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Enhance Efficiency of Vision Transformers at the Edge/3bd82ff4-b9fe-43da-a28f-c5a1697c4ab3_content_list.json @@ -0,0 +1,1488 @@ +[ + { + "type": "text", + "text": "DeepCompress-ViT: Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge", + "text_level": 1, + "bbox": [ + 173, + 130, + 825, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sabbir Ahmed $^{1*}$ , Abdullah Al Arafat $^{2*}$ , Deniz Najafi $^{3*}$ , Akhlak Mahmood $^{4}$ , Mamshad Nayeem Rizve $^{5}$ , Mohaiminul Al Nahian $^{1}$ , Ranyang Zhou $^{3}$ , Shaahin Angizi $^{3}$ , Adnan Siraj Rakin $^{1}$ $^{1}$ Binghamton University (SUNY), $^{2}$ North Carolina State University, $^{3}$ New Jersey Institute of Technology, $^{4}$ Georgia Institute of Technology, $^{5}$ Adobe Inc.", + "bbox": [ + 99, + 202, + 915, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 308, + 326, + 324 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision Transformers (ViTs) excel in tackling complex vision tasks, yet their substantial size poses significant challenges for applications on resource-constrained edge devices. The increased size of these models leads to higher overhead (e.g., energy, latency) when transmitting model weights between the edge device and the server. Hence, ViTs are not ideal for edge devices where the entire model may not fit on the device. Current model compression techniques often achieve high compression ratios at the expense of performance degradation, particularly for ViTs. To overcome the limitations of existing works, we rethink model compression strategy for ViTs from first principle approach and develop an orthogonal strategy called DeepCompress-ViT. The objective of the DeepCompress-ViT is to encode the model weights to a highly compressed encoded representation using a novel training method, denoted as Unified Compression Training (UCT). Proposed UCT is accompanied by a decoding mechanism during inference, which helps to gain any loss of accuracy due to high compression ratio. We further optimize this decoding step by reordering the decoding operation using associative property of matrix multiplication, ensuring that the compressed weights can be decoded during inference without incurring any computational overhead. Our extensive experiments across multiple ViT models on modern edge devices show that DeepCompress-ViT can successfully compress ViTs at high compression ratios $(>14\\times)$ . DeepCompress-ViT enables the entire model to be stored on edge device, resulting in unprecedented reductions in energy consumption $(>1470\\times)$ and latency $(>68\\times)$ for edge ViT inference. Our code is available at https://github.com/ML-Security-Research-LAB/DeepCompress-ViT.", + "bbox": [ + 88, + 339, + 485, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 824, + 223, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The integration of computer vision and deep learning (DL) into the Industrial Internet of Things (IIoT) and edge de", + "bbox": [ + 89, + 849, + 482, + 880 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c021b82f1ded9a591fc796bd3d6bb00c9144042ae1b71403ae3092d189b66af8.jpg", + "image_caption": [ + "Figure 1. Comparison of DeepCompress-ViT with SOTA ViT compression methods [8, 11, 31] for compressing DeiT-S [27] trained onImagenet-1k [22]. Existing compression methods achieve a large compression ratio at the expense of large performance loss, whereas the DeepCompress-ViT achieves the highest compression ratio with the best accuracy among the competition." + ], + "image_footnote": [], + "bbox": [ + 535, + 306, + 885, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "vices has revolutionized data processing, analysis, and action in these systems [3]. By deploying advanced models, such as Vision Transformers (ViTs), on resource-constrained devices, IIoT systems can directly manage complex tasks, including object detection, anomaly detection, and facial recognition on the device. This local processing capability on edge minimizes data transmission to centralized servers, reducing latency and enhancing data privacy by keeping information closer to its source [35].", + "bbox": [ + 509, + 580, + 906, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, Vision Transformers (ViTs) [7] have gained significant attention among deep neural network (DNN) models for their remarkable performance [20]. Their potential to tackle various real-world vision problems, such as object detection [4] and segmentation [26], makes them especially appealing for edge applications. However, the challenge of achieving reliable, real-time inference on resource-constrained devices cannot be underestimated, primarily due to the large model sizes of ViTs in comparison to models like Convolutional Neural Networks [23].", + "bbox": [ + 509, + 718, + 908, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The architectural design of ViTs often exceeds the on-chip memory limits of edge devices (e.g., Espressif ESP32-", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* These authors contributed equally", + "bbox": [ + 114, + 886, + 307, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "30147", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "S3 [1] has 8 MB pseudo-static RAM on-chip memory, but DeiT-S model size is approximately 85 MB), leading to a reliance on off-chip memory from servers to store the entire model. This dependency introduces two critical challenges that significantly impede the use of large ViTs in edge environments [10]. Firstly, computations performed on-chip are estimated to be 10 to 100 times faster than those conducted off-chip (see Table 1 for a detailed numerical comparison of various metrics between on- and off-chip memories). Secondly, transferring sizable model weights demands high communication bandwidth, resulting in elevated energy consumption. As a result, for edge applications (e.g., real-time patient monitoring, autonomous vehicle perception, quality control in production) where latency and power efficiency are critical, the deployment of ViT models is severely limited. Therefore, addressing model size and enhancing memory management are not just challenges; they are essential for unlocking the full potential of ViT models in IoT devices.", + "bbox": [ + 89, + 90, + 483, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To effectively deploy large Vision Transformer (ViT) models at the edge, it is crucial to aggressively compress them to fit into on-chip memory. Aggressive compression reduces reliance on off-chip memory, decreasing latency and energy consumption. However, techniques such as pruning [31] and quantization [11] often face challenges at high compression ratios, leading to significant drops in performance. For instance, the DeiT-Small model, which is approximately $85\\mathrm{MB}$ , would require over $10\\times$ compression to fit into an 8 MB edge device. This extreme compression level can result in severe accuracy loss (please refer to Figure 1). Therefore, it is essential to carefully reconsider and rethink model compression strategies for ViTs to maintain both performance and efficiency at the edge.", + "bbox": [ + 89, + 380, + 483, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we begin by formulating the popular compression strategies from the perspective of weight encoding, as illustrated in Figure 2. Both pruning and quantization are techniques that encode model weights into a compressed format. However, at high compression ratios, this weight encoding mechanism can become lossy, leading to a decline in model performance. Our hypothesis is that to mitigate the performance loss due to encoded weights, it is essential to implement a decoding method during inference that can reconstruct or remap the weights back to their original (decompressed) state. This approach could enhance the model's accuracy during inference by reversing the effects of a lossy compression. Nonetheless, developing an effective compression strategy that achieves high compression while also enabling accurate weight decoding for inference involves overcoming several challenges, which our work aims to resolve.", + "bbox": [ + 89, + 595, + 483, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose a novel and unique perspective on model compression, which enables aggressive compression of ViT models while maintaining a decoding frame", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6289255a14ece7fa96528f50db9adf84d14bd23af8579ab33438e22578d393c6.jpg", + "image_caption": [ + "Figure 2. Existing compression methods can be viewed as a form of weight encoding. However, inference with lossy encoded weights results in performance dorp whereas proposed DeepCompress-ViT maintains an optimized decoding method at test time to maintain model performance." + ], + "image_footnote": [], + "bbox": [ + 527, + 88, + 897, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "work to reconstruct the weights back. The key idea is that the compressed version of the weight and a lightweight decoder will be stored in memory to reduce memory costs. However, these weights will be reconstructed back to their original form using the decoder in a layer-by-layer sequence for model inference and thus help to maintain accuracy. Our proposed DeepCompress-ViT consists of two phases—Unified Compression Training and Optimized Test-Time Decoding. In Unified Compression Training, we train an encoder and decoder alongside the model, learning a highly compressed representation of its parameters through encoded embeddings. After training, we retain only these encoded weights and the decoder, discarding the encoder.", + "bbox": [ + 511, + 431, + 908, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Next, during inference, the goal is to Decode the compressed parameters layer-by-layer systematically to reconstruct the original parameters for each layer to compute the next layers output. Nevertheless, the proposed layer-by-layer decoding approach comes with two notable drawbacks. First, decoding the compressed representation of each layer back to its original form incurs extra computational costs, such as increased energy use and processing time. Additionally, this can lead to significant on-chip memory usage, particularly in larger layers, when decoded weights will be stored on-chip temporarily to compute output of a given layer. Hence, we propose Optimized Test-Time Decoding, eliminating the need to decode embeddings to their original parameters. This optimized decoding step leverages the associative property of matrix multiplication to reorder the decoding operation. This innovation eliminates both computation and memory usage drawback associated with the decoding step, making proposed", + "bbox": [ + 511, + 628, + 908, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "30148", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DeepCompress-ViT best of all worlds (accuracy, memory, energy and latency). Our experiments on SOTA ViTs and edge devices show that DeepCompress-ViT achieves compression ratios exceeding $14 \\times$ while achieving unprecedented reductions in energy ( $>1470 \\times$ ) and latency ( $>68 \\times$ ), all with the least amount of accuracy loss among the SOTA compression methods.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 200, + 232, + 214 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision Transformers. The introduction of Transformer architecture [28] has marked a paradigm shift in machine learning, initially transforming natural language processing. Building on this success, the architecture was adapted for computer vision, leading to the development of Vision Transformer (ViT) [7]. This success has led to a surge in transformer-based models for computer vision. For example, DeiT [27] introduced advanced training techniques and a novel distillation approach to reduce ViT's dependence on large datasets. Further architectural innovations, such as Pyramid Vision Transformer (PVT) [29] and Swin Transformer [17], incorporated hierarchical feature representations enabling transformers to serve as versatile frameworks for diverse computer vision applications. Even though ViTs have demonstrated strong performance, they require significant memory that limits their application in edge devices. Compressing ViTs has thus emerged as an important area of research to address this large memory requirement.", + "bbox": [ + 89, + 219, + 482, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ViT Compression. A widely used approach for compressing Vision Transformers (ViT) is pruning [16, 30-33, 36], which focuses on reducing the number of unimportant weights in the model. Pruning methods for ViT models are commonly divided into two categories: unstructured and structured pruning. Unstructured pruning techniques, such as magnitude-based and Hessian-based methods [24], remove individual weights based on certain importance metrics. However, these techniques result in irregular sparsity patterns, which complicate tensor computations and limit hardware efficiency. Structured pruning mitigates this challenge by removing larger, contiguous structures within the model, such as entire attention heads or rows of weight matrices, which are more compatible with hardware requirements. For instance, [31] proposed a structured pruning method for ViTs that uses a binary mask to distinguish important from unimportant parameters based on magnitude. Another effective approach, introduced in [33], combines pruning, layer skipping, and knowledge distillation within a unified framework to create a compact ViT model.", + "bbox": [ + 89, + 492, + 482, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another widely adopted approach for compressing ViT models is quantization [8, 11-13, 15, 18], which converts floating-point parameters to lower precision values. Several quantization methods tailored to ViT's unique architecture have been proposed. For instance, Q-ViT [11] introduced differentiable quantization for ViTs, treating quantization bit-widths and scales as learnable parameters.", + "bbox": [ + 89, + 795, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PTQ4ViT [18] utilizes twin uniform quantization and applies a Hessian-guided metric to determine optimal scaling factors. FQ-ViT [15] incorporates powers-of-two scale quantization and log-int quantization specifically for Layer-Norm and Softmax operations, respectively.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While both pruning and quantization methods have shown great promise in reducing computational demands, they still experience significant performance degradation at high compression ratios [11, 31], also shown in Table 2, severely limiting their applicability in edge IoT devices.", + "bbox": [ + 511, + 167, + 906, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Challenges and Motivation", + "text_level": 1, + "bbox": [ + 511, + 244, + 764, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To motivate our compression technique, we identify the critical bottleneck hindering efficient inference of Vision Transformers (ViTs) at the edge. We will also assess the limitations of current compression methods, establishing the necessary foundation for our proposed method.", + "bbox": [ + 511, + 267, + 905, + 342 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Challenges of Efficient Edge Inference", + "text_level": 1, + "bbox": [ + 511, + 344, + 841, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The deployment of ViTs on edge devices presents significant challenges due to their substantial memory requirements, which often exceed the on-chip memory capacity of these resource-constrained environments. Consequently, model parameters must be stored in off-chip memory, necessitating a sequential processing approach during inference. This approach involves iteratively loading each layer's weights into on-chip memory and performing computations on that layer before proceeding to the next. While this method enables the inference of ViTs on devices with limited on-chip memory, it introduces significant latency and increased energy consumption due to frequent off-chip memory accesses, both of which are critical concerns in resource-constrained edge environments (e.g., autonomous vehicle perception).", + "bbox": [ + 511, + 364, + 905, + 592 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/e7180f2a1945ffcb2138a5458da92989a234ed29a9eea6d5dfec214528729c57.jpg", + "table_caption": [ + "Table 1. Comparison of On-chip and Off-chip Memory Access Cost in Edge Devices" + ], + "table_footnote": [ + "†32b SRAM Read (32KB), §32b DRAM [10], * For edge AI devices." + ], + "table_body": "
Memory TypeAccess Time (ns)Energy per Access (pJ)Available Storage (MB)
On-chip1-105·20†1-8
Off-chip70-2001300-2600§1024-8192*
", + "bbox": [ + 519, + 631, + 901, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "One potential solution to mitigate this frequent off-chip memory access is model compression. Model compression can reduce the overall memory footprint and allow the entire model to be stored in on-chip memory, which can minimize/eliminate the need for costly memory access. However, as shown in Table 1, the available on-chip memory is often severely constrained (e.g., $\\sim 1 - 8$ MB), and achieving this would require aggressive compression (e.g., greater than $10\\times$ ).", + "bbox": [ + 511, + 689, + 905, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "One of the widely explored approaches for model compression is pruning. Numerous studies [24, 31, 33] have applied pruning techniques on ViTs to reduce their memory and computation costs. While pruning has demonstrated significant success in lowering the computational demands", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "30149", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of these models, our investigation reveals that achieving high compression through pruning in ViTs is challenging without severely impacting model performance. As shown in Table 2, even with a $2.5 \\times$ compression ratio, the model suffers $\\sim 19\\%$ accuracy loss.", + "bbox": [ + 88, + 90, + 480, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Another widely adopted approach for improving model efficiency is quantization [11, 15, 18]. Quantization has proven particularly effective in reducing the memory footprint of large models, such as large language models (LLMs). The existing literature demonstrates that extreme quantization can be successfully applied to LLMs [19] with minimal performance loss. However, quantization applied to ViTs presents a different challenge. Studies focusing on ViTs [11, 34] have shown that these models suffer from significant performance degradation when subjected to extreme quantization (see Table 2).", + "bbox": [ + 88, + 167, + 482, + 332 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/d2f05914e633673795c1ade6b476f84e127eb13917d849972962723883a688b3.jpg", + "table_caption": [ + "Table 2. Evaluating existing compression methods by aggressively compressing a DeiT-S model and highlighting their shortcoming in achieving our ideal objective ( $4^{th}$ row) for edge inference." + ], + "table_footnote": [], + "table_body": "
MethodOriginal Size (MB)Compression RatioAccuracy (%)
Original Model84.11×79.72
Pruning [11]33.72.5×60.51
Quantization [31]6.1813.6×71.90
Our Objective1-8 ( constraint at edge)10-80× (required)79.72 (ideally)
", + "bbox": [ + 116, + 386, + 460, + 443 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we dissect these two popular model compression strategies to determine the fundamental limitation that hurts the state-of-the-art model compression technique and whether we can develop an orthogonal approach to overcome them at our targeting edge applications.", + "bbox": [ + 89, + 455, + 482, + 531 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Motivation", + "text_level": 1, + "bbox": [ + 89, + 532, + 212, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 2, both pruning and quantization can be viewed as a form of encoding original model weights to a compressed representation. The fundamental challenge lies in the way these compression techniques encode model weights. In this work, we postulate that the primary factor contributing to this performance loss can be attributed to the large weight perturbation error introduced by the encoding mechanism of these compression techniques, as formalized in the following lemma.", + "bbox": [ + 88, + 551, + 482, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lemma 3.1. (Error Bound for Compression in DNNs). Let $\\mathbf{w}$ represent the weights of a deep neural network (DNN) with an associated loss function $\\mathcal{L}(\\mathbf{w})$ . Consider a compression technique that encodes the weights using a transformation $\\mathbf{F}$ resulting in $\\mathbf{w}' = \\mathbf{F}(\\mathbf{w})$ and introducing a perturbation $\\delta \\mathbf{w} = \\mathbf{w}' - \\mathbf{w}$ . The change in loss due to this compression can be upper bounded as follows:", + "bbox": [ + 88, + 694, + 482, + 800 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n| \\mathcal {L} (\\mathbf {w} ^ {\\prime}) - \\mathcal {L} (\\mathbf {w}) | \\leq \\| \\nabla_ {\\mathbf {w}} \\mathcal {L} (\\mathbf {w}) \\| \\| \\delta \\mathbf {w} \\| + \\frac {1}{2} \\| H \\| \\| \\delta \\mathbf {w} \\| ^ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 805, + 470, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\nabla_{\\mathbf{w}}\\mathcal{L}(\\mathbf{w})$ is the gradient of the loss function with respect to the original weights $\\mathbf{w}$ , $\\|H\\|$ denotes the norm of the Hessian matrix of $\\mathcal{L}(\\mathbf{w})$ , and $\\|\\delta \\mathbf{w}\\|$ is the norm of the weight perturbation introduced by the compression.", + "bbox": [ + 89, + 839, + 485, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From Lemma 3.1, it is evident that a smaller weight perturbation $\\| \\delta \\mathbf{w}\\|$ leads to a tighter upper bound on the loss difference $|\\mathcal{L}(\\mathbf{w}^{\\prime}) - \\mathcal{L}(\\mathbf{w})|$ . Therefore, an ideal compression method should minimize the weight perturbation error. However, for edge application of ViTs, we are forced to perform aggressive compression that will inevitably lead to a higher $\\| \\delta \\mathbf{w}\\|$ .", + "bbox": [ + 511, + 90, + 903, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Neither pruning nor quantization has a countermeasure against this high $\\| \\delta \\mathbf{w}\\|$ for aggressive compression, laying down the foundation for our proposed method as to whether we can device a technique to reduce $\\| \\delta \\mathbf{w}\\|$ at the inference stage even at a high compression ratio. The research question that motivates our work: Given that weight encoding for compression inevitably introduces significant weight perturbation error at high compression ratio, an effective approach to mitigate this error may lie in coupling the encoding mechanism with a complementary decoding mechanism that can reverse the lossy encoding, as formalized in the following proposition.", + "bbox": [ + 511, + 198, + 906, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proposition 3.2. (Lower Error Bound with Weight Decoding). Let $\\mathbf{w}$ represent the weights of a deep neural network (DNN) and consider a compression method that encodes these weights using a transformation $\\mathbf{F}$ , introducing a weight perturbation $\\delta \\mathbf{w} = \\mathbf{w}' - \\mathbf{w}$ . Now consider a weight decoding mechanism with transformation $\\mathbf{G}$ , where $\\mathbf{G}$ approximates the inverse of $\\mathbf{F}$ . Then, the weight perturbation error after decoding the weights can be bounded as follows:", + "bbox": [ + 511, + 388, + 906, + 511 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\| \\mathbf {G} (\\mathbf {F} (\\mathbf {w})) - \\mathbf {w} \\| \\leq \\| \\delta \\mathbf {w} \\|.\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 522, + 800, + 540 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above proposition demonstrates the potential of a weight decoding strategy to reduce weight perturbation and minimize the impact on model performance at inference. Inspired by Proposition 3.2, we aim to design a novel Encoder-Decoder-based model compression approach that can enable the potential of achieving a high compression ratio while minimizing inference loss.", + "bbox": [ + 511, + 551, + 905, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Proposed Method: DeepCompress-ViT", + "text_level": 1, + "bbox": [ + 511, + 666, + 862, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose DeepCompress-ViT, a novel compression framework designed for achieving a high compression ratio while preserving inference accuracy. As shown in Figure 3, our novel DeepCompress-ViT framework consists of two stages. In the first stage, we propose Unified Compression Training, which jointly trains the encoder and decoder networks (see Figure 3). The encoder network, denoted as $\\mathbf{F}$ , learns to encode the original model weights w from $\\mathbb{R}^d$ to $\\mathbb{R}^r$ , where $r \\ll d$ . And the decoder network, $\\mathbf{G}$ , learns to decode the encoded weights back to $\\mathbb{R}^d$ . After training is complete, only the encoded weights and the decoder network are retained for inference, while the encoder network is discarded. During inference, the proposed DeepCompress-ViT reconstructs each layer's weight one by", + "bbox": [ + 511, + 688, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "30150", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a5a8a34564b1ed522ee446c51bff9b2c9e4bb2c6a9653abfae1f59e50dd998ff.jpg", + "image_caption": [ + "Figure 3. Unified Compression Training. The Encoder and Decoder parameters are optimized jointly to minimize the loss. After training, only encoded weights and decoder network is retained for inference" + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 483, + 214 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "one and performs inference using the decoded version of the weight to help maintain inference accuracy.", + "bbox": [ + 89, + 290, + 483, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While the decoding step is necessary to maintain accuracy, it has two drawbacks. To understand this, lets consider a simplified form the output computation for a given layer: input $\\times$ encoded weight $\\times$ decoder weight. First, the decoding step will be performed using encoded weight $\\times$ decoder weight which introduces additional computation at runtime, and second, the reconstructed version of the weight will increase temporary on-chip memory consumption, especially for larger layers. To address this, we propose optimizing the decoding step by designing a lightweight decoder implemented as a single linear layer. In addition, we leverage the associative property of matrix multiplication to transform the inefficient weight decoding input $\\times$ (encoded weight $\\times$ decoder weight) to optimized test-time decoding as (input $\\times$ encoded weight) $\\times$ decoder weight, which would ensure the computation cost remains unchanged for an optimum level of decoder input (compressed weight size $r$ outlined in equation 4 in details) is selected. This optimization ensures the proposed DeepCompress-ViT does not introduce any computational overhead (Figure 4) in pursuit of compression and accuracy.", + "bbox": [ + 91, + 321, + 483, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Unified Compression Training (UCT)", + "text_level": 1, + "bbox": [ + 89, + 648, + 413, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this stage, an encoder-decoder network is trained to achieve aggressive compression. The encoder network $\\mathbf{F}$ , learns to encode the model's weights to a compressed representation as the encoded embedding, while the decoder network, $\\mathbf{G}$ , learns to decode the weights back to their original dimension as shown in Figure 3.", + "bbox": [ + 89, + 672, + 482, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Consider a ViT model $\\mathbf{H}_{\\mathbf{W}}(\\cdot)$ consisting of $L$ layers, where the weights of the layers are denoted by the set $\\mathbf{W} = \\{\\mathbf{w}_1,\\mathbf{w}_2,\\dots ,\\mathbf{w}_L\\}$ . Let the parameters of the encoder network $\\mathbf{F}(.)$ be represented as $\\mathbf{W}_{\\mathbf{E}}$ , and the parameters of the decoder network $\\mathbf{G}(.)$ be represented as $\\mathbf{W}_{\\mathbf{D}}$ .", + "bbox": [ + 89, + 763, + 482, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During training, each layer's weight $\\mathbf{w}_i$ is passed through the encoder network $\\mathbf{F}$ , which encodes it to a lower-dimensional representation, given by $\\mathbf{z}_i = \\mathbf{F}(\\mathbf{w}_i)$ . The decoder network $\\mathbf{G}$ then decodes $\\mathbf{z}_i$ back to its original di", + "bbox": [ + 89, + 840, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "mensionality as $\\hat{\\mathbf{w}}_i = \\mathbf{G}(\\mathbf{z}_i)$ . The encoder and decoder networks are trained jointly to minimize the mean squared error (MSE) between the original weight set $(\\mathbf{W})$ and the reconstructed weight set $(\\hat{\\mathbf{W}})$ . The weight reconstruction loss is calculated as:", + "bbox": [ + 511, + 90, + 905, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\bf m s e} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\| {\\bf w} _ {i} - {\\bf G} ({\\bf F} ({\\bf w} _ {i})) \\| ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 588, + 175, + 831, + 217 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To optimize this training step further, we unify the encoder-decoder training step with the original ViT-model. Our hypothesis is that only MSE loss-based weight reconstruction may not provide optimal performance [2]. Even though minimizing MSE loss results in the minimization of weight perturbation error, different sets of decoded weights with the same MSE value can have varying weight distributions, which can lead to a performance drop in the ViT model. Hence, it is reasonable to incorporate the ViT model into this training loop to align the ViT model's weight distribution with the decoded version of the weight.", + "bbox": [ + 511, + 227, + 906, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hence, we propose this end-to-end unified framework where the encoder-decoder networks are jointly trained with the ViT model. Our method will incorporate cross-entropy (CE) loss and knowledge distillation (KD) from a pretrained model in training, where CE ensures the ViT model performance is optimized on the decoded weight values w.r.t ground truth, and KD ensures the decoded weight parameters do not drift far apart from the initial weight distribution of a pre-trained ViT model.", + "bbox": [ + 511, + 393, + 905, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The forward pass for the whole end-to-end training after obtaining the decoded weight sets $\\hat{\\mathbf{W}}$ from the decoder is formulated as $\\mathbf{H}_{\\mathbf{W}}(\\cdot) \\rightarrow \\mathbf{H}_{\\hat{\\mathbf{W}}}(\\cdot)$ , which implies that the ViT model inference will always use the decoded weights, i.e., the forward pass of the ViT model becomes $\\hat{\\mathbf{y}} = \\mathbf{H}_{\\hat{\\mathbf{W}}}(\\mathbf{x})$ , where $\\mathbf{x}$ are the input images and $\\hat{\\mathbf{y}}$ are the predictions from the ViT model. Next, using $\\hat{\\mathbf{y}}$ , we compute the cross-entropy loss and knowledge distillation loss as follows:", + "bbox": [ + 511, + 529, + 905, + 664 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathbf {C E}} = - \\sum_ {i} \\mathbf {y} _ {i} \\log (\\hat {\\mathbf {y}} _ {i}), \\quad \\mathcal {L} _ {\\mathbf {K D}} = \\sum_ {i} \\hat {\\mathbf {y}} _ {\\mathrm {t}, i} \\log \\left(\\frac {\\hat {\\mathbf {y}} _ {\\mathrm {t} , i}}{\\hat {\\mathbf {y}} _ {i}}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 674, + 893, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{y}}_{\\mathrm{t}}$ represents the prediction from the pretrained teacher model. The total loss function is then defined as:", + "bbox": [ + 511, + 720, + 905, + 751 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {t o t a l}} = \\mathcal {L} _ {\\mathrm {m s e}} + \\alpha \\cdot \\mathcal {L} _ {\\mathrm {C E}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {K D}},\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 763, + 841, + 780 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are scaling factors controlling the contributions of cross-entropy and knowledge distillation losses, respectively. Finally, the overall loss function is minimized by jointly optimizing the encoder and decoder parameters $\\mathbf{W}_{\\mathbf{E}}$ and $\\mathbf{W}_{\\mathbf{D}}$ as follows:", + "bbox": [ + 511, + 792, + 905, + 868 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {W} _ {\\mathrm {E}}, \\mathbf {W} _ {\\mathrm {D}}} \\mathcal {L} _ {\\mathrm {t o t a l}}\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 875, + 759, + 897 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "30151", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b49711e04362cc903cd5186f5cdd249e35ddb9c27815b80790e38c4406d4d640.jpg", + "image_caption": [ + "Figure 4. Proposed Optimized Test-Time Decoding overview. Decoding the encoded (compressed) weights first and then matrix multiplying with input activation increases FLOPs. The proposed method eliminates extra FLOPs by multiplying input activation with encoded weights first, then passing through decoder. The chosen value of encoding dimension $(r)$ prevents any FLOP increase." + ], + "image_footnote": [], + "bbox": [ + 186, + 88, + 485, + 335 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cb7d7a50faf7fd8b949340c7555f512c031cf39802803af6c3ae83f7e9006519.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 88, + 812, + 335 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After training is complete, for inference, we keep only the encoded weight parameters $\\{\\mathbf{z}_i\\}$ and a lightweight decoder $\\mathbf{W}_{\\mathbf{D}}$ in memory while discarding the encoder $\\mathbf{W}_{\\mathbf{E}}$ .", + "bbox": [ + 89, + 398, + 482, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "At inference, the decoder needs to map compressed weights to their original form layer by layer, which may help preserve accuracy. However, this can introduce two major drawbacks. First, the decoding step will inevitably lead to additional computation at runtime, and second, the decoded weights will increase temporary on-chip memory consumption, particularly for larger layers. Next, we outline our optimized test-time decoding strategy, which ensures these two bottlenecks remain in check.", + "bbox": [ + 89, + 443, + 483, + 578 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Optimized Test-Time Decoding", + "text_level": 1, + "bbox": [ + 89, + 587, + 366, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To mitigate the overhead associated with the decoding step, first design level optimization we propose is to design the decoder $\\mathbf{G}$ as a single linear layer. This design choice minimizes repetitive decoding operations, reducing the computational overhead. Although a single-layer decoder network lowers the computational load relative to a multi-layer decoder, the computation needed for decoding weights using a single layer still persists.", + "bbox": [ + 89, + 609, + 482, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To illustrate the overhead of weight decoding step, consider a fully connected layer in a ViT model with original weights $\\mathbf{w}_i\\in \\mathbb{R}^{C\\times d}$ , whose weights are encoded and the encoded weights are represented by $\\mathbf{z}_i\\in \\mathbb{R}^{C\\times r}$ . During inference of this layer, the weights are first decoded using the single-layer decoder network $\\mathbf{G}$ , where weights of the decoder network is represented by $\\mathbf{w}_D\\in \\mathbb{R}^{r\\times d}$ . This weight decoding computation can be represented as follows:", + "bbox": [ + 89, + 731, + 482, + 852 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {w}} _ {i} = \\mathbf {z} _ {i} \\times \\mathbf {w} _ {D}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 230, + 859, + 482, + 875 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{w}}_i\\in \\mathbb{R}^{C\\times d}$ denotes the decoded weights. One of the", + "bbox": [ + 89, + 883, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "most widely used metrics to evaluate computational complexity is Floating-point Operations (FLOPs) [6], which counts the total number of multiplications and additions performed in a given operation. The FLOPs incurred for the weight decoding operation is $2 \\cdot C \\cdot r \\cdot d$ , corresponding to the matrix multiplication in eqn. (1).", + "bbox": [ + 511, + 398, + 906, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, the usual forward pass of fully connected layer in the ViT model with input activations $\\mathbf{x}_i\\in \\mathbb{R}^{N\\times C}$ and decoded weights $\\hat{\\mathbf{w}}_i$ is computed as follows:", + "bbox": [ + 511, + 488, + 906, + 532 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} \\times \\hat {\\mathbf {w}} _ {i}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 650, + 542, + 903, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_{i + 1}$ represents the output activations of the layer. The FLOPs incurred by this forward pass is $2\\cdot N\\cdot C\\cdot d$ resulting from the matrix multiplication in eqn. (2). Therefore, the total FLOPs incurred in the forward pass with this strategy is $(2\\cdot N\\cdot C\\cdot d + 2\\cdot C\\cdot r\\cdot d)$ where the additional $2\\cdot C\\cdot r\\cdot d$ FLOPs is incurred because of this inefficient weight decoding strategy.", + "bbox": [ + 511, + 566, + 906, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we optimize the decoding step to eliminate this additional $2 \\cdot C \\cdot r \\cdot d$ FLOPs, we propose Optimized Test-Time Decoding. Our proposed decoding approach leverages the associative property of matrix multiplication to reorder computation sequence to maintain or improve overall FLOPs. To illustrate, recall that the overall computation for inefficient decoding strategy is as follows:", + "bbox": [ + 511, + 672, + 906, + 779 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} \\times \\hat {\\mathbf {w}} _ {i} = \\mathbf {x} _ {i} \\times \\left(\\mathbf {z} _ {i} \\times \\mathbf {w} _ {D}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 787, + 903, + 803 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where it shows weight decoding first and then perform the forward pass in the fully connected layer of ViT model. We optimize the decoding step by simply reorder the matrix multiplications as follows:", + "bbox": [ + 511, + 811, + 906, + 871 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} ^ {\\prime} \\times \\mathbf {w} _ {D} = (\\mathbf {x} _ {i} \\times \\mathbf {z} _ {i}) \\times \\mathbf {w} _ {D},\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 880, + 836, + 897 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "30152", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where we first perform input compression $(\\mathbf{x} \\in \\mathbb{R}^{N \\times C} \\to \\mathbf{x}' \\in \\mathbb{R}^{N \\times r})$ and then do the optimized forward pass $(\\mathbf{x}' \\times \\mathbf{w}_D)$ . The proposed strategy is also illustrated in Figure 4.", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The total FLOPs for this optimized approach is $2 \\cdot N \\cdot r \\cdot (C + d)$ . However, with an arbitrary value of $r$ , the overall FLOPs can still go up. Therefore, to ensure that the total FLOPs of the proposed decoding strategy do not exceed the baseline models FLOPs, we derive the optimal $r$ for efficiency by solving the following inequality,", + "bbox": [ + 89, + 136, + 480, + 227 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n2 \\cdot N \\cdot r \\cdot (C + d) \\leq 2 \\cdot N \\cdot C \\cdot d,\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 239, + 403, + 253 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $2 \\cdot N \\cdot C \\cdot d$ is the FLOPs incurred due to normal forward pass in eqn. (2). Solving the inequality, we get:", + "bbox": [ + 89, + 267, + 482, + 297 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nr \\leq \\frac {2 \\cdot N \\cdot C \\cdot d}{2 \\cdot N \\cdot (C + d)} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 306, + 482, + 340 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In summary, by reordering the computation sequence and using optimal $r$ for compression derived in eqn. (4), our innovative decoding optimization does not incur any additional computation.", + "bbox": [ + 89, + 349, + 483, + 411 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 89, + 417, + 295, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Datasets and Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 441, + 410, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets. We conduct our experiments on the ILSVRC12 ImageNet classification dataset [22] consisting 1,000 classes with 1.2 million training images and 50k validation images. Additionally, we evaluate DeepCompress-ViT on the widely used COCO benchmark dataset [14] for object detection and instance segmentation task.", + "bbox": [ + 89, + 462, + 482, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Encoder-Decoder Architecture. We use four encoder network each with 2 linear layers to encode four types of layers: attn_qkv, attnProj, mlp_fcl and mlp_fcl2. Each encoder has an affine transformation before and after the 2 linear layers. Similarly to encoders, we use four single linear layer decoders to decode the four types of layers. Note that each decoder is a shared decoder which decodes a particular type of layer of all ViT blocks. Note that, we exclude the first layer, last layer, and LayerNorm parameters from compression.", + "bbox": [ + 89, + 553, + 482, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experimental Settings. The encoder and decoder models are trained for 275 epochs with a batch size of 256 and a base learning rate of $1 \\times 10^{-4}$ , using a cosine learning rate scheduler. For data augmentation, we apply the standard techniques used in [27] and for knowledge distillation, we use pretrained distilled DeiT models [27] with temperature $\\tau = 1$ . For UCT, we set the value of $\\alpha = 1$ and $\\beta = 3 \\times 10^3$ . The encoded weights are quantized using 4-bit asymmetric quantization, while decoder weights are quantized using 4-bit symmetric quantization, both trained using Quantization Aware Training. Additionally, the patch embedding (first) and classification (last) layers are quantized using 8-bit symmetric quantization. The optimal value of $r$ from", + "bbox": [ + 89, + 704, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "solving (4) is set to 277 for DeiT-S and 502 for DeiT-B. For object detection and instance segmentation, we use the mmdetection library with the standard $1 \\times$ training scheduler and adopt an edge-friendly resolution of $384 \\times 384$ for both training and evaluation.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Results", + "text_level": 1, + "bbox": [ + 511, + 190, + 607, + 204 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image Classification. Performance of the compressed DeiT models with proposed DeepCompress-ViT on the classification task is shown in Table 3. The results demonstrate substantial reductions in model size and energy consumption resulting from DeepCompress-ViT. For instance, the DeepCompress-DeiT-S model achieves a compression ratio of $14.9\\times$ , reducing the model size from $84.1\\mathrm{MB}$ to just $5.64\\mathrm{MB}$ while maintaining an accuracy of $78.74\\%$ on ImageNet. Similarly, DeepCompress-DeiT-B achieves a compression ratio of $17.4\\times$ , decreasing the model size from $330.2\\mathrm{MB}$ to $18.9\\mathrm{MB}$ . Remarkably, both models show an unprecedented energy reduction of $673\\times$ and $1475\\times$ and latency reduction of $44.5\\times$ and $68.4\\times$ respectively (please refer to section 5.3 and Figure 5 for more hardware energy and latency evaluation details). Proposed DeepCompress-ViT achieves this unprecedented level of model compression, energy, and latency reduction, enabling the deployment of ViT models at the edge while only sacrificing a marginal level of accuracy (e.g., for DeiT-B only $\\sim 0.1\\%$ )", + "bbox": [ + 511, + 210, + 906, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Object Detection and Instance Segmentation. Next, table 4 compares the performance of DeepCompress-ViT with baseline (no compression) DeiT-S model on object detection and instance segmentation tasks. We trained both the models on COCO dataset integrating the respective ViT backbones with Mask R-CNN [9]. We evaluate both of the models for these tasks at an edge-friendly resolution of $384 \\times 384$ . Notably, DeepCompress-ViT reduces the ViT backbone (DeiT-S) size from 82.65MB to 5.27MB ( $15.7 \\times$ compression) with a slight drop in $\\mathrm{AP^b}$ and $\\mathrm{AP^m}$ , further highlighting the effectiveness of our compression method on other complex vision tasks.", + "bbox": [ + 511, + 503, + 905, + 684 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with SOTA compression methods. Finally, Table 5 provides a comparative analysis of DeiT-Small models compressed using different pruning and quantization methods. Among the methods, DeepCompress-ViT achieves the highest compression ratio of $14.9 \\times$ , reducing the model size to 5.64 MB while maintaining a top-1 accuracy of $78.74\\%$ . In contrast, popular WDPruning [31], LSQ [8] and Q-ViT [11] achieves achieve much lower accuracies of $60.51\\%$ , $68.00\\%$ and $71.9\\%$ , respectively. Our proposed DeepCompress-ViT consistently outperforms them by large margins of $\\sim 18\\%$ , $\\sim 10\\%$ , and $\\sim 7\\%$ , respectively, making DeepCompress-ViT the only practical choice to maintain accuracy while performing aggressive compression.", + "bbox": [ + 511, + 689, + 905, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "30153", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9746999787ecabd3c4e3ce2e50f849b2c1a2de06a9efb411802d3594d275435d.jpg", + "table_caption": [ + "Table 3. Performance of DeepCompress-ViT on ImageNet-1K. DeepCompress-ViT achieves memory ( $\\geq 15 \\times$ ) and energy consumption ( $\\geq 1531 \\times$ ), while marginal accuracy drop ( $< 1\\%$ )." + ], + "table_footnote": [], + "table_body": "
MethodAccuracy (%)Model Size (MB)Compression RatioGFLOPsExecution Time (s)Energy Consumption (J)
DeiT-S [27]79.7284.11x9.2024.029979.52
DeepCompress-DeiT-S78.745.6414.9x8.880.5414.83
DeiT-B [27]81.74330.21x35.14129.32150895
DeepCompress-DeiT-B81.6218.917.4x30.841.89102.29
", + "bbox": [ + 125, + 118, + 867, + 186 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/448b1858d2a548afa320699e42a8434312c3979d0b5a5d84fc8ef7e82bce2231.jpg", + "table_caption": [ + "Table 4. Performance of DeepCompress-ViT for Object Detection on the COCO validation set with Mask R-CNN evaluated at an edge-friendly resolution of $384 \\times 384$ ." + ], + "table_footnote": [], + "table_body": "
Method\\( {\\mathbf{{AP}}}^{\\mathbf{b}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}} \\)ViT Backbone Size (MB)
DeiT-S [27]26.223.782.65
DeepCompress-ViT23.020.95.27 (15.7×)
", + "bbox": [ + 135, + 246, + 439, + 291 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/320105d2f294d6b6ebd9e51407a00df25edcabf771a3489ba60e95dbfa93028a.jpg", + "table_caption": [ + "Table 5. Performance comparison of DeiT-Small with SOTA compression methods on ImageNet-1K" + ], + "table_footnote": [], + "table_body": "
ModelAccuracy (%)Model Size (MB)Compression Ratio
DeiT-S [27]79.72 (0)84.11x
WDPruning [31]60.51 (↓19.21)33.72.5x
LSQ [8]68.00 (↓11.72)6.1813.6x
Q-ViT [11]71.90 (↓7.82)6.1813.6x
DeepCompress-ViT78.74 (↓0.98)5.6414.9x
", + "bbox": [ + 93, + 335, + 480, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Hardware Evaluation", + "text_level": 1, + "bbox": [ + 89, + 428, + 294, + 443 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "High compression gain gives an understanding of the effectiveness of a compression method in terms of memory savings. But to successfully realize the full potential of our proposed method, we evaluate the energy and latency gain on hardware evaluation platforms. For hardware deployment, we use the gem5-Aladdin platform [25], which effectively captures dynamic interactions between accelerators and the SoC platform, enabling detailed architectural analysis of the proposed compression method. Our setup incorporates a cycle-accurate in-house-developed model based on the Eyeriss accelerator [5] (0.0029 DRAM access/multiply and accumulation (MAC), 33.6 GMAC/s). Performance metrics from gem5-Aladdin are then analyzed using DRAM-Sim2 [21] to model realistic off-chip memory latency and energy characteristics. The total on-chip weight memory is capped at three configurations (2 MB, 4 MB, 8 MB). The analyzed DeiT-S model initially requires 84.1MB of memory, which exceeds the on-chip memory capacity. By applying DeepCompress-ViT algorithm, this requirement is reduced to 5.64 MB, which can readily fit into the 8MB on-chip memory. However, with a smaller memory capacity, it is not feasible to transfer the entire set of weight parameters to the accelerator in a single batch due to the model's memory demands. Therefore, we implemented a weight parser that transmits weight parameters in variable batch sizes to the accelerator. Figure 5 shows the breakdown of energy consumption and latency across MAC, off-chip, and on-chip memory access components for various on-chip memory sizes. For both DeiT-S and DeiT-B, the DeepCompress-ViT algorithm achieves significant energy savings, reduc", + "bbox": [ + 88, + 446, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/295f440da98d769fe480f170d2d3538b2dfee19cbd1ce31f5e99273299ce59e1.jpg", + "image_caption": [ + "Figure 5. Breakdown of (a) Energy consumption, (b) Latency vs. on-chip memory size. For every off-chip memory size, DeiT-S, DeepCompress-ViT-S, DeiT-B, and DeepCompress-ViT-B results are plotted, respectively." + ], + "image_footnote": [], + "bbox": [ + 514, + 189, + 710, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8dda0ecef3cd3d164e89f402b611e539c4551e247cd3c6d059cca3c1bee4cbb4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 191, + 901, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing consumption by approximately $673 \\times$ and $1475 \\times$ , respectively, with an 8MB on-chip memory. This remarkable reduction is primarily due to the DeepCompress-ViT algorithm's ability to minimize off-chip memory access, as visible through the high difference in the red bar plots. This reduction becomes even more pronounced with smaller memory sizes, enabling for the first time the possibility of deploying large ViT models at the edge and performing time-sensitive applications.", + "bbox": [ + 511, + 407, + 906, + 544 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 560, + 633, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present DeepCompress-ViT, a novel approach to achieve highly compressed Vision Transformers optimized for efficient edge deployment. We first analyze the limitations of existing model compression techniques and show that they lead to large weight perturbation error because of their lossy encoding mechanism. Then, to resolve this challenge, we develop an orthogonal compression technique that consists of an encoding for compression and a decoding step to help maintain performance. However, decoding weights repeatedly during inference can lead to additional computation and increase on-chip memory usage, both of which are critical concerns for edge applications. To address these challenges, we propose a novel optimized Test-Time Decoding scheme that enables efficient inference without increased computation and avoids high on-chip memory usage. Our extensive experiments and hardware evaluation show that the proposed DeepCompress-ViT can lead to an unprecedented reduction in energy and execution time with minimal loss of performance, unlocking the possibilities of deploying large-scale ViT models at edge IIoT devices.", + "bbox": [ + 509, + 583, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "30154", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Esp32-s3 designed for aiot applications, 2022. 2", + "[2] Sabbir Ahmed, Uday Kamal, and Md Kamrul Hasan. Dfrtsd: A deep learning based framework for robust traffic sign detection under challenging weather conditions. 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Savit: Structure-aware vision transformer pruning via collaborative optimization. Advances in Neural Information Processing Systems, 35:9010-9023, 2022. 3" + ], + "bbox": [ + 91, + 92, + 480, + 738 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "30156", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/3bd82ff4-b9fe-43da-a28f-c5a1697c4ab3_model.json b/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/3bd82ff4-b9fe-43da-a28f-c5a1697c4ab3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9548ef86a3f545ecad254704552747a8629184ce --- /dev/null +++ b/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/3bd82ff4-b9fe-43da-a28f-c5a1697c4ab3_model.json @@ -0,0 +1,1914 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.131, + 0.826, + 0.176 + ], + "angle": 0, + "content": "DeepCompress-ViT: Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.203, + 0.916, + 0.277 + ], + "angle": 0, + "content": "Sabbir Ahmed\\(^{1*}\\), Abdullah Al Arafat\\(^{2*}\\), Deniz Najafi\\(^{3*}\\), Akhlak Mahmood\\(^{4}\\), Mamshad Nayeem Rizve\\(^{5}\\), Mohaiminul Al Nahian\\(^{1}\\), Ranyang Zhou\\(^{3}\\), Shaahin Angizi\\(^{3}\\), Adnan Siraj Rakin\\(^{1}\\) \n\\(^{1}\\)Binghamton University (SUNY), \\(^{2}\\)North Carolina State University, \\(^{3}\\)New Jersey Institute of Technology, \\(^{4}\\)Georgia Institute of Technology, \\(^{5}\\)Adobe Inc." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.309, + 0.327, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.34, + 0.486, + 0.824 + ], + "angle": 0, + "content": "Vision Transformers (ViTs) excel in tackling complex vision tasks, yet their substantial size poses significant challenges for applications on resource-constrained edge devices. The increased size of these models leads to higher overhead (e.g., energy, latency) when transmitting model weights between the edge device and the server. Hence, ViTs are not ideal for edge devices where the entire model may not fit on the device. Current model compression techniques often achieve high compression ratios at the expense of performance degradation, particularly for ViTs. To overcome the limitations of existing works, we rethink model compression strategy for ViTs from first principle approach and develop an orthogonal strategy called DeepCompress-ViT. The objective of the DeepCompress-ViT is to encode the model weights to a highly compressed encoded representation using a novel training method, denoted as Unified Compression Training (UCT). Proposed UCT is accompanied by a decoding mechanism during inference, which helps to gain any loss of accuracy due to high compression ratio. We further optimize this decoding step by reordering the decoding operation using associative property of matrix multiplication, ensuring that the compressed weights can be decoded during inference without incurring any computational overhead. Our extensive experiments across multiple ViT models on modern edge devices show that DeepCompress-ViT can successfully compress ViTs at high compression ratios \\((>14\\times)\\). DeepCompress-ViT enables the entire model to be stored on edge device, resulting in unprecedented reductions in energy consumption \\((>1470\\times)\\) and latency \\((>68\\times)\\) for edge ViT inference. Our code is available at https://github.com/ML-Security-Research-LAB/DeepCompress-ViT." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.825, + 0.224, + 0.84 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.85, + 0.483, + 0.881 + ], + "angle": 0, + "content": "The integration of computer vision and deep learning (DL) into the Industrial Internet of Things (IIoT) and edge de" + }, + { + "type": "image", + "bbox": [ + 0.537, + 0.308, + 0.886, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.494, + 0.907, + 0.578 + ], + "angle": 0, + "content": "Figure 1. Comparison of DeepCompress-ViT with SOTA ViT compression methods [8, 11, 31] for compressing DeiT-S [27] trained onImagenet-1k [22]. Existing compression methods achieve a large compression ratio at the expense of large performance loss, whereas the DeepCompress-ViT achieves the highest compression ratio with the best accuracy among the competition." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.582, + 0.907, + 0.718 + ], + "angle": 0, + "content": "vices has revolutionized data processing, analysis, and action in these systems [3]. By deploying advanced models, such as Vision Transformers (ViTs), on resource-constrained devices, IIoT systems can directly manage complex tasks, including object detection, anomaly detection, and facial recognition on the device. This local processing capability on edge minimizes data transmission to centralized servers, reducing latency and enhancing data privacy by keeping information closer to its source [35]." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.719, + 0.909, + 0.869 + ], + "angle": 0, + "content": "In recent years, Vision Transformers (ViTs) [7] have gained significant attention among deep neural network (DNN) models for their remarkable performance [20]. Their potential to tackle various real-world vision problems, such as object detection [4] and segmentation [26], makes them especially appealing for edge applications. However, the challenge of achieving reliable, real-time inference on resource-constrained devices cannot be underestimated, primarily due to the large model sizes of ViTs in comparison to models like Convolutional Neural Networks [23]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.902 + ], + "angle": 0, + "content": "The architectural design of ViTs often exceeds the on-chip memory limits of edge devices (e.g., Espressif ESP32-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.887, + 0.308, + 0.901 + ], + "angle": 0, + "content": "* These authors contributed equally" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "30147" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.378 + ], + "angle": 0, + "content": "S3 [1] has 8 MB pseudo-static RAM on-chip memory, but DeiT-S model size is approximately 85 MB), leading to a reliance on off-chip memory from servers to store the entire model. This dependency introduces two critical challenges that significantly impede the use of large ViTs in edge environments [10]. Firstly, computations performed on-chip are estimated to be 10 to 100 times faster than those conducted off-chip (see Table 1 for a detailed numerical comparison of various metrics between on- and off-chip memories). Secondly, transferring sizable model weights demands high communication bandwidth, resulting in elevated energy consumption. As a result, for edge applications (e.g., real-time patient monitoring, autonomous vehicle perception, quality control in production) where latency and power efficiency are critical, the deployment of ViT models is severely limited. Therefore, addressing model size and enhancing memory management are not just challenges; they are essential for unlocking the full potential of ViT models in IoT devices." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.381, + 0.484, + 0.593 + ], + "angle": 0, + "content": "To effectively deploy large Vision Transformer (ViT) models at the edge, it is crucial to aggressively compress them to fit into on-chip memory. Aggressive compression reduces reliance on off-chip memory, decreasing latency and energy consumption. However, techniques such as pruning [31] and quantization [11] often face challenges at high compression ratios, leading to significant drops in performance. For instance, the DeiT-Small model, which is approximately \\(85\\mathrm{MB}\\), would require over \\(10\\times\\) compression to fit into an 8 MB edge device. This extreme compression level can result in severe accuracy loss (please refer to Figure 1). Therefore, it is essential to carefully reconsider and rethink model compression strategies for ViTs to maintain both performance and efficiency at the edge." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.596, + 0.484, + 0.852 + ], + "angle": 0, + "content": "In this work, we begin by formulating the popular compression strategies from the perspective of weight encoding, as illustrated in Figure 2. Both pruning and quantization are techniques that encode model weights into a compressed format. However, at high compression ratios, this weight encoding mechanism can become lossy, leading to a decline in model performance. Our hypothesis is that to mitigate the performance loss due to encoded weights, it is essential to implement a decoding method during inference that can reconstruct or remap the weights back to their original (decompressed) state. This approach could enhance the model's accuracy during inference by reversing the effects of a lossy compression. Nonetheless, developing an effective compression strategy that achieves high compression while also enabling accurate weight decoding for inference involves overcoming several challenges, which our work aims to resolve." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To this end, we propose a novel and unique perspective on model compression, which enables aggressive compression of ViT models while maintaining a decoding frame" + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.089, + 0.898, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.359, + 0.908, + 0.429 + ], + "angle": 0, + "content": "Figure 2. Existing compression methods can be viewed as a form of weight encoding. However, inference with lossy encoded weights results in performance dorp whereas proposed DeepCompress-ViT maintains an optimized decoding method at test time to maintain model performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.432, + 0.909, + 0.629 + ], + "angle": 0, + "content": "work to reconstruct the weights back. The key idea is that the compressed version of the weight and a lightweight decoder will be stored in memory to reduce memory costs. However, these weights will be reconstructed back to their original form using the decoder in a layer-by-layer sequence for model inference and thus help to maintain accuracy. Our proposed DeepCompress-ViT consists of two phases—Unified Compression Training and Optimized Test-Time Decoding. In Unified Compression Training, we train an encoder and decoder alongside the model, learning a highly compressed representation of its parameters through encoded embeddings. After training, we retain only these encoded weights and the decoder, discarding the encoder." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.63, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Next, during inference, the goal is to Decode the compressed parameters layer-by-layer systematically to reconstruct the original parameters for each layer to compute the next layers output. Nevertheless, the proposed layer-by-layer decoding approach comes with two notable drawbacks. First, decoding the compressed representation of each layer back to its original form incurs extra computational costs, such as increased energy use and processing time. Additionally, this can lead to significant on-chip memory usage, particularly in larger layers, when decoded weights will be stored on-chip temporarily to compute output of a given layer. Hence, we propose Optimized Test-Time Decoding, eliminating the need to decode embeddings to their original parameters. This optimized decoding step leverages the associative property of matrix multiplication to reorder the decoding operation. This innovation eliminates both computation and memory usage drawback associated with the decoding step, making proposed" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "30148" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "DeepCompress-ViT best of all worlds (accuracy, memory, energy and latency). Our experiments on SOTA ViTs and edge devices show that DeepCompress-ViT achieves compression ratios exceeding \\(14 \\times\\) while achieving unprecedented reductions in energy (\\(>1470 \\times\\)) and latency (\\(>68 \\times\\)), all with the least amount of accuracy loss among the SOTA compression methods." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.201, + 0.233, + 0.215 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.22, + 0.483, + 0.492 + ], + "angle": 0, + "content": "Vision Transformers. The introduction of Transformer architecture [28] has marked a paradigm shift in machine learning, initially transforming natural language processing. Building on this success, the architecture was adapted for computer vision, leading to the development of Vision Transformer (ViT) [7]. This success has led to a surge in transformer-based models for computer vision. For example, DeiT [27] introduced advanced training techniques and a novel distillation approach to reduce ViT's dependence on large datasets. Further architectural innovations, such as Pyramid Vision Transformer (PVT) [29] and Swin Transformer [17], incorporated hierarchical feature representations enabling transformers to serve as versatile frameworks for diverse computer vision applications. Even though ViTs have demonstrated strong performance, they require significant memory that limits their application in edge devices. Compressing ViTs has thus emerged as an important area of research to address this large memory requirement." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.493, + 0.483, + 0.794 + ], + "angle": 0, + "content": "ViT Compression. A widely used approach for compressing Vision Transformers (ViT) is pruning [16, 30-33, 36], which focuses on reducing the number of unimportant weights in the model. Pruning methods for ViT models are commonly divided into two categories: unstructured and structured pruning. Unstructured pruning techniques, such as magnitude-based and Hessian-based methods [24], remove individual weights based on certain importance metrics. However, these techniques result in irregular sparsity patterns, which complicate tensor computations and limit hardware efficiency. Structured pruning mitigates this challenge by removing larger, contiguous structures within the model, such as entire attention heads or rows of weight matrices, which are more compatible with hardware requirements. For instance, [31] proposed a structured pruning method for ViTs that uses a binary mask to distinguish important from unimportant parameters based on magnitude. Another effective approach, introduced in [33], combines pruning, layer skipping, and knowledge distillation within a unified framework to create a compact ViT model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Another widely adopted approach for compressing ViT models is quantization [8, 11-13, 15, 18], which converts floating-point parameters to lower precision values. Several quantization methods tailored to ViT's unique architecture have been proposed. For instance, Q-ViT [11] introduced differentiable quantization for ViTs, treating quantization bit-widths and scales as learnable parameters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "PTQ4ViT [18] utilizes twin uniform quantization and applies a Hessian-guided metric to determine optimal scaling factors. FQ-ViT [15] incorporates powers-of-two scale quantization and log-int quantization specifically for Layer-Norm and Softmax operations, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.168, + 0.907, + 0.243 + ], + "angle": 0, + "content": "While both pruning and quantization methods have shown great promise in reducing computational demands, they still experience significant performance degradation at high compression ratios [11, 31], also shown in Table 2, severely limiting their applicability in edge IoT devices." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.246, + 0.765, + 0.264 + ], + "angle": 0, + "content": "3. Challenges and Motivation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.268, + 0.906, + 0.343 + ], + "angle": 0, + "content": "To motivate our compression technique, we identify the critical bottleneck hindering efficient inference of Vision Transformers (ViTs) at the edge. We will also assess the limitations of current compression methods, establishing the necessary foundation for our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.345, + 0.843, + 0.361 + ], + "angle": 0, + "content": "3.1. Challenges of Efficient Edge Inference" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.365, + 0.906, + 0.593 + ], + "angle": 0, + "content": "The deployment of ViTs on edge devices presents significant challenges due to their substantial memory requirements, which often exceed the on-chip memory capacity of these resource-constrained environments. Consequently, model parameters must be stored in off-chip memory, necessitating a sequential processing approach during inference. This approach involves iteratively loading each layer's weights into on-chip memory and performing computations on that layer before proceeding to the next. While this method enables the inference of ViTs on devices with limited on-chip memory, it introduces significant latency and increased energy consumption due to frequent off-chip memory accesses, both of which are critical concerns in resource-constrained edge environments (e.g., autonomous vehicle perception)." + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.603, + 0.905, + 0.631 + ], + "angle": 0, + "content": "Table 1. Comparison of On-chip and Off-chip Memory Access Cost in Edge Devices" + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.632, + 0.903, + 0.663 + ], + "angle": 0, + "content": "
Memory TypeAccess Time (ns)Energy per Access (pJ)Available Storage (MB)
On-chip1-105·20†1-8
Off-chip70-2001300-2600§1024-8192*
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.526, + 0.663, + 0.892, + 0.676 + ], + "angle": 0, + "content": "†32b SRAM Read (32KB), §32b DRAM [10], * For edge AI devices." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.906, + 0.825 + ], + "angle": 0, + "content": "One potential solution to mitigate this frequent off-chip memory access is model compression. Model compression can reduce the overall memory footprint and allow the entire model to be stored in on-chip memory, which can minimize/eliminate the need for costly memory access. However, as shown in Table 1, the available on-chip memory is often severely constrained (e.g., \\(\\sim 1 - 8\\) MB), and achieving this would require aggressive compression (e.g., greater than \\(10\\times\\))." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "One of the widely explored approaches for model compression is pruning. Numerous studies [24, 31, 33] have applied pruning techniques on ViTs to reduce their memory and computation costs. While pruning has demonstrated significant success in lowering the computational demands" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30149" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.089, + 0.092, + 0.482, + 0.166 + ], + "angle": 0, + "content": "of these models, our investigation reveals that achieving high compression through pruning in ViTs is challenging without severely impacting model performance. As shown in Table 2, even with a \\(2.5 \\times\\) compression ratio, the model suffers \\(\\sim 19\\%\\) accuracy loss." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.168, + 0.483, + 0.333 + ], + "angle": 0, + "content": "Another widely adopted approach for improving model efficiency is quantization [11, 15, 18]. Quantization has proven particularly effective in reducing the memory footprint of large models, such as large language models (LLMs). The existing literature demonstrates that extreme quantization can be successfully applied to LLMs [19] with minimal performance loss. However, quantization applied to ViTs presents a different challenge. Studies focusing on ViTs [11, 34] have shown that these models suffer from significant performance degradation when subjected to extreme quantization (see Table 2)." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.345, + 0.483, + 0.386 + ], + "angle": 0, + "content": "Table 2. Evaluating existing compression methods by aggressively compressing a DeiT-S model and highlighting their shortcoming in achieving our ideal objective (\\(4^{th}\\) row) for edge inference." + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.387, + 0.462, + 0.444 + ], + "angle": 0, + "content": "
MethodOriginal Size (MB)Compression RatioAccuracy (%)
Original Model84.11×79.72
Pruning [11]33.72.5×60.51
Quantization [31]6.1813.6×71.90
Our Objective1-8 ( constraint at edge)10-80× (required)79.72 (ideally)
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.456, + 0.483, + 0.532 + ], + "angle": 0, + "content": "Next, we dissect these two popular model compression strategies to determine the fundamental limitation that hurts the state-of-the-art model compression technique and whether we can develop an orthogonal approach to overcome them at our targeting edge applications." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.533, + 0.214, + 0.547 + ], + "angle": 0, + "content": "3.2. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.553, + 0.483, + 0.689 + ], + "angle": 0, + "content": "As shown in Figure 2, both pruning and quantization can be viewed as a form of encoding original model weights to a compressed representation. The fundamental challenge lies in the way these compression techniques encode model weights. In this work, we postulate that the primary factor contributing to this performance loss can be attributed to the large weight perturbation error introduced by the encoding mechanism of these compression techniques, as formalized in the following lemma." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.695, + 0.483, + 0.801 + ], + "angle": 0, + "content": "Lemma 3.1. (Error Bound for Compression in DNNs). Let \\(\\mathbf{w}\\) represent the weights of a deep neural network (DNN) with an associated loss function \\(\\mathcal{L}(\\mathbf{w})\\). Consider a compression technique that encodes the weights using a transformation \\(\\mathbf{F}\\) resulting in \\(\\mathbf{w}' = \\mathbf{F}(\\mathbf{w})\\) and introducing a perturbation \\(\\delta \\mathbf{w} = \\mathbf{w}' - \\mathbf{w}\\). The change in loss due to this compression can be upper bounded as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.806, + 0.472, + 0.836 + ], + "angle": 0, + "content": "\\[\n| \\mathcal {L} (\\mathbf {w} ^ {\\prime}) - \\mathcal {L} (\\mathbf {w}) | \\leq \\| \\nabla_ {\\mathbf {w}} \\mathcal {L} (\\mathbf {w}) \\| \\| \\delta \\mathbf {w} \\| + \\frac {1}{2} \\| H \\| \\| \\delta \\mathbf {w} \\| ^ {2},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.486, + 0.902 + ], + "angle": 0, + "content": "where \\(\\nabla_{\\mathbf{w}}\\mathcal{L}(\\mathbf{w})\\) is the gradient of the loss function with respect to the original weights \\(\\mathbf{w}\\), \\(\\|H\\|\\) denotes the norm of the Hessian matrix of \\(\\mathcal{L}(\\mathbf{w})\\), and \\(\\|\\delta \\mathbf{w}\\|\\) is the norm of the weight perturbation introduced by the compression." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.198 + ], + "angle": 0, + "content": "From Lemma 3.1, it is evident that a smaller weight perturbation \\(\\| \\delta \\mathbf{w}\\|\\) leads to a tighter upper bound on the loss difference \\(|\\mathcal{L}(\\mathbf{w}^{\\prime}) - \\mathcal{L}(\\mathbf{w})|\\). Therefore, an ideal compression method should minimize the weight perturbation error. However, for edge application of ViTs, we are forced to perform aggressive compression that will inevitably lead to a higher \\(\\| \\delta \\mathbf{w}\\|\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.199, + 0.907, + 0.38 + ], + "angle": 0, + "content": "Neither pruning nor quantization has a countermeasure against this high \\(\\| \\delta \\mathbf{w}\\|\\) for aggressive compression, laying down the foundation for our proposed method as to whether we can device a technique to reduce \\(\\| \\delta \\mathbf{w}\\|\\) at the inference stage even at a high compression ratio. The research question that motivates our work: Given that weight encoding for compression inevitably introduces significant weight perturbation error at high compression ratio, an effective approach to mitigate this error may lie in coupling the encoding mechanism with a complementary decoding mechanism that can reverse the lossy encoding, as formalized in the following proposition." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.39, + 0.907, + 0.512 + ], + "angle": 0, + "content": "Proposition 3.2. (Lower Error Bound with Weight Decoding). Let \\(\\mathbf{w}\\) represent the weights of a deep neural network (DNN) and consider a compression method that encodes these weights using a transformation \\(\\mathbf{F}\\), introducing a weight perturbation \\(\\delta \\mathbf{w} = \\mathbf{w}' - \\mathbf{w}\\). Now consider a weight decoding mechanism with transformation \\(\\mathbf{G}\\), where \\(\\mathbf{G}\\) approximates the inverse of \\(\\mathbf{F}\\). Then, the weight perturbation error after decoding the weights can be bounded as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.523, + 0.802, + 0.541 + ], + "angle": 0, + "content": "\\[\n\\| \\mathbf {G} (\\mathbf {F} (\\mathbf {w})) - \\mathbf {w} \\| \\leq \\| \\delta \\mathbf {w} \\|.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.906, + 0.659 + ], + "angle": 0, + "content": "The above proposition demonstrates the potential of a weight decoding strategy to reduce weight perturbation and minimize the impact on model performance at inference. Inspired by Proposition 3.2, we aim to design a novel Encoder-Decoder-based model compression approach that can enable the potential of achieving a high compression ratio while minimizing inference loss." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.667, + 0.864, + 0.685 + ], + "angle": 0, + "content": "4. Proposed Method: DeepCompress-ViT" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We propose DeepCompress-ViT, a novel compression framework designed for achieving a high compression ratio while preserving inference accuracy. As shown in Figure 3, our novel DeepCompress-ViT framework consists of two stages. In the first stage, we propose Unified Compression Training, which jointly trains the encoder and decoder networks (see Figure 3). The encoder network, denoted as \\(\\mathbf{F}\\), learns to encode the original model weights w from \\(\\mathbb{R}^d\\) to \\(\\mathbb{R}^r\\), where \\(r \\ll d\\). And the decoder network, \\(\\mathbf{G}\\), learns to decode the encoded weights back to \\(\\mathbb{R}^d\\). After training is complete, only the encoded weights and the decoder network are retained for inference, while the encoder network is discarded. During inference, the proposed DeepCompress-ViT reconstructs each layer's weight one by" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "30150" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.088, + 0.485, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.225, + 0.486, + 0.281 + ], + "angle": 0, + "content": "Figure 3. Unified Compression Training. The Encoder and Decoder parameters are optimized jointly to minimize the loss. After training, only encoded weights and decoder network is retained for inference" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.291, + 0.484, + 0.32 + ], + "angle": 0, + "content": "one and performs inference using the decoded version of the weight to help maintain inference accuracy." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.322, + 0.485, + 0.64 + ], + "angle": 0, + "content": "While the decoding step is necessary to maintain accuracy, it has two drawbacks. To understand this, lets consider a simplified form the output computation for a given layer: input \\(\\times\\) encoded weight \\(\\times\\) decoder weight. First, the decoding step will be performed using encoded weight \\(\\times\\) decoder weight which introduces additional computation at runtime, and second, the reconstructed version of the weight will increase temporary on-chip memory consumption, especially for larger layers. To address this, we propose optimizing the decoding step by designing a lightweight decoder implemented as a single linear layer. In addition, we leverage the associative property of matrix multiplication to transform the inefficient weight decoding input \\(\\times\\) (encoded weight \\(\\times\\) decoder weight) to optimized test-time decoding as (input \\(\\times\\) encoded weight) \\(\\times\\) decoder weight, which would ensure the computation cost remains unchanged for an optimum level of decoder input (compressed weight size \\(r\\) outlined in equation 4 in details) is selected. This optimization ensures the proposed DeepCompress-ViT does not introduce any computational overhead (Figure 4) in pursuit of compression and accuracy." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.649, + 0.415, + 0.667 + ], + "angle": 0, + "content": "4.1. Unified Compression Training (UCT)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.673, + 0.483, + 0.764 + ], + "angle": 0, + "content": "In this stage, an encoder-decoder network is trained to achieve aggressive compression. The encoder network \\(\\mathbf{F}\\), learns to encode the model's weights to a compressed representation as the encoded embedding, while the decoder network, \\(\\mathbf{G}\\), learns to decode the weights back to their original dimension as shown in Figure 3." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.841 + ], + "angle": 0, + "content": "Consider a ViT model \\(\\mathbf{H}_{\\mathbf{W}}(\\cdot)\\) consisting of \\(L\\) layers, where the weights of the layers are denoted by the set \\(\\mathbf{W} = \\{\\mathbf{w}_1,\\mathbf{w}_2,\\dots ,\\mathbf{w}_L\\}\\). Let the parameters of the encoder network \\(\\mathbf{F}(.)\\) be represented as \\(\\mathbf{W}_{\\mathbf{E}}\\), and the parameters of the decoder network \\(\\mathbf{G}(.)\\) be represented as \\(\\mathbf{W}_{\\mathbf{D}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.484, + 0.902 + ], + "angle": 0, + "content": "During training, each layer's weight \\(\\mathbf{w}_i\\) is passed through the encoder network \\(\\mathbf{F}\\), which encodes it to a lower-dimensional representation, given by \\(\\mathbf{z}_i = \\mathbf{F}(\\mathbf{w}_i)\\). The decoder network \\(\\mathbf{G}\\) then decodes \\(\\mathbf{z}_i\\) back to its original di" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.168 + ], + "angle": 0, + "content": "mensionality as \\(\\hat{\\mathbf{w}}_i = \\mathbf{G}(\\mathbf{z}_i)\\). The encoder and decoder networks are trained jointly to minimize the mean squared error (MSE) between the original weight set \\((\\mathbf{W})\\) and the reconstructed weight set \\((\\hat{\\mathbf{W}})\\). The weight reconstruction loss is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.589, + 0.176, + 0.833, + 0.218 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\bf m s e} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\| {\\bf w} _ {i} - {\\bf G} ({\\bf F} ({\\bf w} _ {i})) \\| ^ {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.228, + 0.907, + 0.394 + ], + "angle": 0, + "content": "To optimize this training step further, we unify the encoder-decoder training step with the original ViT-model. Our hypothesis is that only MSE loss-based weight reconstruction may not provide optimal performance [2]. Even though minimizing MSE loss results in the minimization of weight perturbation error, different sets of decoded weights with the same MSE value can have varying weight distributions, which can lead to a performance drop in the ViT model. Hence, it is reasonable to incorporate the ViT model into this training loop to align the ViT model's weight distribution with the decoded version of the weight." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.395, + 0.906, + 0.529 + ], + "angle": 0, + "content": "Hence, we propose this end-to-end unified framework where the encoder-decoder networks are jointly trained with the ViT model. Our method will incorporate cross-entropy (CE) loss and knowledge distillation (KD) from a pretrained model in training, where CE ensures the ViT model performance is optimized on the decoded weight values w.r.t ground truth, and KD ensures the decoded weight parameters do not drift far apart from the initial weight distribution of a pre-trained ViT model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.53, + 0.906, + 0.665 + ], + "angle": 0, + "content": "The forward pass for the whole end-to-end training after obtaining the decoded weight sets \\(\\hat{\\mathbf{W}}\\) from the decoder is formulated as \\(\\mathbf{H}_{\\mathbf{W}}(\\cdot) \\rightarrow \\mathbf{H}_{\\hat{\\mathbf{W}}}(\\cdot)\\), which implies that the ViT model inference will always use the decoded weights, i.e., the forward pass of the ViT model becomes \\(\\hat{\\mathbf{y}} = \\mathbf{H}_{\\hat{\\mathbf{W}}}(\\mathbf{x})\\), where \\(\\mathbf{x}\\) are the input images and \\(\\hat{\\mathbf{y}}\\) are the predictions from the ViT model. Next, using \\(\\hat{\\mathbf{y}}\\), we compute the cross-entropy loss and knowledge distillation loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.675, + 0.895, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathbf {C E}} = - \\sum_ {i} \\mathbf {y} _ {i} \\log (\\hat {\\mathbf {y}} _ {i}), \\quad \\mathcal {L} _ {\\mathbf {K D}} = \\sum_ {i} \\hat {\\mathbf {y}} _ {\\mathrm {t}, i} \\log \\left(\\frac {\\hat {\\mathbf {y}} _ {\\mathrm {t} , i}}{\\hat {\\mathbf {y}} _ {i}}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.722, + 0.906, + 0.752 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{y}}_{\\mathrm{t}}\\) represents the prediction from the pretrained teacher model. The total loss function is then defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.765, + 0.842, + 0.781 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {t o t a l}} = \\mathcal {L} _ {\\mathrm {m s e}} + \\alpha \\cdot \\mathcal {L} _ {\\mathrm {C E}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {K D}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.793, + 0.906, + 0.869 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are scaling factors controlling the contributions of cross-entropy and knowledge distillation losses, respectively. Finally, the overall loss function is minimized by jointly optimizing the encoder and decoder parameters \\(\\mathbf{W}_{\\mathbf{E}}\\) and \\(\\mathbf{W}_{\\mathbf{D}}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.876, + 0.761, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {W} _ {\\mathrm {E}}, \\mathbf {W} _ {\\mathrm {D}}} \\mathcal {L} _ {\\mathrm {t o t a l}}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "30151" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.187, + 0.089, + 0.486, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.089, + 0.813, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.348, + 0.907, + 0.391 + ], + "angle": 0, + "content": "Figure 4. Proposed Optimized Test-Time Decoding overview. Decoding the encoded (compressed) weights first and then matrix multiplying with input activation increases FLOPs. The proposed method eliminates extra FLOPs by multiplying input activation with encoded weights first, then passing through decoder. The chosen value of encoding dimension \\((r)\\) prevents any FLOP increase." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.399, + 0.483, + 0.444 + ], + "angle": 0, + "content": "After training is complete, for inference, we keep only the encoded weight parameters \\(\\{\\mathbf{z}_i\\}\\) and a lightweight decoder \\(\\mathbf{W}_{\\mathbf{D}}\\) in memory while discarding the encoder \\(\\mathbf{W}_{\\mathbf{E}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.444, + 0.484, + 0.579 + ], + "angle": 0, + "content": "At inference, the decoder needs to map compressed weights to their original form layer by layer, which may help preserve accuracy. However, this can introduce two major drawbacks. First, the decoding step will inevitably lead to additional computation at runtime, and second, the decoded weights will increase temporary on-chip memory consumption, particularly for larger layers. Next, we outline our optimized test-time decoding strategy, which ensures these two bottlenecks remain in check." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.588, + 0.367, + 0.604 + ], + "angle": 0, + "content": "4.2. Optimized Test-Time Decoding" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.611, + 0.483, + 0.731 + ], + "angle": 0, + "content": "To mitigate the overhead associated with the decoding step, first design level optimization we propose is to design the decoder \\(\\mathbf{G}\\) as a single linear layer. This design choice minimizes repetitive decoding operations, reducing the computational overhead. Although a single-layer decoder network lowers the computational load relative to a multi-layer decoder, the computation needed for decoding weights using a single layer still persists." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.732, + 0.483, + 0.853 + ], + "angle": 0, + "content": "To illustrate the overhead of weight decoding step, consider a fully connected layer in a ViT model with original weights \\(\\mathbf{w}_i\\in \\mathbb{R}^{C\\times d}\\), whose weights are encoded and the encoded weights are represented by \\(\\mathbf{z}_i\\in \\mathbb{R}^{C\\times r}\\). During inference of this layer, the weights are first decoded using the single-layer decoder network \\(\\mathbf{G}\\), where weights of the decoder network is represented by \\(\\mathbf{w}_D\\in \\mathbb{R}^{r\\times d}\\). This weight decoding computation can be represented as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.232, + 0.86, + 0.483, + 0.875 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {w}} _ {i} = \\mathbf {z} _ {i} \\times \\mathbf {w} _ {D}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.885, + 0.484, + 0.901 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{w}}_i\\in \\mathbb{R}^{C\\times d}\\) denotes the decoded weights. One of the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.399, + 0.907, + 0.489 + ], + "angle": 0, + "content": "most widely used metrics to evaluate computational complexity is Floating-point Operations (FLOPs) [6], which counts the total number of multiplications and additions performed in a given operation. The FLOPs incurred for the weight decoding operation is \\(2 \\cdot C \\cdot r \\cdot d\\), corresponding to the matrix multiplication in eqn. (1)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.489, + 0.907, + 0.534 + ], + "angle": 0, + "content": "Next, the usual forward pass of fully connected layer in the ViT model with input activations \\(\\mathbf{x}_i\\in \\mathbb{R}^{N\\times C}\\) and decoded weights \\(\\hat{\\mathbf{w}}_i\\) is computed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.651, + 0.544, + 0.905, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} \\times \\hat {\\mathbf {w}} _ {i}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.907, + 0.673 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_{i + 1}\\) represents the output activations of the layer. The FLOPs incurred by this forward pass is \\(2\\cdot N\\cdot C\\cdot d\\) resulting from the matrix multiplication in eqn. (2). Therefore, the total FLOPs incurred in the forward pass with this strategy is \\((2\\cdot N\\cdot C\\cdot d + 2\\cdot C\\cdot r\\cdot d)\\) where the additional \\(2\\cdot C\\cdot r\\cdot d\\) FLOPs is incurred because of this inefficient weight decoding strategy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.907, + 0.78 + ], + "angle": 0, + "content": "Next, we optimize the decoding step to eliminate this additional \\(2 \\cdot C \\cdot r \\cdot d\\) FLOPs, we propose Optimized Test-Time Decoding. Our proposed decoding approach leverages the associative property of matrix multiplication to reorder computation sequence to maintain or improve overall FLOPs. To illustrate, recall that the overall computation for inefficient decoding strategy is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.788, + 0.905, + 0.804 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} \\times \\hat {\\mathbf {w}} _ {i} = \\mathbf {x} _ {i} \\times \\left(\\mathbf {z} _ {i} \\times \\mathbf {w} _ {D}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.812, + 0.907, + 0.872 + ], + "angle": 0, + "content": "where it shows weight decoding first and then perform the forward pass in the fully connected layer of ViT model. We optimize the decoding step by simply reorder the matrix multiplications as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.881, + 0.838, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} ^ {\\prime} \\times \\mathbf {w} _ {D} = (\\mathbf {x} _ {i} \\times \\mathbf {z} _ {i}) \\times \\mathbf {w} _ {D},\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30152" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.482, + 0.137 + ], + "angle": 0, + "content": "where we first perform input compression \\((\\mathbf{x} \\in \\mathbb{R}^{N \\times C} \\to \\mathbf{x}' \\in \\mathbb{R}^{N \\times r})\\) and then do the optimized forward pass \\((\\mathbf{x}' \\times \\mathbf{w}_D)\\). The proposed strategy is also illustrated in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.137, + 0.482, + 0.228 + ], + "angle": 0, + "content": "The total FLOPs for this optimized approach is \\(2 \\cdot N \\cdot r \\cdot (C + d)\\). However, with an arbitrary value of \\(r\\), the overall FLOPs can still go up. Therefore, to ensure that the total FLOPs of the proposed decoding strategy do not exceed the baseline models FLOPs, we derive the optimal \\(r\\) for efficiency by solving the following inequality," + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.24, + 0.405, + 0.255 + ], + "angle": 0, + "content": "\\[\n2 \\cdot N \\cdot r \\cdot (C + d) \\leq 2 \\cdot N \\cdot C \\cdot d,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.268, + 0.483, + 0.299 + ], + "angle": 0, + "content": "where \\(2 \\cdot N \\cdot C \\cdot d\\) is the FLOPs incurred due to normal forward pass in eqn. (2). Solving the inequality, we get:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.308, + 0.483, + 0.341 + ], + "angle": 0, + "content": "\\[\nr \\leq \\frac {2 \\cdot N \\cdot C \\cdot d}{2 \\cdot N \\cdot (C + d)} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.351, + 0.484, + 0.412 + ], + "angle": 0, + "content": "In summary, by reordering the computation sequence and using optimal \\( r \\) for compression derived in eqn. (4), our innovative decoding optimization does not incur any additional computation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.419, + 0.296, + 0.435 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.443, + 0.411, + 0.459 + ], + "angle": 0, + "content": "5.1. Datasets and Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.463, + 0.483, + 0.553 + ], + "angle": 0, + "content": "Datasets. We conduct our experiments on the ILSVRC12 ImageNet classification dataset [22] consisting 1,000 classes with 1.2 million training images and 50k validation images. Additionally, we evaluate DeepCompress-ViT on the widely used COCO benchmark dataset [14] for object detection and instance segmentation task." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.554, + 0.483, + 0.704 + ], + "angle": 0, + "content": "Encoder-Decoder Architecture. We use four encoder network each with 2 linear layers to encode four types of layers: attn_qkv, attnProj, mlp_fcl and mlp_fcl2. Each encoder has an affine transformation before and after the 2 linear layers. Similarly to encoders, we use four single linear layer decoders to decode the four types of layers. Note that each decoder is a shared decoder which decodes a particular type of layer of all ViT blocks. Note that, we exclude the first layer, last layer, and LayerNorm parameters from compression." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Experimental Settings. The encoder and decoder models are trained for 275 epochs with a batch size of 256 and a base learning rate of \\(1 \\times 10^{-4}\\), using a cosine learning rate scheduler. For data augmentation, we apply the standard techniques used in [27] and for knowledge distillation, we use pretrained distilled DeiT models [27] with temperature \\(\\tau = 1\\). For UCT, we set the value of \\(\\alpha = 1\\) and \\(\\beta = 3 \\times 10^3\\). The encoded weights are quantized using 4-bit asymmetric quantization, while decoder weights are quantized using 4-bit symmetric quantization, both trained using Quantization Aware Training. Additionally, the patch embedding (first) and classification (last) layers are quantized using 8-bit symmetric quantization. The optimal value of \\(r\\) from" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "solving (4) is set to 277 for DeiT-S and 502 for DeiT-B. For object detection and instance segmentation, we use the mmdetection library with the standard \\(1 \\times\\) training scheduler and adopt an edge-friendly resolution of \\(384 \\times 384\\) for both training and evaluation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.191, + 0.608, + 0.205 + ], + "angle": 0, + "content": "5.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.212, + 0.907, + 0.501 + ], + "angle": 0, + "content": "Image Classification. Performance of the compressed DeiT models with proposed DeepCompress-ViT on the classification task is shown in Table 3. The results demonstrate substantial reductions in model size and energy consumption resulting from DeepCompress-ViT. For instance, the DeepCompress-DeiT-S model achieves a compression ratio of \\(14.9\\times\\), reducing the model size from \\(84.1\\mathrm{MB}\\) to just \\(5.64\\mathrm{MB}\\) while maintaining an accuracy of \\(78.74\\%\\) on ImageNet. Similarly, DeepCompress-DeiT-B achieves a compression ratio of \\(17.4\\times\\), decreasing the model size from \\(330.2\\mathrm{MB}\\) to \\(18.9\\mathrm{MB}\\). Remarkably, both models show an unprecedented energy reduction of \\(673\\times\\) and \\(1475\\times\\) and latency reduction of \\(44.5\\times\\) and \\(68.4\\times\\) respectively (please refer to section 5.3 and Figure 5 for more hardware energy and latency evaluation details). Proposed DeepCompress-ViT achieves this unprecedented level of model compression, energy, and latency reduction, enabling the deployment of ViT models at the edge while only sacrificing a marginal level of accuracy (e.g., for DeiT-B only \\(\\sim 0.1\\%\\))" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.504, + 0.906, + 0.685 + ], + "angle": 0, + "content": "Object Detection and Instance Segmentation. Next, table 4 compares the performance of DeepCompress-ViT with baseline (no compression) DeiT-S model on object detection and instance segmentation tasks. We trained both the models on COCO dataset integrating the respective ViT backbones with Mask R-CNN [9]. We evaluate both of the models for these tasks at an edge-friendly resolution of \\(384 \\times 384\\). Notably, DeepCompress-ViT reduces the ViT backbone (DeiT-S) size from 82.65MB to 5.27MB (\\(15.7 \\times\\) compression) with a slight drop in \\(\\mathrm{AP^b}\\) and \\(\\mathrm{AP^m}\\), further highlighting the effectiveness of our compression method on other complex vision tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.906, + 0.9 + ], + "angle": 0, + "content": "Comparison with SOTA compression methods. Finally, Table 5 provides a comparative analysis of DeiT-Small models compressed using different pruning and quantization methods. Among the methods, DeepCompress-ViT achieves the highest compression ratio of \\(14.9 \\times\\), reducing the model size to 5.64 MB while maintaining a top-1 accuracy of \\(78.74\\%\\). In contrast, popular WDPruning [31], LSQ [8] and Q-ViT [11] achieves achieve much lower accuracies of \\(60.51\\%\\), \\(68.00\\%\\) and \\(71.9\\%\\), respectively. Our proposed DeepCompress-ViT consistently outperforms them by large margins of \\(\\sim 18\\%\\), \\(\\sim 10\\%\\), and \\(\\sim 7\\%\\), respectively, making DeepCompress-ViT the only practical choice to maintain accuracy while performing aggressive compression." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "30153" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.118 + ], + "angle": 0, + "content": "Table 3. Performance of DeepCompress-ViT on ImageNet-1K. DeepCompress-ViT achieves memory (\\( \\geq 15 \\times \\)) and energy consumption (\\( \\geq 1531 \\times \\)), while marginal accuracy drop (\\(< 1\\%\\))." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.119, + 0.868, + 0.188 + ], + "angle": 0, + "content": "
MethodAccuracy (%)Model Size (MB)Compression RatioGFLOPsExecution Time (s)Energy Consumption (J)
DeiT-S [27]79.7284.11x9.2024.029979.52
DeepCompress-DeiT-S78.745.6414.9x8.880.5414.83
DeiT-B [27]81.74330.21x35.14129.32150895
DeepCompress-DeiT-B81.6218.917.4x30.841.89102.29
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.205, + 0.483, + 0.246 + ], + "angle": 0, + "content": "Table 4. Performance of DeepCompress-ViT for Object Detection on the COCO validation set with Mask R-CNN evaluated at an edge-friendly resolution of \\(384 \\times 384\\)." + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.247, + 0.44, + 0.292 + ], + "angle": 0, + "content": "
Method\\( {\\mathbf{{AP}}}^{\\mathbf{b}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}} \\)ViT Backbone Size (MB)
DeiT-S [27]26.223.782.65
DeepCompress-ViT23.020.95.27 (15.7×)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.308, + 0.483, + 0.336 + ], + "angle": 0, + "content": "Table 5. Performance comparison of DeiT-Small with SOTA compression methods on ImageNet-1K" + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.336, + 0.482, + 0.413 + ], + "angle": 0, + "content": "
ModelAccuracy (%)Model Size (MB)Compression Ratio
DeiT-S [27]79.72 (0)84.11x
WDPruning [31]60.51 (↓19.21)33.72.5x
LSQ [8]68.00 (↓11.72)6.1813.6x
Q-ViT [11]71.90 (↓7.82)6.1813.6x
DeepCompress-ViT78.74 (↓0.98)5.6414.9x
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.429, + 0.295, + 0.444 + ], + "angle": 0, + "content": "5.3. Hardware Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.448, + 0.485, + 0.902 + ], + "angle": 0, + "content": "High compression gain gives an understanding of the effectiveness of a compression method in terms of memory savings. But to successfully realize the full potential of our proposed method, we evaluate the energy and latency gain on hardware evaluation platforms. For hardware deployment, we use the gem5-Aladdin platform [25], which effectively captures dynamic interactions between accelerators and the SoC platform, enabling detailed architectural analysis of the proposed compression method. Our setup incorporates a cycle-accurate in-house-developed model based on the Eyeriss accelerator [5] (0.0029 DRAM access/multiply and accumulation (MAC), 33.6 GMAC/s). Performance metrics from gem5-Aladdin are then analyzed using DRAM-Sim2 [21] to model realistic off-chip memory latency and energy characteristics. The total on-chip weight memory is capped at three configurations (2 MB, 4 MB, 8 MB). The analyzed DeiT-S model initially requires 84.1MB of memory, which exceeds the on-chip memory capacity. By applying DeepCompress-ViT algorithm, this requirement is reduced to 5.64 MB, which can readily fit into the 8MB on-chip memory. However, with a smaller memory capacity, it is not feasible to transfer the entire set of weight parameters to the accelerator in a single batch due to the model's memory demands. Therefore, we implemented a weight parser that transmits weight parameters in variable batch sizes to the accelerator. Figure 5 shows the breakdown of energy consumption and latency across MAC, off-chip, and on-chip memory access components for various on-chip memory sizes. For both DeiT-S and DeiT-B, the DeepCompress-ViT algorithm achieves significant energy savings, reduc" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.19, + 0.712, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.192, + 0.903, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.345, + 0.906, + 0.4 + ], + "angle": 0, + "content": "Figure 5. Breakdown of (a) Energy consumption, (b) Latency vs. on-chip memory size. For every off-chip memory size, DeiT-S, DeepCompress-ViT-S, DeiT-B, and DeepCompress-ViT-B results are plotted, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.409, + 0.907, + 0.545 + ], + "angle": 0, + "content": "ing consumption by approximately \\(673 \\times\\) and \\(1475 \\times\\), respectively, with an 8MB on-chip memory. This remarkable reduction is primarily due to the DeepCompress-ViT algorithm's ability to minimize off-chip memory access, as visible through the high difference in the red bar plots. This reduction becomes even more pronounced with smaller memory sizes, enabling for the first time the possibility of deploying large ViT models at the edge and performing time-sensitive applications." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.561, + 0.634, + 0.577 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.584, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this paper, we present DeepCompress-ViT, a novel approach to achieve highly compressed Vision Transformers optimized for efficient edge deployment. We first analyze the limitations of existing model compression techniques and show that they lead to large weight perturbation error because of their lossy encoding mechanism. Then, to resolve this challenge, we develop an orthogonal compression technique that consists of an encoding for compression and a decoding step to help maintain performance. However, decoding weights repeatedly during inference can lead to additional computation and increase on-chip memory usage, both of which are critical concerns for edge applications. To address these challenges, we propose a novel optimized Test-Time Decoding scheme that enables efficient inference without increased computation and avoids high on-chip memory usage. Our extensive experiments and hardware evaluation show that the proposed DeepCompress-ViT can lead to an unprecedented reduction in energy and execution time with minimal loss of performance, unlocking the possibilities of deploying large-scale ViT models at edge IIoT devices." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "30154" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.414, + 0.129 + ], + "angle": 0, + "content": "[1] Esp32-s3 designed for aiot applications, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.131, + 0.483, + 0.198 + ], + "angle": 0, + "content": "[2] Sabbir Ahmed, Uday Kamal, and Md Kamrul Hasan. Dfrtsd: A deep learning based framework for robust traffic sign detection under challenging weather conditions. 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Advances in Neural Information Processing Systems, 35:9010-9023, 2022. 3" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.482, + 0.739 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "30156" + } + ] +] \ No newline at end of file diff --git a/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/3bd82ff4-b9fe-43da-a28f-c5a1697c4ab3_origin.pdf b/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/3bd82ff4-b9fe-43da-a28f-c5a1697c4ab3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f1327eef4d0f07d415366ca2d67aff56ef4a3267 --- /dev/null +++ b/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/3bd82ff4-b9fe-43da-a28f-c5a1697c4ab3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5651a7ef730fbffc5b666af316fed78ea8f823e46320e88096c1b87c7db2a6b9 +size 609195 diff --git a/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/full.md b/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d62cc3a6bb93c9dd11dfd1e5e8ff34b84b4752de --- /dev/null +++ b/2025/DeepCompress-ViT_ Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge/full.md @@ -0,0 +1,296 @@ +# DeepCompress-ViT: Rethinking Model Compression to Enhance Efficiency of Vision Transformers at the Edge + +Sabbir Ahmed $^{1*}$ , Abdullah Al Arafat $^{2*}$ , Deniz Najafi $^{3*}$ , Akhlak Mahmood $^{4}$ , Mamshad Nayeem Rizve $^{5}$ , Mohaiminul Al Nahian $^{1}$ , Ranyang Zhou $^{3}$ , Shaahin Angizi $^{3}$ , Adnan Siraj Rakin $^{1}$ $^{1}$ Binghamton University (SUNY), $^{2}$ North Carolina State University, $^{3}$ New Jersey Institute of Technology, $^{4}$ Georgia Institute of Technology, $^{5}$ Adobe Inc. + +# Abstract + +Vision Transformers (ViTs) excel in tackling complex vision tasks, yet their substantial size poses significant challenges for applications on resource-constrained edge devices. The increased size of these models leads to higher overhead (e.g., energy, latency) when transmitting model weights between the edge device and the server. Hence, ViTs are not ideal for edge devices where the entire model may not fit on the device. Current model compression techniques often achieve high compression ratios at the expense of performance degradation, particularly for ViTs. To overcome the limitations of existing works, we rethink model compression strategy for ViTs from first principle approach and develop an orthogonal strategy called DeepCompress-ViT. The objective of the DeepCompress-ViT is to encode the model weights to a highly compressed encoded representation using a novel training method, denoted as Unified Compression Training (UCT). Proposed UCT is accompanied by a decoding mechanism during inference, which helps to gain any loss of accuracy due to high compression ratio. We further optimize this decoding step by reordering the decoding operation using associative property of matrix multiplication, ensuring that the compressed weights can be decoded during inference without incurring any computational overhead. Our extensive experiments across multiple ViT models on modern edge devices show that DeepCompress-ViT can successfully compress ViTs at high compression ratios $(>14\times)$ . DeepCompress-ViT enables the entire model to be stored on edge device, resulting in unprecedented reductions in energy consumption $(>1470\times)$ and latency $(>68\times)$ for edge ViT inference. Our code is available at https://github.com/ML-Security-Research-LAB/DeepCompress-ViT. + +# 1. Introduction + +The integration of computer vision and deep learning (DL) into the Industrial Internet of Things (IIoT) and edge de + +![](images/c021b82f1ded9a591fc796bd3d6bb00c9144042ae1b71403ae3092d189b66af8.jpg) +Figure 1. Comparison of DeepCompress-ViT with SOTA ViT compression methods [8, 11, 31] for compressing DeiT-S [27] trained onImagenet-1k [22]. Existing compression methods achieve a large compression ratio at the expense of large performance loss, whereas the DeepCompress-ViT achieves the highest compression ratio with the best accuracy among the competition. + +vices has revolutionized data processing, analysis, and action in these systems [3]. By deploying advanced models, such as Vision Transformers (ViTs), on resource-constrained devices, IIoT systems can directly manage complex tasks, including object detection, anomaly detection, and facial recognition on the device. This local processing capability on edge minimizes data transmission to centralized servers, reducing latency and enhancing data privacy by keeping information closer to its source [35]. + +In recent years, Vision Transformers (ViTs) [7] have gained significant attention among deep neural network (DNN) models for their remarkable performance [20]. Their potential to tackle various real-world vision problems, such as object detection [4] and segmentation [26], makes them especially appealing for edge applications. However, the challenge of achieving reliable, real-time inference on resource-constrained devices cannot be underestimated, primarily due to the large model sizes of ViTs in comparison to models like Convolutional Neural Networks [23]. + +The architectural design of ViTs often exceeds the on-chip memory limits of edge devices (e.g., Espressif ESP32- + +S3 [1] has 8 MB pseudo-static RAM on-chip memory, but DeiT-S model size is approximately 85 MB), leading to a reliance on off-chip memory from servers to store the entire model. This dependency introduces two critical challenges that significantly impede the use of large ViTs in edge environments [10]. Firstly, computations performed on-chip are estimated to be 10 to 100 times faster than those conducted off-chip (see Table 1 for a detailed numerical comparison of various metrics between on- and off-chip memories). Secondly, transferring sizable model weights demands high communication bandwidth, resulting in elevated energy consumption. As a result, for edge applications (e.g., real-time patient monitoring, autonomous vehicle perception, quality control in production) where latency and power efficiency are critical, the deployment of ViT models is severely limited. Therefore, addressing model size and enhancing memory management are not just challenges; they are essential for unlocking the full potential of ViT models in IoT devices. + +To effectively deploy large Vision Transformer (ViT) models at the edge, it is crucial to aggressively compress them to fit into on-chip memory. Aggressive compression reduces reliance on off-chip memory, decreasing latency and energy consumption. However, techniques such as pruning [31] and quantization [11] often face challenges at high compression ratios, leading to significant drops in performance. For instance, the DeiT-Small model, which is approximately $85\mathrm{MB}$ , would require over $10\times$ compression to fit into an 8 MB edge device. This extreme compression level can result in severe accuracy loss (please refer to Figure 1). Therefore, it is essential to carefully reconsider and rethink model compression strategies for ViTs to maintain both performance and efficiency at the edge. + +In this work, we begin by formulating the popular compression strategies from the perspective of weight encoding, as illustrated in Figure 2. Both pruning and quantization are techniques that encode model weights into a compressed format. However, at high compression ratios, this weight encoding mechanism can become lossy, leading to a decline in model performance. Our hypothesis is that to mitigate the performance loss due to encoded weights, it is essential to implement a decoding method during inference that can reconstruct or remap the weights back to their original (decompressed) state. This approach could enhance the model's accuracy during inference by reversing the effects of a lossy compression. Nonetheless, developing an effective compression strategy that achieves high compression while also enabling accurate weight decoding for inference involves overcoming several challenges, which our work aims to resolve. + +To this end, we propose a novel and unique perspective on model compression, which enables aggressive compression of ViT models while maintaining a decoding frame + +![](images/6289255a14ece7fa96528f50db9adf84d14bd23af8579ab33438e22578d393c6.jpg) +Figure 2. Existing compression methods can be viewed as a form of weight encoding. However, inference with lossy encoded weights results in performance dorp whereas proposed DeepCompress-ViT maintains an optimized decoding method at test time to maintain model performance. + +work to reconstruct the weights back. The key idea is that the compressed version of the weight and a lightweight decoder will be stored in memory to reduce memory costs. However, these weights will be reconstructed back to their original form using the decoder in a layer-by-layer sequence for model inference and thus help to maintain accuracy. Our proposed DeepCompress-ViT consists of two phases—Unified Compression Training and Optimized Test-Time Decoding. In Unified Compression Training, we train an encoder and decoder alongside the model, learning a highly compressed representation of its parameters through encoded embeddings. After training, we retain only these encoded weights and the decoder, discarding the encoder. + +Next, during inference, the goal is to Decode the compressed parameters layer-by-layer systematically to reconstruct the original parameters for each layer to compute the next layers output. Nevertheless, the proposed layer-by-layer decoding approach comes with two notable drawbacks. First, decoding the compressed representation of each layer back to its original form incurs extra computational costs, such as increased energy use and processing time. Additionally, this can lead to significant on-chip memory usage, particularly in larger layers, when decoded weights will be stored on-chip temporarily to compute output of a given layer. Hence, we propose Optimized Test-Time Decoding, eliminating the need to decode embeddings to their original parameters. This optimized decoding step leverages the associative property of matrix multiplication to reorder the decoding operation. This innovation eliminates both computation and memory usage drawback associated with the decoding step, making proposed + +DeepCompress-ViT best of all worlds (accuracy, memory, energy and latency). Our experiments on SOTA ViTs and edge devices show that DeepCompress-ViT achieves compression ratios exceeding $14 \times$ while achieving unprecedented reductions in energy ( $>1470 \times$ ) and latency ( $>68 \times$ ), all with the least amount of accuracy loss among the SOTA compression methods. + +# 2. Related Work + +Vision Transformers. The introduction of Transformer architecture [28] has marked a paradigm shift in machine learning, initially transforming natural language processing. Building on this success, the architecture was adapted for computer vision, leading to the development of Vision Transformer (ViT) [7]. This success has led to a surge in transformer-based models for computer vision. For example, DeiT [27] introduced advanced training techniques and a novel distillation approach to reduce ViT's dependence on large datasets. Further architectural innovations, such as Pyramid Vision Transformer (PVT) [29] and Swin Transformer [17], incorporated hierarchical feature representations enabling transformers to serve as versatile frameworks for diverse computer vision applications. Even though ViTs have demonstrated strong performance, they require significant memory that limits their application in edge devices. Compressing ViTs has thus emerged as an important area of research to address this large memory requirement. + +ViT Compression. A widely used approach for compressing Vision Transformers (ViT) is pruning [16, 30-33, 36], which focuses on reducing the number of unimportant weights in the model. Pruning methods for ViT models are commonly divided into two categories: unstructured and structured pruning. Unstructured pruning techniques, such as magnitude-based and Hessian-based methods [24], remove individual weights based on certain importance metrics. However, these techniques result in irregular sparsity patterns, which complicate tensor computations and limit hardware efficiency. Structured pruning mitigates this challenge by removing larger, contiguous structures within the model, such as entire attention heads or rows of weight matrices, which are more compatible with hardware requirements. For instance, [31] proposed a structured pruning method for ViTs that uses a binary mask to distinguish important from unimportant parameters based on magnitude. Another effective approach, introduced in [33], combines pruning, layer skipping, and knowledge distillation within a unified framework to create a compact ViT model. + +Another widely adopted approach for compressing ViT models is quantization [8, 11-13, 15, 18], which converts floating-point parameters to lower precision values. Several quantization methods tailored to ViT's unique architecture have been proposed. For instance, Q-ViT [11] introduced differentiable quantization for ViTs, treating quantization bit-widths and scales as learnable parameters. + +PTQ4ViT [18] utilizes twin uniform quantization and applies a Hessian-guided metric to determine optimal scaling factors. FQ-ViT [15] incorporates powers-of-two scale quantization and log-int quantization specifically for Layer-Norm and Softmax operations, respectively. + +While both pruning and quantization methods have shown great promise in reducing computational demands, they still experience significant performance degradation at high compression ratios [11, 31], also shown in Table 2, severely limiting their applicability in edge IoT devices. + +# 3. Challenges and Motivation + +To motivate our compression technique, we identify the critical bottleneck hindering efficient inference of Vision Transformers (ViTs) at the edge. We will also assess the limitations of current compression methods, establishing the necessary foundation for our proposed method. + +# 3.1. Challenges of Efficient Edge Inference + +The deployment of ViTs on edge devices presents significant challenges due to their substantial memory requirements, which often exceed the on-chip memory capacity of these resource-constrained environments. Consequently, model parameters must be stored in off-chip memory, necessitating a sequential processing approach during inference. This approach involves iteratively loading each layer's weights into on-chip memory and performing computations on that layer before proceeding to the next. While this method enables the inference of ViTs on devices with limited on-chip memory, it introduces significant latency and increased energy consumption due to frequent off-chip memory accesses, both of which are critical concerns in resource-constrained edge environments (e.g., autonomous vehicle perception). + +Table 1. Comparison of On-chip and Off-chip Memory Access Cost in Edge Devices + +
Memory TypeAccess Time (ns)Energy per Access (pJ)Available Storage (MB)
On-chip1-105·20†1-8
Off-chip70-2001300-2600§1024-8192*
+ +†32b SRAM Read (32KB), §32b DRAM [10], * For edge AI devices. + +One potential solution to mitigate this frequent off-chip memory access is model compression. Model compression can reduce the overall memory footprint and allow the entire model to be stored in on-chip memory, which can minimize/eliminate the need for costly memory access. However, as shown in Table 1, the available on-chip memory is often severely constrained (e.g., $\sim 1 - 8$ MB), and achieving this would require aggressive compression (e.g., greater than $10\times$ ). + +One of the widely explored approaches for model compression is pruning. Numerous studies [24, 31, 33] have applied pruning techniques on ViTs to reduce their memory and computation costs. While pruning has demonstrated significant success in lowering the computational demands + +of these models, our investigation reveals that achieving high compression through pruning in ViTs is challenging without severely impacting model performance. As shown in Table 2, even with a $2.5 \times$ compression ratio, the model suffers $\sim 19\%$ accuracy loss. + +Another widely adopted approach for improving model efficiency is quantization [11, 15, 18]. Quantization has proven particularly effective in reducing the memory footprint of large models, such as large language models (LLMs). The existing literature demonstrates that extreme quantization can be successfully applied to LLMs [19] with minimal performance loss. However, quantization applied to ViTs presents a different challenge. Studies focusing on ViTs [11, 34] have shown that these models suffer from significant performance degradation when subjected to extreme quantization (see Table 2). + +Table 2. Evaluating existing compression methods by aggressively compressing a DeiT-S model and highlighting their shortcoming in achieving our ideal objective ( $4^{th}$ row) for edge inference. + +
MethodOriginal Size (MB)Compression RatioAccuracy (%)
Original Model84.11×79.72
Pruning [11]33.72.5×60.51
Quantization [31]6.1813.6×71.90
Our Objective1-8 ( constraint at edge)10-80× (required)79.72 (ideally)
+ +Next, we dissect these two popular model compression strategies to determine the fundamental limitation that hurts the state-of-the-art model compression technique and whether we can develop an orthogonal approach to overcome them at our targeting edge applications. + +# 3.2. Motivation + +As shown in Figure 2, both pruning and quantization can be viewed as a form of encoding original model weights to a compressed representation. The fundamental challenge lies in the way these compression techniques encode model weights. In this work, we postulate that the primary factor contributing to this performance loss can be attributed to the large weight perturbation error introduced by the encoding mechanism of these compression techniques, as formalized in the following lemma. + +Lemma 3.1. (Error Bound for Compression in DNNs). Let $\mathbf{w}$ represent the weights of a deep neural network (DNN) with an associated loss function $\mathcal{L}(\mathbf{w})$ . Consider a compression technique that encodes the weights using a transformation $\mathbf{F}$ resulting in $\mathbf{w}' = \mathbf{F}(\mathbf{w})$ and introducing a perturbation $\delta \mathbf{w} = \mathbf{w}' - \mathbf{w}$ . The change in loss due to this compression can be upper bounded as follows: + +$$ +| \mathcal {L} (\mathbf {w} ^ {\prime}) - \mathcal {L} (\mathbf {w}) | \leq \| \nabla_ {\mathbf {w}} \mathcal {L} (\mathbf {w}) \| \| \delta \mathbf {w} \| + \frac {1}{2} \| H \| \| \delta \mathbf {w} \| ^ {2}, +$$ + +where $\nabla_{\mathbf{w}}\mathcal{L}(\mathbf{w})$ is the gradient of the loss function with respect to the original weights $\mathbf{w}$ , $\|H\|$ denotes the norm of the Hessian matrix of $\mathcal{L}(\mathbf{w})$ , and $\|\delta \mathbf{w}\|$ is the norm of the weight perturbation introduced by the compression. + +From Lemma 3.1, it is evident that a smaller weight perturbation $\| \delta \mathbf{w}\|$ leads to a tighter upper bound on the loss difference $|\mathcal{L}(\mathbf{w}^{\prime}) - \mathcal{L}(\mathbf{w})|$ . Therefore, an ideal compression method should minimize the weight perturbation error. However, for edge application of ViTs, we are forced to perform aggressive compression that will inevitably lead to a higher $\| \delta \mathbf{w}\|$ . + +Neither pruning nor quantization has a countermeasure against this high $\| \delta \mathbf{w}\|$ for aggressive compression, laying down the foundation for our proposed method as to whether we can device a technique to reduce $\| \delta \mathbf{w}\|$ at the inference stage even at a high compression ratio. The research question that motivates our work: Given that weight encoding for compression inevitably introduces significant weight perturbation error at high compression ratio, an effective approach to mitigate this error may lie in coupling the encoding mechanism with a complementary decoding mechanism that can reverse the lossy encoding, as formalized in the following proposition. + +Proposition 3.2. (Lower Error Bound with Weight Decoding). Let $\mathbf{w}$ represent the weights of a deep neural network (DNN) and consider a compression method that encodes these weights using a transformation $\mathbf{F}$ , introducing a weight perturbation $\delta \mathbf{w} = \mathbf{w}' - \mathbf{w}$ . Now consider a weight decoding mechanism with transformation $\mathbf{G}$ , where $\mathbf{G}$ approximates the inverse of $\mathbf{F}$ . Then, the weight perturbation error after decoding the weights can be bounded as follows: + +$$ +\| \mathbf {G} (\mathbf {F} (\mathbf {w})) - \mathbf {w} \| \leq \| \delta \mathbf {w} \|. +$$ + +The above proposition demonstrates the potential of a weight decoding strategy to reduce weight perturbation and minimize the impact on model performance at inference. Inspired by Proposition 3.2, we aim to design a novel Encoder-Decoder-based model compression approach that can enable the potential of achieving a high compression ratio while minimizing inference loss. + +# 4. Proposed Method: DeepCompress-ViT + +We propose DeepCompress-ViT, a novel compression framework designed for achieving a high compression ratio while preserving inference accuracy. As shown in Figure 3, our novel DeepCompress-ViT framework consists of two stages. In the first stage, we propose Unified Compression Training, which jointly trains the encoder and decoder networks (see Figure 3). The encoder network, denoted as $\mathbf{F}$ , learns to encode the original model weights w from $\mathbb{R}^d$ to $\mathbb{R}^r$ , where $r \ll d$ . And the decoder network, $\mathbf{G}$ , learns to decode the encoded weights back to $\mathbb{R}^d$ . After training is complete, only the encoded weights and the decoder network are retained for inference, while the encoder network is discarded. During inference, the proposed DeepCompress-ViT reconstructs each layer's weight one by + +![](images/a5a8a34564b1ed522ee446c51bff9b2c9e4bb2c6a9653abfae1f59e50dd998ff.jpg) +Figure 3. Unified Compression Training. The Encoder and Decoder parameters are optimized jointly to minimize the loss. After training, only encoded weights and decoder network is retained for inference + +one and performs inference using the decoded version of the weight to help maintain inference accuracy. + +While the decoding step is necessary to maintain accuracy, it has two drawbacks. To understand this, lets consider a simplified form the output computation for a given layer: input $\times$ encoded weight $\times$ decoder weight. First, the decoding step will be performed using encoded weight $\times$ decoder weight which introduces additional computation at runtime, and second, the reconstructed version of the weight will increase temporary on-chip memory consumption, especially for larger layers. To address this, we propose optimizing the decoding step by designing a lightweight decoder implemented as a single linear layer. In addition, we leverage the associative property of matrix multiplication to transform the inefficient weight decoding input $\times$ (encoded weight $\times$ decoder weight) to optimized test-time decoding as (input $\times$ encoded weight) $\times$ decoder weight, which would ensure the computation cost remains unchanged for an optimum level of decoder input (compressed weight size $r$ outlined in equation 4 in details) is selected. This optimization ensures the proposed DeepCompress-ViT does not introduce any computational overhead (Figure 4) in pursuit of compression and accuracy. + +# 4.1. Unified Compression Training (UCT) + +In this stage, an encoder-decoder network is trained to achieve aggressive compression. The encoder network $\mathbf{F}$ , learns to encode the model's weights to a compressed representation as the encoded embedding, while the decoder network, $\mathbf{G}$ , learns to decode the weights back to their original dimension as shown in Figure 3. + +Consider a ViT model $\mathbf{H}_{\mathbf{W}}(\cdot)$ consisting of $L$ layers, where the weights of the layers are denoted by the set $\mathbf{W} = \{\mathbf{w}_1,\mathbf{w}_2,\dots ,\mathbf{w}_L\}$ . Let the parameters of the encoder network $\mathbf{F}(.)$ be represented as $\mathbf{W}_{\mathbf{E}}$ , and the parameters of the decoder network $\mathbf{G}(.)$ be represented as $\mathbf{W}_{\mathbf{D}}$ . + +During training, each layer's weight $\mathbf{w}_i$ is passed through the encoder network $\mathbf{F}$ , which encodes it to a lower-dimensional representation, given by $\mathbf{z}_i = \mathbf{F}(\mathbf{w}_i)$ . The decoder network $\mathbf{G}$ then decodes $\mathbf{z}_i$ back to its original di + +mensionality as $\hat{\mathbf{w}}_i = \mathbf{G}(\mathbf{z}_i)$ . The encoder and decoder networks are trained jointly to minimize the mean squared error (MSE) between the original weight set $(\mathbf{W})$ and the reconstructed weight set $(\hat{\mathbf{W}})$ . The weight reconstruction loss is calculated as: + +$$ +\mathcal {L} _ {\bf m s e} = \frac {1}{L} \sum_ {i = 1} ^ {L} \| {\bf w} _ {i} - {\bf G} ({\bf F} ({\bf w} _ {i})) \| ^ {2} +$$ + +To optimize this training step further, we unify the encoder-decoder training step with the original ViT-model. Our hypothesis is that only MSE loss-based weight reconstruction may not provide optimal performance [2]. Even though minimizing MSE loss results in the minimization of weight perturbation error, different sets of decoded weights with the same MSE value can have varying weight distributions, which can lead to a performance drop in the ViT model. Hence, it is reasonable to incorporate the ViT model into this training loop to align the ViT model's weight distribution with the decoded version of the weight. + +Hence, we propose this end-to-end unified framework where the encoder-decoder networks are jointly trained with the ViT model. Our method will incorporate cross-entropy (CE) loss and knowledge distillation (KD) from a pretrained model in training, where CE ensures the ViT model performance is optimized on the decoded weight values w.r.t ground truth, and KD ensures the decoded weight parameters do not drift far apart from the initial weight distribution of a pre-trained ViT model. + +The forward pass for the whole end-to-end training after obtaining the decoded weight sets $\hat{\mathbf{W}}$ from the decoder is formulated as $\mathbf{H}_{\mathbf{W}}(\cdot) \rightarrow \mathbf{H}_{\hat{\mathbf{W}}}(\cdot)$ , which implies that the ViT model inference will always use the decoded weights, i.e., the forward pass of the ViT model becomes $\hat{\mathbf{y}} = \mathbf{H}_{\hat{\mathbf{W}}}(\mathbf{x})$ , where $\mathbf{x}$ are the input images and $\hat{\mathbf{y}}$ are the predictions from the ViT model. Next, using $\hat{\mathbf{y}}$ , we compute the cross-entropy loss and knowledge distillation loss as follows: + +$$ +\mathcal {L} _ {\mathbf {C E}} = - \sum_ {i} \mathbf {y} _ {i} \log (\hat {\mathbf {y}} _ {i}), \quad \mathcal {L} _ {\mathbf {K D}} = \sum_ {i} \hat {\mathbf {y}} _ {\mathrm {t}, i} \log \left(\frac {\hat {\mathbf {y}} _ {\mathrm {t} , i}}{\hat {\mathbf {y}} _ {i}}\right) +$$ + +where $\hat{\mathbf{y}}_{\mathrm{t}}$ represents the prediction from the pretrained teacher model. The total loss function is then defined as: + +$$ +\mathcal {L} _ {\mathrm {t o t a l}} = \mathcal {L} _ {\mathrm {m s e}} + \alpha \cdot \mathcal {L} _ {\mathrm {C E}} + \beta \cdot \mathcal {L} _ {\mathrm {K D}}, +$$ + +where $\alpha$ and $\beta$ are scaling factors controlling the contributions of cross-entropy and knowledge distillation losses, respectively. Finally, the overall loss function is minimized by jointly optimizing the encoder and decoder parameters $\mathbf{W}_{\mathbf{E}}$ and $\mathbf{W}_{\mathbf{D}}$ as follows: + +$$ +\min _ {\mathbf {W} _ {\mathrm {E}}, \mathbf {W} _ {\mathrm {D}}} \mathcal {L} _ {\mathrm {t o t a l}} +$$ + +![](images/b49711e04362cc903cd5186f5cdd249e35ddb9c27815b80790e38c4406d4d640.jpg) +Figure 4. Proposed Optimized Test-Time Decoding overview. Decoding the encoded (compressed) weights first and then matrix multiplying with input activation increases FLOPs. The proposed method eliminates extra FLOPs by multiplying input activation with encoded weights first, then passing through decoder. The chosen value of encoding dimension $(r)$ prevents any FLOP increase. + +![](images/cb7d7a50faf7fd8b949340c7555f512c031cf39802803af6c3ae83f7e9006519.jpg) + +After training is complete, for inference, we keep only the encoded weight parameters $\{\mathbf{z}_i\}$ and a lightweight decoder $\mathbf{W}_{\mathbf{D}}$ in memory while discarding the encoder $\mathbf{W}_{\mathbf{E}}$ . + +At inference, the decoder needs to map compressed weights to their original form layer by layer, which may help preserve accuracy. However, this can introduce two major drawbacks. First, the decoding step will inevitably lead to additional computation at runtime, and second, the decoded weights will increase temporary on-chip memory consumption, particularly for larger layers. Next, we outline our optimized test-time decoding strategy, which ensures these two bottlenecks remain in check. + +# 4.2. Optimized Test-Time Decoding + +To mitigate the overhead associated with the decoding step, first design level optimization we propose is to design the decoder $\mathbf{G}$ as a single linear layer. This design choice minimizes repetitive decoding operations, reducing the computational overhead. Although a single-layer decoder network lowers the computational load relative to a multi-layer decoder, the computation needed for decoding weights using a single layer still persists. + +To illustrate the overhead of weight decoding step, consider a fully connected layer in a ViT model with original weights $\mathbf{w}_i\in \mathbb{R}^{C\times d}$ , whose weights are encoded and the encoded weights are represented by $\mathbf{z}_i\in \mathbb{R}^{C\times r}$ . During inference of this layer, the weights are first decoded using the single-layer decoder network $\mathbf{G}$ , where weights of the decoder network is represented by $\mathbf{w}_D\in \mathbb{R}^{r\times d}$ . This weight decoding computation can be represented as follows: + +$$ +\hat {\mathbf {w}} _ {i} = \mathbf {z} _ {i} \times \mathbf {w} _ {D}, \tag {1} +$$ + +where $\hat{\mathbf{w}}_i\in \mathbb{R}^{C\times d}$ denotes the decoded weights. One of the + +most widely used metrics to evaluate computational complexity is Floating-point Operations (FLOPs) [6], which counts the total number of multiplications and additions performed in a given operation. The FLOPs incurred for the weight decoding operation is $2 \cdot C \cdot r \cdot d$ , corresponding to the matrix multiplication in eqn. (1). + +Next, the usual forward pass of fully connected layer in the ViT model with input activations $\mathbf{x}_i\in \mathbb{R}^{N\times C}$ and decoded weights $\hat{\mathbf{w}}_i$ is computed as follows: + +$$ +\mathbf {x} _ {i + 1} = \mathbf {x} _ {i} \times \hat {\mathbf {w}} _ {i}, \tag {2} +$$ + +where $\mathbf{x}_{i + 1}$ represents the output activations of the layer. The FLOPs incurred by this forward pass is $2\cdot N\cdot C\cdot d$ resulting from the matrix multiplication in eqn. (2). Therefore, the total FLOPs incurred in the forward pass with this strategy is $(2\cdot N\cdot C\cdot d + 2\cdot C\cdot r\cdot d)$ where the additional $2\cdot C\cdot r\cdot d$ FLOPs is incurred because of this inefficient weight decoding strategy. + +Next, we optimize the decoding step to eliminate this additional $2 \cdot C \cdot r \cdot d$ FLOPs, we propose Optimized Test-Time Decoding. Our proposed decoding approach leverages the associative property of matrix multiplication to reorder computation sequence to maintain or improve overall FLOPs. To illustrate, recall that the overall computation for inefficient decoding strategy is as follows: + +$$ +\mathbf {x} _ {i + 1} = \mathbf {x} _ {i} \times \hat {\mathbf {w}} _ {i} = \mathbf {x} _ {i} \times \left(\mathbf {z} _ {i} \times \mathbf {w} _ {D}\right), \tag {3} +$$ + +where it shows weight decoding first and then perform the forward pass in the fully connected layer of ViT model. We optimize the decoding step by simply reorder the matrix multiplications as follows: + +$$ +\mathbf {x} _ {i + 1} = \mathbf {x} _ {i} ^ {\prime} \times \mathbf {w} _ {D} = (\mathbf {x} _ {i} \times \mathbf {z} _ {i}) \times \mathbf {w} _ {D}, +$$ + +where we first perform input compression $(\mathbf{x} \in \mathbb{R}^{N \times C} \to \mathbf{x}' \in \mathbb{R}^{N \times r})$ and then do the optimized forward pass $(\mathbf{x}' \times \mathbf{w}_D)$ . The proposed strategy is also illustrated in Figure 4. + +The total FLOPs for this optimized approach is $2 \cdot N \cdot r \cdot (C + d)$ . However, with an arbitrary value of $r$ , the overall FLOPs can still go up. Therefore, to ensure that the total FLOPs of the proposed decoding strategy do not exceed the baseline models FLOPs, we derive the optimal $r$ for efficiency by solving the following inequality, + +$$ +2 \cdot N \cdot r \cdot (C + d) \leq 2 \cdot N \cdot C \cdot d, +$$ + +where $2 \cdot N \cdot C \cdot d$ is the FLOPs incurred due to normal forward pass in eqn. (2). Solving the inequality, we get: + +$$ +r \leq \frac {2 \cdot N \cdot C \cdot d}{2 \cdot N \cdot (C + d)} \tag {4} +$$ + +In summary, by reordering the computation sequence and using optimal $r$ for compression derived in eqn. (4), our innovative decoding optimization does not incur any additional computation. + +# 5. Experimental Results + +# 5.1. Datasets and Implementation Details + +Datasets. We conduct our experiments on the ILSVRC12 ImageNet classification dataset [22] consisting 1,000 classes with 1.2 million training images and 50k validation images. Additionally, we evaluate DeepCompress-ViT on the widely used COCO benchmark dataset [14] for object detection and instance segmentation task. + +Encoder-Decoder Architecture. We use four encoder network each with 2 linear layers to encode four types of layers: attn_qkv, attnProj, mlp_fcl and mlp_fcl2. Each encoder has an affine transformation before and after the 2 linear layers. Similarly to encoders, we use four single linear layer decoders to decode the four types of layers. Note that each decoder is a shared decoder which decodes a particular type of layer of all ViT blocks. Note that, we exclude the first layer, last layer, and LayerNorm parameters from compression. + +Experimental Settings. The encoder and decoder models are trained for 275 epochs with a batch size of 256 and a base learning rate of $1 \times 10^{-4}$ , using a cosine learning rate scheduler. For data augmentation, we apply the standard techniques used in [27] and for knowledge distillation, we use pretrained distilled DeiT models [27] with temperature $\tau = 1$ . For UCT, we set the value of $\alpha = 1$ and $\beta = 3 \times 10^3$ . The encoded weights are quantized using 4-bit asymmetric quantization, while decoder weights are quantized using 4-bit symmetric quantization, both trained using Quantization Aware Training. Additionally, the patch embedding (first) and classification (last) layers are quantized using 8-bit symmetric quantization. The optimal value of $r$ from + +solving (4) is set to 277 for DeiT-S and 502 for DeiT-B. For object detection and instance segmentation, we use the mmdetection library with the standard $1 \times$ training scheduler and adopt an edge-friendly resolution of $384 \times 384$ for both training and evaluation. + +# 5.2. Results + +Image Classification. Performance of the compressed DeiT models with proposed DeepCompress-ViT on the classification task is shown in Table 3. The results demonstrate substantial reductions in model size and energy consumption resulting from DeepCompress-ViT. For instance, the DeepCompress-DeiT-S model achieves a compression ratio of $14.9\times$ , reducing the model size from $84.1\mathrm{MB}$ to just $5.64\mathrm{MB}$ while maintaining an accuracy of $78.74\%$ on ImageNet. Similarly, DeepCompress-DeiT-B achieves a compression ratio of $17.4\times$ , decreasing the model size from $330.2\mathrm{MB}$ to $18.9\mathrm{MB}$ . Remarkably, both models show an unprecedented energy reduction of $673\times$ and $1475\times$ and latency reduction of $44.5\times$ and $68.4\times$ respectively (please refer to section 5.3 and Figure 5 for more hardware energy and latency evaluation details). Proposed DeepCompress-ViT achieves this unprecedented level of model compression, energy, and latency reduction, enabling the deployment of ViT models at the edge while only sacrificing a marginal level of accuracy (e.g., for DeiT-B only $\sim 0.1\%$ ) + +Object Detection and Instance Segmentation. Next, table 4 compares the performance of DeepCompress-ViT with baseline (no compression) DeiT-S model on object detection and instance segmentation tasks. We trained both the models on COCO dataset integrating the respective ViT backbones with Mask R-CNN [9]. We evaluate both of the models for these tasks at an edge-friendly resolution of $384 \times 384$ . Notably, DeepCompress-ViT reduces the ViT backbone (DeiT-S) size from 82.65MB to 5.27MB ( $15.7 \times$ compression) with a slight drop in $\mathrm{AP^b}$ and $\mathrm{AP^m}$ , further highlighting the effectiveness of our compression method on other complex vision tasks. + +Comparison with SOTA compression methods. Finally, Table 5 provides a comparative analysis of DeiT-Small models compressed using different pruning and quantization methods. Among the methods, DeepCompress-ViT achieves the highest compression ratio of $14.9 \times$ , reducing the model size to 5.64 MB while maintaining a top-1 accuracy of $78.74\%$ . In contrast, popular WDPruning [31], LSQ [8] and Q-ViT [11] achieves achieve much lower accuracies of $60.51\%$ , $68.00\%$ and $71.9\%$ , respectively. Our proposed DeepCompress-ViT consistently outperforms them by large margins of $\sim 18\%$ , $\sim 10\%$ , and $\sim 7\%$ , respectively, making DeepCompress-ViT the only practical choice to maintain accuracy while performing aggressive compression. + +Table 3. Performance of DeepCompress-ViT on ImageNet-1K. DeepCompress-ViT achieves memory ( $\geq 15 \times$ ) and energy consumption ( $\geq 1531 \times$ ), while marginal accuracy drop ( $< 1\%$ ). + +
MethodAccuracy (%)Model Size (MB)Compression RatioGFLOPsExecution Time (s)Energy Consumption (J)
DeiT-S [27]79.7284.11x9.2024.029979.52
DeepCompress-DeiT-S78.745.6414.9x8.880.5414.83
DeiT-B [27]81.74330.21x35.14129.32150895
DeepCompress-DeiT-B81.6218.917.4x30.841.89102.29
+ +Table 4. Performance of DeepCompress-ViT for Object Detection on the COCO validation set with Mask R-CNN evaluated at an edge-friendly resolution of $384 \times 384$ . + +
Method\( {\mathbf{{AP}}}^{\mathbf{b}} \)\( {\mathbf{{AP}}}^{\mathbf{m}} \)ViT Backbone Size (MB)
DeiT-S [27]26.223.782.65
DeepCompress-ViT23.020.95.27 (15.7×)
+ +Table 5. Performance comparison of DeiT-Small with SOTA compression methods on ImageNet-1K + +
ModelAccuracy (%)Model Size (MB)Compression Ratio
DeiT-S [27]79.72 (0)84.11x
WDPruning [31]60.51 (↓19.21)33.72.5x
LSQ [8]68.00 (↓11.72)6.1813.6x
Q-ViT [11]71.90 (↓7.82)6.1813.6x
DeepCompress-ViT78.74 (↓0.98)5.6414.9x
+ +# 5.3. Hardware Evaluation + +High compression gain gives an understanding of the effectiveness of a compression method in terms of memory savings. But to successfully realize the full potential of our proposed method, we evaluate the energy and latency gain on hardware evaluation platforms. For hardware deployment, we use the gem5-Aladdin platform [25], which effectively captures dynamic interactions between accelerators and the SoC platform, enabling detailed architectural analysis of the proposed compression method. Our setup incorporates a cycle-accurate in-house-developed model based on the Eyeriss accelerator [5] (0.0029 DRAM access/multiply and accumulation (MAC), 33.6 GMAC/s). Performance metrics from gem5-Aladdin are then analyzed using DRAM-Sim2 [21] to model realistic off-chip memory latency and energy characteristics. The total on-chip weight memory is capped at three configurations (2 MB, 4 MB, 8 MB). The analyzed DeiT-S model initially requires 84.1MB of memory, which exceeds the on-chip memory capacity. By applying DeepCompress-ViT algorithm, this requirement is reduced to 5.64 MB, which can readily fit into the 8MB on-chip memory. However, with a smaller memory capacity, it is not feasible to transfer the entire set of weight parameters to the accelerator in a single batch due to the model's memory demands. Therefore, we implemented a weight parser that transmits weight parameters in variable batch sizes to the accelerator. Figure 5 shows the breakdown of energy consumption and latency across MAC, off-chip, and on-chip memory access components for various on-chip memory sizes. For both DeiT-S and DeiT-B, the DeepCompress-ViT algorithm achieves significant energy savings, reduc + +![](images/295f440da98d769fe480f170d2d3538b2dfee19cbd1ce31f5e99273299ce59e1.jpg) +Figure 5. Breakdown of (a) Energy consumption, (b) Latency vs. on-chip memory size. For every off-chip memory size, DeiT-S, DeepCompress-ViT-S, DeiT-B, and DeepCompress-ViT-B results are plotted, respectively. + +![](images/8dda0ecef3cd3d164e89f402b611e539c4551e247cd3c6d059cca3c1bee4cbb4.jpg) + +ing consumption by approximately $673 \times$ and $1475 \times$ , respectively, with an 8MB on-chip memory. This remarkable reduction is primarily due to the DeepCompress-ViT algorithm's ability to minimize off-chip memory access, as visible through the high difference in the red bar plots. This reduction becomes even more pronounced with smaller memory sizes, enabling for the first time the possibility of deploying large ViT models at the edge and performing time-sensitive applications. + +# 6. Conclusion + +In this paper, we present DeepCompress-ViT, a novel approach to achieve highly compressed Vision Transformers optimized for efficient edge deployment. We first analyze the limitations of existing model compression techniques and show that they lead to large weight perturbation error because of their lossy encoding mechanism. Then, to resolve this challenge, we develop an orthogonal compression technique that consists of an encoding for compression and a decoding step to help maintain performance. However, decoding weights repeatedly during inference can lead to additional computation and increase on-chip memory usage, both of which are critical concerns for edge applications. To address these challenges, we propose a novel optimized Test-Time Decoding scheme that enables efficient inference without increased computation and avoids high on-chip memory usage. 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Savit: Structure-aware vision transformer pruning via collaborative optimization. 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], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "spans": [ + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "type": "text", + "content": "Vision Transformers (ViTs) excel in tackling complex vision tasks, yet their substantial size poses significant challenges for applications on resource-constrained edge devices. The increased size of these models leads to higher overhead (e.g., energy, latency) when transmitting model weights between the edge device and the server. Hence, ViTs are not ideal for edge devices where the entire model may not fit on the device. Current model compression techniques often achieve high compression ratios at the expense of performance degradation, particularly for ViTs. To overcome the limitations of existing works, we rethink model compression strategy for ViTs from first principle approach and develop an orthogonal strategy called DeepCompress-ViT. The objective of the DeepCompress-ViT is to encode the model weights to a highly compressed encoded representation using a novel training method, denoted as Unified Compression Training (UCT). Proposed UCT is accompanied by a decoding mechanism during inference, which helps to gain any loss of accuracy due to high compression ratio. We further optimize this decoding step by reordering the decoding operation using associative property of matrix multiplication, ensuring that the compressed weights can be decoded during inference without incurring any computational overhead. Our extensive experiments across multiple ViT models on modern edge devices show that DeepCompress-ViT can successfully compress ViTs at high compression ratios " + }, + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "type": "inline_equation", + "content": "(>14\\times)" + }, + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "type": "text", + "content": ". DeepCompress-ViT enables the entire model to be stored on edge device, resulting in unprecedented reductions in energy consumption " + }, + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "type": "inline_equation", + "content": "(>1470\\times)" + }, + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "type": "text", + "content": " and latency " + }, + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "type": "inline_equation", + "content": "(>68\\times)" + }, + { + "bbox": [ + 54, + 269, + 297, + 652 + ], + "type": "text", + "content": " for edge ViT inference. Our code is available at https://github.com/ML-Security-Research-LAB/DeepCompress-ViT." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 653, + 137, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 137, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 137, + 665 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 673, + 295, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 673, + 295, + 697 + ], + "spans": [ + { + "bbox": [ + 55, + 673, + 295, + 697 + ], + "type": "text", + "content": "The integration of computer vision and deep learning (DL) into the Industrial Internet of Things (IIoT) and edge de" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 328, + 243, + 542, + 384 + ], + "blocks": [ + { + "bbox": [ + 328, + 243, + 542, + 384 + ], + "lines": [ + { + "bbox": [ + 328, + 243, + 542, + 384 + ], + "spans": [ + { + "bbox": [ + 328, + 243, + 542, + 384 + ], + "type": "image", + "image_path": "c021b82f1ded9a591fc796bd3d6bb00c9144042ae1b71403ae3092d189b66af8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 391, + 555, + 457 + ], + "lines": [ + { + "bbox": [ + 313, + 391, + 555, + 457 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 555, + 457 + ], + "type": "text", + "content": "Figure 1. Comparison of DeepCompress-ViT with SOTA ViT compression methods [8, 11, 31] for compressing DeiT-S [27] trained onImagenet-1k [22]. Existing compression methods achieve a large compression ratio at the expense of large performance loss, whereas the DeepCompress-ViT achieves the highest compression ratio with the best accuracy among the competition." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 460, + 555, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 460, + 555, + 568 + ], + "spans": [ + { + "bbox": [ + 312, + 460, + 555, + 568 + ], + "type": "text", + "content": "vices has revolutionized data processing, analysis, and action in these systems [3]. By deploying advanced models, such as Vision Transformers (ViTs), on resource-constrained devices, IIoT systems can directly manage complex tasks, including object detection, anomaly detection, and facial recognition on the device. This local processing capability on edge minimizes data transmission to centralized servers, reducing latency and enhancing data privacy by keeping information closer to its source [35]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 569, + 556, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 569, + 556, + 688 + ], + "spans": [ + { + "bbox": [ + 312, + 569, + 556, + 688 + ], + "type": "text", + "content": "In recent years, Vision Transformers (ViTs) [7] have gained significant attention among deep neural network (DNN) models for their remarkable performance [20]. Their potential to tackle various real-world vision problems, such as object detection [4] and segmentation [26], makes them especially appealing for edge applications. However, the challenge of achieving reliable, real-time inference on resource-constrained devices cannot be underestimated, primarily due to the large model sizes of ViTs in comparison to models like Convolutional Neural Networks [23]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "The architectural design of ViTs often exceeds the on-chip memory limits of edge devices (e.g., Espressif ESP32-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 702, + 188, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 702, + 188, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 702, + 188, + 713 + ], + "type": "text", + "content": "* These authors contributed equally" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "30147" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 299 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 299 + ], + "type": "text", + "content": "S3 [1] has 8 MB pseudo-static RAM on-chip memory, but DeiT-S model size is approximately 85 MB), leading to a reliance on off-chip memory from servers to store the entire model. This dependency introduces two critical challenges that significantly impede the use of large ViTs in edge environments [10]. Firstly, computations performed on-chip are estimated to be 10 to 100 times faster than those conducted off-chip (see Table 1 for a detailed numerical comparison of various metrics between on- and off-chip memories). Secondly, transferring sizable model weights demands high communication bandwidth, resulting in elevated energy consumption. As a result, for edge applications (e.g., real-time patient monitoring, autonomous vehicle perception, quality control in production) where latency and power efficiency are critical, the deployment of ViT models is severely limited. Therefore, addressing model size and enhancing memory management are not just challenges; they are essential for unlocking the full potential of ViT models in IoT devices." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 301, + 296, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 301, + 296, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 301, + 296, + 469 + ], + "type": "text", + "content": "To effectively deploy large Vision Transformer (ViT) models at the edge, it is crucial to aggressively compress them to fit into on-chip memory. Aggressive compression reduces reliance on off-chip memory, decreasing latency and energy consumption. However, techniques such as pruning [31] and quantization [11] often face challenges at high compression ratios, leading to significant drops in performance. For instance, the DeiT-Small model, which is approximately " + }, + { + "bbox": [ + 55, + 301, + 296, + 469 + ], + "type": "inline_equation", + "content": "85\\mathrm{MB}" + }, + { + "bbox": [ + 55, + 301, + 296, + 469 + ], + "type": "text", + "content": ", would require over " + }, + { + "bbox": [ + 55, + 301, + 296, + 469 + ], + "type": "inline_equation", + "content": "10\\times" + }, + { + "bbox": [ + 55, + 301, + 296, + 469 + ], + "type": "text", + "content": " compression to fit into an 8 MB edge device. This extreme compression level can result in severe accuracy loss (please refer to Figure 1). Therefore, it is essential to carefully reconsider and rethink model compression strategies for ViTs to maintain both performance and efficiency at the edge." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 472, + 296, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 296, + 674 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 296, + 674 + ], + "type": "text", + "content": "In this work, we begin by formulating the popular compression strategies from the perspective of weight encoding, as illustrated in Figure 2. Both pruning and quantization are techniques that encode model weights into a compressed format. However, at high compression ratios, this weight encoding mechanism can become lossy, leading to a decline in model performance. Our hypothesis is that to mitigate the performance loss due to encoded weights, it is essential to implement a decoding method during inference that can reconstruct or remap the weights back to their original (decompressed) state. This approach could enhance the model's accuracy during inference by reversing the effects of a lossy compression. Nonetheless, developing an effective compression strategy that achieves high compression while also enabling accurate weight decoding for inference involves overcoming several challenges, which our work aims to resolve." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "To this end, we propose a novel and unique perspective on model compression, which enables aggressive compression of ViT models while maintaining a decoding frame" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 323, + 70, + 549, + 277 + ], + "blocks": [ + { + "bbox": [ + 323, + 70, + 549, + 277 + ], + "lines": [ + { + "bbox": [ + 323, + 70, + 549, + 277 + ], + "spans": [ + { + "bbox": [ + 323, + 70, + 549, + 277 + ], + "type": "image", + "image_path": "6289255a14ece7fa96528f50db9adf84d14bd23af8579ab33438e22578d393c6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 284, + 555, + 339 + ], + "lines": [ + { + "bbox": [ + 313, + 284, + 555, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 284, + 555, + 339 + ], + "type": "text", + "content": "Figure 2. Existing compression methods can be viewed as a form of weight encoding. However, inference with lossy encoded weights results in performance dorp whereas proposed DeepCompress-ViT maintains an optimized decoding method at test time to maintain model performance." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 342, + 556, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 556, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 556, + 498 + ], + "type": "text", + "content": "work to reconstruct the weights back. The key idea is that the compressed version of the weight and a lightweight decoder will be stored in memory to reduce memory costs. However, these weights will be reconstructed back to their original form using the decoder in a layer-by-layer sequence for model inference and thus help to maintain accuracy. Our proposed DeepCompress-ViT consists of two phases—Unified Compression Training and Optimized Test-Time Decoding. In Unified Compression Training, we train an encoder and decoder alongside the model, learning a highly compressed representation of its parameters through encoded embeddings. After training, we retain only these encoded weights and the decoder, discarding the encoder." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": "Next, during inference, the goal is to Decode the compressed parameters layer-by-layer systematically to reconstruct the original parameters for each layer to compute the next layers output. Nevertheless, the proposed layer-by-layer decoding approach comes with two notable drawbacks. First, decoding the compressed representation of each layer back to its original form incurs extra computational costs, such as increased energy use and processing time. Additionally, this can lead to significant on-chip memory usage, particularly in larger layers, when decoded weights will be stored on-chip temporarily to compute output of a given layer. Hence, we propose Optimized Test-Time Decoding, eliminating the need to decode embeddings to their original parameters. This optimized decoding step leverages the associative property of matrix multiplication to reorder the decoding operation. This innovation eliminates both computation and memory usage drawback associated with the decoding step, making proposed" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "30148" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "DeepCompress-ViT best of all worlds (accuracy, memory, energy and latency). Our experiments on SOTA ViTs and edge devices show that DeepCompress-ViT achieves compression ratios exceeding " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "14 \\times" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " while achieving unprecedented reductions in energy (" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": ">1470 \\times" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": ") and latency (" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": ">68 \\times" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "), all with the least amount of accuracy loss among the SOTA compression methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 159, + 142, + 170 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 159, + 142, + 170 + ], + "spans": [ + { + "bbox": [ + 55, + 159, + 142, + 170 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 174, + 295, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 174, + 295, + 389 + ], + "spans": [ + { + "bbox": [ + 55, + 174, + 295, + 389 + ], + "type": "text", + "content": "Vision Transformers. The introduction of Transformer architecture [28] has marked a paradigm shift in machine learning, initially transforming natural language processing. Building on this success, the architecture was adapted for computer vision, leading to the development of Vision Transformer (ViT) [7]. This success has led to a surge in transformer-based models for computer vision. For example, DeiT [27] introduced advanced training techniques and a novel distillation approach to reduce ViT's dependence on large datasets. Further architectural innovations, such as Pyramid Vision Transformer (PVT) [29] and Swin Transformer [17], incorporated hierarchical feature representations enabling transformers to serve as versatile frameworks for diverse computer vision applications. Even though ViTs have demonstrated strong performance, they require significant memory that limits their application in edge devices. Compressing ViTs has thus emerged as an important area of research to address this large memory requirement." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 390, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 390, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 390, + 295, + 628 + ], + "type": "text", + "content": "ViT Compression. A widely used approach for compressing Vision Transformers (ViT) is pruning [16, 30-33, 36], which focuses on reducing the number of unimportant weights in the model. Pruning methods for ViT models are commonly divided into two categories: unstructured and structured pruning. Unstructured pruning techniques, such as magnitude-based and Hessian-based methods [24], remove individual weights based on certain importance metrics. However, these techniques result in irregular sparsity patterns, which complicate tensor computations and limit hardware efficiency. Structured pruning mitigates this challenge by removing larger, contiguous structures within the model, such as entire attention heads or rows of weight matrices, which are more compatible with hardware requirements. For instance, [31] proposed a structured pruning method for ViTs that uses a binary mask to distinguish important from unimportant parameters based on magnitude. Another effective approach, introduced in [33], combines pruning, layer skipping, and knowledge distillation within a unified framework to create a compact ViT model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 714 + ], + "type": "text", + "content": "Another widely adopted approach for compressing ViT models is quantization [8, 11-13, 15, 18], which converts floating-point parameters to lower precision values. Several quantization methods tailored to ViT's unique architecture have been proposed. For instance, Q-ViT [11] introduced differentiable quantization for ViTs, treating quantization bit-widths and scales as learnable parameters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "PTQ4ViT [18] utilizes twin uniform quantization and applies a Hessian-guided metric to determine optimal scaling factors. FQ-ViT [15] incorporates powers-of-two scale quantization and log-int quantization specifically for Layer-Norm and Softmax operations, respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 133, + 555, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 555, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 555, + 192 + ], + "type": "text", + "content": "While both pruning and quantization methods have shown great promise in reducing computational demands, they still experience significant performance degradation at high compression ratios [11, 31], also shown in Table 2, severely limiting their applicability in edge IoT devices." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 194, + 468, + 209 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 194, + 468, + 209 + ], + "spans": [ + { + "bbox": [ + 313, + 194, + 468, + 209 + ], + "type": "text", + "content": "3. Challenges and Motivation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 212, + 554, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 212, + 554, + 271 + ], + "spans": [ + { + "bbox": [ + 313, + 212, + 554, + 271 + ], + "type": "text", + "content": "To motivate our compression technique, we identify the critical bottleneck hindering efficient inference of Vision Transformers (ViTs) at the edge. We will also assess the limitations of current compression methods, establishing the necessary foundation for our proposed method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 273, + 515, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 273, + 515, + 285 + ], + "spans": [ + { + "bbox": [ + 313, + 273, + 515, + 285 + ], + "type": "text", + "content": "3.1. Challenges of Efficient Edge Inference" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 289, + 554, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 554, + 469 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 554, + 469 + ], + "type": "text", + "content": "The deployment of ViTs on edge devices presents significant challenges due to their substantial memory requirements, which often exceed the on-chip memory capacity of these resource-constrained environments. Consequently, model parameters must be stored in off-chip memory, necessitating a sequential processing approach during inference. This approach involves iteratively loading each layer's weights into on-chip memory and performing computations on that layer before proceeding to the next. While this method enables the inference of ViTs on devices with limited on-chip memory, it introduces significant latency and increased energy consumption due to frequent off-chip memory accesses, both of which are critical concerns in resource-constrained edge environments (e.g., autonomous vehicle perception)." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 318, + 500, + 552, + 525 + ], + "blocks": [ + { + "bbox": [ + 314, + 477, + 553, + 499 + ], + "lines": [ + { + "bbox": [ + 314, + 477, + 553, + 499 + ], + "spans": [ + { + "bbox": [ + 314, + 477, + 553, + 499 + ], + "type": "text", + "content": "Table 1. Comparison of On-chip and Off-chip Memory Access Cost in Edge Devices" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 500, + 552, + 525 + ], + "lines": [ + { + "bbox": [ + 318, + 500, + 552, + 525 + ], + "spans": [ + { + "bbox": [ + 318, + 500, + 552, + 525 + ], + "type": "table", + "html": "
Memory TypeAccess Time (ns)Energy per Access (pJ)Available Storage (MB)
On-chip1-105·20†1-8
Off-chip70-2001300-2600§1024-8192*
", + "image_path": "e7180f2a1945ffcb2138a5458da92989a234ed29a9eea6d5dfec214528729c57.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 321, + 525, + 545, + 535 + ], + "lines": [ + { + "bbox": [ + 321, + 525, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 321, + 525, + 545, + 535 + ], + "type": "text", + "content": "†32b SRAM Read (32KB), §32b DRAM [10], * For edge AI devices." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 546, + 554, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 554, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 554, + 653 + ], + "type": "text", + "content": "One potential solution to mitigate this frequent off-chip memory access is model compression. Model compression can reduce the overall memory footprint and allow the entire model to be stored in on-chip memory, which can minimize/eliminate the need for costly memory access. However, as shown in Table 1, the available on-chip memory is often severely constrained (e.g., " + }, + { + "bbox": [ + 313, + 546, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\sim 1 - 8" + }, + { + "bbox": [ + 313, + 546, + 554, + 653 + ], + "type": "text", + "content": " MB), and achieving this would require aggressive compression (e.g., greater than " + }, + { + "bbox": [ + 313, + 546, + 554, + 653 + ], + "type": "inline_equation", + "content": "10\\times" + }, + { + "bbox": [ + 313, + 546, + 554, + 653 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "One of the widely explored approaches for model compression is pruning. Numerous studies [24, 31, 33] have applied pruning techniques on ViTs to reduce their memory and computation costs. While pruning has demonstrated significant success in lowering the computational demands" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30149" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 72, + 294, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 72, + 294, + 131 + ], + "spans": [ + { + "bbox": [ + 54, + 72, + 294, + 131 + ], + "type": "text", + "content": "of these models, our investigation reveals that achieving high compression through pruning in ViTs is challenging without severely impacting model performance. As shown in Table 2, even with a " + }, + { + "bbox": [ + 54, + 72, + 294, + 131 + ], + "type": "inline_equation", + "content": "2.5 \\times" + }, + { + "bbox": [ + 54, + 72, + 294, + 131 + ], + "type": "text", + "content": " compression ratio, the model suffers " + }, + { + "bbox": [ + 54, + 72, + 294, + 131 + ], + "type": "inline_equation", + "content": "\\sim 19\\%" + }, + { + "bbox": [ + 54, + 72, + 294, + 131 + ], + "type": "text", + "content": " accuracy loss." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 133, + 295, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 133, + 295, + 263 + ], + "spans": [ + { + "bbox": [ + 54, + 133, + 295, + 263 + ], + "type": "text", + "content": "Another widely adopted approach for improving model efficiency is quantization [11, 15, 18]. Quantization has proven particularly effective in reducing the memory footprint of large models, such as large language models (LLMs). The existing literature demonstrates that extreme quantization can be successfully applied to LLMs [19] with minimal performance loss. However, quantization applied to ViTs presents a different challenge. Studies focusing on ViTs [11, 34] have shown that these models suffer from significant performance degradation when subjected to extreme quantization (see Table 2)." + } + ] + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 71, + 306, + 282, + 351 + ], + "blocks": [ + { + "bbox": [ + 55, + 273, + 295, + 305 + ], + "lines": [ + { + "bbox": [ + 55, + 273, + 295, + 305 + ], + "spans": [ + { + "bbox": [ + 55, + 273, + 295, + 305 + ], + "type": "text", + "content": "Table 2. Evaluating existing compression methods by aggressively compressing a DeiT-S model and highlighting their shortcoming in achieving our ideal objective (" + }, + { + "bbox": [ + 55, + 273, + 295, + 305 + ], + "type": "inline_equation", + "content": "4^{th}" + }, + { + "bbox": [ + 55, + 273, + 295, + 305 + ], + "type": "text", + "content": " row) for edge inference." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 306, + 282, + 351 + ], + "lines": [ + { + "bbox": [ + 71, + 306, + 282, + 351 + ], + "spans": [ + { + "bbox": [ + 71, + 306, + 282, + 351 + ], + "type": "table", + "html": "
MethodOriginal Size (MB)Compression RatioAccuracy (%)
Original Model84.11×79.72
Pruning [11]33.72.5×60.51
Quantization [31]6.1813.6×71.90
Our Objective1-8 ( constraint at edge)10-80× (required)79.72 (ideally)
", + "image_path": "d2f05914e633673795c1ade6b476f84e127eb13917d849972962723883a688b3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 361, + 295, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 295, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 295, + 421 + ], + "type": "text", + "content": "Next, we dissect these two popular model compression strategies to determine the fundamental limitation that hurts the state-of-the-art model compression technique and whether we can develop an orthogonal approach to overcome them at our targeting edge applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 422, + 130, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 130, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 130, + 433 + ], + "type": "text", + "content": "3.2. Motivation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 437, + 295, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 437, + 295, + 545 + ], + "spans": [ + { + "bbox": [ + 54, + 437, + 295, + 545 + ], + "type": "text", + "content": "As shown in Figure 2, both pruning and quantization can be viewed as a form of encoding original model weights to a compressed representation. The fundamental challenge lies in the way these compression techniques encode model weights. In this work, we postulate that the primary factor contributing to this performance loss can be attributed to the large weight perturbation error introduced by the encoding mechanism of these compression techniques, as formalized in the following lemma." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "spans": [ + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "text", + "content": "Lemma 3.1. (Error Bound for Compression in DNNs). Let " + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "text", + "content": " represent the weights of a deep neural network (DNN) with an associated loss function " + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\mathbf{w})" + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "text", + "content": ". Consider a compression technique that encodes the weights using a transformation " + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "text", + "content": " resulting in " + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{w}' = \\mathbf{F}(\\mathbf{w})" + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "text", + "content": " and introducing a perturbation " + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "inline_equation", + "content": "\\delta \\mathbf{w} = \\mathbf{w}' - \\mathbf{w}" + }, + { + "bbox": [ + 54, + 550, + 295, + 634 + ], + "type": "text", + "content": ". The change in loss due to this compression can be upper bounded as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 63, + 638, + 288, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 638, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 63, + 638, + 288, + 662 + ], + "type": "interline_equation", + "content": "| \\mathcal {L} (\\mathbf {w} ^ {\\prime}) - \\mathcal {L} (\\mathbf {w}) | \\leq \\| \\nabla_ {\\mathbf {w}} \\mathcal {L} (\\mathbf {w}) \\| \\| \\delta \\mathbf {w} \\| + \\frac {1}{2} \\| H \\| \\| \\delta \\mathbf {w} \\| ^ {2},", + "image_path": "d67959060f244f792ec90a80d10d5f2e7d929d5f4b8ba705ddd19d9ee5a60d6b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{w}}\\mathcal{L}(\\mathbf{w})" + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "content": " is the gradient of the loss function with respect to the original weights " + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "inline_equation", + "content": "\\|H\\|" + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "content": " denotes the norm of the Hessian matrix of " + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\mathbf{w})" + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "inline_equation", + "content": "\\|\\delta \\mathbf{w}\\|" + }, + { + "bbox": [ + 55, + 665, + 297, + 714 + ], + "type": "text", + "content": " is the norm of the weight perturbation introduced by the compression." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "From Lemma 3.1, it is evident that a smaller weight perturbation " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "\\| \\delta \\mathbf{w}\\|" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": " leads to a tighter upper bound on the loss difference " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "|\\mathcal{L}(\\mathbf{w}^{\\prime}) - \\mathcal{L}(\\mathbf{w})|" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": ". Therefore, an ideal compression method should minimize the weight perturbation error. However, for edge application of ViTs, we are forced to perform aggressive compression that will inevitably lead to a higher " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "\\| \\delta \\mathbf{w}\\|" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 157, + 555, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 157, + 555, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 157, + 555, + 300 + ], + "type": "text", + "content": "Neither pruning nor quantization has a countermeasure against this high " + }, + { + "bbox": [ + 313, + 157, + 555, + 300 + ], + "type": "inline_equation", + "content": "\\| \\delta \\mathbf{w}\\|" + }, + { + "bbox": [ + 313, + 157, + 555, + 300 + ], + "type": "text", + "content": " for aggressive compression, laying down the foundation for our proposed method as to whether we can device a technique to reduce " + }, + { + "bbox": [ + 313, + 157, + 555, + 300 + ], + "type": "inline_equation", + "content": "\\| \\delta \\mathbf{w}\\|" + }, + { + "bbox": [ + 313, + 157, + 555, + 300 + ], + "type": "text", + "content": " at the inference stage even at a high compression ratio. The research question that motivates our work: Given that weight encoding for compression inevitably introduces significant weight perturbation error at high compression ratio, an effective approach to mitigate this error may lie in coupling the encoding mechanism with a complementary decoding mechanism that can reverse the lossy encoding, as formalized in the following proposition." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "text", + "content": "Proposition 3.2. (Lower Error Bound with Weight Decoding). Let " + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "text", + "content": " represent the weights of a deep neural network (DNN) and consider a compression method that encodes these weights using a transformation " + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "text", + "content": ", introducing a weight perturbation " + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\delta \\mathbf{w} = \\mathbf{w}' - \\mathbf{w}" + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "text", + "content": ". Now consider a weight decoding mechanism with transformation " + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "text", + "content": " approximates the inverse of " + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 313, + 308, + 555, + 405 + ], + "type": "text", + "content": ". Then, the weight perturbation error after decoding the weights can be bounded as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 377, + 414, + 490, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 414, + 490, + 428 + ], + "spans": [ + { + "bbox": [ + 377, + 414, + 490, + 428 + ], + "type": "interline_equation", + "content": "\\| \\mathbf {G} (\\mathbf {F} (\\mathbf {w})) - \\mathbf {w} \\| \\leq \\| \\delta \\mathbf {w} \\|.", + "image_path": "81b73caae0a2cd30a02d26c37a91de1d76998e2f33bd26b1eec65aeb0d72e3c2.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 437, + 554, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 554, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 554, + 521 + ], + "type": "text", + "content": "The above proposition demonstrates the potential of a weight decoding strategy to reduce weight perturbation and minimize the impact on model performance at inference. Inspired by Proposition 3.2, we aim to design a novel Encoder-Decoder-based model compression approach that can enable the potential of achieving a high compression ratio while minimizing inference loss." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 528, + 528, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 528, + 528, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 528, + 528, + 542 + ], + "type": "text", + "content": "4. Proposed Method: DeepCompress-ViT" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": "We propose DeepCompress-ViT, a novel compression framework designed for achieving a high compression ratio while preserving inference accuracy. As shown in Figure 3, our novel DeepCompress-ViT framework consists of two stages. In the first stage, we propose Unified Compression Training, which jointly trains the encoder and decoder networks (see Figure 3). The encoder network, denoted as " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ", learns to encode the original model weights w from " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^r" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "r \\ll d" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ". And the decoder network, " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ", learns to decode the encoded weights back to " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ". After training is complete, only the encoded weights and the decoder network are retained for inference, while the encoder network is discarded. During inference, the proposed DeepCompress-ViT reconstructs each layer's weight one by" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "30150" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 296, + 170 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 296, + 170 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 296, + 170 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 296, + 170 + ], + "type": "image", + "image_path": "a5a8a34564b1ed522ee446c51bff9b2c9e4bb2c6a9653abfae1f59e50dd998ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 178, + 297, + 222 + ], + "lines": [ + { + "bbox": [ + 54, + 178, + 297, + 222 + ], + "spans": [ + { + "bbox": [ + 54, + 178, + 297, + 222 + ], + "type": "text", + "content": "Figure 3. Unified Compression Training. The Encoder and Decoder parameters are optimized jointly to minimize the loss. After training, only encoded weights and decoder network is retained for inference" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 230, + 296, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 230, + 296, + 253 + ], + "spans": [ + { + "bbox": [ + 55, + 230, + 296, + 253 + ], + "type": "text", + "content": "one and performs inference using the decoded version of the weight to help maintain inference accuracy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "spans": [ + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": "While the decoding step is necessary to maintain accuracy, it has two drawbacks. To understand this, lets consider a simplified form the output computation for a given layer: input " + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": " encoded weight " + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": " decoder weight. First, the decoding step will be performed using encoded weight " + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": " decoder weight which introduces additional computation at runtime, and second, the reconstructed version of the weight will increase temporary on-chip memory consumption, especially for larger layers. To address this, we propose optimizing the decoding step by designing a lightweight decoder implemented as a single linear layer. In addition, we leverage the associative property of matrix multiplication to transform the inefficient weight decoding input " + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": " (encoded weight " + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": " decoder weight) to optimized test-time decoding as (input " + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": " encoded weight) " + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": " decoder weight, which would ensure the computation cost remains unchanged for an optimum level of decoder input (compressed weight size " + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 56, + 255, + 296, + 506 + ], + "type": "text", + "content": " outlined in equation 4 in details) is selected. This optimization ensures the proposed DeepCompress-ViT does not introduce any computational overhead (Figure 4) in pursuit of compression and accuracy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 514, + 253, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 253, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 253, + 528 + ], + "type": "text", + "content": "4.1. Unified Compression Training (UCT)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 533, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 295, + 605 + ], + "type": "text", + "content": "In this stage, an encoder-decoder network is trained to achieve aggressive compression. The encoder network " + }, + { + "bbox": [ + 55, + 533, + 295, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 55, + 533, + 295, + 605 + ], + "type": "text", + "content": ", learns to encode the model's weights to a compressed representation as the encoded embedding, while the decoder network, " + }, + { + "bbox": [ + 55, + 533, + 295, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 55, + 533, + 295, + 605 + ], + "type": "text", + "content": ", learns to decode the weights back to their original dimension as shown in Figure 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": "Consider a ViT model " + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathbf{W}}(\\cdot)" + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": " consisting of " + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": " layers, where the weights of the layers are denoted by the set " + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = \\{\\mathbf{w}_1,\\mathbf{w}_2,\\dots ,\\mathbf{w}_L\\}" + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": ". Let the parameters of the encoder network " + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{F}(.)" + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": " be represented as " + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathbf{E}}" + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": ", and the parameters of the decoder network " + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{G}(.)" + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": " be represented as " + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathbf{D}}" + }, + { + "bbox": [ + 55, + 605, + 295, + 666 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": "During training, each layer's weight " + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": " is passed through the encoder network " + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": ", which encodes it to a lower-dimensional representation, given by " + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i = \\mathbf{F}(\\mathbf{w}_i)" + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": ". The decoder network " + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": " then decodes " + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": " back to its original di" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": "mensionality as " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}_i = \\mathbf{G}(\\mathbf{z}_i)" + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": ". The encoder and decoder networks are trained jointly to minimize the mean squared error (MSE) between the original weight set " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "(\\mathbf{W})" + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": " and the reconstructed weight set " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "(\\hat{\\mathbf{W}})" + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": ". The weight reconstruction loss is calculated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 360, + 139, + 509, + 172 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 139, + 509, + 172 + ], + "spans": [ + { + "bbox": [ + 360, + 139, + 509, + 172 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\bf m s e} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\| {\\bf w} _ {i} - {\\bf G} ({\\bf F} ({\\bf w} _ {i})) \\| ^ {2}", + "image_path": "8d9ed040295061d9029094ed897ce15fe2db44a83494cc99731a0b7be0ba2e1d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 180, + 555, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 555, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 555, + 312 + ], + "type": "text", + "content": "To optimize this training step further, we unify the encoder-decoder training step with the original ViT-model. Our hypothesis is that only MSE loss-based weight reconstruction may not provide optimal performance [2]. Even though minimizing MSE loss results in the minimization of weight perturbation error, different sets of decoded weights with the same MSE value can have varying weight distributions, which can lead to a performance drop in the ViT model. Hence, it is reasonable to incorporate the ViT model into this training loop to align the ViT model's weight distribution with the decoded version of the weight." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 312, + 554, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 554, + 418 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 554, + 418 + ], + "type": "text", + "content": "Hence, we propose this end-to-end unified framework where the encoder-decoder networks are jointly trained with the ViT model. Our method will incorporate cross-entropy (CE) loss and knowledge distillation (KD) from a pretrained model in training, where CE ensures the ViT model performance is optimized on the decoded weight values w.r.t ground truth, and KD ensures the decoded weight parameters do not drift far apart from the initial weight distribution of a pre-trained ViT model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "text", + "content": "The forward pass for the whole end-to-end training after obtaining the decoded weight sets " + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{W}}" + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "text", + "content": " from the decoder is formulated as " + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathbf{W}}(\\cdot) \\rightarrow \\mathbf{H}_{\\hat{\\mathbf{W}}}(\\cdot)" + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "text", + "content": ", which implies that the ViT model inference will always use the decoded weights, i.e., the forward pass of the ViT model becomes " + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}} = \\mathbf{H}_{\\hat{\\mathbf{W}}}(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "text", + "content": " are the input images and " + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "text", + "content": " are the predictions from the ViT model. Next, using " + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 419, + 554, + 526 + ], + "type": "text", + "content": ", we compute the cross-entropy loss and knowledge distillation loss as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 319, + 534, + 547, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 534, + 547, + 563 + ], + "spans": [ + { + "bbox": [ + 319, + 534, + 547, + 563 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathbf {C E}} = - \\sum_ {i} \\mathbf {y} _ {i} \\log (\\hat {\\mathbf {y}} _ {i}), \\quad \\mathcal {L} _ {\\mathbf {K D}} = \\sum_ {i} \\hat {\\mathbf {y}} _ {\\mathrm {t}, i} \\log \\left(\\frac {\\hat {\\mathbf {y}} _ {\\mathrm {t} , i}}{\\hat {\\mathbf {y}} _ {i}}\\right)", + "image_path": "ecaf3dc7fc2655f33e271e5c0b5aa700d9cfea114ebff3814e2d0b547e3c0a65.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 571, + 554, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 571, + 554, + 595 + ], + "spans": [ + { + "bbox": [ + 313, + 571, + 554, + 595 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 571, + 554, + 595 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_{\\mathrm{t}}" + }, + { + "bbox": [ + 313, + 571, + 554, + 595 + ], + "type": "text", + "content": " represents the prediction from the pretrained teacher model. The total loss function is then defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 353, + 605, + 515, + 618 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 605, + 515, + 618 + ], + "spans": [ + { + "bbox": [ + 353, + 605, + 515, + 618 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {t o t a l}} = \\mathcal {L} _ {\\mathrm {m s e}} + \\alpha \\cdot \\mathcal {L} _ {\\mathrm {C E}} + \\beta \\cdot \\mathcal {L} _ {\\mathrm {K D}},", + "image_path": "0ae8813aa7c3533718e53998fdca00e3ebdf2dc6ae71b64c01bf0721ccd798c6.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "text", + "content": " are scaling factors controlling the contributions of cross-entropy and knowledge distillation losses, respectively. Finally, the overall loss function is minimized by jointly optimizing the encoder and decoder parameters " + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathbf{E}}" + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathbf{D}}" + }, + { + "bbox": [ + 313, + 628, + 554, + 688 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 402, + 693, + 465, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 693, + 465, + 711 + ], + "spans": [ + { + "bbox": [ + 402, + 693, + 465, + 711 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {W} _ {\\mathrm {E}}, \\mathbf {W} _ {\\mathrm {D}}} \\mathcal {L} _ {\\mathrm {t o t a l}}", + "image_path": "8aad558a74bb8a10005a0c90dac34bfd3f90dcacc2d68fc3f795febc2618f756.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30151" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 114, + 70, + 297, + 266 + ], + "blocks": [ + { + "bbox": [ + 114, + 70, + 297, + 266 + ], + "lines": [ + { + "bbox": [ + 114, + 70, + 297, + 266 + ], + "spans": [ + { + "bbox": [ + 114, + 70, + 297, + 266 + ], + "type": "image", + "image_path": "b49711e04362cc903cd5186f5cdd249e35ddb9c27815b80790e38c4406d4d640.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 275, + 555, + 309 + ], + "lines": [ + { + "bbox": [ + 54, + 275, + 555, + 309 + ], + "spans": [ + { + "bbox": [ + 54, + 275, + 555, + 309 + ], + "type": "text", + "content": "Figure 4. Proposed Optimized Test-Time Decoding overview. Decoding the encoded (compressed) weights first and then matrix multiplying with input activation increases FLOPs. The proposed method eliminates extra FLOPs by multiplying input activation with encoded weights first, then passing through decoder. The chosen value of encoding dimension " + }, + { + "bbox": [ + 54, + 275, + 555, + 309 + ], + "type": "inline_equation", + "content": "(r)" + }, + { + "bbox": [ + 54, + 275, + 555, + 309 + ], + "type": "text", + "content": " prevents any FLOP increase." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 70, + 497, + 266 + ], + "blocks": [ + { + "bbox": [ + 298, + 70, + 497, + 266 + ], + "lines": [ + { + "bbox": [ + 298, + 70, + 497, + 266 + ], + "spans": [ + { + "bbox": [ + 298, + 70, + 497, + 266 + ], + "type": "image", + "image_path": "cb7d7a50faf7fd8b949340c7555f512c031cf39802803af6c3ae83f7e9006519.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "type": "text", + "content": "After training is complete, for inference, we keep only the encoded weight parameters " + }, + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_i\\}" + }, + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "type": "text", + "content": " and a lightweight decoder " + }, + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathbf{D}}" + }, + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "type": "text", + "content": " in memory while discarding the encoder " + }, + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathbf{E}}" + }, + { + "bbox": [ + 55, + 316, + 295, + 351 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 351, + 296, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 351, + 296, + 458 + ], + "spans": [ + { + "bbox": [ + 55, + 351, + 296, + 458 + ], + "type": "text", + "content": "At inference, the decoder needs to map compressed weights to their original form layer by layer, which may help preserve accuracy. However, this can introduce two major drawbacks. First, the decoding step will inevitably lead to additional computation at runtime, and second, the decoded weights will increase temporary on-chip memory consumption, particularly for larger layers. Next, we outline our optimized test-time decoding strategy, which ensures these two bottlenecks remain in check." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 465, + 224, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 465, + 224, + 478 + ], + "spans": [ + { + "bbox": [ + 55, + 465, + 224, + 478 + ], + "type": "text", + "content": "4.2. Optimized Test-Time Decoding" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 483, + 295, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 295, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 295, + 578 + ], + "type": "text", + "content": "To mitigate the overhead associated with the decoding step, first design level optimization we propose is to design the decoder " + }, + { + "bbox": [ + 55, + 483, + 295, + 578 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 55, + 483, + 295, + 578 + ], + "type": "text", + "content": " as a single linear layer. This design choice minimizes repetitive decoding operations, reducing the computational overhead. Although a single-layer decoder network lowers the computational load relative to a multi-layer decoder, the computation needed for decoding weights using a single layer still persists." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "text", + "content": "To illustrate the overhead of weight decoding step, consider a fully connected layer in a ViT model with original weights " + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i\\in \\mathbb{R}^{C\\times d}" + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "text", + "content": ", whose weights are encoded and the encoded weights are represented by " + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i\\in \\mathbb{R}^{C\\times r}" + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "text", + "content": ". During inference of this layer, the weights are first decoded using the single-layer decoder network " + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "text", + "content": ", where weights of the decoder network is represented by " + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_D\\in \\mathbb{R}^{r\\times d}" + }, + { + "bbox": [ + 55, + 579, + 295, + 675 + ], + "type": "text", + "content": ". This weight decoding computation can be represented as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 681, + 295, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 681, + 295, + 693 + ], + "spans": [ + { + "bbox": [ + 141, + 681, + 295, + 693 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {w}} _ {i} = \\mathbf {z} _ {i} \\times \\mathbf {w} _ {D}, \\tag {1}", + "image_path": "a39be38b4d34a7d6be11239d100b1892f0a41ef2166f2058943f442b14df2a1e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 700, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 700, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 700, + 296, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 700, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}_i\\in \\mathbb{R}^{C\\times d}" + }, + { + "bbox": [ + 55, + 700, + 296, + 713 + ], + "type": "text", + "content": " denotes the decoded weights. One of the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 316, + 555, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 555, + 387 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 555, + 387 + ], + "type": "text", + "content": "most widely used metrics to evaluate computational complexity is Floating-point Operations (FLOPs) [6], which counts the total number of multiplications and additions performed in a given operation. The FLOPs incurred for the weight decoding operation is " + }, + { + "bbox": [ + 313, + 316, + 555, + 387 + ], + "type": "inline_equation", + "content": "2 \\cdot C \\cdot r \\cdot d" + }, + { + "bbox": [ + 313, + 316, + 555, + 387 + ], + "type": "text", + "content": ", corresponding to the matrix multiplication in eqn. (1)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 387, + 555, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 387, + 555, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 555, + 422 + ], + "type": "text", + "content": "Next, the usual forward pass of fully connected layer in the ViT model with input activations " + }, + { + "bbox": [ + 313, + 387, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i\\in \\mathbb{R}^{N\\times C}" + }, + { + "bbox": [ + 313, + 387, + 555, + 422 + ], + "type": "text", + "content": " and decoded weights " + }, + { + "bbox": [ + 313, + 387, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}_i" + }, + { + "bbox": [ + 313, + 387, + 555, + 422 + ], + "type": "text", + "content": " is computed as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 398, + 430, + 553, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 398, + 430, + 553, + 442 + ], + "spans": [ + { + "bbox": [ + 398, + 430, + 553, + 442 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} \\times \\hat {\\mathbf {w}} _ {i}, \\tag {2}", + "image_path": "bbc686823d8c84b712356543f680aa2776d4b9259c3a15dd8ad637e3e3a13a40.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i + 1}" + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "text", + "content": " represents the output activations of the layer. The FLOPs incurred by this forward pass is " + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "inline_equation", + "content": "2\\cdot N\\cdot C\\cdot d" + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "text", + "content": " resulting from the matrix multiplication in eqn. (2). Therefore, the total FLOPs incurred in the forward pass with this strategy is " + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "inline_equation", + "content": "(2\\cdot N\\cdot C\\cdot d + 2\\cdot C\\cdot r\\cdot d)" + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "text", + "content": " where the additional " + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "inline_equation", + "content": "2\\cdot C\\cdot r\\cdot d" + }, + { + "bbox": [ + 313, + 449, + 555, + 533 + ], + "type": "text", + "content": " FLOPs is incurred because of this inefficient weight decoding strategy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 533, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 617 + ], + "type": "text", + "content": "Next, we optimize the decoding step to eliminate this additional " + }, + { + "bbox": [ + 313, + 533, + 555, + 617 + ], + "type": "inline_equation", + "content": "2 \\cdot C \\cdot r \\cdot d" + }, + { + "bbox": [ + 313, + 533, + 555, + 617 + ], + "type": "text", + "content": " FLOPs, we propose Optimized Test-Time Decoding. Our proposed decoding approach leverages the associative property of matrix multiplication to reorder computation sequence to maintain or improve overall FLOPs. To illustrate, recall that the overall computation for inefficient decoding strategy is as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 358, + 624, + 553, + 636 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 624, + 553, + 636 + ], + "spans": [ + { + "bbox": [ + 358, + 624, + 553, + 636 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} \\times \\hat {\\mathbf {w}} _ {i} = \\mathbf {x} _ {i} \\times \\left(\\mathbf {z} _ {i} \\times \\mathbf {w} _ {D}\\right), \\tag {3}", + "image_path": "a04e5bb7e0ce74a26be97f0e6afbade7684ede7143944c83262b7918d5dbc662.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 643, + 555, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 643, + 555, + 690 + ], + "spans": [ + { + "bbox": [ + 313, + 643, + 555, + 690 + ], + "type": "text", + "content": "where it shows weight decoding first and then perform the forward pass in the fully connected layer of ViT model. We optimize the decoding step by simply reorder the matrix multiplications as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 356, + 697, + 512, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 697, + 512, + 711 + ], + "spans": [ + { + "bbox": [ + 356, + 697, + 512, + 711 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} ^ {\\prime} \\times \\mathbf {w} _ {D} = (\\mathbf {x} _ {i} \\times \\mathbf {z} _ {i}) \\times \\mathbf {w} _ {D},", + "image_path": "e04499653a85ffe2b96562d668176b09db089b4bff8b8328b7b42e5d891cf56c.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30152" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "where we first perform input compression " + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "inline_equation", + "content": "(\\mathbf{x} \\in \\mathbb{R}^{N \\times C} \\to \\mathbf{x}' \\in \\mathbb{R}^{N \\times r})" + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": " and then do the optimized forward pass " + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}' \\times \\mathbf{w}_D)" + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": ". The proposed strategy is also illustrated in Figure 4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "type": "text", + "content": "The total FLOPs for this optimized approach is " + }, + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "type": "inline_equation", + "content": "2 \\cdot N \\cdot r \\cdot (C + d)" + }, + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "type": "text", + "content": ". However, with an arbitrary value of " + }, + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "type": "text", + "content": ", the overall FLOPs can still go up. Therefore, to ensure that the total FLOPs of the proposed decoding strategy do not exceed the baseline models FLOPs, we derive the optimal " + }, + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 55, + 108, + 294, + 180 + ], + "type": "text", + "content": " for efficiency by solving the following inequality," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 190, + 247, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 190, + 247, + 201 + ], + "spans": [ + { + "bbox": [ + 104, + 190, + 247, + 201 + ], + "type": "interline_equation", + "content": "2 \\cdot N \\cdot r \\cdot (C + d) \\leq 2 \\cdot N \\cdot C \\cdot d,", + "image_path": "780265ece973562986aa2c07c49dee849969881436c77bf7ed329f81cbc32083.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 212, + 295, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 212, + 295, + 236 + ], + "spans": [ + { + "bbox": [ + 55, + 212, + 295, + 236 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 212, + 295, + 236 + ], + "type": "inline_equation", + "content": "2 \\cdot N \\cdot C \\cdot d" + }, + { + "bbox": [ + 55, + 212, + 295, + 236 + ], + "type": "text", + "content": " is the FLOPs incurred due to normal forward pass in eqn. (2). Solving the inequality, we get:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 132, + 243, + 295, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 243, + 295, + 270 + ], + "spans": [ + { + "bbox": [ + 132, + 243, + 295, + 270 + ], + "type": "interline_equation", + "content": "r \\leq \\frac {2 \\cdot N \\cdot C \\cdot d}{2 \\cdot N \\cdot (C + d)} \\tag {4}", + "image_path": "9c431cf57e8d8280969c628565b68b2761bb03331254c2b1fc7d0801598496f6.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 277, + 296, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 277, + 296, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 296, + 326 + ], + "type": "text", + "content": "In summary, by reordering the computation sequence and using optimal " + }, + { + "bbox": [ + 55, + 277, + 296, + 326 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 55, + 277, + 296, + 326 + ], + "type": "text", + "content": " for compression derived in eqn. (4), our innovative decoding optimization does not incur any additional computation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 331, + 181, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 181, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 181, + 344 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 350, + 251, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 251, + 363 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 251, + 363 + ], + "type": "text", + "content": "5.1. Datasets and Implementation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 366, + 295, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 295, + 437 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 295, + 437 + ], + "type": "text", + "content": "Datasets. We conduct our experiments on the ILSVRC12 ImageNet classification dataset [22] consisting 1,000 classes with 1.2 million training images and 50k validation images. Additionally, we evaluate DeepCompress-ViT on the widely used COCO benchmark dataset [14] for object detection and instance segmentation task." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 438, + 295, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 438, + 295, + 557 + ], + "spans": [ + { + "bbox": [ + 55, + 438, + 295, + 557 + ], + "type": "text", + "content": "Encoder-Decoder Architecture. We use four encoder network each with 2 linear layers to encode four types of layers: attn_qkv, attnProj, mlp_fcl and mlp_fcl2. Each encoder has an affine transformation before and after the 2 linear layers. Similarly to encoders, we use four single linear layer decoders to decode the four types of layers. Note that each decoder is a shared decoder which decodes a particular type of layer of all ViT blocks. Note that, we exclude the first layer, last layer, and LayerNorm parameters from compression." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "content": "Experimental Settings. The encoder and decoder models are trained for 275 epochs with a batch size of 256 and a base learning rate of " + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "content": ", using a cosine learning rate scheduler. For data augmentation, we apply the standard techniques used in [27] and for knowledge distillation, we use pretrained distilled DeiT models [27] with temperature " + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\tau = 1" + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "content": ". For UCT, we set the value of " + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\beta = 3 \\times 10^3" + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "content": ". The encoded weights are quantized using 4-bit asymmetric quantization, while decoder weights are quantized using 4-bit symmetric quantization, both trained using Quantization Aware Training. Additionally, the patch embedding (first) and classification (last) layers are quantized using 8-bit symmetric quantization. The optimal value of " + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 55, + 558, + 295, + 713 + ], + "type": "text", + "content": " from" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "solving (4) is set to 277 for DeiT-S and 502 for DeiT-B. For object detection and instance segmentation, we use the mmdetection library with the standard " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " training scheduler and adopt an edge-friendly resolution of " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " for both training and evaluation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 151, + 372, + 162 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 151, + 372, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 151, + 372, + 162 + ], + "type": "text", + "content": "5.2. Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": "Image Classification. Performance of the compressed DeiT models with proposed DeepCompress-ViT on the classification task is shown in Table 3. The results demonstrate substantial reductions in model size and energy consumption resulting from DeepCompress-ViT. For instance, the DeepCompress-DeiT-S model achieves a compression ratio of " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "14.9\\times" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": ", reducing the model size from " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "84.1\\mathrm{MB}" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": " to just " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "5.64\\mathrm{MB}" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": " while maintaining an accuracy of " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "78.74\\%" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": " on ImageNet. Similarly, DeepCompress-DeiT-B achieves a compression ratio of " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "17.4\\times" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": ", decreasing the model size from " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "330.2\\mathrm{MB}" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "18.9\\mathrm{MB}" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": ". Remarkably, both models show an unprecedented energy reduction of " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "673\\times" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "1475\\times" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": " and latency reduction of " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "44.5\\times" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "68.4\\times" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": " respectively (please refer to section 5.3 and Figure 5 for more hardware energy and latency evaluation details). Proposed DeepCompress-ViT achieves this unprecedented level of model compression, energy, and latency reduction, enabling the deployment of ViT models at the edge while only sacrificing a marginal level of accuracy (e.g., for DeiT-B only " + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\sim 0.1\\%" + }, + { + "bbox": [ + 313, + 167, + 555, + 396 + ], + "type": "text", + "content": ")" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "text", + "content": "Object Detection and Instance Segmentation. Next, table 4 compares the performance of DeepCompress-ViT with baseline (no compression) DeiT-S model on object detection and instance segmentation tasks. We trained both the models on COCO dataset integrating the respective ViT backbones with Mask R-CNN [9]. We evaluate both of the models for these tasks at an edge-friendly resolution of " + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "text", + "content": ". Notably, DeepCompress-ViT reduces the ViT backbone (DeiT-S) size from 82.65MB to 5.27MB (" + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "inline_equation", + "content": "15.7 \\times" + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "text", + "content": " compression) with a slight drop in " + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^b}" + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^m}" + }, + { + "bbox": [ + 313, + 399, + 554, + 542 + ], + "type": "text", + "content": ", further highlighting the effectiveness of our compression method on other complex vision tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": "Comparison with SOTA compression methods. Finally, Table 5 provides a comparative analysis of DeiT-Small models compressed using different pruning and quantization methods. Among the methods, DeepCompress-ViT achieves the highest compression ratio of " + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "inline_equation", + "content": "14.9 \\times" + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": ", reducing the model size to 5.64 MB while maintaining a top-1 accuracy of " + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "inline_equation", + "content": "78.74\\%" + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": ". In contrast, popular WDPruning [31], LSQ [8] and Q-ViT [11] achieves achieve much lower accuracies of " + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "inline_equation", + "content": "60.51\\%" + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "inline_equation", + "content": "68.00\\%" + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "inline_equation", + "content": "71.9\\%" + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": ", respectively. Our proposed DeepCompress-ViT consistently outperforms them by large margins of " + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "inline_equation", + "content": "\\sim 18\\%" + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "inline_equation", + "content": "\\sim 10\\%" + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "inline_equation", + "content": "\\sim 7\\%" + }, + { + "bbox": [ + 313, + 546, + 554, + 712 + ], + "type": "text", + "content": ", respectively, making DeepCompress-ViT the only practical choice to maintain accuracy while performing aggressive compression." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30153" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 94, + 531, + 148 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "text", + "content": "Table 3. Performance of DeepCompress-ViT on ImageNet-1K. DeepCompress-ViT achieves memory (" + }, + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "inline_equation", + "content": "\\geq 15 \\times" + }, + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "text", + "content": ") and energy consumption (" + }, + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "inline_equation", + "content": "\\geq 1531 \\times" + }, + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "text", + "content": "), while marginal accuracy drop (" + }, + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "inline_equation", + "content": "< 1\\%" + }, + { + "bbox": [ + 55, + 70, + 555, + 93 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 94, + 531, + 148 + ], + "lines": [ + { + "bbox": [ + 77, + 94, + 531, + 148 + ], + "spans": [ + { + "bbox": [ + 77, + 94, + 531, + 148 + ], + "type": "table", + "html": "
MethodAccuracy (%)Model Size (MB)Compression RatioGFLOPsExecution Time (s)Energy Consumption (J)
DeiT-S [27]79.7284.11x9.2024.029979.52
DeepCompress-DeiT-S78.745.6414.9x8.880.5414.83
DeiT-B [27]81.74330.21x35.14129.32150895
DeepCompress-DeiT-B81.6218.917.4x30.841.89102.29
", + "image_path": "9746999787ecabd3c4e3ce2e50f849b2c1a2de06a9efb411802d3594d275435d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 83, + 195, + 269, + 231 + ], + "blocks": [ + { + "bbox": [ + 55, + 162, + 295, + 194 + ], + "lines": [ + { + "bbox": [ + 55, + 162, + 295, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 162, + 295, + 194 + ], + "type": "text", + "content": "Table 4. Performance of DeepCompress-ViT for Object Detection on the COCO validation set with Mask R-CNN evaluated at an edge-friendly resolution of " + }, + { + "bbox": [ + 55, + 162, + 295, + 194 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 55, + 162, + 295, + 194 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 195, + 269, + 231 + ], + "lines": [ + { + "bbox": [ + 83, + 195, + 269, + 231 + ], + "spans": [ + { + "bbox": [ + 83, + 195, + 269, + 231 + ], + "type": "table", + "html": "
Method\\( {\\mathbf{{AP}}}^{\\mathbf{b}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}} \\)ViT Backbone Size (MB)
DeiT-S [27]26.223.782.65
DeepCompress-ViT23.020.95.27 (15.7×)
", + "image_path": "448b1858d2a548afa320699e42a8434312c3979d0b5a5d84fc8ef7e82bce2231.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 57, + 266, + 294, + 327 + ], + "blocks": [ + { + "bbox": [ + 55, + 243, + 295, + 266 + ], + "lines": [ + { + "bbox": [ + 55, + 243, + 295, + 266 + ], + "spans": [ + { + "bbox": [ + 55, + 243, + 295, + 266 + ], + "type": "text", + "content": "Table 5. Performance comparison of DeiT-Small with SOTA compression methods on ImageNet-1K" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 266, + 294, + 327 + ], + "lines": [ + { + "bbox": [ + 57, + 266, + 294, + 327 + ], + "spans": [ + { + "bbox": [ + 57, + 266, + 294, + 327 + ], + "type": "table", + "html": "
ModelAccuracy (%)Model Size (MB)Compression Ratio
DeiT-S [27]79.72 (0)84.11x
WDPruning [31]60.51 (↓19.21)33.72.5x
LSQ [8]68.00 (↓11.72)6.1813.6x
Q-ViT [11]71.90 (↓7.82)6.1813.6x
DeepCompress-ViT78.74 (↓0.98)5.6414.9x
", + "image_path": "320105d2f294d6b6ebd9e51407a00df25edcabf771a3489ba60e95dbfa93028a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 339, + 180, + 351 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 339, + 180, + 351 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 180, + 351 + ], + "type": "text", + "content": "5.3. Hardware Evaluation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 354, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 354, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 354, + 296, + 714 + ], + "type": "text", + "content": "High compression gain gives an understanding of the effectiveness of a compression method in terms of memory savings. But to successfully realize the full potential of our proposed method, we evaluate the energy and latency gain on hardware evaluation platforms. For hardware deployment, we use the gem5-Aladdin platform [25], which effectively captures dynamic interactions between accelerators and the SoC platform, enabling detailed architectural analysis of the proposed compression method. Our setup incorporates a cycle-accurate in-house-developed model based on the Eyeriss accelerator [5] (0.0029 DRAM access/multiply and accumulation (MAC), 33.6 GMAC/s). Performance metrics from gem5-Aladdin are then analyzed using DRAM-Sim2 [21] to model realistic off-chip memory latency and energy characteristics. The total on-chip weight memory is capped at three configurations (2 MB, 4 MB, 8 MB). The analyzed DeiT-S model initially requires 84.1MB of memory, which exceeds the on-chip memory capacity. By applying DeepCompress-ViT algorithm, this requirement is reduced to 5.64 MB, which can readily fit into the 8MB on-chip memory. However, with a smaller memory capacity, it is not feasible to transfer the entire set of weight parameters to the accelerator in a single batch due to the model's memory demands. Therefore, we implemented a weight parser that transmits weight parameters in variable batch sizes to the accelerator. Figure 5 shows the breakdown of energy consumption and latency across MAC, off-chip, and on-chip memory access components for various on-chip memory sizes. For both DeiT-S and DeiT-B, the DeepCompress-ViT algorithm achieves significant energy savings, reduc" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 150, + 435, + 271 + ], + "blocks": [ + { + "bbox": [ + 315, + 150, + 435, + 271 + ], + "lines": [ + { + "bbox": [ + 315, + 150, + 435, + 271 + ], + "spans": [ + { + "bbox": [ + 315, + 150, + 435, + 271 + ], + "type": "image", + "image_path": "295f440da98d769fe480f170d2d3538b2dfee19cbd1ce31f5e99273299ce59e1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 273, + 554, + 316 + ], + "lines": [ + { + "bbox": [ + 313, + 273, + 554, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 273, + 554, + 316 + ], + "type": "text", + "content": "Figure 5. Breakdown of (a) Energy consumption, (b) Latency vs. on-chip memory size. For every off-chip memory size, DeiT-S, DeepCompress-ViT-S, DeiT-B, and DeepCompress-ViT-B results are plotted, respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 435, + 152, + 552, + 272 + ], + "blocks": [ + { + "bbox": [ + 435, + 152, + 552, + 272 + ], + "lines": [ + { + "bbox": [ + 435, + 152, + 552, + 272 + ], + "spans": [ + { + "bbox": [ + 435, + 152, + 552, + 272 + ], + "type": "image", + "image_path": "8dda0ecef3cd3d164e89f402b611e539c4551e247cd3c6d059cca3c1bee4cbb4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 323, + 555, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 555, + 431 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 555, + 431 + ], + "type": "text", + "content": "ing consumption by approximately " + }, + { + "bbox": [ + 313, + 323, + 555, + 431 + ], + "type": "inline_equation", + "content": "673 \\times" + }, + { + "bbox": [ + 313, + 323, + 555, + 431 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 323, + 555, + 431 + ], + "type": "inline_equation", + "content": "1475 \\times" + }, + { + "bbox": [ + 313, + 323, + 555, + 431 + ], + "type": "text", + "content": ", respectively, with an 8MB on-chip memory. This remarkable reduction is primarily due to the DeepCompress-ViT algorithm's ability to minimize off-chip memory access, as visible through the high difference in the red bar plots. This reduction becomes even more pronounced with smaller memory sizes, enabling for the first time the possibility of deploying large ViT models at the edge and performing time-sensitive applications." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 444, + 388, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 388, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 388, + 456 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 462, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 462, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 312, + 462, + 555, + 713 + ], + "type": "text", + "content": "In this paper, we present DeepCompress-ViT, a novel approach to achieve highly compressed Vision Transformers optimized for efficient edge deployment. We first analyze the limitations of existing model compression techniques and show that they lead to large weight perturbation error because of their lossy encoding mechanism. Then, to resolve this challenge, we develop an orthogonal compression technique that consists of an encoding for compression and a decoding step to help maintain performance. However, decoding weights repeatedly during inference can lead to additional computation and increase on-chip memory usage, both of which are critical concerns for edge applications. To address these challenges, we propose a novel optimized Test-Time Decoding scheme that enables efficient inference without increased computation and avoids high on-chip memory usage. 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Advances in Neural Information Processing Systems, 35:9010-9023, 2022. 3" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "30156" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/a85e9f83-617a-4a59-8124-97eefae14b9e_content_list.json b/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/a85e9f83-617a-4a59-8124-97eefae14b9e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8daa0c2801306bb8edc6711f1d05f21cf4208fb4 --- /dev/null +++ b/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/a85e9f83-617a-4a59-8124-97eefae14b9e_content_list.json @@ -0,0 +1,1604 @@ +[ + { + "type": "text", + "text": "DeepLA-Net: Very Deep Local Aggregation Networks for Point Cloud Analysis", + "text_level": 1, + "bbox": [ + 99, + 130, + 897, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ziyin Zeng $^{1}$ , Mingyue Dong $^{1}$ , Jian Zhou $^{1*}$ , Huan Qiu $^{1}$ , Zhen Dong $^{1}$ , Man Luo $^{2}$ and Bijun Li $^{1}$ $^{1}$ Wuhan University, $^{2}$ Dongfeng USharing Technology Co.", + "bbox": [ + 129, + 179, + 864, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zengziyin, dongmy, jianzhou, huanqiu, dongzhenwhu, lee}@whu.edu.cn, tc-luoman@dfmc.com.cn", + "bbox": [ + 101, + 219, + 895, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 268, + 328, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to the irregular and disordered data structure in 3D point clouds, prior works have focused on designing more sophisticated local representation methods to capture these complex local patterns. However, the recognition performance has saturated over the past few years, indicating that increasingly complex and redundant designs no longer make improvements to local learning. This phenomenon prompts us to diverge from the trend in 3D vision and instead pursue an alternative and successful solution: deeper neural networks. In this paper, we propose DeepLA-Net, a series of very deep networks for point cloud analysis. The key insight of our approach is to exploit a small but mighty local learning block, which uses $10 \\times$ fewer FLOPs, enabling the construction of very deep networks. Furthermore, we design a training supervision strategy to ensure smooth gradient backpropagation and optimization in very deep networks. We construct the DeepLA-Net family with a depth of up to 120 blocks — at least $5 \\times$ deeper than recent methods — trained on a single RTX 3090. An ensemble of the DeepLA-Net achieves state-of-the-art performance on classification and segmentation tasks of S3DIS Area5 ( $+2.2\\%$ mIoU), ScanNet test set ( $+1.6\\%$ mIoU), ScanObjectNN ( $+2.1\\%$ OA), and ShapeNetPart ( $+0.9\\%$ CLS.mIoU). The code are released at https://github.com/zeng-ziyin/DeepLA-Net.", + "bbox": [ + 88, + 301, + 485, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 696, + 220, + 713 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thanks to the significant development of 3D sensors, 3D point cloud analysis has garnered increasing attention in recent years and is widely applied in autonomous driving, smart cities, and robotics [18, 84]. However, 3D point clouds consist of sparse, discrete, and non-uniform point sets embedded in continuous space [46]. This complex structure poses challenges to local pattern learning.", + "bbox": [ + 89, + 722, + 482, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In order to solve this problem, extensive explorations have been conducted on the local pattern of point clouds to enable fine-grained analysis. Inspired by CNNs, they intro-", + "bbox": [ + 89, + 829, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/010e3b29538d74f2a25cdff83dedeb3c7292b0054646bdae373e01fbf7cdf69f.jpg", + "image_caption": [ + "Figure 1. Illustration of segmentation performance, model efficiency and network depth on S3DIS Area5. DeepLA-24 has already achieved SOTA-equivalent performance with minimal parameters. The deeper architecture DeepLA-120 achieves a milestone (75.7%) by exceeding 75% threshold for the first time, and outperforms Point Transformer v3 [70] with fewer parameters." + ], + "image_footnote": [], + "bbox": [ + 535, + 261, + 887, + 516 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "duce two robust inductive biases: locality and weight sharing, which promote the development of neural networks for analyzing 3D point clouds [47]. Specifically, these studies [10, 20, 33, 48, 56, 83, 85, 86] employ MLPs with shared weights to capture local features from neighbors. We collectively refer to them as local aggregation networks (LANets) in this paper. It is noteworthy that most LANets primarily focus on developing intricate local representation methods to explicitly explore the local patterns of point clouds, achieving success due to the robust inductive biases. However, the performance of increasingly sophisticated LANets on popular benchmarks [1, 9, 64, 80] has gradually saturated, as evidenced by minimal gains compare to PointNeXt [48] over the past few years, such as ScanObjectNN [64] (OA +0.4%, mAcc +0.5%, in Tab. 3) and ShapeNetPart [80] (cls.mIoU +0.4%, Ins.mIoU +0.2%, in Tab. 4). Particularly, the performance of most existing methods on S3DIS [1] has saturated around 73% [62, 70], as shown in Figure 1. The primary reason is that they already adequately", + "bbox": [ + 511, + 612, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* corresponding author: Jian Zhou", + "bbox": [ + 107, + 887, + 290, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1330", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "describe the local geometric properties of point clouds, and more complex designs no longer contribute to capturing additional local patterns [39, 48]. This phenomenon prompts us to rethink the design of LANets.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Interestingly, the development of 3D point cloud analysis is closely related to the evolution of 2D image processing networks [39, 47]. We observe that the design of 2D CNNs shifted towards deeper with the residual connections [19], making deep networks the mainstream backbone for feature extraction with successful performance [2, 35, 52]. Given that LANets for point clouds share similar inductive biases with CNNs, we cannot help but wonder: can we explore an alternative path by leveraging the success of deep CNNs for LANets? Unfortunately, to the best of our knowledge, there has been limited systematic exploration of deepening LANets. Therefore, in this paper, instead of following the tendency to explore sophisticated details, we are in pursuit of very deep LANets for point cloud analysis. For this purpose, we encounter two key challenges: (1) high computational cost, and (2) difficult training optimization.", + "bbox": [ + 89, + 154, + 482, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Obviously, the prevailing philosophy of sophisticated and redundant local learning has significantly increased computational complexity. To circumvent the prohibitive computations, we propose a residual local feature extraction (ResLFE) block that ensures minimal computational cost. Specifically, we first employ stage-level positional embedding instead of redundant and high latency layer-level. We then introduce an efficient vector feature representation and a robust modernization structure that significantly reduces FLOPs while preserving local information interactions. As shown in Figure 2, the proposed ResLFE block shows significant computational efficiency $(10\\times$ fewer FLOPs) and commendable performance improvements $(+1.1\\%$ mIoU). In particular, this remarkable computational efficiency enables the construction of very deep networks.", + "bbox": [ + 89, + 398, + 482, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, very deep networks are difficult to optimize [19, 72], and the complex geometric patterns of point clouds further exacerbate the difficulty of optimization [16, 44, 58]. To address these issues, we introduce a hybrid deep supervision (HDS) strategy to facilitate learning and optimization. We employ two forms of supervision to the outputs of the encoder at each stage. Specifically, we align each output with the ground truth using cross-entropy loss, which promotes smooth gradient propagation. Meanwhile, we also align the outputs with the spatial distribution of the point cloud using mean squared error loss, which benefits in fitting the complex geometric patterns to simplify network optimization. We demonstrate in experiments that the proposed HDS strategy optimizes network training by accelerating model convergence and achieves significant performance improvements $(+3.1\\% \\mathrm{mIoU})$", + "bbox": [ + 89, + 627, + 482, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, we propose very Deep Local Aggregation Networks (DeepLA-Net), constructed from the ResLFE", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "block for lightweight design and the HDS strategy for optimization. In particular, we have successfully trained DeepLA-120—a representative deep network comprising up to 120 ResLFE blocks—on a single RTX 3090 with 24GB memory. The DeepLA-Net family outperforms the SOTA methods across various tasks, including S3DIS [1] and ScanNetV2 [9] for semantic segmentation, ScanObjectNN [64] for object classification, and ShapeNetPart [80] for part segmentation. Figure 1 highlights the superior performance and efficiency of our DeepLA-Net family on S3DIS Area5. Moreover, a step-by-step procedure of constructing the DeepLA-Net and the corresponding results are shown in Figure 2. Our key contributions are:", + "bbox": [ + 511, + 90, + 903, + 287 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a residual local feature extraction block from the perspective of efficiency and performance, enabling the construction of deeper LANets.", + "- We propose a hybrid deep supervision strategy from the perspective of optimization and learning to ensure smooth gradient backpropagation in deeper LANets.", + "- We propose DeepLA-Net, a series of very deep local aggregation networks, surpassing SOTA in classification, part segmentation, and semantic segmentation." + ], + "bbox": [ + 511, + 297, + 903, + 444 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 458, + 653, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deep Learning on Point Clouds", + "text_level": 1, + "bbox": [ + 511, + 483, + 790, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given the disordered and unstructured nature of 3D point clouds, directly applying traditional CNNs to them remains a challenge. Therefore, some methods firstly transform point clouds into intermediate representations such as 2D images [3, 26, 42, 73, 82] or 3D voxels [5, 7, 17, 27, 41, 93] through projection or voxelization, and subsequently employ 2D/3D CNNs to process these structured data. Although promising results have been shown in certain scenarios, the intermediate transformation steps may introduce information loss and computation costs [14, 51, 86]. In contrast, point-based methods [14, 20, 31, 46, 47, 51, 69, 83, 85, 86, 91] are specifically designed to perform feature learning directly on point clouds without using intermediate representations. Moreover, some noteworthy research has leveraged techniques like Recurrent Neural Networks (RNNs) [21, 34, 79], Graph Neural Networks (GNNs) [25, 28, 66, 75, 87], point-voxel hybrid representation [36, 37, 53, 74, 88], and sparse voxel [4, 8, 55, 59, 60], achieving significant performance in various tasks.", + "bbox": [ + 511, + 505, + 903, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Local Aggregation Networks for Point Clouds", + "text_level": 1, + "bbox": [ + 511, + 801, + 898, + 818 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The pioneering PointNet [46] uses point-wise MLPs to learn per-point features, however, it has limitations in capturing local details. To overcome this, PointNet++ [47] improves PointNet by employing shared-weight MLPs in local neighbors, aligning with the inductive biases in CNNs:", + "bbox": [ + 511, + 825, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1331", + "bbox": [ + 483, + 945, + 511, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "localization and weight sharing. Along this direction, numerous subsequent studies [30, 40, 63, 67, 69, 90] have employed the above two inductive biases by local feature aggregation operations. We summarize them as local aggregation networks (LANets). Recent LANets [10, 14, 20, 33, 43, 48, 51, 54, 83, 85, 86] have primarily focused on exploring more robust local representations. For example, Point Transformer [92] designs a local transformer layer based on vector self-attention in local neighbors. PointVector [10] improves local extractor by transforming relative features and positions of input into representative vectors. ConDaFormer [13] enhances local geometric modeling by depth-wise convolutions, capturing both long-range contextual information and local priors. However, with the development of LANets, merely development of more complex LANets is insufficient for further capturing the local patterns. In this paper, we demonstrate that without relying on intricate and complex local representations, designing very deep hierarchical architectures for LANets can also achieve significant breakthroughs in performance.", + "bbox": [ + 89, + 90, + 483, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 89, + 405, + 218, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the preliminary implementation of DeepLA-Net. Most existing LANets have focused on robust local representation to effectively capture the complex local patterns of sparse and discrete point clouds. However, this focus makes them difficult to deepen due to the high computational cost. Therefore, we consider building deep networks based on the simplest PointNet++ [47].", + "bbox": [ + 89, + 430, + 483, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PointNet++ [47], the pioneering LANet for point cloud analysis, can be summarized in two phases: position embedding and feature representation. In the position embedding phase, PointNet++ employs ball query to group points, and then uses relative position differences as position embedding. Subsequently, in the feature representation phase, PointNet++ concatenates position embedding and grouped features to represent local features, and then aggregates them to centroid points by using max pooling. This can be formulated as:", + "bbox": [ + 89, + 539, + 483, + 690 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} p _ {i} ^ {k} = \\operatorname {G r o u p} \\left(p _ {i}\\right) \\\\ P E = \\mathcal {M} \\left(p _ {i} - p _ {i} ^ {k}\\right) \\end{array} \\quad \\left\\{ \\begin{array}{l} F _ {N} = \\mathcal {M} \\left[ f _ {i} ^ {k} \\oplus P E \\right] \\\\ F _ {\\text {o u t}} = \\max \\left(F _ {N}\\right) \\end{array} \\right. \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 710, + 482, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $p_i$ denotes the centroid points, $p_i^k$ denotes the grouped points, $\\mathcal{M}$ denotes the multi-layer perceptron, $\\oplus$ denotes the concatenation, max denotes the max-pooling, and $f_i^k$ denotes the grouped features.", + "bbox": [ + 89, + 760, + 482, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Implementation. Due to its simplicity, we employ PointNet++ [47] as the baseline and demonstrate the step-by-step \"modernization\" into DeepLA-Net. Firstly, we follow the PointNeXt [48] configuration, incorporating data augmentation and optimization techniques such as random height", + "bbox": [ + 89, + 824, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/724b6af3ffb39dd6c145d58ccbb8dd715198ec2ab1fcd23320af0f85c45e3cf7.jpg", + "image_caption": [ + "Figure 2. Illustration of the designs and results of our improvements on S3DIS [1] Area5 step-by-step. The foreground bars denote model accuracy, the stars denote model FLOPs, and hatched bars mean the modification is not adopted solely." + ], + "image_footnote": [], + "bbox": [ + 526, + 84, + 895, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and color dropout. The baseline model achieves $63.4\\%$ mIoU and 11.3G FLOPs1. Subsequently, we directly extend the baseline to 24-block model, following [35] with a block ratio of [1:1:3:1]. This plain-24 model achieves $69.0\\%$ mIoU and 92.2G FLOPs. Despite achieving a respectable mIoU score, the huge FLOPs prevent us from further deepening the network. In addition, deep network poses optimization challenges. Therefore, to construct LANets as deep as possible, we propose the ResLFE block which significantly reduces the computation cost while preserving reliable accuracy. Subsequently, we propose the HDS strategy to ensure smooth gradient backpropagation in deep networks and mitigate training optimization challenges.", + "bbox": [ + 511, + 479, + 906, + 678 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 511, + 689, + 650, + 707 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the key components of our DeepLA-Net: residual local feature extraction (ResLFE) block and hybrid deep supervision (HDS) strategy. To intuitively and clearly demonstrate the role of each design, we illustrate each step of improvement in Figure 2, with all models evaluated on S3DIS Area 5 [1].", + "bbox": [ + 511, + 714, + 905, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Residual Local Feature Extraction Block", + "text_level": 1, + "bbox": [ + 511, + 814, + 862, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To enable the construction of deeper networks, we propose the ResLFE block, as shown in Figure 3, which significantly", + "bbox": [ + 511, + 835, + 905, + 867 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "$^{1}$ FLOPs calculation follows the settings of PointNeXt [48] which evaluated on S3DIS with $16 \\times 15$ , 000 points.", + "bbox": [ + 511, + 875, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1332", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0ef439624a33fe11f9097f47d0e3a0622206be35f49626e59c12f143ba081f6b.jpg", + "image_caption": [ + "Figure 3. Illustration of the proposed ResLFE block. Right: stage-level position embedding. Middle: Vector Feature Representation (VFR.) module. Left: modernization structure." + ], + "image_footnote": [], + "bbox": [ + 122, + 85, + 460, + 265 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fdbd61f09272a97fb4d8c252b5d93ee64616df89f7cdcee15fdc4753ebd19b98.jpg", + "image_caption": [ + "Figure 4. Illustration of the computational latency of position embedding and feature representation phases in different LANets." + ], + "image_footnote": [], + "bbox": [ + 101, + 320, + 473, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "reduces computational cost. The ResLFE block comprises three key aspects: (1) stage-level position embedding, (2) efficient vector feature representation module, and (3) powerful modernization structure.", + "bbox": [ + 89, + 468, + 483, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stage-Level Position Embedding: Existing LANets typically implement position embedding at each learning layer, resulting in high computational costs. As shown in Figure 4, the computational latency of the positional embedding phase constitutes approximately half of the total for each layer, which is unacceptable in deeper networks. As indicated by Eq. 1, we observe that the computation of position embedding relies solely on point coordinates. Considering that the resolution of points remains constant within each stage, layers in the same stage can share an identical position embedding. Therefore, we suggest pre-calculate the position embedding at the beginning of each stage, saving it to cache and reusing it per-layer in that stage to avoid subsequent real-time computations. This approach ensures that the computational costs of position embedding depend solely on the number of stages, rather than the depth of the network, thereby facilitating the efficient application of very deep networks. Our implementation of position embedding is the same as PointNet++. This operation approximately halves the FLOPs (92.2G → 44.6G), with only a minimal decrease in performance (69.0% → 68.6%).", + "bbox": [ + 89, + 532, + 483, + 851 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Vector Feature Representation Module: First, we consider further improvements in computational efficiency during the feature representation phase. We observe that, in", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "most existing LANets, feature abstraction (linear layers in Eq. 1) is typically performed after grouping the features into $f_{i}^{k} \\in \\mathbb{R}^{N \\times K \\times C}$ , which incurs substantial computational costs. To address this issue, we suggest conducting feature abstraction before grouping on $f_{i} \\in \\mathbb{R}^{N \\times C}$ (front-linear). Although this approach may limit local information interactions, it allows for a reduction in FLOPs by $K$ times theoretically, leading to significant efficiency gains. Practically, this operation reduces the $7 \\times$ FLOPs $(44.6\\mathrm{G} \\rightarrow 6.3\\mathrm{G})$ , with a performance degradation of only $1.2\\%$ $(68.6\\% \\rightarrow 67.4\\%)$ .", + "bbox": [ + 511, + 90, + 903, + 242 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Moreover, we suggest employing the vector feature $f_{i} - f_{i}^{k}$ instead of the grouped feature $f_{i}^{k}$ . On the one hand, this approach achieves cost-effective local interaction, which can enhance relation learning. On the other hand, it aligns with the relative position embedding $p_{i} - p_{i}^{k}$ , mitigating the potential semantic gap between position embedding and feature representation. This operation improves performance by $1.2\\%$ ( $67.4\\% \\rightarrow 68.6\\%$ ) without incurring additional computation costs.", + "bbox": [ + 511, + 242, + 903, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, when combining the vector feature with the relative position embedding, we replace concatenation $(\\oplus)$ with simple addition $(+)$ , avoiding duplicating channels, which further reduces computational demands. This operation reduces computation $(6.3\\mathrm{G}\\rightarrow 4.4\\mathrm{G})$ while only marginally decreasing performance $(68.6\\% \\to 68.4\\%)$ . Finally, we employ the simple but effective max pooling for aggregation. The vector feature representation (VFR) module can be formulated as follows:", + "bbox": [ + 511, + 378, + 906, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} f _ {i} ^ {\\prime} = \\mathcal {M} \\left(f _ {i}\\right) \\\\ F _ {i} ^ {k} = f _ {i} ^ {\\prime} - f _ {i} ^ {\\prime k} \\\\ F _ {\\text {o u t}} = \\max \\left(F _ {i} ^ {k} + P E\\right) \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 529, + 903, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modernization Structure: Inspired by powerful Transformers [12, 65], we adopt a modernization structure, as shown in Figure 3-(a). Similar to the Transformer block, we employ a dropout path after normalization to mitigate overfitting in deep networks. Notably, unlike the $4 \\times$ Inverted Bottleneck Feed Forward Network in Transformer, which increases the channel dimension, our implementation maintains the same dimensions in the two linear layers of the FFN to conserve computational resources. We can observe that the vanilla modern structure improves performance by $2.1\\%$ ( $68.4\\% \\rightarrow 70.5\\%$ ), but incurs significant additional computations ( $4.4\\mathrm{G} \\rightarrow 21.2\\mathrm{G}$ ). By removing the $4 \\times$ inverted bottleneck, we reduce the FLOPs by approximately half ( $21.2\\mathrm{G} \\rightarrow 9.2\\mathrm{G}$ ), with only a $0.4\\%$ decrease in performance ( $70.5\\% \\rightarrow 70.1\\%$ ).", + "bbox": [ + 511, + 597, + 905, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At this point, we have construct the vanilla DeepLA-24. Compare to the plain-24 model, the vanilla DeepLA-24 improves performance by $1.1\\%$ $(69.0\\% \\rightarrow 70.1\\%)$ while using only $10\\%$ FLOPs $(92.2\\mathrm{G}\\rightarrow 9.2\\mathrm{G})$ . This small but mighty design enables the construction of deeper networks.", + "bbox": [ + 511, + 825, + 903, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1333", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3d809a700d45b4a50b7f673946e8ef5eb0223cb1782d6536754491b4ebb68bb7.jpg", + "image_caption": [ + "Figure 5. Illustration of the proposed HDS strategy." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 486, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Hybrid Deep Supervision Strategy", + "text_level": 1, + "bbox": [ + 89, + 243, + 390, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we propose the HDS strategy, as illustrated in Figure 5. By incorporating supervision signals at each encoding stage, we facilitate smoother gradient propagation and simplify network optimization. The HDS strategy comprises two key aspects: (1) semantic probability supervision, and (2) spatial distribution supervision.", + "bbox": [ + 89, + 266, + 483, + 358 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Semantic Probability Supervision: Despite employing techniques such as residual connections, normalization, and dropout, optimizing very deep networks remains a challenge. The proposed semantic probability supervision encourages hidden layers to learn discriminative features, which facilitates faster convergence and regularization of the network. Specifically, the outputs of each stage are fed into a VFR module without position embedding, ensuring that the supervised signals closely reflect our training process. Then, they are processed by a plain linear layer to align with the ground truth labels. Finally, we use the widely-used weighted cross-entropy loss to calculate the loss at each stage. The loss for semantic probability supervision $(\\mathcal{L}_{sem})$ is defined as the average of all stages, which can be formulated as follows:", + "bbox": [ + 89, + 362, + 483, + 589 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s e m} (Y, P) = - \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\sum_ {c = 0} ^ {C} y _ {i} ^ {c} \\log p _ {i} ^ {c} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 603, + 482, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y_{i}^{c}$ denotes the label vector of the $i$ -stage, $p_{i}^{c}$ denotes the predicted vector of the $i$ -stage, $C$ is the number of label categories, and $N$ denotes the number of stages. This operation improves performance by $2.1\\%$ ( $70.1\\% \\rightarrow 72.2\\%$ ) without additional inference computational costs.", + "bbox": [ + 89, + 654, + 483, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spatial Distribution Supervision: The sparsity and discreteness of point clouds lead to intricate complex local geometric patterns, which further exacerbate the challenges of optimizing very deep networks. To address this issue, we assume that the feature distribution is potentially consistent with the spatial distribution of the point clouds. In the early epochs of training, feature learning should trend toward fitting these geometric structures. Therefore, we propose the spatial distribution supervision that serves as a manual prior for convergence, explicitly guiding feature learning towards geometric structures during the early epochs of training.", + "bbox": [ + 89, + 734, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we represent the spatial distribution by calculating the grouped points with a learnable linear layer. The weights are initialized as an identity matrix and without bias, while the input and output channels are set to 3. Subsequently, we use this spatial distribution to constrain the grouped features obtained during semantic probability supervision. Finally, we adopt the mean squared error (MSE) loss to minimize the discrepancy between the spatial supervision signals and the grouped features. The loss of spatial distribution supervision $(\\mathcal{L}_{spa})$ is defined as the average of all stages, which can be formulated as follows:", + "bbox": [ + 511, + 90, + 906, + 257 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s p a} (Y, P) = - \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\left(p _ {i} - y _ {i}\\right) ^ {2} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 268, + 906, + 309 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y_{i}$ denotes the spatial supervision signals of the $i$ -stage, $p_{i}$ denotes the predicted results from feature relative differences of the $i$ -stage, and $N$ denotes the number of encoder stages. This operation improves performance by $1.7\\%$ ( $70.1\\% \\rightarrow 71.8\\%$ ).", + "bbox": [ + 511, + 311, + 906, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hybrid Loss: The loss function of the network integrates $L_{sem}$ , $L_{spa}$ , and the segmentation loss of final prediction $(L_{pred})$ , which is calculated via cross-entropy loss. Furthermore, we implement different training weights with exponential decay for $L_{sem}$ and $L_{spa}$ , where the decay factor is defined as the reciprocal of the current epoch number. This strategy ensures that deep supervision provides significant guidance in the early training phases, while gradually diminishes its influence to avoid hindering the primary learning path as training progresses. The hybrid loss can be formulated as:", + "bbox": [ + 511, + 391, + 906, + 556 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {H}} = \\alpha^ {n} \\mathcal {L} _ {s e m} + \\beta^ {n} \\mathcal {L} _ {s p a} + (1 - \\alpha^ {n} - \\beta^ {n}) \\mathcal {L} _ {p r e d} \\quad (5)\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 571, + 906, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are the training weights for supervision, $n$ denotes reciprocal of the current epoch number. This hybrid loss improves performance by $3.1\\%$ ( $70.1\\% \\rightarrow 73.2\\%$ ).", + "bbox": [ + 511, + 595, + 905, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. DeepLA-Net Implementation", + "text_level": 1, + "bbox": [ + 511, + 648, + 774, + 665 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We construct a series of DeepLA-Net with different depths: DeepLA-24/60/120. Following successful previous works [12, 35, 92], the block ratio within each stage is set to [1:1:3:1], and the number of channels doubles in the subsequent stage. The configuration of DeepLA-Net is summarized as follows:", + "bbox": [ + 511, + 670, + 905, + 760 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC = [ 6 4, 1 2 8, 2 5 6, 5 1 2 ]\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 762, + 687, + 777 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- DeepLA-24: $B = \\left\\lbrack {4,4,{12},4}\\right\\rbrack$", + "- DeepLA-60: $B = \\left\\lbrack {{10},{10},{30},{10}}\\right\\rbrack$", + "- DeepLA-120: $B = \\left\\lbrack {{20},{20},{60},{20}}\\right\\rbrack$" + ], + "bbox": [ + 514, + 777, + 756, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $C$ refers to the channels of the output and $B$ denotes the number of ResLFE blocks in each stage. Note that, in this paper, the term \"depth\" specifically refers to the number of blocks rather than linear layers. The network architecture details can be found in Appendix.", + "bbox": [ + 511, + 825, + 905, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1334", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/93202b7c74bc29cbc7a7429b73213e1376c766121acf1debf857d05ff24373c3.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons of semantic segmentation with the SOTA methods on S3DIS in terms of mIoU." + ], + "table_footnote": [], + "table_body": "
YearMethod6-flod (%)Area5 (%)
NIPS 2017PointNet++ [47]83.053.5
NIPS 2018PointCNN [30]65.457.3
CVPR 2019KPConv [61]70.667.1
CVPR 2020RandLA-Net [20]70.062.5
CVPR 2021Point Trans. [92]73.570.4
NIPS 2022PointNeXt [48]74.970.8
CVPR 2023AF-GCN [89]77.772.3
CVPR 2023PointVector [10]78.472.3
CVPR 2023PointMeta [33]77.072.0
AAAI 2024PDNet [81]78.372.3
CVPR 2024KPConvX [62]-73.5
CVPR 2024OneFormer3D [23]75.072.4
CVPR 2024Point Trans. v3 [70]77.773.4
ACM MM 2024OPFR [22]76.972.6
ACM MM 2024LDCNet [38]75.471.8
ACM MM 2024MBSE [68]77.872.4
Ours 2024DeepLA-2477.973.2
Ours 2024DeepLA-6079.074.8
Ours 2024DeepLA-12079.875.7
", + "bbox": [ + 91, + 116, + 480, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 409, + 222, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 89, + 435, + 266, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To comprehensively evaluate the effectiveness of the proposed DeepLA-Net, we conduct experiments on S3DIS [1] and ScanNet v2 [9] for semantic segmentation, ScanObjectNN [64] for object classification, and ShapeNetPart [80] for object part segmentation. We use the following quantitative metrics for evaluation: mean Intersection over Union (mIoU), Overall Accuracy (OA), and mean Accuracy (mAcc). In result tables, Bold indicates the best result, underline indicates the best result excluding ours.", + "bbox": [ + 89, + 458, + 482, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the position embedding phase, we employ the KNN for grouping, with the $K$ specified as 24. For hybrid deep supervision, $\\alpha$ and $\\beta$ are set to 0.3 and 0.005, respectively. All experiments are performed on a Nvidia RTX 3090 GPU with 24GB memory. To ensure a fair comparison, the reported performance for both ours and the compared methods excludes the use of voting, pre-trained model, and test-time augmentation strategies. The implementation details and dataset description can be found in Appendix.", + "bbox": [ + 89, + 594, + 482, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Experiment Results", + "text_level": 1, + "bbox": [ + 89, + 742, + 277, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Semantic Segmentation. We show the results of our DeepLA-Net, including DeepLA-24/60/120, compared with previous state-of-the-art methods on S3DIS and ScanNet v2. In Table 1, for S3DIS, our DeepLA-60 has already surpassed previous methods. Particularly, our DeepLA-120 achieves a more significant breakthrough with an mIoU of $79.8\\%$ in 6-fold $(+1.4\\%)$ and $75.7\\%$ $(+2.2\\%)$ in Area5, surpassing the $75\\%$ threshold for the first time. In Table 2, for ScanNet v2, our DeepLA-24/60 achieve competitive perfor", + "bbox": [ + 89, + 763, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5b79951efd9c147f456edd2ef707456643bab6cf30e090c4729d2240794363bc.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons of semantic segmentation with the SOTA methods on ScanNet v2 in terms of mIoU." + ], + "table_footnote": [], + "table_body": "
YearMethodval (%)test (%)
NIPS 2017PointNet++ [47]53.555.7
NIPS 2018PointCNN [30]-45.8
CVPR 2019KPConv [61]69.268.6
CVPR 2022Stra. Trans. [24]74.373.7
NIPS 2022PointNeXt [48]71.571.2
CVPR 2023LRPNet [29]75.074.2
ICCV 2023Retro-FPN [71]74.074.4
NIPS 2023ConDaFormer [13]75.175.5
AAAI 2024HPENet [94]74.0-
ICLR 2024MVNet [76]75.2-
CVPR 2024KPConvX [62]76.3-
CVPR 2024OneFormer3D [23]76.6-
CVPR 2024OA-CNN [45]76.175.6
CVPR 2024MirageRoom [57]74.9-
ACM MM 2024LDCNet [38]73.3-
Ours 2024DeepLA-2474.1-
Ours 2024DeepLA-6075.9-
Ours 2024DeepLA-12077.677.2
", + "bbox": [ + 514, + 116, + 903, + 388 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/05e7d593bd1dfb8fe244f142cca0ea9d0a5127150ac95f64e45df608b8114e54.jpg", + "table_caption": [ + "Table 3. Quantitative comparisons of classification with the SOTA methods on ScanObjectNN (PB T50 RS)." + ], + "table_footnote": [], + "table_body": "
YearMethodOA (%)mAcc (%)
CVPR 2017PointNet [46]68.263.4
NIPS 2018PointCNN [30]78.575.1
TOG 2019DGCNN [67]78.173.6
TMM 2021GBNet [50]80.577.8
TIP 2021PRANet [6]82.179.1
ICLR 2022PointMLP [39]85.784.4
NIPS 2022PointNeXt [48]88.186.4
PAMI 2023GSLCN [32]85.884.1
ICLR 2023ACT [11]88.2-
CVPR 2023NLGAT [49]88.4-
CVPR 2023PointVector [10]88.286.7
CVPR 2023PointMeta [33]88.186.9
AAAI 2024PDNet [81]88.586.8
AAAI 2024Interpretable3D [15]88.086.5
ICLR 2024MaskFeat3D [77]88.4-
ACM MM 2024OPFR [22]88.186.3
Ours 2024DeepLA-2490.689.5
", + "bbox": [ + 517, + 436, + 903, + 685 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "mance, while DeepLA-120 significantly outperforms previous methods, achieving $77.6\\%$ $(+1.0\\%)$ on the validation set and $77.2\\%$ $(+1.6\\%)$ on the test sets. Note that, due to the submission policy of the ScanNet v2 online test set, we only report the best model on the validation set, i.e., DeepLA-120. Additionally, results on the ScanNet test set have been reported less in recent years because fully supervised methods have not achieved substantial breakthroughs in this dataset. The result of the efficient DeepLA-24 demonstrates the rationality and effectiveness of our design. Furthermore, reasonably deepening the network can significantly improve performance. More detailed per-class results and visualizations can be found in Appendix.", + "bbox": [ + 511, + 703, + 906, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1335", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/154d54665c2d8dbcd0c709717df2c76ddec7f96160051124b14c6effe3175904.jpg", + "table_caption": [ + "Table 4. Quantitative comparisons of part segmentation with the SOTA methods on ShapeNetPart." + ], + "table_footnote": [], + "table_body": "
YearMethodCls. mIoU (%)Ins. mIoU (%)
CVPR 2017PointNet [46]80.483.7
NIPS 2018PointCNN [30]84.686.1
TOG 2019DGCNN [67]82.385.1
CVPR 2020PointASNL [78]-86.1
CVPR 2021Point Trans. [92]83.786.6
ICLR 2022PointMLP [39]84.686.1
NIPS 2022PointNeXt [48]85.287.0
ICLR 2023ACT [11]84.786.1
CVPR 2023PointVector [10]85.186.9
CVPR 2023PointMeta [33]85.187.1
CVPR 2023AF-GCN [89]85.387.0
NIPS 2023ConDaFormer [13]84.686.8
AAAI 2024HPENet [94]85.587.1
AAAI 2024PDNet [81]85.487.2
AAAI 2024Interpretable3D [15]85.687.2
ICLR 2024MVNet [76]85.286.8
ICLR 2024MaskFeat3D [77]85.587.0
Ours 2024DeepLA-2486.588.0
", + "bbox": [ + 94, + 118, + 480, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Object Classification. As shown in Table 3, DeepLA-24 outperforms all baselines with OA of $90.6\\%$ and mAcc of $89.5\\%$ $(+2.1\\%$ OA, $+2.6\\%$ mAcc). DeepLA-24 is the first method to surpass $90\\%$ on OA, with the performance of others stagnating around $88\\%$ for several years. This result indicates that merely developing more complex local representation methods is not sufficient for further advancement in shape recognition. In contrast, deeper networks can make significant contributions to capturing local patterns.", + "bbox": [ + 89, + 393, + 483, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Part Segmentation. The results are reported in Table 4, where we evaluate the performance with the mean class IoU (Cls. mIoU) and mean instance IoU (Ins. mIoU). DeepLA-24 outperforms all baselines with the Cls. mIoU of $86.5\\%$ $(+1.0\\%)$ and the Ins. mIoU of $88.0\\%$ $(+0.8\\%)$ without voting. It is noteworthy that we do not experiment with the deeper variants of DeepLA-Net on object classification and part segmentation datasets due to the limited dataset scale.", + "bbox": [ + 89, + 534, + 483, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 89, + 662, + 254, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies on the proposed DeepLA-Net. All the ablation models are evaluated on S3DIS Area5 [1]. If not specified, the DeepLA-24 is employed as the default model.", + "bbox": [ + 89, + 685, + 482, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hyperparameter settings. We analyze the impact of hyperparameter settings including the bottleneck in ResLFE block, the training weights in HDS strategy, the initial feature channel, and the grouping range $K$ . Table 5 explores different bottleneck settings in ResLFE block. The results illustrate that inverted bottlenecks larger than $1 \\times$ marginally improve performance but significantly increase computation costs. Meanwhile, bottlenecks less than $1 \\times$ slightly reduce computation while causing a more pronounced degradation in performance. Therefore, to balance", + "bbox": [ + 89, + 750, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2c76b93953ea8e260c1ee5352a34e04619966dfcd841e44d1ef44844f9d85cab.jpg", + "table_caption": [ + "Table 5. Ablation results of the bottleneck in ResLFE block in DeepLA-24 on S3DIS Area5." + ], + "table_footnote": [], + "table_body": "
ModelmIoU (%)\\( \\bigtriangleup \\)(%)FLOPs (G)\\( \\bigtriangleup \\)(G)
1× bottleneck73.2-9.3-
0.5× bottleneck72.5-0.77.4-1.9
2× bottleneck73.4+0.213.4+4.1
4× bottleneck73.5+0.321.3+13.0
", + "bbox": [ + 517, + 121, + 903, + 202 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ea37a3ea01f21c1edfe150be23cd40ac27de62cbe196733446141fd58423463f.jpg", + "table_caption": [ + "Table 6. Ablation results of training weights in HDS strategy in DeepLA-24 on S3DIS Area5." + ], + "table_footnote": [], + "table_body": "
α\\β03e-35e-37e-31e-2
070.171.071.871.370.6
0.271.872.372.572.972.0
0.372.272.573.272.872.4
0.472.072.672.472.472.1
0.571.572.072.172.271.7
", + "bbox": [ + 596, + 244, + 774, + 381 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a7b3b6e62ff3ee30916ee598b0f4cacc45a2062e7bb3cff00cdfe00ad884a859.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 262, + 818, + 378 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e6d63b0fe4f276959d7f86fddb5dc9001dbb7570af1fdd2ae2a655a562d742f.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 517, + 396, + 709, + 534 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b8e369ac5d39e8cb04d0731daf8afc7544f995867b81fb2488cfedb0d7b52a49.jpg", + "image_caption": [ + "(b)", + "Figure 6. Ablation results of hyperparameters in DeepLA-24 on S3DIS Area5. (a) initial feature dimension. (b) grouping range K." + ], + "image_footnote": [], + "bbox": [ + 715, + 396, + 903, + 535 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "efficiency and performance, we employ the $1 \\times$ bottleneck. Table 6 shows that the setting of training weights in HDS strategy is generally insensitive, as long as they are neither too large to hinder fitting nor too small to be ineffective. Notably, the training weight for spatial distribution is much smaller than that for semantic probability. This is mainly because spatial distribution supervision encourages the network to focus more on local details rather than abstract semantics, which are more crucial for feature classification. Figure 6 illustrates the impact of different initial feature channel and grouping range $K$ . The results demonstrate that small channel and grouping range lead to limited performance, due to inadequacy in capturing local patterns. Meanwhile, excessively large channel and grouping range tend to overfit the training examples, resulting in poor generalization and a decline in performance.", + "bbox": [ + 511, + 593, + 906, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation of Deep Supervision for Training Process. We demonstrate the performance and segmentation loss values $(L_{pred}$ in Eq. 5) of the network with different deep supervision strategies across training epochs, as shown in Fig-", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1336", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4b91d3264b6e9fcc8fadc4e735c45a81e0cd712e2f784e5191edad67fbd3703a.jpg", + "image_caption": [ + "Figure 7. Training performance and loss value across training epochs in DeepLA-24 with different deep supervision strategies. (a) mIoU score, and (b) loss value." + ], + "image_footnote": [], + "bbox": [ + 93, + 82, + 285, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e30fcbf93fb366c617c14053ee2315291138777a253d7ca7f521d48c8d28ac58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 82, + 482, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ure 7. It is evident that the network without deep supervision exhibits a slow decline in loss, with almost no further decrease after 60 epochs. In contrast, networks using deep supervision consistently achieve higher performance and a rapid convergence in loss. Notably, the network employing the HDS strategy achieves the most reasonable and effective convergence. This result demonstrates that our HDS strategy significantly optimizes network training, facilitating a robust and substantial decline in loss.", + "bbox": [ + 88, + 299, + 483, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation of Network Depth for Feature Learning. We visualize the feature similarity matrix of DeepLA-Net with different depths in Figure 8. The matrix is obtained by calculating the cosine similarities of the point features in the final layer, which are then sorted according to the predicted categories. The results indicate that the feature learning of DeepLA-6 is not robust, resulting in numerous recognition errors during segmentation. In contrast, DeepLA-24 demonstrates stronger feature learning capabilities, though the feature differences between classes are not sufficiently distinct, potentially causing blurred boundaries. DeepLA120 demonstrates the highest confidence in class distinction, showcasing the most powerful feature learning abilities among the three networks. This result demonstrates that deeper networks possess more powerful learning capabilities, enhancing segmentation performance.", + "bbox": [ + 89, + 441, + 483, + 683 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis on Complexity and Latency. We report the performance, model complexity, and latency using the same settings of DeepLA-Net family and previous SOTA methods [10, 48, 62, 81] in Table 7. From the results, the baseline exhibits the fastest inference speed but the lowest performance. Simply deepening the baseline (Plain-24) enhances performance but significantly increases FLOPs $(9\\times$ higher) and decreases inference speed $(4.7\\times$ slower). In contrast, DeepLA-24, equipped with the ResLFE block achieves performance improvements while substantially reducing FLOPs $(10\\times$ fewer) and increasing inference speed $(3.75\\times$ faster). The reduction in FLOPs enables the training of deeper networks. In particular, our DeepLA-120 achieves state-of-the-art performance with an inference", + "bbox": [ + 89, + 689, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/48e817e661350c6a29b71140d9173e197e82b43d3a7580fd1d1266148174144e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 524, + 83, + 689, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1591b2f90acec316254a7c4044f8b27ae0096f692f0b540a82eccb6b9c59ab07.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 82, + 864, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3251716dd3ec5331f4face9036bd32cf5974a1a1f1798d9c9ce34aae3f800142.jpg", + "image_caption": [ + "Figure 8. Visual comparison of interpreting feature similarity matrix with different network depth of the DeepLA-6 (6-block network follows [1:1:3:1] ratio), DeepLA-24, and DeepLA-120." + ], + "image_footnote": [], + "bbox": [ + 524, + 224, + 689, + 364 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e9305bf4d12dc0c26fb7e2b381684b9ea60f2bd6984ee441ab19a54be88b778.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 224, + 893, + 364 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/05093655c495cf54d30d875801ed22f49528336d2b334f3fbe443cd422c3f0f4.jpg", + "table_caption": [ + "Table 7. Quantitative comparisons of performance, model complexity, and latency on S3DIS Area5." + ], + "table_footnote": [], + "table_body": "
MethodmIoU (%)Params. (M)FLOPs (G)Thr. Put (ins./sec.)
PointNeXt-XL [48]70.846.184.843
PointVector-XL [10]72.324.158.540
KPConvX-L [62]73.513.5-47
PDNet-XXL [81]72.335.612.0-
Baseline63.43.111.3207
Plain-2469.09.792.244
DeepLA-2473.26.49.2165
DeepLA-6074.815.821.578
DeepLA-12075.730.342.742
", + "bbox": [ + 517, + 446, + 903, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "speed comparable to Plain-24 and the previous SOTA works [10, 48, 62]. More ablation analysis and discussion details can be found in Appendix.", + "bbox": [ + 511, + 601, + 905, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 511, + 662, + 638, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this study, we demonstrate the efficiency and effectiveness of very deep local aggregation networks for point cloud analysis, addressing two primary challenges: computational cost and training optimization. In contrast to most current approaches that rely on expensive and redundant local representation, we propose a lightweight ResLFE block to significantly reduce the computational cost ( $10 \\times$ fewer FLOPs), and make it possible to construct very deep LANets. Furthermore, the HDS strategy is also introduced to ensure smooth gradient backpropagation and mitigate optimization challenges in deep networks. The DeepLA-Net achieves SOTA performance with high efficiency across segmentation and classification tasks on four benchmarks: S3DIS, ScanNet v2, ScanObjectNN, and ShapeNetPart.", + "bbox": [ + 509, + 688, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1337", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Iro Armeni, Ozan Sener, Amir R. Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3D semantic parsing of large-scale indoor spaces. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021. 2" + ], + "bbox": [ + 91, + 90, + 482, + 892 + ], + "page_idx": 11 + }, + { + "type": "ref_text", + "text": "[94] Yanmei Zou, Hongshan Yu, Zhengeng Yang, Zechuan Li, and Naveed Akhtar. Improved mlp point cloud processing with high-dimensional positional encoding. In AAAI Conference on Artificial Intelligence, 2024. 6, 7", + "bbox": [ + 516, + 90, + 903, + 148 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "1341", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/a85e9f83-617a-4a59-8124-97eefae14b9e_model.json b/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/a85e9f83-617a-4a59-8124-97eefae14b9e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1ebbadc1c7bd1e8689dd0440efaf6ca80e0e73cf --- /dev/null +++ b/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/a85e9f83-617a-4a59-8124-97eefae14b9e_model.json @@ -0,0 +1,2732 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.101, + 0.131, + 0.898, + 0.155 + ], + "angle": 0, + "content": "DeepLA-Net: Very Deep Local Aggregation Networks for Point Cloud Analysis" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.18, + 0.865, + 0.218 + ], + "angle": 0, + "content": "Ziyin Zeng\\(^{1}\\), Mingyue Dong\\(^{1}\\), Jian Zhou\\(^{1*}\\), Huan Qiu\\(^{1}\\), Zhen Dong\\(^{1}\\), Man Luo\\(^{2}\\) and Bijun Li\\(^{1}\\) \n\\(^{1}\\)Wuhan University, \\(^{2}\\)Dongfeng USharing Technology Co." + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.22, + 0.896, + 0.235 + ], + "angle": 0, + "content": "{zengziyin, dongmy, jianzhou, huanqiu, dongzhenwhu, lee}@whu.edu.cn, tc-luoman@dfmc.com.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.269, + 0.329, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.302, + 0.486, + 0.681 + ], + "angle": 0, + "content": "Due to the irregular and disordered data structure in 3D point clouds, prior works have focused on designing more sophisticated local representation methods to capture these complex local patterns. However, the recognition performance has saturated over the past few years, indicating that increasingly complex and redundant designs no longer make improvements to local learning. This phenomenon prompts us to diverge from the trend in 3D vision and instead pursue an alternative and successful solution: deeper neural networks. In this paper, we propose DeepLA-Net, a series of very deep networks for point cloud analysis. The key insight of our approach is to exploit a small but mighty local learning block, which uses \\(10 \\times\\) fewer FLOPs, enabling the construction of very deep networks. Furthermore, we design a training supervision strategy to ensure smooth gradient backpropagation and optimization in very deep networks. We construct the DeepLA-Net family with a depth of up to 120 blocks — at least \\(5 \\times\\) deeper than recent methods — trained on a single RTX 3090. An ensemble of the DeepLA-Net achieves state-of-the-art performance on classification and segmentation tasks of S3DIS Area5 (\\(+2.2\\%\\) mIoU), ScanNet test set (\\(+1.6\\%\\) mIoU), ScanObjectNN (\\(+2.1\\%\\) OA), and ShapeNetPart (\\(+0.9\\%\\)CLS.mIoU). The code are released at https://github.com/zeng-ziyin/DeepLA-Net." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.698, + 0.222, + 0.714 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.723, + 0.483, + 0.829 + ], + "angle": 0, + "content": "Thanks to the significant development of 3D sensors, 3D point cloud analysis has garnered increasing attention in recent years and is widely applied in autonomous driving, smart cities, and robotics [18, 84]. However, 3D point clouds consist of sparse, discrete, and non-uniform point sets embedded in continuous space [46]. This complex structure poses challenges to local pattern learning." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.83, + 0.484, + 0.876 + ], + "angle": 0, + "content": "In order to solve this problem, extensive explorations have been conducted on the local pattern of point clouds to enable fine-grained analysis. Inspired by CNNs, they intro-" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.262, + 0.888, + 0.517 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.518, + 0.908, + 0.603 + ], + "angle": 0, + "content": "Figure 1. Illustration of segmentation performance, model efficiency and network depth on S3DIS Area5. DeepLA-24 has already achieved SOTA-equivalent performance with minimal parameters. The deeper architecture DeepLA-120 achieves a milestone (75.7%) by exceeding 75% threshold for the first time, and outperforms Point Transformer v3 [70] with fewer parameters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.909, + 0.903 + ], + "angle": 0, + "content": "duce two robust inductive biases: locality and weight sharing, which promote the development of neural networks for analyzing 3D point clouds [47]. Specifically, these studies [10, 20, 33, 48, 56, 83, 85, 86] employ MLPs with shared weights to capture local features from neighbors. We collectively refer to them as local aggregation networks (LANets) in this paper. It is noteworthy that most LANets primarily focus on developing intricate local representation methods to explicitly explore the local patterns of point clouds, achieving success due to the robust inductive biases. However, the performance of increasingly sophisticated LANets on popular benchmarks [1, 9, 64, 80] has gradually saturated, as evidenced by minimal gains compare to PointNeXt [48] over the past few years, such as ScanObjectNN [64] (OA +0.4%, mAcc +0.5%, in Tab. 3) and ShapeNetPart [80] (cls.mIoU +0.4%, Ins.mIoU +0.2%, in Tab. 4). Particularly, the performance of most existing methods on S3DIS [1] has saturated around 73% [62, 70], as shown in Figure 1. The primary reason is that they already adequately" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.888, + 0.292, + 0.901 + ], + "angle": 0, + "content": "* corresponding author: Jian Zhou" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1330" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "describe the local geometric properties of point clouds, and more complex designs no longer contribute to capturing additional local patterns [39, 48]. This phenomenon prompts us to rethink the design of LANets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.155, + 0.483, + 0.397 + ], + "angle": 0, + "content": "Interestingly, the development of 3D point cloud analysis is closely related to the evolution of 2D image processing networks [39, 47]. We observe that the design of 2D CNNs shifted towards deeper with the residual connections [19], making deep networks the mainstream backbone for feature extraction with successful performance [2, 35, 52]. Given that LANets for point clouds share similar inductive biases with CNNs, we cannot help but wonder: can we explore an alternative path by leveraging the success of deep CNNs for LANets? Unfortunately, to the best of our knowledge, there has been limited systematic exploration of deepening LANets. Therefore, in this paper, instead of following the tendency to explore sophisticated details, we are in pursuit of very deep LANets for point cloud analysis. For this purpose, we encounter two key challenges: (1) high computational cost, and (2) difficult training optimization." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.399, + 0.483, + 0.625 + ], + "angle": 0, + "content": "Obviously, the prevailing philosophy of sophisticated and redundant local learning has significantly increased computational complexity. To circumvent the prohibitive computations, we propose a residual local feature extraction (ResLFE) block that ensures minimal computational cost. Specifically, we first employ stage-level positional embedding instead of redundant and high latency layer-level. We then introduce an efficient vector feature representation and a robust modernization structure that significantly reduces FLOPs while preserving local information interactions. As shown in Figure 2, the proposed ResLFE block shows significant computational efficiency \\((10\\times\\) fewer FLOPs) and commendable performance improvements \\((+1.1\\%\\) mIoU). In particular, this remarkable computational efficiency enables the construction of very deep networks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.628, + 0.483, + 0.868 + ], + "angle": 0, + "content": "Furthermore, very deep networks are difficult to optimize [19, 72], and the complex geometric patterns of point clouds further exacerbate the difficulty of optimization [16, 44, 58]. To address these issues, we introduce a hybrid deep supervision (HDS) strategy to facilitate learning and optimization. We employ two forms of supervision to the outputs of the encoder at each stage. Specifically, we align each output with the ground truth using cross-entropy loss, which promotes smooth gradient propagation. Meanwhile, we also align the outputs with the spatial distribution of the point cloud using mean squared error loss, which benefits in fitting the complex geometric patterns to simplify network optimization. We demonstrate in experiments that the proposed HDS strategy optimizes network training by accelerating model convergence and achieves significant performance improvements \\((+3.1\\% \\mathrm{mIoU})\\)" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Overall, we propose very Deep Local Aggregation Networks (DeepLA-Net), constructed from the ResLFE" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.289 + ], + "angle": 0, + "content": "block for lightweight design and the HDS strategy for optimization. In particular, we have successfully trained DeepLA-120—a representative deep network comprising up to 120 ResLFE blocks—on a single RTX 3090 with 24GB memory. The DeepLA-Net family outperforms the SOTA methods across various tasks, including S3DIS [1] and ScanNetV2 [9] for semantic segmentation, ScanObjectNN [64] for object classification, and ShapeNetPart [80] for part segmentation. Figure 1 highlights the superior performance and efficiency of our DeepLA-Net family on S3DIS Area5. Moreover, a step-by-step procedure of constructing the DeepLA-Net and the corresponding results are shown in Figure 2. Our key contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.298, + 0.905, + 0.344 + ], + "angle": 0, + "content": "- We propose a residual local feature extraction block from the perspective of efficiency and performance, enabling the construction of deeper LANets." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.349, + 0.905, + 0.394 + ], + "angle": 0, + "content": "- We propose a hybrid deep supervision strategy from the perspective of optimization and learning to ensure smooth gradient backpropagation in deeper LANets." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.399, + 0.905, + 0.445 + ], + "angle": 0, + "content": "- We propose DeepLA-Net, a series of very deep local aggregation networks, surpassing SOTA in classification, part segmentation, and semantic segmentation." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.298, + 0.905, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.459, + 0.655, + 0.473 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.484, + 0.791, + 0.5 + ], + "angle": 0, + "content": "2.1. Deep Learning on Point Clouds" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.506, + 0.905, + 0.793 + ], + "angle": 0, + "content": "Given the disordered and unstructured nature of 3D point clouds, directly applying traditional CNNs to them remains a challenge. Therefore, some methods firstly transform point clouds into intermediate representations such as 2D images [3, 26, 42, 73, 82] or 3D voxels [5, 7, 17, 27, 41, 93] through projection or voxelization, and subsequently employ 2D/3D CNNs to process these structured data. Although promising results have been shown in certain scenarios, the intermediate transformation steps may introduce information loss and computation costs [14, 51, 86]. In contrast, point-based methods [14, 20, 31, 46, 47, 51, 69, 83, 85, 86, 91] are specifically designed to perform feature learning directly on point clouds without using intermediate representations. Moreover, some noteworthy research has leveraged techniques like Recurrent Neural Networks (RNNs) [21, 34, 79], Graph Neural Networks (GNNs) [25, 28, 66, 75, 87], point-voxel hybrid representation [36, 37, 53, 74, 88], and sparse voxel [4, 8, 55, 59, 60], achieving significant performance in various tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.9, + 0.819 + ], + "angle": 0, + "content": "2.2. Local Aggregation Networks for Point Clouds" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.901 + ], + "angle": 0, + "content": "The pioneering PointNet [46] uses point-wise MLPs to learn per-point features, however, it has limitations in capturing local details. To overcome this, PointNet++ [47] improves PointNet by employing shared-weight MLPs in local neighbors, aligning with the inductive biases in CNNs:" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.513, + 0.957 + ], + "angle": 0, + "content": "1331" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.396 + ], + "angle": 0, + "content": "localization and weight sharing. Along this direction, numerous subsequent studies [30, 40, 63, 67, 69, 90] have employed the above two inductive biases by local feature aggregation operations. We summarize them as local aggregation networks (LANets). Recent LANets [10, 14, 20, 33, 43, 48, 51, 54, 83, 85, 86] have primarily focused on exploring more robust local representations. For example, Point Transformer [92] designs a local transformer layer based on vector self-attention in local neighbors. PointVector [10] improves local extractor by transforming relative features and positions of input into representative vectors. ConDaFormer [13] enhances local geometric modeling by depth-wise convolutions, capturing both long-range contextual information and local priors. However, with the development of LANets, merely development of more complex LANets is insufficient for further capturing the local patterns. In this paper, we demonstrate that without relying on intricate and complex local representations, designing very deep hierarchical architectures for LANets can also achieve significant breakthroughs in performance." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.406, + 0.219, + 0.423 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.431, + 0.484, + 0.538 + ], + "angle": 0, + "content": "In this section, we introduce the preliminary implementation of DeepLA-Net. Most existing LANets have focused on robust local representation to effectively capture the complex local patterns of sparse and discrete point clouds. However, this focus makes them difficult to deepen due to the high computational cost. Therefore, we consider building deep networks based on the simplest PointNet++ [47]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.54, + 0.484, + 0.691 + ], + "angle": 0, + "content": "PointNet++ [47], the pioneering LANet for point cloud analysis, can be summarized in two phases: position embedding and feature representation. In the position embedding phase, PointNet++ employs ball query to group points, and then uses relative position differences as position embedding. Subsequently, in the feature representation phase, PointNet++ concatenates position embedding and grouped features to represent local features, and then aggregates them to centroid points by using max pooling. This can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.712, + 0.483, + 0.754 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} p _ {i} ^ {k} = \\operatorname {G r o u p} \\left(p _ {i}\\right) \\\\ P E = \\mathcal {M} \\left(p _ {i} - p _ {i} ^ {k}\\right) \\end{array} \\quad \\left\\{ \\begin{array}{l} F _ {N} = \\mathcal {M} \\left[ f _ {i} ^ {k} \\oplus P E \\right] \\\\ F _ {\\text {o u t}} = \\max \\left(F _ {N}\\right) \\end{array} \\right. \\right. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.761, + 0.483, + 0.824 + ], + "angle": 0, + "content": "where \\( p_i \\) denotes the centroid points, \\( p_i^k \\) denotes the grouped points, \\( \\mathcal{M} \\) denotes the multi-layer perceptron, \\( \\oplus \\) denotes the concatenation, max denotes the max-pooling, and \\( f_i^k \\) denotes the grouped features." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Implementation. Due to its simplicity, we employ PointNet++ [47] as the baseline and demonstrate the step-by-step \"modernization\" into DeepLA-Net. Firstly, we follow the PointNeXt [48] configuration, incorporating data augmentation and optimization techniques such as random height" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.085, + 0.897, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.414, + 0.907, + 0.47 + ], + "angle": 0, + "content": "Figure 2. Illustration of the designs and results of our improvements on S3DIS [1] Area5 step-by-step. The foreground bars denote model accuracy, the stars denote model FLOPs, and hatched bars mean the modification is not adopted solely." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.481, + 0.907, + 0.679 + ], + "angle": 0, + "content": "and color dropout. The baseline model achieves \\(63.4\\%\\) mIoU and 11.3G FLOPs1. Subsequently, we directly extend the baseline to 24-block model, following [35] with a block ratio of [1:1:3:1]. This plain-24 model achieves \\(69.0\\%\\) mIoU and 92.2G FLOPs. Despite achieving a respectable mIoU score, the huge FLOPs prevent us from further deepening the network. In addition, deep network poses optimization challenges. Therefore, to construct LANets as deep as possible, we propose the ResLFE block which significantly reduces the computation cost while preserving reliable accuracy. Subsequently, we propose the HDS strategy to ensure smooth gradient backpropagation in deep networks and mitigate training optimization challenges." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.69, + 0.651, + 0.708 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.715, + 0.906, + 0.807 + ], + "angle": 0, + "content": "In this section, we introduce the key components of our DeepLA-Net: residual local feature extraction (ResLFE) block and hybrid deep supervision (HDS) strategy. To intuitively and clearly demonstrate the role of each design, we illustrate each step of improvement in Figure 2, with all models evaluated on S3DIS Area 5 [1]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.815, + 0.864, + 0.83 + ], + "angle": 0, + "content": "4.1. Residual Local Feature Extraction Block" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.837, + 0.906, + 0.868 + ], + "angle": 0, + "content": "To enable the construction of deeper networks, we propose the ResLFE block, as shown in Figure 3, which significantly" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.906, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)FLOPs calculation follows the settings of PointNeXt [48] which evaluated on S3DIS with \\(16 \\times 15\\), 000 points." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1332" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.086, + 0.462, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.27, + 0.483, + 0.311 + ], + "angle": 0, + "content": "Figure 3. Illustration of the proposed ResLFE block. Right: stage-level position embedding. Middle: Vector Feature Representation (VFR.) module. Left: modernization structure." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.321, + 0.475, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.426, + 0.483, + 0.455 + ], + "angle": 0, + "content": "Figure 4. Illustration of the computational latency of position embedding and feature representation phases in different LANets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.469, + 0.484, + 0.529 + ], + "angle": 0, + "content": "reduces computational cost. The ResLFE block comprises three key aspects: (1) stage-level position embedding, (2) efficient vector feature representation module, and (3) powerful modernization structure." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.534, + 0.484, + 0.852 + ], + "angle": 0, + "content": "Stage-Level Position Embedding: Existing LANets typically implement position embedding at each learning layer, resulting in high computational costs. As shown in Figure 4, the computational latency of the positional embedding phase constitutes approximately half of the total for each layer, which is unacceptable in deeper networks. As indicated by Eq. 1, we observe that the computation of position embedding relies solely on point coordinates. Considering that the resolution of points remains constant within each stage, layers in the same stage can share an identical position embedding. Therefore, we suggest pre-calculate the position embedding at the beginning of each stage, saving it to cache and reusing it per-layer in that stage to avoid subsequent real-time computations. This approach ensures that the computational costs of position embedding depend solely on the number of stages, rather than the depth of the network, thereby facilitating the efficient application of very deep networks. Our implementation of position embedding is the same as PointNet++. This operation approximately halves the FLOPs (92.2G → 44.6G), with only a minimal decrease in performance (69.0% → 68.6%)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Vector Feature Representation Module: First, we consider further improvements in computational efficiency during the feature representation phase. We observe that, in" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.243 + ], + "angle": 0, + "content": "most existing LANets, feature abstraction (linear layers in Eq. 1) is typically performed after grouping the features into \\( f_{i}^{k} \\in \\mathbb{R}^{N \\times K \\times C} \\), which incurs substantial computational costs. To address this issue, we suggest conducting feature abstraction before grouping on \\( f_{i} \\in \\mathbb{R}^{N \\times C} \\) (front-linear). Although this approach may limit local information interactions, it allows for a reduction in FLOPs by \\( K \\) times theoretically, leading to significant efficiency gains. Practically, this operation reduces the \\( 7 \\times \\) FLOPs \\( (44.6\\mathrm{G} \\rightarrow 6.3\\mathrm{G}) \\), with a performance degradation of only \\( 1.2\\% \\) \\( (68.6\\% \\rightarrow 67.4\\%) \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.243, + 0.905, + 0.379 + ], + "angle": 0, + "content": "Moreover, we suggest employing the vector feature \\( f_{i} - f_{i}^{k} \\) instead of the grouped feature \\( f_{i}^{k} \\). On the one hand, this approach achieves cost-effective local interaction, which can enhance relation learning. On the other hand, it aligns with the relative position embedding \\( p_{i} - p_{i}^{k} \\), mitigating the potential semantic gap between position embedding and feature representation. This operation improves performance by \\( 1.2\\% \\) (\\( 67.4\\% \\rightarrow 68.6\\% \\)) without incurring additional computation costs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.38, + 0.907, + 0.515 + ], + "angle": 0, + "content": "Furthermore, when combining the vector feature with the relative position embedding, we replace concatenation \\((\\oplus)\\) with simple addition \\((+)\\), avoiding duplicating channels, which further reduces computational demands. This operation reduces computation \\((6.3\\mathrm{G}\\rightarrow 4.4\\mathrm{G})\\) while only marginally decreasing performance \\((68.6\\% \\to 68.4\\%)\\). Finally, we employ the simple but effective max pooling for aggregation. The vector feature representation (VFR) module can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.53, + 0.905, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} f _ {i} ^ {\\prime} = \\mathcal {M} \\left(f _ {i}\\right) \\\\ F _ {i} ^ {k} = f _ {i} ^ {\\prime} - f _ {i} ^ {\\prime k} \\\\ F _ {\\text {o u t}} = \\max \\left(F _ {i} ^ {k} + P E\\right) \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.598, + 0.906, + 0.824 + ], + "angle": 0, + "content": "Modernization Structure: Inspired by powerful Transformers [12, 65], we adopt a modernization structure, as shown in Figure 3-(a). Similar to the Transformer block, we employ a dropout path after normalization to mitigate overfitting in deep networks. Notably, unlike the \\(4 \\times\\) Inverted Bottleneck Feed Forward Network in Transformer, which increases the channel dimension, our implementation maintains the same dimensions in the two linear layers of the FFN to conserve computational resources. We can observe that the vanilla modern structure improves performance by \\(2.1\\%\\) (\\(68.4\\% \\rightarrow 70.5\\%\\)), but incurs significant additional computations (\\(4.4\\mathrm{G} \\rightarrow 21.2\\mathrm{G}\\)). By removing the \\(4 \\times\\) inverted bottleneck, we reduce the FLOPs by approximately half (\\(21.2\\mathrm{G} \\rightarrow 9.2\\mathrm{G}\\)), with only a \\(0.4\\%\\) decrease in performance (\\(70.5\\% \\rightarrow 70.1\\%\\))." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.901 + ], + "angle": 0, + "content": "At this point, we have construct the vanilla DeepLA-24. Compare to the plain-24 model, the vanilla DeepLA-24 improves performance by \\(1.1\\%\\) \\((69.0\\% \\rightarrow 70.1\\%)\\) while using only \\(10\\%\\) FLOPs \\((92.2\\mathrm{G}\\rightarrow 9.2\\mathrm{G})\\). This small but mighty design enables the construction of deeper networks." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1333" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.488, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.216, + 0.442, + 0.23 + ], + "angle": 0, + "content": "Figure 5. Illustration of the proposed HDS strategy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.244, + 0.391, + 0.261 + ], + "angle": 0, + "content": "4.2. Hybrid Deep Supervision Strategy" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.267, + 0.484, + 0.359 + ], + "angle": 0, + "content": "In this section, we propose the HDS strategy, as illustrated in Figure 5. By incorporating supervision signals at each encoding stage, we facilitate smoother gradient propagation and simplify network optimization. The HDS strategy comprises two key aspects: (1) semantic probability supervision, and (2) spatial distribution supervision." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.363, + 0.484, + 0.59 + ], + "angle": 0, + "content": "Semantic Probability Supervision: Despite employing techniques such as residual connections, normalization, and dropout, optimizing very deep networks remains a challenge. The proposed semantic probability supervision encourages hidden layers to learn discriminative features, which facilitates faster convergence and regularization of the network. Specifically, the outputs of each stage are fed into a VFR module without position embedding, ensuring that the supervised signals closely reflect our training process. Then, they are processed by a plain linear layer to align with the ground truth labels. Finally, we use the widely-used weighted cross-entropy loss to calculate the loss at each stage. The loss for semantic probability supervision \\((\\mathcal{L}_{sem})\\) is defined as the average of all stages, which can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.604, + 0.483, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s e m} (Y, P) = - \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\sum_ {c = 0} ^ {C} y _ {i} ^ {c} \\log p _ {i} ^ {c} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.655, + 0.484, + 0.732 + ], + "angle": 0, + "content": "where \\( y_{i}^{c} \\) denotes the label vector of the \\( i \\)-stage, \\( p_{i}^{c} \\) denotes the predicted vector of the \\( i \\)-stage, \\( C \\) is the number of label categories, and \\( N \\) denotes the number of stages. This operation improves performance by \\( 2.1\\% \\) (\\( 70.1\\% \\rightarrow 72.2\\% \\)) without additional inference computational costs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Spatial Distribution Supervision: The sparsity and discreteness of point clouds lead to intricate complex local geometric patterns, which further exacerbate the challenges of optimizing very deep networks. To address this issue, we assume that the feature distribution is potentially consistent with the spatial distribution of the point clouds. In the early epochs of training, feature learning should trend toward fitting these geometric structures. Therefore, we propose the spatial distribution supervision that serves as a manual prior for convergence, explicitly guiding feature learning towards geometric structures during the early epochs of training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.258 + ], + "angle": 0, + "content": "Specifically, we represent the spatial distribution by calculating the grouped points with a learnable linear layer. The weights are initialized as an identity matrix and without bias, while the input and output channels are set to 3. Subsequently, we use this spatial distribution to constrain the grouped features obtained during semantic probability supervision. Finally, we adopt the mean squared error (MSE) loss to minimize the discrepancy between the spatial supervision signals and the grouped features. The loss of spatial distribution supervision \\((\\mathcal{L}_{spa})\\) is defined as the average of all stages, which can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.269, + 0.907, + 0.31 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s p a} (Y, P) = - \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\left(p _ {i} - y _ {i}\\right) ^ {2} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.313, + 0.907, + 0.388 + ], + "angle": 0, + "content": "where \\( y_{i} \\) denotes the spatial supervision signals of the \\( i \\)-stage, \\( p_{i} \\) denotes the predicted results from feature relative differences of the \\( i \\)-stage, and \\( N \\) denotes the number of encoder stages. This operation improves performance by \\( 1.7\\% \\) (\\( 70.1\\% \\rightarrow 71.8\\% \\))." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.392, + 0.907, + 0.557 + ], + "angle": 0, + "content": "Hybrid Loss: The loss function of the network integrates \\( L_{sem} \\), \\( L_{spa} \\), and the segmentation loss of final prediction \\( (L_{pred}) \\), which is calculated via cross-entropy loss. Furthermore, we implement different training weights with exponential decay for \\( L_{sem} \\) and \\( L_{spa} \\), where the decay factor is defined as the reciprocal of the current epoch number. This strategy ensures that deep supervision provides significant guidance in the early training phases, while gradually diminishes its influence to avoid hindering the primary learning path as training progresses. The hybrid loss can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.572, + 0.907, + 0.591 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {H}} = \\alpha^ {n} \\mathcal {L} _ {s e m} + \\beta^ {n} \\mathcal {L} _ {s p a} + (1 - \\alpha^ {n} - \\beta^ {n}) \\mathcal {L} _ {p r e d} \\quad (5)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.597, + 0.906, + 0.643 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are the training weights for supervision, \\(n\\) denotes reciprocal of the current epoch number. This hybrid loss improves performance by \\(3.1\\%\\) (\\(70.1\\% \\rightarrow 73.2\\%\\))." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.649, + 0.776, + 0.666 + ], + "angle": 0, + "content": "4.3. DeepLA-Net Implementation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.671, + 0.906, + 0.761 + ], + "angle": 0, + "content": "We construct a series of DeepLA-Net with different depths: DeepLA-24/60/120. Following successful previous works [12, 35, 92], the block ratio within each stage is set to [1:1:3:1], and the number of channels doubles in the subsequent stage. The configuration of DeepLA-Net is summarized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.763, + 0.688, + 0.778 + ], + "angle": 0, + "content": "\\[\nC = [ 6 4, 1 2 8, 2 5 6, 5 1 2 ]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.779, + 0.726, + 0.794 + ], + "angle": 0, + "content": "- DeepLA-24: \\( B = \\left\\lbrack {4,4,{12},4}\\right\\rbrack \\)" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.794, + 0.75, + 0.809 + ], + "angle": 0, + "content": "- DeepLA-60: \\( B = \\left\\lbrack {{10},{10},{30},{10}}\\right\\rbrack \\)" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.81, + 0.758, + 0.824 + ], + "angle": 0, + "content": "- DeepLA-120: \\( B = \\left\\lbrack {{20},{20},{60},{20}}\\right\\rbrack \\)" + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.779, + 0.758, + 0.824 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.903 + ], + "angle": 0, + "content": "where \\( C \\) refers to the channels of the output and \\( B \\) denotes the number of ResLFE blocks in each stage. Note that, in this paper, the term \"depth\" specifically refers to the number of blocks rather than linear layers. The network architecture details can be found in Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1334" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.483, + 0.117 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons of semantic segmentation with the SOTA methods on S3DIS in terms of mIoU." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.117, + 0.482, + 0.389 + ], + "angle": 0, + "content": "
YearMethod6-flod (%)Area5 (%)
NIPS 2017PointNet++ [47]83.053.5
NIPS 2018PointCNN [30]65.457.3
CVPR 2019KPConv [61]70.667.1
CVPR 2020RandLA-Net [20]70.062.5
CVPR 2021Point Trans. [92]73.570.4
NIPS 2022PointNeXt [48]74.970.8
CVPR 2023AF-GCN [89]77.772.3
CVPR 2023PointVector [10]78.472.3
CVPR 2023PointMeta [33]77.072.0
AAAI 2024PDNet [81]78.372.3
CVPR 2024KPConvX [62]-73.5
CVPR 2024OneFormer3D [23]75.072.4
CVPR 2024Point Trans. v3 [70]77.773.4
ACM MM 2024OPFR [22]76.972.6
ACM MM 2024LDCNet [38]75.471.8
ACM MM 2024MBSE [68]77.872.4
Ours 2024DeepLA-2477.973.2
Ours 2024DeepLA-6079.074.8
Ours 2024DeepLA-12079.875.7
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.41, + 0.223, + 0.427 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.436, + 0.267, + 0.453 + ], + "angle": 0, + "content": "5.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.459, + 0.483, + 0.594 + ], + "angle": 0, + "content": "To comprehensively evaluate the effectiveness of the proposed DeepLA-Net, we conduct experiments on S3DIS [1] and ScanNet v2 [9] for semantic segmentation, ScanObjectNN [64] for object classification, and ShapeNetPart [80] for object part segmentation. We use the following quantitative metrics for evaluation: mean Intersection over Union (mIoU), Overall Accuracy (OA), and mean Accuracy (mAcc). In result tables, Bold indicates the best result, underline indicates the best result excluding ours." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.595, + 0.483, + 0.732 + ], + "angle": 0, + "content": "In the position embedding phase, we employ the KNN for grouping, with the \\(K\\) specified as 24. For hybrid deep supervision, \\(\\alpha\\) and \\(\\beta\\) are set to 0.3 and 0.005, respectively. All experiments are performed on a Nvidia RTX 3090 GPU with 24GB memory. To ensure a fair comparison, the reported performance for both ours and the compared methods excludes the use of voting, pre-trained model, and test-time augmentation strategies. The implementation details and dataset description can be found in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.743, + 0.279, + 0.759 + ], + "angle": 0, + "content": "5.2. Experiment Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Semantic Segmentation. We show the results of our DeepLA-Net, including DeepLA-24/60/120, compared with previous state-of-the-art methods on S3DIS and ScanNet v2. In Table 1, for S3DIS, our DeepLA-60 has already surpassed previous methods. Particularly, our DeepLA-120 achieves a more significant breakthrough with an mIoU of \\(79.8\\%\\) in 6-fold \\((+1.4\\%)\\) and \\(75.7\\%\\) \\((+2.2\\%)\\) in Area5, surpassing the \\(75\\%\\) threshold for the first time. In Table 2, for ScanNet v2, our DeepLA-24/60 achieve competitive perfor" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.905, + 0.116 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons of semantic segmentation with the SOTA methods on ScanNet v2 in terms of mIoU." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.117, + 0.905, + 0.39 + ], + "angle": 0, + "content": "
YearMethodval (%)test (%)
NIPS 2017PointNet++ [47]53.555.7
NIPS 2018PointCNN [30]-45.8
CVPR 2019KPConv [61]69.268.6
CVPR 2022Stra. Trans. [24]74.373.7
NIPS 2022PointNeXt [48]71.571.2
CVPR 2023LRPNet [29]75.074.2
ICCV 2023Retro-FPN [71]74.074.4
NIPS 2023ConDaFormer [13]75.175.5
AAAI 2024HPENet [94]74.0-
ICLR 2024MVNet [76]75.2-
CVPR 2024KPConvX [62]76.3-
CVPR 2024OneFormer3D [23]76.6-
CVPR 2024OA-CNN [45]76.175.6
CVPR 2024MirageRoom [57]74.9-
ACM MM 2024LDCNet [38]73.3-
Ours 2024DeepLA-2474.1-
Ours 2024DeepLA-6075.9-
Ours 2024DeepLA-12077.677.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.41, + 0.905, + 0.437 + ], + "angle": 0, + "content": "Table 3. Quantitative comparisons of classification with the SOTA methods on ScanObjectNN (PB T50 RS)." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.438, + 0.905, + 0.686 + ], + "angle": 0, + "content": "
YearMethodOA (%)mAcc (%)
CVPR 2017PointNet [46]68.263.4
NIPS 2018PointCNN [30]78.575.1
TOG 2019DGCNN [67]78.173.6
TMM 2021GBNet [50]80.577.8
TIP 2021PRANet [6]82.179.1
ICLR 2022PointMLP [39]85.784.4
NIPS 2022PointNeXt [48]88.186.4
PAMI 2023GSLCN [32]85.884.1
ICLR 2023ACT [11]88.2-
CVPR 2023NLGAT [49]88.4-
CVPR 2023PointVector [10]88.286.7
CVPR 2023PointMeta [33]88.186.9
AAAI 2024PDNet [81]88.586.8
AAAI 2024Interpretable3D [15]88.086.5
ICLR 2024MaskFeat3D [77]88.4-
ACM MM 2024OPFR [22]88.186.3
Ours 2024DeepLA-2490.689.5
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.903 + ], + "angle": 0, + "content": "mance, while DeepLA-120 significantly outperforms previous methods, achieving \\(77.6\\%\\) \\((+1.0\\%)\\) on the validation set and \\(77.2\\%\\) \\((+1.6\\%)\\) on the test sets. Note that, due to the submission policy of the ScanNet v2 online test set, we only report the best model on the validation set, i.e., DeepLA-120. Additionally, results on the ScanNet test set have been reported less in recent years because fully supervised methods have not achieved substantial breakthroughs in this dataset. The result of the efficient DeepLA-24 demonstrates the rationality and effectiveness of our design. Furthermore, reasonably deepening the network can significantly improve performance. More detailed per-class results and visualizations can be found in Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1335" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.483, + 0.117 + ], + "angle": 0, + "content": "Table 4. Quantitative comparisons of part segmentation with the SOTA methods on ShapeNetPart." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.119, + 0.482, + 0.38 + ], + "angle": 0, + "content": "
YearMethodCls. mIoU (%)Ins. mIoU (%)
CVPR 2017PointNet [46]80.483.7
NIPS 2018PointCNN [30]84.686.1
TOG 2019DGCNN [67]82.385.1
CVPR 2020PointASNL [78]-86.1
CVPR 2021Point Trans. [92]83.786.6
ICLR 2022PointMLP [39]84.686.1
NIPS 2022PointNeXt [48]85.287.0
ICLR 2023ACT [11]84.786.1
CVPR 2023PointVector [10]85.186.9
CVPR 2023PointMeta [33]85.187.1
CVPR 2023AF-GCN [89]85.387.0
NIPS 2023ConDaFormer [13]84.686.8
AAAI 2024HPENet [94]85.587.1
AAAI 2024PDNet [81]85.487.2
AAAI 2024Interpretable3D [15]85.687.2
ICLR 2024MVNet [76]85.286.8
ICLR 2024MaskFeat3D [77]85.587.0
Ours 2024DeepLA-2486.588.0
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.394, + 0.484, + 0.531 + ], + "angle": 0, + "content": "Object Classification. As shown in Table 3, DeepLA-24 outperforms all baselines with OA of \\(90.6\\%\\) and mAcc of \\(89.5\\%\\) \\((+2.1\\%\\) OA, \\(+2.6\\%\\) mAcc). DeepLA-24 is the first method to surpass \\(90\\%\\) on OA, with the performance of others stagnating around \\(88\\%\\) for several years. This result indicates that merely developing more complex local representation methods is not sufficient for further advancement in shape recognition. In contrast, deeper networks can make significant contributions to capturing local patterns." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.535, + 0.484, + 0.655 + ], + "angle": 0, + "content": "Part Segmentation. The results are reported in Table 4, where we evaluate the performance with the mean class IoU (Cls. mIoU) and mean instance IoU (Ins. mIoU). DeepLA-24 outperforms all baselines with the Cls. mIoU of \\(86.5\\%\\) \\((+1.0\\%)\\) and the Ins. mIoU of \\(88.0\\%\\) \\((+0.8\\%)\\) without voting. It is noteworthy that we do not experiment with the deeper variants of DeepLA-Net on object classification and part segmentation datasets due to the limited dataset scale." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.664, + 0.255, + 0.679 + ], + "angle": 0, + "content": "5.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.686, + 0.483, + 0.746 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies on the proposed DeepLA-Net. All the ablation models are evaluated on S3DIS Area5 [1]. If not specified, the DeepLA-24 is employed as the default model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Hyperparameter settings. We analyze the impact of hyperparameter settings including the bottleneck in ResLFE block, the training weights in HDS strategy, the initial feature channel, and the grouping range \\( K \\). Table 5 explores different bottleneck settings in ResLFE block. The results illustrate that inverted bottlenecks larger than \\( 1 \\times \\) marginally improve performance but significantly increase computation costs. Meanwhile, bottlenecks less than \\( 1 \\times \\) slightly reduce computation while causing a more pronounced degradation in performance. Therefore, to balance" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.907, + 0.117 + ], + "angle": 0, + "content": "Table 5. Ablation results of the bottleneck in ResLFE block in DeepLA-24 on S3DIS Area5." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.122, + 0.905, + 0.203 + ], + "angle": 0, + "content": "
ModelmIoU (%)\\( \\bigtriangleup \\)(%)FLOPs (G)\\( \\bigtriangleup \\)(G)
1× bottleneck73.2-9.3-
0.5× bottleneck72.5-0.77.4-1.9
2× bottleneck73.4+0.213.4+4.1
4× bottleneck73.5+0.321.3+13.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.214, + 0.907, + 0.241 + ], + "angle": 0, + "content": "Table 6. Ablation results of training weights in HDS strategy in DeepLA-24 on S3DIS Area5." + }, + { + "type": "table", + "bbox": [ + 0.597, + 0.246, + 0.775, + 0.382 + ], + "angle": 0, + "content": "
α\\β03e-35e-37e-31e-2
070.171.071.871.370.6
0.271.872.372.572.972.0
0.372.272.573.272.872.4
0.472.072.672.472.472.1
0.571.572.072.172.271.7
" + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.263, + 0.82, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.397, + 0.71, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.537, + 0.636, + 0.549 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.717, + 0.397, + 0.905, + 0.536 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.818, + 0.537, + 0.835, + 0.548 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.55, + 0.907, + 0.578 + ], + "angle": 0, + "content": "Figure 6. Ablation results of hyperparameters in DeepLA-24 on S3DIS Area5. (a) initial feature dimension. (b) grouping range K." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.594, + 0.907, + 0.837 + ], + "angle": 0, + "content": "efficiency and performance, we employ the \\(1 \\times\\) bottleneck. Table 6 shows that the setting of training weights in HDS strategy is generally insensitive, as long as they are neither too large to hinder fitting nor too small to be ineffective. Notably, the training weight for spatial distribution is much smaller than that for semantic probability. This is mainly because spatial distribution supervision encourages the network to focus more on local details rather than abstract semantics, which are more crucial for feature classification. Figure 6 illustrates the impact of different initial feature channel and grouping range \\(K\\). The results demonstrate that small channel and grouping range lead to limited performance, due to inadequacy in capturing local patterns. Meanwhile, excessively large channel and grouping range tend to overfit the training examples, resulting in poor generalization and a decline in performance." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Ablation of Deep Supervision for Training Process. We demonstrate the performance and segmentation loss values \\((L_{pred}\\) in Eq. 5) of the network with different deep supervision strategies across training epochs, as shown in Fig-" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1336" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.083, + 0.287, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.083, + 0.483, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.242, + 0.483, + 0.282 + ], + "angle": 0, + "content": "Figure 7. Training performance and loss value across training epochs in DeepLA-24 with different deep supervision strategies. (a) mIoU score, and (b) loss value." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.3, + 0.484, + 0.435 + ], + "angle": 0, + "content": "ure 7. It is evident that the network without deep supervision exhibits a slow decline in loss, with almost no further decrease after 60 epochs. In contrast, networks using deep supervision consistently achieve higher performance and a rapid convergence in loss. Notably, the network employing the HDS strategy achieves the most reasonable and effective convergence. This result demonstrates that our HDS strategy significantly optimizes network training, facilitating a robust and substantial decline in loss." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.442, + 0.484, + 0.684 + ], + "angle": 0, + "content": "Ablation of Network Depth for Feature Learning. We visualize the feature similarity matrix of DeepLA-Net with different depths in Figure 8. The matrix is obtained by calculating the cosine similarities of the point features in the final layer, which are then sorted according to the predicted categories. The results indicate that the feature learning of DeepLA-6 is not robust, resulting in numerous recognition errors during segmentation. In contrast, DeepLA-24 demonstrates stronger feature learning capabilities, though the feature differences between classes are not sufficiently distinct, potentially causing blurred boundaries. DeepLA120 demonstrates the highest confidence in class distinction, showcasing the most powerful feature learning abilities among the three networks. This result demonstrates that deeper networks possess more powerful learning capabilities, enhancing segmentation performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Analysis on Complexity and Latency. We report the performance, model complexity, and latency using the same settings of DeepLA-Net family and previous SOTA methods [10, 48, 62, 81] in Table 7. From the results, the baseline exhibits the fastest inference speed but the lowest performance. Simply deepening the baseline (Plain-24) enhances performance but significantly increases FLOPs \\((9\\times\\) higher) and decreases inference speed \\((4.7\\times\\) slower). In contrast, DeepLA-24, equipped with the ResLFE block achieves performance improvements while substantially reducing FLOPs \\((10\\times\\) fewer) and increasing inference speed \\((3.75\\times\\) faster). The reduction in FLOPs enables the training of deeper networks. In particular, our DeepLA-120 achieves state-of-the-art performance with an inference" + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.084, + 0.691, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.083, + 0.865, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.226, + 0.691, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.226, + 0.895, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.367, + 0.905, + 0.409 + ], + "angle": 0, + "content": "Figure 8. Visual comparison of interpreting feature similarity matrix with different network depth of the DeepLA-6 (6-block network follows [1:1:3:1] ratio), DeepLA-24, and DeepLA-120." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.417, + 0.905, + 0.445 + ], + "angle": 0, + "content": "Table 7. Quantitative comparisons of performance, model complexity, and latency on S3DIS Area5." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.447, + 0.905, + 0.589 + ], + "angle": 0, + "content": "
MethodmIoU (%)Params. (M)FLOPs (G)Thr. Put (ins./sec.)
PointNeXt-XL [48]70.846.184.843
PointVector-XL [10]72.324.158.540
KPConvX-L [62]73.513.5-47
PDNet-XXL [81]72.335.612.0-
Baseline63.43.111.3207
Plain-2469.09.792.244
DeepLA-2473.26.49.2165
DeepLA-6074.815.821.578
DeepLA-12075.730.342.742
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.602, + 0.906, + 0.648 + ], + "angle": 0, + "content": "speed comparable to Plain-24 and the previous SOTA works [10, 48, 62]. More ablation analysis and discussion details can be found in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.664, + 0.64, + 0.68 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.689, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this study, we demonstrate the efficiency and effectiveness of very deep local aggregation networks for point cloud analysis, addressing two primary challenges: computational cost and training optimization. In contrast to most current approaches that rely on expensive and redundant local representation, we propose a lightweight ResLFE block to significantly reduce the computational cost (\\(10 \\times\\) fewer FLOPs), and make it possible to construct very deep LANets. Furthermore, the HDS strategy is also introduced to ensure smooth gradient backpropagation and mitigate optimization challenges in deep networks. The DeepLA-Net achieves SOTA performance with high efficiency across segmentation and classification tasks on four benchmarks: S3DIS, ScanNet v2, ScanObjectNN, and ShapeNetPart." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1337" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.484, + 0.184 + ], + "angle": 0, + "content": "[1] Iro Armeni, Ozan Sener, Amir R. Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3D semantic parsing of large-scale indoor spaces. 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However, the recognition performance has saturated over the past few years, indicating that increasingly complex and redundant designs no longer make improvements to local learning. This phenomenon prompts us to diverge from the trend in 3D vision and instead pursue an alternative and successful solution: deeper neural networks. In this paper, we propose DeepLA-Net, a series of very deep networks for point cloud analysis. The key insight of our approach is to exploit a small but mighty local learning block, which uses $10 \times$ fewer FLOPs, enabling the construction of very deep networks. Furthermore, we design a training supervision strategy to ensure smooth gradient backpropagation and optimization in very deep networks. We construct the DeepLA-Net family with a depth of up to 120 blocks — at least $5 \times$ deeper than recent methods — trained on a single RTX 3090. An ensemble of the DeepLA-Net achieves state-of-the-art performance on classification and segmentation tasks of S3DIS Area5 ( $+2.2\%$ mIoU), ScanNet test set ( $+1.6\%$ mIoU), ScanObjectNN ( $+2.1\%$ OA), and ShapeNetPart ( $+0.9\%$ CLS.mIoU). The code are released at https://github.com/zeng-ziyin/DeepLA-Net. + +# 1. Introduction + +Thanks to the significant development of 3D sensors, 3D point cloud analysis has garnered increasing attention in recent years and is widely applied in autonomous driving, smart cities, and robotics [18, 84]. However, 3D point clouds consist of sparse, discrete, and non-uniform point sets embedded in continuous space [46]. This complex structure poses challenges to local pattern learning. + +In order to solve this problem, extensive explorations have been conducted on the local pattern of point clouds to enable fine-grained analysis. Inspired by CNNs, they intro- + +![](images/010e3b29538d74f2a25cdff83dedeb3c7292b0054646bdae373e01fbf7cdf69f.jpg) +Figure 1. Illustration of segmentation performance, model efficiency and network depth on S3DIS Area5. DeepLA-24 has already achieved SOTA-equivalent performance with minimal parameters. The deeper architecture DeepLA-120 achieves a milestone (75.7%) by exceeding 75% threshold for the first time, and outperforms Point Transformer v3 [70] with fewer parameters. + +duce two robust inductive biases: locality and weight sharing, which promote the development of neural networks for analyzing 3D point clouds [47]. Specifically, these studies [10, 20, 33, 48, 56, 83, 85, 86] employ MLPs with shared weights to capture local features from neighbors. We collectively refer to them as local aggregation networks (LANets) in this paper. It is noteworthy that most LANets primarily focus on developing intricate local representation methods to explicitly explore the local patterns of point clouds, achieving success due to the robust inductive biases. However, the performance of increasingly sophisticated LANets on popular benchmarks [1, 9, 64, 80] has gradually saturated, as evidenced by minimal gains compare to PointNeXt [48] over the past few years, such as ScanObjectNN [64] (OA +0.4%, mAcc +0.5%, in Tab. 3) and ShapeNetPart [80] (cls.mIoU +0.4%, Ins.mIoU +0.2%, in Tab. 4). Particularly, the performance of most existing methods on S3DIS [1] has saturated around 73% [62, 70], as shown in Figure 1. The primary reason is that they already adequately + +describe the local geometric properties of point clouds, and more complex designs no longer contribute to capturing additional local patterns [39, 48]. This phenomenon prompts us to rethink the design of LANets. + +Interestingly, the development of 3D point cloud analysis is closely related to the evolution of 2D image processing networks [39, 47]. We observe that the design of 2D CNNs shifted towards deeper with the residual connections [19], making deep networks the mainstream backbone for feature extraction with successful performance [2, 35, 52]. Given that LANets for point clouds share similar inductive biases with CNNs, we cannot help but wonder: can we explore an alternative path by leveraging the success of deep CNNs for LANets? Unfortunately, to the best of our knowledge, there has been limited systematic exploration of deepening LANets. Therefore, in this paper, instead of following the tendency to explore sophisticated details, we are in pursuit of very deep LANets for point cloud analysis. For this purpose, we encounter two key challenges: (1) high computational cost, and (2) difficult training optimization. + +Obviously, the prevailing philosophy of sophisticated and redundant local learning has significantly increased computational complexity. To circumvent the prohibitive computations, we propose a residual local feature extraction (ResLFE) block that ensures minimal computational cost. Specifically, we first employ stage-level positional embedding instead of redundant and high latency layer-level. We then introduce an efficient vector feature representation and a robust modernization structure that significantly reduces FLOPs while preserving local information interactions. As shown in Figure 2, the proposed ResLFE block shows significant computational efficiency $(10\times$ fewer FLOPs) and commendable performance improvements $(+1.1\%$ mIoU). In particular, this remarkable computational efficiency enables the construction of very deep networks. + +Furthermore, very deep networks are difficult to optimize [19, 72], and the complex geometric patterns of point clouds further exacerbate the difficulty of optimization [16, 44, 58]. To address these issues, we introduce a hybrid deep supervision (HDS) strategy to facilitate learning and optimization. We employ two forms of supervision to the outputs of the encoder at each stage. Specifically, we align each output with the ground truth using cross-entropy loss, which promotes smooth gradient propagation. Meanwhile, we also align the outputs with the spatial distribution of the point cloud using mean squared error loss, which benefits in fitting the complex geometric patterns to simplify network optimization. We demonstrate in experiments that the proposed HDS strategy optimizes network training by accelerating model convergence and achieves significant performance improvements $(+3.1\% \mathrm{mIoU})$ + +Overall, we propose very Deep Local Aggregation Networks (DeepLA-Net), constructed from the ResLFE + +block for lightweight design and the HDS strategy for optimization. In particular, we have successfully trained DeepLA-120—a representative deep network comprising up to 120 ResLFE blocks—on a single RTX 3090 with 24GB memory. The DeepLA-Net family outperforms the SOTA methods across various tasks, including S3DIS [1] and ScanNetV2 [9] for semantic segmentation, ScanObjectNN [64] for object classification, and ShapeNetPart [80] for part segmentation. Figure 1 highlights the superior performance and efficiency of our DeepLA-Net family on S3DIS Area5. Moreover, a step-by-step procedure of constructing the DeepLA-Net and the corresponding results are shown in Figure 2. Our key contributions are: + +- We propose a residual local feature extraction block from the perspective of efficiency and performance, enabling the construction of deeper LANets. +- We propose a hybrid deep supervision strategy from the perspective of optimization and learning to ensure smooth gradient backpropagation in deeper LANets. +- We propose DeepLA-Net, a series of very deep local aggregation networks, surpassing SOTA in classification, part segmentation, and semantic segmentation. + +# 2. Related Work + +# 2.1. Deep Learning on Point Clouds + +Given the disordered and unstructured nature of 3D point clouds, directly applying traditional CNNs to them remains a challenge. Therefore, some methods firstly transform point clouds into intermediate representations such as 2D images [3, 26, 42, 73, 82] or 3D voxels [5, 7, 17, 27, 41, 93] through projection or voxelization, and subsequently employ 2D/3D CNNs to process these structured data. Although promising results have been shown in certain scenarios, the intermediate transformation steps may introduce information loss and computation costs [14, 51, 86]. In contrast, point-based methods [14, 20, 31, 46, 47, 51, 69, 83, 85, 86, 91] are specifically designed to perform feature learning directly on point clouds without using intermediate representations. Moreover, some noteworthy research has leveraged techniques like Recurrent Neural Networks (RNNs) [21, 34, 79], Graph Neural Networks (GNNs) [25, 28, 66, 75, 87], point-voxel hybrid representation [36, 37, 53, 74, 88], and sparse voxel [4, 8, 55, 59, 60], achieving significant performance in various tasks. + +# 2.2. Local Aggregation Networks for Point Clouds + +The pioneering PointNet [46] uses point-wise MLPs to learn per-point features, however, it has limitations in capturing local details. To overcome this, PointNet++ [47] improves PointNet by employing shared-weight MLPs in local neighbors, aligning with the inductive biases in CNNs: + +localization and weight sharing. Along this direction, numerous subsequent studies [30, 40, 63, 67, 69, 90] have employed the above two inductive biases by local feature aggregation operations. We summarize them as local aggregation networks (LANets). Recent LANets [10, 14, 20, 33, 43, 48, 51, 54, 83, 85, 86] have primarily focused on exploring more robust local representations. For example, Point Transformer [92] designs a local transformer layer based on vector self-attention in local neighbors. PointVector [10] improves local extractor by transforming relative features and positions of input into representative vectors. ConDaFormer [13] enhances local geometric modeling by depth-wise convolutions, capturing both long-range contextual information and local priors. However, with the development of LANets, merely development of more complex LANets is insufficient for further capturing the local patterns. In this paper, we demonstrate that without relying on intricate and complex local representations, designing very deep hierarchical architectures for LANets can also achieve significant breakthroughs in performance. + +# 3. Preliminary + +In this section, we introduce the preliminary implementation of DeepLA-Net. Most existing LANets have focused on robust local representation to effectively capture the complex local patterns of sparse and discrete point clouds. However, this focus makes them difficult to deepen due to the high computational cost. Therefore, we consider building deep networks based on the simplest PointNet++ [47]. + +PointNet++ [47], the pioneering LANet for point cloud analysis, can be summarized in two phases: position embedding and feature representation. In the position embedding phase, PointNet++ employs ball query to group points, and then uses relative position differences as position embedding. Subsequently, in the feature representation phase, PointNet++ concatenates position embedding and grouped features to represent local features, and then aggregates them to centroid points by using max pooling. This can be formulated as: + +$$ +\left\{ \begin{array}{l} p _ {i} ^ {k} = \operatorname {G r o u p} \left(p _ {i}\right) \\ P E = \mathcal {M} \left(p _ {i} - p _ {i} ^ {k}\right) \end{array} \quad \left\{ \begin{array}{l} F _ {N} = \mathcal {M} \left[ f _ {i} ^ {k} \oplus P E \right] \\ F _ {\text {o u t}} = \max \left(F _ {N}\right) \end{array} \right. \right. \tag {1} +$$ + +where $p_i$ denotes the centroid points, $p_i^k$ denotes the grouped points, $\mathcal{M}$ denotes the multi-layer perceptron, $\oplus$ denotes the concatenation, max denotes the max-pooling, and $f_i^k$ denotes the grouped features. + +Implementation. Due to its simplicity, we employ PointNet++ [47] as the baseline and demonstrate the step-by-step "modernization" into DeepLA-Net. Firstly, we follow the PointNeXt [48] configuration, incorporating data augmentation and optimization techniques such as random height + +![](images/724b6af3ffb39dd6c145d58ccbb8dd715198ec2ab1fcd23320af0f85c45e3cf7.jpg) +Figure 2. Illustration of the designs and results of our improvements on S3DIS [1] Area5 step-by-step. The foreground bars denote model accuracy, the stars denote model FLOPs, and hatched bars mean the modification is not adopted solely. + +and color dropout. The baseline model achieves $63.4\%$ mIoU and 11.3G FLOPs1. Subsequently, we directly extend the baseline to 24-block model, following [35] with a block ratio of [1:1:3:1]. This plain-24 model achieves $69.0\%$ mIoU and 92.2G FLOPs. Despite achieving a respectable mIoU score, the huge FLOPs prevent us from further deepening the network. In addition, deep network poses optimization challenges. Therefore, to construct LANets as deep as possible, we propose the ResLFE block which significantly reduces the computation cost while preserving reliable accuracy. Subsequently, we propose the HDS strategy to ensure smooth gradient backpropagation in deep networks and mitigate training optimization challenges. + +# 4. Methodology + +In this section, we introduce the key components of our DeepLA-Net: residual local feature extraction (ResLFE) block and hybrid deep supervision (HDS) strategy. To intuitively and clearly demonstrate the role of each design, we illustrate each step of improvement in Figure 2, with all models evaluated on S3DIS Area 5 [1]. + +# 4.1. Residual Local Feature Extraction Block + +To enable the construction of deeper networks, we propose the ResLFE block, as shown in Figure 3, which significantly + +![](images/0ef439624a33fe11f9097f47d0e3a0622206be35f49626e59c12f143ba081f6b.jpg) +Figure 3. Illustration of the proposed ResLFE block. Right: stage-level position embedding. Middle: Vector Feature Representation (VFR.) module. Left: modernization structure. + +![](images/fdbd61f09272a97fb4d8c252b5d93ee64616df89f7cdcee15fdc4753ebd19b98.jpg) +Figure 4. Illustration of the computational latency of position embedding and feature representation phases in different LANets. + +reduces computational cost. The ResLFE block comprises three key aspects: (1) stage-level position embedding, (2) efficient vector feature representation module, and (3) powerful modernization structure. + +Stage-Level Position Embedding: Existing LANets typically implement position embedding at each learning layer, resulting in high computational costs. As shown in Figure 4, the computational latency of the positional embedding phase constitutes approximately half of the total for each layer, which is unacceptable in deeper networks. As indicated by Eq. 1, we observe that the computation of position embedding relies solely on point coordinates. Considering that the resolution of points remains constant within each stage, layers in the same stage can share an identical position embedding. Therefore, we suggest pre-calculate the position embedding at the beginning of each stage, saving it to cache and reusing it per-layer in that stage to avoid subsequent real-time computations. This approach ensures that the computational costs of position embedding depend solely on the number of stages, rather than the depth of the network, thereby facilitating the efficient application of very deep networks. Our implementation of position embedding is the same as PointNet++. This operation approximately halves the FLOPs (92.2G → 44.6G), with only a minimal decrease in performance (69.0% → 68.6%). + +Vector Feature Representation Module: First, we consider further improvements in computational efficiency during the feature representation phase. We observe that, in + +most existing LANets, feature abstraction (linear layers in Eq. 1) is typically performed after grouping the features into $f_{i}^{k} \in \mathbb{R}^{N \times K \times C}$ , which incurs substantial computational costs. To address this issue, we suggest conducting feature abstraction before grouping on $f_{i} \in \mathbb{R}^{N \times C}$ (front-linear). Although this approach may limit local information interactions, it allows for a reduction in FLOPs by $K$ times theoretically, leading to significant efficiency gains. Practically, this operation reduces the $7 \times$ FLOPs $(44.6\mathrm{G} \rightarrow 6.3\mathrm{G})$ , with a performance degradation of only $1.2\%$ $(68.6\% \rightarrow 67.4\%)$ . + +Moreover, we suggest employing the vector feature $f_{i} - f_{i}^{k}$ instead of the grouped feature $f_{i}^{k}$ . On the one hand, this approach achieves cost-effective local interaction, which can enhance relation learning. On the other hand, it aligns with the relative position embedding $p_{i} - p_{i}^{k}$ , mitigating the potential semantic gap between position embedding and feature representation. This operation improves performance by $1.2\%$ ( $67.4\% \rightarrow 68.6\%$ ) without incurring additional computation costs. + +Furthermore, when combining the vector feature with the relative position embedding, we replace concatenation $(\oplus)$ with simple addition $(+)$ , avoiding duplicating channels, which further reduces computational demands. This operation reduces computation $(6.3\mathrm{G}\rightarrow 4.4\mathrm{G})$ while only marginally decreasing performance $(68.6\% \to 68.4\%)$ . Finally, we employ the simple but effective max pooling for aggregation. The vector feature representation (VFR) module can be formulated as follows: + +$$ +\left\{ \begin{array}{l} f _ {i} ^ {\prime} = \mathcal {M} \left(f _ {i}\right) \\ F _ {i} ^ {k} = f _ {i} ^ {\prime} - f _ {i} ^ {\prime k} \\ F _ {\text {o u t}} = \max \left(F _ {i} ^ {k} + P E\right) \end{array} \right. \tag {2} +$$ + +Modernization Structure: Inspired by powerful Transformers [12, 65], we adopt a modernization structure, as shown in Figure 3-(a). Similar to the Transformer block, we employ a dropout path after normalization to mitigate overfitting in deep networks. Notably, unlike the $4 \times$ Inverted Bottleneck Feed Forward Network in Transformer, which increases the channel dimension, our implementation maintains the same dimensions in the two linear layers of the FFN to conserve computational resources. We can observe that the vanilla modern structure improves performance by $2.1\%$ ( $68.4\% \rightarrow 70.5\%$ ), but incurs significant additional computations ( $4.4\mathrm{G} \rightarrow 21.2\mathrm{G}$ ). By removing the $4 \times$ inverted bottleneck, we reduce the FLOPs by approximately half ( $21.2\mathrm{G} \rightarrow 9.2\mathrm{G}$ ), with only a $0.4\%$ decrease in performance ( $70.5\% \rightarrow 70.1\%$ ). + +At this point, we have construct the vanilla DeepLA-24. Compare to the plain-24 model, the vanilla DeepLA-24 improves performance by $1.1\%$ $(69.0\% \rightarrow 70.1\%)$ while using only $10\%$ FLOPs $(92.2\mathrm{G}\rightarrow 9.2\mathrm{G})$ . This small but mighty design enables the construction of deeper networks. + +![](images/3d809a700d45b4a50b7f673946e8ef5eb0223cb1782d6536754491b4ebb68bb7.jpg) +Figure 5. Illustration of the proposed HDS strategy. + +# 4.2. Hybrid Deep Supervision Strategy + +In this section, we propose the HDS strategy, as illustrated in Figure 5. By incorporating supervision signals at each encoding stage, we facilitate smoother gradient propagation and simplify network optimization. The HDS strategy comprises two key aspects: (1) semantic probability supervision, and (2) spatial distribution supervision. + +Semantic Probability Supervision: Despite employing techniques such as residual connections, normalization, and dropout, optimizing very deep networks remains a challenge. The proposed semantic probability supervision encourages hidden layers to learn discriminative features, which facilitates faster convergence and regularization of the network. Specifically, the outputs of each stage are fed into a VFR module without position embedding, ensuring that the supervised signals closely reflect our training process. Then, they are processed by a plain linear layer to align with the ground truth labels. Finally, we use the widely-used weighted cross-entropy loss to calculate the loss at each stage. The loss for semantic probability supervision $(\mathcal{L}_{sem})$ is defined as the average of all stages, which can be formulated as follows: + +$$ +\mathcal {L} _ {s e m} (Y, P) = - \frac {1}{N} \sum_ {i = 0} ^ {N} \sum_ {c = 0} ^ {C} y _ {i} ^ {c} \log p _ {i} ^ {c} \tag {3} +$$ + +where $y_{i}^{c}$ denotes the label vector of the $i$ -stage, $p_{i}^{c}$ denotes the predicted vector of the $i$ -stage, $C$ is the number of label categories, and $N$ denotes the number of stages. This operation improves performance by $2.1\%$ ( $70.1\% \rightarrow 72.2\%$ ) without additional inference computational costs. + +Spatial Distribution Supervision: The sparsity and discreteness of point clouds lead to intricate complex local geometric patterns, which further exacerbate the challenges of optimizing very deep networks. To address this issue, we assume that the feature distribution is potentially consistent with the spatial distribution of the point clouds. In the early epochs of training, feature learning should trend toward fitting these geometric structures. Therefore, we propose the spatial distribution supervision that serves as a manual prior for convergence, explicitly guiding feature learning towards geometric structures during the early epochs of training. + +Specifically, we represent the spatial distribution by calculating the grouped points with a learnable linear layer. The weights are initialized as an identity matrix and without bias, while the input and output channels are set to 3. Subsequently, we use this spatial distribution to constrain the grouped features obtained during semantic probability supervision. Finally, we adopt the mean squared error (MSE) loss to minimize the discrepancy between the spatial supervision signals and the grouped features. The loss of spatial distribution supervision $(\mathcal{L}_{spa})$ is defined as the average of all stages, which can be formulated as follows: + +$$ +\mathcal {L} _ {s p a} (Y, P) = - \frac {1}{N} \sum_ {i = 0} ^ {N} \left(p _ {i} - y _ {i}\right) ^ {2} \tag {4} +$$ + +where $y_{i}$ denotes the spatial supervision signals of the $i$ -stage, $p_{i}$ denotes the predicted results from feature relative differences of the $i$ -stage, and $N$ denotes the number of encoder stages. This operation improves performance by $1.7\%$ ( $70.1\% \rightarrow 71.8\%$ ). + +Hybrid Loss: The loss function of the network integrates $L_{sem}$ , $L_{spa}$ , and the segmentation loss of final prediction $(L_{pred})$ , which is calculated via cross-entropy loss. Furthermore, we implement different training weights with exponential decay for $L_{sem}$ and $L_{spa}$ , where the decay factor is defined as the reciprocal of the current epoch number. This strategy ensures that deep supervision provides significant guidance in the early training phases, while gradually diminishes its influence to avoid hindering the primary learning path as training progresses. The hybrid loss can be formulated as: + +$$ +\mathcal {L} _ {\mathcal {H}} = \alpha^ {n} \mathcal {L} _ {s e m} + \beta^ {n} \mathcal {L} _ {s p a} + (1 - \alpha^ {n} - \beta^ {n}) \mathcal {L} _ {p r e d} \quad (5) +$$ + +where $\alpha$ and $\beta$ are the training weights for supervision, $n$ denotes reciprocal of the current epoch number. This hybrid loss improves performance by $3.1\%$ ( $70.1\% \rightarrow 73.2\%$ ). + +# 4.3. DeepLA-Net Implementation + +We construct a series of DeepLA-Net with different depths: DeepLA-24/60/120. Following successful previous works [12, 35, 92], the block ratio within each stage is set to [1:1:3:1], and the number of channels doubles in the subsequent stage. The configuration of DeepLA-Net is summarized as follows: + +$$ +C = [ 6 4, 1 2 8, 2 5 6, 5 1 2 ] +$$ + +- DeepLA-24: $B = \left\lbrack {4,4,{12},4}\right\rbrack$ +- DeepLA-60: $B = \left\lbrack {{10},{10},{30},{10}}\right\rbrack$ +- DeepLA-120: $B = \left\lbrack {{20},{20},{60},{20}}\right\rbrack$ + +where $C$ refers to the channels of the output and $B$ denotes the number of ResLFE blocks in each stage. Note that, in this paper, the term "depth" specifically refers to the number of blocks rather than linear layers. The network architecture details can be found in Appendix. + +Table 1. Quantitative comparisons of semantic segmentation with the SOTA methods on S3DIS in terms of mIoU. + +
YearMethod6-flod (%)Area5 (%)
NIPS 2017PointNet++ [47]83.053.5
NIPS 2018PointCNN [30]65.457.3
CVPR 2019KPConv [61]70.667.1
CVPR 2020RandLA-Net [20]70.062.5
CVPR 2021Point Trans. [92]73.570.4
NIPS 2022PointNeXt [48]74.970.8
CVPR 2023AF-GCN [89]77.772.3
CVPR 2023PointVector [10]78.472.3
CVPR 2023PointMeta [33]77.072.0
AAAI 2024PDNet [81]78.372.3
CVPR 2024KPConvX [62]-73.5
CVPR 2024OneFormer3D [23]75.072.4
CVPR 2024Point Trans. v3 [70]77.773.4
ACM MM 2024OPFR [22]76.972.6
ACM MM 2024LDCNet [38]75.471.8
ACM MM 2024MBSE [68]77.872.4
Ours 2024DeepLA-2477.973.2
Ours 2024DeepLA-6079.074.8
Ours 2024DeepLA-12079.875.7
+ +# 5. Experiments + +# 5.1. Experiment Setup + +To comprehensively evaluate the effectiveness of the proposed DeepLA-Net, we conduct experiments on S3DIS [1] and ScanNet v2 [9] for semantic segmentation, ScanObjectNN [64] for object classification, and ShapeNetPart [80] for object part segmentation. We use the following quantitative metrics for evaluation: mean Intersection over Union (mIoU), Overall Accuracy (OA), and mean Accuracy (mAcc). In result tables, Bold indicates the best result, underline indicates the best result excluding ours. + +In the position embedding phase, we employ the KNN for grouping, with the $K$ specified as 24. For hybrid deep supervision, $\alpha$ and $\beta$ are set to 0.3 and 0.005, respectively. All experiments are performed on a Nvidia RTX 3090 GPU with 24GB memory. To ensure a fair comparison, the reported performance for both ours and the compared methods excludes the use of voting, pre-trained model, and test-time augmentation strategies. The implementation details and dataset description can be found in Appendix. + +# 5.2. Experiment Results + +Semantic Segmentation. We show the results of our DeepLA-Net, including DeepLA-24/60/120, compared with previous state-of-the-art methods on S3DIS and ScanNet v2. In Table 1, for S3DIS, our DeepLA-60 has already surpassed previous methods. Particularly, our DeepLA-120 achieves a more significant breakthrough with an mIoU of $79.8\%$ in 6-fold $(+1.4\%)$ and $75.7\%$ $(+2.2\%)$ in Area5, surpassing the $75\%$ threshold for the first time. In Table 2, for ScanNet v2, our DeepLA-24/60 achieve competitive perfor + +Table 2. Quantitative comparisons of semantic segmentation with the SOTA methods on ScanNet v2 in terms of mIoU. + +
YearMethodval (%)test (%)
NIPS 2017PointNet++ [47]53.555.7
NIPS 2018PointCNN [30]-45.8
CVPR 2019KPConv [61]69.268.6
CVPR 2022Stra. Trans. [24]74.373.7
NIPS 2022PointNeXt [48]71.571.2
CVPR 2023LRPNet [29]75.074.2
ICCV 2023Retro-FPN [71]74.074.4
NIPS 2023ConDaFormer [13]75.175.5
AAAI 2024HPENet [94]74.0-
ICLR 2024MVNet [76]75.2-
CVPR 2024KPConvX [62]76.3-
CVPR 2024OneFormer3D [23]76.6-
CVPR 2024OA-CNN [45]76.175.6
CVPR 2024MirageRoom [57]74.9-
ACM MM 2024LDCNet [38]73.3-
Ours 2024DeepLA-2474.1-
Ours 2024DeepLA-6075.9-
Ours 2024DeepLA-12077.677.2
+ +Table 3. Quantitative comparisons of classification with the SOTA methods on ScanObjectNN (PB T50 RS). + +
YearMethodOA (%)mAcc (%)
CVPR 2017PointNet [46]68.263.4
NIPS 2018PointCNN [30]78.575.1
TOG 2019DGCNN [67]78.173.6
TMM 2021GBNet [50]80.577.8
TIP 2021PRANet [6]82.179.1
ICLR 2022PointMLP [39]85.784.4
NIPS 2022PointNeXt [48]88.186.4
PAMI 2023GSLCN [32]85.884.1
ICLR 2023ACT [11]88.2-
CVPR 2023NLGAT [49]88.4-
CVPR 2023PointVector [10]88.286.7
CVPR 2023PointMeta [33]88.186.9
AAAI 2024PDNet [81]88.586.8
AAAI 2024Interpretable3D [15]88.086.5
ICLR 2024MaskFeat3D [77]88.4-
ACM MM 2024OPFR [22]88.186.3
Ours 2024DeepLA-2490.689.5
+ +mance, while DeepLA-120 significantly outperforms previous methods, achieving $77.6\%$ $(+1.0\%)$ on the validation set and $77.2\%$ $(+1.6\%)$ on the test sets. Note that, due to the submission policy of the ScanNet v2 online test set, we only report the best model on the validation set, i.e., DeepLA-120. Additionally, results on the ScanNet test set have been reported less in recent years because fully supervised methods have not achieved substantial breakthroughs in this dataset. The result of the efficient DeepLA-24 demonstrates the rationality and effectiveness of our design. Furthermore, reasonably deepening the network can significantly improve performance. More detailed per-class results and visualizations can be found in Appendix. + +Table 4. Quantitative comparisons of part segmentation with the SOTA methods on ShapeNetPart. + +
YearMethodCls. mIoU (%)Ins. mIoU (%)
CVPR 2017PointNet [46]80.483.7
NIPS 2018PointCNN [30]84.686.1
TOG 2019DGCNN [67]82.385.1
CVPR 2020PointASNL [78]-86.1
CVPR 2021Point Trans. [92]83.786.6
ICLR 2022PointMLP [39]84.686.1
NIPS 2022PointNeXt [48]85.287.0
ICLR 2023ACT [11]84.786.1
CVPR 2023PointVector [10]85.186.9
CVPR 2023PointMeta [33]85.187.1
CVPR 2023AF-GCN [89]85.387.0
NIPS 2023ConDaFormer [13]84.686.8
AAAI 2024HPENet [94]85.587.1
AAAI 2024PDNet [81]85.487.2
AAAI 2024Interpretable3D [15]85.687.2
ICLR 2024MVNet [76]85.286.8
ICLR 2024MaskFeat3D [77]85.587.0
Ours 2024DeepLA-2486.588.0
+ +Object Classification. As shown in Table 3, DeepLA-24 outperforms all baselines with OA of $90.6\%$ and mAcc of $89.5\%$ $(+2.1\%$ OA, $+2.6\%$ mAcc). DeepLA-24 is the first method to surpass $90\%$ on OA, with the performance of others stagnating around $88\%$ for several years. This result indicates that merely developing more complex local representation methods is not sufficient for further advancement in shape recognition. In contrast, deeper networks can make significant contributions to capturing local patterns. + +Part Segmentation. The results are reported in Table 4, where we evaluate the performance with the mean class IoU (Cls. mIoU) and mean instance IoU (Ins. mIoU). DeepLA-24 outperforms all baselines with the Cls. mIoU of $86.5\%$ $(+1.0\%)$ and the Ins. mIoU of $88.0\%$ $(+0.8\%)$ without voting. It is noteworthy that we do not experiment with the deeper variants of DeepLA-Net on object classification and part segmentation datasets due to the limited dataset scale. + +# 5.3. Ablation Studies + +In this section, we conduct ablation studies on the proposed DeepLA-Net. All the ablation models are evaluated on S3DIS Area5 [1]. If not specified, the DeepLA-24 is employed as the default model. + +Hyperparameter settings. We analyze the impact of hyperparameter settings including the bottleneck in ResLFE block, the training weights in HDS strategy, the initial feature channel, and the grouping range $K$ . Table 5 explores different bottleneck settings in ResLFE block. The results illustrate that inverted bottlenecks larger than $1 \times$ marginally improve performance but significantly increase computation costs. Meanwhile, bottlenecks less than $1 \times$ slightly reduce computation while causing a more pronounced degradation in performance. Therefore, to balance + +Table 5. Ablation results of the bottleneck in ResLFE block in DeepLA-24 on S3DIS Area5. + +
ModelmIoU (%)\( \bigtriangleup \)(%)FLOPs (G)\( \bigtriangleup \)(G)
1× bottleneck73.2-9.3-
0.5× bottleneck72.5-0.77.4-1.9
2× bottleneck73.4+0.213.4+4.1
4× bottleneck73.5+0.321.3+13.0
+ +Table 6. Ablation results of training weights in HDS strategy in DeepLA-24 on S3DIS Area5. + +
α\β03e-35e-37e-31e-2
070.171.071.871.370.6
0.271.872.372.572.972.0
0.372.272.573.272.872.4
0.472.072.672.472.472.1
0.571.572.072.172.271.7
+ +![](images/a7b3b6e62ff3ee30916ee598b0f4cacc45a2062e7bb3cff00cdfe00ad884a859.jpg) + +![](images/0e6d63b0fe4f276959d7f86fddb5dc9001dbb7570af1fdd2ae2a655a562d742f.jpg) +(a) + +![](images/b8e369ac5d39e8cb04d0731daf8afc7544f995867b81fb2488cfedb0d7b52a49.jpg) +(b) +Figure 6. Ablation results of hyperparameters in DeepLA-24 on S3DIS Area5. (a) initial feature dimension. (b) grouping range K. + +efficiency and performance, we employ the $1 \times$ bottleneck. Table 6 shows that the setting of training weights in HDS strategy is generally insensitive, as long as they are neither too large to hinder fitting nor too small to be ineffective. Notably, the training weight for spatial distribution is much smaller than that for semantic probability. This is mainly because spatial distribution supervision encourages the network to focus more on local details rather than abstract semantics, which are more crucial for feature classification. Figure 6 illustrates the impact of different initial feature channel and grouping range $K$ . The results demonstrate that small channel and grouping range lead to limited performance, due to inadequacy in capturing local patterns. Meanwhile, excessively large channel and grouping range tend to overfit the training examples, resulting in poor generalization and a decline in performance. + +Ablation of Deep Supervision for Training Process. We demonstrate the performance and segmentation loss values $(L_{pred}$ in Eq. 5) of the network with different deep supervision strategies across training epochs, as shown in Fig- + +![](images/4b91d3264b6e9fcc8fadc4e735c45a81e0cd712e2f784e5191edad67fbd3703a.jpg) +Figure 7. Training performance and loss value across training epochs in DeepLA-24 with different deep supervision strategies. (a) mIoU score, and (b) loss value. + +![](images/e30fcbf93fb366c617c14053ee2315291138777a253d7ca7f521d48c8d28ac58.jpg) + +ure 7. It is evident that the network without deep supervision exhibits a slow decline in loss, with almost no further decrease after 60 epochs. In contrast, networks using deep supervision consistently achieve higher performance and a rapid convergence in loss. Notably, the network employing the HDS strategy achieves the most reasonable and effective convergence. This result demonstrates that our HDS strategy significantly optimizes network training, facilitating a robust and substantial decline in loss. + +Ablation of Network Depth for Feature Learning. We visualize the feature similarity matrix of DeepLA-Net with different depths in Figure 8. The matrix is obtained by calculating the cosine similarities of the point features in the final layer, which are then sorted according to the predicted categories. The results indicate that the feature learning of DeepLA-6 is not robust, resulting in numerous recognition errors during segmentation. In contrast, DeepLA-24 demonstrates stronger feature learning capabilities, though the feature differences between classes are not sufficiently distinct, potentially causing blurred boundaries. DeepLA120 demonstrates the highest confidence in class distinction, showcasing the most powerful feature learning abilities among the three networks. This result demonstrates that deeper networks possess more powerful learning capabilities, enhancing segmentation performance. + +Analysis on Complexity and Latency. We report the performance, model complexity, and latency using the same settings of DeepLA-Net family and previous SOTA methods [10, 48, 62, 81] in Table 7. From the results, the baseline exhibits the fastest inference speed but the lowest performance. Simply deepening the baseline (Plain-24) enhances performance but significantly increases FLOPs $(9\times$ higher) and decreases inference speed $(4.7\times$ slower). In contrast, DeepLA-24, equipped with the ResLFE block achieves performance improvements while substantially reducing FLOPs $(10\times$ fewer) and increasing inference speed $(3.75\times$ faster). The reduction in FLOPs enables the training of deeper networks. In particular, our DeepLA-120 achieves state-of-the-art performance with an inference + +![](images/48e817e661350c6a29b71140d9173e197e82b43d3a7580fd1d1266148174144e.jpg) + +![](images/1591b2f90acec316254a7c4044f8b27ae0096f692f0b540a82eccb6b9c59ab07.jpg) + +![](images/3251716dd3ec5331f4face9036bd32cf5974a1a1f1798d9c9ce34aae3f800142.jpg) +Figure 8. Visual comparison of interpreting feature similarity matrix with different network depth of the DeepLA-6 (6-block network follows [1:1:3:1] ratio), DeepLA-24, and DeepLA-120. + +![](images/8e9305bf4d12dc0c26fb7e2b381684b9ea60f2bd6984ee441ab19a54be88b778.jpg) + +Table 7. Quantitative comparisons of performance, model complexity, and latency on S3DIS Area5. + +
MethodmIoU (%)Params. (M)FLOPs (G)Thr. Put (ins./sec.)
PointNeXt-XL [48]70.846.184.843
PointVector-XL [10]72.324.158.540
KPConvX-L [62]73.513.5-47
PDNet-XXL [81]72.335.612.0-
Baseline63.43.111.3207
Plain-2469.09.792.244
DeepLA-2473.26.49.2165
DeepLA-6074.815.821.578
DeepLA-12075.730.342.742
+ +speed comparable to Plain-24 and the previous SOTA works [10, 48, 62]. More ablation analysis and discussion details can be found in Appendix. + +# 6. Conclusions + +In this study, we demonstrate the efficiency and effectiveness of very deep local aggregation networks for point cloud analysis, addressing two primary challenges: computational cost and training optimization. In contrast to most current approaches that rely on expensive and redundant local representation, we propose a lightweight ResLFE block to significantly reduce the computational cost ( $10 \times$ fewer FLOPs), and make it possible to construct very deep LANets. Furthermore, the HDS strategy is also introduced to ensure smooth gradient backpropagation and mitigate optimization challenges in deep networks. 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In AAAI Conference on Artificial Intelligence, 2024. 6, 7 \ No newline at end of file diff --git a/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/images.zip b/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..bc141ed9dfe5704e81891c4b04accc81546b3b39 --- /dev/null +++ b/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0aa8ba741bd163ee2adea73ca3ed851a6d9f9762596694a3da67e187257db890 +size 679867 diff --git a/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/layout.json b/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..06dafb9787bf869887c46ff83fadffa94bcc062f --- /dev/null +++ b/2025/DeepLA-Net_ Very Deep Local Aggregation Networks for Point Cloud Analysis/layout.json @@ -0,0 +1,10610 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 61, + 103, + 549, + 122 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 103, + 549, + 122 + ], + "spans": [ + { + "bbox": [ + 61, + 103, + 549, + 122 + ], + "type": "text", + "content": "DeepLA-Net: Very Deep Local Aggregation Networks for Point Cloud Analysis" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "spans": [ + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": "Ziyin Zeng" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": ", Mingyue Dong" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": ", Jian Zhou" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": ", Huan Qiu" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": ", Zhen Dong" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": ", Man Luo" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": " and Bijun Li" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": "Wuhan University, " + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 79, + 142, + 529, + 172 + ], + "type": "text", + "content": "Dongfeng USharing Technology Co." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 174, + 548, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 174, + 548, + 186 + ], + "spans": [ + { + "bbox": [ + 62, + 174, + 548, + 186 + ], + "type": "text", + "content": "{zengziyin, dongmy, jianzhou, huanqiu, dongzhenwhu, lee}@whu.edu.cn, tc-luoman@dfmc.com.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 213, + 201, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 213, + 201, + 225 + ], + "spans": [ + { + "bbox": [ + 151, + 213, + 201, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "spans": [ + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "text", + "content": "Due to the irregular and disordered data structure in 3D point clouds, prior works have focused on designing more sophisticated local representation methods to capture these complex local patterns. However, the recognition performance has saturated over the past few years, indicating that increasingly complex and redundant designs no longer make improvements to local learning. This phenomenon prompts us to diverge from the trend in 3D vision and instead pursue an alternative and successful solution: deeper neural networks. In this paper, we propose DeepLA-Net, a series of very deep networks for point cloud analysis. The key insight of our approach is to exploit a small but mighty local learning block, which uses " + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "text", + "content": " fewer FLOPs, enabling the construction of very deep networks. Furthermore, we design a training supervision strategy to ensure smooth gradient backpropagation and optimization in very deep networks. We construct the DeepLA-Net family with a depth of up to 120 blocks — at least " + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "text", + "content": " deeper than recent methods — trained on a single RTX 3090. An ensemble of the DeepLA-Net achieves state-of-the-art performance on classification and segmentation tasks of S3DIS Area5 (" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "inline_equation", + "content": "+2.2\\%" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "text", + "content": " mIoU), ScanNet test set (" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "inline_equation", + "content": "+1.6\\%" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "text", + "content": " mIoU), ScanObjectNN (" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "inline_equation", + "content": "+2.1\\%" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "text", + "content": " OA), and ShapeNetPart (" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "inline_equation", + "content": "+0.9\\%" + }, + { + "bbox": [ + 54, + 239, + 297, + 539 + ], + "type": "text", + "content": "CLS.mIoU). The code are released at https://github.com/zeng-ziyin/DeepLA-Net." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 552, + 135, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 135, + 565 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 135, + 565 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 572, + 295, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 572, + 295, + 656 + ], + "spans": [ + { + "bbox": [ + 55, + 572, + 295, + 656 + ], + "type": "text", + "content": "Thanks to the significant development of 3D sensors, 3D point cloud analysis has garnered increasing attention in recent years and is widely applied in autonomous driving, smart cities, and robotics [18, 84]. However, 3D point clouds consist of sparse, discrete, and non-uniform point sets embedded in continuous space [46]. This complex structure poses challenges to local pattern learning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 657, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 657, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 657, + 296, + 693 + ], + "type": "text", + "content": "In order to solve this problem, extensive explorations have been conducted on the local pattern of point clouds to enable fine-grained analysis. Inspired by CNNs, they intro-" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 328, + 207, + 543, + 409 + ], + "blocks": [ + { + "bbox": [ + 328, + 207, + 543, + 409 + ], + "lines": [ + { + "bbox": [ + 328, + 207, + 543, + 409 + ], + "spans": [ + { + "bbox": [ + 328, + 207, + 543, + 409 + ], + "type": "image", + "image_path": "010e3b29538d74f2a25cdff83dedeb3c7292b0054646bdae373e01fbf7cdf69f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 410, + 555, + 477 + ], + "lines": [ + { + "bbox": [ + 313, + 410, + 555, + 477 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 555, + 477 + ], + "type": "text", + "content": "Figure 1. Illustration of segmentation performance, model efficiency and network depth on S3DIS Area5. DeepLA-24 has already achieved SOTA-equivalent performance with minimal parameters. The deeper architecture DeepLA-120 achieves a milestone (75.7%) by exceeding 75% threshold for the first time, and outperforms Point Transformer v3 [70] with fewer parameters." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 485, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 556, + 715 + ], + "type": "text", + "content": "duce two robust inductive biases: locality and weight sharing, which promote the development of neural networks for analyzing 3D point clouds [47]. Specifically, these studies [10, 20, 33, 48, 56, 83, 85, 86] employ MLPs with shared weights to capture local features from neighbors. We collectively refer to them as local aggregation networks (LANets) in this paper. It is noteworthy that most LANets primarily focus on developing intricate local representation methods to explicitly explore the local patterns of point clouds, achieving success due to the robust inductive biases. However, the performance of increasingly sophisticated LANets on popular benchmarks [1, 9, 64, 80] has gradually saturated, as evidenced by minimal gains compare to PointNeXt [48] over the past few years, such as ScanObjectNN [64] (OA +0.4%, mAcc +0.5%, in Tab. 3) and ShapeNetPart [80] (cls.mIoU +0.4%, Ins.mIoU +0.2%, in Tab. 4). Particularly, the performance of most existing methods on S3DIS [1] has saturated around 73% [62, 70], as shown in Figure 1. The primary reason is that they already adequately" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 703, + 178, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 703, + 178, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 703, + 178, + 713 + ], + "type": "text", + "content": "* corresponding author: Jian Zhou" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1330" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "describe the local geometric properties of point clouds, and more complex designs no longer contribute to capturing additional local patterns [39, 48]. This phenomenon prompts us to rethink the design of LANets." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 122, + 295, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 122, + 295, + 314 + ], + "spans": [ + { + "bbox": [ + 55, + 122, + 295, + 314 + ], + "type": "text", + "content": "Interestingly, the development of 3D point cloud analysis is closely related to the evolution of 2D image processing networks [39, 47]. We observe that the design of 2D CNNs shifted towards deeper with the residual connections [19], making deep networks the mainstream backbone for feature extraction with successful performance [2, 35, 52]. Given that LANets for point clouds share similar inductive biases with CNNs, we cannot help but wonder: can we explore an alternative path by leveraging the success of deep CNNs for LANets? Unfortunately, to the best of our knowledge, there has been limited systematic exploration of deepening LANets. Therefore, in this paper, instead of following the tendency to explore sophisticated details, we are in pursuit of very deep LANets for point cloud analysis. For this purpose, we encounter two key challenges: (1) high computational cost, and (2) difficult training optimization." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 316, + 295, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 295, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 295, + 495 + ], + "type": "text", + "content": "Obviously, the prevailing philosophy of sophisticated and redundant local learning has significantly increased computational complexity. To circumvent the prohibitive computations, we propose a residual local feature extraction (ResLFE) block that ensures minimal computational cost. Specifically, we first employ stage-level positional embedding instead of redundant and high latency layer-level. We then introduce an efficient vector feature representation and a robust modernization structure that significantly reduces FLOPs while preserving local information interactions. As shown in Figure 2, the proposed ResLFE block shows significant computational efficiency " + }, + { + "bbox": [ + 55, + 316, + 295, + 495 + ], + "type": "inline_equation", + "content": "(10\\times" + }, + { + "bbox": [ + 55, + 316, + 295, + 495 + ], + "type": "text", + "content": " fewer FLOPs) and commendable performance improvements " + }, + { + "bbox": [ + 55, + 316, + 295, + 495 + ], + "type": "inline_equation", + "content": "(+1.1\\%" + }, + { + "bbox": [ + 55, + 316, + 295, + 495 + ], + "type": "text", + "content": " mIoU). In particular, this remarkable computational efficiency enables the construction of very deep networks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 497, + 295, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 497, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 497, + 295, + 687 + ], + "type": "text", + "content": "Furthermore, very deep networks are difficult to optimize [19, 72], and the complex geometric patterns of point clouds further exacerbate the difficulty of optimization [16, 44, 58]. To address these issues, we introduce a hybrid deep supervision (HDS) strategy to facilitate learning and optimization. We employ two forms of supervision to the outputs of the encoder at each stage. Specifically, we align each output with the ground truth using cross-entropy loss, which promotes smooth gradient propagation. Meanwhile, we also align the outputs with the spatial distribution of the point cloud using mean squared error loss, which benefits in fitting the complex geometric patterns to simplify network optimization. We demonstrate in experiments that the proposed HDS strategy optimizes network training by accelerating model convergence and achieves significant performance improvements " + }, + { + "bbox": [ + 55, + 497, + 295, + 687 + ], + "type": "inline_equation", + "content": "(+3.1\\% \\mathrm{mIoU})" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "Overall, we propose very Deep Local Aggregation Networks (DeepLA-Net), constructed from the ResLFE" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 228 + ], + "type": "text", + "content": "block for lightweight design and the HDS strategy for optimization. In particular, we have successfully trained DeepLA-120—a representative deep network comprising up to 120 ResLFE blocks—on a single RTX 3090 with 24GB memory. The DeepLA-Net family outperforms the SOTA methods across various tasks, including S3DIS [1] and ScanNetV2 [9] for semantic segmentation, ScanObjectNN [64] for object classification, and ShapeNetPart [80] for part segmentation. Figure 1 highlights the superior performance and efficiency of our DeepLA-Net family on S3DIS Area5. Moreover, a step-by-step procedure of constructing the DeepLA-Net and the corresponding results are shown in Figure 2. Our key contributions are:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 236, + 553, + 352 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 313, + 236, + 553, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 553, + 272 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 553, + 272 + ], + "type": "text", + "content": "- We propose a residual local feature extraction block from the perspective of efficiency and performance, enabling the construction of deeper LANets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 276, + 553, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 553, + 312 + ], + "type": "text", + "content": "- We propose a hybrid deep supervision strategy from the perspective of optimization and learning to ensure smooth gradient backpropagation in deeper LANets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 316, + 553, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 553, + 352 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 553, + 352 + ], + "type": "text", + "content": "- We propose DeepLA-Net, a series of very deep local aggregation networks, surpassing SOTA in classification, part segmentation, and semantic segmentation." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 363, + 400, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 363, + 400, + 374 + ], + "spans": [ + { + "bbox": [ + 314, + 363, + 400, + 374 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 383, + 484, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 383, + 484, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 383, + 484, + 396 + ], + "type": "text", + "content": "2.1. Deep Learning on Point Clouds" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 400, + 553, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 400, + 553, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 400, + 553, + 628 + ], + "type": "text", + "content": "Given the disordered and unstructured nature of 3D point clouds, directly applying traditional CNNs to them remains a challenge. Therefore, some methods firstly transform point clouds into intermediate representations such as 2D images [3, 26, 42, 73, 82] or 3D voxels [5, 7, 17, 27, 41, 93] through projection or voxelization, and subsequently employ 2D/3D CNNs to process these structured data. Although promising results have been shown in certain scenarios, the intermediate transformation steps may introduce information loss and computation costs [14, 51, 86]. In contrast, point-based methods [14, 20, 31, 46, 47, 51, 69, 83, 85, 86, 91] are specifically designed to perform feature learning directly on point clouds without using intermediate representations. Moreover, some noteworthy research has leveraged techniques like Recurrent Neural Networks (RNNs) [21, 34, 79], Graph Neural Networks (GNNs) [25, 28, 66, 75, 87], point-voxel hybrid representation [36, 37, 53, 74, 88], and sparse voxel [4, 8, 55, 59, 60], achieving significant performance in various tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 635, + 550, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 550, + 648 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 550, + 648 + ], + "type": "text", + "content": "2.2. Local Aggregation Networks for Point Clouds" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": "The pioneering PointNet [46] uses point-wise MLPs to learn per-point features, however, it has limitations in capturing local details. To overcome this, PointNet++ [47] improves PointNet by employing shared-weight MLPs in local neighbors, aligning with the inductive biases in CNNs:" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 313, + 757 + ], + "type": "text", + "content": "1331" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 313 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 313 + ], + "type": "text", + "content": "localization and weight sharing. Along this direction, numerous subsequent studies [30, 40, 63, 67, 69, 90] have employed the above two inductive biases by local feature aggregation operations. We summarize them as local aggregation networks (LANets). Recent LANets [10, 14, 20, 33, 43, 48, 51, 54, 83, 85, 86] have primarily focused on exploring more robust local representations. For example, Point Transformer [92] designs a local transformer layer based on vector self-attention in local neighbors. PointVector [10] improves local extractor by transforming relative features and positions of input into representative vectors. ConDaFormer [13] enhances local geometric modeling by depth-wise convolutions, capturing both long-range contextual information and local priors. However, with the development of LANets, merely development of more complex LANets is insufficient for further capturing the local patterns. In this paper, we demonstrate that without relying on intricate and complex local representations, designing very deep hierarchical architectures for LANets can also achieve significant breakthroughs in performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 321, + 134, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 321, + 134, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 321, + 134, + 335 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 341, + 296, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 341, + 296, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 341, + 296, + 426 + ], + "type": "text", + "content": "In this section, we introduce the preliminary implementation of DeepLA-Net. Most existing LANets have focused on robust local representation to effectively capture the complex local patterns of sparse and discrete point clouds. However, this focus makes them difficult to deepen due to the high computational cost. Therefore, we consider building deep networks based on the simplest PointNet++ [47]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 427, + 296, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 296, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 296, + 547 + ], + "type": "text", + "content": "PointNet++ [47], the pioneering LANet for point cloud analysis, can be summarized in two phases: position embedding and feature representation. In the position embedding phase, PointNet++ employs ball query to group points, and then uses relative position differences as position embedding. Subsequently, in the feature representation phase, PointNet++ concatenates position embedding and grouped features to represent local features, and then aggregates them to centroid points by using max pooling. This can be formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 563, + 295, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 563, + 295, + 597 + ], + "spans": [ + { + "bbox": [ + 62, + 563, + 295, + 597 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} p _ {i} ^ {k} = \\operatorname {G r o u p} \\left(p _ {i}\\right) \\\\ P E = \\mathcal {M} \\left(p _ {i} - p _ {i} ^ {k}\\right) \\end{array} \\quad \\left\\{ \\begin{array}{l} F _ {N} = \\mathcal {M} \\left[ f _ {i} ^ {k} \\oplus P E \\right] \\\\ F _ {\\text {o u t}} = \\max \\left(F _ {N}\\right) \\end{array} \\right. \\right. \\tag {1}", + "image_path": "a6fa0234dd5612b253a7e7a7fc6b61e734c9e81933bf6881d825760bb432acde.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "text", + "content": " denotes the centroid points, " + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "inline_equation", + "content": "p_i^k" + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "text", + "content": " denotes the grouped points, " + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "text", + "content": " denotes the multi-layer perceptron, " + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "text", + "content": " denotes the concatenation, max denotes the max-pooling, and " + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "inline_equation", + "content": "f_i^k" + }, + { + "bbox": [ + 55, + 602, + 295, + 652 + ], + "type": "text", + "content": " denotes the grouped features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": "Implementation. Due to its simplicity, we employ PointNet++ [47] as the baseline and demonstrate the step-by-step \"modernization\" into DeepLA-Net. Firstly, we follow the PointNeXt [48] configuration, incorporating data augmentation and optimization techniques such as random height" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 322, + 67, + 548, + 326 + ], + "blocks": [ + { + "bbox": [ + 322, + 67, + 548, + 326 + ], + "lines": [ + { + "bbox": [ + 322, + 67, + 548, + 326 + ], + "spans": [ + { + "bbox": [ + 322, + 67, + 548, + 326 + ], + "type": "image", + "image_path": "724b6af3ffb39dd6c145d58ccbb8dd715198ec2ab1fcd23320af0f85c45e3cf7.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 327, + 555, + 372 + ], + "lines": [ + { + "bbox": [ + 313, + 327, + 555, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 555, + 372 + ], + "type": "text", + "content": "Figure 2. Illustration of the designs and results of our improvements on S3DIS [1] Area5 step-by-step. The foreground bars denote model accuracy, the stars denote model FLOPs, and hatched bars mean the modification is not adopted solely." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 380, + 555, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 555, + 537 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 555, + 537 + ], + "type": "text", + "content": "and color dropout. The baseline model achieves " + }, + { + "bbox": [ + 313, + 380, + 555, + 537 + ], + "type": "inline_equation", + "content": "63.4\\%" + }, + { + "bbox": [ + 313, + 380, + 555, + 537 + ], + "type": "text", + "content": " mIoU and 11.3G FLOPs1. Subsequently, we directly extend the baseline to 24-block model, following [35] with a block ratio of [1:1:3:1]. This plain-24 model achieves " + }, + { + "bbox": [ + 313, + 380, + 555, + 537 + ], + "type": "inline_equation", + "content": "69.0\\%" + }, + { + "bbox": [ + 313, + 380, + 555, + 537 + ], + "type": "text", + "content": " mIoU and 92.2G FLOPs. Despite achieving a respectable mIoU score, the huge FLOPs prevent us from further deepening the network. In addition, deep network poses optimization challenges. Therefore, to construct LANets as deep as possible, we propose the ResLFE block which significantly reduces the computation cost while preserving reliable accuracy. Subsequently, we propose the HDS strategy to ensure smooth gradient backpropagation in deep networks and mitigate training optimization challenges." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 546, + 398, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 398, + 560 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 398, + 560 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 566, + 554, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 566, + 554, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 554, + 639 + ], + "type": "text", + "content": "In this section, we introduce the key components of our DeepLA-Net: residual local feature extraction (ResLFE) block and hybrid deep supervision (HDS) strategy. To intuitively and clearly demonstrate the role of each design, we illustrate each step of improvement in Figure 2, with all models evaluated on S3DIS Area 5 [1]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 645, + 528, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 645, + 528, + 657 + ], + "spans": [ + { + "bbox": [ + 313, + 645, + 528, + 657 + ], + "type": "text", + "content": "4.1. Residual Local Feature Extraction Block" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 662, + 554, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 662, + 554, + 687 + ], + "spans": [ + { + "bbox": [ + 313, + 662, + 554, + 687 + ], + "type": "text", + "content": "To enable the construction of deeper networks, we propose the ResLFE block, as shown in Figure 3, which significantly" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "text", + "content": "FLOPs calculation follows the settings of PointNeXt [48] which evaluated on S3DIS with " + }, + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "inline_equation", + "content": "16 \\times 15" + }, + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "text", + "content": ", 000 points." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1332" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 68, + 282, + 210 + ], + "blocks": [ + { + "bbox": [ + 75, + 68, + 282, + 210 + ], + "lines": [ + { + "bbox": [ + 75, + 68, + 282, + 210 + ], + "spans": [ + { + "bbox": [ + 75, + 68, + 282, + 210 + ], + "type": "image", + "image_path": "0ef439624a33fe11f9097f47d0e3a0622206be35f49626e59c12f143ba081f6b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 213, + 295, + 246 + ], + "lines": [ + { + "bbox": [ + 55, + 213, + 295, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 295, + 246 + ], + "type": "text", + "content": "Figure 3. Illustration of the proposed ResLFE block. Right: stage-level position embedding. Middle: Vector Feature Representation (VFR.) module. Left: modernization structure." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 62, + 254, + 290, + 335 + ], + "blocks": [ + { + "bbox": [ + 62, + 254, + 290, + 335 + ], + "lines": [ + { + "bbox": [ + 62, + 254, + 290, + 335 + ], + "spans": [ + { + "bbox": [ + 62, + 254, + 290, + 335 + ], + "type": "image", + "image_path": "fdbd61f09272a97fb4d8c252b5d93ee64616df89f7cdcee15fdc4753ebd19b98.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 337, + 295, + 360 + ], + "lines": [ + { + "bbox": [ + 55, + 337, + 295, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 337, + 295, + 360 + ], + "type": "text", + "content": "Figure 4. Illustration of the computational latency of position embedding and feature representation phases in different LANets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 371, + 296, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 371, + 296, + 418 + ], + "spans": [ + { + "bbox": [ + 55, + 371, + 296, + 418 + ], + "type": "text", + "content": "reduces computational cost. The ResLFE block comprises three key aspects: (1) stage-level position embedding, (2) efficient vector feature representation module, and (3) powerful modernization structure." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 422, + 296, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 296, + 674 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 296, + 674 + ], + "type": "text", + "content": "Stage-Level Position Embedding: Existing LANets typically implement position embedding at each learning layer, resulting in high computational costs. As shown in Figure 4, the computational latency of the positional embedding phase constitutes approximately half of the total for each layer, which is unacceptable in deeper networks. As indicated by Eq. 1, we observe that the computation of position embedding relies solely on point coordinates. Considering that the resolution of points remains constant within each stage, layers in the same stage can share an identical position embedding. Therefore, we suggest pre-calculate the position embedding at the beginning of each stage, saving it to cache and reusing it per-layer in that stage to avoid subsequent real-time computations. This approach ensures that the computational costs of position embedding depend solely on the number of stages, rather than the depth of the network, thereby facilitating the efficient application of very deep networks. Our implementation of position embedding is the same as PointNet++. This operation approximately halves the FLOPs (92.2G → 44.6G), with only a minimal decrease in performance (69.0% → 68.6%)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "Vector Feature Representation Module: First, we consider further improvements in computational efficiency during the feature representation phase. We observe that, in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": "most existing LANets, feature abstraction (linear layers in Eq. 1) is typically performed after grouping the features into " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "f_{i}^{k} \\in \\mathbb{R}^{N \\times K \\times C}" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": ", which incurs substantial computational costs. To address this issue, we suggest conducting feature abstraction before grouping on " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "f_{i} \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": " (front-linear). Although this approach may limit local information interactions, it allows for a reduction in FLOPs by " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": " times theoretically, leading to significant efficiency gains. Practically, this operation reduces the " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "7 \\times" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": " FLOPs " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "(44.6\\mathrm{G} \\rightarrow 6.3\\mathrm{G})" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": ", with a performance degradation of only " + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "inline_equation", + "content": "(68.6\\% \\rightarrow 67.4\\%)" + }, + { + "bbox": [ + 313, + 72, + 553, + 192 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "text", + "content": "Moreover, we suggest employing the vector feature " + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "inline_equation", + "content": "f_{i} - f_{i}^{k}" + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "text", + "content": " instead of the grouped feature " + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "inline_equation", + "content": "f_{i}^{k}" + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "text", + "content": ". On the one hand, this approach achieves cost-effective local interaction, which can enhance relation learning. On the other hand, it aligns with the relative position embedding " + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "inline_equation", + "content": "p_{i} - p_{i}^{k}" + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "text", + "content": ", mitigating the potential semantic gap between position embedding and feature representation. This operation improves performance by " + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "inline_equation", + "content": "67.4\\% \\rightarrow 68.6\\%" + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "text", + "content": ") without incurring additional computation costs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "text", + "content": "Furthermore, when combining the vector feature with the relative position embedding, we replace concatenation " + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "inline_equation", + "content": "(\\oplus)" + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "text", + "content": " with simple addition " + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "inline_equation", + "content": "(+)" + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "text", + "content": ", avoiding duplicating channels, which further reduces computational demands. This operation reduces computation " + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "inline_equation", + "content": "(6.3\\mathrm{G}\\rightarrow 4.4\\mathrm{G})" + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "text", + "content": " while only marginally decreasing performance " + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "inline_equation", + "content": "(68.6\\% \\to 68.4\\%)" + }, + { + "bbox": [ + 313, + 300, + 555, + 407 + ], + "type": "text", + "content": ". Finally, we employ the simple but effective max pooling for aggregation. The vector feature representation (VFR) module can be formulated as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 373, + 419, + 553, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 419, + 553, + 464 + ], + "spans": [ + { + "bbox": [ + 373, + 419, + 553, + 464 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} f _ {i} ^ {\\prime} = \\mathcal {M} \\left(f _ {i}\\right) \\\\ F _ {i} ^ {k} = f _ {i} ^ {\\prime} - f _ {i} ^ {\\prime k} \\\\ F _ {\\text {o u t}} = \\max \\left(F _ {i} ^ {k} + P E\\right) \\end{array} \\right. \\tag {2}", + "image_path": "06c4223f4d1504b9270c68fcb23d0051075379cf21a832a0c8d717caee8765f9.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": "Modernization Structure: Inspired by powerful Transformers [12, 65], we adopt a modernization structure, as shown in Figure 3-(a). Similar to the Transformer block, we employ a dropout path after normalization to mitigate overfitting in deep networks. Notably, unlike the " + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": " Inverted Bottleneck Feed Forward Network in Transformer, which increases the channel dimension, our implementation maintains the same dimensions in the two linear layers of the FFN to conserve computational resources. We can observe that the vanilla modern structure improves performance by " + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "inline_equation", + "content": "68.4\\% \\rightarrow 70.5\\%" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": "), but incurs significant additional computations (" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "inline_equation", + "content": "4.4\\mathrm{G} \\rightarrow 21.2\\mathrm{G}" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": "). By removing the " + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": " inverted bottleneck, we reduce the FLOPs by approximately half (" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "inline_equation", + "content": "21.2\\mathrm{G} \\rightarrow 9.2\\mathrm{G}" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": "), with only a " + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": " decrease in performance (" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "inline_equation", + "content": "70.5\\% \\rightarrow 70.1\\%" + }, + { + "bbox": [ + 313, + 473, + 554, + 652 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": "At this point, we have construct the vanilla DeepLA-24. Compare to the plain-24 model, the vanilla DeepLA-24 improves performance by " + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "inline_equation", + "content": "(69.0\\% \\rightarrow 70.1\\%)" + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": " while using only " + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": " FLOPs " + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "inline_equation", + "content": "(92.2\\mathrm{G}\\rightarrow 9.2\\mathrm{G})" + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": ". This small but mighty design enables the construction of deeper networks." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1333" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 298, + 167 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 298, + 167 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 298, + 167 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 298, + 167 + ], + "type": "image", + "image_path": "3d809a700d45b4a50b7f673946e8ef5eb0223cb1782d6536754491b4ebb68bb7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 81, + 171, + 270, + 182 + ], + "lines": [ + { + "bbox": [ + 81, + 171, + 270, + 182 + ], + "spans": [ + { + "bbox": [ + 81, + 171, + 270, + 182 + ], + "type": "text", + "content": "Figure 5. Illustration of the proposed HDS strategy." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 193, + 239, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 193, + 239, + 206 + ], + "spans": [ + { + "bbox": [ + 55, + 193, + 239, + 206 + ], + "type": "text", + "content": "4.2. Hybrid Deep Supervision Strategy" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 211, + 296, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 211, + 296, + 284 + ], + "spans": [ + { + "bbox": [ + 55, + 211, + 296, + 284 + ], + "type": "text", + "content": "In this section, we propose the HDS strategy, as illustrated in Figure 5. By incorporating supervision signals at each encoding stage, we facilitate smoother gradient propagation and simplify network optimization. The HDS strategy comprises two key aspects: (1) semantic probability supervision, and (2) spatial distribution supervision." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 287, + 296, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 287, + 296, + 467 + ], + "spans": [ + { + "bbox": [ + 55, + 287, + 296, + 467 + ], + "type": "text", + "content": "Semantic Probability Supervision: Despite employing techniques such as residual connections, normalization, and dropout, optimizing very deep networks remains a challenge. The proposed semantic probability supervision encourages hidden layers to learn discriminative features, which facilitates faster convergence and regularization of the network. Specifically, the outputs of each stage are fed into a VFR module without position embedding, ensuring that the supervised signals closely reflect our training process. Then, they are processed by a plain linear layer to align with the ground truth labels. Finally, we use the widely-used weighted cross-entropy loss to calculate the loss at each stage. The loss for semantic probability supervision " + }, + { + "bbox": [ + 55, + 287, + 296, + 467 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{sem})" + }, + { + "bbox": [ + 55, + 287, + 296, + 467 + ], + "type": "text", + "content": " is defined as the average of all stages, which can be formulated as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 99, + 478, + 295, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 478, + 295, + 512 + ], + "spans": [ + { + "bbox": [ + 99, + 478, + 295, + 512 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s e m} (Y, P) = - \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\sum_ {c = 0} ^ {C} y _ {i} ^ {c} \\log p _ {i} ^ {c} \\tag {3}", + "image_path": "34d6d1dfe3bdce35a760bb0008d06fd4bd9fad4927cc4387dbebeaaed53fcd80.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "inline_equation", + "content": "y_{i}^{c}" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": " denotes the label vector of the " + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": "-stage, " + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "inline_equation", + "content": "p_{i}^{c}" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": " denotes the predicted vector of the " + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": "-stage, " + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": " is the number of label categories, and " + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": " denotes the number of stages. This operation improves performance by " + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "inline_equation", + "content": "70.1\\% \\rightarrow 72.2\\%" + }, + { + "bbox": [ + 55, + 518, + 296, + 579 + ], + "type": "text", + "content": ") without additional inference computational costs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "content": "Spatial Distribution Supervision: The sparsity and discreteness of point clouds lead to intricate complex local geometric patterns, which further exacerbate the challenges of optimizing very deep networks. To address this issue, we assume that the feature distribution is potentially consistent with the spatial distribution of the point clouds. In the early epochs of training, feature learning should trend toward fitting these geometric structures. Therefore, we propose the spatial distribution supervision that serves as a manual prior for convergence, explicitly guiding feature learning towards geometric structures during the early epochs of training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": "Specifically, we represent the spatial distribution by calculating the grouped points with a learnable linear layer. The weights are initialized as an identity matrix and without bias, while the input and output channels are set to 3. Subsequently, we use this spatial distribution to constrain the grouped features obtained during semantic probability supervision. Finally, we adopt the mean squared error (MSE) loss to minimize the discrepancy between the spatial supervision signals and the grouped features. The loss of spatial distribution supervision " + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{spa})" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": " is defined as the average of all stages, which can be formulated as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 364, + 213, + 555, + 245 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 213, + 555, + 245 + ], + "spans": [ + { + "bbox": [ + 364, + 213, + 555, + 245 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s p a} (Y, P) = - \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\left(p _ {i} - y _ {i}\\right) ^ {2} \\tag {4}", + "image_path": "d25d9d920ef8f77bc6023b5b3ddb90882630c03b58b4ea5a5a01440d5a008dad.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "spans": [ + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "content": " denotes the spatial supervision signals of the " + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "content": "-stage, " + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "inline_equation", + "content": "p_{i}" + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "content": " denotes the predicted results from feature relative differences of the " + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "content": "-stage, and " + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "content": " denotes the number of encoder stages. This operation improves performance by " + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "inline_equation", + "content": "70.1\\% \\rightarrow 71.8\\%" + }, + { + "bbox": [ + 313, + 247, + 555, + 307 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "text", + "content": "Hybrid Loss: The loss function of the network integrates " + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "inline_equation", + "content": "L_{sem}" + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "inline_equation", + "content": "L_{spa}" + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "text", + "content": ", and the segmentation loss of final prediction " + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "inline_equation", + "content": "(L_{pred})" + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "text", + "content": ", which is calculated via cross-entropy loss. Furthermore, we implement different training weights with exponential decay for " + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "inline_equation", + "content": "L_{sem}" + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "inline_equation", + "content": "L_{spa}" + }, + { + "bbox": [ + 313, + 310, + 555, + 441 + ], + "type": "text", + "content": ", where the decay factor is defined as the reciprocal of the current epoch number. This strategy ensures that deep supervision provides significant guidance in the early training phases, while gradually diminishes its influence to avoid hindering the primary learning path as training progresses. The hybrid loss can be formulated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 326, + 453, + 555, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 453, + 555, + 468 + ], + "spans": [ + { + "bbox": [ + 326, + 453, + 555, + 468 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {H}} = \\alpha^ {n} \\mathcal {L} _ {s e m} + \\beta^ {n} \\mathcal {L} _ {s p a} + (1 - \\alpha^ {n} - \\beta^ {n}) \\mathcal {L} _ {p r e d} \\quad (5)", + "image_path": "750eaa55e2f6f9805ed079a27f61284478e52593d803de80c05889a179fd0b9f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "text", + "content": " are the training weights for supervision, " + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "text", + "content": " denotes reciprocal of the current epoch number. This hybrid loss improves performance by " + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "inline_equation", + "content": "3.1\\%" + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "inline_equation", + "content": "70.1\\% \\rightarrow 73.2\\%" + }, + { + "bbox": [ + 313, + 472, + 554, + 509 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 514, + 474, + 527 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 514, + 474, + 527 + ], + "spans": [ + { + "bbox": [ + 313, + 514, + 474, + 527 + ], + "type": "text", + "content": "4.3. DeepLA-Net Implementation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 531, + 554, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 554, + 602 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 554, + 602 + ], + "type": "text", + "content": "We construct a series of DeepLA-Net with different depths: DeepLA-24/60/120. Following successful previous works [12, 35, 92], the block ratio within each stage is set to [1:1:3:1], and the number of channels doubles in the subsequent stage. The configuration of DeepLA-Net is summarized as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 323, + 604, + 421, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 604, + 421, + 616 + ], + "spans": [ + { + "bbox": [ + 323, + 604, + 421, + 616 + ], + "type": "interline_equation", + "content": "C = [ 6 4, 1 2 8, 2 5 6, 5 1 2 ]", + "image_path": "2905c4b4e90102a0f54531f2e90bf1aa5ae6d9fd3500d78b1620ebde87e9a80a.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 616, + 463, + 652 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 315, + 616, + 444, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 616, + 444, + 628 + ], + "spans": [ + { + "bbox": [ + 315, + 616, + 444, + 628 + ], + "type": "text", + "content": "- DeepLA-24: " + }, + { + "bbox": [ + 315, + 616, + 444, + 628 + ], + "type": "inline_equation", + "content": "B = \\left\\lbrack {4,4,{12},4}\\right\\rbrack" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 628, + 459, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 628, + 459, + 640 + ], + "spans": [ + { + "bbox": [ + 315, + 628, + 459, + 640 + ], + "type": "text", + "content": "- DeepLA-60: " + }, + { + "bbox": [ + 315, + 628, + 459, + 640 + ], + "type": "inline_equation", + "content": "B = \\left\\lbrack {{10},{10},{30},{10}}\\right\\rbrack" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 315, + 641, + 463, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 641, + 463, + 652 + ], + "spans": [ + { + "bbox": [ + 315, + 641, + 463, + 652 + ], + "type": "text", + "content": "- DeepLA-120: " + }, + { + "bbox": [ + 315, + 641, + 463, + 652 + ], + "type": "inline_equation", + "content": "B = \\left\\lbrack {{20},{20},{60},{20}}\\right\\rbrack" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "text", + "content": " refers to the channels of the output and " + }, + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "text", + "content": " denotes the number of ResLFE blocks in each stage. Note that, in this paper, the term \"depth\" specifically refers to the number of blocks rather than linear layers. The network architecture details can be found in Appendix." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1334" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 92, + 294, + 308 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 295, + 92 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 295, + 92 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 295, + 92 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons of semantic segmentation with the SOTA methods on S3DIS in terms of mIoU." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 92, + 294, + 308 + ], + "lines": [ + { + "bbox": [ + 56, + 92, + 294, + 308 + ], + "spans": [ + { + "bbox": [ + 56, + 92, + 294, + 308 + ], + "type": "table", + "html": "
YearMethod6-flod (%)Area5 (%)
NIPS 2017PointNet++ [47]83.053.5
NIPS 2018PointCNN [30]65.457.3
CVPR 2019KPConv [61]70.667.1
CVPR 2020RandLA-Net [20]70.062.5
CVPR 2021Point Trans. [92]73.570.4
NIPS 2022PointNeXt [48]74.970.8
CVPR 2023AF-GCN [89]77.772.3
CVPR 2023PointVector [10]78.472.3
CVPR 2023PointMeta [33]77.072.0
AAAI 2024PDNet [81]78.372.3
CVPR 2024KPConvX [62]-73.5
CVPR 2024OneFormer3D [23]75.072.4
CVPR 2024Point Trans. v3 [70]77.773.4
ACM MM 2024OPFR [22]76.972.6
ACM MM 2024LDCNet [38]75.471.8
ACM MM 2024MBSE [68]77.872.4
Ours 2024DeepLA-2477.973.2
Ours 2024DeepLA-6079.074.8
Ours 2024DeepLA-12079.875.7
", + "image_path": "93202b7c74bc29cbc7a7429b73213e1376c766121acf1debf857d05ff24373c3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 324, + 136, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 136, + 338 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 136, + 338 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 345, + 163, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 345, + 163, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 345, + 163, + 358 + ], + "type": "text", + "content": "5.1. Experiment Setup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 363, + 295, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 363, + 295, + 470 + ], + "spans": [ + { + "bbox": [ + 55, + 363, + 295, + 470 + ], + "type": "text", + "content": "To comprehensively evaluate the effectiveness of the proposed DeepLA-Net, we conduct experiments on S3DIS [1] and ScanNet v2 [9] for semantic segmentation, ScanObjectNN [64] for object classification, and ShapeNetPart [80] for object part segmentation. We use the following quantitative metrics for evaluation: mean Intersection over Union (mIoU), Overall Accuracy (OA), and mean Accuracy (mAcc). In result tables, Bold indicates the best result, underline indicates the best result excluding ours." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "type": "text", + "content": "In the position embedding phase, we employ the KNN for grouping, with the " + }, + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "type": "text", + "content": " specified as 24. For hybrid deep supervision, " + }, + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 471, + 295, + 579 + ], + "type": "text", + "content": " are set to 0.3 and 0.005, respectively. All experiments are performed on a Nvidia RTX 3090 GPU with 24GB memory. To ensure a fair comparison, the reported performance for both ours and the compared methods excludes the use of voting, pre-trained model, and test-time augmentation strategies. The implementation details and dataset description can be found in Appendix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 588, + 170, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 588, + 170, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 588, + 170, + 601 + ], + "type": "text", + "content": "5.2. Experiment Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": "Semantic Segmentation. We show the results of our DeepLA-Net, including DeepLA-24/60/120, compared with previous state-of-the-art methods on S3DIS and ScanNet v2. In Table 1, for S3DIS, our DeepLA-60 has already surpassed previous methods. Particularly, our DeepLA-120 achieves a more significant breakthrough with an mIoU of " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "79.8\\%" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " in 6-fold " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "(+1.4\\%)" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "75.7\\%" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "(+2.2\\%)" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " in Area5, surpassing the " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " threshold for the first time. In Table 2, for ScanNet v2, our DeepLA-24/60 achieve competitive perfor" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 92, + 553, + 308 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 553, + 91 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 553, + 91 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 553, + 91 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons of semantic segmentation with the SOTA methods on ScanNet v2 in terms of mIoU." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 92, + 553, + 308 + ], + "lines": [ + { + "bbox": [ + 315, + 92, + 553, + 308 + ], + "spans": [ + { + "bbox": [ + 315, + 92, + 553, + 308 + ], + "type": "table", + "html": "
YearMethodval (%)test (%)
NIPS 2017PointNet++ [47]53.555.7
NIPS 2018PointCNN [30]-45.8
CVPR 2019KPConv [61]69.268.6
CVPR 2022Stra. Trans. [24]74.373.7
NIPS 2022PointNeXt [48]71.571.2
CVPR 2023LRPNet [29]75.074.2
ICCV 2023Retro-FPN [71]74.074.4
NIPS 2023ConDaFormer [13]75.175.5
AAAI 2024HPENet [94]74.0-
ICLR 2024MVNet [76]75.2-
CVPR 2024KPConvX [62]76.3-
CVPR 2024OneFormer3D [23]76.6-
CVPR 2024OA-CNN [45]76.175.6
CVPR 2024MirageRoom [57]74.9-
ACM MM 2024LDCNet [38]73.3-
Ours 2024DeepLA-2474.1-
Ours 2024DeepLA-6075.9-
Ours 2024DeepLA-12077.677.2
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YearMethodOA (%)mAcc (%)
CVPR 2017PointNet [46]68.263.4
NIPS 2018PointCNN [30]78.575.1
TOG 2019DGCNN [67]78.173.6
TMM 2021GBNet [50]80.577.8
TIP 2021PRANet [6]82.179.1
ICLR 2022PointMLP [39]85.784.4
NIPS 2022PointNeXt [48]88.186.4
PAMI 2023GSLCN [32]85.884.1
ICLR 2023ACT [11]88.2-
CVPR 2023NLGAT [49]88.4-
CVPR 2023PointVector [10]88.286.7
CVPR 2023PointMeta [33]88.186.9
AAAI 2024PDNet [81]88.586.8
AAAI 2024Interpretable3D [15]88.086.5
ICLR 2024MaskFeat3D [77]88.4-
ACM MM 2024OPFR [22]88.186.3
Ours 2024DeepLA-2490.689.5
", + "image_path": "05e7d593bd1dfb8fe244f142cca0ea9d0a5127150ac95f64e45df608b8114e54.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "text", + "content": "mance, while DeepLA-120 significantly outperforms previous methods, achieving " + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "inline_equation", + "content": "77.6\\%" + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "inline_equation", + "content": "(+1.0\\%)" + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "text", + "content": " on the validation set and " + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "inline_equation", + "content": "77.2\\%" + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "inline_equation", + "content": "(+1.6\\%)" + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "text", + "content": " on the test sets. Note that, due to the submission policy of the ScanNet v2 online test set, we only report the best model on the validation set, i.e., DeepLA-120. Additionally, results on the ScanNet test set have been reported less in recent years because fully supervised methods have not achieved substantial breakthroughs in this dataset. The result of the efficient DeepLA-24 demonstrates the rationality and effectiveness of our design. Furthermore, reasonably deepening the network can significantly improve performance. More detailed per-class results and visualizations can be found in Appendix." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1335" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 94, + 294, + 300 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 295, + 92 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 295, + 92 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 295, + 92 + ], + "type": "text", + "content": "Table 4. Quantitative comparisons of part segmentation with the SOTA methods on ShapeNetPart." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 94, + 294, + 300 + ], + "lines": [ + { + "bbox": [ + 58, + 94, + 294, + 300 + ], + "spans": [ + { + "bbox": [ + 58, + 94, + 294, + 300 + ], + "type": "table", + "html": "
YearMethodCls. mIoU (%)Ins. mIoU (%)
CVPR 2017PointNet [46]80.483.7
NIPS 2018PointCNN [30]84.686.1
TOG 2019DGCNN [67]82.385.1
CVPR 2020PointASNL [78]-86.1
CVPR 2021Point Trans. [92]83.786.6
ICLR 2022PointMLP [39]84.686.1
NIPS 2022PointNeXt [48]85.287.0
ICLR 2023ACT [11]84.786.1
CVPR 2023PointVector [10]85.186.9
CVPR 2023PointMeta [33]85.187.1
CVPR 2023AF-GCN [89]85.387.0
NIPS 2023ConDaFormer [13]84.686.8
AAAI 2024HPENet [94]85.587.1
AAAI 2024PDNet [81]85.487.2
AAAI 2024Interpretable3D [15]85.687.2
ICLR 2024MVNet [76]85.286.8
ICLR 2024MaskFeat3D [77]85.587.0
Ours 2024DeepLA-2486.588.0
", + "image_path": "154d54665c2d8dbcd0c709717df2c76ddec7f96160051124b14c6effe3175904.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "text", + "content": "Object Classification. As shown in Table 3, DeepLA-24 outperforms all baselines with OA of " + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "inline_equation", + "content": "90.6\\%" + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "text", + "content": " and mAcc of " + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "inline_equation", + "content": "89.5\\%" + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "inline_equation", + "content": "(+2.1\\%" + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "text", + "content": " OA, " + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "inline_equation", + "content": "+2.6\\%" + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "text", + "content": " mAcc). DeepLA-24 is the first method to surpass " + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "text", + "content": " on OA, with the performance of others stagnating around " + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "inline_equation", + "content": "88\\%" + }, + { + "bbox": [ + 55, + 312, + 296, + 420 + ], + "type": "text", + "content": " for several years. This result indicates that merely developing more complex local representation methods is not sufficient for further advancement in shape recognition. In contrast, deeper networks can make significant contributions to capturing local patterns." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "type": "text", + "content": "Part Segmentation. The results are reported in Table 4, where we evaluate the performance with the mean class IoU (Cls. mIoU) and mean instance IoU (Ins. mIoU). DeepLA-24 outperforms all baselines with the Cls. mIoU of " + }, + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "type": "inline_equation", + "content": "86.5\\%" + }, + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "type": "inline_equation", + "content": "(+1.0\\%)" + }, + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "type": "text", + "content": " and the Ins. mIoU of " + }, + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "type": "inline_equation", + "content": "88.0\\%" + }, + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "type": "inline_equation", + "content": "(+0.8\\%)" + }, + { + "bbox": [ + 55, + 423, + 296, + 518 + ], + "type": "text", + "content": " without voting. It is noteworthy that we do not experiment with the deeper variants of DeepLA-Net on object classification and part segmentation datasets due to the limited dataset scale." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 525, + 156, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 525, + 156, + 537 + ], + "spans": [ + { + "bbox": [ + 55, + 525, + 156, + 537 + ], + "type": "text", + "content": "5.3. Ablation Studies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 543, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 543, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 543, + 295, + 590 + ], + "type": "text", + "content": "In this section, we conduct ablation studies on the proposed DeepLA-Net. All the ablation models are evaluated on S3DIS Area5 [1]. If not specified, the DeepLA-24 is employed as the default model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "content": "Hyperparameter settings. We analyze the impact of hyperparameter settings including the bottleneck in ResLFE block, the training weights in HDS strategy, the initial feature channel, and the grouping range " + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "content": ". Table 5 explores different bottleneck settings in ResLFE block. The results illustrate that inverted bottlenecks larger than " + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "content": " marginally improve performance but significantly increase computation costs. Meanwhile, bottlenecks less than " + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "content": " slightly reduce computation while causing a more pronounced degradation in performance. Therefore, to balance" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 317, + 96, + 553, + 160 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 555, + 92 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 555, + 92 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 555, + 92 + ], + "type": "text", + "content": "Table 5. Ablation results of the bottleneck in ResLFE block in DeepLA-24 on S3DIS Area5." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 96, + 553, + 160 + ], + "lines": [ + { + "bbox": [ + 317, + 96, + 553, + 160 + ], + "spans": [ + { + "bbox": [ + 317, + 96, + 553, + 160 + ], + "type": "table", + "html": "
ModelmIoU (%)\\( \\bigtriangleup \\)(%)FLOPs (G)\\( \\bigtriangleup \\)(G)
1× bottleneck73.2-9.3-
0.5× bottleneck72.5-0.77.4-1.9
2× bottleneck73.4+0.213.4+4.1
4× bottleneck73.5+0.321.3+13.0
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α\\β03e-35e-37e-31e-2
070.171.071.871.370.6
0.271.872.372.572.972.0
0.372.272.573.272.872.4
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Ablation results of hyperparameters in DeepLA-24 on S3DIS Area5. (a) initial feature dimension. (b) grouping range K." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 470, + 555, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 470, + 555, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 470, + 555, + 662 + ], + "type": "text", + "content": "efficiency and performance, we employ the " + }, + { + "bbox": [ + 313, + 470, + 555, + 662 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 313, + 470, + 555, + 662 + ], + "type": "text", + "content": " bottleneck. Table 6 shows that the setting of training weights in HDS strategy is generally insensitive, as long as they are neither too large to hinder fitting nor too small to be ineffective. Notably, the training weight for spatial distribution is much smaller than that for semantic probability. This is mainly because spatial distribution supervision encourages the network to focus more on local details rather than abstract semantics, which are more crucial for feature classification. Figure 6 illustrates the impact of different initial feature channel and grouping range " + }, + { + "bbox": [ + 313, + 470, + 555, + 662 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 470, + 555, + 662 + ], + "type": "text", + "content": ". The results demonstrate that small channel and grouping range lead to limited performance, due to inadequacy in capturing local patterns. Meanwhile, excessively large channel and grouping range tend to overfit the training examples, resulting in poor generalization and a decline in performance." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "Ablation of Deep Supervision for Training Process. We demonstrate the performance and segmentation loss values " + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "inline_equation", + "content": "(L_{pred}" + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": " in Eq. 5) of the network with different deep supervision strategies across training epochs, as shown in Fig-" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1336" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 65, + 175, + 190 + ], + "blocks": [ + { + "bbox": [ + 57, + 65, + 175, + 190 + ], + "lines": [ + { + "bbox": [ + 57, + 65, + 175, + 190 + ], + "spans": [ + { + "bbox": [ + 57, + 65, + 175, + 190 + ], + "type": "image", + "image_path": "4b91d3264b6e9fcc8fadc4e735c45a81e0cd712e2f784e5191edad67fbd3703a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 191, + 295, + 223 + ], + "lines": [ + { + "bbox": [ + 55, + 191, + 295, + 223 + ], + "spans": [ + { + "bbox": [ + 55, + 191, + 295, + 223 + ], + "type": "text", + "content": "Figure 7. Training performance and loss value across training epochs in DeepLA-24 with different deep supervision strategies. (a) mIoU score, and (b) loss value." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 65, + 295, + 190 + ], + "blocks": [ + { + "bbox": [ + 175, + 65, + 295, + 190 + ], + "lines": [ + { + "bbox": [ + 175, + 65, + 295, + 190 + ], + "spans": [ + { + "bbox": [ + 175, + 65, + 295, + 190 + ], + "type": "image", + "image_path": "e30fcbf93fb366c617c14053ee2315291138777a253d7ca7f521d48c8d28ac58.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 237, + 296, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 237, + 296, + 344 + ], + "spans": [ + { + "bbox": [ + 54, + 237, + 296, + 344 + ], + "type": "text", + "content": "ure 7. It is evident that the network without deep supervision exhibits a slow decline in loss, with almost no further decrease after 60 epochs. In contrast, networks using deep supervision consistently achieve higher performance and a rapid convergence in loss. Notably, the network employing the HDS strategy achieves the most reasonable and effective convergence. This result demonstrates that our HDS strategy significantly optimizes network training, facilitating a robust and substantial decline in loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 350, + 296, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 296, + 541 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 296, + 541 + ], + "type": "text", + "content": "Ablation of Network Depth for Feature Learning. We visualize the feature similarity matrix of DeepLA-Net with different depths in Figure 8. The matrix is obtained by calculating the cosine similarities of the point features in the final layer, which are then sorted according to the predicted categories. The results indicate that the feature learning of DeepLA-6 is not robust, resulting in numerous recognition errors during segmentation. In contrast, DeepLA-24 demonstrates stronger feature learning capabilities, though the feature differences between classes are not sufficiently distinct, potentially causing blurred boundaries. DeepLA120 demonstrates the highest confidence in class distinction, showcasing the most powerful feature learning abilities among the three networks. This result demonstrates that deeper networks possess more powerful learning capabilities, enhancing segmentation performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "text", + "content": "Analysis on Complexity and Latency. We report the performance, model complexity, and latency using the same settings of DeepLA-Net family and previous SOTA methods [10, 48, 62, 81] in Table 7. From the results, the baseline exhibits the fastest inference speed but the lowest performance. Simply deepening the baseline (Plain-24) enhances performance but significantly increases FLOPs " + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "inline_equation", + "content": "(9\\times" + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "text", + "content": " higher) and decreases inference speed " + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "inline_equation", + "content": "(4.7\\times" + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "text", + "content": " slower). In contrast, DeepLA-24, equipped with the ResLFE block achieves performance improvements while substantially reducing FLOPs " + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "inline_equation", + "content": "(10\\times" + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "text", + "content": " fewer) and increasing inference speed " + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "inline_equation", + "content": "(3.75\\times" + }, + { + "bbox": [ + 55, + 546, + 296, + 713 + ], + "type": "text", + "content": " faster). The reduction in FLOPs enables the training of deeper networks. In particular, our DeepLA-120 achieves state-of-the-art performance with an inference" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 321, + 66, + 422, + 175 + ], + "blocks": [ + { + "bbox": [ + 321, + 66, + 422, + 175 + ], + "lines": [ + { + "bbox": [ + 321, + 66, + 422, + 175 + ], + "spans": [ + { + "bbox": [ + 321, + 66, + 422, + 175 + ], + "type": "image", + "image_path": "48e817e661350c6a29b71140d9173e197e82b43d3a7580fd1d1266148174144e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 426, + 65, + 529, + 175 + ], + "blocks": [ + { + "bbox": [ + 426, + 65, + 529, + 175 + ], + "lines": [ + { + "bbox": [ + 426, + 65, + 529, + 175 + ], + "spans": [ + { + "bbox": [ + 426, + 65, + 529, + 175 + ], + "type": "image", + "image_path": "1591b2f90acec316254a7c4044f8b27ae0096f692f0b540a82eccb6b9c59ab07.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 321, + 178, + 422, + 289 + ], + "blocks": [ + { + "bbox": [ + 321, + 178, + 422, + 289 + ], + "lines": [ + { + "bbox": [ + 321, + 178, + 422, + 289 + ], + "spans": [ + { + "bbox": [ + 321, + 178, + 422, + 289 + ], + "type": "image", + "image_path": "3251716dd3ec5331f4face9036bd32cf5974a1a1f1798d9c9ce34aae3f800142.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 290, + 553, + 323 + ], + "lines": [ + { + "bbox": [ + 313, + 290, + 553, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 290, + 553, + 323 + ], + "type": "text", + "content": "Figure 8. Visual comparison of interpreting feature similarity matrix with different network depth of the DeepLA-6 (6-block network follows [1:1:3:1] ratio), DeepLA-24, and DeepLA-120." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 427, + 178, + 547, + 289 + ], + "blocks": [ + { + "bbox": [ + 427, + 178, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 427, + 178, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 427, + 178, + 547, + 289 + ], + "type": "image", + "image_path": "8e9305bf4d12dc0c26fb7e2b381684b9ea60f2bd6984ee441ab19a54be88b778.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 317, + 354, + 553, + 466 + ], + "blocks": [ + { + "bbox": [ + 313, + 330, + 553, + 352 + ], + "lines": [ + { + "bbox": [ + 313, + 330, + 553, + 352 + ], + "spans": [ + { + "bbox": [ + 313, + 330, + 553, + 352 + ], + "type": "text", + "content": "Table 7. Quantitative comparisons of performance, model complexity, and latency on S3DIS Area5." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 354, + 553, + 466 + ], + "lines": [ + { + "bbox": [ + 317, + 354, + 553, + 466 + ], + "spans": [ + { + "bbox": [ + 317, + 354, + 553, + 466 + ], + "type": "table", + "html": "
MethodmIoU (%)Params. (M)FLOPs (G)Thr. Put (ins./sec.)
PointNeXt-XL [48]70.846.184.843
PointVector-XL [10]72.324.158.540
KPConvX-L [62]73.513.5-47
PDNet-XXL [81]72.335.612.0-
Baseline63.43.111.3207
Plain-2469.09.792.244
DeepLA-2473.26.49.2165
DeepLA-6074.815.821.578
DeepLA-12075.730.342.742
", + "image_path": "05093655c495cf54d30d875801ed22f49528336d2b334f3fbe443cd422c3f0f4.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 476, + 554, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 476, + 554, + 513 + ], + "spans": [ + { + "bbox": [ + 313, + 476, + 554, + 513 + ], + "type": "text", + "content": "speed comparable to Plain-24 and the previous SOTA works [10, 48, 62]. More ablation analysis and discussion details can be found in Appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 525, + 391, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 525, + 391, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 525, + 391, + 538 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 545, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 545, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 312, + 545, + 555, + 713 + ], + "type": "text", + "content": "In this study, we demonstrate the efficiency and effectiveness of very deep local aggregation networks for point cloud analysis, addressing two primary challenges: computational cost and training optimization. In contrast to most current approaches that rely on expensive and redundant local representation, we propose a lightweight ResLFE block to significantly reduce the computational cost (" + }, + { + "bbox": [ + 312, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 312, + 545, + 555, + 713 + ], + "type": "text", + "content": " fewer FLOPs), and make it possible to construct very deep LANets. Furthermore, the HDS strategy is also introduced to ensure smooth gradient backpropagation and mitigate optimization challenges in deep networks. The DeepLA-Net achieves SOTA performance with high efficiency across segmentation and classification tasks on four benchmarks: S3DIS, ScanNet v2, ScanObjectNN, and ShapeNetPart." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1337" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 704 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "type": "text", + "content": "[1] Iro Armeni, Ozan Sener, Amir R. 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In AAAI Conference on Artificial Intelligence, 2024. 6, 7" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1341" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_content_list.json b/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3f2840af162efbfb6ce45c4c8cda16c247f880a3 --- /dev/null +++ b/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_content_list.json @@ -0,0 +1,1627 @@ +[ + { + "type": "text", + "text": "DefMamba: Deformable Visual State Space Model", + "text_level": 1, + "bbox": [ + 243, + 130, + 754, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Leiye Liu $^{1}$ Miao Zhang $^{1,*}$ Jihao Yin $^{1}$ Tingwei Liu $^{1}$ Wei Ji $^{2}$ Yongri Piao $^{1,*}$ Huchuan Lu $^{1}$ $^{1}$ Dalian University of Technology $^{2}$ Yale University", + "bbox": [ + 114, + 179, + 879, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "leiyeliu@mail.dlut.edu.cn,wei.ji@yale.edu,yrpiao@dlut.edu.cn", + "bbox": [ + 225, + 219, + 776, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 268, + 326, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, state space models (SSM), particularly Mamba, have attracted significant attention from scholars due to their ability to effectively balance computational efficiency and performance. However, most existing visual Mamba methods flatten images into 1D sequences using predefined scan orders, which results the model being less capable of utilizing the spatial structural information of the image during the feature extraction process. To address this issue, we proposed a novel visual foundation model called DefMamba. This model includes a multi-scale backbone structure and deformable mamba (DM) blocks, which dynamically adjust the scanning path to prioritize important information, thus enhancing the capture and processing of relevant input features. By combining a deformable scanning (DS) strategy, this model significantly improves its ability to learn image structures and detects changes in object details. Numerous experiments have shown that DefMamba achieves state-of-the-art performance in various visual tasks, including image classification, object detection, instance segmentation, and semantic segmentation. The code is open source on DefMamba.", + "bbox": [ + 89, + 301, + 483, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 650, + 220, + 666 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most existing visual foundation models primarily rely on convolutional neural networks (CNNs) [25, 28, 32] and Transformer architectures [9, 24, 33]. However, CNNs are constrained by their sliding window structure, which limits the receptive field and significantly impedes global information aggregation across the input data. In contrast, Transformers excel in global information aggregation due to their attention mechanism, but their high computational complexity poses a challenge in achieving a balance between efficiency and performance. State space models (SSMs) [12] provide a potential solution to this trade-off. SSMs aggregate previous features through a hidden state matrix to update current features, thereby reducing the computational", + "bbox": [ + 89, + 676, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b746006dc09f3480b8bd51dc483afbf1c6b831768fb42154ddc66bddfbb6e4ae.jpg", + "image_caption": [ + "(a) Raster scanning" + ], + "image_footnote": [], + "bbox": [ + 522, + 268, + 640, + 361 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/240bbbc8ac05aa6eaab697097eb934d8555ac8db10935f13af476b482292acfe.jpg", + "image_caption": [ + "(b) Local scanning" + ], + "image_footnote": [], + "bbox": [ + 650, + 268, + 769, + 361 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c1686f77e4c3a741a8cb279de6aa2bba03e98bf6752142c3280709fa402d6bb.jpg", + "image_caption": [ + "(c) Continuous scanning" + ], + "image_footnote": [], + "bbox": [ + 777, + 268, + 898, + 361 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f0bfe0498799fd4537e7586b332300a82bd9e47fc6866d89d2faa7820a01428c.jpg", + "image_caption": [ + "(d) Deformable scanning" + ], + "image_footnote": [], + "bbox": [ + 521, + 381, + 660, + 488 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d8092b1aad8383b57f24758e18390d11e6faab60ae7a5c6a64693d893f90c4d1.jpg", + "image_caption": [ + "OffsetΔ" + ], + "image_footnote": [], + "bbox": [ + 676, + 391, + 741, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/24bc2d34f3f99430bcfaa0ebd123bcd5f30d4a40e4f22a5d586425df967c10e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 381, + 898, + 488 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4a1ed3c55a890b8b6ae824edec172f1c76c35301654634c492b5ed92e06269cf.jpg", + "image_caption": [ + "Fixed scan order", + "Deformable scan order", + "Figure 1. Comparison of deformable scanning and other scanning methods. (a) Raster scanning [23, 47], (b) Local scanning [19], (c) Continuous scanning [42], (d) Our designed deformable scanning. The blue dots represent the reference points, and the red dots represent the deformable points. The yellow arrows represent the fixed scan order, and the red gradient arrows represent the deformable scan order. Our method exhibits an enhanced capacity to accurately capture the structural characteristics of objects, thereby enabling the development of a more refined scanning approach." + ], + "image_footnote": [], + "bbox": [ + 540, + 506, + 586, + 532 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8f4f10d14633d0f0814c8491ee725ffae41b5567e00e3e2cf349bd469e8b9b1d.jpg", + "image_caption": [ + "Reference point" + ], + "image_footnote": [], + "bbox": [ + 753, + 508, + 769, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a01bbf82bf635c44ae384d019c9896ea46cc498232dd85d19dfec10a6bf7b35b.jpg", + "image_caption": [ + "Deformable point" + ], + "image_footnote": [], + "bbox": [ + 753, + 521, + 769, + 531 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "complexity to a linear relationship with the sequence length. Although SSMs process sequences in a recurrent manner, SSMs can perform calculations on sequences in parallel after simplification. Despite these advantages, SSMs struggle to capture long-range dependencies due to the lack of content-aware perception in the state matrix update process.", + "bbox": [ + 511, + 702, + 906, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, Mamba [11] proposes an improved selection mechanism designed to optimize the training process of SSMs. This innovative mechanism introduces content awareness into the feature extraction pipeline, expands the effective receptive field, and achieves remarkable performance enhancements in various NLP tasks. Consequently, numerous studies have attempted to extend this approach to", + "bbox": [ + 511, + 795, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors.", + "bbox": [ + 109, + 887, + 241, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8838", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the broader field of computer vision [1-4, 10, 22, 30, 40, 43, 46]. The principal challenge in this endeavor is how to effectively map 2D image feature maps into 1D sequences, without losing essential information. Most existing methods employ predefined strategies for mapping, such as raster scanning [23, 47], local scanning [19], and continuous scanning [42]. However, as illustrated in Figure 1, these methods all rely on a fixed scanning path. This results in adjacent tokens no longer being adjacent after flattening. Thereby, they neglect the inherent spatial structure of the image, leading to the loss of structural information. To address this issue, QuadMamba [39] determines the scanning window size based on the amount of information contained in different areas of the image. However, the scanning order in each window is fixed. This leads to an incomplete solution of the aforementioned issues. GrootV [38] adaptively constructs a tree topology based on input features and subsequently extracts features from this topology. Nevertheless, it employs only adjacent features in constructing the topology and distributes attention uniformly across the patch. The aforementioned methods are either based on a fixed scanning order, leading to the loss of structural information, or treat the information in the perception area equally, resulting in insensitivity to variations in object details.", + "bbox": [ + 93, + 90, + 480, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To solve this problem, we proposed a novel framework called DefMamba inspired by deformable mechanisms [6, 36]. However, intuitively applying deformable mechanisms to SSMs still causes structural information loss and increases computational complexity. Therefore, we proposed a deformable state space model and a deformable scanning strategy (DS) to prioritize deformable tokens based on essential information and slide reference points towards the important area. This approach enables the SSMs to capture and process relevant features related to the input more effectively. Specifically, we shifted the reference point by the generated offset from a fixed position to an adjustable one that provided more useful information, thereby facilitating the awareness of changes in object details. On the other hand, we also dynamically adjusted the scanning order by the offset vector for obtaining a structure-aware sequence. In this way, our framework adaptively perceives the variations in object details to find the most suitable feature points, and determines the optimal scanning order consistent with the object structure based on the input image features.", + "bbox": [ + 93, + 458, + 480, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conducted extensive experiments to validate the effectiveness of DefMamba across multiple visual benchmarks, including image classification on ImageNet [8], object detection and instance segmentation on COCO [21], and semantic segmentation on ADE20K [45]. These results demonstrate that our method outperforms existing SSMs based approaches on all benchmarks and remains competitive with CNN and transformer-based methods.", + "bbox": [ + 93, + 780, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 517, + 90, + 653, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Mamba for Visual Applications", + "text_level": 1, + "bbox": [ + 517, + 116, + 787, + 131 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Numerous studies have successfully integrated Mamba [11] into visual tasks [19, 23, 27, 29, 31, 38, 39, 42, 47], demonstrating preliminary achievements. ViM [47] introduces a bidirectional scanning approach to transform 2D image into 1D sequences, which are then fed into SSM for global context modeling, marking the first integration of Mamba into visual tasks. VMamba [23] employs a four-way scanning algorithm to convert 2D image into 1D sequences. PlainMamba [42] modifies the scanning method from raster to continuous, preserving the spatial dependencies of the image. MSVMamba [31] downsamples the sequence based on four scans to reduce computational redundancy and mitigates the issue of information loss. GrootV [38] constructs a minimum spanning tree on a four-way plane graph using the differences between adjacent features, dynamically adjusting the scanning order according to different inputs. QuadMamba [39] adaptively adjusts the window granularity during the scanning process based on the information content of the image to better aggregate local information. While GrootV and QuadMamba can adapt their scanning methods based on input data, GrootV only considers the relationships between adjacent elements when generating the minimum spanning tree, neglecting global information. On the other hand, QuadMamba still relies on predefined scanning methods and does not achieve true dynamic scanning. In contrast, our DefMamba introduces a content-aware deformable scanning strategy that allows the network to dynamically learn the scanning order and the reference points position.", + "bbox": [ + 517, + 138, + 903, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Deformable CNNs and Attention Mechanism", + "text_level": 1, + "bbox": [ + 517, + 590, + 892, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deformable convolution [6, 20, 41, 48] employs a convolution kernel that adapts to geometric variations in the input feature map, thereby overcoming the limitations of traditional convolution, which performs poorly when dealing with complex targets. Recently, the deformable mechanism has been extended to visual transformers [9] to enhance their ability to capture local features and adapt to geometric variations. DPT [5] proposes an adaptive patch embedding method that dynamically adjusts the position and size of patches while preserving their semantic information. PSViT [44] introduces a progressive sampling module prior to ViT [9], which iteratively identifies the most suitable deformable point positions for the current image. DAT [36] integrates the deformable mechanism with the self-attention mechanism in Transformers for the first time, incorporating deformable attention into the visual backbone. This approach learns a set of features corresponding to global keypoints and adapts to spatial variations. Previous approaches have explored various ways to effectively incorporate de", + "bbox": [ + 517, + 613, + 903, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8839", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ae1ba1cc1e661f4023f08f9b73b17db10b6af066bb24446c2126442309318c23.jpg", + "image_caption": [ + "Figure 2. Overview of DefMamba. (a) depicts the overall architecture of our network. (b) illustrates the structure of the deformable Mamba block. LN means LayerNorm and FFN is a feed-forward network." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 903, + 255 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "formable mechanism into transformer architectures. With the recent popularity of Mamba [11], we attempted to introduce deformable mechanism into Mamba. However, directly applying these mechanism has resulted in issues like the loss of structural information and the necessity for additional modules. In this context, our designed DS strategy stands out by effectively prioritizing deformable tokens while directing reference points toward key areas.", + "bbox": [ + 88, + 316, + 483, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 450, + 183, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first summarized the SSMs in Section 3.1. Then, in Section 3.2, we described the overall structure of the proposed network. Section 3.3 introduces a Deformable State Space Model (DSSM). Finally, Section 3.4 presents the designed model configurations across multiple scales.", + "bbox": [ + 89, + 476, + 483, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 575, + 230, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SSMs, including notable implementations like S4 [12] and Mamba [11], are structured sequence architectures that combine elements of recurrent neural networks (RNNs) and CNNs, enabling linear or near-linear scaling with respect to sequence length. These models, derived from continuous systems, define a 1D function-to-function map for an input $u(t) \\in \\mathbb{R}^L$ to an output $y(t) \\in \\mathbb{R}^L$ through a hidden state $h(t) \\in \\mathbb{R}^N$ . Where $t$ represents time. More formally, SSMs are characterized by the continuous-time Ordinary Differential Equation (ODE) [11] presented:", + "bbox": [ + 89, + 597, + 483, + 750 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} h ^ {\\prime} (t) = \\mathbf {A} h (t) + \\mathbf {B} u (t), \\\\ y (t) = \\hat {C} h (t), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 755, + 364, + 791 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $h(t)$ is the current hidden state. $h^{\\prime}(t)$ is the updated hidden state. $u(t)$ is the current input. $y(t)$ is the output. $\\mathbf{A} \\in \\mathbb{R}^{N \\times N}$ is SSM's evolution matrix, and $\\mathbf{B} \\in \\mathbb{R}^{N \\times 1}$ , $\\hat{C} \\in \\mathbb{R}^{1 \\times N}$ are the input and output projection matrices, respectively.", + "bbox": [ + 89, + 794, + 482, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To enable the application of SSMs in sequence modeling tasks within deep learning, they must be discretized,", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "transforming the SSM from a continuous-time function-to-function map into a discrete-time sequence-to-sequence map. S4 [12] and Mamba [11] are examples of discrete adaptations of the continuous system, incorporating a timescale parameter $\\Delta$ to convert the continuous parameters $\\mathbf{A}$ , $\\mathbf{B}$ into their discrete counterparts $\\bar{\\mathbf{A}}$ , $\\bar{\\mathbf{B}}$ . This discretization is typically achieved using the Zero-Order Hold (ZOH) [11] method:", + "bbox": [ + 511, + 316, + 906, + 436 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\bar {\\mathbf {A}} = \\exp (\\Delta \\mathbf {A}), \\\\ \\bar {\\mathbf {B}} = \\left( \\begin{array}{l} (\\Delta \\mathbf {A}) ^ {- 1} (\\exp (\\Delta \\mathbf {A}) - \\mathbf {I}) \\cdot \\Delta \\mathbf {B}, \\end{array} \\right. \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 444, + 903, + 484 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh _ {t} = \\bar {\\mathbf {A}} h _ {t - 1} + \\bar {\\mathbf {B}} u _ {t},\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 482, + 723, + 494 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ny _ {t} = \\mathbf {C} h _ {t}.\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 500, + 663, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While both S4 [12] and Mamba [11] employ a similar discretization process as outlined in Equation 2, Mamba distinguishes itself from S4 by conditioning the parameters $\\Delta \\in \\mathbb{R}^{b\\times L\\times D}$ , $\\mathbf{B}\\in \\mathbb{R}^{b\\times L\\times N}$ , and $\\mathbf{C}\\in \\mathbb{R}^{b\\times L\\times N}$ on the input $u\\in \\mathbb{R}^{b\\times L\\times D}$ through the S6 Selective Scan Mechanism. Here, $b$ represents the batch size, $L$ denotes the sequence length, and $D$ signifies the feature dimension.", + "bbox": [ + 511, + 518, + 906, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overall Model Architecture", + "text_level": 1, + "bbox": [ + 511, + 636, + 764, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DefMamba uses a common multi-scale backbone structure similar to many CNNs [25, 28] and Transformers [24]. As illustrated in Figure 2(a), the image $I \\in \\mathbb{R}^{H \\times W \\times 3}$ is first divided into patches through a patch embedding layer, which produces a 2D feature map with spatial dimensions $H / 4 \\times W / 4$ and channel dimensions $C$ . Subsequently, multiple network stages are used to create hierarchical representations of dimensions $H / 8 \\times W / 8 \\times 2C$ , $H / 16 \\times W / 16 \\times 4C$ , and $H / 32 \\times W / 32 \\times 8C$ . Each stage consists of a stack of Deformable Mamba (DM) blocks followed by a downsampling layer (except the fourth stage). Finally, the features are average-pooled and sent to the classification head to obtain the prediction results. In particular, we followed [38] and used overlapping forms in the patch embedding layer and the downsampling layers. For specific structural details, please refer to the Appendix.", + "bbox": [ + 511, + 659, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8840", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b9eabf434458bbe39aa7301aae2d2af4ec4d3edd5e6eae6096bb601ccaf7c1bd.jpg", + "image_caption": [ + "Figure 3. Illustration of Deformable State Space Model. (a) illustrates the processing flow of the deformable state space model for feature extraction. (b) depicts the processing flow of the deformable scan. The upper part primarily shifts the feature points to enable the model to focus on more salient regions, while the lower part shifts the token positions to facilitate the discovery of a scanning order that is better suited to the current input. To clearly illustrate the process, only nine points are depicted in the figure, however, the actual processing involves a greater number of points. (c) presents the detailed structure of the offset network." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 903, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from the Mamba structure used in language models [11], the DM block follows the popular structure of the Transformer block [9, 24], which consists of two Layer Norm (LN) layers, an FFN, a DSSM (to be introduced in the following subsection) and residual connections, as shown in the Figure 2(b).", + "bbox": [ + 88, + 428, + 483, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Deformable State Space Model", + "text_level": 1, + "bbox": [ + 89, + 529, + 364, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overall architecture of the deformable state space model is presented in Figure 3(a). Inspired by [23, 31, 38], we employed depthwise convolution to replace the original 1D convolution in the vision mamba block [47] and incorporated a deformable branch comprising a deformable scanning and a deformable SSM (DSSM). We maintained the standard forward and backward branches to ensure stable model convergence, as our method introduces more spatial token jumps compared to previous scanning methods, potentially complicating model training and learning. Subsequent experiments validate this (Table 4).", + "bbox": [ + 88, + 551, + 482, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Deformable Scanning. Given the issue of mutual interference between multiple deformable points, we constrained the offset of the deformable points in a certain range. This ensures the relationship between deformable points and reference points remains invariant, allowing us to approximate the relationship after deformation using the relationship before deformation. Furthermore, considering the simplicity of the computation, we employed a parallel approach to simultaneously adjust the reference points and scanning order, thereby reducing the computational burden. The specific structure is illustrated in the Figure 3(b).", + "bbox": [ + 88, + 719, + 482, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an input feature $x \\in \\mathbb{R}^{H \\times W \\times C}$ , where $C$ denotes", + "bbox": [ + 109, + 883, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the channel dimension and $H, W$ represent the spatial resolution. We first generated the offset $o \\in \\mathbb{R}^{H \\times W \\times 3}$ using a subnetwork that utilizes $x$ to output the offset values $o$ for the reference point and the reference token.", + "bbox": [ + 511, + 428, + 906, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We initially implemented the subnetwork as depicted in Figure 3(c). The input features are first processed through a $K \\times K$ depthwise convolution to capture local features. Subsequently, GELU, Layer Normalization (LN), and a $1 \\times 1$ convolution are employed to derive the offset values, which encompass three dimensions in total. The first two dimensions represent the offset of the reference point in two-dimensional space, while the third dimension signifies the offset of the reference token index within the entire patch. During our experiments, we observed that the offset of the token necessitates global perception of the features within the patch, which cannot be achieved solely through convolution. In light of this, and considering the previous method's findings [29, 31] that mamba has redundancy in the channel dimension, we incorporated a Channel Attention (CA) mechanism [18] following the depthwise convolution layer. This mechanism mitigates channel redundancy and facilitates the integration of global contextual information. Notably, following the configuration of DAT [36], we set $K$ to [9, 7, 5, 3] across four stages and omitted the bias in the $1 \\times 1$ convolution.", + "bbox": [ + 511, + 489, + 908, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To stabilize the training process, we employed the tanh function to mitigate the impact of extreme values in $o$ , where $\\hat{o} = \\tanh(o)$ . Subsequently, we split $\\hat{o}$ to 2 parts along the channel dimension, one with 2 channels and one with 1 channel, to obtain the point offset $\\Delta p$ and token index offset $\\Delta t$ . As previously mentioned, we needed to fur", + "bbox": [ + 511, + 809, + 908, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8841", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/56c30ffb3cf9d3882af71d29b6eea984c5713be7261c494a6328b6a3e266b973.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodType#Param.#FLOPsTop-1 Acc.
RegNetY-800M [28]C6M0.8G76.3
GhostNet 1.3× [13]C7M0.2G75.7
DeiT-Ti [33]T6M1.3G72.2
ViM-T [47]S7M1.5G76.1
EffVMamba-T [27]S6M0.8G76.5
LocalVim-T [19]S8M1.5G76.2
PlainMamba-L1 [42]S7M3.0G77.9
MSVMamba-N [31]S7M0.9G77.3
QuadMamba-Li [39]S5M0.8G74.2
DefMamba-TS8M1.2G78.6
RegNetY-4G [28]C21M4.0G80.0
ConvNeXt-T [25]C29M4.5G82.1
Conv2Former-T [17]C27M4.4G83.2
DeiT-S [33]T22M4.6G79.8
Swin-T [24]T29M4.5G81.3
CoAtNet-0 [7]T25M4.0G81.6
CrossFormer-S [35]T31M4.9G82.5
ViM-S [47]S26M5.1G81.0
VMamba-T [23]S22M5.6G82.2
", + "bbox": [ + 99, + 88, + 488, + 377 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e25dd3cadd5b475d456c44d6e443e38cd7ce461bcb39d384fb1db09292832e9b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodType#Param.#FLOPsTop-1 Acc.
LocalVim-S [19]S28M4.8G81.2
LocalVMamba-T [19]S26M5.7G82.7
EffVMamba-B [27]S33M4.6G83.0
MSVMamba-T [31]S33M4.6G82.8
PlainMamba-L2 [42]S25M8.1G81.6
GrootV-T [38]S30M4.8G83.4
QuadMamba-S [39]S31M5.5G82.4
DefMamba-SS32M4.8G83.5
ConvNeXt-S [25]C50M8.7G83.1
Conv2Former [17]C50M8.7G84.1
Swin-S [24]T50M8.7G83.0
CoAtNet-1 [7]T42M8.0G83.3
CrossFormer-B [35]T52M9.2G83.4
VMamba-S [23]S50M8.7G83.6
LocalVMamba-B [19]S50M11.4G83.7
PlainMamba-L3 [42]S50M14.4G82.3
GrootV-S [38]S51M8.5G84.2
QuadMamba-B [39]S50M9.3G83.8
DefMamba-BS51M8.5G84.2
", + "bbox": [ + 503, + 88, + 895, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Image classification performance on ImageNet-1K validation set. C, T and S indicate the model type of CNNs, Transformer and SSM. The best results are shown in bold font.", + "bbox": [ + 89, + 386, + 906, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ther constrain $\\Delta p$ , in order to stabilize training and simplify the structure. We divided the horizontal and vertical dimensions of $\\Delta p$ by $W$ and $H$ , respectively, thereby limiting the offset to the range of a single token. The detailed process is outlined as follows:", + "bbox": [ + 89, + 441, + 482, + 516 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta p, \\Delta t = S p l i t (\\tanh (O f f s e t (x)), \\mathrm {d i m s} = [ 2, 1 ]), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 526, + 482, + 550 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\Delta} p = \\operatorname {N o r m} (\\Delta p).\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 546, + 272, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, we sent the point offset $\\hat{\\Delta p}$ , token index offset $\\Delta t$ , and input feature $x$ to the point offset branch and index branch, to obtain the final output, respectively.", + "bbox": [ + 89, + 566, + 482, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Point Offset. To obtain feature representations that are more sensitive to changes in objects, we dynamically adapted the network's reference points to deformable points that contain more relevant information based on the input. Firstly, we generated reference points $p \\in \\mathbb{R}^{H \\times W \\times 2}$ . The values in $p$ correspond to the two-dimensional coordinates of points ranging from (0, 0) to $(H - 1, W - 1)$ . To simplify network calculations, we normalized $p$ from its original range to $[-1, 1]$ , where $[-1, 1]$ represents the point in the upper left corner and $[1, 1]$ represents the point in the lower right corner. We then added the reference point $p$ and the offset to obtain the deformable point $\\hat{p} = p + \\Delta p$ . Since the offset $\\hat{p}$ contains a decimal part, it cannot be used directly. Therefore, we used bilinear interpolation to extract features at the spatial position corresponding to the offset point $\\hat{p}$ from the input $x$ .", + "bbox": [ + 89, + 613, + 482, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When our model performs point offset, the features will move in space, potentially causing the position encoding added in the initial stage to become ineffective and thereby", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "decreasing model performance. To address this, we designed an offset bias based on the relative position encoding in the Swin Transformer. Specifically, given the feature map of size $H \\times W$ , the relative coordinate displacement of points lies within the range of $[-H, H]$ and $[-W, W]$ in two dimensions, respectively. Therefore, we set a learnable relative offset bias matrix $R \\in \\mathbb{R}^{(2H - 1) \\times (2W - 1)}$ . However, considering that such a matrix would result in a significant increase in parameter count, we performed a downsampling operation on this matrix to obtain $R \\in \\mathbb{R}^{H \\times W}$ . At the same time, we divided the point displacement by 2 to accommodate this change. Then we used the point displacement to calculate the corresponding compensation by interpolating on $R$ . Finally, this compensation is added to the interpolated features. The specific process is as follows:", + "bbox": [ + 511, + 441, + 906, + 667 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {p} = p + \\Delta p, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 676, + 903, + 698 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} = \\phi (x, \\hat {p}) + \\phi (R, \\hat {p}),\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 695, + 782, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi (x,\\hat{p})$ represents the use of bilinear interpolation function to extract the feature corresponding to position $\\hat{p}$ on $x$ .", + "bbox": [ + 511, + 717, + 906, + 761 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Index Offset. We modified the scanning order to enable the model to perceive the structure of the input object effectively by varying the reference token index and the deformable token index. We initially generated the reference token index $t_r \\in \\mathbb{R}^{N \\times 1}$ , where $N = H \\times W$ . The values in $t$ indicate the token positions within the current patch, ranging from 0 to $N - 1$ . To simplify network computations, we normalized $t_r$ from its original range to [-1, 1]. This enables us to compute the deformable token index $t_d = t_r + \\Delta t$ .", + "bbox": [ + 511, + 763, + 908, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8842", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e228cfb0481a6552e8be11dceb1e63b5db963496aa093af33b8f538641cd4a12.jpg", + "table_caption": [ + "Mask R-CNN 1× schedule" + ], + "table_footnote": [], + "table_body": "
Backbone#FLOPs\\( {\\mathbf{{AP}}}^{\\mathbf{b}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{b}}{}_{50} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{b}}{}_{75} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}}{}_{50} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}}{}_{75} \\)
ResNet-50 [15]260G38.258.841.434.755.737.2
Swin-T [24]267G42.765.246.839.362.242.2
ConvNeXt-T [25]262G44.266.648.340.163.342.8
PVTv2-B2 [34]309G45.367.149.441.264.244.4
VMamba-T [23]286G47.469.552.042.766.346.0
LocalVMamba-T [19]291G46.768.750.842.265.745.5
QuadMamba-S [39]301G46.769.051.342.465.945.6
MSVMamba-T [31]252G46.968.851.442.265.645.4
GrootV-T [38]265G47.069.451.542.766.446.0
DefMamba-S268G47.569.651.742.866.346.2
", + "bbox": [ + 93, + 99, + 480, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Object detection and instance segmentation performance on MSCOCO 2017 val set. All using Mask R-CNN framework. $\\mathrm{AP^b}$ and $\\mathrm{AP^m}$ indicate the mean Average Precision (mAP) of detection and segmentation, respectively", + "bbox": [ + 89, + 222, + 482, + 279 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since the derived $t_d$ contain decimal components, they cannot be utilized directly. Consequently, for $t_d$ , we applied a sorting algorithm to determine the indices post-offset based on the magnitude of their values. Finally, we transformed the offset features $\\hat{x}$ into a 1D sequence according to these indices, thereby obtaining a content-adaptive image feature sequence. It is important to note that the sorting algorithm truncates gradients, rendering the network untrainable. To address this, we averaged the gradients of the final image sequence across the dimension and replicate them to $\\Delta t$ to approximate the gradient of the scanning order offset.", + "bbox": [ + 88, + 306, + 482, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 488, + 223, + 506 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Image Classification", + "text_level": 1, + "bbox": [ + 89, + 513, + 282, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. The image classification experiments are conducted using the ImageNet-1K [8] dataset, which comprises over 1.28 million training images and 50,000 validation images across 1,000 categories. Our training setup closely follows the methodology of previous practices [23, 31, 38], incorporating various data augmentations such as random cropping, random horizontal flipping, label-smoothing regularization, mixup, autoaugment, and random erasing. The models are trained for 300 epochs using the AdamW [26] optimizer with a cosine decay learning rate scheduler, including a 20-epoch warm-up period. The total batch size is set to 1,024, with the models trained on $8 \\times$ A800 GPUs. The optimizer parameters are configured with betas set to (0.9, 0.999), momentum set to 0.9, an initial learning rate of $1 \\times 10^{-3}$ , a weight decay of 0.05, and Exponential Moving Average (EMA).", + "bbox": [ + 91, + 537, + 482, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. Table 1 presents a comparison of our proposed DefMamba models (T, S, B) with various state-of-the-art (SOTA) methods. Specifically, DefMamba-T achieves $78.6\\%$ Top-1 Acc., outperforming CNNs based RegNetY800M [28] and transformer based DeiT-Ti [33] by $2.3\\%$ and $6.4\\%$ , respectively. Moreover, DefMamba-T outperforms the recently introduced SSMs models, achieving $2.5\\%$ , $2.4\\%$ , and $1.3\\%$ higher performance than ViM-T", + "bbox": [ + 89, + 780, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8ee24a9a6527c871ed03c6095f7d20f6979c5d77c0f70ac3d9d090f5207274c4.jpg", + "table_caption": [ + "ADE20K with crop size 512" + ], + "table_footnote": [], + "table_body": "
BackbonemIOU (SS)mIOU (MS)#Param.#FLOPs
ResNet-50 [15]42.142.867M953G
Swin-T [24]44.545.860M945G
ConvNeXt-T [25]46.046.760M939G
NAT-T [14]47.148.458M934G
Vim-S [47]44.9-46M-
LocalVim-S [19]46.447.558M297G
VMamba-T [23]47.948.862M949G
PlainMamba-L2 [42]46.8-55M285G
LocalVMamba-T [19]47.949.157M970G
MSVMamba-T [31]47.648.565M942G
QuadMamba-S [39]47.248.162M961G
GrootV-T [38]48.549.460M941G
DefMamba-S48.849.665M946G
", + "bbox": [ + 517, + 102, + 903, + 294 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Semantic segmentation performance on ADE20K val set. The crop size is all set to $512^2$ . SS and MS denote single-scale and multi-scale testing, respectively.", + "bbox": [ + 511, + 304, + 906, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[47], LocalViM-T [19], and MSVMamba-N [31] in terms of parameter and computational complexity. Moreover, it reduces the computational burden by $60\\%$ while achieving a performance improvement of $0.7\\%$ over PlainMamba-L1 [42]. DefMamba-S achieves $83.5\\%$ Top-1 Acc., surpassing GrootV-T [38] and EfficientVMamba-B [27]. Furthermore, DefMamba-B achieves an accuracy of $84.2\\%$ , exceeding VMamba-S [23] by $0.6\\%$ , demonstrating the effectiveness of our methods.", + "bbox": [ + 511, + 369, + 906, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Object Detection", + "text_level": 1, + "bbox": [ + 511, + 515, + 679, + 531 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. We evaluated DefMamba on the MSCOCO 2017 dataset [21] using the Mask R-CNN framework [16] for object detection and instance segmentation tasks. Following prior works [24, 31, 38], we utilized backbones pretrained on ImageNet-1K for initialization. We employed standard training strategies, including $1 \\times (12$ epochs) with MultiScale (MS) training, to ensure a fair comparison.", + "bbox": [ + 511, + 537, + 906, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. As depicted in Table 2, our method outperforms existing methods on most evaluation metrics. Specifically, under $1 \\times$ schedule, DefMamba-S achieves 47.5 in box mAP $(\\mathrm{AP}^{\\mathrm{b}})$ and 42.8 in mask mAP $(\\mathrm{AP}^{\\mathrm{m}})$ . Our model surpassed ResNet-50 [15], Swin-T [24] and ConvNeXt-T [25]. At the same time, our method improved $\\mathrm{AP}^{\\mathrm{m}}$ by 0.6 points compared to LocalVMamba-T [19] and QuadMamba-S [39]. Furthermore, our method exhibited comparable performance to the previous SOTA method, VMamba-T [23], while reducing the computational load by $4\\%$ .", + "bbox": [ + 511, + 643, + 908, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Semantic Segmentation", + "text_level": 1, + "bbox": [ + 511, + 803, + 732, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. To evaluate the semantic segmentation performance of DefMamba, we trained our models using UperNet [37] initialized with pre-trained classification weights on ADE20K [45] for 160,000 iterations. We employed the AdamW optimizer [26] with a learning rate set at $6 \\times 10^{-5}$ .", + "bbox": [ + 511, + 825, + 905, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8843", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4a4f7b0d9a41465af22083c4801c34489458f97a9f3762ef9aa99895a6708778.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
IndexFB-BBCB [42]LB [19]DB#Param.#FLOPsTop-1
(1)✓7.3M1.1G76.9
(2)✓8.1M1.1G76.5
(3)✓✓7.5M1.1G77.3
(4)✓✓7.5M1.1G77.1
(5)✓✓8.3M1.2G78.6
", + "bbox": [ + 98, + 89, + 477, + 161 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/69b055eb0a02c9d6ad79d192e00e4715743367941fd8c9c33fabf5a6fda4b227.jpg", + "table_caption": [ + "Table 4. Comparisons with the different scanning branches in the setting of tiny model size. DB means our deformable branch. The best results are shown in **bold** font." + ], + "table_footnote": [], + "table_body": "
IndexDPDTOBCA#Param.#FLOPsTop-1
(1)7.5M1.1G77.0
(2)✓7.5M1.2G77.4
(3)✓7.5M1.2G77.2
(4)✓✓7.5M1.2G77.9
(5)✓✓✓8.2M1.2G78.2
(6)✓✓✓✓8.3M1.2G78.6
", + "bbox": [ + 99, + 229, + 475, + 328 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Comparisons with the different components of proposed deformable scanning in tiny model size settings on ImageNet-1k. The best results are shown in bold font.", + "bbox": [ + 89, + 339, + 482, + 381 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our experiments are primarily conducted using a default input resolution of $512 \\times 512$ . Additionally, we incorporated Multi-Scale (MS) testing to assess performance variations.", + "bbox": [ + 89, + 410, + 482, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. The DefMamba-S model demonstrates favorable performance in semantic segmentation compared to various SOTA methods, as presented in Table 3. DefMamba-S achieves a mIOU of 48.8 in single-scale and 49.6 in multi-scale evaluation. This outperforms ResNet-50 [15], Swin-T [24], and ConvNeXt-T [25]. Additionally, DefMamba-S exceeds the performance of the recent SSM methods, including GrootV-T [38], QuadMamba-S [39] and MSVMamba-T [31]. Our method achieves improvements of 0.3 points, 1.6 points, and 1.2 points, respectively, on the single-scale mIoU metric.", + "bbox": [ + 89, + 455, + 482, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 635, + 243, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of the Proposed DSSM Structure. To give the evidence for the effectiveness of the proposed deformable branch, we conducted a series of experiments over different branch settings in Table 4. As shown in Table 4, FB-BB refers to the forward and the backward branches for feature extraction. CB represents continuous scanning [42] branch. LB is local scanning [19] branch and DB denotes our proposed deformable branch in Figure 2 (a). By comparing the results in Table 4 (1) and (5), we observed that the proposed deformable branch significantly increased the accuracy of the ImageNet dataset by $1.7\\%$ within a reasonable computational budget, to demonstrate the effectiveness of the proposed deformable branch. Moreover, compared with Table 4 (3), (4) and (5), our method only increased the computational cost by 0.1G, while significantly improving the accuracy on ImageNet dataset by $1.4\\%$ . This further demon-", + "bbox": [ + 89, + 657, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/09baed4a154e94d6c2235b759bb1883c14283e4c331de41876fa79b1ef412300.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 89, + 594, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b6fae81d86ea4e205ec6563dab4fdb5cc749291aa980ab311ea8681c6175d3f7.jpg", + "image_caption": [ + "Image", + "Figure 4. Visualization of activation maps in the specific position. The position is marker by red and orange point. RS stands for raster scanning, DS stands for our deformable scanning." + ], + "image_footnote": [], + "bbox": [ + 516, + 148, + 594, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/47216140e4c4590f434e7f793ae29f58d44143662ab7d43c8dd7e4d25871089d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 596, + 89, + 669, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e0cdb04e68326430b383fa960dfe10dd561e20e24f309c423f55b28490c31e20.jpg", + "image_caption": [ + "RS" + ], + "image_footnote": [], + "bbox": [ + 596, + 148, + 669, + 208 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/166745a0b2523067f384e2bcbef4b4d0857b25f067bef4f69a3761484c211e6f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 671, + 89, + 748, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6b9b73f12108e870d3d0cba1193b5c7ccfe5e9309c564288bb1167bb55b6fbb8.jpg", + "image_caption": [ + "DS" + ], + "image_footnote": [], + "bbox": [ + 671, + 148, + 746, + 208 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c14c85d39fb53a27df055b1fded592e4b072beaa0540990d655d183f5c446d58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 750, + 89, + 825, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9b0a62375488617458d541bafc1bd43e9a7b3cbae1882bb043b5632217b05bdb.jpg", + "image_caption": [ + "RS" + ], + "image_footnote": [], + "bbox": [ + 750, + 148, + 825, + 208 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0232c90e70eeb5784c8fc50b3fbd7966a13a6b58ee085127a6d08a352d997621.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 826, + 89, + 903, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a0f94ca9be6f5d0348760820a3e080d3540009a4e6fd74be31d07c2f66e48612.jpg", + "image_caption": [ + "DS" + ], + "image_footnote": [], + "bbox": [ + 826, + 148, + 903, + 208 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "strates that our deformable scanning approach, as opposed to other fixed scanning methods, is more capable of capturing structural information of objects and enhancing model performance. From Table 4 (1) and (2), we noted that incorporating only the proposed deformable branch would lead to a decrease in performance due to the increased spatial token jumps. To achieve more stable training and higher model performance, we adhered to the previous paradigm by combining the FB-BB and DB in our proposed model.", + "bbox": [ + 511, + 308, + 903, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of the Deformable Scanning Components. To thoroughly evaluate the contributions of each component in our proposed deformable scanning method, we conducted an ablation study in Table 5. As shown in Table 5, DP, DT, OB and CA represent the components of the deformable scanning in Figure 2 (b), respectively. DP (Deformable Points) involves the process of generating deformable points, which includes initializing reference points, an offsets network and a bilinear interpolation. DT (Deformable Tokens) refers to the process of dynamically changing the token order based on predicted offsets, which includes initializing token index and deformable token index, as well as an offsets network. OB represents the operation of generating offset bias. CA denotes channel attention operation in the offset network. By comparing the results in Table 5 (1), (2) and (3), we observed that adding either the DP operation or the DT operation boosting the baseline (1) performance by $0.2 - 0.4\\%$ , with only a minor increases in computational costs (0.1G), demonstrated that the effectiveness of both DP and DT. Moreover, when combining both DP and DT operations (4), the performance further improves by $1\\%$ compared to the baseline, as shown in Table 5 (1) and (4). These results strongly prove that whether adding DT or DP individually, or combining both, the model can better learn the structure of images and facilitate the awareness of changes in object details, thus improving performance. Furthermore, we run ablation experiments to confirm the effectiveness of OB and CA by comparing Table 5 (4) and (5), and Table 5 (5) and (6), respectively. The experiments validate the effectiveness of our methods.", + "bbox": [ + 511, + 446, + 903, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8844", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a4a975e2d4ed761d1256a74adb474d33b63f3521337444a84dfd5293dc89adf7.jpg", + "image_caption": [ + "Figure 5. Visualization of deformable points and deformable token index. In (a), the orange dots represent deformable points, the green dots represent reference points, and the red arrows represent the offset path of the points. In (b) and (c), the gradient from yellow to green represents the scanning path, with the yellow dots being scanned first and the green dots being scanned later." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 212, + 284 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0035e466654ac12b930b27d494414f135eaaf847ea1943c1c955a4dd24a659a9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 217, + 89, + 334, + 284 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0ed8e8653f85ff217bb8ce5c8acd70b4a1dffe6b229bbaf69a89868f7e5321f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 336, + 90, + 480, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization Results. To better demonstrate the superiority of our deformable scanning strategy, we present the activation maps of images at different positions for various methods in Figure 4, marked clearly by red and orange dots in the image. Specifically, we visualized the activation map corresponding to the final layer of the second stage using the method outlined in [23]. As illustrated in the activation map of the pen in the last line of Figure 4, our method demonstrates an enhanced ability to focus on the structural and shape information of objects, even when dealing with complex scenes that contain multiple overlapping objects. This capability allows for more precise recognition and segmentation, further highlighting the effectiveness of our approach in capturing essential details.", + "bbox": [ + 88, + 407, + 482, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also visualized the deformable points and deformable token index to intuitively demonstrate the performance of our method, as shown in the Figure 5. In the red box of Figure 5 (a), we can observe that some focus points outside the object shift towards the object. Such movements allow the network to attend to more object information. Compared with Figure 5 (b), our method (c) adjusts the scanning order to emphasize important tokens. For example, as shown in the first row of the Figure 5, the token corresponding to the snake's head is shifted from the middle position in a raster scan to being the first position in our method. Such offsets are beneficial for the network to learn relevant features.", + "bbox": [ + 89, + 619, + 482, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation", + "text_level": 1, + "bbox": [ + 89, + 829, + 205, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Despite the strong results of our approach, there is still a limitation. In cases where the image contains incomplete object structures or multiple objects arranged in a regular", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d324cf04f66a3b2d46aeb62497af47027e0615ced8c7bf95c00d169828d00335.jpg", + "image_caption": [ + "Figure 6. Failure cases. The blue dots represent deformable points, while the black arrows indicate the scanning order after deformation." + ], + "image_footnote": [], + "bbox": [ + 514, + 88, + 898, + 304 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "pattern, the deformable scanning strategy may be less effective. As illustrated in Figure 6, when the image shows only a portion of a baseball, the deformable mechanism does not capture complete structural information, resulting in offsets that are too small and converge towards the predefined scanning method. Meanwhile, when multiple objects are arranged according to a certain rule, the information variation between adjacent tokens is minimal. Results in the model remaining in an indolent learning process.", + "bbox": [ + 511, + 387, + 906, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 541, + 633, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we made efforts to tackle the challenge arising from existing Mamba-based methods, which rely on fixed scanning techniques to extract features. These methods do not fully leverage the spatial structure information inherent in images. To overcome this limitation, we proposed a novel foundation model named DefMamba, which is grounded in DS. This innovative model aims to enhance the capability of the network to learn and represent complex image structures, as well as to detect subtle changes in object details. The DS principally comprises two key operations: the shifting of focus points and the alteration of the scanning order. The first operation effectively repositions reference points toward significant regions of interest, thereby enhancing the model's sensitivity to variations in object details. The second operation modifies the scanning order to create a structure-aware sequence that is better aligned with the underlying object structure based on the input features. Extensive experimental evaluations on benchmark datasets, including ImageNet, COCO, and ADE20K, robustly demonstrate that our proposed method outperforms existing SSMs and remains competitive when compared to both CNNs and Transformer-based approaches.", + "bbox": [ + 511, + 568, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8845", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China (62172070, 62372080, 62376050, and U22B2052), and the Natural Science Foundation of Liaoning Province (2024-MSBA-24).", + "bbox": [ + 89, + 114, + 483, + 176 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 188, + 187, + 204 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Qi Bi, Jingjun Yi, Hao Zheng, Wei Ji, Haolan Zhan, Yawen Huang, Yuexiang Li, and Yefeng Zheng. 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Grootvl: Tree topology is all you need in state space model. arXiv preprint arXiv:2406.02395, 2024. 2, 3, 4, 5, 6, 7, 1" + ], + "bbox": [ + 91, + 92, + 482, + 898 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[39] Fei Xie, Weijia Zhang, Zhongdao Wang, and Chao Ma. Quadmamba: Learning quadtree-based selective scan for visual state space model. arXiv preprint arXiv:2410.06806, 2024. 2, 5, 6, 7, 1", + "[40] Zhaohu Xing, Tian Ye, Yijun Yang, Guang Liu, and Lei Zhu. Segmamba: Long-range sequential modeling mamba for 3d medical image segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 578-588. Springer, 2024. 2", + "[41] Yuwen Xiong, Zhiqi Li, Yuntao Chen, Feng Wang, Xizhou Zhu, Jiapeng Luo, Wenhai Wang, Tong Lu, Hongsheng Li, Yu Qiao, et al. Efficient deformable convnets: Rethinking dynamic and sparse operator for vision applications. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9308-9316, 2019. 2" + ], + "bbox": [ + 516, + 92, + 903, + 753 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8847", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_model.json b/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf55c15ac01d0c332537d374fe62f327a69539d --- /dev/null +++ b/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_model.json @@ -0,0 +1,2244 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.244, + 0.131, + 0.756, + 0.154 + ], + "angle": 0, + "content": "DefMamba: Deformable Visual State Space Model" + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.18, + 0.88, + 0.218 + ], + "angle": 0, + "content": "Leiye Liu\\(^{1}\\) Miao Zhang\\(^{1,*}\\) Jihao Yin\\(^{1}\\) Tingwei Liu\\(^{1}\\) Wei Ji\\(^{2}\\) Yongri Piao\\(^{1,*}\\) Huchuan Lu\\(^{1}\\) \n\\(^{1}\\)Dalian University of Technology \\(^{2}\\)Yale University" + }, + { + "type": "text", + "bbox": [ + 0.226, + 0.22, + 0.777, + 0.234 + ], + "angle": 0, + "content": "leiyeliu@mail.dlut.edu.cn,wei.ji@yale.edu,yrpiao@dlut.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.302, + 0.485, + 0.62 + ], + "angle": 0, + "content": "Recently, state space models (SSM), particularly Mamba, have attracted significant attention from scholars due to their ability to effectively balance computational efficiency and performance. However, most existing visual Mamba methods flatten images into 1D sequences using predefined scan orders, which results the model being less capable of utilizing the spatial structural information of the image during the feature extraction process. To address this issue, we proposed a novel visual foundation model called DefMamba. This model includes a multi-scale backbone structure and deformable mamba (DM) blocks, which dynamically adjust the scanning path to prioritize important information, thus enhancing the capture and processing of relevant input features. By combining a deformable scanning (DS) strategy, this model significantly improves its ability to learn image structures and detects changes in object details. Numerous experiments have shown that DefMamba achieves state-of-the-art performance in various visual tasks, including image classification, object detection, instance segmentation, and semantic segmentation. The code is open source on DefMamba." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.651, + 0.222, + 0.667 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.678, + 0.484, + 0.875 + ], + "angle": 0, + "content": "Most existing visual foundation models primarily rely on convolutional neural networks (CNNs) [25, 28, 32] and Transformer architectures [9, 24, 33]. However, CNNs are constrained by their sliding window structure, which limits the receptive field and significantly impedes global information aggregation across the input data. In contrast, Transformers excel in global information aggregation due to their attention mechanism, but their high computational complexity poses a challenge in achieving a balance between efficiency and performance. State space models (SSMs) [12] provide a potential solution to this trade-off. SSMs aggregate previous features through a hidden state matrix to update current features, thereby reducing the computational" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.27, + 0.642, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.363, + 0.636, + 0.375 + ], + "angle": 0, + "content": "(a) Raster scanning" + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.27, + 0.771, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.363, + 0.761, + 0.375 + ], + "angle": 0, + "content": "(b) Local scanning" + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.27, + 0.899, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.363, + 0.903, + 0.375 + ], + "angle": 0, + "content": "(c) Continuous scanning" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.382, + 0.661, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.392, + 0.743, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.685, + 0.465, + 0.732, + 0.477 + ], + "angle": 0, + "content": "OffsetΔ" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.382, + 0.899, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.643, + 0.491, + 0.779, + 0.502 + ], + "angle": 0, + "content": "(d) Deformable scanning" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.507, + 0.587, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.594, + 0.508, + 0.685, + 0.519 + ], + "angle": 0, + "content": "Fixed scan order" + }, + { + "type": "image_caption", + "bbox": [ + 0.594, + 0.522, + 0.718, + 0.532 + ], + "angle": 0, + "content": "Deformable scan order" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.509, + 0.771, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.508, + 0.859, + 0.519 + ], + "angle": 0, + "content": "Reference point" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.522, + 0.771, + 0.532 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.522, + 0.869, + 0.533 + ], + "angle": 0, + "content": "Deformable point" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.549, + 0.907, + 0.675 + ], + "angle": 0, + "content": "Figure 1. Comparison of deformable scanning and other scanning methods. (a) Raster scanning [23, 47], (b) Local scanning [19], (c) Continuous scanning [42], (d) Our designed deformable scanning. The blue dots represent the reference points, and the red dots represent the deformable points. The yellow arrows represent the fixed scan order, and the red gradient arrows represent the deformable scan order. Our method exhibits an enhanced capacity to accurately capture the structural characteristics of objects, thereby enabling the development of a more refined scanning approach." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.907, + 0.795 + ], + "angle": 0, + "content": "complexity to a linear relationship with the sequence length. Although SSMs process sequences in a recurrent manner, SSMs can perform calculations on sequences in parallel after simplification. Despite these advantages, SSMs struggle to capture long-range dependencies due to the lack of content-aware perception in the state matrix update process." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recently, Mamba [11] proposes an improved selection mechanism designed to optimize the training process of SSMs. This innovative mechanism introduces content awareness into the feature extraction pipeline, expands the effective receptive field, and achieves remarkable performance enhancements in various NLP tasks. Consequently, numerous studies have attempted to extend this approach to" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.242, + 0.9 + ], + "angle": 0, + "content": "*Corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8838" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.094, + 0.092, + 0.482, + 0.453 + ], + "angle": 0, + "content": "the broader field of computer vision [1-4, 10, 22, 30, 40, 43, 46]. The principal challenge in this endeavor is how to effectively map 2D image feature maps into 1D sequences, without losing essential information. Most existing methods employ predefined strategies for mapping, such as raster scanning [23, 47], local scanning [19], and continuous scanning [42]. However, as illustrated in Figure 1, these methods all rely on a fixed scanning path. This results in adjacent tokens no longer being adjacent after flattening. Thereby, they neglect the inherent spatial structure of the image, leading to the loss of structural information. To address this issue, QuadMamba [39] determines the scanning window size based on the amount of information contained in different areas of the image. However, the scanning order in each window is fixed. This leads to an incomplete solution of the aforementioned issues. GrootV [38] adaptively constructs a tree topology based on input features and subsequently extracts features from this topology. Nevertheless, it employs only adjacent features in constructing the topology and distributes attention uniformly across the patch. The aforementioned methods are either based on a fixed scanning order, leading to the loss of structural information, or treat the information in the perception area equally, resulting in insensitivity to variations in object details." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.459, + 0.482, + 0.775 + ], + "angle": 0, + "content": "To solve this problem, we proposed a novel framework called DefMamba inspired by deformable mechanisms [6, 36]. However, intuitively applying deformable mechanisms to SSMs still causes structural information loss and increases computational complexity. Therefore, we proposed a deformable state space model and a deformable scanning strategy (DS) to prioritize deformable tokens based on essential information and slide reference points towards the important area. This approach enables the SSMs to capture and process relevant features related to the input more effectively. Specifically, we shifted the reference point by the generated offset from a fixed position to an adjustable one that provided more useful information, thereby facilitating the awareness of changes in object details. On the other hand, we also dynamically adjusted the scanning order by the offset vector for obtaining a structure-aware sequence. In this way, our framework adaptively perceives the variations in object details to find the most suitable feature points, and determines the optimal scanning order consistent with the object structure based on the input image features." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.781, + 0.482, + 0.9 + ], + "angle": 0, + "content": "We conducted extensive experiments to validate the effectiveness of DefMamba across multiple visual benchmarks, including image classification on ImageNet [8], object detection and instance segmentation on COCO [21], and semantic segmentation on ADE20K [45]. These results demonstrate that our method outperforms existing SSMs based approaches on all benchmarks and remains competitive with CNN and transformer-based methods." + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.091, + 0.654, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.117, + 0.789, + 0.132 + ], + "angle": 0, + "content": "2.1. Mamba for Visual Applications" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.14, + 0.904, + 0.577 + ], + "angle": 0, + "content": "Numerous studies have successfully integrated Mamba [11] into visual tasks [19, 23, 27, 29, 31, 38, 39, 42, 47], demonstrating preliminary achievements. ViM [47] introduces a bidirectional scanning approach to transform 2D image into 1D sequences, which are then fed into SSM for global context modeling, marking the first integration of Mamba into visual tasks. VMamba [23] employs a four-way scanning algorithm to convert 2D image into 1D sequences. PlainMamba [42] modifies the scanning method from raster to continuous, preserving the spatial dependencies of the image. MSVMamba [31] downsamples the sequence based on four scans to reduce computational redundancy and mitigates the issue of information loss. GrootV [38] constructs a minimum spanning tree on a four-way plane graph using the differences between adjacent features, dynamically adjusting the scanning order according to different inputs. QuadMamba [39] adaptively adjusts the window granularity during the scanning process based on the information content of the image to better aggregate local information. While GrootV and QuadMamba can adapt their scanning methods based on input data, GrootV only considers the relationships between adjacent elements when generating the minimum spanning tree, neglecting global information. On the other hand, QuadMamba still relies on predefined scanning methods and does not achieve true dynamic scanning. In contrast, our DefMamba introduces a content-aware deformable scanning strategy that allows the network to dynamically learn the scanning order and the reference points position." + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.592, + 0.893, + 0.606 + ], + "angle": 0, + "content": "2.2. Deformable CNNs and Attention Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.614, + 0.904, + 0.9 + ], + "angle": 0, + "content": "Deformable convolution [6, 20, 41, 48] employs a convolution kernel that adapts to geometric variations in the input feature map, thereby overcoming the limitations of traditional convolution, which performs poorly when dealing with complex targets. Recently, the deformable mechanism has been extended to visual transformers [9] to enhance their ability to capture local features and adapt to geometric variations. DPT [5] proposes an adaptive patch embedding method that dynamically adjusts the position and size of patches while preserving their semantic information. PSViT [44] introduces a progressive sampling module prior to ViT [9], which iteratively identifies the most suitable deformable point positions for the current image. DAT [36] integrates the deformable mechanism with the self-attention mechanism in Transformers for the first time, incorporating deformable attention into the visual backbone. This approach learns a set of features corresponding to global keypoints and adapts to spatial variations. Previous approaches have explored various ways to effectively incorporate de" + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.514, + 0.956 + ], + "angle": 0, + "content": "8839" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.905, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.263, + 0.908, + 0.293 + ], + "angle": 0, + "content": "Figure 2. Overview of DefMamba. (a) depicts the overall architecture of our network. (b) illustrates the structure of the deformable Mamba block. LN means LayerNorm and FFN is a feed-forward network." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.318, + 0.485, + 0.44 + ], + "angle": 0, + "content": "formable mechanism into transformer architectures. With the recent popularity of Mamba [11], we attempted to introduce deformable mechanism into Mamba. However, directly applying these mechanism has resulted in issues like the loss of structural information and the necessity for additional modules. In this context, our designed DS strategy stands out by effectively prioritizing deformable tokens while directing reference points toward key areas." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.452, + 0.184, + 0.468 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.477, + 0.484, + 0.567 + ], + "angle": 0, + "content": "In this section, we first summarized the SSMs in Section 3.1. Then, in Section 3.2, we described the overall structure of the proposed network. Section 3.3 introduces a Deformable State Space Model (DSSM). Finally, Section 3.4 presents the designed model configurations across multiple scales." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.576, + 0.232, + 0.591 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.598, + 0.484, + 0.75 + ], + "angle": 0, + "content": "SSMs, including notable implementations like S4 [12] and Mamba [11], are structured sequence architectures that combine elements of recurrent neural networks (RNNs) and CNNs, enabling linear or near-linear scaling with respect to sequence length. These models, derived from continuous systems, define a 1D function-to-function map for an input \\( u(t) \\in \\mathbb{R}^L \\) to an output \\( y(t) \\in \\mathbb{R}^L \\) through a hidden state \\( h(t) \\in \\mathbb{R}^N \\). Where \\( t \\) represents time. More formally, SSMs are characterized by the continuous-time Ordinary Differential Equation (ODE) [11] presented:" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.756, + 0.365, + 0.792 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} h ^ {\\prime} (t) = \\mathbf {A} h (t) + \\mathbf {B} u (t), \\\\ y (t) = \\hat {C} h (t), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.483, + 0.871 + ], + "angle": 0, + "content": "where \\( h(t) \\) is the current hidden state. \\( h^{\\prime}(t) \\) is the updated hidden state. \\( u(t) \\) is the current input. \\( y(t) \\) is the output. \\( \\mathbf{A} \\in \\mathbb{R}^{N \\times N} \\) is SSM's evolution matrix, and \\( \\mathbf{B} \\in \\mathbb{R}^{N \\times 1} \\), \\( \\hat{C} \\in \\mathbb{R}^{1 \\times N} \\) are the input and output projection matrices, respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To enable the application of SSMs in sequence modeling tasks within deep learning, they must be discretized," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.318, + 0.907, + 0.438 + ], + "angle": 0, + "content": "transforming the SSM from a continuous-time function-to-function map into a discrete-time sequence-to-sequence map. S4 [12] and Mamba [11] are examples of discrete adaptations of the continuous system, incorporating a timescale parameter \\(\\Delta\\) to convert the continuous parameters \\(\\mathbf{A}\\), \\(\\mathbf{B}\\) into their discrete counterparts \\(\\bar{\\mathbf{A}}\\), \\(\\bar{\\mathbf{B}}\\). This discretization is typically achieved using the Zero-Order Hold (ZOH) [11] method:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.445, + 0.905, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\bar {\\mathbf {A}} = \\exp (\\Delta \\mathbf {A}), \\\\ \\bar {\\mathbf {B}} = \\left( \\begin{array}{l} (\\Delta \\mathbf {A}) ^ {- 1} (\\exp (\\Delta \\mathbf {A}) - \\mathbf {I}) \\cdot \\Delta \\mathbf {B}, \\end{array} \\right. \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.483, + 0.725, + 0.496 + ], + "angle": 0, + "content": "\\[\nh _ {t} = \\bar {\\mathbf {A}} h _ {t - 1} + \\bar {\\mathbf {B}} u _ {t},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.5, + 0.665, + 0.514 + ], + "angle": 0, + "content": "\\[\ny _ {t} = \\mathbf {C} h _ {t}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.907, + 0.627 + ], + "angle": 0, + "content": "While both S4 [12] and Mamba [11] employ a similar discretization process as outlined in Equation 2, Mamba distinguishes itself from S4 by conditioning the parameters \\(\\Delta \\in \\mathbb{R}^{b\\times L\\times D}\\), \\(\\mathbf{B}\\in \\mathbb{R}^{b\\times L\\times N}\\), and \\(\\mathbf{C}\\in \\mathbb{R}^{b\\times L\\times N}\\) on the input \\(u\\in \\mathbb{R}^{b\\times L\\times D}\\) through the S6 Selective Scan Mechanism. Here, \\(b\\) represents the batch size, \\(L\\) denotes the sequence length, and \\(D\\) signifies the feature dimension." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.637, + 0.766, + 0.652 + ], + "angle": 0, + "content": "3.2. Overall Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.907, + 0.902 + ], + "angle": 0, + "content": "DefMamba uses a common multi-scale backbone structure similar to many CNNs [25, 28] and Transformers [24]. As illustrated in Figure 2(a), the image \\(I \\in \\mathbb{R}^{H \\times W \\times 3}\\) is first divided into patches through a patch embedding layer, which produces a 2D feature map with spatial dimensions \\(H / 4 \\times W / 4\\) and channel dimensions \\(C\\). Subsequently, multiple network stages are used to create hierarchical representations of dimensions \\(H / 8 \\times W / 8 \\times 2C\\), \\(H / 16 \\times W / 16 \\times 4C\\), and \\(H / 32 \\times W / 32 \\times 8C\\). Each stage consists of a stack of Deformable Mamba (DM) blocks followed by a downsampling layer (except the fourth stage). Finally, the features are average-pooled and sent to the classification head to obtain the prediction results. In particular, we followed [38] and used overlapping forms in the patch embedding layer and the downsampling layers. For specific structural details, please refer to the Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8840" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.905, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.332, + 0.908, + 0.404 + ], + "angle": 0, + "content": "Figure 3. Illustration of Deformable State Space Model. (a) illustrates the processing flow of the deformable state space model for feature extraction. (b) depicts the processing flow of the deformable scan. The upper part primarily shifts the feature points to enable the model to focus on more salient regions, while the lower part shifts the token positions to facilitate the discovery of a scanning order that is better suited to the current input. To clearly illustrate the process, only nine points are depicted in the figure, however, the actual processing involves a greater number of points. (c) presents the detailed structure of the offset network." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.429, + 0.484, + 0.52 + ], + "angle": 0, + "content": "Different from the Mamba structure used in language models [11], the DM block follows the popular structure of the Transformer block [9, 24], which consists of two Layer Norm (LN) layers, an FFN, a DSSM (to be introduced in the following subsection) and residual connections, as shown in the Figure 2(b)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.53, + 0.365, + 0.547 + ], + "angle": 0, + "content": "3.3. Deformable State Space Model" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.553, + 0.483, + 0.718 + ], + "angle": 0, + "content": "The overall architecture of the deformable state space model is presented in Figure 3(a). Inspired by [23, 31, 38], we employed depthwise convolution to replace the original 1D convolution in the vision mamba block [47] and incorporated a deformable branch comprising a deformable scanning and a deformable SSM (DSSM). We maintained the standard forward and backward branches to ensure stable model convergence, as our method introduces more spatial token jumps compared to previous scanning methods, potentially complicating model training and learning. Subsequent experiments validate this (Table 4)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.72, + 0.483, + 0.884 + ], + "angle": 0, + "content": "Deformable Scanning. Given the issue of mutual interference between multiple deformable points, we constrained the offset of the deformable points in a certain range. This ensures the relationship between deformable points and reference points remains invariant, allowing us to approximate the relationship after deformation using the relationship before deformation. Furthermore, considering the simplicity of the computation, we employed a parallel approach to simultaneously adjust the reference points and scanning order, thereby reducing the computational burden. The specific structure is illustrated in the Figure 3(b)." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.885, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Given an input feature \\( x \\in \\mathbb{R}^{H \\times W \\times C} \\), where \\( C \\) denotes" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.429, + 0.907, + 0.489 + ], + "angle": 0, + "content": "the channel dimension and \\( H, W \\) represent the spatial resolution. We first generated the offset \\( o \\in \\mathbb{R}^{H \\times W \\times 3} \\) using a subnetwork that utilizes \\( x \\) to output the offset values \\( o \\) for the reference point and the reference token." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.491, + 0.909, + 0.807 + ], + "angle": 0, + "content": "We initially implemented the subnetwork as depicted in Figure 3(c). The input features are first processed through a \\( K \\times K \\) depthwise convolution to capture local features. Subsequently, GELU, Layer Normalization (LN), and a \\( 1 \\times 1 \\) convolution are employed to derive the offset values, which encompass three dimensions in total. The first two dimensions represent the offset of the reference point in two-dimensional space, while the third dimension signifies the offset of the reference token index within the entire patch. During our experiments, we observed that the offset of the token necessitates global perception of the features within the patch, which cannot be achieved solely through convolution. In light of this, and considering the previous method's findings [29, 31] that mamba has redundancy in the channel dimension, we incorporated a Channel Attention (CA) mechanism [18] following the depthwise convolution layer. This mechanism mitigates channel redundancy and facilitates the integration of global contextual information. Notably, following the configuration of DAT [36], we set \\( K \\) to [9, 7, 5, 3] across four stages and omitted the bias in the \\( 1 \\times 1 \\) convolution." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.901 + ], + "angle": 0, + "content": "To stabilize the training process, we employed the tanh function to mitigate the impact of extreme values in \\(o\\), where \\(\\hat{o} = \\tanh(o)\\). Subsequently, we split \\(\\hat{o}\\) to 2 parts along the channel dimension, one with 2 channels and one with 1 channel, to obtain the point offset \\(\\Delta p\\) and token index offset \\(\\Delta t\\). As previously mentioned, we needed to fur" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "8841" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.49, + 0.378 + ], + "angle": 0, + "content": "
MethodType#Param.#FLOPsTop-1 Acc.
RegNetY-800M [28]C6M0.8G76.3
GhostNet 1.3× [13]C7M0.2G75.7
DeiT-Ti [33]T6M1.3G72.2
ViM-T [47]S7M1.5G76.1
EffVMamba-T [27]S6M0.8G76.5
LocalVim-T [19]S8M1.5G76.2
PlainMamba-L1 [42]S7M3.0G77.9
MSVMamba-N [31]S7M0.9G77.3
QuadMamba-Li [39]S5M0.8G74.2
DefMamba-TS8M1.2G78.6
RegNetY-4G [28]C21M4.0G80.0
ConvNeXt-T [25]C29M4.5G82.1
Conv2Former-T [17]C27M4.4G83.2
DeiT-S [33]T22M4.6G79.8
Swin-T [24]T29M4.5G81.3
CoAtNet-0 [7]T25M4.0G81.6
CrossFormer-S [35]T31M4.9G82.5
ViM-S [47]S26M5.1G81.0
VMamba-T [23]S22M5.6G82.2
" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.089, + 0.896, + 0.378 + ], + "angle": 0, + "content": "
MethodType#Param.#FLOPsTop-1 Acc.
LocalVim-S [19]S28M4.8G81.2
LocalVMamba-T [19]S26M5.7G82.7
EffVMamba-B [27]S33M4.6G83.0
MSVMamba-T [31]S33M4.6G82.8
PlainMamba-L2 [42]S25M8.1G81.6
GrootV-T [38]S30M4.8G83.4
QuadMamba-S [39]S31M5.5G82.4
DefMamba-SS32M4.8G83.5
ConvNeXt-S [25]C50M8.7G83.1
Conv2Former [17]C50M8.7G84.1
Swin-S [24]T50M8.7G83.0
CoAtNet-1 [7]T42M8.0G83.3
CrossFormer-B [35]T52M9.2G83.4
VMamba-S [23]S50M8.7G83.6
LocalVMamba-B [19]S50M11.4G83.7
PlainMamba-L3 [42]S50M14.4G82.3
GrootV-S [38]S51M8.5G84.2
QuadMamba-B [39]S50M9.3G83.8
DefMamba-BS51M8.5G84.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.387, + 0.908, + 0.416 + ], + "angle": 0, + "content": "Table 1. Image classification performance on ImageNet-1K validation set. C, T and S indicate the model type of CNNs, Transformer and SSM. The best results are shown in bold font." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.442, + 0.483, + 0.517 + ], + "angle": 0, + "content": "ther constrain \\(\\Delta p\\), in order to stabilize training and simplify the structure. We divided the horizontal and vertical dimensions of \\(\\Delta p\\) by \\(W\\) and \\(H\\), respectively, thereby limiting the offset to the range of a single token. The detailed process is outlined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.527, + 0.483, + 0.551 + ], + "angle": 0, + "content": "\\[\n\\Delta p, \\Delta t = S p l i t (\\tanh (O f f s e t (x)), \\mathrm {d i m s} = [ 2, 1 ]), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.547, + 0.274, + 0.562 + ], + "angle": 0, + "content": "\\[\n\\hat {\\Delta} p = \\operatorname {N o r m} (\\Delta p).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.568, + 0.483, + 0.614 + ], + "angle": 0, + "content": "Then, we sent the point offset \\(\\hat{\\Delta p}\\), token index offset \\(\\Delta t\\), and input feature \\(x\\) to the point offset branch and index branch, to obtain the final output, respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.483, + 0.854 + ], + "angle": 0, + "content": "Point Offset. To obtain feature representations that are more sensitive to changes in objects, we dynamically adapted the network's reference points to deformable points that contain more relevant information based on the input. Firstly, we generated reference points \\( p \\in \\mathbb{R}^{H \\times W \\times 2} \\). The values in \\( p \\) correspond to the two-dimensional coordinates of points ranging from (0, 0) to \\( (H - 1, W - 1) \\). To simplify network calculations, we normalized \\( p \\) from its original range to \\( [-1, 1] \\), where \\( [-1, 1] \\) represents the point in the upper left corner and \\( [1, 1] \\) represents the point in the lower right corner. We then added the reference point \\( p \\) and the offset to obtain the deformable point \\( \\hat{p} = p + \\Delta p \\). Since the offset \\( \\hat{p} \\) contains a decimal part, it cannot be used directly. Therefore, we used bilinear interpolation to extract features at the spatial position corresponding to the offset point \\( \\hat{p} \\) from the input \\( x \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "When our model performs point offset, the features will move in space, potentially causing the position encoding added in the initial stage to become ineffective and thereby" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.442, + 0.907, + 0.669 + ], + "angle": 0, + "content": "decreasing model performance. To address this, we designed an offset bias based on the relative position encoding in the Swin Transformer. Specifically, given the feature map of size \\( H \\times W \\), the relative coordinate displacement of points lies within the range of \\([-H, H]\\) and \\([-W, W]\\) in two dimensions, respectively. Therefore, we set a learnable relative offset bias matrix \\( R \\in \\mathbb{R}^{(2H - 1) \\times (2W - 1)} \\). However, considering that such a matrix would result in a significant increase in parameter count, we performed a downsampling operation on this matrix to obtain \\( R \\in \\mathbb{R}^{H \\times W} \\). At the same time, we divided the point displacement by 2 to accommodate this change. Then we used the point displacement to calculate the corresponding compensation by interpolating on \\( R \\). Finally, this compensation is added to the interpolated features. The specific process is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.678, + 0.905, + 0.699 + ], + "angle": 0, + "content": "\\[\n\\hat {p} = p + \\Delta p, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.696, + 0.783, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\hat {x} = \\phi (x, \\hat {p}) + \\phi (R, \\hat {p}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.907, + 0.762 + ], + "angle": 0, + "content": "where \\(\\phi (x,\\hat{p})\\) represents the use of bilinear interpolation function to extract the feature corresponding to position \\(\\hat{p}\\) on \\(x\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Index Offset. We modified the scanning order to enable the model to perceive the structure of the input object effectively by varying the reference token index and the deformable token index. We initially generated the reference token index \\( t_r \\in \\mathbb{R}^{N \\times 1} \\), where \\( N = H \\times W \\). The values in \\( t \\) indicate the token positions within the current patch, ranging from 0 to \\( N - 1 \\). To simplify network computations, we normalized \\( t_r \\) from its original range to [-1, 1]. This enables us to compute the deformable token index \\( t_d = t_r + \\Delta t \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8842" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.227, + 0.091, + 0.349, + 0.1 + ], + "angle": 0, + "content": "Mask R-CNN 1× schedule" + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.1, + 0.481, + 0.213 + ], + "angle": 0, + "content": "
Backbone#FLOPs\\( {\\mathbf{{AP}}}^{\\mathbf{b}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{b}}{}_{50} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{b}}{}_{75} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}}{}_{50} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}}{}_{75} \\)
ResNet-50 [15]260G38.258.841.434.755.737.2
Swin-T [24]267G42.765.246.839.362.242.2
ConvNeXt-T [25]262G44.266.648.340.163.342.8
PVTv2-B2 [34]309G45.367.149.441.264.244.4
VMamba-T [23]286G47.469.552.042.766.346.0
LocalVMamba-T [19]291G46.768.750.842.265.745.5
QuadMamba-S [39]301G46.769.051.342.465.945.6
MSVMamba-T [31]252G46.968.851.442.265.645.4
GrootV-T [38]265G47.069.451.542.766.446.0
DefMamba-S268G47.569.651.742.866.346.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.223, + 0.483, + 0.28 + ], + "angle": 0, + "content": "Table 2. Object detection and instance segmentation performance on MSCOCO 2017 val set. All using Mask R-CNN framework. \\(\\mathrm{AP^b}\\) and \\(\\mathrm{AP^m}\\) indicate the mean Average Precision (mAP) of detection and segmentation, respectively" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.307, + 0.483, + 0.475 + ], + "angle": 0, + "content": "Since the derived \\( t_d \\) contain decimal components, they cannot be utilized directly. Consequently, for \\( t_d \\), we applied a sorting algorithm to determine the indices post-offset based on the magnitude of their values. Finally, we transformed the offset features \\( \\hat{x} \\) into a 1D sequence according to these indices, thereby obtaining a content-adaptive image feature sequence. It is important to note that the sorting algorithm truncates gradients, rendering the network untrainable. To address this, we averaged the gradients of the final image sequence across the dimension and replicate them to \\( \\Delta t \\) to approximate the gradient of the scanning order offset." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.489, + 0.224, + 0.507 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.515, + 0.283, + 0.531 + ], + "angle": 0, + "content": "4.1. Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.538, + 0.483, + 0.779 + ], + "angle": 0, + "content": "Settings. The image classification experiments are conducted using the ImageNet-1K [8] dataset, which comprises over 1.28 million training images and 50,000 validation images across 1,000 categories. Our training setup closely follows the methodology of previous practices [23, 31, 38], incorporating various data augmentations such as random cropping, random horizontal flipping, label-smoothing regularization, mixup, autoaugment, and random erasing. The models are trained for 300 epochs using the AdamW [26] optimizer with a cosine decay learning rate scheduler, including a 20-epoch warm-up period. The total batch size is set to 1,024, with the models trained on \\(8 \\times\\) A800 GPUs. The optimizer parameters are configured with betas set to (0.9, 0.999), momentum set to 0.9, an initial learning rate of \\(1 \\times 10^{-3}\\), a weight decay of 0.05, and Exponential Moving Average (EMA)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Results. Table 1 presents a comparison of our proposed DefMamba models (T, S, B) with various state-of-the-art (SOTA) methods. Specifically, DefMamba-T achieves \\(78.6\\%\\) Top-1 Acc., outperforming CNNs based RegNetY800M [28] and transformer based DeiT-Ti [33] by \\(2.3\\%\\) and \\(6.4\\%\\), respectively. Moreover, DefMamba-T outperforms the recently introduced SSMs models, achieving \\(2.5\\%\\), \\(2.4\\%\\), and \\(1.3\\%\\) higher performance than ViM-T" + }, + { + "type": "table_caption", + "bbox": [ + 0.634, + 0.091, + 0.787, + 0.103 + ], + "angle": 0, + "content": "ADE20K with crop size 512" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.103, + 0.905, + 0.295 + ], + "angle": 0, + "content": "
BackbonemIOU (SS)mIOU (MS)#Param.#FLOPs
ResNet-50 [15]42.142.867M953G
Swin-T [24]44.545.860M945G
ConvNeXt-T [25]46.046.760M939G
NAT-T [14]47.148.458M934G
Vim-S [47]44.9-46M-
LocalVim-S [19]46.447.558M297G
VMamba-T [23]47.948.862M949G
PlainMamba-L2 [42]46.8-55M285G
LocalVMamba-T [19]47.949.157M970G
MSVMamba-T [31]47.648.565M942G
QuadMamba-S [39]47.248.162M961G
GrootV-T [38]48.549.460M941G
DefMamba-S48.849.665M946G
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.305, + 0.907, + 0.348 + ], + "angle": 0, + "content": "Table 3. Semantic segmentation performance on ADE20K val set. The crop size is all set to \\(512^2\\). SS and MS denote single-scale and multi-scale testing, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.371, + 0.907, + 0.508 + ], + "angle": 0, + "content": "[47], LocalViM-T [19], and MSVMamba-N [31] in terms of parameter and computational complexity. Moreover, it reduces the computational burden by \\(60\\%\\) while achieving a performance improvement of \\(0.7\\%\\) over PlainMamba-L1 [42]. DefMamba-S achieves \\(83.5\\%\\) Top-1 Acc., surpassing GrootV-T [38] and EfficientVMamba-B [27]. Furthermore, DefMamba-B achieves an accuracy of \\(84.2\\%\\), exceeding VMamba-S [23] by \\(0.6\\%\\), demonstrating the effectiveness of our methods." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.516, + 0.681, + 0.532 + ], + "angle": 0, + "content": "4.2. Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.538, + 0.907, + 0.645 + ], + "angle": 0, + "content": "Settings. We evaluated DefMamba on the MSCOCO 2017 dataset [21] using the Mask R-CNN framework [16] for object detection and instance segmentation tasks. Following prior works [24, 31, 38], we utilized backbones pretrained on ImageNet-1K for initialization. We employed standard training strategies, including \\(1 \\times (12\\) epochs) with MultiScale (MS) training, to ensure a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.909, + 0.797 + ], + "angle": 0, + "content": "Results. As depicted in Table 2, our method outperforms existing methods on most evaluation metrics. Specifically, under \\(1 \\times\\) schedule, DefMamba-S achieves 47.5 in box mAP \\((\\mathrm{AP}^{\\mathrm{b}})\\) and 42.8 in mask mAP \\((\\mathrm{AP}^{\\mathrm{m}})\\). Our model surpassed ResNet-50 [15], Swin-T [24] and ConvNeXt-T [25]. At the same time, our method improved \\(\\mathrm{AP}^{\\mathrm{m}}\\) by 0.6 points compared to LocalVMamba-T [19] and QuadMamba-S [39]. Furthermore, our method exhibited comparable performance to the previous SOTA method, VMamba-T [23], while reducing the computational load by \\(4\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.804, + 0.733, + 0.82 + ], + "angle": 0, + "content": "4.3. Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Settings. To evaluate the semantic segmentation performance of DefMamba, we trained our models using UperNet [37] initialized with pre-trained classification weights on ADE20K [45] for 160,000 iterations. We employed the AdamW optimizer [26] with a learning rate set at \\(6 \\times 10^{-5}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8843" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.09, + 0.478, + 0.162 + ], + "angle": 0, + "content": "
IndexFB-BBCB [42]LB [19]DB#Param.#FLOPsTop-1
(1)✓7.3M1.1G76.9
(2)✓8.1M1.1G76.5
(3)✓✓7.5M1.1G77.3
(4)✓✓7.5M1.1G77.1
(5)✓✓8.3M1.2G78.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.172, + 0.483, + 0.214 + ], + "angle": 0, + "content": "Table 4. Comparisons with the different scanning branches in the setting of tiny model size. DB means our deformable branch. The best results are shown in **bold** font." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.231, + 0.476, + 0.329 + ], + "angle": 0, + "content": "
IndexDPDTOBCA#Param.#FLOPsTop-1
(1)7.5M1.1G77.0
(2)✓7.5M1.2G77.4
(3)✓7.5M1.2G77.2
(4)✓✓7.5M1.2G77.9
(5)✓✓✓8.2M1.2G78.2
(6)✓✓✓✓8.3M1.2G78.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.34, + 0.483, + 0.382 + ], + "angle": 0, + "content": "Table 5. Comparisons with the different components of proposed deformable scanning in tiny model size settings on ImageNet-1k. The best results are shown in bold font." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.411, + 0.483, + 0.456 + ], + "angle": 0, + "content": "Our experiments are primarily conducted using a default input resolution of \\(512 \\times 512\\). Additionally, we incorporated Multi-Scale (MS) testing to assess performance variations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.457, + 0.483, + 0.623 + ], + "angle": 0, + "content": "Results. The DefMamba-S model demonstrates favorable performance in semantic segmentation compared to various SOTA methods, as presented in Table 3. DefMamba-S achieves a mIOU of 48.8 in single-scale and 49.6 in multi-scale evaluation. This outperforms ResNet-50 [15], Swin-T [24], and ConvNeXt-T [25]. Additionally, DefMamba-S exceeds the performance of the recent SSM methods, including GrootV-T [38], QuadMamba-S [39] and MSVMamba-T [31]. Our method achieves improvements of 0.3 points, 1.6 points, and 1.2 points, respectively, on the single-scale mIoU metric." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.636, + 0.245, + 0.652 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Effect of the Proposed DSSM Structure. To give the evidence for the effectiveness of the proposed deformable branch, we conducted a series of experiments over different branch settings in Table 4. As shown in Table 4, FB-BB refers to the forward and the backward branches for feature extraction. CB represents continuous scanning [42] branch. LB is local scanning [19] branch and DB denotes our proposed deformable branch in Figure 2 (a). By comparing the results in Table 4 (1) and (5), we observed that the proposed deformable branch significantly increased the accuracy of the ImageNet dataset by \\(1.7\\%\\) within a reasonable computational budget, to demonstrate the effectiveness of the proposed deformable branch. Moreover, compared with Table 4 (3), (4) and (5), our method only increased the computational cost by 0.1G, while significantly improving the accuracy on ImageNet dataset by \\(1.4\\%\\). This further demon-" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.09, + 0.596, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.149, + 0.596, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.21, + 0.574, + 0.221 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.597, + 0.09, + 0.671, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.597, + 0.149, + 0.671, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.625, + 0.21, + 0.642, + 0.22 + ], + "angle": 0, + "content": "RS" + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.09, + 0.749, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.149, + 0.748, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.21, + 0.72, + 0.22 + ], + "angle": 0, + "content": "DS" + }, + { + "type": "image", + "bbox": [ + 0.751, + 0.09, + 0.826, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.751, + 0.149, + 0.826, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.21, + 0.798, + 0.22 + ], + "angle": 0, + "content": "RS" + }, + { + "type": "image", + "bbox": [ + 0.828, + 0.09, + 0.905, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.828, + 0.149, + 0.905, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.856, + 0.21, + 0.875, + 0.22 + ], + "angle": 0, + "content": "DS" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.233, + 0.905, + 0.275 + ], + "angle": 0, + "content": "Figure 4. Visualization of activation maps in the specific position. The position is marker by red and orange point. RS stands for raster scanning, DS stands for our deformable scanning." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.309, + 0.905, + 0.445 + ], + "angle": 0, + "content": "strates that our deformable scanning approach, as opposed to other fixed scanning methods, is more capable of capturing structural information of objects and enhancing model performance. From Table 4 (1) and (2), we noted that incorporating only the proposed deformable branch would lead to a decrease in performance due to the increased spatial token jumps. To achieve more stable training and higher model performance, we adhered to the previous paradigm by combining the FB-BB and DB in our proposed model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Effect of the Deformable Scanning Components. To thoroughly evaluate the contributions of each component in our proposed deformable scanning method, we conducted an ablation study in Table 5. As shown in Table 5, DP, DT, OB and CA represent the components of the deformable scanning in Figure 2 (b), respectively. DP (Deformable Points) involves the process of generating deformable points, which includes initializing reference points, an offsets network and a bilinear interpolation. DT (Deformable Tokens) refers to the process of dynamically changing the token order based on predicted offsets, which includes initializing token index and deformable token index, as well as an offsets network. OB represents the operation of generating offset bias. CA denotes channel attention operation in the offset network. By comparing the results in Table 5 (1), (2) and (3), we observed that adding either the DP operation or the DT operation boosting the baseline (1) performance by \\(0.2 - 0.4\\%\\), with only a minor increases in computational costs (0.1G), demonstrated that the effectiveness of both DP and DT. Moreover, when combining both DP and DT operations (4), the performance further improves by \\(1\\%\\) compared to the baseline, as shown in Table 5 (1) and (4). These results strongly prove that whether adding DT or DP individually, or combining both, the model can better learn the structure of images and facilitate the awareness of changes in object details, thus improving performance. Furthermore, we run ablation experiments to confirm the effectiveness of OB and CA by comparing Table 5 (4) and (5), and Table 5 (5) and (6), respectively. The experiments validate the effectiveness of our methods." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8844" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.214, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.09, + 0.336, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.091, + 0.482, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.298, + 0.484, + 0.382 + ], + "angle": 0, + "content": "Figure 5. Visualization of deformable points and deformable token index. In (a), the orange dots represent deformable points, the green dots represent reference points, and the red arrows represent the offset path of the points. In (b) and (c), the gradient from yellow to green represents the scanning path, with the yellow dots being scanned first and the green dots being scanned later." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.409, + 0.483, + 0.619 + ], + "angle": 0, + "content": "Visualization Results. To better demonstrate the superiority of our deformable scanning strategy, we present the activation maps of images at different positions for various methods in Figure 4, marked clearly by red and orange dots in the image. Specifically, we visualized the activation map corresponding to the final layer of the second stage using the method outlined in [23]. As illustrated in the activation map of the pen in the last line of Figure 4, our method demonstrates an enhanced ability to focus on the structural and shape information of objects, even when dealing with complex scenes that contain multiple overlapping objects. This capability allows for more precise recognition and segmentation, further highlighting the effectiveness of our approach in capturing essential details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.621, + 0.483, + 0.816 + ], + "angle": 0, + "content": "We also visualized the deformable points and deformable token index to intuitively demonstrate the performance of our method, as shown in the Figure 5. In the red box of Figure 5 (a), we can observe that some focus points outside the object shift towards the object. Such movements allow the network to attend to more object information. Compared with Figure 5 (b), our method (c) adjusts the scanning order to emphasize important tokens. For example, as shown in the first row of the Figure 5, the token corresponding to the snake's head is shifted from the middle position in a raster scan to being the first position in our method. Such offsets are beneficial for the network to learn relevant features." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.83, + 0.206, + 0.846 + ], + "angle": 0, + "content": "5. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Despite the strong results of our approach, there is still a limitation. In cases where the image contains incomplete object structures or multiple objects arranged in a regular" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.089, + 0.9, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.315, + 0.906, + 0.356 + ], + "angle": 0, + "content": "Figure 6. Failure cases. The blue dots represent deformable points, while the black arrows indicate the scanning order after deformation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.388, + 0.907, + 0.525 + ], + "angle": 0, + "content": "pattern, the deformable scanning strategy may be less effective. As illustrated in Figure 6, when the image shows only a portion of a baseball, the deformable mechanism does not capture complete structural information, resulting in offsets that are too small and converge towards the predefined scanning method. Meanwhile, when multiple objects are arranged according to a certain rule, the information variation between adjacent tokens is minimal. Results in the model remaining in an indolent learning process." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.542, + 0.634, + 0.558 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.907, + 0.903 + ], + "angle": 0, + "content": "In this work, we made efforts to tackle the challenge arising from existing Mamba-based methods, which rely on fixed scanning techniques to extract features. These methods do not fully leverage the spatial structure information inherent in images. To overcome this limitation, we proposed a novel foundation model named DefMamba, which is grounded in DS. This innovative model aims to enhance the capability of the network to learn and represent complex image structures, as well as to detect subtle changes in object details. The DS principally comprises two key operations: the shifting of focus points and the alteration of the scanning order. The first operation effectively repositions reference points toward significant regions of interest, thereby enhancing the model's sensitivity to variations in object details. The second operation modifies the scanning order to create a structure-aware sequence that is better aligned with the underlying object structure based on the input features. Extensive experimental evaluations on benchmark datasets, including ImageNet, COCO, and ADE20K, robustly demonstrate that our proposed method outperforms existing SSMs and remains competitive when compared to both CNNs and Transformer-based approaches." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8845" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.177 + ], + "angle": 0, + "content": "This work was supported by the National Natural Science Foundation of China (62172070, 62372080, 62376050, and U22B2052), and the Natural Science Foundation of Liaoning Province (2024-MSBA-24)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.189, + 0.188, + 0.205 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.213, + 0.484, + 0.284 + ], + "angle": 0, + "content": "[1] Qi Bi, Jingjun Yi, Hao Zheng, Wei Ji, Haolan Zhan, Yawen Huang, Yuexiang Li, and Yefeng Zheng. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9308-9316, 2019. 2" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.755 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8847" + } + ] +] \ No newline at end of file diff --git a/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_origin.pdf b/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..059999b33134129f6b049a0b207a1578e4cad57d --- /dev/null +++ b/2025/DefMamba_ Deformable Visual State Space Model/deb50b63-d2d0-4e53-81b5-8019ea8427b2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:743ff499c64bd1fab2336d7e6a7568494ef41ed5635f4cb563f0f310d0301c8e +size 6788667 diff --git a/2025/DefMamba_ Deformable Visual State Space Model/full.md b/2025/DefMamba_ Deformable Visual State Space Model/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f113900a277c1cc6ac3546fb0cf7a4396a4bae05 --- /dev/null +++ b/2025/DefMamba_ Deformable Visual State Space Model/full.md @@ -0,0 +1,320 @@ +# DefMamba: Deformable Visual State Space Model + +Leiye Liu $^{1}$ Miao Zhang $^{1,*}$ Jihao Yin $^{1}$ Tingwei Liu $^{1}$ Wei Ji $^{2}$ Yongri Piao $^{1,*}$ Huchuan Lu $^{1}$ $^{1}$ Dalian University of Technology $^{2}$ Yale University + +leiyeliu@mail.dlut.edu.cn,wei.ji@yale.edu,yrpiao@dlut.edu.cn + +# Abstract + +Recently, state space models (SSM), particularly Mamba, have attracted significant attention from scholars due to their ability to effectively balance computational efficiency and performance. However, most existing visual Mamba methods flatten images into 1D sequences using predefined scan orders, which results the model being less capable of utilizing the spatial structural information of the image during the feature extraction process. To address this issue, we proposed a novel visual foundation model called DefMamba. This model includes a multi-scale backbone structure and deformable mamba (DM) blocks, which dynamically adjust the scanning path to prioritize important information, thus enhancing the capture and processing of relevant input features. By combining a deformable scanning (DS) strategy, this model significantly improves its ability to learn image structures and detects changes in object details. Numerous experiments have shown that DefMamba achieves state-of-the-art performance in various visual tasks, including image classification, object detection, instance segmentation, and semantic segmentation. The code is open source on DefMamba. + +# 1. Introduction + +Most existing visual foundation models primarily rely on convolutional neural networks (CNNs) [25, 28, 32] and Transformer architectures [9, 24, 33]. However, CNNs are constrained by their sliding window structure, which limits the receptive field and significantly impedes global information aggregation across the input data. In contrast, Transformers excel in global information aggregation due to their attention mechanism, but their high computational complexity poses a challenge in achieving a balance between efficiency and performance. State space models (SSMs) [12] provide a potential solution to this trade-off. SSMs aggregate previous features through a hidden state matrix to update current features, thereby reducing the computational + +![](images/b746006dc09f3480b8bd51dc483afbf1c6b831768fb42154ddc66bddfbb6e4ae.jpg) +(a) Raster scanning + +![](images/240bbbc8ac05aa6eaab697097eb934d8555ac8db10935f13af476b482292acfe.jpg) +(b) Local scanning + +![](images/4c1686f77e4c3a741a8cb279de6aa2bba03e98bf6752142c3280709fa402d6bb.jpg) +(c) Continuous scanning + +![](images/f0bfe0498799fd4537e7586b332300a82bd9e47fc6866d89d2faa7820a01428c.jpg) +(d) Deformable scanning + +![](images/d8092b1aad8383b57f24758e18390d11e6faab60ae7a5c6a64693d893f90c4d1.jpg) +OffsetΔ + +![](images/24bc2d34f3f99430bcfaa0ebd123bcd5f30d4a40e4f22a5d586425df967c10e3.jpg) + +![](images/4a1ed3c55a890b8b6ae824edec172f1c76c35301654634c492b5ed92e06269cf.jpg) +Fixed scan order +Deformable scan order +Figure 1. Comparison of deformable scanning and other scanning methods. (a) Raster scanning [23, 47], (b) Local scanning [19], (c) Continuous scanning [42], (d) Our designed deformable scanning. The blue dots represent the reference points, and the red dots represent the deformable points. The yellow arrows represent the fixed scan order, and the red gradient arrows represent the deformable scan order. Our method exhibits an enhanced capacity to accurately capture the structural characteristics of objects, thereby enabling the development of a more refined scanning approach. + +![](images/8f4f10d14633d0f0814c8491ee725ffae41b5567e00e3e2cf349bd469e8b9b1d.jpg) +Reference point + +![](images/a01bbf82bf635c44ae384d019c9896ea46cc498232dd85d19dfec10a6bf7b35b.jpg) +Deformable point + +complexity to a linear relationship with the sequence length. Although SSMs process sequences in a recurrent manner, SSMs can perform calculations on sequences in parallel after simplification. Despite these advantages, SSMs struggle to capture long-range dependencies due to the lack of content-aware perception in the state matrix update process. + +Recently, Mamba [11] proposes an improved selection mechanism designed to optimize the training process of SSMs. This innovative mechanism introduces content awareness into the feature extraction pipeline, expands the effective receptive field, and achieves remarkable performance enhancements in various NLP tasks. Consequently, numerous studies have attempted to extend this approach to + +the broader field of computer vision [1-4, 10, 22, 30, 40, 43, 46]. The principal challenge in this endeavor is how to effectively map 2D image feature maps into 1D sequences, without losing essential information. Most existing methods employ predefined strategies for mapping, such as raster scanning [23, 47], local scanning [19], and continuous scanning [42]. However, as illustrated in Figure 1, these methods all rely on a fixed scanning path. This results in adjacent tokens no longer being adjacent after flattening. Thereby, they neglect the inherent spatial structure of the image, leading to the loss of structural information. To address this issue, QuadMamba [39] determines the scanning window size based on the amount of information contained in different areas of the image. However, the scanning order in each window is fixed. This leads to an incomplete solution of the aforementioned issues. GrootV [38] adaptively constructs a tree topology based on input features and subsequently extracts features from this topology. Nevertheless, it employs only adjacent features in constructing the topology and distributes attention uniformly across the patch. The aforementioned methods are either based on a fixed scanning order, leading to the loss of structural information, or treat the information in the perception area equally, resulting in insensitivity to variations in object details. + +To solve this problem, we proposed a novel framework called DefMamba inspired by deformable mechanisms [6, 36]. However, intuitively applying deformable mechanisms to SSMs still causes structural information loss and increases computational complexity. Therefore, we proposed a deformable state space model and a deformable scanning strategy (DS) to prioritize deformable tokens based on essential information and slide reference points towards the important area. This approach enables the SSMs to capture and process relevant features related to the input more effectively. Specifically, we shifted the reference point by the generated offset from a fixed position to an adjustable one that provided more useful information, thereby facilitating the awareness of changes in object details. On the other hand, we also dynamically adjusted the scanning order by the offset vector for obtaining a structure-aware sequence. In this way, our framework adaptively perceives the variations in object details to find the most suitable feature points, and determines the optimal scanning order consistent with the object structure based on the input image features. + +We conducted extensive experiments to validate the effectiveness of DefMamba across multiple visual benchmarks, including image classification on ImageNet [8], object detection and instance segmentation on COCO [21], and semantic segmentation on ADE20K [45]. These results demonstrate that our method outperforms existing SSMs based approaches on all benchmarks and remains competitive with CNN and transformer-based methods. + +# 2. Related Work + +# 2.1. Mamba for Visual Applications + +Numerous studies have successfully integrated Mamba [11] into visual tasks [19, 23, 27, 29, 31, 38, 39, 42, 47], demonstrating preliminary achievements. ViM [47] introduces a bidirectional scanning approach to transform 2D image into 1D sequences, which are then fed into SSM for global context modeling, marking the first integration of Mamba into visual tasks. VMamba [23] employs a four-way scanning algorithm to convert 2D image into 1D sequences. PlainMamba [42] modifies the scanning method from raster to continuous, preserving the spatial dependencies of the image. MSVMamba [31] downsamples the sequence based on four scans to reduce computational redundancy and mitigates the issue of information loss. GrootV [38] constructs a minimum spanning tree on a four-way plane graph using the differences between adjacent features, dynamically adjusting the scanning order according to different inputs. QuadMamba [39] adaptively adjusts the window granularity during the scanning process based on the information content of the image to better aggregate local information. While GrootV and QuadMamba can adapt their scanning methods based on input data, GrootV only considers the relationships between adjacent elements when generating the minimum spanning tree, neglecting global information. On the other hand, QuadMamba still relies on predefined scanning methods and does not achieve true dynamic scanning. In contrast, our DefMamba introduces a content-aware deformable scanning strategy that allows the network to dynamically learn the scanning order and the reference points position. + +# 2.2. Deformable CNNs and Attention Mechanism + +Deformable convolution [6, 20, 41, 48] employs a convolution kernel that adapts to geometric variations in the input feature map, thereby overcoming the limitations of traditional convolution, which performs poorly when dealing with complex targets. Recently, the deformable mechanism has been extended to visual transformers [9] to enhance their ability to capture local features and adapt to geometric variations. DPT [5] proposes an adaptive patch embedding method that dynamically adjusts the position and size of patches while preserving their semantic information. PSViT [44] introduces a progressive sampling module prior to ViT [9], which iteratively identifies the most suitable deformable point positions for the current image. DAT [36] integrates the deformable mechanism with the self-attention mechanism in Transformers for the first time, incorporating deformable attention into the visual backbone. This approach learns a set of features corresponding to global keypoints and adapts to spatial variations. Previous approaches have explored various ways to effectively incorporate de + +![](images/ae1ba1cc1e661f4023f08f9b73b17db10b6af066bb24446c2126442309318c23.jpg) +Figure 2. Overview of DefMamba. (a) depicts the overall architecture of our network. (b) illustrates the structure of the deformable Mamba block. LN means LayerNorm and FFN is a feed-forward network. + +formable mechanism into transformer architectures. With the recent popularity of Mamba [11], we attempted to introduce deformable mechanism into Mamba. However, directly applying these mechanism has resulted in issues like the loss of structural information and the necessity for additional modules. In this context, our designed DS strategy stands out by effectively prioritizing deformable tokens while directing reference points toward key areas. + +# 3. Method + +In this section, we first summarized the SSMs in Section 3.1. Then, in Section 3.2, we described the overall structure of the proposed network. Section 3.3 introduces a Deformable State Space Model (DSSM). Finally, Section 3.4 presents the designed model configurations across multiple scales. + +# 3.1. Preliminaries + +SSMs, including notable implementations like S4 [12] and Mamba [11], are structured sequence architectures that combine elements of recurrent neural networks (RNNs) and CNNs, enabling linear or near-linear scaling with respect to sequence length. These models, derived from continuous systems, define a 1D function-to-function map for an input $u(t) \in \mathbb{R}^L$ to an output $y(t) \in \mathbb{R}^L$ through a hidden state $h(t) \in \mathbb{R}^N$ . Where $t$ represents time. More formally, SSMs are characterized by the continuous-time Ordinary Differential Equation (ODE) [11] presented: + +$$ +\begin{array}{l} h ^ {\prime} (t) = \mathbf {A} h (t) + \mathbf {B} u (t), \\ y (t) = \hat {C} h (t), \\ \end{array} +$$ + +where $h(t)$ is the current hidden state. $h^{\prime}(t)$ is the updated hidden state. $u(t)$ is the current input. $y(t)$ is the output. $\mathbf{A} \in \mathbb{R}^{N \times N}$ is SSM's evolution matrix, and $\mathbf{B} \in \mathbb{R}^{N \times 1}$ , $\hat{C} \in \mathbb{R}^{1 \times N}$ are the input and output projection matrices, respectively. + +To enable the application of SSMs in sequence modeling tasks within deep learning, they must be discretized, + +transforming the SSM from a continuous-time function-to-function map into a discrete-time sequence-to-sequence map. S4 [12] and Mamba [11] are examples of discrete adaptations of the continuous system, incorporating a timescale parameter $\Delta$ to convert the continuous parameters $\mathbf{A}$ , $\mathbf{B}$ into their discrete counterparts $\bar{\mathbf{A}}$ , $\bar{\mathbf{B}}$ . This discretization is typically achieved using the Zero-Order Hold (ZOH) [11] method: + +$$ +\begin{array}{l} \bar {\mathbf {A}} = \exp (\Delta \mathbf {A}), \\ \bar {\mathbf {B}} = \left( \begin{array}{l} (\Delta \mathbf {A}) ^ {- 1} (\exp (\Delta \mathbf {A}) - \mathbf {I}) \cdot \Delta \mathbf {B}, \end{array} \right. \tag {2} \\ \end{array} +$$ + +$$ +h _ {t} = \bar {\mathbf {A}} h _ {t - 1} + \bar {\mathbf {B}} u _ {t}, +$$ + +$$ +y _ {t} = \mathbf {C} h _ {t}. +$$ + +While both S4 [12] and Mamba [11] employ a similar discretization process as outlined in Equation 2, Mamba distinguishes itself from S4 by conditioning the parameters $\Delta \in \mathbb{R}^{b\times L\times D}$ , $\mathbf{B}\in \mathbb{R}^{b\times L\times N}$ , and $\mathbf{C}\in \mathbb{R}^{b\times L\times N}$ on the input $u\in \mathbb{R}^{b\times L\times D}$ through the S6 Selective Scan Mechanism. Here, $b$ represents the batch size, $L$ denotes the sequence length, and $D$ signifies the feature dimension. + +# 3.2. Overall Model Architecture + +DefMamba uses a common multi-scale backbone structure similar to many CNNs [25, 28] and Transformers [24]. As illustrated in Figure 2(a), the image $I \in \mathbb{R}^{H \times W \times 3}$ is first divided into patches through a patch embedding layer, which produces a 2D feature map with spatial dimensions $H / 4 \times W / 4$ and channel dimensions $C$ . Subsequently, multiple network stages are used to create hierarchical representations of dimensions $H / 8 \times W / 8 \times 2C$ , $H / 16 \times W / 16 \times 4C$ , and $H / 32 \times W / 32 \times 8C$ . Each stage consists of a stack of Deformable Mamba (DM) blocks followed by a downsampling layer (except the fourth stage). Finally, the features are average-pooled and sent to the classification head to obtain the prediction results. In particular, we followed [38] and used overlapping forms in the patch embedding layer and the downsampling layers. For specific structural details, please refer to the Appendix. + +![](images/b9eabf434458bbe39aa7301aae2d2af4ec4d3edd5e6eae6096bb601ccaf7c1bd.jpg) +Figure 3. Illustration of Deformable State Space Model. (a) illustrates the processing flow of the deformable state space model for feature extraction. (b) depicts the processing flow of the deformable scan. The upper part primarily shifts the feature points to enable the model to focus on more salient regions, while the lower part shifts the token positions to facilitate the discovery of a scanning order that is better suited to the current input. To clearly illustrate the process, only nine points are depicted in the figure, however, the actual processing involves a greater number of points. (c) presents the detailed structure of the offset network. + +Different from the Mamba structure used in language models [11], the DM block follows the popular structure of the Transformer block [9, 24], which consists of two Layer Norm (LN) layers, an FFN, a DSSM (to be introduced in the following subsection) and residual connections, as shown in the Figure 2(b). + +# 3.3. Deformable State Space Model + +The overall architecture of the deformable state space model is presented in Figure 3(a). Inspired by [23, 31, 38], we employed depthwise convolution to replace the original 1D convolution in the vision mamba block [47] and incorporated a deformable branch comprising a deformable scanning and a deformable SSM (DSSM). We maintained the standard forward and backward branches to ensure stable model convergence, as our method introduces more spatial token jumps compared to previous scanning methods, potentially complicating model training and learning. Subsequent experiments validate this (Table 4). + +Deformable Scanning. Given the issue of mutual interference between multiple deformable points, we constrained the offset of the deformable points in a certain range. This ensures the relationship between deformable points and reference points remains invariant, allowing us to approximate the relationship after deformation using the relationship before deformation. Furthermore, considering the simplicity of the computation, we employed a parallel approach to simultaneously adjust the reference points and scanning order, thereby reducing the computational burden. The specific structure is illustrated in the Figure 3(b). + +Given an input feature $x \in \mathbb{R}^{H \times W \times C}$ , where $C$ denotes + +the channel dimension and $H, W$ represent the spatial resolution. We first generated the offset $o \in \mathbb{R}^{H \times W \times 3}$ using a subnetwork that utilizes $x$ to output the offset values $o$ for the reference point and the reference token. + +We initially implemented the subnetwork as depicted in Figure 3(c). The input features are first processed through a $K \times K$ depthwise convolution to capture local features. Subsequently, GELU, Layer Normalization (LN), and a $1 \times 1$ convolution are employed to derive the offset values, which encompass three dimensions in total. The first two dimensions represent the offset of the reference point in two-dimensional space, while the third dimension signifies the offset of the reference token index within the entire patch. During our experiments, we observed that the offset of the token necessitates global perception of the features within the patch, which cannot be achieved solely through convolution. In light of this, and considering the previous method's findings [29, 31] that mamba has redundancy in the channel dimension, we incorporated a Channel Attention (CA) mechanism [18] following the depthwise convolution layer. This mechanism mitigates channel redundancy and facilitates the integration of global contextual information. Notably, following the configuration of DAT [36], we set $K$ to [9, 7, 5, 3] across four stages and omitted the bias in the $1 \times 1$ convolution. + +To stabilize the training process, we employed the tanh function to mitigate the impact of extreme values in $o$ , where $\hat{o} = \tanh(o)$ . Subsequently, we split $\hat{o}$ to 2 parts along the channel dimension, one with 2 channels and one with 1 channel, to obtain the point offset $\Delta p$ and token index offset $\Delta t$ . As previously mentioned, we needed to fur + +
MethodType#Param.#FLOPsTop-1 Acc.
RegNetY-800M [28]C6M0.8G76.3
GhostNet 1.3× [13]C7M0.2G75.7
DeiT-Ti [33]T6M1.3G72.2
ViM-T [47]S7M1.5G76.1
EffVMamba-T [27]S6M0.8G76.5
LocalVim-T [19]S8M1.5G76.2
PlainMamba-L1 [42]S7M3.0G77.9
MSVMamba-N [31]S7M0.9G77.3
QuadMamba-Li [39]S5M0.8G74.2
DefMamba-TS8M1.2G78.6
RegNetY-4G [28]C21M4.0G80.0
ConvNeXt-T [25]C29M4.5G82.1
Conv2Former-T [17]C27M4.4G83.2
DeiT-S [33]T22M4.6G79.8
Swin-T [24]T29M4.5G81.3
CoAtNet-0 [7]T25M4.0G81.6
CrossFormer-S [35]T31M4.9G82.5
ViM-S [47]S26M5.1G81.0
VMamba-T [23]S22M5.6G82.2
+ +
MethodType#Param.#FLOPsTop-1 Acc.
LocalVim-S [19]S28M4.8G81.2
LocalVMamba-T [19]S26M5.7G82.7
EffVMamba-B [27]S33M4.6G83.0
MSVMamba-T [31]S33M4.6G82.8
PlainMamba-L2 [42]S25M8.1G81.6
GrootV-T [38]S30M4.8G83.4
QuadMamba-S [39]S31M5.5G82.4
DefMamba-SS32M4.8G83.5
ConvNeXt-S [25]C50M8.7G83.1
Conv2Former [17]C50M8.7G84.1
Swin-S [24]T50M8.7G83.0
CoAtNet-1 [7]T42M8.0G83.3
CrossFormer-B [35]T52M9.2G83.4
VMamba-S [23]S50M8.7G83.6
LocalVMamba-B [19]S50M11.4G83.7
PlainMamba-L3 [42]S50M14.4G82.3
GrootV-S [38]S51M8.5G84.2
QuadMamba-B [39]S50M9.3G83.8
DefMamba-BS51M8.5G84.2
+ +Table 1. Image classification performance on ImageNet-1K validation set. C, T and S indicate the model type of CNNs, Transformer and SSM. The best results are shown in bold font. + +ther constrain $\Delta p$ , in order to stabilize training and simplify the structure. We divided the horizontal and vertical dimensions of $\Delta p$ by $W$ and $H$ , respectively, thereby limiting the offset to the range of a single token. The detailed process is outlined as follows: + +$$ +\Delta p, \Delta t = S p l i t (\tanh (O f f s e t (x)), \mathrm {d i m s} = [ 2, 1 ]), \tag {3} +$$ + +$$ +\hat {\Delta} p = \operatorname {N o r m} (\Delta p). +$$ + +Then, we sent the point offset $\hat{\Delta p}$ , token index offset $\Delta t$ , and input feature $x$ to the point offset branch and index branch, to obtain the final output, respectively. + +Point Offset. To obtain feature representations that are more sensitive to changes in objects, we dynamically adapted the network's reference points to deformable points that contain more relevant information based on the input. Firstly, we generated reference points $p \in \mathbb{R}^{H \times W \times 2}$ . The values in $p$ correspond to the two-dimensional coordinates of points ranging from (0, 0) to $(H - 1, W - 1)$ . To simplify network calculations, we normalized $p$ from its original range to $[-1, 1]$ , where $[-1, 1]$ represents the point in the upper left corner and $[1, 1]$ represents the point in the lower right corner. We then added the reference point $p$ and the offset to obtain the deformable point $\hat{p} = p + \Delta p$ . Since the offset $\hat{p}$ contains a decimal part, it cannot be used directly. Therefore, we used bilinear interpolation to extract features at the spatial position corresponding to the offset point $\hat{p}$ from the input $x$ . + +When our model performs point offset, the features will move in space, potentially causing the position encoding added in the initial stage to become ineffective and thereby + +decreasing model performance. To address this, we designed an offset bias based on the relative position encoding in the Swin Transformer. Specifically, given the feature map of size $H \times W$ , the relative coordinate displacement of points lies within the range of $[-H, H]$ and $[-W, W]$ in two dimensions, respectively. Therefore, we set a learnable relative offset bias matrix $R \in \mathbb{R}^{(2H - 1) \times (2W - 1)}$ . However, considering that such a matrix would result in a significant increase in parameter count, we performed a downsampling operation on this matrix to obtain $R \in \mathbb{R}^{H \times W}$ . At the same time, we divided the point displacement by 2 to accommodate this change. Then we used the point displacement to calculate the corresponding compensation by interpolating on $R$ . Finally, this compensation is added to the interpolated features. The specific process is as follows: + +$$ +\hat {p} = p + \Delta p, \tag {4} +$$ + +$$ +\hat {x} = \phi (x, \hat {p}) + \phi (R, \hat {p}), +$$ + +where $\phi (x,\hat{p})$ represents the use of bilinear interpolation function to extract the feature corresponding to position $\hat{p}$ on $x$ . + +Index Offset. We modified the scanning order to enable the model to perceive the structure of the input object effectively by varying the reference token index and the deformable token index. We initially generated the reference token index $t_r \in \mathbb{R}^{N \times 1}$ , where $N = H \times W$ . The values in $t$ indicate the token positions within the current patch, ranging from 0 to $N - 1$ . To simplify network computations, we normalized $t_r$ from its original range to [-1, 1]. This enables us to compute the deformable token index $t_d = t_r + \Delta t$ . + +Mask R-CNN 1× schedule + +
Backbone#FLOPs\( {\mathbf{{AP}}}^{\mathbf{b}} \)\( {\mathbf{{AP}}}^{\mathbf{b}}{}_{50} \)\( {\mathbf{{AP}}}^{\mathbf{b}}{}_{75} \)\( {\mathbf{{AP}}}^{\mathbf{m}} \)\( {\mathbf{{AP}}}^{\mathbf{m}}{}_{50} \)\( {\mathbf{{AP}}}^{\mathbf{m}}{}_{75} \)
ResNet-50 [15]260G38.258.841.434.755.737.2
Swin-T [24]267G42.765.246.839.362.242.2
ConvNeXt-T [25]262G44.266.648.340.163.342.8
PVTv2-B2 [34]309G45.367.149.441.264.244.4
VMamba-T [23]286G47.469.552.042.766.346.0
LocalVMamba-T [19]291G46.768.750.842.265.745.5
QuadMamba-S [39]301G46.769.051.342.465.945.6
MSVMamba-T [31]252G46.968.851.442.265.645.4
GrootV-T [38]265G47.069.451.542.766.446.0
DefMamba-S268G47.569.651.742.866.346.2
+ +Table 2. Object detection and instance segmentation performance on MSCOCO 2017 val set. All using Mask R-CNN framework. $\mathrm{AP^b}$ and $\mathrm{AP^m}$ indicate the mean Average Precision (mAP) of detection and segmentation, respectively + +Since the derived $t_d$ contain decimal components, they cannot be utilized directly. Consequently, for $t_d$ , we applied a sorting algorithm to determine the indices post-offset based on the magnitude of their values. Finally, we transformed the offset features $\hat{x}$ into a 1D sequence according to these indices, thereby obtaining a content-adaptive image feature sequence. It is important to note that the sorting algorithm truncates gradients, rendering the network untrainable. To address this, we averaged the gradients of the final image sequence across the dimension and replicate them to $\Delta t$ to approximate the gradient of the scanning order offset. + +# 4. Experiments + +# 4.1. Image Classification + +Settings. The image classification experiments are conducted using the ImageNet-1K [8] dataset, which comprises over 1.28 million training images and 50,000 validation images across 1,000 categories. Our training setup closely follows the methodology of previous practices [23, 31, 38], incorporating various data augmentations such as random cropping, random horizontal flipping, label-smoothing regularization, mixup, autoaugment, and random erasing. The models are trained for 300 epochs using the AdamW [26] optimizer with a cosine decay learning rate scheduler, including a 20-epoch warm-up period. The total batch size is set to 1,024, with the models trained on $8 \times$ A800 GPUs. The optimizer parameters are configured with betas set to (0.9, 0.999), momentum set to 0.9, an initial learning rate of $1 \times 10^{-3}$ , a weight decay of 0.05, and Exponential Moving Average (EMA). + +Results. Table 1 presents a comparison of our proposed DefMamba models (T, S, B) with various state-of-the-art (SOTA) methods. Specifically, DefMamba-T achieves $78.6\%$ Top-1 Acc., outperforming CNNs based RegNetY800M [28] and transformer based DeiT-Ti [33] by $2.3\%$ and $6.4\%$ , respectively. Moreover, DefMamba-T outperforms the recently introduced SSMs models, achieving $2.5\%$ , $2.4\%$ , and $1.3\%$ higher performance than ViM-T + +ADE20K with crop size 512 + +
BackbonemIOU (SS)mIOU (MS)#Param.#FLOPs
ResNet-50 [15]42.142.867M953G
Swin-T [24]44.545.860M945G
ConvNeXt-T [25]46.046.760M939G
NAT-T [14]47.148.458M934G
Vim-S [47]44.9-46M-
LocalVim-S [19]46.447.558M297G
VMamba-T [23]47.948.862M949G
PlainMamba-L2 [42]46.8-55M285G
LocalVMamba-T [19]47.949.157M970G
MSVMamba-T [31]47.648.565M942G
QuadMamba-S [39]47.248.162M961G
GrootV-T [38]48.549.460M941G
DefMamba-S48.849.665M946G
+ +Table 3. Semantic segmentation performance on ADE20K val set. The crop size is all set to $512^2$ . SS and MS denote single-scale and multi-scale testing, respectively. + +[47], LocalViM-T [19], and MSVMamba-N [31] in terms of parameter and computational complexity. Moreover, it reduces the computational burden by $60\%$ while achieving a performance improvement of $0.7\%$ over PlainMamba-L1 [42]. DefMamba-S achieves $83.5\%$ Top-1 Acc., surpassing GrootV-T [38] and EfficientVMamba-B [27]. Furthermore, DefMamba-B achieves an accuracy of $84.2\%$ , exceeding VMamba-S [23] by $0.6\%$ , demonstrating the effectiveness of our methods. + +# 4.2. Object Detection + +Settings. We evaluated DefMamba on the MSCOCO 2017 dataset [21] using the Mask R-CNN framework [16] for object detection and instance segmentation tasks. Following prior works [24, 31, 38], we utilized backbones pretrained on ImageNet-1K for initialization. We employed standard training strategies, including $1 \times (12$ epochs) with MultiScale (MS) training, to ensure a fair comparison. + +Results. As depicted in Table 2, our method outperforms existing methods on most evaluation metrics. Specifically, under $1 \times$ schedule, DefMamba-S achieves 47.5 in box mAP $(\mathrm{AP}^{\mathrm{b}})$ and 42.8 in mask mAP $(\mathrm{AP}^{\mathrm{m}})$ . Our model surpassed ResNet-50 [15], Swin-T [24] and ConvNeXt-T [25]. At the same time, our method improved $\mathrm{AP}^{\mathrm{m}}$ by 0.6 points compared to LocalVMamba-T [19] and QuadMamba-S [39]. Furthermore, our method exhibited comparable performance to the previous SOTA method, VMamba-T [23], while reducing the computational load by $4\%$ . + +# 4.3. Semantic Segmentation + +Settings. To evaluate the semantic segmentation performance of DefMamba, we trained our models using UperNet [37] initialized with pre-trained classification weights on ADE20K [45] for 160,000 iterations. We employed the AdamW optimizer [26] with a learning rate set at $6 \times 10^{-5}$ . + +
IndexFB-BBCB [42]LB [19]DB#Param.#FLOPsTop-1
(1)✓7.3M1.1G76.9
(2)✓8.1M1.1G76.5
(3)✓✓7.5M1.1G77.3
(4)✓✓7.5M1.1G77.1
(5)✓✓8.3M1.2G78.6
+ +Table 4. Comparisons with the different scanning branches in the setting of tiny model size. DB means our deformable branch. The best results are shown in **bold** font. + +
IndexDPDTOBCA#Param.#FLOPsTop-1
(1)7.5M1.1G77.0
(2)✓7.5M1.2G77.4
(3)✓7.5M1.2G77.2
(4)✓✓7.5M1.2G77.9
(5)✓✓✓8.2M1.2G78.2
(6)✓✓✓✓8.3M1.2G78.6
+ +Table 5. Comparisons with the different components of proposed deformable scanning in tiny model size settings on ImageNet-1k. The best results are shown in bold font. + +Our experiments are primarily conducted using a default input resolution of $512 \times 512$ . Additionally, we incorporated Multi-Scale (MS) testing to assess performance variations. + +Results. The DefMamba-S model demonstrates favorable performance in semantic segmentation compared to various SOTA methods, as presented in Table 3. DefMamba-S achieves a mIOU of 48.8 in single-scale and 49.6 in multi-scale evaluation. This outperforms ResNet-50 [15], Swin-T [24], and ConvNeXt-T [25]. Additionally, DefMamba-S exceeds the performance of the recent SSM methods, including GrootV-T [38], QuadMamba-S [39] and MSVMamba-T [31]. Our method achieves improvements of 0.3 points, 1.6 points, and 1.2 points, respectively, on the single-scale mIoU metric. + +# 4.4. Ablation Study + +Effect of the Proposed DSSM Structure. To give the evidence for the effectiveness of the proposed deformable branch, we conducted a series of experiments over different branch settings in Table 4. As shown in Table 4, FB-BB refers to the forward and the backward branches for feature extraction. CB represents continuous scanning [42] branch. LB is local scanning [19] branch and DB denotes our proposed deformable branch in Figure 2 (a). By comparing the results in Table 4 (1) and (5), we observed that the proposed deformable branch significantly increased the accuracy of the ImageNet dataset by $1.7\%$ within a reasonable computational budget, to demonstrate the effectiveness of the proposed deformable branch. Moreover, compared with Table 4 (3), (4) and (5), our method only increased the computational cost by 0.1G, while significantly improving the accuracy on ImageNet dataset by $1.4\%$ . This further demon- + +![](images/09baed4a154e94d6c2235b759bb1883c14283e4c331de41876fa79b1ef412300.jpg) + +![](images/b6fae81d86ea4e205ec6563dab4fdb5cc749291aa980ab311ea8681c6175d3f7.jpg) +Image +Figure 4. Visualization of activation maps in the specific position. The position is marker by red and orange point. RS stands for raster scanning, DS stands for our deformable scanning. + +![](images/47216140e4c4590f434e7f793ae29f58d44143662ab7d43c8dd7e4d25871089d.jpg) + +![](images/e0cdb04e68326430b383fa960dfe10dd561e20e24f309c423f55b28490c31e20.jpg) +RS + +![](images/166745a0b2523067f384e2bcbef4b4d0857b25f067bef4f69a3761484c211e6f.jpg) + +![](images/6b9b73f12108e870d3d0cba1193b5c7ccfe5e9309c564288bb1167bb55b6fbb8.jpg) +DS + +![](images/c14c85d39fb53a27df055b1fded592e4b072beaa0540990d655d183f5c446d58.jpg) + +![](images/9b0a62375488617458d541bafc1bd43e9a7b3cbae1882bb043b5632217b05bdb.jpg) +RS + +![](images/0232c90e70eeb5784c8fc50b3fbd7966a13a6b58ee085127a6d08a352d997621.jpg) + +![](images/a0f94ca9be6f5d0348760820a3e080d3540009a4e6fd74be31d07c2f66e48612.jpg) +DS + +strates that our deformable scanning approach, as opposed to other fixed scanning methods, is more capable of capturing structural information of objects and enhancing model performance. From Table 4 (1) and (2), we noted that incorporating only the proposed deformable branch would lead to a decrease in performance due to the increased spatial token jumps. To achieve more stable training and higher model performance, we adhered to the previous paradigm by combining the FB-BB and DB in our proposed model. + +Effect of the Deformable Scanning Components. To thoroughly evaluate the contributions of each component in our proposed deformable scanning method, we conducted an ablation study in Table 5. As shown in Table 5, DP, DT, OB and CA represent the components of the deformable scanning in Figure 2 (b), respectively. DP (Deformable Points) involves the process of generating deformable points, which includes initializing reference points, an offsets network and a bilinear interpolation. DT (Deformable Tokens) refers to the process of dynamically changing the token order based on predicted offsets, which includes initializing token index and deformable token index, as well as an offsets network. OB represents the operation of generating offset bias. CA denotes channel attention operation in the offset network. By comparing the results in Table 5 (1), (2) and (3), we observed that adding either the DP operation or the DT operation boosting the baseline (1) performance by $0.2 - 0.4\%$ , with only a minor increases in computational costs (0.1G), demonstrated that the effectiveness of both DP and DT. Moreover, when combining both DP and DT operations (4), the performance further improves by $1\%$ compared to the baseline, as shown in Table 5 (1) and (4). These results strongly prove that whether adding DT or DP individually, or combining both, the model can better learn the structure of images and facilitate the awareness of changes in object details, thus improving performance. Furthermore, we run ablation experiments to confirm the effectiveness of OB and CA by comparing Table 5 (4) and (5), and Table 5 (5) and (6), respectively. The experiments validate the effectiveness of our methods. + +![](images/a4a975e2d4ed761d1256a74adb474d33b63f3521337444a84dfd5293dc89adf7.jpg) +Figure 5. Visualization of deformable points and deformable token index. In (a), the orange dots represent deformable points, the green dots represent reference points, and the red arrows represent the offset path of the points. In (b) and (c), the gradient from yellow to green represents the scanning path, with the yellow dots being scanned first and the green dots being scanned later. + +![](images/0035e466654ac12b930b27d494414f135eaaf847ea1943c1c955a4dd24a659a9.jpg) + +![](images/0ed8e8653f85ff217bb8ce5c8acd70b4a1dffe6b229bbaf69a89868f7e5321f1.jpg) + +Visualization Results. To better demonstrate the superiority of our deformable scanning strategy, we present the activation maps of images at different positions for various methods in Figure 4, marked clearly by red and orange dots in the image. Specifically, we visualized the activation map corresponding to the final layer of the second stage using the method outlined in [23]. As illustrated in the activation map of the pen in the last line of Figure 4, our method demonstrates an enhanced ability to focus on the structural and shape information of objects, even when dealing with complex scenes that contain multiple overlapping objects. This capability allows for more precise recognition and segmentation, further highlighting the effectiveness of our approach in capturing essential details. + +We also visualized the deformable points and deformable token index to intuitively demonstrate the performance of our method, as shown in the Figure 5. In the red box of Figure 5 (a), we can observe that some focus points outside the object shift towards the object. Such movements allow the network to attend to more object information. Compared with Figure 5 (b), our method (c) adjusts the scanning order to emphasize important tokens. For example, as shown in the first row of the Figure 5, the token corresponding to the snake's head is shifted from the middle position in a raster scan to being the first position in our method. Such offsets are beneficial for the network to learn relevant features. + +# 5. Limitation + +Despite the strong results of our approach, there is still a limitation. In cases where the image contains incomplete object structures or multiple objects arranged in a regular + +![](images/d324cf04f66a3b2d46aeb62497af47027e0615ced8c7bf95c00d169828d00335.jpg) +Figure 6. Failure cases. The blue dots represent deformable points, while the black arrows indicate the scanning order after deformation. + +pattern, the deformable scanning strategy may be less effective. As illustrated in Figure 6, when the image shows only a portion of a baseball, the deformable mechanism does not capture complete structural information, resulting in offsets that are too small and converge towards the predefined scanning method. Meanwhile, when multiple objects are arranged according to a certain rule, the information variation between adjacent tokens is minimal. Results in the model remaining in an indolent learning process. + +# 6. Conclusion + +In this work, we made efforts to tackle the challenge arising from existing Mamba-based methods, which rely on fixed scanning techniques to extract features. These methods do not fully leverage the spatial structure information inherent in images. To overcome this limitation, we proposed a novel foundation model named DefMamba, which is grounded in DS. This innovative model aims to enhance the capability of the network to learn and represent complex image structures, as well as to detect subtle changes in object details. The DS principally comprises two key operations: the shifting of focus points and the alteration of the scanning order. The first operation effectively repositions reference points toward significant regions of interest, thereby enhancing the model's sensitivity to variations in object details. The second operation modifies the scanning order to create a structure-aware sequence that is better aligned with the underlying object structure based on the input features. Extensive experimental evaluations on benchmark datasets, including ImageNet, COCO, and ADE20K, robustly demonstrate that our proposed method outperforms existing SSMs and remains competitive when compared to both CNNs and Transformer-based approaches. + +# Acknowledgement + +This work was supported by the National Natural Science Foundation of China (62172070, 62372080, 62376050, and U22B2052), and the Natural Science Foundation of Liaoning Province (2024-MSBA-24). + +# References + +[1] Qi Bi, Jingjun Yi, Hao Zheng, Wei Ji, Haolan Zhan, Yawen Huang, Yuexiang Li, and Yefeng Zheng. Samba: Severity-aware recurrent modeling for cross-domain medical image grading. In Advances in Neural Information Processing Systems (NeurIPS), pages 75829-75852, 2024. 2 +[2] Qi Bi, Jingjun Yi, Haolan Zhan, Wei Ji, and Gui-Song Xia. 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Comparison of deformable scanning and other scanning methods. (a) Raster scanning [23, 47], (b) Local scanning [19], (c) Continuous scanning [42], (d) Our designed deformable scanning. The blue dots represent the reference points, and the red dots represent the deformable points. The yellow arrows represent the fixed scan order, and the red gradient arrows represent the deformable scan order. Our method exhibits an enhanced capacity to accurately capture the structural characteristics of objects, thereby enabling the development of a more refined scanning approach." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 461, + 403, + 471, + 411 + ], + "blocks": [ + { + "bbox": [ + 461, + 403, + 471, + 411 + ], + "lines": [ + { + "bbox": [ + 461, + 403, + 471, + 411 + ], + "spans": [ + { + "bbox": [ + 461, + 403, + 471, + 411 + ], + "type": "image", + "image_path": "8f4f10d14633d0f0814c8491ee725ffae41b5567e00e3e2cf349bd469e8b9b1d.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 402, + 525, + 411 + ], + "lines": [ + { + "bbox": [ + 473, + 402, + 525, + 411 + ], + "spans": [ + { + "bbox": [ + 473, + 402, + 525, + 411 + ], + "type": "text", + "content": "Reference point" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 461, + 413, + 471, + 421 + ], + "blocks": [ + { + "bbox": [ + 461, + 413, + 471, + 421 + ], + "lines": [ + { + "bbox": [ + 461, + 413, + 471, + 421 + ], + "spans": [ + { + "bbox": [ + 461, + 413, + 471, + 421 + ], + "type": "image", + "image_path": "a01bbf82bf635c44ae384d019c9896ea46cc498232dd85d19dfec10a6bf7b35b.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 413, + 531, + 422 + ], + "lines": [ + { + "bbox": [ + 473, + 413, + 531, + 422 + ], + "spans": [ + { + "bbox": [ + 473, + 413, + 531, + 422 + ], + "type": "text", + "content": "Deformable point" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 556, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 555, + 629 + ], + "type": "text", + "content": "complexity to a linear relationship with the sequence length. Although SSMs process sequences in a recurrent manner, SSMs can perform calculations on sequences in parallel after simplification. Despite these advantages, SSMs struggle to capture long-range dependencies due to the lack of content-aware perception in the state matrix update process." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": "Recently, Mamba [11] proposes an improved selection mechanism designed to optimize the training process of SSMs. This innovative mechanism introduces content awareness into the feature extraction pipeline, expands the effective receptive field, and achieves remarkable performance enhancements in various NLP tasks. Consequently, numerous studies have attempted to extend this approach to" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 148, + 712 + ], + "type": "text", + "content": "*Corresponding authors." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8838" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 57, + 72, + 294, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 72, + 294, + 358 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 294, + 358 + ], + "type": "text", + "content": "the broader field of computer vision [1-4, 10, 22, 30, 40, 43, 46]. The principal challenge in this endeavor is how to effectively map 2D image feature maps into 1D sequences, without losing essential information. Most existing methods employ predefined strategies for mapping, such as raster scanning [23, 47], local scanning [19], and continuous scanning [42]. However, as illustrated in Figure 1, these methods all rely on a fixed scanning path. This results in adjacent tokens no longer being adjacent after flattening. Thereby, they neglect the inherent spatial structure of the image, leading to the loss of structural information. To address this issue, QuadMamba [39] determines the scanning window size based on the amount of information contained in different areas of the image. However, the scanning order in each window is fixed. This leads to an incomplete solution of the aforementioned issues. GrootV [38] adaptively constructs a tree topology based on input features and subsequently extracts features from this topology. Nevertheless, it employs only adjacent features in constructing the topology and distributes attention uniformly across the patch. The aforementioned methods are either based on a fixed scanning order, leading to the loss of structural information, or treat the information in the perception area equally, resulting in insensitivity to variations in object details." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 363, + 294, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 363, + 294, + 613 + ], + "spans": [ + { + "bbox": [ + 57, + 363, + 294, + 613 + ], + "type": "text", + "content": "To solve this problem, we proposed a novel framework called DefMamba inspired by deformable mechanisms [6, 36]. However, intuitively applying deformable mechanisms to SSMs still causes structural information loss and increases computational complexity. Therefore, we proposed a deformable state space model and a deformable scanning strategy (DS) to prioritize deformable tokens based on essential information and slide reference points towards the important area. This approach enables the SSMs to capture and process relevant features related to the input more effectively. Specifically, we shifted the reference point by the generated offset from a fixed position to an adjustable one that provided more useful information, thereby facilitating the awareness of changes in object details. On the other hand, we also dynamically adjusted the scanning order by the offset vector for obtaining a structure-aware sequence. In this way, our framework adaptively perceives the variations in object details to find the most suitable feature points, and determines the optimal scanning order consistent with the object structure based on the input image features." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 618, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 618, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 618, + 294, + 712 + ], + "type": "text", + "content": "We conducted extensive experiments to validate the effectiveness of DefMamba across multiple visual benchmarks, including image classification on ImageNet [8], object detection and instance segmentation on COCO [21], and semantic segmentation on ADE20K [45]. These results demonstrate that our method outperforms existing SSMs based approaches on all benchmarks and remains competitive with CNN and transformer-based methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 317, + 72, + 400, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 400, + 83 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 400, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 92, + 482, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 92, + 482, + 104 + ], + "spans": [ + { + "bbox": [ + 317, + 92, + 482, + 104 + ], + "type": "text", + "content": "2.1. Mamba for Visual Applications" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 110, + 553, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 110, + 553, + 456 + ], + "spans": [ + { + "bbox": [ + 317, + 110, + 553, + 456 + ], + "type": "text", + "content": "Numerous studies have successfully integrated Mamba [11] into visual tasks [19, 23, 27, 29, 31, 38, 39, 42, 47], demonstrating preliminary achievements. ViM [47] introduces a bidirectional scanning approach to transform 2D image into 1D sequences, which are then fed into SSM for global context modeling, marking the first integration of Mamba into visual tasks. VMamba [23] employs a four-way scanning algorithm to convert 2D image into 1D sequences. PlainMamba [42] modifies the scanning method from raster to continuous, preserving the spatial dependencies of the image. MSVMamba [31] downsamples the sequence based on four scans to reduce computational redundancy and mitigates the issue of information loss. GrootV [38] constructs a minimum spanning tree on a four-way plane graph using the differences between adjacent features, dynamically adjusting the scanning order according to different inputs. QuadMamba [39] adaptively adjusts the window granularity during the scanning process based on the information content of the image to better aggregate local information. While GrootV and QuadMamba can adapt their scanning methods based on input data, GrootV only considers the relationships between adjacent elements when generating the minimum spanning tree, neglecting global information. On the other hand, QuadMamba still relies on predefined scanning methods and does not achieve true dynamic scanning. In contrast, our DefMamba introduces a content-aware deformable scanning strategy that allows the network to dynamically learn the scanning order and the reference points position." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 468, + 546, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 468, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 317, + 468, + 546, + 479 + ], + "type": "text", + "content": "2.2. Deformable CNNs and Attention Mechanism" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 486, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 486, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 486, + 553, + 712 + ], + "type": "text", + "content": "Deformable convolution [6, 20, 41, 48] employs a convolution kernel that adapts to geometric variations in the input feature map, thereby overcoming the limitations of traditional convolution, which performs poorly when dealing with complex targets. Recently, the deformable mechanism has been extended to visual transformers [9] to enhance their ability to capture local features and adapt to geometric variations. DPT [5] proposes an adaptive patch embedding method that dynamically adjusts the position and size of patches while preserving their semantic information. PSViT [44] introduces a progressive sampling module prior to ViT [9], which iteratively identifies the most suitable deformable point positions for the current image. DAT [36] integrates the deformable mechanism with the self-attention mechanism in Transformers for the first time, incorporating deformable attention into the visual backbone. This approach learns a set of features corresponding to global keypoints and adapts to spatial variations. Previous approaches have explored various ways to effectively incorporate de" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "8839" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 553, + 202 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 553, + 202 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 553, + 202 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 553, + 202 + ], + "type": "image", + "image_path": "ae1ba1cc1e661f4023f08f9b73b17db10b6af066bb24446c2126442309318c23.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 208, + 555, + 232 + ], + "lines": [ + { + "bbox": [ + 54, + 208, + 555, + 232 + ], + "spans": [ + { + "bbox": [ + 54, + 208, + 555, + 232 + ], + "type": "text", + "content": "Figure 2. Overview of DefMamba. (a) depicts the overall architecture of our network. (b) illustrates the structure of the deformable Mamba block. LN means LayerNorm and FFN is a feed-forward network." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 251, + 296, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 251, + 296, + 348 + ], + "spans": [ + { + "bbox": [ + 54, + 251, + 296, + 348 + ], + "type": "text", + "content": "formable mechanism into transformer architectures. With the recent popularity of Mamba [11], we attempted to introduce deformable mechanism into Mamba. However, directly applying these mechanism has resulted in issues like the loss of structural information and the necessity for additional modules. In this context, our designed DS strategy stands out by effectively prioritizing deformable tokens while directing reference points toward key areas." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 357, + 112, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 112, + 370 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 112, + 370 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 377, + 296, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 377, + 296, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 377, + 296, + 449 + ], + "type": "text", + "content": "In this section, we first summarized the SSMs in Section 3.1. Then, in Section 3.2, we described the overall structure of the proposed network. Section 3.3 introduces a Deformable State Space Model (DSSM). Finally, Section 3.4 presents the designed model configurations across multiple scales." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 456, + 141, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 456, + 141, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 456, + 141, + 468 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "text", + "content": "SSMs, including notable implementations like S4 [12] and Mamba [11], are structured sequence architectures that combine elements of recurrent neural networks (RNNs) and CNNs, enabling linear or near-linear scaling with respect to sequence length. These models, derived from continuous systems, define a 1D function-to-function map for an input " + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "inline_equation", + "content": "u(t) \\in \\mathbb{R}^L" + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "text", + "content": " to an output " + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "inline_equation", + "content": "y(t) \\in \\mathbb{R}^L" + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "text", + "content": " through a hidden state " + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "inline_equation", + "content": "h(t) \\in \\mathbb{R}^N" + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "text", + "content": ". Where " + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 473, + 296, + 594 + ], + "type": "text", + "content": " represents time. More formally, SSMs are characterized by the continuous-time Ordinary Differential Equation (ODE) [11] presented:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 127, + 598, + 223, + 627 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 598, + 223, + 627 + ], + "spans": [ + { + "bbox": [ + 127, + 598, + 223, + 627 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} h ^ {\\prime} (t) = \\mathbf {A} h (t) + \\mathbf {B} u (t), \\\\ y (t) = \\hat {C} h (t), \\\\ \\end{array}", + "image_path": "fb99f5b84a521e297dc3a0e3cd3d9963d6b22d8b1312f33801284b8d8600fc31.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "inline_equation", + "content": "h(t)" + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "content": " is the current hidden state. " + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "inline_equation", + "content": "h^{\\prime}(t)" + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "content": " is the updated hidden state. " + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "inline_equation", + "content": "u(t)" + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "content": " is the current input. " + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "inline_equation", + "content": "y(t)" + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "content": " is the output. " + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "content": " is SSM's evolution matrix, and " + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{B} \\in \\mathbb{R}^{N \\times 1}" + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\hat{C} \\in \\mathbb{R}^{1 \\times N}" + }, + { + "bbox": [ + 55, + 629, + 295, + 689 + ], + "type": "text", + "content": " are the input and output projection matrices, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "To enable the application of SSMs in sequence modeling tasks within deep learning, they must be discretized," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "text", + "content": "transforming the SSM from a continuous-time function-to-function map into a discrete-time sequence-to-sequence map. S4 [12] and Mamba [11] are examples of discrete adaptations of the continuous system, incorporating a timescale parameter " + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "text", + "content": " to convert the continuous parameters " + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "text", + "content": " into their discrete counterparts " + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{A}}" + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{B}}" + }, + { + "bbox": [ + 313, + 251, + 555, + 346 + ], + "type": "text", + "content": ". This discretization is typically achieved using the Zero-Order Hold (ZOH) [11] method:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 365, + 352, + 553, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 352, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 365, + 352, + 553, + 384 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\bar {\\mathbf {A}} = \\exp (\\Delta \\mathbf {A}), \\\\ \\bar {\\mathbf {B}} = \\left( \\begin{array}{l} (\\Delta \\mathbf {A}) ^ {- 1} (\\exp (\\Delta \\mathbf {A}) - \\mathbf {I}) \\cdot \\Delta \\mathbf {B}, \\end{array} \\right. \\tag {2} \\\\ \\end{array}", + "image_path": "0b58d43bbf6f95d44543ec83885cc03bef8191494d142881ab463a299cf97cb3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 365, + 382, + 443, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 382, + 443, + 392 + ], + "spans": [ + { + "bbox": [ + 365, + 382, + 443, + 392 + ], + "type": "interline_equation", + "content": "h _ {t} = \\bar {\\mathbf {A}} h _ {t - 1} + \\bar {\\mathbf {B}} u _ {t},", + "image_path": "853ee444427d224efcea560cf04b51dde174d730a91cdec82c56f3c3077e51df.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 365, + 396, + 406, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 396, + 406, + 407 + ], + "spans": [ + { + "bbox": [ + 365, + 396, + 406, + 407 + ], + "type": "interline_equation", + "content": "y _ {t} = \\mathbf {C} h _ {t}.", + "image_path": "ac10e8610a2dfefb2f6051deb381bc6b1b10101ec8a4a6b4fe132cfaafbd2cd0.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "content": "While both S4 [12] and Mamba [11] employ a similar discretization process as outlined in Equation 2, Mamba distinguishes itself from S4 by conditioning the parameters " + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "inline_equation", + "content": "\\Delta \\in \\mathbb{R}^{b\\times L\\times D}" + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{B}\\in \\mathbb{R}^{b\\times L\\times N}" + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{C}\\in \\mathbb{R}^{b\\times L\\times N}" + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "content": " on the input " + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "inline_equation", + "content": "u\\in \\mathbb{R}^{b\\times L\\times D}" + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "content": " through the S6 Selective Scan Mechanism. Here, " + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "content": " represents the batch size, " + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "content": " denotes the sequence length, and " + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 411, + 555, + 496 + ], + "type": "text", + "content": " signifies the feature dimension." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 504, + 468, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 504, + 468, + 516 + ], + "spans": [ + { + "bbox": [ + 313, + 504, + 468, + 516 + ], + "type": "text", + "content": "3.2. Overall Model Architecture" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "text", + "content": "DefMamba uses a common multi-scale backbone structure similar to many CNNs [25, 28] and Transformers [24]. As illustrated in Figure 2(a), the image " + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "text", + "content": " is first divided into patches through a patch embedding layer, which produces a 2D feature map with spatial dimensions " + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "inline_equation", + "content": "H / 4 \\times W / 4" + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "text", + "content": " and channel dimensions " + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "text", + "content": ". Subsequently, multiple network stages are used to create hierarchical representations of dimensions " + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "inline_equation", + "content": "H / 8 \\times W / 8 \\times 2C" + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "inline_equation", + "content": "H / 16 \\times W / 16 \\times 4C" + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "inline_equation", + "content": "H / 32 \\times W / 32 \\times 8C" + }, + { + "bbox": [ + 313, + 522, + 555, + 714 + ], + "type": "text", + "content": ". Each stage consists of a stack of Deformable Mamba (DM) blocks followed by a downsampling layer (except the fourth stage). Finally, the features are average-pooled and sent to the classification head to obtain the prediction results. In particular, we followed [38] and used overlapping forms in the patch embedding layer and the downsampling layers. For specific structural details, please refer to the Appendix." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8840" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 553, + 252 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 553, + 252 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 553, + 252 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 553, + 252 + ], + "type": "image", + "image_path": "b9eabf434458bbe39aa7301aae2d2af4ec4d3edd5e6eae6096bb601ccaf7c1bd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 262, + 555, + 319 + ], + "lines": [ + { + "bbox": [ + 54, + 262, + 555, + 319 + ], + "spans": [ + { + "bbox": [ + 54, + 262, + 555, + 319 + ], + "type": "text", + "content": "Figure 3. Illustration of Deformable State Space Model. (a) illustrates the processing flow of the deformable state space model for feature extraction. (b) depicts the processing flow of the deformable scan. The upper part primarily shifts the feature points to enable the model to focus on more salient regions, while the lower part shifts the token positions to facilitate the discovery of a scanning order that is better suited to the current input. To clearly illustrate the process, only nine points are depicted in the figure, however, the actual processing involves a greater number of points. (c) presents the detailed structure of the offset network." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 339, + 296, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 339, + 296, + 411 + ], + "spans": [ + { + "bbox": [ + 54, + 339, + 296, + 411 + ], + "type": "text", + "content": "Different from the Mamba structure used in language models [11], the DM block follows the popular structure of the Transformer block [9, 24], which consists of two Layer Norm (LN) layers, an FFN, a DSSM (to be introduced in the following subsection) and residual connections, as shown in the Figure 2(b)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 419, + 223, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 419, + 223, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 419, + 223, + 433 + ], + "type": "text", + "content": "3.3. Deformable State Space Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 437, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 437, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 54, + 437, + 295, + 568 + ], + "type": "text", + "content": "The overall architecture of the deformable state space model is presented in Figure 3(a). Inspired by [23, 31, 38], we employed depthwise convolution to replace the original 1D convolution in the vision mamba block [47] and incorporated a deformable branch comprising a deformable scanning and a deformable SSM (DSSM). We maintained the standard forward and backward branches to ensure stable model convergence, as our method introduces more spatial token jumps compared to previous scanning methods, potentially complicating model training and learning. Subsequent experiments validate this (Table 4)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 570, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 570, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 54, + 570, + 295, + 700 + ], + "type": "text", + "content": "Deformable Scanning. Given the issue of mutual interference between multiple deformable points, we constrained the offset of the deformable points in a certain range. This ensures the relationship between deformable points and reference points remains invariant, allowing us to approximate the relationship after deformation using the relationship before deformation. Furthermore, considering the simplicity of the computation, we employed a parallel approach to simultaneously adjust the reference points and scanning order, thereby reducing the computational burden. The specific structure is illustrated in the Figure 3(b)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 700, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 700, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 700, + 295, + 713 + ], + "type": "text", + "content": "Given an input feature " + }, + { + "bbox": [ + 67, + 700, + 295, + 713 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 67, + 700, + 295, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 67, + 700, + 295, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 67, + 700, + 295, + 713 + ], + "type": "text", + "content": " denotes" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "text", + "content": "the channel dimension and " + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "text", + "content": " represent the spatial resolution. We first generated the offset " + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "inline_equation", + "content": "o \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "text", + "content": " using a subnetwork that utilizes " + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "text", + "content": " to output the offset values " + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 313, + 339, + 555, + 387 + ], + "type": "text", + "content": " for the reference point and the reference token." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "text", + "content": "We initially implemented the subnetwork as depicted in Figure 3(c). The input features are first processed through a " + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "inline_equation", + "content": "K \\times K" + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "text", + "content": " depthwise convolution to capture local features. Subsequently, GELU, Layer Normalization (LN), and a " + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "text", + "content": " convolution are employed to derive the offset values, which encompass three dimensions in total. The first two dimensions represent the offset of the reference point in two-dimensional space, while the third dimension signifies the offset of the reference token index within the entire patch. During our experiments, we observed that the offset of the token necessitates global perception of the features within the patch, which cannot be achieved solely through convolution. In light of this, and considering the previous method's findings [29, 31] that mamba has redundancy in the channel dimension, we incorporated a Channel Attention (CA) mechanism [18] following the depthwise convolution layer. This mechanism mitigates channel redundancy and facilitates the integration of global contextual information. Notably, following the configuration of DAT [36], we set " + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "text", + "content": " to [9, 7, 5, 3] across four stages and omitted the bias in the " + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 388, + 556, + 639 + ], + "type": "text", + "content": " convolution." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "content": "To stabilize the training process, we employed the tanh function to mitigate the impact of extreme values in " + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\hat{o} = \\tanh(o)" + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "content": ". Subsequently, we split " + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\hat{o}" + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "content": " to 2 parts along the channel dimension, one with 2 channels and one with 1 channel, to obtain the point offset " + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\Delta p" + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "content": " and token index offset " + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 313, + 641, + 556, + 713 + ], + "type": "text", + "content": ". As previously mentioned, we needed to fur" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8841" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 299, + 299 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 299, + 299 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 299, + 299 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 299, + 299 + ], + "type": "table", + "html": "
MethodType#Param.#FLOPsTop-1 Acc.
RegNetY-800M [28]C6M0.8G76.3
GhostNet 1.3× [13]C7M0.2G75.7
DeiT-Ti [33]T6M1.3G72.2
ViM-T [47]S7M1.5G76.1
EffVMamba-T [27]S6M0.8G76.5
LocalVim-T [19]S8M1.5G76.2
PlainMamba-L1 [42]S7M3.0G77.9
MSVMamba-N [31]S7M0.9G77.3
QuadMamba-Li [39]S5M0.8G74.2
DefMamba-TS8M1.2G78.6
RegNetY-4G [28]C21M4.0G80.0
ConvNeXt-T [25]C29M4.5G82.1
Conv2Former-T [17]C27M4.4G83.2
DeiT-S [33]T22M4.6G79.8
Swin-T [24]T29M4.5G81.3
CoAtNet-0 [7]T25M4.0G81.6
CrossFormer-S [35]T31M4.9G82.5
ViM-S [47]S26M5.1G81.0
VMamba-T [23]S22M5.6G82.2
", + "image_path": "56c30ffb3cf9d3882af71d29b6eea984c5713be7261c494a6328b6a3e266b973.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 308, + 70, + 548, + 299 + ], + "blocks": [ + { + "bbox": [ + 308, + 70, + 548, + 299 + ], + "lines": [ + { + "bbox": [ + 308, + 70, + 548, + 299 + ], + "spans": [ + { + "bbox": [ + 308, + 70, + 548, + 299 + ], + "type": "table", + "html": "
MethodType#Param.#FLOPsTop-1 Acc.
LocalVim-S [19]S28M4.8G81.2
LocalVMamba-T [19]S26M5.7G82.7
EffVMamba-B [27]S33M4.6G83.0
MSVMamba-T [31]S33M4.6G82.8
PlainMamba-L2 [42]S25M8.1G81.6
GrootV-T [38]S30M4.8G83.4
QuadMamba-S [39]S31M5.5G82.4
DefMamba-SS32M4.8G83.5
ConvNeXt-S [25]C50M8.7G83.1
Conv2Former [17]C50M8.7G84.1
Swin-S [24]T50M8.7G83.0
CoAtNet-1 [7]T42M8.0G83.3
CrossFormer-B [35]T52M9.2G83.4
VMamba-S [23]S50M8.7G83.6
LocalVMamba-B [19]S50M11.4G83.7
PlainMamba-L3 [42]S50M14.4G82.3
GrootV-S [38]S51M8.5G84.2
QuadMamba-B [39]S50M9.3G83.8
DefMamba-BS51M8.5G84.2
", + "image_path": "e25dd3cadd5b475d456c44d6e443e38cd7ce461bcb39d384fb1db09292832e9b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 306, + 555, + 329 + ], + "lines": [ + { + "bbox": [ + 55, + 306, + 555, + 329 + ], + "spans": [ + { + "bbox": [ + 55, + 306, + 555, + 329 + ], + "type": "text", + "content": "Table 1. Image classification performance on ImageNet-1K validation set. C, T and S indicate the model type of CNNs, Transformer and SSM. The best results are shown in bold font." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "text", + "content": "ther constrain " + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "inline_equation", + "content": "\\Delta p" + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "text", + "content": ", in order to stabilize training and simplify the structure. We divided the horizontal and vertical dimensions of " + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "inline_equation", + "content": "\\Delta p" + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 55, + 350, + 295, + 409 + ], + "type": "text", + "content": ", respectively, thereby limiting the offset to the range of a single token. The detailed process is outlined as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 83, + 417, + 295, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 417, + 295, + 436 + ], + "spans": [ + { + "bbox": [ + 83, + 417, + 295, + 436 + ], + "type": "interline_equation", + "content": "\\Delta p, \\Delta t = S p l i t (\\tanh (O f f s e t (x)), \\mathrm {d i m s} = [ 2, 1 ]), \\tag {3}", + "image_path": "89afb9509bdc7aa388a7cb33c9ca36bc2fac5bee50dcd85848337934a2ef8b61.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 99, + 433, + 167, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 433, + 167, + 445 + ], + "spans": [ + { + "bbox": [ + 99, + 433, + 167, + 445 + ], + "type": "interline_equation", + "content": "\\hat {\\Delta} p = \\operatorname {N o r m} (\\Delta p).", + "image_path": "49a8e57475a55153188d31efd176d190815a0fd0c6c95581e0246e5d4facc8ee.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "type": "text", + "content": "Then, we sent the point offset " + }, + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "type": "inline_equation", + "content": "\\hat{\\Delta p}" + }, + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "type": "text", + "content": ", token index offset " + }, + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "type": "text", + "content": ", and input feature " + }, + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 449, + 295, + 486 + ], + "type": "text", + "content": " to the point offset branch and index branch, to obtain the final output, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": "Point Offset. To obtain feature representations that are more sensitive to changes in objects, we dynamically adapted the network's reference points to deformable points that contain more relevant information based on the input. Firstly, we generated reference points " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "p \\in \\mathbb{R}^{H \\times W \\times 2}" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": ". The values in " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": " correspond to the two-dimensional coordinates of points ranging from (0, 0) to " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "(H - 1, W - 1)" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": ". To simplify network calculations, we normalized " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": " from its original range to " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": " represents the point in the upper left corner and " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "[1, 1]" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": " represents the point in the lower right corner. We then added the reference point " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": " and the offset to obtain the deformable point " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "\\hat{p} = p + \\Delta p" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": ". Since the offset " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "\\hat{p}" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": " contains a decimal part, it cannot be used directly. Therefore, we used bilinear interpolation to extract features at the spatial position corresponding to the offset point " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "\\hat{p}" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": " from the input " + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 486, + 295, + 676 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "When our model performs point offset, the features will move in space, potentially causing the position encoding added in the initial stage to become ineffective and thereby" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "text", + "content": "decreasing model performance. To address this, we designed an offset bias based on the relative position encoding in the Swin Transformer. Specifically, given the feature map of size " + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "text", + "content": ", the relative coordinate displacement of points lies within the range of " + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "inline_equation", + "content": "[-H, H]" + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "inline_equation", + "content": "[-W, W]" + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "text", + "content": " in two dimensions, respectively. Therefore, we set a learnable relative offset bias matrix " + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "inline_equation", + "content": "R \\in \\mathbb{R}^{(2H - 1) \\times (2W - 1)}" + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "text", + "content": ". However, considering that such a matrix would result in a significant increase in parameter count, we performed a downsampling operation on this matrix to obtain " + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "inline_equation", + "content": "R \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "text", + "content": ". At the same time, we divided the point displacement by 2 to accommodate this change. Then we used the point displacement to calculate the corresponding compensation by interpolating on " + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 350, + 555, + 529 + ], + "type": "text", + "content": ". Finally, this compensation is added to the interpolated features. The specific process is as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 389, + 536, + 553, + 553 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 536, + 553, + 553 + ], + "spans": [ + { + "bbox": [ + 389, + 536, + 553, + 553 + ], + "type": "interline_equation", + "content": "\\hat {p} = p + \\Delta p, \\tag {4}", + "image_path": "e3972b4724b790b37cf63aa7303a37c23e800840f97f29403e45e3c1ba9ad68c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 390, + 551, + 479, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 551, + 479, + 562 + ], + "spans": [ + { + "bbox": [ + 390, + 551, + 479, + 562 + ], + "type": "interline_equation", + "content": "\\hat {x} = \\phi (x, \\hat {p}) + \\phi (R, \\hat {p}),", + "image_path": "451f4f03d7e7004846ee5f16fe036c1a7995d9a2ed2f6056e06b07b81a677db0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "type": "inline_equation", + "content": "\\phi (x,\\hat{p})" + }, + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "type": "text", + "content": " represents the use of bilinear interpolation function to extract the feature corresponding to position " + }, + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "type": "inline_equation", + "content": "\\hat{p}" + }, + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 568, + 555, + 603 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": "Index Offset. We modified the scanning order to enable the model to perceive the structure of the input object effectively by varying the reference token index and the deformable token index. We initially generated the reference token index " + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "inline_equation", + "content": "t_r \\in \\mathbb{R}^{N \\times 1}" + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "inline_equation", + "content": "N = H \\times W" + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": ". The values in " + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": " indicate the token positions within the current patch, ranging from 0 to " + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "inline_equation", + "content": "N - 1" + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": ". To simplify network computations, we normalized " + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "inline_equation", + "content": "t_r" + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": " from its original range to [-1, 1]. This enables us to compute the deformable token index " + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "inline_equation", + "content": "t_d = t_r + \\Delta t" + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8842" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 79, + 294, + 168 + ], + "blocks": [ + { + "bbox": [ + 138, + 72, + 213, + 79 + ], + "lines": [ + { + "bbox": [ + 138, + 72, + 213, + 79 + ], + "spans": [ + { + "bbox": [ + 138, + 72, + 213, + 79 + ], + "type": "text", + "content": "Mask R-CNN 1× schedule" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 79, + 294, + 168 + ], + "lines": [ + { + "bbox": [ + 57, + 79, + 294, + 168 + ], + "spans": [ + { + "bbox": [ + 57, + 79, + 294, + 168 + ], + "type": "table", + "html": "
Backbone#FLOPs\\( {\\mathbf{{AP}}}^{\\mathbf{b}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{b}}{}_{50} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{b}}{}_{75} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}}{}_{50} \\)\\( {\\mathbf{{AP}}}^{\\mathbf{m}}{}_{75} \\)
ResNet-50 [15]260G38.258.841.434.755.737.2
Swin-T [24]267G42.765.246.839.362.242.2
ConvNeXt-T [25]262G44.266.648.340.163.342.8
PVTv2-B2 [34]309G45.367.149.441.264.244.4
VMamba-T [23]286G47.469.552.042.766.346.0
LocalVMamba-T [19]291G46.768.750.842.265.745.5
QuadMamba-S [39]301G46.769.051.342.465.945.6
MSVMamba-T [31]252G46.968.851.442.265.645.4
GrootV-T [38]265G47.069.451.542.766.446.0
DefMamba-S268G47.569.651.742.866.346.2
", + "image_path": "e228cfb0481a6552e8be11dceb1e63b5db963496aa093af33b8f538641cd4a12.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 176, + 295, + 221 + ], + "lines": [ + { + "bbox": [ + 55, + 176, + 295, + 221 + ], + "spans": [ + { + "bbox": [ + 55, + 176, + 295, + 221 + ], + "type": "text", + "content": "Table 2. Object detection and instance segmentation performance on MSCOCO 2017 val set. All using Mask R-CNN framework. " + }, + { + "bbox": [ + 55, + 176, + 295, + 221 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^b}" + }, + { + "bbox": [ + 55, + 176, + 295, + 221 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 176, + 295, + 221 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^m}" + }, + { + "bbox": [ + 55, + 176, + 295, + 221 + ], + "type": "text", + "content": " indicate the mean Average Precision (mAP) of detection and segmentation, respectively" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "spans": [ + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "text", + "content": "Since the derived " + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "inline_equation", + "content": "t_d" + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "text", + "content": " contain decimal components, they cannot be utilized directly. Consequently, for " + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "inline_equation", + "content": "t_d" + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "text", + "content": ", we applied a sorting algorithm to determine the indices post-offset based on the magnitude of their values. Finally, we transformed the offset features " + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "text", + "content": " into a 1D sequence according to these indices, thereby obtaining a content-adaptive image feature sequence. It is important to note that the sorting algorithm truncates gradients, rendering the network untrainable. To address this, we averaged the gradients of the final image sequence across the dimension and replicate them to " + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 54, + 243, + 295, + 376 + ], + "type": "text", + "content": " to approximate the gradient of the scanning order offset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 387, + 137, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 137, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 137, + 401 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 407, + 173, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 407, + 173, + 420 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 173, + 420 + ], + "type": "text", + "content": "4.1. Image Classification" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 426, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 426, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 56, + 426, + 295, + 616 + ], + "type": "text", + "content": "Settings. The image classification experiments are conducted using the ImageNet-1K [8] dataset, which comprises over 1.28 million training images and 50,000 validation images across 1,000 categories. Our training setup closely follows the methodology of previous practices [23, 31, 38], incorporating various data augmentations such as random cropping, random horizontal flipping, label-smoothing regularization, mixup, autoaugment, and random erasing. The models are trained for 300 epochs using the AdamW [26] optimizer with a cosine decay learning rate scheduler, including a 20-epoch warm-up period. The total batch size is set to 1,024, with the models trained on " + }, + { + "bbox": [ + 56, + 426, + 295, + 616 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 56, + 426, + 295, + 616 + ], + "type": "text", + "content": " A800 GPUs. The optimizer parameters are configured with betas set to (0.9, 0.999), momentum set to 0.9, an initial learning rate of " + }, + { + "bbox": [ + 56, + 426, + 295, + 616 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 56, + 426, + 295, + 616 + ], + "type": "text", + "content": ", a weight decay of 0.05, and Exponential Moving Average (EMA)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "text", + "content": "Results. Table 1 presents a comparison of our proposed DefMamba models (T, S, B) with various state-of-the-art (SOTA) methods. Specifically, DefMamba-T achieves " + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "inline_equation", + "content": "78.6\\%" + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "text", + "content": " Top-1 Acc., outperforming CNNs based RegNetY800M [28] and transformer based DeiT-Ti [33] by " + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "inline_equation", + "content": "2.3\\%" + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "inline_equation", + "content": "6.4\\%" + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "text", + "content": ", respectively. Moreover, DefMamba-T outperforms the recently introduced SSMs models, achieving " + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 55, + 618, + 295, + 714 + ], + "type": "text", + "content": " higher performance than ViM-T" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 81, + 553, + 233 + ], + "blocks": [ + { + "bbox": [ + 388, + 72, + 481, + 81 + ], + "lines": [ + { + "bbox": [ + 388, + 72, + 481, + 81 + ], + "spans": [ + { + "bbox": [ + 388, + 72, + 481, + 81 + ], + "type": "text", + "content": "ADE20K with crop size 512" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 81, + 553, + 233 + ], + "lines": [ + { + "bbox": [ + 317, + 81, + 553, + 233 + ], + "spans": [ + { + "bbox": [ + 317, + 81, + 553, + 233 + ], + "type": "table", + "html": "
BackbonemIOU (SS)mIOU (MS)#Param.#FLOPs
ResNet-50 [15]42.142.867M953G
Swin-T [24]44.545.860M945G
ConvNeXt-T [25]46.046.760M939G
NAT-T [14]47.148.458M934G
Vim-S [47]44.9-46M-
LocalVim-S [19]46.447.558M297G
VMamba-T [23]47.948.862M949G
PlainMamba-L2 [42]46.8-55M285G
LocalVMamba-T [19]47.949.157M970G
MSVMamba-T [31]47.648.565M942G
QuadMamba-S [39]47.248.162M961G
GrootV-T [38]48.549.460M941G
DefMamba-S48.849.665M946G
", + "image_path": "8ee24a9a6527c871ed03c6095f7d20f6979c5d77c0f70ac3d9d090f5207274c4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 241, + 555, + 275 + ], + "lines": [ + { + "bbox": [ + 313, + 241, + 555, + 275 + ], + "spans": [ + { + "bbox": [ + 313, + 241, + 555, + 275 + ], + "type": "text", + "content": "Table 3. Semantic segmentation performance on ADE20K val set. The crop size is all set to " + }, + { + "bbox": [ + 313, + 241, + 555, + 275 + ], + "type": "inline_equation", + "content": "512^2" + }, + { + "bbox": [ + 313, + 241, + 555, + 275 + ], + "type": "text", + "content": ". SS and MS denote single-scale and multi-scale testing, respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "text", + "content": "[47], LocalViM-T [19], and MSVMamba-N [31] in terms of parameter and computational complexity. Moreover, it reduces the computational burden by " + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "text", + "content": " while achieving a performance improvement of " + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "text", + "content": " over PlainMamba-L1 [42]. DefMamba-S achieves " + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "inline_equation", + "content": "83.5\\%" + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "text", + "content": " Top-1 Acc., surpassing GrootV-T [38] and EfficientVMamba-B [27]. Furthermore, DefMamba-B achieves an accuracy of " + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "inline_equation", + "content": "84.2\\%" + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "text", + "content": ", exceeding VMamba-S [23] by " + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 313, + 293, + 555, + 402 + ], + "type": "text", + "content": ", demonstrating the effectiveness of our methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 408, + 416, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 408, + 416, + 421 + ], + "spans": [ + { + "bbox": [ + 313, + 408, + 416, + 421 + ], + "type": "text", + "content": "4.2. Object Detection" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 426, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 555, + 510 + ], + "type": "text", + "content": "Settings. We evaluated DefMamba on the MSCOCO 2017 dataset [21] using the Mask R-CNN framework [16] for object detection and instance segmentation tasks. Following prior works [24, 31, 38], we utilized backbones pretrained on ImageNet-1K for initialization. We employed standard training strategies, including " + }, + { + "bbox": [ + 313, + 426, + 555, + 510 + ], + "type": "inline_equation", + "content": "1 \\times (12" + }, + { + "bbox": [ + 313, + 426, + 555, + 510 + ], + "type": "text", + "content": " epochs) with MultiScale (MS) training, to ensure a fair comparison." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "text", + "content": "Results. As depicted in Table 2, our method outperforms existing methods on most evaluation metrics. Specifically, under " + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "text", + "content": " schedule, DefMamba-S achieves 47.5 in box mAP " + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}^{\\mathrm{b}})" + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "text", + "content": " and 42.8 in mask mAP " + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}^{\\mathrm{m}})" + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "text", + "content": ". Our model surpassed ResNet-50 [15], Swin-T [24] and ConvNeXt-T [25]. At the same time, our method improved " + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}^{\\mathrm{m}}" + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "text", + "content": " by 0.6 points compared to LocalVMamba-T [19] and QuadMamba-S [39]. Furthermore, our method exhibited comparable performance to the previous SOTA method, VMamba-T [23], while reducing the computational load by " + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 313, + 510, + 556, + 631 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 636, + 448, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 636, + 448, + 649 + ], + "spans": [ + { + "bbox": [ + 313, + 636, + 448, + 649 + ], + "type": "text", + "content": "4.3. Semantic Segmentation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "text", + "content": "Settings. To evaluate the semantic segmentation performance of DefMamba, we trained our models using UperNet [37] initialized with pre-trained classification weights on ADE20K [45] for 160,000 iterations. We employed the AdamW optimizer [26] with a learning rate set at " + }, + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "inline_equation", + "content": "6 \\times 10^{-5}" + }, + { + "bbox": [ + 313, + 654, + 554, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8843" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 71, + 292, + 128 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 292, + 128 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 292, + 128 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 292, + 128 + ], + "type": "table", + "html": "
IndexFB-BBCB [42]LB [19]DB#Param.#FLOPsTop-1
(1)✓7.3M1.1G76.9
(2)✓8.1M1.1G76.5
(3)✓✓7.5M1.1G77.3
(4)✓✓7.5M1.1G77.1
(5)✓✓8.3M1.2G78.6
", + "image_path": "4a4f7b0d9a41465af22083c4801c34489458f97a9f3762ef9aa99895a6708778.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 61, + 182, + 291, + 260 + ], + "blocks": [ + { + "bbox": [ + 55, + 136, + 295, + 169 + ], + "lines": [ + { + "bbox": [ + 55, + 136, + 295, + 169 + ], + "spans": [ + { + "bbox": [ + 55, + 136, + 295, + 169 + ], + "type": "text", + "content": "Table 4. Comparisons with the different scanning branches in the setting of tiny model size. DB means our deformable branch. The best results are shown in **bold** font." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 182, + 291, + 260 + ], + "lines": [ + { + "bbox": [ + 61, + 182, + 291, + 260 + ], + "spans": [ + { + "bbox": [ + 61, + 182, + 291, + 260 + ], + "type": "table", + "html": "
IndexDPDTOBCA#Param.#FLOPsTop-1
(1)7.5M1.1G77.0
(2)✓7.5M1.2G77.4
(3)✓7.5M1.2G77.2
(4)✓✓7.5M1.2G77.9
(5)✓✓✓8.2M1.2G78.2
(6)✓✓✓✓8.3M1.2G78.6
", + "image_path": "69b055eb0a02c9d6ad79d192e00e4715743367941fd8c9c33fabf5a6fda4b227.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 269, + 295, + 302 + ], + "lines": [ + { + "bbox": [ + 55, + 269, + 295, + 302 + ], + "spans": [ + { + "bbox": [ + 55, + 269, + 295, + 302 + ], + "type": "text", + "content": "Table 5. Comparisons with the different components of proposed deformable scanning in tiny model size settings on ImageNet-1k. The best results are shown in bold font." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 325, + 295, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 325, + 295, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 325, + 295, + 361 + ], + "type": "text", + "content": "Our experiments are primarily conducted using a default input resolution of " + }, + { + "bbox": [ + 55, + 325, + 295, + 361 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 325, + 295, + 361 + ], + "type": "text", + "content": ". Additionally, we incorporated Multi-Scale (MS) testing to assess performance variations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 361, + 295, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 295, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 295, + 493 + ], + "type": "text", + "content": "Results. The DefMamba-S model demonstrates favorable performance in semantic segmentation compared to various SOTA methods, as presented in Table 3. DefMamba-S achieves a mIOU of 48.8 in single-scale and 49.6 in multi-scale evaluation. This outperforms ResNet-50 [15], Swin-T [24], and ConvNeXt-T [25]. Additionally, DefMamba-S exceeds the performance of the recent SSM methods, including GrootV-T [38], QuadMamba-S [39] and MSVMamba-T [31]. Our method achieves improvements of 0.3 points, 1.6 points, and 1.2 points, respectively, on the single-scale mIoU metric." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 503, + 149, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 503, + 149, + 516 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 149, + 516 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "text", + "content": "Effect of the Proposed DSSM Structure. To give the evidence for the effectiveness of the proposed deformable branch, we conducted a series of experiments over different branch settings in Table 4. As shown in Table 4, FB-BB refers to the forward and the backward branches for feature extraction. CB represents continuous scanning [42] branch. LB is local scanning [19] branch and DB denotes our proposed deformable branch in Figure 2 (a). By comparing the results in Table 4 (1) and (5), we observed that the proposed deformable branch significantly increased the accuracy of the ImageNet dataset by " + }, + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "text", + "content": " within a reasonable computational budget, to demonstrate the effectiveness of the proposed deformable branch. Moreover, compared with Table 4 (3), (4) and (5), our method only increased the computational cost by 0.1G, while significantly improving the accuracy on ImageNet dataset by " + }, + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "text", + "content": ". This further demon-" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 71, + 364, + 118 + ], + "blocks": [ + { + "bbox": [ + 316, + 71, + 364, + 118 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 364, + 118 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 364, + 118 + ], + "type": "image", + "image_path": "09baed4a154e94d6c2235b759bb1883c14283e4c331de41876fa79b1ef412300.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 118, + 364, + 166 + ], + "blocks": [ + { + "bbox": [ + 316, + 118, + 364, + 166 + ], + "lines": [ + { + "bbox": [ + 316, + 118, + 364, + 166 + ], + "spans": [ + { + "bbox": [ + 316, + 118, + 364, + 166 + ], + "type": "image", + "image_path": "b6fae81d86ea4e205ec6563dab4fdb5cc749291aa980ab311ea8681c6175d3f7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 166, + 351, + 175 + ], + "lines": [ + { + "bbox": [ + 329, + 166, + 351, + 175 + ], + "spans": [ + { + "bbox": [ + 329, + 166, + 351, + 175 + ], + "type": "text", + "content": "Image" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 184, + 553, + 217 + ], + "lines": [ + { + "bbox": [ + 313, + 184, + 553, + 217 + ], + "spans": [ + { + "bbox": [ + 313, + 184, + 553, + 217 + ], + "type": "text", + "content": "Figure 4. Visualization of activation maps in the specific position. The position is marker by red and orange point. RS stands for raster scanning, DS stands for our deformable scanning." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 365, + 71, + 410, + 118 + ], + "blocks": [ + { + "bbox": [ + 365, + 71, + 410, + 118 + ], + "lines": [ + { + "bbox": [ + 365, + 71, + 410, + 118 + ], + "spans": [ + { + "bbox": [ + 365, + 71, + 410, + 118 + ], + "type": "image", + "image_path": "47216140e4c4590f434e7f793ae29f58d44143662ab7d43c8dd7e4d25871089d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 365, + 118, + 410, + 165 + ], + "blocks": [ + { + "bbox": [ + 365, + 118, + 410, + 165 + ], + "lines": [ + { + "bbox": [ + 365, + 118, + 410, + 165 + ], + "spans": [ + { + "bbox": [ + 365, + 118, + 410, + 165 + ], + "type": "image", + "image_path": "e0cdb04e68326430b383fa960dfe10dd561e20e24f309c423f55b28490c31e20.jpg" + } + ] + } + ], + 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"lines": [ + { + "bbox": [ + 313, + 244, + 553, + 352 + ], + "spans": [ + { + "bbox": [ + 313, + 244, + 553, + 352 + ], + "type": "text", + "content": "strates that our deformable scanning approach, as opposed to other fixed scanning methods, is more capable of capturing structural information of objects and enhancing model performance. From Table 4 (1) and (2), we noted that incorporating only the proposed deformable branch would lead to a decrease in performance due to the increased spatial token jumps. To achieve more stable training and higher model performance, we adhered to the previous paradigm by combining the FB-BB and DB in our proposed model." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 354, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 553, + 713 + ], + "type": "text", + "content": "Effect of the Deformable Scanning Components. To thoroughly evaluate the contributions of each component in our proposed deformable scanning method, we conducted an ablation study in Table 5. As shown in Table 5, DP, DT, OB and CA represent the components of the deformable scanning in Figure 2 (b), respectively. DP (Deformable Points) involves the process of generating deformable points, which includes initializing reference points, an offsets network and a bilinear interpolation. DT (Deformable Tokens) refers to the process of dynamically changing the token order based on predicted offsets, which includes initializing token index and deformable token index, as well as an offsets network. OB represents the operation of generating offset bias. CA denotes channel attention operation in the offset network. By comparing the results in Table 5 (1), (2) and (3), we observed that adding either the DP operation or the DT operation boosting the baseline (1) performance by " + }, + { + "bbox": [ + 313, + 354, + 553, + 713 + ], + "type": "inline_equation", + "content": "0.2 - 0.4\\%" + }, + { + "bbox": [ + 313, + 354, + 553, + 713 + ], + "type": "text", + "content": ", with only a minor increases in computational costs (0.1G), demonstrated that the effectiveness of both DP and DT. Moreover, when combining both DP and DT operations (4), the performance further improves by " + }, + { + "bbox": [ + 313, + 354, + 553, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 313, + 354, + 553, + 713 + ], + "type": "text", + "content": " compared to the baseline, as shown in Table 5 (1) and (4). These results strongly prove that whether adding DT or DP individually, or combining both, the model can better learn the structure of images and facilitate the awareness of changes in object details, thus improving performance. Furthermore, we run ablation experiments to confirm the effectiveness of OB and CA by comparing Table 5 (4) and (5), and Table 5 (5) and (6), respectively. The experiments validate the effectiveness of our methods." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8844" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 130, + 225 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 130, + 225 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 130, + 225 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 130, + 225 + ], + "type": "image", + "image_path": "a4a975e2d4ed761d1256a74adb474d33b63f3521337444a84dfd5293dc89adf7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 236, + 296, + 302 + ], + "lines": [ + { + "bbox": [ + 55, + 236, + 296, + 302 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 296, + 302 + ], + "type": "text", + "content": "Figure 5. Visualization of deformable points and deformable token index. In (a), the orange dots represent deformable points, the green dots represent reference points, and the red arrows represent the offset path of the points. In (b) and (c), the gradient from yellow to green represents the scanning path, with the yellow dots being scanned first and the green dots being scanned later." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 133, + 71, + 205, + 225 + ], + "blocks": [ + { + "bbox": [ + 133, + 71, + 205, + 225 + ], + "lines": [ + { + "bbox": [ + 133, + 71, + 205, + 225 + ], + "spans": [ + { + "bbox": [ + 133, + 71, + 205, + 225 + ], + "type": "image", + "image_path": "0035e466654ac12b930b27d494414f135eaaf847ea1943c1c955a4dd24a659a9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 206, + 72, + 294, + 225 + ], + "blocks": [ + { + "bbox": [ + 206, + 72, + 294, + 225 + ], + "lines": [ + { + "bbox": [ + 206, + 72, + 294, + 225 + ], + "spans": [ + { + "bbox": [ + 206, + 72, + 294, + 225 + ], + "type": "image", + "image_path": "0ed8e8653f85ff217bb8ce5c8acd70b4a1dffe6b229bbaf69a89868f7e5321f1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 323, + 295, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 323, + 295, + 490 + ], + "spans": [ + { + "bbox": [ + 54, + 323, + 295, + 490 + ], + "type": "text", + "content": "Visualization Results. To better demonstrate the superiority of our deformable scanning strategy, we present the activation maps of images at different positions for various methods in Figure 4, marked clearly by red and orange dots in the image. Specifically, we visualized the activation map corresponding to the final layer of the second stage using the method outlined in [23]. As illustrated in the activation map of the pen in the last line of Figure 4, our method demonstrates an enhanced ability to focus on the structural and shape information of objects, even when dealing with complex scenes that contain multiple overlapping objects. This capability allows for more precise recognition and segmentation, further highlighting the effectiveness of our approach in capturing essential details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 491, + 295, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 295, + 646 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 295, + 646 + ], + "type": "text", + "content": "We also visualized the deformable points and deformable token index to intuitively demonstrate the performance of our method, as shown in the Figure 5. In the red box of Figure 5 (a), we can observe that some focus points outside the object shift towards the object. Such movements allow the network to attend to more object information. Compared with Figure 5 (b), our method (c) adjusts the scanning order to emphasize important tokens. For example, as shown in the first row of the Figure 5, the token corresponding to the snake's head is shifted from the middle position in a raster scan to being the first position in our method. Such offsets are beneficial for the network to learn relevant features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 657, + 126, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 657, + 126, + 670 + ], + "spans": [ + { + "bbox": [ + 55, + 657, + 126, + 670 + ], + "type": "text", + "content": "5. Limitation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "Despite the strong results of our approach, there is still a limitation. In cases where the image contains incomplete object structures or multiple objects arranged in a regular" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 70, + 550, + 241 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 550, + 241 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 550, + 241 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 550, + 241 + ], + "type": "image", + "image_path": "d324cf04f66a3b2d46aeb62497af47027e0615ced8c7bf95c00d169828d00335.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 249, + 554, + 281 + ], + "lines": [ + { + "bbox": [ + 313, + 249, + 554, + 281 + ], + "spans": [ + { + "bbox": [ + 313, + 249, + 554, + 281 + ], + "type": "text", + "content": "Figure 6. Failure cases. The blue dots represent deformable points, while the black arrows indicate the scanning order after deformation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 307, + 555, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 307, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 307, + 555, + 415 + ], + "type": "text", + "content": "pattern, the deformable scanning strategy may be less effective. As illustrated in Figure 6, when the image shows only a portion of a baseball, the deformable mechanism does not capture complete structural information, resulting in offsets that are too small and converge towards the predefined scanning method. Meanwhile, when multiple objects are arranged according to a certain rule, the information variation between adjacent tokens is minimal. Results in the model remaining in an indolent learning process." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 429, + 388, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 429, + 388, + 441 + ], + "spans": [ + { + "bbox": [ + 314, + 429, + 388, + 441 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "text", + "content": "In this work, we made efforts to tackle the challenge arising from existing Mamba-based methods, which rely on fixed scanning techniques to extract features. These methods do not fully leverage the spatial structure information inherent in images. To overcome this limitation, we proposed a novel foundation model named DefMamba, which is grounded in DS. This innovative model aims to enhance the capability of the network to learn and represent complex image structures, as well as to detect subtle changes in object details. The DS principally comprises two key operations: the shifting of focus points and the alteration of the scanning order. The first operation effectively repositions reference points toward significant regions of interest, thereby enhancing the model's sensitivity to variations in object details. The second operation modifies the scanning order to create a structure-aware sequence that is better aligned with the underlying object structure based on the input features. Extensive experimental evaluations on benchmark datasets, including ImageNet, COCO, and ADE20K, robustly demonstrate that our proposed method outperforms existing SSMs and remains competitive when compared to both CNNs and Transformer-based approaches." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8845" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "type": "text", + "content": "This work was supported by the National Natural Science Foundation of China (62172070, 62372080, 62376050, and U22B2052), and the Natural Science Foundation of Liaoning Province (2024-MSBA-24)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 149, + 115, + 162 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 149, + 115, + 162 + ], + "spans": [ + { + "bbox": [ + 56, + 149, + 115, + 162 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 168, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 168, + 296, + 224 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 168, + 296, + 224 + ], + "spans": [ + { + "bbox": [ + 61, + 168, + 296, + 224 + ], + "type": "text", + "content": "[1] Qi Bi, Jingjun Yi, Hao Zheng, Wei Ji, Haolan Zhan, Yawen Huang, Yuexiang Li, and Yefeng Zheng. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9308-9316, 2019. 2" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8847" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_content_list.json b/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5bc3e1284a0d8ca06713a51f4ec5bd411914df76 --- /dev/null +++ b/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_content_list.json @@ -0,0 +1,1416 @@ +[ + { + "type": "text", + "text": "DefectFill: Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection", + "text_level": 1, + "bbox": [ + 120, + 128, + 875, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jaewoo Song $^{1,2}$ Daemin Park $^{1}$ Kanghyun Baek $^{3}$ Sangyub Lee $^{3}$ Jooyoung Choi $^{1}$ Eunji Kim $^{1}$ Sungroh Yoon $^{1,3,4,*}$", + "bbox": [ + 181, + 200, + 813, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Department of Electrical and Computer Engineering, Seoul National University $^{2}$ Global Technology Research, Samsung Electronics $^{3}$ IPAI, $^{4}$ AIIS, ASRI, INMC, ISRC, Seoul National University", + "bbox": [ + 183, + 239, + 815, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{woo.song, eoalsqkr12, qor6271, nickyub, jy-choi, kce407, sryoon}@snu.ac.kr", + "bbox": [ + 166, + 294, + 823, + 309 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2938ba1622ae50854e20dac74e063d4cd2a2e4f4ebe4bea7546466e895c2f92a.jpg", + "image_caption": [ + "Figure 1. Given a few reference image-mask pairs of a defect (e.g. \"hole\" of a hazelnut), DefectFill learns the defect and realistically fill it onto defect-free objects in desired shapes (e.g. star, square, etc.), generating new defect images that integrate naturally with the objects. These generated images are then used for visual inspection tasks." + ], + "image_footnote": [], + "bbox": [ + 96, + 349, + 903, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 594, + 326, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Developing effective visual inspection models remains challenging due to the scarcity of defect data. While image generation models have been used to synthesize defect images, producing highly realistic defects remains difficult. We propose DefectFill, a novel method for realistic defect generation that requires only a few reference defect images. It leverages a fine-tuned inpainting diffusion model, optimized with our custom loss functions incorporating defect, object, and attention terms. It enables precise capture of detailed, localized defect features and their seamless integration into defect-free objects. Additionally, our Low-Fidelity Selection method further enhances the defect sample quality. Experiments show that DefectFill generates high-quality defect images, enabling visual inspection models to achieve state-of-the-art performance on the MVTec AD dataset.", + "bbox": [ + 88, + 628, + 485, + 857 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 514, + 594, + 643, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automating inspection on manufacturing lines is a crucial step in advancing smart factories. In this context, visual inspection focused on defect detection is a critical application for AI models. With substantial amounts of defective data, high-performance models can be developed through supervised learning [6]. However, collecting large quantities of defective data is challenging in real-world settings. For example, in newly established production lines or semiconductor processes with exceptionally low defect rates, it may be difficult or even impossible to acquire enough data.", + "bbox": [ + 511, + 625, + 906, + 775 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome the limited availability of defect data, various approaches have been developed, including out-of-distribution (OOD) techniques [21] and anomaly detection (AD) [26], which only use non-defective data, as well as active learning [20] and semi-supervised learning [27] with limited defective data. However, these methods have limitations: defect criteria vary across different problems and often require domain expertise, and they struggle to clas-", + "bbox": [ + 511, + 779, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Correspondence to: Sungroh Yoon (sryoon@snu.ac.kr)", + "bbox": [ + 107, + 886, + 406, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18718", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sify defect types accurately. To address these issues, some methods propose generating defect images to train visual inspection models [7, 14, 22, 36]. Yet, a key problem remains: defect images generated by existing methods appear unrealistic, lacking the clarity and natural details of real-world defects, which limits their practical effectiveness.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we focus on generating realistic defect images to improve the accuracy of visual inspection tasks. To achieve this, we address two key considerations: (1) precisely capturing defect details and (2) seamlessly incorporating these defect features into defect-free images.", + "bbox": [ + 89, + 181, + 480, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce DefectFill, a novel approach for generating realistic and detailed defect images using abundant normal images along with a few reference defect samples. We leverage a pre-trained inpainting diffusion model [24] to remove certain areas of a defect-free image and naturally fill those areas with defects. However, accurately filling defects is challenging, as these features often have entirely different textures or appearances compared to the original object. Therefore, we introduce three loss functions: defect loss to capture detailed features of the defect itself, object loss to establish the semantic relationship between the defect and the object, and attention loss to ensure the word representing the defect focuses precisely on the defect area. These carefully designed loss functions are essential for generating realistic defect images, enabling defects to be naturally and authentically \"filled\" within objects. To further refine samples, we implement the Low-Fidelity Selection method, which filters out generated images that fail to represent defects clearly, ensuring only high-quality samples are used.", + "bbox": [ + 91, + 260, + 482, + 546 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Through extensive experiments, we demonstrate our model's ability to generate realistic defect images that outperform state-of-the-art methods in both qualitative and quantitative evaluations. Finally, by leveraging our high-quality generated defect images, we improve performance in visual inspection downstream tasks such as anomaly classification and localization, showing that DefectFill effectively addresses the shortage of defect data.", + "bbox": [ + 89, + 547, + 480, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions include: (1) pioneering the use of an inpainting diffusion model for generating defect images, (2) designing novel loss functions that enable the model to learn embedded defect characteristics within the context of the object, thereby generating realistic defects, (3) introducing the Low-Fidelity Selection method which is used to further enhance the quality of generated samples, and (4) demonstrating that our realistic defect images significantly improve performance in downstream tasks.", + "bbox": [ + 89, + 669, + 482, + 804 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 821, + 232, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Anomaly generation", + "text_level": 1, + "bbox": [ + 89, + 847, + 282, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Various approaches have been proposed to mitigate the scarcity of defective data by generating synthetic de", + "bbox": [ + 89, + 869, + 480, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "fcts [17, 18, 35, 37]. Crop-Paste [18] and CutPaste [17] synthesize data by extracting in-distribution image patches and repositioning them, while PRN [37] and DRAEM [35] incorporate out-of-distribution elements into normal images to generate additional synthetic anomalies. Since these methods solely rely on data augmentation, their ability to generate truly novel defects remains limited, thus constraining diversity. Additionally, the defects synthesized using cross-distribution images often lack realism.", + "bbox": [ + 511, + 90, + 903, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent research has shifted toward direct defect image generation using Generative Adversarial Networks (GANs) [9], including methods like SDGAN [22] and Defect-GAN [36]. However, these approaches require large and diverse defect datasets, which limits their applicability in data-scarce scenarios. DFMGAN [7] addresses this limitation by enabling defect image generation from a small number of reference images, by exploiting a pre-trained StyleGAN2 [15]. Nonetheless, it demands lengthy training times and struggles with generating realistic defects. In contrast to GAN-based models, studies using powerful text-to-image diffusion models [24] have shown promising results. AnomalyDiffusion [14] optimizes word vectors to disentangle the intrinsic characteristics of defects from their positional information, allowing defects to be generated at any specified location. However, these word vectors still fall short in capturing the fine structural details of defects [8], resulting in defects that lack realism.", + "bbox": [ + 511, + 229, + 903, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Personalization", + "text_level": 1, + "bbox": [ + 513, + 521, + 666, + 536 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Leveraging the text-to-image capabilities of diffusion models, personalization research has emerged to learn new objects unknown to these models. This learning process uses a few reference images to enable a unique word token $[V^{*}]$ to represent the new target concept. Once the concept is learned, prompts containing the $[V^{*}]$ token can be used to generate new images of this concept. Most studies primarily focus on learning a main object that occupies most of the image, either by optimizing the unique word token [8] or fine-tuning the diffusion model [16, 28].", + "bbox": [ + 511, + 546, + 903, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, CLiC [29] focuses on learning local concepts rather than the main object and employs cross-attention guidance [5] to transfer these local concepts. We draw inspiration from this approach, though it is primarily designed for realistic scenarios where the target object can naturally exhibit these concepts, unlike defect images. In addition to the previously mentioned studies, there has been an effort to use inpainting diffusion models to learn concepts [33]. This approach focuses on learning a single target image alongside reference images, solely for inpainting that target.", + "bbox": [ + 511, + 700, + 903, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Related to these studies, we aim to learn a defect concept anomalous to objects and generate diverse, realistic defect images to enhance the performance of downstream tasks.", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18719", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/223f8689eb2ab3d1b9ef8a6202a5b2b29bcfd00310f04233512004e44647f010.jpg", + "image_caption": [ + "Figure 2. Defect learning overview. To fine-tune the inpainting diffusion model, we compute three types of loss ( $\\mathcal{L}_{\\text{def}}$ , $\\mathcal{L}_{\\text{attn}}$ , and $\\mathcal{L}_{\\text{obj}}$ ) using an image $I$ and a defect mask $M$ . The image $I$ is duplicated, with each copy combined with different masks ( $M$ and $M_{rand}$ ) and prompts ( $\\mathcal{P}_{\\text{def}}$ : \"A photo of $[V^{*}]$ \", and $\\mathcal{P}_{\\text{obj}}$ : \"A hazelnut with $[V^{*}]'$ ) as inputs to the model. The model prediction using the defect prompt $\\mathcal{P}_{\\text{def}}$ (upper pipeline) is used to compute $\\mathcal{L}_{\\text{def}}$ and, while the prediction using the object prompt $\\mathcal{P}_{\\text{obj}}$ (lower pipeline) is used to compute $\\mathcal{L}_{\\text{attn}}$ and $\\mathcal{L}_{\\text{obj}}$ ." + ], + "image_footnote": [], + "bbox": [ + 91, + 90, + 911, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 89, + 458, + 191, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce DefectFill, a novel method for generating diverse and realistic defect images. By fine-tuning a pretrained inpainting diffusion model, DefectFill efficiently learns defect concepts using only a limited set of reference defect image-mask pairs. During inference, it fills the defect feature into specific areas of defect-free images, thereby enabling the generation of high-quality defect images that enhance performance in visual inspection tasks.", + "bbox": [ + 89, + 484, + 482, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The following sections cover the background on inpainting diffusion models (Sec.3.1), followed by a formal description of our method for learning defects (Sec.3.2) and generating defect images with the learned defects (Sec.3.3). Subsequently, we describe how the generated images can be applied to downstream tasks (Sec.3.4).", + "bbox": [ + 89, + 607, + 483, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 710, + 232, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Latent Diffusion Models. Latent Diffusion Models (LDMs) [24] are a class of diffusion models [12, 30, 32] specifically designed to enhance efficiency by reducing computational complexity. An LDM consists of an encoder $\\mathcal{E}$ that maps image $I$ to a latent space $x_0 = \\mathcal{E}(I)$ , a decoder $\\mathcal{D}$ that reconstructs images as $I = \\mathcal{D}(x_0)$ , and a diffusion model operating in the latent space. The encoder and decoder are pre-trained to accurately reconstruct images from their latent representations such that $\\mathcal{D}(\\mathcal{E}(I)) = I$ , while the diffusion model is trained to predict the noise that needs to be removed from a noisy latent representation.", + "bbox": [ + 89, + 734, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The forward process of the diffusion model gradually adds Gaussian noise $\\epsilon \\sim \\mathcal{N}(0,1)$ to the latent image:", + "bbox": [ + 511, + 460, + 906, + 491 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} = \\sqrt {\\alpha_ {t}} x _ {0} + \\left(\\sqrt {1 - \\alpha_ {t}}\\right) \\epsilon , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 500, + 906, + 520 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\{\\alpha_{t}\\}_{t = 1}^{T}$ is a noise scheduler that determines the proportion of noise added at each timestep $t$ . The reverse process reconstructs the latent image from the noisy input $x_{t}$ . The diffusion model can incorporate a text prompt $\\mathcal{P}$ as conditioning, which is encoded by a text encoder $\\tau_{\\theta}$ , and is trained using the following objective:", + "bbox": [ + 511, + 527, + 906, + 621 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathbb {E} _ {x _ {t}, t, \\epsilon} \\| \\epsilon_ {\\theta} (x _ {t}, t, \\tau_ {\\theta} (\\mathcal {P})) - \\epsilon \\| _ {2} ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 628, + 906, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inpainting Diffusion Models. Inpainting Diffusion Models are fine-tuned versions of LDM, specifically designed to fill content within masked areas. These models learn the inpainting task using both a mask $M$ and a background image $B$ where the masked areas are removed. Specifically, the image $I$ and the background $B$ are mapped into the latent space through the encoder, resulting in $x_0 = \\mathcal{E}(I)$ and $b = \\mathcal{E}(B)$ . Gaussian noise is then added to $x_0$ at a specific timestep $t$ , producing $x_t$ . Subsequently, $x_t^{inpaint}$ is constructed by concatenating $x_t$ , $b$ , and $M$ as follows:", + "bbox": [ + 511, + 665, + 908, + 816 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} ^ {\\text {i n p a i n t}} = \\operatorname {c o n c a t} \\left(x _ {t}, b, M\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 825, + 903, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and is used for training diffusion models via Eq. (2). This process allows the LDM to learn how to accurately fill the masked areas with appropriate content.", + "bbox": [ + 511, + 854, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18720", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/31474b7a442d52806bb0d44d8e18987983241d779b1592de294e3783284eaefd.jpg", + "image_caption": [ + "Figure 3. Low-Fidelity Selection (LFS) for defect of leather's glue. LFS automatically selects the defect image with the most pronounced expression (blue box) by identifying the sample with the lowest fidelity (highest LPIPS score) in the masked area." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 482, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Learning Defect", + "text_level": 1, + "bbox": [ + 89, + 260, + 250, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use a stable diffusion inpainting model [24] to leverage its prior knowledge for seamlessly \"filling\" masked areas with desired defects. To train the model to understand the concept of defects, we fine-tune it using a small set of reference defect images $I$ paired with defect masks $M$ . This fine-tuning enables the model to associate the word token $[V^{*}]$ with defects. Specifically, to efficiently learn various defects while avoiding overfitting [10], we fine-tune only the text encoder $\\tau_{\\theta}$ and the attention layers by using LoRA [13].", + "bbox": [ + 89, + 282, + 483, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More precisely, we aim to achieve three goals to effectively learn local defects: (1) recognizing defects that are not the main object of the image but rather local features dependent on it, (2) understanding the semantic relationship between the defect and the main object to ensure natural blending, and (3) ensuring the word token $[V^{*}]$ corresponds to the defect region of the object. To achieve these goals, we propose three loss terms: defect, object, and attention loss, as illustrated in the overall training scheme shown in Fig. 2", + "bbox": [ + 89, + 420, + 483, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Defect Loss. The key loss term, defect loss $\\mathcal{L}_{def}$ , directly learns the detailed features of the defect concept. By guiding the model to focus exclusively on the intrinsic features of the defect, it enables inpainting of even unusual features that would not typically appear in the object.", + "bbox": [ + 89, + 579, + 482, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, we sample a timestep $t \\sim p(t)$ from the model's timestep distribution and obtain the noise latent $x_{t}$ using Eq. (1). Next, we prepare the defect mask $M$ for $I$ and generate a background image $B_{def} = (1 - M) \\odot I$ where the defect area is masked out. The latent $b_{def} = \\mathcal{E}(B_{def})$ is then concatenated with $x_{t}$ and $M$ to form $x_{t}^{def}$ :", + "bbox": [ + 89, + 656, + 483, + 750 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} ^ {\\text {d e f}} = \\operatorname {c o n c a t} \\left(x _ {t}, b _ {\\text {d e f}}, M\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 761, + 482, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which serves as input to the model.", + "bbox": [ + 89, + 794, + 326, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure the prompt focuses exclusively on the defect, we define it as $\\mathcal{P}_{def} = \"A\\text{photo of}[V^*]\".$ The text encoder $\\tau_{\\theta}$ encodes this prompt to generate the text condition embedding $c^{def} = \\tau_{\\theta}(\\mathcal{P}_{def})$ . Using these inputs, we optimize the $\\mathcal{L}_2$ loss with respect to noise $\\epsilon$ to reconstruct $x_0$ but we compute the loss only over the masked region $M$ to", + "bbox": [ + 89, + 810, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "avoid reconstructing the background:", + "bbox": [ + 511, + 90, + 761, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d e f} = \\mathbb {E} _ {x _ {t} ^ {d e f}, t, \\epsilon} \\left[ \\left\\| M \\odot \\left(\\epsilon - \\epsilon_ {\\theta} \\left(x _ {t} ^ {d e f}, t, c ^ {d e f}\\right)\\right) \\right\\| _ {2} ^ {2} \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 111, + 906, + 145 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Object Loss. The object loss $\\mathcal{L}_{obj}$ learns both the defect and its relationship to the object in which it appears. This ensures the defect blends naturally within the object.", + "bbox": [ + 511, + 159, + 906, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The $\\mathcal{L}_{obj}$ term shares the same sampled values for $\\epsilon$ , $t$ , and $x_{t}$ as the defect loss. To capture the full semantic context of the object, we create a mask with 30 random boxes, $M_{rand}$ , and train the model to fill in the occluded information across the entire image. Similar to the defect loss, we obtain the conditioning background $B_{rand} = (1 - M_{rand}) \\odot I$ and its latent $b_{rand} = \\mathcal{E}(B_{rand})$ . This $b_{rand}$ is then concatenated with $x_{t}$ and $M_{rand}$ to form $x_{t}^{obj}$ :", + "bbox": [ + 511, + 205, + 906, + 328 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} ^ {o b j} = \\operatorname {c o n c a t} \\left(x _ {t}, b _ {\\text {r a n d}}, M _ {\\text {r a n d}}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 334, + 903, + 352 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To express the object's possession of the defect, we set the prompt as $\\mathcal{P}_{obj} = \"A[Object] with [V^*]\"$ and obtain the text embedding $c^{obj} = \\tau_{\\theta}(\\mathcal{P}_{obj})$ . Although it is essential to learn the semantic context of the defect within the object, capturing the fine details of the defect itself is also crucial for authentic inpainting. To address this, we apply a weight of 1 to the defect mask areas and a weight of $\\alpha$ , less than 1, to the background areas, producing an adjusted mask $M'$ :", + "bbox": [ + 511, + 358, + 906, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {o b j} = \\mathbb {E} _ {x _ {t} ^ {o b j}, t, \\epsilon} \\left[ \\left\\| M ^ {\\prime} \\odot \\left(\\epsilon - \\epsilon_ {\\theta} \\left(x _ {t} ^ {o b j}, t, c ^ {o b j}\\right)\\right) \\right\\| _ {2} ^ {2} \\right], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 484, + 903, + 518 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM ^ {\\prime} = M + \\alpha \\cdot (1 - M).\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 520, + 705, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attention Loss. We also utilize cross-attention maps from the forward pass for $\\mathcal{L}_{obj}$ . The maps for a specific token represent the layout of the corresponding object, allowing the model to focus more precisely on that region. This helps the model better attend to the defect's features, resulting in higher-fidelity defect generation. Since the encoder in the UNet [25] does not effectively represent the layout of the corresponding token object [4], we use only decoder-layer maps. To handle varying spatial sizes across decoder layers, we resize them to match the latent size, then average those of the $[V^{*}]$ token to obtain $A_{t}^{[V^{*}]}$ . Finally, we compute the $\\mathcal{L}_2$ loss with the defect mask $M$ , increasing values in the defect region while reducing them in the background:", + "bbox": [ + 511, + 553, + 906, + 752 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a t t n} = \\mathbb {E} \\left[ \\left\\| A _ {t} ^ {[ V ^ {*} ]} - M \\right\\| _ {2} ^ {2} \\right]. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 762, + 903, + 796 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "DefectFill Loss. Finally, we fine-tune the model using a linear combination of these three loss terms:", + "bbox": [ + 511, + 810, + 905, + 839 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {o u r s}} = \\lambda_ {\\text {d e f}} \\cdot \\mathcal {L} _ {\\text {d e f}} + \\lambda_ {\\text {o b j}} \\cdot \\mathcal {L} _ {\\text {o b j}} + \\lambda_ {\\text {a t t n}} \\cdot \\mathcal {L} _ {\\text {a t t n}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 848, + 903, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The weights for each term are set to 0.5, 0.2, and 0.05, based on experiments that account for the scale of each loss.", + "bbox": [ + 511, + 869, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18721", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0e8df6b26facecb642a46b877b7d162f85daaf7d8480d2dd1e2b7e0181ada2b9.jpg", + "image_caption": [ + "Figure 4. Generated Defects by DefectFill. The first row displays the normal images (green boxes), while the second row shows the generated defect images along with their masks, and the third row provides zoomed-in views of the defects (red boxes). The zoomed images highlight the realistic and detailed rendering of the defects." + ], + "image_footnote": [], + "bbox": [ + 93, + 85, + 480, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Generating Defect", + "text_level": 1, + "bbox": [ + 89, + 388, + 267, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sampling. After fine-tuning the inpainting diffusion model with our DefectFill loss to learn the defect concept, we utilize a widely adopted diffusion-based inpainting pipeline [1, 32] to generate diverse defect samples. Specifically, as input, we provide a defect-free image $I$ along with a mask $M$ indicating the exact area intended for defect placement. At each inference step $t$ , we replace the latent representation's background area outside the mask with the latent of the defect-free image diffused with Eq. (1). This approach ensures that the model modifies only the masked region while preserving the background that should remain unchanged. This approach maintains the structure of the original image, allowing for seamless integration of defects without affecting the overall image quality.", + "bbox": [ + 88, + 411, + 482, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Low-Fidelity Selection. Finally, we propose an additional method for selecting samples where the defect is more accurately filled. Since the diffusion model generates diverse samples depending on the initial latent inputs, and due to the nature of the inpainting diffusion model, the masked area is occasionally overly reconstructed, resulting in lower-quality defect. To mitigate this issue, we select the least reconstructed image from the eight samples generated using the same normal image $I$ and defect mask $M$ . This selection is based on a reconstruction metric (e.g. PSNR, SSIM [34], LPIPS [38]) measured only within the masked region (as shown in Fig. 3). This simple yet effective process filters out unclear cases and improves defect generation quality. In particular, for downstream tasks using generated defect images, this approach allows us to automatically select high-quality defects samples without manual effort. In our case, we employ LPIPS as the reconstruction metric.", + "bbox": [ + 89, + 643, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Applying to Visual Inspection", + "text_level": 1, + "bbox": [ + 511, + 90, + 777, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The generated high-quality defect images are used to train a visual inspection model. First, we learn the concept for each defect category (Sec.3.2) and generate defective images (Sec.3.3) for each category. After that, for classification, we train standard classification models (e.g. ResNet [11]) using the generated images labeled by defect category. For localization, we train segmentation models (e.g. UNet [25]) with normal and synthesized defect images along with their corresponding masks, optimizing with focal loss [19].", + "bbox": [ + 511, + 112, + 906, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 263, + 645, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We evaluate DefectFill on the MVTec AD Dataset [2], which consists of 15 industrial objects with multiple defect categories. Each category contains hundreds of normal images and approximately 20 defect images with masks. Instead of traditional anomaly detection, we generate defect images by training on one-third of the defect image-mask pairs and applying the model to the remaining two-thirds of masks with normal images. For reliable quantitative results, we evaluate on 10 objects, while all objects are used for qualitative analysis.", + "bbox": [ + 511, + 289, + 906, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Our approach leverages the Stable-Diffusion-2-inpainting model [24], fine-tuning the text encoder and UNet's attention layers with LoRA (rank 8) [13]. We use a learning rate of 2e-4 for the UNet and 4e-5 for the text encoder. Inference is conducted with a DDIM [31] scheduler with 50 denoising steps. Additional details are provided in the supplementary materials.", + "bbox": [ + 511, + 462, + 906, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metric. We evaluate defect generation quality using Kernel Inception Distance (KID) [3] for quality and IC-LPIPS [23] for diversity, excluding FID and IS due to their limitations on smaller or unreferenced datasets. For defect inspection, we measure classification accuracy, Area Under the ROC Curve (AUROC), Average Precision (AP), $F_{1}$ -max, and Per Region Overlap (PRO).", + "bbox": [ + 511, + 589, + 905, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compare our method against two state-of-the-art defect generation methods: DFMGAN [7], a two-stage GAN-based approach, and AnomalyDiffusion [14], a text-to-image diffusion model that disentangles the appearance and spatial attributes of defects.", + "bbox": [ + 511, + 715, + 905, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Defect Generation Evaluation", + "text_level": 1, + "bbox": [ + 511, + 801, + 779, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Qualitative Results. The generated results are shown in Fig. 4. The first row displays the normal images, the second row shows the generated defect images using the mask in the lower right, and the third row provides a zoomed-in view of the generated defects. Despite using custom-drawn", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18722", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b6ce88eb4e341be5ee06aa3de62c64df136a20722701e6aa7f8e0aaa542060bb.jpg", + "image_caption": [ + "Figure 5. Defect Generation Comparisons. This figure compares the quality of defect images generated by our method (bottom row) with baseline approaches. Our method produces the most realistic results, with defects that blend seamlessly into the objects." + ], + "image_footnote": [], + "bbox": [ + 112, + 85, + 883, + 349 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/edc26efedabba02c60b8d3943ddc94f1c81f183eb0d4b53dfc1adeb9af29d882.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ObjectsDFMGAN*DFMGAN†AnoDiff‡Ours
KID↓IC-LPIPS↑KID↓IC-LPIPS↑KID↓IC-LPIPS↑KID↓IC-LPIPS↑
bottle70.900.1276.750.15131.520.1730.990.12
capsule40.630.10182.830.1754.970.185.600.18
carpet25.140.1346.020.25149.830.2250.370.22
hazelnut21.160.2430.940.3350.610.311.130.31
leather75.850.17501.610.51244.750.4074.660.30
pill123.520.1670.150.2377.690.238.760.23
tile85.280.22254.820.25314.300.4845.140.44
toothbrush46.490.1861.430.2073.310.183.190.15
wood68.130.34406.610.3583.940.354.720.35
zipper78.080.2735.740.26126.650.2434.910.20
", + "bbox": [ + 142, + 398, + 857, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Generation Comparison. This table presents the average KID and IC-LPIPS scores, computed from 1,000 generated images per defect category and averaged across all categories for each object. Our method achieves the best KID scores for all objects except carpet and the highest IC-LPIPS scores for capsule, pill, and wood. DFMGAN*: scores taken directly from the paper. DFMGAN†: scores reproduced by us. AnoDiff‡: scores measured from the generated dataset (poor samples filtered) on their official page.", + "bbox": [ + 88, + 614, + 906, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "masks which are unseen during training, the model generates authentic and well-aligned defects. Notably, for the hazelnut, the model produces a realistic defect that aligns with the object's semantics, even with an unrealistic mask shape for the crack, demonstrating its strong generalization ability. Additionally, the detailed texture within the hazelnut is observable and highlights the realism of the defects.", + "bbox": [ + 88, + 696, + 480, + 803 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 5 presents a qualitative comparison with the baselines. For AnomalyDiffusion, we use the same normal image and mask, while DFMGAN cannot use the same base image as it generates both normal and defect images directly. In the hazelnut case, both baselines struggle with the texture around the hole, whereas our method produces re", + "bbox": [ + 88, + 809, + 485, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "alistic defects that blend seamlessly with the object texture, handling irregular mask shapes and demonstrating Defect-Fill's robustness. In cases such as carpet and tile, where defects are small or thin, the baselines either fail to capture them accurately or omit them entirely, while our model generates well-defined defects. For the toothbrush, DFMGAN blurs the masked area, and AnomalyDiffusion generates defects with colors misaligned with the object context. In contrast, our model produces a realistic blueish defect that reflects the object's context (similar to how the toothbrush in Fig. 4 appears yellowish). This demonstrates our model's ability to integrate object semantics into defect generation.", + "bbox": [ + 511, + 696, + 906, + 880 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18723", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b3af1a8571dd40ab3ce38de8e4e3ce723f433203de207b7e04c3d46a910c85e9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ObjectsDFMGAN†AnoDiff*AnoDiff‡Ours
AUROCAPF1-maxPROAUROCAPF1-maxPROAUROCAPF1-maxPROAUROCAPF1-maxPRO
bottle0.960.800.740.840.990.940.870.940.990.910.830.941.000.960.900.97
capsule0.740.040.090.340.990.570.600.950.980.410.440.841.000.750.690.96
carpet0.950.620.600.840.990.810.750.920.970.740.680.820.990.920.860.96
hazelnut1.000.940.870.961.000.970.910.971.000.960.900.971.000.990.940.99
leather0.960.560.560.841.000.800.710.981.000.800.720.981.000.910.830.98
pill0.990.890.860.911.000.970.910.971.000.970.910.951.000.980.930.98
tile0.990.940.870.960.990.940.860.960.990.950.870.971.000.970.900.98
toothbrush0.980.600.610.890.990.770.730.910.990.710.680.910.990.890.820.94
wood0.720.370.410.730.990.850.750.940.970.790.720.891.000.930.860.98
zipper0.990.820.760.950.990.860.790.961.000.870.800.971.000.900.840.97
", + "bbox": [ + 91, + 88, + 906, + 272 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5e14531c754bf84328e2d58ca26928d6a2b95e272bdbcaad7c08db99d610b5c8.jpg", + "table_caption": [ + "Table 2. Localization Comparison. The table presents AUROC, AP, $F_{1}$ -max, and PRO scores for localization evaluation using a UNet trained on generated defect images. Our method achieves the highest performance across all metrics and objects. AnoDiff*: scores reported in the paper. The others: described in Tab. 1." + ], + "table_footnote": [], + "table_body": "
ObjectsDFMGAN*DFMGAN†AnoDiff*AnoDiff‡Ours
bottle56.5963.4190.7095.3597.56
capsule37.2725.0066.6745.3387.50
carpet47.3142.1158.0664.5287.72
hazelnut81.9486.9685.4289.58100.00
leather49.7332.2061.9065.0893.22
pill29.5244.4459.3864.5897.53
tile74.8581.8284.2196.49100.00
wood49.0245.1671.4378.57100.00
zipper27.6445.4569.5185.3790.91
", + "bbox": [ + 91, + 347, + 480, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Classification Comparison. The table shows classification accuracy (\\%) when a ResNet-34 is trained on generated defect images for defect category prediction. Our method achieves the highest performance across all objects. AnoDiff*: scores reported in the paper. The others: described in Tab. 1.", + "bbox": [ + 89, + 501, + 482, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Results. Tab. 1 compares the KID and IC-LPIPS scores of our method with baseline approaches across various objects. For evaluation, we generate 1,000 images for each defect category within each object, ensuring that all metrics, including KID, are calculated using only defect images excluded from the training set. This approach is necessary as KID often produces overly optimistic values when models overfit and are evaluated on training data.", + "bbox": [ + 89, + 597, + 482, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method outperforms the baselines in KID scores across most objects. For IC-LPIPS, it also achieves the best scores on three objects (capsule, pill, wood). In the case of leather, DFMGAN† and AnoDiff‡ score significantly higher, but this is primarily due to their generation of diverse yet low-quality samples across various masks. The high KID values for these methods further confirm that the quality of their generated defect images is low.", + "bbox": [ + 89, + 718, + 482, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Visual Inspection Evaluation", + "text_level": 1, + "bbox": [ + 89, + 848, + 346, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate that the realistic images generated by DefectFill can enhance performance in downstream visual in", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "spection tasks, we apply it to two tasks: classification and localization. Following the experimental setup of AnomalyDiffusion [14], we use ResNet-34 [11] for classification and UNet [25] for localization. As outlined in the quantitative results (Sec. 4.1), we generate 1,000 defects per category and train the models on this data. Testing is conducted on the remaining two-thirds of the dataset.", + "bbox": [ + 511, + 351, + 906, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Classification. As shown in Tab.3, our method achieves higher classification accuracy across all objects compared to the baselines. Notably, there is a significant improvement for objects with small defect areas, which are typically challenging to generate meaningful defects for, such as capsule $(66.67\\% \\rightarrow 87.50\\%)$ and pill $(64.58\\% \\rightarrow 97.53\\%)$ .", + "bbox": [ + 511, + 474, + 906, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Localization. The UNet is trained to predict defect locations, and the predictions are evaluated using various metrics. As shown in Tab. 2, our model achieves the best performance across all metrics and objects. The capsule is a particularly challenging object for localization, yet our model significantly outperforms the baseline with a notable improvement in AP score $(0.57 \\to 0.75)$ .", + "bbox": [ + 511, + 582, + 905, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 511, + 696, + 679, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inpainting Ablation. We conduct an ablation study to evaluate the impact of leveraging the inpainting diffusion model and our defect-specific loss tailored for this model (Fig. 6). As mentioned in Sec. 2, CLiC [29] is a method that learns local concepts without using the inpainting diffusion model. However, the generated results tend to focus on reconstruction rather than creating actual holes (left image). This is because, unlike general local concepts, the defect concept we aim to learn is an unusual concept unknown to the model's prior. When applying our defect-specific loss (middle image), the model better learns the defect features, resulting in more accurately formed holes. However, the", + "bbox": [ + 511, + 719, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18724", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/36eeea633020dea5d3c353acad5a2b6125a39fc290704c5c282104afad1a1675.jpg", + "image_caption": [ + "Figure 6. Inpainting Ablation. Ablation study comparing three setups: applying CLiC [29] loss to vanilla Stable Diffusion (SD2+CLiC Loss), replacing CLiC with our loss (SD2+Our Loss), and our full approach (SD2-Inpainting+Our Loss). Using the inpainting model with our loss is necessary to produce realistic defects that align well with both the mask and the object." + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 480, + 252 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "thin regions of the mask are still neglected, and the texture around the hole doesn't blend well with the surrounding hazelnut texture. Finally, by leveraging the inpainting diffusion model's strong prior for filling, we generate realistic defects that blend naturally with their surroundings (as shown by the light brown texture around the hole in the right image), and aligning with the thin mask regions.", + "bbox": [ + 89, + 375, + 483, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Loss Ablation. As described in Sec. 3.2, we structure our loss function with three terms to achieve three specific goals. To illustrate the contribution of each term, we perform an ablation study. Fig. 7 shows the defect generation results when each loss term is omitted during training. When the defect loss is excluded, the model tends to reconstruct rather than generate defects. This occurs because the inpainting diffusion model fails to learn the distinctive characteristics of defects and instead fills the masked area with just plausible context. Without the object loss, the model lacks semantic alignment with the object, leading to unnatural defect generation. For example, the middle section of a zipper may appear fused, or a hole may look like it's placed on a carpet rather than genuinely puncturing it. Lastly, when the attention loss is omitted, the model struggles to focus accurately on the defect mask area, resulting in lower defect fidelity (e.g. an awkwardly split zipper or an incomplete hole). Finally, by combining all loss terms, we achieve realistic defects seamlessly filled onto objects.", + "bbox": [ + 89, + 502, + 483, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Low Fidelity Selection. Our simple yet effective Low-Fidelity Selection method enables high-quality defect sampling without human effort. As shown in Fig. 3, it intuitively selects qualitatively good samples. Additionally, as reported in Tab. 4, it improves both the quality (KID) and the diversity (IC-LPIPS) of generated defects.", + "bbox": [ + 89, + 809, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8b6aeeb76bcb84c446109b74d10bc2506b1286daf0578b221a2476b3436e6717.jpg", + "image_caption": [ + "Figure 7. Loss Ablation. This figure illustrates the impact of each loss term on generated defect quality. We show the results when each loss term is individually removed during fine-tuning, as well as the result when all terms are used together. Utilizing all loss terms results in realistic defects that align well with the context." + ], + "image_footnote": [], + "bbox": [ + 516, + 87, + 905, + 324 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4cea0af88d827733768ab2ccfd792b58ec349843c411b220f242315ae1c00028.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Ours w/o LFSOurs
KID↓IC-LPIPS↑KID↓IC-LPIPS↑
28.4850.24725.9470.250
", + "bbox": [ + 566, + 420, + 854, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Generation Comparison with Low-Fidelity Selection. The application of LFS shows improvements in quality (KID) and diversity (IC-LPIPS). The values represent averages calculated for each defect category, and then averaged across objects.", + "bbox": [ + 511, + 500, + 906, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 513, + 580, + 638, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present DefectFill, a novel approach that fine-tunes an inpainting diffusion model to generate realistic and high-fidelity defect images. Our method achieves state-of-the-art performance in both generation quality and visual inspection tasks on the MVtec AD dataset, demonstrating its effectiveness even when limited reference samples are available. These strengths make DefectFill particularly well-suited for widespread industrial applications, especially in scenarios where defect images are scarce.", + "bbox": [ + 511, + 607, + 906, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. While our method excels at generating localized defects—a common real-world scenario—it is less effective for global structural defects that affect the entire object, such as misalignment. This limitation arises because our inpainting-based approach, which focuses on local masked regions. Addressing such global defects remains an area for future research, though our method already robustly handles the majority of practical defect cases, where localized defects are the primary concern.", + "bbox": [ + 511, + 763, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18725", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 258, + 187, + 273 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. Blended latent diffusion. ACM transactions on graphics (TOG), 42 (4):1-11, 2023. 5", + "[2] Paul Bergmann, Michael Fauser, David Sattlegger, and Carsten Steger. Mvtec ad-a comprehensive real-world dataset for unsupervised anomaly detection. 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Prototypical residual networks for anomaly detection and localization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16281-16291, 2023. 2", + "[38] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 5" + ], + "bbox": [ + 514, + 90, + 905, + 231 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18727", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_model.json b/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ca03b9d4e7b4d9e34a9b6244750c064644f4d29a --- /dev/null +++ b/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_model.json @@ -0,0 +1,1837 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.122, + 0.13, + 0.877, + 0.177 + ], + "angle": 0, + "content": "DefectFill: Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection" + }, + { + "type": "text", + "bbox": [ + 0.183, + 0.202, + 0.814, + 0.24 + ], + "angle": 0, + "content": "Jaewoo Song\\(^{1,2}\\) Daemin Park\\(^{1}\\) Kanghyun Baek\\(^{3}\\) Sangyub Lee\\(^{3}\\) Jooyoung Choi\\(^{1}\\) Eunji Kim\\(^{1}\\) Sungroh Yoon\\(^{1,3,4,*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.24, + 0.816, + 0.294 + ], + "angle": 0, + "content": "\\(^{1}\\)Department of Electrical and Computer Engineering, Seoul National University \\(^{2}\\)Global Technology Research, Samsung Electronics \\(^{3}\\)IPAI, \\(^{4}\\)AIIS, ASRI, INMC, ISRC, Seoul National University" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.295, + 0.825, + 0.31 + ], + "angle": 0, + "content": "{woo.song, eoalsqkr12, qor6271, nickyub, jy-choi, kce407, sryoon}@snu.ac.kr" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.351, + 0.905, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.54, + 0.908, + 0.584 + ], + "angle": 0, + "content": "Figure 1. Given a few reference image-mask pairs of a defect (e.g. \"hole\" of a hazelnut), DefectFill learns the defect and realistically fill it onto defect-free objects in desired shapes (e.g. star, square, etc.), generating new defect images that integrate naturally with the objects. These generated images are then used for visual inspection tasks." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.595, + 0.327, + 0.61 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.63, + 0.486, + 0.858 + ], + "angle": 0, + "content": "Developing effective visual inspection models remains challenging due to the scarcity of defect data. While image generation models have been used to synthesize defect images, producing highly realistic defects remains difficult. We propose DefectFill, a novel method for realistic defect generation that requires only a few reference defect images. It leverages a fine-tuned inpainting diffusion model, optimized with our custom loss functions incorporating defect, object, and attention terms. It enables precise capture of detailed, localized defect features and their seamless integration into defect-free objects. Additionally, our Low-Fidelity Selection method further enhances the defect sample quality. Experiments show that DefectFill generates high-quality defect images, enabling visual inspection models to achieve state-of-the-art performance on the MVTec AD dataset." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.595, + 0.645, + 0.61 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.625, + 0.907, + 0.776 + ], + "angle": 0, + "content": "Automating inspection on manufacturing lines is a crucial step in advancing smart factories. In this context, visual inspection focused on defect detection is a critical application for AI models. With substantial amounts of defective data, high-performance models can be developed through supervised learning [6]. However, collecting large quantities of defective data is challenging in real-world settings. For example, in newly established production lines or semiconductor processes with exceptionally low defect rates, it may be difficult or even impossible to acquire enough data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "To overcome the limited availability of defect data, various approaches have been developed, including out-of-distribution (OOD) techniques [21] and anomaly detection (AD) [26], which only use non-defective data, as well as active learning [20] and semi-supervised learning [27] with limited defective data. However, these methods have limitations: defect criteria vary across different problems and often require domain expertise, and they struggle to clas-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.408, + 0.902 + ], + "angle": 0, + "content": "*Correspondence to: Sungroh Yoon (sryoon@snu.ac.kr)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18718" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "sify defect types accurately. To address these issues, some methods propose generating defect images to train visual inspection models [7, 14, 22, 36]. Yet, a key problem remains: defect images generated by existing methods appear unrealistic, lacking the clarity and natural details of real-world defects, which limits their practical effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.183, + 0.482, + 0.259 + ], + "angle": 0, + "content": "In this paper, we focus on generating realistic defect images to improve the accuracy of visual inspection tasks. To achieve this, we address two key considerations: (1) precisely capturing defect details and (2) seamlessly incorporating these defect features into defect-free images." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.261, + 0.483, + 0.547 + ], + "angle": 0, + "content": "We introduce DefectFill, a novel approach for generating realistic and detailed defect images using abundant normal images along with a few reference defect samples. We leverage a pre-trained inpainting diffusion model [24] to remove certain areas of a defect-free image and naturally fill those areas with defects. However, accurately filling defects is challenging, as these features often have entirely different textures or appearances compared to the original object. Therefore, we introduce three loss functions: defect loss to capture detailed features of the defect itself, object loss to establish the semantic relationship between the defect and the object, and attention loss to ensure the word representing the defect focuses precisely on the defect area. These carefully designed loss functions are essential for generating realistic defect images, enabling defects to be naturally and authentically \"filled\" within objects. To further refine samples, we implement the Low-Fidelity Selection method, which filters out generated images that fail to represent defects clearly, ensuring only high-quality samples are used." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.548, + 0.482, + 0.669 + ], + "angle": 0, + "content": "Through extensive experiments, we demonstrate our model's ability to generate realistic defect images that outperform state-of-the-art methods in both qualitative and quantitative evaluations. Finally, by leveraging our high-quality generated defect images, we improve performance in visual inspection downstream tasks such as anomaly classification and localization, showing that DefectFill effectively addresses the shortage of defect data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.483, + 0.805 + ], + "angle": 0, + "content": "Our main contributions include: (1) pioneering the use of an inpainting diffusion model for generating defect images, (2) designing novel loss functions that enable the model to learn embedded defect characteristics within the context of the object, thereby generating realistic defects, (3) introducing the Low-Fidelity Selection method which is used to further enhance the quality of generated samples, and (4) demonstrating that our realistic defect images significantly improve performance in downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.822, + 0.233, + 0.837 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.848, + 0.283, + 0.864 + ], + "angle": 0, + "content": "2.1. Anomaly generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.482, + 0.901 + ], + "angle": 0, + "content": "Various approaches have been proposed to mitigate the scarcity of defective data by generating synthetic de" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.228 + ], + "angle": 0, + "content": "fcts [17, 18, 35, 37]. Crop-Paste [18] and CutPaste [17] synthesize data by extracting in-distribution image patches and repositioning them, while PRN [37] and DRAEM [35] incorporate out-of-distribution elements into normal images to generate additional synthetic anomalies. Since these methods solely rely on data augmentation, their ability to generate truly novel defects remains limited, thus constraining diversity. Additionally, the defects synthesized using cross-distribution images often lack realism." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.231, + 0.905, + 0.502 + ], + "angle": 0, + "content": "Recent research has shifted toward direct defect image generation using Generative Adversarial Networks (GANs) [9], including methods like SDGAN [22] and Defect-GAN [36]. However, these approaches require large and diverse defect datasets, which limits their applicability in data-scarce scenarios. DFMGAN [7] addresses this limitation by enabling defect image generation from a small number of reference images, by exploiting a pre-trained StyleGAN2 [15]. Nonetheless, it demands lengthy training times and struggles with generating realistic defects. In contrast to GAN-based models, studies using powerful text-to-image diffusion models [24] have shown promising results. AnomalyDiffusion [14] optimizes word vectors to disentangle the intrinsic characteristics of defects from their positional information, allowing defects to be generated at any specified location. However, these word vectors still fall short in capturing the fine structural details of defects [8], resulting in defects that lack realism." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.522, + 0.668, + 0.537 + ], + "angle": 0, + "content": "2.2. Personalization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.547, + 0.905, + 0.699 + ], + "angle": 0, + "content": "Leveraging the text-to-image capabilities of diffusion models, personalization research has emerged to learn new objects unknown to these models. This learning process uses a few reference images to enable a unique word token \\([V^{*}]\\) to represent the new target concept. Once the concept is learned, prompts containing the \\([V^{*}]\\) token can be used to generate new images of this concept. Most studies primarily focus on learning a main object that occupies most of the image, either by optimizing the unique word token [8] or fine-tuning the diffusion model [16, 28]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.701, + 0.905, + 0.853 + ], + "angle": 0, + "content": "In contrast, CLiC [29] focuses on learning local concepts rather than the main object and employs cross-attention guidance [5] to transfer these local concepts. We draw inspiration from this approach, though it is primarily designed for realistic scenarios where the target object can naturally exhibit these concepts, unlike defect images. In addition to the previously mentioned studies, there has been an effort to use inpainting diffusion models to learn concepts [33]. This approach focuses on learning a single target image alongside reference images, solely for inpainting that target." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Related to these studies, we aim to learn a defect concept anomalous to objects and generate diverse, realistic defect images to enhance the performance of downstream tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "18719" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.092, + 0.912, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.353, + 0.908, + 0.427 + ], + "angle": 0, + "content": "Figure 2. Defect learning overview. To fine-tune the inpainting diffusion model, we compute three types of loss (\\(\\mathcal{L}_{\\text{def}}\\), \\(\\mathcal{L}_{\\text{attn}}\\), and \\(\\mathcal{L}_{\\text{obj}}\\)) using an image \\(I\\) and a defect mask \\(M\\). The image \\(I\\) is duplicated, with each copy combined with different masks (\\(M\\) and \\(M_{rand}\\)) and prompts (\\(\\mathcal{P}_{\\text{def}}\\): \"A photo of \\([V^{*}]\\)\", and \\(\\mathcal{P}_{\\text{obj}}\\): \"A hazelnut with \\([V^{*}]'\\)) as inputs to the model. The model prediction using the defect prompt \\(\\mathcal{P}_{\\text{def}}\\) (upper pipeline) is used to compute \\(\\mathcal{L}_{\\text{def}}\\) and, while the prediction using the object prompt \\(\\mathcal{P}_{\\text{obj}}\\) (lower pipeline) is used to compute \\(\\mathcal{L}_{\\text{attn}}\\) and \\(\\mathcal{L}_{\\text{obj}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.459, + 0.192, + 0.475 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.486, + 0.483, + 0.607 + ], + "angle": 0, + "content": "We introduce DefectFill, a novel method for generating diverse and realistic defect images. By fine-tuning a pretrained inpainting diffusion model, DefectFill efficiently learns defect concepts using only a limited set of reference defect image-mask pairs. During inference, it fills the defect feature into specific areas of defect-free images, thereby enabling the generation of high-quality defect images that enhance performance in visual inspection tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.608, + 0.484, + 0.699 + ], + "angle": 0, + "content": "The following sections cover the background on inpainting diffusion models (Sec.3.1), followed by a formal description of our method for learning defects (Sec.3.2) and generating defect images with the learned defects (Sec.3.3). Subsequently, we describe how the generated images can be applied to downstream tasks (Sec.3.4)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.711, + 0.233, + 0.726 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Latent Diffusion Models. Latent Diffusion Models (LDMs) [24] are a class of diffusion models [12, 30, 32] specifically designed to enhance efficiency by reducing computational complexity. An LDM consists of an encoder \\(\\mathcal{E}\\) that maps image \\(I\\) to a latent space \\(x_0 = \\mathcal{E}(I)\\), a decoder \\(\\mathcal{D}\\) that reconstructs images as \\(I = \\mathcal{D}(x_0)\\), and a diffusion model operating in the latent space. The encoder and decoder are pre-trained to accurately reconstruct images from their latent representations such that \\(\\mathcal{D}(\\mathcal{E}(I)) = I\\), while the diffusion model is trained to predict the noise that needs to be removed from a noisy latent representation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.461, + 0.907, + 0.492 + ], + "angle": 0, + "content": "The forward process of the diffusion model gradually adds Gaussian noise \\(\\epsilon \\sim \\mathcal{N}(0,1)\\) to the latent image:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.501, + 0.907, + 0.521 + ], + "angle": 0, + "content": "\\[\nx _ {t} = \\sqrt {\\alpha_ {t}} x _ {0} + \\left(\\sqrt {1 - \\alpha_ {t}}\\right) \\epsilon , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.529, + 0.907, + 0.622 + ], + "angle": 0, + "content": "where \\(\\{\\alpha_{t}\\}_{t = 1}^{T}\\) is a noise scheduler that determines the proportion of noise added at each timestep \\(t\\). The reverse process reconstructs the latent image from the noisy input \\(x_{t}\\). The diffusion model can incorporate a text prompt \\(\\mathcal{P}\\) as conditioning, which is encoded by a text encoder \\(\\tau_{\\theta}\\), and is trained using the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.63, + 0.907, + 0.65 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathbb {E} _ {x _ {t}, t, \\epsilon} \\| \\epsilon_ {\\theta} (x _ {t}, t, \\tau_ {\\theta} (\\mathcal {P})) - \\epsilon \\| _ {2} ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.666, + 0.909, + 0.818 + ], + "angle": 0, + "content": "Inpainting Diffusion Models. Inpainting Diffusion Models are fine-tuned versions of LDM, specifically designed to fill content within masked areas. These models learn the inpainting task using both a mask \\( M \\) and a background image \\( B \\) where the masked areas are removed. Specifically, the image \\( I \\) and the background \\( B \\) are mapped into the latent space through the encoder, resulting in \\( x_0 = \\mathcal{E}(I) \\) and \\( b = \\mathcal{E}(B) \\). Gaussian noise is then added to \\( x_0 \\) at a specific timestep \\( t \\), producing \\( x_t \\). Subsequently, \\( x_t^{inpaint} \\) is constructed by concatenating \\( x_t \\), \\( b \\), and \\( M \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.827, + 0.905, + 0.845 + ], + "angle": 0, + "content": "\\[\nx _ {t} ^ {\\text {i n p a i n t}} = \\operatorname {c o n c a t} \\left(x _ {t}, b, M\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.902 + ], + "angle": 0, + "content": "and is used for training diffusion models via Eq. (2). This process allows the LDM to learn how to accurately fill the masked areas with appropriate content." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18720" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.483, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.177, + 0.483, + 0.234 + ], + "angle": 0, + "content": "Figure 3. Low-Fidelity Selection (LFS) for defect of leather's glue. LFS automatically selects the defect image with the most pronounced expression (blue box) by identifying the sample with the lowest fidelity (highest LPIPS score) in the masked area." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.261, + 0.251, + 0.277 + ], + "angle": 0, + "content": "3.2. Learning Defect" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.284, + 0.484, + 0.42 + ], + "angle": 0, + "content": "We use a stable diffusion inpainting model [24] to leverage its prior knowledge for seamlessly \"filling\" masked areas with desired defects. To train the model to understand the concept of defects, we fine-tune it using a small set of reference defect images \\(I\\) paired with defect masks \\(M\\). This fine-tuning enables the model to associate the word token \\([V^{*}]\\) with defects. Specifically, to efficiently learn various defects while avoiding overfitting [10], we fine-tune only the text encoder \\(\\tau_{\\theta}\\) and the attention layers by using LoRA [13]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.421, + 0.484, + 0.557 + ], + "angle": 0, + "content": "More precisely, we aim to achieve three goals to effectively learn local defects: (1) recognizing defects that are not the main object of the image but rather local features dependent on it, (2) understanding the semantic relationship between the defect and the main object to ensure natural blending, and (3) ensuring the word token \\([V^{*}]\\) corresponds to the defect region of the object. To achieve these goals, we propose three loss terms: defect, object, and attention loss, as illustrated in the overall training scheme shown in Fig. 2" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.58, + 0.483, + 0.656 + ], + "angle": 0, + "content": "Defect Loss. The key loss term, defect loss \\(\\mathcal{L}_{def}\\), directly learns the detailed features of the defect concept. By guiding the model to focus exclusively on the intrinsic features of the defect, it enables inpainting of even unusual features that would not typically appear in the object." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.657, + 0.484, + 0.75 + ], + "angle": 0, + "content": "First, we sample a timestep \\( t \\sim p(t) \\) from the model's timestep distribution and obtain the noise latent \\( x_{t} \\) using Eq. (1). Next, we prepare the defect mask \\( M \\) for \\( I \\) and generate a background image \\( B_{def} = (1 - M) \\odot I \\) where the defect area is masked out. The latent \\( b_{def} = \\mathcal{E}(B_{def}) \\) is then concatenated with \\( x_{t} \\) and \\( M \\) to form \\( x_{t}^{def} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.762, + 0.483, + 0.782 + ], + "angle": 0, + "content": "\\[\nx _ {t} ^ {\\text {d e f}} = \\operatorname {c o n c a t} \\left(x _ {t}, b _ {\\text {d e f}}, M\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.795, + 0.327, + 0.809 + ], + "angle": 0, + "content": "which serves as input to the model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To ensure the prompt focuses exclusively on the defect, we define it as \\(\\mathcal{P}_{def} = \"A\\text{photo of}[V^*]\".\\) The text encoder \\(\\tau_{\\theta}\\) encodes this prompt to generate the text condition embedding \\(c^{def} = \\tau_{\\theta}(\\mathcal{P}_{def})\\). Using these inputs, we optimize the \\(\\mathcal{L}_2\\) loss with respect to noise \\(\\epsilon\\) to reconstruct \\(x_0\\) but we compute the loss only over the masked region \\(M\\) to" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.763, + 0.107 + ], + "angle": 0, + "content": "avoid reconstructing the background:" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.112, + 0.907, + 0.146 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d e f} = \\mathbb {E} _ {x _ {t} ^ {d e f}, t, \\epsilon} \\left[ \\left\\| M \\odot \\left(\\epsilon - \\epsilon_ {\\theta} \\left(x _ {t} ^ {d e f}, t, c ^ {d e f}\\right)\\right) \\right\\| _ {2} ^ {2} \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.16, + 0.907, + 0.206 + ], + "angle": 0, + "content": "Object Loss. The object loss \\(\\mathcal{L}_{obj}\\) learns both the defect and its relationship to the object in which it appears. This ensures the defect blends naturally within the object." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.207, + 0.907, + 0.329 + ], + "angle": 0, + "content": "The \\(\\mathcal{L}_{obj}\\) term shares the same sampled values for \\(\\epsilon\\), \\(t\\), and \\(x_{t}\\) as the defect loss. To capture the full semantic context of the object, we create a mask with 30 random boxes, \\(M_{rand}\\), and train the model to fill in the occluded information across the entire image. Similar to the defect loss, we obtain the conditioning background \\(B_{rand} = (1 - M_{rand}) \\odot I\\) and its latent \\(b_{rand} = \\mathcal{E}(B_{rand})\\). This \\(b_{rand}\\) is then concatenated with \\(x_{t}\\) and \\(M_{rand}\\) to form \\(x_{t}^{obj}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.335, + 0.905, + 0.353 + ], + "angle": 0, + "content": "\\[\nx _ {t} ^ {o b j} = \\operatorname {c o n c a t} \\left(x _ {t}, b _ {\\text {r a n d}}, M _ {\\text {r a n d}}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.359, + 0.907, + 0.481 + ], + "angle": 0, + "content": "To express the object's possession of the defect, we set the prompt as \\(\\mathcal{P}_{obj} = \"A[Object] with [V^*]\"\\) and obtain the text embedding \\(c^{obj} = \\tau_{\\theta}(\\mathcal{P}_{obj})\\). Although it is essential to learn the semantic context of the defect within the object, capturing the fine details of the defect itself is also crucial for authentic inpainting. To address this, we apply a weight of 1 to the defect mask areas and a weight of \\(\\alpha\\), less than 1, to the background areas, producing an adjusted mask \\(M'\\):" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.485, + 0.905, + 0.52 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {o b j} = \\mathbb {E} _ {x _ {t} ^ {o b j}, t, \\epsilon} \\left[ \\left\\| M ^ {\\prime} \\odot \\left(\\epsilon - \\epsilon_ {\\theta} \\left(x _ {t} ^ {o b j}, t, c ^ {o b j}\\right)\\right) \\right\\| _ {2} ^ {2} \\right], \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.521, + 0.706, + 0.538 + ], + "angle": 0, + "content": "\\[\nM ^ {\\prime} = M + \\alpha \\cdot (1 - M).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.907, + 0.753 + ], + "angle": 0, + "content": "Attention Loss. We also utilize cross-attention maps from the forward pass for \\(\\mathcal{L}_{obj}\\). The maps for a specific token represent the layout of the corresponding object, allowing the model to focus more precisely on that region. This helps the model better attend to the defect's features, resulting in higher-fidelity defect generation. Since the encoder in the UNet [25] does not effectively represent the layout of the corresponding token object [4], we use only decoder-layer maps. To handle varying spatial sizes across decoder layers, we resize them to match the latent size, then average those of the \\([V^{*}]\\) token to obtain \\(A_{t}^{[V^{*}]}\\). Finally, we compute the \\(\\mathcal{L}_2\\) loss with the defect mask \\(M\\), increasing values in the defect region while reducing them in the background:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.763, + 0.905, + 0.797 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a t t n} = \\mathbb {E} \\left[ \\left\\| A _ {t} ^ {[ V ^ {*} ]} - M \\right\\| _ {2} ^ {2} \\right]. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.811, + 0.906, + 0.84 + ], + "angle": 0, + "content": "DefectFill Loss. Finally, we fine-tune the model using a linear combination of these three loss terms:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.849, + 0.905, + 0.866 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {o u r s}} = \\lambda_ {\\text {d e f}} \\cdot \\mathcal {L} _ {\\text {d e f}} + \\lambda_ {\\text {o b j}} \\cdot \\mathcal {L} _ {\\text {o b j}} + \\lambda_ {\\text {a t t n}} \\cdot \\mathcal {L} _ {\\text {a t t n}}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.901 + ], + "angle": 0, + "content": "The weights for each term are set to 0.5, 0.2, and 0.05, based on experiments that account for the scale of each loss." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18721" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.087, + 0.482, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.293, + 0.485, + 0.365 + ], + "angle": 0, + "content": "Figure 4. Generated Defects by DefectFill. The first row displays the normal images (green boxes), while the second row shows the generated defect images along with their masks, and the third row provides zoomed-in views of the defects (red boxes). The zoomed images highlight the realistic and detailed rendering of the defects." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.39, + 0.269, + 0.406 + ], + "angle": 0, + "content": "3.3. Generating Defect" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.412, + 0.483, + 0.624 + ], + "angle": 0, + "content": "Sampling. After fine-tuning the inpainting diffusion model with our DefectFill loss to learn the defect concept, we utilize a widely adopted diffusion-based inpainting pipeline [1, 32] to generate diverse defect samples. Specifically, as input, we provide a defect-free image \\( I \\) along with a mask \\( M \\) indicating the exact area intended for defect placement. At each inference step \\( t \\), we replace the latent representation's background area outside the mask with the latent of the defect-free image diffused with Eq. (1). This approach ensures that the model modifies only the masked region while preserving the background that should remain unchanged. This approach maintains the structure of the original image, allowing for seamless integration of defects without affecting the overall image quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Low-Fidelity Selection. Finally, we propose an additional method for selecting samples where the defect is more accurately filled. Since the diffusion model generates diverse samples depending on the initial latent inputs, and due to the nature of the inpainting diffusion model, the masked area is occasionally overly reconstructed, resulting in lower-quality defect. To mitigate this issue, we select the least reconstructed image from the eight samples generated using the same normal image \\( I \\) and defect mask \\( M \\). This selection is based on a reconstruction metric (e.g. PSNR, SSIM [34], LPIPS [38]) measured only within the masked region (as shown in Fig. 3). This simple yet effective process filters out unclear cases and improves defect generation quality. In particular, for downstream tasks using generated defect images, this approach allows us to automatically select high-quality defects samples without manual effort. In our case, we employ LPIPS as the reconstruction metric." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.091, + 0.779, + 0.108 + ], + "angle": 0, + "content": "3.4. Applying to Visual Inspection" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.113, + 0.907, + 0.25 + ], + "angle": 0, + "content": "The generated high-quality defect images are used to train a visual inspection model. First, we learn the concept for each defect category (Sec.3.2) and generate defective images (Sec.3.3) for each category. After that, for classification, we train standard classification models (e.g. ResNet [11]) using the generated images labeled by defect category. For localization, we train segmentation models (e.g. UNet [25]) with normal and synthesized defect images along with their corresponding masks, optimizing with focal loss [19]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.265, + 0.646, + 0.281 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.29, + 0.907, + 0.442 + ], + "angle": 0, + "content": "Dataset. We evaluate DefectFill on the MVTec AD Dataset [2], which consists of 15 industrial objects with multiple defect categories. Each category contains hundreds of normal images and approximately 20 defect images with masks. Instead of traditional anomaly detection, we generate defect images by training on one-third of the defect image-mask pairs and applying the model to the remaining two-thirds of masks with normal images. For reliable quantitative results, we evaluate on 10 objects, while all objects are used for qualitative analysis." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.907, + 0.57 + ], + "angle": 0, + "content": "Implementation Details. Our approach leverages the Stable-Diffusion-2-inpainting model [24], fine-tuning the text encoder and UNet's attention layers with LoRA (rank 8) [13]. We use a learning rate of 2e-4 for the UNet and 4e-5 for the text encoder. Inference is conducted with a DDIM [31] scheduler with 50 denoising steps. Additional details are provided in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.59, + 0.906, + 0.696 + ], + "angle": 0, + "content": "Metric. We evaluate defect generation quality using Kernel Inception Distance (KID) [3] for quality and IC-LPIPS [23] for diversity, excluding FID and IS due to their limitations on smaller or unreferenced datasets. For defect inspection, we measure classification accuracy, Area Under the ROC Curve (AUROC), Average Precision (AP), \\(F_{1}\\)-max, and Per Region Overlap (PRO)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.716, + 0.906, + 0.792 + ], + "angle": 0, + "content": "Baselines. We compare our method against two state-of-the-art defect generation methods: DFMGAN [7], a two-stage GAN-based approach, and AnomalyDiffusion [14], a text-to-image diffusion model that disentangles the appearance and spatial attributes of defects." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.78, + 0.818 + ], + "angle": 0, + "content": "4.1. Defect Generation Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Qualitative Results. The generated results are shown in Fig. 4. The first row displays the normal images, the second row shows the generated defect images using the mask in the lower right, and the third row provides a zoomed-in view of the generated defects. Despite using custom-drawn" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18722" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.086, + 0.885, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.359, + 0.908, + 0.389 + ], + "angle": 0, + "content": "Figure 5. Defect Generation Comparisons. This figure compares the quality of defect images generated by our method (bottom row) with baseline approaches. Our method produces the most realistic results, with defects that blend seamlessly into the objects." + }, + { + "type": "table", + "bbox": [ + 0.143, + 0.4, + 0.859, + 0.606 + ], + "angle": 0, + "content": "
ObjectsDFMGAN*DFMGAN†AnoDiff‡Ours
KID↓IC-LPIPS↑KID↓IC-LPIPS↑KID↓IC-LPIPS↑KID↓IC-LPIPS↑
bottle70.900.1276.750.15131.520.1730.990.12
capsule40.630.10182.830.1754.970.185.600.18
carpet25.140.1346.020.25149.830.2250.370.22
hazelnut21.160.2430.940.3350.610.311.130.31
leather75.850.17501.610.51244.750.4074.660.30
pill123.520.1670.150.2377.690.238.760.23
tile85.280.22254.820.25314.300.4845.140.44
toothbrush46.490.1861.430.2073.310.183.190.15
wood68.130.34406.610.3583.940.354.720.35
zipper78.080.2735.740.26126.650.2434.910.20
" + }, + { + "type": "table_caption", + "bbox": [ + 0.089, + 0.615, + 0.908, + 0.677 + ], + "angle": 0, + "content": "Table 1. Generation Comparison. This table presents the average KID and IC-LPIPS scores, computed from 1,000 generated images per defect category and averaged across all categories for each object. Our method achieves the best KID scores for all objects except carpet and the highest IC-LPIPS scores for capsule, pill, and wood. DFMGAN*: scores taken directly from the paper. DFMGAN†: scores reproduced by us. AnoDiff‡: scores measured from the generated dataset (poor samples filtered) on their official page." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.698, + 0.482, + 0.804 + ], + "angle": 0, + "content": "masks which are unseen during training, the model generates authentic and well-aligned defects. Notably, for the hazelnut, the model produces a realistic defect that aligns with the object's semantics, even with an unrealistic mask shape for the crack, demonstrating its strong generalization ability. Additionally, the detailed texture within the hazelnut is observable and highlights the realism of the defects." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.81, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Fig. 5 presents a qualitative comparison with the baselines. For AnomalyDiffusion, we use the same normal image and mask, while DFMGAN cannot use the same base image as it generates both normal and defect images directly. In the hazelnut case, both baselines struggle with the texture around the hole, whereas our method produces re" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.698, + 0.907, + 0.881 + ], + "angle": 0, + "content": "alistic defects that blend seamlessly with the object texture, handling irregular mask shapes and demonstrating Defect-Fill's robustness. In cases such as carpet and tile, where defects are small or thin, the baselines either fail to capture them accurately or omit them entirely, while our model generates well-defined defects. For the toothbrush, DFMGAN blurs the masked area, and AnomalyDiffusion generates defects with colors misaligned with the object context. In contrast, our model produces a realistic blueish defect that reflects the object's context (similar to how the toothbrush in Fig. 4 appears yellowish). This demonstrates our model's ability to integrate object semantics into defect generation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18723" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.907, + 0.273 + ], + "angle": 0, + "content": "
ObjectsDFMGAN†AnoDiff*AnoDiff‡Ours
AUROCAPF1-maxPROAUROCAPF1-maxPROAUROCAPF1-maxPROAUROCAPF1-maxPRO
bottle0.960.800.740.840.990.940.870.940.990.910.830.941.000.960.900.97
capsule0.740.040.090.340.990.570.600.950.980.410.440.841.000.750.690.96
carpet0.950.620.600.840.990.810.750.920.970.740.680.820.990.920.860.96
hazelnut1.000.940.870.961.000.970.910.971.000.960.900.971.000.990.940.99
leather0.960.560.560.841.000.800.710.981.000.800.720.981.000.910.830.98
pill0.990.890.860.911.000.970.910.971.000.970.910.951.000.980.930.98
tile0.990.940.870.960.990.940.860.960.990.950.870.971.000.970.900.98
toothbrush0.980.600.610.890.990.770.730.910.990.710.680.910.990.890.820.94
wood0.720.370.410.730.990.850.750.940.970.790.720.891.000.930.860.98
zipper0.990.820.760.950.990.860.790.961.000.870.800.971.000.900.840.97
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.282, + 0.907, + 0.325 + ], + "angle": 0, + "content": "Table 2. Localization Comparison. The table presents AUROC, AP, \\(F_{1}\\)-max, and PRO scores for localization evaluation using a UNet trained on generated defect images. Our method achieves the highest performance across all metrics and objects. AnoDiff*: scores reported in the paper. The others: described in Tab. 1." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.348, + 0.482, + 0.491 + ], + "angle": 0, + "content": "
ObjectsDFMGAN*DFMGAN†AnoDiff*AnoDiff‡Ours
bottle56.5963.4190.7095.3597.56
capsule37.2725.0066.6745.3387.50
carpet47.3142.1158.0664.5287.72
hazelnut81.9486.9685.4289.58100.00
leather49.7332.2061.9065.0893.22
pill29.5244.4459.3864.5897.53
tile74.8581.8284.2196.49100.00
wood49.0245.1671.4378.57100.00
zipper27.6445.4569.5185.3790.91
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.502, + 0.483, + 0.573 + ], + "angle": 0, + "content": "Table 3. Classification Comparison. The table shows classification accuracy (\\%) when a ResNet-34 is trained on generated defect images for defect category prediction. Our method achieves the highest performance across all objects. AnoDiff*: scores reported in the paper. The others: described in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.598, + 0.483, + 0.718 + ], + "angle": 0, + "content": "Quantitative Results. Tab. 1 compares the KID and IC-LPIPS scores of our method with baseline approaches across various objects. For evaluation, we generate 1,000 images for each defect category within each object, ensuring that all metrics, including KID, are calculated using only defect images excluded from the training set. This approach is necessary as KID often produces overly optimistic values when models overfit and are evaluated on training data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.719, + 0.483, + 0.84 + ], + "angle": 0, + "content": "Our method outperforms the baselines in KID scores across most objects. For IC-LPIPS, it also achieves the best scores on three objects (capsule, pill, wood). In the case of leather, DFMGAN† and AnoDiff‡ score significantly higher, but this is primarily due to their generation of diverse yet low-quality samples across various masks. The high KID values for these methods further confirm that the quality of their generated defect images is low." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.348, + 0.866 + ], + "angle": 0, + "content": "4.2. Visual Inspection Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To demonstrate that the realistic images generated by DefectFill can enhance performance in downstream visual in" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.352, + 0.907, + 0.457 + ], + "angle": 0, + "content": "spection tasks, we apply it to two tasks: classification and localization. Following the experimental setup of AnomalyDiffusion [14], we use ResNet-34 [11] for classification and UNet [25] for localization. As outlined in the quantitative results (Sec. 4.1), we generate 1,000 defects per category and train the models on this data. Testing is conducted on the remaining two-thirds of the dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.475, + 0.907, + 0.567 + ], + "angle": 0, + "content": "Classification. As shown in Tab.3, our method achieves higher classification accuracy across all objects compared to the baselines. Notably, there is a significant improvement for objects with small defect areas, which are typically challenging to generate meaningful defects for, such as capsule \\((66.67\\% \\rightarrow 87.50\\%)\\) and pill \\((64.58\\% \\rightarrow 97.53\\%)\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.906, + 0.689 + ], + "angle": 0, + "content": "Localization. The UNet is trained to predict defect locations, and the predictions are evaluated using various metrics. As shown in Tab. 2, our model achieves the best performance across all metrics and objects. The capsule is a particularly challenging object for localization, yet our model significantly outperforms the baseline with a notable improvement in AP score \\((0.57 \\to 0.75)\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.698, + 0.68, + 0.713 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Inpainting Ablation. We conduct an ablation study to evaluate the impact of leveraging the inpainting diffusion model and our defect-specific loss tailored for this model (Fig. 6). As mentioned in Sec. 2, CLiC [29] is a method that learns local concepts without using the inpainting diffusion model. However, the generated results tend to focus on reconstruction rather than creating actual holes (left image). This is because, unlike general local concepts, the defect concept we aim to learn is an unusual concept unknown to the model's prior. When applying our defect-specific loss (middle image), the model better learns the defect features, resulting in more accurately formed holes. However, the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18724" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.482, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.265, + 0.483, + 0.349 + ], + "angle": 0, + "content": "Figure 6. Inpainting Ablation. Ablation study comparing three setups: applying CLiC [29] loss to vanilla Stable Diffusion (SD2+CLiC Loss), replacing CLiC with our loss (SD2+Our Loss), and our full approach (SD2-Inpainting+Our Loss). Using the inpainting model with our loss is necessary to produce realistic defects that align well with both the mask and the object." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.376, + 0.484, + 0.483 + ], + "angle": 0, + "content": "thin regions of the mask are still neglected, and the texture around the hole doesn't blend well with the surrounding hazelnut texture. Finally, by leveraging the inpainting diffusion model's strong prior for filling, we generate realistic defects that blend naturally with their surroundings (as shown by the light brown texture around the hole in the right image), and aligning with the thin mask regions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.503, + 0.484, + 0.79 + ], + "angle": 0, + "content": "Loss Ablation. As described in Sec. 3.2, we structure our loss function with three terms to achieve three specific goals. To illustrate the contribution of each term, we perform an ablation study. Fig. 7 shows the defect generation results when each loss term is omitted during training. When the defect loss is excluded, the model tends to reconstruct rather than generate defects. This occurs because the inpainting diffusion model fails to learn the distinctive characteristics of defects and instead fills the masked area with just plausible context. Without the object loss, the model lacks semantic alignment with the object, leading to unnatural defect generation. For example, the middle section of a zipper may appear fused, or a hole may look like it's placed on a carpet rather than genuinely puncturing it. Lastly, when the attention loss is omitted, the model struggles to focus accurately on the defect mask area, resulting in lower defect fidelity (e.g. an awkwardly split zipper or an incomplete hole). Finally, by combining all loss terms, we achieve realistic defects seamlessly filled onto objects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Low Fidelity Selection. Our simple yet effective Low-Fidelity Selection method enables high-quality defect sampling without human effort. As shown in Fig. 3, it intuitively selects qualitatively good samples. Additionally, as reported in Tab. 4, it improves both the quality (KID) and the diversity (IC-LPIPS) of generated defects." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.088, + 0.906, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.337, + 0.907, + 0.406 + ], + "angle": 0, + "content": "Figure 7. Loss Ablation. This figure illustrates the impact of each loss term on generated defect quality. We show the results when each loss term is individually removed during fine-tuning, as well as the result when all terms are used together. Utilizing all loss terms results in realistic defects that align well with the context." + }, + { + "type": "table", + "bbox": [ + 0.568, + 0.421, + 0.855, + 0.49 + ], + "angle": 0, + "content": "
Ours w/o LFSOurs
KID↓IC-LPIPS↑KID↓IC-LPIPS↑
28.4850.24725.9470.250
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.5, + 0.907, + 0.556 + ], + "angle": 0, + "content": "Table 4. Generation Comparison with Low-Fidelity Selection. The application of LFS shows improvements in quality (KID) and diversity (IC-LPIPS). The values represent averages calculated for each defect category, and then averaged across objects." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.582, + 0.64, + 0.598 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.608, + 0.907, + 0.745 + ], + "angle": 0, + "content": "In this work, we present DefectFill, a novel approach that fine-tunes an inpainting diffusion model to generate realistic and high-fidelity defect images. Our method achieves state-of-the-art performance in both generation quality and visual inspection tasks on the MVtec AD dataset, demonstrating its effectiveness even when limited reference samples are available. These strengths make DefectFill particularly well-suited for widespread industrial applications, especially in scenarios where defect images are scarce." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Limitations. While our method excels at generating localized defects—a common real-world scenario—it is less effective for global structural defects that affect the entire object, such as misalignment. This limitation arises because our inpainting-based approach, which focuses on local masked regions. Addressing such global defects remains an area for future research, though our method already robustly handles the majority of practical defect cases, where localized defects are the primary concern." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18725" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.244 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) [No. 2022R1A3B1077720], Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) [NO.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)], and the BK21 FOUR program of the Education and Research Program for Future ICT Pioneers, Seoul National University in 2024." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.259, + 0.188, + 0.275 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.285, + 0.484, + 0.326 + ], + "angle": 0, + "content": "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 5" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.092, + 0.906, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18727" + } + ] +] \ No newline at end of file diff --git a/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_origin.pdf b/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..164e53273f2f045eeb1c5b3ba1910d15c8968bb1 --- /dev/null +++ b/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/41a38a7f-989e-4bd9-87f8-8ae83802b924_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8254311b23a6971428f0473683fda7d460204daf78e8e5de0d8dd79f91118a2a +size 6259343 diff --git a/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/full.md b/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4d9d57f88ef11a1c1266efb3830a2e49ba406486 --- /dev/null +++ b/2025/DefectFill_ Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection/full.md @@ -0,0 +1,273 @@ +# DefectFill: Realistic Defect Generation with Inpainting Diffusion Model for Visual Inspection + +Jaewoo Song $^{1,2}$ Daemin Park $^{1}$ Kanghyun Baek $^{3}$ Sangyub Lee $^{3}$ Jooyoung Choi $^{1}$ Eunji Kim $^{1}$ Sungroh Yoon $^{1,3,4,*}$ + +$^{1}$ Department of Electrical and Computer Engineering, Seoul National University $^{2}$ Global Technology Research, Samsung Electronics $^{3}$ IPAI, $^{4}$ AIIS, ASRI, INMC, ISRC, Seoul National University + +{woo.song, eoalsqkr12, qor6271, nickyub, jy-choi, kce407, sryoon}@snu.ac.kr + +![](images/2938ba1622ae50854e20dac74e063d4cd2a2e4f4ebe4bea7546466e895c2f92a.jpg) +Figure 1. Given a few reference image-mask pairs of a defect (e.g. "hole" of a hazelnut), DefectFill learns the defect and realistically fill it onto defect-free objects in desired shapes (e.g. star, square, etc.), generating new defect images that integrate naturally with the objects. These generated images are then used for visual inspection tasks. + +# Abstract + +Developing effective visual inspection models remains challenging due to the scarcity of defect data. While image generation models have been used to synthesize defect images, producing highly realistic defects remains difficult. We propose DefectFill, a novel method for realistic defect generation that requires only a few reference defect images. It leverages a fine-tuned inpainting diffusion model, optimized with our custom loss functions incorporating defect, object, and attention terms. It enables precise capture of detailed, localized defect features and their seamless integration into defect-free objects. Additionally, our Low-Fidelity Selection method further enhances the defect sample quality. Experiments show that DefectFill generates high-quality defect images, enabling visual inspection models to achieve state-of-the-art performance on the MVTec AD dataset. + +# 1. Introduction + +Automating inspection on manufacturing lines is a crucial step in advancing smart factories. In this context, visual inspection focused on defect detection is a critical application for AI models. With substantial amounts of defective data, high-performance models can be developed through supervised learning [6]. However, collecting large quantities of defective data is challenging in real-world settings. For example, in newly established production lines or semiconductor processes with exceptionally low defect rates, it may be difficult or even impossible to acquire enough data. + +To overcome the limited availability of defect data, various approaches have been developed, including out-of-distribution (OOD) techniques [21] and anomaly detection (AD) [26], which only use non-defective data, as well as active learning [20] and semi-supervised learning [27] with limited defective data. However, these methods have limitations: defect criteria vary across different problems and often require domain expertise, and they struggle to clas- + +sify defect types accurately. To address these issues, some methods propose generating defect images to train visual inspection models [7, 14, 22, 36]. Yet, a key problem remains: defect images generated by existing methods appear unrealistic, lacking the clarity and natural details of real-world defects, which limits their practical effectiveness. + +In this paper, we focus on generating realistic defect images to improve the accuracy of visual inspection tasks. To achieve this, we address two key considerations: (1) precisely capturing defect details and (2) seamlessly incorporating these defect features into defect-free images. + +We introduce DefectFill, a novel approach for generating realistic and detailed defect images using abundant normal images along with a few reference defect samples. We leverage a pre-trained inpainting diffusion model [24] to remove certain areas of a defect-free image and naturally fill those areas with defects. However, accurately filling defects is challenging, as these features often have entirely different textures or appearances compared to the original object. Therefore, we introduce three loss functions: defect loss to capture detailed features of the defect itself, object loss to establish the semantic relationship between the defect and the object, and attention loss to ensure the word representing the defect focuses precisely on the defect area. These carefully designed loss functions are essential for generating realistic defect images, enabling defects to be naturally and authentically "filled" within objects. To further refine samples, we implement the Low-Fidelity Selection method, which filters out generated images that fail to represent defects clearly, ensuring only high-quality samples are used. + +Through extensive experiments, we demonstrate our model's ability to generate realistic defect images that outperform state-of-the-art methods in both qualitative and quantitative evaluations. Finally, by leveraging our high-quality generated defect images, we improve performance in visual inspection downstream tasks such as anomaly classification and localization, showing that DefectFill effectively addresses the shortage of defect data. + +Our main contributions include: (1) pioneering the use of an inpainting diffusion model for generating defect images, (2) designing novel loss functions that enable the model to learn embedded defect characteristics within the context of the object, thereby generating realistic defects, (3) introducing the Low-Fidelity Selection method which is used to further enhance the quality of generated samples, and (4) demonstrating that our realistic defect images significantly improve performance in downstream tasks. + +# 2. Related Work + +# 2.1. Anomaly generation + +Various approaches have been proposed to mitigate the scarcity of defective data by generating synthetic de + +fcts [17, 18, 35, 37]. Crop-Paste [18] and CutPaste [17] synthesize data by extracting in-distribution image patches and repositioning them, while PRN [37] and DRAEM [35] incorporate out-of-distribution elements into normal images to generate additional synthetic anomalies. Since these methods solely rely on data augmentation, their ability to generate truly novel defects remains limited, thus constraining diversity. Additionally, the defects synthesized using cross-distribution images often lack realism. + +Recent research has shifted toward direct defect image generation using Generative Adversarial Networks (GANs) [9], including methods like SDGAN [22] and Defect-GAN [36]. However, these approaches require large and diverse defect datasets, which limits their applicability in data-scarce scenarios. DFMGAN [7] addresses this limitation by enabling defect image generation from a small number of reference images, by exploiting a pre-trained StyleGAN2 [15]. Nonetheless, it demands lengthy training times and struggles with generating realistic defects. In contrast to GAN-based models, studies using powerful text-to-image diffusion models [24] have shown promising results. AnomalyDiffusion [14] optimizes word vectors to disentangle the intrinsic characteristics of defects from their positional information, allowing defects to be generated at any specified location. However, these word vectors still fall short in capturing the fine structural details of defects [8], resulting in defects that lack realism. + +# 2.2. Personalization + +Leveraging the text-to-image capabilities of diffusion models, personalization research has emerged to learn new objects unknown to these models. This learning process uses a few reference images to enable a unique word token $[V^{*}]$ to represent the new target concept. Once the concept is learned, prompts containing the $[V^{*}]$ token can be used to generate new images of this concept. Most studies primarily focus on learning a main object that occupies most of the image, either by optimizing the unique word token [8] or fine-tuning the diffusion model [16, 28]. + +In contrast, CLiC [29] focuses on learning local concepts rather than the main object and employs cross-attention guidance [5] to transfer these local concepts. We draw inspiration from this approach, though it is primarily designed for realistic scenarios where the target object can naturally exhibit these concepts, unlike defect images. In addition to the previously mentioned studies, there has been an effort to use inpainting diffusion models to learn concepts [33]. This approach focuses on learning a single target image alongside reference images, solely for inpainting that target. + +Related to these studies, we aim to learn a defect concept anomalous to objects and generate diverse, realistic defect images to enhance the performance of downstream tasks. + +![](images/223f8689eb2ab3d1b9ef8a6202a5b2b29bcfd00310f04233512004e44647f010.jpg) +Figure 2. Defect learning overview. To fine-tune the inpainting diffusion model, we compute three types of loss ( $\mathcal{L}_{\text{def}}$ , $\mathcal{L}_{\text{attn}}$ , and $\mathcal{L}_{\text{obj}}$ ) using an image $I$ and a defect mask $M$ . The image $I$ is duplicated, with each copy combined with different masks ( $M$ and $M_{rand}$ ) and prompts ( $\mathcal{P}_{\text{def}}$ : "A photo of $[V^{*}]$ ", and $\mathcal{P}_{\text{obj}}$ : "A hazelnut with $[V^{*}]'$ ) as inputs to the model. The model prediction using the defect prompt $\mathcal{P}_{\text{def}}$ (upper pipeline) is used to compute $\mathcal{L}_{\text{def}}$ and, while the prediction using the object prompt $\mathcal{P}_{\text{obj}}$ (lower pipeline) is used to compute $\mathcal{L}_{\text{attn}}$ and $\mathcal{L}_{\text{obj}}$ . + +# 3. Methods + +We introduce DefectFill, a novel method for generating diverse and realistic defect images. By fine-tuning a pretrained inpainting diffusion model, DefectFill efficiently learns defect concepts using only a limited set of reference defect image-mask pairs. During inference, it fills the defect feature into specific areas of defect-free images, thereby enabling the generation of high-quality defect images that enhance performance in visual inspection tasks. + +The following sections cover the background on inpainting diffusion models (Sec.3.1), followed by a formal description of our method for learning defects (Sec.3.2) and generating defect images with the learned defects (Sec.3.3). Subsequently, we describe how the generated images can be applied to downstream tasks (Sec.3.4). + +# 3.1. Preliminaries + +Latent Diffusion Models. Latent Diffusion Models (LDMs) [24] are a class of diffusion models [12, 30, 32] specifically designed to enhance efficiency by reducing computational complexity. An LDM consists of an encoder $\mathcal{E}$ that maps image $I$ to a latent space $x_0 = \mathcal{E}(I)$ , a decoder $\mathcal{D}$ that reconstructs images as $I = \mathcal{D}(x_0)$ , and a diffusion model operating in the latent space. The encoder and decoder are pre-trained to accurately reconstruct images from their latent representations such that $\mathcal{D}(\mathcal{E}(I)) = I$ , while the diffusion model is trained to predict the noise that needs to be removed from a noisy latent representation. + +The forward process of the diffusion model gradually adds Gaussian noise $\epsilon \sim \mathcal{N}(0,1)$ to the latent image: + +$$ +x _ {t} = \sqrt {\alpha_ {t}} x _ {0} + \left(\sqrt {1 - \alpha_ {t}}\right) \epsilon , \tag {1} +$$ + +where $\{\alpha_{t}\}_{t = 1}^{T}$ is a noise scheduler that determines the proportion of noise added at each timestep $t$ . The reverse process reconstructs the latent image from the noisy input $x_{t}$ . The diffusion model can incorporate a text prompt $\mathcal{P}$ as conditioning, which is encoded by a text encoder $\tau_{\theta}$ , and is trained using the following objective: + +$$ +\mathcal {L} = \mathbb {E} _ {x _ {t}, t, \epsilon} \| \epsilon_ {\theta} (x _ {t}, t, \tau_ {\theta} (\mathcal {P})) - \epsilon \| _ {2} ^ {2}. \tag {2} +$$ + +Inpainting Diffusion Models. Inpainting Diffusion Models are fine-tuned versions of LDM, specifically designed to fill content within masked areas. These models learn the inpainting task using both a mask $M$ and a background image $B$ where the masked areas are removed. Specifically, the image $I$ and the background $B$ are mapped into the latent space through the encoder, resulting in $x_0 = \mathcal{E}(I)$ and $b = \mathcal{E}(B)$ . Gaussian noise is then added to $x_0$ at a specific timestep $t$ , producing $x_t$ . Subsequently, $x_t^{inpaint}$ is constructed by concatenating $x_t$ , $b$ , and $M$ as follows: + +$$ +x _ {t} ^ {\text {i n p a i n t}} = \operatorname {c o n c a t} \left(x _ {t}, b, M\right), \tag {3} +$$ + +and is used for training diffusion models via Eq. (2). This process allows the LDM to learn how to accurately fill the masked areas with appropriate content. + +![](images/31474b7a442d52806bb0d44d8e18987983241d779b1592de294e3783284eaefd.jpg) +Figure 3. Low-Fidelity Selection (LFS) for defect of leather's glue. LFS automatically selects the defect image with the most pronounced expression (blue box) by identifying the sample with the lowest fidelity (highest LPIPS score) in the masked area. + +# 3.2. Learning Defect + +We use a stable diffusion inpainting model [24] to leverage its prior knowledge for seamlessly "filling" masked areas with desired defects. To train the model to understand the concept of defects, we fine-tune it using a small set of reference defect images $I$ paired with defect masks $M$ . This fine-tuning enables the model to associate the word token $[V^{*}]$ with defects. Specifically, to efficiently learn various defects while avoiding overfitting [10], we fine-tune only the text encoder $\tau_{\theta}$ and the attention layers by using LoRA [13]. + +More precisely, we aim to achieve three goals to effectively learn local defects: (1) recognizing defects that are not the main object of the image but rather local features dependent on it, (2) understanding the semantic relationship between the defect and the main object to ensure natural blending, and (3) ensuring the word token $[V^{*}]$ corresponds to the defect region of the object. To achieve these goals, we propose three loss terms: defect, object, and attention loss, as illustrated in the overall training scheme shown in Fig. 2 + +Defect Loss. The key loss term, defect loss $\mathcal{L}_{def}$ , directly learns the detailed features of the defect concept. By guiding the model to focus exclusively on the intrinsic features of the defect, it enables inpainting of even unusual features that would not typically appear in the object. + +First, we sample a timestep $t \sim p(t)$ from the model's timestep distribution and obtain the noise latent $x_{t}$ using Eq. (1). Next, we prepare the defect mask $M$ for $I$ and generate a background image $B_{def} = (1 - M) \odot I$ where the defect area is masked out. The latent $b_{def} = \mathcal{E}(B_{def})$ is then concatenated with $x_{t}$ and $M$ to form $x_{t}^{def}$ : + +$$ +x _ {t} ^ {\text {d e f}} = \operatorname {c o n c a t} \left(x _ {t}, b _ {\text {d e f}}, M\right), \tag {4} +$$ + +which serves as input to the model. + +To ensure the prompt focuses exclusively on the defect, we define it as $\mathcal{P}_{def} = "A\text{photo of}[V^*]".$ The text encoder $\tau_{\theta}$ encodes this prompt to generate the text condition embedding $c^{def} = \tau_{\theta}(\mathcal{P}_{def})$ . Using these inputs, we optimize the $\mathcal{L}_2$ loss with respect to noise $\epsilon$ to reconstruct $x_0$ but we compute the loss only over the masked region $M$ to + +avoid reconstructing the background: + +$$ +\mathcal {L} _ {d e f} = \mathbb {E} _ {x _ {t} ^ {d e f}, t, \epsilon} \left[ \left\| M \odot \left(\epsilon - \epsilon_ {\theta} \left(x _ {t} ^ {d e f}, t, c ^ {d e f}\right)\right) \right\| _ {2} ^ {2} \right]. \tag {5} +$$ + +Object Loss. The object loss $\mathcal{L}_{obj}$ learns both the defect and its relationship to the object in which it appears. This ensures the defect blends naturally within the object. + +The $\mathcal{L}_{obj}$ term shares the same sampled values for $\epsilon$ , $t$ , and $x_{t}$ as the defect loss. To capture the full semantic context of the object, we create a mask with 30 random boxes, $M_{rand}$ , and train the model to fill in the occluded information across the entire image. Similar to the defect loss, we obtain the conditioning background $B_{rand} = (1 - M_{rand}) \odot I$ and its latent $b_{rand} = \mathcal{E}(B_{rand})$ . This $b_{rand}$ is then concatenated with $x_{t}$ and $M_{rand}$ to form $x_{t}^{obj}$ : + +$$ +x _ {t} ^ {o b j} = \operatorname {c o n c a t} \left(x _ {t}, b _ {\text {r a n d}}, M _ {\text {r a n d}}\right). \tag {6} +$$ + +To express the object's possession of the defect, we set the prompt as $\mathcal{P}_{obj} = "A[Object] with [V^*]"$ and obtain the text embedding $c^{obj} = \tau_{\theta}(\mathcal{P}_{obj})$ . Although it is essential to learn the semantic context of the defect within the object, capturing the fine details of the defect itself is also crucial for authentic inpainting. To address this, we apply a weight of 1 to the defect mask areas and a weight of $\alpha$ , less than 1, to the background areas, producing an adjusted mask $M'$ : + +$$ +\mathcal {L} _ {o b j} = \mathbb {E} _ {x _ {t} ^ {o b j}, t, \epsilon} \left[ \left\| M ^ {\prime} \odot \left(\epsilon - \epsilon_ {\theta} \left(x _ {t} ^ {o b j}, t, c ^ {o b j}\right)\right) \right\| _ {2} ^ {2} \right], \tag {7} +$$ + +$$ +M ^ {\prime} = M + \alpha \cdot (1 - M). +$$ + +Attention Loss. We also utilize cross-attention maps from the forward pass for $\mathcal{L}_{obj}$ . The maps for a specific token represent the layout of the corresponding object, allowing the model to focus more precisely on that region. This helps the model better attend to the defect's features, resulting in higher-fidelity defect generation. Since the encoder in the UNet [25] does not effectively represent the layout of the corresponding token object [4], we use only decoder-layer maps. To handle varying spatial sizes across decoder layers, we resize them to match the latent size, then average those of the $[V^{*}]$ token to obtain $A_{t}^{[V^{*}]}$ . Finally, we compute the $\mathcal{L}_2$ loss with the defect mask $M$ , increasing values in the defect region while reducing them in the background: + +$$ +\mathcal {L} _ {a t t n} = \mathbb {E} \left[ \left\| A _ {t} ^ {[ V ^ {*} ]} - M \right\| _ {2} ^ {2} \right]. \tag {8} +$$ + +DefectFill Loss. Finally, we fine-tune the model using a linear combination of these three loss terms: + +$$ +\mathcal {L} _ {\text {o u r s}} = \lambda_ {\text {d e f}} \cdot \mathcal {L} _ {\text {d e f}} + \lambda_ {\text {o b j}} \cdot \mathcal {L} _ {\text {o b j}} + \lambda_ {\text {a t t n}} \cdot \mathcal {L} _ {\text {a t t n}}. \tag {9} +$$ + +The weights for each term are set to 0.5, 0.2, and 0.05, based on experiments that account for the scale of each loss. + +![](images/0e8df6b26facecb642a46b877b7d162f85daaf7d8480d2dd1e2b7e0181ada2b9.jpg) +Figure 4. Generated Defects by DefectFill. The first row displays the normal images (green boxes), while the second row shows the generated defect images along with their masks, and the third row provides zoomed-in views of the defects (red boxes). The zoomed images highlight the realistic and detailed rendering of the defects. + +# 3.3. Generating Defect + +Sampling. After fine-tuning the inpainting diffusion model with our DefectFill loss to learn the defect concept, we utilize a widely adopted diffusion-based inpainting pipeline [1, 32] to generate diverse defect samples. Specifically, as input, we provide a defect-free image $I$ along with a mask $M$ indicating the exact area intended for defect placement. At each inference step $t$ , we replace the latent representation's background area outside the mask with the latent of the defect-free image diffused with Eq. (1). This approach ensures that the model modifies only the masked region while preserving the background that should remain unchanged. This approach maintains the structure of the original image, allowing for seamless integration of defects without affecting the overall image quality. + +Low-Fidelity Selection. Finally, we propose an additional method for selecting samples where the defect is more accurately filled. Since the diffusion model generates diverse samples depending on the initial latent inputs, and due to the nature of the inpainting diffusion model, the masked area is occasionally overly reconstructed, resulting in lower-quality defect. To mitigate this issue, we select the least reconstructed image from the eight samples generated using the same normal image $I$ and defect mask $M$ . This selection is based on a reconstruction metric (e.g. PSNR, SSIM [34], LPIPS [38]) measured only within the masked region (as shown in Fig. 3). This simple yet effective process filters out unclear cases and improves defect generation quality. In particular, for downstream tasks using generated defect images, this approach allows us to automatically select high-quality defects samples without manual effort. In our case, we employ LPIPS as the reconstruction metric. + +# 3.4. Applying to Visual Inspection + +The generated high-quality defect images are used to train a visual inspection model. First, we learn the concept for each defect category (Sec.3.2) and generate defective images (Sec.3.3) for each category. After that, for classification, we train standard classification models (e.g. ResNet [11]) using the generated images labeled by defect category. For localization, we train segmentation models (e.g. UNet [25]) with normal and synthesized defect images along with their corresponding masks, optimizing with focal loss [19]. + +# 4. Experiments + +Dataset. We evaluate DefectFill on the MVTec AD Dataset [2], which consists of 15 industrial objects with multiple defect categories. Each category contains hundreds of normal images and approximately 20 defect images with masks. Instead of traditional anomaly detection, we generate defect images by training on one-third of the defect image-mask pairs and applying the model to the remaining two-thirds of masks with normal images. For reliable quantitative results, we evaluate on 10 objects, while all objects are used for qualitative analysis. + +Implementation Details. Our approach leverages the Stable-Diffusion-2-inpainting model [24], fine-tuning the text encoder and UNet's attention layers with LoRA (rank 8) [13]. We use a learning rate of 2e-4 for the UNet and 4e-5 for the text encoder. Inference is conducted with a DDIM [31] scheduler with 50 denoising steps. Additional details are provided in the supplementary materials. + +Metric. We evaluate defect generation quality using Kernel Inception Distance (KID) [3] for quality and IC-LPIPS [23] for diversity, excluding FID and IS due to their limitations on smaller or unreferenced datasets. For defect inspection, we measure classification accuracy, Area Under the ROC Curve (AUROC), Average Precision (AP), $F_{1}$ -max, and Per Region Overlap (PRO). + +Baselines. We compare our method against two state-of-the-art defect generation methods: DFMGAN [7], a two-stage GAN-based approach, and AnomalyDiffusion [14], a text-to-image diffusion model that disentangles the appearance and spatial attributes of defects. + +# 4.1. Defect Generation Evaluation + +Qualitative Results. The generated results are shown in Fig. 4. The first row displays the normal images, the second row shows the generated defect images using the mask in the lower right, and the third row provides a zoomed-in view of the generated defects. Despite using custom-drawn + +![](images/b6ce88eb4e341be5ee06aa3de62c64df136a20722701e6aa7f8e0aaa542060bb.jpg) +Figure 5. Defect Generation Comparisons. This figure compares the quality of defect images generated by our method (bottom row) with baseline approaches. Our method produces the most realistic results, with defects that blend seamlessly into the objects. + +
ObjectsDFMGAN*DFMGAN†AnoDiff‡Ours
KID↓IC-LPIPS↑KID↓IC-LPIPS↑KID↓IC-LPIPS↑KID↓IC-LPIPS↑
bottle70.900.1276.750.15131.520.1730.990.12
capsule40.630.10182.830.1754.970.185.600.18
carpet25.140.1346.020.25149.830.2250.370.22
hazelnut21.160.2430.940.3350.610.311.130.31
leather75.850.17501.610.51244.750.4074.660.30
pill123.520.1670.150.2377.690.238.760.23
tile85.280.22254.820.25314.300.4845.140.44
toothbrush46.490.1861.430.2073.310.183.190.15
wood68.130.34406.610.3583.940.354.720.35
zipper78.080.2735.740.26126.650.2434.910.20
+ +Table 1. Generation Comparison. This table presents the average KID and IC-LPIPS scores, computed from 1,000 generated images per defect category and averaged across all categories for each object. Our method achieves the best KID scores for all objects except carpet and the highest IC-LPIPS scores for capsule, pill, and wood. DFMGAN*: scores taken directly from the paper. DFMGAN†: scores reproduced by us. AnoDiff‡: scores measured from the generated dataset (poor samples filtered) on their official page. + +masks which are unseen during training, the model generates authentic and well-aligned defects. Notably, for the hazelnut, the model produces a realistic defect that aligns with the object's semantics, even with an unrealistic mask shape for the crack, demonstrating its strong generalization ability. Additionally, the detailed texture within the hazelnut is observable and highlights the realism of the defects. + +Fig. 5 presents a qualitative comparison with the baselines. For AnomalyDiffusion, we use the same normal image and mask, while DFMGAN cannot use the same base image as it generates both normal and defect images directly. In the hazelnut case, both baselines struggle with the texture around the hole, whereas our method produces re + +alistic defects that blend seamlessly with the object texture, handling irregular mask shapes and demonstrating Defect-Fill's robustness. In cases such as carpet and tile, where defects are small or thin, the baselines either fail to capture them accurately or omit them entirely, while our model generates well-defined defects. For the toothbrush, DFMGAN blurs the masked area, and AnomalyDiffusion generates defects with colors misaligned with the object context. In contrast, our model produces a realistic blueish defect that reflects the object's context (similar to how the toothbrush in Fig. 4 appears yellowish). This demonstrates our model's ability to integrate object semantics into defect generation. + +
ObjectsDFMGAN†AnoDiff*AnoDiff‡Ours
AUROCAPF1-maxPROAUROCAPF1-maxPROAUROCAPF1-maxPROAUROCAPF1-maxPRO
bottle0.960.800.740.840.990.940.870.940.990.910.830.941.000.960.900.97
capsule0.740.040.090.340.990.570.600.950.980.410.440.841.000.750.690.96
carpet0.950.620.600.840.990.810.750.920.970.740.680.820.990.920.860.96
hazelnut1.000.940.870.961.000.970.910.971.000.960.900.971.000.990.940.99
leather0.960.560.560.841.000.800.710.981.000.800.720.981.000.910.830.98
pill0.990.890.860.911.000.970.910.971.000.970.910.951.000.980.930.98
tile0.990.940.870.960.990.940.860.960.990.950.870.971.000.970.900.98
toothbrush0.980.600.610.890.990.770.730.910.990.710.680.910.990.890.820.94
wood0.720.370.410.730.990.850.750.940.970.790.720.891.000.930.860.98
zipper0.990.820.760.950.990.860.790.961.000.870.800.971.000.900.840.97
+ +Table 2. Localization Comparison. The table presents AUROC, AP, $F_{1}$ -max, and PRO scores for localization evaluation using a UNet trained on generated defect images. Our method achieves the highest performance across all metrics and objects. AnoDiff*: scores reported in the paper. The others: described in Tab. 1. + +
ObjectsDFMGAN*DFMGAN†AnoDiff*AnoDiff‡Ours
bottle56.5963.4190.7095.3597.56
capsule37.2725.0066.6745.3387.50
carpet47.3142.1158.0664.5287.72
hazelnut81.9486.9685.4289.58100.00
leather49.7332.2061.9065.0893.22
pill29.5244.4459.3864.5897.53
tile74.8581.8284.2196.49100.00
wood49.0245.1671.4378.57100.00
zipper27.6445.4569.5185.3790.91
+ +Table 3. Classification Comparison. The table shows classification accuracy (\%) when a ResNet-34 is trained on generated defect images for defect category prediction. Our method achieves the highest performance across all objects. AnoDiff*: scores reported in the paper. The others: described in Tab. 1. + +Quantitative Results. Tab. 1 compares the KID and IC-LPIPS scores of our method with baseline approaches across various objects. For evaluation, we generate 1,000 images for each defect category within each object, ensuring that all metrics, including KID, are calculated using only defect images excluded from the training set. This approach is necessary as KID often produces overly optimistic values when models overfit and are evaluated on training data. + +Our method outperforms the baselines in KID scores across most objects. For IC-LPIPS, it also achieves the best scores on three objects (capsule, pill, wood). In the case of leather, DFMGAN† and AnoDiff‡ score significantly higher, but this is primarily due to their generation of diverse yet low-quality samples across various masks. The high KID values for these methods further confirm that the quality of their generated defect images is low. + +# 4.2. Visual Inspection Evaluation + +To demonstrate that the realistic images generated by DefectFill can enhance performance in downstream visual in + +spection tasks, we apply it to two tasks: classification and localization. Following the experimental setup of AnomalyDiffusion [14], we use ResNet-34 [11] for classification and UNet [25] for localization. As outlined in the quantitative results (Sec. 4.1), we generate 1,000 defects per category and train the models on this data. Testing is conducted on the remaining two-thirds of the dataset. + +Classification. As shown in Tab.3, our method achieves higher classification accuracy across all objects compared to the baselines. Notably, there is a significant improvement for objects with small defect areas, which are typically challenging to generate meaningful defects for, such as capsule $(66.67\% \rightarrow 87.50\%)$ and pill $(64.58\% \rightarrow 97.53\%)$ . + +Localization. The UNet is trained to predict defect locations, and the predictions are evaluated using various metrics. As shown in Tab. 2, our model achieves the best performance across all metrics and objects. The capsule is a particularly challenging object for localization, yet our model significantly outperforms the baseline with a notable improvement in AP score $(0.57 \to 0.75)$ . + +# 4.3. Ablation Studies + +Inpainting Ablation. We conduct an ablation study to evaluate the impact of leveraging the inpainting diffusion model and our defect-specific loss tailored for this model (Fig. 6). As mentioned in Sec. 2, CLiC [29] is a method that learns local concepts without using the inpainting diffusion model. However, the generated results tend to focus on reconstruction rather than creating actual holes (left image). This is because, unlike general local concepts, the defect concept we aim to learn is an unusual concept unknown to the model's prior. When applying our defect-specific loss (middle image), the model better learns the defect features, resulting in more accurately formed holes. However, the + +![](images/36eeea633020dea5d3c353acad5a2b6125a39fc290704c5c282104afad1a1675.jpg) +Figure 6. Inpainting Ablation. Ablation study comparing three setups: applying CLiC [29] loss to vanilla Stable Diffusion (SD2+CLiC Loss), replacing CLiC with our loss (SD2+Our Loss), and our full approach (SD2-Inpainting+Our Loss). Using the inpainting model with our loss is necessary to produce realistic defects that align well with both the mask and the object. + +thin regions of the mask are still neglected, and the texture around the hole doesn't blend well with the surrounding hazelnut texture. Finally, by leveraging the inpainting diffusion model's strong prior for filling, we generate realistic defects that blend naturally with their surroundings (as shown by the light brown texture around the hole in the right image), and aligning with the thin mask regions. + +Loss Ablation. As described in Sec. 3.2, we structure our loss function with three terms to achieve three specific goals. To illustrate the contribution of each term, we perform an ablation study. Fig. 7 shows the defect generation results when each loss term is omitted during training. When the defect loss is excluded, the model tends to reconstruct rather than generate defects. This occurs because the inpainting diffusion model fails to learn the distinctive characteristics of defects and instead fills the masked area with just plausible context. Without the object loss, the model lacks semantic alignment with the object, leading to unnatural defect generation. For example, the middle section of a zipper may appear fused, or a hole may look like it's placed on a carpet rather than genuinely puncturing it. Lastly, when the attention loss is omitted, the model struggles to focus accurately on the defect mask area, resulting in lower defect fidelity (e.g. an awkwardly split zipper or an incomplete hole). Finally, by combining all loss terms, we achieve realistic defects seamlessly filled onto objects. + +Low Fidelity Selection. Our simple yet effective Low-Fidelity Selection method enables high-quality defect sampling without human effort. As shown in Fig. 3, it intuitively selects qualitatively good samples. Additionally, as reported in Tab. 4, it improves both the quality (KID) and the diversity (IC-LPIPS) of generated defects. + +![](images/8b6aeeb76bcb84c446109b74d10bc2506b1286daf0578b221a2476b3436e6717.jpg) +Figure 7. Loss Ablation. This figure illustrates the impact of each loss term on generated defect quality. We show the results when each loss term is individually removed during fine-tuning, as well as the result when all terms are used together. Utilizing all loss terms results in realistic defects that align well with the context. + +
Ours w/o LFSOurs
KID↓IC-LPIPS↑KID↓IC-LPIPS↑
28.4850.24725.9470.250
+ +Table 4. Generation Comparison with Low-Fidelity Selection. The application of LFS shows improvements in quality (KID) and diversity (IC-LPIPS). The values represent averages calculated for each defect category, and then averaged across objects. + +# 5. Conclusions + +In this work, we present DefectFill, a novel approach that fine-tunes an inpainting diffusion model to generate realistic and high-fidelity defect images. Our method achieves state-of-the-art performance in both generation quality and visual inspection tasks on the MVtec AD dataset, demonstrating its effectiveness even when limited reference samples are available. These strengths make DefectFill particularly well-suited for widespread industrial applications, especially in scenarios where defect images are scarce. + +Limitations. While our method excels at generating localized defects—a common real-world scenario—it is less effective for global structural defects that affect the entire object, such as misalignment. 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Given a few reference image-mask pairs of a defect (e.g. \"hole\" of a hazelnut), DefectFill learns the defect and realistically fill it onto defect-free objects in desired shapes (e.g. star, square, etc.), generating new defect images that integrate naturally with the objects. These generated images are then used for visual inspection tasks." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 152, + 471, + 200, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 471, + 200, + 483 + ], + "spans": [ + { + "bbox": [ + 152, + 471, + 200, + 483 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 498, + 297, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 498, + 297, + 679 + ], + "spans": [ + { + "bbox": [ + 54, + 498, + 297, + 679 + ], + "type": "text", + "content": "Developing effective visual inspection models remains challenging due to the scarcity of defect data. While image generation models have been used to synthesize defect images, producing highly realistic defects remains difficult. We propose DefectFill, a novel method for realistic defect generation that requires only a few reference defect images. It leverages a fine-tuned inpainting diffusion model, optimized with our custom loss functions incorporating defect, object, and attention terms. It enables precise capture of detailed, localized defect features and their seamless integration into defect-free objects. Additionally, our Low-Fidelity Selection method further enhances the defect sample quality. Experiments show that DefectFill generates high-quality defect images, enabling visual inspection models to achieve state-of-the-art performance on the MVTec AD dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 471, + 394, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 471, + 394, + 483 + ], + "spans": [ + { + "bbox": [ + 315, + 471, + 394, + 483 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 495, + 555, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 555, + 614 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 555, + 614 + ], + "type": "text", + "content": "Automating inspection on manufacturing lines is a crucial step in advancing smart factories. In this context, visual inspection focused on defect detection is a critical application for AI models. With substantial amounts of defective data, high-performance models can be developed through supervised learning [6]. However, collecting large quantities of defective data is challenging in real-world settings. For example, in newly established production lines or semiconductor processes with exceptionally low defect rates, it may be difficult or even impossible to acquire enough data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": "To overcome the limited availability of defect data, various approaches have been developed, including out-of-distribution (OOD) techniques [21] and anomaly detection (AD) [26], which only use non-defective data, as well as active learning [20] and semi-supervised learning [27] with limited defective data. However, these methods have limitations: defect criteria vary across different problems and often require domain expertise, and they struggle to clas-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 249, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 249, + 714 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 249, + 714 + ], + "type": "text", + "content": "*Correspondence to: Sungroh Yoon (sryoon@snu.ac.kr)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18718" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "sify defect types accurately. To address these issues, some methods propose generating defect images to train visual inspection models [7, 14, 22, 36]. Yet, a key problem remains: defect images generated by existing methods appear unrealistic, lacking the clarity and natural details of real-world defects, which limits their practical effectiveness." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 294, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 294, + 205 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 294, + 205 + ], + "type": "text", + "content": "In this paper, we focus on generating realistic defect images to improve the accuracy of visual inspection tasks. To achieve this, we address two key considerations: (1) precisely capturing defect details and (2) seamlessly incorporating these defect features into defect-free images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 206, + 295, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 206, + 295, + 433 + ], + "spans": [ + { + "bbox": [ + 56, + 206, + 295, + 433 + ], + "type": "text", + "content": "We introduce DefectFill, a novel approach for generating realistic and detailed defect images using abundant normal images along with a few reference defect samples. We leverage a pre-trained inpainting diffusion model [24] to remove certain areas of a defect-free image and naturally fill those areas with defects. However, accurately filling defects is challenging, as these features often have entirely different textures or appearances compared to the original object. Therefore, we introduce three loss functions: defect loss to capture detailed features of the defect itself, object loss to establish the semantic relationship between the defect and the object, and attention loss to ensure the word representing the defect focuses precisely on the defect area. These carefully designed loss functions are essential for generating realistic defect images, enabling defects to be naturally and authentically \"filled\" within objects. To further refine samples, we implement the Low-Fidelity Selection method, which filters out generated images that fail to represent defects clearly, ensuring only high-quality samples are used." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 434, + 294, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 294, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 294, + 529 + ], + "type": "text", + "content": "Through extensive experiments, we demonstrate our model's ability to generate realistic defect images that outperform state-of-the-art methods in both qualitative and quantitative evaluations. Finally, by leveraging our high-quality generated defect images, we improve performance in visual inspection downstream tasks such as anomaly classification and localization, showing that DefectFill effectively addresses the shortage of defect data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 530, + 295, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 295, + 637 + ], + "spans": [ + { + "bbox": [ + 55, + 530, + 295, + 637 + ], + "type": "text", + "content": "Our main contributions include: (1) pioneering the use of an inpainting diffusion model for generating defect images, (2) designing novel loss functions that enable the model to learn embedded defect characteristics within the context of the object, thereby generating realistic defects, (3) introducing the Low-Fidelity Selection method which is used to further enhance the quality of generated samples, and (4) demonstrating that our realistic defect images significantly improve performance in downstream tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 651, + 142, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 651, + 142, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 651, + 142, + 662 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 671, + 173, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 671, + 173, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 671, + 173, + 684 + ], + "type": "text", + "content": "2.1. Anomaly generation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "type": "text", + "content": "Various approaches have been proposed to mitigate the scarcity of defective data by generating synthetic de" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "type": "text", + "content": "fcts [17, 18, 35, 37]. Crop-Paste [18] and CutPaste [17] synthesize data by extracting in-distribution image patches and repositioning them, while PRN [37] and DRAEM [35] incorporate out-of-distribution elements into normal images to generate additional synthetic anomalies. Since these methods solely rely on data augmentation, their ability to generate truly novel defects remains limited, thus constraining diversity. Additionally, the defects synthesized using cross-distribution images often lack realism." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 182, + 553, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 182, + 553, + 397 + ], + "spans": [ + { + "bbox": [ + 313, + 182, + 553, + 397 + ], + "type": "text", + "content": "Recent research has shifted toward direct defect image generation using Generative Adversarial Networks (GANs) [9], including methods like SDGAN [22] and Defect-GAN [36]. However, these approaches require large and diverse defect datasets, which limits their applicability in data-scarce scenarios. DFMGAN [7] addresses this limitation by enabling defect image generation from a small number of reference images, by exploiting a pre-trained StyleGAN2 [15]. Nonetheless, it demands lengthy training times and struggles with generating realistic defects. In contrast to GAN-based models, studies using powerful text-to-image diffusion models [24] have shown promising results. AnomalyDiffusion [14] optimizes word vectors to disentangle the intrinsic characteristics of defects from their positional information, allowing defects to be generated at any specified location. However, these word vectors still fall short in capturing the fine structural details of defects [8], resulting in defects that lack realism." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 413, + 408, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 413, + 408, + 425 + ], + "spans": [ + { + "bbox": [ + 314, + 413, + 408, + 425 + ], + "type": "text", + "content": "2.2. Personalization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 433, + 553, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 433, + 553, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 433, + 553, + 553 + ], + "type": "text", + "content": "Leveraging the text-to-image capabilities of diffusion models, personalization research has emerged to learn new objects unknown to these models. This learning process uses a few reference images to enable a unique word token " + }, + { + "bbox": [ + 313, + 433, + 553, + 553 + ], + "type": "inline_equation", + "content": "[V^{*}]" + }, + { + "bbox": [ + 313, + 433, + 553, + 553 + ], + "type": "text", + "content": " to represent the new target concept. Once the concept is learned, prompts containing the " + }, + { + "bbox": [ + 313, + 433, + 553, + 553 + ], + "type": "inline_equation", + "content": "[V^{*}]" + }, + { + "bbox": [ + 313, + 433, + 553, + 553 + ], + "type": "text", + "content": " token can be used to generate new images of this concept. Most studies primarily focus on learning a main object that occupies most of the image, either by optimizing the unique word token [8] or fine-tuning the diffusion model [16, 28]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 555, + 553, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 553, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 553, + 675 + ], + "type": "text", + "content": "In contrast, CLiC [29] focuses on learning local concepts rather than the main object and employs cross-attention guidance [5] to transfer these local concepts. We draw inspiration from this approach, though it is primarily designed for realistic scenarios where the target object can naturally exhibit these concepts, unlike defect images. In addition to the previously mentioned studies, there has been an effort to use inpainting diffusion models to learn concepts [33]. This approach focuses on learning a single target image alongside reference images, solely for inpainting that target." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "Related to these studies, we aim to learn a defect concept anomalous to objects and generate diverse, realistic defect images to enhance the performance of downstream tasks." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18719" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 72, + 558, + 270 + ], + "blocks": [ + { + "bbox": [ + 56, + 72, + 558, + 270 + ], + "lines": [ + { + "bbox": [ + 56, + 72, + 558, + 270 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 558, + 270 + ], + "type": "image", + "image_path": "223f8689eb2ab3d1b9ef8a6202a5b2b29bcfd00310f04233512004e44647f010.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "lines": [ + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": "Figure 2. Defect learning overview. To fine-tune the inpainting diffusion model, we compute three types of loss (" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{def}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{attn}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{obj}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": ") using an image " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": " and a defect mask " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": ". The image " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": " is duplicated, with each copy combined with different masks (" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "M_{rand}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": ") and prompts (" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\text{def}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": ": \"A photo of " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "[V^{*}]" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": "\", and " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\text{obj}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": ": \"A hazelnut with " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "[V^{*}]'" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": ") as inputs to the model. The model prediction using the defect prompt " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\text{def}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": " (upper pipeline) is used to compute " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{def}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": " and, while the prediction using the object prompt " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\text{obj}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": " (lower pipeline) is used to compute " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{attn}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{obj}}" + }, + { + "bbox": [ + 54, + 279, + 555, + 338 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 363, + 117, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 363, + 117, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 363, + 117, + 376 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 384, + 295, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 295, + 480 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 295, + 480 + ], + "type": "text", + "content": "We introduce DefectFill, a novel method for generating diverse and realistic defect images. By fine-tuning a pretrained inpainting diffusion model, DefectFill efficiently learns defect concepts using only a limited set of reference defect image-mask pairs. During inference, it fills the defect feature into specific areas of defect-free images, thereby enabling the generation of high-quality defect images that enhance performance in visual inspection tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 481, + 296, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 481, + 296, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 481, + 296, + 553 + ], + "type": "text", + "content": "The following sections cover the background on inpainting diffusion models (Sec.3.1), followed by a formal description of our method for learning defects (Sec.3.2) and generating defect images with the learned defects (Sec.3.3). Subsequently, we describe how the generated images can be applied to downstream tasks (Sec.3.4)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 563, + 142, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 142, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 142, + 574 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": "Latent Diffusion Models. Latent Diffusion Models (LDMs) [24] are a class of diffusion models [12, 30, 32] specifically designed to enhance efficiency by reducing computational complexity. An LDM consists of an encoder " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " that maps image " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " to a latent space " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "x_0 = \\mathcal{E}(I)" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": ", a decoder " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " that reconstructs images as " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "I = \\mathcal{D}(x_0)" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": ", and a diffusion model operating in the latent space. The encoder and decoder are pre-trained to accurately reconstruct images from their latent representations such that " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathcal{E}(I)) = I" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": ", while the diffusion model is trained to predict the noise that needs to be removed from a noisy latent representation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "type": "text", + "content": "The forward process of the diffusion model gradually adds Gaussian noise " + }, + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,1)" + }, + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "type": "text", + "content": " to the latent image:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 374, + 396, + 555, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 396, + 555, + 412 + ], + "spans": [ + { + "bbox": [ + 374, + 396, + 555, + 412 + ], + "type": "interline_equation", + "content": "x _ {t} = \\sqrt {\\alpha_ {t}} x _ {0} + \\left(\\sqrt {1 - \\alpha_ {t}}\\right) \\epsilon , \\tag {1}", + "image_path": "fe229a2f712cacfb53cc5e294a292453c3339425766b63757ff2f3ea19196e33.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "inline_equation", + "content": "\\{\\alpha_{t}\\}_{t = 1}^{T}" + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "text", + "content": " is a noise scheduler that determines the proportion of noise added at each timestep " + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "text", + "content": ". The reverse process reconstructs the latent image from the noisy input " + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "text", + "content": ". The diffusion model can incorporate a text prompt " + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "text", + "content": " as conditioning, which is encoded by a text encoder " + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 313, + 418, + 555, + 492 + ], + "type": "text", + "content": ", and is trained using the following objective:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 359, + 498, + 555, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 498, + 555, + 514 + ], + "spans": [ + { + "bbox": [ + 359, + 498, + 555, + 514 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathbb {E} _ {x _ {t}, t, \\epsilon} \\| \\epsilon_ {\\theta} (x _ {t}, t, \\tau_ {\\theta} (\\mathcal {P})) - \\epsilon \\| _ {2} ^ {2}. \\tag {2}", + "image_path": "780d8d71f06479e80d6ba6a046f6ddc4c13743e2ae0db54ba33a1adba88f049d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": "Inpainting Diffusion Models. Inpainting Diffusion Models are fine-tuned versions of LDM, specifically designed to fill content within masked areas. These models learn the inpainting task using both a mask " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": " and a background image " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": " where the masked areas are removed. Specifically, the image " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": " and the background " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": " are mapped into the latent space through the encoder, resulting in " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "x_0 = \\mathcal{E}(I)" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "b = \\mathcal{E}(B)" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": ". Gaussian noise is then added to " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": " at a specific timestep " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": ", producing " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": ". Subsequently, " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "x_t^{inpaint}" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": " is constructed by concatenating " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 527, + 556, + 647 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 371, + 654, + 553, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 654, + 553, + 669 + ], + "spans": [ + { + "bbox": [ + 371, + 654, + 553, + 669 + ], + "type": "interline_equation", + "content": "x _ {t} ^ {\\text {i n p a i n t}} = \\operatorname {c o n c a t} \\left(x _ {t}, b, M\\right), \\tag {3}", + "image_path": "ad0b298a2d9f13729abac043f21ff207087a086f8e0af49d178ddcea22618efa.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": "and is used for training diffusion models via Eq. (2). This process allows the LDM to learn how to accurately fill the masked areas with appropriate content." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18720" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 295, + 131 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 295, + 131 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 295, + 131 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 295, + 131 + ], + "type": "image", + "image_path": "31474b7a442d52806bb0d44d8e18987983241d779b1592de294e3783284eaefd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 140, + 295, + 185 + ], + "lines": [ + { + "bbox": [ + 55, + 140, + 295, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 140, + 295, + 185 + ], + "type": "text", + "content": "Figure 3. Low-Fidelity Selection (LFS) for defect of leather's glue. LFS automatically selects the defect image with the most pronounced expression (blue box) by identifying the sample with the lowest fidelity (highest LPIPS score) in the masked area." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 206, + 153, + 219 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 206, + 153, + 219 + ], + "spans": [ + { + "bbox": [ + 55, + 206, + 153, + 219 + ], + "type": "text", + "content": "3.2. Learning Defect" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "spans": [ + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "text", + "content": "We use a stable diffusion inpainting model [24] to leverage its prior knowledge for seamlessly \"filling\" masked areas with desired defects. To train the model to understand the concept of defects, we fine-tune it using a small set of reference defect images " + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "text", + "content": " paired with defect masks " + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "text", + "content": ". This fine-tuning enables the model to associate the word token " + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "inline_equation", + "content": "[V^{*}]" + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "text", + "content": " with defects. Specifically, to efficiently learn various defects while avoiding overfitting [10], we fine-tune only the text encoder " + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 55, + 224, + 296, + 332 + ], + "type": "text", + "content": " and the attention layers by using LoRA [13]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 333, + 296, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 333, + 296, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 333, + 296, + 441 + ], + "type": "text", + "content": "More precisely, we aim to achieve three goals to effectively learn local defects: (1) recognizing defects that are not the main object of the image but rather local features dependent on it, (2) understanding the semantic relationship between the defect and the main object to ensure natural blending, and (3) ensuring the word token " + }, + { + "bbox": [ + 55, + 333, + 296, + 441 + ], + "type": "inline_equation", + "content": "[V^{*}]" + }, + { + "bbox": [ + 55, + 333, + 296, + 441 + ], + "type": "text", + "content": " corresponds to the defect region of the object. To achieve these goals, we propose three loss terms: defect, object, and attention loss, as illustrated in the overall training scheme shown in Fig. 2" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 459, + 295, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 295, + 519 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 295, + 519 + ], + "type": "text", + "content": "Defect Loss. The key loss term, defect loss " + }, + { + "bbox": [ + 55, + 459, + 295, + 519 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{def}" + }, + { + "bbox": [ + 55, + 459, + 295, + 519 + ], + "type": "text", + "content": ", directly learns the detailed features of the defect concept. By guiding the model to focus exclusively on the intrinsic features of the defect, it enables inpainting of even unusual features that would not typically appear in the object." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": "First, we sample a timestep " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "t \\sim p(t)" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": " from the model's timestep distribution and obtain the noise latent " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": " using Eq. (1). Next, we prepare the defect mask " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": " and generate a background image " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "B_{def} = (1 - M) \\odot I" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": " where the defect area is masked out. The latent " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "b_{def} = \\mathcal{E}(B_{def})" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": " is then concatenated with " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": " to form " + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "inline_equation", + "content": "x_{t}^{def}" + }, + { + "bbox": [ + 55, + 520, + 296, + 594 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 113, + 603, + 295, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 603, + 295, + 619 + ], + "spans": [ + { + "bbox": [ + 113, + 603, + 295, + 619 + ], + "type": "interline_equation", + "content": "x _ {t} ^ {\\text {d e f}} = \\operatorname {c o n c a t} \\left(x _ {t}, b _ {\\text {d e f}}, M\\right), \\tag {4}", + "image_path": "d63494d285baf6fbcde15e0d9012b94c843322ab2ded62445244f7053bd4e229.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 629, + 200, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 200, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 200, + 640 + ], + "type": "text", + "content": "which serves as input to the model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": "To ensure the prompt focuses exclusively on the defect, we define it as " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{def} = \"A\\text{photo of}[V^*]\"." + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": " The text encoder " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": " encodes this prompt to generate the text condition embedding " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "c^{def} = \\tau_{\\theta}(\\mathcal{P}_{def})" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": ". Using these inputs, we optimize the " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": " loss with respect to noise " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": " to reconstruct " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": " but we compute the loss only over the masked region " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": " to" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 466, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 466, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 466, + 84 + ], + "type": "text", + "content": "avoid reconstructing the background:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 88, + 555, + 115 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 88, + 555, + 115 + ], + "spans": [ + { + "bbox": [ + 320, + 88, + 555, + 115 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d e f} = \\mathbb {E} _ {x _ {t} ^ {d e f}, t, \\epsilon} \\left[ \\left\\| M \\odot \\left(\\epsilon - \\epsilon_ {\\theta} \\left(x _ {t} ^ {d e f}, t, c ^ {d e f}\\right)\\right) \\right\\| _ {2} ^ {2} \\right]. \\tag {5}", + "image_path": "68e6d552c33bc0187075ec41c6f4cea4cbaa39001556644adbccf8e7d8209385.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 126, + 555, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 126, + 555, + 163 + ], + "spans": [ + { + "bbox": [ + 313, + 126, + 555, + 163 + ], + "type": "text", + "content": "Object Loss. The object loss " + }, + { + "bbox": [ + 313, + 126, + 555, + 163 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{obj}" + }, + { + "bbox": [ + 313, + 126, + 555, + 163 + ], + "type": "text", + "content": " learns both the defect and its relationship to the object in which it appears. This ensures the defect blends naturally within the object." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{obj}" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": " term shares the same sampled values for " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": " as the defect loss. To capture the full semantic context of the object, we create a mask with 30 random boxes, " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "M_{rand}" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": ", and train the model to fill in the occluded information across the entire image. Similar to the defect loss, we obtain the conditioning background " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "B_{rand} = (1 - M_{rand}) \\odot I" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": " and its latent " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "b_{rand} = \\mathcal{E}(B_{rand})" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": ". This " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "b_{rand}" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": " is then concatenated with " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "M_{rand}" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": " to form " + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "inline_equation", + "content": "x_{t}^{obj}" + }, + { + "bbox": [ + 313, + 163, + 555, + 260 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 361, + 265, + 553, + 279 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 265, + 553, + 279 + ], + "spans": [ + { + "bbox": [ + 361, + 265, + 553, + 279 + ], + "type": "interline_equation", + "content": "x _ {t} ^ {o b j} = \\operatorname {c o n c a t} \\left(x _ {t}, b _ {\\text {r a n d}}, M _ {\\text {r a n d}}\\right). \\tag {6}", + "image_path": "62b3735193afcd8ded2fb91de52119ee57e8c6f568f2a0556b6afe706c74ec77.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "spans": [ + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "text", + "content": "To express the object's possession of the defect, we set the prompt as " + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{obj} = \"A[Object] with [V^*]\"" + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "text", + "content": " and obtain the text embedding " + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "inline_equation", + "content": "c^{obj} = \\tau_{\\theta}(\\mathcal{P}_{obj})" + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "text", + "content": ". Although it is essential to learn the semantic context of the defect within the object, capturing the fine details of the defect itself is also crucial for authentic inpainting. To address this, we apply a weight of 1 to the defect mask areas and a weight of " + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "text", + "content": ", less than 1, to the background areas, producing an adjusted mask " + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 313, + 284, + 555, + 380 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 321, + 384, + 553, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 384, + 553, + 411 + ], + "spans": [ + { + "bbox": [ + 321, + 384, + 553, + 411 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {o b j} = \\mathbb {E} _ {x _ {t} ^ {o b j}, t, \\epsilon} \\left[ \\left\\| M ^ {\\prime} \\odot \\left(\\epsilon - \\epsilon_ {\\theta} \\left(x _ {t} ^ {o b j}, t, c ^ {o b j}\\right)\\right) \\right\\| _ {2} ^ {2} \\right], \\tag {7}", + "image_path": "1549f059c060e705f0d4327087ca700a4f4cbce59423d6217b4dcac2fdf57375.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 328, + 412, + 432, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 412, + 432, + 426 + ], + "spans": [ + { + "bbox": [ + 328, + 412, + 432, + 426 + ], + "type": "interline_equation", + "content": "M ^ {\\prime} = M + \\alpha \\cdot (1 - M).", + "image_path": "1632ad3726ba33e27e7f018a570a62a9b21128792a1758ae933d72f72f998965.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "text", + "content": "Attention Loss. We also utilize cross-attention maps from the forward pass for " + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{obj}" + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "text", + "content": ". The maps for a specific token represent the layout of the corresponding object, allowing the model to focus more precisely on that region. This helps the model better attend to the defect's features, resulting in higher-fidelity defect generation. Since the encoder in the UNet [25] does not effectively represent the layout of the corresponding token object [4], we use only decoder-layer maps. To handle varying spatial sizes across decoder layers, we resize them to match the latent size, then average those of the " + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "inline_equation", + "content": "[V^{*}]" + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "text", + "content": " token to obtain " + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "inline_equation", + "content": "A_{t}^{[V^{*}]}" + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "text", + "content": ". Finally, we compute the " + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "text", + "content": " loss with the defect mask " + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 438, + 555, + 596 + ], + "type": "text", + "content": ", increasing values in the defect region while reducing them in the background:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 372, + 604, + 553, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 604, + 553, + 631 + ], + "spans": [ + { + "bbox": [ + 372, + 604, + 553, + 631 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a t t n} = \\mathbb {E} \\left[ \\left\\| A _ {t} ^ {[ V ^ {*} ]} - M \\right\\| _ {2} ^ {2} \\right]. \\tag {8}", + "image_path": "17c2084ed7ee83b23cf3c0ee49fc00e55bce980aaa9eee2cce91e947951c71f4.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 642, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 665 + ], + "type": "text", + "content": "DefectFill Loss. Finally, we fine-tune the model using a linear combination of these three loss terms:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 324, + 672, + 553, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 672, + 553, + 685 + ], + "spans": [ + { + "bbox": [ + 324, + 672, + 553, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {o u r s}} = \\lambda_ {\\text {d e f}} \\cdot \\mathcal {L} _ {\\text {d e f}} + \\lambda_ {\\text {o b j}} \\cdot \\mathcal {L} _ {\\text {o b j}} + \\lambda_ {\\text {a t t n}} \\cdot \\mathcal {L} _ {\\text {a t t n}}. \\tag {9}", + "image_path": "aa0f5f302122243394124fa5a92b3000331aa6798f9e10c6233b338363d97344.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "content": "The weights for each term are set to 0.5, 0.2, and 0.05, based on experiments that account for the scale of each loss." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18721" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 68, + 294, + 223 + ], + "blocks": [ + { + "bbox": [ + 57, + 68, + 294, + 223 + ], + "lines": [ + { + "bbox": [ + 57, + 68, + 294, + 223 + ], + "spans": [ + { + "bbox": [ + 57, + 68, + 294, + 223 + ], + "type": "image", + "image_path": "0e8df6b26facecb642a46b877b7d162f85daaf7d8480d2dd1e2b7e0181ada2b9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 232, + 296, + 289 + ], + "lines": [ + { + "bbox": [ + 55, + 232, + 296, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 232, + 296, + 289 + ], + "type": "text", + "content": "Figure 4. Generated Defects by DefectFill. The first row displays the normal images (green boxes), while the second row shows the generated defect images along with their masks, and the third row provides zoomed-in views of the defects (red boxes). The zoomed images highlight the realistic and detailed rendering of the defects." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 308, + 164, + 321 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 308, + 164, + 321 + ], + "spans": [ + { + "bbox": [ + 55, + 308, + 164, + 321 + ], + "type": "text", + "content": "3.3. Generating Defect" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "spans": [ + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "type": "text", + "content": "Sampling. After fine-tuning the inpainting diffusion model with our DefectFill loss to learn the defect concept, we utilize a widely adopted diffusion-based inpainting pipeline [1, 32] to generate diverse defect samples. Specifically, as input, we provide a defect-free image " + }, + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "type": "text", + "content": " along with a mask " + }, + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "type": "text", + "content": " indicating the exact area intended for defect placement. At each inference step " + }, + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 54, + 326, + 295, + 494 + ], + "type": "text", + "content": ", we replace the latent representation's background area outside the mask with the latent of the defect-free image diffused with Eq. (1). This approach ensures that the model modifies only the masked region while preserving the background that should remain unchanged. This approach maintains the structure of the original image, allowing for seamless integration of defects without affecting the overall image quality." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": "Low-Fidelity Selection. Finally, we propose an additional method for selecting samples where the defect is more accurately filled. Since the diffusion model generates diverse samples depending on the initial latent inputs, and due to the nature of the inpainting diffusion model, the masked area is occasionally overly reconstructed, resulting in lower-quality defect. To mitigate this issue, we select the least reconstructed image from the eight samples generated using the same normal image " + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": " and defect mask " + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": ". This selection is based on a reconstruction metric (e.g. PSNR, SSIM [34], LPIPS [38]) measured only within the masked region (as shown in Fig. 3). This simple yet effective process filters out unclear cases and improves defect generation quality. In particular, for downstream tasks using generated defect images, this approach allows us to automatically select high-quality defects samples without manual effort. In our case, we employ LPIPS as the reconstruction metric." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 476, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 476, + 85 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 476, + 85 + ], + "type": "text", + "content": "3.4. Applying to Visual Inspection" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "spans": [ + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "text", + "content": "The generated high-quality defect images are used to train a visual inspection model. First, we learn the concept for each defect category (Sec.3.2) and generate defective images (Sec.3.3) for each category. After that, for classification, we train standard classification models (e.g. ResNet [11]) using the generated images labeled by defect category. For localization, we train segmentation models (e.g. UNet [25]) with normal and synthesized defect images along with their corresponding masks, optimizing with focal loss [19]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 209, + 395, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 395, + 222 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 395, + 222 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 229, + 555, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 555, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 555, + 350 + ], + "type": "text", + "content": "Dataset. We evaluate DefectFill on the MVTec AD Dataset [2], which consists of 15 industrial objects with multiple defect categories. Each category contains hundreds of normal images and approximately 20 defect images with masks. Instead of traditional anomaly detection, we generate defect images by training on one-third of the defect image-mask pairs and applying the model to the remaining two-thirds of masks with normal images. For reliable quantitative results, we evaluate on 10 objects, while all objects are used for qualitative analysis." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 366, + 555, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 555, + 451 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 555, + 451 + ], + "type": "text", + "content": "Implementation Details. Our approach leverages the Stable-Diffusion-2-inpainting model [24], fine-tuning the text encoder and UNet's attention layers with LoRA (rank 8) [13]. We use a learning rate of 2e-4 for the UNet and 4e-5 for the text encoder. Inference is conducted with a DDIM [31] scheduler with 50 denoising steps. Additional details are provided in the supplementary materials." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 467, + 554, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 554, + 551 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 554, + 551 + ], + "type": "text", + "content": "Metric. We evaluate defect generation quality using Kernel Inception Distance (KID) [3] for quality and IC-LPIPS [23] for diversity, excluding FID and IS due to their limitations on smaller or unreferenced datasets. For defect inspection, we measure classification accuracy, Area Under the ROC Curve (AUROC), Average Precision (AP), " + }, + { + "bbox": [ + 313, + 467, + 554, + 551 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 313, + 467, + 554, + 551 + ], + "type": "text", + "content": "-max, and Per Region Overlap (PRO)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 567, + 554, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 567, + 554, + 627 + ], + "spans": [ + { + "bbox": [ + 313, + 567, + 554, + 627 + ], + "type": "text", + "content": "Baselines. We compare our method against two state-of-the-art defect generation methods: DFMGAN [7], a two-stage GAN-based approach, and AnomalyDiffusion [14], a text-to-image diffusion model that disentangles the appearance and spatial attributes of defects." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 635, + 477, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 477, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 477, + 647 + ], + "type": "text", + "content": "4.1. Defect Generation Evaluation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "Qualitative Results. The generated results are shown in Fig. 4. The first row displays the normal images, the second row shows the generated defect images using the mask in the lower right, and the third row provides a zoomed-in view of the generated defects. Despite using custom-drawn" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18722" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 68, + 541, + 277 + ], + "blocks": [ + { + "bbox": [ + 69, + 68, + 541, + 277 + ], + "lines": [ + { + "bbox": [ + 69, + 68, + 541, + 277 + ], + "spans": [ + { + "bbox": [ + 69, + 68, + 541, + 277 + ], + "type": "image", + "image_path": "b6ce88eb4e341be5ee06aa3de62c64df136a20722701e6aa7f8e0aaa542060bb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 284, + 555, + 308 + ], + "lines": [ + { + "bbox": [ + 54, + 284, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 54, + 284, + 555, + 308 + ], + "type": "text", + "content": "Figure 5. Defect Generation Comparisons. This figure compares the quality of defect images generated by our method (bottom row) with baseline approaches. Our method produces the most realistic results, with defects that blend seamlessly into the objects." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 87, + 316, + 525, + 479 + ], + "blocks": [ + { + "bbox": [ + 87, + 316, + 525, + 479 + ], + "lines": [ + { + "bbox": [ + 87, + 316, + 525, + 479 + ], + "spans": [ + { + "bbox": [ + 87, + 316, + 525, + 479 + ], + "type": "table", + "html": "
ObjectsDFMGAN*DFMGAN†AnoDiff‡Ours
KID↓IC-LPIPS↑KID↓IC-LPIPS↑KID↓IC-LPIPS↑KID↓IC-LPIPS↑
bottle70.900.1276.750.15131.520.1730.990.12
capsule40.630.10182.830.1754.970.185.600.18
carpet25.140.1346.020.25149.830.2250.370.22
hazelnut21.160.2430.940.3350.610.311.130.31
leather75.850.17501.610.51244.750.4074.660.30
pill123.520.1670.150.2377.690.238.760.23
tile85.280.22254.820.25314.300.4845.140.44
toothbrush46.490.1861.430.2073.310.183.190.15
wood68.130.34406.610.3583.940.354.720.35
zipper78.080.2735.740.26126.650.2434.910.20
", + "image_path": "edc26efedabba02c60b8d3943ddc94f1c81f183eb0d4b53dfc1adeb9af29d882.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 487, + 555, + 536 + ], + "lines": [ + { + "bbox": [ + 54, + 487, + 555, + 536 + ], + "spans": [ + { + "bbox": [ + 54, + 487, + 555, + 536 + ], + "type": "text", + "content": "Table 1. Generation Comparison. This table presents the average KID and IC-LPIPS scores, computed from 1,000 generated images per defect category and averaged across all categories for each object. Our method achieves the best KID scores for all objects except carpet and the highest IC-LPIPS scores for capsule, pill, and wood. DFMGAN*: scores taken directly from the paper. DFMGAN†: scores reproduced by us. AnoDiff‡: scores measured from the generated dataset (poor samples filtered) on their official page." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 552, + 294, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 552, + 294, + 636 + ], + "spans": [ + { + "bbox": [ + 54, + 552, + 294, + 636 + ], + "type": "text", + "content": "masks which are unseen during training, the model generates authentic and well-aligned defects. Notably, for the hazelnut, the model produces a realistic defect that aligns with the object's semantics, even with an unrealistic mask shape for the crack, demonstrating its strong generalization ability. Additionally, the detailed texture within the hazelnut is observable and highlights the realism of the defects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 641, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 641, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 641, + 297, + 715 + ], + "type": "text", + "content": "Fig. 5 presents a qualitative comparison with the baselines. For AnomalyDiffusion, we use the same normal image and mask, while DFMGAN cannot use the same base image as it generates both normal and defect images directly. In the hazelnut case, both baselines struggle with the texture around the hole, whereas our method produces re" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 552, + 555, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 555, + 697 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 555, + 697 + ], + "type": "text", + "content": "alistic defects that blend seamlessly with the object texture, handling irregular mask shapes and demonstrating Defect-Fill's robustness. In cases such as carpet and tile, where defects are small or thin, the baselines either fail to capture them accurately or omit them entirely, while our model generates well-defined defects. For the toothbrush, DFMGAN blurs the masked area, and AnomalyDiffusion generates defects with colors misaligned with the object context. In contrast, our model produces a realistic blueish defect that reflects the object's context (similar to how the toothbrush in Fig. 4 appears yellowish). This demonstrates our model's ability to integrate object semantics into defect generation." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18723" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 555, + 216 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 555, + 216 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 555, + 216 + ], + "type": "table", + "html": "
ObjectsDFMGAN†AnoDiff*AnoDiff‡Ours
AUROCAPF1-maxPROAUROCAPF1-maxPROAUROCAPF1-maxPROAUROCAPF1-maxPRO
bottle0.960.800.740.840.990.940.870.940.990.910.830.941.000.960.900.97
capsule0.740.040.090.340.990.570.600.950.980.410.440.841.000.750.690.96
carpet0.950.620.600.840.990.810.750.920.970.740.680.820.990.920.860.96
hazelnut1.000.940.870.961.000.970.910.971.000.960.900.971.000.990.940.99
leather0.960.560.560.841.000.800.710.981.000.800.720.981.000.910.830.98
pill0.990.890.860.911.000.970.910.971.000.970.910.951.000.980.930.98
tile0.990.940.870.960.990.940.860.960.990.950.870.971.000.970.900.98
toothbrush0.980.600.610.890.990.770.730.910.990.710.680.910.990.890.820.94
wood0.720.370.410.730.990.850.750.940.970.790.720.891.000.930.860.98
zipper0.990.820.760.950.990.860.790.961.000.870.800.971.000.900.840.97
", + "image_path": "b3af1a8571dd40ab3ce38de8e4e3ce723f433203de207b7e04c3d46a910c85e9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 275, + 294, + 388 + ], + "blocks": [ + { + "bbox": [ + 55, + 223, + 555, + 257 + ], + "lines": [ + { + "bbox": [ + 55, + 223, + 555, + 257 + ], + "spans": [ + { + "bbox": [ + 55, + 223, + 555, + 257 + ], + "type": "text", + "content": "Table 2. Localization Comparison. The table presents AUROC, AP, " + }, + { + "bbox": [ + 55, + 223, + 555, + 257 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 55, + 223, + 555, + 257 + ], + "type": "text", + "content": "-max, and PRO scores for localization evaluation using a UNet trained on generated defect images. Our method achieves the highest performance across all metrics and objects. AnoDiff*: scores reported in the paper. The others: described in Tab. 1." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 275, + 294, + 388 + ], + "lines": [ + { + "bbox": [ + 56, + 275, + 294, + 388 + ], + "spans": [ + { + "bbox": [ + 56, + 275, + 294, + 388 + ], + "type": "table", + "html": "
ObjectsDFMGAN*DFMGAN†AnoDiff*AnoDiff‡Ours
bottle56.5963.4190.7095.3597.56
capsule37.2725.0066.6745.3387.50
carpet47.3142.1158.0664.5287.72
hazelnut81.9486.9685.4289.58100.00
leather49.7332.2061.9065.0893.22
pill29.5244.4459.3864.5897.53
tile74.8581.8284.2196.49100.00
wood49.0245.1671.4378.57100.00
zipper27.6445.4569.5185.3790.91
", + "image_path": "5e14531c754bf84328e2d58ca26928d6a2b95e272bdbcaad7c08db99d610b5c8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 397, + 295, + 453 + ], + "lines": [ + { + "bbox": [ + 55, + 397, + 295, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 397, + 295, + 453 + ], + "type": "text", + "content": "Table 3. Classification Comparison. The table shows classification accuracy (\\%) when a ResNet-34 is trained on generated defect images for defect category prediction. Our method achieves the highest performance across all objects. AnoDiff*: scores reported in the paper. The others: described in Tab. 1." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 473, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 473, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 473, + 295, + 568 + ], + "type": "text", + "content": "Quantitative Results. Tab. 1 compares the KID and IC-LPIPS scores of our method with baseline approaches across various objects. For evaluation, we generate 1,000 images for each defect category within each object, ensuring that all metrics, including KID, are calculated using only defect images excluded from the training set. This approach is necessary as KID often produces overly optimistic values when models overfit and are evaluated on training data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 569, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 569, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 569, + 295, + 665 + ], + "type": "text", + "content": "Our method outperforms the baselines in KID scores across most objects. For IC-LPIPS, it also achieves the best scores on three objects (capsule, pill, wood). In the case of leather, DFMGAN† and AnoDiff‡ score significantly higher, but this is primarily due to their generation of diverse yet low-quality samples across various masks. The high KID values for these methods further confirm that the quality of their generated defect images is low." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 672, + 212, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 212, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 212, + 685 + ], + "type": "text", + "content": "4.2. Visual Inspection Evaluation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "To demonstrate that the realistic images generated by DefectFill can enhance performance in downstream visual in" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 278, + 555, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 278, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 278, + 555, + 361 + ], + "type": "text", + "content": "spection tasks, we apply it to two tasks: classification and localization. Following the experimental setup of AnomalyDiffusion [14], we use ResNet-34 [11] for classification and UNet [25] for localization. As outlined in the quantitative results (Sec. 4.1), we generate 1,000 defects per category and train the models on this data. Testing is conducted on the remaining two-thirds of the dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 376, + 555, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 555, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 555, + 449 + ], + "type": "text", + "content": "Classification. As shown in Tab.3, our method achieves higher classification accuracy across all objects compared to the baselines. Notably, there is a significant improvement for objects with small defect areas, which are typically challenging to generate meaningful defects for, such as capsule " + }, + { + "bbox": [ + 313, + 376, + 555, + 449 + ], + "type": "inline_equation", + "content": "(66.67\\% \\rightarrow 87.50\\%)" + }, + { + "bbox": [ + 313, + 376, + 555, + 449 + ], + "type": "text", + "content": " and pill " + }, + { + "bbox": [ + 313, + 376, + 555, + 449 + ], + "type": "inline_equation", + "content": "(64.58\\% \\rightarrow 97.53\\%)" + }, + { + "bbox": [ + 313, + 376, + 555, + 449 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 461, + 554, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 554, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 554, + 545 + ], + "type": "text", + "content": "Localization. The UNet is trained to predict defect locations, and the predictions are evaluated using various metrics. As shown in Tab. 2, our model achieves the best performance across all metrics and objects. The capsule is a particularly challenging object for localization, yet our model significantly outperforms the baseline with a notable improvement in AP score " + }, + { + "bbox": [ + 313, + 461, + 554, + 545 + ], + "type": "inline_equation", + "content": "(0.57 \\to 0.75)" + }, + { + "bbox": [ + 313, + 461, + 554, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 552, + 416, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 416, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 416, + 564 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "content": "Inpainting Ablation. We conduct an ablation study to evaluate the impact of leveraging the inpainting diffusion model and our defect-specific loss tailored for this model (Fig. 6). As mentioned in Sec. 2, CLiC [29] is a method that learns local concepts without using the inpainting diffusion model. However, the generated results tend to focus on reconstruction rather than creating actual holes (left image). This is because, unlike general local concepts, the defect concept we aim to learn is an unusual concept unknown to the model's prior. When applying our defect-specific loss (middle image), the model better learns the defect features, resulting in more accurately formed holes. However, the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18724" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 294, + 200 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 294, + 200 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 294, + 200 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 294, + 200 + ], + "type": "image", + "image_path": "36eeea633020dea5d3c353acad5a2b6125a39fc290704c5c282104afad1a1675.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 209, + 295, + 276 + ], + "lines": [ + { + "bbox": [ + 55, + 209, + 295, + 276 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 295, + 276 + ], + "type": "text", + "content": "Figure 6. Inpainting Ablation. Ablation study comparing three setups: applying CLiC [29] loss to vanilla Stable Diffusion (SD2+CLiC Loss), replacing CLiC with our loss (SD2+Our Loss), and our full approach (SD2-Inpainting+Our Loss). Using the inpainting model with our loss is necessary to produce realistic defects that align well with both the mask and the object." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 297, + 296, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 297, + 296, + 382 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 296, + 382 + ], + "type": "text", + "content": "thin regions of the mask are still neglected, and the texture around the hole doesn't blend well with the surrounding hazelnut texture. Finally, by leveraging the inpainting diffusion model's strong prior for filling, we generate realistic defects that blend naturally with their surroundings (as shown by the light brown texture around the hole in the right image), and aligning with the thin mask regions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 398, + 296, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 398, + 296, + 625 + ], + "spans": [ + { + "bbox": [ + 55, + 398, + 296, + 625 + ], + "type": "text", + "content": "Loss Ablation. As described in Sec. 3.2, we structure our loss function with three terms to achieve three specific goals. To illustrate the contribution of each term, we perform an ablation study. Fig. 7 shows the defect generation results when each loss term is omitted during training. When the defect loss is excluded, the model tends to reconstruct rather than generate defects. This occurs because the inpainting diffusion model fails to learn the distinctive characteristics of defects and instead fills the masked area with just plausible context. Without the object loss, the model lacks semantic alignment with the object, leading to unnatural defect generation. For example, the middle section of a zipper may appear fused, or a hole may look like it's placed on a carpet rather than genuinely puncturing it. Lastly, when the attention loss is omitted, the model struggles to focus accurately on the defect mask area, resulting in lower defect fidelity (e.g. an awkwardly split zipper or an incomplete hole). Finally, by combining all loss terms, we achieve realistic defects seamlessly filled onto objects." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": "Low Fidelity Selection. Our simple yet effective Low-Fidelity Selection method enables high-quality defect sampling without human effort. As shown in Fig. 3, it intuitively selects qualitatively good samples. Additionally, as reported in Tab. 4, it improves both the quality (KID) and the diversity (IC-LPIPS) of generated defects." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 316, + 69, + 554, + 257 + ], + "blocks": [ + { + "bbox": [ + 316, + 69, + 554, + 257 + ], + "lines": [ + { + "bbox": [ + 316, + 69, + 554, + 257 + ], + "spans": [ + { + "bbox": [ + 316, + 69, + 554, + 257 + ], + "type": "image", + "image_path": "8b6aeeb76bcb84c446109b74d10bc2506b1286daf0578b221a2476b3436e6717.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 266, + 555, + 321 + ], + "lines": [ + { + "bbox": [ + 313, + 266, + 555, + 321 + ], + "spans": [ + { + "bbox": [ + 313, + 266, + 555, + 321 + ], + "type": "text", + "content": "Figure 7. Loss Ablation. This figure illustrates the impact of each loss term on generated defect quality. We show the results when each loss term is individually removed during fine-tuning, as well as the result when all terms are used together. Utilizing all loss terms results in realistic defects that align well with the context." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 347, + 333, + 523, + 388 + ], + "blocks": [ + { + "bbox": [ + 347, + 333, + 523, + 388 + ], + "lines": [ + { + "bbox": [ + 347, + 333, + 523, + 388 + ], + "spans": [ + { + "bbox": [ + 347, + 333, + 523, + 388 + ], + "type": "table", + "html": "
Ours w/o LFSOurs
KID↓IC-LPIPS↑KID↓IC-LPIPS↑
28.4850.24725.9470.250
", + "image_path": "4cea0af88d827733768ab2ccfd792b58ec349843c411b220f242315ae1c00028.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 396, + 555, + 440 + ], + "lines": [ + { + "bbox": [ + 313, + 396, + 555, + 440 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 555, + 440 + ], + "type": "text", + "content": "Table 4. Generation Comparison with Low-Fidelity Selection. The application of LFS shows improvements in quality (KID) and diversity (IC-LPIPS). The values represent averages calculated for each defect category, and then averaged across objects." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 314, + 460, + 391, + 473 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 460, + 391, + 473 + ], + "spans": [ + { + "bbox": [ + 314, + 460, + 391, + 473 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 481, + 555, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 481, + 555, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 481, + 555, + 590 + ], + "type": "text", + "content": "In this work, we present DefectFill, a novel approach that fine-tunes an inpainting diffusion model to generate realistic and high-fidelity defect images. Our method achieves state-of-the-art performance in both generation quality and visual inspection tasks on the MVtec AD dataset, demonstrating its effectiveness even when limited reference samples are available. These strengths make DefectFill particularly well-suited for widespread industrial applications, especially in scenarios where defect images are scarce." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": "Limitations. While our method excels at generating localized defects—a common real-world scenario—it is less effective for global structural defects that affect the entire object, such as misalignment. This limitation arises because our inpainting-based approach, which focuses on local masked regions. Addressing such global defects remains an area for future research, though our method already robustly handles the majority of practical defect cases, where localized defects are the primary concern." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18725" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 205, + 115, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 205, + 115, + 217 + ], + "spans": [ + { + "bbox": [ + 56, + 205, + 115, + 217 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 225, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 61, + 225, + 296, + 258 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 225, + 296, + 258 + ], + "spans": [ + { + "bbox": [ + 61, + 225, + 296, + 258 + ], + "type": "text", + "content": "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. 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Previous methods have commonly relied on discrete representation like mask, often resulting in local fractures or scattered fragments due to the inherent limitations of the per-pixel classification paradigm. In this work, we introduce DeformCL, a new continuous representation based on Deformable Centerlines, where centerline points act as nodes connected by edges that capture spatial relationships. Compared with previous representations, DeformCL offers three key advantages: natural connectivity, noise robustness, and interaction facility. We present a comprehensive training pipeline structured in a cascaded manner to fully exploit these favorable properties of DeformCL. Extensive experiments on four 3D vessel segmentation datasets demonstrate the effectiveness and superiority of our method. Furthermore, the visualization of curved planar reformation images validates the clinical significance of the proposed framework. We release the code in https://github.com/barry664/DeformCL.", + "bbox": [ + 86, + 411, + 485, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 760, + 220, + 776 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Cerebro-cardiovascular disease is one of the most severe global health threats [22]. Timely detection of potential high-risk locations and prompt intervention are crucial to reducing mortality, relying on accurate extraction, reconstruction, and analysis of major vessels in CTA images [16].", + "bbox": [ + 89, + 786, + 483, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In clinical practice, the primary requirement is to achieve accurate segmentation of primary vessel branches to enable comprehensive vascular system assessment and detailed local analysis.", + "bbox": [ + 511, + 380, + 906, + 441 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous methodologies [1, 21, 25, 26, 29, 31] have predominantly adopted the traditional semantic segmentation approach, which relies on fine-grained, per-pixel classification within a discrete mask representation. As illustrated in the top part of Figure 1, to improve the volumetric scores (e.g. Dice) or topological metrics (e.g. betti number errors) for segmentation, these approaches introduce a variety of innovations, such as incorporating tubular priors into network architecture [13, 21, 25, 31, 36, 39] or designing topology-preserving loss functions [1, 9, 26]. Despite these advancements in the training process, the core issue that the discrete mask representation is not well-suited for the curvilinear vessels remains unchanged, imposing several inherent limitations that restrict the model's performance and applicability, as shown in the top part of Figure 2. Firstly, the neural networks struggle to recognize fragile and tortuous local structures, which may lead to segmentation fractures [21]. Moreover, the discrete representation exhibits poor robustness to local noise [26, 29], such as variations in tissue density, due to the lack of a holistic view of the global morphology. Consequently, it may mistakenly identify the tissues with appearances similar to target vessels. Finally, designing an effective feature aggregation strategy along tubular curves remains challenging, considering the lack of explicit relationships among elements in discrete mask representations.", + "bbox": [ + 511, + 444, + 908, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "These challenges motivate us to seek a continuous representation that can explicitly fit the tubular structures from a holistic view, rather than confined to per-pixel classification paradigm. In this paper, we introduce DeformCL,", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 107, + 875, + 218, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Project lead.", + "bbox": [ + 109, + 887, + 184, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "30896", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3ec4c7541ed469d1737cc92c55bc8129cee23a9be0beeafd54e9deff278f58d4.jpg", + "image_caption": [ + "Figure 1. Previous methods [1, 21, 26, 29, 31] primarily rely on the discrete mask representation, adopting a per-pixel classification paradigm for vessel segmentation. Common techniques in these approaches include incorporating tubular priors and applying topology-preserving loss functions. In contrast, we introduce a new continuous representation, DeformCL, which employs centerline points connected by edges to gradually fit the curvilinear vessels via a template deformation process. Once structured centerlines are obtained, generating segmentation predictions with improved topological accuracy becomes a straightforward task." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 903, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a new representation for vessel extraction in 3D medical image based on Deformable Centerline. As shown in the bottom part of Figure 1, DeformCL employs a graph structure, wherein centerline points serve as nodes connected by edges representing their spatial relationships. This continuously defined representation accurately depicts the curvilinear structures, thus circumventing the drawbacks of discrete mask representation and has its own merits: (1) the incorporation of natural connectivity mitigates centerline ruptures, particularly in the thin and fragile areas; (2) by considering the entire curvilinear structures rather than local pixels, DeformCL ensures a comprehensive understanding of the global morphology, thus reducing local artifacts and false positives; (3) the inherent graph structure facilitates efficient and effective feature aggregation along the tubular curves, enhancing overall segmentation performance.", + "bbox": [ + 88, + 358, + 485, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose a novel framework to learn deformable centerline representation from 3D medical images. Our framework consists of several key steps. Firstly, we adaptively generate an initial continuous centerline template based on the input image, taking anatomical variations among different individuals into account. Next, the centerline points within the template will interact with each other to capture features along tubular curves. The whole centerline template will be iteratively refined by deformation and unpooling layers, gradually aligning with the ground truth centerlines. Finally, after obtaining precise centerlines of tubular structures, crafting a high-quality segmentation algorithm becomes a straightforward task. In our approach, we leverage the distance map derived from the predicted centerline points to execute the final segmentation process effortlessly. Benefiting from the high-quality continuous centerlines, the segmentation performance is improved significantly.", + "bbox": [ + 89, + 606, + 483, + 864 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We benchmark DeformCL on four 3D medical datasets, and the extensive experiments validate the effectiveness of", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "our proposed method. Additionally, due to its continuous nature, DeformCL's centerline predictions can be directly used as a structural representation of vessels, commonly as directional centerlines [10, 24]. This structural representation is crucial in clinical practice, serving as an indispensable component in various subsequent diagnostic tasks, such as curved planar reformation [11] and computational hemodynamics [27]. We qualitatively demonstrate the clinical relevance of DeformCL, highlighting its potential applicability for diagnostic purposes.", + "bbox": [ + 511, + 357, + 906, + 508 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are three-fold:", + "bbox": [ + 532, + 508, + 870, + 522 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a continuous representation, called DeformCL, which possesses several favorable properties for curvilinear vessels in 3D medical image.", + "- We propose a comprehensive pipeline for effectively training DeformCL through a cascaded deformation process.", + "- Our approach significantly bolsters the performance of several baselines on four 3D vessel extraction datasets." + ], + "bbox": [ + 511, + 523, + 906, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 657, + 656, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Vessel Segmentation in 3D Medical Image", + "text_level": 1, + "bbox": [ + 511, + 681, + 870, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vessel segmentation in 3D medical image is a crucial task due to the prevalence of curvilinear vessels in the human body. Classical modern segmentation models like UNet [3, 23] and FCN [17] face challenges in accurately extracting tubular structures due to their complex global morphology and fragile thin structures. Previous methods have adopted various strategies to address these challenges: incorporate tubular priors into network architecture [14, 21, 25, 31, 33, 36, 39], design topology-preserving loss functions [1, 9, 26] or employ more flexible representation [29, 38]. Shit et al. [26] introduces a new connectivity-aware similarity measure called clDice, and the differentiable version can be used to train segmentation models for", + "bbox": [ + 511, + 704, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "30897", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tubular structures. Qi et al. [21] proposes a dynamic snake convolution to let networks adaptively focus on the tubular structures and make more accurate predictions. Wang et al. [29] relies on the flexibility of point set representation which is not restricted to a fixed grid to promote the performance of tubular structure extraction.", + "bbox": [ + 89, + 90, + 483, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Deformable Paradigm", + "text_level": 1, + "bbox": [ + 89, + 190, + 297, + 207 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The deformable paradigm is a widely used technique in deep learning, particularly in computer vision, where it plays a crucial role in capturing complex structures and achieving significant advancements in various tasks. Introduced by Dai et al. [4], deformable convolution extends traditional convolutions to capture complex structures effectively. It has been successfully applied in tasks such as object detection and segmentation, allowing models to adapt to object variations and complex shapes. Deformable DETR [41] combines attention mechanism with deformable paradigm for efficient feature extraction process. In addition, deformable structures have also found applications in 3D reconstruction tasks [2, 14, 30, 32, 34, 40]. For instance, Pixel2Mesh [30] generates 3D shapes represented as triangular meshes from single images by progressively deforming an initial ellipsoid. Similarly, Voxel2Mesh [32] extends this approach to generate organ surfaces from 3D medical volumes, facilitating organ segmentation and visualization. Kong et al. [14] proposed a deep-learning approach to generate whole heart geometries from pre-defined mesh templates, demonstrating the versatility of deformable structures in human anatomical modeling.", + "bbox": [ + 89, + 212, + 483, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 556, + 183, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will first introduce the new representation DeformCL and its favorable properties in Sec 3.1. Sec 3.2 elaborates on the network architecture for learning deformation centerline representation from 3D medical images. Sec 3.3 presents the training losses for the framework.", + "bbox": [ + 89, + 583, + 483, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Representation of DeformCL", + "text_level": 1, + "bbox": [ + 89, + 667, + 352, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In 3D medical imaging, a common representation of a given volume $I \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}$ is its segmentation mask, denoted as $Y \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}$ . Nearly all previous methods [1, 21, 25, 26, 29, 31] rely on this discrete mask representation, framing the task as per-pixel classification. This paradigm inherently possesses several limitations, as illustrated in the top part of Figure 2, which ultimately restrict the model's performance.", + "bbox": [ + 89, + 688, + 483, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we introduce a novel continuous representation called Deformable CenterLine (DeformCL) to efficiently and effectively capture tubular structures in 3D medical image. Instead of relying on segmentation mask, we represent tubular structures using a graph $\\mathcal{G} = \\{\\mathcal{V},\\epsilon \\}$ , where $\\mathcal{V} = \\{v_{i}|v_{i}\\in \\mathbb{R}^{3}\\}_{i = 1}^{N}$ is a set of $N$ vertices standing", + "bbox": [ + 89, + 810, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1f5f80f12b0e2e829c2b8a6f02ac77f186c37a5163018a48fbba69f04679fe37.jpg", + "image_caption": [ + "Figure 2. Three significant properties of DeformCL compared with the discrete mask representation. (Zoom in for more details.)" + ], + "image_footnote": [], + "bbox": [ + 537, + 90, + 882, + 195 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for centerline points, $\\epsilon = \\{(k,w)|1\\leq k,w\\leq N\\}$ is the set of edges connecting adjacent vertices.", + "bbox": [ + 511, + 256, + 903, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in the bottom part of Figure 2, compared with previous discrete representations, DeformCL possesses several favorable properties, making it a reasonable and effective representation for tubular structure modeling.", + "bbox": [ + 511, + 287, + 903, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Natural connectivity. Unlike traditional discrete representations, DeformCL naturally exhibits the connectivity among centerline points, which explicitly models the tubular structures in a continuously defined way. On one hand, this continuous representation helps prevent predictions from breaking in thin and fragile regions. On the other hand, the traditionally complex and time-consuming continuous centerlines extraction [10, 19] from segmentation for curved planner reconstruction [11] is eliminated.", + "bbox": [ + 511, + 349, + 905, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Noise robustness. Thanks to its top-down manner, DeformCL exhibits robustness to noise and local disturbances, such as variations in tissue density or the presence of contrast agents. This inherent property enables DeformCL to effectively filter out local artifacts and false positives, leading to more accurate and reliable tubular structure extraction compared to previous bottom-up methods.", + "bbox": [ + 511, + 486, + 905, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Interaction facility. Constrained by the discrete representation, previous methods [21, 26, 29, 31] lack of an effective approach for tubular feature aggregation. On the contrary, DeformCL's graph structure facilitates feature fusion process via methods like GCN [12] or Transformer [28] along the tubular curve. This global information interaction is significant for the structure completeness and topology correctness of tubular predictions.", + "bbox": [ + 511, + 593, + 905, + 714 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Network Architecture", + "text_level": 1, + "bbox": [ + 511, + 724, + 718, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this subsection, we will introduce the network architecture for learning deformable centerline representation. The whole framework is shown in Figure 3. Given a 3D medical image $I \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}$ , we first pass it through a 3D backbone (e.g. 3D UNet [3]) to obtain hierarchical feature maps $\\{F_i\\}_{i=1}^m$ at different down-sampled rates. Additionally, the backbone network produces a coarse segmentation result $\\hat{Y}_c \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}$ for each category of vessels.", + "bbox": [ + 511, + 748, + 905, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adaptive Template Generation. In order to initialize the graph structure of DeformCL, we attempt to initial-", + "bbox": [ + 511, + 869, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "30898", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4f7468b84536469a2fe97024a46544b872d0a7cecc331ea307f70a81b3474e3b.jpg", + "image_caption": [ + "Figure 3. Overview of the training process. Given a 3D medical image, the segmentation network first outputs a coarse prediction and generates hierarchical downsampled feature maps. An initial template, produced by the Adaptive Template Generation module, is then iteratively fed through deformation and unpooling layers to progressively adapt to the curvilinear structures. Finally, refined segmentation results are generated based on the accurately aligned continuous centerlines. We apply Dice loss to both the coarse and refined segmentation predictions, and local chamfer loss, SDF loss, and regularization loss for centerline predictions." + ], + "image_footnote": [], + "bbox": [ + 133, + 92, + 861, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ize a tubular template motivated by mesh generation methods [30, 32]. However, unlike human organs, tubular structures in 3D medical image, such as coronary arteries, exhibit complex global morphology and variable extension direction, which means that discovering a universal template for such structures poses significant challenges. Therefore, we introduce a new method to adaptively generate initial templates for each image.", + "bbox": [ + 88, + 508, + 482, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The template generation process, illustrated in the Figure 4, is conducted independently for each category of vessels. Firstly, the coarse segmentation result $\\hat{Y}_c$ is converted into discrete centerline points via traditional 3D thinning algorithm [15]. These points are then reconstructed into a graph using the minimum spanning tree algorithm [7] following the strategy in [37]. Next, a set of $k$ control points is selected from the graph at fixed distances, serving as the abstraction of the structure. Finally, curvilinear interpolation (e.g. Bezier Curve Interpolation, Linear Interpolation) is applied based on the control points to generate the initial template, denoted as $\\{v_i^c | v_i^c \\in \\mathbb{R}^3\\}_{i=1}^{N_c}$ . Here, $v_i^c$ represents the $i$ -th point for category $c$ , $N_c$ is the total number of points for category $c$ , and $v_i^c$ is connected with $v_{i+1}^c$ by default.", + "bbox": [ + 89, + 628, + 482, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is worth noting that we adopt a rough template generation strategy using control points instead of directly utilizing the reconstructed tree as the initial template. The reason is that we empirically find overly accurate initial templates", + "bbox": [ + 89, + 840, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "may harm model performance, supported by experimental results shown in Table 3. We speculate that overly accurate initial templates may simplify the deformation task excessively, potentially leading to insufficient model training.", + "bbox": [ + 511, + 508, + 903, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cascaded Deformation Process. After the generation of initial templates, we proceed with the cascaded deformation process to refine the centerline predictions. For clarity, we focus on the centerline points of one category of vessels in the subsequent sections of the paper.", + "bbox": [ + 511, + 569, + 905, + 645 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Firstly, trilinear interpolation is applied to each centerline point $v_{i}$ in the downsampled feature maps $\\{F_i\\}_{i = 1}^m$ , and the hierarchical points features are fused via a linear layer:", + "bbox": [ + 511, + 645, + 905, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf \\left(v _ {i}\\right) = \\operatorname {L i n e a r} \\left(\\left[ \\operatorname {T r i} \\left(F _ {1}, v _ {i}\\right), \\dots , \\operatorname {T r i} \\left(F _ {m}, v _ {i}\\right) \\right]\\right) \\in \\mathbb {R} ^ {C}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 703, + 903, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C$ denotes the channel size, Tri represents the tri-linear interpolation. Next, the points and their corresponding features $\\{v_{i},f(v_{i})\\}$ are fed into Transformer [28] layers for feature aggregation along the tubular curve. The positional encoding $\\mathrm{Pos}(v^l)$ contains learnable embeddings of absolute 3D positions of points and relative positions in the graph. Subsequently, the augmented point features are used to predict an offset $\\delta_i^l$ , which is then applied to update the position of each point $v_{i}^{l}$ to obtain $v_{i}^{l + 1}$ .", + "bbox": [ + 511, + 733, + 905, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since high-accuracy centerlines require a sufficient number of points to capture curvilinear structures accurately, we", + "bbox": [ + 511, + 869, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "30899", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/21fe1120de844ce93b8cd7df0776d53b71b17da688a310172b4c5cf44eb07b6f.jpg", + "image_caption": [ + "Figure 4. Adaptive Template Generation." + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 477, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "apply an unpooling strategy after deformation to increase point density. Specifically, a new point is inserted between each pair of connected points. We reuse the symbol $\\{v_i^{l + 1}\\}$ for clarity. This process is iterated $L$ times for accurate centerline prediction, where the $l$ -th layer is described as follows:", + "bbox": [ + 89, + 196, + 483, + 286 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {f} \\left(v _ {i} ^ {l}\\right) = f \\left(v _ {i} ^ {l}\\right) + \\operatorname {T r a n s f o r m e r} \\left(f \\left(v ^ {l}\\right), \\operatorname {P o s} \\left(v ^ {l}\\right)\\right) \\in \\mathbb {R} ^ {C}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 295, + 480, + 315 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {i} ^ {l} = \\operatorname {T a n h} \\left(\\mathrm {M L P} \\left(\\tilde {f} \\left(v _ {i} ^ {l}\\right)\\right)\\right) \\in \\mathbb {R} ^ {3}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 316, + 482, + 335 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv _ {i} ^ {l + 1} = v _ {i} ^ {l} + \\delta_ {i} ^ {l} \\in \\mathbb {R} ^ {3}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 338, + 482, + 357 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{v _ {i} ^ {l + 1} \\right\\} = \\text {U n p o o l i n g} \\left(\\left\\{v _ {i} ^ {l + 1} \\right\\}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 359, + 482, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After completing the cascaded deformation process, the final set of points $\\{v_i^L\\}$ represents the predicted centerline points, which will be used for subsequent centerline-based segmentation task.", + "bbox": [ + 89, + 388, + 483, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Centerline-based Segmentation. Once accurate centerlines of tubular structures are obtained, predicting the corresponding segmentation results becomes straightforward. In this work, we employ a simple method using distance maps to achieve centerline-based segmentation. Specifically, given the predicted centerline points $V = \\{v_{i}^{L}\\in \\mathbb{R}^{3}\\}$ , we calculate the minimum distance of each voxel in the image to the points in $V$ :", + "bbox": [ + 89, + 449, + 483, + 570 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD [ x, y, z ] = \\min _ {v \\in V} | | (x, y, z) - v | | _ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 583, + 482, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{D} \\times \\mathbb{W}}$ is the distance map based on the centerline points. Finally, the coarse segmentation results $\\hat{Y}_c$ and the distance map $D$ are input to a convolutional layer for fusion, yielding the refined segmentation results $\\hat{Y}_r$ .", + "bbox": [ + 89, + 612, + 483, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Training Loss", + "text_level": 1, + "bbox": [ + 89, + 681, + 233, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this subsection, we will elaborate on the loss functions of the proposed framework. For centerline prediction, we employ a combination of local chamfer distance loss, signed distance function (SDF) loss, and a regularization loss. We utilize Dice loss for segmentation.", + "bbox": [ + 89, + 704, + 483, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Local Chamfer Distance Loss. Tradition global chamfer distance loss calculates the distance between two point cloud sets. However, curvilinear vessels in the human body often exhibit complex global morphology and sparse 3D distribution. As a result, using global chamfer distance loss may lead to larger fluctuations and suboptimal convergence during the training process. To address this issue, we adopt a local version of chamfer distance loss.", + "bbox": [ + 89, + 780, + 483, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To be specific, we begin by employing Farthest Point Sampling (FPS) to select candidate points $\\{u_{i_k}\\}$ from the ground truth centerline points $\\{u_i\\}$ , which are obtained from the ground truth mask via traditional 3D thinning algorithm [15]. Then, we crop local patches with fixed size $M$ centered around each selected point $\\{u_{i_k}\\}$ . The points located within each cropped patch are denoted as $\\omega_{i_k} = \\{p = (x,y,z)|p\\in [u_{i_k} - M / 2,u_{i_k} + M / 2]\\}$ , and the set of patches is denoted as $\\Omega = \\{\\omega_{i_k}\\}$ . The chamfer distance loss is then applied between the predicted point set and the ground truth point set within each cropped patch. Formally, the loss is defined as:", + "bbox": [ + 511, + 90, + 906, + 272 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c h a}} = \\frac {1}{| \\Omega |} \\sum_ {\\omega \\in \\Omega} \\left(\\sum_ {v _ {i} \\in \\omega} \\min _ {u _ {i} \\in \\omega} \\| v _ {i} - u _ {i} \\| _ {2} ^ {2} + \\sum_ {u _ {i} \\in \\omega} \\min _ {v _ {i} \\in \\omega} \\| u _ {i} - v _ {i} \\| _ {2} ^ {2}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 292, + 911, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SDF Loss. Signed Distance Function (SDF) is a well-established concept in computer vision and computer graphics, used to represent the surface of 3D objects through signed distances. We find that SDF is appropriate for ensuring the centrality of predicted centerline points. Firstly, we define the surface of tubular strcutures following [31]:", + "bbox": [ + 511, + 340, + 906, + 446 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS = \\{x \\in \\mathbb {R} ^ {3} | Y [ x ] = 1, \\exists u \\in \\mathcal {N} (x), Y [ u ] = 0 \\}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 455, + 903, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{N}(x)$ denotes the 6-neightbour voxels of $x$ , $Y$ is the ground truth mask. Then, the SDF value of an arbitrary point $p$ in the image can be calculated as:", + "bbox": [ + 511, + 481, + 905, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS D F (p) = \\left\\{ \\begin{array}{l l} - \\min _ {u \\in S} | | p - u | | _ {2} ^ {2}, & \\text {i f} Y [ p ] = 1, \\\\ \\min _ {u \\in S} | | p - u | | _ {2} ^ {2}, & \\text {i f} Y [ p ] = 0. \\end{array} \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 535, + 903, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The SDF values of all predicted centerline points are utilized as the training loss:", + "bbox": [ + 511, + 585, + 905, + 617 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s d f}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} S D F (v _ {i}). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 625, + 903, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated in Figure 5, SDF loss serves two crucial purposes. Firstly, it provides supervision for all predicted centerline points, whereas the local chamfer", + "bbox": [ + 511, + 674, + 668, + 792 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d4d481a2bc9d2f062bdf2a3bf6e9a9aa6146e89ef73b64716a578be2c14c1c69.jpg", + "image_caption": [ + "Figure 5. SDF Loss." + ], + "image_footnote": [], + "bbox": [ + 700, + 676, + 903, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "distance loss can only provide supervision for points within cropped patches, potentially missing outlier predictions. Secondly, it facilitates the gradual deformation of predicted points towards the ideal center of tubular structures, thereby ensuring the centrality of centerlines.", + "bbox": [ + 511, + 795, + 905, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Regularization Loss. To prevent the deformable centerline points from deviating mistakenly, which may result in long", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 4 + }, + { + "type": "footer", + "text": "30900", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "edges between adjacent vertices, we apply a regularization loss to penalize the adjacent points with much long edges:", + "bbox": [ + 89, + 90, + 482, + 122 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left| \\left| v _ {i} - v _ {i - 1} \\right| \\right| _ {2} ^ {2}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 128, + 482, + 170 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Segmentation Loss. We use Dice loss [18] as loss function for the coarse and refined segmentation results $\\hat{Y}_c$ and $\\hat{Y}_r$ :", + "bbox": [ + 89, + 179, + 482, + 209 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s e g}} = \\lambda \\operatorname {D i c e} \\left(Y, \\hat {Y} _ {c}\\right) + \\operatorname {D i c e} \\left(Y, \\hat {Y} _ {r}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 215, + 482, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda$ is set to 0.2.", + "bbox": [ + 89, + 243, + 230, + 256 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that local chamfer distance loss, SDF loss and regularization loss are applied to all intermediate results in the cascaded deformation process. The total training loss is a combination of all loss functions:", + "bbox": [ + 89, + 258, + 483, + 316 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum_ {l = 1} ^ {L} w _ {l} \\left(\\lambda_ {\\mathrm {c h a}} \\mathcal {L} _ {\\mathrm {c h a}} + \\lambda_ {\\mathrm {s d f}} \\mathcal {L} _ {\\mathrm {s d f}} + \\lambda_ {\\mathrm {r e g}} \\mathcal {L} _ {\\mathrm {r e g}}\\right) + \\mathcal {L} _ {\\mathrm {s e g}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 324, + 482, + 366 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$w_{l}$ stands for the weight of the $l$ -th deformation stage.", + "bbox": [ + 89, + 373, + 446, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 400, + 223, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 89, + 425, + 192, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use four datasets to evaluate our proposed framework. HaN-Seg [20] is a public dataset consisting of 56 CT and MR images with 30 categories of head and neck organ pixel annotations. ASOCA [5, 6] is a public dataset in the MICCAI-2020 challenge which aims to automatically segment the coronary artery lumen. It consists of 40 Cardiac Computed Tomography Angiography (CCTA) images with artery segmentation annotations. ImageCAS [35] is a public dataset containing about 1000 3D CTA images with coronary artery segmentation labels. HNCTA is a private head and neck artery dataset with 358 CTA images. More details of datasets can be found in supplementary materials.", + "bbox": [ + 89, + 446, + 483, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 89, + 637, + 274, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We assess the segmentation performance in three main aspects following [21]. For volumetric scores, we report Dice [18] and clDice [26] to evaluate the segmentation results. For topology-based scores, absolute Betti Errors for Betti Numbers $\\beta_0$ and $\\beta_{1}$ and absolute error of Euler characteristic are used to measure the topology and completeness of the extracted vessels following [21, 26, 29]. For distance-based scores, Hausdorff Distance (HD) is employed for measuring the maximum distance between two 3D point sets. All presented metrics in this paper are the average of all vessel categories.", + "bbox": [ + 89, + 659, + 482, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the centerline extraction task, we use F1, Hausdorff Distance, Chamfer Distance and absolute Betti Errors for Betti Numbers $\\beta_0$ as evaluation metrics. For robust evaluation, we apply a three-pixel tolerance region around the ground truth centerline points following [8, 29].", + "bbox": [ + 89, + 825, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/48cd18fa65fabd0ff8e115dd9590ea3bb57509a22f34055d7a0c9502f2f090f7.jpg", + "table_caption": [ + "Table 1. Main results on vessel segmentation task. We mark the best performance by bold numbers. Ours (softDice) denotes that we use softDice as base model with the proposed DeformCL as an additional segmentation head." + ], + "table_footnote": [], + "table_body": "
DatasetMethodVolumetric Scores (%) ↑Topological Error ↓Distance ↓
DiceclDiceβ0β1EulerHD95
HaN-SegDDT [31]75.7685.792.3330.1272.3295.473
softDice [18]76.3085.963.3160.0293.2864.905
Ours (softDice)79.58+3.2888.86+2.902.1230.0892.0344.113
clDice [26]76.2286.502.8610.0652.7965.244
Ours (clDice)78.39+2.1787.32+0.822.2070.2262.0423.838
DSCNet [21]77.1684.633.8580.2953.5644.949
Ours (DSCNet)78.61+1.4586.89+2.262.6020.3582.3184.125
HNCTADDT [31]83.5693.280.1720.0500.2192.666
softDice [18]83.0592.140.2860.0590.3372.924
Ours (softDice)84.69+1.6493.72+1.580.1490.0510.1992.084
clDice [26]83.1391.890.1600.0581.2393.118
Ours (clDice)84.13+1.0093.15+1.260.1500.0520.2002.839
DSCNet [21]83.5492.060.2460.0600.3012.658
Ours (DSCNet)84.80+1.2693.82+1.760.1830.0440.2282.349
ASOCADDT [31]83.0089.630.9980.0941.0907.646
softDice [18]84.0689.810.9300.1190.9966.829
Ours (softDice)85.16+1.1092.41+2.600.4080.1290.5105.082
clDice [26]84.0890.921.0090.1221.0826.299
Ours (clDice)84.77+0.6991.94+1.020.6030.1000.6774.122
DSCNet [21]84.2891.040.8400.1460.9275.286
Ours (DSCNet)85.47+1.1992.87+1.830.5080.0830.5905.212
ImageCASDDT [31]87.5195.320.1890.0650.2784.621
softDice [18]87.5995.150.1900.0620.2684.674
Ours (softDice)88.33+0.7495.48+0.330.0740.0650.1593.580
clDice [26]87.7896.000.1580.0640.2384.021
Ours (clDice)87.85+0.0796.01+0.010.1520.0670.2345.038
DSCNet [21]87.9895.340.2130.0700.2833.751
Ours (DSCNet)88.84+0.8696.38+1.040.1270.0690.2153.291
", + "bbox": [ + 516, + 148, + 911, + 492 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2642c83ca2289e56df07a937b3fcbfcb967fd1950f2f2d5d6154453bb0967e37.jpg", + "table_caption": [ + "Table 2. Main results on centerline extraction task." + ], + "table_footnote": [], + "table_body": "
DatasetMethodMetrics
F1 (%)↑HD95 ↓Chamfer ↓β0 ↓
HaN-SegDDT [31]89.657.67818.9573.136
softDice [18]91.176.98119.1114.318
Ours (softDice)94.56+3.394.2506.3321.727
clDice [26]90.789.02329.2173.636
Ours (clDice)92.36+1.585.2207.1301.409
DSCNet [21]90.457.46218.2954.818
Ours (DSCNet)91.50+1.058.22212.3622.773
HNCTADDT [31]97.293.2917.0830.394
softDice [18]97.053.82111.9940.591
Ours (softDice)98.74+1.692.2504.0720.422
clDice [26]96.693.5669.0970.387
Ours (clDice)98.36+1.672.3216.7610.520
DSCNet [21]97.283.3978.4050.534
Ours (DSCNet)98.59+1.312.1453.8290.419
ASOCADDT [31]91.4310.64163.4872.063
softDice [18]91.5711.95646.3581.905
Ours (softDice)95.23+3.667.42329.0270.810
clDice [26]93.439.16829.9711.554
Ours (clDice)94.77+1.347.27317.7380.929
DSCNet [21]93.467.90823.0521.540
Ours (DSCNet)94.28+0.827.05214.7601.000
ImageCASDDT [31]95.104.88119.3760.538
softDice [18]94.407.13430.3450.687
Ours (softDice)96.67+2.275.12717.3130.123
clDice [26]95.785.04319.4900.385
Ours (clDice)96.64+0.864.74314.9410.333
DSCNet [21]95.325.17017.2390.503
Ours (DSCNet)97.28+1.964.30312.1520.318
", + "bbox": [ + 550, + 536, + 864, + 878 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "30901", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8cec88bf16b6180f7df2fe87c1a5ddc725f67cec92f8d01fc1b4df405ec63aca.jpg", + "image_caption": [ + "Figure 6. Visualizations of the predictions from different methods on four 3D medical image datasets. Different rows and columns stand for different datasets and methods respectively. The arrows point out the areas where models easily exhibit errors. Zoom in for more details." + ], + "image_footnote": [], + "bbox": [ + 96, + 90, + 478, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 496, + 307, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In our experiments, we use 3D UNet [3] as the backbone for all methods. We set the number of hierarchical feature maps $m$ to 5. The number of control points $k$ in template generation is set to 4. The number of deformation stages $L$ is 4, and the channel size for point features $C$ is 24. The centerline template of each vessel category is initialized with $N_{c} = 100$ points by default. All of the coordinates of centerline points are normalized to 0-1 in the framework.", + "bbox": [ + 89, + 518, + 482, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "When computing local chamfer distance loss, the number of local patches is sampled from an even distribution $|\\Omega| \\sim U(60,80)$ . The loss weights $\\lambda_{\\mathrm{cha}}$ , $\\lambda_{\\mathrm{sdf}}$ , $\\lambda_{\\mathrm{reg}}$ are set to 30, 0.5, and 60 by default. The balance weights for different deformation stages $\\{w_l\\}_{l=1}^L$ are set to 0.05, 0.60, 0.95, and 1.00. More implementation details are depicted in the supplementary materials.", + "bbox": [ + 89, + 641, + 482, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Main Results", + "text_level": 1, + "bbox": [ + 89, + 757, + 228, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our approach can be incorporated into common segmentation models, such as softmax [18] or clDice [26], as an additional segmentation head. In this subsection, we present the results of our method implemented on softmax [18], clDice [26] and DSCNet [21], comparing it with competitive segmentation models, including softmax [18], cldice [26], DDT [31] and DSCNet [21]. All models are trained under identical settings, including training sched", + "bbox": [ + 89, + 780, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/deb376b81c8c2a600c84047807a84f600fe8dff834ed3caeb4a6b3b99388b253.jpg", + "table_caption": [ + "Table 3. Ablation on the number of control points k for each category of vessels on HaN-Seg dataset." + ], + "table_footnote": [], + "table_body": "
kVolumetric Scores (%) ↑
DiceclDice
078.8786.89
4*79.5888.86
878.3686.88
1677.2285.93
6477.3785.66
", + "bbox": [ + 624, + 121, + 799, + 229 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0bbc290f4615b322b79bd0a17b4ba290220316803e5e32e7b435e1eea5e69d61.jpg", + "table_caption": [ + "Table 4. Ablation on loss functions on HaN-Seg dataset. w/o $\\mathcal{L}_{\\mathrm{cha}}$ means that we use global chamfer distance loss instead of local chamfer distance loss." + ], + "table_footnote": [], + "table_body": "
Loss FunctionVolumetric Scores (%) ↑
DiceclDice
w/o Lcha78.1886.62
w/o Lreg78.3886.70
w/o Lsdf79.5187.89
full configuration79.5888.86
", + "bbox": [ + 584, + 275, + 836, + 369 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ules and hyper-parameters, etc. We have not included PointScatter [29] and Topoloss [9] in the comparison as it is designed for 2D images and is not applicable to 3D medical images due to GPU memory limitations.", + "bbox": [ + 511, + 397, + 906, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For segmentation, our method demonstrates notable performance improvements when integrated with baseline models as depicted in Table 1. The enhancement is particularly prominent in metrics like cDice and Betti number errors, which primarily reflect vessel completeness and topology correctness. This phenomenon verifies the effectiveness of the continuously defined representation. Furthermore, thanks to the exact prediction of centerlines, the performance of segmentation on the distance metric HD95 has also improved a lot.", + "bbox": [ + 511, + 458, + 905, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For centerline extraction, we present the experimental results on HaN-Seg and ASOCA datasets in Table 2. It can be concluded that DeformCL can improve a range of metrics consistently across multiple baseline models. More experiments can be found in supplementary materials.", + "bbox": [ + 511, + 609, + 905, + 684 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To provide a qualitative assessment of the model performance, we present visualizations of predictions from different methods in Figure 6. These results illustrate that DeformCL effectively captures thin and fragile structures with minimal segmentation fractures. Moreover, the reduction in scattered false positives demonstrates the noise robustness of DeformCL. These results reaffirm that the continuously defined representation offers superior capabilities in curvilinear vessel extraction, owing to its unique properties.", + "bbox": [ + 511, + 685, + 905, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 832, + 666, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct ablation experiments on the HaN-Seg dataset to assess the impact of different components of our method. Other ablation studies are presented in the supplementary", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "30902", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/446a79d30aa43cae1446575c9d97cd66f5ff22d613b7db4576bd7fb37ea932a6.jpg", + "image_caption": [ + "Figure 7. Visual comparison of different loss function configurations. The carnatio masks and yellow lines denote the predicted segmentations and centerlines respectively. The red and green triangles point out the areas to focus on." + ], + "image_footnote": [], + "bbox": [ + 114, + 89, + 460, + 262 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "materials.", + "bbox": [ + 89, + 359, + 158, + 372 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Template Selection. We compare the performance of different template selection strategies in Table 3. $k = 0$ means that we use a straight centerline as the initial template without considering image information. It can be found that adaptive template generation outperforms fixed initial templates $(k = 0)$ . Furthermore, we observe a gradual decline in performance as the number of control points $k$ increases from 4 to 64. We guess that more control points lead to overly accurate initial templates, thus reducing the difficulty and complexity of the deformation task. Consequently, the model may not be sufficiently trained. Therefore, we adopt a rough initial template with $k = 4$ .", + "bbox": [ + 89, + 378, + 483, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Loss Function. We evaluate the effectiveness of different loss functions in Table 4 and Figure 7. It is observed from the results in the table that local chamfer distance loss outperforms global chamfer distance loss, particularly in terms of cldice. We empirically find that the global chamfer distance loss will result in larger fluctuations during training process compared with the local version. The reason is that the tubular structures in human body usually have complex global morphology and sparse 3D distribution, which means that conducting global calculations will have more fluctuations.", + "bbox": [ + 89, + 564, + 483, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although the gains from SDF loss and regularization loss are not as pronounced in the numerical results, visualization comparison in the figure reveal that these losses contribute to more accurate centerline predictions. For instance, without regularization loss, the centerline prediction may be sparse and deviated in local regions, due to the long edges between adjacent vertices. In addition, adding SDF loss augments the centrality of centerline predictions. These properties are significant for the subsequent tasks, such as curved planar reformation [11]. In summary, the full configurations of loss functions achieve the best performance.", + "bbox": [ + 89, + 734, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a0bd91ace274e6390623695c0c1057568f6dc39fc3b460ee52fa6cb6775a4739.jpg", + "image_caption": [ + "Figure 8. Visual comparison of SCPR images reconstructed from the predictions of UNet and DeformCL. Red triangles indicate the regions where the vessel predictions by UNet are not correct, resulting in severe errors on SCPR images, while green ones indicate improved results from our DeformCL. Cyan arrows indicate the areas with plaque and stenosis needing additional clinical diagnosis." + ], + "image_footnote": [], + "bbox": [ + 531, + 89, + 893, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Clinical Significance", + "text_level": 1, + "bbox": [ + 511, + 325, + 705, + 342 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In clinical practice, the generation of straightened curved planar reformation [11] (SCPR) images is vital for radiologists to conduct accurate diagnoses for blood vessels, especially for observing possible plaques and stenosis. High-quality SCPR images require high-quality vessel graphical structures (directional centerlines) that meet the criteria of completeness, smoothness, and centrality. Previous methods often rely on converting discrete segmentation masks into continuous centerlines using traditional tools [10, 19], which may be susceptible to imperfect segmentation predictions. Moreover, this conversion process is complex and time-consuming. In contrast, our DeformCL can directly generate continuous centerlines during model inference without the need for any post-processing.", + "bbox": [ + 511, + 348, + 906, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As depicted in Figure 8, we compare the SCPR images reconstructed from the predictions of UNet and DeformCL. It is evident that the SCPR images generated from UNet exhibit severe bending and breaking, indicated by red arrows, which could hinder plaque diagnosis. These inaccuracies stem from the segmentation masks being fragmented by UNet in fragile regions, potentially containing plaques and stenosis. In contrast, DeformCL produces high-quality SCPR images that reveal diseased regions comprehensively and clearly. These visualizations underscore the potential of DeformCL in assisting the clinical diagnosis process.", + "bbox": [ + 511, + 559, + 908, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 511, + 739, + 640, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose DeformCL, a novel continuously defined representation for 3D vessel segmentation. To fully leverage the advantages of DeformCL, we introduce a cascaded deformation process based on an adaptive template generation strategy. Through this comprehensive training framework, DeformCL demonstrates clear superiority over previous methods. The visualizations highlight DeformCL's potential in generating CPR images for clinical diagnosis, especially for patients with severe stenosis.", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "30903", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported by National Science and Technology Major Project (2022ZD0114902) and National Science Foundation of China (NSFC92470123, NSFC62276005).", + "bbox": [ + 89, + 90, + 485, + 151 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 164, + 187, + 179 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ricardo J Araujo, Jaime S Cardoso, and Helder P Oliveira. Topological similarity index and loss function for blood vessel segmentation. arXiv preprint arXiv:2107.14531, 2021. 1, 2, 3", + "[2] Fabian Bongratz, Anne-Marie Rickmann, Sebastian Pölsterl, and Christian Wachinger. Vox2cortex: fast explicit reconstruction of cortical surfaces from 3d mri scans with geometric deep neural networks. 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Voxel2mesh: 3d mesh model generation from volumetric data. In Medical Image Computing and Computer Assisted Intervention-MICCAI 2020: 23rd International Conference, Lima, Peru, October 4-8, 2020, Proceedings, Part IV 23, pages 299-308. Springer, 2020. 3, 4", + "[33] Qian Wu, Yufei Chen, Wei Liu, Xiaodong Yue, and Xiahai Zhuang. Deep closing: Enhancing topological connectivity in medical tubular segmentation. IEEE Transactions on Medical Imaging, 2024. 2", + "[34] Jiancheng Yang, Udaranga Wickramasinghe, Bingbing Ni, and Pascal Fua. Implicitatlas: learning deformable shape templates in medical imaging. In Proceedings of the" + ], + "bbox": [ + 91, + 90, + 480, + 901 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15861-15871, 2022. 3", + "[35] An Zeng, Chunbiao Wu, Guisen Lin, Wen Xie, Jin Hong, Meiping Huang, Jian Zhuang, Shanshan Bi, Dan Pan, Najeeb Ullah, et al. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 3" + ], + "bbox": [ + 516, + 92, + 903, + 654 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "30905", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/3df80607-397e-48ec-af7c-1eb858969941_model.json b/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/3df80607-397e-48ec-af7c-1eb858969941_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5f03447220d8b3445988c31c97c9592cb951fed4 --- /dev/null +++ b/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/3df80607-397e-48ec-af7c-1eb858969941_model.json @@ -0,0 +1,2167 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.13, + 0.856, + 0.175 + ], + "angle": 0, + "content": "DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image" + }, + { + "type": "text", + "bbox": [ + 0.25, + 0.203, + 0.765, + 0.24 + ], + "angle": 0, + "content": "Ziwei Zhao\\(^{1*}\\) Zhixing Zhang\\(^{2,5*}\\) Yuhang Liu\\(^{1\\dagger}\\) Zhao Zhang\\(^{2}\\) Haojun Yu\\(^{4}\\) Dong Wang\\(^{1}\\) Liwei Wang\\(^{3,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.251, + 0.24, + 0.76, + 0.257 + ], + "angle": 0, + "content": "1Zihun Medical AI Co., Ltd 2Center for Data Science, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.258, + 0.704, + 0.275 + ], + "angle": 0, + "content": "3Center for Machine Learning Research, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.276, + 0.911, + 0.293 + ], + "angle": 0, + "content": "\\(^{4}\\)State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.294, + 0.293, + 0.718, + 0.31 + ], + "angle": 0, + "content": "\\(^{5}\\)Pazhou Laboratory (Huangpu), Guangzhou, Guangdong, China" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.313, + 0.725, + 0.328 + ], + "angle": 0, + "content": "{ziwei.zhao, yuhang.liu, dong.wang}@yzhun-ai.com" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.33, + 0.778, + 0.345 + ], + "angle": 0, + "content": "{zhangzhixing@stu., zhangzh@stu., haojunyu@, wanglw@}pku.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.38, + 0.327, + 0.396 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.412, + 0.486, + 0.73 + ], + "angle": 0, + "content": "In the field of 3D medical imaging, accurately extracting and representing the blood vessels with curvilinear structures holds paramount importance for clinical diagnosis. Previous methods have commonly relied on discrete representation like mask, often resulting in local fractures or scattered fragments due to the inherent limitations of the per-pixel classification paradigm. In this work, we introduce DeformCL, a new continuous representation based on Deformable Centerlines, where centerline points act as nodes connected by edges that capture spatial relationships. Compared with previous representations, DeformCL offers three key advantages: natural connectivity, noise robustness, and interaction facility. We present a comprehensive training pipeline structured in a cascaded manner to fully exploit these favorable properties of DeformCL. Extensive experiments on four 3D vessel segmentation datasets demonstrate the effectiveness and superiority of our method. Furthermore, the visualization of curved planar reformation images validates the clinical significance of the proposed framework. We release the code in https://github.com/barry664/DeformCL." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.761, + 0.222, + 0.777 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.787, + 0.485, + 0.864 + ], + "angle": 0, + "content": "Cerebro-cardiovascular disease is one of the most severe global health threats [22]. Timely detection of potential high-risk locations and prompt intervention are crucial to reducing mortality, relying on accurate extraction, reconstruction, and analysis of major vessels in CTA images [16]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.381, + 0.907, + 0.442 + ], + "angle": 0, + "content": "In clinical practice, the primary requirement is to achieve accurate segmentation of primary vessel branches to enable comprehensive vascular system assessment and detailed local analysis." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.445, + 0.909, + 0.838 + ], + "angle": 0, + "content": "Previous methodologies [1, 21, 25, 26, 29, 31] have predominantly adopted the traditional semantic segmentation approach, which relies on fine-grained, per-pixel classification within a discrete mask representation. As illustrated in the top part of Figure 1, to improve the volumetric scores (e.g. Dice) or topological metrics (e.g. betti number errors) for segmentation, these approaches introduce a variety of innovations, such as incorporating tubular priors into network architecture [13, 21, 25, 31, 36, 39] or designing topology-preserving loss functions [1, 9, 26]. Despite these advancements in the training process, the core issue that the discrete mask representation is not well-suited for the curvilinear vessels remains unchanged, imposing several inherent limitations that restrict the model's performance and applicability, as shown in the top part of Figure 2. Firstly, the neural networks struggle to recognize fragile and tortuous local structures, which may lead to segmentation fractures [21]. Moreover, the discrete representation exhibits poor robustness to local noise [26, 29], such as variations in tissue density, due to the lack of a holistic view of the global morphology. Consequently, it may mistakenly identify the tissues with appearances similar to target vessels. Finally, designing an effective feature aggregation strategy along tubular curves remains challenging, considering the lack of explicit relationships among elements in discrete mask representations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "These challenges motivate us to seek a continuous representation that can explicitly fit the tubular structures from a holistic view, rather than confined to per-pixel classification paradigm. In this paper, we introduce DeformCL," + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.22, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.185, + 0.9 + ], + "angle": 0, + "content": "†Project lead." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "30896" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.26, + 0.908, + 0.331 + ], + "angle": 0, + "content": "Figure 1. Previous methods [1, 21, 26, 29, 31] primarily rely on the discrete mask representation, adopting a per-pixel classification paradigm for vessel segmentation. Common techniques in these approaches include incorporating tubular priors and applying topology-preserving loss functions. In contrast, we introduce a new continuous representation, DeformCL, which employs centerline points connected by edges to gradually fit the curvilinear vessels via a template deformation process. Once structured centerlines are obtained, generating segmentation predictions with improved topological accuracy becomes a straightforward task." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.359, + 0.486, + 0.601 + ], + "angle": 0, + "content": "a new representation for vessel extraction in 3D medical image based on Deformable Centerline. As shown in the bottom part of Figure 1, DeformCL employs a graph structure, wherein centerline points serve as nodes connected by edges representing their spatial relationships. This continuously defined representation accurately depicts the curvilinear structures, thus circumventing the drawbacks of discrete mask representation and has its own merits: (1) the incorporation of natural connectivity mitigates centerline ruptures, particularly in the thin and fragile areas; (2) by considering the entire curvilinear structures rather than local pixels, DeformCL ensures a comprehensive understanding of the global morphology, thus reducing local artifacts and false positives; (3) the inherent graph structure facilitates efficient and effective feature aggregation along the tubular curves, enhancing overall segmentation performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.607, + 0.485, + 0.865 + ], + "angle": 0, + "content": "We propose a novel framework to learn deformable centerline representation from 3D medical images. Our framework consists of several key steps. Firstly, we adaptively generate an initial continuous centerline template based on the input image, taking anatomical variations among different individuals into account. Next, the centerline points within the template will interact with each other to capture features along tubular curves. The whole centerline template will be iteratively refined by deformation and unpooling layers, gradually aligning with the ground truth centerlines. Finally, after obtaining precise centerlines of tubular structures, crafting a high-quality segmentation algorithm becomes a straightforward task. In our approach, we leverage the distance map derived from the predicted centerline points to execute the final segmentation process effortlessly. Benefiting from the high-quality continuous centerlines, the segmentation performance is improved significantly." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.485, + 0.903 + ], + "angle": 0, + "content": "We benchmark DeformCL on four 3D medical datasets, and the extensive experiments validate the effectiveness of" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.358, + 0.907, + 0.51 + ], + "angle": 0, + "content": "our proposed method. Additionally, due to its continuous nature, DeformCL's centerline predictions can be directly used as a structural representation of vessels, commonly as directional centerlines [10, 24]. This structural representation is crucial in clinical practice, serving as an indispensable component in various subsequent diagnostic tasks, such as curved planar reformation [11] and computational hemodynamics [27]. We qualitatively demonstrate the clinical relevance of DeformCL, highlighting its potential applicability for diagnostic purposes." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.51, + 0.871, + 0.523 + ], + "angle": 0, + "content": "In summary, our main contributions are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.524, + 0.906, + 0.569 + ], + "angle": 0, + "content": "- We introduce a continuous representation, called DeformCL, which possesses several favorable properties for curvilinear vessels in 3D medical image." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.57, + 0.907, + 0.613 + ], + "angle": 0, + "content": "- We propose a comprehensive pipeline for effectively training DeformCL through a cascaded deformation process." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.615, + 0.907, + 0.645 + ], + "angle": 0, + "content": "- Our approach significantly bolsters the performance of several baselines on four 3D vessel extraction datasets." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.524, + 0.907, + 0.645 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.658, + 0.657, + 0.673 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.683, + 0.871, + 0.699 + ], + "angle": 0, + "content": "2.1. Vessel Segmentation in 3D Medical Image" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Vessel segmentation in 3D medical image is a crucial task due to the prevalence of curvilinear vessels in the human body. Classical modern segmentation models like UNet [3, 23] and FCN [17] face challenges in accurately extracting tubular structures due to their complex global morphology and fragile thin structures. Previous methods have adopted various strategies to address these challenges: incorporate tubular priors into network architecture [14, 21, 25, 31, 33, 36, 39], design topology-preserving loss functions [1, 9, 26] or employ more flexible representation [29, 38]. Shit et al. [26] introduces a new connectivity-aware similarity measure called clDice, and the differentiable version can be used to train segmentation models for" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "30897" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.182 + ], + "angle": 0, + "content": "tubular structures. Qi et al. [21] proposes a dynamic snake convolution to let networks adaptively focus on the tubular structures and make more accurate predictions. Wang et al. [29] relies on the flexibility of point set representation which is not restricted to a fixed grid to promote the performance of tubular structure extraction." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.191, + 0.299, + 0.208 + ], + "angle": 0, + "content": "2.2. Deformable Paradigm" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.213, + 0.485, + 0.546 + ], + "angle": 0, + "content": "The deformable paradigm is a widely used technique in deep learning, particularly in computer vision, where it plays a crucial role in capturing complex structures and achieving significant advancements in various tasks. Introduced by Dai et al. [4], deformable convolution extends traditional convolutions to capture complex structures effectively. It has been successfully applied in tasks such as object detection and segmentation, allowing models to adapt to object variations and complex shapes. Deformable DETR [41] combines attention mechanism with deformable paradigm for efficient feature extraction process. In addition, deformable structures have also found applications in 3D reconstruction tasks [2, 14, 30, 32, 34, 40]. For instance, Pixel2Mesh [30] generates 3D shapes represented as triangular meshes from single images by progressively deforming an initial ellipsoid. Similarly, Voxel2Mesh [32] extends this approach to generate organ surfaces from 3D medical volumes, facilitating organ segmentation and visualization. Kong et al. [14] proposed a deep-learning approach to generate whole heart geometries from pre-defined mesh templates, demonstrating the versatility of deformable structures in human anatomical modeling." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.558, + 0.184, + 0.573 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.484, + 0.66 + ], + "angle": 0, + "content": "In this section, we will first introduce the new representation DeformCL and its favorable properties in Sec 3.1. Sec 3.2 elaborates on the network architecture for learning deformation centerline representation from 3D medical images. Sec 3.3 presents the training losses for the framework." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.668, + 0.353, + 0.684 + ], + "angle": 0, + "content": "3.1. Representation of DeformCL" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.484, + 0.81 + ], + "angle": 0, + "content": "In 3D medical imaging, a common representation of a given volume \\( I \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}} \\) is its segmentation mask, denoted as \\( Y \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}} \\). Nearly all previous methods [1, 21, 25, 26, 29, 31] rely on this discrete mask representation, framing the task as per-pixel classification. This paradigm inherently possesses several limitations, as illustrated in the top part of Figure 2, which ultimately restrict the model's performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.903 + ], + "angle": 0, + "content": "In this paper, we introduce a novel continuous representation called Deformable CenterLine (DeformCL) to efficiently and effectively capture tubular structures in 3D medical image. Instead of relying on segmentation mask, we represent tubular structures using a graph \\(\\mathcal{G} = \\{\\mathcal{V},\\epsilon \\}\\), where \\(\\mathcal{V} = \\{v_{i}|v_{i}\\in \\mathbb{R}^{3}\\}_{i = 1}^{N}\\) is a set of \\(N\\) vertices standing" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.092, + 0.883, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.199, + 0.907, + 0.227 + ], + "angle": 0, + "content": "Figure 2. Three significant properties of DeformCL compared with the discrete mask representation. (Zoom in for more details.)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.257, + 0.905, + 0.289 + ], + "angle": 0, + "content": "for centerline points, \\(\\epsilon = \\{(k,w)|1\\leq k,w\\leq N\\}\\) is the set of edges connecting adjacent vertices." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.289, + 0.905, + 0.349 + ], + "angle": 0, + "content": "As shown in the bottom part of Figure 2, compared with previous discrete representations, DeformCL possesses several favorable properties, making it a reasonable and effective representation for tubular structure modeling." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.35, + 0.906, + 0.486 + ], + "angle": 0, + "content": "Natural connectivity. Unlike traditional discrete representations, DeformCL naturally exhibits the connectivity among centerline points, which explicitly models the tubular structures in a continuously defined way. On one hand, this continuous representation helps prevent predictions from breaking in thin and fragile regions. On the other hand, the traditionally complex and time-consuming continuous centerlines extraction [10, 19] from segmentation for curved planner reconstruction [11] is eliminated." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.487, + 0.906, + 0.593 + ], + "angle": 0, + "content": "Noise robustness. Thanks to its top-down manner, DeformCL exhibits robustness to noise and local disturbances, such as variations in tissue density or the presence of contrast agents. This inherent property enables DeformCL to effectively filter out local artifacts and false positives, leading to more accurate and reliable tubular structure extraction compared to previous bottom-up methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.594, + 0.906, + 0.715 + ], + "angle": 0, + "content": "Interaction facility. Constrained by the discrete representation, previous methods [21, 26, 29, 31] lack of an effective approach for tubular feature aggregation. On the contrary, DeformCL's graph structure facilitates feature fusion process via methods like GCN [12] or Transformer [28] along the tubular curve. This global information interaction is significant for the structure completeness and topology correctness of tubular predictions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.726, + 0.72, + 0.74 + ], + "angle": 0, + "content": "3.2. Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.906, + 0.87 + ], + "angle": 0, + "content": "In this subsection, we will introduce the network architecture for learning deformable centerline representation. The whole framework is shown in Figure 3. Given a 3D medical image \\(I \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}\\), we first pass it through a 3D backbone (e.g. 3D UNet [3]) to obtain hierarchical feature maps \\(\\{F_i\\}_{i=1}^m\\) at different down-sampled rates. Additionally, the backbone network produces a coarse segmentation result \\(\\hat{Y}_c \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}\\) for each category of vessels." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Adaptive Template Generation. In order to initialize the graph structure of DeformCL, we attempt to initial-" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30898" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.093, + 0.862, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.409, + 0.908, + 0.482 + ], + "angle": 0, + "content": "Figure 3. Overview of the training process. Given a 3D medical image, the segmentation network first outputs a coarse prediction and generates hierarchical downsampled feature maps. An initial template, produced by the Adaptive Template Generation module, is then iteratively fed through deformation and unpooling layers to progressively adapt to the curvilinear structures. Finally, refined segmentation results are generated based on the accurately aligned continuous centerlines. We apply Dice loss to both the coarse and refined segmentation predictions, and local chamfer loss, SDF loss, and regularization loss for centerline predictions." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.509, + 0.483, + 0.629 + ], + "angle": 0, + "content": "ize a tubular template motivated by mesh generation methods [30, 32]. However, unlike human organs, tubular structures in 3D medical image, such as coronary arteries, exhibit complex global morphology and variable extension direction, which means that discovering a universal template for such structures poses significant challenges. Therefore, we introduce a new method to adaptively generate initial templates for each image." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.63, + 0.483, + 0.841 + ], + "angle": 0, + "content": "The template generation process, illustrated in the Figure 4, is conducted independently for each category of vessels. Firstly, the coarse segmentation result \\(\\hat{Y}_c\\) is converted into discrete centerline points via traditional 3D thinning algorithm [15]. These points are then reconstructed into a graph using the minimum spanning tree algorithm [7] following the strategy in [37]. Next, a set of \\(k\\) control points is selected from the graph at fixed distances, serving as the abstraction of the structure. Finally, curvilinear interpolation (e.g. Bezier Curve Interpolation, Linear Interpolation) is applied based on the control points to generate the initial template, denoted as \\(\\{v_i^c | v_i^c \\in \\mathbb{R}^3\\}_{i=1}^{N_c}\\). Here, \\(v_i^c\\) represents the \\(i\\)-th point for category \\(c\\), \\(N_c\\) is the total number of points for category \\(c\\), and \\(v_i^c\\) is connected with \\(v_{i+1}^c\\) by default." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.484, + 0.902 + ], + "angle": 0, + "content": "It is worth noting that we adopt a rough template generation strategy using control points instead of directly utilizing the reconstructed tree as the initial template. The reason is that we empirically find overly accurate initial templates" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.509, + 0.905, + 0.569 + ], + "angle": 0, + "content": "may harm model performance, supported by experimental results shown in Table 3. We speculate that overly accurate initial templates may simplify the deformation task excessively, potentially leading to insufficient model training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.57, + 0.906, + 0.646 + ], + "angle": 0, + "content": "Cascaded Deformation Process. After the generation of initial templates, we proceed with the cascaded deformation process to refine the centerline predictions. For clarity, we focus on the centerline points of one category of vessels in the subsequent sections of the paper." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.646, + 0.906, + 0.692 + ], + "angle": 0, + "content": "Firstly, trilinear interpolation is applied to each centerline point \\( v_{i} \\) in the downsampled feature maps \\( \\{F_i\\}_{i = 1}^m \\), and the hierarchical points features are fused via a linear layer:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.704, + 0.905, + 0.722 + ], + "angle": 0, + "content": "\\[\nf \\left(v _ {i}\\right) = \\operatorname {L i n e a r} \\left(\\left[ \\operatorname {T r i} \\left(F _ {1}, v _ {i}\\right), \\dots , \\operatorname {T r i} \\left(F _ {m}, v _ {i}\\right) \\right]\\right) \\in \\mathbb {R} ^ {C}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.734, + 0.906, + 0.871 + ], + "angle": 0, + "content": "where \\(C\\) denotes the channel size, Tri represents the tri-linear interpolation. Next, the points and their corresponding features \\(\\{v_{i},f(v_{i})\\}\\) are fed into Transformer [28] layers for feature aggregation along the tubular curve. The positional encoding \\(\\mathrm{Pos}(v^l)\\) contains learnable embeddings of absolute 3D positions of points and relative positions in the graph. Subsequently, the augmented point features are used to predict an offset \\(\\delta_i^l\\), which is then applied to update the position of each point \\(v_{i}^{l}\\) to obtain \\(v_{i}^{l + 1}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Since high-accuracy centerlines require a sufficient number of points to capture curvilinear structures accurately, we" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30899" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.09, + 0.478, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.164, + 0.155, + 0.411, + 0.171 + ], + "angle": 0, + "content": "Figure 4. Adaptive Template Generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.198, + 0.484, + 0.287 + ], + "angle": 0, + "content": "apply an unpooling strategy after deformation to increase point density. Specifically, a new point is inserted between each pair of connected points. We reuse the symbol \\(\\{v_i^{l + 1}\\}\\) for clarity. This process is iterated \\(L\\) times for accurate centerline prediction, where the \\(l\\)-th layer is described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.296, + 0.482, + 0.316 + ], + "angle": 0, + "content": "\\[\n\\tilde {f} \\left(v _ {i} ^ {l}\\right) = f \\left(v _ {i} ^ {l}\\right) + \\operatorname {T r a n s f o r m e r} \\left(f \\left(v ^ {l}\\right), \\operatorname {P o s} \\left(v ^ {l}\\right)\\right) \\in \\mathbb {R} ^ {C}, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.318, + 0.483, + 0.337 + ], + "angle": 0, + "content": "\\[\n\\delta_ {i} ^ {l} = \\operatorname {T a n h} \\left(\\mathrm {M L P} \\left(\\tilde {f} \\left(v _ {i} ^ {l}\\right)\\right)\\right) \\in \\mathbb {R} ^ {3}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.339, + 0.483, + 0.358 + ], + "angle": 0, + "content": "\\[\nv _ {i} ^ {l + 1} = v _ {i} ^ {l} + \\delta_ {i} ^ {l} \\in \\mathbb {R} ^ {3}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.36, + 0.483, + 0.38 + ], + "angle": 0, + "content": "\\[\n\\left\\{v _ {i} ^ {l + 1} \\right\\} = \\text {U n p o o l i n g} \\left(\\left\\{v _ {i} ^ {l + 1} \\right\\}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.389, + 0.484, + 0.448 + ], + "angle": 0, + "content": "After completing the cascaded deformation process, the final set of points \\(\\{v_i^L\\}\\) represents the predicted centerline points, which will be used for subsequent centerline-based segmentation task." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.45, + 0.484, + 0.571 + ], + "angle": 0, + "content": "Centerline-based Segmentation. Once accurate centerlines of tubular structures are obtained, predicting the corresponding segmentation results becomes straightforward. In this work, we employ a simple method using distance maps to achieve centerline-based segmentation. Specifically, given the predicted centerline points \\( V = \\{v_{i}^{L}\\in \\mathbb{R}^{3}\\} \\), we calculate the minimum distance of each voxel in the image to the points in \\( V \\):" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.584, + 0.483, + 0.607 + ], + "angle": 0, + "content": "\\[\nD [ x, y, z ] = \\min _ {v \\in V} | | (x, y, z) - v | | _ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.484, + 0.675 + ], + "angle": 0, + "content": "where \\(D \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{D} \\times \\mathbb{W}}\\) is the distance map based on the centerline points. Finally, the coarse segmentation results \\(\\hat{Y}_c\\) and the distance map \\(D\\) are input to a convolutional layer for fusion, yielding the refined segmentation results \\(\\hat{Y}_r\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.682, + 0.235, + 0.699 + ], + "angle": 0, + "content": "3.3. Training Loss" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.484, + 0.78 + ], + "angle": 0, + "content": "In this subsection, we will elaborate on the loss functions of the proposed framework. For centerline prediction, we employ a combination of local chamfer distance loss, signed distance function (SDF) loss, and a regularization loss. We utilize Dice loss for segmentation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.484, + 0.9 + ], + "angle": 0, + "content": "Local Chamfer Distance Loss. Tradition global chamfer distance loss calculates the distance between two point cloud sets. However, curvilinear vessels in the human body often exhibit complex global morphology and sparse 3D distribution. As a result, using global chamfer distance loss may lead to larger fluctuations and suboptimal convergence during the training process. To address this issue, we adopt a local version of chamfer distance loss." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.273 + ], + "angle": 0, + "content": "To be specific, we begin by employing Farthest Point Sampling (FPS) to select candidate points \\(\\{u_{i_k}\\}\\) from the ground truth centerline points \\(\\{u_i\\}\\), which are obtained from the ground truth mask via traditional 3D thinning algorithm [15]. Then, we crop local patches with fixed size \\(M\\) centered around each selected point \\(\\{u_{i_k}\\}\\). The points located within each cropped patch are denoted as \\(\\omega_{i_k} = \\{p = (x,y,z)|p\\in [u_{i_k} - M / 2,u_{i_k} + M / 2]\\}\\), and the set of patches is denoted as \\(\\Omega = \\{\\omega_{i_k}\\}\\). The chamfer distance loss is then applied between the predicted point set and the ground truth point set within each cropped patch. Formally, the loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.293, + 0.913, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c h a}} = \\frac {1}{| \\Omega |} \\sum_ {\\omega \\in \\Omega} \\left(\\sum_ {v _ {i} \\in \\omega} \\min _ {u _ {i} \\in \\omega} \\| v _ {i} - u _ {i} \\| _ {2} ^ {2} + \\sum_ {u _ {i} \\in \\omega} \\min _ {v _ {i} \\in \\omega} \\| u _ {i} - v _ {i} \\| _ {2} ^ {2}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.342, + 0.907, + 0.448 + ], + "angle": 0, + "content": "SDF Loss. Signed Distance Function (SDF) is a well-established concept in computer vision and computer graphics, used to represent the surface of 3D objects through signed distances. We find that SDF is appropriate for ensuring the centrality of predicted centerline points. Firstly, we define the surface of tubular strcutures following [31]:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.456, + 0.905, + 0.475 + ], + "angle": 0, + "content": "\\[\nS = \\{x \\in \\mathbb {R} ^ {3} | Y [ x ] = 1, \\exists u \\in \\mathcal {N} (x), Y [ u ] = 0 \\}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.482, + 0.906, + 0.528 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}(x)\\) denotes the 6-neightbour voxels of \\(x\\), \\(Y\\) is the ground truth mask. Then, the SDF value of an arbitrary point \\(p\\) in the image can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.536, + 0.905, + 0.58 + ], + "angle": 0, + "content": "\\[\nS D F (p) = \\left\\{ \\begin{array}{l l} - \\min _ {u \\in S} | | p - u | | _ {2} ^ {2}, & \\text {i f} Y [ p ] = 1, \\\\ \\min _ {u \\in S} | | p - u | | _ {2} ^ {2}, & \\text {i f} Y [ p ] = 0. \\end{array} \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.587, + 0.906, + 0.618 + ], + "angle": 0, + "content": "The SDF values of all predicted centerline points are utilized as the training loss:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.626, + 0.905, + 0.667 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s d f}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} S D F (v _ {i}). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.675, + 0.669, + 0.794 + ], + "angle": 0, + "content": "As illustrated in Figure 5, SDF loss serves two crucial purposes. Firstly, it provides supervision for all predicted centerline points, whereas the local chamfer" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.678, + 0.905, + 0.774 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.739, + 0.776, + 0.863, + 0.79 + ], + "angle": 0, + "content": "Figure 5. SDF Loss." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.906, + 0.87 + ], + "angle": 0, + "content": "distance loss can only provide supervision for points within cropped patches, potentially missing outlier predictions. Secondly, it facilitates the gradual deformation of predicted points towards the ideal center of tubular structures, thereby ensuring the centrality of centerlines." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Regularization Loss. To prevent the deformable centerline points from deviating mistakenly, which may result in long" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "30900" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.123 + ], + "angle": 0, + "content": "edges between adjacent vertices, we apply a regularization loss to penalize the adjacent points with much long edges:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.13, + 0.483, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left| \\left| v _ {i} - v _ {i - 1} \\right| \\right| _ {2} ^ {2}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.18, + 0.483, + 0.21 + ], + "angle": 0, + "content": "Segmentation Loss. We use Dice loss [18] as loss function for the coarse and refined segmentation results \\(\\hat{Y}_c\\) and \\(\\hat{Y}_r\\):" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.217, + 0.483, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s e g}} = \\lambda \\operatorname {D i c e} \\left(Y, \\hat {Y} _ {c}\\right) + \\operatorname {D i c e} \\left(Y, \\hat {Y} _ {r}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.244, + 0.232, + 0.257 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is set to 0.2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.259, + 0.484, + 0.318 + ], + "angle": 0, + "content": "Note that local chamfer distance loss, SDF loss and regularization loss are applied to all intermediate results in the cascaded deformation process. The total training loss is a combination of all loss functions:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.325, + 0.483, + 0.367 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum_ {l = 1} ^ {L} w _ {l} \\left(\\lambda_ {\\mathrm {c h a}} \\mathcal {L} _ {\\mathrm {c h a}} + \\lambda_ {\\mathrm {s d f}} \\mathcal {L} _ {\\mathrm {s d f}} + \\lambda_ {\\mathrm {r e g}} \\mathcal {L} _ {\\mathrm {r e g}}\\right) + \\mathcal {L} _ {\\mathrm {s e g}}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.374, + 0.447, + 0.389 + ], + "angle": 0, + "content": "\\(w_{l}\\) stands for the weight of the \\(l\\)-th deformation stage." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.401, + 0.224, + 0.418 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.426, + 0.194, + 0.44 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.484, + 0.63 + ], + "angle": 0, + "content": "We use four datasets to evaluate our proposed framework. HaN-Seg [20] is a public dataset consisting of 56 CT and MR images with 30 categories of head and neck organ pixel annotations. ASOCA [5, 6] is a public dataset in the MICCAI-2020 challenge which aims to automatically segment the coronary artery lumen. It consists of 40 Cardiac Computed Tomography Angiography (CCTA) images with artery segmentation annotations. ImageCAS [35] is a public dataset containing about 1000 3D CTA images with coronary artery segmentation labels. HNCTA is a private head and neck artery dataset with 358 CTA images. More details of datasets can be found in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.638, + 0.275, + 0.652 + ], + "angle": 0, + "content": "4.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.483, + 0.825 + ], + "angle": 0, + "content": "We assess the segmentation performance in three main aspects following [21]. For volumetric scores, we report Dice [18] and clDice [26] to evaluate the segmentation results. For topology-based scores, absolute Betti Errors for Betti Numbers \\(\\beta_0\\) and \\(\\beta_{1}\\) and absolute error of Euler characteristic are used to measure the topology and completeness of the extracted vessels following [21, 26, 29]. For distance-based scores, Hausdorff Distance (HD) is employed for measuring the maximum distance between two 3D point sets. All presented metrics in this paper are the average of all vessel categories." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.902 + ], + "angle": 0, + "content": "For the centerline extraction task, we use F1, Hausdorff Distance, Chamfer Distance and absolute Betti Errors for Betti Numbers \\(\\beta_0\\) as evaluation metrics. For robust evaluation, we apply a three-pixel tolerance region around the ground truth centerline points following [8, 29]." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.146 + ], + "angle": 0, + "content": "Table 1. Main results on vessel segmentation task. We mark the best performance by bold numbers. Ours (softDice) denotes that we use softDice as base model with the proposed DeformCL as an additional segmentation head." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.15, + 0.912, + 0.493 + ], + "angle": 0, + "content": "
DatasetMethodVolumetric Scores (%) ↑Topological Error ↓Distance ↓
DiceclDiceβ0β1EulerHD95
HaN-SegDDT [31]75.7685.792.3330.1272.3295.473
softDice [18]76.3085.963.3160.0293.2864.905
Ours (softDice)79.58+3.2888.86+2.902.1230.0892.0344.113
clDice [26]76.2286.502.8610.0652.7965.244
Ours (clDice)78.39+2.1787.32+0.822.2070.2262.0423.838
DSCNet [21]77.1684.633.8580.2953.5644.949
Ours (DSCNet)78.61+1.4586.89+2.262.6020.3582.3184.125
HNCTADDT [31]83.5693.280.1720.0500.2192.666
softDice [18]83.0592.140.2860.0590.3372.924
Ours (softDice)84.69+1.6493.72+1.580.1490.0510.1992.084
clDice [26]83.1391.890.1600.0581.2393.118
Ours (clDice)84.13+1.0093.15+1.260.1500.0520.2002.839
DSCNet [21]83.5492.060.2460.0600.3012.658
Ours (DSCNet)84.80+1.2693.82+1.760.1830.0440.2282.349
ASOCADDT [31]83.0089.630.9980.0941.0907.646
softDice [18]84.0689.810.9300.1190.9966.829
Ours (softDice)85.16+1.1092.41+2.600.4080.1290.5105.082
clDice [26]84.0890.921.0090.1221.0826.299
Ours (clDice)84.77+0.6991.94+1.020.6030.1000.6774.122
DSCNet [21]84.2891.040.8400.1460.9275.286
Ours (DSCNet)85.47+1.1992.87+1.830.5080.0830.5905.212
ImageCASDDT [31]87.5195.320.1890.0650.2784.621
softDice [18]87.5995.150.1900.0620.2684.674
Ours (softDice)88.33+0.7495.48+0.330.0740.0650.1593.580
clDice [26]87.7896.000.1580.0640.2384.021
Ours (clDice)87.85+0.0796.01+0.010.1520.0670.2345.038
DSCNet [21]87.9895.340.2130.0700.2833.751
Ours (DSCNet)88.84+0.8696.38+1.040.1270.0690.2153.291
" + }, + { + "type": "table_caption", + "bbox": [ + 0.559, + 0.52, + 0.86, + 0.534 + ], + "angle": 0, + "content": "Table 2. Main results on centerline extraction task." + }, + { + "type": "table", + "bbox": [ + 0.552, + 0.537, + 0.865, + 0.879 + ], + "angle": 0, + "content": "
DatasetMethodMetrics
F1 (%)↑HD95 ↓Chamfer ↓β0 ↓
HaN-SegDDT [31]89.657.67818.9573.136
softDice [18]91.176.98119.1114.318
Ours (softDice)94.56+3.394.2506.3321.727
clDice [26]90.789.02329.2173.636
Ours (clDice)92.36+1.585.2207.1301.409
DSCNet [21]90.457.46218.2954.818
Ours (DSCNet)91.50+1.058.22212.3622.773
HNCTADDT [31]97.293.2917.0830.394
softDice [18]97.053.82111.9940.591
Ours (softDice)98.74+1.692.2504.0720.422
clDice [26]96.693.5669.0970.387
Ours (clDice)98.36+1.672.3216.7610.520
DSCNet [21]97.283.3978.4050.534
Ours (DSCNet)98.59+1.312.1453.8290.419
ASOCADDT [31]91.4310.64163.4872.063
softDice [18]91.5711.95646.3581.905
Ours (softDice)95.23+3.667.42329.0270.810
clDice [26]93.439.16829.9711.554
Ours (clDice)94.77+1.347.27317.7380.929
DSCNet [21]93.467.90823.0521.540
Ours (DSCNet)94.28+0.827.05214.7601.000
ImageCASDDT [31]95.104.88119.3760.538
softDice [18]94.407.13430.3450.687
Ours (softDice)96.67+2.275.12717.3130.123
clDice [26]95.785.04319.4900.385
Ours (clDice)96.64+0.864.74314.9410.333
DSCNet [21]95.325.17017.2390.503
Ours (DSCNet)97.28+1.964.30312.1520.318
" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "30901" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.091, + 0.48, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.398, + 0.483, + 0.466 + ], + "angle": 0, + "content": "Figure 6. Visualizations of the predictions from different methods on four 3D medical image datasets. Different rows and columns stand for different datasets and methods respectively. The arrows point out the areas where models easily exhibit errors. Zoom in for more details." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.497, + 0.308, + 0.513 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.52, + 0.483, + 0.64 + ], + "angle": 0, + "content": "In our experiments, we use 3D UNet [3] as the backbone for all methods. We set the number of hierarchical feature maps \\( m \\) to 5. The number of control points \\( k \\) in template generation is set to 4. The number of deformation stages \\( L \\) is 4, and the channel size for point features \\( C \\) is 24. The centerline template of each vessel category is initialized with \\( N_{c} = 100 \\) points by default. All of the coordinates of centerline points are normalized to 0-1 in the framework." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.642, + 0.483, + 0.747 + ], + "angle": 0, + "content": "When computing local chamfer distance loss, the number of local patches is sampled from an even distribution \\( |\\Omega| \\sim U(60,80) \\). The loss weights \\( \\lambda_{\\mathrm{cha}} \\), \\( \\lambda_{\\mathrm{sdf}} \\), \\( \\lambda_{\\mathrm{reg}} \\) are set to 30, 0.5, and 60 by default. The balance weights for different deformation stages \\( \\{w_l\\}_{l=1}^L \\) are set to 0.05, 0.60, 0.95, and 1.00. More implementation details are depicted in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.758, + 0.229, + 0.772 + ], + "angle": 0, + "content": "4.4. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Our approach can be incorporated into common segmentation models, such as softmax [18] or clDice [26], as an additional segmentation head. In this subsection, we present the results of our method implemented on softmax [18], clDice [26] and DSCNet [21], comparing it with competitive segmentation models, including softmax [18], cldice [26], DDT [31] and DSCNet [21]. All models are trained under identical settings, including training sched" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.092, + 0.908, + 0.12 + ], + "angle": 0, + "content": "Table 3. Ablation on the number of control points k for each category of vessels on HaN-Seg dataset." + }, + { + "type": "table", + "bbox": [ + 0.625, + 0.122, + 0.8, + 0.23 + ], + "angle": 0, + "content": "
kVolumetric Scores (%) ↑
DiceclDice
078.8786.89
4*79.5888.86
878.3686.88
1677.2285.93
6477.3785.66
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.233, + 0.908, + 0.273 + ], + "angle": 0, + "content": "Table 4. Ablation on loss functions on HaN-Seg dataset. w/o \\(\\mathcal{L}_{\\mathrm{cha}}\\) means that we use global chamfer distance loss instead of local chamfer distance loss." + }, + { + "type": "table", + "bbox": [ + 0.586, + 0.276, + 0.838, + 0.371 + ], + "angle": 0, + "content": "
Loss FunctionVolumetric Scores (%) ↑
DiceclDice
w/o Lcha78.1886.62
w/o Lreg78.3886.70
w/o Lsdf79.5187.89
full configuration79.5888.86
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.907, + 0.457 + ], + "angle": 0, + "content": "ules and hyper-parameters, etc. We have not included PointScatter [29] and Topoloss [9] in the comparison as it is designed for 2D images and is not applicable to 3D medical images due to GPU memory limitations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.459, + 0.906, + 0.609 + ], + "angle": 0, + "content": "For segmentation, our method demonstrates notable performance improvements when integrated with baseline models as depicted in Table 1. The enhancement is particularly prominent in metrics like cDice and Betti number errors, which primarily reflect vessel completeness and topology correctness. This phenomenon verifies the effectiveness of the continuously defined representation. Furthermore, thanks to the exact prediction of centerlines, the performance of segmentation on the distance metric HD95 has also improved a lot." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.61, + 0.906, + 0.685 + ], + "angle": 0, + "content": "For centerline extraction, we present the experimental results on HaN-Seg and ASOCA datasets in Table 2. It can be concluded that DeformCL can improve a range of metrics consistently across multiple baseline models. More experiments can be found in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.686, + 0.906, + 0.822 + ], + "angle": 0, + "content": "To provide a qualitative assessment of the model performance, we present visualizations of predictions from different methods in Figure 6. These results illustrate that DeformCL effectively captures thin and fragile structures with minimal segmentation fractures. Moreover, the reduction in scattered false positives demonstrates the noise robustness of DeformCL. These results reaffirm that the continuously defined representation offers superior capabilities in curvilinear vessel extraction, owing to its unique properties." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.667, + 0.849 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "We conduct ablation experiments on the HaN-Seg dataset to assess the impact of different components of our method. Other ablation studies are presented in the supplementary" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "30902" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.09, + 0.462, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.266, + 0.483, + 0.322 + ], + "angle": 0, + "content": "Figure 7. Visual comparison of different loss function configurations. The carnatio masks and yellow lines denote the predicted segmentations and centerlines respectively. The red and green triangles point out the areas to focus on." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.36, + 0.16, + 0.373 + ], + "angle": 0, + "content": "materials." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.379, + 0.484, + 0.56 + ], + "angle": 0, + "content": "Template Selection. We compare the performance of different template selection strategies in Table 3. \\( k = 0 \\) means that we use a straight centerline as the initial template without considering image information. It can be found that adaptive template generation outperforms fixed initial templates \\( (k = 0) \\). Furthermore, we observe a gradual decline in performance as the number of control points \\( k \\) increases from 4 to 64. We guess that more control points lead to overly accurate initial templates, thus reducing the difficulty and complexity of the deformation task. Consequently, the model may not be sufficiently trained. Therefore, we adopt a rough initial template with \\( k = 4 \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.565, + 0.484, + 0.731 + ], + "angle": 0, + "content": "Loss Function. We evaluate the effectiveness of different loss functions in Table 4 and Figure 7. It is observed from the results in the table that local chamfer distance loss outperforms global chamfer distance loss, particularly in terms of cldice. We empirically find that the global chamfer distance loss will result in larger fluctuations during training process compared with the local version. The reason is that the tubular structures in human body usually have complex global morphology and sparse 3D distribution, which means that conducting global calculations will have more fluctuations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Although the gains from SDF loss and regularization loss are not as pronounced in the numerical results, visualization comparison in the figure reveal that these losses contribute to more accurate centerline predictions. For instance, without regularization loss, the centerline prediction may be sparse and deviated in local regions, due to the long edges between adjacent vertices. In addition, adding SDF loss augments the centrality of centerline predictions. These properties are significant for the subsequent tasks, such as curved planar reformation [11]. In summary, the full configurations of loss functions achieve the best performance." + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.09, + 0.895, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.215, + 0.907, + 0.299 + ], + "angle": 0, + "content": "Figure 8. Visual comparison of SCPR images reconstructed from the predictions of UNet and DeformCL. Red triangles indicate the regions where the vessel predictions by UNet are not correct, resulting in severe errors on SCPR images, while green ones indicate improved results from our DeformCL. Cyan arrows indicate the areas with plaque and stenosis needing additional clinical diagnosis." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.327, + 0.707, + 0.343 + ], + "angle": 0, + "content": "4.6. Clinical Significance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.349, + 0.907, + 0.56 + ], + "angle": 0, + "content": "In clinical practice, the generation of straightened curved planar reformation [11] (SCPR) images is vital for radiologists to conduct accurate diagnoses for blood vessels, especially for observing possible plaques and stenosis. High-quality SCPR images require high-quality vessel graphical structures (directional centerlines) that meet the criteria of completeness, smoothness, and centrality. Previous methods often rely on converting discrete segmentation masks into continuous centerlines using traditional tools [10, 19], which may be susceptible to imperfect segmentation predictions. Moreover, this conversion process is complex and time-consuming. In contrast, our DeformCL can directly generate continuous centerlines during model inference without the need for any post-processing." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.56, + 0.909, + 0.727 + ], + "angle": 0, + "content": "As depicted in Figure 8, we compare the SCPR images reconstructed from the predictions of UNet and DeformCL. It is evident that the SCPR images generated from UNet exhibit severe bending and breaking, indicated by red arrows, which could hinder plaque diagnosis. These inaccuracies stem from the segmentation masks being fragmented by UNet in fragile regions, potentially containing plaques and stenosis. In contrast, DeformCL produces high-quality SCPR images that reveal diseased regions comprehensively and clearly. These visualizations underscore the potential of DeformCL in assisting the clinical diagnosis process." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.74, + 0.642, + 0.755 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose DeformCL, a novel continuously defined representation for 3D vessel segmentation. To fully leverage the advantages of DeformCL, we introduce a cascaded deformation process based on an adaptive template generation strategy. Through this comprehensive training framework, DeformCL demonstrates clear superiority over previous methods. The visualizations highlight DeformCL's potential in generating CPR images for clinical diagnosis, especially for patients with severe stenosis." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "30903" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.152 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported by National Science and Technology Major Project (2022ZD0114902) and National Science Foundation of China (NSFC92470123, NSFC62276005)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.165, + 0.188, + 0.18 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.189, + 0.484, + 0.244 + ], + "angle": 0, + "content": "[1] Ricardo J Araujo, Jaime S Cardoso, and Helder P Oliveira. Topological similarity index and loss function for blood vessel segmentation. arXiv preprint arXiv:2107.14531, 2021. 1, 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.246, + 0.484, + 0.328 + ], + "angle": 0, + "content": "[2] Fabian Bongratz, Anne-Marie Rickmann, Sebastian Pölsterl, and Christian Wachinger. Vox2cortex: fast explicit reconstruction of cortical surfaces from 3d mri scans with geometric deep neural networks. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "30905" + } + ] +] \ No newline at end of file diff --git a/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/3df80607-397e-48ec-af7c-1eb858969941_origin.pdf b/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/3df80607-397e-48ec-af7c-1eb858969941_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7b29549580c247da067e8fd8e238e239520e2d76 --- /dev/null +++ b/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/3df80607-397e-48ec-af7c-1eb858969941_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d12833569d5720cbcdb46728912732daf0b31f46bdd6bf93e1d8985cbdccf391 +size 7105933 diff --git a/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/full.md b/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2e5ebb982da558532137db75be287883f006b508 --- /dev/null +++ b/2025/DeformCL_ Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image/full.md @@ -0,0 +1,329 @@ +# DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image + +Ziwei Zhao $^{1*}$ Zhixing Zhang $^{2,5*}$ Yuhang Liu $^{1\dagger}$ Zhao Zhang $^{2}$ Haojun Yu $^{4}$ Dong Wang $^{1}$ Liwei Wang $^{3,4}$ + +1Zihun Medical AI Co., Ltd 2Center for Data Science, Peking University + +3Center for Machine Learning Research, Peking University + +$^{4}$ State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University + +$^{5}$ Pazhou Laboratory (Huangpu), Guangzhou, Guangdong, China + +{ziwei.zhao, yuhang.liu, dong.wang}@yzhun-ai.com + +{zhangzhixing@stu., zhangzh@stu., haojunyu@, wanglw@}pku.edu.cn + +# Abstract + +In the field of 3D medical imaging, accurately extracting and representing the blood vessels with curvilinear structures holds paramount importance for clinical diagnosis. Previous methods have commonly relied on discrete representation like mask, often resulting in local fractures or scattered fragments due to the inherent limitations of the per-pixel classification paradigm. In this work, we introduce DeformCL, a new continuous representation based on Deformable Centerlines, where centerline points act as nodes connected by edges that capture spatial relationships. Compared with previous representations, DeformCL offers three key advantages: natural connectivity, noise robustness, and interaction facility. We present a comprehensive training pipeline structured in a cascaded manner to fully exploit these favorable properties of DeformCL. Extensive experiments on four 3D vessel segmentation datasets demonstrate the effectiveness and superiority of our method. Furthermore, the visualization of curved planar reformation images validates the clinical significance of the proposed framework. We release the code in https://github.com/barry664/DeformCL. + +# 1. Introduction + +Cerebro-cardiovascular disease is one of the most severe global health threats [22]. Timely detection of potential high-risk locations and prompt intervention are crucial to reducing mortality, relying on accurate extraction, reconstruction, and analysis of major vessels in CTA images [16]. + +In clinical practice, the primary requirement is to achieve accurate segmentation of primary vessel branches to enable comprehensive vascular system assessment and detailed local analysis. + +Previous methodologies [1, 21, 25, 26, 29, 31] have predominantly adopted the traditional semantic segmentation approach, which relies on fine-grained, per-pixel classification within a discrete mask representation. As illustrated in the top part of Figure 1, to improve the volumetric scores (e.g. Dice) or topological metrics (e.g. betti number errors) for segmentation, these approaches introduce a variety of innovations, such as incorporating tubular priors into network architecture [13, 21, 25, 31, 36, 39] or designing topology-preserving loss functions [1, 9, 26]. Despite these advancements in the training process, the core issue that the discrete mask representation is not well-suited for the curvilinear vessels remains unchanged, imposing several inherent limitations that restrict the model's performance and applicability, as shown in the top part of Figure 2. Firstly, the neural networks struggle to recognize fragile and tortuous local structures, which may lead to segmentation fractures [21]. Moreover, the discrete representation exhibits poor robustness to local noise [26, 29], such as variations in tissue density, due to the lack of a holistic view of the global morphology. Consequently, it may mistakenly identify the tissues with appearances similar to target vessels. Finally, designing an effective feature aggregation strategy along tubular curves remains challenging, considering the lack of explicit relationships among elements in discrete mask representations. + +These challenges motivate us to seek a continuous representation that can explicitly fit the tubular structures from a holistic view, rather than confined to per-pixel classification paradigm. In this paper, we introduce DeformCL, + +![](images/3ec4c7541ed469d1737cc92c55bc8129cee23a9be0beeafd54e9deff278f58d4.jpg) +Figure 1. Previous methods [1, 21, 26, 29, 31] primarily rely on the discrete mask representation, adopting a per-pixel classification paradigm for vessel segmentation. Common techniques in these approaches include incorporating tubular priors and applying topology-preserving loss functions. In contrast, we introduce a new continuous representation, DeformCL, which employs centerline points connected by edges to gradually fit the curvilinear vessels via a template deformation process. Once structured centerlines are obtained, generating segmentation predictions with improved topological accuracy becomes a straightforward task. + +a new representation for vessel extraction in 3D medical image based on Deformable Centerline. As shown in the bottom part of Figure 1, DeformCL employs a graph structure, wherein centerline points serve as nodes connected by edges representing their spatial relationships. This continuously defined representation accurately depicts the curvilinear structures, thus circumventing the drawbacks of discrete mask representation and has its own merits: (1) the incorporation of natural connectivity mitigates centerline ruptures, particularly in the thin and fragile areas; (2) by considering the entire curvilinear structures rather than local pixels, DeformCL ensures a comprehensive understanding of the global morphology, thus reducing local artifacts and false positives; (3) the inherent graph structure facilitates efficient and effective feature aggregation along the tubular curves, enhancing overall segmentation performance. + +We propose a novel framework to learn deformable centerline representation from 3D medical images. Our framework consists of several key steps. Firstly, we adaptively generate an initial continuous centerline template based on the input image, taking anatomical variations among different individuals into account. Next, the centerline points within the template will interact with each other to capture features along tubular curves. The whole centerline template will be iteratively refined by deformation and unpooling layers, gradually aligning with the ground truth centerlines. Finally, after obtaining precise centerlines of tubular structures, crafting a high-quality segmentation algorithm becomes a straightforward task. In our approach, we leverage the distance map derived from the predicted centerline points to execute the final segmentation process effortlessly. Benefiting from the high-quality continuous centerlines, the segmentation performance is improved significantly. + +We benchmark DeformCL on four 3D medical datasets, and the extensive experiments validate the effectiveness of + +our proposed method. Additionally, due to its continuous nature, DeformCL's centerline predictions can be directly used as a structural representation of vessels, commonly as directional centerlines [10, 24]. This structural representation is crucial in clinical practice, serving as an indispensable component in various subsequent diagnostic tasks, such as curved planar reformation [11] and computational hemodynamics [27]. We qualitatively demonstrate the clinical relevance of DeformCL, highlighting its potential applicability for diagnostic purposes. + +In summary, our main contributions are three-fold: + +- We introduce a continuous representation, called DeformCL, which possesses several favorable properties for curvilinear vessels in 3D medical image. +- We propose a comprehensive pipeline for effectively training DeformCL through a cascaded deformation process. +- Our approach significantly bolsters the performance of several baselines on four 3D vessel extraction datasets. + +# 2. Related Work + +# 2.1. Vessel Segmentation in 3D Medical Image + +Vessel segmentation in 3D medical image is a crucial task due to the prevalence of curvilinear vessels in the human body. Classical modern segmentation models like UNet [3, 23] and FCN [17] face challenges in accurately extracting tubular structures due to their complex global morphology and fragile thin structures. Previous methods have adopted various strategies to address these challenges: incorporate tubular priors into network architecture [14, 21, 25, 31, 33, 36, 39], design topology-preserving loss functions [1, 9, 26] or employ more flexible representation [29, 38]. Shit et al. [26] introduces a new connectivity-aware similarity measure called clDice, and the differentiable version can be used to train segmentation models for + +tubular structures. Qi et al. [21] proposes a dynamic snake convolution to let networks adaptively focus on the tubular structures and make more accurate predictions. Wang et al. [29] relies on the flexibility of point set representation which is not restricted to a fixed grid to promote the performance of tubular structure extraction. + +# 2.2. Deformable Paradigm + +The deformable paradigm is a widely used technique in deep learning, particularly in computer vision, where it plays a crucial role in capturing complex structures and achieving significant advancements in various tasks. Introduced by Dai et al. [4], deformable convolution extends traditional convolutions to capture complex structures effectively. It has been successfully applied in tasks such as object detection and segmentation, allowing models to adapt to object variations and complex shapes. Deformable DETR [41] combines attention mechanism with deformable paradigm for efficient feature extraction process. In addition, deformable structures have also found applications in 3D reconstruction tasks [2, 14, 30, 32, 34, 40]. For instance, Pixel2Mesh [30] generates 3D shapes represented as triangular meshes from single images by progressively deforming an initial ellipsoid. Similarly, Voxel2Mesh [32] extends this approach to generate organ surfaces from 3D medical volumes, facilitating organ segmentation and visualization. Kong et al. [14] proposed a deep-learning approach to generate whole heart geometries from pre-defined mesh templates, demonstrating the versatility of deformable structures in human anatomical modeling. + +# 3. Method + +In this section, we will first introduce the new representation DeformCL and its favorable properties in Sec 3.1. Sec 3.2 elaborates on the network architecture for learning deformation centerline representation from 3D medical images. Sec 3.3 presents the training losses for the framework. + +# 3.1. Representation of DeformCL + +In 3D medical imaging, a common representation of a given volume $I \in \mathbb{R}^{\mathbb{H} \times \mathbb{W} \times \mathbb{D}}$ is its segmentation mask, denoted as $Y \in \mathbb{R}^{\mathbb{H} \times \mathbb{W} \times \mathbb{D}}$ . Nearly all previous methods [1, 21, 25, 26, 29, 31] rely on this discrete mask representation, framing the task as per-pixel classification. This paradigm inherently possesses several limitations, as illustrated in the top part of Figure 2, which ultimately restrict the model's performance. + +In this paper, we introduce a novel continuous representation called Deformable CenterLine (DeformCL) to efficiently and effectively capture tubular structures in 3D medical image. Instead of relying on segmentation mask, we represent tubular structures using a graph $\mathcal{G} = \{\mathcal{V},\epsilon \}$ , where $\mathcal{V} = \{v_{i}|v_{i}\in \mathbb{R}^{3}\}_{i = 1}^{N}$ is a set of $N$ vertices standing + +![](images/1f5f80f12b0e2e829c2b8a6f02ac77f186c37a5163018a48fbba69f04679fe37.jpg) +Figure 2. Three significant properties of DeformCL compared with the discrete mask representation. (Zoom in for more details.) + +for centerline points, $\epsilon = \{(k,w)|1\leq k,w\leq N\}$ is the set of edges connecting adjacent vertices. + +As shown in the bottom part of Figure 2, compared with previous discrete representations, DeformCL possesses several favorable properties, making it a reasonable and effective representation for tubular structure modeling. + +Natural connectivity. Unlike traditional discrete representations, DeformCL naturally exhibits the connectivity among centerline points, which explicitly models the tubular structures in a continuously defined way. On one hand, this continuous representation helps prevent predictions from breaking in thin and fragile regions. On the other hand, the traditionally complex and time-consuming continuous centerlines extraction [10, 19] from segmentation for curved planner reconstruction [11] is eliminated. + +Noise robustness. Thanks to its top-down manner, DeformCL exhibits robustness to noise and local disturbances, such as variations in tissue density or the presence of contrast agents. This inherent property enables DeformCL to effectively filter out local artifacts and false positives, leading to more accurate and reliable tubular structure extraction compared to previous bottom-up methods. + +Interaction facility. Constrained by the discrete representation, previous methods [21, 26, 29, 31] lack of an effective approach for tubular feature aggregation. On the contrary, DeformCL's graph structure facilitates feature fusion process via methods like GCN [12] or Transformer [28] along the tubular curve. This global information interaction is significant for the structure completeness and topology correctness of tubular predictions. + +# 3.2. Network Architecture + +In this subsection, we will introduce the network architecture for learning deformable centerline representation. The whole framework is shown in Figure 3. Given a 3D medical image $I \in \mathbb{R}^{\mathbb{H} \times \mathbb{W} \times \mathbb{D}}$ , we first pass it through a 3D backbone (e.g. 3D UNet [3]) to obtain hierarchical feature maps $\{F_i\}_{i=1}^m$ at different down-sampled rates. Additionally, the backbone network produces a coarse segmentation result $\hat{Y}_c \in \mathbb{R}^{\mathbb{H} \times \mathbb{W} \times \mathbb{D}}$ for each category of vessels. + +Adaptive Template Generation. In order to initialize the graph structure of DeformCL, we attempt to initial- + +![](images/4f7468b84536469a2fe97024a46544b872d0a7cecc331ea307f70a81b3474e3b.jpg) +Figure 3. Overview of the training process. Given a 3D medical image, the segmentation network first outputs a coarse prediction and generates hierarchical downsampled feature maps. An initial template, produced by the Adaptive Template Generation module, is then iteratively fed through deformation and unpooling layers to progressively adapt to the curvilinear structures. Finally, refined segmentation results are generated based on the accurately aligned continuous centerlines. We apply Dice loss to both the coarse and refined segmentation predictions, and local chamfer loss, SDF loss, and regularization loss for centerline predictions. + +ize a tubular template motivated by mesh generation methods [30, 32]. However, unlike human organs, tubular structures in 3D medical image, such as coronary arteries, exhibit complex global morphology and variable extension direction, which means that discovering a universal template for such structures poses significant challenges. Therefore, we introduce a new method to adaptively generate initial templates for each image. + +The template generation process, illustrated in the Figure 4, is conducted independently for each category of vessels. Firstly, the coarse segmentation result $\hat{Y}_c$ is converted into discrete centerline points via traditional 3D thinning algorithm [15]. These points are then reconstructed into a graph using the minimum spanning tree algorithm [7] following the strategy in [37]. Next, a set of $k$ control points is selected from the graph at fixed distances, serving as the abstraction of the structure. Finally, curvilinear interpolation (e.g. Bezier Curve Interpolation, Linear Interpolation) is applied based on the control points to generate the initial template, denoted as $\{v_i^c | v_i^c \in \mathbb{R}^3\}_{i=1}^{N_c}$ . Here, $v_i^c$ represents the $i$ -th point for category $c$ , $N_c$ is the total number of points for category $c$ , and $v_i^c$ is connected with $v_{i+1}^c$ by default. + +It is worth noting that we adopt a rough template generation strategy using control points instead of directly utilizing the reconstructed tree as the initial template. The reason is that we empirically find overly accurate initial templates + +may harm model performance, supported by experimental results shown in Table 3. We speculate that overly accurate initial templates may simplify the deformation task excessively, potentially leading to insufficient model training. + +Cascaded Deformation Process. After the generation of initial templates, we proceed with the cascaded deformation process to refine the centerline predictions. For clarity, we focus on the centerline points of one category of vessels in the subsequent sections of the paper. + +Firstly, trilinear interpolation is applied to each centerline point $v_{i}$ in the downsampled feature maps $\{F_i\}_{i = 1}^m$ , and the hierarchical points features are fused via a linear layer: + +$$ +f \left(v _ {i}\right) = \operatorname {L i n e a r} \left(\left[ \operatorname {T r i} \left(F _ {1}, v _ {i}\right), \dots , \operatorname {T r i} \left(F _ {m}, v _ {i}\right) \right]\right) \in \mathbb {R} ^ {C}, \tag {1} +$$ + +where $C$ denotes the channel size, Tri represents the tri-linear interpolation. Next, the points and their corresponding features $\{v_{i},f(v_{i})\}$ are fed into Transformer [28] layers for feature aggregation along the tubular curve. The positional encoding $\mathrm{Pos}(v^l)$ contains learnable embeddings of absolute 3D positions of points and relative positions in the graph. Subsequently, the augmented point features are used to predict an offset $\delta_i^l$ , which is then applied to update the position of each point $v_{i}^{l}$ to obtain $v_{i}^{l + 1}$ . + +Since high-accuracy centerlines require a sufficient number of points to capture curvilinear structures accurately, we + +![](images/21fe1120de844ce93b8cd7df0776d53b71b17da688a310172b4c5cf44eb07b6f.jpg) +Figure 4. Adaptive Template Generation. + +apply an unpooling strategy after deformation to increase point density. Specifically, a new point is inserted between each pair of connected points. We reuse the symbol $\{v_i^{l + 1}\}$ for clarity. This process is iterated $L$ times for accurate centerline prediction, where the $l$ -th layer is described as follows: + +$$ +\tilde {f} \left(v _ {i} ^ {l}\right) = f \left(v _ {i} ^ {l}\right) + \operatorname {T r a n s f o r m e r} \left(f \left(v ^ {l}\right), \operatorname {P o s} \left(v ^ {l}\right)\right) \in \mathbb {R} ^ {C}, \tag {2} +$$ + +$$ +\delta_ {i} ^ {l} = \operatorname {T a n h} \left(\mathrm {M L P} \left(\tilde {f} \left(v _ {i} ^ {l}\right)\right)\right) \in \mathbb {R} ^ {3}, \tag {3} +$$ + +$$ +v _ {i} ^ {l + 1} = v _ {i} ^ {l} + \delta_ {i} ^ {l} \in \mathbb {R} ^ {3}, \tag {4} +$$ + +$$ +\left\{v _ {i} ^ {l + 1} \right\} = \text {U n p o o l i n g} \left(\left\{v _ {i} ^ {l + 1} \right\}\right) \tag {5} +$$ + +After completing the cascaded deformation process, the final set of points $\{v_i^L\}$ represents the predicted centerline points, which will be used for subsequent centerline-based segmentation task. + +Centerline-based Segmentation. Once accurate centerlines of tubular structures are obtained, predicting the corresponding segmentation results becomes straightforward. In this work, we employ a simple method using distance maps to achieve centerline-based segmentation. Specifically, given the predicted centerline points $V = \{v_{i}^{L}\in \mathbb{R}^{3}\}$ , we calculate the minimum distance of each voxel in the image to the points in $V$ : + +$$ +D [ x, y, z ] = \min _ {v \in V} | | (x, y, z) - v | | _ {2}, \tag {6} +$$ + +where $D \in \mathbb{R}^{\mathbb{H} \times \mathbb{D} \times \mathbb{W}}$ is the distance map based on the centerline points. Finally, the coarse segmentation results $\hat{Y}_c$ and the distance map $D$ are input to a convolutional layer for fusion, yielding the refined segmentation results $\hat{Y}_r$ . + +# 3.3. Training Loss + +In this subsection, we will elaborate on the loss functions of the proposed framework. For centerline prediction, we employ a combination of local chamfer distance loss, signed distance function (SDF) loss, and a regularization loss. We utilize Dice loss for segmentation. + +Local Chamfer Distance Loss. Tradition global chamfer distance loss calculates the distance between two point cloud sets. However, curvilinear vessels in the human body often exhibit complex global morphology and sparse 3D distribution. As a result, using global chamfer distance loss may lead to larger fluctuations and suboptimal convergence during the training process. To address this issue, we adopt a local version of chamfer distance loss. + +To be specific, we begin by employing Farthest Point Sampling (FPS) to select candidate points $\{u_{i_k}\}$ from the ground truth centerline points $\{u_i\}$ , which are obtained from the ground truth mask via traditional 3D thinning algorithm [15]. Then, we crop local patches with fixed size $M$ centered around each selected point $\{u_{i_k}\}$ . The points located within each cropped patch are denoted as $\omega_{i_k} = \{p = (x,y,z)|p\in [u_{i_k} - M / 2,u_{i_k} + M / 2]\}$ , and the set of patches is denoted as $\Omega = \{\omega_{i_k}\}$ . The chamfer distance loss is then applied between the predicted point set and the ground truth point set within each cropped patch. Formally, the loss is defined as: + +$$ +\mathcal {L} _ {\mathrm {c h a}} = \frac {1}{| \Omega |} \sum_ {\omega \in \Omega} \left(\sum_ {v _ {i} \in \omega} \min _ {u _ {i} \in \omega} \| v _ {i} - u _ {i} \| _ {2} ^ {2} + \sum_ {u _ {i} \in \omega} \min _ {v _ {i} \in \omega} \| u _ {i} - v _ {i} \| _ {2} ^ {2}\right). \tag {7} +$$ + +SDF Loss. Signed Distance Function (SDF) is a well-established concept in computer vision and computer graphics, used to represent the surface of 3D objects through signed distances. We find that SDF is appropriate for ensuring the centrality of predicted centerline points. Firstly, we define the surface of tubular strcutures following [31]: + +$$ +S = \{x \in \mathbb {R} ^ {3} | Y [ x ] = 1, \exists u \in \mathcal {N} (x), Y [ u ] = 0 \}, \tag {8} +$$ + +where $\mathcal{N}(x)$ denotes the 6-neightbour voxels of $x$ , $Y$ is the ground truth mask. Then, the SDF value of an arbitrary point $p$ in the image can be calculated as: + +$$ +S D F (p) = \left\{ \begin{array}{l l} - \min _ {u \in S} | | p - u | | _ {2} ^ {2}, & \text {i f} Y [ p ] = 1, \\ \min _ {u \in S} | | p - u | | _ {2} ^ {2}, & \text {i f} Y [ p ] = 0. \end{array} \right. \tag {9} +$$ + +The SDF values of all predicted centerline points are utilized as the training loss: + +$$ +\mathcal {L} _ {\mathrm {s d f}} = \frac {1}{N} \sum_ {i = 1} ^ {N} S D F (v _ {i}). \tag {10} +$$ + +As illustrated in Figure 5, SDF loss serves two crucial purposes. Firstly, it provides supervision for all predicted centerline points, whereas the local chamfer + +![](images/d4d481a2bc9d2f062bdf2a3bf6e9a9aa6146e89ef73b64716a578be2c14c1c69.jpg) +Figure 5. SDF Loss. + +distance loss can only provide supervision for points within cropped patches, potentially missing outlier predictions. Secondly, it facilitates the gradual deformation of predicted points towards the ideal center of tubular structures, thereby ensuring the centrality of centerlines. + +Regularization Loss. To prevent the deformable centerline points from deviating mistakenly, which may result in long + +edges between adjacent vertices, we apply a regularization loss to penalize the adjacent points with much long edges: + +$$ +\mathcal {L} _ {\text {r e g}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left| \left| v _ {i} - v _ {i - 1} \right| \right| _ {2} ^ {2}. \tag {11} +$$ + +Segmentation Loss. We use Dice loss [18] as loss function for the coarse and refined segmentation results $\hat{Y}_c$ and $\hat{Y}_r$ : + +$$ +\mathcal {L} _ {\mathrm {s e g}} = \lambda \operatorname {D i c e} \left(Y, \hat {Y} _ {c}\right) + \operatorname {D i c e} \left(Y, \hat {Y} _ {r}\right), \tag {12} +$$ + +where $\lambda$ is set to 0.2. + +Note that local chamfer distance loss, SDF loss and regularization loss are applied to all intermediate results in the cascaded deformation process. The total training loss is a combination of all loss functions: + +$$ +\mathcal {L} = \sum_ {l = 1} ^ {L} w _ {l} \left(\lambda_ {\mathrm {c h a}} \mathcal {L} _ {\mathrm {c h a}} + \lambda_ {\mathrm {s d f}} \mathcal {L} _ {\mathrm {s d f}} + \lambda_ {\mathrm {r e g}} \mathcal {L} _ {\mathrm {r e g}}\right) + \mathcal {L} _ {\mathrm {s e g}}, \tag {13} +$$ + +$w_{l}$ stands for the weight of the $l$ -th deformation stage. + +# 4. Experiments + +# 4.1. Datasets + +We use four datasets to evaluate our proposed framework. HaN-Seg [20] is a public dataset consisting of 56 CT and MR images with 30 categories of head and neck organ pixel annotations. ASOCA [5, 6] is a public dataset in the MICCAI-2020 challenge which aims to automatically segment the coronary artery lumen. It consists of 40 Cardiac Computed Tomography Angiography (CCTA) images with artery segmentation annotations. ImageCAS [35] is a public dataset containing about 1000 3D CTA images with coronary artery segmentation labels. HNCTA is a private head and neck artery dataset with 358 CTA images. More details of datasets can be found in supplementary materials. + +# 4.2. Evaluation Metrics + +We assess the segmentation performance in three main aspects following [21]. For volumetric scores, we report Dice [18] and clDice [26] to evaluate the segmentation results. For topology-based scores, absolute Betti Errors for Betti Numbers $\beta_0$ and $\beta_{1}$ and absolute error of Euler characteristic are used to measure the topology and completeness of the extracted vessels following [21, 26, 29]. For distance-based scores, Hausdorff Distance (HD) is employed for measuring the maximum distance between two 3D point sets. All presented metrics in this paper are the average of all vessel categories. + +For the centerline extraction task, we use F1, Hausdorff Distance, Chamfer Distance and absolute Betti Errors for Betti Numbers $\beta_0$ as evaluation metrics. For robust evaluation, we apply a three-pixel tolerance region around the ground truth centerline points following [8, 29]. + +Table 1. Main results on vessel segmentation task. We mark the best performance by bold numbers. Ours (softDice) denotes that we use softDice as base model with the proposed DeformCL as an additional segmentation head. + +
DatasetMethodVolumetric Scores (%) ↑Topological Error ↓Distance ↓
DiceclDiceβ0β1EulerHD95
HaN-SegDDT [31]75.7685.792.3330.1272.3295.473
softDice [18]76.3085.963.3160.0293.2864.905
Ours (softDice)79.58+3.2888.86+2.902.1230.0892.0344.113
clDice [26]76.2286.502.8610.0652.7965.244
Ours (clDice)78.39+2.1787.32+0.822.2070.2262.0423.838
DSCNet [21]77.1684.633.8580.2953.5644.949
Ours (DSCNet)78.61+1.4586.89+2.262.6020.3582.3184.125
HNCTADDT [31]83.5693.280.1720.0500.2192.666
softDice [18]83.0592.140.2860.0590.3372.924
Ours (softDice)84.69+1.6493.72+1.580.1490.0510.1992.084
clDice [26]83.1391.890.1600.0581.2393.118
Ours (clDice)84.13+1.0093.15+1.260.1500.0520.2002.839
DSCNet [21]83.5492.060.2460.0600.3012.658
Ours (DSCNet)84.80+1.2693.82+1.760.1830.0440.2282.349
ASOCADDT [31]83.0089.630.9980.0941.0907.646
softDice [18]84.0689.810.9300.1190.9966.829
Ours (softDice)85.16+1.1092.41+2.600.4080.1290.5105.082
clDice [26]84.0890.921.0090.1221.0826.299
Ours (clDice)84.77+0.6991.94+1.020.6030.1000.6774.122
DSCNet [21]84.2891.040.8400.1460.9275.286
Ours (DSCNet)85.47+1.1992.87+1.830.5080.0830.5905.212
ImageCASDDT [31]87.5195.320.1890.0650.2784.621
softDice [18]87.5995.150.1900.0620.2684.674
Ours (softDice)88.33+0.7495.48+0.330.0740.0650.1593.580
clDice [26]87.7896.000.1580.0640.2384.021
Ours (clDice)87.85+0.0796.01+0.010.1520.0670.2345.038
DSCNet [21]87.9895.340.2130.0700.2833.751
Ours (DSCNet)88.84+0.8696.38+1.040.1270.0690.2153.291
+ +Table 2. Main results on centerline extraction task. + +
DatasetMethodMetrics
F1 (%)↑HD95 ↓Chamfer ↓β0 ↓
HaN-SegDDT [31]89.657.67818.9573.136
softDice [18]91.176.98119.1114.318
Ours (softDice)94.56+3.394.2506.3321.727
clDice [26]90.789.02329.2173.636
Ours (clDice)92.36+1.585.2207.1301.409
DSCNet [21]90.457.46218.2954.818
Ours (DSCNet)91.50+1.058.22212.3622.773
HNCTADDT [31]97.293.2917.0830.394
softDice [18]97.053.82111.9940.591
Ours (softDice)98.74+1.692.2504.0720.422
clDice [26]96.693.5669.0970.387
Ours (clDice)98.36+1.672.3216.7610.520
DSCNet [21]97.283.3978.4050.534
Ours (DSCNet)98.59+1.312.1453.8290.419
ASOCADDT [31]91.4310.64163.4872.063
softDice [18]91.5711.95646.3581.905
Ours (softDice)95.23+3.667.42329.0270.810
clDice [26]93.439.16829.9711.554
Ours (clDice)94.77+1.347.27317.7380.929
DSCNet [21]93.467.90823.0521.540
Ours (DSCNet)94.28+0.827.05214.7601.000
ImageCASDDT [31]95.104.88119.3760.538
softDice [18]94.407.13430.3450.687
Ours (softDice)96.67+2.275.12717.3130.123
clDice [26]95.785.04319.4900.385
Ours (clDice)96.64+0.864.74314.9410.333
DSCNet [21]95.325.17017.2390.503
Ours (DSCNet)97.28+1.964.30312.1520.318
+ +![](images/8cec88bf16b6180f7df2fe87c1a5ddc725f67cec92f8d01fc1b4df405ec63aca.jpg) +Figure 6. Visualizations of the predictions from different methods on four 3D medical image datasets. Different rows and columns stand for different datasets and methods respectively. The arrows point out the areas where models easily exhibit errors. Zoom in for more details. + +# 4.3. Implementation Details + +In our experiments, we use 3D UNet [3] as the backbone for all methods. We set the number of hierarchical feature maps $m$ to 5. The number of control points $k$ in template generation is set to 4. The number of deformation stages $L$ is 4, and the channel size for point features $C$ is 24. The centerline template of each vessel category is initialized with $N_{c} = 100$ points by default. All of the coordinates of centerline points are normalized to 0-1 in the framework. + +When computing local chamfer distance loss, the number of local patches is sampled from an even distribution $|\Omega| \sim U(60,80)$ . The loss weights $\lambda_{\mathrm{cha}}$ , $\lambda_{\mathrm{sdf}}$ , $\lambda_{\mathrm{reg}}$ are set to 30, 0.5, and 60 by default. The balance weights for different deformation stages $\{w_l\}_{l=1}^L$ are set to 0.05, 0.60, 0.95, and 1.00. More implementation details are depicted in the supplementary materials. + +# 4.4. Main Results + +Our approach can be incorporated into common segmentation models, such as softmax [18] or clDice [26], as an additional segmentation head. In this subsection, we present the results of our method implemented on softmax [18], clDice [26] and DSCNet [21], comparing it with competitive segmentation models, including softmax [18], cldice [26], DDT [31] and DSCNet [21]. All models are trained under identical settings, including training sched + +Table 3. Ablation on the number of control points k for each category of vessels on HaN-Seg dataset. + +
kVolumetric Scores (%) ↑
DiceclDice
078.8786.89
4*79.5888.86
878.3686.88
1677.2285.93
6477.3785.66
+ +Table 4. Ablation on loss functions on HaN-Seg dataset. w/o $\mathcal{L}_{\mathrm{cha}}$ means that we use global chamfer distance loss instead of local chamfer distance loss. + +
Loss FunctionVolumetric Scores (%) ↑
DiceclDice
w/o Lcha78.1886.62
w/o Lreg78.3886.70
w/o Lsdf79.5187.89
full configuration79.5888.86
+ +ules and hyper-parameters, etc. We have not included PointScatter [29] and Topoloss [9] in the comparison as it is designed for 2D images and is not applicable to 3D medical images due to GPU memory limitations. + +For segmentation, our method demonstrates notable performance improvements when integrated with baseline models as depicted in Table 1. The enhancement is particularly prominent in metrics like cDice and Betti number errors, which primarily reflect vessel completeness and topology correctness. This phenomenon verifies the effectiveness of the continuously defined representation. Furthermore, thanks to the exact prediction of centerlines, the performance of segmentation on the distance metric HD95 has also improved a lot. + +For centerline extraction, we present the experimental results on HaN-Seg and ASOCA datasets in Table 2. It can be concluded that DeformCL can improve a range of metrics consistently across multiple baseline models. More experiments can be found in supplementary materials. + +To provide a qualitative assessment of the model performance, we present visualizations of predictions from different methods in Figure 6. These results illustrate that DeformCL effectively captures thin and fragile structures with minimal segmentation fractures. Moreover, the reduction in scattered false positives demonstrates the noise robustness of DeformCL. These results reaffirm that the continuously defined representation offers superior capabilities in curvilinear vessel extraction, owing to its unique properties. + +# 4.5. Ablation Study + +We conduct ablation experiments on the HaN-Seg dataset to assess the impact of different components of our method. Other ablation studies are presented in the supplementary + +![](images/446a79d30aa43cae1446575c9d97cd66f5ff22d613b7db4576bd7fb37ea932a6.jpg) +Figure 7. Visual comparison of different loss function configurations. The carnatio masks and yellow lines denote the predicted segmentations and centerlines respectively. The red and green triangles point out the areas to focus on. + +materials. + +Template Selection. We compare the performance of different template selection strategies in Table 3. $k = 0$ means that we use a straight centerline as the initial template without considering image information. It can be found that adaptive template generation outperforms fixed initial templates $(k = 0)$ . Furthermore, we observe a gradual decline in performance as the number of control points $k$ increases from 4 to 64. We guess that more control points lead to overly accurate initial templates, thus reducing the difficulty and complexity of the deformation task. Consequently, the model may not be sufficiently trained. Therefore, we adopt a rough initial template with $k = 4$ . + +Loss Function. We evaluate the effectiveness of different loss functions in Table 4 and Figure 7. It is observed from the results in the table that local chamfer distance loss outperforms global chamfer distance loss, particularly in terms of cldice. We empirically find that the global chamfer distance loss will result in larger fluctuations during training process compared with the local version. The reason is that the tubular structures in human body usually have complex global morphology and sparse 3D distribution, which means that conducting global calculations will have more fluctuations. + +Although the gains from SDF loss and regularization loss are not as pronounced in the numerical results, visualization comparison in the figure reveal that these losses contribute to more accurate centerline predictions. For instance, without regularization loss, the centerline prediction may be sparse and deviated in local regions, due to the long edges between adjacent vertices. In addition, adding SDF loss augments the centrality of centerline predictions. These properties are significant for the subsequent tasks, such as curved planar reformation [11]. In summary, the full configurations of loss functions achieve the best performance. + +![](images/a0bd91ace274e6390623695c0c1057568f6dc39fc3b460ee52fa6cb6775a4739.jpg) +Figure 8. Visual comparison of SCPR images reconstructed from the predictions of UNet and DeformCL. Red triangles indicate the regions where the vessel predictions by UNet are not correct, resulting in severe errors on SCPR images, while green ones indicate improved results from our DeformCL. Cyan arrows indicate the areas with plaque and stenosis needing additional clinical diagnosis. + +# 4.6. Clinical Significance + +In clinical practice, the generation of straightened curved planar reformation [11] (SCPR) images is vital for radiologists to conduct accurate diagnoses for blood vessels, especially for observing possible plaques and stenosis. High-quality SCPR images require high-quality vessel graphical structures (directional centerlines) that meet the criteria of completeness, smoothness, and centrality. Previous methods often rely on converting discrete segmentation masks into continuous centerlines using traditional tools [10, 19], which may be susceptible to imperfect segmentation predictions. Moreover, this conversion process is complex and time-consuming. In contrast, our DeformCL can directly generate continuous centerlines during model inference without the need for any post-processing. + +As depicted in Figure 8, we compare the SCPR images reconstructed from the predictions of UNet and DeformCL. It is evident that the SCPR images generated from UNet exhibit severe bending and breaking, indicated by red arrows, which could hinder plaque diagnosis. These inaccuracies stem from the segmentation masks being fragmented by UNet in fragile regions, potentially containing plaques and stenosis. In contrast, DeformCL produces high-quality SCPR images that reveal diseased regions comprehensively and clearly. These visualizations underscore the potential of DeformCL in assisting the clinical diagnosis process. + +# 5. Conclusions + +In this paper, we propose DeformCL, a novel continuously defined representation for 3D vessel segmentation. To fully leverage the advantages of DeformCL, we introduce a cascaded deformation process based on an adaptive template generation strategy. Through this comprehensive training framework, DeformCL demonstrates clear superiority over previous methods. The visualizations highlight DeformCL's potential in generating CPR images for clinical diagnosis, especially for patients with severe stenosis. + +Acknowledgement. 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Computerized Medical Imaging and Graphics, 109:102287, 2023. 6 +[36] Xiao Zhang, Jingyang Zhang, Lei Ma, Peng Xue, Yan Hu, Dijia Wu, Yiqiang Zhan, Jun Feng, and Dinggang Shen. Progressive deep segmentation of coronary artery via hierarchical topology learning. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 391-400. Springer, 2022. 1, 2 +[37] Zhixing Zhang, Ziwei Zhao, Dong Wang, Shishuang Zhao, Yuhang Liu, Jia Liu, and Liwei Wang. Topology-preserving automatic labeling of coronary arteries via anatomy-aware connection classifier. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 759-769. Springer, 2023. 4 +[38] Zhao Zhang, Ziwei Zhao, Dong Wang, and Liwei Wang. Graphmorph: Tubular structure extraction by morphing predicted graphs. Advances in Neural Information Processing Systems, 37:68472-68499, 2024. 2 +[39] Gangming Zhao, Kongming Liang, Chengwei Pan, Fandong Zhang, Xianpeng Wu, Xinyang Hu, and Yizhou Yu. Graph convolution based cross-network multiscale feature fusion for deep vessel segmentation. IEEE Transactions on Medical Imaging, 42(1):183-195, 2022. 1, 2 +[40] Tianyi Zhao, Kai Cao, Jiawen Yao, Isabella Nogues, Le Lu, Lingyun Huang, Jing Xiao, Zhaozheng Yin, and Ling Zhang. 3d graph anatomy geometry-integrated network for pancreatic mass segmentation, diagnosis, and quantitative patient management. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 13743-13752, 2021. 3 +[41] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. 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Previous methods have commonly relied on discrete representation like mask, often resulting in local fractures or scattered fragments due to the inherent limitations of the per-pixel classification paradigm. In this work, we introduce DeformCL, a new continuous representation based on Deformable Centerlines, where centerline points act as nodes connected by edges that capture spatial relationships. Compared with previous representations, DeformCL offers three key advantages: natural connectivity, noise robustness, and interaction facility. We present a comprehensive training pipeline structured in a cascaded manner to fully exploit these favorable properties of DeformCL. Extensive experiments on four 3D vessel segmentation datasets demonstrate the effectiveness and superiority of our method. Furthermore, the visualization of curved planar reformation images validates the clinical significance of the proposed framework. 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Timely detection of potential high-risk locations and prompt intervention are crucial to reducing mortality, relying on accurate extraction, reconstruction, and analysis of major vessels in CTA images [16]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 301, + 555, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 555, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 555, + 350 + ], + "type": "text", + "content": "In clinical practice, the primary requirement is to achieve accurate segmentation of primary vessel branches to enable comprehensive vascular system assessment and detailed local analysis." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 352, + 556, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 352, + 556, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 352, + 556, + 663 + ], + "type": "text", + "content": "Previous methodologies [1, 21, 25, 26, 29, 31] have predominantly adopted the traditional semantic segmentation approach, which relies on fine-grained, per-pixel classification within a discrete mask representation. As illustrated in the top part of Figure 1, to improve the volumetric scores (e.g. Dice) or topological metrics (e.g. betti number errors) for segmentation, these approaches introduce a variety of innovations, such as incorporating tubular priors into network architecture [13, 21, 25, 31, 36, 39] or designing topology-preserving loss functions [1, 9, 26]. Despite these advancements in the training process, the core issue that the discrete mask representation is not well-suited for the curvilinear vessels remains unchanged, imposing several inherent limitations that restrict the model's performance and applicability, as shown in the top part of Figure 2. Firstly, the neural networks struggle to recognize fragile and tortuous local structures, which may lead to segmentation fractures [21]. Moreover, the discrete representation exhibits poor robustness to local noise [26, 29], such as variations in tissue density, due to the lack of a holistic view of the global morphology. Consequently, it may mistakenly identify the tissues with appearances similar to target vessels. Finally, designing an effective feature aggregation strategy along tubular curves remains challenging, considering the lack of explicit relationships among elements in discrete mask representations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "These challenges motivate us to seek a continuous representation that can explicitly fit the tubular structures from a holistic view, rather than confined to per-pixel classification paradigm. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 134, + 703 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 67, + 703, + 113, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 113, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 113, + 712 + ], + "type": "text", + "content": "†Project lead." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "30896" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 553, + 203 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 203 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 203 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 203 + ], + "type": "image", + "image_path": "3ec4c7541ed469d1737cc92c55bc8129cee23a9be0beeafd54e9deff278f58d4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 205, + 555, + 262 + ], + "lines": [ + { + "bbox": [ + 54, + 205, + 555, + 262 + ], + "spans": [ + { + "bbox": [ + 54, + 205, + 555, + 262 + ], + "type": "text", + "content": "Figure 1. Previous methods [1, 21, 26, 29, 31] primarily rely on the discrete mask representation, adopting a per-pixel classification paradigm for vessel segmentation. Common techniques in these approaches include incorporating tubular priors and applying topology-preserving loss functions. In contrast, we introduce a new continuous representation, DeformCL, which employs centerline points connected by edges to gradually fit the curvilinear vessels via a template deformation process. Once structured centerlines are obtained, generating segmentation predictions with improved topological accuracy becomes a straightforward task." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 284, + 297, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 284, + 297, + 475 + ], + "spans": [ + { + "bbox": [ + 54, + 284, + 297, + 475 + ], + "type": "text", + "content": "a new representation for vessel extraction in 3D medical image based on Deformable Centerline. As shown in the bottom part of Figure 1, DeformCL employs a graph structure, wherein centerline points serve as nodes connected by edges representing their spatial relationships. This continuously defined representation accurately depicts the curvilinear structures, thus circumventing the drawbacks of discrete mask representation and has its own merits: (1) the incorporation of natural connectivity mitigates centerline ruptures, particularly in the thin and fragile areas; (2) by considering the entire curvilinear structures rather than local pixels, DeformCL ensures a comprehensive understanding of the global morphology, thus reducing local artifacts and false positives; (3) the inherent graph structure facilitates efficient and effective feature aggregation along the tubular curves, enhancing overall segmentation performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 480, + 296, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 480, + 296, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 480, + 296, + 685 + ], + "type": "text", + "content": "We propose a novel framework to learn deformable centerline representation from 3D medical images. Our framework consists of several key steps. Firstly, we adaptively generate an initial continuous centerline template based on the input image, taking anatomical variations among different individuals into account. Next, the centerline points within the template will interact with each other to capture features along tubular curves. The whole centerline template will be iteratively refined by deformation and unpooling layers, gradually aligning with the ground truth centerlines. Finally, after obtaining precise centerlines of tubular structures, crafting a high-quality segmentation algorithm becomes a straightforward task. In our approach, we leverage the distance map derived from the predicted centerline points to execute the final segmentation process effortlessly. Benefiting from the high-quality continuous centerlines, the segmentation performance is improved significantly." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "We benchmark DeformCL on four 3D medical datasets, and the extensive experiments validate the effectiveness of" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 283, + 555, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 283, + 555, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 283, + 555, + 403 + ], + "type": "text", + "content": "our proposed method. Additionally, due to its continuous nature, DeformCL's centerline predictions can be directly used as a structural representation of vessels, commonly as directional centerlines [10, 24]. This structural representation is crucial in clinical practice, serving as an indispensable component in various subsequent diagnostic tasks, such as curved planar reformation [11] and computational hemodynamics [27]. We qualitatively demonstrate the clinical relevance of DeformCL, highlighting its potential applicability for diagnostic purposes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 326, + 403, + 533, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 403, + 533, + 414 + ], + "spans": [ + { + "bbox": [ + 326, + 403, + 533, + 414 + ], + "type": "text", + "content": "In summary, our main contributions are three-fold:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 415, + 555, + 510 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 314, + 415, + 554, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 415, + 554, + 450 + ], + "spans": [ + { + "bbox": [ + 314, + 415, + 554, + 450 + ], + "type": "text", + "content": "- We introduce a continuous representation, called DeformCL, which possesses several favorable properties for curvilinear vessels in 3D medical image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 451, + 555, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 451, + 555, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 451, + 555, + 485 + ], + "type": "text", + "content": "- We propose a comprehensive pipeline for effectively training DeformCL through a cascaded deformation process." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 487, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 555, + 510 + ], + "type": "text", + "content": "- Our approach significantly bolsters the performance of several baselines on four 3D vessel extraction datasets." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 521, + 402, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 402, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 402, + 533 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 540, + 533, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 533, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 533, + 553 + ], + "type": "text", + "content": "2.1. Vessel Segmentation in 3D Medical Image" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "type": "text", + "content": "Vessel segmentation in 3D medical image is a crucial task due to the prevalence of curvilinear vessels in the human body. Classical modern segmentation models like UNet [3, 23] and FCN [17] face challenges in accurately extracting tubular structures due to their complex global morphology and fragile thin structures. Previous methods have adopted various strategies to address these challenges: incorporate tubular priors into network architecture [14, 21, 25, 31, 33, 36, 39], design topology-preserving loss functions [1, 9, 26] or employ more flexible representation [29, 38]. Shit et al. [26] introduces a new connectivity-aware similarity measure called clDice, and the differentiable version can be used to train segmentation models for" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "30897" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": "tubular structures. Qi et al. [21] proposes a dynamic snake convolution to let networks adaptively focus on the tubular structures and make more accurate predictions. Wang et al. [29] relies on the flexibility of point set representation which is not restricted to a fixed grid to promote the performance of tubular structure extraction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 151, + 182, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 151, + 182, + 164 + ], + "spans": [ + { + "bbox": [ + 55, + 151, + 182, + 164 + ], + "type": "text", + "content": "2.2. Deformable Paradigm" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 168, + 296, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 168, + 296, + 432 + ], + "spans": [ + { + "bbox": [ + 55, + 168, + 296, + 432 + ], + "type": "text", + "content": "The deformable paradigm is a widely used technique in deep learning, particularly in computer vision, where it plays a crucial role in capturing complex structures and achieving significant advancements in various tasks. Introduced by Dai et al. [4], deformable convolution extends traditional convolutions to capture complex structures effectively. It has been successfully applied in tasks such as object detection and segmentation, allowing models to adapt to object variations and complex shapes. Deformable DETR [41] combines attention mechanism with deformable paradigm for efficient feature extraction process. In addition, deformable structures have also found applications in 3D reconstruction tasks [2, 14, 30, 32, 34, 40]. For instance, Pixel2Mesh [30] generates 3D shapes represented as triangular meshes from single images by progressively deforming an initial ellipsoid. Similarly, Voxel2Mesh [32] extends this approach to generate organ surfaces from 3D medical volumes, facilitating organ segmentation and visualization. Kong et al. [14] proposed a deep-learning approach to generate whole heart geometries from pre-defined mesh templates, demonstrating the versatility of deformable structures in human anatomical modeling." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 441, + 112, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 441, + 112, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 441, + 112, + 453 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 462, + 296, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 296, + 522 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 296, + 522 + ], + "type": "text", + "content": "In this section, we will first introduce the new representation DeformCL and its favorable properties in Sec 3.1. Sec 3.2 elaborates on the network architecture for learning deformation centerline representation from 3D medical images. Sec 3.3 presents the training losses for the framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 529, + 216, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 529, + 216, + 541 + ], + "spans": [ + { + "bbox": [ + 55, + 529, + 216, + 541 + ], + "type": "text", + "content": "3.1. Representation of DeformCL" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 545, + 296, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 296, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 296, + 641 + ], + "type": "text", + "content": "In 3D medical imaging, a common representation of a given volume " + }, + { + "bbox": [ + 55, + 545, + 296, + 641 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}" + }, + { + "bbox": [ + 55, + 545, + 296, + 641 + ], + "type": "text", + "content": " is its segmentation mask, denoted as " + }, + { + "bbox": [ + 55, + 545, + 296, + 641 + ], + "type": "inline_equation", + "content": "Y \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}" + }, + { + "bbox": [ + 55, + 545, + 296, + 641 + ], + "type": "text", + "content": ". Nearly all previous methods [1, 21, 25, 26, 29, 31] rely on this discrete mask representation, framing the task as per-pixel classification. This paradigm inherently possesses several limitations, as illustrated in the top part of Figure 2, which ultimately restrict the model's performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "text", + "content": "In this paper, we introduce a novel continuous representation called Deformable CenterLine (DeformCL) to efficiently and effectively capture tubular structures in 3D medical image. Instead of relying on segmentation mask, we represent tubular structures using a graph " + }, + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = \\{\\mathcal{V},\\epsilon \\}" + }, + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{v_{i}|v_{i}\\in \\mathbb{R}^{3}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "text", + "content": " is a set of " + }, + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "text", + "content": " vertices standing" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 329, + 72, + 540, + 155 + ], + "blocks": [ + { + "bbox": [ + 329, + 72, + 540, + 155 + ], + "lines": [ + { + "bbox": [ + 329, + 72, + 540, + 155 + ], + "spans": [ + { + "bbox": [ + 329, + 72, + 540, + 155 + ], + "type": "image", + "image_path": "1f5f80f12b0e2e829c2b8a6f02ac77f186c37a5163018a48fbba69f04679fe37.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 157, + 555, + 179 + ], + "lines": [ + { + "bbox": [ + 313, + 157, + 555, + 179 + ], + "spans": [ + { + "bbox": [ + 313, + 157, + 555, + 179 + ], + "type": "text", + "content": "Figure 2. Three significant properties of DeformCL compared with the discrete mask representation. (Zoom in for more details.)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 203, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 203, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 203, + 553, + 228 + ], + "type": "text", + "content": "for centerline points, " + }, + { + "bbox": [ + 313, + 203, + 553, + 228 + ], + "type": "inline_equation", + "content": "\\epsilon = \\{(k,w)|1\\leq k,w\\leq N\\}" + }, + { + "bbox": [ + 313, + 203, + 553, + 228 + ], + "type": "text", + "content": " is the set of edges connecting adjacent vertices." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 228, + 553, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 276 + ], + "type": "text", + "content": "As shown in the bottom part of Figure 2, compared with previous discrete representations, DeformCL possesses several favorable properties, making it a reasonable and effective representation for tubular structure modeling." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 277, + 554, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 554, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 554, + 384 + ], + "type": "text", + "content": "Natural connectivity. Unlike traditional discrete representations, DeformCL naturally exhibits the connectivity among centerline points, which explicitly models the tubular structures in a continuously defined way. On one hand, this continuous representation helps prevent predictions from breaking in thin and fragile regions. On the other hand, the traditionally complex and time-consuming continuous centerlines extraction [10, 19] from segmentation for curved planner reconstruction [11] is eliminated." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 385, + 554, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 385, + 554, + 469 + ], + "spans": [ + { + "bbox": [ + 313, + 385, + 554, + 469 + ], + "type": "text", + "content": "Noise robustness. Thanks to its top-down manner, DeformCL exhibits robustness to noise and local disturbances, such as variations in tissue density or the presence of contrast agents. This inherent property enables DeformCL to effectively filter out local artifacts and false positives, leading to more accurate and reliable tubular structure extraction compared to previous bottom-up methods." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 470, + 554, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 470, + 554, + 566 + ], + "spans": [ + { + "bbox": [ + 313, + 470, + 554, + 566 + ], + "type": "text", + "content": "Interaction facility. Constrained by the discrete representation, previous methods [21, 26, 29, 31] lack of an effective approach for tubular feature aggregation. On the contrary, DeformCL's graph structure facilitates feature fusion process via methods like GCN [12] or Transformer [28] along the tubular curve. This global information interaction is significant for the structure completeness and topology correctness of tubular predictions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 574, + 440, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 440, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 440, + 586 + ], + "type": "text", + "content": "3.2. Network Architecture" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "type": "text", + "content": "In this subsection, we will introduce the network architecture for learning deformable centerline representation. The whole framework is shown in Figure 3. Given a 3D medical image " + }, + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}" + }, + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "type": "text", + "content": ", we first pass it through a 3D backbone (e.g. 3D UNet [3]) to obtain hierarchical feature maps " + }, + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\{F_i\\}_{i=1}^m" + }, + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "type": "text", + "content": " at different down-sampled rates. Additionally, the backbone network produces a coarse segmentation result " + }, + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\hat{Y}_c \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{W} \\times \\mathbb{D}}" + }, + { + "bbox": [ + 313, + 593, + 554, + 689 + ], + "type": "text", + "content": " for each category of vessels." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "content": "Adaptive Template Generation. In order to initialize the graph structure of DeformCL, we attempt to initial-" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30898" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 73, + 527, + 320 + ], + "blocks": [ + { + "bbox": [ + 82, + 73, + 527, + 320 + ], + "lines": [ + { + "bbox": [ + 82, + 73, + 527, + 320 + ], + "spans": [ + { + "bbox": [ + 82, + 73, + 527, + 320 + ], + "type": "image", + "image_path": "4f7468b84536469a2fe97024a46544b872d0a7cecc331ea307f70a81b3474e3b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 323, + 555, + 381 + ], + "lines": [ + { + "bbox": [ + 54, + 323, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 54, + 323, + 555, + 381 + ], + "type": "text", + "content": "Figure 3. Overview of the training process. Given a 3D medical image, the segmentation network first outputs a coarse prediction and generates hierarchical downsampled feature maps. An initial template, produced by the Adaptive Template Generation module, is then iteratively fed through deformation and unpooling layers to progressively adapt to the curvilinear structures. Finally, refined segmentation results are generated based on the accurately aligned continuous centerlines. We apply Dice loss to both the coarse and refined segmentation predictions, and local chamfer loss, SDF loss, and regularization loss for centerline predictions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 403, + 295, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 403, + 295, + 498 + ], + "spans": [ + { + "bbox": [ + 54, + 403, + 295, + 498 + ], + "type": "text", + "content": "ize a tubular template motivated by mesh generation methods [30, 32]. However, unlike human organs, tubular structures in 3D medical image, such as coronary arteries, exhibit complex global morphology and variable extension direction, which means that discovering a universal template for such structures poses significant challenges. Therefore, we introduce a new method to adaptively generate initial templates for each image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": "The template generation process, illustrated in the Figure 4, is conducted independently for each category of vessels. Firstly, the coarse segmentation result " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "\\hat{Y}_c" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": " is converted into discrete centerline points via traditional 3D thinning algorithm [15]. These points are then reconstructed into a graph using the minimum spanning tree algorithm [7] following the strategy in [37]. Next, a set of " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": " control points is selected from the graph at fixed distances, serving as the abstraction of the structure. Finally, curvilinear interpolation (e.g. Bezier Curve Interpolation, Linear Interpolation) is applied based on the control points to generate the initial template, denoted as " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "\\{v_i^c | v_i^c \\in \\mathbb{R}^3\\}_{i=1}^{N_c}" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "v_i^c" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": "-th point for category " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "N_c" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": " is the total number of points for category " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "v_i^c" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": " is connected with " + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "inline_equation", + "content": "v_{i+1}^c" + }, + { + "bbox": [ + 55, + 498, + 295, + 666 + ], + "type": "text", + "content": " by default." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": "It is worth noting that we adopt a rough template generation strategy using control points instead of directly utilizing the reconstructed tree as the initial template. The reason is that we empirically find overly accurate initial templates" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 403, + 553, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 553, + 450 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 553, + 450 + ], + "type": "text", + "content": "may harm model performance, supported by experimental results shown in Table 3. We speculate that overly accurate initial templates may simplify the deformation task excessively, potentially leading to insufficient model training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 451, + 554, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 451, + 554, + 511 + ], + "spans": [ + { + "bbox": [ + 313, + 451, + 554, + 511 + ], + "type": "text", + "content": "Cascaded Deformation Process. After the generation of initial templates, we proceed with the cascaded deformation process to refine the centerline predictions. For clarity, we focus on the centerline points of one category of vessels in the subsequent sections of the paper." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 511, + 554, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 554, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 554, + 548 + ], + "type": "text", + "content": "Firstly, trilinear interpolation is applied to each centerline point " + }, + { + "bbox": [ + 313, + 511, + 554, + 548 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 313, + 511, + 554, + 548 + ], + "type": "text", + "content": " in the downsampled feature maps " + }, + { + "bbox": [ + 313, + 511, + 554, + 548 + ], + "type": "inline_equation", + "content": "\\{F_i\\}_{i = 1}^m" + }, + { + "bbox": [ + 313, + 511, + 554, + 548 + ], + "type": "text", + "content": ", and the hierarchical points features are fused via a linear layer:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 321, + 557, + 553, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 557, + 553, + 571 + ], + "spans": [ + { + "bbox": [ + 321, + 557, + 553, + 571 + ], + "type": "interline_equation", + "content": "f \\left(v _ {i}\\right) = \\operatorname {L i n e a r} \\left(\\left[ \\operatorname {T r i} \\left(F _ {1}, v _ {i}\\right), \\dots , \\operatorname {T r i} \\left(F _ {m}, v _ {i}\\right) \\right]\\right) \\in \\mathbb {R} ^ {C}, \\tag {1}", + "image_path": "7626265fcdfa5f6f4eeca3511e3b90dd60bbe02e4e3114c0f5e7546f381834b4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "text", + "content": " denotes the channel size, Tri represents the tri-linear interpolation. Next, the points and their corresponding features " + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\{v_{i},f(v_{i})\\}" + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "text", + "content": " are fed into Transformer [28] layers for feature aggregation along the tubular curve. The positional encoding " + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{Pos}(v^l)" + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "text", + "content": " contains learnable embeddings of absolute 3D positions of points and relative positions in the graph. Subsequently, the augmented point features are used to predict an offset " + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "inline_equation", + "content": "\\delta_i^l" + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "text", + "content": ", which is then applied to update the position of each point " + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "inline_equation", + "content": "v_{i}^{l}" + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "inline_equation", + "content": "v_{i}^{l + 1}" + }, + { + "bbox": [ + 313, + 581, + 554, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "content": "Since high-accuracy centerlines require a sufficient number of points to capture curvilinear structures accurately, we" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30899" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 292, + 121 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 292, + 121 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 292, + 121 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 292, + 121 + ], + "type": "image", + "image_path": "21fe1120de844ce93b8cd7df0776d53b71b17da688a310172b4c5cf44eb07b6f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 100, + 122, + 251, + 135 + ], + "lines": [ + { + "bbox": [ + 100, + 122, + 251, + 135 + ], + "spans": [ + { + "bbox": [ + 100, + 122, + 251, + 135 + ], + "type": "text", + "content": "Figure 4. Adaptive Template Generation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "spans": [ + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "type": "text", + "content": "apply an unpooling strategy after deformation to increase point density. Specifically, a new point is inserted between each pair of connected points. We reuse the symbol " + }, + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "type": "inline_equation", + "content": "\\{v_i^{l + 1}\\}" + }, + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "type": "text", + "content": " for clarity. This process is iterated " + }, + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "type": "text", + "content": " times for accurate centerline prediction, where the " + }, + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 156, + 296, + 227 + ], + "type": "text", + "content": "-th layer is described as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 234, + 294, + 250 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 234, + 294, + 250 + ], + "spans": [ + { + "bbox": [ + 61, + 234, + 294, + 250 + ], + "type": "interline_equation", + "content": "\\tilde {f} \\left(v _ {i} ^ {l}\\right) = f \\left(v _ {i} ^ {l}\\right) + \\operatorname {T r a n s f o r m e r} \\left(f \\left(v ^ {l}\\right), \\operatorname {P o s} \\left(v ^ {l}\\right)\\right) \\in \\mathbb {R} ^ {C}, \\tag {2}", + "image_path": "1acef1cf8022361e13f2c9e770d823e24f636a30fe599a1952c985c95870d81e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 251, + 295, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 251, + 295, + 266 + ], + "spans": [ + { + "bbox": [ + 62, + 251, + 295, + 266 + ], + "type": "interline_equation", + "content": "\\delta_ {i} ^ {l} = \\operatorname {T a n h} \\left(\\mathrm {M L P} \\left(\\tilde {f} \\left(v _ {i} ^ {l}\\right)\\right)\\right) \\in \\mathbb {R} ^ {3}, \\tag {3}", + "image_path": "0dfb33a3cf2865de70fc569b30ac322523d3bd809a537ba2573eb981f8156429.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 268, + 295, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 268, + 295, + 283 + ], + "spans": [ + { + "bbox": [ + 62, + 268, + 295, + 283 + ], + "type": "interline_equation", + "content": "v _ {i} ^ {l + 1} = v _ {i} ^ {l} + \\delta_ {i} ^ {l} \\in \\mathbb {R} ^ {3}, \\tag {4}", + "image_path": "7953479a289d9b0ec24c5389e3b46e003c1854d3737e46b4fc17fc0c01b529ae.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 285, + 295, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 285, + 295, + 300 + ], + "spans": [ + { + "bbox": [ + 63, + 285, + 295, + 300 + ], + "type": "interline_equation", + "content": "\\left\\{v _ {i} ^ {l + 1} \\right\\} = \\text {U n p o o l i n g} \\left(\\left\\{v _ {i} ^ {l + 1} \\right\\}\\right) \\tag {5}", + "image_path": "f941730a92dd6f9ac13657b140a27c204b6ec893ae4ca1968ebea62609cc817a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 308, + 296, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 308, + 296, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 308, + 296, + 354 + ], + "type": "text", + "content": "After completing the cascaded deformation process, the final set of points " + }, + { + "bbox": [ + 55, + 308, + 296, + 354 + ], + "type": "inline_equation", + "content": "\\{v_i^L\\}" + }, + { + "bbox": [ + 55, + 308, + 296, + 354 + ], + "type": "text", + "content": " represents the predicted centerline points, which will be used for subsequent centerline-based segmentation task." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 356, + 296, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 356, + 296, + 452 + ], + "spans": [ + { + "bbox": [ + 55, + 356, + 296, + 452 + ], + "type": "text", + "content": "Centerline-based Segmentation. Once accurate centerlines of tubular structures are obtained, predicting the corresponding segmentation results becomes straightforward. In this work, we employ a simple method using distance maps to achieve centerline-based segmentation. Specifically, given the predicted centerline points " + }, + { + "bbox": [ + 55, + 356, + 296, + 452 + ], + "type": "inline_equation", + "content": "V = \\{v_{i}^{L}\\in \\mathbb{R}^{3}\\}" + }, + { + "bbox": [ + 55, + 356, + 296, + 452 + ], + "type": "text", + "content": ", we calculate the minimum distance of each voxel in the image to the points in " + }, + { + "bbox": [ + 55, + 356, + 296, + 452 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 55, + 356, + 296, + 452 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 462, + 295, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 462, + 295, + 480 + ], + "spans": [ + { + "bbox": [ + 104, + 462, + 295, + 480 + ], + "type": "interline_equation", + "content": "D [ x, y, z ] = \\min _ {v \\in V} | | (x, y, z) - v | | _ {2}, \\tag {6}", + "image_path": "e68b36995a241f2f15e989199c803ee527921c99b0b75f0cda9f063dd87abb70.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "inline_equation", + "content": "D \\in \\mathbb{R}^{\\mathbb{H} \\times \\mathbb{D} \\times \\mathbb{W}}" + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "text", + "content": " is the distance map based on the centerline points. Finally, the coarse segmentation results " + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\hat{Y}_c" + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "text", + "content": " and the distance map " + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "text", + "content": " are input to a convolutional layer for fusion, yielding the refined segmentation results " + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\hat{Y}_r" + }, + { + "bbox": [ + 55, + 485, + 296, + 534 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 540, + 143, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 143, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 143, + 553 + ], + "type": "text", + "content": "3.3. Training Loss" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 558, + 296, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 296, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 296, + 617 + ], + "type": "text", + "content": "In this subsection, we will elaborate on the loss functions of the proposed framework. For centerline prediction, we employ a combination of local chamfer distance loss, signed distance function (SDF) loss, and a regularization loss. We utilize Dice loss for segmentation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 618, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 712 + ], + "type": "text", + "content": "Local Chamfer Distance Loss. Tradition global chamfer distance loss calculates the distance between two point cloud sets. However, curvilinear vessels in the human body often exhibit complex global morphology and sparse 3D distribution. As a result, using global chamfer distance loss may lead to larger fluctuations and suboptimal convergence during the training process. To address this issue, we adopt a local version of chamfer distance loss." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": "To be specific, we begin by employing Farthest Point Sampling (FPS) to select candidate points " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\{u_{i_k}\\}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " from the ground truth centerline points " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\{u_i\\}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": ", which are obtained from the ground truth mask via traditional 3D thinning algorithm [15]. Then, we crop local patches with fixed size " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " centered around each selected point " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\{u_{i_k}\\}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": ". The points located within each cropped patch are denoted as " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\omega_{i_k} = \\{p = (x,y,z)|p\\in [u_{i_k} - M / 2,u_{i_k} + M / 2]\\}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": ", and the set of patches is denoted as " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\Omega = \\{\\omega_{i_k}\\}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": ". The chamfer distance loss is then applied between the predicted point set and the ground truth point set within each cropped patch. Formally, the loss is defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 232, + 558, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 232, + 558, + 270 + ], + "spans": [ + { + "bbox": [ + 314, + 232, + 558, + 270 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c h a}} = \\frac {1}{| \\Omega |} \\sum_ {\\omega \\in \\Omega} \\left(\\sum_ {v _ {i} \\in \\omega} \\min _ {u _ {i} \\in \\omega} \\| v _ {i} - u _ {i} \\| _ {2} ^ {2} + \\sum_ {u _ {i} \\in \\omega} \\min _ {v _ {i} \\in \\omega} \\| u _ {i} - v _ {i} \\| _ {2} ^ {2}\\right). \\tag {7}", + "image_path": "6c361bc7c725fdb8f2acea0b2c787898823861b9401d8a519c05a8ea7544124b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 270, + 555, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 270, + 555, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 555, + 354 + ], + "type": "text", + "content": "SDF Loss. Signed Distance Function (SDF) is a well-established concept in computer vision and computer graphics, used to represent the surface of 3D objects through signed distances. We find that SDF is appropriate for ensuring the centrality of predicted centerline points. Firstly, we define the surface of tubular strcutures following [31]:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 328, + 361, + 553, + 376 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 361, + 553, + 376 + ], + "spans": [ + { + "bbox": [ + 328, + 361, + 553, + 376 + ], + "type": "interline_equation", + "content": "S = \\{x \\in \\mathbb {R} ^ {3} | Y [ x ] = 1, \\exists u \\in \\mathcal {N} (x), Y [ u ] = 0 \\}, \\tag {8}", + "image_path": "b8c54ac2ce53f2471eb124c688e025e43601a2b7f3d9ee6a53e37dddae086c0d.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "spans": [ + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(x)" + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "text", + "content": " denotes the 6-neightbour voxels of " + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "text", + "content": " is the ground truth mask. Then, the SDF value of an arbitrary point " + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 381, + 554, + 418 + ], + "type": "text", + "content": " in the image can be calculated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 328, + 424, + 553, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 424, + 553, + 459 + ], + "spans": [ + { + "bbox": [ + 328, + 424, + 553, + 459 + ], + "type": "interline_equation", + "content": "S D F (p) = \\left\\{ \\begin{array}{l l} - \\min _ {u \\in S} | | p - u | | _ {2} ^ {2}, & \\text {i f} Y [ p ] = 1, \\\\ \\min _ {u \\in S} | | p - u | | _ {2} ^ {2}, & \\text {i f} Y [ p ] = 0. \\end{array} \\right. \\tag {9}", + "image_path": "c9353718482823b5274616ab9941d88c2ad6165ae096c2630d9d1d4e2a84401e.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 464, + 554, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 554, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 554, + 489 + ], + "type": "text", + "content": "The SDF values of all predicted centerline points are utilized as the training loss:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 382, + 495, + 553, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 495, + 553, + 528 + ], + "spans": [ + { + "bbox": [ + 382, + 495, + 553, + 528 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s d f}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} S D F (v _ {i}). \\tag {10}", + "image_path": "ac56f9baa1bb6a440521f41c3bd37a9dc3902a88ab6a6e9e330b8c86135b58b1.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 534, + 409, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 409, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 409, + 628 + ], + "type": "text", + "content": "As illustrated in Figure 5, SDF loss serves two crucial purposes. Firstly, it provides supervision for all predicted centerline points, whereas the local chamfer" + } + ] + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 429, + 536, + 553, + 613 + ], + "blocks": [ + { + "bbox": [ + 429, + 536, + 553, + 613 + ], + "lines": [ + { + "bbox": [ + 429, + 536, + 553, + 613 + ], + "spans": [ + { + "bbox": [ + 429, + 536, + 553, + 613 + ], + "type": "image", + "image_path": "d4d481a2bc9d2f062bdf2a3bf6e9a9aa6146e89ef73b64716a578be2c14c1c69.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 452, + 614, + 528, + 625 + ], + "lines": [ + { + "bbox": [ + 452, + 614, + 528, + 625 + ], + "spans": [ + { + "bbox": [ + 452, + 614, + 528, + 625 + ], + "type": "text", + "content": "Figure 5. SDF Loss." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 630, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 554, + 689 + ], + "type": "text", + "content": "distance loss can only provide supervision for points within cropped patches, potentially missing outlier predictions. Secondly, it facilitates the gradual deformation of predicted points towards the ideal center of tubular structures, thereby ensuring the centrality of centerlines." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "Regularization Loss. To prevent the deformable centerline points from deviating mistakenly, which may result in long" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "30900" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 97 + ], + "type": "text", + "content": "edges between adjacent vertices, we apply a regularization loss to penalize the adjacent points with much long edges:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 116, + 102, + 295, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 102, + 295, + 135 + ], + "spans": [ + { + "bbox": [ + 116, + 102, + 295, + 135 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e g}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left| \\left| v _ {i} - v _ {i - 1} \\right| \\right| _ {2} ^ {2}. \\tag {11}", + "image_path": "755274f47d5da89c518edee583602ca265914456ce7c311a3c3601480d41a5bb.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 142, + 295, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 142, + 295, + 166 + ], + "spans": [ + { + "bbox": [ + 55, + 142, + 295, + 166 + ], + "type": "text", + "content": "Segmentation Loss. We use Dice loss [18] as loss function for the coarse and refined segmentation results " + }, + { + "bbox": [ + 55, + 142, + 295, + 166 + ], + "type": "inline_equation", + "content": "\\hat{Y}_c" + }, + { + "bbox": [ + 55, + 142, + 295, + 166 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 142, + 295, + 166 + ], + "type": "inline_equation", + "content": "\\hat{Y}_r" + }, + { + "bbox": [ + 55, + 142, + 295, + 166 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 101, + 171, + 295, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 171, + 295, + 186 + ], + "spans": [ + { + "bbox": [ + 101, + 171, + 295, + 186 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s e g}} = \\lambda \\operatorname {D i c e} \\left(Y, \\hat {Y} _ {c}\\right) + \\operatorname {D i c e} \\left(Y, \\hat {Y} _ {r}\\right), \\tag {12}", + "image_path": "4a5d683552cab2ea6b2fd4da1990de1bc1cbe343cf6ee30e1b433690907d7723.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 193, + 141, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 193, + 141, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 193, + 141, + 203 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 193, + 141, + 203 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 193, + 141, + 203 + ], + "type": "text", + "content": " is set to 0.2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 205, + 296, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 205, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 205, + 296, + 251 + ], + "type": "text", + "content": "Note that local chamfer distance loss, SDF loss and regularization loss are applied to all intermediate results in the cascaded deformation process. The total training loss is a combination of all loss functions:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 257, + 295, + 290 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 257, + 295, + 290 + ], + "spans": [ + { + "bbox": [ + 63, + 257, + 295, + 290 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum_ {l = 1} ^ {L} w _ {l} \\left(\\lambda_ {\\mathrm {c h a}} \\mathcal {L} _ {\\mathrm {c h a}} + \\lambda_ {\\mathrm {s d f}} \\mathcal {L} _ {\\mathrm {s d f}} + \\lambda_ {\\mathrm {r e g}} \\mathcal {L} _ {\\mathrm {r e g}}\\right) + \\mathcal {L} _ {\\mathrm {s e g}}, \\tag {13}", + "image_path": "79fbebcbf000d73ebf68c0acfa96351ce8bd0417271b538ce9ed74362b1dacc9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 296, + 273, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 296, + 273, + 308 + ], + "spans": [ + { + "bbox": [ + 55, + 296, + 273, + 308 + ], + "type": "inline_equation", + "content": "w_{l}" + }, + { + "bbox": [ + 55, + 296, + 273, + 308 + ], + "type": "text", + "content": " stands for the weight of the " + }, + { + "bbox": [ + 55, + 296, + 273, + 308 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 296, + 273, + 308 + ], + "type": "text", + "content": "-th deformation stage." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 317, + 137, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 317, + 137, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 317, + 137, + 331 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 337, + 118, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 337, + 118, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 337, + 118, + 348 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 354, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 296, + 498 + ], + "type": "text", + "content": "We use four datasets to evaluate our proposed framework. HaN-Seg [20] is a public dataset consisting of 56 CT and MR images with 30 categories of head and neck organ pixel annotations. ASOCA [5, 6] is a public dataset in the MICCAI-2020 challenge which aims to automatically segment the coronary artery lumen. It consists of 40 Cardiac Computed Tomography Angiography (CCTA) images with artery segmentation annotations. ImageCAS [35] is a public dataset containing about 1000 3D CTA images with coronary artery segmentation labels. HNCTA is a private head and neck artery dataset with 358 CTA images. More details of datasets can be found in supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 505, + 168, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 168, + 516 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 168, + 516 + ], + "type": "text", + "content": "4.2. Evaluation Metrics" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 522, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 295, + 653 + ], + "type": "text", + "content": "We assess the segmentation performance in three main aspects following [21]. For volumetric scores, we report Dice [18] and clDice [26] to evaluate the segmentation results. For topology-based scores, absolute Betti Errors for Betti Numbers " + }, + { + "bbox": [ + 55, + 522, + 295, + 653 + ], + "type": "inline_equation", + "content": "\\beta_0" + }, + { + "bbox": [ + 55, + 522, + 295, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 522, + 295, + 653 + ], + "type": "inline_equation", + "content": "\\beta_{1}" + }, + { + "bbox": [ + 55, + 522, + 295, + 653 + ], + "type": "text", + "content": " and absolute error of Euler characteristic are used to measure the topology and completeness of the extracted vessels following [21, 26, 29]. For distance-based scores, Hausdorff Distance (HD) is employed for measuring the maximum distance between two 3D point sets. All presented metrics in this paper are the average of all vessel categories." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": "For the centerline extraction task, we use F1, Hausdorff Distance, Chamfer Distance and absolute Betti Errors for Betti Numbers " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\beta_0" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": " as evaluation metrics. For robust evaluation, we apply a three-pixel tolerance region around the ground truth centerline points following [8, 29]." + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 316, + 118, + 558, + 390 + ], + "blocks": [ + { + "bbox": [ + 313, + 72, + 555, + 115 + ], + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 115 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 115 + ], + "type": "text", + "content": "Table 1. Main results on vessel segmentation task. We mark the best performance by bold numbers. Ours (softDice) denotes that we use softDice as base model with the proposed DeformCL as an additional segmentation head." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 118, + 558, + 390 + ], + "lines": [ + { + "bbox": [ + 316, + 118, + 558, + 390 + ], + "spans": [ + { + "bbox": [ + 316, + 118, + 558, + 390 + ], + "type": "table", + "html": "
DatasetMethodVolumetric Scores (%) ↑Topological Error ↓Distance ↓
DiceclDiceβ0β1EulerHD95
HaN-SegDDT [31]75.7685.792.3330.1272.3295.473
softDice [18]76.3085.963.3160.0293.2864.905
Ours (softDice)79.58+3.2888.86+2.902.1230.0892.0344.113
clDice [26]76.2286.502.8610.0652.7965.244
Ours (clDice)78.39+2.1787.32+0.822.2070.2262.0423.838
DSCNet [21]77.1684.633.8580.2953.5644.949
Ours (DSCNet)78.61+1.4586.89+2.262.6020.3582.3184.125
HNCTADDT [31]83.5693.280.1720.0500.2192.666
softDice [18]83.0592.140.2860.0590.3372.924
Ours (softDice)84.69+1.6493.72+1.580.1490.0510.1992.084
clDice [26]83.1391.890.1600.0581.2393.118
Ours (clDice)84.13+1.0093.15+1.260.1500.0520.2002.839
DSCNet [21]83.5492.060.2460.0600.3012.658
Ours (DSCNet)84.80+1.2693.82+1.760.1830.0440.2282.349
ASOCADDT [31]83.0089.630.9980.0941.0907.646
softDice [18]84.0689.810.9300.1190.9966.829
Ours (softDice)85.16+1.1092.41+2.600.4080.1290.5105.082
clDice [26]84.0890.921.0090.1221.0826.299
Ours (clDice)84.77+0.6991.94+1.020.6030.1000.6774.122
DSCNet [21]84.2891.040.8400.1460.9275.286
Ours (DSCNet)85.47+1.1992.87+1.830.5080.0830.5905.212
ImageCASDDT [31]87.5195.320.1890.0650.2784.621
softDice [18]87.5995.150.1900.0620.2684.674
Ours (softDice)88.33+0.7495.48+0.330.0740.0650.1593.580
clDice [26]87.7896.000.1580.0640.2384.021
Ours (clDice)87.85+0.0796.01+0.010.1520.0670.2345.038
DSCNet [21]87.9895.340.2130.0700.2833.751
Ours (DSCNet)88.84+0.8696.38+1.040.1270.0690.2153.291
", + "image_path": "48cd18fa65fabd0ff8e115dd9590ea3bb57509a22f34055d7a0c9502f2f090f7.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 337, + 425, + 529, + 696 + ], + "blocks": [ + { + "bbox": [ + 342, + 411, + 526, + 422 + ], + "lines": [ + { + "bbox": [ + 342, + 411, + 526, + 422 + ], + "spans": [ + { + "bbox": [ + 342, + 411, + 526, + 422 + ], + "type": "text", + "content": "Table 2. Main results on centerline extraction task." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 337, + 425, + 529, + 696 + ], + "lines": [ + { + "bbox": [ + 337, + 425, + 529, + 696 + ], + "spans": [ + { + "bbox": [ + 337, + 425, + 529, + 696 + ], + "type": "table", + "html": "
DatasetMethodMetrics
F1 (%)↑HD95 ↓Chamfer ↓β0 ↓
HaN-SegDDT [31]89.657.67818.9573.136
softDice [18]91.176.98119.1114.318
Ours (softDice)94.56+3.394.2506.3321.727
clDice [26]90.789.02329.2173.636
Ours (clDice)92.36+1.585.2207.1301.409
DSCNet [21]90.457.46218.2954.818
Ours (DSCNet)91.50+1.058.22212.3622.773
HNCTADDT [31]97.293.2917.0830.394
softDice [18]97.053.82111.9940.591
Ours (softDice)98.74+1.692.2504.0720.422
clDice [26]96.693.5669.0970.387
Ours (clDice)98.36+1.672.3216.7610.520
DSCNet [21]97.283.3978.4050.534
Ours (DSCNet)98.59+1.312.1453.8290.419
ASOCADDT [31]91.4310.64163.4872.063
softDice [18]91.5711.95646.3581.905
Ours (softDice)95.23+3.667.42329.0270.810
clDice [26]93.439.16829.9711.554
Ours (clDice)94.77+1.347.27317.7380.929
DSCNet [21]93.467.90823.0521.540
Ours (DSCNet)94.28+0.827.05214.7601.000
ImageCASDDT [31]95.104.88119.3760.538
softDice [18]94.407.13430.3450.687
Ours (softDice)96.67+2.275.12717.3130.123
clDice [26]95.785.04319.4900.385
Ours (clDice)96.64+0.864.74314.9410.333
DSCNet [21]95.325.17017.2390.503
Ours (DSCNet)97.28+1.964.30312.1520.318
", + "image_path": "2642c83ca2289e56df07a937b3fcbfcb967fd1950f2f2d5d6154453bb0967e37.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30901" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 72, + 293, + 312 + ], + "blocks": [ + { + "bbox": [ + 59, + 72, + 293, + 312 + ], + "lines": [ + { + "bbox": [ + 59, + 72, + 293, + 312 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 293, + 312 + ], + "type": "image", + "image_path": "8cec88bf16b6180f7df2fe87c1a5ddc725f67cec92f8d01fc1b4df405ec63aca.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 315, + 295, + 369 + ], + "lines": [ + { + "bbox": [ + 55, + 315, + 295, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 315, + 295, + 369 + ], + "type": "text", + "content": "Figure 6. Visualizations of the predictions from different methods on four 3D medical image datasets. Different rows and columns stand for different datasets and methods respectively. The arrows point out the areas where models easily exhibit errors. Zoom in for more details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 393, + 188, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 393, + 188, + 406 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 188, + 406 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "text", + "content": "In our experiments, we use 3D UNet [3] as the backbone for all methods. We set the number of hierarchical feature maps " + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "text", + "content": " to 5. The number of control points " + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "text", + "content": " in template generation is set to 4. The number of deformation stages " + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "text", + "content": " is 4, and the channel size for point features " + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "text", + "content": " is 24. The centerline template of each vessel category is initialized with " + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "inline_equation", + "content": "N_{c} = 100" + }, + { + "bbox": [ + 55, + 411, + 295, + 506 + ], + "type": "text", + "content": " points by default. All of the coordinates of centerline points are normalized to 0-1 in the framework." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "spans": [ + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "text", + "content": "When computing local chamfer distance loss, the number of local patches is sampled from an even distribution " + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "inline_equation", + "content": "|\\Omega| \\sim U(60,80)" + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "text", + "content": ". The loss weights " + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{cha}}" + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{sdf}}" + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{reg}}" + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "text", + "content": " are set to 30, 0.5, and 60 by default. The balance weights for different deformation stages " + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "inline_equation", + "content": "\\{w_l\\}_{l=1}^L" + }, + { + "bbox": [ + 55, + 508, + 295, + 591 + ], + "type": "text", + "content": " are set to 0.05, 0.60, 0.95, and 1.00. More implementation details are depicted in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 600, + 140, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 600, + 140, + 611 + ], + "spans": [ + { + "bbox": [ + 55, + 600, + 140, + 611 + ], + "type": "text", + "content": "4.4. Main Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "type": "text", + "content": "Our approach can be incorporated into common segmentation models, such as softmax [18] or clDice [26], as an additional segmentation head. In this subsection, we present the results of our method implemented on softmax [18], clDice [26] and DSCNet [21], comparing it with competitive segmentation models, including softmax [18], cldice [26], DDT [31] and DSCNet [21]. All models are trained under identical settings, including training sched" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 382, + 96, + 489, + 182 + ], + "blocks": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "text", + "content": "Table 3. Ablation on the number of control points k for each category of vessels on HaN-Seg dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 382, + 96, + 489, + 182 + ], + "lines": [ + { + "bbox": [ + 382, + 96, + 489, + 182 + ], + "spans": [ + { + "bbox": [ + 382, + 96, + 489, + 182 + ], + "type": "table", + "html": "
kVolumetric Scores (%) ↑
DiceclDice
078.8786.89
4*79.5888.86
878.3686.88
1677.2285.93
6477.3785.66
", + "image_path": "deb376b81c8c2a600c84047807a84f600fe8dff834ed3caeb4a6b3b99388b253.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 358, + 218, + 512, + 293 + ], + "blocks": [ + { + "bbox": [ + 313, + 184, + 555, + 216 + ], + "lines": [ + { + "bbox": [ + 313, + 184, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 184, + 555, + 216 + ], + "type": "text", + "content": "Table 4. Ablation on loss functions on HaN-Seg dataset. w/o " + }, + { + "bbox": [ + 313, + 184, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cha}}" + }, + { + "bbox": [ + 313, + 184, + 555, + 216 + ], + "type": "text", + "content": " means that we use global chamfer distance loss instead of local chamfer distance loss." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 358, + 218, + 512, + 293 + ], + "lines": [ + { + "bbox": [ + 358, + 218, + 512, + 293 + ], + "spans": [ + { + "bbox": [ + 358, + 218, + 512, + 293 + ], + "type": "table", + "html": "
Loss FunctionVolumetric Scores (%) ↑
DiceclDice
w/o Lcha78.1886.62
w/o Lreg78.3886.70
w/o Lsdf79.5187.89
full configuration79.5888.86
", + "image_path": "0bbc290f4615b322b79bd0a17b4ba290220316803e5e32e7b435e1eea5e69d61.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 315, + 555, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 555, + 361 + ], + "type": "text", + "content": "ules and hyper-parameters, etc. We have not included PointScatter [29] and Topoloss [9] in the comparison as it is designed for 2D images and is not applicable to 3D medical images due to GPU memory limitations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 363, + 554, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 363, + 554, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 363, + 554, + 482 + ], + "type": "text", + "content": "For segmentation, our method demonstrates notable performance improvements when integrated with baseline models as depicted in Table 1. The enhancement is particularly prominent in metrics like cDice and Betti number errors, which primarily reflect vessel completeness and topology correctness. This phenomenon verifies the effectiveness of the continuously defined representation. Furthermore, thanks to the exact prediction of centerlines, the performance of segmentation on the distance metric HD95 has also improved a lot." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 483, + 554, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 554, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 554, + 542 + ], + "type": "text", + "content": "For centerline extraction, we present the experimental results on HaN-Seg and ASOCA datasets in Table 2. It can be concluded that DeformCL can improve a range of metrics consistently across multiple baseline models. More experiments can be found in supplementary materials." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 543, + 554, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 543, + 554, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 543, + 554, + 651 + ], + "type": "text", + "content": "To provide a qualitative assessment of the model performance, we present visualizations of predictions from different methods in Figure 6. These results illustrate that DeformCL effectively captures thin and fragile structures with minimal segmentation fractures. Moreover, the reduction in scattered false positives demonstrates the noise robustness of DeformCL. These results reaffirm that the continuously defined representation offers superior capabilities in curvilinear vessel extraction, owing to its unique properties." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 659, + 408, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 408, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 408, + 672 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "We conduct ablation experiments on the HaN-Seg dataset to assess the impact of different components of our method. Other ablation studies are presented in the supplementary" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30902" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 71, + 282, + 208 + ], + "blocks": [ + { + "bbox": [ + 70, + 71, + 282, + 208 + ], + "lines": [ + { + "bbox": [ + 70, + 71, + 282, + 208 + ], + "spans": [ + { + "bbox": [ + 70, + 71, + 282, + 208 + ], + "type": "image", + "image_path": "446a79d30aa43cae1446575c9d97cd66f5ff22d613b7db4576bd7fb37ea932a6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 210, + 295, + 255 + ], + "lines": [ + { + "bbox": [ + 55, + 210, + 295, + 255 + ], + "spans": [ + { + "bbox": [ + 55, + 210, + 295, + 255 + ], + "type": "text", + "content": "Figure 7. Visual comparison of different loss function configurations. The carnatio masks and yellow lines denote the predicted segmentations and centerlines respectively. The red and green triangles point out the areas to focus on." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 285, + 97, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 285, + 97, + 295 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 97, + 295 + ], + "type": "text", + "content": "materials." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "text", + "content": "Template Selection. We compare the performance of different template selection strategies in Table 3. " + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "inline_equation", + "content": "k = 0" + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "text", + "content": " means that we use a straight centerline as the initial template without considering image information. It can be found that adaptive template generation outperforms fixed initial templates " + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "inline_equation", + "content": "(k = 0)" + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "text", + "content": ". Furthermore, we observe a gradual decline in performance as the number of control points " + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "text", + "content": " increases from 4 to 64. We guess that more control points lead to overly accurate initial templates, thus reducing the difficulty and complexity of the deformation task. Consequently, the model may not be sufficiently trained. Therefore, we adopt a rough initial template with " + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "inline_equation", + "content": "k = 4" + }, + { + "bbox": [ + 55, + 300, + 296, + 443 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 447, + 296, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 296, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 296, + 578 + ], + "type": "text", + "content": "Loss Function. We evaluate the effectiveness of different loss functions in Table 4 and Figure 7. It is observed from the results in the table that local chamfer distance loss outperforms global chamfer distance loss, particularly in terms of cldice. We empirically find that the global chamfer distance loss will result in larger fluctuations during training process compared with the local version. The reason is that the tubular structures in human body usually have complex global morphology and sparse 3D distribution, which means that conducting global calculations will have more fluctuations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "content": "Although the gains from SDF loss and regularization loss are not as pronounced in the numerical results, visualization comparison in the figure reveal that these losses contribute to more accurate centerline predictions. For instance, without regularization loss, the centerline prediction may be sparse and deviated in local regions, due to the long edges between adjacent vertices. In addition, adding SDF loss augments the centrality of centerline predictions. These properties are significant for the subsequent tasks, such as curved planar reformation [11]. In summary, the full configurations of loss functions achieve the best performance." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 325, + 71, + 547, + 168 + ], + "blocks": [ + { + "bbox": [ + 325, + 71, + 547, + 168 + ], + "lines": [ + { + "bbox": [ + 325, + 71, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 325, + 71, + 547, + 168 + ], + "type": "image", + "image_path": "a0bd91ace274e6390623695c0c1057568f6dc39fc3b460ee52fa6cb6775a4739.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 170, + 555, + 236 + ], + "lines": [ + { + "bbox": [ + 313, + 170, + 555, + 236 + ], + "spans": [ + { + "bbox": [ + 313, + 170, + 555, + 236 + ], + "type": "text", + "content": "Figure 8. Visual comparison of SCPR images reconstructed from the predictions of UNet and DeformCL. Red triangles indicate the regions where the vessel predictions by UNet are not correct, resulting in severe errors on SCPR images, while green ones indicate improved results from our DeformCL. Cyan arrows indicate the areas with plaque and stenosis needing additional clinical diagnosis." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 258, + 432, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 258, + 432, + 271 + ], + "spans": [ + { + "bbox": [ + 313, + 258, + 432, + 271 + ], + "type": "text", + "content": "4.6. Clinical Significance" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 276, + 555, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 555, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 555, + 443 + ], + "type": "text", + "content": "In clinical practice, the generation of straightened curved planar reformation [11] (SCPR) images is vital for radiologists to conduct accurate diagnoses for blood vessels, especially for observing possible plaques and stenosis. High-quality SCPR images require high-quality vessel graphical structures (directional centerlines) that meet the criteria of completeness, smoothness, and centrality. Previous methods often rely on converting discrete segmentation masks into continuous centerlines using traditional tools [10, 19], which may be susceptible to imperfect segmentation predictions. Moreover, this conversion process is complex and time-consuming. In contrast, our DeformCL can directly generate continuous centerlines during model inference without the need for any post-processing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 443, + 556, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 443, + 556, + 575 + ], + "spans": [ + { + "bbox": [ + 313, + 443, + 556, + 575 + ], + "type": "text", + "content": "As depicted in Figure 8, we compare the SCPR images reconstructed from the predictions of UNet and DeformCL. It is evident that the SCPR images generated from UNet exhibit severe bending and breaking, indicated by red arrows, which could hinder plaque diagnosis. These inaccuracies stem from the segmentation masks being fragmented by UNet in fragile regions, potentially containing plaques and stenosis. In contrast, DeformCL produces high-quality SCPR images that reveal diseased regions comprehensively and clearly. These visualizations underscore the potential of DeformCL in assisting the clinical diagnosis process." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 586, + 392, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 586, + 392, + 597 + ], + "spans": [ + { + "bbox": [ + 313, + 586, + 392, + 597 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "In this paper, we propose DeformCL, a novel continuously defined representation for 3D vessel segmentation. To fully leverage the advantages of DeformCL, we introduce a cascaded deformation process based on an adaptive template generation strategy. Through this comprehensive training framework, DeformCL demonstrates clear superiority over previous methods. The visualizations highlight DeformCL's potential in generating CPR images for clinical diagnosis, especially for patients with severe stenosis." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "30903" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 120 + ], + "type": "text", + "content": "Acknowledgement. This work is supported by National Science and Technology Major Project (2022ZD0114902) and National Science Foundation of China (NSFC92470123, NSFC62276005)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 130, + 115, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 130, + 115, + 142 + ], + "spans": [ + { + "bbox": [ + 56, + 130, + 115, + 142 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 149, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 149, + 296, + 193 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 149, + 296, + 193 + ], + "spans": [ + { + "bbox": [ + 61, + 149, + 296, + 193 + ], + "type": "text", + "content": "[1] Ricardo J Araujo, Jaime S Cardoso, and Helder P Oliveira. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 3" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "30905" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Deformable Radial Kernel Splatting/3fdb69e1-a3c3-48aa-8f3c-430c977f4a43_content_list.json b/2025/Deformable Radial Kernel Splatting/3fdb69e1-a3c3-48aa-8f3c-430c977f4a43_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dc2a1878821fa0a285ba6d04519440feb4094620 --- /dev/null +++ b/2025/Deformable Radial Kernel Splatting/3fdb69e1-a3c3-48aa-8f3c-430c977f4a43_content_list.json @@ -0,0 +1,1889 @@ +[ + { + "type": "text", + "text": "Deformable Radial Kernel Splitting", + "text_level": 1, + "bbox": [ + 315, + 130, + 684, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yi-Hua Huang $^{1}$ Ming-Xian Lin $^{1}$ Yang-Tian Sun $^{1}$ Ziyi Yang $^{1}$ Xiaoyang Lyu $^{1}$ Yan-Pei Cao $^{2\\dagger}$ Xiaojuan Qi $^{1\\dagger}$ $^{1}$ The University of Hong Kong ${}^{2}$ VAST", + "bbox": [ + 171, + 178, + 823, + 236 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b9c7fb755f47de4b54ea3cca66415ad172c037146c5745763ed990856be95d3c.jpg", + "image_caption": [ + "Target", + "Figure 1. Gaussian Splatting (GS) vs. Deformable Radial Kernel (DRK) Splatting: GS requires thousands of Gaussians to approximate detailed textures and shapes. In contrast, DRK efficiently fits the target pattern with just 30 primitives, achieving superior results." + ], + "image_footnote": [], + "bbox": [ + 91, + 263, + 297, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4d045abfcec963bbee65cdefcd089858594f118eacd495125e7445f788420235.jpg", + "image_caption": [ + "GS (50)" + ], + "image_footnote": [], + "bbox": [ + 302, + 263, + 406, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cc7f88a3c76c887a6b1326d3e5a1b121e2841e2eb52c9539fabf4ad8757627e2.jpg", + "image_caption": [ + "GS (500)" + ], + "image_footnote": [], + "bbox": [ + 406, + 263, + 511, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1c59c8561d94ab15a7728e4d766d1cd94b5d7031cf918ce7161a14b4041cff56.jpg", + "image_caption": [ + "GS (5K)" + ], + "image_footnote": [], + "bbox": [ + 514, + 263, + 617, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d44e537bbbdad0d6d98a2df34ad337c062f16a33960e6816477d4bd63e0f1649.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 624, + 263, + 776, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c27c9734889a32f247c2dcabdcfe428dab7adb6f2e5d71dbfc6a3af253c2af99.jpg", + "image_caption": [ + "DRK (50)", + "Render Scale-Down" + ], + "image_footnote": [], + "bbox": [ + 782, + 263, + 885, + 404 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 450, + 326, + 467 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, Gaussian splatting has emerged as a robust technique for representing 3D scenes, enabling real-time rasterization and high-fidelity rendering. However, Gaussians' inherent radial symmetry and smoothness constraints limit their ability to represent complex shapes, often requiring thousands of primitives to approximate detailed geometry. We introduce Deformable Radial Kernel (DRK), which extends Gaussian splatting into a more general and flexible framework. Through learnable radial bases with adjustable angles and scales, DRK efficiently models diverse shape primitives while enabling precise control over edge sharpness and boundary curvature. Even DRK's planar nature, we further develop accurate ray-primitive intersection computation for depth sorting and introduce efficient kernel culling strategies for improved rasterization efficiency. Extensive experiments demonstrate that DRK outperforms existing methods in both representation efficiency and rendering quality, achieving state-of-the-art performance while dramatically reducing primitive count.", + "bbox": [ + 88, + 481, + 485, + 770 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 797, + 223, + 813 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D Gaussian Splitting [27] (3D-GS) has emerged as a leading 3D representation method thanks to its rapid rasterization and superior rendering quality. Its key advantages—ex", + "bbox": [ + 89, + 821, + 483, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "plicit point-based representation, flexibility for manipulation, and MLP-free rendering- have positioned it as a dominant approach in novel view synthesis. However, this success raises an intriguing question: Is the Gaussian kernel truly optimal for representing 3D scenes?", + "bbox": [ + 511, + 452, + 906, + 527 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Natural scenes often consist of primitives with diverse shapes (see Fig. 2), such as rectangles, triangles, and ellipses, which cannot be fully captured by Gaussians alone. Moreover, the inherently smooth nature of Gaussian kernels makes them less effective at representing sharp transitions. As a result, densely packed or numerous Gaussians are frequently required to accurately model scene primitives with non-Gaussian geometries or sharp boundaries (see Fig. 1), leading to inefficiencies in both computation and memory.", + "bbox": [ + 511, + 532, + 908, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent works have explored modifications to the Gaussian kernel to better handle discontinuities. For example, GES [20] adaptively adjusts the exponent values to control the sharpness of Gaussians, while still maintaining rotational symmetry, which limits its representational flexibility. DisC-GS [43] and 3D-HGS [30] introduce curve-and half-cutting techniques to the Gaussian kernel, respectively, improving its ability to capture discontinuous transitions. However, these cutting-based approaches remain fundamentally constrained by the inherent smoothness of the Gaussian kernel. Another line of research [8, 16, 19, 22] leverages 2D Gaussians to represent 3D scenes. While this approach offers better surface reconstruction compared to 3DGS, it is still constrained by the inherent limitations of the Gaussian framework, which restricts the flexibility", + "bbox": [ + 511, + 674, + 910, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding Author", + "bbox": [ + 89, + 875, + 223, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Project page: https://yihua7.github.io/DRK-web/.", + "bbox": [ + 91, + 888, + 429, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21513", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of the representation. Notably, the concurrent work 3D-CS [21] employs novel 3D smooth convex shapes as primitives for geometry modeling with satisfactory results.", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, our objective is to design new shape primitives that can adapt to complex 3D scenes. Motivated by the success of 2D Gaussian Splatting (2D-GS), we focus on developing adaptive 2D planar kernels. Specifically, we introduce the 2D Deformable Radial Kernel (DRK), a flexible planar primitive for representing 3D scenes (see Fig. 4). At its core, DRK extends traditional radial bases with learnable parameters that enable precise control over shape deformation through three key features: 1) multiple radial bases with learnable polar angles and scale parameters allow the kernel to adaptively stretch, rotate, and shrink, providing significantly more flexibility than fixed Gaussian functions; 2) a hybrid distance metric combining $L1$ and $L2$ norms with learnable weights enables DRK to naturally represent both curved surfaces and sharp geometric features; and 3) an adaptive piecewise linear remapping function provides fine-grained control over value distributions, particularly enhancing the representation of sharp boundaries. Despite its enhanced expressiveness, DRK maintains a simple parametric form that is easy to optimize and efficient to render. The DRK determines the location and orientation of the tangent plane through its center and rotation parameters, building upon these radial bases as its structural foundation to conform to target shapes, bypassing the geometric and smoothness constraints typically imposed by Gaussian functions. As shown in Fig. 2, a single DRK primitive can flexibly model a wide range of shape primitives, whereas many Gaussians are often required to represent similar shapes. The formulation is also backwards-compatible - DRK naturally reduces to a Gaussian kernel when using two orthogonal major bases with different decay rates, while achieving superior rendering quality with comparable computational efficiency.", + "bbox": [ + 91, + 138, + 483, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We experimentally validate $DRK$ on our proposed dataset (DiverseScene) covering various scenarios, including rich textures, fine geometry, specular effects, and large spatial scale. We also evaluate $DRK$ on unbounded MipNeRF 360 [2] datasets. Experimental results demonstrate our method has advantages in preserving visual details more effectively and efficiently.", + "bbox": [ + 89, + 638, + 482, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, our work makes the following contributions:", + "bbox": [ + 109, + 747, + 462, + 762 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce Deformable Radial Kernel (DRK), a novel primitive that generalizes conventional Gaussian splattig. DRK enables flexible shape modeling through learnable radial bases, hybrid distance metrics, and adaptive sharpness control, significantly reducing the number of primitives needed for high-quality scene representation.", + "- We develop a differentiable and efficient rendering pipeline for DRK, featuring polygon-based tile culling and cache-sorting strategies to enhance both rendering ef" + ], + "bbox": [ + 89, + 763, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ficiency and view consistency.", + "bbox": [ + 527, + 90, + 730, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We created DiverseScenes, a new dataset covering rich textures, fine geometry, specular effects, and large scenes for more effectively evaluating the ability to model complex scenarios of different algorithms.", + "bbox": [ + 513, + 106, + 906, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 181, + 653, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Novel View Synthesis", + "text_level": 1, + "bbox": [ + 513, + 207, + 712, + 222 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Novel view synthesis from multi-view images represents a fundamental challenge in computer graphics and computer vision. The field has evolved through increasingly sophisticated 3D scene representations. Traditional light field approaches [10, 18, 29] attempt to model the entire scene through a single 4D function of ray-slice intersections, but this implicit representation struggles with sparse inputs and complex geometry. Advancing beyond single-function modeling, Multi-Plane-Images (MPI) [38, 51, 55, 58, 69] introduced a layered representation using multiple depth planes, offering better 3D structure modeling. However, its discrete depth layering limits the handling of large viewpoint changes, particularly in rotational views. To achieve continuous depth modeling, subsequent works adopted explicit 3D proxies including meshes [5, 11, 35, 56, 59], point clouds [1, 7, 37, 41, 57], and voxels [14, 32, 48, 49]. These representations offer more flexible geometry modeling, with point-based methods further enhanced by neural networks [45, 46] for improved stability.", + "bbox": [ + 511, + 229, + 906, + 518 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most recently, continuous neural representations have emerged as a powerful alternative, replacing discrete geometric proxies with MLPs that directly map 3D coordinates to scene properties. NeRF [39] pioneered this approach with radiance fields, spawning numerous extensions for faster inference [15, 26, 40], large-scale scenes [2, 17, 53, 61, 66], dynamic content [31, 42, 50], reflection modeling [3, 24, 28, 62], and stylization [9, 13, 23, 67].", + "bbox": [ + 511, + 518, + 905, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Gaussian Splitting", + "text_level": 1, + "bbox": [ + 513, + 648, + 694, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Point-based rendering approaches have made the rendering process of point clouds differentiable, enabling end-to-end training for novel view synthesis. 3D Gaussian Splating (3D-GS) [27] introduced scene modeling using 3D Gaussian distributions, compositing the appearance of intersected Gaussians along viewing rays through $\\alpha$ -blending. This seminal work has inspired numerous extensions across various applications, including dynamic scene view synthesis [25, 34, 65], 3D content generation [54, 70], geometry reconstruction [22, 36], video representation [52] and neural network-enhanced high-fidelity view synthesis [33, 64]. The flexible representation, computational efficiency, and superior rendering quality of 3D-GS have established it as a prominent approach in the field [60].", + "bbox": [ + 511, + 672, + 906, + 885 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The key innovation of 3D-GS lies in its use of Gaussian", + "bbox": [ + 532, + 885, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21514", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "kernels for point effect decay, where the continuous nature of these functions facilitates the optimization of discrete representations. Subsequent research has focused on both constraining and extending these Gaussian kernels for specific applications. Notable developments include the constraint of 3D Gaussians to 2D space [8, 19, 22], yielding planar representations that better approximate scene surfaces for precise geometry reconstruction. Other works have extended the framework to 4D space [12, 63], enabling temporal dynamic modeling through 3D slicing of 4D Gaussians for view synthesis. To address limitations in representing sharp edges, researchers have proposed modifications to the Gaussian shape using curve-cutting [43], hemispheric truncation [30], and novel 3D convex shapes [21].", + "bbox": [ + 89, + 90, + 483, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 319, + 230, + 334 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first review 3D Gaussian Splitting (3D-GS) and 2D Gaussian Splitting (2D-GS), and their mathematical formulations (Sec. 3.1 and Sec. 3.2). We then introduce our general kernel splitting framework that extends beyond traditional Gaussian primitives (Sec. 3.3). Finally, we analyze the inherent limitations of Gaussian-based representations, motivating the need for our proposed deformable radial kernel formulation (Sec. 3.4).", + "bbox": [ + 89, + 345, + 483, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. 3D Gaussian Splitting (3D-GS)", + "text_level": 1, + "bbox": [ + 89, + 478, + 369, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D Gaussian Splatting represents scenes using colored 3D Gaussians [27]. Each Gaussian $G$ is parameterized by a 3D center $\\mu$ , covariance matrix $\\Sigma = R S S^T R^T$ (where $R$ is a rotation matrix from quaternion $q \\in \\mathbf{SO}(3)$ and $S$ is a scaling matrix from vector $s$ ), opacity $o$ , and spherical harmonic coefficients $sh$ for view-dependent appearance. A scene is represented as $\\mathcal{G} = \\{G_j : \\mu_j, q_j, s_j, o_j, sh_j\\}$ .", + "bbox": [ + 89, + 502, + 483, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rendering involves projecting Gaussians onto the image plane with 2D covariance $\\Sigma^{\\prime} = JW\\Sigma W^{T}J^{T}$ and center $\\mu^{\\prime} = JW\\mu$ . The pixel color $C(u)$ is computed via neural point-based $\\alpha$ -blending:", + "bbox": [ + 89, + 609, + 483, + 670 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC (u) = \\sum_ {i \\in N} T _ {i} \\alpha_ {i} \\mathcal {S H} \\left(s h _ {i}, v _ {i}\\right), \\text {w h e r e} T _ {i} = \\Pi_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 681, + 483, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{SH}$ evaluates spherical harmonics with view direction $v_{i}$ , and $\\alpha_{i}$ is:", + "bbox": [ + 89, + 715, + 482, + 744 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i} = o _ {i} e ^ {- \\frac {1}{2} (p - \\mu_ {i} ^ {\\prime}) ^ {T} \\Sigma_ {i} ^ {\\prime} (p - \\mu_ {i} ^ {\\prime})}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 756, + 482, + 775 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By optimizing these Gaussian parameters and adaptively adjusting their density, 3D-GS achieves high-quality scene representation with real-time rendering capabilities.", + "bbox": [ + 89, + 789, + 483, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. 2D Gaussian Splitting (2D-GS)", + "text_level": 1, + "bbox": [ + 89, + 845, + 367, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recognizing that real-world scenes primarily consist of surface structures where 3D Gaussians naturally compress into", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "planar formations, recent works [8, 22] proposed 2D Gaussian Splatting (2D-GS). The opacity $\\alpha$ is computed using local coordinates $(u,v)$ on the tangent plane:", + "bbox": [ + 511, + 90, + 905, + 137 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\frac {u ^ {2}}{s _ {u} ^ {2}} + \\frac {v ^ {2}}{s _ {v} ^ {2}}\\right)\\right), \\qquad (3)\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 147, + 906, + 184 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $s_u^2$ and $s_v^2$ denote the variances along the U and V axes. This surface-centric formulation aligns with the success of polygon meshes in 3D modeling, offering a more compact scene representation.", + "bbox": [ + 511, + 191, + 906, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. General Kernel Splitting", + "text_level": 1, + "bbox": [ + 511, + 263, + 743, + 279 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We extend conventional 2D Gaussians by introducing a more general planar kernel splating formulation (Fig. 3). Given a ray from position $r_o \\in \\mathbb{R}^3$ with direction $r_d \\in \\mathbb{R}^3$ intersecting a tangent plane centered at $\\mu$ with rotation $R \\in SO(3)$ , the intersection point is:", + "bbox": [ + 511, + 286, + 905, + 362 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ni = r _ {o} + \\frac {\\left(\\mu - r _ {o}\\right) ^ {T} R _ {z}}{r _ {d} ^ {T} R _ {z}} r _ {d}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 371, + 906, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $R_{z}$ is the plane normal. The local UV coordinates at this intersection are:", + "bbox": [ + 511, + 411, + 905, + 440 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\binom {u} {v} = \\binom {R _ {x} ^ {T}} {R _ {y} ^ {T}} (i - \\mu), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 446, + 905, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $R_x^T$ and $R_y^T$ are the first and second rows of $R$ . The kernel splating function then maps these UV coordinates to a density value $\\alpha$ , determining the primitive's shape.", + "bbox": [ + 511, + 488, + 905, + 536 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/06925da25236c608d0b84ba3b2e2acbc7e39399f748872753f9a433e3a97d5d2.jpg", + "image_caption": [ + "Figure 3. Illustration of general planar kernel splitting: UV coordinates of ray-plane intersections are mapped to density values via a kernel function that determines the primitive's shape." + ], + "image_footnote": [], + "bbox": [ + 514, + 544, + 905, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.4. Discussions", + "text_level": 1, + "bbox": [ + 511, + 696, + 638, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While 3D-GS demonstrates remarkable efficacy, our analysis reveals several inherent limitations. First, screen-space projection of Gaussians yields 2D elliptical distributions with rotational symmetry, constraining their ability to approximate diverse primitive shapes. Second, their conic curve boundaries (derived by the $L2$ norm) challenge the representation of linear edges and intermediate edge forms. Third, Gaussian distributions inherently couple decay rate with spatial extent through the covariance matrix—sharp features necessitate narrow distributions, making it challenging to simultaneously capture abrupt transitions and extended spatial regions.", + "bbox": [ + 511, + 719, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21515", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/90b549a05a564ded20b6dcf86d6f433becb3a6175851252be815003c6fd3a2c0.jpg", + "image_caption": [ + "Figure 2. Comparison of 3D-GS versus a single $DRK$ : $DRK$ achieves superior geometric fidelity with just one primitive compared to multiple Gaussians. We visualize the contours of 3D-GS and $DRK$ to better illustrate primitive count, scale, and position." + ], + "image_footnote": [], + "bbox": [ + 127, + 85, + 313, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6b072a01261154279bcf9e81adb3c1b1f15824ed64178ed7123322fecfd52ba4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 87, + 504, + 205 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/06a905b352cfa0d7d8c1ca4d20bf425bb918fbbd7a22d5876f80199b7c4024de.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 513, + 85, + 694, + 205 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/937d773db46c267312745cbbe3a56d81751a733b3dbb6e89520c6ef1049c4306.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 85, + 862, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These constraints necessitate millions of fine-grained Gaussians to approximate arbitrary shapes, leading to overparameterization while still failing to achieve perfect fidelity under practical constraints. As shown in Fig. 2, even elementary shapes like triangles and rectangles—which can be described concisely—require numerous Gaussians for approximation, exhibiting artifacts like interior inconsistencies and external floating points (last column). Our deformable radial kernel (DRK) addresses these limitations through radial basis functions with varying lengths $s_k$ and polar angles $\\theta_k$ , controlled by parameters $\\eta$ and $\\tau$ for contour curvature and sharpness (Fig. 4).", + "bbox": [ + 89, + 244, + 483, + 428 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Deformable Radial Kernel Splitting", + "text_level": 1, + "bbox": [ + 89, + 445, + 418, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Deformable Radial Kernel (DRK) is a novel primitive for 3D scene representation characterized by a set of parameters $\\Theta = \\{\\mu, q, s_k, \\theta_k, \\eta, \\tau, o, sh\\}$ , where:", + "bbox": [ + 89, + 472, + 482, + 517 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $\\mu \\in \\mathbb{R}^3$ , $q \\in SO(3)$ , $o$ , and $sh$ follow 3D-GS for position, orientation, opacity, and view-dependent appearance", + "- $\\{s_k, \\theta_k\\}_{k=1}^K$ define radial basis lengths and angles that control the kernel shape", + "- $\\eta \\in (0,1)$ and $\\tau \\in (-1,1)$ control boundary curvature and sharpness, respectively" + ], + "bbox": [ + 89, + 518, + 482, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the following sections, we detail each component of DRK. First, we introduce the radial basis formulation (Sec. 4.1), showing that traditional 2D Gaussians are a special case within our framework. Then, we discuss $L1\\& L2$ norm blending and edge sharpening in Sec. 4.2 and Sec. 4.3, which enable flexible control of boundary curvature and sharpness. Finally, in Sec. 4.4, we explore efficient rasterization strategies specifically tailored for DRK, including low-pass filtering, kernel culling, and cache sorting.", + "bbox": [ + 89, + 611, + 482, + 748 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/58e3d301b862f3a363a03ff8d54587ae48c856279b6c442f16063a854b6eb868.jpg", + "image_caption": [ + "Figure 4. $DRK$ defines a deformable shape using radial basis functions characterized by lengths $s_k$ and polar angles $\\theta_k$ , with parameters $\\eta$ and $\\tau$ governing the shape's curvature and sharpness respectively." + ], + "image_footnote": [], + "bbox": [ + 91, + 752, + 187, + 838 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d6f816574cfea7d7acf27ffe665c35d06936ada7cbcf1fd04fe39ebad6d1e332.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 191, + 752, + 321, + 838 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/dd71778987ce77a99abdf95b06a9ba6dc400d15d608bd8c47016101ff0943411.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 325, + 752, + 482, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Radial Basis", + "text_level": 1, + "bbox": [ + 511, + 244, + 645, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our radial basis defines a kernel's shape through $K$ control points in polar coordinates $\\{s_k,\\theta_k\\}$ , where $s_k > 0$ represents each radial length and angles are ordered as $0 < \\theta_0 < \\ldots < \\theta_K \\leq 2\\pi$ . For any point with local tangent coordinates $(u,v)$ , we compute its polar representation using $L2$ norm $r_2 = \\sqrt{u^2 + v^2}$ and angle $\\theta = \\arccos (u / r_2)$ . Given a point lying between basis $k$ and $k + 1$ (i.e., $\\theta_{k} < \\theta \\leq \\theta_{k + 1}$ ), we define its relative angular distance as $\\Delta \\theta_{k} = \\frac{(\\theta - \\theta_{k})\\pi}{\\theta_{k + 1} - \\theta_{k}}$ . The kernel function is then formulated as:", + "bbox": [ + 511, + 268, + 906, + 407 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha = o \\cdot \\exp \\left(- \\frac {r _ {2} ^ {2}}{2} \\left(\\frac {1 + \\cos (\\Delta \\theta_ {k})}{2 s _ {k} ^ {2}} + \\frac {1 - \\cos (\\Delta \\theta_ {k})}{2 s _ {k + 1} ^ {2}}\\right)\\right). (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 415, + 906, + 449 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This formulation smoothly interpolates between adjacent radial bases using cosine weighting terms, ensuring continuous transitions in the kernel's shape.", + "bbox": [ + 511, + 455, + 906, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2D Gaussian as a Special Case. Our formulation generalizes 2D Gaussian kernels. By setting $K = 4$ with $\\theta_{k} = \\frac{k\\pi}{2}$ and $s_0 = s_2 = s_u$ , $s_1 = s_3 = s_v$ , we can derive the 2D Gaussian form in Eq. (3). For points in the first UV quadrant where $\\Delta \\theta_{k} = 2\\theta$ :", + "bbox": [ + 511, + 508, + 905, + 584 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\alpha = o \\cdot \\exp \\left(- \\frac {r _ {2} ^ {2}}{2} \\left(\\frac {\\cos^ {2} \\theta}{s _ {0} ^ {2}} + \\frac {\\cos^ {2} \\theta}{s _ {1} ^ {2}}\\right)\\right) \\\\ = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\frac {u ^ {2}}{s _ {0} ^ {2}} + \\frac {v ^ {2}}{s _ {1} ^ {2}}\\right)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 595, + 846, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we use the identity $\\cos (\\Delta \\theta_k) = \\cos (2\\theta) = 2\\cos^2\\theta -1$ . The derivation extends to other quadrants by symmetry.", + "bbox": [ + 511, + 676, + 906, + 723 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. L1&L2 Norm Blending", + "text_level": 1, + "bbox": [ + 511, + 733, + 723, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The scaling term $\\frac{1}{\\bar{s}^2} = \\left(\\frac{1 + \\cos(\\Delta\\theta_k)}{2s_k^2} +\\frac{1 - \\cos(\\Delta\\theta_k)}{2s_{k + 1}^2}\\right)$ in Eq. (6) enforces smooth contours at radial endpoints, where $\\frac{d\\bar{s}}{d\\Delta\\theta_k} = 0$ at $\\Delta \\theta_{k} = 0$ or $\\pi$ . However, since radials converge at the kernel center and are not parallel, this $L2$ formulation inherently produces conic curves, limiting its ability to represent straight edges common in man-made environments.", + "bbox": [ + 511, + 755, + 905, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address this limitation, we incorporate $L1$ norm into our $DRK$ formulation. For a point $(u,v)$ between radial", + "bbox": [ + 511, + 869, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21516", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "endpoints $e_i = (s_i \\cos(\\theta_i), s_i \\sin(\\theta_i))$ and $e_{i+1}$ , we compute its $L1$ norm as:", + "bbox": [ + 89, + 90, + 482, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {1} = \\left\\| \\left( \\begin{array}{l l} e _ {i} & e _ {i + 1} \\end{array} \\right) ^ {- 1} \\binom {u} {v} \\right\\| _ {1}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 132, + 482, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This transformation maps the diamond-shaped $L1$ unit ball $(|x| + |y| = 1,0\\leq x,y\\leq 1)$ to the segment between adjacent endpoints, enabling straight-line boundaries.", + "bbox": [ + 89, + 175, + 482, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We then introduce a blending weight $\\eta \\in (0,1)$ to smoothly interpolate between $L1$ and $L2$ norms, yielding our complete kernel function:", + "bbox": [ + 89, + 220, + 483, + 266 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\eta r _ {1} ^ {2} + (1 - \\eta) \\frac {r _ {2} ^ {2}}{\\bar {s} ^ {2}}\\right)\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 277, + 482, + 310 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that $r_1^2$ requires no explicit scaling term as it is inherently scaled through the inverse transformation in Eq. (7). Please see Fig. 4 (right) for illustration.", + "bbox": [ + 89, + 321, + 483, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Edge Sharpening", + "text_level": 1, + "bbox": [ + 89, + 380, + 261, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 2, Gaussian functions inherently couple scale and edge sharpness through their variance parameter, making it challenging to achieve precise shape approximation even with thousands of Gaussians. To decouple these properties, we introduce a sharpening coefficient $\\tau \\in (-1,1)$ that adaptively adjusts edge tran", + "bbox": [ + 89, + 404, + 310, + 569 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f5ad3c746395127b8c4aee24cb987ce3a5e45c06575d7b4cc75c687d665f310d.jpg", + "image_caption": [ + "Figure 5. Sharpening function illustration." + ], + "image_footnote": [], + "bbox": [ + 316, + 405, + 483, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "sitions. Given the exponential term $g$ (i.e., the density value before opacity scaling) in Eq. (8), our sharpening function is:", + "bbox": [ + 89, + 571, + 483, + 614 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Psi (g) = \\left\\{ \\begin{array}{l l} \\frac {1 - \\tau}{1 + \\tau} g & \\text {i f} \\quad 0 \\quad \\leq g < \\frac {1 + \\tau}{4}, \\\\ \\frac {1 + \\tau}{1 - \\tau} g - \\frac {\\tau}{1 - \\tau} & \\text {i f} \\quad \\frac {1 + \\tau}{4} \\quad \\leq g < \\frac {3 - \\tau}{4}, \\\\ \\frac {1 - \\tau}{1 + \\tau} g + \\frac {2 \\tau}{1 + \\tau} & \\text {i f} \\quad \\frac {3 - \\tau}{4} \\quad \\leq g \\leq 1. \\end{array} \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 625, + 482, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated in Fig. 5, this piecewise function reshapes the alpha values toward 0 or 1, creating sharper edge transitions while maintaining the kernel's spatial extent. The final kernel opacity is computed as $\\alpha = o\\cdot \\Psi (g)$", + "bbox": [ + 89, + 681, + 483, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Rasterization", + "text_level": 1, + "bbox": [ + 89, + 755, + 230, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Low-pass Filtering. Camera-captured images represent discretely sampled signals from scene rays, inherently limiting the maximum recoverable frequency of 3D content. Without proper frequency constraints, optimization tends to generate small, floating primitives that overfit to individual training views. These primitives become too fine-grained (smaller than ray coverage) and only contribute to specific rays, resulting in poor generalization.", + "bbox": [ + 89, + 780, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While 3D-GS leverages EWA splatting for closed-form Gaussian low-pass filtering, $DRK$ requires an alternative approach. Following Botsch et al. [4], we approximate filtering by taking the maximum between the kernel function and a view-dependent low-pass filter. Since $DRK$ represents planar primitives, its frequency should be bounded on its tangent plane while potentially unbounded when viewed orthogonally, so we scale the filter size by the cosine of the view angle:", + "bbox": [ + 511, + 90, + 906, + 227 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\alpha} = \\max (\\alpha , o \\cdot \\exp (- \\frac {1}{2 \\left| r _ {d} \\cdot R _ {z} \\right| ^ {2}} \\left(\\frac {\\Delta p _ {w} ^ {2}}{s _ {l} ^ {2}} + \\frac {\\Delta p _ {h} ^ {2}}{s _ {l} ^ {2}}\\right))), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 237, + 906, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Delta p_h$ and $\\Delta p_w$ are image space distances between the pixel and the projected kernel center, $r_d \\cdot R_z$ accounts for view-dependent scaling, and $s_l$ controls the filter radius.", + "bbox": [ + 511, + 279, + 906, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Tile Culling. Our rendering pipeline, based on 3D-GS, performs image rendering using 2D thread grids on CUDA. The process begins by dividing images into $16 \\times 16$ tiles, with each tile corresponding to potentially intersecting primitives (kernels or 3D Gaussians). While 3D-GS projects the major axis of a 3D Gaussian onto the image plane to create a square axis-aligned bounding box (AABB) for tile coverage, this method can be computationally inefficient for primitives that project as highly anisotropic or elongated shapes, as shown in Fig. 6. This inefficiency becomes particularly evident in $DRK$ due to its diverse shape representations. To address this, we introduce a more precise radius calculation and an improved tile culling strategy.", + "bbox": [ + 511, + 347, + 906, + 544 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fc685348f0cc435f77b9844f0bc04c2f23c00dfa7fbf718bd21a12643ebabafa.jpg", + "image_caption": [ + "Figure 6. Polygon-based tile culling using radial basis endpoints enables efficient rasterization by eliminating untouched tiles." + ], + "image_footnote": [], + "bbox": [ + 516, + 547, + 905, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The effective range of $DRK$ is governed by its radial basis, whose endpoints define the kernel's boundary. Following the 3-σ principle, we define the boundary radius $s_k^c$ , but extend it to account for opacity $o$ and sharpness $\\tau$ parameters. The calibrated radial length $s_k^c$ is defined as:", + "bbox": [ + 511, + 684, + 905, + 761 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {k} ^ {c} = s _ {k} \\sqrt {- \\log \\left(\\Psi^ {- 1} \\left(\\frac {e ^ {- 3 2}}{o}\\right)\\right)}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 773, + 903, + 814 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The derivation details are provided in the Supplementary Material. Using this calibrated length, we calculate each radial basis endpoint $v_{k}$ :", + "bbox": [ + 511, + 825, + 905, + 871 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv _ {k} = \\mu + s _ {k} ^ {c} (\\cos \\theta_ {k} R _ {x} + \\sin \\theta_ {k} R _ {y}). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 885, + 903, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21517", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ef1ce67b2064c48837e08ed8abbd92a1b957d2675758d7bb1ed3053f7efff957.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsSimpleTextureGeometrySpecularLargeAverage
PSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIM
2D-GS42.10.0209.996942.59.0624.983429.90.0513.970027.18.0570.955027.80.2500.838833.92.0881.9514
3D-GS39.51.0311.994144.57.0628.996829.14.0552.965827.16.0758.952332.19.2054.901734.41.0861.9621
3D-HGS41.41.0199.993146.19.0397.991230.42.0406.959827.27.0512.944733.17.1672.872135.68.0637.9521
GES40.95.0266.995545.23.0579.997730.36.0468.970427.04.0632.955031.67.2074.898735.05.0804.9634
DRK (S2)40.34.0283.994647.67.0537.997630.68.0477.970927.07.0704.957031.57.2090.898535.03.0823.9637
DRK (S1)42.24.0168.997447.86.0410.998831.67.0394.978827.77.0631.960333.78.1685.919636.62.0668.9701
DRK43.46.0105.998549.08.0396.999031.93.0366.980328.19.0592.961535.28.1348.937237.58.0564.9752
", + "bbox": [ + 93, + 88, + 898, + 212 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e57fd26b15a657cce25ec3da2985a3244a7964cf39c8273b84928e7ab0cd74ae.jpg", + "table_caption": [ + "Table 1. Rendering quality evaluation on DiverseScene datasets across various categories" + ], + "table_footnote": [], + "table_body": "
2DGS3DGS3DHGSGESDRK(S2)DRK(S1)DRK
Num(↓)359K336K373K330K42 K109K260K
MB(↓)83.679.789.678.112.332.176.6
FPS(↑)251.3247.1154.5227.4234.9119.277.5
", + "bbox": [ + 94, + 237, + 480, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Evaluation results of average primitive number (Num), model size (MB), and rendering speed (FPS) on DiverseScene.", + "bbox": [ + 89, + 295, + 480, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These endpoints form a polygon that accurately approximates the kernel's boundary. By projecting this polygon onto the image plane, we can efficiently identify and cull tiles that don't intersect with the kernel, making the rasterization more efficient.", + "bbox": [ + 89, + 351, + 482, + 425 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0740a8d4f73f30787f7472318146e0e8a484aa4609808025b3971bfe1ed22d55.jpg", + "image_caption": [ + "Figure 7. Our cache-sorting uses $r_t$ as keys in cache-sorting to rectify the sorting order while preventing popping artifacts." + ], + "image_footnote": [], + "bbox": [ + 93, + 426, + 295, + 520 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7c6e4e5757952293201c78226a9ee5589e72c6929448f8ec9df92a3106fb0d76.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 428, + 480, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cache Sorting. 3D-GS sorts the Gaussian using the depth of the center $\\mu$ , which can lead to inconsistencies across multiple views. While Radl et al. [44] address this by estimating the depth of the Gaussian at the point of maximum density and applying a hierarchical sorting solution to mitigate popping artifacts caused by inconsistent sorting, we propose a simpler yet effective solution. In our approach, the distance $r_t$ from the camera to the intersection between the ray and $DRK$ is calculated as:", + "bbox": [ + 89, + 569, + 482, + 705 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nr _ {t} = \\frac {\\left(\\mu - r _ {o}\\right) ^ {T} R _ {z}}{r _ {d} ^ {T} R _ {z}}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 717, + 480, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During rendering, each thread processes a pixel using an sorted array to cache the $r_t$ values and kernel indices, as illustrated in Fig. 7. The array is kept sorted by performing insert sorting for each new-coming kernel. If the array is full, the kernel with the smallest $r_t$ is popped out for processing. A dynamic cursor is used to record the scanning. We maintain an array length of 8, which is sufficient for approximating a more accurate sort. Fig. 7 demonstrates our method's effectiveness in handling multiple overlapping", + "bbox": [ + 89, + 763, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "kernels with identical center depths, comparing rasterization results with and without cache-sorting, preventing popping artifacts while maintaining rendering efficiency.", + "bbox": [ + 511, + 241, + 903, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 511, + 300, + 637, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 511, + 324, + 799, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate our method's performance across diverse scenarios, we focused on four key aspects: texture complexity, geometric detail, view-dependent effects, and scene scale. We collected 10 representative 3D scenes from Sketchfab1, with two scenes per category: simple objects, richly textured surfaces, intricate geometric details, specular materials, and large-scale environments. The dataset, namely DiverseScenes, serves as a benchmark to assess our representation method's capabilities. Detailed information about DiverseScenes can be found in the supplementary materials. For the evaluation on unbounded real-world scenes, we utilized the Mip-NeRF360 dataset [2], which contains multi-view images captured in open environments. Camera poses were estimated using COLMAP [47]. We assessed performance using three metrics: Peak Signal-to-Noise Ratio (PSNR) for overall reconstruction accuracy, Structural Similarity Index (SSIM) for perceptual quality and Learned Perceptual Image Patch Similarity (LPIPS) [68] for human-perceived visual fidelity. We observed that the number of primitives significantly impacts rendering quality. To evaluate DRK's performance across different densities, we present results using various hyper-parameters (details provided in the Supp), where the density decreases progressively from $DRK$ to $DRK(S2)$ and then to $DRK(S1)$ .", + "bbox": [ + 511, + 348, + 906, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2.Quantitative Comparisons", + "text_level": 1, + "bbox": [ + 511, + 719, + 751, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DiverseScenes. We compare our method, $DRK$ , against state-of-the-art Gaussian representations: 3D-GS [27], 2D-GS [22], 3D-HGS [30], and GES [20], using their official implementations. To ensure a fair comparison focused on kernel representation, we adjust the gradient threshold for densification in these methods, aligning their primitive count with that of 3D-GS $(300\\mathrm{K}+)$ . The results for each dataset category are shown in Table 1, demonstrating that our method achieves the best average performance. This", + "bbox": [ + 511, + 742, + 905, + 878 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1https://sketchfab.com/", + "bbox": [ + 531, + 886, + 658, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21518", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1c5cbff6b0244e704362d31e14ccc71d6840e362f3ab1641ec33ad693fb3c311.jpg", + "image_caption": [ + "Figure 8. Qualitative comparisons of $DRK$ with state-of-the-art methods across various scenarios show that $DRK$ effectively captures sharp texture and geometry boundaries." + ], + "image_footnote": [], + "bbox": [ + 107, + 84, + 883, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "is followed by our sparser version, $DRK$ (S1). $DRK$ (S2) also performs comparably to other state-of-the-art methods, with significantly fewer primitives and lower space occupancy, while maintaining comparable FPS, as detailed in Table 2. Although our method requires more computation, the rendering frameres remain efficient (FPS > 50).", + "bbox": [ + 89, + 640, + 482, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Mip-NeRF360 Datasets. We also tested $DRK$ on Mip-NeRF360 datasets, known for accurate camera poses and unbounded scenes. Results are shown in Tab. 3. On unbounded scenes, $DRK$ still excels in perceptual quality (LPIPS, SSIM), it shows less advantage in PSNR, especially with sparser kernels. We hypothesize that DRK may tend to overfit distant regions with limited supervision. To address this, we used MiVOS[6] to mask image sequences, training on original images but evaluating only the foreground. The results (M-PSNR) indicate our method's strength in well-supervised central regions.", + "bbox": [ + 89, + 734, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a1a5899899d079f6b3ad9219d5fc13818ebed436ae5d0b47b033eadd5963dada.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsPSNR(↑)M-PSNR(↑)LPIPS(↓)SSIM(↑)Num(↓)Size(↓)
2D-GS26.3232.01.2987.7617928 K216.0 M
3D-GS26.4832.23.3045.7537811 K191.3 M
3D-GS (L)26.9432.75.2688.77991191 K281.6 M
3D-HGS26.7432.51.2999.7561842 K202.4 M
GES26.6232.11.3047.7542824 K195.0 M
DRK (S2)26.2032.31.2781.7601388 K125.9 M
DRK (S1)26.4032.56.2601.7722551 K161.9 M
DRK26.7632.81.2364.7871952 K279.1 M
", + "bbox": [ + 517, + 637, + 901, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Quantitative evaluation on Mip-NeRF360 scenes [2].", + "bbox": [ + 524, + 750, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Qualitative Comparison", + "text_level": 1, + "bbox": [ + 511, + 782, + 735, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conducted qualitative comparisons to highlight the advantages of DRK over other state-of-the-art kernel representations. Fig.8 shows results across different scene categories, where our method achieves better texture and geometry fitting with a comparable or smaller number of kernels. Fig.9 demonstrates that DRK effectively handles fine ge", + "bbox": [ + 511, + 810, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21519", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce129829ec4e9d1b3936bc747c80fee4861b9355f5fe3f6a0a68d0cb9a92d8da.jpg", + "image_caption": [ + "Figure 9. Comparisons on the MipNeRF 360 dataset show our method achieves clearer details and high-fidelity rendering." + ], + "image_footnote": [], + "bbox": [ + 98, + 64, + 893, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "omtries, such as flowers and leaves, and detailed textures, like tags and bark, outperforming other representations that may have used more primitives (see Tab. 3).", + "bbox": [ + 89, + 458, + 482, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Converting Mesh to DRK", + "text_level": 1, + "bbox": [ + 89, + 513, + 323, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "All existing \"Splatting\" methods [20, 22, 27, 30] fail to seamlessly integrate with traditional assets. In contrast, our $DRK$ framework provides a versatile representation that allows for effortless conversion of triangle and polygon faces into $DRK$ . This is accomplished by placing the $DRK$ endpoints at the polygon vertices and adjusting the parameters $\\tau$ and $\\eta$ to control sharpness, with both $L1$ and $L2$ curvature set to 1. This process eliminates the need for training data rendering or model optimization. Consequently, rich 3D assets can be seamlessly transferred into $DRK$ , bridging the gap between millions of traditional 3D assets and our fast, high-quality reconstruction representation. Figure 10 illustrates the potential applications of Mesh2DRK.", + "bbox": [ + 89, + 537, + 483, + 733 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dbdd6816b4b53211bf74f4ba522e15e0e630220817fdc117055621b7e65a2784.jpg", + "image_caption": [ + "Figure 10. The conversion from Mesh to $DRK$ demonstrates the efficiency of using $DRK$ to incorporate traditional 3D assets into any $DRK$ scene at low cost." + ], + "image_footnote": [], + "bbox": [ + 89, + 737, + 483, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 455, + 633, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present $DRK$ , a novel primitive representation that generalizes and enhances Gaussian splatting. By incorporating learnable radial bases, adaptive shape control, and efficient rendering strategies, $DRK$ effectively addresses the fundamental limitations of Gaussian kernels in representing diverse geometric features. Our experiments on both synthetic and real-world scenes demonstrate that $DRK$ achieves superior rendering quality with significantly fewer primitives, while maintaining computational efficiency through carefully designed rasterization optimizations. Leveraging the flexibility of $DRK$ , traditional triangle or polygon mesh representations can be seamlessly converted into $DRK$ without requiring any training. This capability bridges rich 3D assets with reconstructed scenes, paving the way for future applications such as real-scene editing, VR digital world creation, and AR scene enhancement.", + "bbox": [ + 511, + 482, + 906, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 513, + 739, + 671, + 756 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work has been supported in part by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621), General Research Fund Scheme (Grant No. 17202422, 17212923), Theme-based Research (Grant No. T45-701/22-R) and Shenzhen Science and Technology Innovation Commission (SGDX20220530111405040). Part of the described research work is conducted in the JC STEM Lab of Robotics for Soft Materials funded by The Hong Kong Jockey Club Charities Trust.", + "bbox": [ + 511, + 763, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21520", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. Neural point-based graphics. In Proceedings of the European Conference on Computer Vision (ECCV), pages 696-712. Springer, 2020. 2", + "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Mip-NeRF 360: Unbounded anti-aliased neural radiance fields. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10324-10335, 2024. 2" + ], + "bbox": [ + 516, + 92, + 906, + 232 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21523", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Deformable Radial Kernel Splatting/3fdb69e1-a3c3-48aa-8f3c-430c977f4a43_model.json b/2025/Deformable Radial Kernel Splatting/3fdb69e1-a3c3-48aa-8f3c-430c977f4a43_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b6b0a0f4a8f37aae78a4ba8bf1f8b71968cd16c4 --- /dev/null +++ b/2025/Deformable Radial Kernel Splatting/3fdb69e1-a3c3-48aa-8f3c-430c977f4a43_model.json @@ -0,0 +1,2752 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.316, + 0.131, + 0.685, + 0.154 + ], + "angle": 0, + "content": "Deformable Radial Kernel Splitting" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.179, + 0.825, + 0.237 + ], + "angle": 0, + "content": "Yi-Hua Huang\\(^{1}\\) Ming-Xian Lin\\(^{1}\\) Yang-Tian Sun\\(^{1}\\) Ziyi Yang\\(^{1}\\) Xiaoyang Lyu\\(^{1}\\) Yan-Pei Cao\\(^{2\\dagger}\\) Xiaojuan Qi\\(^{1\\dagger}\\) \n\\(^{1}\\) The University of Hong Kong \\({}^{2}\\) VAST" + }, + { + "type": "image_caption", + "bbox": [ + 0.167, + 0.251, + 0.213, + 0.265 + ], + "angle": 0, + "content": "Target" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.265, + 0.299, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.323, + 0.251, + 0.378, + 0.265 + ], + "angle": 0, + "content": "GS (50)" + }, + { + "type": "image", + "bbox": [ + 0.303, + 0.265, + 0.407, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.427, + 0.251, + 0.488, + 0.265 + ], + "angle": 0, + "content": "GS (500)" + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.265, + 0.512, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.251, + 0.594, + 0.265 + ], + "angle": 0, + "content": "GS (5K)" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.265, + 0.618, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.265, + 0.777, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.799, + 0.251, + 0.866, + 0.265 + ], + "angle": 0, + "content": "DRK (50)" + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.265, + 0.887, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.889, + 0.279, + 0.905, + 0.397 + ], + "angle": 0, + "content": "Render Scale-Down" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.41, + 0.908, + 0.439 + ], + "angle": 0, + "content": "Figure 1. Gaussian Splatting (GS) vs. Deformable Radial Kernel (DRK) Splatting: GS requires thousands of Gaussians to approximate detailed textures and shapes. In contrast, DRK efficiently fits the target pattern with just 30 primitives, achieving superior results." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.451, + 0.328, + 0.468 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.482, + 0.486, + 0.771 + ], + "angle": 0, + "content": "Recently, Gaussian splatting has emerged as a robust technique for representing 3D scenes, enabling real-time rasterization and high-fidelity rendering. However, Gaussians' inherent radial symmetry and smoothness constraints limit their ability to represent complex shapes, often requiring thousands of primitives to approximate detailed geometry. We introduce Deformable Radial Kernel (DRK), which extends Gaussian splatting into a more general and flexible framework. Through learnable radial bases with adjustable angles and scales, DRK efficiently models diverse shape primitives while enabling precise control over edge sharpness and boundary curvature. Even DRK's planar nature, we further develop accurate ray-primitive intersection computation for depth sorting and introduce efficient kernel culling strategies for improved rasterization efficiency. Extensive experiments demonstrate that DRK outperforms existing methods in both representation efficiency and rendering quality, achieving state-of-the-art performance while dramatically reducing primitive count." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.798, + 0.224, + 0.814 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.823, + 0.485, + 0.87 + ], + "angle": 0, + "content": "3D Gaussian Splitting [27] (3D-GS) has emerged as a leading 3D representation method thanks to its rapid rasterization and superior rendering quality. Its key advantages—ex" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.453, + 0.907, + 0.529 + ], + "angle": 0, + "content": "plicit point-based representation, flexibility for manipulation, and MLP-free rendering- have positioned it as a dominant approach in novel view synthesis. However, this success raises an intriguing question: Is the Gaussian kernel truly optimal for representing 3D scenes?" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.533, + 0.909, + 0.67 + ], + "angle": 0, + "content": "Natural scenes often consist of primitives with diverse shapes (see Fig. 2), such as rectangles, triangles, and ellipses, which cannot be fully captured by Gaussians alone. Moreover, the inherently smooth nature of Gaussian kernels makes them less effective at representing sharp transitions. As a result, densely packed or numerous Gaussians are frequently required to accurately model scene primitives with non-Gaussian geometries or sharp boundaries (see Fig. 1), leading to inefficiencies in both computation and memory." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.911, + 0.903 + ], + "angle": 0, + "content": "Recent works have explored modifications to the Gaussian kernel to better handle discontinuities. For example, GES [20] adaptively adjusts the exponent values to control the sharpness of Gaussians, while still maintaining rotational symmetry, which limits its representational flexibility. DisC-GS [43] and 3D-HGS [30] introduce curve-and half-cutting techniques to the Gaussian kernel, respectively, improving its ability to capture discontinuous transitions. However, these cutting-based approaches remain fundamentally constrained by the inherent smoothness of the Gaussian kernel. Another line of research [8, 16, 19, 22] leverages 2D Gaussians to represent 3D scenes. While this approach offers better surface reconstruction compared to 3DGS, it is still constrained by the inherent limitations of the Gaussian framework, which restricts the flexibility" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.876, + 0.225, + 0.888 + ], + "angle": 0, + "content": "†Corresponding Author" + }, + { + "type": "page_footnote", + "bbox": [ + 0.093, + 0.889, + 0.43, + 0.901 + ], + "angle": 0, + "content": "Project page: https://yihua7.github.io/DRK-web/." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.876, + 0.43, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21513" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.137 + ], + "angle": 0, + "content": "of the representation. Notably, the concurrent work 3D-CS [21] employs novel 3D smooth convex shapes as primitives for geometry modeling with satisfactory results." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.139, + 0.485, + 0.639 + ], + "angle": 0, + "content": "In this work, our objective is to design new shape primitives that can adapt to complex 3D scenes. Motivated by the success of 2D Gaussian Splatting (2D-GS), we focus on developing adaptive 2D planar kernels. Specifically, we introduce the 2D Deformable Radial Kernel (DRK), a flexible planar primitive for representing 3D scenes (see Fig. 4). At its core, DRK extends traditional radial bases with learnable parameters that enable precise control over shape deformation through three key features: 1) multiple radial bases with learnable polar angles and scale parameters allow the kernel to adaptively stretch, rotate, and shrink, providing significantly more flexibility than fixed Gaussian functions; 2) a hybrid distance metric combining \\( L1 \\) and \\( L2 \\) norms with learnable weights enables DRK to naturally represent both curved surfaces and sharp geometric features; and 3) an adaptive piecewise linear remapping function provides fine-grained control over value distributions, particularly enhancing the representation of sharp boundaries. Despite its enhanced expressiveness, DRK maintains a simple parametric form that is easy to optimize and efficient to render. The DRK determines the location and orientation of the tangent plane through its center and rotation parameters, building upon these radial bases as its structural foundation to conform to target shapes, bypassing the geometric and smoothness constraints typically imposed by Gaussian functions. As shown in Fig. 2, a single DRK primitive can flexibly model a wide range of shape primitives, whereas many Gaussians are often required to represent similar shapes. The formulation is also backwards-compatible - DRK naturally reduces to a Gaussian kernel when using two orthogonal major bases with different decay rates, while achieving superior rendering quality with comparable computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.64, + 0.483, + 0.746 + ], + "angle": 0, + "content": "We experimentally validate \\( DRK \\) on our proposed dataset (DiverseScene) covering various scenarios, including rich textures, fine geometry, specular effects, and large spatial scale. We also evaluate \\( DRK \\) on unbounded MipNeRF 360 [2] datasets. Experimental results demonstrate our method has advantages in preserving visual details more effectively and efficiently." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.748, + 0.464, + 0.763 + ], + "angle": 0, + "content": "Overall, our work makes the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.765, + 0.483, + 0.856 + ], + "angle": 0, + "content": "- We introduce Deformable Radial Kernel (DRK), a novel primitive that generalizes conventional Gaussian splattig. DRK enables flexible shape modeling through learnable radial bases, hybrid distance metrics, and adaptive sharpness control, significantly reducing the number of primitives needed for high-quality scene representation." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "- We develop a differentiable and efficient rendering pipeline for DRK, featuring polygon-based tile culling and cache-sorting strategies to enhance both rendering ef" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.765, + 0.484, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.092, + 0.731, + 0.107 + ], + "angle": 0, + "content": "ficiency and view consistency." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.107, + 0.907, + 0.168 + ], + "angle": 0, + "content": "- We created DiverseScenes, a new dataset covering rich textures, fine geometry, specular effects, and large scenes for more effectively evaluating the ability to model complex scenarios of different algorithms." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.182, + 0.655, + 0.198 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.208, + 0.714, + 0.223 + ], + "angle": 0, + "content": "2.1. Novel View Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.231, + 0.907, + 0.519 + ], + "angle": 0, + "content": "Novel view synthesis from multi-view images represents a fundamental challenge in computer graphics and computer vision. The field has evolved through increasingly sophisticated 3D scene representations. Traditional light field approaches [10, 18, 29] attempt to model the entire scene through a single 4D function of ray-slice intersections, but this implicit representation struggles with sparse inputs and complex geometry. Advancing beyond single-function modeling, Multi-Plane-Images (MPI) [38, 51, 55, 58, 69] introduced a layered representation using multiple depth planes, offering better 3D structure modeling. However, its discrete depth layering limits the handling of large viewpoint changes, particularly in rotational views. To achieve continuous depth modeling, subsequent works adopted explicit 3D proxies including meshes [5, 11, 35, 56, 59], point clouds [1, 7, 37, 41, 57], and voxels [14, 32, 48, 49]. These representations offer more flexible geometry modeling, with point-based methods further enhanced by neural networks [45, 46] for improved stability." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.519, + 0.906, + 0.64 + ], + "angle": 0, + "content": "Most recently, continuous neural representations have emerged as a powerful alternative, replacing discrete geometric proxies with MLPs that directly map 3D coordinates to scene properties. NeRF [39] pioneered this approach with radiance fields, spawning numerous extensions for faster inference [15, 26, 40], large-scale scenes [2, 17, 53, 61, 66], dynamic content [31, 42, 50], reflection modeling [3, 24, 28, 62], and stylization [9, 13, 23, 67]." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.65, + 0.696, + 0.667 + ], + "angle": 0, + "content": "2.2. Gaussian Splitting" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.907, + 0.886 + ], + "angle": 0, + "content": "Point-based rendering approaches have made the rendering process of point clouds differentiable, enabling end-to-end training for novel view synthesis. 3D Gaussian Splating (3D-GS) [27] introduced scene modeling using 3D Gaussian distributions, compositing the appearance of intersected Gaussians along viewing rays through \\(\\alpha\\)-blending. This seminal work has inspired numerous extensions across various applications, including dynamic scene view synthesis [25, 34, 65], 3D content generation [54, 70], geometry reconstruction [22, 36], video representation [52] and neural network-enhanced high-fidelity view synthesis [33, 64]. The flexible representation, computational efficiency, and superior rendering quality of 3D-GS have established it as a prominent approach in the field [60]." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.886, + 0.905, + 0.901 + ], + "angle": 0, + "content": "The key innovation of 3D-GS lies in its use of Gaussian" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21514" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.304 + ], + "angle": 0, + "content": "kernels for point effect decay, where the continuous nature of these functions facilitates the optimization of discrete representations. Subsequent research has focused on both constraining and extending these Gaussian kernels for specific applications. Notable developments include the constraint of 3D Gaussians to 2D space [8, 19, 22], yielding planar representations that better approximate scene surfaces for precise geometry reconstruction. Other works have extended the framework to 4D space [12, 63], enabling temporal dynamic modeling through 3D slicing of 4D Gaussians for view synthesis. To address limitations in representing sharp edges, researchers have proposed modifications to the Gaussian shape using curve-cutting [43], hemispheric truncation [30], and novel 3D convex shapes [21]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.32, + 0.231, + 0.335 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.346, + 0.484, + 0.466 + ], + "angle": 0, + "content": "In this section, we first review 3D Gaussian Splitting (3D-GS) and 2D Gaussian Splitting (2D-GS), and their mathematical formulations (Sec. 3.1 and Sec. 3.2). We then introduce our general kernel splitting framework that extends beyond traditional Gaussian primitives (Sec. 3.3). Finally, we analyze the inherent limitations of Gaussian-based representations, motivating the need for our proposed deformable radial kernel formulation (Sec. 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.479, + 0.37, + 0.495 + ], + "angle": 0, + "content": "3.1. 3D Gaussian Splitting (3D-GS)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.503, + 0.484, + 0.61 + ], + "angle": 0, + "content": "3D Gaussian Splatting represents scenes using colored 3D Gaussians [27]. Each Gaussian \\(G\\) is parameterized by a 3D center \\(\\mu\\), covariance matrix \\(\\Sigma = R S S^T R^T\\) (where \\(R\\) is a rotation matrix from quaternion \\(q \\in \\mathbf{SO}(3)\\) and \\(S\\) is a scaling matrix from vector \\(s\\)), opacity \\(o\\), and spherical harmonic coefficients \\(sh\\) for view-dependent appearance. A scene is represented as \\(\\mathcal{G} = \\{G_j : \\mu_j, q_j, s_j, o_j, sh_j\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.61, + 0.484, + 0.671 + ], + "angle": 0, + "content": "Rendering involves projecting Gaussians onto the image plane with 2D covariance \\(\\Sigma^{\\prime} = JW\\Sigma W^{T}J^{T}\\) and center \\(\\mu^{\\prime} = JW\\mu\\) . The pixel color \\(C(u)\\) is computed via neural point-based \\(\\alpha\\) -blending:" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.683, + 0.484, + 0.711 + ], + "angle": 0, + "content": "\\[\nC (u) = \\sum_ {i \\in N} T _ {i} \\alpha_ {i} \\mathcal {S H} \\left(s h _ {i}, v _ {i}\\right), \\text {w h e r e} T _ {i} = \\Pi_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.716, + 0.483, + 0.746 + ], + "angle": 0, + "content": "where \\(\\mathcal{SH}\\) evaluates spherical harmonics with view direction \\(v_{i}\\), and \\(\\alpha_{i}\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.757, + 0.483, + 0.776 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i} = o _ {i} e ^ {- \\frac {1}{2} (p - \\mu_ {i} ^ {\\prime}) ^ {T} \\Sigma_ {i} ^ {\\prime} (p - \\mu_ {i} ^ {\\prime})}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.79, + 0.484, + 0.835 + ], + "angle": 0, + "content": "By optimizing these Gaussian parameters and adaptively adjusting their density, 3D-GS achieves high-quality scene representation with real-time rendering capabilities." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.847, + 0.369, + 0.863 + ], + "angle": 0, + "content": "3.2. 2D Gaussian Splitting (2D-GS)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Recognizing that real-world scenes primarily consist of surface structures where 3D Gaussians naturally compress into" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.138 + ], + "angle": 0, + "content": "planar formations, recent works [8, 22] proposed 2D Gaussian Splatting (2D-GS). The opacity \\(\\alpha\\) is computed using local coordinates \\((u,v)\\) on the tangent plane:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.148, + 0.907, + 0.185 + ], + "angle": 0, + "content": "\\[\n\\alpha = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\frac {u ^ {2}}{s _ {u} ^ {2}} + \\frac {v ^ {2}}{s _ {v} ^ {2}}\\right)\\right), \\qquad (3)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.193, + 0.907, + 0.255 + ], + "angle": 0, + "content": "where \\( s_u^2 \\) and \\( s_v^2 \\) denote the variances along the U and V axes. This surface-centric formulation aligns with the success of polygon meshes in 3D modeling, offering a more compact scene representation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.264, + 0.745, + 0.28 + ], + "angle": 0, + "content": "3.3. General Kernel Splitting" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.287, + 0.906, + 0.363 + ], + "angle": 0, + "content": "We extend conventional 2D Gaussians by introducing a more general planar kernel splating formulation (Fig. 3). Given a ray from position \\(r_o \\in \\mathbb{R}^3\\) with direction \\(r_d \\in \\mathbb{R}^3\\) intersecting a tangent plane centered at \\(\\mu\\) with rotation \\(R \\in SO(3)\\), the intersection point is:" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.372, + 0.907, + 0.405 + ], + "angle": 0, + "content": "\\[\ni = r _ {o} + \\frac {\\left(\\mu - r _ {o}\\right) ^ {T} R _ {z}}{r _ {d} ^ {T} R _ {z}} r _ {d}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.412, + 0.906, + 0.441 + ], + "angle": 0, + "content": "where \\( R_{z} \\) is the plane normal. The local UV coordinates at this intersection are:" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.448, + 0.906, + 0.481 + ], + "angle": 0, + "content": "\\[\n\\binom {u} {v} = \\binom {R _ {x} ^ {T}} {R _ {y} ^ {T}} (i - \\mu), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.489, + 0.906, + 0.537 + ], + "angle": 0, + "content": "where \\( R_x^T \\) and \\( R_y^T \\) are the first and second rows of \\( R \\). The kernel splating function then maps these UV coordinates to a density value \\( \\alpha \\), determining the primitive's shape." + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.545, + 0.906, + 0.634 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.636, + 0.906, + 0.678 + ], + "angle": 0, + "content": "Figure 3. Illustration of general planar kernel splitting: UV coordinates of ray-plane intersections are mapped to density values via a kernel function that determines the primitive's shape." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.697, + 0.64, + 0.712 + ], + "angle": 0, + "content": "3.4. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.901 + ], + "angle": 0, + "content": "While 3D-GS demonstrates remarkable efficacy, our analysis reveals several inherent limitations. First, screen-space projection of Gaussians yields 2D elliptical distributions with rotational symmetry, constraining their ability to approximate diverse primitive shapes. Second, their conic curve boundaries (derived by the \\(L2\\) norm) challenge the representation of linear edges and intermediate edge forms. Third, Gaussian distributions inherently couple decay rate with spatial extent through the covariance matrix—sharp features necessitate narrow distributions, making it challenging to simultaneously capture abrupt transitions and extended spatial regions." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21515" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.087, + 0.315, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.322, + 0.088, + 0.506, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.087, + 0.695, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.087, + 0.864, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.209, + 0.908, + 0.239 + ], + "angle": 0, + "content": "Figure 2. Comparison of 3D-GS versus a single \\(DRK\\): \\(DRK\\) achieves superior geometric fidelity with just one primitive compared to multiple Gaussians. We visualize the contours of 3D-GS and \\(DRK\\) to better illustrate primitive count, scale, and position." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.246, + 0.485, + 0.429 + ], + "angle": 0, + "content": "These constraints necessitate millions of fine-grained Gaussians to approximate arbitrary shapes, leading to overparameterization while still failing to achieve perfect fidelity under practical constraints. As shown in Fig. 2, even elementary shapes like triangles and rectangles—which can be described concisely—require numerous Gaussians for approximation, exhibiting artifacts like interior inconsistencies and external floating points (last column). Our deformable radial kernel (DRK) addresses these limitations through radial basis functions with varying lengths \\( s_k \\) and polar angles \\( \\theta_k \\), controlled by parameters \\( \\eta \\) and \\( \\tau \\) for contour curvature and sharpness (Fig. 4)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.446, + 0.419, + 0.465 + ], + "angle": 0, + "content": "4. Deformable Radial Kernel Splitting" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.473, + 0.483, + 0.518 + ], + "angle": 0, + "content": "Deformable Radial Kernel (DRK) is a novel primitive for 3D scene representation characterized by a set of parameters \\(\\Theta = \\{\\mu, q, s_k, \\theta_k, \\eta, \\tau, o, sh\\}\\), where:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.52, + 0.483, + 0.551 + ], + "angle": 0, + "content": "- \\(\\mu \\in \\mathbb{R}^3\\), \\(q \\in SO(3)\\), \\(o\\), and \\(sh\\) follow 3D-GS for position, orientation, opacity, and view-dependent appearance" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.551, + 0.483, + 0.58 + ], + "angle": 0, + "content": "- \\(\\{s_k, \\theta_k\\}_{k=1}^K\\) define radial basis lengths and angles that control the kernel shape" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.58, + 0.483, + 0.611 + ], + "angle": 0, + "content": "- \\(\\eta \\in (0,1)\\) and \\(\\tau \\in (-1,1)\\) control boundary curvature and sharpness, respectively" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.52, + 0.483, + 0.611 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.483, + 0.749 + ], + "angle": 0, + "content": "In the following sections, we detail each component of DRK. First, we introduce the radial basis formulation (Sec. 4.1), showing that traditional 2D Gaussians are a special case within our framework. Then, we discuss \\(L1\\& L2\\) norm blending and edge sharpening in Sec. 4.2 and Sec. 4.3, which enable flexible control of boundary curvature and sharpness. Finally, in Sec. 4.4, we explore efficient rasterization strategies specifically tailored for DRK, including low-pass filtering, kernel culling, and cache sorting." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.753, + 0.188, + 0.839 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.192, + 0.753, + 0.323, + 0.839 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.326, + 0.753, + 0.483, + 0.839 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.842, + 0.485, + 0.898 + ], + "angle": 0, + "content": "Figure 4. \\( DRK \\) defines a deformable shape using radial basis functions characterized by lengths \\( s_k \\) and polar angles \\( \\theta_k \\), with parameters \\( \\eta \\) and \\( \\tau \\) governing the shape's curvature and sharpness respectively." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.246, + 0.646, + 0.26 + ], + "angle": 0, + "content": "4.1. Radial Basis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.269, + 0.907, + 0.409 + ], + "angle": 0, + "content": "Our radial basis defines a kernel's shape through \\(K\\) control points in polar coordinates \\(\\{s_k,\\theta_k\\}\\), where \\(s_k > 0\\) represents each radial length and angles are ordered as \\(0 < \\theta_0 < \\ldots < \\theta_K \\leq 2\\pi\\). For any point with local tangent coordinates \\((u,v)\\), we compute its polar representation using \\(L2\\) norm \\(r_2 = \\sqrt{u^2 + v^2}\\) and angle \\(\\theta = \\arccos (u / r_2)\\). Given a point lying between basis \\(k\\) and \\(k + 1\\) (i.e., \\(\\theta_{k} < \\theta \\leq \\theta_{k + 1}\\)), we define its relative angular distance as \\(\\Delta \\theta_{k} = \\frac{(\\theta - \\theta_{k})\\pi}{\\theta_{k + 1} - \\theta_{k}}\\). The kernel function is then formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.416, + 0.907, + 0.45 + ], + "angle": 0, + "content": "\\[\n\\alpha = o \\cdot \\exp \\left(- \\frac {r _ {2} ^ {2}}{2} \\left(\\frac {1 + \\cos (\\Delta \\theta_ {k})}{2 s _ {k} ^ {2}} + \\frac {1 - \\cos (\\Delta \\theta_ {k})}{2 s _ {k + 1} ^ {2}}\\right)\\right). (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.457, + 0.907, + 0.504 + ], + "angle": 0, + "content": "This formulation smoothly interpolates between adjacent radial bases using cosine weighting terms, ensuring continuous transitions in the kernel's shape." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.51, + 0.906, + 0.585 + ], + "angle": 0, + "content": "2D Gaussian as a Special Case. Our formulation generalizes 2D Gaussian kernels. By setting \\( K = 4 \\) with \\( \\theta_{k} = \\frac{k\\pi}{2} \\) and \\( s_0 = s_2 = s_u \\), \\( s_1 = s_3 = s_v \\), we can derive the 2D Gaussian form in Eq. (3). For points in the first UV quadrant where \\( \\Delta \\theta_{k} = 2\\theta \\):" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.596, + 0.847, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\alpha = o \\cdot \\exp \\left(- \\frac {r _ {2} ^ {2}}{2} \\left(\\frac {\\cos^ {2} \\theta}{s _ {0} ^ {2}} + \\frac {\\cos^ {2} \\theta}{s _ {1} ^ {2}}\\right)\\right) \\\\ = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\frac {u ^ {2}}{s _ {0} ^ {2}} + \\frac {v ^ {2}}{s _ {1} ^ {2}}\\right)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.678, + 0.907, + 0.724 + ], + "angle": 0, + "content": "where we use the identity \\(\\cos (\\Delta \\theta_k) = \\cos (2\\theta) = 2\\cos^2\\theta -1\\). The derivation extends to other quadrants by symmetry." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.734, + 0.725, + 0.75 + ], + "angle": 0, + "content": "4.2. L1&L2 Norm Blending" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.756, + 0.906, + 0.869 + ], + "angle": 0, + "content": "The scaling term \\(\\frac{1}{\\bar{s}^2} = \\left(\\frac{1 + \\cos(\\Delta\\theta_k)}{2s_k^2} +\\frac{1 - \\cos(\\Delta\\theta_k)}{2s_{k + 1}^2}\\right)\\) in Eq. (6) enforces smooth contours at radial endpoints, where \\(\\frac{d\\bar{s}}{d\\Delta\\theta_k} = 0\\) at \\(\\Delta \\theta_{k} = 0\\) or \\(\\pi\\). However, since radials converge at the kernel center and are not parallel, this \\(L2\\) formulation inherently produces conic curves, limiting its ability to represent straight edges common in man-made environments." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.907, + 0.901 + ], + "angle": 0, + "content": "To address this limitation, we incorporate \\( L1 \\) norm into our \\( DRK \\) formulation. For a point \\( (u,v) \\) between radial" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21516" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.122 + ], + "angle": 0, + "content": "endpoints \\( e_i = (s_i \\cos(\\theta_i), s_i \\sin(\\theta_i)) \\) and \\( e_{i+1} \\), we compute its \\( L1 \\) norm as:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.133, + 0.483, + 0.166 + ], + "angle": 0, + "content": "\\[\nr _ {1} = \\left\\| \\left( \\begin{array}{l l} e _ {i} & e _ {i + 1} \\end{array} \\right) ^ {- 1} \\binom {u} {v} \\right\\| _ {1}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.176, + 0.483, + 0.221 + ], + "angle": 0, + "content": "This transformation maps the diamond-shaped \\( L1 \\) unit ball \\( (|x| + |y| = 1,0\\leq x,y\\leq 1) \\) to the segment between adjacent endpoints, enabling straight-line boundaries." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.222, + 0.484, + 0.267 + ], + "angle": 0, + "content": "We then introduce a blending weight \\(\\eta \\in (0,1)\\) to smoothly interpolate between \\(L1\\) and \\(L2\\) norms, yielding our complete kernel function:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.279, + 0.483, + 0.311 + ], + "angle": 0, + "content": "\\[\n\\alpha = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\eta r _ {1} ^ {2} + (1 - \\eta) \\frac {r _ {2} ^ {2}}{\\bar {s} ^ {2}}\\right)\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.323, + 0.484, + 0.368 + ], + "angle": 0, + "content": "Note that \\( r_1^2 \\) requires no explicit scaling term as it is inherently scaled through the inverse transformation in Eq. (7). Please see Fig. 4 (right) for illustration." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.381, + 0.262, + 0.397 + ], + "angle": 0, + "content": "4.3. Edge Sharpening" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.405, + 0.311, + 0.57 + ], + "angle": 0, + "content": "As shown in Fig. 2, Gaussian functions inherently couple scale and edge sharpness through their variance parameter, making it challenging to achieve precise shape approximation even with thousands of Gaussians. To decouple these properties, we introduce a sharpening coefficient \\(\\tau \\in (-1,1)\\) that adaptively adjusts edge tran" + }, + { + "type": "image", + "bbox": [ + 0.317, + 0.406, + 0.484, + 0.529 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.34, + 0.535, + 0.483, + 0.561 + ], + "angle": 0, + "content": "Figure 5. Sharpening function illustration." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.572, + 0.484, + 0.615 + ], + "angle": 0, + "content": "sitions. Given the exponential term \\( g \\) (i.e., the density value before opacity scaling) in Eq. (8), our sharpening function is:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.625, + 0.483, + 0.672 + ], + "angle": 0, + "content": "\\[\n\\Psi (g) = \\left\\{ \\begin{array}{l l} \\frac {1 - \\tau}{1 + \\tau} g & \\text {i f} \\quad 0 \\quad \\leq g < \\frac {1 + \\tau}{4}, \\\\ \\frac {1 + \\tau}{1 - \\tau} g - \\frac {\\tau}{1 - \\tau} & \\text {i f} \\quad \\frac {1 + \\tau}{4} \\quad \\leq g < \\frac {3 - \\tau}{4}, \\\\ \\frac {1 - \\tau}{1 + \\tau} g + \\frac {2 \\tau}{1 + \\tau} & \\text {i f} \\quad \\frac {3 - \\tau}{4} \\quad \\leq g \\leq 1. \\end{array} \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.683, + 0.484, + 0.745 + ], + "angle": 0, + "content": "As illustrated in Fig. 5, this piecewise function reshapes the alpha values toward 0 or 1, creating sharper edge transitions while maintaining the kernel's spatial extent. The final kernel opacity is computed as \\(\\alpha = o\\cdot \\Psi (g)\\)" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.756, + 0.231, + 0.77 + ], + "angle": 0, + "content": "4.4. Rasterization" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Low-pass Filtering. Camera-captured images represent discretely sampled signals from scene rays, inherently limiting the maximum recoverable frequency of 3D content. Without proper frequency constraints, optimization tends to generate small, floating primitives that overfit to individual training views. These primitives become too fine-grained (smaller than ray coverage) and only contribute to specific rays, resulting in poor generalization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.228 + ], + "angle": 0, + "content": "While 3D-GS leverages EWA splatting for closed-form Gaussian low-pass filtering, \\( DRK \\) requires an alternative approach. Following Botsch et al. [4], we approximate filtering by taking the maximum between the kernel function and a view-dependent low-pass filter. Since \\( DRK \\) represents planar primitives, its frequency should be bounded on its tangent plane while potentially unbounded when viewed orthogonally, so we scale the filter size by the cosine of the view angle:" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.238, + 0.907, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\alpha} = \\max (\\alpha , o \\cdot \\exp (- \\frac {1}{2 \\left| r _ {d} \\cdot R _ {z} \\right| ^ {2}} \\left(\\frac {\\Delta p _ {w} ^ {2}}{s _ {l} ^ {2}} + \\frac {\\Delta p _ {h} ^ {2}}{s _ {l} ^ {2}}\\right))), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.28, + 0.907, + 0.326 + ], + "angle": 0, + "content": "where \\(\\Delta p_h\\) and \\(\\Delta p_w\\) are image space distances between the pixel and the projected kernel center, \\(r_d \\cdot R_z\\) accounts for view-dependent scaling, and \\(s_l\\) controls the filter radius." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.348, + 0.907, + 0.545 + ], + "angle": 0, + "content": "Tile Culling. Our rendering pipeline, based on 3D-GS, performs image rendering using 2D thread grids on CUDA. The process begins by dividing images into \\(16 \\times 16\\) tiles, with each tile corresponding to potentially intersecting primitives (kernels or 3D Gaussians). While 3D-GS projects the major axis of a 3D Gaussian onto the image plane to create a square axis-aligned bounding box (AABB) for tile coverage, this method can be computationally inefficient for primitives that project as highly anisotropic or elongated shapes, as shown in Fig. 6. This inefficiency becomes particularly evident in \\(DRK\\) due to its diverse shape representations. To address this, we introduce a more precise radius calculation and an improved tile culling strategy." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.548, + 0.906, + 0.647 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.65, + 0.906, + 0.678 + ], + "angle": 0, + "content": "Figure 6. Polygon-based tile culling using radial basis endpoints enables efficient rasterization by eliminating untouched tiles." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.685, + 0.906, + 0.762 + ], + "angle": 0, + "content": "The effective range of \\( DRK \\) is governed by its radial basis, whose endpoints define the kernel's boundary. Following the 3-σ principle, we define the boundary radius \\( s_k^c \\), but extend it to account for opacity \\( o \\) and sharpness \\( \\tau \\) parameters. The calibrated radial length \\( s_k^c \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.775, + 0.905, + 0.815 + ], + "angle": 0, + "content": "\\[\ns _ {k} ^ {c} = s _ {k} \\sqrt {- \\log \\left(\\Psi^ {- 1} \\left(\\frac {e ^ {- 3 2}}{o}\\right)\\right)}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.906, + 0.872 + ], + "angle": 0, + "content": "The derivation details are provided in the Supplementary Material. Using this calibrated length, we calculate each radial basis endpoint \\( v_{k} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.886, + 0.905, + 0.903 + ], + "angle": 0, + "content": "\\[\nv _ {k} = \\mu + s _ {k} ^ {c} (\\cos \\theta_ {k} R _ {x} + \\sin \\theta_ {k} R _ {y}). \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21517" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.9, + 0.213 + ], + "angle": 0, + "content": "
MethodsSimpleTextureGeometrySpecularLargeAverage
PSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIM
2D-GS42.10.0209.996942.59.0624.983429.90.0513.970027.18.0570.955027.80.2500.838833.92.0881.9514
3D-GS39.51.0311.994144.57.0628.996829.14.0552.965827.16.0758.952332.19.2054.901734.41.0861.9621
3D-HGS41.41.0199.993146.19.0397.991230.42.0406.959827.27.0512.944733.17.1672.872135.68.0637.9521
GES40.95.0266.995545.23.0579.997730.36.0468.970427.04.0632.955031.67.2074.898735.05.0804.9634
DRK (S2)40.34.0283.994647.67.0537.997630.68.0477.970927.07.0704.957031.57.2090.898535.03.0823.9637
DRK (S1)42.24.0168.997447.86.0410.998831.67.0394.978827.77.0631.960333.78.1685.919636.62.0668.9701
DRK43.46.0105.998549.08.0396.999031.93.0366.980328.19.0592.961535.28.1348.937237.58.0564.9752
" + }, + { + "type": "table_caption", + "bbox": [ + 0.235, + 0.215, + 0.762, + 0.229 + ], + "angle": 0, + "content": "Table 1. Rendering quality evaluation on DiverseScene datasets across various categories" + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.238, + 0.482, + 0.294 + ], + "angle": 0, + "content": "
2DGS3DGS3DHGSGESDRK(S2)DRK(S1)DRK
Num(↓)359K336K373K330K42 K109K260K
MB(↓)83.679.789.678.112.332.176.6
FPS(↑)251.3247.1154.5227.4234.9119.277.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.296, + 0.482, + 0.324 + ], + "angle": 0, + "content": "Table 2. Evaluation results of average primitive number (Num), model size (MB), and rendering speed (FPS) on DiverseScene." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.352, + 0.483, + 0.426 + ], + "angle": 0, + "content": "These endpoints form a polygon that accurately approximates the kernel's boundary. By projecting this polygon onto the image plane, we can efficiently identify and cull tiles that don't intersect with the kernel, making the rasterization more efficient." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.428, + 0.297, + 0.521 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.429, + 0.482, + 0.521 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.522, + 0.483, + 0.551 + ], + "angle": 0, + "content": "Figure 7. Our cache-sorting uses \\( r_t \\) as keys in cache-sorting to rectify the sorting order while preventing popping artifacts." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.57, + 0.483, + 0.706 + ], + "angle": 0, + "content": "Cache Sorting. 3D-GS sorts the Gaussian using the depth of the center \\(\\mu\\), which can lead to inconsistencies across multiple views. While Radl et al. [44] address this by estimating the depth of the Gaussian at the point of maximum density and applying a hierarchical sorting solution to mitigate popping artifacts caused by inconsistent sorting, we propose a simpler yet effective solution. In our approach, the distance \\(r_t\\) from the camera to the intersection between the ray and \\(DRK\\) is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.718, + 0.482, + 0.754 + ], + "angle": 0, + "content": "\\[\nr _ {t} = \\frac {\\left(\\mu - r _ {o}\\right) ^ {T} R _ {z}}{r _ {d} ^ {T} R _ {z}}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.902 + ], + "angle": 0, + "content": "During rendering, each thread processes a pixel using an sorted array to cache the \\( r_t \\) values and kernel indices, as illustrated in Fig. 7. The array is kept sorted by performing insert sorting for each new-coming kernel. If the array is full, the kernel with the smallest \\( r_t \\) is popped out for processing. A dynamic cursor is used to record the scanning. We maintain an array length of 8, which is sufficient for approximating a more accurate sort. Fig. 7 demonstrates our method's effectiveness in handling multiple overlapping" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.242, + 0.905, + 0.288 + ], + "angle": 0, + "content": "kernels with identical center depths, comparing rasterization results with and without cache-sorting, preventing popping artifacts while maintaining rendering efficiency." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.301, + 0.638, + 0.317 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.325, + 0.8, + 0.34 + ], + "angle": 0, + "content": "5.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.349, + 0.907, + 0.711 + ], + "angle": 0, + "content": "To evaluate our method's performance across diverse scenarios, we focused on four key aspects: texture complexity, geometric detail, view-dependent effects, and scene scale. We collected 10 representative 3D scenes from Sketchfab1, with two scenes per category: simple objects, richly textured surfaces, intricate geometric details, specular materials, and large-scale environments. The dataset, namely DiverseScenes, serves as a benchmark to assess our representation method's capabilities. Detailed information about DiverseScenes can be found in the supplementary materials. For the evaluation on unbounded real-world scenes, we utilized the Mip-NeRF360 dataset [2], which contains multi-view images captured in open environments. Camera poses were estimated using COLMAP [47]. We assessed performance using three metrics: Peak Signal-to-Noise Ratio (PSNR) for overall reconstruction accuracy, Structural Similarity Index (SSIM) for perceptual quality and Learned Perceptual Image Patch Similarity (LPIPS) [68] for human-perceived visual fidelity. We observed that the number of primitives significantly impacts rendering quality. To evaluate DRK's performance across different densities, we present results using various hyper-parameters (details provided in the Supp), where the density decreases progressively from \\(DRK\\) to \\(DRK(S2)\\) and then to \\(DRK(S1)\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.72, + 0.753, + 0.736 + ], + "angle": 0, + "content": "5.2.Quantitative Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.743, + 0.906, + 0.879 + ], + "angle": 0, + "content": "DiverseScenes. We compare our method, \\(DRK\\), against state-of-the-art Gaussian representations: 3D-GS [27], 2D-GS [22], 3D-HGS [30], and GES [20], using their official implementations. To ensure a fair comparison focused on kernel representation, we adjust the gradient threshold for densification in these methods, aligning their primitive count with that of 3D-GS \\((300\\mathrm{K}+)\\). The results for each dataset category are shown in Table 1, demonstrating that our method achieves the best average performance. This" + }, + { + "type": "page_footnote", + "bbox": [ + 0.532, + 0.887, + 0.659, + 0.9 + ], + "angle": 0, + "content": "1https://sketchfab.com/" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21518" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.108, + 0.085, + 0.885, + 0.607 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.608, + 0.907, + 0.636 + ], + "angle": 0, + "content": "Figure 8. Qualitative comparisons of \\( DRK \\) with state-of-the-art methods across various scenarios show that \\( DRK \\) effectively captures sharp texture and geometry boundaries." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.641, + 0.483, + 0.732 + ], + "angle": 0, + "content": "is followed by our sparser version, \\( DRK \\) (S1). \\( DRK \\) (S2) also performs comparably to other state-of-the-art methods, with significantly fewer primitives and lower space occupancy, while maintaining comparable FPS, as detailed in Table 2. Although our method requires more computation, the rendering frameres remain efficient (FPS > 50)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Mip-NeRF360 Datasets. We also tested \\( DRK \\) on Mip-NeRF360 datasets, known for accurate camera poses and unbounded scenes. Results are shown in Tab. 3. On unbounded scenes, \\( DRK \\) still excels in perceptual quality (LPIPS, SSIM), it shows less advantage in PSNR, especially with sparser kernels. We hypothesize that DRK may tend to overfit distant regions with limited supervision. To address this, we used MiVOS[6] to mask image sequences, training on original images but evaluating only the foreground. The results (M-PSNR) indicate our method's strength in well-supervised central regions." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.638, + 0.902, + 0.743 + ], + "angle": 0, + "content": "
MethodsPSNR(↑)M-PSNR(↑)LPIPS(↓)SSIM(↑)Num(↓)Size(↓)
2D-GS26.3232.01.2987.7617928 K216.0 M
3D-GS26.4832.23.3045.7537811 K191.3 M
3D-GS (L)26.9432.75.2688.77991191 K281.6 M
3D-HGS26.7432.51.2999.7561842 K202.4 M
GES26.6232.11.3047.7542824 K195.0 M
DRK (S2)26.2032.31.2781.7601388 K125.9 M
DRK (S1)26.4032.56.2601.7722551 K161.9 M
DRK26.7632.81.2364.7871952 K279.1 M
" + }, + { + "type": "table_caption", + "bbox": [ + 0.525, + 0.751, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation on Mip-NeRF360 scenes [2]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.784, + 0.736, + 0.801 + ], + "angle": 0, + "content": "5.3. Qualitative Comparison" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We conducted qualitative comparisons to highlight the advantages of DRK over other state-of-the-art kernel representations. Fig.8 shows results across different scene categories, where our method achieves better texture and geometry fitting with a comparable or smaller number of kernels. Fig.9 demonstrates that DRK effectively handles fine ge" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21519" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.065, + 0.894, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.137, + 0.432, + 0.858, + 0.446 + ], + "angle": 0, + "content": "Figure 9. Comparisons on the MipNeRF 360 dataset show our method achieves clearer details and high-fidelity rendering." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.459, + 0.483, + 0.504 + ], + "angle": 0, + "content": "omtries, such as flowers and leaves, and detailed textures, like tags and bark, outperforming other representations that may have used more primitives (see Tab. 3)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.514, + 0.325, + 0.53 + ], + "angle": 0, + "content": "5.4. Converting Mesh to DRK" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.538, + 0.484, + 0.734 + ], + "angle": 0, + "content": "All existing \"Splatting\" methods [20, 22, 27, 30] fail to seamlessly integrate with traditional assets. In contrast, our \\(DRK\\) framework provides a versatile representation that allows for effortless conversion of triangle and polygon faces into \\(DRK\\). This is accomplished by placing the \\(DRK\\) endpoints at the polygon vertices and adjusting the parameters \\(\\tau\\) and \\(\\eta\\) to control sharpness, with both \\(L1\\) and \\(L2\\) curvature set to 1. This process eliminates the need for training data rendering or model optimization. Consequently, rich 3D assets can be seamlessly transferred into \\(DRK\\), bridging the gap between millions of traditional 3D assets and our fast, high-quality reconstruction representation. Figure 10 illustrates the potential applications of Mesh2DRK." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.738, + 0.484, + 0.871 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.873, + 0.483, + 0.915 + ], + "angle": 0, + "content": "Figure 10. The conversion from Mesh to \\( DRK \\) demonstrates the efficiency of using \\( DRK \\) to incorporate traditional 3D assets into any \\( DRK \\) scene at low cost." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.457, + 0.634, + 0.473 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.483, + 0.907, + 0.725 + ], + "angle": 0, + "content": "We present \\(DRK\\), a novel primitive representation that generalizes and enhances Gaussian splatting. By incorporating learnable radial bases, adaptive shape control, and efficient rendering strategies, \\(DRK\\) effectively addresses the fundamental limitations of Gaussian kernels in representing diverse geometric features. Our experiments on both synthetic and real-world scenes demonstrate that \\(DRK\\) achieves superior rendering quality with significantly fewer primitives, while maintaining computational efficiency through carefully designed rasterization optimizations. Leveraging the flexibility of \\(DRK\\), traditional triangle or polygon mesh representations can be seamlessly converted into \\(DRK\\) without requiring any training. This capability bridges rich 3D assets with reconstructed scenes, paving the way for future applications such as real-scene editing, VR digital world creation, and AR scene enhancement." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.74, + 0.673, + 0.757 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.903 + ], + "angle": 0, + "content": "This work has been supported in part by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621), General Research Fund Scheme (Grant No. 17202422, 17212923), Theme-based Research (Grant No. T45-701/22-R) and Shenzhen Science and Technology Innovation Commission (SGDX20220530111405040). Part of the described research work is conducted in the JC STEM Lab of Robotics for Soft Materials funded by The Hong Kong Jockey Club Charities Trust." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21520" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.171 + ], + "angle": 0, + "content": "[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. Neural point-based graphics. In Proceedings of the European Conference on Computer Vision (ECCV), pages 696-712. Springer, 2020. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.173, + 0.483, + 0.227 + ], + "angle": 0, + "content": "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Mip-NeRF 360: Unbounded anti-aliased neural radiance fields. 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Gaussian Splatting (GS) vs. Deformable Radial Kernel (DRK) Splatting: GS requires thousands of Gaussians to approximate detailed textures and shapes. In contrast, DRK efficiently fits the target pattern with just 30 primitives, achieving superior results. + +![](images/4d045abfcec963bbee65cdefcd089858594f118eacd495125e7445f788420235.jpg) +GS (50) + +![](images/cc7f88a3c76c887a6b1326d3e5a1b121e2841e2eb52c9539fabf4ad8757627e2.jpg) +GS (500) + +![](images/1c59c8561d94ab15a7728e4d766d1cd94b5d7031cf918ce7161a14b4041cff56.jpg) +GS (5K) + +![](images/d44e537bbbdad0d6d98a2df34ad337c062f16a33960e6816477d4bd63e0f1649.jpg) + +![](images/c27c9734889a32f247c2dcabdcfe428dab7adb6f2e5d71dbfc6a3af253c2af99.jpg) +DRK (50) +Render Scale-Down + +# Abstract + +Recently, Gaussian splatting has emerged as a robust technique for representing 3D scenes, enabling real-time rasterization and high-fidelity rendering. However, Gaussians' inherent radial symmetry and smoothness constraints limit their ability to represent complex shapes, often requiring thousands of primitives to approximate detailed geometry. We introduce Deformable Radial Kernel (DRK), which extends Gaussian splatting into a more general and flexible framework. Through learnable radial bases with adjustable angles and scales, DRK efficiently models diverse shape primitives while enabling precise control over edge sharpness and boundary curvature. Even DRK's planar nature, we further develop accurate ray-primitive intersection computation for depth sorting and introduce efficient kernel culling strategies for improved rasterization efficiency. Extensive experiments demonstrate that DRK outperforms existing methods in both representation efficiency and rendering quality, achieving state-of-the-art performance while dramatically reducing primitive count. + +# 1. Introduction + +3D Gaussian Splitting [27] (3D-GS) has emerged as a leading 3D representation method thanks to its rapid rasterization and superior rendering quality. Its key advantages—ex + +plicit point-based representation, flexibility for manipulation, and MLP-free rendering- have positioned it as a dominant approach in novel view synthesis. However, this success raises an intriguing question: Is the Gaussian kernel truly optimal for representing 3D scenes? + +Natural scenes often consist of primitives with diverse shapes (see Fig. 2), such as rectangles, triangles, and ellipses, which cannot be fully captured by Gaussians alone. Moreover, the inherently smooth nature of Gaussian kernels makes them less effective at representing sharp transitions. As a result, densely packed or numerous Gaussians are frequently required to accurately model scene primitives with non-Gaussian geometries or sharp boundaries (see Fig. 1), leading to inefficiencies in both computation and memory. + +Recent works have explored modifications to the Gaussian kernel to better handle discontinuities. For example, GES [20] adaptively adjusts the exponent values to control the sharpness of Gaussians, while still maintaining rotational symmetry, which limits its representational flexibility. DisC-GS [43] and 3D-HGS [30] introduce curve-and half-cutting techniques to the Gaussian kernel, respectively, improving its ability to capture discontinuous transitions. However, these cutting-based approaches remain fundamentally constrained by the inherent smoothness of the Gaussian kernel. Another line of research [8, 16, 19, 22] leverages 2D Gaussians to represent 3D scenes. While this approach offers better surface reconstruction compared to 3DGS, it is still constrained by the inherent limitations of the Gaussian framework, which restricts the flexibility + +of the representation. Notably, the concurrent work 3D-CS [21] employs novel 3D smooth convex shapes as primitives for geometry modeling with satisfactory results. + +In this work, our objective is to design new shape primitives that can adapt to complex 3D scenes. Motivated by the success of 2D Gaussian Splatting (2D-GS), we focus on developing adaptive 2D planar kernels. Specifically, we introduce the 2D Deformable Radial Kernel (DRK), a flexible planar primitive for representing 3D scenes (see Fig. 4). At its core, DRK extends traditional radial bases with learnable parameters that enable precise control over shape deformation through three key features: 1) multiple radial bases with learnable polar angles and scale parameters allow the kernel to adaptively stretch, rotate, and shrink, providing significantly more flexibility than fixed Gaussian functions; 2) a hybrid distance metric combining $L1$ and $L2$ norms with learnable weights enables DRK to naturally represent both curved surfaces and sharp geometric features; and 3) an adaptive piecewise linear remapping function provides fine-grained control over value distributions, particularly enhancing the representation of sharp boundaries. Despite its enhanced expressiveness, DRK maintains a simple parametric form that is easy to optimize and efficient to render. The DRK determines the location and orientation of the tangent plane through its center and rotation parameters, building upon these radial bases as its structural foundation to conform to target shapes, bypassing the geometric and smoothness constraints typically imposed by Gaussian functions. As shown in Fig. 2, a single DRK primitive can flexibly model a wide range of shape primitives, whereas many Gaussians are often required to represent similar shapes. The formulation is also backwards-compatible - DRK naturally reduces to a Gaussian kernel when using two orthogonal major bases with different decay rates, while achieving superior rendering quality with comparable computational efficiency. + +We experimentally validate $DRK$ on our proposed dataset (DiverseScene) covering various scenarios, including rich textures, fine geometry, specular effects, and large spatial scale. We also evaluate $DRK$ on unbounded MipNeRF 360 [2] datasets. Experimental results demonstrate our method has advantages in preserving visual details more effectively and efficiently. + +Overall, our work makes the following contributions: + +- We introduce Deformable Radial Kernel (DRK), a novel primitive that generalizes conventional Gaussian splattig. DRK enables flexible shape modeling through learnable radial bases, hybrid distance metrics, and adaptive sharpness control, significantly reducing the number of primitives needed for high-quality scene representation. +- We develop a differentiable and efficient rendering pipeline for DRK, featuring polygon-based tile culling and cache-sorting strategies to enhance both rendering ef + +ficiency and view consistency. + +- We created DiverseScenes, a new dataset covering rich textures, fine geometry, specular effects, and large scenes for more effectively evaluating the ability to model complex scenarios of different algorithms. + +# 2. Related Work + +# 2.1. Novel View Synthesis + +Novel view synthesis from multi-view images represents a fundamental challenge in computer graphics and computer vision. The field has evolved through increasingly sophisticated 3D scene representations. Traditional light field approaches [10, 18, 29] attempt to model the entire scene through a single 4D function of ray-slice intersections, but this implicit representation struggles with sparse inputs and complex geometry. Advancing beyond single-function modeling, Multi-Plane-Images (MPI) [38, 51, 55, 58, 69] introduced a layered representation using multiple depth planes, offering better 3D structure modeling. However, its discrete depth layering limits the handling of large viewpoint changes, particularly in rotational views. To achieve continuous depth modeling, subsequent works adopted explicit 3D proxies including meshes [5, 11, 35, 56, 59], point clouds [1, 7, 37, 41, 57], and voxels [14, 32, 48, 49]. These representations offer more flexible geometry modeling, with point-based methods further enhanced by neural networks [45, 46] for improved stability. + +Most recently, continuous neural representations have emerged as a powerful alternative, replacing discrete geometric proxies with MLPs that directly map 3D coordinates to scene properties. NeRF [39] pioneered this approach with radiance fields, spawning numerous extensions for faster inference [15, 26, 40], large-scale scenes [2, 17, 53, 61, 66], dynamic content [31, 42, 50], reflection modeling [3, 24, 28, 62], and stylization [9, 13, 23, 67]. + +# 2.2. Gaussian Splitting + +Point-based rendering approaches have made the rendering process of point clouds differentiable, enabling end-to-end training for novel view synthesis. 3D Gaussian Splating (3D-GS) [27] introduced scene modeling using 3D Gaussian distributions, compositing the appearance of intersected Gaussians along viewing rays through $\alpha$ -blending. This seminal work has inspired numerous extensions across various applications, including dynamic scene view synthesis [25, 34, 65], 3D content generation [54, 70], geometry reconstruction [22, 36], video representation [52] and neural network-enhanced high-fidelity view synthesis [33, 64]. The flexible representation, computational efficiency, and superior rendering quality of 3D-GS have established it as a prominent approach in the field [60]. + +The key innovation of 3D-GS lies in its use of Gaussian + +kernels for point effect decay, where the continuous nature of these functions facilitates the optimization of discrete representations. Subsequent research has focused on both constraining and extending these Gaussian kernels for specific applications. Notable developments include the constraint of 3D Gaussians to 2D space [8, 19, 22], yielding planar representations that better approximate scene surfaces for precise geometry reconstruction. Other works have extended the framework to 4D space [12, 63], enabling temporal dynamic modeling through 3D slicing of 4D Gaussians for view synthesis. To address limitations in representing sharp edges, researchers have proposed modifications to the Gaussian shape using curve-cutting [43], hemispheric truncation [30], and novel 3D convex shapes [21]. + +# 3. Preliminaries + +In this section, we first review 3D Gaussian Splitting (3D-GS) and 2D Gaussian Splitting (2D-GS), and their mathematical formulations (Sec. 3.1 and Sec. 3.2). We then introduce our general kernel splitting framework that extends beyond traditional Gaussian primitives (Sec. 3.3). Finally, we analyze the inherent limitations of Gaussian-based representations, motivating the need for our proposed deformable radial kernel formulation (Sec. 3.4). + +# 3.1. 3D Gaussian Splitting (3D-GS) + +3D Gaussian Splatting represents scenes using colored 3D Gaussians [27]. Each Gaussian $G$ is parameterized by a 3D center $\mu$ , covariance matrix $\Sigma = R S S^T R^T$ (where $R$ is a rotation matrix from quaternion $q \in \mathbf{SO}(3)$ and $S$ is a scaling matrix from vector $s$ ), opacity $o$ , and spherical harmonic coefficients $sh$ for view-dependent appearance. A scene is represented as $\mathcal{G} = \{G_j : \mu_j, q_j, s_j, o_j, sh_j\}$ . + +Rendering involves projecting Gaussians onto the image plane with 2D covariance $\Sigma^{\prime} = JW\Sigma W^{T}J^{T}$ and center $\mu^{\prime} = JW\mu$ . The pixel color $C(u)$ is computed via neural point-based $\alpha$ -blending: + +$$ +C (u) = \sum_ {i \in N} T _ {i} \alpha_ {i} \mathcal {S H} \left(s h _ {i}, v _ {i}\right), \text {w h e r e} T _ {i} = \Pi_ {j = 1} ^ {i - 1} \left(1 - \alpha_ {j}\right), \tag {1} +$$ + +where $\mathcal{SH}$ evaluates spherical harmonics with view direction $v_{i}$ , and $\alpha_{i}$ is: + +$$ +\alpha_ {i} = o _ {i} e ^ {- \frac {1}{2} (p - \mu_ {i} ^ {\prime}) ^ {T} \Sigma_ {i} ^ {\prime} (p - \mu_ {i} ^ {\prime})}. \tag {2} +$$ + +By optimizing these Gaussian parameters and adaptively adjusting their density, 3D-GS achieves high-quality scene representation with real-time rendering capabilities. + +# 3.2. 2D Gaussian Splitting (2D-GS) + +Recognizing that real-world scenes primarily consist of surface structures where 3D Gaussians naturally compress into + +planar formations, recent works [8, 22] proposed 2D Gaussian Splatting (2D-GS). The opacity $\alpha$ is computed using local coordinates $(u,v)$ on the tangent plane: + +$$ +\alpha = o \cdot \exp \left(- \frac {1}{2} \left(\frac {u ^ {2}}{s _ {u} ^ {2}} + \frac {v ^ {2}}{s _ {v} ^ {2}}\right)\right), \qquad (3) +$$ + +where $s_u^2$ and $s_v^2$ denote the variances along the U and V axes. This surface-centric formulation aligns with the success of polygon meshes in 3D modeling, offering a more compact scene representation. + +# 3.3. General Kernel Splitting + +We extend conventional 2D Gaussians by introducing a more general planar kernel splating formulation (Fig. 3). Given a ray from position $r_o \in \mathbb{R}^3$ with direction $r_d \in \mathbb{R}^3$ intersecting a tangent plane centered at $\mu$ with rotation $R \in SO(3)$ , the intersection point is: + +$$ +i = r _ {o} + \frac {\left(\mu - r _ {o}\right) ^ {T} R _ {z}}{r _ {d} ^ {T} R _ {z}} r _ {d}, \tag {4} +$$ + +where $R_{z}$ is the plane normal. The local UV coordinates at this intersection are: + +$$ +\binom {u} {v} = \binom {R _ {x} ^ {T}} {R _ {y} ^ {T}} (i - \mu), \tag {5} +$$ + +where $R_x^T$ and $R_y^T$ are the first and second rows of $R$ . The kernel splating function then maps these UV coordinates to a density value $\alpha$ , determining the primitive's shape. + +![](images/06925da25236c608d0b84ba3b2e2acbc7e39399f748872753f9a433e3a97d5d2.jpg) +Figure 3. Illustration of general planar kernel splitting: UV coordinates of ray-plane intersections are mapped to density values via a kernel function that determines the primitive's shape. + +# 3.4. Discussions + +While 3D-GS demonstrates remarkable efficacy, our analysis reveals several inherent limitations. First, screen-space projection of Gaussians yields 2D elliptical distributions with rotational symmetry, constraining their ability to approximate diverse primitive shapes. Second, their conic curve boundaries (derived by the $L2$ norm) challenge the representation of linear edges and intermediate edge forms. Third, Gaussian distributions inherently couple decay rate with spatial extent through the covariance matrix—sharp features necessitate narrow distributions, making it challenging to simultaneously capture abrupt transitions and extended spatial regions. + +![](images/90b549a05a564ded20b6dcf86d6f433becb3a6175851252be815003c6fd3a2c0.jpg) +Figure 2. Comparison of 3D-GS versus a single $DRK$ : $DRK$ achieves superior geometric fidelity with just one primitive compared to multiple Gaussians. We visualize the contours of 3D-GS and $DRK$ to better illustrate primitive count, scale, and position. + +![](images/6b072a01261154279bcf9e81adb3c1b1f15824ed64178ed7123322fecfd52ba4.jpg) + +![](images/06a905b352cfa0d7d8c1ca4d20bf425bb918fbbd7a22d5876f80199b7c4024de.jpg) + +![](images/937d773db46c267312745cbbe3a56d81751a733b3dbb6e89520c6ef1049c4306.jpg) + +These constraints necessitate millions of fine-grained Gaussians to approximate arbitrary shapes, leading to overparameterization while still failing to achieve perfect fidelity under practical constraints. As shown in Fig. 2, even elementary shapes like triangles and rectangles—which can be described concisely—require numerous Gaussians for approximation, exhibiting artifacts like interior inconsistencies and external floating points (last column). Our deformable radial kernel (DRK) addresses these limitations through radial basis functions with varying lengths $s_k$ and polar angles $\theta_k$ , controlled by parameters $\eta$ and $\tau$ for contour curvature and sharpness (Fig. 4). + +# 4. Deformable Radial Kernel Splitting + +Deformable Radial Kernel (DRK) is a novel primitive for 3D scene representation characterized by a set of parameters $\Theta = \{\mu, q, s_k, \theta_k, \eta, \tau, o, sh\}$ , where: + +- $\mu \in \mathbb{R}^3$ , $q \in SO(3)$ , $o$ , and $sh$ follow 3D-GS for position, orientation, opacity, and view-dependent appearance +- $\{s_k, \theta_k\}_{k=1}^K$ define radial basis lengths and angles that control the kernel shape +- $\eta \in (0,1)$ and $\tau \in (-1,1)$ control boundary curvature and sharpness, respectively + +In the following sections, we detail each component of DRK. First, we introduce the radial basis formulation (Sec. 4.1), showing that traditional 2D Gaussians are a special case within our framework. Then, we discuss $L1\& L2$ norm blending and edge sharpening in Sec. 4.2 and Sec. 4.3, which enable flexible control of boundary curvature and sharpness. Finally, in Sec. 4.4, we explore efficient rasterization strategies specifically tailored for DRK, including low-pass filtering, kernel culling, and cache sorting. + +![](images/58e3d301b862f3a363a03ff8d54587ae48c856279b6c442f16063a854b6eb868.jpg) +Figure 4. $DRK$ defines a deformable shape using radial basis functions characterized by lengths $s_k$ and polar angles $\theta_k$ , with parameters $\eta$ and $\tau$ governing the shape's curvature and sharpness respectively. + +![](images/d6f816574cfea7d7acf27ffe665c35d06936ada7cbcf1fd04fe39ebad6d1e332.jpg) + +![](images/dd71778987ce77a99abdf95b06a9ba6dc400d15d608bd8c47016101ff0943411.jpg) + +# 4.1. Radial Basis + +Our radial basis defines a kernel's shape through $K$ control points in polar coordinates $\{s_k,\theta_k\}$ , where $s_k > 0$ represents each radial length and angles are ordered as $0 < \theta_0 < \ldots < \theta_K \leq 2\pi$ . For any point with local tangent coordinates $(u,v)$ , we compute its polar representation using $L2$ norm $r_2 = \sqrt{u^2 + v^2}$ and angle $\theta = \arccos (u / r_2)$ . Given a point lying between basis $k$ and $k + 1$ (i.e., $\theta_{k} < \theta \leq \theta_{k + 1}$ ), we define its relative angular distance as $\Delta \theta_{k} = \frac{(\theta - \theta_{k})\pi}{\theta_{k + 1} - \theta_{k}}$ . The kernel function is then formulated as: + +$$ +\alpha = o \cdot \exp \left(- \frac {r _ {2} ^ {2}}{2} \left(\frac {1 + \cos (\Delta \theta_ {k})}{2 s _ {k} ^ {2}} + \frac {1 - \cos (\Delta \theta_ {k})}{2 s _ {k + 1} ^ {2}}\right)\right). (6) +$$ + +This formulation smoothly interpolates between adjacent radial bases using cosine weighting terms, ensuring continuous transitions in the kernel's shape. + +2D Gaussian as a Special Case. Our formulation generalizes 2D Gaussian kernels. By setting $K = 4$ with $\theta_{k} = \frac{k\pi}{2}$ and $s_0 = s_2 = s_u$ , $s_1 = s_3 = s_v$ , we can derive the 2D Gaussian form in Eq. (3). For points in the first UV quadrant where $\Delta \theta_{k} = 2\theta$ : + +$$ +\begin{array}{l} \alpha = o \cdot \exp \left(- \frac {r _ {2} ^ {2}}{2} \left(\frac {\cos^ {2} \theta}{s _ {0} ^ {2}} + \frac {\cos^ {2} \theta}{s _ {1} ^ {2}}\right)\right) \\ = o \cdot \exp \left(- \frac {1}{2} \left(\frac {u ^ {2}}{s _ {0} ^ {2}} + \frac {v ^ {2}}{s _ {1} ^ {2}}\right)\right), \\ \end{array} +$$ + +where we use the identity $\cos (\Delta \theta_k) = \cos (2\theta) = 2\cos^2\theta -1$ . The derivation extends to other quadrants by symmetry. + +# 4.2. L1&L2 Norm Blending + +The scaling term $\frac{1}{\bar{s}^2} = \left(\frac{1 + \cos(\Delta\theta_k)}{2s_k^2} +\frac{1 - \cos(\Delta\theta_k)}{2s_{k + 1}^2}\right)$ in Eq. (6) enforces smooth contours at radial endpoints, where $\frac{d\bar{s}}{d\Delta\theta_k} = 0$ at $\Delta \theta_{k} = 0$ or $\pi$ . However, since radials converge at the kernel center and are not parallel, this $L2$ formulation inherently produces conic curves, limiting its ability to represent straight edges common in man-made environments. + +To address this limitation, we incorporate $L1$ norm into our $DRK$ formulation. For a point $(u,v)$ between radial + +endpoints $e_i = (s_i \cos(\theta_i), s_i \sin(\theta_i))$ and $e_{i+1}$ , we compute its $L1$ norm as: + +$$ +r _ {1} = \left\| \left( \begin{array}{l l} e _ {i} & e _ {i + 1} \end{array} \right) ^ {- 1} \binom {u} {v} \right\| _ {1}. \tag {7} +$$ + +This transformation maps the diamond-shaped $L1$ unit ball $(|x| + |y| = 1,0\leq x,y\leq 1)$ to the segment between adjacent endpoints, enabling straight-line boundaries. + +We then introduce a blending weight $\eta \in (0,1)$ to smoothly interpolate between $L1$ and $L2$ norms, yielding our complete kernel function: + +$$ +\alpha = o \cdot \exp \left(- \frac {1}{2} \left(\eta r _ {1} ^ {2} + (1 - \eta) \frac {r _ {2} ^ {2}}{\bar {s} ^ {2}}\right)\right). \tag {8} +$$ + +Note that $r_1^2$ requires no explicit scaling term as it is inherently scaled through the inverse transformation in Eq. (7). Please see Fig. 4 (right) for illustration. + +# 4.3. Edge Sharpening + +As shown in Fig. 2, Gaussian functions inherently couple scale and edge sharpness through their variance parameter, making it challenging to achieve precise shape approximation even with thousands of Gaussians. To decouple these properties, we introduce a sharpening coefficient $\tau \in (-1,1)$ that adaptively adjusts edge tran + +![](images/f5ad3c746395127b8c4aee24cb987ce3a5e45c06575d7b4cc75c687d665f310d.jpg) +Figure 5. Sharpening function illustration. + +sitions. Given the exponential term $g$ (i.e., the density value before opacity scaling) in Eq. (8), our sharpening function is: + +$$ +\Psi (g) = \left\{ \begin{array}{l l} \frac {1 - \tau}{1 + \tau} g & \text {i f} \quad 0 \quad \leq g < \frac {1 + \tau}{4}, \\ \frac {1 + \tau}{1 - \tau} g - \frac {\tau}{1 - \tau} & \text {i f} \quad \frac {1 + \tau}{4} \quad \leq g < \frac {3 - \tau}{4}, \\ \frac {1 - \tau}{1 + \tau} g + \frac {2 \tau}{1 + \tau} & \text {i f} \quad \frac {3 - \tau}{4} \quad \leq g \leq 1. \end{array} \right. \tag {9} +$$ + +As illustrated in Fig. 5, this piecewise function reshapes the alpha values toward 0 or 1, creating sharper edge transitions while maintaining the kernel's spatial extent. The final kernel opacity is computed as $\alpha = o\cdot \Psi (g)$ + +# 4.4. Rasterization + +Low-pass Filtering. Camera-captured images represent discretely sampled signals from scene rays, inherently limiting the maximum recoverable frequency of 3D content. Without proper frequency constraints, optimization tends to generate small, floating primitives that overfit to individual training views. These primitives become too fine-grained (smaller than ray coverage) and only contribute to specific rays, resulting in poor generalization. + +While 3D-GS leverages EWA splatting for closed-form Gaussian low-pass filtering, $DRK$ requires an alternative approach. Following Botsch et al. [4], we approximate filtering by taking the maximum between the kernel function and a view-dependent low-pass filter. Since $DRK$ represents planar primitives, its frequency should be bounded on its tangent plane while potentially unbounded when viewed orthogonally, so we scale the filter size by the cosine of the view angle: + +$$ +\tilde {\alpha} = \max (\alpha , o \cdot \exp (- \frac {1}{2 \left| r _ {d} \cdot R _ {z} \right| ^ {2}} \left(\frac {\Delta p _ {w} ^ {2}}{s _ {l} ^ {2}} + \frac {\Delta p _ {h} ^ {2}}{s _ {l} ^ {2}}\right))), \tag {10} +$$ + +where $\Delta p_h$ and $\Delta p_w$ are image space distances between the pixel and the projected kernel center, $r_d \cdot R_z$ accounts for view-dependent scaling, and $s_l$ controls the filter radius. + +Tile Culling. Our rendering pipeline, based on 3D-GS, performs image rendering using 2D thread grids on CUDA. The process begins by dividing images into $16 \times 16$ tiles, with each tile corresponding to potentially intersecting primitives (kernels or 3D Gaussians). While 3D-GS projects the major axis of a 3D Gaussian onto the image plane to create a square axis-aligned bounding box (AABB) for tile coverage, this method can be computationally inefficient for primitives that project as highly anisotropic or elongated shapes, as shown in Fig. 6. This inefficiency becomes particularly evident in $DRK$ due to its diverse shape representations. To address this, we introduce a more precise radius calculation and an improved tile culling strategy. + +![](images/fc685348f0cc435f77b9844f0bc04c2f23c00dfa7fbf718bd21a12643ebabafa.jpg) +Figure 6. Polygon-based tile culling using radial basis endpoints enables efficient rasterization by eliminating untouched tiles. + +The effective range of $DRK$ is governed by its radial basis, whose endpoints define the kernel's boundary. Following the 3-σ principle, we define the boundary radius $s_k^c$ , but extend it to account for opacity $o$ and sharpness $\tau$ parameters. The calibrated radial length $s_k^c$ is defined as: + +$$ +s _ {k} ^ {c} = s _ {k} \sqrt {- \log \left(\Psi^ {- 1} \left(\frac {e ^ {- 3 2}}{o}\right)\right)}. \tag {11} +$$ + +The derivation details are provided in the Supplementary Material. Using this calibrated length, we calculate each radial basis endpoint $v_{k}$ : + +$$ +v _ {k} = \mu + s _ {k} ^ {c} (\cos \theta_ {k} R _ {x} + \sin \theta_ {k} R _ {y}). \tag {12} +$$ + +
MethodsSimpleTextureGeometrySpecularLargeAverage
PSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIM
2D-GS42.10.0209.996942.59.0624.983429.90.0513.970027.18.0570.955027.80.2500.838833.92.0881.9514
3D-GS39.51.0311.994144.57.0628.996829.14.0552.965827.16.0758.952332.19.2054.901734.41.0861.9621
3D-HGS41.41.0199.993146.19.0397.991230.42.0406.959827.27.0512.944733.17.1672.872135.68.0637.9521
GES40.95.0266.995545.23.0579.997730.36.0468.970427.04.0632.955031.67.2074.898735.05.0804.9634
DRK (S2)40.34.0283.994647.67.0537.997630.68.0477.970927.07.0704.957031.57.2090.898535.03.0823.9637
DRK (S1)42.24.0168.997447.86.0410.998831.67.0394.978827.77.0631.960333.78.1685.919636.62.0668.9701
DRK43.46.0105.998549.08.0396.999031.93.0366.980328.19.0592.961535.28.1348.937237.58.0564.9752
+ +Table 1. Rendering quality evaluation on DiverseScene datasets across various categories + +
2DGS3DGS3DHGSGESDRK(S2)DRK(S1)DRK
Num(↓)359K336K373K330K42 K109K260K
MB(↓)83.679.789.678.112.332.176.6
FPS(↑)251.3247.1154.5227.4234.9119.277.5
+ +Table 2. Evaluation results of average primitive number (Num), model size (MB), and rendering speed (FPS) on DiverseScene. + +These endpoints form a polygon that accurately approximates the kernel's boundary. By projecting this polygon onto the image plane, we can efficiently identify and cull tiles that don't intersect with the kernel, making the rasterization more efficient. + +![](images/0740a8d4f73f30787f7472318146e0e8a484aa4609808025b3971bfe1ed22d55.jpg) +Figure 7. Our cache-sorting uses $r_t$ as keys in cache-sorting to rectify the sorting order while preventing popping artifacts. + +![](images/7c6e4e5757952293201c78226a9ee5589e72c6929448f8ec9df92a3106fb0d76.jpg) + +Cache Sorting. 3D-GS sorts the Gaussian using the depth of the center $\mu$ , which can lead to inconsistencies across multiple views. While Radl et al. [44] address this by estimating the depth of the Gaussian at the point of maximum density and applying a hierarchical sorting solution to mitigate popping artifacts caused by inconsistent sorting, we propose a simpler yet effective solution. In our approach, the distance $r_t$ from the camera to the intersection between the ray and $DRK$ is calculated as: + +$$ +r _ {t} = \frac {\left(\mu - r _ {o}\right) ^ {T} R _ {z}}{r _ {d} ^ {T} R _ {z}}. \tag {13} +$$ + +During rendering, each thread processes a pixel using an sorted array to cache the $r_t$ values and kernel indices, as illustrated in Fig. 7. The array is kept sorted by performing insert sorting for each new-coming kernel. If the array is full, the kernel with the smallest $r_t$ is popped out for processing. A dynamic cursor is used to record the scanning. We maintain an array length of 8, which is sufficient for approximating a more accurate sort. Fig. 7 demonstrates our method's effectiveness in handling multiple overlapping + +kernels with identical center depths, comparing rasterization results with and without cache-sorting, preventing popping artifacts while maintaining rendering efficiency. + +# 5. Experiment + +# 5.1. Datasets and Evaluation Metrics + +To evaluate our method's performance across diverse scenarios, we focused on four key aspects: texture complexity, geometric detail, view-dependent effects, and scene scale. We collected 10 representative 3D scenes from Sketchfab1, with two scenes per category: simple objects, richly textured surfaces, intricate geometric details, specular materials, and large-scale environments. The dataset, namely DiverseScenes, serves as a benchmark to assess our representation method's capabilities. Detailed information about DiverseScenes can be found in the supplementary materials. For the evaluation on unbounded real-world scenes, we utilized the Mip-NeRF360 dataset [2], which contains multi-view images captured in open environments. Camera poses were estimated using COLMAP [47]. We assessed performance using three metrics: Peak Signal-to-Noise Ratio (PSNR) for overall reconstruction accuracy, Structural Similarity Index (SSIM) for perceptual quality and Learned Perceptual Image Patch Similarity (LPIPS) [68] for human-perceived visual fidelity. We observed that the number of primitives significantly impacts rendering quality. To evaluate DRK's performance across different densities, we present results using various hyper-parameters (details provided in the Supp), where the density decreases progressively from $DRK$ to $DRK(S2)$ and then to $DRK(S1)$ . + +# 5.2.Quantitative Comparisons + +DiverseScenes. We compare our method, $DRK$ , against state-of-the-art Gaussian representations: 3D-GS [27], 2D-GS [22], 3D-HGS [30], and GES [20], using their official implementations. To ensure a fair comparison focused on kernel representation, we adjust the gradient threshold for densification in these methods, aligning their primitive count with that of 3D-GS $(300\mathrm{K}+)$ . The results for each dataset category are shown in Table 1, demonstrating that our method achieves the best average performance. This + +![](images/1c5cbff6b0244e704362d31e14ccc71d6840e362f3ab1641ec33ad693fb3c311.jpg) +Figure 8. Qualitative comparisons of $DRK$ with state-of-the-art methods across various scenarios show that $DRK$ effectively captures sharp texture and geometry boundaries. + +is followed by our sparser version, $DRK$ (S1). $DRK$ (S2) also performs comparably to other state-of-the-art methods, with significantly fewer primitives and lower space occupancy, while maintaining comparable FPS, as detailed in Table 2. Although our method requires more computation, the rendering frameres remain efficient (FPS > 50). + +Mip-NeRF360 Datasets. We also tested $DRK$ on Mip-NeRF360 datasets, known for accurate camera poses and unbounded scenes. Results are shown in Tab. 3. On unbounded scenes, $DRK$ still excels in perceptual quality (LPIPS, SSIM), it shows less advantage in PSNR, especially with sparser kernels. We hypothesize that DRK may tend to overfit distant regions with limited supervision. To address this, we used MiVOS[6] to mask image sequences, training on original images but evaluating only the foreground. The results (M-PSNR) indicate our method's strength in well-supervised central regions. + +
MethodsPSNR(↑)M-PSNR(↑)LPIPS(↓)SSIM(↑)Num(↓)Size(↓)
2D-GS26.3232.01.2987.7617928 K216.0 M
3D-GS26.4832.23.3045.7537811 K191.3 M
3D-GS (L)26.9432.75.2688.77991191 K281.6 M
3D-HGS26.7432.51.2999.7561842 K202.4 M
GES26.6232.11.3047.7542824 K195.0 M
DRK (S2)26.2032.31.2781.7601388 K125.9 M
DRK (S1)26.4032.56.2601.7722551 K161.9 M
DRK26.7632.81.2364.7871952 K279.1 M
+ +Table 3. Quantitative evaluation on Mip-NeRF360 scenes [2]. + +# 5.3. Qualitative Comparison + +We conducted qualitative comparisons to highlight the advantages of DRK over other state-of-the-art kernel representations. Fig.8 shows results across different scene categories, where our method achieves better texture and geometry fitting with a comparable or smaller number of kernels. Fig.9 demonstrates that DRK effectively handles fine ge + +![](images/ce129829ec4e9d1b3936bc747c80fee4861b9355f5fe3f6a0a68d0cb9a92d8da.jpg) +Figure 9. Comparisons on the MipNeRF 360 dataset show our method achieves clearer details and high-fidelity rendering. + +omtries, such as flowers and leaves, and detailed textures, like tags and bark, outperforming other representations that may have used more primitives (see Tab. 3). + +# 5.4. Converting Mesh to DRK + +All existing "Splatting" methods [20, 22, 27, 30] fail to seamlessly integrate with traditional assets. In contrast, our $DRK$ framework provides a versatile representation that allows for effortless conversion of triangle and polygon faces into $DRK$ . This is accomplished by placing the $DRK$ endpoints at the polygon vertices and adjusting the parameters $\tau$ and $\eta$ to control sharpness, with both $L1$ and $L2$ curvature set to 1. This process eliminates the need for training data rendering or model optimization. Consequently, rich 3D assets can be seamlessly transferred into $DRK$ , bridging the gap between millions of traditional 3D assets and our fast, high-quality reconstruction representation. Figure 10 illustrates the potential applications of Mesh2DRK. + +![](images/dbdd6816b4b53211bf74f4ba522e15e0e630220817fdc117055621b7e65a2784.jpg) +Figure 10. The conversion from Mesh to $DRK$ demonstrates the efficiency of using $DRK$ to incorporate traditional 3D assets into any $DRK$ scene at low cost. + +# 6. Conclusion + +We present $DRK$ , a novel primitive representation that generalizes and enhances Gaussian splatting. By incorporating learnable radial bases, adaptive shape control, and efficient rendering strategies, $DRK$ effectively addresses the fundamental limitations of Gaussian kernels in representing diverse geometric features. Our experiments on both synthetic and real-world scenes demonstrate that $DRK$ achieves superior rendering quality with significantly fewer primitives, while maintaining computational efficiency through carefully designed rasterization optimizations. Leveraging the flexibility of $DRK$ , traditional triangle or polygon mesh representations can be seamlessly converted into $DRK$ without requiring any training. This capability bridges rich 3D assets with reconstructed scenes, paving the way for future applications such as real-scene editing, VR digital world creation, and AR scene enhancement. + +# Acknowledgement + +This work has been supported in part by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621), General Research Fund Scheme (Grant No. 17202422, 17212923), Theme-based Research (Grant No. T45-701/22-R) and Shenzhen Science and Technology Innovation Commission (SGDX20220530111405040). Part of the described research work is conducted in the JC STEM Lab of Robotics for Soft Materials funded by The Hong Kong Jockey Club Charities Trust. + +# References + +[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. Neural point-based graphics. In Proceedings of the European Conference on Computer Vision (ECCV), pages 696-712. 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Triplane meets gaussian splatting: Fast and generalizable single-view 3d reconstruction with transformers. 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Gaussian Splatting (GS) vs. Deformable Radial Kernel (DRK) Splatting: GS requires thousands of Gaussians to approximate detailed textures and shapes. 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However, Gaussians' inherent radial symmetry and smoothness constraints limit their ability to represent complex shapes, often requiring thousands of primitives to approximate detailed geometry. We introduce Deformable Radial Kernel (DRK), which extends Gaussian splatting into a more general and flexible framework. Through learnable radial bases with adjustable angles and scales, DRK efficiently models diverse shape primitives while enabling precise control over edge sharpness and boundary curvature. Even DRK's planar nature, we further develop accurate ray-primitive intersection computation for depth sorting and introduce efficient kernel culling strategies for improved rasterization efficiency. Extensive experiments demonstrate that DRK outperforms existing methods in both representation efficiency and rendering quality, achieving state-of-the-art performance while dramatically reducing primitive count." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 55, + 632, + 137, + 644 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 632, + 137, + 644 + ], + "spans": [ + { + "bbox": [ + 55, + 632, + 137, + 644 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 55, + 651, + 296, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 651, + 296, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 651, + 296, + 689 + ], + "type": "text", + "content": "3D Gaussian Splitting [27] (3D-GS) has emerged as a leading 3D representation method thanks to its rapid rasterization and superior rendering quality. Its key advantages—ex" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 358, + 555, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 358, + 555, + 418 + ], + "spans": [ + { + "bbox": [ + 313, + 358, + 555, + 418 + ], + "type": "text", + "content": "plicit point-based representation, flexibility for manipulation, and MLP-free rendering- have positioned it as a dominant approach in novel view synthesis. However, this success raises an intriguing question: Is the Gaussian kernel truly optimal for representing 3D scenes?" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 422, + 556, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 556, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 556, + 530 + ], + "type": "text", + "content": "Natural scenes often consist of primitives with diverse shapes (see Fig. 2), such as rectangles, triangles, and ellipses, which cannot be fully captured by Gaussians alone. Moreover, the inherently smooth nature of Gaussian kernels makes them less effective at representing sharp transitions. As a result, densely packed or numerous Gaussians are frequently required to accurately model scene primitives with non-Gaussian geometries or sharp boundaries (see Fig. 1), leading to inefficiencies in both computation and memory." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 534, + 557, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 557, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 557, + 715 + ], + "type": "text", + "content": "Recent works have explored modifications to the Gaussian kernel to better handle discontinuities. For example, GES [20] adaptively adjusts the exponent values to control the sharpness of Gaussians, while still maintaining rotational symmetry, which limits its representational flexibility. DisC-GS [43] and 3D-HGS [30] introduce curve-and half-cutting techniques to the Gaussian kernel, respectively, improving its ability to capture discontinuous transitions. However, these cutting-based approaches remain fundamentally constrained by the inherent smoothness of the Gaussian kernel. Another line of research [8, 16, 19, 22] leverages 2D Gaussians to represent 3D scenes. While this approach offers better surface reconstruction compared to 3DGS, it is still constrained by the inherent limitations of the Gaussian framework, which restricts the flexibility" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 693, + 137, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 693, + 137, + 703 + ], + "spans": [ + { + "bbox": [ + 55, + 693, + 137, + 703 + ], + "type": "text", + "content": "†Corresponding Author" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 56, + 704, + 263, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 704, + 263, + 713 + ], + "spans": [ + { + "bbox": [ + 56, + 704, + 263, + 713 + ], + "type": "text", + "content": "Project page: https://yihua7.github.io/DRK-web/." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21513" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "of the representation. Notably, the concurrent work 3D-CS [21] employs novel 3D smooth convex shapes as primitives for geometry modeling with satisfactory results." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 110, + 296, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 110, + 296, + 506 + ], + "spans": [ + { + "bbox": [ + 56, + 110, + 296, + 506 + ], + "type": "text", + "content": "In this work, our objective is to design new shape primitives that can adapt to complex 3D scenes. Motivated by the success of 2D Gaussian Splatting (2D-GS), we focus on developing adaptive 2D planar kernels. Specifically, we introduce the 2D Deformable Radial Kernel (DRK), a flexible planar primitive for representing 3D scenes (see Fig. 4). At its core, DRK extends traditional radial bases with learnable parameters that enable precise control over shape deformation through three key features: 1) multiple radial bases with learnable polar angles and scale parameters allow the kernel to adaptively stretch, rotate, and shrink, providing significantly more flexibility than fixed Gaussian functions; 2) a hybrid distance metric combining " + }, + { + "bbox": [ + 56, + 110, + 296, + 506 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 56, + 110, + 296, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 56, + 110, + 296, + 506 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 56, + 110, + 296, + 506 + ], + "type": "text", + "content": " norms with learnable weights enables DRK to naturally represent both curved surfaces and sharp geometric features; and 3) an adaptive piecewise linear remapping function provides fine-grained control over value distributions, particularly enhancing the representation of sharp boundaries. Despite its enhanced expressiveness, DRK maintains a simple parametric form that is easy to optimize and efficient to render. The DRK determines the location and orientation of the tangent plane through its center and rotation parameters, building upon these radial bases as its structural foundation to conform to target shapes, bypassing the geometric and smoothness constraints typically imposed by Gaussian functions. As shown in Fig. 2, a single DRK primitive can flexibly model a wide range of shape primitives, whereas many Gaussians are often required to represent similar shapes. The formulation is also backwards-compatible - DRK naturally reduces to a Gaussian kernel when using two orthogonal major bases with different decay rates, while achieving superior rendering quality with comparable computational efficiency." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "text", + "content": "We experimentally validate " + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "text", + "content": " on our proposed dataset (DiverseScene) covering various scenarios, including rich textures, fine geometry, specular effects, and large spatial scale. We also evaluate " + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 506, + 295, + 590 + ], + "type": "text", + "content": " on unbounded MipNeRF 360 [2] datasets. Experimental results demonstrate our method has advantages in preserving visual details more effectively and efficiently." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 592, + 283, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 592, + 283, + 604 + ], + "spans": [ + { + "bbox": [ + 67, + 592, + 283, + 604 + ], + "type": "text", + "content": "Overall, our work makes the following contributions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 605, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 677 + ], + "type": "text", + "content": "- We introduce Deformable Radial Kernel (DRK), a novel primitive that generalizes conventional Gaussian splattig. DRK enables flexible shape modeling through learnable radial bases, hybrid distance metrics, and adaptive sharpness control, significantly reducing the number of primitives needed for high-quality scene representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "- We develop a differentiable and efficient rendering pipeline for DRK, featuring polygon-based tile culling and cache-sorting strategies to enhance both rendering ef" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 323, + 72, + 447, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 72, + 447, + 84 + ], + "spans": [ + { + "bbox": [ + 323, + 72, + 447, + 84 + ], + "type": "text", + "content": "ficiency and view consistency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 84, + 555, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 84, + 555, + 133 + ], + "spans": [ + { + "bbox": [ + 314, + 84, + 555, + 133 + ], + "type": "text", + "content": "- We created DiverseScenes, a new dataset covering rich textures, fine geometry, specular effects, and large scenes for more effectively evaluating the ability to model complex scenarios of different algorithms." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 144, + 400, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 144, + 400, + 156 + ], + "spans": [ + { + "bbox": [ + 314, + 144, + 400, + 156 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 164, + 436, + 176 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 164, + 436, + 176 + ], + "spans": [ + { + "bbox": [ + 314, + 164, + 436, + 176 + ], + "type": "text", + "content": "2.1. Novel View Synthesis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 182, + 555, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 182, + 555, + 411 + ], + "spans": [ + { + "bbox": [ + 313, + 182, + 555, + 411 + ], + "type": "text", + "content": "Novel view synthesis from multi-view images represents a fundamental challenge in computer graphics and computer vision. The field has evolved through increasingly sophisticated 3D scene representations. Traditional light field approaches [10, 18, 29] attempt to model the entire scene through a single 4D function of ray-slice intersections, but this implicit representation struggles with sparse inputs and complex geometry. Advancing beyond single-function modeling, Multi-Plane-Images (MPI) [38, 51, 55, 58, 69] introduced a layered representation using multiple depth planes, offering better 3D structure modeling. However, its discrete depth layering limits the handling of large viewpoint changes, particularly in rotational views. To achieve continuous depth modeling, subsequent works adopted explicit 3D proxies including meshes [5, 11, 35, 56, 59], point clouds [1, 7, 37, 41, 57], and voxels [14, 32, 48, 49]. These representations offer more flexible geometry modeling, with point-based methods further enhanced by neural networks [45, 46] for improved stability." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 411, + 554, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 554, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 554, + 506 + ], + "type": "text", + "content": "Most recently, continuous neural representations have emerged as a powerful alternative, replacing discrete geometric proxies with MLPs that directly map 3D coordinates to scene properties. NeRF [39] pioneered this approach with radiance fields, spawning numerous extensions for faster inference [15, 26, 40], large-scale scenes [2, 17, 53, 61, 66], dynamic content [31, 42, 50], reflection modeling [3, 24, 28, 62], and stylization [9, 13, 23, 67]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 514, + 425, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 514, + 425, + 528 + ], + "spans": [ + { + "bbox": [ + 314, + 514, + 425, + 528 + ], + "type": "text", + "content": "2.2. Gaussian Splitting" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 533, + 555, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 701 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 701 + ], + "type": "text", + "content": "Point-based rendering approaches have made the rendering process of point clouds differentiable, enabling end-to-end training for novel view synthesis. 3D Gaussian Splating (3D-GS) [27] introduced scene modeling using 3D Gaussian distributions, compositing the appearance of intersected Gaussians along viewing rays through " + }, + { + "bbox": [ + 313, + 533, + 555, + 701 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 533, + 555, + 701 + ], + "type": "text", + "content": "-blending. This seminal work has inspired numerous extensions across various applications, including dynamic scene view synthesis [25, 34, 65], 3D content generation [54, 70], geometry reconstruction [22, 36], video representation [52] and neural network-enhanced high-fidelity view synthesis [33, 64]. The flexible representation, computational efficiency, and superior rendering quality of 3D-GS have established it as a prominent approach in the field [60]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 326, + 701, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 553, + 713 + ], + "type": "text", + "content": "The key innovation of 3D-GS lies in its use of Gaussian" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21514" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 240 + ], + "type": "text", + "content": "kernels for point effect decay, where the continuous nature of these functions facilitates the optimization of discrete representations. Subsequent research has focused on both constraining and extending these Gaussian kernels for specific applications. Notable developments include the constraint of 3D Gaussians to 2D space [8, 19, 22], yielding planar representations that better approximate scene surfaces for precise geometry reconstruction. Other works have extended the framework to 4D space [12, 63], enabling temporal dynamic modeling through 3D slicing of 4D Gaussians for view synthesis. To address limitations in representing sharp edges, researchers have proposed modifications to the Gaussian shape using curve-cutting [43], hemispheric truncation [30], and novel 3D convex shapes [21]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 253, + 141, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 253, + 141, + 265 + ], + "spans": [ + { + "bbox": [ + 55, + 253, + 141, + 265 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 274, + 296, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 274, + 296, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 274, + 296, + 369 + ], + "type": "text", + "content": "In this section, we first review 3D Gaussian Splitting (3D-GS) and 2D Gaussian Splitting (2D-GS), and their mathematical formulations (Sec. 3.1 and Sec. 3.2). We then introduce our general kernel splitting framework that extends beyond traditional Gaussian primitives (Sec. 3.3). Finally, we analyze the inherent limitations of Gaussian-based representations, motivating the need for our proposed deformable radial kernel formulation (Sec. 3.4)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 379, + 226, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 379, + 226, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 379, + 226, + 392 + ], + "type": "text", + "content": "3.1. 3D Gaussian Splitting (3D-GS)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": "3D Gaussian Splatting represents scenes using colored 3D Gaussians [27]. Each Gaussian " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": " is parameterized by a 3D center " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": ", covariance matrix " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\Sigma = R S S^T R^T" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": " (where " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": " is a rotation matrix from quaternion " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "q \\in \\mathbf{SO}(3)" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": " is a scaling matrix from vector " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": "), opacity " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": ", and spherical harmonic coefficients " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "sh" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": " for view-dependent appearance. A scene is represented as " + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = \\{G_j : \\mu_j, q_j, s_j, o_j, sh_j\\}" + }, + { + "bbox": [ + 55, + 398, + 296, + 483 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "text", + "content": "Rendering involves projecting Gaussians onto the image plane with 2D covariance " + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "inline_equation", + "content": "\\Sigma^{\\prime} = JW\\Sigma W^{T}J^{T}" + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "text", + "content": " and center " + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "inline_equation", + "content": "\\mu^{\\prime} = JW\\mu" + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "text", + "content": " . The pixel color " + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "inline_equation", + "content": "C(u)" + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "text", + "content": " is computed via neural point-based " + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 483, + 296, + 531 + ], + "type": "text", + "content": " -blending:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 540, + 296, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 540, + 296, + 563 + ], + "spans": [ + { + "bbox": [ + 59, + 540, + 296, + 563 + ], + "type": "interline_equation", + "content": "C (u) = \\sum_ {i \\in N} T _ {i} \\alpha_ {i} \\mathcal {S H} \\left(s h _ {i}, v _ {i}\\right), \\text {w h e r e} T _ {i} = \\Pi_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j}\\right), \\tag {1}", + "image_path": "2568ffc75b219916557813d2a11deeb77151f8584d129a9aa170d24a6657b13b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{SH}" + }, + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "type": "text", + "content": " evaluates spherical harmonics with view direction " + }, + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 55, + 567, + 295, + 590 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 119, + 599, + 295, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 599, + 295, + 614 + ], + "spans": [ + { + "bbox": [ + 119, + 599, + 295, + 614 + ], + "type": "interline_equation", + "content": "\\alpha_ {i} = o _ {i} e ^ {- \\frac {1}{2} (p - \\mu_ {i} ^ {\\prime}) ^ {T} \\Sigma_ {i} ^ {\\prime} (p - \\mu_ {i} ^ {\\prime})}. \\tag {2}", + "image_path": "03e67bc2bef5304b94a3b249943ca206f9234c001eaa512a7f81741b1b3a9e95.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 625, + 296, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 625, + 296, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 625, + 296, + 661 + ], + "type": "text", + "content": "By optimizing these Gaussian parameters and adaptively adjusting their density, 3D-GS achieves high-quality scene representation with real-time rendering capabilities." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 670, + 225, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 670, + 225, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 670, + 225, + 683 + ], + "type": "text", + "content": "3.2. 2D Gaussian Splitting (2D-GS)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Recognizing that real-world scenes primarily consist of surface structures where 3D Gaussians naturally compress into" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": "planar formations, recent works [8, 22] proposed 2D Gaussian Splatting (2D-GS). The opacity " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": " is computed using local coordinates " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": " on the tangent plane:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 364, + 117, + 555, + 146 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 117, + 555, + 146 + ], + "spans": [ + { + "bbox": [ + 364, + 117, + 555, + 146 + ], + "type": "interline_equation", + "content": "\\alpha = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\frac {u ^ {2}}{s _ {u} ^ {2}} + \\frac {v ^ {2}}{s _ {v} ^ {2}}\\right)\\right), \\qquad (3)", + "image_path": "d7e4556eef739dfa6d509199c87a6e6faa34b489825cec6da8dc9e1344441b29.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 152, + 555, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 152, + 555, + 201 + ], + "spans": [ + { + "bbox": [ + 313, + 152, + 555, + 201 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 152, + 555, + 201 + ], + "type": "inline_equation", + "content": "s_u^2" + }, + { + "bbox": [ + 313, + 152, + 555, + 201 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 152, + 555, + 201 + ], + "type": "inline_equation", + "content": "s_v^2" + }, + { + "bbox": [ + 313, + 152, + 555, + 201 + ], + "type": "text", + "content": " denote the variances along the U and V axes. This surface-centric formulation aligns with the success of polygon meshes in 3D modeling, offering a more compact scene representation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 209, + 455, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 455, + 221 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 455, + 221 + ], + "type": "text", + "content": "3.3. General Kernel Splitting" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "spans": [ + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "text", + "content": "We extend conventional 2D Gaussians by introducing a more general planar kernel splating formulation (Fig. 3). Given a ray from position " + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "inline_equation", + "content": "r_o \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "text", + "content": " with direction " + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "inline_equation", + "content": "r_d \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "text", + "content": " intersecting a tangent plane centered at " + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "text", + "content": " with rotation " + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "inline_equation", + "content": "R \\in SO(3)" + }, + { + "bbox": [ + 313, + 227, + 554, + 287 + ], + "type": "text", + "content": ", the intersection point is:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 383, + 294, + 555, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 294, + 555, + 320 + ], + "spans": [ + { + "bbox": [ + 383, + 294, + 555, + 320 + ], + "type": "interline_equation", + "content": "i = r _ {o} + \\frac {\\left(\\mu - r _ {o}\\right) ^ {T} R _ {z}}{r _ {d} ^ {T} R _ {z}} r _ {d}, \\tag {4}", + "image_path": "d63133c25cb3814185ae124860447fe81f614312cae4de180d9cce3863cb6818.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 326, + 554, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 326, + 554, + 349 + ], + "spans": [ + { + "bbox": [ + 313, + 326, + 554, + 349 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 326, + 554, + 349 + ], + "type": "inline_equation", + "content": "R_{z}" + }, + { + "bbox": [ + 313, + 326, + 554, + 349 + ], + "type": "text", + "content": " is the plane normal. The local UV coordinates at this intersection are:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 389, + 354, + 554, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 354, + 554, + 380 + ], + "spans": [ + { + "bbox": [ + 389, + 354, + 554, + 380 + ], + "type": "interline_equation", + "content": "\\binom {u} {v} = \\binom {R _ {x} ^ {T}} {R _ {y} ^ {T}} (i - \\mu), \\tag {5}", + "image_path": "bfcf6f3124ba0ea5e0709bafd70255a4ca8cd6f38705de8332f09bfdd083f94e.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "inline_equation", + "content": "R_x^T" + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "inline_equation", + "content": "R_y^T" + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "text", + "content": " are the first and second rows of " + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "text", + "content": ". The kernel splating function then maps these UV coordinates to a density value " + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 387, + 554, + 425 + ], + "type": "text", + "content": ", determining the primitive's shape." + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 315, + 431, + 554, + 502 + ], + "blocks": [ + { + "bbox": [ + 315, + 431, + 554, + 502 + ], + "lines": [ + { + "bbox": [ + 315, + 431, + 554, + 502 + ], + "spans": [ + { + "bbox": [ + 315, + 431, + 554, + 502 + ], + "type": "image", + "image_path": "06925da25236c608d0b84ba3b2e2acbc7e39399f748872753f9a433e3a97d5d2.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 503, + 554, + 536 + ], + "lines": [ + { + "bbox": [ + 313, + 503, + 554, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 503, + 554, + 536 + ], + "type": "text", + "content": "Figure 3. Illustration of general planar kernel splitting: UV coordinates of ray-plane intersections are mapped to density values via a kernel function that determines the primitive's shape." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 552, + 391, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 391, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 391, + 563 + ], + "type": "text", + "content": "3.4. Discussions" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "content": "While 3D-GS demonstrates remarkable efficacy, our analysis reveals several inherent limitations. First, screen-space projection of Gaussians yields 2D elliptical distributions with rotational symmetry, constraining their ability to approximate diverse primitive shapes. Second, their conic curve boundaries (derived by the " + }, + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "content": " norm) challenge the representation of linear edges and intermediate edge forms. Third, Gaussian distributions inherently couple decay rate with spatial extent through the covariance matrix—sharp features necessitate narrow distributions, making it challenging to simultaneously capture abrupt transitions and extended spatial regions." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21515" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 68, + 192, + 162 + ], + "blocks": [ + { + "bbox": [ + 78, + 68, + 192, + 162 + ], + "lines": [ + { + "bbox": [ + 78, + 68, + 192, + 162 + ], + "spans": [ + { + "bbox": [ + 78, + 68, + 192, + 162 + ], + "type": "image", + "image_path": "90b549a05a564ded20b6dcf86d6f433becb3a6175851252be815003c6fd3a2c0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "lines": [ + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "spans": [ + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "type": "text", + "content": "Figure 2. Comparison of 3D-GS versus a single " + }, + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "type": "text", + "content": " achieves superior geometric fidelity with just one primitive compared to multiple Gaussians. We visualize the contours of 3D-GS and " + }, + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 165, + 555, + 189 + ], + "type": "text", + "content": " to better illustrate primitive count, scale, and position." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 197, + 69, + 309, + 163 + ], + "blocks": [ + { + "bbox": [ + 197, + 69, + 309, + 163 + ], + "lines": [ + { + "bbox": [ + 197, + 69, + 309, + 163 + ], + "spans": [ + { + "bbox": [ + 197, + 69, + 309, + 163 + ], + "type": "image", + "image_path": "6b072a01261154279bcf9e81adb3c1b1f15824ed64178ed7123322fecfd52ba4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 314, + 68, + 425, + 163 + ], + "blocks": [ + { + "bbox": [ + 314, + 68, + 425, + 163 + ], + "lines": [ + { + "bbox": [ + 314, + 68, + 425, + 163 + ], + "spans": [ + { + "bbox": [ + 314, + 68, + 425, + 163 + ], + "type": "image", + "image_path": "06a905b352cfa0d7d8c1ca4d20bf425bb918fbbd7a22d5876f80199b7c4024de.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 432, + 68, + 528, + 163 + ], + "blocks": [ + { + "bbox": [ + 432, + 68, + 528, + 163 + ], + "lines": [ + { + "bbox": [ + 432, + 68, + 528, + 163 + ], + "spans": [ + { + "bbox": [ + 432, + 68, + 528, + 163 + ], + "type": "image", + "image_path": "937d773db46c267312745cbbe3a56d81751a733b3dbb6e89520c6ef1049c4306.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "spans": [ + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "text", + "content": "These constraints necessitate millions of fine-grained Gaussians to approximate arbitrary shapes, leading to overparameterization while still failing to achieve perfect fidelity under practical constraints. As shown in Fig. 2, even elementary shapes like triangles and rectangles—which can be described concisely—require numerous Gaussians for approximation, exhibiting artifacts like interior inconsistencies and external floating points (last column). Our deformable radial kernel (DRK) addresses these limitations through radial basis functions with varying lengths " + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "text", + "content": " and polar angles " + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "inline_equation", + "content": "\\theta_k" + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "text", + "content": ", controlled by parameters " + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 194, + 296, + 339 + ], + "type": "text", + "content": " for contour curvature and sharpness (Fig. 4)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 353, + 256, + 368 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 353, + 256, + 368 + ], + "spans": [ + { + "bbox": [ + 55, + 353, + 256, + 368 + ], + "type": "text", + "content": "4. Deformable Radial Kernel Splitting" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 374, + 295, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 374, + 295, + 410 + ], + "spans": [ + { + "bbox": [ + 55, + 374, + 295, + 410 + ], + "type": "text", + "content": "Deformable Radial Kernel (DRK) is a novel primitive for 3D scene representation characterized by a set of parameters " + }, + { + "bbox": [ + 55, + 374, + 295, + 410 + ], + "type": "inline_equation", + "content": "\\Theta = \\{\\mu, q, s_k, \\theta_k, \\eta, \\tau, o, sh\\}" + }, + { + "bbox": [ + 55, + 374, + 295, + 410 + ], + "type": "text", + "content": ", where:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 411, + 295, + 483 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "inline_equation", + "content": "\\mu \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "inline_equation", + "content": "q \\in SO(3)" + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "inline_equation", + "content": "sh" + }, + { + "bbox": [ + 55, + 411, + 295, + 436 + ], + "type": "text", + "content": " follow 3D-GS for position, orientation, opacity, and view-dependent appearance" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 436, + 295, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 436, + 295, + 459 + ], + "spans": [ + { + "bbox": [ + 55, + 436, + 295, + 459 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 55, + 436, + 295, + 459 + ], + "type": "inline_equation", + "content": "\\{s_k, \\theta_k\\}_{k=1}^K" + }, + { + "bbox": [ + 55, + 436, + 295, + 459 + ], + "type": "text", + "content": " define radial basis lengths and angles that control the kernel shape" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 459, + 295, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 295, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 295, + 483 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 55, + 459, + 295, + 483 + ], + "type": "inline_equation", + "content": "\\eta \\in (0,1)" + }, + { + "bbox": [ + 55, + 459, + 295, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 459, + 295, + 483 + ], + "type": "inline_equation", + "content": "\\tau \\in (-1,1)" + }, + { + "bbox": [ + 55, + 459, + 295, + 483 + ], + "type": "text", + "content": " control boundary curvature and sharpness, respectively" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 484, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 295, + 593 + ], + "type": "text", + "content": "In the following sections, we detail each component of DRK. First, we introduce the radial basis formulation (Sec. 4.1), showing that traditional 2D Gaussians are a special case within our framework. Then, we discuss " + }, + { + "bbox": [ + 55, + 484, + 295, + 593 + ], + "type": "inline_equation", + "content": "L1\\& L2" + }, + { + "bbox": [ + 55, + 484, + 295, + 593 + ], + "type": "text", + "content": " norm blending and edge sharpening in Sec. 4.2 and Sec. 4.3, which enable flexible control of boundary curvature and sharpness. Finally, in Sec. 4.4, we explore efficient rasterization strategies specifically tailored for DRK, including low-pass filtering, kernel culling, and cache sorting." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 56, + 596, + 115, + 664 + ], + "blocks": [ + { + "bbox": [ + 56, + 596, + 115, + 664 + ], + "lines": [ + { + "bbox": [ + 56, + 596, + 115, + 664 + ], + "spans": [ + { + "bbox": [ + 56, + 596, + 115, + 664 + ], + "type": "image", + "image_path": "58e3d301b862f3a363a03ff8d54587ae48c856279b6c442f16063a854b6eb868.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "text", + "content": "Figure 4. " + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "text", + "content": " defines a deformable shape using radial basis functions characterized by lengths " + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "text", + "content": " and polar angles " + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "inline_equation", + "content": "\\theta_k" + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "text", + "content": ", with parameters " + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 666, + 296, + 711 + ], + "type": "text", + "content": " governing the shape's curvature and sharpness respectively." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 117, + 596, + 197, + 664 + ], + "blocks": [ + { + "bbox": [ + 117, + 596, + 197, + 664 + ], + "lines": [ + { + "bbox": [ + 117, + 596, + 197, + 664 + ], + "spans": [ + { + "bbox": [ + 117, + 596, + 197, + 664 + ], + "type": "image", + "image_path": "d6f816574cfea7d7acf27ffe665c35d06936ada7cbcf1fd04fe39ebad6d1e332.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 199, + 596, + 295, + 664 + ], + "blocks": [ + { + "bbox": [ + 199, + 596, + 295, + 664 + ], + "lines": [ + { + "bbox": [ + 199, + 596, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 199, + 596, + 295, + 664 + ], + "type": "image", + "image_path": "dd71778987ce77a99abdf95b06a9ba6dc400d15d608bd8c47016101ff0943411.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 194, + 395, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 194, + 395, + 205 + ], + "spans": [ + { + "bbox": [ + 313, + 194, + 395, + 205 + ], + "type": "text", + "content": "4.1. Radial Basis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": "Our radial basis defines a kernel's shape through " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": " control points in polar coordinates " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "\\{s_k,\\theta_k\\}" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "s_k > 0" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": " represents each radial length and angles are ordered as " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "0 < \\theta_0 < \\ldots < \\theta_K \\leq 2\\pi" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": ". For any point with local tangent coordinates " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": ", we compute its polar representation using " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": " norm " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "r_2 = \\sqrt{u^2 + v^2}" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": " and angle " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "\\theta = \\arccos (u / r_2)" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": ". Given a point lying between basis " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "k + 1" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "\\theta_{k} < \\theta \\leq \\theta_{k + 1}" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": "), we define its relative angular distance as " + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "inline_equation", + "content": "\\Delta \\theta_{k} = \\frac{(\\theta - \\theta_{k})\\pi}{\\theta_{k + 1} - \\theta_{k}}" + }, + { + "bbox": [ + 313, + 213, + 555, + 323 + ], + "type": "text", + "content": ". The kernel function is then formulated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 318, + 329, + 555, + 356 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 329, + 555, + 356 + ], + "spans": [ + { + "bbox": [ + 318, + 329, + 555, + 356 + ], + "type": "interline_equation", + "content": "\\alpha = o \\cdot \\exp \\left(- \\frac {r _ {2} ^ {2}}{2} \\left(\\frac {1 + \\cos (\\Delta \\theta_ {k})}{2 s _ {k} ^ {2}} + \\frac {1 - \\cos (\\Delta \\theta_ {k})}{2 s _ {k + 1} ^ {2}}\\right)\\right). (6)", + "image_path": "09245f430b18dd937f30a72fb44b5a36ee24b7fbb721e694ff1b67db17fddb1d.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 361, + 555, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 555, + 399 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 555, + 399 + ], + "type": "text", + "content": "This formulation smoothly interpolates between adjacent radial bases using cosine weighting terms, ensuring continuous transitions in the kernel's shape." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "text", + "content": "2D Gaussian as a Special Case. Our formulation generalizes 2D Gaussian kernels. By setting " + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "inline_equation", + "content": "\\theta_{k} = \\frac{k\\pi}{2}" + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "inline_equation", + "content": "s_0 = s_2 = s_u" + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "inline_equation", + "content": "s_1 = s_3 = s_v" + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "text", + "content": ", we can derive the 2D Gaussian form in Eq. (3). For points in the first UV quadrant where " + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "inline_equation", + "content": "\\Delta \\theta_{k} = 2\\theta" + }, + { + "bbox": [ + 313, + 403, + 554, + 463 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 349, + 472, + 518, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 472, + 518, + 529 + ], + "spans": [ + { + "bbox": [ + 349, + 472, + 518, + 529 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\alpha = o \\cdot \\exp \\left(- \\frac {r _ {2} ^ {2}}{2} \\left(\\frac {\\cos^ {2} \\theta}{s _ {0} ^ {2}} + \\frac {\\cos^ {2} \\theta}{s _ {1} ^ {2}}\\right)\\right) \\\\ = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\frac {u ^ {2}}{s _ {0} ^ {2}} + \\frac {v ^ {2}}{s _ {1} ^ {2}}\\right)\\right), \\\\ \\end{array}", + "image_path": "a01b5a2a8d813971fbb3c7117577ed0b8f3b0037ed65a3b769e959382ed31d33.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 536, + 555, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 555, + 573 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 555, + 573 + ], + "type": "text", + "content": "where we use the identity " + }, + { + "bbox": [ + 313, + 536, + 555, + 573 + ], + "type": "inline_equation", + "content": "\\cos (\\Delta \\theta_k) = \\cos (2\\theta) = 2\\cos^2\\theta -1" + }, + { + "bbox": [ + 313, + 536, + 555, + 573 + ], + "type": "text", + "content": ". The derivation extends to other quadrants by symmetry." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 581, + 443, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 581, + 443, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 581, + 443, + 594 + ], + "type": "text", + "content": "4.2. L1&L2 Norm Blending" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "text", + "content": "The scaling term " + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "inline_equation", + "content": "\\frac{1}{\\bar{s}^2} = \\left(\\frac{1 + \\cos(\\Delta\\theta_k)}{2s_k^2} +\\frac{1 - \\cos(\\Delta\\theta_k)}{2s_{k + 1}^2}\\right)" + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "text", + "content": " in Eq. (6) enforces smooth contours at radial endpoints, where " + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "inline_equation", + "content": "\\frac{d\\bar{s}}{d\\Delta\\theta_k} = 0" + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "inline_equation", + "content": "\\Delta \\theta_{k} = 0" + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "text", + "content": ". However, since radials converge at the kernel center and are not parallel, this " + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 313, + 598, + 554, + 688 + ], + "type": "text", + "content": " formulation inherently produces conic curves, limiting its ability to represent straight edges common in man-made environments." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": "To address this limitation, we incorporate " + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": " norm into our " + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": " formulation. For a point " + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": " between radial" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21516" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "content": "endpoints " + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "inline_equation", + "content": "e_i = (s_i \\cos(\\theta_i), s_i \\sin(\\theta_i))" + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "inline_equation", + "content": "e_{i+1}" + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "content": ", we compute its " + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 55, + 72, + 295, + 96 + ], + "type": "text", + "content": " norm as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 117, + 105, + 295, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 105, + 295, + 131 + ], + "spans": [ + { + "bbox": [ + 117, + 105, + 295, + 131 + ], + "type": "interline_equation", + "content": "r _ {1} = \\left\\| \\left( \\begin{array}{l l} e _ {i} & e _ {i + 1} \\end{array} \\right) ^ {- 1} \\binom {u} {v} \\right\\| _ {1}. \\tag {7}", + "image_path": "a018245b94614cd3840c680af7f7364140592a667d3225303e40e88c95206fa1.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 139, + 295, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 139, + 295, + 175 + ], + "spans": [ + { + "bbox": [ + 55, + 139, + 295, + 175 + ], + "type": "text", + "content": "This transformation maps the diamond-shaped " + }, + { + "bbox": [ + 55, + 139, + 295, + 175 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 55, + 139, + 295, + 175 + ], + "type": "text", + "content": " unit ball " + }, + { + "bbox": [ + 55, + 139, + 295, + 175 + ], + "type": "inline_equation", + "content": "(|x| + |y| = 1,0\\leq x,y\\leq 1)" + }, + { + "bbox": [ + 55, + 139, + 295, + 175 + ], + "type": "text", + "content": " to the segment between adjacent endpoints, enabling straight-line boundaries." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "spans": [ + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "type": "text", + "content": "We then introduce a blending weight " + }, + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "type": "inline_equation", + "content": "\\eta \\in (0,1)" + }, + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "type": "text", + "content": " to smoothly interpolate between " + }, + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 55, + 175, + 296, + 211 + ], + "type": "text", + "content": " norms, yielding our complete kernel function:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 95, + 220, + 295, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 220, + 295, + 246 + ], + "spans": [ + { + "bbox": [ + 95, + 220, + 295, + 246 + ], + "type": "interline_equation", + "content": "\\alpha = o \\cdot \\exp \\left(- \\frac {1}{2} \\left(\\eta r _ {1} ^ {2} + (1 - \\eta) \\frac {r _ {2} ^ {2}}{\\bar {s} ^ {2}}\\right)\\right). \\tag {8}", + "image_path": "d87cceaeaed1bd40a5f32af3dc73ce149219b1b14bc753e2ced751ce62b58d99.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 255, + 296, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 255, + 296, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 255, + 296, + 291 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 55, + 255, + 296, + 291 + ], + "type": "inline_equation", + "content": "r_1^2" + }, + { + "bbox": [ + 55, + 255, + 296, + 291 + ], + "type": "text", + "content": " requires no explicit scaling term as it is inherently scaled through the inverse transformation in Eq. (7). Please see Fig. 4 (right) for illustration." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 301, + 160, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 301, + 160, + 314 + ], + "spans": [ + { + "bbox": [ + 55, + 301, + 160, + 314 + ], + "type": "text", + "content": "4.3. Edge Sharpening" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 320, + 190, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 320, + 190, + 451 + ], + "spans": [ + { + "bbox": [ + 55, + 320, + 190, + 451 + ], + "type": "text", + "content": "As shown in Fig. 2, Gaussian functions inherently couple scale and edge sharpness through their variance parameter, making it challenging to achieve precise shape approximation even with thousands of Gaussians. To decouple these properties, we introduce a sharpening coefficient " + }, + { + "bbox": [ + 55, + 320, + 190, + 451 + ], + "type": "inline_equation", + "content": "\\tau \\in (-1,1)" + }, + { + "bbox": [ + 55, + 320, + 190, + 451 + ], + "type": "text", + "content": " that adaptively adjusts edge tran" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 194, + 321, + 296, + 418 + ], + "blocks": [ + { + "bbox": [ + 194, + 321, + 296, + 418 + ], + "lines": [ + { + "bbox": [ + 194, + 321, + 296, + 418 + ], + "spans": [ + { + "bbox": [ + 194, + 321, + 296, + 418 + ], + "type": "image", + "image_path": "f5ad3c746395127b8c4aee24cb987ce3a5e45c06575d7b4cc75c687d665f310d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 208, + 423, + 295, + 444 + ], + "lines": [ + { + "bbox": [ + 208, + 423, + 295, + 444 + ], + "spans": [ + { + "bbox": [ + 208, + 423, + 295, + 444 + ], + "type": "text", + "content": "Figure 5. Sharpening function illustration." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "spans": [ + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "type": "text", + "content": "sitions. Given the exponential term " + }, + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 453, + 296, + 487 + ], + "type": "text", + "content": " (i.e., the density value before opacity scaling) in Eq. (8), our sharpening function is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 70, + 495, + 295, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 495, + 295, + 532 + ], + "spans": [ + { + "bbox": [ + 70, + 495, + 295, + 532 + ], + "type": "interline_equation", + "content": "\\Psi (g) = \\left\\{ \\begin{array}{l l} \\frac {1 - \\tau}{1 + \\tau} g & \\text {i f} \\quad 0 \\quad \\leq g < \\frac {1 + \\tau}{4}, \\\\ \\frac {1 + \\tau}{1 - \\tau} g - \\frac {\\tau}{1 - \\tau} & \\text {i f} \\quad \\frac {1 + \\tau}{4} \\quad \\leq g < \\frac {3 - \\tau}{4}, \\\\ \\frac {1 - \\tau}{1 + \\tau} g + \\frac {2 \\tau}{1 + \\tau} & \\text {i f} \\quad \\frac {3 - \\tau}{4} \\quad \\leq g \\leq 1. \\end{array} \\right. \\tag {9}", + "image_path": "0dfd2c77c351a67ab34e3326f6ed5f47bfdc3c22dc931816dd899f47bbc60c3b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 540, + 296, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 296, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 296, + 590 + ], + "type": "text", + "content": "As illustrated in Fig. 5, this piecewise function reshapes the alpha values toward 0 or 1, creating sharper edge transitions while maintaining the kernel's spatial extent. The final kernel opacity is computed as " + }, + { + "bbox": [ + 55, + 540, + 296, + 590 + ], + "type": "inline_equation", + "content": "\\alpha = o\\cdot \\Psi (g)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 598, + 141, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 598, + 141, + 609 + ], + "spans": [ + { + "bbox": [ + 55, + 598, + 141, + 609 + ], + "type": "text", + "content": "4.4. Rasterization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 618, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 713 + ], + "type": "text", + "content": "Low-pass Filtering. Camera-captured images represent discretely sampled signals from scene rays, inherently limiting the maximum recoverable frequency of 3D content. Without proper frequency constraints, optimization tends to generate small, floating primitives that overfit to individual training views. These primitives become too fine-grained (smaller than ray coverage) and only contribute to specific rays, resulting in poor generalization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": "While 3D-GS leverages EWA splatting for closed-form Gaussian low-pass filtering, " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": " requires an alternative approach. Following Botsch et al. [4], we approximate filtering by taking the maximum between the kernel function and a view-dependent low-pass filter. Since " + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 72, + 555, + 180 + ], + "type": "text", + "content": " represents planar primitives, its frequency should be bounded on its tangent plane while potentially unbounded when viewed orthogonally, so we scale the filter size by the cosine of the view angle:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 327, + 188, + 555, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 188, + 555, + 214 + ], + "spans": [ + { + "bbox": [ + 327, + 188, + 555, + 214 + ], + "type": "interline_equation", + "content": "\\tilde {\\alpha} = \\max (\\alpha , o \\cdot \\exp (- \\frac {1}{2 \\left| r _ {d} \\cdot R _ {z} \\right| ^ {2}} \\left(\\frac {\\Delta p _ {w} ^ {2}}{s _ {l} ^ {2}} + \\frac {\\Delta p _ {h} ^ {2}}{s _ {l} ^ {2}}\\right))), \\tag {10}", + "image_path": "b139dab23440dd98e85858b6c8550120f8660537c10a089d5012b212ee8411b1.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "spans": [ + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "inline_equation", + "content": "\\Delta p_h" + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "inline_equation", + "content": "\\Delta p_w" + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "text", + "content": " are image space distances between the pixel and the projected kernel center, " + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "inline_equation", + "content": "r_d \\cdot R_z" + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "text", + "content": " accounts for view-dependent scaling, and " + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "inline_equation", + "content": "s_l" + }, + { + "bbox": [ + 313, + 221, + 555, + 258 + ], + "type": "text", + "content": " controls the filter radius." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 275, + 555, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 275, + 555, + 431 + ], + "spans": [ + { + "bbox": [ + 313, + 275, + 555, + 431 + ], + "type": "text", + "content": "Tile Culling. Our rendering pipeline, based on 3D-GS, performs image rendering using 2D thread grids on CUDA. The process begins by dividing images into " + }, + { + "bbox": [ + 313, + 275, + 555, + 431 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 313, + 275, + 555, + 431 + ], + "type": "text", + "content": " tiles, with each tile corresponding to potentially intersecting primitives (kernels or 3D Gaussians). While 3D-GS projects the major axis of a 3D Gaussian onto the image plane to create a square axis-aligned bounding box (AABB) for tile coverage, this method can be computationally inefficient for primitives that project as highly anisotropic or elongated shapes, as shown in Fig. 6. This inefficiency becomes particularly evident in " + }, + { + "bbox": [ + 313, + 275, + 555, + 431 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 275, + 555, + 431 + ], + "type": "text", + "content": " due to its diverse shape representations. To address this, we introduce a more precise radius calculation and an improved tile culling strategy." + } + ] + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 316, + 434, + 554, + 512 + ], + "blocks": [ + { + "bbox": [ + 316, + 434, + 554, + 512 + ], + "lines": [ + { + "bbox": [ + 316, + 434, + 554, + 512 + ], + "spans": [ + { + "bbox": [ + 316, + 434, + 554, + 512 + ], + "type": "image", + "image_path": "fc685348f0cc435f77b9844f0bc04c2f23c00dfa7fbf718bd21a12643ebabafa.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 514, + 554, + 536 + ], + "lines": [ + { + "bbox": [ + 313, + 514, + 554, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 514, + 554, + 536 + ], + "type": "text", + "content": "Figure 6. Polygon-based tile culling using radial basis endpoints enables efficient rasterization by eliminating untouched tiles." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "spans": [ + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "text", + "content": "The effective range of " + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "text", + "content": " is governed by its radial basis, whose endpoints define the kernel's boundary. Following the 3-σ principle, we define the boundary radius " + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "inline_equation", + "content": "s_k^c" + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "text", + "content": ", but extend it to account for opacity " + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "text", + "content": " and sharpness " + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "text", + "content": " parameters. The calibrated radial length " + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "inline_equation", + "content": "s_k^c" + }, + { + "bbox": [ + 313, + 542, + 554, + 603 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 366, + 613, + 553, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 613, + 553, + 645 + ], + "spans": [ + { + "bbox": [ + 366, + 613, + 553, + 645 + ], + "type": "interline_equation", + "content": "s _ {k} ^ {c} = s _ {k} \\sqrt {- \\log \\left(\\Psi^ {- 1} \\left(\\frac {e ^ {- 3 2}}{o}\\right)\\right)}. \\tag {11}", + "image_path": "101667dd5a4d0d0b5a6c1149120d6db3c20f5cd7c782a550b8ee7717f21a5214.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 654, + 554, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 690 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 690 + ], + "type": "text", + "content": "The derivation details are provided in the Supplementary Material. Using this calibrated length, we calculate each radial basis endpoint " + }, + { + "bbox": [ + 313, + 654, + 554, + 690 + ], + "type": "inline_equation", + "content": "v_{k}" + }, + { + "bbox": [ + 313, + 654, + 554, + 690 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 359, + 701, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 701, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 359, + 701, + 553, + 715 + ], + "type": "interline_equation", + "content": "v _ {k} = \\mu + s _ {k} ^ {c} (\\cos \\theta_ {k} R _ {x} + \\sin \\theta_ {k} R _ {y}). \\tag {12}", + "image_path": "26651cf19fd0316b87da85cacc6f19feb9030136625ee32fdd9e07717916e7e2.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21517" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 550, + 168 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 550, + 168 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 550, + 168 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 550, + 168 + ], + "type": "table", + "html": "
MethodsSimpleTextureGeometrySpecularLargeAverage
PSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIMPSNRLPIPSSSIM
2D-GS42.10.0209.996942.59.0624.983429.90.0513.970027.18.0570.955027.80.2500.838833.92.0881.9514
3D-GS39.51.0311.994144.57.0628.996829.14.0552.965827.16.0758.952332.19.2054.901734.41.0861.9621
3D-HGS41.41.0199.993146.19.0397.991230.42.0406.959827.27.0512.944733.17.1672.872135.68.0637.9521
GES40.95.0266.995545.23.0579.997730.36.0468.970427.04.0632.955031.67.2074.898735.05.0804.9634
DRK (S2)40.34.0283.994647.67.0537.997630.68.0477.970927.07.0704.957031.57.2090.898535.03.0823.9637
DRK (S1)42.24.0168.997447.86.0410.998831.67.0394.978827.77.0631.960333.78.1685.919636.62.0668.9701
DRK43.46.0105.998549.08.0396.999031.93.0366.980328.19.0592.961535.28.1348.937237.58.0564.9752
", + "image_path": "ef1ce67b2064c48837e08ed8abbd92a1b957d2675758d7bb1ed3053f7efff957.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 188, + 294, + 232 + ], + "blocks": [ + { + "bbox": [ + 143, + 170, + 466, + 181 + ], + "lines": [ + { + "bbox": [ + 143, + 170, + 466, + 181 + ], + "spans": [ + { + "bbox": [ + 143, + 170, + 466, + 181 + ], + "type": "text", + "content": "Table 1. Rendering quality evaluation on DiverseScene datasets across various categories" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 188, + 294, + 232 + ], + "lines": [ + { + "bbox": [ + 58, + 188, + 294, + 232 + ], + "spans": [ + { + "bbox": [ + 58, + 188, + 294, + 232 + ], + "type": "table", + "html": "
2DGS3DGS3DHGSGESDRK(S2)DRK(S1)DRK
Num(↓)359K336K373K330K42 K109K260K
MB(↓)83.679.789.678.112.332.176.6
FPS(↑)251.3247.1154.5227.4234.9119.277.5
", + "image_path": "e57fd26b15a657cce25ec3da2985a3244a7964cf39c8273b84928e7ab0cd74ae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 234, + 294, + 256 + ], + "lines": [ + { + "bbox": [ + 55, + 234, + 294, + 256 + ], + "spans": [ + { + "bbox": [ + 55, + 234, + 294, + 256 + ], + "type": "text", + "content": "Table 2. Evaluation results of average primitive number (Num), model size (MB), and rendering speed (FPS) on DiverseScene." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 278, + 295, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 278, + 295, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 278, + 295, + 337 + ], + "type": "text", + "content": "These endpoints form a polygon that accurately approximates the kernel's boundary. By projecting this polygon onto the image plane, we can efficiently identify and cull tiles that don't intersect with the kernel, making the rasterization more efficient." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 57, + 338, + 181, + 412 + ], + "blocks": [ + { + "bbox": [ + 57, + 338, + 181, + 412 + ], + "lines": [ + { + "bbox": [ + 57, + 338, + 181, + 412 + ], + "spans": [ + { + "bbox": [ + 57, + 338, + 181, + 412 + ], + "type": "image", + "image_path": "0740a8d4f73f30787f7472318146e0e8a484aa4609808025b3971bfe1ed22d55.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 413, + 295, + 436 + ], + "lines": [ + { + "bbox": [ + 55, + 413, + 295, + 436 + ], + "spans": [ + { + "bbox": [ + 55, + 413, + 295, + 436 + ], + "type": "text", + "content": "Figure 7. Our cache-sorting uses " + }, + { + "bbox": [ + 55, + 413, + 295, + 436 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 55, + 413, + 295, + 436 + ], + "type": "text", + "content": " as keys in cache-sorting to rectify the sorting order while preventing popping artifacts." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 184, + 339, + 294, + 412 + ], + "blocks": [ + { + "bbox": [ + 184, + 339, + 294, + 412 + ], + "lines": [ + { + "bbox": [ + 184, + 339, + 294, + 412 + ], + "spans": [ + { + "bbox": [ + 184, + 339, + 294, + 412 + ], + "type": "image", + "image_path": "7c6e4e5757952293201c78226a9ee5589e72c6929448f8ec9df92a3106fb0d76.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "spans": [ + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "type": "text", + "content": "Cache Sorting. 3D-GS sorts the Gaussian using the depth of the center " + }, + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "type": "text", + "content": ", which can lead to inconsistencies across multiple views. While Radl et al. [44] address this by estimating the depth of the Gaussian at the point of maximum density and applying a hierarchical sorting solution to mitigate popping artifacts caused by inconsistent sorting, we propose a simpler yet effective solution. In our approach, the distance " + }, + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "type": "text", + "content": " from the camera to the intersection between the ray and " + }, + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 451, + 295, + 559 + ], + "type": "text", + "content": " is calculated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 133, + 568, + 294, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 568, + 294, + 597 + ], + "spans": [ + { + "bbox": [ + 133, + 568, + 294, + 597 + ], + "type": "interline_equation", + "content": "r _ {t} = \\frac {\\left(\\mu - r _ {o}\\right) ^ {T} R _ {z}}{r _ {d} ^ {T} R _ {z}}. \\tag {13}", + "image_path": "64e6a537b5cbf85a2969748a2465131aaedc1a0b8ffdb897540e418154ccae09.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": "During rendering, each thread processes a pixel using an sorted array to cache the " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " values and kernel indices, as illustrated in Fig. 7. The array is kept sorted by performing insert sorting for each new-coming kernel. If the array is full, the kernel with the smallest " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " is popped out for processing. A dynamic cursor is used to record the scanning. We maintain an array length of 8, which is sufficient for approximating a more accurate sort. Fig. 7 demonstrates our method's effectiveness in handling multiple overlapping" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 191, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 191, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 191, + 553, + 228 + ], + "type": "text", + "content": "kernels with identical center depths, comparing rasterization results with and without cache-sorting, preventing popping artifacts while maintaining rendering efficiency." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 238, + 390, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 238, + 390, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 238, + 390, + 251 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 257, + 489, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 257, + 489, + 269 + ], + "spans": [ + { + "bbox": [ + 313, + 257, + 489, + 269 + ], + "type": "text", + "content": "5.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "type": "text", + "content": "To evaluate our method's performance across diverse scenarios, we focused on four key aspects: texture complexity, geometric detail, view-dependent effects, and scene scale. We collected 10 representative 3D scenes from Sketchfab1, with two scenes per category: simple objects, richly textured surfaces, intricate geometric details, specular materials, and large-scale environments. The dataset, namely DiverseScenes, serves as a benchmark to assess our representation method's capabilities. Detailed information about DiverseScenes can be found in the supplementary materials. For the evaluation on unbounded real-world scenes, we utilized the Mip-NeRF360 dataset [2], which contains multi-view images captured in open environments. Camera poses were estimated using COLMAP [47]. We assessed performance using three metrics: Peak Signal-to-Noise Ratio (PSNR) for overall reconstruction accuracy, Structural Similarity Index (SSIM) for perceptual quality and Learned Perceptual Image Patch Similarity (LPIPS) [68] for human-perceived visual fidelity. We observed that the number of primitives significantly impacts rendering quality. To evaluate DRK's performance across different densities, we present results using various hyper-parameters (details provided in the Supp), where the density decreases progressively from " + }, + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "type": "inline_equation", + "content": "DRK(S2)" + }, + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "type": "text", + "content": " and then to " + }, + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "type": "inline_equation", + "content": "DRK(S1)" + }, + { + "bbox": [ + 313, + 276, + 555, + 563 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 570, + 460, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 460, + 582 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 460, + 582 + ], + "type": "text", + "content": "5.2.Quantitative Comparisons" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 588, + 554, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 588, + 554, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 588, + 554, + 696 + ], + "type": "text", + "content": "DiverseScenes. We compare our method, " + }, + { + "bbox": [ + 313, + 588, + 554, + 696 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 588, + 554, + 696 + ], + "type": "text", + "content": ", against state-of-the-art Gaussian representations: 3D-GS [27], 2D-GS [22], 3D-HGS [30], and GES [20], using their official implementations. To ensure a fair comparison focused on kernel representation, we adjust the gradient threshold for densification in these methods, aligning their primitive count with that of 3D-GS " + }, + { + "bbox": [ + 313, + 588, + 554, + 696 + ], + "type": "inline_equation", + "content": "(300\\mathrm{K}+)" + }, + { + "bbox": [ + 313, + 588, + 554, + 696 + ], + "type": "text", + "content": ". The results for each dataset category are shown in Table 1, demonstrating that our method achieves the best average performance. This" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 325, + 702, + 403, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 702, + 403, + 712 + ], + "spans": [ + { + "bbox": [ + 325, + 702, + 403, + 712 + ], + "type": "text", + "content": "1https://sketchfab.com/" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21518" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 67, + 541, + 480 + ], + "blocks": [ + { + "bbox": [ + 66, + 67, + 541, + 480 + ], + "lines": [ + { + "bbox": [ + 66, + 67, + 541, + 480 + ], + "spans": [ + { + "bbox": [ + 66, + 67, + 541, + 480 + ], + "type": "image", + "image_path": "1c5cbff6b0244e704362d31e14ccc71d6840e362f3ab1641ec33ad693fb3c311.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 481, + 555, + 503 + ], + "lines": [ + { + "bbox": [ + 55, + 481, + 555, + 503 + ], + "spans": [ + { + "bbox": [ + 55, + 481, + 555, + 503 + ], + "type": "text", + "content": "Figure 8. Qualitative comparisons of " + }, + { + "bbox": [ + 55, + 481, + 555, + 503 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 481, + 555, + 503 + ], + "type": "text", + "content": " with state-of-the-art methods across various scenarios show that " + }, + { + "bbox": [ + 55, + 481, + 555, + 503 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 481, + 555, + 503 + ], + "type": "text", + "content": " effectively captures sharp texture and geometry boundaries." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": "is followed by our sparser version, " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": " (S1). " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": " (S2) also performs comparably to other state-of-the-art methods, with significantly fewer primitives and lower space occupancy, while maintaining comparable FPS, as detailed in Table 2. Although our method requires more computation, the rendering frameres remain efficient (FPS > 50)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 582, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 715 + ], + "type": "text", + "content": "Mip-NeRF360 Datasets. We also tested " + }, + { + "bbox": [ + 55, + 582, + 295, + 715 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 582, + 295, + 715 + ], + "type": "text", + "content": " on Mip-NeRF360 datasets, known for accurate camera poses and unbounded scenes. Results are shown in Tab. 3. On unbounded scenes, " + }, + { + "bbox": [ + 55, + 582, + 295, + 715 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 582, + 295, + 715 + ], + "type": "text", + "content": " still excels in perceptual quality (LPIPS, SSIM), it shows less advantage in PSNR, especially with sparser kernels. We hypothesize that DRK may tend to overfit distant regions with limited supervision. To address this, we used MiVOS[6] to mask image sequences, training on original images but evaluating only the foreground. The results (M-PSNR) indicate our method's strength in well-supervised central regions." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 317, + 505, + 552, + 588 + ], + "blocks": [ + { + "bbox": [ + 317, + 505, + 552, + 588 + ], + "lines": [ + { + "bbox": [ + 317, + 505, + 552, + 588 + ], + "spans": [ + { + "bbox": [ + 317, + 505, + 552, + 588 + ], + "type": "table", + "html": "
MethodsPSNR(↑)M-PSNR(↑)LPIPS(↓)SSIM(↑)Num(↓)Size(↓)
2D-GS26.3232.01.2987.7617928 K216.0 M
3D-GS26.4832.23.3045.7537811 K191.3 M
3D-GS (L)26.9432.75.2688.77991191 K281.6 M
3D-HGS26.7432.51.2999.7561842 K202.4 M
GES26.6232.11.3047.7542824 K195.0 M
DRK (S2)26.2032.31.2781.7601388 K125.9 M
DRK (S1)26.4032.56.2601.7722551 K161.9 M
DRK26.7632.81.2364.7871952 K279.1 M
", + "image_path": "a1a5899899d079f6b3ad9219d5fc13818ebed436ae5d0b47b033eadd5963dada.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 321, + 594, + 545, + 605 + ], + "lines": [ + { + "bbox": [ + 321, + 594, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 321, + 594, + 545, + 605 + ], + "type": "text", + "content": "Table 3. Quantitative evaluation on Mip-NeRF360 scenes [2]." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 620, + 450, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 620, + 450, + 634 + ], + "spans": [ + { + "bbox": [ + 313, + 620, + 450, + 634 + ], + "type": "text", + "content": "5.3. Qualitative Comparison" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 555, + 715 + ], + "type": "text", + "content": "We conducted qualitative comparisons to highlight the advantages of DRK over other state-of-the-art kernel representations. Fig.8 shows results across different scene categories, where our method achieves better texture and geometry fitting with a comparable or smaller number of kernels. Fig.9 demonstrates that DRK effectively handles fine ge" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21519" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 51, + 547, + 339 + ], + "blocks": [ + { + "bbox": [ + 60, + 51, + 547, + 339 + ], + "lines": [ + { + "bbox": [ + 60, + 51, + 547, + 339 + ], + "spans": [ + { + "bbox": [ + 60, + 51, + 547, + 339 + ], + "type": "image", + "image_path": "ce129829ec4e9d1b3936bc747c80fee4861b9355f5fe3f6a0a68d0cb9a92d8da.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 342, + 525, + 353 + ], + "lines": [ + { + "bbox": [ + 83, + 342, + 525, + 353 + ], + "spans": [ + { + "bbox": [ + 83, + 342, + 525, + 353 + ], + "type": "text", + "content": "Figure 9. Comparisons on the MipNeRF 360 dataset show our method achieves clearer details and high-fidelity rendering." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 363, + 295, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 363, + 295, + 399 + ], + "spans": [ + { + "bbox": [ + 55, + 363, + 295, + 399 + ], + "type": "text", + "content": "omtries, such as flowers and leaves, and detailed textures, like tags and bark, outperforming other representations that may have used more primitives (see Tab. 3)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 407, + 198, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 407, + 198, + 419 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 198, + 419 + ], + "type": "text", + "content": "5.4. Converting Mesh to DRK" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": "All existing \"Splatting\" methods [20, 22, 27, 30] fail to seamlessly integrate with traditional assets. In contrast, our " + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": " framework provides a versatile representation that allows for effortless conversion of triangle and polygon faces into " + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": ". This is accomplished by placing the " + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": " endpoints at the polygon vertices and adjusting the parameters " + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": " to control sharpness, with both " + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": " curvature set to 1. This process eliminates the need for training data rendering or model optimization. Consequently, rich 3D assets can be seamlessly transferred into " + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 426, + 296, + 581 + ], + "type": "text", + "content": ", bridging the gap between millions of traditional 3D assets and our fast, high-quality reconstruction representation. Figure 10 illustrates the potential applications of Mesh2DRK." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 55, + 584, + 296, + 689 + ], + "blocks": [ + { + "bbox": [ + 55, + 584, + 296, + 689 + ], + "lines": [ + { + "bbox": [ + 55, + 584, + 296, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 584, + 296, + 689 + ], + "type": "image", + "image_path": "dbdd6816b4b53211bf74f4ba522e15e0e630220817fdc117055621b7e65a2784.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "lines": [ + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "spans": [ + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "type": "text", + "content": "Figure 10. The conversion from Mesh to " + }, + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "type": "text", + "content": " demonstrates the efficiency of using " + }, + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "type": "text", + "content": " to incorporate traditional 3D assets into any " + }, + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 55, + 691, + 295, + 724 + ], + "type": "text", + "content": " scene at low cost." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 361, + 388, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 361, + 388, + 374 + ], + "spans": [ + { + "bbox": [ + 314, + 361, + 388, + 374 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "text", + "content": "We present " + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "text", + "content": ", a novel primitive representation that generalizes and enhances Gaussian splatting. By incorporating learnable radial bases, adaptive shape control, and efficient rendering strategies, " + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "text", + "content": " effectively addresses the fundamental limitations of Gaussian kernels in representing diverse geometric features. Our experiments on both synthetic and real-world scenes demonstrate that " + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "text", + "content": " achieves superior rendering quality with significantly fewer primitives, while maintaining computational efficiency through carefully designed rasterization optimizations. Leveraging the flexibility of " + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "text", + "content": ", traditional triangle or polygon mesh representations can be seamlessly converted into " + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "inline_equation", + "content": "DRK" + }, + { + "bbox": [ + 313, + 382, + 555, + 574 + ], + "type": "text", + "content": " without requiring any training. This capability bridges rich 3D assets with reconstructed scenes, paving the way for future applications such as real-scene editing, VR digital world creation, and AR scene enhancement." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 586, + 411, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 586, + 411, + 599 + ], + "spans": [ + { + "bbox": [ + 314, + 586, + 411, + 599 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 715 + ], + "type": "text", + "content": "This work has been supported in part by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621), General Research Fund Scheme (Grant No. 17202422, 17212923), Theme-based Research (Grant No. T45-701/22-R) and Shenzhen Science and Technology Innovation Commission (SGDX20220530111405040). Part of the described research work is conducted in the JC STEM Lab of Robotics for Soft Materials funded by The Hong Kong Jockey Club Charities Trust." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21520" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 135 + ], + "type": "text", + "content": "[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10324-10335, 2024. 2" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "21523" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_content_list.json b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5353c49fd2e43245a289ec59b8b97b355e081af3 --- /dev/null +++ b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_content_list.json @@ -0,0 +1,1329 @@ +[ + { + "type": "text", + "text": "Degradation-Aware Feature Perturbation for All-in-One Image Restoration", + "text_level": 1, + "bbox": [ + 117, + 130, + 879, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiangpeng Tian, Xiangyu Liao, Xiao Liu, Meng Li, Chao Ren* \nCollege of Electronics and Information Engineering, Sichuan University, China \n{tianxp, liaoxiangyul, liux, limeng.scu}@stu.scu.edu.cn, chaoren@scu.edu.cn", + "bbox": [ + 163, + 181, + 823, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 268, + 326, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "All-in-one image restoration aims to recover clear images from various degradation types and levels with a unified model. Nonetheless, the significant variations among degradation types present challenges for training a universal model, often resulting in task interference, where the gradient update directions of different tasks may diverge due to shared parameters. To address this issue, motivated by the routing strategy, we propose DFPIR, a novel all-in-one image restorer that introduces Degradation-aware Feature Perturbations(DFP) to adjust the feature space to align with the unified parameter space. In this paper, the feature perturbations primarily include channel-wise perturbations and attention-wise perturbations. Specifically, channel-wise perturbations are implemented by shuffling the channels in high-dimensional space guided by degradation types, while attention-wise perturbations are achieved through selective masking in the attention space. To achieve these goals, we propose a Degradation-Guided Perturbation Block (DGPB) to implement these two functions, positioned between the encoding and decoding stages of the encoder-decoder architecture. Extensive experimental results demonstrate that DFPIR achieves state-of-the-art performance on several all-in-one image restoration tasks including image denoising, image dehazing, image deraining, motion deblurring, and low-light image enhancement. Our codes are available at https://github.com/TxpHome/DFPIR.", + "bbox": [ + 88, + 301, + 485, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 726, + 220, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image restoration, a fundamental task in computer vision, has been widely studied, with a primary focus on addressing individual degradation types, such as noise, haze, rain, or blur. Recently, deep learning-based approaches have achieved remarkable progress in single-degradation restoration tasks, including denoising [15, 26, 35, 36, 42, 61], deraining [2, 17, 22, 48, 54], dehazing [5, 9, 40, 45, 51], and deblurring [7, 19, 37, 37, 60]. While these single-", + "bbox": [ + 89, + 752, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2e84e4e7408236d6469ddb43aa4924c222e57fda975d2dde6a9a5ac3f09638c4.jpg", + "image_caption": [ + "Figure 1. This figure demonstrates the channel-wise perturbation method of DFPIR, where channel shuffle assigns unique channel orders for different degradation types." + ], + "image_footnote": [], + "bbox": [ + 516, + 270, + 903, + 409 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "degradation solutions perform well under specific conditions, they often struggle to generalize effectively to multiple degradation scenarios. Consequently, recent research has shifted toward multi-degradation restoration techniques, delivering state-of-the-art performance for known combinations of degradations [3, 33, 56, 57]. However, these approaches typically require separate networks for each degradation type, leading to large model sizes and high computational demands.", + "bbox": [ + 511, + 488, + 906, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, all-in-one approaches(also known as multi-degradation or multi-task image restoration) have gained prominence by addressing multiple image degradations within a unified model [6, 21, 38, 39, 49, 55, 59]. While these methods have achieved state-of-the-art results, they often overlook the relationships and distinctive characteristics among different degradation types due to shared parameters. For example, MedIR [55] demonstrates that the gradient update directions between different tasks are inconsistent or even opposite. According to the characteristics of existing methods, current all-in-one image restoration methods can be roughly divided into two categories: (1) one solution is to modify the parameter space to fit the model for different degradations [21, 38, 49, 59]; (2) and the other solution is to modify the feature space to align with the shared parameter space [8, 39, 55]. Both approaches require incorporating degradation information into the network to mitigate the interference between different degras", + "bbox": [ + 511, + 628, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 109, + 887, + 233, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28165", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ce12d81db4d13d5a5a88a4ec631eff8aa58a7a829399ea71a4008b0ca21ea86a.jpg", + "image_caption": [ + "Without attention disturbance: Select all attention maps." + ], + "image_footnote": [], + "bbox": [ + 112, + 125, + 263, + 239 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6c6b59ee92b42ef29baa71d45038cf18e5d5fca980f043ca29a1a14191faaf26.jpg", + "image_caption": [ + "With attention disturbance: Select partial attention maps." + ], + "image_footnote": [], + "bbox": [ + 308, + 125, + 460, + 239 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/05174b5e62c78d6233d2594e558d7b470c08010641b89eebc164ba727875f283.jpg", + "image_caption": [ + "Figure 2. This figure showcases our attention-wise perturbation, where DFPIR applies attention selection to perturb image features, discarding a portion of attention for each degradation type." + ], + "image_footnote": [], + "bbox": [ + 94, + 247, + 475, + 265 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "dations. Although the approach (1) can effectively enhance network performance, it usually requires a large number of additional degradation parameters or a more complex network structure, increasing computational complexity.", + "bbox": [ + 89, + 339, + 482, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared to the approach (1), the method (2) is more prevalent in the \"All-in-One\" image restoration framework. The approach (2) typically involves introducing a degradation type prompt, which modulates features to align with the shared network parameters. Specifically, PromptIR [39] conducts multi-degradation processing by introducing additional implicit prompts. However, although this implicit cue in the feature domain utilizes the inherent features of the image, it neglects the influence of degradation types, making it challenging to reduce the mutual influence among multiple degradation types, which ultimately leads to suboptimal results. MedIR [55] introduces multiple experts into the feature space modulation to implement a task-adaptive routing strategy. Although this \"hard\" routing strategy effectively reduces the influence between tasks, it may overlook the inherent features of the image among multiple degradations. InstructIR [8] introduces text commands for multi-task restoration, showcasing the potential of using text prompts to guide image restoration. However, InstructIR [8] modulates features through channel attention using text prompts, which may make it challenging to mitigate the mutual influence among different degradations.", + "bbox": [ + 89, + 401, + 482, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome these challenges, this paper analyzes the design philosophy and rationale behind the success of prompts and presents a degradation-aware feature perturbation approach to adjust the feature space to align with the unified parameter space for all-in-one image restoration. Our method modulates features through perturbations which include channel-wise and attention-wise perturbations to align with shared network parameters or structures, guided by degradation type prompts. Specifically, channel-wise perturbations involve shuffling the channels in high-dimensional space rather than using the conventional", + "bbox": [ + 89, + 734, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "channel attention mechanism (see Fig.1). This shuffling approach preserves the inherent features of the image while reducing the mutual influence of degradation features. While attention-wise perturbations involve selectively masking the features after channel shuffling to achieve channel-adapted attention perturbation (see Fig.2). This approach not only preserves the inherent feature information of the image but also adaptively reduces the mutual influence between different degradation types, achieving a good balance between influence and inherent features. The main contributions of our method are as follows:", + "bbox": [ + 511, + 90, + 906, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose a novel degradation-aware feature perturbation all-in-one restoration framework, DFPIR, which adaptively adjusts the feature space in high-dimensional space to align with the unified parameter space, guided by degradation type prompts.", + "bbox": [ + 513, + 257, + 903, + 332 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We design a Degradation-Guided Perturbation Block (DGPB), consisting of a Degradation-Guided Channel Perturbation Module (DGCPM) and a Channel-Adapted Attention Perturbation Module (CAAPM), to apply perturbation modulation to features along the channel and attention dimensions, aligning with the encoder-decoder architecture with unified parameters.", + "- Extensive experiments demonstrate that our network achieves state-of-the-art performance in all-in-one image restoration. Especially for all-in-one restoration, 0.45dB PSNR improvement is obtained in comparison with InstructIR [8]." + ], + "bbox": [ + 513, + 333, + 903, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 527, + 661, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Single Task Image Restoration. Single task image restoration seeks to recover a high-quality image from its low-quality version. Due to the ill-posed nature of the task, early methods primarily focused on designing effective handcrafted priors to constrain the solution space. In contrast, recent deep learning-based approaches have significantly advanced the performance of various image restoration tasks, such as denoising [13, 26, 35, 36, 42, 43], detraining [2, 22, 24, 27, 47], dehazing [5, 9, 29, 40, 45, 51], deblurring [4, 7, 18, 19, 37, 37, 60], and low-light enhancement [12, 31, 52], by learning generalizable priors from large-scale datasets. We focus on general purpose restoration models [3, 25, 57], as these architectures can be independently trained for a variety of tasks. NAFNet [3] simplifies the network structure with lightweight channel attention and gated mechanisms, offering an alternative to non-linear activations. Meanwhile, Restormer [57] leverages transformer architectures to enhance low-level restoration tasks while minimizing computational overhead. In this study, we adopt Restormer [57] as the backbone for our DFPIR model due to its efficient design and high performance across multiple restoration tasks. However, these models are primarily designed for single-degradation scenarios, limiting their ef", + "bbox": [ + 511, + 553, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28166", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "fectiveness when applied directly to all-in-one restoration tasks.", + "bbox": [ + 89, + 90, + 485, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "All-In-One Image Restoration. Multi-task image restoration aims to address multiple tasks using the same network design [8, 21, 38, 39, 49, 55, 59]. Compared to single-task image restoration, the key challenge in multi-task image restoration is how to reduce the mutual influence of different degradation features while preserving the inherent features of the image. One approach is to adjust the network's parameter space to accommodate different degradation types. Several works have explored these strategies to handle diverse degradations. Li et al. [23] introduce a single-encoder, multi-decoder framework targeting weather-based degradations using the Rain-Haze-Snow dataset. Chen et al. [6] propose a two-stage knowledge transfer mechanism, employing a multi-teacher, single-student approach to handle various degradation types. Li et al. [21] propose an all-in-one framework capable of restoring multiple degraded images without requiring prior knowledge of degradation types or levels. Zhang et al. [59] propose an ingredient-oriented strategy that supports up to five restoration tasks within a single model, significantly enhancing scalability. Similarly, Zhang et al. [58] introduce a representation learning network guided by degradation classification, using its strong classification capabilities to effectively steer the restoration process. Another approach is to introduce image or degradation prompts to modulate the features, adapting to a unified parameter space [8, 39, 55]. PromptIR [39] encodes degradation-specific information through prompts, using them to dynamically guide the restoration network. In contrast, InstructIR [8] allows for model-driven image editing based on instructions that specify the desired actions, rather than relying on text labels, captions, or descriptions of input and output images.", + "bbox": [ + 91, + 146, + 483, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 89, + 662, + 264, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In \"All-In-One\" image restoration, the objective is to develop a single model $\\mathbf{M}$ capable of restoring a clean image $\\hat{\\mathbf{I}}$ from a degraded input image $\\mathbf{I}$ affected by a degradation $\\mathbf{D}$ . Within this framework, under the same network parameters and architecture, different types of degradation mutually influence each other. For example, degraded images contain both inherent image features and degradation features. While inherent image features help the network learn latent parameters, thereby enhancing restoration performance, degradation features may negatively impact each other, reducing restoration effectiveness. In order to fully utilize the inherent features of the image while reducing the influence of different degradation features, motivated by the \"hard\" routing strategy [55] and PromptIR [39], we propose", + "bbox": [ + 89, + 688, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d7e704d2c354c66f078f1502c41fb2dc1ec481ed9b503e27e7a0bc580332a2e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 89, + 694, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3b70733a0733a3919e535dff7d3db8aef6583aa077056658cd9b96f6dc79703f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 728, + 90, + 898, + 189 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ec8c2b758214f6d49685e1a185f0c06a0b23c7ea68b270f8d78b5ce5ea5ce2b2.jpg", + "image_caption": [ + "Noisy: CBSD68" + ], + "image_footnote": [], + "bbox": [ + 517, + 191, + 638, + 224 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9dd11401eed88882eaaf5bd52e9dcda4f4bc27b36c689c9991214749f91dfe0a.jpg", + "image_caption": [ + "Rainy: Rain100L" + ], + "image_footnote": [], + "bbox": [ + 651, + 191, + 771, + 224 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a4692ea5232598541fe181489e449de6059f58e4251d5e12656cb0cdce69ce3c.jpg", + "image_caption": [ + "Hazy: SOTS", + "Figure 3. The figure provides t-SNE plots of the intermediate features from DFPIR (our method) and PromptIR on the test datasets (CBSD68, Rain100L, and SOTS) under the three-task setting. In our model, the features for each task exhibit tighter clustering, highlighting the effectiveness of our degradation-aware feature perturbation strategy in enhancing restoration performance." + ], + "image_footnote": [], + "bbox": [ + 779, + 191, + 901, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a degradation-aware feature perturbation modulation network, DFPIR, that adjusts the feature space through perturbation modulation to align with the shared-parameter network structure, thereby enhancing multi-degradation image restoration performance. The perturbation is divided into two parts: channel-wise perturbation and attention-wise perturbation. Channel-wise perturbation is implemented through channel shuffle, while attention-wise perturbation is achieved by selecting a portion of the attention maps. The details of these two perturbation mechanisms are provided in Section 3.3. The pipeline of the proposed DFPIR framework is illustrated in Fig.4. In the following sections, we describe the overall structure of DFPIR in detail.", + "bbox": [ + 511, + 353, + 906, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overall Pipeline", + "text_level": 1, + "bbox": [ + 511, + 560, + 673, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a degraded input image $\\mathbf{I} \\in R^{H \\times W \\times 3}$ , the DFPIR initially extracts shallow features $\\mathbf{F_0} \\in R^{H \\times W \\times C}$ using a $3 \\times 3$ convolution layer; where $H \\times W$ is the spatial size and $C$ denotes the channels. Next, these features $\\mathbf{F_0}$ undergo a 4-level encoder-decoder network, transforming into deep features $\\mathbf{F_r} \\in R^{H \\times W \\times 2C}$ . Each level of the encoder-decoder employs multiple Transformer blocks [57], where the number of blocks gradually increases from the top level to the bottom level, facilitating a computationally efficient design. Beginning with the high-resolution input, the encoder aims to gradually decrease spatial resolution while increasing channel capacity, resulting in a low-resolution latent representation $\\mathbf{F_e} \\in R^{\\frac{H}{8} \\times \\frac{W}{8} \\times 8C}$ . Given the low-resolution latent features $\\mathbf{F_e}$ , the objective of the decoder is to progressively restore the high-resolution clean output. To assist the recovery process, the encoder features are concatenated with the decoder features via skip connections [44]. We insert our Degradation-Guided Perturbation Block (DGPB) between the encoder and decoder, specifically within the skip-connection stage, to perturb the encoded feature space, which is guided by degradation type", + "bbox": [ + 511, + 582, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28167", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/557326d963e3f73764ffeb10fa721b634f4a4d5d11c49e9014c7453fae9a9646.jpg", + "image_caption": [ + "Figure 4. Overview of the DFPIR framework. We employ Restormer [57], an encoder-decoder network with transformer blocks in the encoding and decoding stages, as our backbone. The primary component of the framework, the Degradation-Guided Perturbation Block (DGPB), consists of two submodules, i.e., Degradation-Guided Channel Perturbation Module (DGCPM) and Channel-Adapted Attention Perturbation Module (CAAPM). The DGCPM module introduces conventional dimensional perturbations to image features in the form of channel shuffling, guided by degradation-type prompts. The CAAPM module applies attention perturbation to the channel-shuffled features through a top-K masking strategy." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 903, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "prompts, and align it with the shared-parameter decoder. To obtain degradation type prompts, we utilize a pre-trained CLIP [41] model to encode the textual degradation type descriptions. In the following sections, we describe the proposed DGPB and its core building modules in detail.", + "bbox": [ + 89, + 539, + 482, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Degradation-Guided Perturbation Block (DGPB)", + "text_level": 1, + "bbox": [ + 89, + 623, + 482, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In all-in-one setting, shared parameters are challenging to handle all-in-one image restoration effectively. We specifically design a Degradation-Guided Perturbation Block (DGPB) to apply perturbations to the encoded features, better aligning them with the shared decoder in multi-task scenarios, guided by the degradation type prompts (as shown in Fig.4). Given as inputs both the image feature $\\mathbf{F_n} \\in R^{\\widehat{H} \\times \\widehat{W} \\times \\widehat{C}}$ and degradation type prompts $\\mathbf{P_e} \\in T^{\\widehat{L} \\times 1}$ , the overall process of DGPB is defined as:", + "bbox": [ + 89, + 661, + 482, + 800 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F _ {b}} = \\operatorname {C A A P M} (\\operatorname {D G C P M} (\\mathbf {F _ {n}}, \\operatorname {D G M} (\\mathbf {P _ {e}})), \\mathbf {F _ {n}}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 811, + 482, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{F_n}$ represents the encoder output. The DGPB comprises two core components: the Degradation-Guided Channel Perturbation Module (DGCPM) and the Channel-Adapted Attention Perturbation Module (CAAPM).", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Degradation-Guided Channel Perturbation Module (DGCPM)", + "text_level": 1, + "bbox": [ + 513, + 537, + 906, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In DGCPM, the objective is to add perturbations to the feature channels through channel shuffling, guided by degradation type prompts. However, directly shuffling the channels on the feature $\\mathbf{F_n}$ may make it difficult to converge due to excessive perturbation and may also affect the quality of the reconstruction. To address this issue, we initially expand the number of channels in the image feature $\\mathbf{F_n}$ by $2\\mathrm{x}$ to introduce channel perturbations in a higher-dimensional channel space, guided by the Degradation Guidance Module(DGM). After channel expansion, the size of feature $\\mathbf{F_n}$ becomes $\\mathbf{F}_{2\\mathbf{n}}\\in R^{\\widehat{H}\\times \\widehat{W}\\times 2\\widehat{C}}$ . In DGM, the degradation type prompts $(\\mathbf{P_e})$ are used to adaptively apply channel shuffle. To maintain the dimensionality of $\\mathbf{P_e}$ consistent with the channel dimensionality of $\\mathbf{F_{2n}}$ , we employ a Multi-Layer Perceptron (MLP) which consisting of two linear layers to achieve dimension matching. Thus, MLP transforms the input feature $\\mathbf{P_e}$ into $\\mathbf{P_{ec}}\\in T^{2\\widehat{C}\\times 1}$ . For degradation type prompts, see the supplementary document. In channel shuffle stage, we get the index value corresponding to the top- $\\mathrm{K}(\\mathrm{K} = 2\\widehat{\\mathrm{C}})$ value of $\\mathbf{P_{ec}}$ , and use these index values to reorder the channels. Finally, halve the number of channels", + "bbox": [ + 511, + 579, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28168", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/05627f8b35b98f5271dacb43bf5bd2fe062416f6d363acdec64fe6760ad8f009.jpg", + "table_caption": [ + "Table 1. Comparison to state-of-the-art on three tasks. PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images. On average PSNR, our DFPIR provides a significant gain of 0.45 dB over the previous all-in-one method InstructIR [8]." + ], + "table_footnote": [], + "table_body": "
MethodDehazing on SOTSDeraining on Rain100LDenoising on CBSD68 datasetAverage
σ = 15σ = 25σ = 50
DL [11]26.92 / 0.39132.62 / 0.93133.05 / 0.91430.41 / 0.86126.90 / 0.74029.98 / 0.875
FDGAN [10]24.71 / 0.92429.89 / 0.93330.25 / 0.91028.81 / 0.86826.43 / 0.77628.02 / 0.883
MPRNet [56]25.28 / 0.95433.57 / 0.95433.54 / 0.92730.89 / 0.88027.56 / 0.77930.17 / 0.899
AirNet [21]27.94 / 0.96234.90 / 0.96733.92 / 0.93331.26 / 0.88828.00 / 0.79731.20 / 0.910
Restormer [57]30.43 / 0.97536.55 / 0.97533.84 / 0.93131.18 / 0.88527.90 / 0.79031.98 / 0.911
PromptIR [39]30.58 / 0.97436.37 / 0.97233.98 / 0.93331.31 / 0.88828.06 / 0.79932.06 / 0.913
InstructIR [8]30.22 / 0.95937.98 / 0.97834.15 / 0.93331.52 / 0.89028.30 / 0.80432.43 / 0.913
DFPIR(Ours)31.87 / 0.98038.65 / 0.98234.14 / 0.93531.47 / 0.89328.25 / 0.80632.88 / 0.919
", + "bbox": [ + 91, + 127, + 906, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "after the shuffle to keep the channel count consistent before and after the transformation. Overall, the DGCPM process is summarized as:", + "bbox": [ + 89, + 309, + 480, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} = \\operatorname {C o n v h} \\left(\\mathbf {C S} _ {\\text {t o p} K} \\left(\\operatorname {C o n v k} \\left(\\mathbf {F} _ {\\mathbf {n}}\\right) | \\mathrm {D G M} \\left(\\mathbf {P} _ {\\mathbf {e}}\\right)\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 363, + 482, + 381 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the operation $\\mathbf{CStopK}(\\bullet|\\mathrm{DGM}(\\mathbf{Pe}))$ denotes top-K channel shuffling guided by $\\mathrm{DGM}(\\mathbf{P_e})$ , while Convk ( $\\bullet$ ) and Convh ( $\\bullet$ ) represent the operations of doubling and halving the feature channels, respectively. After DGCPM, we obtain feature $\\mathbf{Q} \\in R^{\\widehat{H} \\times \\widehat{W} \\times \\widehat{C}}$ .", + "bbox": [ + 89, + 388, + 483, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Channel-Adapted Attention Perturbation Module(CAAPM)", + "text_level": 1, + "bbox": [ + 89, + 484, + 483, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although the shuffled features can adapt well to specific degradations, directly using them for reconstruction may not yield optimal results. This is because the shuffled features carry degradation-type information but lack interaction with the original feature information. To address this, we designed the Channel-Adapted Attention Perturbation Module (CAAPM). CAAPM has two main functions: facilitating information interaction between the shuffled and original features, and adding perturbations in the attention dimension. Motivated by Restormer [57], we design a cross-attention mechanism in the channel dimension to aggregate the shuffled and original features. To add perturbations to the attention map, we introduce a mask matrix $\\mathbf{M} \\in R^{\\widehat{C} \\times \\widehat{C}}$ to select part of the attention map from each row using a top-K approach with a perturbation factor parameter $\\gamma$ . The process of obtaining the perturbed attention map $\\mathbf{PAM} \\in R^{\\widehat{H}\\widehat{W} \\times \\widehat{C}}$ can be described as:", + "bbox": [ + 89, + 523, + 483, + 785 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P A M} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {s o f t m a x} (\\mathbf {M} \\odot (\\mathbf {Q} _ {*} \\mathbf {K} _ {*} ^ {T} / \\sqrt {d _ {k}})) \\mathbf {V} _ {*} (3)\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 792, + 482, + 818 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the query $\\mathbf{Q}_{*}$ is derived from shuffled feature $\\mathbf{Q}$ , and the key $\\mathbf{K}_{*}$ and value $\\mathbf{V}_{*}$ are derived from original features $\\mathbf{F_{n}}$ . $\\mathbf{M}$ represents the selection mask matrix. $\\odot$ represents the element-wise multiplication. Then, we use a $1\\times 1$ convolution to obtain the feature $\\mathbf{F_{a}}$ with attention perturbations.", + "bbox": [ + 89, + 824, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we obtain the final output through an FFN network. This can be expressed as:", + "bbox": [ + 511, + 309, + 903, + 339 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {\\mathbf {b}} = \\mathbf {F} _ {\\mathbf {a}} + \\operatorname {F F N} \\left(\\mathbf {F} _ {\\mathbf {a}}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 352, + 906, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The selection of the perturbation factor $\\gamma$ needs to comprehensively consider the extent of interference magnitude between tasks and information loss. Fig.4 illustrates the relationship between $\\gamma$ , interference size, and information loss. In our paper, the parameter is $\\gamma$ fixed at 0.9, and the ablation study presents the experimental results for different values of $\\gamma$ .", + "bbox": [ + 511, + 380, + 906, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Analysis of Our Feature Perturbation Strategy", + "text_level": 1, + "bbox": [ + 511, + 494, + 903, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The task-aware feature perturbation strategy we propose involves both channel and attention dimensions. By perturbing these two dimensions, it not only preserves the inherent features of the image but also reduces the mutual influence of degradation features. Fig.3 illustrates that our model excels in learning discriminative degradation contexts.", + "bbox": [ + 511, + 518, + 905, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Channel-wise Perturbation Strategy. Directly performing channel shuffle in a low-dimensional space causes excessive perturbation, making network training difficult to converge. Therefore, we propose a degradation-aware adaptive channel shuffle strategy (as shown in Fig.1), which adaptively reorders the feature channels for each task in a high-dimensional feature space. Given a image feature which contains $N$ channels $\\mathbf{F_{nc}} = \\{C_1,C_2,\\dots ,C_r,\\dots ,C_N\\} (\\mathrm{r}\\leq N)$ and M tasks, our channel shuffle strategy adopts different channel orders for each degradation restoration task. For any given task $\\mathrm{T_m(m\\leq M)}$ , the channel index vector after channel shuffle is defined as $\\mathbf{S}^N = \\{S_1^N,S_2^N,\\dots ,S_N^N\\}$ . Finally, the feature obtained after channel shuffle is $\\mathbf{F}_{\\mathbf{m}} = \\{C_{S_1^N},C_{S_2^N},\\dots ,C_{S_N^N}\\}$ . The adjustment of this channel order is adaptively random under the guidance of degradation prompts. This random adaptive shuffle strategy reduces interference between feature channels while preserving the", + "bbox": [ + 511, + 628, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28169", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f2ba637c86223dcbdb3594c0bb4820e0ed398d1c747c630c83023d3595fb8358.jpg", + "table_caption": [ + "Table 2. Comparison to state-of-the-art on five tasks. PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images with (*) denoting general image restorers, others are specialized all-in-one approaches. Denoising results are reported for the noise level $\\sigma = 25$ ." + ], + "table_footnote": [], + "table_body": "
MethodDehazing on SOTSDeraining on Rain100LDenoising on CBSD68Deblurring on GoproLow-light Enh. on LOLAverage
DGUNet* [33]24.78 / 0.94036.62 / 0.97131.10 / 0.88327.25 / 0.83721.87 / 0.82328.32 / 0.891
SwinIR* [25]21.50 / 0.89130.78 / 0.92330.59 / 0.86824.52 / 0.77317.81 / 0.72325.04 / 0.835
Restomer* [57]24.09 / 0.92734.81 / 0.96231.49 / 0.88427.22 / 0.82920.41 / 0.80627.60 / 0.881
NAFNet* [3]25.23 / 0.93935.56 / 0.96731.02 / 0.88326.53 / 0.80820.49 / 0.80927.76 / 0.881
DL [11]20.54 / 0.82621.96 / 0.76223.09 / 0.74519.86 / 0.67219.83 / 0.71221.05 / 0.743
Transweather [46]21.32 / 0.88529.43 / 0.90529.00 / 0.84125.12 / 0.75721.21 / 0.79225.22 / 0.836
TAPE [28]22.16 / 0.86129.67 / 0.90430.18 / 0.85524.47 / 0.76318.97 / 0.62125.09 / 0.801
AirNet [21]21.04 / 0.88432.98 / 0.95130.91 / 0.88224.35 / 0.78118.18 / 0.73525.49 / 0.846
IDR [59]25.24 / 0.94335.63 / 0.96531.60 / 0.88727.87 / 0.84621.34 / 0.82628.34 / 0.893
InstructIR [8]27.10 / 0.95636.84 / 0.97331.40 / 0.88729.40 / 0.88623.00 / 0.83629.55 / 0.907
DFPIR(Ours)31.64 / 0.97937.62 / 0.97831.29 / 0.88928.82 / 0.87323.82 / 0.84330.64 / 0.913
", + "bbox": [ + 94, + 127, + 903, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "inherent characteristics of the image (as channel shuffling does not result in channel feature loss), thereby improving reconstruction quality.", + "bbox": [ + 89, + 354, + 482, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Attention-wise Perturbation Strategy. The main purpose of channel shuffle is to minimize the influence of degradation features while preserving the inherent characteristics of the image. However, this reduction is not thorough enough, meaning its effectiveness is limited. To address this, we directly discard a portion of the attention in the attention maps to further mitigate the impact of multiple degradation features (as shown in Fig.2). Specifically, we compute the transposed cross attention map $\\mathbf{A}_{tt} \\in R^{\\widehat{C} \\times \\widehat{C}}$ . We select a portion of the attention map values from each column of $\\mathbf{A}_{tt}$ using the top-K method to generate a disturbance mask matrix $\\mathbf{M} \\in R^{\\widehat{C} \\times \\widehat{C}}$ , where the values that are not selected are set to 0, and the remaining values are set to 1. Then, the matrix $\\mathbf{M}$ is multiplied element-wise with $\\mathbf{A}_{tt}$ to obtain a new attention map $\\mathbf{A}_{ttn}$ , achieving perturbation in the attention dimension. In other words, $\\mathbf{A}_{ttn} = \\mathbf{A}_{tt} \\odot \\mathbf{M}$ , where $\\mathbf{A}_{tt}$ is $\\mathbf{Q}_*\\mathbf{K}_*^T / \\sqrt{d_k}$ in equation 3.", + "bbox": [ + 89, + 419, + 483, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 694, + 223, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we follow the protocols of prior state-of-the-art works [21, 39] to conduct experiments under two settings: (a) all-in-one and (b) single-task. For the all-in-one setting, a unified model is trained to handle multiple degradation types, with experiments conducted across three and five distinct degradations. In contrast, the single-task setting involves training separate models, each specialized for a specific restoration task. The image quality metrics—PSNR and SSIM [16]—for the top-performing methods are highlighted in red and the second-best results are highlighted in blue in the result tables. Single-task results and more visual experiments are in the supplementary material.", + "bbox": [ + 89, + 719, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 511, + 354, + 720, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. In line with previous work [21, 39], we prepare datasets tailored for various restoration tasks. For single-task image denoising, we merge images from the BSD400 [1] and WED [30] datasets to train the model. Testing is conducted on the CBSD68 [32] and Urban100 [14] datasets. For image dehazing, we use the SOTS [20] dataset, while Rain100L [53] is employed for image deraining. Deblurring and low-light enhancement tasks utilize the GoPro [34] and LOL-v1 [34] datasets, respectively. In the all-in-one setting, a unified model is trained on the combined training datasets mentioned above and tested directly across multiple restoration tasks. Additional dataset details can be found in the supplementary materials.", + "bbox": [ + 511, + 388, + 906, + 587 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. Our DFPIR provides an end-to-end trainable solution, removing the necessity for pretraining any individual components. Following the configuration of PromptIR [39], our DFPIR architecture features a 4-level encoder-decoder structure, comprising varying numbers of Transformer blocks at each level, specifically [4, 6, 6, 8] from level-1 to level-4. We integrate our Degradation-Guided Perturbation Block (DGPB) between the encoder and decoder, with a total of four DGPBs distributed throughout the network. We conduct our experiments using PyTorch on a single NVIDIA GeForce RTX 3090 GPU. For training, we run for 80 epochs with an initial learning rate of $1e^{-4}$ , followed by fine-tuning for 5 epochs at a learning rate of $1e^{-5}$ . Initially, we set the patch size to $128^2$ with the batch size of 5, and for fine-tuning, the patch size is adjusted to $192^2$ with a batch size of 3. The network is optimized using the L1 loss function in conjunction with the Adam optimizer (with parameters $\\beta_{1} = 0.9$ and $\\beta_{2} = 0.999$ ). We train on cropped patches and augment the dataset with random horizontal and vertical flips.", + "bbox": [ + 511, + 598, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28170", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/acb9365ca31a97e0485dd698a7fe410c8b935a454592935105d718ed31b596ed.jpg", + "image_caption": [ + "Figure 5. Visual comparison of DFPIR with state-of-the-art methods on challenging cases for the All-in-One setting considering three degradations. Zoom in for better view." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 903, + 381 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Results Comparisons on Three Tasks", + "text_level": 1, + "bbox": [ + 89, + 435, + 410, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We assess the performance of our all-in-one DFPIR across three distinct restoration tasks: dehazing, deraining, and denoising. Our DFPIR is compared with various general image restoration methods, including Restormer [57], FDGAN [10], and MPRNet [56], as well as specialized all-in-one approaches such as DL [11], AirNet [21], PromptIR [39], and InstructIR [8]. As shown in Tab. 1, the proposed DFPIR consistently outperforms the other competing methods. On average across the different restoration tasks, our algorithm achieves a performance improvement of $0.45\\mathrm{dB}$ over the previous best method, InstructIR [8], and $0.82\\mathrm{dB}$ over the second-best approach, PromptIR [39]. Specifically, DFPIR demonstrates a notable increase of $0.67\\mathrm{dB}$ on the deraining task and $1.65\\mathrm{dB}$ on the dehazing task compared to InstructIR [8].", + "bbox": [ + 88, + 459, + 482, + 685 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Results Comparisons on Five Tasks", + "text_level": 1, + "bbox": [ + 89, + 695, + 397, + 710 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To further validate the method's effectiveness in addressing a broader range of tasks, building upon the recent research conducted by IDR [59] and InstructIR [8], we extend our investigation into the efficacy of DFPIR by conducting experiments across five restoration tasks: dehazing, deraining, denoising, deblurring, and low-light image enhancement. To achieve this, we train a comprehensive DFPIR on combined datasets compiled for five distinct tasks. These encompass datasets from the previously mentioned threetask scenario, alongside additional datasets: GoPro [34] for motion deblurring and LOL [50] for low-light image enhancement. Tab. 2 demonstrates that DFPIR achieves a 1.09", + "bbox": [ + 88, + 719, + 482, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dB improvement compared to the recent leading method InstructIR [8], when averaged across five restoration tasks. Additionally, we compare our method to general image restoration models that were trained in the same All-in-One setting. Notably, our method surpasses Restormer[57] and NAFNet [3] on average PSNR by 3.04 dB and 2.88 dB, respectively, validating the effectiveness of our approach in handling multiple degradations.", + "bbox": [ + 511, + 436, + 906, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Visual Results", + "text_level": 1, + "bbox": [ + 511, + 571, + 660, + 587 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual examples illustrating our results for dehazing, de- raining, and denoising are provided in Fig.5. Compared to PromptIR [39] and InstructIR [8], our method is more effective in challenging dehazing scenarios. Additionally, our model's deraining results are closer to the ground-truth images. Furthermore, in image denoising, our model recovers more details from heavily degraded noisy inputs. We visualized the results of channel shuffling, as shown in Fig.7. After channel shuffling, the channel order for each task changed accordingly, which validates the effectiveness of our proposed channel shuffling strategy. Additionally, we also visualized the feature perturbations before and after for the $\\mathbf{F}_1$ layer, as shown in Fig.6. As can be seen, after channel dimension perturbation (DGCPM), the network extracts the image's inherent features from multi-degradation scenarios, reducing the impact of degradation-specific features. With the addition of perturbation in the attention dimension (DGCPM+CAAPM), the intrinsic detail features of the image are further enhanced, while the degradation features are more effectively suppressed. This demonstrates the efficacy", + "bbox": [ + 511, + 598, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28171", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e0be6a4e4db7fb1572a3a41d94b7999a2c4228d61c7ff8fcedf4a64b1c71c34d.jpg", + "image_caption": [ + "Figure 6. Feature visualization. DGCPM extracts the intrinsic features of the image while suppressing degradation characteristics. DGCPM + CAAPM enhances intrinsic features while further reducing the impact of degradation. Zoom in for better view." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 480, + 248 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of our proposed channel and attention perturbation strategy.", + "bbox": [ + 89, + 330, + 482, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablations Studies", + "text_level": 1, + "bbox": [ + 89, + 354, + 261, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct several ablation experiments to demonstrate the effectiveness of our proposed degradation-guided perurbation block. We report the results of training an all-in-one model on combined datasets from three restoration tasks. More detailed ablation experiments can be found in the supplementary materials.", + "bbox": [ + 89, + 378, + 482, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of key components. As illustrated in the Tab. 3(a), using channel attention (Method (a)) directly improves by $0.36\\mathrm{dB}$ compared to the baseline [57], but it is $0.15\\mathrm{dB}$ lower than channel shuffle (Method (c)). This also validates the effectiveness of the channel shuffle strategy we proposed. Channel shuffle preserves inherent image features with degradation info but offers limited reduction in cross-degradation interference. By applying attention-wise perturbation, restoration quality is significantly enhanced (DGCPM+CAAPM). The average PSNR increased from 32.49 to 32.88, reflecting an improvement of $0.39\\mathrm{dB}$ . However, Method (b) (CA+CAAPM) results in a lower performance than DFPIR, indicating that the perturbations in channel and attention dimensions produce a synergistic enhancement effect.", + "bbox": [ + 89, + 469, + 482, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of parameter $\\gamma$ . As illustrated in the Tab. 3(b), if the perturbation in the attention dimension is too high ( $\\gamma = 0.5$ ) or absent ( $\\gamma = 1.0$ ), the performance is not optimal. This is because excessive perturbation, while reducing the interference between images with different degradations, increases information loss, leading to suboptimal performance. Similarly, if the perturbation is too small, the interference between tasks becomes more significant, resulting in suboptimal performance as well.", + "bbox": [ + 89, + 696, + 482, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 844, + 209, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a novel all-in-one image restoration framework, DFPIR, which introduces Degradation-", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/503f7c2f2d491d90de4da4c7ba625b1245934e85a90b544420f09026f12dddf2.jpg", + "table_caption": [ + "Table 3. Ablation study results on three tasks. Average PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images. The CA stands for Channel Attention.", + "(a) Impact of key components." + ], + "table_footnote": [], + "table_body": "
MethodCADGCPMCAAPMPSNR/SSIM
baseline×××31.98 / 0.911
(a)✓××32.34 / 0.914
(b)✓×✓32.65 / 0.917
(c)×✓×32.49 / 0.910
DFPIR×✓✓32.88 / 0.919
", + "bbox": [ + 514, + 167, + 759, + 268 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2eeac9a2eb697846aa2fb703ef66b3736cfaf699547c3d0d318f52f8f9257f91.jpg", + "table_caption": [ + "(b) Impact of $\\gamma$" + ], + "table_footnote": [], + "table_body": "
γPSNR / SSIM
0.532.67 / 0.913
0.732.81 / 0.919
0.832.84 / 0.919
0.932.88 / 0.919
1.032.83 / 0.919
", + "bbox": [ + 767, + 167, + 893, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ddefacbba56e202c78d3c95b08110ebb8b6c206288fd36715ef52cab409ab7b4.jpg", + "image_caption": [ + "Figure 7. Channel shuffle visualization. After channel shuffling, the feature channel order for each task has changed compared to the original order." + ], + "image_footnote": [], + "bbox": [ + 514, + 282, + 903, + 406 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "aware Feature Perturbations (DFP) to adjust the feature space in alignment with a unified parameter space. Our approach incorporates both channel-wise and attentionwise perturbations, dynamically guided by degradation type prompts. Specifically, channel-wise perturbations are achieved by shuffling channels in a high-dimensional space, while attention-wise perturbations are implemented through selective masking in the attention space. To effectively realize these operations, we design a Degradation-Guided Perturbation Block (DGPB), which integrates channel shuffling and attention masking, strategically placed between the encoding and decoding stages of the encoder-decoder architecture. The proposed DGPB demonstrates its efficacy in enhancing comprehensive image restoration when integrated into a state-of-the-art model, yielding notable improvements in the all-in-one restoration setting.", + "bbox": [ + 511, + 472, + 906, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgment", + "text_level": 1, + "bbox": [ + 511, + 724, + 684, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China under Grant 62171304 and partly by the Natural Science Foundation of Sichuan Province under Grant 2024NSFSC1423, Cooperation Science and Technology Project of Sichuan University and Dazhou City under Grant 2022CDDZ-09, the TCL Science and Technology Innovation Fund under grant 25JZH008, and the Young Faculty Technology Innovation Capacity Enhancement Program of Sichuan University under Grant 2024SCUQJTX025.", + "bbox": [ + 511, + 750, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28172", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10255-10264, 2019. 1" + ], + "bbox": [ + 516, + 92, + 903, + 203 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "28175", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_model.json b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..44a388a6c716c04e5572173a592768648606ed0e --- /dev/null +++ b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_model.json @@ -0,0 +1,2081 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.119, + 0.131, + 0.88, + 0.154 + ], + "angle": 0, + "content": "Degradation-Aware Feature Perturbation for All-in-One Image Restoration" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.182, + 0.825, + 0.234 + ], + "angle": 0, + "content": "Xiangpeng Tian, Xiangyu Liao, Xiao Liu, Meng Li, Chao Ren* \nCollege of Electronics and Information Engineering, Sichuan University, China \n{tianxp, liaoxiangyul, liux, limeng.scu}@stu.scu.edu.cn, chaoren@scu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.302, + 0.486, + 0.695 + ], + "angle": 0, + "content": "All-in-one image restoration aims to recover clear images from various degradation types and levels with a unified model. Nonetheless, the significant variations among degradation types present challenges for training a universal model, often resulting in task interference, where the gradient update directions of different tasks may diverge due to shared parameters. To address this issue, motivated by the routing strategy, we propose DFPIR, a novel all-in-one image restorer that introduces Degradation-aware Feature Perturbations(DFP) to adjust the feature space to align with the unified parameter space. In this paper, the feature perturbations primarily include channel-wise perturbations and attention-wise perturbations. Specifically, channel-wise perturbations are implemented by shuffling the channels in high-dimensional space guided by degradation types, while attention-wise perturbations are achieved through selective masking in the attention space. To achieve these goals, we propose a Degradation-Guided Perturbation Block (DGPB) to implement these two functions, positioned between the encoding and decoding stages of the encoder-decoder architecture. Extensive experimental results demonstrate that DFPIR achieves state-of-the-art performance on several all-in-one image restoration tasks including image denoising, image dehazing, image deraining, motion deblurring, and low-light image enhancement. Our codes are available at https://github.com/TxpHome/DFPIR." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.727, + 0.222, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.753, + 0.484, + 0.875 + ], + "angle": 0, + "content": "Image restoration, a fundamental task in computer vision, has been widely studied, with a primary focus on addressing individual degradation types, such as noise, haze, rain, or blur. Recently, deep learning-based approaches have achieved remarkable progress in single-degradation restoration tasks, including denoising [15, 26, 35, 36, 42, 61], deraining [2, 17, 22, 48, 54], dehazing [5, 9, 40, 45, 51], and deblurring [7, 19, 37, 37, 60]. While these single-" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.271, + 0.905, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.411, + 0.907, + 0.454 + ], + "angle": 0, + "content": "Figure 1. This figure demonstrates the channel-wise perturbation method of DFPIR, where channel shuffle assigns unique channel orders for different degradation types." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.489, + 0.907, + 0.625 + ], + "angle": 0, + "content": "degradation solutions perform well under specific conditions, they often struggle to generalize effectively to multiple degradation scenarios. Consequently, recent research has shifted toward multi-degradation restoration techniques, delivering state-of-the-art performance for known combinations of degradations [3, 33, 56, 57]. However, these approaches typically require separate networks for each degradation type, leading to large model sizes and high computational demands." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recently, all-in-one approaches(also known as multi-degradation or multi-task image restoration) have gained prominence by addressing multiple image degradations within a unified model [6, 21, 38, 39, 49, 55, 59]. While these methods have achieved state-of-the-art results, they often overlook the relationships and distinctive characteristics among different degradation types due to shared parameters. For example, MedIR [55] demonstrates that the gradient update directions between different tasks are inconsistent or even opposite. According to the characteristics of existing methods, current all-in-one image restoration methods can be roughly divided into two categories: (1) one solution is to modify the parameter space to fit the model for different degradations [21, 38, 49, 59]; (2) and the other solution is to modify the feature space to align with the shared parameter space [8, 39, 55]. Both approaches require incorporating degradation information into the network to mitigate the interference between different degras" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.235, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28165" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.097, + 0.262, + 0.123 + ], + "angle": 0, + "content": "Without attention disturbance: Select all attention maps." + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.126, + 0.264, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.098, + 0.464, + 0.123 + ], + "angle": 0, + "content": "With attention disturbance: Select partial attention maps." + }, + { + "type": "image", + "bbox": [ + 0.31, + 0.125, + 0.462, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.248, + 0.477, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.268, + 0.482, + 0.31 + ], + "angle": 0, + "content": "Figure 2. This figure showcases our attention-wise perturbation, where DFPIR applies attention selection to perturb image features, discarding a portion of attention for each degradation type." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.34, + 0.483, + 0.4 + ], + "angle": 0, + "content": "dations. Although the approach (1) can effectively enhance network performance, it usually requires a large number of additional degradation parameters or a more complex network structure, increasing computational complexity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.402, + 0.483, + 0.734 + ], + "angle": 0, + "content": "Compared to the approach (1), the method (2) is more prevalent in the \"All-in-One\" image restoration framework. The approach (2) typically involves introducing a degradation type prompt, which modulates features to align with the shared network parameters. Specifically, PromptIR [39] conducts multi-degradation processing by introducing additional implicit prompts. However, although this implicit cue in the feature domain utilizes the inherent features of the image, it neglects the influence of degradation types, making it challenging to reduce the mutual influence among multiple degradation types, which ultimately leads to suboptimal results. MedIR [55] introduces multiple experts into the feature space modulation to implement a task-adaptive routing strategy. Although this \"hard\" routing strategy effectively reduces the influence between tasks, it may overlook the inherent features of the image among multiple degradations. InstructIR [8] introduces text commands for multi-task restoration, showcasing the potential of using text prompts to guide image restoration. However, InstructIR [8] modulates features through channel attention using text prompts, which may make it challenging to mitigate the mutual influence among different degradations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.902 + ], + "angle": 0, + "content": "To overcome these challenges, this paper analyzes the design philosophy and rationale behind the success of prompts and presents a degradation-aware feature perturbation approach to adjust the feature space to align with the unified parameter space for all-in-one image restoration. Our method modulates features through perturbations which include channel-wise and attention-wise perturbations to align with shared network parameters or structures, guided by degradation type prompts. Specifically, channel-wise perturbations involve shuffling the channels in high-dimensional space rather than using the conventional" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.257 + ], + "angle": 0, + "content": "channel attention mechanism (see Fig.1). This shuffling approach preserves the inherent features of the image while reducing the mutual influence of degradation features. While attention-wise perturbations involve selectively masking the features after channel shuffling to achieve channel-adapted attention perturbation (see Fig.2). This approach not only preserves the inherent feature information of the image but also adaptively reduces the mutual influence between different degradation types, achieving a good balance between influence and inherent features. The main contributions of our method are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.258, + 0.905, + 0.333 + ], + "angle": 0, + "content": "- We propose a novel degradation-aware feature perturbation all-in-one restoration framework, DFPIR, which adaptively adjusts the feature space in high-dimensional space to align with the unified parameter space, guided by degradation type prompts." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.334, + 0.905, + 0.438 + ], + "angle": 0, + "content": "- We design a Degradation-Guided Perturbation Block (DGPB), consisting of a Degradation-Guided Channel Perturbation Module (DGCPM) and a Channel-Adapted Attention Perturbation Module (CAAPM), to apply perturbation modulation to features along the channel and attention dimensions, aligning with the encoder-decoder architecture with unified parameters." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.44, + 0.905, + 0.514 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that our network achieves state-of-the-art performance in all-in-one image restoration. Especially for all-in-one restoration, 0.45dB PSNR improvement is obtained in comparison with InstructIR [8]." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.334, + 0.905, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.529, + 0.663, + 0.544 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Single Task Image Restoration. Single task image restoration seeks to recover a high-quality image from its low-quality version. Due to the ill-posed nature of the task, early methods primarily focused on designing effective handcrafted priors to constrain the solution space. In contrast, recent deep learning-based approaches have significantly advanced the performance of various image restoration tasks, such as denoising [13, 26, 35, 36, 42, 43], detraining [2, 22, 24, 27, 47], dehazing [5, 9, 29, 40, 45, 51], deblurring [4, 7, 18, 19, 37, 37, 60], and low-light enhancement [12, 31, 52], by learning generalizable priors from large-scale datasets. We focus on general purpose restoration models [3, 25, 57], as these architectures can be independently trained for a variety of tasks. NAFNet [3] simplifies the network structure with lightweight channel attention and gated mechanisms, offering an alternative to non-linear activations. Meanwhile, Restormer [57] leverages transformer architectures to enhance low-level restoration tasks while minimizing computational overhead. In this study, we adopt Restormer [57] as the backbone for our DFPIR model due to its efficient design and high performance across multiple restoration tasks. However, these models are primarily designed for single-degradation scenarios, limiting their ef" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28166" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.122 + ], + "angle": 0, + "content": "fectiveness when applied directly to all-in-one restoration tasks." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.147, + 0.485, + 0.648 + ], + "angle": 0, + "content": "All-In-One Image Restoration. Multi-task image restoration aims to address multiple tasks using the same network design [8, 21, 38, 39, 49, 55, 59]. Compared to single-task image restoration, the key challenge in multi-task image restoration is how to reduce the mutual influence of different degradation features while preserving the inherent features of the image. One approach is to adjust the network's parameter space to accommodate different degradation types. Several works have explored these strategies to handle diverse degradations. Li et al. [23] introduce a single-encoder, multi-decoder framework targeting weather-based degradations using the Rain-Haze-Snow dataset. Chen et al. [6] propose a two-stage knowledge transfer mechanism, employing a multi-teacher, single-student approach to handle various degradation types. Li et al. [21] propose an all-in-one framework capable of restoring multiple degraded images without requiring prior knowledge of degradation types or levels. Zhang et al. [59] propose an ingredient-oriented strategy that supports up to five restoration tasks within a single model, significantly enhancing scalability. Similarly, Zhang et al. [58] introduce a representation learning network guided by degradation classification, using its strong classification capabilities to effectively steer the restoration process. Another approach is to introduce image or degradation prompts to modulate the features, adapting to a unified parameter space [8, 39, 55]. PromptIR [39] encodes degradation-specific information through prompts, using them to dynamically guide the restoration network. In contrast, InstructIR [8] allows for model-driven image editing based on instructions that specify the desired actions, rather than relying on text labels, captions, or descriptions of input and output images." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.663, + 0.265, + 0.68 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In \"All-In-One\" image restoration, the objective is to develop a single model \\(\\mathbf{M}\\) capable of restoring a clean image \\(\\hat{\\mathbf{I}}\\) from a degraded input image \\(\\mathbf{I}\\) affected by a degradation \\(\\mathbf{D}\\). Within this framework, under the same network parameters and architecture, different types of degradation mutually influence each other. For example, degraded images contain both inherent image features and degradation features. While inherent image features help the network learn latent parameters, thereby enhancing restoration performance, degradation features may negatively impact each other, reducing restoration effectiveness. In order to fully utilize the inherent features of the image while reducing the influence of different degradation features, motivated by the \"hard\" routing strategy [55] and PromptIR [39], we propose" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.09, + 0.695, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.729, + 0.092, + 0.899, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.193, + 0.64, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.228, + 0.625, + 0.24 + ], + "angle": 0, + "content": "Noisy: CBSD68" + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.193, + 0.772, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.655, + 0.228, + 0.758, + 0.24 + ], + "angle": 0, + "content": "Rainy: Rain100L" + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.193, + 0.902, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.228, + 0.869, + 0.24 + ], + "angle": 0, + "content": "Hazy: SOTS" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.244, + 0.907, + 0.328 + ], + "angle": 0, + "content": "Figure 3. The figure provides t-SNE plots of the intermediate features from DFPIR (our method) and PromptIR on the test datasets (CBSD68, Rain100L, and SOTS) under the three-task setting. In our model, the features for each task exhibit tighter clustering, highlighting the effectiveness of our degradation-aware feature perturbation strategy in enhancing restoration performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.354, + 0.907, + 0.55 + ], + "angle": 0, + "content": "a degradation-aware feature perturbation modulation network, DFPIR, that adjusts the feature space through perturbation modulation to align with the shared-parameter network structure, thereby enhancing multi-degradation image restoration performance. The perturbation is divided into two parts: channel-wise perturbation and attention-wise perturbation. Channel-wise perturbation is implemented through channel shuffle, while attention-wise perturbation is achieved by selecting a portion of the attention maps. The details of these two perturbation mechanisms are provided in Section 3.3. The pipeline of the proposed DFPIR framework is illustrated in Fig.4. In the following sections, we describe the overall structure of DFPIR in detail." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.561, + 0.674, + 0.577 + ], + "angle": 0, + "content": "3.1. Overall Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Given a degraded input image \\(\\mathbf{I} \\in R^{H \\times W \\times 3}\\), the DFPIR initially extracts shallow features \\(\\mathbf{F_0} \\in R^{H \\times W \\times C}\\) using a \\(3 \\times 3\\) convolution layer; where \\(H \\times W\\) is the spatial size and \\(C\\) denotes the channels. Next, these features \\(\\mathbf{F_0}\\) undergo a 4-level encoder-decoder network, transforming into deep features \\(\\mathbf{F_r} \\in R^{H \\times W \\times 2C}\\). Each level of the encoder-decoder employs multiple Transformer blocks [57], where the number of blocks gradually increases from the top level to the bottom level, facilitating a computationally efficient design. Beginning with the high-resolution input, the encoder aims to gradually decrease spatial resolution while increasing channel capacity, resulting in a low-resolution latent representation \\(\\mathbf{F_e} \\in R^{\\frac{H}{8} \\times \\frac{W}{8} \\times 8C}\\). Given the low-resolution latent features \\(\\mathbf{F_e}\\), the objective of the decoder is to progressively restore the high-resolution clean output. To assist the recovery process, the encoder features are concatenated with the decoder features via skip connections [44]. We insert our Degradation-Guided Perturbation Block (DGPB) between the encoder and decoder, specifically within the skip-connection stage, to perturb the encoded feature space, which is guided by degradation type" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28167" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.904, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.429, + 0.907, + 0.513 + ], + "angle": 0, + "content": "Figure 4. Overview of the DFPIR framework. We employ Restormer [57], an encoder-decoder network with transformer blocks in the encoding and decoding stages, as our backbone. The primary component of the framework, the Degradation-Guided Perturbation Block (DGPB), consists of two submodules, i.e., Degradation-Guided Channel Perturbation Module (DGCPM) and Channel-Adapted Attention Perturbation Module (CAAPM). The DGCPM module introduces conventional dimensional perturbations to image features in the form of channel shuffling, guided by degradation-type prompts. The CAAPM module applies attention perturbation to the channel-shuffled features through a top-K masking strategy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.54, + 0.483, + 0.614 + ], + "angle": 0, + "content": "prompts, and align it with the shared-parameter decoder. To obtain degradation type prompts, we utilize a pre-trained CLIP [41] model to encode the textual degradation type descriptions. In the following sections, we describe the proposed DGPB and its core building modules in detail." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.624, + 0.483, + 0.654 + ], + "angle": 0, + "content": "3.2. Degradation-Guided Perturbation Block (DGPB)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.662, + 0.483, + 0.801 + ], + "angle": 0, + "content": "In all-in-one setting, shared parameters are challenging to handle all-in-one image restoration effectively. We specifically design a Degradation-Guided Perturbation Block (DGPB) to apply perturbations to the encoded features, better aligning them with the shared decoder in multi-task scenarios, guided by the degradation type prompts (as shown in Fig.4). Given as inputs both the image feature \\(\\mathbf{F_n} \\in R^{\\widehat{H} \\times \\widehat{W} \\times \\widehat{C}}\\) and degradation type prompts \\(\\mathbf{P_e} \\in T^{\\widehat{L} \\times 1}\\), the overall process of DGPB is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.813, + 0.483, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F _ {b}} = \\operatorname {C A A P M} (\\operatorname {D G C P M} (\\mathbf {F _ {n}}, \\operatorname {D G M} (\\mathbf {P _ {e}})), \\mathbf {F _ {n}}) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{F_n}\\) represents the encoder output. The DGPB comprises two core components: the Degradation-Guided Channel Perturbation Module (DGCPM) and the Channel-Adapted Attention Perturbation Module (CAAPM)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.539, + 0.907, + 0.569 + ], + "angle": 0, + "content": "3.2.1 Degradation-Guided Channel Perturbation Module (DGCPM)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In DGCPM, the objective is to add perturbations to the feature channels through channel shuffling, guided by degradation type prompts. However, directly shuffling the channels on the feature \\(\\mathbf{F_n}\\) may make it difficult to converge due to excessive perturbation and may also affect the quality of the reconstruction. To address this issue, we initially expand the number of channels in the image feature \\(\\mathbf{F_n}\\) by \\(2\\mathrm{x}\\) to introduce channel perturbations in a higher-dimensional channel space, guided by the Degradation Guidance Module(DGM). After channel expansion, the size of feature \\(\\mathbf{F_n}\\) becomes \\(\\mathbf{F}_{2\\mathbf{n}}\\in R^{\\widehat{H}\\times \\widehat{W}\\times 2\\widehat{C}}\\) . In DGM, the degradation type prompts \\((\\mathbf{P_e})\\) are used to adaptively apply channel shuffle. To maintain the dimensionality of \\(\\mathbf{P_e}\\) consistent with the channel dimensionality of \\(\\mathbf{F_{2n}}\\) , we employ a Multi-Layer Perceptron (MLP) which consisting of two linear layers to achieve dimension matching. Thus, MLP transforms the input feature \\(\\mathbf{P_e}\\) into \\(\\mathbf{P_{ec}}\\in T^{2\\widehat{C}\\times 1}\\) . For degradation type prompts, see the supplementary document. In channel shuffle stage, we get the index value corresponding to the top- \\(\\mathrm{K}(\\mathrm{K} = 2\\widehat{\\mathrm{C}})\\) value of \\(\\mathbf{P_{ec}}\\) , and use these index values to reorder the channels. Finally, halve the number of channels" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28168" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.119 + ], + "angle": 0, + "content": "Table 1. Comparison to state-of-the-art on three tasks. PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images. On average PSNR, our DFPIR provides a significant gain of 0.45 dB over the previous all-in-one method InstructIR [8]." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.128, + 0.907, + 0.287 + ], + "angle": 0, + "content": "
MethodDehazing on SOTSDeraining on Rain100LDenoising on CBSD68 datasetAverage
σ = 15σ = 25σ = 50
DL [11]26.92 / 0.39132.62 / 0.93133.05 / 0.91430.41 / 0.86126.90 / 0.74029.98 / 0.875
FDGAN [10]24.71 / 0.92429.89 / 0.93330.25 / 0.91028.81 / 0.86826.43 / 0.77628.02 / 0.883
MPRNet [56]25.28 / 0.95433.57 / 0.95433.54 / 0.92730.89 / 0.88027.56 / 0.77930.17 / 0.899
AirNet [21]27.94 / 0.96234.90 / 0.96733.92 / 0.93331.26 / 0.88828.00 / 0.79731.20 / 0.910
Restormer [57]30.43 / 0.97536.55 / 0.97533.84 / 0.93131.18 / 0.88527.90 / 0.79031.98 / 0.911
PromptIR [39]30.58 / 0.97436.37 / 0.97233.98 / 0.93331.31 / 0.88828.06 / 0.79932.06 / 0.913
InstructIR [8]30.22 / 0.95937.98 / 0.97834.15 / 0.93331.52 / 0.89028.30 / 0.80432.43 / 0.913
DFPIR(Ours)31.87 / 0.98038.65 / 0.98234.14 / 0.93531.47 / 0.89328.25 / 0.80632.88 / 0.919
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.31, + 0.482, + 0.355 + ], + "angle": 0, + "content": "after the shuffle to keep the channel count consistent before and after the transformation. Overall, the DGCPM process is summarized as:" + }, + { + "type": "equation", + "bbox": [ + 0.119, + 0.364, + 0.483, + 0.382 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} = \\operatorname {C o n v h} \\left(\\mathbf {C S} _ {\\text {t o p} K} \\left(\\operatorname {C o n v k} \\left(\\mathbf {F} _ {\\mathbf {n}}\\right) | \\mathrm {D G M} \\left(\\mathbf {P} _ {\\mathbf {e}}\\right)\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.389, + 0.484, + 0.468 + ], + "angle": 0, + "content": "where the operation \\(\\mathbf{CStopK}(\\bullet|\\mathrm{DGM}(\\mathbf{Pe}))\\) denotes top-K channel shuffling guided by \\(\\mathrm{DGM}(\\mathbf{P_e})\\), while Convk (\\(\\bullet\\)) and Convh (\\(\\bullet\\)) represent the operations of doubling and halving the feature channels, respectively. After DGCPM, we obtain feature \\(\\mathbf{Q} \\in R^{\\widehat{H} \\times \\widehat{W} \\times \\widehat{C}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.485, + 0.484, + 0.515 + ], + "angle": 0, + "content": "3.2.2 Channel-Adapted Attention Perturbation Module(CAAPM)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.524, + 0.484, + 0.786 + ], + "angle": 0, + "content": "Although the shuffled features can adapt well to specific degradations, directly using them for reconstruction may not yield optimal results. This is because the shuffled features carry degradation-type information but lack interaction with the original feature information. To address this, we designed the Channel-Adapted Attention Perturbation Module (CAAPM). CAAPM has two main functions: facilitating information interaction between the shuffled and original features, and adding perturbations in the attention dimension. Motivated by Restormer [57], we design a cross-attention mechanism in the channel dimension to aggregate the shuffled and original features. To add perturbations to the attention map, we introduce a mask matrix \\(\\mathbf{M} \\in R^{\\widehat{C} \\times \\widehat{C}}\\) to select part of the attention map from each row using a top-K approach with a perturbation factor parameter \\(\\gamma\\). The process of obtaining the perturbed attention map \\(\\mathbf{PAM} \\in R^{\\widehat{H}\\widehat{W} \\times \\widehat{C}}\\) can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.793, + 0.483, + 0.819 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P A M} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {s o f t m a x} (\\mathbf {M} \\odot (\\mathbf {Q} _ {*} \\mathbf {K} _ {*} ^ {T} / \\sqrt {d _ {k}})) \\mathbf {V} _ {*} (3)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where the query \\(\\mathbf{Q}_{*}\\) is derived from shuffled feature \\(\\mathbf{Q}\\), and the key \\(\\mathbf{K}_{*}\\) and value \\(\\mathbf{V}_{*}\\) are derived from original features \\(\\mathbf{F_{n}}\\). \\(\\mathbf{M}\\) represents the selection mask matrix. \\(\\odot\\) represents the element-wise multiplication. Then, we use a \\(1\\times 1\\) convolution to obtain the feature \\(\\mathbf{F_{a}}\\) with attention perturbations." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.31, + 0.905, + 0.34 + ], + "angle": 0, + "content": "Finally, we obtain the final output through an FFN network. This can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.353, + 0.907, + 0.37 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {\\mathbf {b}} = \\mathbf {F} _ {\\mathbf {a}} + \\operatorname {F F N} \\left(\\mathbf {F} _ {\\mathbf {a}}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.381, + 0.907, + 0.487 + ], + "angle": 0, + "content": "The selection of the perturbation factor \\(\\gamma\\) needs to comprehensively consider the extent of interference magnitude between tasks and information loss. Fig.4 illustrates the relationship between \\(\\gamma\\), interference size, and information loss. In our paper, the parameter is \\(\\gamma\\) fixed at 0.9, and the ablation study presents the experimental results for different values of \\(\\gamma\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.496, + 0.905, + 0.513 + ], + "angle": 0, + "content": "3.3. Analysis of Our Feature Perturbation Strategy" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.906, + 0.611 + ], + "angle": 0, + "content": "The task-aware feature perturbation strategy we propose involves both channel and attention dimensions. By perturbing these two dimensions, it not only preserves the inherent features of the image but also reduces the mutual influence of degradation features. Fig.3 illustrates that our model excels in learning discriminative degradation contexts." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Channel-wise Perturbation Strategy. Directly performing channel shuffle in a low-dimensional space causes excessive perturbation, making network training difficult to converge. Therefore, we propose a degradation-aware adaptive channel shuffle strategy (as shown in Fig.1), which adaptively reorders the feature channels for each task in a high-dimensional feature space. Given a image feature which contains \\(N\\) channels \\(\\mathbf{F_{nc}} = \\{C_1,C_2,\\dots ,C_r,\\dots ,C_N\\} (\\mathrm{r}\\leq N)\\) and M tasks, our channel shuffle strategy adopts different channel orders for each degradation restoration task. For any given task \\(\\mathrm{T_m(m\\leq M)}\\), the channel index vector after channel shuffle is defined as \\(\\mathbf{S}^N = \\{S_1^N,S_2^N,\\dots ,S_N^N\\}\\). Finally, the feature obtained after channel shuffle is \\(\\mathbf{F}_{\\mathbf{m}} = \\{C_{S_1^N},C_{S_2^N},\\dots ,C_{S_N^N}\\}\\). The adjustment of this channel order is adaptively random under the guidance of degradation prompts. This random adaptive shuffle strategy reduces interference between feature channels while preserving the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28169" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.119 + ], + "angle": 0, + "content": "Table 2. Comparison to state-of-the-art on five tasks. PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images with (*) denoting general image restorers, others are specialized all-in-one approaches. Denoising results are reported for the noise level \\( \\sigma = 25 \\)." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.128, + 0.905, + 0.332 + ], + "angle": 0, + "content": "
MethodDehazing on SOTSDeraining on Rain100LDenoising on CBSD68Deblurring on GoproLow-light Enh. on LOLAverage
DGUNet* [33]24.78 / 0.94036.62 / 0.97131.10 / 0.88327.25 / 0.83721.87 / 0.82328.32 / 0.891
SwinIR* [25]21.50 / 0.89130.78 / 0.92330.59 / 0.86824.52 / 0.77317.81 / 0.72325.04 / 0.835
Restomer* [57]24.09 / 0.92734.81 / 0.96231.49 / 0.88427.22 / 0.82920.41 / 0.80627.60 / 0.881
NAFNet* [3]25.23 / 0.93935.56 / 0.96731.02 / 0.88326.53 / 0.80820.49 / 0.80927.76 / 0.881
DL [11]20.54 / 0.82621.96 / 0.76223.09 / 0.74519.86 / 0.67219.83 / 0.71221.05 / 0.743
Transweather [46]21.32 / 0.88529.43 / 0.90529.00 / 0.84125.12 / 0.75721.21 / 0.79225.22 / 0.836
TAPE [28]22.16 / 0.86129.67 / 0.90430.18 / 0.85524.47 / 0.76318.97 / 0.62125.09 / 0.801
AirNet [21]21.04 / 0.88432.98 / 0.95130.91 / 0.88224.35 / 0.78118.18 / 0.73525.49 / 0.846
IDR [59]25.24 / 0.94335.63 / 0.96531.60 / 0.88727.87 / 0.84621.34 / 0.82628.34 / 0.893
InstructIR [8]27.10 / 0.95636.84 / 0.97331.40 / 0.88729.40 / 0.88623.00 / 0.83629.55 / 0.907
DFPIR(Ours)31.64 / 0.97937.62 / 0.97831.29 / 0.88928.82 / 0.87323.82 / 0.84330.64 / 0.913
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.356, + 0.483, + 0.403 + ], + "angle": 0, + "content": "inherent characteristics of the image (as channel shuffling does not result in channel feature loss), thereby improving reconstruction quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.42, + 0.484, + 0.683 + ], + "angle": 0, + "content": "Attention-wise Perturbation Strategy. The main purpose of channel shuffle is to minimize the influence of degradation features while preserving the inherent characteristics of the image. However, this reduction is not thorough enough, meaning its effectiveness is limited. To address this, we directly discard a portion of the attention in the attention maps to further mitigate the impact of multiple degradation features (as shown in Fig.2). Specifically, we compute the transposed cross attention map \\(\\mathbf{A}_{tt} \\in R^{\\widehat{C} \\times \\widehat{C}}\\). We select a portion of the attention map values from each column of \\(\\mathbf{A}_{tt}\\) using the top-K method to generate a disturbance mask matrix \\(\\mathbf{M} \\in R^{\\widehat{C} \\times \\widehat{C}}\\), where the values that are not selected are set to 0, and the remaining values are set to 1. Then, the matrix \\(\\mathbf{M}\\) is multiplied element-wise with \\(\\mathbf{A}_{tt}\\) to obtain a new attention map \\(\\mathbf{A}_{ttn}\\), achieving perturbation in the attention dimension. In other words, \\(\\mathbf{A}_{ttn} = \\mathbf{A}_{tt} \\odot \\mathbf{M}\\), where \\(\\mathbf{A}_{tt}\\) is \\(\\mathbf{Q}_*\\mathbf{K}_*^T / \\sqrt{d_k}\\) in equation 3." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.695, + 0.224, + 0.712 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this section, we follow the protocols of prior state-of-the-art works [21, 39] to conduct experiments under two settings: (a) all-in-one and (b) single-task. For the all-in-one setting, a unified model is trained to handle multiple degradation types, with experiments conducted across three and five distinct degradations. In contrast, the single-task setting involves training separate models, each specialized for a specific restoration task. The image quality metrics—PSNR and SSIM [16]—for the top-performing methods are highlighted in red and the second-best results are highlighted in blue in the result tables. Single-task results and more visual experiments are in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.355, + 0.722, + 0.372 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.39, + 0.907, + 0.588 + ], + "angle": 0, + "content": "Datasets. In line with previous work [21, 39], we prepare datasets tailored for various restoration tasks. For single-task image denoising, we merge images from the BSD400 [1] and WED [30] datasets to train the model. Testing is conducted on the CBSD68 [32] and Urban100 [14] datasets. For image dehazing, we use the SOTS [20] dataset, while Rain100L [53] is employed for image deraining. Deblurring and low-light enhancement tasks utilize the GoPro [34] and LOL-v1 [34] datasets, respectively. In the all-in-one setting, a unified model is trained on the combined training datasets mentioned above and tested directly across multiple restoration tasks. Additional dataset details can be found in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Implementation Details. Our DFPIR provides an end-to-end trainable solution, removing the necessity for pretraining any individual components. Following the configuration of PromptIR [39], our DFPIR architecture features a 4-level encoder-decoder structure, comprising varying numbers of Transformer blocks at each level, specifically [4, 6, 6, 8] from level-1 to level-4. We integrate our Degradation-Guided Perturbation Block (DGPB) between the encoder and decoder, with a total of four DGPBs distributed throughout the network. We conduct our experiments using PyTorch on a single NVIDIA GeForce RTX 3090 GPU. For training, we run for 80 epochs with an initial learning rate of \\(1e^{-4}\\), followed by fine-tuning for 5 epochs at a learning rate of \\(1e^{-5}\\). Initially, we set the patch size to \\(128^2\\) with the batch size of 5, and for fine-tuning, the patch size is adjusted to \\(192^2\\) with a batch size of 3. The network is optimized using the L1 loss function in conjunction with the Adam optimizer (with parameters \\(\\beta_{1} = 0.9\\) and \\(\\beta_{2} = 0.999\\)). We train on cropped patches and augment the dataset with random horizontal and vertical flips." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28170" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.383, + 0.908, + 0.41 + ], + "angle": 0, + "content": "Figure 5. Visual comparison of DFPIR with state-of-the-art methods on challenging cases for the All-in-One setting considering three degradations. Zoom in for better view." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.436, + 0.411, + 0.452 + ], + "angle": 0, + "content": "4.2. Results Comparisons on Three Tasks" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.46, + 0.483, + 0.686 + ], + "angle": 0, + "content": "We assess the performance of our all-in-one DFPIR across three distinct restoration tasks: dehazing, deraining, and denoising. Our DFPIR is compared with various general image restoration methods, including Restormer [57], FDGAN [10], and MPRNet [56], as well as specialized all-in-one approaches such as DL [11], AirNet [21], PromptIR [39], and InstructIR [8]. As shown in Tab. 1, the proposed DFPIR consistently outperforms the other competing methods. On average across the different restoration tasks, our algorithm achieves a performance improvement of \\(0.45\\mathrm{dB}\\) over the previous best method, InstructIR [8], and \\(0.82\\mathrm{dB}\\) over the second-best approach, PromptIR [39]. Specifically, DFPIR demonstrates a notable increase of \\(0.67\\mathrm{dB}\\) on the deraining task and \\(1.65\\mathrm{dB}\\) on the dehazing task compared to InstructIR [8]." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.696, + 0.398, + 0.712 + ], + "angle": 0, + "content": "4.3. Results Comparisons on Five Tasks" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.72, + 0.483, + 0.9 + ], + "angle": 0, + "content": "To further validate the method's effectiveness in addressing a broader range of tasks, building upon the recent research conducted by IDR [59] and InstructIR [8], we extend our investigation into the efficacy of DFPIR by conducting experiments across five restoration tasks: dehazing, deraining, denoising, deblurring, and low-light image enhancement. To achieve this, we train a comprehensive DFPIR on combined datasets compiled for five distinct tasks. These encompass datasets from the previously mentioned threetask scenario, alongside additional datasets: GoPro [34] for motion deblurring and LOL [50] for low-light image enhancement. Tab. 2 demonstrates that DFPIR achieves a 1.09" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.437, + 0.907, + 0.558 + ], + "angle": 0, + "content": "dB improvement compared to the recent leading method InstructIR [8], when averaged across five restoration tasks. Additionally, we compare our method to general image restoration models that were trained in the same All-in-One setting. Notably, our method surpasses Restormer[57] and NAFNet [3] on average PSNR by 3.04 dB and 2.88 dB, respectively, validating the effectiveness of our approach in handling multiple degradations." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.573, + 0.661, + 0.588 + ], + "angle": 0, + "content": "4.4. Visual Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Visual examples illustrating our results for dehazing, de- raining, and denoising are provided in Fig.5. Compared to PromptIR [39] and InstructIR [8], our method is more effective in challenging dehazing scenarios. Additionally, our model's deraining results are closer to the ground-truth images. Furthermore, in image denoising, our model recovers more details from heavily degraded noisy inputs. We visualized the results of channel shuffling, as shown in Fig.7. After channel shuffling, the channel order for each task changed accordingly, which validates the effectiveness of our proposed channel shuffling strategy. Additionally, we also visualized the feature perturbations before and after for the \\(\\mathbf{F}_1\\) layer, as shown in Fig.6. As can be seen, after channel dimension perturbation (DGCPM), the network extracts the image's inherent features from multi-degradation scenarios, reducing the impact of degradation-specific features. With the addition of perturbation in the attention dimension (DGCPM+CAAPM), the intrinsic detail features of the image are further enhanced, while the degradation features are more effectively suppressed. This demonstrates the efficacy" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28171" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.482, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.25, + 0.483, + 0.306 + ], + "angle": 0, + "content": "Figure 6. Feature visualization. DGCPM extracts the intrinsic features of the image while suppressing degradation characteristics. DGCPM + CAAPM enhances intrinsic features while further reducing the impact of degradation. Zoom in for better view." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.331, + 0.483, + 0.348 + ], + "angle": 0, + "content": "of our proposed channel and attention perturbation strategy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.356, + 0.262, + 0.371 + ], + "angle": 0, + "content": "4.5. Ablations Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.379, + 0.483, + 0.469 + ], + "angle": 0, + "content": "We conduct several ablation experiments to demonstrate the effectiveness of our proposed degradation-guided perurbation block. We report the results of training an all-in-one model on combined datasets from three restoration tasks. More detailed ablation experiments can be found in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.47, + 0.483, + 0.695 + ], + "angle": 0, + "content": "Impact of key components. As illustrated in the Tab. 3(a), using channel attention (Method (a)) directly improves by \\(0.36\\mathrm{dB}\\) compared to the baseline [57], but it is \\(0.15\\mathrm{dB}\\) lower than channel shuffle (Method (c)). This also validates the effectiveness of the channel shuffle strategy we proposed. Channel shuffle preserves inherent image features with degradation info but offers limited reduction in cross-degradation interference. By applying attention-wise perturbation, restoration quality is significantly enhanced (DGCPM+CAAPM). The average PSNR increased from 32.49 to 32.88, reflecting an improvement of \\(0.39\\mathrm{dB}\\). However, Method (b) (CA+CAAPM) results in a lower performance than DFPIR, indicating that the perturbations in channel and attention dimensions produce a synergistic enhancement effect." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.697, + 0.483, + 0.833 + ], + "angle": 0, + "content": "Impact of parameter \\(\\gamma\\). As illustrated in the Tab. 3(b), if the perturbation in the attention dimension is too high (\\(\\gamma = 0.5\\)) or absent (\\(\\gamma = 1.0\\)), the performance is not optimal. This is because excessive perturbation, while reducing the interference between images with different degradations, increases information loss, leading to suboptimal performance. Similarly, if the perturbation is too small, the interference between tasks becomes more significant, resulting in suboptimal performance as well." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.845, + 0.21, + 0.861 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this paper, we present a novel all-in-one image restoration framework, DFPIR, which introduces Degradation-" + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.089, + 0.907, + 0.131 + ], + "angle": 0, + "content": "Table 3. Ablation study results on three tasks. Average PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images. The CA stands for Channel Attention." + }, + { + "type": "table_caption", + "bbox": [ + 0.536, + 0.144, + 0.717, + 0.158 + ], + "angle": 0, + "content": "(a) Impact of key components." + }, + { + "type": "table_caption", + "bbox": [ + 0.783, + 0.144, + 0.878, + 0.158 + ], + "angle": 0, + "content": "(b) Impact of \\(\\gamma\\)" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.169, + 0.761, + 0.269 + ], + "angle": 0, + "content": "
MethodCADGCPMCAAPMPSNR/SSIM
baseline×××31.98 / 0.911
(a)✓××32.34 / 0.914
(b)✓×✓32.65 / 0.917
(c)×✓×32.49 / 0.910
DFPIR×✓✓32.88 / 0.919
" + }, + { + "type": "table", + "bbox": [ + 0.768, + 0.169, + 0.895, + 0.269 + ], + "angle": 0, + "content": "
γPSNR / SSIM
0.532.67 / 0.913
0.732.81 / 0.919
0.832.84 / 0.919
0.932.88 / 0.919
1.032.83 / 0.919
" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.283, + 0.905, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.407, + 0.907, + 0.448 + ], + "angle": 0, + "content": "Figure 7. Channel shuffle visualization. After channel shuffling, the feature channel order for each task has changed compared to the original order." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.473, + 0.907, + 0.716 + ], + "angle": 0, + "content": "aware Feature Perturbations (DFP) to adjust the feature space in alignment with a unified parameter space. Our approach incorporates both channel-wise and attentionwise perturbations, dynamically guided by degradation type prompts. Specifically, channel-wise perturbations are achieved by shuffling channels in a high-dimensional space, while attention-wise perturbations are implemented through selective masking in the attention space. To effectively realize these operations, we design a Degradation-Guided Perturbation Block (DGPB), which integrates channel shuffling and attention masking, strategically placed between the encoding and decoding stages of the encoder-decoder architecture. The proposed DGPB demonstrates its efficacy in enhancing comprehensive image restoration when integrated into a state-of-the-art model, yielding notable improvements in the all-in-one restoration setting." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.725, + 0.685, + 0.743 + ], + "angle": 0, + "content": "6. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.901 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China under Grant 62171304 and partly by the Natural Science Foundation of Sichuan Province under Grant 2024NSFSC1423, Cooperation Science and Technology Project of Sichuan University and Dazhou City under Grant 2022CDDZ-09, the TCL Science and Technology Innovation Fund under grant 25JZH008, and the Young Faculty Technology Innovation Capacity Enhancement Program of Sichuan University under Grant 2024SCUQJTX025." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28172" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. 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In Proceedings of the IEEE/CVF conference on" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.092, + 0.483, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "ref_text", + "bbox": [ + 0.548, + 0.093, + 0.905, + 0.119 + ], + "angle": 0, + "content": "computer vision and pattern recognition, pages 2737-2746, 2020.1,2" + }, + { + "type": "ref_text", + "bbox": [ + 0.517, + 0.121, + 0.905, + 0.204 + ], + "angle": 0, + "content": "[61] Magaiya Zhussip, Shakarim Soltanayev, and Se Young Chun. Training deep learning based image denoisers from undersampled measurements without ground truth and without image prior. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10255-10264, 2019. 1" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "28175" + } + ] +] \ No newline at end of file diff --git a/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_origin.pdf b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9aebffa57fe7dd8cf9e30ce74fde14deb8c007ff --- /dev/null +++ b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/dd15326b-1f78-4e60-9709-e2819267a8c5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f767756cab2d317057612f15359d4c3bcc03a5b94cb76372b2ca32b0b9c2792d +size 2188552 diff --git a/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/full.md b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..13c09d79a08e9e471931c68d98b77d54169f17bf --- /dev/null +++ b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/full.md @@ -0,0 +1,270 @@ +# Degradation-Aware Feature Perturbation for All-in-One Image Restoration + +Xiangpeng Tian, Xiangyu Liao, Xiao Liu, Meng Li, Chao Ren* +College of Electronics and Information Engineering, Sichuan University, China +{tianxp, liaoxiangyul, liux, limeng.scu}@stu.scu.edu.cn, chaoren@scu.edu.cn + +# Abstract + +All-in-one image restoration aims to recover clear images from various degradation types and levels with a unified model. Nonetheless, the significant variations among degradation types present challenges for training a universal model, often resulting in task interference, where the gradient update directions of different tasks may diverge due to shared parameters. To address this issue, motivated by the routing strategy, we propose DFPIR, a novel all-in-one image restorer that introduces Degradation-aware Feature Perturbations(DFP) to adjust the feature space to align with the unified parameter space. In this paper, the feature perturbations primarily include channel-wise perturbations and attention-wise perturbations. Specifically, channel-wise perturbations are implemented by shuffling the channels in high-dimensional space guided by degradation types, while attention-wise perturbations are achieved through selective masking in the attention space. To achieve these goals, we propose a Degradation-Guided Perturbation Block (DGPB) to implement these two functions, positioned between the encoding and decoding stages of the encoder-decoder architecture. Extensive experimental results demonstrate that DFPIR achieves state-of-the-art performance on several all-in-one image restoration tasks including image denoising, image dehazing, image deraining, motion deblurring, and low-light image enhancement. Our codes are available at https://github.com/TxpHome/DFPIR. + +# 1. Introduction + +Image restoration, a fundamental task in computer vision, has been widely studied, with a primary focus on addressing individual degradation types, such as noise, haze, rain, or blur. Recently, deep learning-based approaches have achieved remarkable progress in single-degradation restoration tasks, including denoising [15, 26, 35, 36, 42, 61], deraining [2, 17, 22, 48, 54], dehazing [5, 9, 40, 45, 51], and deblurring [7, 19, 37, 37, 60]. While these single- + +![](images/2e84e4e7408236d6469ddb43aa4924c222e57fda975d2dde6a9a5ac3f09638c4.jpg) +Figure 1. This figure demonstrates the channel-wise perturbation method of DFPIR, where channel shuffle assigns unique channel orders for different degradation types. + +degradation solutions perform well under specific conditions, they often struggle to generalize effectively to multiple degradation scenarios. Consequently, recent research has shifted toward multi-degradation restoration techniques, delivering state-of-the-art performance for known combinations of degradations [3, 33, 56, 57]. However, these approaches typically require separate networks for each degradation type, leading to large model sizes and high computational demands. + +Recently, all-in-one approaches(also known as multi-degradation or multi-task image restoration) have gained prominence by addressing multiple image degradations within a unified model [6, 21, 38, 39, 49, 55, 59]. While these methods have achieved state-of-the-art results, they often overlook the relationships and distinctive characteristics among different degradation types due to shared parameters. For example, MedIR [55] demonstrates that the gradient update directions between different tasks are inconsistent or even opposite. According to the characteristics of existing methods, current all-in-one image restoration methods can be roughly divided into two categories: (1) one solution is to modify the parameter space to fit the model for different degradations [21, 38, 49, 59]; (2) and the other solution is to modify the feature space to align with the shared parameter space [8, 39, 55]. Both approaches require incorporating degradation information into the network to mitigate the interference between different degras + +![](images/ce12d81db4d13d5a5a88a4ec631eff8aa58a7a829399ea71a4008b0ca21ea86a.jpg) +Without attention disturbance: Select all attention maps. + +![](images/6c6b59ee92b42ef29baa71d45038cf18e5d5fca980f043ca29a1a14191faaf26.jpg) +With attention disturbance: Select partial attention maps. + +![](images/05174b5e62c78d6233d2594e558d7b470c08010641b89eebc164ba727875f283.jpg) +Figure 2. This figure showcases our attention-wise perturbation, where DFPIR applies attention selection to perturb image features, discarding a portion of attention for each degradation type. + +dations. Although the approach (1) can effectively enhance network performance, it usually requires a large number of additional degradation parameters or a more complex network structure, increasing computational complexity. + +Compared to the approach (1), the method (2) is more prevalent in the "All-in-One" image restoration framework. The approach (2) typically involves introducing a degradation type prompt, which modulates features to align with the shared network parameters. Specifically, PromptIR [39] conducts multi-degradation processing by introducing additional implicit prompts. However, although this implicit cue in the feature domain utilizes the inherent features of the image, it neglects the influence of degradation types, making it challenging to reduce the mutual influence among multiple degradation types, which ultimately leads to suboptimal results. MedIR [55] introduces multiple experts into the feature space modulation to implement a task-adaptive routing strategy. Although this "hard" routing strategy effectively reduces the influence between tasks, it may overlook the inherent features of the image among multiple degradations. InstructIR [8] introduces text commands for multi-task restoration, showcasing the potential of using text prompts to guide image restoration. However, InstructIR [8] modulates features through channel attention using text prompts, which may make it challenging to mitigate the mutual influence among different degradations. + +To overcome these challenges, this paper analyzes the design philosophy and rationale behind the success of prompts and presents a degradation-aware feature perturbation approach to adjust the feature space to align with the unified parameter space for all-in-one image restoration. Our method modulates features through perturbations which include channel-wise and attention-wise perturbations to align with shared network parameters or structures, guided by degradation type prompts. Specifically, channel-wise perturbations involve shuffling the channels in high-dimensional space rather than using the conventional + +channel attention mechanism (see Fig.1). This shuffling approach preserves the inherent features of the image while reducing the mutual influence of degradation features. While attention-wise perturbations involve selectively masking the features after channel shuffling to achieve channel-adapted attention perturbation (see Fig.2). This approach not only preserves the inherent feature information of the image but also adaptively reduces the mutual influence between different degradation types, achieving a good balance between influence and inherent features. The main contributions of our method are as follows: + +- We propose a novel degradation-aware feature perturbation all-in-one restoration framework, DFPIR, which adaptively adjusts the feature space in high-dimensional space to align with the unified parameter space, guided by degradation type prompts. + +- We design a Degradation-Guided Perturbation Block (DGPB), consisting of a Degradation-Guided Channel Perturbation Module (DGCPM) and a Channel-Adapted Attention Perturbation Module (CAAPM), to apply perturbation modulation to features along the channel and attention dimensions, aligning with the encoder-decoder architecture with unified parameters. +- Extensive experiments demonstrate that our network achieves state-of-the-art performance in all-in-one image restoration. Especially for all-in-one restoration, 0.45dB PSNR improvement is obtained in comparison with InstructIR [8]. + +# 2. Related Works + +Single Task Image Restoration. Single task image restoration seeks to recover a high-quality image from its low-quality version. Due to the ill-posed nature of the task, early methods primarily focused on designing effective handcrafted priors to constrain the solution space. In contrast, recent deep learning-based approaches have significantly advanced the performance of various image restoration tasks, such as denoising [13, 26, 35, 36, 42, 43], detraining [2, 22, 24, 27, 47], dehazing [5, 9, 29, 40, 45, 51], deblurring [4, 7, 18, 19, 37, 37, 60], and low-light enhancement [12, 31, 52], by learning generalizable priors from large-scale datasets. We focus on general purpose restoration models [3, 25, 57], as these architectures can be independently trained for a variety of tasks. NAFNet [3] simplifies the network structure with lightweight channel attention and gated mechanisms, offering an alternative to non-linear activations. Meanwhile, Restormer [57] leverages transformer architectures to enhance low-level restoration tasks while minimizing computational overhead. In this study, we adopt Restormer [57] as the backbone for our DFPIR model due to its efficient design and high performance across multiple restoration tasks. However, these models are primarily designed for single-degradation scenarios, limiting their ef + +fectiveness when applied directly to all-in-one restoration tasks. + +All-In-One Image Restoration. Multi-task image restoration aims to address multiple tasks using the same network design [8, 21, 38, 39, 49, 55, 59]. Compared to single-task image restoration, the key challenge in multi-task image restoration is how to reduce the mutual influence of different degradation features while preserving the inherent features of the image. One approach is to adjust the network's parameter space to accommodate different degradation types. Several works have explored these strategies to handle diverse degradations. Li et al. [23] introduce a single-encoder, multi-decoder framework targeting weather-based degradations using the Rain-Haze-Snow dataset. Chen et al. [6] propose a two-stage knowledge transfer mechanism, employing a multi-teacher, single-student approach to handle various degradation types. Li et al. [21] propose an all-in-one framework capable of restoring multiple degraded images without requiring prior knowledge of degradation types or levels. Zhang et al. [59] propose an ingredient-oriented strategy that supports up to five restoration tasks within a single model, significantly enhancing scalability. Similarly, Zhang et al. [58] introduce a representation learning network guided by degradation classification, using its strong classification capabilities to effectively steer the restoration process. Another approach is to introduce image or degradation prompts to modulate the features, adapting to a unified parameter space [8, 39, 55]. PromptIR [39] encodes degradation-specific information through prompts, using them to dynamically guide the restoration network. In contrast, InstructIR [8] allows for model-driven image editing based on instructions that specify the desired actions, rather than relying on text labels, captions, or descriptions of input and output images. + +# 3. Proposed Method + +In "All-In-One" image restoration, the objective is to develop a single model $\mathbf{M}$ capable of restoring a clean image $\hat{\mathbf{I}}$ from a degraded input image $\mathbf{I}$ affected by a degradation $\mathbf{D}$ . Within this framework, under the same network parameters and architecture, different types of degradation mutually influence each other. For example, degraded images contain both inherent image features and degradation features. While inherent image features help the network learn latent parameters, thereby enhancing restoration performance, degradation features may negatively impact each other, reducing restoration effectiveness. In order to fully utilize the inherent features of the image while reducing the influence of different degradation features, motivated by the "hard" routing strategy [55] and PromptIR [39], we propose + +![](images/d7e704d2c354c66f078f1502c41fb2dc1ec481ed9b503e27e7a0bc580332a2e3.jpg) + +![](images/3b70733a0733a3919e535dff7d3db8aef6583aa077056658cd9b96f6dc79703f.jpg) + +![](images/ec8c2b758214f6d49685e1a185f0c06a0b23c7ea68b270f8d78b5ce5ea5ce2b2.jpg) +Noisy: CBSD68 + +![](images/9dd11401eed88882eaaf5bd52e9dcda4f4bc27b36c689c9991214749f91dfe0a.jpg) +Rainy: Rain100L + +![](images/a4692ea5232598541fe181489e449de6059f58e4251d5e12656cb0cdce69ce3c.jpg) +Hazy: SOTS +Figure 3. The figure provides t-SNE plots of the intermediate features from DFPIR (our method) and PromptIR on the test datasets (CBSD68, Rain100L, and SOTS) under the three-task setting. In our model, the features for each task exhibit tighter clustering, highlighting the effectiveness of our degradation-aware feature perturbation strategy in enhancing restoration performance. + +a degradation-aware feature perturbation modulation network, DFPIR, that adjusts the feature space through perturbation modulation to align with the shared-parameter network structure, thereby enhancing multi-degradation image restoration performance. The perturbation is divided into two parts: channel-wise perturbation and attention-wise perturbation. Channel-wise perturbation is implemented through channel shuffle, while attention-wise perturbation is achieved by selecting a portion of the attention maps. The details of these two perturbation mechanisms are provided in Section 3.3. The pipeline of the proposed DFPIR framework is illustrated in Fig.4. In the following sections, we describe the overall structure of DFPIR in detail. + +# 3.1. Overall Pipeline + +Given a degraded input image $\mathbf{I} \in R^{H \times W \times 3}$ , the DFPIR initially extracts shallow features $\mathbf{F_0} \in R^{H \times W \times C}$ using a $3 \times 3$ convolution layer; where $H \times W$ is the spatial size and $C$ denotes the channels. Next, these features $\mathbf{F_0}$ undergo a 4-level encoder-decoder network, transforming into deep features $\mathbf{F_r} \in R^{H \times W \times 2C}$ . Each level of the encoder-decoder employs multiple Transformer blocks [57], where the number of blocks gradually increases from the top level to the bottom level, facilitating a computationally efficient design. Beginning with the high-resolution input, the encoder aims to gradually decrease spatial resolution while increasing channel capacity, resulting in a low-resolution latent representation $\mathbf{F_e} \in R^{\frac{H}{8} \times \frac{W}{8} \times 8C}$ . Given the low-resolution latent features $\mathbf{F_e}$ , the objective of the decoder is to progressively restore the high-resolution clean output. To assist the recovery process, the encoder features are concatenated with the decoder features via skip connections [44]. We insert our Degradation-Guided Perturbation Block (DGPB) between the encoder and decoder, specifically within the skip-connection stage, to perturb the encoded feature space, which is guided by degradation type + +![](images/557326d963e3f73764ffeb10fa721b634f4a4d5d11c49e9014c7453fae9a9646.jpg) +Figure 4. Overview of the DFPIR framework. We employ Restormer [57], an encoder-decoder network with transformer blocks in the encoding and decoding stages, as our backbone. The primary component of the framework, the Degradation-Guided Perturbation Block (DGPB), consists of two submodules, i.e., Degradation-Guided Channel Perturbation Module (DGCPM) and Channel-Adapted Attention Perturbation Module (CAAPM). The DGCPM module introduces conventional dimensional perturbations to image features in the form of channel shuffling, guided by degradation-type prompts. The CAAPM module applies attention perturbation to the channel-shuffled features through a top-K masking strategy. + +prompts, and align it with the shared-parameter decoder. To obtain degradation type prompts, we utilize a pre-trained CLIP [41] model to encode the textual degradation type descriptions. In the following sections, we describe the proposed DGPB and its core building modules in detail. + +# 3.2. Degradation-Guided Perturbation Block (DGPB) + +In all-in-one setting, shared parameters are challenging to handle all-in-one image restoration effectively. We specifically design a Degradation-Guided Perturbation Block (DGPB) to apply perturbations to the encoded features, better aligning them with the shared decoder in multi-task scenarios, guided by the degradation type prompts (as shown in Fig.4). Given as inputs both the image feature $\mathbf{F_n} \in R^{\widehat{H} \times \widehat{W} \times \widehat{C}}$ and degradation type prompts $\mathbf{P_e} \in T^{\widehat{L} \times 1}$ , the overall process of DGPB is defined as: + +$$ +\mathbf {F _ {b}} = \operatorname {C A A P M} (\operatorname {D G C P M} (\mathbf {F _ {n}}, \operatorname {D G M} (\mathbf {P _ {e}})), \mathbf {F _ {n}}) \tag {1} +$$ + +where $\mathbf{F_n}$ represents the encoder output. The DGPB comprises two core components: the Degradation-Guided Channel Perturbation Module (DGCPM) and the Channel-Adapted Attention Perturbation Module (CAAPM). + +# 3.2.1 Degradation-Guided Channel Perturbation Module (DGCPM) + +In DGCPM, the objective is to add perturbations to the feature channels through channel shuffling, guided by degradation type prompts. However, directly shuffling the channels on the feature $\mathbf{F_n}$ may make it difficult to converge due to excessive perturbation and may also affect the quality of the reconstruction. To address this issue, we initially expand the number of channels in the image feature $\mathbf{F_n}$ by $2\mathrm{x}$ to introduce channel perturbations in a higher-dimensional channel space, guided by the Degradation Guidance Module(DGM). After channel expansion, the size of feature $\mathbf{F_n}$ becomes $\mathbf{F}_{2\mathbf{n}}\in R^{\widehat{H}\times \widehat{W}\times 2\widehat{C}}$ . In DGM, the degradation type prompts $(\mathbf{P_e})$ are used to adaptively apply channel shuffle. To maintain the dimensionality of $\mathbf{P_e}$ consistent with the channel dimensionality of $\mathbf{F_{2n}}$ , we employ a Multi-Layer Perceptron (MLP) which consisting of two linear layers to achieve dimension matching. Thus, MLP transforms the input feature $\mathbf{P_e}$ into $\mathbf{P_{ec}}\in T^{2\widehat{C}\times 1}$ . For degradation type prompts, see the supplementary document. In channel shuffle stage, we get the index value corresponding to the top- $\mathrm{K}(\mathrm{K} = 2\widehat{\mathrm{C}})$ value of $\mathbf{P_{ec}}$ , and use these index values to reorder the channels. Finally, halve the number of channels + +Table 1. Comparison to state-of-the-art on three tasks. PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images. On average PSNR, our DFPIR provides a significant gain of 0.45 dB over the previous all-in-one method InstructIR [8]. + +
MethodDehazing on SOTSDeraining on Rain100LDenoising on CBSD68 datasetAverage
σ = 15σ = 25σ = 50
DL [11]26.92 / 0.39132.62 / 0.93133.05 / 0.91430.41 / 0.86126.90 / 0.74029.98 / 0.875
FDGAN [10]24.71 / 0.92429.89 / 0.93330.25 / 0.91028.81 / 0.86826.43 / 0.77628.02 / 0.883
MPRNet [56]25.28 / 0.95433.57 / 0.95433.54 / 0.92730.89 / 0.88027.56 / 0.77930.17 / 0.899
AirNet [21]27.94 / 0.96234.90 / 0.96733.92 / 0.93331.26 / 0.88828.00 / 0.79731.20 / 0.910
Restormer [57]30.43 / 0.97536.55 / 0.97533.84 / 0.93131.18 / 0.88527.90 / 0.79031.98 / 0.911
PromptIR [39]30.58 / 0.97436.37 / 0.97233.98 / 0.93331.31 / 0.88828.06 / 0.79932.06 / 0.913
InstructIR [8]30.22 / 0.95937.98 / 0.97834.15 / 0.93331.52 / 0.89028.30 / 0.80432.43 / 0.913
DFPIR(Ours)31.87 / 0.98038.65 / 0.98234.14 / 0.93531.47 / 0.89328.25 / 0.80632.88 / 0.919
+ +after the shuffle to keep the channel count consistent before and after the transformation. Overall, the DGCPM process is summarized as: + +$$ +\mathbf {Q} = \operatorname {C o n v h} \left(\mathbf {C S} _ {\text {t o p} K} \left(\operatorname {C o n v k} \left(\mathbf {F} _ {\mathbf {n}}\right) | \mathrm {D G M} \left(\mathbf {P} _ {\mathbf {e}}\right)\right)\right) \tag {2} +$$ + +where the operation $\mathbf{CStopK}(\bullet|\mathrm{DGM}(\mathbf{Pe}))$ denotes top-K channel shuffling guided by $\mathrm{DGM}(\mathbf{P_e})$ , while Convk ( $\bullet$ ) and Convh ( $\bullet$ ) represent the operations of doubling and halving the feature channels, respectively. After DGCPM, we obtain feature $\mathbf{Q} \in R^{\widehat{H} \times \widehat{W} \times \widehat{C}}$ . + +# 3.2.2 Channel-Adapted Attention Perturbation Module(CAAPM) + +Although the shuffled features can adapt well to specific degradations, directly using them for reconstruction may not yield optimal results. This is because the shuffled features carry degradation-type information but lack interaction with the original feature information. To address this, we designed the Channel-Adapted Attention Perturbation Module (CAAPM). CAAPM has two main functions: facilitating information interaction between the shuffled and original features, and adding perturbations in the attention dimension. Motivated by Restormer [57], we design a cross-attention mechanism in the channel dimension to aggregate the shuffled and original features. To add perturbations to the attention map, we introduce a mask matrix $\mathbf{M} \in R^{\widehat{C} \times \widehat{C}}$ to select part of the attention map from each row using a top-K approach with a perturbation factor parameter $\gamma$ . The process of obtaining the perturbed attention map $\mathbf{PAM} \in R^{\widehat{H}\widehat{W} \times \widehat{C}}$ can be described as: + +$$ +\mathbf {P A M} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \operatorname {s o f t m a x} (\mathbf {M} \odot (\mathbf {Q} _ {*} \mathbf {K} _ {*} ^ {T} / \sqrt {d _ {k}})) \mathbf {V} _ {*} (3) +$$ + +where the query $\mathbf{Q}_{*}$ is derived from shuffled feature $\mathbf{Q}$ , and the key $\mathbf{K}_{*}$ and value $\mathbf{V}_{*}$ are derived from original features $\mathbf{F_{n}}$ . $\mathbf{M}$ represents the selection mask matrix. $\odot$ represents the element-wise multiplication. Then, we use a $1\times 1$ convolution to obtain the feature $\mathbf{F_{a}}$ with attention perturbations. + +Finally, we obtain the final output through an FFN network. This can be expressed as: + +$$ +\mathbf {F} _ {\mathbf {b}} = \mathbf {F} _ {\mathbf {a}} + \operatorname {F F N} \left(\mathbf {F} _ {\mathbf {a}}\right) \tag {4} +$$ + +The selection of the perturbation factor $\gamma$ needs to comprehensively consider the extent of interference magnitude between tasks and information loss. Fig.4 illustrates the relationship between $\gamma$ , interference size, and information loss. In our paper, the parameter is $\gamma$ fixed at 0.9, and the ablation study presents the experimental results for different values of $\gamma$ . + +# 3.3. Analysis of Our Feature Perturbation Strategy + +The task-aware feature perturbation strategy we propose involves both channel and attention dimensions. By perturbing these two dimensions, it not only preserves the inherent features of the image but also reduces the mutual influence of degradation features. Fig.3 illustrates that our model excels in learning discriminative degradation contexts. + +Channel-wise Perturbation Strategy. Directly performing channel shuffle in a low-dimensional space causes excessive perturbation, making network training difficult to converge. Therefore, we propose a degradation-aware adaptive channel shuffle strategy (as shown in Fig.1), which adaptively reorders the feature channels for each task in a high-dimensional feature space. Given a image feature which contains $N$ channels $\mathbf{F_{nc}} = \{C_1,C_2,\dots ,C_r,\dots ,C_N\} (\mathrm{r}\leq N)$ and M tasks, our channel shuffle strategy adopts different channel orders for each degradation restoration task. For any given task $\mathrm{T_m(m\leq M)}$ , the channel index vector after channel shuffle is defined as $\mathbf{S}^N = \{S_1^N,S_2^N,\dots ,S_N^N\}$ . Finally, the feature obtained after channel shuffle is $\mathbf{F}_{\mathbf{m}} = \{C_{S_1^N},C_{S_2^N},\dots ,C_{S_N^N}\}$ . The adjustment of this channel order is adaptively random under the guidance of degradation prompts. This random adaptive shuffle strategy reduces interference between feature channels while preserving the + +Table 2. Comparison to state-of-the-art on five tasks. PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images with (*) denoting general image restorers, others are specialized all-in-one approaches. Denoising results are reported for the noise level $\sigma = 25$ . + +
MethodDehazing on SOTSDeraining on Rain100LDenoising on CBSD68Deblurring on GoproLow-light Enh. on LOLAverage
DGUNet* [33]24.78 / 0.94036.62 / 0.97131.10 / 0.88327.25 / 0.83721.87 / 0.82328.32 / 0.891
SwinIR* [25]21.50 / 0.89130.78 / 0.92330.59 / 0.86824.52 / 0.77317.81 / 0.72325.04 / 0.835
Restomer* [57]24.09 / 0.92734.81 / 0.96231.49 / 0.88427.22 / 0.82920.41 / 0.80627.60 / 0.881
NAFNet* [3]25.23 / 0.93935.56 / 0.96731.02 / 0.88326.53 / 0.80820.49 / 0.80927.76 / 0.881
DL [11]20.54 / 0.82621.96 / 0.76223.09 / 0.74519.86 / 0.67219.83 / 0.71221.05 / 0.743
Transweather [46]21.32 / 0.88529.43 / 0.90529.00 / 0.84125.12 / 0.75721.21 / 0.79225.22 / 0.836
TAPE [28]22.16 / 0.86129.67 / 0.90430.18 / 0.85524.47 / 0.76318.97 / 0.62125.09 / 0.801
AirNet [21]21.04 / 0.88432.98 / 0.95130.91 / 0.88224.35 / 0.78118.18 / 0.73525.49 / 0.846
IDR [59]25.24 / 0.94335.63 / 0.96531.60 / 0.88727.87 / 0.84621.34 / 0.82628.34 / 0.893
InstructIR [8]27.10 / 0.95636.84 / 0.97331.40 / 0.88729.40 / 0.88623.00 / 0.83629.55 / 0.907
DFPIR(Ours)31.64 / 0.97937.62 / 0.97831.29 / 0.88928.82 / 0.87323.82 / 0.84330.64 / 0.913
+ +inherent characteristics of the image (as channel shuffling does not result in channel feature loss), thereby improving reconstruction quality. + +Attention-wise Perturbation Strategy. The main purpose of channel shuffle is to minimize the influence of degradation features while preserving the inherent characteristics of the image. However, this reduction is not thorough enough, meaning its effectiveness is limited. To address this, we directly discard a portion of the attention in the attention maps to further mitigate the impact of multiple degradation features (as shown in Fig.2). Specifically, we compute the transposed cross attention map $\mathbf{A}_{tt} \in R^{\widehat{C} \times \widehat{C}}$ . We select a portion of the attention map values from each column of $\mathbf{A}_{tt}$ using the top-K method to generate a disturbance mask matrix $\mathbf{M} \in R^{\widehat{C} \times \widehat{C}}$ , where the values that are not selected are set to 0, and the remaining values are set to 1. Then, the matrix $\mathbf{M}$ is multiplied element-wise with $\mathbf{A}_{tt}$ to obtain a new attention map $\mathbf{A}_{ttn}$ , achieving perturbation in the attention dimension. In other words, $\mathbf{A}_{ttn} = \mathbf{A}_{tt} \odot \mathbf{M}$ , where $\mathbf{A}_{tt}$ is $\mathbf{Q}_*\mathbf{K}_*^T / \sqrt{d_k}$ in equation 3. + +# 4. Experiments + +In this section, we follow the protocols of prior state-of-the-art works [21, 39] to conduct experiments under two settings: (a) all-in-one and (b) single-task. For the all-in-one setting, a unified model is trained to handle multiple degradation types, with experiments conducted across three and five distinct degradations. In contrast, the single-task setting involves training separate models, each specialized for a specific restoration task. The image quality metrics—PSNR and SSIM [16]—for the top-performing methods are highlighted in red and the second-best results are highlighted in blue in the result tables. Single-task results and more visual experiments are in the supplementary material. + +# 4.1. Experimental Settings + +Datasets. In line with previous work [21, 39], we prepare datasets tailored for various restoration tasks. For single-task image denoising, we merge images from the BSD400 [1] and WED [30] datasets to train the model. Testing is conducted on the CBSD68 [32] and Urban100 [14] datasets. For image dehazing, we use the SOTS [20] dataset, while Rain100L [53] is employed for image deraining. Deblurring and low-light enhancement tasks utilize the GoPro [34] and LOL-v1 [34] datasets, respectively. In the all-in-one setting, a unified model is trained on the combined training datasets mentioned above and tested directly across multiple restoration tasks. Additional dataset details can be found in the supplementary materials. + +Implementation Details. Our DFPIR provides an end-to-end trainable solution, removing the necessity for pretraining any individual components. Following the configuration of PromptIR [39], our DFPIR architecture features a 4-level encoder-decoder structure, comprising varying numbers of Transformer blocks at each level, specifically [4, 6, 6, 8] from level-1 to level-4. We integrate our Degradation-Guided Perturbation Block (DGPB) between the encoder and decoder, with a total of four DGPBs distributed throughout the network. We conduct our experiments using PyTorch on a single NVIDIA GeForce RTX 3090 GPU. For training, we run for 80 epochs with an initial learning rate of $1e^{-4}$ , followed by fine-tuning for 5 epochs at a learning rate of $1e^{-5}$ . Initially, we set the patch size to $128^2$ with the batch size of 5, and for fine-tuning, the patch size is adjusted to $192^2$ with a batch size of 3. The network is optimized using the L1 loss function in conjunction with the Adam optimizer (with parameters $\beta_{1} = 0.9$ and $\beta_{2} = 0.999$ ). We train on cropped patches and augment the dataset with random horizontal and vertical flips. + +![](images/acb9365ca31a97e0485dd698a7fe410c8b935a454592935105d718ed31b596ed.jpg) +Figure 5. Visual comparison of DFPIR with state-of-the-art methods on challenging cases for the All-in-One setting considering three degradations. Zoom in for better view. + +# 4.2. Results Comparisons on Three Tasks + +We assess the performance of our all-in-one DFPIR across three distinct restoration tasks: dehazing, deraining, and denoising. Our DFPIR is compared with various general image restoration methods, including Restormer [57], FDGAN [10], and MPRNet [56], as well as specialized all-in-one approaches such as DL [11], AirNet [21], PromptIR [39], and InstructIR [8]. As shown in Tab. 1, the proposed DFPIR consistently outperforms the other competing methods. On average across the different restoration tasks, our algorithm achieves a performance improvement of $0.45\mathrm{dB}$ over the previous best method, InstructIR [8], and $0.82\mathrm{dB}$ over the second-best approach, PromptIR [39]. Specifically, DFPIR demonstrates a notable increase of $0.67\mathrm{dB}$ on the deraining task and $1.65\mathrm{dB}$ on the dehazing task compared to InstructIR [8]. + +# 4.3. Results Comparisons on Five Tasks + +To further validate the method's effectiveness in addressing a broader range of tasks, building upon the recent research conducted by IDR [59] and InstructIR [8], we extend our investigation into the efficacy of DFPIR by conducting experiments across five restoration tasks: dehazing, deraining, denoising, deblurring, and low-light image enhancement. To achieve this, we train a comprehensive DFPIR on combined datasets compiled for five distinct tasks. These encompass datasets from the previously mentioned threetask scenario, alongside additional datasets: GoPro [34] for motion deblurring and LOL [50] for low-light image enhancement. Tab. 2 demonstrates that DFPIR achieves a 1.09 + +dB improvement compared to the recent leading method InstructIR [8], when averaged across five restoration tasks. Additionally, we compare our method to general image restoration models that were trained in the same All-in-One setting. Notably, our method surpasses Restormer[57] and NAFNet [3] on average PSNR by 3.04 dB and 2.88 dB, respectively, validating the effectiveness of our approach in handling multiple degradations. + +# 4.4. Visual Results + +Visual examples illustrating our results for dehazing, de- raining, and denoising are provided in Fig.5. Compared to PromptIR [39] and InstructIR [8], our method is more effective in challenging dehazing scenarios. Additionally, our model's deraining results are closer to the ground-truth images. Furthermore, in image denoising, our model recovers more details from heavily degraded noisy inputs. We visualized the results of channel shuffling, as shown in Fig.7. After channel shuffling, the channel order for each task changed accordingly, which validates the effectiveness of our proposed channel shuffling strategy. Additionally, we also visualized the feature perturbations before and after for the $\mathbf{F}_1$ layer, as shown in Fig.6. As can be seen, after channel dimension perturbation (DGCPM), the network extracts the image's inherent features from multi-degradation scenarios, reducing the impact of degradation-specific features. With the addition of perturbation in the attention dimension (DGCPM+CAAPM), the intrinsic detail features of the image are further enhanced, while the degradation features are more effectively suppressed. This demonstrates the efficacy + +![](images/e0be6a4e4db7fb1572a3a41d94b7999a2c4228d61c7ff8fcedf4a64b1c71c34d.jpg) +Figure 6. Feature visualization. DGCPM extracts the intrinsic features of the image while suppressing degradation characteristics. DGCPM + CAAPM enhances intrinsic features while further reducing the impact of degradation. Zoom in for better view. + +of our proposed channel and attention perturbation strategy. + +# 4.5. Ablations Studies + +We conduct several ablation experiments to demonstrate the effectiveness of our proposed degradation-guided perurbation block. We report the results of training an all-in-one model on combined datasets from three restoration tasks. More detailed ablation experiments can be found in the supplementary materials. + +Impact of key components. As illustrated in the Tab. 3(a), using channel attention (Method (a)) directly improves by $0.36\mathrm{dB}$ compared to the baseline [57], but it is $0.15\mathrm{dB}$ lower than channel shuffle (Method (c)). This also validates the effectiveness of the channel shuffle strategy we proposed. Channel shuffle preserves inherent image features with degradation info but offers limited reduction in cross-degradation interference. By applying attention-wise perturbation, restoration quality is significantly enhanced (DGCPM+CAAPM). The average PSNR increased from 32.49 to 32.88, reflecting an improvement of $0.39\mathrm{dB}$ . However, Method (b) (CA+CAAPM) results in a lower performance than DFPIR, indicating that the perturbations in channel and attention dimensions produce a synergistic enhancement effect. + +Impact of parameter $\gamma$ . As illustrated in the Tab. 3(b), if the perturbation in the attention dimension is too high ( $\gamma = 0.5$ ) or absent ( $\gamma = 1.0$ ), the performance is not optimal. This is because excessive perturbation, while reducing the interference between images with different degradations, increases information loss, leading to suboptimal performance. Similarly, if the perturbation is too small, the interference between tasks becomes more significant, resulting in suboptimal performance as well. + +# 5. Conclusion + +In this paper, we present a novel all-in-one image restoration framework, DFPIR, which introduces Degradation- + +Table 3. Ablation study results on three tasks. Average PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images. The CA stands for Channel Attention. +(a) Impact of key components. + +
MethodCADGCPMCAAPMPSNR/SSIM
baseline×××31.98 / 0.911
(a)✓××32.34 / 0.914
(b)✓×✓32.65 / 0.917
(c)×✓×32.49 / 0.910
DFPIR×✓✓32.88 / 0.919
+ +(b) Impact of $\gamma$ + +
γPSNR / SSIM
0.532.67 / 0.913
0.732.81 / 0.919
0.832.84 / 0.919
0.932.88 / 0.919
1.032.83 / 0.919
+ +![](images/ddefacbba56e202c78d3c95b08110ebb8b6c206288fd36715ef52cab409ab7b4.jpg) +Figure 7. Channel shuffle visualization. After channel shuffling, the feature channel order for each task has changed compared to the original order. + +aware Feature Perturbations (DFP) to adjust the feature space in alignment with a unified parameter space. Our approach incorporates both channel-wise and attentionwise perturbations, dynamically guided by degradation type prompts. Specifically, channel-wise perturbations are achieved by shuffling channels in a high-dimensional space, while attention-wise perturbations are implemented through selective masking in the attention space. To effectively realize these operations, we design a Degradation-Guided Perturbation Block (DGPB), which integrates channel shuffling and attention masking, strategically placed between the encoding and decoding stages of the encoder-decoder architecture. The proposed DGPB demonstrates its efficacy in enhancing comprehensive image restoration when integrated into a state-of-the-art model, yielding notable improvements in the all-in-one restoration setting. + +# 6. Acknowledgment + +This work was supported in part by the National Natural Science Foundation of China under Grant 62171304 and partly by the Natural Science Foundation of Sichuan Province under Grant 2024NSFSC1423, Cooperation Science and Technology Project of Sichuan University and Dazhou City under Grant 2022CDDZ-09, the TCL Science and Technology Innovation Fund under grant 25JZH008, and the Young Faculty Technology Innovation Capacity Enhancement Program of Sichuan University under Grant 2024SCUQJTX025. + +# References + +[1] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. Contour detection and hierarchical image segmentation. IEEE transactions on pattern analysis and machine intelligence, 33(5):898-916, 2010. 6 +[2] Chenghao Chen and Hao Li. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10255-10264, 2019. 1 \ No newline at end of file diff --git a/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/images.zip b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..59f7be04daa8a4ff26046a5b9062090e9b4aca85 --- /dev/null +++ b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:68b6cd85c4367192a3f4d760e7847ffa327a154adadb5e622a692d1d8fda20c2 +size 807416 diff --git a/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/layout.json b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ebbd1721e28924eabf15a033f0e63be4235adc9a --- /dev/null +++ b/2025/Degradation-Aware Feature Perturbation for All-in-One Image Restoration/layout.json @@ -0,0 +1,8007 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 72, + 103, + 538, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 103, + 538, + 121 + ], + "spans": [ + { + "bbox": [ + 72, + 103, + 538, + 121 + ], + "type": "text", + "content": "Degradation-Aware Feature Perturbation for All-in-One Image Restoration" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 100, + 144, + 504, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 144, + 504, + 185 + ], + "spans": [ + { + "bbox": [ + 100, + 144, + 504, + 185 + ], + "type": "text", + "content": "Xiangpeng Tian, Xiangyu Liao, Xiao Liu, Meng Li, Chao Ren* \nCollege of Electronics and Information Engineering, Sichuan University, China \n{tianxp, liaoxiangyul, liux, limeng.scu}@stu.scu.edu.cn, chaoren@scu.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 152, + 213, + 200, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 213, + 200, + 225 + ], + "spans": [ + { + "bbox": [ + 152, + 213, + 200, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 239, + 297, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 239, + 297, + 550 + ], + "spans": [ + { + "bbox": [ + 54, + 239, + 297, + 550 + ], + "type": "text", + "content": "All-in-one image restoration aims to recover clear images from various degradation types and levels with a unified model. Nonetheless, the significant variations among degradation types present challenges for training a universal model, often resulting in task interference, where the gradient update directions of different tasks may diverge due to shared parameters. To address this issue, motivated by the routing strategy, we propose DFPIR, a novel all-in-one image restorer that introduces Degradation-aware Feature Perturbations(DFP) to adjust the feature space to align with the unified parameter space. In this paper, the feature perturbations primarily include channel-wise perturbations and attention-wise perturbations. Specifically, channel-wise perturbations are implemented by shuffling the channels in high-dimensional space guided by degradation types, while attention-wise perturbations are achieved through selective masking in the attention space. To achieve these goals, we propose a Degradation-Guided Perturbation Block (DGPB) to implement these two functions, positioned between the encoding and decoding stages of the encoder-decoder architecture. Extensive experimental results demonstrate that DFPIR achieves state-of-the-art performance on several all-in-one image restoration tasks including image denoising, image dehazing, image deraining, motion deblurring, and low-light image enhancement. Our codes are available at https://github.com/TxpHome/DFPIR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 575, + 135, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 135, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 135, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 596, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 596, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 596, + 296, + 693 + ], + "type": "text", + "content": "Image restoration, a fundamental task in computer vision, has been widely studied, with a primary focus on addressing individual degradation types, such as noise, haze, rain, or blur. Recently, deep learning-based approaches have achieved remarkable progress in single-degradation restoration tasks, including denoising [15, 26, 35, 36, 42, 61], deraining [2, 17, 22, 48, 54], dehazing [5, 9, 40, 45, 51], and deblurring [7, 19, 37, 37, 60]. While these single-" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 214, + 553, + 324 + ], + "blocks": [ + { + "bbox": [ + 316, + 214, + 553, + 324 + ], + "lines": [ + { + "bbox": [ + 316, + 214, + 553, + 324 + ], + "spans": [ + { + "bbox": [ + 316, + 214, + 553, + 324 + ], + "type": "image", + "image_path": "2e84e4e7408236d6469ddb43aa4924c222e57fda975d2dde6a9a5ac3f09638c4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 325, + 555, + 359 + ], + "lines": [ + { + "bbox": [ + 313, + 325, + 555, + 359 + ], + "spans": [ + { + "bbox": [ + 313, + 325, + 555, + 359 + ], + "type": "text", + "content": "Figure 1. This figure demonstrates the channel-wise perturbation method of DFPIR, where channel shuffle assigns unique channel orders for different degradation types." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 387, + 555, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 387, + 555, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 555, + 495 + ], + "type": "text", + "content": "degradation solutions perform well under specific conditions, they often struggle to generalize effectively to multiple degradation scenarios. Consequently, recent research has shifted toward multi-degradation restoration techniques, delivering state-of-the-art performance for known combinations of degradations [3, 33, 56, 57]. However, these approaches typically require separate networks for each degradation type, leading to large model sizes and high computational demands." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "type": "text", + "content": "Recently, all-in-one approaches(also known as multi-degradation or multi-task image restoration) have gained prominence by addressing multiple image degradations within a unified model [6, 21, 38, 39, 49, 55, 59]. While these methods have achieved state-of-the-art results, they often overlook the relationships and distinctive characteristics among different degradation types due to shared parameters. For example, MedIR [55] demonstrates that the gradient update directions between different tasks are inconsistent or even opposite. According to the characteristics of existing methods, current all-in-one image restoration methods can be roughly divided into two categories: (1) one solution is to modify the parameter space to fit the model for different degradations [21, 38, 49, 59]; (2) and the other solution is to modify the feature space to align with the shared parameter space [8, 39, 55]. Both approaches require incorporating degradation information into the network to mitigate the interference between different degras" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28165" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 99, + 161, + 190 + ], + "blocks": [ + { + "bbox": [ + 59, + 76, + 160, + 97 + ], + "lines": [ + { + "bbox": [ + 59, + 76, + 160, + 97 + ], + "spans": [ + { + "bbox": [ + 59, + 76, + 160, + 97 + ], + "type": "text", + "content": "Without attention disturbance: Select all attention maps." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 69, + 99, + 161, + 190 + ], + "lines": [ + { + "bbox": [ + 69, + 99, + 161, + 190 + ], + "spans": [ + { + "bbox": [ + 69, + 99, + 161, + 190 + ], + "type": "image", + "image_path": "ce12d81db4d13d5a5a88a4ec631eff8aa58a7a829399ea71a4008b0ca21ea86a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 189, + 99, + 282, + 190 + ], + "blocks": [ + { + "bbox": [ + 188, + 77, + 283, + 97 + ], + "lines": [ + { + "bbox": [ + 188, + 77, + 283, + 97 + ], + "spans": [ + { + "bbox": [ + 188, + 77, + 283, + 97 + ], + "type": "text", + "content": "With attention disturbance: Select partial attention maps." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 189, + 99, + 282, + 190 + ], + "lines": [ + { + "bbox": [ + 189, + 99, + 282, + 190 + ], + "spans": [ + { + "bbox": [ + 189, + 99, + 282, + 190 + ], + "type": "image", + "image_path": "6c6b59ee92b42ef29baa71d45038cf18e5d5fca980f043ca29a1a14191faaf26.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 58, + 196, + 291, + 210 + ], + "blocks": [ + { + "bbox": [ + 58, + 196, + 291, + 210 + ], + "lines": [ + { + "bbox": [ + 58, + 196, + 291, + 210 + ], + "spans": [ + { + "bbox": [ + 58, + 196, + 291, + 210 + ], + "type": "image", + "image_path": "05174b5e62c78d6233d2594e558d7b470c08010641b89eebc164ba727875f283.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 212, + 294, + 245 + ], + "lines": [ + { + "bbox": [ + 55, + 212, + 294, + 245 + ], + "spans": [ + { + "bbox": [ + 55, + 212, + 294, + 245 + ], + "type": "text", + "content": "Figure 2. This figure showcases our attention-wise perturbation, where DFPIR applies attention selection to perturb image features, discarding a portion of attention for each degradation type." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 269, + 295, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 269, + 295, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 269, + 295, + 316 + ], + "type": "text", + "content": "dations. Although the approach (1) can effectively enhance network performance, it usually requires a large number of additional degradation parameters or a more complex network structure, increasing computational complexity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 318, + 295, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 295, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 295, + 581 + ], + "type": "text", + "content": "Compared to the approach (1), the method (2) is more prevalent in the \"All-in-One\" image restoration framework. The approach (2) typically involves introducing a degradation type prompt, which modulates features to align with the shared network parameters. Specifically, PromptIR [39] conducts multi-degradation processing by introducing additional implicit prompts. However, although this implicit cue in the feature domain utilizes the inherent features of the image, it neglects the influence of degradation types, making it challenging to reduce the mutual influence among multiple degradation types, which ultimately leads to suboptimal results. MedIR [55] introduces multiple experts into the feature space modulation to implement a task-adaptive routing strategy. Although this \"hard\" routing strategy effectively reduces the influence between tasks, it may overlook the inherent features of the image among multiple degradations. InstructIR [8] introduces text commands for multi-task restoration, showcasing the potential of using text prompts to guide image restoration. However, InstructIR [8] modulates features through channel attention using text prompts, which may make it challenging to mitigate the mutual influence among different degradations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "text", + "content": "To overcome these challenges, this paper analyzes the design philosophy and rationale behind the success of prompts and presents a degradation-aware feature perturbation approach to adjust the feature space to align with the unified parameter space for all-in-one image restoration. Our method modulates features through perturbations which include channel-wise and attention-wise perturbations to align with shared network parameters or structures, guided by degradation type prompts. Specifically, channel-wise perturbations involve shuffling the channels in high-dimensional space rather than using the conventional" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 555, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 203 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 203 + ], + "type": "text", + "content": "channel attention mechanism (see Fig.1). This shuffling approach preserves the inherent features of the image while reducing the mutual influence of degradation features. While attention-wise perturbations involve selectively masking the features after channel shuffling to achieve channel-adapted attention perturbation (see Fig.2). This approach not only preserves the inherent feature information of the image but also adaptively reduces the mutual influence between different degradation types, achieving a good balance between influence and inherent features. The main contributions of our method are as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 204, + 553, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 204, + 553, + 263 + ], + "spans": [ + { + "bbox": [ + 314, + 204, + 553, + 263 + ], + "type": "text", + "content": "- We propose a novel degradation-aware feature perturbation all-in-one restoration framework, DFPIR, which adaptively adjusts the feature space in high-dimensional space to align with the unified parameter space, guided by degradation type prompts." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 264, + 553, + 407 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 314, + 264, + 553, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 264, + 553, + 346 + ], + "spans": [ + { + "bbox": [ + 314, + 264, + 553, + 346 + ], + "type": "text", + "content": "- We design a Degradation-Guided Perturbation Block (DGPB), consisting of a Degradation-Guided Channel Perturbation Module (DGCPM) and a Channel-Adapted Attention Perturbation Module (CAAPM), to apply perturbation modulation to features along the channel and attention dimensions, aligning with the encoder-decoder architecture with unified parameters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 348, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 348, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 314, + 348, + 553, + 407 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that our network achieves state-of-the-art performance in all-in-one image restoration. Especially for all-in-one restoration, 0.45dB PSNR improvement is obtained in comparison with InstructIR [8]." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 418, + 405, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 418, + 405, + 430 + ], + "spans": [ + { + "bbox": [ + 314, + 418, + 405, + 430 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "type": "text", + "content": "Single Task Image Restoration. Single task image restoration seeks to recover a high-quality image from its low-quality version. Due to the ill-posed nature of the task, early methods primarily focused on designing effective handcrafted priors to constrain the solution space. In contrast, recent deep learning-based approaches have significantly advanced the performance of various image restoration tasks, such as denoising [13, 26, 35, 36, 42, 43], detraining [2, 22, 24, 27, 47], dehazing [5, 9, 29, 40, 45, 51], deblurring [4, 7, 18, 19, 37, 37, 60], and low-light enhancement [12, 31, 52], by learning generalizable priors from large-scale datasets. We focus on general purpose restoration models [3, 25, 57], as these architectures can be independently trained for a variety of tasks. NAFNet [3] simplifies the network structure with lightweight channel attention and gated mechanisms, offering an alternative to non-linear activations. Meanwhile, Restormer [57] leverages transformer architectures to enhance low-level restoration tasks while minimizing computational overhead. In this study, we adopt Restormer [57] as the backbone for our DFPIR model due to its efficient design and high performance across multiple restoration tasks. However, these models are primarily designed for single-degradation scenarios, limiting their ef" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28166" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 96 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 96 + ], + "type": "text", + "content": "fectiveness when applied directly to all-in-one restoration tasks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 116, + 296, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 116, + 296, + 513 + ], + "spans": [ + { + "bbox": [ + 56, + 116, + 296, + 513 + ], + "type": "text", + "content": "All-In-One Image Restoration. Multi-task image restoration aims to address multiple tasks using the same network design [8, 21, 38, 39, 49, 55, 59]. Compared to single-task image restoration, the key challenge in multi-task image restoration is how to reduce the mutual influence of different degradation features while preserving the inherent features of the image. One approach is to adjust the network's parameter space to accommodate different degradation types. Several works have explored these strategies to handle diverse degradations. Li et al. [23] introduce a single-encoder, multi-decoder framework targeting weather-based degradations using the Rain-Haze-Snow dataset. Chen et al. [6] propose a two-stage knowledge transfer mechanism, employing a multi-teacher, single-student approach to handle various degradation types. Li et al. [21] propose an all-in-one framework capable of restoring multiple degraded images without requiring prior knowledge of degradation types or levels. Zhang et al. [59] propose an ingredient-oriented strategy that supports up to five restoration tasks within a single model, significantly enhancing scalability. Similarly, Zhang et al. [58] introduce a representation learning network guided by degradation classification, using its strong classification capabilities to effectively steer the restoration process. Another approach is to introduce image or degradation prompts to modulate the features, adapting to a unified parameter space [8, 39, 55]. PromptIR [39] encodes degradation-specific information through prompts, using them to dynamically guide the restoration network. In contrast, InstructIR [8] allows for model-driven image editing based on instructions that specify the desired actions, rather than relying on text labels, captions, or descriptions of input and output images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 525, + 162, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 525, + 162, + 538 + ], + "spans": [ + { + "bbox": [ + 55, + 525, + 162, + 538 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "text", + "content": "In \"All-In-One\" image restoration, the objective is to develop a single model " + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "text", + "content": " capable of restoring a clean image " + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}" + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "text", + "content": " from a degraded input image " + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "text", + "content": " affected by a degradation " + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "text", + "content": ". Within this framework, under the same network parameters and architecture, different types of degradation mutually influence each other. For example, degraded images contain both inherent image features and degradation features. While inherent image features help the network learn latent parameters, thereby enhancing restoration performance, degradation features may negatively impact each other, reducing restoration effectiveness. In order to fully utilize the inherent features of the image while reducing the influence of different degradation features, motivated by the \"hard\" routing strategy [55] and PromptIR [39], we propose" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 317, + 71, + 425, + 151 + ], + "blocks": [ + { + "bbox": [ + 317, + 71, + 425, + 151 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 425, + 151 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 425, + 151 + ], + "type": "image", + "image_path": "d7e704d2c354c66f078f1502c41fb2dc1ec481ed9b503e27e7a0bc580332a2e3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 446, + 72, + 550, + 150 + ], + "blocks": [ + { + "bbox": [ + 446, + 72, + 550, + 150 + ], + "lines": [ + { + "bbox": [ + 446, + 72, + 550, + 150 + ], + "spans": [ + { + "bbox": [ + 446, + 72, + 550, + 150 + ], + "type": "image", + "image_path": "3b70733a0733a3919e535dff7d3db8aef6583aa077056658cd9b96f6dc79703f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 317, + 152, + 391, + 178 + ], + "blocks": [ + { + "bbox": [ + 317, + 152, + 391, + 178 + ], + "lines": [ + { + "bbox": [ + 317, + 152, + 391, + 178 + ], + "spans": [ + { + "bbox": [ + 317, + 152, + 391, + 178 + ], + "type": "image", + "image_path": "ec8c2b758214f6d49685e1a185f0c06a0b23c7ea68b270f8d78b5ce5ea5ce2b2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 180, + 382, + 190 + ], + "lines": [ + { + "bbox": [ + 318, + 180, + 382, + 190 + ], + "spans": [ + { + "bbox": [ + 318, + 180, + 382, + 190 + ], + "type": "text", + "content": "Noisy: CBSD68" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 399, + 152, + 472, + 178 + ], + "blocks": [ + { + "bbox": [ + 399, + 152, + 472, + 178 + ], + "lines": [ + { + "bbox": [ + 399, + 152, + 472, + 178 + ], + "spans": [ + { + "bbox": [ + 399, + 152, + 472, + 178 + ], + "type": "image", + "image_path": "9dd11401eed88882eaaf5bd52e9dcda4f4bc27b36c689c9991214749f91dfe0a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 400, + 180, + 463, + 190 + ], + "lines": [ + { + "bbox": [ + 400, + 180, + 463, + 190 + ], + "spans": [ + { + "bbox": [ + 400, + 180, + 463, + 190 + ], + "type": "text", + "content": "Rainy: Rain100L" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 477, + 152, + 552, + 178 + ], + "blocks": [ + { + "bbox": [ + 477, + 152, + 552, + 178 + ], + "lines": [ + { + "bbox": [ + 477, + 152, + 552, + 178 + ], + "spans": [ + { + "bbox": [ + 477, + 152, + 552, + 178 + ], + "type": "image", + "image_path": "a4692ea5232598541fe181489e449de6059f58e4251d5e12656cb0cdce69ce3c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 478, + 180, + 531, + 190 + ], + "lines": [ + { + "bbox": [ + 478, + 180, + 531, + 190 + ], + "spans": [ + { + "bbox": [ + 478, + 180, + 531, + 190 + ], + "type": "text", + "content": "Hazy: SOTS" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 193, + 555, + 259 + ], + "lines": [ + { + "bbox": [ + 313, + 193, + 555, + 259 + ], + "spans": [ + { + "bbox": [ + 313, + 193, + 555, + 259 + ], + "type": "text", + "content": "Figure 3. The figure provides t-SNE plots of the intermediate features from DFPIR (our method) and PromptIR on the test datasets (CBSD68, Rain100L, and SOTS) under the three-task setting. In our model, the features for each task exhibit tighter clustering, highlighting the effectiveness of our degradation-aware feature perturbation strategy in enhancing restoration performance." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 280, + 555, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 280, + 555, + 435 + ], + "spans": [ + { + "bbox": [ + 313, + 280, + 555, + 435 + ], + "type": "text", + "content": "a degradation-aware feature perturbation modulation network, DFPIR, that adjusts the feature space through perturbation modulation to align with the shared-parameter network structure, thereby enhancing multi-degradation image restoration performance. The perturbation is divided into two parts: channel-wise perturbation and attention-wise perturbation. Channel-wise perturbation is implemented through channel shuffle, while attention-wise perturbation is achieved by selecting a portion of the attention maps. The details of these two perturbation mechanisms are provided in Section 3.3. The pipeline of the proposed DFPIR framework is illustrated in Fig.4. In the following sections, we describe the overall structure of DFPIR in detail." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 444, + 412, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 412, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 412, + 456 + ], + "type": "text", + "content": "3.1. Overall Pipeline" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": "Given a degraded input image " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in R^{H \\times W \\times 3}" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": ", the DFPIR initially extracts shallow features " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F_0} \\in R^{H \\times W \\times C}" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": " using a " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": " convolution layer; where " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": " is the spatial size and " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": " denotes the channels. Next, these features " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F_0}" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": " undergo a 4-level encoder-decoder network, transforming into deep features " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F_r} \\in R^{H \\times W \\times 2C}" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": ". Each level of the encoder-decoder employs multiple Transformer blocks [57], where the number of blocks gradually increases from the top level to the bottom level, facilitating a computationally efficient design. Beginning with the high-resolution input, the encoder aims to gradually decrease spatial resolution while increasing channel capacity, resulting in a low-resolution latent representation " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F_e} \\in R^{\\frac{H}{8} \\times \\frac{W}{8} \\times 8C}" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": ". Given the low-resolution latent features " + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F_e}" + }, + { + "bbox": [ + 313, + 461, + 556, + 715 + ], + "type": "text", + "content": ", the objective of the decoder is to progressively restore the high-resolution clean output. To assist the recovery process, the encoder features are concatenated with the decoder features via skip connections [44]. We insert our Degradation-Guided Perturbation Block (DGPB) between the encoder and decoder, specifically within the skip-connection stage, to perturb the encoded feature space, which is guided by degradation type" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28167" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 553, + 338 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 553, + 338 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 553, + 338 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 553, + 338 + ], + "type": "image", + "image_path": "557326d963e3f73764ffeb10fa721b634f4a4d5d11c49e9014c7453fae9a9646.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 339, + 555, + 406 + ], + "lines": [ + { + "bbox": [ + 55, + 339, + 555, + 406 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 555, + 406 + ], + "type": "text", + "content": "Figure 4. Overview of the DFPIR framework. We employ Restormer [57], an encoder-decoder network with transformer blocks in the encoding and decoding stages, as our backbone. The primary component of the framework, the Degradation-Guided Perturbation Block (DGPB), consists of two submodules, i.e., Degradation-Guided Channel Perturbation Module (DGCPM) and Channel-Adapted Attention Perturbation Module (CAAPM). The DGCPM module introduces conventional dimensional perturbations to image features in the form of channel shuffling, guided by degradation-type prompts. The CAAPM module applies attention perturbation to the channel-shuffled features through a top-K masking strategy." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 427, + 295, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 295, + 486 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 295, + 486 + ], + "type": "text", + "content": "prompts, and align it with the shared-parameter decoder. To obtain degradation type prompts, we utilize a pre-trained CLIP [41] model to encode the textual degradation type descriptions. In the following sections, we describe the proposed DGPB and its core building modules in detail." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 494, + 295, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 494, + 295, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 494, + 295, + 517 + ], + "type": "text", + "content": "3.2. Degradation-Guided Perturbation Block (DGPB)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 524, + 295, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 524, + 295, + 634 + ], + "spans": [ + { + "bbox": [ + 55, + 524, + 295, + 634 + ], + "type": "text", + "content": "In all-in-one setting, shared parameters are challenging to handle all-in-one image restoration effectively. We specifically design a Degradation-Guided Perturbation Block (DGPB) to apply perturbations to the encoded features, better aligning them with the shared decoder in multi-task scenarios, guided by the degradation type prompts (as shown in Fig.4). Given as inputs both the image feature " + }, + { + "bbox": [ + 55, + 524, + 295, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{F_n} \\in R^{\\widehat{H} \\times \\widehat{W} \\times \\widehat{C}}" + }, + { + "bbox": [ + 55, + 524, + 295, + 634 + ], + "type": "text", + "content": " and degradation type prompts " + }, + { + "bbox": [ + 55, + 524, + 295, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{P_e} \\in T^{\\widehat{L} \\times 1}" + }, + { + "bbox": [ + 55, + 524, + 295, + 634 + ], + "type": "text", + "content": ", the overall process of DGPB is defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 71, + 643, + 295, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 643, + 295, + 657 + ], + "spans": [ + { + "bbox": [ + 71, + 643, + 295, + 657 + ], + "type": "interline_equation", + "content": "\\mathbf {F _ {b}} = \\operatorname {C A A P M} (\\operatorname {D G C P M} (\\mathbf {F _ {n}}, \\operatorname {D G M} (\\mathbf {P _ {e}})), \\mathbf {F _ {n}}) \\tag {1}", + "image_path": "c9d5f7f0407f4194619665e8cd9504d92e7e319f340f2c305cd42b6f34f3f6bc.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F_n}" + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": " represents the encoder output. The DGPB comprises two core components: the Degradation-Guided Channel Perturbation Module (DGCPM) and the Channel-Adapted Attention Perturbation Module (CAAPM)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 426, + 555, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 426, + 555, + 450 + ], + "spans": [ + { + "bbox": [ + 314, + 426, + 555, + 450 + ], + "type": "text", + "content": "3.2.1 Degradation-Guided Channel Perturbation Module (DGCPM)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": "In DGCPM, the objective is to add perturbations to the feature channels through channel shuffling, guided by degradation type prompts. However, directly shuffling the channels on the feature " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F_n}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " may make it difficult to converge due to excessive perturbation and may also affect the quality of the reconstruction. To address this issue, we initially expand the number of channels in the image feature " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F_n}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "2\\mathrm{x}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " to introduce channel perturbations in a higher-dimensional channel space, guided by the Degradation Guidance Module(DGM). After channel expansion, the size of feature " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F_n}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " becomes " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{2\\mathbf{n}}\\in R^{\\widehat{H}\\times \\widehat{W}\\times 2\\widehat{C}}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " . In DGM, the degradation type prompts " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "(\\mathbf{P_e})" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " are used to adaptively apply channel shuffle. To maintain the dimensionality of " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P_e}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " consistent with the channel dimensionality of " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F_{2n}}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " , we employ a Multi-Layer Perceptron (MLP) which consisting of two linear layers to achieve dimension matching. Thus, MLP transforms the input feature " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P_e}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P_{ec}}\\in T^{2\\widehat{C}\\times 1}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " . For degradation type prompts, see the supplementary document. In channel shuffle stage, we get the index value corresponding to the top- " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{K}(\\mathrm{K} = 2\\widehat{\\mathrm{C}})" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " value of " + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P_{ec}}" + }, + { + "bbox": [ + 313, + 459, + 555, + 713 + ], + "type": "text", + "content": " , and use these index values to reorder the channels. Finally, halve the number of channels" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28168" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 101, + 555, + 227 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": "Table 1. Comparison to state-of-the-art on three tasks. PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images. On average PSNR, our DFPIR provides a significant gain of 0.45 dB over the previous all-in-one method InstructIR [8]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 101, + 555, + 227 + ], + "lines": [ + { + "bbox": [ + 56, + 101, + 555, + 227 + ], + "spans": [ + { + "bbox": [ + 56, + 101, + 555, + 227 + ], + "type": "table", + "html": "
MethodDehazing on SOTSDeraining on Rain100LDenoising on CBSD68 datasetAverage
σ = 15σ = 25σ = 50
DL [11]26.92 / 0.39132.62 / 0.93133.05 / 0.91430.41 / 0.86126.90 / 0.74029.98 / 0.875
FDGAN [10]24.71 / 0.92429.89 / 0.93330.25 / 0.91028.81 / 0.86826.43 / 0.77628.02 / 0.883
MPRNet [56]25.28 / 0.95433.57 / 0.95433.54 / 0.92730.89 / 0.88027.56 / 0.77930.17 / 0.899
AirNet [21]27.94 / 0.96234.90 / 0.96733.92 / 0.93331.26 / 0.88828.00 / 0.79731.20 / 0.910
Restormer [57]30.43 / 0.97536.55 / 0.97533.84 / 0.93131.18 / 0.88527.90 / 0.79031.98 / 0.911
PromptIR [39]30.58 / 0.97436.37 / 0.97233.98 / 0.93331.31 / 0.88828.06 / 0.79932.06 / 0.913
InstructIR [8]30.22 / 0.95937.98 / 0.97834.15 / 0.93331.52 / 0.89028.30 / 0.80432.43 / 0.913
DFPIR(Ours)31.87 / 0.98038.65 / 0.98234.14 / 0.93531.47 / 0.89328.25 / 0.80632.88 / 0.919
", + "image_path": "05627f8b35b98f5271dacb43bf5bd2fe062416f6d363acdec64fe6760ad8f009.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 245, + 294, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 245, + 294, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 245, + 294, + 281 + ], + "type": "text", + "content": "after the shuffle to keep the channel count consistent before and after the transformation. Overall, the DGCPM process is summarized as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 72, + 288, + 295, + 302 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 288, + 295, + 302 + ], + "spans": [ + { + "bbox": [ + 72, + 288, + 295, + 302 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} = \\operatorname {C o n v h} \\left(\\mathbf {C S} _ {\\text {t o p} K} \\left(\\operatorname {C o n v k} \\left(\\mathbf {F} _ {\\mathbf {n}}\\right) | \\mathrm {D G M} \\left(\\mathbf {P} _ {\\mathbf {e}}\\right)\\right)\\right) \\tag {2}", + "image_path": "af03c4285383fca5399f6580bd22173102e0b719d5fb6f02b89b007e8ce604b7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "spans": [ + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "text", + "content": "where the operation " + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "inline_equation", + "content": "\\mathbf{CStopK}(\\bullet|\\mathrm{DGM}(\\mathbf{Pe}))" + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "text", + "content": " denotes top-K channel shuffling guided by " + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "inline_equation", + "content": "\\mathrm{DGM}(\\mathbf{P_e})" + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "text", + "content": ", while Convk (" + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "text", + "content": ") and Convh (" + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "text", + "content": ") represent the operations of doubling and halving the feature channels, respectively. After DGCPM, we obtain feature " + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} \\in R^{\\widehat{H} \\times \\widehat{W} \\times \\widehat{C}}" + }, + { + "bbox": [ + 55, + 308, + 296, + 370 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 384, + 296, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 296, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 296, + 407 + ], + "type": "text", + "content": "3.2.2 Channel-Adapted Attention Perturbation Module(CAAPM)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "spans": [ + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "type": "text", + "content": "Although the shuffled features can adapt well to specific degradations, directly using them for reconstruction may not yield optimal results. This is because the shuffled features carry degradation-type information but lack interaction with the original feature information. To address this, we designed the Channel-Adapted Attention Perturbation Module (CAAPM). CAAPM has two main functions: facilitating information interaction between the shuffled and original features, and adding perturbations in the attention dimension. Motivated by Restormer [57], we design a cross-attention mechanism in the channel dimension to aggregate the shuffled and original features. To add perturbations to the attention map, we introduce a mask matrix " + }, + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in R^{\\widehat{C} \\times \\widehat{C}}" + }, + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "type": "text", + "content": " to select part of the attention map from each row using a top-K approach with a perturbation factor parameter " + }, + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "type": "text", + "content": ". The process of obtaining the perturbed attention map " + }, + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{PAM} \\in R^{\\widehat{H}\\widehat{W} \\times \\widehat{C}}" + }, + { + "bbox": [ + 55, + 415, + 296, + 622 + ], + "type": "text", + "content": " can be described as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 628, + 295, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 628, + 295, + 648 + ], + "spans": [ + { + "bbox": [ + 63, + 628, + 295, + 648 + ], + "type": "interline_equation", + "content": "\\mathbf {P A M} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {s o f t m a x} (\\mathbf {M} \\odot (\\mathbf {Q} _ {*} \\mathbf {K} _ {*} ^ {T} / \\sqrt {d _ {k}})) \\mathbf {V} _ {*} (3)", + "image_path": "8d0afd1e2e3db1dbaa4d1b76518383eaf1739fcd42c71949efff2b850895926e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": "where the query " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{*}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " is derived from shuffled feature " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": ", and the key " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{*}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " and value " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{*}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " are derived from original features " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F_{n}}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " represents the selection mask matrix. " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " represents the element-wise multiplication. Then, we use a " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " convolution to obtain the feature " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F_{a}}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " with attention perturbations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 245, + 553, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 245, + 553, + 269 + ], + "spans": [ + { + "bbox": [ + 313, + 245, + 553, + 269 + ], + "type": "text", + "content": "Finally, we obtain the final output through an FFN network. This can be expressed as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 389, + 279, + 555, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 279, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 389, + 279, + 555, + 293 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {\\mathbf {b}} = \\mathbf {F} _ {\\mathbf {a}} + \\operatorname {F F N} \\left(\\mathbf {F} _ {\\mathbf {a}}\\right) \\tag {4}", + "image_path": "45d8543a0bd56e0d270f9abf21922354b1013ad773cdfbfd9e122c07ec4c228a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "text", + "content": "The selection of the perturbation factor " + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "text", + "content": " needs to comprehensively consider the extent of interference magnitude between tasks and information loss. Fig.4 illustrates the relationship between " + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "text", + "content": ", interference size, and information loss. In our paper, the parameter is " + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "text", + "content": " fixed at 0.9, and the ablation study presents the experimental results for different values of " + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 301, + 555, + 385 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 392, + 553, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 553, + 406 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 553, + 406 + ], + "type": "text", + "content": "3.3. Analysis of Our Feature Perturbation Strategy" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "text", + "content": "The task-aware feature perturbation strategy we propose involves both channel and attention dimensions. By perturbing these two dimensions, it not only preserves the inherent features of the image but also reduces the mutual influence of degradation features. Fig.3 illustrates that our model excels in learning discriminative degradation contexts." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": "Channel-wise Perturbation Strategy. Directly performing channel shuffle in a low-dimensional space causes excessive perturbation, making network training difficult to converge. Therefore, we propose a degradation-aware adaptive channel shuffle strategy (as shown in Fig.1), which adaptively reorders the feature channels for each task in a high-dimensional feature space. Given a image feature which contains " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " channels " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F_{nc}} = \\{C_1,C_2,\\dots ,C_r,\\dots ,C_N\\} (\\mathrm{r}\\leq N)" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": " and M tasks, our channel shuffle strategy adopts different channel orders for each degradation restoration task. For any given task " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{T_m(m\\leq M)}" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": ", the channel index vector after channel shuffle is defined as " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^N = \\{S_1^N,S_2^N,\\dots ,S_N^N\\}" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": ". Finally, the feature obtained after channel shuffle is " + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{m}} = \\{C_{S_1^N},C_{S_2^N},\\dots ,C_{S_N^N}\\}" + }, + { + "bbox": [ + 313, + 498, + 555, + 713 + ], + "type": "text", + "content": ". The adjustment of this channel order is adaptively random under the guidance of degradation prompts. This random adaptive shuffle strategy reduces interference between feature channels while preserving the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28169" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 101, + 553, + 262 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": "Table 2. Comparison to state-of-the-art on five tasks. PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images with (*) denoting general image restorers, others are specialized all-in-one approaches. Denoising results are reported for the noise level " + }, + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "inline_equation", + "content": "\\sigma = 25" + }, + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 101, + 553, + 262 + ], + "lines": [ + { + "bbox": [ + 58, + 101, + 553, + 262 + ], + "spans": [ + { + "bbox": [ + 58, + 101, + 553, + 262 + ], + "type": "table", + "html": "
MethodDehazing on SOTSDeraining on Rain100LDenoising on CBSD68Deblurring on GoproLow-light Enh. on LOLAverage
DGUNet* [33]24.78 / 0.94036.62 / 0.97131.10 / 0.88327.25 / 0.83721.87 / 0.82328.32 / 0.891
SwinIR* [25]21.50 / 0.89130.78 / 0.92330.59 / 0.86824.52 / 0.77317.81 / 0.72325.04 / 0.835
Restomer* [57]24.09 / 0.92734.81 / 0.96231.49 / 0.88427.22 / 0.82920.41 / 0.80627.60 / 0.881
NAFNet* [3]25.23 / 0.93935.56 / 0.96731.02 / 0.88326.53 / 0.80820.49 / 0.80927.76 / 0.881
DL [11]20.54 / 0.82621.96 / 0.76223.09 / 0.74519.86 / 0.67219.83 / 0.71221.05 / 0.743
Transweather [46]21.32 / 0.88529.43 / 0.90529.00 / 0.84125.12 / 0.75721.21 / 0.79225.22 / 0.836
TAPE [28]22.16 / 0.86129.67 / 0.90430.18 / 0.85524.47 / 0.76318.97 / 0.62125.09 / 0.801
AirNet [21]21.04 / 0.88432.98 / 0.95130.91 / 0.88224.35 / 0.78118.18 / 0.73525.49 / 0.846
IDR [59]25.24 / 0.94335.63 / 0.96531.60 / 0.88727.87 / 0.84621.34 / 0.82628.34 / 0.893
InstructIR [8]27.10 / 0.95636.84 / 0.97331.40 / 0.88729.40 / 0.88623.00 / 0.83629.55 / 0.907
DFPIR(Ours)31.64 / 0.97937.62 / 0.97831.29 / 0.88928.82 / 0.87323.82 / 0.84330.64 / 0.913
", + "image_path": "f2ba637c86223dcbdb3594c0bb4820e0ed398d1c747c630c83023d3595fb8358.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 281, + 295, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 295, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 295, + 319 + ], + "type": "text", + "content": "inherent characteristics of the image (as channel shuffling does not result in channel feature loss), thereby improving reconstruction quality." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": "Attention-wise Perturbation Strategy. The main purpose of channel shuffle is to minimize the influence of degradation features while preserving the inherent characteristics of the image. However, this reduction is not thorough enough, meaning its effectiveness is limited. To address this, we directly discard a portion of the attention in the attention maps to further mitigate the impact of multiple degradation features (as shown in Fig.2). Specifically, we compute the transposed cross attention map " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{tt} \\in R^{\\widehat{C} \\times \\widehat{C}}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": ". We select a portion of the attention map values from each column of " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{tt}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": " using the top-K method to generate a disturbance mask matrix " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in R^{\\widehat{C} \\times \\widehat{C}}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": ", where the values that are not selected are set to 0, and the remaining values are set to 1. Then, the matrix " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": " is multiplied element-wise with " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{tt}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": " to obtain a new attention map " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{ttn}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": ", achieving perturbation in the attention dimension. In other words, " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{ttn} = \\mathbf{A}_{tt} \\odot \\mathbf{M}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{tt}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_*\\mathbf{K}_*^T / \\sqrt{d_k}" + }, + { + "bbox": [ + 55, + 332, + 296, + 540 + ], + "type": "text", + "content": " in equation 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 550, + 137, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 550, + 137, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 550, + 137, + 563 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 570, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 713 + ], + "type": "text", + "content": "In this section, we follow the protocols of prior state-of-the-art works [21, 39] to conduct experiments under two settings: (a) all-in-one and (b) single-task. For the all-in-one setting, a unified model is trained to handle multiple degradation types, with experiments conducted across three and five distinct degradations. In contrast, the single-task setting involves training separate models, each specialized for a specific restoration task. The image quality metrics—PSNR and SSIM [16]—for the top-performing methods are highlighted in red and the second-best results are highlighted in blue in the result tables. Single-task results and more visual experiments are in the supplementary material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 281, + 441, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 441, + 294 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 441, + 294 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 308, + 555, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 555, + 465 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 555, + 465 + ], + "type": "text", + "content": "Datasets. In line with previous work [21, 39], we prepare datasets tailored for various restoration tasks. For single-task image denoising, we merge images from the BSD400 [1] and WED [30] datasets to train the model. Testing is conducted on the CBSD68 [32] and Urban100 [14] datasets. For image dehazing, we use the SOTS [20] dataset, while Rain100L [53] is employed for image deraining. Deblurring and low-light enhancement tasks utilize the GoPro [34] and LOL-v1 [34] datasets, respectively. In the all-in-one setting, a unified model is trained on the combined training datasets mentioned above and tested directly across multiple restoration tasks. Additional dataset details can be found in the supplementary materials." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": "Implementation Details. Our DFPIR provides an end-to-end trainable solution, removing the necessity for pretraining any individual components. Following the configuration of PromptIR [39], our DFPIR architecture features a 4-level encoder-decoder structure, comprising varying numbers of Transformer blocks at each level, specifically [4, 6, 6, 8] from level-1 to level-4. We integrate our Degradation-Guided Perturbation Block (DGPB) between the encoder and decoder, with a total of four DGPBs distributed throughout the network. We conduct our experiments using PyTorch on a single NVIDIA GeForce RTX 3090 GPU. For training, we run for 80 epochs with an initial learning rate of " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": ", followed by fine-tuning for 5 epochs at a learning rate of " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "1e^{-5}" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": ". Initially, we set the patch size to " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "128^2" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " with the batch size of 5, and for fine-tuning, the patch size is adjusted to " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "192^2" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " with a batch size of 3. The network is optimized using the L1 loss function in conjunction with the Adam optimizer (with parameters " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": "). We train on cropped patches and augment the dataset with random horizontal and vertical flips." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28170" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 553, + 302 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 302 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 302 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 302 + ], + "type": "image", + "image_path": "acb9365ca31a97e0485dd698a7fe410c8b935a454592935105d718ed31b596ed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 303, + 555, + 324 + ], + "lines": [ + { + "bbox": [ + 55, + 303, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 55, + 303, + 555, + 324 + ], + "type": "text", + "content": "Figure 5. Visual comparison of DFPIR with state-of-the-art methods on challenging cases for the All-in-One setting considering three degradations. Zoom in for better view." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 345, + 251, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 345, + 251, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 345, + 251, + 357 + ], + "type": "text", + "content": "4.2. Results Comparisons on Three Tasks" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "spans": [ + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "text", + "content": "We assess the performance of our all-in-one DFPIR across three distinct restoration tasks: dehazing, deraining, and denoising. Our DFPIR is compared with various general image restoration methods, including Restormer [57], FDGAN [10], and MPRNet [56], as well as specialized all-in-one approaches such as DL [11], AirNet [21], PromptIR [39], and InstructIR [8]. As shown in Tab. 1, the proposed DFPIR consistently outperforms the other competing methods. On average across the different restoration tasks, our algorithm achieves a performance improvement of " + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "inline_equation", + "content": "0.45\\mathrm{dB}" + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "text", + "content": " over the previous best method, InstructIR [8], and " + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "inline_equation", + "content": "0.82\\mathrm{dB}" + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "text", + "content": " over the second-best approach, PromptIR [39]. Specifically, DFPIR demonstrates a notable increase of " + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "inline_equation", + "content": "0.67\\mathrm{dB}" + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "text", + "content": " on the deraining task and " + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "inline_equation", + "content": "1.65\\mathrm{dB}" + }, + { + "bbox": [ + 54, + 364, + 295, + 543 + ], + "type": "text", + "content": " on the dehazing task compared to InstructIR [8]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 551, + 243, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 551, + 243, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 551, + 243, + 563 + ], + "type": "text", + "content": "4.3. Results Comparisons on Five Tasks" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 570, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 570, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 54, + 570, + 295, + 712 + ], + "type": "text", + "content": "To further validate the method's effectiveness in addressing a broader range of tasks, building upon the recent research conducted by IDR [59] and InstructIR [8], we extend our investigation into the efficacy of DFPIR by conducting experiments across five restoration tasks: dehazing, deraining, denoising, deblurring, and low-light image enhancement. To achieve this, we train a comprehensive DFPIR on combined datasets compiled for five distinct tasks. These encompass datasets from the previously mentioned threetask scenario, alongside additional datasets: GoPro [34] for motion deblurring and LOL [50] for low-light image enhancement. Tab. 2 demonstrates that DFPIR achieves a 1.09" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 346, + 555, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 555, + 441 + ], + "type": "text", + "content": "dB improvement compared to the recent leading method InstructIR [8], when averaged across five restoration tasks. Additionally, we compare our method to general image restoration models that were trained in the same All-in-One setting. Notably, our method surpasses Restormer[57] and NAFNet [3] on average PSNR by 3.04 dB and 2.88 dB, respectively, validating the effectiveness of our approach in handling multiple degradations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 453, + 404, + 465 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 404, + 465 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 404, + 465 + ], + "type": "text", + "content": "4.4. Visual Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 474, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 555, + 715 + ], + "type": "text", + "content": "Visual examples illustrating our results for dehazing, de- raining, and denoising are provided in Fig.5. Compared to PromptIR [39] and InstructIR [8], our method is more effective in challenging dehazing scenarios. Additionally, our model's deraining results are closer to the ground-truth images. Furthermore, in image denoising, our model recovers more details from heavily degraded noisy inputs. We visualized the results of channel shuffling, as shown in Fig.7. After channel shuffling, the channel order for each task changed accordingly, which validates the effectiveness of our proposed channel shuffling strategy. Additionally, we also visualized the feature perturbations before and after for the " + }, + { + "bbox": [ + 313, + 474, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_1" + }, + { + "bbox": [ + 313, + 474, + 555, + 715 + ], + "type": "text", + "content": " layer, as shown in Fig.6. As can be seen, after channel dimension perturbation (DGCPM), the network extracts the image's inherent features from multi-degradation scenarios, reducing the impact of degradation-specific features. With the addition of perturbation in the attention dimension (DGCPM+CAAPM), the intrinsic detail features of the image are further enhanced, while the degradation features are more effectively suppressed. This demonstrates the efficacy" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28171" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 294, + 197 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 294, + 197 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 294, + 197 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 294, + 197 + ], + "type": "image", + "image_path": "e0be6a4e4db7fb1572a3a41d94b7999a2c4228d61c7ff8fcedf4a64b1c71c34d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 198, + 295, + 242 + ], + "lines": [ + { + "bbox": [ + 55, + 198, + 295, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 198, + 295, + 242 + ], + "type": "text", + "content": "Figure 6. Feature visualization. DGCPM extracts the intrinsic features of the image while suppressing degradation characteristics. DGCPM + CAAPM enhances intrinsic features while further reducing the impact of degradation. Zoom in for better view." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 262, + 295, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 262, + 295, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 295, + 275 + ], + "type": "text", + "content": "of our proposed channel and attention perturbation strategy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 281, + 160, + 293 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 160, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 160, + 293 + ], + "type": "text", + "content": "4.5. Ablations Studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 300, + 295, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 295, + 371 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 295, + 371 + ], + "type": "text", + "content": "We conduct several ablation experiments to demonstrate the effectiveness of our proposed degradation-guided perurbation block. We report the results of training an all-in-one model on combined datasets from three restoration tasks. More detailed ablation experiments can be found in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "spans": [ + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "type": "text", + "content": "Impact of key components. As illustrated in the Tab. 3(a), using channel attention (Method (a)) directly improves by " + }, + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "type": "inline_equation", + "content": "0.36\\mathrm{dB}" + }, + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "type": "text", + "content": " compared to the baseline [57], but it is " + }, + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "type": "inline_equation", + "content": "0.15\\mathrm{dB}" + }, + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "type": "text", + "content": " lower than channel shuffle (Method (c)). This also validates the effectiveness of the channel shuffle strategy we proposed. Channel shuffle preserves inherent image features with degradation info but offers limited reduction in cross-degradation interference. By applying attention-wise perturbation, restoration quality is significantly enhanced (DGCPM+CAAPM). The average PSNR increased from 32.49 to 32.88, reflecting an improvement of " + }, + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "type": "inline_equation", + "content": "0.39\\mathrm{dB}" + }, + { + "bbox": [ + 55, + 372, + 295, + 550 + ], + "type": "text", + "content": ". However, Method (b) (CA+CAAPM) results in a lower performance than DFPIR, indicating that the perturbations in channel and attention dimensions produce a synergistic enhancement effect." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "type": "text", + "content": "Impact of parameter " + }, + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "type": "text", + "content": ". As illustrated in the Tab. 3(b), if the perturbation in the attention dimension is too high (" + }, + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "type": "inline_equation", + "content": "\\gamma = 0.5" + }, + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "type": "text", + "content": ") or absent (" + }, + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "type": "inline_equation", + "content": "\\gamma = 1.0" + }, + { + "bbox": [ + 55, + 552, + 295, + 659 + ], + "type": "text", + "content": "), the performance is not optimal. This is because excessive perturbation, while reducing the interference between images with different degradations, increases information loss, leading to suboptimal performance. Similarly, if the perturbation is too small, the interference between tasks becomes more significant, resulting in suboptimal performance as well." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 669, + 128, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 128, + 681 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 128, + 681 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "In this paper, we present a novel all-in-one image restoration framework, DFPIR, which introduces Degradation-" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 315, + 133, + 465, + 213 + ], + "blocks": [ + { + "bbox": [ + 314, + 70, + 555, + 103 + ], + "lines": [ + { + "bbox": [ + 314, + 70, + 555, + 103 + ], + "spans": [ + { + "bbox": [ + 314, + 70, + 555, + 103 + ], + "type": "text", + "content": "Table 3. Ablation study results on three tasks. Average PSNR (dB, ↑) and SSIM (↑) metrics are reported on the full RGB images. The CA stands for Channel Attention." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 114, + 438, + 125 + ], + "lines": [ + { + "bbox": [ + 328, + 114, + 438, + 125 + ], + "spans": [ + { + "bbox": [ + 328, + 114, + 438, + 125 + ], + "type": "text", + "content": "(a) Impact of key components." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 133, + 465, + 213 + ], + "lines": [ + { + "bbox": [ + 315, + 133, + 465, + 213 + ], + "spans": [ + { + "bbox": [ + 315, + 133, + 465, + 213 + ], + "type": "table", + "html": "
MethodCADGCPMCAAPMPSNR/SSIM
baseline×××31.98 / 0.911
(a)✓××32.34 / 0.914
(b)✓×✓32.65 / 0.917
(c)×✓×32.49 / 0.910
DFPIR×✓✓32.88 / 0.919
", + "image_path": "503f7c2f2d491d90de4da4c7ba625b1245934e85a90b544420f09026f12dddf2.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 470, + 133, + 547, + 213 + ], + "blocks": [ + { + "bbox": [ + 479, + 114, + 537, + 125 + ], + "lines": [ + { + "bbox": [ + 479, + 114, + 537, + 125 + ], + "spans": [ + { + "bbox": [ + 479, + 114, + 537, + 125 + ], + "type": "text", + "content": "(b) Impact of " + }, + { + "bbox": [ + 479, + 114, + 537, + 125 + ], + "type": "inline_equation", + "content": "\\gamma" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 470, + 133, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 470, + 133, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 470, + 133, + 547, + 213 + ], + "type": "table", + "html": "
γPSNR / SSIM
0.532.67 / 0.913
0.732.81 / 0.919
0.832.84 / 0.919
0.932.88 / 0.919
1.032.83 / 0.919
", + "image_path": "2eeac9a2eb697846aa2fb703ef66b3736cfaf699547c3d0d318f52f8f9257f91.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 315, + 224, + 553, + 322 + ], + "blocks": [ + { + "bbox": [ + 315, + 224, + 553, + 322 + ], + "lines": [ + { + "bbox": [ + 315, + 224, + 553, + 322 + ], + "spans": [ + { + "bbox": [ + 315, + 224, + 553, + 322 + ], + "type": "image", + "image_path": "ddefacbba56e202c78d3c95b08110ebb8b6c206288fd36715ef52cab409ab7b4.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 322, + 555, + 354 + ], + "lines": [ + { + "bbox": [ + 313, + 322, + 555, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 322, + 555, + 354 + ], + "type": "text", + "content": "Figure 7. Channel shuffle visualization. After channel shuffling, the feature channel order for each task has changed compared to the original order." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 374, + 555, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 374, + 555, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 374, + 555, + 567 + ], + "type": "text", + "content": "aware Feature Perturbations (DFP) to adjust the feature space in alignment with a unified parameter space. Our approach incorporates both channel-wise and attentionwise perturbations, dynamically guided by degradation type prompts. Specifically, channel-wise perturbations are achieved by shuffling channels in a high-dimensional space, while attention-wise perturbations are implemented through selective masking in the attention space. To effectively realize these operations, we design a Degradation-Guided Perturbation Block (DGPB), which integrates channel shuffling and attention masking, strategically placed between the encoding and decoding stages of the encoder-decoder architecture. The proposed DGPB demonstrates its efficacy in enhancing comprehensive image restoration when integrated into a state-of-the-art model, yielding notable improvements in the all-in-one restoration setting." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 574, + 419, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 419, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 419, + 588 + ], + "type": "text", + "content": "6. Acknowledgment" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China under Grant 62171304 and partly by the Natural Science Foundation of Sichuan Province under Grant 2024NSFSC1423, Cooperation Science and Technology Project of Sichuan University and Dazhou City under Grant 2022CDDZ-09, the TCL Science and Technology Innovation Fund under grant 25JZH008, and the Young Faculty Technology Innovation Capacity Enhancement Program of Sichuan University under Grant 2024SCUQJTX025." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28172" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. 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However, these large models typically process videos by averaging embedding outputs from multiple clips over time to produce fixed-length representations. This approach fails to account for a variety of time-related features, such as variable video durations, chronological order of events, and temporal variance in feature significance. While methods for temporal modeling do exist, they often require significant architectural changes and expensive retraining, making them impractical for off-the-shelf, fine-tuned large encoders. To overcome these limitations, we propose DejaVid, an encoder-agnostic method that enhances model performance without the need for retraining or altering the architecture. Our framework converts a video into a variable-length temporal sequence of embeddings (TSE). A TSE naturally preserves temporal order and accommodates variable video durations. We then learn per-timestep, per-feature weights over the encoded TSE frames, allowing us to account for variations in feature importance over time. We introduce a new neural network architecture inspired by traditional time series alignment algorithms for this learning task. Our evaluation demonstrates that DejaVid substantially improves the performance of a state-of-the-art large encoder, achieving leading Top-1 accuracy of $77.2\\%$ on Something-Something V2, $89.1\\%$ on Kinetics-400, and $88.6\\%$ on HMDB51, while adding fewer than $1.8\\%$ additional learnable parameters and requiring less than 3 hours of training time. Our code is available at https://github.com/darrylho/DejaVid.", + "bbox": [ + 88, + 320, + 485, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 787, + 220, + 803 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video action recognition has seen remarkable progress with the rise of transformer-based video models [2, 7, 10]. To improve their performance, one of the most straightforward and effective approaches is to upscale the model and training data [33]. As such, the leaderboards of major action recognition benchmarks have come to be dom", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c4c3a1c57f32e388d56cea0f15fbbef3842597e6b37526e5b5e4eb0229cf446d.jpg", + "image_caption": [ + "Pre-training Training" + ], + "image_footnote": [], + "bbox": [ + 516, + 303, + 903, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/28e85de19bb4088a6c6512d8bcb9a5ac8cb516bb5aeb3a8f0f73fce4856bf5d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 402, + 903, + 508 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4fa947fdd9646b701df09c0a16ede581f80bcbf524bb8ce939e3f8fba843fd2f.jpg", + "image_caption": [ + "Figure 1. DejaVid system diagram. We first transform a video into a variable-length temporal sequence of embeddings (TSE) then use Dynamic Time Warping Barycenter Averaging (DBA) [21] to calculate a reasonably \"average\" TSE per class for its centroid initialization. We then learn per-timestep, per-feature weights for the encoded TSE frames, enabling us to accommodate variations in feature importance over time, as well as finetune the centroid TSE for each output class. For this task, we introduce a new neural network architecture inspired by traditional time series alignment algorithms. In testing, we freeze the post-training centroids and weights and use the same pre-training pipeline to generate TSEs to feed into DejaVid for predictions." + ], + "image_footnote": [], + "bbox": [ + 516, + 510, + 905, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "inated by 100M-1B+ parameter large video transformers [14, 16, 18, 22, 28-30].", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24023", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "These large encoders process videos with fixed frame counts, heights, and widths, generating a single embedding. On datasets with varying durations, the common approach is to pass multiple temporal clips and spatial crops through the encoder and then average the resulting logits for class prediction [22, 28-30]. However, while the height and width of videos in a dataset are usually constant, their duration can vary significantly [14]. Furthermore, temporal order is far more critical. Unlike image flipping [17], reversing time can alter semantics, such as opening vs. closing a door. When averaging logits from different temporal clips, sequential information in these clips is lost. Moreover, the significance of each feature within a video can change over time. For example, in a basketball three-point shot, early frames emphasize player position, while later frames focus on whether the ball goes in. Although encoders might not explicitly model semantically interpretable features like these, temporal variation in feature importance can also occur for arbitrary features, which mean-pooling fails to capture adequately. This motivates a key observation of our work: by failing to carefully account for temporal dimensions, state-of-the-art large models leave significant accuracy gains on the table.", + "bbox": [ + 93, + 90, + 480, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Improving the temporal performance of large encoders is not trivial. Existing temporal-focused methods require invasive changes to the model, such as inserting temporal-specific layers between transformer blocks [27, 31] or creating model duplications to focus on different input views [11, 32]. These approaches are costly to apply to off-the-shelf pre-trained encoders because they require extensive changes in implementation and costly re-training.", + "bbox": [ + 93, + 443, + 480, + 563 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These insights motivate DejaVid, a lightweight encoder-agnostic temporal approach that substantially boosts model classification performance. The simple yet crucial idea behind DejaVid is that a video is more effectively represented as a temporal sequence of embeddings (TSE) rather than as a single embedding. This representation naturally preserves chronological order while supporting varying time lengths, addressing the aforementioned shortcomings. DejaVid is naturally able to use any pre-trained model by consuming a sliding-window of encoded video to generate a TSE, without requiring changes to the model's architecture, retraining, or fine-tuning. DejaVid is inspired by the well-known Dynamic Time Warping (DTW) algorithm [4], which dynamically aligns similar data points between two temporal sequences while maintaining their chronological order. In particular, DejaVid introduces a novel neural network architecture inspired by DTW but with learned per-timestep, per-feature weights to handle the temporal variance of feature importance. Additionally, we develop a custom high-performance CUDA kernel for efficient computation and backpropagation of the (time-weighted) warping distance that outperforms a naive DTW-based implementation by 2", + "bbox": [ + 93, + 569, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "orders of magnitude.", + "bbox": [ + 517, + 92, + 651, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate DejaVid by layering it on top of the largest (ViT-g) variant of VideoMAE V2 [28] (abbr. VideoMAE V2-g) as the backbone encoder to evaluate DejaVid on three popular action recognition datasets: Kinetics-400 [16], Something-Something V2 [14], and HMDB51 [18]. We show that DejaVid significantly improves on the strongest VideoMAE V2-g baseline, thereby achieving new state-of-the-art performance. In particular, DejaVid achieves Top-1 accuracy of $77.2\\%$ on Something-Something V2, $89.1\\%$ on Kinetics-400, and $88.6\\%$ on HMDB51, while adding fewer than $1.8\\%$ additional learnable parameters and requiring less than 3 hours of training time. We also show that our proposed modifications to DTW, including the temporal weights, can further improve prediction performance.", + "bbox": [ + 517, + 108, + 903, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 517, + 332, + 651, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "State-of-the-Art in Action Recognition. Major action recognition benchmarks are topped by massive video transformers with hundreds of millions or billions of parameters. As of the time of writing, according to Papers with Code, the top performers on Kinetics-400 and Something-Something V2 with verifiable parameter counts have between 600M and 6B parameters [14, 16, 22, 28-30]. However, their evaluations on these two datasets all apply spatial and temporal mean-pooling to the logits at the end, which suffers from the time-related shortfalls related to variable video durations, chronological order of events, and temporal variance in feature significance, as described in Sec. 1.", + "bbox": [ + 517, + 354, + 903, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Temporal-focused Methods for Action Recognition. There have been various works on improving the temporal modeling capability of video transformers. One general approach is to introduce temporal-specific layers in between transformer blocks. For example, ILA employs a mask-based layer that predicts interactive points between frame pairs to implicitly align features [27], ATM applies basic arithmetic operations to pairs-of-frame features between ViT blocks [31], and TAM inserts an attention-based temporal adaptive module between 2D convolutions within a ResNet block [19]. Another line of work is to fuse multiple temporal views in different ways. For example, SlowFast networks feed two different frame rates of a video into separate encoders and add lateral connections between them to fuse information across views [11], and MTV deploys a similar idea but for both spatial and temporal dimensions [32]. However, their performance is not competitive against the aforementioned large state-of-the-art models, partly due to their smaller size. Implementing these methods within the large models would involve considerable implementation changes and expensive retraining.", + "bbox": [ + 517, + 537, + 903, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning Temporal Sequence Alignments. DTW is one of the most classic methods for calculating similarities between univariate time series or multivariate ones like our", + "bbox": [ + 517, + 856, + 903, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24024", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "TSEs [4, 23]. Its traditional formulation is a dynamic programming scheme, but recent work has explored making it differentiable and then applying it to various fields. SoftDTW [9] shows that DTW makes a good loss function when the min operator is replaced with soft-min. DTWnet [5] proposes using DTW learning for time series feature extraction, and D3TW, OTAM, and FTCL [6, 8, 12] similarly do this for weakly-supervised and few-shot video understanding. While these works have some similarities to our DTW-based temporal representation learning, our method is technically different and superior in three ways:", + "bbox": [ + 89, + 90, + 483, + 256 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. DejaVid models and learns the temporal variance in feature importance, which none of the other methods do. While classical DTW typically only works for a few dimensions (10-100) that require handcrafting or hand-picking [3], by adding learned weights, we extend DTW to high-dimensional use cases $(1000 - 10000+)$ like video recognition by letting it learn the important dimensions.", + "2. We reformulate our DTW-inspired temporal learning algorithm as a new neural network architecture that boosts parallelizability and facilitates differentiability.", + "3. We introduce changes to DTW to improve model stability, including removing the diagonal transition of DTW." + ], + "bbox": [ + 91, + 257, + 482, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 449, + 181, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As described in Sec. 1, we represent a video as a temporal sequence of embeddings (TSE). In this section, we assume all videos have been converted into TSEs, and operate in this TSE space. DejaVid feeds a video encoder a sliding-window stream of frames of an input video to generate a TSE, so the shape of a TSE is $T \\times N_{f}$ , where each index along $T$ represents the encoding of a window of frames, and thus $T$ can vary depending on individual video duration. $N_{f}$ is the size of the embedding vector of the backbone encoder and is constant.", + "bbox": [ + 89, + 474, + 483, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our problem is to classify TSEs. Specifically, we are given a training set of TSEs with class labels among $N_{c}$ classes, and our goal is to predict the classes of our validation TSEs. We solve this problem in three broad steps:", + "bbox": [ + 89, + 626, + 483, + 686 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. For each class, we calculate a centroid TSE from the training TSEs of that class.", + "2. We optimize the centroid TSEs according to some loss function w.r.t. the training TSEs.", + "3. For each validation TSE, we calculate which class's centroid TSE is the most similar to it." + ], + "bbox": [ + 91, + 686, + 482, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, Steps 1 and 3 require a definition of distance (or similarity) between TSE pairs, and Step 2 requires the distance metric to be backpropagateable. The following Secs. 3.1 and 3.2 describe how we solve these two problems.", + "bbox": [ + 89, + 780, + 483, + 842 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Definitions", + "text_level": 1, + "bbox": [ + 89, + 848, + 210, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There are multiple ways in which one can define the distance between two TSEs [4, 24], but in this paper, we focus", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "on a standard time series distance metric: Dynamic Time Warping (DTW), as given in Algorithm 1 (without the red text). DTW aligns two sequences that vary in time or speed by minimizing the distance between corresponding points. The two sequences are aligned by aligning each timestep in the first sequence to one or more consecutive timesteps in the second sequence while maintaining a monotonic relationship where a later timestep in the first must map to a later interval in the second. Monotonicity is maintained in Line 5 of Algorithm 1, where each step only moves forward in time for either sequence (from $i - 1$ to $i$ or $j - 1$ to $j$ ). This alignment minimizes cumulative distance and is commonly visualized as a \"warping path\" on a 2D grid, which shows the optimal alignment of the two sequences, each depicted in one grid axis.", + "bbox": [ + 511, + 90, + 906, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Algorithm 1 The Standard DTW Algorithm (without diagonal transition) vs. the Time-Weighted DTW Algorithm (red) \nInput: Two TSEs $a, b \\in \\mathbb{R}^{n \\times N_f}, \\mathbb{R}^{m \\times N_f}$ ; a distance function $dist_w$ ; $u \\in \\mathbb{R}_{>0}^{n \\times N_f}$ temporal feature weights of $a$ \nOutput: Distance between $a$ and $b$", + "bbox": [ + 511, + 330, + 906, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "1: $D \\gets \\operatorname{array}[n, m]$ {Out-of-bounds access returns $+\\infty$ }", + "bbox": [ + 522, + 414, + 903, + 431 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "2: $D_{0,0}\\gets dist_w(u_0,a_0,b_0)$", + "3: for $i$ in $[0, n - 1]$ do", + "4: for $j$ in $([0, m - 1]$ if $i > 0$ else $[1, m - 1]$ ) do", + "5: $D_{i,j}\\gets \\min (D_{i - 1,j},D_{i,j - 1}) + dist_w(u_i,a_i,b_j)$", + "6: end for", + "7: end for", + "8: return $D_{n-1,m-1}$" + ], + "bbox": [ + 522, + 444, + 893, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the standard Algorithm 1, we use the Manhattan distance for the pointwise distance function $dist$ . Also, although the original DTW algorithm includes a diagonal transition $D_{i-1,j-1}$ in the min clause, we omit this in DejaVid because it improves model stability. We discuss this decision in more detail in Sec. 3.4.", + "bbox": [ + 511, + 561, + 906, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $D_v(a,b)$ denote the DTW distance between TSEs $a$ and $b$ as returned by the standard Algorithm 1, and let $C \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}$ represent the centroid TSEs for the $N_c$ classes. Intuitively, we want to assign each TSE to the class it is nearest to in the DTW space. To do this, we define the predicted probability distribution $\\hat{\\mathbf{y}}_v$ for a training or validation TSE $m \\in \\mathbb{R}^{T_m \\times N_f^1}$ , and the loss $\\mathcal{L}_v$ for $m$ under centroids $C$ and one-hot ground truth vector $\\mathbf{y}$ :", + "bbox": [ + 511, + 652, + 906, + 773 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {y}} _ {v} (C, m) := \\underset {0 \\leq i < N _ {c}} {\\operatorname {s o f t m i n}} \\left(D _ {v} \\left(C _ {i}, m\\right)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 776, + 823, + 799 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v} (C, m) := \\operatorname {C r o s s E n t r o p y} (\\mathbf {y}, \\hat {\\mathbf {y}} _ {v} (C, m))\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 800, + 849, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, as described in Sec. 1, we observe that the importance of each feature of a video can vary as time progresses. This observation motivates our time-weighted", + "bbox": [ + 511, + 821, + 905, + 867 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "In practice, we perform a LayerNorm operation before the soft-min, but this doesn't qualitatively change our approach.", + "bbox": [ + 511, + 875, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24025", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DTW distance metric, given in Algorithm 1 with modifications shown in red. The difference is the additional weight input $u$ , which denotes the change in feature importance over time for $a$ . We also modify the pointwise Manhattan distance function to incorporate $u$ : $dist_w(u_i, a_i, b_j) := \\sum_{k=0}^{N_f-1} u_{i,k} |a_{i,k} - b_{j,k}|$ . The changes are colored in Lines 2 and 5 of Algorithm 1. Intuitively, when Algorithm 1 calculates the distance between two sequences, our time-weighted modification allows it to weight some timesteps more than some other timesteps in the first series, and different features can have different weights as well. Let $D_w(u, a, b)$ denote the time-weighted DTW distance between TSEs $a$ and $b$ as returned by the time-weighted Algorithm 1. We aim to learn the temporal variance of feature importance of the centroids $C$ , so we define $U \\in \\mathbb{R}_{>0}^{N_c \\times T_c \\times N_f}$ of the same shape as $C$ to be the time-varying feature weights. To maintain the positivity of distances, we constrain $U$ to be positive. The time-weighted variant of predicted probability distribution $\\hat{\\mathbf{y}}_w$ and loss $\\mathcal{L}_w$ are defined similarly as before:", + "bbox": [ + 89, + 90, + 483, + 398 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {y}} _ {w} (U, C, m) := \\operatorname * {s o f t m i n} _ {0 \\leq i < N _ {c}} \\left(D _ {w} \\left(U _ {i}, C _ {i}, m\\right)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 404, + 424, + 426 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {w} (u, C, m) := \\operatorname {C r o s s E n t r o p y} (\\mathbf {y}, \\hat {\\mathbf {y}} _ {w} (u, C, m))\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 430, + 444, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From now on, we focus on the time-weighted Algorithm 1, since one can set $U = \\mathbf{1}_{N_c\\times T_c\\times N_f}$ to recover standard DTW in Algorithm 1.", + "bbox": [ + 89, + 449, + 482, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Parallelizability & Differentiability", + "text_level": 1, + "bbox": [ + 89, + 498, + 397, + 513 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d3b9dc2a9adf3207121ce6722fa7b2e5bf936b2e8b234a8ba6752ecf9ef2465e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 515, + 285, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 285, + 515, + 480, + 603 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f9a81c43fd45cbba525cffa70af147d5b4be9b45ef721c0dc7a5560ba0b182fa.jpg", + "image_caption": [ + "Figure 2. 1. Each cell of the DTW 2D grid executes a min operation and then an add-dist operation. Checkmarks show completed cells in row-major order. 2. In diagonal order, a diagonal can be executed as soon as the previous diagonal has finished. Checkmarks show completed cells in diagonal order. 3. We can view each diagonal as a min-pooling layer with kernel size 2 and stride 1, followed by an additive skip-connection layer. 4. We reformulate the algorithm into a serial stack of min-pooling layers interlaced with additive skip-connections." + ], + "image_footnote": [], + "bbox": [ + 94, + 604, + 285, + 691 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/78c89e18579b5ea8cc2f3c2be1e42e29dfb997bd69f3f31f186c4734b9a45c51.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 515, + 480, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 2 given an equivalent neural-network formulation for Algorithm 1; this formulation facilitates the use of backpropagation for optimizing weights and enhances parallelizability. Before providing the details of the algorithm, we provide some intuition as to how and why it works.", + "bbox": [ + 89, + 825, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 2 depicts the 2D grid commonly used for representing DTW warping path(s) between two sequences, as described in Sec. 3.1. We visualize each operation in the nested loop in Algorithm 1 onto the corresponding cell in the grid. We can see that each cell executes a min operation on the outputs of its left-adjacent and bottom-adjacent cells, followed by an addition of some pointwise weighted distance $dist_w$ . Note that cells are executed in a row-major order in Algorithm 1. Therefore, the critical path length is quadratic $(O(nm))$ .", + "bbox": [ + 511, + 90, + 905, + 241 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, we leverage a critical property of Algorithm 1 that enables a reformulation of the algorithm, which is that each cell can be executed as soon as its left and bottom neighbors have finished. Therefore, we reformulate Algorithm 1 to execute in diagonal order and observe that the $l$ -th diagonal can be executed as soon as the $(l - 1)$ -th diagonal has finished. Here, we define the $l$ -th diagonal to be the cells $\\{(i,j) \\mid i + j = l\\}$ . For example, the top-right of Fig. 2 shows the 4th diagonal. Furthermore, elements in the same diagonal are mutually independent, so the work within each diagonal is parallelized. So we have reduced the critical path length to the number of diagonals, obtaining the linear runtime $O(n + m)$ .", + "bbox": [ + 511, + 242, + 906, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Because each cell executes at Line 5 of Algorithm 1 a min operation on two consecutive cells of the previous diagonal and then adds some $dist_w$ term, we can express the new formulation as a neural net where each diagonal is a min-pooling layer with kernel size 2 and stride 1 followed by an additive skip-connection layer. Each min-pooling layer is executed after its previous skip-connection and min-pooling are completed. So Algorithm 1 is equivalent to a serial stack of min-pooling layers, with skip-connections interlacing in between. These descriptions are formalized in Algorithm 2, where one can see the execution of the interlaced layers at Lines 10 and 11. For differentiability, we rewrite the time-weighted DTW distance $D_w$ as:", + "bbox": [ + 511, + 438, + 908, + 635 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} D _ {w} := S C _ {n + m - 2} + M P _ {n + m - 2} \\left(S C _ {n + m - 3} + M P _ {n + m - 3}\\right) \\\\ \\ldots + S C _ {1} + M P _ {1} \\left(S C _ {0}\\right) \\dots)) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 637, + 906, + 670 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $MP_{l}$ and $SC_{l}$ are the $l$ -th min-pooling and skipconnection as show in Algorithm 2. Because both min-pooling and additive skip-connections are standard neural network operations, loss gradients trivially propagate through them. In a nutshell, the loss backpropagates to only the $dist_{w}(u_{i},a_{i},b_{j})$ functions on the optimal warping path, which enables gradient-based optimization on $U$ and $C$ . We leave the detailed formulas for loss gradients $\\frac{\\partial L_w}{\\partial C}$ and $\\frac{\\partial L_w}{\\partial U}$ in Supplementary Material.", + "bbox": [ + 511, + 676, + 905, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. System Overview", + "text_level": 1, + "bbox": [ + 511, + 821, + 684, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the definitions introduced in Secs. 3.1 and 3.2, we now formalize the 3-step solution outlined at the start of Sec. 3. Fig. 1 provides an overview of the DejaVid system. The video encoder takes as input a video clip of fixed duration", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24026", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [], + "code_body": "Algorithm 2 Time-Weighted DTW Neural Network \nInput: Two TSEs $a, b \\in \\mathbb{R}^{n \\times N_f}, \\mathbb{R}^{m \\times N_f}$ ; a distance func \ntion $dist_w$ ; $u \\in \\mathbb{R}_{>0}^{n \\times N_f}$ temporal feature weights of $a$ \nOutput: Distance between $a$ and $b$ \n1: {Out-of-bounds access to $D$ or $SC$ returns $+\\infty$ } \n2: $SC_{0,0} \\gets dist_w(u_0, a_0, b_0)$ {The 0-th skip- \nconnection} \n3: $D_{0,0} \\gets SC_{0,0}$ \n4: for $l$ in $[1, n + m - 2]$ do \n5: {The $l$ -th diagonal} \n6: start, end $\\leftarrow \\max(0, l - m + 1)$ , $\\min(n - 1, l)$ \n7: $SC_l \\gets [dist_w(u_t, a_t, b_{l-t})]_{t=start}^{\\text{end}}$ \n8: $D_l \\gets \\text{array[end - start + 1]}$ \n9: kernel, stride $\\leftarrow 2, 1$ \n10: for $i$ in range(0, end - start + 1, stride) do \n11: $D_{l,i} \\gets SC_{l,i} + \\min_{s=0}^{kernel-1}(D_{l-1,i-s})$ \n12: end for \n13: end for \n14: return $D_{n+m-2,0}$", + "bbox": [ + 91, + 89, + 483, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and outputs an embedding $e \\in \\mathbb{R}^{N_f}$ . Given any off-the-shelf video encoder, we apply a sliding window over each video to produce a sequence of clips, which we then feed into the encoder to produce a temporal sequence of embeddings $E = \\{e_0, e_1, \\dots, e_{T-1}\\} \\in \\mathbb{R}^{T \\times N_f}$ , which forms a TSE for each video sample in the dataset. Then, we produce a centroid TSE of shape $T_c \\times N_f^2$ for each class by feeding the training TSEs to the DBA (Dynamic Time Warping Barycenter Averaging) [21] algorithm, which calculates a reasonable \"average\" time series of the inputs while accounting for imperfect temporal alignment. Intuitively, each centroid TSE represents how the class-wide average of the $N_f$ features changes over time. Ultimately, we obtain many training TSEs, each with shape $T \\times N_f$ for some varying $T$ , and a stack of centroid TSEs $C$ of shape $N_c \\times T_c \\times N_f$ , where $N_c$ is the number of classes. This concludes the pretraining stage of DejaVid.", + "bbox": [ + 89, + 417, + 483, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the training phase, to account for temporal variance in feature importance over time, each centroid TSE is paired with a positive weight tensor of the same shape $T_{c} \\times N_{f}$ that represents the importance of each feature over time. The positivity is to maintain that the pointwise distance $\\text{dist}_{w}$ is always positive. We denote the stack of weight TSEs $U$ with shape $N_{c} \\times T_{c} \\times N_{f}$ . At initialization, the weight TSEs are either filled with ones or random positive values.", + "bbox": [ + 89, + 676, + 482, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In each epoch, we calculate the weighted DTW distance $D_w$ from each training TSE $m \\in \\mathbb{R}^{T \\times N_f}$ to every centroid TSE to get the logit vector $\\mathbf{z} = \\{D_w(U_i, C_i, m)\\}_{i=0}^{N_c-1} \\in \\mathbb{R}^{N_c}$ , on which we apply softmax to get the class prediction $\\hat{\\mathbf{y}}$ and cross-entropy loss $\\mathcal{L}_w$ w.r.t. the ground truth $\\mathbf{y}$ . The", + "bbox": [ + 89, + 799, + 483, + 875 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "weights $U$ and centroids $C$ TSEs are updated during backpropagation. To accelerate forward and backward passes, we implement a custom DTW CUDA kernel that efficiently calculates a slope tensor $S \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}$ and an intercept tensor $B \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}$ such that $\\text{torch.sum}(U \\odot (C \\odot S + B), \\dim = (-2, -1))$ equals the logit vector $\\mathbf{z}$ and the effective gradients w.r.t. $U$ and $C$ equals $\\frac{\\partial L_w}{\\partial U}$ and $\\frac{\\partial L_w}{\\partial C}$ . The implementation of the CUDA kernel, roughly speaking, leverages the fact that a weighted DTW distance is essentially the sum of many terms of $u \\cdot |c - b|$ , which equals $u \\cdot (c \\cdot (\\pm 1) + (\\mp 1)b)$ , where the $(\\pm 1)$ term contributes to slope $S$ and $(\\mp 1)b$ to intercept $B$ .", + "bbox": [ + 511, + 90, + 906, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Modifications to Standard DTW", + "text_level": 1, + "bbox": [ + 511, + 277, + 797, + 291 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As mentioned in Sec. 3.1, unlike the original DTW algorithm, we exclude the diagonal transitions (i.e., transitioning from $D_{i-1,j-1}$ to $D_{i,j}$ in Algorithm 1) for DejaVid. The reason is due to model stability. When matching two series of length $n$ and $m$ , by disallowing diagonal transitions, the warping path from $D_{0,0}$ to $D_{n-1,m-1}$ always takes $n+m-1$ steps, and so the DTW distance will always be the sum of $n+m-1$ step-wise distances. If diagonal transitions are allowed, the number of step-wise distances on the warping path can vary, destabilizing the model. Although beyond the scope of this paper, we note that there could be other ways to deal with diagonal transitions, such as assigning or learning a multiplicative or additive distance bias for diagonal vs. non-diagonal transitions, such as in Move-Split-Merge (MSM) [24], a more modern replacement of DTW that treats diagonal transitions differently from non-diagonal ones.", + "bbox": [ + 511, + 294, + 906, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Another modification we made is to fix epoch centroids and weights. That is, at the beginning of an epoch, we make a frozen copy of the current centroids and weights, and then during the epoch, use them to calculate the warping path for each centroid-training TSE pair. Then, along the path, we calculate the pointwise distance using the (non-frozen) originals and perform backpropagation on them. Note that the frozen copies are not updated per batch but instead per epoch. The reason for this modification is again due to model stability. We found that if the warping path calculation mechanism is updated every batch, the distances become noisier from batch to batch, and the model has a harder time converging.", + "bbox": [ + 511, + 551, + 905, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We discuss the effect of these modifications in Sec. 4.4.", + "bbox": [ + 532, + 748, + 898, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Evaluation", + "text_level": 1, + "bbox": [ + 511, + 766, + 630, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we describe our implementation and evaluation of DejaVid.", + "bbox": [ + 511, + 787, + 905, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 511, + 821, + 799, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We test DejaVid on three different popular action recognition datasets: Something-Something V2 [14], Kinetics-400 [16], and HMDB51 [18]. The first two are large-scale datasets: Something-Something V2 has 168,913 videos for", + "bbox": [ + 511, + 840, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2We set $T_{c} = 8$ for all experiments in this work.", + "bbox": [ + 107, + 886, + 367, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24027", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "training and 24,777 for validation, while Kinetics-400 has 240,436 training and 19,787 validation videos. In contrast, HMDB51 only has 3,570 training and 1,530 validation videos, but its smaller size can help us study the model's performance when the training set is smaller.", + "bbox": [ + 89, + 90, + 480, + 165 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Something-Something V2 has 174 action classes that are object and motion-centric, which requires learning the subtle differences between motions and object interactions. Kinetics-400 covers 400 classes of everyday human actions derived from real-world scenarios on YouTube and can be human-object or human-human interactions. Its videos are also longer than those of Something-Something V2 on average ( $\\sim$ 300 frames vs. $\\sim$ 40 frames), which can help differentiate the temporal modeling capabilities between models. HMDB51 has 51 human-dominated action classes, like Kinetics-400, containing some individual and some human-human behaviors.", + "bbox": [ + 89, + 167, + 480, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For all these datasets, we train DejaVid on the training sets and test on the validation sets using the same evaluation protocols as those in VideoMAE V2 [28]. We report the top-1 and top-5 accuracy for every experiment on Something-Something V2 and Kinetics-400. Due to the smaller action set of HMDB51, we only report top-1 for experiments on it.", + "bbox": [ + 89, + 348, + 480, + 454 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 460, + 307, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pre-training. We use the largest (ViT-g) model from VideoMAE V2 [28] (abbr. VideoMAE V2-g) as the video encoder.3 VideoMAE V2-g is the only model we experiment with because it is the only SOTA model4 that publishes finetuned weights on large datasets like Kinetics-400 and Something-Something V2, which we cannot afford to finetune ourselves. To show that DejaVid is model-agnostic, we apply the same method to other non-SOTA video encoders in Supplementary Material. The native embedding output length of VideoMAE V2 is 1408, which is then converted into $N_{c}$ logits for class prediction, so we let $N_{f} \\coloneqq 1408 + N_{c}$ denote the length of the entire output of VideoMAE V2-g. For DejaVid, we apply a temporal sliding window across the input video $T$ times to feed into the encoder, resulting in a TSE of shape $T \\times N_{f}$ . We then randomly sample some TSEs for each action class to calculate its initial centroid TSE using the DBA algorithm [21]. $T$ can be different across different datasets and within the same dataset. In particular, we use $T = 33$ for Kinetics-400 and HMDB51, and $T = 4|vid|$ for Something-Something V2, where $|vid|$ is the length of an individual video. For a detailed description of our pre-training configuration and the choice of width and stride for the sliding window of each dataset, please refer to the Additional Implementation", + "bbox": [ + 89, + 478, + 482, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Details section in Supplementary Material.", + "bbox": [ + 511, + 90, + 795, + 106 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training & Testing. The pre-training stage gives us a TSE $m$ for each training or validation video as well as the centroid TSEs $C$ . The weight tensor $U$ is either randomly initialized or one-initialized (i.e., filled with ones). To enforce positivity, we actually store the log of the weights and exponentiate them during forward passes. These log-of-weights are randomly initialized or zero-initialized (i.e., filled with zeros). We use the AdamW optimizer with betas (0.9, 0.999) and no weight decay. The initial learning rate for the log-of-weights is 1e-3 for both Something-Something V2 and Kinetics-400, and 8e-3 for HMDB51. The learning rates for the centroid TSEs are one-third of the log-of-weights. We use batch size 48 and train for 36 epochs. We use a cosine scheduler across all 36 epochs. A validation run is performed after every epoch, and we report the top accuracy recorded across all epochs.", + "bbox": [ + 511, + 111, + 903, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 511, + 361, + 651, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This section compares our results with previous other temporal-related and state-of-the-art methods. The main baseline is VideoMAE V2-g, which is a billion-parameter video encoder that is state-of-the-art or near state-of-the-art on all evaluation datasets [14, 16, 18, 28]. We test our method on each dataset with three different settings: random-initialization for the weight TSEs $U$ (denoted as full learning; $w$ -init-rnd in the following charts), one-initialization for $U$ (denoted as full learning; $w$ -init-one), and finally one-initialization for $U$ but freezing it throughout (i.e., disallowing optimizer step() to act on $U$ ; denoted as frozen weights; $w$ -init-one). Note that the last setting is for experimenting with the unweighted DTW distance as in Algorithm 1, so frozen weights with random initialization don't make sense.", + "bbox": [ + 511, + 380, + 903, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Kinetics-400. As shown in Tab. 1, our method achieves leading accuracy on Kinetics-400. We improve on the strongest VideoMAE V2-g baseline by $0.7\\%$ . DejaVid only requires 5.8M parameters, less than $0.6\\%$ of the encoder's parameter count, to achieve this gain. For comparison, the gain from VideoMAE V1 to VideoMAE V2 uses 380M extra parameters to increase the accuracy by only $0.4\\%$ . Note that our results are achieved without refinetuning the encoder, so the training cost is minimal compared to training the encoder. In short, DejaVid is a comparatively tiny add-on that significantly boosts the performance of an off-the-shelf frozen model.", + "bbox": [ + 511, + 612, + 903, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The performance gain of DejaVid is not only due to temporal supersampling. We test this by averaging the temporal dimension of each sample TSE to get a length- $(1408 + N_{c})$ vector and using the last $N_{c}$ elements for class prediction; the result is shown as VideoMAE V2 (temporal supersampling) Tab. 1. When compared against the original setting at VideoMAE V2 $5\\times 3$ , we see this alone does not improve", + "bbox": [ + 511, + 795, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3VideoMAE V2 publishes different finetuned weights for Kinetics-400 and Something-Something V2, and the script for finetuning on HMDB51, which we can afford to run thanks to the small dataset size. We use the respective finetuned weights for the pre-training stage of each dataset.", + "bbox": [ + 89, + 849, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24028", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the accuracy. Also, the temporal weight-learning does not provide additional benefits on top of our centroid-finetuning for Kinetics-400. We suspect the reason is that the temporal weights increase the expressivity of our method, so overfitting becomes more likely; one future work is to look into regularization for DejaVid.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on HMDB51. The results in Tab. 1 show that our model also achieves state-of-the-art accuracy on the HMDB51. We achieve a $0.5\\%$ performance gain against the strongest VideoMAE V2-g baseline. To the best of our knowledge and according to Papers with Code, this is the highest accuracy recorded on the HMDB51 action recognition benchmark to date (as of Nov, 2024). This shows that DejaVid works well in a training data-scarce scenario. We draw similar conclusions to those from Kinetics-400 in parameter efficiency – our parameter count is 1.19M, which is less than $0.12\\%$ of that of VideoMAE V2-g – and temporal supersampling alone does not improve performance.", + "bbox": [ + 89, + 186, + 482, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Something-Something V2. Tab. 1 compares our results on Something-Something V2 against other works. We outperform the top VideoMAE V2-g baseline with a performance gain of $0.5\\%$ . To the best of our knowledge and according to Papers with Code, DejaVid achieves the highest top-5 accuracy and one of the highest top-1 accuracies on the Something-Something V2 action recognition benchmark to date (as of Nov, 2024).", + "bbox": [ + 89, + 372, + 482, + 492 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Progress on Something-Something V2 has slowed in recent years, with top accuracy improving by no more than $0.3\\%$ between 2022 and 2024 [20]. Such gains often require massive model scaling; for example, InternVideo2 added over 5 billion parameters for a $0.4\\%$ boost [30]. In contrast, DejaVid achieves comparable improvements with just 17.6M parameters—fewer than $1.8\\%$ of VideoMAE V2-g. This efficiency highlights the significance of our $+0.5\\%$ accuracy gain, which equates to more than two years of recent progress [28-30].", + "bbox": [ + 89, + 493, + 482, + 643 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "However, the performance gain is smaller than on Kinetics-400. One possible reason could be the difference in average video length: $\\sim 40$ for Something-Something V2 and $\\sim 300$ for Kinetics-400. Because Kinetics-400 videos are longer, there may be more temporal information", + "bbox": [ + 89, + 645, + 482, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for DejaVid to capture. Another reason may be that the encoder is trained with variable video durations, as described in Sec. 4.2, so one future work would be to re-finetune the encoder with video clips of constant frame-count and retry our experiments.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 511, + 172, + 678, + 186 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Centroid vs. Weight Learning. In Tab. 2, we analyze the impacts of centroid and weight learning of DejaVid by freezing one component at a time and comparing the results. As seen, both frozen-centroid and frozen-weight variants yield meaningful accuracy gains against the VideoMAE V2-g baseline, and so both components are indeed beneficial. The centroid component has a greater performance gain on average across the three datasets, giving $+0.43\\%$ top-1 accuracy gain vs. $0.25\\%$ for the weights, but the weight component seems to be more useful when training data is scarce. As for the training data-rich cases, the weight component seems to be more useful in Something-Something V2 than in Kinetics-400, potentially because we have 4 different feature sets from the different sliding window widths, and these features should naturally have different importance, so the one-initialized weights are further away from the global optimal.", + "bbox": [ + 511, + 191, + 906, + 448 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e8195f4e028746b9117ccbff6ad2c0d2f5fd8958ba7d77fa5056dacfac056db5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSth-Sth2K400HMDB
top-1top-5top-1top-5top-1
VideoMAE V2-g @ best [28]76.7595.8588.498.088.1
Frozen centroids (w-init-rnd)76.896.288.698.088.4
Frozen centroids (w-init-one)76.996.288.898.188.4
Frozen weights (w-init-one)77.196.389.198.288.3
Full learning (w-init-rnd)77.296.388.998.188.6
Full learning (w-init-one)77.096.389.098.288.6
", + "bbox": [ + 516, + 463, + 903, + 578 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5a28d5ff27995ea53f0042163d360d6218c00f74c7099da1a38490bd1b7825d0.jpg", + "table_caption": [ + "Table 2. Ablation study on centroid & weight learning." + ], + "table_footnote": [], + "table_body": "
MethodSth-Sth2K400HMDB
top-1top-5top-1top-5top-1
DT on, otherwise best77.096.288.698.088.5
FECW off, otherwise best77.196.289.098.288.5
Best (DT off, FECW on)77.296.389.198.288.6
", + "bbox": [ + 516, + 604, + 901, + 681 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d18bdec49750a5a7de046e5b8404793481762a684b499c102d41a9d472d65412.jpg", + "table_caption": [ + "Table 3. Ablation studies on diagonal transition (DT) and fixed epoch centroids & weights (FECW)." + ], + "table_footnote": [], + "table_body": "
MethodSth-Sth2K400HMDB
Naive DTW implementation4.79e471.17e57294
Custom DTW CUDA kernel2971561.01
", + "bbox": [ + 517, + 723, + 901, + 781 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation study on the custom DTW CUDA kernel. Table shows runtime per training epoch in seconds.", + "bbox": [ + 511, + 785, + 903, + 813 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Diagonal Transition of DTW. Tab. 3 presents a comparison between the best (highest top-1 accuracy $^{8}$ ) setting of", + "bbox": [ + 511, + 820, + 903, + 851 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "Estimated by running 3 batches.", + "bbox": [ + 532, + 862, + 709, + 875 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "In the case of tied top-1 accuracies, we apply the same change to each tied setting and average their resulting accuracies after the change.", + "bbox": [ + 514, + 876, + 903, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "4We were unable to run InternVideo2 on our machine due to one of its required packages, flash-attn, being incompatible with our machine. 5The authors of VideoMAE V2 report 77.0 and 95.9 for top-1 and top-5 accuracy, respectively, but we measure only 76.7 and 95.8 using their published weights. We suspect the discrepancy is due to the input video loading mechanism. The official GitHub repo of VideoMAE V2 has inconsistent descriptions about the data preparation for Something-Something V2, but as of the time of writing, the source code assumes each video has been converted to a folder ofjpeg images, and VideoMAE V2 loads theseJPEG files instead of the source video. But when we do exactly that, the top-1 accuracy measures only 75.7. This is understandable since JPEG uses lossy compression. So we modified the source code to use opencv2 to directly load each video, which gives 76.7 and 95.8.", + "bbox": [ + 89, + 729, + 482, + 886 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "The definition of these clips are described in Sec. 4.2.", + "bbox": [ + 107, + 887, + 398, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24029", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1f6c23252ef2c13fa7dbaab48cc9307f236138362529b4ce7ce351f1c350ede1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodW.A.Kinetics-400Something-Something V2HMDB51
ParamsClipsxCropsTop-1Top-5ParamsClipsxCropsTop-1Top-5ParamsClipsxCropsTop-1
Other State-of-the-Art Large Models
TubeViT [22]No632M4×390.998.9307M-76.195.2---
MVD [29]No633M5×387.297.4633M2×377.395.7---
InternVideo2-1B [30]Yes41B4×391.6-1B2×377.1----
InternVideo2-6B [30]No6B4×392.1-6B5×377.5----
Other Temporal-Focused Methods
ILA [27]--4×388.797.8-4×370.291.8---
ATM [31]--4×389.498.3-2×374.694.4---
TAM [19]--4×379.394.1-2×366.090.1---
SlowFast [11]--10×379.893.9--61.7----
MTV [32]--4×389.198.2--68.590.4---
Main Baselines
VideoMAE V1-H [28]Yes633M5×388.1--------
VideoMAE V1-L (32-frame input) [25, 28]Yes----305M2×375.495.2---
VideoMAE V2-g [28]Yes1013M5×388.498.01013M2×376.7595.851013M5×388.1
VideoMAE V2-g (temporal supersampling) [28]Yes1013M336×188.197.81013M(4|vid|)6×176.295.71013M336×188.0
Our Results
Ours (frozen weights; w-init-one)-+5.8M36×189.198.2+8.8M(4|vid|)6×177.196.3+0.60M88.3
Ours (full learning; w-init-rnd)-+11.6M88.998.1+17.6M77.296.3+1.19M336×188.6
Ours (full learning; w-init-one)-+11.6M89.098.2+17.6M77.096.3+1.19M88.6
", + "bbox": [ + 91, + 88, + 903, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. Comparison with the VideoMAE V2-g baseline and other relevant variants, SOTA, or temporal methods on Kinetics-400, Something-Something V2, and HMDB51. All accuracies are reported in percent (\\%). W.A. = Weights Available. Dashes (-) = N/A.", + "bbox": [ + 89, + 349, + 906, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 2 for each dataset and the same setting but with diagonal transitions turned on. Enabling diagonal transitions consistently performs worse on all datasets. This justifies our choice of disabling diagonal transitions in DejaVid and verifies the insight behind this choice as described in Sec. 3.4.", + "bbox": [ + 88, + 382, + 480, + 457 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fixed Epoch Centroids & Weights for DTW Learning. We use Tab. 3 to compare the best setting (highest top-1 accuracy8) from Tab. 2 for each dataset with the same setting but disabling fixed epoch centroids & weights, where we do not make frozen copies of the centroids and weights for warping-path determination (shown as FECW off). Again, the inferior performance of this group compared to when FECW is on across all datasets justifies our design for DejaVid, aligning with the reasons detailed in Sec. 3.4 about model stability. However, the gap is less significant than that for the diagonal transition. This suggests there may be room for improvement by tweaking the path-determination mechanism, such as only updating every other epoch instead of each epoch.", + "bbox": [ + 88, + 458, + 482, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Custom CUDA Kernel for Accelerating DTW. Tab. 4 summarizes the runtime per epoch of the best-performing settings on all datasets compared to using a naive Python implementation of DTW. All experiments are conducted on a single node with 8 NVIDIA H100 GPUs. We can see that our custom CUDA kernel provides a speedup between $161\\mathrm{x}$ and $750\\mathrm{x}$ . The most technically significant speedup comes from reducing the critical path length from quadratic to linear, as discussed in Sec. 3.2. Other factors contributing to the speedup include the Python/C++ speed difference and architecture and locality-aware, LibTorch-native implementation of the CUDA-kernel.", + "bbox": [ + 89, + 669, + 482, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 852, + 209, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented DejaVid, an encoder-agnostic method that boosts video classification performance without retraining", + "bbox": [ + 89, + 869, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the encoder or changing its architecture. Instead of converting a video into a single fixed-length embedding like most state-of-the-art encoders do, we feed a backbone encoder a sliding-window stream of frames to obtain a variable-length temporal sequence of embeddings (TSE), which preserves temporal order and supports variable video durations. We then introduce a novel neural network architecture based on Dynamic Time Warping (DTW) with learnable, per-timestamp feature weights to address temporal variance in feature significance. Our ablation studies compare and justify various design choices and modifications to classical DTW, and our evaluation shows that DejaVid achieves state-of-the-art video classification results on a variety of benchmarks, significantly improves the accuracy of a cutting-edge large encoder, and outperforms other temporal methods. In particular, we achieve leading Top-1 accuracy of $77.2\\%$ on Something-Something V2, $89.1\\%$ on Kinetics-400, and $88.6\\%$ on HMDB51, representing a 0.5- $0.7\\%$ accuracy gain over VideoMAE V2-g while adding less than $1.8\\%$ additional learnable parameters and less than 3 hours of training time.", + "bbox": [ + 511, + 382, + 906, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Future Work", + "text_level": 1, + "bbox": [ + 511, + 708, + 648, + 723 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we selected video classification as the evaluation task due to its foundational role in computer vision [15, 16, 26], its real-world importance [1, 11, 13], and the significant amount of highly competitive research focused on it [2, 11, 19, 22, 25, 27-32]. With that said, we can also see the potential of DejaVid – and of the power of fine-grained temporal alignment learning in general – in action segmentation, video captioning, text-to-video retrieval, and any other tasks that can benefit from detailed temporal modeling.", + "bbox": [ + 511, + 729, + 906, + 878 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24030", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. Youtube-8m: A large-scale video classification benchmark. arXiv preprint arXiv:1609.08675, 2016. 8", + "[2] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 12104-12113, 2022. 1" + ], + "bbox": [ + 91, + 90, + 482, + 640 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24032", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DejaVid_ Encoder-Agnostic Learned Temporal Matching for Video Classification/b75bb180-204a-4d50-a1dd-1f6046fc0819_model.json b/2025/DejaVid_ Encoder-Agnostic Learned Temporal Matching for Video Classification/b75bb180-204a-4d50-a1dd-1f6046fc0819_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4c543756a24a67479ff13194f0415cc3eafddc67 --- /dev/null +++ b/2025/DejaVid_ Encoder-Agnostic Learned Temporal Matching for Video Classification/b75bb180-204a-4d50-a1dd-1f6046fc0819_model.json @@ -0,0 +1,2057 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.131, + 0.908, + 0.155 + ], + "angle": 0, + "content": "DejaVid: Encoder-Agnostic Learned Temporal Matching for Video Classification" + }, + { + "type": "text", + "bbox": [ + 0.328, + 0.182, + 0.421, + 0.199 + ], + "angle": 0, + "content": "Darryl Ho" + }, + { + "type": "text", + "bbox": [ + 0.324, + 0.2, + 0.425, + 0.215 + ], + "angle": 0, + "content": "MIT CSAIL" + }, + { + "type": "text", + "bbox": [ + 0.287, + 0.217, + 0.463, + 0.234 + ], + "angle": 0, + "content": "Cambridge MA, USA" + }, + { + "type": "text", + "bbox": [ + 0.276, + 0.238, + 0.473, + 0.251 + ], + "angle": 0, + "content": "darrylho@csail.mit.edu" + }, + { + "type": "text", + "bbox": [ + 0.559, + 0.182, + 0.701, + 0.198 + ], + "angle": 0, + "content": "Samuel Madden" + }, + { + "type": "text", + "bbox": [ + 0.579, + 0.2, + 0.681, + 0.215 + ], + "angle": 0, + "content": "MIT CSAIL" + }, + { + "type": "text", + "bbox": [ + 0.542, + 0.217, + 0.718, + 0.234 + ], + "angle": 0, + "content": "Cambridge MA, USA" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.238, + 0.718, + 0.251 + ], + "angle": 0, + "content": "madden@csail.mit.edu" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.321, + 0.486, + 0.775 + ], + "angle": 0, + "content": "In recent years, large transformer-based video encoder models have greatly advanced state-of-the-art performance on video classification tasks. However, these large models typically process videos by averaging embedding outputs from multiple clips over time to produce fixed-length representations. This approach fails to account for a variety of time-related features, such as variable video durations, chronological order of events, and temporal variance in feature significance. While methods for temporal modeling do exist, they often require significant architectural changes and expensive retraining, making them impractical for off-the-shelf, fine-tuned large encoders. To overcome these limitations, we propose DejaVid, an encoder-agnostic method that enhances model performance without the need for retraining or altering the architecture. Our framework converts a video into a variable-length temporal sequence of embeddings (TSE). A TSE naturally preserves temporal order and accommodates variable video durations. We then learn per-timestep, per-feature weights over the encoded TSE frames, allowing us to account for variations in feature importance over time. We introduce a new neural network architecture inspired by traditional time series alignment algorithms for this learning task. Our evaluation demonstrates that DejaVid substantially improves the performance of a state-of-the-art large encoder, achieving leading Top-1 accuracy of \\(77.2\\%\\) on Something-Something V2, \\(89.1\\%\\) on Kinetics-400, and \\(88.6\\%\\) on HMDB51, while adding fewer than \\(1.8\\%\\) additional learnable parameters and requiring less than 3 hours of training time. Our code is available at https://github.com/darrylho/DejaVid." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.789, + 0.222, + 0.804 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.485, + 0.902 + ], + "angle": 0, + "content": "Video action recognition has seen remarkable progress with the rise of transformer-based video models [2, 7, 10]. To improve their performance, one of the most straightforward and effective approaches is to upscale the model and training data [33]. As such, the leaderboards of major action recognition benchmarks have come to be dom" + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.287, + 0.681, + 0.304 + ], + "angle": 0, + "content": "Pre-training Training" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.304, + 0.905, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.404, + 0.904, + 0.51 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.511, + 0.906, + 0.683 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.69, + 0.907, + 0.858 + ], + "angle": 0, + "content": "Figure 1. DejaVid system diagram. We first transform a video into a variable-length temporal sequence of embeddings (TSE) then use Dynamic Time Warping Barycenter Averaging (DBA) [21] to calculate a reasonably \"average\" TSE per class for its centroid initialization. We then learn per-timestep, per-feature weights for the encoded TSE frames, enabling us to accommodate variations in feature importance over time, as well as finetune the centroid TSE for each output class. For this task, we introduce a new neural network architecture inspired by traditional time series alignment algorithms. In testing, we freeze the post-training centroids and weights and use the same pre-training pipeline to generate TSEs to feed into DejaVid for predictions." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "inated by 100M-1B+ parameter large video transformers [14, 16, 18, 22, 28-30]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24023" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.094, + 0.092, + 0.482, + 0.438 + ], + "angle": 0, + "content": "These large encoders process videos with fixed frame counts, heights, and widths, generating a single embedding. On datasets with varying durations, the common approach is to pass multiple temporal clips and spatial crops through the encoder and then average the resulting logits for class prediction [22, 28-30]. However, while the height and width of videos in a dataset are usually constant, their duration can vary significantly [14]. Furthermore, temporal order is far more critical. Unlike image flipping [17], reversing time can alter semantics, such as opening vs. closing a door. When averaging logits from different temporal clips, sequential information in these clips is lost. Moreover, the significance of each feature within a video can change over time. For example, in a basketball three-point shot, early frames emphasize player position, while later frames focus on whether the ball goes in. Although encoders might not explicitly model semantically interpretable features like these, temporal variation in feature importance can also occur for arbitrary features, which mean-pooling fails to capture adequately. This motivates a key observation of our work: by failing to carefully account for temporal dimensions, state-of-the-art large models leave significant accuracy gains on the table." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.444, + 0.482, + 0.564 + ], + "angle": 0, + "content": "Improving the temporal performance of large encoders is not trivial. Existing temporal-focused methods require invasive changes to the model, such as inserting temporal-specific layers between transformer blocks [27, 31] or creating model duplications to focus on different input views [11, 32]. These approaches are costly to apply to off-the-shelf pre-trained encoders because they require extensive changes in implementation and costly re-training." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.57, + 0.482, + 0.9 + ], + "angle": 0, + "content": "These insights motivate DejaVid, a lightweight encoder-agnostic temporal approach that substantially boosts model classification performance. The simple yet crucial idea behind DejaVid is that a video is more effectively represented as a temporal sequence of embeddings (TSE) rather than as a single embedding. This representation naturally preserves chronological order while supporting varying time lengths, addressing the aforementioned shortcomings. DejaVid is naturally able to use any pre-trained model by consuming a sliding-window of encoded video to generate a TSE, without requiring changes to the model's architecture, retraining, or fine-tuning. DejaVid is inspired by the well-known Dynamic Time Warping (DTW) algorithm [4], which dynamically aligns similar data points between two temporal sequences while maintaining their chronological order. In particular, DejaVid introduces a novel neural network architecture inspired by DTW but with learned per-timestep, per-feature weights to handle the temporal variance of feature importance. Additionally, we develop a custom high-performance CUDA kernel for efficient computation and backpropagation of the (time-weighted) warping distance that outperforms a naive DTW-based implementation by 2" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.093, + 0.652, + 0.107 + ], + "angle": 0, + "content": "orders of magnitude." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.109, + 0.904, + 0.319 + ], + "angle": 0, + "content": "We evaluate DejaVid by layering it on top of the largest (ViT-g) variant of VideoMAE V2 [28] (abbr. VideoMAE V2-g) as the backbone encoder to evaluate DejaVid on three popular action recognition datasets: Kinetics-400 [16], Something-Something V2 [14], and HMDB51 [18]. We show that DejaVid significantly improves on the strongest VideoMAE V2-g baseline, thereby achieving new state-of-the-art performance. In particular, DejaVid achieves Top-1 accuracy of \\(77.2\\%\\) on Something-Something V2, \\(89.1\\%\\) on Kinetics-400, and \\(88.6\\%\\) on HMDB51, while adding fewer than \\(1.8\\%\\) additional learnable parameters and requiring less than 3 hours of training time. We also show that our proposed modifications to DTW, including the temporal weights, can further improve prediction performance." + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.333, + 0.653, + 0.348 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.355, + 0.904, + 0.535 + ], + "angle": 0, + "content": "State-of-the-Art in Action Recognition. Major action recognition benchmarks are topped by massive video transformers with hundreds of millions or billions of parameters. As of the time of writing, according to Papers with Code, the top performers on Kinetics-400 and Something-Something V2 with verifiable parameter counts have between 600M and 6B parameters [14, 16, 22, 28-30]. However, their evaluations on these two datasets all apply spatial and temporal mean-pooling to the logits at the end, which suffers from the time-related shortfalls related to variable video durations, chronological order of events, and temporal variance in feature significance, as described in Sec. 1." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.538, + 0.904, + 0.853 + ], + "angle": 0, + "content": "Temporal-focused Methods for Action Recognition. There have been various works on improving the temporal modeling capability of video transformers. One general approach is to introduce temporal-specific layers in between transformer blocks. For example, ILA employs a mask-based layer that predicts interactive points between frame pairs to implicitly align features [27], ATM applies basic arithmetic operations to pairs-of-frame features between ViT blocks [31], and TAM inserts an attention-based temporal adaptive module between 2D convolutions within a ResNet block [19]. Another line of work is to fuse multiple temporal views in different ways. For example, SlowFast networks feed two different frame rates of a video into separate encoders and add lateral connections between them to fuse information across views [11], and MTV deploys a similar idea but for both spatial and temporal dimensions [32]. However, their performance is not competitive against the aforementioned large state-of-the-art models, partly due to their smaller size. Implementing these methods within the large models would involve considerable implementation changes and expensive retraining." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.857, + 0.904, + 0.899 + ], + "angle": 0, + "content": "Learning Temporal Sequence Alignments. DTW is one of the most classic methods for calculating similarities between univariate time series or multivariate ones like our" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24024" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.257 + ], + "angle": 0, + "content": "TSEs [4, 23]. Its traditional formulation is a dynamic programming scheme, but recent work has explored making it differentiable and then applying it to various fields. SoftDTW [9] shows that DTW makes a good loss function when the min operator is replaced with soft-min. DTWnet [5] proposes using DTW learning for time series feature extraction, and D3TW, OTAM, and FTCL [6, 8, 12] similarly do this for weakly-supervised and few-shot video understanding. While these works have some similarities to our DTW-based temporal representation learning, our method is technically different and superior in three ways:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.258, + 0.483, + 0.363 + ], + "angle": 0, + "content": "1. DejaVid models and learns the temporal variance in feature importance, which none of the other methods do. While classical DTW typically only works for a few dimensions (10-100) that require handcrafting or hand-picking [3], by adding learned weights, we extend DTW to high-dimensional use cases \\((1000 - 10000+)\\) like video recognition by letting it learn the important dimensions." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.364, + 0.482, + 0.409 + ], + "angle": 0, + "content": "2. We reformulate our DTW-inspired temporal learning algorithm as a new neural network architecture that boosts parallelizability and facilitates differentiability." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.409, + 0.482, + 0.439 + ], + "angle": 0, + "content": "3. We introduce changes to DTW to improve model stability, including removing the diagonal transition of DTW." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.258, + 0.483, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.45, + 0.182, + 0.466 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.476, + 0.484, + 0.626 + ], + "angle": 0, + "content": "As described in Sec. 1, we represent a video as a temporal sequence of embeddings (TSE). In this section, we assume all videos have been converted into TSEs, and operate in this TSE space. DejaVid feeds a video encoder a sliding-window stream of frames of an input video to generate a TSE, so the shape of a TSE is \\( T \\times N_{f} \\), where each index along \\( T \\) represents the encoding of a window of frames, and thus \\( T \\) can vary depending on individual video duration. \\( N_{f} \\) is the size of the embedding vector of the backbone encoder and is constant." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.627, + 0.484, + 0.687 + ], + "angle": 0, + "content": "Our problem is to classify TSEs. Specifically, we are given a training set of TSEs with class labels among \\( N_{c} \\) classes, and our goal is to predict the classes of our validation TSEs. We solve this problem in three broad steps:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.688, + 0.483, + 0.718 + ], + "angle": 0, + "content": "1. For each class, we calculate a centroid TSE from the training TSEs of that class." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.719, + 0.483, + 0.749 + ], + "angle": 0, + "content": "2. We optimize the centroid TSEs according to some loss function w.r.t. the training TSEs." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.749, + 0.483, + 0.778 + ], + "angle": 0, + "content": "3. For each validation TSE, we calculate which class's centroid TSE is the most similar to it." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.688, + 0.483, + 0.778 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.484, + 0.843 + ], + "angle": 0, + "content": "Here, Steps 1 and 3 require a definition of distance (or similarity) between TSE pairs, and Step 2 requires the distance metric to be backpropagateable. The following Secs. 3.1 and 3.2 describe how we solve these two problems." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.212, + 0.864 + ], + "angle": 0, + "content": "3.1. Definitions" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "There are multiple ways in which one can define the distance between two TSEs [4, 24], but in this paper, we focus" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.319 + ], + "angle": 0, + "content": "on a standard time series distance metric: Dynamic Time Warping (DTW), as given in Algorithm 1 (without the red text). DTW aligns two sequences that vary in time or speed by minimizing the distance between corresponding points. The two sequences are aligned by aligning each timestep in the first sequence to one or more consecutive timesteps in the second sequence while maintaining a monotonic relationship where a later timestep in the first must map to a later interval in the second. Monotonicity is maintained in Line 5 of Algorithm 1, where each step only moves forward in time for either sequence (from \\( i - 1 \\) to \\( i \\) or \\( j - 1 \\) to \\( j \\)). This alignment minimizes cumulative distance and is commonly visualized as a \"warping path\" on a 2D grid, which shows the optimal alignment of the two sequences, each depicted in one grid axis." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.332, + 0.907, + 0.413 + ], + "angle": 0, + "content": "Algorithm 1 The Standard DTW Algorithm (without diagonal transition) vs. the Time-Weighted DTW Algorithm (red) \nInput: Two TSEs \\( a, b \\in \\mathbb{R}^{n \\times N_f}, \\mathbb{R}^{m \\times N_f} \\); a distance function \\( dist_w \\); \\( u \\in \\mathbb{R}_{>0}^{n \\times N_f} \\) temporal feature weights of \\( a \\) \nOutput: Distance between \\( a \\) and \\( b \\)" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.415, + 0.904, + 0.432 + ], + "angle": 0, + "content": "1: \\(D \\gets \\operatorname{array}[n, m]\\) {Out-of-bounds access returns \\(+\\infty\\)}" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.445, + 0.713, + 0.461 + ], + "angle": 0, + "content": "2: \\(D_{0,0}\\gets dist_w(u_0,a_0,b_0)\\)" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.461, + 0.682, + 0.476 + ], + "angle": 0, + "content": "3: for \\( i \\) in \\( [0, n - 1] \\) do" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.476, + 0.871, + 0.491 + ], + "angle": 0, + "content": "4: for \\( j \\) in \\( ([0, m - 1] \\) if \\( i > 0 \\) else \\( [1, m - 1] \\)) do" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.491, + 0.895, + 0.508 + ], + "angle": 0, + "content": "5: \\(D_{i,j}\\gets \\min (D_{i - 1,j},D_{i,j - 1}) + dist_w(u_i,a_i,b_j)\\)" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.508, + 0.613, + 0.52 + ], + "angle": 0, + "content": "6: end for" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.521, + 0.597, + 0.535 + ], + "angle": 0, + "content": "7: end for" + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.536, + 0.67, + 0.552 + ], + "angle": 0, + "content": "8: return \\( D_{n-1,m-1} \\)" + }, + { + "type": "list", + "bbox": [ + 0.523, + 0.445, + 0.895, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.562, + 0.907, + 0.652 + ], + "angle": 0, + "content": "In the standard Algorithm 1, we use the Manhattan distance for the pointwise distance function \\(dist\\). Also, although the original DTW algorithm includes a diagonal transition \\(D_{i-1,j-1}\\) in the min clause, we omit this in DejaVid because it improves model stability. We discuss this decision in more detail in Sec. 3.4." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.653, + 0.907, + 0.774 + ], + "angle": 0, + "content": "Let \\(D_v(a,b)\\) denote the DTW distance between TSEs \\(a\\) and \\(b\\) as returned by the standard Algorithm 1, and let \\(C \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}\\) represent the centroid TSEs for the \\(N_c\\) classes. Intuitively, we want to assign each TSE to the class it is nearest to in the DTW space. To do this, we define the predicted probability distribution \\(\\hat{\\mathbf{y}}_v\\) for a training or validation TSE \\(m \\in \\mathbb{R}^{T_m \\times N_f^1}\\), and the loss \\(\\mathcal{L}_v\\) for \\(m\\) under centroids \\(C\\) and one-hot ground truth vector \\(\\mathbf{y}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.777, + 0.824, + 0.8 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {y}} _ {v} (C, m) := \\underset {0 \\leq i < N _ {c}} {\\operatorname {s o f t m i n}} \\left(D _ {v} \\left(C _ {i}, m\\right)\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.801, + 0.85, + 0.818 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v} (C, m) := \\operatorname {C r o s s E n t r o p y} (\\mathbf {y}, \\hat {\\mathbf {y}} _ {v} (C, m))\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.822, + 0.906, + 0.868 + ], + "angle": 0, + "content": "However, as described in Sec. 1, we observe that the importance of each feature of a video can vary as time progresses. This observation motivates our time-weighted" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.906, + 0.901 + ], + "angle": 0, + "content": "In practice, we perform a LayerNorm operation before the soft-min, but this doesn't qualitatively change our approach." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24025" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.399 + ], + "angle": 0, + "content": "DTW distance metric, given in Algorithm 1 with modifications shown in red. The difference is the additional weight input \\( u \\), which denotes the change in feature importance over time for \\( a \\). We also modify the pointwise Manhattan distance function to incorporate \\( u \\): \\( dist_w(u_i, a_i, b_j) := \\sum_{k=0}^{N_f-1} u_{i,k} |a_{i,k} - b_{j,k}| \\). The changes are colored in Lines 2 and 5 of Algorithm 1. Intuitively, when Algorithm 1 calculates the distance between two sequences, our time-weighted modification allows it to weight some timesteps more than some other timesteps in the first series, and different features can have different weights as well. Let \\( D_w(u, a, b) \\) denote the time-weighted DTW distance between TSEs \\( a \\) and \\( b \\) as returned by the time-weighted Algorithm 1. We aim to learn the temporal variance of feature importance of the centroids \\( C \\), so we define \\( U \\in \\mathbb{R}_{>0}^{N_c \\times T_c \\times N_f} \\) of the same shape as \\( C \\) to be the time-varying feature weights. To maintain the positivity of distances, we constrain \\( U \\) to be positive. The time-weighted variant of predicted probability distribution \\( \\hat{\\mathbf{y}}_w \\) and loss \\( \\mathcal{L}_w \\) are defined similarly as before:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.405, + 0.426, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {y}} _ {w} (U, C, m) := \\operatorname * {s o f t m i n} _ {0 \\leq i < N _ {c}} \\left(D _ {w} \\left(U _ {i}, C _ {i}, m\\right)\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.431, + 0.446, + 0.448 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {w} (u, C, m) := \\operatorname {C r o s s E n t r o p y} (\\mathbf {y}, \\hat {\\mathbf {y}} _ {w} (u, C, m))\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.45, + 0.483, + 0.495 + ], + "angle": 0, + "content": "From now on, we focus on the time-weighted Algorithm 1, since one can set \\( U = \\mathbf{1}_{N_c\\times T_c\\times N_f} \\) to recover standard DTW in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.499, + 0.398, + 0.515 + ], + "angle": 0, + "content": "3.2. Parallelizability & Differentiability" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.516, + 0.287, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.516, + 0.482, + 0.604 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.606, + 0.286, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.516, + 0.482, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.694, + 0.483, + 0.819 + ], + "angle": 0, + "content": "Figure 2. 1. Each cell of the DTW 2D grid executes a min operation and then an add-dist operation. Checkmarks show completed cells in row-major order. 2. In diagonal order, a diagonal can be executed as soon as the previous diagonal has finished. Checkmarks show completed cells in diagonal order. 3. We can view each diagonal as a min-pooling layer with kernel size 2 and stride 1, followed by an additive skip-connection layer. 4. We reformulate the algorithm into a serial stack of min-pooling layers interlaced with additive skip-connections." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Algorithm 2 given an equivalent neural-network formulation for Algorithm 1; this formulation facilitates the use of backpropagation for optimizing weights and enhances parallelizability. Before providing the details of the algorithm, we provide some intuition as to how and why it works." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.242 + ], + "angle": 0, + "content": "Fig. 2 depicts the 2D grid commonly used for representing DTW warping path(s) between two sequences, as described in Sec. 3.1. We visualize each operation in the nested loop in Algorithm 1 onto the corresponding cell in the grid. We can see that each cell executes a min operation on the outputs of its left-adjacent and bottom-adjacent cells, followed by an addition of some pointwise weighted distance \\(dist_w\\). Note that cells are executed in a row-major order in Algorithm 1. Therefore, the critical path length is quadratic \\((O(nm))\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.243, + 0.907, + 0.438 + ], + "angle": 0, + "content": "However, we leverage a critical property of Algorithm 1 that enables a reformulation of the algorithm, which is that each cell can be executed as soon as its left and bottom neighbors have finished. Therefore, we reformulate Algorithm 1 to execute in diagonal order and observe that the \\( l \\)-th diagonal can be executed as soon as the \\( (l - 1) \\)-th diagonal has finished. Here, we define the \\( l \\)-th diagonal to be the cells \\( \\{(i,j) \\mid i + j = l\\} \\). For example, the top-right of Fig. 2 shows the 4th diagonal. Furthermore, elements in the same diagonal are mutually independent, so the work within each diagonal is parallelized. So we have reduced the critical path length to the number of diagonals, obtaining the linear runtime \\( O(n + m) \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.439, + 0.909, + 0.636 + ], + "angle": 0, + "content": "Because each cell executes at Line 5 of Algorithm 1 a min operation on two consecutive cells of the previous diagonal and then adds some \\(dist_w\\) term, we can express the new formulation as a neural net where each diagonal is a min-pooling layer with kernel size 2 and stride 1 followed by an additive skip-connection layer. Each min-pooling layer is executed after its previous skip-connection and min-pooling are completed. So Algorithm 1 is equivalent to a serial stack of min-pooling layers, with skip-connections interlacing in between. These descriptions are formalized in Algorithm 2, where one can see the execution of the interlaced layers at Lines 10 and 11. For differentiability, we rewrite the time-weighted DTW distance \\(D_w\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.638, + 0.907, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} D _ {w} := S C _ {n + m - 2} + M P _ {n + m - 2} \\left(S C _ {n + m - 3} + M P _ {n + m - 3}\\right) \\\\ \\ldots + S C _ {1} + M P _ {1} \\left(S C _ {0}\\right) \\dots)) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.677, + 0.906, + 0.815 + ], + "angle": 0, + "content": "where \\( MP_{l} \\) and \\( SC_{l} \\) are the \\( l \\)-th min-pooling and skipconnection as show in Algorithm 2. Because both min-pooling and additive skip-connections are standard neural network operations, loss gradients trivially propagate through them. In a nutshell, the loss backpropagates to only the \\( dist_{w}(u_{i},a_{i},b_{j}) \\) functions on the optimal warping path, which enables gradient-based optimization on \\( U \\) and \\( C \\). We leave the detailed formulas for loss gradients \\( \\frac{\\partial L_w}{\\partial C} \\) and \\( \\frac{\\partial L_w}{\\partial U} \\) in Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.823, + 0.685, + 0.838 + ], + "angle": 0, + "content": "3.3. System Overview" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "With the definitions introduced in Secs. 3.1 and 3.2, we now formalize the 3-step solution outlined at the start of Sec. 3. Fig. 1 provides an overview of the DejaVid system. The video encoder takes as input a video clip of fixed duration" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24026" + } + ], + [ + { + "type": "algorithm", + "bbox": [ + 0.092, + 0.09, + 0.484, + 0.39 + ], + "angle": 0, + "content": "Algorithm 2 Time-Weighted DTW Neural Network \nInput: Two TSEs \\(a, b \\in \\mathbb{R}^{n \\times N_f}, \\mathbb{R}^{m \\times N_f}\\); a distance func \ntion \\(dist_w\\); \\(u \\in \\mathbb{R}_{>0}^{n \\times N_f}\\) temporal feature weights of \\(a\\) \nOutput: Distance between \\(a\\) and \\(b\\) \n1: {Out-of-bounds access to \\(D\\) or \\(SC\\) returns \\(+\\infty\\)} \n2: \\(SC_{0,0} \\gets dist_w(u_0, a_0, b_0)\\) {The 0-th skip- \nconnection} \n3: \\(D_{0,0} \\gets SC_{0,0}\\) \n4: for \\(l\\) in \\([1, n + m - 2]\\) do \n5: {The \\(l\\)-th diagonal} \n6: start, end \\(\\leftarrow \\max(0, l - m + 1)\\), \\(\\min(n - 1, l)\\) \n7: \\(SC_l \\gets [dist_w(u_t, a_t, b_{l-t})]_{t=start}^{\\text{end}}\\) \n8: \\(D_l \\gets \\text{array[end - start + 1]}\\) \n9: kernel, stride \\(\\leftarrow 2, 1\\) \n10: for \\(i\\) in range(0, end - start + 1, stride) do \n11: \\(D_{l,i} \\gets SC_{l,i} + \\min_{s=0}^{kernel-1}(D_{l-1,i-s})\\) \n12: end for \n13: end for \n14: return \\(D_{n+m-2,0}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.419, + 0.484, + 0.677 + ], + "angle": 0, + "content": "and outputs an embedding \\( e \\in \\mathbb{R}^{N_f} \\). Given any off-the-shelf video encoder, we apply a sliding window over each video to produce a sequence of clips, which we then feed into the encoder to produce a temporal sequence of embeddings \\( E = \\{e_0, e_1, \\dots, e_{T-1}\\} \\in \\mathbb{R}^{T \\times N_f} \\), which forms a TSE for each video sample in the dataset. Then, we produce a centroid TSE of shape \\( T_c \\times N_f^2 \\) for each class by feeding the training TSEs to the DBA (Dynamic Time Warping Barycenter Averaging) [21] algorithm, which calculates a reasonable \"average\" time series of the inputs while accounting for imperfect temporal alignment. Intuitively, each centroid TSE represents how the class-wide average of the \\( N_f \\) features changes over time. Ultimately, we obtain many training TSEs, each with shape \\( T \\times N_f \\) for some varying \\( T \\), and a stack of centroid TSEs \\( C \\) of shape \\( N_c \\times T_c \\times N_f \\), where \\( N_c \\) is the number of classes. This concludes the pretraining stage of DejaVid." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.678, + 0.483, + 0.798 + ], + "angle": 0, + "content": "In the training phase, to account for temporal variance in feature importance over time, each centroid TSE is paired with a positive weight tensor of the same shape \\(T_{c} \\times N_{f}\\) that represents the importance of each feature over time. The positivity is to maintain that the pointwise distance \\(\\text{dist}_{w}\\) is always positive. We denote the stack of weight TSEs \\(U\\) with shape \\(N_{c} \\times T_{c} \\times N_{f}\\). At initialization, the weight TSEs are either filled with ones or random positive values." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.8, + 0.484, + 0.876 + ], + "angle": 0, + "content": "In each epoch, we calculate the weighted DTW distance \\(D_w\\) from each training TSE \\(m \\in \\mathbb{R}^{T \\times N_f}\\) to every centroid TSE to get the logit vector \\(\\mathbf{z} = \\{D_w(U_i, C_i, m)\\}_{i=0}^{N_c-1} \\in \\mathbb{R}^{N_c}\\), on which we apply softmax to get the class prediction \\(\\hat{\\mathbf{y}}\\) and cross-entropy loss \\(\\mathcal{L}_w\\) w.r.t. the ground truth \\(\\mathbf{y}\\). The" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.273 + ], + "angle": 0, + "content": "weights \\(U\\) and centroids \\(C\\) TSEs are updated during backpropagation. To accelerate forward and backward passes, we implement a custom DTW CUDA kernel that efficiently calculates a slope tensor \\(S \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}\\) and an intercept tensor \\(B \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}\\) such that \\(\\text{torch.sum}(U \\odot (C \\odot S + B), \\dim = (-2, -1))\\) equals the logit vector \\(\\mathbf{z}\\) and the effective gradients w.r.t. \\(U\\) and \\(C\\) equals \\(\\frac{\\partial L_w}{\\partial U}\\) and \\(\\frac{\\partial L_w}{\\partial C}\\). The implementation of the CUDA kernel, roughly speaking, leverages the fact that a weighted DTW distance is essentially the sum of many terms of \\(u \\cdot |c - b|\\), which equals \\(u \\cdot (c \\cdot (\\pm 1) + (\\mp 1)b)\\), where the \\((\\pm 1)\\) term contributes to slope \\(S\\) and \\((\\mp 1)b\\) to intercept \\(B\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.278, + 0.798, + 0.292 + ], + "angle": 0, + "content": "3.4. Modifications to Standard DTW" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.295, + 0.907, + 0.552 + ], + "angle": 0, + "content": "As mentioned in Sec. 3.1, unlike the original DTW algorithm, we exclude the diagonal transitions (i.e., transitioning from \\( D_{i-1,j-1} \\) to \\( D_{i,j} \\) in Algorithm 1) for DejaVid. The reason is due to model stability. When matching two series of length \\( n \\) and \\( m \\), by disallowing diagonal transitions, the warping path from \\( D_{0,0} \\) to \\( D_{n-1,m-1} \\) always takes \\( n+m-1 \\) steps, and so the DTW distance will always be the sum of \\( n+m-1 \\) step-wise distances. If diagonal transitions are allowed, the number of step-wise distances on the warping path can vary, destabilizing the model. Although beyond the scope of this paper, we note that there could be other ways to deal with diagonal transitions, such as assigning or learning a multiplicative or additive distance bias for diagonal vs. non-diagonal transitions, such as in Move-Split-Merge (MSM) [24], a more modern replacement of DTW that treats diagonal transitions differently from non-diagonal ones." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.906, + 0.749 + ], + "angle": 0, + "content": "Another modification we made is to fix epoch centroids and weights. That is, at the beginning of an epoch, we make a frozen copy of the current centroids and weights, and then during the epoch, use them to calculate the warping path for each centroid-training TSE pair. Then, along the path, we calculate the pointwise distance using the (non-frozen) originals and perform backpropagation on them. Note that the frozen copies are not updated per batch but instead per epoch. The reason for this modification is again due to model stability. We found that if the warping path calculation mechanism is updated every batch, the distances become noisier from batch to batch, and the model has a harder time converging." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.749, + 0.9, + 0.763 + ], + "angle": 0, + "content": "We discuss the effect of these modifications in Sec. 4.4." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.767, + 0.631, + 0.782 + ], + "angle": 0, + "content": "4. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.788, + 0.906, + 0.818 + ], + "angle": 0, + "content": "In this section, we describe our implementation and evaluation of DejaVid." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.823, + 0.8, + 0.837 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.901 + ], + "angle": 0, + "content": "We test DejaVid on three different popular action recognition datasets: Something-Something V2 [14], Kinetics-400 [16], and HMDB51 [18]. The first two are large-scale datasets: Something-Something V2 has 168,913 videos for" + }, + { + "type": "page_footnote", + "bbox": [ + 0.108, + 0.887, + 0.368, + 0.9 + ], + "angle": 0, + "content": "2We set \\(T_{c} = 8\\) for all experiments in this work." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24027" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.166 + ], + "angle": 0, + "content": "training and 24,777 for validation, while Kinetics-400 has 240,436 training and 19,787 validation videos. In contrast, HMDB51 only has 3,570 training and 1,530 validation videos, but its smaller size can help us study the model's performance when the training set is smaller." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.168, + 0.482, + 0.348 + ], + "angle": 0, + "content": "Something-Something V2 has 174 action classes that are object and motion-centric, which requires learning the subtle differences between motions and object interactions. Kinetics-400 covers 400 classes of everyday human actions derived from real-world scenarios on YouTube and can be human-object or human-human interactions. Its videos are also longer than those of Something-Something V2 on average (\\(\\sim\\)300 frames vs. \\(\\sim\\)40 frames), which can help differentiate the temporal modeling capabilities between models. HMDB51 has 51 human-dominated action classes, like Kinetics-400, containing some individual and some human-human behaviors." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.349, + 0.482, + 0.455 + ], + "angle": 0, + "content": "For all these datasets, we train DejaVid on the training sets and test on the validation sets using the same evaluation protocols as those in VideoMAE V2 [28]. We report the top-1 and top-5 accuracy for every experiment on Something-Something V2 and Kinetics-400. Due to the smaller action set of HMDB51, we only report top-1 for experiments on it." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.461, + 0.308, + 0.476 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.479, + 0.483, + 0.841 + ], + "angle": 0, + "content": "Pre-training. We use the largest (ViT-g) model from VideoMAE V2 [28] (abbr. VideoMAE V2-g) as the video encoder.3 VideoMAE V2-g is the only model we experiment with because it is the only SOTA model4 that publishes finetuned weights on large datasets like Kinetics-400 and Something-Something V2, which we cannot afford to finetune ourselves. To show that DejaVid is model-agnostic, we apply the same method to other non-SOTA video encoders in Supplementary Material. The native embedding output length of VideoMAE V2 is 1408, which is then converted into \\( N_{c} \\) logits for class prediction, so we let \\( N_{f} \\coloneqq 1408 + N_{c} \\) denote the length of the entire output of VideoMAE V2-g. For DejaVid, we apply a temporal sliding window across the input video \\( T \\) times to feed into the encoder, resulting in a TSE of shape \\( T \\times N_{f} \\). We then randomly sample some TSEs for each action class to calculate its initial centroid TSE using the DBA algorithm [21]. \\( T \\) can be different across different datasets and within the same dataset. In particular, we use \\( T = 33 \\) for Kinetics-400 and HMDB51, and \\( T = 4|vid| \\) for Something-Something V2, where \\( |vid| \\) is the length of an individual video. For a detailed description of our pre-training configuration and the choice of width and stride for the sliding window of each dataset, please refer to the Additional Implementation" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.797, + 0.107 + ], + "angle": 0, + "content": "Details section in Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.112, + 0.905, + 0.354 + ], + "angle": 0, + "content": "Training & Testing. The pre-training stage gives us a TSE \\( m \\) for each training or validation video as well as the centroid TSEs \\( C \\). The weight tensor \\( U \\) is either randomly initialized or one-initialized (i.e., filled with ones). To enforce positivity, we actually store the log of the weights and exponentiate them during forward passes. These log-of-weights are randomly initialized or zero-initialized (i.e., filled with zeros). We use the AdamW optimizer with betas (0.9, 0.999) and no weight decay. The initial learning rate for the log-of-weights is 1e-3 for both Something-Something V2 and Kinetics-400, and 8e-3 for HMDB51. The learning rates for the centroid TSEs are one-third of the log-of-weights. We use batch size 48 and train for 36 epochs. We use a cosine scheduler across all 36 epochs. A validation run is performed after every epoch, and we report the top accuracy recorded across all epochs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.362, + 0.652, + 0.376 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.381, + 0.905, + 0.606 + ], + "angle": 0, + "content": "This section compares our results with previous other temporal-related and state-of-the-art methods. The main baseline is VideoMAE V2-g, which is a billion-parameter video encoder that is state-of-the-art or near state-of-the-art on all evaluation datasets [14, 16, 18, 28]. We test our method on each dataset with three different settings: random-initialization for the weight TSEs \\( U \\) (denoted as full learning; \\( w \\)-init-rnd in the following charts), one-initialization for \\( U \\) (denoted as full learning; \\( w \\)-init-one), and finally one-initialization for \\( U \\) but freezing it throughout (i.e., disallowing optimizer step() to act on \\( U \\); denoted as frozen weights; \\( w \\)-init-one). Note that the last setting is for experimenting with the unweighted DTW distance as in Algorithm 1, so frozen weights with random initialization don't make sense." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.905, + 0.793 + ], + "angle": 0, + "content": "Results on Kinetics-400. As shown in Tab. 1, our method achieves leading accuracy on Kinetics-400. We improve on the strongest VideoMAE V2-g baseline by \\(0.7\\%\\). DejaVid only requires 5.8M parameters, less than \\(0.6\\%\\) of the encoder's parameter count, to achieve this gain. For comparison, the gain from VideoMAE V1 to VideoMAE V2 uses 380M extra parameters to increase the accuracy by only \\(0.4\\%\\). Note that our results are achieved without refinetuning the encoder, so the training cost is minimal compared to training the encoder. In short, DejaVid is a comparatively tiny add-on that significantly boosts the performance of an off-the-shelf frozen model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.905, + 0.901 + ], + "angle": 0, + "content": "The performance gain of DejaVid is not only due to temporal supersampling. We test this by averaging the temporal dimension of each sample TSE to get a length- \\((1408 + N_{c})\\) vector and using the last \\(N_{c}\\) elements for class prediction; the result is shown as VideoMAE V2 (temporal supersampling) Tab. 1. When compared against the original setting at VideoMAE V2 \\(5\\times 3\\), we see this alone does not improve" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.85, + 0.483, + 0.901 + ], + "angle": 0, + "content": "3VideoMAE V2 publishes different finetuned weights for Kinetics-400 and Something-Something V2, and the script for finetuning on HMDB51, which we can afford to run thanks to the small dataset size. We use the respective finetuned weights for the pre-training stage of each dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24028" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "the accuracy. Also, the temporal weight-learning does not provide additional benefits on top of our centroid-finetuning for Kinetics-400. We suspect the reason is that the temporal weights increase the expressivity of our method, so overfitting becomes more likely; one future work is to look into regularization for DejaVid." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.187, + 0.483, + 0.368 + ], + "angle": 0, + "content": "Results on HMDB51. The results in Tab. 1 show that our model also achieves state-of-the-art accuracy on the HMDB51. We achieve a \\(0.5\\%\\) performance gain against the strongest VideoMAE V2-g baseline. To the best of our knowledge and according to Papers with Code, this is the highest accuracy recorded on the HMDB51 action recognition benchmark to date (as of Nov, 2024). This shows that DejaVid works well in a training data-scarce scenario. We draw similar conclusions to those from Kinetics-400 in parameter efficiency – our parameter count is 1.19M, which is less than \\(0.12\\%\\) of that of VideoMAE V2-g – and temporal supersampling alone does not improve performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.373, + 0.483, + 0.493 + ], + "angle": 0, + "content": "Results on Something-Something V2. Tab. 1 compares our results on Something-Something V2 against other works. We outperform the top VideoMAE V2-g baseline with a performance gain of \\(0.5\\%\\). To the best of our knowledge and according to Papers with Code, DejaVid achieves the highest top-5 accuracy and one of the highest top-1 accuracies on the Something-Something V2 action recognition benchmark to date (as of Nov, 2024)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.494, + 0.483, + 0.645 + ], + "angle": 0, + "content": "Progress on Something-Something V2 has slowed in recent years, with top accuracy improving by no more than \\(0.3\\%\\) between 2022 and 2024 [20]. Such gains often require massive model scaling; for example, InternVideo2 added over 5 billion parameters for a \\(0.4\\%\\) boost [30]. In contrast, DejaVid achieves comparable improvements with just 17.6M parameters—fewer than \\(1.8\\%\\) of VideoMAE V2-g. This efficiency highlights the significance of our \\(+0.5\\%\\) accuracy gain, which equates to more than two years of recent progress [28-30]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.646, + 0.483, + 0.721 + ], + "angle": 0, + "content": "However, the performance gain is smaller than on Kinetics-400. One possible reason could be the difference in average video length: \\(\\sim 40\\) for Something-Something V2 and \\(\\sim 300\\) for Kinetics-400. Because Kinetics-400 videos are longer, there may be more temporal information" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "for DejaVid to capture. Another reason may be that the encoder is trained with variable video durations, as described in Sec. 4.2, so one future work would be to re-finetune the encoder with video clips of constant frame-count and retry our experiments." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.174, + 0.679, + 0.188 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.192, + 0.907, + 0.449 + ], + "angle": 0, + "content": "Centroid vs. Weight Learning. In Tab. 2, we analyze the impacts of centroid and weight learning of DejaVid by freezing one component at a time and comparing the results. As seen, both frozen-centroid and frozen-weight variants yield meaningful accuracy gains against the VideoMAE V2-g baseline, and so both components are indeed beneficial. The centroid component has a greater performance gain on average across the three datasets, giving \\(+0.43\\%\\) top-1 accuracy gain vs. \\(0.25\\%\\) for the weights, but the weight component seems to be more useful when training data is scarce. As for the training data-rich cases, the weight component seems to be more useful in Something-Something V2 than in Kinetics-400, potentially because we have 4 different feature sets from the different sliding window widths, and these features should naturally have different importance, so the one-initialized weights are further away from the global optimal." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.464, + 0.905, + 0.579 + ], + "angle": 0, + "content": "
MethodSth-Sth2K400HMDB
top-1top-5top-1top-5top-1
VideoMAE V2-g @ best [28]76.7595.8588.498.088.1
Frozen centroids (w-init-rnd)76.896.288.698.088.4
Frozen centroids (w-init-one)76.996.288.898.188.4
Frozen weights (w-init-one)77.196.389.198.288.3
Full learning (w-init-rnd)77.296.388.998.188.6
Full learning (w-init-one)77.096.389.098.288.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.546, + 0.582, + 0.874, + 0.596 + ], + "angle": 0, + "content": "Table 2. Ablation study on centroid & weight learning." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.606, + 0.903, + 0.683 + ], + "angle": 0, + "content": "
MethodSth-Sth2K400HMDB
top-1top-5top-1top-5top-1
DT on, otherwise best77.096.288.698.088.5
FECW off, otherwise best77.196.289.098.288.5
Best (DT off, FECW on)77.296.389.198.288.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.686, + 0.905, + 0.714 + ], + "angle": 0, + "content": "Table 3. Ablation studies on diagonal transition (DT) and fixed epoch centroids & weights (FECW)." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.724, + 0.903, + 0.782 + ], + "angle": 0, + "content": "
MethodSth-Sth2K400HMDB
Naive DTW implementation4.79e471.17e57294
Custom DTW CUDA kernel2971561.01
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.786, + 0.905, + 0.814 + ], + "angle": 0, + "content": "Table 4. Ablation study on the custom DTW CUDA kernel. Table shows runtime per training epoch in seconds." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.821, + 0.905, + 0.852 + ], + "angle": 0, + "content": "Diagonal Transition of DTW. Tab. 3 presents a comparison between the best (highest top-1 accuracy\\(^{8}\\)) setting of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.533, + 0.863, + 0.71, + 0.876 + ], + "angle": 0, + "content": "Estimated by running 3 batches." + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.877, + 0.905, + 0.901 + ], + "angle": 0, + "content": "In the case of tied top-1 accuracies, we apply the same change to each tied setting and average their resulting accuracies after the change." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.863, + 0.905, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.731, + 0.483, + 0.887 + ], + "angle": 0, + "content": "4We were unable to run InternVideo2 on our machine due to one of its required packages, flash-attn, being incompatible with our machine. 5The authors of VideoMAE V2 report 77.0 and 95.9 for top-1 and top-5 accuracy, respectively, but we measure only 76.7 and 95.8 using their published weights. We suspect the discrepancy is due to the input video loading mechanism. The official GitHub repo of VideoMAE V2 has inconsistent descriptions about the data preparation for Something-Something V2, but as of the time of writing, the source code assumes each video has been converted to a folder ofjpeg images, and VideoMAE V2 loads theseJPEG files instead of the source video. But when we do exactly that, the top-1 accuracy measures only 75.7. This is understandable since JPEG uses lossy compression. So we modified the source code to use opencv2 to directly load each video, which gives 76.7 and 95.8." + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.888, + 0.399, + 0.9 + ], + "angle": 0, + "content": "The definition of these clips are described in Sec. 4.2." + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.731, + 0.483, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24029" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.905, + 0.341 + ], + "angle": 0, + "content": "
MethodW.A.Kinetics-400Something-Something V2HMDB51
ParamsClipsxCropsTop-1Top-5ParamsClipsxCropsTop-1Top-5ParamsClipsxCropsTop-1
Other State-of-the-Art Large Models
TubeViT [22]No632M4×390.998.9307M-76.195.2---
MVD [29]No633M5×387.297.4633M2×377.395.7---
InternVideo2-1B [30]Yes41B4×391.6-1B2×377.1----
InternVideo2-6B [30]No6B4×392.1-6B5×377.5----
Other Temporal-Focused Methods
ILA [27]--4×388.797.8-4×370.291.8---
ATM [31]--4×389.498.3-2×374.694.4---
TAM [19]--4×379.394.1-2×366.090.1---
SlowFast [11]--10×379.893.9--61.7----
MTV [32]--4×389.198.2--68.590.4---
Main Baselines
VideoMAE V1-H [28]Yes633M5×388.1--------
VideoMAE V1-L (32-frame input) [25, 28]Yes----305M2×375.495.2---
VideoMAE V2-g [28]Yes1013M5×388.498.01013M2×376.7595.851013M5×388.1
VideoMAE V2-g (temporal supersampling) [28]Yes1013M336×188.197.81013M(4|vid|)6×176.295.71013M336×188.0
Our Results
Ours (frozen weights; w-init-one)-+5.8M36×189.198.2+8.8M(4|vid|)6×177.196.3+0.60M88.3
Ours (full learning; w-init-rnd)-+11.6M88.998.1+17.6M77.296.3+1.19M336×188.6
Ours (full learning; w-init-one)-+11.6M89.098.2+17.6M77.096.3+1.19M88.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.351, + 0.907, + 0.379 + ], + "angle": 0, + "content": "Table 1. Comparison with the VideoMAE V2-g baseline and other relevant variants, SOTA, or temporal methods on Kinetics-400, Something-Something V2, and HMDB51. All accuracies are reported in percent (\\%). W.A. = Weights Available. Dashes (-) = N/A." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.383, + 0.482, + 0.458 + ], + "angle": 0, + "content": "Tab. 2 for each dataset and the same setting but with diagonal transitions turned on. Enabling diagonal transitions consistently performs worse on all datasets. This justifies our choice of disabling diagonal transitions in DejaVid and verifies the insight behind this choice as described in Sec. 3.4." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.459, + 0.483, + 0.669 + ], + "angle": 0, + "content": "Fixed Epoch Centroids & Weights for DTW Learning. We use Tab. 3 to compare the best setting (highest top-1 accuracy8) from Tab. 2 for each dataset with the same setting but disabling fixed epoch centroids & weights, where we do not make frozen copies of the centroids and weights for warping-path determination (shown as FECW off). Again, the inferior performance of this group compared to when FECW is on across all datasets justifies our design for DejaVid, aligning with the reasons detailed in Sec. 3.4 about model stability. However, the gap is less significant than that for the diagonal transition. This suggests there may be room for improvement by tweaking the path-determination mechanism, such as only updating every other epoch instead of each epoch." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.483, + 0.851 + ], + "angle": 0, + "content": "Custom CUDA Kernel for Accelerating DTW. Tab. 4 summarizes the runtime per epoch of the best-performing settings on all datasets compared to using a naive Python implementation of DTW. All experiments are conducted on a single node with 8 NVIDIA H100 GPUs. We can see that our custom CUDA kernel provides a speedup between \\(161\\mathrm{x}\\) and \\(750\\mathrm{x}\\). The most technically significant speedup comes from reducing the critical path length from quadratic to linear, as discussed in Sec. 3.2. Other factors contributing to the speedup include the Python/C++ speed difference and architecture and locality-aware, LibTorch-native implementation of the CUDA-kernel." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.853, + 0.21, + 0.868 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.903 + ], + "angle": 0, + "content": "We presented DejaVid, an encoder-agnostic method that boosts video classification performance without retraining" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.383, + 0.908, + 0.701 + ], + "angle": 0, + "content": "the encoder or changing its architecture. Instead of converting a video into a single fixed-length embedding like most state-of-the-art encoders do, we feed a backbone encoder a sliding-window stream of frames to obtain a variable-length temporal sequence of embeddings (TSE), which preserves temporal order and supports variable video durations. We then introduce a novel neural network architecture based on Dynamic Time Warping (DTW) with learnable, per-timestamp feature weights to address temporal variance in feature significance. Our ablation studies compare and justify various design choices and modifications to classical DTW, and our evaluation shows that DejaVid achieves state-of-the-art video classification results on a variety of benchmarks, significantly improves the accuracy of a cutting-edge large encoder, and outperforms other temporal methods. In particular, we achieve leading Top-1 accuracy of \\(77.2\\%\\) on Something-Something V2, \\(89.1\\%\\) on Kinetics-400, and \\(88.6\\%\\) on HMDB51, representing a 0.5- \\(0.7\\%\\) accuracy gain over VideoMAE V2-g while adding less than \\(1.8\\%\\) additional learnable parameters and less than 3 hours of training time." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.709, + 0.649, + 0.724 + ], + "angle": 0, + "content": "6. Future Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.73, + 0.907, + 0.88 + ], + "angle": 0, + "content": "In this paper, we selected video classification as the evaluation task due to its foundational role in computer vision [15, 16, 26], its real-world importance [1, 11, 13], and the significant amount of highly competitive research focused on it [2, 11, 19, 22, 25, 27-32]. With that said, we can also see the potential of DejaVid – and of the power of fine-grained temporal alignment learning in general – in action segmentation, video captioning, text-to-video retrieval, and any other tasks that can benefit from detailed temporal modeling." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24030" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.184 + ], + "angle": 0, + "content": "[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. 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However, these large models typically process videos by averaging embedding outputs from multiple clips over time to produce fixed-length representations. This approach fails to account for a variety of time-related features, such as variable video durations, chronological order of events, and temporal variance in feature significance. While methods for temporal modeling do exist, they often require significant architectural changes and expensive retraining, making them impractical for off-the-shelf, fine-tuned large encoders. To overcome these limitations, we propose DejaVid, an encoder-agnostic method that enhances model performance without the need for retraining or altering the architecture. Our framework converts a video into a variable-length temporal sequence of embeddings (TSE). A TSE naturally preserves temporal order and accommodates variable video durations. We then learn per-timestep, per-feature weights over the encoded TSE frames, allowing us to account for variations in feature importance over time. We introduce a new neural network architecture inspired by traditional time series alignment algorithms for this learning task. Our evaluation demonstrates that DejaVid substantially improves the performance of a state-of-the-art large encoder, achieving leading Top-1 accuracy of $77.2\%$ on Something-Something V2, $89.1\%$ on Kinetics-400, and $88.6\%$ on HMDB51, while adding fewer than $1.8\%$ additional learnable parameters and requiring less than 3 hours of training time. Our code is available at https://github.com/darrylho/DejaVid. + +# 1. Introduction + +Video action recognition has seen remarkable progress with the rise of transformer-based video models [2, 7, 10]. To improve their performance, one of the most straightforward and effective approaches is to upscale the model and training data [33]. As such, the leaderboards of major action recognition benchmarks have come to be dom + +![](images/c4c3a1c57f32e388d56cea0f15fbbef3842597e6b37526e5b5e4eb0229cf446d.jpg) +Pre-training Training + +![](images/28e85de19bb4088a6c6512d8bcb9a5ac8cb516bb5aeb3a8f0f73fce4856bf5d4.jpg) + +![](images/4fa947fdd9646b701df09c0a16ede581f80bcbf524bb8ce939e3f8fba843fd2f.jpg) +Figure 1. DejaVid system diagram. We first transform a video into a variable-length temporal sequence of embeddings (TSE) then use Dynamic Time Warping Barycenter Averaging (DBA) [21] to calculate a reasonably "average" TSE per class for its centroid initialization. We then learn per-timestep, per-feature weights for the encoded TSE frames, enabling us to accommodate variations in feature importance over time, as well as finetune the centroid TSE for each output class. For this task, we introduce a new neural network architecture inspired by traditional time series alignment algorithms. In testing, we freeze the post-training centroids and weights and use the same pre-training pipeline to generate TSEs to feed into DejaVid for predictions. + +inated by 100M-1B+ parameter large video transformers [14, 16, 18, 22, 28-30]. + +These large encoders process videos with fixed frame counts, heights, and widths, generating a single embedding. On datasets with varying durations, the common approach is to pass multiple temporal clips and spatial crops through the encoder and then average the resulting logits for class prediction [22, 28-30]. However, while the height and width of videos in a dataset are usually constant, their duration can vary significantly [14]. Furthermore, temporal order is far more critical. Unlike image flipping [17], reversing time can alter semantics, such as opening vs. closing a door. When averaging logits from different temporal clips, sequential information in these clips is lost. Moreover, the significance of each feature within a video can change over time. For example, in a basketball three-point shot, early frames emphasize player position, while later frames focus on whether the ball goes in. Although encoders might not explicitly model semantically interpretable features like these, temporal variation in feature importance can also occur for arbitrary features, which mean-pooling fails to capture adequately. This motivates a key observation of our work: by failing to carefully account for temporal dimensions, state-of-the-art large models leave significant accuracy gains on the table. + +Improving the temporal performance of large encoders is not trivial. Existing temporal-focused methods require invasive changes to the model, such as inserting temporal-specific layers between transformer blocks [27, 31] or creating model duplications to focus on different input views [11, 32]. These approaches are costly to apply to off-the-shelf pre-trained encoders because they require extensive changes in implementation and costly re-training. + +These insights motivate DejaVid, a lightweight encoder-agnostic temporal approach that substantially boosts model classification performance. The simple yet crucial idea behind DejaVid is that a video is more effectively represented as a temporal sequence of embeddings (TSE) rather than as a single embedding. This representation naturally preserves chronological order while supporting varying time lengths, addressing the aforementioned shortcomings. DejaVid is naturally able to use any pre-trained model by consuming a sliding-window of encoded video to generate a TSE, without requiring changes to the model's architecture, retraining, or fine-tuning. DejaVid is inspired by the well-known Dynamic Time Warping (DTW) algorithm [4], which dynamically aligns similar data points between two temporal sequences while maintaining their chronological order. In particular, DejaVid introduces a novel neural network architecture inspired by DTW but with learned per-timestep, per-feature weights to handle the temporal variance of feature importance. Additionally, we develop a custom high-performance CUDA kernel for efficient computation and backpropagation of the (time-weighted) warping distance that outperforms a naive DTW-based implementation by 2 + +orders of magnitude. + +We evaluate DejaVid by layering it on top of the largest (ViT-g) variant of VideoMAE V2 [28] (abbr. VideoMAE V2-g) as the backbone encoder to evaluate DejaVid on three popular action recognition datasets: Kinetics-400 [16], Something-Something V2 [14], and HMDB51 [18]. We show that DejaVid significantly improves on the strongest VideoMAE V2-g baseline, thereby achieving new state-of-the-art performance. In particular, DejaVid achieves Top-1 accuracy of $77.2\%$ on Something-Something V2, $89.1\%$ on Kinetics-400, and $88.6\%$ on HMDB51, while adding fewer than $1.8\%$ additional learnable parameters and requiring less than 3 hours of training time. We also show that our proposed modifications to DTW, including the temporal weights, can further improve prediction performance. + +# 2. Related Work + +State-of-the-Art in Action Recognition. Major action recognition benchmarks are topped by massive video transformers with hundreds of millions or billions of parameters. As of the time of writing, according to Papers with Code, the top performers on Kinetics-400 and Something-Something V2 with verifiable parameter counts have between 600M and 6B parameters [14, 16, 22, 28-30]. However, their evaluations on these two datasets all apply spatial and temporal mean-pooling to the logits at the end, which suffers from the time-related shortfalls related to variable video durations, chronological order of events, and temporal variance in feature significance, as described in Sec. 1. + +Temporal-focused Methods for Action Recognition. There have been various works on improving the temporal modeling capability of video transformers. One general approach is to introduce temporal-specific layers in between transformer blocks. For example, ILA employs a mask-based layer that predicts interactive points between frame pairs to implicitly align features [27], ATM applies basic arithmetic operations to pairs-of-frame features between ViT blocks [31], and TAM inserts an attention-based temporal adaptive module between 2D convolutions within a ResNet block [19]. Another line of work is to fuse multiple temporal views in different ways. For example, SlowFast networks feed two different frame rates of a video into separate encoders and add lateral connections between them to fuse information across views [11], and MTV deploys a similar idea but for both spatial and temporal dimensions [32]. However, their performance is not competitive against the aforementioned large state-of-the-art models, partly due to their smaller size. Implementing these methods within the large models would involve considerable implementation changes and expensive retraining. + +Learning Temporal Sequence Alignments. DTW is one of the most classic methods for calculating similarities between univariate time series or multivariate ones like our + +TSEs [4, 23]. Its traditional formulation is a dynamic programming scheme, but recent work has explored making it differentiable and then applying it to various fields. SoftDTW [9] shows that DTW makes a good loss function when the min operator is replaced with soft-min. DTWnet [5] proposes using DTW learning for time series feature extraction, and D3TW, OTAM, and FTCL [6, 8, 12] similarly do this for weakly-supervised and few-shot video understanding. While these works have some similarities to our DTW-based temporal representation learning, our method is technically different and superior in three ways: + +1. DejaVid models and learns the temporal variance in feature importance, which none of the other methods do. While classical DTW typically only works for a few dimensions (10-100) that require handcrafting or hand-picking [3], by adding learned weights, we extend DTW to high-dimensional use cases $(1000 - 10000+)$ like video recognition by letting it learn the important dimensions. +2. We reformulate our DTW-inspired temporal learning algorithm as a new neural network architecture that boosts parallelizability and facilitates differentiability. +3. We introduce changes to DTW to improve model stability, including removing the diagonal transition of DTW. + +# 3. Method + +As described in Sec. 1, we represent a video as a temporal sequence of embeddings (TSE). In this section, we assume all videos have been converted into TSEs, and operate in this TSE space. DejaVid feeds a video encoder a sliding-window stream of frames of an input video to generate a TSE, so the shape of a TSE is $T \times N_{f}$ , where each index along $T$ represents the encoding of a window of frames, and thus $T$ can vary depending on individual video duration. $N_{f}$ is the size of the embedding vector of the backbone encoder and is constant. + +Our problem is to classify TSEs. Specifically, we are given a training set of TSEs with class labels among $N_{c}$ classes, and our goal is to predict the classes of our validation TSEs. We solve this problem in three broad steps: + +1. For each class, we calculate a centroid TSE from the training TSEs of that class. +2. We optimize the centroid TSEs according to some loss function w.r.t. the training TSEs. +3. For each validation TSE, we calculate which class's centroid TSE is the most similar to it. + +Here, Steps 1 and 3 require a definition of distance (or similarity) between TSE pairs, and Step 2 requires the distance metric to be backpropagateable. The following Secs. 3.1 and 3.2 describe how we solve these two problems. + +# 3.1. Definitions + +There are multiple ways in which one can define the distance between two TSEs [4, 24], but in this paper, we focus + +on a standard time series distance metric: Dynamic Time Warping (DTW), as given in Algorithm 1 (without the red text). DTW aligns two sequences that vary in time or speed by minimizing the distance between corresponding points. The two sequences are aligned by aligning each timestep in the first sequence to one or more consecutive timesteps in the second sequence while maintaining a monotonic relationship where a later timestep in the first must map to a later interval in the second. Monotonicity is maintained in Line 5 of Algorithm 1, where each step only moves forward in time for either sequence (from $i - 1$ to $i$ or $j - 1$ to $j$ ). This alignment minimizes cumulative distance and is commonly visualized as a "warping path" on a 2D grid, which shows the optimal alignment of the two sequences, each depicted in one grid axis. + +Algorithm 1 The Standard DTW Algorithm (without diagonal transition) vs. the Time-Weighted DTW Algorithm (red) +Input: Two TSEs $a, b \in \mathbb{R}^{n \times N_f}, \mathbb{R}^{m \times N_f}$ ; a distance function $dist_w$ ; $u \in \mathbb{R}_{>0}^{n \times N_f}$ temporal feature weights of $a$ +Output: Distance between $a$ and $b$ + +1: $D \gets \operatorname{array}[n, m]$ {Out-of-bounds access returns $+\infty$ } + +2: $D_{0,0}\gets dist_w(u_0,a_0,b_0)$ +3: for $i$ in $[0, n - 1]$ do +4: for $j$ in $([0, m - 1]$ if $i > 0$ else $[1, m - 1]$ ) do +5: $D_{i,j}\gets \min (D_{i - 1,j},D_{i,j - 1}) + dist_w(u_i,a_i,b_j)$ +6: end for +7: end for +8: return $D_{n-1,m-1}$ + +In the standard Algorithm 1, we use the Manhattan distance for the pointwise distance function $dist$ . Also, although the original DTW algorithm includes a diagonal transition $D_{i-1,j-1}$ in the min clause, we omit this in DejaVid because it improves model stability. We discuss this decision in more detail in Sec. 3.4. + +Let $D_v(a,b)$ denote the DTW distance between TSEs $a$ and $b$ as returned by the standard Algorithm 1, and let $C \in \mathbb{R}^{N_c \times T_c \times N_f}$ represent the centroid TSEs for the $N_c$ classes. Intuitively, we want to assign each TSE to the class it is nearest to in the DTW space. To do this, we define the predicted probability distribution $\hat{\mathbf{y}}_v$ for a training or validation TSE $m \in \mathbb{R}^{T_m \times N_f^1}$ , and the loss $\mathcal{L}_v$ for $m$ under centroids $C$ and one-hot ground truth vector $\mathbf{y}$ : + +$$ +\hat {\mathbf {y}} _ {v} (C, m) := \underset {0 \leq i < N _ {c}} {\operatorname {s o f t m i n}} \left(D _ {v} \left(C _ {i}, m\right)\right) +$$ + +$$ +\mathcal {L} _ {v} (C, m) := \operatorname {C r o s s E n t r o p y} (\mathbf {y}, \hat {\mathbf {y}} _ {v} (C, m)) +$$ + +However, as described in Sec. 1, we observe that the importance of each feature of a video can vary as time progresses. This observation motivates our time-weighted + +DTW distance metric, given in Algorithm 1 with modifications shown in red. The difference is the additional weight input $u$ , which denotes the change in feature importance over time for $a$ . We also modify the pointwise Manhattan distance function to incorporate $u$ : $dist_w(u_i, a_i, b_j) := \sum_{k=0}^{N_f-1} u_{i,k} |a_{i,k} - b_{j,k}|$ . The changes are colored in Lines 2 and 5 of Algorithm 1. Intuitively, when Algorithm 1 calculates the distance between two sequences, our time-weighted modification allows it to weight some timesteps more than some other timesteps in the first series, and different features can have different weights as well. Let $D_w(u, a, b)$ denote the time-weighted DTW distance between TSEs $a$ and $b$ as returned by the time-weighted Algorithm 1. We aim to learn the temporal variance of feature importance of the centroids $C$ , so we define $U \in \mathbb{R}_{>0}^{N_c \times T_c \times N_f}$ of the same shape as $C$ to be the time-varying feature weights. To maintain the positivity of distances, we constrain $U$ to be positive. The time-weighted variant of predicted probability distribution $\hat{\mathbf{y}}_w$ and loss $\mathcal{L}_w$ are defined similarly as before: + +$$ +\hat {\mathbf {y}} _ {w} (U, C, m) := \operatorname * {s o f t m i n} _ {0 \leq i < N _ {c}} \left(D _ {w} \left(U _ {i}, C _ {i}, m\right)\right) +$$ + +$$ +\mathcal {L} _ {w} (u, C, m) := \operatorname {C r o s s E n t r o p y} (\mathbf {y}, \hat {\mathbf {y}} _ {w} (u, C, m)) +$$ + +From now on, we focus on the time-weighted Algorithm 1, since one can set $U = \mathbf{1}_{N_c\times T_c\times N_f}$ to recover standard DTW in Algorithm 1. + +# 3.2. Parallelizability & Differentiability + +![](images/d3b9dc2a9adf3207121ce6722fa7b2e5bf936b2e8b234a8ba6752ecf9ef2465e.jpg) + +![](images/f9a81c43fd45cbba525cffa70af147d5b4be9b45ef721c0dc7a5560ba0b182fa.jpg) +Figure 2. 1. Each cell of the DTW 2D grid executes a min operation and then an add-dist operation. Checkmarks show completed cells in row-major order. 2. In diagonal order, a diagonal can be executed as soon as the previous diagonal has finished. Checkmarks show completed cells in diagonal order. 3. We can view each diagonal as a min-pooling layer with kernel size 2 and stride 1, followed by an additive skip-connection layer. 4. We reformulate the algorithm into a serial stack of min-pooling layers interlaced with additive skip-connections. + +![](images/78c89e18579b5ea8cc2f3c2be1e42e29dfb997bd69f3f31f186c4734b9a45c51.jpg) + +Algorithm 2 given an equivalent neural-network formulation for Algorithm 1; this formulation facilitates the use of backpropagation for optimizing weights and enhances parallelizability. Before providing the details of the algorithm, we provide some intuition as to how and why it works. + +Fig. 2 depicts the 2D grid commonly used for representing DTW warping path(s) between two sequences, as described in Sec. 3.1. We visualize each operation in the nested loop in Algorithm 1 onto the corresponding cell in the grid. We can see that each cell executes a min operation on the outputs of its left-adjacent and bottom-adjacent cells, followed by an addition of some pointwise weighted distance $dist_w$ . Note that cells are executed in a row-major order in Algorithm 1. Therefore, the critical path length is quadratic $(O(nm))$ . + +However, we leverage a critical property of Algorithm 1 that enables a reformulation of the algorithm, which is that each cell can be executed as soon as its left and bottom neighbors have finished. Therefore, we reformulate Algorithm 1 to execute in diagonal order and observe that the $l$ -th diagonal can be executed as soon as the $(l - 1)$ -th diagonal has finished. Here, we define the $l$ -th diagonal to be the cells $\{(i,j) \mid i + j = l\}$ . For example, the top-right of Fig. 2 shows the 4th diagonal. Furthermore, elements in the same diagonal are mutually independent, so the work within each diagonal is parallelized. So we have reduced the critical path length to the number of diagonals, obtaining the linear runtime $O(n + m)$ . + +Because each cell executes at Line 5 of Algorithm 1 a min operation on two consecutive cells of the previous diagonal and then adds some $dist_w$ term, we can express the new formulation as a neural net where each diagonal is a min-pooling layer with kernel size 2 and stride 1 followed by an additive skip-connection layer. Each min-pooling layer is executed after its previous skip-connection and min-pooling are completed. So Algorithm 1 is equivalent to a serial stack of min-pooling layers, with skip-connections interlacing in between. These descriptions are formalized in Algorithm 2, where one can see the execution of the interlaced layers at Lines 10 and 11. For differentiability, we rewrite the time-weighted DTW distance $D_w$ as: + +$$ +\begin{array}{l} D _ {w} := S C _ {n + m - 2} + M P _ {n + m - 2} \left(S C _ {n + m - 3} + M P _ {n + m - 3}\right) \\ \ldots + S C _ {1} + M P _ {1} \left(S C _ {0}\right) \dots)) \\ \end{array} +$$ + +where $MP_{l}$ and $SC_{l}$ are the $l$ -th min-pooling and skipconnection as show in Algorithm 2. Because both min-pooling and additive skip-connections are standard neural network operations, loss gradients trivially propagate through them. In a nutshell, the loss backpropagates to only the $dist_{w}(u_{i},a_{i},b_{j})$ functions on the optimal warping path, which enables gradient-based optimization on $U$ and $C$ . We leave the detailed formulas for loss gradients $\frac{\partial L_w}{\partial C}$ and $\frac{\partial L_w}{\partial U}$ in Supplementary Material. + +# 3.3. System Overview + +With the definitions introduced in Secs. 3.1 and 3.2, we now formalize the 3-step solution outlined at the start of Sec. 3. Fig. 1 provides an overview of the DejaVid system. The video encoder takes as input a video clip of fixed duration + +Algorithm 2 Time-Weighted DTW Neural Network +Input: Two TSEs $a, b \in \mathbb{R}^{n \times N_f}, \mathbb{R}^{m \times N_f}$ ; a distance func +tion $dist_w$ ; $u \in \mathbb{R}_{>0}^{n \times N_f}$ temporal feature weights of $a$ +Output: Distance between $a$ and $b$ +1: {Out-of-bounds access to $D$ or $SC$ returns $+\infty$ } +2: $SC_{0,0} \gets dist_w(u_0, a_0, b_0)$ {The 0-th skip- +connection} +3: $D_{0,0} \gets SC_{0,0}$ +4: for $l$ in $[1, n + m - 2]$ do +5: {The $l$ -th diagonal} +6: start, end $\leftarrow \max(0, l - m + 1)$ , $\min(n - 1, l)$ +7: $SC_l \gets [dist_w(u_t, a_t, b_{l-t})]_{t=start}^{\text{end}}$ +8: $D_l \gets \text{array[end - start + 1]}$ +9: kernel, stride $\leftarrow 2, 1$ +10: for $i$ in range(0, end - start + 1, stride) do +11: $D_{l,i} \gets SC_{l,i} + \min_{s=0}^{kernel-1}(D_{l-1,i-s})$ +12: end for +13: end for +14: return $D_{n+m-2,0}$ + +and outputs an embedding $e \in \mathbb{R}^{N_f}$ . Given any off-the-shelf video encoder, we apply a sliding window over each video to produce a sequence of clips, which we then feed into the encoder to produce a temporal sequence of embeddings $E = \{e_0, e_1, \dots, e_{T-1}\} \in \mathbb{R}^{T \times N_f}$ , which forms a TSE for each video sample in the dataset. Then, we produce a centroid TSE of shape $T_c \times N_f^2$ for each class by feeding the training TSEs to the DBA (Dynamic Time Warping Barycenter Averaging) [21] algorithm, which calculates a reasonable "average" time series of the inputs while accounting for imperfect temporal alignment. Intuitively, each centroid TSE represents how the class-wide average of the $N_f$ features changes over time. Ultimately, we obtain many training TSEs, each with shape $T \times N_f$ for some varying $T$ , and a stack of centroid TSEs $C$ of shape $N_c \times T_c \times N_f$ , where $N_c$ is the number of classes. This concludes the pretraining stage of DejaVid. + +In the training phase, to account for temporal variance in feature importance over time, each centroid TSE is paired with a positive weight tensor of the same shape $T_{c} \times N_{f}$ that represents the importance of each feature over time. The positivity is to maintain that the pointwise distance $\text{dist}_{w}$ is always positive. We denote the stack of weight TSEs $U$ with shape $N_{c} \times T_{c} \times N_{f}$ . At initialization, the weight TSEs are either filled with ones or random positive values. + +In each epoch, we calculate the weighted DTW distance $D_w$ from each training TSE $m \in \mathbb{R}^{T \times N_f}$ to every centroid TSE to get the logit vector $\mathbf{z} = \{D_w(U_i, C_i, m)\}_{i=0}^{N_c-1} \in \mathbb{R}^{N_c}$ , on which we apply softmax to get the class prediction $\hat{\mathbf{y}}$ and cross-entropy loss $\mathcal{L}_w$ w.r.t. the ground truth $\mathbf{y}$ . The + +weights $U$ and centroids $C$ TSEs are updated during backpropagation. To accelerate forward and backward passes, we implement a custom DTW CUDA kernel that efficiently calculates a slope tensor $S \in \mathbb{R}^{N_c \times T_c \times N_f}$ and an intercept tensor $B \in \mathbb{R}^{N_c \times T_c \times N_f}$ such that $\text{torch.sum}(U \odot (C \odot S + B), \dim = (-2, -1))$ equals the logit vector $\mathbf{z}$ and the effective gradients w.r.t. $U$ and $C$ equals $\frac{\partial L_w}{\partial U}$ and $\frac{\partial L_w}{\partial C}$ . The implementation of the CUDA kernel, roughly speaking, leverages the fact that a weighted DTW distance is essentially the sum of many terms of $u \cdot |c - b|$ , which equals $u \cdot (c \cdot (\pm 1) + (\mp 1)b)$ , where the $(\pm 1)$ term contributes to slope $S$ and $(\mp 1)b$ to intercept $B$ . + +# 3.4. Modifications to Standard DTW + +As mentioned in Sec. 3.1, unlike the original DTW algorithm, we exclude the diagonal transitions (i.e., transitioning from $D_{i-1,j-1}$ to $D_{i,j}$ in Algorithm 1) for DejaVid. The reason is due to model stability. When matching two series of length $n$ and $m$ , by disallowing diagonal transitions, the warping path from $D_{0,0}$ to $D_{n-1,m-1}$ always takes $n+m-1$ steps, and so the DTW distance will always be the sum of $n+m-1$ step-wise distances. If diagonal transitions are allowed, the number of step-wise distances on the warping path can vary, destabilizing the model. Although beyond the scope of this paper, we note that there could be other ways to deal with diagonal transitions, such as assigning or learning a multiplicative or additive distance bias for diagonal vs. non-diagonal transitions, such as in Move-Split-Merge (MSM) [24], a more modern replacement of DTW that treats diagonal transitions differently from non-diagonal ones. + +Another modification we made is to fix epoch centroids and weights. That is, at the beginning of an epoch, we make a frozen copy of the current centroids and weights, and then during the epoch, use them to calculate the warping path for each centroid-training TSE pair. Then, along the path, we calculate the pointwise distance using the (non-frozen) originals and perform backpropagation on them. Note that the frozen copies are not updated per batch but instead per epoch. The reason for this modification is again due to model stability. We found that if the warping path calculation mechanism is updated every batch, the distances become noisier from batch to batch, and the model has a harder time converging. + +We discuss the effect of these modifications in Sec. 4.4. + +# 4. Evaluation + +In this section, we describe our implementation and evaluation of DejaVid. + +# 4.1. Datasets and Evaluation Metrics + +We test DejaVid on three different popular action recognition datasets: Something-Something V2 [14], Kinetics-400 [16], and HMDB51 [18]. The first two are large-scale datasets: Something-Something V2 has 168,913 videos for + +training and 24,777 for validation, while Kinetics-400 has 240,436 training and 19,787 validation videos. In contrast, HMDB51 only has 3,570 training and 1,530 validation videos, but its smaller size can help us study the model's performance when the training set is smaller. + +Something-Something V2 has 174 action classes that are object and motion-centric, which requires learning the subtle differences between motions and object interactions. Kinetics-400 covers 400 classes of everyday human actions derived from real-world scenarios on YouTube and can be human-object or human-human interactions. Its videos are also longer than those of Something-Something V2 on average ( $\sim$ 300 frames vs. $\sim$ 40 frames), which can help differentiate the temporal modeling capabilities between models. HMDB51 has 51 human-dominated action classes, like Kinetics-400, containing some individual and some human-human behaviors. + +For all these datasets, we train DejaVid on the training sets and test on the validation sets using the same evaluation protocols as those in VideoMAE V2 [28]. We report the top-1 and top-5 accuracy for every experiment on Something-Something V2 and Kinetics-400. Due to the smaller action set of HMDB51, we only report top-1 for experiments on it. + +# 4.2. Implementation Details + +Pre-training. We use the largest (ViT-g) model from VideoMAE V2 [28] (abbr. VideoMAE V2-g) as the video encoder.3 VideoMAE V2-g is the only model we experiment with because it is the only SOTA model4 that publishes finetuned weights on large datasets like Kinetics-400 and Something-Something V2, which we cannot afford to finetune ourselves. To show that DejaVid is model-agnostic, we apply the same method to other non-SOTA video encoders in Supplementary Material. The native embedding output length of VideoMAE V2 is 1408, which is then converted into $N_{c}$ logits for class prediction, so we let $N_{f} \coloneqq 1408 + N_{c}$ denote the length of the entire output of VideoMAE V2-g. For DejaVid, we apply a temporal sliding window across the input video $T$ times to feed into the encoder, resulting in a TSE of shape $T \times N_{f}$ . We then randomly sample some TSEs for each action class to calculate its initial centroid TSE using the DBA algorithm [21]. $T$ can be different across different datasets and within the same dataset. In particular, we use $T = 33$ for Kinetics-400 and HMDB51, and $T = 4|vid|$ for Something-Something V2, where $|vid|$ is the length of an individual video. For a detailed description of our pre-training configuration and the choice of width and stride for the sliding window of each dataset, please refer to the Additional Implementation + +Details section in Supplementary Material. + +Training & Testing. The pre-training stage gives us a TSE $m$ for each training or validation video as well as the centroid TSEs $C$ . The weight tensor $U$ is either randomly initialized or one-initialized (i.e., filled with ones). To enforce positivity, we actually store the log of the weights and exponentiate them during forward passes. These log-of-weights are randomly initialized or zero-initialized (i.e., filled with zeros). We use the AdamW optimizer with betas (0.9, 0.999) and no weight decay. The initial learning rate for the log-of-weights is 1e-3 for both Something-Something V2 and Kinetics-400, and 8e-3 for HMDB51. The learning rates for the centroid TSEs are one-third of the log-of-weights. We use batch size 48 and train for 36 epochs. We use a cosine scheduler across all 36 epochs. A validation run is performed after every epoch, and we report the top accuracy recorded across all epochs. + +# 4.3. Main Results + +This section compares our results with previous other temporal-related and state-of-the-art methods. The main baseline is VideoMAE V2-g, which is a billion-parameter video encoder that is state-of-the-art or near state-of-the-art on all evaluation datasets [14, 16, 18, 28]. We test our method on each dataset with three different settings: random-initialization for the weight TSEs $U$ (denoted as full learning; $w$ -init-rnd in the following charts), one-initialization for $U$ (denoted as full learning; $w$ -init-one), and finally one-initialization for $U$ but freezing it throughout (i.e., disallowing optimizer step() to act on $U$ ; denoted as frozen weights; $w$ -init-one). Note that the last setting is for experimenting with the unweighted DTW distance as in Algorithm 1, so frozen weights with random initialization don't make sense. + +Results on Kinetics-400. As shown in Tab. 1, our method achieves leading accuracy on Kinetics-400. We improve on the strongest VideoMAE V2-g baseline by $0.7\%$ . DejaVid only requires 5.8M parameters, less than $0.6\%$ of the encoder's parameter count, to achieve this gain. For comparison, the gain from VideoMAE V1 to VideoMAE V2 uses 380M extra parameters to increase the accuracy by only $0.4\%$ . Note that our results are achieved without refinetuning the encoder, so the training cost is minimal compared to training the encoder. In short, DejaVid is a comparatively tiny add-on that significantly boosts the performance of an off-the-shelf frozen model. + +The performance gain of DejaVid is not only due to temporal supersampling. We test this by averaging the temporal dimension of each sample TSE to get a length- $(1408 + N_{c})$ vector and using the last $N_{c}$ elements for class prediction; the result is shown as VideoMAE V2 (temporal supersampling) Tab. 1. When compared against the original setting at VideoMAE V2 $5\times 3$ , we see this alone does not improve + +the accuracy. Also, the temporal weight-learning does not provide additional benefits on top of our centroid-finetuning for Kinetics-400. We suspect the reason is that the temporal weights increase the expressivity of our method, so overfitting becomes more likely; one future work is to look into regularization for DejaVid. + +Results on HMDB51. The results in Tab. 1 show that our model also achieves state-of-the-art accuracy on the HMDB51. We achieve a $0.5\%$ performance gain against the strongest VideoMAE V2-g baseline. To the best of our knowledge and according to Papers with Code, this is the highest accuracy recorded on the HMDB51 action recognition benchmark to date (as of Nov, 2024). This shows that DejaVid works well in a training data-scarce scenario. We draw similar conclusions to those from Kinetics-400 in parameter efficiency – our parameter count is 1.19M, which is less than $0.12\%$ of that of VideoMAE V2-g – and temporal supersampling alone does not improve performance. + +Results on Something-Something V2. Tab. 1 compares our results on Something-Something V2 against other works. We outperform the top VideoMAE V2-g baseline with a performance gain of $0.5\%$ . To the best of our knowledge and according to Papers with Code, DejaVid achieves the highest top-5 accuracy and one of the highest top-1 accuracies on the Something-Something V2 action recognition benchmark to date (as of Nov, 2024). + +Progress on Something-Something V2 has slowed in recent years, with top accuracy improving by no more than $0.3\%$ between 2022 and 2024 [20]. Such gains often require massive model scaling; for example, InternVideo2 added over 5 billion parameters for a $0.4\%$ boost [30]. In contrast, DejaVid achieves comparable improvements with just 17.6M parameters—fewer than $1.8\%$ of VideoMAE V2-g. This efficiency highlights the significance of our $+0.5\%$ accuracy gain, which equates to more than two years of recent progress [28-30]. + +However, the performance gain is smaller than on Kinetics-400. One possible reason could be the difference in average video length: $\sim 40$ for Something-Something V2 and $\sim 300$ for Kinetics-400. Because Kinetics-400 videos are longer, there may be more temporal information + +for DejaVid to capture. Another reason may be that the encoder is trained with variable video durations, as described in Sec. 4.2, so one future work would be to re-finetune the encoder with video clips of constant frame-count and retry our experiments. + +# 4.4. Ablation Studies + +Centroid vs. Weight Learning. In Tab. 2, we analyze the impacts of centroid and weight learning of DejaVid by freezing one component at a time and comparing the results. As seen, both frozen-centroid and frozen-weight variants yield meaningful accuracy gains against the VideoMAE V2-g baseline, and so both components are indeed beneficial. The centroid component has a greater performance gain on average across the three datasets, giving $+0.43\%$ top-1 accuracy gain vs. $0.25\%$ for the weights, but the weight component seems to be more useful when training data is scarce. As for the training data-rich cases, the weight component seems to be more useful in Something-Something V2 than in Kinetics-400, potentially because we have 4 different feature sets from the different sliding window widths, and these features should naturally have different importance, so the one-initialized weights are further away from the global optimal. + +
MethodSth-Sth2K400HMDB
top-1top-5top-1top-5top-1
VideoMAE V2-g @ best [28]76.7595.8588.498.088.1
Frozen centroids (w-init-rnd)76.896.288.698.088.4
Frozen centroids (w-init-one)76.996.288.898.188.4
Frozen weights (w-init-one)77.196.389.198.288.3
Full learning (w-init-rnd)77.296.388.998.188.6
Full learning (w-init-one)77.096.389.098.288.6
+ +Table 2. Ablation study on centroid & weight learning. + +
MethodSth-Sth2K400HMDB
top-1top-5top-1top-5top-1
DT on, otherwise best77.096.288.698.088.5
FECW off, otherwise best77.196.289.098.288.5
Best (DT off, FECW on)77.296.389.198.288.6
+ +Table 3. Ablation studies on diagonal transition (DT) and fixed epoch centroids & weights (FECW). + +
MethodSth-Sth2K400HMDB
Naive DTW implementation4.79e471.17e57294
Custom DTW CUDA kernel2971561.01
+ +Table 4. Ablation study on the custom DTW CUDA kernel. Table shows runtime per training epoch in seconds. + +Diagonal Transition of DTW. Tab. 3 presents a comparison between the best (highest top-1 accuracy $^{8}$ ) setting of + +
MethodW.A.Kinetics-400Something-Something V2HMDB51
ParamsClipsxCropsTop-1Top-5ParamsClipsxCropsTop-1Top-5ParamsClipsxCropsTop-1
Other State-of-the-Art Large Models
TubeViT [22]No632M4×390.998.9307M-76.195.2---
MVD [29]No633M5×387.297.4633M2×377.395.7---
InternVideo2-1B [30]Yes41B4×391.6-1B2×377.1----
InternVideo2-6B [30]No6B4×392.1-6B5×377.5----
Other Temporal-Focused Methods
ILA [27]--4×388.797.8-4×370.291.8---
ATM [31]--4×389.498.3-2×374.694.4---
TAM [19]--4×379.394.1-2×366.090.1---
SlowFast [11]--10×379.893.9--61.7----
MTV [32]--4×389.198.2--68.590.4---
Main Baselines
VideoMAE V1-H [28]Yes633M5×388.1--------
VideoMAE V1-L (32-frame input) [25, 28]Yes----305M2×375.495.2---
VideoMAE V2-g [28]Yes1013M5×388.498.01013M2×376.7595.851013M5×388.1
VideoMAE V2-g (temporal supersampling) [28]Yes1013M336×188.197.81013M(4|vid|)6×176.295.71013M336×188.0
Our Results
Ours (frozen weights; w-init-one)-+5.8M36×189.198.2+8.8M(4|vid|)6×177.196.3+0.60M88.3
Ours (full learning; w-init-rnd)-+11.6M88.998.1+17.6M77.296.3+1.19M336×188.6
Ours (full learning; w-init-one)-+11.6M89.098.2+17.6M77.096.3+1.19M88.6
+ +Table 1. Comparison with the VideoMAE V2-g baseline and other relevant variants, SOTA, or temporal methods on Kinetics-400, Something-Something V2, and HMDB51. All accuracies are reported in percent (\%). W.A. = Weights Available. Dashes (-) = N/A. + +Tab. 2 for each dataset and the same setting but with diagonal transitions turned on. Enabling diagonal transitions consistently performs worse on all datasets. This justifies our choice of disabling diagonal transitions in DejaVid and verifies the insight behind this choice as described in Sec. 3.4. + +Fixed Epoch Centroids & Weights for DTW Learning. We use Tab. 3 to compare the best setting (highest top-1 accuracy8) from Tab. 2 for each dataset with the same setting but disabling fixed epoch centroids & weights, where we do not make frozen copies of the centroids and weights for warping-path determination (shown as FECW off). Again, the inferior performance of this group compared to when FECW is on across all datasets justifies our design for DejaVid, aligning with the reasons detailed in Sec. 3.4 about model stability. However, the gap is less significant than that for the diagonal transition. This suggests there may be room for improvement by tweaking the path-determination mechanism, such as only updating every other epoch instead of each epoch. + +Custom CUDA Kernel for Accelerating DTW. Tab. 4 summarizes the runtime per epoch of the best-performing settings on all datasets compared to using a naive Python implementation of DTW. All experiments are conducted on a single node with 8 NVIDIA H100 GPUs. We can see that our custom CUDA kernel provides a speedup between $161\mathrm{x}$ and $750\mathrm{x}$ . The most technically significant speedup comes from reducing the critical path length from quadratic to linear, as discussed in Sec. 3.2. Other factors contributing to the speedup include the Python/C++ speed difference and architecture and locality-aware, LibTorch-native implementation of the CUDA-kernel. + +# 5. Conclusion + +We presented DejaVid, an encoder-agnostic method that boosts video classification performance without retraining + +the encoder or changing its architecture. Instead of converting a video into a single fixed-length embedding like most state-of-the-art encoders do, we feed a backbone encoder a sliding-window stream of frames to obtain a variable-length temporal sequence of embeddings (TSE), which preserves temporal order and supports variable video durations. We then introduce a novel neural network architecture based on Dynamic Time Warping (DTW) with learnable, per-timestamp feature weights to address temporal variance in feature significance. Our ablation studies compare and justify various design choices and modifications to classical DTW, and our evaluation shows that DejaVid achieves state-of-the-art video classification results on a variety of benchmarks, significantly improves the accuracy of a cutting-edge large encoder, and outperforms other temporal methods. In particular, we achieve leading Top-1 accuracy of $77.2\%$ on Something-Something V2, $89.1\%$ on Kinetics-400, and $88.6\%$ on HMDB51, representing a 0.5- $0.7\%$ accuracy gain over VideoMAE V2-g while adding less than $1.8\%$ additional learnable parameters and less than 3 hours of training time. + +# 6. Future Work + +In this paper, we selected video classification as the evaluation task due to its foundational role in computer vision [15, 16, 26], its real-world importance [1, 11, 13], and the significant amount of highly competitive research focused on it [2, 11, 19, 22, 25, 27-32]. With that said, we can also see the potential of DejaVid – and of the power of fine-grained temporal alignment learning in general – in action segmentation, video captioning, text-to-video retrieval, and any other tasks that can benefit from detailed temporal modeling. + +# References + +[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. Youtube-8m: A large-scale video classification benchmark. arXiv preprint arXiv:1609.08675, 2016. 8 +[2] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. In Proceedings of the IEEE/CVF international conference on computer vision, pages 6836-6846, 2021. 1, 8 +[3] Anthony Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn Keogh. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 6299-6308, 2017. 1 +[8] Chien-Yi Chang, De-An Huang, Yanan Sui, Li Fei-Fei, and Juan Carlos Niebles. D3tw: Discriminative differentiable dynamic time warping for weakly supervised action alignment and segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3546-3555, 2019. 3 +[9] Marco Cuturi and Mathieu Blondel. Soft-dtw: a differentiable loss function for time-series. In International conference on machine learning, pages 894-903. PMLR, 2017. 3 +[10] Alexey Dosovitskiy. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020. 1 +[11] Christoph Feichtenhofer, Haoqi Fan, Jitendra Malik, and Kaiming He. Slowfast networks for video recognition. 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In Proceedings of the IEEE international conference on computer vision, pages 5842-5850, 2017. 1, 2, 5, 6 +[15] Andrej Karpathy, George Toderici, Sanketh Shetty, Thomas Leung, Rahul Sukthankar, and Li Fei-Fei. Large-scale video classification with convolutional neural networks. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pages 1725–1732, 2014. 8 +[16] Will Kay, Joao Carreira, Karen Simonyan, Brian Zhang, Chloe Hillier, Sudheendra Vijayanarasimhan, Fabio Viola, Tim Green, Trevor Back, Paul Natsev, et al. The kinetics human action video dataset. arXiv preprint arXiv:1705.06950, 2017. 1, 2, 5, 6, 8 +[17] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25, 2012. 2 +[18] Hildegard Kuehne, Hueihan Jhuang, Estíbaliz Garrote, Tomaso Poggio, and Thomas Serre. Hmdb: a large video database for human motion recognition. In 2011 International conference on computer vision, pages 2556-2563. IEEE, 2011. 1, 2, 5, 6 +[19] Zhaoyang Liu, Limin Wang, Wayne Wu, Chen Qian, and Tong Lu. Tam: Temporal adaptive module for video recognition. In Proceedings of the IEEE/CVF international conference on computer vision, pages 13708-13718, 2021. 2, 8 +[20] Papers with Code. Action recognition on something-something v2 leaderboard. https : / / paperswithcode . com / sota / action - recognition - in - videos - on - something, 2024. Accessed: 2024-11-04. 7 +[21] François Petitjean, Alain Ketterlin, and Pierre Gançarski. A global averaging method for dynamic time warping, with applications to clustering. Pattern recognition, 44(3):678-693, 2011. 1, 5, 6 +[22] AJ Piergiovanni, Weicheng Kuo, and Anelia Angelova. Rethinking video vits: Sparse video tubes for joint image and video learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2214-2224, 2023. 1, 2, 8 +[23] Pavel Senin. Dynamic time warping algorithm review. Information and Computer Science Department University of Hawaii at Manoa Honolulu, USA, 855(1-23):40, 2008. 3 +[24] Alexandra Stefan, Vassilis Athitsos, and Gautam Das. The move-split-merge metric for time series. IEEE transactions on Knowledge and Data Engineering, 25(6):1425-1438, 2012. 3, 5 +[25] Zhan Tong, Yibing Song, Jue Wang, and Limin Wang. Videomae: Masked autoencoders are data-efficient learners for self-supervised video pre-training. Advances in neural information processing systems, 35:10078-10093, 2022. 8 +[26] Du Tran, Lubomir Bourdev, Rob Fergus, Lorenzo Torresani, and Manohar Paluri. Learning spatiotemporal features with + +3d convolutional networks. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 4489-4497, 2015. 8 +[27] Shuyuan Tu, Qi Dai, Zuxuan Wu, Zhi-Qi Cheng, Han Hu, and Yu-Gang Jiang. Implicit temporal modeling with learnable alignment for video recognition. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 19936-19947, 2023. 2, 8 +[28] Limin Wang, Bingkun Huang, Zhiyu Zhao, Zhan Tong, Yi-nan He, Yi Wang, Yali Wang, and Yu Qiao. Videomae v2: Scaling video masked autoencoders with dual masking. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14549-14560, 2023. 1, 2, 6, 7, 8 +[29] Rui Wang, Dongdong Chen, Zuxuan Wu, Yinpeng Chen, Xiyang Dai, Mengchen Liu, Lu Yuan, and Yu-Gang Jiang. Masked video distillation: Rethinking masked feature modeling for self-supervised video representation learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 6312-6322, 2023. 8 +[30] Yi Wang, Kunchang Li, Xinhao Li, Jiashuo Yu, Yinan He, Guo Chen, Baoqi Pei, Rongkun Zheng, Jilan Xu, Zun Wang, et al. Internvideo2: Scaling video foundation models for multimodal video understanding. arXiv preprint arXiv:2403.15377, 2024. 1, 2, 7, 8 +[31] Wenhao Wu, Yuxin Song, Zhun Sun, Jingdong Wang, Chang Xu, and Wanli Ouyang. What can simple arithmetic operations do for temporal modeling? In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 13712-13722, 2023. 2, 8 +[32] Shen Yan, Xuehan Xiong, Anurag Arnab, Zhichao Lu, Mi Zhang, Chen Sun, and Cordelia Schmid. Multiview transformers for video recognition. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3333-3343, 2022. 2, 8 +[33] Xiaohua Zhai, Alexander Kolesnikov, Neil Houlsby, and Lucas Beyer. Scaling vision transformers. 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However, these large models typically process videos by averaging embedding outputs from multiple clips over time to produce fixed-length representations. This approach fails to account for a variety of time-related features, such as variable video durations, chronological order of events, and temporal variance in feature significance. While methods for temporal modeling do exist, they often require significant architectural changes and expensive retraining, making them impractical for off-the-shelf, fine-tuned large encoders. To overcome these limitations, we propose DejaVid, an encoder-agnostic method that enhances model performance without the need for retraining or altering the architecture. Our framework converts a video into a variable-length temporal sequence of embeddings (TSE). A TSE naturally preserves temporal order and accommodates variable video durations. 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DejaVid system diagram. We first transform a video into a variable-length temporal sequence of embeddings (TSE) then use Dynamic Time Warping Barycenter Averaging (DBA) [21] to calculate a reasonably \"average\" TSE per class for its centroid initialization. We then learn per-timestep, per-feature weights for the encoded TSE frames, enabling us to accommodate variations in feature importance over time, as well as finetune the centroid TSE for each output class. For this task, we introduce a new neural network architecture inspired by traditional time series alignment algorithms. In testing, we freeze the post-training centroids and weights and use the same pre-training pipeline to generate TSEs to feed into DejaVid for predictions." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "inated by 100M-1B+ parameter large video transformers [14, 16, 18, 22, 28-30]." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24023" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 57, + 72, + 294, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 72, + 294, + 346 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 294, + 346 + ], + "type": "text", + "content": "These large encoders process videos with fixed frame counts, heights, and widths, generating a single embedding. On datasets with varying durations, the common approach is to pass multiple temporal clips and spatial crops through the encoder and then average the resulting logits for class prediction [22, 28-30]. However, while the height and width of videos in a dataset are usually constant, their duration can vary significantly [14]. Furthermore, temporal order is far more critical. Unlike image flipping [17], reversing time can alter semantics, such as opening vs. closing a door. When averaging logits from different temporal clips, sequential information in these clips is lost. Moreover, the significance of each feature within a video can change over time. For example, in a basketball three-point shot, early frames emphasize player position, while later frames focus on whether the ball goes in. Although encoders might not explicitly model semantically interpretable features like these, temporal variation in feature importance can also occur for arbitrary features, which mean-pooling fails to capture adequately. This motivates a key observation of our work: by failing to carefully account for temporal dimensions, state-of-the-art large models leave significant accuracy gains on the table." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 351, + 294, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 351, + 294, + 446 + ], + "spans": [ + { + "bbox": [ + 57, + 351, + 294, + 446 + ], + "type": "text", + "content": "Improving the temporal performance of large encoders is not trivial. Existing temporal-focused methods require invasive changes to the model, such as inserting temporal-specific layers between transformer blocks [27, 31] or creating model duplications to focus on different input views [11, 32]. These approaches are costly to apply to off-the-shelf pre-trained encoders because they require extensive changes in implementation and costly re-training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 451, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 451, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 451, + 294, + 712 + ], + "type": "text", + "content": "These insights motivate DejaVid, a lightweight encoder-agnostic temporal approach that substantially boosts model classification performance. The simple yet crucial idea behind DejaVid is that a video is more effectively represented as a temporal sequence of embeddings (TSE) rather than as a single embedding. This representation naturally preserves chronological order while supporting varying time lengths, addressing the aforementioned shortcomings. DejaVid is naturally able to use any pre-trained model by consuming a sliding-window of encoded video to generate a TSE, without requiring changes to the model's architecture, retraining, or fine-tuning. DejaVid is inspired by the well-known Dynamic Time Warping (DTW) algorithm [4], which dynamically aligns similar data points between two temporal sequences while maintaining their chronological order. In particular, DejaVid introduces a novel neural network architecture inspired by DTW but with learned per-timestep, per-feature weights to handle the temporal variance of feature importance. Additionally, we develop a custom high-performance CUDA kernel for efficient computation and backpropagation of the (time-weighted) warping distance that outperforms a naive DTW-based implementation by 2" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 317, + 73, + 399, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 73, + 399, + 84 + ], + "spans": [ + { + "bbox": [ + 317, + 73, + 399, + 84 + ], + "type": "text", + "content": "orders of magnitude." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "spans": [ + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "text", + "content": "We evaluate DejaVid by layering it on top of the largest (ViT-g) variant of VideoMAE V2 [28] (abbr. VideoMAE V2-g) as the backbone encoder to evaluate DejaVid on three popular action recognition datasets: Kinetics-400 [16], Something-Something V2 [14], and HMDB51 [18]. We show that DejaVid significantly improves on the strongest VideoMAE V2-g baseline, thereby achieving new state-of-the-art performance. In particular, DejaVid achieves Top-1 accuracy of " + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "inline_equation", + "content": "77.2\\%" + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "text", + "content": " on Something-Something V2, " + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "inline_equation", + "content": "89.1\\%" + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "text", + "content": " on Kinetics-400, and " + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "inline_equation", + "content": "88.6\\%" + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "text", + "content": " on HMDB51, while adding fewer than " + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 317, + 86, + 553, + 252 + ], + "type": "text", + "content": " additional learnable parameters and requiring less than 3 hours of training time. We also show that our proposed modifications to DTW, including the temporal weights, can further improve prediction performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 263, + 399, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 263, + 399, + 275 + ], + "spans": [ + { + "bbox": [ + 317, + 263, + 399, + 275 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 281, + 553, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 281, + 553, + 423 + ], + "spans": [ + { + "bbox": [ + 317, + 281, + 553, + 423 + ], + "type": "text", + "content": "State-of-the-Art in Action Recognition. Major action recognition benchmarks are topped by massive video transformers with hundreds of millions or billions of parameters. As of the time of writing, according to Papers with Code, the top performers on Kinetics-400 and Something-Something V2 with verifiable parameter counts have between 600M and 6B parameters [14, 16, 22, 28-30]. However, their evaluations on these two datasets all apply spatial and temporal mean-pooling to the logits at the end, which suffers from the time-related shortfalls related to variable video durations, chronological order of events, and temporal variance in feature significance, as described in Sec. 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 426, + 553, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 426, + 553, + 675 + ], + "spans": [ + { + "bbox": [ + 317, + 426, + 553, + 675 + ], + "type": "text", + "content": "Temporal-focused Methods for Action Recognition. There have been various works on improving the temporal modeling capability of video transformers. One general approach is to introduce temporal-specific layers in between transformer blocks. For example, ILA employs a mask-based layer that predicts interactive points between frame pairs to implicitly align features [27], ATM applies basic arithmetic operations to pairs-of-frame features between ViT blocks [31], and TAM inserts an attention-based temporal adaptive module between 2D convolutions within a ResNet block [19]. Another line of work is to fuse multiple temporal views in different ways. For example, SlowFast networks feed two different frame rates of a video into separate encoders and add lateral connections between them to fuse information across views [11], and MTV deploys a similar idea but for both spatial and temporal dimensions [32]. However, their performance is not competitive against the aforementioned large state-of-the-art models, partly due to their smaller size. Implementing these methods within the large models would involve considerable implementation changes and expensive retraining." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 678, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 678, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 678, + 553, + 712 + ], + "type": "text", + "content": "Learning Temporal Sequence Alignments. DTW is one of the most classic methods for calculating similarities between univariate time series or multivariate ones like our" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24024" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 203 + ], + "type": "text", + "content": "TSEs [4, 23]. Its traditional formulation is a dynamic programming scheme, but recent work has explored making it differentiable and then applying it to various fields. SoftDTW [9] shows that DTW makes a good loss function when the min operator is replaced with soft-min. DTWnet [5] proposes using DTW learning for time series feature extraction, and D3TW, OTAM, and FTCL [6, 8, 12] similarly do this for weakly-supervised and few-shot video understanding. While these works have some similarities to our DTW-based temporal representation learning, our method is technically different and superior in three ways:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 204, + 295, + 347 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 56, + 204, + 295, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 204, + 295, + 287 + ], + "spans": [ + { + "bbox": [ + 56, + 204, + 295, + 287 + ], + "type": "text", + "content": "1. DejaVid models and learns the temporal variance in feature importance, which none of the other methods do. While classical DTW typically only works for a few dimensions (10-100) that require handcrafting or hand-picking [3], by adding learned weights, we extend DTW to high-dimensional use cases " + }, + { + "bbox": [ + 56, + 204, + 295, + 287 + ], + "type": "inline_equation", + "content": "(1000 - 10000+)" + }, + { + "bbox": [ + 56, + 204, + 295, + 287 + ], + "type": "text", + "content": " like video recognition by letting it learn the important dimensions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 288, + 294, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 288, + 294, + 323 + ], + "spans": [ + { + "bbox": [ + 56, + 288, + 294, + 323 + ], + "type": "text", + "content": "2. We reformulate our DTW-inspired temporal learning algorithm as a new neural network architecture that boosts parallelizability and facilitates differentiability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 323, + 294, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 323, + 294, + 347 + ], + "spans": [ + { + "bbox": [ + 56, + 323, + 294, + 347 + ], + "type": "text", + "content": "3. We introduce changes to DTW to improve model stability, including removing the diagonal transition of DTW." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 356, + 111, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 356, + 111, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 356, + 111, + 369 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "text", + "content": "As described in Sec. 1, we represent a video as a temporal sequence of embeddings (TSE). In this section, we assume all videos have been converted into TSEs, and operate in this TSE space. DejaVid feeds a video encoder a sliding-window stream of frames of an input video to generate a TSE, so the shape of a TSE is " + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "inline_equation", + "content": "T \\times N_{f}" + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "text", + "content": ", where each index along " + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "text", + "content": " represents the encoding of a window of frames, and thus " + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "text", + "content": " can vary depending on individual video duration. " + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "inline_equation", + "content": "N_{f}" + }, + { + "bbox": [ + 55, + 376, + 296, + 495 + ], + "type": "text", + "content": " is the size of the embedding vector of the backbone encoder and is constant." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 496, + 296, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 496, + 296, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 496, + 296, + 544 + ], + "type": "text", + "content": "Our problem is to classify TSEs. Specifically, we are given a training set of TSEs with class labels among " + }, + { + "bbox": [ + 55, + 496, + 296, + 544 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 55, + 496, + 296, + 544 + ], + "type": "text", + "content": " classes, and our goal is to predict the classes of our validation TSEs. We solve this problem in three broad steps:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 544, + 295, + 616 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 56, + 544, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 544, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 56, + 544, + 295, + 568 + ], + "type": "text", + "content": "1. For each class, we calculate a centroid TSE from the training TSEs of that class." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 569, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 569, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 56, + 569, + 295, + 593 + ], + "type": "text", + "content": "2. We optimize the centroid TSEs according to some loss function w.r.t. the training TSEs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 56, + 593, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 593, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 56, + 593, + 295, + 616 + ], + "type": "text", + "content": "3. For each validation TSE, we calculate which class's centroid TSE is the most similar to it." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 618, + 296, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 667 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 667 + ], + "type": "text", + "content": "Here, Steps 1 and 3 require a definition of distance (or similarity) between TSE pairs, and Step 2 requires the distance metric to be backpropagateable. The following Secs. 3.1 and 3.2 describe how we solve these two problems." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 672, + 129, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 129, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 129, + 684 + ], + "type": "text", + "content": "3.1. Definitions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "There are multiple ways in which one can define the distance between two TSEs [4, 24], but in this paper, we focus" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": "on a standard time series distance metric: Dynamic Time Warping (DTW), as given in Algorithm 1 (without the red text). DTW aligns two sequences that vary in time or speed by minimizing the distance between corresponding points. The two sequences are aligned by aligning each timestep in the first sequence to one or more consecutive timesteps in the second sequence while maintaining a monotonic relationship where a later timestep in the first must map to a later interval in the second. Monotonicity is maintained in Line 5 of Algorithm 1, where each step only moves forward in time for either sequence (from " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "i - 1" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "j - 1" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 72, + 555, + 252 + ], + "type": "text", + "content": "). This alignment minimizes cumulative distance and is commonly visualized as a \"warping path\" on a 2D grid, which shows the optimal alignment of the two sequences, each depicted in one grid axis." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "spans": [ + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "text", + "content": "Algorithm 1 The Standard DTW Algorithm (without diagonal transition) vs. the Time-Weighted DTW Algorithm (red) \nInput: Two TSEs " + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "inline_equation", + "content": "a, b \\in \\mathbb{R}^{n \\times N_f}, \\mathbb{R}^{m \\times N_f}" + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "text", + "content": "; a distance function " + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "inline_equation", + "content": "dist_w" + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "inline_equation", + "content": "u \\in \\mathbb{R}_{>0}^{n \\times N_f}" + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "text", + "content": " temporal feature weights of " + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "text", + "content": " \nOutput: Distance between " + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 262, + 555, + 327 + ], + "type": "inline_equation", + "content": "b" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 328, + 553, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 328, + 553, + 342 + ], + "spans": [ + { + "bbox": [ + 320, + 328, + 553, + 342 + ], + "type": "text", + "content": "1: " + }, + { + "bbox": [ + 320, + 328, + 553, + 342 + ], + "type": "inline_equation", + "content": "D \\gets \\operatorname{array}[n, m]" + }, + { + "bbox": [ + 320, + 328, + 553, + 342 + ], + "type": "text", + "content": " {Out-of-bounds access returns " + }, + { + "bbox": [ + 320, + 328, + 553, + 342 + ], + "type": "inline_equation", + "content": "+\\infty" + }, + { + "bbox": [ + 320, + 328, + 553, + 342 + ], + "type": "text", + "content": "}" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 320, + 352, + 547, + 437 + ], + "type": "list", + "angle": 0, + "index": 25, + "blocks": [ + { + "bbox": [ + 320, + 352, + 436, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 352, + 436, + 365 + ], + "spans": [ + { + "bbox": [ + 320, + 352, + 436, + 365 + ], + "type": "text", + "content": "2: " + }, + { + "bbox": [ + 320, + 352, + 436, + 365 + ], + "type": "inline_equation", + "content": "D_{0,0}\\gets dist_w(u_0,a_0,b_0)" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 320, + 365, + 417, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 365, + 417, + 376 + ], + "spans": [ + { + "bbox": [ + 320, + 365, + 417, + 376 + ], + "type": "text", + "content": "3: for " + }, + { + "bbox": [ + 320, + 365, + 417, + 376 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 320, + 365, + 417, + 376 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 320, + 365, + 417, + 376 + ], + "type": "inline_equation", + "content": "[0, n - 1]" + }, + { + "bbox": [ + 320, + 365, + 417, + 376 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "spans": [ + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "text", + "content": "4: for " + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "inline_equation", + "content": "([0, m - 1]" + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "inline_equation", + "content": "i > 0" + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "text", + "content": " else " + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "inline_equation", + "content": "[1, m - 1]" + }, + { + "bbox": [ + 320, + 376, + 533, + 388 + ], + "type": "text", + "content": ") do" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 320, + 388, + 547, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 388, + 547, + 402 + ], + "spans": [ + { + "bbox": [ + 320, + 388, + 547, + 402 + ], + "type": "text", + "content": "5: " + }, + { + "bbox": [ + 320, + 388, + 547, + 402 + ], + "type": "inline_equation", + "content": "D_{i,j}\\gets \\min (D_{i - 1,j},D_{i,j - 1}) + dist_w(u_i,a_i,b_j)" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 320, + 402, + 375, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 402, + 375, + 411 + ], + "spans": [ + { + "bbox": [ + 320, + 402, + 375, + 411 + ], + "type": "text", + "content": "6: end for" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 320, + 412, + 365, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 412, + 365, + 423 + ], + "spans": [ + { + "bbox": [ + 320, + 412, + 365, + 423 + ], + "type": "text", + "content": "7: end for" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 320, + 424, + 410, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 424, + 410, + 437 + ], + "spans": [ + { + "bbox": [ + 320, + 424, + 410, + 437 + ], + "type": "text", + "content": "8: return " + }, + { + "bbox": [ + 320, + 424, + 410, + 437 + ], + "type": "inline_equation", + "content": "D_{n-1,m-1}" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 445, + 555, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 445, + 555, + 516 + ], + "spans": [ + { + "bbox": [ + 313, + 445, + 555, + 516 + ], + "type": "text", + "content": "In the standard Algorithm 1, we use the Manhattan distance for the pointwise distance function " + }, + { + "bbox": [ + 313, + 445, + 555, + 516 + ], + "type": "inline_equation", + "content": "dist" + }, + { + "bbox": [ + 313, + 445, + 555, + 516 + ], + "type": "text", + "content": ". Also, although the original DTW algorithm includes a diagonal transition " + }, + { + "bbox": [ + 313, + 445, + 555, + 516 + ], + "type": "inline_equation", + "content": "D_{i-1,j-1}" + }, + { + "bbox": [ + 313, + 445, + 555, + 516 + ], + "type": "text", + "content": " in the min clause, we omit this in DejaVid because it improves model stability. We discuss this decision in more detail in Sec. 3.4." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "D_v(a,b)" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " denote the DTW distance between TSEs " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " as returned by the standard Algorithm 1, and let " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "C \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " represent the centroid TSEs for the " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "N_c" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " classes. Intuitively, we want to assign each TSE to the class it is nearest to in the DTW space. To do this, we define the predicted probability distribution " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_v" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " for a training or validation TSE " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "m \\in \\mathbb{R}^{T_m \\times N_f^1}" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": ", and the loss " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_v" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " under centroids " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": " and one-hot ground truth vector " + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 313, + 517, + 555, + 613 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 363, + 615, + 504, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 615, + 504, + 633 + ], + "spans": [ + { + "bbox": [ + 363, + 615, + 504, + 633 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {y}} _ {v} (C, m) := \\underset {0 \\leq i < N _ {c}} {\\operatorname {s o f t m i n}} \\left(D _ {v} \\left(C _ {i}, m\\right)\\right)", + "image_path": "a1ce5dcb49e4a16e81288c583e197ee2cef0e7c7a42263234d641890c55a3578.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 349, + 634, + 520, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 634, + 520, + 647 + ], + "spans": [ + { + "bbox": [ + 349, + 634, + 520, + 647 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v} (C, m) := \\operatorname {C r o s s E n t r o p y} (\\mathbf {y}, \\hat {\\mathbf {y}} _ {v} (C, m))", + "image_path": "1cc4f942d6ad99ba0d8d12ae5c8456a2e5f6536f44c6d535d4cb5628ae826b34.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 651, + 554, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 651, + 554, + 687 + ], + "spans": [ + { + "bbox": [ + 313, + 651, + 554, + 687 + ], + "type": "text", + "content": "However, as described in Sec. 1, we observe that the importance of each feature of a video can vary as time progresses. This observation motivates our time-weighted" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "text", + "content": "In practice, we perform a LayerNorm operation before the soft-min, but this doesn't qualitatively change our approach." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24025" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": "DTW distance metric, given in Algorithm 1 with modifications shown in red. The difference is the additional weight input " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": ", which denotes the change in feature importance over time for " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": ". We also modify the pointwise Manhattan distance function to incorporate " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "dist_w(u_i, a_i, b_j) := \\sum_{k=0}^{N_f-1} u_{i,k} |a_{i,k} - b_{j,k}|" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": ". The changes are colored in Lines 2 and 5 of Algorithm 1. Intuitively, when Algorithm 1 calculates the distance between two sequences, our time-weighted modification allows it to weight some timesteps more than some other timesteps in the first series, and different features can have different weights as well. Let " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "D_w(u, a, b)" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": " denote the time-weighted DTW distance between TSEs " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": " as returned by the time-weighted Algorithm 1. We aim to learn the temporal variance of feature importance of the centroids " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": ", so we define " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "U \\in \\mathbb{R}_{>0}^{N_c \\times T_c \\times N_f}" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": " of the same shape as " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": " to be the time-varying feature weights. To maintain the positivity of distances, we constrain " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": " to be positive. The time-weighted variant of predicted probability distribution " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_w" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": " and loss " + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 55, + 72, + 296, + 316 + ], + "type": "text", + "content": " are defined similarly as before:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 89, + 320, + 260, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 320, + 260, + 338 + ], + "spans": [ + { + "bbox": [ + 89, + 320, + 260, + 338 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {y}} _ {w} (U, C, m) := \\operatorname * {s o f t m i n} _ {0 \\leq i < N _ {c}} \\left(D _ {w} \\left(U _ {i}, C _ {i}, m\\right)\\right)", + "image_path": "21cc896268562b3e4214f0d8f0d3090b3daea51c353865cc28fa4c2326091e9b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 78, + 341, + 272, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 341, + 272, + 354 + ], + "spans": [ + { + "bbox": [ + 78, + 341, + 272, + 354 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {w} (u, C, m) := \\operatorname {C r o s s E n t r o p y} (\\mathbf {y}, \\hat {\\mathbf {y}} _ {w} (u, C, m))", + "image_path": "e919c530adb73ad6a97513a3b54ed4a62004cca9724179ea71ac4f2c0692edfa.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 356, + 295, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 356, + 295, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 356, + 295, + 392 + ], + "type": "text", + "content": "From now on, we focus on the time-weighted Algorithm 1, since one can set " + }, + { + "bbox": [ + 55, + 356, + 295, + 392 + ], + "type": "inline_equation", + "content": "U = \\mathbf{1}_{N_c\\times T_c\\times N_f}" + }, + { + "bbox": [ + 55, + 356, + 295, + 392 + ], + "type": "text", + "content": " to recover standard DTW in Algorithm 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 395, + 243, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 395, + 243, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 395, + 243, + 407 + ], + "type": "text", + "content": "3.2. Parallelizability & Differentiability" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 58, + 408, + 175, + 479 + ], + "blocks": [ + { + "bbox": [ + 58, + 408, + 175, + 479 + ], + "lines": [ + { + "bbox": [ + 58, + 408, + 175, + 479 + ], + "spans": [ + { + "bbox": [ + 58, + 408, + 175, + 479 + ], + "type": "image", + "image_path": "d3b9dc2a9adf3207121ce6722fa7b2e5bf936b2e8b234a8ba6752ecf9ef2465e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 175, + 408, + 294, + 478 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 408, + 294, + 478 + ], + "spans": [ + { + "bbox": [ + 175, + 408, + 294, + 478 + ], + "type": "image", + "image_path": "d607ecd8393867e956dbc99b000a8be11ef12285b2335096e2ed1d0b53cb340d.jpg" + } + ] + } + ], + "index": 6, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 58, + 479, + 175, + 548 + ], + "blocks": [ + { + "bbox": [ + 58, + 479, + 175, + 548 + ], + "lines": [ + { + "bbox": [ + 58, + 479, + 175, + 548 + ], + "spans": [ + { + "bbox": [ + 58, + 479, + 175, + 548 + ], + "type": "image", + "image_path": "f9a81c43fd45cbba525cffa70af147d5b4be9b45ef721c0dc7a5560ba0b182fa.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 549, + 295, + 648 + ], + "lines": [ + { + "bbox": [ + 55, + 549, + 295, + 648 + ], + "spans": [ + { + "bbox": [ + 55, + 549, + 295, + 648 + ], + "type": "text", + "content": "Figure 2. 1. Each cell of the DTW 2D grid executes a min operation and then an add-dist operation. Checkmarks show completed cells in row-major order. 2. In diagonal order, a diagonal can be executed as soon as the previous diagonal has finished. Checkmarks show completed cells in diagonal order. 3. We can view each diagonal as a min-pooling layer with kernel size 2 and stride 1, followed by an additive skip-connection layer. 4. We reformulate the algorithm into a serial stack of min-pooling layers interlaced with additive skip-connections." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 175, + 408, + 294, + 548 + ], + "blocks": [ + { + "bbox": [ + 175, + 408, + 294, + 548 + ], + "lines": [ + { + "bbox": [ + 175, + 408, + 294, + 548 + ], + "spans": [ + { + "bbox": [ + 175, + 408, + 294, + 548 + ], + "type": "image", + "image_path": "78c89e18579b5ea8cc2f3c2be1e42e29dfb997bd69f3f31f186c4734b9a45c51.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": "Algorithm 2 given an equivalent neural-network formulation for Algorithm 1; this formulation facilitates the use of backpropagation for optimizing weights and enhances parallelizability. Before providing the details of the algorithm, we provide some intuition as to how and why it works." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 554, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 191 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 191 + ], + "type": "text", + "content": "Fig. 2 depicts the 2D grid commonly used for representing DTW warping path(s) between two sequences, as described in Sec. 3.1. We visualize each operation in the nested loop in Algorithm 1 onto the corresponding cell in the grid. We can see that each cell executes a min operation on the outputs of its left-adjacent and bottom-adjacent cells, followed by an addition of some pointwise weighted distance " + }, + { + "bbox": [ + 313, + 72, + 554, + 191 + ], + "type": "inline_equation", + "content": "dist_w" + }, + { + "bbox": [ + 313, + 72, + 554, + 191 + ], + "type": "text", + "content": ". Note that cells are executed in a row-major order in Algorithm 1. Therefore, the critical path length is quadratic " + }, + { + "bbox": [ + 313, + 72, + 554, + 191 + ], + "type": "inline_equation", + "content": "(O(nm))" + }, + { + "bbox": [ + 313, + 72, + 554, + 191 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "text", + "content": "However, we leverage a critical property of Algorithm 1 that enables a reformulation of the algorithm, which is that each cell can be executed as soon as its left and bottom neighbors have finished. Therefore, we reformulate Algorithm 1 to execute in diagonal order and observe that the " + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "text", + "content": "-th diagonal can be executed as soon as the " + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "inline_equation", + "content": "(l - 1)" + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "text", + "content": "-th diagonal has finished. Here, we define the " + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "text", + "content": "-th diagonal to be the cells " + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "inline_equation", + "content": "\\{(i,j) \\mid i + j = l\\}" + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "text", + "content": ". For example, the top-right of Fig. 2 shows the 4th diagonal. Furthermore, elements in the same diagonal are mutually independent, so the work within each diagonal is parallelized. So we have reduced the critical path length to the number of diagonals, obtaining the linear runtime " + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "inline_equation", + "content": "O(n + m)" + }, + { + "bbox": [ + 313, + 192, + 555, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 347, + 556, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 347, + 556, + 503 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 556, + 503 + ], + "type": "text", + "content": "Because each cell executes at Line 5 of Algorithm 1 a min operation on two consecutive cells of the previous diagonal and then adds some " + }, + { + "bbox": [ + 313, + 347, + 556, + 503 + ], + "type": "inline_equation", + "content": "dist_w" + }, + { + "bbox": [ + 313, + 347, + 556, + 503 + ], + "type": "text", + "content": " term, we can express the new formulation as a neural net where each diagonal is a min-pooling layer with kernel size 2 and stride 1 followed by an additive skip-connection layer. Each min-pooling layer is executed after its previous skip-connection and min-pooling are completed. So Algorithm 1 is equivalent to a serial stack of min-pooling layers, with skip-connections interlacing in between. These descriptions are formalized in Algorithm 2, where one can see the execution of the interlaced layers at Lines 10 and 11. For differentiability, we rewrite the time-weighted DTW distance " + }, + { + "bbox": [ + 313, + 347, + 556, + 503 + ], + "type": "inline_equation", + "content": "D_w" + }, + { + "bbox": [ + 313, + 347, + 556, + 503 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 505, + 555, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 505, + 555, + 531 + ], + "spans": [ + { + "bbox": [ + 315, + 505, + 555, + 531 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} D _ {w} := S C _ {n + m - 2} + M P _ {n + m - 2} \\left(S C _ {n + m - 3} + M P _ {n + m - 3}\\right) \\\\ \\ldots + S C _ {1} + M P _ {1} \\left(S C _ {0}\\right) \\dots)) \\\\ \\end{array}", + "image_path": "c6a7476a4b60d9849c16c60a35f27aa80b070202de4c09a40870bcc2d0bcf626.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "inline_equation", + "content": "MP_{l}" + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "inline_equation", + "content": "SC_{l}" + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": "-th min-pooling and skipconnection as show in Algorithm 2. Because both min-pooling and additive skip-connections are standard neural network operations, loss gradients trivially propagate through them. In a nutshell, the loss backpropagates to only the " + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "inline_equation", + "content": "dist_{w}(u_{i},a_{i},b_{j})" + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": " functions on the optimal warping path, which enables gradient-based optimization on " + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": ". We leave the detailed formulas for loss gradients " + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L_w}{\\partial C}" + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L_w}{\\partial U}" + }, + { + "bbox": [ + 313, + 536, + 554, + 645 + ], + "type": "text", + "content": " in Supplementary Material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 651, + 419, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 651, + 419, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 651, + 419, + 663 + ], + "type": "text", + "content": "3.3. System Overview" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "With the definitions introduced in Secs. 3.1 and 3.2, we now formalize the 3-step solution outlined at the start of Sec. 3. Fig. 1 provides an overview of the DejaVid system. The video encoder takes as input a video clip of fixed duration" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24026" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 56, + 71, + 296, + 308 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": "Algorithm 2 Time-Weighted DTW Neural Network \nInput: Two TSEs " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "a, b \\in \\mathbb{R}^{n \\times N_f}, \\mathbb{R}^{m \\times N_f}" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": "; a distance func \ntion " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "dist_w" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "u \\in \\mathbb{R}_{>0}^{n \\times N_f}" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " temporal feature weights of " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " \nOutput: Distance between " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " \n1: {Out-of-bounds access to " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "SC" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " returns " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "+\\infty" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": "} \n2: " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "SC_{0,0} \\gets dist_w(u_0, a_0, b_0)" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " {The 0-th skip- \nconnection} \n3: " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "D_{0,0} \\gets SC_{0,0}" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " \n4: for " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "[1, n + m - 2]" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " do \n5: {The " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": "-th diagonal} \n6: start, end " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "\\leftarrow \\max(0, l - m + 1)" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "\\min(n - 1, l)" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " \n7: " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "SC_l \\gets [dist_w(u_t, a_t, b_{l-t})]_{t=start}^{\\text{end}}" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " \n8: " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "D_l \\gets \\text{array[end - start + 1]}" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " \n9: kernel, stride " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "\\leftarrow 2, 1" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " \n10: for " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " in range(0, end - start + 1, stride) do \n11: " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "D_{l,i} \\gets SC_{l,i} + \\min_{s=0}^{kernel-1}(D_{l-1,i-s})" + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "text", + "content": " \n12: end for \n13: end for \n14: return " + }, + { + "bbox": [ + 56, + 71, + 296, + 308 + ], + "type": "inline_equation", + "content": "D_{n+m-2,0}" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_body" + } + ], + "index": 0, + "sub_type": "algorithm" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": "and outputs an embedding " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "e \\in \\mathbb{R}^{N_f}" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": ". Given any off-the-shelf video encoder, we apply a sliding window over each video to produce a sequence of clips, which we then feed into the encoder to produce a temporal sequence of embeddings " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "E = \\{e_0, e_1, \\dots, e_{T-1}\\} \\in \\mathbb{R}^{T \\times N_f}" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": ", which forms a TSE for each video sample in the dataset. Then, we produce a centroid TSE of shape " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "T_c \\times N_f^2" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": " for each class by feeding the training TSEs to the DBA (Dynamic Time Warping Barycenter Averaging) [21] algorithm, which calculates a reasonable \"average\" time series of the inputs while accounting for imperfect temporal alignment. Intuitively, each centroid TSE represents how the class-wide average of the " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "N_f" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": " features changes over time. Ultimately, we obtain many training TSEs, each with shape " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "T \\times N_f" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": " for some varying " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": ", and a stack of centroid TSEs " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": " of shape " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "N_c \\times T_c \\times N_f" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "inline_equation", + "content": "N_c" + }, + { + "bbox": [ + 55, + 331, + 296, + 536 + ], + "type": "text", + "content": " is the number of classes. This concludes the pretraining stage of DejaVid." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "text", + "content": "In the training phase, to account for temporal variance in feature importance over time, each centroid TSE is paired with a positive weight tensor of the same shape " + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "inline_equation", + "content": "T_{c} \\times N_{f}" + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "text", + "content": " that represents the importance of each feature over time. The positivity is to maintain that the pointwise distance " + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "inline_equation", + "content": "\\text{dist}_{w}" + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "text", + "content": " is always positive. We denote the stack of weight TSEs " + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "text", + "content": " with shape " + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "inline_equation", + "content": "N_{c} \\times T_{c} \\times N_{f}" + }, + { + "bbox": [ + 55, + 536, + 295, + 632 + ], + "type": "text", + "content": ". At initialization, the weight TSEs are either filled with ones or random positive values." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "text", + "content": "In each epoch, we calculate the weighted DTW distance " + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "inline_equation", + "content": "D_w" + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "text", + "content": " from each training TSE " + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "inline_equation", + "content": "m \\in \\mathbb{R}^{T \\times N_f}" + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "text", + "content": " to every centroid TSE to get the logit vector " + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\{D_w(U_i, C_i, m)\\}_{i=0}^{N_c-1} \\in \\mathbb{R}^{N_c}" + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "text", + "content": ", on which we apply softmax to get the class prediction " + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "text", + "content": " and cross-entropy loss " + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "text", + "content": " w.r.t. the ground truth " + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 55, + 633, + 296, + 693 + ], + "type": "text", + "content": ". The" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": "weights " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " and centroids " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " TSEs are updated during backpropagation. To accelerate forward and backward passes, we implement a custom DTW CUDA kernel that efficiently calculates a slope tensor " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " and an intercept tensor " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "B \\in \\mathbb{R}^{N_c \\times T_c \\times N_f}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\text{torch.sum}(U \\odot (C \\odot S + B), \\dim = (-2, -1))" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " equals the logit vector " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " and the effective gradients w.r.t. " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " equals " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L_w}{\\partial U}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L_w}{\\partial C}" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": ". The implementation of the CUDA kernel, roughly speaking, leverages the fact that a weighted DTW distance is essentially the sum of many terms of " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "u \\cdot |c - b|" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": ", which equals " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "u \\cdot (c \\cdot (\\pm 1) + (\\mp 1)b)" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": ", where the " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "(\\pm 1)" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " term contributes to slope " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "(\\mp 1)b" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": " to intercept " + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 72, + 555, + 216 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 220, + 488, + 231 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 220, + 488, + 231 + ], + "spans": [ + { + "bbox": [ + 313, + 220, + 488, + 231 + ], + "type": "text", + "content": "3.4. Modifications to Standard DTW" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": "As mentioned in Sec. 3.1, unlike the original DTW algorithm, we exclude the diagonal transitions (i.e., transitioning from " + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "inline_equation", + "content": "D_{i-1,j-1}" + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "inline_equation", + "content": "D_{i,j}" + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": " in Algorithm 1) for DejaVid. The reason is due to model stability. When matching two series of length " + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": ", by disallowing diagonal transitions, the warping path from " + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "inline_equation", + "content": "D_{0,0}" + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "inline_equation", + "content": "D_{n-1,m-1}" + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": " always takes " + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "inline_equation", + "content": "n+m-1" + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": " steps, and so the DTW distance will always be the sum of " + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "inline_equation", + "content": "n+m-1" + }, + { + "bbox": [ + 313, + 233, + 555, + 437 + ], + "type": "text", + "content": " step-wise distances. If diagonal transitions are allowed, the number of step-wise distances on the warping path can vary, destabilizing the model. Although beyond the scope of this paper, we note that there could be other ways to deal with diagonal transitions, such as assigning or learning a multiplicative or additive distance bias for diagonal vs. non-diagonal transitions, such as in Move-Split-Merge (MSM) [24], a more modern replacement of DTW that treats diagonal transitions differently from non-diagonal ones." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 437, + 554, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 554, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 554, + 593 + ], + "type": "text", + "content": "Another modification we made is to fix epoch centroids and weights. That is, at the beginning of an epoch, we make a frozen copy of the current centroids and weights, and then during the epoch, use them to calculate the warping path for each centroid-training TSE pair. Then, along the path, we calculate the pointwise distance using the (non-frozen) originals and perform backpropagation on them. Note that the frozen copies are not updated per batch but instead per epoch. The reason for this modification is again due to model stability. We found that if the warping path calculation mechanism is updated every batch, the distances become noisier from batch to batch, and the model has a harder time converging." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 326, + 593, + 550, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 593, + 550, + 604 + ], + "spans": [ + { + "bbox": [ + 326, + 593, + 550, + 604 + ], + "type": "text", + "content": "We discuss the effect of these modifications in Sec. 4.4." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 607, + 386, + 619 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 607, + 386, + 619 + ], + "spans": [ + { + "bbox": [ + 313, + 607, + 386, + 619 + ], + "type": "text", + "content": "4. Evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 624, + 554, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 554, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 554, + 647 + ], + "type": "text", + "content": "In this section, we describe our implementation and evaluation of DejaVid." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 651, + 489, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 651, + 489, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 651, + 489, + 662 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": "We test DejaVid on three different popular action recognition datasets: Something-Something V2 [14], Kinetics-400 [16], and HMDB51 [18]. The first two are large-scale datasets: Something-Something V2 has 168,913 videos for" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 66, + 702, + 225, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 225, + 712 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 225, + 712 + ], + "type": "text", + "content": "2We set " + }, + { + "bbox": [ + 66, + 702, + 225, + 712 + ], + "type": "inline_equation", + "content": "T_{c} = 8" + }, + { + "bbox": [ + 66, + 702, + 225, + 712 + ], + "type": "text", + "content": " for all experiments in this work." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24027" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 131 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 131 + ], + "type": "text", + "content": "training and 24,777 for validation, while Kinetics-400 has 240,436 training and 19,787 validation videos. In contrast, HMDB51 only has 3,570 training and 1,530 validation videos, but its smaller size can help us study the model's performance when the training set is smaller." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 133, + 294, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 133, + 294, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 294, + 275 + ], + "type": "text", + "content": "Something-Something V2 has 174 action classes that are object and motion-centric, which requires learning the subtle differences between motions and object interactions. Kinetics-400 covers 400 classes of everyday human actions derived from real-world scenarios on YouTube and can be human-object or human-human interactions. Its videos are also longer than those of Something-Something V2 on average (" + }, + { + "bbox": [ + 55, + 133, + 294, + 275 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 55, + 133, + 294, + 275 + ], + "type": "text", + "content": "300 frames vs. " + }, + { + "bbox": [ + 55, + 133, + 294, + 275 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 55, + 133, + 294, + 275 + ], + "type": "text", + "content": "40 frames), which can help differentiate the temporal modeling capabilities between models. HMDB51 has 51 human-dominated action classes, like Kinetics-400, containing some individual and some human-human behaviors." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 276, + 294, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 276, + 294, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 276, + 294, + 360 + ], + "type": "text", + "content": "For all these datasets, we train DejaVid on the training sets and test on the validation sets using the same evaluation protocols as those in VideoMAE V2 [28]. We report the top-1 and top-5 accuracy for every experiment on Something-Something V2 and Kinetics-400. Due to the smaller action set of HMDB51, we only report top-1 for experiments on it." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 365, + 188, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 188, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 188, + 376 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": "Pre-training. We use the largest (ViT-g) model from VideoMAE V2 [28] (abbr. VideoMAE V2-g) as the video encoder.3 VideoMAE V2-g is the only model we experiment with because it is the only SOTA model4 that publishes finetuned weights on large datasets like Kinetics-400 and Something-Something V2, which we cannot afford to finetune ourselves. To show that DejaVid is model-agnostic, we apply the same method to other non-SOTA video encoders in Supplementary Material. The native embedding output length of VideoMAE V2 is 1408, which is then converted into " + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": " logits for class prediction, so we let " + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "inline_equation", + "content": "N_{f} \\coloneqq 1408 + N_{c}" + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": " denote the length of the entire output of VideoMAE V2-g. For DejaVid, we apply a temporal sliding window across the input video " + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": " times to feed into the encoder, resulting in a TSE of shape " + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "inline_equation", + "content": "T \\times N_{f}" + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": ". We then randomly sample some TSEs for each action class to calculate its initial centroid TSE using the DBA algorithm [21]. " + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": " can be different across different datasets and within the same dataset. In particular, we use " + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "inline_equation", + "content": "T = 33" + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": " for Kinetics-400 and HMDB51, and " + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "inline_equation", + "content": "T = 4|vid|" + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": " for Something-Something V2, where " + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "inline_equation", + "content": "|vid|" + }, + { + "bbox": [ + 55, + 379, + 295, + 666 + ], + "type": "text", + "content": " is the length of an individual video. For a detailed description of our pre-training configuration and the choice of width and stride for the sliding window of each dataset, please refer to the Additional Implementation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 487, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 487, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 487, + 84 + ], + "type": "text", + "content": "Details section in Supplementary Material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "spans": [ + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "type": "text", + "content": "Training & Testing. The pre-training stage gives us a TSE " + }, + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "type": "text", + "content": " for each training or validation video as well as the centroid TSEs " + }, + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "type": "text", + "content": ". The weight tensor " + }, + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 313, + 88, + 553, + 280 + ], + "type": "text", + "content": " is either randomly initialized or one-initialized (i.e., filled with ones). To enforce positivity, we actually store the log of the weights and exponentiate them during forward passes. These log-of-weights are randomly initialized or zero-initialized (i.e., filled with zeros). We use the AdamW optimizer with betas (0.9, 0.999) and no weight decay. The initial learning rate for the log-of-weights is 1e-3 for both Something-Something V2 and Kinetics-400, and 8e-3 for HMDB51. The learning rates for the centroid TSEs are one-third of the log-of-weights. We use batch size 48 and train for 36 epochs. We use a cosine scheduler across all 36 epochs. A validation run is performed after every epoch, and we report the top accuracy recorded across all epochs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 286, + 399, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 286, + 399, + 297 + ], + "spans": [ + { + "bbox": [ + 313, + 286, + 399, + 297 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "content": "This section compares our results with previous other temporal-related and state-of-the-art methods. The main baseline is VideoMAE V2-g, which is a billion-parameter video encoder that is state-of-the-art or near state-of-the-art on all evaluation datasets [14, 16, 18, 28]. We test our method on each dataset with three different settings: random-initialization for the weight TSEs " + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "content": " (denoted as full learning; " + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "content": "-init-rnd in the following charts), one-initialization for " + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "content": " (denoted as full learning; " + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "content": "-init-one), and finally one-initialization for " + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "content": " but freezing it throughout (i.e., disallowing optimizer step() to act on " + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "content": "; denoted as frozen weights; " + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 313, + 301, + 553, + 479 + ], + "type": "text", + "content": "-init-one). Note that the last setting is for experimenting with the unweighted DTW distance as in Algorithm 1, so frozen weights with random initialization don't make sense." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "type": "text", + "content": "Results on Kinetics-400. As shown in Tab. 1, our method achieves leading accuracy on Kinetics-400. We improve on the strongest VideoMAE V2-g baseline by " + }, + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "type": "text", + "content": ". DejaVid only requires 5.8M parameters, less than " + }, + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "type": "text", + "content": " of the encoder's parameter count, to achieve this gain. For comparison, the gain from VideoMAE V1 to VideoMAE V2 uses 380M extra parameters to increase the accuracy by only " + }, + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 313, + 485, + 553, + 628 + ], + "type": "text", + "content": ". Note that our results are achieved without refinetuning the encoder, so the training cost is minimal compared to training the encoder. In short, DejaVid is a comparatively tiny add-on that significantly boosts the performance of an off-the-shelf frozen model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "text", + "content": "The performance gain of DejaVid is not only due to temporal supersampling. We test this by averaging the temporal dimension of each sample TSE to get a length- " + }, + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "inline_equation", + "content": "(1408 + N_{c})" + }, + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "text", + "content": " vector and using the last " + }, + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "text", + "content": " elements for class prediction; the result is shown as VideoMAE V2 (temporal supersampling) Tab. 1. When compared against the original setting at VideoMAE V2 " + }, + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "inline_equation", + "content": "5\\times 3" + }, + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "text", + "content": ", we see this alone does not improve" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 673, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 673, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 673, + 295, + 713 + ], + "type": "text", + "content": "3VideoMAE V2 publishes different finetuned weights for Kinetics-400 and Something-Something V2, and the script for finetuning on HMDB51, which we can afford to run thanks to the small dataset size. We use the respective finetuned weights for the pre-training stage of each dataset." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24028" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "the accuracy. Also, the temporal weight-learning does not provide additional benefits on top of our centroid-finetuning for Kinetics-400. We suspect the reason is that the temporal weights increase the expressivity of our method, so overfitting becomes more likely; one future work is to look into regularization for DejaVid." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 148, + 295, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 148, + 295, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 148, + 295, + 291 + ], + "type": "text", + "content": "Results on HMDB51. The results in Tab. 1 show that our model also achieves state-of-the-art accuracy on the HMDB51. We achieve a " + }, + { + "bbox": [ + 55, + 148, + 295, + 291 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 55, + 148, + 295, + 291 + ], + "type": "text", + "content": " performance gain against the strongest VideoMAE V2-g baseline. To the best of our knowledge and according to Papers with Code, this is the highest accuracy recorded on the HMDB51 action recognition benchmark to date (as of Nov, 2024). This shows that DejaVid works well in a training data-scarce scenario. We draw similar conclusions to those from Kinetics-400 in parameter efficiency – our parameter count is 1.19M, which is less than " + }, + { + "bbox": [ + 55, + 148, + 295, + 291 + ], + "type": "inline_equation", + "content": "0.12\\%" + }, + { + "bbox": [ + 55, + 148, + 295, + 291 + ], + "type": "text", + "content": " of that of VideoMAE V2-g – and temporal supersampling alone does not improve performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 295, + 295, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 295, + 295, + 390 + ], + "spans": [ + { + "bbox": [ + 55, + 295, + 295, + 390 + ], + "type": "text", + "content": "Results on Something-Something V2. Tab. 1 compares our results on Something-Something V2 against other works. We outperform the top VideoMAE V2-g baseline with a performance gain of " + }, + { + "bbox": [ + 55, + 295, + 295, + 390 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 55, + 295, + 295, + 390 + ], + "type": "text", + "content": ". To the best of our knowledge and according to Papers with Code, DejaVid achieves the highest top-5 accuracy and one of the highest top-1 accuracies on the Something-Something V2 action recognition benchmark to date (as of Nov, 2024)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "text", + "content": "Progress on Something-Something V2 has slowed in recent years, with top accuracy improving by no more than " + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "text", + "content": " between 2022 and 2024 [20]. Such gains often require massive model scaling; for example, InternVideo2 added over 5 billion parameters for a " + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "text", + "content": " boost [30]. In contrast, DejaVid achieves comparable improvements with just 17.6M parameters—fewer than " + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "text", + "content": " of VideoMAE V2-g. This efficiency highlights the significance of our " + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "inline_equation", + "content": "+0.5\\%" + }, + { + "bbox": [ + 55, + 391, + 295, + 510 + ], + "type": "text", + "content": " accuracy gain, which equates to more than two years of recent progress [28-30]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 511, + 295, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 511, + 295, + 571 + ], + "spans": [ + { + "bbox": [ + 55, + 511, + 295, + 571 + ], + "type": "text", + "content": "However, the performance gain is smaller than on Kinetics-400. One possible reason could be the difference in average video length: " + }, + { + "bbox": [ + 55, + 511, + 295, + 571 + ], + "type": "inline_equation", + "content": "\\sim 40" + }, + { + "bbox": [ + 55, + 511, + 295, + 571 + ], + "type": "text", + "content": " for Something-Something V2 and " + }, + { + "bbox": [ + 55, + 511, + 295, + 571 + ], + "type": "inline_equation", + "content": "\\sim 300" + }, + { + "bbox": [ + 55, + 511, + 295, + 571 + ], + "type": "text", + "content": " for Kinetics-400. Because Kinetics-400 videos are longer, there may be more temporal information" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "for DejaVid to capture. Another reason may be that the encoder is trained with variable video durations, as described in Sec. 4.2, so one future work would be to re-finetune the encoder with video clips of constant frame-count and retry our experiments." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 137, + 415, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 137, + 415, + 148 + ], + "spans": [ + { + "bbox": [ + 313, + 137, + 415, + 148 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 152, + 555, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 152, + 555, + 355 + ], + "spans": [ + { + "bbox": [ + 313, + 152, + 555, + 355 + ], + "type": "text", + "content": "Centroid vs. Weight Learning. In Tab. 2, we analyze the impacts of centroid and weight learning of DejaVid by freezing one component at a time and comparing the results. As seen, both frozen-centroid and frozen-weight variants yield meaningful accuracy gains against the VideoMAE V2-g baseline, and so both components are indeed beneficial. The centroid component has a greater performance gain on average across the three datasets, giving " + }, + { + "bbox": [ + 313, + 152, + 555, + 355 + ], + "type": "inline_equation", + "content": "+0.43\\%" + }, + { + "bbox": [ + 313, + 152, + 555, + 355 + ], + "type": "text", + "content": " top-1 accuracy gain vs. " + }, + { + "bbox": [ + 313, + 152, + 555, + 355 + ], + "type": "inline_equation", + "content": "0.25\\%" + }, + { + "bbox": [ + 313, + 152, + 555, + 355 + ], + "type": "text", + "content": " for the weights, but the weight component seems to be more useful when training data is scarce. As for the training data-rich cases, the weight component seems to be more useful in Something-Something V2 than in Kinetics-400, potentially because we have 4 different feature sets from the different sliding window widths, and these features should naturally have different importance, so the one-initialized weights are further away from the global optimal." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 316, + 367, + 553, + 458 + ], + "blocks": [ + { + "bbox": [ + 316, + 367, + 553, + 458 + ], + "lines": [ + { + "bbox": [ + 316, + 367, + 553, + 458 + ], + "spans": [ + { + "bbox": [ + 316, + 367, + 553, + 458 + ], + "type": "table", + "html": "
MethodSth-Sth2K400HMDB
top-1top-5top-1top-5top-1
VideoMAE V2-g @ best [28]76.7595.8588.498.088.1
Frozen centroids (w-init-rnd)76.896.288.698.088.4
Frozen centroids (w-init-one)76.996.288.898.188.4
Frozen weights (w-init-one)77.196.389.198.288.3
Full learning (w-init-rnd)77.296.388.998.188.6
Full learning (w-init-one)77.096.389.098.288.6
", + "image_path": "e8195f4e028746b9117ccbff6ad2c0d2f5fd8958ba7d77fa5056dacfac056db5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 316, + 479, + 552, + 540 + ], + "blocks": [ + { + "bbox": [ + 334, + 460, + 534, + 472 + ], + "lines": [ + { + "bbox": [ + 334, + 460, + 534, + 472 + ], + "spans": [ + { + "bbox": [ + 334, + 460, + 534, + 472 + ], + "type": "text", + "content": "Table 2. Ablation study on centroid & weight learning." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 479, + 552, + 540 + ], + "lines": [ + { + "bbox": [ + 316, + 479, + 552, + 540 + ], + "spans": [ + { + "bbox": [ + 316, + 479, + 552, + 540 + ], + "type": "table", + "html": "
MethodSth-Sth2K400HMDB
top-1top-5top-1top-5top-1
DT on, otherwise best77.096.288.698.088.5
FECW off, otherwise best77.196.289.098.288.5
Best (DT off, FECW on)77.296.389.198.288.6
", + "image_path": "5a28d5ff27995ea53f0042163d360d6218c00f74c7099da1a38490bd1b7825d0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 317, + 573, + 552, + 619 + ], + "blocks": [ + { + "bbox": [ + 313, + 543, + 553, + 565 + ], + "lines": [ + { + "bbox": [ + 313, + 543, + 553, + 565 + ], + "spans": [ + { + "bbox": [ + 313, + 543, + 553, + 565 + ], + "type": "text", + "content": "Table 3. Ablation studies on diagonal transition (DT) and fixed epoch centroids & weights (FECW)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 573, + 552, + 619 + ], + "lines": [ + { + "bbox": [ + 317, + 573, + 552, + 619 + ], + "spans": [ + { + "bbox": [ + 317, + 573, + 552, + 619 + ], + "type": "table", + "html": "
MethodSth-Sth2K400HMDB
Naive DTW implementation4.79e471.17e57294
Custom DTW CUDA kernel2971561.01
", + "image_path": "d18bdec49750a5a7de046e5b8404793481762a684b499c102d41a9d472d65412.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 622, + 553, + 644 + ], + "lines": [ + { + "bbox": [ + 313, + 622, + 553, + 644 + ], + "spans": [ + { + "bbox": [ + 313, + 622, + 553, + 644 + ], + "type": "text", + "content": "Table 4. Ablation study on the custom DTW CUDA kernel. Table shows runtime per training epoch in seconds." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 650, + 553, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 650, + 553, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 650, + 553, + 674 + ], + "type": "text", + "content": "Diagonal Transition of DTW. Tab. 3 presents a comparison between the best (highest top-1 accuracy" + }, + { + "bbox": [ + 313, + 650, + 553, + 674 + ], + "type": "inline_equation", + "content": "^{8}" + }, + { + "bbox": [ + 313, + 650, + 553, + 674 + ], + "type": "text", + "content": ") setting of" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 326, + 683, + 434, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 683, + 434, + 693 + ], + "spans": [ + { + "bbox": [ + 326, + 683, + 434, + 693 + ], + "type": "text", + "content": "Estimated by running 3 batches." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 694, + 553, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 694, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 694, + 553, + 713 + ], + "type": "text", + "content": "In the case of tied top-1 accuracies, we apply the same change to each tied setting and average their resulting accuracies after the change." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 55, + 578, + 295, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 295, + 702 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 295, + 702 + ], + "type": "text", + "content": "4We were unable to run InternVideo2 on our machine due to one of its required packages, flash-attn, being incompatible with our machine. 5The authors of VideoMAE V2 report 77.0 and 95.9 for top-1 and top-5 accuracy, respectively, but we measure only 76.7 and 95.8 using their published weights. We suspect the discrepancy is due to the input video loading mechanism. The official GitHub repo of VideoMAE V2 has inconsistent descriptions about the data preparation for Something-Something V2, but as of the time of writing, the source code assumes each video has been converted to a folder ofjpeg images, and VideoMAE V2 loads theseJPEG files instead of the source video. But when we do exactly that, the top-1 accuracy measures only 75.7. This is understandable since JPEG uses lossy compression. So we modified the source code to use opencv2 to directly load each video, which gives 76.7 and 95.8." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 66, + 703, + 244, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 703, + 244, + 712 + ], + "spans": [ + { + "bbox": [ + 66, + 703, + 244, + 712 + ], + "type": "text", + "content": "The definition of these clips are described in Sec. 4.2." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24029" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 553, + 270 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 553, + 270 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 553, + 270 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 553, + 270 + ], + "type": "table", + "html": "
MethodW.A.Kinetics-400Something-Something V2HMDB51
ParamsClipsxCropsTop-1Top-5ParamsClipsxCropsTop-1Top-5ParamsClipsxCropsTop-1
Other State-of-the-Art Large Models
TubeViT [22]No632M4×390.998.9307M-76.195.2---
MVD [29]No633M5×387.297.4633M2×377.395.7---
InternVideo2-1B [30]Yes41B4×391.6-1B2×377.1----
InternVideo2-6B [30]No6B4×392.1-6B5×377.5----
Other Temporal-Focused Methods
ILA [27]--4×388.797.8-4×370.291.8---
ATM [31]--4×389.498.3-2×374.694.4---
TAM [19]--4×379.394.1-2×366.090.1---
SlowFast [11]--10×379.893.9--61.7----
MTV [32]--4×389.198.2--68.590.4---
Main Baselines
VideoMAE V1-H [28]Yes633M5×388.1--------
VideoMAE V1-L (32-frame input) [25, 28]Yes----305M2×375.495.2---
VideoMAE V2-g [28]Yes1013M5×388.498.01013M2×376.7595.851013M5×388.1
VideoMAE V2-g (temporal supersampling) [28]Yes1013M336×188.197.81013M(4|vid|)6×176.295.71013M336×188.0
Our Results
Ours (frozen weights; w-init-one)-+5.8M36×189.198.2+8.8M(4|vid|)6×177.196.3+0.60M88.3
Ours (full learning; w-init-rnd)-+11.6M88.998.1+17.6M77.296.3+1.19M336×188.6
Ours (full learning; w-init-one)-+11.6M89.098.2+17.6M77.096.3+1.19M88.6
", + "image_path": "1f6c23252ef2c13fa7dbaab48cc9307f236138362529b4ce7ce351f1c350ede1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 277, + 555, + 300 + ], + "lines": [ + { + "bbox": [ + 55, + 277, + 555, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 555, + 300 + ], + "type": "text", + "content": "Table 1. Comparison with the VideoMAE V2-g baseline and other relevant variants, SOTA, or temporal methods on Kinetics-400, Something-Something V2, and HMDB51. All accuracies are reported in percent (\\%). W.A. = Weights Available. Dashes (-) = N/A." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 303, + 294, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 303, + 294, + 362 + ], + "spans": [ + { + "bbox": [ + 54, + 303, + 294, + 362 + ], + "type": "text", + "content": "Tab. 2 for each dataset and the same setting but with diagonal transitions turned on. Enabling diagonal transitions consistently performs worse on all datasets. This justifies our choice of disabling diagonal transitions in DejaVid and verifies the insight behind this choice as described in Sec. 3.4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 363, + 295, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 363, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 54, + 363, + 295, + 529 + ], + "type": "text", + "content": "Fixed Epoch Centroids & Weights for DTW Learning. We use Tab. 3 to compare the best setting (highest top-1 accuracy8) from Tab. 2 for each dataset with the same setting but disabling fixed epoch centroids & weights, where we do not make frozen copies of the centroids and weights for warping-path determination (shown as FECW off). Again, the inferior performance of this group compared to when FECW is on across all datasets justifies our design for DejaVid, aligning with the reasons detailed in Sec. 3.4 about model stability. However, the gap is less significant than that for the diagonal transition. This suggests there may be room for improvement by tweaking the path-determination mechanism, such as only updating every other epoch instead of each epoch." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 530, + 295, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 295, + 673 + ], + "spans": [ + { + "bbox": [ + 55, + 530, + 295, + 673 + ], + "type": "text", + "content": "Custom CUDA Kernel for Accelerating DTW. Tab. 4 summarizes the runtime per epoch of the best-performing settings on all datasets compared to using a naive Python implementation of DTW. All experiments are conducted on a single node with 8 NVIDIA H100 GPUs. We can see that our custom CUDA kernel provides a speedup between " + }, + { + "bbox": [ + 55, + 530, + 295, + 673 + ], + "type": "inline_equation", + "content": "161\\mathrm{x}" + }, + { + "bbox": [ + 55, + 530, + 295, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 530, + 295, + 673 + ], + "type": "inline_equation", + "content": "750\\mathrm{x}" + }, + { + "bbox": [ + 55, + 530, + 295, + 673 + ], + "type": "text", + "content": ". The most technically significant speedup comes from reducing the critical path length from quadratic to linear, as discussed in Sec. 3.2. Other factors contributing to the speedup include the Python/C++ speed difference and architecture and locality-aware, LibTorch-native implementation of the CUDA-kernel." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 675, + 128, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 675, + 128, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 675, + 128, + 687 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "content": "We presented DejaVid, an encoder-agnostic method that boosts video classification performance without retraining" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "text", + "content": "the encoder or changing its architecture. Instead of converting a video into a single fixed-length embedding like most state-of-the-art encoders do, we feed a backbone encoder a sliding-window stream of frames to obtain a variable-length temporal sequence of embeddings (TSE), which preserves temporal order and supports variable video durations. We then introduce a novel neural network architecture based on Dynamic Time Warping (DTW) with learnable, per-timestamp feature weights to address temporal variance in feature significance. Our ablation studies compare and justify various design choices and modifications to classical DTW, and our evaluation shows that DejaVid achieves state-of-the-art video classification results on a variety of benchmarks, significantly improves the accuracy of a cutting-edge large encoder, and outperforms other temporal methods. In particular, we achieve leading Top-1 accuracy of " + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "inline_equation", + "content": "77.2\\%" + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "text", + "content": " on Something-Something V2, " + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "inline_equation", + "content": "89.1\\%" + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "text", + "content": " on Kinetics-400, and " + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "inline_equation", + "content": "88.6\\%" + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "text", + "content": " on HMDB51, representing a 0.5- " + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "text", + "content": " accuracy gain over VideoMAE V2-g while adding less than " + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 313, + 303, + 555, + 555 + ], + "type": "text", + "content": " additional learnable parameters and less than 3 hours of training time." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 561, + 397, + 573 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 561, + 397, + 573 + ], + "spans": [ + { + "bbox": [ + 313, + 561, + 397, + 573 + ], + "type": "text", + "content": "6. Future Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 578, + 555, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 578, + 555, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 578, + 555, + 696 + ], + "type": "text", + "content": "In this paper, we selected video classification as the evaluation task due to its foundational role in computer vision [15, 16, 26], its real-world importance [1, 11, 13], and the significant amount of highly competitive research focused on it [2, 11, 19, 22, 25, 27-32]. With that said, we can also see the potential of DejaVid – and of the power of fine-grained temporal alignment learning in general – in action segmentation, video captioning, text-to-video retrieval, and any other tasks that can benefit from detailed temporal modeling." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24030" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "type": "text", + "content": "[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 12104-12113, 2022. 1" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24032" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Denoising Functional Maps_ Diffusion Models for Shape Correspondence/2c4c8aae-c014-423b-a2aa-0d67eb2103ed_content_list.json b/2025/Denoising Functional Maps_ Diffusion Models for Shape Correspondence/2c4c8aae-c014-423b-a2aa-0d67eb2103ed_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..94e156af06242429f149ee9a0b3fb6dd9ba90a51 --- /dev/null +++ b/2025/Denoising Functional Maps_ Diffusion Models for Shape Correspondence/2c4c8aae-c014-423b-a2aa-0d67eb2103ed_content_list.json @@ -0,0 +1,1809 @@ +[ + { + "type": "text", + "text": "Denoising Functional Maps: Diffusion Models for Shape Correspondence", + "text_level": 1, + "bbox": [ + 127, + 130, + 869, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Aleksei Zhuravlev", + "bbox": [ + 233, + 179, + 387, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Bonn", + "bbox": [ + 222, + 198, + 383, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zorah Lähner1, 2", + "bbox": [ + 428, + 179, + 558, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Lamarr Institute", + "bbox": [ + 411, + 198, + 549, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vladislav Golyanik3", + "bbox": [ + 599, + 180, + 763, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ MPI for Informatics, SIC", + "bbox": [ + 576, + 198, + 787, + 215 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6a20d093a6aa6f0492c5ced4ce3fe33c6d44579e6940055eae638f620839de52.jpg", + "image_caption": [ + "+Challenging Human Shapes", + "+ Zero-Shot on Humanoids", + "+ Animal Shapes", + "Figure 1. We propose DenoisFM, a novel method for predicting shape correspondences in the form of functional maps using denoising diffusion models. (Left:) Challenging examples our method can handle, with color-coded correspondences. (Right:) By sequentially denoising samples of random noise, the diffusion model can predict the correct functional map between a pair of shapes." + ], + "image_footnote": [], + "bbox": [ + 91, + 239, + 563, + 353 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 413, + 244, + 563, + 353 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d11d7c96ca80f393dcd2c171ae5fdd2616573871bf6b5e38e2142cf2d237073a.jpg", + "image_caption": [ + "Predict Functional Maps using DDPMs", + "Gaussian Noise $x_{T}$", + "$x_{t - 1}\\coloneqq \\mathbf{DDPM}(x_t;y)$", + "Functional Map" + ], + "image_footnote": [], + "bbox": [ + 589, + 280, + 885, + 342 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 433, + 325, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape deformation methods. See our project page1 for the source code2 and the datasets.", + "bbox": [ + 86, + 470, + 483, + 816 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 514, + 433, + 643, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A long-standing problem in computer graphics and vision is to find corresponding points in a pair of 3D shapes [9, 11, 19, 42, 49, 64, 69]. The point map can then be used for texture [14], segmentation [63] and deformation transfer [68], statistical shape analysis [13], and construction of parametric models [37, 55]. A popular approach to solving the correspondence problem involves the functional map framework [49], which represents the correspondence as a small matrix that maps between the eigenfunctions of the Laplace operator on each shape. This representation is compact and allows to regularize constraints on the correspondences, such as bijectivity or area preservation. The functional map framework has been extended in numerous works, such as matching shapes with partiality [4, 58], analyzing the properties of shape collections [13] or improving accuracy through iterative refinement [19, 44, 57].", + "bbox": [ + 511, + 460, + 906, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous functional map approaches focused on using small datasets, rarely exceeding a hundred unique shapes. This favored training models with lightweight architectures that could learn as much as possible with limited data, but these methods may face challenges with generalization to broad shape categories. To develop a unified model that is applicable to various tasks, we draw attention to denoising diffusion models [25, 66, 67], which have impressive generalization ability when trained on large amounts of data. In our work, we apply this approach to correspondence estimation using functional maps.", + "bbox": [ + 511, + 703, + 908, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Based on the idea of sequentially denoising samples of random noise into samples from the data distribution, dif-", + "bbox": [ + 511, + 869, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Project page: https://alekseizhuravlev.github.io/ denoising-functional-maps/", + "bbox": [ + 89, + 849, + 482, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Source code: https://github.com/alekseizhuravlev/ denoising-functional-maps/", + "bbox": [ + 89, + 875, + 480, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26899", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "fusion models have achieved unprecedented performance in high-fidelity, diverse, and controllable image synthesis [53]. The scalable U-Net architecture [60] allows them to be trained on large datasets with hundreds of thousands of high-resolution images. The application of diffusion models to shape matching has been limited so far, mainly focusing on feature extraction from pre-trained foundational models [1, 17]. Interestingly, functional maps appear well-suited to bridge diffusion models and shape correspondence. They are small-sized single-channel matrices, making standard architectures developed for images readily applicable to them. Large amounts of shape data for training are then available through parametric models such as SMPL [37], an approach that has already been used for matching tasks [23, 72] and is also suitable for diffusion models.", + "bbox": [ + 89, + 90, + 480, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present Denoising Functional Maps (DenoisFM), an approach to directly predict the functional map between shapes using a denoising diffusion model; see Fig. 1 for the overview. For training, we create a large dataset of functional maps between $2.3 \\cdot 10^{5}$ human shapes from the SURREAL dataset [73] and a template shape. Using template-wise maps instead of pair-wise ones allows to reduce the complexity of training and inference. The conditioning information is inferred directly from the geometric shape structure. Additionally, we propose to exploit the probabilistic nature of diffusion models by predicting several initial maps instead of a single one, and selecting the best map based on the Dirichlet energy [52].", + "bbox": [ + 89, + 334, + 480, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An important property of functional maps is that they are defined in the basis of the first $n$ eigenvectors of the Laplacian operator for each shape. The basis is not unique due to the sign ambiguity of the eigenvectors, and there are potentially $2^{n}$ possible basis combinations for each shape. To address this problem, we propose an unsupervised approach which selects the signs of the basis vectors using per-vertex features extracted in an unsupervised way (Sec. 3.2). This reduces the number of possible functional maps between shapes, further lowering the training complexity.", + "bbox": [ + 89, + 532, + 480, + 684 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. Overall, the technical contributions of this paper can be summarized as follows:", + "bbox": [ + 89, + 685, + 482, + 715 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- DenoisFM, a fundamentally new approach to shape correspondence estimation based on predicting functional maps using denoising diffusion models;", + "- An unsupervised method to address the sign ambiguity of eigenvectors of the Laplacian, which reduces the complexity of the prediction problem." + ], + "bbox": [ + 89, + 717, + 482, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our model performs on par with existing shape matching methods on human benchmark datasets, achieves generalization to non-isometric humanoid shapes without learning on them, and is also applicable to animal shapes. See our project page1 for the source code2 and the datasets of functional maps used to train our models.", + "bbox": [ + 89, + 810, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 89, + 653, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Shape Correspondence Estimation. Learning-based shape correspondence methods can be roughly divided into two categories: first, approaches that predict pointwise descriptors suitable for computing functional maps [49, 50], a low-rank representation of the point-wise correspondence in Laplace-Beltrami eigenbasis; second, deformation-based methods that directly align input shapes and typically require much larger training datasets than descriptor-based methods.", + "bbox": [ + 511, + 114, + 903, + 251 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the standard functional map pipeline, point-wise descriptor functions that encode the surface geometry are first computed on each shape [5, 9, 71], and then the functional map is estimated using the descriptors in a least-squares optimization. With the advent of deep learning, network architectures were introduced to learn descriptor functions directly from the data [35, 65]. While the initial methods were supervised [15, 35], recent works estimate the descriptors in an unsupervised manner [11, 62]. Most shape matching datasets consist of fewer than a hundred unique meshes and focus on a specific category of shapes [3, 7, 40, 43]. Therefore, the most effective descriptor-based models use lightweight architectures to infer as much geometric information as possible from limited training data.", + "bbox": [ + 511, + 252, + 903, + 464 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another group of works use large-scale datasets of synthetic data for training. 3D-CODED [23] is an encoder-decoder architecture that predicts the correspondence by learning a surface parameterization and attempts to estimate the deformation from the template shape to the test one. Transmatch [72] is a transformer-based model that uses an attention mechanism to learn the underlying structure of the geometry. Other works utilizing large amounts of data [10, 31, 76] mainly focus on point cloud registration, and a group of works learn the shape deformation using data-efficient architectures [20, 70].", + "bbox": [ + 511, + 465, + 903, + 631 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We combine the advantages of both categories of models by training a large-scale method based on functional maps that leverages the power of denoising diffusion models.", + "bbox": [ + 511, + 632, + 903, + 676 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Denoising Diffusion Models. Diffusion models have become popular in many areas of visual computing; see the recent survey for details [53]. Several diffusion-based generative models have been proposed [66, 67], and the simplified learning process of denoising diffusion probabilistic models (DDPMs) enabled the image synthesis at unprecedented quality [25]. Various conditioning mechanisms such as class labels, textual descriptions, or segmentation maps have been used to guide the diffusion process [59]. While diffusion models quickly found applications in areas beyond imaging such as video [26, 27] and 3D content generation [36, 54], their application to shape correspondence estimation has been limited so far to extracting descriptors from images of meshes [17] or segmentation maps [1] gen", + "bbox": [ + 511, + 688, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26900", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "erated by foundational models. Our work is the first to use DDPMs to directly predict the functional maps between pairs of shapes to obtain the correspondences.", + "bbox": [ + 89, + 90, + 482, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sign Ambiguity of Laplacian Eigenvectors. Since for any eigenvector $\\phi_i$ , its negative version $-\\phi_i$ is also an eigenvector, the Laplace-Beltrami eigenbasis has an inherent sign ambiguity. Additionally, the eigenvalues can have higher multiplicity and make the intrinsic ordering non-unique. This symmetry needs to be taken into account when processing the eigenvectors [8, 48, 63].", + "bbox": [ + 89, + 146, + 482, + 251 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In graph learning, Laplacian eigenvectors are used to encode information about the structure of a graph [6, 32], and several methods were proposed to address the sign ambiguity. Laplacian Canonization [38] proposes to find the coordinate axis on which the projection of the eigenvector has the largest angle and fixes the projection to be positive. SAN [30] obtains sign-invariant operators using absolute subtraction and product between a pair of nodes, this only considers the relative sign between queries. SignNet [34] learns a sign-invariant embedding and Dwivedi et al. [18] learns on all possible sign combinations.", + "bbox": [ + 88, + 252, + 482, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The methods described above are designed for graphs with a small number of vertices. For point clouds, Linearly Invariant Embedding [41] considered the problem of learning the basis functions directly from the input data. However, the majority of works on 3D shapes employ the sign-equivariant approach, where a sign-dependent functional map is computed from descriptor functions in a precomputed Laplace-Beltrami eigenbasis. In our work, we propose to address the sign ambiguity problem using a learning-based method that assigns a specific combination of signs to the eigenvectors of any human shape, which is learned directly from the data in an unsupervised way.", + "bbox": [ + 89, + 417, + 482, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 89, + 614, + 218, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notation. Given a shape $S$ represented as a triangular mesh with $v$ vertices, we compute its Laplace matrix $L$ [45] and the first $n$ eigenvectors of $L$ corresponding to the eigenvalues $\\lambda_1 \\leqslant \\ldots \\leqslant \\lambda_n$ . $A$ is the diagonal vertex-area matrix associated with $L$ , computed by assigning one-third of the total area of all faces incident to the corresponding vertex.", + "bbox": [ + 89, + 640, + 482, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We denote matrices of $n$ functions on the vertices of $S$ by uppercase letters: $\\Phi \\in \\mathbb{R}^{v \\times n}$ for the matrix of eigenvectors, $\\Sigma \\in \\mathbb{R}^{v \\times n}$ for the matrix of learned features. The individual eigenvectors and feature vectors are denoted by lowercase letters: $\\phi_i \\in \\mathbb{R}^v$ for the $i$ -th eigenvector, $s_i \\in \\mathbb{R}^v$ for the $i$ -th feature vector. Finally, $\\sigma \\in \\{-1, 1\\}^n$ represents a vector consisting of $n$ signs.", + "bbox": [ + 89, + 732, + 482, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Functional Maps", + "text_level": 1, + "bbox": [ + 89, + 848, + 256, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method is built upon the framework of functional maps [49, 50]. Consider the point-wise map $\\Pi_{21} \\in \\{0,1\\}^{v_2 \\times v_1}$", + "bbox": [ + 89, + 869, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "between two meshes $S_{1}$ and $S_{2}$ . The point-wise map is a permutation matrix, and due to its large size, it cannot be processed efficiently. The functional map $C_{12} \\in \\mathbb{R}^{n \\times n}$ is the spectral representation of $\\Pi_{21}$ , which is computed as", + "bbox": [ + 511, + 90, + 905, + 151 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC _ {1 2} = \\Phi_ {2} ^ {\\dagger} \\Pi_ {2 1} \\Phi_ {1}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 165, + 906, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where “ $\\dagger$ ” denotes the pseudo-inverse. The functional map efficiently encodes the point-wise map in a low-dimensional representation, since $n \\ll v_1, v_2$ .", + "bbox": [ + 511, + 186, + 905, + 233 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In a standard pipeline, learned or handcrafted $p$ -dimensional descriptor functions are computed on each shape, $F_{1} \\in \\mathbb{R}^{v_{1} \\times p}$ , $F_{2} \\in \\mathbb{R}^{v_{2} \\times p}$ . The functional map is then obtained by solving the linear system [50]:", + "bbox": [ + 511, + 234, + 905, + 294 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC _ {1 2} = \\underset {C} {\\arg \\min } \\left\\| C \\Phi_ {1} ^ {\\dagger} F _ {1} - \\Phi_ {2} ^ {\\dagger} F _ {2} \\right\\| _ {2} ^ {2}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 304, + 905, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which is usually further regularized [15, 47]. The pointwise map can be recovered from the functional map and the eigenvectors using nearest neighbor search [49, 51].", + "bbox": [ + 511, + 340, + 905, + 386 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Sign Ambiguity", + "text_level": 1, + "bbox": [ + 511, + 393, + 669, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The functional map is defined in a basis spanned by the eigenvectors of the Laplacian on each shape, as can be seen from Eq. (1). However, this basis is not unique since for each eigenvector $\\phi_i$ , $-\\phi_i$ is also a valid eigenvector corresponding to the same eigenvalue $\\lambda_i$ . Due to sign ambiguity, there are $2^n$ possible basis combinations on each shape.", + "bbox": [ + 511, + 416, + 905, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The eigenvectors returned by a numerical eigensolver will have a random sign combination, and mathematically it is impossible to select some specific sign of eigenvectors. However, several works demonstrate that the choice of the sign can be determined by the underlying data using the projection operator [8, 34, 38]. An intuitive example arises in the principal component analysis: Each eigenvector should point in the same direction as the points it is representing. This can be achieved by projecting the singular vector onto the data vectors and changing its sign to make the projection positive. This approach allows to select a canonical direction for the first few eigenvectors.", + "bbox": [ + 511, + 507, + 905, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sign ambiguity is a special case of basis ambiguity when all eigenvalues are distinct. The more general basis ambiguity occurs if an eigenvalue $\\lambda_{i}$ has multiplicity degree $d_{i} > 1$ . Then any $d_{i}$ vectors forming an orthogonal basis in the subspace spanned by its eigenvectors $(\\phi_{i + 1},\\phi_{i + 2}\\dots \\phi_{i + d_i})$ are also valid eigenvectors. Although the basis ambiguity is difficult to deal with, in practice high multiplicities do not occur often in low-order eigenvectors [29, 50].", + "bbox": [ + 511, + 688, + 905, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Denoising Diffusion Models", + "text_level": 1, + "bbox": [ + 511, + 816, + 761, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a dataset of examples drawn independently from a data distribution $q(x)$ , diffusion models aim to learn the underlying data distribution by sequentially denoising random noise samples [25, 53, 66].", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26901", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The forward diffusion process takes a real data point $x_0$ and incrementally adds to it a small amount of Gaussian noise, producing a sequence of $T$ noisy samples $x_1, \\ldots, x_T$ . The step sizes are controlled by a variance schedule $\\{\\beta_t \\in (0, 1)\\}_{t=1}^T$ . With the larger steps $t$ , the noisy sample $x_t$ further deviates from the original sample. At $T \\to \\infty$ , it is close to the Gaussian distribution, $x_T \\sim N(x_T; 0, I)$ . The reverse process recreates the original sample by iteratively removing noise from an input $x_T$ drawn from the Gaussian distribution. Assuming that the reverse conditional probability is conditioned on $x_0$ , $q(x_{t-1} \\mid x_t, x_0) = N\\left(x_{t-1}; \\tilde{\\mu}(x_t, x_0), \\tilde{\\beta}_t I\\right)$ , we can obtain $\\tilde{\\mu}_t = \\frac{1}{\\sqrt{\\alpha_t}}\\left(x_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\tilde{\\alpha}_t}}\\epsilon_t\\right)$ , where $\\alpha_t = 1 - \\beta_t$ and $\\bar{\\alpha}_t = \\prod_{i=1}^T \\alpha_i$ .", + "bbox": [ + 89, + 90, + 483, + 324 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead of directly predicting the denoised sample $\\tilde{\\mu}_t$ with a neural network, we can predict the noise content $\\epsilon_{\\theta}(x_t,t)$ from the input $x_{t}$ at time step $t$ [25]. Such a model is trained with a denoising score-matching objective: $\\mathcal{L}_t = E_{t\\sim [1,T],x_0,\\epsilon_t}\\left[\\| \\epsilon_t - \\epsilon_\\theta (x_t,t)\\| ^2\\right]$ .", + "bbox": [ + 89, + 328, + 483, + 415 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Denoising Functional Maps", + "text_level": 1, + "bbox": [ + 89, + 445, + 344, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This section introduces Denoising Functional Maps (DenoisFM), our approach for shape correspondence estimation; see Fig. 2 for the method overview. Since functional maps are square low-dimensional matrices (see Sec. 3.1), we use a standard neural architecture based on a 2D U-Net [61] as a backbone. We aim to train our model on a large collection of shapes with diverse geometry. Since functional maps are defined for shape pairs, for a dataset with $m$ shapes the model would have to learn $m^2$ functional maps. Instead of this naive approach, we consider the correspondences to a single template shape, following previous works [23, 72]. As a result, the training data includes only $m$ functional maps, one for each shape in the dataset.", + "bbox": [ + 89, + 478, + 483, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A functional map is defined in a specific basis of Laplacian eigenvectors, and knowing the exact basis combination is necessary to convert it to a point-wise correspondence map. Therefore, we compute the basis first and then condition the diffusion model on it; the model then returns the corresponding functional map. To reduce the complexity of the problem caused by the sign ambiguity of basis eigenvectors, we utilize a sign correction network to select a specific combination of signs for the basis.", + "bbox": [ + 89, + 681, + 483, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "DenoisFM consists of two components: the DDPM for functional map prediction (Sec. 4.1) with post-processing that filters out low-quality solutions using Dirichlet energy of the point-wise map (Sec. 4.1.1), and the sign corrector for the Laplacian eigenvectors (Sec. 4.2).", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Denoising Diffusion Component", + "text_level": 1, + "bbox": [ + 513, + 90, + 797, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We next describe the training and inference of the diffusion component of DenoisFM. For training, we use a large collection of shapes and a template. For each shape $S$ in the dataset, we compute an eigenbasis $\\Phi$ , a template-wise functional map $C_{1T}$ , and conditioning $y = y(S,\\Phi)$ which incorporates geometric details of the input shape and information about the basis. The exact form of conditioning will be specified in Sec. 4.3. We use the training objective of denoising diffusion probabilistic models (DDPMs) [25]: $\\mathcal{L}_{\\mathrm{DDPM}} = E_{x,\\epsilon \\sim N(0,1),t}\\left[\\| \\epsilon -\\epsilon_{\\theta}(x_t,t,y)\\| _2^2\\right]$ , where $\\epsilon_{\\theta}$ is the amount of noise predicted by a 2D UNet [60], $x_{t}$ is a noisy version of the input $x_0\\coloneqq C_{1T}$ , and $t$ is the time step uniformly sampled from $\\{1,\\ldots ,T\\}$ .", + "bbox": [ + 511, + 116, + 906, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The inference pipeline consists of two stages, see Fig. 2a. In the template stage, for each individual shape $S$ in the evaluation dataset, we obtain an eigenbasis $\\Phi$ , calculate the conditioning $y$ , and predict the template-wise functional map $C_{1T}$ using the diffusion model. Note that the inference of DDPMs is time-consuming due to the large number of denoising steps and can take several hours for high-dimensional functional maps. Because the predicted maps refer to the template, we need to run the denoising process only once for each shape.", + "bbox": [ + 511, + 323, + 906, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the pairwise stage, for each test pair, we convert the respective template-wise functional maps into pairwise ones using the composition property [49]: $C_{12} = C_{1T}(C_{2T})^{-1}$ . We then apply the Zoomout refinement [44] to increase the resolution of the functional maps. This spectral upsampling step has been shown to improve their accuracy, and our framework benefits from it without additional modifications. Finally, the functional map is converted into a pointwise map $\\Pi_{21}$ using nearest neighbor search.", + "bbox": [ + 511, + 479, + 908, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1.1. Post-Processing of the Samples", + "text_level": 1, + "bbox": [ + 513, + 636, + 774, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion models are inherently probabilistic and their outputs may differ given the same conditioning but different initial noise [25]. To address this, we repeat the denoising process multiple times and filter out the low-quality results. The selection is based on the Dirichlet energy of the pointwise map [21, 40]: an accurate map should be smooth, with neighboring vertices on one shape matching neighboring vertices on the other. Therefore, we repeat both the template step and the pairwise step to produce multiple point-wise maps. We can then either report the map with the lowest Dirichlet energy or combine the results of several smoothest maps. To do this, for each query point on the source mesh, we gather potential matching points on the target mesh and select the one with the smallest total distance to the other candidates (see Supp. B.3). The map selection step has a major impact on the accuracy of our method.", + "bbox": [ + 511, + 657, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26902", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/37b7c3ee91cde8dc1f79b48cab49ee57ada7aa9d751bb45cd7d53faa6cefa407.jpg", + "image_caption": [ + "(a) Functional map prediction using a diffusion model. For each unique shape $S$ in the dataset, we obtain feature vectors $\\Sigma$ using a feature extractor $\\Theta$ , as well as a sign-corrected eigenbasis $\\hat{\\Phi}$ (Fig. 2b, Sec. 4.2). Both are used for conditional prediction of the template-wise functional map $C_{1T}$ using a diffusion model, performed separately for each shape. The pairwise functional maps $C_{12}$ are obtained through the map composition property, upsampled using ZoomOut [44], and converted to pointwise maps $\\Pi_{21}$ ." + ], + "image_footnote": [], + "bbox": [ + 117, + 89, + 883, + 271 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0b1dfdf25910845f8b3aeb3adff0ad9b12e122dfed0db6ab664405e132ac55f1.jpg", + "image_caption": [ + "(b) Learned sign correction. The eigenvectors $\\Phi$ returned by a numerical eigensolver have random signs. To select a specific sign, we project the eigenvectors onto the feature vectors $\\Sigma$ obtained with a feature extractor $\\Theta$ , and make the projection positive. The sign correction network is trained in an unsupervised manner: learning to correct eigenvectors that have random signs. The learned features $\\Sigma$ are also used for the conditional prediction of the template-wise functional map using a diffusion model (Fig. 2a).", + "Figure 2. Overview of DenoisFM. (a) A pair of shapes is matched using a DDPM model. (b) The signs of eigenvectors are corrected through learned features." + ], + "image_footnote": [], + "bbox": [ + 178, + 335, + 823, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Learned Sign Correction", + "text_level": 1, + "bbox": [ + 89, + 587, + 318, + 603 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The diffusion model needs to be conditioned on the basis eigenvectors and predict the functional map for that particular basis. Theoretically, the model could be trained using random basis combinations, as was done in Dwivedi et al. [18] for graph networks. However, this would significantly increase the amount of training data.", + "bbox": [ + 89, + 609, + 483, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hence, we follow a more effective approach: we select a specific basis by fixing the sign of the Laplacian eigenvectors on each shape. Previous works infer the sign from the underlying data using the projection operator (see Sec. 3.2). Therefore, suppose that $\\Sigma \\coloneqq \\Theta(S) \\in \\mathbb{R}^{v \\times n}$ is a set of pervertex feature vectors inferred from the geometry of shape $S$ by a trainable feature extractor $\\Theta$ , one for each eigenvector. The sign of the eigenvectors can be selected by projecting the features $\\Sigma$ onto the eigenvectors $\\Phi$ and making the corresponding projections positive:", + "bbox": [ + 89, + 700, + 483, + 852 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\sigma} := \\operatorname {s i g n} \\left[ \\operatorname {d i a g} \\left(\\Sigma^ {T} A \\Phi\\right) \\right], \\tag {3} \\\\ \\hat {\\Phi} := \\Phi \\hat {\\sigma}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 863, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where “ $\\mathrm{diag}(\\cdot)$ ” and “ $\\mathrm{sign}(\\cdot)$ ” denote matrix diagonal and sign extraction operators, $A$ is the diagonal vertex-area matrix. To illustrate, suppose we have a human mesh and a single feature vector $\\varsigma_{i}$ , which is a binary vector with ones for points on the left hand, and zeros otherwise. After performing the procedure described in Eq. (3), the corrected eigenvector $\\hat{\\phi}_i$ will be mostly positive on the left hand.", + "bbox": [ + 511, + 588, + 906, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1. Training the Sign Corrector", + "text_level": 1, + "bbox": [ + 511, + 700, + 756, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The sign correction network is trained in an unsupervised manner by learning to correct eigenvectors that have random signs. If we perform the eigendecomposition with a numerical solver twice on the same mesh and get two sets of eigenvectors $\\Phi_1$ and $\\Phi_2$ , due to the sign ambiguity, the difference between them can be written as $\\Phi_2 = \\Phi_1\\sigma$ , where $\\sigma \\in \\{-1,1\\}^n$ is the ground-truth sign difference. Now we perform the sign correction using Eq. (3), after which we expect the corrected eigenvectors to be equal to each other:", + "bbox": [ + 511, + 719, + 906, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\Phi} _ {1} = \\hat {\\Phi} _ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 674, + 866, + 903, + 891 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi_ {1} \\hat {\\sigma} _ {1} = \\Phi_ {2} \\hat {\\sigma} _ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 888, + 761, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "26903", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\sigma}_1, \\hat{\\sigma}_2 \\in \\{-1, 1\\}^n$ are the predicted combinations of correction signs. After substitution and using $\\hat{\\sigma}_1 \\hat{\\sigma}_1 = I$ :", + "bbox": [ + 89, + 90, + 485, + 122 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi_ {1} \\hat {\\sigma} _ {1} = \\Phi_ {1} \\sigma \\hat {\\sigma} _ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 136, + 346, + 152 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {1} = \\sigma \\hat {\\sigma} _ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 250, + 156, + 480, + 170 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {1} \\hat {\\sigma} _ {2} = \\sigma .\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 175, + 305, + 189 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As a result, the difference between the predicted correction signs should be the same as the ground-truth sign difference, and we can use this as our unsupervised training objective with a mean square error function:", + "bbox": [ + 89, + 205, + 483, + 266 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s i g n}} = \\operatorname {M S E} (\\hat {\\sigma} _ {1} \\hat {\\sigma} _ {2}; \\sigma) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 287, + 483, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that the sign operator in Eq. (3) is not differentiable. Therefore, during training, we set $\\hat{\\sigma}_1$ and $\\hat{\\sigma}_2$ to be the diagonal elements of the projections, rather than their signs, assuming that the feature vectors and eigenvectors have unit norm. The training objective of the feature extractor (Eq. 6) then forces the elements of $\\hat{\\sigma}_1$ and $\\hat{\\sigma}_2$ to be as close to $-1$ or $1$ as possible. The absolute value can be interpreted as confidence in the predicted sign: values close to $\\pm 1$ mean high confidence.", + "bbox": [ + 89, + 316, + 483, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In practice, we found that a network trained this way quickly converges on a dataset of human or animal meshes. Our method returns the same corrected eigenbasis $95 - 99\\%$ of the time for the first hundred Laplacian eigenvectors. The accuracy of the sign correction and its impact on the distribution of functional maps are discussed in Supp. A.", + "bbox": [ + 89, + 454, + 483, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Choice of Conditioning", + "text_level": 1, + "bbox": [ + 89, + 559, + 305, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Conditioning of the diffusion model should include two parts: the basis information and the geometric properties of the shape. The former can be provided simply via the sign-corrected eigenvectors $\\hat{\\Phi}$ . They additionally represent the spectral embedding of the shape and convey the full intrinsic information. As for the latter, during the training of the sign-correction network, the useful properties will be encoded in the learned feature vectors $\\Sigma$ . Therefore, we propose to project the feature vectors onto the sign-corrected eigenvectors:", + "bbox": [ + 89, + 582, + 483, + 733 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\text {C o n d i t i o n g} y = \\Sigma^ {T} A \\hat {\\Phi}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 747, + 482, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This form of conditioning has two important properties. First, it has the same dimensions as the functional map. Therefore, we can condition the diffusion model using a simple concatenation, where the conditioning matrix is concatenated with the intermediate denoising targets and passed through the score estimator as input [25, 75]. Second, it is independent of the number of vertices, making it scalable to large meshes.", + "bbox": [ + 89, + 780, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Training and Experimental Results", + "text_level": 1, + "bbox": [ + 511, + 90, + 831, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This section describes the steps for generating the training data for our model (Sec. 5.1) as well as the experimental results on several challenging datasets (Secs. 5.2-5.5). The evaluation of the sign correction network, additional comparison, implementation details, and the ablation studies can be found in Supp. A to C. Since our model is designed to be trained on large and diverse shape collections, it can be applied to multiple (reminiscent) shape classes without retraining. This reduces the need for small category-specific training sets. We focus on datasets with human-like shapes as their combined volume allows versatile comparison of our approach with the previous works.", + "bbox": [ + 511, + 114, + 906, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Training Data and Implementation", + "text_level": 1, + "bbox": [ + 511, + 306, + 818, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our model consists of two independent components: a denoising diffusion model that predicts the functional map and a sign correction network based on a per-vertex feature extractor, trained separately on their respective datasets.", + "bbox": [ + 511, + 330, + 905, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1.1. Denoising Diffusion", + "text_level": 1, + "bbox": [ + 511, + 398, + 697, + 414 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Diffusion models require large amounts of training data with hundreds of thousands of examples. Therefore, we follow 3D-CODED [23] and use the SURREAL [73] dataset with 230,000 human meshes generated with SMPL [37]. All its meshes are smooth and have the same vertex structure. To make the connectivity more diverse, we remesh each mesh [28, 46] and randomly simplify the number of faces using Quadric Edge Collapse [22]. In $65\\%$ of the cases, we simplify the entire mesh resulting in uniform connectivity. In the remaining $35\\%$ of the cases, we simplify only a small subset of the mesh to add non-even connectivity to the training data. After remeshing, we correct the signs of the eigenvectors using a pre-trained sign correction network (Sec. 4.2) and compute the functional map to the template shape. We only store the functional maps and conditioning matrices to save memory requirements. The data generation takes 10 hours using parallel processing.", + "bbox": [ + 511, + 417, + 906, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use the standard DDPM [25] implemented in Diffusers [74] and distributed training with Accelerate [24]. We train models that predict 32, 64, and 96-dimensional functional maps for 100 epochs on eight A40 GPUs, which takes 1, 8, and 30 hours respectively. The inference at the template stage takes 1, 7, and 27 minutes for each shape in the dataset. The pairwise stage takes 30 seconds per pair.", + "bbox": [ + 511, + 676, + 905, + 782 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1.2. Sign Correction Network", + "text_level": 1, + "bbox": [ + 511, + 790, + 735, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The per-vertex feature extractor of the sign correction network is based on DiffusionNet [65] (not to be confused with denoising diffusion) with six blocks and 128 WKS descriptors [5] as input. This architecture was designed for small shape matching datasets, so we used 1000 randomly selected meshes from SURREAL for training. Each", + "bbox": [ + 511, + 810, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "26904", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of them was randomly remeshed and simplified without adding anisotropy. The sign correction network is trained for $5 \\cdot 10^{4}$ iterations, which takes one hour on a single A40 GPU; the inference takes a few seconds per shape.", + "bbox": [ + 89, + 90, + 482, + 151 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Near-Isometric Shape Matching", + "text_level": 1, + "bbox": [ + 89, + 162, + 372, + 179 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets. We evaluate our method on three widely used datasets: FAUST [7], SCAPE [3] and SHREC'19 [43]. Following previous works, we use their more challenging remeshed versions [15, 56]:", + "bbox": [ + 89, + 184, + 482, + 244 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The FAUST dataset contains meshes of 10 human classes in 10 poses, 100 in total. The train/test split is 80/20.", + "- The SCAPE dataset includes 71 meshes of the same person in different poses, the last 20 are used for testing.", + "- The SHREC'19 dataset is composed of 44 shapes with diverse body types and poses, arguably the most challenging of the three. This dataset does not have a train split and is used for testing only. Following [11], we removed shape 40 since it is the only partial non-closed shape." + ], + "bbox": [ + 89, + 246, + 482, + 380 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. We compare our approach with two categories of non-rigid shape correspondence methods. The first includes large-scale template-based models trained on SURREAL: 3D-CODED [23] and TransMatch [72], i.e., our main competitors as our work belongs to the same group. The second category includes descriptor-based models: ULRSSM [11], DiffZO [39], ConsistentFMaps [69], GeomFMaps [15], AttentiveFMaps [33], DUO-FMNet [16], SSL [10], SmS [12]. Since our and other methods can be applied to any shape class, we do not include template fitting methods such as NICP [42], which typically focus on human scans and incorporate explicit human body priors.", + "bbox": [ + 89, + 391, + 482, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To compare both categories of baselines fairly, we note that SCAPE is too small to train large models. On the other hand, FAUST was created with SMPL [37] like SURREAL, and includes a sufficient diversity of body types and poses. Therefore, we follow [10, 11, 69] and train large models on SURREAL, descriptor-based models on FAUST, and evaluate them on three test datasets. A comparison with the baselines trained on FAUST+SCAPE can be found in Supp. C.2.", + "bbox": [ + 89, + 573, + 482, + 694 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. We report the mean geodesic error of our model and the baselines in Table 1. Compared to other large-scale methods trained on SURREAL, our work generalizes well to meshes from SCAPE and SHREC'19. A common problem in large-scale baselines is predicted point maps with incorrect symmetry. This is caused by the fact that the geometry of the evaluation meshes has fewer fine-scale details such as fingers, which help to disambiguate the internal symmetry. Our work avoids overfitting to fine-scale details of SURREAL by using data augmentation (Sec. 5.1). As a result, we can utilize large amounts of data more effectively.", + "bbox": [ + 89, + 703, + 482, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared to descriptor-based methods, our results are on par on all datasets (especially SHREC'19), demonstrat", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ec5c7e1b984ad0955ff3146e95e5b04728d5fae73c349d016101ecd2de806064.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelCategoryF_rS_rS’19_r
3D-CODEDLarge-2.516.117.3
TransMatchScale1.715.321.0
DUO-FMNet2.54.26.4
GeomFMaps1.92.47.9
AttentiveFMaps1.92.65.8
ConsistentFMapsDescriptor-2.32.63.8
SSLBased2.03.14.0
DiffZO1.92.44.2
ULRSSM1.62.25.7
SmS1.43.36.2
Ours - 64×641.82.33.5
Ours - 96×961.72.13.9
", + "bbox": [ + 532, + 87, + 890, + 273 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Mean geodesic errors $(\\times 100)$ on the remeshed FAUST, SCAPE, and SHREC'19 datasets. The best results are highlighted. Large-scale methods are trained on SURREAL, and descriptor-based methods on FAUST. Here and in the following, the results of our model are averaged across 5 runs.", + "bbox": [ + 511, + 282, + 903, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ab7467989956d412eb654a556da4be94f761993c744f635626c8106c37feed95.jpg", + "image_caption": [ + "Figure 3. Qualitative results by our approach on SHREC'19 (top) and DT4D (bottom) datasets; see also Supp. C.1." + ], + "image_footnote": [], + "bbox": [ + 516, + 369, + 906, + 539 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing our excellent performance on diverse shape classes. We can see that most descriptor-based methods can generalize to non-SMPL meshes, but none of them show competitive performance on all three datasets simultaneously.", + "bbox": [ + 511, + 604, + 903, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the qualitative results of our model on several challenging meshes from SHREC'19 in Fig. 3. Even though these shapes include high-frequency details such as muscles, in contrast to the smooth shapes typically generated by SMPL, our model is able to obtain correct correspondences.", + "bbox": [ + 511, + 667, + 905, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Matching with Anisotropic Meshing", + "text_level": 1, + "bbox": [ + 511, + 756, + 826, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets. To evaluate the robustness of our method to different connectivity, we use the anisotropically remeshed versions of FAUST and SCAPE [16], denoted F_a and S_a, respectively. In these datasets, the triangle scale is uneven, ranging from small and densely packed triangles on one side of the mesh to large and coarse triangulation on the other. As a result, models that are sensitive to mesh connectivity will likely fail to predict the correct maps.", + "bbox": [ + 511, + 779, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "26905", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b24cffbc698cb31d5feb047e8f2ed41062215614a20f10c5ca1074f0c2e3675e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelCategoryF_aS_a
3D-CODEDLarge2.916.9
TransMatchScale2.716.2
DUO-FMNet3.04.4
GeomFMapsDescriptor3.23.8
AttentiveFMapsBased2.42.8
ConsistentFMaps2.62.7
ULRSSM1.92.4
Ours - 64×642.12.3
Ours - 96×962.02.2
", + "bbox": [ + 140, + 88, + 433, + 231 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/83f30f3e682ce8047afe0a811e4f74d1ec009e92735802750bf10f6a1af98f0c.jpg", + "table_caption": [ + "Table 2. Results on the anisotropic FAUST and SCAPE." + ], + "table_footnote": [], + "table_body": "
ClassIntraInter
Ours[11][69]Ours[11][69]
manneq.1.01.01.63.34.04.5
zlorp1.11.32.14.26.94.2
crypto1.11.52.4---
prisoner1.11.12.129.620.526.7
ninja1.45.62.24.316.27.1
ortiz9.34.42.5---
mousey10.22.75.2---
drake10.61.02.110.48.24.5
skeletonz.16.31.41.449.436.548.0
", + "bbox": [ + 106, + 270, + 467, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results. Table 2 shows the matching results. Both large-scale and descriptor-based methods experience performance drops on anisotropically remeshed datasets. In contrast, our method is more robust to changes in mesh connectivity. We attribute this to our design choices, such as diversifying the vertex structure of the training data and using conditioning that is independent of the number of vertices.", + "bbox": [ + 89, + 498, + 483, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Zero-Shot Shape Matching", + "text_level": 1, + "bbox": [ + 89, + 613, + 334, + 630 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Datasets. Generalization to shape types not observed during training is a desirable property in many shape matching applications. To evaluate our model on unseen data, we use the non-isometric DT4D dataset [40] that consists of nine humanoid shape classes. While typically, 198 shapes are defined for training and 95 for testing, we instead make the evaluation more challenging by training on human datasets, SURREAL or FAUST. This can be viewed as a zero-shot setting, since most of the test shapes are different from the training data (see Supp. C.1 for an illustration).", + "bbox": [ + 89, + 635, + 483, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results. Our proposed experimental setup is challenging due to the differences between the training and test shapes. We use a lower-resolution model predicting a $32 \\times 32$ functional map, results of all our models are shown in Supp. C.5. We compare our method with recent descriptor-based approaches: ConsistentFMaps [69] and ULRSSM [11].", + "bbox": [ + 89, + 794, + 482, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The mean geodesic errors per class for inter- and intra", + "bbox": [ + 109, + 886, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c02b7320a2b03afe74322ed08c312e861328770ee0e02a9204f750c23bbae47c.jpg", + "table_caption": [ + "Table 3. Results on shape classes from DT4D. Classes mousey and ortiz are not present in inter-class split. All inter-class evaluation pairs have the format \"crypto vs other class\", so crypto is excluded." + ], + "table_footnote": [], + "table_body": "
ClassOurs[11][69]
wolf3.53.54.4
dog3.53.54.5
horse3.73.84.4
cow3.83.84.4
lion4.03.84.9
fox4.73.64.9
hippo7.69.97.9
mean4.34.34.8
", + "bbox": [ + 524, + 88, + 722, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1c3fb53794170792745041786366ccb6398ee75f3b5805c62c650d87615d1102.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 728, + 89, + 885, + 210 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Results on the SMAL dataset [16], all categories are present in train/test sets. Format: category vs. everything.", + "bbox": [ + 511, + 227, + 905, + 257 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "category splits are shown in Table 3, with further comparisons in Supp. C.7. Our method achieves accurate matching for most shape classes in both splits, demonstrating the generalization of our method to data unseen during training. We show the qualitative examples in Fig. 3.", + "bbox": [ + 511, + 275, + 905, + 351 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Application to Animal Shapes", + "text_level": 1, + "bbox": [ + 511, + 361, + 777, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Datasets. To demonstrate the applicability of our method to shape classes other than humans, we test our approach on the SMAL dataset containing seven animal types. We take the 32/17 split from [16], where all categories are present in train/test sets. While the original training set is sufficient for descriptor-based baselines, it is too small for our model. To address this, we use the fitted parameters of the SMAL parametric model [77] and randomly vary the pose of each training animal, generating a total of 64,000 meshes. We use the mean SMAL shape as a template. Note that this generated dataset conveys little new information, since e.g., there are only three different types of lions.", + "bbox": [ + 511, + 383, + 906, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results. Table 4 shows the results of our $64 \\times 64$ model. Although the training data for our method lacks sufficient diversity, we achieve comparable performance to the baselines. Therefore, given enough training data, we believe our method can be applied to any shape class.", + "bbox": [ + 511, + 574, + 905, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 662, + 633, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented DenoisFM, an approach of a new class for shape correspondence estimation. Our model is trained on a large dataset of synthetic human meshes and predicts the functional map between a pair of shapes using a denoising diffusion model. DenoisFM achieves correspondence accuracy on par with state-of-the-art methods across multiple datasets. The key advantage of our work is its generalization ability to human and humanoid shapes that differ noticeably from the training data, as well as competitive performance on animal shapes. Therefore, DenoisFM bridges the gap between previous large-scale and descriptor-based approaches by efficiently leveraging large amounts of data, opening up a new direction for using diffusion models in shape correspondence estimation.", + "bbox": [ + 511, + 689, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "26906", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ZL acknowledges the support of the DFG Sachbeihilfe grant LA 5191/2-1.", + "bbox": [ + 89, + 116, + 483, + 147 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 164, + 187, + 181 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ahmed Abdelreheem, Abdelrahman Eldesokey, Maks Ovsjanikov, and Peter Wonka. 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What are diffusion models? lilian-weng.github.io, 2021. 6", + "[76] Yiming Zeng, Yue Qian, Zhiyu Zhu, Junhui Hou, Hui Yuan, and Ying He. Corrnet3d: Unsupervised end-to-end learning of dense correspondence for 3d point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6052-6061, 2021. 2", + "[77] Silvia Zuffi, Angjoo Kanazawa, David W Jacobs, and Michael J Black. 3d menagerie: Modeling the 3d shape and pose of animals. In Computer Vision and Pattern Recognition (CVPR), pages 6365-6373, 2017. 8" + ], + "bbox": [ + 514, + 90, + 903, + 515 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "26909", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Denoising Functional Maps_ Diffusion Models for Shape Correspondence/2c4c8aae-c014-423b-a2aa-0d67eb2103ed_model.json b/2025/Denoising Functional Maps_ Diffusion Models for Shape Correspondence/2c4c8aae-c014-423b-a2aa-0d67eb2103ed_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ada8b1ce28bd4a063b3c584a77a08cc38fec9245 --- /dev/null +++ b/2025/Denoising Functional Maps_ Diffusion Models for Shape Correspondence/2c4c8aae-c014-423b-a2aa-0d67eb2103ed_model.json @@ -0,0 +1,2730 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.129, + 0.131, + 0.87, + 0.154 + ], + "angle": 0, + "content": "Denoising Functional Maps: Diffusion Models for Shape Correspondence" + }, + { + "type": "text", + "bbox": [ + 0.234, + 0.18, + 0.388, + 0.198 + ], + "angle": 0, + "content": "Aleksei Zhuravlev" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.199, + 0.384, + 0.217 + ], + "angle": 0, + "content": "1University of Bonn" + }, + { + "type": "text", + "bbox": [ + 0.429, + 0.18, + 0.56, + 0.198 + ], + "angle": 0, + "content": "Zorah Lähner1, 2" + }, + { + "type": "text", + "bbox": [ + 0.412, + 0.199, + 0.55, + 0.216 + ], + "angle": 0, + "content": "\\(^{2}\\)Lamarr Institute" + }, + { + "type": "text", + "bbox": [ + 0.601, + 0.181, + 0.764, + 0.199 + ], + "angle": 0, + "content": "Vladislav Golyanik3" + }, + { + "type": "text", + "bbox": [ + 0.578, + 0.199, + 0.788, + 0.216 + ], + "angle": 0, + "content": "\\(^{3}\\)MPI for Informatics, SIC" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.24, + 0.565, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.355, + 0.26, + 0.368 + ], + "angle": 0, + "content": "+Challenging Human Shapes" + }, + { + "type": "image_caption", + "bbox": [ + 0.271, + 0.354, + 0.41, + 0.367 + ], + "angle": 0, + "content": "+ Zero-Shot on Humanoids" + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.245, + 0.565, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.445, + 0.356, + 0.533, + 0.368 + ], + "angle": 0, + "content": "+ Animal Shapes" + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.258, + 0.87, + 0.272 + ], + "angle": 0, + "content": "Predict Functional Maps using DDPMs" + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.281, + 0.886, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.589, + 0.343, + 0.684, + 0.354 + ], + "angle": 0, + "content": "Gaussian Noise \\(x_{T}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.692, + 0.344, + 0.787, + 0.354 + ], + "angle": 0, + "content": "\\(x_{t - 1}\\coloneqq \\mathbf{DDPM}(x_t;y)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.804, + 0.343, + 0.887, + 0.354 + ], + "angle": 0, + "content": "Functional Map" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.381, + 0.907, + 0.424 + ], + "angle": 0, + "content": "Figure 1. We propose DenoisFM, a novel method for predicting shape correspondences in the form of functional maps using denoising diffusion models. (Left:) Challenging examples our method can handle, with color-coded correspondences. (Right:) By sequentially denoising samples of random noise, the diffusion model can predict the correct functional map between a pair of shapes." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.434, + 0.326, + 0.449 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.472, + 0.485, + 0.818 + ], + "angle": 0, + "content": "Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape deformation methods. See our project page1 for the source code2 and the datasets." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.434, + 0.645, + 0.449 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.461, + 0.907, + 0.702 + ], + "angle": 0, + "content": "A long-standing problem in computer graphics and vision is to find corresponding points in a pair of 3D shapes [9, 11, 19, 42, 49, 64, 69]. The point map can then be used for texture [14], segmentation [63] and deformation transfer [68], statistical shape analysis [13], and construction of parametric models [37, 55]. A popular approach to solving the correspondence problem involves the functional map framework [49], which represents the correspondence as a small matrix that maps between the eigenfunctions of the Laplace operator on each shape. This representation is compact and allows to regularize constraints on the correspondences, such as bijectivity or area preservation. The functional map framework has been extended in numerous works, such as matching shapes with partiality [4, 58], analyzing the properties of shape collections [13] or improving accuracy through iterative refinement [19, 44, 57]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.909, + 0.87 + ], + "angle": 0, + "content": "Previous functional map approaches focused on using small datasets, rarely exceeding a hundred unique shapes. This favored training models with lightweight architectures that could learn as much as possible with limited data, but these methods may face challenges with generalization to broad shape categories. To develop a unified model that is applicable to various tasks, we draw attention to denoising diffusion models [25, 66, 67], which have impressive generalization ability when trained on large amounts of data. In our work, we apply this approach to correspondence estimation using functional maps." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.908, + 0.901 + ], + "angle": 0, + "content": "Based on the idea of sequentially denoising samples of random noise into samples from the data distribution, dif-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.85, + 0.483, + 0.876 + ], + "angle": 0, + "content": "1Project page: https://alekseizhuravlev.github.io/ denoising-functional-maps/" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.876, + 0.482, + 0.901 + ], + "angle": 0, + "content": "Source code: https://github.com/alekseizhuravlev/ denoising-functional-maps/" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.85, + 0.483, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26899" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.332 + ], + "angle": 0, + "content": "fusion models have achieved unprecedented performance in high-fidelity, diverse, and controllable image synthesis [53]. The scalable U-Net architecture [60] allows them to be trained on large datasets with hundreds of thousands of high-resolution images. The application of diffusion models to shape matching has been limited so far, mainly focusing on feature extraction from pre-trained foundational models [1, 17]. Interestingly, functional maps appear well-suited to bridge diffusion models and shape correspondence. They are small-sized single-channel matrices, making standard architectures developed for images readily applicable to them. Large amounts of shape data for training are then available through parametric models such as SMPL [37], an approach that has already been used for matching tasks [23, 72] and is also suitable for diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.335, + 0.482, + 0.532 + ], + "angle": 0, + "content": "In this work, we present Denoising Functional Maps (DenoisFM), an approach to directly predict the functional map between shapes using a denoising diffusion model; see Fig. 1 for the overview. For training, we create a large dataset of functional maps between \\(2.3 \\cdot 10^{5}\\) human shapes from the SURREAL dataset [73] and a template shape. Using template-wise maps instead of pair-wise ones allows to reduce the complexity of training and inference. The conditioning information is inferred directly from the geometric shape structure. Additionally, we propose to exploit the probabilistic nature of diffusion models by predicting several initial maps instead of a single one, and selecting the best map based on the Dirichlet energy [52]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.534, + 0.482, + 0.685 + ], + "angle": 0, + "content": "An important property of functional maps is that they are defined in the basis of the first \\( n \\) eigenvectors of the Laplacian operator for each shape. The basis is not unique due to the sign ambiguity of the eigenvectors, and there are potentially \\( 2^{n} \\) possible basis combinations for each shape. To address this problem, we propose an unsupervised approach which selects the signs of the basis vectors using per-vertex features extracted in an unsupervised way (Sec. 3.2). This reduces the number of possible functional maps between shapes, further lowering the training complexity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.686, + 0.483, + 0.716 + ], + "angle": 0, + "content": "Contributions. Overall, the technical contributions of this paper can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.718, + 0.483, + 0.763 + ], + "angle": 0, + "content": "- DenoisFM, a fundamentally new approach to shape correspondence estimation based on predicting functional maps using denoising diffusion models;" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.763, + 0.483, + 0.809 + ], + "angle": 0, + "content": "- An unsupervised method to address the sign ambiguity of eigenvectors of the Laplacian, which reduces the complexity of the prediction problem." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.718, + 0.483, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Our model performs on par with existing shape matching methods on human benchmark datasets, achieves generalization to non-isometric humanoid shapes without learning on them, and is also applicable to animal shapes. See our project page1 for the source code2 and the datasets of functional maps used to train our models." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.655, + 0.105 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.116, + 0.905, + 0.252 + ], + "angle": 0, + "content": "Shape Correspondence Estimation. Learning-based shape correspondence methods can be roughly divided into two categories: first, approaches that predict pointwise descriptors suitable for computing functional maps [49, 50], a low-rank representation of the point-wise correspondence in Laplace-Beltrami eigenbasis; second, deformation-based methods that directly align input shapes and typically require much larger training datasets than descriptor-based methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.253, + 0.905, + 0.465 + ], + "angle": 0, + "content": "In the standard functional map pipeline, point-wise descriptor functions that encode the surface geometry are first computed on each shape [5, 9, 71], and then the functional map is estimated using the descriptors in a least-squares optimization. With the advent of deep learning, network architectures were introduced to learn descriptor functions directly from the data [35, 65]. While the initial methods were supervised [15, 35], recent works estimate the descriptors in an unsupervised manner [11, 62]. Most shape matching datasets consist of fewer than a hundred unique meshes and focus on a specific category of shapes [3, 7, 40, 43]. Therefore, the most effective descriptor-based models use lightweight architectures to infer as much geometric information as possible from limited training data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.905, + 0.632 + ], + "angle": 0, + "content": "Another group of works use large-scale datasets of synthetic data for training. 3D-CODED [23] is an encoder-decoder architecture that predicts the correspondence by learning a surface parameterization and attempts to estimate the deformation from the template shape to the test one. Transmatch [72] is a transformer-based model that uses an attention mechanism to learn the underlying structure of the geometry. Other works utilizing large amounts of data [10, 31, 76] mainly focus on point cloud registration, and a group of works learn the shape deformation using data-efficient architectures [20, 70]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.633, + 0.905, + 0.678 + ], + "angle": 0, + "content": "We combine the advantages of both categories of models by training a large-scale method based on functional maps that leverages the power of denoising diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Denoising Diffusion Models. Diffusion models have become popular in many areas of visual computing; see the recent survey for details [53]. Several diffusion-based generative models have been proposed [66, 67], and the simplified learning process of denoising diffusion probabilistic models (DDPMs) enabled the image synthesis at unprecedented quality [25]. Various conditioning mechanisms such as class labels, textual descriptions, or segmentation maps have been used to guide the diffusion process [59]. While diffusion models quickly found applications in areas beyond imaging such as video [26, 27] and 3D content generation [36, 54], their application to shape correspondence estimation has been limited so far to extracting descriptors from images of meshes [17] or segmentation maps [1] gen" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26900" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.138 + ], + "angle": 0, + "content": "erated by foundational models. Our work is the first to use DDPMs to directly predict the functional maps between pairs of shapes to obtain the correspondences." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.147, + 0.483, + 0.252 + ], + "angle": 0, + "content": "Sign Ambiguity of Laplacian Eigenvectors. Since for any eigenvector \\(\\phi_i\\), its negative version \\(-\\phi_i\\) is also an eigenvector, the Laplace-Beltrami eigenbasis has an inherent sign ambiguity. Additionally, the eigenvalues can have higher multiplicity and make the intrinsic ordering non-unique. This symmetry needs to be taken into account when processing the eigenvectors [8, 48, 63]." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.253, + 0.483, + 0.418 + ], + "angle": 0, + "content": "In graph learning, Laplacian eigenvectors are used to encode information about the structure of a graph [6, 32], and several methods were proposed to address the sign ambiguity. Laplacian Canonization [38] proposes to find the coordinate axis on which the projection of the eigenvector has the largest angle and fixes the projection to be positive. SAN [30] obtains sign-invariant operators using absolute subtraction and product between a pair of nodes, this only considers the relative sign between queries. SignNet [34] learns a sign-invariant embedding and Dwivedi et al. [18] learns on all possible sign combinations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.419, + 0.483, + 0.601 + ], + "angle": 0, + "content": "The methods described above are designed for graphs with a small number of vertices. For point clouds, Linearly Invariant Embedding [41] considered the problem of learning the basis functions directly from the input data. However, the majority of works on 3D shapes employ the sign-equivariant approach, where a sign-dependent functional map is computed from descriptor functions in a precomputed Laplace-Beltrami eigenbasis. In our work, we propose to address the sign ambiguity problem using a learning-based method that assigns a specific combination of signs to the eigenvectors of any human shape, which is learned directly from the data in an unsupervised way." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.616, + 0.22, + 0.633 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.641, + 0.483, + 0.732 + ], + "angle": 0, + "content": "Notation. Given a shape \\( S \\) represented as a triangular mesh with \\( v \\) vertices, we compute its Laplace matrix \\( L \\) [45] and the first \\( n \\) eigenvectors of \\( L \\) corresponding to the eigenvalues \\( \\lambda_1 \\leqslant \\ldots \\leqslant \\lambda_n \\). \\( A \\) is the diagonal vertex-area matrix associated with \\( L \\), computed by assigning one-third of the total area of all faces incident to the corresponding vertex." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.733, + 0.483, + 0.839 + ], + "angle": 0, + "content": "We denote matrices of \\( n \\) functions on the vertices of \\( S \\) by uppercase letters: \\( \\Phi \\in \\mathbb{R}^{v \\times n} \\) for the matrix of eigenvectors, \\( \\Sigma \\in \\mathbb{R}^{v \\times n} \\) for the matrix of learned features. The individual eigenvectors and feature vectors are denoted by lowercase letters: \\( \\phi_i \\in \\mathbb{R}^v \\) for the \\( i \\)-th eigenvector, \\( s_i \\in \\mathbb{R}^v \\) for the \\( i \\)-th feature vector. Finally, \\( \\sigma \\in \\{-1, 1\\}^n \\) represents a vector consisting of \\( n \\) signs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.258, + 0.865 + ], + "angle": 0, + "content": "3.1. Functional Maps" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Our method is built upon the framework of functional maps [49, 50]. Consider the point-wise map \\(\\Pi_{21} \\in \\{0,1\\}^{v_2 \\times v_1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.152 + ], + "angle": 0, + "content": "between two meshes \\( S_{1} \\) and \\( S_{2} \\). The point-wise map is a permutation matrix, and due to its large size, it cannot be processed efficiently. The functional map \\( C_{12} \\in \\mathbb{R}^{n \\times n} \\) is the spectral representation of \\( \\Pi_{21} \\), which is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.649, + 0.166, + 0.907, + 0.183 + ], + "angle": 0, + "content": "\\[\nC _ {1 2} = \\Phi_ {2} ^ {\\dagger} \\Pi_ {2 1} \\Phi_ {1}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.188, + 0.906, + 0.234 + ], + "angle": 0, + "content": "where “\\(\\dagger\\)” denotes the pseudo-inverse. The functional map efficiently encodes the point-wise map in a low-dimensional representation, since \\(n \\ll v_1, v_2\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.235, + 0.906, + 0.295 + ], + "angle": 0, + "content": "In a standard pipeline, learned or handcrafted \\(p\\)-dimensional descriptor functions are computed on each shape, \\(F_{1} \\in \\mathbb{R}^{v_{1} \\times p}\\), \\(F_{2} \\in \\mathbb{R}^{v_{2} \\times p}\\). The functional map is then obtained by solving the linear system [50]:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.305, + 0.906, + 0.337 + ], + "angle": 0, + "content": "\\[\nC _ {1 2} = \\underset {C} {\\arg \\min } \\left\\| C \\Phi_ {1} ^ {\\dagger} F _ {1} - \\Phi_ {2} ^ {\\dagger} F _ {2} \\right\\| _ {2} ^ {2}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.341, + 0.906, + 0.387 + ], + "angle": 0, + "content": "which is usually further regularized [15, 47]. The pointwise map can be recovered from the functional map and the eigenvectors using nearest neighbor search [49, 51]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.395, + 0.671, + 0.412 + ], + "angle": 0, + "content": "3.2. Sign Ambiguity" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.417, + 0.906, + 0.508 + ], + "angle": 0, + "content": "The functional map is defined in a basis spanned by the eigenvectors of the Laplacian on each shape, as can be seen from Eq. (1). However, this basis is not unique since for each eigenvector \\(\\phi_i\\), \\(-\\phi_i\\) is also a valid eigenvector corresponding to the same eigenvalue \\(\\lambda_i\\). Due to sign ambiguity, there are \\(2^n\\) possible basis combinations on each shape." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.508, + 0.906, + 0.689 + ], + "angle": 0, + "content": "The eigenvectors returned by a numerical eigensolver will have a random sign combination, and mathematically it is impossible to select some specific sign of eigenvectors. However, several works demonstrate that the choice of the sign can be determined by the underlying data using the projection operator [8, 34, 38]. An intuitive example arises in the principal component analysis: Each eigenvector should point in the same direction as the points it is representing. This can be achieved by projecting the singular vector onto the data vectors and changing its sign to make the projection positive. This approach allows to select a canonical direction for the first few eigenvectors." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.81 + ], + "angle": 0, + "content": "Sign ambiguity is a special case of basis ambiguity when all eigenvalues are distinct. The more general basis ambiguity occurs if an eigenvalue \\(\\lambda_{i}\\) has multiplicity degree \\(d_{i} > 1\\). Then any \\(d_{i}\\) vectors forming an orthogonal basis in the subspace spanned by its eigenvectors \\((\\phi_{i + 1},\\phi_{i + 2}\\dots \\phi_{i + d_i})\\) are also valid eigenvectors. Although the basis ambiguity is difficult to deal with, in practice high multiplicities do not occur often in low-order eigenvectors [29, 50]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.818, + 0.763, + 0.835 + ], + "angle": 0, + "content": "3.3. Denoising Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Given a dataset of examples drawn independently from a data distribution \\( q(x) \\), diffusion models aim to learn the underlying data distribution by sequentially denoising random noise samples [25, 53, 66]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26901" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.325 + ], + "angle": 0, + "content": "The forward diffusion process takes a real data point \\( x_0 \\) and incrementally adds to it a small amount of Gaussian noise, producing a sequence of \\( T \\) noisy samples \\( x_1, \\ldots, x_T \\). The step sizes are controlled by a variance schedule \\( \\{\\beta_t \\in (0, 1)\\}_{t=1}^T \\). With the larger steps \\( t \\), the noisy sample \\( x_t \\) further deviates from the original sample. At \\( T \\to \\infty \\), it is close to the Gaussian distribution, \\( x_T \\sim N(x_T; 0, I) \\). The reverse process recreates the original sample by iteratively removing noise from an input \\( x_T \\) drawn from the Gaussian distribution. Assuming that the reverse conditional probability is conditioned on \\( x_0 \\), \\( q(x_{t-1} \\mid x_t, x_0) = N\\left(x_{t-1}; \\tilde{\\mu}(x_t, x_0), \\tilde{\\beta}_t I\\right) \\), we can obtain \\( \\tilde{\\mu}_t = \\frac{1}{\\sqrt{\\alpha_t}}\\left(x_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\tilde{\\alpha}_t}}\\epsilon_t\\right) \\), where \\( \\alpha_t = 1 - \\beta_t \\) and \\( \\bar{\\alpha}_t = \\prod_{i=1}^T \\alpha_i \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.329, + 0.484, + 0.416 + ], + "angle": 0, + "content": "Instead of directly predicting the denoised sample \\(\\tilde{\\mu}_t\\) with a neural network, we can predict the noise content \\(\\epsilon_{\\theta}(x_t,t)\\) from the input \\(x_{t}\\) at time step \\(t\\) [25]. Such a model is trained with a denoising score-matching objective: \\(\\mathcal{L}_t = E_{t\\sim [1,T],x_0,\\epsilon_t}\\left[\\| \\epsilon_t - \\epsilon_\\theta (x_t,t)\\| ^2\\right]\\)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.446, + 0.345, + 0.465 + ], + "angle": 0, + "content": "4. Denoising Functional Maps" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.479, + 0.484, + 0.678 + ], + "angle": 0, + "content": "This section introduces Denoising Functional Maps (DenoisFM), our approach for shape correspondence estimation; see Fig. 2 for the method overview. Since functional maps are square low-dimensional matrices (see Sec. 3.1), we use a standard neural architecture based on a 2D U-Net [61] as a backbone. We aim to train our model on a large collection of shapes with diverse geometry. Since functional maps are defined for shape pairs, for a dataset with \\( m \\) shapes the model would have to learn \\( m^2 \\) functional maps. Instead of this naive approach, we consider the correspondences to a single template shape, following previous works [23, 72]. As a result, the training data includes only \\( m \\) functional maps, one for each shape in the dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.682, + 0.484, + 0.82 + ], + "angle": 0, + "content": "A functional map is defined in a specific basis of Laplacian eigenvectors, and knowing the exact basis combination is necessary to convert it to a point-wise correspondence map. Therefore, we compute the basis first and then condition the diffusion model on it; the model then returns the corresponding functional map. To reduce the complexity of the problem caused by the sign ambiguity of basis eigenvectors, we utilize a sign correction network to select a specific combination of signs for the basis." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "DenoisFM consists of two components: the DDPM for functional map prediction (Sec. 4.1) with post-processing that filters out low-quality solutions using Dirichlet energy of the point-wise map (Sec. 4.1.1), and the sign corrector for the Laplacian eigenvectors (Sec. 4.2)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.798, + 0.108 + ], + "angle": 0, + "content": "4.1. Denoising Diffusion Component" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.117, + 0.907, + 0.322 + ], + "angle": 0, + "content": "We next describe the training and inference of the diffusion component of DenoisFM. For training, we use a large collection of shapes and a template. For each shape \\(S\\) in the dataset, we compute an eigenbasis \\(\\Phi\\), a template-wise functional map \\(C_{1T}\\), and conditioning \\(y = y(S,\\Phi)\\) which incorporates geometric details of the input shape and information about the basis. The exact form of conditioning will be specified in Sec. 4.3. We use the training objective of denoising diffusion probabilistic models (DDPMs) [25]: \\(\\mathcal{L}_{\\mathrm{DDPM}} = E_{x,\\epsilon \\sim N(0,1),t}\\left[\\| \\epsilon -\\epsilon_{\\theta}(x_t,t,y)\\| _2^2\\right]\\), where \\(\\epsilon_{\\theta}\\) is the amount of noise predicted by a 2D UNet [60], \\(x_{t}\\) is a noisy version of the input \\(x_0\\coloneqq C_{1T}\\), and \\(t\\) is the time step uniformly sampled from \\(\\{1,\\ldots ,T\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.324, + 0.907, + 0.476 + ], + "angle": 0, + "content": "The inference pipeline consists of two stages, see Fig. 2a. In the template stage, for each individual shape \\( S \\) in the evaluation dataset, we obtain an eigenbasis \\( \\Phi \\), calculate the conditioning \\( y \\), and predict the template-wise functional map \\( C_{1T} \\) using the diffusion model. Note that the inference of DDPMs is time-consuming due to the large number of denoising steps and can take several hours for high-dimensional functional maps. Because the predicted maps refer to the template, we need to run the denoising process only once for each shape." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.48, + 0.909, + 0.618 + ], + "angle": 0, + "content": "In the pairwise stage, for each test pair, we convert the respective template-wise functional maps into pairwise ones using the composition property [49]: \\( C_{12} = C_{1T}(C_{2T})^{-1} \\). We then apply the Zoomout refinement [44] to increase the resolution of the functional maps. This spectral upsampling step has been shown to improve their accuracy, and our framework benefits from it without additional modifications. Finally, the functional map is converted into a pointwise map \\( \\Pi_{21} \\) using nearest neighbor search." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.637, + 0.776, + 0.652 + ], + "angle": 0, + "content": "4.1.1. Post-Processing of the Samples" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.659, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Diffusion models are inherently probabilistic and their outputs may differ given the same conditioning but different initial noise [25]. To address this, we repeat the denoising process multiple times and filter out the low-quality results. The selection is based on the Dirichlet energy of the pointwise map [21, 40]: an accurate map should be smooth, with neighboring vertices on one shape matching neighboring vertices on the other. Therefore, we repeat both the template step and the pairwise step to produce multiple point-wise maps. We can then either report the map with the lowest Dirichlet energy or combine the results of several smoothest maps. To do this, for each query point on the source mesh, we gather potential matching points on the target mesh and select the one with the smallest total distance to the other candidates (see Supp. B.3). The map selection step has a major impact on the accuracy of our method." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26902" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.09, + 0.885, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.276, + 0.907, + 0.327 + ], + "angle": 0, + "content": "(a) Functional map prediction using a diffusion model. For each unique shape \\(S\\) in the dataset, we obtain feature vectors \\(\\Sigma\\) using a feature extractor \\(\\Theta\\), as well as a sign-corrected eigenbasis \\(\\hat{\\Phi}\\) (Fig. 2b, Sec. 4.2). Both are used for conditional prediction of the template-wise functional map \\(C_{1T}\\) using a diffusion model, performed separately for each shape. The pairwise functional maps \\(C_{12}\\) are obtained through the map composition property, upsampled using ZoomOut [44], and converted to pointwise maps \\(\\Pi_{21}\\)." + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.336, + 0.825, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.473, + 0.908, + 0.524 + ], + "angle": 0, + "content": "(b) Learned sign correction. The eigenvectors \\(\\Phi\\) returned by a numerical eigensolver have random signs. To select a specific sign, we project the eigenvectors onto the feature vectors \\(\\Sigma\\) obtained with a feature extractor \\(\\Theta\\), and make the projection positive. The sign correction network is trained in an unsupervised manner: learning to correct eigenvectors that have random signs. The learned features \\(\\Sigma\\) are also used for the conditional prediction of the template-wise functional map using a diffusion model (Fig. 2a)." + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.534, + 0.908, + 0.562 + ], + "angle": 0, + "content": "Figure 2. Overview of DenoisFM. (a) A pair of shapes is matched using a DDPM model. (b) The signs of eigenvectors are corrected through learned features." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.588, + 0.32, + 0.604 + ], + "angle": 0, + "content": "4.2. Learned Sign Correction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.61, + 0.484, + 0.701 + ], + "angle": 0, + "content": "The diffusion model needs to be conditioned on the basis eigenvectors and predict the functional map for that particular basis. Theoretically, the model could be trained using random basis combinations, as was done in Dwivedi et al. [18] for graph networks. However, this would significantly increase the amount of training data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.702, + 0.484, + 0.853 + ], + "angle": 0, + "content": "Hence, we follow a more effective approach: we select a specific basis by fixing the sign of the Laplacian eigenvectors on each shape. Previous works infer the sign from the underlying data using the projection operator (see Sec. 3.2). Therefore, suppose that \\(\\Sigma \\coloneqq \\Theta(S) \\in \\mathbb{R}^{v \\times n}\\) is a set of pervertex feature vectors inferred from the geometry of shape \\(S\\) by a trainable feature extractor \\(\\Theta\\), one for each eigenvector. The sign of the eigenvectors can be selected by projecting the features \\(\\Sigma\\) onto the eigenvectors \\(\\Phi\\) and making the corresponding projections positive:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.864, + 0.483, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\sigma} := \\operatorname {s i g n} \\left[ \\operatorname {d i a g} \\left(\\Sigma^ {T} A \\Phi\\right) \\right], \\tag {3} \\\\ \\hat {\\Phi} := \\Phi \\hat {\\sigma}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.589, + 0.907, + 0.695 + ], + "angle": 0, + "content": "where “\\(\\mathrm{diag}(\\cdot)\\)” and “\\(\\mathrm{sign}(\\cdot)\\)” denote matrix diagonal and sign extraction operators, \\(A\\) is the diagonal vertex-area matrix. To illustrate, suppose we have a human mesh and a single feature vector \\(\\varsigma_{i}\\), which is a binary vector with ones for points on the left hand, and zeros otherwise. After performing the procedure described in Eq. (3), the corrected eigenvector \\(\\hat{\\phi}_i\\) will be mostly positive on the left hand." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.701, + 0.757, + 0.716 + ], + "angle": 0, + "content": "4.2.1. Training the Sign Corrector" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.856 + ], + "angle": 0, + "content": "The sign correction network is trained in an unsupervised manner by learning to correct eigenvectors that have random signs. If we perform the eigendecomposition with a numerical solver twice on the same mesh and get two sets of eigenvectors \\(\\Phi_1\\) and \\(\\Phi_2\\), due to the sign ambiguity, the difference between them can be written as \\(\\Phi_2 = \\Phi_1\\sigma\\), where \\(\\sigma \\in \\{-1,1\\}^n\\) is the ground-truth sign difference. Now we perform the sign correction using Eq. (3), after which we expect the corrected eigenvectors to be equal to each other:" + }, + { + "type": "equation", + "bbox": [ + 0.676, + 0.867, + 0.905, + 0.892 + ], + "angle": 0, + "content": "\\[\n\\hat {\\Phi} _ {1} = \\hat {\\Phi} _ {2}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.889, + 0.763, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\Phi_ {1} \\hat {\\sigma} _ {1} = \\Phi_ {2} \\hat {\\sigma} _ {2},\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26903" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.123 + ], + "angle": 0, + "content": "where \\(\\hat{\\sigma}_1, \\hat{\\sigma}_2 \\in \\{-1, 1\\}^n\\) are the predicted combinations of correction signs. After substitution and using \\(\\hat{\\sigma}_1 \\hat{\\sigma}_1 = I\\):" + }, + { + "type": "equation", + "bbox": [ + 0.226, + 0.137, + 0.348, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\Phi_ {1} \\hat {\\sigma} _ {1} = \\Phi_ {1} \\sigma \\hat {\\sigma} _ {2},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.25, + 0.157, + 0.482, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {1} = \\sigma \\hat {\\sigma} _ {2}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.229, + 0.176, + 0.306, + 0.19 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {1} \\hat {\\sigma} _ {2} = \\sigma .\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.207, + 0.485, + 0.267 + ], + "angle": 0, + "content": "As a result, the difference between the predicted correction signs should be the same as the ground-truth sign difference, and we can use this as our unsupervised training objective with a mean square error function:" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.288, + 0.484, + 0.304 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s i g n}} = \\operatorname {M S E} (\\hat {\\sigma} _ {1} \\hat {\\sigma} _ {2}; \\sigma) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.317, + 0.484, + 0.452 + ], + "angle": 0, + "content": "Note that the sign operator in Eq. (3) is not differentiable. Therefore, during training, we set \\(\\hat{\\sigma}_1\\) and \\(\\hat{\\sigma}_2\\) to be the diagonal elements of the projections, rather than their signs, assuming that the feature vectors and eigenvectors have unit norm. The training objective of the feature extractor (Eq. 6) then forces the elements of \\(\\hat{\\sigma}_1\\) and \\(\\hat{\\sigma}_2\\) to be as close to \\(-1\\) or \\(1\\) as possible. The absolute value can be interpreted as confidence in the predicted sign: values close to \\(\\pm 1\\) mean high confidence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.455, + 0.484, + 0.547 + ], + "angle": 0, + "content": "In practice, we found that a network trained this way quickly converges on a dataset of human or animal meshes. Our method returns the same corrected eigenbasis \\(95 - 99\\%\\) of the time for the first hundred Laplacian eigenvectors. The accuracy of the sign correction and its impact on the distribution of functional maps are discussed in Supp. A." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.56, + 0.307, + 0.575 + ], + "angle": 0, + "content": "4.3. Choice of Conditioning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.583, + 0.484, + 0.734 + ], + "angle": 0, + "content": "Conditioning of the diffusion model should include two parts: the basis information and the geometric properties of the shape. The former can be provided simply via the sign-corrected eigenvectors \\(\\hat{\\Phi}\\). They additionally represent the spectral embedding of the shape and convey the full intrinsic information. As for the latter, during the training of the sign-correction network, the useful properties will be encoded in the learned feature vectors \\(\\Sigma\\). Therefore, we propose to project the feature vectors onto the sign-corrected eigenvectors:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.748, + 0.483, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\text {C o n d i t i o n g} y = \\Sigma^ {T} A \\hat {\\Phi}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.484, + 0.901 + ], + "angle": 0, + "content": "This form of conditioning has two important properties. First, it has the same dimensions as the functional map. Therefore, we can condition the diffusion model using a simple concatenation, where the conditioning matrix is concatenated with the intermediate denoising targets and passed through the score estimator as input [25, 75]. Second, it is independent of the number of vertices, making it scalable to large meshes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.091, + 0.833, + 0.108 + ], + "angle": 0, + "content": "5. Training and Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.116, + 0.907, + 0.299 + ], + "angle": 0, + "content": "This section describes the steps for generating the training data for our model (Sec. 5.1) as well as the experimental results on several challenging datasets (Secs. 5.2-5.5). The evaluation of the sign correction network, additional comparison, implementation details, and the ablation studies can be found in Supp. A to C. Since our model is designed to be trained on large and diverse shape collections, it can be applied to multiple (reminiscent) shape classes without retraining. This reduces the need for small category-specific training sets. We focus on datasets with human-like shapes as their combined volume allows versatile comparison of our approach with the previous works." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.308, + 0.82, + 0.324 + ], + "angle": 0, + "content": "5.1. Training Data and Implementation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.331, + 0.906, + 0.392 + ], + "angle": 0, + "content": "Our model consists of two independent components: a denoising diffusion model that predicts the functional map and a sign correction network based on a per-vertex feature extractor, trained separately on their respective datasets." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.4, + 0.698, + 0.415 + ], + "angle": 0, + "content": "5.1.1. Denoising Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.419, + 0.907, + 0.677 + ], + "angle": 0, + "content": "Diffusion models require large amounts of training data with hundreds of thousands of examples. Therefore, we follow 3D-CODED [23] and use the SURREAL [73] dataset with 230,000 human meshes generated with SMPL [37]. All its meshes are smooth and have the same vertex structure. To make the connectivity more diverse, we remesh each mesh [28, 46] and randomly simplify the number of faces using Quadric Edge Collapse [22]. In \\(65\\%\\) of the cases, we simplify the entire mesh resulting in uniform connectivity. In the remaining \\(35\\%\\) of the cases, we simplify only a small subset of the mesh to add non-even connectivity to the training data. After remeshing, we correct the signs of the eigenvectors using a pre-trained sign correction network (Sec. 4.2) and compute the functional map to the template shape. We only store the functional maps and conditioning matrices to save memory requirements. The data generation takes 10 hours using parallel processing." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.677, + 0.906, + 0.783 + ], + "angle": 0, + "content": "We use the standard DDPM [25] implemented in Diffusers [74] and distributed training with Accelerate [24]. We train models that predict 32, 64, and 96-dimensional functional maps for 100 epochs on eight A40 GPUs, which takes 1, 8, and 30 hours respectively. The inference at the template stage takes 1, 7, and 27 minutes for each shape in the dataset. The pairwise stage takes 30 seconds per pair." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.791, + 0.736, + 0.806 + ], + "angle": 0, + "content": "5.1.2. Sign Correction Network" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.901 + ], + "angle": 0, + "content": "The per-vertex feature extractor of the sign correction network is based on DiffusionNet [65] (not to be confused with denoising diffusion) with six blocks and 128 WKS descriptors [5] as input. This architecture was designed for small shape matching datasets, so we used 1000 randomly selected meshes from SURREAL for training. Each" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26904" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.152 + ], + "angle": 0, + "content": "of them was randomly remeshed and simplified without adding anisotropy. The sign correction network is trained for \\(5 \\cdot 10^{4}\\) iterations, which takes one hour on a single A40 GPU; the inference takes a few seconds per shape." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.163, + 0.373, + 0.18 + ], + "angle": 0, + "content": "5.2. Near-Isometric Shape Matching" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.185, + 0.483, + 0.245 + ], + "angle": 0, + "content": "Datasets. We evaluate our method on three widely used datasets: FAUST [7], SCAPE [3] and SHREC'19 [43]. Following previous works, we use their more challenging remeshed versions [15, 56]:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.247, + 0.483, + 0.275 + ], + "angle": 0, + "content": "- The FAUST dataset contains meshes of 10 human classes in 10 poses, 100 in total. The train/test split is 80/20." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.277, + 0.482, + 0.306 + ], + "angle": 0, + "content": "- The SCAPE dataset includes 71 meshes of the same person in different poses, the last 20 are used for testing." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.307, + 0.482, + 0.381 + ], + "angle": 0, + "content": "- The SHREC'19 dataset is composed of 44 shapes with diverse body types and poses, arguably the most challenging of the three. This dataset does not have a train split and is used for testing only. Following [11], we removed shape 40 since it is the only partial non-closed shape." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.247, + 0.483, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.392, + 0.483, + 0.573 + ], + "angle": 0, + "content": "Baselines. We compare our approach with two categories of non-rigid shape correspondence methods. The first includes large-scale template-based models trained on SURREAL: 3D-CODED [23] and TransMatch [72], i.e., our main competitors as our work belongs to the same group. The second category includes descriptor-based models: ULRSSM [11], DiffZO [39], ConsistentFMaps [69], GeomFMaps [15], AttentiveFMaps [33], DUO-FMNet [16], SSL [10], SmS [12]. Since our and other methods can be applied to any shape class, we do not include template fitting methods such as NICP [42], which typically focus on human scans and incorporate explicit human body priors." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.574, + 0.483, + 0.695 + ], + "angle": 0, + "content": "To compare both categories of baselines fairly, we note that SCAPE is too small to train large models. On the other hand, FAUST was created with SMPL [37] like SURREAL, and includes a sufficient diversity of body types and poses. Therefore, we follow [10, 11, 69] and train large models on SURREAL, descriptor-based models on FAUST, and evaluate them on three test datasets. A comparison with the baselines trained on FAUST+SCAPE can be found in Supp. C.2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.483, + 0.87 + ], + "angle": 0, + "content": "Results. We report the mean geodesic error of our model and the baselines in Table 1. Compared to other large-scale methods trained on SURREAL, our work generalizes well to meshes from SCAPE and SHREC'19. A common problem in large-scale baselines is predicted point maps with incorrect symmetry. This is caused by the fact that the geometry of the evaluation meshes has fewer fine-scale details such as fingers, which help to disambiguate the internal symmetry. Our work avoids overfitting to fine-scale details of SURREAL by using data augmentation (Sec. 5.1). As a result, we can utilize large amounts of data more effectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Compared to descriptor-based methods, our results are on par on all datasets (especially SHREC'19), demonstrat" + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.088, + 0.891, + 0.274 + ], + "angle": 0, + "content": "
ModelCategoryF_rS_rS’19_r
3D-CODEDLarge-2.516.117.3
TransMatchScale1.715.321.0
DUO-FMNet2.54.26.4
GeomFMaps1.92.47.9
AttentiveFMaps1.92.65.8
ConsistentFMapsDescriptor-2.32.63.8
SSLBased2.03.14.0
DiffZO1.92.44.2
ULRSSM1.62.25.7
SmS1.43.36.2
Ours - 64×641.82.33.5
Ours - 96×961.72.13.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.284, + 0.905, + 0.354 + ], + "angle": 0, + "content": "Table 1. Mean geodesic errors \\((\\times 100)\\) on the remeshed FAUST, SCAPE, and SHREC'19 datasets. The best results are highlighted. Large-scale methods are trained on SURREAL, and descriptor-based methods on FAUST. Here and in the following, the results of our model are averaged across 5 runs." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.371, + 0.907, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.556, + 0.907, + 0.585 + ], + "angle": 0, + "content": "Figure 3. Qualitative results by our approach on SHREC'19 (top) and DT4D (bottom) datasets; see also Supp. C.1." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.606, + 0.905, + 0.667 + ], + "angle": 0, + "content": "ing our excellent performance on diverse shape classes. We can see that most descriptor-based methods can generalize to non-SMPL meshes, but none of them show competitive performance on all three datasets simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.668, + 0.906, + 0.743 + ], + "angle": 0, + "content": "We show the qualitative results of our model on several challenging meshes from SHREC'19 in Fig. 3. Even though these shapes include high-frequency details such as muscles, in contrast to the smooth shapes typically generated by SMPL, our model is able to obtain correct correspondences." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.757, + 0.828, + 0.773 + ], + "angle": 0, + "content": "5.3. Matching with Anisotropic Meshing" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Datasets. To evaluate the robustness of our method to different connectivity, we use the anisotropically remeshed versions of FAUST and SCAPE [16], denoted F_a and S_a, respectively. In these datasets, the triangle scale is uneven, ranging from small and densely packed triangles on one side of the mesh to large and coarse triangulation on the other. As a result, models that are sensitive to mesh connectivity will likely fail to predict the correct maps." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26905" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.141, + 0.089, + 0.434, + 0.232 + ], + "angle": 0, + "content": "
ModelCategoryF_aS_a
3D-CODEDLarge2.916.9
TransMatchScale2.716.2
DUO-FMNet3.04.4
GeomFMapsDescriptor3.23.8
AttentiveFMapsBased2.42.8
ConsistentFMaps2.62.7
ULRSSM1.92.4
Ours - 64×642.12.3
Ours - 96×962.02.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.243, + 0.454, + 0.257 + ], + "angle": 0, + "content": "Table 2. Results on the anisotropic FAUST and SCAPE." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.271, + 0.468, + 0.428 + ], + "angle": 0, + "content": "
ClassIntraInter
Ours[11][69]Ours[11][69]
manneq.1.01.01.63.34.04.5
zlorp1.11.32.14.26.94.2
crypto1.11.52.4---
prisoner1.11.12.129.620.526.7
ninja1.45.62.24.316.27.1
ortiz9.34.42.5---
mousey10.22.75.2---
drake10.61.02.110.48.24.5
skeletonz.16.31.41.449.436.548.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.438, + 0.483, + 0.482 + ], + "angle": 0, + "content": "Table 3. Results on shape classes from DT4D. Classes mousey and ortiz are not present in inter-class split. All inter-class evaluation pairs have the format \"crypto vs other class\", so crypto is excluded." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.499, + 0.484, + 0.606 + ], + "angle": 0, + "content": "Results. Table 2 shows the matching results. Both large-scale and descriptor-based methods experience performance drops on anisotropically remeshed datasets. In contrast, our method is more robust to changes in mesh connectivity. We attribute this to our design choices, such as diversifying the vertex structure of the training data and using conditioning that is independent of the number of vertices." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.614, + 0.336, + 0.631 + ], + "angle": 0, + "content": "5.4. Zero-Shot Shape Matching" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.636, + 0.484, + 0.788 + ], + "angle": 0, + "content": "Datasets. Generalization to shape types not observed during training is a desirable property in many shape matching applications. To evaluate our model on unseen data, we use the non-isometric DT4D dataset [40] that consists of nine humanoid shape classes. While typically, 198 shapes are defined for training and 95 for testing, we instead make the evaluation more challenging by training on human datasets, SURREAL or FAUST. This can be viewed as a zero-shot setting, since most of the test shapes are different from the training data (see Supp. C.1 for an illustration)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.483, + 0.886 + ], + "angle": 0, + "content": "Results. Our proposed experimental setup is challenging due to the differences between the training and test shapes. We use a lower-resolution model predicting a \\(32 \\times 32\\) functional map, results of all our models are shown in Supp. C.5. We compare our method with recent descriptor-based approaches: ConsistentFMaps [69] and ULRSSM [11]." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.887, + 0.483, + 0.901 + ], + "angle": 0, + "content": "The mean geodesic errors per class for inter- and intra" + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.089, + 0.723, + 0.219 + ], + "angle": 0, + "content": "
ClassOurs[11][69]
wolf3.53.54.4
dog3.53.54.5
horse3.73.84.4
cow3.83.84.4
lion4.03.84.9
fox4.73.64.9
hippo7.69.97.9
mean4.34.34.8
" + }, + { + "type": "image", + "bbox": [ + 0.729, + 0.09, + 0.886, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.228, + 0.906, + 0.258 + ], + "angle": 0, + "content": "Table 4. Results on the SMAL dataset [16], all categories are present in train/test sets. Format: category vs. everything." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.276, + 0.906, + 0.352 + ], + "angle": 0, + "content": "category splits are shown in Table 3, with further comparisons in Supp. C.7. Our method achieves accurate matching for most shape classes in both splits, demonstrating the generalization of our method to data unseen during training. We show the qualitative examples in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.362, + 0.779, + 0.379 + ], + "angle": 0, + "content": "5.5. Application to Animal Shapes" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.384, + 0.907, + 0.566 + ], + "angle": 0, + "content": "Datasets. To demonstrate the applicability of our method to shape classes other than humans, we test our approach on the SMAL dataset containing seven animal types. We take the 32/17 split from [16], where all categories are present in train/test sets. While the original training set is sufficient for descriptor-based baselines, it is too small for our model. To address this, we use the fitted parameters of the SMAL parametric model [77] and randomly vary the pose of each training animal, generating a total of 64,000 meshes. We use the mean SMAL shape as a template. Note that this generated dataset conveys little new information, since e.g., there are only three different types of lions." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.575, + 0.906, + 0.651 + ], + "angle": 0, + "content": "Results. Table 4 shows the results of our \\(64 \\times 64\\) model. Although the training data for our method lacks sufficient diversity, we achieve comparable performance to the baselines. Therefore, given enough training data, we believe our method can be applied to any shape class." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.664, + 0.634, + 0.68 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We presented DenoisFM, an approach of a new class for shape correspondence estimation. Our model is trained on a large dataset of synthetic human meshes and predicts the functional map between a pair of shapes using a denoising diffusion model. DenoisFM achieves correspondence accuracy on par with state-of-the-art methods across multiple datasets. The key advantage of our work is its generalization ability to human and humanoid shapes that differ noticeably from the training data, as well as competitive performance on animal shapes. Therefore, DenoisFM bridges the gap between previous large-scale and descriptor-based approaches by efficiently leveraging large amounts of data, opening up a new direction for using diffusion models in shape correspondence estimation." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26906" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.117, + 0.484, + 0.148 + ], + "angle": 0, + "content": "ZL acknowledges the support of the DFG Sachbeihilfe grant LA 5191/2-1." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.165, + 0.188, + 0.182 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.19, + 0.484, + 0.233 + ], + "angle": 0, + "content": "[1] Ahmed Abdelreheem, Abdelrahman Eldesokey, Maks Ovsjanikov, and Peter Wonka. 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We propose DenoisFM, a novel method for predicting shape correspondences in the form of functional maps using denoising diffusion models. (Left:) Challenging examples our method can handle, with color-coded correspondences. (Right:) By sequentially denoising samples of random noise, the diffusion model can predict the correct functional map between a pair of shapes. + +![](images/d11d7c96ca80f393dcd2c171ae5fdd2616573871bf6b5e38e2142cf2d237073a.jpg) +Predict Functional Maps using DDPMs +Gaussian Noise $x_{T}$ +$x_{t - 1}\coloneqq \mathbf{DDPM}(x_t;y)$ +Functional Map + +# Abstract + +Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape deformation methods. See our project page1 for the source code2 and the datasets. + +# 1. Introduction + +A long-standing problem in computer graphics and vision is to find corresponding points in a pair of 3D shapes [9, 11, 19, 42, 49, 64, 69]. The point map can then be used for texture [14], segmentation [63] and deformation transfer [68], statistical shape analysis [13], and construction of parametric models [37, 55]. A popular approach to solving the correspondence problem involves the functional map framework [49], which represents the correspondence as a small matrix that maps between the eigenfunctions of the Laplace operator on each shape. This representation is compact and allows to regularize constraints on the correspondences, such as bijectivity or area preservation. The functional map framework has been extended in numerous works, such as matching shapes with partiality [4, 58], analyzing the properties of shape collections [13] or improving accuracy through iterative refinement [19, 44, 57]. + +Previous functional map approaches focused on using small datasets, rarely exceeding a hundred unique shapes. This favored training models with lightweight architectures that could learn as much as possible with limited data, but these methods may face challenges with generalization to broad shape categories. To develop a unified model that is applicable to various tasks, we draw attention to denoising diffusion models [25, 66, 67], which have impressive generalization ability when trained on large amounts of data. In our work, we apply this approach to correspondence estimation using functional maps. + +Based on the idea of sequentially denoising samples of random noise into samples from the data distribution, dif- + +fusion models have achieved unprecedented performance in high-fidelity, diverse, and controllable image synthesis [53]. The scalable U-Net architecture [60] allows them to be trained on large datasets with hundreds of thousands of high-resolution images. The application of diffusion models to shape matching has been limited so far, mainly focusing on feature extraction from pre-trained foundational models [1, 17]. Interestingly, functional maps appear well-suited to bridge diffusion models and shape correspondence. They are small-sized single-channel matrices, making standard architectures developed for images readily applicable to them. Large amounts of shape data for training are then available through parametric models such as SMPL [37], an approach that has already been used for matching tasks [23, 72] and is also suitable for diffusion models. + +In this work, we present Denoising Functional Maps (DenoisFM), an approach to directly predict the functional map between shapes using a denoising diffusion model; see Fig. 1 for the overview. For training, we create a large dataset of functional maps between $2.3 \cdot 10^{5}$ human shapes from the SURREAL dataset [73] and a template shape. Using template-wise maps instead of pair-wise ones allows to reduce the complexity of training and inference. The conditioning information is inferred directly from the geometric shape structure. Additionally, we propose to exploit the probabilistic nature of diffusion models by predicting several initial maps instead of a single one, and selecting the best map based on the Dirichlet energy [52]. + +An important property of functional maps is that they are defined in the basis of the first $n$ eigenvectors of the Laplacian operator for each shape. The basis is not unique due to the sign ambiguity of the eigenvectors, and there are potentially $2^{n}$ possible basis combinations for each shape. To address this problem, we propose an unsupervised approach which selects the signs of the basis vectors using per-vertex features extracted in an unsupervised way (Sec. 3.2). This reduces the number of possible functional maps between shapes, further lowering the training complexity. + +Contributions. Overall, the technical contributions of this paper can be summarized as follows: + +- DenoisFM, a fundamentally new approach to shape correspondence estimation based on predicting functional maps using denoising diffusion models; +- An unsupervised method to address the sign ambiguity of eigenvectors of the Laplacian, which reduces the complexity of the prediction problem. + +Our model performs on par with existing shape matching methods on human benchmark datasets, achieves generalization to non-isometric humanoid shapes without learning on them, and is also applicable to animal shapes. See our project page1 for the source code2 and the datasets of functional maps used to train our models. + +# 2. Related Work + +Shape Correspondence Estimation. Learning-based shape correspondence methods can be roughly divided into two categories: first, approaches that predict pointwise descriptors suitable for computing functional maps [49, 50], a low-rank representation of the point-wise correspondence in Laplace-Beltrami eigenbasis; second, deformation-based methods that directly align input shapes and typically require much larger training datasets than descriptor-based methods. + +In the standard functional map pipeline, point-wise descriptor functions that encode the surface geometry are first computed on each shape [5, 9, 71], and then the functional map is estimated using the descriptors in a least-squares optimization. With the advent of deep learning, network architectures were introduced to learn descriptor functions directly from the data [35, 65]. While the initial methods were supervised [15, 35], recent works estimate the descriptors in an unsupervised manner [11, 62]. Most shape matching datasets consist of fewer than a hundred unique meshes and focus on a specific category of shapes [3, 7, 40, 43]. Therefore, the most effective descriptor-based models use lightweight architectures to infer as much geometric information as possible from limited training data. + +Another group of works use large-scale datasets of synthetic data for training. 3D-CODED [23] is an encoder-decoder architecture that predicts the correspondence by learning a surface parameterization and attempts to estimate the deformation from the template shape to the test one. Transmatch [72] is a transformer-based model that uses an attention mechanism to learn the underlying structure of the geometry. Other works utilizing large amounts of data [10, 31, 76] mainly focus on point cloud registration, and a group of works learn the shape deformation using data-efficient architectures [20, 70]. + +We combine the advantages of both categories of models by training a large-scale method based on functional maps that leverages the power of denoising diffusion models. + +Denoising Diffusion Models. Diffusion models have become popular in many areas of visual computing; see the recent survey for details [53]. Several diffusion-based generative models have been proposed [66, 67], and the simplified learning process of denoising diffusion probabilistic models (DDPMs) enabled the image synthesis at unprecedented quality [25]. Various conditioning mechanisms such as class labels, textual descriptions, or segmentation maps have been used to guide the diffusion process [59]. While diffusion models quickly found applications in areas beyond imaging such as video [26, 27] and 3D content generation [36, 54], their application to shape correspondence estimation has been limited so far to extracting descriptors from images of meshes [17] or segmentation maps [1] gen + +erated by foundational models. Our work is the first to use DDPMs to directly predict the functional maps between pairs of shapes to obtain the correspondences. + +Sign Ambiguity of Laplacian Eigenvectors. Since for any eigenvector $\phi_i$ , its negative version $-\phi_i$ is also an eigenvector, the Laplace-Beltrami eigenbasis has an inherent sign ambiguity. Additionally, the eigenvalues can have higher multiplicity and make the intrinsic ordering non-unique. This symmetry needs to be taken into account when processing the eigenvectors [8, 48, 63]. + +In graph learning, Laplacian eigenvectors are used to encode information about the structure of a graph [6, 32], and several methods were proposed to address the sign ambiguity. Laplacian Canonization [38] proposes to find the coordinate axis on which the projection of the eigenvector has the largest angle and fixes the projection to be positive. SAN [30] obtains sign-invariant operators using absolute subtraction and product between a pair of nodes, this only considers the relative sign between queries. SignNet [34] learns a sign-invariant embedding and Dwivedi et al. [18] learns on all possible sign combinations. + +The methods described above are designed for graphs with a small number of vertices. For point clouds, Linearly Invariant Embedding [41] considered the problem of learning the basis functions directly from the input data. However, the majority of works on 3D shapes employ the sign-equivariant approach, where a sign-dependent functional map is computed from descriptor functions in a precomputed Laplace-Beltrami eigenbasis. In our work, we propose to address the sign ambiguity problem using a learning-based method that assigns a specific combination of signs to the eigenvectors of any human shape, which is learned directly from the data in an unsupervised way. + +# 3. Background + +Notation. Given a shape $S$ represented as a triangular mesh with $v$ vertices, we compute its Laplace matrix $L$ [45] and the first $n$ eigenvectors of $L$ corresponding to the eigenvalues $\lambda_1 \leqslant \ldots \leqslant \lambda_n$ . $A$ is the diagonal vertex-area matrix associated with $L$ , computed by assigning one-third of the total area of all faces incident to the corresponding vertex. + +We denote matrices of $n$ functions on the vertices of $S$ by uppercase letters: $\Phi \in \mathbb{R}^{v \times n}$ for the matrix of eigenvectors, $\Sigma \in \mathbb{R}^{v \times n}$ for the matrix of learned features. The individual eigenvectors and feature vectors are denoted by lowercase letters: $\phi_i \in \mathbb{R}^v$ for the $i$ -th eigenvector, $s_i \in \mathbb{R}^v$ for the $i$ -th feature vector. Finally, $\sigma \in \{-1, 1\}^n$ represents a vector consisting of $n$ signs. + +# 3.1. Functional Maps + +Our method is built upon the framework of functional maps [49, 50]. Consider the point-wise map $\Pi_{21} \in \{0,1\}^{v_2 \times v_1}$ + +between two meshes $S_{1}$ and $S_{2}$ . The point-wise map is a permutation matrix, and due to its large size, it cannot be processed efficiently. The functional map $C_{12} \in \mathbb{R}^{n \times n}$ is the spectral representation of $\Pi_{21}$ , which is computed as + +$$ +C _ {1 2} = \Phi_ {2} ^ {\dagger} \Pi_ {2 1} \Phi_ {1}, \tag {1} +$$ + +where “ $\dagger$ ” denotes the pseudo-inverse. The functional map efficiently encodes the point-wise map in a low-dimensional representation, since $n \ll v_1, v_2$ . + +In a standard pipeline, learned or handcrafted $p$ -dimensional descriptor functions are computed on each shape, $F_{1} \in \mathbb{R}^{v_{1} \times p}$ , $F_{2} \in \mathbb{R}^{v_{2} \times p}$ . The functional map is then obtained by solving the linear system [50]: + +$$ +C _ {1 2} = \underset {C} {\arg \min } \left\| C \Phi_ {1} ^ {\dagger} F _ {1} - \Phi_ {2} ^ {\dagger} F _ {2} \right\| _ {2} ^ {2}, \tag {2} +$$ + +which is usually further regularized [15, 47]. The pointwise map can be recovered from the functional map and the eigenvectors using nearest neighbor search [49, 51]. + +# 3.2. Sign Ambiguity + +The functional map is defined in a basis spanned by the eigenvectors of the Laplacian on each shape, as can be seen from Eq. (1). However, this basis is not unique since for each eigenvector $\phi_i$ , $-\phi_i$ is also a valid eigenvector corresponding to the same eigenvalue $\lambda_i$ . Due to sign ambiguity, there are $2^n$ possible basis combinations on each shape. + +The eigenvectors returned by a numerical eigensolver will have a random sign combination, and mathematically it is impossible to select some specific sign of eigenvectors. However, several works demonstrate that the choice of the sign can be determined by the underlying data using the projection operator [8, 34, 38]. An intuitive example arises in the principal component analysis: Each eigenvector should point in the same direction as the points it is representing. This can be achieved by projecting the singular vector onto the data vectors and changing its sign to make the projection positive. This approach allows to select a canonical direction for the first few eigenvectors. + +Sign ambiguity is a special case of basis ambiguity when all eigenvalues are distinct. The more general basis ambiguity occurs if an eigenvalue $\lambda_{i}$ has multiplicity degree $d_{i} > 1$ . Then any $d_{i}$ vectors forming an orthogonal basis in the subspace spanned by its eigenvectors $(\phi_{i + 1},\phi_{i + 2}\dots \phi_{i + d_i})$ are also valid eigenvectors. Although the basis ambiguity is difficult to deal with, in practice high multiplicities do not occur often in low-order eigenvectors [29, 50]. + +# 3.3. Denoising Diffusion Models + +Given a dataset of examples drawn independently from a data distribution $q(x)$ , diffusion models aim to learn the underlying data distribution by sequentially denoising random noise samples [25, 53, 66]. + +The forward diffusion process takes a real data point $x_0$ and incrementally adds to it a small amount of Gaussian noise, producing a sequence of $T$ noisy samples $x_1, \ldots, x_T$ . The step sizes are controlled by a variance schedule $\{\beta_t \in (0, 1)\}_{t=1}^T$ . With the larger steps $t$ , the noisy sample $x_t$ further deviates from the original sample. At $T \to \infty$ , it is close to the Gaussian distribution, $x_T \sim N(x_T; 0, I)$ . The reverse process recreates the original sample by iteratively removing noise from an input $x_T$ drawn from the Gaussian distribution. Assuming that the reverse conditional probability is conditioned on $x_0$ , $q(x_{t-1} \mid x_t, x_0) = N\left(x_{t-1}; \tilde{\mu}(x_t, x_0), \tilde{\beta}_t I\right)$ , we can obtain $\tilde{\mu}_t = \frac{1}{\sqrt{\alpha_t}}\left(x_t - \frac{1 - \alpha_t}{\sqrt{1 - \tilde{\alpha}_t}}\epsilon_t\right)$ , where $\alpha_t = 1 - \beta_t$ and $\bar{\alpha}_t = \prod_{i=1}^T \alpha_i$ . + +Instead of directly predicting the denoised sample $\tilde{\mu}_t$ with a neural network, we can predict the noise content $\epsilon_{\theta}(x_t,t)$ from the input $x_{t}$ at time step $t$ [25]. Such a model is trained with a denoising score-matching objective: $\mathcal{L}_t = E_{t\sim [1,T],x_0,\epsilon_t}\left[\| \epsilon_t - \epsilon_\theta (x_t,t)\| ^2\right]$ . + +# 4. Denoising Functional Maps + +This section introduces Denoising Functional Maps (DenoisFM), our approach for shape correspondence estimation; see Fig. 2 for the method overview. Since functional maps are square low-dimensional matrices (see Sec. 3.1), we use a standard neural architecture based on a 2D U-Net [61] as a backbone. We aim to train our model on a large collection of shapes with diverse geometry. Since functional maps are defined for shape pairs, for a dataset with $m$ shapes the model would have to learn $m^2$ functional maps. Instead of this naive approach, we consider the correspondences to a single template shape, following previous works [23, 72]. As a result, the training data includes only $m$ functional maps, one for each shape in the dataset. + +A functional map is defined in a specific basis of Laplacian eigenvectors, and knowing the exact basis combination is necessary to convert it to a point-wise correspondence map. Therefore, we compute the basis first and then condition the diffusion model on it; the model then returns the corresponding functional map. To reduce the complexity of the problem caused by the sign ambiguity of basis eigenvectors, we utilize a sign correction network to select a specific combination of signs for the basis. + +DenoisFM consists of two components: the DDPM for functional map prediction (Sec. 4.1) with post-processing that filters out low-quality solutions using Dirichlet energy of the point-wise map (Sec. 4.1.1), and the sign corrector for the Laplacian eigenvectors (Sec. 4.2). + +# 4.1. Denoising Diffusion Component + +We next describe the training and inference of the diffusion component of DenoisFM. For training, we use a large collection of shapes and a template. For each shape $S$ in the dataset, we compute an eigenbasis $\Phi$ , a template-wise functional map $C_{1T}$ , and conditioning $y = y(S,\Phi)$ which incorporates geometric details of the input shape and information about the basis. The exact form of conditioning will be specified in Sec. 4.3. We use the training objective of denoising diffusion probabilistic models (DDPMs) [25]: $\mathcal{L}_{\mathrm{DDPM}} = E_{x,\epsilon \sim N(0,1),t}\left[\| \epsilon -\epsilon_{\theta}(x_t,t,y)\| _2^2\right]$ , where $\epsilon_{\theta}$ is the amount of noise predicted by a 2D UNet [60], $x_{t}$ is a noisy version of the input $x_0\coloneqq C_{1T}$ , and $t$ is the time step uniformly sampled from $\{1,\ldots ,T\}$ . + +The inference pipeline consists of two stages, see Fig. 2a. In the template stage, for each individual shape $S$ in the evaluation dataset, we obtain an eigenbasis $\Phi$ , calculate the conditioning $y$ , and predict the template-wise functional map $C_{1T}$ using the diffusion model. Note that the inference of DDPMs is time-consuming due to the large number of denoising steps and can take several hours for high-dimensional functional maps. Because the predicted maps refer to the template, we need to run the denoising process only once for each shape. + +In the pairwise stage, for each test pair, we convert the respective template-wise functional maps into pairwise ones using the composition property [49]: $C_{12} = C_{1T}(C_{2T})^{-1}$ . We then apply the Zoomout refinement [44] to increase the resolution of the functional maps. This spectral upsampling step has been shown to improve their accuracy, and our framework benefits from it without additional modifications. Finally, the functional map is converted into a pointwise map $\Pi_{21}$ using nearest neighbor search. + +# 4.1.1. Post-Processing of the Samples + +Diffusion models are inherently probabilistic and their outputs may differ given the same conditioning but different initial noise [25]. To address this, we repeat the denoising process multiple times and filter out the low-quality results. The selection is based on the Dirichlet energy of the pointwise map [21, 40]: an accurate map should be smooth, with neighboring vertices on one shape matching neighboring vertices on the other. Therefore, we repeat both the template step and the pairwise step to produce multiple point-wise maps. We can then either report the map with the lowest Dirichlet energy or combine the results of several smoothest maps. To do this, for each query point on the source mesh, we gather potential matching points on the target mesh and select the one with the smallest total distance to the other candidates (see Supp. B.3). The map selection step has a major impact on the accuracy of our method. + +![](images/37b7c3ee91cde8dc1f79b48cab49ee57ada7aa9d751bb45cd7d53faa6cefa407.jpg) +(a) Functional map prediction using a diffusion model. For each unique shape $S$ in the dataset, we obtain feature vectors $\Sigma$ using a feature extractor $\Theta$ , as well as a sign-corrected eigenbasis $\hat{\Phi}$ (Fig. 2b, Sec. 4.2). Both are used for conditional prediction of the template-wise functional map $C_{1T}$ using a diffusion model, performed separately for each shape. The pairwise functional maps $C_{12}$ are obtained through the map composition property, upsampled using ZoomOut [44], and converted to pointwise maps $\Pi_{21}$ . + +![](images/0b1dfdf25910845f8b3aeb3adff0ad9b12e122dfed0db6ab664405e132ac55f1.jpg) +(b) Learned sign correction. The eigenvectors $\Phi$ returned by a numerical eigensolver have random signs. To select a specific sign, we project the eigenvectors onto the feature vectors $\Sigma$ obtained with a feature extractor $\Theta$ , and make the projection positive. The sign correction network is trained in an unsupervised manner: learning to correct eigenvectors that have random signs. The learned features $\Sigma$ are also used for the conditional prediction of the template-wise functional map using a diffusion model (Fig. 2a). +Figure 2. Overview of DenoisFM. (a) A pair of shapes is matched using a DDPM model. (b) The signs of eigenvectors are corrected through learned features. + +# 4.2. Learned Sign Correction + +The diffusion model needs to be conditioned on the basis eigenvectors and predict the functional map for that particular basis. Theoretically, the model could be trained using random basis combinations, as was done in Dwivedi et al. [18] for graph networks. However, this would significantly increase the amount of training data. + +Hence, we follow a more effective approach: we select a specific basis by fixing the sign of the Laplacian eigenvectors on each shape. Previous works infer the sign from the underlying data using the projection operator (see Sec. 3.2). Therefore, suppose that $\Sigma \coloneqq \Theta(S) \in \mathbb{R}^{v \times n}$ is a set of pervertex feature vectors inferred from the geometry of shape $S$ by a trainable feature extractor $\Theta$ , one for each eigenvector. The sign of the eigenvectors can be selected by projecting the features $\Sigma$ onto the eigenvectors $\Phi$ and making the corresponding projections positive: + +$$ +\begin{array}{l} \hat {\sigma} := \operatorname {s i g n} \left[ \operatorname {d i a g} \left(\Sigma^ {T} A \Phi\right) \right], \tag {3} \\ \hat {\Phi} := \Phi \hat {\sigma}, \\ \end{array} +$$ + +where “ $\mathrm{diag}(\cdot)$ ” and “ $\mathrm{sign}(\cdot)$ ” denote matrix diagonal and sign extraction operators, $A$ is the diagonal vertex-area matrix. To illustrate, suppose we have a human mesh and a single feature vector $\varsigma_{i}$ , which is a binary vector with ones for points on the left hand, and zeros otherwise. After performing the procedure described in Eq. (3), the corrected eigenvector $\hat{\phi}_i$ will be mostly positive on the left hand. + +# 4.2.1. Training the Sign Corrector + +The sign correction network is trained in an unsupervised manner by learning to correct eigenvectors that have random signs. If we perform the eigendecomposition with a numerical solver twice on the same mesh and get two sets of eigenvectors $\Phi_1$ and $\Phi_2$ , due to the sign ambiguity, the difference between them can be written as $\Phi_2 = \Phi_1\sigma$ , where $\sigma \in \{-1,1\}^n$ is the ground-truth sign difference. Now we perform the sign correction using Eq. (3), after which we expect the corrected eigenvectors to be equal to each other: + +$$ +\hat {\Phi} _ {1} = \hat {\Phi} _ {2}, \tag {4} +$$ + +$$ +\Phi_ {1} \hat {\sigma} _ {1} = \Phi_ {2} \hat {\sigma} _ {2}, +$$ + +where $\hat{\sigma}_1, \hat{\sigma}_2 \in \{-1, 1\}^n$ are the predicted combinations of correction signs. After substitution and using $\hat{\sigma}_1 \hat{\sigma}_1 = I$ : + +$$ +\Phi_ {1} \hat {\sigma} _ {1} = \Phi_ {1} \sigma \hat {\sigma} _ {2}, +$$ + +$$ +\hat {\sigma} _ {1} = \sigma \hat {\sigma} _ {2}, \tag {5} +$$ + +$$ +\hat {\sigma} _ {1} \hat {\sigma} _ {2} = \sigma . +$$ + +As a result, the difference between the predicted correction signs should be the same as the ground-truth sign difference, and we can use this as our unsupervised training objective with a mean square error function: + +$$ +\mathcal {L} _ {\text {s i g n}} = \operatorname {M S E} (\hat {\sigma} _ {1} \hat {\sigma} _ {2}; \sigma) \tag {6} +$$ + +Note that the sign operator in Eq. (3) is not differentiable. Therefore, during training, we set $\hat{\sigma}_1$ and $\hat{\sigma}_2$ to be the diagonal elements of the projections, rather than their signs, assuming that the feature vectors and eigenvectors have unit norm. The training objective of the feature extractor (Eq. 6) then forces the elements of $\hat{\sigma}_1$ and $\hat{\sigma}_2$ to be as close to $-1$ or $1$ as possible. The absolute value can be interpreted as confidence in the predicted sign: values close to $\pm 1$ mean high confidence. + +In practice, we found that a network trained this way quickly converges on a dataset of human or animal meshes. Our method returns the same corrected eigenbasis $95 - 99\%$ of the time for the first hundred Laplacian eigenvectors. The accuracy of the sign correction and its impact on the distribution of functional maps are discussed in Supp. A. + +# 4.3. Choice of Conditioning + +Conditioning of the diffusion model should include two parts: the basis information and the geometric properties of the shape. The former can be provided simply via the sign-corrected eigenvectors $\hat{\Phi}$ . They additionally represent the spectral embedding of the shape and convey the full intrinsic information. As for the latter, during the training of the sign-correction network, the useful properties will be encoded in the learned feature vectors $\Sigma$ . Therefore, we propose to project the feature vectors onto the sign-corrected eigenvectors: + +$$ +\text {C o n d i t i o n g} y = \Sigma^ {T} A \hat {\Phi}. \tag {7} +$$ + +This form of conditioning has two important properties. First, it has the same dimensions as the functional map. Therefore, we can condition the diffusion model using a simple concatenation, where the conditioning matrix is concatenated with the intermediate denoising targets and passed through the score estimator as input [25, 75]. Second, it is independent of the number of vertices, making it scalable to large meshes. + +# 5. Training and Experimental Results + +This section describes the steps for generating the training data for our model (Sec. 5.1) as well as the experimental results on several challenging datasets (Secs. 5.2-5.5). The evaluation of the sign correction network, additional comparison, implementation details, and the ablation studies can be found in Supp. A to C. Since our model is designed to be trained on large and diverse shape collections, it can be applied to multiple (reminiscent) shape classes without retraining. This reduces the need for small category-specific training sets. We focus on datasets with human-like shapes as their combined volume allows versatile comparison of our approach with the previous works. + +# 5.1. Training Data and Implementation + +Our model consists of two independent components: a denoising diffusion model that predicts the functional map and a sign correction network based on a per-vertex feature extractor, trained separately on their respective datasets. + +# 5.1.1. Denoising Diffusion + +Diffusion models require large amounts of training data with hundreds of thousands of examples. Therefore, we follow 3D-CODED [23] and use the SURREAL [73] dataset with 230,000 human meshes generated with SMPL [37]. All its meshes are smooth and have the same vertex structure. To make the connectivity more diverse, we remesh each mesh [28, 46] and randomly simplify the number of faces using Quadric Edge Collapse [22]. In $65\%$ of the cases, we simplify the entire mesh resulting in uniform connectivity. In the remaining $35\%$ of the cases, we simplify only a small subset of the mesh to add non-even connectivity to the training data. After remeshing, we correct the signs of the eigenvectors using a pre-trained sign correction network (Sec. 4.2) and compute the functional map to the template shape. We only store the functional maps and conditioning matrices to save memory requirements. The data generation takes 10 hours using parallel processing. + +We use the standard DDPM [25] implemented in Diffusers [74] and distributed training with Accelerate [24]. We train models that predict 32, 64, and 96-dimensional functional maps for 100 epochs on eight A40 GPUs, which takes 1, 8, and 30 hours respectively. The inference at the template stage takes 1, 7, and 27 minutes for each shape in the dataset. The pairwise stage takes 30 seconds per pair. + +# 5.1.2. Sign Correction Network + +The per-vertex feature extractor of the sign correction network is based on DiffusionNet [65] (not to be confused with denoising diffusion) with six blocks and 128 WKS descriptors [5] as input. This architecture was designed for small shape matching datasets, so we used 1000 randomly selected meshes from SURREAL for training. Each + +of them was randomly remeshed and simplified without adding anisotropy. The sign correction network is trained for $5 \cdot 10^{4}$ iterations, which takes one hour on a single A40 GPU; the inference takes a few seconds per shape. + +# 5.2. Near-Isometric Shape Matching + +Datasets. We evaluate our method on three widely used datasets: FAUST [7], SCAPE [3] and SHREC'19 [43]. Following previous works, we use their more challenging remeshed versions [15, 56]: + +- The FAUST dataset contains meshes of 10 human classes in 10 poses, 100 in total. The train/test split is 80/20. +- The SCAPE dataset includes 71 meshes of the same person in different poses, the last 20 are used for testing. +- The SHREC'19 dataset is composed of 44 shapes with diverse body types and poses, arguably the most challenging of the three. This dataset does not have a train split and is used for testing only. Following [11], we removed shape 40 since it is the only partial non-closed shape. + +Baselines. We compare our approach with two categories of non-rigid shape correspondence methods. The first includes large-scale template-based models trained on SURREAL: 3D-CODED [23] and TransMatch [72], i.e., our main competitors as our work belongs to the same group. The second category includes descriptor-based models: ULRSSM [11], DiffZO [39], ConsistentFMaps [69], GeomFMaps [15], AttentiveFMaps [33], DUO-FMNet [16], SSL [10], SmS [12]. Since our and other methods can be applied to any shape class, we do not include template fitting methods such as NICP [42], which typically focus on human scans and incorporate explicit human body priors. + +To compare both categories of baselines fairly, we note that SCAPE is too small to train large models. On the other hand, FAUST was created with SMPL [37] like SURREAL, and includes a sufficient diversity of body types and poses. Therefore, we follow [10, 11, 69] and train large models on SURREAL, descriptor-based models on FAUST, and evaluate them on three test datasets. A comparison with the baselines trained on FAUST+SCAPE can be found in Supp. C.2. + +Results. We report the mean geodesic error of our model and the baselines in Table 1. Compared to other large-scale methods trained on SURREAL, our work generalizes well to meshes from SCAPE and SHREC'19. A common problem in large-scale baselines is predicted point maps with incorrect symmetry. This is caused by the fact that the geometry of the evaluation meshes has fewer fine-scale details such as fingers, which help to disambiguate the internal symmetry. Our work avoids overfitting to fine-scale details of SURREAL by using data augmentation (Sec. 5.1). As a result, we can utilize large amounts of data more effectively. + +Compared to descriptor-based methods, our results are on par on all datasets (especially SHREC'19), demonstrat + +
ModelCategoryF_rS_rS’19_r
3D-CODEDLarge-2.516.117.3
TransMatchScale1.715.321.0
DUO-FMNet2.54.26.4
GeomFMaps1.92.47.9
AttentiveFMaps1.92.65.8
ConsistentFMapsDescriptor-2.32.63.8
SSLBased2.03.14.0
DiffZO1.92.44.2
ULRSSM1.62.25.7
SmS1.43.36.2
Ours - 64×641.82.33.5
Ours - 96×961.72.13.9
+ +Table 1. Mean geodesic errors $(\times 100)$ on the remeshed FAUST, SCAPE, and SHREC'19 datasets. The best results are highlighted. Large-scale methods are trained on SURREAL, and descriptor-based methods on FAUST. Here and in the following, the results of our model are averaged across 5 runs. + +![](images/ab7467989956d412eb654a556da4be94f761993c744f635626c8106c37feed95.jpg) +Figure 3. Qualitative results by our approach on SHREC'19 (top) and DT4D (bottom) datasets; see also Supp. C.1. + +ing our excellent performance on diverse shape classes. We can see that most descriptor-based methods can generalize to non-SMPL meshes, but none of them show competitive performance on all three datasets simultaneously. + +We show the qualitative results of our model on several challenging meshes from SHREC'19 in Fig. 3. Even though these shapes include high-frequency details such as muscles, in contrast to the smooth shapes typically generated by SMPL, our model is able to obtain correct correspondences. + +# 5.3. Matching with Anisotropic Meshing + +Datasets. To evaluate the robustness of our method to different connectivity, we use the anisotropically remeshed versions of FAUST and SCAPE [16], denoted F_a and S_a, respectively. In these datasets, the triangle scale is uneven, ranging from small and densely packed triangles on one side of the mesh to large and coarse triangulation on the other. As a result, models that are sensitive to mesh connectivity will likely fail to predict the correct maps. + +
ModelCategoryF_aS_a
3D-CODEDLarge2.916.9
TransMatchScale2.716.2
DUO-FMNet3.04.4
GeomFMapsDescriptor3.23.8
AttentiveFMapsBased2.42.8
ConsistentFMaps2.62.7
ULRSSM1.92.4
Ours - 64×642.12.3
Ours - 96×962.02.2
+ +Table 2. Results on the anisotropic FAUST and SCAPE. + +
ClassIntraInter
Ours[11][69]Ours[11][69]
manneq.1.01.01.63.34.04.5
zlorp1.11.32.14.26.94.2
crypto1.11.52.4---
prisoner1.11.12.129.620.526.7
ninja1.45.62.24.316.27.1
ortiz9.34.42.5---
mousey10.22.75.2---
drake10.61.02.110.48.24.5
skeletonz.16.31.41.449.436.548.0
+ +Results. Table 2 shows the matching results. Both large-scale and descriptor-based methods experience performance drops on anisotropically remeshed datasets. In contrast, our method is more robust to changes in mesh connectivity. We attribute this to our design choices, such as diversifying the vertex structure of the training data and using conditioning that is independent of the number of vertices. + +# 5.4. Zero-Shot Shape Matching + +Datasets. Generalization to shape types not observed during training is a desirable property in many shape matching applications. To evaluate our model on unseen data, we use the non-isometric DT4D dataset [40] that consists of nine humanoid shape classes. While typically, 198 shapes are defined for training and 95 for testing, we instead make the evaluation more challenging by training on human datasets, SURREAL or FAUST. This can be viewed as a zero-shot setting, since most of the test shapes are different from the training data (see Supp. C.1 for an illustration). + +Results. Our proposed experimental setup is challenging due to the differences between the training and test shapes. We use a lower-resolution model predicting a $32 \times 32$ functional map, results of all our models are shown in Supp. C.5. We compare our method with recent descriptor-based approaches: ConsistentFMaps [69] and ULRSSM [11]. + +The mean geodesic errors per class for inter- and intra + +Table 3. Results on shape classes from DT4D. Classes mousey and ortiz are not present in inter-class split. All inter-class evaluation pairs have the format "crypto vs other class", so crypto is excluded. + +
ClassOurs[11][69]
wolf3.53.54.4
dog3.53.54.5
horse3.73.84.4
cow3.83.84.4
lion4.03.84.9
fox4.73.64.9
hippo7.69.97.9
mean4.34.34.8
+ +![](images/1c3fb53794170792745041786366ccb6398ee75f3b5805c62c650d87615d1102.jpg) + +Table 4. Results on the SMAL dataset [16], all categories are present in train/test sets. Format: category vs. everything. + +category splits are shown in Table 3, with further comparisons in Supp. C.7. Our method achieves accurate matching for most shape classes in both splits, demonstrating the generalization of our method to data unseen during training. We show the qualitative examples in Fig. 3. + +# 5.5. Application to Animal Shapes + +Datasets. To demonstrate the applicability of our method to shape classes other than humans, we test our approach on the SMAL dataset containing seven animal types. We take the 32/17 split from [16], where all categories are present in train/test sets. While the original training set is sufficient for descriptor-based baselines, it is too small for our model. To address this, we use the fitted parameters of the SMAL parametric model [77] and randomly vary the pose of each training animal, generating a total of 64,000 meshes. We use the mean SMAL shape as a template. Note that this generated dataset conveys little new information, since e.g., there are only three different types of lions. + +Results. Table 4 shows the results of our $64 \times 64$ model. Although the training data for our method lacks sufficient diversity, we achieve comparable performance to the baselines. Therefore, given enough training data, we believe our method can be applied to any shape class. + +# 6. Conclusion + +We presented DenoisFM, an approach of a new class for shape correspondence estimation. Our model is trained on a large dataset of synthetic human meshes and predicts the functional map between a pair of shapes using a denoising diffusion model. DenoisFM achieves correspondence accuracy on par with state-of-the-art methods across multiple datasets. The key advantage of our work is its generalization ability to human and humanoid shapes that differ noticeably from the training data, as well as competitive performance on animal shapes. Therefore, DenoisFM bridges the gap between previous large-scale and descriptor-based approaches by efficiently leveraging large amounts of data, opening up a new direction for using diffusion models in shape correspondence estimation. + +# Acknowledgement + +ZL acknowledges the support of the DFG Sachbeihilfe grant LA 5191/2-1. + +# References + +[1] Ahmed Abdelreheem, Abdelrahman Eldesokey, Maks Ovsjanikov, and Peter Wonka. Zero-shot 3d shape correspondence. In SIGGRAPH Asia Conference Papers, 2023. 2 +[2] Hervé Abdi and Lynne J Williams. Principal component analysis. Wiley interdisciplinary reviews: computational statistics, 2(4):433-459, 2010. 1 +[3] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. 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We propose DenoisFM, a novel method for predicting shape correspondences in the form of functional maps using denoising diffusion models. (Left:) Challenging examples our method can handle, with color-coded correspondences. (Right:) By sequentially denoising samples of random noise, the diffusion model can predict the correct functional map between a pair of shapes." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 253, + 194, + 345, + 280 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 253, + 194, + 345, + 280 + ], + "spans": [ + { + "bbox": [ + 253, + 194, + 345, + 280 + ], + "type": "image", + "image_path": "4c831f22c8deb0f481e22fa77cbfbcf587ea86a4cd8a4d2686af5a0df2f3b345.jpg" + } + ] + } + ], + "index": 12, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 361, + 222, + 542, + 271 + ], + "blocks": [ + { + "bbox": [ + 371, + 204, + 532, + 215 + ], + "lines": [ + { + "bbox": [ + 371, + 204, + 532, + 215 + ], + "spans": [ + { + "bbox": [ + 371, + 204, + 532, + 215 + ], + "type": "text", + "content": "Predict Functional Maps using DDPMs" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 361, + 222, + 542, + 271 + ], + "lines": [ + { + "bbox": [ + 361, + 222, + 542, + 271 + ], + "spans": [ + { + "bbox": [ + 361, + 222, + 542, + 271 + ], + "type": "image", + "image_path": "d11d7c96ca80f393dcd2c171ae5fdd2616573871bf6b5e38e2142cf2d237073a.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 360, + 271, + 418, + 280 + ], + "lines": [ + { + "bbox": [ + 360, + 271, + 418, + 280 + ], + "spans": [ + { + "bbox": [ + 360, + 271, + 418, + 280 + ], + "type": "text", + "content": "Gaussian Noise " + }, + { + "bbox": [ + 360, + 271, + 418, + 280 + ], + "type": "inline_equation", + "content": "x_{T}" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 423, + 272, + 481, + 280 + ], + "lines": [ + { + "bbox": [ + 423, + 272, + 481, + 280 + ], + "spans": [ + { + "bbox": [ + 423, + 272, + 481, + 280 + ], + "type": "inline_equation", + "content": "x_{t - 1}\\coloneqq \\mathbf{DDPM}(x_t;y)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 492, + 271, + 542, + 280 + ], + "lines": [ + { + "bbox": [ + 492, + 271, + 542, + 280 + ], + "spans": [ + { + "bbox": [ + 492, + 271, + 542, + 280 + ], + "type": "text", + "content": "Functional Map" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 152, + 343, + 199, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 343, + 199, + 355 + ], + "spans": [ + { + "bbox": [ + 152, + 343, + 199, + 355 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 53, + 373, + 296, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 373, + 296, + 647 + ], + "spans": [ + { + "bbox": [ + 53, + 373, + 296, + 647 + ], + "type": "text", + "content": "Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape deformation methods. See our project page1 for the source code2 and the datasets." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 315, + 343, + 394, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 343, + 394, + 355 + ], + "spans": [ + { + "bbox": [ + 315, + 343, + 394, + 355 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 365, + 555, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 555, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 555, + 555 + ], + "type": "text", + "content": "A long-standing problem in computer graphics and vision is to find corresponding points in a pair of 3D shapes [9, 11, 19, 42, 49, 64, 69]. The point map can then be used for texture [14], segmentation [63] and deformation transfer [68], statistical shape analysis [13], and construction of parametric models [37, 55]. A popular approach to solving the correspondence problem involves the functional map framework [49], which represents the correspondence as a small matrix that maps between the eigenfunctions of the Laplace operator on each shape. This representation is compact and allows to regularize constraints on the correspondences, such as bijectivity or area preservation. The functional map framework has been extended in numerous works, such as matching shapes with partiality [4, 58], analyzing the properties of shape collections [13] or improving accuracy through iterative refinement [19, 44, 57]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 557, + 556, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 556, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 556, + 689 + ], + "type": "text", + "content": "Previous functional map approaches focused on using small datasets, rarely exceeding a hundred unique shapes. This favored training models with lightweight architectures that could learn as much as possible with limited data, but these methods may face challenges with generalization to broad shape categories. To develop a unified model that is applicable to various tasks, we draw attention to denoising diffusion models [25, 66, 67], which have impressive generalization ability when trained on large amounts of data. In our work, we apply this approach to correspondence estimation using functional maps." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": "Based on the idea of sequentially denoising samples of random noise into samples from the data distribution, dif-" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 673, + 295, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 673, + 295, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 673, + 295, + 693 + ], + "type": "text", + "content": "1Project page: https://alekseizhuravlev.github.io/ denoising-functional-maps/" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 55, + 693, + 294, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 693, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 693, + 294, + 713 + ], + "type": "text", + "content": "Source code: https://github.com/alekseizhuravlev/ denoising-functional-maps/" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26899" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 262 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 262 + ], + "type": "text", + "content": "fusion models have achieved unprecedented performance in high-fidelity, diverse, and controllable image synthesis [53]. The scalable U-Net architecture [60] allows them to be trained on large datasets with hundreds of thousands of high-resolution images. The application of diffusion models to shape matching has been limited so far, mainly focusing on feature extraction from pre-trained foundational models [1, 17]. Interestingly, functional maps appear well-suited to bridge diffusion models and shape correspondence. They are small-sized single-channel matrices, making standard architectures developed for images readily applicable to them. Large amounts of shape data for training are then available through parametric models such as SMPL [37], an approach that has already been used for matching tasks [23, 72] and is also suitable for diffusion models." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 265, + 294, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 265, + 294, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 265, + 294, + 421 + ], + "type": "text", + "content": "In this work, we present Denoising Functional Maps (DenoisFM), an approach to directly predict the functional map between shapes using a denoising diffusion model; see Fig. 1 for the overview. For training, we create a large dataset of functional maps between " + }, + { + "bbox": [ + 55, + 265, + 294, + 421 + ], + "type": "inline_equation", + "content": "2.3 \\cdot 10^{5}" + }, + { + "bbox": [ + 55, + 265, + 294, + 421 + ], + "type": "text", + "content": " human shapes from the SURREAL dataset [73] and a template shape. Using template-wise maps instead of pair-wise ones allows to reduce the complexity of training and inference. The conditioning information is inferred directly from the geometric shape structure. Additionally, we propose to exploit the probabilistic nature of diffusion models by predicting several initial maps instead of a single one, and selecting the best map based on the Dirichlet energy [52]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 422, + 294, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 294, + 542 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 294, + 542 + ], + "type": "text", + "content": "An important property of functional maps is that they are defined in the basis of the first " + }, + { + "bbox": [ + 55, + 422, + 294, + 542 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 422, + 294, + 542 + ], + "type": "text", + "content": " eigenvectors of the Laplacian operator for each shape. The basis is not unique due to the sign ambiguity of the eigenvectors, and there are potentially " + }, + { + "bbox": [ + 55, + 422, + 294, + 542 + ], + "type": "inline_equation", + "content": "2^{n}" + }, + { + "bbox": [ + 55, + 422, + 294, + 542 + ], + "type": "text", + "content": " possible basis combinations for each shape. To address this problem, we propose an unsupervised approach which selects the signs of the basis vectors using per-vertex features extracted in an unsupervised way (Sec. 3.2). This reduces the number of possible functional maps between shapes, further lowering the training complexity." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 543, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 543, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 543, + 295, + 567 + ], + "type": "text", + "content": "Contributions. Overall, the technical contributions of this paper can be summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 568, + 295, + 640 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 568, + 295, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 568, + 295, + 604 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 295, + 604 + ], + "type": "text", + "content": "- DenoisFM, a fundamentally new approach to shape correspondence estimation based on predicting functional maps using denoising diffusion models;" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 604, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 604, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 604, + 295, + 640 + ], + "type": "text", + "content": "- An unsupervised method to address the sign ambiguity of eigenvectors of the Laplacian, which reduces the complexity of the prediction problem." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 713 + ], + "type": "text", + "content": "Our model performs on par with existing shape matching methods on human benchmark datasets, achieves generalization to non-isometric humanoid shapes without learning on them, and is also applicable to animal shapes. See our project page1 for the source code2 and the datasets of functional maps used to train our models." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 91, + 553, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 199 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 199 + ], + "type": "text", + "content": "Shape Correspondence Estimation. Learning-based shape correspondence methods can be roughly divided into two categories: first, approaches that predict pointwise descriptors suitable for computing functional maps [49, 50], a low-rank representation of the point-wise correspondence in Laplace-Beltrami eigenbasis; second, deformation-based methods that directly align input shapes and typically require much larger training datasets than descriptor-based methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 200, + 553, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 200, + 553, + 368 + ], + "spans": [ + { + "bbox": [ + 313, + 200, + 553, + 368 + ], + "type": "text", + "content": "In the standard functional map pipeline, point-wise descriptor functions that encode the surface geometry are first computed on each shape [5, 9, 71], and then the functional map is estimated using the descriptors in a least-squares optimization. With the advent of deep learning, network architectures were introduced to learn descriptor functions directly from the data [35, 65]. While the initial methods were supervised [15, 35], recent works estimate the descriptors in an unsupervised manner [11, 62]. Most shape matching datasets consist of fewer than a hundred unique meshes and focus on a specific category of shapes [3, 7, 40, 43]. Therefore, the most effective descriptor-based models use lightweight architectures to infer as much geometric information as possible from limited training data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 369, + 553, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 553, + 500 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 553, + 500 + ], + "type": "text", + "content": "Another group of works use large-scale datasets of synthetic data for training. 3D-CODED [23] is an encoder-decoder architecture that predicts the correspondence by learning a surface parameterization and attempts to estimate the deformation from the template shape to the test one. Transmatch [72] is a transformer-based model that uses an attention mechanism to learn the underlying structure of the geometry. Other works utilizing large amounts of data [10, 31, 76] mainly focus on point cloud registration, and a group of works learn the shape deformation using data-efficient architectures [20, 70]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 501, + 553, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 501, + 553, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 501, + 553, + 536 + ], + "type": "text", + "content": "We combine the advantages of both categories of models by training a large-scale method based on functional maps that leverages the power of denoising diffusion models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 545, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 553, + 713 + ], + "type": "text", + "content": "Denoising Diffusion Models. Diffusion models have become popular in many areas of visual computing; see the recent survey for details [53]. Several diffusion-based generative models have been proposed [66, 67], and the simplified learning process of denoising diffusion probabilistic models (DDPMs) enabled the image synthesis at unprecedented quality [25]. Various conditioning mechanisms such as class labels, textual descriptions, or segmentation maps have been used to guide the diffusion process [59]. While diffusion models quickly found applications in areas beyond imaging such as video [26, 27] and 3D content generation [36, 54], their application to shape correspondence estimation has been limited so far to extracting descriptors from images of meshes [17] or segmentation maps [1] gen" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26900" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": "erated by foundational models. Our work is the first to use DDPMs to directly predict the functional maps between pairs of shapes to obtain the correspondences." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 116, + 295, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 116, + 295, + 199 + ], + "spans": [ + { + "bbox": [ + 55, + 116, + 295, + 199 + ], + "type": "text", + "content": "Sign Ambiguity of Laplacian Eigenvectors. Since for any eigenvector " + }, + { + "bbox": [ + 55, + 116, + 295, + 199 + ], + "type": "inline_equation", + "content": "\\phi_i" + }, + { + "bbox": [ + 55, + 116, + 295, + 199 + ], + "type": "text", + "content": ", its negative version " + }, + { + "bbox": [ + 55, + 116, + 295, + 199 + ], + "type": "inline_equation", + "content": "-\\phi_i" + }, + { + "bbox": [ + 55, + 116, + 295, + 199 + ], + "type": "text", + "content": " is also an eigenvector, the Laplace-Beltrami eigenbasis has an inherent sign ambiguity. Additionally, the eigenvalues can have higher multiplicity and make the intrinsic ordering non-unique. This symmetry needs to be taken into account when processing the eigenvectors [8, 48, 63]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 200, + 295, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 200, + 295, + 331 + ], + "spans": [ + { + "bbox": [ + 54, + 200, + 295, + 331 + ], + "type": "text", + "content": "In graph learning, Laplacian eigenvectors are used to encode information about the structure of a graph [6, 32], and several methods were proposed to address the sign ambiguity. Laplacian Canonization [38] proposes to find the coordinate axis on which the projection of the eigenvector has the largest angle and fixes the projection to be positive. SAN [30] obtains sign-invariant operators using absolute subtraction and product between a pair of nodes, this only considers the relative sign between queries. SignNet [34] learns a sign-invariant embedding and Dwivedi et al. [18] learns on all possible sign combinations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 331, + 295, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 295, + 475 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 295, + 475 + ], + "type": "text", + "content": "The methods described above are designed for graphs with a small number of vertices. For point clouds, Linearly Invariant Embedding [41] considered the problem of learning the basis functions directly from the input data. However, the majority of works on 3D shapes employ the sign-equivariant approach, where a sign-dependent functional map is computed from descriptor functions in a precomputed Laplace-Beltrami eigenbasis. In our work, we propose to address the sign ambiguity problem using a learning-based method that assigns a specific combination of signs to the eigenvectors of any human shape, which is learned directly from the data in an unsupervised way." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 487, + 134, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 134, + 501 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 134, + 501 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": "Notation. Given a shape " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": " represented as a triangular mesh with " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": " vertices, we compute its Laplace matrix " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": " [45] and the first " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": " eigenvectors of " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": " corresponding to the eigenvalues " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "\\lambda_1 \\leqslant \\ldots \\leqslant \\lambda_n" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": " is the diagonal vertex-area matrix associated with " + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 507, + 295, + 579 + ], + "type": "text", + "content": ", computed by assigning one-third of the total area of all faces incident to the corresponding vertex." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": "We denote matrices of " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": " functions on the vertices of " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": " by uppercase letters: " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\Phi \\in \\mathbb{R}^{v \\times n}" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": " for the matrix of eigenvectors, " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\Sigma \\in \\mathbb{R}^{v \\times n}" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": " for the matrix of learned features. The individual eigenvectors and feature vectors are denoted by lowercase letters: " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\phi_i \\in \\mathbb{R}^v" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": "-th eigenvector, " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "s_i \\in \\mathbb{R}^v" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": "-th feature vector. Finally, " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\{-1, 1\\}^n" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": " represents a vector consisting of " + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 580, + 295, + 664 + ], + "type": "text", + "content": " signs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 672, + 157, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 157, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 157, + 685 + ], + "type": "text", + "content": "3.1. Functional Maps" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "content": "Our method is built upon the framework of functional maps [49, 50]. Consider the point-wise map " + }, + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\Pi_{21} \\in \\{0,1\\}^{v_2 \\times v_1}" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": "between two meshes " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "S_{1}" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "S_{2}" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": ". The point-wise map is a permutation matrix, and due to its large size, it cannot be processed efficiently. The functional map " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "C_{12} \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": " is the spectral representation of " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "\\Pi_{21}" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": ", which is computed as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 397, + 131, + 555, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 131, + 555, + 144 + ], + "spans": [ + { + "bbox": [ + 397, + 131, + 555, + 144 + ], + "type": "interline_equation", + "content": "C _ {1 2} = \\Phi_ {2} ^ {\\dagger} \\Pi_ {2 1} \\Phi_ {1}, \\tag {1}", + "image_path": "f6310ed0881146b44899a7ddcb4b3badfa08a17dede2cb096edf50e328f1c5e3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 148, + 554, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 148, + 554, + 185 + ], + "spans": [ + { + "bbox": [ + 313, + 148, + 554, + 185 + ], + "type": "text", + "content": "where “" + }, + { + "bbox": [ + 313, + 148, + 554, + 185 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 313, + 148, + 554, + 185 + ], + "type": "text", + "content": "” denotes the pseudo-inverse. The functional map efficiently encodes the point-wise map in a low-dimensional representation, since " + }, + { + "bbox": [ + 313, + 148, + 554, + 185 + ], + "type": "inline_equation", + "content": "n \\ll v_1, v_2" + }, + { + "bbox": [ + 313, + 148, + 554, + 185 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "spans": [ + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "type": "text", + "content": "In a standard pipeline, learned or handcrafted " + }, + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "type": "text", + "content": "-dimensional descriptor functions are computed on each shape, " + }, + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "type": "inline_equation", + "content": "F_{1} \\in \\mathbb{R}^{v_{1} \\times p}" + }, + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "type": "inline_equation", + "content": "F_{2} \\in \\mathbb{R}^{v_{2} \\times p}" + }, + { + "bbox": [ + 313, + 186, + 554, + 233 + ], + "type": "text", + "content": ". The functional map is then obtained by solving the linear system [50]:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 358, + 241, + 554, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 241, + 554, + 266 + ], + "spans": [ + { + "bbox": [ + 358, + 241, + 554, + 266 + ], + "type": "interline_equation", + "content": "C _ {1 2} = \\underset {C} {\\arg \\min } \\left\\| C \\Phi_ {1} ^ {\\dagger} F _ {1} - \\Phi_ {2} ^ {\\dagger} F _ {2} \\right\\| _ {2} ^ {2}, \\tag {2}", + "image_path": "7841f4122ed0438e251879251c4874131f85260beb7ee10bd35b91f8b0fdd5bc.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 270, + 554, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 270, + 554, + 306 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 554, + 306 + ], + "type": "text", + "content": "which is usually further regularized [15, 47]. The pointwise map can be recovered from the functional map and the eigenvectors using nearest neighbor search [49, 51]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 312, + 410, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 410, + 326 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 410, + 326 + ], + "type": "text", + "content": "3.2. Sign Ambiguity" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "spans": [ + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "text", + "content": "The functional map is defined in a basis spanned by the eigenvectors of the Laplacian on each shape, as can be seen from Eq. (1). However, this basis is not unique since for each eigenvector " + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "inline_equation", + "content": "\\phi_i" + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "inline_equation", + "content": "-\\phi_i" + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "text", + "content": " is also a valid eigenvector corresponding to the same eigenvalue " + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "inline_equation", + "content": "\\lambda_i" + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "text", + "content": ". Due to sign ambiguity, there are " + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "inline_equation", + "content": "2^n" + }, + { + "bbox": [ + 313, + 330, + 554, + 402 + ], + "type": "text", + "content": " possible basis combinations on each shape." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 402, + 554, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 402, + 554, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 402, + 554, + 545 + ], + "type": "text", + "content": "The eigenvectors returned by a numerical eigensolver will have a random sign combination, and mathematically it is impossible to select some specific sign of eigenvectors. However, several works demonstrate that the choice of the sign can be determined by the underlying data using the projection operator [8, 34, 38]. An intuitive example arises in the principal component analysis: Each eigenvector should point in the same direction as the points it is representing. This can be achieved by projecting the singular vector onto the data vectors and changing its sign to make the projection positive. This approach allows to select a canonical direction for the first few eigenvectors." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "text", + "content": "Sign ambiguity is a special case of basis ambiguity when all eigenvalues are distinct. The more general basis ambiguity occurs if an eigenvalue " + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "inline_equation", + "content": "\\lambda_{i}" + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "text", + "content": " has multiplicity degree " + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "inline_equation", + "content": "d_{i} > 1" + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "text", + "content": ". Then any " + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "text", + "content": " vectors forming an orthogonal basis in the subspace spanned by its eigenvectors " + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "inline_equation", + "content": "(\\phi_{i + 1},\\phi_{i + 2}\\dots \\phi_{i + d_i})" + }, + { + "bbox": [ + 313, + 545, + 554, + 641 + ], + "type": "text", + "content": " are also valid eigenvectors. Although the basis ambiguity is difficult to deal with, in practice high multiplicities do not occur often in low-order eigenvectors [29, 50]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 647, + 466, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 466, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 466, + 661 + ], + "type": "text", + "content": "3.3. Denoising Diffusion Models" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "Given a dataset of examples drawn independently from a data distribution " + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "inline_equation", + "content": "q(x)" + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": ", diffusion models aim to learn the underlying data distribution by sequentially denoising random noise samples [25, 53, 66]." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26901" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": "The forward diffusion process takes a real data point " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": " and incrementally adds to it a small amount of Gaussian noise, producing a sequence of " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": " noisy samples " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "x_1, \\ldots, x_T" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": ". The step sizes are controlled by a variance schedule " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "\\{\\beta_t \\in (0, 1)\\}_{t=1}^T" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": ". With the larger steps " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": ", the noisy sample " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": " further deviates from the original sample. At " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "T \\to \\infty" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": ", it is close to the Gaussian distribution, " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "x_T \\sim N(x_T; 0, I)" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": ". The reverse process recreates the original sample by iteratively removing noise from an input " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "x_T" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": " drawn from the Gaussian distribution. Assuming that the reverse conditional probability is conditioned on " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "q(x_{t-1} \\mid x_t, x_0) = N\\left(x_{t-1}; \\tilde{\\mu}(x_t, x_0), \\tilde{\\beta}_t I\\right)" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": ", we can obtain " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "\\tilde{\\mu}_t = \\frac{1}{\\sqrt{\\alpha_t}}\\left(x_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\tilde{\\alpha}_t}}\\epsilon_t\\right)" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "\\alpha_t = 1 - \\beta_t" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_t = \\prod_{i=1}^T \\alpha_i" + }, + { + "bbox": [ + 55, + 72, + 296, + 257 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "spans": [ + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "text", + "content": "Instead of directly predicting the denoised sample " + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "inline_equation", + "content": "\\tilde{\\mu}_t" + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "text", + "content": " with a neural network, we can predict the noise content " + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "text", + "content": " from the input " + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "text", + "content": " at time step " + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "text", + "content": " [25]. Such a model is trained with a denoising score-matching objective: " + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_t = E_{t\\sim [1,T],x_0,\\epsilon_t}\\left[\\| \\epsilon_t - \\epsilon_\\theta (x_t,t)\\| ^2\\right]" + }, + { + "bbox": [ + 55, + 260, + 296, + 329 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 353, + 211, + 368 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 353, + 211, + 368 + ], + "spans": [ + { + "bbox": [ + 55, + 353, + 211, + 368 + ], + "type": "text", + "content": "4. Denoising Functional Maps" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "spans": [ + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "type": "text", + "content": "This section introduces Denoising Functional Maps (DenoisFM), our approach for shape correspondence estimation; see Fig. 2 for the method overview. Since functional maps are square low-dimensional matrices (see Sec. 3.1), we use a standard neural architecture based on a 2D U-Net [61] as a backbone. We aim to train our model on a large collection of shapes with diverse geometry. Since functional maps are defined for shape pairs, for a dataset with " + }, + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "type": "text", + "content": " shapes the model would have to learn " + }, + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "type": "inline_equation", + "content": "m^2" + }, + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "type": "text", + "content": " functional maps. Instead of this naive approach, we consider the correspondences to a single template shape, following previous works [23, 72]. As a result, the training data includes only " + }, + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 379, + 296, + 536 + ], + "type": "text", + "content": " functional maps, one for each shape in the dataset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 540, + 296, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 296, + 649 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 296, + 649 + ], + "type": "text", + "content": "A functional map is defined in a specific basis of Laplacian eigenvectors, and knowing the exact basis combination is necessary to convert it to a point-wise correspondence map. Therefore, we compute the basis first and then condition the diffusion model on it; the model then returns the corresponding functional map. To reduce the complexity of the problem caused by the sign ambiguity of basis eigenvectors, we utilize a sign correction network to select a specific combination of signs for the basis." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "DenoisFM consists of two components: the DDPM for functional map prediction (Sec. 4.1) with post-processing that filters out low-quality solutions using Dirichlet energy of the point-wise map (Sec. 4.1.1), and the sign corrector for the Laplacian eigenvectors (Sec. 4.2)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 72, + 488, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 488, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 488, + 85 + ], + "type": "text", + "content": "4.1. Denoising Diffusion Component" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "spans": [ + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": "We next describe the training and inference of the diffusion component of DenoisFM. For training, we use a large collection of shapes and a template. For each shape " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": " in the dataset, we compute an eigenbasis " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": ", a template-wise functional map " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "C_{1T}" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": ", and conditioning " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "y = y(S,\\Phi)" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": " which incorporates geometric details of the input shape and information about the basis. The exact form of conditioning will be specified in Sec. 4.3. We use the training objective of denoising diffusion probabilistic models (DDPMs) [25]: " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{DDPM}} = E_{x,\\epsilon \\sim N(0,1),t}\\left[\\| \\epsilon -\\epsilon_{\\theta}(x_t,t,y)\\| _2^2\\right]" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": " is the amount of noise predicted by a 2D UNet [60], " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": " is a noisy version of the input " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "x_0\\coloneqq C_{1T}" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": " is the time step uniformly sampled from " + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "inline_equation", + "content": "\\{1,\\ldots ,T\\}" + }, + { + "bbox": [ + 313, + 92, + 555, + 255 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "content": "The inference pipeline consists of two stages, see Fig. 2a. In the template stage, for each individual shape " + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "content": " in the evaluation dataset, we obtain an eigenbasis " + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "content": ", calculate the conditioning " + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "content": ", and predict the template-wise functional map " + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "inline_equation", + "content": "C_{1T}" + }, + { + "bbox": [ + 313, + 256, + 555, + 376 + ], + "type": "text", + "content": " using the diffusion model. Note that the inference of DDPMs is time-consuming due to the large number of denoising steps and can take several hours for high-dimensional functional maps. Because the predicted maps refer to the template, we need to run the denoising process only once for each shape." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 380, + 556, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 556, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 556, + 489 + ], + "type": "text", + "content": "In the pairwise stage, for each test pair, we convert the respective template-wise functional maps into pairwise ones using the composition property [49]: " + }, + { + "bbox": [ + 313, + 380, + 556, + 489 + ], + "type": "inline_equation", + "content": "C_{12} = C_{1T}(C_{2T})^{-1}" + }, + { + "bbox": [ + 313, + 380, + 556, + 489 + ], + "type": "text", + "content": ". We then apply the Zoomout refinement [44] to increase the resolution of the functional maps. This spectral upsampling step has been shown to improve their accuracy, and our framework benefits from it without additional modifications. Finally, the functional map is converted into a pointwise map " + }, + { + "bbox": [ + 313, + 380, + 556, + 489 + ], + "type": "inline_equation", + "content": "\\Pi_{21}" + }, + { + "bbox": [ + 313, + 380, + 556, + 489 + ], + "type": "text", + "content": " using nearest neighbor search." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 504, + 474, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 504, + 474, + 516 + ], + "spans": [ + { + "bbox": [ + 314, + 504, + 474, + 516 + ], + "type": "text", + "content": "4.1.1. Post-Processing of the Samples" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "type": "text", + "content": "Diffusion models are inherently probabilistic and their outputs may differ given the same conditioning but different initial noise [25]. To address this, we repeat the denoising process multiple times and filter out the low-quality results. The selection is based on the Dirichlet energy of the pointwise map [21, 40]: an accurate map should be smooth, with neighboring vertices on one shape matching neighboring vertices on the other. Therefore, we repeat both the template step and the pairwise step to produce multiple point-wise maps. We can then either report the map with the lowest Dirichlet energy or combine the results of several smoothest maps. To do this, for each query point on the source mesh, we gather potential matching points on the target mesh and select the one with the smallest total distance to the other candidates (see Supp. B.3). The map selection step has a major impact on the accuracy of our method." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "26902" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 71, + 541, + 215 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 541, + 215 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 541, + 215 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 541, + 215 + ], + "type": "image", + "image_path": "37b7c3ee91cde8dc1f79b48cab49ee57ada7aa9d751bb45cd7d53faa6cefa407.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "lines": [ + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "text", + "content": "(a) Functional map prediction using a diffusion model. For each unique shape " + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "text", + "content": " in the dataset, we obtain feature vectors " + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "text", + "content": " using a feature extractor " + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "text", + "content": ", as well as a sign-corrected eigenbasis " + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "inline_equation", + "content": "\\hat{\\Phi}" + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "text", + "content": " (Fig. 2b, Sec. 4.2). Both are used for conditional prediction of the template-wise functional map " + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "inline_equation", + "content": "C_{1T}" + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "text", + "content": " using a diffusion model, performed separately for each shape. The pairwise functional maps " + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "inline_equation", + "content": "C_{12}" + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "text", + "content": " are obtained through the map composition property, upsampled using ZoomOut [44], and converted to pointwise maps " + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "inline_equation", + "content": "\\Pi_{21}" + }, + { + "bbox": [ + 55, + 218, + 555, + 258 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 109, + 266, + 504, + 373 + ], + "blocks": [ + { + "bbox": [ + 109, + 266, + 504, + 373 + ], + "lines": [ + { + "bbox": [ + 109, + 266, + 504, + 373 + ], + "spans": [ + { + "bbox": [ + 109, + 266, + 504, + 373 + ], + "type": "image", + "image_path": "0b1dfdf25910845f8b3aeb3adff0ad9b12e122dfed0db6ab664405e132ac55f1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "lines": [ + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "text", + "content": "(b) Learned sign correction. The eigenvectors " + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "text", + "content": " returned by a numerical eigensolver have random signs. To select a specific sign, we project the eigenvectors onto the feature vectors " + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "text", + "content": " obtained with a feature extractor " + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "text", + "content": ", and make the projection positive. The sign correction network is trained in an unsupervised manner: learning to correct eigenvectors that have random signs. The learned features " + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 374, + 555, + 415 + ], + "type": "text", + "content": " are also used for the conditional prediction of the template-wise functional map using a diffusion model (Fig. 2a)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 422, + 555, + 445 + ], + "lines": [ + { + "bbox": [ + 54, + 422, + 555, + 445 + ], + "spans": [ + { + "bbox": [ + 54, + 422, + 555, + 445 + ], + "type": "text", + "content": "Figure 2. Overview of DenoisFM. (a) A pair of shapes is matched using a DDPM model. (b) The signs of eigenvectors are corrected through learned features." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 465, + 195, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 465, + 195, + 478 + ], + "spans": [ + { + "bbox": [ + 55, + 465, + 195, + 478 + ], + "type": "text", + "content": "4.2. Learned Sign Correction" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "text", + "content": "The diffusion model needs to be conditioned on the basis eigenvectors and predict the functional map for that particular basis. Theoretically, the model could be trained using random basis combinations, as was done in Dwivedi et al. [18] for graph networks. However, this would significantly increase the amount of training data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "content": "Hence, we follow a more effective approach: we select a specific basis by fixing the sign of the Laplacian eigenvectors on each shape. Previous works infer the sign from the underlying data using the projection operator (see Sec. 3.2). Therefore, suppose that " + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "inline_equation", + "content": "\\Sigma \\coloneqq \\Theta(S) \\in \\mathbb{R}^{v \\times n}" + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "content": " is a set of pervertex feature vectors inferred from the geometry of shape " + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "content": " by a trainable feature extractor " + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "content": ", one for each eigenvector. The sign of the eigenvectors can be selected by projecting the features " + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "content": " onto the eigenvectors " + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "content": " and making the corresponding projections positive:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 119, + 684, + 295, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 684, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 119, + 684, + 295, + 714 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\sigma} := \\operatorname {s i g n} \\left[ \\operatorname {d i a g} \\left(\\Sigma^ {T} A \\Phi\\right) \\right], \\tag {3} \\\\ \\hat {\\Phi} := \\Phi \\hat {\\sigma}, \\\\ \\end{array}", + "image_path": "ca83c14156e9216a9b5d7065753fad0c3997d73fe3e736e8f84115e9f11337c1.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "spans": [ + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "text", + "content": "where “" + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "inline_equation", + "content": "\\mathrm{diag}(\\cdot)" + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "text", + "content": "” and “" + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "inline_equation", + "content": "\\mathrm{sign}(\\cdot)" + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "text", + "content": "” denote matrix diagonal and sign extraction operators, " + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "text", + "content": " is the diagonal vertex-area matrix. To illustrate, suppose we have a human mesh and a single feature vector " + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "inline_equation", + "content": "\\varsigma_{i}" + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "text", + "content": ", which is a binary vector with ones for points on the left hand, and zeros otherwise. After performing the procedure described in Eq. (3), the corrected eigenvector " + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "inline_equation", + "content": "\\hat{\\phi}_i" + }, + { + "bbox": [ + 313, + 466, + 555, + 550 + ], + "type": "text", + "content": " will be mostly positive on the left hand." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 555, + 463, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 463, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 463, + 567 + ], + "type": "text", + "content": "4.2.1. Training the Sign Corrector" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "text", + "content": "The sign correction network is trained in an unsupervised manner by learning to correct eigenvectors that have random signs. If we perform the eigendecomposition with a numerical solver twice on the same mesh and get two sets of eigenvectors " + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "inline_equation", + "content": "\\Phi_1" + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "inline_equation", + "content": "\\Phi_2" + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "text", + "content": ", due to the sign ambiguity, the difference between them can be written as " + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "inline_equation", + "content": "\\Phi_2 = \\Phi_1\\sigma" + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\{-1,1\\}^n" + }, + { + "bbox": [ + 313, + 570, + 555, + 677 + ], + "type": "text", + "content": " is the ground-truth sign difference. Now we perform the sign correction using Eq. (3), after which we expect the corrected eigenvectors to be equal to each other:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 413, + 686, + 553, + 706 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 413, + 686, + 553, + 706 + ], + "spans": [ + { + "bbox": [ + 413, + 686, + 553, + 706 + ], + "type": "interline_equation", + "content": "\\hat {\\Phi} _ {1} = \\hat {\\Phi} _ {2}, \\tag {4}", + "image_path": "e92f8bc1ae3246bf3a00b0a2ebc97ffad3d7766bc408e923197ad53b65684424.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 402, + 704, + 466, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 704, + 466, + 715 + ], + "spans": [ + { + "bbox": [ + 402, + 704, + 466, + 715 + ], + "type": "interline_equation", + "content": "\\Phi_ {1} \\hat {\\sigma} _ {1} = \\Phi_ {2} \\hat {\\sigma} _ {2},", + "image_path": "46d8ab44b975a376f232be866ffb6a16a58c68a8a0161826a768d7dd8d14a6ba.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26903" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_1, \\hat{\\sigma}_2 \\in \\{-1, 1\\}^n" + }, + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "content": " are the predicted combinations of correction signs. After substitution and using " + }, + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_1 \\hat{\\sigma}_1 = I" + }, + { + "bbox": [ + 55, + 72, + 297, + 97 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 138, + 108, + 212, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 108, + 212, + 121 + ], + "spans": [ + { + "bbox": [ + 138, + 108, + 212, + 121 + ], + "type": "interline_equation", + "content": "\\Phi_ {1} \\hat {\\sigma} _ {1} = \\Phi_ {1} \\sigma \\hat {\\sigma} _ {2},", + "image_path": "cb5acdd3e68dd6ac0aaf358e289852e1d720b621a5bc4fe9ecc47dcfd3d985ef.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 153, + 124, + 294, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 153, + 124, + 294, + 135 + ], + "spans": [ + { + "bbox": [ + 153, + 124, + 294, + 135 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {1} = \\sigma \\hat {\\sigma} _ {2}, \\tag {5}", + "image_path": "065fb1977646143dc566806618e959e5d5b28ac6a9a235f4d40db05b40e680ac.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 140, + 139, + 187, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 139, + 187, + 150 + ], + "spans": [ + { + "bbox": [ + 140, + 139, + 187, + 150 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {1} \\hat {\\sigma} _ {2} = \\sigma .", + "image_path": "a319d88d26be0ebb37c10e69a147d4d43b53e0f159619b3462dcc40be31dc70c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 163, + 296, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 163, + 296, + 211 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 296, + 211 + ], + "type": "text", + "content": "As a result, the difference between the predicted correction signs should be the same as the ground-truth sign difference, and we can use this as our unsupervised training objective with a mean square error function:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 126, + 228, + 296, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 228, + 296, + 240 + ], + "spans": [ + { + "bbox": [ + 126, + 228, + 296, + 240 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s i g n}} = \\operatorname {M S E} (\\hat {\\sigma} _ {1} \\hat {\\sigma} _ {2}; \\sigma) \\tag {6}", + "image_path": "cc4c402d074a0e88078bbdfc7115609e22a8e151dbe545d2b4c67be0d20d9432.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "content": "Note that the sign operator in Eq. (3) is not differentiable. Therefore, during training, we set " + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_1" + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_2" + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "content": " to be the diagonal elements of the projections, rather than their signs, assuming that the feature vectors and eigenvectors have unit norm. The training objective of the feature extractor (Eq. 6) then forces the elements of " + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_1" + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_2" + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "content": " to be as close to " + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "inline_equation", + "content": "1" + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "content": " as possible. The absolute value can be interpreted as confidence in the predicted sign: values close to " + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\pm 1" + }, + { + "bbox": [ + 55, + 251, + 296, + 357 + ], + "type": "text", + "content": " mean high confidence." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 360, + 296, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 360, + 296, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 360, + 296, + 433 + ], + "type": "text", + "content": "In practice, we found that a network trained this way quickly converges on a dataset of human or animal meshes. Our method returns the same corrected eigenbasis " + }, + { + "bbox": [ + 55, + 360, + 296, + 433 + ], + "type": "inline_equation", + "content": "95 - 99\\%" + }, + { + "bbox": [ + 55, + 360, + 296, + 433 + ], + "type": "text", + "content": " of the time for the first hundred Laplacian eigenvectors. The accuracy of the sign correction and its impact on the distribution of functional maps are discussed in Supp. A." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 443, + 187, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 443, + 187, + 455 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 187, + 455 + ], + "type": "text", + "content": "4.3. Choice of Conditioning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 461, + 296, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 296, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 296, + 581 + ], + "type": "text", + "content": "Conditioning of the diffusion model should include two parts: the basis information and the geometric properties of the shape. The former can be provided simply via the sign-corrected eigenvectors " + }, + { + "bbox": [ + 55, + 461, + 296, + 581 + ], + "type": "inline_equation", + "content": "\\hat{\\Phi}" + }, + { + "bbox": [ + 55, + 461, + 296, + 581 + ], + "type": "text", + "content": ". They additionally represent the spectral embedding of the shape and convey the full intrinsic information. As for the latter, during the training of the sign-correction network, the useful properties will be encoded in the learned feature vectors " + }, + { + "bbox": [ + 55, + 461, + 296, + 581 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 461, + 296, + 581 + ], + "type": "text", + "content": ". Therefore, we propose to project the feature vectors onto the sign-corrected eigenvectors:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 119, + 592, + 295, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 592, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 119, + 592, + 295, + 605 + ], + "type": "interline_equation", + "content": "\\text {C o n d i t i o n g} y = \\Sigma^ {T} A \\hat {\\Phi}. \\tag {7}", + "image_path": "34217fc3bfef1e53c803a26ba52e98cdba9f6a070057e261794f5b50a167cdd8.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 618, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 713 + ], + "type": "text", + "content": "This form of conditioning has two important properties. First, it has the same dimensions as the functional map. Therefore, we can condition the diffusion model using a simple concatenation, where the conditioning matrix is concatenated with the intermediate denoising targets and passed through the score estimator as input [25, 75]. Second, it is independent of the number of vertices, making it scalable to large meshes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 509, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 509, + 85 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 509, + 85 + ], + "type": "text", + "content": "5. Training and Experimental Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 91, + 555, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 236 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 236 + ], + "type": "text", + "content": "This section describes the steps for generating the training data for our model (Sec. 5.1) as well as the experimental results on several challenging datasets (Secs. 5.2-5.5). The evaluation of the sign correction network, additional comparison, implementation details, and the ablation studies can be found in Supp. A to C. Since our model is designed to be trained on large and diverse shape collections, it can be applied to multiple (reminiscent) shape classes without retraining. This reduces the need for small category-specific training sets. We focus on datasets with human-like shapes as their combined volume allows versatile comparison of our approach with the previous works." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 243, + 501, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 501, + 256 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 501, + 256 + ], + "type": "text", + "content": "5.1. Training Data and Implementation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 262, + 554, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 262, + 554, + 310 + ], + "spans": [ + { + "bbox": [ + 313, + 262, + 554, + 310 + ], + "type": "text", + "content": "Our model consists of two independent components: a denoising diffusion model that predicts the functional map and a sign correction network based on a per-vertex feature extractor, trained separately on their respective datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 316, + 427, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 427, + 328 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 427, + 328 + ], + "type": "text", + "content": "5.1.1. Denoising Diffusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 331, + 555, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 555, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 555, + 536 + ], + "type": "text", + "content": "Diffusion models require large amounts of training data with hundreds of thousands of examples. Therefore, we follow 3D-CODED [23] and use the SURREAL [73] dataset with 230,000 human meshes generated with SMPL [37]. All its meshes are smooth and have the same vertex structure. To make the connectivity more diverse, we remesh each mesh [28, 46] and randomly simplify the number of faces using Quadric Edge Collapse [22]. In " + }, + { + "bbox": [ + 313, + 331, + 555, + 536 + ], + "type": "inline_equation", + "content": "65\\%" + }, + { + "bbox": [ + 313, + 331, + 555, + 536 + ], + "type": "text", + "content": " of the cases, we simplify the entire mesh resulting in uniform connectivity. In the remaining " + }, + { + "bbox": [ + 313, + 331, + 555, + 536 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 313, + 331, + 555, + 536 + ], + "type": "text", + "content": " of the cases, we simplify only a small subset of the mesh to add non-even connectivity to the training data. After remeshing, we correct the signs of the eigenvectors using a pre-trained sign correction network (Sec. 4.2) and compute the functional map to the template shape. We only store the functional maps and conditioning matrices to save memory requirements. The data generation takes 10 hours using parallel processing." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 536, + 554, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 554, + 620 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 554, + 620 + ], + "type": "text", + "content": "We use the standard DDPM [25] implemented in Diffusers [74] and distributed training with Accelerate [24]. We train models that predict 32, 64, and 96-dimensional functional maps for 100 epochs on eight A40 GPUs, which takes 1, 8, and 30 hours respectively. The inference at the template stage takes 1, 7, and 27 minutes for each shape in the dataset. The pairwise stage takes 30 seconds per pair." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 626, + 450, + 638 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 626, + 450, + 638 + ], + "spans": [ + { + "bbox": [ + 313, + 626, + 450, + 638 + ], + "type": "text", + "content": "5.1.2. Sign Correction Network" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "content": "The per-vertex feature extractor of the sign correction network is based on DiffusionNet [65] (not to be confused with denoising diffusion) with six blocks and 128 WKS descriptors [5] as input. This architecture was designed for small shape matching datasets, so we used 1000 randomly selected meshes from SURREAL for training. Each" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "26904" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "content": "of them was randomly remeshed and simplified without adding anisotropy. The sign correction network is trained for " + }, + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "inline_equation", + "content": "5 \\cdot 10^{4}" + }, + { + "bbox": [ + 55, + 72, + 295, + 120 + ], + "type": "text", + "content": " iterations, which takes one hour on a single A40 GPU; the inference takes a few seconds per shape." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 129, + 228, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 129, + 228, + 142 + ], + "spans": [ + { + "bbox": [ + 55, + 129, + 228, + 142 + ], + "type": "text", + "content": "5.2. Near-Isometric Shape Matching" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 146, + 295, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 146, + 295, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 295, + 194 + ], + "type": "text", + "content": "Datasets. We evaluate our method on three widely used datasets: FAUST [7], SCAPE [3] and SHREC'19 [43]. Following previous works, we use their more challenging remeshed versions [15, 56]:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 195, + 295, + 301 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 195, + 295, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 195, + 295, + 217 + ], + "spans": [ + { + "bbox": [ + 55, + 195, + 295, + 217 + ], + "type": "text", + "content": "- The FAUST dataset contains meshes of 10 human classes in 10 poses, 100 in total. The train/test split is 80/20." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 219, + 294, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 219, + 294, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 219, + 294, + 242 + ], + "type": "text", + "content": "- The SCAPE dataset includes 71 meshes of the same person in different poses, the last 20 are used for testing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 243, + 294, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 243, + 294, + 301 + ], + "spans": [ + { + "bbox": [ + 55, + 243, + 294, + 301 + ], + "type": "text", + "content": "- The SHREC'19 dataset is composed of 44 shapes with diverse body types and poses, arguably the most challenging of the three. This dataset does not have a train split and is used for testing only. Following [11], we removed shape 40 since it is the only partial non-closed shape." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 310, + 295, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 310, + 295, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 310, + 295, + 453 + ], + "type": "text", + "content": "Baselines. We compare our approach with two categories of non-rigid shape correspondence methods. The first includes large-scale template-based models trained on SURREAL: 3D-CODED [23] and TransMatch [72], i.e., our main competitors as our work belongs to the same group. The second category includes descriptor-based models: ULRSSM [11], DiffZO [39], ConsistentFMaps [69], GeomFMaps [15], AttentiveFMaps [33], DUO-FMNet [16], SSL [10], SmS [12]. Since our and other methods can be applied to any shape class, we do not include template fitting methods such as NICP [42], which typically focus on human scans and incorporate explicit human body priors." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 454, + 295, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 454, + 295, + 550 + ], + "spans": [ + { + "bbox": [ + 55, + 454, + 295, + 550 + ], + "type": "text", + "content": "To compare both categories of baselines fairly, we note that SCAPE is too small to train large models. On the other hand, FAUST was created with SMPL [37] like SURREAL, and includes a sufficient diversity of body types and poses. Therefore, we follow [10, 11, 69] and train large models on SURREAL, descriptor-based models on FAUST, and evaluate them on three test datasets. A comparison with the baselines trained on FAUST+SCAPE can be found in Supp. C.2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 557, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 295, + 689 + ], + "type": "text", + "content": "Results. We report the mean geodesic error of our model and the baselines in Table 1. Compared to other large-scale methods trained on SURREAL, our work generalizes well to meshes from SCAPE and SHREC'19. A common problem in large-scale baselines is predicted point maps with incorrect symmetry. This is caused by the fact that the geometry of the evaluation meshes has fewer fine-scale details such as fingers, which help to disambiguate the internal symmetry. Our work avoids overfitting to fine-scale details of SURREAL by using data augmentation (Sec. 5.1). As a result, we can utilize large amounts of data more effectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "Compared to descriptor-based methods, our results are on par on all datasets (especially SHREC'19), demonstrat" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 326, + 69, + 545, + 217 + ], + "blocks": [ + { + "bbox": [ + 326, + 69, + 545, + 217 + ], + "lines": [ + { + "bbox": [ + 326, + 69, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 326, + 69, + 545, + 217 + ], + "type": "table", + "html": "
ModelCategoryF_rS_rS’19_r
3D-CODEDLarge-2.516.117.3
TransMatchScale1.715.321.0
DUO-FMNet2.54.26.4
GeomFMaps1.92.47.9
AttentiveFMaps1.92.65.8
ConsistentFMapsDescriptor-2.32.63.8
SSLBased2.03.14.0
DiffZO1.92.44.2
ULRSSM1.62.25.7
SmS1.43.36.2
Ours - 64×641.82.33.5
Ours - 96×961.72.13.9
", + "image_path": "ec5c7e1b984ad0955ff3146e95e5b04728d5fae73c349d016101ecd2de806064.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 224, + 553, + 280 + ], + "lines": [ + { + "bbox": [ + 313, + 224, + 553, + 280 + ], + "spans": [ + { + "bbox": [ + 313, + 224, + 553, + 280 + ], + "type": "text", + "content": "Table 1. Mean geodesic errors " + }, + { + "bbox": [ + 313, + 224, + 553, + 280 + ], + "type": "inline_equation", + "content": "(\\times 100)" + }, + { + "bbox": [ + 313, + 224, + 553, + 280 + ], + "type": "text", + "content": " on the remeshed FAUST, SCAPE, and SHREC'19 datasets. The best results are highlighted. Large-scale methods are trained on SURREAL, and descriptor-based methods on FAUST. Here and in the following, the results of our model are averaged across 5 runs." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 316, + 293, + 555, + 427 + ], + "blocks": [ + { + "bbox": [ + 316, + 293, + 555, + 427 + ], + "lines": [ + { + "bbox": [ + 316, + 293, + 555, + 427 + ], + "spans": [ + { + "bbox": [ + 316, + 293, + 555, + 427 + ], + "type": "image", + "image_path": "ab7467989956d412eb654a556da4be94f761993c744f635626c8106c37feed95.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 440, + 555, + 463 + ], + "lines": [ + { + "bbox": [ + 313, + 440, + 555, + 463 + ], + "spans": [ + { + "bbox": [ + 313, + 440, + 555, + 463 + ], + "type": "text", + "content": "Figure 3. Qualitative results by our approach on SHREC'19 (top) and DT4D (bottom) datasets; see also Supp. C.1." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 479, + 553, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 553, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 553, + 528 + ], + "type": "text", + "content": "ing our excellent performance on diverse shape classes. We can see that most descriptor-based methods can generalize to non-SMPL meshes, but none of them show competitive performance on all three datasets simultaneously." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 529, + 554, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 554, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 554, + 588 + ], + "type": "text", + "content": "We show the qualitative results of our model on several challenging meshes from SHREC'19 in Fig. 3. Even though these shapes include high-frequency details such as muscles, in contrast to the smooth shapes typically generated by SMPL, our model is able to obtain correct correspondences." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 599, + 506, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 599, + 506, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 599, + 506, + 612 + ], + "type": "text", + "content": "5.3. Matching with Anisotropic Meshing" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 713 + ], + "type": "text", + "content": "Datasets. To evaluate the robustness of our method to different connectivity, we use the anisotropically remeshed versions of FAUST and SCAPE [16], denoted F_a and S_a, respectively. In these datasets, the triangle scale is uneven, ranging from small and densely packed triangles on one side of the mesh to large and coarse triangulation on the other. As a result, models that are sensitive to mesh connectivity will likely fail to predict the correct maps." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "26905" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 70, + 265, + 183 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 265, + 183 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 265, + 183 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 265, + 183 + ], + "type": "table", + "html": "
ModelCategoryF_aS_a
3D-CODEDLarge2.916.9
TransMatchScale2.716.2
DUO-FMNet3.04.4
GeomFMapsDescriptor3.23.8
AttentiveFMapsBased2.42.8
ConsistentFMaps2.62.7
ULRSSM1.92.4
Ours - 64×642.12.3
Ours - 96×962.02.2
", + "image_path": "b24cffbc698cb31d5feb047e8f2ed41062215614a20f10c5ca1074f0c2e3675e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 65, + 214, + 286, + 338 + ], + "blocks": [ + { + "bbox": [ + 73, + 192, + 277, + 203 + ], + "lines": [ + { + "bbox": [ + 73, + 192, + 277, + 203 + ], + "spans": [ + { + "bbox": [ + 73, + 192, + 277, + 203 + ], + "type": "text", + "content": "Table 2. Results on the anisotropic FAUST and SCAPE." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 214, + 286, + 338 + ], + "lines": [ + { + "bbox": [ + 65, + 214, + 286, + 338 + ], + "spans": [ + { + "bbox": [ + 65, + 214, + 286, + 338 + ], + "type": "table", + "html": "
ClassIntraInter
Ours[11][69]Ours[11][69]
manneq.1.01.01.63.34.04.5
zlorp1.11.32.14.26.94.2
crypto1.11.52.4---
prisoner1.11.12.129.620.526.7
ninja1.45.62.24.316.27.1
ortiz9.34.42.5---
mousey10.22.75.2---
drake10.61.02.110.48.24.5
skeletonz.16.31.41.449.436.548.0
", + "image_path": "83f30f3e682ce8047afe0a811e4f74d1ec009e92735802750bf10f6a1af98f0c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 395, + 296, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 395, + 296, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 395, + 296, + 479 + ], + "type": "text", + "content": "Results. Table 2 shows the matching results. Both large-scale and descriptor-based methods experience performance drops on anisotropically remeshed datasets. In contrast, our method is more robust to changes in mesh connectivity. We attribute this to our design choices, such as diversifying the vertex structure of the training data and using conditioning that is independent of the number of vertices." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 486, + 205, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 205, + 499 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 205, + 499 + ], + "type": "text", + "content": "5.4. Zero-Shot Shape Matching" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 503, + 296, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 503, + 296, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 296, + 624 + ], + "type": "text", + "content": "Datasets. Generalization to shape types not observed during training is a desirable property in many shape matching applications. To evaluate our model on unseen data, we use the non-isometric DT4D dataset [40] that consists of nine humanoid shape classes. While typically, 198 shapes are defined for training and 95 for testing, we instead make the evaluation more challenging by training on human datasets, SURREAL or FAUST. This can be viewed as a zero-shot setting, since most of the test shapes are different from the training data (see Supp. C.1 for an illustration)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 629, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 295, + 701 + ], + "type": "text", + "content": "Results. Our proposed experimental setup is challenging due to the differences between the training and test shapes. We use a lower-resolution model predicting a " + }, + { + "bbox": [ + 55, + 629, + 295, + 701 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 55, + 629, + 295, + 701 + ], + "type": "text", + "content": " functional map, results of all our models are shown in Supp. C.5. We compare our method with recent descriptor-based approaches: ConsistentFMaps [69] and ULRSSM [11]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 702, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 295, + 713 + ], + "type": "text", + "content": "The mean geodesic errors per class for inter- and intra" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 321, + 70, + 442, + 173 + ], + "blocks": [ + { + "bbox": [ + 55, + 346, + 295, + 381 + ], + "lines": [ + { + "bbox": [ + 55, + 346, + 295, + 381 + ], + "spans": [ + { + "bbox": [ + 55, + 346, + 295, + 381 + ], + "type": "text", + "content": "Table 3. Results on shape classes from DT4D. Classes mousey and ortiz are not present in inter-class split. All inter-class evaluation pairs have the format \"crypto vs other class\", so crypto is excluded." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 70, + 442, + 173 + ], + "lines": [ + { + "bbox": [ + 321, + 70, + 442, + 173 + ], + "spans": [ + { + "bbox": [ + 321, + 70, + 442, + 173 + ], + "type": "table", + "html": "
ClassOurs[11][69]
wolf3.53.54.4
dog3.53.54.5
horse3.73.84.4
cow3.83.84.4
lion4.03.84.9
fox4.73.64.9
hippo7.69.97.9
mean4.34.34.8
", + "image_path": "c02b7320a2b03afe74322ed08c312e861328770ee0e02a9204f750c23bbae47c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 446, + 71, + 542, + 167 + ], + "blocks": [ + { + "bbox": [ + 446, + 71, + 542, + 167 + ], + "lines": [ + { + "bbox": [ + 446, + 71, + 542, + 167 + ], + "spans": [ + { + "bbox": [ + 446, + 71, + 542, + 167 + ], + "type": "image", + "image_path": "1c3fb53794170792745041786366ccb6398ee75f3b5805c62c650d87615d1102.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 180, + 554, + 204 + ], + "lines": [ + { + "bbox": [ + 313, + 180, + 554, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 554, + 204 + ], + "type": "text", + "content": "Table 4. Results on the SMAL dataset [16], all categories are present in train/test sets. Format: category vs. everything." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 218, + 554, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 218, + 554, + 278 + ], + "spans": [ + { + "bbox": [ + 313, + 218, + 554, + 278 + ], + "type": "text", + "content": "category splits are shown in Table 3, with further comparisons in Supp. C.7. Our method achieves accurate matching for most shape classes in both splits, demonstrating the generalization of our method to data unseen during training. We show the qualitative examples in Fig. 3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 286, + 476, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 286, + 476, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 286, + 476, + 300 + ], + "type": "text", + "content": "5.5. Application to Animal Shapes" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 304, + 555, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 304, + 555, + 448 + ], + "spans": [ + { + "bbox": [ + 313, + 304, + 555, + 448 + ], + "type": "text", + "content": "Datasets. To demonstrate the applicability of our method to shape classes other than humans, we test our approach on the SMAL dataset containing seven animal types. We take the 32/17 split from [16], where all categories are present in train/test sets. While the original training set is sufficient for descriptor-based baselines, it is too small for our model. To address this, we use the fitted parameters of the SMAL parametric model [77] and randomly vary the pose of each training animal, generating a total of 64,000 meshes. We use the mean SMAL shape as a template. Note that this generated dataset conveys little new information, since e.g., there are only three different types of lions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 455, + 554, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 455, + 554, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 455, + 554, + 515 + ], + "type": "text", + "content": "Results. Table 4 shows the results of our " + }, + { + "bbox": [ + 313, + 455, + 554, + 515 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 313, + 455, + 554, + 515 + ], + "type": "text", + "content": " model. Although the training data for our method lacks sufficient diversity, we achieve comparable performance to the baselines. Therefore, given enough training data, we believe our method can be applied to any shape class." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 525, + 388, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 525, + 388, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 525, + 388, + 538 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 555, + 713 + ], + "type": "text", + "content": "We presented DenoisFM, an approach of a new class for shape correspondence estimation. Our model is trained on a large dataset of synthetic human meshes and predicts the functional map between a pair of shapes using a denoising diffusion model. DenoisFM achieves correspondence accuracy on par with state-of-the-art methods across multiple datasets. The key advantage of our work is its generalization ability to human and humanoid shapes that differ noticeably from the training data, as well as competitive performance on animal shapes. Therefore, DenoisFM bridges the gap between previous large-scale and descriptor-based approaches by efficiently leveraging large amounts of data, opening up a new direction for using diffusion models in shape correspondence estimation." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "26906" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 92, + 296, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 92, + 296, + 117 + ], + "spans": [ + { + "bbox": [ + 55, + 92, + 296, + 117 + ], + "type": "text", + "content": "ZL acknowledges the support of the DFG Sachbeihilfe grant LA 5191/2-1." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 130, + 115, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 130, + 115, + 144 + ], + "spans": [ + { + "bbox": [ + 56, + 130, + 115, + 144 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 150, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 150, + 296, + 184 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 150, + 296, + 184 + ], + "spans": [ + { + "bbox": [ + 61, + 150, + 296, + 184 + ], + "type": "text", + "content": "[1] Ahmed Abdelreheem, Abdelrahman Eldesokey, Maks Ovsjanikov, and Peter Wonka. 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In Computer Vision and Pattern Recognition (CVPR), pages 6365-6373, 2017. 8" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "26909" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_content_list.json b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e3d7354b5e8169ec55429914b1c03f951541e21b --- /dev/null +++ b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_content_list.json @@ -0,0 +1,1810 @@ +[ + { + "type": "text", + "text": "Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes", + "text_level": 1, + "bbox": [ + 246, + 130, + 750, + 176 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/89156821aabbee6877038a1ecc316ab45776a5ab47da7330b32b36759717e8f0.jpg", + "image_caption": [ + "Suhyun Shin POSTECH", + "Seungwoo Yoon POSTECH", + "Ryota Maeda \nPOSTECH, University of Hyogo" + ], + "image_footnote": [], + "bbox": [ + 91, + 243, + 483, + 513 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6e782d289ebd3330b8c812f85d23601e17e77e499cf30157e74646c2c887d6c1.jpg", + "image_caption": [ + "Seung-Hwan Baek POSTECH" + ], + "image_footnote": [], + "bbox": [ + 483, + 243, + 743, + 513 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/47e2faf80318818f08b87b483d3dbb28c5a256317a1e5e4643839c505dcb5c2c.jpg", + "image_caption": [ + "Figure 1. We introduce a spectrally multiplexed Dense Dispersed Structured Light (DDSL), accurate hyperspectral 3D imaging method for dynamic scenes. (a) Capture configuration, (b) estimated hyperspectral image in sRGB and depth image for dynamic scenes, (c) estimated hyperspectral image, (d) comparison with spectroradiometer measurements." + ], + "image_footnote": [], + "bbox": [ + 743, + 243, + 905, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 566, + 326, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyperspectral 3D imaging captures both depth maps and hyperspectral images, enabling comprehensive geometric and material analysis. Recent methods achieve high spectral and depth accuracy; however, they require long acquisition times—often over several minutes—or rely on large, expensive systems, restricting their use to static scenes. We present Dense Dispersed Structured Light (DDSL), an accurate hyperspectral 3D imaging method for dynamic scenes that utilizes stereo RGB cameras and an RGB projector equipped with an affordable diffraction grating film. We design spectrally multiplexed DDSL patterns that significantly reduce the number of required projector patterns, thereby accelerating acquisition speed. Additionally, we formulate an image formation model and a reconstruction method to estimate a hyperspectral image and depth map from captured stereo images. As the first practical and accurate hyperspectral 3D imaging method for dynamic scenes, we experimentally demonstrate that DDSL achieves a spectral resolution of $15.5\\mathrm{nm}$ full width at half maximum (FWHM), $4\\mathrm{mm}$ depth error, and $6.6\\mathrm{fps}$ .", + "bbox": [ + 86, + 598, + 485, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 514, + 566, + 643, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyperspectral imaging captures a scene across multiple spectral channels beyond the three-channel RGB imaging, thereby providing both spectral and spatial information about the scene. Expanding on this, hyperspectral 3D imaging has recently received interest, as it captures both spectral and geometric information in the form of a depth map and a hyperspectral image. It has proven useful in scientific analysis of real-world materials, with applications in object classification [15], food ripeness detection [20], cultural heritage analysis, and geology [12]. Recently, dispersed structured light has been proposed as a cost-effective and compact solution for accurate hyperspectral 3D imaging [19]. However, its applicability remains limited to static scenes due to the need for projecting hundreds of patterns, resulting in acquisition times of several minutes.", + "bbox": [ + 511, + 595, + 906, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Increasing the acquisition speed of hyperspectral 3D imaging could make it feasible to analyze the geometric and material properties of objects and scenes in motion. Existing methods rely on expensive, bulky systems, such as coded-aperture snapshot spectral imagers (CASSI) [24]", + "bbox": [ + 511, + 824, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16589", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9319688cf13debe69675821ad1d37d0bf62a1794eabec186c08e3a3209fb01f7.jpg", + "image_caption": [ + "(a) Imaging system" + ], + "image_footnote": [], + "bbox": [ + 114, + 85, + 330, + 196 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/585a66eb6ae7457b18225b6e53f89ab400acbab9f50261f3daaf570f0ccb73c0.jpg", + "image_caption": [ + "(b) Schematic diagram", + "Figure 2. Imaging System. (a) Our active stereo system comprises RGB stereo cameras and a RGB projector equipped with a diffraction grating. (b) The diffraction grating introduces dispersion to the projector light. (c) Spectral sensitivity and emission functions of the camera and the projector. (d) Diffraction grating efficiency." + ], + "image_footnote": [], + "bbox": [ + 330, + 87, + 486, + 196 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/92a0f6003b9a1f51faf14ef80d8f8097fcfb471f553bf9e5e43b51194fc7b3f5.jpg", + "image_caption": [ + "(c) Radiometric parameters" + ], + "image_footnote": [], + "bbox": [ + 491, + 89, + 687, + 196 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/de440bcaf7a4fe78764a108d48bac5d8dfaae474710747fdbd6b4b5070a42af0.jpg", + "image_caption": [ + "(d) Diffraction grating efficiency $\\eta_{\\lambda}$" + ], + "image_footnote": [], + "bbox": [ + 689, + 90, + 883, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "paired with stereo cameras or time-of-flight setups [10, 17, 25-27]. While compact, practical PSF-based systems exist [4, 18], they significantly compromise either depth or spectral accuracy.", + "bbox": [ + 89, + 268, + 482, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose DDSL, an accurate hyperspectral 3D imaging method for dynamic scenes, using a compact and affordable system. Figure 1 shows the capture configuration using our prototype, which consists of stereo RGB cameras and an RGB projector equipped with an affordable diffraction-grating film that generates structured-light projections with wavelength-dependent dispersion.", + "bbox": [ + 89, + 332, + 482, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We design DDSL patterns for the projector that produce spectrally multiplexed light projections, allowing us to use fewer than ten projections, enabling rapid image acquisition for dynamic scenes. We analyze the stereo images captured under these repeating DDSL patterns by developing an image formation model and a reconstruction method for depth maps and hyperspectral images.", + "bbox": [ + 89, + 440, + 483, + 546 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DDSL enables accurate depth and spectral estimation even for high-frequency spectral variations, where existing affordable methods fall short. We demonstrate that DDSL achieves a depth error of $4\\mathrm{mm}$ , a spectral FWHM of $15.5\\mathrm{nm}$ in the visible spectrum, and acquisition speed of 6.6 FPS. Our dynamic imaging is achieved through software synchronization between the cameras and the projector. The use of a compact and affordable active-stereo setup enhanced with a diffraction grating film makes DDSL a promising approach for practical and accurate hyperspectral 3D imaging of dynamic scenes.", + "bbox": [ + 89, + 547, + 482, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions as follows:", + "bbox": [ + 109, + 717, + 401, + 731 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce Dense Dispersed Structured Light (DDSL), which enables high-quality hyperspectral 3D imaging for dynamic scenes using an affordable active-stereo setup composed of RGB stereo cameras and an RGB projector augmented with a diffraction grating film.", + "- We design DDSL patterns and develop an image formation model and hyperspectral 3D reconstruction method for dynamic scenes, obtaining a depth map and a hyperspectral images from stereo RGB images.", + "- We demonstrate that DDSL outperforms state-of-the-art affordable hyperspectral 3D imaging methods in acquisi" + ], + "bbox": [ + 89, + 734, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion speed with high reconstruction accuracy, achieving a depth error of $4\\mathrm{mm}$ , a spectral FWHM of $15.5\\mathrm{nm}$ , and a frame rate of 6.6 FPS.", + "bbox": [ + 524, + 268, + 906, + 314 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 325, + 653, + 342 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Hyperspectral 3D Imaging Various hyperspectral 3D imaging systems have been developed. Kim et al. [12] combined a laser scanner with a CASSI system for accurate hyperspectral 3D imaging, while Li et al. [13] employed a practical projector-camera setup, though at the cost of reduced spectral accuracy. Shin et al. [19] introduced a compact projector-camera system using dispersed structured light with a diffraction grating. However, these previous approaches are generally limited to static scenes due to their long acquisition times, often lasting several minutes. For dynamic scenes, a common approach is to use depth video cameras in conjunction with hyperspectral video cameras. However, hyperspectral video cameras tend to be large and expensive [1, 2, 6, 10, 17, 23, 25, 26]. While solutions using point spread function (PSF) engineering offer single-shot hyperspectral 3D imaging in a compact setup through custom micro- or nano-optical elements, they generally have limited spectral and depth accuracy [4, 18]. Our method achieves accurate hyperspectral 3D imaging for dynamic scenes using a practical setup: stereo RGB cameras and an RGB projector with a diffraction grating film.", + "bbox": [ + 511, + 352, + 906, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Active Stereo Active stereo employs a stereo camera and an illumination module projecting structured-light patterns for robust 3D imaging [3, 5, 11, 16, 29]. Heist et al. [10] repurposed an active stereo system with a high-speed projector and hyperspectral video cameras for hyperspectral 3D imaging of dynamic scenes. However, the use of hyperspectral video cameras significantly increases instrumentation costs. We leverage a diffraction grating film in front of an RGB projector with RGB stereo cameras, eliminating the need for hyperspectral cameras and enabling practical, accurate hyperspectral 3D imaging for dynamic scenes.", + "bbox": [ + 511, + 686, + 906, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dispersive Optics Dispersive optics, including prisms and diffraction gratings, are widely used in hyperspectral", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16590", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "imaging. CASSI systems utilize relay lenses with dispersive elements and coded masks for precise spectral reconstruction. Cao et al. [6] minimized system size by using a prism and coded mask without relay lenses. Recently, diffractive optical elements have been employed to create spectrally varying point spread functions [4, 18]. Shin et al. [19] integrated a diffraction grating film into a projector-camera system, though it required hundreds of projected patterns, resulting in long capture times. Our method achieves rapid acquisition at 6.6 fps with high spectral and depth accuracy, through our active stereo setup, DDSL patterns, image formation model, and reconstruction method.", + "bbox": [ + 89, + 90, + 483, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Imaging System", + "text_level": 1, + "bbox": [ + 89, + 287, + 250, + 304 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce a practical and affordable active stereo system. We use stereo RGB cameras (FLIR GS3-U3-32S4C-C) and an RGB projector (Epson CO-FH02) equipped with diffraction grating film (Edmund 54-509) placed in front of the projector (see Figure 2(a)). The diffraction grating film, which costs less than 20 USD, disperses the broadband projector light according to the light wavelength $\\lambda$ as shown Figure 2(b). Each dispersed light ray of a specific wavelength $\\lambda$ then propagates to a scene, creating spatially-distributed narrow-band spectral illumination. The stereo cameras capture the scene illuminated by the dispersed light. We set the camera fields of view to capture first-order diffracted light [9]. For color channel $c\\in \\{R,G,B\\}$ and wavelength $\\lambda$ , we calibrate and refine the projector spectral emission $\\Omega_{c,\\lambda}^{\\mathrm{proj}}$ , camera spectral sensitivity $\\Omega_{c,\\lambda}^{\\mathrm{cam}}$ , and diffraction-grating efficiency $\\eta_{\\lambda}$ (Figures 2(c) and (d)).", + "bbox": [ + 89, + 311, + 483, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Image Formation", + "text_level": 1, + "bbox": [ + 89, + 569, + 261, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We develop an image formation model for the active stereo system given a pattern image $P$ that we set to the projector.", + "bbox": [ + 89, + 594, + 483, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Projector Light Given the projector pattern $P(q, c)$ where $q$ is a projector pixel and $c \\in \\{R, G, B\\}$ is a color channel, we model the light intensity $L(q, \\lambda)$ emitted from the pixel $q$ at wavelength $\\lambda$ as", + "bbox": [ + 89, + 643, + 483, + 705 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL (q, \\lambda) = \\sum_ {c} \\Omega_ {c, \\lambda} ^ {\\operatorname {p r o j}} P (q, c). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 717, + 482, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dispersed Light Projection Model The light ray of wavelength $\\lambda$ emitted by the projector pixel $q$ is diffracted by the diffraction grating and propagates to a scene. We model such dispersed projection in a backward manner as shown Figure 3(a). That is, from a scene point $\\mathbf{p}$ and given wavelength $\\lambda$ , we model its corresponding projector pixel $q_{\\lambda}$ that emits the ray:", + "bbox": [ + 89, + 766, + 483, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq _ {\\lambda} = \\psi (\\mathbf {p}, \\lambda). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 233, + 885, + 482, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/869eacad7267465a184c9ec68cb15b9a9f0e17d62991c1dc485c8fb9dae07aa7.jpg", + "image_caption": [ + "(b) Sub-pixel accurate sample collection for data-driven backward modeling" + ], + "image_footnote": [], + "bbox": [ + 521, + 85, + 903, + 414 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/490a5e55a5678412de3401313909f8ece324ad07054d1fd80fabd27a3fac44bb.jpg", + "image_caption": [ + "(d) Depth dependent backward mapping model $\\psi$ for specific wavelength", + "Figure 3. Image Formation. (a) Light transport of the dispersed light projection of the mapping function $\\psi$ . (b) Sub-pixel accurate sample collection for data-driven backward modeling. Calibrated backward mapping model that relates pixel point to projector horizontal position (c) for depth given a specific wavelength and (d) for wavelength given a fixed depth value." + ], + "image_footnote": [], + "bbox": [ + 519, + 441, + 681, + 547 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0cda267d6a27220d8f59242f547799af8b0462390028e6b1f73e742b123ffd28.jpg", + "image_caption": [ + "(e) Wavelength dependent backward mapping model $\\psi$ for specific depth" + ], + "image_footnote": [], + "bbox": [ + 683, + 444, + 895, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To construct the backward model $\\psi$ , we use a data-driven approach. First, we acquire the samples $q_{\\lambda} \\in \\mathbb{S}_q$ , $\\lambda \\in \\mathbb{S}_{\\lambda}$ , $\\mathbf{p} \\in \\mathbb{S}_{\\mathbf{p}}$ by capturing Spectralon images under column-wise scan-line patterns per each narrow-band spectrum $\\lambda$ using spectral bandpass filters as shown in Figure 3(b). Using the scan-line patterns and sub-pixel accurate Gaussian fitting, we obtain the scene point $\\mathbf{p}$ via triangulation, and its projector pixel $q_{\\lambda}$ can be obtained for the horizontal coordinate. Note that we model the horizontal coordinate only as dispersion occurs in the horizontal direction. Second, we apply non-linear interpolation using a power function along the depth coordinate of the scene point $\\mathbf{p}'_z \\in \\mathbb{S}_{\\mathbf{p}}$ , where $\\mathbf{p}'_z$ denotes the z-coordinate of", + "bbox": [ + 511, + 704, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16591", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cb23e322efac1e8225df6acf5cba4a4c52550ebc86994656211872ab809084a2.jpg", + "image_caption": [ + "Figure 4. DDSL Pattern Design. (a) Three parameters of DDSL patterns. We visualize the issues raised from large or small values for each parameter (b) line offset, (c) line shift, (d) line width. Refer to the text for details. (e) We project DDSL patterns and a single black pattern, and the captured images under such patterns are spectrally multiplexed. (f) Illuminated wavelengths for DDSL and black patterns onto the scene point." + ], + "image_footnote": [], + "bbox": [ + 91, + 85, + 911, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a scene point $\\mathbf{p}'$ , and then linearly interpolate wavelength samples $\\lambda' \\in \\mathbb{S}_{\\lambda}$ and spatial samples $p' \\in \\mathbb{S}_p$ . As a result, we obtain the mapping function $\\psi$ with a sub-pixel reprojection error of 0.66 pixel. More details of the sample acquisition and interpolation can be found in the Supplemental Document.", + "bbox": [ + 88, + 453, + 480, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stereo Imaging The camera $k \\in \\{\\text{left, right}\\}$ captures the scene point $\\mathbf{p}$ at a camera pixel $p_k$ through perspective projection:", + "bbox": [ + 88, + 561, + 482, + 606 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} = z _ {k} \\mathbf {E} _ {k} ^ {- 1} \\mathbf {K} _ {k} ^ {- 1} \\dot {p} _ {k}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 606, + 480, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_{k}$ is the depth, $\\mathbf{E}_k$ is the extrinsic matrix, $\\mathbf{K}_k$ is the intrinsic matrix, and $\\dot{p}_k$ is the homogeneous coordinate of pixel $p_k$ . The captured intensity $I_{k}(p_{k},c)$ for the color channel $c$ is modeled as", + "bbox": [ + 89, + 628, + 483, + 689 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {k} \\left(p _ {k}, c\\right) = \\sum_ {\\lambda \\in \\Lambda} \\Omega_ {c, \\lambda} ^ {\\mathrm {c a m}} H _ {k} \\left(p _ {k}, \\lambda\\right) \\frac {\\eta_ {\\lambda}}{d (\\mathbf {p}) ^ {2}} L \\left(q _ {\\lambda}, \\lambda\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 696, + 482, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $H_{k}(p_{k},\\lambda)$ is the hyperspectral image and $d(\\mathbf{p})$ is the distance between the scene point $\\mathbf{p}$ and the projector. The model integrates over wavelengths $\\lambda \\in \\Lambda$ , effectively ranging from $440\\mathrm{nm}$ to $660\\mathrm{nm}$ at $10\\mathrm{nm}$ intervals: $\\Lambda = \\{\\lambda_1 = 440\\mathrm{nm},\\dots ,\\lambda_N = 660\\mathrm{nm}\\}$ , where $N = 23$ is the number of spectral bands.", + "bbox": [ + 89, + 739, + 483, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Dense Dispersed Structured Light", + "text_level": 1, + "bbox": [ + 89, + 844, + 398, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We design DDSL patterns $\\{P_i\\}_{i=1}^M$ that enable hyperspectral 3D imaging for dynamic scenes on our active stereo", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "setup. Each DDSL pattern $P_{i}$ is composed of multiple vertical lines, defined as:", + "bbox": [ + 511, + 453, + 903, + 483 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {i} (q, \\forall) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\mod \\left(\\left| q _ {x} - i \\times l _ {\\text {s h i f t}} \\right|, l _ {\\text {o f f s e t}}\\right) \\leq \\frac {l _ {\\text {w i d t h}}}{2}, \\\\ 0 & \\text {e l s e}, \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 494, + 903, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $q_{x}$ is the column index of a projector pixel $q$ , $l_{\\mathrm{shift}}$ is the line shift between neighboring patterns $P_{i}$ and $P_{i + 1}$ , $l_{\\mathrm{offset}}$ is the line offset between neighboring lines in a pattern, $l_{\\mathrm{width}}$ is the line width, and $\\mathrm{mod}(x,y) = x\\% y$ is the modulo operator.", + "bbox": [ + 511, + 547, + 905, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We project $M$ DDSL patterns $\\{P_1, \\ldots, P_M\\}$ and one black pattern $P_B$ repeatedly, capturing corresponding stereo images $I_k^1, \\ldots, I_k^M, I_k^B$ for $k \\in \\{\\text{left}, \\text{right}\\}$ . The black pattern $P_B$ is used to compensate for the non-zero projector intensity for the zero-valued pattern and to enable robust motion compensation which we detail in Section 6. The DDSL patterns create dispersion for each vertical white line, and the dispersed patterns can overlap depending on the settings for three parameters: line offset $l_{\\text{offset}}$ , line width $l_{\\text{width}}$ , and line shift $l_{\\text{shift}}$ . Figure 4(a) and (e) shows the DDSL patterns and captured images with our chosen parameters $l_{\\text{offset}}$ , $l_{\\text{width}}$ , and $l_{\\text{shift}}$ . Below, we discuss our design choices for these parameters.", + "bbox": [ + 511, + 623, + 906, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Line Offset The line offset $l_{\\mathrm{offset}}$ defines the spacing between vertical lines in pattern $P_{i}$ . A small $l_{\\mathrm{offset}}$ increases overlap between dispersed patterns, resulting in more spectrally multiplexed illumination (Figure 4(b)). This reduces", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16592", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/16d2da3c835f03ae0d30637729705b22577a353205594abebfe799161e096026.jpg", + "image_caption": [ + "Figure 5. Black Optical Flow. We warp adjacent frame image to a target frame using naive optical flow under DDSL patterns and our black optical flow method to show the effectiveness of our method. We estimate optical flows using pretrained RAFT network [22] for both methods. Note that the target frame and adjacent frames are captured under different DDSL patterns. Therefore, the evaluation should primarily focus on geometric alignment rather than color consistency. (a) Warped images based on naive optical flow and black optical flow. (b) Visualization of the interpolated optical flows using the black optical flow." + ], + "image_footnote": [], + "bbox": [ + 91, + 85, + 906, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the number of patterns $M$ , though it may decrease spectral accuracy due to blurred illumination. A larger $l_{\\mathrm{offset}}$ reduces multiplexing, improving spectral accuracy at the cost of more patterns. We set $l_{\\mathrm{offset}} = 40\\mathrm{px}$ to multiplex three spectral bands aligned with the camera RGB channels, balancing spectral accuracy and pattern count.", + "bbox": [ + 88, + 500, + 482, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Line Shift The line shift $l_{\\mathrm{shift}}$ specifies the shift between lines in neighboring patterns $P_{i}$ and $P_{i + 1}$ . A small $l_{\\mathrm{shift}}$ densely samples the spectral axis, increasing potential spectral channels but requiring more patterns $M$ (Figure 4(c)). To achieve spectral channels from $440\\mathrm{nm}$ to $660\\mathrm{nm}$ at $10\\mathrm{nm}$ intervals, we set $l_{\\mathrm{shift}} = 5\\mathrm{px}$ , providing a $10\\mathrm{nm}$ spectral step size while minimizing the number of patterns.", + "bbox": [ + 89, + 608, + 482, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Line Width A larger line width $l_{\\mathrm{width}}$ increases spectral overlapping across RGB channels, smoothing the illumination spectrum and potentially lowering spectral accuracy (Figure 4(d)). A very narrow $l_{\\mathrm{width}}$ results in low illumination power, introducing noise in captured images. We set $l_{\\mathrm{width}} = 5$ pixels to optimize illumination intensity without sacrificing spectral accuracy.", + "bbox": [ + 89, + 731, + 482, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Summary We use eight DDSL patterns ( $M = 8$ ) with $l_{\\mathrm{shift}} = 5$ , $l_{\\mathrm{width}} = 5$ , and $l_{\\mathrm{offset}} = 40$ , enabling accurate hyperspectral 3D reconstruction in our experimental", + "bbox": [ + 89, + 854, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "setup. Figure 4(f) shows the spectral power distribution of the DDSL-pattern illumination projected onto a scene point $\\mathbf{p}$ . For each $i$ -th DDSL pattern, we have three peaks over the RGB spectrum. Using only $M = 8$ DDSL patterns, we can densely sample wavelengths with $10\\mathrm{nm}$ step, allowing for accurate hyperspectral 3D imaging, contrast to using hundreds of pattern images as in the previous work [19].", + "bbox": [ + 511, + 500, + 906, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Hyperspectral 3D Reconstruction", + "text_level": 1, + "bbox": [ + 511, + 619, + 818, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the captured stereo images $I_{k}^{1}, \\ldots, I_{k}^{M}, I_{k}^{B}$ for DDSL patterns $P_{1}, \\ldots, P_{M}$ and one black pattern $P_{B}$ , we reconstruct a hyperspectral image $H_{k}$ and a depth map $z_{k}$ .", + "bbox": [ + 511, + 645, + 905, + 693 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth Estimation We estimate depth from stereo images $I_{\\mathrm{left}}^i$ and $I_{\\mathrm{right}}^i$ for each frame $i$ . The captured stereo images are rectified, and disparity is estimated using the pretrained RAFT-Stereo network [14]. Depth is then computed from disparity using calibrated camera parameters, followed by un-rectification.", + "bbox": [ + 511, + 712, + 905, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Black Optical Flow Dynamic objects move while capturing the images $I_{k}^{1}, \\ldots, I_{k}^{M}, I_{k}^{B}$ under the varying projector patterns $P_{1}, \\ldots, P_{M}, P_{B}$ , which needs compensation for robust hyperspectral image reconstruction. One straightforward approach is to estimate optical flow $\\nabla p_{k}^{M/2 \\to i}$ from", + "bbox": [ + 511, + 823, + 905, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16593", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e2308f8b473c946507c39dec0b93e34cfe17a303c0b6dee0b0ee3a2798f141cf.jpg", + "image_caption": [ + "(a) Reconstructed sRGB" + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 232, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d584090927628e490589a5f2fdeea428845a823492f93097fa1459b78d144a24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 235, + 88, + 405, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/62f35e2feee4c730a3263fd6794c024389d99c978ba015f4c129670b8242dbb7.jpg", + "image_caption": [ + "(b) Point cloud of color checker", + "(c) Color checker evaluation", + "Figure 6. Spectral Accuracy. Color checker evaluation. (a) Reconstructed hyperspectral image of color checker in sRGB, (b) point cloud of color checker, (c) hyperspectral intensity of color checker. High-frequency spectral data evaluation comparing other methods with Shin et al. [19] and Li et al. [13]. (d) $10\\mathrm{nm}$ -FWHM spectral band pass filters and acquisition time for the three methods, (e) reconstructed hyperspectral intensity." + ], + "image_footnote": [], + "bbox": [ + 91, + 161, + 403, + 329 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0d60f23425f15b12ebb9fe1fb22578a3ca33e0422b7f0512b1ff4a83081f868f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 411, + 88, + 506, + 157 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c62081495fd8f323c839e3fbdd0ade8301bf4ddfe4a32a64a63744cca3c2bced.jpg", + "image_caption": [ + "(d) High frequency spectral band pass filters" + ], + "image_footnote": [], + "bbox": [ + 411, + 161, + 506, + 316 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2ebfb5bb9c9688d267e006fd6742bf4048fa806cae24eff49aba437b2bb6dca7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 88, + 642, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9bdffb863199093b469bfd6a1be0fc92fbfdd4caa60ad9f3f4dd92a73df415da.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 162, + 643, + 237 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3e64fba54e22097a50440e859dce3002f557f7c0d33fb66245ac37917f6a6ae1.jpg", + "image_caption": [ + "(e) Reconstructed hyperspectral intensity of each spectral filters" + ], + "image_footnote": [], + "bbox": [ + 509, + 237, + 643, + 316 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f6e7df7a57044eb5ec226e2dba2ff533d33978d435c21e973e51c21a2df83501.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 88, + 774, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a4ad7546050c138a81cf070d366915792c1da016028f089e8e8b74b5241f7109.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 162, + 774, + 236 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/48174738bdef1419be65b46747b586b6ff695ffb0b9b0dd1cb686dbfe3599659.jpg", + "image_caption": [ + "Wavelength[nm]" + ], + "image_footnote": [], + "bbox": [ + 645, + 236, + 774, + 316 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/25e6ea90394c77eff9c57d3d244265f6efde3708685fe6c4a26eb3ec1163270b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 88, + 905, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0b5570e3cb00412ae1cf1ac455f9db85c20e4c94d42ab78a2c575e9182bec81e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 162, + 905, + 236 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d5992a4d761958cbb8ce245c80f270d46a3ac4d64f5567e2f9e1eab0abdb1e76.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 236, + 905, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the center frame $M / 2$ to each frame $i$ :", + "bbox": [ + 89, + 426, + 344, + 441 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\np _ {k} ^ {i} = p _ {k} ^ {M / 2} + \\nabla p _ {k} ^ {M / 2 \\rightarrow i}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 454, + 482, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "However, this approach is challenging due to the inconsistent illumination at corresponding pixels since each image $\\{I_k^i\\}_{i = 1}^M$ is illuminated by a different DDSL pattern $\\{P_i\\}_{i = 1}^M$ . Figure 5(a) depicts how naive optical flow between adjacent DDSL patterns fails to accurately capture the motion. Instead, we estimate the black optical flow, which is the flow between successive black-pattern images $I_{k}^{B}$ , avoiding illumination inconsistency. We then interpolate the black optical flow to obtain the target optical flow $\\nabla p_k^{M / 2\\rightarrow i}$ , enabling robust optical-flow estimation, as illustrated in Figure 5. Using the estimated flow, we align the images $I_{k}^{1},\\ldots ,I_{k}^{M}$ captured under the DDSL patterns to the center frame $I_{k}^{M / 2}$ .", + "bbox": [ + 89, + 484, + 483, + 689 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Multi-pattern Image Formation Using the aligned images $I_{k}^{1}, \\ldots, I_{k}^{M}$ captured under $M$ DDSL patterns, we reformulate the image formation model from Section 4. For the $i$ -th DDSL pattern, the aligned image $I_{k}^{i}$ is modeled as:", + "bbox": [ + 89, + 705, + 483, + 767 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nI _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) = \\sum_ {\\lambda \\in \\Lambda} \\Omega_ {c, \\lambda} ^ {\\mathrm {c a m}} H _ {k} \\left(p _ {k} ^ {i}, \\lambda\\right) \\frac {\\eta_ {\\lambda}}{d \\left(\\mathbf {p} _ {k} ^ {i}\\right) ^ {2}} L ^ {i} \\left(q _ {\\lambda} ^ {i}, \\lambda\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 777, + 482, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{p}_k^i$ is the corresponding scene point at frame $i$ , and $q_{\\lambda}^{i}$ is the corresponding projector pixel obtained using the backward model $\\psi \\colon q_{\\lambda}^{i} = \\psi \\left(\\mathbf{p}_{k}^{i},\\lambda\\right)$ .", + "bbox": [ + 89, + 824, + 482, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We then subtract the black pattern captured image $I_k^B$ from all the captured images $\\{I_k^i(p_k^i, c)\\}_{i=1}^M$ to remove the", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "undesired residual light intensity for the black pattern:", + "bbox": [ + 511, + 426, + 870, + 441 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nI _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) \\leftarrow I _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) - I _ {k} ^ {B} \\left(p _ {k} ^ {B}, c\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 446, + 903, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We rewrite the image formation as a matrix-vector multiplication:", + "bbox": [ + 511, + 470, + 903, + 500 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {k} = \\mathbf {L H} _ {k}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 669, + 502, + 903, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{I}_k$ is the intensity vector of captured image under $M$ DDSL patterns, $\\mathbf{L}$ is the system matrix, and $\\mathbf{H}_k$ is the hyperspectral image:", + "bbox": [ + 511, + 521, + 905, + 566 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {k} = \\left[ I _ {k} ^ {1} \\left(p _ {k} ^ {1}, R\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, R\\right), \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 571, + 784, + 589 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nI _ {k} ^ {1} \\left(p _ {k} ^ {1}, G\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, G\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 592, + 784, + 609 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left. I _ {k} ^ {1} \\left(p _ {k} ^ {1}, B\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, B\\right) \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {3 M \\times 1}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 613, + 903, + 631 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} = \\left[ \\mathbf {L} _ {R}; \\mathbf {L} _ {G}; \\mathbf {L} _ {B} \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {3 M \\times N}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 633, + 903, + 652 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} _ {c} (i, j) = \\Omega_ {c, \\lambda_ {j}} ^ {\\mathrm {c a m}} \\eta_ {\\lambda_ {j}} \\left(L ^ {i} * G\\right) \\left(q _ {\\lambda_ {j}} ^ {i}, \\lambda_ {j}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 655, + 903, + 680 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} _ {k} = \\left[ H \\left(p _ {k} ^ {M / 2}, \\lambda_ {1}\\right), \\dots , H \\left(p _ {k} ^ {M / 2}, \\lambda_ {N}\\right) \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {N \\times 1}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 681, + 903, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $i = 1, \\ldots, M$ , $j = 1, \\ldots, N$ , and $G$ is a Gaussian blur kernel accounting for the imaging system's blur; details can be found in the Supplemental Document.", + "bbox": [ + 511, + 722, + 905, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyperspectral Reconstruction We reconstruct per-pixel hyperspectral reflectance $\\mathbf{H}_k$ by solving the following:", + "bbox": [ + 511, + 785, + 905, + 816 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {H} _ {k}} {\\operatorname {a r g m i n}} \\underbrace {\\| \\mathbf {L} \\mathbf {H} _ {k} - \\mathbf {I} _ {k} \\| _ {2} ^ {2}} _ {\\text {D a t a t e r m}} + \\underbrace {\\kappa_ {\\lambda} \\| \\nabla_ {\\lambda} \\mathbf {H} _ {k} \\| _ {2} ^ {2}} _ {\\text {S p e c t r a l s m o o t h n e s s}} +\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 820, + 846, + 857 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\underbrace {\\kappa_ {x y} \\left(\\left\\| \\nabla_ {x} \\mathbf {H} _ {k} \\right\\| _ {1} + \\left\\| \\nabla_ {y} \\mathbf {H} _ {k} \\right\\| _ {1}\\right)} _ {\\text {S p a t i a l r e g u l a r i z a t i o n}}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 861, + 903, + 896 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16594", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/458bbae01d34750ba029195fa632226b66e952ee48224bffdaee377cb440e015.jpg", + "image_caption": [ + "Stair case object" + ], + "image_footnote": [], + "bbox": [ + 127, + 88, + 240, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8410a0e3317413ee4c4aab6055290c654123a6b8e446643200eb5f8b11d55037.jpg", + "image_caption": [ + "Reconstructed depth under $P_{j}$" + ], + "image_footnote": [], + "bbox": [ + 240, + 88, + 341, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2547c209d82bafacc3011322825a64aa53d983d4edb9af27ece1c46b110807c8.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 343, + 88, + 483, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d02991550bcbf745631b5af8b4107faecce3123867e4ce5c338fd72fc149531e.jpg", + "image_caption": [ + "(a) Depth reconstructed results", + "(b) Absolute depth evaluation" + ], + "image_footnote": [], + "bbox": [ + 91, + 227, + 287, + 345 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b9bafe675ba08526d770ddac2a21272e9d8c76421d517653a3d44d527d18967.jpg", + "image_caption": [ + "(c) Consistency between different DDSL patterns" + ], + "image_footnote": [], + "bbox": [ + 287, + 227, + 483, + 345 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\nabla_{\\lambda}, \\nabla_{x}$ , and $\\nabla_{y}$ are gradient operators along the spectral and spatial axes, respectively. The first term corresponds to the data term, penalizing reconstruction error, while the second and third terms enforce spectral smoothness and spatial total variation. The coefficients $\\kappa_{\\lambda} = 3$ and $\\kappa_{xy} = 0.05$ are balancing weights. We solve the per-pixel optimization problem using ADAM [7]. Optimization details are provided in the Supplemental Document.", + "bbox": [ + 89, + 465, + 483, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "7. Calibration", + "text_level": 1, + "bbox": [ + 89, + 613, + 212, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform a one-time calibration of the projector, camera, and diffraction grating. We obtain the geometric parameters of the stereo cameras and the projector using checkerboard methods [21, 30] without attaching the diffraction grating film. To measure the diffraction efficiency $\\eta_{\\lambda}$ of the diffraction grating, shown in Figure 2(d), we filter the dispersed light using spectral bandpass filters with a $10\\mathrm{nm}$ bandwidth, covering wavelengths from $440\\mathrm{nm}$ to $660\\mathrm{nm}$ , and capture the intensity reflected from a Spectralon target. We calibrate the camera response function $\\Omega_{c,\\lambda}^{\\mathrm{cam}}$ also using spectral bandpass filters under LED light, and measure the projector spectral emission function $\\Omega_{c,\\lambda}^{\\mathrm{proj}}$ by projecting RGB dots onto a Spectralon target and capturing the reflected radiance with a spectroradiometer (JETI Specbos 1211). To enhance reconstruction accuracy, we further optimize the radiometric parameters for both the projector and camera; detailed methods are provided in the Supplemental Document.", + "bbox": [ + 89, + 643, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a71c81b20630a457fbf9f56bf0be492679abc592282e2511f5baa807bce40852.jpg", + "image_caption": [ + "(a) Reconstructed sRGB" + ], + "image_footnote": [], + "bbox": [ + 517, + 106, + 640, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4b24bb8c29d12c72c5337b45d35a0b85f4c6c704154b610cff6b75119cbe8abe.jpg", + "image_caption": [ + "(b) Reconstructed depth" + ], + "image_footnote": [], + "bbox": [ + 640, + 106, + 792, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e4375e7068cbfac86a5d2c5911766940563834811c82f755a67e1c642a18d76.jpg", + "image_caption": [ + "(c) Hyperspectral intensity" + ], + "image_footnote": [], + "bbox": [ + 794, + 107, + 903, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce0d140846c098bf6c96933b2a1d9d8619e3f06878ccfda1dbb0dfd4901c8071.jpg", + "image_caption": [ + "Figure 7. Depth Validation. (a) Stair case depth reconstructed results. (b) Absolute depth evaluation. (c) Consistency between depth reconstructed results between different DDSL patterns for the stair position index of 3.", + "Figure 8. Fake and Real Oranges. We compare real and artificial fruit(orange), showing the differences in their hyperspectral image curves and corresponding images. (a) Reconstructed hyperspectral image in sRGB, (b) depth (c) spectral graph and (d) hyperspectral images of metameric samples." + ], + "image_footnote": [], + "bbox": [ + 517, + 232, + 614, + 367 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d5ff9187b4592a5dc0dc08675d6894d90dfcf1febfe1fd4f740ddb352db6f6f4.jpg", + "image_caption": [ + "(d) Hyperspectral images" + ], + "image_footnote": [], + "bbox": [ + 616, + 232, + 661, + 367 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/45fc81c4e7cb276ea10a046b299db40d55da07a4da15cd98516a1f97dfa4844e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 663, + 232, + 709, + 367 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/07e6c6fec8031128a6f848b9431d2d0c069da3ec218c8293ed7012682b4ad0e8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 232, + 756, + 367 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8f298918dd244986fd3a81c166f5ddc44edd1595af5086d1f2dc1392b82fb204.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 232, + 805, + 367 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4accad497cb941b44e43c64105835fe82c5e74978b9165c74e099e29ad8e4ce0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 807, + 232, + 854, + 367 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eb0591a8aa7928478be611b7abcb12acee0d888d7ac8cb157bead493a744ee8e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 856, + 232, + 903, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "8. Results", + "text_level": 1, + "bbox": [ + 513, + 484, + 599, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spectral Accuracy Figure 6 (a), (b) and (c) shows the reconstructed hyperspectral image in sRGB, depth, and hyperspectral curves of a ColorChecker chart, demonstrating accurate reconstruction. To measure spectral FWHM of our system, we capture nine narrow-band spectral filters as shown in Figure 6(d). The FWHM of those bandpass filters is $10\\mathrm{nm}$ . Figure 6(e) shows that our method achieves a FWHM of $15.5\\mathrm{nm}$ compared to the ground-truth hyperspectral data of the filters, outperforming state-of-the-art affordable hyperspectral 3D imaging methods by Li et al. [13] and Shin et al. [19]. Li et al.[13] shows a FWHM of $40\\mathrm{nm}$ due to the use of broadband RGB illumination of a conventional projector. Shin et al.[19] attains $18\\mathrm{nm}$ FWHM. Moreover, its acquisition time for a scene is 10 minutes whereas our method only requires 0.15 seconds, representing $\\times 4000$ speed increase, thus enabling hyperspectral 3D imaging for dynamic scenes.", + "bbox": [ + 511, + 512, + 906, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Depth Accuracy We evaluate the accuracy of depth estimation. Ground-truth depth is obtained using the binary-coded structured light method [8]. Figure 7(a) evaluates the absolute depth error by capturing a 3D-printed stair object. We achieve an average depth error of $4\\mathrm{mm}$ in the area of each step compared to the ground truth, with a maximum error of $8\\mathrm{mm}$ . Figure 7(b) shows the difference be", + "bbox": [ + 511, + 794, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16595", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/617aa3fc25b1e4665b26f0421afd6eaef23b9a180bef0430dcd0174e7d87837d.jpg", + "image_caption": [ + "Figure 9. Dynamic Scene. We show the reconstructed depth and spectral results of a dynamic scene. (a) Reconstructed depth. (b) Reconstructed hyperspectral image in sRGB. (c) Reconstructed hyperspectral image. (d) Hyperspectral intensity." + ], + "image_footnote": [], + "bbox": [ + 91, + 95, + 911, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tween depth results for each DDSL pattern. The consistency across different DDSL patterns is evident, with a difference of less than $2\\mathrm{mm}$ between patterns.", + "bbox": [ + 89, + 357, + 482, + 405 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dynamic Scenes By using spectrally multiplexed DDSL patterns, we reduce the required number of projections from over hundred patterns with naive scanning [19] to 8 DDSL patterns. This enables accurate hyperspectral 3D imaging for dynamic scenes at 6.6 fps, by software synchronizing camera and projector, as shown in Figure 1, Figure 9, and the Supplemental Video.", + "bbox": [ + 89, + 426, + 483, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of Pattern Parameters Table 1 shows the impact of different parameter settings of DDSL patterns. Our empirically-set pattern parameters $l_{\\mathrm{offset}}$ , $l_{\\mathrm{width}}$ , $l_{\\mathrm{shift}}$ result in the best spectral and depth accuracy with a short capture time. The depth accuracy remains unchanged due to the robustness of RaftStereo [14] for correspondence matching.", + "bbox": [ + 89, + 556, + 483, + 647 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d41de2b2a9c038726a47314ac26f9d452102ed1eaff7cad7bda41ff7e4dde61b.jpg", + "table_caption": [ + "Table 1. Ablation study on pattern parameters: ${l}_{\\text{offset }},{l}_{\\text{width }},{l}_{\\text{shift }}$ ." + ], + "table_footnote": [], + "table_body": "
Indexl_offsetl_widthlshift# of patterns ∝ capture time↓Spectral FWHM [nm]↓Depth MAE [mm]↓
#160551215.54
#220554174
#3402058FailFail
#440158504
#5405103Fail4
#640522015.54
chosen4055815.54
", + "bbox": [ + 91, + 676, + 483, + 781 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Real and Fake Oranges Figure 8 presents a comparison between artificial and real oranges with reconstructed hyperspectral images in sRGB and depth with spectral curves of each fruits. We can differentiate between the objects in detailed spectral analysis. Ground-truth intensity measurements are acquired using a spectroradiometer.", + "bbox": [ + 89, + 810, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "9. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 354, + 633, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have introduced DDSL, an accurate and compact method for hyperspectral 3D imaging for dynamic scenes. We use a conventional RGB stereo camera-projector system paired with a sub-millimeter diffraction grating, implemented as a practical experimental prototype. We design the DDSL patterns, generating spectrally-multiplexed illumination, enabling rapid and high-quality hyperspectral 3D imaging. Our method incorporates the dispersion-aware image formation model using the sub-pixel accurate backward mapping. Experimental results demonstrate that we outperform prior affordable methods in both accuracy and also acquisition time, achieving 6.6 fps with a depth error of $4\\mathrm{mm}$ and a spectral accuracy of 15.5 FWHM. We envision that our DDSL method opens up new applications of geometric and material analysis for dynamic objects.", + "bbox": [ + 511, + 381, + 906, + 608 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and Future work While our method enables rapid, accurate, and practical hyperspectral 3D imaging for dynamic scenes, it is currently constrained to low-speed motion, achieving a frame rate of 6.6 fps due to the slow software-based synchronization between the camera and projector. To address this limitation, hardware synchronization and a high-speed, affordable projector-camera system could significantly increase frame rates [28]. The limited diffraction efficiency also restricts the range of scene positions. Thus, using a high efficiency diffraction grating for the first-order light would enhance the effective range.", + "bbox": [ + 511, + 625, + 908, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, RS-2024-00438532), Korea IITP MSIT (RS-2019-II191906, Artificial Intelligence Graduate School Program-POSTECH, RS-2024-00437866), POSCO, and 2024 POSTECH International Joint Research Project.", + "bbox": [ + 511, + 810, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16596", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Reza Arablouei, Ethan Goan, Stephen Gensemer, and Branislav Kusy. Fast and robust pushbroom hyperspectral imaging via dmd-based scanning. 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IEEE Transactions on pattern analysis and machine intelligence, 22(11):1330-1334, 2000. 7" + ], + "bbox": [ + 91, + 90, + 483, + 190 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16598", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_model.json b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9d8aa4563fcde1ad7fcc4ef82aad55278b44de6c --- /dev/null +++ b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_model.json @@ -0,0 +1,2387 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.131, + 0.75, + 0.177 + ], + "angle": 0, + "content": "Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes" + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.204, + 0.223, + 0.238 + ], + "angle": 0, + "content": "Suhyun Shin POSTECH" + }, + { + "type": "image_caption", + "bbox": [ + 0.259, + 0.204, + 0.393, + 0.238 + ], + "angle": 0, + "content": "Seungwoo Yoon POSTECH" + }, + { + "type": "image_caption", + "bbox": [ + 0.43, + 0.204, + 0.692, + 0.24 + ], + "angle": 0, + "content": "Ryota Maeda \nPOSTECH, University of Hyogo" + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.204, + 0.882, + 0.238 + ], + "angle": 0, + "content": "Seung-Hwan Baek POSTECH" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.244, + 0.484, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.244, + 0.745, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.745, + 0.244, + 0.906, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.52, + 0.908, + 0.562 + ], + "angle": 0, + "content": "Figure 1. We introduce a spectrally multiplexed Dense Dispersed Structured Light (DDSL), accurate hyperspectral 3D imaging method for dynamic scenes. (a) Capture configuration, (b) estimated hyperspectral image in sRGB and depth image for dynamic scenes, (c) estimated hyperspectral image, (d) comparison with spectroradiometer measurements." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.567, + 0.327, + 0.583 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.599, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Hyperspectral 3D imaging captures both depth maps and hyperspectral images, enabling comprehensive geometric and material analysis. Recent methods achieve high spectral and depth accuracy; however, they require long acquisition times—often over several minutes—or rely on large, expensive systems, restricting their use to static scenes. We present Dense Dispersed Structured Light (DDSL), an accurate hyperspectral 3D imaging method for dynamic scenes that utilizes stereo RGB cameras and an RGB projector equipped with an affordable diffraction grating film. We design spectrally multiplexed DDSL patterns that significantly reduce the number of required projector patterns, thereby accelerating acquisition speed. Additionally, we formulate an image formation model and a reconstruction method to estimate a hyperspectral image and depth map from captured stereo images. As the first practical and accurate hyperspectral 3D imaging method for dynamic scenes, we experimentally demonstrate that DDSL achieves a spectral resolution of \\(15.5\\mathrm{nm}\\) full width at half maximum (FWHM), \\(4\\mathrm{mm}\\) depth error, and \\(6.6\\mathrm{fps}\\)." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.567, + 0.645, + 0.583 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.596, + 0.907, + 0.822 + ], + "angle": 0, + "content": "Hyperspectral imaging captures a scene across multiple spectral channels beyond the three-channel RGB imaging, thereby providing both spectral and spatial information about the scene. Expanding on this, hyperspectral 3D imaging has recently received interest, as it captures both spectral and geometric information in the form of a depth map and a hyperspectral image. It has proven useful in scientific analysis of real-world materials, with applications in object classification [15], food ripeness detection [20], cultural heritage analysis, and geology [12]. Recently, dispersed structured light has been proposed as a cost-effective and compact solution for accurate hyperspectral 3D imaging [19]. However, its applicability remains limited to static scenes due to the need for projecting hundreds of patterns, resulting in acquisition times of several minutes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Increasing the acquisition speed of hyperspectral 3D imaging could make it feasible to analyze the geometric and material properties of objects and scenes in motion. Existing methods rely on expensive, bulky systems, such as coded-aperture snapshot spectral imagers (CASSI) [24]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16589" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.087, + 0.331, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.168, + 0.199, + 0.272, + 0.211 + ], + "angle": 0, + "content": "(a) Imaging system" + }, + { + "type": "image", + "bbox": [ + 0.331, + 0.088, + 0.488, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.199, + 0.483, + 0.211 + ], + "angle": 0, + "content": "(b) Schematic diagram" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.09, + 0.689, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.199, + 0.676, + 0.211 + ], + "angle": 0, + "content": "(c) Radiometric parameters" + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.091, + 0.885, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.199, + 0.892, + 0.211 + ], + "angle": 0, + "content": "(d) Diffraction grating efficiency \\(\\eta_{\\lambda}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.219, + 0.907, + 0.262 + ], + "angle": 0, + "content": "Figure 2. Imaging System. (a) Our active stereo system comprises RGB stereo cameras and a RGB projector equipped with a diffraction grating. (b) The diffraction grating introduces dispersion to the projector light. (c) Spectral sensitivity and emission functions of the camera and the projector. (d) Diffraction grating efficiency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.27, + 0.483, + 0.331 + ], + "angle": 0, + "content": "paired with stereo cameras or time-of-flight setups [10, 17, 25-27]. While compact, practical PSF-based systems exist [4, 18], they significantly compromise either depth or spectral accuracy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.333, + 0.483, + 0.44 + ], + "angle": 0, + "content": "In this paper, we propose DDSL, an accurate hyperspectral 3D imaging method for dynamic scenes, using a compact and affordable system. Figure 1 shows the capture configuration using our prototype, which consists of stereo RGB cameras and an RGB projector equipped with an affordable diffraction-grating film that generates structured-light projections with wavelength-dependent dispersion." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.441, + 0.484, + 0.547 + ], + "angle": 0, + "content": "We design DDSL patterns for the projector that produce spectrally multiplexed light projections, allowing us to use fewer than ten projections, enabling rapid image acquisition for dynamic scenes. We analyze the stereo images captured under these repeating DDSL patterns by developing an image formation model and a reconstruction method for depth maps and hyperspectral images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.549, + 0.483, + 0.716 + ], + "angle": 0, + "content": "DDSL enables accurate depth and spectral estimation even for high-frequency spectral variations, where existing affordable methods fall short. We demonstrate that DDSL achieves a depth error of \\(4\\mathrm{mm}\\), a spectral FWHM of \\(15.5\\mathrm{nm}\\) in the visible spectrum, and acquisition speed of 6.6 FPS. Our dynamic imaging is achieved through software synchronization between the cameras and the projector. The use of a compact and affordable active-stereo setup enhanced with a diffraction grating film makes DDSL a promising approach for practical and accurate hyperspectral 3D imaging of dynamic scenes." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.718, + 0.403, + 0.732 + ], + "angle": 0, + "content": "We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.735, + 0.483, + 0.81 + ], + "angle": 0, + "content": "- We introduce Dense Dispersed Structured Light (DDSL), which enables high-quality hyperspectral 3D imaging for dynamic scenes using an affordable active-stereo setup composed of RGB stereo cameras and an RGB projector augmented with a diffraction grating film." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.811, + 0.483, + 0.871 + ], + "angle": 0, + "content": "- We design DDSL patterns and develop an image formation model and hyperspectral 3D reconstruction method for dynamic scenes, obtaining a depth map and a hyperspectral images from stereo RGB images." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "- We demonstrate that DDSL outperforms state-of-the-art affordable hyperspectral 3D imaging methods in acquisi" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.735, + 0.483, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.27, + 0.907, + 0.315 + ], + "angle": 0, + "content": "tion speed with high reconstruction accuracy, achieving a depth error of \\(4\\mathrm{mm}\\), a spectral FWHM of \\(15.5\\mathrm{nm}\\), and a frame rate of 6.6 FPS." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.327, + 0.655, + 0.343 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.353, + 0.907, + 0.671 + ], + "angle": 0, + "content": "Hyperspectral 3D Imaging Various hyperspectral 3D imaging systems have been developed. Kim et al. [12] combined a laser scanner with a CASSI system for accurate hyperspectral 3D imaging, while Li et al. [13] employed a practical projector-camera setup, though at the cost of reduced spectral accuracy. Shin et al. [19] introduced a compact projector-camera system using dispersed structured light with a diffraction grating. However, these previous approaches are generally limited to static scenes due to their long acquisition times, often lasting several minutes. For dynamic scenes, a common approach is to use depth video cameras in conjunction with hyperspectral video cameras. However, hyperspectral video cameras tend to be large and expensive [1, 2, 6, 10, 17, 23, 25, 26]. While solutions using point spread function (PSF) engineering offer single-shot hyperspectral 3D imaging in a compact setup through custom micro- or nano-optical elements, they generally have limited spectral and depth accuracy [4, 18]. Our method achieves accurate hyperspectral 3D imaging for dynamic scenes using a practical setup: stereo RGB cameras and an RGB projector with a diffraction grating film." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.687, + 0.907, + 0.854 + ], + "angle": 0, + "content": "Active Stereo Active stereo employs a stereo camera and an illumination module projecting structured-light patterns for robust 3D imaging [3, 5, 11, 16, 29]. Heist et al. [10] repurposed an active stereo system with a high-speed projector and hyperspectral video cameras for hyperspectral 3D imaging of dynamic scenes. However, the use of hyperspectral video cameras significantly increases instrumentation costs. We leverage a diffraction grating film in front of an RGB projector with RGB stereo cameras, eliminating the need for hyperspectral cameras and enabling practical, accurate hyperspectral 3D imaging for dynamic scenes." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Dispersive Optics Dispersive optics, including prisms and diffraction gratings, are widely used in hyperspectral" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16590" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.273 + ], + "angle": 0, + "content": "imaging. CASSI systems utilize relay lenses with dispersive elements and coded masks for precise spectral reconstruction. Cao et al. [6] minimized system size by using a prism and coded mask without relay lenses. Recently, diffractive optical elements have been employed to create spectrally varying point spread functions [4, 18]. Shin et al. [19] integrated a diffraction grating film into a projector-camera system, though it required hundreds of projected patterns, resulting in long capture times. Our method achieves rapid acquisition at 6.6 fps with high spectral and depth accuracy, through our active stereo setup, DDSL patterns, image formation model, and reconstruction method." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.288, + 0.251, + 0.305 + ], + "angle": 0, + "content": "3. Imaging System" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.313, + 0.485, + 0.555 + ], + "angle": 0, + "content": "We introduce a practical and affordable active stereo system. We use stereo RGB cameras (FLIR GS3-U3-32S4C-C) and an RGB projector (Epson CO-FH02) equipped with diffraction grating film (Edmund 54-509) placed in front of the projector (see Figure 2(a)). The diffraction grating film, which costs less than 20 USD, disperses the broadband projector light according to the light wavelength \\(\\lambda\\) as shown Figure 2(b). Each dispersed light ray of a specific wavelength \\(\\lambda\\) then propagates to a scene, creating spatially-distributed narrow-band spectral illumination. The stereo cameras capture the scene illuminated by the dispersed light. We set the camera fields of view to capture first-order diffracted light [9]. For color channel \\(c\\in \\{R,G,B\\}\\) and wavelength \\(\\lambda\\), we calibrate and refine the projector spectral emission \\(\\Omega_{c,\\lambda}^{\\mathrm{proj}}\\), camera spectral sensitivity \\(\\Omega_{c,\\lambda}^{\\mathrm{cam}}\\), and diffraction-grating efficiency \\(\\eta_{\\lambda}\\) (Figures 2(c) and (d))." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.57, + 0.262, + 0.587 + ], + "angle": 0, + "content": "4. Image Formation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.595, + 0.484, + 0.627 + ], + "angle": 0, + "content": "We develop an image formation model for the active stereo system given a pattern image \\(P\\) that we set to the projector." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.484, + 0.707 + ], + "angle": 0, + "content": "Projector Light Given the projector pattern \\( P(q, c) \\) where \\( q \\) is a projector pixel and \\( c \\in \\{R, G, B\\} \\) is a color channel, we model the light intensity \\( L(q, \\lambda) \\) emitted from the pixel \\( q \\) at wavelength \\( \\lambda \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.718, + 0.483, + 0.749 + ], + "angle": 0, + "content": "\\[\nL (q, \\lambda) = \\sum_ {c} \\Omega_ {c, \\lambda} ^ {\\operatorname {p r o j}} P (q, c). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.767, + 0.484, + 0.873 + ], + "angle": 0, + "content": "Dispersed Light Projection Model The light ray of wavelength \\(\\lambda\\) emitted by the projector pixel \\(q\\) is diffracted by the diffraction grating and propagates to a scene. We model such dispersed projection in a backward manner as shown Figure 3(a). That is, from a scene point \\(\\mathbf{p}\\) and given wavelength \\(\\lambda\\), we model its corresponding projector pixel \\(q_{\\lambda}\\) that emits the ray:" + }, + { + "type": "equation", + "bbox": [ + 0.235, + 0.886, + 0.483, + 0.903 + ], + "angle": 0, + "content": "\\[\nq _ {\\lambda} = \\psi (\\mathbf {p}, \\lambda). \\tag {2}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.087, + 0.905, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.416, + 0.907, + 0.43 + ], + "angle": 0, + "content": "(b) Sub-pixel accurate sample collection for data-driven backward modeling" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.443, + 0.683, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.54, + 0.556, + 0.692, + 0.591 + ], + "angle": 0, + "content": "(d) Depth dependent backward mapping model \\(\\psi\\) for specific wavelength" + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.445, + 0.897, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.556, + 0.877, + 0.59 + ], + "angle": 0, + "content": "(e) Wavelength dependent backward mapping model \\(\\psi\\) for specific depth" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.595, + 0.907, + 0.678 + ], + "angle": 0, + "content": "Figure 3. Image Formation. (a) Light transport of the dispersed light projection of the mapping function \\(\\psi\\). (b) Sub-pixel accurate sample collection for data-driven backward modeling. Calibrated backward mapping model that relates pixel point to projector horizontal position (c) for depth given a specific wavelength and (d) for wavelength given a fixed depth value." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.909, + 0.903 + ], + "angle": 0, + "content": "To construct the backward model \\(\\psi\\), we use a data-driven approach. First, we acquire the samples \\(q_{\\lambda} \\in \\mathbb{S}_q\\), \\(\\lambda \\in \\mathbb{S}_{\\lambda}\\), \\(\\mathbf{p} \\in \\mathbb{S}_{\\mathbf{p}}\\) by capturing Spectralon images under column-wise scan-line patterns per each narrow-band spectrum \\(\\lambda\\) using spectral bandpass filters as shown in Figure 3(b). Using the scan-line patterns and sub-pixel accurate Gaussian fitting, we obtain the scene point \\(\\mathbf{p}\\) via triangulation, and its projector pixel \\(q_{\\lambda}\\) can be obtained for the horizontal coordinate. Note that we model the horizontal coordinate only as dispersion occurs in the horizontal direction. Second, we apply non-linear interpolation using a power function along the depth coordinate of the scene point \\(\\mathbf{p}'_z \\in \\mathbb{S}_{\\mathbf{p}}\\), where \\(\\mathbf{p}'_z\\) denotes the z-coordinate of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16591" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.087, + 0.912, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.379, + 0.908, + 0.437 + ], + "angle": 0, + "content": "Figure 4. DDSL Pattern Design. (a) Three parameters of DDSL patterns. We visualize the issues raised from large or small values for each parameter (b) line offset, (c) line shift, (d) line width. Refer to the text for details. (e) We project DDSL patterns and a single black pattern, and the captured images under such patterns are spectrally multiplexed. (f) Illuminated wavelengths for DDSL and black patterns onto the scene point." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.454, + 0.482, + 0.545 + ], + "angle": 0, + "content": "a scene point \\(\\mathbf{p}'\\), and then linearly interpolate wavelength samples \\(\\lambda' \\in \\mathbb{S}_{\\lambda}\\) and spatial samples \\(p' \\in \\mathbb{S}_p\\). As a result, we obtain the mapping function \\(\\psi\\) with a sub-pixel reprojection error of 0.66 pixel. More details of the sample acquisition and interpolation can be found in the Supplemental Document." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.563, + 0.483, + 0.607 + ], + "angle": 0, + "content": "Stereo Imaging The camera \\( k \\in \\{\\text{left, right}\\} \\) captures the scene point \\( \\mathbf{p} \\) at a camera pixel \\( p_k \\) through perspective projection:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.607, + 0.482, + 0.626 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} = z _ {k} \\mathbf {E} _ {k} ^ {- 1} \\mathbf {K} _ {k} ^ {- 1} \\dot {p} _ {k}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.63, + 0.484, + 0.69 + ], + "angle": 0, + "content": "where \\(z_{k}\\) is the depth, \\(\\mathbf{E}_k\\) is the extrinsic matrix, \\(\\mathbf{K}_k\\) is the intrinsic matrix, and \\(\\dot{p}_k\\) is the homogeneous coordinate of pixel \\(p_k\\). The captured intensity \\(I_{k}(p_{k},c)\\) for the color channel \\(c\\) is modeled as" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.698, + 0.483, + 0.731 + ], + "angle": 0, + "content": "\\[\nI _ {k} \\left(p _ {k}, c\\right) = \\sum_ {\\lambda \\in \\Lambda} \\Omega_ {c, \\lambda} ^ {\\mathrm {c a m}} H _ {k} \\left(p _ {k}, \\lambda\\right) \\frac {\\eta_ {\\lambda}}{d (\\mathbf {p}) ^ {2}} L \\left(q _ {\\lambda}, \\lambda\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.741, + 0.484, + 0.833 + ], + "angle": 0, + "content": "where \\( H_{k}(p_{k},\\lambda) \\) is the hyperspectral image and \\( d(\\mathbf{p}) \\) is the distance between the scene point \\( \\mathbf{p} \\) and the projector. The model integrates over wavelengths \\( \\lambda \\in \\Lambda \\), effectively ranging from \\( 440\\mathrm{nm} \\) to \\( 660\\mathrm{nm} \\) at \\( 10\\mathrm{nm} \\) intervals: \\( \\Lambda = \\{\\lambda_1 = 440\\mathrm{nm},\\dots ,\\lambda_N = 660\\mathrm{nm}\\} \\), where \\( N = 23 \\) is the number of spectral bands." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.845, + 0.4, + 0.863 + ], + "angle": 0, + "content": "5. Dense Dispersed Structured Light" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.87, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We design DDSL patterns \\(\\{P_i\\}_{i=1}^M\\) that enable hyperspectral 3D imaging for dynamic scenes on our active stereo" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.454, + 0.905, + 0.484 + ], + "angle": 0, + "content": "setup. Each DDSL pattern \\(P_{i}\\) is composed of multiple vertical lines, defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.495, + 0.905, + 0.548 + ], + "angle": 0, + "content": "\\[\nP _ {i} (q, \\forall) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\mod \\left(\\left| q _ {x} - i \\times l _ {\\text {s h i f t}} \\right|, l _ {\\text {o f f s e t}}\\right) \\leq \\frac {l _ {\\text {w i d t h}}}{2}, \\\\ 0 & \\text {e l s e}, \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.549, + 0.906, + 0.623 + ], + "angle": 0, + "content": "where \\( q_{x} \\) is the column index of a projector pixel \\( q \\), \\( l_{\\mathrm{shift}} \\) is the line shift between neighboring patterns \\( P_{i} \\) and \\( P_{i + 1} \\), \\( l_{\\mathrm{offset}} \\) is the line offset between neighboring lines in a pattern, \\( l_{\\mathrm{width}} \\) is the line width, and \\( \\mathrm{mod}(x,y) = x\\% y \\) is the modulo operator." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.624, + 0.907, + 0.821 + ], + "angle": 0, + "content": "We project \\(M\\) DDSL patterns \\(\\{P_1, \\ldots, P_M\\}\\) and one black pattern \\(P_B\\) repeatedly, capturing corresponding stereo images \\(I_k^1, \\ldots, I_k^M, I_k^B\\) for \\(k \\in \\{\\text{left}, \\text{right}\\}\\). The black pattern \\(P_B\\) is used to compensate for the non-zero projector intensity for the zero-valued pattern and to enable robust motion compensation which we detail in Section 6. The DDSL patterns create dispersion for each vertical white line, and the dispersed patterns can overlap depending on the settings for three parameters: line offset \\(l_{\\text{offset}}\\), line width \\(l_{\\text{width}}\\), and line shift \\(l_{\\text{shift}}\\). Figure 4(a) and (e) shows the DDSL patterns and captured images with our chosen parameters \\(l_{\\text{offset}}\\), \\(l_{\\text{width}}\\), and \\(l_{\\text{shift}}\\). Below, we discuss our design choices for these parameters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Line Offset The line offset \\( l_{\\mathrm{offset}} \\) defines the spacing between vertical lines in pattern \\( P_{i} \\). A small \\( l_{\\mathrm{offset}} \\) increases overlap between dispersed patterns, resulting in more spectrally multiplexed illumination (Figure 4(b)). This reduces" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16592" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.086, + 0.907, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.411, + 0.907, + 0.482 + ], + "angle": 0, + "content": "Figure 5. Black Optical Flow. We warp adjacent frame image to a target frame using naive optical flow under DDSL patterns and our black optical flow method to show the effectiveness of our method. We estimate optical flows using pretrained RAFT network [22] for both methods. Note that the target frame and adjacent frames are captured under different DDSL patterns. Therefore, the evaluation should primarily focus on geometric alignment rather than color consistency. (a) Warped images based on naive optical flow and black optical flow. (b) Visualization of the interpolated optical flows using the black optical flow." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.501, + 0.483, + 0.593 + ], + "angle": 0, + "content": "the number of patterns \\(M\\), though it may decrease spectral accuracy due to blurred illumination. A larger \\(l_{\\mathrm{offset}}\\) reduces multiplexing, improving spectral accuracy at the cost of more patterns. We set \\(l_{\\mathrm{offset}} = 40\\mathrm{px}\\) to multiplex three spectral bands aligned with the camera RGB channels, balancing spectral accuracy and pattern count." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.609, + 0.483, + 0.716 + ], + "angle": 0, + "content": "Line Shift The line shift \\( l_{\\mathrm{shift}} \\) specifies the shift between lines in neighboring patterns \\( P_{i} \\) and \\( P_{i + 1} \\). A small \\( l_{\\mathrm{shift}} \\) densely samples the spectral axis, increasing potential spectral channels but requiring more patterns \\( M \\) (Figure 4(c)). To achieve spectral channels from \\( 440\\mathrm{nm} \\) to \\( 660\\mathrm{nm} \\) at \\( 10\\mathrm{nm} \\) intervals, we set \\( l_{\\mathrm{shift}} = 5\\mathrm{px} \\), providing a \\( 10\\mathrm{nm} \\) spectral step size while minimizing the number of patterns." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.732, + 0.483, + 0.839 + ], + "angle": 0, + "content": "Line Width A larger line width \\( l_{\\mathrm{width}} \\) increases spectral overlapping across RGB channels, smoothing the illumination spectrum and potentially lowering spectral accuracy (Figure 4(d)). A very narrow \\( l_{\\mathrm{width}} \\) results in low illumination power, introducing noise in captured images. We set \\( l_{\\mathrm{width}} = 5 \\) pixels to optimize illumination intensity without sacrificing spectral accuracy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Summary We use eight DDSL patterns (\\(M = 8\\)) with \\(l_{\\mathrm{shift}} = 5\\), \\(l_{\\mathrm{width}} = 5\\), and \\(l_{\\mathrm{offset}} = 40\\), enabling accurate hyperspectral 3D reconstruction in our experimental" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.501, + 0.907, + 0.607 + ], + "angle": 0, + "content": "setup. Figure 4(f) shows the spectral power distribution of the DDSL-pattern illumination projected onto a scene point \\(\\mathbf{p}\\). For each \\(i\\)-th DDSL pattern, we have three peaks over the RGB spectrum. Using only \\(M = 8\\) DDSL patterns, we can densely sample wavelengths with \\(10\\mathrm{nm}\\) step, allowing for accurate hyperspectral 3D imaging, contrast to using hundreds of pattern images as in the previous work [19]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.621, + 0.819, + 0.639 + ], + "angle": 0, + "content": "6. Hyperspectral 3D Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.646, + 0.906, + 0.694 + ], + "angle": 0, + "content": "Given the captured stereo images \\( I_{k}^{1}, \\ldots, I_{k}^{M}, I_{k}^{B} \\) for DDSL patterns \\( P_{1}, \\ldots, P_{M} \\) and one black pattern \\( P_{B} \\), we reconstruct a hyperspectral image \\( H_{k} \\) and a depth map \\( z_{k} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.713, + 0.906, + 0.803 + ], + "angle": 0, + "content": "Depth Estimation We estimate depth from stereo images \\( I_{\\mathrm{left}}^i \\) and \\( I_{\\mathrm{right}}^i \\) for each frame \\( i \\). The captured stereo images are rectified, and disparity is estimated using the pretrained RAFT-Stereo network [14]. Depth is then computed from disparity using calibrated camera parameters, followed by un-rectification." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.824, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Black Optical Flow Dynamic objects move while capturing the images \\( I_{k}^{1}, \\ldots, I_{k}^{M}, I_{k}^{B} \\) under the varying projector patterns \\( P_{1}, \\ldots, P_{M}, P_{B} \\), which needs compensation for robust hyperspectral image reconstruction. One straightforward approach is to estimate optical flow \\( \\nabla p_{k}^{M/2 \\to i} \\) from" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16593" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.089, + 0.233, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.153, + 0.23, + 0.162 + ], + "angle": 0, + "content": "(a) Reconstructed sRGB" + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.089, + 0.406, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.247, + 0.153, + 0.393, + 0.162 + ], + "angle": 0, + "content": "(b) Point cloud of color checker" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.162, + 0.405, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.186, + 0.331, + 0.328, + 0.341 + ], + "angle": 0, + "content": "(c) Color checker evaluation" + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.089, + 0.508, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.162, + 0.508, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.419, + 0.32, + 0.528, + 0.341 + ], + "angle": 0, + "content": "(d) High frequency spectral band pass filters" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.089, + 0.643, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.163, + 0.644, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.238, + 0.644, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.089, + 0.775, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.163, + 0.775, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.237, + 0.775, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.318, + 0.75, + 0.328 + ], + "angle": 0, + "content": "Wavelength[nm]" + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.089, + 0.906, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.163, + 0.906, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.237, + 0.906, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.329, + 0.87, + 0.341 + ], + "angle": 0, + "content": "(e) Reconstructed hyperspectral intensity of each spectral filters" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.352, + 0.907, + 0.409 + ], + "angle": 0, + "content": "Figure 6. Spectral Accuracy. Color checker evaluation. (a) Reconstructed hyperspectral image of color checker in sRGB, (b) point cloud of color checker, (c) hyperspectral intensity of color checker. High-frequency spectral data evaluation comparing other methods with Shin et al. [19] and Li et al. [13]. (d) \\(10\\mathrm{nm}\\)-FWHM spectral band pass filters and acquisition time for the three methods, (e) reconstructed hyperspectral intensity." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.428, + 0.346, + 0.443 + ], + "angle": 0, + "content": "the center frame \\(M / 2\\) to each frame \\(i\\):" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.455, + 0.483, + 0.475 + ], + "angle": 0, + "content": "\\[\np _ {k} ^ {i} = p _ {k} ^ {M / 2} + \\nabla p _ {k} ^ {M / 2 \\rightarrow i}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.486, + 0.484, + 0.69 + ], + "angle": 0, + "content": "However, this approach is challenging due to the inconsistent illumination at corresponding pixels since each image \\(\\{I_k^i\\}_{i = 1}^M\\) is illuminated by a different DDSL pattern \\(\\{P_i\\}_{i = 1}^M\\). Figure 5(a) depicts how naive optical flow between adjacent DDSL patterns fails to accurately capture the motion. Instead, we estimate the black optical flow, which is the flow between successive black-pattern images \\(I_{k}^{B}\\), avoiding illumination inconsistency. We then interpolate the black optical flow to obtain the target optical flow \\(\\nabla p_k^{M / 2\\rightarrow i}\\), enabling robust optical-flow estimation, as illustrated in Figure 5. Using the estimated flow, we align the images \\(I_{k}^{1},\\ldots ,I_{k}^{M}\\) captured under the DDSL patterns to the center frame \\(I_{k}^{M / 2}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.707, + 0.484, + 0.768 + ], + "angle": 0, + "content": "Multi-pattern Image Formation Using the aligned images \\( I_{k}^{1}, \\ldots, I_{k}^{M} \\) captured under \\( M \\) DDSL patterns, we reformulate the image formation model from Section 4. For the \\( i \\)-th DDSL pattern, the aligned image \\( I_{k}^{i} \\) is modeled as:" + }, + { + "type": "equation", + "bbox": [ + 0.109, + 0.779, + 0.483, + 0.813 + ], + "angle": 0, + "content": "\\[\nI _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) = \\sum_ {\\lambda \\in \\Lambda} \\Omega_ {c, \\lambda} ^ {\\mathrm {c a m}} H _ {k} \\left(p _ {k} ^ {i}, \\lambda\\right) \\frac {\\eta_ {\\lambda}}{d \\left(\\mathbf {p} _ {k} ^ {i}\\right) ^ {2}} L ^ {i} \\left(q _ {\\lambda} ^ {i}, \\lambda\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.483, + 0.871 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}_k^i\\) is the corresponding scene point at frame \\(i\\), and \\(q_{\\lambda}^{i}\\) is the corresponding projector pixel obtained using the backward model \\(\\psi \\colon q_{\\lambda}^{i} = \\psi \\left(\\mathbf{p}_{k}^{i},\\lambda\\right)\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We then subtract the black pattern captured image \\( I_k^B \\) from all the captured images \\( \\{I_k^i(p_k^i, c)\\}_{i=1}^M \\) to remove the" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.428, + 0.872, + 0.443 + ], + "angle": 0, + "content": "undesired residual light intensity for the black pattern:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.448, + 0.905, + 0.467 + ], + "angle": 0, + "content": "\\[\nI _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) \\leftarrow I _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) - I _ {k} ^ {B} \\left(p _ {k} ^ {B}, c\\right) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.472, + 0.905, + 0.501 + ], + "angle": 0, + "content": "We rewrite the image formation as a matrix-vector multiplication:" + }, + { + "type": "equation", + "bbox": [ + 0.67, + 0.503, + 0.905, + 0.518 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {k} = \\mathbf {L H} _ {k}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.522, + 0.906, + 0.567 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}_k\\) is the intensity vector of captured image under \\(M\\) DDSL patterns, \\(\\mathbf{L}\\) is the system matrix, and \\(\\mathbf{H}_k\\) is the hyperspectral image:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.572, + 0.785, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {k} = \\left[ I _ {k} ^ {1} \\left(p _ {k} ^ {1}, R\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, R\\right), \\right.\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.593, + 0.785, + 0.611 + ], + "angle": 0, + "content": "\\[\nI _ {k} ^ {1} \\left(p _ {k} ^ {1}, G\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, G\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.614, + 0.904, + 0.632 + ], + "angle": 0, + "content": "\\[\n\\left. I _ {k} ^ {1} \\left(p _ {k} ^ {1}, B\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, B\\right) \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {3 M \\times 1}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.635, + 0.905, + 0.653 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} = \\left[ \\mathbf {L} _ {R}; \\mathbf {L} _ {G}; \\mathbf {L} _ {B} \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {3 M \\times N}, \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.656, + 0.905, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} _ {c} (i, j) = \\Omega_ {c, \\lambda_ {j}} ^ {\\mathrm {c a m}} \\eta_ {\\lambda_ {j}} \\left(L ^ {i} * G\\right) \\left(q _ {\\lambda_ {j}} ^ {i}, \\lambda_ {j}\\right), \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.683, + 0.905, + 0.717 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} _ {k} = \\left[ H \\left(p _ {k} ^ {M / 2}, \\lambda_ {1}\\right), \\dots , H \\left(p _ {k} ^ {M / 2}, \\lambda_ {N}\\right) \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {N \\times 1}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.723, + 0.906, + 0.769 + ], + "angle": 0, + "content": "where \\( i = 1, \\ldots, M \\), \\( j = 1, \\ldots, N \\), and \\( G \\) is a Gaussian blur kernel accounting for the imaging system's blur; details can be found in the Supplemental Document." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.786, + 0.906, + 0.817 + ], + "angle": 0, + "content": "Hyperspectral Reconstruction We reconstruct per-pixel hyperspectral reflectance \\(\\mathbf{H}_k\\) by solving the following:" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.821, + 0.848, + 0.858 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {H} _ {k}} {\\operatorname {a r g m i n}} \\underbrace {\\| \\mathbf {L} \\mathbf {H} _ {k} - \\mathbf {I} _ {k} \\| _ {2} ^ {2}} _ {\\text {D a t a t e r m}} + \\underbrace {\\kappa_ {\\lambda} \\| \\nabla_ {\\lambda} \\mathbf {H} _ {k} \\| _ {2} ^ {2}} _ {\\text {S p e c t r a l s m o o t h n e s s}} +\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.624, + 0.862, + 0.905, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\underbrace {\\kappa_ {x y} \\left(\\left\\| \\nabla_ {x} \\mathbf {H} _ {k} \\right\\| _ {1} + \\left\\| \\nabla_ {y} \\mathbf {H} _ {k} \\right\\| _ {1}\\right)} _ {\\text {S p a t i a l r e g u l a r i z a t i o n}}, \\tag {14}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16594" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.089, + 0.241, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.198, + 0.227, + 0.208 + ], + "angle": 0, + "content": "Stair case object" + }, + { + "type": "image", + "bbox": [ + 0.241, + 0.089, + 0.342, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.251, + 0.194, + 0.333, + 0.214 + ], + "angle": 0, + "content": "Reconstructed depth under \\(P_{j}\\)" + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.089, + 0.484, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.195, + 0.404, + 0.205 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.204, + 0.215, + 0.37, + 0.227 + ], + "angle": 0, + "content": "(a) Depth reconstructed results" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.228, + 0.289, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.12, + 0.353, + 0.277, + 0.365 + ], + "angle": 0, + "content": "(b) Absolute depth evaluation" + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.228, + 0.484, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.328, + 0.347, + 0.46, + 0.37 + ], + "angle": 0, + "content": "(c) Consistency between different DDSL patterns" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.38, + 0.484, + 0.437 + ], + "angle": 0, + "content": "Figure 7. Depth Validation. (a) Stair case depth reconstructed results. (b) Absolute depth evaluation. (c) Consistency between depth reconstructed results between different DDSL patterns for the stair position index of 3." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.466, + 0.484, + 0.587 + ], + "angle": 0, + "content": "where \\(\\nabla_{\\lambda}, \\nabla_{x}\\), and \\(\\nabla_{y}\\) are gradient operators along the spectral and spatial axes, respectively. The first term corresponds to the data term, penalizing reconstruction error, while the second and third terms enforce spectral smoothness and spatial total variation. The coefficients \\(\\kappa_{\\lambda} = 3\\) and \\(\\kappa_{xy} = 0.05\\) are balancing weights. We solve the per-pixel optimization problem using ADAM [7]. Optimization details are provided in the Supplemental Document." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.614, + 0.214, + 0.63 + ], + "angle": 0, + "content": "7. Calibration" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.483, + 0.901 + ], + "angle": 0, + "content": "We perform a one-time calibration of the projector, camera, and diffraction grating. We obtain the geometric parameters of the stereo cameras and the projector using checkerboard methods [21, 30] without attaching the diffraction grating film. To measure the diffraction efficiency \\(\\eta_{\\lambda}\\) of the diffraction grating, shown in Figure 2(d), we filter the dispersed light using spectral bandpass filters with a \\(10\\mathrm{nm}\\) bandwidth, covering wavelengths from \\(440\\mathrm{nm}\\) to \\(660\\mathrm{nm}\\), and capture the intensity reflected from a Spectralon target. We calibrate the camera response function \\(\\Omega_{c,\\lambda}^{\\mathrm{cam}}\\) also using spectral bandpass filters under LED light, and measure the projector spectral emission function \\(\\Omega_{c,\\lambda}^{\\mathrm{proj}}\\) by projecting RGB dots onto a Spectralon target and capturing the reflected radiance with a spectroradiometer (JETI Specbos 1211). To enhance reconstruction accuracy, we further optimize the radiometric parameters for both the projector and camera; detailed methods are provided in the Supplemental Document." + }, + { + "type": "image_caption", + "bbox": [ + 0.517, + 0.097, + 0.642, + 0.107 + ], + "angle": 0, + "content": "(a) Reconstructed sRGB" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.107, + 0.642, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.668, + 0.096, + 0.793, + 0.107 + ], + "angle": 0, + "content": "(b) Reconstructed depth" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.107, + 0.793, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.088, + 0.903, + 0.108 + ], + "angle": 0, + "content": "(c) Hyperspectral intensity" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.108, + 0.905, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.233, + 0.616, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.233, + 0.663, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.664, + 0.233, + 0.71, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.233, + 0.758, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.233, + 0.807, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.808, + 0.233, + 0.855, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.857, + 0.233, + 0.904, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.65, + 0.37, + 0.78, + 0.382 + ], + "angle": 0, + "content": "(d) Hyperspectral images" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.392, + 0.906, + 0.462 + ], + "angle": 0, + "content": "Figure 8. Fake and Real Oranges. We compare real and artificial fruit(orange), showing the differences in their hyperspectral image curves and corresponding images. (a) Reconstructed hyperspectral image in sRGB, (b) depth (c) spectral graph and (d) hyperspectral images of metameric samples." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.486, + 0.6, + 0.501 + ], + "angle": 0, + "content": "8. Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.513, + 0.907, + 0.77 + ], + "angle": 0, + "content": "Spectral Accuracy Figure 6 (a), (b) and (c) shows the reconstructed hyperspectral image in sRGB, depth, and hyperspectral curves of a ColorChecker chart, demonstrating accurate reconstruction. To measure spectral FWHM of our system, we capture nine narrow-band spectral filters as shown in Figure 6(d). The FWHM of those bandpass filters is \\(10\\mathrm{nm}\\). Figure 6(e) shows that our method achieves a FWHM of \\(15.5\\mathrm{nm}\\) compared to the ground-truth hyperspectral data of the filters, outperforming state-of-the-art affordable hyperspectral 3D imaging methods by Li et al. [13] and Shin et al. [19]. Li et al.[13] shows a FWHM of \\(40\\mathrm{nm}\\) due to the use of broadband RGB illumination of a conventional projector. Shin et al.[19] attains \\(18\\mathrm{nm}\\) FWHM. Moreover, its acquisition time for a scene is 10 minutes whereas our method only requires 0.15 seconds, representing \\(\\times 4000\\) speed increase, thus enabling hyperspectral 3D imaging for dynamic scenes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Depth Accuracy We evaluate the accuracy of depth estimation. Ground-truth depth is obtained using the binary-coded structured light method [8]. Figure 7(a) evaluates the absolute depth error by capturing a 3D-printed stair object. We achieve an average depth error of \\(4\\mathrm{mm}\\) in the area of each step compared to the ground truth, with a maximum error of \\(8\\mathrm{mm}\\). Figure 7(b) shows the difference be" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16595" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.096, + 0.912, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.31, + 0.908, + 0.34 + ], + "angle": 0, + "content": "Figure 9. Dynamic Scene. We show the reconstructed depth and spectral results of a dynamic scene. (a) Reconstructed depth. (b) Reconstructed hyperspectral image in sRGB. (c) Reconstructed hyperspectral image. (d) Hyperspectral intensity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.406 + ], + "angle": 0, + "content": "tween depth results for each DDSL pattern. The consistency across different DDSL patterns is evident, with a difference of less than \\(2\\mathrm{mm}\\) between patterns." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.427, + 0.484, + 0.534 + ], + "angle": 0, + "content": "Dynamic Scenes By using spectrally multiplexed DDSL patterns, we reduce the required number of projections from over hundred patterns with naive scanning [19] to 8 DDSL patterns. This enables accurate hyperspectral 3D imaging for dynamic scenes at 6.6 fps, by software synchronizing camera and projector, as shown in Figure 1, Figure 9, and the Supplemental Video." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.557, + 0.484, + 0.648 + ], + "angle": 0, + "content": "Impact of Pattern Parameters Table 1 shows the impact of different parameter settings of DDSL patterns. Our empirically-set pattern parameters \\( l_{\\mathrm{offset}} \\), \\( l_{\\mathrm{width}} \\), \\( l_{\\mathrm{shift}} \\) result in the best spectral and depth accuracy with a short capture time. The depth accuracy remains unchanged due to the robustness of RaftStereo [14] for correspondence matching." + }, + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.662, + 0.476, + 0.677 + ], + "angle": 0, + "content": "Table 1. Ablation study on pattern parameters: \\( {l}_{\\text{offset }},{l}_{\\text{width }},{l}_{\\text{shift }} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.678, + 0.485, + 0.782 + ], + "angle": 0, + "content": "
Indexl_offsetl_widthlshift# of patterns ∝ capture time↓Spectral FWHM [nm]↓Depth MAE [mm]↓
#160551215.54
#220554174
#3402058FailFail
#440158504
#5405103Fail4
#640522015.54
chosen4055815.54
" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Real and Fake Oranges Figure 8 presents a comparison between artificial and real oranges with reconstructed hyperspectral images in sRGB and depth with spectral curves of each fruits. We can differentiate between the objects in detailed spectral analysis. Ground-truth intensity measurements are acquired using a spectroradiometer." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.356, + 0.634, + 0.372 + ], + "angle": 0, + "content": "9. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.382, + 0.907, + 0.609 + ], + "angle": 0, + "content": "We have introduced DDSL, an accurate and compact method for hyperspectral 3D imaging for dynamic scenes. We use a conventional RGB stereo camera-projector system paired with a sub-millimeter diffraction grating, implemented as a practical experimental prototype. We design the DDSL patterns, generating spectrally-multiplexed illumination, enabling rapid and high-quality hyperspectral 3D imaging. Our method incorporates the dispersion-aware image formation model using the sub-pixel accurate backward mapping. Experimental results demonstrate that we outperform prior affordable methods in both accuracy and also acquisition time, achieving 6.6 fps with a depth error of \\(4\\mathrm{mm}\\) and a spectral accuracy of 15.5 FWHM. We envision that our DDSL method opens up new applications of geometric and material analysis for dynamic objects." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.626, + 0.909, + 0.793 + ], + "angle": 0, + "content": "Limitations and Future work While our method enables rapid, accurate, and practical hyperspectral 3D imaging for dynamic scenes, it is currently constrained to low-speed motion, achieving a frame rate of 6.6 fps due to the slow software-based synchronization between the camera and projector. To address this limitation, hardware synchronization and a high-speed, affordable projector-camera system could significantly increase frame rates [28]. The limited diffraction efficiency also restricts the range of scene positions. Thus, using a high efficiency diffraction grating for the first-order light would enhance the effective range." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Acknowledgments Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, RS-2024-00438532), Korea IITP MSIT (RS-2019-II191906, Artificial Intelligence Graduate School Program-POSTECH, RS-2024-00437866), POSCO, and 2024 POSTECH International Joint Research Project." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16596" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Reza Arablouei, Ethan Goan, Stephen Gensemer, and Branislav Kusy. Fast and robust pushbroom hyperspectral imaging via dmd-based scanning. 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IEEE Transactions on pattern analysis and machine intelligence, 22(11):1330-1334, 2000. 7" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.484, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16598" + } + ] +] \ No newline at end of file diff --git a/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_origin.pdf b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ae10afe808263e3bb43a42562e2001c0daa9b6c1 --- /dev/null +++ b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/e6f27c19-909f-43c9-8505-0dcb89ae13c2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0508d81add2228299df248fd4cdc2aed45f02248f84b382ea24018851acec4fb +size 8412396 diff --git a/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/full.md b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/full.md new file mode 100644 index 0000000000000000000000000000000000000000..39efd77ca977cf1a79dc5bc1874f510b63fc2b2e --- /dev/null +++ b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/full.md @@ -0,0 +1,366 @@ +# Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes + +![](images/89156821aabbee6877038a1ecc316ab45776a5ab47da7330b32b36759717e8f0.jpg) +Suhyun Shin POSTECH +Seungwoo Yoon POSTECH +Ryota Maeda +POSTECH, University of Hyogo + +![](images/6e782d289ebd3330b8c812f85d23601e17e77e499cf30157e74646c2c887d6c1.jpg) +Seung-Hwan Baek POSTECH + +![](images/47e2faf80318818f08b87b483d3dbb28c5a256317a1e5e4643839c505dcb5c2c.jpg) +Figure 1. We introduce a spectrally multiplexed Dense Dispersed Structured Light (DDSL), accurate hyperspectral 3D imaging method for dynamic scenes. (a) Capture configuration, (b) estimated hyperspectral image in sRGB and depth image for dynamic scenes, (c) estimated hyperspectral image, (d) comparison with spectroradiometer measurements. + +# Abstract + +Hyperspectral 3D imaging captures both depth maps and hyperspectral images, enabling comprehensive geometric and material analysis. Recent methods achieve high spectral and depth accuracy; however, they require long acquisition times—often over several minutes—or rely on large, expensive systems, restricting their use to static scenes. We present Dense Dispersed Structured Light (DDSL), an accurate hyperspectral 3D imaging method for dynamic scenes that utilizes stereo RGB cameras and an RGB projector equipped with an affordable diffraction grating film. We design spectrally multiplexed DDSL patterns that significantly reduce the number of required projector patterns, thereby accelerating acquisition speed. Additionally, we formulate an image formation model and a reconstruction method to estimate a hyperspectral image and depth map from captured stereo images. As the first practical and accurate hyperspectral 3D imaging method for dynamic scenes, we experimentally demonstrate that DDSL achieves a spectral resolution of $15.5\mathrm{nm}$ full width at half maximum (FWHM), $4\mathrm{mm}$ depth error, and $6.6\mathrm{fps}$ . + +# 1. Introduction + +Hyperspectral imaging captures a scene across multiple spectral channels beyond the three-channel RGB imaging, thereby providing both spectral and spatial information about the scene. Expanding on this, hyperspectral 3D imaging has recently received interest, as it captures both spectral and geometric information in the form of a depth map and a hyperspectral image. It has proven useful in scientific analysis of real-world materials, with applications in object classification [15], food ripeness detection [20], cultural heritage analysis, and geology [12]. Recently, dispersed structured light has been proposed as a cost-effective and compact solution for accurate hyperspectral 3D imaging [19]. However, its applicability remains limited to static scenes due to the need for projecting hundreds of patterns, resulting in acquisition times of several minutes. + +Increasing the acquisition speed of hyperspectral 3D imaging could make it feasible to analyze the geometric and material properties of objects and scenes in motion. Existing methods rely on expensive, bulky systems, such as coded-aperture snapshot spectral imagers (CASSI) [24] + +![](images/9319688cf13debe69675821ad1d37d0bf62a1794eabec186c08e3a3209fb01f7.jpg) +(a) Imaging system + +![](images/585a66eb6ae7457b18225b6e53f89ab400acbab9f50261f3daaf570f0ccb73c0.jpg) +(b) Schematic diagram +Figure 2. Imaging System. (a) Our active stereo system comprises RGB stereo cameras and a RGB projector equipped with a diffraction grating. (b) The diffraction grating introduces dispersion to the projector light. (c) Spectral sensitivity and emission functions of the camera and the projector. (d) Diffraction grating efficiency. + +![](images/92a0f6003b9a1f51faf14ef80d8f8097fcfb471f553bf9e5e43b51194fc7b3f5.jpg) +(c) Radiometric parameters + +![](images/de440bcaf7a4fe78764a108d48bac5d8dfaae474710747fdbd6b4b5070a42af0.jpg) +(d) Diffraction grating efficiency $\eta_{\lambda}$ + +paired with stereo cameras or time-of-flight setups [10, 17, 25-27]. While compact, practical PSF-based systems exist [4, 18], they significantly compromise either depth or spectral accuracy. + +In this paper, we propose DDSL, an accurate hyperspectral 3D imaging method for dynamic scenes, using a compact and affordable system. Figure 1 shows the capture configuration using our prototype, which consists of stereo RGB cameras and an RGB projector equipped with an affordable diffraction-grating film that generates structured-light projections with wavelength-dependent dispersion. + +We design DDSL patterns for the projector that produce spectrally multiplexed light projections, allowing us to use fewer than ten projections, enabling rapid image acquisition for dynamic scenes. We analyze the stereo images captured under these repeating DDSL patterns by developing an image formation model and a reconstruction method for depth maps and hyperspectral images. + +DDSL enables accurate depth and spectral estimation even for high-frequency spectral variations, where existing affordable methods fall short. We demonstrate that DDSL achieves a depth error of $4\mathrm{mm}$ , a spectral FWHM of $15.5\mathrm{nm}$ in the visible spectrum, and acquisition speed of 6.6 FPS. Our dynamic imaging is achieved through software synchronization between the cameras and the projector. The use of a compact and affordable active-stereo setup enhanced with a diffraction grating film makes DDSL a promising approach for practical and accurate hyperspectral 3D imaging of dynamic scenes. + +We summarize our contributions as follows: + +- We introduce Dense Dispersed Structured Light (DDSL), which enables high-quality hyperspectral 3D imaging for dynamic scenes using an affordable active-stereo setup composed of RGB stereo cameras and an RGB projector augmented with a diffraction grating film. +- We design DDSL patterns and develop an image formation model and hyperspectral 3D reconstruction method for dynamic scenes, obtaining a depth map and a hyperspectral images from stereo RGB images. +- We demonstrate that DDSL outperforms state-of-the-art affordable hyperspectral 3D imaging methods in acquisi + +tion speed with high reconstruction accuracy, achieving a depth error of $4\mathrm{mm}$ , a spectral FWHM of $15.5\mathrm{nm}$ , and a frame rate of 6.6 FPS. + +# 2. Related Work + +Hyperspectral 3D Imaging Various hyperspectral 3D imaging systems have been developed. Kim et al. [12] combined a laser scanner with a CASSI system for accurate hyperspectral 3D imaging, while Li et al. [13] employed a practical projector-camera setup, though at the cost of reduced spectral accuracy. Shin et al. [19] introduced a compact projector-camera system using dispersed structured light with a diffraction grating. However, these previous approaches are generally limited to static scenes due to their long acquisition times, often lasting several minutes. For dynamic scenes, a common approach is to use depth video cameras in conjunction with hyperspectral video cameras. However, hyperspectral video cameras tend to be large and expensive [1, 2, 6, 10, 17, 23, 25, 26]. While solutions using point spread function (PSF) engineering offer single-shot hyperspectral 3D imaging in a compact setup through custom micro- or nano-optical elements, they generally have limited spectral and depth accuracy [4, 18]. Our method achieves accurate hyperspectral 3D imaging for dynamic scenes using a practical setup: stereo RGB cameras and an RGB projector with a diffraction grating film. + +Active Stereo Active stereo employs a stereo camera and an illumination module projecting structured-light patterns for robust 3D imaging [3, 5, 11, 16, 29]. Heist et al. [10] repurposed an active stereo system with a high-speed projector and hyperspectral video cameras for hyperspectral 3D imaging of dynamic scenes. However, the use of hyperspectral video cameras significantly increases instrumentation costs. We leverage a diffraction grating film in front of an RGB projector with RGB stereo cameras, eliminating the need for hyperspectral cameras and enabling practical, accurate hyperspectral 3D imaging for dynamic scenes. + +Dispersive Optics Dispersive optics, including prisms and diffraction gratings, are widely used in hyperspectral + +imaging. CASSI systems utilize relay lenses with dispersive elements and coded masks for precise spectral reconstruction. Cao et al. [6] minimized system size by using a prism and coded mask without relay lenses. Recently, diffractive optical elements have been employed to create spectrally varying point spread functions [4, 18]. Shin et al. [19] integrated a diffraction grating film into a projector-camera system, though it required hundreds of projected patterns, resulting in long capture times. Our method achieves rapid acquisition at 6.6 fps with high spectral and depth accuracy, through our active stereo setup, DDSL patterns, image formation model, and reconstruction method. + +# 3. Imaging System + +We introduce a practical and affordable active stereo system. We use stereo RGB cameras (FLIR GS3-U3-32S4C-C) and an RGB projector (Epson CO-FH02) equipped with diffraction grating film (Edmund 54-509) placed in front of the projector (see Figure 2(a)). The diffraction grating film, which costs less than 20 USD, disperses the broadband projector light according to the light wavelength $\lambda$ as shown Figure 2(b). Each dispersed light ray of a specific wavelength $\lambda$ then propagates to a scene, creating spatially-distributed narrow-band spectral illumination. The stereo cameras capture the scene illuminated by the dispersed light. We set the camera fields of view to capture first-order diffracted light [9]. For color channel $c\in \{R,G,B\}$ and wavelength $\lambda$ , we calibrate and refine the projector spectral emission $\Omega_{c,\lambda}^{\mathrm{proj}}$ , camera spectral sensitivity $\Omega_{c,\lambda}^{\mathrm{cam}}$ , and diffraction-grating efficiency $\eta_{\lambda}$ (Figures 2(c) and (d)). + +# 4. Image Formation + +We develop an image formation model for the active stereo system given a pattern image $P$ that we set to the projector. + +Projector Light Given the projector pattern $P(q, c)$ where $q$ is a projector pixel and $c \in \{R, G, B\}$ is a color channel, we model the light intensity $L(q, \lambda)$ emitted from the pixel $q$ at wavelength $\lambda$ as + +$$ +L (q, \lambda) = \sum_ {c} \Omega_ {c, \lambda} ^ {\operatorname {p r o j}} P (q, c). \tag {1} +$$ + +Dispersed Light Projection Model The light ray of wavelength $\lambda$ emitted by the projector pixel $q$ is diffracted by the diffraction grating and propagates to a scene. We model such dispersed projection in a backward manner as shown Figure 3(a). That is, from a scene point $\mathbf{p}$ and given wavelength $\lambda$ , we model its corresponding projector pixel $q_{\lambda}$ that emits the ray: + +$$ +q _ {\lambda} = \psi (\mathbf {p}, \lambda). \tag {2} +$$ + +![](images/869eacad7267465a184c9ec68cb15b9a9f0e17d62991c1dc485c8fb9dae07aa7.jpg) +(b) Sub-pixel accurate sample collection for data-driven backward modeling + +![](images/490a5e55a5678412de3401313909f8ece324ad07054d1fd80fabd27a3fac44bb.jpg) +(d) Depth dependent backward mapping model $\psi$ for specific wavelength +Figure 3. Image Formation. (a) Light transport of the dispersed light projection of the mapping function $\psi$ . (b) Sub-pixel accurate sample collection for data-driven backward modeling. Calibrated backward mapping model that relates pixel point to projector horizontal position (c) for depth given a specific wavelength and (d) for wavelength given a fixed depth value. + +![](images/0cda267d6a27220d8f59242f547799af8b0462390028e6b1f73e742b123ffd28.jpg) +(e) Wavelength dependent backward mapping model $\psi$ for specific depth + +To construct the backward model $\psi$ , we use a data-driven approach. First, we acquire the samples $q_{\lambda} \in \mathbb{S}_q$ , $\lambda \in \mathbb{S}_{\lambda}$ , $\mathbf{p} \in \mathbb{S}_{\mathbf{p}}$ by capturing Spectralon images under column-wise scan-line patterns per each narrow-band spectrum $\lambda$ using spectral bandpass filters as shown in Figure 3(b). Using the scan-line patterns and sub-pixel accurate Gaussian fitting, we obtain the scene point $\mathbf{p}$ via triangulation, and its projector pixel $q_{\lambda}$ can be obtained for the horizontal coordinate. Note that we model the horizontal coordinate only as dispersion occurs in the horizontal direction. Second, we apply non-linear interpolation using a power function along the depth coordinate of the scene point $\mathbf{p}'_z \in \mathbb{S}_{\mathbf{p}}$ , where $\mathbf{p}'_z$ denotes the z-coordinate of + +![](images/cb23e322efac1e8225df6acf5cba4a4c52550ebc86994656211872ab809084a2.jpg) +Figure 4. DDSL Pattern Design. (a) Three parameters of DDSL patterns. We visualize the issues raised from large or small values for each parameter (b) line offset, (c) line shift, (d) line width. Refer to the text for details. (e) We project DDSL patterns and a single black pattern, and the captured images under such patterns are spectrally multiplexed. (f) Illuminated wavelengths for DDSL and black patterns onto the scene point. + +a scene point $\mathbf{p}'$ , and then linearly interpolate wavelength samples $\lambda' \in \mathbb{S}_{\lambda}$ and spatial samples $p' \in \mathbb{S}_p$ . As a result, we obtain the mapping function $\psi$ with a sub-pixel reprojection error of 0.66 pixel. More details of the sample acquisition and interpolation can be found in the Supplemental Document. + +Stereo Imaging The camera $k \in \{\text{left, right}\}$ captures the scene point $\mathbf{p}$ at a camera pixel $p_k$ through perspective projection: + +$$ +\mathbf {p} = z _ {k} \mathbf {E} _ {k} ^ {- 1} \mathbf {K} _ {k} ^ {- 1} \dot {p} _ {k}, \tag {3} +$$ + +where $z_{k}$ is the depth, $\mathbf{E}_k$ is the extrinsic matrix, $\mathbf{K}_k$ is the intrinsic matrix, and $\dot{p}_k$ is the homogeneous coordinate of pixel $p_k$ . The captured intensity $I_{k}(p_{k},c)$ for the color channel $c$ is modeled as + +$$ +I _ {k} \left(p _ {k}, c\right) = \sum_ {\lambda \in \Lambda} \Omega_ {c, \lambda} ^ {\mathrm {c a m}} H _ {k} \left(p _ {k}, \lambda\right) \frac {\eta_ {\lambda}}{d (\mathbf {p}) ^ {2}} L \left(q _ {\lambda}, \lambda\right), \tag {4} +$$ + +where $H_{k}(p_{k},\lambda)$ is the hyperspectral image and $d(\mathbf{p})$ is the distance between the scene point $\mathbf{p}$ and the projector. The model integrates over wavelengths $\lambda \in \Lambda$ , effectively ranging from $440\mathrm{nm}$ to $660\mathrm{nm}$ at $10\mathrm{nm}$ intervals: $\Lambda = \{\lambda_1 = 440\mathrm{nm},\dots ,\lambda_N = 660\mathrm{nm}\}$ , where $N = 23$ is the number of spectral bands. + +# 5. Dense Dispersed Structured Light + +We design DDSL patterns $\{P_i\}_{i=1}^M$ that enable hyperspectral 3D imaging for dynamic scenes on our active stereo + +setup. Each DDSL pattern $P_{i}$ is composed of multiple vertical lines, defined as: + +$$ +P _ {i} (q, \forall) = \left\{ \begin{array}{l l} 1 & \text {i f} \mod \left(\left| q _ {x} - i \times l _ {\text {s h i f t}} \right|, l _ {\text {o f f s e t}}\right) \leq \frac {l _ {\text {w i d t h}}}{2}, \\ 0 & \text {e l s e}, \end{array} \right. \tag {5} +$$ + +where $q_{x}$ is the column index of a projector pixel $q$ , $l_{\mathrm{shift}}$ is the line shift between neighboring patterns $P_{i}$ and $P_{i + 1}$ , $l_{\mathrm{offset}}$ is the line offset between neighboring lines in a pattern, $l_{\mathrm{width}}$ is the line width, and $\mathrm{mod}(x,y) = x\% y$ is the modulo operator. + +We project $M$ DDSL patterns $\{P_1, \ldots, P_M\}$ and one black pattern $P_B$ repeatedly, capturing corresponding stereo images $I_k^1, \ldots, I_k^M, I_k^B$ for $k \in \{\text{left}, \text{right}\}$ . The black pattern $P_B$ is used to compensate for the non-zero projector intensity for the zero-valued pattern and to enable robust motion compensation which we detail in Section 6. The DDSL patterns create dispersion for each vertical white line, and the dispersed patterns can overlap depending on the settings for three parameters: line offset $l_{\text{offset}}$ , line width $l_{\text{width}}$ , and line shift $l_{\text{shift}}$ . Figure 4(a) and (e) shows the DDSL patterns and captured images with our chosen parameters $l_{\text{offset}}$ , $l_{\text{width}}$ , and $l_{\text{shift}}$ . Below, we discuss our design choices for these parameters. + +Line Offset The line offset $l_{\mathrm{offset}}$ defines the spacing between vertical lines in pattern $P_{i}$ . A small $l_{\mathrm{offset}}$ increases overlap between dispersed patterns, resulting in more spectrally multiplexed illumination (Figure 4(b)). This reduces + +![](images/16d2da3c835f03ae0d30637729705b22577a353205594abebfe799161e096026.jpg) +Figure 5. Black Optical Flow. We warp adjacent frame image to a target frame using naive optical flow under DDSL patterns and our black optical flow method to show the effectiveness of our method. We estimate optical flows using pretrained RAFT network [22] for both methods. Note that the target frame and adjacent frames are captured under different DDSL patterns. Therefore, the evaluation should primarily focus on geometric alignment rather than color consistency. (a) Warped images based on naive optical flow and black optical flow. (b) Visualization of the interpolated optical flows using the black optical flow. + +the number of patterns $M$ , though it may decrease spectral accuracy due to blurred illumination. A larger $l_{\mathrm{offset}}$ reduces multiplexing, improving spectral accuracy at the cost of more patterns. We set $l_{\mathrm{offset}} = 40\mathrm{px}$ to multiplex three spectral bands aligned with the camera RGB channels, balancing spectral accuracy and pattern count. + +Line Shift The line shift $l_{\mathrm{shift}}$ specifies the shift between lines in neighboring patterns $P_{i}$ and $P_{i + 1}$ . A small $l_{\mathrm{shift}}$ densely samples the spectral axis, increasing potential spectral channels but requiring more patterns $M$ (Figure 4(c)). To achieve spectral channels from $440\mathrm{nm}$ to $660\mathrm{nm}$ at $10\mathrm{nm}$ intervals, we set $l_{\mathrm{shift}} = 5\mathrm{px}$ , providing a $10\mathrm{nm}$ spectral step size while minimizing the number of patterns. + +Line Width A larger line width $l_{\mathrm{width}}$ increases spectral overlapping across RGB channels, smoothing the illumination spectrum and potentially lowering spectral accuracy (Figure 4(d)). A very narrow $l_{\mathrm{width}}$ results in low illumination power, introducing noise in captured images. We set $l_{\mathrm{width}} = 5$ pixels to optimize illumination intensity without sacrificing spectral accuracy. + +Summary We use eight DDSL patterns ( $M = 8$ ) with $l_{\mathrm{shift}} = 5$ , $l_{\mathrm{width}} = 5$ , and $l_{\mathrm{offset}} = 40$ , enabling accurate hyperspectral 3D reconstruction in our experimental + +setup. Figure 4(f) shows the spectral power distribution of the DDSL-pattern illumination projected onto a scene point $\mathbf{p}$ . For each $i$ -th DDSL pattern, we have three peaks over the RGB spectrum. Using only $M = 8$ DDSL patterns, we can densely sample wavelengths with $10\mathrm{nm}$ step, allowing for accurate hyperspectral 3D imaging, contrast to using hundreds of pattern images as in the previous work [19]. + +# 6. Hyperspectral 3D Reconstruction + +Given the captured stereo images $I_{k}^{1}, \ldots, I_{k}^{M}, I_{k}^{B}$ for DDSL patterns $P_{1}, \ldots, P_{M}$ and one black pattern $P_{B}$ , we reconstruct a hyperspectral image $H_{k}$ and a depth map $z_{k}$ . + +Depth Estimation We estimate depth from stereo images $I_{\mathrm{left}}^i$ and $I_{\mathrm{right}}^i$ for each frame $i$ . The captured stereo images are rectified, and disparity is estimated using the pretrained RAFT-Stereo network [14]. Depth is then computed from disparity using calibrated camera parameters, followed by un-rectification. + +Black Optical Flow Dynamic objects move while capturing the images $I_{k}^{1}, \ldots, I_{k}^{M}, I_{k}^{B}$ under the varying projector patterns $P_{1}, \ldots, P_{M}, P_{B}$ , which needs compensation for robust hyperspectral image reconstruction. One straightforward approach is to estimate optical flow $\nabla p_{k}^{M/2 \to i}$ from + +![](images/e2308f8b473c946507c39dec0b93e34cfe17a303c0b6dee0b0ee3a2798f141cf.jpg) +(a) Reconstructed sRGB + +![](images/d584090927628e490589a5f2fdeea428845a823492f93097fa1459b78d144a24.jpg) + +![](images/62f35e2feee4c730a3263fd6794c024389d99c978ba015f4c129670b8242dbb7.jpg) +(b) Point cloud of color checker +(c) Color checker evaluation +Figure 6. Spectral Accuracy. Color checker evaluation. (a) Reconstructed hyperspectral image of color checker in sRGB, (b) point cloud of color checker, (c) hyperspectral intensity of color checker. High-frequency spectral data evaluation comparing other methods with Shin et al. [19] and Li et al. [13]. (d) $10\mathrm{nm}$ -FWHM spectral band pass filters and acquisition time for the three methods, (e) reconstructed hyperspectral intensity. + +![](images/0d60f23425f15b12ebb9fe1fb22578a3ca33e0422b7f0512b1ff4a83081f868f.jpg) + +![](images/c62081495fd8f323c839e3fbdd0ade8301bf4ddfe4a32a64a63744cca3c2bced.jpg) +(d) High frequency spectral band pass filters + +![](images/2ebfb5bb9c9688d267e006fd6742bf4048fa806cae24eff49aba437b2bb6dca7.jpg) + +![](images/9bdffb863199093b469bfd6a1be0fc92fbfdd4caa60ad9f3f4dd92a73df415da.jpg) + +![](images/3e64fba54e22097a50440e859dce3002f557f7c0d33fb66245ac37917f6a6ae1.jpg) +(e) Reconstructed hyperspectral intensity of each spectral filters + +![](images/f6e7df7a57044eb5ec226e2dba2ff533d33978d435c21e973e51c21a2df83501.jpg) + +![](images/a4ad7546050c138a81cf070d366915792c1da016028f089e8e8b74b5241f7109.jpg) + +![](images/48174738bdef1419be65b46747b586b6ff695ffb0b9b0dd1cb686dbfe3599659.jpg) +Wavelength[nm] + +![](images/25e6ea90394c77eff9c57d3d244265f6efde3708685fe6c4a26eb3ec1163270b.jpg) + +![](images/0b5570e3cb00412ae1cf1ac455f9db85c20e4c94d42ab78a2c575e9182bec81e.jpg) + +![](images/d5992a4d761958cbb8ce245c80f270d46a3ac4d64f5567e2f9e1eab0abdb1e76.jpg) + +the center frame $M / 2$ to each frame $i$ : + +$$ +p _ {k} ^ {i} = p _ {k} ^ {M / 2} + \nabla p _ {k} ^ {M / 2 \rightarrow i}. \tag {6} +$$ + +However, this approach is challenging due to the inconsistent illumination at corresponding pixels since each image $\{I_k^i\}_{i = 1}^M$ is illuminated by a different DDSL pattern $\{P_i\}_{i = 1}^M$ . Figure 5(a) depicts how naive optical flow between adjacent DDSL patterns fails to accurately capture the motion. Instead, we estimate the black optical flow, which is the flow between successive black-pattern images $I_{k}^{B}$ , avoiding illumination inconsistency. We then interpolate the black optical flow to obtain the target optical flow $\nabla p_k^{M / 2\rightarrow i}$ , enabling robust optical-flow estimation, as illustrated in Figure 5. Using the estimated flow, we align the images $I_{k}^{1},\ldots ,I_{k}^{M}$ captured under the DDSL patterns to the center frame $I_{k}^{M / 2}$ . + +Multi-pattern Image Formation Using the aligned images $I_{k}^{1}, \ldots, I_{k}^{M}$ captured under $M$ DDSL patterns, we reformulate the image formation model from Section 4. For the $i$ -th DDSL pattern, the aligned image $I_{k}^{i}$ is modeled as: + +$$ +I _ {k} ^ {i} \left(p _ {k} ^ {i}, c\right) = \sum_ {\lambda \in \Lambda} \Omega_ {c, \lambda} ^ {\mathrm {c a m}} H _ {k} \left(p _ {k} ^ {i}, \lambda\right) \frac {\eta_ {\lambda}}{d \left(\mathbf {p} _ {k} ^ {i}\right) ^ {2}} L ^ {i} \left(q _ {\lambda} ^ {i}, \lambda\right), \tag {7} +$$ + +where $\mathbf{p}_k^i$ is the corresponding scene point at frame $i$ , and $q_{\lambda}^{i}$ is the corresponding projector pixel obtained using the backward model $\psi \colon q_{\lambda}^{i} = \psi \left(\mathbf{p}_{k}^{i},\lambda\right)$ . + +We then subtract the black pattern captured image $I_k^B$ from all the captured images $\{I_k^i(p_k^i, c)\}_{i=1}^M$ to remove the + +undesired residual light intensity for the black pattern: + +$$ +I _ {k} ^ {i} \left(p _ {k} ^ {i}, c\right) \leftarrow I _ {k} ^ {i} \left(p _ {k} ^ {i}, c\right) - I _ {k} ^ {B} \left(p _ {k} ^ {B}, c\right) \tag {8} +$$ + +We rewrite the image formation as a matrix-vector multiplication: + +$$ +\mathbf {I} _ {k} = \mathbf {L H} _ {k}, \tag {9} +$$ + +where $\mathbf{I}_k$ is the intensity vector of captured image under $M$ DDSL patterns, $\mathbf{L}$ is the system matrix, and $\mathbf{H}_k$ is the hyperspectral image: + +$$ +\mathbf {I} _ {k} = \left[ I _ {k} ^ {1} \left(p _ {k} ^ {1}, R\right), \dots , I _ {k} ^ {M} \left(p _ {k} ^ {M}, R\right), \right. +$$ + +$$ +I _ {k} ^ {1} \left(p _ {k} ^ {1}, G\right), \dots , I _ {k} ^ {M} \left(p _ {k} ^ {M}, G\right), +$$ + +$$ +\left. I _ {k} ^ {1} \left(p _ {k} ^ {1}, B\right), \dots , I _ {k} ^ {M} \left(p _ {k} ^ {M}, B\right) \right] ^ {\intercal} \in \mathbb {R} ^ {3 M \times 1}, \tag {10} +$$ + +$$ +\mathbf {L} = \left[ \mathbf {L} _ {R}; \mathbf {L} _ {G}; \mathbf {L} _ {B} \right] ^ {\intercal} \in \mathbb {R} ^ {3 M \times N}, \tag {11} +$$ + +$$ +\mathbf {L} _ {c} (i, j) = \Omega_ {c, \lambda_ {j}} ^ {\mathrm {c a m}} \eta_ {\lambda_ {j}} \left(L ^ {i} * G\right) \left(q _ {\lambda_ {j}} ^ {i}, \lambda_ {j}\right), \tag {12} +$$ + +$$ +\mathbf {H} _ {k} = \left[ H \left(p _ {k} ^ {M / 2}, \lambda_ {1}\right), \dots , H \left(p _ {k} ^ {M / 2}, \lambda_ {N}\right) \right] ^ {\intercal} \in \mathbb {R} ^ {N \times 1}, \tag {13} +$$ + +where $i = 1, \ldots, M$ , $j = 1, \ldots, N$ , and $G$ is a Gaussian blur kernel accounting for the imaging system's blur; details can be found in the Supplemental Document. + +Hyperspectral Reconstruction We reconstruct per-pixel hyperspectral reflectance $\mathbf{H}_k$ by solving the following: + +$$ +\underset {\mathbf {H} _ {k}} {\operatorname {a r g m i n}} \underbrace {\| \mathbf {L} \mathbf {H} _ {k} - \mathbf {I} _ {k} \| _ {2} ^ {2}} _ {\text {D a t a t e r m}} + \underbrace {\kappa_ {\lambda} \| \nabla_ {\lambda} \mathbf {H} _ {k} \| _ {2} ^ {2}} _ {\text {S p e c t r a l s m o o t h n e s s}} + +$$ + +$$ +\underbrace {\kappa_ {x y} \left(\left\| \nabla_ {x} \mathbf {H} _ {k} \right\| _ {1} + \left\| \nabla_ {y} \mathbf {H} _ {k} \right\| _ {1}\right)} _ {\text {S p a t i a l r e g u l a r i z a t i o n}}, \tag {14} +$$ + +![](images/458bbae01d34750ba029195fa632226b66e952ee48224bffdaee377cb440e015.jpg) +Stair case object + +![](images/8410a0e3317413ee4c4aab6055290c654123a6b8e446643200eb5f8b11d55037.jpg) +Reconstructed depth under $P_{j}$ + +![](images/2547c209d82bafacc3011322825a64aa53d983d4edb9af27ece1c46b110807c8.jpg) +GT + +![](images/d02991550bcbf745631b5af8b4107faecce3123867e4ce5c338fd72fc149531e.jpg) +(a) Depth reconstructed results +(b) Absolute depth evaluation + +![](images/5b9bafe675ba08526d770ddac2a21272e9d8c76421d517653a3d44d527d18967.jpg) +(c) Consistency between different DDSL patterns + +where $\nabla_{\lambda}, \nabla_{x}$ , and $\nabla_{y}$ are gradient operators along the spectral and spatial axes, respectively. The first term corresponds to the data term, penalizing reconstruction error, while the second and third terms enforce spectral smoothness and spatial total variation. The coefficients $\kappa_{\lambda} = 3$ and $\kappa_{xy} = 0.05$ are balancing weights. We solve the per-pixel optimization problem using ADAM [7]. Optimization details are provided in the Supplemental Document. + +# 7. Calibration + +We perform a one-time calibration of the projector, camera, and diffraction grating. We obtain the geometric parameters of the stereo cameras and the projector using checkerboard methods [21, 30] without attaching the diffraction grating film. To measure the diffraction efficiency $\eta_{\lambda}$ of the diffraction grating, shown in Figure 2(d), we filter the dispersed light using spectral bandpass filters with a $10\mathrm{nm}$ bandwidth, covering wavelengths from $440\mathrm{nm}$ to $660\mathrm{nm}$ , and capture the intensity reflected from a Spectralon target. We calibrate the camera response function $\Omega_{c,\lambda}^{\mathrm{cam}}$ also using spectral bandpass filters under LED light, and measure the projector spectral emission function $\Omega_{c,\lambda}^{\mathrm{proj}}$ by projecting RGB dots onto a Spectralon target and capturing the reflected radiance with a spectroradiometer (JETI Specbos 1211). To enhance reconstruction accuracy, we further optimize the radiometric parameters for both the projector and camera; detailed methods are provided in the Supplemental Document. + +![](images/a71c81b20630a457fbf9f56bf0be492679abc592282e2511f5baa807bce40852.jpg) +(a) Reconstructed sRGB + +![](images/4b24bb8c29d12c72c5337b45d35a0b85f4c6c704154b610cff6b75119cbe8abe.jpg) +(b) Reconstructed depth + +![](images/6e4375e7068cbfac86a5d2c5911766940563834811c82f755a67e1c642a18d76.jpg) +(c) Hyperspectral intensity + +![](images/ce0d140846c098bf6c96933b2a1d9d8619e3f06878ccfda1dbb0dfd4901c8071.jpg) +Figure 7. Depth Validation. (a) Stair case depth reconstructed results. (b) Absolute depth evaluation. (c) Consistency between depth reconstructed results between different DDSL patterns for the stair position index of 3. +Figure 8. Fake and Real Oranges. We compare real and artificial fruit(orange), showing the differences in their hyperspectral image curves and corresponding images. (a) Reconstructed hyperspectral image in sRGB, (b) depth (c) spectral graph and (d) hyperspectral images of metameric samples. + +![](images/d5ff9187b4592a5dc0dc08675d6894d90dfcf1febfe1fd4f740ddb352db6f6f4.jpg) +(d) Hyperspectral images + +![](images/45fc81c4e7cb276ea10a046b299db40d55da07a4da15cd98516a1f97dfa4844e.jpg) + +![](images/07e6c6fec8031128a6f848b9431d2d0c069da3ec218c8293ed7012682b4ad0e8.jpg) + +![](images/8f298918dd244986fd3a81c166f5ddc44edd1595af5086d1f2dc1392b82fb204.jpg) + +![](images/4accad497cb941b44e43c64105835fe82c5e74978b9165c74e099e29ad8e4ce0.jpg) + +![](images/eb0591a8aa7928478be611b7abcb12acee0d888d7ac8cb157bead493a744ee8e.jpg) + +# 8. Results + +Spectral Accuracy Figure 6 (a), (b) and (c) shows the reconstructed hyperspectral image in sRGB, depth, and hyperspectral curves of a ColorChecker chart, demonstrating accurate reconstruction. To measure spectral FWHM of our system, we capture nine narrow-band spectral filters as shown in Figure 6(d). The FWHM of those bandpass filters is $10\mathrm{nm}$ . Figure 6(e) shows that our method achieves a FWHM of $15.5\mathrm{nm}$ compared to the ground-truth hyperspectral data of the filters, outperforming state-of-the-art affordable hyperspectral 3D imaging methods by Li et al. [13] and Shin et al. [19]. Li et al.[13] shows a FWHM of $40\mathrm{nm}$ due to the use of broadband RGB illumination of a conventional projector. Shin et al.[19] attains $18\mathrm{nm}$ FWHM. Moreover, its acquisition time for a scene is 10 minutes whereas our method only requires 0.15 seconds, representing $\times 4000$ speed increase, thus enabling hyperspectral 3D imaging for dynamic scenes. + +Depth Accuracy We evaluate the accuracy of depth estimation. Ground-truth depth is obtained using the binary-coded structured light method [8]. Figure 7(a) evaluates the absolute depth error by capturing a 3D-printed stair object. We achieve an average depth error of $4\mathrm{mm}$ in the area of each step compared to the ground truth, with a maximum error of $8\mathrm{mm}$ . Figure 7(b) shows the difference be + +![](images/617aa3fc25b1e4665b26f0421afd6eaef23b9a180bef0430dcd0174e7d87837d.jpg) +Figure 9. Dynamic Scene. We show the reconstructed depth and spectral results of a dynamic scene. (a) Reconstructed depth. (b) Reconstructed hyperspectral image in sRGB. (c) Reconstructed hyperspectral image. (d) Hyperspectral intensity. + +tween depth results for each DDSL pattern. The consistency across different DDSL patterns is evident, with a difference of less than $2\mathrm{mm}$ between patterns. + +Dynamic Scenes By using spectrally multiplexed DDSL patterns, we reduce the required number of projections from over hundred patterns with naive scanning [19] to 8 DDSL patterns. This enables accurate hyperspectral 3D imaging for dynamic scenes at 6.6 fps, by software synchronizing camera and projector, as shown in Figure 1, Figure 9, and the Supplemental Video. + +Impact of Pattern Parameters Table 1 shows the impact of different parameter settings of DDSL patterns. Our empirically-set pattern parameters $l_{\mathrm{offset}}$ , $l_{\mathrm{width}}$ , $l_{\mathrm{shift}}$ result in the best spectral and depth accuracy with a short capture time. The depth accuracy remains unchanged due to the robustness of RaftStereo [14] for correspondence matching. + +Table 1. Ablation study on pattern parameters: ${l}_{\text{offset }},{l}_{\text{width }},{l}_{\text{shift }}$ . + +
Indexl_offsetl_widthlshift# of patterns ∝ capture time↓Spectral FWHM [nm]↓Depth MAE [mm]↓
#160551215.54
#220554174
#3402058FailFail
#440158504
#5405103Fail4
#640522015.54
chosen4055815.54
+ +Real and Fake Oranges Figure 8 presents a comparison between artificial and real oranges with reconstructed hyperspectral images in sRGB and depth with spectral curves of each fruits. We can differentiate between the objects in detailed spectral analysis. Ground-truth intensity measurements are acquired using a spectroradiometer. + +# 9. Conclusion + +We have introduced DDSL, an accurate and compact method for hyperspectral 3D imaging for dynamic scenes. We use a conventional RGB stereo camera-projector system paired with a sub-millimeter diffraction grating, implemented as a practical experimental prototype. We design the DDSL patterns, generating spectrally-multiplexed illumination, enabling rapid and high-quality hyperspectral 3D imaging. Our method incorporates the dispersion-aware image formation model using the sub-pixel accurate backward mapping. Experimental results demonstrate that we outperform prior affordable methods in both accuracy and also acquisition time, achieving 6.6 fps with a depth error of $4\mathrm{mm}$ and a spectral accuracy of 15.5 FWHM. We envision that our DDSL method opens up new applications of geometric and material analysis for dynamic objects. + +Limitations and Future work While our method enables rapid, accurate, and practical hyperspectral 3D imaging for dynamic scenes, it is currently constrained to low-speed motion, achieving a frame rate of 6.6 fps due to the slow software-based synchronization between the camera and projector. To address this limitation, hardware synchronization and a high-speed, affordable projector-camera system could significantly increase frame rates [28]. The limited diffraction efficiency also restricts the range of scene positions. Thus, using a high efficiency diffraction grating for the first-order light would enhance the effective range. + +Acknowledgments Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, RS-2024-00438532), Korea IITP MSIT (RS-2019-II191906, Artificial Intelligence Graduate School Program-POSTECH, RS-2024-00437866), POSCO, and 2024 POSTECH International Joint Research Project. + +# References + +[1] Reza Arablouei, Ethan Goan, Stephen Gensemer, and Branislav Kusy. Fast and robust pushbroom hyperspectral imaging via dmd-based scanning. In Novel Optical Systems Design and Optimization XIX, pages 7-17. SPIE, 2016. 2 +[2] Charles M Bachmann, Rehman S Eon, Christopher S Lapszynski, Gregory P Badura, Anthony Vodacek, Matthew J Hoffman, Donald McKeown, Robert L Kremens, Michael Richardson, Timothy Bauch, et al. A low-rate video approach to hyperspectral imaging of dynamic scenes. Journal of Imaging, 5(1):6, 2018. 2 +[3] Seung-Hwan Baek and Felix Heide. 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IEEE Transactions on pattern analysis and machine intelligence, 22(11):1330-1334, 2000. 7 \ No newline at end of file diff --git a/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/images.zip b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ae5b624f5fe3c9359a9348b0c07588113f91f1f1 --- /dev/null +++ b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:763b33322fe4d29fedadc4ab153fc3d74150cf3a3294be4b752abe3c5a5ada54 +size 1010058 diff --git a/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/layout.json b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f2820c31a409a6a56048f33a7e3afb905daa1623 --- /dev/null +++ b/2025/Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes/layout.json @@ -0,0 +1,11109 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 151, + 103, + 459, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 103, + 459, + 140 + ], + "spans": [ + { + "bbox": [ + 151, + 103, + 459, + 140 + ], + "type": "text", + "content": "Dense Dispersed Structured Light for Hyperspectral 3D Imaging of Dynamic Scenes" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 56, + 193, + 296, + 407 + ], + "blocks": [ + { + "bbox": [ + 71, + 161, + 136, + 188 + ], + "lines": [ + { + "bbox": [ + 71, + 161, + 136, + 188 + ], + "spans": [ + { + "bbox": [ + 71, + 161, + 136, + 188 + ], + "type": "text", + "content": "Suhyun Shin POSTECH" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 158, + 161, + 240, + 188 + ], + "lines": [ + { + "bbox": [ + 158, + 161, + 240, + 188 + ], + "spans": [ + { + "bbox": [ + 158, + 161, + 240, + 188 + ], + "type": "text", + "content": "Seungwoo Yoon POSTECH" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 263, + 161, + 423, + 190 + ], + "lines": [ + { + "bbox": [ + 263, + 161, + 423, + 190 + ], + "spans": [ + { + "bbox": [ + 263, + 161, + 423, + 190 + ], + "type": "text", + "content": "Ryota Maeda \nPOSTECH, University of Hyogo" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 56, + 193, + 296, + 407 + ], + "lines": [ + { + "bbox": [ + 56, + 193, + 296, + 407 + ], + "spans": [ + { + "bbox": [ + 56, + 193, + 296, + 407 + ], + "type": "image", + "image_path": "89156821aabbee6877038a1ecc316ab45776a5ab47da7330b32b36759717e8f0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 296, + 193, + 455, + 407 + ], + "blocks": [ + { + "bbox": [ + 446, + 161, + 539, + 188 + ], + "lines": [ + { + "bbox": [ + 446, + 161, + 539, + 188 + ], + "spans": [ + { + "bbox": [ + 446, + 161, + 539, + 188 + ], + "type": "text", + "content": "Seung-Hwan Baek POSTECH" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 296, + 193, + 455, + 407 + ], + "lines": [ + { + "bbox": [ + 296, + 193, + 455, + 407 + ], + "spans": [ + { + "bbox": [ + 296, + 193, + 455, + 407 + ], + "type": "image", + "image_path": "6e782d289ebd3330b8c812f85d23601e17e77e499cf30157e74646c2c887d6c1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 455, + 193, + 554, + 411 + ], + "blocks": [ + { + "bbox": [ + 455, + 193, + 554, + 411 + ], + "lines": [ + { + "bbox": [ + 455, + 193, + 554, + 411 + ], + "spans": [ + { + "bbox": [ + 455, + 193, + 554, + 411 + ], + "type": "image", + "image_path": "47e2faf80318818f08b87b483d3dbb28c5a256317a1e5e4643839c505dcb5c2c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 411, + 555, + 445 + ], + "lines": [ + { + "bbox": [ + 55, + 411, + 555, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 555, + 445 + ], + "type": "text", + "content": "Figure 1. We introduce a spectrally multiplexed Dense Dispersed Structured Light (DDSL), accurate hyperspectral 3D imaging method for dynamic scenes. (a) Capture configuration, (b) estimated hyperspectral image in sRGB and depth image for dynamic scenes, (c) estimated hyperspectral image, (d) comparison with spectroradiometer measurements." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 152, + 449, + 200, + 461 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 449, + 200, + 461 + ], + "spans": [ + { + "bbox": [ + 152, + 449, + 200, + 461 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "type": "text", + "content": "Hyperspectral 3D imaging captures both depth maps and hyperspectral images, enabling comprehensive geometric and material analysis. Recent methods achieve high spectral and depth accuracy; however, they require long acquisition times—often over several minutes—or rely on large, expensive systems, restricting their use to static scenes. We present Dense Dispersed Structured Light (DDSL), an accurate hyperspectral 3D imaging method for dynamic scenes that utilizes stereo RGB cameras and an RGB projector equipped with an affordable diffraction grating film. We design spectrally multiplexed DDSL patterns that significantly reduce the number of required projector patterns, thereby accelerating acquisition speed. Additionally, we formulate an image formation model and a reconstruction method to estimate a hyperspectral image and depth map from captured stereo images. As the first practical and accurate hyperspectral 3D imaging method for dynamic scenes, we experimentally demonstrate that DDSL achieves a spectral resolution of " + }, + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "type": "inline_equation", + "content": "15.5\\mathrm{nm}" + }, + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "type": "text", + "content": " full width at half maximum (FWHM), " + }, + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "type": "inline_equation", + "content": "4\\mathrm{mm}" + }, + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "type": "text", + "content": " depth error, and " + }, + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "type": "inline_equation", + "content": "6.6\\mathrm{fps}" + }, + { + "bbox": [ + 53, + 474, + 297, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 449, + 394, + 461 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 449, + 394, + 461 + ], + "spans": [ + { + "bbox": [ + 315, + 449, + 394, + 461 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 472, + 555, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 555, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 555, + 651 + ], + "type": "text", + "content": "Hyperspectral imaging captures a scene across multiple spectral channels beyond the three-channel RGB imaging, thereby providing both spectral and spatial information about the scene. Expanding on this, hyperspectral 3D imaging has recently received interest, as it captures both spectral and geometric information in the form of a depth map and a hyperspectral image. It has proven useful in scientific analysis of real-world materials, with applications in object classification [15], food ripeness detection [20], cultural heritage analysis, and geology [12]. Recently, dispersed structured light has been proposed as a cost-effective and compact solution for accurate hyperspectral 3D imaging [19]. However, its applicability remains limited to static scenes due to the need for projecting hundreds of patterns, resulting in acquisition times of several minutes." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "content": "Increasing the acquisition speed of hyperspectral 3D imaging could make it feasible to analyze the geometric and material properties of objects and scenes in motion. Existing methods rely on expensive, bulky systems, such as coded-aperture snapshot spectral imagers (CASSI) [24]" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16589" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 68, + 202, + 156 + ], + "blocks": [ + { + "bbox": [ + 70, + 68, + 202, + 156 + ], + "lines": [ + { + "bbox": [ + 70, + 68, + 202, + 156 + ], + "spans": [ + { + "bbox": [ + 70, + 68, + 202, + 156 + ], + "type": "image", + "image_path": "9319688cf13debe69675821ad1d37d0bf62a1794eabec186c08e3a3209fb01f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 102, + 157, + 166, + 167 + ], + "lines": [ + { + "bbox": [ + 102, + 157, + 166, + 167 + ], + "spans": [ + { + "bbox": [ + 102, + 157, + 166, + 167 + ], + "type": "text", + "content": "(a) Imaging system" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 202, + 69, + 298, + 156 + ], + "blocks": [ + { + "bbox": [ + 202, + 69, + 298, + 156 + ], + "lines": [ + { + "bbox": [ + 202, + 69, + 298, + 156 + ], + "spans": [ + { + "bbox": [ + 202, + 69, + 298, + 156 + ], + "type": "image", + "image_path": "585a66eb6ae7457b18225b6e53f89ab400acbab9f50261f3daaf570f0ccb73c0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 157, + 295, + 167 + ], + "lines": [ + { + "bbox": [ + 220, + 157, + 295, + 167 + ], + "spans": [ + { + "bbox": [ + 220, + 157, + 295, + 167 + ], + "type": "text", + "content": "(b) Schematic diagram" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 173, + 555, + 207 + ], + "lines": [ + { + "bbox": [ + 55, + 173, + 555, + 207 + ], + "spans": [ + { + "bbox": [ + 55, + 173, + 555, + 207 + ], + "type": "text", + "content": "Figure 2. Imaging System. (a) Our active stereo system comprises RGB stereo cameras and a RGB projector equipped with a diffraction grating. (b) The diffraction grating introduces dispersion to the projector light. (c) Spectral sensitivity and emission functions of the camera and the projector. (d) Diffraction grating efficiency." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 301, + 71, + 421, + 156 + ], + "blocks": [ + { + "bbox": [ + 301, + 71, + 421, + 156 + ], + "lines": [ + { + "bbox": [ + 301, + 71, + 421, + 156 + ], + "spans": [ + { + "bbox": [ + 301, + 71, + 421, + 156 + ], + "type": "image", + "image_path": "92a0f6003b9a1f51faf14ef80d8f8097fcfb471f553bf9e5e43b51194fc7b3f5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 157, + 413, + 167 + ], + "lines": [ + { + "bbox": [ + 324, + 157, + 413, + 167 + ], + "spans": [ + { + "bbox": [ + 324, + 157, + 413, + 167 + ], + "type": "text", + "content": "(c) Radiometric parameters" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 422, + 72, + 541, + 156 + ], + "blocks": [ + { + "bbox": [ + 422, + 72, + 541, + 156 + ], + "lines": [ + { + "bbox": [ + 422, + 72, + 541, + 156 + ], + "spans": [ + { + "bbox": [ + 422, + 72, + 541, + 156 + ], + "type": "image", + "image_path": "de440bcaf7a4fe78764a108d48bac5d8dfaae474710747fdbd6b4b5070a42af0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 157, + 545, + 167 + ], + "lines": [ + { + "bbox": [ + 432, + 157, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 432, + 157, + 545, + 167 + ], + "type": "text", + "content": "(d) Diffraction grating efficiency " + }, + { + "bbox": [ + 432, + 157, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\eta_{\\lambda}" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 213, + 295, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 213, + 295, + 262 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 295, + 262 + ], + "type": "text", + "content": "paired with stereo cameras or time-of-flight setups [10, 17, 25-27]. While compact, practical PSF-based systems exist [4, 18], they significantly compromise either depth or spectral accuracy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 263, + 295, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 263, + 295, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 263, + 295, + 348 + ], + "type": "text", + "content": "In this paper, we propose DDSL, an accurate hyperspectral 3D imaging method for dynamic scenes, using a compact and affordable system. Figure 1 shows the capture configuration using our prototype, which consists of stereo RGB cameras and an RGB projector equipped with an affordable diffraction-grating film that generates structured-light projections with wavelength-dependent dispersion." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 349, + 296, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 296, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 296, + 433 + ], + "type": "text", + "content": "We design DDSL patterns for the projector that produce spectrally multiplexed light projections, allowing us to use fewer than ten projections, enabling rapid image acquisition for dynamic scenes. We analyze the stereo images captured under these repeating DDSL patterns by developing an image formation model and a reconstruction method for depth maps and hyperspectral images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 434, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 295, + 567 + ], + "type": "text", + "content": "DDSL enables accurate depth and spectral estimation even for high-frequency spectral variations, where existing affordable methods fall short. We demonstrate that DDSL achieves a depth error of " + }, + { + "bbox": [ + 55, + 434, + 295, + 567 + ], + "type": "inline_equation", + "content": "4\\mathrm{mm}" + }, + { + "bbox": [ + 55, + 434, + 295, + 567 + ], + "type": "text", + "content": ", a spectral FWHM of " + }, + { + "bbox": [ + 55, + 434, + 295, + 567 + ], + "type": "inline_equation", + "content": "15.5\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 434, + 295, + 567 + ], + "type": "text", + "content": " in the visible spectrum, and acquisition speed of 6.6 FPS. Our dynamic imaging is achieved through software synchronization between the cameras and the projector. The use of a compact and affordable active-stereo setup enhanced with a diffraction grating film makes DDSL a promising approach for practical and accurate hyperspectral 3D imaging of dynamic scenes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 67, + 568, + 246, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 568, + 246, + 579 + ], + "spans": [ + { + "bbox": [ + 67, + 568, + 246, + 579 + ], + "type": "text", + "content": "We summarize our contributions as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 582, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 55, + 582, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 641 + ], + "type": "text", + "content": "- We introduce Dense Dispersed Structured Light (DDSL), which enables high-quality hyperspectral 3D imaging for dynamic scenes using an affordable active-stereo setup composed of RGB stereo cameras and an RGB projector augmented with a diffraction grating film." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "content": "- We design DDSL patterns and develop an image formation model and hyperspectral 3D reconstruction method for dynamic scenes, obtaining a depth map and a hyperspectral images from stereo RGB images." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "- We demonstrate that DDSL outperforms state-of-the-art affordable hyperspectral 3D imaging methods in acquisi" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 321, + 213, + 555, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 213, + 555, + 249 + ], + "spans": [ + { + "bbox": [ + 321, + 213, + 555, + 249 + ], + "type": "text", + "content": "tion speed with high reconstruction accuracy, achieving a depth error of " + }, + { + "bbox": [ + 321, + 213, + 555, + 249 + ], + "type": "inline_equation", + "content": "4\\mathrm{mm}" + }, + { + "bbox": [ + 321, + 213, + 555, + 249 + ], + "type": "text", + "content": ", a spectral FWHM of " + }, + { + "bbox": [ + 321, + 213, + 555, + 249 + ], + "type": "inline_equation", + "content": "15.5\\mathrm{nm}" + }, + { + "bbox": [ + 321, + 213, + 555, + 249 + ], + "type": "text", + "content": ", and a frame rate of 6.6 FPS." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 314, + 258, + 400, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 258, + 400, + 271 + ], + "spans": [ + { + "bbox": [ + 314, + 258, + 400, + 271 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 279, + 555, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 279, + 555, + 531 + ], + "spans": [ + { + "bbox": [ + 313, + 279, + 555, + 531 + ], + "type": "text", + "content": "Hyperspectral 3D Imaging Various hyperspectral 3D imaging systems have been developed. Kim et al. [12] combined a laser scanner with a CASSI system for accurate hyperspectral 3D imaging, while Li et al. [13] employed a practical projector-camera setup, though at the cost of reduced spectral accuracy. Shin et al. [19] introduced a compact projector-camera system using dispersed structured light with a diffraction grating. However, these previous approaches are generally limited to static scenes due to their long acquisition times, often lasting several minutes. For dynamic scenes, a common approach is to use depth video cameras in conjunction with hyperspectral video cameras. However, hyperspectral video cameras tend to be large and expensive [1, 2, 6, 10, 17, 23, 25, 26]. While solutions using point spread function (PSF) engineering offer single-shot hyperspectral 3D imaging in a compact setup through custom micro- or nano-optical elements, they generally have limited spectral and depth accuracy [4, 18]. Our method achieves accurate hyperspectral 3D imaging for dynamic scenes using a practical setup: stereo RGB cameras and an RGB projector with a diffraction grating film." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 544, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 555, + 676 + ], + "type": "text", + "content": "Active Stereo Active stereo employs a stereo camera and an illumination module projecting structured-light patterns for robust 3D imaging [3, 5, 11, 16, 29]. Heist et al. [10] repurposed an active stereo system with a high-speed projector and hyperspectral video cameras for hyperspectral 3D imaging of dynamic scenes. However, the use of hyperspectral video cameras significantly increases instrumentation costs. We leverage a diffraction grating film in front of an RGB projector with RGB stereo cameras, eliminating the need for hyperspectral cameras and enabling practical, accurate hyperspectral 3D imaging for dynamic scenes." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "Dispersive Optics Dispersive optics, including prisms and diffraction gratings, are widely used in hyperspectral" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16590" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "type": "text", + "content": "imaging. CASSI systems utilize relay lenses with dispersive elements and coded masks for precise spectral reconstruction. Cao et al. [6] minimized system size by using a prism and coded mask without relay lenses. Recently, diffractive optical elements have been employed to create spectrally varying point spread functions [4, 18]. Shin et al. [19] integrated a diffraction grating film into a projector-camera system, though it required hundreds of projected patterns, resulting in long capture times. Our method achieves rapid acquisition at 6.6 fps with high spectral and depth accuracy, through our active stereo setup, DDSL patterns, image formation model, and reconstruction method." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 228, + 153, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 153, + 241 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 153, + 241 + ], + "type": "text", + "content": "3. Imaging System" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "content": "We introduce a practical and affordable active stereo system. We use stereo RGB cameras (FLIR GS3-U3-32S4C-C) and an RGB projector (Epson CO-FH02) equipped with diffraction grating film (Edmund 54-509) placed in front of the projector (see Figure 2(a)). The diffraction grating film, which costs less than 20 USD, disperses the broadband projector light according to the light wavelength " + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "content": " as shown Figure 2(b). Each dispersed light ray of a specific wavelength " + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "content": " then propagates to a scene, creating spatially-distributed narrow-band spectral illumination. The stereo cameras capture the scene illuminated by the dispersed light. We set the camera fields of view to capture first-order diffracted light [9]. For color channel " + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "inline_equation", + "content": "c\\in \\{R,G,B\\}" + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "content": " and wavelength " + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "content": ", we calibrate and refine the projector spectral emission " + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "inline_equation", + "content": "\\Omega_{c,\\lambda}^{\\mathrm{proj}}" + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "content": ", camera spectral sensitivity " + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "inline_equation", + "content": "\\Omega_{c,\\lambda}^{\\mathrm{cam}}" + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "content": ", and diffraction-grating efficiency " + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "inline_equation", + "content": "\\eta_{\\lambda}" + }, + { + "bbox": [ + 55, + 247, + 296, + 439 + ], + "type": "text", + "content": " (Figures 2(c) and (d))." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 451, + 160, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 451, + 160, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 451, + 160, + 464 + ], + "type": "text", + "content": "4. Image Formation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 471, + 296, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 471, + 296, + 496 + ], + "spans": [ + { + "bbox": [ + 55, + 471, + 296, + 496 + ], + "type": "text", + "content": "We develop an image formation model for the active stereo system given a pattern image " + }, + { + "bbox": [ + 55, + 471, + 296, + 496 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 471, + 296, + 496 + ], + "type": "text", + "content": " that we set to the projector." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "text", + "content": "Projector Light Given the projector pattern " + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "inline_equation", + "content": "P(q, c)" + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "text", + "content": " is a projector pixel and " + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "inline_equation", + "content": "c \\in \\{R, G, B\\}" + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "text", + "content": " is a color channel, we model the light intensity " + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "inline_equation", + "content": "L(q, \\lambda)" + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "text", + "content": " emitted from the pixel " + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "text", + "content": " at wavelength " + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 510, + 296, + 559 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 118, + 568, + 295, + 593 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 568, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 118, + 568, + 295, + 593 + ], + "type": "interline_equation", + "content": "L (q, \\lambda) = \\sum_ {c} \\Omega_ {c, \\lambda} ^ {\\operatorname {p r o j}} P (q, c). \\tag {1}", + "image_path": "bf1688ba89c868139e4b5ddfe98de7ab8835411ac9d79506401fe6c8a53c8f8f.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "spans": [ + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "text", + "content": "Dispersed Light Projection Model The light ray of wavelength " + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "text", + "content": " emitted by the projector pixel " + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "text", + "content": " is diffracted by the diffraction grating and propagates to a scene. We model such dispersed projection in a backward manner as shown Figure 3(a). That is, from a scene point " + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "text", + "content": " and given wavelength " + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "text", + "content": ", we model its corresponding projector pixel " + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "inline_equation", + "content": "q_{\\lambda}" + }, + { + "bbox": [ + 55, + 607, + 296, + 691 + ], + "type": "text", + "content": " that emits the ray:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 701, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 701, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 143, + 701, + 295, + 715 + ], + "type": "interline_equation", + "content": "q _ {\\lambda} = \\psi (\\mathbf {p}, \\lambda). \\tag {2}", + "image_path": "c162bea3f9ebef2a36d7b860c2ab5820f50543478f28fcb267eaa62fb32832bc.jpg" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 319, + 68, + 553, + 328 + ], + "blocks": [ + { + "bbox": [ + 319, + 68, + 553, + 328 + ], + "lines": [ + { + "bbox": [ + 319, + 68, + 553, + 328 + ], + "spans": [ + { + "bbox": [ + 319, + 68, + 553, + 328 + ], + "type": "image", + "image_path": "869eacad7267465a184c9ec68cb15b9a9f0e17d62991c1dc485c8fb9dae07aa7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 329, + 555, + 340 + ], + "lines": [ + { + "bbox": [ + 315, + 329, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 315, + 329, + 555, + 340 + ], + "type": "text", + "content": "(b) Sub-pixel accurate sample collection for data-driven backward modeling" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 350, + 417, + 434 + ], + "blocks": [ + { + "bbox": [ + 318, + 350, + 417, + 434 + ], + "lines": [ + { + "bbox": [ + 318, + 350, + 417, + 434 + ], + "spans": [ + { + "bbox": [ + 318, + 350, + 417, + 434 + ], + "type": "image", + "image_path": "490a5e55a5678412de3401313909f8ece324ad07054d1fd80fabd27a3fac44bb.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 330, + 440, + 423, + 468 + ], + "lines": [ + { + "bbox": [ + 330, + 440, + 423, + 468 + ], + "spans": [ + { + "bbox": [ + 330, + 440, + 423, + 468 + ], + "type": "text", + "content": "(d) Depth dependent backward mapping model " + }, + { + "bbox": [ + 330, + 440, + 423, + 468 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 330, + 440, + 423, + 468 + ], + "type": "text", + "content": " for specific wavelength" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 471, + 555, + 536 + ], + "lines": [ + { + "bbox": [ + 313, + 471, + 555, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 471, + 555, + 536 + ], + "type": "text", + "content": "Figure 3. Image Formation. (a) Light transport of the dispersed light projection of the mapping function " + }, + { + "bbox": [ + 313, + 471, + 555, + 536 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 313, + 471, + 555, + 536 + ], + "type": "text", + "content": ". (b) Sub-pixel accurate sample collection for data-driven backward modeling. Calibrated backward mapping model that relates pixel point to projector horizontal position (c) for depth given a specific wavelength and (d) for wavelength given a fixed depth value." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 418, + 352, + 548, + 434 + ], + "blocks": [ + { + "bbox": [ + 418, + 352, + 548, + 434 + ], + "lines": [ + { + "bbox": [ + 418, + 352, + 548, + 434 + ], + "spans": [ + { + "bbox": [ + 418, + 352, + 548, + 434 + ], + "type": "image", + "image_path": "0cda267d6a27220d8f59242f547799af8b0462390028e6b1f73e742b123ffd28.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 440, + 536, + 467 + ], + "lines": [ + { + "bbox": [ + 443, + 440, + 536, + 467 + ], + "spans": [ + { + "bbox": [ + 443, + 440, + 536, + 467 + ], + "type": "text", + "content": "(e) Wavelength dependent backward mapping model " + }, + { + "bbox": [ + 443, + 440, + 536, + 467 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 443, + 440, + 536, + 467 + ], + "type": "text", + "content": " for specific depth" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": "To construct the backward model " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": ", we use a data-driven approach. First, we acquire the samples " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "q_{\\lambda} \\in \\mathbb{S}_q" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\lambda \\in \\mathbb{S}_{\\lambda}" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbb{S}_{\\mathbf{p}}" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": " by capturing Spectralon images under column-wise scan-line patterns per each narrow-band spectrum " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": " using spectral bandpass filters as shown in Figure 3(b). Using the scan-line patterns and sub-pixel accurate Gaussian fitting, we obtain the scene point " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": " via triangulation, and its projector pixel " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "q_{\\lambda}" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": " can be obtained for the horizontal coordinate. Note that we model the horizontal coordinate only as dispersion occurs in the horizontal direction. Second, we apply non-linear interpolation using a power function along the depth coordinate of the scene point " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}'_z \\in \\mathbb{S}_{\\mathbf{p}}" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}'_z" + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": " denotes the z-coordinate of" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16591" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 68, + 558, + 297 + ], + "blocks": [ + { + "bbox": [ + 56, + 68, + 558, + 297 + ], + "lines": [ + { + "bbox": [ + 56, + 68, + 558, + 297 + ], + "spans": [ + { + "bbox": [ + 56, + 68, + 558, + 297 + ], + "type": "image", + "image_path": "cb23e322efac1e8225df6acf5cba4a4c52550ebc86994656211872ab809084a2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 300, + 555, + 346 + ], + "lines": [ + { + "bbox": [ + 54, + 300, + 555, + 346 + ], + "spans": [ + { + "bbox": [ + 54, + 300, + 555, + 346 + ], + "type": "text", + "content": "Figure 4. DDSL Pattern Design. (a) Three parameters of DDSL patterns. We visualize the issues raised from large or small values for each parameter (b) line offset, (c) line shift, (d) line width. Refer to the text for details. (e) We project DDSL patterns and a single black pattern, and the captured images under such patterns are spectrally multiplexed. (f) Illuminated wavelengths for DDSL and black patterns onto the scene point." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "spans": [ + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "text", + "content": "a scene point " + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{p}'" + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "text", + "content": ", and then linearly interpolate wavelength samples " + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "inline_equation", + "content": "\\lambda' \\in \\mathbb{S}_{\\lambda}" + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "text", + "content": " and spatial samples " + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "inline_equation", + "content": "p' \\in \\mathbb{S}_p" + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "text", + "content": ". As a result, we obtain the mapping function " + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 54, + 359, + 294, + 431 + ], + "type": "text", + "content": " with a sub-pixel reprojection error of 0.66 pixel. More details of the sample acquisition and interpolation can be found in the Supplemental Document." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "spans": [ + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "type": "text", + "content": "Stereo Imaging The camera " + }, + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "type": "inline_equation", + "content": "k \\in \\{\\text{left, right}\\}" + }, + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "type": "text", + "content": " captures the scene point " + }, + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "type": "text", + "content": " at a camera pixel " + }, + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "type": "inline_equation", + "content": "p_k" + }, + { + "bbox": [ + 54, + 445, + 295, + 480 + ], + "type": "text", + "content": " through perspective projection:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 480, + 294, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 480, + 294, + 495 + ], + "spans": [ + { + "bbox": [ + 133, + 480, + 294, + 495 + ], + "type": "interline_equation", + "content": "\\mathbf {p} = z _ {k} \\mathbf {E} _ {k} ^ {- 1} \\mathbf {K} _ {k} ^ {- 1} \\dot {p} _ {k}, \\tag {3}", + "image_path": "04dd7d7759c480de1441b55d5716c31978bf8541e4b4cafc30b177d07ac028d3.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "inline_equation", + "content": "z_{k}" + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "content": " is the depth, " + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_k" + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "content": " is the extrinsic matrix, " + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_k" + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "content": " is the intrinsic matrix, and " + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "inline_equation", + "content": "\\dot{p}_k" + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "content": " is the homogeneous coordinate of pixel " + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "inline_equation", + "content": "p_k" + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "content": ". The captured intensity " + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "inline_equation", + "content": "I_{k}(p_{k},c)" + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "content": " for the color channel " + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 498, + 296, + 546 + ], + "type": "text", + "content": " is modeled as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 73, + 552, + 295, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 552, + 295, + 578 + ], + "spans": [ + { + "bbox": [ + 73, + 552, + 295, + 578 + ], + "type": "interline_equation", + "content": "I _ {k} \\left(p _ {k}, c\\right) = \\sum_ {\\lambda \\in \\Lambda} \\Omega_ {c, \\lambda} ^ {\\mathrm {c a m}} H _ {k} \\left(p _ {k}, \\lambda\\right) \\frac {\\eta_ {\\lambda}}{d (\\mathbf {p}) ^ {2}} L \\left(q _ {\\lambda}, \\lambda\\right), \\tag {4}", + "image_path": "e7de3f81f9c5dcdda16f911a294b194f23661937fd7756d6d651aaf23c1f5f73.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "H_{k}(p_{k},\\lambda)" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": " is the hyperspectral image and " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "d(\\mathbf{p})" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": " is the distance between the scene point " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": " and the projector. The model integrates over wavelengths " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\lambda \\in \\Lambda" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": ", effectively ranging from " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "440\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "660\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "10\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": " intervals: " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\Lambda = \\{\\lambda_1 = 440\\mathrm{nm},\\dots ,\\lambda_N = 660\\mathrm{nm}\\}" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "inline_equation", + "content": "N = 23" + }, + { + "bbox": [ + 55, + 586, + 296, + 659 + ], + "type": "text", + "content": " is the number of spectral bands." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 669, + 244, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 244, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 244, + 683 + ], + "type": "text", + "content": "5. Dense Dispersed Structured Light" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "We design DDSL patterns " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\{P_i\\}_{i=1}^M" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " that enable hyperspectral 3D imaging for dynamic scenes on our active stereo" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 359, + 553, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 359, + 553, + 383 + ], + "spans": [ + { + "bbox": [ + 313, + 359, + 553, + 383 + ], + "type": "text", + "content": "setup. Each DDSL pattern " + }, + { + "bbox": [ + 313, + 359, + 553, + 383 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 313, + 359, + 553, + 383 + ], + "type": "text", + "content": " is composed of multiple vertical lines, defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 392, + 553, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 392, + 553, + 434 + ], + "spans": [ + { + "bbox": [ + 317, + 392, + 553, + 434 + ], + "type": "interline_equation", + "content": "P _ {i} (q, \\forall) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\mod \\left(\\left| q _ {x} - i \\times l _ {\\text {s h i f t}} \\right|, l _ {\\text {o f f s e t}}\\right) \\leq \\frac {l _ {\\text {w i d t h}}}{2}, \\\\ 0 & \\text {e l s e}, \\end{array} \\right. \\tag {5}", + "image_path": "067c764f5b6e91875e0860fb5744ed7557ad1fb46554ffcad546edb759dc0f7f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "inline_equation", + "content": "q_{x}" + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": " is the column index of a projector pixel " + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{shift}}" + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": " is the line shift between neighboring patterns " + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "inline_equation", + "content": "P_{i + 1}" + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{offset}}" + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": " is the line offset between neighboring lines in a pattern, " + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{width}}" + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": " is the line width, and " + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "inline_equation", + "content": "\\mathrm{mod}(x,y) = x\\% y" + }, + { + "bbox": [ + 313, + 434, + 554, + 493 + ], + "type": "text", + "content": " is the modulo operator." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "spans": [ + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": "We project " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": " DDSL patterns " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "\\{P_1, \\ldots, P_M\\}" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": " and one black pattern " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "P_B" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": " repeatedly, capturing corresponding stereo images " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "I_k^1, \\ldots, I_k^M, I_k^B" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "k \\in \\{\\text{left}, \\text{right}\\}" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": ". The black pattern " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "P_B" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": " is used to compensate for the non-zero projector intensity for the zero-valued pattern and to enable robust motion compensation which we detail in Section 6. The DDSL patterns create dispersion for each vertical white line, and the dispersed patterns can overlap depending on the settings for three parameters: line offset " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "l_{\\text{offset}}" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": ", line width " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "l_{\\text{width}}" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": ", and line shift " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "l_{\\text{shift}}" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": ". Figure 4(a) and (e) shows the DDSL patterns and captured images with our chosen parameters " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "l_{\\text{offset}}" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "l_{\\text{width}}" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "inline_equation", + "content": "l_{\\text{shift}}" + }, + { + "bbox": [ + 313, + 494, + 555, + 650 + ], + "type": "text", + "content": ". Below, we discuss our design choices for these parameters." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "Line Offset The line offset " + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{offset}}" + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": " defines the spacing between vertical lines in pattern " + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": ". A small " + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{offset}}" + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": " increases overlap between dispersed patterns, resulting in more spectrally multiplexed illumination (Figure 4(b)). This reduces" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16592" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 68, + 555, + 320 + ], + "blocks": [ + { + "bbox": [ + 56, + 68, + 555, + 320 + ], + "lines": [ + { + "bbox": [ + 56, + 68, + 555, + 320 + ], + "spans": [ + { + "bbox": [ + 56, + 68, + 555, + 320 + ], + "type": "image", + "image_path": "16d2da3c835f03ae0d30637729705b22577a353205594abebfe799161e096026.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 325, + 555, + 381 + ], + "lines": [ + { + "bbox": [ + 54, + 325, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 54, + 325, + 555, + 381 + ], + "type": "text", + "content": "Figure 5. Black Optical Flow. We warp adjacent frame image to a target frame using naive optical flow under DDSL patterns and our black optical flow method to show the effectiveness of our method. We estimate optical flows using pretrained RAFT network [22] for both methods. Note that the target frame and adjacent frames are captured under different DDSL patterns. Therefore, the evaluation should primarily focus on geometric alignment rather than color consistency. (a) Warped images based on naive optical flow and black optical flow. (b) Visualization of the interpolated optical flows using the black optical flow." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "spans": [ + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "type": "text", + "content": "the number of patterns " + }, + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "type": "text", + "content": ", though it may decrease spectral accuracy due to blurred illumination. A larger " + }, + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{offset}}" + }, + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "type": "text", + "content": " reduces multiplexing, improving spectral accuracy at the cost of more patterns. We set " + }, + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{offset}} = 40\\mathrm{px}" + }, + { + "bbox": [ + 54, + 396, + 295, + 469 + ], + "type": "text", + "content": " to multiplex three spectral bands aligned with the camera RGB channels, balancing spectral accuracy and pattern count." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": "Line Shift The line shift " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{shift}}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": " specifies the shift between lines in neighboring patterns " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "P_{i + 1}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": ". A small " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{shift}}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": " densely samples the spectral axis, increasing potential spectral channels but requiring more patterns " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": " (Figure 4(c)). To achieve spectral channels from " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "440\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "660\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "10\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": " intervals, we set " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{shift}} = 5\\mathrm{px}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": ", providing a " + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "inline_equation", + "content": "10\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 482, + 295, + 567 + ], + "type": "text", + "content": " spectral step size while minimizing the number of patterns." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "type": "text", + "content": "Line Width A larger line width " + }, + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{width}}" + }, + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "type": "text", + "content": " increases spectral overlapping across RGB channels, smoothing the illumination spectrum and potentially lowering spectral accuracy (Figure 4(d)). A very narrow " + }, + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{width}}" + }, + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "type": "text", + "content": " results in low illumination power, introducing noise in captured images. We set " + }, + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{width}} = 5" + }, + { + "bbox": [ + 55, + 579, + 295, + 664 + ], + "type": "text", + "content": " pixels to optimize illumination intensity without sacrificing spectral accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "content": "Summary We use eight DDSL patterns (" + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "inline_equation", + "content": "M = 8" + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "content": ") with " + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{shift}} = 5" + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{width}} = 5" + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{offset}} = 40" + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "content": ", enabling accurate hyperspectral 3D reconstruction in our experimental" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "text", + "content": "setup. Figure 4(f) shows the spectral power distribution of the DDSL-pattern illumination projected onto a scene point " + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "text", + "content": ". For each " + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "text", + "content": "-th DDSL pattern, we have three peaks over the RGB spectrum. Using only " + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "inline_equation", + "content": "M = 8" + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "text", + "content": " DDSL patterns, we can densely sample wavelengths with " + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "inline_equation", + "content": "10\\mathrm{nm}" + }, + { + "bbox": [ + 313, + 396, + 555, + 480 + ], + "type": "text", + "content": " step, allowing for accurate hyperspectral 3D imaging, contrast to using hundreds of pattern images as in the previous work [19]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 491, + 501, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 501, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 501, + 506 + ], + "type": "text", + "content": "6. Hyperspectral 3D Reconstruction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "text", + "content": "Given the captured stereo images " + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "inline_equation", + "content": "I_{k}^{1}, \\ldots, I_{k}^{M}, I_{k}^{B}" + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "text", + "content": " for DDSL patterns " + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "inline_equation", + "content": "P_{1}, \\ldots, P_{M}" + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "text", + "content": " and one black pattern " + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "inline_equation", + "content": "P_{B}" + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "text", + "content": ", we reconstruct a hyperspectral image " + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "inline_equation", + "content": "H_{k}" + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "text", + "content": " and a depth map " + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "inline_equation", + "content": "z_{k}" + }, + { + "bbox": [ + 313, + 511, + 554, + 549 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "type": "text", + "content": "Depth Estimation We estimate depth from stereo images " + }, + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{left}}^i" + }, + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{right}}^i" + }, + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "type": "text", + "content": " for each frame " + }, + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 564, + 554, + 635 + ], + "type": "text", + "content": ". The captured stereo images are rectified, and disparity is estimated using the pretrained RAFT-Stereo network [14]. Depth is then computed from disparity using calibrated camera parameters, followed by un-rectification." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "type": "text", + "content": "Black Optical Flow Dynamic objects move while capturing the images " + }, + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "type": "inline_equation", + "content": "I_{k}^{1}, \\ldots, I_{k}^{M}, I_{k}^{B}" + }, + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "type": "text", + "content": " under the varying projector patterns " + }, + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "type": "inline_equation", + "content": "P_{1}, \\ldots, P_{M}, P_{B}" + }, + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "type": "text", + "content": ", which needs compensation for robust hyperspectral image reconstruction. One straightforward approach is to estimate optical flow " + }, + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\nabla p_{k}^{M/2 \\to i}" + }, + { + "bbox": [ + 313, + 652, + 554, + 715 + ], + "type": "text", + "content": " from" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16593" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 142, + 121 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 142, + 121 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 142, + 121 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 142, + 121 + ], + "type": "image", + "image_path": "e2308f8b473c946507c39dec0b93e34cfe17a303c0b6dee0b0ee3a2798f141cf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 121, + 140, + 128 + ], + "lines": [ + { + "bbox": [ + 70, + 121, + 140, + 128 + ], + "spans": [ + { + "bbox": [ + 70, + 121, + 140, + 128 + ], + "type": "text", + "content": "(a) Reconstructed sRGB" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 144, + 70, + 248, + 121 + ], + "blocks": [ + { + "bbox": [ + 144, + 70, + 248, + 121 + ], + "lines": [ + { + "bbox": [ + 144, + 70, + 248, + 121 + ], + "spans": [ + { + "bbox": [ + 144, + 70, + 248, + 121 + ], + "type": "image", + "image_path": "d584090927628e490589a5f2fdeea428845a823492f93097fa1459b78d144a24.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 56, + 128, + 247, + 261 + ], + "blocks": [ + { + "bbox": [ + 151, + 121, + 240, + 128 + ], + "lines": [ + { + "bbox": [ + 151, + 121, + 240, + 128 + ], + "spans": [ + { + "bbox": [ + 151, + 121, + 240, + 128 + ], + "type": "text", + "content": "(b) Point cloud of color checker" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 56, + 128, + 247, + 261 + ], + "lines": [ + { + "bbox": [ + 56, + 128, + 247, + 261 + ], + "spans": [ + { + "bbox": [ + 56, + 128, + 247, + 261 + ], + "type": "image", + "image_path": "62f35e2feee4c730a3263fd6794c024389d99c978ba015f4c129670b8242dbb7.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 113, + 262, + 200, + 270 + ], + "lines": [ + { + "bbox": [ + 113, + 262, + 200, + 270 + ], + "spans": [ + { + "bbox": [ + 113, + 262, + 200, + 270 + ], + "type": "text", + "content": "(c) Color checker evaluation" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 278, + 555, + 323 + ], + "lines": [ + { + "bbox": [ + 54, + 278, + 555, + 323 + ], + "spans": [ + { + "bbox": [ + 54, + 278, + 555, + 323 + ], + "type": "text", + "content": "Figure 6. Spectral Accuracy. Color checker evaluation. (a) Reconstructed hyperspectral image of color checker in sRGB, (b) point cloud of color checker, (c) hyperspectral intensity of color checker. High-frequency spectral data evaluation comparing other methods with Shin et al. [19] and Li et al. [13]. (d) " + }, + { + "bbox": [ + 54, + 278, + 555, + 323 + ], + "type": "inline_equation", + "content": "10\\mathrm{nm}" + }, + { + "bbox": [ + 54, + 278, + 555, + 323 + ], + "type": "text", + "content": "-FWHM spectral band pass filters and acquisition time for the three methods, (e) reconstructed hyperspectral intensity." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 252, + 70, + 310, + 125 + ], + "blocks": [ + { + "bbox": [ + 252, + 70, + 310, + 125 + ], + "lines": [ + { + "bbox": [ + 252, + 70, + 310, + 125 + ], + "spans": [ + { + "bbox": [ + 252, + 70, + 310, + 125 + ], + "type": "image", + "image_path": "0d60f23425f15b12ebb9fe1fb22578a3ca33e0422b7f0512b1ff4a83081f868f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 252, + 128, + 310, + 251 + ], + "blocks": [ + { + "bbox": [ + 252, + 128, + 310, + 251 + ], + 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] + } + ], + "index": 21 + }, + { + "bbox": [ + 123, + 360, + 295, + 376 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 360, + 295, + 376 + ], + "spans": [ + { + "bbox": [ + 123, + 360, + 295, + 376 + ], + "type": "interline_equation", + "content": "p _ {k} ^ {i} = p _ {k} ^ {M / 2} + \\nabla p _ {k} ^ {M / 2 \\rightarrow i}. \\tag {6}", + "image_path": "b1612496edec5b93532dfe39e19318bc374044e5106daf337d067c590dc4326b.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "text", + "content": "However, this approach is challenging due to the inconsistent illumination at corresponding pixels since each image " + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "inline_equation", + "content": "\\{I_k^i\\}_{i = 1}^M" + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "text", + "content": " is illuminated by a different DDSL pattern " + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "inline_equation", + "content": "\\{P_i\\}_{i = 1}^M" + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "text", + "content": ". Figure 5(a) depicts how naive optical flow between adjacent DDSL patterns fails to accurately capture the motion. Instead, we estimate the black optical flow, which is the flow between successive black-pattern images " + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "inline_equation", + "content": "I_{k}^{B}" + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "text", + "content": ", avoiding illumination inconsistency. We then interpolate the black optical flow to obtain the target optical flow " + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "inline_equation", + "content": "\\nabla p_k^{M / 2\\rightarrow i}" + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "text", + "content": ", enabling robust optical-flow estimation, as illustrated in Figure 5. Using the estimated flow, we align the images " + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "inline_equation", + "content": "I_{k}^{1},\\ldots ,I_{k}^{M}" + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "text", + "content": " captured under the DDSL patterns to the center frame " + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "inline_equation", + "content": "I_{k}^{M / 2}" + }, + { + "bbox": [ + 55, + 384, + 296, + 546 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "spans": [ + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "text", + "content": "Multi-pattern Image Formation Using the aligned images " + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "inline_equation", + "content": "I_{k}^{1}, \\ldots, I_{k}^{M}" + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "text", + "content": " captured under " + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "text", + "content": " DDSL patterns, we reformulate the image formation model from Section 4. For the " + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "text", + "content": "-th DDSL pattern, the aligned image " + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "inline_equation", + "content": "I_{k}^{i}" + }, + { + "bbox": [ + 55, + 559, + 296, + 608 + ], + "type": "text", + "content": " is modeled as:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 66, + 616, + 295, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 616, + 295, + 643 + ], + "spans": [ + { + "bbox": [ + 66, + 616, + 295, + 643 + ], + "type": "interline_equation", + "content": "I _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) = \\sum_ {\\lambda \\in \\Lambda} \\Omega_ {c, \\lambda} ^ {\\mathrm {c a m}} H _ {k} \\left(p _ {k} ^ {i}, \\lambda\\right) \\frac {\\eta_ {\\lambda}}{d \\left(\\mathbf {p} _ {k} ^ {i}\\right) ^ {2}} L ^ {i} \\left(q _ {\\lambda} ^ {i}, \\lambda\\right), \\tag {7}", + "image_path": "962be56617e9b02ec69fb71319c42f5235c7861624623a40fbe497ebe28a1f42.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_k^i" + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": " is the corresponding scene point at frame " + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "inline_equation", + "content": "q_{\\lambda}^{i}" + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": " is the corresponding projector pixel obtained using the backward model " + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\psi \\colon q_{\\lambda}^{i} = \\psi \\left(\\mathbf{p}_{k}^{i},\\lambda\\right)" + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "We then subtract the black pattern captured image " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "I_k^B" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": " from all the captured images " + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\{I_k^i(p_k^i, c)\\}_{i=1}^M" + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": " to remove the" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 338, + 533, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 533, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 533, + 350 + ], + "type": "text", + "content": "undesired residual light intensity for the black pattern:" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 363, + 354, + 553, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 354, + 553, + 369 + ], + "spans": [ + { + "bbox": [ + 363, + 354, + 553, + 369 + ], + "type": "interline_equation", + "content": "I _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) \\leftarrow I _ {k} ^ {i} \\left(p _ {k} ^ {i}, c\\right) - I _ {k} ^ {B} \\left(p _ {k} ^ {B}, c\\right) \\tag {8}", + "image_path": "42c5df9e7277f8412afa9fbd23918b9f6c04203838b5a303f35eb3f645b915ed.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 373, + 553, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 373, + 553, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 553, + 396 + ], + "type": "text", + "content": "We rewrite the image formation as a matrix-vector multiplication:" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 410, + 398, + 553, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 410, + 398, + 553, + 410 + ], + "spans": [ + { + "bbox": [ + 410, + 398, + 553, + 410 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {k} = \\mathbf {L H} _ {k}, \\tag {9}", + "image_path": "e99a73703241446d2224122b3ab47740715581d48c8b8242298958444c6a1118.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_k" + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "text", + "content": " is the intensity vector of captured image under " + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "text", + "content": " DDSL patterns, " + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{L}" + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "text", + "content": " is the system matrix, and " + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_k" + }, + { + "bbox": [ + 313, + 413, + 554, + 449 + ], + "type": "text", + "content": " is the hyperspectral image:" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 342, + 453, + 480, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 453, + 480, + 467 + ], + "spans": [ + { + "bbox": [ + 342, + 453, + 480, + 467 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {k} = \\left[ I _ {k} ^ {1} \\left(p _ {k} ^ {1}, R\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, R\\right), \\right.", + "image_path": "23725ad7a3338f8c4fd059dd84eefe53c91083762435536bd1ec560f48a4afcf.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 366, + 469, + 480, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 469, + 480, + 483 + ], + "spans": [ + { + "bbox": [ + 366, + 469, + 480, + 483 + ], + "type": "interline_equation", + "content": "I _ {k} ^ {1} \\left(p _ {k} ^ {1}, G\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, G\\right),", + "image_path": "5eae4e43fbba3af882811b3372c9e78d903401397e0faa4b93d8996485269228.jpg" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 366, + 486, + 553, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 486, + 553, + 500 + ], + "spans": [ + { + "bbox": [ + 366, + 486, + 553, + 500 + ], + "type": "interline_equation", + "content": "\\left. I _ {k} ^ {1} \\left(p _ {k} ^ {1}, B\\right), \\dots , I _ {k} ^ {M} \\left(p _ {k} ^ {M}, B\\right) \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {3 M \\times 1}, \\tag {10}", + "image_path": "e57234f2aa01dbea0de141f0d18b9fd03191a7b38ba85e2e6e0e3de0a92ea7e7.jpg" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 346, + 502, + 553, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 502, + 553, + 517 + ], + "spans": [ + { + "bbox": [ + 346, + 502, + 553, + 517 + ], + "type": "interline_equation", + "content": "\\mathbf {L} = \\left[ \\mathbf {L} _ {R}; \\mathbf {L} _ {G}; \\mathbf {L} _ {B} \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {3 M \\times N}, \\tag {11}", + "image_path": "28778a7d4d437337170038be40b17408ab40f73bcf44de5538c9817c7314036e.jpg" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 320, + 519, + 553, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 519, + 553, + 539 + ], + "spans": [ + { + "bbox": [ + 320, + 519, + 553, + 539 + ], + "type": "interline_equation", + "content": "\\mathbf {L} _ {c} (i, j) = \\Omega_ {c, \\lambda_ {j}} ^ {\\mathrm {c a m}} \\eta_ {\\lambda_ {j}} \\left(L ^ {i} * G\\right) \\left(q _ {\\lambda_ {j}} ^ {i}, \\lambda_ {j}\\right), \\tag {12}", + "image_path": "f7a63ba3a44e78ba27450c10df037eff54558a4e28a5f3d1ee4f2255d2c6020e.jpg" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 338, + 540, + 553, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 540, + 553, + 567 + ], + "spans": [ + { + "bbox": [ + 338, + 540, + 553, + 567 + ], + "type": "interline_equation", + "content": "\\mathbf {H} _ {k} = \\left[ H \\left(p _ {k} ^ {M / 2}, \\lambda_ {1}\\right), \\dots , H \\left(p _ {k} ^ {M / 2}, \\lambda_ {N}\\right) \\right] ^ {\\intercal} \\in \\mathbb {R} ^ {N \\times 1}, \\tag {13}", + "image_path": "cc737fe12e199417f3c60fabd67a170179eae57bbbb5c9c29f5795fc2b245440.jpg" + } + ] + } + 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{2}} _ {\\text {D a t a t e r m}} + \\underbrace {\\kappa_ {\\lambda} \\| \\nabla_ {\\lambda} \\mathbf {H} _ {k} \\| _ {2} ^ {2}} _ {\\text {S p e c t r a l s m o o t h n e s s}} +", + "image_path": "47086acf11e431362a7a84166c756ae2f6b83c125a3520e99f747209e8c7965a.jpg" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 381, + 682, + 553, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 682, + 553, + 710 + ], + "spans": [ + { + "bbox": [ + 381, + 682, + 553, + 710 + ], + "type": "interline_equation", + "content": "\\underbrace {\\kappa_ {x y} \\left(\\left\\| \\nabla_ {x} \\mathbf {H} _ {k} \\right\\| _ {1} + \\left\\| \\nabla_ {y} \\mathbf {H} _ {k} \\right\\| _ {1}\\right)} _ {\\text {S p a t i a l r e g u l a r i z a t i o n}}, \\tag {14}", + "image_path": "69e00e42e0307409961bdb42b5accfc9cb311072158c27ce5a95ff7afca90aab.jpg" + } + ] + } + ], + "index": 42 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], 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+ ], + "type": "inline_equation", + "content": "\\nabla_{y}" + }, + { + "bbox": [ + 55, + 369, + 296, + 464 + ], + "type": "text", + "content": " are gradient operators along the spectral and spatial axes, respectively. The first term corresponds to the data term, penalizing reconstruction error, while the second and third terms enforce spectral smoothness and spatial total variation. The coefficients " + }, + { + "bbox": [ + 55, + 369, + 296, + 464 + ], + "type": "inline_equation", + "content": "\\kappa_{\\lambda} = 3" + }, + { + "bbox": [ + 55, + 369, + 296, + 464 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 369, + 296, + 464 + ], + "type": "inline_equation", + "content": "\\kappa_{xy} = 0.05" + }, + { + "bbox": [ + 55, + 369, + 296, + 464 + ], + "type": "text", + "content": " are balancing weights. We solve the per-pixel optimization problem using ADAM [7]. Optimization details are provided in the Supplemental Document." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 486, + 130, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 130, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 130, + 498 + ], + "type": "text", + "content": "7. Calibration" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": "We perform a one-time calibration of the projector, camera, and diffraction grating. We obtain the geometric parameters of the stereo cameras and the projector using checkerboard methods [21, 30] without attaching the diffraction grating film. To measure the diffraction efficiency " + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\eta_{\\lambda}" + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": " of the diffraction grating, shown in Figure 2(d), we filter the dispersed light using spectral bandpass filters with a " + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "inline_equation", + "content": "10\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": " bandwidth, covering wavelengths from " + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "inline_equation", + "content": "440\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "inline_equation", + "content": "660\\mathrm{nm}" + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": ", and capture the intensity reflected from a Spectralon target. We calibrate the camera response function " + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\Omega_{c,\\lambda}^{\\mathrm{cam}}" + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": " also using spectral bandpass filters under LED light, and measure the projector spectral emission function " + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\Omega_{c,\\lambda}^{\\mathrm{proj}}" + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": " by projecting RGB dots onto a Spectralon target and capturing the reflected radiance with a spectroradiometer (JETI Specbos 1211). To enhance reconstruction accuracy, we further optimize the radiometric parameters for both the projector and camera; detailed methods are provided in the Supplemental Document." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 317, + 84, + 392, + 175 + ], + "blocks": [ + { + "bbox": [ + 316, + 76, + 392, + 84 + ], + "lines": [ + { + "bbox": [ + 316, + 76, + 392, + 84 + ], + "spans": [ + { + "bbox": [ + 316, + 76, + 392, + 84 + ], + "type": "text", + "content": "(a) Reconstructed sRGB" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 84, + 392, + 175 + ], + "lines": [ + { + "bbox": [ + 317, + 84, + 392, + 175 + ], + "spans": [ + { + "bbox": [ + 317, + 84, + 392, + 175 + ], + "type": "image", + "image_path": "a71c81b20630a457fbf9f56bf0be492679abc592282e2511f5baa807bce40852.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 392, + 84, + 485, + 175 + ], + "blocks": [ + { + "bbox": [ + 408, + 76, + 485, + 84 + ], + "lines": [ + { + "bbox": [ + 408, + 76, + 485, + 84 + ], + "spans": [ + { + "bbox": [ + 408, + 76, + 485, + 84 + ], + "type": "text", + "content": "(b) Reconstructed depth" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 392, + 84, + 485, + 175 + ], + "lines": [ + { + "bbox": [ + 392, + 84, + 485, + 175 + ], + "spans": [ + { + "bbox": [ + 392, + 84, + 485, + 175 + ], + "type": "image", + "image_path": "4b24bb8c29d12c72c5337b45d35a0b85f4c6c704154b610cff6b75119cbe8abe.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 486, + 85, + 553, + 182 + ], + "blocks": [ + { + "bbox": [ + 497, + 69, + 552, + 85 + ], + "lines": [ + { + "bbox": [ + 497, + 69, + 552, + 85 + ], + "spans": [ + { + "bbox": [ + 497, + 69, + 552, + 85 + ], + "type": "text", + "content": "(c) Hyperspectral intensity" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 486, + 85, + 553, + 182 + ], + "lines": [ + { + "bbox": [ + 486, + 85, + 553, + 182 + ], + "spans": [ + { + "bbox": [ + 486, + 85, + 553, + 182 + ], + "type": "image", + "image_path": "6e4375e7068cbfac86a5d2c5911766940563834811c82f755a67e1c642a18d76.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 317, + 184, + 376, + 291 + ], + "blocks": [ + { + "bbox": [ + 55, + 300, + 296, + 346 + ], + "lines": [ + { + "bbox": [ + 55, + 300, + 296, + 346 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 296, + 346 + ], + "type": "text", + "content": "Figure 7. Depth Validation. (a) Stair case depth reconstructed results. (b) Absolute depth evaluation. (c) Consistency between depth reconstructed results between different DDSL patterns for the stair position index of 3." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 184, + 376, + 291 + ], + "lines": [ + { + "bbox": [ + 317, + 184, + 376, + 291 + ], + "spans": [ + { + "bbox": [ + 317, + 184, + 376, + 291 + ], + "type": "image", + "image_path": "ce0d140846c098bf6c96933b2a1d9d8619e3f06878ccfda1dbb0dfd4901c8071.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 310, + 554, + 365 + ], + "lines": [ + { + "bbox": [ + 313, + 310, + 554, + 365 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 554, + 365 + ], + "type": "text", + "content": "Figure 8. Fake and Real Oranges. We compare real and artificial fruit(orange), showing the differences in their hyperspectral image curves and corresponding images. (a) Reconstructed hyperspectral image in sRGB, (b) depth (c) spectral graph and (d) hyperspectral images of metameric samples." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 377, + 184, + 405, + 291 + ], + "blocks": [ + { + "bbox": [ + 377, + 184, + 405, + 291 + ], + "lines": [ + { + "bbox": [ + 377, + 184, + 405, + 291 + ], + "spans": [ + { + "bbox": [ + 377, + 184, + 405, + 291 + ], + "type": "image", + "image_path": "d5ff9187b4592a5dc0dc08675d6894d90dfcf1febfe1fd4f740ddb352db6f6f4.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 293, + 477, + 302 + ], + "lines": [ + { + "bbox": [ + 397, + 293, + 477, + 302 + ], + "spans": [ + { + "bbox": [ + 397, + 293, + 477, + 302 + ], + "type": "text", + "content": "(d) Hyperspectral images" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 406, + 184, + 434, + 291 + ], + "blocks": [ + { + "bbox": [ + 406, + 184, + 434, + 291 + ], + "lines": [ + { + "bbox": [ + 406, + 184, + 434, + 291 + ], + "spans": [ + { + "bbox": [ + 406, + 184, + 434, + 291 + ], + "type": "image", + "image_path": "45fc81c4e7cb276ea10a046b299db40d55da07a4da15cd98516a1f97dfa4844e.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 435, + 184, + 463, + 291 + ], + "blocks": [ + { + "bbox": [ + 435, + 184, + 463, + 291 + ], + "lines": [ + { + "bbox": [ + 435, + 184, + 463, + 291 + ], + "spans": [ + { + "bbox": [ + 435, + 184, + 463, + 291 + ], + "type": "image", + "image_path": "07e6c6fec8031128a6f848b9431d2d0c069da3ec218c8293ed7012682b4ad0e8.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 465, + 184, + 493, + 291 + ], + "blocks": [ + { + "bbox": [ + 465, + 184, + 493, + 291 + ], + "lines": [ + { + "bbox": [ + 465, + 184, + 493, + 291 + ], + "spans": [ + { + "bbox": [ + 465, + 184, + 493, + 291 + ], + "type": "image", + "image_path": "8f298918dd244986fd3a81c166f5ddc44edd1595af5086d1f2dc1392b82fb204.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 494, + 184, + 523, + 291 + ], + "blocks": [ + { + "bbox": [ + 494, + 184, + 523, + 291 + ], + "lines": [ + { + "bbox": [ + 494, + 184, + 523, + 291 + ], + "spans": [ + { + "bbox": [ + 494, + 184, + 523, + 291 + ], + "type": "image", + "image_path": "4accad497cb941b44e43c64105835fe82c5e74978b9165c74e099e29ad8e4ce0.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 524, + 184, + 553, + 291 + ], + "blocks": [ + { + "bbox": [ + 524, + 184, + 553, + 291 + ], + "lines": [ + { + "bbox": [ + 524, + 184, + 553, + 291 + ], + "spans": [ + { + "bbox": [ + 524, + 184, + 553, + 291 + ], + "type": "image", + "image_path": "eb0591a8aa7928478be611b7abcb12acee0d888d7ac8cb157bead493a744ee8e.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + } + ], + "index": 27 + }, + { + "bbox": [ + 314, + 384, + 367, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 384, + 367, + 396 + ], + "spans": [ + { + "bbox": [ + 314, + 384, + 367, + 396 + ], + "type": "text", + "content": "8. Results" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "spans": [ + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "text", + "content": "Spectral Accuracy Figure 6 (a), (b) and (c) shows the reconstructed hyperspectral image in sRGB, depth, and hyperspectral curves of a ColorChecker chart, demonstrating accurate reconstruction. To measure spectral FWHM of our system, we capture nine narrow-band spectral filters as shown in Figure 6(d). The FWHM of those bandpass filters is " + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "inline_equation", + "content": "10\\mathrm{nm}" + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "text", + "content": ". Figure 6(e) shows that our method achieves a FWHM of " + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "inline_equation", + "content": "15.5\\mathrm{nm}" + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "text", + "content": " compared to the ground-truth hyperspectral data of the filters, outperforming state-of-the-art affordable hyperspectral 3D imaging methods by Li et al. [13] and Shin et al. [19]. Li et al.[13] shows a FWHM of " + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "inline_equation", + "content": "40\\mathrm{nm}" + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "text", + "content": " due to the use of broadband RGB illumination of a conventional projector. Shin et al.[19] attains " + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "inline_equation", + "content": "18\\mathrm{nm}" + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "text", + "content": " FWHM. Moreover, its acquisition time for a scene is 10 minutes whereas our method only requires 0.15 seconds, representing " + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "inline_equation", + "content": "\\times 4000" + }, + { + "bbox": [ + 313, + 406, + 555, + 609 + ], + "type": "text", + "content": " speed increase, thus enabling hyperspectral 3D imaging for dynamic scenes." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "type": "text", + "content": "Depth Accuracy We evaluate the accuracy of depth estimation. Ground-truth depth is obtained using the binary-coded structured light method [8]. Figure 7(a) evaluates the absolute depth error by capturing a 3D-printed stair object. We achieve an average depth error of " + }, + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "type": "inline_equation", + "content": "4\\mathrm{mm}" + }, + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "type": "text", + "content": " in the area of each step compared to the ground truth, with a maximum error of " + }, + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "type": "inline_equation", + "content": "8\\mathrm{mm}" + }, + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "type": "text", + "content": ". Figure 7(b) shows the difference be" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16595" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 76, + 558, + 239 + ], + "blocks": [ + { + "bbox": [ + 56, + 76, + 558, + 239 + ], + "lines": [ + { + "bbox": [ + 56, + 76, + 558, + 239 + ], + "spans": [ + { + "bbox": [ + 56, + 76, + 558, + 239 + ], + "type": "image", + "image_path": "617aa3fc25b1e4665b26f0421afd6eaef23b9a180bef0430dcd0174e7d87837d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 245, + 555, + 269 + ], + "lines": [ + { + "bbox": [ + 55, + 245, + 555, + 269 + ], + "spans": [ + { + "bbox": [ + 55, + 245, + 555, + 269 + ], + "type": "text", + "content": "Figure 9. Dynamic Scene. We show the reconstructed depth and spectral results of a dynamic scene. (a) Reconstructed depth. (b) Reconstructed hyperspectral image in sRGB. (c) Reconstructed hyperspectral image. (d) Hyperspectral intensity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 283, + 295, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 321 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 321 + ], + "type": "text", + "content": "tween depth results for each DDSL pattern. The consistency across different DDSL patterns is evident, with a difference of less than " + }, + { + "bbox": [ + 55, + 283, + 295, + 321 + ], + "type": "inline_equation", + "content": "2\\mathrm{mm}" + }, + { + "bbox": [ + 55, + 283, + 295, + 321 + ], + "type": "text", + "content": " between patterns." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 338, + 296, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 296, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 296, + 422 + ], + "type": "text", + "content": "Dynamic Scenes By using spectrally multiplexed DDSL patterns, we reduce the required number of projections from over hundred patterns with naive scanning [19] to 8 DDSL patterns. This enables accurate hyperspectral 3D imaging for dynamic scenes at 6.6 fps, by software synchronizing camera and projector, as shown in Figure 1, Figure 9, and the Supplemental Video." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "spans": [ + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "type": "text", + "content": "Impact of Pattern Parameters Table 1 shows the impact of different parameter settings of DDSL patterns. Our empirically-set pattern parameters " + }, + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{offset}}" + }, + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{width}}" + }, + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{shift}}" + }, + { + "bbox": [ + 55, + 441, + 296, + 513 + ], + "type": "text", + "content": " result in the best spectral and depth accuracy with a short capture time. The depth accuracy remains unchanged due to the robustness of RaftStereo [14] for correspondence matching." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 56, + 536, + 296, + 619 + ], + "blocks": [ + { + "bbox": [ + 59, + 524, + 291, + 536 + ], + "lines": [ + { + "bbox": [ + 59, + 524, + 291, + 536 + ], + "spans": [ + { + "bbox": [ + 59, + 524, + 291, + 536 + ], + "type": "text", + "content": "Table 1. Ablation study on pattern parameters: " + }, + { + "bbox": [ + 59, + 524, + 291, + 536 + ], + "type": "inline_equation", + "content": "{l}_{\\text{offset }},{l}_{\\text{width }},{l}_{\\text{shift }}" + }, + { + "bbox": [ + 59, + 524, + 291, + 536 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 536, + 296, + 619 + ], + "lines": [ + { + "bbox": [ + 56, + 536, + 296, + 619 + ], + "spans": [ + { + "bbox": [ + 56, + 536, + 296, + 619 + ], + "type": "table", + "html": "
Indexl_offsetl_widthlshift# of patterns ∝ capture time↓Spectral FWHM [nm]↓Depth MAE [mm]↓
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Ground-truth intensity measurements are acquired using a spectroradiometer." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 281, + 388, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 388, + 294 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 388, + 294 + ], + "type": "text", + "content": "9. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 302, + 555, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 302, + 555, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 302, + 555, + 482 + ], + "type": "text", + "content": "We have introduced DDSL, an accurate and compact method for hyperspectral 3D imaging for dynamic scenes. We use a conventional RGB stereo camera-projector system paired with a sub-millimeter diffraction grating, implemented as a practical experimental prototype. We design the DDSL patterns, generating spectrally-multiplexed illumination, enabling rapid and high-quality hyperspectral 3D imaging. Our method incorporates the dispersion-aware image formation model using the sub-pixel accurate backward mapping. Experimental results demonstrate that we outperform prior affordable methods in both accuracy and also acquisition time, achieving 6.6 fps with a depth error of " + }, + { + "bbox": [ + 313, + 302, + 555, + 482 + ], + "type": "inline_equation", + "content": "4\\mathrm{mm}" + }, + { + "bbox": [ + 313, + 302, + 555, + 482 + ], + "type": "text", + "content": " and a spectral accuracy of 15.5 FWHM. We envision that our DDSL method opens up new applications of geometric and material analysis for dynamic objects." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 495, + 556, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 556, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 556, + 628 + ], + "type": "text", + "content": "Limitations and Future work While our method enables rapid, accurate, and practical hyperspectral 3D imaging for dynamic scenes, it is currently constrained to low-speed motion, achieving a frame rate of 6.6 fps due to the slow software-based synchronization between the camera and projector. To address this limitation, hardware synchronization and a high-speed, affordable projector-camera system could significantly increase frame rates [28]. The limited diffraction efficiency also restricts the range of scene positions. Thus, using a high efficiency diffraction grating for the first-order light would enhance the effective range." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 715 + ], + "type": "text", + "content": "Acknowledgments Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, RS-2024-00438532), Korea IITP MSIT (RS-2019-II191906, Artificial Intelligence Graduate School Program-POSTECH, RS-2024-00437866), POSCO, and 2024 POSTECH International Joint Research Project." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16596" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Reza Arablouei, Ethan Goan, Stephen Gensemer, and Branislav Kusy. 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Activestereonet: End-to-end self-supervised learning for active stereo systems. In Proceedings of the European conference on computer vision (ECCV), pages 784-801, 2018. 2" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 118, + 295, + 151 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 118, + 295, + 151 + ], + "spans": [ + { + "bbox": [ + 56, + 118, + 295, + 151 + ], + "type": "text", + "content": "[30] Zhengyou Zhang. A flexible new technique for camera calibration. IEEE Transactions on pattern analysis and machine intelligence, 22(11):1330-1334, 2000. 7" + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16598" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_content_list.json b/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f0aa8ae5c0acf4bf039e498789e51b761a22532e --- /dev/null +++ b/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_content_list.json @@ -0,0 +1,1682 @@ +[ + { + "type": "text", + "text": "Dense Match Summarization for Faster Two-view Estimation", + "text_level": 1, + "bbox": [ + 189, + 130, + 807, + 150 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jonathan Astermark, Anders Heyden, and Viktor Larsson \nCentre for Mathematical Sciences, Lund University", + "bbox": [ + 271, + 181, + 723, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{jonathan.astermark, anders.heyden, viktor.larsson}@math.lth.se", + "bbox": [ + 217, + 219, + 772, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 268, + 326, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we speed up robust two-view relative pose from dense correspondences. Previous work has shown that dense matchers can significantly improve both accuracy and robustness in the resulting pose. However, the large number of matches comes with a significantly increased runtime during robust estimation in RANSAC. To avoid this, we propose an efficient match summarization scheme which provides comparable accuracy to using the full set of dense matches, while having 10-100x faster runtime. We validate our approach on standard benchmark datasets together with multiple state-of-the-art dense matchers.", + "bbox": [ + 88, + 301, + 485, + 467 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 496, + 220, + 511 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Determining the two-view camera geometry is an important sub-task in many computer vision problems, e.g. for Simultaneous Localization and Mapping or Structure-from-Motion. The most common approach is to first detect corresponding points in the two views, followed by robust estimation using RANdom Sample Consensus (RANSAC) [18] which both estimates the relative pose and identifies potential outlier matches. Traditionally, keypoint matching is performed by independently detecting keypoints in each view, followed by a matching step, either directly comparing descriptor similarity or using a learned matcher.", + "bbox": [ + 89, + 522, + 482, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, a lot of attention has been given to so-called detector-free matching, which takes the images as input and directly establishes (semi-)dense correspondences. These matchers produce significantly more matches, compared to the detector-based counterparts, especially in weakly textured image regions, such as walls, floors, and ceilings. Dense matching shows great promise and currently achieves the most accurate two-view estimates in standard benchmarks. However, this comes with a trade-off in runtime, both for running the matching and in the subsequent robust estimation (i.e. RANSAC).", + "bbox": [ + 89, + 688, + 482, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we aim to improve the runtime of the robust estimation step. We show that when using dense matchers, most of the matches provide redundant geometric con", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e54d6597b5d5d93351611c7428ff027264c33f56117977237f42e4f27d936c8b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 266, + 903, + 368 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/12f4d89663cf79382f11299172b903411bd47a7c500e264ace515b2feacbc45c.jpg", + "image_caption": [ + "Figure 1. Relative Pose Estimation from Dense Matches. The top images show 10,000 semi-dense matches from DKM [15] with same colors indicating corresponding points. The large number of matches makes robust estimation with RANSAC accurate (pose error $\\epsilon = 0.38^{\\circ}$ ) but slow (runtime $t = 98$ ms). In this paper we show that we can get comparable accuracy with significantly lower runtime by sparsifying the dense matches (bottom images). Each sparsified match is represented by a $9 \\times 9$ -matrix that summarizes the geometric constraints from nearby matches." + ], + "image_footnote": [], + "bbox": [ + 517, + 369, + 903, + 470 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "straints, and we present an efficient match summarization scheme that selects a subset of $\\approx 1\\%$ of the matches, which we call representative matches, that are used for robust estimation. Using this smaller set of matches, we can obtain a 10-100x speedup with a marginal loss in pose accuracy. In addition, we present an approximation approach for enriching each representative match to capture the geometric constraints of nearby correspondences in a single $9\\times 9$ -matrix (regardless of how many neighboring matches are included). This enrichment allows for an even smaller loss of pose accuracy, while still being significantly faster compared to dense correspondence. In Figure 1 we visualize one example from MegaDepth [26].", + "bbox": [ + 511, + 638, + 906, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We validate our claims and our approach with extensive experiments and ablation studies on standard benchmarks with different state-of-the-art dense matchers.", + "bbox": [ + 511, + 837, + 903, + 882 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In summary, our contributions are:", + "bbox": [ + 532, + 885, + 764, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1093", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A scheme for summarizing any dense matches into sparse representative matches, which speeds up the robust estimation by a factor 10-100x, with only a very small loss in accuracy.", + "- An approximation-based approach to summarize the contributions of each cluster, which we use to refine the output from RANSAC. This lets us maintain the high accuracy from dense matches, with only a small increase in runtime compared to the approach above.", + "- In experiments on standard benchmarks, with multiple state-of-the-art dense matchers, we are able to consistently show a significant speedup. Furthermore, our experiments show that sparsified dense matches outperform state-of-the-art sparse matches in terms of accuracy." + ], + "bbox": [ + 89, + 90, + 482, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1.1. Related Work", + "text_level": 1, + "bbox": [ + 91, + 316, + 233, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Matching and Correspondences. Image correspondence for geometric estimation traditionally works with a detect-then-match paradigm that first identifies keypoints (e.g. SIFT [28], SuperPoint [12]) independently in each image, followed by a matching step. The matching is either done by comparing descriptor similarity ([12, 14, 28]) or more recently via learned matchers ([27, 35]). In [36] the authors instead proposed to perform detection-free matching, which takes an image pair as input and directly regresses semi-dense pixel correspondences. This started a series of work on dense matching ([7, 15, 16, 20]) which improved on the initial work. Common for all dense methods is that they produce significantly more matches compared to classical detector-based methods. By considering both images jointly, the methods are able to propagate strong matches to weaker ones, allowing for even weakly textured regions to be matched between images.", + "bbox": [ + 89, + 339, + 483, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In benchmarks for two-view relative pose estimation, these methods significantly improve the results in terms of pose accuracy. However, this comes at a trade-off with runtime, as the large number of matches makes robust estimation more costly. In this work, we offset some of this cost by speeding up the robust estimation. Our method is not specific to a particular matcher and can be applied to any dense correspondences.", + "bbox": [ + 89, + 597, + 483, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robust Estimation. For robust geometric estimation problems in computer vision, the RANSAC algorithm, originally introduced by Fischler and Bolles [18] in 1981, is the de facto standard. Modern RANSAC variants, while still working with similar principles as the original, usually incorporate some form of local optimization (LORANSAC [10, 24]) as well a more complex scoring beyond simple inlier counting, e.g. MSAC [37] or MAGSAC [3]. Other works improve by integrating various learned components in the pipeline, see e.g. [4, 6, 39]. There are also several works which focus on making RANSAC faster. In [9], the authors propose a probabilistic method (SPRT) for de", + "bbox": [ + 89, + 719, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ciding when to early exit. In [22], the authors propose to only perform scoring once two similar models are found. Rais et al. [32] instead aggregate multiple model hypotheses to form the final output. Barath et al. [2] speed up scoring by filtering out regions of the matches which cannot contain inlier correspondences for the current model. PROSAC [8] leverages per-match confidences to sample good models earlier, to speed up convergence. Ni et al. [30] group correspondences and model different inlier ratios for each cluster, which is used both for sampling and stopping criterion.", + "bbox": [ + 511, + 90, + 903, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The match summarization method proposed in this paper is orthogonal (and could be combined) with the improvements in the above methods. In particular, most prior work focuses on either speeding up the scoring or reducing the number of iterations, but do not consider refinement which is particularly costly with a large number of matches.", + "bbox": [ + 511, + 242, + 903, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Richer Correspondences. For affine-correspondences (ACs) each match is associated with a $2 \\times 2$ matrix representing a local transformation around the keypoints. These matrices can be interpreted as a linearization of the local planar homography [33]. Affine correspondences have been used to derive more efficient minimal estimators ([5, 17, 33, 38]) as well as provide constraints for normal estimation [19]. In this paper, we derive a summarized correspondence expressed with a $9 \\times 9$ -matrix. While this matrix is similar to ACs in that it encodes additional local geometric constraints, it does not make assumption on local planarity and yields stronger geometric constraints, even allowing estimation from a single correspondence (see Section 4.4).", + "bbox": [ + 511, + 333, + 906, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background", + "text_level": 1, + "bbox": [ + 513, + 542, + 640, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Each 2D-point correspondence $(\\pmb{x},\\bar{\\pmb{x}})\\in \\mathbb{R}^3\\times \\mathbb{R}^3$ (in homogeneous coordinates) constrain the relative pose by", + "bbox": [ + 511, + 566, + 903, + 598 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x} = 0, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 666, + 606, + 903, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $E = [t]_{\\times}R$ is the essential matrix. As the points $(\\pmb{x},\\bar{\\pmb{x}})$ are measurements from the images, they will contain noise and will not satisfy (1) exactly, even if the match is correct. Thus, in the optimization, a residual such as the Sampson error is commonly used instead,", + "bbox": [ + 511, + 633, + 903, + 710 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}) = \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {x} \\| ^ {2} + \\left\\| \\left(E ^ {T}\\right) _ {1 2} \\bar {\\boldsymbol {x}} \\right\\| ^ {2}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 719, + 903, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $E_{12}$ is the first two rows of $E$ . The Sampson error approximates the squared reprojection error, and is used to determine match correctness (inlier or outlier). Most RANSAC-variants additionally use some form of MSAC-scoring [37] for the models, i.e. the essential matrix is chosen by minimizing the sum of truncated residuals", + "bbox": [ + 511, + 762, + 906, + 853 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nf (E) = \\sum_ {i = 1} ^ {N} \\min \\left\\{\\mathcal {E} \\left(E, \\boldsymbol {x} _ {i}, \\bar {\\boldsymbol {x}} _ {i}\\right), \\tau^ {2} \\right\\}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 862, + 903, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1094", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $N$ denotes the number of matches and $\\tau \\in \\mathbb{R}_+$ is the inlier threshold. The model-scoring function $f(E)$ is used both for selecting the best model, and for non-linear refinement. As the number of matches $N$ grows large, evaluating $f(E)$ will dominate the runtime cost in RANSAC.", + "bbox": [ + 89, + 90, + 483, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 179, + 181, + 194 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present a method for efficiently summarizing the geometric constraints given by the dense matches. The idea is to first cluster the correspondences into subsets that yield similar geometric constraints, and replace each cluster with a single representative match used in robust estimation. Next, we compute a proxy residual that summarizes the geometric constraints from each cluster into a $9 \\times 9$ -matrix, irrespective of cluster size. This allows us to refine the pose without evaluating the full residual (3) in each step of the optimization. Figure 2 shows an overview of our method. In Section 3.1 we discuss different approaches for performing the clustering and selecting representative matches, and in Section 3.2 we derive the proxy residual.", + "bbox": [ + 89, + 205, + 483, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the paper we focus the presentation on the calibrated case (essential matrix), but the approach is directly applicable to the uncalibrated (fundamental matrix) setting as well.", + "bbox": [ + 89, + 401, + 483, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Clustering and Representative Matches", + "text_level": 1, + "bbox": [ + 89, + 455, + 429, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a set of dense matches, our goal is to find a sparse subset of representative matches that capture the same geometric constraints as the full set. To do this, we begin by clustering correspondences that contribute with similar residuals. From each cluster, we then select a single match which serves as a representative of that cluster.", + "bbox": [ + 89, + 477, + 483, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We base our clustering on the assumption that matches close to each other should lead to similar residuals in (3). This motivates us to group matches based on their position in the two images. A simple approach is to use a standard clustering method, e.g. K-means, applied on the 4-dimensional match vectors (i.e. concatenated keypoint coordinates from both images). Alternatively, matches could be clustered based on the images, e.g. using superpixels. In Section 4.2, we discuss and compare different approaches for clustering and their trade-off in terms of runtime and accuracy for our method.", + "bbox": [ + 89, + 568, + 483, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For each cluster, we then select the match closest to the cluster centroid (in 4D match space) as the representative match. The set of representative matches $\\{(c_i,\\bar{c}_i)\\}_{i = 1}^K\\subset$ $\\{(x_{i},\\bar{x}_{i})\\}_{i = 1}^{N}$ , where $K$ is the number of clusters, can be used directly in RANSAC to estimate the relative pose, using the sub-sampled cost", + "bbox": [ + 89, + 734, + 483, + 825 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {c} (E) = \\sum_ {i = 1} ^ {K} \\min \\left\\{\\mathcal {E} \\left(E, \\boldsymbol {c} _ {i}, \\bar {\\boldsymbol {c}} _ {i}\\right), \\tau^ {2} \\right\\}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 834, + 483, + 875 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the runtime of RANSAC is generally dominated by", + "bbox": [ + 89, + 885, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "scoring and refinement, which grows linearly with the number of matches, significant subsampling can drastically reduce the runtime. In our experiments (Section 4) we show that even when severely subsampling ( $K \\approx N / 80$ ), leading to $55\\mathrm{x}$ speedup, we can still obtain good relative pose estimates when using this method. This highlights that most constraints in the dense matches are redundant. However, the sparsified matches still will lead to a slight drop in accuracy. In the next section, we propose an approximation which enriches each of the matches to also encode the geometric constraints from the full cluster.", + "bbox": [ + 511, + 90, + 906, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Dense Match Summarization", + "text_level": 1, + "bbox": [ + 511, + 265, + 774, + 279 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now present a method for approximating the full cost in (3) using the clustering. The idea is to replace the dense matches in each cluster with a more computationally efficient proxy residual. While we in the previous section reduced the number of residuals from $N$ to $K$ by only considering the representative matches, in this section we will capture more of the geometry per cluster by increasing this number to $9K$ . We do this in two steps; first by assuming that each cluster is either all-inlier or all-outler, and second by approximating the Sampson error in each cluster.", + "bbox": [ + 511, + 287, + 906, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathcal{M} \\subset \\mathbb{R}^3 \\times \\mathbb{R}^3$ be the set of dense input matches, and let $\\mathcal{C}_1, \\ldots, \\mathcal{C}_K \\subset \\mathcal{M}$ be a disjoint clustering of these with associated representative matches $\\{(c_k, \\bar{c}_k)\\}_{k=1}^K$ . By assuming that the matches in each cluster are either all inliers or all outliers, (3) can be rewritten as", + "bbox": [ + 511, + 436, + 905, + 513 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} f (E) = \\sum_ {k = 1} ^ {K} \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C} _ {k}} \\min \\left\\{\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tau^ {2} \\right\\} (5) \\\\ \\approx \\sum_ {k = 1} ^ {K} \\min \\left\\{\\sum_ {\\left(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}\\right) \\in \\mathcal {C} _ {k}} \\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), | \\mathcal {C} _ {k} | \\tau^ {2} \\right\\}, (6) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 521, + 906, + 616 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $|\\mathcal{C}_k|$ denotes the number of matches in cluster $\\mathcal{C}_k$ . This means that each cluster either contributes the sum of all its dense residuals, or the constant factor $|\\mathcal{C}_k| \\tau^2 -$ whichever is smallest.", + "bbox": [ + 511, + 622, + 906, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Now, consider a single cluster $\\mathcal{C}$ with representative match $(c,\\bar{c})$ . The sum of all its dense residuals is", + "bbox": [ + 511, + 683, + 905, + 713 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {c l} (E; \\mathcal {C}) = \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 720, + 906, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "i.e. the inner sum in (6). By construction, each match $(\\pmb{x},\\bar{\\pmb{x}})\\in \\mathcal{C}$ will lie relatively close to the cluster's representative match $(c,\\bar{c})$ . This motivates us to approximate the Sampson error (2) for each dense match as", + "bbox": [ + 511, + 762, + 905, + 821 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\approx \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {c} \\| ^ {2} + \\| (E ^ {T}) _ {1 2} \\bar {\\boldsymbol {c}} \\| ^ {2}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 828, + 905, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "i.e. by replacing $(\\pmb {x},\\bar{\\pmb{x}})$ in the denominator with $(c,\\overline{c})$ .For brevity, we introduce $\\alpha (E;\\mathcal{C}) = \\| E_{12}\\pmb {c}\\| ^2 +\\| (E^T)_{12}\\overline{\\pmb{c}}\\| ^2.$", + "bbox": [ + 511, + 869, + 905, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1095", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/598ee4f4384d4bf9369cf9cfbb0463f0b786ef44892799680322330bca3e0c2a.jpg", + "image_caption": [ + "Figure 2. Overview of our Summarization Scheme. As input, our method takes a set of dense matches $\\{(\\pmb{x}_i,\\bar{\\pmb{x}}_i)\\}_{i = 1}^N$ , where typically $N = 10000$ . Through clustering, the matches are grouped into clusters $\\mathcal{C}_1,\\ldots ,\\mathcal{C}_K$ , $K\\ll N$ , which yield approximately the same geometric constraints on the relative pose. For each cluster, we then perform match summarization, which replaces each group of matches with a representative match $(c_k,\\bar{c}_k)$ and a $9\\times 9$ -matrix $M_{k}$ that encodes the geometric constraints. These summarized meta-matches can then used for robust two-view estimation with significant speedup for a very small accuracy loss." + ], + "image_footnote": [], + "bbox": [ + 91, + 73, + 903, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then the approximation in (8) lets us write the sum of residuals for a cluster more compactly as", + "bbox": [ + 89, + 362, + 482, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} f _ {\\mathrm {c l}} (E; \\mathcal {C}) \\approx \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\alpha (E ; \\mathcal {C})} (9) \\\\ = \\frac {1}{\\alpha (E ; \\mathcal {C})} \\left\\| \\left( \\begin{array}{c} \\bar {\\boldsymbol {x}} _ {1} ^ {T} E \\boldsymbol {x} _ {1} \\\\ \\vdots \\\\ \\bar {\\boldsymbol {x}} _ {n} ^ {T} E \\boldsymbol {x} _ {n} \\end{array} \\right) \\right\\| ^ {2} = \\frac {1}{\\alpha (E ; \\mathcal {C})} \\| A e \\| ^ {2}, (10) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 401, + 482, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $n = |\\mathcal{C}_k|$ ; $\\pmb{e} \\in \\mathbb{R}^9$ is a vector containing the elements of $E$ , and $A \\in \\mathbb{R}^{n \\times 9}$ is the matrix with rows $A_i = (\\pmb{x}_i \\otimes \\bar{\\pmb{x}}_i)^T$ for all $(\\pmb{x}_i, \\bar{\\pmb{x}}_i) \\in \\mathcal{C}$ . Here, $\\otimes$ denotes the Kronecker product. The trick to efficiently evaluating (10) is that the large matrix $A$ can be replaced with the reduced measurement matrix [34] $M \\in \\mathbb{R}^{9 \\times 9}$ using Cholesky factorization $A^T A = M^T M$ , since", + "bbox": [ + 89, + 534, + 483, + 640 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| A \\boldsymbol {e} \\right\\| ^ {2} = \\boldsymbol {e} ^ {T} A ^ {T} A \\boldsymbol {e} = \\boldsymbol {e} ^ {T} M ^ {T} M \\boldsymbol {e} = \\left\\| M \\boldsymbol {e} \\right\\| ^ {2}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 651, + 482, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that this is very fast to compute (in our experiments a total of $0.2\\mathrm{ms}$ for 128 clusters with $N = 10,000$ ) and only needs to be done once for each clustering.", + "bbox": [ + 89, + 681, + 482, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The final approximate cost function for all matches, to be evaluated in each step of the optimization, is", + "bbox": [ + 89, + 728, + 482, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\text {a p p r o x}} (E) = \\sum_ {k = 1} ^ {K} \\min \\left\\{\\frac {1}{\\alpha \\left(E ; \\mathcal {C} _ {k}\\right)} \\| M _ {k} e \\| ^ {2}, | \\mathcal {C} _ {k} | \\tau^ {2} \\right\\}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 770, + 480, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our experiments (Section 4.3) we show that this provides a tight approximation to the sum of Sampson errors, while being significantly faster to compute.", + "bbox": [ + 89, + 825, + 482, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Above, the approximation was applied to the Sampson residual, but it is in principle also applicable to residuals", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with similar form, e.g. Symmetric Epipolar Distance:", + "bbox": [ + 511, + 362, + 864, + 377 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}})} \\left(\\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {x} \\| ^ {2}} + \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} ^ {T} \\bar {\\boldsymbol {x}} \\| ^ {2}}\\right) \\approx \\frac {\\| A \\boldsymbol {e} \\| ^ {2}}{\\| E _ {1 2} \\boldsymbol {c} \\| ^ {2}} + \\frac {\\| A \\boldsymbol {e} \\| ^ {2}}{\\| E _ {1 2} ^ {T} \\bar {\\boldsymbol {c}} \\| ^ {2}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 385, + 903, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 436, + 645, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we evaluate the match clustering and summarization scheme presented in Section 3, through experiments on real image pairs. First, in Section 4.2, we compare clustering methods and perform an ablation study on both the clustering method and number of clusters. In Section 4.3, this is followed by an evaluation of the approximation error of our summarization scheme. Next, in Section 4.4, we perform an ablation study on the integration of our summarization scheme in RANSAC.", + "bbox": [ + 511, + 462, + 906, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use two standard benchmarks for relative pose estimation, ScanNet-1500 [11, 35] and MegaDepth-1500 [26, 36], which each contain 1500 image pairs of indoor and outdoor scenes, respectively. For inlier thresholds, we use 1.0 pixels in MegaDepth-1500, and 2.5 pixels in ScanNet-1500. Following prior work, we report the pose error (max of rotation and translation error in degrees) with the Area Under Curve (AUC) up to some threshold. For our ablations and approximation evaluation, we evaluate on MegaDepth-1500, using $N = 10000$ dense matches from DKM [15]. Finally, in Section 4.5 we show that our results generalize to other state-of-the-art dense matchers and other datasets. We also present results on estimation of the fundamental matrix on the challenging WxBS dataset [29].", + "bbox": [ + 511, + 598, + 908, + 811 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 511, + 818, + 732, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We implement our approximate residual in an LO-RANSAC framework building on PoseLib [23], which is a state-of-the-art robust estimation library in $\\mathrm{C + + }$ . To get a fair comparison with the dense and subsampled methods,", + "bbox": [ + 511, + 839, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1096", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we implement the standard Sampson residual in the same framework. For the ablations and evaluations in the following sections, our method runs RANSAC using the representative matches from Section 3.1, followed by refinement using the approximate residuals described in Section 3.2. All timings are measured on a modern desktop CPU.", + "bbox": [ + 89, + 90, + 483, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Ablation on Clustering", + "text_level": 1, + "bbox": [ + 89, + 194, + 305, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we explore different approaches for performing the match clustering. We explore both keypoint-based and image-based clustering methods. For the keypoint-based methods, we evaluate K-means clustering on both the 4-dimensional match vectors and the 2-dimensional keypoints from one of the images. Motivated by the geometric constraints in (10), we also evaluate clustering in the 9-dimensional constraint vectors $A_{i} = \\boldsymbol{x}_{i}\\otimes \\bar{\\boldsymbol{x}}_{i}\\in \\mathbb{R}^{9}$ . For the K-means clustering experiments we use FAISS [13] on a CPU, running a maximum of 5 iterations.", + "bbox": [ + 89, + 217, + 483, + 368 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For image-based clustering, we first segment one of the images, then consider all matches within the same segment as a cluster. We evaluate both a simple 2D-grid segmentation, and a more sophisticated superpixel detection. The 2D grid is created by dividing the image region between the minimum and maximum keypoint coordinates into $m^2$ equally sized rectangles, where $m = \\lceil \\sqrt{K} \\rceil$ . For the superpixel detection, we use SLIC [1, 21]. For each clustering method, we select the representative match by finding the match closest to the centroid.", + "bbox": [ + 89, + 369, + 483, + 520 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Figure 3, we show some qualitative examples of the different clusterings on two example image pairs from MegaDepth-1500 and ScanNet-1500, respectively. In the top example, we see that the keypoint-based methods (2D, 4D, 9D) all give similar clustering patterns, while in the bottom example 2D clustering leads to a coarser clustering in the second image. This is explained by the smaller image overlap; while 4D and 9D clustering takes the keypoint density in both images into account, 2D clustering only sees the keypoints from one of the images. The image-based methods (Grid and SLIC), on the other hand, lead to larger clusters in both of the image pairs. This is because the segmentation is not proportional to the match density, so they may \"waste\" clusters on image regions with few or no matches.", + "bbox": [ + 89, + 521, + 483, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Table 1, we compare the errors and runtimes for different clustering methods on MegaDepth-1500, using a cluster size of 128. We report both the time for clustering, and for estimation using the clusters. We assume that grid-clustering can be done at negligible runtime with an efficient implementation. In the table, we see that the difference between clustering methods is quite small, except for SLIC which is markedly more expensive to calculate. A key difference with image-based clustering, however, is that it only needs to be done once per image. Keypoint-based clustering, on the other hand, needs to be done once per image", + "bbox": [ + 89, + 734, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pair, which can lead to many more total evaluations. For large datasets with high co-visibility, this may be important to consider.", + "bbox": [ + 511, + 90, + 906, + 136 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/eb6bfbfe3d12235da0665e5d9162e610ae8dbc860ebfcc6c1e223af1d7da05dd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAUC@5°εavgRuntime
ClusteringRANSAC
K-means 2D66.43.621.53 ms1.46 ms
K-means 4D66.93.281.22 ms1.44 ms
K-means 9D66.63.251.38 ms1.43 ms
Grid65.93.73≈0 ms1.34 ms
SLIC [21]64.54.0722.38 ms0.97 ms
", + "bbox": [ + 519, + 145, + 901, + 266 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Clustering Method Ablation. The table shows the pose errors for each clustering approach on MegaDepth-1500, as well as the average runtime for each clustering strategy.", + "bbox": [ + 511, + 276, + 906, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we evaluate the impact of the number of clusters. Figure 4 shows the AUC@5° (left) and runtime (center) plotted against the number of clusters, as well as AUC@5° vs. runtime (right). We also include the dense baseline (dashed). The results further indicate that all K-means clustering variants perform similarly, and that the performance gets close to the dense baseline as number of clusters increases. Based on these results, we select K-means 4D with $K = 128$ as our main clustering method to be used in the experiments, but note that other choices are viable as well.", + "bbox": [ + 511, + 335, + 906, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Evaluation of Approximation Error", + "text_level": 1, + "bbox": [ + 511, + 496, + 823, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Section 3.2, we introduced a proxy residual to approximate the sum of squared Sampson residuals for a cluster. In this section, we experimentally validate this approximation and show that it provides a tight approximation of the true residual. We use 128 clusters per image pair obtained via Kmeans-9D, as defined in the previous section. For each cluster $\\mathcal{C}$ , we compute the per-cluster average Sampson residuals exactly as", + "bbox": [ + 511, + 518, + 906, + 638 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\varepsilon_ {S} ^ {2} = \\frac {1}{| \\mathcal {C} |} \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\mathcal {E} (E _ {g t}, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 647, + 906, + 685 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and the squared approximate cluster residual as", + "bbox": [ + 511, + 696, + 830, + 710 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\varepsilon_ {a} ^ {2} = \\frac {1}{| \\mathcal {C} |} \\frac {\\left\\| M \\operatorname {v e c} \\left(E _ {g t}\\right) \\right\\| ^ {2}}{\\left\\| \\left(E _ {g t}\\right) _ {1 2} \\boldsymbol {c} \\right\\| ^ {2} + \\left\\| \\left(E _ {g t} ^ {T}\\right) _ {1 2} \\bar {\\boldsymbol {c}} \\right\\| ^ {2}}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 720, + 906, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Figure 5 we show the distribution of the difference $\\varepsilon_{S} - \\varepsilon_{a}$ between the true residual and the approximation, computed on the 1500 image pairs from MegaDepth-1500 with 10000 DKM matches. The residuals are evaluated for the ground truth essential matrix $E_{gt} = [t_{gt}]_{\\times}R_{gt}$ . Note that positive values indicate that the approximation gives too small residuals, while negative values correspond to the approximation giving too large residuals. We plot residuals between the $1^{\\mathrm{st}}$ and $99^{\\mathrm{th}}$ percentile. Thus we see that more", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1097", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e2695a197f0d53daa56a4b0d29e393217e34604da1b0de9c4e849fb28dafc417.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 85, + 362, + 164 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/07e2bed2aa36df75402502d2c8f09588915185c7d5a24caf016b91567496eb1c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 165, + 362, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/edcbcc4e432edc190795e23a7688c283dc3664ce9220e3458c200c60e31fe7b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 85, + 625, + 164 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e99ce44fcc900571c8158167ae367f452983ab42d04a80db824d97034613d702.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 164, + 625, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/21e053569e8ec5184868169a0488ca2231ddcc15c8c9e95d0eac50a16002d974.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 88, + 890, + 164 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8cd241df394c8c8548e9695183cae986dba7080f9320a71f050bf37d379ed586.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 165, + 890, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bff4ebdd4c26f419166404ac88fc61f3573fd570f3420427e56a3664e1352af2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 244, + 366, + 324 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f42f3a3b74bc5ef11444ba96d01f22cb0f44e1063fba11a54660e69815d0c402.jpg", + "image_caption": [ + "Figure 3. Qualitative Comparison of Clustering Methods. We compare different clustering methods on a single image pair from MegaDepth-1500 (top 2 rows) and ScanNet-1500 (bottom 2 rows), respectively. Dense matches from DKM are clustered using three keypoint-based methods (2D, 3D, 9D) and two image-based methods (Grid, SLIC)." + ], + "image_footnote": [], + "bbox": [ + 102, + 324, + 366, + 402 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fd2c134b8051ae07f7cc6be05ef1d3c90ad339bcc7dc29370597c80a2b40e6ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 244, + 627, + 324 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d5468c86cbd3499afc411c60a69eaf39e54f66b626c691e13fda64708a27cc40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 324, + 627, + 402 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/abcda61a2fc71b8597f7004707e7b0306e9fc01053f617232553f1b586f79210.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 244, + 892, + 324 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9158f0c8316b4cdf0ca63692ab4157772f88fa1194c9c54ff2049cedd6952348.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 324, + 892, + 402 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6f1b36f531eab4e74693b2ff4a5f5e55ac1c32133264c10b6a4f292ae7c8f13e.jpg", + "image_caption": [ + "Figure 4. Clustering Method and Hyperparameter Ablation. The plots show AUC@5° (left), runtime (middle) and AUC-runtime-tradeoff (right) for different clustering methods and number of clusters $K$ . We include AUC@5° for the dense baseline as reference." + ], + "image_footnote": [], + "bbox": [ + 96, + 472, + 364, + 609 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/feb8553163b7861b180c92976f93a5b306b138e8c9a57de25e303d61f9c38bba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 472, + 627, + 609 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/46cf91a0b9056a2f1ea8bafed7c97ff470ffe97f2d21cd1eee3275f38aaa1b5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 472, + 898, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "than $98\\%$ of the residuals have an absolute approximation error of less than 0.1 pixels, with a small bias towards getting too large residuals.", + "bbox": [ + 89, + 679, + 482, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 2 we compare the inlier ratios obtained through exact and approximate residuals, using the ground-truth pose. We compute average inlier ratios for each of the 1500 image pairs in MegaDepth-1500. Note that we compute the ratio of inlier clusters for $\\varepsilon_{a}$ , while for the exact residual $\\varepsilon_{S}$ the inlier ratio is computed per match. We also include the runtime for computing the two residuals for an image pair (equivalent to scoring a model in RANSAC). We see that the approximated residual gives slightly lower inlier ratios, which decrease slowly for coarser clustering, while the speedup in computing time is significant.", + "bbox": [ + 89, + 734, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation on Integration in RANSAC", + "text_level": 1, + "bbox": [ + 511, + 679, + 830, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we explore different ways of integrating our method in robust estimation with RANSAC. Robust estimation is typically done in two stages: the hypothesize-and-verify loop, which alternates between estimating and scoring models, and model refinement, which is done on the best model after the stop criterion is reached.", + "bbox": [ + 511, + 702, + 906, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the effect of our summarization scheme both on the model scoring and refinement stages of the estimation. For both stages, we evaluate usage of the representative match residuals (4), and the approximate residuals (12). We will refer to these methods as Center and Approximate, respectively. For the refinement stage, we also evaluate usage of the original residuals (3), referred to as the Dense", + "bbox": [ + 511, + 795, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1098", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/315b11a65b2a3c76df529fa1f1670a2d623ef8b44ee706040628a104c3dc02ef.jpg", + "image_caption": [ + "Figure 5. Histogram over Approximation Error. The graph shows the distribution of differences between the true and approximated residuals, i.e. $\\varepsilon_{S} - \\varepsilon_{a}$ , scaled with focal length. Statistic taken over all clusters from all image pairs in MegaDepth-1500." + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 480, + 295 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0926d1ebeba640c812517da4b0e3672c59936c1bcad0ee7f3b32b00399f49af9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Type of residualInlier ratioRuntime (μs)
Med.Avg.Avg.Speedup
Exact0.870.82155.81.0x
Approx. K = 10240.850.8031.15.0x
Approx. K = 5120.840.8014.810.5x
Approx. K = 2560.840.797.121.9x
Approx. K = 1280.820.783.248.7x
Approx. K = 640.800.761.3119.8x
", + "bbox": [ + 94, + 375, + 478, + 510 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "method. With two model scoring costs to evaluate (Center and Approximate) and three refinement costs (Center, Approximate, and Dense) this results in 6 possible combinations for our ablation study, in addition to the fully dense baseline. However, we omit Approximate scoring followed by Center refinement, since this would use less information in the refinement than what was used for the model scoring.", + "bbox": [ + 89, + 657, + 482, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For all of the above methods, we perform model estimation using the 5-point solver [31], sampling from the representative matches. Note that this sampling has no effect on runtime compared to sampling from the dense matches, since convergence of RANSAC is only based on the scoring. Since we get up to 9 constraints from each $M_{k}$ matrix, it is in principle also possible to estimate a model from a single summarized correspondence. However, we found that this generally gives worse performance, see suppl. material.", + "bbox": [ + 89, + 763, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 3, we show AUC@5° and median runtime for the different combinations of model scoring and refinement costs, compared with a fully dense baseline. We report the average and standard deviation of the AUC for 10 runs using different seeds. In the table, we abbreviate the methods using a three letter combination, where the first letter denotes sampling method, the second letter denotes scoring method, and the third letter denotes refinement method. We see that scoring using Approximate or Center residuals are both significantly faster than Dense. Center scoring is the fastest while not significantly less accurate than Approximate. For refinement, however, Approximate residuals give a small but significant improvement in score over Center, but at an increased runtime. This gives us a possible trade-off, where we can sacrifice some runtime for better accuracy.", + "bbox": [ + 511, + 90, + 903, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also compare our ablated methods with a dense baseline on subsampled DKM-matches, obtained by querying the balanced DKM sampler for a lower number of correspondences. In Figure 6, we plot AUC@5° vs. runtime for our methods and different number of DKM matches. We see that compared to subsampling, most of our methods give shorter runtime for the same performance; in particular CCC and CCA. This indicates that our summarization better preserves the geometric constraints, compared to reducing the number of correspondences extracted from the matcher.", + "bbox": [ + 511, + 316, + 903, + 484 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ee2a8be2febe748ae8a4526c13133f107fdc0c5af1765185d265e1b59bec521e.jpg", + "table_caption": [ + "Table 2. Comparison of RANSAC Scoring. We compare the inlier ratios when calculating exact and approximate residuals for different numbers of clusters $K$ , using the ground-truth essential matrix on all image pairs in MegaDepth-1500. The average and median ratios over all image pairs is reported. Note that inlier ratios are calculated per match for the exact residuals, and per cluster for approximate residuals. The runtime shows the average cost of scoring a model with MSAC in RANSAC." + ], + "table_footnote": [], + "table_body": "
MethodAUC@5°RT (ms)Speedup
DDD (baseline)67.38±0.1066.01.0x
CAD67.21±0.086.89.8x
CCD67.12±0.085.312.3x
CAA66.87±0.072.724.6x
CCA66.70±0.061.545.2x
CCC65.95±0.101.255.0x
", + "bbox": [ + 524, + 494, + 890, + 618 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation on RANSAC Integration. We compare usage of our two summarization schemes in different stages of the estimation. Method names denote the what data is used in sampling, scoring, and refinement. For example, \"CAD\" means sampling from representative matches (C), scoring with the summarized approximation (A), and refinement with the dense matches (D).", + "bbox": [ + 511, + 627, + 903, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Comparative Evaluation in RANSAC", + "text_level": 1, + "bbox": [ + 511, + 741, + 836, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate our match summarization scheme on robust estimation using different dense matchers. We run both the CCC- and CCA-methods, since they represent a possible trade-off between accuracy and runtime. We compare with a fully dense baseline on the full set of matches. To show that our results do not depend on the dense matcher, we report results using DKM [15], RoMA [16], and ASPanFormer [7]. From DKM and RoMA, we always sample 10000 matches, while ASPanFormer gives a variable", + "bbox": [ + 511, + 763, + 903, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1099", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5216068451ad400fe0d20de0a4ffb377b8c0509ed42226e632e72e32ef471d68.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MatchesEstimatorMegaDepth-1500ScanNet-1500
AUC@5°AUC@10°AUC@20°RT (ms)SpeedupAUC@5°AUC@10°AUC@20°RT (ms)Speedup
DKMDense67.479.688.066.61.0x31.352.669.968.81.0x
Ours CCA66.779.187.51.545.2x30.952.169.61.546.7x
Ours CCC66.078.787.31.255.0x30.451.769.31.258.6x
RoMADense70.181.589.360.61.0x33.355.272.264.61.0x
Ours CCA70.181.689.41.442.2x33.054.972.01.446.3x
Ours CCC69.381.189.21.252.1x32.854.771.81.158.3x
ASpan-FormerDense66.378.887.514.41.0x30.350.566.515.21.0x
Ours CCA65.878.587.41.59.6x29.749.966.11.510.3x
Ours CCC64.177.486.81.212.1x28.949.265.71.213.0x
SP+LGDense63.777.286.55.0N/A21.839.655.63.0N/A
", + "bbox": [ + 102, + 88, + 893, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7cb304f8e6f2ae911030eed053ce0f034e3a1372592042da6e86f1426b2ad7b1.jpg", + "image_caption": [ + "Figure 6. AUC-Runtime Trade-off in Ablation Study. The methods in Table 3 are plotted together with dense baseline for different samplings from DKM." + ], + "image_footnote": [], + "bbox": [ + 89, + 313, + 480, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "amount of matches. For image pairs where ASpanFormer gives less than 128 matches, we fall back to using dense estimation. The average results from 10 different seeds are shown in Table 4. The reported runtime is the median over all image pairs. For the convenience of the reader, we have also included estimation from sparse SuperPoint [12] + LightGlue [27] keypoints. In summary, we see that our summarization scheme achieves comparable accuracy to the dense baseline at a fraction of the runtime, irrespective of the dense keypoint matcher used.", + "bbox": [ + 88, + 608, + 482, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we present an experiment on the WxBS benchmark [29]. This benchmark contains extremely challenging wide-baseline image pairs, where GT-correspondences are provided. As it does not provide intrinsics, we evaluate fundamental matrix estimation. The metrics are computed by checking consistency of the estimated $F$ with the GT matches. For comparison, we also run on dense matches extracted with MASt3R [25], where we disabled subsampling in the fast reciprocal matching. The results in Table 5", + "bbox": [ + 88, + 763, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/93879fb2891e21614572830974e06332cca6c2fae415c7bc15934fc5f8827e46.jpg", + "table_caption": [ + "Table 4. Comparison with State-of-the-art. We compare our method with a dense baseline for several dense matchers on both MegaDepth-1500 and ScanNet-1500. For comparison, we also include AUC and runtime for state-of-the-art sparse matches (SP+LG)." + ], + "table_footnote": [], + "table_body": "
MatchesEstimatorRecall (10px)↑RT (ms)↓Speedup↑
RoMaDense86.363.01.0x
Ours CCA85.11.4543.3x
Ours CCC83.80.8277.0x
MASt3RDense63.437.11.0x
Ours CCA63.21.4325.8x
Ours CCC61.60.7649.6x
", + "bbox": [ + 532, + 313, + 883, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Fundamental Matrix Estimation on WxBS.", + "bbox": [ + 545, + 417, + 872, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "are qualitatively similar to the calibrated setting, showing that our method significantly speeds up the robust estimation with a marginal loss in accuracy.", + "bbox": [ + 511, + 460, + 903, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 523, + 633, + 540 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we have shown that dense keypoint matches, while they improve estimation compared to sparse matches, contain significant redundancies. This redundancy makes it possible to heavily subsample the matches while keeping most of the geometric constraints. We demonstrated a method to significantly speed up geometric estimation with little effect on the estimation accuracy. We additionally showed that this reduction in accuracy can be partially recovered by using our proposed summarized metacorrespondences. With this scheme, we were able to reduce the number of residuals per image pair from the number of matches $N$ , to $9K$ where $K$ is the number of clusters – a hyperparameter we can choose such that $N \\ll 9K$ . We also get a potential compression ratio in terms of storage, since the constraints from each cluster is entirely contained in a $9 \\times 9$ -matrix, plus a single correspondence. A limitation is that the method only makes sense if the original number of matches is very large. Another limitation of the paper is that we have only focused on speeding up the robust estimation step, while a large part of the total runtime comes from the dense matcher itself.", + "bbox": [ + 511, + 551, + 906, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. The project was supported by ELLIIT and the Swedish Research Council (Grant No. 2023-05424).", + "bbox": [ + 511, + 869, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1100", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süssstrunk. Slic superpixels compared to state-of-the-art superpixel methods. 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In International Conference on Computer Vision (ICCV), 2023. 2" + ], + "bbox": [ + 89, + 92, + 482, + 445 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1102", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_model.json b/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fce8be54d9d90cf8d765ff5321419cf930eba80b --- /dev/null +++ b/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_model.json @@ -0,0 +1,2112 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.19, + 0.131, + 0.808, + 0.151 + ], + "angle": 0, + "content": "Dense Match Summarization for Faster Two-view Estimation" + }, + { + "type": "text", + "bbox": [ + 0.272, + 0.182, + 0.725, + 0.218 + ], + "angle": 0, + "content": "Jonathan Astermark, Anders Heyden, and Viktor Larsson \nCentre for Mathematical Sciences, Lund University" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.22, + 0.774, + 0.234 + ], + "angle": 0, + "content": "{jonathan.astermark, anders.heyden, viktor.larsson}@math.lth.se" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.302, + 0.486, + 0.468 + ], + "angle": 0, + "content": "In this paper, we speed up robust two-view relative pose from dense correspondences. Previous work has shown that dense matchers can significantly improve both accuracy and robustness in the resulting pose. However, the large number of matches comes with a significantly increased runtime during robust estimation in RANSAC. To avoid this, we propose an efficient match summarization scheme which provides comparable accuracy to using the full set of dense matches, while having 10-100x faster runtime. We validate our approach on standard benchmark datasets together with multiple state-of-the-art dense matchers." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.497, + 0.222, + 0.512 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.523, + 0.483, + 0.688 + ], + "angle": 0, + "content": "Determining the two-view camera geometry is an important sub-task in many computer vision problems, e.g. for Simultaneous Localization and Mapping or Structure-from-Motion. The most common approach is to first detect corresponding points in the two views, followed by robust estimation using RANdom Sample Consensus (RANSAC) [18] which both estimates the relative pose and identifies potential outlier matches. Traditionally, keypoint matching is performed by independently detecting keypoints in each view, followed by a matching step, either directly comparing descriptor similarity or using a learned matcher." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.855 + ], + "angle": 0, + "content": "Recently, a lot of attention has been given to so-called detector-free matching, which takes the images as input and directly establishes (semi-)dense correspondences. These matchers produce significantly more matches, compared to the detector-based counterparts, especially in weakly textured image regions, such as walls, floors, and ceilings. Dense matching shows great promise and currently achieves the most accurate two-view estimates in standard benchmarks. However, this comes with a trade-off in runtime, both for running the matching and in the subsequent robust estimation (i.e. RANSAC)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "In this paper, we aim to improve the runtime of the robust estimation step. We show that when using dense matchers, most of the matches provide redundant geometric con" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.267, + 0.905, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.371, + 0.905, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.483, + 0.907, + 0.608 + ], + "angle": 0, + "content": "Figure 1. Relative Pose Estimation from Dense Matches. The top images show 10,000 semi-dense matches from DKM [15] with same colors indicating corresponding points. The large number of matches makes robust estimation with RANSAC accurate (pose error \\(\\epsilon = 0.38^{\\circ}\\)) but slow (runtime \\(t = 98\\) ms). In this paper we show that we can get comparable accuracy with significantly lower runtime by sparsifying the dense matches (bottom images). Each sparsified match is represented by a \\(9 \\times 9\\)-matrix that summarizes the geometric constraints from nearby matches." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.64, + 0.907, + 0.836 + ], + "angle": 0, + "content": "straints, and we present an efficient match summarization scheme that selects a subset of \\(\\approx 1\\%\\) of the matches, which we call representative matches, that are used for robust estimation. Using this smaller set of matches, we can obtain a 10-100x speedup with a marginal loss in pose accuracy. In addition, we present an approximation approach for enriching each representative match to capture the geometric constraints of nearby correspondences in a single \\(9\\times 9\\)-matrix (regardless of how many neighboring matches are included). This enrichment allows for an even smaller loss of pose accuracy, while still being significantly faster compared to dense correspondence. In Figure 1 we visualize one example from MegaDepth [26]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.838, + 0.905, + 0.883 + ], + "angle": 0, + "content": "We validate our claims and our approach with extensive experiments and ablation studies on standard benchmarks with different state-of-the-art dense matchers." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.886, + 0.766, + 0.901 + ], + "angle": 0, + "content": "In summary, our contributions are:" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1093" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.482, + 0.151 + ], + "angle": 0, + "content": "- A scheme for summarizing any dense matches into sparse representative matches, which speeds up the robust estimation by a factor 10-100x, with only a very small loss in accuracy." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.153, + 0.483, + 0.227 + ], + "angle": 0, + "content": "- An approximation-based approach to summarize the contributions of each cluster, which we use to refine the output from RANSAC. This lets us maintain the high accuracy from dense matches, with only a small increase in runtime compared to the approach above." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.228, + 0.482, + 0.303 + ], + "angle": 0, + "content": "- In experiments on standard benchmarks, with multiple state-of-the-art dense matchers, we are able to consistently show a significant speedup. Furthermore, our experiments show that sparsified dense matches outperform state-of-the-art sparse matches in terms of accuracy." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.092, + 0.483, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.317, + 0.235, + 0.331 + ], + "angle": 0, + "content": "1.1. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.34, + 0.484, + 0.597 + ], + "angle": 0, + "content": "Matching and Correspondences. Image correspondence for geometric estimation traditionally works with a detect-then-match paradigm that first identifies keypoints (e.g. SIFT [28], SuperPoint [12]) independently in each image, followed by a matching step. The matching is either done by comparing descriptor similarity ([12, 14, 28]) or more recently via learned matchers ([27, 35]). In [36] the authors instead proposed to perform detection-free matching, which takes an image pair as input and directly regresses semi-dense pixel correspondences. This started a series of work on dense matching ([7, 15, 16, 20]) which improved on the initial work. Common for all dense methods is that they produce significantly more matches compared to classical detector-based methods. By considering both images jointly, the methods are able to propagate strong matches to weaker ones, allowing for even weakly textured regions to be matched between images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.598, + 0.484, + 0.718 + ], + "angle": 0, + "content": "In benchmarks for two-view relative pose estimation, these methods significantly improve the results in terms of pose accuracy. However, this comes at a trade-off with runtime, as the large number of matches makes robust estimation more costly. In this work, we offset some of this cost by speeding up the robust estimation. Our method is not specific to a particular matcher and can be applied to any dense correspondences." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Robust Estimation. For robust geometric estimation problems in computer vision, the RANSAC algorithm, originally introduced by Fischler and Bolles [18] in 1981, is the de facto standard. Modern RANSAC variants, while still working with similar principles as the original, usually incorporate some form of local optimization (LORANSAC [10, 24]) as well a more complex scoring beyond simple inlier counting, e.g. MSAC [37] or MAGSAC [3]. Other works improve by integrating various learned components in the pipeline, see e.g. [4, 6, 39]. There are also several works which focus on making RANSAC faster. In [9], the authors propose a probabilistic method (SPRT) for de" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.242 + ], + "angle": 0, + "content": "ciding when to early exit. In [22], the authors propose to only perform scoring once two similar models are found. Rais et al. [32] instead aggregate multiple model hypotheses to form the final output. Barath et al. [2] speed up scoring by filtering out regions of the matches which cannot contain inlier correspondences for the current model. PROSAC [8] leverages per-match confidences to sample good models earlier, to speed up convergence. Ni et al. [30] group correspondences and model different inlier ratios for each cluster, which is used both for sampling and stopping criterion." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.243, + 0.905, + 0.333 + ], + "angle": 0, + "content": "The match summarization method proposed in this paper is orthogonal (and could be combined) with the improvements in the above methods. In particular, most prior work focuses on either speeding up the scoring or reducing the number of iterations, but do not consider refinement which is particularly costly with a large number of matches." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.334, + 0.907, + 0.53 + ], + "angle": 0, + "content": "Richer Correspondences. For affine-correspondences (ACs) each match is associated with a \\(2 \\times 2\\) matrix representing a local transformation around the keypoints. These matrices can be interpreted as a linearization of the local planar homography [33]. Affine correspondences have been used to derive more efficient minimal estimators ([5, 17, 33, 38]) as well as provide constraints for normal estimation [19]. In this paper, we derive a summarized correspondence expressed with a \\(9 \\times 9\\)-matrix. While this matrix is similar to ACs in that it encodes additional local geometric constraints, it does not make assumption on local planarity and yields stronger geometric constraints, even allowing estimation from a single correspondence (see Section 4.4)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.543, + 0.642, + 0.56 + ], + "angle": 0, + "content": "2. Background" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.567, + 0.905, + 0.599 + ], + "angle": 0, + "content": "Each 2D-point correspondence \\((\\pmb{x},\\bar{\\pmb{x}})\\in \\mathbb{R}^3\\times \\mathbb{R}^3\\) (in homogeneous coordinates) constrain the relative pose by" + }, + { + "type": "equation", + "bbox": [ + 0.668, + 0.607, + 0.905, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x} = 0, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.635, + 0.905, + 0.711 + ], + "angle": 0, + "content": "where \\( E = [t]_{\\times}R \\) is the essential matrix. As the points \\( (\\pmb{x},\\bar{\\pmb{x}}) \\) are measurements from the images, they will contain noise and will not satisfy (1) exactly, even if the match is correct. Thus, in the optimization, a residual such as the Sampson error is commonly used instead," + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.72, + 0.905, + 0.756 + ], + "angle": 0, + "content": "\\[\n\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}) = \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {x} \\| ^ {2} + \\left\\| \\left(E ^ {T}\\right) _ {1 2} \\bar {\\boldsymbol {x}} \\right\\| ^ {2}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.763, + 0.907, + 0.854 + ], + "angle": 0, + "content": "where \\( E_{12} \\) is the first two rows of \\( E \\). The Sampson error approximates the squared reprojection error, and is used to determine match correctness (inlier or outlier). Most RANSAC-variants additionally use some form of MSAC-scoring [37] for the models, i.e. the essential matrix is chosen by minimizing the sum of truncated residuals" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.863, + 0.905, + 0.904 + ], + "angle": 0, + "content": "\\[\nf (E) = \\sum_ {i = 1} ^ {N} \\min \\left\\{\\mathcal {E} \\left(E, \\boldsymbol {x} _ {i}, \\bar {\\boldsymbol {x}} _ {i}\\right), \\tau^ {2} \\right\\}, \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1094" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.168 + ], + "angle": 0, + "content": "where \\(N\\) denotes the number of matches and \\(\\tau \\in \\mathbb{R}_+\\) is the inlier threshold. The model-scoring function \\(f(E)\\) is used both for selecting the best model, and for non-linear refinement. As the number of matches \\(N\\) grows large, evaluating \\(f(E)\\) will dominate the runtime cost in RANSAC." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.18, + 0.182, + 0.195 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.206, + 0.484, + 0.401 + ], + "angle": 0, + "content": "In this section, we present a method for efficiently summarizing the geometric constraints given by the dense matches. The idea is to first cluster the correspondences into subsets that yield similar geometric constraints, and replace each cluster with a single representative match used in robust estimation. Next, we compute a proxy residual that summarizes the geometric constraints from each cluster into a \\(9 \\times 9\\)-matrix, irrespective of cluster size. This allows us to refine the pose without evaluating the full residual (3) in each step of the optimization. Figure 2 shows an overview of our method. In Section 3.1 we discuss different approaches for performing the clustering and selecting representative matches, and in Section 3.2 we derive the proxy residual." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.402, + 0.484, + 0.448 + ], + "angle": 0, + "content": "In the paper we focus the presentation on the calibrated case (essential matrix), but the approach is directly applicable to the uncalibrated (fundamental matrix) setting as well." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.456, + 0.43, + 0.472 + ], + "angle": 0, + "content": "3.1. Clustering and Representative Matches" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.478, + 0.484, + 0.568 + ], + "angle": 0, + "content": "Given a set of dense matches, our goal is to find a sparse subset of representative matches that capture the same geometric constraints as the full set. To do this, we begin by clustering correspondences that contribute with similar residuals. From each cluster, we then select a single match which serves as a representative of that cluster." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.569, + 0.484, + 0.734 + ], + "angle": 0, + "content": "We base our clustering on the assumption that matches close to each other should lead to similar residuals in (3). This motivates us to group matches based on their position in the two images. A simple approach is to use a standard clustering method, e.g. K-means, applied on the 4-dimensional match vectors (i.e. concatenated keypoint coordinates from both images). Alternatively, matches could be clustered based on the images, e.g. using superpixels. In Section 4.2, we discuss and compare different approaches for clustering and their trade-off in terms of runtime and accuracy for our method." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.735, + 0.484, + 0.826 + ], + "angle": 0, + "content": "For each cluster, we then select the match closest to the cluster centroid (in 4D match space) as the representative match. The set of representative matches \\(\\{(c_i,\\bar{c}_i)\\}_{i = 1}^K\\subset\\) \\(\\{(x_{i},\\bar{x}_{i})\\}_{i = 1}^{N}\\), where \\(K\\) is the number of clusters, can be used directly in RANSAC to estimate the relative pose, using the sub-sampled cost" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.835, + 0.484, + 0.876 + ], + "angle": 0, + "content": "\\[\nf _ {c} (E) = \\sum_ {i = 1} ^ {K} \\min \\left\\{\\mathcal {E} \\left(E, \\boldsymbol {c} _ {i}, \\bar {\\boldsymbol {c}} _ {i}\\right), \\tau^ {2} \\right\\}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Since the runtime of RANSAC is generally dominated by" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.258 + ], + "angle": 0, + "content": "scoring and refinement, which grows linearly with the number of matches, significant subsampling can drastically reduce the runtime. In our experiments (Section 4) we show that even when severely subsampling (\\( K \\approx N / 80 \\)), leading to \\( 55\\mathrm{x} \\) speedup, we can still obtain good relative pose estimates when using this method. This highlights that most constraints in the dense matches are redundant. However, the sparsified matches still will lead to a slight drop in accuracy. In the next section, we propose an approximation which enriches each of the matches to also encode the geometric constraints from the full cluster." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.266, + 0.776, + 0.28 + ], + "angle": 0, + "content": "3.2. Dense Match Summarization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.907, + 0.438 + ], + "angle": 0, + "content": "We now present a method for approximating the full cost in (3) using the clustering. The idea is to replace the dense matches in each cluster with a more computationally efficient proxy residual. While we in the previous section reduced the number of residuals from \\( N \\) to \\( K \\) by only considering the representative matches, in this section we will capture more of the geometry per cluster by increasing this number to \\( 9K \\). We do this in two steps; first by assuming that each cluster is either all-inlier or all-outler, and second by approximating the Sampson error in each cluster." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.438, + 0.906, + 0.514 + ], + "angle": 0, + "content": "Let \\(\\mathcal{M} \\subset \\mathbb{R}^3 \\times \\mathbb{R}^3\\) be the set of dense input matches, and let \\(\\mathcal{C}_1, \\ldots, \\mathcal{C}_K \\subset \\mathcal{M}\\) be a disjoint clustering of these with associated representative matches \\(\\{(c_k, \\bar{c}_k)\\}_{k=1}^K\\). By assuming that the matches in each cluster are either all inliers or all outliers, (3) can be rewritten as" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.522, + 0.907, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} f (E) = \\sum_ {k = 1} ^ {K} \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C} _ {k}} \\min \\left\\{\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tau^ {2} \\right\\} (5) \\\\ \\approx \\sum_ {k = 1} ^ {K} \\min \\left\\{\\sum_ {\\left(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}\\right) \\in \\mathcal {C} _ {k}} \\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), | \\mathcal {C} _ {k} | \\tau^ {2} \\right\\}, (6) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.623, + 0.907, + 0.681 + ], + "angle": 0, + "content": "where \\(|\\mathcal{C}_k|\\) denotes the number of matches in cluster \\(\\mathcal{C}_k\\). This means that each cluster either contributes the sum of all its dense residuals, or the constant factor \\(|\\mathcal{C}_k| \\tau^2 -\\) whichever is smallest." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.684, + 0.906, + 0.714 + ], + "angle": 0, + "content": "Now, consider a single cluster \\(\\mathcal{C}\\) with representative match \\((c,\\bar{c})\\). The sum of all its dense residuals is" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.721, + 0.907, + 0.755 + ], + "angle": 0, + "content": "\\[\nf _ {c l} (E; \\mathcal {C}) = \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.763, + 0.906, + 0.823 + ], + "angle": 0, + "content": "i.e. the inner sum in (6). By construction, each match \\((\\pmb{x},\\bar{\\pmb{x}})\\in \\mathcal{C}\\) will lie relatively close to the cluster's representative match \\((c,\\bar{c})\\). This motivates us to approximate the Sampson error (2) for each dense match as" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.829, + 0.906, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\approx \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {c} \\| ^ {2} + \\| (E ^ {T}) _ {1 2} \\bar {\\boldsymbol {c}} \\| ^ {2}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.906, + 0.903 + ], + "angle": 0, + "content": "i.e. by replacing \\((\\pmb {x},\\bar{\\pmb{x}})\\) in the denominator with \\((c,\\overline{c})\\) .For brevity, we introduce \\(\\alpha (E;\\mathcal{C}) = \\| E_{12}\\pmb {c}\\| ^2 +\\| (E^T)_{12}\\overline{\\pmb{c}}\\| ^2.\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1095" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.074, + 0.905, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.265, + 0.908, + 0.337 + ], + "angle": 0, + "content": "Figure 2. Overview of our Summarization Scheme. As input, our method takes a set of dense matches \\(\\{(\\pmb{x}_i,\\bar{\\pmb{x}}_i)\\}_{i = 1}^N\\), where typically \\(N = 10000\\). Through clustering, the matches are grouped into clusters \\(\\mathcal{C}_1,\\ldots ,\\mathcal{C}_K\\), \\(K\\ll N\\), which yield approximately the same geometric constraints on the relative pose. For each cluster, we then perform match summarization, which replaces each group of matches with a representative match \\((c_k,\\bar{c}_k)\\) and a \\(9\\times 9\\) -matrix \\(M_{k}\\) that encodes the geometric constraints. These summarized meta-matches can then used for robust two-view estimation with significant speedup for a very small accuracy loss." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.363, + 0.483, + 0.394 + ], + "angle": 0, + "content": "Then the approximation in (8) lets us write the sum of residuals for a cluster more compactly as" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.402, + 0.483, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} f _ {\\mathrm {c l}} (E; \\mathcal {C}) \\approx \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\alpha (E ; \\mathcal {C})} (9) \\\\ = \\frac {1}{\\alpha (E ; \\mathcal {C})} \\left\\| \\left( \\begin{array}{c} \\bar {\\boldsymbol {x}} _ {1} ^ {T} E \\boldsymbol {x} _ {1} \\\\ \\vdots \\\\ \\bar {\\boldsymbol {x}} _ {n} ^ {T} E \\boldsymbol {x} _ {n} \\end{array} \\right) \\right\\| ^ {2} = \\frac {1}{\\alpha (E ; \\mathcal {C})} \\| A e \\| ^ {2}, (10) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.535, + 0.484, + 0.641 + ], + "angle": 0, + "content": "where \\(n = |\\mathcal{C}_k|\\); \\(\\pmb{e} \\in \\mathbb{R}^9\\) is a vector containing the elements of \\(E\\), and \\(A \\in \\mathbb{R}^{n \\times 9}\\) is the matrix with rows \\(A_i = (\\pmb{x}_i \\otimes \\bar{\\pmb{x}}_i)^T\\) for all \\((\\pmb{x}_i, \\bar{\\pmb{x}}_i) \\in \\mathcal{C}\\). Here, \\(\\otimes\\) denotes the Kronecker product. The trick to efficiently evaluating (10) is that the large matrix \\(A\\) can be replaced with the reduced measurement matrix [34] \\(M \\in \\mathbb{R}^{9 \\times 9}\\) using Cholesky factorization \\(A^T A = M^T M\\), since" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.652, + 0.483, + 0.672 + ], + "angle": 0, + "content": "\\[\n\\left\\| A \\boldsymbol {e} \\right\\| ^ {2} = \\boldsymbol {e} ^ {T} A ^ {T} A \\boldsymbol {e} = \\boldsymbol {e} ^ {T} M ^ {T} M \\boldsymbol {e} = \\left\\| M \\boldsymbol {e} \\right\\| ^ {2}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.683, + 0.483, + 0.728 + ], + "angle": 0, + "content": "Note that this is very fast to compute (in our experiments a total of \\(0.2\\mathrm{ms}\\) for 128 clusters with \\(N = 10,000\\)) and only needs to be done once for each clustering." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.729, + 0.483, + 0.76 + ], + "angle": 0, + "content": "The final approximate cost function for all matches, to be evaluated in each step of the optimization, is" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.771, + 0.482, + 0.825 + ], + "angle": 0, + "content": "\\[\nf _ {\\text {a p p r o x}} (E) = \\sum_ {k = 1} ^ {K} \\min \\left\\{\\frac {1}{\\alpha \\left(E ; \\mathcal {C} _ {k}\\right)} \\| M _ {k} e \\| ^ {2}, | \\mathcal {C} _ {k} | \\tau^ {2} \\right\\}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.483, + 0.871 + ], + "angle": 0, + "content": "In our experiments (Section 4.3) we show that this provides a tight approximation to the sum of Sampson errors, while being significantly faster to compute." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Above, the approximation was applied to the Sampson residual, but it is in principle also applicable to residuals" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.363, + 0.866, + 0.378 + ], + "angle": 0, + "content": "with similar form, e.g. Symmetric Epipolar Distance:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.386, + 0.905, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}})} \\left(\\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {x} \\| ^ {2}} + \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} ^ {T} \\bar {\\boldsymbol {x}} \\| ^ {2}}\\right) \\approx \\frac {\\| A \\boldsymbol {e} \\| ^ {2}}{\\| E _ {1 2} \\boldsymbol {c} \\| ^ {2}} + \\frac {\\| A \\boldsymbol {e} \\| ^ {2}}{\\| E _ {1 2} ^ {T} \\bar {\\boldsymbol {c}} \\| ^ {2}}.\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.437, + 0.646, + 0.455 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.907, + 0.597 + ], + "angle": 0, + "content": "In this section, we evaluate the match clustering and summarization scheme presented in Section 3, through experiments on real image pairs. First, in Section 4.2, we compare clustering methods and perform an ablation study on both the clustering method and number of clusters. In Section 4.3, this is followed by an evaluation of the approximation error of our summarization scheme. Next, in Section 4.4, we perform an ablation study on the integration of our summarization scheme in RANSAC." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.909, + 0.812 + ], + "angle": 0, + "content": "We use two standard benchmarks for relative pose estimation, ScanNet-1500 [11, 35] and MegaDepth-1500 [26, 36], which each contain 1500 image pairs of indoor and outdoor scenes, respectively. For inlier thresholds, we use 1.0 pixels in MegaDepth-1500, and 2.5 pixels in ScanNet-1500. Following prior work, we report the pose error (max of rotation and translation error in degrees) with the Area Under Curve (AUC) up to some threshold. For our ablations and approximation evaluation, we evaluate on MegaDepth-1500, using \\( N = 10000 \\) dense matches from DKM [15]. Finally, in Section 4.5 we show that our results generalize to other state-of-the-art dense matchers and other datasets. We also present results on estimation of the fundamental matrix on the challenging WxBS dataset [29]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.733, + 0.835 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.908, + 0.902 + ], + "angle": 0, + "content": "We implement our approximate residual in an LO-RANSAC framework building on PoseLib [23], which is a state-of-the-art robust estimation library in \\(\\mathrm{C + + }\\) . To get a fair comparison with the dense and subsampled methods," + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1096" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.184 + ], + "angle": 0, + "content": "we implement the standard Sampson residual in the same framework. For the ablations and evaluations in the following sections, our method runs RANSAC using the representative matches from Section 3.1, followed by refinement using the approximate residuals described in Section 3.2. All timings are measured on a modern desktop CPU." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.195, + 0.306, + 0.213 + ], + "angle": 0, + "content": "4.2. Ablation on Clustering" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.218, + 0.484, + 0.369 + ], + "angle": 0, + "content": "First, we explore different approaches for performing the match clustering. We explore both keypoint-based and image-based clustering methods. For the keypoint-based methods, we evaluate K-means clustering on both the 4-dimensional match vectors and the 2-dimensional keypoints from one of the images. Motivated by the geometric constraints in (10), we also evaluate clustering in the 9-dimensional constraint vectors \\( A_{i} = \\boldsymbol{x}_{i}\\otimes \\bar{\\boldsymbol{x}}_{i}\\in \\mathbb{R}^{9} \\). For the K-means clustering experiments we use FAISS [13] on a CPU, running a maximum of 5 iterations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.371, + 0.484, + 0.521 + ], + "angle": 0, + "content": "For image-based clustering, we first segment one of the images, then consider all matches within the same segment as a cluster. We evaluate both a simple 2D-grid segmentation, and a more sophisticated superpixel detection. The 2D grid is created by dividing the image region between the minimum and maximum keypoint coordinates into \\( m^2 \\) equally sized rectangles, where \\( m = \\lceil \\sqrt{K} \\rceil \\). For the superpixel detection, we use SLIC [1, 21]. For each clustering method, we select the representative match by finding the match closest to the centroid." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.522, + 0.484, + 0.734 + ], + "angle": 0, + "content": "In Figure 3, we show some qualitative examples of the different clusterings on two example image pairs from MegaDepth-1500 and ScanNet-1500, respectively. In the top example, we see that the keypoint-based methods (2D, 4D, 9D) all give similar clustering patterns, while in the bottom example 2D clustering leads to a coarser clustering in the second image. This is explained by the smaller image overlap; while 4D and 9D clustering takes the keypoint density in both images into account, 2D clustering only sees the keypoints from one of the images. The image-based methods (Grid and SLIC), on the other hand, lead to larger clusters in both of the image pairs. This is because the segmentation is not proportional to the match density, so they may \"waste\" clusters on image regions with few or no matches." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.903 + ], + "angle": 0, + "content": "In Table 1, we compare the errors and runtimes for different clustering methods on MegaDepth-1500, using a cluster size of 128. We report both the time for clustering, and for estimation using the clusters. We assume that grid-clustering can be done at negligible runtime with an efficient implementation. In the table, we see that the difference between clustering methods is quite small, except for SLIC which is markedly more expensive to calculate. A key difference with image-based clustering, however, is that it only needs to be done once per image. Keypoint-based clustering, on the other hand, needs to be done once per image" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.137 + ], + "angle": 0, + "content": "pair, which can lead to many more total evaluations. For large datasets with high co-visibility, this may be important to consider." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.146, + 0.903, + 0.267 + ], + "angle": 0, + "content": "
MethodAUC@5°εavgRuntime
ClusteringRANSAC
K-means 2D66.43.621.53 ms1.46 ms
K-means 4D66.93.281.22 ms1.44 ms
K-means 9D66.63.251.38 ms1.43 ms
Grid65.93.73≈0 ms1.34 ms
SLIC [21]64.54.0722.38 ms0.97 ms
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.277, + 0.908, + 0.32 + ], + "angle": 0, + "content": "Table 1. Clustering Method Ablation. The table shows the pose errors for each clustering approach on MegaDepth-1500, as well as the average runtime for each clustering strategy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.337, + 0.907, + 0.489 + ], + "angle": 0, + "content": "Next, we evaluate the impact of the number of clusters. Figure 4 shows the AUC@5° (left) and runtime (center) plotted against the number of clusters, as well as AUC@5° vs. runtime (right). We also include the dense baseline (dashed). The results further indicate that all K-means clustering variants perform similarly, and that the performance gets close to the dense baseline as number of clusters increases. Based on these results, we select K-means 4D with \\(K = 128\\) as our main clustering method to be used in the experiments, but note that other choices are viable as well." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.497, + 0.825, + 0.514 + ], + "angle": 0, + "content": "4.3. Evaluation of Approximation Error" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.519, + 0.907, + 0.64 + ], + "angle": 0, + "content": "In Section 3.2, we introduced a proxy residual to approximate the sum of squared Sampson residuals for a cluster. In this section, we experimentally validate this approximation and show that it provides a tight approximation of the true residual. We use 128 clusters per image pair obtained via Kmeans-9D, as defined in the previous section. For each cluster \\(\\mathcal{C}\\), we compute the per-cluster average Sampson residuals exactly as" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.648, + 0.907, + 0.686 + ], + "angle": 0, + "content": "\\[\n\\varepsilon_ {S} ^ {2} = \\frac {1}{| \\mathcal {C} |} \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\mathcal {E} (E _ {g t}, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.697, + 0.831, + 0.712 + ], + "angle": 0, + "content": "and the squared approximate cluster residual as" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.721, + 0.907, + 0.757 + ], + "angle": 0, + "content": "\\[\n\\varepsilon_ {a} ^ {2} = \\frac {1}{| \\mathcal {C} |} \\frac {\\left\\| M \\operatorname {v e c} \\left(E _ {g t}\\right) \\right\\| ^ {2}}{\\left\\| \\left(E _ {g t}\\right) _ {1 2} \\boldsymbol {c} \\right\\| ^ {2} + \\left\\| \\left(E _ {g t} ^ {T}\\right) _ {1 2} \\bar {\\boldsymbol {c}} \\right\\| ^ {2}}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In Figure 5 we show the distribution of the difference \\(\\varepsilon_{S} - \\varepsilon_{a}\\) between the true residual and the approximation, computed on the 1500 image pairs from MegaDepth-1500 with 10000 DKM matches. The residuals are evaluated for the ground truth essential matrix \\(E_{gt} = [t_{gt}]_{\\times}R_{gt}\\). Note that positive values indicate that the approximation gives too small residuals, while negative values correspond to the approximation giving too large residuals. We plot residuals between the \\(1^{\\mathrm{st}}\\) and \\(99^{\\mathrm{th}}\\) percentile. Thus we see that more" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1097" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.087, + 0.363, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.166, + 0.363, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.087, + 0.627, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.165, + 0.627, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.089, + 0.892, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.166, + 0.892, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.246, + 0.367, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.325, + 0.367, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.246, + 0.629, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.325, + 0.629, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.246, + 0.893, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.325, + 0.893, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.413, + 0.907, + 0.456 + ], + "angle": 0, + "content": "Figure 3. Qualitative Comparison of Clustering Methods. We compare different clustering methods on a single image pair from MegaDepth-1500 (top 2 rows) and ScanNet-1500 (bottom 2 rows), respectively. Dense matches from DKM are clustered using three keypoint-based methods (2D, 3D, 9D) and two image-based methods (Grid, SLIC)." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.473, + 0.365, + 0.611 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.473, + 0.628, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.634, + 0.473, + 0.9, + 0.611 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.625, + 0.907, + 0.655 + ], + "angle": 0, + "content": "Figure 4. Clustering Method and Hyperparameter Ablation. The plots show AUC@5° (left), runtime (middle) and AUC-runtime-tradeoff (right) for different clustering methods and number of clusters \\( K \\). We include AUC@5° for the dense baseline as reference." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.68, + 0.483, + 0.725 + ], + "angle": 0, + "content": "than \\(98\\%\\) of the residuals have an absolute approximation error of less than 0.1 pixels, with a small bias towards getting too large residuals." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In Table 2 we compare the inlier ratios obtained through exact and approximate residuals, using the ground-truth pose. We compute average inlier ratios for each of the 1500 image pairs in MegaDepth-1500. Note that we compute the ratio of inlier clusters for \\(\\varepsilon_{a}\\), while for the exact residual \\(\\varepsilon_{S}\\) the inlier ratio is computed per match. We also include the runtime for computing the two residuals for an image pair (equivalent to scoring a model in RANSAC). We see that the approximated residual gives slightly lower inlier ratios, which decrease slowly for coarser clustering, while the speedup in computing time is significant." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.68, + 0.831, + 0.696 + ], + "angle": 0, + "content": "4.4. Ablation on Integration in RANSAC" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.907, + 0.794 + ], + "angle": 0, + "content": "In this section, we explore different ways of integrating our method in robust estimation with RANSAC. Robust estimation is typically done in two stages: the hypothesize-and-verify loop, which alternates between estimating and scoring models, and model refinement, which is done on the best model after the stop criterion is reached." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We evaluate the effect of our summarization scheme both on the model scoring and refinement stages of the estimation. For both stages, we evaluate usage of the representative match residuals (4), and the approximate residuals (12). We will refer to these methods as Center and Approximate, respectively. For the refinement stage, we also evaluate usage of the original residuals (3), referred to as the Dense" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1098" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.482, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.305, + 0.483, + 0.362 + ], + "angle": 0, + "content": "Figure 5. Histogram over Approximation Error. The graph shows the distribution of differences between the true and approximated residuals, i.e. \\(\\varepsilon_{S} - \\varepsilon_{a}\\), scaled with focal length. Statistic taken over all clusters from all image pairs in MegaDepth-1500." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.375, + 0.48, + 0.511 + ], + "angle": 0, + "content": "
Type of residualInlier ratioRuntime (μs)
Med.Avg.Avg.Speedup
Exact0.870.82155.81.0x
Approx. K = 10240.850.8031.15.0x
Approx. K = 5120.840.8014.810.5x
Approx. K = 2560.840.797.121.9x
Approx. K = 1280.820.783.248.7x
Approx. K = 640.800.761.3119.8x
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.521, + 0.484, + 0.633 + ], + "angle": 0, + "content": "Table 2. Comparison of RANSAC Scoring. We compare the inlier ratios when calculating exact and approximate residuals for different numbers of clusters \\( K \\), using the ground-truth essential matrix on all image pairs in MegaDepth-1500. The average and median ratios over all image pairs is reported. Note that inlier ratios are calculated per match for the exact residuals, and per cluster for approximate residuals. The runtime shows the average cost of scoring a model with MSAC in RANSAC." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.765 + ], + "angle": 0, + "content": "method. With two model scoring costs to evaluate (Center and Approximate) and three refinement costs (Center, Approximate, and Dense) this results in 6 possible combinations for our ablation study, in addition to the fully dense baseline. However, we omit Approximate scoring followed by Center refinement, since this would use less information in the refinement than what was used for the model scoring." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.902 + ], + "angle": 0, + "content": "For all of the above methods, we perform model estimation using the 5-point solver [31], sampling from the representative matches. Note that this sampling has no effect on runtime compared to sampling from the dense matches, since convergence of RANSAC is only based on the scoring. Since we get up to 9 constraints from each \\(M_{k}\\) matrix, it is in principle also possible to estimate a model from a single summarized correspondence. However, we found that this generally gives worse performance, see suppl. material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.318 + ], + "angle": 0, + "content": "In Table 3, we show AUC@5° and median runtime for the different combinations of model scoring and refinement costs, compared with a fully dense baseline. We report the average and standard deviation of the AUC for 10 runs using different seeds. In the table, we abbreviate the methods using a three letter combination, where the first letter denotes sampling method, the second letter denotes scoring method, and the third letter denotes refinement method. We see that scoring using Approximate or Center residuals are both significantly faster than Dense. Center scoring is the fastest while not significantly less accurate than Approximate. For refinement, however, Approximate residuals give a small but significant improvement in score over Center, but at an increased runtime. This gives us a possible trade-off, where we can sacrifice some runtime for better accuracy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.318, + 0.905, + 0.485 + ], + "angle": 0, + "content": "We also compare our ablated methods with a dense baseline on subsampled DKM-matches, obtained by querying the balanced DKM sampler for a lower number of correspondences. In Figure 6, we plot AUC@5° vs. runtime for our methods and different number of DKM matches. We see that compared to subsampling, most of our methods give shorter runtime for the same performance; in particular CCC and CCA. This indicates that our summarization better preserves the geometric constraints, compared to reducing the number of correspondences extracted from the matcher." + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.495, + 0.892, + 0.619 + ], + "angle": 0, + "content": "
MethodAUC@5°RT (ms)Speedup
DDD (baseline)67.38±0.1066.01.0x
CAD67.21±0.086.89.8x
CCD67.12±0.085.312.3x
CAA66.87±0.072.724.6x
CCA66.70±0.061.545.2x
CCC65.95±0.101.255.0x
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.628, + 0.905, + 0.713 + ], + "angle": 0, + "content": "Table 3. Ablation on RANSAC Integration. We compare usage of our two summarization schemes in different stages of the estimation. Method names denote the what data is used in sampling, scoring, and refinement. For example, \"CAD\" means sampling from representative matches (C), scoring with the summarized approximation (A), and refinement with the dense matches (D)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.742, + 0.837, + 0.759 + ], + "angle": 0, + "content": "4.5. Comparative Evaluation in RANSAC" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.905, + 0.903 + ], + "angle": 0, + "content": "We evaluate our match summarization scheme on robust estimation using different dense matchers. We run both the CCC- and CCA-methods, since they represent a possible trade-off between accuracy and runtime. We compare with a fully dense baseline on the full set of matches. To show that our results do not depend on the dense matcher, we report results using DKM [15], RoMA [16], and ASPanFormer [7]. From DKM and RoMA, we always sample 10000 matches, while ASPanFormer gives a variable" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1099" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.104, + 0.089, + 0.894, + 0.251 + ], + "angle": 0, + "content": "
MatchesEstimatorMegaDepth-1500ScanNet-1500
AUC@5°AUC@10°AUC@20°RT (ms)SpeedupAUC@5°AUC@10°AUC@20°RT (ms)Speedup
DKMDense67.479.688.066.61.0x31.352.669.968.81.0x
Ours CCA66.779.187.51.545.2x30.952.169.61.546.7x
Ours CCC66.078.787.31.255.0x30.451.769.31.258.6x
RoMADense70.181.589.360.61.0x33.355.272.264.61.0x
Ours CCA70.181.689.41.442.2x33.054.972.01.446.3x
Ours CCC69.381.189.21.252.1x32.854.771.81.158.3x
ASpan-FormerDense66.378.887.514.41.0x30.350.566.515.21.0x
Ours CCA65.878.587.41.59.6x29.749.966.11.510.3x
Ours CCC64.177.486.81.212.1x28.949.265.71.213.0x
SP+LGDense63.777.286.55.0N/A21.839.655.63.0N/A
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.262, + 0.905, + 0.292 + ], + "angle": 0, + "content": "Table 4. Comparison with State-of-the-art. We compare our method with a dense baseline for several dense matchers on both MegaDepth-1500 and ScanNet-1500. For comparison, we also include AUC and runtime for state-of-the-art sparse matches (SP+LG)." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.314, + 0.482, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.531, + 0.483, + 0.575 + ], + "angle": 0, + "content": "Figure 6. AUC-Runtime Trade-off in Ablation Study. The methods in Table 3 are plotted together with dense baseline for different samplings from DKM." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.609, + 0.483, + 0.761 + ], + "angle": 0, + "content": "amount of matches. For image pairs where ASpanFormer gives less than 128 matches, we fall back to using dense estimation. The average results from 10 different seeds are shown in Table 4. The reported runtime is the median over all image pairs. For the convenience of the reader, we have also included estimation from sparse SuperPoint [12] + LightGlue [27] keypoints. In summary, we see that our summarization scheme achieves comparable accuracy to the dense baseline at a fraction of the runtime, irrespective of the dense keypoint matcher used." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.765, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Finally, we present an experiment on the WxBS benchmark [29]. This benchmark contains extremely challenging wide-baseline image pairs, where GT-correspondences are provided. As it does not provide intrinsics, we evaluate fundamental matrix estimation. The metrics are computed by checking consistency of the estimated \\(F\\) with the GT matches. For comparison, we also run on dense matches extracted with MASt3R [25], where we disabled subsampling in the fast reciprocal matching. The results in Table 5" + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.314, + 0.885, + 0.408 + ], + "angle": 0, + "content": "
MatchesEstimatorRecall (10px)↑RT (ms)↓Speedup↑
RoMaDense86.363.01.0x
Ours CCA85.11.4543.3x
Ours CCC83.80.8277.0x
MASt3RDense63.437.11.0x
Ours CCA63.21.4325.8x
Ours CCC61.60.7649.6x
" + }, + { + "type": "table_caption", + "bbox": [ + 0.546, + 0.418, + 0.874, + 0.432 + ], + "angle": 0, + "content": "Table 5. Fundamental Matrix Estimation on WxBS." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.462, + 0.905, + 0.509 + ], + "angle": 0, + "content": "are qualitatively similar to the calibrated setting, showing that our method significantly speeds up the robust estimation with a marginal loss in accuracy." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.525, + 0.634, + 0.541 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.552, + 0.907, + 0.869 + ], + "angle": 0, + "content": "In this work, we have shown that dense keypoint matches, while they improve estimation compared to sparse matches, contain significant redundancies. This redundancy makes it possible to heavily subsample the matches while keeping most of the geometric constraints. We demonstrated a method to significantly speed up geometric estimation with little effect on the estimation accuracy. We additionally showed that this reduction in accuracy can be partially recovered by using our proposed summarized metacorrespondences. With this scheme, we were able to reduce the number of residuals per image pair from the number of matches \\( N \\), to \\( 9K \\) where \\( K \\) is the number of clusters – a hyperparameter we can choose such that \\( N \\ll 9K \\). We also get a potential compression ratio in terms of storage, since the constraints from each cluster is entirely contained in a \\( 9 \\times 9 \\)-matrix, plus a single correspondence. A limitation is that the method only makes sense if the original number of matches is very large. Another limitation of the paper is that we have only focused on speeding up the robust estimation step, while a large part of the total runtime comes from the dense matcher itself." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. The project was supported by ELLIIT and the Swedish Research Council (Grant No. 2023-05424)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1100" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.184 + ], + "angle": 0, + "content": "[1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süssstrunk. Slic superpixels compared to state-of-the-art superpixel methods. 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In International Conference on Computer Vision (ICCV), 2023. 2" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.093, + 0.483, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1102" + } + ] +] \ No newline at end of file diff --git a/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_origin.pdf b/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..004c8fbae562e5ebec7e024540a79012c306f987 --- /dev/null +++ b/2025/Dense Match Summarization for Faster Two-view Estimation/cc201b1e-b30f-4c1e-aa8e-8a269c75e076_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:03122666d8fb5659bb8c16136d068520da03503751b62a85315541a6a4e76ac7 +size 9727543 diff --git a/2025/Dense Match Summarization for Faster Two-view Estimation/full.md b/2025/Dense Match Summarization for Faster Two-view Estimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bb1aa51bfa8207fdc0ce36029f9c0822c6a56e6e --- /dev/null +++ b/2025/Dense Match Summarization for Faster Two-view Estimation/full.md @@ -0,0 +1,329 @@ +# Dense Match Summarization for Faster Two-view Estimation + +Jonathan Astermark, Anders Heyden, and Viktor Larsson +Centre for Mathematical Sciences, Lund University + +{jonathan.astermark, anders.heyden, viktor.larsson}@math.lth.se + +# Abstract + +In this paper, we speed up robust two-view relative pose from dense correspondences. Previous work has shown that dense matchers can significantly improve both accuracy and robustness in the resulting pose. However, the large number of matches comes with a significantly increased runtime during robust estimation in RANSAC. To avoid this, we propose an efficient match summarization scheme which provides comparable accuracy to using the full set of dense matches, while having 10-100x faster runtime. We validate our approach on standard benchmark datasets together with multiple state-of-the-art dense matchers. + +# 1. Introduction + +Determining the two-view camera geometry is an important sub-task in many computer vision problems, e.g. for Simultaneous Localization and Mapping or Structure-from-Motion. The most common approach is to first detect corresponding points in the two views, followed by robust estimation using RANdom Sample Consensus (RANSAC) [18] which both estimates the relative pose and identifies potential outlier matches. Traditionally, keypoint matching is performed by independently detecting keypoints in each view, followed by a matching step, either directly comparing descriptor similarity or using a learned matcher. + +Recently, a lot of attention has been given to so-called detector-free matching, which takes the images as input and directly establishes (semi-)dense correspondences. These matchers produce significantly more matches, compared to the detector-based counterparts, especially in weakly textured image regions, such as walls, floors, and ceilings. Dense matching shows great promise and currently achieves the most accurate two-view estimates in standard benchmarks. However, this comes with a trade-off in runtime, both for running the matching and in the subsequent robust estimation (i.e. RANSAC). + +In this paper, we aim to improve the runtime of the robust estimation step. We show that when using dense matchers, most of the matches provide redundant geometric con + +![](images/e54d6597b5d5d93351611c7428ff027264c33f56117977237f42e4f27d936c8b.jpg) + +![](images/12f4d89663cf79382f11299172b903411bd47a7c500e264ace515b2feacbc45c.jpg) +Figure 1. Relative Pose Estimation from Dense Matches. The top images show 10,000 semi-dense matches from DKM [15] with same colors indicating corresponding points. The large number of matches makes robust estimation with RANSAC accurate (pose error $\epsilon = 0.38^{\circ}$ ) but slow (runtime $t = 98$ ms). In this paper we show that we can get comparable accuracy with significantly lower runtime by sparsifying the dense matches (bottom images). Each sparsified match is represented by a $9 \times 9$ -matrix that summarizes the geometric constraints from nearby matches. + +straints, and we present an efficient match summarization scheme that selects a subset of $\approx 1\%$ of the matches, which we call representative matches, that are used for robust estimation. Using this smaller set of matches, we can obtain a 10-100x speedup with a marginal loss in pose accuracy. In addition, we present an approximation approach for enriching each representative match to capture the geometric constraints of nearby correspondences in a single $9\times 9$ -matrix (regardless of how many neighboring matches are included). This enrichment allows for an even smaller loss of pose accuracy, while still being significantly faster compared to dense correspondence. In Figure 1 we visualize one example from MegaDepth [26]. + +We validate our claims and our approach with extensive experiments and ablation studies on standard benchmarks with different state-of-the-art dense matchers. + +In summary, our contributions are: + +- A scheme for summarizing any dense matches into sparse representative matches, which speeds up the robust estimation by a factor 10-100x, with only a very small loss in accuracy. +- An approximation-based approach to summarize the contributions of each cluster, which we use to refine the output from RANSAC. This lets us maintain the high accuracy from dense matches, with only a small increase in runtime compared to the approach above. +- In experiments on standard benchmarks, with multiple state-of-the-art dense matchers, we are able to consistently show a significant speedup. Furthermore, our experiments show that sparsified dense matches outperform state-of-the-art sparse matches in terms of accuracy. + +# 1.1. Related Work + +Matching and Correspondences. Image correspondence for geometric estimation traditionally works with a detect-then-match paradigm that first identifies keypoints (e.g. SIFT [28], SuperPoint [12]) independently in each image, followed by a matching step. The matching is either done by comparing descriptor similarity ([12, 14, 28]) or more recently via learned matchers ([27, 35]). In [36] the authors instead proposed to perform detection-free matching, which takes an image pair as input and directly regresses semi-dense pixel correspondences. This started a series of work on dense matching ([7, 15, 16, 20]) which improved on the initial work. Common for all dense methods is that they produce significantly more matches compared to classical detector-based methods. By considering both images jointly, the methods are able to propagate strong matches to weaker ones, allowing for even weakly textured regions to be matched between images. + +In benchmarks for two-view relative pose estimation, these methods significantly improve the results in terms of pose accuracy. However, this comes at a trade-off with runtime, as the large number of matches makes robust estimation more costly. In this work, we offset some of this cost by speeding up the robust estimation. Our method is not specific to a particular matcher and can be applied to any dense correspondences. + +Robust Estimation. For robust geometric estimation problems in computer vision, the RANSAC algorithm, originally introduced by Fischler and Bolles [18] in 1981, is the de facto standard. Modern RANSAC variants, while still working with similar principles as the original, usually incorporate some form of local optimization (LORANSAC [10, 24]) as well a more complex scoring beyond simple inlier counting, e.g. MSAC [37] or MAGSAC [3]. Other works improve by integrating various learned components in the pipeline, see e.g. [4, 6, 39]. There are also several works which focus on making RANSAC faster. In [9], the authors propose a probabilistic method (SPRT) for de + +ciding when to early exit. In [22], the authors propose to only perform scoring once two similar models are found. Rais et al. [32] instead aggregate multiple model hypotheses to form the final output. Barath et al. [2] speed up scoring by filtering out regions of the matches which cannot contain inlier correspondences for the current model. PROSAC [8] leverages per-match confidences to sample good models earlier, to speed up convergence. Ni et al. [30] group correspondences and model different inlier ratios for each cluster, which is used both for sampling and stopping criterion. + +The match summarization method proposed in this paper is orthogonal (and could be combined) with the improvements in the above methods. In particular, most prior work focuses on either speeding up the scoring or reducing the number of iterations, but do not consider refinement which is particularly costly with a large number of matches. + +Richer Correspondences. For affine-correspondences (ACs) each match is associated with a $2 \times 2$ matrix representing a local transformation around the keypoints. These matrices can be interpreted as a linearization of the local planar homography [33]. Affine correspondences have been used to derive more efficient minimal estimators ([5, 17, 33, 38]) as well as provide constraints for normal estimation [19]. In this paper, we derive a summarized correspondence expressed with a $9 \times 9$ -matrix. While this matrix is similar to ACs in that it encodes additional local geometric constraints, it does not make assumption on local planarity and yields stronger geometric constraints, even allowing estimation from a single correspondence (see Section 4.4). + +# 2. Background + +Each 2D-point correspondence $(\pmb{x},\bar{\pmb{x}})\in \mathbb{R}^3\times \mathbb{R}^3$ (in homogeneous coordinates) constrain the relative pose by + +$$ +\bar {\boldsymbol {x}} ^ {T} E \boldsymbol {x} = 0, \tag {1} +$$ + +where $E = [t]_{\times}R$ is the essential matrix. As the points $(\pmb{x},\bar{\pmb{x}})$ are measurements from the images, they will contain noise and will not satisfy (1) exactly, even if the match is correct. Thus, in the optimization, a residual such as the Sampson error is commonly used instead, + +$$ +\mathcal {E} (E, \boldsymbol {x}, \bar {\boldsymbol {x}}) = \frac {(\bar {\boldsymbol {x}} ^ {T} E \boldsymbol {x}) ^ {2}}{\| E _ {1 2} \boldsymbol {x} \| ^ {2} + \left\| \left(E ^ {T}\right) _ {1 2} \bar {\boldsymbol {x}} \right\| ^ {2}}, \tag {2} +$$ + +where $E_{12}$ is the first two rows of $E$ . The Sampson error approximates the squared reprojection error, and is used to determine match correctness (inlier or outlier). Most RANSAC-variants additionally use some form of MSAC-scoring [37] for the models, i.e. the essential matrix is chosen by minimizing the sum of truncated residuals + +$$ +f (E) = \sum_ {i = 1} ^ {N} \min \left\{\mathcal {E} \left(E, \boldsymbol {x} _ {i}, \bar {\boldsymbol {x}} _ {i}\right), \tau^ {2} \right\}, \tag {3} +$$ + +where $N$ denotes the number of matches and $\tau \in \mathbb{R}_+$ is the inlier threshold. The model-scoring function $f(E)$ is used both for selecting the best model, and for non-linear refinement. As the number of matches $N$ grows large, evaluating $f(E)$ will dominate the runtime cost in RANSAC. + +# 3. Method + +In this section, we present a method for efficiently summarizing the geometric constraints given by the dense matches. The idea is to first cluster the correspondences into subsets that yield similar geometric constraints, and replace each cluster with a single representative match used in robust estimation. Next, we compute a proxy residual that summarizes the geometric constraints from each cluster into a $9 \times 9$ -matrix, irrespective of cluster size. This allows us to refine the pose without evaluating the full residual (3) in each step of the optimization. Figure 2 shows an overview of our method. In Section 3.1 we discuss different approaches for performing the clustering and selecting representative matches, and in Section 3.2 we derive the proxy residual. + +In the paper we focus the presentation on the calibrated case (essential matrix), but the approach is directly applicable to the uncalibrated (fundamental matrix) setting as well. + +# 3.1. Clustering and Representative Matches + +Given a set of dense matches, our goal is to find a sparse subset of representative matches that capture the same geometric constraints as the full set. To do this, we begin by clustering correspondences that contribute with similar residuals. From each cluster, we then select a single match which serves as a representative of that cluster. + +We base our clustering on the assumption that matches close to each other should lead to similar residuals in (3). This motivates us to group matches based on their position in the two images. A simple approach is to use a standard clustering method, e.g. K-means, applied on the 4-dimensional match vectors (i.e. concatenated keypoint coordinates from both images). Alternatively, matches could be clustered based on the images, e.g. using superpixels. In Section 4.2, we discuss and compare different approaches for clustering and their trade-off in terms of runtime and accuracy for our method. + +For each cluster, we then select the match closest to the cluster centroid (in 4D match space) as the representative match. The set of representative matches $\{(c_i,\bar{c}_i)\}_{i = 1}^K\subset$ $\{(x_{i},\bar{x}_{i})\}_{i = 1}^{N}$ , where $K$ is the number of clusters, can be used directly in RANSAC to estimate the relative pose, using the sub-sampled cost + +$$ +f _ {c} (E) = \sum_ {i = 1} ^ {K} \min \left\{\mathcal {E} \left(E, \boldsymbol {c} _ {i}, \bar {\boldsymbol {c}} _ {i}\right), \tau^ {2} \right\}. \tag {4} +$$ + +Since the runtime of RANSAC is generally dominated by + +scoring and refinement, which grows linearly with the number of matches, significant subsampling can drastically reduce the runtime. In our experiments (Section 4) we show that even when severely subsampling ( $K \approx N / 80$ ), leading to $55\mathrm{x}$ speedup, we can still obtain good relative pose estimates when using this method. This highlights that most constraints in the dense matches are redundant. However, the sparsified matches still will lead to a slight drop in accuracy. In the next section, we propose an approximation which enriches each of the matches to also encode the geometric constraints from the full cluster. + +# 3.2. Dense Match Summarization + +We now present a method for approximating the full cost in (3) using the clustering. The idea is to replace the dense matches in each cluster with a more computationally efficient proxy residual. While we in the previous section reduced the number of residuals from $N$ to $K$ by only considering the representative matches, in this section we will capture more of the geometry per cluster by increasing this number to $9K$ . We do this in two steps; first by assuming that each cluster is either all-inlier or all-outler, and second by approximating the Sampson error in each cluster. + +Let $\mathcal{M} \subset \mathbb{R}^3 \times \mathbb{R}^3$ be the set of dense input matches, and let $\mathcal{C}_1, \ldots, \mathcal{C}_K \subset \mathcal{M}$ be a disjoint clustering of these with associated representative matches $\{(c_k, \bar{c}_k)\}_{k=1}^K$ . By assuming that the matches in each cluster are either all inliers or all outliers, (3) can be rewritten as + +$$ +\begin{array}{l} f (E) = \sum_ {k = 1} ^ {K} \sum_ {(\boldsymbol {x}, \bar {\boldsymbol {x}}) \in \mathcal {C} _ {k}} \min \left\{\mathcal {E} (E, \boldsymbol {x}, \bar {\boldsymbol {x}}), \tau^ {2} \right\} (5) \\ \approx \sum_ {k = 1} ^ {K} \min \left\{\sum_ {\left(\boldsymbol {x}, \bar {\boldsymbol {x}}\right) \in \mathcal {C} _ {k}} \mathcal {E} (E, \boldsymbol {x}, \bar {\boldsymbol {x}}), | \mathcal {C} _ {k} | \tau^ {2} \right\}, (6) \\ \end{array} +$$ + +where $|\mathcal{C}_k|$ denotes the number of matches in cluster $\mathcal{C}_k$ . This means that each cluster either contributes the sum of all its dense residuals, or the constant factor $|\mathcal{C}_k| \tau^2 -$ whichever is smallest. + +Now, consider a single cluster $\mathcal{C}$ with representative match $(c,\bar{c})$ . The sum of all its dense residuals is + +$$ +f _ {c l} (E; \mathcal {C}) = \sum_ {(\boldsymbol {x}, \bar {\boldsymbol {x}}) \in \mathcal {C}} \mathcal {E} (E, \boldsymbol {x}, \bar {\boldsymbol {x}}), \tag {7} +$$ + +i.e. the inner sum in (6). By construction, each match $(\pmb{x},\bar{\pmb{x}})\in \mathcal{C}$ will lie relatively close to the cluster's representative match $(c,\bar{c})$ . This motivates us to approximate the Sampson error (2) for each dense match as + +$$ +\mathcal {E} (E, \boldsymbol {x}, \bar {\boldsymbol {x}}) \approx \frac {(\bar {\boldsymbol {x}} ^ {T} E \boldsymbol {x}) ^ {2}}{\| E _ {1 2} \boldsymbol {c} \| ^ {2} + \| (E ^ {T}) _ {1 2} \bar {\boldsymbol {c}} \| ^ {2}}, \tag {8} +$$ + +i.e. by replacing $(\pmb {x},\bar{\pmb{x}})$ in the denominator with $(c,\overline{c})$ .For brevity, we introduce $\alpha (E;\mathcal{C}) = \| E_{12}\pmb {c}\| ^2 +\| (E^T)_{12}\overline{\pmb{c}}\| ^2.$ + +![](images/598ee4f4384d4bf9369cf9cfbb0463f0b786ef44892799680322330bca3e0c2a.jpg) +Figure 2. Overview of our Summarization Scheme. As input, our method takes a set of dense matches $\{(\pmb{x}_i,\bar{\pmb{x}}_i)\}_{i = 1}^N$ , where typically $N = 10000$ . Through clustering, the matches are grouped into clusters $\mathcal{C}_1,\ldots ,\mathcal{C}_K$ , $K\ll N$ , which yield approximately the same geometric constraints on the relative pose. For each cluster, we then perform match summarization, which replaces each group of matches with a representative match $(c_k,\bar{c}_k)$ and a $9\times 9$ -matrix $M_{k}$ that encodes the geometric constraints. These summarized meta-matches can then used for robust two-view estimation with significant speedup for a very small accuracy loss. + +Then the approximation in (8) lets us write the sum of residuals for a cluster more compactly as + +$$ +\begin{array}{l} f _ {\mathrm {c l}} (E; \mathcal {C}) \approx \sum_ {(\boldsymbol {x}, \bar {\boldsymbol {x}}) \in \mathcal {C}} \frac {(\bar {\boldsymbol {x}} ^ {T} E \boldsymbol {x}) ^ {2}}{\alpha (E ; \mathcal {C})} (9) \\ = \frac {1}{\alpha (E ; \mathcal {C})} \left\| \left( \begin{array}{c} \bar {\boldsymbol {x}} _ {1} ^ {T} E \boldsymbol {x} _ {1} \\ \vdots \\ \bar {\boldsymbol {x}} _ {n} ^ {T} E \boldsymbol {x} _ {n} \end{array} \right) \right\| ^ {2} = \frac {1}{\alpha (E ; \mathcal {C})} \| A e \| ^ {2}, (10) \\ \end{array} +$$ + +where $n = |\mathcal{C}_k|$ ; $\pmb{e} \in \mathbb{R}^9$ is a vector containing the elements of $E$ , and $A \in \mathbb{R}^{n \times 9}$ is the matrix with rows $A_i = (\pmb{x}_i \otimes \bar{\pmb{x}}_i)^T$ for all $(\pmb{x}_i, \bar{\pmb{x}}_i) \in \mathcal{C}$ . Here, $\otimes$ denotes the Kronecker product. The trick to efficiently evaluating (10) is that the large matrix $A$ can be replaced with the reduced measurement matrix [34] $M \in \mathbb{R}^{9 \times 9}$ using Cholesky factorization $A^T A = M^T M$ , since + +$$ +\left\| A \boldsymbol {e} \right\| ^ {2} = \boldsymbol {e} ^ {T} A ^ {T} A \boldsymbol {e} = \boldsymbol {e} ^ {T} M ^ {T} M \boldsymbol {e} = \left\| M \boldsymbol {e} \right\| ^ {2}. \tag {11} +$$ + +Note that this is very fast to compute (in our experiments a total of $0.2\mathrm{ms}$ for 128 clusters with $N = 10,000$ ) and only needs to be done once for each clustering. + +The final approximate cost function for all matches, to be evaluated in each step of the optimization, is + +$$ +f _ {\text {a p p r o x}} (E) = \sum_ {k = 1} ^ {K} \min \left\{\frac {1}{\alpha \left(E ; \mathcal {C} _ {k}\right)} \| M _ {k} e \| ^ {2}, | \mathcal {C} _ {k} | \tau^ {2} \right\}. \tag {12} +$$ + +In our experiments (Section 4.3) we show that this provides a tight approximation to the sum of Sampson errors, while being significantly faster to compute. + +Above, the approximation was applied to the Sampson residual, but it is in principle also applicable to residuals + +with similar form, e.g. Symmetric Epipolar Distance: + +$$ +\sum_ {(\boldsymbol {x}, \bar {\boldsymbol {x}})} \left(\frac {(\bar {\boldsymbol {x}} ^ {T} E \boldsymbol {x}) ^ {2}}{\| E _ {1 2} \boldsymbol {x} \| ^ {2}} + \frac {(\bar {\boldsymbol {x}} ^ {T} E \boldsymbol {x}) ^ {2}}{\| E _ {1 2} ^ {T} \bar {\boldsymbol {x}} \| ^ {2}}\right) \approx \frac {\| A \boldsymbol {e} \| ^ {2}}{\| E _ {1 2} \boldsymbol {c} \| ^ {2}} + \frac {\| A \boldsymbol {e} \| ^ {2}}{\| E _ {1 2} ^ {T} \bar {\boldsymbol {c}} \| ^ {2}}. +$$ + +# 4. Experiments + +In this section, we evaluate the match clustering and summarization scheme presented in Section 3, through experiments on real image pairs. First, in Section 4.2, we compare clustering methods and perform an ablation study on both the clustering method and number of clusters. In Section 4.3, this is followed by an evaluation of the approximation error of our summarization scheme. Next, in Section 4.4, we perform an ablation study on the integration of our summarization scheme in RANSAC. + +We use two standard benchmarks for relative pose estimation, ScanNet-1500 [11, 35] and MegaDepth-1500 [26, 36], which each contain 1500 image pairs of indoor and outdoor scenes, respectively. For inlier thresholds, we use 1.0 pixels in MegaDepth-1500, and 2.5 pixels in ScanNet-1500. Following prior work, we report the pose error (max of rotation and translation error in degrees) with the Area Under Curve (AUC) up to some threshold. For our ablations and approximation evaluation, we evaluate on MegaDepth-1500, using $N = 10000$ dense matches from DKM [15]. Finally, in Section 4.5 we show that our results generalize to other state-of-the-art dense matchers and other datasets. We also present results on estimation of the fundamental matrix on the challenging WxBS dataset [29]. + +# 4.1. Implementation Details + +We implement our approximate residual in an LO-RANSAC framework building on PoseLib [23], which is a state-of-the-art robust estimation library in $\mathrm{C + + }$ . To get a fair comparison with the dense and subsampled methods, + +we implement the standard Sampson residual in the same framework. For the ablations and evaluations in the following sections, our method runs RANSAC using the representative matches from Section 3.1, followed by refinement using the approximate residuals described in Section 3.2. All timings are measured on a modern desktop CPU. + +# 4.2. Ablation on Clustering + +First, we explore different approaches for performing the match clustering. We explore both keypoint-based and image-based clustering methods. For the keypoint-based methods, we evaluate K-means clustering on both the 4-dimensional match vectors and the 2-dimensional keypoints from one of the images. Motivated by the geometric constraints in (10), we also evaluate clustering in the 9-dimensional constraint vectors $A_{i} = \boldsymbol{x}_{i}\otimes \bar{\boldsymbol{x}}_{i}\in \mathbb{R}^{9}$ . For the K-means clustering experiments we use FAISS [13] on a CPU, running a maximum of 5 iterations. + +For image-based clustering, we first segment one of the images, then consider all matches within the same segment as a cluster. We evaluate both a simple 2D-grid segmentation, and a more sophisticated superpixel detection. The 2D grid is created by dividing the image region between the minimum and maximum keypoint coordinates into $m^2$ equally sized rectangles, where $m = \lceil \sqrt{K} \rceil$ . For the superpixel detection, we use SLIC [1, 21]. For each clustering method, we select the representative match by finding the match closest to the centroid. + +In Figure 3, we show some qualitative examples of the different clusterings on two example image pairs from MegaDepth-1500 and ScanNet-1500, respectively. In the top example, we see that the keypoint-based methods (2D, 4D, 9D) all give similar clustering patterns, while in the bottom example 2D clustering leads to a coarser clustering in the second image. This is explained by the smaller image overlap; while 4D and 9D clustering takes the keypoint density in both images into account, 2D clustering only sees the keypoints from one of the images. The image-based methods (Grid and SLIC), on the other hand, lead to larger clusters in both of the image pairs. This is because the segmentation is not proportional to the match density, so they may "waste" clusters on image regions with few or no matches. + +In Table 1, we compare the errors and runtimes for different clustering methods on MegaDepth-1500, using a cluster size of 128. We report both the time for clustering, and for estimation using the clusters. We assume that grid-clustering can be done at negligible runtime with an efficient implementation. In the table, we see that the difference between clustering methods is quite small, except for SLIC which is markedly more expensive to calculate. A key difference with image-based clustering, however, is that it only needs to be done once per image. Keypoint-based clustering, on the other hand, needs to be done once per image + +pair, which can lead to many more total evaluations. For large datasets with high co-visibility, this may be important to consider. + +
MethodAUC@5°εavgRuntime
ClusteringRANSAC
K-means 2D66.43.621.53 ms1.46 ms
K-means 4D66.93.281.22 ms1.44 ms
K-means 9D66.63.251.38 ms1.43 ms
Grid65.93.73≈0 ms1.34 ms
SLIC [21]64.54.0722.38 ms0.97 ms
+ +Table 1. Clustering Method Ablation. The table shows the pose errors for each clustering approach on MegaDepth-1500, as well as the average runtime for each clustering strategy. + +Next, we evaluate the impact of the number of clusters. Figure 4 shows the AUC@5° (left) and runtime (center) plotted against the number of clusters, as well as AUC@5° vs. runtime (right). We also include the dense baseline (dashed). The results further indicate that all K-means clustering variants perform similarly, and that the performance gets close to the dense baseline as number of clusters increases. Based on these results, we select K-means 4D with $K = 128$ as our main clustering method to be used in the experiments, but note that other choices are viable as well. + +# 4.3. Evaluation of Approximation Error + +In Section 3.2, we introduced a proxy residual to approximate the sum of squared Sampson residuals for a cluster. In this section, we experimentally validate this approximation and show that it provides a tight approximation of the true residual. We use 128 clusters per image pair obtained via Kmeans-9D, as defined in the previous section. For each cluster $\mathcal{C}$ , we compute the per-cluster average Sampson residuals exactly as + +$$ +\varepsilon_ {S} ^ {2} = \frac {1}{| \mathcal {C} |} \sum_ {(\boldsymbol {x}, \bar {\boldsymbol {x}}) \in \mathcal {C}} \mathcal {E} (E _ {g t}, \boldsymbol {x}, \bar {\boldsymbol {x}}), \tag {13} +$$ + +and the squared approximate cluster residual as + +$$ +\varepsilon_ {a} ^ {2} = \frac {1}{| \mathcal {C} |} \frac {\left\| M \operatorname {v e c} \left(E _ {g t}\right) \right\| ^ {2}}{\left\| \left(E _ {g t}\right) _ {1 2} \boldsymbol {c} \right\| ^ {2} + \left\| \left(E _ {g t} ^ {T}\right) _ {1 2} \bar {\boldsymbol {c}} \right\| ^ {2}}. \tag {14} +$$ + +In Figure 5 we show the distribution of the difference $\varepsilon_{S} - \varepsilon_{a}$ between the true residual and the approximation, computed on the 1500 image pairs from MegaDepth-1500 with 10000 DKM matches. The residuals are evaluated for the ground truth essential matrix $E_{gt} = [t_{gt}]_{\times}R_{gt}$ . Note that positive values indicate that the approximation gives too small residuals, while negative values correspond to the approximation giving too large residuals. We plot residuals between the $1^{\mathrm{st}}$ and $99^{\mathrm{th}}$ percentile. Thus we see that more + +![](images/e2695a197f0d53daa56a4b0d29e393217e34604da1b0de9c4e849fb28dafc417.jpg) + +![](images/07e2bed2aa36df75402502d2c8f09588915185c7d5a24caf016b91567496eb1c.jpg) + +![](images/edcbcc4e432edc190795e23a7688c283dc3664ce9220e3458c200c60e31fe7b9.jpg) + +![](images/e99ce44fcc900571c8158167ae367f452983ab42d04a80db824d97034613d702.jpg) + +![](images/21e053569e8ec5184868169a0488ca2231ddcc15c8c9e95d0eac50a16002d974.jpg) + +![](images/8cd241df394c8c8548e9695183cae986dba7080f9320a71f050bf37d379ed586.jpg) + +![](images/bff4ebdd4c26f419166404ac88fc61f3573fd570f3420427e56a3664e1352af2.jpg) + +![](images/f42f3a3b74bc5ef11444ba96d01f22cb0f44e1063fba11a54660e69815d0c402.jpg) +Figure 3. Qualitative Comparison of Clustering Methods. We compare different clustering methods on a single image pair from MegaDepth-1500 (top 2 rows) and ScanNet-1500 (bottom 2 rows), respectively. Dense matches from DKM are clustered using three keypoint-based methods (2D, 3D, 9D) and two image-based methods (Grid, SLIC). + +![](images/fd2c134b8051ae07f7cc6be05ef1d3c90ad339bcc7dc29370597c80a2b40e6ec.jpg) + +![](images/d5468c86cbd3499afc411c60a69eaf39e54f66b626c691e13fda64708a27cc40.jpg) + +![](images/abcda61a2fc71b8597f7004707e7b0306e9fc01053f617232553f1b586f79210.jpg) + +![](images/9158f0c8316b4cdf0ca63692ab4157772f88fa1194c9c54ff2049cedd6952348.jpg) + +![](images/6f1b36f531eab4e74693b2ff4a5f5e55ac1c32133264c10b6a4f292ae7c8f13e.jpg) +Figure 4. Clustering Method and Hyperparameter Ablation. The plots show AUC@5° (left), runtime (middle) and AUC-runtime-tradeoff (right) for different clustering methods and number of clusters $K$ . We include AUC@5° for the dense baseline as reference. + +![](images/feb8553163b7861b180c92976f93a5b306b138e8c9a57de25e303d61f9c38bba.jpg) + +![](images/46cf91a0b9056a2f1ea8bafed7c97ff470ffe97f2d21cd1eee3275f38aaa1b5e.jpg) + +than $98\%$ of the residuals have an absolute approximation error of less than 0.1 pixels, with a small bias towards getting too large residuals. + +In Table 2 we compare the inlier ratios obtained through exact and approximate residuals, using the ground-truth pose. We compute average inlier ratios for each of the 1500 image pairs in MegaDepth-1500. Note that we compute the ratio of inlier clusters for $\varepsilon_{a}$ , while for the exact residual $\varepsilon_{S}$ the inlier ratio is computed per match. We also include the runtime for computing the two residuals for an image pair (equivalent to scoring a model in RANSAC). We see that the approximated residual gives slightly lower inlier ratios, which decrease slowly for coarser clustering, while the speedup in computing time is significant. + +# 4.4. Ablation on Integration in RANSAC + +In this section, we explore different ways of integrating our method in robust estimation with RANSAC. Robust estimation is typically done in two stages: the hypothesize-and-verify loop, which alternates between estimating and scoring models, and model refinement, which is done on the best model after the stop criterion is reached. + +We evaluate the effect of our summarization scheme both on the model scoring and refinement stages of the estimation. For both stages, we evaluate usage of the representative match residuals (4), and the approximate residuals (12). We will refer to these methods as Center and Approximate, respectively. For the refinement stage, we also evaluate usage of the original residuals (3), referred to as the Dense + +![](images/315b11a65b2a3c76df529fa1f1670a2d623ef8b44ee706040628a104c3dc02ef.jpg) +Figure 5. Histogram over Approximation Error. The graph shows the distribution of differences between the true and approximated residuals, i.e. $\varepsilon_{S} - \varepsilon_{a}$ , scaled with focal length. Statistic taken over all clusters from all image pairs in MegaDepth-1500. + +
Type of residualInlier ratioRuntime (μs)
Med.Avg.Avg.Speedup
Exact0.870.82155.81.0x
Approx. K = 10240.850.8031.15.0x
Approx. K = 5120.840.8014.810.5x
Approx. K = 2560.840.797.121.9x
Approx. K = 1280.820.783.248.7x
Approx. K = 640.800.761.3119.8x
+ +method. With two model scoring costs to evaluate (Center and Approximate) and three refinement costs (Center, Approximate, and Dense) this results in 6 possible combinations for our ablation study, in addition to the fully dense baseline. However, we omit Approximate scoring followed by Center refinement, since this would use less information in the refinement than what was used for the model scoring. + +For all of the above methods, we perform model estimation using the 5-point solver [31], sampling from the representative matches. Note that this sampling has no effect on runtime compared to sampling from the dense matches, since convergence of RANSAC is only based on the scoring. Since we get up to 9 constraints from each $M_{k}$ matrix, it is in principle also possible to estimate a model from a single summarized correspondence. However, we found that this generally gives worse performance, see suppl. material. + +In Table 3, we show AUC@5° and median runtime for the different combinations of model scoring and refinement costs, compared with a fully dense baseline. We report the average and standard deviation of the AUC for 10 runs using different seeds. In the table, we abbreviate the methods using a three letter combination, where the first letter denotes sampling method, the second letter denotes scoring method, and the third letter denotes refinement method. We see that scoring using Approximate or Center residuals are both significantly faster than Dense. Center scoring is the fastest while not significantly less accurate than Approximate. For refinement, however, Approximate residuals give a small but significant improvement in score over Center, but at an increased runtime. This gives us a possible trade-off, where we can sacrifice some runtime for better accuracy. + +We also compare our ablated methods with a dense baseline on subsampled DKM-matches, obtained by querying the balanced DKM sampler for a lower number of correspondences. In Figure 6, we plot AUC@5° vs. runtime for our methods and different number of DKM matches. We see that compared to subsampling, most of our methods give shorter runtime for the same performance; in particular CCC and CCA. This indicates that our summarization better preserves the geometric constraints, compared to reducing the number of correspondences extracted from the matcher. + +Table 2. Comparison of RANSAC Scoring. We compare the inlier ratios when calculating exact and approximate residuals for different numbers of clusters $K$ , using the ground-truth essential matrix on all image pairs in MegaDepth-1500. The average and median ratios over all image pairs is reported. Note that inlier ratios are calculated per match for the exact residuals, and per cluster for approximate residuals. The runtime shows the average cost of scoring a model with MSAC in RANSAC. + +
MethodAUC@5°RT (ms)Speedup
DDD (baseline)67.38±0.1066.01.0x
CAD67.21±0.086.89.8x
CCD67.12±0.085.312.3x
CAA66.87±0.072.724.6x
CCA66.70±0.061.545.2x
CCC65.95±0.101.255.0x
+ +Table 3. Ablation on RANSAC Integration. We compare usage of our two summarization schemes in different stages of the estimation. Method names denote the what data is used in sampling, scoring, and refinement. For example, "CAD" means sampling from representative matches (C), scoring with the summarized approximation (A), and refinement with the dense matches (D). + +# 4.5. Comparative Evaluation in RANSAC + +We evaluate our match summarization scheme on robust estimation using different dense matchers. We run both the CCC- and CCA-methods, since they represent a possible trade-off between accuracy and runtime. We compare with a fully dense baseline on the full set of matches. To show that our results do not depend on the dense matcher, we report results using DKM [15], RoMA [16], and ASPanFormer [7]. From DKM and RoMA, we always sample 10000 matches, while ASPanFormer gives a variable + +
MatchesEstimatorMegaDepth-1500ScanNet-1500
AUC@5°AUC@10°AUC@20°RT (ms)SpeedupAUC@5°AUC@10°AUC@20°RT (ms)Speedup
DKMDense67.479.688.066.61.0x31.352.669.968.81.0x
Ours CCA66.779.187.51.545.2x30.952.169.61.546.7x
Ours CCC66.078.787.31.255.0x30.451.769.31.258.6x
RoMADense70.181.589.360.61.0x33.355.272.264.61.0x
Ours CCA70.181.689.41.442.2x33.054.972.01.446.3x
Ours CCC69.381.189.21.252.1x32.854.771.81.158.3x
ASpan-FormerDense66.378.887.514.41.0x30.350.566.515.21.0x
Ours CCA65.878.587.41.59.6x29.749.966.11.510.3x
Ours CCC64.177.486.81.212.1x28.949.265.71.213.0x
SP+LGDense63.777.286.55.0N/A21.839.655.63.0N/A
+ +![](images/7cb304f8e6f2ae911030eed053ce0f034e3a1372592042da6e86f1426b2ad7b1.jpg) +Figure 6. AUC-Runtime Trade-off in Ablation Study. The methods in Table 3 are plotted together with dense baseline for different samplings from DKM. + +amount of matches. For image pairs where ASpanFormer gives less than 128 matches, we fall back to using dense estimation. The average results from 10 different seeds are shown in Table 4. The reported runtime is the median over all image pairs. For the convenience of the reader, we have also included estimation from sparse SuperPoint [12] + LightGlue [27] keypoints. In summary, we see that our summarization scheme achieves comparable accuracy to the dense baseline at a fraction of the runtime, irrespective of the dense keypoint matcher used. + +Finally, we present an experiment on the WxBS benchmark [29]. This benchmark contains extremely challenging wide-baseline image pairs, where GT-correspondences are provided. As it does not provide intrinsics, we evaluate fundamental matrix estimation. The metrics are computed by checking consistency of the estimated $F$ with the GT matches. For comparison, we also run on dense matches extracted with MASt3R [25], where we disabled subsampling in the fast reciprocal matching. The results in Table 5 + +Table 4. Comparison with State-of-the-art. We compare our method with a dense baseline for several dense matchers on both MegaDepth-1500 and ScanNet-1500. For comparison, we also include AUC and runtime for state-of-the-art sparse matches (SP+LG). + +
MatchesEstimatorRecall (10px)↑RT (ms)↓Speedup↑
RoMaDense86.363.01.0x
Ours CCA85.11.4543.3x
Ours CCC83.80.8277.0x
MASt3RDense63.437.11.0x
Ours CCA63.21.4325.8x
Ours CCC61.60.7649.6x
+ +Table 5. Fundamental Matrix Estimation on WxBS. + +are qualitatively similar to the calibrated setting, showing that our method significantly speeds up the robust estimation with a marginal loss in accuracy. + +# 5. Conclusion + +In this work, we have shown that dense keypoint matches, while they improve estimation compared to sparse matches, contain significant redundancies. This redundancy makes it possible to heavily subsample the matches while keeping most of the geometric constraints. We demonstrated a method to significantly speed up geometric estimation with little effect on the estimation accuracy. We additionally showed that this reduction in accuracy can be partially recovered by using our proposed summarized metacorrespondences. With this scheme, we were able to reduce the number of residuals per image pair from the number of matches $N$ , to $9K$ where $K$ is the number of clusters – a hyperparameter we can choose such that $N \ll 9K$ . We also get a potential compression ratio in terms of storage, since the constraints from each cluster is entirely contained in a $9 \times 9$ -matrix, plus a single correspondence. A limitation is that the method only makes sense if the original number of matches is very large. Another limitation of the paper is that we have only focused on speeding up the robust estimation step, while a large part of the total runtime comes from the dense matcher itself. + +Acknowledgments. The project was supported by ELLIIT and the Swedish Research Council (Grant No. 2023-05424). + +# References + +[1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süssstrunk. Slic superpixels compared to state-of-the-art superpixel methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(11):2274-2282, 2012. 5 +[2] Daniel Barath and Gábor Valasek. Space-partitioning ransac. In European Conference on Computer Vision (ECCV), 2022. 2 +[3] Daniel Barath, Jiri Matas, and Jana Noskova. MAGSAC: marginalizing sample consensus. In Computer Vision and Pattern Recognition (CVPR), 2019. 2 +[4] Axel Barroso-Laguna, Eric Brachmann, Victor Adrian Prisacariu, Gabriel J Brostow, and Daniyar Turmukhambetov. Two-view geometry scoring without correspondences. In Computer Vision and Pattern Recognition (CVPR), 2023. 2 +[5] Jacob Bentolila and Joseph M Francos. Conic epipolar constraints from affine correspondences. Computer Vision and Image Understanding (CVIU), 2014. 2 +[6] Luca Cavalli, Daniel Barath, Marc Pollefeys, and Viktor Larsson. Consensus-adaptive ransac. arXiv preprint arXiv:2307.14030, 2023. 2 +[7] Hongkai Chen, Zixin Luo, Lei Zhou, Yurun Tian, Mingmin Zhen, Tian Fang, David McKinnon, Yanghai Tsin, and Long Quan. Aspanformer: Detector-free image matching with adaptive span transformer. European Conference on Computer Vision (ECCV), 2022. 2, 7 +[8] O. Chum and J. Matas. Matching with prosac - progressive sample consensus. In Computer Vision and Pattern Recognition (CVPR), 2005. 2 +[9] Ondřej Chum and Jiří Matas. Optimal randomized ransac. IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI), 2008. 2 +[10] Ondrej Chum, Jiří Matas, and Josef Kittler. Locally optimized ransac. In Pattern Recognition, pages 236-243, Berlin, Heidelberg, 2003. Springer Berlin Heidelberg. 2 +[11] Angela Dai, Angel X. Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In Computer Vision and Pattern Recognition (CVPR), 2017. 4 +[12] Daniel DeTone, Tomasz Malisiewicz, and Andrew Rabinovich. Superpoint: Self-supervised interest point detection and description. In Computer Vision and Pattern Recognition Workshops (CVPRW), 2018. 2, 8 +[13] Matthijs Douze, Alexandr Guzhva, Chengqi Deng, Jeff Johnson, Gergely Szilvasy, Pierre-Emmanuel Mazaré, Maria Lomeli, Lucas Hosseini, and Hervé Jégou. The faiss library. arXiv preprint arXiv:2401.08281, 2024. 5 +[14] Mihai Dusmanu, Ignacio Rocco, Tomas Pajdla, Marc Pollefeys, Josef Sivic, Akihiko Torii, and Torsten Sattler. D2-net: A trainable cnn for joint description and detection of local features. In Computer Vision and Pattern Recognition (CVPR), 2019. 2 +[15] Johan Edstedt, Ioannis Athanasiadis, Mårten Wadenbäck, and Michael Felsberg. DKM: Dense kernelized feature + +matching for geometry estimation. In Computer Vision and Pattern Recognition (CVPR), 2023. 1, 2, 4, 7 +[16] Johan Edstedt, Qiyu Sun, Georg Bokman, Mårten Wadenback, and Michael Felsberg. RoMa: Robust Dense Feature Matching. Computer Vision and Pattern Recognition (CVPR), 2024. 2, 7 +[17] Ivan Eichhardt and Dmitry Chetverikov. Affine correspondences between central cameras for rapid relative pose estimation. In European Conference on Computer Vision (ECCV), 2018. 2 +[18] Martin A Fischler and Robert C Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381-395, 1981. 1, 2 +[19] Levente Hajder, Lajos Lóczni, and Daniel Barath. Fast globally optimal surface normal estimation from an affine correspondence. In International Conference on Computer Vision (ICCV), 2023. 2 +[20] Wei Jiang, Eduard Trulls, Jan Hosang, Andrea Tagliasacchi, and Kwang Moo Yi. Cotr: Correspondence transformer for matching across images. In International Conference on Computer Vision (ICCV), 2021. 2 +[21] Alchan Kim. Fast-slic. https://github.com/Algy/fast-slic, 2019.5 +[22] Simon Korman and Roee Litman. Latent ransac. In Computer Vision and Pattern Recognition (CVPR), 2018. 2 +[23] Viktor Larsson and contributors. PoseLib - Minimal Solvers for Camera Pose Estimation. https://github.com/vlarsson/PoseLib, 2020.4 +[24] Karel Lebeda, Jiri Matas, and Ondrej Chum. Fixing the locally optimized ransac-full experimental evaluation. In British Machine Vision Conference (BMVC), 2012. 2 +[25] Vincent Leroy, Yohann Cabon, and Jérôme Revaud. Grounding image matching in 3d with mast3r. In European Conference on Computer Vision (ECCV), 2024. 8 +[26] Zhengqi Li and Noah Snavely. Megadepth: Learning single-view depth prediction from internet photos. In Computer Vision and Pattern Recognition (CVPR), 2018. 1, 4 +[27] Philipp Lindenberger, Paul-Edouard Sarlin, and Marc Pollefeys. LightGlue: Local Feature Matching at Light Speed. In International Conference on Computer Vision (ICCV), 2023. 2, 8 +[28] David G Lowe. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision (IJCV), 60:91-110, 2004. 2 +[29] Dmytro Mishkin, Jiri Matas, Michal Perdoch, and Karel Lenc. WxBS: Wide baseline stereo generalizations. In British Machine Vision Conference (BMVC), 2015. 4, 8 +[30] Kai Ni, Hailin Jin, and Frank Dellaert. Groupsac: Efficient consensus in the presence of groupings. In International Conference on Computer Vision (ICCV), 2009. 2 +[31] David Nister. An efficient solution to the five-point relative pose problem. IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI), 2004. 7 +[32] Martin Rais, Gabriele Facciolo, Enric Meinhardt-Llopis, Jean-Michel Morel, Antoni Buades, and Bartomeu Coll. Accurate motion estimation through random sample aggregated consensus. arXiv preprint arXiv:1701.05268, 2017. 2 + +[33] Carolina Raposo and Joao P Barreto. Theory and practice of structure-from-motion using affine correspondences. In Computer Vision and Pattern Recognition (CVPR), 2016. 2 +[34] A. L. Rodríguez, P. E. López-de Teruel, and A. Ruiz. Reduced epipolar cost for accelerated incremental SfM. In Computer Vision and Pattern Recognition (CVPR), 2011. 4 +[35] Paul-Edouard Sarlin, Daniel DeTone, Tomasz Malisiewicz, and Andrew Rabinovich. Superglue: Learning feature matching with graph neural networks. In Computer Vision and Pattern Recognition (CVPR), 2020. 2, 4 +[36] Jiaming Sun, Zehong Shen, Yuang Wang, Hujun Bao, and Xiaowei Zhou. LoFTR: Detector-free local feature matching with transformers. Computer Vision and Pattern Recognition (CVPR), 2021. 2, 4 +[37] P.H.S. Torr and A. Zisserman. MLESAC: A New Robust Estimator with Application to Estimating Image Geometry. Computer Vision and Image Understanding (CVIU), 78(1): 138-156, 2000. 2 +[38] Jonathan Ventura, Zuzana Kukelova, Torsten Sattler, and Daniel Barath. P1ac: Revisiting absolute pose from a single affine correspondence. In International Conference on Computer Vision (ICCV), 2023. 2 +[39] Tong Wei, Jiri Matas, and Daniel Barath. Adaptive reordering sampler with neurally guided magsac. In International Conference on Computer Vision (ICCV), 2023. 2 \ No newline at end of file diff --git a/2025/Dense Match Summarization for Faster Two-view Estimation/images.zip b/2025/Dense Match Summarization for Faster Two-view Estimation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..5979c33b9e4bd240635b31406e4165d5a2c4295d --- /dev/null +++ b/2025/Dense Match Summarization for Faster Two-view Estimation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:09dabfb411b60ba4cee0e67ffef2e261c732773d717c62a6030807f63abc60d4 +size 695819 diff --git a/2025/Dense Match Summarization for Faster Two-view Estimation/layout.json b/2025/Dense Match Summarization for Faster Two-view Estimation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..dd56153e00a8a7b00ee6d865997b5dd100729479 --- /dev/null +++ b/2025/Dense Match Summarization for Faster Two-view Estimation/layout.json @@ -0,0 +1,8248 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 116, + 103, + 494, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 103, + 494, + 119 + ], + "spans": [ + { + "bbox": [ + 116, + 103, + 494, + 119 + ], + "type": "text", + "content": "Dense Match Summarization for Faster Two-view Estimation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 166, + 144, + 443, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 166, + 144, + 443, + 172 + ], + "spans": [ + { + "bbox": [ + 166, + 144, + 443, + 172 + ], + "type": "text", + "content": "Jonathan Astermark, Anders Heyden, and Viktor Larsson \nCentre for Mathematical Sciences, Lund University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 174, + 473, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 174, + 473, + 185 + ], + "spans": [ + { + "bbox": [ + 133, + 174, + 473, + 185 + ], + "type": "text", + "content": "{jonathan.astermark, anders.heyden, viktor.larsson}@math.lth.se" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "spans": [ + { + "bbox": [ + 151, + 213, + 200, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 239, + 297, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 239, + 297, + 370 + ], + "spans": [ + { + "bbox": [ + 54, + 239, + 297, + 370 + ], + "type": "text", + "content": "In this paper, we speed up robust two-view relative pose from dense correspondences. Previous work has shown that dense matchers can significantly improve both accuracy and robustness in the resulting pose. However, the large number of matches comes with a significantly increased runtime during robust estimation in RANSAC. To avoid this, we propose an efficient match summarization scheme which provides comparable accuracy to using the full set of dense matches, while having 10-100x faster runtime. We validate our approach on standard benchmark datasets together with multiple state-of-the-art dense matchers." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 393, + 135, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 393, + 135, + 405 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 135, + 405 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 414, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 414, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 414, + 295, + 544 + ], + "type": "text", + "content": "Determining the two-view camera geometry is an important sub-task in many computer vision problems, e.g. for Simultaneous Localization and Mapping or Structure-from-Motion. The most common approach is to first detect corresponding points in the two views, followed by robust estimation using RANdom Sample Consensus (RANSAC) [18] which both estimates the relative pose and identifies potential outlier matches. Traditionally, keypoint matching is performed by independently detecting keypoints in each view, followed by a matching step, either directly comparing descriptor similarity or using a learned matcher." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 545, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 677 + ], + "type": "text", + "content": "Recently, a lot of attention has been given to so-called detector-free matching, which takes the images as input and directly establishes (semi-)dense correspondences. These matchers produce significantly more matches, compared to the detector-based counterparts, especially in weakly textured image regions, such as walls, floors, and ceilings. Dense matching shows great promise and currently achieves the most accurate two-view estimates in standard benchmarks. However, this comes with a trade-off in runtime, both for running the matching and in the subsequent robust estimation (i.e. RANSAC)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "In this paper, we aim to improve the runtime of the robust estimation step. 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Relative Pose Estimation from Dense Matches. The top images show 10,000 semi-dense matches from DKM [15] with same colors indicating corresponding points. The large number of matches makes robust estimation with RANSAC accurate (pose error " + }, + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "type": "inline_equation", + "content": "\\epsilon = 0.38^{\\circ}" + }, + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "type": "text", + "content": ") but slow (runtime " + }, + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "type": "inline_equation", + "content": "t = 98" + }, + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "type": "text", + "content": " ms). In this paper we show that we can get comparable accuracy with significantly lower runtime by sparsifying the dense matches (bottom images). Each sparsified match is represented by a " + }, + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "type": "text", + "content": "-matrix that summarizes the geometric constraints from nearby matches." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 506, + 555, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 555, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 555, + 662 + ], + "type": "text", + "content": "straints, and we present an efficient match summarization scheme that selects a subset of " + }, + { + "bbox": [ + 313, + 506, + 555, + 662 + ], + "type": "inline_equation", + "content": "\\approx 1\\%" + }, + { + "bbox": [ + 313, + 506, + 555, + 662 + ], + "type": "text", + "content": " of the matches, which we call representative matches, that are used for robust estimation. Using this smaller set of matches, we can obtain a 10-100x speedup with a marginal loss in pose accuracy. In addition, we present an approximation approach for enriching each representative match to capture the geometric constraints of nearby correspondences in a single " + }, + { + "bbox": [ + 313, + 506, + 555, + 662 + ], + "type": "inline_equation", + "content": "9\\times 9" + }, + { + "bbox": [ + 313, + 506, + 555, + 662 + ], + "type": "text", + "content": "-matrix (regardless of how many neighboring matches are included). This enrichment allows for an even smaller loss of pose accuracy, while still being significantly faster compared to dense correspondence. In Figure 1 we visualize one example from MegaDepth [26]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 663, + 553, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 663, + 553, + 699 + ], + "spans": [ + { + "bbox": [ + 313, + 663, + 553, + 699 + ], + "type": "text", + "content": "We validate our claims and our approach with extensive experiments and ablation studies on standard benchmarks with different state-of-the-art dense matchers." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 701, + 468, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 468, + 713 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 468, + 713 + ], + "type": "text", + "content": "In summary, our contributions are:" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1093" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 239 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "content": "- A scheme for summarizing any dense matches into sparse representative matches, which speeds up the robust estimation by a factor 10-100x, with only a very small loss in accuracy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 121, + 295, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 121, + 295, + 179 + ], + "spans": [ + { + "bbox": [ + 56, + 121, + 295, + 179 + ], + "type": "text", + "content": "- An approximation-based approach to summarize the contributions of each cluster, which we use to refine the output from RANSAC. This lets us maintain the high accuracy from dense matches, with only a small increase in runtime compared to the approach above." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 180, + 294, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 180, + 294, + 239 + ], + "spans": [ + { + "bbox": [ + 55, + 180, + 294, + 239 + ], + "type": "text", + "content": "- In experiments on standard benchmarks, with multiple state-of-the-art dense matchers, we are able to consistently show a significant speedup. Furthermore, our experiments show that sparsified dense matches outperform state-of-the-art sparse matches in terms of accuracy." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 56, + 251, + 143, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 251, + 143, + 262 + ], + "spans": [ + { + "bbox": [ + 56, + 251, + 143, + 262 + ], + "type": "text", + "content": "1.1. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 269, + 296, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 269, + 296, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 269, + 296, + 472 + ], + "type": "text", + "content": "Matching and Correspondences. Image correspondence for geometric estimation traditionally works with a detect-then-match paradigm that first identifies keypoints (e.g. SIFT [28], SuperPoint [12]) independently in each image, followed by a matching step. The matching is either done by comparing descriptor similarity ([12, 14, 28]) or more recently via learned matchers ([27, 35]). In [36] the authors instead proposed to perform detection-free matching, which takes an image pair as input and directly regresses semi-dense pixel correspondences. This started a series of work on dense matching ([7, 15, 16, 20]) which improved on the initial work. Common for all dense methods is that they produce significantly more matches compared to classical detector-based methods. By considering both images jointly, the methods are able to propagate strong matches to weaker ones, allowing for even weakly textured regions to be matched between images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 473, + 296, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 473, + 296, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 473, + 296, + 568 + ], + "type": "text", + "content": "In benchmarks for two-view relative pose estimation, these methods significantly improve the results in terms of pose accuracy. However, this comes at a trade-off with runtime, as the large number of matches makes robust estimation more costly. In this work, we offset some of this cost by speeding up the robust estimation. Our method is not specific to a particular matcher and can be applied to any dense correspondences." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "content": "Robust Estimation. For robust geometric estimation problems in computer vision, the RANSAC algorithm, originally introduced by Fischler and Bolles [18] in 1981, is the de facto standard. Modern RANSAC variants, while still working with similar principles as the original, usually incorporate some form of local optimization (LORANSAC [10, 24]) as well a more complex scoring beyond simple inlier counting, e.g. MSAC [37] or MAGSAC [3]. Other works improve by integrating various learned components in the pipeline, see e.g. [4, 6, 39]. There are also several works which focus on making RANSAC faster. In [9], the authors propose a probabilistic method (SPRT) for de" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 191 + ], + "type": "text", + "content": "ciding when to early exit. In [22], the authors propose to only perform scoring once two similar models are found. Rais et al. [32] instead aggregate multiple model hypotheses to form the final output. Barath et al. [2] speed up scoring by filtering out regions of the matches which cannot contain inlier correspondences for the current model. PROSAC [8] leverages per-match confidences to sample good models earlier, to speed up convergence. Ni et al. [30] group correspondences and model different inlier ratios for each cluster, which is used both for sampling and stopping criterion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 192, + 553, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 192, + 553, + 263 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 553, + 263 + ], + "type": "text", + "content": "The match summarization method proposed in this paper is orthogonal (and could be combined) with the improvements in the above methods. In particular, most prior work focuses on either speeding up the scoring or reducing the number of iterations, but do not consider refinement which is particularly costly with a large number of matches." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 264, + 555, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 264, + 555, + 419 + ], + "spans": [ + { + "bbox": [ + 313, + 264, + 555, + 419 + ], + "type": "text", + "content": "Richer Correspondences. For affine-correspondences (ACs) each match is associated with a " + }, + { + "bbox": [ + 313, + 264, + 555, + 419 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 264, + 555, + 419 + ], + "type": "text", + "content": " matrix representing a local transformation around the keypoints. These matrices can be interpreted as a linearization of the local planar homography [33]. Affine correspondences have been used to derive more efficient minimal estimators ([5, 17, 33, 38]) as well as provide constraints for normal estimation [19]. In this paper, we derive a summarized correspondence expressed with a " + }, + { + "bbox": [ + 313, + 264, + 555, + 419 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 313, + 264, + 555, + 419 + ], + "type": "text", + "content": "-matrix. While this matrix is similar to ACs in that it encodes additional local geometric constraints, it does not make assumption on local planarity and yields stronger geometric constraints, even allowing estimation from a single correspondence (see Section 4.4)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 430, + 392, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 430, + 392, + 443 + ], + "spans": [ + { + "bbox": [ + 314, + 430, + 392, + 443 + ], + "type": "text", + "content": "2. Background" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 449, + 553, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 553, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 553, + 474 + ], + "type": "text", + "content": "Each 2D-point correspondence " + }, + { + "bbox": [ + 313, + 449, + 553, + 474 + ], + "type": "inline_equation", + "content": "(\\pmb{x},\\bar{\\pmb{x}})\\in \\mathbb{R}^3\\times \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 449, + 553, + 474 + ], + "type": "text", + "content": " (in homogeneous coordinates) constrain the relative pose by" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 408, + 480, + 553, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 408, + 480, + 553, + 495 + ], + "spans": [ + { + "bbox": [ + 408, + 480, + 553, + 495 + ], + "type": "interline_equation", + "content": "\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x} = 0, \\tag {1}", + "image_path": "2e58751a09e4df725ce813032bde0e07167df3ee2e626b7c24ff6f9f48b64dda.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 502, + 553, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 553, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 553, + 563 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 502, + 553, + 563 + ], + "type": "inline_equation", + "content": "E = [t]_{\\times}R" + }, + { + "bbox": [ + 313, + 502, + 553, + 563 + ], + "type": "text", + "content": " is the essential matrix. As the points " + }, + { + "bbox": [ + 313, + 502, + 553, + 563 + ], + "type": "inline_equation", + "content": "(\\pmb{x},\\bar{\\pmb{x}})" + }, + { + "bbox": [ + 313, + 502, + 553, + 563 + ], + "type": "text", + "content": " are measurements from the images, they will contain noise and will not satisfy (1) exactly, even if the match is correct. Thus, in the optimization, a residual such as the Sampson error is commonly used instead," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 570, + 553, + 598 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 570, + 553, + 598 + ], + "spans": [ + { + "bbox": [ + 350, + 570, + 553, + 598 + ], + "type": "interline_equation", + "content": "\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}) = \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {x} \\| ^ {2} + \\left\\| \\left(E ^ {T}\\right) _ {1 2} \\bar {\\boldsymbol {x}} \\right\\| ^ {2}}, \\tag {2}", + "image_path": "7c909b9a47e62996ee8450cada9030b4a87852b001be640fec9caa2f7fbacbc5.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 604, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 604, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 604, + 555, + 676 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 604, + 555, + 676 + ], + "type": "inline_equation", + "content": "E_{12}" + }, + { + "bbox": [ + 313, + 604, + 555, + 676 + ], + "type": "text", + "content": " is the first two rows of " + }, + { + "bbox": [ + 313, + 604, + 555, + 676 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 604, + 555, + 676 + ], + "type": "text", + "content": ". The Sampson error approximates the squared reprojection error, and is used to determine match correctness (inlier or outlier). Most RANSAC-variants additionally use some form of MSAC-scoring [37] for the models, i.e. the essential matrix is chosen by minimizing the sum of truncated residuals" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 356, + 683, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 683, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 356, + 683, + 553, + 715 + ], + "type": "interline_equation", + "content": "f (E) = \\sum_ {i = 1} ^ {N} \\min \\left\\{\\mathcal {E} \\left(E, \\boldsymbol {x} _ {i}, \\bar {\\boldsymbol {x}} _ {i}\\right), \\tau^ {2} \\right\\}, \\tag {3}", + "image_path": "72d6ac931beab83d55482dfce64137711c2d916b2881bfc0641ee3a447305f7c.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1094" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " denotes the number of matches and " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "\\tau \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " is the inlier threshold. The model-scoring function " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "f(E)" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " is used both for selecting the best model, and for non-linear refinement. As the number of matches " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " grows large, evaluating " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "f(E)" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " will dominate the runtime cost in RANSAC." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 142, + 111, + 154 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 142, + 111, + 154 + ], + "spans": [ + { + "bbox": [ + 55, + 142, + 111, + 154 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 163, + 296, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 163, + 296, + 317 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 296, + 317 + ], + "type": "text", + "content": "In this section, we present a method for efficiently summarizing the geometric constraints given by the dense matches. The idea is to first cluster the correspondences into subsets that yield similar geometric constraints, and replace each cluster with a single representative match used in robust estimation. Next, we compute a proxy residual that summarizes the geometric constraints from each cluster into a " + }, + { + "bbox": [ + 55, + 163, + 296, + 317 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 55, + 163, + 296, + 317 + ], + "type": "text", + "content": "-matrix, irrespective of cluster size. This allows us to refine the pose without evaluating the full residual (3) in each step of the optimization. Figure 2 shows an overview of our method. In Section 3.1 we discuss different approaches for performing the clustering and selecting representative matches, and in Section 3.2 we derive the proxy residual." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 318, + 296, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 296, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 296, + 354 + ], + "type": "text", + "content": "In the paper we focus the presentation on the calibrated case (essential matrix), but the approach is directly applicable to the uncalibrated (fundamental matrix) setting as well." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 361, + 263, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 263, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 263, + 373 + ], + "type": "text", + "content": "3.1. Clustering and Representative Matches" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 378, + 296, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 378, + 296, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 378, + 296, + 449 + ], + "type": "text", + "content": "Given a set of dense matches, our goal is to find a sparse subset of representative matches that capture the same geometric constraints as the full set. To do this, we begin by clustering correspondences that contribute with similar residuals. From each cluster, we then select a single match which serves as a representative of that cluster." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 450, + 296, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 296, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 296, + 581 + ], + "type": "text", + "content": "We base our clustering on the assumption that matches close to each other should lead to similar residuals in (3). This motivates us to group matches based on their position in the two images. A simple approach is to use a standard clustering method, e.g. K-means, applied on the 4-dimensional match vectors (i.e. concatenated keypoint coordinates from both images). Alternatively, matches could be clustered based on the images, e.g. using superpixels. In Section 4.2, we discuss and compare different approaches for clustering and their trade-off in terms of runtime and accuracy for our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 582, + 296, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 654 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 654 + ], + "type": "text", + "content": "For each cluster, we then select the match closest to the cluster centroid (in 4D match space) as the representative match. The set of representative matches " + }, + { + "bbox": [ + 55, + 582, + 296, + 654 + ], + "type": "inline_equation", + "content": "\\{(c_i,\\bar{c}_i)\\}_{i = 1}^K\\subset" + }, + { + "bbox": [ + 55, + 582, + 296, + 654 + ], + "type": "inline_equation", + "content": "\\{(x_{i},\\bar{x}_{i})\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 55, + 582, + 296, + 654 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 582, + 296, + 654 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 582, + 296, + 654 + ], + "type": "text", + "content": " is the number of clusters, can be used directly in RANSAC to estimate the relative pose, using the sub-sampled cost" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 97, + 661, + 296, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 661, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 97, + 661, + 296, + 693 + ], + "type": "interline_equation", + "content": "f _ {c} (E) = \\sum_ {i = 1} ^ {K} \\min \\left\\{\\mathcal {E} \\left(E, \\boldsymbol {c} _ {i}, \\bar {\\boldsymbol {c}} _ {i}\\right), \\tau^ {2} \\right\\}. \\tag {4}", + "image_path": "06906aeb161ee11c44c65b3c9b996fafb5cf07f479bdfe7898dcb83c58f6b45a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "content": "Since the runtime of RANSAC is generally dominated by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": "scoring and refinement, which grows linearly with the number of matches, significant subsampling can drastically reduce the runtime. In our experiments (Section 4) we show that even when severely subsampling (" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "inline_equation", + "content": "K \\approx N / 80" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": "), leading to " + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "inline_equation", + "content": "55\\mathrm{x}" + }, + { + "bbox": [ + 313, + 72, + 555, + 204 + ], + "type": "text", + "content": " speedup, we can still obtain good relative pose estimates when using this method. This highlights that most constraints in the dense matches are redundant. However, the sparsified matches still will lead to a slight drop in accuracy. In the next section, we propose an approximation which enriches each of the matches to also encode the geometric constraints from the full cluster." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 210, + 474, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 210, + 474, + 221 + ], + "spans": [ + { + "bbox": [ + 313, + 210, + 474, + 221 + ], + "type": "text", + "content": "3.2. Dense Match Summarization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "type": "text", + "content": "We now present a method for approximating the full cost in (3) using the clustering. The idea is to replace the dense matches in each cluster with a more computationally efficient proxy residual. While we in the previous section reduced the number of residuals from " + }, + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "type": "text", + "content": " by only considering the representative matches, in this section we will capture more of the geometry per cluster by increasing this number to " + }, + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "type": "inline_equation", + "content": "9K" + }, + { + "bbox": [ + 313, + 228, + 555, + 346 + ], + "type": "text", + "content": ". We do this in two steps; first by assuming that each cluster is either all-inlier or all-outler, and second by approximating the Sampson error in each cluster." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{M} \\subset \\mathbb{R}^3 \\times \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "type": "text", + "content": " be the set of dense input matches, and let " + }, + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1, \\ldots, \\mathcal{C}_K \\subset \\mathcal{M}" + }, + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "type": "text", + "content": " be a disjoint clustering of these with associated representative matches " + }, + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "type": "inline_equation", + "content": "\\{(c_k, \\bar{c}_k)\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 346, + 554, + 407 + ], + "type": "text", + "content": ". By assuming that the matches in each cluster are either all inliers or all outliers, (3) can be rewritten as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 325, + 413, + 555, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 413, + 555, + 488 + ], + "spans": [ + { + "bbox": [ + 325, + 413, + 555, + 488 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} f (E) = \\sum_ {k = 1} ^ {K} \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C} _ {k}} \\min \\left\\{\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tau^ {2} \\right\\} (5) \\\\ \\approx \\sum_ {k = 1} ^ {K} \\min \\left\\{\\sum_ {\\left(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}\\right) \\in \\mathcal {C} _ {k}} \\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), | \\mathcal {C} _ {k} | \\tau^ {2} \\right\\}, (6) \\\\ \\end{array}", + "image_path": "e009f3eb0920ff4130c395d41946e21bb92870ff47ffbb059bfc63f6c93ef1a1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "type": "inline_equation", + "content": "|\\mathcal{C}_k|" + }, + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "type": "text", + "content": " denotes the number of matches in cluster " + }, + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_k" + }, + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "type": "text", + "content": ". This means that each cluster either contributes the sum of all its dense residuals, or the constant factor " + }, + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "type": "inline_equation", + "content": "|\\mathcal{C}_k| \\tau^2 -" + }, + { + "bbox": [ + 313, + 493, + 555, + 539 + ], + "type": "text", + "content": " whichever is smallest." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 541, + 554, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 541, + 554, + 565 + ], + "spans": [ + { + "bbox": [ + 313, + 541, + 554, + 565 + ], + "type": "text", + "content": "Now, consider a single cluster " + }, + { + "bbox": [ + 313, + 541, + 554, + 565 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 313, + 541, + 554, + 565 + ], + "type": "text", + "content": " with representative match " + }, + { + "bbox": [ + 313, + 541, + 554, + 565 + ], + "type": "inline_equation", + "content": "(c,\\bar{c})" + }, + { + "bbox": [ + 313, + 541, + 554, + 565 + ], + "type": "text", + "content": ". The sum of all its dense residuals is" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 368, + 571, + 555, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 571, + 555, + 597 + ], + "spans": [ + { + "bbox": [ + 368, + 571, + 555, + 597 + ], + "type": "interline_equation", + "content": "f _ {c l} (E; \\mathcal {C}) = \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tag {7}", + "image_path": "4185332077b148b7c4616bb3c804f09e998c985e004600eaa01a83ba2bb93ebe.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 604, + 554, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 604, + 554, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 604, + 554, + 651 + ], + "type": "text", + "content": "i.e. the inner sum in (6). By construction, each match " + }, + { + "bbox": [ + 313, + 604, + 554, + 651 + ], + "type": "inline_equation", + "content": "(\\pmb{x},\\bar{\\pmb{x}})\\in \\mathcal{C}" + }, + { + "bbox": [ + 313, + 604, + 554, + 651 + ], + "type": "text", + "content": " will lie relatively close to the cluster's representative match " + }, + { + "bbox": [ + 313, + 604, + 554, + 651 + ], + "type": "inline_equation", + "content": "(c,\\bar{c})" + }, + { + "bbox": [ + 313, + 604, + 554, + 651 + ], + "type": "text", + "content": ". This motivates us to approximate the Sampson error (2) for each dense match as" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 352, + 656, + 554, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 656, + 554, + 685 + ], + "spans": [ + { + "bbox": [ + 352, + 656, + 554, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {E} (E, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\approx \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {c} \\| ^ {2} + \\| (E ^ {T}) _ {1 2} \\bar {\\boldsymbol {c}} \\| ^ {2}}, \\tag {8}", + "image_path": "1762f65f4561a20d14bee17f487dacbe9d57b5bd7ab77d096f502c6e5993b218.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": "i.e. by replacing " + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "inline_equation", + "content": "(\\pmb {x},\\bar{\\pmb{x}})" + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": " in the denominator with " + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "inline_equation", + "content": "(c,\\overline{c})" + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "text", + "content": " .For brevity, we introduce " + }, + { + "bbox": [ + 313, + 689, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\alpha (E;\\mathcal{C}) = \\| E_{12}\\pmb {c}\\| ^2 +\\| (E^T)_{12}\\overline{\\pmb{c}}\\| ^2." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1095" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 58, + 553, + 205 + ], + "blocks": [ + { + "bbox": [ + 56, + 58, + 553, + 205 + ], + "lines": [ + { + "bbox": [ + 56, + 58, + 553, + 205 + ], + "spans": [ + { + "bbox": [ + 56, + 58, + 553, + 205 + ], + "type": "image", + "image_path": "598ee4f4384d4bf9369cf9cfbb0463f0b786ef44892799680322330bca3e0c2a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "lines": [ + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "text", + "content": "Figure 2. Overview of our Summarization Scheme. As input, our method takes a set of dense matches " + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "inline_equation", + "content": "\\{(\\pmb{x}_i,\\bar{\\pmb{x}}_i)\\}_{i = 1}^N" + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "text", + "content": ", where typically " + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "inline_equation", + "content": "N = 10000" + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "text", + "content": ". Through clustering, the matches are grouped into clusters " + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1,\\ldots ,\\mathcal{C}_K" + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "inline_equation", + "content": "K\\ll N" + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "text", + "content": ", which yield approximately the same geometric constraints on the relative pose. For each cluster, we then perform match summarization, which replaces each group of matches with a representative match " + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "inline_equation", + "content": "(c_k,\\bar{c}_k)" + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "text", + "content": " and a " + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "inline_equation", + "content": "9\\times 9" + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "text", + "content": " -matrix " + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "inline_equation", + "content": "M_{k}" + }, + { + "bbox": [ + 55, + 209, + 555, + 266 + ], + "type": "text", + "content": " that encodes the geometric constraints. These summarized meta-matches can then used for robust two-view estimation with significant speedup for a very small accuracy loss." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 287, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 287, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 287, + 295, + 312 + ], + "type": "text", + "content": "Then the approximation in (8) lets us write the sum of residuals for a cluster more compactly as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 318, + 295, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 318, + 295, + 413 + ], + "spans": [ + { + "bbox": [ + 58, + 318, + 295, + 413 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} f _ {\\mathrm {c l}} (E; \\mathcal {C}) \\approx \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\alpha (E ; \\mathcal {C})} (9) \\\\ = \\frac {1}{\\alpha (E ; \\mathcal {C})} \\left\\| \\left( \\begin{array}{c} \\bar {\\boldsymbol {x}} _ {1} ^ {T} E \\boldsymbol {x} _ {1} \\\\ \\vdots \\\\ \\bar {\\boldsymbol {x}} _ {n} ^ {T} E \\boldsymbol {x} _ {n} \\end{array} \\right) \\right\\| ^ {2} = \\frac {1}{\\alpha (E ; \\mathcal {C})} \\| A e \\| ^ {2}, (10) \\\\ \\end{array}", + "image_path": "30b87922ce20a6b166d3e4b7fd1685cb31ce826fe90c752a14b8f885ca11ac04.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "n = |\\mathcal{C}_k|" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "\\pmb{e} \\in \\mathbb{R}^9" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": " is a vector containing the elements of " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "A \\in \\mathbb{R}^{n \\times 9}" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": " is the matrix with rows " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "A_i = (\\pmb{x}_i \\otimes \\bar{\\pmb{x}}_i)^T" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "(\\pmb{x}_i, \\bar{\\pmb{x}}_i) \\in \\mathcal{C}" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": " denotes the Kronecker product. The trick to efficiently evaluating (10) is that the large matrix " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": " can be replaced with the reduced measurement matrix [34] " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{R}^{9 \\times 9}" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": " using Cholesky factorization " + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "inline_equation", + "content": "A^T A = M^T M" + }, + { + "bbox": [ + 55, + 423, + 296, + 507 + ], + "type": "text", + "content": ", since" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 73, + 516, + 295, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 516, + 295, + 532 + ], + "spans": [ + { + "bbox": [ + 73, + 516, + 295, + 532 + ], + "type": "interline_equation", + "content": "\\left\\| A \\boldsymbol {e} \\right\\| ^ {2} = \\boldsymbol {e} ^ {T} A ^ {T} A \\boldsymbol {e} = \\boldsymbol {e} ^ {T} M ^ {T} M \\boldsymbol {e} = \\left\\| M \\boldsymbol {e} \\right\\| ^ {2}. \\tag {11}", + "image_path": "d6212f2544521bfd8ca6904198ba8dce23fa518ebdddbd1fde9779dcf3c6ff11.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 540, + 295, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 295, + 576 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 295, + 576 + ], + "type": "text", + "content": "Note that this is very fast to compute (in our experiments a total of " + }, + { + "bbox": [ + 55, + 540, + 295, + 576 + ], + "type": "inline_equation", + "content": "0.2\\mathrm{ms}" + }, + { + "bbox": [ + 55, + 540, + 295, + 576 + ], + "type": "text", + "content": " for 128 clusters with " + }, + { + "bbox": [ + 55, + 540, + 295, + 576 + ], + "type": "inline_equation", + "content": "N = 10,000" + }, + { + "bbox": [ + 55, + 540, + 295, + 576 + ], + "type": "text", + "content": ") and only needs to be done once for each clustering." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 577, + 295, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 577, + 295, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 577, + 295, + 601 + ], + "type": "text", + "content": "The final approximate cost function for all matches, to be evaluated in each step of the optimization, is" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 63, + 610, + 294, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 610, + 294, + 653 + ], + "spans": [ + { + "bbox": [ + 63, + 610, + 294, + 653 + ], + "type": "interline_equation", + "content": "f _ {\\text {a p p r o x}} (E) = \\sum_ {k = 1} ^ {K} \\min \\left\\{\\frac {1}{\\alpha \\left(E ; \\mathcal {C} _ {k}\\right)} \\| M _ {k} e \\| ^ {2}, | \\mathcal {C} _ {k} | \\tau^ {2} \\right\\}. \\tag {12}", + "image_path": "6ae281ffc2cb768cc08bf08552ee82339c77b49307d9bc3d76cec1e2454845df.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 295, + 689 + ], + "type": "text", + "content": "In our experiments (Section 4.3) we show that this provides a tight approximation to the sum of Sampson errors, while being significantly faster to compute." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Above, the approximation was applied to the Sampson residual, but it is in principle also applicable to residuals" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 287, + 529, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 287, + 529, + 299 + ], + "spans": [ + { + "bbox": [ + 313, + 287, + 529, + 299 + ], + "type": "text", + "content": "with similar form, e.g. Symmetric Epipolar Distance:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 305, + 553, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 305, + 553, + 338 + ], + "spans": [ + { + "bbox": [ + 315, + 305, + 553, + 338 + ], + "type": "interline_equation", + "content": "\\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}})} \\left(\\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} \\boldsymbol {x} \\| ^ {2}} + \\frac {(\\bar {\\boldsymbol {x}} ^ {T} E \\boldsymbol {x}) ^ {2}}{\\| E _ {1 2} ^ {T} \\bar {\\boldsymbol {x}} \\| ^ {2}}\\right) \\approx \\frac {\\| A \\boldsymbol {e} \\| ^ {2}}{\\| E _ {1 2} \\boldsymbol {c} \\| ^ {2}} + \\frac {\\| A \\boldsymbol {e} \\| ^ {2}}{\\| E _ {1 2} ^ {T} \\bar {\\boldsymbol {c}} \\| ^ {2}}.", + "image_path": "32dac32955d68aea315ec15a271900bd763e3bcd51742fd901b76b12023239e0.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 346, + 395, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 395, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 395, + 360 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 366, + 555, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 555, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 555, + 472 + ], + "type": "text", + "content": "In this section, we evaluate the match clustering and summarization scheme presented in Section 3, through experiments on real image pairs. First, in Section 4.2, we compare clustering methods and perform an ablation study on both the clustering method and number of clusters. In Section 4.3, this is followed by an evaluation of the approximation error of our summarization scheme. Next, in Section 4.4, we perform an ablation study on the integration of our summarization scheme in RANSAC." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 474, + 556, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 556, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 556, + 643 + ], + "type": "text", + "content": "We use two standard benchmarks for relative pose estimation, ScanNet-1500 [11, 35] and MegaDepth-1500 [26, 36], which each contain 1500 image pairs of indoor and outdoor scenes, respectively. For inlier thresholds, we use 1.0 pixels in MegaDepth-1500, and 2.5 pixels in ScanNet-1500. Following prior work, we report the pose error (max of rotation and translation error in degrees) with the Area Under Curve (AUC) up to some threshold. For our ablations and approximation evaluation, we evaluate on MegaDepth-1500, using " + }, + { + "bbox": [ + 313, + 474, + 556, + 643 + ], + "type": "inline_equation", + "content": "N = 10000" + }, + { + "bbox": [ + 313, + 474, + 556, + 643 + ], + "type": "text", + "content": " dense matches from DKM [15]. Finally, in Section 4.5 we show that our results generalize to other state-of-the-art dense matchers and other datasets. We also present results on estimation of the fundamental matrix on the challenging WxBS dataset [29]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 648, + 448, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 448, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 448, + 661 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "content": "We implement our approximate residual in an LO-RANSAC framework building on PoseLib [23], which is a state-of-the-art robust estimation library in " + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{C + + }" + }, + { + "bbox": [ + 313, + 665, + 555, + 714 + ], + "type": "text", + "content": " . To get a fair comparison with the dense and subsampled methods," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1096" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "text", + "content": "we implement the standard Sampson residual in the same framework. For the ablations and evaluations in the following sections, our method runs RANSAC using the representative matches from Section 3.1, followed by refinement using the approximate residuals described in Section 3.2. All timings are measured on a modern desktop CPU." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 154, + 187, + 168 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 154, + 187, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 154, + 187, + 168 + ], + "type": "text", + "content": "4.2. Ablation on Clustering" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 172, + 296, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 172, + 296, + 292 + ], + "spans": [ + { + "bbox": [ + 55, + 172, + 296, + 292 + ], + "type": "text", + "content": "First, we explore different approaches for performing the match clustering. We explore both keypoint-based and image-based clustering methods. For the keypoint-based methods, we evaluate K-means clustering on both the 4-dimensional match vectors and the 2-dimensional keypoints from one of the images. Motivated by the geometric constraints in (10), we also evaluate clustering in the 9-dimensional constraint vectors " + }, + { + "bbox": [ + 55, + 172, + 296, + 292 + ], + "type": "inline_equation", + "content": "A_{i} = \\boldsymbol{x}_{i}\\otimes \\bar{\\boldsymbol{x}}_{i}\\in \\mathbb{R}^{9}" + }, + { + "bbox": [ + 55, + 172, + 296, + 292 + ], + "type": "text", + "content": ". For the K-means clustering experiments we use FAISS [13] on a CPU, running a maximum of 5 iterations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 293, + 296, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 293, + 296, + 412 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 296, + 412 + ], + "type": "text", + "content": "For image-based clustering, we first segment one of the images, then consider all matches within the same segment as a cluster. We evaluate both a simple 2D-grid segmentation, and a more sophisticated superpixel detection. The 2D grid is created by dividing the image region between the minimum and maximum keypoint coordinates into " + }, + { + "bbox": [ + 55, + 293, + 296, + 412 + ], + "type": "inline_equation", + "content": "m^2" + }, + { + "bbox": [ + 55, + 293, + 296, + 412 + ], + "type": "text", + "content": " equally sized rectangles, where " + }, + { + "bbox": [ + 55, + 293, + 296, + 412 + ], + "type": "inline_equation", + "content": "m = \\lceil \\sqrt{K} \\rceil" + }, + { + "bbox": [ + 55, + 293, + 296, + 412 + ], + "type": "text", + "content": ". For the superpixel detection, we use SLIC [1, 21]. For each clustering method, we select the representative match by finding the match closest to the centroid." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 413, + 296, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 413, + 296, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 413, + 296, + 581 + ], + "type": "text", + "content": "In Figure 3, we show some qualitative examples of the different clusterings on two example image pairs from MegaDepth-1500 and ScanNet-1500, respectively. In the top example, we see that the keypoint-based methods (2D, 4D, 9D) all give similar clustering patterns, while in the bottom example 2D clustering leads to a coarser clustering in the second image. This is explained by the smaller image overlap; while 4D and 9D clustering takes the keypoint density in both images into account, 2D clustering only sees the keypoints from one of the images. The image-based methods (Grid and SLIC), on the other hand, lead to larger clusters in both of the image pairs. This is because the segmentation is not proportional to the match density, so they may \"waste\" clusters on image regions with few or no matches." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "content": "In Table 1, we compare the errors and runtimes for different clustering methods on MegaDepth-1500, using a cluster size of 128. We report both the time for clustering, and for estimation using the clusters. We assume that grid-clustering can be done at negligible runtime with an efficient implementation. In the table, we see that the difference between clustering methods is quite small, except for SLIC which is markedly more expensive to calculate. A key difference with image-based clustering, however, is that it only needs to be done once per image. Keypoint-based clustering, on the other hand, needs to be done once per image" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "content": "pair, which can lead to many more total evaluations. For large datasets with high co-visibility, this may be important to consider." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 318, + 115, + 552, + 211 + ], + "blocks": [ + { + "bbox": [ + 318, + 115, + 552, + 211 + ], + "lines": [ + { + "bbox": [ + 318, + 115, + 552, + 211 + ], + "spans": [ + { + "bbox": [ + 318, + 115, + 552, + 211 + ], + "type": "table", + "html": "
MethodAUC@5°εavgRuntime
ClusteringRANSAC
K-means 2D66.43.621.53 ms1.46 ms
K-means 4D66.93.281.22 ms1.44 ms
K-means 9D66.63.251.38 ms1.43 ms
Grid65.93.73≈0 ms1.34 ms
SLIC [21]64.54.0722.38 ms0.97 ms
", + "image_path": "eb6bfbfe3d12235da0665e5d9162e610ae8dbc860ebfcc6c1e223af1d7da05dd.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 219, + 555, + 253 + ], + "lines": [ + { + "bbox": [ + 313, + 219, + 555, + 253 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 555, + 253 + ], + "type": "text", + "content": "Table 1. Clustering Method Ablation. The table shows the pose errors for each clustering approach on MegaDepth-1500, as well as the average runtime for each clustering strategy." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 266, + 555, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 266, + 555, + 387 + ], + "spans": [ + { + "bbox": [ + 313, + 266, + 555, + 387 + ], + "type": "text", + "content": "Next, we evaluate the impact of the number of clusters. Figure 4 shows the AUC@5° (left) and runtime (center) plotted against the number of clusters, as well as AUC@5° vs. runtime (right). We also include the dense baseline (dashed). The results further indicate that all K-means clustering variants perform similarly, and that the performance gets close to the dense baseline as number of clusters increases. Based on these results, we select K-means 4D with " + }, + { + "bbox": [ + 313, + 266, + 555, + 387 + ], + "type": "inline_equation", + "content": "K = 128" + }, + { + "bbox": [ + 313, + 266, + 555, + 387 + ], + "type": "text", + "content": " as our main clustering method to be used in the experiments, but note that other choices are viable as well." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 393, + 504, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 393, + 504, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 393, + 504, + 407 + ], + "type": "text", + "content": "4.3. Evaluation of Approximation Error" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 411, + 555, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 555, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 555, + 506 + ], + "type": "text", + "content": "In Section 3.2, we introduced a proxy residual to approximate the sum of squared Sampson residuals for a cluster. In this section, we experimentally validate this approximation and show that it provides a tight approximation of the true residual. We use 128 clusters per image pair obtained via Kmeans-9D, as defined in the previous section. For each cluster " + }, + { + "bbox": [ + 313, + 411, + 555, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 313, + 411, + 555, + 506 + ], + "type": "text", + "content": ", we compute the per-cluster average Sampson residuals exactly as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 370, + 513, + 555, + 543 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 513, + 555, + 543 + ], + "spans": [ + { + "bbox": [ + 370, + 513, + 555, + 543 + ], + "type": "interline_equation", + "content": "\\varepsilon_ {S} ^ {2} = \\frac {1}{| \\mathcal {C} |} \\sum_ {(\\boldsymbol {x}, \\bar {\\boldsymbol {x}}) \\in \\mathcal {C}} \\mathcal {E} (E _ {g t}, \\boldsymbol {x}, \\bar {\\boldsymbol {x}}), \\tag {13}", + "image_path": "2639cf3824e9c3a63dbd9bfcfd509edd63bf36fbc066312c592f2b64c36e9706.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 552, + 508, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 508, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 508, + 563 + ], + "type": "text", + "content": "and the squared approximate cluster residual as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 354, + 571, + 555, + 599 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 571, + 555, + 599 + ], + "spans": [ + { + "bbox": [ + 354, + 571, + 555, + 599 + ], + "type": "interline_equation", + "content": "\\varepsilon_ {a} ^ {2} = \\frac {1}{| \\mathcal {C} |} \\frac {\\left\\| M \\operatorname {v e c} \\left(E _ {g t}\\right) \\right\\| ^ {2}}{\\left\\| \\left(E _ {g t}\\right) _ {1 2} \\boldsymbol {c} \\right\\| ^ {2} + \\left\\| \\left(E _ {g t} ^ {T}\\right) _ {1 2} \\bar {\\boldsymbol {c}} \\right\\| ^ {2}}. \\tag {14}", + "image_path": "c28e885668dd91a802dddb2ed3d0056a74403d06bd0a9f94767f180f8cf32ffe.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "In Figure 5 we show the distribution of the difference " + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\varepsilon_{S} - \\varepsilon_{a}" + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": " between the true residual and the approximation, computed on the 1500 image pairs from MegaDepth-1500 with 10000 DKM matches. The residuals are evaluated for the ground truth essential matrix " + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "inline_equation", + "content": "E_{gt} = [t_{gt}]_{\\times}R_{gt}" + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": ". Note that positive values indicate that the approximation gives too small residuals, while negative values correspond to the approximation giving too large residuals. We plot residuals between the " + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "inline_equation", + "content": "1^{\\mathrm{st}}" + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "inline_equation", + "content": "99^{\\mathrm{th}}" + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": " percentile. Thus we see that more" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1097" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 68, + 222, + 130 + ], + "blocks": [ + { + "bbox": [ + 63, + 68, + 222, + 130 + ], + "lines": [ + { + "bbox": [ + 63, + 68, + 222, + 130 + ], + "spans": [ + { + "bbox": [ + 63, + 68, + 222, + 130 + ], + "type": "image", + "image_path": "e2695a197f0d53daa56a4b0d29e393217e34604da1b0de9c4e849fb28dafc417.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 63, + 131, + 222, + 191 + ], + "blocks": [ + { + "bbox": [ + 63, + 131, + 222, + 191 + ], + "lines": [ + { + "bbox": [ + 63, + 131, + 222, + 191 + ], + "spans": [ + { + "bbox": [ + 63, + 131, + 222, + 191 + ], + "type": "image", + "image_path": "07e2bed2aa36df75402502d2c8f09588915185c7d5a24caf016b91567496eb1c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 225, + 68, + 383, + 130 + ], + "blocks": [ + { + "bbox": [ + 225, + 68, + 383, + 130 + ], + "lines": [ + { + "bbox": [ + 225, + 68, + 383, + 130 + ], + "spans": [ + { + "bbox": [ + 225, + 68, + 383, + 130 + ], + "type": "image", + "image_path": "edcbcc4e432edc190795e23a7688c283dc3664ce9220e3458c200c60e31fe7b9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 225, + 130, + 383, + 191 + ], + "blocks": [ + { + "bbox": [ + 225, + 130, + 383, + 191 + ], + "lines": [ + { + "bbox": [ + 225, + 130, + 383, + 191 + ], + "spans": [ + { + "bbox": [ + 225, + 130, + 383, + 191 + ], + "type": "image", + "image_path": "e99ce44fcc900571c8158167ae367f452983ab42d04a80db824d97034613d702.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 386, + 70, + 545, + 130 + ], + "blocks": [ + { + "bbox": [ + 386, + 70, + 545, + 130 + ], + "lines": [ + { + "bbox": [ + 386, + 70, + 545, + 130 + ], + "spans": [ + { + "bbox": [ + 386, + 70, + 545, + 130 + ], + "type": "image", + "image_path": "21e053569e8ec5184868169a0488ca2231ddcc15c8c9e95d0eac50a16002d974.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 386, + 131, + 545, + 191 + ], + "blocks": [ + { + "bbox": [ + 386, + 131, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 386, + 131, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 386, + 131, + 545, + 191 + ], + "type": "image", + "image_path": "8cd241df394c8c8548e9695183cae986dba7080f9320a71f050bf37d379ed586.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 63, + 194, + 224, + 257 + ], + "blocks": [ + { + "bbox": [ + 63, + 194, + 224, + 257 + ], + "lines": [ + { + "bbox": [ + 63, + 194, + 224, + 257 + ], + "spans": [ + { + "bbox": [ + 63, + 194, + 224, + 257 + ], + "type": "image", + "image_path": "bff4ebdd4c26f419166404ac88fc61f3573fd570f3420427e56a3664e1352af2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 63, + 257, + 224, + 319 + ], + "blocks": [ + { + "bbox": [ + 63, + 257, + 224, + 319 + ], + "lines": [ + { + "bbox": [ + 63, + 257, + 224, + 319 + ], + "spans": [ + { + "bbox": [ + 63, + 257, + 224, + 319 + ], + "type": "image", + "image_path": "f42f3a3b74bc5ef11444ba96d01f22cb0f44e1063fba11a54660e69815d0c402.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 327, + 555, + 361 + ], + "lines": [ + { + "bbox": [ + 55, + 327, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 555, + 361 + ], + "type": "text", + "content": "Figure 3. Qualitative Comparison of Clustering Methods. We compare different clustering methods on a single image pair from MegaDepth-1500 (top 2 rows) and ScanNet-1500 (bottom 2 rows), respectively. Dense matches from DKM are clustered using three keypoint-based methods (2D, 3D, 9D) and two image-based methods (Grid, SLIC)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 225, + 194, + 384, + 257 + ], + "blocks": [ + { + "bbox": [ + 225, + 194, + 384, + 257 + ], + "lines": [ + { + "bbox": [ + 225, + 194, + 384, + 257 + ], + "spans": [ + { + "bbox": [ + 225, + 194, + 384, + 257 + ], + "type": "image", + "image_path": "fd2c134b8051ae07f7cc6be05ef1d3c90ad339bcc7dc29370597c80a2b40e6ec.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 225, + 257, + 384, + 319 + ], + "blocks": [ + { + "bbox": [ + 225, + 257, + 384, + 319 + ], + "lines": [ + { + "bbox": [ + 225, + 257, + 384, + 319 + ], + "spans": [ + { + "bbox": [ + 225, + 257, + 384, + 319 + ], + "type": "image", + "image_path": "d5468c86cbd3499afc411c60a69eaf39e54f66b626c691e13fda64708a27cc40.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 386, + 194, + 546, + 257 + ], + "blocks": [ + { + "bbox": [ + 386, + 194, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 386, + 194, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 386, + 194, + 546, + 257 + ], + "type": "image", + "image_path": "abcda61a2fc71b8597f7004707e7b0306e9fc01053f617232553f1b586f79210.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 386, + 257, + 546, + 319 + ], + "blocks": [ + { + "bbox": [ + 386, + 257, + 546, + 319 + ], + "lines": [ + { + "bbox": [ + 386, + 257, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 386, + 257, + 546, + 319 + ], + "type": "image", + "image_path": "9158f0c8316b4cdf0ca63692ab4157772f88fa1194c9c54ff2049cedd6952348.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 59, + 374, + 223, + 483 + ], + "blocks": [ + { + "bbox": [ + 59, + 374, + 223, + 483 + ], + "lines": [ + { + "bbox": [ + 59, + 374, + 223, + 483 + ], + "spans": [ + { + "bbox": [ + 59, + 374, + 223, + 483 + ], + "type": "image", + "image_path": "6f1b36f531eab4e74693b2ff4a5f5e55ac1c32133264c10b6a4f292ae7c8f13e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 495, + 555, + 518 + ], + "lines": [ + { + "bbox": [ + 55, + 495, + 555, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 555, + 518 + ], + "type": "text", + "content": "Figure 4. Clustering Method and Hyperparameter Ablation. The plots show AUC@5° (left), runtime (middle) and AUC-runtime-tradeoff (right) for different clustering methods and number of clusters " + }, + { + "bbox": [ + 55, + 495, + 555, + 518 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 495, + 555, + 518 + ], + "type": "text", + "content": ". We include AUC@5° for the dense baseline as reference." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 225, + 374, + 384, + 483 + ], + "blocks": [ + { + "bbox": [ + 225, + 374, + 384, + 483 + ], + "lines": [ + { + "bbox": [ + 225, + 374, + 384, + 483 + ], + "spans": [ + { + "bbox": [ + 225, + 374, + 384, + 483 + ], + "type": "image", + "image_path": "feb8553163b7861b180c92976f93a5b306b138e8c9a57de25e303d61f9c38bba.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 388, + 374, + 550, + 483 + ], + "blocks": [ + { + "bbox": [ + 388, + 374, + 550, + 483 + ], + "lines": [ + { + "bbox": [ + 388, + 374, + 550, + 483 + ], + "spans": [ + { + "bbox": [ + 388, + 374, + 550, + 483 + ], + "type": "image", + "image_path": "46cf91a0b9056a2f1ea8bafed7c97ff470ffe97f2d21cd1eee3275f38aaa1b5e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 538, + 295, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 538, + 295, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 538, + 295, + 574 + ], + "type": "text", + "content": "than " + }, + { + "bbox": [ + 55, + 538, + 295, + 574 + ], + "type": "inline_equation", + "content": "98\\%" + }, + { + "bbox": [ + 55, + 538, + 295, + 574 + ], + "type": "text", + "content": " of the residuals have an absolute approximation error of less than 0.1 pixels, with a small bias towards getting too large residuals." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": "In Table 2 we compare the inlier ratios obtained through exact and approximate residuals, using the ground-truth pose. We compute average inlier ratios for each of the 1500 image pairs in MegaDepth-1500. Note that we compute the ratio of inlier clusters for " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\varepsilon_{a}" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": ", while for the exact residual " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\varepsilon_{S}" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " the inlier ratio is computed per match. We also include the runtime for computing the two residuals for an image pair (equivalent to scoring a model in RANSAC). We see that the approximated residual gives slightly lower inlier ratios, which decrease slowly for coarser clustering, while the speedup in computing time is significant." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 538, + 508, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 538, + 508, + 551 + ], + "spans": [ + { + "bbox": [ + 313, + 538, + 508, + 551 + ], + "type": "text", + "content": "4.4. Ablation on Integration in RANSAC" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 556, + 555, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 555, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 555, + 628 + ], + "type": "text", + "content": "In this section, we explore different ways of integrating our method in robust estimation with RANSAC. Robust estimation is typically done in two stages: the hypothesize-and-verify loop, which alternates between estimating and scoring models, and model refinement, which is done on the best model after the stop criterion is reached." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": "We evaluate the effect of our summarization scheme both on the model scoring and refinement stages of the estimation. For both stages, we evaluate usage of the representative match residuals (4), and the approximate residuals (12). We will refer to these methods as Center and Approximate, respectively. For the refinement stage, we also evaluate usage of the original residuals (3), referred to as the Dense" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1098" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 294, + 234 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 294, + 234 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 294, + 234 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 294, + 234 + ], + "type": "image", + "image_path": "315b11a65b2a3c76df529fa1f1670a2d623ef8b44ee706040628a104c3dc02ef.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 241, + 295, + 286 + ], + "lines": [ + { + "bbox": [ + 55, + 241, + 295, + 286 + ], + "spans": [ + { + "bbox": [ + 55, + 241, + 295, + 286 + ], + "type": "text", + "content": "Figure 5. Histogram over Approximation Error. The graph shows the distribution of differences between the true and approximated residuals, i.e. " + }, + { + "bbox": [ + 55, + 241, + 295, + 286 + ], + "type": "inline_equation", + "content": "\\varepsilon_{S} - \\varepsilon_{a}" + }, + { + "bbox": [ + 55, + 241, + 295, + 286 + ], + "type": "text", + "content": ", scaled with focal length. Statistic taken over all clusters from all image pairs in MegaDepth-1500." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 297, + 293, + 404 + ], + "blocks": [ + { + "bbox": [ + 58, + 297, + 293, + 404 + ], + "lines": [ + { + "bbox": [ + 58, + 297, + 293, + 404 + ], + "spans": [ + { + "bbox": [ + 58, + 297, + 293, + 404 + ], + "type": "table", + "html": "
Type of residualInlier ratioRuntime (μs)
Med.Avg.Avg.Speedup
Exact0.870.82155.81.0x
Approx. K = 10240.850.8031.15.0x
Approx. K = 5120.840.8014.810.5x
Approx. K = 2560.840.797.121.9x
Approx. K = 1280.820.783.248.7x
Approx. K = 640.800.761.3119.8x
", + "image_path": "0926d1ebeba640c812517da4b0e3672c59936c1bcad0ee7f3b32b00399f49af9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 521, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 605 + ], + "type": "text", + "content": "method. With two model scoring costs to evaluate (Center and Approximate) and three refinement costs (Center, Approximate, and Dense) this results in 6 possible combinations for our ablation study, in addition to the fully dense baseline. However, we omit Approximate scoring followed by Center refinement, since this would use less information in the refinement than what was used for the model scoring." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": "For all of the above methods, we perform model estimation using the 5-point solver [31], sampling from the representative matches. Note that this sampling has no effect on runtime compared to sampling from the dense matches, since convergence of RANSAC is only based on the scoring. Since we get up to 9 constraints from each " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "M_{k}" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " matrix, it is in principle also possible to estimate a model from a single summarized correspondence. However, we found that this generally gives worse performance, see suppl. material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": "In Table 3, we show AUC@5° and median runtime for the different combinations of model scoring and refinement costs, compared with a fully dense baseline. We report the average and standard deviation of the AUC for 10 runs using different seeds. In the table, we abbreviate the methods using a three letter combination, where the first letter denotes sampling method, the second letter denotes scoring method, and the third letter denotes refinement method. We see that scoring using Approximate or Center residuals are both significantly faster than Dense. Center scoring is the fastest while not significantly less accurate than Approximate. For refinement, however, Approximate residuals give a small but significant improvement in score over Center, but at an increased runtime. This gives us a possible trade-off, where we can sacrifice some runtime for better accuracy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 251, + 553, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 553, + 384 + ], + "type": "text", + "content": "We also compare our ablated methods with a dense baseline on subsampled DKM-matches, obtained by querying the balanced DKM sampler for a lower number of correspondences. In Figure 6, we plot AUC@5° vs. runtime for our methods and different number of DKM matches. We see that compared to subsampling, most of our methods give shorter runtime for the same performance; in particular CCC and CCA. This indicates that our summarization better preserves the geometric constraints, compared to reducing the number of correspondences extracted from the matcher." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 321, + 392, + 545, + 490 + ], + "blocks": [ + { + "bbox": [ + 55, + 412, + 296, + 501 + ], + "lines": [ + { + "bbox": [ + 55, + 412, + 296, + 501 + ], + "spans": [ + { + "bbox": [ + 55, + 412, + 296, + 501 + ], + "type": "text", + "content": "Table 2. Comparison of RANSAC Scoring. We compare the inlier ratios when calculating exact and approximate residuals for different numbers of clusters " + }, + { + "bbox": [ + 55, + 412, + 296, + 501 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 412, + 296, + 501 + ], + "type": "text", + "content": ", using the ground-truth essential matrix on all image pairs in MegaDepth-1500. The average and median ratios over all image pairs is reported. Note that inlier ratios are calculated per match for the exact residuals, and per cluster for approximate residuals. The runtime shows the average cost of scoring a model with MSAC in RANSAC." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 392, + 545, + 490 + ], + "lines": [ + { + "bbox": [ + 321, + 392, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 321, + 392, + 545, + 490 + ], + "type": "table", + "html": "
MethodAUC@5°RT (ms)Speedup
DDD (baseline)67.38±0.1066.01.0x
CAD67.21±0.086.89.8x
CCD67.12±0.085.312.3x
CAA66.87±0.072.724.6x
CCA66.70±0.061.545.2x
CCC65.95±0.101.255.0x
", + "image_path": "ee2a8be2febe748ae8a4526c13133f107fdc0c5af1765185d265e1b59bec521e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 497, + 553, + 564 + ], + "lines": [ + { + "bbox": [ + 313, + 497, + 553, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 553, + 564 + ], + "type": "text", + "content": "Table 3. Ablation on RANSAC Integration. We compare usage of our two summarization schemes in different stages of the estimation. Method names denote the what data is used in sampling, scoring, and refinement. For example, \"CAD\" means sampling from representative matches (C), scoring with the summarized approximation (A), and refinement with the dense matches (D)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 587, + 512, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 587, + 512, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 587, + 512, + 601 + ], + "type": "text", + "content": "4.5. Comparative Evaluation in RANSAC" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 605, + 553, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 553, + 715 + ], + "type": "text", + "content": "We evaluate our match summarization scheme on robust estimation using different dense matchers. We run both the CCC- and CCA-methods, since they represent a possible trade-off between accuracy and runtime. We compare with a fully dense baseline on the full set of matches. To show that our results do not depend on the dense matcher, we report results using DKM [15], RoMA [16], and ASPanFormer [7]. From DKM and RoMA, we always sample 10000 matches, while ASPanFormer gives a variable" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1099" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 70, + 547, + 198 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 547, + 198 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 547, + 198 + ], + "type": "table", + "html": "
MatchesEstimatorMegaDepth-1500ScanNet-1500
AUC@5°AUC@10°AUC@20°RT (ms)SpeedupAUC@5°AUC@10°AUC@20°RT (ms)Speedup
DKMDense67.479.688.066.61.0x31.352.669.968.81.0x
Ours CCA66.779.187.51.545.2x30.952.169.61.546.7x
Ours CCC66.078.787.31.255.0x30.451.769.31.258.6x
RoMADense70.181.589.360.61.0x33.355.272.264.61.0x
Ours CCA70.181.689.41.442.2x33.054.972.01.446.3x
Ours CCC69.381.189.21.252.1x32.854.771.81.158.3x
ASpan-FormerDense66.378.887.514.41.0x30.350.566.515.21.0x
Ours CCA65.878.587.41.59.6x29.749.966.11.510.3x
Ours CCC64.177.486.81.212.1x28.949.265.71.213.0x
SP+LGDense63.777.286.55.0N/A21.839.655.63.0N/A
", + "image_path": "5216068451ad400fe0d20de0a4ffb377b8c0509ed42226e632e72e32ef471d68.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 248, + 294, + 413 + ], + "blocks": [ + { + "bbox": [ + 55, + 248, + 294, + 413 + ], + "lines": [ + { + "bbox": [ + 55, + 248, + 294, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 248, + 294, + 413 + ], + "type": "image", + "image_path": "7cb304f8e6f2ae911030eed053ce0f034e3a1372592042da6e86f1426b2ad7b1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 420, + 295, + 455 + ], + "lines": [ + { + "bbox": [ + 55, + 420, + 295, + 455 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 295, + 455 + ], + "type": "text", + "content": "Figure 6. AUC-Runtime Trade-off in Ablation Study. The methods in Table 3 are plotted together with dense baseline for different samplings from DKM." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 482, + 295, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 482, + 295, + 602 + ], + "spans": [ + { + "bbox": [ + 54, + 482, + 295, + 602 + ], + "type": "text", + "content": "amount of matches. For image pairs where ASpanFormer gives less than 128 matches, we fall back to using dense estimation. The average results from 10 different seeds are shown in Table 4. The reported runtime is the median over all image pairs. For the convenience of the reader, we have also included estimation from sparse SuperPoint [12] + LightGlue [27] keypoints. In summary, we see that our summarization scheme achieves comparable accuracy to the dense baseline at a fraction of the runtime, irrespective of the dense keypoint matcher used." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "content": "Finally, we present an experiment on the WxBS benchmark [29]. This benchmark contains extremely challenging wide-baseline image pairs, where GT-correspondences are provided. As it does not provide intrinsics, we evaluate fundamental matrix estimation. The metrics are computed by checking consistency of the estimated " + }, + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 54, + 605, + 295, + 715 + ], + "type": "text", + "content": " with the GT matches. For comparison, we also run on dense matches extracted with MASt3R [25], where we disabled subsampling in the fast reciprocal matching. The results in Table 5" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 326, + 248, + 541, + 323 + ], + "blocks": [ + { + "bbox": [ + 55, + 207, + 553, + 231 + ], + "lines": [ + { + "bbox": [ + 55, + 207, + 553, + 231 + ], + "spans": [ + { + "bbox": [ + 55, + 207, + 553, + 231 + ], + "type": "text", + "content": "Table 4. Comparison with State-of-the-art. We compare our method with a dense baseline for several dense matchers on both MegaDepth-1500 and ScanNet-1500. For comparison, we also include AUC and runtime for state-of-the-art sparse matches (SP+LG)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 248, + 541, + 323 + ], + "lines": [ + { + "bbox": [ + 326, + 248, + 541, + 323 + ], + "spans": [ + { + "bbox": [ + 326, + 248, + 541, + 323 + ], + "type": "table", + "html": "
MatchesEstimatorRecall (10px)↑RT (ms)↓Speedup↑
RoMaDense86.363.01.0x
Ours CCA85.11.4543.3x
Ours CCC83.80.8277.0x
MASt3RDense63.437.11.0x
Ours CCA63.21.4325.8x
Ours CCC61.60.7649.6x
", + "image_path": "93879fb2891e21614572830974e06332cca6c2fae415c7bc15934fc5f8827e46.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 334, + 331, + 534, + 342 + ], + "lines": [ + { + "bbox": [ + 334, + 331, + 534, + 342 + ], + "spans": [ + { + "bbox": [ + 334, + 331, + 534, + 342 + ], + "type": "text", + "content": "Table 5. Fundamental Matrix Estimation on WxBS." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 365, + 553, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 553, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 553, + 403 + ], + "type": "text", + "content": "are qualitatively similar to the calibrated setting, showing that our method significantly speeds up the robust estimation with a marginal loss in accuracy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 415, + 388, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 415, + 388, + 428 + ], + "spans": [ + { + "bbox": [ + 313, + 415, + 388, + 428 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "text", + "content": "In this work, we have shown that dense keypoint matches, while they improve estimation compared to sparse matches, contain significant redundancies. This redundancy makes it possible to heavily subsample the matches while keeping most of the geometric constraints. We demonstrated a method to significantly speed up geometric estimation with little effect on the estimation accuracy. We additionally showed that this reduction in accuracy can be partially recovered by using our proposed summarized metacorrespondences. With this scheme, we were able to reduce the number of residuals per image pair from the number of matches " + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "text", + "content": ", to " + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "inline_equation", + "content": "9K" + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "text", + "content": " is the number of clusters – a hyperparameter we can choose such that " + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "inline_equation", + "content": "N \\ll 9K" + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "text", + "content": ". We also get a potential compression ratio in terms of storage, since the constraints from each cluster is entirely contained in a " + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 313, + 437, + 555, + 688 + ], + "type": "text", + "content": "-matrix, plus a single correspondence. A limitation is that the method only makes sense if the original number of matches is very large. Another limitation of the paper is that we have only focused on speeding up the robust estimation step, while a large part of the total runtime comes from the dense matcher itself." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": "Acknowledgments. 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Computer Vision and Image Understanding (CVIU), 78(1): 138-156, 2000. 2" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 276, + 294, + 319 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 276, + 294, + 319 + ], + "spans": [ + { + "bbox": [ + 57, + 276, + 294, + 319 + ], + "type": "text", + "content": "[38] Jonathan Ventura, Zuzana Kukelova, Torsten Sattler, and Daniel Barath. P1ac: Revisiting absolute pose from a single affine correspondence. In International Conference on Computer Vision (ICCV), 2023. 2" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 320, + 294, + 353 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 320, + 294, + 353 + ], + "spans": [ + { + "bbox": [ + 57, + 320, + 294, + 353 + ], + "type": "text", + "content": "[39] Tong Wei, Jiri Matas, and Daniel Barath. Adaptive reordering sampler with neurally guided magsac. In International Conference on Computer Vision (ICCV), 2023. 2" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1102" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_content_list.json b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fa427755a0e67bc6f045cab731626780e4c70b09 --- /dev/null +++ b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_content_list.json @@ -0,0 +1,1689 @@ +[ + { + "type": "text", + "text": "Dense-SfM: Structure from Motion with Dense Consistent Matching", + "text_level": 1, + "bbox": [ + 153, + 130, + 843, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "JongMin Lee \nSeoul National University \njongmin.cy@gmail.com", + "bbox": [ + 259, + 181, + 467, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sungjoo Yoo Seoul National University sungjoo.yoo@gmail.com", + "bbox": [ + 527, + 181, + 736, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 268, + 326, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present Dense-SfM, a novel Structure from Motion (SfM) framework designed for dense and accurate 3D reconstruction from multi-view images. Sparse keypoint matching, which traditional SfM methods often rely on, limits both accuracy and point density, especially in textureless areas. Dense-SfM addresses this limitation by integrating dense matching with a Gaussian Splatting (GS) based track extension which gives more consistent, longer feature tracks. To further improve reconstruction accuracy, Dense-SfM is equipped with a multi-view kernelized matching module leveraging transformer and Gaussian Process architectures, for robust track refinement across multi-views. Evaluations on the ETH3D and Texture-Poor SfM datasets show that Dense-SfM offers significant improvements in accuracy and density over state-of-the-art methods. Project page: https://icetea-cv.github.io/densesfm/.", + "bbox": [ + 89, + 301, + 483, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 587, + 220, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Structure from Motion (SfM) is a fundamental task in computer vision that enables the reconstruction of 3D structures from multi-view images of a scene. It has been a widely researched problem, focusing on reconstructing accurate camera poses and 3D point cloud of a scene, benefiting a variety of downstream tasks such as visual localization [19, 43, 46, 48, 58], AR/VR [39, 70], multi-view stereo [20, 50, 52] and neural rendering [27, 34, 72]. Over the years, several well-established methods have been developed to address the SfM pipeline [36, 40, 49, 55, 68].", + "bbox": [ + 89, + 612, + 483, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, there has been an increasing demand for dense and accurate 3D reconstructions in various 3D vision tasks, including dense reconstruction [17, 65], object pose estimation [5, 23, 57] and neural rendering [27, 72]. However, existing detector-based methods have limitations in achieving sufficient accuracy and density of 3D points, especially in texture-less regions where obtaining matchable keypoints is challenging, limiting the performance of downstream tasks. With the advent of deep learning and atten", + "bbox": [ + 89, + 765, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/35a41e1a450f0fe8c2f80e11ae7367195ba37a4fbf6ac14ff8e8609a7c1947b8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 268, + 901, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e93e564a471819a50fe507198a7a44fb4bc399881700a0ae0c1a8113d00f7e51.jpg", + "image_caption": [ + "Figure 1. Comparison of SfM results between quantized-matching and our matching. To solve the fragmentary track problem, DFSfM [24] uses quantized matching, which can compromise the accuracy and completeness of 3D points due to quantization. In contrast, our Dense-SfM pipeline leverages Gaussian Splatting to solve the problem, offering more accurate and dense 3D points. Thanks to dense matching, our pipeline can also be applied to texture-less objects, further improving the quality of 3D points and pose estimation." + ], + "image_footnote": [], + "bbox": [ + 522, + 521, + 901, + 614 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion mechanism [62], semi-dense and dense matching methods [6, 14, 15, 56, 66] have been introduced, enabling the reliable matches even in low-texture areas and producing denser match results than classical detector-based methods. This advancement has led to improved performance across many tasks, including homography and relative pose estimation [2, 7, 29]. However, due to their pairwise matching approach, the matching methods usually yield fragmented", + "bbox": [ + 511, + 779, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6404", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tracks $^1$ as mentioned in Detector-Free SfM (DFSfM) [24], making direct integration with existing SfM pipelines challenging. To solve this inconsistency issue, DFSfM applied quantization to the matched keypoints, and then refined the multi-view tracks to obtain accurate camera pose and point cloud. While the quantization strategy can increase track length and consistency, enhancing the multi-view refinement results, it can significantly limit the number of matches and accuracy, reducing the quality of the resulting SfM model, as exemplified in Fig. 1.", + "bbox": [ + 89, + 90, + 480, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel SfM framework that leverages dense matching while addressing the limitations of pairwise matching methods. As shown in Fig. 1, our approach reconstructs a dense and accurate 3D point cloud, avoiding the inherent limitations of quantized matching. Specifically, our framework first performs dense matching using a dense matcher, e.g., DKM [14] or RoMa [15], to construct an initial SfM model, where most tracks are initially fragmentary, i.e., of short (mostly a pair of images) lengths. Next, we initialize small 3D Gaussians based on the initial SfM's point cloud, integrating attributes like color and position. These Gaussians are then optimized and denified through Gaussian Splatting (GS) [27, 72], filling in the scene while keeping the initial Gaussians' (SfM points') positions fixed. We then infer the visibility of each initial SfM point per image by rendering through the ray from camera poses. In case that the 3D point is visible on the image, we include the image into the track of the 3D point thereby increasing the track length—a process we refer to as Track Extension. Note that Track Extension enables us to resolve the problem of short tracks in pairwise matching. Lastly, we perform our proposed SfM refinement pipeline, which includes a multi-view kernelized matching module and geometric bundle adjustment, to further optimize the camera poses and 3D points. Our track refinement module is mainly built on two architectures, transformer and Gaussian Process [41], which incorporate both feature-based and positional information, resulting in notable performance gains over existing refinement modules as demonstrated in our ablation study (Tab. 3).", + "bbox": [ + 91, + 243, + 483, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our Dense-SfM framework on the ETH3D, Texture-Poor SfM and Image Matching Challenge (IMC) 2021 datasets, where it outperforms state-of-the-art SfM systems across multiple metrics. Thanks to the dense matching coupled with track extension via Gaussian Splating, as well as our novel track refinement module, our framework achieves accurate camera pose estimations and dense 3D reconstructions.", + "bbox": [ + 89, + 696, + 482, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions:", + "text_level": 1, + "bbox": [ + 89, + 832, + 199, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- A novel SfM framework optimized for dense matchers,", + "bbox": [ + 89, + 848, + 482, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "capable of reconstructing highly accurate and dense 3D models, even in texture-less regions.", + "bbox": [ + 526, + 90, + 903, + 119 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A track extension method that, based on Gaussian Splatting, helps find new images on which 3D point is visible, thereby increasing track length of the 3D point.", + "- A new track refinement pipeline that leverages transformer and Gaussian Process architectures to enhance the consistency of feature tracks and refine the overall reconstruction quality.", + "- Extensive evaluations across diverse metrics demonstrate that our framework achieves state-of-the-art performance." + ], + "bbox": [ + 511, + 121, + 903, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 268, + 655, + 284 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Matching. Establishing 2D correspondences through feature matching is a fundamental component for SfM and visual SLAM. Traditional feature matching typically involves i) detecting keypoints [8, 11, 31, 42, 44, 45], ii) computing descriptors [13, 32, 33, 37, 59, 61] and iii) performing descriptor matching [18, 47, 71]. Despite its efficiency, it struggles in challenging scenarios such as low-textured regions, where keypoint detection is unreliable, and repetitive patterns, where matching often fails—leading to suboptimal SfM results.", + "bbox": [ + 511, + 294, + 906, + 445 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these limitations, more recent methods bypass the need for keypoint detection and instead directly perform semi-dense [6, 56, 66] or dense [14, 15] matching between image pairs. These approaches benefit from global receptive fields provided by transformers [62] or correlations computed from CNN or ViT features [9, 38], which allows them to achieve better performance in texture-poor areas where traditional methods often fail.", + "bbox": [ + 511, + 446, + 905, + 565 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, semi-dense and dense matching often results in fragmentary feature tracks, making it difficult to apply on SfM pipeline [53]. To solve this, DFSfM [24] introduced quantization matching that merges nearby subpixel matches into grid nodes, improving track consistency. Yet, this approach can compromise the accuracy of the initial camera poses and point clouds, heavily relying on refinement modules and reducing point cloud density.", + "bbox": [ + 511, + 566, + 905, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, our framework leverages Gaussian Splatting to assess visibility of 3D points. By projecting 3D points onto new images on which the points are visible, we obtain longer and consistent tracks without sacrificing the initial matching accuracy, which leads to improved refinement performance and, finally, better SfM results.", + "bbox": [ + 511, + 686, + 905, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Structure From Motion. Feature correspondence-based SfM methods have been extensively studied [3, 16, 35]. Incremental SfM [1, 55, 68] has become a widely adopted approach, with COLMAP [49] recognized as one of the most popular frameworks.", + "bbox": [ + 511, + 794, + 905, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, differentiable SfM methods [4, 10, 54, 63, 64, 67] have aimed to simplify or entirely replace the traditional", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1A keypoint is assigned a set of 2D coordinates, called feature track or track in short, on neighbor images where the keypoint is matched.", + "bbox": [ + 89, + 875, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6405", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b5504cd38dce0bc0f9e03ce98cd773a1eb575dd82ce21e65dbd4513ce5b446d8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 88, + 504, + 212 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/85b1842134afd64004d2e058898812f42f6b6ecaa4125a4500d2b8677b4cd64d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 89, + 903, + 212 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0cb4eddbb99e02a74a0286456273d380d874764f1c967aa9949ca4cff64c84cf.jpg", + "image_caption": [ + "Figure 2. Pipeline Overview. From a set of images, we construct an initial SfM model using dense two-view matching, filtering unreliable matches through mutual verification. To extend track length, we project 3D points onto additional images, using a visibility filter based on Gaussian Splatting. We then refine these extended tracks with our track refinement module and perform geometric bundle adjustment to improve the accuracy of SfM model." + ], + "image_footnote": [], + "bbox": [ + 96, + 213, + 903, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SfM pipeline. VGGSfM [64] manages all SfM components as fully differentiable, enabling end-to-end training. DUSt3R [67] predicts pairwise pointmaps and refines them through optimization-based global alignment. Its successors, MASt3R [28] and MASt3R-SfM [10], improve pixel matching for localization by predicting additional per-pixel features and leveraging its encoder for fast image retrieval, leading to a newly proposed SfM pipeline.", + "bbox": [ + 89, + 410, + 483, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-view Refinement. Inconsistent feature points across multiple views can impact the accuracy of reconstructed point cloud and camera poses in SfM. Hence, precise multi-view correspondences are essential for accurately recovering 3D structures and camera parameters in SfM pipelines.", + "bbox": [ + 89, + 551, + 483, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address this, several previous methods have proposed multi-view keypoint refinement models based on flow [12] or dense features [30], which lead to significant improvements in SfM accuracy. PatchFlow [12] refines keypoint locations using a geometric cost constrained by local flow between two views, followed by global optimization using a multi-view graph of relative feature geometry constraints. Similarly, PixSfM [30] refines keypoint locations through feature-metric keypoint adjustment by optimizing a direct cost over discriminative dense feature maps along the tracks. DFSfM [24], introduces a multi-view matching module that iteratively refines the tracks obtained from the COLMAP framework. The module extracts local patches from each image and feeds them into a transformer-based network to refine the keypoint's location by enforcing multi-view consistency.", + "bbox": [ + 89, + 643, + 482, + 885 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Building on these recent advancements, we propose a", + "bbox": [ + 109, + 886, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "novel refinement module that leverages both feature and positional information to refine the keypoint coordinates within the tracks. Instead of relying on statistical methods to select the refined tracks, our module fully regresses and learns the confidence (certainty) per track, resulting in more accurate refinement. As demonstrated in our ablation study (Tab. 3), our approach outperforms the existing refinement methods.", + "bbox": [ + 511, + 410, + 906, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 542, + 604, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of our Dense-SfM framework is shown in Fig. 2. Given $N$ images $\\{I_i\\}$ of a scene, our goal is to estimate the camera poses and reconstruct the 3D point cloud representing the scene.", + "bbox": [ + 511, + 568, + 906, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We design our framework as a three-stage pipeline. First, we construct an initial SfM model using correspondences between image pairs from a two-view dense matcher (e.g., DKM [14] and RoMa [15]). Next, we extend the track length of each 3D point by projecting it onto new images where it is visible, verifying visibility through Gaussian Splatting [27]. Finally, we perform iterative SfM refinement to enhance the accuracy of poses and point cloud.", + "bbox": [ + 511, + 628, + 905, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Initial SfM via Dense Matching", + "text_level": 1, + "bbox": [ + 511, + 757, + 790, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our framework employs dense feature matching between image pairs, unlike traditional SfM pipelines [49] which rely on sparse keypoints [8, 31]. By employing dense matching, our approach improves the reconstruction of texture-poor scenes and enables the registration of dense 3D points, which is challenging for conventional methods.", + "bbox": [ + 511, + 780, + 905, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For efficiency, we first sample matches from the dense matching using non-max suppression [8], based on per", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6406", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bcc3fe6f952ef0889c80a6dbd3e7c2cd99034912fcf9c428940e485c65185fb2.jpg", + "image_caption": [ + "Figure 3. Bidirectional verification on two-view dense matching. The match result $p_b$ from $\\mathcal{M}_{A \\to B}$ is re-used as input to $\\mathcal{M}_{B \\to A}$ to estimate $p_{a'}$ . We then compute the distance between $p_a$ and $p_{a'}$ , where a smaller distance indicates higher reliability of the match between $p_a$ and $p_b$ ." + ], + "image_footnote": [], + "bbox": [ + 150, + 88, + 421, + 204 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "pixel confidence scores from the dense matching model's output. Then, we sort out reliable matches by a method called mutual verification using bi-directional dense matching, similar to the mutual-nearest neighbor approach commonly used in detector-based methods.", + "bbox": [ + 89, + 292, + 483, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 3, from the bi-directional dense matching results $M_{A\\rightarrow B}$ and $M_{B\\rightarrow A}$ between images $A$ and $B$ , we define the pixel coordinates $p_b$ and $p_{a'}$ as", + "bbox": [ + 89, + 369, + 483, + 415 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {b} = \\mathcal {M} _ {A \\rightarrow B} [ p _ {a} ], \\quad p _ {a ^ {\\prime}} = \\mathcal {M} _ {B \\rightarrow A} [ p _ {b} ] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 425, + 482, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p_{a'}$ is sampled using bilinear-interpolation.", + "bbox": [ + 109, + 453, + 437, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure more reliable matches, we filter out correspondences using a binary mask, which is obtained with the distance from $p_a$ to $p_{a'}$ as follows:", + "bbox": [ + 89, + 468, + 483, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nB = \\left[ \\left\\| p _ {a} - p _ {a ^ {\\prime}} \\right\\| _ {2} \\leq \\epsilon_ {p} \\right] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 523, + 482, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using these filtered matches, we construct the initial SfM by triangulating 3D points through dense two-view fine matching. If camera poses are not provided for the reconstruction task, we first perform match quantization [24] and incremental mapping [49] to obtain coarse poses. We then triangulate 3D points using raw matching with the coarse pose and refine both the point cloud and camera poses through the refinement process, as explained in Sec. 3.3.", + "bbox": [ + 89, + 551, + 483, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Track Extension via Gaussian Splitting", + "text_level": 1, + "bbox": [ + 89, + 681, + 431, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the initial SfM, most of the tracks are short, i.e. consisting of mostly two images, due to the fragmentary nature of feature tracks in pair-wise matching, which can limit the performance of track refinement, as shown in DFSfM [24].", + "bbox": [ + 89, + 704, + 482, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Longer tracks, which offer more information on 3D geometry, could improve the track refinement performance. Thus, we generate new matching pairs on the existing matches for consistent multi-view matches, extending the length of track. We achieve this by projecting 3D points (triangulated by two-view matches) onto additional images on which, if successfully projected, the point is considered as visible from the camera pose as illustrated (by the blue dashed line) in Fig. 2.", + "bbox": [ + 89, + 763, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To determine the visibility of each 3D point from a camera pose, we apply a visibility filter using Gaussian Splating (GS) [27, 72], which supports fast training and rendering. We initialize a GS model with the 3D points obtained in the initial SfM. Specifically, we treat them as small 3D Gaussians setting each mean $\\mu \\in \\mathbb{R}^3$ to the 3D point coordinates, rotation $R$ to the identity matrix, opacity $\\alpha$ to 1, and scale $S$ based on the policy from Splatam [26], which uses focal length and depth information. These Gaussians are optimized and densified to cover the entire scene, while keeping the initial Gaussian's parameters fixed. The details of initialization and training process is described in supplementary material.", + "bbox": [ + 511, + 90, + 903, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After training the GS model, we utilize it for evaluating the visibility $M$ of all SfM points (represented as small Gaussians) from each camera pose using the following formula:", + "bbox": [ + 511, + 287, + 903, + 345 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM = \\left[ \\max _ {r \\in R} \\left\\{\\alpha_ {\\mathrm {S f M}} \\prod_ {j = 1} ^ {N _ {S f M} - 1} (1 - \\alpha_ {j}) \\right\\} > \\epsilon_ {v} \\right] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 340, + 903, + 385 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $R$ is the set of rays from the camera center (of a camera pose) for rendering the image, $\\alpha_{\\mathrm{SfM}}$ is the opacity of Gaussian representing the SfM point (set to 1), $N_{SfM}$ the number of Gaussians along the ray $r$ from the camera center to the SfM point, and $\\alpha_{j}$ the opacity of $j$ -th intermediate Gaussian. If the highest visibility score among the pixels rendered from the Gaussian representing the SfM point is larger than $\\epsilon_{\\nu}$ , we consider the SfM point, i.e. $N_{SfM}$ -th Gaussian, visible from the view of the camera pose. For each 3D point, we extend its track by adding its projected 2D point(s) onto the visible view(s). To do that, we project a 3D point $P_{j}$ onto the visible image using camera pose $\\{R_i,t_i\\}$ and intrinsic matrix $C_i$ as follows:", + "bbox": [ + 511, + 388, + 906, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {i j} = \\Pi \\left(R _ {i} P _ {j} + t _ {i}, C _ {i}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 592, + 903, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we verify the correspondence between the newly obtained 2D point $p_{ij}$ and its associated original 2D keypoint with geometric verification [49] using initial SfM's camera poses. After verified, we add the new 2D point to the track of the 3D point $P_j$ , which extends the length of $P_j$ 's track.", + "bbox": [ + 511, + 614, + 905, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that we project the 3D point onto the images that were not involved in the initial triangulation (i.e., establishing a new one-to-one correspondence of 2D-3D matches per image as illustrated with green lines in Fig. 2 (Stage 2). As will be demonstrated in our experiments (Tab. 3), the proposed Track extension enables the subsequent track refinement to produce more refined tracks, which leads to more accurate 3D points in the SfM model.", + "bbox": [ + 511, + 705, + 905, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Iterative SfM Refinement", + "text_level": 1, + "bbox": [ + 511, + 833, + 745, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using the extended tracks, we refine the initial SfM model to obtain improved camera poses and point cloud. Specifically, we iteratively improve the accuracy of feature tracks", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6407", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5c14b51d1a7394ad3699c195deba40c33974e8a8b2ec30b1eafb635f8889a17a.jpg", + "image_caption": [ + "Figure 4. Multi-view kernelized matching architecture. The feature maps from the reference and query views are processed in two ways: first, by a multi-view transformer, applying self and cross-attention and secondly, by a Gaussian Process that computes the posterior mean conditioned on the feature of each query view. All results are concatenated and fed into a CNN decoder, yielding probability distribution of coordinates for refinement $\\mathbf{P}_{Q_i}$ and corresponding confidence score $\\mathbf{S}_{Q_i}$ for each query view." + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 483, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "by employing our multi-view kernelized matching module alongside bundle adjustment, jointly optimizing camera poses and point cloud.", + "bbox": [ + 89, + 397, + 483, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.1. Feature Track Refinement", + "text_level": 1, + "bbox": [ + 89, + 450, + 320, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A feature track (or track) $\\mathcal{T}_j = \\{\\mathbf{x}_k\\in \\mathbb{R}^2 |k = 1:N_j\\}$ represents a set of 2D keypoint locations on multi-view $(N_{j})$ images that correspond to a 3D point $P_{j}$ . In our proposed method of feature track refinement, each track goes through a multi-view kernelized matching architecture (Fig. 4) and the regression of refined coordinates (Fig. 5). The matching architecture produces two outputs, a probability distribution of coordinate per pixel $P_{Q_i}$ and confidence score $S_{Q_i}$ per view. Then, the regression from these outputs produces a refined track by adjusting the keypoint locations.", + "bbox": [ + 89, + 470, + 483, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multi-view kernelized matching. Following DFSfM, we split a track into the keypoint of a reference view and those of query views (views from the track except the reference view) with a policy of median depth value. Then, we feed image patches centered at each keypoint into a CNN feature extractor, obtaining feature maps $\\mathbf{F}_R$ , $\\mathbf{F}_{Q_i} \\in \\mathbb{R}^{p \\times p \\times c}$ , where $\\mathbf{F}_R$ is from the reference view and $\\mathbf{F}_{Q_i}$ 's are from query views. As shown in Fig. 4, our multi-view kernelized matching architecture takes as input these feature maps of reference and query views.", + "bbox": [ + 89, + 643, + 483, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our proposed matching architecture consists of two paths, feature-based and coordinate-embedding-based ones. On the feature-based path (denoted with Multi-view Transformer in Fig. 4), we utilize a local feature transformer to obtain the transformed feature map $\\hat{\\mathbf{F}}_R$ and $\\hat{\\mathbf{F}}_{Q_i}$ 's through self and cross-attention between $\\mathbf{F}_R$ and $\\mathbf{F}_Q$ 's. On the coordinate-embedding-based path (denoted with Gaussian", + "bbox": [ + 89, + 795, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/593bdd7af826a6c00bb3827019f3e14e38bcb5c2041e368781f72e10095bae0e.jpg", + "image_caption": [ + "Figure 5. Regression of refined coordinate. Top: Selection of refined coordinate on the reference view: From the set of $S_{Q_i}$ values, representing the correspondence scores from the reference view to each query view $Q_i$ , we sum over $S_{Q_i}$ 's and select the pixel with the highest score as the refined coordinate for the reference view. Bottom: Regression of refined coordinate on each query view: We apply a channel-wise softmax to obtain a probability distribution of coordinates for each pixel, then calculate a weighted average to determine the correspondence from the reference view to query view $Q_i$ ." + ], + "image_footnote": [], + "bbox": [ + 519, + 88, + 906, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Process in Fig. 4), we employ a Gaussian Process [41] to utilize the positional information, deriving a coordinate embedding feature $\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})$ for each query view. Following DKM [14], we use an exponential cosine similarity kernel:", + "bbox": [ + 511, + 412, + 905, + 473 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nk \\left(f _ {A}, f _ {B}\\right) = \\exp (- \\tau) \\exp \\left(\\tau \\frac {\\langle f _ {A} , f _ {B} \\rangle}{\\sqrt {\\langle f _ {A} , f _ {A} \\rangle \\langle f _ {B} , f _ {B} \\rangle + \\varepsilon}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 477, + 903, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{A}$ and $f_{B}$ each is a feature vector from $\\mathbf{F}_A$ and $\\mathbf{F}_B$ , respectively. From this kernel function, we build kernel matrices $K^{\\mathcal{R}\\mathcal{Q}_i}$ , $K^{\\mathcal{Q}_i\\mathcal{Q}_i} \\in \\mathbb{R}^{p^2 \\times p^2}$ to obtain posterior mean $\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})$ as follows:", + "bbox": [ + 511, + 526, + 905, + 588 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mu \\left(\\mathbf {F} _ {R} \\mid \\mathbf {F} _ {Q _ {i}}\\right) = K ^ {R Q _ {i}} \\left(K ^ {Q _ {i} Q _ {i}} + \\sigma_ {n} ^ {2} I\\right) ^ {- 1} \\chi^ {Q _ {i}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 593, + 903, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\chi^{\\mathcal{Q}_i}$ is the Fourier positional encoding [34] of $F_{Q_i}$ 's pixel coordinate. Finally, we concatenate the transformed feature maps $\\hat{\\mathbf{F}}_R$ , $\\hat{\\mathbf{F}}_{Q_i}$ and coordinate embedding $\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})$ , and feed them into a CNN decoder $D_{\\theta}$ :", + "bbox": [ + 511, + 622, + 906, + 686 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP _ {Q _ {i}}, S _ {Q _ {i}} = D _ {\\theta} \\left(\\hat {\\mathbf {F}} _ {R} \\oplus \\hat {\\mathbf {F}} _ {Q _ {i}} \\oplus \\mu \\left(\\mathbf {F} _ {R} \\mid \\mathbf {F} _ {Q _ {i}}\\right)\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 700, + 903, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we obtain a probability distribution of coordinate per pixel $P_{Q_i} \\in \\mathbb{R}^{C^2 \\times w \\times w}$ and confidence score $S_{Q_i} \\in \\mathbb{R}^{w \\times w}$ , $C^2$ is the number of distribution's anchors, and $w \\times w$ a search boundary for refined coordinates.", + "bbox": [ + 511, + 729, + 905, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Regression of keypoint's location. Fig. 5 illustrates how the refined track is obtained. First, we obtain the refined coordinate of keypoint on the reference view. From the output of multi-view kernelized matching, $\\{S_{Q_i}\\}$ , we estimate the confidence value of each pixel as the candidate of refined coordinate on the reference view. As shown in Fig. 5 (top),", + "bbox": [ + 511, + 809, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6408", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we select, as the refined coordinate on the reference view, the pixel with the highest value, i.e. the highest confidence from $\\sum_{i}S_{Q_i}$", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then, as shown in Fig. 5 (bottom), from the refined coordinate on the reference view (calculated above), we estimate the refined coordinate of keypoint for each query view $Q_{i}$ . For each patch of $P_{Q_i}$ of size $w\\times w$ , we apply softmax across channels from the pixel of refined coordinate for the reference view, to obtain a probability distribution over a $C\\times C$ grid. The refined coordinate for the query view $Q_{i}$ is then computed as a weighted average, where each pixel's probability serves as its weight. By multiplying each probability by its corresponding pixel coordinate and summing these weighted values, we derive a refined coordinate for query view $Q_{i}$ . Finally, we construct the final refined track $T_{j}^{*}$ , consisting of the refined coordinates for the reference view and all query views.", + "bbox": [ + 89, + 137, + 482, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training setup and loss function. We set up training as in DFSfM [24] using MegaDepth dataset [29]. We use image bags sampled from the SfM model provided in the dataset, in which ground truth tracks are derived from the given camera pose and MVS depth map. For training, we perturb the ground truth 2D locations of tracks in the query views with random noise, providing these as input to our refinement module. Unlike DFSfM, which relies on statistics (variance) as uncertainty measure, we directly learn confidence score through a neural network. Consequently, our loss function is not simply formulated as an $L_{2}$ loss to minimize the distance between the refined tracks and the ground truth tracks. Instead, we jointly predict and learn the confidence $S_{Q_i} > 0$ for each query view, and include it in the regression loss as follows:", + "bbox": [ + 89, + 364, + 482, + 592 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\frac {1}{N} \\sum_ {j \\in n _ {t}} \\sum_ {i \\in n _ {j}} s _ {Q _ {i}} \\cdot \\| p _ {Q _ {i}} - p _ {g t} \\| _ {2} - \\alpha \\log s _ {Q _ {i}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 597, + 482, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $n_t$ is the number of feature tracks, $n_j$ the number of query views in a track $j$ , $N$ the total number of refined keypoints on all the query views, $p_{Q_i}$ and $p_{gt}$ the learned 2D coordinate from $Q_i$ (as illustrated in Fig. 5) and the ground truth 2D coordinate, respectively, and $s_{Q_i}$ the confidence score of prediction $p_{Q_i}$ , which is obtained, from $S_{Q_i}$ , at the pixel of the reference view's ground truth keypoint. The second term in the loss is used to avoid being underconfident, where we set $\\alpha$ as 20.", + "bbox": [ + 89, + 641, + 482, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3.2. Bundle Adjustment", + "text_level": 1, + "bbox": [ + 89, + 782, + 272, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Using the refined feature tracks, we iteratively perform geometric bundle adjustment (BA) [60] to refine the intrinsic parameters $\\{C_i\\}$ , camera poses $\\{\\xi_i\\}$ , and 3D points' coordinates $\\{P_j\\}$ . Formally, we minimize the reprojection error $E$ defined as:", + "bbox": [ + 89, + 801, + 482, + 875 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nE = \\sum_ {j} \\sum_ {x _ {k} ^ {*} \\in \\mathcal {T} _ {j} ^ {*}} \\rho \\big (\\| \\pi (\\pmb {\\xi} _ {i} \\cdot P _ {j}, C _ {i}) - x _ {k} ^ {*} \\| _ {2} ^ {2} \\big) ,\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 882, + 439, + 904 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\pi (\\cdot)$ projects points to image plane using intrinsic parameter $C_i$ , and $\\rho (\\cdot)$ is a robust loss function [21]. We then filter outliers [49, 68] by rejecting points that exceed the maximum reprojection error threshold $\\epsilon_{f}$ . After performing BA and outlier filtering, the refined SfM can be passed to the next iteration of feature track refinement and BA.", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 200, + 645, + 217 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 511, + 226, + 614, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use the ETH3D [51], Texture-Poor SfM datasets [24], and Image Matching Challenge (IMC) 2021 dataset [25], each presenting unique challenges across different types of scenes. The ETH3D dataset includes indoor and outdoor scenes with sparsely captured, high-resolution images, and ground truth poses calibrated using Lidar. The Texture-Poor SfM dataset focuses on object-centric scenes with low texture, comprising subsampled image sets. We use all test scenes from the IMC Phototourism dataset, evaluating them with subsampled image bags. The main challenge of this dataset lies in its sparse views, accompanied by significant variations in viewpoint and illumination.", + "bbox": [ + 511, + 250, + 906, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 511, + 444, + 730, + 459 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For efficiency, we apply non-max suppression [8] with a radius of 4 pixels for ETH3D and 2 pixels for Texture-Poor SfM and IMC dataset. For mutual verification, we filter out matches with a distance exceeding $\\epsilon_{p} = 3\\mathrm{px}$ in Eq. 2.", + "bbox": [ + 511, + 467, + 905, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To determine the visibility of Gaussians (SfM points) from a camera pose, we set the visibility threshold $\\epsilon_{\\nu}$ to 0.5 in Eq. 3. Details of training and implementation of Gaussian Splatting are provided in the supplementary material.", + "bbox": [ + 511, + 529, + 905, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use S2Dnet [18] as a CNN backbone for our refinement architecture, and adopt the multi-view transformer architecture from DFSfM [24]. To ensure a fair comparison, we apply the same refinement parameters as in DFSfM, including a local patch size $(p = 15)$ from the feature maps $\\mathbf{F}_R$ and $\\mathbf{F}_Q$ , obtained from the CNN backbone, and a search boundary for reference view's refined keypoints set to $w = 7$ . The number of distribution anchors $C^2$ is set to $7^2$ . For the CNN decoder in Fig. 4, we use a series of residual blocks [22] and channel attention blocks [69]. During bundle adjustment, matches with reprojection errors exceeding $\\epsilon_f = 3\\mathrm{px}$ are discarded. The total SfM refinement process is iterated twice. More implementation details are reported in the supplementary material.", + "bbox": [ + 511, + 590, + 906, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. 3D Triangulation", + "text_level": 1, + "bbox": [ + 511, + 816, + 681, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Accurately triangulating scene point clouds, given known camera poses and intrinsics, is an important task in SfM. In this section, we evaluate the accuracy and completeness of the reconstructed point clouds.", + "bbox": [ + 511, + 840, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6409", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/03ccdeda1831897372558d09e9f97f51398ac8ba230bc83bf82d9f0d00ca46bd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TypeMethodAccuracy (%)Completeness (%)
1cm2cm5cm1cm2cm5cm
Detector-BasedSIFT [31] + NN + PixSfM [30]76.1885.6093.160.170.713.29
D2Net [11] + NN + PixSfM74.7583.8191.980.832.698.95
R2D2 [42] + NN + PixSfM74.1284.4991.980.431.586.71
SP [8] + SG [47] + PixSfM79.0187.0493.800.752.7711.28
Semi-Dense MatchingLoFTR [56] + PixSfM74.4284.0892.632.919.3927.31
LoFTR + DFSfM [24]80.3889.0195.833.7311.0729.54
AspanTrans. [6] + DFSfM77.6387.4095.023.9712.1832.42
MatchFormer [66] + DFSfM79.8688.5195.483.7611.0629.05
Dense-MatchingRoMa + DFSfM79.3288.4295.823.139.7929.10
DKM + Ours84.0591.9697.395.9513.9531.03
RoMa + Ours84.7992.6297.777.3817.0636.35
DeepVGGSfM [64]80.6289.4996.524.5213.1133.96
Point-BasedMast3r-SfM [10]42.0259.7480.582.058.7631.73
Mast3r-SfM + Our Refinement (Sec. 3.3)77.2286.4794.052.408.2627.17
", + "bbox": [ + 96, + 88, + 480, + 243 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Results of 3D Triangulation. Our method is compared with the baselines on the ETH3D [51] dataset using accuracy and completeness metrics with different thresholds.", + "bbox": [ + 89, + 250, + 482, + 292 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation. We use the ETH3D training set, comprising 13 indoor and outdoor scenes with millimeter-accurate dense point clouds as ground truth. Following the protocol in PixSfM [30] and DFSfM [24], we triangulate 3D points using fixed camera poses and intrinsics, then evaluate the resulting point clouds for accuracy and completeness using the ETH3D benchmark [51]. The results are reported at varying distance thresholds (1cm, 2cm, 5cm), averaged across all scenes. Consistent with the benchmark setup, accuracy and completeness are measured by the proportion of triangulated points that fall within the specified distances from the ground truth points.", + "bbox": [ + 89, + 297, + 483, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. The results are shown in Tab. 1. While there is a trade-off between accuracy and completeness, our Dense-SfM framework achieves superior performances on both metrics. Compared to the state-of-the-art baseline LoFTR + DFSfM, our pipeline with RoMa achieves higher accuracy and completeness, thanks to employing dense matching and our proposed pipeline. Also, compared to the RoMa + DFSfM, where we apply quantization on dense matching and refine the tracks as in DFSfM, our method achieves higher performance in terms of both accuracy and completeness, highlighting the effectiveness of our SfM framework. More results with detector-based and semi-dense matching are reported in the supplementary material.", + "bbox": [ + 89, + 500, + 483, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Multi-View Camera Pose Estimation", + "text_level": 1, + "bbox": [ + 89, + 705, + 408, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we evaluate the recovered multi-view poses.", + "bbox": [ + 89, + 729, + 482, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation protocols. For the evaluation, we use a subset of ETH3D training and test dataset, which includes 22 indoor and outdoor scenes, the Texture-Poor SfM dataset, and the test scenes of IMC 2021 dataset. We evaluate the accuracy of the estimated multi-view poses using the AUC of pose error at various thresholds. For the evaluation of IMC 2021 dataset, due to the high occlusion and appearance changes in many test scenes, directly applying track extension via GS is challenging. Instead, we adopt a", + "bbox": [ + 89, + 763, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "quantization method [24] on the matching results, focusing on comparing our multi-view kernelized matching module with DFSfM's refinement module. Specifically, we apply quantization to the matched keypoints with a radius of 4, and then use our refinement module to refine the quantized keypoints.", + "bbox": [ + 511, + 90, + 906, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d71db4223592121d4edf85d100411088846adf93f1457a223172a1a88f39e55.jpg", + "image_caption": [ + "Figure 6. Qualitative Results on Texture-Poor SfM and IMC dataset. Our method with the dense matcher RoMa is qualitatively compared with the baseline LoFTR + DFSfM. The red cameras are ground truth poses while the blue cameras are recovered poses." + ], + "image_footnote": [], + "bbox": [ + 519, + 189, + 897, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. As shown in Tab. 2, our Dense-SfM framework outperforms existing baselines over all datasets. On the ETH3D dataset, our framework with dense matching achieves the highest multi-view pose accuracy, with a particularly large improvement at the highest threshold.", + "bbox": [ + 511, + 659, + 905, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Fig. 6, our framework successfully reconstructs dense and accurate 3D points thanks to dense matching and our pipeline, even in challenging low-textured regions with viewpoint changes, leading to much higher pose estimation accuracy.", + "bbox": [ + 511, + 734, + 905, + 810 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 511, + 818, + 679, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct several experiments to evaluate the key components of our pipeline, including the matching design used as input for SfM and the architectural choices of the refinement module, on the ETH3D dataset using triangulation metrics.", + "bbox": [ + 511, + 840, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6410", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/efd97d89e819bf74b36c96ab77a91345d96be6b56db1640eedfd5a5ed3629989.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TypeMethodETH3D DatasetTexture-Poor SfM DatasetIMC Dataset
AUC@1°AUC@3°AUC@5°AUC@3°AUC@5°AUC@10°AUC@3°AUC@5°AUC@10°
Detector-BasedCOLMAP (SIFT+NN) [49]26.7138.8642.142.873.854.9523.5823.6644.79
SIFT [31] + NN + PixSfM [30]26.9439.0142.193.134.085.0925.5434.8046.73
D2Net [11] + NN + PixSfM34.5049.7753.581.542.634.548.9112.2616.79
R2D2 [42] + NN + PixSfM43.5862.0966.893.795.517.8431.4141.8054.65
SP [8] + SG [47] + PixSfM50.8268.5272.8614.0019.2324.5545.1957.2270.47
Semi-Dense MatchingLoFTR [56] + PixSfM54.3573.9778.8620.6630.4942.0144.0656.1669.61
LoFTR + DFSIM [24]59.1275.5979.5326.0735.7745.4346.5558.7472.19
AspanTrans. [6] + DFSfM57.2373.7177.7025.7835.6945.6446.7959.0172.50
MatchFormer [66] + DFSfM56.7073.0076.8426.9037.5748.5545.8357.8871.22
Dense MatchingRoMa + DFSfM57.9777.0281.5934.2850.0169.0147.4359.8473.19
DKM + Ours59.0477.7382.2041.1957.2672.9548.6561.0974.37
RoMa + Ours60.9278.4182.6349.9466.2381.4148.4860.7973.90
DeepVGGsF M [64]28.0944.4149.911.866.2621.1045.2358.8973.92
Point-BasedMast3r-SfM [10]35.8558.4665.0343.4661.5178.9742.2654.5367.97
Mast3r-SfM + Our Refinement37.5059.1865.4848.0364.4880.3144.9857.0970.09
", + "bbox": [ + 114, + 88, + 883, + 275 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/79c60a1446de2c3344bef957769052dd14243be57ef0378dc7014270b5ef1fd7.jpg", + "table_caption": [ + "Table 2. Results of Multi-View Camera Pose Estimation. Our framework is compared with detector-based, detector-free and dense-matching baselines by the AUC of pose error at different thresholds. Bold and underline indicate the best and second-best results." + ], + "table_footnote": [], + "table_body": "
Design ChoiceAccu. (%)Complete. (%)
1cm2cm1cm2cm
(1) Matching designsFull model84.7992.627.3817.06
w/o Mutual Verification84.0392.068.1418.68
w/o GS Extension77.4587.809.4521.64
Quantized Matching (r=4)82.8290.753.5310.62
(2) Refinement designsFull model84.7992.627.3817.06
Multi-view Trans. [24]80.5990.046.0415.2
w/o Gaussian Process72.4784.724.7812.59
w/o Multi-view Trans.83.3991.637.0416.49
w/o ref. confidence selection83.8192.158.8319.85
(3) Number of iterationsNo refine.69.7782.598.6120.4
1 iter81.1290.527.6217.86
2 iter84.7992.67.3817.06
3 iter85.0192.756.7415.91
", + "bbox": [ + 96, + 320, + 480, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation Studies. On the ETH3D dataset, we quantitatively evaluate the impact of design choice of matching and refinement module, and the number of iterations of refinement. The reported triangulation accuracy and completeness are averaged across all scenes.", + "bbox": [ + 89, + 486, + 482, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Matching Designs. Tab. 3 (1) demonstrates the benefits of our proposed matching filtering (mutual verification) and track extension via Gaussian Splatting (GS). Compared to the configurations without mutual verification, where all matches are used for reconstructing the initial SfM, incorporating mutual verification improves accuracy, with a tradeoff in completeness due to filtering. Moreover, extending match pairs through GS significantly improves accuracy, which shows that using more views for multi-view kernelized matching contribute to higher performance of accuracy.", + "bbox": [ + 88, + 564, + 482, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For a comparison with DFSfM [24], which applies quantization to matched keypoints to address the fragmented track problem, we replaced our GS track extension with their quantization approach, using a rounding ratio of $r = 4$ . Results indicate that our GS track extension not only maintains completeness by avoiding the limitations of quantization but also achieves superior accuracy.", + "bbox": [ + 89, + 715, + 482, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Refinement designs. Table 3 (2) shows the benefit of our proposed multi-view kernelized matching's components in Fig. 4 and confidence-based track selection in Fig. 5.", + "bbox": [ + 89, + 839, + 482, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We first compare our refinement module to the multi-", + "bbox": [ + 109, + 885, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "view refinement module in DFSfM [24], by substituting our refinement module with it. The result shows that our refinement module consistently outperforms the existing approach, achieving higher accuracy and completeness.", + "bbox": [ + 511, + 323, + 906, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Next, we evaluate the contributions of each component in our refinement architecture (Fig. 4) by testing configurations where either the multi-view transformer or Gaussian Process is removed. The results show that our full model, which integrates both components, achieves the highest performance in accuracy and completeness, confirming that combining feature-based and positional information yields more precise refinement. Furthermore, our strategy of selecting a final refined track based on predicted confidence in the reference view further enhances accuracy.", + "bbox": [ + 511, + 388, + 908, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of iterations. Table 3 (3) reports the results after each refinement iteration. The initial SfM point cloud is less accurate due to reliance solely on initial two-view matching. As the iterations progress, the accuracy of the SfM point cloud gets improved. However, further refinement beyond two iterations gives little gains. So, we limit the refinement to two iterations for efficiency.", + "bbox": [ + 511, + 584, + 908, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 719, + 633, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces a novel Dense-SfM framework aimed at reconstructing dense point cloud and estimating camera poses from a set of images. Unlike conventional SfM systems that often rely on initial 2D matches, our framework leverages Gaussian Splatting to generate new matching pairs, producing longer tracks that significantly enhance both the accuracy and density of the reconstructed point cloud. Extensive evaluations on diverse datasets show that our framework consistently outperforms existing SfM baselines across multiple metrics.", + "bbox": [ + 511, + 750, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6411", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 89, + 90, + 269, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research was supported in part by Samsung Advanced Institute of Technology (SAIT), the Naver-Intel Co-Lab, Inter-university Semiconductor Research Center (ISRC), and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) [NO.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)].", + "bbox": [ + 89, + 114, + 483, + 238 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 250, + 187, + 266 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sameer Agarwal, Noah Snavely, Ian Simon, Steven M. Seitz, and Richard Szeliski. Building rome in a day. 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In ACCV, 2022. 1, 2, 7, 8", + "[67] Shuzhe Wang, Vincent Leroy, Yohann Cabon, Boris Chidlovskii, and Jerome Revaud. Dust3r: Geometric 3d vision made easy. In CVPR, 2024. 2, 3", + "[68] Changchang Wu. Towards linear-time incremental structure from motion. In 2013 International Conference on 3D Vision - 3DV 2013, pages 127-134, 2013. 1, 2, 6", + "[69] Changqian Yu, Jingbo Wang, Chao Peng, Changxin Gao, Gang Yu, and Nong Sang. Learning a discriminative feature network for semantic segmentation. CoRR, abs/1804.09337, 2018. 6", + "[70] Harry Zhang, Jeffrey Ichnowski, Yahav Avigal, Joseph Gonzales, Ion Stoica, and Ken Goldberg. Dex-net ar: Distributed deep grasp planning using a commodity cellphone and augmented reality app. In 2020 IEEE International Conference on Robotics and Automation (ICRA), pages 552-558, 2020. 1", + "[71] Jiahui Zhang, Dawei Sun, Zixin Luo, Anbang Yao, Lei Zhou, Tianwei Shen, Yurong Chen, Long Quan, and Honggen Liao. Learning two-view correspondences and geometry using order-aware network. International Conference on Computer Vision (ICCV), 2019. 2", + "[72] Zehao Zhu, Zhiwen Fan, Yifan Jiang, and Zhangyang Wang. Fsgs: Real-time few-shot view synthesis using gaussian splatting, 2024. 1, 2, 4" + ], + "bbox": [ + 91, + 90, + 480, + 883 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "6414", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_model.json b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b9d9494e9da1c35062bc2df895b7158007a149c7 --- /dev/null +++ b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_model.json @@ -0,0 +1,2466 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.155, + 0.131, + 0.844, + 0.154 + ], + "angle": 0, + "content": "Dense-SfM: Structure from Motion with Dense Consistent Matching" + }, + { + "type": "text", + "bbox": [ + 0.26, + 0.182, + 0.468, + 0.234 + ], + "angle": 0, + "content": "JongMin Lee \nSeoul National University \njongmin.cy@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.529, + 0.182, + 0.738, + 0.234 + ], + "angle": 0, + "content": "Sungjoo Yoo Seoul National University sungjoo.yoo@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.302, + 0.485, + 0.558 + ], + "angle": 0, + "content": "We present Dense-SfM, a novel Structure from Motion (SfM) framework designed for dense and accurate 3D reconstruction from multi-view images. Sparse keypoint matching, which traditional SfM methods often rely on, limits both accuracy and point density, especially in textureless areas. Dense-SfM addresses this limitation by integrating dense matching with a Gaussian Splatting (GS) based track extension which gives more consistent, longer feature tracks. To further improve reconstruction accuracy, Dense-SfM is equipped with a multi-view kernelized matching module leveraging transformer and Gaussian Process architectures, for robust track refinement across multi-views. Evaluations on the ETH3D and Texture-Poor SfM datasets show that Dense-SfM offers significant improvements in accuracy and density over state-of-the-art methods. Project page: https://icetea-cv.github.io/densesfm/." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.588, + 0.222, + 0.604 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.484, + 0.765 + ], + "angle": 0, + "content": "Structure from Motion (SfM) is a fundamental task in computer vision that enables the reconstruction of 3D structures from multi-view images of a scene. It has been a widely researched problem, focusing on reconstructing accurate camera poses and 3D point cloud of a scene, benefiting a variety of downstream tasks such as visual localization [19, 43, 46, 48, 58], AR/VR [39, 70], multi-view stereo [20, 50, 52] and neural rendering [27, 34, 72]. Over the years, several well-established methods have been developed to address the SfM pipeline [36, 40, 49, 55, 68]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.766, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Recently, there has been an increasing demand for dense and accurate 3D reconstructions in various 3D vision tasks, including dense reconstruction [17, 65], object pose estimation [5, 23, 57] and neural rendering [27, 72]. However, existing detector-based methods have limitations in achieving sufficient accuracy and density of 3D points, especially in texture-less regions where obtaining matchable keypoints is challenging, limiting the performance of downstream tasks. With the advent of deep learning and atten" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.27, + 0.902, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.522, + 0.902, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.622, + 0.907, + 0.747 + ], + "angle": 0, + "content": "Figure 1. Comparison of SfM results between quantized-matching and our matching. To solve the fragmentary track problem, DFSfM [24] uses quantized matching, which can compromise the accuracy and completeness of 3D points due to quantization. In contrast, our Dense-SfM pipeline leverages Gaussian Splatting to solve the problem, offering more accurate and dense 3D points. Thanks to dense matching, our pipeline can also be applied to texture-less objects, further improving the quality of 3D points and pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.903 + ], + "angle": 0, + "content": "tion mechanism [62], semi-dense and dense matching methods [6, 14, 15, 56, 66] have been introduced, enabling the reliable matches even in low-texture areas and producing denser match results than classical detector-based methods. This advancement has led to improved performance across many tasks, including homography and relative pose estimation [2, 7, 29]. However, due to their pairwise matching approach, the matching methods usually yield fragmented" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6404" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.482, + 0.242 + ], + "angle": 0, + "content": "tracks\\(^1\\) as mentioned in Detector-Free SfM (DFSfM) [24], making direct integration with existing SfM pipelines challenging. To solve this inconsistency issue, DFSfM applied quantization to the matched keypoints, and then refined the multi-view tracks to obtain accurate camera pose and point cloud. While the quantization strategy can increase track length and consistency, enhancing the multi-view refinement results, it can significantly limit the number of matches and accuracy, reducing the quality of the resulting SfM model, as exemplified in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.244, + 0.485, + 0.695 + ], + "angle": 0, + "content": "In this paper, we propose a novel SfM framework that leverages dense matching while addressing the limitations of pairwise matching methods. As shown in Fig. 1, our approach reconstructs a dense and accurate 3D point cloud, avoiding the inherent limitations of quantized matching. Specifically, our framework first performs dense matching using a dense matcher, e.g., DKM [14] or RoMa [15], to construct an initial SfM model, where most tracks are initially fragmentary, i.e., of short (mostly a pair of images) lengths. Next, we initialize small 3D Gaussians based on the initial SfM's point cloud, integrating attributes like color and position. These Gaussians are then optimized and denified through Gaussian Splatting (GS) [27, 72], filling in the scene while keeping the initial Gaussians' (SfM points') positions fixed. We then infer the visibility of each initial SfM point per image by rendering through the ray from camera poses. In case that the 3D point is visible on the image, we include the image into the track of the 3D point thereby increasing the track length—a process we refer to as Track Extension. Note that Track Extension enables us to resolve the problem of short tracks in pairwise matching. Lastly, we perform our proposed SfM refinement pipeline, which includes a multi-view kernelized matching module and geometric bundle adjustment, to further optimize the camera poses and 3D points. Our track refinement module is mainly built on two architectures, transformer and Gaussian Process [41], which incorporate both feature-based and positional information, resulting in notable performance gains over existing refinement modules as demonstrated in our ablation study (Tab. 3)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.697, + 0.483, + 0.817 + ], + "angle": 0, + "content": "We evaluate our Dense-SfM framework on the ETH3D, Texture-Poor SfM and Image Matching Challenge (IMC) 2021 datasets, where it outperforms state-of-the-art SfM systems across multiple metrics. Thanks to the dense matching coupled with track extension via Gaussian Splating, as well as our novel track refinement module, our framework achieves accurate camera pose estimations and dense 3D reconstructions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.833, + 0.2, + 0.846 + ], + "angle": 0, + "content": "Contributions:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.849, + 0.483, + 0.864 + ], + "angle": 0, + "content": "- A novel SfM framework optimized for dense matchers," + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "capable of reconstructing highly accurate and dense 3D models, even in texture-less regions." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.122, + 0.905, + 0.167 + ], + "angle": 0, + "content": "- A track extension method that, based on Gaussian Splatting, helps find new images on which 3D point is visible, thereby increasing track length of the 3D point." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.168, + 0.905, + 0.228 + ], + "angle": 0, + "content": "- A new track refinement pipeline that leverages transformer and Gaussian Process architectures to enhance the consistency of feature tracks and refine the overall reconstruction quality." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.228, + 0.905, + 0.258 + ], + "angle": 0, + "content": "- Extensive evaluations across diverse metrics demonstrate that our framework achieves state-of-the-art performance." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.122, + 0.905, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.269, + 0.656, + 0.285 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.295, + 0.907, + 0.446 + ], + "angle": 0, + "content": "Image Matching. Establishing 2D correspondences through feature matching is a fundamental component for SfM and visual SLAM. Traditional feature matching typically involves i) detecting keypoints [8, 11, 31, 42, 44, 45], ii) computing descriptors [13, 32, 33, 37, 59, 61] and iii) performing descriptor matching [18, 47, 71]. Despite its efficiency, it struggles in challenging scenarios such as low-textured regions, where keypoint detection is unreliable, and repetitive patterns, where matching often fails—leading to suboptimal SfM results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.447, + 0.906, + 0.566 + ], + "angle": 0, + "content": "To address these limitations, more recent methods bypass the need for keypoint detection and instead directly perform semi-dense [6, 56, 66] or dense [14, 15] matching between image pairs. These approaches benefit from global receptive fields provided by transformers [62] or correlations computed from CNN or ViT features [9, 38], which allows them to achieve better performance in texture-poor areas where traditional methods often fail." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.906, + 0.687 + ], + "angle": 0, + "content": "However, semi-dense and dense matching often results in fragmentary feature tracks, making it difficult to apply on SfM pipeline [53]. To solve this, DFSfM [24] introduced quantization matching that merges nearby subpixel matches into grid nodes, improving track consistency. Yet, this approach can compromise the accuracy of the initial camera poses and point clouds, heavily relying on refinement modules and reducing point cloud density." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.688, + 0.906, + 0.779 + ], + "angle": 0, + "content": "In contrast, our framework leverages Gaussian Splatting to assess visibility of 3D points. By projecting 3D points onto new images on which the points are visible, we obtain longer and consistent tracks without sacrificing the initial matching accuracy, which leads to improved refinement performance and, finally, better SfM results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.87 + ], + "angle": 0, + "content": "Structure From Motion. Feature correspondence-based SfM methods have been extensively studied [3, 16, 35]. Incremental SfM [1, 55, 68] has become a widely adopted approach, with COLMAP [49] recognized as one of the most popular frameworks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Recently, differentiable SfM methods [4, 10, 54, 63, 64, 67] have aimed to simplify or entirely replace the traditional" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.875, + 0.483, + 0.901 + ], + "angle": 0, + "content": "1A keypoint is assigned a set of 2D coordinates, called feature track or track in short, on neighbor images where the keypoint is matched." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6405" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.089, + 0.505, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.09, + 0.904, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.214, + 0.904, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.339, + 0.908, + 0.396 + ], + "angle": 0, + "content": "Figure 2. Pipeline Overview. From a set of images, we construct an initial SfM model using dense two-view matching, filtering unreliable matches through mutual verification. To extend track length, we project 3D points onto additional images, using a visibility filter based on Gaussian Splatting. We then refine these extended tracks with our track refinement module and perform geometric bundle adjustment to improve the accuracy of SfM model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.411, + 0.484, + 0.534 + ], + "angle": 0, + "content": "SfM pipeline. VGGSfM [64] manages all SfM components as fully differentiable, enabling end-to-end training. DUSt3R [67] predicts pairwise pointmaps and refines them through optimization-based global alignment. Its successors, MASt3R [28] and MASt3R-SfM [10], improve pixel matching for localization by predicting additional per-pixel features and leveraging its encoder for fast image retrieval, leading to a newly proposed SfM pipeline." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.484, + 0.644 + ], + "angle": 0, + "content": "Multi-view Refinement. Inconsistent feature points across multiple views can impact the accuracy of reconstructed point cloud and camera poses in SfM. Hence, precise multi-view correspondences are essential for accurately recovering 3D structures and camera parameters in SfM pipelines." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.483, + 0.886 + ], + "angle": 0, + "content": "To address this, several previous methods have proposed multi-view keypoint refinement models based on flow [12] or dense features [30], which lead to significant improvements in SfM accuracy. PatchFlow [12] refines keypoint locations using a geometric cost constrained by local flow between two views, followed by global optimization using a multi-view graph of relative feature geometry constraints. Similarly, PixSfM [30] refines keypoint locations through feature-metric keypoint adjustment by optimizing a direct cost over discriminative dense feature maps along the tracks. DFSfM [24], introduces a multi-view matching module that iteratively refines the tracks obtained from the COLMAP framework. The module extracts local patches from each image and feeds them into a transformer-based network to refine the keypoint's location by enforcing multi-view consistency." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.887, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Building on these recent advancements, we propose a" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.411, + 0.907, + 0.531 + ], + "angle": 0, + "content": "novel refinement module that leverages both feature and positional information to refine the keypoint coordinates within the tracks. Instead of relying on statistical methods to select the refined tracks, our module fully regresses and learns the confidence (certainty) per track, resulting in more accurate refinement. As demonstrated in our ablation study (Tab. 3), our approach outperforms the existing refinement methods." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.543, + 0.605, + 0.559 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.907, + 0.629 + ], + "angle": 0, + "content": "An overview of our Dense-SfM framework is shown in Fig. 2. Given \\(N\\) images \\(\\{I_i\\}\\) of a scene, our goal is to estimate the camera poses and reconstruct the 3D point cloud representing the scene." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.63, + 0.906, + 0.751 + ], + "angle": 0, + "content": "We design our framework as a three-stage pipeline. First, we construct an initial SfM model using correspondences between image pairs from a two-view dense matcher (e.g., DKM [14] and RoMa [15]). Next, we extend the track length of each 3D point by projecting it onto new images where it is visible, verifying visibility through Gaussian Splatting [27]. Finally, we perform iterative SfM refinement to enhance the accuracy of poses and point cloud." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.758, + 0.791, + 0.774 + ], + "angle": 0, + "content": "3.1. Initial SfM via Dense Matching" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.906, + 0.871 + ], + "angle": 0, + "content": "Our framework employs dense feature matching between image pairs, unlike traditional SfM pipelines [49] which rely on sparse keypoints [8, 31]. By employing dense matching, our approach improves the reconstruction of texture-poor scenes and enables the registration of dense 3D points, which is challenging for conventional methods." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "For efficiency, we first sample matches from the dense matching using non-max suppression [8], based on per" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6406" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.151, + 0.089, + 0.422, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.209, + 0.485, + 0.281 + ], + "angle": 0, + "content": "Figure 3. Bidirectional verification on two-view dense matching. The match result \\( p_b \\) from \\( \\mathcal{M}_{A \\to B} \\) is re-used as input to \\( \\mathcal{M}_{B \\to A} \\) to estimate \\( p_{a'} \\). We then compute the distance between \\( p_a \\) and \\( p_{a'} \\), where a smaller distance indicates higher reliability of the match between \\( p_a \\) and \\( p_b \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.294, + 0.484, + 0.369 + ], + "angle": 0, + "content": "pixel confidence scores from the dense matching model's output. Then, we sort out reliable matches by a method called mutual verification using bi-directional dense matching, similar to the mutual-nearest neighbor approach commonly used in detector-based methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.37, + 0.484, + 0.416 + ], + "angle": 0, + "content": "As shown in Fig. 3, from the bi-directional dense matching results \\( M_{A\\rightarrow B} \\) and \\( M_{B\\rightarrow A} \\) between images \\( A \\) and \\( B \\), we define the pixel coordinates \\( p_b \\) and \\( p_{a'} \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.426, + 0.483, + 0.445 + ], + "angle": 0, + "content": "\\[\np _ {b} = \\mathcal {M} _ {A \\rightarrow B} [ p _ {a} ], \\quad p _ {a ^ {\\prime}} = \\mathcal {M} _ {B \\rightarrow A} [ p _ {b} ] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.454, + 0.439, + 0.469 + ], + "angle": 0, + "content": "where \\(p_{a'}\\) is sampled using bilinear-interpolation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.469, + 0.484, + 0.515 + ], + "angle": 0, + "content": "To ensure more reliable matches, we filter out correspondences using a binary mask, which is obtained with the distance from \\( p_a \\) to \\( p_{a'} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.525, + 0.483, + 0.543 + ], + "angle": 0, + "content": "\\[\nB = \\left[ \\left\\| p _ {a} - p _ {a ^ {\\prime}} \\right\\| _ {2} \\leq \\epsilon_ {p} \\right] \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.484, + 0.675 + ], + "angle": 0, + "content": "Using these filtered matches, we construct the initial SfM by triangulating 3D points through dense two-view fine matching. If camera poses are not provided for the reconstruction task, we first perform match quantization [24] and incremental mapping [49] to obtain coarse poses. We then triangulate 3D points using raw matching with the coarse pose and refine both the point cloud and camera poses through the refinement process, as explained in Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.682, + 0.433, + 0.699 + ], + "angle": 0, + "content": "3.2. Track Extension via Gaussian Splitting" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.483, + 0.765 + ], + "angle": 0, + "content": "In the initial SfM, most of the tracks are short, i.e. consisting of mostly two images, due to the fragmentary nature of feature tracks in pair-wise matching, which can limit the performance of track refinement, as shown in DFSfM [24]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Longer tracks, which offer more information on 3D geometry, could improve the track refinement performance. Thus, we generate new matching pairs on the existing matches for consistent multi-view matches, extending the length of track. We achieve this by projecting 3D points (triangulated by two-view matches) onto additional images on which, if successfully projected, the point is considered as visible from the camera pose as illustrated (by the blue dashed line) in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.287 + ], + "angle": 0, + "content": "To determine the visibility of each 3D point from a camera pose, we apply a visibility filter using Gaussian Splating (GS) [27, 72], which supports fast training and rendering. We initialize a GS model with the 3D points obtained in the initial SfM. Specifically, we treat them as small 3D Gaussians setting each mean \\(\\mu \\in \\mathbb{R}^3\\) to the 3D point coordinates, rotation \\(R\\) to the identity matrix, opacity \\(\\alpha\\) to 1, and scale \\(S\\) based on the policy from Splatam [26], which uses focal length and depth information. These Gaussians are optimized and densified to cover the entire scene, while keeping the initial Gaussian's parameters fixed. The details of initialization and training process is described in supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.905, + 0.346 + ], + "angle": 0, + "content": "After training the GS model, we utilize it for evaluating the visibility \\( M \\) of all SfM points (represented as small Gaussians) from each camera pose using the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.342, + 0.905, + 0.386 + ], + "angle": 0, + "content": "\\[\nM = \\left[ \\max _ {r \\in R} \\left\\{\\alpha_ {\\mathrm {S f M}} \\prod_ {j = 1} ^ {N _ {S f M} - 1} (1 - \\alpha_ {j}) \\right\\} > \\epsilon_ {v} \\right] \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.39, + 0.907, + 0.587 + ], + "angle": 0, + "content": "where \\(R\\) is the set of rays from the camera center (of a camera pose) for rendering the image, \\(\\alpha_{\\mathrm{SfM}}\\) is the opacity of Gaussian representing the SfM point (set to 1), \\(N_{SfM}\\) the number of Gaussians along the ray \\(r\\) from the camera center to the SfM point, and \\(\\alpha_{j}\\) the opacity of \\(j\\)-th intermediate Gaussian. If the highest visibility score among the pixels rendered from the Gaussian representing the SfM point is larger than \\(\\epsilon_{\\nu}\\), we consider the SfM point, i.e. \\(N_{SfM}\\)-th Gaussian, visible from the view of the camera pose. For each 3D point, we extend its track by adding its projected 2D point(s) onto the visible view(s). To do that, we project a 3D point \\(P_{j}\\) onto the visible image using camera pose \\(\\{R_i,t_i\\}\\) and intrinsic matrix \\(C_i\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.626, + 0.593, + 0.905, + 0.611 + ], + "angle": 0, + "content": "\\[\np _ {i j} = \\Pi \\left(R _ {i} P _ {j} + t _ {i}, C _ {i}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.615, + 0.906, + 0.705 + ], + "angle": 0, + "content": "Then, we verify the correspondence between the newly obtained 2D point \\( p_{ij} \\) and its associated original 2D keypoint with geometric verification [49] using initial SfM's camera poses. After verified, we add the new 2D point to the track of the 3D point \\( P_j \\), which extends the length of \\( P_j \\)'s track." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.706, + 0.906, + 0.827 + ], + "angle": 0, + "content": "Note that we project the 3D point onto the images that were not involved in the initial triangulation (i.e., establishing a new one-to-one correspondence of 2D-3D matches per image as illustrated with green lines in Fig. 2 (Stage 2). As will be demonstrated in our experiments (Tab. 3), the proposed Track extension enables the subsequent track refinement to produce more refined tracks, which leads to more accurate 3D points in the SfM model." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.834, + 0.746, + 0.849 + ], + "angle": 0, + "content": "3.3. Iterative SfM Refinement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Using the extended tracks, we refine the initial SfM model to obtain improved camera poses and point cloud. Specifically, we iteratively improve the accuracy of feature tracks" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6407" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.485, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.273, + 0.485, + 0.387 + ], + "angle": 0, + "content": "Figure 4. Multi-view kernelized matching architecture. The feature maps from the reference and query views are processed in two ways: first, by a multi-view transformer, applying self and cross-attention and secondly, by a Gaussian Process that computes the posterior mean conditioned on the feature of each query view. All results are concatenated and fed into a CNN decoder, yielding probability distribution of coordinates for refinement \\(\\mathbf{P}_{Q_i}\\) and corresponding confidence score \\(\\mathbf{S}_{Q_i}\\) for each query view." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.398, + 0.484, + 0.445 + ], + "angle": 0, + "content": "by employing our multi-view kernelized matching module alongside bundle adjustment, jointly optimizing camera poses and point cloud." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.452, + 0.321, + 0.466 + ], + "angle": 0, + "content": "3.3.1. Feature Track Refinement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.471, + 0.484, + 0.624 + ], + "angle": 0, + "content": "A feature track (or track) \\(\\mathcal{T}_j = \\{\\mathbf{x}_k\\in \\mathbb{R}^2 |k = 1:N_j\\}\\) represents a set of 2D keypoint locations on multi-view \\((N_{j})\\) images that correspond to a 3D point \\(P_{j}\\). In our proposed method of feature track refinement, each track goes through a multi-view kernelized matching architecture (Fig. 4) and the regression of refined coordinates (Fig. 5). The matching architecture produces two outputs, a probability distribution of coordinate per pixel \\(P_{Q_i}\\) and confidence score \\(S_{Q_i}\\) per view. Then, the regression from these outputs produces a refined track by adjusting the keypoint locations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.484, + 0.795 + ], + "angle": 0, + "content": "Multi-view kernelized matching. Following DFSfM, we split a track into the keypoint of a reference view and those of query views (views from the track except the reference view) with a policy of median depth value. Then, we feed image patches centered at each keypoint into a CNN feature extractor, obtaining feature maps \\(\\mathbf{F}_R\\), \\(\\mathbf{F}_{Q_i} \\in \\mathbb{R}^{p \\times p \\times c}\\), where \\(\\mathbf{F}_R\\) is from the reference view and \\(\\mathbf{F}_{Q_i}\\)'s are from query views. As shown in Fig. 4, our multi-view kernelized matching architecture takes as input these feature maps of reference and query views." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Our proposed matching architecture consists of two paths, feature-based and coordinate-embedding-based ones. On the feature-based path (denoted with Multi-view Transformer in Fig. 4), we utilize a local feature transformer to obtain the transformed feature map \\(\\hat{\\mathbf{F}}_R\\) and \\(\\hat{\\mathbf{F}}_{Q_i}\\) 's through self and cross-attention between \\(\\mathbf{F}_R\\) and \\(\\mathbf{F}_Q\\)'s. On the coordinate-embedding-based path (denoted with Gaussian" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.089, + 0.907, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.266, + 0.907, + 0.406 + ], + "angle": 0, + "content": "Figure 5. Regression of refined coordinate. Top: Selection of refined coordinate on the reference view: From the set of \\( S_{Q_i} \\) values, representing the correspondence scores from the reference view to each query view \\( Q_i \\), we sum over \\( S_{Q_i} \\)'s and select the pixel with the highest score as the refined coordinate for the reference view. Bottom: Regression of refined coordinate on each query view: We apply a channel-wise softmax to obtain a probability distribution of coordinates for each pixel, then calculate a weighted average to determine the correspondence from the reference view to query view \\( Q_i \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.413, + 0.906, + 0.474 + ], + "angle": 0, + "content": "Process in Fig. 4), we employ a Gaussian Process [41] to utilize the positional information, deriving a coordinate embedding feature \\(\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})\\) for each query view. Following DKM [14], we use an exponential cosine similarity kernel:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.478, + 0.905, + 0.526 + ], + "angle": 0, + "content": "\\[\nk \\left(f _ {A}, f _ {B}\\right) = \\exp (- \\tau) \\exp \\left(\\tau \\frac {\\langle f _ {A} , f _ {B} \\rangle}{\\sqrt {\\langle f _ {A} , f _ {A} \\rangle \\langle f _ {B} , f _ {B} \\rangle + \\varepsilon}}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.527, + 0.906, + 0.589 + ], + "angle": 0, + "content": "where \\(f_{A}\\) and \\(f_{B}\\) each is a feature vector from \\(\\mathbf{F}_A\\) and \\(\\mathbf{F}_B\\), respectively. From this kernel function, we build kernel matrices \\(K^{\\mathcal{R}\\mathcal{Q}_i}\\), \\(K^{\\mathcal{Q}_i\\mathcal{Q}_i} \\in \\mathbb{R}^{p^2 \\times p^2}\\) to obtain posterior mean \\(\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.594, + 0.905, + 0.614 + ], + "angle": 0, + "content": "\\[\n\\mu \\left(\\mathbf {F} _ {R} \\mid \\mathbf {F} _ {Q _ {i}}\\right) = K ^ {R Q _ {i}} \\left(K ^ {Q _ {i} Q _ {i}} + \\sigma_ {n} ^ {2} I\\right) ^ {- 1} \\chi^ {Q _ {i}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.623, + 0.907, + 0.688 + ], + "angle": 0, + "content": "where \\(\\chi^{\\mathcal{Q}_i}\\) is the Fourier positional encoding [34] of \\(F_{Q_i}\\)'s pixel coordinate. Finally, we concatenate the transformed feature maps \\(\\hat{\\mathbf{F}}_R\\), \\(\\hat{\\mathbf{F}}_{Q_i}\\) and coordinate embedding \\(\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})\\), and feed them into a CNN decoder \\(D_{\\theta}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.701, + 0.905, + 0.721 + ], + "angle": 0, + "content": "\\[\nP _ {Q _ {i}}, S _ {Q _ {i}} = D _ {\\theta} \\left(\\hat {\\mathbf {F}} _ {R} \\oplus \\hat {\\mathbf {F}} _ {Q _ {i}} \\oplus \\mu \\left(\\mathbf {F} _ {R} \\mid \\mathbf {F} _ {Q _ {i}}\\right)\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.731, + 0.906, + 0.793 + ], + "angle": 0, + "content": "where we obtain a probability distribution of coordinate per pixel \\( P_{Q_i} \\in \\mathbb{R}^{C^2 \\times w \\times w} \\) and confidence score \\( S_{Q_i} \\in \\mathbb{R}^{w \\times w} \\), \\( C^2 \\) is the number of distribution's anchors, and \\( w \\times w \\) a search boundary for refined coordinates." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Regression of keypoint's location. Fig. 5 illustrates how the refined track is obtained. First, we obtain the refined coordinate of keypoint on the reference view. From the output of multi-view kernelized matching, \\(\\{S_{Q_i}\\}\\), we estimate the confidence value of each pixel as the candidate of refined coordinate on the reference view. As shown in Fig. 5 (top)," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6408" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.137 + ], + "angle": 0, + "content": "we select, as the refined coordinate on the reference view, the pixel with the highest value, i.e. the highest confidence from \\(\\sum_{i}S_{Q_i}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.138, + 0.483, + 0.349 + ], + "angle": 0, + "content": "Then, as shown in Fig. 5 (bottom), from the refined coordinate on the reference view (calculated above), we estimate the refined coordinate of keypoint for each query view \\( Q_{i} \\). For each patch of \\( P_{Q_i} \\) of size \\( w\\times w \\), we apply softmax across channels from the pixel of refined coordinate for the reference view, to obtain a probability distribution over a \\( C\\times C \\) grid. The refined coordinate for the query view \\( Q_{i} \\) is then computed as a weighted average, where each pixel's probability serves as its weight. By multiplying each probability by its corresponding pixel coordinate and summing these weighted values, we derive a refined coordinate for query view \\( Q_{i} \\). Finally, we construct the final refined track \\( T_{j}^{*} \\), consisting of the refined coordinates for the reference view and all query views." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.366, + 0.483, + 0.593 + ], + "angle": 0, + "content": "Training setup and loss function. We set up training as in DFSfM [24] using MegaDepth dataset [29]. We use image bags sampled from the SfM model provided in the dataset, in which ground truth tracks are derived from the given camera pose and MVS depth map. For training, we perturb the ground truth 2D locations of tracks in the query views with random noise, providing these as input to our refinement module. Unlike DFSfM, which relies on statistics (variance) as uncertainty measure, we directly learn confidence score through a neural network. Consequently, our loss function is not simply formulated as an \\( L_{2} \\) loss to minimize the distance between the refined tracks and the ground truth tracks. Instead, we jointly predict and learn the confidence \\( S_{Q_i} > 0 \\) for each query view, and include it in the regression loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.598, + 0.483, + 0.636 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\frac {1}{N} \\sum_ {j \\in n _ {t}} \\sum_ {i \\in n _ {j}} s _ {Q _ {i}} \\cdot \\| p _ {Q _ {i}} - p _ {g t} \\| _ {2} - \\alpha \\log s _ {Q _ {i}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.642, + 0.483, + 0.777 + ], + "angle": 0, + "content": "where \\( n_t \\) is the number of feature tracks, \\( n_j \\) the number of query views in a track \\( j \\), \\( N \\) the total number of refined keypoints on all the query views, \\( p_{Q_i} \\) and \\( p_{gt} \\) the learned 2D coordinate from \\( Q_i \\) (as illustrated in Fig. 5) and the ground truth 2D coordinate, respectively, and \\( s_{Q_i} \\) the confidence score of prediction \\( p_{Q_i} \\), which is obtained, from \\( S_{Q_i} \\), at the pixel of the reference view's ground truth keypoint. The second term in the loss is used to avoid being underconfident, where we set \\( \\alpha \\) as 20." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.783, + 0.274, + 0.798 + ], + "angle": 0, + "content": "3.3.2. Bundle Adjustment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.802, + 0.483, + 0.876 + ], + "angle": 0, + "content": "Using the refined feature tracks, we iteratively perform geometric bundle adjustment (BA) [60] to refine the intrinsic parameters \\(\\{C_i\\}\\), camera poses \\(\\{\\xi_i\\}\\), and 3D points' coordinates \\(\\{P_j\\}\\). Formally, we minimize the reprojection error \\(E\\) defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.883, + 0.441, + 0.905 + ], + "angle": 0, + "content": "\\[\nE = \\sum_ {j} \\sum_ {x _ {k} ^ {*} \\in \\mathcal {T} _ {j} ^ {*}} \\rho \\big (\\| \\pi (\\pmb {\\xi} _ {i} \\cdot P _ {j}, C _ {i}) - x _ {k} ^ {*} \\| _ {2} ^ {2} \\big) ,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.182 + ], + "angle": 0, + "content": "where \\(\\pi (\\cdot)\\) projects points to image plane using intrinsic parameter \\(C_i\\), and \\(\\rho (\\cdot)\\) is a robust loss function [21]. We then filter outliers [49, 68] by rejecting points that exceed the maximum reprojection error threshold \\(\\epsilon_{f}\\). After performing BA and outlier filtering, the refined SfM can be passed to the next iteration of feature track refinement and BA." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.201, + 0.646, + 0.218 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.227, + 0.616, + 0.241 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.25, + 0.907, + 0.432 + ], + "angle": 0, + "content": "We use the ETH3D [51], Texture-Poor SfM datasets [24], and Image Matching Challenge (IMC) 2021 dataset [25], each presenting unique challenges across different types of scenes. The ETH3D dataset includes indoor and outdoor scenes with sparsely captured, high-resolution images, and ground truth poses calibrated using Lidar. The Texture-Poor SfM dataset focuses on object-centric scenes with low texture, comprising subsampled image sets. We use all test scenes from the IMC Phototourism dataset, evaluating them with subsampled image bags. The main challenge of this dataset lies in its sparse views, accompanied by significant variations in viewpoint and illumination." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.445, + 0.731, + 0.46 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.468, + 0.906, + 0.529 + ], + "angle": 0, + "content": "For efficiency, we apply non-max suppression [8] with a radius of 4 pixels for ETH3D and 2 pixels for Texture-Poor SfM and IMC dataset. For mutual verification, we filter out matches with a distance exceeding \\(\\epsilon_{p} = 3\\mathrm{px}\\) in Eq. 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.53, + 0.906, + 0.591 + ], + "angle": 0, + "content": "To determine the visibility of Gaussians (SfM points) from a camera pose, we set the visibility threshold \\(\\epsilon_{\\nu}\\) to 0.5 in Eq. 3. Details of training and implementation of Gaussian Splatting are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.592, + 0.907, + 0.803 + ], + "angle": 0, + "content": "We use S2Dnet [18] as a CNN backbone for our refinement architecture, and adopt the multi-view transformer architecture from DFSfM [24]. To ensure a fair comparison, we apply the same refinement parameters as in DFSfM, including a local patch size \\((p = 15)\\) from the feature maps \\(\\mathbf{F}_R\\) and \\(\\mathbf{F}_Q\\), obtained from the CNN backbone, and a search boundary for reference view's refined keypoints set to \\(w = 7\\). The number of distribution anchors \\(C^2\\) is set to \\(7^2\\). For the CNN decoder in Fig. 4, we use a series of residual blocks [22] and channel attention blocks [69]. During bundle adjustment, matches with reprojection errors exceeding \\(\\epsilon_f = 3\\mathrm{px}\\) are discarded. The total SfM refinement process is iterated twice. More implementation details are reported in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.817, + 0.682, + 0.833 + ], + "angle": 0, + "content": "4.3. 3D Triangulation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Accurately triangulating scene point clouds, given known camera poses and intrinsics, is an important task in SfM. In this section, we evaluate the accuracy and completeness of the reconstructed point clouds." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6409" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.089, + 0.481, + 0.244 + ], + "angle": 0, + "content": "
TypeMethodAccuracy (%)Completeness (%)
1cm2cm5cm1cm2cm5cm
Detector-BasedSIFT [31] + NN + PixSfM [30]76.1885.6093.160.170.713.29
D2Net [11] + NN + PixSfM74.7583.8191.980.832.698.95
R2D2 [42] + NN + PixSfM74.1284.4991.980.431.586.71
SP [8] + SG [47] + PixSfM79.0187.0493.800.752.7711.28
Semi-Dense MatchingLoFTR [56] + PixSfM74.4284.0892.632.919.3927.31
LoFTR + DFSfM [24]80.3889.0195.833.7311.0729.54
AspanTrans. [6] + DFSfM77.6387.4095.023.9712.1832.42
MatchFormer [66] + DFSfM79.8688.5195.483.7611.0629.05
Dense-MatchingRoMa + DFSfM79.3288.4295.823.139.7929.10
DKM + Ours84.0591.9697.395.9513.9531.03
RoMa + Ours84.7992.6297.777.3817.0636.35
DeepVGGSfM [64]80.6289.4996.524.5213.1133.96
Point-BasedMast3r-SfM [10]42.0259.7480.582.058.7631.73
Mast3r-SfM + Our Refinement (Sec. 3.3)77.2286.4794.052.408.2627.17
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.251, + 0.483, + 0.293 + ], + "angle": 0, + "content": "Table 1. Results of 3D Triangulation. Our method is compared with the baselines on the ETH3D [51] dataset using accuracy and completeness metrics with different thresholds." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.299, + 0.484, + 0.48 + ], + "angle": 0, + "content": "Evaluation. We use the ETH3D training set, comprising 13 indoor and outdoor scenes with millimeter-accurate dense point clouds as ground truth. Following the protocol in PixSfM [30] and DFSfM [24], we triangulate 3D points using fixed camera poses and intrinsics, then evaluate the resulting point clouds for accuracy and completeness using the ETH3D benchmark [51]. The results are reported at varying distance thresholds (1cm, 2cm, 5cm), averaged across all scenes. Consistent with the benchmark setup, accuracy and completeness are measured by the proportion of triangulated points that fall within the specified distances from the ground truth points." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.501, + 0.484, + 0.698 + ], + "angle": 0, + "content": "Results. The results are shown in Tab. 1. While there is a trade-off between accuracy and completeness, our Dense-SfM framework achieves superior performances on both metrics. Compared to the state-of-the-art baseline LoFTR + DFSfM, our pipeline with RoMa achieves higher accuracy and completeness, thanks to employing dense matching and our proposed pipeline. Also, compared to the RoMa + DFSfM, where we apply quantization on dense matching and refine the tracks as in DFSfM, our method achieves higher performance in terms of both accuracy and completeness, highlighting the effectiveness of our SfM framework. More results with detector-based and semi-dense matching are reported in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.707, + 0.409, + 0.723 + ], + "angle": 0, + "content": "4.4. Multi-View Camera Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.73, + 0.483, + 0.745 + ], + "angle": 0, + "content": "In this section, we evaluate the recovered multi-view poses." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Evaluation protocols. For the evaluation, we use a subset of ETH3D training and test dataset, which includes 22 indoor and outdoor scenes, the Texture-Poor SfM dataset, and the test scenes of IMC 2021 dataset. We evaluate the accuracy of the estimated multi-view poses using the AUC of pose error at various thresholds. For the evaluation of IMC 2021 dataset, due to the high occlusion and appearance changes in many test scenes, directly applying track extension via GS is challenging. Instead, we adopt a" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.183 + ], + "angle": 0, + "content": "quantization method [24] on the matching results, focusing on comparing our multi-view kernelized matching module with DFSfM's refinement module. Specifically, we apply quantization to the matched keypoints with a radius of 4, and then use our refinement module to refine the quantized keypoints." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.19, + 0.898, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.593, + 0.907, + 0.651 + ], + "angle": 0, + "content": "Figure 6. Qualitative Results on Texture-Poor SfM and IMC dataset. Our method with the dense matcher RoMa is qualitatively compared with the baseline LoFTR + DFSfM. The red cameras are ground truth poses while the blue cameras are recovered poses." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.906, + 0.735 + ], + "angle": 0, + "content": "Results. As shown in Tab. 2, our Dense-SfM framework outperforms existing baselines over all datasets. On the ETH3D dataset, our framework with dense matching achieves the highest multi-view pose accuracy, with a particularly large improvement at the highest threshold." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.736, + 0.906, + 0.811 + ], + "angle": 0, + "content": "As shown in Fig. 6, our framework successfully reconstructs dense and accurate 3D points thanks to dense matching and our pipeline, even in challenging low-textured regions with viewpoint changes, leading to much higher pose estimation accuracy." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.68, + 0.833 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.901 + ], + "angle": 0, + "content": "We conduct several experiments to evaluate the key components of our pipeline, including the matching design used as input for SfM and the architectural choices of the refinement module, on the ETH3D dataset using triangulation metrics." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6410" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.115, + 0.089, + 0.885, + 0.276 + ], + "angle": 0, + "content": "
TypeMethodETH3D DatasetTexture-Poor SfM DatasetIMC Dataset
AUC@1°AUC@3°AUC@5°AUC@3°AUC@5°AUC@10°AUC@3°AUC@5°AUC@10°
Detector-BasedCOLMAP (SIFT+NN) [49]26.7138.8642.142.873.854.9523.5823.6644.79
SIFT [31] + NN + PixSfM [30]26.9439.0142.193.134.085.0925.5434.8046.73
D2Net [11] + NN + PixSfM34.5049.7753.581.542.634.548.9112.2616.79
R2D2 [42] + NN + PixSfM43.5862.0966.893.795.517.8431.4141.8054.65
SP [8] + SG [47] + PixSfM50.8268.5272.8614.0019.2324.5545.1957.2270.47
Semi-Dense MatchingLoFTR [56] + PixSfM54.3573.9778.8620.6630.4942.0144.0656.1669.61
LoFTR + DFSIM [24]59.1275.5979.5326.0735.7745.4346.5558.7472.19
AspanTrans. [6] + DFSfM57.2373.7177.7025.7835.6945.6446.7959.0172.50
MatchFormer [66] + DFSfM56.7073.0076.8426.9037.5748.5545.8357.8871.22
Dense MatchingRoMa + DFSfM57.9777.0281.5934.2850.0169.0147.4359.8473.19
DKM + Ours59.0477.7382.2041.1957.2672.9548.6561.0974.37
RoMa + Ours60.9278.4182.6349.9466.2381.4148.4860.7973.90
DeepVGGsF M [64]28.0944.4149.911.866.2621.1045.2358.8973.92
Point-BasedMast3r-SfM [10]35.8558.4665.0343.4661.5178.9742.2654.5367.97
Mast3r-SfM + Our Refinement37.5059.1865.4848.0364.4880.3144.9857.0970.09
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.281, + 0.907, + 0.311 + ], + "angle": 0, + "content": "Table 2. Results of Multi-View Camera Pose Estimation. Our framework is compared with detector-based, detector-free and dense-matching baselines by the AUC of pose error at different thresholds. Bold and underline indicate the best and second-best results." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.321, + 0.481, + 0.483 + ], + "angle": 0, + "content": "
Design ChoiceAccu. (%)Complete. (%)
1cm2cm1cm2cm
(1) Matching designsFull model84.7992.627.3817.06
w/o Mutual Verification84.0392.068.1418.68
w/o GS Extension77.4587.809.4521.64
Quantized Matching (r=4)82.8290.753.5310.62
(2) Refinement designsFull model84.7992.627.3817.06
Multi-view Trans. [24]80.5990.046.0415.2
w/o Gaussian Process72.4784.724.7812.59
w/o Multi-view Trans.83.3991.637.0416.49
w/o ref. confidence selection83.8192.158.8319.85
(3) Number of iterationsNo refine.69.7782.598.6120.4
1 iter81.1290.527.6217.86
2 iter84.7992.67.3817.06
3 iter85.0192.756.7415.91
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.487, + 0.483, + 0.558 + ], + "angle": 0, + "content": "Table 3. Ablation Studies. On the ETH3D dataset, we quantitatively evaluate the impact of design choice of matching and refinement module, and the number of iterations of refinement. The reported triangulation accuracy and completeness are averaged across all scenes." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.565, + 0.483, + 0.716 + ], + "angle": 0, + "content": "Matching Designs. Tab. 3 (1) demonstrates the benefits of our proposed matching filtering (mutual verification) and track extension via Gaussian Splatting (GS). Compared to the configurations without mutual verification, where all matches are used for reconstructing the initial SfM, incorporating mutual verification improves accuracy, with a tradeoff in completeness due to filtering. Moreover, extending match pairs through GS significantly improves accuracy, which shows that using more views for multi-view kernelized matching contribute to higher performance of accuracy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.717, + 0.483, + 0.824 + ], + "angle": 0, + "content": "For a comparison with DFSfM [24], which applies quantization to matched keypoints to address the fragmented track problem, we replaced our GS track extension with their quantization approach, using a rounding ratio of \\( r = 4 \\). Results indicate that our GS track extension not only maintains completeness by avoiding the limitations of quantization but also achieves superior accuracy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.886 + ], + "angle": 0, + "content": "Refinement designs. Table 3 (2) shows the benefit of our proposed multi-view kernelized matching's components in Fig. 4 and confidence-based track selection in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We first compare our refinement module to the multi-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.324, + 0.907, + 0.385 + ], + "angle": 0, + "content": "view refinement module in DFSfM [24], by substituting our refinement module with it. The result shows that our refinement module consistently outperforms the existing approach, achieving higher accuracy and completeness." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.389, + 0.909, + 0.542 + ], + "angle": 0, + "content": "Next, we evaluate the contributions of each component in our refinement architecture (Fig. 4) by testing configurations where either the multi-view transformer or Gaussian Process is removed. The results show that our full model, which integrates both components, achieves the highest performance in accuracy and completeness, confirming that combining feature-based and positional information yields more precise refinement. Furthermore, our strategy of selecting a final refined track based on predicted confidence in the reference view further enhances accuracy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.585, + 0.909, + 0.693 + ], + "angle": 0, + "content": "Impact of iterations. Table 3 (3) reports the results after each refinement iteration. The initial SfM point cloud is less accurate due to reliance solely on initial two-view matching. As the iterations progress, the accuracy of the SfM point cloud gets improved. However, further refinement beyond two iterations gives little gains. So, we limit the refinement to two iterations for efficiency." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.72, + 0.634, + 0.736 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.903 + ], + "angle": 0, + "content": "This paper introduces a novel Dense-SfM framework aimed at reconstructing dense point cloud and estimating camera poses from a set of images. Unlike conventional SfM systems that often rely on initial 2D matches, our framework leverages Gaussian Splatting to generate new matching pairs, producing longer tracks that significantly enhance both the accuracy and density of the reconstructed point cloud. Extensive evaluations on diverse datasets show that our framework consistently outperforms existing SfM baselines across multiple metrics." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "6411" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.271, + 0.108 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.484, + 0.239 + ], + "angle": 0, + "content": "This research was supported in part by Samsung Advanced Institute of Technology (SAIT), the Naver-Intel Co-Lab, Inter-university Semiconductor Research Center (ISRC), and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) [NO.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)]." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.251, + 0.188, + 0.267 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.277, + 0.484, + 0.331 + ], + "angle": 0, + "content": "[1] Sameer Agarwal, Noah Snavely, Ian Simon, Steven M. Seitz, and Richard Szeliski. Building rome in a day. 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Fsgs: Real-time few-shot view synthesis using gaussian splatting, 2024. 1, 2, 4" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.482, + 0.885 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6414" + } + ] +] \ No newline at end of file diff --git a/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_origin.pdf b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f719d622b5d4ac2244da09304ddf79c06ee68530 --- /dev/null +++ b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/39fcbf6f-a095-433d-809d-0e3787aefd05_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d65b039dc8b7665cd82719948a58facd64d681a638ff16ae026a5391d4e0b433 +size 6749917 diff --git a/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/full.md b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e4fb4c96d8bbff8778ccf348a453f9b5bd15eb96 --- /dev/null +++ b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/full.md @@ -0,0 +1,347 @@ +# Dense-SfM: Structure from Motion with Dense Consistent Matching + +JongMin Lee +Seoul National University +jongmin.cy@gmail.com + +Sungjoo Yoo Seoul National University sungjoo.yoo@gmail.com + +# Abstract + +We present Dense-SfM, a novel Structure from Motion (SfM) framework designed for dense and accurate 3D reconstruction from multi-view images. Sparse keypoint matching, which traditional SfM methods often rely on, limits both accuracy and point density, especially in textureless areas. Dense-SfM addresses this limitation by integrating dense matching with a Gaussian Splatting (GS) based track extension which gives more consistent, longer feature tracks. To further improve reconstruction accuracy, Dense-SfM is equipped with a multi-view kernelized matching module leveraging transformer and Gaussian Process architectures, for robust track refinement across multi-views. Evaluations on the ETH3D and Texture-Poor SfM datasets show that Dense-SfM offers significant improvements in accuracy and density over state-of-the-art methods. Project page: https://icetea-cv.github.io/densesfm/. + +# 1. Introduction + +Structure from Motion (SfM) is a fundamental task in computer vision that enables the reconstruction of 3D structures from multi-view images of a scene. It has been a widely researched problem, focusing on reconstructing accurate camera poses and 3D point cloud of a scene, benefiting a variety of downstream tasks such as visual localization [19, 43, 46, 48, 58], AR/VR [39, 70], multi-view stereo [20, 50, 52] and neural rendering [27, 34, 72]. Over the years, several well-established methods have been developed to address the SfM pipeline [36, 40, 49, 55, 68]. + +Recently, there has been an increasing demand for dense and accurate 3D reconstructions in various 3D vision tasks, including dense reconstruction [17, 65], object pose estimation [5, 23, 57] and neural rendering [27, 72]. However, existing detector-based methods have limitations in achieving sufficient accuracy and density of 3D points, especially in texture-less regions where obtaining matchable keypoints is challenging, limiting the performance of downstream tasks. With the advent of deep learning and atten + +![](images/35a41e1a450f0fe8c2f80e11ae7367195ba37a4fbf6ac14ff8e8609a7c1947b8.jpg) + +![](images/e93e564a471819a50fe507198a7a44fb4bc399881700a0ae0c1a8113d00f7e51.jpg) +Figure 1. Comparison of SfM results between quantized-matching and our matching. To solve the fragmentary track problem, DFSfM [24] uses quantized matching, which can compromise the accuracy and completeness of 3D points due to quantization. In contrast, our Dense-SfM pipeline leverages Gaussian Splatting to solve the problem, offering more accurate and dense 3D points. Thanks to dense matching, our pipeline can also be applied to texture-less objects, further improving the quality of 3D points and pose estimation. + +tion mechanism [62], semi-dense and dense matching methods [6, 14, 15, 56, 66] have been introduced, enabling the reliable matches even in low-texture areas and producing denser match results than classical detector-based methods. This advancement has led to improved performance across many tasks, including homography and relative pose estimation [2, 7, 29]. However, due to their pairwise matching approach, the matching methods usually yield fragmented + +tracks $^1$ as mentioned in Detector-Free SfM (DFSfM) [24], making direct integration with existing SfM pipelines challenging. To solve this inconsistency issue, DFSfM applied quantization to the matched keypoints, and then refined the multi-view tracks to obtain accurate camera pose and point cloud. While the quantization strategy can increase track length and consistency, enhancing the multi-view refinement results, it can significantly limit the number of matches and accuracy, reducing the quality of the resulting SfM model, as exemplified in Fig. 1. + +In this paper, we propose a novel SfM framework that leverages dense matching while addressing the limitations of pairwise matching methods. As shown in Fig. 1, our approach reconstructs a dense and accurate 3D point cloud, avoiding the inherent limitations of quantized matching. Specifically, our framework first performs dense matching using a dense matcher, e.g., DKM [14] or RoMa [15], to construct an initial SfM model, where most tracks are initially fragmentary, i.e., of short (mostly a pair of images) lengths. Next, we initialize small 3D Gaussians based on the initial SfM's point cloud, integrating attributes like color and position. These Gaussians are then optimized and denified through Gaussian Splatting (GS) [27, 72], filling in the scene while keeping the initial Gaussians' (SfM points') positions fixed. We then infer the visibility of each initial SfM point per image by rendering through the ray from camera poses. In case that the 3D point is visible on the image, we include the image into the track of the 3D point thereby increasing the track length—a process we refer to as Track Extension. Note that Track Extension enables us to resolve the problem of short tracks in pairwise matching. Lastly, we perform our proposed SfM refinement pipeline, which includes a multi-view kernelized matching module and geometric bundle adjustment, to further optimize the camera poses and 3D points. Our track refinement module is mainly built on two architectures, transformer and Gaussian Process [41], which incorporate both feature-based and positional information, resulting in notable performance gains over existing refinement modules as demonstrated in our ablation study (Tab. 3). + +We evaluate our Dense-SfM framework on the ETH3D, Texture-Poor SfM and Image Matching Challenge (IMC) 2021 datasets, where it outperforms state-of-the-art SfM systems across multiple metrics. Thanks to the dense matching coupled with track extension via Gaussian Splating, as well as our novel track refinement module, our framework achieves accurate camera pose estimations and dense 3D reconstructions. + +# Contributions: + +- A novel SfM framework optimized for dense matchers, + +capable of reconstructing highly accurate and dense 3D models, even in texture-less regions. + +- A track extension method that, based on Gaussian Splatting, helps find new images on which 3D point is visible, thereby increasing track length of the 3D point. +- A new track refinement pipeline that leverages transformer and Gaussian Process architectures to enhance the consistency of feature tracks and refine the overall reconstruction quality. +- Extensive evaluations across diverse metrics demonstrate that our framework achieves state-of-the-art performance. + +# 2. Related Work + +Image Matching. Establishing 2D correspondences through feature matching is a fundamental component for SfM and visual SLAM. Traditional feature matching typically involves i) detecting keypoints [8, 11, 31, 42, 44, 45], ii) computing descriptors [13, 32, 33, 37, 59, 61] and iii) performing descriptor matching [18, 47, 71]. Despite its efficiency, it struggles in challenging scenarios such as low-textured regions, where keypoint detection is unreliable, and repetitive patterns, where matching often fails—leading to suboptimal SfM results. + +To address these limitations, more recent methods bypass the need for keypoint detection and instead directly perform semi-dense [6, 56, 66] or dense [14, 15] matching between image pairs. These approaches benefit from global receptive fields provided by transformers [62] or correlations computed from CNN or ViT features [9, 38], which allows them to achieve better performance in texture-poor areas where traditional methods often fail. + +However, semi-dense and dense matching often results in fragmentary feature tracks, making it difficult to apply on SfM pipeline [53]. To solve this, DFSfM [24] introduced quantization matching that merges nearby subpixel matches into grid nodes, improving track consistency. Yet, this approach can compromise the accuracy of the initial camera poses and point clouds, heavily relying on refinement modules and reducing point cloud density. + +In contrast, our framework leverages Gaussian Splatting to assess visibility of 3D points. By projecting 3D points onto new images on which the points are visible, we obtain longer and consistent tracks without sacrificing the initial matching accuracy, which leads to improved refinement performance and, finally, better SfM results. + +Structure From Motion. Feature correspondence-based SfM methods have been extensively studied [3, 16, 35]. Incremental SfM [1, 55, 68] has become a widely adopted approach, with COLMAP [49] recognized as one of the most popular frameworks. + +Recently, differentiable SfM methods [4, 10, 54, 63, 64, 67] have aimed to simplify or entirely replace the traditional + +![](images/b5504cd38dce0bc0f9e03ce98cd773a1eb575dd82ce21e65dbd4513ce5b446d8.jpg) + +![](images/85b1842134afd64004d2e058898812f42f6b6ecaa4125a4500d2b8677b4cd64d.jpg) + +![](images/0cb4eddbb99e02a74a0286456273d380d874764f1c967aa9949ca4cff64c84cf.jpg) +Figure 2. Pipeline Overview. From a set of images, we construct an initial SfM model using dense two-view matching, filtering unreliable matches through mutual verification. To extend track length, we project 3D points onto additional images, using a visibility filter based on Gaussian Splatting. We then refine these extended tracks with our track refinement module and perform geometric bundle adjustment to improve the accuracy of SfM model. + +SfM pipeline. VGGSfM [64] manages all SfM components as fully differentiable, enabling end-to-end training. DUSt3R [67] predicts pairwise pointmaps and refines them through optimization-based global alignment. Its successors, MASt3R [28] and MASt3R-SfM [10], improve pixel matching for localization by predicting additional per-pixel features and leveraging its encoder for fast image retrieval, leading to a newly proposed SfM pipeline. + +Multi-view Refinement. Inconsistent feature points across multiple views can impact the accuracy of reconstructed point cloud and camera poses in SfM. Hence, precise multi-view correspondences are essential for accurately recovering 3D structures and camera parameters in SfM pipelines. + +To address this, several previous methods have proposed multi-view keypoint refinement models based on flow [12] or dense features [30], which lead to significant improvements in SfM accuracy. PatchFlow [12] refines keypoint locations using a geometric cost constrained by local flow between two views, followed by global optimization using a multi-view graph of relative feature geometry constraints. Similarly, PixSfM [30] refines keypoint locations through feature-metric keypoint adjustment by optimizing a direct cost over discriminative dense feature maps along the tracks. DFSfM [24], introduces a multi-view matching module that iteratively refines the tracks obtained from the COLMAP framework. The module extracts local patches from each image and feeds them into a transformer-based network to refine the keypoint's location by enforcing multi-view consistency. + +Building on these recent advancements, we propose a + +novel refinement module that leverages both feature and positional information to refine the keypoint coordinates within the tracks. Instead of relying on statistical methods to select the refined tracks, our module fully regresses and learns the confidence (certainty) per track, resulting in more accurate refinement. As demonstrated in our ablation study (Tab. 3), our approach outperforms the existing refinement methods. + +# 3. Method + +An overview of our Dense-SfM framework is shown in Fig. 2. Given $N$ images $\{I_i\}$ of a scene, our goal is to estimate the camera poses and reconstruct the 3D point cloud representing the scene. + +We design our framework as a three-stage pipeline. First, we construct an initial SfM model using correspondences between image pairs from a two-view dense matcher (e.g., DKM [14] and RoMa [15]). Next, we extend the track length of each 3D point by projecting it onto new images where it is visible, verifying visibility through Gaussian Splatting [27]. Finally, we perform iterative SfM refinement to enhance the accuracy of poses and point cloud. + +# 3.1. Initial SfM via Dense Matching + +Our framework employs dense feature matching between image pairs, unlike traditional SfM pipelines [49] which rely on sparse keypoints [8, 31]. By employing dense matching, our approach improves the reconstruction of texture-poor scenes and enables the registration of dense 3D points, which is challenging for conventional methods. + +For efficiency, we first sample matches from the dense matching using non-max suppression [8], based on per + +![](images/bcc3fe6f952ef0889c80a6dbd3e7c2cd99034912fcf9c428940e485c65185fb2.jpg) +Figure 3. Bidirectional verification on two-view dense matching. The match result $p_b$ from $\mathcal{M}_{A \to B}$ is re-used as input to $\mathcal{M}_{B \to A}$ to estimate $p_{a'}$ . We then compute the distance between $p_a$ and $p_{a'}$ , where a smaller distance indicates higher reliability of the match between $p_a$ and $p_b$ . + +pixel confidence scores from the dense matching model's output. Then, we sort out reliable matches by a method called mutual verification using bi-directional dense matching, similar to the mutual-nearest neighbor approach commonly used in detector-based methods. + +As shown in Fig. 3, from the bi-directional dense matching results $M_{A\rightarrow B}$ and $M_{B\rightarrow A}$ between images $A$ and $B$ , we define the pixel coordinates $p_b$ and $p_{a'}$ as + +$$ +p _ {b} = \mathcal {M} _ {A \rightarrow B} [ p _ {a} ], \quad p _ {a ^ {\prime}} = \mathcal {M} _ {B \rightarrow A} [ p _ {b} ] \tag {1} +$$ + +where $p_{a'}$ is sampled using bilinear-interpolation. + +To ensure more reliable matches, we filter out correspondences using a binary mask, which is obtained with the distance from $p_a$ to $p_{a'}$ as follows: + +$$ +B = \left[ \left\| p _ {a} - p _ {a ^ {\prime}} \right\| _ {2} \leq \epsilon_ {p} \right] \tag {2} +$$ + +Using these filtered matches, we construct the initial SfM by triangulating 3D points through dense two-view fine matching. If camera poses are not provided for the reconstruction task, we first perform match quantization [24] and incremental mapping [49] to obtain coarse poses. We then triangulate 3D points using raw matching with the coarse pose and refine both the point cloud and camera poses through the refinement process, as explained in Sec. 3.3. + +# 3.2. Track Extension via Gaussian Splitting + +In the initial SfM, most of the tracks are short, i.e. consisting of mostly two images, due to the fragmentary nature of feature tracks in pair-wise matching, which can limit the performance of track refinement, as shown in DFSfM [24]. + +Longer tracks, which offer more information on 3D geometry, could improve the track refinement performance. Thus, we generate new matching pairs on the existing matches for consistent multi-view matches, extending the length of track. We achieve this by projecting 3D points (triangulated by two-view matches) onto additional images on which, if successfully projected, the point is considered as visible from the camera pose as illustrated (by the blue dashed line) in Fig. 2. + +To determine the visibility of each 3D point from a camera pose, we apply a visibility filter using Gaussian Splating (GS) [27, 72], which supports fast training and rendering. We initialize a GS model with the 3D points obtained in the initial SfM. Specifically, we treat them as small 3D Gaussians setting each mean $\mu \in \mathbb{R}^3$ to the 3D point coordinates, rotation $R$ to the identity matrix, opacity $\alpha$ to 1, and scale $S$ based on the policy from Splatam [26], which uses focal length and depth information. These Gaussians are optimized and densified to cover the entire scene, while keeping the initial Gaussian's parameters fixed. The details of initialization and training process is described in supplementary material. + +After training the GS model, we utilize it for evaluating the visibility $M$ of all SfM points (represented as small Gaussians) from each camera pose using the following formula: + +$$ +M = \left[ \max _ {r \in R} \left\{\alpha_ {\mathrm {S f M}} \prod_ {j = 1} ^ {N _ {S f M} - 1} (1 - \alpha_ {j}) \right\} > \epsilon_ {v} \right] \tag {3} +$$ + +where $R$ is the set of rays from the camera center (of a camera pose) for rendering the image, $\alpha_{\mathrm{SfM}}$ is the opacity of Gaussian representing the SfM point (set to 1), $N_{SfM}$ the number of Gaussians along the ray $r$ from the camera center to the SfM point, and $\alpha_{j}$ the opacity of $j$ -th intermediate Gaussian. If the highest visibility score among the pixels rendered from the Gaussian representing the SfM point is larger than $\epsilon_{\nu}$ , we consider the SfM point, i.e. $N_{SfM}$ -th Gaussian, visible from the view of the camera pose. For each 3D point, we extend its track by adding its projected 2D point(s) onto the visible view(s). To do that, we project a 3D point $P_{j}$ onto the visible image using camera pose $\{R_i,t_i\}$ and intrinsic matrix $C_i$ as follows: + +$$ +p _ {i j} = \Pi \left(R _ {i} P _ {j} + t _ {i}, C _ {i}\right) \tag {4} +$$ + +Then, we verify the correspondence between the newly obtained 2D point $p_{ij}$ and its associated original 2D keypoint with geometric verification [49] using initial SfM's camera poses. After verified, we add the new 2D point to the track of the 3D point $P_j$ , which extends the length of $P_j$ 's track. + +Note that we project the 3D point onto the images that were not involved in the initial triangulation (i.e., establishing a new one-to-one correspondence of 2D-3D matches per image as illustrated with green lines in Fig. 2 (Stage 2). As will be demonstrated in our experiments (Tab. 3), the proposed Track extension enables the subsequent track refinement to produce more refined tracks, which leads to more accurate 3D points in the SfM model. + +# 3.3. Iterative SfM Refinement + +Using the extended tracks, we refine the initial SfM model to obtain improved camera poses and point cloud. Specifically, we iteratively improve the accuracy of feature tracks + +![](images/5c14b51d1a7394ad3699c195deba40c33974e8a8b2ec30b1eafb635f8889a17a.jpg) +Figure 4. Multi-view kernelized matching architecture. The feature maps from the reference and query views are processed in two ways: first, by a multi-view transformer, applying self and cross-attention and secondly, by a Gaussian Process that computes the posterior mean conditioned on the feature of each query view. All results are concatenated and fed into a CNN decoder, yielding probability distribution of coordinates for refinement $\mathbf{P}_{Q_i}$ and corresponding confidence score $\mathbf{S}_{Q_i}$ for each query view. + +by employing our multi-view kernelized matching module alongside bundle adjustment, jointly optimizing camera poses and point cloud. + +# 3.3.1. Feature Track Refinement + +A feature track (or track) $\mathcal{T}_j = \{\mathbf{x}_k\in \mathbb{R}^2 |k = 1:N_j\}$ represents a set of 2D keypoint locations on multi-view $(N_{j})$ images that correspond to a 3D point $P_{j}$ . In our proposed method of feature track refinement, each track goes through a multi-view kernelized matching architecture (Fig. 4) and the regression of refined coordinates (Fig. 5). The matching architecture produces two outputs, a probability distribution of coordinate per pixel $P_{Q_i}$ and confidence score $S_{Q_i}$ per view. Then, the regression from these outputs produces a refined track by adjusting the keypoint locations. + +Multi-view kernelized matching. Following DFSfM, we split a track into the keypoint of a reference view and those of query views (views from the track except the reference view) with a policy of median depth value. Then, we feed image patches centered at each keypoint into a CNN feature extractor, obtaining feature maps $\mathbf{F}_R$ , $\mathbf{F}_{Q_i} \in \mathbb{R}^{p \times p \times c}$ , where $\mathbf{F}_R$ is from the reference view and $\mathbf{F}_{Q_i}$ 's are from query views. As shown in Fig. 4, our multi-view kernelized matching architecture takes as input these feature maps of reference and query views. + +Our proposed matching architecture consists of two paths, feature-based and coordinate-embedding-based ones. On the feature-based path (denoted with Multi-view Transformer in Fig. 4), we utilize a local feature transformer to obtain the transformed feature map $\hat{\mathbf{F}}_R$ and $\hat{\mathbf{F}}_{Q_i}$ 's through self and cross-attention between $\mathbf{F}_R$ and $\mathbf{F}_Q$ 's. On the coordinate-embedding-based path (denoted with Gaussian + +![](images/593bdd7af826a6c00bb3827019f3e14e38bcb5c2041e368781f72e10095bae0e.jpg) +Figure 5. Regression of refined coordinate. Top: Selection of refined coordinate on the reference view: From the set of $S_{Q_i}$ values, representing the correspondence scores from the reference view to each query view $Q_i$ , we sum over $S_{Q_i}$ 's and select the pixel with the highest score as the refined coordinate for the reference view. Bottom: Regression of refined coordinate on each query view: We apply a channel-wise softmax to obtain a probability distribution of coordinates for each pixel, then calculate a weighted average to determine the correspondence from the reference view to query view $Q_i$ . + +Process in Fig. 4), we employ a Gaussian Process [41] to utilize the positional information, deriving a coordinate embedding feature $\mu (\mathbf{F}_R|\mathbf{F}_{Q_i})$ for each query view. Following DKM [14], we use an exponential cosine similarity kernel: + +$$ +k \left(f _ {A}, f _ {B}\right) = \exp (- \tau) \exp \left(\tau \frac {\langle f _ {A} , f _ {B} \rangle}{\sqrt {\langle f _ {A} , f _ {A} \rangle \langle f _ {B} , f _ {B} \rangle + \varepsilon}}\right), \tag {5} +$$ + +where $f_{A}$ and $f_{B}$ each is a feature vector from $\mathbf{F}_A$ and $\mathbf{F}_B$ , respectively. From this kernel function, we build kernel matrices $K^{\mathcal{R}\mathcal{Q}_i}$ , $K^{\mathcal{Q}_i\mathcal{Q}_i} \in \mathbb{R}^{p^2 \times p^2}$ to obtain posterior mean $\mu (\mathbf{F}_R|\mathbf{F}_{Q_i})$ as follows: + +$$ +\mu \left(\mathbf {F} _ {R} \mid \mathbf {F} _ {Q _ {i}}\right) = K ^ {R Q _ {i}} \left(K ^ {Q _ {i} Q _ {i}} + \sigma_ {n} ^ {2} I\right) ^ {- 1} \chi^ {Q _ {i}} \tag {6} +$$ + +where $\chi^{\mathcal{Q}_i}$ is the Fourier positional encoding [34] of $F_{Q_i}$ 's pixel coordinate. Finally, we concatenate the transformed feature maps $\hat{\mathbf{F}}_R$ , $\hat{\mathbf{F}}_{Q_i}$ and coordinate embedding $\mu (\mathbf{F}_R|\mathbf{F}_{Q_i})$ , and feed them into a CNN decoder $D_{\theta}$ : + +$$ +P _ {Q _ {i}}, S _ {Q _ {i}} = D _ {\theta} \left(\hat {\mathbf {F}} _ {R} \oplus \hat {\mathbf {F}} _ {Q _ {i}} \oplus \mu \left(\mathbf {F} _ {R} \mid \mathbf {F} _ {Q _ {i}}\right)\right) \tag {7} +$$ + +where we obtain a probability distribution of coordinate per pixel $P_{Q_i} \in \mathbb{R}^{C^2 \times w \times w}$ and confidence score $S_{Q_i} \in \mathbb{R}^{w \times w}$ , $C^2$ is the number of distribution's anchors, and $w \times w$ a search boundary for refined coordinates. + +Regression of keypoint's location. Fig. 5 illustrates how the refined track is obtained. First, we obtain the refined coordinate of keypoint on the reference view. From the output of multi-view kernelized matching, $\{S_{Q_i}\}$ , we estimate the confidence value of each pixel as the candidate of refined coordinate on the reference view. As shown in Fig. 5 (top), + +we select, as the refined coordinate on the reference view, the pixel with the highest value, i.e. the highest confidence from $\sum_{i}S_{Q_i}$ + +Then, as shown in Fig. 5 (bottom), from the refined coordinate on the reference view (calculated above), we estimate the refined coordinate of keypoint for each query view $Q_{i}$ . For each patch of $P_{Q_i}$ of size $w\times w$ , we apply softmax across channels from the pixel of refined coordinate for the reference view, to obtain a probability distribution over a $C\times C$ grid. The refined coordinate for the query view $Q_{i}$ is then computed as a weighted average, where each pixel's probability serves as its weight. By multiplying each probability by its corresponding pixel coordinate and summing these weighted values, we derive a refined coordinate for query view $Q_{i}$ . Finally, we construct the final refined track $T_{j}^{*}$ , consisting of the refined coordinates for the reference view and all query views. + +Training setup and loss function. We set up training as in DFSfM [24] using MegaDepth dataset [29]. We use image bags sampled from the SfM model provided in the dataset, in which ground truth tracks are derived from the given camera pose and MVS depth map. For training, we perturb the ground truth 2D locations of tracks in the query views with random noise, providing these as input to our refinement module. Unlike DFSfM, which relies on statistics (variance) as uncertainty measure, we directly learn confidence score through a neural network. Consequently, our loss function is not simply formulated as an $L_{2}$ loss to minimize the distance between the refined tracks and the ground truth tracks. Instead, we jointly predict and learn the confidence $S_{Q_i} > 0$ for each query view, and include it in the regression loss as follows: + +$$ +\mathcal {L} = \frac {1}{N} \sum_ {j \in n _ {t}} \sum_ {i \in n _ {j}} s _ {Q _ {i}} \cdot \| p _ {Q _ {i}} - p _ {g t} \| _ {2} - \alpha \log s _ {Q _ {i}}. \tag {8} +$$ + +where $n_t$ is the number of feature tracks, $n_j$ the number of query views in a track $j$ , $N$ the total number of refined keypoints on all the query views, $p_{Q_i}$ and $p_{gt}$ the learned 2D coordinate from $Q_i$ (as illustrated in Fig. 5) and the ground truth 2D coordinate, respectively, and $s_{Q_i}$ the confidence score of prediction $p_{Q_i}$ , which is obtained, from $S_{Q_i}$ , at the pixel of the reference view's ground truth keypoint. The second term in the loss is used to avoid being underconfident, where we set $\alpha$ as 20. + +# 3.3.2. Bundle Adjustment + +Using the refined feature tracks, we iteratively perform geometric bundle adjustment (BA) [60] to refine the intrinsic parameters $\{C_i\}$ , camera poses $\{\xi_i\}$ , and 3D points' coordinates $\{P_j\}$ . Formally, we minimize the reprojection error $E$ defined as: + +$$ +E = \sum_ {j} \sum_ {x _ {k} ^ {*} \in \mathcal {T} _ {j} ^ {*}} \rho \big (\| \pi (\pmb {\xi} _ {i} \cdot P _ {j}, C _ {i}) - x _ {k} ^ {*} \| _ {2} ^ {2} \big) , +$$ + +where $\pi (\cdot)$ projects points to image plane using intrinsic parameter $C_i$ , and $\rho (\cdot)$ is a robust loss function [21]. We then filter outliers [49, 68] by rejecting points that exceed the maximum reprojection error threshold $\epsilon_{f}$ . After performing BA and outlier filtering, the refined SfM can be passed to the next iteration of feature track refinement and BA. + +# 4. Experiments + +# 4.1. Datasets + +We use the ETH3D [51], Texture-Poor SfM datasets [24], and Image Matching Challenge (IMC) 2021 dataset [25], each presenting unique challenges across different types of scenes. The ETH3D dataset includes indoor and outdoor scenes with sparsely captured, high-resolution images, and ground truth poses calibrated using Lidar. The Texture-Poor SfM dataset focuses on object-centric scenes with low texture, comprising subsampled image sets. We use all test scenes from the IMC Phototourism dataset, evaluating them with subsampled image bags. The main challenge of this dataset lies in its sparse views, accompanied by significant variations in viewpoint and illumination. + +# 4.2. Implementation Details + +For efficiency, we apply non-max suppression [8] with a radius of 4 pixels for ETH3D and 2 pixels for Texture-Poor SfM and IMC dataset. For mutual verification, we filter out matches with a distance exceeding $\epsilon_{p} = 3\mathrm{px}$ in Eq. 2. + +To determine the visibility of Gaussians (SfM points) from a camera pose, we set the visibility threshold $\epsilon_{\nu}$ to 0.5 in Eq. 3. Details of training and implementation of Gaussian Splatting are provided in the supplementary material. + +We use S2Dnet [18] as a CNN backbone for our refinement architecture, and adopt the multi-view transformer architecture from DFSfM [24]. To ensure a fair comparison, we apply the same refinement parameters as in DFSfM, including a local patch size $(p = 15)$ from the feature maps $\mathbf{F}_R$ and $\mathbf{F}_Q$ , obtained from the CNN backbone, and a search boundary for reference view's refined keypoints set to $w = 7$ . The number of distribution anchors $C^2$ is set to $7^2$ . For the CNN decoder in Fig. 4, we use a series of residual blocks [22] and channel attention blocks [69]. During bundle adjustment, matches with reprojection errors exceeding $\epsilon_f = 3\mathrm{px}$ are discarded. The total SfM refinement process is iterated twice. More implementation details are reported in the supplementary material. + +# 4.3. 3D Triangulation + +Accurately triangulating scene point clouds, given known camera poses and intrinsics, is an important task in SfM. In this section, we evaluate the accuracy and completeness of the reconstructed point clouds. + +
TypeMethodAccuracy (%)Completeness (%)
1cm2cm5cm1cm2cm5cm
Detector-BasedSIFT [31] + NN + PixSfM [30]76.1885.6093.160.170.713.29
D2Net [11] + NN + PixSfM74.7583.8191.980.832.698.95
R2D2 [42] + NN + PixSfM74.1284.4991.980.431.586.71
SP [8] + SG [47] + PixSfM79.0187.0493.800.752.7711.28
Semi-Dense MatchingLoFTR [56] + PixSfM74.4284.0892.632.919.3927.31
LoFTR + DFSfM [24]80.3889.0195.833.7311.0729.54
AspanTrans. [6] + DFSfM77.6387.4095.023.9712.1832.42
MatchFormer [66] + DFSfM79.8688.5195.483.7611.0629.05
Dense-MatchingRoMa + DFSfM79.3288.4295.823.139.7929.10
DKM + Ours84.0591.9697.395.9513.9531.03
RoMa + Ours84.7992.6297.777.3817.0636.35
DeepVGGSfM [64]80.6289.4996.524.5213.1133.96
Point-BasedMast3r-SfM [10]42.0259.7480.582.058.7631.73
Mast3r-SfM + Our Refinement (Sec. 3.3)77.2286.4794.052.408.2627.17
+ +Table 1. Results of 3D Triangulation. Our method is compared with the baselines on the ETH3D [51] dataset using accuracy and completeness metrics with different thresholds. + +Evaluation. We use the ETH3D training set, comprising 13 indoor and outdoor scenes with millimeter-accurate dense point clouds as ground truth. Following the protocol in PixSfM [30] and DFSfM [24], we triangulate 3D points using fixed camera poses and intrinsics, then evaluate the resulting point clouds for accuracy and completeness using the ETH3D benchmark [51]. The results are reported at varying distance thresholds (1cm, 2cm, 5cm), averaged across all scenes. Consistent with the benchmark setup, accuracy and completeness are measured by the proportion of triangulated points that fall within the specified distances from the ground truth points. + +Results. The results are shown in Tab. 1. While there is a trade-off between accuracy and completeness, our Dense-SfM framework achieves superior performances on both metrics. Compared to the state-of-the-art baseline LoFTR + DFSfM, our pipeline with RoMa achieves higher accuracy and completeness, thanks to employing dense matching and our proposed pipeline. Also, compared to the RoMa + DFSfM, where we apply quantization on dense matching and refine the tracks as in DFSfM, our method achieves higher performance in terms of both accuracy and completeness, highlighting the effectiveness of our SfM framework. More results with detector-based and semi-dense matching are reported in the supplementary material. + +# 4.4. Multi-View Camera Pose Estimation + +In this section, we evaluate the recovered multi-view poses. + +Evaluation protocols. For the evaluation, we use a subset of ETH3D training and test dataset, which includes 22 indoor and outdoor scenes, the Texture-Poor SfM dataset, and the test scenes of IMC 2021 dataset. We evaluate the accuracy of the estimated multi-view poses using the AUC of pose error at various thresholds. For the evaluation of IMC 2021 dataset, due to the high occlusion and appearance changes in many test scenes, directly applying track extension via GS is challenging. Instead, we adopt a + +quantization method [24] on the matching results, focusing on comparing our multi-view kernelized matching module with DFSfM's refinement module. Specifically, we apply quantization to the matched keypoints with a radius of 4, and then use our refinement module to refine the quantized keypoints. + +![](images/4d71db4223592121d4edf85d100411088846adf93f1457a223172a1a88f39e55.jpg) +Figure 6. Qualitative Results on Texture-Poor SfM and IMC dataset. Our method with the dense matcher RoMa is qualitatively compared with the baseline LoFTR + DFSfM. The red cameras are ground truth poses while the blue cameras are recovered poses. + +Results. As shown in Tab. 2, our Dense-SfM framework outperforms existing baselines over all datasets. On the ETH3D dataset, our framework with dense matching achieves the highest multi-view pose accuracy, with a particularly large improvement at the highest threshold. + +As shown in Fig. 6, our framework successfully reconstructs dense and accurate 3D points thanks to dense matching and our pipeline, even in challenging low-textured regions with viewpoint changes, leading to much higher pose estimation accuracy. + +# 4.5. Ablation Studies + +We conduct several experiments to evaluate the key components of our pipeline, including the matching design used as input for SfM and the architectural choices of the refinement module, on the ETH3D dataset using triangulation metrics. + +
TypeMethodETH3D DatasetTexture-Poor SfM DatasetIMC Dataset
AUC@1°AUC@3°AUC@5°AUC@3°AUC@5°AUC@10°AUC@3°AUC@5°AUC@10°
Detector-BasedCOLMAP (SIFT+NN) [49]26.7138.8642.142.873.854.9523.5823.6644.79
SIFT [31] + NN + PixSfM [30]26.9439.0142.193.134.085.0925.5434.8046.73
D2Net [11] + NN + PixSfM34.5049.7753.581.542.634.548.9112.2616.79
R2D2 [42] + NN + PixSfM43.5862.0966.893.795.517.8431.4141.8054.65
SP [8] + SG [47] + PixSfM50.8268.5272.8614.0019.2324.5545.1957.2270.47
Semi-Dense MatchingLoFTR [56] + PixSfM54.3573.9778.8620.6630.4942.0144.0656.1669.61
LoFTR + DFSIM [24]59.1275.5979.5326.0735.7745.4346.5558.7472.19
AspanTrans. [6] + DFSfM57.2373.7177.7025.7835.6945.6446.7959.0172.50
MatchFormer [66] + DFSfM56.7073.0076.8426.9037.5748.5545.8357.8871.22
Dense MatchingRoMa + DFSfM57.9777.0281.5934.2850.0169.0147.4359.8473.19
DKM + Ours59.0477.7382.2041.1957.2672.9548.6561.0974.37
RoMa + Ours60.9278.4182.6349.9466.2381.4148.4860.7973.90
DeepVGGsF M [64]28.0944.4149.911.866.2621.1045.2358.8973.92
Point-BasedMast3r-SfM [10]35.8558.4665.0343.4661.5178.9742.2654.5367.97
Mast3r-SfM + Our Refinement37.5059.1865.4848.0364.4880.3144.9857.0970.09
+ +Table 2. Results of Multi-View Camera Pose Estimation. Our framework is compared with detector-based, detector-free and dense-matching baselines by the AUC of pose error at different thresholds. Bold and underline indicate the best and second-best results. + +
Design ChoiceAccu. (%)Complete. (%)
1cm2cm1cm2cm
(1) Matching designsFull model84.7992.627.3817.06
w/o Mutual Verification84.0392.068.1418.68
w/o GS Extension77.4587.809.4521.64
Quantized Matching (r=4)82.8290.753.5310.62
(2) Refinement designsFull model84.7992.627.3817.06
Multi-view Trans. [24]80.5990.046.0415.2
w/o Gaussian Process72.4784.724.7812.59
w/o Multi-view Trans.83.3991.637.0416.49
w/o ref. confidence selection83.8192.158.8319.85
(3) Number of iterationsNo refine.69.7782.598.6120.4
1 iter81.1290.527.6217.86
2 iter84.7992.67.3817.06
3 iter85.0192.756.7415.91
+ +Table 3. Ablation Studies. On the ETH3D dataset, we quantitatively evaluate the impact of design choice of matching and refinement module, and the number of iterations of refinement. The reported triangulation accuracy and completeness are averaged across all scenes. + +Matching Designs. Tab. 3 (1) demonstrates the benefits of our proposed matching filtering (mutual verification) and track extension via Gaussian Splatting (GS). Compared to the configurations without mutual verification, where all matches are used for reconstructing the initial SfM, incorporating mutual verification improves accuracy, with a tradeoff in completeness due to filtering. Moreover, extending match pairs through GS significantly improves accuracy, which shows that using more views for multi-view kernelized matching contribute to higher performance of accuracy. + +For a comparison with DFSfM [24], which applies quantization to matched keypoints to address the fragmented track problem, we replaced our GS track extension with their quantization approach, using a rounding ratio of $r = 4$ . Results indicate that our GS track extension not only maintains completeness by avoiding the limitations of quantization but also achieves superior accuracy. + +Refinement designs. Table 3 (2) shows the benefit of our proposed multi-view kernelized matching's components in Fig. 4 and confidence-based track selection in Fig. 5. + +We first compare our refinement module to the multi- + +view refinement module in DFSfM [24], by substituting our refinement module with it. The result shows that our refinement module consistently outperforms the existing approach, achieving higher accuracy and completeness. + +Next, we evaluate the contributions of each component in our refinement architecture (Fig. 4) by testing configurations where either the multi-view transformer or Gaussian Process is removed. The results show that our full model, which integrates both components, achieves the highest performance in accuracy and completeness, confirming that combining feature-based and positional information yields more precise refinement. Furthermore, our strategy of selecting a final refined track based on predicted confidence in the reference view further enhances accuracy. + +Impact of iterations. Table 3 (3) reports the results after each refinement iteration. The initial SfM point cloud is less accurate due to reliance solely on initial two-view matching. As the iterations progress, the accuracy of the SfM point cloud gets improved. However, further refinement beyond two iterations gives little gains. So, we limit the refinement to two iterations for efficiency. + +# 5. Conclusion + +This paper introduces a novel Dense-SfM framework aimed at reconstructing dense point cloud and estimating camera poses from a set of images. Unlike conventional SfM systems that often rely on initial 2D matches, our framework leverages Gaussian Splatting to generate new matching pairs, producing longer tracks that significantly enhance both the accuracy and density of the reconstructed point cloud. Extensive evaluations on diverse datasets show that our framework consistently outperforms existing SfM baselines across multiple metrics. + +# 6. Acknowledgement + +This research was supported in part by Samsung Advanced Institute of Technology (SAIT), the Naver-Intel Co-Lab, Inter-university Semiconductor Research Center (ISRC), and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) [NO.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)]. + +# References + +[1] Sameer Agarwal, Noah Snavely, Ian Simon, Steven M. Seitz, and Richard Szeliski. Building rome in a day. In 2009 IEEE 12th International Conference on Computer Vision, pages 72-79, 2009. 2 +[2] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. Hpatches: A benchmark and evaluation of handcrafted and learned local descriptors, 2017. 1 +[3] Paul A. Beardsley, Philip H. S. Torr, and Andrew Zisserman. 3d model acquisition from extended image sequences. 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Fsgs: Real-time few-shot view synthesis using gaussian splatting, 2024. 1, 2, 4 \ No newline at end of file diff --git a/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/images.zip b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2d4fec99c2a9d9d6ceb3ae8e5289d2c700c691c2 --- /dev/null +++ b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cb5e6c43f04f4602f7cad25c7168d4751a5f32e06b0fae939ebb9d7561718070 +size 569955 diff --git a/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/layout.json b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..c70b4430da3578c656623a5edf7fe37b5f8ed335 --- /dev/null +++ b/2025/Dense-SfM_ Structure from Motion with Dense Consistent Matching/layout.json @@ -0,0 +1,9805 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 94, + 103, + 516, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 103, + 516, + 121 + ], + "spans": [ + { + "bbox": [ + 94, + 103, + 516, + 121 + ], + "type": "text", + "content": "Dense-SfM: Structure from Motion with Dense Consistent Matching" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 159, + 144, + 286, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 144, + 286, + 185 + ], + "spans": [ + { + "bbox": [ + 159, + 144, + 286, + 185 + ], + "type": "text", + "content": "JongMin Lee \nSeoul National University \njongmin.cy@gmail.com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 323, + 144, + 451, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 144, + 451, + 185 + ], + "spans": [ + { + "bbox": [ + 323, + 144, + 451, + 185 + ], + "type": "text", + "content": "Sungjoo Yoo Seoul National University sungjoo.yoo@gmail.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 152, + 213, + 200, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 213, + 200, + 225 + ], + "spans": [ + { + "bbox": [ + 152, + 213, + 200, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 239, + 296, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 239, + 296, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 239, + 296, + 441 + ], + "type": "text", + "content": "We present Dense-SfM, a novel Structure from Motion (SfM) framework designed for dense and accurate 3D reconstruction from multi-view images. Sparse keypoint matching, which traditional SfM methods often rely on, limits both accuracy and point density, especially in textureless areas. Dense-SfM addresses this limitation by integrating dense matching with a Gaussian Splatting (GS) based track extension which gives more consistent, longer feature tracks. To further improve reconstruction accuracy, Dense-SfM is equipped with a multi-view kernelized matching module leveraging transformer and Gaussian Process architectures, for robust track refinement across multi-views. Evaluations on the ETH3D and Texture-Poor SfM datasets show that Dense-SfM offers significant improvements in accuracy and density over state-of-the-art methods. Project page: https://icetea-cv.github.io/densesfm/." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 465, + 135, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 465, + 135, + 478 + ], + "spans": [ + { + "bbox": [ + 55, + 465, + 135, + 478 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 485, + 296, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 296, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 296, + 605 + ], + "type": "text", + "content": "Structure from Motion (SfM) is a fundamental task in computer vision that enables the reconstruction of 3D structures from multi-view images of a scene. It has been a widely researched problem, focusing on reconstructing accurate camera poses and 3D point cloud of a scene, benefiting a variety of downstream tasks such as visual localization [19, 43, 46, 48, 58], AR/VR [39, 70], multi-view stereo [20, 50, 52] and neural rendering [27, 34, 72]. Over the years, several well-established methods have been developed to address the SfM pipeline [36, 40, 49, 55, 68]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 606, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 606, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 606, + 296, + 714 + ], + "type": "text", + "content": "Recently, there has been an increasing demand for dense and accurate 3D reconstructions in various 3D vision tasks, including dense reconstruction [17, 65], object pose estimation [5, 23, 57] and neural rendering [27, 72]. However, existing detector-based methods have limitations in achieving sufficient accuracy and density of 3D points, especially in texture-less regions where obtaining matchable keypoints is challenging, limiting the performance of downstream tasks. 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Comparison of SfM results between quantized-matching and our matching. To solve the fragmentary track problem, DFSfM [24] uses quantized matching, which can compromise the accuracy and completeness of 3D points due to quantization. In contrast, our Dense-SfM pipeline leverages Gaussian Splatting to solve the problem, offering more accurate and dense 3D points. Thanks to dense matching, our pipeline can also be applied to texture-less objects, further improving the quality of 3D points and pose estimation." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 715 + ], + "type": "text", + "content": "tion mechanism [62], semi-dense and dense matching methods [6, 14, 15, 56, 66] have been introduced, enabling the reliable matches even in low-texture areas and producing denser match results than classical detector-based methods. This advancement has led to improved performance across many tasks, including homography and relative pose estimation [2, 7, 29]. However, due to their pairwise matching approach, the matching methods usually yield fragmented" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6404" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 191 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 191 + ], + "type": "text", + "content": "tracks" + }, + { + "bbox": [ + 55, + 72, + 294, + 191 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 55, + 72, + 294, + 191 + ], + "type": "text", + "content": " as mentioned in Detector-Free SfM (DFSfM) [24], making direct integration with existing SfM pipelines challenging. To solve this inconsistency issue, DFSfM applied quantization to the matched keypoints, and then refined the multi-view tracks to obtain accurate camera pose and point cloud. While the quantization strategy can increase track length and consistency, enhancing the multi-view refinement results, it can significantly limit the number of matches and accuracy, reducing the quality of the resulting SfM model, as exemplified in Fig. 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 193, + 296, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 193, + 296, + 550 + ], + "spans": [ + { + "bbox": [ + 56, + 193, + 296, + 550 + ], + "type": "text", + "content": "In this paper, we propose a novel SfM framework that leverages dense matching while addressing the limitations of pairwise matching methods. As shown in Fig. 1, our approach reconstructs a dense and accurate 3D point cloud, avoiding the inherent limitations of quantized matching. Specifically, our framework first performs dense matching using a dense matcher, e.g., DKM [14] or RoMa [15], to construct an initial SfM model, where most tracks are initially fragmentary, i.e., of short (mostly a pair of images) lengths. Next, we initialize small 3D Gaussians based on the initial SfM's point cloud, integrating attributes like color and position. These Gaussians are then optimized and denified through Gaussian Splatting (GS) [27, 72], filling in the scene while keeping the initial Gaussians' (SfM points') positions fixed. We then infer the visibility of each initial SfM point per image by rendering through the ray from camera poses. In case that the 3D point is visible on the image, we include the image into the track of the 3D point thereby increasing the track length—a process we refer to as Track Extension. Note that Track Extension enables us to resolve the problem of short tracks in pairwise matching. Lastly, we perform our proposed SfM refinement pipeline, which includes a multi-view kernelized matching module and geometric bundle adjustment, to further optimize the camera poses and 3D points. Our track refinement module is mainly built on two architectures, transformer and Gaussian Process [41], which incorporate both feature-based and positional information, resulting in notable performance gains over existing refinement modules as demonstrated in our ablation study (Tab. 3)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 552, + 295, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 647 + ], + "type": "text", + "content": "We evaluate our Dense-SfM framework on the ETH3D, Texture-Poor SfM and Image Matching Challenge (IMC) 2021 datasets, where it outperforms state-of-the-art SfM systems across multiple metrics. Thanks to the dense matching coupled with track extension via Gaussian Splating, as well as our novel track refinement module, our framework achieves accurate camera pose estimations and dense 3D reconstructions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 659, + 122, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 659, + 122, + 670 + ], + "spans": [ + { + "bbox": [ + 55, + 659, + 122, + 670 + ], + "type": "text", + "content": "Contributions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 672, + 295, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 295, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 295, + 684 + ], + "type": "text", + "content": "- A novel SfM framework optimized for dense matchers," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 322, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 322, + 72, + 553, + 95 + ], + "type": "text", + "content": "capable of reconstructing highly accurate and dense 3D models, even in texture-less regions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 96, + 553, + 204 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 314, + 96, + 553, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 96, + 553, + 132 + ], + "spans": [ + { + "bbox": [ + 314, + 96, + 553, + 132 + ], + "type": "text", + "content": "- A track extension method that, based on Gaussian Splatting, helps find new images on which 3D point is visible, thereby increasing track length of the 3D point." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 133, + 553, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 553, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 553, + 180 + ], + "type": "text", + "content": "- A new track refinement pipeline that leverages transformer and Gaussian Process architectures to enhance the consistency of feature tracks and refine the overall reconstruction quality." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 180, + 553, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 553, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 553, + 204 + ], + "type": "text", + "content": "- Extensive evaluations across diverse metrics demonstrate that our framework achieves state-of-the-art performance." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 213, + 401, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 213, + 401, + 225 + ], + "spans": [ + { + "bbox": [ + 314, + 213, + 401, + 225 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 233, + 555, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 233, + 555, + 353 + ], + "spans": [ + { + "bbox": [ + 313, + 233, + 555, + 353 + ], + "type": "text", + "content": "Image Matching. Establishing 2D correspondences through feature matching is a fundamental component for SfM and visual SLAM. Traditional feature matching typically involves i) detecting keypoints [8, 11, 31, 42, 44, 45], ii) computing descriptors [13, 32, 33, 37, 59, 61] and iii) performing descriptor matching [18, 47, 71]. Despite its efficiency, it struggles in challenging scenarios such as low-textured regions, where keypoint detection is unreliable, and repetitive patterns, where matching often fails—leading to suboptimal SfM results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 354, + 554, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 554, + 448 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 554, + 448 + ], + "type": "text", + "content": "To address these limitations, more recent methods bypass the need for keypoint detection and instead directly perform semi-dense [6, 56, 66] or dense [14, 15] matching between image pairs. These approaches benefit from global receptive fields provided by transformers [62] or correlations computed from CNN or ViT features [9, 38], which allows them to achieve better performance in texture-poor areas where traditional methods often fail." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 554, + 544 + ], + "type": "text", + "content": "However, semi-dense and dense matching often results in fragmentary feature tracks, making it difficult to apply on SfM pipeline [53]. To solve this, DFSfM [24] introduced quantization matching that merges nearby subpixel matches into grid nodes, improving track consistency. Yet, this approach can compromise the accuracy of the initial camera poses and point clouds, heavily relying on refinement modules and reducing point cloud density." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 544, + 554, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 554, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 554, + 616 + ], + "type": "text", + "content": "In contrast, our framework leverages Gaussian Splatting to assess visibility of 3D points. By projecting 3D points onto new images on which the points are visible, we obtain longer and consistent tracks without sacrificing the initial matching accuracy, which leads to improved refinement performance and, finally, better SfM results." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 629, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 689 + ], + "type": "text", + "content": "Structure From Motion. Feature correspondence-based SfM methods have been extensively studied [3, 16, 35]. Incremental SfM [1, 55, 68] has become a widely adopted approach, with COLMAP [49] recognized as one of the most popular frameworks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "Recently, differentiable SfM methods [4, 10, 54, 63, 64, 67] have aimed to simplify or entirely replace the traditional" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 693, + 295, + 713 + ], + "type": "text", + "content": "1A keypoint is assigned a set of 2D coordinates, called feature track or track in short, on neighbor images where the keypoint is matched." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6405" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 309, + 168 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 309, + 168 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 309, + 168 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 309, + 168 + ], + "type": "image", + "image_path": "b5504cd38dce0bc0f9e03ce98cd773a1eb575dd82ce21e65dbd4513ce5b446d8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 553, + 168 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 553, + 168 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 553, + 168 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 553, + 168 + ], + "type": "image", + "image_path": "85b1842134afd64004d2e058898812f42f6b6ecaa4125a4500d2b8677b4cd64d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 59, + 169, + 553, + 262 + ], + "blocks": [ + { + "bbox": [ + 59, + 169, + 553, + 262 + ], + "lines": [ + { + "bbox": [ + 59, + 169, + 553, + 262 + ], + "spans": [ + { + "bbox": [ + 59, + 169, + 553, + 262 + ], + "type": "image", + "image_path": "0cb4eddbb99e02a74a0286456273d380d874764f1c967aa9949ca4cff64c84cf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 268, + 555, + 313 + ], + "lines": [ + { + "bbox": [ + 55, + 268, + 555, + 313 + ], + "spans": [ + { + "bbox": [ + 55, + 268, + 555, + 313 + ], + "type": "text", + "content": "Figure 2. Pipeline Overview. From a set of images, we construct an initial SfM model using dense two-view matching, filtering unreliable matches through mutual verification. To extend track length, we project 3D points onto additional images, using a visibility filter based on Gaussian Splatting. We then refine these extended tracks with our track refinement module and perform geometric bundle adjustment to improve the accuracy of SfM model." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 325, + 296, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 325, + 296, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 325, + 296, + 422 + ], + "type": "text", + "content": "SfM pipeline. VGGSfM [64] manages all SfM components as fully differentiable, enabling end-to-end training. DUSt3R [67] predicts pairwise pointmaps and refines them through optimization-based global alignment. Its successors, MASt3R [28] and MASt3R-SfM [10], improve pixel matching for localization by predicting additional per-pixel features and leveraging its encoder for fast image retrieval, leading to a newly proposed SfM pipeline." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 437, + 296, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 296, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 296, + 510 + ], + "type": "text", + "content": "Multi-view Refinement. Inconsistent feature points across multiple views can impact the accuracy of reconstructed point cloud and camera poses in SfM. Hence, precise multi-view correspondences are essential for accurately recovering 3D structures and camera parameters in SfM pipelines." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 510, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 701 + ], + "type": "text", + "content": "To address this, several previous methods have proposed multi-view keypoint refinement models based on flow [12] or dense features [30], which lead to significant improvements in SfM accuracy. PatchFlow [12] refines keypoint locations using a geometric cost constrained by local flow between two views, followed by global optimization using a multi-view graph of relative feature geometry constraints. Similarly, PixSfM [30] refines keypoint locations through feature-metric keypoint adjustment by optimizing a direct cost over discriminative dense feature maps along the tracks. DFSfM [24], introduces a multi-view matching module that iteratively refines the tracks obtained from the COLMAP framework. The module extracts local patches from each image and feeds them into a transformer-based network to refine the keypoint's location by enforcing multi-view consistency." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 702, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 295, + 714 + ], + "type": "text", + "content": "Building on these recent advancements, we propose a" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 325, + 555, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 325, + 555, + 420 + ], + "spans": [ + { + "bbox": [ + 313, + 325, + 555, + 420 + ], + "type": "text", + "content": "novel refinement module that leverages both feature and positional information to refine the keypoint coordinates within the tracks. Instead of relying on statistical methods to select the refined tracks, our module fully regresses and learns the confidence (certainty) per track, resulting in more accurate refinement. As demonstrated in our ablation study (Tab. 3), our approach outperforms the existing refinement methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 430, + 370, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 430, + 370, + 442 + ], + "spans": [ + { + "bbox": [ + 314, + 430, + 370, + 442 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 450, + 555, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 555, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 555, + 498 + ], + "type": "text", + "content": "An overview of our Dense-SfM framework is shown in Fig. 2. Given " + }, + { + "bbox": [ + 313, + 450, + 555, + 498 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 450, + 555, + 498 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 313, + 450, + 555, + 498 + ], + "type": "inline_equation", + "content": "\\{I_i\\}" + }, + { + "bbox": [ + 313, + 450, + 555, + 498 + ], + "type": "text", + "content": " of a scene, our goal is to estimate the camera poses and reconstruct the 3D point cloud representing the scene." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 498, + 554, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 594 + ], + "type": "text", + "content": "We design our framework as a three-stage pipeline. First, we construct an initial SfM model using correspondences between image pairs from a two-view dense matcher (e.g., DKM [14] and RoMa [15]). Next, we extend the track length of each 3D point by projecting it onto new images where it is visible, verifying visibility through Gaussian Splatting [27]. Finally, we perform iterative SfM refinement to enhance the accuracy of poses and point cloud." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 600, + 484, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 600, + 484, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 600, + 484, + 613 + ], + "type": "text", + "content": "3.1. Initial SfM via Dense Matching" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 618, + 554, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 554, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 554, + 689 + ], + "type": "text", + "content": "Our framework employs dense feature matching between image pairs, unlike traditional SfM pipelines [49] which rely on sparse keypoints [8, 31]. By employing dense matching, our approach improves the reconstruction of texture-poor scenes and enables the registration of dense 3D points, which is challenging for conventional methods." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "For efficiency, we first sample matches from the dense matching using non-max suppression [8], based on per" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6406" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 92, + 70, + 258, + 162 + ], + "blocks": [ + { + "bbox": [ + 92, + 70, + 258, + 162 + ], + "lines": [ + { + "bbox": [ + 92, + 70, + 258, + 162 + ], + "spans": [ + { + "bbox": [ + 92, + 70, + 258, + 162 + ], + "type": "image", + "image_path": "bcc3fe6f952ef0889c80a6dbd3e7c2cd99034912fcf9c428940e485c65185fb2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "lines": [ + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "spans": [ + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": "Figure 3. Bidirectional verification on two-view dense matching. The match result " + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "inline_equation", + "content": "p_b" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{A \\to B}" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": " is re-used as input to " + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{B \\to A}" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": " to estimate " + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "inline_equation", + "content": "p_{a'}" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": ". We then compute the distance between " + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "inline_equation", + "content": "p_{a'}" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": ", where a smaller distance indicates higher reliability of the match between " + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "inline_equation", + "content": "p_b" + }, + { + "bbox": [ + 55, + 165, + 296, + 222 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 232, + 296, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 232, + 296, + 292 + ], + "spans": [ + { + "bbox": [ + 55, + 232, + 296, + 292 + ], + "type": "text", + "content": "pixel confidence scores from the dense matching model's output. Then, we sort out reliable matches by a method called mutual verification using bi-directional dense matching, similar to the mutual-nearest neighbor approach commonly used in detector-based methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "text", + "content": "As shown in Fig. 3, from the bi-directional dense matching results " + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "inline_equation", + "content": "M_{A\\rightarrow B}" + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "inline_equation", + "content": "M_{B\\rightarrow A}" + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "text", + "content": " between images " + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "text", + "content": ", we define the pixel coordinates " + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "inline_equation", + "content": "p_b" + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "inline_equation", + "content": "p_{a'}" + }, + { + "bbox": [ + 55, + 293, + 296, + 329 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 99, + 337, + 295, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 337, + 295, + 352 + ], + "spans": [ + { + "bbox": [ + 99, + 337, + 295, + 352 + ], + "type": "interline_equation", + "content": "p _ {b} = \\mathcal {M} _ {A \\rightarrow B} [ p _ {a} ], \\quad p _ {a ^ {\\prime}} = \\mathcal {M} _ {B \\rightarrow A} [ p _ {b} ] \\tag {1}", + "image_path": "3bba43ca7de792d7ddcfedff9cda5548a6214e0d85cb9d0eb22235830b3ed995.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 359, + 268, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 359, + 268, + 371 + ], + "spans": [ + { + "bbox": [ + 67, + 359, + 268, + 371 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 67, + 359, + 268, + 371 + ], + "type": "inline_equation", + "content": "p_{a'}" + }, + { + "bbox": [ + 67, + 359, + 268, + 371 + ], + "type": "text", + "content": " is sampled using bilinear-interpolation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 371, + 296, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 371, + 296, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 371, + 296, + 407 + ], + "type": "text", + "content": "To ensure more reliable matches, we filter out correspondences using a binary mask, which is obtained with the distance from " + }, + { + "bbox": [ + 55, + 371, + 296, + 407 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 55, + 371, + 296, + 407 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 371, + 296, + 407 + ], + "type": "inline_equation", + "content": "p_{a'}" + }, + { + "bbox": [ + 55, + 371, + 296, + 407 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 124, + 415, + 295, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 415, + 295, + 430 + ], + "spans": [ + { + "bbox": [ + 124, + 415, + 295, + 430 + ], + "type": "interline_equation", + "content": "B = \\left[ \\left\\| p _ {a} - p _ {a ^ {\\prime}} \\right\\| _ {2} \\leq \\epsilon_ {p} \\right] \\tag {2}", + "image_path": "e0fed9e0268d848b6fb3ce7a6e17b73c7e7b8429bfa11807e299acc0c321e33c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 437, + 296, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 296, + 534 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 296, + 534 + ], + "type": "text", + "content": "Using these filtered matches, we construct the initial SfM by triangulating 3D points through dense two-view fine matching. If camera poses are not provided for the reconstruction task, we first perform match quantization [24] and incremental mapping [49] to obtain coarse poses. We then triangulate 3D points using raw matching with the coarse pose and refine both the point cloud and camera poses through the refinement process, as explained in Sec. 3.3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 540, + 264, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 264, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 264, + 553 + ], + "type": "text", + "content": "3.2. Track Extension via Gaussian Splitting" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 558, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 295, + 605 + ], + "type": "text", + "content": "In the initial SfM, most of the tracks are short, i.e. consisting of mostly two images, due to the fragmentary nature of feature tracks in pair-wise matching, which can limit the performance of track refinement, as shown in DFSfM [24]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": "Longer tracks, which offer more information on 3D geometry, could improve the track refinement performance. Thus, we generate new matching pairs on the existing matches for consistent multi-view matches, extending the length of track. We achieve this by projecting 3D points (triangulated by two-view matches) onto additional images on which, if successfully projected, the point is considered as visible from the camera pose as illustrated (by the blue dashed line) in Fig. 2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "content": "To determine the visibility of each 3D point from a camera pose, we apply a visibility filter using Gaussian Splating (GS) [27, 72], which supports fast training and rendering. We initialize a GS model with the 3D points obtained in the initial SfM. Specifically, we treat them as small 3D Gaussians setting each mean " + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "inline_equation", + "content": "\\mu \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "content": " to the 3D point coordinates, rotation " + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "content": " to the identity matrix, opacity " + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "content": " to 1, and scale " + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "content": " based on the policy from Splatam [26], which uses focal length and depth information. These Gaussians are optimized and densified to cover the entire scene, while keeping the initial Gaussian's parameters fixed. The details of initialization and training process is described in supplementary material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 228, + 553, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 274 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 274 + ], + "type": "text", + "content": "After training the GS model, we utilize it for evaluating the visibility " + }, + { + "bbox": [ + 313, + 228, + 553, + 274 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 228, + 553, + 274 + ], + "type": "text", + "content": " of all SfM points (represented as small Gaussians) from each camera pose using the following formula:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 346, + 270, + 553, + 305 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 270, + 553, + 305 + ], + "spans": [ + { + "bbox": [ + 346, + 270, + 553, + 305 + ], + "type": "interline_equation", + "content": "M = \\left[ \\max _ {r \\in R} \\left\\{\\alpha_ {\\mathrm {S f M}} \\prod_ {j = 1} ^ {N _ {S f M} - 1} (1 - \\alpha_ {j}) \\right\\} > \\epsilon_ {v} \\right] \\tag {3}", + "image_path": "405f29c5ea572ec6828877212e8958084d9f4cfc71ddb6b6638b33b25ee41346.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": " is the set of rays from the camera center (of a camera pose) for rendering the image, " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "\\alpha_{\\mathrm{SfM}}" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": " is the opacity of Gaussian representing the SfM point (set to 1), " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "N_{SfM}" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": " the number of Gaussians along the ray " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": " from the camera center to the SfM point, and " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "\\alpha_{j}" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": " the opacity of " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": "-th intermediate Gaussian. If the highest visibility score among the pixels rendered from the Gaussian representing the SfM point is larger than " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\nu}" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": ", we consider the SfM point, i.e. " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "N_{SfM}" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": "-th Gaussian, visible from the view of the camera pose. For each 3D point, we extend its track by adding its projected 2D point(s) onto the visible view(s). To do that, we project a 3D point " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "P_{j}" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": " onto the visible image using camera pose " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "\\{R_i,t_i\\}" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": " and intrinsic matrix " + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 313, + 308, + 555, + 464 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 383, + 469, + 553, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 469, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 383, + 469, + 553, + 483 + ], + "type": "interline_equation", + "content": "p _ {i j} = \\Pi \\left(R _ {i} P _ {j} + t _ {i}, C _ {i}\\right) \\tag {4}", + "image_path": "5e84019151e4386a2d6683fbde447eda1ca7a8fcf341c80728469d90b9804ef3.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "type": "text", + "content": "Then, we verify the correspondence between the newly obtained 2D point " + }, + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "type": "inline_equation", + "content": "p_{ij}" + }, + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "type": "text", + "content": " and its associated original 2D keypoint with geometric verification [49] using initial SfM's camera poses. After verified, we add the new 2D point to the track of the 3D point " + }, + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "type": "inline_equation", + "content": "P_j" + }, + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "type": "text", + "content": ", which extends the length of " + }, + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "type": "inline_equation", + "content": "P_j" + }, + { + "bbox": [ + 313, + 487, + 554, + 558 + ], + "type": "text", + "content": "'s track." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 559, + 554, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 559, + 554, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 559, + 554, + 654 + ], + "type": "text", + "content": "Note that we project the 3D point onto the images that were not involved in the initial triangulation (i.e., establishing a new one-to-one correspondence of 2D-3D matches per image as illustrated with green lines in Fig. 2 (Stage 2). As will be demonstrated in our experiments (Tab. 3), the proposed Track extension enables the subsequent track refinement to produce more refined tracks, which leads to more accurate 3D points in the SfM model." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 660, + 456, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 660, + 456, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 660, + 456, + 672 + ], + "type": "text", + "content": "3.3. Iterative SfM Refinement" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Using the extended tracks, we refine the initial SfM model to obtain improved camera poses and point cloud. Specifically, we iteratively improve the accuracy of feature tracks" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6407" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 296, + 208 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 296, + 208 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 296, + 208 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 296, + 208 + ], + "type": "image", + "image_path": "5c14b51d1a7394ad3699c195deba40c33974e8a8b2ec30b1eafb635f8889a17a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 216, + 296, + 306 + ], + "lines": [ + { + "bbox": [ + 55, + 216, + 296, + 306 + ], + "spans": [ + { + "bbox": [ + 55, + 216, + 296, + 306 + ], + "type": "text", + "content": "Figure 4. Multi-view kernelized matching architecture. The feature maps from the reference and query views are processed in two ways: first, by a multi-view transformer, applying self and cross-attention and secondly, by a Gaussian Process that computes the posterior mean conditioned on the feature of each query view. All results are concatenated and fed into a CNN decoder, yielding probability distribution of coordinates for refinement " + }, + { + "bbox": [ + 55, + 216, + 296, + 306 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{Q_i}" + }, + { + "bbox": [ + 55, + 216, + 296, + 306 + ], + "type": "text", + "content": " and corresponding confidence score " + }, + { + "bbox": [ + 55, + 216, + 296, + 306 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{Q_i}" + }, + { + "bbox": [ + 55, + 216, + 296, + 306 + ], + "type": "text", + "content": " for each query view." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 315, + 296, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 315, + 296, + 352 + ], + "spans": [ + { + "bbox": [ + 55, + 315, + 296, + 352 + ], + "type": "text", + "content": "by employing our multi-view kernelized matching module alongside bundle adjustment, jointly optimizing camera poses and point cloud." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 357, + 196, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 196, + 369 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 196, + 369 + ], + "type": "text", + "content": "3.3.1. Feature Track Refinement" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "spans": [ + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "text", + "content": "A feature track (or track) " + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_j = \\{\\mathbf{x}_k\\in \\mathbb{R}^2 |k = 1:N_j\\}" + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "text", + "content": " represents a set of 2D keypoint locations on multi-view " + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "inline_equation", + "content": "(N_{j})" + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "text", + "content": " images that correspond to a 3D point " + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "inline_equation", + "content": "P_{j}" + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "text", + "content": ". In our proposed method of feature track refinement, each track goes through a multi-view kernelized matching architecture (Fig. 4) and the regression of refined coordinates (Fig. 5). The matching architecture produces two outputs, a probability distribution of coordinate per pixel " + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "inline_equation", + "content": "P_{Q_i}" + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "text", + "content": " and confidence score " + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "inline_equation", + "content": "S_{Q_i}" + }, + { + "bbox": [ + 55, + 373, + 296, + 494 + ], + "type": "text", + "content": " per view. Then, the regression from these outputs produces a refined track by adjusting the keypoint locations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "text", + "content": "Multi-view kernelized matching. Following DFSfM, we split a track into the keypoint of a reference view and those of query views (views from the track except the reference view) with a policy of median depth value. Then, we feed image patches centered at each keypoint into a CNN feature extractor, obtaining feature maps " + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_R" + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{Q_i} \\in \\mathbb{R}^{p \\times p \\times c}" + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_R" + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "text", + "content": " is from the reference view and " + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{Q_i}" + }, + { + "bbox": [ + 55, + 510, + 296, + 629 + ], + "type": "text", + "content": "'s are from query views. As shown in Fig. 4, our multi-view kernelized matching architecture takes as input these feature maps of reference and query views." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": "Our proposed matching architecture consists of two paths, feature-based and coordinate-embedding-based ones. On the feature-based path (denoted with Multi-view Transformer in Fig. 4), we utilize a local feature transformer to obtain the transformed feature map " + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_R" + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{Q_i}" + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": " 's through self and cross-attention between " + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_R" + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_Q" + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": "'s. On the coordinate-embedding-based path (denoted with Gaussian" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 318, + 70, + 555, + 205 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 555, + 205 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 555, + 205 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 555, + 205 + ], + "type": "image", + "image_path": "593bdd7af826a6c00bb3827019f3e14e38bcb5c2041e368781f72e10095bae0e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "lines": [ + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "spans": [ + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "text", + "content": "Figure 5. Regression of refined coordinate. Top: Selection of refined coordinate on the reference view: From the set of " + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "inline_equation", + "content": "S_{Q_i}" + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "text", + "content": " values, representing the correspondence scores from the reference view to each query view " + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "inline_equation", + "content": "Q_i" + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "text", + "content": ", we sum over " + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "inline_equation", + "content": "S_{Q_i}" + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "text", + "content": "'s and select the pixel with the highest score as the refined coordinate for the reference view. Bottom: Regression of refined coordinate on each query view: We apply a channel-wise softmax to obtain a probability distribution of coordinates for each pixel, then calculate a weighted average to determine the correspondence from the reference view to query view " + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "inline_equation", + "content": "Q_i" + }, + { + "bbox": [ + 313, + 210, + 555, + 321 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 327, + 554, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 327, + 554, + 375 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 554, + 375 + ], + "type": "text", + "content": "Process in Fig. 4), we employ a Gaussian Process [41] to utilize the positional information, deriving a coordinate embedding feature " + }, + { + "bbox": [ + 313, + 327, + 554, + 375 + ], + "type": "inline_equation", + "content": "\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})" + }, + { + "bbox": [ + 313, + 327, + 554, + 375 + ], + "type": "text", + "content": " for each query view. Following DKM [14], we use an exponential cosine similarity kernel:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 378, + 553, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 378, + 553, + 416 + ], + "spans": [ + { + "bbox": [ + 315, + 378, + 553, + 416 + ], + "type": "interline_equation", + "content": "k \\left(f _ {A}, f _ {B}\\right) = \\exp (- \\tau) \\exp \\left(\\tau \\frac {\\langle f _ {A} , f _ {B} \\rangle}{\\sqrt {\\langle f _ {A} , f _ {A} \\rangle \\langle f _ {B} , f _ {B} \\rangle + \\varepsilon}}\\right), \\tag {5}", + "image_path": "47ea994d5f79f74dd0362d6184e7f8d047ee045f09f3ff2356442bf8d394a819.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "spans": [ + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "inline_equation", + "content": "f_{A}" + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "inline_equation", + "content": "f_{B}" + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "content": " each is a feature vector from " + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_A" + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_B" + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "content": ", respectively. From this kernel function, we build kernel matrices " + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "inline_equation", + "content": "K^{\\mathcal{R}\\mathcal{Q}_i}" + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "inline_equation", + "content": "K^{\\mathcal{Q}_i\\mathcal{Q}_i} \\in \\mathbb{R}^{p^2 \\times p^2}" + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "content": " to obtain posterior mean " + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "inline_equation", + "content": "\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})" + }, + { + "bbox": [ + 313, + 417, + 554, + 466 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 343, + 470, + 553, + 486 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 470, + 553, + 486 + ], + "spans": [ + { + "bbox": [ + 343, + 470, + 553, + 486 + ], + "type": "interline_equation", + "content": "\\mu \\left(\\mathbf {F} _ {R} \\mid \\mathbf {F} _ {Q _ {i}}\\right) = K ^ {R Q _ {i}} \\left(K ^ {Q _ {i} Q _ {i}} + \\sigma_ {n} ^ {2} I\\right) ^ {- 1} \\chi^ {Q _ {i}} \\tag {6}", + "image_path": "61ee3866b0a453a331e7cbd0aec1857970cbb56ef437ea7eff05041d7097dd2c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "inline_equation", + "content": "\\chi^{\\mathcal{Q}_i}" + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "text", + "content": " is the Fourier positional encoding [34] of " + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "inline_equation", + "content": "F_{Q_i}" + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "text", + "content": "'s pixel coordinate. Finally, we concatenate the transformed feature maps " + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_R" + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{Q_i}" + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "text", + "content": " and coordinate embedding " + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "inline_equation", + "content": "\\mu (\\mathbf{F}_R|\\mathbf{F}_{Q_i})" + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "text", + "content": ", and feed them into a CNN decoder " + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "inline_equation", + "content": "D_{\\theta}" + }, + { + "bbox": [ + 313, + 493, + 555, + 544 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 345, + 555, + 553, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 555, + 553, + 571 + ], + "spans": [ + { + "bbox": [ + 345, + 555, + 553, + 571 + ], + "type": "interline_equation", + "content": "P _ {Q _ {i}}, S _ {Q _ {i}} = D _ {\\theta} \\left(\\hat {\\mathbf {F}} _ {R} \\oplus \\hat {\\mathbf {F}} _ {Q _ {i}} \\oplus \\mu \\left(\\mathbf {F} _ {R} \\mid \\mathbf {F} _ {Q _ {i}}\\right)\\right) \\tag {7}", + "image_path": "ff11aaaeb2fff4cbc9b027a424e41885bcef2db04e76bc35552d235b251ac1e7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "text", + "content": "where we obtain a probability distribution of coordinate per pixel " + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "inline_equation", + "content": "P_{Q_i} \\in \\mathbb{R}^{C^2 \\times w \\times w}" + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "text", + "content": " and confidence score " + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "inline_equation", + "content": "S_{Q_i} \\in \\mathbb{R}^{w \\times w}" + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "inline_equation", + "content": "C^2" + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "text", + "content": " is the number of distribution's anchors, and " + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "inline_equation", + "content": "w \\times w" + }, + { + "bbox": [ + 313, + 578, + 554, + 628 + ], + "type": "text", + "content": " a search boundary for refined coordinates." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "text", + "content": "Regression of keypoint's location. Fig. 5 illustrates how the refined track is obtained. First, we obtain the refined coordinate of keypoint on the reference view. From the output of multi-view kernelized matching, " + }, + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\{S_{Q_i}\\}" + }, + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "text", + "content": ", we estimate the confidence value of each pixel as the candidate of refined coordinate on the reference view. As shown in Fig. 5 (top)," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6408" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "we select, as the refined coordinate on the reference view, the pixel with the highest value, i.e. the highest confidence from " + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "inline_equation", + "content": "\\sum_{i}S_{Q_i}" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "spans": [ + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "content": "Then, as shown in Fig. 5 (bottom), from the refined coordinate on the reference view (calculated above), we estimate the refined coordinate of keypoint for each query view " + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "inline_equation", + "content": "Q_{i}" + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "content": ". For each patch of " + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "inline_equation", + "content": "P_{Q_i}" + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "inline_equation", + "content": "w\\times w" + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "content": ", we apply softmax across channels from the pixel of refined coordinate for the reference view, to obtain a probability distribution over a " + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "inline_equation", + "content": "C\\times C" + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "content": " grid. The refined coordinate for the query view " + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "inline_equation", + "content": "Q_{i}" + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "content": " is then computed as a weighted average, where each pixel's probability serves as its weight. By multiplying each probability by its corresponding pixel coordinate and summing these weighted values, we derive a refined coordinate for query view " + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "inline_equation", + "content": "Q_{i}" + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "content": ". Finally, we construct the final refined track " + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "inline_equation", + "content": "T_{j}^{*}" + }, + { + "bbox": [ + 55, + 109, + 295, + 276 + ], + "type": "text", + "content": ", consisting of the refined coordinates for the reference view and all query views." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 289, + 295, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 289, + 295, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 289, + 295, + 469 + ], + "type": "text", + "content": "Training setup and loss function. We set up training as in DFSfM [24] using MegaDepth dataset [29]. We use image bags sampled from the SfM model provided in the dataset, in which ground truth tracks are derived from the given camera pose and MVS depth map. For training, we perturb the ground truth 2D locations of tracks in the query views with random noise, providing these as input to our refinement module. Unlike DFSfM, which relies on statistics (variance) as uncertainty measure, we directly learn confidence score through a neural network. Consequently, our loss function is not simply formulated as an " + }, + { + "bbox": [ + 55, + 289, + 295, + 469 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 55, + 289, + 295, + 469 + ], + "type": "text", + "content": " loss to minimize the distance between the refined tracks and the ground truth tracks. Instead, we jointly predict and learn the confidence " + }, + { + "bbox": [ + 55, + 289, + 295, + 469 + ], + "type": "inline_equation", + "content": "S_{Q_i} > 0" + }, + { + "bbox": [ + 55, + 289, + 295, + 469 + ], + "type": "text", + "content": " for each query view, and include it in the regression loss as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 473, + 295, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 473, + 295, + 503 + ], + "spans": [ + { + "bbox": [ + 69, + 473, + 295, + 503 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\frac {1}{N} \\sum_ {j \\in n _ {t}} \\sum_ {i \\in n _ {j}} s _ {Q _ {i}} \\cdot \\| p _ {Q _ {i}} - p _ {g t} \\| _ {2} - \\alpha \\log s _ {Q _ {i}}. \\tag {8}", + "image_path": "c92b052b18dff10e457756ba1e7d4b37de31b6e477b519b2772934cba341f962.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "spans": [ + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": " is the number of feature tracks, " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "n_j" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": " the number of query views in a track " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": " the total number of refined keypoints on all the query views, " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "p_{Q_i}" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "p_{gt}" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": " the learned 2D coordinate from " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "Q_i" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": " (as illustrated in Fig. 5) and the ground truth 2D coordinate, respectively, and " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "s_{Q_i}" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": " the confidence score of prediction " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "p_{Q_i}" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": ", which is obtained, from " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "S_{Q_i}" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": ", at the pixel of the reference view's ground truth keypoint. The second term in the loss is used to avoid being underconfident, where we set " + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 508, + 295, + 615 + ], + "type": "text", + "content": " as 20." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 620, + 167, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 620, + 167, + 632 + ], + "spans": [ + { + "bbox": [ + 55, + 620, + 167, + 632 + ], + "type": "text", + "content": "3.3.2. Bundle Adjustment" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "text", + "content": "Using the refined feature tracks, we iteratively perform geometric bundle adjustment (BA) [60] to refine the intrinsic parameters " + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "inline_equation", + "content": "\\{C_i\\}" + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "text", + "content": ", camera poses " + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "inline_equation", + "content": "\\{\\xi_i\\}" + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "text", + "content": ", and 3D points' coordinates " + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "inline_equation", + "content": "\\{P_j\\}" + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "text", + "content": ". Formally, we minimize the reprojection error " + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 635, + 295, + 693 + ], + "type": "text", + "content": " defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 82, + 699, + 269, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 699, + 269, + 716 + ], + "spans": [ + { + "bbox": [ + 82, + 699, + 269, + 716 + ], + "type": "interline_equation", + "content": "E = \\sum_ {j} \\sum_ {x _ {k} ^ {*} \\in \\mathcal {T} _ {j} ^ {*}} \\rho \\big (\\| \\pi (\\pmb {\\xi} _ {i} \\cdot P _ {j}, C _ {i}) - x _ {k} ^ {*} \\| _ {2} ^ {2} \\big) ,", + "image_path": "b0ba76d304b375b9c2280a3b62ee37923b1c1dbe89e2b637732a70aac8f34dd6.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\pi (\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": " projects points to image plane using intrinsic parameter " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\rho (\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": " is a robust loss function [21]. We then filter outliers [49, 68] by rejecting points that exceed the maximum reprojection error threshold " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\epsilon_{f}" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": ". After performing BA and outlier filtering, the refined SfM can be passed to the next iteration of feature track refinement and BA." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 159, + 395, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 159, + 395, + 172 + ], + "spans": [ + { + "bbox": [ + 313, + 159, + 395, + 172 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 179, + 376, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 179, + 376, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 179, + 376, + 190 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 198, + 555, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 198, + 555, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 555, + 342 + ], + "type": "text", + "content": "We use the ETH3D [51], Texture-Poor SfM datasets [24], and Image Matching Challenge (IMC) 2021 dataset [25], each presenting unique challenges across different types of scenes. The ETH3D dataset includes indoor and outdoor scenes with sparsely captured, high-resolution images, and ground truth poses calibrated using Lidar. The Texture-Poor SfM dataset focuses on object-centric scenes with low texture, comprising subsampled image sets. We use all test scenes from the IMC Phototourism dataset, evaluating them with subsampled image bags. The main challenge of this dataset lies in its sparse views, accompanied by significant variations in viewpoint and illumination." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 352, + 447, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 352, + 447, + 364 + ], + "spans": [ + { + "bbox": [ + 313, + 352, + 447, + 364 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 370, + 554, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 370, + 554, + 418 + ], + "spans": [ + { + "bbox": [ + 313, + 370, + 554, + 418 + ], + "type": "text", + "content": "For efficiency, we apply non-max suppression [8] with a radius of 4 pixels for ETH3D and 2 pixels for Texture-Poor SfM and IMC dataset. For mutual verification, we filter out matches with a distance exceeding " + }, + { + "bbox": [ + 313, + 370, + 554, + 418 + ], + "type": "inline_equation", + "content": "\\epsilon_{p} = 3\\mathrm{px}" + }, + { + "bbox": [ + 313, + 370, + 554, + 418 + ], + "type": "text", + "content": " in Eq. 2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 419, + 554, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 419, + 554, + 468 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 554, + 468 + ], + "type": "text", + "content": "To determine the visibility of Gaussians (SfM points) from a camera pose, we set the visibility threshold " + }, + { + "bbox": [ + 313, + 419, + 554, + 468 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\nu}" + }, + { + "bbox": [ + 313, + 419, + 554, + 468 + ], + "type": "text", + "content": " to 0.5 in Eq. 3. Details of training and implementation of Gaussian Splatting are provided in the supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "content": "We use S2Dnet [18] as a CNN backbone for our refinement architecture, and adopt the multi-view transformer architecture from DFSfM [24]. To ensure a fair comparison, we apply the same refinement parameters as in DFSfM, including a local patch size " + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "inline_equation", + "content": "(p = 15)" + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "content": " from the feature maps " + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_R" + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_Q" + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "content": ", obtained from the CNN backbone, and a search boundary for reference view's refined keypoints set to " + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "inline_equation", + "content": "w = 7" + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "content": ". The number of distribution anchors " + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "inline_equation", + "content": "C^2" + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "inline_equation", + "content": "7^2" + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "content": ". For the CNN decoder in Fig. 4, we use a series of residual blocks [22] and channel attention blocks [69]. During bundle adjustment, matches with reprojection errors exceeding " + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "inline_equation", + "content": "\\epsilon_f = 3\\mathrm{px}" + }, + { + "bbox": [ + 313, + 468, + 555, + 635 + ], + "type": "text", + "content": " are discarded. The total SfM refinement process is iterated twice. More implementation details are reported in the supplementary material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 647, + 417, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 417, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 417, + 659 + ], + "type": "text", + "content": "4.3. 3D Triangulation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": "Accurately triangulating scene point clouds, given known camera poses and intrinsics, is an important task in SfM. In this section, we evaluate the accuracy and completeness of the reconstructed point clouds." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6409" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 294, + 193 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 294, + 193 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 294, + 193 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 294, + 193 + ], + "type": "table", + "html": "
TypeMethodAccuracy (%)Completeness (%)
1cm2cm5cm1cm2cm5cm
Detector-BasedSIFT [31] + NN + PixSfM [30]76.1885.6093.160.170.713.29
D2Net [11] + NN + PixSfM74.7583.8191.980.832.698.95
R2D2 [42] + NN + PixSfM74.1284.4991.980.431.586.71
SP [8] + SG [47] + PixSfM79.0187.0493.800.752.7711.28
Semi-Dense MatchingLoFTR [56] + PixSfM74.4284.0892.632.919.3927.31
LoFTR + DFSfM [24]80.3889.0195.833.7311.0729.54
AspanTrans. [6] + DFSfM77.6387.4095.023.9712.1832.42
MatchFormer [66] + DFSfM79.8688.5195.483.7611.0629.05
Dense-MatchingRoMa + DFSfM79.3288.4295.823.139.7929.10
DKM + Ours84.0591.9697.395.9513.9531.03
RoMa + Ours84.7992.6297.777.3817.0636.35
DeepVGGSfM [64]80.6289.4996.524.5213.1133.96
Point-BasedMast3r-SfM [10]42.0259.7480.582.058.7631.73
Mast3r-SfM + Our Refinement (Sec. 3.3)77.2286.4794.052.408.2627.17
", + "image_path": "03ccdeda1831897372558d09e9f97f51398ac8ba230bc83bf82d9f0d00ca46bd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 198, + 295, + 232 + ], + "lines": [ + { + "bbox": [ + 55, + 198, + 295, + 232 + ], + "spans": [ + { + "bbox": [ + 55, + 198, + 295, + 232 + ], + "type": "text", + "content": "Table 1. Results of 3D Triangulation. Our method is compared with the baselines on the ETH3D [51] dataset using accuracy and completeness metrics with different thresholds." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 236, + 296, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 236, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 296, + 380 + ], + "type": "text", + "content": "Evaluation. We use the ETH3D training set, comprising 13 indoor and outdoor scenes with millimeter-accurate dense point clouds as ground truth. Following the protocol in PixSfM [30] and DFSfM [24], we triangulate 3D points using fixed camera poses and intrinsics, then evaluate the resulting point clouds for accuracy and completeness using the ETH3D benchmark [51]. The results are reported at varying distance thresholds (1cm, 2cm, 5cm), averaged across all scenes. Consistent with the benchmark setup, accuracy and completeness are measured by the proportion of triangulated points that fall within the specified distances from the ground truth points." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 396, + 296, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 552 + ], + "type": "text", + "content": "Results. The results are shown in Tab. 1. While there is a trade-off between accuracy and completeness, our Dense-SfM framework achieves superior performances on both metrics. Compared to the state-of-the-art baseline LoFTR + DFSfM, our pipeline with RoMa achieves higher accuracy and completeness, thanks to employing dense matching and our proposed pipeline. Also, compared to the RoMa + DFSfM, where we apply quantization on dense matching and refine the tracks as in DFSfM, our method achieves higher performance in terms of both accuracy and completeness, highlighting the effectiveness of our SfM framework. More results with detector-based and semi-dense matching are reported in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 559, + 250, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 559, + 250, + 572 + ], + "spans": [ + { + "bbox": [ + 55, + 559, + 250, + 572 + ], + "type": "text", + "content": "4.4. Multi-View Camera Pose Estimation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 578, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 295, + 590 + ], + "type": "text", + "content": "In this section, we evaluate the recovered multi-view poses." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": "Evaluation protocols. For the evaluation, we use a subset of ETH3D training and test dataset, which includes 22 indoor and outdoor scenes, the Texture-Poor SfM dataset, and the test scenes of IMC 2021 dataset. We evaluate the accuracy of the estimated multi-view poses using the AUC of pose error at various thresholds. For the evaluation of IMC 2021 dataset, due to the high occlusion and appearance changes in many test scenes, directly applying track extension via GS is challenging. Instead, we adopt a" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "type": "text", + "content": "quantization method [24] on the matching results, focusing on comparing our multi-view kernelized matching module with DFSfM's refinement module. Specifically, we apply quantization to the matched keypoints with a radius of 4, and then use our refinement module to refine the quantized keypoints." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 318, + 150, + 549, + 466 + ], + "blocks": [ + { + "bbox": [ + 318, + 150, + 549, + 466 + ], + "lines": [ + { + "bbox": [ + 318, + 150, + 549, + 466 + ], + "spans": [ + { + "bbox": [ + 318, + 150, + 549, + 466 + ], + "type": "image", + "image_path": "4d71db4223592121d4edf85d100411088846adf93f1457a223172a1a88f39e55.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 469, + 555, + 515 + ], + "lines": [ + { + "bbox": [ + 313, + 469, + 555, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 555, + 515 + ], + "type": "text", + "content": "Figure 6. Qualitative Results on Texture-Poor SfM and IMC dataset. Our method with the dense matcher RoMa is qualitatively compared with the baseline LoFTR + DFSfM. The red cameras are ground truth poses while the blue cameras are recovered poses." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 522, + 554, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 554, + 582 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 554, + 582 + ], + "type": "text", + "content": "Results. As shown in Tab. 2, our Dense-SfM framework outperforms existing baselines over all datasets. On the ETH3D dataset, our framework with dense matching achieves the highest multi-view pose accuracy, with a particularly large improvement at the highest threshold." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 582, + 554, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 554, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 554, + 642 + ], + "type": "text", + "content": "As shown in Fig. 6, our framework successfully reconstructs dense and accurate 3D points thanks to dense matching and our pipeline, even in challenging low-textured regions with viewpoint changes, leading to much higher pose estimation accuracy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 648, + 416, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 416, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 416, + 659 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": "We conduct several experiments to evaluate the key components of our pipeline, including the matching design used as input for SfM and the architectural choices of the refinement module, on the ETH3D dataset using triangulation metrics." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6410" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 70, + 541, + 218 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 541, + 218 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 541, + 218 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 541, + 218 + ], + "type": "table", + "html": "
TypeMethodETH3D DatasetTexture-Poor SfM DatasetIMC Dataset
AUC@1°AUC@3°AUC@5°AUC@3°AUC@5°AUC@10°AUC@3°AUC@5°AUC@10°
Detector-BasedCOLMAP (SIFT+NN) [49]26.7138.8642.142.873.854.9523.5823.6644.79
SIFT [31] + NN + PixSfM [30]26.9439.0142.193.134.085.0925.5434.8046.73
D2Net [11] + NN + PixSfM34.5049.7753.581.542.634.548.9112.2616.79
R2D2 [42] + NN + PixSfM43.5862.0966.893.795.517.8431.4141.8054.65
SP [8] + SG [47] + PixSfM50.8268.5272.8614.0019.2324.5545.1957.2270.47
Semi-Dense MatchingLoFTR [56] + PixSfM54.3573.9778.8620.6630.4942.0144.0656.1669.61
LoFTR + DFSIM [24]59.1275.5979.5326.0735.7745.4346.5558.7472.19
AspanTrans. [6] + DFSfM57.2373.7177.7025.7835.6945.6446.7959.0172.50
MatchFormer [66] + DFSfM56.7073.0076.8426.9037.5748.5545.8357.8871.22
Dense MatchingRoMa + DFSfM57.9777.0281.5934.2850.0169.0147.4359.8473.19
DKM + Ours59.0477.7382.2041.1957.2672.9548.6561.0974.37
RoMa + Ours60.9278.4182.6349.9466.2381.4148.4860.7973.90
DeepVGGsF M [64]28.0944.4149.911.866.2621.1045.2358.8973.92
Point-BasedMast3r-SfM [10]35.8558.4665.0343.4661.5178.9742.2654.5367.97
Mast3r-SfM + Our Refinement37.5059.1865.4848.0364.4880.3144.9857.0970.09
", + "image_path": "efd97d89e819bf74b36c96ab77a91345d96be6b56db1640eedfd5a5ed3629989.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 254, + 294, + 382 + ], + "blocks": [ + { + "bbox": [ + 55, + 222, + 555, + 246 + ], + "lines": [ + { + "bbox": [ + 55, + 222, + 555, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 222, + 555, + 246 + ], + "type": "text", + "content": "Table 2. Results of Multi-View Camera Pose Estimation. Our framework is compared with detector-based, detector-free and dense-matching baselines by the AUC of pose error at different thresholds. Bold and underline indicate the best and second-best results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 254, + 294, + 382 + ], + "lines": [ + { + "bbox": [ + 59, + 254, + 294, + 382 + ], + "spans": [ + { + "bbox": [ + 59, + 254, + 294, + 382 + ], + "type": "table", + "html": "
Design ChoiceAccu. (%)Complete. (%)
1cm2cm1cm2cm
(1) Matching designsFull model84.7992.627.3817.06
w/o Mutual Verification84.0392.068.1418.68
w/o GS Extension77.4587.809.4521.64
Quantized Matching (r=4)82.8290.753.5310.62
(2) Refinement designsFull model84.7992.627.3817.06
Multi-view Trans. [24]80.5990.046.0415.2
w/o Gaussian Process72.4784.724.7812.59
w/o Multi-view Trans.83.3991.637.0416.49
w/o ref. confidence selection83.8192.158.8319.85
(3) Number of iterationsNo refine.69.7782.598.6120.4
1 iter81.1290.527.6217.86
2 iter84.7992.67.3817.06
3 iter85.0192.756.7415.91
", + "image_path": "79c60a1446de2c3344bef957769052dd14243be57ef0378dc7014270b5ef1fd7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 385, + 295, + 441 + ], + "lines": [ + { + "bbox": [ + 55, + 385, + 295, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 295, + 441 + ], + "type": "text", + "content": "Table 3. Ablation Studies. On the ETH3D dataset, we quantitatively evaluate the impact of design choice of matching and refinement module, and the number of iterations of refinement. The reported triangulation accuracy and completeness are averaged across all scenes." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 447, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 447, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 54, + 447, + 295, + 567 + ], + "type": "text", + "content": "Matching Designs. Tab. 3 (1) demonstrates the benefits of our proposed matching filtering (mutual verification) and track extension via Gaussian Splatting (GS). Compared to the configurations without mutual verification, where all matches are used for reconstructing the initial SfM, incorporating mutual verification improves accuracy, with a tradeoff in completeness due to filtering. Moreover, extending match pairs through GS significantly improves accuracy, which shows that using more views for multi-view kernelized matching contribute to higher performance of accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 567, + 295, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 295, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 295, + 652 + ], + "type": "text", + "content": "For a comparison with DFSfM [24], which applies quantization to matched keypoints to address the fragmented track problem, we replaced our GS track extension with their quantization approach, using a rounding ratio of " + }, + { + "bbox": [ + 55, + 567, + 295, + 652 + ], + "type": "inline_equation", + "content": "r = 4" + }, + { + "bbox": [ + 55, + 567, + 295, + 652 + ], + "type": "text", + "content": ". Results indicate that our GS track extension not only maintains completeness by avoiding the limitations of quantization but also achieves superior accuracy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 701 + ], + "type": "text", + "content": "Refinement designs. Table 3 (2) shows the benefit of our proposed multi-view kernelized matching's components in Fig. 4 and confidence-based track selection in Fig. 5." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "type": "text", + "content": "We first compare our refinement module to the multi-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 256, + 555, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 256, + 555, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 555, + 304 + ], + "type": "text", + "content": "view refinement module in DFSfM [24], by substituting our refinement module with it. The result shows that our refinement module consistently outperforms the existing approach, achieving higher accuracy and completeness." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 308, + 556, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 556, + 429 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 556, + 429 + ], + "type": "text", + "content": "Next, we evaluate the contributions of each component in our refinement architecture (Fig. 4) by testing configurations where either the multi-view transformer or Gaussian Process is removed. The results show that our full model, which integrates both components, achieves the highest performance in accuracy and completeness, confirming that combining feature-based and positional information yields more precise refinement. Furthermore, our strategy of selecting a final refined track based on predicted confidence in the reference view further enhances accuracy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 463, + 556, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 463, + 556, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 463, + 556, + 548 + ], + "type": "text", + "content": "Impact of iterations. Table 3 (3) reports the results after each refinement iteration. The initial SfM point cloud is less accurate due to reliance solely on initial two-view matching. As the iterations progress, the accuracy of the SfM point cloud gets improved. However, further refinement beyond two iterations gives little gains. So, we limit the refinement to two iterations for efficiency." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 570, + 388, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 388, + 582 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 388, + 582 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "content": "This paper introduces a novel Dense-SfM framework aimed at reconstructing dense point cloud and estimating camera poses from a set of images. Unlike conventional SfM systems that often rely on initial 2D matches, our framework leverages Gaussian Splatting to generate new matching pairs, producing longer tracks that significantly enhance both the accuracy and density of the reconstructed point cloud. Extensive evaluations on diverse datasets show that our framework consistently outperforms existing SfM baselines across multiple metrics." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "6411" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 165, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 165, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 165, + 85 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 189 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 189 + ], + "type": "text", + "content": "This research was supported in part by Samsung Advanced Institute of Technology (SAIT), the Naver-Intel Co-Lab, Inter-university Semiconductor Research Center (ISRC), and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) [NO.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 198, + 115, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 198, + 115, + 211 + ], + "spans": [ + { + "bbox": [ + 56, + 198, + 115, + 211 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 219, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 219, + 296, + 262 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 219, + 296, + 262 + ], + "spans": [ + { + "bbox": [ + 61, + 219, + 296, + 262 + ], + "type": "text", + "content": "[1] Sameer Agarwal, Noah Snavely, Ian Simon, Steven M. 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Mahdi H. Miangoleh $^{3}$ , Xinyu Huang $^{1}$ , Liu Ren $^{1}$", + "bbox": [ + 165, + 179, + 828, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Bosch Research North America & Bosch Center for Artificial Intelligence (BCAI)", + "bbox": [ + 251, + 200, + 745, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Carnegie Mellon University $^{3}$ Simon Fraser University", + "bbox": [ + 326, + 218, + 669, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[yluliang.quo2,xingyu.huang,liu. ren]@us.bosch.com", + "bbox": [ + 282, + 234, + 714, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ sparshg@andrew.cmu.edu $^{3}$ smh31@sfu.ca", + "bbox": [ + 328, + 253, + 666, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://yuliangguo.github.io/depth-any-camera", + "bbox": [ + 294, + 272, + 696, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 321, + 326, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While recent depth foundation models exhibit strong zero-shot generalization, achieving accurate metric depth across diverse camera types—particularly those with large fields of view (FoV) such as fisheye and 360-degree cameras—remains a significant challenge. This paper presents Depth Any Camera (DAC), a powerful zero-shot metric depth estimation framework that extends a perspective-trained model to effectively handle cameras with varying FoVs. The framework is designed to ensure that all existing 3D data can be leveraged, regardless of the specific camera types used in new applications. Remarkably, DAC is trained exclusively on perspective images but generalizes seamlessly to fisheye and 360-degree cameras without the need for specialized training data. DAC employs Equi-Rectangular Projection (ERP) as a unified image representation, enabling consistent processing of images with diverse FoVs. Its core components include pitch-aware Image-to-ERP conversion with efficient online augmentation to simulate distorted ERP patches from undistorted inputs, FoV alignment operations to enable effective training across a wide range of FoVs, and multi-resolution data augmentation to further address resolution disparities between training and testing. DAC achieves state-of-the-art zero-shot metric depth estimation, improving $\\delta_{1}$ accuracy by up to $50\\%$ on multiple fisheye and 360-degree datasets compared to prior metric depth foundation models, demonstrating robust generalization across camera types.", + "bbox": [ + 88, + 354, + 483, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 792, + 220, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Depth estimation from monocular cameras is a foundational challenge for applications like autonomous driving, AR/VR, and robotics. While early deep learning methods", + "bbox": [ + 89, + 816, + 483, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eca003ef65b3c695ab9c932d5824bbf4561a2832f026b7c56fdf8e4dfad385b9.jpg", + "image_caption": [ + "Figure 1. We introduce Depth Any Camera (DAC) framework, which leverages large-scale datasets containing perspective camera images to train a single depth estimation model capable of conducting zero-shot metric depth estimation on images captured various types of cameras, including those captured from large FoV fisheye and $360^{\\circ}$ cameras." + ], + "image_footnote": [], + "bbox": [ + 526, + 319, + 893, + 478 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "relied on supervised training using single datasets and depth sensor [24] supervision [3, 25, 36], monocular depth estimation remains challenging due to scale-depth ambiguity. Expanding training datasets has been a key strategy to enhance robustness, with self-supervised approaches using sequential frames [13, 46, 48]. However, these methods often underperform due to self-supervision ambiguity, view inconsistencies and dynamic objects. Recent methods, such as MiDaS [37], leverage large-scale datasets with 3D supervision, normalizing scale differences across datasets to enable zero-shot testing. However, they primarily provide relative depth rather than metric depth.", + "bbox": [ + 509, + 593, + 906, + 775 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent methods tackle zero-shot metric depth estimation by addressing the challenges of inconsistent scaling factors in depth ground truth caused by varying camera intrinsic parameters. Several works demonstrate impressive generalization capabilities on novel images [4, 20, 33, 53, 57], establishing themselves as foundational depth models for downstream tasks. However, these approaches often struggle with large field-of-view (FoV) cameras like fisheye and", + "bbox": [ + 509, + 779, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 107, + 875, + 236, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Equal technical contribution.", + "bbox": [ + 109, + 887, + 269, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26996", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$360^{\\circ}$ cameras, where performance significantly declines compared to standard perspective cameras.", + "bbox": [ + 89, + 90, + 482, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As illustrated in Fig. 2, large FoV images can be represented in multiple formats, but generating the best-performing undistorted image for perspective-based depth models often leads to substantial FoV loss. Despite these limitations, large FoV inputs are crucial for efficiency-critical downstream applications such as large-scale detection [34, 52], segmentation [55, 58], SLAM [11, 44, 45, 62], interactive 3D scene generation [59], and robotic demonstration capturing [6, 14, 49].", + "bbox": [ + 88, + 122, + 482, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Achieving zero-shot depth generalization across any FoV camera presents several challenges: (1) selecting a unified camera model to represent diverse FoVs, (2) effectively leveraging perspective training datasets to generalize to data spaces observable only from large FoV cameras, (3) managing drastically different training image sizes in the unified space caused by varying FoVs, and (4) handling resolution inconsistencies between training and testing phases.", + "bbox": [ + 88, + 260, + 482, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present Depth Any Camera (DAC), a novel zero-shot metric depth estimation framework that enables a depth model trained exclusively on perspective images to generalize across cameras with widely varying FoVs, including fisheye and $360^{\\circ}$ cameras (see Fig. 1). DAC employs Equi-Rectangular Projection (ERP) as a canonical representation to unify images from diverse FoVs into a shared space. A key innovation is the introduction of an efficient pitch-aware Image-to-ERP conversion based on grid sampling and Gnomonic Geometry [47], enabling seamless ERP-space data augmentations. Specifically, pitch-aware ERP conversion with pitch-angle augmentation projects perspective images into high-distortion regions of the ERP space, effectively simulating observations unique to large-FoV cameras. This enhances DAC's zero-shot generalization, allowing it to extrapolate beyond the perspective domain to a broader range of camera types. To facilitate learning from mixed datasets, we propose a FoV alignment process that normalizes diverse-FoV training samples to a predefined ERP patch size, preserving content while minimizing computational overhead. Additionally, multi-resolution augmentation is applied to address resolution mismatches, allowing the model to learn scale-equivariant features and adapt to a flexible range of testing resolutions. In summary, our contributions are as follows:", + "bbox": [ + 91, + 383, + 483, + 760 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel zero-shot metric depth estimation framework capable of handling images from any camera type, including fisheye and $360^{\\circ}$ images, using a model trained exclusively on perspective data.", + "- We introduce an efficient pitch-aware perspective-to-ERP patch conversion that simulates the high-distortion characteristics of large-FoV cameras from perspective inputs, enhancing zero-shot generalization.", + "- We develop a FoV alignment process that enables effic" + ], + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tive training across cameras with diverse FoVs within a unified ERP space, along with a multi-resolution training strategy to address resolution mismatches between training ERP patches and testing images.", + "bbox": [ + 524, + 90, + 903, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our method achieves State-of-The-Art (SoTA) zero-shot performance on all large FoV testing datasets, delivering up to a $50\\%$ improvement in $\\delta_{1}$ accuracy on indoor fisheye and $360^{\\circ}$ datasets, showcasing strong generalization across diverse camera types.", + "bbox": [ + 513, + 152, + 903, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/51c412acdd7c4f5b81303d9f168de1ff9ca81e75a60d8815cf31788ffb2ce2ae.jpg", + "image_caption": [ + "Figure 2. Challenges on zero-shot test on large FoV camera images. Metric depth estimation models trained on perspective images (e.g., Metric3Dv2 [20]) experience significant performance degradation when applied to fisheye images. Degradation is less pronounced when using an undistorted portion with a highly limited FoV or its ERP conversion." + ], + "image_footnote": [], + "bbox": [ + 516, + 237, + 903, + 369 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 474, + 663, + 491 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Zero-Shot Monocular Depth Estimation", + "text_level": 1, + "bbox": [ + 511, + 500, + 856, + 515 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent approaches to zero-shot metric depth estimation tackle the challenge of inconsistent scaling factors in depth ground truth due to varying camera intrinsic parameters [4, 16, 20, 33, 53, 54, 57]. Zoedepth [4] introduces an advanced network architecture, while DepthAnything [53, 54] employs a sophisticated unsupervised learning paradigm. However, their performance in metric depth estimation is limited without tackling inconsistency camera intrinsics. Metric3D [20, 57] and UniDepth [33] address scaling inconsistencies by converting images into a canonical camera space. Metric3D uses intrinsic parameters for this preprocessing, whereas UniDepth incorporates a network branch to estimate and convert intrinsics on the fly. Despite these advances, none of these methods achieve satisfactory zero-shot performance on large FoV images, presenting unique challenges in unifying diverse FoVs and supporting effective model learning.", + "bbox": [ + 511, + 523, + 906, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Depth Estimation from Large FoV Cameras", + "text_level": 1, + "bbox": [ + 511, + 786, + 885, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Depth estimation for fisheye, $360^{\\circ}$ cameras has grown in popularity, as large FoVs capture richer contextual information that enhances depth estimation [1, 21, 26, 41, 60]. A key challenge for these cameras is managing position-dependent distortions, which vary by camera models. Approaches to address this include deformable CNNs [42, 50,", + "bbox": [ + 511, + 809, + 905, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26997", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "63], which adapt kernel shapes to compensate for distortions, as well as methods that segment ERP images to reduce distortion effects before merging [21, 38]. More recent methods leverage transformers to handle these distortions [10, 26, 41, 60]. While transformer-based networks have improved in-domain performance, they are approaching saturation, indicating that distortion is not the only challenge. Instead, the lack of large-scale FoV-specific training data is a key bottleneck for generalization. No current methods enable an unified depth estimation model trained on mixed large-scale perspective datasets to achieve zero-shot generalization on ERP or fisheye images.", + "bbox": [ + 89, + 90, + 483, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Notations and Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 285, + 349, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Depth Scaling Operations. Monocular depth estimation is inherently ill-posed, as different 3D object sizes and depths can produce the same 2D appearance. Deep learning models rely on learning an object's 3D dimensions from its 2D appearance [16, 17, 43] to infer depth, leading to the scaling operation illustrated in the right panel of Fig. 3. When using mixed camera data, apparent object size also depends on focal length, making accurate 2D-to-depth mapping dependent on appropriately scaling ground-truth depths when converting a perspective model to a canonical model, as shown in the left panel of Fig. 3. These scaling operations are central to the Metric3D [20, 57] pipeline and are integrated into our ERP-based approach.", + "bbox": [ + 89, + 310, + 483, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "EquiRectangular Projection (ERP). Equi-Rectangular Projection (ERP) is an image representation based on a spherical camera model, where each pixel corresponds to a specific latitude $\\lambda$ and longitude $\\phi$ . A full ERP space spans $180^{\\circ}$ in latitude and $360^{\\circ}$ in longitude, making it ideal for handling diverse FoV cameras. The ERP image height is the only parameter needed to define the ERP space, allowing both training and testing images to be consistently converted into this space, regardless of the original FoV.", + "bbox": [ + 89, + 507, + 483, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformations between standard images and ERP images use Gnomonic Projection transformation [47], which offers a closed-form mapping between tangent image coordinates $(x_{t},y_{t})$ and spherical coordinates $(\\lambda ,\\phi)$ , assuming a tangent plane centered at $(\\lambda_c,\\phi_c)$ of a unit sphere. Specifically, as shown in Fig. 5, this mapping is given by:", + "bbox": [ + 89, + 642, + 483, + 726 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} = \\frac {\\bar {x}}{\\cos c} = \\frac {\\cos \\phi \\sin (\\lambda - \\lambda_ {c})}{\\cos c} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 732, + 482, + 760 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ny _ {t} = \\frac {\\bar {y}}{\\cos c} = \\frac {\\cos \\phi_ {c} \\sin \\phi - \\sin \\phi_ {c} \\cos \\phi \\cos (\\lambda - \\lambda_ {c})}{\\cos c} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 762, + 480, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $(\\bar{x},\\bar{y},\\cos c)$ represents a point on the unit sphere, and $c$ is the angular distance between $(\\lambda ,\\phi)$ and $(\\lambda_c,\\phi_c)$ , can be calculated as:", + "bbox": [ + 89, + 795, + 482, + 837 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\cos c = \\sin \\phi_ {c} \\sin \\phi + \\cos \\phi_ {c} \\cos \\phi \\cos (\\lambda - \\lambda_ {c}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 847, + 482, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use these transformations to enable an efficient ERP conversion and data augmentation process, creating a", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/243f816124080811df05945fad13bf5f8e7b73db2064f4ef58c8219591096bb4.jpg", + "image_caption": [ + "Camera Conversion", + "Figure 3. Depth Scaling in Canonical Model Conversion and Image Resizing. The apparent 2D size of an object $u$ in an image depends on its 3D dimensions $X$ , depth $Z$ , and camera focal length $f_{x}$ . Left: Converting a perspective camera model to a canonical model with a different focal length $\\hat{f}_{x}$ requires scaling the depth values proportionally, so $\\hat{Z} = \\frac{\\hat{f}_{x}Z}{\\hat{f}_{x}}$ . Center: The original camera setup, showing the direct relationship between object size, depth, and focal length. Right: When the camera model is fixed but the image is resized to $u'$ , this simulates viewing the same 3D object at a different distance, necessitating depth scaling for accurate metric depth, with $Z' = \\frac{uZ}{u'}$ ." + ], + "image_footnote": [], + "bbox": [ + 521, + 89, + 640, + 215 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/044bbd9a554cd2f80eac9b2957819b84475f0c01b0ea2f5ea11cd3fbd6486961.jpg", + "image_caption": [ + "Original Cam" + ], + "image_footnote": [], + "bbox": [ + 653, + 89, + 774, + 215 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b5183e01cde5e7f9043d1aad9ea2c2bbbf1095ec6ab390a338c1005454bd4880.jpg", + "image_caption": [ + "Image Resizing" + ], + "image_footnote": [], + "bbox": [ + 781, + 89, + 900, + 215 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "streamlined pipeline that supports zero-shot generalization for depth estimation across various FoV cameras.", + "bbox": [ + 511, + 405, + 905, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Depth Any Camera", + "text_level": 1, + "bbox": [ + 511, + 450, + 702, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose Depth Any Camera (DAC), a depth model training framework designed to achieve zero-shot generalization across diverse camera models, including perspective, fisheye, and $360^{\\circ}$ cameras. As illustrated in Fig. 4, images from different camera types and FoVs are transformed into a canonical ERP space during both the training and testing phases. For training, we leverage the extensive perspective image datasets by converting them into smaller ERP patches for efficient learning. During testing, large FoV images are similarly converted into the canonical ERP space, allowing the trained model to predict metric depth consistently, without getting confused by different camera intrinsic and distortion parameters.", + "bbox": [ + 511, + 476, + 906, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Several key components are designed to address specific challenges in implementing the DAC framework. In Sec. 4.1, we present an efficient pitch-aware Image-to-ERP conversion method that simulate large-FoV images at patch level and supports online augmentation within the ERP space. Sec. 4.2 introduces a FoV alignment process, an effective data augmentation technique that maximizes content inclusion while minimizing computational waste on background areas, using a single predefined ERP patch size. In Sec. 4.3, we describe a multi-resolution data augmentation approach aimed at training a transformer-based network capable of handling a broad range of testing resolutions.", + "bbox": [ + 511, + 672, + 908, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed DAC framework is compatible with various depth estimation network architectures, which are not the primary focus of this paper. Without loss of generality,", + "bbox": [ + 511, + 854, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26998", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c5379d3552bf1603bb40886272ce8e00d7cd45b37beb62cbc73beed7e2b01fbf.jpg", + "image_caption": [ + "Figure 4. Depth Any Camera Pipeline. Our DAC framework converts data from any camera type into a canonical ERP space, enabling a model trained solely on perspective images to process large-FOV test data consistently for metric depth estimation. During training, we introduce an effective pitch-aware Image-to-ERP conversion with online data augmentation to simulate high-distortion regions unique to large-FOV images. The proposed FoV-Align process normalizes diverse-FOV data to a predefined ERP patch size, maximizing training efficiency. During inference, images from any camera type are converted into ERP space for depth estimation, with an optional step to map the ERP output back to the original image space for visualization." + ], + "image_footnote": [], + "bbox": [ + 112, + 89, + 883, + 385 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we employ iDisc [32] for its simplicity and effectiveness, and for its incorporation of two prototypical attention modules, namely cross-attention and self-attention. We use the SIlog loss function [9] for training our models.", + "bbox": [ + 89, + 494, + 483, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Pitch-Aware Image-to-ERP Conversion", + "text_level": 1, + "bbox": [ + 89, + 564, + 429, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An input image can be efficiently converted to its corresponding ERP patch through grid sampling combined with gnomonic projection. Assuming an ERP space with height $H_{E}$ , width $W_{E} = 2H_{E}$ , and the image center at latitude $\\lambda_{c}$ , longitude $\\phi_{c}$ , with a target ERP patch size of $H_{e} \\times W_{e}$ , the ERP patch coordinates $(u_{e}, v_{e})$ can be mapped to spherical coordinates as $\\phi = \\frac{2\\pi W_{e}}{W_{E}} (u_{e} - \\frac{W_{e}}{2}) + \\phi_{c}$ , and $\\lambda = \\frac{\\pi H_{e}}{H_{E}} (v_{e} - \\frac{H_{e}}{2}) + \\lambda_{c}$ . Using Gnomonic Geometry presented in Eq. 1 and Eq. 2, we obtain the corresponding normalized image coordinate $(x_{t}, y_{t}, 1)$ in the tangent plane and $(\\bar{x}, \\bar{y}, \\cos c)$ on the unit sphere. To map this coordinate to the actual image coordinate $(u, v)$ , we apply distortion and projection functions based on the given camera parameters:", + "bbox": [ + 89, + 585, + 483, + 776 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(x _ {d}, y _ {d}\\right) = f _ {d} (\\bar {x}, \\bar {y}, \\cos c, D _ {c}) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 782, + 482, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n(u, v) = f _ {p} \\left(x _ {d}, y _ {d}, K _ {c}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 209, + 801, + 482, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{d}$ is the distortion function with distortion parameters $D_{c}$ , and $f_{p}$ is the projection function with intrinsic parameters $K_{c}$ . If the input image has no distortion, projection function is directly applied to $(x_{t}, y_{t})$ . Details on applying distortion models are included in Supplemental Sec. 8.", + "bbox": [ + 89, + 824, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 5, with uniformly sampled grid points within the target ERP patch, each grid point can be mapped directly to a corresponding location in the input image. This mapping facilitates efficient transformation of the captured image into an ERP patch via grid sampling. Essentially, each grid point in the ERP patch maps to a specific floating-point position in the input image, and its value is obtained by interpolating from the neighboring pixel values.", + "bbox": [ + 511, + 494, + 906, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This ERP conversion enables a powerful training pipeline when the latitude of the tangent plane center $\\lambda_{c}$ is defined by the camera's pitch angle in training. When camera orientation is available or can be estimated [22], perspective data can be projected to various latitudes in the ERP space, enabling the simulation of regions uniquely visible from large-FoV cameras, as shown in Fig. 5, and Supplemental Fig. 7. This pitch-aware conversion is crucial for improving the generalization of trained models to previously unobserved large-FoV data, as demonstrated in Sec. 5.3, because neural networks alone have limited capacity to generalize to extrapolated data spaces [51].", + "bbox": [ + 511, + 621, + 908, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Another notable advantage is the seamless ability to perform online augmentation efficiently in the ERP space. For datasets with limited pitch variation [12, 15, 19, 61], a unique pitch augmentation can be efficiently applied by adding noise to $\\lambda_{c}$ , generating ERP patches with varying shapes, as shown in Fig. 4. In addition, common augmenta", + "bbox": [ + 511, + 810, + 908, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26999", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bf161515b70df72a299dee603fdf820daa98320baa68833764ef08ccf70ac55b.jpg", + "image_caption": [ + "Grid Sampling via Gnomonic Geometry", + "Figure 5. Pitch-Aware ERP Conversion and FoV Alignment. Top: Grid Sampling is applied for an efficient Image-to-ERP conversion. Each ERP grid sample's corresponding location in the input image is computed using gnomonic geometry and specific camera projection parameters. Given the patch center latitude $\\lambda$ determined by the camera's pitch angle, it makes the converted patch to represent high-distortion regions in the ERP space. Bottom: The FoV-Align process normalizes diverse-FoV ERP patches (shown in red and green) to match the height of a single predefined ERP patch (outlined in blue), ensuring efficient training." + ], + "image_footnote": [], + "bbox": [ + 106, + 104, + 468, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tions, such as scaling, rotation, and translation—commonly applied to perspective images—can be directly applied to the normalized image coordinates $(x_{t},y_{t})$ as follows:", + "bbox": [ + 89, + 397, + 483, + 444 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\begin{array}{l} x _ {t} ^ {\\prime} \\\\ y _ {t} ^ {\\prime} \\end{array} \\right] = s _ {\\sigma} \\left[ \\begin{array}{l l} R _ {\\sigma} & T _ {\\sigma} \\end{array} \\right] \\left[ \\begin{array}{l} x _ {t} \\\\ y _ {t} \\end{array} \\right] \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 450, + 482, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s_{\\sigma}$ is a scale factor, $R_{\\sigma}$ is 2D rotation matrix, and $T_{\\sigma}$ is a 2D translation vector corresponding to the applied augmentations.", + "bbox": [ + 89, + 491, + 483, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. FoV Alignment", + "text_level": 1, + "bbox": [ + 89, + 544, + 246, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When training data include a wide range of camera FoVs within perspective images, such as in the HM3D [35] dataset produced by OmniData [8], the corresponding ERP regions can vary significantly in size, as shown in Fig. 5. There is no single crop size that can consistently capture most content information for certain images without wasting substantial computation on background padding for others. This creates a dilemma in prioritizing between training efficiency and richness of information, and it can also reduce training quality when samples exhibit drastically different content-to-background ratios.", + "bbox": [ + 89, + 568, + 482, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address this challenge, we introduce a simple yet effective FoV Alignment operation that adjusts the FoV of each input image to match the predetermined crop area FoV. Specifically, this process applies a specific scaling augmentation, as described in Sec. 4.1 and Eq. 6, specifically $\\mathrm{Fov}_e = \\frac{H_e\\pi}{H_E}$ and $s_\\sigma = \\frac{\\mathrm{Fov}_c}{\\mathrm{Fov}_e}$ , where $\\mathrm{Fov}_c$ is derived from actual camera parameters, and $\\mathrm{Fov}_e$ is ERP patch's vertical FoV. As illustrated in Fig. 5, this approach allows a single predefined ERP patch size to maximize the inclusion of relevant content and minimize computational waste on background, making it ideal for an efficient training pipeline.", + "bbox": [ + 89, + 734, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Multi-Resolution Training", + "text_level": 1, + "bbox": [ + 513, + 90, + 754, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training ERP patches and testing images may prefer inconsistent resolutions for various reasons, e.g. drastically different aspect ratio, edge device limitation. When testing resolutions differ from the training patch size, model performance can degrade significantly, particularly with attention modules that aggregate different numbers of image tokens.", + "bbox": [ + 511, + 114, + 903, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address this issue, we adopt a multi-resolution training scheme. As illustrated in Fig. 4, each ERP patch is resized to two additional lower resolutions (typically 0.7 and 0.4 of the original) to incorporate varied image resolutions in training. The training feeds the model three batches of images at different resolutions and sums the losses.", + "bbox": [ + 511, + 205, + 905, + 295 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 309, + 645, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 513, + 333, + 702, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In-Domain Training Datasets. For indoor experiments, we use Habitat-Matterport 3D (HM3D) [35], Taskonomy [61], and Hypersim [39], totaling 670K perspective images with distinct characteristics. To streamline training, we use the first 50 scenes from HM3D and Taskonomy (tiny versions provided by OmniData [8]). For outdoor data, we use DDAD [15] and LYFT [19], totaling 130K images. Table 1 summarizes the datasets in use, showing varying distributions in FoV, pitch angles, sources, and image quality.", + "bbox": [ + 511, + 356, + 906, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Zero-Shot Testing Datasets. We evaluate DAC on two $360^{\\circ}$ datasets—Matterport3D [5] and Pano3DGV2 [2]—and two fisheye datasets—ScanNet++ [56] and KITTI360 [27]—all featuring larger FoVs than perspective images. Our primary experiments focus on these datasets to assess zero-shot generalization to large FoV cameras. Additional evaluations on NYUv2 [30] and KITTI [12] are provided in the supplementary material, demonstrating DAC's performance on perspective data relative to SoTA methods.", + "bbox": [ + 511, + 492, + 905, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Details. We assess DAC's generalization to large FoV cameras across both indoor and outdoor scenes, training separate models for each without data mixing to simplify training. For fair comparison, competing models are either re-trained with the same data splits or use their largest versions trained on extensive datasets. Evaluations are conducted using metric depth metrics: $\\delta_1\\uparrow ,\\delta_2\\uparrow ,\\delta_3\\uparrow$ Abs Rel↓, RMSE↓, and log10↓.", + "bbox": [ + 511, + 628, + 905, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compare DAC with the following baselines:", + "bbox": [ + 513, + 750, + 903, + 763 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Metric3Dv2 [20]: A SoTA foundation model in zero-shot metric depth estimation, built upon perspective canonical camera model to standardize datasets.", + "- UniDepth [33]: A more recent SoTA foundation depth model leveraging network designs to handle diverse camera parameters. We test its ability to handle large FoV cameras not included in training.", + "- iDisc [32]: Selected as a network baseline due to its use of self-attention and cross-attention modules in a straight-" + ], + "bbox": [ + 514, + 765, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "27000", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/656e4e3d269ab98eb35dfe2a601dbddc449625739640a88f0088e527a6b50559.jpg", + "table_caption": [ + "Table 1. Overview of Datasets. This table summarizes the training and testing datasets used in this work. The training datasets span a range of FoVs, pitch angles, and image quality, each potentially impacting performance on different test datasets in varying degrees." + ], + "table_footnote": [], + "table_body": "
Train Dataset# ImagesScenexFoV (deg.)# CamsPitch (deg.)SourceImg Qual.Test DatasetCam TypexFoV (deg.)Scene
HM3D-tiny [35]310KIndoor36° - 124°10K+3σ = 75°ReconLowMatterport3D [5]ERP360°Indoor
Taskonomy-tiny [61]300KIndoor45° - 75°10K+3σ = 24°RealHighPano3D-GV2 [2]ERP360°Indoor
Hypersim [39]54KIndoor60°13σ = 60°SimHigh+ScanNet++ [56]Fisheye150°Indoor
DDAD [15]80KOutdoor45° - 60°36+3σ ~ 10°RealHighKITTI360 [27]Fisheye180°Outdoor
LYFT [19]50KOutdoor20° - 60°6+3σ ~ 10°RealHigh
", + "bbox": [ + 91, + 125, + 919, + 200 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0880769ad30e5eb8ef19156cb7415bb7b4aed7e95a875121490b127ab3bef850.jpg", + "table_caption": [ + "Table 2. Zero-Shot Test on ${360}^{ \\circ }$ and Fisheye Datasets. DAC is compared with SoTA metric depth models across four large-ForV datasets." + ], + "table_footnote": [], + "table_body": "
Test DatasetMethodsTrain DatasetBackboneδ1↑δ2↑δ3↑Abs Rel↓RMSE↓log10↓
Matterport3D [5]UniDepth [33]Mix 3MViT-L [7]0.25760.51140.70910.76481.38270.2208
Metric3Dv2 [20]Mix 16MDinov2 [31]0.43810.73110.87350.29240.88420.1546
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.42870.78540.93330.27880.89610.1352
iDisc [32]Indoor 670KResnet101 [18]0.52870.82600.93980.27570.77710.1147
DAC (Ours)Indoor 670KResnet101 [18]0.77270.95620.98220.1560.61850.0707
Pano3D-GV2 [2]UniDepth [33]Mix 3MViT-L [7]0.24690.49770.70840.78921.26810.2231
Metric3Dv2 [20]Mix 16MDinov2 [31]0.40400.69290.84990.30700.85490.1664
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.50600.81760.93600.26080.72480.1201
iDisc [32]Indoor 670KResnet101 [18]0.56290.82220.93320.26570.64460.1122
DAC (Ours)Indoor 670KResnet101 [18]0.81150.95490.98600.13870.47800.0623
ScanNet++ [56]UniDepth [33]Mix 3MViT-L [7]0.36380.64610.83580.49711.16590.1648
Metric3Dv2 [20]Mix 16MDinov2 [31]0.53600.82180.93500.22290.89500.1177
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.64890.89200.95580.19150.97790.0938
iDisc [32]Indoor 670KResnet101 [18]0.61500.87800.96170.27120.48350.0972
DAC (Ours)Indoor 670KResnet101 [18]0.85170.96930.99220.13230.30860.0532
KITTI360 [27]UniDepth [33]Mix 3MViT-L [7]0.48100.83970.94060.29396.56420.1221
Metric3Dv2 [20]Mix 16MDinov2 [31]0.71590.93230.97710.19974.57690.0811
Metric3Dv2 [20]Outdoor 130KDinov2 [31]0.76750.93700.97560.15214.66100.0723
iDisc [32]Outdoor 130KResnet101 [18]0.78330.93840.97530.15984.91220.0704
DAC (Ours)Outdoor 130KResnet101 [18]0.78580.93880.97750.15594.36140.0684
", + "bbox": [ + 161, + 244, + 836, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "forward yet effective network, and strong in-domain performance. As iDisc alone does not handle mixed camera parameters, we train it with Metric3Dv2 [20], and compare it to the same network trained with ours.", + "bbox": [ + 102, + 526, + 482, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. In the DAC training pipeline, we set the full ERP height to $H_{\\mathrm{erp}} = 1400$ pixels, with an ERP patch size of $500 \\times 700$ pixels for both indoor and outdoor models. We use $10^{\\circ}$ latitude augmentations for both and additionally $10^{\\circ}$ rotation augmentation for indoor. When training the iDisc [32] model using the Metric3D [57] pipeline, we use canonical focal lengths of $f_{\\mathrm{cano}} = 519$ (NYU dataset [30]) for indoor models and $f_{\\mathrm{cano}} = 721$ (KITTI dataset [12]) for outdoor models.", + "bbox": [ + 89, + 588, + 482, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To test perspective models on ERP and fisheye images, specific adjustments are required. For $360^{\\circ}$ (ERP) images, which lack a defined focal length, we calculate a virtual focal length $f_{\\mathrm{virtual}}$ based on pixels per latitude degree: $\\frac{1}{f_{\\mathrm{virtual}}} = \\tan \\left(\\frac{\\pi}{H_{\\mathrm{ep}}}\\right)$ , scaling the predicted depth with $\\frac{f_{\\mathrm{cano}}}{f_{\\mathrm{virtual}}}$ for ground-truth alignment. For fisheye images, aligning $f_{\\mathrm{cano}}$ with the post-distortion focal length introduces significant errors, so we first convert fisheye images to ERP space and apply $\\frac{f_{\\mathrm{cano}}}{f_{\\mathrm{virtual}}}$ for metric depth evaluation.", + "bbox": [ + 89, + 726, + 482, + 871 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For testing resolution, if the original resolution is less than twice the training resolution, we use it directly; for", + "bbox": [ + 89, + 871, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "larger resolutions, we maintain the aspect ratio and align it with the training resolution. Based on this rule, we evaluate Matterport3D [5] and Pano3D-GV2 [2] at $512 \\times 1024$ , ScanNet++ [56] at $500 \\times 750$ , and KITTI360 [27] at $700 \\times 700$ . For competing methods that are not adaptable to inconsistent resolutions compared to training, we report the higher score obtained from the two settings to ensure fairness.", + "bbox": [ + 511, + 526, + 906, + 632 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In experiments, ResNet101 [18]-backbone models are trained for 60k iterations with a batch size of 48, while Swin-L [28] and DINOv2 [31] models are trained for 120k iterations with a batch size of 48. Finally, to support all FoV types, depth is represented as Euclidean Distance from the camera center rather than Z-buffer format, as the latter is incompatible with spherical projections and would yield inaccurate low depth values for fisheye or ERP images.", + "bbox": [ + 511, + 633, + 908, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison with the SoTA", + "text_level": 1, + "bbox": [ + 511, + 768, + 759, + 786 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare DAC with primary baselines in zero-shot generalization tests on large FoV datasets, with quantitative results reported in Table 2, and qualitative results shown in Fig. 6. In indoor experiments, DAC significantly outperforms pre-trained models UniDepth [33] and Metric3Dv2 [20], even when using a lighter ResNet101 [18] backbone and a much smaller training dataset. DAC", + "bbox": [ + 511, + 794, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "27001", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "achieves superior performance across both $360^{\\circ}$ datasets and the fisheye dataset ScanNet++ [56]. Compared to the iDisc [32] network trained with the Metric3Dv2 pipeline, DAC shows substantial improvements across all metrics on all datasets. Notably, DAC improves the next-best method by nearly $50\\%$ in the most differentiating metric, $\\delta_{1}$ .", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In outdoor tests, DAC significantly outperforms Metric3Dv2 [57] and UniDepth [33], even with much larger backbones. However, it achieves only marginal improvements over iDisc [32] under the same network configuration, with less pronounced gains compared to indoor settings. This is likely due to the limited camera pitch variance in the outdoor training data (Table 1), reducing the ability to simulate highly distorted regions. Moreover, KITTI360 [27] LiDAR points are concentrated in less distorted areas (Fig. 6), making the evaluation less distinctive.", + "bbox": [ + 89, + 181, + 480, + 332 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Particularly, a notable observation is that while UniDepth [33] utilizes a network-based spherical conversion, it struggles with large FoV cameras, exposing the limitations of deep learning in extrapolated domains [51]. In contrast, DAC's success underscores the effectiveness of our geometry-based training pipeline.", + "bbox": [ + 89, + 333, + 480, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Additional results of DAC models using SwinL [28] backbones are provided in Supplemental Table 5. These models outperform their ResNet101 [18] counterparts in most cases, except on the $360^{\\circ}$ datasets.", + "bbox": [ + 89, + 422, + 480, + 483 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5f2ec13ffc3c2be9eb6bb133e210fe8c9fe5c567f6c7cdadbdf95b314833c5eb.jpg", + "table_caption": [ + "Table 3. Impact of Key Components and Network. We conduct the main ablation study on indoor datasets by training with HM3D [35] and performing zero-shot testing on Pano3D-GV2 [2] and ScanNet++ [56]. We compare the performance of the DAC framework with specific components removed, as well as different network architectures trained under the Metric3D [57] pipeline." + ], + "table_footnote": [], + "table_body": "
Test DatasetMethodsδ1↑δ2↑A.Rel↓
Pano3D-GV2 [2]Metric3Dv2 [20]0.56230.83410.2479
iDisc-cnn [32]0.30260.55650.3548
iDisc [32]0.41300.68440.3043
DAC (Ours)0.72510.92540.1729
w\\o Pitch-Aware ERP0.49110.79040.2422
w\\o Pitch Aug 10°0.69120.93110.188
w\\o FoV Align0.40750.75850.2610
w\\o Multi-Reso0.51280.77840.2437
ScanNet++ [56]Metric3Dv2 [20]0.45690.74630.2818
iDisc-cnn [32]0.46390.76530.3045
iDisc [32]0.53010.80480.3237
DAC (Ours)0.65390.90830.1951
w\\o Pitch-Aware ERP0.47110.80680.2508
w\\o Pitch Aug 10°0.67410.90660.1914
w\\o FoV Align0.54280.86440.2200
w\\o Multi-Reso0.55040.84640.2231
", + "bbox": [ + 102, + 585, + 470, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 816, + 243, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Key Components and Network Architecture. We evaluate the effect of the FoV Align and Multi-Reso Training components by removing each individually, while keeping the rest of the DAC framework unchanged. This ablation", + "bbox": [ + 89, + 839, + 480, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2ded7b0f56317789a40f5adcd7485cbd89fab74a109c53413253109f714608b5.jpg", + "table_caption": [ + "Table 4. Impact of Train Dataset. Models are trained separately on each training dataset and evaluated in zero-shot tests on $360^{\\circ}$ and fisheye datasets. Due to the unique characteristics of each training dataset, their contributions and importance to generalization across different testing datasets vary." + ], + "table_footnote": [], + "table_body": "
Test DatasetsTrain DatasetMethodsδ1↑A.Rel↓
Pano3D-GV2 [2]HM3D-tiny [35]Metric3Dv2 [20]0.56230.2479
iDisc [32]0.41300.3043
DAC (Ours)0.72510.1729
Taskonomy-tiny [61]Metric3Dv2 [20]0.37850.2959
iDisc [32]0.38880.4076
DAC (Ours)0.64110.1972
Hypersim [39]Metric3Dv2 [20]0.30850.5583
iDisc [32]0.33720.3288
DAC (Ours)0.52080.1792
ScanNet++ [56]HM3D-tiny [35]Metric3Dv2 [20]0.45690.2818
iDisc [32]0.53010.3237
DAC (Ours)0.65390.1951
Taskonomy-tiny [61]Metric3Dv2 [20]0.63180.2148
iDisc [32]0.67430.1977
DAC (Ours)0.79810.1447
Hypersim [39]Metric3Dv2 [20]0.50500.2269
iDisc [32]0.66560.2213
DAC (Ours)0.74780.1762
", + "bbox": [ + 526, + 164, + 897, + 375 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "is conducted on the challenging HM3D-tiny [35] indoor dataset, which includes varied camera FoVs, pitch angles, and lower-quality images from reconstructed scenes. We also test the impact of removing attention modules from iDisc [32] and compare to Metric3Dv2 [20] to isolate the influence of the iDisc architecture. Both iDisc-based methods and DAC use ResNet101 backbones, while Metric3Dv2 uses Dinov2. Table 3 provides a summary; full metrics and Matterport3D [5] results are in the Supplemental Table 6.", + "bbox": [ + 511, + 398, + 903, + 535 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 highlights the pivotal role of pitch-aware ERP conversion in generalizing perspective-trained models to large FoV datasets by effectively simulating high-distortion regions uniquely observed in large FoV images (Fig. 7). This approach turns the wide pitch angle variance in datasets like HM3D [35] into an advantage. While additional pitch augmentation does not appear essential when the training dataset like HM3D intricately spans a large range of pitch angle. However, its effectiveness varies across datasets, as detailed in Supplemental Table 6.", + "bbox": [ + 511, + 536, + 905, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results in Table 3 also show that removing FoV Align or Multi-Reso Training significantly reduces DAC performance, particularly for zero-shot generalization on $360^{\\circ}$ images. Compared to the iDisc network trained with the Metric3D pipeline, DAC achieves notable improvements for large FoV cameras, with attention modules in iDisc proving effective for large FoV test data. Although Metric3Dv2 uses a heavier backbone, it shows limited zero-shot generalization on large FoV images without DAC. More comprehensive results can be found both in Supplemental Table 6.", + "bbox": [ + 511, + 688, + 905, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of Training Dataset. Each dataset has unique characteristics (Table 1). To evaluate their impact on generalization to large FoV data, we trained models separately on HM3D-tiny, Taskonomy-tiny [61], and Hypersim [39], then", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "27002", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d8a91233206937f0c25f40a96afb7676773b84c426efe09874af7dd342c79295.jpg", + "image_caption": [ + "Figure 6. Zero-Shot Qualitative Results. For each dataset, an example is presented in two consecutive rows. The left column shows the original image and Ground-Truth depth map, followed by results from various methods. For each method, the top row displays the A.Rel map $\\downarrow$ and the bottom row shows the predicted depth map. The color range for depth and A.Rel maps is indicated in the last column." + ], + "image_footnote": [], + "bbox": [ + 117, + 87, + 883, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tested them in zero-shot mode on indoor large FoV datasets. Results are summarized in Table 4, with full results in Supplemental Table 7.", + "bbox": [ + 89, + 671, + 482, + 717 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For Pano3D-GV2 [2], broader FoV and pitch angle coverage in HM3D training improve generalization across all methods, despite HM3D's lower quality due to rendering artifacts. For fisheye data in ScanNet++ [56], FoV diversity appears less crucial, as the single-camera Hypersim dataset, despite limited training data, outperforms HM3D, indicating that image quality plays a key role in ScanNet++ test.", + "bbox": [ + 89, + 724, + 482, + 833 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparing individually trained models with results from mixed training in Table 2 shows that DAC effectively leverages the synergy of diverse datasets, significantly enhancing generalization to large FoV datasets.", + "bbox": [ + 89, + 839, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 670, + 633, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduced the Depth Any Camera (DAC) framework for zero-shot metric depth estimation across diverse camera types, including perspective, fisheye, and $360^{\\circ}$ cameras. By leveraging a highly effective pitch-aware Image-to-ERP transformation, FoV alignment, and multi-resolution training, DAC addresses the challenges posed by varying FoVs and resolution inconsistencies and enables robust generalization on large FoV datasets. Our results demonstrate that DAC significantly outperforms state-of-the-art methods and adapts seamlessly to different backbone networks. In practice, DAC ensures that every piece of previously collected 3D data remains valuable, regardless of the camera type used in new applications.", + "bbox": [ + 511, + 703, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "27003", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hao Ai, Zidong Cao, Yan-Pei Cao, Ying Shan, and Lin Wang. 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Fisheyebevseg: Surround view fisheye cameras based bird's-eye view segmentation for autonomous driving. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2024 - Workshops, Seattle, WA, USA, June 17-18, 2024, 2024. 2", + "[59] Hong-Xing Yu, Haoyi Duan, Charles Herrmann, William T. Freeman, and Jiajun Wu. Wonderworld: Interactive 3d scene generation from a single image. CoRR, 2024. 2", + "[60] Ilwi Yun, Chanyong Shin, Hyunku Lee, Hyuk-Jae Lee, and Chae-Eun Rhee. Egformer: Equirectangular geometry-biased transformer for 360 depth estimation. In IEEE/CVF International Conference on Computer Vision, ICCV 2023, Paris, France, October 1-6, 2023, 2, 3", + "[61] Amir Zamir, Alexander Sax, William B. Shen, Leonidas J. Guibas, Jitendra Malik, and Silvio Savarese. Taskonomy: Disentangling task transfer learning. 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Deformable convnets V2: more deformable, better results. 2019. 3" + ], + "bbox": [ + 516, + 92, + 906, + 498 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "27006", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/d2be3c71-7e44-4cd1-ae50-da4952c81a8f_model.json b/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/d2be3c71-7e44-4cd1-ae50-da4952c81a8f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ccb7478baa1d71ebe309e54bd9bb9240b9f7d3eb --- /dev/null +++ b/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/d2be3c71-7e44-4cd1-ae50-da4952c81a8f_model.json @@ -0,0 +1,2312 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.118, + 0.131, + 0.88, + 0.153 + ], + "angle": 0, + "content": "Depth Any Camera: Zero-Shot Metric Depth Estimation from Any Camera" + }, + { + "type": "text", + "bbox": [ + 0.166, + 0.18, + 0.83, + 0.201 + ], + "angle": 0, + "content": "Yuliang Guo\\(^{1*}\\), Sparsh Garg\\(^{2*}\\), S. Mahdi H. Miangoleh\\(^{3}\\), Xinyu Huang\\(^{1}\\), Liu Ren\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.253, + 0.201, + 0.746, + 0.217 + ], + "angle": 0, + "content": "1Bosch Research North America & Bosch Center for Artificial Intelligence (BCAI)" + }, + { + "type": "text", + "bbox": [ + 0.327, + 0.219, + 0.671, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\)Carnegie Mellon University \\(^{3}\\)Simon Fraser University" + }, + { + "type": "text", + "bbox": [ + 0.283, + 0.235, + 0.715, + 0.252 + ], + "angle": 0, + "content": "[yluliang.quo2,xingyu.huang,liu. ren]@us.bosch.com" + }, + { + "type": "text", + "bbox": [ + 0.329, + 0.254, + 0.668, + 0.269 + ], + "angle": 0, + "content": "\\(^{2}\\)sparshg@andrew.cmu.edu \\(^{3}\\)smh31@sfu.ca" + }, + { + "type": "text", + "bbox": [ + 0.295, + 0.273, + 0.697, + 0.287 + ], + "angle": 0, + "content": "https://yuliangguo.github.io/depth-any-camera" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.322, + 0.327, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.355, + 0.485, + 0.764 + ], + "angle": 0, + "content": "While recent depth foundation models exhibit strong zero-shot generalization, achieving accurate metric depth across diverse camera types—particularly those with large fields of view (FoV) such as fisheye and 360-degree cameras—remains a significant challenge. This paper presents Depth Any Camera (DAC), a powerful zero-shot metric depth estimation framework that extends a perspective-trained model to effectively handle cameras with varying FoVs. The framework is designed to ensure that all existing 3D data can be leveraged, regardless of the specific camera types used in new applications. Remarkably, DAC is trained exclusively on perspective images but generalizes seamlessly to fisheye and 360-degree cameras without the need for specialized training data. DAC employs Equi-Rectangular Projection (ERP) as a unified image representation, enabling consistent processing of images with diverse FoVs. Its core components include pitch-aware Image-to-ERP conversion with efficient online augmentation to simulate distorted ERP patches from undistorted inputs, FoV alignment operations to enable effective training across a wide range of FoVs, and multi-resolution data augmentation to further address resolution disparities between training and testing. DAC achieves state-of-the-art zero-shot metric depth estimation, improving \\(\\delta_{1}\\) accuracy by up to \\(50\\%\\) on multiple fisheye and 360-degree datasets compared to prior metric depth foundation models, demonstrating robust generalization across camera types." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.793, + 0.222, + 0.809 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.818, + 0.484, + 0.865 + ], + "angle": 0, + "content": "Depth estimation from monocular cameras is a foundational challenge for applications like autonomous driving, AR/VR, and robotics. While early deep learning methods" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.32, + 0.895, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.489, + 0.908, + 0.573 + ], + "angle": 0, + "content": "Figure 1. We introduce Depth Any Camera (DAC) framework, which leverages large-scale datasets containing perspective camera images to train a single depth estimation model capable of conducting zero-shot metric depth estimation on images captured various types of cameras, including those captured from large FoV fisheye and \\(360^{\\circ}\\) cameras." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.594, + 0.907, + 0.776 + ], + "angle": 0, + "content": "relied on supervised training using single datasets and depth sensor [24] supervision [3, 25, 36], monocular depth estimation remains challenging due to scale-depth ambiguity. Expanding training datasets has been a key strategy to enhance robustness, with self-supervised approaches using sequential frames [13, 46, 48]. However, these methods often underperform due to self-supervision ambiguity, view inconsistencies and dynamic objects. Recent methods, such as MiDaS [37], leverage large-scale datasets with 3D supervision, normalizing scale differences across datasets to enable zero-shot testing. However, they primarily provide relative depth rather than metric depth." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recent methods tackle zero-shot metric depth estimation by addressing the challenges of inconsistent scaling factors in depth ground truth caused by varying camera intrinsic parameters. Several works demonstrate impressive generalization capabilities on novel images [4, 20, 33, 53, 57], establishing themselves as foundational depth models for downstream tasks. However, these approaches often struggle with large field-of-view (FoV) cameras like fisheye and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.237, + 0.888 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.27, + 0.9 + ], + "angle": 0, + "content": "\\(\\dagger\\) Equal technical contribution." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.27, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26996" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.121 + ], + "angle": 0, + "content": "\\(360^{\\circ}\\) cameras, where performance significantly declines compared to standard perspective cameras." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.123, + 0.483, + 0.26 + ], + "angle": 0, + "content": "As illustrated in Fig. 2, large FoV images can be represented in multiple formats, but generating the best-performing undistorted image for perspective-based depth models often leads to substantial FoV loss. Despite these limitations, large FoV inputs are crucial for efficiency-critical downstream applications such as large-scale detection [34, 52], segmentation [55, 58], SLAM [11, 44, 45, 62], interactive 3D scene generation [59], and robotic demonstration capturing [6, 14, 49]." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.261, + 0.483, + 0.382 + ], + "angle": 0, + "content": "Achieving zero-shot depth generalization across any FoV camera presents several challenges: (1) selecting a unified camera model to represent diverse FoVs, (2) effectively leveraging perspective training datasets to generalize to data spaces observable only from large FoV cameras, (3) managing drastically different training image sizes in the unified space caused by varying FoVs, and (4) handling resolution inconsistencies between training and testing phases." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.384, + 0.485, + 0.761 + ], + "angle": 0, + "content": "In this paper, we present Depth Any Camera (DAC), a novel zero-shot metric depth estimation framework that enables a depth model trained exclusively on perspective images to generalize across cameras with widely varying FoVs, including fisheye and \\(360^{\\circ}\\) cameras (see Fig. 1). DAC employs Equi-Rectangular Projection (ERP) as a canonical representation to unify images from diverse FoVs into a shared space. A key innovation is the introduction of an efficient pitch-aware Image-to-ERP conversion based on grid sampling and Gnomonic Geometry [47], enabling seamless ERP-space data augmentations. Specifically, pitch-aware ERP conversion with pitch-angle augmentation projects perspective images into high-distortion regions of the ERP space, effectively simulating observations unique to large-FoV cameras. This enhances DAC's zero-shot generalization, allowing it to extrapolate beyond the perspective domain to a broader range of camera types. To facilitate learning from mixed datasets, we propose a FoV alignment process that normalizes diverse-FoV training samples to a predefined ERP patch size, preserving content while minimizing computational overhead. Additionally, multi-resolution augmentation is applied to address resolution mismatches, allowing the model to learn scale-equivariant features and adapt to a flexible range of testing resolutions. In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.765, + 0.483, + 0.825 + ], + "angle": 0, + "content": "- We propose a novel zero-shot metric depth estimation framework capable of handling images from any camera type, including fisheye and \\(360^{\\circ}\\) images, using a model trained exclusively on perspective data." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.826, + 0.483, + 0.886 + ], + "angle": 0, + "content": "- We introduce an efficient pitch-aware perspective-to-ERP patch conversion that simulates the high-distortion characteristics of large-FoV cameras from perspective inputs, enhancing zero-shot generalization." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- We develop a FoV alignment process that enables effic" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "tive training across cameras with diverse FoVs within a unified ERP space, along with a multi-resolution training strategy to address resolution mismatches between training ERP patches and testing images." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.153, + 0.905, + 0.228 + ], + "angle": 0, + "content": "- Our method achieves State-of-The-Art (SoTA) zero-shot performance on all large FoV testing datasets, delivering up to a \\(50\\%\\) improvement in \\(\\delta_{1}\\) accuracy on indoor fisheye and \\(360^{\\circ}\\) datasets, showcasing strong generalization across diverse camera types." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.238, + 0.905, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.381, + 0.907, + 0.465 + ], + "angle": 0, + "content": "Figure 2. Challenges on zero-shot test on large FoV camera images. Metric depth estimation models trained on perspective images (e.g., Metric3Dv2 [20]) experience significant performance degradation when applied to fisheye images. Degradation is less pronounced when using an undistorted portion with a highly limited FoV or its ERP conversion." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.476, + 0.665, + 0.492 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.5, + 0.857, + 0.516 + ], + "angle": 0, + "content": "2.1. Zero-Shot Monocular Depth Estimation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.524, + 0.907, + 0.78 + ], + "angle": 0, + "content": "Recent approaches to zero-shot metric depth estimation tackle the challenge of inconsistent scaling factors in depth ground truth due to varying camera intrinsic parameters [4, 16, 20, 33, 53, 54, 57]. Zoedepth [4] introduces an advanced network architecture, while DepthAnything [53, 54] employs a sophisticated unsupervised learning paradigm. However, their performance in metric depth estimation is limited without tackling inconsistency camera intrinsics. Metric3D [20, 57] and UniDepth [33] address scaling inconsistencies by converting images into a canonical camera space. Metric3D uses intrinsic parameters for this preprocessing, whereas UniDepth incorporates a network branch to estimate and convert intrinsics on the fly. Despite these advances, none of these methods achieve satisfactory zero-shot performance on large FoV images, presenting unique challenges in unifying diverse FoVs and supporting effective model learning." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.787, + 0.887, + 0.803 + ], + "angle": 0, + "content": "2.2. Depth Estimation from Large FoV Cameras" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Depth estimation for fisheye, \\(360^{\\circ}\\) cameras has grown in popularity, as large FoVs capture richer contextual information that enhances depth estimation [1, 21, 26, 41, 60]. A key challenge for these cameras is managing position-dependent distortions, which vary by camera models. Approaches to address this include deformable CNNs [42, 50," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26997" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.273 + ], + "angle": 0, + "content": "63], which adapt kernel shapes to compensate for distortions, as well as methods that segment ERP images to reduce distortion effects before merging [21, 38]. More recent methods leverage transformers to handle these distortions [10, 26, 41, 60]. While transformer-based networks have improved in-domain performance, they are approaching saturation, indicating that distortion is not the only challenge. Instead, the lack of large-scale FoV-specific training data is a key bottleneck for generalization. No current methods enable an unified depth estimation model trained on mixed large-scale perspective datasets to achieve zero-shot generalization on ERP or fisheye images." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.286, + 0.351, + 0.303 + ], + "angle": 0, + "content": "3. Notations and Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.311, + 0.484, + 0.506 + ], + "angle": 0, + "content": "Depth Scaling Operations. Monocular depth estimation is inherently ill-posed, as different 3D object sizes and depths can produce the same 2D appearance. Deep learning models rely on learning an object's 3D dimensions from its 2D appearance [16, 17, 43] to infer depth, leading to the scaling operation illustrated in the right panel of Fig. 3. When using mixed camera data, apparent object size also depends on focal length, making accurate 2D-to-depth mapping dependent on appropriately scaling ground-truth depths when converting a perspective model to a canonical model, as shown in the left panel of Fig. 3. These scaling operations are central to the Metric3D [20, 57] pipeline and are integrated into our ERP-based approach." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.508, + 0.484, + 0.643 + ], + "angle": 0, + "content": "EquiRectangular Projection (ERP). Equi-Rectangular Projection (ERP) is an image representation based on a spherical camera model, where each pixel corresponds to a specific latitude \\(\\lambda\\) and longitude \\(\\phi\\). A full ERP space spans \\(180^{\\circ}\\) in latitude and \\(360^{\\circ}\\) in longitude, making it ideal for handling diverse FoV cameras. The ERP image height is the only parameter needed to define the ERP space, allowing both training and testing images to be consistently converted into this space, regardless of the original FoV." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.643, + 0.484, + 0.727 + ], + "angle": 0, + "content": "Transformations between standard images and ERP images use Gnomonic Projection transformation [47], which offers a closed-form mapping between tangent image coordinates \\((x_{t},y_{t})\\) and spherical coordinates \\((\\lambda ,\\phi)\\), assuming a tangent plane centered at \\((\\lambda_c,\\phi_c)\\) of a unit sphere. Specifically, as shown in Fig. 5, this mapping is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.733, + 0.483, + 0.761 + ], + "angle": 0, + "content": "\\[\nx _ {t} = \\frac {\\bar {x}}{\\cos c} = \\frac {\\cos \\phi \\sin (\\lambda - \\lambda_ {c})}{\\cos c} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.763, + 0.482, + 0.79 + ], + "angle": 0, + "content": "\\[\ny _ {t} = \\frac {\\bar {y}}{\\cos c} = \\frac {\\cos \\phi_ {c} \\sin \\phi - \\sin \\phi_ {c} \\cos \\phi \\cos (\\lambda - \\lambda_ {c})}{\\cos c} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.796, + 0.483, + 0.838 + ], + "angle": 0, + "content": "where \\((\\bar{x},\\bar{y},\\cos c)\\) represents a point on the unit sphere, and \\(c\\) is the angular distance between \\((\\lambda ,\\phi)\\) and \\((\\lambda_c,\\phi_c)\\), can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.848, + 0.483, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\cos c = \\sin \\phi_ {c} \\sin \\phi + \\cos \\phi_ {c} \\cos \\phi \\cos (\\lambda - \\lambda_ {c}) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We use these transformations to enable an efficient ERP conversion and data augmentation process, creating a" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.09, + 0.641, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.216, + 0.624, + 0.226 + ], + "angle": 0, + "content": "Camera Conversion" + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.09, + 0.775, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.216, + 0.741, + 0.226 + ], + "angle": 0, + "content": "Original Cam" + }, + { + "type": "image", + "bbox": [ + 0.782, + 0.09, + 0.901, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.81, + 0.216, + 0.882, + 0.226 + ], + "angle": 0, + "content": "Image Resizing" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.238, + 0.907, + 0.395 + ], + "angle": 0, + "content": "Figure 3. Depth Scaling in Canonical Model Conversion and Image Resizing. The apparent 2D size of an object \\( u \\) in an image depends on its 3D dimensions \\( X \\), depth \\( Z \\), and camera focal length \\( f_{x} \\). Left: Converting a perspective camera model to a canonical model with a different focal length \\( \\hat{f}_{x} \\) requires scaling the depth values proportionally, so \\( \\hat{Z} = \\frac{\\hat{f}_{x}Z}{\\hat{f}_{x}} \\). Center: The original camera setup, showing the direct relationship between object size, depth, and focal length. Right: When the camera model is fixed but the image is resized to \\( u' \\), this simulates viewing the same 3D object at a different distance, necessitating depth scaling for accurate metric depth, with \\( Z' = \\frac{uZ}{u'} \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.406, + 0.906, + 0.436 + ], + "angle": 0, + "content": "streamlined pipeline that supports zero-shot generalization for depth estimation across various FoV cameras." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.451, + 0.704, + 0.469 + ], + "angle": 0, + "content": "4. Depth Any Camera" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.477, + 0.907, + 0.674 + ], + "angle": 0, + "content": "We propose Depth Any Camera (DAC), a depth model training framework designed to achieve zero-shot generalization across diverse camera models, including perspective, fisheye, and \\(360^{\\circ}\\) cameras. As illustrated in Fig. 4, images from different camera types and FoVs are transformed into a canonical ERP space during both the training and testing phases. For training, we leverage the extensive perspective image datasets by converting them into smaller ERP patches for efficient learning. During testing, large FoV images are similarly converted into the canonical ERP space, allowing the trained model to predict metric depth consistently, without getting confused by different camera intrinsic and distortion parameters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.909, + 0.856 + ], + "angle": 0, + "content": "Several key components are designed to address specific challenges in implementing the DAC framework. In Sec. 4.1, we present an efficient pitch-aware Image-to-ERP conversion method that simulate large-FoV images at patch level and supports online augmentation within the ERP space. Sec. 4.2 introduces a FoV alignment process, an effective data augmentation technique that maximizes content inclusion while minimizing computational waste on background areas, using a single predefined ERP patch size. In Sec. 4.3, we describe a multi-resolution data augmentation approach aimed at training a transformer-based network capable of handling a broad range of testing resolutions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.902 + ], + "angle": 0, + "content": "The proposed DAC framework is compatible with various depth estimation network architectures, which are not the primary focus of this paper. Without loss of generality," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26998" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.09, + 0.885, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.399, + 0.908, + 0.485 + ], + "angle": 0, + "content": "Figure 4. Depth Any Camera Pipeline. Our DAC framework converts data from any camera type into a canonical ERP space, enabling a model trained solely on perspective images to process large-FOV test data consistently for metric depth estimation. During training, we introduce an effective pitch-aware Image-to-ERP conversion with online data augmentation to simulate high-distortion regions unique to large-FOV images. The proposed FoV-Align process normalizes diverse-FOV data to a predefined ERP patch size, maximizing training efficiency. During inference, images from any camera type are converted into ERP space for depth estimation, with an optional step to map the ERP output back to the original image space for visualization." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.495, + 0.484, + 0.556 + ], + "angle": 0, + "content": "we employ iDisc [32] for its simplicity and effectiveness, and for its incorporation of two prototypical attention modules, namely cross-attention and self-attention. We use the SIlog loss function [9] for training our models." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.565, + 0.43, + 0.581 + ], + "angle": 0, + "content": "4.1. Pitch-Aware Image-to-ERP Conversion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.587, + 0.484, + 0.777 + ], + "angle": 0, + "content": "An input image can be efficiently converted to its corresponding ERP patch through grid sampling combined with gnomonic projection. Assuming an ERP space with height \\( H_{E} \\), width \\( W_{E} = 2H_{E} \\), and the image center at latitude \\( \\lambda_{c} \\), longitude \\( \\phi_{c} \\), with a target ERP patch size of \\( H_{e} \\times W_{e} \\), the ERP patch coordinates \\( (u_{e}, v_{e}) \\) can be mapped to spherical coordinates as \\( \\phi = \\frac{2\\pi W_{e}}{W_{E}} (u_{e} - \\frac{W_{e}}{2}) + \\phi_{c} \\), and \\( \\lambda = \\frac{\\pi H_{e}}{H_{E}} (v_{e} - \\frac{H_{e}}{2}) + \\lambda_{c} \\). Using Gnomonic Geometry presented in Eq. 1 and Eq. 2, we obtain the corresponding normalized image coordinate \\( (x_{t}, y_{t}, 1) \\) in the tangent plane and \\( (\\bar{x}, \\bar{y}, \\cos c) \\) on the unit sphere. To map this coordinate to the actual image coordinate \\( (u, v) \\), we apply distortion and projection functions based on the given camera parameters:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.784, + 0.483, + 0.799 + ], + "angle": 0, + "content": "\\[\n\\left(x _ {d}, y _ {d}\\right) = f _ {d} (\\bar {x}, \\bar {y}, \\cos c, D _ {c}) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.802, + 0.483, + 0.817 + ], + "angle": 0, + "content": "\\[\n(u, v) = f _ {p} \\left(x _ {d}, y _ {d}, K _ {c}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\( f_{d} \\) is the distortion function with distortion parameters \\( D_{c} \\), and \\( f_{p} \\) is the projection function with intrinsic parameters \\( K_{c} \\). If the input image has no distortion, projection function is directly applied to \\( (x_{t}, y_{t}) \\). Details on applying distortion models are included in Supplemental Sec. 8." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.495, + 0.907, + 0.618 + ], + "angle": 0, + "content": "As shown in Fig. 5, with uniformly sampled grid points within the target ERP patch, each grid point can be mapped directly to a corresponding location in the input image. This mapping facilitates efficient transformation of the captured image into an ERP patch via grid sampling. Essentially, each grid point in the ERP patch maps to a specific floating-point position in the input image, and its value is obtained by interpolating from the neighboring pixel values." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.622, + 0.909, + 0.804 + ], + "angle": 0, + "content": "This ERP conversion enables a powerful training pipeline when the latitude of the tangent plane center \\(\\lambda_{c}\\) is defined by the camera's pitch angle in training. When camera orientation is available or can be estimated [22], perspective data can be projected to various latitudes in the ERP space, enabling the simulation of regions uniquely visible from large-FoV cameras, as shown in Fig. 5, and Supplemental Fig. 7. This pitch-aware conversion is crucial for improving the generalization of trained models to previously unobserved large-FoV data, as demonstrated in Sec. 5.3, because neural networks alone have limited capacity to generalize to extrapolated data spaces [51]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Another notable advantage is the seamless ability to perform online augmentation efficiently in the ERP space. For datasets with limited pitch variation [12, 15, 19, 61], a unique pitch augmentation can be efficiently applied by adding noise to \\(\\lambda_{c}\\), generating ERP patches with varying shapes, as shown in Fig. 4. In addition, common augmenta" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26999" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.191, + 0.089, + 0.4, + 0.102 + ], + "angle": 0, + "content": "Grid Sampling via Gnomonic Geometry" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.106, + 0.47, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.249, + 0.485, + 0.388 + ], + "angle": 0, + "content": "Figure 5. Pitch-Aware ERP Conversion and FoV Alignment. Top: Grid Sampling is applied for an efficient Image-to-ERP conversion. Each ERP grid sample's corresponding location in the input image is computed using gnomonic geometry and specific camera projection parameters. Given the patch center latitude \\(\\lambda\\) determined by the camera's pitch angle, it makes the converted patch to represent high-distortion regions in the ERP space. Bottom: The FoV-Align process normalizes diverse-FoV ERP patches (shown in red and green) to match the height of a single predefined ERP patch (outlined in blue), ensuring efficient training." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.398, + 0.484, + 0.445 + ], + "angle": 0, + "content": "tions, such as scaling, rotation, and translation—commonly applied to perspective images—can be directly applied to the normalized image coordinates \\((x_{t},y_{t})\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.451, + 0.483, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\left[ \\begin{array}{l} x _ {t} ^ {\\prime} \\\\ y _ {t} ^ {\\prime} \\end{array} \\right] = s _ {\\sigma} \\left[ \\begin{array}{l l} R _ {\\sigma} & T _ {\\sigma} \\end{array} \\right] \\left[ \\begin{array}{l} x _ {t} \\\\ y _ {t} \\end{array} \\right] \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.492, + 0.484, + 0.538 + ], + "angle": 0, + "content": "where \\( s_{\\sigma} \\) is a scale factor, \\( R_{\\sigma} \\) is 2D rotation matrix, and \\( T_{\\sigma} \\) is a 2D translation vector corresponding to the applied augmentations." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.545, + 0.247, + 0.563 + ], + "angle": 0, + "content": "4.2. FoV Alignment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.569, + 0.483, + 0.734 + ], + "angle": 0, + "content": "When training data include a wide range of camera FoVs within perspective images, such as in the HM3D [35] dataset produced by OmniData [8], the corresponding ERP regions can vary significantly in size, as shown in Fig. 5. There is no single crop size that can consistently capture most content information for certain images without wasting substantial computation on background padding for others. This creates a dilemma in prioritizing between training efficiency and richness of information, and it can also reduce training quality when samples exhibit drastically different content-to-background ratios." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To address this challenge, we introduce a simple yet effective FoV Alignment operation that adjusts the FoV of each input image to match the predetermined crop area FoV. Specifically, this process applies a specific scaling augmentation, as described in Sec. 4.1 and Eq. 6, specifically \\(\\mathrm{Fov}_e = \\frac{H_e\\pi}{H_E}\\) and \\(s_\\sigma = \\frac{\\mathrm{Fov}_c}{\\mathrm{Fov}_e}\\), where \\(\\mathrm{Fov}_c\\) is derived from actual camera parameters, and \\(\\mathrm{Fov}_e\\) is ERP patch's vertical FoV. As illustrated in Fig. 5, this approach allows a single predefined ERP patch size to maximize the inclusion of relevant content and minimize computational waste on background, making it ideal for an efficient training pipeline." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.755, + 0.108 + ], + "angle": 0, + "content": "4.3. Multi-Resolution Training" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.115, + 0.905, + 0.205 + ], + "angle": 0, + "content": "Training ERP patches and testing images may prefer inconsistent resolutions for various reasons, e.g. drastically different aspect ratio, edge device limitation. When testing resolutions differ from the training patch size, model performance can degrade significantly, particularly with attention modules that aggregate different numbers of image tokens." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.206, + 0.906, + 0.296 + ], + "angle": 0, + "content": "To address this issue, we adopt a multi-resolution training scheme. As illustrated in Fig. 4, each ERP patch is resized to two additional lower resolutions (typically 0.7 and 0.4 of the original) to incorporate varied image resolutions in training. The training feeds the model three batches of images at different resolutions and sums the losses." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.31, + 0.646, + 0.327 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.334, + 0.704, + 0.351 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.357, + 0.907, + 0.493 + ], + "angle": 0, + "content": "In-Domain Training Datasets. For indoor experiments, we use Habitat-Matterport 3D (HM3D) [35], Taskonomy [61], and Hypersim [39], totaling 670K perspective images with distinct characteristics. To streamline training, we use the first 50 scenes from HM3D and Taskonomy (tiny versions provided by OmniData [8]). For outdoor data, we use DDAD [15] and LYFT [19], totaling 130K images. Table 1 summarizes the datasets in use, showing varying distributions in FoV, pitch angles, sources, and image quality." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.493, + 0.906, + 0.629 + ], + "angle": 0, + "content": "Zero-Shot Testing Datasets. We evaluate DAC on two \\(360^{\\circ}\\) datasets—Matterport3D [5] and Pano3DGV2 [2]—and two fisheye datasets—ScanNet++ [56] and KITTI360 [27]—all featuring larger FoVs than perspective images. Our primary experiments focus on these datasets to assess zero-shot generalization to large FoV cameras. Additional evaluations on NYUv2 [30] and KITTI [12] are provided in the supplementary material, demonstrating DAC's performance on perspective data relative to SoTA methods." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.63, + 0.906, + 0.75 + ], + "angle": 0, + "content": "Evaluation Details. We assess DAC's generalization to large FoV cameras across both indoor and outdoor scenes, training separate models for each without data mixing to simplify training. For fair comparison, competing models are either re-trained with the same data splits or use their largest versions trained on extensive datasets. Evaluations are conducted using metric depth metrics: \\(\\delta_1\\uparrow ,\\delta_2\\uparrow ,\\delta_3\\uparrow\\) Abs Rel↓, RMSE↓, and log10↓." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.75, + 0.905, + 0.765 + ], + "angle": 0, + "content": "Baselines. We compare DAC with the following baselines:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.766, + 0.905, + 0.809 + ], + "angle": 0, + "content": "- Metric3Dv2 [20]: A SoTA foundation model in zero-shot metric depth estimation, built upon perspective canonical camera model to standardize datasets." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.811, + 0.905, + 0.87 + ], + "angle": 0, + "content": "- UniDepth [33]: A more recent SoTA foundation depth model leveraging network designs to handle diverse camera parameters. We test its ability to handle large FoV cameras not included in training." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "- iDisc [32]: Selected as a network baseline due to its use of self-attention and cross-attention modules in a straight-" + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.766, + 0.905, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27000" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.119 + ], + "angle": 0, + "content": "Table 1. Overview of Datasets. This table summarizes the training and testing datasets used in this work. The training datasets span a range of FoVs, pitch angles, and image quality, each potentially impacting performance on different test datasets in varying degrees." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.125, + 0.92, + 0.202 + ], + "angle": 0, + "content": "
Train Dataset# ImagesScenexFoV (deg.)# CamsPitch (deg.)SourceImg Qual.Test DatasetCam TypexFoV (deg.)Scene
HM3D-tiny [35]310KIndoor36° - 124°10K+3σ = 75°ReconLowMatterport3D [5]ERP360°Indoor
Taskonomy-tiny [61]300KIndoor45° - 75°10K+3σ = 24°RealHighPano3D-GV2 [2]ERP360°Indoor
Hypersim [39]54KIndoor60°13σ = 60°SimHigh+ScanNet++ [56]Fisheye150°Indoor
DDAD [15]80KOutdoor45° - 60°36+3σ ~ 10°RealHighKITTI360 [27]Fisheye180°Outdoor
LYFT [19]50KOutdoor20° - 60°6+3σ ~ 10°RealHigh
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.226, + 0.908, + 0.241 + ], + "angle": 0, + "content": "Table 2. Zero-Shot Test on \\( {360}^{ \\circ } \\) and Fisheye Datasets. DAC is compared with SoTA metric depth models across four large-ForV datasets." + }, + { + "type": "table", + "bbox": [ + 0.163, + 0.246, + 0.837, + 0.505 + ], + "angle": 0, + "content": "
Test DatasetMethodsTrain DatasetBackboneδ1↑δ2↑δ3↑Abs Rel↓RMSE↓log10↓
Matterport3D [5]UniDepth [33]Mix 3MViT-L [7]0.25760.51140.70910.76481.38270.2208
Metric3Dv2 [20]Mix 16MDinov2 [31]0.43810.73110.87350.29240.88420.1546
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.42870.78540.93330.27880.89610.1352
iDisc [32]Indoor 670KResnet101 [18]0.52870.82600.93980.27570.77710.1147
DAC (Ours)Indoor 670KResnet101 [18]0.77270.95620.98220.1560.61850.0707
Pano3D-GV2 [2]UniDepth [33]Mix 3MViT-L [7]0.24690.49770.70840.78921.26810.2231
Metric3Dv2 [20]Mix 16MDinov2 [31]0.40400.69290.84990.30700.85490.1664
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.50600.81760.93600.26080.72480.1201
iDisc [32]Indoor 670KResnet101 [18]0.56290.82220.93320.26570.64460.1122
DAC (Ours)Indoor 670KResnet101 [18]0.81150.95490.98600.13870.47800.0623
ScanNet++ [56]UniDepth [33]Mix 3MViT-L [7]0.36380.64610.83580.49711.16590.1648
Metric3Dv2 [20]Mix 16MDinov2 [31]0.53600.82180.93500.22290.89500.1177
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.64890.89200.95580.19150.97790.0938
iDisc [32]Indoor 670KResnet101 [18]0.61500.87800.96170.27120.48350.0972
DAC (Ours)Indoor 670KResnet101 [18]0.85170.96930.99220.13230.30860.0532
KITTI360 [27]UniDepth [33]Mix 3MViT-L [7]0.48100.83970.94060.29396.56420.1221
Metric3Dv2 [20]Mix 16MDinov2 [31]0.71590.93230.97710.19974.57690.0811
Metric3Dv2 [20]Outdoor 130KDinov2 [31]0.76750.93700.97560.15214.66100.0723
iDisc [32]Outdoor 130KResnet101 [18]0.78330.93840.97530.15984.91220.0704
DAC (Ours)Outdoor 130KResnet101 [18]0.78580.93880.97750.15594.36140.0684
" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.527, + 0.483, + 0.587 + ], + "angle": 0, + "content": "forward yet effective network, and strong in-domain performance. As iDisc alone does not handle mixed camera parameters, we train it with Metric3Dv2 [20], and compare it to the same network trained with ours." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.589, + 0.483, + 0.725 + ], + "angle": 0, + "content": "Implementation Details. In the DAC training pipeline, we set the full ERP height to \\( H_{\\mathrm{erp}} = 1400 \\) pixels, with an ERP patch size of \\( 500 \\times 700 \\) pixels for both indoor and outdoor models. We use \\( 10^{\\circ} \\) latitude augmentations for both and additionally \\( 10^{\\circ} \\) rotation augmentation for indoor. When training the iDisc [32] model using the Metric3D [57] pipeline, we use canonical focal lengths of \\( f_{\\mathrm{cano}} = 519 \\) (NYU dataset [30]) for indoor models and \\( f_{\\mathrm{cano}} = 721 \\) (KITTI dataset [12]) for outdoor models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.727, + 0.483, + 0.872 + ], + "angle": 0, + "content": "To test perspective models on ERP and fisheye images, specific adjustments are required. For \\(360^{\\circ}\\) (ERP) images, which lack a defined focal length, we calculate a virtual focal length \\(f_{\\mathrm{virtual}}\\) based on pixels per latitude degree: \\(\\frac{1}{f_{\\mathrm{virtual}}} = \\tan \\left(\\frac{\\pi}{H_{\\mathrm{ep}}}\\right)\\), scaling the predicted depth with \\(\\frac{f_{\\mathrm{cano}}}{f_{\\mathrm{virtual}}}\\) for ground-truth alignment. For fisheye images, aligning \\(f_{\\mathrm{cano}}\\) with the post-distortion focal length introduces significant errors, so we first convert fisheye images to ERP space and apply \\(\\frac{f_{\\mathrm{cano}}}{f_{\\mathrm{virtual}}}\\) for metric depth evaluation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.872, + 0.483, + 0.901 + ], + "angle": 0, + "content": "For testing resolution, if the original resolution is less than twice the training resolution, we use it directly; for" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.527, + 0.907, + 0.633 + ], + "angle": 0, + "content": "larger resolutions, we maintain the aspect ratio and align it with the training resolution. Based on this rule, we evaluate Matterport3D [5] and Pano3D-GV2 [2] at \\(512 \\times 1024\\), ScanNet++ [56] at \\(500 \\times 750\\), and KITTI360 [27] at \\(700 \\times 700\\). For competing methods that are not adaptable to inconsistent resolutions compared to training, we report the higher score obtained from the two settings to ensure fairness." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.635, + 0.909, + 0.756 + ], + "angle": 0, + "content": "In experiments, ResNet101 [18]-backbone models are trained for 60k iterations with a batch size of 48, while Swin-L [28] and DINOv2 [31] models are trained for 120k iterations with a batch size of 48. Finally, to support all FoV types, depth is represented as Euclidean Distance from the camera center rather than Z-buffer format, as the latter is incompatible with spherical projections and would yield inaccurate low depth values for fisheye or ERP images." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.77, + 0.76, + 0.787 + ], + "angle": 0, + "content": "5.2. Comparison with the SoTA" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In this section, we compare DAC with primary baselines in zero-shot generalization tests on large FoV datasets, with quantitative results reported in Table 2, and qualitative results shown in Fig. 6. In indoor experiments, DAC significantly outperforms pre-trained models UniDepth [33] and Metric3Dv2 [20], even when using a lighter ResNet101 [18] backbone and a much smaller training dataset. DAC" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27001" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "achieves superior performance across both \\(360^{\\circ}\\) datasets and the fisheye dataset ScanNet++ [56]. Compared to the iDisc [32] network trained with the Metric3Dv2 pipeline, DAC shows substantial improvements across all metrics on all datasets. Notably, DAC improves the next-best method by nearly \\(50\\%\\) in the most differentiating metric, \\(\\delta_{1}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.183, + 0.482, + 0.333 + ], + "angle": 0, + "content": "In outdoor tests, DAC significantly outperforms Metric3Dv2 [57] and UniDepth [33], even with much larger backbones. However, it achieves only marginal improvements over iDisc [32] under the same network configuration, with less pronounced gains compared to indoor settings. This is likely due to the limited camera pitch variance in the outdoor training data (Table 1), reducing the ability to simulate highly distorted regions. Moreover, KITTI360 [27] LiDAR points are concentrated in less distorted areas (Fig. 6), making the evaluation less distinctive." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.334, + 0.482, + 0.424 + ], + "angle": 0, + "content": "Particularly, a notable observation is that while UniDepth [33] utilizes a network-based spherical conversion, it struggles with large FoV cameras, exposing the limitations of deep learning in extrapolated domains [51]. In contrast, DAC's success underscores the effectiveness of our geometry-based training pipeline." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.424, + 0.482, + 0.484 + ], + "angle": 0, + "content": "Additional results of DAC models using SwinL [28] backbones are provided in Supplemental Table 5. These models outperform their ResNet101 [18] counterparts in most cases, except on the \\(360^{\\circ}\\) datasets." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.497, + 0.482, + 0.581 + ], + "angle": 0, + "content": "Table 3. Impact of Key Components and Network. We conduct the main ablation study on indoor datasets by training with HM3D [35] and performing zero-shot testing on Pano3D-GV2 [2] and ScanNet++ [56]. We compare the performance of the DAC framework with specific components removed, as well as different network architectures trained under the Metric3D [57] pipeline." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.587, + 0.472, + 0.794 + ], + "angle": 0, + "content": "
Test DatasetMethodsδ1↑δ2↑A.Rel↓
Pano3D-GV2 [2]Metric3Dv2 [20]0.56230.83410.2479
iDisc-cnn [32]0.30260.55650.3548
iDisc [32]0.41300.68440.3043
DAC (Ours)0.72510.92540.1729
w\\o Pitch-Aware ERP0.49110.79040.2422
w\\o Pitch Aug 10°0.69120.93110.188
w\\o FoV Align0.40750.75850.2610
w\\o Multi-Reso0.51280.77840.2437
ScanNet++ [56]Metric3Dv2 [20]0.45690.74630.2818
iDisc-cnn [32]0.46390.76530.3045
iDisc [32]0.53010.80480.3237
DAC (Ours)0.65390.90830.1951
w\\o Pitch-Aware ERP0.47110.80680.2508
w\\o Pitch Aug 10°0.67410.90660.1914
w\\o FoV Align0.54280.86440.2200
w\\o Multi-Reso0.55040.84640.2231
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.245, + 0.833 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.482, + 0.901 + ], + "angle": 0, + "content": "Key Components and Network Architecture. We evaluate the effect of the FoV Align and Multi-Reso Training components by removing each individually, while keeping the rest of the DAC framework unchanged. This ablation" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.905, + 0.16 + ], + "angle": 0, + "content": "Table 4. Impact of Train Dataset. Models are trained separately on each training dataset and evaluated in zero-shot tests on \\(360^{\\circ}\\) and fisheye datasets. Due to the unique characteristics of each training dataset, their contributions and importance to generalization across different testing datasets vary." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.165, + 0.898, + 0.375 + ], + "angle": 0, + "content": "
Test DatasetsTrain DatasetMethodsδ1↑A.Rel↓
Pano3D-GV2 [2]HM3D-tiny [35]Metric3Dv2 [20]0.56230.2479
iDisc [32]0.41300.3043
DAC (Ours)0.72510.1729
Taskonomy-tiny [61]Metric3Dv2 [20]0.37850.2959
iDisc [32]0.38880.4076
DAC (Ours)0.64110.1972
Hypersim [39]Metric3Dv2 [20]0.30850.5583
iDisc [32]0.33720.3288
DAC (Ours)0.52080.1792
ScanNet++ [56]HM3D-tiny [35]Metric3Dv2 [20]0.45690.2818
iDisc [32]0.53010.3237
DAC (Ours)0.65390.1951
Taskonomy-tiny [61]Metric3Dv2 [20]0.63180.2148
iDisc [32]0.67430.1977
DAC (Ours)0.79810.1447
Hypersim [39]Metric3Dv2 [20]0.50500.2269
iDisc [32]0.66560.2213
DAC (Ours)0.74780.1762
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.4, + 0.905, + 0.536 + ], + "angle": 0, + "content": "is conducted on the challenging HM3D-tiny [35] indoor dataset, which includes varied camera FoVs, pitch angles, and lower-quality images from reconstructed scenes. We also test the impact of removing attention modules from iDisc [32] and compare to Metric3Dv2 [20] to isolate the influence of the iDisc architecture. Both iDisc-based methods and DAC use ResNet101 backbones, while Metric3Dv2 uses Dinov2. Table 3 provides a summary; full metrics and Matterport3D [5] results are in the Supplemental Table 6." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.537, + 0.906, + 0.688 + ], + "angle": 0, + "content": "Table 3 highlights the pivotal role of pitch-aware ERP conversion in generalizing perspective-trained models to large FoV datasets by effectively simulating high-distortion regions uniquely observed in large FoV images (Fig. 7). This approach turns the wide pitch angle variance in datasets like HM3D [35] into an advantage. While additional pitch augmentation does not appear essential when the training dataset like HM3D intricately spans a large range of pitch angle. However, its effectiveness varies across datasets, as detailed in Supplemental Table 6." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.84 + ], + "angle": 0, + "content": "Results in Table 3 also show that removing FoV Align or Multi-Reso Training significantly reduces DAC performance, particularly for zero-shot generalization on \\(360^{\\circ}\\) images. Compared to the iDisc network trained with the Metric3D pipeline, DAC achieves notable improvements for large FoV cameras, with attention modules in iDisc proving effective for large FoV test data. Although Metric3Dv2 uses a heavier backbone, it shows limited zero-shot generalization on large FoV images without DAC. More comprehensive results can be found both in Supplemental Table 6." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Impact of Training Dataset. Each dataset has unique characteristics (Table 1). To evaluate their impact on generalization to large FoV data, we trained models separately on HM3D-tiny, Taskonomy-tiny [61], and Hypersim [39], then" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27002" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.088, + 0.885, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.603, + 0.908, + 0.648 + ], + "angle": 0, + "content": "Figure 6. Zero-Shot Qualitative Results. For each dataset, an example is presented in two consecutive rows. The left column shows the original image and Ground-Truth depth map, followed by results from various methods. For each method, the top row displays the A.Rel map \\(\\downarrow\\) and the bottom row shows the predicted depth map. The color range for depth and A.Rel maps is indicated in the last column." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.672, + 0.483, + 0.718 + ], + "angle": 0, + "content": "tested them in zero-shot mode on indoor large FoV datasets. Results are summarized in Table 4, with full results in Supplemental Table 7." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.726, + 0.483, + 0.834 + ], + "angle": 0, + "content": "For Pano3D-GV2 [2], broader FoV and pitch angle coverage in HM3D training improve generalization across all methods, despite HM3D's lower quality due to rendering artifacts. For fisheye data in ScanNet++ [56], FoV diversity appears less crucial, as the single-camera Hypersim dataset, despite limited training data, outperforms HM3D, indicating that image quality plays a key role in ScanNet++ test." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Comparing individually trained models with results from mixed training in Table 2 shows that DAC effectively leverages the synergy of diverse datasets, significantly enhancing generalization to large FoV datasets." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.671, + 0.634, + 0.687 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We introduced the Depth Any Camera (DAC) framework for zero-shot metric depth estimation across diverse camera types, including perspective, fisheye, and \\(360^{\\circ}\\) cameras. By leveraging a highly effective pitch-aware Image-to-ERP transformation, FoV alignment, and multi-resolution training, DAC addresses the challenges posed by varying FoVs and resolution inconsistencies and enables robust generalization on large FoV datasets. Our results demonstrate that DAC significantly outperforms state-of-the-art methods and adapts seamlessly to different backbone networks. In practice, DAC ensures that every piece of previously collected 3D data remains valuable, regardless of the camera type used in new applications." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "27003" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.198 + ], + "angle": 0, + "content": "[1] Hao Ai, Zidong Cao, Yan-Pei Cao, Ying Shan, and Lin Wang. 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Deformable convnets V2: more deformable, better results. 2019. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.907, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27006" + } + ] +] \ No newline at end of file diff --git a/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/d2be3c71-7e44-4cd1-ae50-da4952c81a8f_origin.pdf b/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/d2be3c71-7e44-4cd1-ae50-da4952c81a8f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f3ee7d19794f85d488851483e1ebe0f27847f6e2 --- /dev/null +++ b/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/d2be3c71-7e44-4cd1-ae50-da4952c81a8f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a40e80d66eedc2e29ad58519f4f1606350eec9c26480ea22ee736a761b0b086f +size 1774757 diff --git a/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/full.md b/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/full.md new file mode 100644 index 0000000000000000000000000000000000000000..69e88b793beec39ea2f53a9f7eaca4f0d3c0aac6 --- /dev/null +++ b/2025/Depth Any Camera_ Zero-Shot Metric Depth Estimation from Any Camera/full.md @@ -0,0 +1,306 @@ +# Depth Any Camera: Zero-Shot Metric Depth Estimation from Any Camera + +Yuliang Guo $^{1*}$ , Sparsh Garg $^{2*}$ , S. Mahdi H. Miangoleh $^{3}$ , Xinyu Huang $^{1}$ , Liu Ren $^{1}$ + +1Bosch Research North America & Bosch Center for Artificial Intelligence (BCAI) + +$^{2}$ Carnegie Mellon University $^{3}$ Simon Fraser University + +[yluliang.quo2,xingyu.huang,liu. ren]@us.bosch.com + +$^{2}$ sparshg@andrew.cmu.edu $^{3}$ smh31@sfu.ca + +https://yuliangguo.github.io/depth-any-camera + +# Abstract + +While recent depth foundation models exhibit strong zero-shot generalization, achieving accurate metric depth across diverse camera types—particularly those with large fields of view (FoV) such as fisheye and 360-degree cameras—remains a significant challenge. This paper presents Depth Any Camera (DAC), a powerful zero-shot metric depth estimation framework that extends a perspective-trained model to effectively handle cameras with varying FoVs. The framework is designed to ensure that all existing 3D data can be leveraged, regardless of the specific camera types used in new applications. Remarkably, DAC is trained exclusively on perspective images but generalizes seamlessly to fisheye and 360-degree cameras without the need for specialized training data. DAC employs Equi-Rectangular Projection (ERP) as a unified image representation, enabling consistent processing of images with diverse FoVs. Its core components include pitch-aware Image-to-ERP conversion with efficient online augmentation to simulate distorted ERP patches from undistorted inputs, FoV alignment operations to enable effective training across a wide range of FoVs, and multi-resolution data augmentation to further address resolution disparities between training and testing. DAC achieves state-of-the-art zero-shot metric depth estimation, improving $\delta_{1}$ accuracy by up to $50\%$ on multiple fisheye and 360-degree datasets compared to prior metric depth foundation models, demonstrating robust generalization across camera types. + +# 1. Introduction + +Depth estimation from monocular cameras is a foundational challenge for applications like autonomous driving, AR/VR, and robotics. While early deep learning methods + +![](images/eca003ef65b3c695ab9c932d5824bbf4561a2832f026b7c56fdf8e4dfad385b9.jpg) +Figure 1. We introduce Depth Any Camera (DAC) framework, which leverages large-scale datasets containing perspective camera images to train a single depth estimation model capable of conducting zero-shot metric depth estimation on images captured various types of cameras, including those captured from large FoV fisheye and $360^{\circ}$ cameras. + +relied on supervised training using single datasets and depth sensor [24] supervision [3, 25, 36], monocular depth estimation remains challenging due to scale-depth ambiguity. Expanding training datasets has been a key strategy to enhance robustness, with self-supervised approaches using sequential frames [13, 46, 48]. However, these methods often underperform due to self-supervision ambiguity, view inconsistencies and dynamic objects. Recent methods, such as MiDaS [37], leverage large-scale datasets with 3D supervision, normalizing scale differences across datasets to enable zero-shot testing. However, they primarily provide relative depth rather than metric depth. + +Recent methods tackle zero-shot metric depth estimation by addressing the challenges of inconsistent scaling factors in depth ground truth caused by varying camera intrinsic parameters. Several works demonstrate impressive generalization capabilities on novel images [4, 20, 33, 53, 57], establishing themselves as foundational depth models for downstream tasks. However, these approaches often struggle with large field-of-view (FoV) cameras like fisheye and + +$360^{\circ}$ cameras, where performance significantly declines compared to standard perspective cameras. + +As illustrated in Fig. 2, large FoV images can be represented in multiple formats, but generating the best-performing undistorted image for perspective-based depth models often leads to substantial FoV loss. Despite these limitations, large FoV inputs are crucial for efficiency-critical downstream applications such as large-scale detection [34, 52], segmentation [55, 58], SLAM [11, 44, 45, 62], interactive 3D scene generation [59], and robotic demonstration capturing [6, 14, 49]. + +Achieving zero-shot depth generalization across any FoV camera presents several challenges: (1) selecting a unified camera model to represent diverse FoVs, (2) effectively leveraging perspective training datasets to generalize to data spaces observable only from large FoV cameras, (3) managing drastically different training image sizes in the unified space caused by varying FoVs, and (4) handling resolution inconsistencies between training and testing phases. + +In this paper, we present Depth Any Camera (DAC), a novel zero-shot metric depth estimation framework that enables a depth model trained exclusively on perspective images to generalize across cameras with widely varying FoVs, including fisheye and $360^{\circ}$ cameras (see Fig. 1). DAC employs Equi-Rectangular Projection (ERP) as a canonical representation to unify images from diverse FoVs into a shared space. A key innovation is the introduction of an efficient pitch-aware Image-to-ERP conversion based on grid sampling and Gnomonic Geometry [47], enabling seamless ERP-space data augmentations. Specifically, pitch-aware ERP conversion with pitch-angle augmentation projects perspective images into high-distortion regions of the ERP space, effectively simulating observations unique to large-FoV cameras. This enhances DAC's zero-shot generalization, allowing it to extrapolate beyond the perspective domain to a broader range of camera types. To facilitate learning from mixed datasets, we propose a FoV alignment process that normalizes diverse-FoV training samples to a predefined ERP patch size, preserving content while minimizing computational overhead. Additionally, multi-resolution augmentation is applied to address resolution mismatches, allowing the model to learn scale-equivariant features and adapt to a flexible range of testing resolutions. In summary, our contributions are as follows: + +- We propose a novel zero-shot metric depth estimation framework capable of handling images from any camera type, including fisheye and $360^{\circ}$ images, using a model trained exclusively on perspective data. +- We introduce an efficient pitch-aware perspective-to-ERP patch conversion that simulates the high-distortion characteristics of large-FoV cameras from perspective inputs, enhancing zero-shot generalization. +- We develop a FoV alignment process that enables effic + +tive training across cameras with diverse FoVs within a unified ERP space, along with a multi-resolution training strategy to address resolution mismatches between training ERP patches and testing images. + +- Our method achieves State-of-The-Art (SoTA) zero-shot performance on all large FoV testing datasets, delivering up to a $50\%$ improvement in $\delta_{1}$ accuracy on indoor fisheye and $360^{\circ}$ datasets, showcasing strong generalization across diverse camera types. + +![](images/51c412acdd7c4f5b81303d9f168de1ff9ca81e75a60d8815cf31788ffb2ce2ae.jpg) +Figure 2. Challenges on zero-shot test on large FoV camera images. Metric depth estimation models trained on perspective images (e.g., Metric3Dv2 [20]) experience significant performance degradation when applied to fisheye images. Degradation is less pronounced when using an undistorted portion with a highly limited FoV or its ERP conversion. + +# 2. Related Works + +# 2.1. Zero-Shot Monocular Depth Estimation + +Recent approaches to zero-shot metric depth estimation tackle the challenge of inconsistent scaling factors in depth ground truth due to varying camera intrinsic parameters [4, 16, 20, 33, 53, 54, 57]. Zoedepth [4] introduces an advanced network architecture, while DepthAnything [53, 54] employs a sophisticated unsupervised learning paradigm. However, their performance in metric depth estimation is limited without tackling inconsistency camera intrinsics. Metric3D [20, 57] and UniDepth [33] address scaling inconsistencies by converting images into a canonical camera space. Metric3D uses intrinsic parameters for this preprocessing, whereas UniDepth incorporates a network branch to estimate and convert intrinsics on the fly. Despite these advances, none of these methods achieve satisfactory zero-shot performance on large FoV images, presenting unique challenges in unifying diverse FoVs and supporting effective model learning. + +# 2.2. Depth Estimation from Large FoV Cameras + +Depth estimation for fisheye, $360^{\circ}$ cameras has grown in popularity, as large FoVs capture richer contextual information that enhances depth estimation [1, 21, 26, 41, 60]. A key challenge for these cameras is managing position-dependent distortions, which vary by camera models. Approaches to address this include deformable CNNs [42, 50, + +63], which adapt kernel shapes to compensate for distortions, as well as methods that segment ERP images to reduce distortion effects before merging [21, 38]. More recent methods leverage transformers to handle these distortions [10, 26, 41, 60]. While transformer-based networks have improved in-domain performance, they are approaching saturation, indicating that distortion is not the only challenge. Instead, the lack of large-scale FoV-specific training data is a key bottleneck for generalization. No current methods enable an unified depth estimation model trained on mixed large-scale perspective datasets to achieve zero-shot generalization on ERP or fisheye images. + +# 3. Notations and Preliminaries + +Depth Scaling Operations. Monocular depth estimation is inherently ill-posed, as different 3D object sizes and depths can produce the same 2D appearance. Deep learning models rely on learning an object's 3D dimensions from its 2D appearance [16, 17, 43] to infer depth, leading to the scaling operation illustrated in the right panel of Fig. 3. When using mixed camera data, apparent object size also depends on focal length, making accurate 2D-to-depth mapping dependent on appropriately scaling ground-truth depths when converting a perspective model to a canonical model, as shown in the left panel of Fig. 3. These scaling operations are central to the Metric3D [20, 57] pipeline and are integrated into our ERP-based approach. + +EquiRectangular Projection (ERP). Equi-Rectangular Projection (ERP) is an image representation based on a spherical camera model, where each pixel corresponds to a specific latitude $\lambda$ and longitude $\phi$ . A full ERP space spans $180^{\circ}$ in latitude and $360^{\circ}$ in longitude, making it ideal for handling diverse FoV cameras. The ERP image height is the only parameter needed to define the ERP space, allowing both training and testing images to be consistently converted into this space, regardless of the original FoV. + +Transformations between standard images and ERP images use Gnomonic Projection transformation [47], which offers a closed-form mapping between tangent image coordinates $(x_{t},y_{t})$ and spherical coordinates $(\lambda ,\phi)$ , assuming a tangent plane centered at $(\lambda_c,\phi_c)$ of a unit sphere. Specifically, as shown in Fig. 5, this mapping is given by: + +$$ +x _ {t} = \frac {\bar {x}}{\cos c} = \frac {\cos \phi \sin (\lambda - \lambda_ {c})}{\cos c} \tag {1} +$$ + +$$ +y _ {t} = \frac {\bar {y}}{\cos c} = \frac {\cos \phi_ {c} \sin \phi - \sin \phi_ {c} \cos \phi \cos (\lambda - \lambda_ {c})}{\cos c} \tag {2} +$$ + +where $(\bar{x},\bar{y},\cos c)$ represents a point on the unit sphere, and $c$ is the angular distance between $(\lambda ,\phi)$ and $(\lambda_c,\phi_c)$ , can be calculated as: + +$$ +\cos c = \sin \phi_ {c} \sin \phi + \cos \phi_ {c} \cos \phi \cos (\lambda - \lambda_ {c}) \tag {3} +$$ + +We use these transformations to enable an efficient ERP conversion and data augmentation process, creating a + +![](images/243f816124080811df05945fad13bf5f8e7b73db2064f4ef58c8219591096bb4.jpg) +Camera Conversion +Figure 3. Depth Scaling in Canonical Model Conversion and Image Resizing. The apparent 2D size of an object $u$ in an image depends on its 3D dimensions $X$ , depth $Z$ , and camera focal length $f_{x}$ . Left: Converting a perspective camera model to a canonical model with a different focal length $\hat{f}_{x}$ requires scaling the depth values proportionally, so $\hat{Z} = \frac{\hat{f}_{x}Z}{\hat{f}_{x}}$ . Center: The original camera setup, showing the direct relationship between object size, depth, and focal length. Right: When the camera model is fixed but the image is resized to $u'$ , this simulates viewing the same 3D object at a different distance, necessitating depth scaling for accurate metric depth, with $Z' = \frac{uZ}{u'}$ . + +![](images/044bbd9a554cd2f80eac9b2957819b84475f0c01b0ea2f5ea11cd3fbd6486961.jpg) +Original Cam + +![](images/b5183e01cde5e7f9043d1aad9ea2c2bbbf1095ec6ab390a338c1005454bd4880.jpg) +Image Resizing + +streamlined pipeline that supports zero-shot generalization for depth estimation across various FoV cameras. + +# 4. Depth Any Camera + +We propose Depth Any Camera (DAC), a depth model training framework designed to achieve zero-shot generalization across diverse camera models, including perspective, fisheye, and $360^{\circ}$ cameras. As illustrated in Fig. 4, images from different camera types and FoVs are transformed into a canonical ERP space during both the training and testing phases. For training, we leverage the extensive perspective image datasets by converting them into smaller ERP patches for efficient learning. During testing, large FoV images are similarly converted into the canonical ERP space, allowing the trained model to predict metric depth consistently, without getting confused by different camera intrinsic and distortion parameters. + +Several key components are designed to address specific challenges in implementing the DAC framework. In Sec. 4.1, we present an efficient pitch-aware Image-to-ERP conversion method that simulate large-FoV images at patch level and supports online augmentation within the ERP space. Sec. 4.2 introduces a FoV alignment process, an effective data augmentation technique that maximizes content inclusion while minimizing computational waste on background areas, using a single predefined ERP patch size. In Sec. 4.3, we describe a multi-resolution data augmentation approach aimed at training a transformer-based network capable of handling a broad range of testing resolutions. + +The proposed DAC framework is compatible with various depth estimation network architectures, which are not the primary focus of this paper. Without loss of generality, + +![](images/c5379d3552bf1603bb40886272ce8e00d7cd45b37beb62cbc73beed7e2b01fbf.jpg) +Figure 4. Depth Any Camera Pipeline. Our DAC framework converts data from any camera type into a canonical ERP space, enabling a model trained solely on perspective images to process large-FOV test data consistently for metric depth estimation. During training, we introduce an effective pitch-aware Image-to-ERP conversion with online data augmentation to simulate high-distortion regions unique to large-FOV images. The proposed FoV-Align process normalizes diverse-FOV data to a predefined ERP patch size, maximizing training efficiency. During inference, images from any camera type are converted into ERP space for depth estimation, with an optional step to map the ERP output back to the original image space for visualization. + +we employ iDisc [32] for its simplicity and effectiveness, and for its incorporation of two prototypical attention modules, namely cross-attention and self-attention. We use the SIlog loss function [9] for training our models. + +# 4.1. Pitch-Aware Image-to-ERP Conversion + +An input image can be efficiently converted to its corresponding ERP patch through grid sampling combined with gnomonic projection. Assuming an ERP space with height $H_{E}$ , width $W_{E} = 2H_{E}$ , and the image center at latitude $\lambda_{c}$ , longitude $\phi_{c}$ , with a target ERP patch size of $H_{e} \times W_{e}$ , the ERP patch coordinates $(u_{e}, v_{e})$ can be mapped to spherical coordinates as $\phi = \frac{2\pi W_{e}}{W_{E}} (u_{e} - \frac{W_{e}}{2}) + \phi_{c}$ , and $\lambda = \frac{\pi H_{e}}{H_{E}} (v_{e} - \frac{H_{e}}{2}) + \lambda_{c}$ . Using Gnomonic Geometry presented in Eq. 1 and Eq. 2, we obtain the corresponding normalized image coordinate $(x_{t}, y_{t}, 1)$ in the tangent plane and $(\bar{x}, \bar{y}, \cos c)$ on the unit sphere. To map this coordinate to the actual image coordinate $(u, v)$ , we apply distortion and projection functions based on the given camera parameters: + +$$ +\left(x _ {d}, y _ {d}\right) = f _ {d} (\bar {x}, \bar {y}, \cos c, D _ {c}) \tag {4} +$$ + +$$ +(u, v) = f _ {p} \left(x _ {d}, y _ {d}, K _ {c}\right) \tag {5} +$$ + +where $f_{d}$ is the distortion function with distortion parameters $D_{c}$ , and $f_{p}$ is the projection function with intrinsic parameters $K_{c}$ . If the input image has no distortion, projection function is directly applied to $(x_{t}, y_{t})$ . Details on applying distortion models are included in Supplemental Sec. 8. + +As shown in Fig. 5, with uniformly sampled grid points within the target ERP patch, each grid point can be mapped directly to a corresponding location in the input image. This mapping facilitates efficient transformation of the captured image into an ERP patch via grid sampling. Essentially, each grid point in the ERP patch maps to a specific floating-point position in the input image, and its value is obtained by interpolating from the neighboring pixel values. + +This ERP conversion enables a powerful training pipeline when the latitude of the tangent plane center $\lambda_{c}$ is defined by the camera's pitch angle in training. When camera orientation is available or can be estimated [22], perspective data can be projected to various latitudes in the ERP space, enabling the simulation of regions uniquely visible from large-FoV cameras, as shown in Fig. 5, and Supplemental Fig. 7. This pitch-aware conversion is crucial for improving the generalization of trained models to previously unobserved large-FoV data, as demonstrated in Sec. 5.3, because neural networks alone have limited capacity to generalize to extrapolated data spaces [51]. + +Another notable advantage is the seamless ability to perform online augmentation efficiently in the ERP space. For datasets with limited pitch variation [12, 15, 19, 61], a unique pitch augmentation can be efficiently applied by adding noise to $\lambda_{c}$ , generating ERP patches with varying shapes, as shown in Fig. 4. In addition, common augmenta + +![](images/bf161515b70df72a299dee603fdf820daa98320baa68833764ef08ccf70ac55b.jpg) +Grid Sampling via Gnomonic Geometry +Figure 5. Pitch-Aware ERP Conversion and FoV Alignment. Top: Grid Sampling is applied for an efficient Image-to-ERP conversion. Each ERP grid sample's corresponding location in the input image is computed using gnomonic geometry and specific camera projection parameters. Given the patch center latitude $\lambda$ determined by the camera's pitch angle, it makes the converted patch to represent high-distortion regions in the ERP space. Bottom: The FoV-Align process normalizes diverse-FoV ERP patches (shown in red and green) to match the height of a single predefined ERP patch (outlined in blue), ensuring efficient training. + +tions, such as scaling, rotation, and translation—commonly applied to perspective images—can be directly applied to the normalized image coordinates $(x_{t},y_{t})$ as follows: + +$$ +\left[ \begin{array}{l} x _ {t} ^ {\prime} \\ y _ {t} ^ {\prime} \end{array} \right] = s _ {\sigma} \left[ \begin{array}{l l} R _ {\sigma} & T _ {\sigma} \end{array} \right] \left[ \begin{array}{l} x _ {t} \\ y _ {t} \end{array} \right] \tag {6} +$$ + +where $s_{\sigma}$ is a scale factor, $R_{\sigma}$ is 2D rotation matrix, and $T_{\sigma}$ is a 2D translation vector corresponding to the applied augmentations. + +# 4.2. FoV Alignment + +When training data include a wide range of camera FoVs within perspective images, such as in the HM3D [35] dataset produced by OmniData [8], the corresponding ERP regions can vary significantly in size, as shown in Fig. 5. There is no single crop size that can consistently capture most content information for certain images without wasting substantial computation on background padding for others. This creates a dilemma in prioritizing between training efficiency and richness of information, and it can also reduce training quality when samples exhibit drastically different content-to-background ratios. + +To address this challenge, we introduce a simple yet effective FoV Alignment operation that adjusts the FoV of each input image to match the predetermined crop area FoV. Specifically, this process applies a specific scaling augmentation, as described in Sec. 4.1 and Eq. 6, specifically $\mathrm{Fov}_e = \frac{H_e\pi}{H_E}$ and $s_\sigma = \frac{\mathrm{Fov}_c}{\mathrm{Fov}_e}$ , where $\mathrm{Fov}_c$ is derived from actual camera parameters, and $\mathrm{Fov}_e$ is ERP patch's vertical FoV. As illustrated in Fig. 5, this approach allows a single predefined ERP patch size to maximize the inclusion of relevant content and minimize computational waste on background, making it ideal for an efficient training pipeline. + +# 4.3. Multi-Resolution Training + +Training ERP patches and testing images may prefer inconsistent resolutions for various reasons, e.g. drastically different aspect ratio, edge device limitation. When testing resolutions differ from the training patch size, model performance can degrade significantly, particularly with attention modules that aggregate different numbers of image tokens. + +To address this issue, we adopt a multi-resolution training scheme. As illustrated in Fig. 4, each ERP patch is resized to two additional lower resolutions (typically 0.7 and 0.4 of the original) to incorporate varied image resolutions in training. The training feeds the model three batches of images at different resolutions and sums the losses. + +# 5. Experiments + +# 5.1. Experimental Setup + +In-Domain Training Datasets. For indoor experiments, we use Habitat-Matterport 3D (HM3D) [35], Taskonomy [61], and Hypersim [39], totaling 670K perspective images with distinct characteristics. To streamline training, we use the first 50 scenes from HM3D and Taskonomy (tiny versions provided by OmniData [8]). For outdoor data, we use DDAD [15] and LYFT [19], totaling 130K images. Table 1 summarizes the datasets in use, showing varying distributions in FoV, pitch angles, sources, and image quality. + +Zero-Shot Testing Datasets. We evaluate DAC on two $360^{\circ}$ datasets—Matterport3D [5] and Pano3DGV2 [2]—and two fisheye datasets—ScanNet++ [56] and KITTI360 [27]—all featuring larger FoVs than perspective images. Our primary experiments focus on these datasets to assess zero-shot generalization to large FoV cameras. Additional evaluations on NYUv2 [30] and KITTI [12] are provided in the supplementary material, demonstrating DAC's performance on perspective data relative to SoTA methods. + +Evaluation Details. We assess DAC's generalization to large FoV cameras across both indoor and outdoor scenes, training separate models for each without data mixing to simplify training. For fair comparison, competing models are either re-trained with the same data splits or use their largest versions trained on extensive datasets. Evaluations are conducted using metric depth metrics: $\delta_1\uparrow ,\delta_2\uparrow ,\delta_3\uparrow$ Abs Rel↓, RMSE↓, and log10↓. + +Baselines. We compare DAC with the following baselines: + +- Metric3Dv2 [20]: A SoTA foundation model in zero-shot metric depth estimation, built upon perspective canonical camera model to standardize datasets. +- UniDepth [33]: A more recent SoTA foundation depth model leveraging network designs to handle diverse camera parameters. We test its ability to handle large FoV cameras not included in training. +- iDisc [32]: Selected as a network baseline due to its use of self-attention and cross-attention modules in a straight- + +Table 1. Overview of Datasets. This table summarizes the training and testing datasets used in this work. The training datasets span a range of FoVs, pitch angles, and image quality, each potentially impacting performance on different test datasets in varying degrees. + +
Train Dataset# ImagesScenexFoV (deg.)# CamsPitch (deg.)SourceImg Qual.Test DatasetCam TypexFoV (deg.)Scene
HM3D-tiny [35]310KIndoor36° - 124°10K+3σ = 75°ReconLowMatterport3D [5]ERP360°Indoor
Taskonomy-tiny [61]300KIndoor45° - 75°10K+3σ = 24°RealHighPano3D-GV2 [2]ERP360°Indoor
Hypersim [39]54KIndoor60°13σ = 60°SimHigh+ScanNet++ [56]Fisheye150°Indoor
DDAD [15]80KOutdoor45° - 60°36+3σ ~ 10°RealHighKITTI360 [27]Fisheye180°Outdoor
LYFT [19]50KOutdoor20° - 60°6+3σ ~ 10°RealHigh
+ +Table 2. Zero-Shot Test on ${360}^{ \circ }$ and Fisheye Datasets. DAC is compared with SoTA metric depth models across four large-ForV datasets. + +
Test DatasetMethodsTrain DatasetBackboneδ1↑δ2↑δ3↑Abs Rel↓RMSE↓log10↓
Matterport3D [5]UniDepth [33]Mix 3MViT-L [7]0.25760.51140.70910.76481.38270.2208
Metric3Dv2 [20]Mix 16MDinov2 [31]0.43810.73110.87350.29240.88420.1546
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.42870.78540.93330.27880.89610.1352
iDisc [32]Indoor 670KResnet101 [18]0.52870.82600.93980.27570.77710.1147
DAC (Ours)Indoor 670KResnet101 [18]0.77270.95620.98220.1560.61850.0707
Pano3D-GV2 [2]UniDepth [33]Mix 3MViT-L [7]0.24690.49770.70840.78921.26810.2231
Metric3Dv2 [20]Mix 16MDinov2 [31]0.40400.69290.84990.30700.85490.1664
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.50600.81760.93600.26080.72480.1201
iDisc [32]Indoor 670KResnet101 [18]0.56290.82220.93320.26570.64460.1122
DAC (Ours)Indoor 670KResnet101 [18]0.81150.95490.98600.13870.47800.0623
ScanNet++ [56]UniDepth [33]Mix 3MViT-L [7]0.36380.64610.83580.49711.16590.1648
Metric3Dv2 [20]Mix 16MDinov2 [31]0.53600.82180.93500.22290.89500.1177
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.64890.89200.95580.19150.97790.0938
iDisc [32]Indoor 670KResnet101 [18]0.61500.87800.96170.27120.48350.0972
DAC (Ours)Indoor 670KResnet101 [18]0.85170.96930.99220.13230.30860.0532
KITTI360 [27]UniDepth [33]Mix 3MViT-L [7]0.48100.83970.94060.29396.56420.1221
Metric3Dv2 [20]Mix 16MDinov2 [31]0.71590.93230.97710.19974.57690.0811
Metric3Dv2 [20]Outdoor 130KDinov2 [31]0.76750.93700.97560.15214.66100.0723
iDisc [32]Outdoor 130KResnet101 [18]0.78330.93840.97530.15984.91220.0704
DAC (Ours)Outdoor 130KResnet101 [18]0.78580.93880.97750.15594.36140.0684
+ +forward yet effective network, and strong in-domain performance. As iDisc alone does not handle mixed camera parameters, we train it with Metric3Dv2 [20], and compare it to the same network trained with ours. + +Implementation Details. In the DAC training pipeline, we set the full ERP height to $H_{\mathrm{erp}} = 1400$ pixels, with an ERP patch size of $500 \times 700$ pixels for both indoor and outdoor models. We use $10^{\circ}$ latitude augmentations for both and additionally $10^{\circ}$ rotation augmentation for indoor. When training the iDisc [32] model using the Metric3D [57] pipeline, we use canonical focal lengths of $f_{\mathrm{cano}} = 519$ (NYU dataset [30]) for indoor models and $f_{\mathrm{cano}} = 721$ (KITTI dataset [12]) for outdoor models. + +To test perspective models on ERP and fisheye images, specific adjustments are required. For $360^{\circ}$ (ERP) images, which lack a defined focal length, we calculate a virtual focal length $f_{\mathrm{virtual}}$ based on pixels per latitude degree: $\frac{1}{f_{\mathrm{virtual}}} = \tan \left(\frac{\pi}{H_{\mathrm{ep}}}\right)$ , scaling the predicted depth with $\frac{f_{\mathrm{cano}}}{f_{\mathrm{virtual}}}$ for ground-truth alignment. For fisheye images, aligning $f_{\mathrm{cano}}$ with the post-distortion focal length introduces significant errors, so we first convert fisheye images to ERP space and apply $\frac{f_{\mathrm{cano}}}{f_{\mathrm{virtual}}}$ for metric depth evaluation. + +For testing resolution, if the original resolution is less than twice the training resolution, we use it directly; for + +larger resolutions, we maintain the aspect ratio and align it with the training resolution. Based on this rule, we evaluate Matterport3D [5] and Pano3D-GV2 [2] at $512 \times 1024$ , ScanNet++ [56] at $500 \times 750$ , and KITTI360 [27] at $700 \times 700$ . For competing methods that are not adaptable to inconsistent resolutions compared to training, we report the higher score obtained from the two settings to ensure fairness. + +In experiments, ResNet101 [18]-backbone models are trained for 60k iterations with a batch size of 48, while Swin-L [28] and DINOv2 [31] models are trained for 120k iterations with a batch size of 48. Finally, to support all FoV types, depth is represented as Euclidean Distance from the camera center rather than Z-buffer format, as the latter is incompatible with spherical projections and would yield inaccurate low depth values for fisheye or ERP images. + +# 5.2. Comparison with the SoTA + +In this section, we compare DAC with primary baselines in zero-shot generalization tests on large FoV datasets, with quantitative results reported in Table 2, and qualitative results shown in Fig. 6. In indoor experiments, DAC significantly outperforms pre-trained models UniDepth [33] and Metric3Dv2 [20], even when using a lighter ResNet101 [18] backbone and a much smaller training dataset. DAC + +achieves superior performance across both $360^{\circ}$ datasets and the fisheye dataset ScanNet++ [56]. Compared to the iDisc [32] network trained with the Metric3Dv2 pipeline, DAC shows substantial improvements across all metrics on all datasets. Notably, DAC improves the next-best method by nearly $50\%$ in the most differentiating metric, $\delta_{1}$ . + +In outdoor tests, DAC significantly outperforms Metric3Dv2 [57] and UniDepth [33], even with much larger backbones. However, it achieves only marginal improvements over iDisc [32] under the same network configuration, with less pronounced gains compared to indoor settings. This is likely due to the limited camera pitch variance in the outdoor training data (Table 1), reducing the ability to simulate highly distorted regions. Moreover, KITTI360 [27] LiDAR points are concentrated in less distorted areas (Fig. 6), making the evaluation less distinctive. + +Particularly, a notable observation is that while UniDepth [33] utilizes a network-based spherical conversion, it struggles with large FoV cameras, exposing the limitations of deep learning in extrapolated domains [51]. In contrast, DAC's success underscores the effectiveness of our geometry-based training pipeline. + +Additional results of DAC models using SwinL [28] backbones are provided in Supplemental Table 5. These models outperform their ResNet101 [18] counterparts in most cases, except on the $360^{\circ}$ datasets. + +Table 3. Impact of Key Components and Network. We conduct the main ablation study on indoor datasets by training with HM3D [35] and performing zero-shot testing on Pano3D-GV2 [2] and ScanNet++ [56]. We compare the performance of the DAC framework with specific components removed, as well as different network architectures trained under the Metric3D [57] pipeline. + +
Test DatasetMethodsδ1↑δ2↑A.Rel↓
Pano3D-GV2 [2]Metric3Dv2 [20]0.56230.83410.2479
iDisc-cnn [32]0.30260.55650.3548
iDisc [32]0.41300.68440.3043
DAC (Ours)0.72510.92540.1729
w\o Pitch-Aware ERP0.49110.79040.2422
w\o Pitch Aug 10°0.69120.93110.188
w\o FoV Align0.40750.75850.2610
w\o Multi-Reso0.51280.77840.2437
ScanNet++ [56]Metric3Dv2 [20]0.45690.74630.2818
iDisc-cnn [32]0.46390.76530.3045
iDisc [32]0.53010.80480.3237
DAC (Ours)0.65390.90830.1951
w\o Pitch-Aware ERP0.47110.80680.2508
w\o Pitch Aug 10°0.67410.90660.1914
w\o FoV Align0.54280.86440.2200
w\o Multi-Reso0.55040.84640.2231
+ +# 5.3. Ablation Study + +Key Components and Network Architecture. We evaluate the effect of the FoV Align and Multi-Reso Training components by removing each individually, while keeping the rest of the DAC framework unchanged. This ablation + +Table 4. Impact of Train Dataset. Models are trained separately on each training dataset and evaluated in zero-shot tests on $360^{\circ}$ and fisheye datasets. Due to the unique characteristics of each training dataset, their contributions and importance to generalization across different testing datasets vary. + +
Test DatasetsTrain DatasetMethodsδ1↑A.Rel↓
Pano3D-GV2 [2]HM3D-tiny [35]Metric3Dv2 [20]0.56230.2479
iDisc [32]0.41300.3043
DAC (Ours)0.72510.1729
Taskonomy-tiny [61]Metric3Dv2 [20]0.37850.2959
iDisc [32]0.38880.4076
DAC (Ours)0.64110.1972
Hypersim [39]Metric3Dv2 [20]0.30850.5583
iDisc [32]0.33720.3288
DAC (Ours)0.52080.1792
ScanNet++ [56]HM3D-tiny [35]Metric3Dv2 [20]0.45690.2818
iDisc [32]0.53010.3237
DAC (Ours)0.65390.1951
Taskonomy-tiny [61]Metric3Dv2 [20]0.63180.2148
iDisc [32]0.67430.1977
DAC (Ours)0.79810.1447
Hypersim [39]Metric3Dv2 [20]0.50500.2269
iDisc [32]0.66560.2213
DAC (Ours)0.74780.1762
+ +is conducted on the challenging HM3D-tiny [35] indoor dataset, which includes varied camera FoVs, pitch angles, and lower-quality images from reconstructed scenes. We also test the impact of removing attention modules from iDisc [32] and compare to Metric3Dv2 [20] to isolate the influence of the iDisc architecture. Both iDisc-based methods and DAC use ResNet101 backbones, while Metric3Dv2 uses Dinov2. Table 3 provides a summary; full metrics and Matterport3D [5] results are in the Supplemental Table 6. + +Table 3 highlights the pivotal role of pitch-aware ERP conversion in generalizing perspective-trained models to large FoV datasets by effectively simulating high-distortion regions uniquely observed in large FoV images (Fig. 7). This approach turns the wide pitch angle variance in datasets like HM3D [35] into an advantage. While additional pitch augmentation does not appear essential when the training dataset like HM3D intricately spans a large range of pitch angle. However, its effectiveness varies across datasets, as detailed in Supplemental Table 6. + +Results in Table 3 also show that removing FoV Align or Multi-Reso Training significantly reduces DAC performance, particularly for zero-shot generalization on $360^{\circ}$ images. Compared to the iDisc network trained with the Metric3D pipeline, DAC achieves notable improvements for large FoV cameras, with attention modules in iDisc proving effective for large FoV test data. Although Metric3Dv2 uses a heavier backbone, it shows limited zero-shot generalization on large FoV images without DAC. More comprehensive results can be found both in Supplemental Table 6. + +Impact of Training Dataset. Each dataset has unique characteristics (Table 1). To evaluate their impact on generalization to large FoV data, we trained models separately on HM3D-tiny, Taskonomy-tiny [61], and Hypersim [39], then + +![](images/d8a91233206937f0c25f40a96afb7676773b84c426efe09874af7dd342c79295.jpg) +Figure 6. Zero-Shot Qualitative Results. For each dataset, an example is presented in two consecutive rows. The left column shows the original image and Ground-Truth depth map, followed by results from various methods. For each method, the top row displays the A.Rel map $\downarrow$ and the bottom row shows the predicted depth map. The color range for depth and A.Rel maps is indicated in the last column. + +tested them in zero-shot mode on indoor large FoV datasets. Results are summarized in Table 4, with full results in Supplemental Table 7. + +For Pano3D-GV2 [2], broader FoV and pitch angle coverage in HM3D training improve generalization across all methods, despite HM3D's lower quality due to rendering artifacts. For fisheye data in ScanNet++ [56], FoV diversity appears less crucial, as the single-camera Hypersim dataset, despite limited training data, outperforms HM3D, indicating that image quality plays a key role in ScanNet++ test. + +Comparing individually trained models with results from mixed training in Table 2 shows that DAC effectively leverages the synergy of diverse datasets, significantly enhancing generalization to large FoV datasets. + +# 6. Conclusion + +We introduced the Depth Any Camera (DAC) framework for zero-shot metric depth estimation across diverse camera types, including perspective, fisheye, and $360^{\circ}$ cameras. By leveraging a highly effective pitch-aware Image-to-ERP transformation, FoV alignment, and multi-resolution training, DAC addresses the challenges posed by varying FoVs and resolution inconsistencies and enables robust generalization on large FoV datasets. Our results demonstrate that DAC significantly outperforms state-of-the-art methods and adapts seamlessly to different backbone networks. In practice, DAC ensures that every piece of previously collected 3D data remains valuable, regardless of the camera type used in new applications. + +# References + +[1] Hao Ai, Zidong Cao, Yan-Pei Cao, Ying Shan, and Lin Wang. Hrdfuse: Monocular $360^{\circ}$ depth estimation by collaboratively learning holistic-with-regional depth distributions. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023, 2023. 2 +[2] Georgios Albanis, Nikolaos Zioulis, Petros Drakoulis, Vasileios Gkitsas, Vladimirovs Sterzentsenko, Federico Alvarez, Dimitrios Zarpalas, and Petros Daras. Pano3d: A holistic benchmark and a solid baseline for 360deg depth estimation. 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This paper presents Depth Any Camera (DAC), a powerful zero-shot metric depth estimation framework that extends a perspective-trained model to effectively handle cameras with varying FoVs. The framework is designed to ensure that all existing 3D data can be leveraged, regardless of the specific camera types used in new applications. Remarkably, DAC is trained exclusively on perspective images but generalizes seamlessly to fisheye and 360-degree cameras without the need for specialized training data. DAC employs Equi-Rectangular Projection (ERP) as a unified image representation, enabling consistent processing of images with diverse FoVs. Its core components include pitch-aware Image-to-ERP conversion with efficient online augmentation to simulate distorted ERP patches from undistorted inputs, FoV alignment operations to enable effective training across a wide range of FoVs, and multi-resolution data augmentation to further address resolution disparities between training and testing. DAC achieves state-of-the-art zero-shot metric depth estimation, improving " + }, + { + "bbox": [ + 54, + 281, + 296, + 605 + ], + "type": "inline_equation", + "content": "\\delta_{1}" + }, + { + "bbox": [ + 54, + 281, + 296, + 605 + ], + "type": "text", + "content": " accuracy by up to " + }, + { + "bbox": [ + 54, + 281, + 296, + 605 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 54, + 281, + 296, + 605 + ], + "type": "text", + "content": " on multiple fisheye and 360-degree datasets compared to prior metric depth foundation models, demonstrating robust generalization across camera types." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 56, + 628, + 135, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 628, + 135, + 640 + ], + "spans": [ + { + "bbox": [ + 56, + 628, + 135, + 640 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 647, + 296, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 296, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 296, + 685 + ], + "type": "text", + "content": "Depth estimation from monocular cameras is a foundational challenge for applications like autonomous driving, AR/VR, and robotics. While early deep learning methods" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 322, + 253, + 547, + 379 + ], + "blocks": [ + { + "bbox": [ + 322, + 253, + 547, + 379 + ], + "lines": [ + { + "bbox": [ + 322, + 253, + 547, + 379 + ], + "spans": [ + { + "bbox": [ + 322, + 253, + 547, + 379 + ], + "type": "image", + "image_path": "eca003ef65b3c695ab9c932d5824bbf4561a2832f026b7c56fdf8e4dfad385b9.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 387, + 555, + 453 + ], + "lines": [ + { + "bbox": [ + 313, + 387, + 555, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 555, + 453 + ], + "type": "text", + "content": "Figure 1. We introduce Depth Any Camera (DAC) framework, which leverages large-scale datasets containing perspective camera images to train a single depth estimation model capable of conducting zero-shot metric depth estimation on images captured various types of cameras, including those captured from large FoV fisheye and " + }, + { + "bbox": [ + 313, + 387, + 555, + 453 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 313, + 387, + 555, + 453 + ], + "type": "text", + "content": " cameras." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 470, + 555, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 470, + 555, + 614 + ], + "spans": [ + { + "bbox": [ + 312, + 470, + 555, + 614 + ], + "type": "text", + "content": "relied on supervised training using single datasets and depth sensor [24] supervision [3, 25, 36], monocular depth estimation remains challenging due to scale-depth ambiguity. Expanding training datasets has been a key strategy to enhance robustness, with self-supervised approaches using sequential frames [13, 46, 48]. However, these methods often underperform due to self-supervision ambiguity, view inconsistencies and dynamic objects. Recent methods, such as MiDaS [37], leverage large-scale datasets with 3D supervision, normalizing scale differences across datasets to enable zero-shot testing. However, they primarily provide relative depth rather than metric depth." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 312, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 617, + 556, + 715 + ], + "type": "text", + "content": "Recent methods tackle zero-shot metric depth estimation by addressing the challenges of inconsistent scaling factors in depth ground truth caused by varying camera intrinsic parameters. Several works demonstrate impressive generalization capabilities on novel images [4, 20, 33, 53, 57], establishing themselves as foundational depth models for downstream tasks. However, these approaches often struggle with large field-of-view (FoV) cameras like fisheye and" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 145, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 145, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 145, + 703 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 67, + 703, + 165, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 165, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 165, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 67, + 703, + 165, + 712 + ], + "type": "text", + "content": " Equal technical contribution." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26996" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": " cameras, where performance significantly declines compared to standard perspective cameras." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 97, + 295, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 97, + 295, + 205 + ], + "spans": [ + { + "bbox": [ + 54, + 97, + 295, + 205 + ], + "type": "text", + "content": "As illustrated in Fig. 2, large FoV images can be represented in multiple formats, but generating the best-performing undistorted image for perspective-based depth models often leads to substantial FoV loss. Despite these limitations, large FoV inputs are crucial for efficiency-critical downstream applications such as large-scale detection [34, 52], segmentation [55, 58], SLAM [11, 44, 45, 62], interactive 3D scene generation [59], and robotic demonstration capturing [6, 14, 49]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 206, + 295, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 206, + 295, + 302 + ], + "spans": [ + { + "bbox": [ + 54, + 206, + 295, + 302 + ], + "type": "text", + "content": "Achieving zero-shot depth generalization across any FoV camera presents several challenges: (1) selecting a unified camera model to represent diverse FoVs, (2) effectively leveraging perspective training datasets to generalize to data spaces observable only from large FoV cameras, (3) managing drastically different training image sizes in the unified space caused by varying FoVs, and (4) handling resolution inconsistencies between training and testing phases." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 304, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 304, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 56, + 304, + 296, + 602 + ], + "type": "text", + "content": "In this paper, we present Depth Any Camera (DAC), a novel zero-shot metric depth estimation framework that enables a depth model trained exclusively on perspective images to generalize across cameras with widely varying FoVs, including fisheye and " + }, + { + "bbox": [ + 56, + 304, + 296, + 602 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 56, + 304, + 296, + 602 + ], + "type": "text", + "content": " cameras (see Fig. 1). DAC employs Equi-Rectangular Projection (ERP) as a canonical representation to unify images from diverse FoVs into a shared space. A key innovation is the introduction of an efficient pitch-aware Image-to-ERP conversion based on grid sampling and Gnomonic Geometry [47], enabling seamless ERP-space data augmentations. Specifically, pitch-aware ERP conversion with pitch-angle augmentation projects perspective images into high-distortion regions of the ERP space, effectively simulating observations unique to large-FoV cameras. This enhances DAC's zero-shot generalization, allowing it to extrapolate beyond the perspective domain to a broader range of camera types. To facilitate learning from mixed datasets, we propose a FoV alignment process that normalizes diverse-FoV training samples to a predefined ERP patch size, preserving content while minimizing computational overhead. Additionally, multi-resolution augmentation is applied to address resolution mismatches, allowing the model to learn scale-equivariant features and adapt to a flexible range of testing resolutions. In summary, our contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 55, + 605, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 653 + ], + "type": "text", + "content": "- We propose a novel zero-shot metric depth estimation framework capable of handling images from any camera type, including fisheye and " + }, + { + "bbox": [ + 55, + 605, + 295, + 653 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 605, + 295, + 653 + ], + "type": "text", + "content": " images, using a model trained exclusively on perspective data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 654, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 295, + 701 + ], + "type": "text", + "content": "- We introduce an efficient pitch-aware perspective-to-ERP patch conversion that simulates the high-distortion characteristics of large-FoV cameras from perspective inputs, enhancing zero-shot generalization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "content": "- We develop a FoV alignment process that enables effic" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "text", + "content": "tive training across cameras with diverse FoVs within a unified ERP space, along with a multi-resolution training strategy to address resolution mismatches between training ERP patches and testing images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "spans": [ + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "text", + "content": "- Our method achieves State-of-The-Art (SoTA) zero-shot performance on all large FoV testing datasets, delivering up to a " + }, + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "text", + "content": " improvement in " + }, + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "inline_equation", + "content": "\\delta_{1}" + }, + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "text", + "content": " accuracy on indoor fisheye and " + }, + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 314, + 121, + 553, + 180 + ], + "type": "text", + "content": " datasets, showcasing strong generalization across diverse camera types." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 316, + 188, + 553, + 293 + ], + "blocks": [ + { + "bbox": [ + 316, + 188, + 553, + 293 + ], + "lines": [ + { + "bbox": [ + 316, + 188, + 553, + 293 + ], + "spans": [ + { + "bbox": [ + 316, + 188, + 553, + 293 + ], + "type": "image", + "image_path": "51c412acdd7c4f5b81303d9f168de1ff9ca81e75a60d8815cf31788ffb2ce2ae.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 301, + 555, + 368 + ], + "lines": [ + { + "bbox": [ + 313, + 301, + 555, + 368 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 555, + 368 + ], + "type": "text", + "content": "Figure 2. Challenges on zero-shot test on large FoV camera images. Metric depth estimation models trained on perspective images (e.g., Metric3Dv2 [20]) experience significant performance degradation when applied to fisheye images. Degradation is less pronounced when using an undistorted portion with a highly limited FoV or its ERP conversion." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 376, + 406, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 376, + 406, + 389 + ], + "spans": [ + { + "bbox": [ + 314, + 376, + 406, + 389 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 396, + 524, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 524, + 408 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 524, + 408 + ], + "type": "text", + "content": "2.1. Zero-Shot Monocular Depth Estimation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 415, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 415, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 415, + 555, + 617 + ], + "type": "text", + "content": "Recent approaches to zero-shot metric depth estimation tackle the challenge of inconsistent scaling factors in depth ground truth due to varying camera intrinsic parameters [4, 16, 20, 33, 53, 54, 57]. Zoedepth [4] introduces an advanced network architecture, while DepthAnything [53, 54] employs a sophisticated unsupervised learning paradigm. However, their performance in metric depth estimation is limited without tackling inconsistency camera intrinsics. Metric3D [20, 57] and UniDepth [33] address scaling inconsistencies by converting images into a canonical camera space. Metric3D uses intrinsic parameters for this preprocessing, whereas UniDepth incorporates a network branch to estimate and convert intrinsics on the fly. Despite these advances, none of these methods achieve satisfactory zero-shot performance on large FoV images, presenting unique challenges in unifying diverse FoVs and supporting effective model learning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 623, + 542, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 623, + 542, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 623, + 542, + 635 + ], + "type": "text", + "content": "2.2. Depth Estimation from Large FoV Cameras" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "type": "text", + "content": "Depth estimation for fisheye, " + }, + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 313, + 641, + 554, + 715 + ], + "type": "text", + "content": " cameras has grown in popularity, as large FoVs capture richer contextual information that enhances depth estimation [1, 21, 26, 41, 60]. A key challenge for these cameras is managing position-dependent distortions, which vary by camera models. Approaches to address this include deformable CNNs [42, 50," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26997" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 216 + ], + "type": "text", + "content": "63], which adapt kernel shapes to compensate for distortions, as well as methods that segment ERP images to reduce distortion effects before merging [21, 38]. More recent methods leverage transformers to handle these distortions [10, 26, 41, 60]. While transformer-based networks have improved in-domain performance, they are approaching saturation, indicating that distortion is not the only challenge. Instead, the lack of large-scale FoV-specific training data is a key bottleneck for generalization. No current methods enable an unified depth estimation model trained on mixed large-scale perspective datasets to achieve zero-shot generalization on ERP or fisheye images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 226, + 214, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 226, + 214, + 239 + ], + "spans": [ + { + "bbox": [ + 55, + 226, + 214, + 239 + ], + "type": "text", + "content": "3. Notations and Preliminaries" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 246, + 296, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 246, + 296, + 400 + ], + "spans": [ + { + "bbox": [ + 55, + 246, + 296, + 400 + ], + "type": "text", + "content": "Depth Scaling Operations. Monocular depth estimation is inherently ill-posed, as different 3D object sizes and depths can produce the same 2D appearance. Deep learning models rely on learning an object's 3D dimensions from its 2D appearance [16, 17, 43] to infer depth, leading to the scaling operation illustrated in the right panel of Fig. 3. When using mixed camera data, apparent object size also depends on focal length, making accurate 2D-to-depth mapping dependent on appropriately scaling ground-truth depths when converting a perspective model to a canonical model, as shown in the left panel of Fig. 3. These scaling operations are central to the Metric3D [20, 57] pipeline and are integrated into our ERP-based approach." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "spans": [ + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "text", + "content": "EquiRectangular Projection (ERP). Equi-Rectangular Projection (ERP) is an image representation based on a spherical camera model, where each pixel corresponds to a specific latitude " + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "text", + "content": " and longitude " + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "text", + "content": ". A full ERP space spans " + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "text", + "content": " in latitude and " + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 402, + 296, + 509 + ], + "type": "text", + "content": " in longitude, making it ideal for handling diverse FoV cameras. The ERP image height is the only parameter needed to define the ERP space, allowing both training and testing images to be consistently converted into this space, regardless of the original FoV." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "type": "text", + "content": "Transformations between standard images and ERP images use Gnomonic Projection transformation [47], which offers a closed-form mapping between tangent image coordinates " + }, + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "type": "inline_equation", + "content": "(x_{t},y_{t})" + }, + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "type": "text", + "content": " and spherical coordinates " + }, + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "type": "inline_equation", + "content": "(\\lambda ,\\phi)" + }, + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "type": "text", + "content": ", assuming a tangent plane centered at " + }, + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "type": "inline_equation", + "content": "(\\lambda_c,\\phi_c)" + }, + { + "bbox": [ + 55, + 509, + 296, + 575 + ], + "type": "text", + "content": " of a unit sphere. Specifically, as shown in Fig. 5, this mapping is given by:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 580, + 295, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 580, + 295, + 602 + ], + "spans": [ + { + "bbox": [ + 67, + 580, + 295, + 602 + ], + "type": "interline_equation", + "content": "x _ {t} = \\frac {\\bar {x}}{\\cos c} = \\frac {\\cos \\phi \\sin (\\lambda - \\lambda_ {c})}{\\cos c} \\tag {1}", + "image_path": "a9cfffab3ff358621518371f81721e64a611e6b982734e426961edb89f2c3567.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 604, + 294, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 604, + 294, + 625 + ], + "spans": [ + { + "bbox": [ + 69, + 604, + 294, + 625 + ], + "type": "interline_equation", + "content": "y _ {t} = \\frac {\\bar {y}}{\\cos c} = \\frac {\\cos \\phi_ {c} \\sin \\phi - \\sin \\phi_ {c} \\cos \\phi \\cos (\\lambda - \\lambda_ {c})}{\\cos c} \\tag {2}", + "image_path": "17a9091e6afd10cd2550cbddf3825bcac6cb130a8b0d2a548381260d82126c6f.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "inline_equation", + "content": "(\\bar{x},\\bar{y},\\cos c)" + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "text", + "content": " represents a point on the unit sphere, and " + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "text", + "content": " is the angular distance between " + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "inline_equation", + "content": "(\\lambda ,\\phi)" + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "inline_equation", + "content": "(\\lambda_c,\\phi_c)" + }, + { + "bbox": [ + 55, + 630, + 295, + 663 + ], + "type": "text", + "content": ", can be calculated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 671, + 295, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 671, + 295, + 683 + ], + "spans": [ + { + "bbox": [ + 86, + 671, + 295, + 683 + ], + "type": "interline_equation", + "content": "\\cos c = \\sin \\phi_ {c} \\sin \\phi + \\cos \\phi_ {c} \\cos \\phi \\cos (\\lambda - \\lambda_ {c}) \\tag {3}", + "image_path": "52acf5d738429e65e6b2551100112b9a190c75c73787c8f491ab0a9f08fd6e90.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "We use these transformations to enable an efficient ERP conversion and data augmentation process, creating a" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 319, + 71, + 392, + 171 + ], + "blocks": [ + { + "bbox": [ + 319, + 71, + 392, + 171 + ], + "lines": [ + { + "bbox": [ + 319, + 71, + 392, + 171 + ], + "spans": [ + { + "bbox": [ + 319, + 71, + 392, + 171 + ], + "type": "image", + "image_path": "243f816124080811df05945fad13bf5f8e7b73db2064f4ef58c8219591096bb4.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 325, + 171, + 381, + 178 + ], + "lines": [ + { + "bbox": [ + 325, + 171, + 381, + 178 + ], + "spans": [ + { + "bbox": [ + 325, + 171, + 381, + 178 + ], + "type": "text", + "content": "Camera Conversion" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "lines": [ + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": "Figure 3. Depth Scaling in Canonical Model Conversion and Image Resizing. The apparent 2D size of an object " + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": " in an image depends on its 3D dimensions " + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": ", depth " + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": ", and camera focal length " + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "inline_equation", + "content": "f_{x}" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": ". Left: Converting a perspective camera model to a canonical model with a different focal length " + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "inline_equation", + "content": "\\hat{f}_{x}" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": " requires scaling the depth values proportionally, so " + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "inline_equation", + "content": "\\hat{Z} = \\frac{\\hat{f}_{x}Z}{\\hat{f}_{x}}" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": ". Center: The original camera setup, showing the direct relationship between object size, depth, and focal length. Right: When the camera model is fixed but the image is resized to " + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "inline_equation", + "content": "u'" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": ", this simulates viewing the same 3D object at a different distance, necessitating depth scaling for accurate metric depth, with " + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "inline_equation", + "content": "Z' = \\frac{uZ}{u'}" + }, + { + "bbox": [ + 313, + 188, + 555, + 312 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 400, + 71, + 474, + 171 + ], + "blocks": [ + { + "bbox": [ + 400, + 71, + 474, + 171 + ], + "lines": [ + { + "bbox": [ + 400, + 71, + 474, + 171 + ], + "spans": [ + { + "bbox": [ + 400, + 71, + 474, + 171 + ], + "type": "image", + "image_path": "044bbd9a554cd2f80eac9b2957819b84475f0c01b0ea2f5ea11cd3fbd6486961.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 414, + 171, + 453, + 178 + ], + "lines": [ + { + "bbox": [ + 414, + 171, + 453, + 178 + ], + "spans": [ + { + "bbox": [ + 414, + 171, + 453, + 178 + ], + "type": "text", + "content": "Original Cam" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 478, + 71, + 551, + 171 + ], + "blocks": [ + { + "bbox": [ + 478, + 71, + 551, + 171 + ], + "lines": [ + { + "bbox": [ + 478, + 71, + 551, + 171 + ], + "spans": [ + { + "bbox": [ + 478, + 71, + 551, + 171 + ], + "type": "image", + "image_path": "b5183e01cde5e7f9043d1aad9ea2c2bbbf1095ec6ab390a338c1005454bd4880.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 495, + 171, + 539, + 178 + ], + "lines": [ + { + "bbox": [ + 495, + 171, + 539, + 178 + ], + "spans": [ + { + "bbox": [ + 495, + 171, + 539, + 178 + ], + "type": "text", + "content": "Image Resizing" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "spans": [ + { + "bbox": [ + 313, + 321, + 554, + 345 + ], + "type": "text", + "content": "streamlined pipeline that supports zero-shot generalization for depth estimation across various FoV cameras." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 357, + 430, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 430, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 430, + 371 + ], + "type": "text", + "content": "4. Depth Any Camera" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 377, + 555, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 377, + 555, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 377, + 555, + 533 + ], + "type": "text", + "content": "We propose Depth Any Camera (DAC), a depth model training framework designed to achieve zero-shot generalization across diverse camera models, including perspective, fisheye, and " + }, + { + "bbox": [ + 313, + 377, + 555, + 533 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 313, + 377, + 555, + 533 + ], + "type": "text", + "content": " cameras. As illustrated in Fig. 4, images from different camera types and FoVs are transformed into a canonical ERP space during both the training and testing phases. For training, we leverage the extensive perspective image datasets by converting them into smaller ERP patches for efficient learning. During testing, large FoV images are similarly converted into the canonical ERP space, allowing the trained model to predict metric depth consistently, without getting confused by different camera intrinsic and distortion parameters." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 533, + 556, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 556, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 556, + 677 + ], + "type": "text", + "content": "Several key components are designed to address specific challenges in implementing the DAC framework. In Sec. 4.1, we present an efficient pitch-aware Image-to-ERP conversion method that simulate large-FoV images at patch level and supports online augmentation within the ERP space. Sec. 4.2 introduces a FoV alignment process, an effective data augmentation technique that maximizes content inclusion while minimizing computational waste on background areas, using a single predefined ERP patch size. In Sec. 4.3, we describe a multi-resolution data augmentation approach aimed at training a transformer-based network capable of handling a broad range of testing resolutions." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": "The proposed DAC framework is compatible with various depth estimation network architectures, which are not the primary focus of this paper. Without loss of generality," + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26998" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 71, + 541, + 305 + ], + "blocks": [ + { + "bbox": [ + 69, + 71, + 541, + 305 + ], + "lines": [ + { + "bbox": [ + 69, + 71, + 541, + 305 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 541, + 305 + ], + "type": "image", + "image_path": "c5379d3552bf1603bb40886272ce8e00d7cd45b37beb62cbc73beed7e2b01fbf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 316, + 555, + 384 + ], + "lines": [ + { + "bbox": [ + 54, + 316, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 54, + 316, + 555, + 384 + ], + "type": "text", + "content": "Figure 4. Depth Any Camera Pipeline. Our DAC framework converts data from any camera type into a canonical ERP space, enabling a model trained solely on perspective images to process large-FOV test data consistently for metric depth estimation. During training, we introduce an effective pitch-aware Image-to-ERP conversion with online data augmentation to simulate high-distortion regions unique to large-FOV images. The proposed FoV-Align process normalizes diverse-FOV data to a predefined ERP patch size, maximizing training efficiency. During inference, images from any camera type are converted into ERP space for depth estimation, with an optional step to map the ERP output back to the original image space for visualization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 392, + 296, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 392, + 296, + 440 + ], + "spans": [ + { + "bbox": [ + 55, + 392, + 296, + 440 + ], + "type": "text", + "content": "we employ iDisc [32] for its simplicity and effectiveness, and for its incorporation of two prototypical attention modules, namely cross-attention and self-attention. We use the SIlog loss function [9] for training our models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 447, + 263, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 263, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 263, + 460 + ], + "type": "text", + "content": "4.1. Pitch-Aware Image-to-ERP Conversion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "spans": [ + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": "An input image can be efficiently converted to its corresponding ERP patch through grid sampling combined with gnomonic projection. Assuming an ERP space with height " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "H_{E}" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": ", width " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "W_{E} = 2H_{E}" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": ", and the image center at latitude " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": ", longitude " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "\\phi_{c}" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": ", with a target ERP patch size of " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "H_{e} \\times W_{e}" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": ", the ERP patch coordinates " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "(u_{e}, v_{e})" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": " can be mapped to spherical coordinates as " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "\\phi = \\frac{2\\pi W_{e}}{W_{E}} (u_{e} - \\frac{W_{e}}{2}) + \\phi_{c}" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "\\lambda = \\frac{\\pi H_{e}}{H_{E}} (v_{e} - \\frac{H_{e}}{2}) + \\lambda_{c}" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": ". Using Gnomonic Geometry presented in Eq. 1 and Eq. 2, we obtain the corresponding normalized image coordinate " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "(x_{t}, y_{t}, 1)" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": " in the tangent plane and " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "(\\bar{x}, \\bar{y}, \\cos c)" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": " on the unit sphere. To map this coordinate to the actual image coordinate " + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "inline_equation", + "content": "(u, v)" + }, + { + "bbox": [ + 55, + 464, + 296, + 615 + ], + "type": "text", + "content": ", we apply distortion and projection functions based on the given camera parameters:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 119, + 620, + 295, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 620, + 295, + 632 + ], + "spans": [ + { + "bbox": [ + 119, + 620, + 295, + 632 + ], + "type": "interline_equation", + "content": "\\left(x _ {d}, y _ {d}\\right) = f _ {d} (\\bar {x}, \\bar {y}, \\cos c, D _ {c}) \\tag {4}", + "image_path": "eb4835248b5b228ddb2e727a8d76fd68a6879a9a809f5559e579c582902e0484.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 128, + 635, + 295, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 635, + 295, + 647 + ], + "spans": [ + { + "bbox": [ + 128, + 635, + 295, + 647 + ], + "type": "interline_equation", + "content": "(u, v) = f _ {p} \\left(x _ {d}, y _ {d}, K _ {c}\\right) \\tag {5}", + "image_path": "d8f4332debd66bdaa2c577c197b4ab60c9c3bfeacf0e3cae478e26aec627aa61.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "f_{d}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " is the distortion function with distortion parameters " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "D_{c}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "f_{p}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " is the projection function with intrinsic parameters " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "K_{c}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": ". If the input image has no distortion, projection function is directly applied to " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "(x_{t}, y_{t})" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": ". Details on applying distortion models are included in Supplemental Sec. 8." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 392, + 555, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 555, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 555, + 489 + ], + "type": "text", + "content": "As shown in Fig. 5, with uniformly sampled grid points within the target ERP patch, each grid point can be mapped directly to a corresponding location in the input image. This mapping facilitates efficient transformation of the captured image into an ERP patch via grid sampling. Essentially, each grid point in the ERP patch maps to a specific floating-point position in the input image, and its value is obtained by interpolating from the neighboring pixel values." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 492, + 556, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 556, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 556, + 636 + ], + "type": "text", + "content": "This ERP conversion enables a powerful training pipeline when the latitude of the tangent plane center " + }, + { + "bbox": [ + 313, + 492, + 556, + 636 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 313, + 492, + 556, + 636 + ], + "type": "text", + "content": " is defined by the camera's pitch angle in training. When camera orientation is available or can be estimated [22], perspective data can be projected to various latitudes in the ERP space, enabling the simulation of regions uniquely visible from large-FoV cameras, as shown in Fig. 5, and Supplemental Fig. 7. This pitch-aware conversion is crucial for improving the generalization of trained models to previously unobserved large-FoV data, as demonstrated in Sec. 5.3, because neural networks alone have limited capacity to generalize to extrapolated data spaces [51]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "Another notable advantage is the seamless ability to perform online augmentation efficiently in the ERP space. For datasets with limited pitch variation [12, 15, 19, 61], a unique pitch augmentation can be efficiently applied by adding noise to " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": ", generating ERP patches with varying shapes, as shown in Fig. 4. In addition, common augmenta" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26999" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 83, + 287, + 187 + ], + "blocks": [ + { + "bbox": [ + 116, + 70, + 244, + 80 + ], + "lines": [ + { + "bbox": [ + 116, + 70, + 244, + 80 + ], + "spans": [ + { + "bbox": [ + 116, + 70, + 244, + 80 + ], + "type": "text", + "content": "Grid Sampling via Gnomonic Geometry" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 65, + 83, + 287, + 187 + ], + "lines": [ + { + "bbox": [ + 65, + 83, + 287, + 187 + ], + "spans": [ + { + "bbox": [ + 65, + 83, + 287, + 187 + ], + "type": "image", + "image_path": "bf161515b70df72a299dee603fdf820daa98320baa68833764ef08ccf70ac55b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 197, + 296, + 307 + ], + "lines": [ + { + "bbox": [ + 55, + 197, + 296, + 307 + ], + "spans": [ + { + "bbox": [ + 55, + 197, + 296, + 307 + ], + "type": "text", + "content": "Figure 5. Pitch-Aware ERP Conversion and FoV Alignment. Top: Grid Sampling is applied for an efficient Image-to-ERP conversion. Each ERP grid sample's corresponding location in the input image is computed using gnomonic geometry and specific camera projection parameters. Given the patch center latitude " + }, + { + "bbox": [ + 55, + 197, + 296, + 307 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 197, + 296, + 307 + ], + "type": "text", + "content": " determined by the camera's pitch angle, it makes the converted patch to represent high-distortion regions in the ERP space. Bottom: The FoV-Align process normalizes diverse-FoV ERP patches (shown in red and green) to match the height of a single predefined ERP patch (outlined in blue), ensuring efficient training." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 315, + 296, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 315, + 296, + 352 + ], + "spans": [ + { + "bbox": [ + 55, + 315, + 296, + 352 + ], + "type": "text", + "content": "tions, such as scaling, rotation, and translation—commonly applied to perspective images—can be directly applied to the normalized image coordinates " + }, + { + "bbox": [ + 55, + 315, + 296, + 352 + ], + "type": "inline_equation", + "content": "(x_{t},y_{t})" + }, + { + "bbox": [ + 55, + 315, + 296, + 352 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 123, + 357, + 295, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 357, + 295, + 385 + ], + "spans": [ + { + "bbox": [ + 123, + 357, + 295, + 385 + ], + "type": "interline_equation", + "content": "\\left[ \\begin{array}{l} x _ {t} ^ {\\prime} \\\\ y _ {t} ^ {\\prime} \\end{array} \\right] = s _ {\\sigma} \\left[ \\begin{array}{l l} R _ {\\sigma} & T _ {\\sigma} \\end{array} \\right] \\left[ \\begin{array}{l} x _ {t} \\\\ y _ {t} \\end{array} \\right] \\tag {6}", + "image_path": "7494e4524ad2634d1a77fc6dd300699f3bfe782926aba1182e5c6047ecd40827.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "type": "inline_equation", + "content": "s_{\\sigma}" + }, + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "type": "text", + "content": " is a scale factor, " + }, + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "type": "inline_equation", + "content": "R_{\\sigma}" + }, + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "type": "text", + "content": " is 2D rotation matrix, and " + }, + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "type": "inline_equation", + "content": "T_{\\sigma}" + }, + { + "bbox": [ + 55, + 389, + 296, + 426 + ], + "type": "text", + "content": " is a 2D translation vector corresponding to the applied augmentations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 431, + 151, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 431, + 151, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 431, + 151, + 445 + ], + "type": "text", + "content": "4.2. FoV Alignment" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 450, + 295, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 295, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 295, + 581 + ], + "type": "text", + "content": "When training data include a wide range of camera FoVs within perspective images, such as in the HM3D [35] dataset produced by OmniData [8], the corresponding ERP regions can vary significantly in size, as shown in Fig. 5. There is no single crop size that can consistently capture most content information for certain images without wasting substantial computation on background padding for others. This creates a dilemma in prioritizing between training efficiency and richness of information, and it can also reduce training quality when samples exhibit drastically different content-to-background ratios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": "To address this challenge, we introduce a simple yet effective FoV Alignment operation that adjusts the FoV of each input image to match the predetermined crop area FoV. Specifically, this process applies a specific scaling augmentation, as described in Sec. 4.1 and Eq. 6, specifically " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{Fov}_e = \\frac{H_e\\pi}{H_E}" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "s_\\sigma = \\frac{\\mathrm{Fov}_c}{\\mathrm{Fov}_e}" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{Fov}_c" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " is derived from actual camera parameters, and " + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{Fov}_e" + }, + { + "bbox": [ + 55, + 582, + 296, + 714 + ], + "type": "text", + "content": " is ERP patch's vertical FoV. As illustrated in Fig. 5, this approach allows a single predefined ERP patch size to maximize the inclusion of relevant content and minimize computational waste on background, making it ideal for an efficient training pipeline." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 72, + 462, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 462, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 462, + 85 + ], + "type": "text", + "content": "4.3. Multi-Resolution Training" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 91, + 553, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 162 + ], + "type": "text", + "content": "Training ERP patches and testing images may prefer inconsistent resolutions for various reasons, e.g. drastically different aspect ratio, edge device limitation. When testing resolutions differ from the training patch size, model performance can degrade significantly, particularly with attention modules that aggregate different numbers of image tokens." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 163, + 554, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 554, + 234 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 554, + 234 + ], + "type": "text", + "content": "To address this issue, we adopt a multi-resolution training scheme. As illustrated in Fig. 4, each ERP patch is resized to two additional lower resolutions (typically 0.7 and 0.4 of the original) to incorporate varied image resolutions in training. The training feeds the model three batches of images at different resolutions and sums the losses." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 245, + 395, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 245, + 395, + 258 + ], + "spans": [ + { + "bbox": [ + 314, + 245, + 395, + 258 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 264, + 430, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 264, + 430, + 277 + ], + "spans": [ + { + "bbox": [ + 314, + 264, + 430, + 277 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 282, + 555, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 282, + 555, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 282, + 555, + 390 + ], + "type": "text", + "content": "In-Domain Training Datasets. For indoor experiments, we use Habitat-Matterport 3D (HM3D) [35], Taskonomy [61], and Hypersim [39], totaling 670K perspective images with distinct characteristics. To streamline training, we use the first 50 scenes from HM3D and Taskonomy (tiny versions provided by OmniData [8]). For outdoor data, we use DDAD [15] and LYFT [19], totaling 130K images. Table 1 summarizes the datasets in use, showing varying distributions in FoV, pitch angles, sources, and image quality." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 390, + 554, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 390, + 554, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 390, + 554, + 498 + ], + "type": "text", + "content": "Zero-Shot Testing Datasets. We evaluate DAC on two " + }, + { + "bbox": [ + 313, + 390, + 554, + 498 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 313, + 390, + 554, + 498 + ], + "type": "text", + "content": " datasets—Matterport3D [5] and Pano3DGV2 [2]—and two fisheye datasets—ScanNet++ [56] and KITTI360 [27]—all featuring larger FoVs than perspective images. Our primary experiments focus on these datasets to assess zero-shot generalization to large FoV cameras. Additional evaluations on NYUv2 [30] and KITTI [12] are provided in the supplementary material, demonstrating DAC's performance on perspective data relative to SoTA methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 498, + 554, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 594 + ], + "type": "text", + "content": "Evaluation Details. We assess DAC's generalization to large FoV cameras across both indoor and outdoor scenes, training separate models for each without data mixing to simplify training. For fair comparison, competing models are either re-trained with the same data splits or use their largest versions trained on extensive datasets. Evaluations are conducted using metric depth metrics: " + }, + { + "bbox": [ + 313, + 498, + 554, + 594 + ], + "type": "inline_equation", + "content": "\\delta_1\\uparrow ,\\delta_2\\uparrow ,\\delta_3\\uparrow" + }, + { + "bbox": [ + 313, + 498, + 554, + 594 + ], + "type": "text", + "content": " Abs Rel↓, RMSE↓, and log10↓." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 594, + 553, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 594, + 553, + 605 + ], + "spans": [ + { + "bbox": [ + 314, + 594, + 553, + 605 + ], + "type": "text", + "content": "Baselines. We compare DAC with the following baselines:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 606, + 553, + 713 + ], + "type": "list", + "angle": 0, + "index": 21, + "blocks": [ + { + "bbox": [ + 315, + 606, + 553, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 606, + 553, + 640 + ], + "spans": [ + { + "bbox": [ + 315, + 606, + 553, + 640 + ], + "type": "text", + "content": "- Metric3Dv2 [20]: A SoTA foundation model in zero-shot metric depth estimation, built upon perspective canonical camera model to standardize datasets." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 315, + 642, + 553, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 642, + 553, + 689 + ], + "spans": [ + { + "bbox": [ + 315, + 642, + 553, + 689 + ], + "type": "text", + "content": "- UniDepth [33]: A more recent SoTA foundation depth model leveraging network designs to handle diverse camera parameters. We test its ability to handle large FoV cameras not included in training." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 315, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 689, + 553, + 713 + ], + "type": "text", + "content": "- iDisc [32]: Selected as a network baseline due to its use of self-attention and cross-attention modules in a straight-" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27000" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 99, + 563, + 159 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": "Table 1. Overview of Datasets. This table summarizes the training and testing datasets used in this work. The training datasets span a range of FoVs, pitch angles, and image quality, each potentially impacting performance on different test datasets in varying degrees." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 99, + 563, + 159 + ], + "lines": [ + { + "bbox": [ + 56, + 99, + 563, + 159 + ], + "spans": [ + { + "bbox": [ + 56, + 99, + 563, + 159 + ], + "type": "table", + "html": "
Train Dataset# ImagesScenexFoV (deg.)# CamsPitch (deg.)SourceImg Qual.Test DatasetCam TypexFoV (deg.)Scene
HM3D-tiny [35]310KIndoor36° - 124°10K+3σ = 75°ReconLowMatterport3D [5]ERP360°Indoor
Taskonomy-tiny [61]300KIndoor45° - 75°10K+3σ = 24°RealHighPano3D-GV2 [2]ERP360°Indoor
Hypersim [39]54KIndoor60°13σ = 60°SimHigh+ScanNet++ [56]Fisheye150°Indoor
DDAD [15]80KOutdoor45° - 60°36+3σ ~ 10°RealHighKITTI360 [27]Fisheye180°Outdoor
LYFT [19]50KOutdoor20° - 60°6+3σ ~ 10°RealHigh
", + "image_path": "656e4e3d269ab98eb35dfe2a601dbddc449625739640a88f0088e527a6b50559.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 99, + 194, + 512, + 399 + ], + "blocks": [ + { + "bbox": [ + 55, + 178, + 555, + 190 + ], + "lines": [ + { + "bbox": [ + 55, + 178, + 555, + 190 + ], + "spans": [ + { + "bbox": [ + 55, + 178, + 555, + 190 + ], + "type": "text", + "content": "Table 2. Zero-Shot Test on " + }, + { + "bbox": [ + 55, + 178, + 555, + 190 + ], + "type": "inline_equation", + "content": "{360}^{ \\circ }" + }, + { + "bbox": [ + 55, + 178, + 555, + 190 + ], + "type": "text", + "content": " and Fisheye Datasets. DAC is compared with SoTA metric depth models across four large-ForV datasets." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 99, + 194, + 512, + 399 + ], + "lines": [ + { + "bbox": [ + 99, + 194, + 512, + 399 + ], + "spans": [ + { + "bbox": [ + 99, + 194, + 512, + 399 + ], + "type": "table", + "html": "
Test DatasetMethodsTrain DatasetBackboneδ1↑δ2↑δ3↑Abs Rel↓RMSE↓log10↓
Matterport3D [5]UniDepth [33]Mix 3MViT-L [7]0.25760.51140.70910.76481.38270.2208
Metric3Dv2 [20]Mix 16MDinov2 [31]0.43810.73110.87350.29240.88420.1546
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.42870.78540.93330.27880.89610.1352
iDisc [32]Indoor 670KResnet101 [18]0.52870.82600.93980.27570.77710.1147
DAC (Ours)Indoor 670KResnet101 [18]0.77270.95620.98220.1560.61850.0707
Pano3D-GV2 [2]UniDepth [33]Mix 3MViT-L [7]0.24690.49770.70840.78921.26810.2231
Metric3Dv2 [20]Mix 16MDinov2 [31]0.40400.69290.84990.30700.85490.1664
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.50600.81760.93600.26080.72480.1201
iDisc [32]Indoor 670KResnet101 [18]0.56290.82220.93320.26570.64460.1122
DAC (Ours)Indoor 670KResnet101 [18]0.81150.95490.98600.13870.47800.0623
ScanNet++ [56]UniDepth [33]Mix 3MViT-L [7]0.36380.64610.83580.49711.16590.1648
Metric3Dv2 [20]Mix 16MDinov2 [31]0.53600.82180.93500.22290.89500.1177
Metric3Dv2 [20]Indoor 670KDinov2 [31]0.64890.89200.95580.19150.97790.0938
iDisc [32]Indoor 670KResnet101 [18]0.61500.87800.96170.27120.48350.0972
DAC (Ours)Indoor 670KResnet101 [18]0.85170.96930.99220.13230.30860.0532
KITTI360 [27]UniDepth [33]Mix 3MViT-L [7]0.48100.83970.94060.29396.56420.1221
Metric3Dv2 [20]Mix 16MDinov2 [31]0.71590.93230.97710.19974.57690.0811
Metric3Dv2 [20]Outdoor 130KDinov2 [31]0.76750.93700.97560.15214.66100.0723
iDisc [32]Outdoor 130KResnet101 [18]0.78330.93840.97530.15984.91220.0704
DAC (Ours)Outdoor 130KResnet101 [18]0.78580.93880.97750.15594.36140.0684
", + "image_path": "0880769ad30e5eb8ef19156cb7415bb7b4aed7e95a875121490b127ab3bef850.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 63, + 417, + 295, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 417, + 295, + 464 + ], + "spans": [ + { + "bbox": [ + 63, + 417, + 295, + 464 + ], + "type": "text", + "content": "forward yet effective network, and strong in-domain performance. As iDisc alone does not handle mixed camera parameters, we train it with Metric3Dv2 [20], and compare it to the same network trained with ours." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "text", + "content": "Implementation Details. In the DAC training pipeline, we set the full ERP height to " + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "inline_equation", + "content": "H_{\\mathrm{erp}} = 1400" + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "text", + "content": " pixels, with an ERP patch size of " + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "inline_equation", + "content": "500 \\times 700" + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "text", + "content": " pixels for both indoor and outdoor models. We use " + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "inline_equation", + "content": "10^{\\circ}" + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "text", + "content": " latitude augmentations for both and additionally " + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "inline_equation", + "content": "10^{\\circ}" + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "text", + "content": " rotation augmentation for indoor. When training the iDisc [32] model using the Metric3D [57] pipeline, we use canonical focal lengths of " + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{cano}} = 519" + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "text", + "content": " (NYU dataset [30]) for indoor models and " + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{cano}} = 721" + }, + { + "bbox": [ + 55, + 466, + 295, + 574 + ], + "type": "text", + "content": " (KITTI dataset [12]) for outdoor models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "text", + "content": "To test perspective models on ERP and fisheye images, specific adjustments are required. For " + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "text", + "content": " (ERP) images, which lack a defined focal length, we calculate a virtual focal length " + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{virtual}}" + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "text", + "content": " based on pixels per latitude degree: " + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "inline_equation", + "content": "\\frac{1}{f_{\\mathrm{virtual}}} = \\tan \\left(\\frac{\\pi}{H_{\\mathrm{ep}}}\\right)" + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "text", + "content": ", scaling the predicted depth with " + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "inline_equation", + "content": "\\frac{f_{\\mathrm{cano}}}{f_{\\mathrm{virtual}}}" + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "text", + "content": " for ground-truth alignment. For fisheye images, aligning " + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{cano}}" + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "text", + "content": " with the post-distortion focal length introduces significant errors, so we first convert fisheye images to ERP space and apply " + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "inline_equation", + "content": "\\frac{f_{\\mathrm{cano}}}{f_{\\mathrm{virtual}}}" + }, + { + "bbox": [ + 55, + 575, + 295, + 690 + ], + "type": "text", + "content": " for metric depth evaluation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 690, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 690, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 690, + 295, + 713 + ], + "type": "text", + "content": "For testing resolution, if the original resolution is less than twice the training resolution, we use it directly; for" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "type": "text", + "content": "larger resolutions, we maintain the aspect ratio and align it with the training resolution. Based on this rule, we evaluate Matterport3D [5] and Pano3D-GV2 [2] at " + }, + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "type": "inline_equation", + "content": "512 \\times 1024" + }, + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "type": "text", + "content": ", ScanNet++ [56] at " + }, + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "type": "inline_equation", + "content": "500 \\times 750" + }, + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "type": "text", + "content": ", and KITTI360 [27] at " + }, + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "type": "inline_equation", + "content": "700 \\times 700" + }, + { + "bbox": [ + 313, + 417, + 555, + 501 + ], + "type": "text", + "content": ". For competing methods that are not adaptable to inconsistent resolutions compared to training, we report the higher score obtained from the two settings to ensure fairness." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 502, + 556, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 556, + 598 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 556, + 598 + ], + "type": "text", + "content": "In experiments, ResNet101 [18]-backbone models are trained for 60k iterations with a batch size of 48, while Swin-L [28] and DINOv2 [31] models are trained for 120k iterations with a batch size of 48. Finally, to support all FoV types, depth is represented as Euclidean Distance from the camera center rather than Z-buffer format, as the latter is incompatible with spherical projections and would yield inaccurate low depth values for fisheye or ERP images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 609, + 465, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 609, + 465, + 623 + ], + "spans": [ + { + "bbox": [ + 313, + 609, + 465, + 623 + ], + "type": "text", + "content": "5.2. Comparison with the SoTA" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": "In this section, we compare DAC with primary baselines in zero-shot generalization tests on large FoV datasets, with quantitative results reported in Table 2, and qualitative results shown in Fig. 6. In indoor experiments, DAC significantly outperforms pre-trained models UniDepth [33] and Metric3Dv2 [20], even when using a lighter ResNet101 [18] backbone and a much smaller training dataset. DAC" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27001" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "achieves superior performance across both " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " datasets and the fisheye dataset ScanNet++ [56]. Compared to the iDisc [32] network trained with the Metric3Dv2 pipeline, DAC shows substantial improvements across all metrics on all datasets. Notably, DAC improves the next-best method by nearly " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " in the most differentiating metric, " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\delta_{1}" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 294, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 294, + 263 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 294, + 263 + ], + "type": "text", + "content": "In outdoor tests, DAC significantly outperforms Metric3Dv2 [57] and UniDepth [33], even with much larger backbones. However, it achieves only marginal improvements over iDisc [32] under the same network configuration, with less pronounced gains compared to indoor settings. This is likely due to the limited camera pitch variance in the outdoor training data (Table 1), reducing the ability to simulate highly distorted regions. Moreover, KITTI360 [27] LiDAR points are concentrated in less distorted areas (Fig. 6), making the evaluation less distinctive." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 264, + 294, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 264, + 294, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 264, + 294, + 335 + ], + "type": "text", + "content": "Particularly, a notable observation is that while UniDepth [33] utilizes a network-based spherical conversion, it struggles with large FoV cameras, exposing the limitations of deep learning in extrapolated domains [51]. In contrast, DAC's success underscores the effectiveness of our geometry-based training pipeline." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 335, + 294, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 335, + 294, + 383 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 294, + 383 + ], + "type": "text", + "content": "Additional results of DAC models using SwinL [28] backbones are provided in Supplemental Table 5. These models outperform their ResNet101 [18] counterparts in most cases, except on the " + }, + { + "bbox": [ + 55, + 335, + 294, + 383 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 335, + 294, + 383 + ], + "type": "text", + "content": " datasets." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 63, + 464, + 288, + 628 + ], + "blocks": [ + { + "bbox": [ + 55, + 393, + 294, + 460 + ], + "lines": [ + { + "bbox": [ + 55, + 393, + 294, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 294, + 460 + ], + "type": "text", + "content": "Table 3. Impact of Key Components and Network. We conduct the main ablation study on indoor datasets by training with HM3D [35] and performing zero-shot testing on Pano3D-GV2 [2] and ScanNet++ [56]. We compare the performance of the DAC framework with specific components removed, as well as different network architectures trained under the Metric3D [57] pipeline." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 464, + 288, + 628 + ], + "lines": [ + { + "bbox": [ + 63, + 464, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 63, + 464, + 288, + 628 + ], + "type": "table", + "html": "
Test DatasetMethodsδ1↑δ2↑A.Rel↓
Pano3D-GV2 [2]Metric3Dv2 [20]0.56230.83410.2479
iDisc-cnn [32]0.30260.55650.3548
iDisc [32]0.41300.68440.3043
DAC (Ours)0.72510.92540.1729
w\\o Pitch-Aware ERP0.49110.79040.2422
w\\o Pitch Aug 10°0.69120.93110.188
w\\o FoV Align0.40750.75850.2610
w\\o Multi-Reso0.51280.77840.2437
ScanNet++ [56]Metric3Dv2 [20]0.45690.74630.2818
iDisc-cnn [32]0.46390.76530.3045
iDisc [32]0.53010.80480.3237
DAC (Ours)0.65390.90830.1951
w\\o Pitch-Aware ERP0.47110.80680.2508
w\\o Pitch Aug 10°0.67410.90660.1914
w\\o FoV Align0.54280.86440.2200
w\\o Multi-Reso0.55040.84640.2231
", + "image_path": "5f2ec13ffc3c2be9eb6bb133e210fe8c9fe5c567f6c7cdadbdf95b314833c5eb.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 647, + 149, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 149, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 149, + 659 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 294, + 713 + ], + "type": "text", + "content": "Key Components and Network Architecture. We evaluate the effect of the FoV Align and Multi-Reso Training components by removing each individually, while keeping the rest of the DAC framework unchanged. This ablation" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 322, + 130, + 549, + 297 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 553, + 126 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 553, + 126 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 553, + 126 + ], + "type": "text", + "content": "Table 4. Impact of Train Dataset. Models are trained separately on each training dataset and evaluated in zero-shot tests on " + }, + { + "bbox": [ + 313, + 71, + 553, + 126 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 313, + 71, + 553, + 126 + ], + "type": "text", + "content": " and fisheye datasets. Due to the unique characteristics of each training dataset, their contributions and importance to generalization across different testing datasets vary." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 130, + 549, + 297 + ], + "lines": [ + { + "bbox": [ + 322, + 130, + 549, + 297 + ], + "spans": [ + { + "bbox": [ + 322, + 130, + 549, + 297 + ], + "type": "table", + "html": "
Test DatasetsTrain DatasetMethodsδ1↑A.Rel↓
Pano3D-GV2 [2]HM3D-tiny [35]Metric3Dv2 [20]0.56230.2479
iDisc [32]0.41300.3043
DAC (Ours)0.72510.1729
Taskonomy-tiny [61]Metric3Dv2 [20]0.37850.2959
iDisc [32]0.38880.4076
DAC (Ours)0.64110.1972
Hypersim [39]Metric3Dv2 [20]0.30850.5583
iDisc [32]0.33720.3288
DAC (Ours)0.52080.1792
ScanNet++ [56]HM3D-tiny [35]Metric3Dv2 [20]0.45690.2818
iDisc [32]0.53010.3237
DAC (Ours)0.65390.1951
Taskonomy-tiny [61]Metric3Dv2 [20]0.63180.2148
iDisc [32]0.67430.1977
DAC (Ours)0.79810.1447
Hypersim [39]Metric3Dv2 [20]0.50500.2269
iDisc [32]0.66560.2213
DAC (Ours)0.74780.1762
", + "image_path": "2ded7b0f56317789a40f5adcd7485cbd89fab74a109c53413253109f714608b5.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 316, + 553, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 553, + 424 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 553, + 424 + ], + "type": "text", + "content": "is conducted on the challenging HM3D-tiny [35] indoor dataset, which includes varied camera FoVs, pitch angles, and lower-quality images from reconstructed scenes. We also test the impact of removing attention modules from iDisc [32] and compare to Metric3Dv2 [20] to isolate the influence of the iDisc architecture. Both iDisc-based methods and DAC use ResNet101 backbones, while Metric3Dv2 uses Dinov2. Table 3 provides a summary; full metrics and Matterport3D [5] results are in the Supplemental Table 6." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 425, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 425, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 425, + 554, + 544 + ], + "type": "text", + "content": "Table 3 highlights the pivotal role of pitch-aware ERP conversion in generalizing perspective-trained models to large FoV datasets by effectively simulating high-distortion regions uniquely observed in large FoV images (Fig. 7). This approach turns the wide pitch angle variance in datasets like HM3D [35] into an advantage. While additional pitch augmentation does not appear essential when the training dataset like HM3D intricately spans a large range of pitch angle. However, its effectiveness varies across datasets, as detailed in Supplemental Table 6." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "text", + "content": "Results in Table 3 also show that removing FoV Align or Multi-Reso Training significantly reduces DAC performance, particularly for zero-shot generalization on " + }, + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "text", + "content": " images. Compared to the iDisc network trained with the Metric3D pipeline, DAC achieves notable improvements for large FoV cameras, with attention modules in iDisc proving effective for large FoV test data. Although Metric3Dv2 uses a heavier backbone, it shows limited zero-shot generalization on large FoV images without DAC. More comprehensive results can be found both in Supplemental Table 6." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "Impact of Training Dataset. Each dataset has unique characteristics (Table 1). To evaluate their impact on generalization to large FoV data, we trained models separately on HM3D-tiny, Taskonomy-tiny [61], and Hypersim [39], then" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27002" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 69, + 541, + 469 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 541, + 469 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 541, + 469 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 541, + 469 + ], + "type": "image", + "image_path": "d8a91233206937f0c25f40a96afb7676773b84c426efe09874af7dd342c79295.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 477, + 555, + 513 + ], + "lines": [ + { + "bbox": [ + 55, + 477, + 555, + 513 + ], + "spans": [ + { + "bbox": [ + 55, + 477, + 555, + 513 + ], + "type": "text", + "content": "Figure 6. Zero-Shot Qualitative Results. For each dataset, an example is presented in two consecutive rows. The left column shows the original image and Ground-Truth depth map, followed by results from various methods. For each method, the top row displays the A.Rel map " + }, + { + "bbox": [ + 55, + 477, + 555, + 513 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 55, + 477, + 555, + 513 + ], + "type": "text", + "content": " and the bottom row shows the predicted depth map. The color range for depth and A.Rel maps is indicated in the last column." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 532, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 532, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 295, + 568 + ], + "type": "text", + "content": "tested them in zero-shot mode on indoor large FoV datasets. Results are summarized in Table 4, with full results in Supplemental Table 7." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 574, + 295, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 574, + 295, + 660 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 295, + 660 + ], + "type": "text", + "content": "For Pano3D-GV2 [2], broader FoV and pitch angle coverage in HM3D training improve generalization across all methods, despite HM3D's lower quality due to rendering artifacts. For fisheye data in ScanNet++ [56], FoV diversity appears less crucial, as the single-camera Hypersim dataset, despite limited training data, outperforms HM3D, indicating that image quality plays a key role in ScanNet++ test." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": "Comparing individually trained models with results from mixed training in Table 2 shows that DAC effectively leverages the synergy of diverse datasets, significantly enhancing generalization to large FoV datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 531, + 388, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 531, + 388, + 544 + ], + "spans": [ + { + "bbox": [ + 314, + 531, + 388, + 544 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "text", + "content": "We introduced the Depth Any Camera (DAC) framework for zero-shot metric depth estimation across diverse camera types, including perspective, fisheye, and " + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 313, + 557, + 555, + 715 + ], + "type": "text", + "content": " cameras. By leveraging a highly effective pitch-aware Image-to-ERP transformation, FoV alignment, and multi-resolution training, DAC addresses the challenges posed by varying FoVs and resolution inconsistencies and enables robust generalization on large FoV datasets. Our results demonstrate that DAC significantly outperforms state-of-the-art methods and adapts seamlessly to different backbone networks. In practice, DAC ensures that every piece of previously collected 3D data remains valuable, regardless of the camera type used in new applications." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "27003" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 156 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 156 + ], + "type": "text", + "content": "[1] Hao Ai, Zidong Cao, Yan-Pei Cao, Ying Shan, and Lin Wang. 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Deformable convnets V2: more deformable, better results. 2019. 3" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "27006" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Depth-Guided Bundle Sampling for Efficient Generalizable Neural Radiance Field Reconstruction/8a97af03-ecf0-4b44-846e-a010c9f066c8_content_list.json b/2025/Depth-Guided Bundle Sampling for Efficient Generalizable Neural Radiance Field Reconstruction/8a97af03-ecf0-4b44-846e-a010c9f066c8_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b7a35db2de24fb2884b4233cfbd66d2943e61a1e --- /dev/null +++ b/2025/Depth-Guided Bundle Sampling for Efficient Generalizable Neural Radiance Field Reconstruction/8a97af03-ecf0-4b44-846e-a010c9f066c8_content_list.json @@ -0,0 +1,1453 @@ +[ + { + "type": "text", + "text": "Depth-Guided Bundle Sampling for Efficient Generalizable Neural Radiance Field Reconstruction*", + "text_level": 1, + "bbox": [ + 112, + 107, + 883, + 150 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Li Fang $^{1}$ Hao Zhu $^{2}$ Longlong Chen $^{1}$ Fei Hu $^{1\\dagger}$ Long Ye $^{1}$ Zhan Ma $^{2}$", + "bbox": [ + 186, + 180, + 807, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Key Laboratory of Media Audio and Video (Communication University of China), Ministry of Education, Beijing 100024, China", + "bbox": [ + 169, + 199, + 826, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China", + "bbox": [ + 135, + 234, + 859, + 253 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{lifang8902, chenll, hufei, yelong}@cuc.edu.cn {zhuhao/photo, mazhan}@nju.edu.cn", + "bbox": [ + 138, + 253, + 852, + 270 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 305, + 326, + 320 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advancements in generalizable novel view synthesis have achieved impressive quality through interpolation between nearby views. However, rendering high-resolution images remains computationally intensive due to the need for dense sampling of all rays. Recognizing that natural scenes are typically piecewise smooth and sampling all rays is often redundant, we propose a novel depth-guided bundle sampling strategy to accelerate rendering. By grouping adjacent rays into a bundle and sampling them collectively, a shared representation is generated for decoding all rays within the bundle. To further optimize efficiency, our adaptive sampling strategy dynamically allocates samples based on depth confidence, concentrating more samples in complex regions while reducing them in smoother areas. When applied to ENeRF, our method achieves up to a 1.27 dB PSNR improvement and a $47\\%$ increase in FPS on the DTU dataset. Extensive experiments on synthetic and real-world datasets demonstrate state-of-the-art rendering quality and up to $2\\times$ faster rendering compared to existing generalizable methods. Code is available at https://github.com/KLMAV-CUC/GDB-NeRF.", + "bbox": [ + 89, + 335, + 483, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 681, + 220, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Novel view synthesis aims to generate photorealistic images from new perspectives using a sparse set of input images. The advent of Neural Radiance Field (NeRF) [28] and subsequent advancements [34] have significantly improved the quality of view synthesis, garnering substantial interest in both academia and industry. NeRF models scenes as continuous radiance and density fields, producing high-quality images. However, this comes at a cost: NeRF's volume rendering process requires numerous samples per ray, leading", + "bbox": [ + 89, + 705, + 482, + 843 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/035d5169a777617d5c2818f4c9d0d92c197afcc4918193f037b9052383a02201.jpg", + "image_caption": [ + "Figure 1. Rendering Quality (PSNR) vs. Speed (FPS) on the DTU Dataset [1] under 3-view setting. ENeRF+Ours achieves state-of-the-art rendering quality and faster rendering speed, outperforming existing generalizable novel view synthesis methods [8, 10, 22, 24, 40, 43]. Model parameter counts are also provided." + ], + "image_footnote": [], + "bbox": [ + 529, + 306, + 890, + 482 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to significant computational demands and impeding real-time, high-resolution synthesis. Additionally, NeRF models are typically scene-specific, requiring lengthy training for each new scene.", + "bbox": [ + 511, + 595, + 906, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent efforts to improve NeRF efficiency have focused on compact data structures and lightweight MLP decoders to store radiance fields, significantly reducing both training and rendering times for scene-specific NeRFs [11, 13, 14, 29, 42]. Techniques like baking and empty space skipping have also contributed to these improvements. However, these methods require per-scene optimization, limiting their ability to generalize to novel scenes. Generalizable NeRFs address this limitation by predicting radiance fields from multi-view images, enabling novel view synthesis for previously unseen scenes [8, 12, 16, 21, 22, 25, 26, 31, 36, 37, 39, 40, 43, 45]. Although promising, generalizable methods often face slower rendering speeds, as scene-specific optimizations are incompatible. While some approaches attempt to reduce per-ray sampling [22, 30], real-time rendering remains challenging.", + "bbox": [ + 511, + 657, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work is supported by National Key R&D Program of China under Grant No. 2021YFF0900701, and the National Natural Science Foundation of China under Grant No. 62001432.", + "bbox": [ + 89, + 851, + 482, + 886 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 111, + 887, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11217", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The expensive computational cost in NeRF-related methods is primarily due to the need for dense sampling across all pixels. From a plenoptic sampling perspective [5], this full-pixel sampling implicitly assumes high-frequency information is uniform across the scene. However, natural scenes are usually piecewise smooth, with high-frequency details in specific areas like object boundaries and depth discontinuities. Based on this observation, we propose a novel bundle sampling strategy. This method groups adjacent rays and samples them jointly at a global, low sampling rate for smooth regions. In non-smooth areas, high-frequency information is captured by increasing samples along the depth dimension. Furthermore, samples within each bundle are further constrained to a small range using depth maps. As a result, this approach significantly reduces the overall number of samples, greatly improving efficiency.", + "bbox": [ + 89, + 90, + 480, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We integrate this depth-guided bundle sampling strategy into a representative generalizable NeRF, ENeRF [22]. Instead of sampling points along individual rays, our method samples 3D areas along bundles of adjacent rays by casting a cone that encompasses the corresponding pixels. Within this cone, inscribed spheres are sampled and featurized with pre-filtered features extracted from the source views. Through depth-guided adaptive sampling, sampling is constrained to a predicted depth range, with the number of samples adjusted dynamically: in smooth regions with a narrow depth range, fewer samples suffice for accurate reconstruction, while areas with a broader depth range require more samples to capture finer details. This adaptive approach aligns with the plenoptic principle [5], ensuring each sample covers a narrow depth range near surfaces. A bundle representation is then computed via volume rendering and decoded to predict the color of each ray. We also apply this depth-guided bundle sampling strategy to a recent generalizable 3D Gaussian splatting (3D-GS) method [24]. Extensive experiments demonstrate that our method significantly improves the efficiency of base models and achieves synthesis quality comparable to state-of-the-art generalizable models, with significant improvements in rendering speed.", + "bbox": [ + 91, + 335, + 482, + 683 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows:", + "bbox": [ + 109, + 686, + 470, + 700 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel bundle sampling strategy that jointly samples bundles of adjacent rays, significantly reducing the number of samples needed and improving both rendering speed and quality.", + "- We introduce a depth-guided adaptive sampling method that dynamically adjusts the number of samples based on local depth range, achieving over a $50\\%$ increase in rendering speed without sacrificing quality.", + "- We validate our method on both generalizable NeRF and 3D-GS across various datasets. Our method achieves state-of-the-art rendering quality and up to $2 \\times$ faster rendering than existing generalizable NeRFs. It also offers flexibility, allowing adjustments between quality and effi" + ], + "bbox": [ + 91, + 704, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ciency depending on practical requirements.", + "bbox": [ + 527, + 90, + 820, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 121, + 663, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accelerating NeRF. NeRFs represent scenes as continuous color and density fields using neural networks, achieving high-quality view synthesis via volume rendering. Despite their success, NeRFs suffer from high computational demands, slowing training and inference. To address this, recent methods have replaced large neural representations with local sparse feature fields and shallow MLP decoders [9, 23, 29, 33, 44], or spherical harmonics embeddings [9, 13, 17]. Other solutions utilize voxel grids [23], octrees [13], tensor decompositions [9], or 3D Gaussians [18], as well as efficient sampling [14, 20, 22, 30] and image-space convolutions [4, 38], leading to significant speed-ups. However, these improvements remain scene-specific, requiring training for each new scene.", + "bbox": [ + 511, + 147, + 906, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generalizable NeRF. These methods generalize NeRF by encoding features for each 3D point and decoding them into volume density and radiance, akin to image-based rendering through NeRF-like volume rendering techniques [8, 10, 12, 16, 21, 22, 25, 26, 31, 36, 37, 39, 40, 45]. While these methods improve across-scene generalizability, they remain limited by slow optimization and rendering. CG-NeRF [31] predicts coarse radiance fields and depth, refining fine-scale features sampled near the estimated depth. ConvGLR [36] processes all camera rays in a low-resolution latent space, which improves quality in sparse-view synthesis. GeFu [25] improves generalizable NeRFs through geometry-aware reconstruction with Adaptive Cost Aggregation and Consistency-Aware Fusion. Most of these methods lack real-time rendering capability. ENeRF [22] accelerates generalizable NeRFs with depth-guided sampling but uses a fixed number of samples per ray, leading to inefficiency. In contrast, our method adaptively samples ray bundles based on local scene complexity, providing greater flexibility and efficiency.", + "bbox": [ + 511, + 380, + 906, + 681 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generalizable 3D-GS. Recent advancements in generalizable Gaussian splatting methods have significantly enhanced the efficiency of novel view synthesis. These approaches eliminate the need for per-scene optimization by directly regressing Gaussian parameters through a feedforward architecture. PixelSplat [7] tackles scale ambiguity by utilizing a multiview epipolar transformer and scale-aware features to predict pixel-aligned 3D Gaussian primitives, though its design is limited to image pair inputs. GPS-Gaussian [47] extends this approach to stereo matching, incorporating epipolar rectification, disparity estimation, and feature encoding. However, its reliance on ground-truth depth maps restricts its applicability. Splatter Image [35]", + "bbox": [ + 511, + 704, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11218", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "proposes a single-view reconstruction approach based on Gaussian splatting, though its focus on object-centric reconstruction constrains its generalization to unseen scenes. MVSGaussian [24] combines multi-view stereo with a generalizable 3D Gaussian representation for real-time novel view synthesis. However, its single-sample-per-ray strategy necessitates highly accurate depth estimations and hinders further efficiency improvements.", + "bbox": [ + 89, + 90, + 480, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 89, + 223, + 218, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminaries on Generalizable NeRF. Given input multi-view images with intrinsic and extrinsic camera matrices, NeRF constructs the scene's radiance fields using a coordinate-based network. However, optimizing this network for each individual scene is computationally intensive. To address this, generalizable NeRF incorporates an additional geometry-aware feature, $\\pmb{f}_p$ , extracted from the source images and included in the network input:", + "bbox": [ + 89, + 250, + 482, + 369 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {p}, c _ {p} = N N _ {\\theta} \\left(\\boldsymbol {x} _ {p}, \\boldsymbol {d} _ {p}, \\boldsymbol {f} _ {p}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 378, + 482, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\boldsymbol{x}_p$ and $\\boldsymbol{d}_p$ represent the coordinates and viewing direction of the 3D point $p$ , respectively. Here, $\\sigma_p$ and $c_p$ denote the density and color of $p$ , defining the radiance field properties at this point. The coordinate network, $NN_{\\theta}$ , decodes these radiance field attributes. Once the radiance fields for the entire scene are constructed, volume rendering techniques can synthesize the color for a pixel from any desired viewpoint.", + "bbox": [ + 89, + 402, + 482, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For an image of resolution $H \\times W$ , NeRF samples $N$ points along the ray passing through each pixel, leading to a computational complexity of approximately $\\mathcal{O}(HWN)$ . As the number of samples increases, so does the computational burden, posing challenges for rendering efficiency and motivating the need for optimized sampling and rendering strategies.", + "bbox": [ + 89, + 523, + 482, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Plenoptic Sampling Theory. To enhance efficiency, existing generalizable NeRFs aim to reduce the number of samples along each ray by concentrating sampling near scene surfaces [22, 24, 25]. However, these methods do not explore the reduction of the total number of rays required for rendering; instead, they uniformly sample all rays with a fixed number of samples. Some approaches attempt to reduce ray sampling needs through super-resolution techniques, though these are often constrained to specific content types such as faces [6].", + "bbox": [ + 89, + 647, + 482, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Plenoptic sampling theory, introduced in [5], investigates the sampling bounds in light field rendering to determine the minimum angular density required for accurate reconstruction. The theory defines the maximum allowable camera spacing as:", + "bbox": [ + 89, + 797, + 482, + 873 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta t \\leq \\frac {\\operatorname* {m a x} \\left(2 \\Delta v , 1 / B _ {v} ^ {s}\\right)}{f \\cdot h _ {d}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 872, + 482, + 905 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f$ is the focal length, $\\Delta v$ is the spacing between camera rays, $B_v^s$ is the highest texture frequency, and $h_d$ is the disparity range defined as $h_d = \\frac{1}{z_{\\mathrm{min}}} - \\frac{1}{z_{\\mathrm{max}}}$ , with $z_{\\mathrm{min}}$ and $z_{\\mathrm{max}}$ denoting the minimum and maximum scene depths, respectively. Eq. (2) first implies that the ray spacing $\\Delta v$ must satisfy the Nyquist sampling criterion, i.e., $\\Delta v \\leq \\frac{1}{2B_v^s}$ , to avoid aliasing; it then highlights that geometric accuracy affects the sampling rate required for image capture: by decomposing the scene into $D$ depth ranges and sampling the light field in each range separately, the camera sampling interval can be increased by a factor of $D$ .", + "bbox": [ + 511, + 90, + 903, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Considering the relation between light fields and NeRFs [32], plenoptic sampling theory inspires our depth-guided bundle sampling strategy. On the one hand, the piecewise smooth nature of natural scenes means that high-frequency content is localized, with most regions being smooth. This allows for reduced sampling rates in smooth areas by effectively lowering the camera resolution (i.e., increasing $\\Delta v$ ). However, this may cause aliasing in high-frequency regions (e.g., edges, textures, thin structures). On the other hand, given a fixed camera spacing $\\Delta t$ , each sample in NeRF can be regarded as a local light field confined to a small disparity range, $h_d \\leq \\frac{\\max(2\\Delta v, \\frac{1}{B_v^s})}{f \\cdot \\Delta t}$ . For high-frequency regions, they often suffer from inaccurate depth estimation, necessitating more samples to ensure each sample covers a small disparity range. These observations motivate our depth-guided bundle sampling strategy, which adapts the sampling density based on scene complexity.", + "bbox": [ + 511, + 258, + 906, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 511, + 537, + 604, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method is designed to synthesize target views from $V$ nearby source views $\\{I_i\\}_{i=1}^V$ at interactive frame rates, addressing challenges in efficient sampling. The proposed depth-guided bundle sampling strategy includes two main innovations: a novel bundle sampling approach that groups adjacent rays in the target view for joint sampling, and a depth-guided adaptive sampling method that dynamically allocates samples based on depth confidence. This adaptive approach reduces the overall number of samples while maintaining consistency with the plenoptic sampling principles. We apply our method to representative ENeRF [22] and MVSGaussian [24] to demonstrate its effectiveness in generalizable NeRF and 3D-GS, respectively. Fig. 2 presents the architecture of ENeRF+Ours, and a similar architecture is employed in MVSGaussian, where the sample features are also decoded into 3D-GS parameters.", + "bbox": [ + 511, + 564, + 906, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Bundle Sampling", + "text_level": 1, + "bbox": [ + 511, + 816, + 684, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our bundle sampling method improves efficiency by reducing the number of sampled rays. Adjacent rays in the target view are grouped into bundles, modeled as cones, with inscribed spheres sampled within each cone, as illustrated in", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11219", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/08854d534b6547fb2ec48a4acb6399f7408643f0d22e46ad4dde94d4530a55df.jpg", + "image_caption": [ + "Figure 2. Network architecture of the proposed depth-guided bundle sampling strategy on ENeRF [22], denoted as ENeRF+Ours, which consists of four main components: (1) Multi-scale feature extraction; (2) Depth estimation to predict depth range; (3) Depth-guided bundle sampling, where rays are grouped into bundles and sampled adaptively based on predicted depth confidence; and (4) Radiance field prediction, which decodes each bundle's representation into individual ray colors." + ], + "image_footnote": [], + "bbox": [ + 125, + 85, + 890, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 3. This design broadens the angular coverage per sample, effectively reducing the total number of rays required. A similar sphere-based sampling approach is used in [15], where spheres are cast for each ray's cone to achieve anti-aliasing. In contrast, our method casts spheres for a cone of grouped rays, enabling collective sampling across multiple rays rather than treating them individually. However, this expanded coverage inevitably leads to loss of high-frequency details in the rendered image. To mitigate this, we encode each sample with both a joint bundle representation and a ray-specific representation, ensuring efficiency while preserving the necessary level of detail.", + "bbox": [ + 88, + 484, + 485, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1.1 Sphere-based cone sampling", + "text_level": 1, + "bbox": [ + 89, + 691, + 344, + 707 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our method models bundles of rays as cones passing through groups of adjacent pixels in the target view. We begin by casting rays from the camera's projection center $o$ through each pixel center $p_o$ , with ray directions defined as $d_r = p_o - o$ . Points along each ray are parameterized as $x_r = o + t d_r$ , where $t$ is the distance along the ray.", + "bbox": [ + 89, + 715, + 483, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 3(b), for a bundle of $K \\times K$ rays, the corresponding region on the target image plane is modeled as a disk with radius $r_{\\mathrm{tar}} = K \\cdot r_p$ , where $r_p = \\sqrt{\\Delta x \\cdot \\Delta y / \\pi}$ is the radius of a single-pixel disk, and $\\Delta x$ and $\\Delta y$ are the pixel's width and height in world coordinates, derived from camera parameters. The cone $\\mathcal{C}$ is", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "emitted from the camera's projection center along the average direction $\\pmb{d}_{\\mathcal{C}} = \\sum_{\\pmb{r} \\in \\mathcal{C}} \\pmb{d}_{\\pmb{r}} / K^2$ , and intersects the image plane at the disk, with the cone's axis defined as $\\pmb{a}(t) = \\pmb{o} + t \\pmb{d}_{\\mathcal{C}}$ . The cone is sampled using a set of inscribed spheres, $S(\\dot{\\pmb{x}}, \\dot{\\pmb{r}})$ , defined by their centers $\\dot{\\pmb{x}}$ and radii $\\dot{\\pmb{r}}$ as follows:", + "bbox": [ + 511, + 484, + 906, + 575 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\dot {\\boldsymbol {x}} = \\frac {1}{K ^ {2}} \\sum_ {\\boldsymbol {r} \\in \\mathcal {C}} \\boldsymbol {x} _ {\\boldsymbol {r}},\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 583, + 658, + 619 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\dot {r} = \\frac {\\left\\| \\dot {\\boldsymbol {x}} - \\boldsymbol {o} \\right\\| _ {2} \\cdot f \\cdot r _ {\\mathrm {t a r}}}{\\left\\| \\boldsymbol {d} _ {\\mathcal {C}} \\right\\| _ {2} \\cdot \\sqrt {\\left(\\sqrt {\\left\\| \\boldsymbol {d} _ {\\mathcal {C}} \\right\\| _ {2} ^ {2} - f ^ {2}} - r _ {\\mathrm {t a r}}\\right) ^ {2} + f ^ {2}}}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 622, + 906, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given sorted distances $\\{t_n\\}_{n = 1}^V$ , the sphere centers $\\dot{\\pmb{x}}_n$ and radii $\\dot{r}_n$ are computed.", + "bbox": [ + 511, + 691, + 905, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For a target view with resolution $H \\times W$ , the image is divided into $\\frac{H}{K} \\times \\frac{W}{K}$ bundles, each consisting of $K \\times K$ pixels. This reduces the total number of samples by approximately $1 / K^2$ , ensuring efficient angular coverage without sacrificing essential surface detail.", + "bbox": [ + 511, + 722, + 906, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1.2 Multi-view image-based sphere encoding", + "text_level": 1, + "bbox": [ + 511, + 816, + 852, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Each sphere covers a broad angular range, which extends to its feature representation. As shown in Fig. 3(b), we extract features based on the area occupied by each sphere, forming a joint bundle representation. However, this approach may", + "bbox": [ + 511, + 839, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11220", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c18be417532e9edc8b061289f556f86f55d5ac248dfdfad3f048e1584940e2ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 106, + 90, + 477, + 224 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9cd2ae2304267912c9f11f82dca83113c51f9d90dd175e7b29eef4d617a8ce0d.jpg", + "image_caption": [ + "(a) Ray Sampling", + "(b) Bundle Sampling", + "Figure 3. Comparison of ray sampling strategies: (a) Traditional ray sampling, which processes each ray individually; (b) Proposed bundle sampling, which jointly samples neighboring rays to leverage scene coherence." + ], + "image_footnote": [], + "bbox": [ + 106, + 241, + 475, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "omit high-frequency details. To retain fine-grained information from individual rays, we augment the joint bundle representation with a ray-specific representation.", + "bbox": [ + 89, + 505, + 482, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The joint bundle representation is derived from the area occupied by the spheres, necessitating an adjustment of the source view pixel spacing $\\Delta v$ in Eq. (2). Inspired by area-sampling techniques used in scene-specific anti-aliasing NeRFs [2, 3, 15], we incorporate mipmap representations from [15] into a multi-view image-based encoding framework. We extract features $\\{F_i\\}_{i=1}^V$ from source views and convert them into mipmaps $\\{M_i\\}_{i=1}^V$ , creating a hierarchical structure that represents the pre-filtered feature space. The base level $M_i^{l_0}$ is the original feature map $F_i$ , with each subsequent level reducing the spatial resolution by a factor of two. To compute the feature vector $\\{f_{S,i}\\}_{i=1}^V$ for sphere $S(\\dot{x},\\dot{r})$ , we project it onto the $i$ -th source view to create a disc, with its radius $r_{\\mathrm{src}}$ calculated as:", + "bbox": [ + 89, + 551, + 482, + 763 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {\\mathrm {s r c}} = \\frac {\\left\\| \\boldsymbol {d} _ {i} \\right\\| _ {2} ^ {2}}{f \\cdot \\sqrt {\\left(\\frac {\\| \\dot {\\boldsymbol {x}} - \\boldsymbol {o} _ {i} \\| _ {2}}{\\dot {r}}\\right) ^ {2} - 1} + \\sqrt {\\left\\| \\boldsymbol {d} _ {i} \\right\\| _ {2} ^ {2} - f ^ {2}}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 773, + 482, + 828 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{o}_i$ is the camera's projection center of the $i$ -th source view, and $\\| \\pmb{d}_i \\|_2$ is the distance from the projection of $\\dot{\\pmb{x}}$ onto the image plane to $\\pmb{o}_i$ (see Fig. 3(b)). The appropriate mipmap level $l$ corresponding to the sphere is determined", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "using:", + "bbox": [ + 513, + 92, + 558, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nl = \\log_ {2} \\left(\\frac {r _ {\\mathrm {s r c}}}{r _ {p}}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 104, + 906, + 138 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This process aligns the radius $r_{\\mathrm{src}}$ of the sphere's projection with the corresponding feature elements' radius at a specific level $l$ within $M_i^l$ , which is equivalent to adjusting the spacing $\\Delta v$ of the sampling camera. Once the appropriate mipmap level is identified, the feature vector $f_{S,i}$ can be accurately extracted from the mipmap $M_i$ via trilinear interpolation at $(x,y,l)$ .", + "bbox": [ + 511, + 138, + 906, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For ray-specific representation, the 3D points $\\boldsymbol{x}_r$ associated with the sphere $S(\\dot{\\boldsymbol{x}},\\dot{r})$ are projected onto the source views $\\{I_i\\}_{i = 1}^V$ to extract pixel-aligned colors. The extracted colors corresponding to the $K\\times K$ rays within each bundle are concatenated to form the ray-specific representation, denoted as $\\{f_{r,i}\\}_{i = 1}^{V}$ , which captures high-frequency information for the rays as projected onto source views.", + "bbox": [ + 511, + 244, + 905, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By combining the joint bundle representation and ray-specific representation, our approach efficiently encodes the bundle samples while maintaining necessary scene details for accurate reconstruction.", + "bbox": [ + 511, + 351, + 905, + 410 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Depth-guided Adaptive Sampling", + "text_level": 1, + "bbox": [ + 511, + 417, + 805, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further optimize sampling, we restrict it to a predicted depth range, $R$ , estimated based on the depth value and associated confidence interval [22, 24, 25]. According to Eq. (2), for a fixed camera spacing $\\Delta t$ , the disparity range covered by the local light field of each sample must satisfy $h_d \\leq \\frac{\\max(2\\Delta v, 1 / B_v^s)}{f \\cdot \\Delta t}$ , representing the maximum sampling spacing along the depth. Consequently, in smooth regions with a narrow depth range, fewer samples are sufficient for accurate reconstruction, while regions with a larger depth range require additional samples. Our depth-guided adaptive sampling strategy dynamically allocates samples near surfaces, ensuring that each sample covers a narrow depth range. The number of samples per bundle is computed as:", + "bbox": [ + 511, + 441, + 906, + 640 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nN _ {\\mathcal {C}} = \\max \\left(\\operatorname {c e i l} \\left(2 \\cdot \\boldsymbol {R} / \\delta_ {s}\\right), N _ {\\max }\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 645, + 906, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\delta_{s}$ denotes the minimum inter-sample spacing, with a maximum limit of $N_{\\mathrm{max}}$ samples. The depth range is then divided into $N_{C}$ uniform intervals, with sampling performed at the center of each interval. For cases requiring only one sample, the sample is placed at the predicted surface point.", + "bbox": [ + 511, + 667, + 905, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unlike existing depth-guided methods that apply uniform ray sampling with a fixed number of points, our adaptive approach dynamically adjusts the number of samples along the depth according to plenoptic sampling theory, significantly enhancing both efficiency and adaptability.", + "bbox": [ + 511, + 743, + 905, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Radiance Field Prediction", + "text_level": 1, + "bbox": [ + 511, + 825, + 750, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each sampled sphere, we predict the density $\\sigma$ and blending weights $\\{w_i\\}_{i=1}^V$ as follows:", + "bbox": [ + 511, + 848, + 905, + 880 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma , \\left\\{w _ {i} \\right\\} _ {i = 1} ^ {V} = \\operatorname {M L P} \\left(\\left\\{\\boldsymbol {f} _ {\\mathcal {S}, i} \\right\\} _ {i = 1} ^ {V}, \\boldsymbol {f} _ {\\text {v o x e l}}, \\left\\{\\Delta \\boldsymbol {d} _ {i} \\right\\} _ {i = 1} ^ {V}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 883, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11221", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{\\mathrm{voxel}}$ is the voxel-aligned feature extracted from the feature volume (from depth estimation, see Fig. 2) by applying trilinear interpolation at the sphere center $\\dot{x}$ . $\\Delta d_i$ is the concatenation of the norm and direction of $d_i - d_c$ , with $d_i$ as the direction of $\\dot{x}$ in the $i$ -th source view. The network design is adapted from [22]. The blending weights $\\{w_i\\}_{i=1}^V$ combine the features using softmax:", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {f} _ {\\mathcal {S}}, \\boldsymbol {f} _ {\\boldsymbol {r}} \\right\\} = \\sum_ {i = 1} ^ {V} \\frac {\\exp \\left(w _ {i}\\right) \\cdot \\left\\{\\boldsymbol {f} _ {\\mathcal {S} , i} \\boldsymbol {f} _ {\\boldsymbol {r} , i} \\right\\}}{\\sum_ {j = 1} ^ {V} \\exp \\left(w _ {j}\\right)}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 205, + 482, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We employ volume rendering to compute the per-bundle features $\\{\\pmb{F}_{\\mathcal{C}},\\pmb{F}_{\\pmb{r}}\\}$ by accumulating the features $\\{\\pmb{f}_S,\\pmb{f}_r\\} _n$ across the $N_{\\mathcal{C}}$ sampled spheres along the cone $\\mathcal{C}$ :", + "bbox": [ + 89, + 256, + 482, + 301 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {F} _ {\\mathcal {C}}, \\boldsymbol {F} _ {\\boldsymbol {r}} \\right\\} = \\sum_ {n = 1} ^ {N _ {\\mathcal {C}}} \\tau_ {n} \\left(1 - \\exp (- \\sigma_ {n})\\right) \\left\\{\\boldsymbol {f} _ {\\mathcal {S}}, \\boldsymbol {f} _ {\\boldsymbol {r}} \\right\\} _ {n}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 311, + 482, + 352 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\tau_{n}$ is the accumulated volume transmittance from the cone apex to the sphere center, computed as:", + "bbox": [ + 89, + 361, + 482, + 391 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\tau_ {n} = \\exp \\left(- \\sum_ {j = 1} ^ {n - 1} \\sigma_ {j}\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 400, + 480, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Neural renderer: For the target view with spatial dimensions $H \\times W$ , the image is divided into $\\frac{H}{K} \\times \\frac{W}{K}$ non-overlapping bundles, each containing $K \\times K$ rays. Using Eq. (9), we generate a feature map $\\{\\pmb{F}_{\\mathcal{C}}^{i}, \\pmb{F}_{r}^{i}\\}_{i=1}^{\\frac{H}{K} \\times \\frac{W}{K}}$ . Here, $\\pmb{F}_{\\mathcal{C}}^{i}$ represents the aggregated joint bundle representation, which is processed through several residual convolutional blocks and decoded into coarse ray colors via sub-pixel convolution, yielding a coarse RGB map $\\hat{\\pmb{I}}_{c}$ of dimensions $H \\times W \\times 3$ . The second component, $\\pmb{F}_{r}^{i}$ , contains the folded RGB values for individual rays and is unfolded to generate a fine RGB map $\\hat{\\pmb{I}}_{f}$ of dimensions $H \\times W \\times 3$ , preserving high-frequency details. The final high-resolution target view is obtained by summing these two components:", + "bbox": [ + 89, + 450, + 483, + 652 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {I}} _ {\\mathrm {t a r}} = \\hat {\\boldsymbol {I}} _ {c} + \\hat {\\boldsymbol {I}} _ {f}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 232, + 660, + 482, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For application to MVSGaussian [24], the renderer not only outputs the rendered target view image but also produces a feature map, which is subsequently processed to generate 3D-GS parameters following [24].", + "bbox": [ + 89, + 688, + 483, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 762, + 222, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Settings", + "text_level": 1, + "bbox": [ + 89, + 786, + 189, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Following MVSNeRF [8, 22, 24], we train the generalizable model on the DTU training set [1] and evaluate it on the DTU test set. We also perform cross-dataset evaluation on the Real Forward-facing [27] and NeRF Synthetic [28] datasets using the trained model without fin-tuning. These datasets introduce significant variations in", + "bbox": [ + 89, + 809, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "view distribution and scene content compared to the DTU dataset. The quality of the synthesized novel views is measured using the PSNR, SSIM [41], and LPIPS [46] metrics.", + "bbox": [ + 511, + 90, + 905, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We compare our method against several state-of-the-art generalizable NeRF methods [8, 10, 22, 31, 36, 40, 43, 45], as well as the recent generalizable 3D-GS method [24]. We follow the same experimental settings as [8, 22, 24] and borrow some results reported in the respective papers. For additional baselines, such as [39, 43], we evaluate their performance using publicly released models.", + "bbox": [ + 511, + 160, + 906, + 267 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. To verify the effectiveness of the proposed depth-guided bundle sampling, we integrate it with two representative methods, ENeRF [22] and MVS-Gaussian [24], keeping hyperparameters consistent with their original configurations. Both models are trained with the loss function from [24]. We observed that direct training can sometimes result in instability during the initial stages. To address this, we employ a pre-training phase that uniformly samples $N_{\\mathrm{max}}$ spheres within each bundle's depth range for 100 epochs. For the depth-guided adaptive sampling phase, we set $N_{\\mathrm{max}} = 6$ and $\\delta_s$ to 1/64 of the scene depth range, as defined in Eq. (6). For ENeRF+Ours, we evaluate different bundle sizes to assess the effectiveness of bundle sampling, with $2 \\times 2$ and $4 \\times 4$ indicating the bundle size. All models are trained and tested on an RTX A6000 GPU using the Adam optimizer [19].", + "bbox": [ + 511, + 289, + 906, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Results", + "text_level": 1, + "bbox": [ + 511, + 544, + 607, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We report quantitative results on the DTU test set in Tab. 1. Additional results on two other datasets are provided in Tab. 2. Notably, ENeRF [22] and MVSGaussian [24] achieve promising speeds by sampling only 1-2 points per ray, while other methods experience slower inference times due to the large number of samples required for accurate reconstruction. We can see that ENeRF+Ours $(2 \\times 2)$ improves PSNR by 1.27 dB and increases FPS by $47\\%$ compared to original ENeRF on DTU. Additionally, ENeRF+Ours $(4 \\times 4)$ demonstrates better performance with over twice the speed of the original ENeRF. Performance is not significantly impacted by bundle size. For MVSGaussian+Ours, improvements are limited due to fewer sampling points and dependency on additional post-processing network layers; further performance gains may require a more integrated approach. Thanks to our efficient depth-guided bundle sampling strategy, ENeRF+Ours achieves competitive performance compared to state-of-the-art approaches, while also maintaining high inference speeds. The ability to adjust bundle size provides flexibility, allowing our method to balance speed and quality across different practical applications. Qualitative results in Fig. 4 show that ENeRF+Ours", + "bbox": [ + 511, + 568, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11222", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/460897e4fead37569871256dd755fd2a22ddcb0c82a1d48bcd8cd0cdcf2d24f1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methods3-view2-view
PSNR ↑SSIM ↑LPIPS ↓Avg. samples per rayFPS ↑PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [45]19.310.7890.382960.019---
IBRNet [40]26.040.9170.1911280.217---
MVSNeRF [8]26.630.9310.1681280.41624.030.9140.192
ENeRF [22]27.610.9570.089219.525.480.9420.107
MatchNeRF [10]26.910.9340.1591281.0425.030.9190.181
GNT [39]26.390.9230.1561920.0124.320.9030.201
CG-NeRF [31]28.210.9300.17042.56---
MuRF [43]28.760.9610.077800.93425.610.9380.104
ConvGLR [36]31.650.9520.0801280.825---
MVSGaussian [24]28.210.9630.076121.525.780.9470.095
ENeRF+Ours (2 × 2)28.860.9640.0730.4228.626.390.9490.089
ENeRF+Ours (4 × 4)28.210.9570.0880.1043.626.090.9420.105
MVSGaussian+Ours28.400.9620.076123.426.160.9460.093
", + "bbox": [ + 122, + 88, + 874, + 306 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8765f4e712b469a71be871e456055f7aa721a4a655713d558bd4e3dc0cbec46d.jpg", + "table_caption": [ + "Table 1. Quantitative results of generalization on the DTU testset [1] $(512\\times 640)$ . The best result is highlighted in bold, while the second-best is underlined." + ], + "table_footnote": [], + "table_body": "
MethodsSettingsReal Forward-facingNeRF Synthetic
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [45]11.240.4860.6717.390.6580.411
IBRNet [40]21.790.7860.27922.440.8740.195
MVSNeRF [8]21.930.7950.25223.620.8970.176
ENeRF [22]23.630.8430.18226.170.9430.085
MatchNeRF [10]22.430.8050.24423.200.8970.164
GNT [39]3-view22.980.7610.22125.800.9050.104
CG-NeRF [31]23.930.8200.21025.010.9000.190
MuRF [43]23.700.8600.18124.370.8850.117
MVSGaussian [24]24.070.8570.16426.460.9480.071
ENeRF+Ours (2 × 2)24.330.8600.16226.490.9480.075
ENeRF+Ours (4 × 4)23.840.8510.17426.000.9430.083
MVSGaussian+Ours24.150.8580.16526.480.9470.070
MVSNeRF [8]20.220.7630.28720.560.8560.243
ENeRF [22]22.780.8210.19124.830.9310.117
MatchNeRF [10]20.590.7750.27620.570.8640.200
GNT [39]2-view20.910.6830.29323.470.8770.151
MuRF [43]22.550.8200.21822.960.8660.137
MVSGaussian [24]23.110.8340.17525.060.9370.079
ENeRF+Ours (2 × 2)23.060.8240.18625.010.9370.087
ENeRF+Ours (4 × 4)23.060.8260.18724.650.9320.098
MVSGaussian+Ours23.130.8340.17525.100.9370.079
", + "bbox": [ + 187, + 358, + 808, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Cross-dataset evaluation results on Real Forward-facing [27] (640 × 960) and NeRF Synthetic [28] (800 × 640) datasets. The best result is highlighted in bold, while the second-best is underlined.", + "bbox": [ + 89, + 698, + 903, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$(2 \\times 2)$ generates high-quality views with enhanced scene detail and fewer artifacts.", + "bbox": [ + 89, + 753, + 482, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablations and Analysis", + "text_level": 1, + "bbox": [ + 89, + 810, + 303, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct a series of ablation studies to evaluate the effectiveness of our design. For efficiency, we limited our experiments to a 3-view configuration on the DTU dataset, employing bundle sizes of $2 \\times 2$ and $4 \\times 4$ on ENeRF [22].", + "bbox": [ + 89, + 839, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sampling Strategy. A unique aspect of our approach is the sphere-based bundle sampling (see Fig. 3), where we sample features from the mipmap of source view feature maps according to the area occupied by each sampled sphere. As shown in Tab. 3, substituting our sphere-based sampling with a pixel-aligned feature extraction at sphere centers results in a PSNR decrease of $1.2\\mathrm{dB}$ .", + "bbox": [ + 511, + 753, + 906, + 859 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11223", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f247432ca24828e12c1d58bb5f71da5dfea7885e3e569e80ddea573e73b2fbf.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of ENeRF+Ours $(2\\times 2)$ with state-of-the-art methods [10, 22, 24] under 3-view setting. Each image triplet includes: the reconstructed image on the left, a zoomed-in view on the upper right, and the error map on the lower right." + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 885, + 297 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/88359cae4ddcca676a33b1715a3049628f79471349e1a08621ac75d7716b8759.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Sphere SamplingX✓✓✓✓
Adaptive Sampling✓X✓✓✓
Joint Bundle Representation✓✓✓X✓
Ray-Specific Representation✓✓X✓✓
2×2PSNR ↑27.6628.8528.4727.8328.86
SSIM ↑0.9490.9640.9580.9590.964
LPIPS ↓0.0900.0760.0780.9330.073
FPS ↑29.217.029.433.7428.6
4×4PSNR ↑25.9328.0626.7427.4228.21
SSIM ↑0.9400.9540.9280.9550.957
LPIPS ↓0.1050.0950.1120.0990.088
FPS ↑44.229.145.349.643.6
", + "bbox": [ + 93, + 359, + 480, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablations. The best result is highlighted in bold.", + "bbox": [ + 114, + 599, + 457, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Depth-Guided Strategy. The proposed depth-guided adaptive sampling strategy enhances efficiency by not only skipping empty regions but also dynamically adjusting the number of samples according to depth confidence. As illustrated in Fig. 5, this approach allocates more samples at object boundaries and areas with depth discontinuities, where detail is essential. As presented in Tab. 3, this method achieves a $50\\%$ increase in FPS while maintaining comparable image quality.", + "bbox": [ + 88, + 640, + 482, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Encoding Strategy. The joint bundle representation, containing pre-filtered features for the sampled spheres, is inherently smooth and lacks high-frequency details. To enhance detail preservation, we integrate a ray-specific representation that provides pixel-aligned colors for individual ray samples within each sphere. As illustrated in Tab. 3, adding this ray-specific representation boosts PSNR by 0.39", + "bbox": [ + 88, + 794, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/65da9d82e39d9e39419a9f85f15b997e0faf0495a6c59161a5d3860d4751bacd.jpg", + "image_caption": [ + "(a) Target View" + ], + "image_footnote": [], + "bbox": [ + 524, + 361, + 709, + 458 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/26708861635e1d35df585d489d4db5f33ab5fa04de73aa0d93e2b831cc7de14e.jpg", + "image_caption": [ + "(b) Sample Distribution", + "Figure 5. Visualization of sample allocation in depth-guided adaptive sampling." + ], + "image_footnote": [], + "bbox": [ + 712, + 361, + 900, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dB for a $2 \\times 2$ bundle configuration and $1.47\\mathrm{dB}$ for a $4 \\times 4$ bundle configuration, with slight impact on FPS.", + "bbox": [ + 511, + 547, + 906, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 607, + 633, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed a novel bundle sampling strategy for generalizable novel view synthesis, inspired by plenoptic sampling theory to exploit the piece-wise smoothness of natural scenes. By grouping adjacent rays into bundles and sampling collectively, our approach reduces sampling redundancy while preserving rendering quality. Additionally, our depth-guided adaptive sampling method further optimizes efficiency by dynamically adjusting the number of samples based on depth confidence, concentrating samples at complex regions such as object boundaries and depth discontinuities. Applied to existing methods, our method achieved significant improvements in speed and fidelity. Experimental results on multiple datasets show that our method provides competitive quality with a substantial speed advantage over existing generalizable radiance field models. The flexibility to adjust bundle size also enables trade-offs between speed and quality, broadening its practical applicability to high-resolution, real-time applications.", + "bbox": [ + 509, + 636, + 906, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11224", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Henrik Aanaes, Rasmus Ramsbøl Jensen, George Vogiatzis, Engin Tola, and Anders Bjorholm Dahl. Large-scale data for multiple-view stereopsis. International Journal of Computer Vision, 120:153-168, 2016. 1, 6, 7", + "[2] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19680-19690, 2024. 2" + ], + "bbox": [ + 516, + 92, + 906, + 838 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11226", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Depth-Guided Bundle Sampling for Efficient Generalizable Neural Radiance Field Reconstruction/8a97af03-ecf0-4b44-846e-a010c9f066c8_model.json b/2025/Depth-Guided Bundle Sampling for Efficient Generalizable Neural Radiance Field Reconstruction/8a97af03-ecf0-4b44-846e-a010c9f066c8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..030f316ca97d4dc953708b1257a612df86b65076 --- /dev/null +++ b/2025/Depth-Guided Bundle Sampling for Efficient Generalizable Neural Radiance Field Reconstruction/8a97af03-ecf0-4b44-846e-a010c9f066c8_model.json @@ -0,0 +1,2035 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.108, + 0.885, + 0.151 + ], + "angle": 0, + "content": "Depth-Guided Bundle Sampling for Efficient Generalizable Neural Radiance Field Reconstruction*" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.181, + 0.808, + 0.2 + ], + "angle": 0, + "content": "Li Fang\\(^{1}\\) Hao Zhu\\(^{2}\\) Longlong Chen\\(^{1}\\) Fei Hu\\(^{1\\dagger}\\) Long Ye\\(^{1}\\) Zhan Ma\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.2, + 0.827, + 0.235 + ], + "angle": 0, + "content": "1Key Laboratory of Media Audio and Video (Communication University of China), Ministry of Education, Beijing 100024, China" + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.235, + 0.86, + 0.254 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.255, + 0.853, + 0.271 + ], + "angle": 0, + "content": "{lifang8902, chenll, hufei, yelong}@cuc.edu.cn {zhuhao/photo, mazhan}@nju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.306, + 0.327, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.337, + 0.485, + 0.655 + ], + "angle": 0, + "content": "Recent advancements in generalizable novel view synthesis have achieved impressive quality through interpolation between nearby views. However, rendering high-resolution images remains computationally intensive due to the need for dense sampling of all rays. Recognizing that natural scenes are typically piecewise smooth and sampling all rays is often redundant, we propose a novel depth-guided bundle sampling strategy to accelerate rendering. By grouping adjacent rays into a bundle and sampling them collectively, a shared representation is generated for decoding all rays within the bundle. To further optimize efficiency, our adaptive sampling strategy dynamically allocates samples based on depth confidence, concentrating more samples in complex regions while reducing them in smoother areas. When applied to ENeRF, our method achieves up to a 1.27 dB PSNR improvement and a \\(47\\%\\) increase in FPS on the DTU dataset. Extensive experiments on synthetic and real-world datasets demonstrate state-of-the-art rendering quality and up to \\(2\\times\\) faster rendering compared to existing generalizable methods. Code is available at https://github.com/KLMAV-CUC/GDB-NeRF." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.682, + 0.222, + 0.698 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.707, + 0.483, + 0.844 + ], + "angle": 0, + "content": "Novel view synthesis aims to generate photorealistic images from new perspectives using a sparse set of input images. The advent of Neural Radiance Field (NeRF) [28] and subsequent advancements [34] have significantly improved the quality of view synthesis, garnering substantial interest in both academia and industry. NeRF models scenes as continuous radiance and density fields, producing high-quality images. However, this comes at a cost: NeRF's volume rendering process requires numerous samples per ray, leading" + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.308, + 0.891, + 0.483 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.496, + 0.907, + 0.568 + ], + "angle": 0, + "content": "Figure 1. Rendering Quality (PSNR) vs. Speed (FPS) on the DTU Dataset [1] under 3-view setting. ENeRF+Ours achieves state-of-the-art rendering quality and faster rendering speed, outperforming existing generalizable novel view synthesis methods [8, 10, 22, 24, 40, 43]. Model parameter counts are also provided." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.597, + 0.907, + 0.656 + ], + "angle": 0, + "content": "to significant computational demands and impeding real-time, high-resolution synthesis. Additionally, NeRF models are typically scene-specific, requiring lengthy training for each new scene." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recent efforts to improve NeRF efficiency have focused on compact data structures and lightweight MLP decoders to store radiance fields, significantly reducing both training and rendering times for scene-specific NeRFs [11, 13, 14, 29, 42]. Techniques like baking and empty space skipping have also contributed to these improvements. However, these methods require per-scene optimization, limiting their ability to generalize to novel scenes. Generalizable NeRFs address this limitation by predicting radiance fields from multi-view images, enabling novel view synthesis for previously unseen scenes [8, 12, 16, 21, 22, 25, 26, 31, 36, 37, 39, 40, 43, 45]. Although promising, generalizable methods often face slower rendering speeds, as scene-specific optimizations are incompatible. While some approaches attempt to reduce per-ray sampling [22, 30], real-time rendering remains challenging." + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.852, + 0.483, + 0.887 + ], + "angle": 0, + "content": "*This work is supported by National Key R&D Program of China under Grant No. 2021YFF0900701, and the National Natural Science Foundation of China under Grant No. 62001432." + }, + { + "type": "page_footnote", + "bbox": [ + 0.112, + 0.888, + 0.236, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.852, + 0.483, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11217" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.333 + ], + "angle": 0, + "content": "The expensive computational cost in NeRF-related methods is primarily due to the need for dense sampling across all pixels. From a plenoptic sampling perspective [5], this full-pixel sampling implicitly assumes high-frequency information is uniform across the scene. However, natural scenes are usually piecewise smooth, with high-frequency details in specific areas like object boundaries and depth discontinuities. Based on this observation, we propose a novel bundle sampling strategy. This method groups adjacent rays and samples them jointly at a global, low sampling rate for smooth regions. In non-smooth areas, high-frequency information is captured by increasing samples along the depth dimension. Furthermore, samples within each bundle are further constrained to a small range using depth maps. As a result, this approach significantly reduces the overall number of samples, greatly improving efficiency." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.336, + 0.483, + 0.684 + ], + "angle": 0, + "content": "We integrate this depth-guided bundle sampling strategy into a representative generalizable NeRF, ENeRF [22]. Instead of sampling points along individual rays, our method samples 3D areas along bundles of adjacent rays by casting a cone that encompasses the corresponding pixels. Within this cone, inscribed spheres are sampled and featurized with pre-filtered features extracted from the source views. Through depth-guided adaptive sampling, sampling is constrained to a predicted depth range, with the number of samples adjusted dynamically: in smooth regions with a narrow depth range, fewer samples suffice for accurate reconstruction, while areas with a broader depth range require more samples to capture finer details. This adaptive approach aligns with the plenoptic principle [5], ensuring each sample covers a narrow depth range near surfaces. A bundle representation is then computed via volume rendering and decoded to predict the color of each ray. We also apply this depth-guided bundle sampling strategy to a recent generalizable 3D Gaussian splatting (3D-GS) method [24]. Extensive experiments demonstrate that our method significantly improves the efficiency of base models and achieves synthesis quality comparable to state-of-the-art generalizable models, with significant improvements in rendering speed." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.687, + 0.472, + 0.701 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.705, + 0.483, + 0.765 + ], + "angle": 0, + "content": "- We propose a novel bundle sampling strategy that jointly samples bundles of adjacent rays, significantly reducing the number of samples needed and improving both rendering speed and quality." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.766, + 0.483, + 0.826 + ], + "angle": 0, + "content": "- We introduce a depth-guided adaptive sampling method that dynamically adjusts the number of samples based on local depth range, achieving over a \\(50\\%\\) increase in rendering speed without sacrificing quality." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.826, + 0.483, + 0.902 + ], + "angle": 0, + "content": "- We validate our method on both generalizable NeRF and 3D-GS across various datasets. Our method achieves state-of-the-art rendering quality and up to \\(2 \\times\\) faster rendering than existing generalizable NeRFs. It also offers flexibility, allowing adjustments between quality and effi" + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.705, + 0.483, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.092, + 0.821, + 0.107 + ], + "angle": 0, + "content": "ciency depending on practical requirements." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.122, + 0.664, + 0.137 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.148, + 0.907, + 0.36 + ], + "angle": 0, + "content": "Accelerating NeRF. NeRFs represent scenes as continuous color and density fields using neural networks, achieving high-quality view synthesis via volume rendering. Despite their success, NeRFs suffer from high computational demands, slowing training and inference. To address this, recent methods have replaced large neural representations with local sparse feature fields and shallow MLP decoders [9, 23, 29, 33, 44], or spherical harmonics embeddings [9, 13, 17]. Other solutions utilize voxel grids [23], octrees [13], tensor decompositions [9], or 3D Gaussians [18], as well as efficient sampling [14, 20, 22, 30] and image-space convolutions [4, 38], leading to significant speed-ups. However, these improvements remain scene-specific, requiring training for each new scene." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.381, + 0.908, + 0.683 + ], + "angle": 0, + "content": "Generalizable NeRF. These methods generalize NeRF by encoding features for each 3D point and decoding them into volume density and radiance, akin to image-based rendering through NeRF-like volume rendering techniques [8, 10, 12, 16, 21, 22, 25, 26, 31, 36, 37, 39, 40, 45]. While these methods improve across-scene generalizability, they remain limited by slow optimization and rendering. CG-NeRF [31] predicts coarse radiance fields and depth, refining fine-scale features sampled near the estimated depth. ConvGLR [36] processes all camera rays in a low-resolution latent space, which improves quality in sparse-view synthesis. GeFu [25] improves generalizable NeRFs through geometry-aware reconstruction with Adaptive Cost Aggregation and Consistency-Aware Fusion. Most of these methods lack real-time rendering capability. ENeRF [22] accelerates generalizable NeRFs with depth-guided sampling but uses a fixed number of samples per ray, leading to inefficiency. In contrast, our method adaptively samples ray bundles based on local scene complexity, providing greater flexibility and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.705, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Generalizable 3D-GS. Recent advancements in generalizable Gaussian splatting methods have significantly enhanced the efficiency of novel view synthesis. These approaches eliminate the need for per-scene optimization by directly regressing Gaussian parameters through a feedforward architecture. PixelSplat [7] tackles scale ambiguity by utilizing a multiview epipolar transformer and scale-aware features to predict pixel-aligned 3D Gaussian primitives, though its design is limited to image pair inputs. GPS-Gaussian [47] extends this approach to stereo matching, incorporating epipolar rectification, disparity estimation, and feature encoding. However, its reliance on ground-truth depth maps restricts its applicability. Splatter Image [35]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11218" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.213 + ], + "angle": 0, + "content": "proposes a single-view reconstruction approach based on Gaussian splatting, though its focus on object-centric reconstruction constrains its generalization to unseen scenes. MVSGaussian [24] combines multi-view stereo with a generalizable 3D Gaussian representation for real-time novel view synthesis. However, its single-sample-per-ray strategy necessitates highly accurate depth estimations and hinders further efficiency improvements." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.224, + 0.22, + 0.243 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.25, + 0.483, + 0.371 + ], + "angle": 0, + "content": "Preliminaries on Generalizable NeRF. Given input multi-view images with intrinsic and extrinsic camera matrices, NeRF constructs the scene's radiance fields using a coordinate-based network. However, optimizing this network for each individual scene is computationally intensive. To address this, generalizable NeRF incorporates an additional geometry-aware feature, \\( \\pmb{f}_p \\), extracted from the source images and included in the network input:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.379, + 0.483, + 0.398 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {p}, c _ {p} = N N _ {\\theta} \\left(\\boldsymbol {x} _ {p}, \\boldsymbol {d} _ {p}, \\boldsymbol {f} _ {p}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.404, + 0.483, + 0.525 + ], + "angle": 0, + "content": "where \\( \\boldsymbol{x}_p \\) and \\( \\boldsymbol{d}_p \\) represent the coordinates and viewing direction of the 3D point \\( p \\), respectively. Here, \\( \\sigma_p \\) and \\( c_p \\) denote the density and color of \\( p \\), defining the radiance field properties at this point. The coordinate network, \\( NN_{\\theta} \\), decodes these radiance field attributes. Once the radiance fields for the entire scene are constructed, volume rendering techniques can synthesize the color for a pixel from any desired viewpoint." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.525, + 0.483, + 0.631 + ], + "angle": 0, + "content": "For an image of resolution \\( H \\times W \\), NeRF samples \\( N \\) points along the ray passing through each pixel, leading to a computational complexity of approximately \\( \\mathcal{O}(HWN) \\). As the number of samples increases, so does the computational burden, posing challenges for rendering efficiency and motivating the need for optimized sampling and rendering strategies." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.648, + 0.483, + 0.799 + ], + "angle": 0, + "content": "Plenoptic Sampling Theory. To enhance efficiency, existing generalizable NeRFs aim to reduce the number of samples along each ray by concentrating sampling near scene surfaces [22, 24, 25]. However, these methods do not explore the reduction of the total number of rays required for rendering; instead, they uniformly sample all rays with a fixed number of samples. Some approaches attempt to reduce ray sampling needs through super-resolution techniques, though these are often constrained to specific content types such as faces [6]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.799, + 0.483, + 0.874 + ], + "angle": 0, + "content": "Plenoptic sampling theory, introduced in [5], investigates the sampling bounds in light field rendering to determine the minimum angular density required for accurate reconstruction. The theory defines the maximum allowable camera spacing as:" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.873, + 0.483, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\Delta t \\leq \\frac {\\operatorname* {m a x} \\left(2 \\Delta v , 1 / B _ {v} ^ {s}\\right)}{f \\cdot h _ {d}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.259 + ], + "angle": 0, + "content": "where \\( f \\) is the focal length, \\( \\Delta v \\) is the spacing between camera rays, \\( B_v^s \\) is the highest texture frequency, and \\( h_d \\) is the disparity range defined as \\( h_d = \\frac{1}{z_{\\mathrm{min}}} - \\frac{1}{z_{\\mathrm{max}}} \\), with \\( z_{\\mathrm{min}} \\) and \\( z_{\\mathrm{max}} \\) denoting the minimum and maximum scene depths, respectively. Eq. (2) first implies that the ray spacing \\( \\Delta v \\) must satisfy the Nyquist sampling criterion, i.e., \\( \\Delta v \\leq \\frac{1}{2B_v^s} \\), to avoid aliasing; it then highlights that geometric accuracy affects the sampling rate required for image capture: by decomposing the scene into \\( D \\) depth ranges and sampling the light field in each range separately, the camera sampling interval can be increased by a factor of \\( D \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.26, + 0.907, + 0.527 + ], + "angle": 0, + "content": "Considering the relation between light fields and NeRFs [32], plenoptic sampling theory inspires our depth-guided bundle sampling strategy. On the one hand, the piecewise smooth nature of natural scenes means that high-frequency content is localized, with most regions being smooth. This allows for reduced sampling rates in smooth areas by effectively lowering the camera resolution (i.e., increasing \\(\\Delta v\\)). However, this may cause aliasing in high-frequency regions (e.g., edges, textures, thin structures). On the other hand, given a fixed camera spacing \\(\\Delta t\\), each sample in NeRF can be regarded as a local light field confined to a small disparity range, \\(h_d \\leq \\frac{\\max(2\\Delta v, \\frac{1}{B_v^s})}{f \\cdot \\Delta t}\\). For high-frequency regions, they often suffer from inaccurate depth estimation, necessitating more samples to ensure each sample covers a small disparity range. These observations motivate our depth-guided bundle sampling strategy, which adapts the sampling density based on scene complexity." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.539, + 0.605, + 0.555 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.565, + 0.907, + 0.807 + ], + "angle": 0, + "content": "Our method is designed to synthesize target views from \\(V\\) nearby source views \\(\\{I_i\\}_{i=1}^V\\) at interactive frame rates, addressing challenges in efficient sampling. The proposed depth-guided bundle sampling strategy includes two main innovations: a novel bundle sampling approach that groups adjacent rays in the target view for joint sampling, and a depth-guided adaptive sampling method that dynamically allocates samples based on depth confidence. This adaptive approach reduces the overall number of samples while maintaining consistency with the plenoptic sampling principles. We apply our method to representative ENeRF [22] and MVSGaussian [24] to demonstrate its effectiveness in generalizable NeRF and 3D-GS, respectively. Fig. 2 presents the architecture of ENeRF+Ours, and a similar architecture is employed in MVSGaussian, where the sample features are also decoded into 3D-GS parameters." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.817, + 0.685, + 0.833 + ], + "angle": 0, + "content": "4.1. Bundle Sampling" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Our bundle sampling method improves efficiency by reducing the number of sampled rays. Adjacent rays in the target view are grouped into bundles, modeled as cones, with inscribed spheres sampled within each cone, as illustrated in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11219" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.087, + 0.891, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.404, + 0.908, + 0.462 + ], + "angle": 0, + "content": "Figure 2. Network architecture of the proposed depth-guided bundle sampling strategy on ENeRF [22], denoted as ENeRF+Ours, which consists of four main components: (1) Multi-scale feature extraction; (2) Depth estimation to predict depth range; (3) Depth-guided bundle sampling, where rays are grouped into bundles and sampled adaptively based on predicted depth confidence; and (4) Radiance field prediction, which decodes each bundle's representation into individual ray colors." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.486, + 0.486, + 0.669 + ], + "angle": 0, + "content": "Fig. 3. This design broadens the angular coverage per sample, effectively reducing the total number of rays required. A similar sphere-based sampling approach is used in [15], where spheres are cast for each ray's cone to achieve anti-aliasing. In contrast, our method casts spheres for a cone of grouped rays, enabling collective sampling across multiple rays rather than treating them individually. However, this expanded coverage inevitably leads to loss of high-frequency details in the rendered image. To mitigate this, we encode each sample with both a joint bundle representation and a ray-specific representation, ensuring efficiency while preserving the necessary level of detail." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.692, + 0.345, + 0.708 + ], + "angle": 0, + "content": "4.1.1 Sphere-based cone sampling" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.717, + 0.484, + 0.809 + ], + "angle": 0, + "content": "Our method models bundles of rays as cones passing through groups of adjacent pixels in the target view. We begin by casting rays from the camera's projection center \\(o\\) through each pixel center \\(p_o\\), with ray directions defined as \\(d_r = p_o - o\\). Points along each ray are parameterized as \\(x_r = o + t d_r\\), where \\(t\\) is the distance along the ray." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 3(b), for a bundle of \\( K \\times K \\) rays, the corresponding region on the target image plane is modeled as a disk with radius \\( r_{\\mathrm{tar}} = K \\cdot r_p \\), where \\( r_p = \\sqrt{\\Delta x \\cdot \\Delta y / \\pi} \\) is the radius of a single-pixel disk, and \\( \\Delta x \\) and \\( \\Delta y \\) are the pixel's width and height in world coordinates, derived from camera parameters. The cone \\( \\mathcal{C} \\) is" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.486, + 0.907, + 0.576 + ], + "angle": 0, + "content": "emitted from the camera's projection center along the average direction \\( \\pmb{d}_{\\mathcal{C}} = \\sum_{\\pmb{r} \\in \\mathcal{C}} \\pmb{d}_{\\pmb{r}} / K^2 \\), and intersects the image plane at the disk, with the cone's axis defined as \\( \\pmb{a}(t) = \\pmb{o} + t \\pmb{d}_{\\mathcal{C}} \\). The cone is sampled using a set of inscribed spheres, \\( S(\\dot{\\pmb{x}}, \\dot{\\pmb{r}}) \\), defined by their centers \\( \\dot{\\pmb{x}} \\) and radii \\( \\dot{\\pmb{r}} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.584, + 0.66, + 0.621 + ], + "angle": 0, + "content": "\\[\n\\dot {\\boldsymbol {x}} = \\frac {1}{K ^ {2}} \\sum_ {\\boldsymbol {r} \\in \\mathcal {C}} \\boldsymbol {x} _ {\\boldsymbol {r}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.623, + 0.907, + 0.682 + ], + "angle": 0, + "content": "\\[\n\\dot {r} = \\frac {\\left\\| \\dot {\\boldsymbol {x}} - \\boldsymbol {o} \\right\\| _ {2} \\cdot f \\cdot r _ {\\mathrm {t a r}}}{\\left\\| \\boldsymbol {d} _ {\\mathcal {C}} \\right\\| _ {2} \\cdot \\sqrt {\\left(\\sqrt {\\left\\| \\boldsymbol {d} _ {\\mathcal {C}} \\right\\| _ {2} ^ {2} - f ^ {2}} - r _ {\\mathrm {t a r}}\\right) ^ {2} + f ^ {2}}}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.693, + 0.906, + 0.723 + ], + "angle": 0, + "content": "Given sorted distances \\(\\{t_n\\}_{n = 1}^V\\), the sphere centers \\(\\dot{\\pmb{x}}_n\\) and radii \\(\\dot{r}_n\\) are computed." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.723, + 0.907, + 0.799 + ], + "angle": 0, + "content": "For a target view with resolution \\( H \\times W \\), the image is divided into \\( \\frac{H}{K} \\times \\frac{W}{K} \\) bundles, each consisting of \\( K \\times K \\) pixels. This reduces the total number of samples by approximately \\( 1 / K^2 \\), ensuring efficient angular coverage without sacrificing essential surface detail." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.817, + 0.854, + 0.833 + ], + "angle": 0, + "content": "4.1.2 Multi-view image-based sphere encoding" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Each sphere covers a broad angular range, which extends to its feature representation. As shown in Fig. 3(b), we extract features based on the area occupied by each sphere, forming a joint bundle representation. However, this approach may" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11220" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.091, + 0.478, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.24, + 0.23, + 0.336, + 0.242 + ], + "angle": 0, + "content": "(a) Ray Sampling" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.242, + 0.476, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.231, + 0.397, + 0.345, + 0.41 + ], + "angle": 0, + "content": "(b) Bundle Sampling" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.421, + 0.483, + 0.478 + ], + "angle": 0, + "content": "Figure 3. Comparison of ray sampling strategies: (a) Traditional ray sampling, which processes each ray individually; (b) Proposed bundle sampling, which jointly samples neighboring rays to leverage scene coherence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.506, + 0.483, + 0.552 + ], + "angle": 0, + "content": "omit high-frequency details. To retain fine-grained information from individual rays, we augment the joint bundle representation with a ray-specific representation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.552, + 0.483, + 0.764 + ], + "angle": 0, + "content": "The joint bundle representation is derived from the area occupied by the spheres, necessitating an adjustment of the source view pixel spacing \\(\\Delta v\\) in Eq. (2). Inspired by area-sampling techniques used in scene-specific anti-aliasing NeRFs [2, 3, 15], we incorporate mipmap representations from [15] into a multi-view image-based encoding framework. We extract features \\(\\{F_i\\}_{i=1}^V\\) from source views and convert them into mipmaps \\(\\{M_i\\}_{i=1}^V\\), creating a hierarchical structure that represents the pre-filtered feature space. The base level \\(M_i^{l_0}\\) is the original feature map \\(F_i\\), with each subsequent level reducing the spatial resolution by a factor of two. To compute the feature vector \\(\\{f_{S,i}\\}_{i=1}^V\\) for sphere \\(S(\\dot{x},\\dot{r})\\), we project it onto the \\(i\\)-th source view to create a disc, with its radius \\(r_{\\mathrm{src}}\\) calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.775, + 0.483, + 0.829 + ], + "angle": 0, + "content": "\\[\nr _ {\\mathrm {s r c}} = \\frac {\\left\\| \\boldsymbol {d} _ {i} \\right\\| _ {2} ^ {2}}{f \\cdot \\sqrt {\\left(\\frac {\\| \\dot {\\boldsymbol {x}} - \\boldsymbol {o} _ {i} \\| _ {2}}{\\dot {r}}\\right) ^ {2} - 1} + \\sqrt {\\left\\| \\boldsymbol {d} _ {i} \\right\\| _ {2} ^ {2} - f ^ {2}}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\( \\pmb{o}_i \\) is the camera's projection center of the \\( i \\)-th source view, and \\( \\| \\pmb{d}_i \\|_2 \\) is the distance from the projection of \\( \\dot{\\pmb{x}} \\) onto the image plane to \\( \\pmb{o}_i \\) (see Fig. 3(b)). The appropriate mipmap level \\( l \\) corresponding to the sphere is determined" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.093, + 0.56, + 0.107 + ], + "angle": 0, + "content": "using:" + }, + { + "type": "equation", + "bbox": [ + 0.649, + 0.106, + 0.907, + 0.139 + ], + "angle": 0, + "content": "\\[\nl = \\log_ {2} \\left(\\frac {r _ {\\mathrm {s r c}}}{r _ {p}}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.14, + 0.907, + 0.246 + ], + "angle": 0, + "content": "This process aligns the radius \\( r_{\\mathrm{src}} \\) of the sphere's projection with the corresponding feature elements' radius at a specific level \\( l \\) within \\( M_i^l \\), which is equivalent to adjusting the spacing \\( \\Delta v \\) of the sampling camera. Once the appropriate mipmap level is identified, the feature vector \\( f_{S,i} \\) can be accurately extracted from the mipmap \\( M_i \\) via trilinear interpolation at \\( (x,y,l) \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.246, + 0.906, + 0.351 + ], + "angle": 0, + "content": "For ray-specific representation, the 3D points \\( \\boldsymbol{x}_r \\) associated with the sphere \\( S(\\dot{\\boldsymbol{x}},\\dot{r}) \\) are projected onto the source views \\( \\{I_i\\}_{i = 1}^V \\) to extract pixel-aligned colors. The extracted colors corresponding to the \\( K\\times K \\) rays within each bundle are concatenated to form the ray-specific representation, denoted as \\( \\{f_{r,i}\\}_{i = 1}^{V} \\), which captures high-frequency information for the rays as projected onto source views." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.352, + 0.906, + 0.411 + ], + "angle": 0, + "content": "By combining the joint bundle representation and ray-specific representation, our approach efficiently encodes the bundle samples while maintaining necessary scene details for accurate reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.419, + 0.807, + 0.435 + ], + "angle": 0, + "content": "4.2. Depth-guided Adaptive Sampling" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.442, + 0.907, + 0.641 + ], + "angle": 0, + "content": "To further optimize sampling, we restrict it to a predicted depth range, \\( R \\), estimated based on the depth value and associated confidence interval [22, 24, 25]. According to Eq. (2), for a fixed camera spacing \\( \\Delta t \\), the disparity range covered by the local light field of each sample must satisfy \\( h_d \\leq \\frac{\\max(2\\Delta v, 1 / B_v^s)}{f \\cdot \\Delta t} \\), representing the maximum sampling spacing along the depth. Consequently, in smooth regions with a narrow depth range, fewer samples are sufficient for accurate reconstruction, while regions with a larger depth range require additional samples. Our depth-guided adaptive sampling strategy dynamically allocates samples near surfaces, ensuring that each sample covers a narrow depth range. The number of samples per bundle is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.646, + 0.907, + 0.663 + ], + "angle": 0, + "content": "\\[\nN _ {\\mathcal {C}} = \\max \\left(\\operatorname {c e i l} \\left(2 \\cdot \\boldsymbol {R} / \\delta_ {s}\\right), N _ {\\max }\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.668, + 0.906, + 0.744 + ], + "angle": 0, + "content": "where \\(\\delta_{s}\\) denotes the minimum inter-sample spacing, with a maximum limit of \\(N_{\\mathrm{max}}\\) samples. The depth range is then divided into \\(N_{C}\\) uniform intervals, with sampling performed at the center of each interval. For cases requiring only one sample, the sample is placed at the predicted surface point." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.744, + 0.906, + 0.82 + ], + "angle": 0, + "content": "Unlike existing depth-guided methods that apply uniform ray sampling with a fixed number of points, our adaptive approach dynamically adjusts the number of samples along the depth according to plenoptic sampling theory, significantly enhancing both efficiency and adaptability." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.826, + 0.75, + 0.841 + ], + "angle": 0, + "content": "4.3. Radiance Field Prediction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.849, + 0.906, + 0.881 + ], + "angle": 0, + "content": "For each sampled sphere, we predict the density \\(\\sigma\\) and blending weights \\(\\{w_i\\}_{i=1}^V\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.884, + 0.907, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\sigma , \\left\\{w _ {i} \\right\\} _ {i = 1} ^ {V} = \\operatorname {M L P} \\left(\\left\\{\\boldsymbol {f} _ {\\mathcal {S}, i} \\right\\} _ {i = 1} ^ {V}, \\boldsymbol {f} _ {\\text {v o x e l}}, \\left\\{\\Delta \\boldsymbol {d} _ {i} \\right\\} _ {i = 1} ^ {V}\\right), \\tag {7}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11221" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "where \\( f_{\\mathrm{voxel}} \\) is the voxel-aligned feature extracted from the feature volume (from depth estimation, see Fig. 2) by applying trilinear interpolation at the sphere center \\( \\dot{x} \\). \\( \\Delta d_i \\) is the concatenation of the norm and direction of \\( d_i - d_c \\), with \\( d_i \\) as the direction of \\( \\dot{x} \\) in the \\( i \\)-th source view. The network design is adapted from [22]. The blending weights \\( \\{w_i\\}_{i=1}^V \\) combine the features using softmax:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.207, + 0.483, + 0.25 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {f} _ {\\mathcal {S}}, \\boldsymbol {f} _ {\\boldsymbol {r}} \\right\\} = \\sum_ {i = 1} ^ {V} \\frac {\\exp \\left(w _ {i}\\right) \\cdot \\left\\{\\boldsymbol {f} _ {\\mathcal {S} , i} \\boldsymbol {f} _ {\\boldsymbol {r} , i} \\right\\}}{\\sum_ {j = 1} ^ {V} \\exp \\left(w _ {j}\\right)}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.257, + 0.483, + 0.303 + ], + "angle": 0, + "content": "We employ volume rendering to compute the per-bundle features \\(\\{\\pmb{F}_{\\mathcal{C}},\\pmb{F}_{\\pmb{r}}\\}\\) by accumulating the features \\(\\{\\pmb{f}_S,\\pmb{f}_r\\} _n\\) across the \\(N_{\\mathcal{C}}\\) sampled spheres along the cone \\(\\mathcal{C}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.312, + 0.483, + 0.353 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {F} _ {\\mathcal {C}}, \\boldsymbol {F} _ {\\boldsymbol {r}} \\right\\} = \\sum_ {n = 1} ^ {N _ {\\mathcal {C}}} \\tau_ {n} \\left(1 - \\exp (- \\sigma_ {n})\\right) \\left\\{\\boldsymbol {f} _ {\\mathcal {S}}, \\boldsymbol {f} _ {\\boldsymbol {r}} \\right\\} _ {n}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.362, + 0.483, + 0.392 + ], + "angle": 0, + "content": "where \\(\\tau_{n}\\) is the accumulated volume transmittance from the cone apex to the sphere center, computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.401, + 0.482, + 0.443 + ], + "angle": 0, + "content": "\\[\n\\tau_ {n} = \\exp \\left(- \\sum_ {j = 1} ^ {n - 1} \\sigma_ {j}\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.452, + 0.484, + 0.653 + ], + "angle": 0, + "content": "Neural renderer: For the target view with spatial dimensions \\(H \\times W\\), the image is divided into \\(\\frac{H}{K} \\times \\frac{W}{K}\\) non-overlapping bundles, each containing \\(K \\times K\\) rays. Using Eq. (9), we generate a feature map \\(\\{\\pmb{F}_{\\mathcal{C}}^{i}, \\pmb{F}_{r}^{i}\\}_{i=1}^{\\frac{H}{K} \\times \\frac{W}{K}}\\). Here, \\(\\pmb{F}_{\\mathcal{C}}^{i}\\) represents the aggregated joint bundle representation, which is processed through several residual convolutional blocks and decoded into coarse ray colors via sub-pixel convolution, yielding a coarse RGB map \\(\\hat{\\pmb{I}}_{c}\\) of dimensions \\(H \\times W \\times 3\\). The second component, \\(\\pmb{F}_{r}^{i}\\), contains the folded RGB values for individual rays and is unfolded to generate a fine RGB map \\(\\hat{\\pmb{I}}_{f}\\) of dimensions \\(H \\times W \\times 3\\), preserving high-frequency details. The final high-resolution target view is obtained by summing these two components:" + }, + { + "type": "equation", + "bbox": [ + 0.233, + 0.661, + 0.483, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {I}} _ {\\mathrm {t a r}} = \\hat {\\boldsymbol {I}} _ {c} + \\hat {\\boldsymbol {I}} _ {f}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.484, + 0.751 + ], + "angle": 0, + "content": "For application to MVSGaussian [24], the renderer not only outputs the rendered target view image but also produces a feature map, which is subsequently processed to generate 3D-GS parameters following [24]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.763, + 0.223, + 0.78 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.787, + 0.19, + 0.803 + ], + "angle": 0, + "content": "5.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Datasets. Following MVSNeRF [8, 22, 24], we train the generalizable model on the DTU training set [1] and evaluate it on the DTU test set. We also perform cross-dataset evaluation on the Real Forward-facing [27] and NeRF Synthetic [28] datasets using the trained model without fin-tuning. These datasets introduce significant variations in" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.138 + ], + "angle": 0, + "content": "view distribution and scene content compared to the DTU dataset. The quality of the synthesized novel views is measured using the PSNR, SSIM [41], and LPIPS [46] metrics." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.161, + 0.907, + 0.268 + ], + "angle": 0, + "content": "Baselines. We compare our method against several state-of-the-art generalizable NeRF methods [8, 10, 22, 31, 36, 40, 43, 45], as well as the recent generalizable 3D-GS method [24]. We follow the same experimental settings as [8, 22, 24] and borrow some results reported in the respective papers. For additional baselines, such as [39, 43], we evaluate their performance using publicly released models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.29, + 0.908, + 0.533 + ], + "angle": 0, + "content": "Implementation Details. To verify the effectiveness of the proposed depth-guided bundle sampling, we integrate it with two representative methods, ENeRF [22] and MVS-Gaussian [24], keeping hyperparameters consistent with their original configurations. Both models are trained with the loss function from [24]. We observed that direct training can sometimes result in instability during the initial stages. To address this, we employ a pre-training phase that uniformly samples \\( N_{\\mathrm{max}} \\) spheres within each bundle's depth range for 100 epochs. For the depth-guided adaptive sampling phase, we set \\( N_{\\mathrm{max}} = 6 \\) and \\( \\delta_s \\) to 1/64 of the scene depth range, as defined in Eq. (6). For ENeRF+Ours, we evaluate different bundle sizes to assess the effectiveness of bundle sampling, with \\( 2 \\times 2 \\) and \\( 4 \\times 4 \\) indicating the bundle size. All models are trained and tested on an RTX A6000 GPU using the Adam optimizer [19]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.545, + 0.608, + 0.559 + ], + "angle": 0, + "content": "5.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We report quantitative results on the DTU test set in Tab. 1. Additional results on two other datasets are provided in Tab. 2. Notably, ENeRF [22] and MVSGaussian [24] achieve promising speeds by sampling only 1-2 points per ray, while other methods experience slower inference times due to the large number of samples required for accurate reconstruction. We can see that ENeRF+Ours \\((2 \\times 2)\\) improves PSNR by 1.27 dB and increases FPS by \\(47\\%\\) compared to original ENeRF on DTU. Additionally, ENeRF+Ours \\((4 \\times 4)\\) demonstrates better performance with over twice the speed of the original ENeRF. Performance is not significantly impacted by bundle size. For MVSGaussian+Ours, improvements are limited due to fewer sampling points and dependency on additional post-processing network layers; further performance gains may require a more integrated approach. Thanks to our efficient depth-guided bundle sampling strategy, ENeRF+Ours achieves competitive performance compared to state-of-the-art approaches, while also maintaining high inference speeds. The ability to adjust bundle size provides flexibility, allowing our method to balance speed and quality across different practical applications. Qualitative results in Fig. 4 show that ENeRF+Ours" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11222" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.089, + 0.875, + 0.307 + ], + "angle": 0, + "content": "
Methods3-view2-view
PSNR ↑SSIM ↑LPIPS ↓Avg. samples per rayFPS ↑PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [45]19.310.7890.382960.019---
IBRNet [40]26.040.9170.1911280.217---
MVSNeRF [8]26.630.9310.1681280.41624.030.9140.192
ENeRF [22]27.610.9570.089219.525.480.9420.107
MatchNeRF [10]26.910.9340.1591281.0425.030.9190.181
GNT [39]26.390.9230.1561920.0124.320.9030.201
CG-NeRF [31]28.210.9300.17042.56---
MuRF [43]28.760.9610.077800.93425.610.9380.104
ConvGLR [36]31.650.9520.0801280.825---
MVSGaussian [24]28.210.9630.076121.525.780.9470.095
ENeRF+Ours (2 × 2)28.860.9640.0730.4228.626.390.9490.089
ENeRF+Ours (4 × 4)28.210.9570.0880.1043.626.090.9420.105
MVSGaussian+Ours28.400.9620.076123.426.160.9460.093
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.318, + 0.904, + 0.345 + ], + "angle": 0, + "content": "Table 1. Quantitative results of generalization on the DTU testset [1] \\((512\\times 640)\\). The best result is highlighted in bold, while the second-best is underlined." + }, + { + "type": "table", + "bbox": [ + 0.189, + 0.359, + 0.809, + 0.688 + ], + "angle": 0, + "content": "
MethodsSettingsReal Forward-facingNeRF Synthetic
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [45]11.240.4860.6717.390.6580.411
IBRNet [40]21.790.7860.27922.440.8740.195
MVSNeRF [8]21.930.7950.25223.620.8970.176
ENeRF [22]23.630.8430.18226.170.9430.085
MatchNeRF [10]22.430.8050.24423.200.8970.164
GNT [39]3-view22.980.7610.22125.800.9050.104
CG-NeRF [31]23.930.8200.21025.010.9000.190
MuRF [43]23.700.8600.18124.370.8850.117
MVSGaussian [24]24.070.8570.16426.460.9480.071
ENeRF+Ours (2 × 2)24.330.8600.16226.490.9480.075
ENeRF+Ours (4 × 4)23.840.8510.17426.000.9430.083
MVSGaussian+Ours24.150.8580.16526.480.9470.070
MVSNeRF [8]20.220.7630.28720.560.8560.243
ENeRF [22]22.780.8210.19124.830.9310.117
MatchNeRF [10]20.590.7750.27620.570.8640.200
GNT [39]2-view20.910.6830.29323.470.8770.151
MuRF [43]22.550.8200.21822.960.8660.137
MVSGaussian [24]23.110.8340.17525.060.9370.079
ENeRF+Ours (2 × 2)23.060.8240.18625.010.9370.087
ENeRF+Ours (4 × 4)23.060.8260.18724.650.9320.098
MVSGaussian+Ours23.130.8340.17525.100.9370.079
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.699, + 0.905, + 0.727 + ], + "angle": 0, + "content": "Table 2. Cross-dataset evaluation results on Real Forward-facing [27] (640 × 960) and NeRF Synthetic [28] (800 × 640) datasets. The best result is highlighted in bold, while the second-best is underlined." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.754, + 0.483, + 0.784 + ], + "angle": 0, + "content": "\\((2 \\times 2)\\) generates high-quality views with enhanced scene detail and fewer artifacts." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.811, + 0.305, + 0.827 + ], + "angle": 0, + "content": "5.3. Ablations and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We conduct a series of ablation studies to evaluate the effectiveness of our design. For efficiency, we limited our experiments to a 3-view configuration on the DTU dataset, employing bundle sizes of \\(2 \\times 2\\) and \\(4 \\times 4\\) on ENeRF [22]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.754, + 0.907, + 0.86 + ], + "angle": 0, + "content": "Sampling Strategy. A unique aspect of our approach is the sphere-based bundle sampling (see Fig. 3), where we sample features from the mipmap of source view feature maps according to the area occupied by each sampled sphere. As shown in Tab. 3, substituting our sphere-based sampling with a pixel-aligned feature extraction at sphere centers results in a PSNR decrease of \\(1.2\\mathrm{dB}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11223" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.089, + 0.887, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.31, + 0.908, + 0.34 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of ENeRF+Ours \\((2\\times 2)\\) with state-of-the-art methods [10, 22, 24] under 3-view setting. Each image triplet includes: the reconstructed image on the left, a zoomed-in view on the upper right, and the error map on the lower right." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.361, + 0.482, + 0.59 + ], + "angle": 0, + "content": "
Sphere SamplingX✓✓✓✓
Adaptive Sampling✓X✓✓✓
Joint Bundle Representation✓✓✓X✓
Ray-Specific Representation✓✓X✓✓
2×2PSNR ↑27.6628.8528.4727.8328.86
SSIM ↑0.9490.9640.9580.9590.964
LPIPS ↓0.0900.0760.0780.9330.073
FPS ↑29.217.029.433.7428.6
4×4PSNR ↑25.9328.0626.7427.4228.21
SSIM ↑0.9400.9540.9280.9550.957
LPIPS ↓0.1050.0950.1120.0990.088
FPS ↑44.229.145.349.643.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.116, + 0.6, + 0.458, + 0.615 + ], + "angle": 0, + "content": "Table 3. Ablations. The best result is highlighted in bold." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.641, + 0.483, + 0.779 + ], + "angle": 0, + "content": "Depth-Guided Strategy. The proposed depth-guided adaptive sampling strategy enhances efficiency by not only skipping empty regions but also dynamically adjusting the number of samples according to depth confidence. As illustrated in Fig. 5, this approach allocates more samples at object boundaries and areas with depth discontinuities, where detail is essential. As presented in Tab. 3, this method achieves a \\(50\\%\\) increase in FPS while maintaining comparable image quality." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.795, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Encoding Strategy. The joint bundle representation, containing pre-filtered features for the sampled spheres, is inherently smooth and lacks high-frequency details. To enhance detail preservation, we integrate a ray-specific representation that provides pixel-aligned colors for individual ray samples within each sphere. As illustrated in Tab. 3, adding this ray-specific representation boosts PSNR by 0.39" + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.362, + 0.71, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.574, + 0.46, + 0.658, + 0.473 + ], + "angle": 0, + "content": "(a) Target View" + }, + { + "type": "image", + "bbox": [ + 0.714, + 0.362, + 0.901, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.743, + 0.46, + 0.869, + 0.473 + ], + "angle": 0, + "content": "(b) Sample Distribution" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.485, + 0.907, + 0.514 + ], + "angle": 0, + "content": "Figure 5. Visualization of sample allocation in depth-guided adaptive sampling." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.549, + 0.907, + 0.581 + ], + "angle": 0, + "content": "dB for a \\(2 \\times 2\\) bundle configuration and \\(1.47\\mathrm{dB}\\) for a \\(4 \\times 4\\) bundle configuration, with slight impact on FPS." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.608, + 0.634, + 0.624 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.637, + 0.907, + 0.89 + ], + "angle": 0, + "content": "We proposed a novel bundle sampling strategy for generalizable novel view synthesis, inspired by plenoptic sampling theory to exploit the piece-wise smoothness of natural scenes. By grouping adjacent rays into bundles and sampling collectively, our approach reduces sampling redundancy while preserving rendering quality. Additionally, our depth-guided adaptive sampling method further optimizes efficiency by dynamically adjusting the number of samples based on depth confidence, concentrating samples at complex regions such as object boundaries and depth discontinuities. Applied to existing methods, our method achieved significant improvements in speed and fidelity. Experimental results on multiple datasets show that our method provides competitive quality with a substantial speed advantage over existing generalizable radiance field models. The flexibility to adjust bundle size also enables trade-offs between speed and quality, broadening its practical applicability to high-resolution, real-time applications." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11224" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.17 + ], + "angle": 0, + "content": "[1] Henrik Aanaes, Rasmus Ramsbøl Jensen, George Vogiatzis, Engin Tola, and Anders Bjorholm Dahl. Large-scale data for multiple-view stereopsis. International Journal of Computer Vision, 120:153-168, 2016. 1, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.171, + 0.484, + 0.254 + ], + "angle": 0, + "content": "[2] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. 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However, rendering high-resolution images remains computationally intensive due to the need for dense sampling of all rays. Recognizing that natural scenes are typically piecewise smooth and sampling all rays is often redundant, we propose a novel depth-guided bundle sampling strategy to accelerate rendering. By grouping adjacent rays into a bundle and sampling them collectively, a shared representation is generated for decoding all rays within the bundle. To further optimize efficiency, our adaptive sampling strategy dynamically allocates samples based on depth confidence, concentrating more samples in complex regions while reducing them in smoother areas. When applied to ENeRF, our method achieves up to a 1.27 dB PSNR improvement and a $47\%$ increase in FPS on the DTU dataset. Extensive experiments on synthetic and real-world datasets demonstrate state-of-the-art rendering quality and up to $2\times$ faster rendering compared to existing generalizable methods. Code is available at https://github.com/KLMAV-CUC/GDB-NeRF. + +# 1. Introduction + +Novel view synthesis aims to generate photorealistic images from new perspectives using a sparse set of input images. The advent of Neural Radiance Field (NeRF) [28] and subsequent advancements [34] have significantly improved the quality of view synthesis, garnering substantial interest in both academia and industry. NeRF models scenes as continuous radiance and density fields, producing high-quality images. However, this comes at a cost: NeRF's volume rendering process requires numerous samples per ray, leading + +![](images/035d5169a777617d5c2818f4c9d0d92c197afcc4918193f037b9052383a02201.jpg) +Figure 1. Rendering Quality (PSNR) vs. Speed (FPS) on the DTU Dataset [1] under 3-view setting. ENeRF+Ours achieves state-of-the-art rendering quality and faster rendering speed, outperforming existing generalizable novel view synthesis methods [8, 10, 22, 24, 40, 43]. Model parameter counts are also provided. + +to significant computational demands and impeding real-time, high-resolution synthesis. Additionally, NeRF models are typically scene-specific, requiring lengthy training for each new scene. + +Recent efforts to improve NeRF efficiency have focused on compact data structures and lightweight MLP decoders to store radiance fields, significantly reducing both training and rendering times for scene-specific NeRFs [11, 13, 14, 29, 42]. Techniques like baking and empty space skipping have also contributed to these improvements. However, these methods require per-scene optimization, limiting their ability to generalize to novel scenes. Generalizable NeRFs address this limitation by predicting radiance fields from multi-view images, enabling novel view synthesis for previously unseen scenes [8, 12, 16, 21, 22, 25, 26, 31, 36, 37, 39, 40, 43, 45]. Although promising, generalizable methods often face slower rendering speeds, as scene-specific optimizations are incompatible. While some approaches attempt to reduce per-ray sampling [22, 30], real-time rendering remains challenging. + +The expensive computational cost in NeRF-related methods is primarily due to the need for dense sampling across all pixels. From a plenoptic sampling perspective [5], this full-pixel sampling implicitly assumes high-frequency information is uniform across the scene. However, natural scenes are usually piecewise smooth, with high-frequency details in specific areas like object boundaries and depth discontinuities. Based on this observation, we propose a novel bundle sampling strategy. This method groups adjacent rays and samples them jointly at a global, low sampling rate for smooth regions. In non-smooth areas, high-frequency information is captured by increasing samples along the depth dimension. Furthermore, samples within each bundle are further constrained to a small range using depth maps. As a result, this approach significantly reduces the overall number of samples, greatly improving efficiency. + +We integrate this depth-guided bundle sampling strategy into a representative generalizable NeRF, ENeRF [22]. Instead of sampling points along individual rays, our method samples 3D areas along bundles of adjacent rays by casting a cone that encompasses the corresponding pixels. Within this cone, inscribed spheres are sampled and featurized with pre-filtered features extracted from the source views. Through depth-guided adaptive sampling, sampling is constrained to a predicted depth range, with the number of samples adjusted dynamically: in smooth regions with a narrow depth range, fewer samples suffice for accurate reconstruction, while areas with a broader depth range require more samples to capture finer details. This adaptive approach aligns with the plenoptic principle [5], ensuring each sample covers a narrow depth range near surfaces. A bundle representation is then computed via volume rendering and decoded to predict the color of each ray. We also apply this depth-guided bundle sampling strategy to a recent generalizable 3D Gaussian splatting (3D-GS) method [24]. Extensive experiments demonstrate that our method significantly improves the efficiency of base models and achieves synthesis quality comparable to state-of-the-art generalizable models, with significant improvements in rendering speed. + +Our main contributions can be summarized as follows: + +- We propose a novel bundle sampling strategy that jointly samples bundles of adjacent rays, significantly reducing the number of samples needed and improving both rendering speed and quality. +- We introduce a depth-guided adaptive sampling method that dynamically adjusts the number of samples based on local depth range, achieving over a $50\%$ increase in rendering speed without sacrificing quality. +- We validate our method on both generalizable NeRF and 3D-GS across various datasets. Our method achieves state-of-the-art rendering quality and up to $2 \times$ faster rendering than existing generalizable NeRFs. It also offers flexibility, allowing adjustments between quality and effi + +ciency depending on practical requirements. + +# 2. Related Works + +Accelerating NeRF. NeRFs represent scenes as continuous color and density fields using neural networks, achieving high-quality view synthesis via volume rendering. Despite their success, NeRFs suffer from high computational demands, slowing training and inference. To address this, recent methods have replaced large neural representations with local sparse feature fields and shallow MLP decoders [9, 23, 29, 33, 44], or spherical harmonics embeddings [9, 13, 17]. Other solutions utilize voxel grids [23], octrees [13], tensor decompositions [9], or 3D Gaussians [18], as well as efficient sampling [14, 20, 22, 30] and image-space convolutions [4, 38], leading to significant speed-ups. However, these improvements remain scene-specific, requiring training for each new scene. + +Generalizable NeRF. These methods generalize NeRF by encoding features for each 3D point and decoding them into volume density and radiance, akin to image-based rendering through NeRF-like volume rendering techniques [8, 10, 12, 16, 21, 22, 25, 26, 31, 36, 37, 39, 40, 45]. While these methods improve across-scene generalizability, they remain limited by slow optimization and rendering. CG-NeRF [31] predicts coarse radiance fields and depth, refining fine-scale features sampled near the estimated depth. ConvGLR [36] processes all camera rays in a low-resolution latent space, which improves quality in sparse-view synthesis. GeFu [25] improves generalizable NeRFs through geometry-aware reconstruction with Adaptive Cost Aggregation and Consistency-Aware Fusion. Most of these methods lack real-time rendering capability. ENeRF [22] accelerates generalizable NeRFs with depth-guided sampling but uses a fixed number of samples per ray, leading to inefficiency. In contrast, our method adaptively samples ray bundles based on local scene complexity, providing greater flexibility and efficiency. + +Generalizable 3D-GS. Recent advancements in generalizable Gaussian splatting methods have significantly enhanced the efficiency of novel view synthesis. These approaches eliminate the need for per-scene optimization by directly regressing Gaussian parameters through a feedforward architecture. PixelSplat [7] tackles scale ambiguity by utilizing a multiview epipolar transformer and scale-aware features to predict pixel-aligned 3D Gaussian primitives, though its design is limited to image pair inputs. GPS-Gaussian [47] extends this approach to stereo matching, incorporating epipolar rectification, disparity estimation, and feature encoding. However, its reliance on ground-truth depth maps restricts its applicability. Splatter Image [35] + +proposes a single-view reconstruction approach based on Gaussian splatting, though its focus on object-centric reconstruction constrains its generalization to unseen scenes. MVSGaussian [24] combines multi-view stereo with a generalizable 3D Gaussian representation for real-time novel view synthesis. However, its single-sample-per-ray strategy necessitates highly accurate depth estimations and hinders further efficiency improvements. + +# 3. Background + +Preliminaries on Generalizable NeRF. Given input multi-view images with intrinsic and extrinsic camera matrices, NeRF constructs the scene's radiance fields using a coordinate-based network. However, optimizing this network for each individual scene is computationally intensive. To address this, generalizable NeRF incorporates an additional geometry-aware feature, $\pmb{f}_p$ , extracted from the source images and included in the network input: + +$$ +\sigma_ {p}, c _ {p} = N N _ {\theta} \left(\boldsymbol {x} _ {p}, \boldsymbol {d} _ {p}, \boldsymbol {f} _ {p}\right), \tag {1} +$$ + +where $\boldsymbol{x}_p$ and $\boldsymbol{d}_p$ represent the coordinates and viewing direction of the 3D point $p$ , respectively. Here, $\sigma_p$ and $c_p$ denote the density and color of $p$ , defining the radiance field properties at this point. The coordinate network, $NN_{\theta}$ , decodes these radiance field attributes. Once the radiance fields for the entire scene are constructed, volume rendering techniques can synthesize the color for a pixel from any desired viewpoint. + +For an image of resolution $H \times W$ , NeRF samples $N$ points along the ray passing through each pixel, leading to a computational complexity of approximately $\mathcal{O}(HWN)$ . As the number of samples increases, so does the computational burden, posing challenges for rendering efficiency and motivating the need for optimized sampling and rendering strategies. + +Plenoptic Sampling Theory. To enhance efficiency, existing generalizable NeRFs aim to reduce the number of samples along each ray by concentrating sampling near scene surfaces [22, 24, 25]. However, these methods do not explore the reduction of the total number of rays required for rendering; instead, they uniformly sample all rays with a fixed number of samples. Some approaches attempt to reduce ray sampling needs through super-resolution techniques, though these are often constrained to specific content types such as faces [6]. + +Plenoptic sampling theory, introduced in [5], investigates the sampling bounds in light field rendering to determine the minimum angular density required for accurate reconstruction. The theory defines the maximum allowable camera spacing as: + +$$ +\Delta t \leq \frac {\operatorname* {m a x} \left(2 \Delta v , 1 / B _ {v} ^ {s}\right)}{f \cdot h _ {d}}, \tag {2} +$$ + +where $f$ is the focal length, $\Delta v$ is the spacing between camera rays, $B_v^s$ is the highest texture frequency, and $h_d$ is the disparity range defined as $h_d = \frac{1}{z_{\mathrm{min}}} - \frac{1}{z_{\mathrm{max}}}$ , with $z_{\mathrm{min}}$ and $z_{\mathrm{max}}$ denoting the minimum and maximum scene depths, respectively. Eq. (2) first implies that the ray spacing $\Delta v$ must satisfy the Nyquist sampling criterion, i.e., $\Delta v \leq \frac{1}{2B_v^s}$ , to avoid aliasing; it then highlights that geometric accuracy affects the sampling rate required for image capture: by decomposing the scene into $D$ depth ranges and sampling the light field in each range separately, the camera sampling interval can be increased by a factor of $D$ . + +Considering the relation between light fields and NeRFs [32], plenoptic sampling theory inspires our depth-guided bundle sampling strategy. On the one hand, the piecewise smooth nature of natural scenes means that high-frequency content is localized, with most regions being smooth. This allows for reduced sampling rates in smooth areas by effectively lowering the camera resolution (i.e., increasing $\Delta v$ ). However, this may cause aliasing in high-frequency regions (e.g., edges, textures, thin structures). On the other hand, given a fixed camera spacing $\Delta t$ , each sample in NeRF can be regarded as a local light field confined to a small disparity range, $h_d \leq \frac{\max(2\Delta v, \frac{1}{B_v^s})}{f \cdot \Delta t}$ . For high-frequency regions, they often suffer from inaccurate depth estimation, necessitating more samples to ensure each sample covers a small disparity range. These observations motivate our depth-guided bundle sampling strategy, which adapts the sampling density based on scene complexity. + +# 4. Method + +Our method is designed to synthesize target views from $V$ nearby source views $\{I_i\}_{i=1}^V$ at interactive frame rates, addressing challenges in efficient sampling. The proposed depth-guided bundle sampling strategy includes two main innovations: a novel bundle sampling approach that groups adjacent rays in the target view for joint sampling, and a depth-guided adaptive sampling method that dynamically allocates samples based on depth confidence. This adaptive approach reduces the overall number of samples while maintaining consistency with the plenoptic sampling principles. We apply our method to representative ENeRF [22] and MVSGaussian [24] to demonstrate its effectiveness in generalizable NeRF and 3D-GS, respectively. Fig. 2 presents the architecture of ENeRF+Ours, and a similar architecture is employed in MVSGaussian, where the sample features are also decoded into 3D-GS parameters. + +# 4.1. Bundle Sampling + +Our bundle sampling method improves efficiency by reducing the number of sampled rays. Adjacent rays in the target view are grouped into bundles, modeled as cones, with inscribed spheres sampled within each cone, as illustrated in + +![](images/08854d534b6547fb2ec48a4acb6399f7408643f0d22e46ad4dde94d4530a55df.jpg) +Figure 2. Network architecture of the proposed depth-guided bundle sampling strategy on ENeRF [22], denoted as ENeRF+Ours, which consists of four main components: (1) Multi-scale feature extraction; (2) Depth estimation to predict depth range; (3) Depth-guided bundle sampling, where rays are grouped into bundles and sampled adaptively based on predicted depth confidence; and (4) Radiance field prediction, which decodes each bundle's representation into individual ray colors. + +Fig. 3. This design broadens the angular coverage per sample, effectively reducing the total number of rays required. A similar sphere-based sampling approach is used in [15], where spheres are cast for each ray's cone to achieve anti-aliasing. In contrast, our method casts spheres for a cone of grouped rays, enabling collective sampling across multiple rays rather than treating them individually. However, this expanded coverage inevitably leads to loss of high-frequency details in the rendered image. To mitigate this, we encode each sample with both a joint bundle representation and a ray-specific representation, ensuring efficiency while preserving the necessary level of detail. + +# 4.1.1 Sphere-based cone sampling + +Our method models bundles of rays as cones passing through groups of adjacent pixels in the target view. We begin by casting rays from the camera's projection center $o$ through each pixel center $p_o$ , with ray directions defined as $d_r = p_o - o$ . Points along each ray are parameterized as $x_r = o + t d_r$ , where $t$ is the distance along the ray. + +As shown in Fig. 3(b), for a bundle of $K \times K$ rays, the corresponding region on the target image plane is modeled as a disk with radius $r_{\mathrm{tar}} = K \cdot r_p$ , where $r_p = \sqrt{\Delta x \cdot \Delta y / \pi}$ is the radius of a single-pixel disk, and $\Delta x$ and $\Delta y$ are the pixel's width and height in world coordinates, derived from camera parameters. The cone $\mathcal{C}$ is + +emitted from the camera's projection center along the average direction $\pmb{d}_{\mathcal{C}} = \sum_{\pmb{r} \in \mathcal{C}} \pmb{d}_{\pmb{r}} / K^2$ , and intersects the image plane at the disk, with the cone's axis defined as $\pmb{a}(t) = \pmb{o} + t \pmb{d}_{\mathcal{C}}$ . The cone is sampled using a set of inscribed spheres, $S(\dot{\pmb{x}}, \dot{\pmb{r}})$ , defined by their centers $\dot{\pmb{x}}$ and radii $\dot{\pmb{r}}$ as follows: + +$$ +\dot {\boldsymbol {x}} = \frac {1}{K ^ {2}} \sum_ {\boldsymbol {r} \in \mathcal {C}} \boldsymbol {x} _ {\boldsymbol {r}}, +$$ + +$$ +\dot {r} = \frac {\left\| \dot {\boldsymbol {x}} - \boldsymbol {o} \right\| _ {2} \cdot f \cdot r _ {\mathrm {t a r}}}{\left\| \boldsymbol {d} _ {\mathcal {C}} \right\| _ {2} \cdot \sqrt {\left(\sqrt {\left\| \boldsymbol {d} _ {\mathcal {C}} \right\| _ {2} ^ {2} - f ^ {2}} - r _ {\mathrm {t a r}}\right) ^ {2} + f ^ {2}}}. \tag {3} +$$ + +Given sorted distances $\{t_n\}_{n = 1}^V$ , the sphere centers $\dot{\pmb{x}}_n$ and radii $\dot{r}_n$ are computed. + +For a target view with resolution $H \times W$ , the image is divided into $\frac{H}{K} \times \frac{W}{K}$ bundles, each consisting of $K \times K$ pixels. This reduces the total number of samples by approximately $1 / K^2$ , ensuring efficient angular coverage without sacrificing essential surface detail. + +# 4.1.2 Multi-view image-based sphere encoding + +Each sphere covers a broad angular range, which extends to its feature representation. As shown in Fig. 3(b), we extract features based on the area occupied by each sphere, forming a joint bundle representation. However, this approach may + +![](images/c18be417532e9edc8b061289f556f86f55d5ac248dfdfad3f048e1584940e2ec.jpg) + +![](images/9cd2ae2304267912c9f11f82dca83113c51f9d90dd175e7b29eef4d617a8ce0d.jpg) +(a) Ray Sampling +(b) Bundle Sampling +Figure 3. Comparison of ray sampling strategies: (a) Traditional ray sampling, which processes each ray individually; (b) Proposed bundle sampling, which jointly samples neighboring rays to leverage scene coherence. + +omit high-frequency details. To retain fine-grained information from individual rays, we augment the joint bundle representation with a ray-specific representation. + +The joint bundle representation is derived from the area occupied by the spheres, necessitating an adjustment of the source view pixel spacing $\Delta v$ in Eq. (2). Inspired by area-sampling techniques used in scene-specific anti-aliasing NeRFs [2, 3, 15], we incorporate mipmap representations from [15] into a multi-view image-based encoding framework. We extract features $\{F_i\}_{i=1}^V$ from source views and convert them into mipmaps $\{M_i\}_{i=1}^V$ , creating a hierarchical structure that represents the pre-filtered feature space. The base level $M_i^{l_0}$ is the original feature map $F_i$ , with each subsequent level reducing the spatial resolution by a factor of two. To compute the feature vector $\{f_{S,i}\}_{i=1}^V$ for sphere $S(\dot{x},\dot{r})$ , we project it onto the $i$ -th source view to create a disc, with its radius $r_{\mathrm{src}}$ calculated as: + +$$ +r _ {\mathrm {s r c}} = \frac {\left\| \boldsymbol {d} _ {i} \right\| _ {2} ^ {2}}{f \cdot \sqrt {\left(\frac {\| \dot {\boldsymbol {x}} - \boldsymbol {o} _ {i} \| _ {2}}{\dot {r}}\right) ^ {2} - 1} + \sqrt {\left\| \boldsymbol {d} _ {i} \right\| _ {2} ^ {2} - f ^ {2}}}, \tag {4} +$$ + +where $\pmb{o}_i$ is the camera's projection center of the $i$ -th source view, and $\| \pmb{d}_i \|_2$ is the distance from the projection of $\dot{\pmb{x}}$ onto the image plane to $\pmb{o}_i$ (see Fig. 3(b)). The appropriate mipmap level $l$ corresponding to the sphere is determined + +using: + +$$ +l = \log_ {2} \left(\frac {r _ {\mathrm {s r c}}}{r _ {p}}\right). \tag {5} +$$ + +This process aligns the radius $r_{\mathrm{src}}$ of the sphere's projection with the corresponding feature elements' radius at a specific level $l$ within $M_i^l$ , which is equivalent to adjusting the spacing $\Delta v$ of the sampling camera. Once the appropriate mipmap level is identified, the feature vector $f_{S,i}$ can be accurately extracted from the mipmap $M_i$ via trilinear interpolation at $(x,y,l)$ . + +For ray-specific representation, the 3D points $\boldsymbol{x}_r$ associated with the sphere $S(\dot{\boldsymbol{x}},\dot{r})$ are projected onto the source views $\{I_i\}_{i = 1}^V$ to extract pixel-aligned colors. The extracted colors corresponding to the $K\times K$ rays within each bundle are concatenated to form the ray-specific representation, denoted as $\{f_{r,i}\}_{i = 1}^{V}$ , which captures high-frequency information for the rays as projected onto source views. + +By combining the joint bundle representation and ray-specific representation, our approach efficiently encodes the bundle samples while maintaining necessary scene details for accurate reconstruction. + +# 4.2. Depth-guided Adaptive Sampling + +To further optimize sampling, we restrict it to a predicted depth range, $R$ , estimated based on the depth value and associated confidence interval [22, 24, 25]. According to Eq. (2), for a fixed camera spacing $\Delta t$ , the disparity range covered by the local light field of each sample must satisfy $h_d \leq \frac{\max(2\Delta v, 1 / B_v^s)}{f \cdot \Delta t}$ , representing the maximum sampling spacing along the depth. Consequently, in smooth regions with a narrow depth range, fewer samples are sufficient for accurate reconstruction, while regions with a larger depth range require additional samples. Our depth-guided adaptive sampling strategy dynamically allocates samples near surfaces, ensuring that each sample covers a narrow depth range. The number of samples per bundle is computed as: + +$$ +N _ {\mathcal {C}} = \max \left(\operatorname {c e i l} \left(2 \cdot \boldsymbol {R} / \delta_ {s}\right), N _ {\max }\right), \tag {6} +$$ + +where $\delta_{s}$ denotes the minimum inter-sample spacing, with a maximum limit of $N_{\mathrm{max}}$ samples. The depth range is then divided into $N_{C}$ uniform intervals, with sampling performed at the center of each interval. For cases requiring only one sample, the sample is placed at the predicted surface point. + +Unlike existing depth-guided methods that apply uniform ray sampling with a fixed number of points, our adaptive approach dynamically adjusts the number of samples along the depth according to plenoptic sampling theory, significantly enhancing both efficiency and adaptability. + +# 4.3. Radiance Field Prediction + +For each sampled sphere, we predict the density $\sigma$ and blending weights $\{w_i\}_{i=1}^V$ as follows: + +$$ +\sigma , \left\{w _ {i} \right\} _ {i = 1} ^ {V} = \operatorname {M L P} \left(\left\{\boldsymbol {f} _ {\mathcal {S}, i} \right\} _ {i = 1} ^ {V}, \boldsymbol {f} _ {\text {v o x e l}}, \left\{\Delta \boldsymbol {d} _ {i} \right\} _ {i = 1} ^ {V}\right), \tag {7} +$$ + +where $f_{\mathrm{voxel}}$ is the voxel-aligned feature extracted from the feature volume (from depth estimation, see Fig. 2) by applying trilinear interpolation at the sphere center $\dot{x}$ . $\Delta d_i$ is the concatenation of the norm and direction of $d_i - d_c$ , with $d_i$ as the direction of $\dot{x}$ in the $i$ -th source view. The network design is adapted from [22]. The blending weights $\{w_i\}_{i=1}^V$ combine the features using softmax: + +$$ +\left\{\boldsymbol {f} _ {\mathcal {S}}, \boldsymbol {f} _ {\boldsymbol {r}} \right\} = \sum_ {i = 1} ^ {V} \frac {\exp \left(w _ {i}\right) \cdot \left\{\boldsymbol {f} _ {\mathcal {S} , i} \boldsymbol {f} _ {\boldsymbol {r} , i} \right\}}{\sum_ {j = 1} ^ {V} \exp \left(w _ {j}\right)}. \tag {8} +$$ + +We employ volume rendering to compute the per-bundle features $\{\pmb{F}_{\mathcal{C}},\pmb{F}_{\pmb{r}}\}$ by accumulating the features $\{\pmb{f}_S,\pmb{f}_r\} _n$ across the $N_{\mathcal{C}}$ sampled spheres along the cone $\mathcal{C}$ : + +$$ +\left\{\boldsymbol {F} _ {\mathcal {C}}, \boldsymbol {F} _ {\boldsymbol {r}} \right\} = \sum_ {n = 1} ^ {N _ {\mathcal {C}}} \tau_ {n} \left(1 - \exp (- \sigma_ {n})\right) \left\{\boldsymbol {f} _ {\mathcal {S}}, \boldsymbol {f} _ {\boldsymbol {r}} \right\} _ {n}, \tag {9} +$$ + +where $\tau_{n}$ is the accumulated volume transmittance from the cone apex to the sphere center, computed as: + +$$ +\tau_ {n} = \exp \left(- \sum_ {j = 1} ^ {n - 1} \sigma_ {j}\right). \tag {10} +$$ + +Neural renderer: For the target view with spatial dimensions $H \times W$ , the image is divided into $\frac{H}{K} \times \frac{W}{K}$ non-overlapping bundles, each containing $K \times K$ rays. Using Eq. (9), we generate a feature map $\{\pmb{F}_{\mathcal{C}}^{i}, \pmb{F}_{r}^{i}\}_{i=1}^{\frac{H}{K} \times \frac{W}{K}}$ . Here, $\pmb{F}_{\mathcal{C}}^{i}$ represents the aggregated joint bundle representation, which is processed through several residual convolutional blocks and decoded into coarse ray colors via sub-pixel convolution, yielding a coarse RGB map $\hat{\pmb{I}}_{c}$ of dimensions $H \times W \times 3$ . The second component, $\pmb{F}_{r}^{i}$ , contains the folded RGB values for individual rays and is unfolded to generate a fine RGB map $\hat{\pmb{I}}_{f}$ of dimensions $H \times W \times 3$ , preserving high-frequency details. The final high-resolution target view is obtained by summing these two components: + +$$ +\hat {\boldsymbol {I}} _ {\mathrm {t a r}} = \hat {\boldsymbol {I}} _ {c} + \hat {\boldsymbol {I}} _ {f}. \tag {11} +$$ + +For application to MVSGaussian [24], the renderer not only outputs the rendered target view image but also produces a feature map, which is subsequently processed to generate 3D-GS parameters following [24]. + +# 5. Experiments + +# 5.1. Settings + +Datasets. Following MVSNeRF [8, 22, 24], we train the generalizable model on the DTU training set [1] and evaluate it on the DTU test set. We also perform cross-dataset evaluation on the Real Forward-facing [27] and NeRF Synthetic [28] datasets using the trained model without fin-tuning. These datasets introduce significant variations in + +view distribution and scene content compared to the DTU dataset. The quality of the synthesized novel views is measured using the PSNR, SSIM [41], and LPIPS [46] metrics. + +Baselines. We compare our method against several state-of-the-art generalizable NeRF methods [8, 10, 22, 31, 36, 40, 43, 45], as well as the recent generalizable 3D-GS method [24]. We follow the same experimental settings as [8, 22, 24] and borrow some results reported in the respective papers. For additional baselines, such as [39, 43], we evaluate their performance using publicly released models. + +Implementation Details. To verify the effectiveness of the proposed depth-guided bundle sampling, we integrate it with two representative methods, ENeRF [22] and MVS-Gaussian [24], keeping hyperparameters consistent with their original configurations. Both models are trained with the loss function from [24]. We observed that direct training can sometimes result in instability during the initial stages. To address this, we employ a pre-training phase that uniformly samples $N_{\mathrm{max}}$ spheres within each bundle's depth range for 100 epochs. For the depth-guided adaptive sampling phase, we set $N_{\mathrm{max}} = 6$ and $\delta_s$ to 1/64 of the scene depth range, as defined in Eq. (6). For ENeRF+Ours, we evaluate different bundle sizes to assess the effectiveness of bundle sampling, with $2 \times 2$ and $4 \times 4$ indicating the bundle size. All models are trained and tested on an RTX A6000 GPU using the Adam optimizer [19]. + +# 5.2. Results + +We report quantitative results on the DTU test set in Tab. 1. Additional results on two other datasets are provided in Tab. 2. Notably, ENeRF [22] and MVSGaussian [24] achieve promising speeds by sampling only 1-2 points per ray, while other methods experience slower inference times due to the large number of samples required for accurate reconstruction. We can see that ENeRF+Ours $(2 \times 2)$ improves PSNR by 1.27 dB and increases FPS by $47\%$ compared to original ENeRF on DTU. Additionally, ENeRF+Ours $(4 \times 4)$ demonstrates better performance with over twice the speed of the original ENeRF. Performance is not significantly impacted by bundle size. For MVSGaussian+Ours, improvements are limited due to fewer sampling points and dependency on additional post-processing network layers; further performance gains may require a more integrated approach. Thanks to our efficient depth-guided bundle sampling strategy, ENeRF+Ours achieves competitive performance compared to state-of-the-art approaches, while also maintaining high inference speeds. The ability to adjust bundle size provides flexibility, allowing our method to balance speed and quality across different practical applications. Qualitative results in Fig. 4 show that ENeRF+Ours + +
Methods3-view2-view
PSNR ↑SSIM ↑LPIPS ↓Avg. samples per rayFPS ↑PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [45]19.310.7890.382960.019---
IBRNet [40]26.040.9170.1911280.217---
MVSNeRF [8]26.630.9310.1681280.41624.030.9140.192
ENeRF [22]27.610.9570.089219.525.480.9420.107
MatchNeRF [10]26.910.9340.1591281.0425.030.9190.181
GNT [39]26.390.9230.1561920.0124.320.9030.201
CG-NeRF [31]28.210.9300.17042.56---
MuRF [43]28.760.9610.077800.93425.610.9380.104
ConvGLR [36]31.650.9520.0801280.825---
MVSGaussian [24]28.210.9630.076121.525.780.9470.095
ENeRF+Ours (2 × 2)28.860.9640.0730.4228.626.390.9490.089
ENeRF+Ours (4 × 4)28.210.9570.0880.1043.626.090.9420.105
MVSGaussian+Ours28.400.9620.076123.426.160.9460.093
+ +Table 1. Quantitative results of generalization on the DTU testset [1] $(512\times 640)$ . The best result is highlighted in bold, while the second-best is underlined. + +
MethodsSettingsReal Forward-facingNeRF Synthetic
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [45]11.240.4860.6717.390.6580.411
IBRNet [40]21.790.7860.27922.440.8740.195
MVSNeRF [8]21.930.7950.25223.620.8970.176
ENeRF [22]23.630.8430.18226.170.9430.085
MatchNeRF [10]22.430.8050.24423.200.8970.164
GNT [39]3-view22.980.7610.22125.800.9050.104
CG-NeRF [31]23.930.8200.21025.010.9000.190
MuRF [43]23.700.8600.18124.370.8850.117
MVSGaussian [24]24.070.8570.16426.460.9480.071
ENeRF+Ours (2 × 2)24.330.8600.16226.490.9480.075
ENeRF+Ours (4 × 4)23.840.8510.17426.000.9430.083
MVSGaussian+Ours24.150.8580.16526.480.9470.070
MVSNeRF [8]20.220.7630.28720.560.8560.243
ENeRF [22]22.780.8210.19124.830.9310.117
MatchNeRF [10]20.590.7750.27620.570.8640.200
GNT [39]2-view20.910.6830.29323.470.8770.151
MuRF [43]22.550.8200.21822.960.8660.137
MVSGaussian [24]23.110.8340.17525.060.9370.079
ENeRF+Ours (2 × 2)23.060.8240.18625.010.9370.087
ENeRF+Ours (4 × 4)23.060.8260.18724.650.9320.098
MVSGaussian+Ours23.130.8340.17525.100.9370.079
+ +Table 2. Cross-dataset evaluation results on Real Forward-facing [27] (640 × 960) and NeRF Synthetic [28] (800 × 640) datasets. The best result is highlighted in bold, while the second-best is underlined. + +$(2 \times 2)$ generates high-quality views with enhanced scene detail and fewer artifacts. + +# 5.3. Ablations and Analysis + +We conduct a series of ablation studies to evaluate the effectiveness of our design. For efficiency, we limited our experiments to a 3-view configuration on the DTU dataset, employing bundle sizes of $2 \times 2$ and $4 \times 4$ on ENeRF [22]. + +Sampling Strategy. A unique aspect of our approach is the sphere-based bundle sampling (see Fig. 3), where we sample features from the mipmap of source view feature maps according to the area occupied by each sampled sphere. As shown in Tab. 3, substituting our sphere-based sampling with a pixel-aligned feature extraction at sphere centers results in a PSNR decrease of $1.2\mathrm{dB}$ . + +![](images/0f247432ca24828e12c1d58bb5f71da5dfea7885e3e569e80ddea573e73b2fbf.jpg) +Figure 4. Qualitative comparison of ENeRF+Ours $(2\times 2)$ with state-of-the-art methods [10, 22, 24] under 3-view setting. Each image triplet includes: the reconstructed image on the left, a zoomed-in view on the upper right, and the error map on the lower right. + +
Sphere SamplingX✓✓✓✓
Adaptive Sampling✓X✓✓✓
Joint Bundle Representation✓✓✓X✓
Ray-Specific Representation✓✓X✓✓
2×2PSNR ↑27.6628.8528.4727.8328.86
SSIM ↑0.9490.9640.9580.9590.964
LPIPS ↓0.0900.0760.0780.9330.073
FPS ↑29.217.029.433.7428.6
4×4PSNR ↑25.9328.0626.7427.4228.21
SSIM ↑0.9400.9540.9280.9550.957
LPIPS ↓0.1050.0950.1120.0990.088
FPS ↑44.229.145.349.643.6
+ +Table 3. Ablations. The best result is highlighted in bold. + +Depth-Guided Strategy. The proposed depth-guided adaptive sampling strategy enhances efficiency by not only skipping empty regions but also dynamically adjusting the number of samples according to depth confidence. As illustrated in Fig. 5, this approach allocates more samples at object boundaries and areas with depth discontinuities, where detail is essential. As presented in Tab. 3, this method achieves a $50\%$ increase in FPS while maintaining comparable image quality. + +Encoding Strategy. The joint bundle representation, containing pre-filtered features for the sampled spheres, is inherently smooth and lacks high-frequency details. To enhance detail preservation, we integrate a ray-specific representation that provides pixel-aligned colors for individual ray samples within each sphere. As illustrated in Tab. 3, adding this ray-specific representation boosts PSNR by 0.39 + +![](images/65da9d82e39d9e39419a9f85f15b997e0faf0495a6c59161a5d3860d4751bacd.jpg) +(a) Target View + +![](images/26708861635e1d35df585d489d4db5f33ab5fa04de73aa0d93e2b831cc7de14e.jpg) +(b) Sample Distribution +Figure 5. Visualization of sample allocation in depth-guided adaptive sampling. + +dB for a $2 \times 2$ bundle configuration and $1.47\mathrm{dB}$ for a $4 \times 4$ bundle configuration, with slight impact on FPS. + +# 6. Conclusion + +We proposed a novel bundle sampling strategy for generalizable novel view synthesis, inspired by plenoptic sampling theory to exploit the piece-wise smoothness of natural scenes. By grouping adjacent rays into bundles and sampling collectively, our approach reduces sampling redundancy while preserving rendering quality. Additionally, our depth-guided adaptive sampling method further optimizes efficiency by dynamically adjusting the number of samples based on depth confidence, concentrating samples at complex regions such as object boundaries and depth discontinuities. Applied to existing methods, our method achieved significant improvements in speed and fidelity. Experimental results on multiple datasets show that our method provides competitive quality with a substantial speed advantage over existing generalizable radiance field models. The flexibility to adjust bundle size also enables trade-offs between speed and quality, broadening its practical applicability to high-resolution, real-time applications. + +# References + +[1] Henrik Aanaes, Rasmus Ramsbøl Jensen, George Vogiatzis, Engin Tola, and Anders Bjorholm Dahl. Large-scale data for multiple-view stereopsis. 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However, rendering high-resolution images remains computationally intensive due to the need for dense sampling of all rays. Recognizing that natural scenes are typically piecewise smooth and sampling all rays is often redundant, we propose a novel depth-guided bundle sampling strategy to accelerate rendering. By grouping adjacent rays into a bundle and sampling them collectively, a shared representation is generated for decoding all rays within the bundle. To further optimize efficiency, our adaptive sampling strategy dynamically allocates samples based on depth confidence, concentrating more samples in complex regions while reducing them in smoother areas. When applied to ENeRF, our method achieves up to a 1.27 dB PSNR improvement and a " + }, + { + "bbox": [ + 55, + 266, + 296, + 518 + ], + "type": "inline_equation", + "content": "47\\%" + }, + { + "bbox": [ + 55, + 266, + 296, + 518 + ], + "type": "text", + "content": " increase in FPS on the DTU dataset. Extensive experiments on synthetic and real-world datasets demonstrate state-of-the-art rendering quality and up to " + }, + { + "bbox": [ + 55, + 266, + 296, + 518 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 55, + 266, + 296, + 518 + ], + "type": "text", + "content": " faster rendering compared to existing generalizable methods. Code is available at https://github.com/KLMAV-CUC/GDB-NeRF." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 540, + 135, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 135, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 135, + 552 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 559, + 295, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 559, + 295, + 668 + ], + "spans": [ + { + "bbox": [ + 55, + 559, + 295, + 668 + ], + "type": "text", + "content": "Novel view synthesis aims to generate photorealistic images from new perspectives using a sparse set of input images. The advent of Neural Radiance Field (NeRF) [28] and subsequent advancements [34] have significantly improved the quality of view synthesis, garnering substantial interest in both academia and industry. NeRF models scenes as continuous radiance and density fields, producing high-quality images. However, this comes at a cost: NeRF's volume rendering process requires numerous samples per ray, leading" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 324, + 243, + 545, + 382 + ], + "blocks": [ + { + "bbox": [ + 324, + 243, + 545, + 382 + ], + "lines": [ + { + "bbox": [ + 324, + 243, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 324, + 243, + 545, + 382 + ], + "type": "image", + "image_path": "035d5169a777617d5c2818f4c9d0d92c197afcc4918193f037b9052383a02201.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 392, + 555, + 449 + ], + "lines": [ + { + "bbox": [ + 313, + 392, + 555, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 555, + 449 + ], + "type": "text", + "content": "Figure 1. Rendering Quality (PSNR) vs. Speed (FPS) on the DTU Dataset [1] under 3-view setting. ENeRF+Ours achieves state-of-the-art rendering quality and faster rendering speed, outperforming existing generalizable novel view synthesis methods [8, 10, 22, 24, 40, 43]. Model parameter counts are also provided." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 472, + 555, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 555, + 519 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 555, + 519 + ], + "type": "text", + "content": "to significant computational demands and impeding real-time, high-resolution synthesis. Additionally, NeRF models are typically scene-specific, requiring lengthy training for each new scene." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "type": "text", + "content": "Recent efforts to improve NeRF efficiency have focused on compact data structures and lightweight MLP decoders to store radiance fields, significantly reducing both training and rendering times for scene-specific NeRFs [11, 13, 14, 29, 42]. Techniques like baking and empty space skipping have also contributed to these improvements. However, these methods require per-scene optimization, limiting their ability to generalize to novel scenes. Generalizable NeRFs address this limitation by predicting radiance fields from multi-view images, enabling novel view synthesis for previously unseen scenes [8, 12, 16, 21, 22, 25, 26, 31, 36, 37, 39, 40, 43, 45]. Although promising, generalizable methods often face slower rendering speeds, as scene-specific optimizations are incompatible. While some approaches attempt to reduce per-ray sampling [22, 30], real-time rendering remains challenging." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 674, + 295, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 674, + 295, + 702 + ], + "spans": [ + { + "bbox": [ + 55, + 674, + 295, + 702 + ], + "type": "text", + "content": "*This work is supported by National Key R&D Program of China under Grant No. 2021YFF0900701, and the National Natural Science Foundation of China under Grant No. 62001432." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 68, + 703, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 703, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 68, + 703, + 144, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11217" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "content": "The expensive computational cost in NeRF-related methods is primarily due to the need for dense sampling across all pixels. From a plenoptic sampling perspective [5], this full-pixel sampling implicitly assumes high-frequency information is uniform across the scene. However, natural scenes are usually piecewise smooth, with high-frequency details in specific areas like object boundaries and depth discontinuities. Based on this observation, we propose a novel bundle sampling strategy. This method groups adjacent rays and samples them jointly at a global, low sampling rate for smooth regions. In non-smooth areas, high-frequency information is captured by increasing samples along the depth dimension. Furthermore, samples within each bundle are further constrained to a small range using depth maps. As a result, this approach significantly reduces the overall number of samples, greatly improving efficiency." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 266, + 295, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 266, + 295, + 541 + ], + "spans": [ + { + "bbox": [ + 56, + 266, + 295, + 541 + ], + "type": "text", + "content": "We integrate this depth-guided bundle sampling strategy into a representative generalizable NeRF, ENeRF [22]. Instead of sampling points along individual rays, our method samples 3D areas along bundles of adjacent rays by casting a cone that encompasses the corresponding pixels. Within this cone, inscribed spheres are sampled and featurized with pre-filtered features extracted from the source views. Through depth-guided adaptive sampling, sampling is constrained to a predicted depth range, with the number of samples adjusted dynamically: in smooth regions with a narrow depth range, fewer samples suffice for accurate reconstruction, while areas with a broader depth range require more samples to capture finer details. This adaptive approach aligns with the plenoptic principle [5], ensuring each sample covers a narrow depth range near surfaces. A bundle representation is then computed via volume rendering and decoded to predict the color of each ray. We also apply this depth-guided bundle sampling strategy to a recent generalizable 3D Gaussian splatting (3D-GS) method [24]. Extensive experiments demonstrate that our method significantly improves the efficiency of base models and achieves synthesis quality comparable to state-of-the-art generalizable models, with significant improvements in rendering speed." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 544, + 288, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 544, + 288, + 555 + ], + "spans": [ + { + "bbox": [ + 67, + 544, + 288, + 555 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 558, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 56, + 558, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 558, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 56, + 558, + 295, + 605 + ], + "type": "text", + "content": "- We propose a novel bundle sampling strategy that jointly samples bundles of adjacent rays, significantly reducing the number of samples needed and improving both rendering speed and quality." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 606, + 295, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 606, + 295, + 654 + ], + "spans": [ + { + "bbox": [ + 56, + 606, + 295, + 654 + ], + "type": "text", + "content": "- We introduce a depth-guided adaptive sampling method that dynamically adjusts the number of samples based on local depth range, achieving over a " + }, + { + "bbox": [ + 56, + 606, + 295, + 654 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 56, + 606, + 295, + 654 + ], + "type": "text", + "content": " increase in rendering speed without sacrificing quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 654, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 654, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 654, + 295, + 714 + ], + "type": "text", + "content": "- We validate our method on both generalizable NeRF and 3D-GS across various datasets. Our method achieves state-of-the-art rendering quality and up to " + }, + { + "bbox": [ + 56, + 654, + 295, + 714 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 56, + 654, + 295, + 714 + ], + "type": "text", + "content": " faster rendering than existing generalizable NeRFs. It also offers flexibility, allowing adjustments between quality and effi" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 323, + 72, + 502, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 72, + 502, + 84 + ], + "spans": [ + { + "bbox": [ + 323, + 72, + 502, + 84 + ], + "type": "text", + "content": "ciency depending on practical requirements." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 96, + 406, + 108 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 96, + 406, + 108 + ], + "spans": [ + { + "bbox": [ + 314, + 96, + 406, + 108 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 117, + 555, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 117, + 555, + 285 + ], + "spans": [ + { + "bbox": [ + 313, + 117, + 555, + 285 + ], + "type": "text", + "content": "Accelerating NeRF. NeRFs represent scenes as continuous color and density fields using neural networks, achieving high-quality view synthesis via volume rendering. Despite their success, NeRFs suffer from high computational demands, slowing training and inference. To address this, recent methods have replaced large neural representations with local sparse feature fields and shallow MLP decoders [9, 23, 29, 33, 44], or spherical harmonics embeddings [9, 13, 17]. Other solutions utilize voxel grids [23], octrees [13], tensor decompositions [9], or 3D Gaussians [18], as well as efficient sampling [14, 20, 22, 30] and image-space convolutions [4, 38], leading to significant speed-ups. However, these improvements remain scene-specific, requiring training for each new scene." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 301, + 555, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 555, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 555, + 540 + ], + "type": "text", + "content": "Generalizable NeRF. These methods generalize NeRF by encoding features for each 3D point and decoding them into volume density and radiance, akin to image-based rendering through NeRF-like volume rendering techniques [8, 10, 12, 16, 21, 22, 25, 26, 31, 36, 37, 39, 40, 45]. While these methods improve across-scene generalizability, they remain limited by slow optimization and rendering. CG-NeRF [31] predicts coarse radiance fields and depth, refining fine-scale features sampled near the estimated depth. ConvGLR [36] processes all camera rays in a low-resolution latent space, which improves quality in sparse-view synthesis. GeFu [25] improves generalizable NeRFs through geometry-aware reconstruction with Adaptive Cost Aggregation and Consistency-Aware Fusion. Most of these methods lack real-time rendering capability. ENeRF [22] accelerates generalizable NeRFs with depth-guided sampling but uses a fixed number of samples per ray, leading to inefficiency. In contrast, our method adaptively samples ray bundles based on local scene complexity, providing greater flexibility and efficiency." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 556, + 715 + ], + "type": "text", + "content": "Generalizable 3D-GS. Recent advancements in generalizable Gaussian splatting methods have significantly enhanced the efficiency of novel view synthesis. These approaches eliminate the need for per-scene optimization by directly regressing Gaussian parameters through a feedforward architecture. PixelSplat [7] tackles scale ambiguity by utilizing a multiview epipolar transformer and scale-aware features to predict pixel-aligned 3D Gaussian primitives, though its design is limited to image pair inputs. GPS-Gaussian [47] extends this approach to stereo matching, incorporating epipolar rectification, disparity estimation, and feature encoding. However, its reliance on ground-truth depth maps restricts its applicability. Splatter Image [35]" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "11218" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 168 + ], + "type": "text", + "content": "proposes a single-view reconstruction approach based on Gaussian splatting, though its focus on object-centric reconstruction constrains its generalization to unseen scenes. MVSGaussian [24] combines multi-view stereo with a generalizable 3D Gaussian representation for real-time novel view synthesis. However, its single-sample-per-ray strategy necessitates highly accurate depth estimations and hinders further efficiency improvements." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 177, + 134, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 177, + 134, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 177, + 134, + 192 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 198, + 295, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 198, + 295, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 198, + 295, + 293 + ], + "type": "text", + "content": "Preliminaries on Generalizable NeRF. Given input multi-view images with intrinsic and extrinsic camera matrices, NeRF constructs the scene's radiance fields using a coordinate-based network. However, optimizing this network for each individual scene is computationally intensive. To address this, generalizable NeRF incorporates an additional geometry-aware feature, " + }, + { + "bbox": [ + 55, + 198, + 295, + 293 + ], + "type": "inline_equation", + "content": "\\pmb{f}_p" + }, + { + "bbox": [ + 55, + 198, + 295, + 293 + ], + "type": "text", + "content": ", extracted from the source images and included in the network input:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 117, + 300, + 295, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 300, + 295, + 315 + ], + "spans": [ + { + "bbox": [ + 117, + 300, + 295, + 315 + ], + "type": "interline_equation", + "content": "\\sigma_ {p}, c _ {p} = N N _ {\\theta} \\left(\\boldsymbol {x} _ {p}, \\boldsymbol {d} _ {p}, \\boldsymbol {f} _ {p}\\right), \\tag {1}", + "image_path": "f4045dd01388612ad70a014584ab2eb4f0f80dd4bb171cf696ad179a5ed17430.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_p" + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "inline_equation", + "content": "\\boldsymbol{d}_p" + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "content": " represent the coordinates and viewing direction of the 3D point " + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "content": ", respectively. Here, " + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "inline_equation", + "content": "\\sigma_p" + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "inline_equation", + "content": "c_p" + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "content": " denote the density and color of " + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "content": ", defining the radiance field properties at this point. The coordinate network, " + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "inline_equation", + "content": "NN_{\\theta}" + }, + { + "bbox": [ + 55, + 319, + 295, + 415 + ], + "type": "text", + "content": ", decodes these radiance field attributes. Once the radiance fields for the entire scene are constructed, volume rendering techniques can synthesize the color for a pixel from any desired viewpoint." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "spans": [ + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "type": "text", + "content": "For an image of resolution " + }, + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "type": "text", + "content": ", NeRF samples " + }, + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "type": "text", + "content": " points along the ray passing through each pixel, leading to a computational complexity of approximately " + }, + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(HWN)" + }, + { + "bbox": [ + 55, + 415, + 295, + 499 + ], + "type": "text", + "content": ". As the number of samples increases, so does the computational burden, posing challenges for rendering efficiency and motivating the need for optimized sampling and rendering strategies." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 513, + 295, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 513, + 295, + 632 + ], + "spans": [ + { + "bbox": [ + 55, + 513, + 295, + 632 + ], + "type": "text", + "content": "Plenoptic Sampling Theory. To enhance efficiency, existing generalizable NeRFs aim to reduce the number of samples along each ray by concentrating sampling near scene surfaces [22, 24, 25]. However, these methods do not explore the reduction of the total number of rays required for rendering; instead, they uniformly sample all rays with a fixed number of samples. Some approaches attempt to reduce ray sampling needs through super-resolution techniques, though these are often constrained to specific content types such as faces [6]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 632, + 295, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 632, + 295, + 692 + ], + "spans": [ + { + "bbox": [ + 55, + 632, + 295, + 692 + ], + "type": "text", + "content": "Plenoptic sampling theory, introduced in [5], investigates the sampling bounds in light field rendering to determine the minimum angular density required for accurate reconstruction. The theory defines the maximum allowable camera spacing as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 123, + 691, + 295, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 691, + 295, + 717 + ], + "spans": [ + { + "bbox": [ + 123, + 691, + 295, + 717 + ], + "type": "interline_equation", + "content": "\\Delta t \\leq \\frac {\\operatorname* {m a x} \\left(2 \\Delta v , 1 / B _ {v} ^ {s}\\right)}{f \\cdot h _ {d}}, \\tag {2}", + "image_path": "f408f149f5dd2d17a9ef675eaac41bc4cf8a319977c94e6e86282a674c48545c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": " is the focal length, " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "\\Delta v" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": " is the spacing between camera rays, " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "B_v^s" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": " is the highest texture frequency, and " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "h_d" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": " is the disparity range defined as " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "h_d = \\frac{1}{z_{\\mathrm{min}}} - \\frac{1}{z_{\\mathrm{max}}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{min}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{max}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": " denoting the minimum and maximum scene depths, respectively. Eq. (2) first implies that the ray spacing " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "\\Delta v" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": " must satisfy the Nyquist sampling criterion, i.e., " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "\\Delta v \\leq \\frac{1}{2B_v^s}" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": ", to avoid aliasing; it then highlights that geometric accuracy affects the sampling rate required for image capture: by decomposing the scene into " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": " depth ranges and sampling the light field in each range separately, the camera sampling interval can be increased by a factor of " + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "spans": [ + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "type": "text", + "content": "Considering the relation between light fields and NeRFs [32], plenoptic sampling theory inspires our depth-guided bundle sampling strategy. On the one hand, the piecewise smooth nature of natural scenes means that high-frequency content is localized, with most regions being smooth. This allows for reduced sampling rates in smooth areas by effectively lowering the camera resolution (i.e., increasing " + }, + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "type": "inline_equation", + "content": "\\Delta v" + }, + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "type": "text", + "content": "). However, this may cause aliasing in high-frequency regions (e.g., edges, textures, thin structures). On the other hand, given a fixed camera spacing " + }, + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "type": "text", + "content": ", each sample in NeRF can be regarded as a local light field confined to a small disparity range, " + }, + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "type": "inline_equation", + "content": "h_d \\leq \\frac{\\max(2\\Delta v, \\frac{1}{B_v^s})}{f \\cdot \\Delta t}" + }, + { + "bbox": [ + 313, + 205, + 555, + 417 + ], + "type": "text", + "content": ". For high-frequency regions, they often suffer from inaccurate depth estimation, necessitating more samples to ensure each sample covers a small disparity range. These observations motivate our depth-guided bundle sampling strategy, which adapts the sampling density based on scene complexity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 426, + 370, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 370, + 439 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 370, + 439 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 447, + 555, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 447, + 555, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 447, + 555, + 639 + ], + "type": "text", + "content": "Our method is designed to synthesize target views from " + }, + { + "bbox": [ + 313, + 447, + 555, + 639 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 313, + 447, + 555, + 639 + ], + "type": "text", + "content": " nearby source views " + }, + { + "bbox": [ + 313, + 447, + 555, + 639 + ], + "type": "inline_equation", + "content": "\\{I_i\\}_{i=1}^V" + }, + { + "bbox": [ + 313, + 447, + 555, + 639 + ], + "type": "text", + "content": " at interactive frame rates, addressing challenges in efficient sampling. The proposed depth-guided bundle sampling strategy includes two main innovations: a novel bundle sampling approach that groups adjacent rays in the target view for joint sampling, and a depth-guided adaptive sampling method that dynamically allocates samples based on depth confidence. This adaptive approach reduces the overall number of samples while maintaining consistency with the plenoptic sampling principles. We apply our method to representative ENeRF [22] and MVSGaussian [24] to demonstrate its effectiveness in generalizable NeRF and 3D-GS, respectively. Fig. 2 presents the architecture of ENeRF+Ours, and a similar architecture is employed in MVSGaussian, where the sample features are also decoded into 3D-GS parameters." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 647, + 419, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 419, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 419, + 659 + ], + "type": "text", + "content": "4.1. Bundle Sampling" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "Our bundle sampling method improves efficiency by reducing the number of sampled rays. Adjacent rays in the target view are grouped into bundles, modeled as cones, with inscribed spheres sampled within each cone, as illustrated in" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11219" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 68, + 545, + 312 + ], + "blocks": [ + { + "bbox": [ + 77, + 68, + 545, + 312 + ], + "lines": [ + { + "bbox": [ + 77, + 68, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 77, + 68, + 545, + 312 + ], + "type": "image", + "image_path": "08854d534b6547fb2ec48a4acb6399f7408643f0d22e46ad4dde94d4530a55df.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 319, + 555, + 365 + ], + "lines": [ + { + "bbox": [ + 54, + 319, + 555, + 365 + ], + "spans": [ + { + "bbox": [ + 54, + 319, + 555, + 365 + ], + "type": "text", + "content": "Figure 2. Network architecture of the proposed depth-guided bundle sampling strategy on ENeRF [22], denoted as ENeRF+Ours, which consists of four main components: (1) Multi-scale feature extraction; (2) Depth estimation to predict depth range; (3) Depth-guided bundle sampling, where rays are grouped into bundles and sampled adaptively based on predicted depth confidence; and (4) Radiance field prediction, which decodes each bundle's representation into individual ray colors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 384, + 297, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 384, + 297, + 529 + ], + "spans": [ + { + "bbox": [ + 54, + 384, + 297, + 529 + ], + "type": "text", + "content": "Fig. 3. This design broadens the angular coverage per sample, effectively reducing the total number of rays required. A similar sphere-based sampling approach is used in [15], where spheres are cast for each ray's cone to achieve anti-aliasing. In contrast, our method casts spheres for a cone of grouped rays, enabling collective sampling across multiple rays rather than treating them individually. However, this expanded coverage inevitably leads to loss of high-frequency details in the rendered image. To mitigate this, we encode each sample with both a joint bundle representation and a ray-specific representation, ensuring efficiency while preserving the necessary level of detail." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 548, + 211, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 211, + 560 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 211, + 560 + ], + "type": "text", + "content": "4.1.1 Sphere-based cone sampling" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "text", + "content": "Our method models bundles of rays as cones passing through groups of adjacent pixels in the target view. We begin by casting rays from the camera's projection center " + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "text", + "content": " through each pixel center " + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "text", + "content": ", with ray directions defined as " + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "inline_equation", + "content": "d_r = p_o - o" + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "text", + "content": ". Points along each ray are parameterized as " + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "inline_equation", + "content": "x_r = o + t d_r" + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 567, + 296, + 640 + ], + "type": "text", + "content": " is the distance along the ray." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "As shown in Fig. 3(b), for a bundle of " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "K \\times K" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": " rays, the corresponding region on the target image plane is modeled as a disk with radius " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{tar}} = K \\cdot r_p" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "r_p = \\sqrt{\\Delta x \\cdot \\Delta y / \\pi}" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": " is the radius of a single-pixel disk, and " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\Delta x" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\Delta y" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": " are the pixel's width and height in world coordinates, derived from camera parameters. The cone " + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "text", + "content": "emitted from the camera's projection center along the average direction " + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "inline_equation", + "content": "\\pmb{d}_{\\mathcal{C}} = \\sum_{\\pmb{r} \\in \\mathcal{C}} \\pmb{d}_{\\pmb{r}} / K^2" + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "text", + "content": ", and intersects the image plane at the disk, with the cone's axis defined as " + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "inline_equation", + "content": "\\pmb{a}(t) = \\pmb{o} + t \\pmb{d}_{\\mathcal{C}}" + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "text", + "content": ". The cone is sampled using a set of inscribed spheres, " + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "inline_equation", + "content": "S(\\dot{\\pmb{x}}, \\dot{\\pmb{r}})" + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "text", + "content": ", defined by their centers " + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "inline_equation", + "content": "\\dot{\\pmb{x}}" + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "text", + "content": " and radii " + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "inline_equation", + "content": "\\dot{\\pmb{r}}" + }, + { + "bbox": [ + 313, + 384, + 555, + 456 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 330, + 462, + 403, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 462, + 403, + 491 + ], + "spans": [ + { + "bbox": [ + 330, + 462, + 403, + 491 + ], + "type": "interline_equation", + "content": "\\dot {\\boldsymbol {x}} = \\frac {1}{K ^ {2}} \\sum_ {\\boldsymbol {r} \\in \\mathcal {C}} \\boldsymbol {x} _ {\\boldsymbol {r}},", + "image_path": "4eaafe1a30657a379354f884bd9925c88ba9ccdecbcfec55f31386efe6bf6c26.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 330, + 493, + 555, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 493, + 555, + 540 + ], + "spans": [ + { + "bbox": [ + 330, + 493, + 555, + 540 + ], + "type": "interline_equation", + "content": "\\dot {r} = \\frac {\\left\\| \\dot {\\boldsymbol {x}} - \\boldsymbol {o} \\right\\| _ {2} \\cdot f \\cdot r _ {\\mathrm {t a r}}}{\\left\\| \\boldsymbol {d} _ {\\mathcal {C}} \\right\\| _ {2} \\cdot \\sqrt {\\left(\\sqrt {\\left\\| \\boldsymbol {d} _ {\\mathcal {C}} \\right\\| _ {2} ^ {2} - f ^ {2}} - r _ {\\mathrm {t a r}}\\right) ^ {2} + f ^ {2}}}. \\tag {3}", + "image_path": "cc00faa1f93b0e1d6ce9868393947e4c8ae1ed6221e79443118b2fbc71ff3f11.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "type": "text", + "content": "Given sorted distances " + }, + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "type": "inline_equation", + "content": "\\{t_n\\}_{n = 1}^V" + }, + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "type": "text", + "content": ", the sphere centers " + }, + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "type": "inline_equation", + "content": "\\dot{\\pmb{x}}_n" + }, + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "type": "text", + "content": " and radii " + }, + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "type": "inline_equation", + "content": "\\dot{r}_n" + }, + { + "bbox": [ + 313, + 548, + 554, + 572 + ], + "type": "text", + "content": " are computed." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "spans": [ + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "text", + "content": "For a target view with resolution " + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "text", + "content": ", the image is divided into " + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "inline_equation", + "content": "\\frac{H}{K} \\times \\frac{W}{K}" + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "text", + "content": " bundles, each consisting of " + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "inline_equation", + "content": "K \\times K" + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "text", + "content": " pixels. This reduces the total number of samples by approximately " + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "inline_equation", + "content": "1 / K^2" + }, + { + "bbox": [ + 313, + 572, + 555, + 632 + ], + "type": "text", + "content": ", ensuring efficient angular coverage without sacrificing essential surface detail." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 647, + 522, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 522, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 522, + 659 + ], + "type": "text", + "content": "4.1.2 Multi-view image-based sphere encoding" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 715 + ], + "type": "text", + "content": "Each sphere covers a broad angular range, which extends to its feature representation. As shown in Fig. 3(b), we extract features based on the area occupied by each sphere, forming a joint bundle representation. However, this approach may" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11220" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 72, + 292, + 178 + ], + "blocks": [ + { + "bbox": [ + 65, + 72, + 292, + 178 + ], + "lines": [ + { + "bbox": [ + 65, + 72, + 292, + 178 + ], + "spans": [ + { + "bbox": [ + 65, + 72, + 292, + 178 + ], + "type": "image", + "image_path": "c18be417532e9edc8b061289f556f86f55d5ac248dfdfad3f048e1584940e2ec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 65, + 191, + 291, + 312 + ], + "blocks": [ + { + "bbox": [ + 146, + 182, + 205, + 191 + ], + "lines": [ + { + "bbox": [ + 146, + 182, + 205, + 191 + ], + "spans": [ + { + "bbox": [ + 146, + 182, + 205, + 191 + ], + "type": "text", + "content": "(a) Ray Sampling" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 65, + 191, + 291, + 312 + ], + "lines": [ + { + "bbox": [ + 65, + 191, + 291, + 312 + ], + "spans": [ + { + "bbox": [ + 65, + 191, + 291, + 312 + ], + "type": "image", + "image_path": "9cd2ae2304267912c9f11f82dca83113c51f9d90dd175e7b29eef4d617a8ce0d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 141, + 314, + 211, + 324 + ], + "lines": [ + { + "bbox": [ + 141, + 314, + 211, + 324 + ], + "spans": [ + { + "bbox": [ + 141, + 314, + 211, + 324 + ], + "type": "text", + "content": "(b) Bundle Sampling" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 333, + 295, + 378 + ], + "lines": [ + { + "bbox": [ + 55, + 333, + 295, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 333, + 295, + 378 + ], + "type": "text", + "content": "Figure 3. Comparison of ray sampling strategies: (a) Traditional ray sampling, which processes each ray individually; (b) Proposed bundle sampling, which jointly samples neighboring rays to leverage scene coherence." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 400, + 295, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 400, + 295, + 437 + ], + "spans": [ + { + "bbox": [ + 55, + 400, + 295, + 437 + ], + "type": "text", + "content": "omit high-frequency details. To retain fine-grained information from individual rays, we augment the joint bundle representation with a ray-specific representation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": "The joint bundle representation is derived from the area occupied by the spheres, necessitating an adjustment of the source view pixel spacing " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "\\Delta v" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": " in Eq. (2). Inspired by area-sampling techniques used in scene-specific anti-aliasing NeRFs [2, 3, 15], we incorporate mipmap representations from [15] into a multi-view image-based encoding framework. We extract features " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "\\{F_i\\}_{i=1}^V" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": " from source views and convert them into mipmaps " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "\\{M_i\\}_{i=1}^V" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": ", creating a hierarchical structure that represents the pre-filtered feature space. The base level " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "M_i^{l_0}" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": " is the original feature map " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "F_i" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": ", with each subsequent level reducing the spatial resolution by a factor of two. To compute the feature vector " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "\\{f_{S,i}\\}_{i=1}^V" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": " for sphere " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "S(\\dot{x},\\dot{r})" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": ", we project it onto the " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": "-th source view to create a disc, with its radius " + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{src}}" + }, + { + "bbox": [ + 55, + 437, + 295, + 605 + ], + "type": "text", + "content": " calculated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 72, + 613, + 295, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 613, + 295, + 656 + ], + "spans": [ + { + "bbox": [ + 72, + 613, + 295, + 656 + ], + "type": "interline_equation", + "content": "r _ {\\mathrm {s r c}} = \\frac {\\left\\| \\boldsymbol {d} _ {i} \\right\\| _ {2} ^ {2}}{f \\cdot \\sqrt {\\left(\\frac {\\| \\dot {\\boldsymbol {x}} - \\boldsymbol {o} _ {i} \\| _ {2}}{\\dot {r}}\\right) ^ {2} - 1} + \\sqrt {\\left\\| \\boldsymbol {d} _ {i} \\right\\| _ {2} ^ {2} - f ^ {2}}}, \\tag {4}", + "image_path": "ba5087cbb5ef6d5e6ac033c450008f682cb6d23e51724da6fc82462e7126b892.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{o}_i" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " is the camera's projection center of the " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "-th source view, and " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\| \\pmb{d}_i \\|_2" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " is the distance from the projection of " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\dot{\\pmb{x}}" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " onto the image plane to " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{o}_i" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " (see Fig. 3(b)). The appropriate mipmap level " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " corresponding to the sphere is determined" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 73, + 342, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 73, + 342, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 73, + 342, + 84 + ], + "type": "text", + "content": "using:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 397, + 83, + 555, + 110 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 83, + 555, + 110 + ], + "spans": [ + { + "bbox": [ + 397, + 83, + 555, + 110 + ], + "type": "interline_equation", + "content": "l = \\log_ {2} \\left(\\frac {r _ {\\mathrm {s r c}}}{r _ {p}}\\right). \\tag {5}", + "image_path": "4e2111e074e06fbdbcc47cdb903126ad2480480c67801da3402a41efc88703d0.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "spans": [ + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "content": "This process aligns the radius " + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{src}}" + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "content": " of the sphere's projection with the corresponding feature elements' radius at a specific level " + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "content": " within " + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "inline_equation", + "content": "M_i^l" + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "content": ", which is equivalent to adjusting the spacing " + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "inline_equation", + "content": "\\Delta v" + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "content": " of the sampling camera. Once the appropriate mipmap level is identified, the feature vector " + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "inline_equation", + "content": "f_{S,i}" + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "content": " can be accurately extracted from the mipmap " + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "inline_equation", + "content": "M_i" + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "content": " via trilinear interpolation at " + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "inline_equation", + "content": "(x,y,l)" + }, + { + "bbox": [ + 313, + 110, + 555, + 194 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "text", + "content": "For ray-specific representation, the 3D points " + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_r" + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "text", + "content": " associated with the sphere " + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "inline_equation", + "content": "S(\\dot{\\boldsymbol{x}},\\dot{r})" + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "text", + "content": " are projected onto the source views " + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "inline_equation", + "content": "\\{I_i\\}_{i = 1}^V" + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "text", + "content": " to extract pixel-aligned colors. The extracted colors corresponding to the " + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "inline_equation", + "content": "K\\times K" + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "text", + "content": " rays within each bundle are concatenated to form the ray-specific representation, denoted as " + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "inline_equation", + "content": "\\{f_{r,i}\\}_{i = 1}^{V}" + }, + { + "bbox": [ + 313, + 194, + 554, + 277 + ], + "type": "text", + "content": ", which captures high-frequency information for the rays as projected onto source views." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 278, + 554, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 278, + 554, + 325 + ], + "spans": [ + { + "bbox": [ + 313, + 278, + 554, + 325 + ], + "type": "text", + "content": "By combining the joint bundle representation and ray-specific representation, our approach efficiently encodes the bundle samples while maintaining necessary scene details for accurate reconstruction." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 331, + 493, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 493, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 493, + 344 + ], + "type": "text", + "content": "4.2. Depth-guided Adaptive Sampling" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "type": "text", + "content": "To further optimize sampling, we restrict it to a predicted depth range, " + }, + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "type": "text", + "content": ", estimated based on the depth value and associated confidence interval [22, 24, 25]. According to Eq. (2), for a fixed camera spacing " + }, + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "type": "text", + "content": ", the disparity range covered by the local light field of each sample must satisfy " + }, + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "type": "inline_equation", + "content": "h_d \\leq \\frac{\\max(2\\Delta v, 1 / B_v^s)}{f \\cdot \\Delta t}" + }, + { + "bbox": [ + 313, + 350, + 555, + 507 + ], + "type": "text", + "content": ", representing the maximum sampling spacing along the depth. Consequently, in smooth regions with a narrow depth range, fewer samples are sufficient for accurate reconstruction, while regions with a larger depth range require additional samples. Our depth-guided adaptive sampling strategy dynamically allocates samples near surfaces, ensuring that each sample covers a narrow depth range. The number of samples per bundle is computed as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 361, + 511, + 555, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 511, + 555, + 525 + ], + "spans": [ + { + "bbox": [ + 361, + 511, + 555, + 525 + ], + "type": "interline_equation", + "content": "N _ {\\mathcal {C}} = \\max \\left(\\operatorname {c e i l} \\left(2 \\cdot \\boldsymbol {R} / \\delta_ {s}\\right), N _ {\\max }\\right), \\tag {6}", + "image_path": "f3c8f9693c3b474c05d68f9e5ff1ea5551bcd2ff7eb6fedc934177cd9d893057.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "type": "inline_equation", + "content": "\\delta_{s}" + }, + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "type": "text", + "content": " denotes the minimum inter-sample spacing, with a maximum limit of " + }, + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{max}}" + }, + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "type": "text", + "content": " samples. The depth range is then divided into " + }, + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "type": "inline_equation", + "content": "N_{C}" + }, + { + "bbox": [ + 313, + 529, + 554, + 589 + ], + "type": "text", + "content": " uniform intervals, with sampling performed at the center of each interval. For cases requiring only one sample, the sample is placed at the predicted surface point." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 589, + 554, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 589, + 554, + 649 + ], + "spans": [ + { + "bbox": [ + 313, + 589, + 554, + 649 + ], + "type": "text", + "content": "Unlike existing depth-guided methods that apply uniform ray sampling with a fixed number of points, our adaptive approach dynamically adjusts the number of samples along the depth according to plenoptic sampling theory, significantly enhancing both efficiency and adaptability." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 654, + 459, + 666 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 459, + 666 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 459, + 666 + ], + "type": "text", + "content": "4.3. Radiance Field Prediction" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 672, + 554, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 672, + 554, + 697 + ], + "spans": [ + { + "bbox": [ + 313, + 672, + 554, + 697 + ], + "type": "text", + "content": "For each sampled sphere, we predict the density " + }, + { + "bbox": [ + 313, + 672, + 554, + 697 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 672, + 554, + 697 + ], + "type": "text", + "content": " and blending weights " + }, + { + "bbox": [ + 313, + 672, + 554, + 697 + ], + "type": "inline_equation", + "content": "\\{w_i\\}_{i=1}^V" + }, + { + "bbox": [ + 313, + 672, + 554, + 697 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 323, + 700, + 555, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 700, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 323, + 700, + 555, + 715 + ], + "type": "interline_equation", + "content": "\\sigma , \\left\\{w _ {i} \\right\\} _ {i = 1} ^ {V} = \\operatorname {M L P} \\left(\\left\\{\\boldsymbol {f} _ {\\mathcal {S}, i} \\right\\} _ {i = 1} ^ {V}, \\boldsymbol {f} _ {\\text {v o x e l}}, \\left\\{\\Delta \\boldsymbol {d} _ {i} \\right\\} _ {i = 1} ^ {V}\\right), \\tag {7}", + "image_path": "d678ff43f04a021ae16ecbd3869b1b6700a26bfed9f8a9258687d9ef42c3c635.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11221" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{voxel}}" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " is the voxel-aligned feature extracted from the feature volume (from depth estimation, see Fig. 2) by applying trilinear interpolation at the sphere center " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "\\dot{x}" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "\\Delta d_i" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " is the concatenation of the norm and direction of " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "d_i - d_c" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " as the direction of " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "\\dot{x}" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "-th source view. The network design is adapted from [22]. The blending weights " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "\\{w_i\\}_{i=1}^V" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": " combine the features using softmax:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 95, + 163, + 295, + 198 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 163, + 295, + 198 + ], + "spans": [ + { + "bbox": [ + 95, + 163, + 295, + 198 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {f} _ {\\mathcal {S}}, \\boldsymbol {f} _ {\\boldsymbol {r}} \\right\\} = \\sum_ {i = 1} ^ {V} \\frac {\\exp \\left(w _ {i}\\right) \\cdot \\left\\{\\boldsymbol {f} _ {\\mathcal {S} , i} \\boldsymbol {f} _ {\\boldsymbol {r} , i} \\right\\}}{\\sum_ {j = 1} ^ {V} \\exp \\left(w _ {j}\\right)}. \\tag {8}", + "image_path": "e9b530f4f98ee94e2d633b870b804464abb4ddfdc25a4c6c4e8b1791e5d961eb.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "spans": [ + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "text", + "content": "We employ volume rendering to compute the per-bundle features " + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "inline_equation", + "content": "\\{\\pmb{F}_{\\mathcal{C}},\\pmb{F}_{\\pmb{r}}\\}" + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "text", + "content": " by accumulating the features " + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "inline_equation", + "content": "\\{\\pmb{f}_S,\\pmb{f}_r\\} _n" + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "text", + "content": " across the " + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "inline_equation", + "content": "N_{\\mathcal{C}}" + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "text", + "content": " sampled spheres along the cone " + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 55, + 203, + 295, + 239 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 247, + 295, + 279 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 247, + 295, + 279 + ], + "spans": [ + { + "bbox": [ + 69, + 247, + 295, + 279 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {F} _ {\\mathcal {C}}, \\boldsymbol {F} _ {\\boldsymbol {r}} \\right\\} = \\sum_ {n = 1} ^ {N _ {\\mathcal {C}}} \\tau_ {n} \\left(1 - \\exp (- \\sigma_ {n})\\right) \\left\\{\\boldsymbol {f} _ {\\mathcal {S}}, \\boldsymbol {f} _ {\\boldsymbol {r}} \\right\\} _ {n}, \\tag {9}", + "image_path": "f16ed82e487f319b50487c347c6f0c9facefa315848e9280b63506650b576284.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 286, + 295, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 286, + 295, + 310 + ], + "spans": [ + { + "bbox": [ + 55, + 286, + 295, + 310 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 286, + 295, + 310 + ], + "type": "inline_equation", + "content": "\\tau_{n}" + }, + { + "bbox": [ + 55, + 286, + 295, + 310 + ], + "type": "text", + "content": " is the accumulated volume transmittance from the cone apex to the sphere center, computed as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 131, + 317, + 294, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 317, + 294, + 350 + ], + "spans": [ + { + "bbox": [ + 131, + 317, + 294, + 350 + ], + "type": "interline_equation", + "content": "\\tau_ {n} = \\exp \\left(- \\sum_ {j = 1} ^ {n - 1} \\sigma_ {j}\\right). \\tag {10}", + "image_path": "20eedc61057f3159888b245c71a7d2abb1d2b1e4383cc2863d7ffa12fb180ea8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": "Neural renderer: For the target view with spatial dimensions " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": ", the image is divided into " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\frac{H}{K} \\times \\frac{W}{K}" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": " non-overlapping bundles, each containing " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "K \\times K" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": " rays. Using Eq. (9), we generate a feature map " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\{\\pmb{F}_{\\mathcal{C}}^{i}, \\pmb{F}_{r}^{i}\\}_{i=1}^{\\frac{H}{K} \\times \\frac{W}{K}}" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{\\mathcal{C}}^{i}" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": " represents the aggregated joint bundle representation, which is processed through several residual convolutional blocks and decoded into coarse ray colors via sub-pixel convolution, yielding a coarse RGB map " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{I}}_{c}" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": " of dimensions " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "H \\times W \\times 3" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": ". The second component, " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{r}^{i}" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": ", contains the folded RGB values for individual rays and is unfolded to generate a fine RGB map " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{I}}_{f}" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": " of dimensions " + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "inline_equation", + "content": "H \\times W \\times 3" + }, + { + "bbox": [ + 55, + 357, + 296, + 517 + ], + "type": "text", + "content": ", preserving high-frequency details. The final high-resolution target view is obtained by summing these two components:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 142, + 523, + 295, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 142, + 523, + 295, + 539 + ], + "spans": [ + { + "bbox": [ + 142, + 523, + 295, + 539 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {I}} _ {\\mathrm {t a r}} = \\hat {\\boldsymbol {I}} _ {c} + \\hat {\\boldsymbol {I}} _ {f}. \\tag {11}", + "image_path": "8ae0c8a6d2faa44592b046fd6fada034c545a76c737daf36776fa1c842f43bf3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 545, + 296, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 296, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 296, + 594 + ], + "type": "text", + "content": "For application to MVSGaussian [24], the renderer not only outputs the rendered target view image but also produces a feature map, which is subsequently processed to generate 3D-GS parameters following [24]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 604, + 136, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 604, + 136, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 604, + 136, + 617 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 623, + 116, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 623, + 116, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 623, + 116, + 635 + ], + "type": "text", + "content": "5.1. Settings" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": "Datasets. Following MVSNeRF [8, 22, 24], we train the generalizable model on the DTU training set [1] and evaluate it on the DTU test set. We also perform cross-dataset evaluation on the Real Forward-facing [27] and NeRF Synthetic [28] datasets using the trained model without fin-tuning. These datasets introduce significant variations in" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": "view distribution and scene content compared to the DTU dataset. The quality of the synthesized novel views is measured using the PSNR, SSIM [41], and LPIPS [46] metrics." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 127, + 555, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 127, + 555, + 212 + ], + "spans": [ + { + "bbox": [ + 313, + 127, + 555, + 212 + ], + "type": "text", + "content": "Baselines. We compare our method against several state-of-the-art generalizable NeRF methods [8, 10, 22, 31, 36, 40, 43, 45], as well as the recent generalizable 3D-GS method [24]. We follow the same experimental settings as [8, 22, 24] and borrow some results reported in the respective papers. For additional baselines, such as [39, 43], we evaluate their performance using publicly released models." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "text", + "content": "Implementation Details. To verify the effectiveness of the proposed depth-guided bundle sampling, we integrate it with two representative methods, ENeRF [22] and MVS-Gaussian [24], keeping hyperparameters consistent with their original configurations. Both models are trained with the loss function from [24]. We observed that direct training can sometimes result in instability during the initial stages. To address this, we employ a pre-training phase that uniformly samples " + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{max}}" + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "text", + "content": " spheres within each bundle's depth range for 100 epochs. For the depth-guided adaptive sampling phase, we set " + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{max}} = 6" + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "inline_equation", + "content": "\\delta_s" + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "text", + "content": " to 1/64 of the scene depth range, as defined in Eq. (6). For ENeRF+Ours, we evaluate different bundle sizes to assess the effectiveness of bundle sampling, with " + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 313, + 229, + 555, + 422 + ], + "type": "text", + "content": " indicating the bundle size. All models are trained and tested on an RTX A6000 GPU using the Adam optimizer [19]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 431, + 372, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 372, + 442 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 372, + 442 + ], + "type": "text", + "content": "5.2. Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "content": "We report quantitative results on the DTU test set in Tab. 1. Additional results on two other datasets are provided in Tab. 2. Notably, ENeRF [22] and MVSGaussian [24] achieve promising speeds by sampling only 1-2 points per ray, while other methods experience slower inference times due to the large number of samples required for accurate reconstruction. We can see that ENeRF+Ours " + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "inline_equation", + "content": "(2 \\times 2)" + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "content": " improves PSNR by 1.27 dB and increases FPS by " + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "inline_equation", + "content": "47\\%" + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "content": " compared to original ENeRF on DTU. Additionally, ENeRF+Ours " + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "inline_equation", + "content": "(4 \\times 4)" + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "content": " demonstrates better performance with over twice the speed of the original ENeRF. Performance is not significantly impacted by bundle size. For MVSGaussian+Ours, improvements are limited due to fewer sampling points and dependency on additional post-processing network layers; further performance gains may require a more integrated approach. Thanks to our efficient depth-guided bundle sampling strategy, ENeRF+Ours achieves competitive performance compared to state-of-the-art approaches, while also maintaining high inference speeds. The ability to adjust bundle size provides flexibility, allowing our method to balance speed and quality across different practical applications. Qualitative results in Fig. 4 show that ENeRF+Ours" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11222" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 70, + 535, + 243 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 535, + 243 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 535, + 243 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 535, + 243 + ], + "type": "table", + "html": "
Methods3-view2-view
PSNR ↑SSIM ↑LPIPS ↓Avg. samples per rayFPS ↑PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [45]19.310.7890.382960.019---
IBRNet [40]26.040.9170.1911280.217---
MVSNeRF [8]26.630.9310.1681280.41624.030.9140.192
ENeRF [22]27.610.9570.089219.525.480.9420.107
MatchNeRF [10]26.910.9340.1591281.0425.030.9190.181
GNT [39]26.390.9230.1561920.0124.320.9030.201
CG-NeRF [31]28.210.9300.17042.56---
MuRF [43]28.760.9610.077800.93425.610.9380.104
ConvGLR [36]31.650.9520.0801280.825---
MVSGaussian [24]28.210.9630.076121.525.780.9470.095
ENeRF+Ours (2 × 2)28.860.9640.0730.4228.626.390.9490.089
ENeRF+Ours (4 × 4)28.210.9570.0880.1043.626.090.9420.105
MVSGaussian+Ours28.400.9620.076123.426.160.9460.093
", + "image_path": "460897e4fead37569871256dd755fd2a22ddcb0c82a1d48bcd8cd0cdcf2d24f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 115, + 284, + 495, + 544 + ], + "blocks": [ + { + "bbox": [ + 55, + 251, + 553, + 273 + ], + "lines": [ + { + "bbox": [ + 55, + 251, + 553, + 273 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 553, + 273 + ], + "type": "text", + "content": "Table 1. Quantitative results of generalization on the DTU testset [1] " + }, + { + "bbox": [ + 55, + 251, + 553, + 273 + ], + "type": "inline_equation", + "content": "(512\\times 640)" + }, + { + "bbox": [ + 55, + 251, + 553, + 273 + ], + "type": "text", + "content": ". The best result is highlighted in bold, while the second-best is underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 115, + 284, + 495, + 544 + ], + "lines": [ + { + "bbox": [ + 115, + 284, + 495, + 544 + ], + "spans": [ + { + "bbox": [ + 115, + 284, + 495, + 544 + ], + "type": "table", + "html": "
MethodsSettingsReal Forward-facingNeRF Synthetic
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [45]11.240.4860.6717.390.6580.411
IBRNet [40]21.790.7860.27922.440.8740.195
MVSNeRF [8]21.930.7950.25223.620.8970.176
ENeRF [22]23.630.8430.18226.170.9430.085
MatchNeRF [10]22.430.8050.24423.200.8970.164
GNT [39]3-view22.980.7610.22125.800.9050.104
CG-NeRF [31]23.930.8200.21025.010.9000.190
MuRF [43]23.700.8600.18124.370.8850.117
MVSGaussian [24]24.070.8570.16426.460.9480.071
ENeRF+Ours (2 × 2)24.330.8600.16226.490.9480.075
ENeRF+Ours (4 × 4)23.840.8510.17426.000.9430.083
MVSGaussian+Ours24.150.8580.16526.480.9470.070
MVSNeRF [8]20.220.7630.28720.560.8560.243
ENeRF [22]22.780.8210.19124.830.9310.117
MatchNeRF [10]20.590.7750.27620.570.8640.200
GNT [39]2-view20.910.6830.29323.470.8770.151
MuRF [43]22.550.8200.21822.960.8660.137
MVSGaussian [24]23.110.8340.17525.060.9370.079
ENeRF+Ours (2 × 2)23.060.8240.18625.010.9370.087
ENeRF+Ours (4 × 4)23.060.8260.18724.650.9320.098
MVSGaussian+Ours23.130.8340.17525.100.9370.079
", + "image_path": "8765f4e712b469a71be871e456055f7aa721a4a655713d558bd4e3dc0cbec46d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 553, + 553, + 575 + ], + "lines": [ + { + "bbox": [ + 55, + 553, + 553, + 575 + ], + "spans": [ + { + "bbox": [ + 55, + 553, + 553, + 575 + ], + "type": "text", + "content": "Table 2. Cross-dataset evaluation results on Real Forward-facing [27] (640 × 960) and NeRF Synthetic [28] (800 × 640) datasets. The best result is highlighted in bold, while the second-best is underlined." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 597, + 295, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 295, + 620 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 295, + 620 + ], + "type": "inline_equation", + "content": "(2 \\times 2)" + }, + { + "bbox": [ + 55, + 597, + 295, + 620 + ], + "type": "text", + "content": " generates high-quality views with enhanced scene detail and fewer artifacts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 642, + 186, + 654 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 186, + 654 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 186, + 654 + ], + "type": "text", + "content": "5.3. Ablations and Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": "We conduct a series of ablation studies to evaluate the effectiveness of our design. For efficiency, we limited our experiments to a 3-view configuration on the DTU dataset, employing bundle sizes of " + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": " on ENeRF [22]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 597, + 555, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 597, + 555, + 681 + ], + "spans": [ + { + "bbox": [ + 313, + 597, + 555, + 681 + ], + "type": "text", + "content": "Sampling Strategy. A unique aspect of our approach is the sphere-based bundle sampling (see Fig. 3), where we sample features from the mipmap of source view feature maps according to the area occupied by each sampled sphere. As shown in Tab. 3, substituting our sphere-based sampling with a pixel-aligned feature extraction at sphere centers results in a PSNR decrease of " + }, + { + "bbox": [ + 313, + 597, + 555, + 681 + ], + "type": "inline_equation", + "content": "1.2\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 597, + 555, + 681 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11223" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 542, + 236 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 542, + 236 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 542, + 236 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 542, + 236 + ], + "type": "image", + "image_path": "0f247432ca24828e12c1d58bb5f71da5dfea7885e3e569e80ddea573e73b2fbf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 245, + 555, + 269 + ], + "lines": [ + { + "bbox": [ + 55, + 245, + 555, + 269 + ], + "spans": [ + { + "bbox": [ + 55, + 245, + 555, + 269 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of ENeRF+Ours " + }, + { + "bbox": [ + 55, + 245, + 555, + 269 + ], + "type": "inline_equation", + "content": "(2\\times 2)" + }, + { + "bbox": [ + 55, + 245, + 555, + 269 + ], + "type": "text", + "content": " with state-of-the-art methods [10, 22, 24] under 3-view setting. Each image triplet includes: the reconstructed image on the left, a zoomed-in view on the upper right, and the error map on the lower right." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 57, + 285, + 294, + 467 + ], + "blocks": [ + { + "bbox": [ + 57, + 285, + 294, + 467 + ], + "lines": [ + { + "bbox": [ + 57, + 285, + 294, + 467 + ], + "spans": [ + { + "bbox": [ + 57, + 285, + 294, + 467 + ], + "type": "table", + "html": "
Sphere SamplingX✓✓✓✓
Adaptive Sampling✓X✓✓✓
Joint Bundle Representation✓✓✓X✓
Ray-Specific Representation✓✓X✓✓
2×2PSNR ↑27.6628.8528.4727.8328.86
SSIM ↑0.9490.9640.9580.9590.964
LPIPS ↓0.0900.0760.0780.9330.073
FPS ↑29.217.029.433.7428.6
4×4PSNR ↑25.9328.0626.7427.4228.21
SSIM ↑0.9400.9540.9280.9550.957
LPIPS ↓0.1050.0950.1120.0990.088
FPS ↑44.229.145.349.643.6
", + "image_path": "88359cae4ddcca676a33b1715a3049628f79471349e1a08621ac75d7716b8759.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 70, + 475, + 280, + 487 + ], + "lines": [ + { + "bbox": [ + 70, + 475, + 280, + 487 + ], + "spans": [ + { + "bbox": [ + 70, + 475, + 280, + 487 + ], + "type": "text", + "content": "Table 3. Ablations. The best result is highlighted in bold." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 507, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 507, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 54, + 507, + 295, + 616 + ], + "type": "text", + "content": "Depth-Guided Strategy. The proposed depth-guided adaptive sampling strategy enhances efficiency by not only skipping empty regions but also dynamically adjusting the number of samples according to depth confidence. As illustrated in Fig. 5, this approach allocates more samples at object boundaries and areas with depth discontinuities, where detail is essential. As presented in Tab. 3, this method achieves a " + }, + { + "bbox": [ + 54, + 507, + 295, + 616 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 54, + 507, + 295, + 616 + ], + "type": "text", + "content": " increase in FPS while maintaining comparable image quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 629, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 629, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 629, + 295, + 715 + ], + "type": "text", + "content": "Encoding Strategy. The joint bundle representation, containing pre-filtered features for the sampled spheres, is inherently smooth and lacks high-frequency details. To enhance detail preservation, we integrate a ray-specific representation that provides pixel-aligned colors for individual ray samples within each sphere. As illustrated in Tab. 3, adding this ray-specific representation boosts PSNR by 0.39" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 321, + 286, + 434, + 363 + ], + "blocks": [ + { + "bbox": [ + 321, + 286, + 434, + 363 + ], + "lines": [ + { + "bbox": [ + 321, + 286, + 434, + 363 + ], + "spans": [ + { + "bbox": [ + 321, + 286, + 434, + 363 + ], + "type": "image", + "image_path": "65da9d82e39d9e39419a9f85f15b997e0faf0495a6c59161a5d3860d4751bacd.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 351, + 364, + 402, + 374 + ], + "lines": [ + { + "bbox": [ + 351, + 364, + 402, + 374 + ], + "spans": [ + { + "bbox": [ + 351, + 364, + 402, + 374 + ], + "type": "text", + "content": "(a) Target View" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 436, + 286, + 551, + 363 + ], + "blocks": [ + { + "bbox": [ + 436, + 286, + 551, + 363 + ], + "lines": [ + { + "bbox": [ + 436, + 286, + 551, + 363 + ], + "spans": [ + { + "bbox": [ + 436, + 286, + 551, + 363 + ], + "type": "image", + "image_path": "26708861635e1d35df585d489d4db5f33ab5fa04de73aa0d93e2b831cc7de14e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 454, + 364, + 531, + 374 + ], + "lines": [ + { + "bbox": [ + 454, + 364, + 531, + 374 + ], + "spans": [ + { + "bbox": [ + 454, + 364, + 531, + 374 + ], + "type": "text", + "content": "(b) Sample Distribution" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 384, + 555, + 407 + ], + "lines": [ + { + "bbox": [ + 313, + 384, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 555, + 407 + ], + "type": "text", + "content": "Figure 5. Visualization of sample allocation in depth-guided adaptive sampling." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "type": "text", + "content": "dB for a " + }, + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "type": "text", + "content": " bundle configuration and " + }, + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "type": "inline_equation", + "content": "1.47\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "type": "text", + "content": " for a " + }, + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 313, + 434, + 555, + 460 + ], + "type": "text", + "content": " bundle configuration, with slight impact on FPS." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 481, + 388, + 494 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 481, + 388, + 494 + ], + "spans": [ + { + "bbox": [ + 313, + 481, + 388, + 494 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 504, + 555, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 504, + 555, + 704 + ], + "spans": [ + { + "bbox": [ + 312, + 504, + 555, + 704 + ], + "type": "text", + "content": "We proposed a novel bundle sampling strategy for generalizable novel view synthesis, inspired by plenoptic sampling theory to exploit the piece-wise smoothness of natural scenes. By grouping adjacent rays into bundles and sampling collectively, our approach reduces sampling redundancy while preserving rendering quality. Additionally, our depth-guided adaptive sampling method further optimizes efficiency by dynamically adjusting the number of samples based on depth confidence, concentrating samples at complex regions such as object boundaries and depth discontinuities. Applied to existing methods, our method achieved significant improvements in speed and fidelity. Experimental results on multiple datasets show that our method provides competitive quality with a substantial speed advantage over existing generalizable radiance field models. The flexibility to adjust bundle size also enables trade-offs between speed and quality, broadening its practical applicability to high-resolution, real-time applications." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11224" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "text", + "content": "[1] Henrik Aanaes, Rasmus Ramsbøl Jensen, George Vogiatzis, Engin Tola, and Anders Bjorholm Dahl. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19680-19690, 2024. 2" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "11226" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_content_list.json b/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..87c0d190567f0a775b483b490c458217556d5a56 --- /dev/null +++ b/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_content_list.json @@ -0,0 +1,1697 @@ +[ + { + "type": "text", + "text": "DepthCrafter: Generating Consistent Long Depth Sequences for Open-world Videos", + "text_level": 1, + "bbox": [ + 191, + 130, + 805, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wenbo Hu $^{1* \\dagger}$ Xiangjun Gao $^{2*}$ Xiaoyu Li $^{1* \\dagger}$ Sijie Zhao $^{1}$ Xiaodong Cun $^{1}$ Yong Zhang $^{1}$ Long Quan $^{2}$ Ying Shan $^{3,1}$", + "bbox": [ + 245, + 200, + 746, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Tencent AI Lab $^{2}$ The Hong Kong University of Science and Technology $^{3}$ ARC Lab, Tencent PCG https://depthcrafter.github.io", + "bbox": [ + 101, + 244, + 898, + 280 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d812dbdf926a8eb8de9c622c1ccc1ac6903524080180c231f60cc61a54740793.jpg", + "image_caption": [ + "Figure 1. We innovate DepthCrafter, a novel video depth estimation approach, that can generate temporally consistent long depth sequences with fine-grained details for open-world videos, without requiring additional information such as camera poses or optical flow." + ], + "image_footnote": [], + "bbox": [ + 101, + 290, + 890, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 604, + 326, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Estimating video depth in open-world scenarios is challenging due to the diversity of videos in appearance, content motion, camera movement, and length. We present DepthCrafter, an innovative method for generating temporally consistent long depth sequences with intricate details for open-world videos, without requiring any supplementary information such as camera poses or optical flow. The generalization ability to open-world videos is achieved by training the video-to-depth model from a pretrained image-to-video diffusion model, through our meticulously designed three-stage training strategy. Our training approach enables the model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both precise depth details and rich content diversity from realistic and synthetic datasets. We also propose an inference strategy that can process extremely", + "bbox": [ + 88, + 637, + 485, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "long videos through segment-wise estimation and seamless stitching. Comprehensive evaluations on multiple datasets reveal that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. Furthermore, DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation.", + "bbox": [ + 511, + 607, + 906, + 713 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 739, + 643, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Monocular depth estimation, serving as the bridge linking 2D observations and the 3D world, has been a long-standing fundamental problem in computer vision. It plays a crucial role in a wide range of downstream applications, e.g., mixed reality, AI-generated content, autonomous driving, and robotics [14, 24, 27, 28, 40, 57, 72, 73]. The inherent ambiguity makes it challenging, as the observed information from a single view is insufficient to determine the depth of a scene uniquely.", + "bbox": [ + 509, + 763, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Joint first authors. † Corresponding authors.", + "bbox": [ + 107, + 886, + 364, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2005", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With recent advances in foundation models, we have witnessed significant progress in depth estimation from monocular images [13, 18, 32, 43, 47, 67, 68, 71]. However, all these methods are tailored for static images, without considering the temporal information in videos. Temporal inconsistency, or flickering, would be observed when directly applying them to videos, as shown in Fig. 1. Existing video depth estimation methods [35, 41, 58, 63, 77] typically try to optimize temporally consistent depth sequences from a pre-trained image depth model, with a given or learnable camera poses. Their performance is sensitive to both the proportion of dynamic content and the quality of the camera poses. Yet, videos in the open world are diverse in content, motion, camera movement, and length, making these methods hard to perform well in practice. Moreover, the required camera poses are usually non-trivial to obtain in open-world videos, particularly for long videos and videos with abundant dynamic content.", + "bbox": [ + 89, + 90, + 480, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we aim to generate temporally consistent long depth sequences with high-fidelity details for diverse open-world videos, without requiring any additional information. Observing the strong capability of diffusion models in generating various types of videos [3, 4, 6, 8, 9, 23, 64, 65], we propose DepthCrafter, to leverage the video diffusion model for video depth estimation, while maintaining the generalization ability to open-world videos. To train our DepthCrafter, a video-to-depth model, from a pre-trained image-to-video diffusion model, we compile paired videodepth datasets in two styles, i.e. realistic and synthetic, since the realistic dataset provides rich content diversity and the synthetic dataset offers precise depth details. On the aspect of temporal context, most existing video diffusion models can only produce a fixed and small number of frames at one time, e.g., 25 frames in Stable Video Diffusion (SVD) [3], which, however, is usually too short for open-world video depth estimation to accurately arrange depth distributions throughout the video. To enable variable long temporal context and fuse the respective advantages of the two-styled datasets, we present a three-stage training strategy to progressively train certain layers of the diffusion model on different datasets with variable lengths. By doing so, we can adapt the video diffusion model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both the precise depth details and rich content diversity. To further support extremely long videos, we tailor an inference strategy to process the video in overlapped segments and seamlessly stitch them together.", + "bbox": [ + 91, + 368, + 482, + 805 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We extensively evaluate our DepthCrafter on diverse datasets, including indoor, outdoor, static, dynamic, realistic, and synthetic videos, under zero-shot settings. Both qualitative and quantitative results demonstrate that our DepthCrafter achieves state-of-the-art performance in openworld video depth estimation, outperforming existing meth", + "bbox": [ + 89, + 810, + 480, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ods by a large margin. Besides, we demonstrate that our DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation. Our contributions are summarized below:", + "bbox": [ + 511, + 90, + 903, + 150 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We innovate DepthCrafter, a novel method to generate temporally consistent long depth sequences with fine-grained details for open-world videos, outperforming existing approaches by a large margin.", + "- We present a three-stage training strategy to enable generating depth sequences with a long and variable temporal context, up to 110 frames. It also allows us to harvest both the precise depth details and rich content diversity from synthetic and realistic datasets.", + "- We design an inference strategy to segment-wisely process videos beyond 110 frames and seamlessly stitch them together, facilitating depth estimation for extremely long videos." + ], + "bbox": [ + 511, + 152, + 903, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 369, + 653, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image depth estimation. Image depth estimation aims at predicting the depth map from a single image [1, 15, 17, 36, 38, 45, 66]. However, the generalization ability to diverse open-world scenes is hindered by the limited training data. To this end, MiDaS [49] presented the affine-invariant depth representation, enabling mixed training datasets. Depth-Anything (V2) [67, 68] followed this idea and proposed to train the model on both labeled and large-scale unlabeled images, achieving good generalization ability. Marigold [32] and follow-up works [18, 21, 42] leverage the diffusion priors to realize zero-shot transfer to unseen datasets. Besides the affine-invariant depth, another stream of methods tried to estimate the absolute metric depth [2, 5, 25, 47, 71]. All these methods are tailored for static images without considering the temporal consistency, while our work aims to generate temporally consistent long depth sequences for open-world videos.", + "bbox": [ + 511, + 397, + 906, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video depth estimation. Existing video depth estimation methods could be categorized into two classes: test-time optimization and feed-forward prediction. Test-time optimization methods [11, 35, 41, 77] involve an optimization procedure for each video during inference, which typically requires camera poses or optical flow. Their results are usually consistent, but the requirement of camera poses or optical flow would limit their applicability to open-world videos. Feed-forward prediction methods directly predict depth sequences from videos [39, 58, 60, 61, 63, 69, 70, 74], e.g., DeepV2D [58] combines camera motion estimation with depth estimation, MAMO [69] leverages memory attention, and NVDS [63] introduces a plug-and-play stabilization network. However, due to the limited video depth training data, these methods often fail to address the in-the-wild videos with diverse content. By leveraging the pre", + "bbox": [ + 511, + 657, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2006", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/511e4c99dea41bbb4f686e1dfcf9c2d187c09705f24eac16902168839d66ab8b.jpg", + "image_caption": [ + "Figure 2. Overview of our DepthCrafter. It is a conditional diffusion model that models the distribution $p(\\mathbf{d} \\mid \\mathbf{v})$ over the depth sequence $\\mathbf{d}$ conditioned on the input video $\\mathbf{v}$ . We train the model in three stages, where the spatial or temporal layers of the diffusion model are progressively learned on our compiled realistic or synthetic datasets with variable lengths $T$ . During inference, given an open-world video, it can generate temporally consistent long depth sequences with fine-grained details for the entire video from initialized Gaussian noise, without requiring any supplementary information, such as camera poses or optical flow." + ], + "image_footnote": [], + "bbox": [ + 109, + 85, + 890, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "trained video diffusion model and our designed three-stage training strategy, our method demonstrates a powerful ability for open-world video depth estimation.", + "bbox": [ + 88, + 376, + 480, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video diffusion models. Diffusion models [22, 56] have shown remarkable video generation ability [3, 4, 6, 8, 9, 23, 64, 65]. Among these methods, VDM [23] presents the first results on video generation using diffusion models, Sora [6] achieves impressive performance in this area, and SVD [3] provides the popular open-source models for image-to-video generation. Trained on a well-curated video dataset, SVD can generate high-quality videos and is used as the model prior for various video-related tasks. In this paper, we leverage the video diffusion model for high-fidelity consistent video depth estimation, such that the generalization ability to open-world videos can be maintained. Concurrent to our work, ChronoDepth [54] also explores video depth estimation with video diffusion priors. However, ChronoDepth only supports a short temporal context, which is insufficient to accurately arrange depth distributions throughout the video. In contrast, our method not only supports variable-length temporal context at one time, up to 110 frames, but also can estimate depth sequences for videos of arbitrary lengths.", + "bbox": [ + 91, + 424, + 483, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 739, + 181, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an open-world video, $\\mathbf{v} \\in \\mathbb{R}^{T \\times H \\times W \\times 3}$ , our goal is to estimate temporally consistent depth sequences, $\\mathbf{d} \\in \\mathbb{R}^{T \\times H \\times W}$ , with fine-grained details. Considering the diversity of open-world videos in appearance, content motion, camera movement, and length, the challenges to achieving our goal are threefold: 1.) a comprehensive understanding of video content for generalization ability; 2.) a long and variable temporal context to arrange the entire depth distributions accurately and keep temporal consistency; and 3.)", + "bbox": [ + 89, + 762, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the ability to process extremely long videos. As shown in Fig. 2, we tackle these challenges by formulating the video depth estimation as a conditional diffusion generation problem $p(\\mathbf{d} \\mid \\mathbf{v})$ . We train a video-to-depth model from a pretrained image-to-video diffusion model through a meticulously designed three-stage training strategy with compiled paired video-depth datasets, and tailor an inference strategy to process extremely long videos through segment-wise estimation and seamless stitching.", + "bbox": [ + 511, + 376, + 906, + 512 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries of Video Diffusion Models", + "text_level": 1, + "bbox": [ + 511, + 518, + 857, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models [22, 56] learn the data distribution $p(\\mathbf{x})$ by a forward diffusion process to gradually noise the data to a target distribution, e.g. the Gaussian distribution, and a reverse denoising process to iteratively recover the data from the noise by a learned denoiser. In this paper, our study is conducted based on the stale video diffusion (SVD) [3], which is a famous open-source video diffusion model. SVD adopts the EDM [31] diffusion framework. The diffusion process is achieved by adding i.i.d. $\\sigma_t^2$ -variance Gaussian noise to the data $\\mathbf{x}_0 \\sim p(\\mathbf{x})$ :", + "bbox": [ + 511, + 542, + 906, + 694 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\mathbf {x} _ {0} + \\sigma_ {t} ^ {2} \\epsilon , \\quad \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 700, + 906, + 719 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_t\\sim p(\\mathbf{x};\\sigma_t)$ is the data with noise level $\\sigma_{t}$ . When $\\sigma_{t}$ is large enough $(\\sigma_{\\mathrm{max}})$ , the distribution would be indistinguishable from the Gaussian distribution. Based on this fact, the diffusion model starts from a high-variance Gaussian noise $\\epsilon \\sim \\mathcal{N}\\big(\\mathbf{0},\\sigma_{\\mathrm{max}}^2\\mathbf{I}\\big)$ and gradually denoises it towards $\\sigma_0 = 0$ to generate the data. The denoiser $D_{\\theta}$ is a learnable function that tries to predict the clean data, i.e. $\\tilde{\\mathbf{x}}_0 = D_\\theta (\\mathbf{x}_t;\\sigma_t)$ . Its training objective is the denoising score matching:", + "bbox": [ + 511, + 724, + 908, + 862 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\mathbf {x} _ {t} \\sim p (\\mathbf {x}; \\sigma_ {t}), \\sigma_ {t} \\sim p (\\sigma)} \\left[ \\lambda_ {\\sigma_ {t}} \\left\\| D _ {\\theta} (\\mathbf {x} _ {t}; \\sigma_ {t}; \\mathbf {c}) - \\mathbf {x} _ {0} \\right\\| _ {2} ^ {2} \\right], \\quad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 867, + 906, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2007", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $p(\\sigma)$ is the noise level distribution during training, $\\mathbf{c}$ denotes the conditioning information, and $\\lambda_{\\sigma_t}$ is the weight for the denoising loss at time $t$ . To promote the learning, EDM adopts the preconditioning strategy [31, 53], to parameterize the denoiser $D_{\\theta}$ as:", + "bbox": [ + 89, + 90, + 483, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\theta} \\left(\\mathbf {x} _ {t}; \\sigma_ {t}; \\mathbf {c}\\right) = \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 176, + 482, + 200 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc _ {\\text {s k i p}} \\left(\\sigma_ {t}\\right) \\mathbf {x} _ {t} + c _ {\\text {o u t}} \\left(\\sigma_ {t}\\right) F _ {\\theta} \\left(c _ {\\text {i n}} \\mathbf {x} _ {t}; c _ {\\text {n o i s e}} \\left(\\sigma_ {t}\\right); \\mathbf {c}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 196, + 434, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $F_{\\theta}$ is implemented as a learnable U-Net [52], and $c_{\\mathrm{in}}$ , $c_{\\mathrm{out}}$ , $c_{\\mathrm{skip}}$ , and $c_{\\mathrm{noise}}$ are preconditioning functions.", + "bbox": [ + 89, + 224, + 482, + 256 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Formulation with Diffusion Models", + "text_level": 1, + "bbox": [ + 89, + 263, + 398, + 279 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Latent space transformation. To generate high-resolution depth sequences without sacrificing computational efficiency, we adopt the framework of Latent Diffusion Models (LDMs) [51] that perform in a low-dimensional latent space. The transformation between the latent and data spaces is achieved by a Variational Autoencoder (VAE) [33], which was originally designed for encoding and decoding video frames in SVD [3]. Fortunately, we found it can be directly used for depth sequences with only a negligible reconstruction error, which is similar to the observation in Marigold [32] for image depth estimation. As shown in Fig. 2, the latent space transformation is formulated as:", + "bbox": [ + 89, + 287, + 483, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} ^ {(\\mathbf {x})} = \\mathcal {E} (\\mathbf {x}), \\quad \\hat {\\mathbf {x}} = \\mathcal {D} \\left(\\mathbf {z} ^ {(\\mathbf {x})}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 481, + 480, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{x}$ is either the video $\\mathbf{v}$ or the depth sequence $\\mathbf{d}$ , $\\mathbf{z}^{(\\mathbf{x})}$ is the latent representation of the data, $\\hat{\\mathbf{x}}$ is the reconstructed data, $\\mathcal{E}$ and $\\mathcal{D}$ are encoder and decoder of the VAE, respectively. For the depth sequence, we replicate it three times to meet the 3-channel input format of the encoder in VAE and average the three channels of the decoder output to obtain the final latent of the depth sequence. Following the practice in image depth estimation [32, 49, 50, 67, 68], we adopt the relative depth, i.e. the affine-invariant depth, which is normalized to [0, 1]. But differently, our predicted depth sequence shares the same scale and shift across frames, rather than a per-frame normalization, which is crucial for maintaining temporal consistency.", + "bbox": [ + 89, + 507, + 483, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conditioning on the video. SVD is an image-to-video diffusion model that generates videos conditioned on a single image. The conditional image is fed into the U-Net in two ways, i.e., concatenating its latent to the input latent, and injecting its CLIP [48] embedding to the intermediate features via cross-attention. Yet, our DepthCrafter involves the generation of depth sequences conditioned on video frames in a frame-to-frame fashion. Therefore, we adapt the conditioning mechanism to meet our video-to-depth generation task. As shown in Fig. 2, given the encoded latent of depth sequence $\\mathbf{z}^{(\\mathrm{d})}$ and video frames $\\mathbf{z}^{(\\mathrm{v})}$ from Eq. (4), we concatenate the video latent to the input noisy depth latent frame-wisely, rather than only the first frame, to condition", + "bbox": [ + 89, + 704, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the denoiser for generating the depth sequence. For high-level semantic information, we embed the video frames using CLIP and then inject the embeddings in a frame-to-frame manner to the denoiser via cross-attention. Compared to the original conditioning mechanism, our adapted conditioning provides comprehensive information from the video frames to the denoiser, which guarantees the alignment between the generated depth sequences and the video content.", + "bbox": [ + 511, + 90, + 905, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Training Strategy", + "text_level": 1, + "bbox": [ + 511, + 224, + 686, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To train our DepthCrafter, we need a large amount of high-quality paired video-depth sequences. Although there are several video depth datasets available, e.g., KITTI [19], Scannet [12], VDW [62], DynamicReplica [30], and MatrixCity [37], they are either lacking high-quality depth annotations or restricted to a specific domain, e.g., driving scenes, indoor scenes, or synthetic scenes.", + "bbox": [ + 511, + 248, + 905, + 353 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dataset construction. To this end, we compiled paired datasets of two styles, i.e. realistic and synthetic, where the realistic dataset is large-scale and diverse, and the synthetic dataset is miniature but fine-grained and accurate. The realistic dataset is constructed from a large number of binocular videos with a wide range of scene and motion diversity. We cut the videos according to scene changes, and apply the state-of-the-art video stereo matching method, e.g., BiDAStereo [29], to generate temporally consistent depth sequences. Finally, we obtained $\\sim 200\\mathrm{K}$ paired video-depth sequences with the length of 50-200 frames. The synthetic dataset is a combination of the DynamicReplica [30] and MatrixCity [37] datasets, which contains $\\sim 3\\mathrm{K}$ fine-grained depth annotations with a length of 150 frames.", + "bbox": [ + 511, + 354, + 906, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Challenges of variable long temporal context. Different from image depth estimation which can determine the distribution of relative depth from a single frame, the video depth estimation requires a long temporal context to arrange the depth distributions accurately for the entire video and keep the temporal consistency. Besides, the model should support variable-length estimation as the length of open-world videos may vary significantly. However, existing open-source video diffusion models can only generate a fixed small number of frames at a time, e.g., 25 frames in SVD [3]. It is non-trivial to adapt the pre-trained model to meet this requirement, as directly fine-tuning it with long sequences is memory-consuming, for example, modern GPUs with 40GB memory can only support the training of a 25-frame sequence in SVD.", + "bbox": [ + 511, + 566, + 908, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Three-stage training. Considering both the two-style paired datasets and the long temporal context requirement, we design a three-stage training strategy to harvest the variety of video content, the precise depth details, as well as the support for long and variable sequences. As shown in Fig. 2, we train our DepthCrafter from the pre-trained SVD in three stages. We first train it on our large realistic", + "bbox": [ + 511, + 795, + 908, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2008", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/885be172efed77e1a780dfb22b9689e975c54a8a0bae0c26fc08ff81744b2a1f.jpg", + "image_caption": [ + "Figure 3. Inference for extremely long videos. We divide the video into overlapped segments and estimate the depth sequence for each segment with a noise initialization strategy to anchor the scale and shift of depth distributions. These depth segments are then seamlessly stitched together with a latent interpolation strategy to form the entire depth sequence. The overlapped frames and their interpolation weights are denoted as $o_i$ , $w_i$ and $1 - w_i$ , respectively." + ], + "image_footnote": [], + "bbox": [ + 93, + 85, + 486, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "dataset to adapt the model to the video-to-depth generation task. The sequence length in this stage is randomly sampled from [1, 25] frames, such that the model can learn to generate depth sequences with variable lengths. In the second stage, we only fine-tune the temporal layers of the model, still on our large realistic dataset, but with the sequence length randomly sampled from [1, 110] frames. The reason why we only fine-tune the temporal layers is that the temporal layers are more sensitive to the sequence length while the spatial layers are already adapted to the video-to-depth generation task in the first stage, and doing so significantly reduces memory consumption compared to fine-tuning the full model. The long temporal context in this stage enables the model to precisely arrange the entire depth distributions for long and variable sequences. In the third stage, we fine-tune the spatial layers of the model on our small synthetic dataset, with a fixed sequence length of 45 frames since the model has already learned to generate depth sequences with variable lengths in the first two stages and tuning the spatial layers would not affect the temporal context. As the depth annotations in the synthetic dataset are more accurate and fine-grained, the model can learn more precise depth details in this stage. The three-stage training strategy makes our DepthCrafter capable of generating high-quality depth sequences for open-world videos with variable lengths.", + "bbox": [ + 91, + 415, + 483, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Inference for Extremely Long Videos", + "text_level": 1, + "bbox": [ + 89, + 801, + 413, + 818 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although the model can estimate depth sequences up to the length of 110 frames after training, it is still far from long enough for open-world videos, which can even contain hundreds or thousands of frames. To this end, we design an inference strategy to infer extremely long depth sequences in", + "bbox": [ + 89, + 825, + 485, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "a segment-wise manner and seamlessly stitch them together to form the entire depth sequence. As shown in Fig. 3, we first divide the video into overlapped segments, whose lengths are up to 110 frames. Then we estimate the depth sequences for each segment. Rather than purely initializing the input latent with Gaussian noise $\\epsilon \\sim \\mathcal{N}\\big(\\mathbf{0},\\sigma_{\\max}^2\\mathbf{I}\\big)$ , we initialize the latent of the overlapped frames by adding noise to the denoised latent from the previous segment, to anchor the scale and shift of the depth distributions. Finally, to further ensure the temporal smoothness across segments, we craft a mortise-and-tenon style latent interpolation strategy to stitch consecutive segments together, inspired by [75]. Specifically, we interpolate the latent of the overlapped frames $o_i$ from the two segments with the interpolation weights $w_i$ and $1 - w_i$ , respectively, where $w_i$ is linearly decreased from 1 to 0. The final estimated depth sequence is obtained by decoding the stitched latent segments with the decoder $\\mathcal{D}$ in the VAE. With the training and inference strategies, our DepthCrafter can generate temporally consistent long depth sequences for open-world videos.", + "bbox": [ + 511, + 90, + 906, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 409, + 648, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation", + "text_level": 1, + "bbox": [ + 511, + 433, + 671, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We implemented our DepthCrafter based on SVD [3], using the diffusers [59] library. We train our model at the resolution of $320 \\times 640$ for efficiency, but we can estimate depth sequences at any resolution, e.g., $576 \\times 1024$ , during inference. We use the Adam optimizer [34] with a learning rate of $1 \\times 10^{-5}$ and a batch size of 8. The number of iterations in the three stages of training is $80K$ , $40K$ , and $10K$ , respectively. We employed eight GPUs for training, with a total training time of about five days. Except for specific explanations, the number of denoising steps is set to 5 during inference. Please refer to the supplementary material for more implementation details.", + "bbox": [ + 511, + 457, + 908, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluation", + "text_level": 1, + "bbox": [ + 511, + 650, + 635, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation datasets. We evaluate our model on four video datasets, a single-image dataset, as well as the DAVIS dataset [46] and in-the-wild videos for qualitative results. The evaluations are conducted under the zero-shot setting, where the testing datasets cover a variety of scenes, including synthetic and realistic scenes, indoor and outdoor scenes, and static and dynamic scenes, to evaluate the generalization ability of our model across various open-world scenarios. Sintel [7] is a synthetic dataset with precise depth labels, featuring dynamic scenes with diverse content and camera motion. It contains 23 sequences with a length of around 50 frames. ScanNet v2 [12] is an indoor dataset with depth maps obtained from a Kinect sensor. We extracted 90 frames at a rate of 15 frames per second from each sequence of the test set, which includes 100 RGB-D video se", + "bbox": [ + 511, + 674, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2009", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e28963603ea69592df8d354d9cef326c2894d2c89f653f12ed3894a42fe7597a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 90, + 290, + 138 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1e7e8cd22d3c76947376eaf4eeae19e94feea64da2a4c9a7620b420c1a07a48e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 90, + 491, + 138 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2a36cd4d0c2c30ec6cc14bd730cf74d06160449f190ba26c7796b0480f3beea7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 90, + 696, + 138 + ], + "page_idx": 5 + }, + { + "type": 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+ 289, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/95731a019221ad07cc1f1ff75b0bb6d58d3b343a2207b4b971c18b7e0c00b791.jpg", + "image_caption": [ + "Depth-Anything-V2" + ], + "image_footnote": [], + "bbox": [ + 300, + 494, + 491, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d640e0e7adf3f5766b77e2a41cfb31adf6d43dc7be95dd5e3411ee7203d2b05d.jpg", + "image_caption": [ + "NVDS", + "Figure 4. Qualitative comparison for open-world video depth estimation. We compare with the representative single-image depth estimation method Depth-Anything-V2 [68] and the video depth estimation method NVDS [63]. For better visualizing the temporal quality, we show the temporal profiles of each result in green boxes, by slicing the depth values along the time axis at the green line positions." + ], + "image_footnote": [], + "bbox": [ + 504, + 494, + 696, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1118163b71229008e3614461b7f4d06f745c187b234bf609c856a01cdad86ee1.jpg", + "image_caption": [ + "DepthCrafter (Ours)" + ], + "image_footnote": [], + "bbox": [ + 709, + 494, + 900, + 549 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "quences of various scenes. Since ScanNet v2 contains only static indoor scenes, we further introduced 5 dynamic indoor RGB-D videos with a length of 110 frames each from the Bonn [44] dataset to better evaluate the performance of our model on dynamic scenes. KITTI [19] is a street-scene outdoor dataset for autonomous driving, with sparse metric depths captured by a LiDAR sensor. We adopted the validation set, which includes 13 scenes, and extracted 13 videos from it with a length of 110 frames each. Besides, we also evaluated our model for single-image depth estimation on the NYU-v2 [55] test set, which contains 654 images.", + "bbox": [ + 89, + 618, + 483, + 785 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. Following practice in affine-invariant depth estimation [14, 32, 67, 68], we align the estimated depth maps with the ground truth using a scale and shift, and calculate two metrics: AbsRel $\\downarrow$ (absolute relative error: $|\\hat{\\mathbf{d}} -\\mathbf{d}| / \\mathbf{d}$ ) and $\\delta_{1}\\uparrow$ (percentage of $\\max (\\mathbf{d} / \\hat{\\mathbf{d}},\\hat{\\mathbf{d}} /\\mathbf{d}) < 1.25$ ). Different from previous methods that optimize the scale and shift individually for each frame, we optimize $a$", + "bbox": [ + 89, + 794, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "shared scale and shift across the entire video, which is more challenging, but necessary, for video depth estimation to ensure temporal consistency.", + "bbox": [ + 511, + 618, + 906, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results. We compare our DepthCrafter with the representative methods for both image and video depth estimation, i.e. Marigold [32], Depth-Anything [67], Depth-Anything-V2 [68], NVDS [63], and ChronoDepth [54]. For Depth-Anything (V2), we use its official code, and the large model variant for best performance, while for Marigold we adopt the LCM version with an ensemble size of 5. As shown in Tab. 1, our DepthCrafter achieves state-of-the-art performance in all four video datasets, thanks to the powerful open-world video understanding capability of the video diffusion models and the three-stage training strategy that leverages both realistic and synthetic datasets. For Sintel and KITTI, characterized by significant camera motion and fast-moving objects, our DepthCrafter outperforms the strong Depth-Anything (V2) model trenen", + "bbox": [ + 511, + 674, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2010", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b4e53ba8dbb5a1a8bde8f78f17958e2aff6085d2c3bd968a8cff552ebd134fc1.jpg", + "table_caption": [ + "Table 1. Zero-shot depth estimation results. We compare with the best single-image depth estimation model, Marigold [32], and Depth Anything (V2) [67, 68], as well as the representative video depth estimation models, NVDS [63] and ChronoDepth [54]. Best and second best results are highlighted." + ], + "table_footnote": [], + "table_body": "
MethodSintel (~50 frames)Scannet (90 frames)KITTI (110 frames)Bonn (110 frames)NYU-v2 (1 frame)
AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑
NVDS [63]0.4080.4830.1870.6770.2530.5880.1670.7660.1510.780
ChronoDepth [54]0.5870.4860.1590.7830.1670.7590.1000.9110.0730.941
Marigold [32]0.5320.5150.1660.7690.1490.7960.0910.9310.0700.946
Depth-Anything [67]0.3250.5640.1300.8380.1420.8030.0780.9390.0420.981
Depth-Anything-V2 [68]0.3670.5540.1350.8220.1400.8040.1060.9210.0430.978
DepthCrafter (Ours)0.2700.6970.1230.8560.1040.8960.0710.9720.0720.948
", + "bbox": [ + 94, + 135, + 903, + 268 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0db688633f645d601867bb003e5d85ebfa442598568b05e74a9704e520f4f4d1.jpg", + "image_caption": [ + "Figure 5. Single-image depth estimation. We compare with the representative single-image depth estimation method Depth-Anything-V2 [68]." + ], + "image_footnote": [], + "bbox": [ + 94, + 277, + 220, + 428 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7af9ee42bc25c6c46eda85bbb6432300c658e393414b0f8d51d649ad0b6423b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 223, + 277, + 349, + 428 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f6a118f6a2af5c01117ae0b3a0c86257ed5370e804cd38317e12e93910f61fba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 277, + 480, + 428 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dously in terms of both the AbsRel and $\\delta_{1}$ metrics, e.g. $25.7\\% = (0.140 - 0.104) / 0.140$ improvement in AbsRel on KITTI. For indoor datasets like Scannet and Bonn, featuring minimal camera motion and roughly the same room scales, Depth-Anything has exhibited good performance. Nevertheless, we still have performance enhancements over it, e.g. $5.4\\% = (0.130 - 0.123) / 0.130$ improvement in AbsRel on Scannet. Note that the sequence length of these datasets varies from 50 to 110 frames, and our model can generalize well across different video lengths.", + "bbox": [ + 89, + 487, + 482, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative results. To further demonstrate the effectiveness of our model, we present the qualitative results from the DAVIS dataset [46], Sora generated videos [6], and open-world videos, including human actions, animals, architectures, cartoons, and games, where the sequence length varies from 90 to 195 frames. As shown in Fig. 4, we show the temporal profiles of the estimated depth sequences in the green line position by slicing the depth values along the time axis, to better visualize the temporal consistency of the estimated depth sequences, following the practice in [26, 63]. We can observe that our DepthCrafter can produce temporally consistent depth sequences with fine-grained details across various open-world videos, while both NVDS and Depth-Anything exhibit zigzag artifacts in the temporal profiles, indicating the flickering artifacts in the estimated depth sequences. These results demonstrate the effectiveness of our DepthCrafter in generating temporally", + "bbox": [ + 89, + 643, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cdd400e7c673f3626c44472a66470beaeb15aff69e024b8a45c3607085193848.jpg", + "table_caption": [ + "Table 2. Ablation study on the Sintel dataset. We evaluate the performance of our model at the end of different stages of training." + ], + "table_footnote": [], + "table_body": "
stage 1stage 2stage 3
AbsRel ↓0.3220.3160.270
δ1 ↑0.6260.6750.697
", + "bbox": [ + 517, + 313, + 901, + 375 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "consistent long depth sequences with high-fidelity details for open-world videos.", + "bbox": [ + 511, + 383, + 903, + 412 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Single-image depth estimation. Although our model is designed for video depth estimation, it can also perform single-image depth estimation, as our DepthCrafter can estimate video depth of any length. As shown in Tab. 1, our DepthCrafter achieves competitive performance in single-image depth estimation on the NYU-v2 dataset. Since the depth labels in the NYU-v2 dataset are sparse and noisy, we also provide the qualitative results in Fig. 5 to demonstrate the effectiveness of our model in estimating depth maps from static images. We can observe that our DepthCrafter can even produce more detailed depth maps than Depth-Anything-V2, which is the existing state-of-the-art single-image depth estimation model. These results demonstrate the ability of our DepthCrafter for processing both video and single-image depth estimation tasks.", + "bbox": [ + 511, + 414, + 906, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 511, + 650, + 679, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the three-stage training strategy. We first ablate the effectiveness of the three-stage training strategy by evaluating the performance of our model at the end of each stage on the Sintel dataset [7], since it contains precise depth annotations on dynamic scenes. From Tab. 2, we can observe that the performance of our model consistently improves as the number of training stages increases, indicating the effectiveness of the three-stage training strategy. More ablation results on other datasets are available in the supplementary material.", + "bbox": [ + 511, + 674, + 905, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the inference strategy. To ablate the effectiveness of our inference strategy components, we consider these variants: baseline, which independently infers each segment and directly averages the overlapped frames; + initialization, which contains the same initialization of", + "bbox": [ + 511, + 825, + 906, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2011", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b85c35f4aa8ddc1705c3607c70b70f6162f3698d2026c3dbebade49a263e00e1.jpg", + "image_caption": [ + "Figure 6. Ablation studies on the effectiveness of the inference strategy. We profile the estimated depth sequences of different variants on the green line position. The yellow and blue arrows point to the static and dynamic regions, respectively." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 480, + 189 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "overlapped latents as our method, but without the stitching process; + initialization & stitching, which is our full method. We visually compare the temporal profiles of the estimated depth sequences of these variants in Fig. 6. We can observe the overlapped jaggies in both the static regions (pointed by the yellow arrow) and the dynamic regions (pointed by the blue arrow) in temporal profiles of the \"baseline\" method, which indicates the flickering artifacts. The \"+\" initialization\" method can alleviate the flickering artifacts in the static regions, but still has jaggies in the dynamic regions, while our full method can produce smooth depth sequences in both static and dynamic regions.", + "bbox": [ + 88, + 261, + 482, + 443 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Applications", + "text_level": 1, + "bbox": [ + 89, + 452, + 225, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our DepthCrafter can facilitate various downstream applications, e.g., foreground matting, depth slicing, fog effects, and depth-conditioned video generation, by providing temporally consistent depth sequences with fine-grained details for open-world videos. We show example results of fog effects and depth-conditioned video generation in Fig. 7, while more visual effects results are available in the supplementary material. For the fog effect, we blend the fog map with the input video frames based on the depth values to simulate varying transparency levels in fog. And many recent conditioned video generation models [10, 16, 20, 76] employ depth maps as the structure conditions for video generation or editing. We adopt Control-A-Video [10] and video depth of our method as conditions to generate a video with prompts \"a rider walking through stars, artstation\". The visual effects of these applications rely heavily on the accuracy and consistency of the video depth, which demonstrates the wide applicability of our DepthCrafter in various downstream tasks.", + "bbox": [ + 89, + 474, + 482, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Limitations", + "text_level": 1, + "bbox": [ + 89, + 771, + 217, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although our DepthCrafter achieves state-of-the-art performance in open-world video depth estimation, there are still some limitations to be addressed in the future. First, the computation and memory consumption of our model is relatively high, which is mainly due to the large model size and the iterative denoising process in the diffusion model. As shown in Tab. 3, we report the inference speed of our model,", + "bbox": [ + 89, + 794, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ae4147316eaf6770300f5a7b8ef5de7b8a79cd8992dc0930d1dc1044b949e2ff.jpg", + "image_caption": [ + "Figure 7. Examples of visual effectiveness that could benefit from our DepthCrafter, including adding fog effects and depth-conditioned video generation. More visual effects results are available on our website." + ], + "image_footnote": [], + "bbox": [ + 514, + 89, + 903, + 215 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/521d1365acaaab4f672fa4e3fa390084afc51510eb33acaaae761671c1e69c62.jpg", + "table_caption": [ + "Table 3. Inference time per frame (ms) of our model, Depth-Anything (V2), and Marigold, with the resolution of $1024 \\times 576$ ." + ], + "table_footnote": [], + "table_body": "
MethodEncodingDenoisingDecodingAll
Depth-Anything (V2)N/AN/AN/A180.46
Marigold256.40114.53699.361070.29
DepthCrafter (Ours)51.85160.93253.06465.84
", + "bbox": [ + 517, + 321, + 901, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Depth-Anything (V2), and Marigold, with the resolution of $1024 \\times 576$ on a single NVIDIA A100 GPU. We can see that Depth-Anything (V2) is faster than our model, while our method is much faster than Marigold since it ensembles five inference results. Our model achieves the best quality without ensembling, and its inference speed of 465.84 ms per frame is acceptable for many applications. Second, our method requires around 24GB GPU memory to process a video with the resolution of $1024 \\times 576$ and a segment length of 110 frames. But note that, with the segment length of 40 frames, the memory consumption can be reduced to 12GB, which is acceptable for most modern GPUs, and we can still infer videos of any length by our inference strategy under this setting. We believe that further engineering efforts, such as model distillation and quantization, can help further promote the practicality of our method.", + "bbox": [ + 511, + 393, + 906, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 648, + 633, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present DepthCrafter, a novel open-world video depth estimation method that leverages video diffusion models. It can generate temporally consistent depth sequences with fine-grained details for video width diverse content, motion, and camera movement, without requiring any additional information. It also supports videos of variable lengths, ranging from one frame (static image) to extremely long videos. This is achieved through our meticulously designed three-stage training strategy, compiled paired video-depth datasets, and an inference strategy. Extensive evaluations have demonstrated that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. It also facilitates various downstream applications, including depth-based visual effects and conditional video generation.", + "bbox": [ + 511, + 674, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2012", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shubhra Aich, Jean Marie Uwabeza Vianney, Md Amirul Islam, and Mannat Kaur Bingbing Liu. Bidirectional attention network for monocular depth estimation. In ICRA, 2021. 2", + "[2] Shariq Farooq Bhat, Reiner Birkl, Diana Wofk, Peter Wonka, and Matthias Müller. 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TOG (Proceedings of ACM SIGGRAPH), 40(4):1-12, 2021. 2", + "bbox": [ + 547, + 92, + 903, + 118 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "2015", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_model.json b/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8eb0c44c3adf0fe6261840fe00a921ad368a6683 --- /dev/null +++ b/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_model.json @@ -0,0 +1,2543 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.192, + 0.131, + 0.806, + 0.176 + ], + "angle": 0, + "content": "DepthCrafter: Generating Consistent Long Depth Sequences for Open-world Videos" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.202, + 0.748, + 0.24 + ], + "angle": 0, + "content": "Wenbo Hu\\(^{1* \\dagger}\\) Xiangjun Gao\\(^{2*}\\) Xiaoyu Li\\(^{1* \\dagger}\\) Sijie Zhao\\(^{1}\\) Xiaodong Cun\\(^{1}\\) Yong Zhang\\(^{1}\\) Long Quan\\(^{2}\\) Ying Shan\\(^{3,1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.245, + 0.9, + 0.281 + ], + "angle": 0, + "content": "\\(^{1}\\)Tencent AI Lab \\(^{2}\\)The Hong Kong University of Science and Technology \\(^{3}\\)ARC Lab, Tencent PCG https://depthcrafter.github.io" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.291, + 0.891, + 0.562 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.568, + 0.908, + 0.596 + ], + "angle": 0, + "content": "Figure 1. We innovate DepthCrafter, a novel video depth estimation approach, that can generate temporally consistent long depth sequences with fine-grained details for open-world videos, without requiring additional information such as camera poses or optical flow." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.606, + 0.327, + 0.621 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.638, + 0.486, + 0.88 + ], + "angle": 0, + "content": "Estimating video depth in open-world scenarios is challenging due to the diversity of videos in appearance, content motion, camera movement, and length. We present DepthCrafter, an innovative method for generating temporally consistent long depth sequences with intricate details for open-world videos, without requiring any supplementary information such as camera poses or optical flow. The generalization ability to open-world videos is achieved by training the video-to-depth model from a pretrained image-to-video diffusion model, through our meticulously designed three-stage training strategy. Our training approach enables the model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both precise depth details and rich content diversity from realistic and synthetic datasets. We also propose an inference strategy that can process extremely" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.608, + 0.907, + 0.714 + ], + "angle": 0, + "content": "long videos through segment-wise estimation and seamless stitching. Comprehensive evaluations on multiple datasets reveal that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. Furthermore, DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.74, + 0.645, + 0.755 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.765, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Monocular depth estimation, serving as the bridge linking 2D observations and the 3D world, has been a long-standing fundamental problem in computer vision. It plays a crucial role in a wide range of downstream applications, e.g., mixed reality, AI-generated content, autonomous driving, and robotics [14, 24, 27, 28, 40, 57, 72, 73]. The inherent ambiguity makes it challenging, as the observed information from a single view is insufficient to determine the depth of a scene uniquely." + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.366, + 0.901 + ], + "angle": 0, + "content": "* Joint first authors. † Corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2005" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.364 + ], + "angle": 0, + "content": "With recent advances in foundation models, we have witnessed significant progress in depth estimation from monocular images [13, 18, 32, 43, 47, 67, 68, 71]. However, all these methods are tailored for static images, without considering the temporal information in videos. Temporal inconsistency, or flickering, would be observed when directly applying them to videos, as shown in Fig. 1. Existing video depth estimation methods [35, 41, 58, 63, 77] typically try to optimize temporally consistent depth sequences from a pre-trained image depth model, with a given or learnable camera poses. Their performance is sensitive to both the proportion of dynamic content and the quality of the camera poses. Yet, videos in the open world are diverse in content, motion, camera movement, and length, making these methods hard to perform well in practice. Moreover, the required camera poses are usually non-trivial to obtain in open-world videos, particularly for long videos and videos with abundant dynamic content." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.369, + 0.483, + 0.806 + ], + "angle": 0, + "content": "In this paper, we aim to generate temporally consistent long depth sequences with high-fidelity details for diverse open-world videos, without requiring any additional information. Observing the strong capability of diffusion models in generating various types of videos [3, 4, 6, 8, 9, 23, 64, 65], we propose DepthCrafter, to leverage the video diffusion model for video depth estimation, while maintaining the generalization ability to open-world videos. To train our DepthCrafter, a video-to-depth model, from a pre-trained image-to-video diffusion model, we compile paired videodepth datasets in two styles, i.e. realistic and synthetic, since the realistic dataset provides rich content diversity and the synthetic dataset offers precise depth details. On the aspect of temporal context, most existing video diffusion models can only produce a fixed and small number of frames at one time, e.g., 25 frames in Stable Video Diffusion (SVD) [3], which, however, is usually too short for open-world video depth estimation to accurately arrange depth distributions throughout the video. To enable variable long temporal context and fuse the respective advantages of the two-styled datasets, we present a three-stage training strategy to progressively train certain layers of the diffusion model on different datasets with variable lengths. By doing so, we can adapt the video diffusion model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both the precise depth details and rich content diversity. To further support extremely long videos, we tailor an inference strategy to process the video in overlapped segments and seamlessly stitch them together." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.482, + 0.902 + ], + "angle": 0, + "content": "We extensively evaluate our DepthCrafter on diverse datasets, including indoor, outdoor, static, dynamic, realistic, and synthetic videos, under zero-shot settings. Both qualitative and quantitative results demonstrate that our DepthCrafter achieves state-of-the-art performance in openworld video depth estimation, outperforming existing meth" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.151 + ], + "angle": 0, + "content": "ods by a large margin. Besides, we demonstrate that our DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation. Our contributions are summarized below:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.154, + 0.905, + 0.214 + ], + "angle": 0, + "content": "- We innovate DepthCrafter, a novel method to generate temporally consistent long depth sequences with fine-grained details for open-world videos, outperforming existing approaches by a large margin." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.215, + 0.905, + 0.289 + ], + "angle": 0, + "content": "- We present a three-stage training strategy to enable generating depth sequences with a long and variable temporal context, up to 110 frames. It also allows us to harvest both the precise depth details and rich content diversity from synthetic and realistic datasets." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.29, + 0.905, + 0.35 + ], + "angle": 0, + "content": "- We design an inference strategy to segment-wisely process videos beyond 110 frames and seamlessly stitch them together, facilitating depth estimation for extremely long videos." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.154, + 0.905, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.37, + 0.655, + 0.385 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.907, + 0.655 + ], + "angle": 0, + "content": "Image depth estimation. Image depth estimation aims at predicting the depth map from a single image [1, 15, 17, 36, 38, 45, 66]. However, the generalization ability to diverse open-world scenes is hindered by the limited training data. To this end, MiDaS [49] presented the affine-invariant depth representation, enabling mixed training datasets. Depth-Anything (V2) [67, 68] followed this idea and proposed to train the model on both labeled and large-scale unlabeled images, achieving good generalization ability. Marigold [32] and follow-up works [18, 21, 42] leverage the diffusion priors to realize zero-shot transfer to unseen datasets. Besides the affine-invariant depth, another stream of methods tried to estimate the absolute metric depth [2, 5, 25, 47, 71]. All these methods are tailored for static images without considering the temporal consistency, while our work aims to generate temporally consistent long depth sequences for open-world videos." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Video depth estimation. Existing video depth estimation methods could be categorized into two classes: test-time optimization and feed-forward prediction. Test-time optimization methods [11, 35, 41, 77] involve an optimization procedure for each video during inference, which typically requires camera poses or optical flow. Their results are usually consistent, but the requirement of camera poses or optical flow would limit their applicability to open-world videos. Feed-forward prediction methods directly predict depth sequences from videos [39, 58, 60, 61, 63, 69, 70, 74], e.g., DeepV2D [58] combines camera motion estimation with depth estimation, MAMO [69] leverages memory attention, and NVDS [63] introduces a plug-and-play stabilization network. However, due to the limited video depth training data, these methods often fail to address the in-the-wild videos with diverse content. By leveraging the pre" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2006" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.086, + 0.891, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.292, + 0.908, + 0.366 + ], + "angle": 0, + "content": "Figure 2. Overview of our DepthCrafter. It is a conditional diffusion model that models the distribution \\( p(\\mathbf{d} \\mid \\mathbf{v}) \\) over the depth sequence \\( \\mathbf{d} \\) conditioned on the input video \\( \\mathbf{v} \\). We train the model in three stages, where the spatial or temporal layers of the diffusion model are progressively learned on our compiled realistic or synthetic datasets with variable lengths \\( T \\). During inference, given an open-world video, it can generate temporally consistent long depth sequences with fine-grained details for the entire video from initialized Gaussian noise, without requiring any supplementary information, such as camera poses or optical flow." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.377, + 0.482, + 0.422 + ], + "angle": 0, + "content": "trained video diffusion model and our designed three-stage training strategy, our method demonstrates a powerful ability for open-world video depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.425, + 0.485, + 0.729 + ], + "angle": 0, + "content": "Video diffusion models. Diffusion models [22, 56] have shown remarkable video generation ability [3, 4, 6, 8, 9, 23, 64, 65]. Among these methods, VDM [23] presents the first results on video generation using diffusion models, Sora [6] achieves impressive performance in this area, and SVD [3] provides the popular open-source models for image-to-video generation. Trained on a well-curated video dataset, SVD can generate high-quality videos and is used as the model prior for various video-related tasks. In this paper, we leverage the video diffusion model for high-fidelity consistent video depth estimation, such that the generalization ability to open-world videos can be maintained. Concurrent to our work, ChronoDepth [54] also explores video depth estimation with video diffusion priors. However, ChronoDepth only supports a short temporal context, which is insufficient to accurately arrange depth distributions throughout the video. In contrast, our method not only supports variable-length temporal context at one time, up to 110 frames, but also can estimate depth sequences for videos of arbitrary lengths." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.74, + 0.182, + 0.755 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.763, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Given an open-world video, \\(\\mathbf{v} \\in \\mathbb{R}^{T \\times H \\times W \\times 3}\\), our goal is to estimate temporally consistent depth sequences, \\(\\mathbf{d} \\in \\mathbb{R}^{T \\times H \\times W}\\), with fine-grained details. Considering the diversity of open-world videos in appearance, content motion, camera movement, and length, the challenges to achieving our goal are threefold: 1.) a comprehensive understanding of video content for generalization ability; 2.) a long and variable temporal context to arrange the entire depth distributions accurately and keep temporal consistency; and 3.)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.377, + 0.907, + 0.513 + ], + "angle": 0, + "content": "the ability to process extremely long videos. As shown in Fig. 2, we tackle these challenges by formulating the video depth estimation as a conditional diffusion generation problem \\( p(\\mathbf{d} \\mid \\mathbf{v}) \\). We train a video-to-depth model from a pretrained image-to-video diffusion model through a meticulously designed three-stage training strategy with compiled paired video-depth datasets, and tailor an inference strategy to process extremely long videos through segment-wise estimation and seamless stitching." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.52, + 0.859, + 0.535 + ], + "angle": 0, + "content": "3.1. Preliminaries of Video Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.543, + 0.907, + 0.695 + ], + "angle": 0, + "content": "Diffusion models [22, 56] learn the data distribution \\( p(\\mathbf{x}) \\) by a forward diffusion process to gradually noise the data to a target distribution, e.g. the Gaussian distribution, and a reverse denoising process to iteratively recover the data from the noise by a learned denoiser. In this paper, our study is conducted based on the stale video diffusion (SVD) [3], which is a famous open-source video diffusion model. SVD adopts the EDM [31] diffusion framework. The diffusion process is achieved by adding i.i.d. \\( \\sigma_t^2 \\)-variance Gaussian noise to the data \\( \\mathbf{x}_0 \\sim p(\\mathbf{x}) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.701, + 0.907, + 0.72 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\mathbf {x} _ {0} + \\sigma_ {t} ^ {2} \\epsilon , \\quad \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.726, + 0.909, + 0.863 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_t\\sim p(\\mathbf{x};\\sigma_t)\\) is the data with noise level \\(\\sigma_{t}\\). When \\(\\sigma_{t}\\) is large enough \\((\\sigma_{\\mathrm{max}})\\), the distribution would be indistinguishable from the Gaussian distribution. Based on this fact, the diffusion model starts from a high-variance Gaussian noise \\(\\epsilon \\sim \\mathcal{N}\\big(\\mathbf{0},\\sigma_{\\mathrm{max}}^2\\mathbf{I}\\big)\\) and gradually denoises it towards \\(\\sigma_0 = 0\\) to generate the data. The denoiser \\(D_{\\theta}\\) is a learnable function that tries to predict the clean data, i.e. \\(\\tilde{\\mathbf{x}}_0 = D_\\theta (\\mathbf{x}_t;\\sigma_t)\\). Its training objective is the denoising score matching:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.868, + 0.907, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\mathbf {x} _ {t} \\sim p (\\mathbf {x}; \\sigma_ {t}), \\sigma_ {t} \\sim p (\\sigma)} \\left[ \\lambda_ {\\sigma_ {t}} \\left\\| D _ {\\theta} (\\mathbf {x} _ {t}; \\sigma_ {t}; \\mathbf {c}) - \\mathbf {x} _ {0} \\right\\| _ {2} ^ {2} \\right], \\quad (2)\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2007" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.168 + ], + "angle": 0, + "content": "where \\(p(\\sigma)\\) is the noise level distribution during training, \\(\\mathbf{c}\\) denotes the conditioning information, and \\(\\lambda_{\\sigma_t}\\) is the weight for the denoising loss at time \\(t\\). To promote the learning, EDM adopts the preconditioning strategy [31, 53], to parameterize the denoiser \\(D_{\\theta}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.177, + 0.483, + 0.202 + ], + "angle": 0, + "content": "\\[\nD _ {\\theta} \\left(\\mathbf {x} _ {t}; \\sigma_ {t}; \\mathbf {c}\\right) = \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.198, + 0.436, + 0.216 + ], + "angle": 0, + "content": "\\[\nc _ {\\text {s k i p}} \\left(\\sigma_ {t}\\right) \\mathbf {x} _ {t} + c _ {\\text {o u t}} \\left(\\sigma_ {t}\\right) F _ {\\theta} \\left(c _ {\\text {i n}} \\mathbf {x} _ {t}; c _ {\\text {n o i s e}} \\left(\\sigma_ {t}\\right); \\mathbf {c}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.225, + 0.483, + 0.257 + ], + "angle": 0, + "content": "where \\(F_{\\theta}\\) is implemented as a learnable U-Net [52], and \\(c_{\\mathrm{in}}\\), \\(c_{\\mathrm{out}}\\), \\(c_{\\mathrm{skip}}\\), and \\(c_{\\mathrm{noise}}\\) are preconditioning functions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.265, + 0.4, + 0.28 + ], + "angle": 0, + "content": "3.2. Formulation with Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.288, + 0.484, + 0.481 + ], + "angle": 0, + "content": "Latent space transformation. To generate high-resolution depth sequences without sacrificing computational efficiency, we adopt the framework of Latent Diffusion Models (LDMs) [51] that perform in a low-dimensional latent space. The transformation between the latent and data spaces is achieved by a Variational Autoencoder (VAE) [33], which was originally designed for encoding and decoding video frames in SVD [3]. Fortunately, we found it can be directly used for depth sequences with only a negligible reconstruction error, which is similar to the observation in Marigold [32] for image depth estimation. As shown in Fig. 2, the latent space transformation is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.482, + 0.482, + 0.501 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} ^ {(\\mathbf {x})} = \\mathcal {E} (\\mathbf {x}), \\quad \\hat {\\mathbf {x}} = \\mathcal {D} \\left(\\mathbf {z} ^ {(\\mathbf {x})}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.508, + 0.484, + 0.705 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}\\) is either the video \\(\\mathbf{v}\\) or the depth sequence \\(\\mathbf{d}\\), \\(\\mathbf{z}^{(\\mathbf{x})}\\) is the latent representation of the data, \\(\\hat{\\mathbf{x}}\\) is the reconstructed data, \\(\\mathcal{E}\\) and \\(\\mathcal{D}\\) are encoder and decoder of the VAE, respectively. For the depth sequence, we replicate it three times to meet the 3-channel input format of the encoder in VAE and average the three channels of the decoder output to obtain the final latent of the depth sequence. Following the practice in image depth estimation [32, 49, 50, 67, 68], we adopt the relative depth, i.e. the affine-invariant depth, which is normalized to [0, 1]. But differently, our predicted depth sequence shares the same scale and shift across frames, rather than a per-frame normalization, which is crucial for maintaining temporal consistency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Conditioning on the video. SVD is an image-to-video diffusion model that generates videos conditioned on a single image. The conditional image is fed into the U-Net in two ways, i.e., concatenating its latent to the input latent, and injecting its CLIP [48] embedding to the intermediate features via cross-attention. Yet, our DepthCrafter involves the generation of depth sequences conditioned on video frames in a frame-to-frame fashion. Therefore, we adapt the conditioning mechanism to meet our video-to-depth generation task. As shown in Fig. 2, given the encoded latent of depth sequence \\(\\mathbf{z}^{(\\mathrm{d})}\\) and video frames \\(\\mathbf{z}^{(\\mathrm{v})}\\) from Eq. (4), we concatenate the video latent to the input noisy depth latent frame-wisely, rather than only the first frame, to condition" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.213 + ], + "angle": 0, + "content": "the denoiser for generating the depth sequence. For high-level semantic information, we embed the video frames using CLIP and then inject the embeddings in a frame-to-frame manner to the denoiser via cross-attention. Compared to the original conditioning mechanism, our adapted conditioning provides comprehensive information from the video frames to the denoiser, which guarantees the alignment between the generated depth sequences and the video content." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.225, + 0.687, + 0.241 + ], + "angle": 0, + "content": "3.3. Training Strategy" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.249, + 0.906, + 0.354 + ], + "angle": 0, + "content": "To train our DepthCrafter, we need a large amount of high-quality paired video-depth sequences. Although there are several video depth datasets available, e.g., KITTI [19], Scannet [12], VDW [62], DynamicReplica [30], and MatrixCity [37], they are either lacking high-quality depth annotations or restricted to a specific domain, e.g., driving scenes, indoor scenes, or synthetic scenes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.356, + 0.907, + 0.567 + ], + "angle": 0, + "content": "Dataset construction. To this end, we compiled paired datasets of two styles, i.e. realistic and synthetic, where the realistic dataset is large-scale and diverse, and the synthetic dataset is miniature but fine-grained and accurate. The realistic dataset is constructed from a large number of binocular videos with a wide range of scene and motion diversity. We cut the videos according to scene changes, and apply the state-of-the-art video stereo matching method, e.g., BiDAStereo [29], to generate temporally consistent depth sequences. Finally, we obtained \\(\\sim 200\\mathrm{K}\\) paired video-depth sequences with the length of 50-200 frames. The synthetic dataset is a combination of the DynamicReplica [30] and MatrixCity [37] datasets, which contains \\(\\sim 3\\mathrm{K}\\) fine-grained depth annotations with a length of 150 frames." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.909, + 0.794 + ], + "angle": 0, + "content": "Challenges of variable long temporal context. Different from image depth estimation which can determine the distribution of relative depth from a single frame, the video depth estimation requires a long temporal context to arrange the depth distributions accurately for the entire video and keep the temporal consistency. Besides, the model should support variable-length estimation as the length of open-world videos may vary significantly. However, existing open-source video diffusion models can only generate a fixed small number of frames at a time, e.g., 25 frames in SVD [3]. It is non-trivial to adapt the pre-trained model to meet this requirement, as directly fine-tuning it with long sequences is memory-consuming, for example, modern GPUs with 40GB memory can only support the training of a 25-frame sequence in SVD." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Three-stage training. Considering both the two-style paired datasets and the long temporal context requirement, we design a three-stage training strategy to harvest the variety of video content, the precise depth details, as well as the support for long and variable sequences. As shown in Fig. 2, we train our DepthCrafter from the pre-trained SVD in three stages. We first train it on our large realistic" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2008" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.087, + 0.488, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.304, + 0.486, + 0.405 + ], + "angle": 0, + "content": "Figure 3. Inference for extremely long videos. We divide the video into overlapped segments and estimate the depth sequence for each segment with a noise initialization strategy to anchor the scale and shift of depth distributions. These depth segments are then seamlessly stitched together with a latent interpolation strategy to form the entire depth sequence. The overlapped frames and their interpolation weights are denoted as \\( o_i \\), \\( w_i \\) and \\( 1 - w_i \\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.416, + 0.485, + 0.794 + ], + "angle": 0, + "content": "dataset to adapt the model to the video-to-depth generation task. The sequence length in this stage is randomly sampled from [1, 25] frames, such that the model can learn to generate depth sequences with variable lengths. In the second stage, we only fine-tune the temporal layers of the model, still on our large realistic dataset, but with the sequence length randomly sampled from [1, 110] frames. The reason why we only fine-tune the temporal layers is that the temporal layers are more sensitive to the sequence length while the spatial layers are already adapted to the video-to-depth generation task in the first stage, and doing so significantly reduces memory consumption compared to fine-tuning the full model. The long temporal context in this stage enables the model to precisely arrange the entire depth distributions for long and variable sequences. In the third stage, we fine-tune the spatial layers of the model on our small synthetic dataset, with a fixed sequence length of 45 frames since the model has already learned to generate depth sequences with variable lengths in the first two stages and tuning the spatial layers would not affect the temporal context. As the depth annotations in the synthetic dataset are more accurate and fine-grained, the model can learn more precise depth details in this stage. The three-stage training strategy makes our DepthCrafter capable of generating high-quality depth sequences for open-world videos with variable lengths." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.802, + 0.414, + 0.819 + ], + "angle": 0, + "content": "3.4. Inference for Extremely Long Videos" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Although the model can estimate depth sequences up to the length of 110 frames after training, it is still far from long enough for open-world videos, which can even contain hundreds or thousands of frames. To this end, we design an inference strategy to infer extremely long depth sequences in" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.396 + ], + "angle": 0, + "content": "a segment-wise manner and seamlessly stitch them together to form the entire depth sequence. As shown in Fig. 3, we first divide the video into overlapped segments, whose lengths are up to 110 frames. Then we estimate the depth sequences for each segment. Rather than purely initializing the input latent with Gaussian noise \\(\\epsilon \\sim \\mathcal{N}\\big(\\mathbf{0},\\sigma_{\\max}^2\\mathbf{I}\\big)\\), we initialize the latent of the overlapped frames by adding noise to the denoised latent from the previous segment, to anchor the scale and shift of the depth distributions. Finally, to further ensure the temporal smoothness across segments, we craft a mortise-and-tenon style latent interpolation strategy to stitch consecutive segments together, inspired by [75]. Specifically, we interpolate the latent of the overlapped frames \\(o_i\\) from the two segments with the interpolation weights \\(w_i\\) and \\(1 - w_i\\), respectively, where \\(w_i\\) is linearly decreased from 1 to 0. The final estimated depth sequence is obtained by decoding the stitched latent segments with the decoder \\(\\mathcal{D}\\) in the VAE. With the training and inference strategies, our DepthCrafter can generate temporally consistent long depth sequences for open-world videos." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.41, + 0.649, + 0.426 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.434, + 0.673, + 0.451 + ], + "angle": 0, + "content": "4.1. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.458, + 0.909, + 0.641 + ], + "angle": 0, + "content": "We implemented our DepthCrafter based on SVD [3], using the diffusers [59] library. We train our model at the resolution of \\( 320 \\times 640 \\) for efficiency, but we can estimate depth sequences at any resolution, e.g., \\( 576 \\times 1024 \\), during inference. We use the Adam optimizer [34] with a learning rate of \\( 1 \\times 10^{-5} \\) and a batch size of 8. The number of iterations in the three stages of training is \\( 80K \\), \\( 40K \\), and \\( 10K \\), respectively. We employed eight GPUs for training, with a total training time of about five days. Except for specific explanations, the number of denoising steps is set to 5 during inference. Please refer to the supplementary material for more implementation details." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.651, + 0.637, + 0.667 + ], + "angle": 0, + "content": "4.2. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Evaluation datasets. We evaluate our model on four video datasets, a single-image dataset, as well as the DAVIS dataset [46] and in-the-wild videos for qualitative results. The evaluations are conducted under the zero-shot setting, where the testing datasets cover a variety of scenes, including synthetic and realistic scenes, indoor and outdoor scenes, and static and dynamic scenes, to evaluate the generalization ability of our model across various open-world scenarios. Sintel [7] is a synthetic dataset with precise depth labels, featuring dynamic scenes with diverse content and camera motion. It contains 23 sequences with a length of around 50 frames. ScanNet v2 [12] is an indoor dataset with depth maps obtained from a Kinect sensor. We extracted 90 frames at a rate of 15 frames per second from each sequence of the test set, which includes 100 RGB-D video se" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "2009" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.092, + 0.291, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.092, + 0.493, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.092, + 0.697, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.092, + 0.901, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.149, + 0.29, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.149, + 0.493, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.149, + 0.697, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.15, + 0.901, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.208, + 0.29, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.208, + 0.493, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.208, + 0.697, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.208, + 0.901, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.266, + 0.29, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.266, + 0.493, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.266, + 0.697, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.266, + 0.901, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.324, + 0.29, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.324, + 0.493, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.324, + 0.697, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.324, + 0.901, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.383, + 0.29, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.383, + 0.493, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.383, + 0.697, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.383, + 0.901, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.442, + 0.29, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.442, + 0.493, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.442, + 0.697, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.442, + 0.901, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.496, + 0.29, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.159, + 0.552, + 0.227, + 0.564 + ], + "angle": 0, + "content": "Input video" + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.496, + 0.493, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.341, + 0.552, + 0.454, + 0.564 + ], + "angle": 0, + "content": "Depth-Anything-V2" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.496, + 0.697, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.584, + 0.552, + 0.619, + 0.563 + ], + "angle": 0, + "content": "NVDS" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.496, + 0.901, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.552, + 0.864, + 0.564 + ], + "angle": 0, + "content": "DepthCrafter (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.569, + 0.907, + 0.611 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison for open-world video depth estimation. We compare with the representative single-image depth estimation method Depth-Anything-V2 [68] and the video depth estimation method NVDS [63]. For better visualizing the temporal quality, we show the temporal profiles of each result in green boxes, by slicing the depth values along the time axis at the green line positions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.619, + 0.484, + 0.786 + ], + "angle": 0, + "content": "quences of various scenes. Since ScanNet v2 contains only static indoor scenes, we further introduced 5 dynamic indoor RGB-D videos with a length of 110 frames each from the Bonn [44] dataset to better evaluate the performance of our model on dynamic scenes. KITTI [19] is a street-scene outdoor dataset for autonomous driving, with sparse metric depths captured by a LiDAR sensor. We adopted the validation set, which includes 13 scenes, and extracted 13 videos from it with a length of 110 frames each. Besides, we also evaluated our model for single-image depth estimation on the NYU-v2 [55] test set, which contains 654 images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Evaluation metrics. Following practice in affine-invariant depth estimation [14, 32, 67, 68], we align the estimated depth maps with the ground truth using a scale and shift, and calculate two metrics: AbsRel \\(\\downarrow\\) (absolute relative error: \\(|\\hat{\\mathbf{d}} -\\mathbf{d}| / \\mathbf{d}\\)) and \\(\\delta_{1}\\uparrow\\) (percentage of \\(\\max (\\mathbf{d} / \\hat{\\mathbf{d}},\\hat{\\mathbf{d}} /\\mathbf{d}) < 1.25\\)). Different from previous methods that optimize the scale and shift individually for each frame, we optimize \\(a\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.619, + 0.907, + 0.665 + ], + "angle": 0, + "content": "shared scale and shift across the entire video, which is more challenging, but necessary, for video depth estimation to ensure temporal consistency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Quantitative results. We compare our DepthCrafter with the representative methods for both image and video depth estimation, i.e. Marigold [32], Depth-Anything [67], Depth-Anything-V2 [68], NVDS [63], and ChronoDepth [54]. For Depth-Anything (V2), we use its official code, and the large model variant for best performance, while for Marigold we adopt the LCM version with an ensemble size of 5. As shown in Tab. 1, our DepthCrafter achieves state-of-the-art performance in all four video datasets, thanks to the powerful open-world video understanding capability of the video diffusion models and the three-stage training strategy that leverages both realistic and synthetic datasets. For Sintel and KITTI, characterized by significant camera motion and fast-moving objects, our DepthCrafter outperforms the strong Depth-Anything (V2) model trenen" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2010" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.131 + ], + "angle": 0, + "content": "Table 1. Zero-shot depth estimation results. We compare with the best single-image depth estimation model, Marigold [32], and Depth Anything (V2) [67, 68], as well as the representative video depth estimation models, NVDS [63] and ChronoDepth [54]. Best and second best results are highlighted." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.136, + 0.905, + 0.269 + ], + "angle": 0, + "content": "
MethodSintel (~50 frames)Scannet (90 frames)KITTI (110 frames)Bonn (110 frames)NYU-v2 (1 frame)
AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑
NVDS [63]0.4080.4830.1870.6770.2530.5880.1670.7660.1510.780
ChronoDepth [54]0.5870.4860.1590.7830.1670.7590.1000.9110.0730.941
Marigold [32]0.5320.5150.1660.7690.1490.7960.0910.9310.0700.946
Depth-Anything [67]0.3250.5640.1300.8380.1420.8030.0780.9390.0420.981
Depth-Anything-V2 [68]0.3670.5540.1350.8220.1400.8040.1060.9210.0430.978
DepthCrafter (Ours)0.2700.6970.1230.8560.1040.8960.0710.9720.0720.948
" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.279, + 0.221, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.279, + 0.351, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.279, + 0.482, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.435, + 0.483, + 0.478 + ], + "angle": 0, + "content": "Figure 5. Single-image depth estimation. We compare with the representative single-image depth estimation method Depth-Anything-V2 [68]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.488, + 0.483, + 0.64 + ], + "angle": 0, + "content": "dously in terms of both the AbsRel and \\(\\delta_{1}\\) metrics, e.g. \\(25.7\\% = (0.140 - 0.104) / 0.140\\) improvement in AbsRel on KITTI. For indoor datasets like Scannet and Bonn, featuring minimal camera motion and roughly the same room scales, Depth-Anything has exhibited good performance. Nevertheless, we still have performance enhancements over it, e.g. \\(5.4\\% = (0.130 - 0.123) / 0.130\\) improvement in AbsRel on Scannet. Note that the sequence length of these datasets varies from 50 to 110 frames, and our model can generalize well across different video lengths." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Qualitative results. To further demonstrate the effectiveness of our model, we present the qualitative results from the DAVIS dataset [46], Sora generated videos [6], and open-world videos, including human actions, animals, architectures, cartoons, and games, where the sequence length varies from 90 to 195 frames. As shown in Fig. 4, we show the temporal profiles of the estimated depth sequences in the green line position by slicing the depth values along the time axis, to better visualize the temporal consistency of the estimated depth sequences, following the practice in [26, 63]. We can observe that our DepthCrafter can produce temporally consistent depth sequences with fine-grained details across various open-world videos, while both NVDS and Depth-Anything exhibit zigzag artifacts in the temporal profiles, indicating the flickering artifacts in the estimated depth sequences. These results demonstrate the effectiveness of our DepthCrafter in generating temporally" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.28, + 0.907, + 0.308 + ], + "angle": 0, + "content": "Table 2. Ablation study on the Sintel dataset. We evaluate the performance of our model at the end of different stages of training." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.314, + 0.903, + 0.375 + ], + "angle": 0, + "content": "
stage 1stage 2stage 3
AbsRel ↓0.3220.3160.270
δ1 ↑0.6260.6750.697
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.384, + 0.905, + 0.413 + ], + "angle": 0, + "content": "consistent long depth sequences with high-fidelity details for open-world videos." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.415, + 0.907, + 0.642 + ], + "angle": 0, + "content": "Single-image depth estimation. Although our model is designed for video depth estimation, it can also perform single-image depth estimation, as our DepthCrafter can estimate video depth of any length. As shown in Tab. 1, our DepthCrafter achieves competitive performance in single-image depth estimation on the NYU-v2 dataset. Since the depth labels in the NYU-v2 dataset are sparse and noisy, we also provide the qualitative results in Fig. 5 to demonstrate the effectiveness of our model in estimating depth maps from static images. We can observe that our DepthCrafter can even produce more detailed depth maps than Depth-Anything-V2, which is the existing state-of-the-art single-image depth estimation model. These results demonstrate the ability of our DepthCrafter for processing both video and single-image depth estimation tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.651, + 0.68, + 0.665 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.906, + 0.825 + ], + "angle": 0, + "content": "Effectiveness of the three-stage training strategy. We first ablate the effectiveness of the three-stage training strategy by evaluating the performance of our model at the end of each stage on the Sintel dataset [7], since it contains precise depth annotations on dynamic scenes. From Tab. 2, we can observe that the performance of our model consistently improves as the number of training stages increases, indicating the effectiveness of the three-stage training strategy. More ablation results on other datasets are available in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.907, + 0.9 + ], + "angle": 0, + "content": "Effectiveness of the inference strategy. To ablate the effectiveness of our inference strategy components, we consider these variants: baseline, which independently infers each segment and directly averages the overlapped frames; + initialization, which contains the same initialization of" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2011" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.482, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.199, + 0.483, + 0.255 + ], + "angle": 0, + "content": "Figure 6. Ablation studies on the effectiveness of the inference strategy. We profile the estimated depth sequences of different variants on the green line position. The yellow and blue arrows point to the static and dynamic regions, respectively." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.262, + 0.483, + 0.444 + ], + "angle": 0, + "content": "overlapped latents as our method, but without the stitching process; + initialization & stitching, which is our full method. We visually compare the temporal profiles of the estimated depth sequences of these variants in Fig. 6. We can observe the overlapped jaggies in both the static regions (pointed by the yellow arrow) and the dynamic regions (pointed by the blue arrow) in temporal profiles of the \"baseline\" method, which indicates the flickering artifacts. The \"+\" initialization\" method can alleviate the flickering artifacts in the static regions, but still has jaggies in the dynamic regions, while our full method can produce smooth depth sequences in both static and dynamic regions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.453, + 0.226, + 0.469 + ], + "angle": 0, + "content": "4.4. Applications" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.476, + 0.483, + 0.763 + ], + "angle": 0, + "content": "Our DepthCrafter can facilitate various downstream applications, e.g., foreground matting, depth slicing, fog effects, and depth-conditioned video generation, by providing temporally consistent depth sequences with fine-grained details for open-world videos. We show example results of fog effects and depth-conditioned video generation in Fig. 7, while more visual effects results are available in the supplementary material. For the fog effect, we blend the fog map with the input video frames based on the depth values to simulate varying transparency levels in fog. And many recent conditioned video generation models [10, 16, 20, 76] employ depth maps as the structure conditions for video generation or editing. We adopt Control-A-Video [10] and video depth of our method as conditions to generate a video with prompts \"a rider walking through stars, artstation\". The visual effects of these applications rely heavily on the accuracy and consistency of the video depth, which demonstrates the wide applicability of our DepthCrafter in various downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.772, + 0.218, + 0.787 + ], + "angle": 0, + "content": "4.5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Although our DepthCrafter achieves state-of-the-art performance in open-world video depth estimation, there are still some limitations to be addressed in the future. First, the computation and memory consumption of our model is relatively high, which is mainly due to the large model size and the iterative denoising process in the diffusion model. As shown in Tab. 3, we report the inference speed of our model," + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.09, + 0.905, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.224, + 0.905, + 0.28 + ], + "angle": 0, + "content": "Figure 7. Examples of visual effectiveness that could benefit from our DepthCrafter, including adding fog effects and depth-conditioned video generation. More visual effects results are available on our website." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.288, + 0.905, + 0.317 + ], + "angle": 0, + "content": "Table 3. Inference time per frame (ms) of our model, Depth-Anything (V2), and Marigold, with the resolution of \\(1024 \\times 576\\)." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.322, + 0.903, + 0.389 + ], + "angle": 0, + "content": "
MethodEncodingDenoisingDecodingAll
Depth-Anything (V2)N/AN/AN/A180.46
Marigold256.40114.53699.361070.29
DepthCrafter (Ours)51.85160.93253.06465.84
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.394, + 0.907, + 0.636 + ], + "angle": 0, + "content": "Depth-Anything (V2), and Marigold, with the resolution of \\(1024 \\times 576\\) on a single NVIDIA A100 GPU. We can see that Depth-Anything (V2) is faster than our model, while our method is much faster than Marigold since it ensembles five inference results. Our model achieves the best quality without ensembling, and its inference speed of 465.84 ms per frame is acceptable for many applications. Second, our method requires around 24GB GPU memory to process a video with the resolution of \\(1024 \\times 576\\) and a segment length of 110 frames. But note that, with the segment length of 40 frames, the memory consumption can be reduced to 12GB, which is acceptable for most modern GPUs, and we can still infer videos of any length by our inference strategy under this setting. We believe that further engineering efforts, such as model distillation and quantization, can help further promote the practicality of our method." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.649, + 0.634, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We present DepthCrafter, a novel open-world video depth estimation method that leverages video diffusion models. It can generate temporally consistent depth sequences with fine-grained details for video width diverse content, motion, and camera movement, without requiring any additional information. It also supports videos of variable lengths, ranging from one frame (static image) to extremely long videos. This is achieved through our meticulously designed three-stage training strategy, compiled paired video-depth datasets, and an inference strategy. Extensive evaluations have demonstrated that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. It also facilitates various downstream applications, including depth-based visual effects and conditional video generation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2012" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.156 + ], + "angle": 0, + "content": "[1] Shubhra Aich, Jean Marie Uwabeza Vianney, Md Amirul Islam, and Mannat Kaur Bingbing Liu. Bidirectional attention network for monocular depth estimation. 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TOG (Proceedings of ACM SIGGRAPH), 40(4):1-12, 2021. 2" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2015" + } + ] +] \ No newline at end of file diff --git a/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_origin.pdf b/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..07cc27c348cffde13db02b17648fa18c27615ebe --- /dev/null +++ b/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/7820448d-f4cd-4ec7-b539-aef2413229a4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1d591d0975884b2e085ca7163597875b378a9e65eac08784895f38f7159523d1 +size 9539591 diff --git a/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/full.md b/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d076024597e6837699427743856044a6e4dc9588 --- /dev/null +++ b/2025/DepthCrafter_ Generating Consistent Long Depth Sequences for Open-world Videos/full.md @@ -0,0 +1,340 @@ +# DepthCrafter: Generating Consistent Long Depth Sequences for Open-world Videos + +Wenbo Hu $^{1* \dagger}$ Xiangjun Gao $^{2*}$ Xiaoyu Li $^{1* \dagger}$ Sijie Zhao $^{1}$ Xiaodong Cun $^{1}$ Yong Zhang $^{1}$ Long Quan $^{2}$ Ying Shan $^{3,1}$ + +$^{1}$ Tencent AI Lab $^{2}$ The Hong Kong University of Science and Technology $^{3}$ ARC Lab, Tencent PCG https://depthcrafter.github.io + +![](images/d812dbdf926a8eb8de9c622c1ccc1ac6903524080180c231f60cc61a54740793.jpg) +Figure 1. We innovate DepthCrafter, a novel video depth estimation approach, that can generate temporally consistent long depth sequences with fine-grained details for open-world videos, without requiring additional information such as camera poses or optical flow. + +# Abstract + +Estimating video depth in open-world scenarios is challenging due to the diversity of videos in appearance, content motion, camera movement, and length. We present DepthCrafter, an innovative method for generating temporally consistent long depth sequences with intricate details for open-world videos, without requiring any supplementary information such as camera poses or optical flow. The generalization ability to open-world videos is achieved by training the video-to-depth model from a pretrained image-to-video diffusion model, through our meticulously designed three-stage training strategy. Our training approach enables the model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both precise depth details and rich content diversity from realistic and synthetic datasets. We also propose an inference strategy that can process extremely + +long videos through segment-wise estimation and seamless stitching. Comprehensive evaluations on multiple datasets reveal that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. Furthermore, DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation. + +# 1. Introduction + +Monocular depth estimation, serving as the bridge linking 2D observations and the 3D world, has been a long-standing fundamental problem in computer vision. It plays a crucial role in a wide range of downstream applications, e.g., mixed reality, AI-generated content, autonomous driving, and robotics [14, 24, 27, 28, 40, 57, 72, 73]. The inherent ambiguity makes it challenging, as the observed information from a single view is insufficient to determine the depth of a scene uniquely. + +With recent advances in foundation models, we have witnessed significant progress in depth estimation from monocular images [13, 18, 32, 43, 47, 67, 68, 71]. However, all these methods are tailored for static images, without considering the temporal information in videos. Temporal inconsistency, or flickering, would be observed when directly applying them to videos, as shown in Fig. 1. Existing video depth estimation methods [35, 41, 58, 63, 77] typically try to optimize temporally consistent depth sequences from a pre-trained image depth model, with a given or learnable camera poses. Their performance is sensitive to both the proportion of dynamic content and the quality of the camera poses. Yet, videos in the open world are diverse in content, motion, camera movement, and length, making these methods hard to perform well in practice. Moreover, the required camera poses are usually non-trivial to obtain in open-world videos, particularly for long videos and videos with abundant dynamic content. + +In this paper, we aim to generate temporally consistent long depth sequences with high-fidelity details for diverse open-world videos, without requiring any additional information. Observing the strong capability of diffusion models in generating various types of videos [3, 4, 6, 8, 9, 23, 64, 65], we propose DepthCrafter, to leverage the video diffusion model for video depth estimation, while maintaining the generalization ability to open-world videos. To train our DepthCrafter, a video-to-depth model, from a pre-trained image-to-video diffusion model, we compile paired videodepth datasets in two styles, i.e. realistic and synthetic, since the realistic dataset provides rich content diversity and the synthetic dataset offers precise depth details. On the aspect of temporal context, most existing video diffusion models can only produce a fixed and small number of frames at one time, e.g., 25 frames in Stable Video Diffusion (SVD) [3], which, however, is usually too short for open-world video depth estimation to accurately arrange depth distributions throughout the video. To enable variable long temporal context and fuse the respective advantages of the two-styled datasets, we present a three-stage training strategy to progressively train certain layers of the diffusion model on different datasets with variable lengths. By doing so, we can adapt the video diffusion model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both the precise depth details and rich content diversity. To further support extremely long videos, we tailor an inference strategy to process the video in overlapped segments and seamlessly stitch them together. + +We extensively evaluate our DepthCrafter on diverse datasets, including indoor, outdoor, static, dynamic, realistic, and synthetic videos, under zero-shot settings. Both qualitative and quantitative results demonstrate that our DepthCrafter achieves state-of-the-art performance in openworld video depth estimation, outperforming existing meth + +ods by a large margin. Besides, we demonstrate that our DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation. Our contributions are summarized below: + +- We innovate DepthCrafter, a novel method to generate temporally consistent long depth sequences with fine-grained details for open-world videos, outperforming existing approaches by a large margin. +- We present a three-stage training strategy to enable generating depth sequences with a long and variable temporal context, up to 110 frames. It also allows us to harvest both the precise depth details and rich content diversity from synthetic and realistic datasets. +- We design an inference strategy to segment-wisely process videos beyond 110 frames and seamlessly stitch them together, facilitating depth estimation for extremely long videos. + +# 2. Related Work + +Image depth estimation. Image depth estimation aims at predicting the depth map from a single image [1, 15, 17, 36, 38, 45, 66]. However, the generalization ability to diverse open-world scenes is hindered by the limited training data. To this end, MiDaS [49] presented the affine-invariant depth representation, enabling mixed training datasets. Depth-Anything (V2) [67, 68] followed this idea and proposed to train the model on both labeled and large-scale unlabeled images, achieving good generalization ability. Marigold [32] and follow-up works [18, 21, 42] leverage the diffusion priors to realize zero-shot transfer to unseen datasets. Besides the affine-invariant depth, another stream of methods tried to estimate the absolute metric depth [2, 5, 25, 47, 71]. All these methods are tailored for static images without considering the temporal consistency, while our work aims to generate temporally consistent long depth sequences for open-world videos. + +Video depth estimation. Existing video depth estimation methods could be categorized into two classes: test-time optimization and feed-forward prediction. Test-time optimization methods [11, 35, 41, 77] involve an optimization procedure for each video during inference, which typically requires camera poses or optical flow. Their results are usually consistent, but the requirement of camera poses or optical flow would limit their applicability to open-world videos. Feed-forward prediction methods directly predict depth sequences from videos [39, 58, 60, 61, 63, 69, 70, 74], e.g., DeepV2D [58] combines camera motion estimation with depth estimation, MAMO [69] leverages memory attention, and NVDS [63] introduces a plug-and-play stabilization network. However, due to the limited video depth training data, these methods often fail to address the in-the-wild videos with diverse content. By leveraging the pre + +![](images/511e4c99dea41bbb4f686e1dfcf9c2d187c09705f24eac16902168839d66ab8b.jpg) +Figure 2. Overview of our DepthCrafter. It is a conditional diffusion model that models the distribution $p(\mathbf{d} \mid \mathbf{v})$ over the depth sequence $\mathbf{d}$ conditioned on the input video $\mathbf{v}$ . We train the model in three stages, where the spatial or temporal layers of the diffusion model are progressively learned on our compiled realistic or synthetic datasets with variable lengths $T$ . During inference, given an open-world video, it can generate temporally consistent long depth sequences with fine-grained details for the entire video from initialized Gaussian noise, without requiring any supplementary information, such as camera poses or optical flow. + +trained video diffusion model and our designed three-stage training strategy, our method demonstrates a powerful ability for open-world video depth estimation. + +Video diffusion models. Diffusion models [22, 56] have shown remarkable video generation ability [3, 4, 6, 8, 9, 23, 64, 65]. Among these methods, VDM [23] presents the first results on video generation using diffusion models, Sora [6] achieves impressive performance in this area, and SVD [3] provides the popular open-source models for image-to-video generation. Trained on a well-curated video dataset, SVD can generate high-quality videos and is used as the model prior for various video-related tasks. In this paper, we leverage the video diffusion model for high-fidelity consistent video depth estimation, such that the generalization ability to open-world videos can be maintained. Concurrent to our work, ChronoDepth [54] also explores video depth estimation with video diffusion priors. However, ChronoDepth only supports a short temporal context, which is insufficient to accurately arrange depth distributions throughout the video. In contrast, our method not only supports variable-length temporal context at one time, up to 110 frames, but also can estimate depth sequences for videos of arbitrary lengths. + +# 3. Method + +Given an open-world video, $\mathbf{v} \in \mathbb{R}^{T \times H \times W \times 3}$ , our goal is to estimate temporally consistent depth sequences, $\mathbf{d} \in \mathbb{R}^{T \times H \times W}$ , with fine-grained details. Considering the diversity of open-world videos in appearance, content motion, camera movement, and length, the challenges to achieving our goal are threefold: 1.) a comprehensive understanding of video content for generalization ability; 2.) a long and variable temporal context to arrange the entire depth distributions accurately and keep temporal consistency; and 3.) + +the ability to process extremely long videos. As shown in Fig. 2, we tackle these challenges by formulating the video depth estimation as a conditional diffusion generation problem $p(\mathbf{d} \mid \mathbf{v})$ . We train a video-to-depth model from a pretrained image-to-video diffusion model through a meticulously designed three-stage training strategy with compiled paired video-depth datasets, and tailor an inference strategy to process extremely long videos through segment-wise estimation and seamless stitching. + +# 3.1. Preliminaries of Video Diffusion Models + +Diffusion models [22, 56] learn the data distribution $p(\mathbf{x})$ by a forward diffusion process to gradually noise the data to a target distribution, e.g. the Gaussian distribution, and a reverse denoising process to iteratively recover the data from the noise by a learned denoiser. In this paper, our study is conducted based on the stale video diffusion (SVD) [3], which is a famous open-source video diffusion model. SVD adopts the EDM [31] diffusion framework. The diffusion process is achieved by adding i.i.d. $\sigma_t^2$ -variance Gaussian noise to the data $\mathbf{x}_0 \sim p(\mathbf{x})$ : + +$$ +\mathbf {x} _ {t} = \mathbf {x} _ {0} + \sigma_ {t} ^ {2} \epsilon , \quad \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {I}), \tag {1} +$$ + +where $\mathbf{x}_t\sim p(\mathbf{x};\sigma_t)$ is the data with noise level $\sigma_{t}$ . When $\sigma_{t}$ is large enough $(\sigma_{\mathrm{max}})$ , the distribution would be indistinguishable from the Gaussian distribution. Based on this fact, the diffusion model starts from a high-variance Gaussian noise $\epsilon \sim \mathcal{N}\big(\mathbf{0},\sigma_{\mathrm{max}}^2\mathbf{I}\big)$ and gradually denoises it towards $\sigma_0 = 0$ to generate the data. The denoiser $D_{\theta}$ is a learnable function that tries to predict the clean data, i.e. $\tilde{\mathbf{x}}_0 = D_\theta (\mathbf{x}_t;\sigma_t)$ . Its training objective is the denoising score matching: + +$$ +\mathbb {E} _ {\mathbf {x} _ {t} \sim p (\mathbf {x}; \sigma_ {t}), \sigma_ {t} \sim p (\sigma)} \left[ \lambda_ {\sigma_ {t}} \left\| D _ {\theta} (\mathbf {x} _ {t}; \sigma_ {t}; \mathbf {c}) - \mathbf {x} _ {0} \right\| _ {2} ^ {2} \right], \quad (2) +$$ + +where $p(\sigma)$ is the noise level distribution during training, $\mathbf{c}$ denotes the conditioning information, and $\lambda_{\sigma_t}$ is the weight for the denoising loss at time $t$ . To promote the learning, EDM adopts the preconditioning strategy [31, 53], to parameterize the denoiser $D_{\theta}$ as: + +$$ +D _ {\theta} \left(\mathbf {x} _ {t}; \sigma_ {t}; \mathbf {c}\right) = \tag {3} +$$ + +$$ +c _ {\text {s k i p}} \left(\sigma_ {t}\right) \mathbf {x} _ {t} + c _ {\text {o u t}} \left(\sigma_ {t}\right) F _ {\theta} \left(c _ {\text {i n}} \mathbf {x} _ {t}; c _ {\text {n o i s e}} \left(\sigma_ {t}\right); \mathbf {c}\right), +$$ + +where $F_{\theta}$ is implemented as a learnable U-Net [52], and $c_{\mathrm{in}}$ , $c_{\mathrm{out}}$ , $c_{\mathrm{skip}}$ , and $c_{\mathrm{noise}}$ are preconditioning functions. + +# 3.2. Formulation with Diffusion Models + +Latent space transformation. To generate high-resolution depth sequences without sacrificing computational efficiency, we adopt the framework of Latent Diffusion Models (LDMs) [51] that perform in a low-dimensional latent space. The transformation between the latent and data spaces is achieved by a Variational Autoencoder (VAE) [33], which was originally designed for encoding and decoding video frames in SVD [3]. Fortunately, we found it can be directly used for depth sequences with only a negligible reconstruction error, which is similar to the observation in Marigold [32] for image depth estimation. As shown in Fig. 2, the latent space transformation is formulated as: + +$$ +\mathbf {z} ^ {(\mathbf {x})} = \mathcal {E} (\mathbf {x}), \quad \hat {\mathbf {x}} = \mathcal {D} \left(\mathbf {z} ^ {(\mathbf {x})}\right), \tag {4} +$$ + +where $\mathbf{x}$ is either the video $\mathbf{v}$ or the depth sequence $\mathbf{d}$ , $\mathbf{z}^{(\mathbf{x})}$ is the latent representation of the data, $\hat{\mathbf{x}}$ is the reconstructed data, $\mathcal{E}$ and $\mathcal{D}$ are encoder and decoder of the VAE, respectively. For the depth sequence, we replicate it three times to meet the 3-channel input format of the encoder in VAE and average the three channels of the decoder output to obtain the final latent of the depth sequence. Following the practice in image depth estimation [32, 49, 50, 67, 68], we adopt the relative depth, i.e. the affine-invariant depth, which is normalized to [0, 1]. But differently, our predicted depth sequence shares the same scale and shift across frames, rather than a per-frame normalization, which is crucial for maintaining temporal consistency. + +Conditioning on the video. SVD is an image-to-video diffusion model that generates videos conditioned on a single image. The conditional image is fed into the U-Net in two ways, i.e., concatenating its latent to the input latent, and injecting its CLIP [48] embedding to the intermediate features via cross-attention. Yet, our DepthCrafter involves the generation of depth sequences conditioned on video frames in a frame-to-frame fashion. Therefore, we adapt the conditioning mechanism to meet our video-to-depth generation task. As shown in Fig. 2, given the encoded latent of depth sequence $\mathbf{z}^{(\mathrm{d})}$ and video frames $\mathbf{z}^{(\mathrm{v})}$ from Eq. (4), we concatenate the video latent to the input noisy depth latent frame-wisely, rather than only the first frame, to condition + +the denoiser for generating the depth sequence. For high-level semantic information, we embed the video frames using CLIP and then inject the embeddings in a frame-to-frame manner to the denoiser via cross-attention. Compared to the original conditioning mechanism, our adapted conditioning provides comprehensive information from the video frames to the denoiser, which guarantees the alignment between the generated depth sequences and the video content. + +# 3.3. Training Strategy + +To train our DepthCrafter, we need a large amount of high-quality paired video-depth sequences. Although there are several video depth datasets available, e.g., KITTI [19], Scannet [12], VDW [62], DynamicReplica [30], and MatrixCity [37], they are either lacking high-quality depth annotations or restricted to a specific domain, e.g., driving scenes, indoor scenes, or synthetic scenes. + +Dataset construction. To this end, we compiled paired datasets of two styles, i.e. realistic and synthetic, where the realistic dataset is large-scale and diverse, and the synthetic dataset is miniature but fine-grained and accurate. The realistic dataset is constructed from a large number of binocular videos with a wide range of scene and motion diversity. We cut the videos according to scene changes, and apply the state-of-the-art video stereo matching method, e.g., BiDAStereo [29], to generate temporally consistent depth sequences. Finally, we obtained $\sim 200\mathrm{K}$ paired video-depth sequences with the length of 50-200 frames. The synthetic dataset is a combination of the DynamicReplica [30] and MatrixCity [37] datasets, which contains $\sim 3\mathrm{K}$ fine-grained depth annotations with a length of 150 frames. + +Challenges of variable long temporal context. Different from image depth estimation which can determine the distribution of relative depth from a single frame, the video depth estimation requires a long temporal context to arrange the depth distributions accurately for the entire video and keep the temporal consistency. Besides, the model should support variable-length estimation as the length of open-world videos may vary significantly. However, existing open-source video diffusion models can only generate a fixed small number of frames at a time, e.g., 25 frames in SVD [3]. It is non-trivial to adapt the pre-trained model to meet this requirement, as directly fine-tuning it with long sequences is memory-consuming, for example, modern GPUs with 40GB memory can only support the training of a 25-frame sequence in SVD. + +Three-stage training. Considering both the two-style paired datasets and the long temporal context requirement, we design a three-stage training strategy to harvest the variety of video content, the precise depth details, as well as the support for long and variable sequences. As shown in Fig. 2, we train our DepthCrafter from the pre-trained SVD in three stages. We first train it on our large realistic + +![](images/885be172efed77e1a780dfb22b9689e975c54a8a0bae0c26fc08ff81744b2a1f.jpg) +Figure 3. Inference for extremely long videos. We divide the video into overlapped segments and estimate the depth sequence for each segment with a noise initialization strategy to anchor the scale and shift of depth distributions. These depth segments are then seamlessly stitched together with a latent interpolation strategy to form the entire depth sequence. The overlapped frames and their interpolation weights are denoted as $o_i$ , $w_i$ and $1 - w_i$ , respectively. + +dataset to adapt the model to the video-to-depth generation task. The sequence length in this stage is randomly sampled from [1, 25] frames, such that the model can learn to generate depth sequences with variable lengths. In the second stage, we only fine-tune the temporal layers of the model, still on our large realistic dataset, but with the sequence length randomly sampled from [1, 110] frames. The reason why we only fine-tune the temporal layers is that the temporal layers are more sensitive to the sequence length while the spatial layers are already adapted to the video-to-depth generation task in the first stage, and doing so significantly reduces memory consumption compared to fine-tuning the full model. The long temporal context in this stage enables the model to precisely arrange the entire depth distributions for long and variable sequences. In the third stage, we fine-tune the spatial layers of the model on our small synthetic dataset, with a fixed sequence length of 45 frames since the model has already learned to generate depth sequences with variable lengths in the first two stages and tuning the spatial layers would not affect the temporal context. As the depth annotations in the synthetic dataset are more accurate and fine-grained, the model can learn more precise depth details in this stage. The three-stage training strategy makes our DepthCrafter capable of generating high-quality depth sequences for open-world videos with variable lengths. + +# 3.4. Inference for Extremely Long Videos + +Although the model can estimate depth sequences up to the length of 110 frames after training, it is still far from long enough for open-world videos, which can even contain hundreds or thousands of frames. To this end, we design an inference strategy to infer extremely long depth sequences in + +a segment-wise manner and seamlessly stitch them together to form the entire depth sequence. As shown in Fig. 3, we first divide the video into overlapped segments, whose lengths are up to 110 frames. Then we estimate the depth sequences for each segment. Rather than purely initializing the input latent with Gaussian noise $\epsilon \sim \mathcal{N}\big(\mathbf{0},\sigma_{\max}^2\mathbf{I}\big)$ , we initialize the latent of the overlapped frames by adding noise to the denoised latent from the previous segment, to anchor the scale and shift of the depth distributions. Finally, to further ensure the temporal smoothness across segments, we craft a mortise-and-tenon style latent interpolation strategy to stitch consecutive segments together, inspired by [75]. Specifically, we interpolate the latent of the overlapped frames $o_i$ from the two segments with the interpolation weights $w_i$ and $1 - w_i$ , respectively, where $w_i$ is linearly decreased from 1 to 0. The final estimated depth sequence is obtained by decoding the stitched latent segments with the decoder $\mathcal{D}$ in the VAE. With the training and inference strategies, our DepthCrafter can generate temporally consistent long depth sequences for open-world videos. + +# 4. Experiments + +# 4.1. Implementation + +We implemented our DepthCrafter based on SVD [3], using the diffusers [59] library. We train our model at the resolution of $320 \times 640$ for efficiency, but we can estimate depth sequences at any resolution, e.g., $576 \times 1024$ , during inference. We use the Adam optimizer [34] with a learning rate of $1 \times 10^{-5}$ and a batch size of 8. The number of iterations in the three stages of training is $80K$ , $40K$ , and $10K$ , respectively. We employed eight GPUs for training, with a total training time of about five days. Except for specific explanations, the number of denoising steps is set to 5 during inference. Please refer to the supplementary material for more implementation details. + +# 4.2. Evaluation + +Evaluation datasets. We evaluate our model on four video datasets, a single-image dataset, as well as the DAVIS dataset [46] and in-the-wild videos for qualitative results. The evaluations are conducted under the zero-shot setting, where the testing datasets cover a variety of scenes, including synthetic and realistic scenes, indoor and outdoor scenes, and static and dynamic scenes, to evaluate the generalization ability of our model across various open-world scenarios. Sintel [7] is a synthetic dataset with precise depth labels, featuring dynamic scenes with diverse content and camera motion. It contains 23 sequences with a length of around 50 frames. ScanNet v2 [12] is an indoor dataset with depth maps obtained from a Kinect sensor. We extracted 90 frames at a rate of 15 frames per second from each sequence of the test set, which includes 100 RGB-D video se + +![](images/e28963603ea69592df8d354d9cef326c2894d2c89f653f12ed3894a42fe7597a.jpg) + +![](images/1e7e8cd22d3c76947376eaf4eeae19e94feea64da2a4c9a7620b420c1a07a48e.jpg) + +![](images/2a36cd4d0c2c30ec6cc14bd730cf74d06160449f190ba26c7796b0480f3beea7.jpg) + +![](images/b119115cf6bb5e8c0f55e81c6b3ecc28aeef6564eb25f7ce3adf3004de1e537b.jpg) + +![](images/40ee4d0916bc092d1921746effaeba9c0897c847d3eb8688a741378d3cbf9fbc.jpg) + +![](images/a406e4ba125187321b48ba7c6b1c2e9215aca56daa77dc5405d84e9431f12c49.jpg) + +![](images/0950b4028335a9f8fd877453dfac937f4ceb6fd15c516a42486020fe6b05dd53.jpg) + +![](images/2528093c0b92626fbf19f143612ab8fa89287b3313a546e57065b5a73756be35.jpg) + +![](images/2099a1118cf4ebe1d83236e159e96597f23bf222c41f07425f9972b691b53345.jpg) + +![](images/2adab3323b4169a1b7e5e12a9e585153cad7f97f1800859076ae6542a0637fd9.jpg) + +![](images/df18958f1f9a3f97b07756975b9edd393532c1af1e24f34ac79a0ce36cbb47aa.jpg) + +![](images/679230ccdb24ca16d3eddf1caf468af9d16d1cca7c2060bf5f8d9558476c1758.jpg) + +![](images/a2befe351f17de866de2c14eee0f9944bc52199f63e1446ce68a9e5cd9a97eb2.jpg) + +![](images/65ad094612fd9f11323f1c58f668b039f9ae4b4588491000e0a3d39db9cdb501.jpg) + +![](images/689ba4a3b278540f1820a05b6a7f517c7adf8b96d2c4ab36e98080539fb1c165.jpg) + +![](images/e8c45d823356dd8e66831ae0c4dc489358267a531c4b87abda548d46140f41ae.jpg) + +![](images/a5755a3a7c8e419b4f9012707baf457807346eb55654e5ae5550f6cd0603e186.jpg) + +![](images/ff0859ee0374d008f284ced332ad31d68ce9351b237d8f6fda75daf7e1ec0ea8.jpg) + +![](images/f923979d975a64a07ccbad5b1c940730f6450ca1fba5f406ee77588cc7712f21.jpg) + +![](images/5a7ee9bcc9ad71560586641bce21511bb95204ae56705ff5e5cf3d7b4df5e9bf.jpg) + +![](images/6c355a98a5905da8abb5c38f7a85d47eed7c4d6db189b9e8a0abd46b540eff15.jpg) + +![](images/a43755677f7778d3a3c0b390259cebdb77136ef4c2152bcc731380afa83d5c8f.jpg) + +![](images/1fbaa74e3dda8a26fd93156606fa744200210b337bb95501199d7cff8808f8e3.jpg) + +![](images/6520c5bf18fb4dcdd2f8e91bc88974401acb5272e4bbdcb381eed8e7d4c9cbcd.jpg) + +![](images/4b4b95b4fa28a2145159f8eeb49f252c090a456e41ee004d1b00837405dfdf87.jpg) + +![](images/6660c22b0912052666f36f120df68e8659dce1018b31d007ec40128a28c3d1c5.jpg) + +![](images/f0bec7520fa99daa4c8395977b7e1f7e5b3e72ebf49187c99fd68acd6ed697ac.jpg) + +![](images/69084b8180bb42b47ad959e7d18c47962e9c29ba7cd0ff430a9a2aada647c421.jpg) + +![](images/b9bea47768f541668b8c41013b029bb9fde7a88b94eb92b7188f5a6bb9a71cf3.jpg) +Input video + +![](images/95731a019221ad07cc1f1ff75b0bb6d58d3b343a2207b4b971c18b7e0c00b791.jpg) +Depth-Anything-V2 + +![](images/d640e0e7adf3f5766b77e2a41cfb31adf6d43dc7be95dd5e3411ee7203d2b05d.jpg) +NVDS +Figure 4. Qualitative comparison for open-world video depth estimation. We compare with the representative single-image depth estimation method Depth-Anything-V2 [68] and the video depth estimation method NVDS [63]. For better visualizing the temporal quality, we show the temporal profiles of each result in green boxes, by slicing the depth values along the time axis at the green line positions. + +![](images/1118163b71229008e3614461b7f4d06f745c187b234bf609c856a01cdad86ee1.jpg) +DepthCrafter (Ours) + +quences of various scenes. Since ScanNet v2 contains only static indoor scenes, we further introduced 5 dynamic indoor RGB-D videos with a length of 110 frames each from the Bonn [44] dataset to better evaluate the performance of our model on dynamic scenes. KITTI [19] is a street-scene outdoor dataset for autonomous driving, with sparse metric depths captured by a LiDAR sensor. We adopted the validation set, which includes 13 scenes, and extracted 13 videos from it with a length of 110 frames each. Besides, we also evaluated our model for single-image depth estimation on the NYU-v2 [55] test set, which contains 654 images. + +Evaluation metrics. Following practice in affine-invariant depth estimation [14, 32, 67, 68], we align the estimated depth maps with the ground truth using a scale and shift, and calculate two metrics: AbsRel $\downarrow$ (absolute relative error: $|\hat{\mathbf{d}} -\mathbf{d}| / \mathbf{d}$ ) and $\delta_{1}\uparrow$ (percentage of $\max (\mathbf{d} / \hat{\mathbf{d}},\hat{\mathbf{d}} /\mathbf{d}) < 1.25$ ). Different from previous methods that optimize the scale and shift individually for each frame, we optimize $a$ + +shared scale and shift across the entire video, which is more challenging, but necessary, for video depth estimation to ensure temporal consistency. + +Quantitative results. We compare our DepthCrafter with the representative methods for both image and video depth estimation, i.e. Marigold [32], Depth-Anything [67], Depth-Anything-V2 [68], NVDS [63], and ChronoDepth [54]. For Depth-Anything (V2), we use its official code, and the large model variant for best performance, while for Marigold we adopt the LCM version with an ensemble size of 5. As shown in Tab. 1, our DepthCrafter achieves state-of-the-art performance in all four video datasets, thanks to the powerful open-world video understanding capability of the video diffusion models and the three-stage training strategy that leverages both realistic and synthetic datasets. For Sintel and KITTI, characterized by significant camera motion and fast-moving objects, our DepthCrafter outperforms the strong Depth-Anything (V2) model trenen + +Table 1. Zero-shot depth estimation results. We compare with the best single-image depth estimation model, Marigold [32], and Depth Anything (V2) [67, 68], as well as the representative video depth estimation models, NVDS [63] and ChronoDepth [54]. Best and second best results are highlighted. + +
MethodSintel (~50 frames)Scannet (90 frames)KITTI (110 frames)Bonn (110 frames)NYU-v2 (1 frame)
AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑
NVDS [63]0.4080.4830.1870.6770.2530.5880.1670.7660.1510.780
ChronoDepth [54]0.5870.4860.1590.7830.1670.7590.1000.9110.0730.941
Marigold [32]0.5320.5150.1660.7690.1490.7960.0910.9310.0700.946
Depth-Anything [67]0.3250.5640.1300.8380.1420.8030.0780.9390.0420.981
Depth-Anything-V2 [68]0.3670.5540.1350.8220.1400.8040.1060.9210.0430.978
DepthCrafter (Ours)0.2700.6970.1230.8560.1040.8960.0710.9720.0720.948
+ +![](images/0db688633f645d601867bb003e5d85ebfa442598568b05e74a9704e520f4f4d1.jpg) +Figure 5. Single-image depth estimation. We compare with the representative single-image depth estimation method Depth-Anything-V2 [68]. + +![](images/7af9ee42bc25c6c46eda85bbb6432300c658e393414b0f8d51d649ad0b6423b1.jpg) + +![](images/f6a118f6a2af5c01117ae0b3a0c86257ed5370e804cd38317e12e93910f61fba.jpg) + +dously in terms of both the AbsRel and $\delta_{1}$ metrics, e.g. $25.7\% = (0.140 - 0.104) / 0.140$ improvement in AbsRel on KITTI. For indoor datasets like Scannet and Bonn, featuring minimal camera motion and roughly the same room scales, Depth-Anything has exhibited good performance. Nevertheless, we still have performance enhancements over it, e.g. $5.4\% = (0.130 - 0.123) / 0.130$ improvement in AbsRel on Scannet. Note that the sequence length of these datasets varies from 50 to 110 frames, and our model can generalize well across different video lengths. + +Qualitative results. To further demonstrate the effectiveness of our model, we present the qualitative results from the DAVIS dataset [46], Sora generated videos [6], and open-world videos, including human actions, animals, architectures, cartoons, and games, where the sequence length varies from 90 to 195 frames. As shown in Fig. 4, we show the temporal profiles of the estimated depth sequences in the green line position by slicing the depth values along the time axis, to better visualize the temporal consistency of the estimated depth sequences, following the practice in [26, 63]. We can observe that our DepthCrafter can produce temporally consistent depth sequences with fine-grained details across various open-world videos, while both NVDS and Depth-Anything exhibit zigzag artifacts in the temporal profiles, indicating the flickering artifacts in the estimated depth sequences. These results demonstrate the effectiveness of our DepthCrafter in generating temporally + +Table 2. Ablation study on the Sintel dataset. We evaluate the performance of our model at the end of different stages of training. + +
stage 1stage 2stage 3
AbsRel ↓0.3220.3160.270
δ1 ↑0.6260.6750.697
+ +consistent long depth sequences with high-fidelity details for open-world videos. + +Single-image depth estimation. Although our model is designed for video depth estimation, it can also perform single-image depth estimation, as our DepthCrafter can estimate video depth of any length. As shown in Tab. 1, our DepthCrafter achieves competitive performance in single-image depth estimation on the NYU-v2 dataset. Since the depth labels in the NYU-v2 dataset are sparse and noisy, we also provide the qualitative results in Fig. 5 to demonstrate the effectiveness of our model in estimating depth maps from static images. We can observe that our DepthCrafter can even produce more detailed depth maps than Depth-Anything-V2, which is the existing state-of-the-art single-image depth estimation model. These results demonstrate the ability of our DepthCrafter for processing both video and single-image depth estimation tasks. + +# 4.3. Ablation Studies + +Effectiveness of the three-stage training strategy. We first ablate the effectiveness of the three-stage training strategy by evaluating the performance of our model at the end of each stage on the Sintel dataset [7], since it contains precise depth annotations on dynamic scenes. From Tab. 2, we can observe that the performance of our model consistently improves as the number of training stages increases, indicating the effectiveness of the three-stage training strategy. More ablation results on other datasets are available in the supplementary material. + +Effectiveness of the inference strategy. To ablate the effectiveness of our inference strategy components, we consider these variants: baseline, which independently infers each segment and directly averages the overlapped frames; + initialization, which contains the same initialization of + +![](images/b85c35f4aa8ddc1705c3607c70b70f6162f3698d2026c3dbebade49a263e00e1.jpg) +Figure 6. Ablation studies on the effectiveness of the inference strategy. We profile the estimated depth sequences of different variants on the green line position. The yellow and blue arrows point to the static and dynamic regions, respectively. + +overlapped latents as our method, but without the stitching process; + initialization & stitching, which is our full method. We visually compare the temporal profiles of the estimated depth sequences of these variants in Fig. 6. We can observe the overlapped jaggies in both the static regions (pointed by the yellow arrow) and the dynamic regions (pointed by the blue arrow) in temporal profiles of the "baseline" method, which indicates the flickering artifacts. The "+" initialization" method can alleviate the flickering artifacts in the static regions, but still has jaggies in the dynamic regions, while our full method can produce smooth depth sequences in both static and dynamic regions. + +# 4.4. Applications + +Our DepthCrafter can facilitate various downstream applications, e.g., foreground matting, depth slicing, fog effects, and depth-conditioned video generation, by providing temporally consistent depth sequences with fine-grained details for open-world videos. We show example results of fog effects and depth-conditioned video generation in Fig. 7, while more visual effects results are available in the supplementary material. For the fog effect, we blend the fog map with the input video frames based on the depth values to simulate varying transparency levels in fog. And many recent conditioned video generation models [10, 16, 20, 76] employ depth maps as the structure conditions for video generation or editing. We adopt Control-A-Video [10] and video depth of our method as conditions to generate a video with prompts "a rider walking through stars, artstation". The visual effects of these applications rely heavily on the accuracy and consistency of the video depth, which demonstrates the wide applicability of our DepthCrafter in various downstream tasks. + +# 4.5. Limitations + +Although our DepthCrafter achieves state-of-the-art performance in open-world video depth estimation, there are still some limitations to be addressed in the future. First, the computation and memory consumption of our model is relatively high, which is mainly due to the large model size and the iterative denoising process in the diffusion model. As shown in Tab. 3, we report the inference speed of our model, + +![](images/ae4147316eaf6770300f5a7b8ef5de7b8a79cd8992dc0930d1dc1044b949e2ff.jpg) +Figure 7. Examples of visual effectiveness that could benefit from our DepthCrafter, including adding fog effects and depth-conditioned video generation. More visual effects results are available on our website. + +Table 3. Inference time per frame (ms) of our model, Depth-Anything (V2), and Marigold, with the resolution of $1024 \times 576$ . + +
MethodEncodingDenoisingDecodingAll
Depth-Anything (V2)N/AN/AN/A180.46
Marigold256.40114.53699.361070.29
DepthCrafter (Ours)51.85160.93253.06465.84
+ +Depth-Anything (V2), and Marigold, with the resolution of $1024 \times 576$ on a single NVIDIA A100 GPU. We can see that Depth-Anything (V2) is faster than our model, while our method is much faster than Marigold since it ensembles five inference results. Our model achieves the best quality without ensembling, and its inference speed of 465.84 ms per frame is acceptable for many applications. Second, our method requires around 24GB GPU memory to process a video with the resolution of $1024 \times 576$ and a segment length of 110 frames. But note that, with the segment length of 40 frames, the memory consumption can be reduced to 12GB, which is acceptable for most modern GPUs, and we can still infer videos of any length by our inference strategy under this setting. We believe that further engineering efforts, such as model distillation and quantization, can help further promote the practicality of our method. + +# 5. Conclusion + +We present DepthCrafter, a novel open-world video depth estimation method that leverages video diffusion models. It can generate temporally consistent depth sequences with fine-grained details for video width diverse content, motion, and camera movement, without requiring any additional information. It also supports videos of variable lengths, ranging from one frame (static image) to extremely long videos. This is achieved through our meticulously designed three-stage training strategy, compiled paired video-depth datasets, and an inference strategy. Extensive evaluations have demonstrated that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. It also facilitates various downstream applications, including depth-based visual effects and conditional video generation. + +# References + +[1] Shubhra Aich, Jean Marie Uwabeza Vianney, Md Amirul Islam, and Mannat Kaur Bingbing Liu. 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We innovate DepthCrafter, a novel video depth estimation approach, that can generate temporally consistent long depth sequences with fine-grained details for open-world videos, without requiring additional information such as camera poses or optical flow." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 479, + 200, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 479, + 200, + 491 + ], + "spans": [ + { + "bbox": [ + 151, + 479, + 200, + 491 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 505, + 297, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 505, + 297, + 696 + ], + "spans": [ + { + "bbox": [ + 54, + 505, + 297, + 696 + ], + "type": "text", + "content": "Estimating video depth in open-world scenarios is challenging due to the diversity of videos in appearance, content motion, camera movement, and length. We present DepthCrafter, an innovative method for generating temporally consistent long depth sequences with intricate details for open-world videos, without requiring any supplementary information such as camera poses or optical flow. The generalization ability to open-world videos is achieved by training the video-to-depth model from a pretrained image-to-video diffusion model, through our meticulously designed three-stage training strategy. Our training approach enables the model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both precise depth details and rich content diversity from realistic and synthetic datasets. We also propose an inference strategy that can process extremely" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 481, + 555, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 481, + 555, + 565 + ], + "spans": [ + { + "bbox": [ + 313, + 481, + 555, + 565 + ], + "type": "text", + "content": "long videos through segment-wise estimation and seamless stitching. Comprehensive evaluations on multiple datasets reveal that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. Furthermore, DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 586, + 394, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 586, + 394, + 597 + ], + "spans": [ + { + "bbox": [ + 314, + 586, + 394, + 597 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 605, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 605, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 605, + 555, + 715 + ], + "type": "text", + "content": "Monocular depth estimation, serving as the bridge linking 2D observations and the 3D world, has been a long-standing fundamental problem in computer vision. It plays a crucial role in a wide range of downstream applications, e.g., mixed reality, AI-generated content, autonomous driving, and robotics [14, 24, 27, 28, 40, 57, 72, 73]. The inherent ambiguity makes it challenging, as the observed information from a single view is insufficient to determine the depth of a scene uniquely." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 223, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 223, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 223, + 713 + ], + "type": "text", + "content": "* Joint first authors. † Corresponding authors." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2005" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 288 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 288 + ], + "type": "text", + "content": "With recent advances in foundation models, we have witnessed significant progress in depth estimation from monocular images [13, 18, 32, 43, 47, 67, 68, 71]. However, all these methods are tailored for static images, without considering the temporal information in videos. Temporal inconsistency, or flickering, would be observed when directly applying them to videos, as shown in Fig. 1. Existing video depth estimation methods [35, 41, 58, 63, 77] typically try to optimize temporally consistent depth sequences from a pre-trained image depth model, with a given or learnable camera poses. Their performance is sensitive to both the proportion of dynamic content and the quality of the camera poses. Yet, videos in the open world are diverse in content, motion, camera movement, and length, making these methods hard to perform well in practice. Moreover, the required camera poses are usually non-trivial to obtain in open-world videos, particularly for long videos and videos with abundant dynamic content." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 292, + 295, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 292, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 56, + 292, + 295, + 638 + ], + "type": "text", + "content": "In this paper, we aim to generate temporally consistent long depth sequences with high-fidelity details for diverse open-world videos, without requiring any additional information. Observing the strong capability of diffusion models in generating various types of videos [3, 4, 6, 8, 9, 23, 64, 65], we propose DepthCrafter, to leverage the video diffusion model for video depth estimation, while maintaining the generalization ability to open-world videos. To train our DepthCrafter, a video-to-depth model, from a pre-trained image-to-video diffusion model, we compile paired videodepth datasets in two styles, i.e. realistic and synthetic, since the realistic dataset provides rich content diversity and the synthetic dataset offers precise depth details. On the aspect of temporal context, most existing video diffusion models can only produce a fixed and small number of frames at one time, e.g., 25 frames in Stable Video Diffusion (SVD) [3], which, however, is usually too short for open-world video depth estimation to accurately arrange depth distributions throughout the video. To enable variable long temporal context and fuse the respective advantages of the two-styled datasets, we present a three-stage training strategy to progressively train certain layers of the diffusion model on different datasets with variable lengths. By doing so, we can adapt the video diffusion model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both the precise depth details and rich content diversity. To further support extremely long videos, we tailor an inference strategy to process the video in overlapped segments and seamlessly stitch them together." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 642, + 294, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 294, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 294, + 714 + ], + "type": "text", + "content": "We extensively evaluate our DepthCrafter on diverse datasets, including indoor, outdoor, static, dynamic, realistic, and synthetic videos, under zero-shot settings. Both qualitative and quantitative results demonstrate that our DepthCrafter achieves state-of-the-art performance in openworld video depth estimation, outperforming existing meth" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 119 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 119 + ], + "type": "text", + "content": "ods by a large margin. Besides, we demonstrate that our DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation. Our contributions are summarized below:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 121, + 553, + 277 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 314, + 121, + 553, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 121, + 553, + 169 + ], + "spans": [ + { + "bbox": [ + 314, + 121, + 553, + 169 + ], + "type": "text", + "content": "- We innovate DepthCrafter, a novel method to generate temporally consistent long depth sequences with fine-grained details for open-world videos, outperforming existing approaches by a large margin." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 170, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 170, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 170, + 553, + 228 + ], + "type": "text", + "content": "- We present a three-stage training strategy to enable generating depth sequences with a long and variable temporal context, up to 110 frames. It also allows us to harvest both the precise depth details and rich content diversity from synthetic and realistic datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 229, + 553, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 553, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 553, + 277 + ], + "type": "text", + "content": "- We design an inference strategy to segment-wisely process videos beyond 110 frames and seamlessly stitch them together, facilitating depth estimation for extremely long videos." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 293, + 400, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 293, + 400, + 304 + ], + "spans": [ + { + "bbox": [ + 314, + 293, + 400, + 304 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 315, + 555, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 555, + 518 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 555, + 518 + ], + "type": "text", + "content": "Image depth estimation. Image depth estimation aims at predicting the depth map from a single image [1, 15, 17, 36, 38, 45, 66]. However, the generalization ability to diverse open-world scenes is hindered by the limited training data. To this end, MiDaS [49] presented the affine-invariant depth representation, enabling mixed training datasets. Depth-Anything (V2) [67, 68] followed this idea and proposed to train the model on both labeled and large-scale unlabeled images, achieving good generalization ability. Marigold [32] and follow-up works [18, 21, 42] leverage the diffusion priors to realize zero-shot transfer to unseen datasets. Besides the affine-invariant depth, another stream of methods tried to estimate the absolute metric depth [2, 5, 25, 47, 71]. All these methods are tailored for static images without considering the temporal consistency, while our work aims to generate temporally consistent long depth sequences for open-world videos." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "type": "text", + "content": "Video depth estimation. Existing video depth estimation methods could be categorized into two classes: test-time optimization and feed-forward prediction. Test-time optimization methods [11, 35, 41, 77] involve an optimization procedure for each video during inference, which typically requires camera poses or optical flow. Their results are usually consistent, but the requirement of camera poses or optical flow would limit their applicability to open-world videos. Feed-forward prediction methods directly predict depth sequences from videos [39, 58, 60, 61, 63, 69, 70, 74], e.g., DeepV2D [58] combines camera motion estimation with depth estimation, MAMO [69] leverages memory attention, and NVDS [63] introduces a plug-and-play stabilization network. However, due to the limited video depth training data, these methods often fail to address the in-the-wild videos with diverse content. By leveraging the pre" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2006" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 68, + 545, + 228 + ], + "blocks": [ + { + "bbox": [ + 67, + 68, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 67, + 68, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 67, + 68, + 545, + 228 + ], + "type": "image", + "image_path": "511e4c99dea41bbb4f686e1dfcf9c2d187c09705f24eac16902168839d66ab8b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "lines": [ + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "spans": [ + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "text", + "content": "Figure 2. Overview of our DepthCrafter. It is a conditional diffusion model that models the distribution " + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "inline_equation", + "content": "p(\\mathbf{d} \\mid \\mathbf{v})" + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "text", + "content": " over the depth sequence " + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "text", + "content": " conditioned on the input video " + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "text", + "content": ". We train the model in three stages, where the spatial or temporal layers of the diffusion model are progressively learned on our compiled realistic or synthetic datasets with variable lengths " + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 54, + 231, + 555, + 289 + ], + "type": "text", + "content": ". During inference, given an open-world video, it can generate temporally consistent long depth sequences with fine-grained details for the entire video from initialized Gaussian noise, without requiring any supplementary information, such as camera poses or optical flow." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 298, + 294, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 298, + 294, + 334 + ], + "spans": [ + { + "bbox": [ + 54, + 298, + 294, + 334 + ], + "type": "text", + "content": "trained video diffusion model and our designed three-stage training strategy, our method demonstrates a powerful ability for open-world video depth estimation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 336, + 296, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 336, + 296, + 577 + ], + "spans": [ + { + "bbox": [ + 56, + 336, + 296, + 577 + ], + "type": "text", + "content": "Video diffusion models. Diffusion models [22, 56] have shown remarkable video generation ability [3, 4, 6, 8, 9, 23, 64, 65]. Among these methods, VDM [23] presents the first results on video generation using diffusion models, Sora [6] achieves impressive performance in this area, and SVD [3] provides the popular open-source models for image-to-video generation. Trained on a well-curated video dataset, SVD can generate high-quality videos and is used as the model prior for various video-related tasks. In this paper, we leverage the video diffusion model for high-fidelity consistent video depth estimation, such that the generalization ability to open-world videos can be maintained. Concurrent to our work, ChronoDepth [54] also explores video depth estimation with video diffusion priors. However, ChronoDepth only supports a short temporal context, which is insufficient to accurately arrange depth distributions throughout the video. In contrast, our method not only supports variable-length temporal context at one time, up to 110 frames, but also can estimate depth sequences for videos of arbitrary lengths." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 586, + 111, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 111, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 111, + 597 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 604, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 604, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 604, + 295, + 714 + ], + "type": "text", + "content": "Given an open-world video, " + }, + { + "bbox": [ + 55, + 604, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{v} \\in \\mathbb{R}^{T \\times H \\times W \\times 3}" + }, + { + "bbox": [ + 55, + 604, + 295, + 714 + ], + "type": "text", + "content": ", our goal is to estimate temporally consistent depth sequences, " + }, + { + "bbox": [ + 55, + 604, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{d} \\in \\mathbb{R}^{T \\times H \\times W}" + }, + { + "bbox": [ + 55, + 604, + 295, + 714 + ], + "type": "text", + "content": ", with fine-grained details. Considering the diversity of open-world videos in appearance, content motion, camera movement, and length, the challenges to achieving our goal are threefold: 1.) a comprehensive understanding of video content for generalization ability; 2.) a long and variable temporal context to arrange the entire depth distributions accurately and keep temporal consistency; and 3.)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 298, + 555, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 298, + 555, + 406 + ], + "spans": [ + { + "bbox": [ + 313, + 298, + 555, + 406 + ], + "type": "text", + "content": "the ability to process extremely long videos. As shown in Fig. 2, we tackle these challenges by formulating the video depth estimation as a conditional diffusion generation problem " + }, + { + "bbox": [ + 313, + 298, + 555, + 406 + ], + "type": "inline_equation", + "content": "p(\\mathbf{d} \\mid \\mathbf{v})" + }, + { + "bbox": [ + 313, + 298, + 555, + 406 + ], + "type": "text", + "content": ". We train a video-to-depth model from a pretrained image-to-video diffusion model through a meticulously designed three-stage training strategy with compiled paired video-depth datasets, and tailor an inference strategy to process extremely long videos through segment-wise estimation and seamless stitching." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 411, + 525, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 525, + 423 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 525, + 423 + ], + "type": "text", + "content": "3.1. Preliminaries of Video Diffusion Models" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "type": "text", + "content": "Diffusion models [22, 56] learn the data distribution " + }, + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "type": "inline_equation", + "content": "p(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "type": "text", + "content": " by a forward diffusion process to gradually noise the data to a target distribution, e.g. the Gaussian distribution, and a reverse denoising process to iteratively recover the data from the noise by a learned denoiser. In this paper, our study is conducted based on the stale video diffusion (SVD) [3], which is a famous open-source video diffusion model. SVD adopts the EDM [31] diffusion framework. The diffusion process is achieved by adding i.i.d. " + }, + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "type": "inline_equation", + "content": "\\sigma_t^2" + }, + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "type": "text", + "content": "-variance Gaussian noise to the data " + }, + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0 \\sim p(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 430, + 555, + 550 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 367, + 555, + 555, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 555, + 555, + 570 + ], + "spans": [ + { + "bbox": [ + 367, + 555, + 555, + 570 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\mathbf {x} _ {0} + \\sigma_ {t} ^ {2} \\epsilon , \\quad \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}), \\tag {1}", + "image_path": "8c44818fc3335d120231d6bf5506aad2f666f7e2d16e7d4426060dc9930d7dfb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t\\sim p(\\mathbf{x};\\sigma_t)" + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": " is the data with noise level " + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": " is large enough " + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "inline_equation", + "content": "(\\sigma_{\\mathrm{max}})" + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": ", the distribution would be indistinguishable from the Gaussian distribution. Based on this fact, the diffusion model starts from a high-variance Gaussian noise " + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}\\big(\\mathbf{0},\\sigma_{\\mathrm{max}}^2\\mathbf{I}\\big)" + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": " and gradually denoises it towards " + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "inline_equation", + "content": "\\sigma_0 = 0" + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": " to generate the data. The denoiser " + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "inline_equation", + "content": "D_{\\theta}" + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": " is a learnable function that tries to predict the clean data, i.e. " + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}_0 = D_\\theta (\\mathbf{x}_t;\\sigma_t)" + }, + { + "bbox": [ + 313, + 574, + 556, + 683 + ], + "type": "text", + "content": ". Its training objective is the denoising score matching:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 326, + 687, + 555, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 687, + 555, + 717 + ], + "spans": [ + { + "bbox": [ + 326, + 687, + 555, + 717 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\mathbf {x} _ {t} \\sim p (\\mathbf {x}; \\sigma_ {t}), \\sigma_ {t} \\sim p (\\sigma)} \\left[ \\lambda_ {\\sigma_ {t}} \\left\\| D _ {\\theta} (\\mathbf {x} _ {t}; \\sigma_ {t}; \\mathbf {c}) - \\mathbf {x} _ {0} \\right\\| _ {2} ^ {2} \\right], \\quad (2)", + "image_path": "8dd420855eb54d381275ed753b42977e36298b8ac5b47ced5466af128fda485c.jpg" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2007" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "p(\\sigma)" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " is the noise level distribution during training, " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " denotes the conditioning information, and " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "\\lambda_{\\sigma_t}" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " is the weight for the denoising loss at time " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": ". To promote the learning, EDM adopts the preconditioning strategy [31, 53], to parameterize the denoiser " + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "inline_equation", + "content": "D_{\\theta}" + }, + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 73, + 140, + 295, + 159 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 140, + 295, + 159 + ], + "spans": [ + { + "bbox": [ + 73, + 140, + 295, + 159 + ], + "type": "interline_equation", + "content": "D _ {\\theta} \\left(\\mathbf {x} _ {t}; \\sigma_ {t}; \\mathbf {c}\\right) = \\tag {3}", + "image_path": "34c762b563ae772a309d75b647bac0e1ac3b556cc59b7239044f03bab66dc3ad.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 86, + 156, + 266, + 171 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 156, + 266, + 171 + ], + "spans": [ + { + "bbox": [ + 86, + 156, + 266, + 171 + ], + "type": "interline_equation", + "content": "c _ {\\text {s k i p}} \\left(\\sigma_ {t}\\right) \\mathbf {x} _ {t} + c _ {\\text {o u t}} \\left(\\sigma_ {t}\\right) F _ {\\theta} \\left(c _ {\\text {i n}} \\mathbf {x} _ {t}; c _ {\\text {n o i s e}} \\left(\\sigma_ {t}\\right); \\mathbf {c}\\right),", + "image_path": "49deb15971b01f53fb0631bcb2b868e8c1549b971a711bd6458c307c7e7637a6.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "text", + "content": " is implemented as a learnable U-Net [52], and " + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}}" + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{out}}" + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{skip}}" + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{noise}}" + }, + { + "bbox": [ + 55, + 178, + 295, + 203 + ], + "type": "text", + "content": " are preconditioning functions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 209, + 244, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 209, + 244, + 221 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 244, + 221 + ], + "type": "text", + "content": "3.2. Formulation with Diffusion Models" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 228, + 296, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 296, + 380 + ], + "type": "text", + "content": "Latent space transformation. To generate high-resolution depth sequences without sacrificing computational efficiency, we adopt the framework of Latent Diffusion Models (LDMs) [51] that perform in a low-dimensional latent space. The transformation between the latent and data spaces is achieved by a Variational Autoencoder (VAE) [33], which was originally designed for encoding and decoding video frames in SVD [3]. Fortunately, we found it can be directly used for depth sequences with only a negligible reconstruction error, which is similar to the observation in Marigold [32] for image depth estimation. As shown in Fig. 2, the latent space transformation is formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 381, + 294, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 381, + 294, + 396 + ], + "spans": [ + { + "bbox": [ + 113, + 381, + 294, + 396 + ], + "type": "interline_equation", + "content": "\\mathbf {z} ^ {(\\mathbf {x})} = \\mathcal {E} (\\mathbf {x}), \\quad \\hat {\\mathbf {x}} = \\mathcal {D} \\left(\\mathbf {z} ^ {(\\mathbf {x})}\\right), \\tag {4}", + "image_path": "7c882228447c1ab260e3195c9236840138f11c97c8e983a0b8995b6de7d66768.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "spans": [ + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "content": " is either the video " + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "content": " or the depth sequence " + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{(\\mathbf{x})}" + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "content": " is the latent representation of the data, " + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "content": " is the reconstructed data, " + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 402, + 296, + 558 + ], + "type": "text", + "content": " are encoder and decoder of the VAE, respectively. For the depth sequence, we replicate it three times to meet the 3-channel input format of the encoder in VAE and average the three channels of the decoder output to obtain the final latent of the depth sequence. Following the practice in image depth estimation [32, 49, 50, 67, 68], we adopt the relative depth, i.e. the affine-invariant depth, which is normalized to [0, 1]. But differently, our predicted depth sequence shares the same scale and shift across frames, rather than a per-frame normalization, which is crucial for maintaining temporal consistency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": "Conditioning on the video. SVD is an image-to-video diffusion model that generates videos conditioned on a single image. The conditional image is fed into the U-Net in two ways, i.e., concatenating its latent to the input latent, and injecting its CLIP [48] embedding to the intermediate features via cross-attention. Yet, our DepthCrafter involves the generation of depth sequences conditioned on video frames in a frame-to-frame fashion. Therefore, we adapt the conditioning mechanism to meet our video-to-depth generation task. As shown in Fig. 2, given the encoded latent of depth sequence " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{(\\mathrm{d})}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " and video frames " + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{(\\mathrm{v})}" + }, + { + "bbox": [ + 55, + 558, + 296, + 713 + ], + "type": "text", + "content": " from Eq. (4), we concatenate the video latent to the input noisy depth latent frame-wisely, rather than only the first frame, to condition" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 554, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 168 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 168 + ], + "type": "text", + "content": "the denoiser for generating the depth sequence. For high-level semantic information, we embed the video frames using CLIP and then inject the embeddings in a frame-to-frame manner to the denoiser via cross-attention. Compared to the original conditioning mechanism, our adapted conditioning provides comprehensive information from the video frames to the denoiser, which guarantees the alignment between the generated depth sequences and the video content." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 178, + 420, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 178, + 420, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 178, + 420, + 190 + ], + "type": "text", + "content": "3.3. Training Strategy" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 197, + 554, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 197, + 554, + 280 + ], + "spans": [ + { + "bbox": [ + 313, + 197, + 554, + 280 + ], + "type": "text", + "content": "To train our DepthCrafter, we need a large amount of high-quality paired video-depth sequences. Although there are several video depth datasets available, e.g., KITTI [19], Scannet [12], VDW [62], DynamicReplica [30], and MatrixCity [37], they are either lacking high-quality depth annotations or restricted to a specific domain, e.g., driving scenes, indoor scenes, or synthetic scenes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "text", + "content": "Dataset construction. To this end, we compiled paired datasets of two styles, i.e. realistic and synthetic, where the realistic dataset is large-scale and diverse, and the synthetic dataset is miniature but fine-grained and accurate. The realistic dataset is constructed from a large number of binocular videos with a wide range of scene and motion diversity. We cut the videos according to scene changes, and apply the state-of-the-art video stereo matching method, e.g., BiDAStereo [29], to generate temporally consistent depth sequences. Finally, we obtained " + }, + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "inline_equation", + "content": "\\sim 200\\mathrm{K}" + }, + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "text", + "content": " paired video-depth sequences with the length of 50-200 frames. The synthetic dataset is a combination of the DynamicReplica [30] and MatrixCity [37] datasets, which contains " + }, + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "inline_equation", + "content": "\\sim 3\\mathrm{K}" + }, + { + "bbox": [ + 313, + 281, + 555, + 449 + ], + "type": "text", + "content": " fine-grained depth annotations with a length of 150 frames." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 449, + 556, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 556, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 556, + 628 + ], + "type": "text", + "content": "Challenges of variable long temporal context. Different from image depth estimation which can determine the distribution of relative depth from a single frame, the video depth estimation requires a long temporal context to arrange the depth distributions accurately for the entire video and keep the temporal consistency. Besides, the model should support variable-length estimation as the length of open-world videos may vary significantly. However, existing open-source video diffusion models can only generate a fixed small number of frames at a time, e.g., 25 frames in SVD [3]. It is non-trivial to adapt the pre-trained model to meet this requirement, as directly fine-tuning it with long sequences is memory-consuming, for example, modern GPUs with 40GB memory can only support the training of a 25-frame sequence in SVD." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 630, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 556, + 713 + ], + "type": "text", + "content": "Three-stage training. Considering both the two-style paired datasets and the long temporal context requirement, we design a three-stage training strategy to harvest the variety of video content, the precise depth details, as well as the support for long and variable sequences. As shown in Fig. 2, we train our DepthCrafter from the pre-trained SVD in three stages. We first train it on our large realistic" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2008" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 68, + 298, + 236 + ], + "blocks": [ + { + "bbox": [ + 57, + 68, + 298, + 236 + ], + "lines": [ + { + "bbox": [ + 57, + 68, + 298, + 236 + ], + "spans": [ + { + "bbox": [ + 57, + 68, + 298, + 236 + ], + "type": "image", + "image_path": "885be172efed77e1a780dfb22b9689e975c54a8a0bae0c26fc08ff81744b2a1f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "lines": [ + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "spans": [ + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "type": "text", + "content": "Figure 3. Inference for extremely long videos. We divide the video into overlapped segments and estimate the depth sequence for each segment with a noise initialization strategy to anchor the scale and shift of depth distributions. These depth segments are then seamlessly stitched together with a latent interpolation strategy to form the entire depth sequence. The overlapped frames and their interpolation weights are denoted as " + }, + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "type": "inline_equation", + "content": "w_i" + }, + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "type": "inline_equation", + "content": "1 - w_i" + }, + { + "bbox": [ + 55, + 240, + 297, + 320 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 329, + 296, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 329, + 296, + 628 + ], + "spans": [ + { + "bbox": [ + 56, + 329, + 296, + 628 + ], + "type": "text", + "content": "dataset to adapt the model to the video-to-depth generation task. The sequence length in this stage is randomly sampled from [1, 25] frames, such that the model can learn to generate depth sequences with variable lengths. In the second stage, we only fine-tune the temporal layers of the model, still on our large realistic dataset, but with the sequence length randomly sampled from [1, 110] frames. The reason why we only fine-tune the temporal layers is that the temporal layers are more sensitive to the sequence length while the spatial layers are already adapted to the video-to-depth generation task in the first stage, and doing so significantly reduces memory consumption compared to fine-tuning the full model. The long temporal context in this stage enables the model to precisely arrange the entire depth distributions for long and variable sequences. In the third stage, we fine-tune the spatial layers of the model on our small synthetic dataset, with a fixed sequence length of 45 frames since the model has already learned to generate depth sequences with variable lengths in the first two stages and tuning the spatial layers would not affect the temporal context. As the depth annotations in the synthetic dataset are more accurate and fine-grained, the model can learn more precise depth details in this stage. The three-stage training strategy makes our DepthCrafter capable of generating high-quality depth sequences for open-world videos with variable lengths." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 635, + 253, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 253, + 648 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 253, + 648 + ], + "type": "text", + "content": "3.4. Inference for Extremely Long Videos" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": "Although the model can estimate depth sequences up to the length of 110 frames after training, it is still far from long enough for open-world videos, which can even contain hundreds or thousands of frames. To this end, we design an inference strategy to infer extremely long depth sequences in" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "text", + "content": "a segment-wise manner and seamlessly stitch them together to form the entire depth sequence. As shown in Fig. 3, we first divide the video into overlapped segments, whose lengths are up to 110 frames. Then we estimate the depth sequences for each segment. Rather than purely initializing the input latent with Gaussian noise " + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}\\big(\\mathbf{0},\\sigma_{\\max}^2\\mathbf{I}\\big)" + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "text", + "content": ", we initialize the latent of the overlapped frames by adding noise to the denoised latent from the previous segment, to anchor the scale and shift of the depth distributions. Finally, to further ensure the temporal smoothness across segments, we craft a mortise-and-tenon style latent interpolation strategy to stitch consecutive segments together, inspired by [75]. Specifically, we interpolate the latent of the overlapped frames " + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "text", + "content": " from the two segments with the interpolation weights " + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "inline_equation", + "content": "w_i" + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "inline_equation", + "content": "1 - w_i" + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "text", + "content": ", respectively, where " + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "inline_equation", + "content": "w_i" + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "text", + "content": " is linearly decreased from 1 to 0. The final estimated depth sequence is obtained by decoding the stitched latent segments with the decoder " + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 72, + 555, + 313 + ], + "type": "text", + "content": " in the VAE. With the training and inference strategies, our DepthCrafter can generate temporally consistent long depth sequences for open-world videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 324, + 397, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 324, + 397, + 337 + ], + "spans": [ + { + "bbox": [ + 313, + 324, + 397, + 337 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 343, + 411, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 343, + 411, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 343, + 411, + 357 + ], + "type": "text", + "content": "4.1. Implementation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "spans": [ + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "text", + "content": "We implemented our DepthCrafter based on SVD [3], using the diffusers [59] library. We train our model at the resolution of " + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "inline_equation", + "content": "320 \\times 640" + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "text", + "content": " for efficiency, but we can estimate depth sequences at any resolution, e.g., " + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "inline_equation", + "content": "576 \\times 1024" + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "text", + "content": ", during inference. We use the Adam optimizer [34] with a learning rate of " + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-5}" + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "text", + "content": " and a batch size of 8. The number of iterations in the three stages of training is " + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "inline_equation", + "content": "80K" + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "inline_equation", + "content": "40K" + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "inline_equation", + "content": "10K" + }, + { + "bbox": [ + 313, + 362, + 556, + 507 + ], + "type": "text", + "content": ", respectively. We employed eight GPUs for training, with a total training time of about five days. Except for specific explanations, the number of denoising steps is set to 5 during inference. Please refer to the supplementary material for more implementation details." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 515, + 389, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 515, + 389, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 515, + 389, + 528 + ], + "type": "text", + "content": "4.2. Evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": "Evaluation datasets. We evaluate our model on four video datasets, a single-image dataset, as well as the DAVIS dataset [46] and in-the-wild videos for qualitative results. 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"type": "image", + "image_path": "d640e0e7adf3f5766b77e2a41cfb31adf6d43dc7be95dd5e3411ee7203d2b05d.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 357, + 437, + 378, + 445 + ], + "lines": [ + { + "bbox": [ + 357, + 437, + 378, + 445 + ], + "spans": [ + { + "bbox": [ + 357, + 437, + 378, + 445 + ], + "type": "text", + "content": "NVDS" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 450, + 555, + 483 + ], + "lines": [ + { + "bbox": [ + 55, + 450, + 555, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 555, + 483 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison for open-world video depth estimation. We compare with the representative single-image depth estimation method Depth-Anything-V2 [68] and the video depth estimation method NVDS [63]. For better visualizing the temporal quality, we show the temporal profiles of each result in green boxes, by slicing the depth values along the time axis at the green line positions." + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 434, + 392, + 551, + 435 + ], + "blocks": [ + { + "bbox": [ + 434, + 392, + 551, + 435 + ], + "lines": [ + { + "bbox": [ + 434, + 392, + 551, + 435 + ], + "spans": [ + { + "bbox": [ + 434, + 392, + 551, + 435 + ], + "type": "image", + "image_path": "1118163b71229008e3614461b7f4d06f745c187b234bf609c856a01cdad86ee1.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 456, + 437, + 528, + 446 + ], + "lines": [ + { + "bbox": [ + 456, + 437, + 528, + 446 + ], + "spans": [ + { + "bbox": [ + 456, + 437, + 528, + 446 + ], + "type": "text", + "content": "DepthCrafter (Ours)" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 34 + }, + { + "bbox": [ + 55, + 490, + 296, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 490, + 296, + 622 + ], + "spans": [ + { + "bbox": [ + 55, + 490, + 296, + 622 + ], + "type": "text", + "content": "quences of various scenes. Since ScanNet v2 contains only static indoor scenes, we further introduced 5 dynamic indoor RGB-D videos with a length of 110 frames each from the Bonn [44] dataset to better evaluate the performance of our model on dynamic scenes. KITTI [19] is a street-scene outdoor dataset for autonomous driving, with sparse metric depths captured by a LiDAR sensor. We adopted the validation set, which includes 13 scenes, and extracted 13 videos from it with a length of 110 frames each. Besides, we also evaluated our model for single-image depth estimation on the NYU-v2 [55] test set, which contains 654 images." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": "Evaluation metrics. Following practice in affine-invariant depth estimation [14, 32, 67, 68], we align the estimated depth maps with the ground truth using a scale and shift, and calculate two metrics: AbsRel " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " (absolute relative error: " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "|\\hat{\\mathbf{d}} -\\mathbf{d}| / \\mathbf{d}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{1}\\uparrow" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " (percentage of " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\max (\\mathbf{d} / \\hat{\\mathbf{d}},\\hat{\\mathbf{d}} /\\mathbf{d}) < 1.25" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": "). Different from previous methods that optimize the scale and shift individually for each frame, we optimize " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "a" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "type": "text", + "content": "shared scale and shift across the entire video, which is more challenging, but necessary, for video depth estimation to ensure temporal consistency." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": "Quantitative results. We compare our DepthCrafter with the representative methods for both image and video depth estimation, i.e. Marigold [32], Depth-Anything [67], Depth-Anything-V2 [68], NVDS [63], and ChronoDepth [54]. For Depth-Anything (V2), we use its official code, and the large model variant for best performance, while for Marigold we adopt the LCM version with an ensemble size of 5. As shown in Tab. 1, our DepthCrafter achieves state-of-the-art performance in all four video datasets, thanks to the powerful open-world video understanding capability of the video diffusion models and the three-stage training strategy that leverages both realistic and synthetic datasets. For Sintel and KITTI, characterized by significant camera motion and fast-moving objects, our DepthCrafter outperforms the strong Depth-Anything (V2) model trenen" + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2010" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 107, + 553, + 213 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 103 + ], + "type": "text", + "content": "Table 1. Zero-shot depth estimation results. We compare with the best single-image depth estimation model, Marigold [32], and Depth Anything (V2) [67, 68], as well as the representative video depth estimation models, NVDS [63] and ChronoDepth [54]. Best and second best results are highlighted." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 107, + 553, + 213 + ], + "lines": [ + { + "bbox": [ + 58, + 107, + 553, + 213 + ], + "spans": [ + { + "bbox": [ + 58, + 107, + 553, + 213 + ], + "type": "table", + "html": "
MethodSintel (~50 frames)Scannet (90 frames)KITTI (110 frames)Bonn (110 frames)NYU-v2 (1 frame)
AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑AbsRel ↓δ1 ↑
NVDS [63]0.4080.4830.1870.6770.2530.5880.1670.7660.1510.780
ChronoDepth [54]0.5870.4860.1590.7830.1670.7590.1000.9110.0730.941
Marigold [32]0.5320.5150.1660.7690.1490.7960.0910.9310.0700.946
Depth-Anything [67]0.3250.5640.1300.8380.1420.8030.0780.9390.0420.981
Depth-Anything-V2 [68]0.3670.5540.1350.8220.1400.8040.1060.9210.0430.978
DepthCrafter (Ours)0.2700.6970.1230.8560.1040.8960.0710.9720.0720.948
", + "image_path": "b4e53ba8dbb5a1a8bde8f78f17958e2aff6085d2c3bd968a8cff552ebd134fc1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 58, + 220, + 135, + 339 + ], + "blocks": [ + { + "bbox": [ + 58, + 220, + 135, + 339 + ], + "lines": [ + { + "bbox": [ + 58, + 220, + 135, + 339 + ], + "spans": [ + { + "bbox": [ + 58, + 220, + 135, + 339 + ], + "type": "image", + "image_path": "0db688633f645d601867bb003e5d85ebfa442598568b05e74a9704e520f4f4d1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 344, + 295, + 378 + ], + "lines": [ + { + "bbox": [ + 55, + 344, + 295, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 295, + 378 + ], + "type": "text", + "content": "Figure 5. Single-image depth estimation. We compare with the representative single-image depth estimation method Depth-Anything-V2 [68]." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 137, + 220, + 214, + 339 + ], + "blocks": [ + { + "bbox": [ + 137, + 220, + 214, + 339 + ], + "lines": [ + { + "bbox": [ + 137, + 220, + 214, + 339 + ], + "spans": [ + { + "bbox": [ + 137, + 220, + 214, + 339 + ], + "type": "image", + "image_path": "7af9ee42bc25c6c46eda85bbb6432300c658e393414b0f8d51d649ad0b6423b1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 217, + 220, + 294, + 339 + ], + "blocks": [ + { + "bbox": [ + 217, + 220, + 294, + 339 + ], + "lines": [ + { + "bbox": [ + 217, + 220, + 294, + 339 + ], + "spans": [ + { + "bbox": [ + 217, + 220, + 294, + 339 + ], + "type": "image", + "image_path": "f6a118f6a2af5c01117ae0b3a0c86257ed5370e804cd38317e12e93910f61fba.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "type": "text", + "content": "dously in terms of both the AbsRel and " + }, + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "type": "inline_equation", + "content": "\\delta_{1}" + }, + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "type": "text", + "content": " metrics, e.g. " + }, + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "type": "inline_equation", + "content": "25.7\\% = (0.140 - 0.104) / 0.140" + }, + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "type": "text", + "content": " improvement in AbsRel on KITTI. For indoor datasets like Scannet and Bonn, featuring minimal camera motion and roughly the same room scales, Depth-Anything has exhibited good performance. Nevertheless, we still have performance enhancements over it, e.g. " + }, + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "type": "inline_equation", + "content": "5.4\\% = (0.130 - 0.123) / 0.130" + }, + { + "bbox": [ + 55, + 386, + 295, + 506 + ], + "type": "text", + "content": " improvement in AbsRel on Scannet. Note that the sequence length of these datasets varies from 50 to 110 frames, and our model can generalize well across different video lengths." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 510, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 714 + ], + "type": "text", + "content": "Qualitative results. To further demonstrate the effectiveness of our model, we present the qualitative results from the DAVIS dataset [46], Sora generated videos [6], and open-world videos, including human actions, animals, architectures, cartoons, and games, where the sequence length varies from 90 to 195 frames. As shown in Fig. 4, we show the temporal profiles of the estimated depth sequences in the green line position by slicing the depth values along the time axis, to better visualize the temporal consistency of the estimated depth sequences, following the practice in [26, 63]. We can observe that our DepthCrafter can produce temporally consistent depth sequences with fine-grained details across various open-world videos, while both NVDS and Depth-Anything exhibit zigzag artifacts in the temporal profiles, indicating the flickering artifacts in the estimated depth sequences. These results demonstrate the effectiveness of our DepthCrafter in generating temporally" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 248, + 552, + 297 + ], + "blocks": [ + { + "bbox": [ + 313, + 221, + 555, + 243 + ], + "lines": [ + { + "bbox": [ + 313, + 221, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 313, + 221, + 555, + 243 + ], + "type": "text", + "content": "Table 2. Ablation study on the Sintel dataset. We evaluate the performance of our model at the end of different stages of training." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 248, + 552, + 297 + ], + "lines": [ + { + "bbox": [ + 317, + 248, + 552, + 297 + ], + "spans": [ + { + "bbox": [ + 317, + 248, + 552, + 297 + ], + "type": "table", + "html": "
stage 1stage 2stage 3
AbsRel ↓0.3220.3160.270
δ1 ↑0.6260.6750.697
", + "image_path": "cdd400e7c673f3626c44472a66470beaeb15aff69e024b8a45c3607085193848.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 304, + 553, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 304, + 553, + 327 + ], + "spans": [ + { + "bbox": [ + 313, + 304, + 553, + 327 + ], + "type": "text", + "content": "consistent long depth sequences with high-fidelity details for open-world videos." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 328, + 555, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 328, + 555, + 508 + ], + "spans": [ + { + "bbox": [ + 313, + 328, + 555, + 508 + ], + "type": "text", + "content": "Single-image depth estimation. Although our model is designed for video depth estimation, it can also perform single-image depth estimation, as our DepthCrafter can estimate video depth of any length. As shown in Tab. 1, our DepthCrafter achieves competitive performance in single-image depth estimation on the NYU-v2 dataset. Since the depth labels in the NYU-v2 dataset are sparse and noisy, we also provide the qualitative results in Fig. 5 to demonstrate the effectiveness of our model in estimating depth maps from static images. We can observe that our DepthCrafter can even produce more detailed depth maps than Depth-Anything-V2, which is the existing state-of-the-art single-image depth estimation model. These results demonstrate the ability of our DepthCrafter for processing both video and single-image depth estimation tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 515, + 416, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 515, + 416, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 515, + 416, + 526 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "content": "Effectiveness of the three-stage training strategy. We first ablate the effectiveness of the three-stage training strategy by evaluating the performance of our model at the end of each stage on the Sintel dataset [7], since it contains precise depth annotations on dynamic scenes. From Tab. 2, we can observe that the performance of our model consistently improves as the number of training stages increases, indicating the effectiveness of the three-stage training strategy. More ablation results on other datasets are available in the supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 654, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 712 + ], + "type": "text", + "content": "Effectiveness of the inference strategy. To ablate the effectiveness of our inference strategy components, we consider these variants: baseline, which independently infers each segment and directly averages the overlapped frames; + initialization, which contains the same initialization of" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2011" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 294, + 150 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 294, + 150 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 294, + 150 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 294, + 150 + ], + "type": "image", + "image_path": "b85c35f4aa8ddc1705c3607c70b70f6162f3698d2026c3dbebade49a263e00e1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 157, + 295, + 201 + ], + "lines": [ + { + "bbox": [ + 55, + 157, + 295, + 201 + ], + "spans": [ + { + "bbox": [ + 55, + 157, + 295, + 201 + ], + "type": "text", + "content": "Figure 6. Ablation studies on the effectiveness of the inference strategy. We profile the estimated depth sequences of different variants on the green line position. The yellow and blue arrows point to the static and dynamic regions, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 207, + 295, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 207, + 295, + 351 + ], + "spans": [ + { + "bbox": [ + 54, + 207, + 295, + 351 + ], + "type": "text", + "content": "overlapped latents as our method, but without the stitching process; + initialization & stitching, which is our full method. We visually compare the temporal profiles of the estimated depth sequences of these variants in Fig. 6. We can observe the overlapped jaggies in both the static regions (pointed by the yellow arrow) and the dynamic regions (pointed by the blue arrow) in temporal profiles of the \"baseline\" method, which indicates the flickering artifacts. The \"+\" initialization\" method can alleviate the flickering artifacts in the static regions, but still has jaggies in the dynamic regions, while our full method can produce smooth depth sequences in both static and dynamic regions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 358, + 138, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 358, + 138, + 371 + ], + "spans": [ + { + "bbox": [ + 55, + 358, + 138, + 371 + ], + "type": "text", + "content": "4.4. Applications" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 376, + 295, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 295, + 604 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 295, + 604 + ], + "type": "text", + "content": "Our DepthCrafter can facilitate various downstream applications, e.g., foreground matting, depth slicing, fog effects, and depth-conditioned video generation, by providing temporally consistent depth sequences with fine-grained details for open-world videos. We show example results of fog effects and depth-conditioned video generation in Fig. 7, while more visual effects results are available in the supplementary material. For the fog effect, we blend the fog map with the input video frames based on the depth values to simulate varying transparency levels in fog. And many recent conditioned video generation models [10, 16, 20, 76] employ depth maps as the structure conditions for video generation or editing. We adopt Control-A-Video [10] and video depth of our method as conditions to generate a video with prompts \"a rider walking through stars, artstation\". The visual effects of these applications rely heavily on the accuracy and consistency of the video depth, which demonstrates the wide applicability of our DepthCrafter in various downstream tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 611, + 133, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 611, + 133, + 623 + ], + "spans": [ + { + "bbox": [ + 55, + 611, + 133, + 623 + ], + "type": "text", + "content": "4.5. Limitations" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 629, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 295, + 713 + ], + "type": "text", + "content": "Although our DepthCrafter achieves state-of-the-art performance in open-world video depth estimation, there are still some limitations to be addressed in the future. First, the computation and memory consumption of our model is relatively high, which is mainly due to the large model size and the iterative denoising process in the diffusion model. As shown in Tab. 3, we report the inference speed of our model," + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 315, + 71, + 553, + 171 + ], + "blocks": [ + { + "bbox": [ + 315, + 71, + 553, + 171 + ], + "lines": [ + { + "bbox": [ + 315, + 71, + 553, + 171 + ], + "spans": [ + { + "bbox": [ + 315, + 71, + 553, + 171 + ], + "type": "image", + "image_path": "ae4147316eaf6770300f5a7b8ef5de7b8a79cd8992dc0930d1dc1044b949e2ff.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 177, + 553, + 221 + ], + "lines": [ + { + "bbox": [ + 313, + 177, + 553, + 221 + ], + "spans": [ + { + "bbox": [ + 313, + 177, + 553, + 221 + ], + "type": "text", + "content": "Figure 7. Examples of visual effectiveness that could benefit from our DepthCrafter, including adding fog effects and depth-conditioned video generation. More visual effects results are available on our website." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 255, + 552, + 308 + ], + "blocks": [ + { + "bbox": [ + 313, + 228, + 553, + 251 + ], + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 251 + ], + "type": "text", + "content": "Table 3. Inference time per frame (ms) of our model, Depth-Anything (V2), and Marigold, with the resolution of " + }, + { + "bbox": [ + 313, + 228, + 553, + 251 + ], + "type": "inline_equation", + "content": "1024 \\times 576" + }, + { + "bbox": [ + 313, + 228, + 553, + 251 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 255, + 552, + 308 + ], + "lines": [ + { + "bbox": [ + 317, + 255, + 552, + 308 + ], + "spans": [ + { + "bbox": [ + 317, + 255, + 552, + 308 + ], + "type": "table", + "html": "
MethodEncodingDenoisingDecodingAll
Depth-Anything (V2)N/AN/AN/A180.46
Marigold256.40114.53699.361070.29
DepthCrafter (Ours)51.85160.93253.06465.84
", + "image_path": "521d1365acaaab4f672fa4e3fa390084afc51510eb33acaaae761671c1e69c62.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 312, + 555, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 555, + 503 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 555, + 503 + ], + "type": "text", + "content": "Depth-Anything (V2), and Marigold, with the resolution of " + }, + { + "bbox": [ + 313, + 312, + 555, + 503 + ], + "type": "inline_equation", + "content": "1024 \\times 576" + }, + { + "bbox": [ + 313, + 312, + 555, + 503 + ], + "type": "text", + "content": " on a single NVIDIA A100 GPU. We can see that Depth-Anything (V2) is faster than our model, while our method is much faster than Marigold since it ensembles five inference results. Our model achieves the best quality without ensembling, and its inference speed of 465.84 ms per frame is acceptable for many applications. Second, our method requires around 24GB GPU memory to process a video with the resolution of " + }, + { + "bbox": [ + 313, + 312, + 555, + 503 + ], + "type": "inline_equation", + "content": "1024 \\times 576" + }, + { + "bbox": [ + 313, + 312, + 555, + 503 + ], + "type": "text", + "content": " and a segment length of 110 frames. But note that, with the segment length of 40 frames, the memory consumption can be reduced to 12GB, which is acceptable for most modern GPUs, and we can still infer videos of any length by our inference strategy under this setting. We believe that further engineering efforts, such as model distillation and quantization, can help further promote the practicality of our method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "spans": [ + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "content": "We present DepthCrafter, a novel open-world video depth estimation method that leverages video diffusion models. It can generate temporally consistent depth sequences with fine-grained details for video width diverse content, motion, and camera movement, without requiring any additional information. It also supports videos of variable lengths, ranging from one frame (static image) to extremely long videos. This is achieved through our meticulously designed three-stage training strategy, compiled paired video-depth datasets, and an inference strategy. Extensive evaluations have demonstrated that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. It also facilitates various downstream applications, including depth-based visual effects and conditional video generation." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2012" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 123 + ], + "type": "text", + "content": "[1] Shubhra Aich, Jean Marie Uwabeza Vianney, Md Amirul Islam, and Mannat Kaur Bingbing Liu. 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TOG (Proceedings of ACM SIGGRAPH), 40(4):1-12, 2021. 2" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2015" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/ba2594dd-8284-4f56-b7c2-2adbb7e80d5c_content_list.json b/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/ba2594dd-8284-4f56-b7c2-2adbb7e80d5c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..cdb4f03c0c367523dca7f657a8f90b14e507ccac --- /dev/null +++ b/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/ba2594dd-8284-4f56-b7c2-2adbb7e80d5c_content_list.json @@ -0,0 +1,1506 @@ +[ + { + "type": "text", + "text": "DepthCues: Evaluating Monocular Depth Perception in Large Vision Models", + "text_level": 1, + "bbox": [ + 111, + 130, + 883, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Duolikun Danier Mehmet Aygün Changjian Li Hakan Bilen Oisin Mac Aodha University of Edinburgh", + "bbox": [ + 148, + 180, + 846, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://danier97.github.io/depthcues", + "bbox": [ + 334, + 224, + 656, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 273, + 326, + 290 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large-scale pre-trained vision models are becoming increasingly prevalent, offering expressive and generalizable visual representations that benefit various downstream tasks. Recent studies on the emergent properties of these models have revealed their high-level geometric understanding, in particular in the context of depth perception. However, it remains unclear how depth perception arises in these models without explicit depth supervision provided during pre-training. To investigate this, we examine whether the monocular depth cues, similar to those used by the human visual system, emerge in these models. We introduce a new benchmark, DepthCues, designed to evaluate depth cue understanding, and present findings across 20 diverse and representative pre-trained vision models. Our analysis shows that human-like depth cues emerge in more recent larger models. We also explore enhancing depth perception in large vision models by fine-tuning on DepthCues, and find that even without dense depth supervision, this improves depth estimation. To support further research, our benchmark and evaluation code will be made publicly available for studying depth perception in vision models.", + "bbox": [ + 89, + 308, + 485, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 659, + 220, + 674 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To ensure safe, accurate, and robust interaction with the 3D world, it is important for computer vision models to understand geometric properties from their projections onto 2D images. Of particular significance is the perception of depth from single images, which has been found to benefit various downstream tasks including segmentation [43], object detection [36], and image and video generation [46, 77], among others. Monocular depth estimation models traditionally rely on dense depth supervision, but obtaining high-quality depth ground truth at scale is challenging, unlike the abundance of large 2D image-only datasets.", + "bbox": [ + 89, + 686, + 482, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large-scale pre-trained vision models like Stable Diffusion [59] and DINOv2 [54], trained solely on 2D images, have shown strong generalization when fine-tuned on var", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/536455f60307367e277d7de5b82e90329adcb883a603ba5dd4f389452616c14e.jpg", + "image_caption": [ + "Figure 1. Human-like monocular depth cues emerge in large vision models. We present DepthCues, a comprehensive benchmark suite designed to probe the understanding of human monocular depth cues in vision models. We analyse a diverse set of vision models and find that recent self-supervised and geometry estimation models demonstrate a notably stronger grasp of these cues, even in cases where models (e.g., DINOv2) were not explicitly pre-trained on any depth-related tasks." + ], + "image_footnote": [], + "bbox": [ + 519, + 281, + 901, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ious computer vision tasks, including multi-view [10, 38] and monocular depth estimation [17, 22, 76], even reaching human-level performance in ordering objects by depth [47]. As a result, numerous recent monocular depth estimation approaches [28, 40, 72] leverage these models' depth priors to achieve state-of-the-art performance. This naturally raises an important question: How does depth perception arise in these large vision models?", + "bbox": [ + 511, + 628, + 906, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Studies on the human visual system [9, 39] suggest that humans infer monocular depth using various visual cues such as elevation, light and shadow, occlusion, perspective, size, and texture gradient [7, 44] (see the top part of Fig. 2). Although these visual cues could emerge in large vision models during pre-training, it remains unclear to what extent this is true. Existing benchmarks [4, 17, 22, 47, 76] focus on evaluating the depth estimation performance of large vision models but do not investigate their understanding of the underlying visual cues. To address this gap, we eval", + "bbox": [ + 511, + 750, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20049", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "uate how well the large vision models understand and utilize human-like monocular depth cues. Our goal is to provide insights into current models' depth estimation behavior, enable a more systematic analysis of their strengths and limitations, and indicate areas for improvement.", + "bbox": [ + 89, + 90, + 480, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce a new benchmark named DepthCues consisting of six depth related tasks (see Fig. 2) where each task is designed to test a given models' ability to estimate a visual cue that is ubiquitous to human depth perception. Specifically, lightweight probing models (referred to as the probes hereafter) placed on top of the frozen features of large vision models are trained and tested on the associated dataset for each task. The assumption is that the more effectively the probe can learn to solve a task using the features of a model, the better the model understands the task-specific cue. Under this protocol, we examine 20 vision models pre-trained at scale under various settings, including self-supervised learning (DINOv2 [54]), image generation (StableDiffusion) [59], vision-language supervision (CLIP [56]), single-view reconstruction (LRM [33]), cross-view completion (CroCo [68]), and also a recent general purpose depth estimation model DepthAnything v2 [72].", + "bbox": [ + 91, + 169, + 482, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our results reveal the following observations: First, the performance of models on DepthCues is highly correlated with their depth estimation performance, validating the effectiveness of DepthCues for investigating depth perception. Second, more recent self-supervised and geometry estimation models exhibit a stronger understanding of human monocular depth cues (see Fig. 1), with DepthAnythingv2 ranking first, and DINOv2 and StableDiffusion ranking top-five. Third, none of the benchmarked models consistently excel on all six of the depth tasks. Finally, recent single-view pre-trained models are limited in their perception of texture gradient, while multi-view trained models are better at this low-level geometric cue. Additionally, we explore enhancing depth awareness of vision models by injecting depth cue priors, demonstrating that fine-tuning on our DepthCues benchmark results in improved depth estimation, despite the significant sparsity of the supervision compared to dense annotations. Our contributions are:", + "bbox": [ + 91, + 428, + 482, + 698 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We develop and make available DepthCues, a benchmark suite for evaluating the emergence of human monocular depth cues in large vision models.", + "- We evaluate 20 diverse vision models across a range of pre-training settings, and analyze their relative strengths and weaknesses in capturing monocular depth cues.", + "- We show that human depth perception cues emerge from self-supervised pre-training on single images, with stronger alignment found in more recent, larger models.", + "- We conduct an exploratory study on enhancing the depth awareness of a model by fine-tuning on DepthCues, showing that explicitly injecting human-like depth priors can improve depth perception." + ], + "bbox": [ + 89, + 702, + 482, + 897 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 89, + 653, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Monocular Depth Estimation. Monocular depth estimation is an inherently ill-posed and challenging problem, yet deep learning-based methods have made significant strides in addressing it. Initial progress was driven by supervised methods [6, 16, 19] that were trained on various labeled datasets [23, 52]. Later, self-supervised approaches advanced the field further by leveraging stereo [21, 25] or temporal consistency [26, 27, 80]. More recently, general purpose methods [40, 58, 71, 72] leveraging large vision backbone models pre-trained with self-supervised [54] or generative objectives [59] and then fine-tuned on very largescale supervised depth datasets have been shown to result in strong monocular depth estimation performance. However, it remains unclear how depth perception develops in the pre-trained models without explicit depth supervision during pre-training. In this paper, we try to shed light on the emergence of these monocular depth cues used by the human visual system in large vision models.", + "bbox": [ + 511, + 114, + 903, + 385 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Depth Perception in Pre-trained Vision Models. Several recent efforts have begun to analyze the 3D and depth perception abilities of pre-trained large vision models, with a focus on 3D awareness [17], 3D scene understanding [50], depth and height perception [4], and 3D physical understanding [76]. Complementary to these efforts, several studies have attempted to enhance the capabilities of these models by integrating 3D and depth information [3, 45, 73, 78]. Unlike these works, we focus on monocular depth estimation, emphasising evaluating the emergence of monocular cues essential for human depth perception. Some of the cues we study are also explored in a concurrent work [76], however, we focus on depth perception with diverse data and analyze a broader range of vision models.", + "bbox": [ + 511, + 387, + 903, + 597 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent work [22, 62] has analyzed monocular depth estimation models, examining properties like the backbone architectures, loss functions, and training datasets. However, they do not explore whether or how these models actually utilize monocular cues for depth estimation. In our work, we focus on analyzing the existence of intrinsic depth cues without direct depth supervision across various large vision models. Closely related to our approach, [63] investigates whether predictions of a monocular depth estimation model [58] violate perceptual cues. However, a prediction that violates a perceptual cue does not necessarily indicate the absence of the cue in the model itself. Instead, we directly examine the presence of these cues across multiple models, including, but not limited to, monocular depth models using our newly introduced benchmark suite.", + "bbox": [ + 511, + 599, + 903, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Comparing Humans to Neural Networks. Human and animal vision systems have long inspired computational vision methods [31, 37, 55]. Many studies have sought to compare biological vision with modern neural network-based computer vision systems across tasks such as ob", + "bbox": [ + 511, + 825, + 903, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20050", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3e83b1ca219705e4a8761ac72012df0e36be3eadb3c5e0b74e94941fdc9217f1.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 96, + 88, + 227, + 265 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0f6566bf1784fe9dd026731779efcfbd360af35f599bd2415ffde757d8c4e751.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 232, + 88, + 362, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/24c7f4de898117948f541d4cb5ad2a40d960440cb33e4e3d13b39eca16083161.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 366, + 88, + 496, + 265 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/65cf4ce19a0f8e8660bae2d143020ce18057725e8eeecc441d463e903d5a1816.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 500, + 88, + 632, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e6cf0077c9181df073e72cca677512ba4118e21a30c3edd144c2562f5bc9bfa1.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 635, + 88, + 764, + 265 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7c23e351b7e4c782f85c27d4a93b6cffb0284c94b949841dd9f49bd03a1138eb.jpg", + "image_caption": [ + "(f)", + "Figure 2. Overview of DepthCues. Monocular depth cues, the associated tasks, and example instances from our proposed benchmark." + ], + "image_footnote": [], + "bbox": [ + 767, + 88, + 900, + 266 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/40668941fb613c51bafd8f6fa74adc992bb0fa77289337fa5966678fde56a36b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Depth CueSource#Images#Train#Val#Test
ElevationHLW [69]18,39015,7618281,801
Light-shadowSOBA [67]7984,716862860
OcclusionCOCOA [83]5,57324,40212,90614,862
PerspectiveNaturalScene [81]2,2752,000125150
SizeKITTI [23], SUN [61]2,7171,986330712
Texture-gradDTD [13]6,0004,0001,0001,000
", + "bbox": [ + 94, + 315, + 478, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Summary of the datasets in DepthCues benchmark. We report total image and data statistics across all splits.", + "bbox": [ + 89, + 407, + 480, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ject recognition [57], shape-bias [24], multi-view consistency [8, 53], visual perspective-taking [47], and perceptual judgments of similarity [20]. In our work, rather than measuring alignment between human and large-scale vision systems, we focus on the emergence of monocular cues that are well-established in the human vision science community [7, 9, 39, 44], i.e., the cues that are crucial for monocular depth estimation in human vision. Recent work has incorporated additional high-level human vision-inspired cues, specifically semantics, object size, and spatial relationships, in an attempt to improve automated monocular depth estimation [1, 2]. These cues, extracted using pre-trained semantic segmentation and language embedding models, are shown to enhance depth prediction accuracy. We hope that our results and analyses will inspire similar approaches and foster new directions.", + "bbox": [ + 88, + 450, + 483, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. DepthCues: Benchmark and Dataset", + "text_level": 1, + "bbox": [ + 89, + 708, + 419, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce DepthCues, a new benchmark to investigate how large-scale pre-trained image models perceive depth by assessing their understanding of a set of monocular depth cues used by humans to perceive depth: elevation, light and shadow, occlusion, perspective, size, and texture gradient [9, 39]. Our benchmark comprises a suite of six tasks with constituent datasets specifically designed to capture the essence of each individual monocular depth cue. For each task, DepthCues provides training and test sets with an evaluation protocol for image models, along with a performance metric to assess how well a given model under", + "bbox": [ + 89, + 734, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "stands each depth cue. Fig. 2 illustrates the task for each cue, and shows a representative instance from the associated dataset. We summarize the statistics of our datasets in Tab. 1. Next, we describe the construction of each task and the data used. In each case, we adapt existing datasets that have been designed for bespoke vision tasks. We use the original train, validation, and test splits of data sources and keep the classes balanced for binary tasks unless specified. Additional details about dataset construction are provided in Appendix B.", + "bbox": [ + 511, + 318, + 906, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Elevation", + "text_level": 1, + "bbox": [ + 511, + 479, + 622, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Objects on the ground plane are farther away as they get closer to the horizon.", + "bbox": [ + 511, + 503, + 905, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Task. The elevation cue relies on perceiving the horizon line, which is defined as the projection of all the points where light rays from the observer's viewpoint are tangent to Earth's surface. Therefore, we adopt the task of horizon line estimation [42, 69]. Note, the horizon line is not always visible, and is different from the skyline, which separates the sky and the entities on the ground. The task is posed as a regression problem where the goal is to estimate the target line, i.e., its slope and y-intercept, in the image.", + "bbox": [ + 511, + 532, + 905, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dataset. We adopt the HLW dataset [69], which provides pairs of images and annotations of the horizon lines. To increase the slope variation, we augment the images by rotating them (and the line annotations) randomly between $-30^{\\circ}$ and $30^{\\circ}$ . An example from the dataset is shown in Fig. 2 (a).", + "bbox": [ + 511, + 670, + 905, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Light and Shadow", + "text_level": 1, + "bbox": [ + 511, + 755, + 689, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The way shadow is cast provides useful cue for orientation and depth of objects. For convenience, we refer to this cue as light-shadow.", + "bbox": [ + 511, + 779, + 905, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Task. To capture the understanding of this cue, we propose a task of associating shadows with objects.", + "bbox": [ + 511, + 825, + 903, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dataset. The SOBA [67] dataset contains images with segmentation masks of objects and their associated shadows. From those, we create a dataset containing tuples of", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20051", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$(I,M_A,M_B,y)$ , where $M_A$ is the mask of the object $A$ in image $I$ , and $M_B$ is the mask of a shadow $B$ in the image. The label $y$ is 1 if $B$ is associated with $A$ , and O otherwise. An example is depicted in Fig. 2 (b).", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.Occlusion", + "text_level": 1, + "bbox": [ + 89, + 161, + 204, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An object that partially blocks another, from the perspective of the viewer, is perceived as closer.", + "bbox": [ + 89, + 184, + 482, + 213 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Task. To test whether models understand occlusion, we propose the task of identifying whether an object is occluded or not by another object.", + "bbox": [ + 89, + 215, + 482, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dataset. We use the COCOA [83] dataset, providing manually annotated segmentation masks for visible and invisible object parts with occlusion rates. From the original annotations, we construct a dataset that contains triplets of image $I$ , the segmentation mask $M_A$ of the visible part of the object $A$ , and the corresponding label $y$ , which is 1 if the object is occluded, and 0 otherwise. In the example in Fig. 2 (c), the car highlighted with a red mask is occluded.", + "bbox": [ + 89, + 260, + 483, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Perspective", + "text_level": 1, + "bbox": [ + 89, + 390, + 215, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Parallel lines converging at infinity offer a strong cue for perceiving depth.", + "bbox": [ + 89, + 414, + 482, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Task. This cue is closely tied to vanishing point [48], which is defined as the point on the image plane where 2D perspective projections of 3D parallel lines intersect. Therefore, we use the task of vanishing point estimation to investigate the understanding of perspective. While there exist different versions of the task that define different numbers of vanishing points [64, 74], we adopt a simplified version that focuses on a single dominant vanishing point. Given an image $I$ , the objective is to estimate the $\\mathbf{p} = (x,y)$ coordinates of the vanishing point in the image coordinate system.", + "bbox": [ + 89, + 444, + 482, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dataset. The NaturalScene dataset [81] contains images from diverse outdoor scenes with one manually annotated dominant vanishing point $\\mathbf{p}$ in each. We use the original dataset and create validation and test sets by dividing the original validation set. An example is shown in Fig. 2 (d) with the vanishing point indicated by the red dot.", + "bbox": [ + 89, + 595, + 482, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Size", + "text_level": 1, + "bbox": [ + 89, + 695, + 158, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "People infer depth based on known object sizes (in 3D) and their apparent retinal sizes (e.g., an object farther away appears smaller). This cue is particularly effective when comparing objects of similar expected sizes.", + "bbox": [ + 89, + 719, + 482, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Task. Using this cue requires prior knowledge of object sizes. Thus we propose a binary classification task: determining if object $A$ is larger than object $B$ in 3D.", + "bbox": [ + 89, + 779, + 482, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dataset. We use 3D object detection datasets KITTI [23] and SUN-RGBD [61] which provide 3D bounding boxes of objects in outdoor and indoor scenes respectively. Given an image $I$ , we sample two objects, $A$ and $B$ , and compare their sizes using the volumes of their 3D bounding boxes.", + "bbox": [ + 89, + 824, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Object masks $M_A$ and $M_B$ in image space are estimated using SAM [41] with bounding box queries and additional filtering to ensure segmentation quality. The final dataset contains tuples $(I, M_A, M_B, y)$ , where the label $y = 1$ if object $A$ is larger, and 0 otherwise. We filtered pairs where the volume difference was under a threshold to reduce errors caused by imprecise labeling. See Fig. 2 (e) for an example.", + "bbox": [ + 511, + 90, + 905, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.6. Texture Gradient", + "text_level": 1, + "bbox": [ + 513, + 205, + 684, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When a region on a surface is further away from the viewer, its texture appears denser and more compressed, with a higher spatial frequency, compared to the same texture viewed nearby. We denote this cue as texture-grad.", + "bbox": [ + 511, + 228, + 903, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Task. This cue is especially helpful on textured surfaces. To assess the existence of this cue, we use the task of depth ordering of regions on a textured plane, where the model must infer depth based solely on texture.", + "bbox": [ + 511, + 289, + 903, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dataset. To ensure that only the texture gradient cue is used for perceiving depth order, we created a synthetic dataset using Blender. First, we initialized a 3D plane, and applied textures sampled from the DTD dataset [13] which contains various real-world, as well as synthetic, textures. Then, fixing both the viewing direction of the camera (to always point at the plane center) and its distance to the plane center, we randomly set the camera elevation angle between $30^{\\circ}$ and $60^{\\circ}$ , and project the textured plane on the camera imaging plane to obtain an image with its depth map.", + "bbox": [ + 511, + 349, + 905, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From each image $I$ , we randomly sample two equal-sized regions $A$ and $B$ (with their masks $M_A, M_B$ ), then set label $y$ to 1 if $A$ is closer than $B$ and 0 otherwise. To avoid the region higher up in the image always being farther away, we apply random horizontal and vertical flips, so that the task cannot be solved solely from locations of the regions. An example image is shown in Fig. 2 (f).", + "bbox": [ + 511, + 500, + 905, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Evaluation Protocol", + "text_level": 1, + "bbox": [ + 513, + 618, + 705, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following previous work [17, 76], we use probing of visual features as our evaluation protocol. Below, we explain how we obtain task-specific input features from visual models, how we probe these features, and how we measure success. An illustrative figure is included in Appendix C.1.", + "bbox": [ + 511, + 643, + 905, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Task Specific Visual Features", + "text_level": 1, + "bbox": [ + 511, + 727, + 772, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a pre-trained vision model $\\phi(\\cdot)$ , we assess its understanding of a cue by training a lightweight probe $g_{\\theta}$ with parameters $\\theta$ on the target task, using the features extracted by $\\phi$ . We obtain features $\\mathbf{f}$ for each task as described below.", + "bbox": [ + 511, + 750, + 905, + 811 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Occlusion. We extract a feature map $\\phi(I)$ from the image $I$ and up-sample it to match the spatial size of the object mask $M_A$ . We mask the feature map and apply spatial pooling:", + "bbox": [ + 511, + 811, + 903, + 857 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} = \\frac {\\sum_ {h , w} M _ {A} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {A}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 866, + 903, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20052", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $h, w$ index the height and width of $I$ , $\\odot$ is element-wise multiplication, and $\\mathrm{up}(\\cdot)$ denotes bilinear upsampling. This results in $\\mathbf{f} \\in \\mathbb{R}^D$ where $D$ is the feature dimension and changes depending on the vision model $\\phi$ .", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Light-shadow, Size, and Texture-grad. For these tasks, we calculate the difference between the masked average features of objects $A$ and $B$ :", + "bbox": [ + 89, + 151, + 482, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} = \\frac {\\sum_ {h , w} M _ {A} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {A}} - \\frac {\\sum_ {h , w} M _ {B} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {B}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 207, + 480, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Elevation and Perspective. These tasks are not object/region specific, so we use the entire image feature, i.e., $\\mathbf{f} = \\phi(I) \\in \\mathbb{R}^{H_{\\mathbf{f}} \\times W_{\\mathbf{f}} \\times D}$ , where $H_{\\mathbf{f}}, W_{\\mathbf{f}}$ are the height and width of the feature map.", + "bbox": [ + 89, + 258, + 482, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Probing Features", + "text_level": 1, + "bbox": [ + 89, + 329, + 261, + 344 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For light-shadow, occlusion, size, and texture-grad, where the task-specific features $\\mathbf{f}$ are $D$ -dimensional vectors, we implement the probe $g_{\\theta}$ as a multi-layer perception (MLP) with two layers and an intermediate GELU activation [32]. Though linear probing has been used commonly for probing large vision models [54], it is not obvious that the solutions to our tasks should be a linear function of the model features. Thus, we use non-linear probes, which empirically outperform linear probes (see Appendix A.2) For elevation and perspective, which require global information, we use an attentive probe [5, 18]. This probe aggregates global features through cross-attention and uses a two-layer MLP for final predictions. We observed via empirical results that the attentive probe achieves better performance than a standard MLP probe on these tasks.", + "bbox": [ + 89, + 352, + 482, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training and Optimization. We train the MLP probes for light-shadow, occlusion, size and texture-grad tasks using binary cross-entropy loss, as these tasks involve binary classification. For elevation and perspective, we use mean squared error loss to train the attentive probes, as the tasks are formulated as regression problems. Additional details on the probe optimization are provided in Appendix C.1.", + "bbox": [ + 89, + 579, + 482, + 685 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following [54, 76], we perform a hyper-parameter search on the layers of model $\\phi$ . For each task, we extract features from different layers of $\\phi$ which is frozen, and train a probe on these features under the same setting. The best layer is then selected based on the validation performance, and the probing on this layer is repeated five times using different random seeds. We report the mean and standard deviation of the test performance.", + "bbox": [ + 89, + 685, + 482, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 89, + 816, + 274, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For light-shadow, occlusion, size and texture-grad which are binary tasks, we report classification accuracy. For the vanishing point estimation task of the perspective cue, while Euclidean distance (between the predicted and ground-truth", + "bbox": [ + 89, + 839, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "vanishing points) is a sensible metric, we instead report success rate to align this metric more closely with accuracy. Specifically, if the Euclidean distance of a prediction falls below a pre-defined threshold, it is interpreted as success. For elevation, we convert the horizon detection error [69] to an accuracy-based measure using a similar approach. More details are provided in Appendix C.2.", + "bbox": [ + 511, + 90, + 903, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 213, + 645, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Monocular Depth Cues in Vision Models", + "text_level": 1, + "bbox": [ + 511, + 239, + 861, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate 20 pre-trained large vision models [11, 15, 29, 30, 33, 35, 41, 49, 54, 56, 58, 59, 65, 66, 68, 70, 72, 75, 79] spanning diverse pre-training objectives, modalities, and model architectures to assess their understanding of monocular depth perception cues in our DepthCues benchmark.", + "bbox": [ + 511, + 263, + 903, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Where possible, we focus on model architectures equivalent to ViT-Base and denote the architecture size (and patch size for transformers) using postfixes, e.g., DINOv2-b14. More details about the models and their architecture are provided in Appendix D. For consistency, we use only patch tokens for all ViT-based models [15], as some do not include a class token.", + "bbox": [ + 511, + 339, + 903, + 445 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Additional Baselines. During the probing of certain cues, we explicitly use mask information to construct the input feature, f. Although these masks are not directly used by the probes, they could theoretically be leveraged to solve tasks. To verify that any additional information from this step is insufficient to solve the task, we designed a trivial baseline in which model features are replaced with simple 2D coordinate maps i.e., $\\phi (I)$ in Eqs. (1) and (2) becomes $C\\in \\mathbb{R}^{H\\times W\\times 2}$ where $C_{h,w} = [h,w]^T$ . Moreover, for each cue, we include an end-to-end baseline, where we train ResNet18 [29] and ViT-B/16 [15] models from scratch in an end-to-end fashion and select the best. We concatenate the masks with the input images channel-wise, allowing us to assess how much of each task can be solved without relying on sophisticated pre-trained features. Finally, to confirm that the tasks are readily solvable by humans, we evaluate our own performance on a random sample from the test sets, and obtained an accuracy of $95\\% \\pm 1.48\\%$ across tasks.", + "bbox": [ + 511, + 446, + 905, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Additional Tasks. To extend our analysis, we also evaluate vision models for monocular depth estimation (on NYUv2 [60] and DIW [12]) and image classification (on ImageNet-1k [14]) using a linear probe, a standard approach in previous work [3, 54, 73] for probing these datasets. Following the previous works [6, 12, 17], For NYUv2, we report accuracy as the percentage of pixels where the ratio between predicted and ground-truth depth is less than 1.25. We report top-1 accuracy for ImageNet. More details on these tasks are provided in Appendix A.1, and we show the linear probing results of these models on NYUv2 in Fig. 3.", + "bbox": [ + 511, + 719, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20053", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8506f87e3c6f4368397432c811f9ce2838601f06a6b2bc2f719a45c56b305810.jpg", + "image_caption": [ + "Figure 3. DepthCues Benchmark Results. We evaluate 20 vision models with diverse pre-training settings (indicated by color) on the DepthCues benchmark, which assesses six different monocular depth cues (each row) ubiquitous to humans. The models are ranked based on their average performance on the six cues. We include an end-to-end trained baseline (blue dotted line) as an oracle and a trivial baseline (red dotted line) to mark floor performance. Additionally, depth estimation linear probing results on NYUv2 are shown on the bottom row." + ], + "image_footnote": [], + "bbox": [ + 99, + 95, + 898, + 852 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20054", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. The probing results of 20 pre-trained vision models and the additional baselines on our DepthCues benchmark are summarized in Fig. 3, where the models are ranked by average performance over all cues. Moreover, we measured Spearman Ranked-order Correlation between each pair of tasks in DepthCues using the ranks of the models evaluated, and also how they correlate with the depth estimation and image classification performance of models, which is visualized in Fig. 4. We discuss our observations below, and present additional analysis, such as how pretraining data size impacts performance, in Appendix A.1.", + "bbox": [ + 89, + 90, + 480, + 257 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(i) Depth cues emerge in more recent large vision models. Firstly, the specialized depth estimation model, DepthAnythingv2, achieved the highest overall performance on DepthCues, indicating the possibility that it leverages such cues to estimate depth. We also observe the emergence of human-like monocular depth cues in recent large vision models, such as DINOv2 and Stable Diffusion. Notably, newer large vision models demonstrate a stronger grasp of these depth cues, as illustrated in Fig. 1. DINOv2 and Stable Diffusion have proven useful for developing monocular depth estimation models [40, 72]. However, the reasons behind these models' effectiveness for depth inference remain unclear, given the lack of explicit depth supervision during pre-training. Our results provide an insight on the development of depth perception in these models: they develop an awareness of human-like monocular depth cues, which might aid depth inference.", + "(ii) Depth models do not always have the strongest knowledge of depth cues. While DepthAnythingv2 achieves the best overall performance on DepthCues, another specialized depth estimation model, MiDaS, is outperformed by several models pre-trained without depth supervision, e.g., DeiT, SigLIP, and DINO. These models also exhibit competitive depth estimation performance (under linear probing) to MiDaS. This suggests that other pretraining recipes than dense depth supervision can effectively enhance depth perception, although they may be less data-efficient – for instance, SigLIP is trained on around 10,000 times more data than MiDaS.", + "(iii) Vision-language models exhibit varying levels of depth cue understanding. CLIP obtains the lowest performance on DepthCues, explaining its limited depth estimation ability as seen in Fig. 3 and in recent work [17]. CLIP's limited understanding of the visual concepts tested in DepthCues may present challenges for downstream tasks that require geometric understanding [82]. In contrast, SigLIP, also trained on matching images to captions but on significantly more data ( $\\times 9$ more data than CLIP), has a significantly better grasp of the depth cues.", + "(iv) Multi-view models are better at the texture-grad task than single-view models. On all depth cues except texture-grad, recent models which are pre-trained with" + ], + "bbox": [ + 89, + 260, + 486, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/08b33ab5117dea7823b78f908fb579c5186a7a9ff0d3865acdb900f8a9cad2e8.jpg", + "image_caption": [ + "Figure 4. Task correlation. We measure the Spearman Ranked-order Correlation between each pair of tasks in DepthCues benchmark, and how they correlate with depth estimation and image classification performance of models. A correlation score of one indicates the same ranking of models for two tasks." + ], + "image_footnote": [], + "bbox": [ + 521, + 94, + 898, + 330 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "single-view images showed overall better performance than multi-view ones. However, on texture-grad, all three multiview models (i.e., CroCo, LRM, and DUSt3R) ranked within the top four, outperforming strong SSL competitors such as DINOV2. While the other five cues operate at the scene or object level, texture-grad uniquely requires a more localized, surface-level understanding. Multi-view pre-trained models are often more effective at capturing such details than single-view models because, during pretraining, they are exposed to variations in the same surface across different viewpoints. For instance, CroCo, which achieves the best performance on the texture-grad task, is trained to reconstruct parts of a scene from different viewpoints, requiring attention to finer local details. Moreover, LRM and DUSt3R are pre-trained on 3D object and scene reconstruction tasks, which require understanding correspondences across views by leveraging local surface details. (v) Performance on DepthCues correlates with depth estimation performance. As shown in Fig. 4, all DepthCues tasks exhibit moderate to high levels of correlation with depth estimation, supporting the importance of depth cues for this task. However, all tasks have a low correlation with ImageNet-1k classification. Interestingly, a relatively higher alignment with classification is observed for occlusion and size, which are also highly correlated with each other. This is reasonable as understanding occlusion and size requires object-level semantics (e.g., 'What does the recognized object look like when not occluded?' and 'Is category A larger than category B?'). Apart from texture-grad, each cue has a high correlation ( $>0.75$ ) with at least one other cue. As discussed above, the texture-grad cue requires understanding surface details and provides local", + "bbox": [ + 511, + 417, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20055", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1ddd8109324d1459782649b45f8864a0f555518caf6abfbb50bda39ba9305e2f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelNYUv2 Acc. (%)↑DIW WHDR (%)↓
DINOv287.7811.99
DINOv2+DC87.0611.95
concat(DINOv2, noise)87.5612.20
concat(DINOv2, DINOv2+DC)88.4611.72
CLIP43.7835.25
CLIP+DC43.5935.45
concat(CLIP, noise)43.3835.39
concat(CLIP, CLIP+DC)44.3233.53
", + "bbox": [ + 93, + 88, + 480, + 200 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. Linear probing on downstream depth estimation. For each model, we probe the patch tokens from the final layer. Models with $+DC$ are fine-tuned using supervision on our DepthCues benchmark. The best results in each subset are bolded.", + "bbox": [ + 89, + 205, + 482, + 262 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ized depth information; perception of this cue is found to be weaker in single-view image models. We note that texture-grad is the only cue that uses synthetic data, which might also contribute to its lower correlation with other cues.", + "bbox": [ + 89, + 276, + 483, + 338 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Learning Depth Cues", + "text_level": 1, + "bbox": [ + 89, + 347, + 292, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We observed that the depth estimation performance of a model highly correlates with its awareness of human-like monocular depth cues. Here we ask if enhanced depth cue awareness improves depth estimation? To investigate this, we fine-tune single-image pre-trained vision models on the training set of DepthCues in a multi-task manner, then evaluate the fine-tuned model on downstream depth estimation. Here we focus on two models widely adopted for various downstream applications: DINOv2 and CLIP.", + "bbox": [ + 88, + 371, + 482, + 507 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We use low-rank adaptation (LoRA) [34] for efficient fine-tuning of pre-trained models. Further details of multitask learning and LoRA implementation are provided in Appendix C.3. We evaluate the pre-trained and fine-tuned models on NYUv2 [60] and DIW [12] depth datasets using linear probes. We experiment with two different variations: first, we evaluate the features from fine-tuned models (denoted as $+DC$ in Tab. 2); second, we concatenate the features from fine-tuned models with the features from the original pre-trained models. The latter approach was also adopted in [51, 73] to preserve the generalization ability of the pre-trained models. As before, we report accuracy for NYUv2, and use Weighted Human Disagreement Rate (WHDR) to measure performance on DIW. It is noted the dataset for the size cue in DepthCues contains a subset of NYUv2 images (due to the use of SUNRGBD), so evaluation on DIW offers a fairer comparison.", + "bbox": [ + 89, + 507, + 482, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We observe in Tab. 2 that for both models, fine-tuning on DepthCues resulted in improved depth perception. Notably, the fine-tuned features often need to be concatenated with the original features to bring improvements, a similar observation also made in previous works [51, 73]. A possible explanation for the decreased generalization in the models is due to the limited size and diversity of the fine-tuning data in DepthCues. We also investigate whether the improvements in the concatenated variations come from the", + "bbox": [ + 89, + 763, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "increased parameters in the probe (due to higher dimensional input), by training linear probes on a combination of original model features and random noise (denoted as concat(·, noise)), which did not result in improvements.", + "bbox": [ + 511, + 90, + 903, + 151 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Discussion", + "text_level": 1, + "bbox": [ + 511, + 159, + 633, + 174 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results in Sec. 5.1 indicate that recent large vision models understand several human-like monocular depth cues, with performance on these cues correlating with depth estimation performance. This suggests that models may use such cues to infer depth, even without explicit depth supervision. For example, the popular self-supervised model, DINOv2, has developed features that help reason about these cues (except texture-grad), which can support depth estimation. Interestingly, the results in Sec. 5.2 show that DepthCues enables the learning of depth cues, which benefit downstream depth performance in a linear probing setting, even though DepthCues has a moderate size (fewer than 35k training images, much smaller than the large datasets used to pre-train the base models), is not designed specifically for end-to-end fine-tuning, and only provides image-level sparse annotations (as opposed to dense depth maps). This suggests promising directions for enhancing depth estimation from sparse annotations.", + "bbox": [ + 511, + 181, + 903, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our analysis focuses only on widely used pretrained model weights but not directly on the impact of various pre-training objectives and their training datasets on the emergence of depth cues. While depth from ego-motion and scene motion are also important cues for humans, our focus is primarily on assessing monocular cues learned by large vision models trained on static image collections and not image sequences (except CroCo, LRM, and DUSt3R).", + "bbox": [ + 511, + 455, + 905, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 511, + 588, + 640, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduced DepthCues, a benchmark suite for evaluating human-like monocular depth cues in large vision models. Testing 20 diverse models, we found that depth perception cues, similar to those used by humans, emerge across various pre-training objectives, with more recent and larger models demonstrating stronger alignment with human depth perception. Furthermore, our fine-tuning experiments on DepthCues indicate that a model's depth perception can be enhanced by explicitly incorporating human-like depth priors, suggesting promising directions for improving depth performance in future models. We hope DepthCues will serve as a valuable resource for advancing research in depth-aware vision systems, particularly for applications requiring robust 3D spatial understanding from 2D inputs.", + "bbox": [ + 511, + 613, + 903, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. Funding was provided by ELIAI (the Edinburgh Laboratory for Integrated Artificial Intelligence) - EPSRC (EP/W002876/1). HB was supported by the EPSRC Visual AI grant EP/T028572/1, and CJ was supported by a gift from Adobe.", + "bbox": [ + 511, + 825, + 903, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20056", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Dylan Auty and Krystian Mikolajczyk. Monocular depth estimation using cues inspired by biological vision systems. In ICPR, 2022. 3", + "[2] Dylan Auty and Krystian Mikolajczyk. Language-based depth hints for monocular depth estimation. arXiv:2403.15551, 2024. 3", + "[3] Mehmet Aygun, Prithviraj Dhar, Zhicheng Yan, Oisin Mac Aodha, and Rakesh Ranjan. Enhancing 2d representation learning with a 3d prior. 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In CVPR, 2017. 3, 4" + ], + "bbox": [ + 516, + 92, + 903, + 244 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20059", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/ba2594dd-8284-4f56-b7c2-2adbb7e80d5c_model.json b/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/ba2594dd-8284-4f56-b7c2-2adbb7e80d5c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..225d0c54034ed47f357d53bd133a4da0cb62ec65 --- /dev/null +++ b/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/ba2594dd-8284-4f56-b7c2-2adbb7e80d5c_model.json @@ -0,0 +1,2466 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.112, + 0.131, + 0.885, + 0.153 + ], + "angle": 0, + "content": "DepthCues: Evaluating Monocular Depth Perception in Large Vision Models" + }, + { + "type": "text", + "bbox": [ + 0.15, + 0.181, + 0.847, + 0.223 + ], + "angle": 0, + "content": "Duolikun Danier Mehmet Aygün Changjian Li Hakan Bilen Oisin Mac Aodha University of Edinburgh" + }, + { + "type": "text", + "bbox": [ + 0.336, + 0.226, + 0.658, + 0.24 + ], + "angle": 0, + "content": "https://danier97.github.io/depthcues" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.275, + 0.327, + 0.291 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.309, + 0.486, + 0.626 + ], + "angle": 0, + "content": "Large-scale pre-trained vision models are becoming increasingly prevalent, offering expressive and generalizable visual representations that benefit various downstream tasks. Recent studies on the emergent properties of these models have revealed their high-level geometric understanding, in particular in the context of depth perception. However, it remains unclear how depth perception arises in these models without explicit depth supervision provided during pre-training. To investigate this, we examine whether the monocular depth cues, similar to those used by the human visual system, emerge in these models. We introduce a new benchmark, DepthCues, designed to evaluate depth cue understanding, and present findings across 20 diverse and representative pre-trained vision models. Our analysis shows that human-like depth cues emerge in more recent larger models. We also explore enhancing depth perception in large vision models by fine-tuning on DepthCues, and find that even without dense depth supervision, this improves depth estimation. To support further research, our benchmark and evaluation code will be made publicly available for studying depth perception in vision models." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.66, + 0.222, + 0.675 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.687, + 0.483, + 0.854 + ], + "angle": 0, + "content": "To ensure safe, accurate, and robust interaction with the 3D world, it is important for computer vision models to understand geometric properties from their projections onto 2D images. Of particular significance is the perception of depth from single images, which has been found to benefit various downstream tasks including segmentation [43], object detection [36], and image and video generation [46, 77], among others. Monocular depth estimation models traditionally rely on dense depth supervision, but obtaining high-quality depth ground truth at scale is challenging, unlike the abundance of large 2D image-only datasets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Large-scale pre-trained vision models like Stable Diffusion [59] and DINOv2 [54], trained solely on 2D images, have shown strong generalization when fine-tuned on var" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.282, + 0.903, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.503, + 0.907, + 0.616 + ], + "angle": 0, + "content": "Figure 1. Human-like monocular depth cues emerge in large vision models. We present DepthCues, a comprehensive benchmark suite designed to probe the understanding of human monocular depth cues in vision models. We analyse a diverse set of vision models and find that recent self-supervised and geometry estimation models demonstrate a notably stronger grasp of these cues, even in cases where models (e.g., DINOv2) were not explicitly pre-trained on any depth-related tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.907, + 0.75 + ], + "angle": 0, + "content": "ious computer vision tasks, including multi-view [10, 38] and monocular depth estimation [17, 22, 76], even reaching human-level performance in ordering objects by depth [47]. As a result, numerous recent monocular depth estimation approaches [28, 40, 72] leverage these models' depth priors to achieve state-of-the-art performance. This naturally raises an important question: How does depth perception arise in these large vision models?" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Studies on the human visual system [9, 39] suggest that humans infer monocular depth using various visual cues such as elevation, light and shadow, occlusion, perspective, size, and texture gradient [7, 44] (see the top part of Fig. 2). Although these visual cues could emerge in large vision models during pre-training, it remains unclear to what extent this is true. Existing benchmarks [4, 17, 22, 47, 76] focus on evaluating the depth estimation performance of large vision models but do not investigate their understanding of the underlying visual cues. To address this gap, we eval" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20049" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.168 + ], + "angle": 0, + "content": "uate how well the large vision models understand and utilize human-like monocular depth cues. Our goal is to provide insights into current models' depth estimation behavior, enable a more systematic analysis of their strengths and limitations, and indicate areas for improvement." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.17, + 0.483, + 0.426 + ], + "angle": 0, + "content": "We introduce a new benchmark named DepthCues consisting of six depth related tasks (see Fig. 2) where each task is designed to test a given models' ability to estimate a visual cue that is ubiquitous to human depth perception. Specifically, lightweight probing models (referred to as the probes hereafter) placed on top of the frozen features of large vision models are trained and tested on the associated dataset for each task. The assumption is that the more effectively the probe can learn to solve a task using the features of a model, the better the model understands the task-specific cue. Under this protocol, we examine 20 vision models pre-trained at scale under various settings, including self-supervised learning (DINOv2 [54]), image generation (StableDiffusion) [59], vision-language supervision (CLIP [56]), single-view reconstruction (LRM [33]), cross-view completion (CroCo [68]), and also a recent general purpose depth estimation model DepthAnything v2 [72]." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.429, + 0.483, + 0.699 + ], + "angle": 0, + "content": "Our results reveal the following observations: First, the performance of models on DepthCues is highly correlated with their depth estimation performance, validating the effectiveness of DepthCues for investigating depth perception. Second, more recent self-supervised and geometry estimation models exhibit a stronger understanding of human monocular depth cues (see Fig. 1), with DepthAnythingv2 ranking first, and DINOv2 and StableDiffusion ranking top-five. Third, none of the benchmarked models consistently excel on all six of the depth tasks. Finally, recent single-view pre-trained models are limited in their perception of texture gradient, while multi-view trained models are better at this low-level geometric cue. Additionally, we explore enhancing depth awareness of vision models by injecting depth cue priors, demonstrating that fine-tuning on our DepthCues benchmark results in improved depth estimation, despite the significant sparsity of the supervision compared to dense annotations. Our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.703, + 0.483, + 0.746 + ], + "angle": 0, + "content": "- We develop and make available DepthCues, a benchmark suite for evaluating the emergence of human monocular depth cues in large vision models." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.748, + 0.483, + 0.792 + ], + "angle": 0, + "content": "- We evaluate 20 diverse vision models across a range of pre-training settings, and analyze their relative strengths and weaknesses in capturing monocular depth cues." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.794, + 0.483, + 0.837 + ], + "angle": 0, + "content": "- We show that human depth perception cues emerge from self-supervised pre-training on single images, with stronger alignment found in more recent, larger models." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.839, + 0.483, + 0.898 + ], + "angle": 0, + "content": "- We conduct an exploratory study on enhancing the depth awareness of a model by fine-tuning on DepthCues, showing that explicitly injecting human-like depth priors can improve depth perception." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.703, + 0.483, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.655, + 0.105 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.905, + 0.386 + ], + "angle": 0, + "content": "Monocular Depth Estimation. Monocular depth estimation is an inherently ill-posed and challenging problem, yet deep learning-based methods have made significant strides in addressing it. Initial progress was driven by supervised methods [6, 16, 19] that were trained on various labeled datasets [23, 52]. Later, self-supervised approaches advanced the field further by leveraging stereo [21, 25] or temporal consistency [26, 27, 80]. More recently, general purpose methods [40, 58, 71, 72] leveraging large vision backbone models pre-trained with self-supervised [54] or generative objectives [59] and then fine-tuned on very largescale supervised depth datasets have been shown to result in strong monocular depth estimation performance. However, it remains unclear how depth perception develops in the pre-trained models without explicit depth supervision during pre-training. In this paper, we try to shed light on the emergence of these monocular depth cues used by the human visual system in large vision models." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.388, + 0.905, + 0.598 + ], + "angle": 0, + "content": "Depth Perception in Pre-trained Vision Models. Several recent efforts have begun to analyze the 3D and depth perception abilities of pre-trained large vision models, with a focus on 3D awareness [17], 3D scene understanding [50], depth and height perception [4], and 3D physical understanding [76]. Complementary to these efforts, several studies have attempted to enhance the capabilities of these models by integrating 3D and depth information [3, 45, 73, 78]. Unlike these works, we focus on monocular depth estimation, emphasising evaluating the emergence of monocular cues essential for human depth perception. Some of the cues we study are also explored in a concurrent work [76], however, we focus on depth perception with diverse data and analyze a broader range of vision models." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.6, + 0.905, + 0.825 + ], + "angle": 0, + "content": "Recent work [22, 62] has analyzed monocular depth estimation models, examining properties like the backbone architectures, loss functions, and training datasets. However, they do not explore whether or how these models actually utilize monocular cues for depth estimation. In our work, we focus on analyzing the existence of intrinsic depth cues without direct depth supervision across various large vision models. Closely related to our approach, [63] investigates whether predictions of a monocular depth estimation model [58] violate perceptual cues. However, a prediction that violates a perceptual cue does not necessarily indicate the absence of the cue in the model itself. Instead, we directly examine the presence of these cues across multiple models, including, but not limited to, monocular depth models using our newly introduced benchmark suite." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.905, + 0.9 + ], + "angle": 0, + "content": "Comparing Humans to Neural Networks. Human and animal vision systems have long inspired computational vision methods [31, 37, 55]. Many studies have sought to compare biological vision with modern neural network-based computer vision systems across tasks such as ob" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20050" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.089, + 0.228, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.155, + 0.269, + 0.172, + 0.28 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.233, + 0.089, + 0.364, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.288, + 0.268, + 0.307, + 0.28 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.089, + 0.498, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.424, + 0.268, + 0.442, + 0.28 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.633, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.559, + 0.268, + 0.576, + 0.28 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.089, + 0.766, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.693, + 0.268, + 0.71, + 0.28 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image", + "bbox": [ + 0.769, + 0.089, + 0.901, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.268, + 0.844, + 0.279 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.288, + 0.894, + 0.302 + ], + "angle": 0, + "content": "Figure 2. Overview of DepthCues. Monocular depth cues, the associated tasks, and example instances from our proposed benchmark." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.316, + 0.48, + 0.403 + ], + "angle": 0, + "content": "
Depth CueSource#Images#Train#Val#Test
ElevationHLW [69]18,39015,7618281,801
Light-shadowSOBA [67]7984,716862860
OcclusionCOCOA [83]5,57324,40212,90614,862
PerspectiveNaturalScene [81]2,2752,000125150
SizeKITTI [23], SUN [61]2,7171,986330712
Texture-gradDTD [13]6,0004,0001,0001,000
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.408, + 0.482, + 0.437 + ], + "angle": 0, + "content": "Table 1. Summary of the datasets in DepthCues benchmark. We report total image and data statistics across all splits." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.452, + 0.484, + 0.693 + ], + "angle": 0, + "content": "ject recognition [57], shape-bias [24], multi-view consistency [8, 53], visual perspective-taking [47], and perceptual judgments of similarity [20]. In our work, rather than measuring alignment between human and large-scale vision systems, we focus on the emergence of monocular cues that are well-established in the human vision science community [7, 9, 39, 44], i.e., the cues that are crucial for monocular depth estimation in human vision. Recent work has incorporated additional high-level human vision-inspired cues, specifically semantics, object size, and spatial relationships, in an attempt to improve automated monocular depth estimation [1, 2]. These cues, extracted using pre-trained semantic segmentation and language embedding models, are shown to enhance depth prediction accuracy. We hope that our results and analyses will inspire similar approaches and foster new directions." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.709, + 0.421, + 0.726 + ], + "angle": 0, + "content": "3. DepthCues: Benchmark and Dataset" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We introduce DepthCues, a new benchmark to investigate how large-scale pre-trained image models perceive depth by assessing their understanding of a set of monocular depth cues used by humans to perceive depth: elevation, light and shadow, occlusion, perspective, size, and texture gradient [9, 39]. Our benchmark comprises a suite of six tasks with constituent datasets specifically designed to capture the essence of each individual monocular depth cue. For each task, DepthCues provides training and test sets with an evaluation protocol for image models, along with a performance metric to assess how well a given model under" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.319, + 0.907, + 0.47 + ], + "angle": 0, + "content": "stands each depth cue. Fig. 2 illustrates the task for each cue, and shows a representative instance from the associated dataset. We summarize the statistics of our datasets in Tab. 1. Next, we describe the construction of each task and the data used. In each case, we adapt existing datasets that have been designed for bespoke vision tasks. We use the original train, validation, and test splits of data sources and keep the classes balanced for binary tasks unless specified. Additional details about dataset construction are provided in Appendix B." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.48, + 0.623, + 0.495 + ], + "angle": 0, + "content": "3.1. Elevation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.504, + 0.906, + 0.533 + ], + "angle": 0, + "content": "Objects on the ground plane are farther away as they get closer to the horizon." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.534, + 0.906, + 0.67 + ], + "angle": 0, + "content": "Task. The elevation cue relies on perceiving the horizon line, which is defined as the projection of all the points where light rays from the observer's viewpoint are tangent to Earth's surface. Therefore, we adopt the task of horizon line estimation [42, 69]. Note, the horizon line is not always visible, and is different from the skyline, which separates the sky and the entities on the ground. The task is posed as a regression problem where the goal is to estimate the target line, i.e., its slope and y-intercept, in the image." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.671, + 0.906, + 0.746 + ], + "angle": 0, + "content": "Dataset. We adopt the HLW dataset [69], which provides pairs of images and annotations of the horizon lines. To increase the slope variation, we augment the images by rotating them (and the line annotations) randomly between \\(-30^{\\circ}\\) and \\(30^{\\circ}\\). An example from the dataset is shown in Fig. 2 (a)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.756, + 0.691, + 0.772 + ], + "angle": 0, + "content": "3.2. Light and Shadow" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.906, + 0.825 + ], + "angle": 0, + "content": "The way shadow is cast provides useful cue for orientation and depth of objects. For convenience, we refer to this cue as light-shadow." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.856 + ], + "angle": 0, + "content": "Task. To capture the understanding of this cue, we propose a task of associating shadows with objects." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Dataset. The SOBA [67] dataset contains images with segmentation masks of objects and their associated shadows. From those, we create a dataset containing tuples of" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20051" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.482, + 0.152 + ], + "angle": 0, + "content": "\\((I,M_A,M_B,y)\\) , where \\(M_A\\) is the mask of the object \\(A\\) in image \\(I\\) , and \\(M_B\\) is the mask of a shadow \\(B\\) in the image. The label \\(y\\) is 1 if \\(B\\) is associated with \\(A\\) , and O otherwise. An example is depicted in Fig. 2 (b)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.162, + 0.205, + 0.177 + ], + "angle": 0, + "content": "3.3.Occlusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.185, + 0.483, + 0.214 + ], + "angle": 0, + "content": "An object that partially blocks another, from the perspective of the viewer, is perceived as closer." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.216, + 0.483, + 0.26 + ], + "angle": 0, + "content": "Task. To test whether models understand occlusion, we propose the task of identifying whether an object is occluded or not by another object." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.261, + 0.484, + 0.381 + ], + "angle": 0, + "content": "Dataset. We use the COCOA [83] dataset, providing manually annotated segmentation masks for visible and invisible object parts with occlusion rates. From the original annotations, we construct a dataset that contains triplets of image \\(I\\), the segmentation mask \\(M_A\\) of the visible part of the object \\(A\\), and the corresponding label \\(y\\), which is 1 if the object is occluded, and 0 otherwise. In the example in Fig. 2 (c), the car highlighted with a red mask is occluded." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.391, + 0.216, + 0.407 + ], + "angle": 0, + "content": "3.4. Perspective" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.415, + 0.483, + 0.445 + ], + "angle": 0, + "content": "Parallel lines converging at infinity offer a strong cue for perceiving depth." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.445, + 0.483, + 0.596 + ], + "angle": 0, + "content": "Task. This cue is closely tied to vanishing point [48], which is defined as the point on the image plane where 2D perspective projections of 3D parallel lines intersect. Therefore, we use the task of vanishing point estimation to investigate the understanding of perspective. While there exist different versions of the task that define different numbers of vanishing points [64, 74], we adopt a simplified version that focuses on a single dominant vanishing point. Given an image \\(I\\), the objective is to estimate the \\(\\mathbf{p} = (x,y)\\) coordinates of the vanishing point in the image coordinate system." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.596, + 0.483, + 0.687 + ], + "angle": 0, + "content": "Dataset. The NaturalScene dataset [81] contains images from diverse outdoor scenes with one manually annotated dominant vanishing point \\(\\mathbf{p}\\) in each. We use the original dataset and create validation and test sets by dividing the original validation set. An example is shown in Fig. 2 (d) with the vanishing point indicated by the red dot." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.696, + 0.16, + 0.71 + ], + "angle": 0, + "content": "3.5. Size" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.78 + ], + "angle": 0, + "content": "People infer depth based on known object sizes (in 3D) and their apparent retinal sizes (e.g., an object farther away appears smaller). This cue is particularly effective when comparing objects of similar expected sizes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.825 + ], + "angle": 0, + "content": "Task. Using this cue requires prior knowledge of object sizes. Thus we propose a binary classification task: determining if object \\( A \\) is larger than object \\( B \\) in 3D." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Dataset. We use 3D object detection datasets KITTI [23] and SUN-RGBD [61] which provide 3D bounding boxes of objects in outdoor and indoor scenes respectively. Given an image \\(I\\), we sample two objects, \\(A\\) and \\(B\\), and compare their sizes using the volumes of their 3D bounding boxes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.198 + ], + "angle": 0, + "content": "Object masks \\( M_A \\) and \\( M_B \\) in image space are estimated using SAM [41] with bounding box queries and additional filtering to ensure segmentation quality. The final dataset contains tuples \\( (I, M_A, M_B, y) \\), where the label \\( y = 1 \\) if object \\( A \\) is larger, and 0 otherwise. We filtered pairs where the volume difference was under a threshold to reduce errors caused by imprecise labeling. See Fig. 2 (e) for an example." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.206, + 0.685, + 0.22 + ], + "angle": 0, + "content": "3.6. Texture Gradient" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.229, + 0.905, + 0.289 + ], + "angle": 0, + "content": "When a region on a surface is further away from the viewer, its texture appears denser and more compressed, with a higher spatial frequency, compared to the same texture viewed nearby. We denote this cue as texture-grad." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.29, + 0.905, + 0.349 + ], + "angle": 0, + "content": "Task. This cue is especially helpful on textured surfaces. To assess the existence of this cue, we use the task of depth ordering of regions on a textured plane, where the model must infer depth based solely on texture." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.35, + 0.906, + 0.501 + ], + "angle": 0, + "content": "Dataset. To ensure that only the texture gradient cue is used for perceiving depth order, we created a synthetic dataset using Blender. First, we initialized a 3D plane, and applied textures sampled from the DTD dataset [13] which contains various real-world, as well as synthetic, textures. Then, fixing both the viewing direction of the camera (to always point at the plane center) and its distance to the plane center, we randomly set the camera elevation angle between \\(30^{\\circ}\\) and \\(60^{\\circ}\\), and project the textured plane on the camera imaging plane to obtain an image with its depth map." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.501, + 0.906, + 0.607 + ], + "angle": 0, + "content": "From each image \\( I \\), we randomly sample two equal-sized regions \\( A \\) and \\( B \\) (with their masks \\( M_A, M_B \\)), then set label \\( y \\) to 1 if \\( A \\) is closer than \\( B \\) and 0 otherwise. To avoid the region higher up in the image always being farther away, we apply random horizontal and vertical flips, so that the task cannot be solved solely from locations of the regions. An example image is shown in Fig. 2 (f)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.619, + 0.706, + 0.635 + ], + "angle": 0, + "content": "4. Evaluation Protocol" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.906, + 0.72 + ], + "angle": 0, + "content": "Following previous work [17, 76], we use probing of visual features as our evaluation protocol. Below, we explain how we obtain task-specific input features from visual models, how we probe these features, and how we measure success. An illustrative figure is included in Appendix C.1." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.728, + 0.774, + 0.744 + ], + "angle": 0, + "content": "4.1. Task Specific Visual Features" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.751, + 0.906, + 0.812 + ], + "angle": 0, + "content": "Given a pre-trained vision model \\(\\phi(\\cdot)\\), we assess its understanding of a cue by training a lightweight probe \\(g_{\\theta}\\) with parameters \\(\\theta\\) on the target task, using the features extracted by \\(\\phi\\). We obtain features \\(\\mathbf{f}\\) for each task as described below." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.812, + 0.905, + 0.858 + ], + "angle": 0, + "content": "Occlusion. We extract a feature map \\(\\phi(I)\\) from the image \\(I\\) and up-sample it to match the spatial size of the object mask \\(M_A\\). We mask the feature map and apply spatial pooling:" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.867, + 0.905, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} = \\frac {\\sum_ {h , w} M _ {A} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {A}}, \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20052" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "where \\(h, w\\) index the height and width of \\(I\\), \\(\\odot\\) is element-wise multiplication, and \\(\\mathrm{up}(\\cdot)\\) denotes bilinear upsampling. This results in \\(\\mathbf{f} \\in \\mathbb{R}^D\\) where \\(D\\) is the feature dimension and changes depending on the vision model \\(\\phi\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.152, + 0.483, + 0.198 + ], + "angle": 0, + "content": "Light-shadow, Size, and Texture-grad. For these tasks, we calculate the difference between the masked average features of objects \\( A \\) and \\( B \\):" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.208, + 0.482, + 0.258 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} = \\frac {\\sum_ {h , w} M _ {A} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {A}} - \\frac {\\sum_ {h , w} M _ {B} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {B}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.259, + 0.483, + 0.32 + ], + "angle": 0, + "content": "Elevation and Perspective. These tasks are not object/region specific, so we use the entire image feature, i.e., \\(\\mathbf{f} = \\phi(I) \\in \\mathbb{R}^{H_{\\mathbf{f}} \\times W_{\\mathbf{f}} \\times D}\\), where \\(H_{\\mathbf{f}}, W_{\\mathbf{f}}\\) are the height and width of the feature map." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.33, + 0.262, + 0.345 + ], + "angle": 0, + "content": "4.2. Probing Features" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.353, + 0.483, + 0.579 + ], + "angle": 0, + "content": "For light-shadow, occlusion, size, and texture-grad, where the task-specific features \\( \\mathbf{f} \\) are \\( D \\)-dimensional vectors, we implement the probe \\( g_{\\theta} \\) as a multi-layer perception (MLP) with two layers and an intermediate GELU activation [32]. Though linear probing has been used commonly for probing large vision models [54], it is not obvious that the solutions to our tasks should be a linear function of the model features. Thus, we use non-linear probes, which empirically outperform linear probes (see Appendix A.2) For elevation and perspective, which require global information, we use an attentive probe [5, 18]. This probe aggregates global features through cross-attention and uses a two-layer MLP for final predictions. We observed via empirical results that the attentive probe achieves better performance than a standard MLP probe on these tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.58, + 0.483, + 0.686 + ], + "angle": 0, + "content": "Training and Optimization. We train the MLP probes for light-shadow, occlusion, size and texture-grad tasks using binary cross-entropy loss, as these tasks involve binary classification. For elevation and perspective, we use mean squared error loss to train the attentive probes, as the tasks are formulated as regression problems. Additional details on the probe optimization are provided in Appendix C.1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.686, + 0.483, + 0.807 + ], + "angle": 0, + "content": "Following [54, 76], we perform a hyper-parameter search on the layers of model \\(\\phi\\). For each task, we extract features from different layers of \\(\\phi\\) which is frozen, and train a probe on these features under the same setting. The best layer is then selected based on the validation performance, and the probing on this layer is repeated five times using different random seeds. We report the mean and standard deviation of the test performance." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.817, + 0.275, + 0.832 + ], + "angle": 0, + "content": "4.3. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "For light-shadow, occlusion, size and texture-grad which are binary tasks, we report classification accuracy. For the vanishing point estimation task of the perspective cue, while Euclidean distance (between the predicted and ground-truth" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.198 + ], + "angle": 0, + "content": "vanishing points) is a sensible metric, we instead report success rate to align this metric more closely with accuracy. Specifically, if the Euclidean distance of a prediction falls below a pre-defined threshold, it is interpreted as success. For elevation, we convert the horizon detection error [69] to an accuracy-based measure using a similar approach. More details are provided in Appendix C.2." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.214, + 0.646, + 0.231 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.24, + 0.862, + 0.257 + ], + "angle": 0, + "content": "5.1. Monocular Depth Cues in Vision Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.264, + 0.905, + 0.34 + ], + "angle": 0, + "content": "We evaluate 20 pre-trained large vision models [11, 15, 29, 30, 33, 35, 41, 49, 54, 56, 58, 59, 65, 66, 68, 70, 72, 75, 79] spanning diverse pre-training objectives, modalities, and model architectures to assess their understanding of monocular depth perception cues in our DepthCues benchmark." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.34, + 0.905, + 0.446 + ], + "angle": 0, + "content": "Implementation Details. Where possible, we focus on model architectures equivalent to ViT-Base and denote the architecture size (and patch size for transformers) using postfixes, e.g., DINOv2-b14. More details about the models and their architecture are provided in Appendix D. For consistency, we use only patch tokens for all ViT-based models [15], as some do not include a class token." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.906, + 0.719 + ], + "angle": 0, + "content": "Additional Baselines. During the probing of certain cues, we explicitly use mask information to construct the input feature, f. Although these masks are not directly used by the probes, they could theoretically be leveraged to solve tasks. To verify that any additional information from this step is insufficient to solve the task, we designed a trivial baseline in which model features are replaced with simple 2D coordinate maps i.e., \\(\\phi (I)\\) in Eqs. (1) and (2) becomes \\(C\\in \\mathbb{R}^{H\\times W\\times 2}\\) where \\(C_{h,w} = [h,w]^T\\). Moreover, for each cue, we include an end-to-end baseline, where we train ResNet18 [29] and ViT-B/16 [15] models from scratch in an end-to-end fashion and select the best. We concatenate the masks with the input images channel-wise, allowing us to assess how much of each task can be solved without relying on sophisticated pre-trained features. Finally, to confirm that the tasks are readily solvable by humans, we evaluate our own performance on a random sample from the test sets, and obtained an accuracy of \\(95\\% \\pm 1.48\\%\\) across tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Additional Tasks. To extend our analysis, we also evaluate vision models for monocular depth estimation (on NYUv2 [60] and DIW [12]) and image classification (on ImageNet-1k [14]) using a linear probe, a standard approach in previous work [3, 54, 73] for probing these datasets. Following the previous works [6, 12, 17], For NYUv2, we report accuracy as the percentage of pixels where the ratio between predicted and ground-truth depth is less than 1.25. We report top-1 accuracy for ImageNet. More details on these tasks are provided in Appendix A.1, and we show the linear probing results of these models on NYUv2 in Fig. 3." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20053" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.096, + 0.899, + 0.853 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.856, + 0.908, + 0.913 + ], + "angle": 0, + "content": "Figure 3. DepthCues Benchmark Results. We evaluate 20 vision models with diverse pre-training settings (indicated by color) on the DepthCues benchmark, which assesses six different monocular depth cues (each row) ubiquitous to humans. The models are ranked based on their average performance on the six cues. We include an end-to-end trained baseline (blue dotted line) as an oracle and a trivial baseline (red dotted line) to mark floor performance. Additionally, depth estimation linear probing results on NYUv2 are shown on the bottom row." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20054" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.258 + ], + "angle": 0, + "content": "Results. The probing results of 20 pre-trained vision models and the additional baselines on our DepthCues benchmark are summarized in Fig. 3, where the models are ranked by average performance over all cues. Moreover, we measured Spearman Ranked-order Correlation between each pair of tasks in DepthCues using the ranks of the models evaluated, and also how they correlate with the depth estimation and image classification performance of models, which is visualized in Fig. 4. We discuss our observations below, and present additional analysis, such as how pretraining data size impacts performance, in Appendix A.1." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.261, + 0.487, + 0.517 + ], + "angle": 0, + "content": "(i) Depth cues emerge in more recent large vision models. Firstly, the specialized depth estimation model, DepthAnythingv2, achieved the highest overall performance on DepthCues, indicating the possibility that it leverages such cues to estimate depth. We also observe the emergence of human-like monocular depth cues in recent large vision models, such as DINOv2 and Stable Diffusion. Notably, newer large vision models demonstrate a stronger grasp of these depth cues, as illustrated in Fig. 1. DINOv2 and Stable Diffusion have proven useful for developing monocular depth estimation models [40, 72]. However, the reasons behind these models' effectiveness for depth inference remain unclear, given the lack of explicit depth supervision during pre-training. Our results provide an insight on the development of depth perception in these models: they develop an awareness of human-like monocular depth cues, which might aid depth inference." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.519, + 0.484, + 0.699 + ], + "angle": 0, + "content": "(ii) Depth models do not always have the strongest knowledge of depth cues. While DepthAnythingv2 achieves the best overall performance on DepthCues, another specialized depth estimation model, MiDaS, is outperformed by several models pre-trained without depth supervision, e.g., DeiT, SigLIP, and DINO. These models also exhibit competitive depth estimation performance (under linear probing) to MiDaS. This suggests that other pretraining recipes than dense depth supervision can effectively enhance depth perception, although they may be less data-efficient – for instance, SigLIP is trained on around 10,000 times more data than MiDaS." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.702, + 0.484, + 0.853 + ], + "angle": 0, + "content": "(iii) Vision-language models exhibit varying levels of depth cue understanding. CLIP obtains the lowest performance on DepthCues, explaining its limited depth estimation ability as seen in Fig. 3 and in recent work [17]. CLIP's limited understanding of the visual concepts tested in DepthCues may present challenges for downstream tasks that require geometric understanding [82]. In contrast, SigLIP, also trained on matching images to captions but on significantly more data (\\( \\times 9 \\) more data than CLIP), has a significantly better grasp of the depth cues." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "(iv) Multi-view models are better at the texture-grad task than single-view models. On all depth cues except texture-grad, recent models which are pre-trained with" + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.261, + 0.487, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.095, + 0.9, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.339, + 0.907, + 0.409 + ], + "angle": 0, + "content": "Figure 4. Task correlation. We measure the Spearman Ranked-order Correlation between each pair of tasks in DepthCues benchmark, and how they correlate with depth estimation and image classification performance of models. A correlation score of one indicates the same ranking of models for two tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.418, + 0.909, + 0.903 + ], + "angle": 0, + "content": "single-view images showed overall better performance than multi-view ones. However, on texture-grad, all three multiview models (i.e., CroCo, LRM, and DUSt3R) ranked within the top four, outperforming strong SSL competitors such as DINOV2. While the other five cues operate at the scene or object level, texture-grad uniquely requires a more localized, surface-level understanding. Multi-view pre-trained models are often more effective at capturing such details than single-view models because, during pretraining, they are exposed to variations in the same surface across different viewpoints. For instance, CroCo, which achieves the best performance on the texture-grad task, is trained to reconstruct parts of a scene from different viewpoints, requiring attention to finer local details. Moreover, LRM and DUSt3R are pre-trained on 3D object and scene reconstruction tasks, which require understanding correspondences across views by leveraging local surface details. (v) Performance on DepthCues correlates with depth estimation performance. As shown in Fig. 4, all DepthCues tasks exhibit moderate to high levels of correlation with depth estimation, supporting the importance of depth cues for this task. However, all tasks have a low correlation with ImageNet-1k classification. Interestingly, a relatively higher alignment with classification is observed for occlusion and size, which are also highly correlated with each other. This is reasonable as understanding occlusion and size requires object-level semantics (e.g., 'What does the recognized object look like when not occluded?' and 'Is category A larger than category B?'). Apart from texture-grad, each cue has a high correlation (\\(>0.75\\)) with at least one other cue. As discussed above, the texture-grad cue requires understanding surface details and provides local" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20055" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.481, + 0.201 + ], + "angle": 0, + "content": "
ModelNYUv2 Acc. (%)↑DIW WHDR (%)↓
DINOv287.7811.99
DINOv2+DC87.0611.95
concat(DINOv2, noise)87.5612.20
concat(DINOv2, DINOv2+DC)88.4611.72
CLIP43.7835.25
CLIP+DC43.5935.45
concat(CLIP, noise)43.3835.39
concat(CLIP, CLIP+DC)44.3233.53
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.207, + 0.483, + 0.263 + ], + "angle": 0, + "content": "Table 2. Linear probing on downstream depth estimation. For each model, we probe the patch tokens from the final layer. Models with \\(+DC\\) are fine-tuned using supervision on our DepthCues benchmark. The best results in each subset are bolded." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.277, + 0.484, + 0.339 + ], + "angle": 0, + "content": "ized depth information; perception of this cue is found to be weaker in single-view image models. We note that texture-grad is the only cue that uses synthetic data, which might also contribute to its lower correlation with other cues." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.348, + 0.293, + 0.365 + ], + "angle": 0, + "content": "5.2. Learning Depth Cues" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.372, + 0.483, + 0.508 + ], + "angle": 0, + "content": "We observed that the depth estimation performance of a model highly correlates with its awareness of human-like monocular depth cues. Here we ask if enhanced depth cue awareness improves depth estimation? To investigate this, we fine-tune single-image pre-trained vision models on the training set of DepthCues in a multi-task manner, then evaluate the fine-tuned model on downstream depth estimation. Here we focus on two models widely adopted for various downstream applications: DINOv2 and CLIP." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.508, + 0.483, + 0.765 + ], + "angle": 0, + "content": "We use low-rank adaptation (LoRA) [34] for efficient fine-tuning of pre-trained models. Further details of multitask learning and LoRA implementation are provided in Appendix C.3. We evaluate the pre-trained and fine-tuned models on NYUv2 [60] and DIW [12] depth datasets using linear probes. We experiment with two different variations: first, we evaluate the features from fine-tuned models (denoted as \\(+DC\\) in Tab. 2); second, we concatenate the features from fine-tuned models with the features from the original pre-trained models. The latter approach was also adopted in [51, 73] to preserve the generalization ability of the pre-trained models. As before, we report accuracy for NYUv2, and use Weighted Human Disagreement Rate (WHDR) to measure performance on DIW. It is noted the dataset for the size cue in DepthCues contains a subset of NYUv2 images (due to the use of SUNRGBD), so evaluation on DIW offers a fairer comparison." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.903 + ], + "angle": 0, + "content": "We observe in Tab. 2 that for both models, fine-tuning on DepthCues resulted in improved depth perception. Notably, the fine-tuned features often need to be concatenated with the original features to bring improvements, a similar observation also made in previous works [51, 73]. A possible explanation for the decreased generalization in the models is due to the limited size and diversity of the fine-tuning data in DepthCues. We also investigate whether the improvements in the concatenated variations come from the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "increased parameters in the probe (due to higher dimensional input), by training linear probes on a combination of original model features and random noise (denoted as concat(·, noise)), which did not result in improvements." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.16, + 0.634, + 0.175 + ], + "angle": 0, + "content": "5.3. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.183, + 0.905, + 0.456 + ], + "angle": 0, + "content": "The results in Sec. 5.1 indicate that recent large vision models understand several human-like monocular depth cues, with performance on these cues correlating with depth estimation performance. This suggests that models may use such cues to infer depth, even without explicit depth supervision. For example, the popular self-supervised model, DINOv2, has developed features that help reason about these cues (except texture-grad), which can support depth estimation. Interestingly, the results in Sec. 5.2 show that DepthCues enables the learning of depth cues, which benefit downstream depth performance in a linear probing setting, even though DepthCues has a moderate size (fewer than 35k training images, much smaller than the large datasets used to pre-train the base models), is not designed specifically for end-to-end fine-tuning, and only provides image-level sparse annotations (as opposed to dense depth maps). This suggests promising directions for enhancing depth estimation from sparse annotations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.456, + 0.906, + 0.577 + ], + "angle": 0, + "content": "Limitations. Our analysis focuses only on widely used pretrained model weights but not directly on the impact of various pre-training objectives and their training datasets on the emergence of depth cues. While depth from ego-motion and scene motion are also important cues for humans, our focus is primarily on assessing monocular cues learned by large vision models trained on static image collections and not image sequences (except CroCo, LRM, and DUSt3R)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.589, + 0.642, + 0.605 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.905, + 0.825 + ], + "angle": 0, + "content": "We introduced DepthCues, a benchmark suite for evaluating human-like monocular depth cues in large vision models. Testing 20 diverse models, we found that depth perception cues, similar to those used by humans, emerge across various pre-training objectives, with more recent and larger models demonstrating stronger alignment with human depth perception. Furthermore, our fine-tuning experiments on DepthCues indicate that a model's depth perception can be enhanced by explicitly incorporating human-like depth priors, suggesting promising directions for improving depth performance in future models. We hope DepthCues will serve as a valuable resource for advancing research in depth-aware vision systems, particularly for applications requiring robust 3D spatial understanding from 2D inputs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Acknowledgments. Funding was provided by ELIAI (the Edinburgh Laboratory for Integrated Artificial Intelligence) - EPSRC (EP/W002876/1). HB was supported by the EPSRC Visual AI grant EP/T028572/1, and CJ was supported by a gift from Adobe." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20056" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.156 + ], + "angle": 0, + "content": "[1] Dylan Auty and Krystian Mikolajczyk. Monocular depth estimation using cues inspired by biological vision systems. In ICPR, 2022. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.16, + 0.484, + 0.201 + ], + "angle": 0, + "content": "[2] Dylan Auty and Krystian Mikolajczyk. 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Recent studies on the emergent properties of these models have revealed their high-level geometric understanding, in particular in the context of depth perception. However, it remains unclear how depth perception arises in these models without explicit depth supervision provided during pre-training. To investigate this, we examine whether the monocular depth cues, similar to those used by the human visual system, emerge in these models. We introduce a new benchmark, DepthCues, designed to evaluate depth cue understanding, and present findings across 20 diverse and representative pre-trained vision models. Our analysis shows that human-like depth cues emerge in more recent larger models. We also explore enhancing depth perception in large vision models by fine-tuning on DepthCues, and find that even without dense depth supervision, this improves depth estimation. To support further research, our benchmark and evaluation code will be made publicly available for studying depth perception in vision models. + +# 1. Introduction + +To ensure safe, accurate, and robust interaction with the 3D world, it is important for computer vision models to understand geometric properties from their projections onto 2D images. Of particular significance is the perception of depth from single images, which has been found to benefit various downstream tasks including segmentation [43], object detection [36], and image and video generation [46, 77], among others. Monocular depth estimation models traditionally rely on dense depth supervision, but obtaining high-quality depth ground truth at scale is challenging, unlike the abundance of large 2D image-only datasets. + +Large-scale pre-trained vision models like Stable Diffusion [59] and DINOv2 [54], trained solely on 2D images, have shown strong generalization when fine-tuned on var + +![](images/536455f60307367e277d7de5b82e90329adcb883a603ba5dd4f389452616c14e.jpg) +Figure 1. Human-like monocular depth cues emerge in large vision models. We present DepthCues, a comprehensive benchmark suite designed to probe the understanding of human monocular depth cues in vision models. We analyse a diverse set of vision models and find that recent self-supervised and geometry estimation models demonstrate a notably stronger grasp of these cues, even in cases where models (e.g., DINOv2) were not explicitly pre-trained on any depth-related tasks. + +ious computer vision tasks, including multi-view [10, 38] and monocular depth estimation [17, 22, 76], even reaching human-level performance in ordering objects by depth [47]. As a result, numerous recent monocular depth estimation approaches [28, 40, 72] leverage these models' depth priors to achieve state-of-the-art performance. This naturally raises an important question: How does depth perception arise in these large vision models? + +Studies on the human visual system [9, 39] suggest that humans infer monocular depth using various visual cues such as elevation, light and shadow, occlusion, perspective, size, and texture gradient [7, 44] (see the top part of Fig. 2). Although these visual cues could emerge in large vision models during pre-training, it remains unclear to what extent this is true. Existing benchmarks [4, 17, 22, 47, 76] focus on evaluating the depth estimation performance of large vision models but do not investigate their understanding of the underlying visual cues. To address this gap, we eval + +uate how well the large vision models understand and utilize human-like monocular depth cues. Our goal is to provide insights into current models' depth estimation behavior, enable a more systematic analysis of their strengths and limitations, and indicate areas for improvement. + +We introduce a new benchmark named DepthCues consisting of six depth related tasks (see Fig. 2) where each task is designed to test a given models' ability to estimate a visual cue that is ubiquitous to human depth perception. Specifically, lightweight probing models (referred to as the probes hereafter) placed on top of the frozen features of large vision models are trained and tested on the associated dataset for each task. The assumption is that the more effectively the probe can learn to solve a task using the features of a model, the better the model understands the task-specific cue. Under this protocol, we examine 20 vision models pre-trained at scale under various settings, including self-supervised learning (DINOv2 [54]), image generation (StableDiffusion) [59], vision-language supervision (CLIP [56]), single-view reconstruction (LRM [33]), cross-view completion (CroCo [68]), and also a recent general purpose depth estimation model DepthAnything v2 [72]. + +Our results reveal the following observations: First, the performance of models on DepthCues is highly correlated with their depth estimation performance, validating the effectiveness of DepthCues for investigating depth perception. Second, more recent self-supervised and geometry estimation models exhibit a stronger understanding of human monocular depth cues (see Fig. 1), with DepthAnythingv2 ranking first, and DINOv2 and StableDiffusion ranking top-five. Third, none of the benchmarked models consistently excel on all six of the depth tasks. Finally, recent single-view pre-trained models are limited in their perception of texture gradient, while multi-view trained models are better at this low-level geometric cue. Additionally, we explore enhancing depth awareness of vision models by injecting depth cue priors, demonstrating that fine-tuning on our DepthCues benchmark results in improved depth estimation, despite the significant sparsity of the supervision compared to dense annotations. Our contributions are: + +- We develop and make available DepthCues, a benchmark suite for evaluating the emergence of human monocular depth cues in large vision models. +- We evaluate 20 diverse vision models across a range of pre-training settings, and analyze their relative strengths and weaknesses in capturing monocular depth cues. +- We show that human depth perception cues emerge from self-supervised pre-training on single images, with stronger alignment found in more recent, larger models. +- We conduct an exploratory study on enhancing the depth awareness of a model by fine-tuning on DepthCues, showing that explicitly injecting human-like depth priors can improve depth perception. + +# 2. Related Work + +Monocular Depth Estimation. Monocular depth estimation is an inherently ill-posed and challenging problem, yet deep learning-based methods have made significant strides in addressing it. Initial progress was driven by supervised methods [6, 16, 19] that were trained on various labeled datasets [23, 52]. Later, self-supervised approaches advanced the field further by leveraging stereo [21, 25] or temporal consistency [26, 27, 80]. More recently, general purpose methods [40, 58, 71, 72] leveraging large vision backbone models pre-trained with self-supervised [54] or generative objectives [59] and then fine-tuned on very largescale supervised depth datasets have been shown to result in strong monocular depth estimation performance. However, it remains unclear how depth perception develops in the pre-trained models without explicit depth supervision during pre-training. In this paper, we try to shed light on the emergence of these monocular depth cues used by the human visual system in large vision models. + +Depth Perception in Pre-trained Vision Models. Several recent efforts have begun to analyze the 3D and depth perception abilities of pre-trained large vision models, with a focus on 3D awareness [17], 3D scene understanding [50], depth and height perception [4], and 3D physical understanding [76]. Complementary to these efforts, several studies have attempted to enhance the capabilities of these models by integrating 3D and depth information [3, 45, 73, 78]. Unlike these works, we focus on monocular depth estimation, emphasising evaluating the emergence of monocular cues essential for human depth perception. Some of the cues we study are also explored in a concurrent work [76], however, we focus on depth perception with diverse data and analyze a broader range of vision models. + +Recent work [22, 62] has analyzed monocular depth estimation models, examining properties like the backbone architectures, loss functions, and training datasets. However, they do not explore whether or how these models actually utilize monocular cues for depth estimation. In our work, we focus on analyzing the existence of intrinsic depth cues without direct depth supervision across various large vision models. Closely related to our approach, [63] investigates whether predictions of a monocular depth estimation model [58] violate perceptual cues. However, a prediction that violates a perceptual cue does not necessarily indicate the absence of the cue in the model itself. Instead, we directly examine the presence of these cues across multiple models, including, but not limited to, monocular depth models using our newly introduced benchmark suite. + +Comparing Humans to Neural Networks. Human and animal vision systems have long inspired computational vision methods [31, 37, 55]. Many studies have sought to compare biological vision with modern neural network-based computer vision systems across tasks such as ob + +![](images/3e83b1ca219705e4a8761ac72012df0e36be3eadb3c5e0b74e94941fdc9217f1.jpg) +(a) + +![](images/0f6566bf1784fe9dd026731779efcfbd360af35f599bd2415ffde757d8c4e751.jpg) +(b) + +![](images/24c7f4de898117948f541d4cb5ad2a40d960440cb33e4e3d13b39eca16083161.jpg) +(c) + +![](images/65cf4ce19a0f8e8660bae2d143020ce18057725e8eeecc441d463e903d5a1816.jpg) +(d) + +![](images/e6cf0077c9181df073e72cca677512ba4118e21a30c3edd144c2562f5bc9bfa1.jpg) +(e) + +![](images/7c23e351b7e4c782f85c27d4a93b6cffb0284c94b949841dd9f49bd03a1138eb.jpg) +(f) +Figure 2. Overview of DepthCues. Monocular depth cues, the associated tasks, and example instances from our proposed benchmark. + +
Depth CueSource#Images#Train#Val#Test
ElevationHLW [69]18,39015,7618281,801
Light-shadowSOBA [67]7984,716862860
OcclusionCOCOA [83]5,57324,40212,90614,862
PerspectiveNaturalScene [81]2,2752,000125150
SizeKITTI [23], SUN [61]2,7171,986330712
Texture-gradDTD [13]6,0004,0001,0001,000
+ +Table 1. Summary of the datasets in DepthCues benchmark. We report total image and data statistics across all splits. + +ject recognition [57], shape-bias [24], multi-view consistency [8, 53], visual perspective-taking [47], and perceptual judgments of similarity [20]. In our work, rather than measuring alignment between human and large-scale vision systems, we focus on the emergence of monocular cues that are well-established in the human vision science community [7, 9, 39, 44], i.e., the cues that are crucial for monocular depth estimation in human vision. Recent work has incorporated additional high-level human vision-inspired cues, specifically semantics, object size, and spatial relationships, in an attempt to improve automated monocular depth estimation [1, 2]. These cues, extracted using pre-trained semantic segmentation and language embedding models, are shown to enhance depth prediction accuracy. We hope that our results and analyses will inspire similar approaches and foster new directions. + +# 3. DepthCues: Benchmark and Dataset + +We introduce DepthCues, a new benchmark to investigate how large-scale pre-trained image models perceive depth by assessing their understanding of a set of monocular depth cues used by humans to perceive depth: elevation, light and shadow, occlusion, perspective, size, and texture gradient [9, 39]. Our benchmark comprises a suite of six tasks with constituent datasets specifically designed to capture the essence of each individual monocular depth cue. For each task, DepthCues provides training and test sets with an evaluation protocol for image models, along with a performance metric to assess how well a given model under + +stands each depth cue. Fig. 2 illustrates the task for each cue, and shows a representative instance from the associated dataset. We summarize the statistics of our datasets in Tab. 1. Next, we describe the construction of each task and the data used. In each case, we adapt existing datasets that have been designed for bespoke vision tasks. We use the original train, validation, and test splits of data sources and keep the classes balanced for binary tasks unless specified. Additional details about dataset construction are provided in Appendix B. + +# 3.1. Elevation + +Objects on the ground plane are farther away as they get closer to the horizon. + +Task. The elevation cue relies on perceiving the horizon line, which is defined as the projection of all the points where light rays from the observer's viewpoint are tangent to Earth's surface. Therefore, we adopt the task of horizon line estimation [42, 69]. Note, the horizon line is not always visible, and is different from the skyline, which separates the sky and the entities on the ground. The task is posed as a regression problem where the goal is to estimate the target line, i.e., its slope and y-intercept, in the image. + +Dataset. We adopt the HLW dataset [69], which provides pairs of images and annotations of the horizon lines. To increase the slope variation, we augment the images by rotating them (and the line annotations) randomly between $-30^{\circ}$ and $30^{\circ}$ . An example from the dataset is shown in Fig. 2 (a). + +# 3.2. Light and Shadow + +The way shadow is cast provides useful cue for orientation and depth of objects. For convenience, we refer to this cue as light-shadow. + +Task. To capture the understanding of this cue, we propose a task of associating shadows with objects. + +Dataset. The SOBA [67] dataset contains images with segmentation masks of objects and their associated shadows. From those, we create a dataset containing tuples of + +$(I,M_A,M_B,y)$ , where $M_A$ is the mask of the object $A$ in image $I$ , and $M_B$ is the mask of a shadow $B$ in the image. The label $y$ is 1 if $B$ is associated with $A$ , and O otherwise. An example is depicted in Fig. 2 (b). + +# 3.3.Occlusion + +An object that partially blocks another, from the perspective of the viewer, is perceived as closer. + +Task. To test whether models understand occlusion, we propose the task of identifying whether an object is occluded or not by another object. + +Dataset. We use the COCOA [83] dataset, providing manually annotated segmentation masks for visible and invisible object parts with occlusion rates. From the original annotations, we construct a dataset that contains triplets of image $I$ , the segmentation mask $M_A$ of the visible part of the object $A$ , and the corresponding label $y$ , which is 1 if the object is occluded, and 0 otherwise. In the example in Fig. 2 (c), the car highlighted with a red mask is occluded. + +# 3.4. Perspective + +Parallel lines converging at infinity offer a strong cue for perceiving depth. + +Task. This cue is closely tied to vanishing point [48], which is defined as the point on the image plane where 2D perspective projections of 3D parallel lines intersect. Therefore, we use the task of vanishing point estimation to investigate the understanding of perspective. While there exist different versions of the task that define different numbers of vanishing points [64, 74], we adopt a simplified version that focuses on a single dominant vanishing point. Given an image $I$ , the objective is to estimate the $\mathbf{p} = (x,y)$ coordinates of the vanishing point in the image coordinate system. + +Dataset. The NaturalScene dataset [81] contains images from diverse outdoor scenes with one manually annotated dominant vanishing point $\mathbf{p}$ in each. We use the original dataset and create validation and test sets by dividing the original validation set. An example is shown in Fig. 2 (d) with the vanishing point indicated by the red dot. + +# 3.5. Size + +People infer depth based on known object sizes (in 3D) and their apparent retinal sizes (e.g., an object farther away appears smaller). This cue is particularly effective when comparing objects of similar expected sizes. + +Task. Using this cue requires prior knowledge of object sizes. Thus we propose a binary classification task: determining if object $A$ is larger than object $B$ in 3D. + +Dataset. We use 3D object detection datasets KITTI [23] and SUN-RGBD [61] which provide 3D bounding boxes of objects in outdoor and indoor scenes respectively. Given an image $I$ , we sample two objects, $A$ and $B$ , and compare their sizes using the volumes of their 3D bounding boxes. + +Object masks $M_A$ and $M_B$ in image space are estimated using SAM [41] with bounding box queries and additional filtering to ensure segmentation quality. The final dataset contains tuples $(I, M_A, M_B, y)$ , where the label $y = 1$ if object $A$ is larger, and 0 otherwise. We filtered pairs where the volume difference was under a threshold to reduce errors caused by imprecise labeling. See Fig. 2 (e) for an example. + +# 3.6. Texture Gradient + +When a region on a surface is further away from the viewer, its texture appears denser and more compressed, with a higher spatial frequency, compared to the same texture viewed nearby. We denote this cue as texture-grad. + +Task. This cue is especially helpful on textured surfaces. To assess the existence of this cue, we use the task of depth ordering of regions on a textured plane, where the model must infer depth based solely on texture. + +Dataset. To ensure that only the texture gradient cue is used for perceiving depth order, we created a synthetic dataset using Blender. First, we initialized a 3D plane, and applied textures sampled from the DTD dataset [13] which contains various real-world, as well as synthetic, textures. Then, fixing both the viewing direction of the camera (to always point at the plane center) and its distance to the plane center, we randomly set the camera elevation angle between $30^{\circ}$ and $60^{\circ}$ , and project the textured plane on the camera imaging plane to obtain an image with its depth map. + +From each image $I$ , we randomly sample two equal-sized regions $A$ and $B$ (with their masks $M_A, M_B$ ), then set label $y$ to 1 if $A$ is closer than $B$ and 0 otherwise. To avoid the region higher up in the image always being farther away, we apply random horizontal and vertical flips, so that the task cannot be solved solely from locations of the regions. An example image is shown in Fig. 2 (f). + +# 4. Evaluation Protocol + +Following previous work [17, 76], we use probing of visual features as our evaluation protocol. Below, we explain how we obtain task-specific input features from visual models, how we probe these features, and how we measure success. An illustrative figure is included in Appendix C.1. + +# 4.1. Task Specific Visual Features + +Given a pre-trained vision model $\phi(\cdot)$ , we assess its understanding of a cue by training a lightweight probe $g_{\theta}$ with parameters $\theta$ on the target task, using the features extracted by $\phi$ . We obtain features $\mathbf{f}$ for each task as described below. + +Occlusion. We extract a feature map $\phi(I)$ from the image $I$ and up-sample it to match the spatial size of the object mask $M_A$ . We mask the feature map and apply spatial pooling: + +$$ +\mathbf {f} = \frac {\sum_ {h , w} M _ {A} \odot \operatorname {u p} (\phi (I))}{\sum_ {h , w} M _ {A}}, \tag {1} +$$ + +where $h, w$ index the height and width of $I$ , $\odot$ is element-wise multiplication, and $\mathrm{up}(\cdot)$ denotes bilinear upsampling. This results in $\mathbf{f} \in \mathbb{R}^D$ where $D$ is the feature dimension and changes depending on the vision model $\phi$ . + +Light-shadow, Size, and Texture-grad. For these tasks, we calculate the difference between the masked average features of objects $A$ and $B$ : + +$$ +\mathbf {f} = \frac {\sum_ {h , w} M _ {A} \odot \operatorname {u p} (\phi (I))}{\sum_ {h , w} M _ {A}} - \frac {\sum_ {h , w} M _ {B} \odot \operatorname {u p} (\phi (I))}{\sum_ {h , w} M _ {B}}. \tag {2} +$$ + +Elevation and Perspective. These tasks are not object/region specific, so we use the entire image feature, i.e., $\mathbf{f} = \phi(I) \in \mathbb{R}^{H_{\mathbf{f}} \times W_{\mathbf{f}} \times D}$ , where $H_{\mathbf{f}}, W_{\mathbf{f}}$ are the height and width of the feature map. + +# 4.2. Probing Features + +For light-shadow, occlusion, size, and texture-grad, where the task-specific features $\mathbf{f}$ are $D$ -dimensional vectors, we implement the probe $g_{\theta}$ as a multi-layer perception (MLP) with two layers and an intermediate GELU activation [32]. Though linear probing has been used commonly for probing large vision models [54], it is not obvious that the solutions to our tasks should be a linear function of the model features. Thus, we use non-linear probes, which empirically outperform linear probes (see Appendix A.2) For elevation and perspective, which require global information, we use an attentive probe [5, 18]. This probe aggregates global features through cross-attention and uses a two-layer MLP for final predictions. We observed via empirical results that the attentive probe achieves better performance than a standard MLP probe on these tasks. + +Training and Optimization. We train the MLP probes for light-shadow, occlusion, size and texture-grad tasks using binary cross-entropy loss, as these tasks involve binary classification. For elevation and perspective, we use mean squared error loss to train the attentive probes, as the tasks are formulated as regression problems. Additional details on the probe optimization are provided in Appendix C.1. + +Following [54, 76], we perform a hyper-parameter search on the layers of model $\phi$ . For each task, we extract features from different layers of $\phi$ which is frozen, and train a probe on these features under the same setting. The best layer is then selected based on the validation performance, and the probing on this layer is repeated five times using different random seeds. We report the mean and standard deviation of the test performance. + +# 4.3. Evaluation Metrics + +For light-shadow, occlusion, size and texture-grad which are binary tasks, we report classification accuracy. For the vanishing point estimation task of the perspective cue, while Euclidean distance (between the predicted and ground-truth + +vanishing points) is a sensible metric, we instead report success rate to align this metric more closely with accuracy. Specifically, if the Euclidean distance of a prediction falls below a pre-defined threshold, it is interpreted as success. For elevation, we convert the horizon detection error [69] to an accuracy-based measure using a similar approach. More details are provided in Appendix C.2. + +# 5. Experiments + +# 5.1. Monocular Depth Cues in Vision Models + +We evaluate 20 pre-trained large vision models [11, 15, 29, 30, 33, 35, 41, 49, 54, 56, 58, 59, 65, 66, 68, 70, 72, 75, 79] spanning diverse pre-training objectives, modalities, and model architectures to assess their understanding of monocular depth perception cues in our DepthCues benchmark. + +Implementation Details. Where possible, we focus on model architectures equivalent to ViT-Base and denote the architecture size (and patch size for transformers) using postfixes, e.g., DINOv2-b14. More details about the models and their architecture are provided in Appendix D. For consistency, we use only patch tokens for all ViT-based models [15], as some do not include a class token. + +Additional Baselines. During the probing of certain cues, we explicitly use mask information to construct the input feature, f. Although these masks are not directly used by the probes, they could theoretically be leveraged to solve tasks. To verify that any additional information from this step is insufficient to solve the task, we designed a trivial baseline in which model features are replaced with simple 2D coordinate maps i.e., $\phi (I)$ in Eqs. (1) and (2) becomes $C\in \mathbb{R}^{H\times W\times 2}$ where $C_{h,w} = [h,w]^T$ . Moreover, for each cue, we include an end-to-end baseline, where we train ResNet18 [29] and ViT-B/16 [15] models from scratch in an end-to-end fashion and select the best. We concatenate the masks with the input images channel-wise, allowing us to assess how much of each task can be solved without relying on sophisticated pre-trained features. Finally, to confirm that the tasks are readily solvable by humans, we evaluate our own performance on a random sample from the test sets, and obtained an accuracy of $95\% \pm 1.48\%$ across tasks. + +Additional Tasks. To extend our analysis, we also evaluate vision models for monocular depth estimation (on NYUv2 [60] and DIW [12]) and image classification (on ImageNet-1k [14]) using a linear probe, a standard approach in previous work [3, 54, 73] for probing these datasets. Following the previous works [6, 12, 17], For NYUv2, we report accuracy as the percentage of pixels where the ratio between predicted and ground-truth depth is less than 1.25. We report top-1 accuracy for ImageNet. More details on these tasks are provided in Appendix A.1, and we show the linear probing results of these models on NYUv2 in Fig. 3. + +![](images/8506f87e3c6f4368397432c811f9ce2838601f06a6b2bc2f719a45c56b305810.jpg) +Figure 3. DepthCues Benchmark Results. We evaluate 20 vision models with diverse pre-training settings (indicated by color) on the DepthCues benchmark, which assesses six different monocular depth cues (each row) ubiquitous to humans. The models are ranked based on their average performance on the six cues. We include an end-to-end trained baseline (blue dotted line) as an oracle and a trivial baseline (red dotted line) to mark floor performance. Additionally, depth estimation linear probing results on NYUv2 are shown on the bottom row. + +Results. The probing results of 20 pre-trained vision models and the additional baselines on our DepthCues benchmark are summarized in Fig. 3, where the models are ranked by average performance over all cues. Moreover, we measured Spearman Ranked-order Correlation between each pair of tasks in DepthCues using the ranks of the models evaluated, and also how they correlate with the depth estimation and image classification performance of models, which is visualized in Fig. 4. We discuss our observations below, and present additional analysis, such as how pretraining data size impacts performance, in Appendix A.1. + +(i) Depth cues emerge in more recent large vision models. Firstly, the specialized depth estimation model, DepthAnythingv2, achieved the highest overall performance on DepthCues, indicating the possibility that it leverages such cues to estimate depth. We also observe the emergence of human-like monocular depth cues in recent large vision models, such as DINOv2 and Stable Diffusion. Notably, newer large vision models demonstrate a stronger grasp of these depth cues, as illustrated in Fig. 1. DINOv2 and Stable Diffusion have proven useful for developing monocular depth estimation models [40, 72]. However, the reasons behind these models' effectiveness for depth inference remain unclear, given the lack of explicit depth supervision during pre-training. Our results provide an insight on the development of depth perception in these models: they develop an awareness of human-like monocular depth cues, which might aid depth inference. +(ii) Depth models do not always have the strongest knowledge of depth cues. While DepthAnythingv2 achieves the best overall performance on DepthCues, another specialized depth estimation model, MiDaS, is outperformed by several models pre-trained without depth supervision, e.g., DeiT, SigLIP, and DINO. These models also exhibit competitive depth estimation performance (under linear probing) to MiDaS. This suggests that other pretraining recipes than dense depth supervision can effectively enhance depth perception, although they may be less data-efficient – for instance, SigLIP is trained on around 10,000 times more data than MiDaS. +(iii) Vision-language models exhibit varying levels of depth cue understanding. CLIP obtains the lowest performance on DepthCues, explaining its limited depth estimation ability as seen in Fig. 3 and in recent work [17]. CLIP's limited understanding of the visual concepts tested in DepthCues may present challenges for downstream tasks that require geometric understanding [82]. In contrast, SigLIP, also trained on matching images to captions but on significantly more data ( $\times 9$ more data than CLIP), has a significantly better grasp of the depth cues. +(iv) Multi-view models are better at the texture-grad task than single-view models. On all depth cues except texture-grad, recent models which are pre-trained with + +![](images/08b33ab5117dea7823b78f908fb579c5186a7a9ff0d3865acdb900f8a9cad2e8.jpg) +Figure 4. Task correlation. We measure the Spearman Ranked-order Correlation between each pair of tasks in DepthCues benchmark, and how they correlate with depth estimation and image classification performance of models. A correlation score of one indicates the same ranking of models for two tasks. + +single-view images showed overall better performance than multi-view ones. However, on texture-grad, all three multiview models (i.e., CroCo, LRM, and DUSt3R) ranked within the top four, outperforming strong SSL competitors such as DINOV2. While the other five cues operate at the scene or object level, texture-grad uniquely requires a more localized, surface-level understanding. Multi-view pre-trained models are often more effective at capturing such details than single-view models because, during pretraining, they are exposed to variations in the same surface across different viewpoints. For instance, CroCo, which achieves the best performance on the texture-grad task, is trained to reconstruct parts of a scene from different viewpoints, requiring attention to finer local details. Moreover, LRM and DUSt3R are pre-trained on 3D object and scene reconstruction tasks, which require understanding correspondences across views by leveraging local surface details. (v) Performance on DepthCues correlates with depth estimation performance. As shown in Fig. 4, all DepthCues tasks exhibit moderate to high levels of correlation with depth estimation, supporting the importance of depth cues for this task. However, all tasks have a low correlation with ImageNet-1k classification. Interestingly, a relatively higher alignment with classification is observed for occlusion and size, which are also highly correlated with each other. This is reasonable as understanding occlusion and size requires object-level semantics (e.g., 'What does the recognized object look like when not occluded?' and 'Is category A larger than category B?'). Apart from texture-grad, each cue has a high correlation ( $>0.75$ ) with at least one other cue. As discussed above, the texture-grad cue requires understanding surface details and provides local + +
ModelNYUv2 Acc. (%)↑DIW WHDR (%)↓
DINOv287.7811.99
DINOv2+DC87.0611.95
concat(DINOv2, noise)87.5612.20
concat(DINOv2, DINOv2+DC)88.4611.72
CLIP43.7835.25
CLIP+DC43.5935.45
concat(CLIP, noise)43.3835.39
concat(CLIP, CLIP+DC)44.3233.53
+ +Table 2. Linear probing on downstream depth estimation. For each model, we probe the patch tokens from the final layer. Models with $+DC$ are fine-tuned using supervision on our DepthCues benchmark. The best results in each subset are bolded. + +ized depth information; perception of this cue is found to be weaker in single-view image models. We note that texture-grad is the only cue that uses synthetic data, which might also contribute to its lower correlation with other cues. + +# 5.2. Learning Depth Cues + +We observed that the depth estimation performance of a model highly correlates with its awareness of human-like monocular depth cues. Here we ask if enhanced depth cue awareness improves depth estimation? To investigate this, we fine-tune single-image pre-trained vision models on the training set of DepthCues in a multi-task manner, then evaluate the fine-tuned model on downstream depth estimation. Here we focus on two models widely adopted for various downstream applications: DINOv2 and CLIP. + +We use low-rank adaptation (LoRA) [34] for efficient fine-tuning of pre-trained models. Further details of multitask learning and LoRA implementation are provided in Appendix C.3. We evaluate the pre-trained and fine-tuned models on NYUv2 [60] and DIW [12] depth datasets using linear probes. We experiment with two different variations: first, we evaluate the features from fine-tuned models (denoted as $+DC$ in Tab. 2); second, we concatenate the features from fine-tuned models with the features from the original pre-trained models. The latter approach was also adopted in [51, 73] to preserve the generalization ability of the pre-trained models. As before, we report accuracy for NYUv2, and use Weighted Human Disagreement Rate (WHDR) to measure performance on DIW. It is noted the dataset for the size cue in DepthCues contains a subset of NYUv2 images (due to the use of SUNRGBD), so evaluation on DIW offers a fairer comparison. + +We observe in Tab. 2 that for both models, fine-tuning on DepthCues resulted in improved depth perception. Notably, the fine-tuned features often need to be concatenated with the original features to bring improvements, a similar observation also made in previous works [51, 73]. A possible explanation for the decreased generalization in the models is due to the limited size and diversity of the fine-tuning data in DepthCues. We also investigate whether the improvements in the concatenated variations come from the + +increased parameters in the probe (due to higher dimensional input), by training linear probes on a combination of original model features and random noise (denoted as concat(·, noise)), which did not result in improvements. + +# 5.3. Discussion + +The results in Sec. 5.1 indicate that recent large vision models understand several human-like monocular depth cues, with performance on these cues correlating with depth estimation performance. This suggests that models may use such cues to infer depth, even without explicit depth supervision. For example, the popular self-supervised model, DINOv2, has developed features that help reason about these cues (except texture-grad), which can support depth estimation. Interestingly, the results in Sec. 5.2 show that DepthCues enables the learning of depth cues, which benefit downstream depth performance in a linear probing setting, even though DepthCues has a moderate size (fewer than 35k training images, much smaller than the large datasets used to pre-train the base models), is not designed specifically for end-to-end fine-tuning, and only provides image-level sparse annotations (as opposed to dense depth maps). This suggests promising directions for enhancing depth estimation from sparse annotations. + +Limitations. Our analysis focuses only on widely used pretrained model weights but not directly on the impact of various pre-training objectives and their training datasets on the emergence of depth cues. While depth from ego-motion and scene motion are also important cues for humans, our focus is primarily on assessing monocular cues learned by large vision models trained on static image collections and not image sequences (except CroCo, LRM, and DUSt3R). + +# 6. Conclusions + +We introduced DepthCues, a benchmark suite for evaluating human-like monocular depth cues in large vision models. Testing 20 diverse models, we found that depth perception cues, similar to those used by humans, emerge across various pre-training objectives, with more recent and larger models demonstrating stronger alignment with human depth perception. Furthermore, our fine-tuning experiments on DepthCues indicate that a model's depth perception can be enhanced by explicitly incorporating human-like depth priors, suggesting promising directions for improving depth performance in future models. We hope DepthCues will serve as a valuable resource for advancing research in depth-aware vision systems, particularly for applications requiring robust 3D spatial understanding from 2D inputs. + +Acknowledgments. Funding was provided by ELIAI (the Edinburgh Laboratory for Integrated Artificial Intelligence) - EPSRC (EP/W002876/1). HB was supported by the EPSRC Visual AI grant EP/T028572/1, and CJ was supported by a gift from Adobe. + +# References + +[1] Dylan Auty and Krystian Mikolajczyk. Monocular depth estimation using cues inspired by biological vision systems. In ICPR, 2022. 3 +[2] Dylan Auty and Krystian Mikolajczyk. 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In CVPR, 2017. 3, 4 \ No newline at end of file diff --git a/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/images.zip b/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..3ad0cb6821f6657c451b354d01eb8a1a26451985 --- /dev/null +++ b/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:aa5d07a1059daa32787cdb986051cd76741cb5d041e67e4116e5eb51c4cf5a45 +size 451424 diff --git a/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/layout.json b/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..2e13da8b3cee8ed9a26057851223bc4a1cea1b6f --- /dev/null +++ b/2025/DepthCues_ Evaluating Monocular Depth Perception in Large Vision Models/layout.json @@ -0,0 +1,8807 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 68, + 103, + 541, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 103, + 541, + 121 + ], + "spans": [ + { + "bbox": [ + 68, + 103, + 541, + 121 + ], + "type": "text", + "content": "DepthCues: Evaluating Monocular Depth Perception in Large Vision Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 143, + 518, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 143, + 518, + 176 + ], + "spans": [ + { + "bbox": [ + 91, + 143, + 518, + 176 + ], + "type": "text", + "content": "Duolikun Danier Mehmet Aygün Changjian Li Hakan Bilen Oisin Mac Aodha University of Edinburgh" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 205, + 178, + 402, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 205, + 178, + 402, + 190 + ], + "spans": [ + { + "bbox": [ + 205, + 178, + 402, + 190 + ], + "type": "text", + "content": "https://danier97.github.io/depthcues" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 217, + 200, + 230 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 217, + 200, + 230 + ], + "spans": [ + { + "bbox": [ + 151, + 217, + 200, + 230 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 244, + 297, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 244, + 297, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 244, + 297, + 495 + ], + "type": "text", + "content": "Large-scale pre-trained vision models are becoming increasingly prevalent, offering expressive and generalizable visual representations that benefit various downstream tasks. Recent studies on the emergent properties of these models have revealed their high-level geometric understanding, in particular in the context of depth perception. However, it remains unclear how depth perception arises in these models without explicit depth supervision provided during pre-training. To investigate this, we examine whether the monocular depth cues, similar to those used by the human visual system, emerge in these models. We introduce a new benchmark, DepthCues, designed to evaluate depth cue understanding, and present findings across 20 diverse and representative pre-trained vision models. Our analysis shows that human-like depth cues emerge in more recent larger models. We also explore enhancing depth perception in large vision models by fine-tuning on DepthCues, and find that even without dense depth supervision, this improves depth estimation. To support further research, our benchmark and evaluation code will be made publicly available for studying depth perception in vision models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 522, + 135, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 522, + 135, + 534 + ], + "spans": [ + { + "bbox": [ + 56, + 522, + 135, + 534 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 544, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 295, + 676 + ], + "type": "text", + "content": "To ensure safe, accurate, and robust interaction with the 3D world, it is important for computer vision models to understand geometric properties from their projections onto 2D images. Of particular significance is the perception of depth from single images, which has been found to benefit various downstream tasks including segmentation [43], object detection [36], and image and video generation [46, 77], among others. Monocular depth estimation models traditionally rely on dense depth supervision, but obtaining high-quality depth ground truth at scale is challenging, unlike the abundance of large 2D image-only datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "Large-scale pre-trained vision models like Stable Diffusion [59] and DINOv2 [54], trained solely on 2D images, have shown strong generalization when fine-tuned on var" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 223, + 552, + 392 + ], + "blocks": [ + { + "bbox": [ + 318, + 223, + 552, + 392 + ], + "lines": [ + { + "bbox": [ + 318, + 223, + 552, + 392 + ], + "spans": [ + { + "bbox": [ + 318, + 223, + 552, + 392 + ], + "type": "image", + "image_path": "536455f60307367e277d7de5b82e90329adcb883a603ba5dd4f389452616c14e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 398, + 555, + 487 + ], + "lines": [ + { + "bbox": [ + 313, + 398, + 555, + 487 + ], + "spans": [ + { + "bbox": [ + 313, + 398, + 555, + 487 + ], + "type": "text", + "content": "Figure 1. Human-like monocular depth cues emerge in large vision models. We present DepthCues, a comprehensive benchmark suite designed to probe the understanding of human monocular depth cues in vision models. We analyse a diverse set of vision models and find that recent self-supervised and geometry estimation models demonstrate a notably stronger grasp of these cues, even in cases where models (e.g., DINOv2) were not explicitly pre-trained on any depth-related tasks." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 498, + 555, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 555, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 555, + 594 + ], + "type": "text", + "content": "ious computer vision tasks, including multi-view [10, 38] and monocular depth estimation [17, 22, 76], even reaching human-level performance in ordering objects by depth [47]. As a result, numerous recent monocular depth estimation approaches [28, 40, 72] leverage these models' depth priors to achieve state-of-the-art performance. This naturally raises an important question: How does depth perception arise in these large vision models?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 714 + ], + "type": "text", + "content": "Studies on the human visual system [9, 39] suggest that humans infer monocular depth using various visual cues such as elevation, light and shadow, occlusion, perspective, size, and texture gradient [7, 44] (see the top part of Fig. 2). Although these visual cues could emerge in large vision models during pre-training, it remains unclear to what extent this is true. Existing benchmarks [4, 17, 22, 47, 76] focus on evaluating the depth estimation performance of large vision models but do not investigate their understanding of the underlying visual cues. To address this gap, we eval" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20049" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": "uate how well the large vision models understand and utilize human-like monocular depth cues. Our goal is to provide insights into current models' depth estimation behavior, enable a more systematic analysis of their strengths and limitations, and indicate areas for improvement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 134, + 295, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 134, + 295, + 337 + ], + "spans": [ + { + "bbox": [ + 56, + 134, + 295, + 337 + ], + "type": "text", + "content": "We introduce a new benchmark named DepthCues consisting of six depth related tasks (see Fig. 2) where each task is designed to test a given models' ability to estimate a visual cue that is ubiquitous to human depth perception. Specifically, lightweight probing models (referred to as the probes hereafter) placed on top of the frozen features of large vision models are trained and tested on the associated dataset for each task. The assumption is that the more effectively the probe can learn to solve a task using the features of a model, the better the model understands the task-specific cue. Under this protocol, we examine 20 vision models pre-trained at scale under various settings, including self-supervised learning (DINOv2 [54]), image generation (StableDiffusion) [59], vision-language supervision (CLIP [56]), single-view reconstruction (LRM [33]), cross-view completion (CroCo [68]), and also a recent general purpose depth estimation model DepthAnything v2 [72]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 339, + 295, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 339, + 295, + 553 + ], + "spans": [ + { + "bbox": [ + 56, + 339, + 295, + 553 + ], + "type": "text", + "content": "Our results reveal the following observations: First, the performance of models on DepthCues is highly correlated with their depth estimation performance, validating the effectiveness of DepthCues for investigating depth perception. Second, more recent self-supervised and geometry estimation models exhibit a stronger understanding of human monocular depth cues (see Fig. 1), with DepthAnythingv2 ranking first, and DINOv2 and StableDiffusion ranking top-five. Third, none of the benchmarked models consistently excel on all six of the depth tasks. Finally, recent single-view pre-trained models are limited in their perception of texture gradient, while multi-view trained models are better at this low-level geometric cue. Additionally, we explore enhancing depth awareness of vision models by injecting depth cue priors, demonstrating that fine-tuning on our DepthCues benchmark results in improved depth estimation, despite the significant sparsity of the supervision compared to dense annotations. Our contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 556, + 295, + 711 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 55, + 556, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 556, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 556, + 295, + 590 + ], + "type": "text", + "content": "- We develop and make available DepthCues, a benchmark suite for evaluating the emergence of human monocular depth cues in large vision models." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 592, + 295, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 592, + 295, + 627 + ], + "spans": [ + { + "bbox": [ + 56, + 592, + 295, + 627 + ], + "type": "text", + "content": "- We evaluate 20 diverse vision models across a range of pre-training settings, and analyze their relative strengths and weaknesses in capturing monocular depth cues." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 628, + 295, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 628, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 56, + 628, + 295, + 662 + ], + "type": "text", + "content": "- We show that human depth perception cues emerge from self-supervised pre-training on single images, with stronger alignment found in more recent, larger models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 664, + 295, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 664, + 295, + 711 + ], + "spans": [ + { + "bbox": [ + 56, + 664, + 295, + 711 + ], + "type": "text", + "content": "- We conduct an exploratory study on enhancing the depth awareness of a model by fine-tuning on DepthCues, showing that explicitly injecting human-like depth priors can improve depth perception." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 400, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 91, + 553, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 305 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 305 + ], + "type": "text", + "content": "Monocular Depth Estimation. Monocular depth estimation is an inherently ill-posed and challenging problem, yet deep learning-based methods have made significant strides in addressing it. Initial progress was driven by supervised methods [6, 16, 19] that were trained on various labeled datasets [23, 52]. Later, self-supervised approaches advanced the field further by leveraging stereo [21, 25] or temporal consistency [26, 27, 80]. More recently, general purpose methods [40, 58, 71, 72] leveraging large vision backbone models pre-trained with self-supervised [54] or generative objectives [59] and then fine-tuned on very largescale supervised depth datasets have been shown to result in strong monocular depth estimation performance. However, it remains unclear how depth perception develops in the pre-trained models without explicit depth supervision during pre-training. In this paper, we try to shed light on the emergence of these monocular depth cues used by the human visual system in large vision models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 307, + 553, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 307, + 553, + 473 + ], + "spans": [ + { + "bbox": [ + 313, + 307, + 553, + 473 + ], + "type": "text", + "content": "Depth Perception in Pre-trained Vision Models. Several recent efforts have begun to analyze the 3D and depth perception abilities of pre-trained large vision models, with a focus on 3D awareness [17], 3D scene understanding [50], depth and height perception [4], and 3D physical understanding [76]. Complementary to these efforts, several studies have attempted to enhance the capabilities of these models by integrating 3D and depth information [3, 45, 73, 78]. Unlike these works, we focus on monocular depth estimation, emphasising evaluating the emergence of monocular cues essential for human depth perception. Some of the cues we study are also explored in a concurrent work [76], however, we focus on depth perception with diverse data and analyze a broader range of vision models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 475, + 553, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 553, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 553, + 653 + ], + "type": "text", + "content": "Recent work [22, 62] has analyzed monocular depth estimation models, examining properties like the backbone architectures, loss functions, and training datasets. However, they do not explore whether or how these models actually utilize monocular cues for depth estimation. In our work, we focus on analyzing the existence of intrinsic depth cues without direct depth supervision across various large vision models. Closely related to our approach, [63] investigates whether predictions of a monocular depth estimation model [58] violate perceptual cues. However, a prediction that violates a perceptual cue does not necessarily indicate the absence of the cue in the model itself. Instead, we directly examine the presence of these cues across multiple models, including, but not limited to, monocular depth models using our newly introduced benchmark suite." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 654, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 712 + ], + "type": "text", + "content": "Comparing Humans to Neural Networks. Human and animal vision systems have long inspired computational vision methods [31, 37, 55]. Many studies have sought to compare biological vision with modern neural network-based computer vision systems across tasks such as ob" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20050" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 139, + 210 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 139, + 210 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 139, + 210 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 139, + 210 + ], + "type": "image", + "image_path": "3e83b1ca219705e4a8761ac72012df0e36be3eadb3c5e0b74e94941fdc9217f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + 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Overview of DepthCues. Monocular depth cues, the associated tasks, and example instances from our proposed benchmark." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 58, + 250, + 293, + 319 + ], + "blocks": [ + { + "bbox": [ + 58, + 250, + 293, + 319 + ], + "lines": [ + { + "bbox": [ + 58, + 250, + 293, + 319 + ], + "spans": [ + { + "bbox": [ + 58, + 250, + 293, + 319 + ], + "type": "table", + "html": "
Depth CueSource#Images#Train#Val#Test
ElevationHLW [69]18,39015,7618281,801
Light-shadowSOBA [67]7984,716862860
OcclusionCOCOA [83]5,57324,40212,90614,862
PerspectiveNaturalScene [81]2,2752,000125150
SizeKITTI [23], SUN [61]2,7171,986330712
Texture-gradDTD [13]6,0004,0001,0001,000
", + "image_path": "40668941fb613c51bafd8f6fa74adc992bb0fa77289337fa5966678fde56a36b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 323, + 294, + 346 + ], + "lines": [ + { + "bbox": [ + 55, + 323, + 294, + 346 + ], + "spans": [ + { + "bbox": [ + 55, + 323, + 294, + 346 + ], + "type": "text", + "content": "Table 1. Summary of the datasets in DepthCues benchmark. We report total image and data statistics across all splits." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 357, + 296, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 357, + 296, + 548 + ], + "spans": [ + { + "bbox": [ + 54, + 357, + 296, + 548 + ], + "type": "text", + "content": "ject recognition [57], shape-bias [24], multi-view consistency [8, 53], visual perspective-taking [47], and perceptual judgments of similarity [20]. In our work, rather than measuring alignment between human and large-scale vision systems, we focus on the emergence of monocular cues that are well-established in the human vision science community [7, 9, 39, 44], i.e., the cues that are crucial for monocular depth estimation in human vision. Recent work has incorporated additional high-level human vision-inspired cues, specifically semantics, object size, and spatial relationships, in an attempt to improve automated monocular depth estimation [1, 2]. These cues, extracted using pre-trained semantic segmentation and language embedding models, are shown to enhance depth prediction accuracy. We hope that our results and analyses will inspire similar approaches and foster new directions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 561, + 257, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 561, + 257, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 561, + 257, + 574 + ], + "type": "text", + "content": "3. DepthCues: Benchmark and Dataset" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 55, + 582, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 713 + ], + "type": "text", + "content": "We introduce DepthCues, a new benchmark to investigate how large-scale pre-trained image models perceive depth by assessing their understanding of a set of monocular depth cues used by humans to perceive depth: elevation, light and shadow, occlusion, perspective, size, and texture gradient [9, 39]. Our benchmark comprises a suite of six tasks with constituent datasets specifically designed to capture the essence of each individual monocular depth cue. For each task, DepthCues provides training and test sets with an evaluation protocol for image models, along with a performance metric to assess how well a given model under" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 252, + 555, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 252, + 555, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 252, + 555, + 372 + ], + "type": "text", + "content": "stands each depth cue. Fig. 2 illustrates the task for each cue, and shows a representative instance from the associated dataset. We summarize the statistics of our datasets in Tab. 1. Next, we describe the construction of each task and the data used. In each case, we adapt existing datasets that have been designed for bespoke vision tasks. We use the original train, validation, and test splits of data sources and keep the classes balanced for binary tasks unless specified. Additional details about dataset construction are provided in Appendix B." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 380, + 381, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 381, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 381, + 392 + ], + "type": "text", + "content": "3.1. Elevation" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 399, + 554, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 554, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 554, + 422 + ], + "type": "text", + "content": "Objects on the ground plane are farther away as they get closer to the horizon." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 422, + 554, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 554, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 554, + 530 + ], + "type": "text", + "content": "Task. The elevation cue relies on perceiving the horizon line, which is defined as the projection of all the points where light rays from the observer's viewpoint are tangent to Earth's surface. Therefore, we adopt the task of horizon line estimation [42, 69]. Note, the horizon line is not always visible, and is different from the skyline, which separates the sky and the entities on the ground. The task is posed as a regression problem where the goal is to estimate the target line, i.e., its slope and y-intercept, in the image." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 531, + 554, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 554, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 554, + 590 + ], + "type": "text", + "content": "Dataset. We adopt the HLW dataset [69], which provides pairs of images and annotations of the horizon lines. To increase the slope variation, we augment the images by rotating them (and the line annotations) randomly between " + }, + { + "bbox": [ + 313, + 531, + 554, + 590 + ], + "type": "inline_equation", + "content": "-30^{\\circ}" + }, + { + "bbox": [ + 313, + 531, + 554, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 531, + 554, + 590 + ], + "type": "inline_equation", + "content": "30^{\\circ}" + }, + { + "bbox": [ + 313, + 531, + 554, + 590 + ], + "type": "text", + "content": ". An example from the dataset is shown in Fig. 2 (a)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 598, + 422, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 598, + 422, + 611 + ], + "spans": [ + { + "bbox": [ + 313, + 598, + 422, + 611 + ], + "type": "text", + "content": "3.2. Light and Shadow" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 617, + 554, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 554, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 554, + 653 + ], + "type": "text", + "content": "The way shadow is cast provides useful cue for orientation and depth of objects. For convenience, we refer to this cue as light-shadow." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 654, + 553, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 677 + ], + "type": "text", + "content": "Task. To capture the understanding of this cue, we propose a task of associating shadows with objects." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Dataset. The SOBA [67] dataset contains images with segmentation masks of objects and their associated shadows. From those, we create a dataset containing tuples of" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20051" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "(I,M_A,M_B,y)" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "M_A" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " is the mask of the object " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " in image " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "M_B" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " is the mask of a shadow " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " in the image. The label " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " is 1 if " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " is associated with " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " , and O otherwise. An example is depicted in Fig. 2 (b)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 128, + 125, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 128, + 125, + 140 + ], + "spans": [ + { + "bbox": [ + 55, + 128, + 125, + 140 + ], + "type": "text", + "content": "3.3.Occlusion" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 146, + 295, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 146, + 295, + 169 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 295, + 169 + ], + "type": "text", + "content": "An object that partially blocks another, from the perspective of the viewer, is perceived as closer." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 171, + 295, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 171, + 295, + 205 + ], + "spans": [ + { + "bbox": [ + 55, + 171, + 295, + 205 + ], + "type": "text", + "content": "Task. To test whether models understand occlusion, we propose the task of identifying whether an object is occluded or not by another object." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "spans": [ + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "text", + "content": "Dataset. We use the COCOA [83] dataset, providing manually annotated segmentation masks for visible and invisible object parts with occlusion rates. From the original annotations, we construct a dataset that contains triplets of image " + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "text", + "content": ", the segmentation mask " + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "inline_equation", + "content": "M_A" + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "text", + "content": " of the visible part of the object " + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "text", + "content": ", and the corresponding label " + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 206, + 296, + 301 + ], + "type": "text", + "content": ", which is 1 if the object is occluded, and 0 otherwise. In the example in Fig. 2 (c), the car highlighted with a red mask is occluded." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 309, + 132, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 309, + 132, + 322 + ], + "spans": [ + { + "bbox": [ + 55, + 309, + 132, + 322 + ], + "type": "text", + "content": "3.4. Perspective" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 328, + 295, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 328, + 295, + 352 + ], + "spans": [ + { + "bbox": [ + 55, + 328, + 295, + 352 + ], + "type": "text", + "content": "Parallel lines converging at infinity offer a strong cue for perceiving depth." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 352, + 295, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 352, + 295, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 352, + 295, + 472 + ], + "type": "text", + "content": "Task. This cue is closely tied to vanishing point [48], which is defined as the point on the image plane where 2D perspective projections of 3D parallel lines intersect. Therefore, we use the task of vanishing point estimation to investigate the understanding of perspective. While there exist different versions of the task that define different numbers of vanishing points [64, 74], we adopt a simplified version that focuses on a single dominant vanishing point. Given an image " + }, + { + "bbox": [ + 55, + 352, + 295, + 472 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 352, + 295, + 472 + ], + "type": "text", + "content": ", the objective is to estimate the " + }, + { + "bbox": [ + 55, + 352, + 295, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = (x,y)" + }, + { + "bbox": [ + 55, + 352, + 295, + 472 + ], + "type": "text", + "content": " coordinates of the vanishing point in the image coordinate system." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 472, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 295, + 544 + ], + "type": "text", + "content": "Dataset. The NaturalScene dataset [81] contains images from diverse outdoor scenes with one manually annotated dominant vanishing point " + }, + { + "bbox": [ + 55, + 472, + 295, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 472, + 295, + 544 + ], + "type": "text", + "content": " in each. We use the original dataset and create validation and test sets by dividing the original validation set. An example is shown in Fig. 2 (d) with the vanishing point indicated by the red dot." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 551, + 97, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 551, + 97, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 551, + 97, + 562 + ], + "type": "text", + "content": "3.5. Size" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 570, + 295, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 617 + ], + "type": "text", + "content": "People infer depth based on known object sizes (in 3D) and their apparent retinal sizes (e.g., an object farther away appears smaller). This cue is particularly effective when comparing objects of similar expected sizes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 617, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 653 + ], + "type": "text", + "content": "Task. Using this cue requires prior knowledge of object sizes. Thus we propose a binary classification task: determining if object " + }, + { + "bbox": [ + 55, + 617, + 295, + 653 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 617, + 295, + 653 + ], + "type": "text", + "content": " is larger than object " + }, + { + "bbox": [ + 55, + 617, + 295, + 653 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 617, + 295, + 653 + ], + "type": "text", + "content": " in 3D." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "text", + "content": "Dataset. We use 3D object detection datasets KITTI [23] and SUN-RGBD [61] which provide 3D bounding boxes of objects in outdoor and indoor scenes respectively. Given an image " + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "text", + "content": ", we sample two objects, " + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 653, + 295, + 713 + ], + "type": "text", + "content": ", and compare their sizes using the volumes of their 3D bounding boxes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": "Object masks " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "M_A" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "M_B" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " in image space are estimated using SAM [41] with bounding box queries and additional filtering to ensure segmentation quality. The final dataset contains tuples " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "(I, M_A, M_B, y)" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": ", where the label " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "y = 1" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " if object " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " is larger, and 0 otherwise. We filtered pairs where the volume difference was under a threshold to reduce errors caused by imprecise labeling. See Fig. 2 (e) for an example." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 163, + 419, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 163, + 419, + 174 + ], + "spans": [ + { + "bbox": [ + 314, + 163, + 419, + 174 + ], + "type": "text", + "content": "3.6. Texture Gradient" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 181, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 181, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 181, + 553, + 228 + ], + "type": "text", + "content": "When a region on a surface is further away from the viewer, its texture appears denser and more compressed, with a higher spatial frequency, compared to the same texture viewed nearby. We denote this cue as texture-grad." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 229, + 553, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 553, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 553, + 276 + ], + "type": "text", + "content": "Task. This cue is especially helpful on textured surfaces. To assess the existence of this cue, we use the task of depth ordering of regions on a textured plane, where the model must infer depth based solely on texture." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 277, + 554, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 554, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 554, + 396 + ], + "type": "text", + "content": "Dataset. To ensure that only the texture gradient cue is used for perceiving depth order, we created a synthetic dataset using Blender. First, we initialized a 3D plane, and applied textures sampled from the DTD dataset [13] which contains various real-world, as well as synthetic, textures. Then, fixing both the viewing direction of the camera (to always point at the plane center) and its distance to the plane center, we randomly set the camera elevation angle between " + }, + { + "bbox": [ + 313, + 277, + 554, + 396 + ], + "type": "inline_equation", + "content": "30^{\\circ}" + }, + { + "bbox": [ + 313, + 277, + 554, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 277, + 554, + 396 + ], + "type": "inline_equation", + "content": "60^{\\circ}" + }, + { + "bbox": [ + 313, + 277, + 554, + 396 + ], + "type": "text", + "content": ", and project the textured plane on the camera imaging plane to obtain an image with its depth map." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "content": "From each image " + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "content": ", we randomly sample two equal-sized regions " + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "content": " (with their masks " + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "inline_equation", + "content": "M_A, M_B" + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "content": "), then set label " + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "content": " to 1 if " + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "content": " is closer than " + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 396, + 554, + 480 + ], + "type": "text", + "content": " and 0 otherwise. To avoid the region higher up in the image always being farther away, we apply random horizontal and vertical flips, so that the task cannot be solved solely from locations of the regions. An example image is shown in Fig. 2 (f)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 314, + 490, + 432, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 490, + 432, + 502 + ], + "spans": [ + { + "bbox": [ + 314, + 490, + 432, + 502 + ], + "type": "text", + "content": "4. Evaluation Protocol" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 510, + 554, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 554, + 570 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 554, + 570 + ], + "type": "text", + "content": "Following previous work [17, 76], we use probing of visual features as our evaluation protocol. Below, we explain how we obtain task-specific input features from visual models, how we probe these features, and how we measure success. An illustrative figure is included in Appendix C.1." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 576, + 473, + 589 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 576, + 473, + 589 + ], + "spans": [ + { + "bbox": [ + 313, + 576, + 473, + 589 + ], + "type": "text", + "content": "4.1. Task Specific Visual Features" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "text", + "content": "Given a pre-trained vision model " + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "text", + "content": ", we assess its understanding of a cue by training a lightweight probe " + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "inline_equation", + "content": "g_{\\theta}" + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "text", + "content": " on the target task, using the features extracted by " + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "text", + "content": ". We obtain features " + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 313, + 594, + 554, + 643 + ], + "type": "text", + "content": " for each task as described below." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "spans": [ + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "type": "text", + "content": "Occlusion. We extract a feature map " + }, + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "type": "inline_equation", + "content": "\\phi(I)" + }, + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "type": "text", + "content": " from the image " + }, + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "type": "text", + "content": " and up-sample it to match the spatial size of the object mask " + }, + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "type": "inline_equation", + "content": "M_A" + }, + { + "bbox": [ + 313, + 643, + 553, + 679 + ], + "type": "text", + "content": ". We mask the feature map and apply spatial pooling:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 375, + 686, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 686, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 375, + 686, + 553, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {f} = \\frac {\\sum_ {h , w} M _ {A} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {A}}, \\tag {1}", + "image_path": "a25d7849586a1d8d301e60d8a5da8a0fe78adb5e5b3865926df37b9ca8bbe9f7.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20052" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "h, w" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " index the height and width of " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " is element-wise multiplication, and " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\mathrm{up}(\\cdot)" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " denotes bilinear upsampling. This results in " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{f} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " is the feature dimension and changes depending on the vision model " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 120, + 295, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 120, + 295, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 120, + 295, + 156 + ], + "type": "text", + "content": "Light-shadow, Size, and Texture-grad. For these tasks, we calculate the difference between the masked average features of objects " + }, + { + "bbox": [ + 55, + 120, + 295, + 156 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 120, + 295, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 120, + 295, + 156 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 120, + 295, + 156 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 164, + 294, + 204 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 164, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 62, + 164, + 294, + 204 + ], + "type": "interline_equation", + "content": "\\mathbf {f} = \\frac {\\sum_ {h , w} M _ {A} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {A}} - \\frac {\\sum_ {h , w} M _ {B} \\odot \\operatorname {u p} (\\phi (I))}{\\sum_ {h , w} M _ {B}}. \\tag {2}", + "image_path": "cbcd303e2f7eb3cbf9d32c1027d2a3792d56c4d9311ec449c55eb5cef78e32fc.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 205, + 295, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 205, + 295, + 253 + ], + "spans": [ + { + "bbox": [ + 55, + 205, + 295, + 253 + ], + "type": "text", + "content": "Elevation and Perspective. These tasks are not object/region specific, so we use the entire image feature, i.e., " + }, + { + "bbox": [ + 55, + 205, + 295, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{f} = \\phi(I) \\in \\mathbb{R}^{H_{\\mathbf{f}} \\times W_{\\mathbf{f}} \\times D}" + }, + { + "bbox": [ + 55, + 205, + 295, + 253 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 205, + 295, + 253 + ], + "type": "inline_equation", + "content": "H_{\\mathbf{f}}, W_{\\mathbf{f}}" + }, + { + "bbox": [ + 55, + 205, + 295, + 253 + ], + "type": "text", + "content": " are the height and width of the feature map." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 261, + 160, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 261, + 160, + 273 + ], + "spans": [ + { + "bbox": [ + 55, + 261, + 160, + 273 + ], + "type": "text", + "content": "4.2. Probing Features" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "spans": [ + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "type": "text", + "content": "For light-shadow, occlusion, size, and texture-grad, where the task-specific features " + }, + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "type": "text", + "content": "-dimensional vectors, we implement the probe " + }, + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "type": "inline_equation", + "content": "g_{\\theta}" + }, + { + "bbox": [ + 55, + 279, + 295, + 458 + ], + "type": "text", + "content": " as a multi-layer perception (MLP) with two layers and an intermediate GELU activation [32]. Though linear probing has been used commonly for probing large vision models [54], it is not obvious that the solutions to our tasks should be a linear function of the model features. Thus, we use non-linear probes, which empirically outperform linear probes (see Appendix A.2) For elevation and perspective, which require global information, we use an attentive probe [5, 18]. This probe aggregates global features through cross-attention and uses a two-layer MLP for final predictions. We observed via empirical results that the attentive probe achieves better performance than a standard MLP probe on these tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 459, + 295, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 295, + 543 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 295, + 543 + ], + "type": "text", + "content": "Training and Optimization. We train the MLP probes for light-shadow, occlusion, size and texture-grad tasks using binary cross-entropy loss, as these tasks involve binary classification. For elevation and perspective, we use mean squared error loss to train the attentive probes, as the tasks are formulated as regression problems. Additional details on the probe optimization are provided in Appendix C.1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 543, + 295, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 543, + 295, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 543, + 295, + 639 + ], + "type": "text", + "content": "Following [54, 76], we perform a hyper-parameter search on the layers of model " + }, + { + "bbox": [ + 55, + 543, + 295, + 639 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 543, + 295, + 639 + ], + "type": "text", + "content": ". For each task, we extract features from different layers of " + }, + { + "bbox": [ + 55, + 543, + 295, + 639 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 543, + 295, + 639 + ], + "type": "text", + "content": " which is frozen, and train a probe on these features under the same setting. The best layer is then selected based on the validation performance, and the probing on this layer is repeated five times using different random seeds. We report the mean and standard deviation of the test performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 647, + 168, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 168, + 658 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 168, + 658 + ], + "type": "text", + "content": "4.3. Evaluation Metrics" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "For light-shadow, occlusion, size and texture-grad which are binary tasks, we report classification accuracy. For the vanishing point estimation task of the perspective cue, while Euclidean distance (between the predicted and ground-truth" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "vanishing points) is a sensible metric, we instead report success rate to align this metric more closely with accuracy. Specifically, if the Euclidean distance of a prediction falls below a pre-defined threshold, it is interpreted as success. For elevation, we convert the horizon detection error [69] to an accuracy-based measure using a similar approach. More details are provided in Appendix C.2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 169, + 395, + 182 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 169, + 395, + 182 + ], + "spans": [ + { + "bbox": [ + 314, + 169, + 395, + 182 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 190, + 527, + 203 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 190, + 527, + 203 + ], + "spans": [ + { + "bbox": [ + 313, + 190, + 527, + 203 + ], + "type": "text", + "content": "5.1. Monocular Depth Cues in Vision Models" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 209, + 553, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 553, + 269 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 553, + 269 + ], + "type": "text", + "content": "We evaluate 20 pre-trained large vision models [11, 15, 29, 30, 33, 35, 41, 49, 54, 56, 58, 59, 65, 66, 68, 70, 72, 75, 79] spanning diverse pre-training objectives, modalities, and model architectures to assess their understanding of monocular depth perception cues in our DepthCues benchmark." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 269, + 553, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 269, + 553, + 353 + ], + "spans": [ + { + "bbox": [ + 313, + 269, + 553, + 353 + ], + "type": "text", + "content": "Implementation Details. Where possible, we focus on model architectures equivalent to ViT-Base and denote the architecture size (and patch size for transformers) using postfixes, e.g., DINOv2-b14. More details about the models and their architecture are provided in Appendix D. For consistency, we use only patch tokens for all ViT-based models [15], as some do not include a class token." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "text", + "content": "Additional Baselines. During the probing of certain cues, we explicitly use mask information to construct the input feature, f. Although these masks are not directly used by the probes, they could theoretically be leveraged to solve tasks. To verify that any additional information from this step is insufficient to solve the task, we designed a trivial baseline in which model features are replaced with simple 2D coordinate maps i.e., " + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "inline_equation", + "content": "\\phi (I)" + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "text", + "content": " in Eqs. (1) and (2) becomes " + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "inline_equation", + "content": "C\\in \\mathbb{R}^{H\\times W\\times 2}" + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "inline_equation", + "content": "C_{h,w} = [h,w]^T" + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "text", + "content": ". Moreover, for each cue, we include an end-to-end baseline, where we train ResNet18 [29] and ViT-B/16 [15] models from scratch in an end-to-end fashion and select the best. We concatenate the masks with the input images channel-wise, allowing us to assess how much of each task can be solved without relying on sophisticated pre-trained features. Finally, to confirm that the tasks are readily solvable by humans, we evaluate our own performance on a random sample from the test sets, and obtained an accuracy of " + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "inline_equation", + "content": "95\\% \\pm 1.48\\%" + }, + { + "bbox": [ + 313, + 354, + 554, + 569 + ], + "type": "text", + "content": " across tasks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "type": "text", + "content": "Additional Tasks. To extend our analysis, we also evaluate vision models for monocular depth estimation (on NYUv2 [60] and DIW [12]) and image classification (on ImageNet-1k [14]) using a linear probe, a standard approach in previous work [3, 54, 73] for probing these datasets. Following the previous works [6, 12, 17], For NYUv2, we report accuracy as the percentage of pixels where the ratio between predicted and ground-truth depth is less than 1.25. We report top-1 accuracy for ImageNet. More details on these tasks are provided in Appendix A.1, and we show the linear probing results of these models on NYUv2 in Fig. 3." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20053" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 76, + 550, + 675 + ], + "blocks": [ + { + "bbox": [ + 61, + 76, + 550, + 675 + ], + "lines": [ + { + "bbox": [ + 61, + 76, + 550, + 675 + ], + "spans": [ + { + "bbox": [ + 61, + 76, + 550, + 675 + ], + "type": "image", + "image_path": "8506f87e3c6f4368397432c811f9ce2838601f06a6b2bc2f719a45c56b305810.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 677, + 555, + 723 + ], + "lines": [ + { + "bbox": [ + 55, + 677, + 555, + 723 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 555, + 723 + ], + "type": "text", + "content": "Figure 3. DepthCues Benchmark Results. We evaluate 20 vision models with diverse pre-training settings (indicated by color) on the DepthCues benchmark, which assesses six different monocular depth cues (each row) ubiquitous to humans. The models are ranked based on their average performance on the six cues. We include an end-to-end trained baseline (blue dotted line) as an oracle and a trivial baseline (red dotted line) to mark floor performance. Additionally, depth estimation linear probing results on NYUv2 are shown on the bottom row." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "20054" + } + ] + } + ], + "index": 2 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": "Results. The probing results of 20 pre-trained vision models and the additional baselines on our DepthCues benchmark are summarized in Fig. 3, where the models are ranked by average performance over all cues. Moreover, we measured Spearman Ranked-order Correlation between each pair of tasks in DepthCues using the ranks of the models evaluated, and also how they correlate with the depth estimation and image classification performance of models, which is visualized in Fig. 4. We discuss our observations below, and present additional analysis, such as how pretraining data size impacts performance, in Appendix A.1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 206, + 298, + 713 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 56, + 206, + 298, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 206, + 298, + 409 + ], + "spans": [ + { + "bbox": [ + 56, + 206, + 298, + 409 + ], + "type": "text", + "content": "(i) Depth cues emerge in more recent large vision models. Firstly, the specialized depth estimation model, DepthAnythingv2, achieved the highest overall performance on DepthCues, indicating the possibility that it leverages such cues to estimate depth. We also observe the emergence of human-like monocular depth cues in recent large vision models, such as DINOv2 and Stable Diffusion. Notably, newer large vision models demonstrate a stronger grasp of these depth cues, as illustrated in Fig. 1. DINOv2 and Stable Diffusion have proven useful for developing monocular depth estimation models [40, 72]. However, the reasons behind these models' effectiveness for depth inference remain unclear, given the lack of explicit depth supervision during pre-training. Our results provide an insight on the development of depth perception in these models: they develop an awareness of human-like monocular depth cues, which might aid depth inference." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 411, + 296, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 296, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 296, + 553 + ], + "type": "text", + "content": "(ii) Depth models do not always have the strongest knowledge of depth cues. While DepthAnythingv2 achieves the best overall performance on DepthCues, another specialized depth estimation model, MiDaS, is outperformed by several models pre-trained without depth supervision, e.g., DeiT, SigLIP, and DINO. These models also exhibit competitive depth estimation performance (under linear probing) to MiDaS. This suggests that other pretraining recipes than dense depth supervision can effectively enhance depth perception, although they may be less data-efficient – for instance, SigLIP is trained on around 10,000 times more data than MiDaS." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "content": "(iii) Vision-language models exhibit varying levels of depth cue understanding. CLIP obtains the lowest performance on DepthCues, explaining its limited depth estimation ability as seen in Fig. 3 and in recent work [17]. CLIP's limited understanding of the visual concepts tested in DepthCues may present challenges for downstream tasks that require geometric understanding [82]. In contrast, SigLIP, also trained on matching images to captions but on significantly more data (" + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "inline_equation", + "content": "\\times 9" + }, + { + "bbox": [ + 55, + 555, + 296, + 675 + ], + "type": "text", + "content": " more data than CLIP), has a significantly better grasp of the depth cues." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "(iv) Multi-view models are better at the texture-grad task than single-view models. On all depth cues except texture-grad, recent models which are pre-trained with" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 319, + 75, + 550, + 262 + ], + "blocks": [ + { + "bbox": [ + 319, + 75, + 550, + 262 + ], + "lines": [ + { + "bbox": [ + 319, + 75, + 550, + 262 + ], + "spans": [ + { + "bbox": [ + 319, + 75, + 550, + 262 + ], + "type": "image", + "image_path": "08b33ab5117dea7823b78f908fb579c5186a7a9ff0d3865acdb900f8a9cad2e8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 268, + 555, + 323 + ], + "lines": [ + { + "bbox": [ + 313, + 268, + 555, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 268, + 555, + 323 + ], + "type": "text", + "content": "Figure 4. Task correlation. We measure the Spearman Ranked-order Correlation between each pair of tasks in DepthCues benchmark, and how they correlate with depth estimation and image classification performance of models. A correlation score of one indicates the same ranking of models for two tasks." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 331, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 556, + 715 + ], + "type": "text", + "content": "single-view images showed overall better performance than multi-view ones. However, on texture-grad, all three multiview models (i.e., CroCo, LRM, and DUSt3R) ranked within the top four, outperforming strong SSL competitors such as DINOV2. While the other five cues operate at the scene or object level, texture-grad uniquely requires a more localized, surface-level understanding. Multi-view pre-trained models are often more effective at capturing such details than single-view models because, during pretraining, they are exposed to variations in the same surface across different viewpoints. For instance, CroCo, which achieves the best performance on the texture-grad task, is trained to reconstruct parts of a scene from different viewpoints, requiring attention to finer local details. Moreover, LRM and DUSt3R are pre-trained on 3D object and scene reconstruction tasks, which require understanding correspondences across views by leveraging local surface details. (v) Performance on DepthCues correlates with depth estimation performance. As shown in Fig. 4, all DepthCues tasks exhibit moderate to high levels of correlation with depth estimation, supporting the importance of depth cues for this task. However, all tasks have a low correlation with ImageNet-1k classification. Interestingly, a relatively higher alignment with classification is observed for occlusion and size, which are also highly correlated with each other. This is reasonable as understanding occlusion and size requires object-level semantics (e.g., 'What does the recognized object look like when not occluded?' and 'Is category A larger than category B?'). Apart from texture-grad, each cue has a high correlation (" + }, + { + "bbox": [ + 313, + 331, + 556, + 715 + ], + "type": "inline_equation", + "content": ">0.75" + }, + { + "bbox": [ + 313, + 331, + 556, + 715 + ], + "type": "text", + "content": ") with at least one other cue. As discussed above, the texture-grad cue requires understanding surface details and provides local" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20055" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 294, + 159 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 294, + 159 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 294, + 159 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 294, + 159 + ], + "type": "table", + "html": "
ModelNYUv2 Acc. (%)↑DIW WHDR (%)↓
DINOv287.7811.99
DINOv2+DC87.0611.95
concat(DINOv2, noise)87.5612.20
concat(DINOv2, DINOv2+DC)88.4611.72
CLIP43.7835.25
CLIP+DC43.5935.45
concat(CLIP, noise)43.3835.39
concat(CLIP, CLIP+DC)44.3233.53
", + "image_path": "1ddd8109324d1459782649b45f8864a0f555518caf6abfbb50bda39ba9305e2f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 163, + 295, + 208 + ], + "lines": [ + { + "bbox": [ + 55, + 163, + 295, + 208 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 295, + 208 + ], + "type": "text", + "content": "Table 2. Linear probing on downstream depth estimation. For each model, we probe the patch tokens from the final layer. Models with " + }, + { + "bbox": [ + 55, + 163, + 295, + 208 + ], + "type": "inline_equation", + "content": "+DC" + }, + { + "bbox": [ + 55, + 163, + 295, + 208 + ], + "type": "text", + "content": " are fine-tuned using supervision on our DepthCues benchmark. The best results in each subset are bolded." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 219, + 296, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 219, + 296, + 268 + ], + "spans": [ + { + "bbox": [ + 55, + 219, + 296, + 268 + ], + "type": "text", + "content": "ized depth information; perception of this cue is found to be weaker in single-view image models. We note that texture-grad is the only cue that uses synthetic data, which might also contribute to its lower correlation with other cues." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 275, + 179, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 275, + 179, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 275, + 179, + 289 + ], + "type": "text", + "content": "5.2. Learning Depth Cues" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 294, + 295, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 294, + 295, + 402 + ], + "spans": [ + { + "bbox": [ + 54, + 294, + 295, + 402 + ], + "type": "text", + "content": "We observed that the depth estimation performance of a model highly correlates with its awareness of human-like monocular depth cues. Here we ask if enhanced depth cue awareness improves depth estimation? To investigate this, we fine-tune single-image pre-trained vision models on the training set of DepthCues in a multi-task manner, then evaluate the fine-tuned model on downstream depth estimation. Here we focus on two models widely adopted for various downstream applications: DINOv2 and CLIP." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 402, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 402, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 402, + 295, + 605 + ], + "type": "text", + "content": "We use low-rank adaptation (LoRA) [34] for efficient fine-tuning of pre-trained models. Further details of multitask learning and LoRA implementation are provided in Appendix C.3. We evaluate the pre-trained and fine-tuned models on NYUv2 [60] and DIW [12] depth datasets using linear probes. We experiment with two different variations: first, we evaluate the features from fine-tuned models (denoted as " + }, + { + "bbox": [ + 55, + 402, + 295, + 605 + ], + "type": "inline_equation", + "content": "+DC" + }, + { + "bbox": [ + 55, + 402, + 295, + 605 + ], + "type": "text", + "content": " in Tab. 2); second, we concatenate the features from fine-tuned models with the features from the original pre-trained models. The latter approach was also adopted in [51, 73] to preserve the generalization ability of the pre-trained models. As before, we report accuracy for NYUv2, and use Weighted Human Disagreement Rate (WHDR) to measure performance on DIW. It is noted the dataset for the size cue in DepthCues contains a subset of NYUv2 images (due to the use of SUNRGBD), so evaluation on DIW offers a fairer comparison." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "content": "We observe in Tab. 2 that for both models, fine-tuning on DepthCues resulted in improved depth perception. Notably, the fine-tuned features often need to be concatenated with the original features to bring improvements, a similar observation also made in previous works [51, 73]. A possible explanation for the decreased generalization in the models is due to the limited size and diversity of the fine-tuning data in DepthCues. We also investigate whether the improvements in the concatenated variations come from the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "increased parameters in the probe (due to higher dimensional input), by training linear probes on a combination of original model features and random noise (denoted as concat(·, noise)), which did not result in improvements." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 126, + 388, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 126, + 388, + 138 + ], + "spans": [ + { + "bbox": [ + 313, + 126, + 388, + 138 + ], + "type": "text", + "content": "5.3. Discussion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 144, + 553, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 553, + 361 + ], + "type": "text", + "content": "The results in Sec. 5.1 indicate that recent large vision models understand several human-like monocular depth cues, with performance on these cues correlating with depth estimation performance. This suggests that models may use such cues to infer depth, even without explicit depth supervision. For example, the popular self-supervised model, DINOv2, has developed features that help reason about these cues (except texture-grad), which can support depth estimation. Interestingly, the results in Sec. 5.2 show that DepthCues enables the learning of depth cues, which benefit downstream depth performance in a linear probing setting, even though DepthCues has a moderate size (fewer than 35k training images, much smaller than the large datasets used to pre-train the base models), is not designed specifically for end-to-end fine-tuning, and only provides image-level sparse annotations (as opposed to dense depth maps). This suggests promising directions for enhancing depth estimation from sparse annotations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 361, + 554, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 554, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 554, + 456 + ], + "type": "text", + "content": "Limitations. Our analysis focuses only on widely used pretrained model weights but not directly on the impact of various pre-training objectives and their training datasets on the emergence of depth cues. While depth from ego-motion and scene motion are also important cues for humans, our focus is primarily on assessing monocular cues learned by large vision models trained on static image collections and not image sequences (except CroCo, LRM, and DUSt3R)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 466, + 392, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 466, + 392, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 466, + 392, + 479 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 486, + 553, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 553, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 553, + 653 + ], + "type": "text", + "content": "We introduced DepthCues, a benchmark suite for evaluating human-like monocular depth cues in large vision models. Testing 20 diverse models, we found that depth perception cues, similar to those used by humans, emerge across various pre-training objectives, with more recent and larger models demonstrating stronger alignment with human depth perception. Furthermore, our fine-tuning experiments on DepthCues indicate that a model's depth perception can be enhanced by explicitly incorporating human-like depth priors, suggesting promising directions for improving depth performance in future models. We hope DepthCues will serve as a valuable resource for advancing research in depth-aware vision systems, particularly for applications requiring robust 3D spatial understanding from 2D inputs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 654, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 714 + ], + "type": "text", + "content": "Acknowledgments. Funding was provided by ELIAI (the Edinburgh Laboratory for Integrated Artificial Intelligence) - EPSRC (EP/W002876/1). HB was supported by the EPSRC Visual AI grant EP/T028572/1, and CJ was supported by a gift from Adobe." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20056" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "type": "text", + "content": "[1] Dylan Auty and Krystian Mikolajczyk. 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DepthSplat enables cross-task interactions between Gaussian splatting and depth. Left: Better depth leads to improved Gaussian splatting reconstruction. Right: Unsupervised depth pre-training with Gaussian splatting leads to reduced depth prediction error." + ], + "image_footnote": [], + "bbox": [ + 96, + 284, + 493, + 460 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ecffa3f78856e2b9a04eb03840e571e9359c85a7054991dd25906c7c2d88464d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 498, + 284, + 633, + 417 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/19be01ccce055d534016650cd5979db4890b22f4da7670c6e5b58964ad3f5fc6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 285, + 903, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 513, + 326, + 529 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gaussian splatting and single-view depth estimation are typically studied in isolation. In this paper, we present DepthSplat to connect Gaussian splatting and depth estimation and study their interactions. More specifically, we first contribute a robust multi-view depth model by leveraging pretrained monocular depth features, leading to high-quality feed-forward 3D Gaussian splatting reconstructions. We also show that Gaussian splatting can serve as an unsupervised pre-training objective for learning powerful depth models from large-scale multi-view posed datasets. We validate the synergy between Gaussian splatting and depth estimation through extensive ablation and cross-task transfer experiments. Our DepthSplat achieves state-of-the-art performance on ScanNet, RealEstate10K and DL3DV datasets in terms of both depth estimation and novel view synthesis, demonstrating the mutual benefits of connecting both tasks. In addition, DepthSplat enables feed-forward reconstruction from 12 input views (512 × 960 resolutions) in 0.6 seconds.", + "bbox": [ + 86, + 544, + 485, + 818 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 844, + 220, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Novel view synthesis [4, 82] and depth prediction [20, 44] are two fundamental tasks in computer vision, serving as the", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "driving force behind numerous applications ranging from augmented reality to robotics and autonomous driving. There have been notable advancements in both areas recently.", + "bbox": [ + 511, + 513, + 906, + 559 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "For novel view synthesis, 3D Gaussian Splatting (3DGS) [29] has emerged as a popular technique due to its impressive real-time performance while attaining high visual fidelity. Recently, advances in feed-forward 3DGS models [7, 9, 48] have been introduced to alleviate the need for tedious per-scene optimization, also enabling few-view 3D reconstruction. The state-of-the-art sparse-view method MVSplat [9] relies on feature matching-based multi-view depth estimation [65] to localize the 3D Gaussian positions, which makes it suffer from similar limitations (e.g., occlusions, texture-less regions, and reflective surfaces) as other multi-view depth methods [18, 25, 44, 56, 71].", + "bbox": [ + 509, + 561, + 908, + 743 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "On the other hand, significant progress has been made in monocular depth estimation, with recent models [19, 22, 28, 40, 69, 74] achieving robust predictions on diverse in-the-wild data. However, these depths typically lack consistent scales across multiple views, constraining their performance in downstream tasks like 3D reconstruction [59, 73].", + "bbox": [ + 511, + 746, + 908, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The integration of 3DGS with single-view depth estimation presents a compelling solution to overcome the individual limitations of each technique while at the same time enhancing their strengths. To this end, we introduce", + "bbox": [ + 511, + 839, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16453", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "DepthSplat, which exploits the complementary nature of sparse-view feed-forward 3DGS and robust monocular depth estimation to improve the performance for both tasks.", + "bbox": [ + 89, + 90, + 482, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we first contribute a robust multi-view depth model by integrating pre-trained monocular depth features [70] to the multi-view feature matching branch, which not only maintains the consistency of multi-view depth models but also leads to more robust results in situations that are hard to match (e.g., occlusions, texture-less regions and reflective surfaces). The predicted multi-view depth maps are then unprojected to 3D as the Gaussian centers, and we use an additional lightweight network to predict other remaining Gaussian parameters. They are combined together to achieve novel view synthesis with the splatting operation [29].", + "bbox": [ + 88, + 136, + 482, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While previous methods [1, 11, 31] also try to fuse monocular and multi-view depths, they usually rely on sophisticated architectures. In contrast, we identify the power of off-the-shelf pre-trained monocular depth models and propose to augment multi-view cost volumes with monocular features, leading to a simpler model and stronger performance.", + "bbox": [ + 89, + 301, + 482, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Thanks to our improved multi-view depth model, the quality of novel view synthesis with Gaussian splatting is also significantly enhanced (see Fig. 1 left). In addition, our Gaussian splatting module is fully differentiable, which requires only photometric supervision to optimize all model components. This provides a new, unsupervised way to pre-train depth prediction models on large-scale multi-view posed datasets without requiring ground truth geometry information. The pre-trained depth model can be further fine-tuned for specific depth tasks and achieves superior results over training from scratch (see Fig. 1 right, where unsupervised pre-training leads to improved performance).", + "bbox": [ + 91, + 393, + 482, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct extensive experiments on the large-scale TartanAir [58], ScanNet [14] and RealEstate10K [82] datasets for depth estimation and Gaussian splatting tasks, as well as the recently introduced DL3DV [32] dataset, which features complex real-world scenes and thus is more challenging. Under various evaluation settings, our DepthSplat achieves state-of-the-art results. We also achieve promising feedforward reconstruction results of large-scale or 360 scenes from 12 input views ( $512 \\times 960$ resolutions) in 0.6 seconds. The strong performance on both tasks demonstrates the mutual benefits of connecting Gaussian splatting and depth.", + "bbox": [ + 89, + 574, + 482, + 741 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 751, + 232, + 767 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-View Depth Estimation. As a core component of classical multi-view stereo pipelines [44], multi-view depth estimation exploits multi-view photometric consistency across multiple images to perform feature matching and predict the depth map of the reference image. In recent years, many learning-based methods [6, 15, 18, 25, 56, 57, 71] have been proposed to improve depth accuracy. Though these learning-based methods significantly improve the depth qual", + "bbox": [ + 89, + 779, + 482, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ity compared to traditional methods [23, 44, 67], they cannot handle challenging situations where the multi-view photometric consistency assumption is not guaranteed, e.g., occlusions, low-textured areas, and non-Lambertian surfaces.", + "bbox": [ + 511, + 90, + 906, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Monocular Depth Estimation. Recently, we have witnessed significant progress in depth estimation from a single image [2, 28, 40, 69, 74], and existing methods can produce surprisingly accurate results on diverse in-the-wild data. However, monocular depth methods inherently suffer from scale ambiguities, which makes it challenging to use them for downstream tasks like 3D reconstruction [73]. In this paper, we leverage the powerful features from a pre-trained monocular depth model [70] to augment feature-matching based multi-view depth estimation, which not only maintains the multi-view consistency but also leads to significantly improved robustness in challenging situations such as low-textured regions and reflective surfaces.", + "bbox": [ + 511, + 154, + 908, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Feed-Forward Gaussian Splatting. Several feed-forward 3D Gaussian splatting models [7-10, 48, 51, 62, 68, 77] have been proposed in literature thanks to its efficiency and ability to handle sparse views. In particular, pixelSplat [7] and Splatter Image [48] predict 3D Gaussians from image features, while MVSplat [9] encodes the feature matching information with cost volumes and achieves better geometry. However, it inherently suffers from the limitation of feature matching in challenging situations like texture-less regions and reflective surfaces. In this paper, we propose to integrate monocular features from pre-trained monocular depth models [70] for more robust depth prediction and 3D Gaussian reconstruction. Another line of work like LGM [51], GRM [68], and GS-LRM [77] relies significantly on the training data and compute, discarding explicit feature matching cues and learning priors purely from data. This makes them expensive to train (e.g., GS-LRM [77] is trained with 64 A100 GPUs for 2 days), while our model can be trained in 2 days with 4 GPUs. Moreover, our Gaussian splatting module enables pre-training depth model from large-scale multi-view posed datasets without ground truth depth supervision.", + "bbox": [ + 511, + 353, + 908, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Depth and Gaussian Splatting. Flash3D [49] explores a pre-trained monocular depth model [39] for single-image 3D Gaussian reconstruction. In contrast, we target large-scale scene reconstruction from multiple views. TranSplat [76] leverages monocular depth to improve Gaussian reconstruction. However, a crucial difference is that TranSplat uses monocular features to refine the coarse depth predicted from a cost volume, which makes it inherently vulnerable to the error in the coarse stage and, thus, suffers from the error propagation issue. In contrast, we avoid this by combining cost volume and monocular features early, which performs significantly better than TranSplat (Tab. 6). Another line of work [12, 53] applies an additional depth loss to the Gaussian optimization process. We note that these two approaches (feed-forward vs. per-scene optimization) are orthogonal.", + "bbox": [ + 511, + 674, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16454", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7b20ba694cdf6e70fc3b5782f4f7e4ff58219cfddfd7c4b9fc91f73c4845c951.jpg", + "image_caption": [ + "Figure 2. DepthSplat connects depth estimation and 3D Gaussian splatting with a shared architecture, which enables cross-task transfer. In particular, DepthSplat consists of a multi-view branch to model feature-matching information and a single-view branch to extract monocular features. The per-view cost volumes and monocular features are concatenated for depth regression with a 2D U-Net architecture. For the depth estimation task, we train the depth model with ground truth depth supervision. For the Gaussian splatting task, we first unproject all depth maps to 3D as the Gaussian centers, and in parallel, we use an additional head to predict the remaining Gaussian parameters. Novel views are rendered with the splatting operation. The full model for novel view synthesis is trained with the photometric rendering loss, which can also be used as an unsupervised pre-training stage for the depth model." + ], + "image_footnote": [], + "bbox": [ + 135, + 87, + 869, + 265 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. DepthSplat", + "text_level": 1, + "bbox": [ + 89, + 386, + 210, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given $N$ input images $\\{\\pmb{I}^i\\}_{i=1}^N$ , $(\\pmb{I}^i \\in \\mathbb{R}^{H \\times W \\times 3}$ , where $H$ and $W$ are the image sizes) with corresponding projection matrices $\\{\\mathbf{P}_i\\}_{i=1}^N$ , $(\\mathbf{P}_i \\in \\mathbb{R}^{3 \\times 4}$ , computed from the intrinsic and extrinsic matrices), our goal is to predict dense per-pixel depth $\\mathbf{D}_i \\in \\mathbb{R}^{H \\times W}$ and per-pixel Gaussian parameters $\\{(\\pmb{\\mu}_j, \\alpha_j, \\pmb{\\Sigma}_j, c_j)\\}_{j=1}^{H \\times W \\times N}$ for each image, where $\\pmb{\\mu}_j, \\alpha_j, \\pmb{\\Sigma}_j$ and $c_j$ are the 3D Gaussian's position, opacity, covariance, and color. As shown in Fig. 2, key to our method is a multi-view depth model augmented with monocular depth features, where we obtain the position $\\pmb{\\mu}_j$ of each Gaussian by unprojecting depth with camera parameters, and other Gaussian parameters are predicted by an additional head.", + "bbox": [ + 89, + 410, + 483, + 593 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "More specifically, our depth model consists of two branches: one for modeling feature matching using cost volumes, and another for extracting monocular features from a pre-trained monocular depth network. The cost volumes and monocular features are concatenated together for subsequent depth regression with a 2D U-Net and a softmax layer. For the depth task, we train our depth model with ground truth depth supervision. Our full model for novel view synthesis is trained with the rendering loss, which can also be used as an unsupervised pre-training stage for the depth model. We introduce the individual components below.", + "bbox": [ + 89, + 594, + 483, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Multi-View Feature Matching", + "text_level": 1, + "bbox": [ + 89, + 768, + 357, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this branch, we extract multi-view features with a multiview Transformer architecture and then build multiple cost volumes that correspond to each input view.", + "bbox": [ + 89, + 792, + 483, + 837 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-View Feature Extraction. For $N$ input images, we first use a lightweight weight-sharing ResNet [27] architecture to get $s \\times$ downsampled features for each image independently. To handle different image resolutions, we", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "make the downsampling factor $s$ flexible by controlling the number of stride-2 $3 \\times 3$ convolutions. For example, the downsampling factor $s$ is 4 if two stride-2 convolutions are used and 8 if three are used. To exchange information across different views, we use a multi-view Swin Transformer [34, 64, 65] which contains six stacked self- and cross-attention layers to obtain multi-view-aware features $\\{F_i\\}_{i=1}^N$ , $F^i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C}$ , where $C$ is the feature dimension. When more than two images ( $N > 2$ ) are given as input, we perform cross-attention between each reference view and its top-2 nearest neighboring views, which are selected based on their camera distances to the reference view. This makes computation tractable with many input views.", + "bbox": [ + 511, + 388, + 908, + 584 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature Matching. We encode the feature matching information across different views with the plane-sweep stereo approach [13, 65]. More specifically, for each view $i$ , we first uniformly sample $D$ depth candidates $\\{d_m\\}_{m=1}^D$ from the near and far depth ranges and then warp the feature $F^j$ of view $j$ to view $i$ with the camera projection matrix and each depth candidate $d_m$ . Then we obtain $D$ warped features $\\{F_{d_m}^{j \\rightarrow i}\\}_{m=1}^D$ that correspond to feature $F^i$ . We then measure their feature correlations with the dot-product operation [9, 63]. The cost volume $C_i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times D}$ for image $i$ is obtained by stacking all correlations. Accordingly, we obtain cost volumes $\\{C_i\\}_{i=1}^N$ for all input images $\\{I_i\\}_{i=1}^N$ . For more than two input views, similar to the strategy in cross-view attention computation, we select the top-2 nearest views for each reference view and compute feature correlations with only the selected views. This enables our cost volume construction to achieve a good speed-accuracy trade-off and scale efficiently to a larger number of input views. The correlation values for the two selected views are combined with averaging.", + "bbox": [ + 511, + 598, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16455", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Monocular Depth Feature Extraction", + "text_level": 1, + "bbox": [ + 89, + 90, + 413, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Despite the remarkable progress in multi-view feature matching-based depth estimation [57, 65, 71] and Gaussian splatting [9], they inherently suffer from limitations in challenging situations like occlusions, texture-less regions, and reflective surfaces. Thus, we propose to integrate pre-trained monocular depth features into the cost volume to handle scenarios that are challenging or impossible to match.", + "bbox": [ + 89, + 116, + 483, + 223 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More specifically, we leverage the pre-trained monocular depth backbone from the recent Depth Anything V2 [70] model thanks to its impressive performance on diverse in-the-wild data. The monocular backbone is a ViT [16, 37] model, which has a patch size of 14 and outputs a feature map that is $1/14$ spatial resolution of the original image. We simply bilinearly interpolate the spatial resolution of the monocular features to the same resolution as the cost volume in Sec. 3.1 and obtain the monocular feature $\\mathbf{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}}$ for input image $\\mathbf{I}_i$ , where $C_{\\mathrm{mono}}$ is the dimension of the monocular feature. This process is performed for all input images in parallel and we obtain monocular features $\\{\\mathbf{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}}\\}_{i=1}^{N}$ , which are subsequently used for per-view depth map estimations.", + "bbox": [ + 89, + 226, + 483, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Feature Fusion and Depth Regression", + "text_level": 1, + "bbox": [ + 89, + 460, + 415, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve robust and multi-view consistent depth predictions, we combine the monocular feature $\\pmb{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}}$ and cost volume $C_i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times D}$ via simple concatenation in the channel dimension. A subsequent 2D U-Net [42, 43] is used to regress depth from the concatenated monocular features and cost volumes. This process is performed for all the input images in parallel and for each image, it outputs a tensor of shape $\\frac{H}{s} \\times \\frac{W}{s} \\times D$ , where $D$ is the number of depth candidates. We normalize the $D$ dimension with the softmax operation and perform a weighted average of all depth candidates to obtain the depth output.", + "bbox": [ + 89, + 487, + 483, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also apply a hierarchical matching [25] architecture where an additional refinement step at $2 \\times$ higher feature resolution is employed to improve the performance further. More specifically, based on the coarse depth prediction, we perform a correspondence search on the $2 \\times$ higher feature maps within the neighbors of the $2 \\times$ upsampled coarse depth prediction. Since we already have a coarse depth prediction, we only need to search a smaller range at the higher resolution, and thus, we construct a smaller cost volume compared to the coarse stage. Such a 2-scale hierarchical architecture not only leads to improved efficiency since most computation is spent on low resolution, but also leads to better results thanks to the use of higher-resolution features [25]. Similar feature fusion and depth regression procedure is used to get higher-resolution depth predictions, which are subsequently upsampled with a DPT head [41] to the full resolution.", + "bbox": [ + 89, + 659, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Gaussian Parameter Prediction", + "text_level": 1, + "bbox": [ + 513, + 90, + 790, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the task of 3D Gaussian splatting, we directly unproject the per-pixel depth maps to 3D with the camera parameters as the Gaussian centers $\\pmb{\\mu}_j$ . To predict other remaining Gaussian parameters $\\alpha_{j}$ (opacity), $\\Sigma_{j}$ (covariance) and $c_{j}$ (color), we use an additional DPT head [41], where it takes the concatenated image, depth and feature information as input and outputs all the remaining Gaussian parameters. With all the predicted 3D Gaussians, we can render novel views with the Gaussian splatting operation [29].", + "bbox": [ + 511, + 112, + 906, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Training Loss", + "text_level": 1, + "bbox": [ + 511, + 260, + 656, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We study the properties of our proposed model on two tasks: depth estimation and novel view synthesis with 3D Gaussian splatting [29]. The loss functions are introduced below.", + "bbox": [ + 511, + 282, + 906, + 328 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Depth estimation. We train our depth model (without the Gaussian splatting head) with $\\ell_1$ loss and gradient loss between the inverse depths of prediction and ground truth:", + "bbox": [ + 511, + 332, + 906, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\text {d e p t h}} = \\alpha \\cdot | \\boldsymbol {D} _ {\\text {p r e d}} - \\boldsymbol {D} _ {\\text {g t}} | + \\beta \\cdot | \\partial_ {x} \\boldsymbol {D} _ {\\text {p r e d}} - \\partial_ {x} \\boldsymbol {D} _ {\\text {g t}} | \\\\ + \\beta \\cdot \\left| \\partial_ {y} \\boldsymbol {D} _ {\\text {p r e d}} - \\partial_ {y} \\boldsymbol {D} _ {\\mathrm {g t}} \\right|), \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 390, + 906, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\partial_x$ and $\\partial_y$ denotes the gradients on the $x$ and $y$ directions, respectively. Following UniMatch [65], we use $\\alpha = 20$ and $\\beta = 20$ .", + "bbox": [ + 511, + 439, + 906, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "View synthesis. We train our full model with a combination of mean squared error (MSE) and LPIPS [78] losses between rendered and ground truth image colors:", + "bbox": [ + 511, + 487, + 905, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {g s}} = \\sum_ {m = 1} ^ {M} \\left(\\operatorname {M S E} \\left(I _ {\\text {r e n d e r}} ^ {m}, I _ {\\mathrm {g t}} ^ {m}\\right) + \\lambda \\cdot \\operatorname {L P I P S} \\left(I _ {\\text {r e n d e r}} ^ {m}, I _ {\\mathrm {g t}} ^ {m}\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 546, + 908, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M$ is the number of novel views to render in a single forward pass. The LPIPS loss weight $\\lambda$ is set to 0.05 [9].", + "bbox": [ + 511, + 599, + 905, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 645, + 643, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Implementation Details. We implement our method in PyTorch [38] and optimize our model with the AdamW [36] optimizer and cosine learning rate schedule. We adopt the xFormers [30] library for our monocular ViT backbone implementation. We use a lower learning rate $2 \\times 10^{-6}$ for the pre-trained Depth Anything V2 [70] backbone, and other remaining layers use a learning rate of $2 \\times 10^{-4}$ . The feature downsampling factor $s$ in our multi-view branch (Sec. 3.1) is chosen based on the image resolution. More specifically, for experiments on the $256 \\times 256$ resolution RealEstate10K [82] dataset, we choose $s = 4$ . For higher resolution datasets (e.g., TartanAir [58], ScanNet [14], KITTI [24] and DL3DV [32]), we choose $s = 8$ . Our hierarchical matching models in Sec. 3.3 use 2-scale features, i.e., $1/8$ and $1/4$ , or $1/4$ and $1/2$ resolutions.", + "bbox": [ + 511, + 674, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16456", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/18c3341dacda733a2db320f7e851f6945e5d3488b3333e552e722a5c68dcdf8b.jpg", + "table_caption": [ + "Table 1. DepthSplat model variants. We evaluate different monocular backbones and different multi-view models (1-scale and 2-scale features for hierarchical matching as described in Sec. 3.3), where both larger monocular backbones and 2-scale hierarchical models lead to consistently improved performance for both depth and view synthesis tasks. The inference time is measured on a single A100 GPU for two input views at $256 \\times 256$ resolutions." + ], + "table_footnote": [], + "table_body": "
MonoMulti-ViewDepth (TartanAir)3DGS (RealEstate10K)Param (M)Time (s)
Abs Rel ↓δ1 ↑PSNR ↑SSIM ↑LPIPS ↓
ViT-S1-scale8.4693.0226.840.8780.122380.050
ViT-B1-scale6.9494.4627.060.8820.1191150.053
ViT-L1-scale6.0795.5227.230.8850.1163470.061
ViT-S2-scale7.0194.5627.120.8840.119410.062
ViT-B2-scale6.2295.3127.340.8870.1161200.070
ViT-L2-scale5.5796.0727.470.8890.1143540.079
", + "bbox": [ + 89, + 189, + 480, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Details. For depth experiments on ScanNet [14], we train our depth model on $4 \\times$ GH200 GPUs for 100K iterations with a total batch size of 32. For the ablation experiments on depth task, we mainly use synthetic datasets (TartanAir [58] and VKITTI2 [5]) for training since they provide high-quality ground truth depths. For Gaussian splatting experiments, we consider both low-resolution and high-resolution images. In particular, for comparisons with previous methods [7, 9], we mainly use $256 \\times 256$ resolution RealEstate10K [82] and $256 \\times 448$ resolution DL3DV [32] datasets. We also report high-resolution $(512 \\times 960)$ results on RealEstate10K and DL3DV datasets for qualitative evaluations. For experiments on the $256 \\times 256$ RealEstate10K dataset, we train our model on $4 \\times$ GH200 GPUs for 150K iterations with a total batch size of 32, which takes 1 day for the small model and 2 days for the large model. For experiments on the $256 \\times 448$ DL3DV [32] dataset, we fine-tune our RealEstate10K pre-trained model on $4 \\times$ GH200 GPUs for 100K iterations with a total batch size of 4, where the number of input views is randomly sampled from 2 to 6. We evaluate the model's performance on different number of input views (2, 4, 6). For high-resolution results, we fine-tune our low-resolution pre-trained models on high-resolution images. More training details are provided in the appendix. Our code and training scripts are available at github.com/cvg/deepsplat to ease reproducibility.", + "bbox": [ + 91, + 325, + 483, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Model Variants", + "text_level": 1, + "bbox": [ + 89, + 727, + 246, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first study several different model variants for both depth estimation and view synthesis tasks. In particular, we explore different monocular backbones [70] (ViT-S, ViT-B, ViT-L) and different multi-view models (1-scale and 2-scale). We conduct depth experiments on the large-scale TartanAir [58] synthetic dataset, which features both indoor and outdoor scenes and has perfect ground truth depth. The Gaussian splatting experiments are conducted on the standard RealEstate10K [82] dataset. Following community standards, we report the depth evaluation metrics [20] of", + "bbox": [ + 89, + 750, + 485, + 901 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b01ed7c06a80b67e697754d290c69dfb8f8f763bd3cb48c33634709fa8076b4a.jpg", + "table_caption": [ + "Table 2. Ablations. We evaluate the contribution of the monocular feature branch and the cost volume branch (1st group of experiments), as well as different monocular features (2nd group of experiments). Our results indicate that the monocular feature and cost volume are complementary, with large performance drops when removing either one. The pre-trained Depth Anything V2 model weights achieve the best view synthesis results." + ], + "table_footnote": [], + "table_body": "
ComponentsDepth (TartanAir)3DGS (RealEstate10K)
Abs Rel ↓δ1 ↑PSNR ↑SSIM ↑LPIPS ↓
Full8.4693.0226.840.8780.122
w/o mono feature12.2588.0026.040.8640.134
w/o cost volume11.3490.0223.240.7660.184
ConvNeXt-T10.5091.1326.110.8650.134
Midas9.5391.6126.460.8720.128
DINO V28.9392.4926.760.8770.123
Depth Anything V18.3893.2326.760.8770.124
Depth Anything V28.4693.0226.840.8780.122
", + "bbox": [ + 516, + 191, + 903, + 342 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Abs Rel (relative $\\ell_1$ error) and $\\delta_{1}$ (percentage of correctly estimated pixels within a threshold) and novel view synthesis metrics [29] of PSNR, SSIM, and LPIPS. The results in Tab. 1 demonstrate that both larger monocular backbones and 2-scale hierarchical models lead to consistently improved performance for both tasks. We name three different model sizes with \"Small\": \"ViT-S monocular, 1-scale multi-view\", \"Base\": \"ViT-B monocular, 2-scale multi-view\", and \"Large\": \"ViT-L monocular, 2-scale multi-view\".", + "bbox": [ + 511, + 362, + 908, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "From Tab. 1, we can also observe that better depth network architecture leads to improved view synthesis. In the appendix, we conduct additional experiments to study the effect of different initializations for the depth network to the view synthesis performance. Our results show that a better depth model initialization also contributes to improved rendering quality. In summary, both better depth network architecture and better depth model initialization lead to improved novel view synthesis results.", + "bbox": [ + 511, + 500, + 908, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Ablation and Analysis", + "text_level": 1, + "bbox": [ + 511, + 648, + 720, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we study the properties of our key components on the TartanAir dataset (for depth) and RealEstate10K dataset (for view synthesis with Gaussian splatting).", + "bbox": [ + 511, + 671, + 906, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Monocular Features for Depth and Gaussian Splatting. In Tab. 2, we compare our full model (Full) with the model variant where the monocular depth feature branch (with a ViT-S model pre-trained by Depth Anything V2 [70]) is removed (w/o mono feature), leaving only the multi-view branch. We can observe a clear performance drop for both depth and view synthesis tasks. In Fig. 3, we visualize the depth predictions and error maps of both models on the ScanNet dataset. The pure multi-view feature matching-based approach struggles a lot at texture-less regions and reflective surfaces. At the same time, our full model achieves reliable results thanks to the powerful prior captured in monocular", + "bbox": [ + 511, + 719, + 908, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16457", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/12d56b8927c8a335e2db48feaebcbe9ecf40ba77e49ede0fe43f357427c223a9.jpg", + "image_caption": [ + "Image 1" + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 225, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dff632b6de3821e7a046d76e406984b149be22862378f248bd991e2f118422d2.jpg", + "image_caption": [ + "Depth (w/o mono feature)" + ], + "image_footnote": [], + "bbox": [ + 227, + 88, + 362, + 165 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/67e00739ecf694e4e180fe1973272330ec6b62d4e59f272bd3e1048da9d877b0.jpg", + "image_caption": [ + "Error (w/o mono feature)" + ], + "image_footnote": [], + "bbox": [ + 364, + 88, + 496, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a79285763d2939c77ce236a7acd9381676287caa9224a7bf3044c3e8c4ae7cf1.jpg", + "image_caption": [ + "Image 1" + ], + "image_footnote": [], + "bbox": [ + 500, + 88, + 633, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/073b55e6a4e835018bcb466a13cd155eee9ed576e4b3d0b6e64666f4ecec420a.jpg", + "image_caption": [ + "Depth (w/o mono feature)" + ], + "image_footnote": [], + "bbox": [ + 635, + 88, + 769, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/147317fd5799aa61e49a3714c4e1df234935f624fbe820822c951b4ad7483339.jpg", + "image_caption": [ + "Error (w/o mono feature)" + ], + "image_footnote": [], + "bbox": [ + 771, + 88, + 903, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/72cc76c0970e9e92133fedda75b207d5b64e1b08cbedb6369e9f61dfd4088157.jpg", + "image_caption": [ + "Image 2" + ], + "image_footnote": [], + "bbox": [ + 91, + 179, + 225, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4b3a4b278fa8a294d4a751e982ec0cf8d18fe8ce73c035d96cc7e68cb7a26878.jpg", + "image_caption": [ + "Depth (w/ mono feature)" + ], + "image_footnote": [], + "bbox": [ + 227, + 180, + 362, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0669fca24201a8b2554aa690ff980b3b91e860472e5ad30c95cd4129947fae41.jpg", + "image_caption": [ + "Error (w/ mono feature)" + ], + "image_footnote": [], + "bbox": [ + 364, + 180, + 496, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a41149169555bdb61738202243723fae3971695a2df7d62f7e07aa656ef1b1e2.jpg", + "image_caption": [ + "Image 2" + ], + "image_footnote": [], + "bbox": [ + 500, + 180, + 633, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3303663fbb1e501328a389c180f813cca297b64b7b5e001630045cac3c90edf0.jpg", + "image_caption": [ + "Depth (w/ mono feature)" + ], + "image_footnote": [], + "bbox": [ + 635, + 180, + 769, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cd0143524ad7b1441341f013f242190c9e5b1d9356b444bcc1c684b37c97f808.jpg", + "image_caption": [ + "Error (w/ mono feature)" + ], + "image_footnote": [], + "bbox": [ + 771, + 180, + 903, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/024ddd21965b9818414e0b149b0121516ae21be89044f1c04ecdb0f500e35d77.jpg", + "image_caption": [ + "Figure 3. Effect of monocular features for depth on ScanNet. The monocular feature greatly improves challenging situations like texture-less regions (e.g., the wall in the first example) and reflective surfaces (e.g., the refrigerator in the second example).", + "Input Image 1" + ], + "image_footnote": [], + "bbox": [ + 91, + 314, + 223, + 416 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2aea3bbfe2b5136278a6847f1d409f795052ed6203c27a2cf405d633f57e9cb7.jpg", + "image_caption": [ + "Image 1: Depth (w/ mono feature)" + ], + "image_footnote": [], + "bbox": [ + 227, + 315, + 356, + 416 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dc519e7765a8083212e15f7d836356dbc46afe5290cb27f168ffaa272da76b94.jpg", + "image_caption": [ + "Image 1: Depth (w/o mono feature)" + ], + "image_footnote": [], + "bbox": [ + 364, + 315, + 493, + 416 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/eb692571fdb314adbd3a24ceb74f1fc1c258c3da29aed62b982ffdc3adc0519d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 315, + 627, + 416 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fdcf12098869025cbd207c1471d07c58db5972f15837363905d11492d4f640dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 315, + 764, + 416 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/557a0988583caf230dd57779b5ca336b982900cfc230b87a7de9274cb9302e05.jpg", + "image_caption": [ + "GT Novel View" + ], + "image_footnote": [], + "bbox": [ + 767, + 315, + 898, + 416 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e5c15727c6ea1fb169ba3eddb5d07ede7d3c6013c282ea3fa2b907c927c18781.jpg", + "image_caption": [ + "Input Image 2", + "Image 2: Depth (w/ mono feature)", + "Figure 4. Effect of monocular features for 3DGS on RealEstate10K. Without monocular features, the model struggles at predicting reliable depth for pixels that are not able to find correspondences (e.g., the lounger chair highlighted with the read rectangle), which subsequently causes misalignment in the rendered image due to the incorrect geometry." + ], + "image_footnote": [], + "bbox": [ + 91, + 450, + 223, + 553 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b699c3363bb1d4ebcd3abd59e6b4ea591cffc6b9719af9eb4ce8923d3a6da0c7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 227, + 450, + 357, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/02b200dbfb77a299a03a5fed46b926ec3097c6444de9a112c9dc0e9838b6c107.jpg", + "image_caption": [ + "Image 2: Depth (w/o mono feature)" + ], + "image_footnote": [], + "bbox": [ + 364, + 450, + 493, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/de5cba7f18f45c51e3f4aedf08b922fb285de516fcb8fc46a630103c4f4432da.jpg", + "image_caption": [ + "Render Error (w/o mono feature)", + "Render Error (w/ mono feature)" + ], + "image_footnote": [], + "bbox": [ + 500, + 450, + 627, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0cc53cd888a9cc8de0664050325017c0fca60d195026e5bca69dfaf08d4fa5a6.jpg", + "image_caption": [ + "Novel View Render (w/o mono feature)" + ], + "image_footnote": [], + "bbox": [ + 633, + 450, + 764, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3c289b29c14ac875a76663ff14ccece14021f53c616ad492407e20dc54735e25.jpg", + "image_caption": [ + "Novel View Render (w/ mono feature)", + "GT Novel View" + ], + "image_footnote": [], + "bbox": [ + 767, + 452, + 898, + 553 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "depth features. We also show the visual comparisons for the Gaussian splatting task in Fig. 4 with two input views. For regions (e.g., the lounge chairs) that only appear in a single image, the pure multi-view method is unable to find correspondences. It thus produces unreliable depth predictions, leading to misalignment in the rendered novel views due to the incorrect geometry.", + "bbox": [ + 89, + 662, + 483, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also experiment with removing the cost volume (w/o cost volume) in the multi-view branch and observed a significant performance drop. This indicates that obtaining scale-and multi-view consistent predictions with a pure monocular depth backbone is challenging, which constrains achieving high-quality results for 3D Gaussian reconstruction.", + "bbox": [ + 89, + 773, + 483, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Different Monocular Features. In Tab. 2, we also evaluate different monocular features, including the ConvNeXt", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/40ad96b9c18269453a6cf0a01b3fccfe0c7ff032ff7f3f19d2e9cf57286533a6.jpg", + "table_caption": [ + "Table 3. Monocular fusion strategy. Our simple concatenation performs surprisingly good compared to other alternatives." + ], + "table_footnote": [], + "table_body": "
MethodAbs Rel ↓δ1 ↑
Cost volume from ViT11.2690.84
Explicit scale align9.1390.21
Attention fusion8.4092.95
Concatenation (Ours)8.4693.02
", + "bbox": [ + 576, + 700, + 844, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "T [35] features used in AFNet [11], and other popular monocular features including Midas [40] and DINOv2 [37]. The pre-trained Depth Anything V2 [70] monocular features achieve the best view synthesis results.", + "bbox": [ + 511, + 806, + 906, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Monocular Fusion Strategy. We compare with alternative strategies for fusing the monocular features for multi-view", + "bbox": [ + 511, + 869, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16458", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e0ba58e0ca2a06513195cade0872b1549dc39bfe8e2ae0b98f90e7c49594dbbe.jpg", + "table_caption": [ + "Table 4. Unsupervised Depth Pre-Training with Gaussian Splat-ting. We evaluate the same architecture but with different weights. The pre-training is performed on RealEstate10K, and fine-tuning is performed on TartanAir and VKITTI2. Unsupervised pre-training (2nd row) produces improved depth predictions compared to random initialization (1st). The performance can be further improved with additional fine-tuning (4th), where the benefit of pre-training is especially significant on challenging datasets like TartanAir and KITTI compared to training from random initialization (3rd)." + ], + "table_footnote": [], + "table_body": "
Pre-TrainFine-TuneTartanAirScanNetKITTI
Abs Rel ↓δ1 ↑Abs Rel ↓δ1 ↑Abs Rel ↓δ1 ↑
XX76.223.4339.9722.5690.690.00
✓X29.5353.1621.5176.0956.8346.26
X✓10.8690.556.7096.1411.5687.27
✓✓10.2091.106.6096.2710.6889.92
", + "bbox": [ + 89, + 217, + 480, + 305 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5b6487fac3039c2736eb9605ab84e2aafbeb0775f81e6dfdc621e8a861534418.jpg", + "table_caption": [ + "Table 5. Two-view Depth Estimation on ScanNet. Our Depth-Spat outperforms all prior methods by clear margins." + ], + "table_footnote": [], + "table_body": "
MethodAbs Rel ↓RMSE ↓RMSElog ↓
DeMoN [54]23.10.7610.289
BA-Net [50]16.10.3460.214
DeepV2D [52]5.70.1680.080
NeuralRecon [47]4.70.1640.093
DRO [26]5.30.1680.081
UniMatch [65]5.90.1790.082
DepthSplat (w/o GS pre-train)4.50.1250.061
DepthSplat (w/ GS pre-train)3.80.1140.055
", + "bbox": [ + 89, + 354, + 480, + 498 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "depth estimation in Sec. 4.2. In particular, we first compare with MVSFormer [6] that constructs the cost volume with monocular ViT features, which leads to a single-branch architecture. We can observe that our fusion strategy performs significantly better than the single-branch design, potentially because our two-branch design disentangles feature matching and monocular priors, which makes the learning task easier. We also compare with fusing the monocular depth maps (instead of monocular features in our model) by first aligning the monocular depth scale using the multi-view depth and then fusing the depth maps together with an additional network. Again, our simple concatenation performs better. We further compare our concatenation with the attention-based adaptive fusion and observe very similar results. Thus we opt to the simpler concatenation design.", + "bbox": [ + 88, + 522, + 485, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Unsupervised Depth Pre-Training with Gaussian Splitting", + "text_level": 1, + "bbox": [ + 89, + 757, + 483, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "By connecting Gaussian splatting and depth, our DepthSplat provides a way to pre-train the depth model in a fully unsupervised manner. In particular, we first train our full model on the large-scale multi-view posed RealEstate10K dataset (contains $\\sim 67\\mathrm{K}$ Youtube videos) with only the Gaussian splatting rendering loss (Eq. (2)), without any direct supervision on the depth predictions. After pre-training, we take", + "bbox": [ + 89, + 794, + 485, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/462295142a2627b9f37f69f43b5f67c1e3bfacb28f30a50d973c0f1ccd42e1d3.jpg", + "table_caption": [ + "Table 6. Two-view 3DGS on RealEstate10K. Our DepthSplat achieves the best performance." + ], + "table_footnote": [], + "table_body": "
MethodPSNR ↑SSIM ↑LPIPS ↓
pixelNeRF [75]20.430.5890.550
GPNR [46]24.110.7930.255
AttnRend [17]24.780.8200.213
MuRF [66]26.100.8580.143
pixelSplat [7]25.890.8580.142
MVSplat [9]26.390.8690.128
TranSplat [76]26.690.8750.125
DepthSplat27.470.8890.114
", + "bbox": [ + 537, + 119, + 883, + 272 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cd6d1a336b22f28e6d77f099f808b471c626864648a0c45f79657fe8e8c33f79.jpg", + "image_caption": [ + "Input", + "GT" + ], + "image_footnote": [], + "bbox": [ + 514, + 284, + 645, + 419 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ec42f13f1fda6087e9aa2d4e88fcf0c8e41d1ec936b0022efb14597a4703796.jpg", + "image_caption": [ + "pixelSplat" + ], + "image_footnote": [], + "bbox": [ + 640, + 285, + 730, + 419 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c1f579fa78a26eab5f96447e863047d7e20823b6f04b9e5d59418a6ad09e22d.jpg", + "image_caption": [ + "MVSplat", + "Figure 5. Novel view synthesis on RealEstate10K. Our DepthSplat performs significantly better than pixelSplat [7] and MVSplat [9] in challenging regions." + ], + "image_footnote": [], + "bbox": [ + 730, + 286, + 818, + 419 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9e3526351c2763b67c01ddaaef8a47ffdb58df66d7d7b145d3ce3ae56e7c0115.jpg", + "image_caption": [ + "DepthSplat" + ], + "image_footnote": [], + "bbox": [ + 818, + 286, + 903, + 419 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the pre-trained depth model and further fine-tune it to the depth task on the mixed TartanAir [58] and VKITTI2 [5] datasets with ground truth depth supervision. In Tab. 4, we evaluate the performance on both in-domain TartanAir test set and the zero-shot generalization on unseen ScanNet and KITTI datasets. We can observe that the benefit of pretraining is especially significant on the challenging datasets like TartanAir and KITTI. The results align well with the observation in [21] which suggests that the pre-training acts as regularization and guides the learning towards better minima and enables better generalization to out-of-distribution datasets. The visual comparison results are provided in the appendix. Given the increasing popularity of view synthesis [61, 81] and multi-view generative models [3, 45], new multi-view datasets [32] and models [55] are gradually introduced, our approach provides a way to pre-train depth models on large-scale multi-view posed image datasets.", + "bbox": [ + 511, + 503, + 908, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Benchmark Comparisons", + "text_level": 1, + "bbox": [ + 511, + 770, + 746, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons on ScanNet and RealEstate10K. Tab. 5 and Tab. 6 compare the depth and novel view synthesis results on the standard ScanNet and RealEstate10K benchmarks, respectively. We can see clearly that our DepthSplat achieves state-of-the-art performance on both datasets for both tasks. The visual comparison with previous methods is shown in Fig. 5, where our method significantly improves the perfor", + "bbox": [ + 511, + 794, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16459", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/48af6100928045d4de8010b18d34d08f0ad98264e16495ed58f3599e8a41640d.jpg", + "table_caption": [ + "Table 7. Comparisons on DL3DV. Our DepthSplat not only consistently outperforms MVSplat on different number of input views, but also scales more efficiently to more input views." + ], + "table_footnote": [], + "table_body": "
Method#ViewsPSNR ↑SSIM ↑LPIPS ↓Time (s)
MVSplat [9]217.540.5290.4020.072
DepthSplat19.310.6150.3100.083
MVSplat [9]421.630.7210.2330.146
DepthSplat23.120.7800.1780.107
MVSplat [9]622.930.7750.1930.263
DepthSplat24.190.8230.1470.132
", + "bbox": [ + 94, + 143, + 477, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/92b82c384beb990a0b540395883f26289f4d29702dc4a14794a0177ac8b75bd6.jpg", + "image_caption": [ + "Figure 6. Visual comparisons on DL3DV. Our DepthSplat performs significantly better than MVSplat [9] on regions that hard to match (e.g., repeated patterns)." + ], + "image_footnote": [], + "bbox": [ + 96, + 282, + 480, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mance on challenging scenarios like texture-less regions and occlusions. For the depth results on ScanNet, we report our base models (with ViT-B and two-scale feature matching) trained with and without Gaussian splatting pre-training on the mixed RealEstate10K and DL3DV datasets. Our model significantly outperforms previous methods and can benefit from additional Gaussian splatting pre-training.", + "bbox": [ + 89, + 547, + 483, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparisons on DL3DV. To evaluate the performance on complex real-world scenes, we conduct comparisons with the representative model MVSplat [9] on the recently introduced DL3DV dataset [32]. We also compare the results of different numbers of input views (2, 4 and 6) on this dataset. We fine-tune MVSplat and our RealEstate10K pre-trained models on DL3DV training scenes and report the results on the benchmark test set in Tab. 7. Our DepthSplat consistently outperforms MVSplat in all metrics, and our improvements are more significant with fewer input views, which indicates that our model is more robust to sparse views. Visual comparisons with MVSplat on the DL3DV dataset are shown in Fig. 6, where MVSplat's depth quality lags behind our DepthSplat due to matching failure, which leads to blurry and distorted view synthesis results. We show more visual comparison results in the appendix. It is also worth noting", + "bbox": [ + 89, + 657, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7744f25098b080d9a75393146953b8fd9aa8c5ea97f4c5fba569ac469b587b56.jpg", + "table_caption": [ + "Table 8. Cross-dataset generalization. When generalizing to DL3DV and ACID with RealEstate10K pre-trained models, our DepthSplat is consistently better than MVSplat, especially on the more challenging DL3DV dataset." + ], + "table_footnote": [], + "table_body": "
MethodDL3DVACID
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
MVSplat [9]24.140.8080.14928.150.8410.147
DepthSplat27.660.8950.09628.370.8470.141
", + "bbox": [ + 516, + 150, + 903, + 217 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "that our method scales more efficiently to more input views thanks to our lightweight local feature matching approach (Sec. 3.1), which is unlike the expensive global pair-wise matching used in MVSplat.", + "bbox": [ + 511, + 236, + 906, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Cross-Dataset Generalization. We evaluate the cross-dataset generalization capability by directly testing on DL3DV [32] and ACID [33] datasets with RealEstate10K [82] pre-trained models. The results are shown in Tab. 8, where our DepthSplat consistently outperforms MVSplat on both datasets, especially on the more challenging DL3DV dataset which features complex scene structures. The visual comparison results are shown in the appendix.", + "bbox": [ + 511, + 300, + 908, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "High-Resolution Results. In addition to the comparison results on the $256 \\times 256$ resolution RealEstate10K and $256 \\times 448$ resolution DL3DV dataets, we show more high-resolution $(512 \\times 960)$ qualitative results in the appendix. We also invite the readers to our project page haofelixu.github.io/deathsplat for high-resolution $(512 \\times 960)$ video results on different number of input views (6 and 12), where our DepthSplat is able to reconstruct larger-scale or 360 scenes from more input views.", + "bbox": [ + 511, + 441, + 908, + 578 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 597, + 633, + 612 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce DepthSplat, a new approach to connecting Gaussian splatting and depth to achieve state-of-the-art results on ScanNet, RealEstate10K and DL3DV datasets for both depth and view synthesis tasks. We show that our model enables unsupervised depth pre-training with Gaussian splatting rendering loss, providing a way to leverage large-scale posed multi-view image datasets for training more robust and generalizable multi-view depth models.", + "bbox": [ + 511, + 625, + 908, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our current model requires camera poses as input along with the multi-view images, which might be challenging to obtain when the input views are extremely sparse. An interesting future direction is to remove this requirement by exploring pose-free models [72, 80]. In addition, our model predicts pixel-aligned Gaussians, where the number of Gaussians will be significantly large when processing a large number of input views [60, 79]. Further improving the geometry representation and the scalability to many input views would be exciting future work.", + "bbox": [ + 511, + 750, + 910, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16460", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We thank Yuedong Chen for his generous help with the DL3DV dataset. Andreas Geiger was supported by the ERC Starting Grant LEGO-3D (850533) and the DFG EXC number 2064/1 - project number 390727645. This work was supported as part of the Swiss AI Initiative by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID a03 on Alps. H. Blum is also with the Lamarr Institute and D. 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ACM TOG, 2018. 1, 2, 4, 5, 8" + ], + "bbox": [ + 516, + 92, + 905, + 231 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16463", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/3c38ee77-2762-4a1c-ad37-7a37f09eab09_model.json b/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/3c38ee77-2762-4a1c-ad37-7a37f09eab09_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4464f1add3cd3d84309eb8a28ef216dffe8d908d --- /dev/null +++ b/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/3c38ee77-2762-4a1c-ad37-7a37f09eab09_model.json @@ -0,0 +1,2917 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.221, + 0.131, + 0.778, + 0.154 + ], + "angle": 0, + "content": "DepthSplat: Connecting Gaussian Splatting and Depth" + }, + { + "type": "text", + "bbox": [ + 0.122, + 0.179, + 0.877, + 0.269 + ], + "angle": 0, + "content": "Haofei Xu\\(^{1,2}\\) Songyou Peng\\(^{1}\\) Fangjinhua Wang\\(^{1}\\) Hermann Blum\\(^{1,4}\\) Daniel Barath\\(^{1}\\) Andreas Geiger\\(^{2}\\) Marc Pollefeys\\(^{1,3}\\) \n\\(^{1}\\)ETH Zurich \\(^{2}\\)University of Tübingen, Tübingen AI Center \\(^{3}\\)Microsoft \\(^{4}\\)University of Bonn haofeixu.github.io/dephthsplat" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.285, + 0.495, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.285, + 0.634, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.286, + 0.904, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.473, + 0.907, + 0.503 + ], + "angle": 0, + "content": "Figure 1. DepthSplat enables cross-task interactions between Gaussian splatting and depth. Left: Better depth leads to improved Gaussian splatting reconstruction. Right: Unsupervised depth pre-training with Gaussian splatting leads to reduced depth prediction error." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.514, + 0.327, + 0.53 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.545, + 0.486, + 0.819 + ], + "angle": 0, + "content": "Gaussian splatting and single-view depth estimation are typically studied in isolation. In this paper, we present DepthSplat to connect Gaussian splatting and depth estimation and study their interactions. More specifically, we first contribute a robust multi-view depth model by leveraging pretrained monocular depth features, leading to high-quality feed-forward 3D Gaussian splatting reconstructions. We also show that Gaussian splatting can serve as an unsupervised pre-training objective for learning powerful depth models from large-scale multi-view posed datasets. We validate the synergy between Gaussian splatting and depth estimation through extensive ablation and cross-task transfer experiments. Our DepthSplat achieves state-of-the-art performance on ScanNet, RealEstate10K and DL3DV datasets in terms of both depth estimation and novel view synthesis, demonstrating the mutual benefits of connecting both tasks. In addition, DepthSplat enables feed-forward reconstruction from 12 input views (512 × 960 resolutions) in 0.6 seconds." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.845, + 0.222, + 0.86 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.87, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Novel view synthesis [4, 82] and depth prediction [20, 44] are two fundamental tasks in computer vision, serving as the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.515, + 0.907, + 0.56 + ], + "angle": 0, + "content": "driving force behind numerous applications ranging from augmented reality to robotics and autonomous driving. There have been notable advancements in both areas recently." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.563, + 0.909, + 0.744 + ], + "angle": 0, + "content": "For novel view synthesis, 3D Gaussian Splatting (3DGS) [29] has emerged as a popular technique due to its impressive real-time performance while attaining high visual fidelity. Recently, advances in feed-forward 3DGS models [7, 9, 48] have been introduced to alleviate the need for tedious per-scene optimization, also enabling few-view 3D reconstruction. The state-of-the-art sparse-view method MVSplat [9] relies on feature matching-based multi-view depth estimation [65] to localize the 3D Gaussian positions, which makes it suffer from similar limitations (e.g., occlusions, texture-less regions, and reflective surfaces) as other multi-view depth methods [18, 25, 44, 56, 71]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.747, + 0.909, + 0.838 + ], + "angle": 0, + "content": "On the other hand, significant progress has been made in monocular depth estimation, with recent models [19, 22, 28, 40, 69, 74] achieving robust predictions on diverse in-the-wild data. However, these depths typically lack consistent scales across multiple views, constraining their performance in downstream tasks like 3D reconstruction [59, 73]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.901 + ], + "angle": 0, + "content": "The integration of 3DGS with single-view depth estimation presents a compelling solution to overcome the individual limitations of each technique while at the same time enhancing their strengths. To this end, we introduce" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16453" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.137 + ], + "angle": 0, + "content": "DepthSplat, which exploits the complementary nature of sparse-view feed-forward 3DGS and robust monocular depth estimation to improve the performance for both tasks." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.137, + 0.483, + 0.303 + ], + "angle": 0, + "content": "Specifically, we first contribute a robust multi-view depth model by integrating pre-trained monocular depth features [70] to the multi-view feature matching branch, which not only maintains the consistency of multi-view depth models but also leads to more robust results in situations that are hard to match (e.g., occlusions, texture-less regions and reflective surfaces). The predicted multi-view depth maps are then unprojected to 3D as the Gaussian centers, and we use an additional lightweight network to predict other remaining Gaussian parameters. They are combined together to achieve novel view synthesis with the splatting operation [29]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.303, + 0.483, + 0.394 + ], + "angle": 0, + "content": "While previous methods [1, 11, 31] also try to fuse monocular and multi-view depths, they usually rely on sophisticated architectures. In contrast, we identify the power of off-the-shelf pre-trained monocular depth models and propose to augment multi-view cost volumes with monocular features, leading to a simpler model and stronger performance." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.394, + 0.483, + 0.575 + ], + "angle": 0, + "content": "Thanks to our improved multi-view depth model, the quality of novel view synthesis with Gaussian splatting is also significantly enhanced (see Fig. 1 left). In addition, our Gaussian splatting module is fully differentiable, which requires only photometric supervision to optimize all model components. This provides a new, unsupervised way to pre-train depth prediction models on large-scale multi-view posed datasets without requiring ground truth geometry information. The pre-trained depth model can be further fine-tuned for specific depth tasks and achieves superior results over training from scratch (see Fig. 1 right, where unsupervised pre-training leads to improved performance)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.575, + 0.483, + 0.742 + ], + "angle": 0, + "content": "We conduct extensive experiments on the large-scale TartanAir [58], ScanNet [14] and RealEstate10K [82] datasets for depth estimation and Gaussian splatting tasks, as well as the recently introduced DL3DV [32] dataset, which features complex real-world scenes and thus is more challenging. Under various evaluation settings, our DepthSplat achieves state-of-the-art results. We also achieve promising feedforward reconstruction results of large-scale or 360 scenes from 12 input views (\\(512 \\times 960\\) resolutions) in 0.6 seconds. The strong performance on both tasks demonstrates the mutual benefits of connecting Gaussian splatting and depth." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.752, + 0.233, + 0.768 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Multi-View Depth Estimation. As a core component of classical multi-view stereo pipelines [44], multi-view depth estimation exploits multi-view photometric consistency across multiple images to perform feature matching and predict the depth map of the reference image. In recent years, many learning-based methods [6, 15, 18, 25, 56, 57, 71] have been proposed to improve depth accuracy. Though these learning-based methods significantly improve the depth qual" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.908, + 0.152 + ], + "angle": 0, + "content": "ity compared to traditional methods [23, 44, 67], they cannot handle challenging situations where the multi-view photometric consistency assumption is not guaranteed, e.g., occlusions, low-textured areas, and non-Lambertian surfaces." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.155, + 0.909, + 0.352 + ], + "angle": 0, + "content": "Monocular Depth Estimation. Recently, we have witnessed significant progress in depth estimation from a single image [2, 28, 40, 69, 74], and existing methods can produce surprisingly accurate results on diverse in-the-wild data. However, monocular depth methods inherently suffer from scale ambiguities, which makes it challenging to use them for downstream tasks like 3D reconstruction [73]. In this paper, we leverage the powerful features from a pre-trained monocular depth model [70] to augment feature-matching based multi-view depth estimation, which not only maintains the multi-view consistency but also leads to significantly improved robustness in challenging situations such as low-textured regions and reflective surfaces." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.354, + 0.909, + 0.672 + ], + "angle": 0, + "content": "Feed-Forward Gaussian Splatting. Several feed-forward 3D Gaussian splatting models [7-10, 48, 51, 62, 68, 77] have been proposed in literature thanks to its efficiency and ability to handle sparse views. In particular, pixelSplat [7] and Splatter Image [48] predict 3D Gaussians from image features, while MVSplat [9] encodes the feature matching information with cost volumes and achieves better geometry. However, it inherently suffers from the limitation of feature matching in challenging situations like texture-less regions and reflective surfaces. In this paper, we propose to integrate monocular features from pre-trained monocular depth models [70] for more robust depth prediction and 3D Gaussian reconstruction. Another line of work like LGM [51], GRM [68], and GS-LRM [77] relies significantly on the training data and compute, discarding explicit feature matching cues and learning priors purely from data. This makes them expensive to train (e.g., GS-LRM [77] is trained with 64 A100 GPUs for 2 days), while our model can be trained in 2 days with 4 GPUs. Moreover, our Gaussian splatting module enables pre-training depth model from large-scale multi-view posed datasets without ground truth depth supervision." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.675, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Depth and Gaussian Splatting. Flash3D [49] explores a pre-trained monocular depth model [39] for single-image 3D Gaussian reconstruction. In contrast, we target large-scale scene reconstruction from multiple views. TranSplat [76] leverages monocular depth to improve Gaussian reconstruction. However, a crucial difference is that TranSplat uses monocular features to refine the coarse depth predicted from a cost volume, which makes it inherently vulnerable to the error in the coarse stage and, thus, suffers from the error propagation issue. In contrast, we avoid this by combining cost volume and monocular features early, which performs significantly better than TranSplat (Tab. 6). Another line of work [12, 53] applies an additional depth loss to the Gaussian optimization process. We note that these two approaches (feed-forward vs. per-scene optimization) are orthogonal." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16454" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.137, + 0.088, + 0.87, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.279, + 0.908, + 0.378 + ], + "angle": 0, + "content": "Figure 2. DepthSplat connects depth estimation and 3D Gaussian splatting with a shared architecture, which enables cross-task transfer. In particular, DepthSplat consists of a multi-view branch to model feature-matching information and a single-view branch to extract monocular features. The per-view cost volumes and monocular features are concatenated for depth regression with a 2D U-Net architecture. For the depth estimation task, we train the depth model with ground truth depth supervision. For the Gaussian splatting task, we first unproject all depth maps to 3D as the Gaussian centers, and in parallel, we use an additional head to predict the remaining Gaussian parameters. Novel views are rendered with the splatting operation. The full model for novel view synthesis is trained with the photometric rendering loss, which can also be used as an unsupervised pre-training stage for the depth model." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.387, + 0.212, + 0.405 + ], + "angle": 0, + "content": "3. DepthSplat" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.411, + 0.484, + 0.594 + ], + "angle": 0, + "content": "Given \\(N\\) input images \\(\\{\\pmb{I}^i\\}_{i=1}^N\\), \\((\\pmb{I}^i \\in \\mathbb{R}^{H \\times W \\times 3}\\), where \\(H\\) and \\(W\\) are the image sizes) with corresponding projection matrices \\(\\{\\mathbf{P}_i\\}_{i=1}^N\\), \\((\\mathbf{P}_i \\in \\mathbb{R}^{3 \\times 4}\\), computed from the intrinsic and extrinsic matrices), our goal is to predict dense per-pixel depth \\(\\mathbf{D}_i \\in \\mathbb{R}^{H \\times W}\\) and per-pixel Gaussian parameters \\(\\{(\\pmb{\\mu}_j, \\alpha_j, \\pmb{\\Sigma}_j, c_j)\\}_{j=1}^{H \\times W \\times N}\\) for each image, where \\(\\pmb{\\mu}_j, \\alpha_j, \\pmb{\\Sigma}_j\\) and \\(c_j\\) are the 3D Gaussian's position, opacity, covariance, and color. As shown in Fig. 2, key to our method is a multi-view depth model augmented with monocular depth features, where we obtain the position \\(\\pmb{\\mu}_j\\) of each Gaussian by unprojecting depth with camera parameters, and other Gaussian parameters are predicted by an additional head." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.595, + 0.484, + 0.761 + ], + "angle": 0, + "content": "More specifically, our depth model consists of two branches: one for modeling feature matching using cost volumes, and another for extracting monocular features from a pre-trained monocular depth network. The cost volumes and monocular features are concatenated together for subsequent depth regression with a 2D U-Net and a softmax layer. For the depth task, we train our depth model with ground truth depth supervision. Our full model for novel view synthesis is trained with the rendering loss, which can also be used as an unsupervised pre-training stage for the depth model. We introduce the individual components below." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.77, + 0.358, + 0.788 + ], + "angle": 0, + "content": "3.1. Multi-View Feature Matching" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.793, + 0.484, + 0.838 + ], + "angle": 0, + "content": "In this branch, we extract multi-view features with a multiview Transformer architecture and then build multiple cost volumes that correspond to each input view." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Multi-View Feature Extraction. For \\(N\\) input images, we first use a lightweight weight-sharing ResNet [27] architecture to get \\(s \\times\\) downsampled features for each image independently. To handle different image resolutions, we" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.389, + 0.909, + 0.585 + ], + "angle": 0, + "content": "make the downsampling factor \\(s\\) flexible by controlling the number of stride-2 \\(3 \\times 3\\) convolutions. For example, the downsampling factor \\(s\\) is 4 if two stride-2 convolutions are used and 8 if three are used. To exchange information across different views, we use a multi-view Swin Transformer [34, 64, 65] which contains six stacked self- and cross-attention layers to obtain multi-view-aware features \\(\\{F_i\\}_{i=1}^N\\), \\(F^i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C}\\), where \\(C\\) is the feature dimension. When more than two images (\\(N > 2\\)) are given as input, we perform cross-attention between each reference view and its top-2 nearest neighboring views, which are selected based on their camera distances to the reference view. This makes computation tractable with many input views." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Feature Matching. We encode the feature matching information across different views with the plane-sweep stereo approach [13, 65]. More specifically, for each view \\(i\\), we first uniformly sample \\(D\\) depth candidates \\(\\{d_m\\}_{m=1}^D\\) from the near and far depth ranges and then warp the feature \\(F^j\\) of view \\(j\\) to view \\(i\\) with the camera projection matrix and each depth candidate \\(d_m\\). Then we obtain \\(D\\) warped features \\(\\{F_{d_m}^{j \\rightarrow i}\\}_{m=1}^D\\) that correspond to feature \\(F^i\\). We then measure their feature correlations with the dot-product operation [9, 63]. The cost volume \\(C_i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times D}\\) for image \\(i\\) is obtained by stacking all correlations. Accordingly, we obtain cost volumes \\(\\{C_i\\}_{i=1}^N\\) for all input images \\(\\{I_i\\}_{i=1}^N\\). For more than two input views, similar to the strategy in cross-view attention computation, we select the top-2 nearest views for each reference view and compute feature correlations with only the selected views. This enables our cost volume construction to achieve a good speed-accuracy trade-off and scale efficiently to a larger number of input views. The correlation values for the two selected views are combined with averaging." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16455" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.414, + 0.108 + ], + "angle": 0, + "content": "3.2. Monocular Depth Feature Extraction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.117, + 0.484, + 0.224 + ], + "angle": 0, + "content": "Despite the remarkable progress in multi-view feature matching-based depth estimation [57, 65, 71] and Gaussian splatting [9], they inherently suffer from limitations in challenging situations like occlusions, texture-less regions, and reflective surfaces. Thus, we propose to integrate pre-trained monocular depth features into the cost volume to handle scenarios that are challenging or impossible to match." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.227, + 0.484, + 0.44 + ], + "angle": 0, + "content": "More specifically, we leverage the pre-trained monocular depth backbone from the recent Depth Anything V2 [70] model thanks to its impressive performance on diverse in-the-wild data. The monocular backbone is a ViT [16, 37] model, which has a patch size of 14 and outputs a feature map that is \\(1/14\\) spatial resolution of the original image. We simply bilinearly interpolate the spatial resolution of the monocular features to the same resolution as the cost volume in Sec. 3.1 and obtain the monocular feature \\(\\mathbf{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}}\\) for input image \\(\\mathbf{I}_i\\), where \\(C_{\\mathrm{mono}}\\) is the dimension of the monocular feature. This process is performed for all input images in parallel and we obtain monocular features \\(\\{\\mathbf{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}}\\}_{i=1}^{N}\\), which are subsequently used for per-view depth map estimations." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.461, + 0.416, + 0.478 + ], + "angle": 0, + "content": "3.3. Feature Fusion and Depth Regression" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.488, + 0.485, + 0.655 + ], + "angle": 0, + "content": "To achieve robust and multi-view consistent depth predictions, we combine the monocular feature \\( \\pmb{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}} \\) and cost volume \\( C_i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times D} \\) via simple concatenation in the channel dimension. A subsequent 2D U-Net [42, 43] is used to regress depth from the concatenated monocular features and cost volumes. This process is performed for all the input images in parallel and for each image, it outputs a tensor of shape \\( \\frac{H}{s} \\times \\frac{W}{s} \\times D \\), where \\( D \\) is the number of depth candidates. We normalize the \\( D \\) dimension with the softmax operation and perform a weighted average of all depth candidates to obtain the depth output." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We also apply a hierarchical matching [25] architecture where an additional refinement step at \\( 2 \\times \\) higher feature resolution is employed to improve the performance further. More specifically, based on the coarse depth prediction, we perform a correspondence search on the \\( 2 \\times \\) higher feature maps within the neighbors of the \\( 2 \\times \\) upsampled coarse depth prediction. Since we already have a coarse depth prediction, we only need to search a smaller range at the higher resolution, and thus, we construct a smaller cost volume compared to the coarse stage. Such a 2-scale hierarchical architecture not only leads to improved efficiency since most computation is spent on low resolution, but also leads to better results thanks to the use of higher-resolution features [25]. Similar feature fusion and depth regression procedure is used to get higher-resolution depth predictions, which are subsequently upsampled with a DPT head [41] to the full resolution." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.791, + 0.106 + ], + "angle": 0, + "content": "3.4. Gaussian Parameter Prediction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.113, + 0.907, + 0.25 + ], + "angle": 0, + "content": "For the task of 3D Gaussian splatting, we directly unproject the per-pixel depth maps to 3D with the camera parameters as the Gaussian centers \\(\\pmb{\\mu}_j\\). To predict other remaining Gaussian parameters \\(\\alpha_{j}\\) (opacity), \\(\\Sigma_{j}\\) (covariance) and \\(c_{j}\\) (color), we use an additional DPT head [41], where it takes the concatenated image, depth and feature information as input and outputs all the remaining Gaussian parameters. With all the predicted 3D Gaussians, we can render novel views with the Gaussian splatting operation [29]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.261, + 0.657, + 0.277 + ], + "angle": 0, + "content": "3.5. Training Loss" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.284, + 0.907, + 0.329 + ], + "angle": 0, + "content": "We study the properties of our proposed model on two tasks: depth estimation and novel view synthesis with 3D Gaussian splatting [29]. The loss functions are introduced below." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.333, + 0.907, + 0.379 + ], + "angle": 0, + "content": "Depth estimation. We train our depth model (without the Gaussian splatting head) with \\(\\ell_1\\) loss and gradient loss between the inverse depths of prediction and ground truth:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.391, + 0.907, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\text {d e p t h}} = \\alpha \\cdot | \\boldsymbol {D} _ {\\text {p r e d}} - \\boldsymbol {D} _ {\\text {g t}} | + \\beta \\cdot | \\partial_ {x} \\boldsymbol {D} _ {\\text {p r e d}} - \\partial_ {x} \\boldsymbol {D} _ {\\text {g t}} | \\\\ + \\beta \\cdot \\left| \\partial_ {y} \\boldsymbol {D} _ {\\text {p r e d}} - \\partial_ {y} \\boldsymbol {D} _ {\\mathrm {g t}} \\right|), \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.44, + 0.907, + 0.485 + ], + "angle": 0, + "content": "where \\(\\partial_x\\) and \\(\\partial_y\\) denotes the gradients on the \\(x\\) and \\(y\\) directions, respectively. Following UniMatch [65], we use \\(\\alpha = 20\\) and \\(\\beta = 20\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.488, + 0.906, + 0.534 + ], + "angle": 0, + "content": "View synthesis. We train our full model with a combination of mean squared error (MSE) and LPIPS [78] losses between rendered and ground truth image colors:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.547, + 0.91, + 0.599 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {g s}} = \\sum_ {m = 1} ^ {M} \\left(\\operatorname {M S E} \\left(I _ {\\text {r e n d e r}} ^ {m}, I _ {\\mathrm {g t}} ^ {m}\\right) + \\lambda \\cdot \\operatorname {L P I P S} \\left(I _ {\\text {r e n d e r}} ^ {m}, I _ {\\mathrm {g t}} ^ {m}\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.6, + 0.906, + 0.631 + ], + "angle": 0, + "content": "where \\(M\\) is the number of novel views to render in a single forward pass. The LPIPS loss weight \\(\\lambda\\) is set to 0.05 [9]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.646, + 0.645, + 0.663 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Implementation Details. We implement our method in PyTorch [38] and optimize our model with the AdamW [36] optimizer and cosine learning rate schedule. We adopt the xFormers [30] library for our monocular ViT backbone implementation. We use a lower learning rate \\(2 \\times 10^{-6}\\) for the pre-trained Depth Anything V2 [70] backbone, and other remaining layers use a learning rate of \\(2 \\times 10^{-4}\\). The feature downsampling factor \\(s\\) in our multi-view branch (Sec. 3.1) is chosen based on the image resolution. More specifically, for experiments on the \\(256 \\times 256\\) resolution RealEstate10K [82] dataset, we choose \\(s = 4\\). For higher resolution datasets (e.g., TartanAir [58], ScanNet [14], KITTI [24] and DL3DV [32]), we choose \\(s = 8\\). Our hierarchical matching models in Sec. 3.3 use 2-scale features, i.e., \\(1/8\\) and \\(1/4\\), or \\(1/4\\) and \\(1/2\\) resolutions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16456" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.486, + 0.188 + ], + "angle": 0, + "content": "Table 1. DepthSplat model variants. We evaluate different monocular backbones and different multi-view models (1-scale and 2-scale features for hierarchical matching as described in Sec. 3.3), where both larger monocular backbones and 2-scale hierarchical models lead to consistently improved performance for both depth and view synthesis tasks. The inference time is measured on a single A100 GPU for two input views at \\(256 \\times 256\\) resolutions." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.19, + 0.482, + 0.304 + ], + "angle": 0, + "content": "
MonoMulti-ViewDepth (TartanAir)3DGS (RealEstate10K)Param (M)Time (s)
Abs Rel ↓δ1 ↑PSNR ↑SSIM ↑LPIPS ↓
ViT-S1-scale8.4693.0226.840.8780.122380.050
ViT-B1-scale6.9494.4627.060.8820.1191150.053
ViT-L1-scale6.0795.5227.230.8850.1163470.061
ViT-S2-scale7.0194.5627.120.8840.119410.062
ViT-B2-scale6.2295.3127.340.8870.1161200.070
ViT-L2-scale5.5796.0727.470.8890.1143540.079
" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.326, + 0.485, + 0.719 + ], + "angle": 0, + "content": "Training Details. For depth experiments on ScanNet [14], we train our depth model on \\( 4 \\times \\) GH200 GPUs for 100K iterations with a total batch size of 32. For the ablation experiments on depth task, we mainly use synthetic datasets (TartanAir [58] and VKITTI2 [5]) for training since they provide high-quality ground truth depths. For Gaussian splatting experiments, we consider both low-resolution and high-resolution images. In particular, for comparisons with previous methods [7, 9], we mainly use \\( 256 \\times 256 \\) resolution RealEstate10K [82] and \\( 256 \\times 448 \\) resolution DL3DV [32] datasets. We also report high-resolution \\( (512 \\times 960) \\) results on RealEstate10K and DL3DV datasets for qualitative evaluations. For experiments on the \\( 256 \\times 256 \\) RealEstate10K dataset, we train our model on \\( 4 \\times \\) GH200 GPUs for 150K iterations with a total batch size of 32, which takes 1 day for the small model and 2 days for the large model. For experiments on the \\( 256 \\times 448 \\) DL3DV [32] dataset, we fine-tune our RealEstate10K pre-trained model on \\( 4 \\times \\) GH200 GPUs for 100K iterations with a total batch size of 4, where the number of input views is randomly sampled from 2 to 6. We evaluate the model's performance on different number of input views (2, 4, 6). For high-resolution results, we fine-tune our low-resolution pre-trained models on high-resolution images. More training details are provided in the appendix. Our code and training scripts are available at github.com/cvg/deepsplat to ease reproducibility." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.728, + 0.248, + 0.743 + ], + "angle": 0, + "content": "4.1. Model Variants" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.486, + 0.902 + ], + "angle": 0, + "content": "We first study several different model variants for both depth estimation and view synthesis tasks. In particular, we explore different monocular backbones [70] (ViT-S, ViT-B, ViT-L) and different multi-view models (1-scale and 2-scale). We conduct depth experiments on the large-scale TartanAir [58] synthetic dataset, which features both indoor and outdoor scenes and has perfect ground truth depth. The Gaussian splatting experiments are conducted on the standard RealEstate10K [82] dataset. Following community standards, we report the depth evaluation metrics [20] of" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.089, + 0.908, + 0.188 + ], + "angle": 0, + "content": "Table 2. Ablations. We evaluate the contribution of the monocular feature branch and the cost volume branch (1st group of experiments), as well as different monocular features (2nd group of experiments). Our results indicate that the monocular feature and cost volume are complementary, with large performance drops when removing either one. The pre-trained Depth Anything V2 model weights achieve the best view synthesis results." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.192, + 0.905, + 0.343 + ], + "angle": 0, + "content": "
ComponentsDepth (TartanAir)3DGS (RealEstate10K)
Abs Rel ↓δ1 ↑PSNR ↑SSIM ↑LPIPS ↓
Full8.4693.0226.840.8780.122
w/o mono feature12.2588.0026.040.8640.134
w/o cost volume11.3490.0223.240.7660.184
ConvNeXt-T10.5091.1326.110.8650.134
Midas9.5391.6126.460.8720.128
DINO V28.9392.4926.760.8770.123
Depth Anything V18.3893.2326.760.8770.124
Depth Anything V28.4693.0226.840.8780.122
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.363, + 0.909, + 0.499 + ], + "angle": 0, + "content": "Abs Rel (relative \\(\\ell_1\\) error) and \\(\\delta_{1}\\) (percentage of correctly estimated pixels within a threshold) and novel view synthesis metrics [29] of PSNR, SSIM, and LPIPS. The results in Tab. 1 demonstrate that both larger monocular backbones and 2-scale hierarchical models lead to consistently improved performance for both tasks. We name three different model sizes with \"Small\": \"ViT-S monocular, 1-scale multi-view\", \"Base\": \"ViT-B monocular, 2-scale multi-view\", and \"Large\": \"ViT-L monocular, 2-scale multi-view\"." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.501, + 0.909, + 0.637 + ], + "angle": 0, + "content": "From Tab. 1, we can also observe that better depth network architecture leads to improved view synthesis. In the appendix, we conduct additional experiments to study the effect of different initializations for the depth network to the view synthesis performance. Our results show that a better depth model initialization also contributes to improved rendering quality. In summary, both better depth network architecture and better depth model initialization lead to improved novel view synthesis results." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.649, + 0.722, + 0.665 + ], + "angle": 0, + "content": "4.2. Ablation and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.672, + 0.908, + 0.717 + ], + "angle": 0, + "content": "In this section, we study the properties of our key components on the TartanAir dataset (for depth) and RealEstate10K dataset (for view synthesis with Gaussian splatting)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Monocular Features for Depth and Gaussian Splatting. In Tab. 2, we compare our full model (Full) with the model variant where the monocular depth feature branch (with a ViT-S model pre-trained by Depth Anything V2 [70]) is removed (w/o mono feature), leaving only the multi-view branch. We can observe a clear performance drop for both depth and view synthesis tasks. In Fig. 3, we visualize the depth predictions and error maps of both models on the ScanNet dataset. The pure multi-view feature matching-based approach struggles a lot at texture-less regions and reflective surfaces. At the same time, our full model achieves reliable results thanks to the powerful prior captured in monocular" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16457" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.226, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.168, + 0.177, + 0.177 + ], + "angle": 0, + "content": "Image 1" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.089, + 0.363, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.231, + 0.167, + 0.361, + 0.177 + ], + "angle": 0, + "content": "Depth (w/o mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.089, + 0.498, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.168, + 0.495, + 0.177 + ], + "angle": 0, + "content": "Error (w/o mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.635, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.168, + 0.585, + 0.177 + ], + "angle": 0, + "content": "Image 1" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.089, + 0.77, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.639, + 0.168, + 0.767, + 0.177 + ], + "angle": 0, + "content": "Depth (w/o mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.772, + 0.089, + 0.905, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.777, + 0.168, + 0.9, + 0.177 + ], + "angle": 0, + "content": "Error (w/o mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.18, + 0.226, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.139, + 0.259, + 0.181, + 0.268 + ], + "angle": 0, + "content": "Image 2" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.181, + 0.363, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.234, + 0.258, + 0.358, + 0.268 + ], + "angle": 0, + "content": "Depth (w/ mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.181, + 0.498, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.367, + 0.258, + 0.487, + 0.268 + ], + "angle": 0, + "content": "Error (w/ mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.181, + 0.635, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.259, + 0.588, + 0.268 + ], + "angle": 0, + "content": "Image 2" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.181, + 0.77, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.258, + 0.765, + 0.268 + ], + "angle": 0, + "content": "Depth (w/ mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.772, + 0.181, + 0.905, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.258, + 0.894, + 0.268 + ], + "angle": 0, + "content": "Error (w/ mono feature)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.274, + 0.907, + 0.302 + ], + "angle": 0, + "content": "Figure 3. Effect of monocular features for depth on ScanNet. The monocular feature greatly improves challenging situations like texture-less regions (e.g., the wall in the first example) and reflective surfaces (e.g., the refrigerator in the second example)." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.315, + 0.225, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.424, + 0.204, + 0.438 + ], + "angle": 0, + "content": "Input Image 1" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.316, + 0.357, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.42, + 0.356, + 0.447 + ], + "angle": 0, + "content": "Image 1: Depth (w/ mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.316, + 0.495, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.42, + 0.497, + 0.448 + ], + "angle": 0, + "content": "Image 1: Depth (w/o mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.316, + 0.629, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.421, + 0.631, + 0.449 + ], + "angle": 0, + "content": "Render Error (w/o mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.316, + 0.766, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.639, + 0.421, + 0.767, + 0.449 + ], + "angle": 0, + "content": "Novel View Render (w/o mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.769, + 0.316, + 0.9, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.429, + 0.887, + 0.441 + ], + "angle": 0, + "content": "GT Novel View" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.452, + 0.225, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.567, + 0.205, + 0.581 + ], + "angle": 0, + "content": "Input Image 2" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.452, + 0.358, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.23, + 0.561, + 0.352, + 0.59 + ], + "angle": 0, + "content": "Image 2: Depth (w/ mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.452, + 0.495, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.369, + 0.561, + 0.496, + 0.589 + ], + "angle": 0, + "content": "Image 2: Depth (w/o mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.452, + 0.629, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.561, + 0.631, + 0.589 + ], + "angle": 0, + "content": "Render Error (w/ mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.452, + 0.765, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.639, + 0.561, + 0.766, + 0.589 + ], + "angle": 0, + "content": "Novel View Render (w/ mono feature)" + }, + { + "type": "image", + "bbox": [ + 0.769, + 0.453, + 0.9, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.571, + 0.886, + 0.584 + ], + "angle": 0, + "content": "GT Novel View" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.605, + 0.907, + 0.647 + ], + "angle": 0, + "content": "Figure 4. Effect of monocular features for 3DGS on RealEstate10K. Without monocular features, the model struggles at predicting reliable depth for pixels that are not able to find correspondences (e.g., the lounger chair highlighted with the read rectangle), which subsequently causes misalignment in the rendered image due to the incorrect geometry." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.664, + 0.484, + 0.77 + ], + "angle": 0, + "content": "depth features. We also show the visual comparisons for the Gaussian splatting task in Fig. 4 with two input views. For regions (e.g., the lounge chairs) that only appear in a single image, the pure multi-view method is unable to find correspondences. It thus produces unreliable depth predictions, leading to misalignment in the rendered novel views due to the incorrect geometry." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.774, + 0.484, + 0.864 + ], + "angle": 0, + "content": "We also experiment with removing the cost volume (w/o cost volume) in the multi-view branch and observed a significant performance drop. This indicates that obtaining scale-and multi-view consistent predictions with a pure monocular depth backbone is challenging, which constrains achieving high-quality results for 3D Gaussian reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Different Monocular Features. In Tab. 2, we also evaluate different monocular features, including the ConvNeXt" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.661, + 0.906, + 0.69 + ], + "angle": 0, + "content": "Table 3. Monocular fusion strategy. Our simple concatenation performs surprisingly good compared to other alternatives." + }, + { + "type": "table", + "bbox": [ + 0.578, + 0.701, + 0.845, + 0.788 + ], + "angle": 0, + "content": "
MethodAbs Rel ↓δ1 ↑
Cost volume from ViT11.2690.84
Explicit scale align9.1390.21
Attention fusion8.4092.95
Concatenation (Ours)8.4693.02
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.807, + 0.907, + 0.867 + ], + "angle": 0, + "content": "T [35] features used in AFNet [11], and other popular monocular features including Midas [40] and DINOv2 [37]. The pre-trained Depth Anything V2 [70] monocular features achieve the best view synthesis results." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Monocular Fusion Strategy. We compare with alternative strategies for fusing the monocular features for multi-view" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16458" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.487, + 0.215 + ], + "angle": 0, + "content": "Table 4. Unsupervised Depth Pre-Training with Gaussian Splat-ting. We evaluate the same architecture but with different weights. The pre-training is performed on RealEstate10K, and fine-tuning is performed on TartanAir and VKITTI2. Unsupervised pre-training (2nd row) produces improved depth predictions compared to random initialization (1st). The performance can be further improved with additional fine-tuning (4th), where the benefit of pre-training is especially significant on challenging datasets like TartanAir and KITTI compared to training from random initialization (3rd)." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.218, + 0.482, + 0.306 + ], + "angle": 0, + "content": "
Pre-TrainFine-TuneTartanAirScanNetKITTI
Abs Rel ↓δ1 ↑Abs Rel ↓δ1 ↑Abs Rel ↓δ1 ↑
XX76.223.4339.9722.5690.690.00
✓X29.5353.1621.5176.0956.8346.26
X✓10.8690.556.7096.1411.5687.27
✓✓10.2091.106.6096.2710.6889.92
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.324, + 0.485, + 0.354 + ], + "angle": 0, + "content": "Table 5. Two-view Depth Estimation on ScanNet. Our Depth-Spat outperforms all prior methods by clear margins." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.356, + 0.482, + 0.499 + ], + "angle": 0, + "content": "
MethodAbs Rel ↓RMSE ↓RMSElog ↓
DeMoN [54]23.10.7610.289
BA-Net [50]16.10.3460.214
DeepV2D [52]5.70.1680.080
NeuralRecon [47]4.70.1640.093
DRO [26]5.30.1680.081
UniMatch [65]5.90.1790.082
DepthSplat (w/o GS pre-train)4.50.1250.061
DepthSplat (w/ GS pre-train)3.80.1140.055
" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.523, + 0.486, + 0.75 + ], + "angle": 0, + "content": "depth estimation in Sec. 4.2. In particular, we first compare with MVSFormer [6] that constructs the cost volume with monocular ViT features, which leads to a single-branch architecture. We can observe that our fusion strategy performs significantly better than the single-branch design, potentially because our two-branch design disentangles feature matching and monocular priors, which makes the learning task easier. We also compare with fusing the monocular depth maps (instead of monocular features in our model) by first aligning the monocular depth scale using the multi-view depth and then fusing the depth maps together with an additional network. Again, our simple concatenation performs better. We further compare our concatenation with the attention-based adaptive fusion and observe very similar results. Thus we opt to the simpler concatenation design." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.758, + 0.485, + 0.79 + ], + "angle": 0, + "content": "4.3. Unsupervised Depth Pre-Training with Gaussian Splitting" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.486, + 0.903 + ], + "angle": 0, + "content": "By connecting Gaussian splatting and depth, our DepthSplat provides a way to pre-train the depth model in a fully unsupervised manner. In particular, we first train our full model on the large-scale multi-view posed RealEstate10K dataset (contains \\(\\sim 67\\mathrm{K}\\) Youtube videos) with only the Gaussian splatting rendering loss (Eq. (2)), without any direct supervision on the depth predictions. After pre-training, we take" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.118 + ], + "angle": 0, + "content": "Table 6. Two-view 3DGS on RealEstate10K. Our DepthSplat achieves the best performance." + }, + { + "type": "table", + "bbox": [ + 0.538, + 0.121, + 0.885, + 0.273 + ], + "angle": 0, + "content": "
MethodPSNR ↑SSIM ↑LPIPS ↓
pixelNeRF [75]20.430.5890.550
GPNR [46]24.110.7930.255
AttnRend [17]24.780.8200.213
MuRF [66]26.100.8580.143
pixelSplat [7]25.890.8580.142
MVSplat [9]26.390.8690.128
TranSplat [76]26.690.8750.125
DepthSplat27.470.8890.114
" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.285, + 0.646, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.421, + 0.548, + 0.43 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.602, + 0.421, + 0.615, + 0.429 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.286, + 0.732, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.666, + 0.421, + 0.703, + 0.43 + ], + "angle": 0, + "content": "pixelSplat" + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.287, + 0.819, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.755, + 0.421, + 0.787, + 0.429 + ], + "angle": 0, + "content": "MVSplat" + }, + { + "type": "image", + "bbox": [ + 0.82, + 0.287, + 0.905, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.844, + 0.421, + 0.884, + 0.429 + ], + "angle": 0, + "content": "DepthSplat" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.438, + 0.909, + 0.482 + ], + "angle": 0, + "content": "Figure 5. Novel view synthesis on RealEstate10K. Our DepthSplat performs significantly better than pixelSplat [7] and MVSplat [9] in challenging regions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.505, + 0.909, + 0.763 + ], + "angle": 0, + "content": "the pre-trained depth model and further fine-tune it to the depth task on the mixed TartanAir [58] and VKITTI2 [5] datasets with ground truth depth supervision. In Tab. 4, we evaluate the performance on both in-domain TartanAir test set and the zero-shot generalization on unseen ScanNet and KITTI datasets. We can observe that the benefit of pretraining is especially significant on the challenging datasets like TartanAir and KITTI. The results align well with the observation in [21] which suggests that the pre-training acts as regularization and guides the learning towards better minima and enables better generalization to out-of-distribution datasets. The visual comparison results are provided in the appendix. Given the increasing popularity of view synthesis [61, 81] and multi-view generative models [3, 45], new multi-view datasets [32] and models [55] are gradually introduced, our approach provides a way to pre-train depth models on large-scale multi-view posed image datasets." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.771, + 0.748, + 0.788 + ], + "angle": 0, + "content": "4.4. Benchmark Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Comparisons on ScanNet and RealEstate10K. Tab. 5 and Tab. 6 compare the depth and novel view synthesis results on the standard ScanNet and RealEstate10K benchmarks, respectively. We can see clearly that our DepthSplat achieves state-of-the-art performance on both datasets for both tasks. The visual comparison with previous methods is shown in Fig. 5, where our method significantly improves the perfor" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16459" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.486, + 0.132 + ], + "angle": 0, + "content": "Table 7. Comparisons on DL3DV. Our DepthSplat not only consistently outperforms MVSplat on different number of input views, but also scales more efficiently to more input views." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.144, + 0.478, + 0.255 + ], + "angle": 0, + "content": "
Method#ViewsPSNR ↑SSIM ↑LPIPS ↓Time (s)
MVSplat [9]217.540.5290.4020.072
DepthSplat19.310.6150.3100.083
MVSplat [9]421.630.7210.2330.146
DepthSplat23.120.7800.1780.107
MVSplat [9]622.930.7750.1930.263
DepthSplat24.190.8230.1470.132
" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.284, + 0.482, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.474, + 0.485, + 0.517 + ], + "angle": 0, + "content": "Figure 6. Visual comparisons on DL3DV. Our DepthSplat performs significantly better than MVSplat [9] on regions that hard to match (e.g., repeated patterns)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.548, + 0.484, + 0.655 + ], + "angle": 0, + "content": "mance on challenging scenarios like texture-less regions and occlusions. For the depth results on ScanNet, we report our base models (with ViT-B and two-scale feature matching) trained with and without Gaussian splatting pre-training on the mixed RealEstate10K and DL3DV datasets. Our model significantly outperforms previous methods and can benefit from additional Gaussian splatting pre-training." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Comparisons on DL3DV. To evaluate the performance on complex real-world scenes, we conduct comparisons with the representative model MVSplat [9] on the recently introduced DL3DV dataset [32]. We also compare the results of different numbers of input views (2, 4 and 6) on this dataset. We fine-tune MVSplat and our RealEstate10K pre-trained models on DL3DV training scenes and report the results on the benchmark test set in Tab. 7. Our DepthSplat consistently outperforms MVSplat in all metrics, and our improvements are more significant with fewer input views, which indicates that our model is more robust to sparse views. Visual comparisons with MVSplat on the DL3DV dataset are shown in Fig. 6, where MVSplat's depth quality lags behind our DepthSplat due to matching failure, which leads to blurry and distorted view synthesis results. We show more visual comparison results in the appendix. It is also worth noting" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.146 + ], + "angle": 0, + "content": "Table 8. Cross-dataset generalization. When generalizing to DL3DV and ACID with RealEstate10K pre-trained models, our DepthSplat is consistently better than MVSplat, especially on the more challenging DL3DV dataset." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.151, + 0.905, + 0.218 + ], + "angle": 0, + "content": "
MethodDL3DVACID
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
MVSplat [9]24.140.8080.14928.150.8410.147
DepthSplat27.660.8950.09628.370.8470.141
" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.237, + 0.907, + 0.298 + ], + "angle": 0, + "content": "that our method scales more efficiently to more input views thanks to our lightweight local feature matching approach (Sec. 3.1), which is unlike the expensive global pair-wise matching used in MVSplat." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.301, + 0.909, + 0.438 + ], + "angle": 0, + "content": "Cross-Dataset Generalization. We evaluate the cross-dataset generalization capability by directly testing on DL3DV [32] and ACID [33] datasets with RealEstate10K [82] pre-trained models. The results are shown in Tab. 8, where our DepthSplat consistently outperforms MVSplat on both datasets, especially on the more challenging DL3DV dataset which features complex scene structures. The visual comparison results are shown in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.442, + 0.909, + 0.579 + ], + "angle": 0, + "content": "High-Resolution Results. In addition to the comparison results on the \\(256 \\times 256\\) resolution RealEstate10K and \\(256 \\times 448\\) resolution DL3DV dataets, we show more high-resolution \\((512 \\times 960)\\) qualitative results in the appendix. We also invite the readers to our project page haofelixu.github.io/deathsplat for high-resolution \\((512 \\times 960)\\) video results on different number of input views (6 and 12), where our DepthSplat is able to reconstruct larger-scale or 360 scenes from more input views." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.598, + 0.634, + 0.613 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.625, + 0.909, + 0.746 + ], + "angle": 0, + "content": "In this paper, we introduce DepthSplat, a new approach to connecting Gaussian splatting and depth to achieve state-of-the-art results on ScanNet, RealEstate10K and DL3DV datasets for both depth and view synthesis tasks. We show that our model enables unsupervised depth pre-training with Gaussian splatting rendering loss, providing a way to leverage large-scale posed multi-view image datasets for training more robust and generalizable multi-view depth models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.911, + 0.901 + ], + "angle": 0, + "content": "Limitations. Our current model requires camera poses as input along with the multi-view images, which might be challenging to obtain when the input views are extremely sparse. An interesting future direction is to remove this requirement by exploring pose-free models [72, 80]. In addition, our model predicts pixel-aligned Gaussians, where the number of Gaussians will be significantly large when processing a large number of input views [60, 79]. Further improving the geometry representation and the scalability to many input views would be exciting future work." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16460" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.486, + 0.239 + ], + "angle": 0, + "content": "We thank Yuedong Chen for his generous help with the DL3DV dataset. Andreas Geiger was supported by the ERC Starting Grant LEGO-3D (850533) and the DFG EXC number 2064/1 - project number 390727645. This work was supported as part of the Swiss AI Initiative by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID a03 on Alps. H. Blum is also with the Lamarr Institute and D. 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ACM TOG, 2018. 1, 2, 4, 5, 8" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.906, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16463" + } + ] +] \ No newline at end of file diff --git a/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/3c38ee77-2762-4a1c-ad37-7a37f09eab09_origin.pdf b/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/3c38ee77-2762-4a1c-ad37-7a37f09eab09_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a7782894d33a728ef4099190efc0c278d7a15459 --- /dev/null +++ b/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/3c38ee77-2762-4a1c-ad37-7a37f09eab09_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6918c8a9f84af814e900c184b751f2359be8aaa4f9c2fe1dc7a8bff5718dbbfe +size 3848020 diff --git a/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/full.md b/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ccb003f8c738e044454926543b0251fa92cfe8d8 --- /dev/null +++ b/2025/DepthSplat_ Connecting Gaussian Splatting and Depth/full.md @@ -0,0 +1,379 @@ +# DepthSplat: Connecting Gaussian Splatting and Depth + +Haofei Xu $^{1,2}$ Songyou Peng $^{1}$ Fangjinhua Wang $^{1}$ Hermann Blum $^{1,4}$ Daniel Barath $^{1}$ Andreas Geiger $^{2}$ Marc Pollefeys $^{1,3}$ $^{1}$ ETH Zurich $^{2}$ University of Tübingen, Tübingen AI Center $^{3}$ Microsoft $^{4}$ University of Bonn haofeixu.github.io/dephthsplat + +![](images/d5dbafa4b2dfed924e7ccfb619b1f9c04809f645465ede8e10bd43e85263298e.jpg) +Figure 1. DepthSplat enables cross-task interactions between Gaussian splatting and depth. Left: Better depth leads to improved Gaussian splatting reconstruction. Right: Unsupervised depth pre-training with Gaussian splatting leads to reduced depth prediction error. + +![](images/ecffa3f78856e2b9a04eb03840e571e9359c85a7054991dd25906c7c2d88464d.jpg) + +![](images/19be01ccce055d534016650cd5979db4890b22f4da7670c6e5b58964ad3f5fc6.jpg) + +# Abstract + +Gaussian splatting and single-view depth estimation are typically studied in isolation. In this paper, we present DepthSplat to connect Gaussian splatting and depth estimation and study their interactions. More specifically, we first contribute a robust multi-view depth model by leveraging pretrained monocular depth features, leading to high-quality feed-forward 3D Gaussian splatting reconstructions. We also show that Gaussian splatting can serve as an unsupervised pre-training objective for learning powerful depth models from large-scale multi-view posed datasets. We validate the synergy between Gaussian splatting and depth estimation through extensive ablation and cross-task transfer experiments. Our DepthSplat achieves state-of-the-art performance on ScanNet, RealEstate10K and DL3DV datasets in terms of both depth estimation and novel view synthesis, demonstrating the mutual benefits of connecting both tasks. In addition, DepthSplat enables feed-forward reconstruction from 12 input views (512 × 960 resolutions) in 0.6 seconds. + +# 1. Introduction + +Novel view synthesis [4, 82] and depth prediction [20, 44] are two fundamental tasks in computer vision, serving as the + +driving force behind numerous applications ranging from augmented reality to robotics and autonomous driving. There have been notable advancements in both areas recently. + +For novel view synthesis, 3D Gaussian Splatting (3DGS) [29] has emerged as a popular technique due to its impressive real-time performance while attaining high visual fidelity. Recently, advances in feed-forward 3DGS models [7, 9, 48] have been introduced to alleviate the need for tedious per-scene optimization, also enabling few-view 3D reconstruction. The state-of-the-art sparse-view method MVSplat [9] relies on feature matching-based multi-view depth estimation [65] to localize the 3D Gaussian positions, which makes it suffer from similar limitations (e.g., occlusions, texture-less regions, and reflective surfaces) as other multi-view depth methods [18, 25, 44, 56, 71]. + +On the other hand, significant progress has been made in monocular depth estimation, with recent models [19, 22, 28, 40, 69, 74] achieving robust predictions on diverse in-the-wild data. However, these depths typically lack consistent scales across multiple views, constraining their performance in downstream tasks like 3D reconstruction [59, 73]. + +The integration of 3DGS with single-view depth estimation presents a compelling solution to overcome the individual limitations of each technique while at the same time enhancing their strengths. To this end, we introduce + +DepthSplat, which exploits the complementary nature of sparse-view feed-forward 3DGS and robust monocular depth estimation to improve the performance for both tasks. + +Specifically, we first contribute a robust multi-view depth model by integrating pre-trained monocular depth features [70] to the multi-view feature matching branch, which not only maintains the consistency of multi-view depth models but also leads to more robust results in situations that are hard to match (e.g., occlusions, texture-less regions and reflective surfaces). The predicted multi-view depth maps are then unprojected to 3D as the Gaussian centers, and we use an additional lightweight network to predict other remaining Gaussian parameters. They are combined together to achieve novel view synthesis with the splatting operation [29]. + +While previous methods [1, 11, 31] also try to fuse monocular and multi-view depths, they usually rely on sophisticated architectures. In contrast, we identify the power of off-the-shelf pre-trained monocular depth models and propose to augment multi-view cost volumes with monocular features, leading to a simpler model and stronger performance. + +Thanks to our improved multi-view depth model, the quality of novel view synthesis with Gaussian splatting is also significantly enhanced (see Fig. 1 left). In addition, our Gaussian splatting module is fully differentiable, which requires only photometric supervision to optimize all model components. This provides a new, unsupervised way to pre-train depth prediction models on large-scale multi-view posed datasets without requiring ground truth geometry information. The pre-trained depth model can be further fine-tuned for specific depth tasks and achieves superior results over training from scratch (see Fig. 1 right, where unsupervised pre-training leads to improved performance). + +We conduct extensive experiments on the large-scale TartanAir [58], ScanNet [14] and RealEstate10K [82] datasets for depth estimation and Gaussian splatting tasks, as well as the recently introduced DL3DV [32] dataset, which features complex real-world scenes and thus is more challenging. Under various evaluation settings, our DepthSplat achieves state-of-the-art results. We also achieve promising feedforward reconstruction results of large-scale or 360 scenes from 12 input views ( $512 \times 960$ resolutions) in 0.6 seconds. The strong performance on both tasks demonstrates the mutual benefits of connecting Gaussian splatting and depth. + +# 2. Related Work + +Multi-View Depth Estimation. As a core component of classical multi-view stereo pipelines [44], multi-view depth estimation exploits multi-view photometric consistency across multiple images to perform feature matching and predict the depth map of the reference image. In recent years, many learning-based methods [6, 15, 18, 25, 56, 57, 71] have been proposed to improve depth accuracy. Though these learning-based methods significantly improve the depth qual + +ity compared to traditional methods [23, 44, 67], they cannot handle challenging situations where the multi-view photometric consistency assumption is not guaranteed, e.g., occlusions, low-textured areas, and non-Lambertian surfaces. + +Monocular Depth Estimation. Recently, we have witnessed significant progress in depth estimation from a single image [2, 28, 40, 69, 74], and existing methods can produce surprisingly accurate results on diverse in-the-wild data. However, monocular depth methods inherently suffer from scale ambiguities, which makes it challenging to use them for downstream tasks like 3D reconstruction [73]. In this paper, we leverage the powerful features from a pre-trained monocular depth model [70] to augment feature-matching based multi-view depth estimation, which not only maintains the multi-view consistency but also leads to significantly improved robustness in challenging situations such as low-textured regions and reflective surfaces. + +Feed-Forward Gaussian Splatting. Several feed-forward 3D Gaussian splatting models [7-10, 48, 51, 62, 68, 77] have been proposed in literature thanks to its efficiency and ability to handle sparse views. In particular, pixelSplat [7] and Splatter Image [48] predict 3D Gaussians from image features, while MVSplat [9] encodes the feature matching information with cost volumes and achieves better geometry. However, it inherently suffers from the limitation of feature matching in challenging situations like texture-less regions and reflective surfaces. In this paper, we propose to integrate monocular features from pre-trained monocular depth models [70] for more robust depth prediction and 3D Gaussian reconstruction. Another line of work like LGM [51], GRM [68], and GS-LRM [77] relies significantly on the training data and compute, discarding explicit feature matching cues and learning priors purely from data. This makes them expensive to train (e.g., GS-LRM [77] is trained with 64 A100 GPUs for 2 days), while our model can be trained in 2 days with 4 GPUs. Moreover, our Gaussian splatting module enables pre-training depth model from large-scale multi-view posed datasets without ground truth depth supervision. + +Depth and Gaussian Splatting. Flash3D [49] explores a pre-trained monocular depth model [39] for single-image 3D Gaussian reconstruction. In contrast, we target large-scale scene reconstruction from multiple views. TranSplat [76] leverages monocular depth to improve Gaussian reconstruction. However, a crucial difference is that TranSplat uses monocular features to refine the coarse depth predicted from a cost volume, which makes it inherently vulnerable to the error in the coarse stage and, thus, suffers from the error propagation issue. In contrast, we avoid this by combining cost volume and monocular features early, which performs significantly better than TranSplat (Tab. 6). Another line of work [12, 53] applies an additional depth loss to the Gaussian optimization process. We note that these two approaches (feed-forward vs. per-scene optimization) are orthogonal. + +![](images/7b20ba694cdf6e70fc3b5782f4f7e4ff58219cfddfd7c4b9fc91f73c4845c951.jpg) +Figure 2. DepthSplat connects depth estimation and 3D Gaussian splatting with a shared architecture, which enables cross-task transfer. In particular, DepthSplat consists of a multi-view branch to model feature-matching information and a single-view branch to extract monocular features. The per-view cost volumes and monocular features are concatenated for depth regression with a 2D U-Net architecture. For the depth estimation task, we train the depth model with ground truth depth supervision. For the Gaussian splatting task, we first unproject all depth maps to 3D as the Gaussian centers, and in parallel, we use an additional head to predict the remaining Gaussian parameters. Novel views are rendered with the splatting operation. The full model for novel view synthesis is trained with the photometric rendering loss, which can also be used as an unsupervised pre-training stage for the depth model. + +# 3. DepthSplat + +Given $N$ input images $\{\pmb{I}^i\}_{i=1}^N$ , $(\pmb{I}^i \in \mathbb{R}^{H \times W \times 3}$ , where $H$ and $W$ are the image sizes) with corresponding projection matrices $\{\mathbf{P}_i\}_{i=1}^N$ , $(\mathbf{P}_i \in \mathbb{R}^{3 \times 4}$ , computed from the intrinsic and extrinsic matrices), our goal is to predict dense per-pixel depth $\mathbf{D}_i \in \mathbb{R}^{H \times W}$ and per-pixel Gaussian parameters $\{(\pmb{\mu}_j, \alpha_j, \pmb{\Sigma}_j, c_j)\}_{j=1}^{H \times W \times N}$ for each image, where $\pmb{\mu}_j, \alpha_j, \pmb{\Sigma}_j$ and $c_j$ are the 3D Gaussian's position, opacity, covariance, and color. As shown in Fig. 2, key to our method is a multi-view depth model augmented with monocular depth features, where we obtain the position $\pmb{\mu}_j$ of each Gaussian by unprojecting depth with camera parameters, and other Gaussian parameters are predicted by an additional head. + +More specifically, our depth model consists of two branches: one for modeling feature matching using cost volumes, and another for extracting monocular features from a pre-trained monocular depth network. The cost volumes and monocular features are concatenated together for subsequent depth regression with a 2D U-Net and a softmax layer. For the depth task, we train our depth model with ground truth depth supervision. Our full model for novel view synthesis is trained with the rendering loss, which can also be used as an unsupervised pre-training stage for the depth model. We introduce the individual components below. + +# 3.1. Multi-View Feature Matching + +In this branch, we extract multi-view features with a multiview Transformer architecture and then build multiple cost volumes that correspond to each input view. + +Multi-View Feature Extraction. For $N$ input images, we first use a lightweight weight-sharing ResNet [27] architecture to get $s \times$ downsampled features for each image independently. To handle different image resolutions, we + +make the downsampling factor $s$ flexible by controlling the number of stride-2 $3 \times 3$ convolutions. For example, the downsampling factor $s$ is 4 if two stride-2 convolutions are used and 8 if three are used. To exchange information across different views, we use a multi-view Swin Transformer [34, 64, 65] which contains six stacked self- and cross-attention layers to obtain multi-view-aware features $\{F_i\}_{i=1}^N$ , $F^i \in \mathbb{R}^{\frac{H}{s} \times \frac{W}{s} \times C}$ , where $C$ is the feature dimension. When more than two images ( $N > 2$ ) are given as input, we perform cross-attention between each reference view and its top-2 nearest neighboring views, which are selected based on their camera distances to the reference view. This makes computation tractable with many input views. + +Feature Matching. We encode the feature matching information across different views with the plane-sweep stereo approach [13, 65]. More specifically, for each view $i$ , we first uniformly sample $D$ depth candidates $\{d_m\}_{m=1}^D$ from the near and far depth ranges and then warp the feature $F^j$ of view $j$ to view $i$ with the camera projection matrix and each depth candidate $d_m$ . Then we obtain $D$ warped features $\{F_{d_m}^{j \rightarrow i}\}_{m=1}^D$ that correspond to feature $F^i$ . We then measure their feature correlations with the dot-product operation [9, 63]. The cost volume $C_i \in \mathbb{R}^{\frac{H}{s} \times \frac{W}{s} \times D}$ for image $i$ is obtained by stacking all correlations. Accordingly, we obtain cost volumes $\{C_i\}_{i=1}^N$ for all input images $\{I_i\}_{i=1}^N$ . For more than two input views, similar to the strategy in cross-view attention computation, we select the top-2 nearest views for each reference view and compute feature correlations with only the selected views. This enables our cost volume construction to achieve a good speed-accuracy trade-off and scale efficiently to a larger number of input views. The correlation values for the two selected views are combined with averaging. + +# 3.2. Monocular Depth Feature Extraction + +Despite the remarkable progress in multi-view feature matching-based depth estimation [57, 65, 71] and Gaussian splatting [9], they inherently suffer from limitations in challenging situations like occlusions, texture-less regions, and reflective surfaces. Thus, we propose to integrate pre-trained monocular depth features into the cost volume to handle scenarios that are challenging or impossible to match. + +More specifically, we leverage the pre-trained monocular depth backbone from the recent Depth Anything V2 [70] model thanks to its impressive performance on diverse in-the-wild data. The monocular backbone is a ViT [16, 37] model, which has a patch size of 14 and outputs a feature map that is $1/14$ spatial resolution of the original image. We simply bilinearly interpolate the spatial resolution of the monocular features to the same resolution as the cost volume in Sec. 3.1 and obtain the monocular feature $\mathbf{F}_{\mathrm{mono}}^{i} \in \mathbb{R}^{\frac{H}{s} \times \frac{W}{s} \times C_{\mathrm{mono}}}$ for input image $\mathbf{I}_i$ , where $C_{\mathrm{mono}}$ is the dimension of the monocular feature. This process is performed for all input images in parallel and we obtain monocular features $\{\mathbf{F}_{\mathrm{mono}}^{i} \in \mathbb{R}^{\frac{H}{s} \times \frac{W}{s} \times C_{\mathrm{mono}}}\}_{i=1}^{N}$ , which are subsequently used for per-view depth map estimations. + +# 3.3. Feature Fusion and Depth Regression + +To achieve robust and multi-view consistent depth predictions, we combine the monocular feature $\pmb{F}_{\mathrm{mono}}^{i} \in \mathbb{R}^{\frac{H}{s} \times \frac{W}{s} \times C_{\mathrm{mono}}}$ and cost volume $C_i \in \mathbb{R}^{\frac{H}{s} \times \frac{W}{s} \times D}$ via simple concatenation in the channel dimension. A subsequent 2D U-Net [42, 43] is used to regress depth from the concatenated monocular features and cost volumes. This process is performed for all the input images in parallel and for each image, it outputs a tensor of shape $\frac{H}{s} \times \frac{W}{s} \times D$ , where $D$ is the number of depth candidates. We normalize the $D$ dimension with the softmax operation and perform a weighted average of all depth candidates to obtain the depth output. + +We also apply a hierarchical matching [25] architecture where an additional refinement step at $2 \times$ higher feature resolution is employed to improve the performance further. More specifically, based on the coarse depth prediction, we perform a correspondence search on the $2 \times$ higher feature maps within the neighbors of the $2 \times$ upsampled coarse depth prediction. Since we already have a coarse depth prediction, we only need to search a smaller range at the higher resolution, and thus, we construct a smaller cost volume compared to the coarse stage. Such a 2-scale hierarchical architecture not only leads to improved efficiency since most computation is spent on low resolution, but also leads to better results thanks to the use of higher-resolution features [25]. Similar feature fusion and depth regression procedure is used to get higher-resolution depth predictions, which are subsequently upsampled with a DPT head [41] to the full resolution. + +# 3.4. Gaussian Parameter Prediction + +For the task of 3D Gaussian splatting, we directly unproject the per-pixel depth maps to 3D with the camera parameters as the Gaussian centers $\pmb{\mu}_j$ . To predict other remaining Gaussian parameters $\alpha_{j}$ (opacity), $\Sigma_{j}$ (covariance) and $c_{j}$ (color), we use an additional DPT head [41], where it takes the concatenated image, depth and feature information as input and outputs all the remaining Gaussian parameters. With all the predicted 3D Gaussians, we can render novel views with the Gaussian splatting operation [29]. + +# 3.5. Training Loss + +We study the properties of our proposed model on two tasks: depth estimation and novel view synthesis with 3D Gaussian splatting [29]. The loss functions are introduced below. + +Depth estimation. We train our depth model (without the Gaussian splatting head) with $\ell_1$ loss and gradient loss between the inverse depths of prediction and ground truth: + +$$ +\begin{array}{l} L _ {\text {d e p t h}} = \alpha \cdot | \boldsymbol {D} _ {\text {p r e d}} - \boldsymbol {D} _ {\text {g t}} | + \beta \cdot | \partial_ {x} \boldsymbol {D} _ {\text {p r e d}} - \partial_ {x} \boldsymbol {D} _ {\text {g t}} | \\ + \beta \cdot \left| \partial_ {y} \boldsymbol {D} _ {\text {p r e d}} - \partial_ {y} \boldsymbol {D} _ {\mathrm {g t}} \right|), \tag {1} \\ \end{array} +$$ + +where $\partial_x$ and $\partial_y$ denotes the gradients on the $x$ and $y$ directions, respectively. Following UniMatch [65], we use $\alpha = 20$ and $\beta = 20$ . + +View synthesis. We train our full model with a combination of mean squared error (MSE) and LPIPS [78] losses between rendered and ground truth image colors: + +$$ +L _ {\mathrm {g s}} = \sum_ {m = 1} ^ {M} \left(\operatorname {M S E} \left(I _ {\text {r e n d e r}} ^ {m}, I _ {\mathrm {g t}} ^ {m}\right) + \lambda \cdot \operatorname {L P I P S} \left(I _ {\text {r e n d e r}} ^ {m}, I _ {\mathrm {g t}} ^ {m}\right)\right), \tag {2} +$$ + +where $M$ is the number of novel views to render in a single forward pass. The LPIPS loss weight $\lambda$ is set to 0.05 [9]. + +# 4. Experiments + +Implementation Details. We implement our method in PyTorch [38] and optimize our model with the AdamW [36] optimizer and cosine learning rate schedule. We adopt the xFormers [30] library for our monocular ViT backbone implementation. We use a lower learning rate $2 \times 10^{-6}$ for the pre-trained Depth Anything V2 [70] backbone, and other remaining layers use a learning rate of $2 \times 10^{-4}$ . The feature downsampling factor $s$ in our multi-view branch (Sec. 3.1) is chosen based on the image resolution. More specifically, for experiments on the $256 \times 256$ resolution RealEstate10K [82] dataset, we choose $s = 4$ . For higher resolution datasets (e.g., TartanAir [58], ScanNet [14], KITTI [24] and DL3DV [32]), we choose $s = 8$ . Our hierarchical matching models in Sec. 3.3 use 2-scale features, i.e., $1/8$ and $1/4$ , or $1/4$ and $1/2$ resolutions. + +Table 1. DepthSplat model variants. We evaluate different monocular backbones and different multi-view models (1-scale and 2-scale features for hierarchical matching as described in Sec. 3.3), where both larger monocular backbones and 2-scale hierarchical models lead to consistently improved performance for both depth and view synthesis tasks. The inference time is measured on a single A100 GPU for two input views at $256 \times 256$ resolutions. + +
MonoMulti-ViewDepth (TartanAir)3DGS (RealEstate10K)Param (M)Time (s)
Abs Rel ↓δ1 ↑PSNR ↑SSIM ↑LPIPS ↓
ViT-S1-scale8.4693.0226.840.8780.122380.050
ViT-B1-scale6.9494.4627.060.8820.1191150.053
ViT-L1-scale6.0795.5227.230.8850.1163470.061
ViT-S2-scale7.0194.5627.120.8840.119410.062
ViT-B2-scale6.2295.3127.340.8870.1161200.070
ViT-L2-scale5.5796.0727.470.8890.1143540.079
+ +Training Details. For depth experiments on ScanNet [14], we train our depth model on $4 \times$ GH200 GPUs for 100K iterations with a total batch size of 32. For the ablation experiments on depth task, we mainly use synthetic datasets (TartanAir [58] and VKITTI2 [5]) for training since they provide high-quality ground truth depths. For Gaussian splatting experiments, we consider both low-resolution and high-resolution images. In particular, for comparisons with previous methods [7, 9], we mainly use $256 \times 256$ resolution RealEstate10K [82] and $256 \times 448$ resolution DL3DV [32] datasets. We also report high-resolution $(512 \times 960)$ results on RealEstate10K and DL3DV datasets for qualitative evaluations. For experiments on the $256 \times 256$ RealEstate10K dataset, we train our model on $4 \times$ GH200 GPUs for 150K iterations with a total batch size of 32, which takes 1 day for the small model and 2 days for the large model. For experiments on the $256 \times 448$ DL3DV [32] dataset, we fine-tune our RealEstate10K pre-trained model on $4 \times$ GH200 GPUs for 100K iterations with a total batch size of 4, where the number of input views is randomly sampled from 2 to 6. We evaluate the model's performance on different number of input views (2, 4, 6). For high-resolution results, we fine-tune our low-resolution pre-trained models on high-resolution images. More training details are provided in the appendix. Our code and training scripts are available at github.com/cvg/deepsplat to ease reproducibility. + +# 4.1. Model Variants + +We first study several different model variants for both depth estimation and view synthesis tasks. In particular, we explore different monocular backbones [70] (ViT-S, ViT-B, ViT-L) and different multi-view models (1-scale and 2-scale). We conduct depth experiments on the large-scale TartanAir [58] synthetic dataset, which features both indoor and outdoor scenes and has perfect ground truth depth. The Gaussian splatting experiments are conducted on the standard RealEstate10K [82] dataset. Following community standards, we report the depth evaluation metrics [20] of + +Table 2. Ablations. We evaluate the contribution of the monocular feature branch and the cost volume branch (1st group of experiments), as well as different monocular features (2nd group of experiments). Our results indicate that the monocular feature and cost volume are complementary, with large performance drops when removing either one. The pre-trained Depth Anything V2 model weights achieve the best view synthesis results. + +
ComponentsDepth (TartanAir)3DGS (RealEstate10K)
Abs Rel ↓δ1 ↑PSNR ↑SSIM ↑LPIPS ↓
Full8.4693.0226.840.8780.122
w/o mono feature12.2588.0026.040.8640.134
w/o cost volume11.3490.0223.240.7660.184
ConvNeXt-T10.5091.1326.110.8650.134
Midas9.5391.6126.460.8720.128
DINO V28.9392.4926.760.8770.123
Depth Anything V18.3893.2326.760.8770.124
Depth Anything V28.4693.0226.840.8780.122
+ +Abs Rel (relative $\ell_1$ error) and $\delta_{1}$ (percentage of correctly estimated pixels within a threshold) and novel view synthesis metrics [29] of PSNR, SSIM, and LPIPS. The results in Tab. 1 demonstrate that both larger monocular backbones and 2-scale hierarchical models lead to consistently improved performance for both tasks. We name three different model sizes with "Small": "ViT-S monocular, 1-scale multi-view", "Base": "ViT-B monocular, 2-scale multi-view", and "Large": "ViT-L monocular, 2-scale multi-view". + +From Tab. 1, we can also observe that better depth network architecture leads to improved view synthesis. In the appendix, we conduct additional experiments to study the effect of different initializations for the depth network to the view synthesis performance. Our results show that a better depth model initialization also contributes to improved rendering quality. In summary, both better depth network architecture and better depth model initialization lead to improved novel view synthesis results. + +# 4.2. Ablation and Analysis + +In this section, we study the properties of our key components on the TartanAir dataset (for depth) and RealEstate10K dataset (for view synthesis with Gaussian splatting). + +Monocular Features for Depth and Gaussian Splatting. In Tab. 2, we compare our full model (Full) with the model variant where the monocular depth feature branch (with a ViT-S model pre-trained by Depth Anything V2 [70]) is removed (w/o mono feature), leaving only the multi-view branch. We can observe a clear performance drop for both depth and view synthesis tasks. In Fig. 3, we visualize the depth predictions and error maps of both models on the ScanNet dataset. The pure multi-view feature matching-based approach struggles a lot at texture-less regions and reflective surfaces. At the same time, our full model achieves reliable results thanks to the powerful prior captured in monocular + +![](images/12d56b8927c8a335e2db48feaebcbe9ecf40ba77e49ede0fe43f357427c223a9.jpg) +Image 1 + +![](images/dff632b6de3821e7a046d76e406984b149be22862378f248bd991e2f118422d2.jpg) +Depth (w/o mono feature) + +![](images/67e00739ecf694e4e180fe1973272330ec6b62d4e59f272bd3e1048da9d877b0.jpg) +Error (w/o mono feature) + +![](images/a79285763d2939c77ce236a7acd9381676287caa9224a7bf3044c3e8c4ae7cf1.jpg) +Image 1 + +![](images/073b55e6a4e835018bcb466a13cd155eee9ed576e4b3d0b6e64666f4ecec420a.jpg) +Depth (w/o mono feature) + +![](images/147317fd5799aa61e49a3714c4e1df234935f624fbe820822c951b4ad7483339.jpg) +Error (w/o mono feature) + +![](images/72cc76c0970e9e92133fedda75b207d5b64e1b08cbedb6369e9f61dfd4088157.jpg) +Image 2 + +![](images/4b3a4b278fa8a294d4a751e982ec0cf8d18fe8ce73c035d96cc7e68cb7a26878.jpg) +Depth (w/ mono feature) + +![](images/0669fca24201a8b2554aa690ff980b3b91e860472e5ad30c95cd4129947fae41.jpg) +Error (w/ mono feature) + +![](images/a41149169555bdb61738202243723fae3971695a2df7d62f7e07aa656ef1b1e2.jpg) +Image 2 + +![](images/3303663fbb1e501328a389c180f813cca297b64b7b5e001630045cac3c90edf0.jpg) +Depth (w/ mono feature) + +![](images/cd0143524ad7b1441341f013f242190c9e5b1d9356b444bcc1c684b37c97f808.jpg) +Error (w/ mono feature) + +![](images/024ddd21965b9818414e0b149b0121516ae21be89044f1c04ecdb0f500e35d77.jpg) +Figure 3. Effect of monocular features for depth on ScanNet. The monocular feature greatly improves challenging situations like texture-less regions (e.g., the wall in the first example) and reflective surfaces (e.g., the refrigerator in the second example). +Input Image 1 + +![](images/2aea3bbfe2b5136278a6847f1d409f795052ed6203c27a2cf405d633f57e9cb7.jpg) +Image 1: Depth (w/ mono feature) + +![](images/dc519e7765a8083212e15f7d836356dbc46afe5290cb27f168ffaa272da76b94.jpg) +Image 1: Depth (w/o mono feature) + +![](images/eb692571fdb314adbd3a24ceb74f1fc1c258c3da29aed62b982ffdc3adc0519d.jpg) + +![](images/fdcf12098869025cbd207c1471d07c58db5972f15837363905d11492d4f640dd.jpg) + +![](images/557a0988583caf230dd57779b5ca336b982900cfc230b87a7de9274cb9302e05.jpg) +GT Novel View + +![](images/e5c15727c6ea1fb169ba3eddb5d07ede7d3c6013c282ea3fa2b907c927c18781.jpg) +Input Image 2 +Image 2: Depth (w/ mono feature) +Figure 4. Effect of monocular features for 3DGS on RealEstate10K. Without monocular features, the model struggles at predicting reliable depth for pixels that are not able to find correspondences (e.g., the lounger chair highlighted with the read rectangle), which subsequently causes misalignment in the rendered image due to the incorrect geometry. + +![](images/b699c3363bb1d4ebcd3abd59e6b4ea591cffc6b9719af9eb4ce8923d3a6da0c7.jpg) + +![](images/02b200dbfb77a299a03a5fed46b926ec3097c6444de9a112c9dc0e9838b6c107.jpg) +Image 2: Depth (w/o mono feature) + +![](images/de5cba7f18f45c51e3f4aedf08b922fb285de516fcb8fc46a630103c4f4432da.jpg) +Render Error (w/o mono feature) +Render Error (w/ mono feature) + +![](images/0cc53cd888a9cc8de0664050325017c0fca60d195026e5bca69dfaf08d4fa5a6.jpg) +Novel View Render (w/o mono feature) + +![](images/3c289b29c14ac875a76663ff14ccece14021f53c616ad492407e20dc54735e25.jpg) +Novel View Render (w/ mono feature) +GT Novel View + +depth features. We also show the visual comparisons for the Gaussian splatting task in Fig. 4 with two input views. For regions (e.g., the lounge chairs) that only appear in a single image, the pure multi-view method is unable to find correspondences. It thus produces unreliable depth predictions, leading to misalignment in the rendered novel views due to the incorrect geometry. + +We also experiment with removing the cost volume (w/o cost volume) in the multi-view branch and observed a significant performance drop. This indicates that obtaining scale-and multi-view consistent predictions with a pure monocular depth backbone is challenging, which constrains achieving high-quality results for 3D Gaussian reconstruction. + +Different Monocular Features. In Tab. 2, we also evaluate different monocular features, including the ConvNeXt + +Table 3. Monocular fusion strategy. Our simple concatenation performs surprisingly good compared to other alternatives. + +
MethodAbs Rel ↓δ1 ↑
Cost volume from ViT11.2690.84
Explicit scale align9.1390.21
Attention fusion8.4092.95
Concatenation (Ours)8.4693.02
+ +T [35] features used in AFNet [11], and other popular monocular features including Midas [40] and DINOv2 [37]. The pre-trained Depth Anything V2 [70] monocular features achieve the best view synthesis results. + +Monocular Fusion Strategy. We compare with alternative strategies for fusing the monocular features for multi-view + +Table 4. Unsupervised Depth Pre-Training with Gaussian Splat-ting. We evaluate the same architecture but with different weights. The pre-training is performed on RealEstate10K, and fine-tuning is performed on TartanAir and VKITTI2. Unsupervised pre-training (2nd row) produces improved depth predictions compared to random initialization (1st). The performance can be further improved with additional fine-tuning (4th), where the benefit of pre-training is especially significant on challenging datasets like TartanAir and KITTI compared to training from random initialization (3rd). + +
Pre-TrainFine-TuneTartanAirScanNetKITTI
Abs Rel ↓δ1 ↑Abs Rel ↓δ1 ↑Abs Rel ↓δ1 ↑
XX76.223.4339.9722.5690.690.00
✓X29.5353.1621.5176.0956.8346.26
X✓10.8690.556.7096.1411.5687.27
✓✓10.2091.106.6096.2710.6889.92
+ +Table 5. Two-view Depth Estimation on ScanNet. Our Depth-Spat outperforms all prior methods by clear margins. + +
MethodAbs Rel ↓RMSE ↓RMSElog ↓
DeMoN [54]23.10.7610.289
BA-Net [50]16.10.3460.214
DeepV2D [52]5.70.1680.080
NeuralRecon [47]4.70.1640.093
DRO [26]5.30.1680.081
UniMatch [65]5.90.1790.082
DepthSplat (w/o GS pre-train)4.50.1250.061
DepthSplat (w/ GS pre-train)3.80.1140.055
+ +depth estimation in Sec. 4.2. In particular, we first compare with MVSFormer [6] that constructs the cost volume with monocular ViT features, which leads to a single-branch architecture. We can observe that our fusion strategy performs significantly better than the single-branch design, potentially because our two-branch design disentangles feature matching and monocular priors, which makes the learning task easier. We also compare with fusing the monocular depth maps (instead of monocular features in our model) by first aligning the monocular depth scale using the multi-view depth and then fusing the depth maps together with an additional network. Again, our simple concatenation performs better. We further compare our concatenation with the attention-based adaptive fusion and observe very similar results. Thus we opt to the simpler concatenation design. + +# 4.3. Unsupervised Depth Pre-Training with Gaussian Splitting + +By connecting Gaussian splatting and depth, our DepthSplat provides a way to pre-train the depth model in a fully unsupervised manner. In particular, we first train our full model on the large-scale multi-view posed RealEstate10K dataset (contains $\sim 67\mathrm{K}$ Youtube videos) with only the Gaussian splatting rendering loss (Eq. (2)), without any direct supervision on the depth predictions. After pre-training, we take + +Table 6. Two-view 3DGS on RealEstate10K. Our DepthSplat achieves the best performance. + +
MethodPSNR ↑SSIM ↑LPIPS ↓
pixelNeRF [75]20.430.5890.550
GPNR [46]24.110.7930.255
AttnRend [17]24.780.8200.213
MuRF [66]26.100.8580.143
pixelSplat [7]25.890.8580.142
MVSplat [9]26.390.8690.128
TranSplat [76]26.690.8750.125
DepthSplat27.470.8890.114
+ +![](images/cd6d1a336b22f28e6d77f099f808b471c626864648a0c45f79657fe8e8c33f79.jpg) +Input +GT + +![](images/7ec42f13f1fda6087e9aa2d4e88fcf0c8e41d1ec936b0022efb14597a4703796.jpg) +pixelSplat + +![](images/8c1f579fa78a26eab5f96447e863047d7e20823b6f04b9e5d59418a6ad09e22d.jpg) +MVSplat +Figure 5. Novel view synthesis on RealEstate10K. Our DepthSplat performs significantly better than pixelSplat [7] and MVSplat [9] in challenging regions. + +![](images/9e3526351c2763b67c01ddaaef8a47ffdb58df66d7d7b145d3ce3ae56e7c0115.jpg) +DepthSplat + +the pre-trained depth model and further fine-tune it to the depth task on the mixed TartanAir [58] and VKITTI2 [5] datasets with ground truth depth supervision. In Tab. 4, we evaluate the performance on both in-domain TartanAir test set and the zero-shot generalization on unseen ScanNet and KITTI datasets. We can observe that the benefit of pretraining is especially significant on the challenging datasets like TartanAir and KITTI. The results align well with the observation in [21] which suggests that the pre-training acts as regularization and guides the learning towards better minima and enables better generalization to out-of-distribution datasets. The visual comparison results are provided in the appendix. Given the increasing popularity of view synthesis [61, 81] and multi-view generative models [3, 45], new multi-view datasets [32] and models [55] are gradually introduced, our approach provides a way to pre-train depth models on large-scale multi-view posed image datasets. + +# 4.4. Benchmark Comparisons + +Comparisons on ScanNet and RealEstate10K. Tab. 5 and Tab. 6 compare the depth and novel view synthesis results on the standard ScanNet and RealEstate10K benchmarks, respectively. We can see clearly that our DepthSplat achieves state-of-the-art performance on both datasets for both tasks. The visual comparison with previous methods is shown in Fig. 5, where our method significantly improves the perfor + +Table 7. Comparisons on DL3DV. Our DepthSplat not only consistently outperforms MVSplat on different number of input views, but also scales more efficiently to more input views. + +
Method#ViewsPSNR ↑SSIM ↑LPIPS ↓Time (s)
MVSplat [9]217.540.5290.4020.072
DepthSplat19.310.6150.3100.083
MVSplat [9]421.630.7210.2330.146
DepthSplat23.120.7800.1780.107
MVSplat [9]622.930.7750.1930.263
DepthSplat24.190.8230.1470.132
+ +![](images/92b82c384beb990a0b540395883f26289f4d29702dc4a14794a0177ac8b75bd6.jpg) +Figure 6. Visual comparisons on DL3DV. Our DepthSplat performs significantly better than MVSplat [9] on regions that hard to match (e.g., repeated patterns). + +mance on challenging scenarios like texture-less regions and occlusions. For the depth results on ScanNet, we report our base models (with ViT-B and two-scale feature matching) trained with and without Gaussian splatting pre-training on the mixed RealEstate10K and DL3DV datasets. Our model significantly outperforms previous methods and can benefit from additional Gaussian splatting pre-training. + +Comparisons on DL3DV. To evaluate the performance on complex real-world scenes, we conduct comparisons with the representative model MVSplat [9] on the recently introduced DL3DV dataset [32]. We also compare the results of different numbers of input views (2, 4 and 6) on this dataset. We fine-tune MVSplat and our RealEstate10K pre-trained models on DL3DV training scenes and report the results on the benchmark test set in Tab. 7. Our DepthSplat consistently outperforms MVSplat in all metrics, and our improvements are more significant with fewer input views, which indicates that our model is more robust to sparse views. Visual comparisons with MVSplat on the DL3DV dataset are shown in Fig. 6, where MVSplat's depth quality lags behind our DepthSplat due to matching failure, which leads to blurry and distorted view synthesis results. We show more visual comparison results in the appendix. It is also worth noting + +Table 8. Cross-dataset generalization. When generalizing to DL3DV and ACID with RealEstate10K pre-trained models, our DepthSplat is consistently better than MVSplat, especially on the more challenging DL3DV dataset. + +
MethodDL3DVACID
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
MVSplat [9]24.140.8080.14928.150.8410.147
DepthSplat27.660.8950.09628.370.8470.141
+ +that our method scales more efficiently to more input views thanks to our lightweight local feature matching approach (Sec. 3.1), which is unlike the expensive global pair-wise matching used in MVSplat. + +Cross-Dataset Generalization. We evaluate the cross-dataset generalization capability by directly testing on DL3DV [32] and ACID [33] datasets with RealEstate10K [82] pre-trained models. The results are shown in Tab. 8, where our DepthSplat consistently outperforms MVSplat on both datasets, especially on the more challenging DL3DV dataset which features complex scene structures. The visual comparison results are shown in the appendix. + +High-Resolution Results. In addition to the comparison results on the $256 \times 256$ resolution RealEstate10K and $256 \times 448$ resolution DL3DV dataets, we show more high-resolution $(512 \times 960)$ qualitative results in the appendix. We also invite the readers to our project page haofelixu.github.io/deathsplat for high-resolution $(512 \times 960)$ video results on different number of input views (6 and 12), where our DepthSplat is able to reconstruct larger-scale or 360 scenes from more input views. + +# 5. Conclusion + +In this paper, we introduce DepthSplat, a new approach to connecting Gaussian splatting and depth to achieve state-of-the-art results on ScanNet, RealEstate10K and DL3DV datasets for both depth and view synthesis tasks. We show that our model enables unsupervised depth pre-training with Gaussian splatting rendering loss, providing a way to leverage large-scale posed multi-view image datasets for training more robust and generalizable multi-view depth models. + +Limitations. Our current model requires camera poses as input along with the multi-view images, which might be challenging to obtain when the input views are extremely sparse. An interesting future direction is to remove this requirement by exploring pose-free models [72, 80]. In addition, our model predicts pixel-aligned Gaussians, where the number of Gaussians will be significantly large when processing a large number of input views [60, 79]. Further improving the geometry representation and the scalability to many input views would be exciting future work. + +# Acknowledgement + +We thank Yuedong Chen for his generous help with the DL3DV dataset. Andreas Geiger was supported by the ERC Starting Grant LEGO-3D (850533) and the DFG EXC number 2064/1 - project number 390727645. This work was supported as part of the Swiss AI Initiative by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID a03 on Alps. H. Blum is also with the Lamarr Institute and D. Barath is also with HUN-REN SZTAKI. + +# References + +[1] Gwangbin Bae, Ignas Budvyitis, and Roberto Cipolla. 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In this paper, we present DepthSplat to connect Gaussian splatting and depth estimation and study their interactions. More specifically, we first contribute a robust multi-view depth model by leveraging pretrained monocular depth features, leading to high-quality feed-forward 3D Gaussian splatting reconstructions. We also show that Gaussian splatting can serve as an unsupervised pre-training objective for learning powerful depth models from large-scale multi-view posed datasets. We validate the synergy between Gaussian splatting and depth estimation through extensive ablation and cross-task transfer experiments. Our DepthSplat achieves state-of-the-art performance on ScanNet, RealEstate10K and DL3DV datasets in terms of both depth estimation and novel view synthesis, demonstrating the mutual benefits of connecting both tasks. In addition, DepthSplat enables feed-forward reconstruction from 12 input views (512 × 960 resolutions) in 0.6 seconds." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 56, + 669, + 135, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 669, + 135, + 681 + ], + "spans": [ + { + "bbox": [ + 56, + 669, + 135, + 681 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Novel view synthesis [4, 82] and depth prediction [20, 44] are two fundamental tasks in computer vision, serving as the" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 407, + 555, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 443 + ], + "type": "text", + "content": "driving force behind numerous applications ranging from augmented reality to robotics and autonomous driving. There have been notable advancements in both areas recently." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 445, + 556, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 445, + 556, + 589 + ], + "spans": [ + { + "bbox": [ + 312, + 445, + 556, + 589 + ], + "type": "text", + "content": "For novel view synthesis, 3D Gaussian Splatting (3DGS) [29] has emerged as a popular technique due to its impressive real-time performance while attaining high visual fidelity. Recently, advances in feed-forward 3DGS models [7, 9, 48] have been introduced to alleviate the need for tedious per-scene optimization, also enabling few-view 3D reconstruction. The state-of-the-art sparse-view method MVSplat [9] relies on feature matching-based multi-view depth estimation [65] to localize the 3D Gaussian positions, which makes it suffer from similar limitations (e.g., occlusions, texture-less regions, and reflective surfaces) as other multi-view depth methods [18, 25, 44, 56, 71]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 591, + 556, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 591, + 556, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 591, + 556, + 663 + ], + "type": "text", + "content": "On the other hand, significant progress has been made in monocular depth estimation, with recent models [19, 22, 28, 40, 69, 74] achieving robust predictions on diverse in-the-wild data. However, these depths typically lack consistent scales across multiple views, constraining their performance in downstream tasks like 3D reconstruction [59, 73]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 665, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 713 + ], + "type": "text", + "content": "The integration of 3DGS with single-view depth estimation presents a compelling solution to overcome the individual limitations of each technique while at the same time enhancing their strengths. To this end, we introduce" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16453" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "content": "DepthSplat, which exploits the complementary nature of sparse-view feed-forward 3DGS and robust monocular depth estimation to improve the performance for both tasks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 108, + 295, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 108, + 295, + 239 + ], + "spans": [ + { + "bbox": [ + 54, + 108, + 295, + 239 + ], + "type": "text", + "content": "Specifically, we first contribute a robust multi-view depth model by integrating pre-trained monocular depth features [70] to the multi-view feature matching branch, which not only maintains the consistency of multi-view depth models but also leads to more robust results in situations that are hard to match (e.g., occlusions, texture-less regions and reflective surfaces). The predicted multi-view depth maps are then unprojected to 3D as the Gaussian centers, and we use an additional lightweight network to predict other remaining Gaussian parameters. They are combined together to achieve novel view synthesis with the splatting operation [29]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 239, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 239, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 239, + 295, + 312 + ], + "type": "text", + "content": "While previous methods [1, 11, 31] also try to fuse monocular and multi-view depths, they usually rely on sophisticated architectures. In contrast, we identify the power of off-the-shelf pre-trained monocular depth models and propose to augment multi-view cost volumes with monocular features, leading to a simpler model and stronger performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 312, + 295, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 312, + 295, + 455 + ], + "spans": [ + { + "bbox": [ + 56, + 312, + 295, + 455 + ], + "type": "text", + "content": "Thanks to our improved multi-view depth model, the quality of novel view synthesis with Gaussian splatting is also significantly enhanced (see Fig. 1 left). In addition, our Gaussian splatting module is fully differentiable, which requires only photometric supervision to optimize all model components. This provides a new, unsupervised way to pre-train depth prediction models on large-scale multi-view posed datasets without requiring ground truth geometry information. The pre-trained depth model can be further fine-tuned for specific depth tasks and achieves superior results over training from scratch (see Fig. 1 right, where unsupervised pre-training leads to improved performance)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 455, + 295, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 295, + 587 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 295, + 587 + ], + "type": "text", + "content": "We conduct extensive experiments on the large-scale TartanAir [58], ScanNet [14] and RealEstate10K [82] datasets for depth estimation and Gaussian splatting tasks, as well as the recently introduced DL3DV [32] dataset, which features complex real-world scenes and thus is more challenging. Under various evaluation settings, our DepthSplat achieves state-of-the-art results. We also achieve promising feedforward reconstruction results of large-scale or 360 scenes from 12 input views (" + }, + { + "bbox": [ + 55, + 455, + 295, + 587 + ], + "type": "inline_equation", + "content": "512 \\times 960" + }, + { + "bbox": [ + 55, + 455, + 295, + 587 + ], + "type": "text", + "content": " resolutions) in 0.6 seconds. The strong performance on both tasks demonstrates the mutual benefits of connecting Gaussian splatting and depth." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 595, + 142, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 595, + 142, + 608 + ], + "spans": [ + { + "bbox": [ + 55, + 595, + 142, + 608 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": "Multi-View Depth Estimation. As a core component of classical multi-view stereo pipelines [44], multi-view depth estimation exploits multi-view photometric consistency across multiple images to perform feature matching and predict the depth map of the reference image. In recent years, many learning-based methods [6, 15, 18, 25, 56, 57, 71] have been proposed to improve depth accuracy. Though these learning-based methods significantly improve the depth qual" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "type": "text", + "content": "ity compared to traditional methods [23, 44, 67], they cannot handle challenging situations where the multi-view photometric consistency assumption is not guaranteed, e.g., occlusions, low-textured areas, and non-Lambertian surfaces." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 122, + 556, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 122, + 556, + 278 + ], + "spans": [ + { + "bbox": [ + 313, + 122, + 556, + 278 + ], + "type": "text", + "content": "Monocular Depth Estimation. Recently, we have witnessed significant progress in depth estimation from a single image [2, 28, 40, 69, 74], and existing methods can produce surprisingly accurate results on diverse in-the-wild data. However, monocular depth methods inherently suffer from scale ambiguities, which makes it challenging to use them for downstream tasks like 3D reconstruction [73]. In this paper, we leverage the powerful features from a pre-trained monocular depth model [70] to augment feature-matching based multi-view depth estimation, which not only maintains the multi-view consistency but also leads to significantly improved robustness in challenging situations such as low-textured regions and reflective surfaces." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 280, + 556, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 280, + 556, + 532 + ], + "spans": [ + { + "bbox": [ + 313, + 280, + 556, + 532 + ], + "type": "text", + "content": "Feed-Forward Gaussian Splatting. Several feed-forward 3D Gaussian splatting models [7-10, 48, 51, 62, 68, 77] have been proposed in literature thanks to its efficiency and ability to handle sparse views. In particular, pixelSplat [7] and Splatter Image [48] predict 3D Gaussians from image features, while MVSplat [9] encodes the feature matching information with cost volumes and achieves better geometry. However, it inherently suffers from the limitation of feature matching in challenging situations like texture-less regions and reflective surfaces. In this paper, we propose to integrate monocular features from pre-trained monocular depth models [70] for more robust depth prediction and 3D Gaussian reconstruction. Another line of work like LGM [51], GRM [68], and GS-LRM [77] relies significantly on the training data and compute, discarding explicit feature matching cues and learning priors purely from data. This makes them expensive to train (e.g., GS-LRM [77] is trained with 64 A100 GPUs for 2 days), while our model can be trained in 2 days with 4 GPUs. Moreover, our Gaussian splatting module enables pre-training depth model from large-scale multi-view posed datasets without ground truth depth supervision." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": "Depth and Gaussian Splatting. Flash3D [49] explores a pre-trained monocular depth model [39] for single-image 3D Gaussian reconstruction. In contrast, we target large-scale scene reconstruction from multiple views. TranSplat [76] leverages monocular depth to improve Gaussian reconstruction. However, a crucial difference is that TranSplat uses monocular features to refine the coarse depth predicted from a cost volume, which makes it inherently vulnerable to the error in the coarse stage and, thus, suffers from the error propagation issue. In contrast, we avoid this by combining cost volume and monocular features early, which performs significantly better than TranSplat (Tab. 6). Another line of work [12, 53] applies an additional depth loss to the Gaussian optimization process. We note that these two approaches (feed-forward vs. per-scene optimization) are orthogonal." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16454" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 69, + 532, + 210 + ], + "blocks": [ + { + "bbox": [ + 83, + 69, + 532, + 210 + ], + "lines": [ + { + "bbox": [ + 83, + 69, + 532, + 210 + ], + "spans": [ + { + "bbox": [ + 83, + 69, + 532, + 210 + ], + "type": "image", + "image_path": "7b20ba694cdf6e70fc3b5782f4f7e4ff58219cfddfd7c4b9fc91f73c4845c951.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 220, + 555, + 299 + ], + "lines": [ + { + "bbox": [ + 54, + 220, + 555, + 299 + ], + "spans": [ + { + "bbox": [ + 54, + 220, + 555, + 299 + ], + "type": "text", + "content": "Figure 2. DepthSplat connects depth estimation and 3D Gaussian splatting with a shared architecture, which enables cross-task transfer. In particular, DepthSplat consists of a multi-view branch to model feature-matching information and a single-view branch to extract monocular features. The per-view cost volumes and monocular features are concatenated for depth regression with a 2D U-Net architecture. For the depth estimation task, we train the depth model with ground truth depth supervision. For the Gaussian splatting task, we first unproject all depth maps to 3D as the Gaussian centers, and in parallel, we use an additional head to predict the remaining Gaussian parameters. Novel views are rendered with the splatting operation. The full model for novel view synthesis is trained with the photometric rendering loss, which can also be used as an unsupervised pre-training stage for the depth model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 306, + 129, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 306, + 129, + 320 + ], + "spans": [ + { + "bbox": [ + 55, + 306, + 129, + 320 + ], + "type": "text", + "content": "3. DepthSplat" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "spans": [ + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": " input images " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "\\{\\pmb{I}^i\\}_{i=1}^N" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "(\\pmb{I}^i \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": " are the image sizes) with corresponding projection matrices " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{P}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "(\\mathbf{P}_i \\in \\mathbb{R}^{3 \\times 4}" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": ", computed from the intrinsic and extrinsic matrices), our goal is to predict dense per-pixel depth " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_i \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": " and per-pixel Gaussian parameters " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "\\{(\\pmb{\\mu}_j, \\alpha_j, \\pmb{\\Sigma}_j, c_j)\\}_{j=1}^{H \\times W \\times N}" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": " for each image, where " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_j, \\alpha_j, \\pmb{\\Sigma}_j" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "c_j" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": " are the 3D Gaussian's position, opacity, covariance, and color. As shown in Fig. 2, key to our method is a multi-view depth model augmented with monocular depth features, where we obtain the position " + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_j" + }, + { + "bbox": [ + 55, + 325, + 296, + 470 + ], + "type": "text", + "content": " of each Gaussian by unprojecting depth with camera parameters, and other Gaussian parameters are predicted by an additional head." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "text", + "content": "More specifically, our depth model consists of two branches: one for modeling feature matching using cost volumes, and another for extracting monocular features from a pre-trained monocular depth network. The cost volumes and monocular features are concatenated together for subsequent depth regression with a 2D U-Net and a softmax layer. For the depth task, we train our depth model with ground truth depth supervision. Our full model for novel view synthesis is trained with the rendering loss, which can also be used as an unsupervised pre-training stage for the depth model. We introduce the individual components below." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 609, + 219, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 609, + 219, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 609, + 219, + 624 + ], + "type": "text", + "content": "3.1. Multi-View Feature Matching" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 628, + 296, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 296, + 663 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 296, + 663 + ], + "type": "text", + "content": "In this branch, we extract multi-view features with a multiview Transformer architecture and then build multiple cost volumes that correspond to each input view." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "Multi-View Feature Extraction. For " + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": " input images, we first use a lightweight weight-sharing ResNet [27] architecture to get " + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "inline_equation", + "content": "s \\times" + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": " downsampled features for each image independently. To handle different image resolutions, we" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "content": "make the downsampling factor " + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "content": " flexible by controlling the number of stride-2 " + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "content": " convolutions. For example, the downsampling factor " + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "content": " is 4 if two stride-2 convolutions are used and 8 if three are used. To exchange information across different views, we use a multi-view Swin Transformer [34, 64, 65] which contains six stacked self- and cross-attention layers to obtain multi-view-aware features " + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "inline_equation", + "content": "\\{F_i\\}_{i=1}^N" + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "inline_equation", + "content": "F^i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C}" + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "content": " is the feature dimension. When more than two images (" + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "inline_equation", + "content": "N > 2" + }, + { + "bbox": [ + 313, + 308, + 556, + 463 + ], + "type": "text", + "content": ") are given as input, we perform cross-attention between each reference view and its top-2 nearest neighboring views, which are selected based on their camera distances to the reference view. This makes computation tractable with many input views." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": "Feature Matching. We encode the feature matching information across different views with the plane-sweep stereo approach [13, 65]. More specifically, for each view " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": ", we first uniformly sample " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " depth candidates " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\{d_m\\}_{m=1}^D" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " from the near and far depth ranges and then warp the feature " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "F^j" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " of view " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " to view " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " with the camera projection matrix and each depth candidate " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "d_m" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": ". Then we obtain " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " warped features " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\{F_{d_m}^{j \\rightarrow i}\\}_{m=1}^D" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " that correspond to feature " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "F^i" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": ". We then measure their feature correlations with the dot-product operation [9, 63]. The cost volume " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "C_i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times D}" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " for image " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " is obtained by stacking all correlations. Accordingly, we obtain cost volumes " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\{C_i\\}_{i=1}^N" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " for all input images " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\{I_i\\}_{i=1}^N" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": ". For more than two input views, similar to the strategy in cross-view attention computation, we select the top-2 nearest views for each reference view and compute feature correlations with only the selected views. This enables our cost volume construction to achieve a good speed-accuracy trade-off and scale efficiently to a larger number of input views. The correlation values for the two selected views are combined with averaging." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16455" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 253, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 253, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 253, + 85 + ], + "type": "text", + "content": "3.2. Monocular Depth Feature Extraction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 92, + 296, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 92, + 296, + 177 + ], + "spans": [ + { + "bbox": [ + 55, + 92, + 296, + 177 + ], + "type": "text", + "content": "Despite the remarkable progress in multi-view feature matching-based depth estimation [57, 65, 71] and Gaussian splatting [9], they inherently suffer from limitations in challenging situations like occlusions, texture-less regions, and reflective surfaces. Thus, we propose to integrate pre-trained monocular depth features into the cost volume to handle scenarios that are challenging or impossible to match." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "text", + "content": "More specifically, we leverage the pre-trained monocular depth backbone from the recent Depth Anything V2 [70] model thanks to its impressive performance on diverse in-the-wild data. The monocular backbone is a ViT [16, 37] model, which has a patch size of 14 and outputs a feature map that is " + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "inline_equation", + "content": "1/14" + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "text", + "content": " spatial resolution of the original image. We simply bilinearly interpolate the spatial resolution of the monocular features to the same resolution as the cost volume in Sec. 3.1 and obtain the monocular feature " + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}}" + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "text", + "content": " for input image " + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_i" + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{mono}}" + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "text", + "content": " is the dimension of the monocular feature. This process is performed for all input images in parallel and we obtain monocular features " + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}}\\}_{i=1}^{N}" + }, + { + "bbox": [ + 55, + 179, + 296, + 348 + ], + "type": "text", + "content": ", which are subsequently used for per-view depth map estimations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 365, + 254, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 254, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 254, + 378 + ], + "type": "text", + "content": "3.3. Feature Fusion and Depth Regression" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "text", + "content": "To achieve robust and multi-view consistent depth predictions, we combine the monocular feature " + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{\\mathrm{mono}}^{i} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times C_{\\mathrm{mono}}}" + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "text", + "content": " and cost volume " + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "inline_equation", + "content": "C_i \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times D}" + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "text", + "content": " via simple concatenation in the channel dimension. A subsequent 2D U-Net [42, 43] is used to regress depth from the concatenated monocular features and cost volumes. This process is performed for all the input images in parallel and for each image, it outputs a tensor of shape " + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "inline_equation", + "content": "\\frac{H}{s} \\times \\frac{W}{s} \\times D" + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "text", + "content": " is the number of depth candidates. We normalize the " + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 386, + 296, + 518 + ], + "type": "text", + "content": " dimension with the softmax operation and perform a weighted average of all depth candidates to obtain the depth output." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "content": "We also apply a hierarchical matching [25] architecture where an additional refinement step at " + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "content": " higher feature resolution is employed to improve the performance further. More specifically, based on the coarse depth prediction, we perform a correspondence search on the " + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "content": " higher feature maps within the neighbors of the " + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "content": " upsampled coarse depth prediction. Since we already have a coarse depth prediction, we only need to search a smaller range at the higher resolution, and thus, we construct a smaller cost volume compared to the coarse stage. Such a 2-scale hierarchical architecture not only leads to improved efficiency since most computation is spent on low resolution, but also leads to better results thanks to the use of higher-resolution features [25]. Similar feature fusion and depth regression procedure is used to get higher-resolution depth predictions, which are subsequently upsampled with a DPT head [41] to the full resolution." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 72, + 484, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 484, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 484, + 83 + ], + "type": "text", + "content": "3.4. Gaussian Parameter Prediction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "spans": [ + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "text", + "content": "For the task of 3D Gaussian splatting, we directly unproject the per-pixel depth maps to 3D with the camera parameters as the Gaussian centers " + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_j" + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "text", + "content": ". To predict other remaining Gaussian parameters " + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "inline_equation", + "content": "\\alpha_{j}" + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "text", + "content": " (opacity), " + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "inline_equation", + "content": "\\Sigma_{j}" + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "text", + "content": " (covariance) and " + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "inline_equation", + "content": "c_{j}" + }, + { + "bbox": [ + 313, + 89, + 555, + 198 + ], + "type": "text", + "content": " (color), we use an additional DPT head [41], where it takes the concatenated image, depth and feature information as input and outputs all the remaining Gaussian parameters. With all the predicted 3D Gaussians, we can render novel views with the Gaussian splatting operation [29]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 206, + 402, + 219 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 206, + 402, + 219 + ], + "spans": [ + { + "bbox": [ + 313, + 206, + 402, + 219 + ], + "type": "text", + "content": "3.5. Training Loss" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 224, + 555, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 224, + 555, + 260 + ], + "spans": [ + { + "bbox": [ + 313, + 224, + 555, + 260 + ], + "type": "text", + "content": "We study the properties of our proposed model on two tasks: depth estimation and novel view synthesis with 3D Gaussian splatting [29]. The loss functions are introduced below." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 263, + 555, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 263, + 555, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 263, + 555, + 300 + ], + "type": "text", + "content": "Depth estimation. We train our depth model (without the Gaussian splatting head) with " + }, + { + "bbox": [ + 313, + 263, + 555, + 300 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 313, + 263, + 555, + 300 + ], + "type": "text", + "content": " loss and gradient loss between the inverse depths of prediction and ground truth:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 309, + 555, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 309, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 321, + 309, + 555, + 338 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\text {d e p t h}} = \\alpha \\cdot | \\boldsymbol {D} _ {\\text {p r e d}} - \\boldsymbol {D} _ {\\text {g t}} | + \\beta \\cdot | \\partial_ {x} \\boldsymbol {D} _ {\\text {p r e d}} - \\partial_ {x} \\boldsymbol {D} _ {\\text {g t}} | \\\\ + \\beta \\cdot \\left| \\partial_ {y} \\boldsymbol {D} _ {\\text {p r e d}} - \\partial_ {y} \\boldsymbol {D} _ {\\mathrm {g t}} \\right|), \\tag {1} \\\\ \\end{array}", + "image_path": "c5c519f56741929e32e4034ee602e5e7d0a84d4d11c733dcc881230a8a935fd8.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "inline_equation", + "content": "\\partial_x" + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "inline_equation", + "content": "\\partial_y" + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "text", + "content": " denotes the gradients on the " + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "text", + "content": " directions, respectively. Following UniMatch [65], we use " + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "inline_equation", + "content": "\\alpha = 20" + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "inline_equation", + "content": "\\beta = 20" + }, + { + "bbox": [ + 313, + 348, + 555, + 384 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 386, + 554, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 386, + 554, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 386, + 554, + 422 + ], + "type": "text", + "content": "View synthesis. We train our full model with a combination of mean squared error (MSE) and LPIPS [78] losses between rendered and ground truth image colors:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 433, + 556, + 474 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 433, + 556, + 474 + ], + "spans": [ + { + "bbox": [ + 314, + 433, + 556, + 474 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {g s}} = \\sum_ {m = 1} ^ {M} \\left(\\operatorname {M S E} \\left(I _ {\\text {r e n d e r}} ^ {m}, I _ {\\mathrm {g t}} ^ {m}\\right) + \\lambda \\cdot \\operatorname {L P I P S} \\left(I _ {\\text {r e n d e r}} ^ {m}, I _ {\\mathrm {g t}} ^ {m}\\right)\\right), \\tag {2}", + "image_path": "3d8657b720595353ba9b61a9fa052546f2bb1922c4545b03ffb96370b1dfbc03.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "type": "text", + "content": " is the number of novel views to render in a single forward pass. The LPIPS loss weight " + }, + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 475, + 554, + 499 + ], + "type": "text", + "content": " is set to 0.05 [9]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 511, + 394, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 394, + 525 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 394, + 525 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": "Implementation Details. We implement our method in PyTorch [38] and optimize our model with the AdamW [36] optimizer and cosine learning rate schedule. We adopt the xFormers [30] library for our monocular ViT backbone implementation. We use a lower learning rate " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-6}" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": " for the pre-trained Depth Anything V2 [70] backbone, and other remaining layers use a learning rate of " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-4}" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": ". The feature downsampling factor " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": " in our multi-view branch (Sec. 3.1) is chosen based on the image resolution. More specifically, for experiments on the " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": " resolution RealEstate10K [82] dataset, we choose " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "s = 4" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": ". For higher resolution datasets (e.g., TartanAir [58], ScanNet [14], KITTI [24] and DL3DV [32]), we choose " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "s = 8" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": ". Our hierarchical matching models in Sec. 3.3 use 2-scale features, i.e., " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "1/8" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": ", or " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 313, + 534, + 556, + 715 + ], + "type": "text", + "content": " resolutions." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16456" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 150, + 294, + 240 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 148 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 148 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 148 + ], + "type": "text", + "content": "Table 1. DepthSplat model variants. We evaluate different monocular backbones and different multi-view models (1-scale and 2-scale features for hierarchical matching as described in Sec. 3.3), where both larger monocular backbones and 2-scale hierarchical models lead to consistently improved performance for both depth and view synthesis tasks. The inference time is measured on a single A100 GPU for two input views at " + }, + { + "bbox": [ + 55, + 70, + 297, + 148 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 70, + 297, + 148 + ], + "type": "text", + "content": " resolutions." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 150, + 294, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 150, + 294, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 150, + 294, + 240 + ], + "type": "table", + "html": "
MonoMulti-ViewDepth (TartanAir)3DGS (RealEstate10K)Param (M)Time (s)
Abs Rel ↓δ1 ↑PSNR ↑SSIM ↑LPIPS ↓
ViT-S1-scale8.4693.0226.840.8780.122380.050
ViT-B1-scale6.9494.4627.060.8820.1191150.053
ViT-L1-scale6.0795.5227.230.8850.1163470.061
ViT-S2-scale7.0194.5627.120.8840.119410.062
ViT-B2-scale6.2295.3127.340.8870.1161200.070
ViT-L2-scale5.5796.0727.470.8890.1143540.079
", + "image_path": "18c3341dacda733a2db320f7e851f6945e5d3488b3333e552e722a5c68dcdf8b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "spans": [ + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": "Training Details. For depth experiments on ScanNet [14], we train our depth model on " + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": " GH200 GPUs for 100K iterations with a total batch size of 32. For the ablation experiments on depth task, we mainly use synthetic datasets (TartanAir [58] and VKITTI2 [5]) for training since they provide high-quality ground truth depths. For Gaussian splatting experiments, we consider both low-resolution and high-resolution images. In particular, for comparisons with previous methods [7, 9], we mainly use " + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": " resolution RealEstate10K [82] and " + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "inline_equation", + "content": "256 \\times 448" + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": " resolution DL3DV [32] datasets. We also report high-resolution " + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "inline_equation", + "content": "(512 \\times 960)" + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": " results on RealEstate10K and DL3DV datasets for qualitative evaluations. For experiments on the " + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": " RealEstate10K dataset, we train our model on " + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": " GH200 GPUs for 150K iterations with a total batch size of 32, which takes 1 day for the small model and 2 days for the large model. For experiments on the " + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "inline_equation", + "content": "256 \\times 448" + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": " DL3DV [32] dataset, we fine-tune our RealEstate10K pre-trained model on " + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 56, + 258, + 296, + 569 + ], + "type": "text", + "content": " GH200 GPUs for 100K iterations with a total batch size of 4, where the number of input views is randomly sampled from 2 to 6. We evaluate the model's performance on different number of input views (2, 4, 6). For high-resolution results, we fine-tune our low-resolution pre-trained models on high-resolution images. More training details are provided in the appendix. Our code and training scripts are available at github.com/cvg/deepsplat to ease reproducibility." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 576, + 151, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 576, + 151, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 576, + 151, + 588 + ], + "type": "text", + "content": "4.1. Model Variants" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "text", + "content": "We first study several different model variants for both depth estimation and view synthesis tasks. In particular, we explore different monocular backbones [70] (ViT-S, ViT-B, ViT-L) and different multi-view models (1-scale and 2-scale). We conduct depth experiments on the large-scale TartanAir [58] synthetic dataset, which features both indoor and outdoor scenes and has perfect ground truth depth. The Gaussian splatting experiments are conducted on the standard RealEstate10K [82] dataset. Following community standards, we report the depth evaluation metrics [20] of" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 316, + 152, + 553, + 271 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 148 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 148 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 148 + ], + "type": "text", + "content": "Table 2. Ablations. We evaluate the contribution of the monocular feature branch and the cost volume branch (1st group of experiments), as well as different monocular features (2nd group of experiments). Our results indicate that the monocular feature and cost volume are complementary, with large performance drops when removing either one. The pre-trained Depth Anything V2 model weights achieve the best view synthesis results." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 152, + 553, + 271 + ], + "lines": [ + { + "bbox": [ + 316, + 152, + 553, + 271 + ], + "spans": [ + { + "bbox": [ + 316, + 152, + 553, + 271 + ], + "type": "table", + "html": "
ComponentsDepth (TartanAir)3DGS (RealEstate10K)
Abs Rel ↓δ1 ↑PSNR ↑SSIM ↑LPIPS ↓
Full8.4693.0226.840.8780.122
w/o mono feature12.2588.0026.040.8640.134
w/o cost volume11.3490.0223.240.7660.184
ConvNeXt-T10.5091.1326.110.8650.134
Midas9.5391.6126.460.8720.128
DINO V28.9392.4926.760.8770.123
Depth Anything V18.3893.2326.760.8770.124
Depth Anything V28.4693.0226.840.8780.122
", + "image_path": "b01ed7c06a80b67e697754d290c69dfb8f8f763bd3cb48c33634709fa8076b4a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 287, + 556, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 287, + 556, + 395 + ], + "spans": [ + { + "bbox": [ + 313, + 287, + 556, + 395 + ], + "type": "text", + "content": "Abs Rel (relative " + }, + { + "bbox": [ + 313, + 287, + 556, + 395 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 313, + 287, + 556, + 395 + ], + "type": "text", + "content": " error) and " + }, + { + "bbox": [ + 313, + 287, + 556, + 395 + ], + "type": "inline_equation", + "content": "\\delta_{1}" + }, + { + "bbox": [ + 313, + 287, + 556, + 395 + ], + "type": "text", + "content": " (percentage of correctly estimated pixels within a threshold) and novel view synthesis metrics [29] of PSNR, SSIM, and LPIPS. The results in Tab. 1 demonstrate that both larger monocular backbones and 2-scale hierarchical models lead to consistently improved performance for both tasks. We name three different model sizes with \"Small\": \"ViT-S monocular, 1-scale multi-view\", \"Base\": \"ViT-B monocular, 2-scale multi-view\", and \"Large\": \"ViT-L monocular, 2-scale multi-view\"." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 396, + 556, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 556, + 504 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 556, + 504 + ], + "type": "text", + "content": "From Tab. 1, we can also observe that better depth network architecture leads to improved view synthesis. In the appendix, we conduct additional experiments to study the effect of different initializations for the depth network to the view synthesis performance. Our results show that a better depth model initialization also contributes to improved rendering quality. In summary, both better depth network architecture and better depth model initialization lead to improved novel view synthesis results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 514, + 441, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 514, + 441, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 514, + 441, + 526 + ], + "type": "text", + "content": "4.2. Ablation and Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 532, + 555, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 532, + 555, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 532, + 555, + 567 + ], + "type": "text", + "content": "In this section, we study the properties of our key components on the TartanAir dataset (for depth) and RealEstate10K dataset (for view synthesis with Gaussian splatting)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "content": "Monocular Features for Depth and Gaussian Splatting. In Tab. 2, we compare our full model (Full) with the model variant where the monocular depth feature branch (with a ViT-S model pre-trained by Depth Anything V2 [70]) is removed (w/o mono feature), leaving only the multi-view branch. We can observe a clear performance drop for both depth and view synthesis tasks. In Fig. 3, we visualize the depth predictions and error maps of both models on the ScanNet dataset. The pure multi-view feature matching-based approach struggles a lot at texture-less regions and reflective surfaces. At the same time, our full model achieves reliable results thanks to the powerful prior captured in monocular" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16457" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 138, + 132 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 138, + 132 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 138, + 132 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 138, + 132 + ], + "type": "image", + "image_path": "12d56b8927c8a335e2db48feaebcbe9ecf40ba77e49ede0fe43f357427c223a9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 84, + 133, + 108, 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Effect of monocular features for depth on ScanNet. 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Effect of monocular features for 3DGS on RealEstate10K. 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We also show the visual comparisons for the Gaussian splatting task in Fig. 4 with two input views. For regions (e.g., the lounge chairs) that only appear in a single image, the pure multi-view method is unable to find correspondences. It thus produces unreliable depth predictions, leading to misalignment in the rendered novel views due to the incorrect geometry." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 55, + 613, + 296, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 613, + 296, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 613, + 296, + 684 + ], + "type": "text", + "content": "We also experiment with removing the cost volume (w/o cost volume) in the multi-view branch and observed a significant performance drop. This indicates that obtaining scale-and multi-view consistent predictions with a pure monocular depth backbone is challenging, which constrains achieving high-quality results for 3D Gaussian reconstruction." + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "Different Monocular Features. In Tab. 2, we also evaluate different monocular features, including the ConvNeXt" + } + ] + } + ], + "index": 52 + }, + { + "type": "table", + "bbox": [ + 353, + 555, + 517, + 624 + ], + "blocks": [ + { + "bbox": [ + 313, + 523, + 554, + 546 + ], + "lines": [ + { + "bbox": [ + 313, + 523, + 554, + 546 + ], + "spans": [ + { + "bbox": [ + 313, + 523, + 554, + 546 + ], + "type": "text", + "content": "Table 3. Monocular fusion strategy. Our simple concatenation performs surprisingly good compared to other alternatives." + } + ] + } + ], + "index": 53, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 353, + 555, + 517, + 624 + ], + "lines": [ + { + "bbox": [ + 353, + 555, + 517, + 624 + ], + "spans": [ + { + "bbox": [ + 353, + 555, + 517, + 624 + ], + "type": "table", + "html": "
MethodAbs Rel ↓δ1 ↑
Cost volume from ViT11.2690.84
Explicit scale align9.1390.21
Attention fusion8.4092.95
Concatenation (Ours)8.4693.02
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Pre-TrainFine-TuneTartanAirScanNetKITTI
Abs Rel ↓δ1 ↑Abs Rel ↓δ1 ↑Abs Rel ↓δ1 ↑
XX76.223.4339.9722.5690.690.00
✓X29.5353.1621.5176.0956.8346.26
X✓10.8690.556.7096.1411.5687.27
✓✓10.2091.106.6096.2710.6889.92
", + "image_path": "e0ba58e0ca2a06513195cade0872b1549dc39bfe8e2ae0b98f90e7c49594dbbe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 55, + 281, + 294, + 395 + ], + "blocks": [ + { + "bbox": [ + 55, + 256, + 296, + 280 + ], + "lines": [ + { + "bbox": [ + 55, + 256, + 296, + 280 + ], + "spans": [ + { + "bbox": [ + 55, + 256, + 296, + 280 + ], + "type": "text", + "content": "Table 5. Two-view Depth Estimation on ScanNet. Our Depth-Spat outperforms all prior methods by clear margins." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 281, + 294, + 395 + ], + "lines": [ + { + "bbox": [ + 55, + 281, + 294, + 395 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 294, + 395 + ], + "type": "table", + "html": "
MethodAbs Rel ↓RMSE ↓RMSElog ↓
DeMoN [54]23.10.7610.289
BA-Net [50]16.10.3460.214
DeepV2D [52]5.70.1680.080
NeuralRecon [47]4.70.1640.093
DRO [26]5.30.1680.081
UniMatch [65]5.90.1790.082
DepthSplat (w/o GS pre-train)4.50.1250.061
DepthSplat (w/ GS pre-train)3.80.1140.055
", + "image_path": "5b6487fac3039c2736eb9605ab84e2aafbeb0775f81e6dfdc621e8a861534418.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 414, + 297, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 414, + 297, + 594 + ], + "spans": [ + { + "bbox": [ + 54, + 414, + 297, + 594 + ], + "type": "text", + "content": "depth estimation in Sec. 4.2. In particular, we first compare with MVSFormer [6] that constructs the cost volume with monocular ViT features, which leads to a single-branch architecture. We can observe that our fusion strategy performs significantly better than the single-branch design, potentially because our two-branch design disentangles feature matching and monocular priors, which makes the learning task easier. We also compare with fusing the monocular depth maps (instead of monocular features in our model) by first aligning the monocular depth scale using the multi-view depth and then fusing the depth maps together with an additional network. Again, our simple concatenation performs better. We further compare our concatenation with the attention-based adaptive fusion and observe very similar results. Thus we opt to the simpler concatenation design." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 600, + 296, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 600, + 296, + 625 + ], + "spans": [ + { + "bbox": [ + 55, + 600, + 296, + 625 + ], + "type": "text", + "content": "4.3. Unsupervised Depth Pre-Training with Gaussian Splitting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 629, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 297, + 715 + ], + "type": "text", + "content": "By connecting Gaussian splatting and depth, our DepthSplat provides a way to pre-train the depth model in a fully unsupervised manner. In particular, we first train our full model on the large-scale multi-view posed RealEstate10K dataset (contains " + }, + { + "bbox": [ + 55, + 629, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\sim 67\\mathrm{K}" + }, + { + "bbox": [ + 55, + 629, + 297, + 715 + ], + "type": "text", + "content": " Youtube videos) with only the Gaussian splatting rendering loss (Eq. (2)), without any direct supervision on the depth predictions. After pre-training, we take" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 329, + 95, + 541, + 216 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 93 + ], + "type": "text", + "content": "Table 6. Two-view 3DGS on RealEstate10K. Our DepthSplat achieves the best performance." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 329, + 95, + 541, + 216 + ], + "lines": [ + { + "bbox": [ + 329, + 95, + 541, + 216 + ], + "spans": [ + { + "bbox": [ + 329, + 95, + 541, + 216 + ], + "type": "table", + "html": "
MethodPSNR ↑SSIM ↑LPIPS ↓
pixelNeRF [75]20.430.5890.550
GPNR [46]24.110.7930.255
AttnRend [17]24.780.8200.213
MuRF [66]26.100.8580.143
pixelSplat [7]25.890.8580.142
MVSplat [9]26.390.8690.128
TranSplat [76]26.690.8750.125
DepthSplat27.470.8890.114
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Novel view synthesis on RealEstate10K. Our DepthSplat performs significantly better than pixelSplat [7] and MVSplat [9] in challenging regions." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 501, + 227, + 553, + 332 + ], + "blocks": [ + { + "bbox": [ + 501, + 227, + 553, + 332 + ], + "lines": [ + { + "bbox": [ + 501, + 227, + 553, + 332 + ], + "spans": [ + { + "bbox": [ + 501, + 227, + 553, + 332 + ], + "type": "image", + "image_path": "9e3526351c2763b67c01ddaaef8a47ffdb58df66d7d7b145d3ce3ae56e7c0115.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 516, + 333, + 541, + 339 + ], + "lines": [ + { + "bbox": [ + 516, + 333, + 541, + 339 + ], + "spans": [ + { + "bbox": [ + 516, + 333, + 541, + 339 + ], + "type": "text", + "content": "DepthSplat" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 399, + 556, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 556, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 556, + 604 + ], + "type": "text", + "content": "the pre-trained depth model and further fine-tune it to the depth task on the mixed TartanAir [58] and VKITTI2 [5] datasets with ground truth depth supervision. In Tab. 4, we evaluate the performance on both in-domain TartanAir test set and the zero-shot generalization on unseen ScanNet and KITTI datasets. We can observe that the benefit of pretraining is especially significant on the challenging datasets like TartanAir and KITTI. The results align well with the observation in [21] which suggests that the pre-training acts as regularization and guides the learning towards better minima and enables better generalization to out-of-distribution datasets. The visual comparison results are provided in the appendix. Given the increasing popularity of view synthesis [61, 81] and multi-view generative models [3, 45], new multi-view datasets [32] and models [55] are gradually introduced, our approach provides a way to pre-train depth models on large-scale multi-view posed image datasets." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 610, + 457, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 610, + 457, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 610, + 457, + 624 + ], + "type": "text", + "content": "4.4. Benchmark Comparisons" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": "Comparisons on ScanNet and RealEstate10K. Tab. 5 and Tab. 6 compare the depth and novel view synthesis results on the standard ScanNet and RealEstate10K benchmarks, respectively. We can see clearly that our DepthSplat achieves state-of-the-art performance on both datasets for both tasks. The visual comparison with previous methods is shown in Fig. 5, where our method significantly improves the perfor" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16459" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 114, + 292, + 201 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 104 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 104 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 104 + ], + "type": "text", + "content": "Table 7. Comparisons on DL3DV. Our DepthSplat not only consistently outperforms MVSplat on different number of input views, but also scales more efficiently to more input views." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 114, + 292, + 201 + ], + "lines": [ + { + "bbox": [ + 58, + 114, + 292, + 201 + ], + "spans": [ + { + "bbox": [ + 58, + 114, + 292, + 201 + ], + "type": "table", + "html": "
Method#ViewsPSNR ↑SSIM ↑LPIPS ↓Time (s)
MVSplat [9]217.540.5290.4020.072
DepthSplat19.310.6150.3100.083
MVSplat [9]421.630.7210.2330.146
DepthSplat23.120.7800.1780.107
MVSplat [9]622.930.7750.1930.263
DepthSplat24.190.8230.1470.132
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MethodDL3DVACID
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
MVSplat [9]24.140.8080.14928.150.8410.147
DepthSplat27.660.8950.09628.370.8470.141
", + "image_path": "7744f25098b080d9a75393146953b8fd9aa8c5ea97f4c5fba569ac469b587b56.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 187, + 555, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 187, + 555, + 236 + ], + "spans": [ + { + "bbox": [ + 313, + 187, + 555, + 236 + ], + "type": "text", + "content": "that our method scales more efficiently to more input views thanks to our lightweight local feature matching approach (Sec. 3.1), which is unlike the expensive global pair-wise matching used in MVSplat." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 238, + 556, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 238, + 556, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 238, + 556, + 346 + ], + "type": "text", + "content": "Cross-Dataset Generalization. We evaluate the cross-dataset generalization capability by directly testing on DL3DV [32] and ACID [33] datasets with RealEstate10K [82] pre-trained models. The results are shown in Tab. 8, where our DepthSplat consistently outperforms MVSplat on both datasets, especially on the more challenging DL3DV dataset which features complex scene structures. The visual comparison results are shown in the appendix." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "text", + "content": "High-Resolution Results. In addition to the comparison results on the " + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "text", + "content": " resolution RealEstate10K and " + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "inline_equation", + "content": "256 \\times 448" + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "text", + "content": " resolution DL3DV dataets, we show more high-resolution " + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "inline_equation", + "content": "(512 \\times 960)" + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "text", + "content": " qualitative results in the appendix. We also invite the readers to our project page haofelixu.github.io/deathsplat for high-resolution " + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "inline_equation", + "content": "(512 \\times 960)" + }, + { + "bbox": [ + 313, + 350, + 556, + 458 + ], + "type": "text", + "content": " video results on different number of input views (6 and 12), where our DepthSplat is able to reconstruct larger-scale or 360 scenes from more input views." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 473, + 388, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 473, + 388, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 473, + 388, + 485 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 495, + 556, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 556, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 556, + 590 + ], + "type": "text", + "content": "In this paper, we introduce DepthSplat, a new approach to connecting Gaussian splatting and depth to achieve state-of-the-art results on ScanNet, RealEstate10K and DL3DV datasets for both depth and view synthesis tasks. We show that our model enables unsupervised depth pre-training with Gaussian splatting rendering loss, providing a way to leverage large-scale posed multi-view image datasets for training more robust and generalizable multi-view depth models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 594, + 557, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 557, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 557, + 713 + ], + "type": "text", + "content": "Limitations. Our current model requires camera poses as input along with the multi-view images, which might be challenging to obtain when the input views are extremely sparse. An interesting future direction is to remove this requirement by exploring pose-free models [72, 80]. In addition, our model predicts pixel-aligned Gaussians, where the number of Gaussians will be significantly large when processing a large number of input views [60, 79]. Further improving the geometry representation and the scalability to many input views would be exciting future work." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16460" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 297, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 297, + 189 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 297, + 189 + ], + "type": "text", + "content": "We thank Yuedong Chen for his generous help with the DL3DV dataset. Andreas Geiger was supported by the ERC Starting Grant LEGO-3D (850533) and the DFG EXC number 2064/1 - project number 390727645. This work was supported as part of the Swiss AI Initiative by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID a03 on Alps. H. Blum is also with the Lamarr Institute and D. 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ACM TOG, 2018. 1, 2, 4, 5, 8" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16463" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_content_list.json b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..04e5738544bc7ee3d2424a2acae602bec69ce3c0 --- /dev/null +++ b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_content_list.json @@ -0,0 +1,1928 @@ +[ + { + "type": "text", + "text": "Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI", + "text_level": 1, + "bbox": [ + 124, + 130, + 872, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Won Jun Kim $^{1*}$", + "bbox": [ + 196, + 179, + 323, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyungjin Chung\\*", + "bbox": [ + 356, + 180, + 504, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jaemin $\\mathrm{Kim}^{1*}$", + "bbox": [ + 537, + 180, + 651, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sangmin Lee", + "bbox": [ + 684, + 180, + 797, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Byeongsu Sim", + "bbox": [ + 356, + 198, + 477, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jong Chul Ye1", + "bbox": [ + 519, + 199, + 633, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 KAIST", + "bbox": [ + 403, + 222, + 475, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2 EverEx", + "bbox": [ + 516, + 222, + 589, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{wonjun, kjm981995, leeeeesang, byeongsu.s,jong.ye}@kaist.ac.kr hj.chung@everex.co.kr", + "bbox": [ + 169, + 243, + 821, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 292, + 326, + 308 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gradient-based methods are a prototypical family of \"explainability for AI\" (XAI) techniques, especially for image-based models. However, they (1) require white-box access to models, (2) are vulnerable to adversarial attacks, and (3) produce attributions that lie off the image manifold, leading to explanations that are not amenable to human perception. To overcome these challenges, we introduce Derivative-Free Diffusion Manifold-Constrained Gradients (FreeMCG): by leveraging ensemble Kalman filters and diffusion models, we derive a derivative-free approximation of the model's gradient projected onto the data manifold, requiring access only to the model's outputs (i.e., black-box setting). We demonstrate the effectiveness of FreeMCG by applying it to both counterfactual generation and feature attribution, which have traditionally been treated as different tasks requiring distinct methods. Through comprehensive evaluation on both counterfactual explanation and feature attribution we show that our method yields state-of-the-art results for both tasks while preserving the essential properties expected of XAI tools. Code: https://github.com/one-june/FreeMCG.", + "bbox": [ + 86, + 325, + 483, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 672, + 220, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding the decision-making process of complex deep neural networks is crucial for their deployment in high-stakes applications such as medical imaging [6, 7], autonomous systems [2, 43], etc. Explanable AI (XAI) seeks to address this challenge by providing insights into how models arrive at specific predictions, thus enhancing trust, accountability, and usability in critical applications. Two widely used tools for XAI are counterfactual explanation [59] and feature attribution1 [31].", + "bbox": [ + 89, + 696, + 482, + 833 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among various XAI methods, the gradient of the target (e.g. classifier) model is the prototypical method of under", + "bbox": [ + 89, + 834, + 483, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9e0e2a8baae79d60bf61427842776a71d0eed0d52535ada408b5b09cf6de14b2.jpg", + "image_caption": [ + "Figure 1. Representative results of FreeMCG, operating as a universal framework for black box XAI." + ], + "image_footnote": [], + "bbox": [ + 519, + 286, + 903, + 594 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "standing the local behavior of a function around a given input data point. It has thus been used since the beginning of the rise of neural networks to explain their decisions [50]. There have been many subsequent works improving the vanilla gradient to serve as better feature attributions for a deep neural network [3, 46, 47, 55, 57, 61]. Gradients are also utilized for generating counterfactual explanations [4, 25, 44], in which the gradient of the target model serves as the direction that guides the change $\\delta$ made to the original image so that prediction of the model flips to another class.", + "bbox": [ + 511, + 642, + 906, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While gradient-based methods are popular explainable AI (XAI) tools, they suffer from three significant limitations:", + "bbox": [ + 511, + 809, + 906, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Access to model gradients is not always feasible: Obtaining gradients requires access to the model's internal weights, which is often not possible in practice. For", + "bbox": [ + 514, + 854, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 107, + 875, + 215, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1The term \"saliency maps\" are also often used interchangeably.", + "bbox": [ + 109, + 887, + 444, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23795", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Feature attribution", + "text_level": 1, + "bbox": [ + 178, + 92, + 269, + 102 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Q. Which features (pixels) are most important for the classifier's decision?", + "bbox": [ + 184, + 109, + 316, + 138 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a1fcf6699108d17e88f44beceaf1c48983af9ea6232d50c2b469d4193c36405f.jpg", + "image_caption": [ + "Counterfactuals on the manifold" + ], + "image_footnote": [], + "bbox": [ + 183, + 157, + 315, + 300 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Counterfactual explanation", + "text_level": 1, + "bbox": [ + 179, + 309, + 307, + 319 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Q. What changes to the input image shift the decision of the classifier to another class?", + "bbox": [ + 184, + 325, + 305, + 361 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1e7e652fda6f4d40e621822d5f06a6472586cd19ae6f8d266a8ee2e8c4b483eb.jpg", + "image_caption": [ + "Adversarial attack", + "$\\otimes$ Off-manifold, Unreliable" + ], + "image_footnote": [], + "bbox": [ + 359, + 107, + 504, + 203 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f2778b9467771786939e56e6ca060a94368fdd026567db59ef3fa66f04fc66e6.jpg", + "image_caption": [ + "$\\odot$ On-manifold, Explainable", + "Figure 2. Unified framework of XAI for feature attribution and counterfactual explanation using our method, Derivative-Free Diffusion Manifold Constrained Gradients (FreeMCG). Naive gradients not only violate the black box assumption but also is unreliable and hard to interpret as they produce adversarial attacks. Using diffusion models to produce on-manifold ensembles, and using the covariance of these particles as the preconditioner of the gradient, FreeMCG approximates gradients on the manifold, which is more reliable and interpretable." + ], + "image_footnote": [], + "bbox": [ + 333, + 260, + 493, + 342 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d7bf2af8fa70264542e3a1eae4753d69717d9abc4f3d04446d735671628ec43b.jpg", + "image_caption": [ + "(i) Spread particles" + ], + "image_footnote": [], + "bbox": [ + 542, + 132, + 607, + 215 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/990e21a3903188cdfdb5b31d8877efeaeeb377964758a43590c6b8d6572a3d2d.jpg", + "image_caption": [ + "FreeMCG", + "(ii) Approximate gradient on manifold" + ], + "image_footnote": [], + "bbox": [ + 627, + 138, + 790, + 220 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0e04c4a1052129324119a402a174e01aa80140cf1b733e8495ea8042382cdcd2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 542, + 253, + 776, + 332 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {g} _ {\\text {F r e e}} \\cong C _ {x x} \\nabla_ {x} f (\\boldsymbol {e} _ {c} - \\boldsymbol {p})\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 340, + 767, + 354 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "many neural-network based services, users can only interact with these systems through their outputs.", + "bbox": [ + 109, + 464, + 482, + 493 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "2. Gradients provide unreliable explanations: As shown in [1, 37, 51], gradient-based methods often fail to generate meaningful explanations of model behavior. These explanations are closely related to adversarial examples [58], and many traditional methods resort to using models that have been trained to be adversarially robust [4, 44]. Moreover, gradients typically do not align with the underlying data manifold, leading to explanations that are misaligned with human perception.", + "3. Lack of a unified framework for feature attribution and counterfactual explanations: The literature on feature attribution and counterfactual explanations remains largely separate. This is because real gradients produce adversarial attacks rather than counterfactual explanations and additional techniques are required to introduce perceptible changes. In theory, gradients should be usable for both applications. This raises the question of whether a single framework can effectively handle both types of explanations." + ], + "bbox": [ + 89, + 493, + 483, + 781 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, in this work, we propose Derivative-Free Diffusion Manifold Constrained Gradients (FreeMCG), a unified framework that can be used both for feature attribution and counterfactual explanation with only black-box access to the target model. By leveraging diffusion models and their powerful ability to model data manifolds, we can produce on-manifold perturbations of input", + "bbox": [ + 89, + 795, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "data points, which, combined with ideas from Ensemble Kalman Filters (EnKF) [45], can be used to approximate manifold-projected model gradients. In Fig. 1, we show the representative results of FreeMCG, acting as a unified framework for XAI. Our contributions can be summarized as follows:", + "bbox": [ + 511, + 463, + 906, + 551 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present the first unified framework that encompasses both feature attribution and counterfactual explanation.", + "- We derive a novel method of estimating the gradient of the target classifier with black-box access (i.e. without access to model weights) by leveraging diffusion models and the theory of EnKF.", + "- We demonstrate that FreeMCG achieves state-of-the-art performance, even compared to white-box methods." + ], + "bbox": [ + 511, + 556, + 905, + 676 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background & Related Works", + "text_level": 1, + "bbox": [ + 511, + 690, + 790, + 707 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Gradient-based XAI", + "text_level": 1, + "bbox": [ + 511, + 715, + 707, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Consider the following classifier", + "bbox": [ + 511, + 737, + 730, + 753 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\np (y = c | \\boldsymbol {x}) = \\frac {\\exp \\left(\\boldsymbol {f} _ {c} (\\boldsymbol {x})\\right)}{\\sum_ {c ^ {\\prime} = 1} ^ {C} \\exp \\left(\\boldsymbol {f} _ {c ^ {\\prime}} (\\boldsymbol {x})\\right)}, \\boldsymbol {f}: \\mathbb {R} ^ {d} \\mapsto \\mathbb {R} ^ {n}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 763, + 903, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $n$ is the number of classes, and $f(\\pmb{x}) := [f_1(\\pmb{x}), \\dots, f_n(\\pmb{x})]$ . Taking the softmax would induce the probability vector $\\pmb{p} = \\text{softmax}(\\pmb{f}(\\pmb{x}))$ . When $\\pmb{x}$ belongs to some class $c$ , let $\\text{class}(\\pmb{x}) = c$ be a labeling function. The task of feature attribution for images is to find an attribution $\\pmb{a} \\in [0, 1]^d$ that has high values in the indices where", + "bbox": [ + 511, + 809, + 906, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23796", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "its influence to $\\pmb{p}$ is pronounced. On the other hand, the task of counterfactual explanation aims to find a vector $\\pmb{x}^{\\prime}$ that belongs to a target class $c^\\prime$ , i.e. $\\operatorname{class}(\\pmb{x}^{\\prime}) = c^{\\prime}$ , but stays in proximity to $\\pmb{x}$ .", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature attribution. Gradients provide a direct representation of the local behavior of a function by encapsulating how the function changes linearly in the gradient vector [50]. Integrated Gradients improve upon the vanilla gradient and satisfies certain desirable properties such as sensitivity, completeness, linearity, and implementation invariance by integrating the gradients along a path from a fixed baseline (often a black image) [57]. Other follow-up works have extended this approach by modifying the integration region [33, 56, 60] or altering the integrand [23, 27, 49], among others.", + "bbox": [ + 89, + 152, + 482, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Counterfactuals and adversarial attacks. Gradients obtained with respect to the input can be used to perform gradient ascent/descent to change the input towards a direction that maximizes or minimizes the model output. However, for high-dimensional input data such as images, gradient ascent or descent often yields changes that are imperceptible to humans. This is known as an adversarial attack [18], because it changes the model output for a given input while the image itself remains effectively unchanged to human perception, thus having the effect of \"fooling\" a model. The adversarial attack phenomenon occurs because gradient ascent/descent using simple gradients perturbs the image in a direction that lifts the image off the image manifold and into the ambient space [14].", + "bbox": [ + 89, + 316, + 482, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Counterfactuals, on the other hand, should yield a semantically meaningful change to the original input $x$ such that the target model changes its prediction. In other words, the change should be on-manifold. Naturally, to induce this on-manifold change, generative models such as GANs and diffusion models [4, 25] have been used. However, most of these methods require access to model gradients, some even requiring that the model be adversarially robust. Moreover, these methods can be considered guided generation methods, making them inapplicable for feature attribution.", + "bbox": [ + 89, + 529, + 482, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Diffusion Models", + "text_level": 1, + "bbox": [ + 89, + 686, + 259, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion model [22, 28, 54] is a class of generative models that sample images through a Gaussian denoising path. This path is constructed by starting from the initial data (i.e. image) distribution $p_0(\\pmb{x})$ , $\\pmb{x} \\in \\mathbb{R}^d$ , gradually adding Gaussian noise, and reaching approximately the Gaussian distribution $p_T(\\pmb{x}) \\approx \\mathcal{N}(\\pmb{0}, \\pmb{I})$ at $t = T$ . For the choice of the Gaussian perturbation $p(\\pmb{x}_t | \\pmb{x}_0) = \\mathcal{N}(\\pmb{x}_0, \\sigma_t^2 \\pmb{I})$ , the reverse generation trajectory reads", + "bbox": [ + 89, + 708, + 482, + 830 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd \\boldsymbol {x} _ {t} = - \\sigma_ {t} \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t}) d t = \\frac {\\boldsymbol {x} _ {t} - \\mathbb {E} [ \\boldsymbol {x} _ {0} | \\boldsymbol {x} _ {t} ]}{\\sigma_ {t}} d t, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 834, + 482, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the initial point is sampled from the reference distribution $\\pmb{x}_T \\sim p_T(\\pmb{x}_T)$ . Here, Tweedie's formula [15]", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbb{E}[\\pmb{x}_0|\\pmb{x}_t] = \\pmb{x}_t + \\sigma_t^2\\nabla_{\\pmb{x}_t}\\log p(\\pmb{x}_t)$ is used for the second equality. Diffusion models are trained as denoisers that estimate this posterior mean", + "bbox": [ + 511, + 90, + 903, + 136 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta^ {*} = \\underset {\\theta} {\\arg \\min } \\mathbb {E} _ {t, \\boldsymbol {x} _ {t}, \\boldsymbol {x} _ {0}} \\left[ \\| D _ {\\theta} (\\boldsymbol {x} _ {t}) - \\boldsymbol {x} _ {0} \\| _ {2} ^ {2} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 148, + 903, + 172 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which can be plugged into (2) as $\\mathbb{E}[\\pmb{x}_0|\\pmb{x}_t]\\approx D_{\\theta^*}(\\pmb{x}_t)$ at test time.", + "bbox": [ + 511, + 185, + 903, + 213 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Chung et al. [8], assuming that $\\mathcal{M}$ is a locally linear subspace, it was further shown that the distribution of noisy data $p(\\boldsymbol{x}_t)$ is then concentrated on shell-like manifold $\\mathcal{M}_t$ . Moreover, one can show that Tweedie's formula is an orthogonal projection from $\\mathcal{M}_t$ to $\\mathcal{M}$ . In other words, when the goal is to produce samples on the manifold $\\mathcal{M}$ in a cost-effective way, one can use Tweedie's formula to generate samples in one step. This matches our intuition up to moderate values of $t$ , where the posterior mean gives us a relatively good approximation of the real samples.", + "bbox": [ + 511, + 215, + 906, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Guided sampling. Often, it is desirable to sample from the posterior $p(\\boldsymbol{x}|\\boldsymbol{y})$ instead of from the prior. A standard approach to achieve this is to use guided sampling by Bayes decomposition", + "bbox": [ + 511, + 386, + 905, + 446 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t} | \\boldsymbol {y}) = \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t}) + \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {y} | \\boldsymbol {x} _ {t}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 459, + 903, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the gradient of the log-likelihood term measures the fidelity with respect to the condition $\\pmb{y}$ . One can either train a separate neural network (e.g. classifier [13, 54]) to estimate the term or use some form of approximation [9, 53]. Sampling from the posterior then boils down to iterating the denoising steps of the unconditional PF-ODE in (2) and the gradient step that maximizes fidelity. However, regardless of the forward model2, most of the methods require access to the gradient of the forward model, which is often hard to compute due to reasons including safety and complexity.", + "bbox": [ + 511, + 503, + 905, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Gradient-free optimization and XAI", + "text_level": 1, + "bbox": [ + 511, + 664, + 826, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When one can only evaluate $f$ but cannot compute its gradient, gradient-free (zeroth-order) optimization [30], where a single or multiple set of samples can be used to calculate the finite difference, alongside techniques such as Gaussian smoothing [35] can be used to estimate the true gradient. Ensemble Kalman Filters (EnKF) [45], in terms of inverse problem solving, is also a widely used method for derivative-free optimization, where the ensemble of particles and its covariance information is used as a proxy for gradient information. In a similar vein, Ensemble Kalman Inversion (EKI) [19, 29] was proposed as a derivative-free", + "bbox": [ + 511, + 686, + 905, + 853 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2For instance, in image restoration, the degradation operator is the forward model. In classification, the neural network classifier is the forward model, as in (1).", + "bbox": [ + 511, + 862, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23797", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "method for training neural networks. Recently, the use of EnKF was extended to inverse problem-solving with diffusion models [62], showing that the technique can be readily used for diffusion guidance. In the proposed method, we leverage EnKF to approximate the unknown gradient.", + "bbox": [ + 89, + 90, + 483, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Black-box feature attribution While white-box methods typically rely on gradient information, this dependency limits the applicability of XAI techniques to scenarios where gradients can be accessed. Several works [17, 31, 36, 40, 61] have introduced perturbation-based approaches for feature attribution. These methods generally involve perturbing the input—commonly by masking out pixel groups at random—and measuring the resulting change in class probabilities. While conceptually similar to FreeMCG in that they only require forward passes through the neural network, perturbation-based methods differ in two key ways: (1) masking pixels typically moves the input off the underlying data manifold, and (2) these methods are exclusively employed for feature attribution and cannot produce counterfactual explanations, as they do not approximate the decision boundary.", + "bbox": [ + 89, + 184, + 483, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Main Contribution: FreeMCG", + "text_level": 1, + "bbox": [ + 89, + 438, + 372, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Derivation of FreeMCG", + "text_level": 1, + "bbox": [ + 89, + 462, + 310, + 478 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From (1), one can derive that", + "bbox": [ + 89, + 484, + 287, + 500 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial}{\\partial \\boldsymbol {f} _ {c ^ {\\prime}}} \\log p (y = c | \\boldsymbol {f} _ {c ^ {\\prime}}) = \\delta_ {c c ^ {\\prime}} - p \\left(c ^ {\\prime} | \\boldsymbol {f} _ {c ^ {\\prime}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 506, + 480, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\delta_{cc'}$ is the Kronecker delta function which evaluates to 1 if and only if $c' = c$ . Vector form of (5) reads", + "bbox": [ + 89, + 546, + 482, + 575 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\boldsymbol {f}} \\log p (y = c | \\boldsymbol {f}) = \\boldsymbol {e} _ {c} - \\boldsymbol {p}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 585, + 480, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $e_{c}$ is a one-hot vector with one at index $c$ , and $\\pmb{p} \\in \\mathbb{R}^{n}$ is the classifier probability. From (6), we further have that", + "bbox": [ + 89, + 609, + 480, + 640 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\boldsymbol {x}} \\log p (y = c | \\boldsymbol {x}) = \\left(\\frac {\\partial \\boldsymbol {f} (\\boldsymbol {x})}{\\partial \\boldsymbol {x}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 647, + 482, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we wrote $\\pmb{p}(\\pmb{x})$ to emphasize that the probability vector is a function of $\\pmb{x}$ . In the context of EnKF, we consider a set of $K$ particles $\\{\\pmb{x}^{(k)}\\}_{k=1}^{K}$ to represent a state, where each particle corresponds to a sample of the random variable $\\pmb{x}$ . To leverage the ideas from EnKF, we are interested in the pre-conditioned version of the gradient, where the covariance of the particles is used", + "bbox": [ + 89, + 691, + 483, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {g} _ {\\text {F r e e}} := \\boldsymbol {C} _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\log p (c | \\boldsymbol {x}) = \\boldsymbol {C} _ {\\boldsymbol {x x}} \\left(\\frac {\\partial \\boldsymbol {f} (\\boldsymbol {x})}{\\partial \\boldsymbol {x}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 805, + 496, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C_{\\pmb{x}\\pmb{x}}:= \\frac{1}{K}\\sum_{k = 1}^{K}(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})^{\\top}$ , and we use $\\bar{\\pmb{x}}$ to denote the sample mean $\\mathbb{E}[\\pmb{x}^{(k)}]$ .", + "bbox": [ + 89, + 864, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9d2ade8800c84df7ba57b4966f1c09414e0a71213624ee3258cecf1185239a16.jpg", + "image_caption": [ + "Figure 3. Toy example of FreeMCG, illustrating the gradient (red arrow) and the gradient aligned with the tangent of manifold (gray dashed) approximated by (9) (green arrow), using neighbor data points (blue dots)." + ], + "image_footnote": [], + "bbox": [ + 521, + 95, + 709, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/32c71bc1d23e6ccda5c279b7736fafd572a38fe0701edc4e85dbfbf2fdda6e82.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 95, + 898, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "FreeMCG produces on-manifold gradients. One may question the need for preconditioning the gradient with the empirical covariance matrix. In Theorem 1, we show that this preconditioning yields gradients that are on the data manifold $\\mathcal{M}$ , producing results that are well-aligned with human perception, and robust to adversarial attacks. The proof can be found in Appendix A.", + "bbox": [ + 511, + 329, + 905, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1. Suppose that $\\mathcal{M}$ is locally linear at $x$ , meaning that in the neighborhood of $x$ , the manifold aligns with its tangent space $\\mathcal{T}_x\\mathcal{M}$ . Suppose further, that the particles $\\boldsymbol{x}^{(k)} \\in \\mathcal{M}$ . Then, $\\boldsymbol{g}_{\\mathrm{Free}}$ approximately lies within $\\mathcal{M}$ . Precisely, $\\boldsymbol{C}_{xx}$ acts as a linear transformation, expanding along $\\mathcal{T}_x\\mathcal{M}$ and contracting the vectors normal to $\\mathcal{T}_x\\mathcal{M}$ .", + "bbox": [ + 511, + 445, + 905, + 536 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 states that when the particles $\\boldsymbol{x}^{(k)}$ lies on the manifold surrounding the original data point $\\boldsymbol{x}$ , $C_{xx}$ captures the geometric properties of the tangent space $T_{x}\\mathcal{M}$ . Specifically, the covariance matrix refines the vanilla gradient by contracting direction that lead off the manifold, which helps prevent the possibility of adversarial examples. Additionally, it expands along the direction of greater variability among the particles, reducing the likelihood of converging to a single original point.", + "bbox": [ + 511, + 545, + 905, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "EnKF for derivative-free gradient However, notice that $C_{xx} \\left( \\frac{\\partial f(x)}{\\partial x} \\right)^\\top$ is hard to compute, as we do not have access to the gradient of $f$ . Thus, we invoke the following.", + "bbox": [ + 511, + 699, + 905, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 2. Suppose $\\| \\nabla_{\\pmb{x}}^{2}\\pmb{f}(\\pmb{x})\\|$ be uniformly bounded and there exists $\\delta >0$ such that $\\pmb{x}^{(k)}\\in \\{\\pmb {x}\\in \\mathbb{R}^d:\\| \\pmb {x} - \\bar{\\pmb{x}}\\| \\leq \\delta \\}$ for all $k$ . Then, the following approximation holds", + "bbox": [ + 511, + 763, + 905, + 823 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC _ {\\boldsymbol {x} \\boldsymbol {f}} = C _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\boldsymbol {f} (\\boldsymbol {x}) ^ {\\top} + \\mathcal {O} \\left(\\delta^ {3}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 834, + 903, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C_{\\pmb{x}\\pmb{f}} := \\frac{1}{K}\\sum_{k=1}^{K}(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb{f}(\\pmb{x}^{(k)}) - \\bar{\\pmb{f}})^{\\top}$ and $\\bar{\\pmb{f}} := \\frac{1}{K}\\sum_{k=1}^{K}\\pmb{f}(\\pmb{x}^{(k)})$ .", + "bbox": [ + 511, + 864, + 905, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23798", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proof along with a formal treatment on approximation errors can be found in Appendix A. Apply Theorem 2 to (8), we have", + "bbox": [ + 89, + 90, + 483, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {C} _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\log p (y = c | \\boldsymbol {x}) \\approx \\boldsymbol {C} _ {\\boldsymbol {x f}} \\left(e _ {c} - \\boldsymbol {p}\\right) \\\\ = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\boldsymbol {x} ^ {(k)} - \\bar {\\boldsymbol {x}}\\right) \\left(\\boldsymbol {f} \\left(\\boldsymbol {x} ^ {(k)}\\right) - \\bar {\\boldsymbol {f}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 150, + 482, + 213 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "given the particles $\\pmb{x}^{(k)}$ . We provide the pseudocode for computing FreeMCG in Alg. 1.", + "bbox": [ + 89, + 227, + 483, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although we now have the machinery to compute the approximate gradient, notice that we have to choose the position of the particles $\\pmb{x}^{(k)}$ . For this, three conditions must be met. The particles should be 1) near $\\pmb{x}$ , 2) on-manifold, and 3) fast to generate. The first two conditions are met by perturbing $\\pmb{x}$ to obtain forward-diffused samples $\\pmb{x}_t^{(k)}$ , and running reverse PF-ODE to all the particles, as used in [32, 62]. However, since this would be prohibitively slow, we simply choose to use the Tweedie denoised estimates, which we denote as $\\pmb{x}_{0|t}^{(k)}$ . In short, our gradient reads", + "bbox": [ + 89, + 260, + 483, + 416 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {g} _ {\\text {F r e e}} := \\mathbb {E} \\left[ \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)} - \\bar {\\boldsymbol {x}} _ {0 | t} ^ {(k)}\\right) \\left(\\boldsymbol {f} \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)}\\right) - \\bar {\\boldsymbol {f}} \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)}\\right)\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p}\\right) \\right], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 429, + 488, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the expectation is over the diffusion timesteps $t$ and the number of particles $k$ . Notice that under our assumption of local linearity, we can use Proposition 2 of [8], which states that Tweedie's formula [15] is locally an orthogonal projection to the manifold $\\mathcal{M}$ , satisfying the assumption of Thm. 1.", + "bbox": [ + 89, + 484, + 483, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We illustrate a 2D toy example in Fig. 3. Considering $f = -x + y^2$ with its gradient $\\nabla_{\\pmb{x}}f(\\pmb{x}) = (-1,2y)$ , we sample particles around the point $\\pmb{x}$ and calculate the covariance matrix. Then, applying (9), we obtain a gradient aligned with the direction of the manifold without directly computing the gradient of the $f$ . In our main experiments, we show that FreeMCG indeed produces a gradient that produces on-manifold gradients so that it avoids being an adversarial attack. In the following, we elaborate on practical implementations of (11) for feature attribution and counterfactual explanation, as well as their intuition, respectively.", + "bbox": [ + 89, + 575, + 483, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Applications of FreeMCG", + "text_level": 1, + "bbox": [ + 89, + 756, + 326, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FreeMCG for feature attribution. This corresponds to the case where the target class $c'$ aligns with the prediction of the classifier $c$ . Notice that $f(\\boldsymbol{x}^{(k)}) - \\bar{f} \\in \\mathbb{R}^n$ where $f_c$ indicates the average drop in logit value after the Tweedie perturbation. Moreover, when $c' = c$ , the only positive entry in $e_c - p$ will be at the index $c$ , positively weighting the part that changes the predicted class label, while negatively weighting the part that is irrelevant. As a concrete example,", + "bbox": [ + 89, + 779, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 FreeMCG Gradient Computation" + ], + "code_body": "1: function FREEMCG $(\\pmb {f},\\{\\pmb{x}^{(k)}\\}_{k = 1}^{K},e_{c},\\pmb {p})$ \n2: $\\bar{\\pmb{x}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb{x}^{(k)}$ \n3: $\\bar{\\pmb{f}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb {f}(\\pmb{x}^{(k)})$ \n4: for $k = 1$ to $K$ do \n5: $\\Delta^{(k)}\\gets (\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb {f}(\\pmb{x}^{(k)}) - \\bar{\\pmb{f}})^{\\top}(\\pmb {e}_c - \\pmb {p})$ \n6: end for \n7: return $\\pmb{g}_{\\mathrm{Free}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb{\\Delta}^{(k)}$ \n8: end function", + "bbox": [ + 521, + 109, + 890, + 239 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 2 FreeMCG for feature attribution" + ], + "code_body": "Require: Classifier $f$ , Diffusion model $\\epsilon_{\\theta}$ , Input $x$ , Number of particles $K$ , Target class vector $e_c$ , Diffusion timestep range $[l, u]$ \n1: $p = \\text{softmax}(f(x))$ \n2: $x_0 \\gets x$ \n3: for $k = 1$ to $K$ do \n4: $t \\sim \\mathcal{U}[l, u]$ \n5: $x_t^{(k)} \\sim p(x_t | x_0)$ \n6: $x_{0|t}^{(k)} \\gets (x_t - \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon_\\theta(x_t)) / \\sqrt{\\bar{\\alpha}_t}$ \n7: end for \n8: $g_{\\text{Free}} \\gets \\text{FREEMCG}(f, \\epsilon_\\theta, x, \\{x_{0|t}^{(k)}\\}_{k=1}^K, e_c, p)$ \n9: return $g_{\\text{Free}}$", + "bbox": [ + 514, + 273, + 906, + 481 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 3 FreeMCG for CE with reverse diffusion" + ], + "code_body": "Require: Classifier $f$ , Diffusion model $\\epsilon_{\\theta}$ Input $\\pmb{x}$ Number of particles $K$ , Target class vector $e_{c^{\\prime}}$ , Diffusion params $t^\\prime ,\\tilde{\\beta}_t,\\bar{\\alpha}_t,\\eta ,\\gamma_t$ \n1: $\\pmb {x}_0\\gets \\pmb{x}$ \n2: $[\\pmb{x}_{t'}^{(k)}]\\sim p(\\pmb{x}_{t'}|\\pmb{x}_0)\\quad \\triangleright [\\cdot ]$ denotes $K$ batched particles \n3: for $t = t^{\\prime}$ to 1 do reverse diffusion \n4: $[\\hat{\\epsilon}_t^{(k)}]\\gets \\epsilon_\\theta ([\\pmb{x}_t^{(k)}])$ \n5: $[\\pmb{x}_{0|t}^{(k)}]\\gets ([\\pmb{x}_t^{(k)}] - \\sqrt{1 - \\bar{\\alpha}_t} [\\hat{\\epsilon}_t^{(k)}]) / \\sqrt{\\bar{\\alpha}_t}$ Tweedie denoising \n6: $[\\pmb{p}^{(k)}]\\gets \\mathrm{softmax}(\\pmb {f}([\\pmb{x}_{0|t}^{(k)}]))$ \n7: $[\\pmb{g}_{\\mathrm{Free}}^{(k)}]\\gets \\mathrm{FREEMCG}(\\pmb {f},[\\pmb{x}_{0|t}^{(k)}],\\pmb{e}_{c'},\\pmb{p}^{(k)})$ \n8: $[\\pmb{g}^{(k)}]\\gets \\alpha [\\pmb{g}_{\\mathrm{Free}}^{(k)}] + \\beta (\\pmb {x} - [\\pmb{x}_{0|t}^{(k)})]$ \n9: $[\\pmb {\\epsilon}^{(k)}]\\sim \\mathcal{N}(0,\\pmb {I})$ \n10: $[\\pmb{x}_{t - 1}]\\gets \\sqrt{\\bar{\\alpha}_{t - 1}} [\\pmb{x}_{0|t}]^{(k)} + \\sqrt{1 - \\bar{\\alpha}_{t - 1} - \\eta^2\\tilde{\\beta}_t^2} [\\hat{\\epsilon}_t]$ $+\\eta \\tilde{\\beta}_t[\\epsilon^{(k)}] + \\gamma_t[\\pmb {g}^{(k)}]$ \n11: end for \n12: return $x^{\\mathrm{(CE)}} = \\frac{1}{K}\\sum_{k = 1}^{K}x_0$ Average of particles", + "bbox": [ + 514, + 513, + 906, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "consider the following 4-class example", + "bbox": [ + 511, + 833, + 774, + 849 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {e} _ {c} = [ 1, 0, 0, 0 ] ^ {\\top}, \\boldsymbol {p} = [ 0. 7, 0. 1, 0. 1, 0. 1 ] ^ {\\top}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 857, + 849, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {e} _ {c} - \\boldsymbol {p} = [ 0. 3, - 0. 1, - 0. 1, - 0. 1 ] ^ {\\top}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 878, + 905, + 897 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23799", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where only the perturbations that dropped the probability of the first class will be positively weighted, while for the other indices, there will be an opposite force.", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For implementation, we found that using multiple levels of $t$ was crucial for encapsulating the attribution that acts both for coarse and fine scales. Similar to how score distillation sampling (SDS) [39] is recently used [48], we constrain the time range to $t \\in [0.1, 0.7]$ . For visualization purposes, we take the mean across the color channels and plot the absolute value. The algorithm for feature attribution using FreeMCG is presented in Alg. 2.", + "bbox": [ + 89, + 136, + 480, + 256 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FreeMCG for counterfactual explanation. While (11) can directly serve as the attribution, for counterfactual explanation, the gradient should be used as the direction of ascent toward a counterfactual sample. Here, we can iteratively apply gradient ascent with FreeMCG, i.e.", + "bbox": [ + 89, + 257, + 482, + 332 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {x} _ {i + 1} = \\boldsymbol {x} _ {i} + \\alpha \\mathbf {g} _ {\\text {F r e e}} (\\boldsymbol {x} _ {i}) + \\beta (\\boldsymbol {x} - \\boldsymbol {x} _ {i}), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 345, + 482, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha$ is the step size weighting the FreeMCG, and $\\beta$ weights the proximal regularization to the initial point $\\pmb{x}$ . Notice that the implementation of FreeMCG for counterfactual explanation differs from that of feature attribution, as we have a different target class $c^{\\prime}$ from $c$ . For instance, consider the example in (12), but the target class is now 2. Then, in the earlier stage of gradient ascent, we have", + "bbox": [ + 89, + 372, + 483, + 477 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {e} _ {c} = [ 0, 1, 0, 0 ] ^ {\\top}, \\boldsymbol {p} = [ 0. 7, 0. 1, 0. 1, 0. 1 ] ^ {\\top}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 488, + 424, + 505 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {e} _ {c} - \\boldsymbol {p} = \\left[ - 0. 7, 0. 9, - 0. 1, - 0. 1 \\right] ^ {\\top}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 510, + 480, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In other words, the components correlated with the original class $c$ is strongly negatively pulled down, whereas the components correlated with the target class $c'$ are strongly positively pushed up.", + "bbox": [ + 89, + 537, + 482, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FreeMCG meets reverse diffusion. While iterative gradient ascents using FreeMCG in (13) gives us a fast way to generate counterfactual explanations, we find that this process is sensitive to hyperparameters and produces suboptimal results. To fully leverage the generative nature of diffusion models, we instead propose a variant that utilizes reverse diffusion, as is done in other methods that use diffusion models for counterfactual explanation [4, 16, 24]. Specifically, we use an SDEdit [32]-like approach, where we forward diffuse our initial sample up to time $t'$ and run reverse guided sampling in (13) to the Tweedie denoised estimates. The algorithm is presented in Alg. 3. Notice that we do not incorporate the Jacobian of $\\epsilon_{\\theta}$ , which is typically done in methods like [9, 53], and simply resort to the gradients with respect to the Tweedie estimates [10] to save computation. For further details, see Appendix G. This approach may be slower as it requires reverse diffusion, but produces higher-fidelity results (Fig. 4). Therefore, all experiments on counterfactual explanation with FreeMCG use this reverse diffusion approach unless specified otherwise.", + "bbox": [ + 89, + 599, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 513, + 90, + 643, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We demonstrate our method from both feature attribution and counterfactual perspectives. To evaluate generalization and domain-specific performance, we compare our method on ImageNet [12] and MIMIC CXR [26] dataset, using images with a resolution of $256 \\times 256$ . We use regular pretrained classifier models with the ResNet-50 [20] and unconditional diffusion models [13] trained on each dataset. Experimental details are provided in Appendix H.", + "bbox": [ + 511, + 114, + 903, + 237 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation protocol", + "text_level": 1, + "bbox": [ + 511, + 250, + 702, + 265 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Counterfactuals. An ideal counterfactual makes semantically meaningful, human-interpretable yet minimal changes to the input image so that it is classified as the target class. This allows the user to gain visual insight into the decision boundary of the model. The aim is to create an example at a point on or near the decision boundary closest to the input image (Fig 2), so the generated counterfactual must be anchored on the original input image and should not be an unconditionally generated image of the target class. Therefore, evaluation involves the following criteria:", + "bbox": [ + 511, + 271, + 903, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1. Meaningful change towards target class", + "text_level": 1, + "bbox": [ + 514, + 426, + 815, + 441 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) Flip rate: Is the generated counterfactual classified as the intended target class by the model of interest?", + "(b) Perceived change: Does the generated counterfactual contain semantically meaningful changes to a human perceiver? (i.e. can it be distinguished from an adversarial attack?)" + ], + "bbox": [ + 537, + 443, + 903, + 531 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2. Similarity to the input", + "text_level": 1, + "bbox": [ + 514, + 534, + 692, + 547 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) L2 distance: Are generated counterfactuals close to the input images in terms of distance?", + "(b) Perceived similarity: Do generated counterfactuals and input appear similar to a human perceiver?" + ], + "bbox": [ + 537, + 547, + 903, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3. Realism of generated image", + "text_level": 1, + "bbox": [ + 514, + 609, + 732, + 623 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) Frechet Inception Distance (FID) [21]: Is the distribution of the generated counterfactual images similar to distribution of original input images?", + "(b) Perceived realism: Do the images appear realistic to a human perceiver?" + ], + "bbox": [ + 537, + 625, + 903, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Crucially, note that these metrics must be interpreted in concert, rather than as separate measures. In particular, an adversarial attack [11, 18], which flips the decision of the classification neural network but does not introduce changes to the input image that are meaningful to a human perceiver (which are meaningless as explainability tools), can speciously score well on aspects such as similarity or realism.", + "bbox": [ + 511, + 702, + 903, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Flip rate, L2 distance, and FID are computed using 1K generated counterfactuals (one from each class of the ImageNet validation set). Following the experimentation scheme in LDCE [16], we select the category closest to the input image based on the WordNet [34] hierarchy as the tar", + "bbox": [ + 511, + 825, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23800", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7c3d41d52b13645da70458f8ba90795bf3a91008ba2a3e4050360ce1f42d5eea.jpg", + "image_caption": [ + "Figure 4. Counterfactual Generation. Images on the leftmost column are given as input, and the counterfactual for the target class (shown in blue) are generated using each method. Baseline methods generate counterfactuals by perturbing the image towards the direction of a given classification neural network's gradients. Not only are these methods not applicable to situations without access to model weights, gradients almost always point away from the image manifold and into the ambient space, leading to imperceptible changes (i.e., adversarial attack) or changes that produce unnatural, off-manifold, images. FreeMCG on the other hand produces semantically meaningful changes while keeping the image on-manifold. *DVCE without cone projection." + ], + "image_footnote": [], + "bbox": [ + 109, + 89, + 500, + 376 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a0b54f6c5cbcb98e92468e624eff1b6a8623bc56571dee09bdb652bda936cf26.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 90, + 888, + 376 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "get class for counterfactual generation. Perceived change, similarity, and realism were measured through a human user study (details in Appendix I). Results are provided in Table 1.", + "bbox": [ + 88, + 488, + 480, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We select DVCE [4] and LDCE [16] as baselines, leveraging diffusion models to generate counterfactuals. Note that these baseline methods require access to the model weights while FreeMCG does not. In addition, while the proposed method of DVCE includes cone projection of model weights to the weights of an adversariably robust classifier, we use DVCE with only a regular non-robust classifier (i.e. without cone projection) for comparison throughout this paper as we are assuming lack of access to adversarially robust weights.", + "bbox": [ + 88, + 558, + 482, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature attribution. Feature attributions can be evaluated by observing the change in model predictions whilst removing the pixels in order of purported importance from the attribution. We compare our approach with existing gradient-based attribution methods, including the vanilla gradient [50], Integrated Gradients [49] and InputXGradient [47]. We provide Shapley additive explanation (SHAP) [31] attributions - which are removal-based, not gradient-based - as a reference that is highly aligned with removal-based evaluation such as Remove-and-Debias (ROAD) [42] used to assess the faithfulness of feature attributions.", + "bbox": [ + 88, + 719, + 482, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 513, + 487, + 606, + 501 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Counterfactual generation. Counterfactual generation results are shown in Fig 4. The generation results show that FreeMCG is able to robustly approximate the direction of the gradient and push the image towards the decision boundary of the classifier. Quantitative results and human user study results for the criteria outlined in Section 4.1 are shown in Table 1. Because baseline methods make use of model gradients while FreeMCG does not, the flip rate of the model's decision is lower for FreeMCG than gradient-based baselines. However, FreeMCG yields by far the most human-perceived changes (Tab. 1 and Fig. 4). In fact, FreeMCG-based counterfactuals often contain informative changes without changing the decision of the classifier while gradient-based baselines commonly produce counterfactuals that fool the classifier to predict a different class but do not introduce semantically meaningful changes. Gradient-based methods are thus closer to adversarial attacks, while FreeMCG better serves the purpose of counterfactual generation and produces interpretable, on-manifold changes towards the target class.", + "bbox": [ + 509, + 515, + 906, + 818 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature attribution. Feature attributions from representative gradient-based methods for both ImageNet and MIMIC-CXR are shown in Fig. 5(a). ROAD evaluation results are also shown in Fig. 5(b). We see that baseline gradient methods provide feature attributions that are", + "bbox": [ + 511, + 825, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23801", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7255a5e172f3bc5d472c8f6b2879df16a5c45fe45544c7c65d99c0b5982424ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 116, + 89, + 620, + 243 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ec567ae129404c123dcda64ce5e61c7b323be36a54504bbda34146e7e2a81d16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 90, + 879, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/234dab938883febed07a39c87c2564236174551f0f7ad6f36c4111d1d531dbc5.jpg", + "image_caption": [ + "Figure 5. (a) Feature attribution maps obtained using each method, (b) Corresponding ROAD [42] evaluation results. Steeper decline is better, and SHAP is given as reference for the lower bound of this decline. For ImageNet, ROAD is calculated as described in [42]. For MIMIC chest X-ray data, results for decline in prediction accuracy was noisy due to the lower starting accuracy of the classifier, low number of classes, and severe data imbalance between classes; therefore, we instead measure the drop in prediction for the originally predicted class. The principle remains the same in that features (pixels) are removed in order of purported importance from each feature attribution map to observe the change in classifier predictions." + ], + "image_footnote": [], + "bbox": [ + 114, + 246, + 619, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1382ce5c029d951fc38ecb870073adfa26d52a305888cc3de124163b8672ba2c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 250, + 879, + 388 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3ab8c47a4851c35d45a77c9235da95763c987c911eb3e36998a742bb659323a2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ChangeSimilarityRealism
Flip Rate ↑Perceived change ↓L2 ↓Perceived similarity ↓FID ↓Perceived realism ↓
DVCE* [4]85.82.35995.922.3471.382.30
LDCE [16]61.72.001351.391.9063.041.87
Ours51.51.651001.021.7666.891.83
", + "bbox": [ + 174, + 506, + 823, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. Quantitative (Flip Rate / L2 / FID) and human user study (perceived change/similarity/realism) results. *DVCE without cone projection.", + "bbox": [ + 88, + 599, + 906, + 630 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "similar to adversarial attacks, hence hardly interpretable. SHAP attributions provide less informative patch-like artifact. FreeMCG, on the other hand, produces high quality and interpretable attributions that are similar to SHAP, but retaining the high-frequency details as it does not rely on arbitrary pixel clustering. In ROAD evaluation, we see that FreeMCG achieves the steepest decline in model prediction among gradient-based methods, corresponding to better feature attributions, closer to the lower-bound computed by SHAP. Additional comparison against other removal-based black-box methods [36, 38] can be found in Appendix E.", + "bbox": [ + 88, + 641, + 482, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 842, + 209, + 858 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We developed Derivative-Free Diffusion Mainfold Constrained Gradients (FreeMCG), an approximation of a neu", + "bbox": [ + 89, + 869, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ral network's gradient tangent to the data manifold, obtained without access to the model weights or its real gradients. Previous explainability literature on gradient-based feature attribution and counterfactual generation have remained largely separate because the gradient could not be readily employed for counterfactual generation as it produces adversarial attacks. With FreeMCG, one can obtain gradient directions on the image manifold that produce semantically meaningful counterfactual explanations and feature attributions. We demonstrate through experiments that FreeMCG enables a unified framework for both explainability methods with state-of-the-art results, all without access to model weights. FreeMCG still assumes black-box access to the model's logits; in more restricted scenarios where only class predictions are available, FreeMCG would not be applicable, highlighting a limitation that could inspire future work on extending FreeMCG to such settings.", + "bbox": [ + 511, + 641, + 906, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23802", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 258, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the National Research Foundation of Korea (NRF) under Grants RS-2024-00336454 and RS-2023-00262527, and by the Institute for Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (RS-2019-II190075, Artificial Intelligence Graduate School Program, KAIST).", + "bbox": [ + 89, + 114, + 483, + 220 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 232, + 187, + 248 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. 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Ensemble kalman diffusion guidance: A derivative-free method for inverse problems. arXiv preprint arXiv:2409.20175, 2024. 4, 5, 10" + ], + "bbox": [ + 91, + 92, + 482, + 517 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "23805", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_model.json b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..afcdd7ad6eebe29275a3080d2a4849f9c8e90d77 --- /dev/null +++ b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_model.json @@ -0,0 +1,2752 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.125, + 0.131, + 0.873, + 0.152 + ], + "angle": 0, + "content": "Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI" + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.18, + 0.324, + 0.199 + ], + "angle": 0, + "content": "Won Jun Kim\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.357, + 0.181, + 0.505, + 0.199 + ], + "angle": 0, + "content": "Hyungjin Chung\\*" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.181, + 0.652, + 0.198 + ], + "angle": 0, + "content": "Jaemin \\(\\mathrm{Kim}^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.686, + 0.181, + 0.798, + 0.199 + ], + "angle": 0, + "content": "Sangmin Lee" + }, + { + "type": "text", + "bbox": [ + 0.357, + 0.199, + 0.478, + 0.217 + ], + "angle": 0, + "content": "Byeongsu Sim" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.2, + 0.635, + 0.217 + ], + "angle": 0, + "content": "Jong Chul Ye1" + }, + { + "type": "text", + "bbox": [ + 0.404, + 0.223, + 0.476, + 0.239 + ], + "angle": 0, + "content": "1 KAIST" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.223, + 0.591, + 0.239 + ], + "angle": 0, + "content": "2 EverEx" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.244, + 0.822, + 0.259 + ], + "angle": 0, + "content": "{wonjun, kjm981995, leeeeesang, byeongsu.s,jong.ye}@kaist.ac.kr hj.chung@everex.co.kr" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.294, + 0.327, + 0.309 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.326, + 0.485, + 0.643 + ], + "angle": 0, + "content": "Gradient-based methods are a prototypical family of \"explainability for AI\" (XAI) techniques, especially for image-based models. However, they (1) require white-box access to models, (2) are vulnerable to adversarial attacks, and (3) produce attributions that lie off the image manifold, leading to explanations that are not amenable to human perception. To overcome these challenges, we introduce Derivative-Free Diffusion Manifold-Constrained Gradients (FreeMCG): by leveraging ensemble Kalman filters and diffusion models, we derive a derivative-free approximation of the model's gradient projected onto the data manifold, requiring access only to the model's outputs (i.e., black-box setting). We demonstrate the effectiveness of FreeMCG by applying it to both counterfactual generation and feature attribution, which have traditionally been treated as different tasks requiring distinct methods. Through comprehensive evaluation on both counterfactual explanation and feature attribution we show that our method yields state-of-the-art results for both tasks while preserving the essential properties expected of XAI tools. Code: https://github.com/one-june/FreeMCG." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.673, + 0.222, + 0.688 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.698, + 0.483, + 0.834 + ], + "angle": 0, + "content": "Understanding the decision-making process of complex deep neural networks is crucial for their deployment in high-stakes applications such as medical imaging [6, 7], autonomous systems [2, 43], etc. Explanable AI (XAI) seeks to address this challenge by providing insights into how models arrive at specific predictions, thus enhancing trust, accountability, and usability in critical applications. Two widely used tools for XAI are counterfactual explanation [59] and feature attribution1 [31]." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.835, + 0.484, + 0.866 + ], + "angle": 0, + "content": "Among various XAI methods, the gradient of the target (e.g. classifier) model is the prototypical method of under" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.287, + 0.905, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.606, + 0.905, + 0.634 + ], + "angle": 0, + "content": "Figure 1. Representative results of FreeMCG, operating as a universal framework for black box XAI." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.907, + 0.809 + ], + "angle": 0, + "content": "standing the local behavior of a function around a given input data point. It has thus been used since the beginning of the rise of neural networks to explain their decisions [50]. There have been many subsequent works improving the vanilla gradient to serve as better feature attributions for a deep neural network [3, 46, 47, 55, 57, 61]. Gradients are also utilized for generating counterfactual explanations [4, 25, 44], in which the gradient of the target model serves as the direction that guides the change \\(\\delta\\) made to the original image so that prediction of the model flips to another class." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.81, + 0.907, + 0.855 + ], + "angle": 0, + "content": "While gradient-based methods are popular explainable AI (XAI) tools, they suffer from three significant limitations:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.856, + 0.909, + 0.902 + ], + "angle": 0, + "content": "1. Access to model gradients is not always feasible: Obtaining gradients requires access to the model's internal weights, which is often not possible in practice. For" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.217, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.445, + 0.901 + ], + "angle": 0, + "content": "1The term \"saliency maps\" are also often used interchangeably." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.445, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23795" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.179, + 0.093, + 0.27, + 0.103 + ], + "angle": 0, + "content": "Feature attribution" + }, + { + "type": "text", + "bbox": [ + 0.185, + 0.111, + 0.318, + 0.139 + ], + "angle": 0, + "content": "Q. Which features (pixels) are most important for the classifier's decision?" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.159, + 0.316, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.18, + 0.31, + 0.308, + 0.32 + ], + "angle": 0, + "content": "Counterfactual explanation" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.326, + 0.306, + 0.362 + ], + "angle": 0, + "content": "Q. What changes to the input image shift the decision of the classifier to another class?" + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.096, + 0.473, + 0.106 + ], + "angle": 0, + "content": "Adversarial attack" + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.108, + 0.506, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.341, + 0.209, + 0.49, + 0.22 + ], + "angle": 0, + "content": "\\(\\otimes\\) Off-manifold, Unreliable" + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.238, + 0.514, + 0.248 + ], + "angle": 0, + "content": "Counterfactuals on the manifold" + }, + { + "type": "image", + "bbox": [ + 0.334, + 0.261, + 0.494, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.341, + 0.348, + 0.494, + 0.359 + ], + "angle": 0, + "content": "\\(\\odot\\) On-manifold, Explainable" + }, + { + "type": "image_caption", + "bbox": [ + 0.645, + 0.096, + 0.712, + 0.107 + ], + "angle": 0, + "content": "FreeMCG" + }, + { + "type": "image_caption", + "bbox": [ + 0.544, + 0.114, + 0.645, + 0.124 + ], + "angle": 0, + "content": "(i) Spread particles" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.133, + 0.609, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.14, + 0.791, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.544, + 0.231, + 0.738, + 0.241 + ], + "angle": 0, + "content": "(ii) Approximate gradient on manifold" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.255, + 0.777, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.341, + 0.768, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {g} _ {\\text {F r e e}} \\cong C _ {x x} \\nabla_ {x} f (\\boldsymbol {e} _ {c} - \\boldsymbol {p})\n\\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.378, + 0.907, + 0.435 + ], + "angle": 0, + "content": "Figure 2. Unified framework of XAI for feature attribution and counterfactual explanation using our method, Derivative-Free Diffusion Manifold Constrained Gradients (FreeMCG). Naive gradients not only violate the black box assumption but also is unreliable and hard to interpret as they produce adversarial attacks. Using diffusion models to produce on-manifold ensembles, and using the covariance of these particles as the preconditioner of the gradient, FreeMCG approximates gradients on the manifold, which is more reliable and interpretable." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.465, + 0.483, + 0.494 + ], + "angle": 0, + "content": "many neural-network based services, users can only interact with these systems through their outputs." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.494, + 0.484, + 0.63 + ], + "angle": 0, + "content": "2. Gradients provide unreliable explanations: As shown in [1, 37, 51], gradient-based methods often fail to generate meaningful explanations of model behavior. These explanations are closely related to adversarial examples [58], and many traditional methods resort to using models that have been trained to be adversarially robust [4, 44]. Moreover, gradients typically do not align with the underlying data manifold, leading to explanations that are misaligned with human perception." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.631, + 0.484, + 0.782 + ], + "angle": 0, + "content": "3. Lack of a unified framework for feature attribution and counterfactual explanations: The literature on feature attribution and counterfactual explanations remains largely separate. This is because real gradients produce adversarial attacks rather than counterfactual explanations and additional techniques are required to introduce perceptible changes. In theory, gradients should be usable for both applications. This raises the question of whether a single framework can effectively handle both types of explanations." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.494, + 0.484, + 0.782 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To address these challenges, in this work, we propose Derivative-Free Diffusion Manifold Constrained Gradients (FreeMCG), a unified framework that can be used both for feature attribution and counterfactual explanation with only black-box access to the target model. By leveraging diffusion models and their powerful ability to model data manifolds, we can produce on-manifold perturbations of input" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.464, + 0.907, + 0.553 + ], + "angle": 0, + "content": "data points, which, combined with ideas from Ensemble Kalman Filters (EnKF) [45], can be used to approximate manifold-projected model gradients. In Fig. 1, we show the representative results of FreeMCG, acting as a unified framework for XAI. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.557, + 0.905, + 0.587 + ], + "angle": 0, + "content": "- We present the first unified framework that encompasses both feature attribution and counterfactual explanation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.588, + 0.906, + 0.647 + ], + "angle": 0, + "content": "- We derive a novel method of estimating the gradient of the target classifier with black-box access (i.e. without access to model weights) by leveraging diffusion models and the theory of EnKF." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.648, + 0.905, + 0.678 + ], + "angle": 0, + "content": "- We demonstrate that FreeMCG achieves state-of-the-art performance, even compared to white-box methods." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.557, + 0.906, + 0.678 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.691, + 0.791, + 0.708 + ], + "angle": 0, + "content": "2. Background & Related Works" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.716, + 0.708, + 0.731 + ], + "angle": 0, + "content": "2.1. Gradient-based XAI" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.738, + 0.731, + 0.754 + ], + "angle": 0, + "content": "Consider the following classifier" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.764, + 0.905, + 0.801 + ], + "angle": 0, + "content": "\\[\np (y = c | \\boldsymbol {x}) = \\frac {\\exp \\left(\\boldsymbol {f} _ {c} (\\boldsymbol {x})\\right)}{\\sum_ {c ^ {\\prime} = 1} ^ {C} \\exp \\left(\\boldsymbol {f} _ {c ^ {\\prime}} (\\boldsymbol {x})\\right)}, \\boldsymbol {f}: \\mathbb {R} ^ {d} \\mapsto \\mathbb {R} ^ {n}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.907, + 0.902 + ], + "angle": 0, + "content": "where \\( n \\) is the number of classes, and \\( f(\\pmb{x}) := [f_1(\\pmb{x}), \\dots, f_n(\\pmb{x})] \\). Taking the softmax would induce the probability vector \\( \\pmb{p} = \\text{softmax}(\\pmb{f}(\\pmb{x})) \\). When \\( \\pmb{x} \\) belongs to some class \\( c \\), let \\( \\text{class}(\\pmb{x}) = c \\) be a labeling function. The task of feature attribution for images is to find an attribution \\( \\pmb{a} \\in [0, 1]^d \\) that has high values in the indices where" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23796" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "its influence to \\(\\pmb{p}\\) is pronounced. On the other hand, the task of counterfactual explanation aims to find a vector \\(\\pmb{x}^{\\prime}\\) that belongs to a target class \\(c^\\prime\\), i.e. \\(\\operatorname{class}(\\pmb{x}^{\\prime}) = c^{\\prime}\\), but stays in proximity to \\(\\pmb{x}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.483, + 0.318 + ], + "angle": 0, + "content": "Feature attribution. Gradients provide a direct representation of the local behavior of a function by encapsulating how the function changes linearly in the gradient vector [50]. Integrated Gradients improve upon the vanilla gradient and satisfies certain desirable properties such as sensitivity, completeness, linearity, and implementation invariance by integrating the gradients along a path from a fixed baseline (often a black image) [57]. Other follow-up works have extended this approach by modifying the integration region [33, 56, 60] or altering the integrand [23, 27, 49], among others." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.318, + 0.483, + 0.529 + ], + "angle": 0, + "content": "Counterfactuals and adversarial attacks. Gradients obtained with respect to the input can be used to perform gradient ascent/descent to change the input towards a direction that maximizes or minimizes the model output. However, for high-dimensional input data such as images, gradient ascent or descent often yields changes that are imperceptible to humans. This is known as an adversarial attack [18], because it changes the model output for a given input while the image itself remains effectively unchanged to human perception, thus having the effect of \"fooling\" a model. The adversarial attack phenomenon occurs because gradient ascent/descent using simple gradients perturbs the image in a direction that lifts the image off the image manifold and into the ambient space [14]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.53, + 0.483, + 0.681 + ], + "angle": 0, + "content": "Counterfactuals, on the other hand, should yield a semantically meaningful change to the original input \\( x \\) such that the target model changes its prediction. In other words, the change should be on-manifold. Naturally, to induce this on-manifold change, generative models such as GANs and diffusion models [4, 25] have been used. However, most of these methods require access to model gradients, some even requiring that the model be adversarially robust. Moreover, these methods can be considered guided generation methods, making them inapplicable for feature attribution." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.687, + 0.26, + 0.702 + ], + "angle": 0, + "content": "2.2. Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.709, + 0.483, + 0.831 + ], + "angle": 0, + "content": "Diffusion model [22, 28, 54] is a class of generative models that sample images through a Gaussian denoising path. This path is constructed by starting from the initial data (i.e. image) distribution \\( p_0(\\pmb{x}) \\), \\( \\pmb{x} \\in \\mathbb{R}^d \\), gradually adding Gaussian noise, and reaching approximately the Gaussian distribution \\( p_T(\\pmb{x}) \\approx \\mathcal{N}(\\pmb{0}, \\pmb{I}) \\) at \\( t = T \\). For the choice of the Gaussian perturbation \\( p(\\pmb{x}_t | \\pmb{x}_0) = \\mathcal{N}(\\pmb{x}_0, \\sigma_t^2 \\pmb{I}) \\), the reverse generation trajectory reads" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.835, + 0.483, + 0.868 + ], + "angle": 0, + "content": "\\[\nd \\boldsymbol {x} _ {t} = - \\sigma_ {t} \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t}) d t = \\frac {\\boldsymbol {x} _ {t} - \\mathbb {E} [ \\boldsymbol {x} _ {0} | \\boldsymbol {x} _ {t} ]}{\\sigma_ {t}} d t, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where the initial point is sampled from the reference distribution \\( \\pmb{x}_T \\sim p_T(\\pmb{x}_T) \\). Here, Tweedie's formula [15]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.091, + 0.905, + 0.137 + ], + "angle": 0, + "content": "\\(\\mathbb{E}[\\pmb{x}_0|\\pmb{x}_t] = \\pmb{x}_t + \\sigma_t^2\\nabla_{\\pmb{x}_t}\\log p(\\pmb{x}_t)\\) is used for the second equality. Diffusion models are trained as denoisers that estimate this posterior mean" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.149, + 0.905, + 0.174 + ], + "angle": 0, + "content": "\\[\n\\theta^ {*} = \\underset {\\theta} {\\arg \\min } \\mathbb {E} _ {t, \\boldsymbol {x} _ {t}, \\boldsymbol {x} _ {0}} \\left[ \\| D _ {\\theta} (\\boldsymbol {x} _ {t}) - \\boldsymbol {x} _ {0} \\| _ {2} ^ {2} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.186, + 0.905, + 0.214 + ], + "angle": 0, + "content": "which can be plugged into (2) as \\(\\mathbb{E}[\\pmb{x}_0|\\pmb{x}_t]\\approx D_{\\theta^*}(\\pmb{x}_t)\\) at test time." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.216, + 0.907, + 0.368 + ], + "angle": 0, + "content": "In Chung et al. [8], assuming that \\(\\mathcal{M}\\) is a locally linear subspace, it was further shown that the distribution of noisy data \\(p(\\boldsymbol{x}_t)\\) is then concentrated on shell-like manifold \\(\\mathcal{M}_t\\). Moreover, one can show that Tweedie's formula is an orthogonal projection from \\(\\mathcal{M}_t\\) to \\(\\mathcal{M}\\). In other words, when the goal is to produce samples on the manifold \\(\\mathcal{M}\\) in a cost-effective way, one can use Tweedie's formula to generate samples in one step. This matches our intuition up to moderate values of \\(t\\), where the posterior mean gives us a relatively good approximation of the real samples." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.387, + 0.906, + 0.448 + ], + "angle": 0, + "content": "Guided sampling. Often, it is desirable to sample from the posterior \\( p(\\boldsymbol{x}|\\boldsymbol{y}) \\) instead of from the prior. A standard approach to achieve this is to use guided sampling by Bayes decomposition" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.46, + 0.905, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t} | \\boldsymbol {y}) = \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t}) + \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {y} | \\boldsymbol {x} _ {t}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.504, + 0.906, + 0.655 + ], + "angle": 0, + "content": "where the gradient of the log-likelihood term measures the fidelity with respect to the condition \\( \\pmb{y} \\). One can either train a separate neural network (e.g. classifier [13, 54]) to estimate the term or use some form of approximation [9, 53]. Sampling from the posterior then boils down to iterating the denoising steps of the unconditional PF-ODE in (2) and the gradient step that maximizes fidelity. However, regardless of the forward model2, most of the methods require access to the gradient of the forward model, which is often hard to compute due to reasons including safety and complexity." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.665, + 0.828, + 0.681 + ], + "angle": 0, + "content": "2.3. Gradient-free optimization and XAI" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.687, + 0.906, + 0.854 + ], + "angle": 0, + "content": "When one can only evaluate \\( f \\) but cannot compute its gradient, gradient-free (zeroth-order) optimization [30], where a single or multiple set of samples can be used to calculate the finite difference, alongside techniques such as Gaussian smoothing [35] can be used to estimate the true gradient. Ensemble Kalman Filters (EnKF) [45], in terms of inverse problem solving, is also a widely used method for derivative-free optimization, where the ensemble of particles and its covariance information is used as a proxy for gradient information. In a similar vein, Ensemble Kalman Inversion (EKI) [19, 29] was proposed as a derivative-free" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.863, + 0.906, + 0.901 + ], + "angle": 0, + "content": "2For instance, in image restoration, the degradation operator is the forward model. In classification, the neural network classifier is the forward model, as in (1)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23797" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.168 + ], + "angle": 0, + "content": "method for training neural networks. Recently, the use of EnKF was extended to inverse problem-solving with diffusion models [62], showing that the technique can be readily used for diffusion guidance. In the proposed method, we leverage EnKF to approximate the unknown gradient." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.185, + 0.484, + 0.427 + ], + "angle": 0, + "content": "Black-box feature attribution While white-box methods typically rely on gradient information, this dependency limits the applicability of XAI techniques to scenarios where gradients can be accessed. Several works [17, 31, 36, 40, 61] have introduced perturbation-based approaches for feature attribution. These methods generally involve perturbing the input—commonly by masking out pixel groups at random—and measuring the resulting change in class probabilities. While conceptually similar to FreeMCG in that they only require forward passes through the neural network, perturbation-based methods differ in two key ways: (1) masking pixels typically moves the input off the underlying data manifold, and (2) these methods are exclusively employed for feature attribution and cannot produce counterfactual explanations, as they do not approximate the decision boundary." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.439, + 0.373, + 0.455 + ], + "angle": 0, + "content": "3. Main Contribution: FreeMCG" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.463, + 0.312, + 0.479 + ], + "angle": 0, + "content": "3.1. Derivation of FreeMCG" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.486, + 0.288, + 0.5 + ], + "angle": 0, + "content": "From (1), one can derive that" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.507, + 0.482, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial}{\\partial \\boldsymbol {f} _ {c ^ {\\prime}}} \\log p (y = c | \\boldsymbol {f} _ {c ^ {\\prime}}) = \\delta_ {c c ^ {\\prime}} - p \\left(c ^ {\\prime} | \\boldsymbol {f} _ {c ^ {\\prime}}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.547, + 0.483, + 0.577 + ], + "angle": 0, + "content": "where \\(\\delta_{cc'}\\) is the Kronecker delta function which evaluates to 1 if and only if \\(c' = c\\). Vector form of (5) reads" + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.586, + 0.482, + 0.603 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\boldsymbol {f}} \\log p (y = c | \\boldsymbol {f}) = \\boldsymbol {e} _ {c} - \\boldsymbol {p}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.61, + 0.482, + 0.641 + ], + "angle": 0, + "content": "where \\( e_{c} \\) is a one-hot vector with one at index \\( c \\), and \\( \\pmb{p} \\in \\mathbb{R}^{n} \\) is the classifier probability. From (6), we further have that" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.648, + 0.483, + 0.685 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\boldsymbol {x}} \\log p (y = c | \\boldsymbol {x}) = \\left(\\frac {\\partial \\boldsymbol {f} (\\boldsymbol {x})}{\\partial \\boldsymbol {x}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.693, + 0.484, + 0.798 + ], + "angle": 0, + "content": "where we wrote \\( \\pmb{p}(\\pmb{x}) \\) to emphasize that the probability vector is a function of \\( \\pmb{x} \\). In the context of EnKF, we consider a set of \\( K \\) particles \\( \\{\\pmb{x}^{(k)}\\}_{k=1}^{K} \\) to represent a state, where each particle corresponds to a sample of the random variable \\( \\pmb{x} \\). To leverage the ideas from EnKF, we are interested in the pre-conditioned version of the gradient, where the covariance of the particles is used" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.806, + 0.498, + 0.856 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {g} _ {\\text {F r e e}} := \\boldsymbol {C} _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\log p (c | \\boldsymbol {x}) = \\boldsymbol {C} _ {\\boldsymbol {x x}} \\left(\\frac {\\partial \\boldsymbol {f} (\\boldsymbol {x})}{\\partial \\boldsymbol {x}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.866, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\(C_{\\pmb{x}\\pmb{x}}:= \\frac{1}{K}\\sum_{k = 1}^{K}(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})^{\\top}\\), and we use \\(\\bar{\\pmb{x}}\\) to denote the sample mean \\(\\mathbb{E}[\\pmb{x}^{(k)}]\\)." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.096, + 0.71, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.096, + 0.899, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.258, + 0.906, + 0.314 + ], + "angle": 0, + "content": "Figure 3. Toy example of FreeMCG, illustrating the gradient (red arrow) and the gradient aligned with the tangent of manifold (gray dashed) approximated by (9) (green arrow), using neighbor data points (blue dots)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.33, + 0.906, + 0.436 + ], + "angle": 0, + "content": "FreeMCG produces on-manifold gradients. One may question the need for preconditioning the gradient with the empirical covariance matrix. In Theorem 1, we show that this preconditioning yields gradients that are on the data manifold \\(\\mathcal{M}\\), producing results that are well-aligned with human perception, and robust to adversarial attacks. The proof can be found in Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.446, + 0.906, + 0.537 + ], + "angle": 0, + "content": "Theorem 1. Suppose that \\(\\mathcal{M}\\) is locally linear at \\(x\\), meaning that in the neighborhood of \\(x\\), the manifold aligns with its tangent space \\(\\mathcal{T}_x\\mathcal{M}\\). Suppose further, that the particles \\(\\boldsymbol{x}^{(k)} \\in \\mathcal{M}\\). Then, \\(\\boldsymbol{g}_{\\mathrm{Free}}\\) approximately lies within \\(\\mathcal{M}\\). Precisely, \\(\\boldsymbol{C}_{xx}\\) acts as a linear transformation, expanding along \\(\\mathcal{T}_x\\mathcal{M}\\) and contracting the vectors normal to \\(\\mathcal{T}_x\\mathcal{M}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.546, + 0.906, + 0.683 + ], + "angle": 0, + "content": "Theorem 1 states that when the particles \\( \\boldsymbol{x}^{(k)} \\) lies on the manifold surrounding the original data point \\( \\boldsymbol{x} \\), \\( C_{xx} \\) captures the geometric properties of the tangent space \\( T_{x}\\mathcal{M} \\). Specifically, the covariance matrix refines the vanilla gradient by contracting direction that lead off the manifold, which helps prevent the possibility of adversarial examples. Additionally, it expands along the direction of greater variability among the particles, reducing the likelihood of converging to a single original point." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.7, + 0.906, + 0.756 + ], + "angle": 0, + "content": "EnKF for derivative-free gradient However, notice that \\( C_{xx} \\left( \\frac{\\partial f(x)}{\\partial x} \\right)^\\top \\) is hard to compute, as we do not have access to the gradient of \\( f \\). Thus, we invoke the following." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.765, + 0.906, + 0.824 + ], + "angle": 0, + "content": "Theorem 2. Suppose \\(\\| \\nabla_{\\pmb{x}}^{2}\\pmb{f}(\\pmb{x})\\|\\) be uniformly bounded and there exists \\(\\delta >0\\) such that \\(\\pmb{x}^{(k)}\\in \\{\\pmb {x}\\in \\mathbb{R}^d:\\| \\pmb {x} - \\bar{\\pmb{x}}\\| \\leq \\delta \\}\\) for all \\(k\\). Then, the following approximation holds" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.835, + 0.905, + 0.854 + ], + "angle": 0, + "content": "\\[\nC _ {\\boldsymbol {x} \\boldsymbol {f}} = C _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\boldsymbol {f} (\\boldsymbol {x}) ^ {\\top} + \\mathcal {O} \\left(\\delta^ {3}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.865, + 0.906, + 0.904 + ], + "angle": 0, + "content": "where \\(C_{\\pmb{x}\\pmb{f}} := \\frac{1}{K}\\sum_{k=1}^{K}(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb{f}(\\pmb{x}^{(k)}) - \\bar{\\pmb{f}})^{\\top}\\) and \\(\\bar{\\pmb{f}} := \\frac{1}{K}\\sum_{k=1}^{K}\\pmb{f}(\\pmb{x}^{(k)})\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23798" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.138 + ], + "angle": 0, + "content": "The proof along with a formal treatment on approximation errors can be found in Appendix A. Apply Theorem 2 to (8), we have" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.151, + 0.483, + 0.214 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {C} _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\log p (y = c | \\boldsymbol {x}) \\approx \\boldsymbol {C} _ {\\boldsymbol {x f}} \\left(e _ {c} - \\boldsymbol {p}\\right) \\\\ = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\boldsymbol {x} ^ {(k)} - \\bar {\\boldsymbol {x}}\\right) \\left(\\boldsymbol {f} \\left(\\boldsymbol {x} ^ {(k)}\\right) - \\bar {\\boldsymbol {f}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.228, + 0.484, + 0.259 + ], + "angle": 0, + "content": "given the particles \\( \\pmb{x}^{(k)} \\). We provide the pseudocode for computing FreeMCG in Alg. 1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.261, + 0.484, + 0.417 + ], + "angle": 0, + "content": "Although we now have the machinery to compute the approximate gradient, notice that we have to choose the position of the particles \\( \\pmb{x}^{(k)} \\). For this, three conditions must be met. The particles should be 1) near \\( \\pmb{x} \\), 2) on-manifold, and 3) fast to generate. The first two conditions are met by perturbing \\( \\pmb{x} \\) to obtain forward-diffused samples \\( \\pmb{x}_t^{(k)} \\), and running reverse PF-ODE to all the particles, as used in [32, 62]. However, since this would be prohibitively slow, we simply choose to use the Tweedie denoised estimates, which we denote as \\( \\pmb{x}_{0|t}^{(k)} \\). In short, our gradient reads" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.43, + 0.49, + 0.472 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {g} _ {\\text {F r e e}} := \\mathbb {E} \\left[ \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)} - \\bar {\\boldsymbol {x}} _ {0 | t} ^ {(k)}\\right) \\left(\\boldsymbol {f} \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)}\\right) - \\bar {\\boldsymbol {f}} \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)}\\right)\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p}\\right) \\right], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.485, + 0.484, + 0.573 + ], + "angle": 0, + "content": "where the expectation is over the diffusion timesteps \\(t\\) and the number of particles \\(k\\). Notice that under our assumption of local linearity, we can use Proposition 2 of [8], which states that Tweedie's formula [15] is locally an orthogonal projection to the manifold \\(\\mathcal{M}\\), satisfying the assumption of Thm. 1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.577, + 0.484, + 0.744 + ], + "angle": 0, + "content": "We illustrate a 2D toy example in Fig. 3. Considering \\( f = -x + y^2 \\) with its gradient \\( \\nabla_{\\pmb{x}}f(\\pmb{x}) = (-1,2y) \\), we sample particles around the point \\( \\pmb{x} \\) and calculate the covariance matrix. Then, applying (9), we obtain a gradient aligned with the direction of the manifold without directly computing the gradient of the \\( f \\). In our main experiments, we show that FreeMCG indeed produces a gradient that produces on-manifold gradients so that it avoids being an adversarial attack. In the following, we elaborate on practical implementations of (11) for feature attribution and counterfactual explanation, as well as their intuition, respectively." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.757, + 0.327, + 0.773 + ], + "angle": 0, + "content": "3.2. Applications of FreeMCG" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.484, + 0.902 + ], + "angle": 0, + "content": "FreeMCG for feature attribution. This corresponds to the case where the target class \\( c' \\) aligns with the prediction of the classifier \\( c \\). Notice that \\( f(\\boldsymbol{x}^{(k)}) - \\bar{f} \\in \\mathbb{R}^n \\) where \\( f_c \\) indicates the average drop in logit value after the Tweedie perturbation. Moreover, when \\( c' = c \\), the only positive entry in \\( e_c - p \\) will be at the index \\( c \\), positively weighting the part that changes the predicted class label, while negatively weighting the part that is irrelevant. As a concrete example," + }, + { + "type": "code_caption", + "bbox": [ + 0.516, + 0.091, + 0.825, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 FreeMCG Gradient Computation" + }, + { + "type": "algorithm", + "bbox": [ + 0.522, + 0.111, + 0.892, + 0.24 + ], + "angle": 0, + "content": "1: function FREEMCG \\((\\pmb {f},\\{\\pmb{x}^{(k)}\\}_{k = 1}^{K},e_{c},\\pmb {p})\\) \n2: \\(\\bar{\\pmb{x}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb{x}^{(k)}\\) \n3: \\(\\bar{\\pmb{f}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb {f}(\\pmb{x}^{(k)})\\) \n4: for \\(k = 1\\) to \\(K\\) do \n5: \\(\\Delta^{(k)}\\gets (\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb {f}(\\pmb{x}^{(k)}) - \\bar{\\pmb{f}})^{\\top}(\\pmb {e}_c - \\pmb {p})\\) \n6: end for \n7: return \\(\\pmb{g}_{\\mathrm{Free}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb{\\Delta}^{(k)}\\) \n8: end function" + }, + { + "type": "code_caption", + "bbox": [ + 0.515, + 0.256, + 0.819, + 0.271 + ], + "angle": 0, + "content": "Algorithm 2 FreeMCG for feature attribution" + }, + { + "type": "algorithm", + "bbox": [ + 0.516, + 0.275, + 0.907, + 0.482 + ], + "angle": 0, + "content": "Require: Classifier \\(f\\), Diffusion model \\(\\epsilon_{\\theta}\\), Input \\(x\\), Number of particles \\(K\\), Target class vector \\(e_c\\), Diffusion timestep range \\([l, u]\\) \n1: \\(p = \\text{softmax}(f(x))\\) \n2: \\(x_0 \\gets x\\) \n3: for \\(k = 1\\) to \\(K\\) do \n4: \\(t \\sim \\mathcal{U}[l, u]\\) \n5: \\(x_t^{(k)} \\sim p(x_t | x_0)\\) \n6: \\(x_{0|t}^{(k)} \\gets (x_t - \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon_\\theta(x_t)) / \\sqrt{\\bar{\\alpha}_t}\\) \n7: end for \n8: \\(g_{\\text{Free}} \\gets \\text{FREEMCG}(f, \\epsilon_\\theta, x, \\{x_{0|t}^{(k)}\\}_{k=1}^K, e_c, p)\\) \n9: return \\(g_{\\text{Free}}\\)" + }, + { + "type": "code_caption", + "bbox": [ + 0.516, + 0.496, + 0.868, + 0.511 + ], + "angle": 0, + "content": "Algorithm 3 FreeMCG for CE with reverse diffusion" + }, + { + "type": "algorithm", + "bbox": [ + 0.516, + 0.515, + 0.907, + 0.809 + ], + "angle": 0, + "content": "Require: Classifier \\(f\\) , Diffusion model \\(\\epsilon_{\\theta}\\) Input \\(\\pmb{x}\\) Number of particles \\(K\\) , Target class vector \\(e_{c^{\\prime}}\\) , Diffusion params \\(t^\\prime ,\\tilde{\\beta}_t,\\bar{\\alpha}_t,\\eta ,\\gamma_t\\) \n1: \\(\\pmb {x}_0\\gets \\pmb{x}\\) \n2: \\([\\pmb{x}_{t'}^{(k)}]\\sim p(\\pmb{x}_{t'}|\\pmb{x}_0)\\quad \\triangleright [\\cdot ]\\) denotes \\(K\\) batched particles \n3: for \\(t = t^{\\prime}\\) to 1 do reverse diffusion \n4: \\([\\hat{\\epsilon}_t^{(k)}]\\gets \\epsilon_\\theta ([\\pmb{x}_t^{(k)}])\\) \n5: \\([\\pmb{x}_{0|t}^{(k)}]\\gets ([\\pmb{x}_t^{(k)}] - \\sqrt{1 - \\bar{\\alpha}_t} [\\hat{\\epsilon}_t^{(k)}]) / \\sqrt{\\bar{\\alpha}_t}\\) Tweedie denoising \n6: \\([\\pmb{p}^{(k)}]\\gets \\mathrm{softmax}(\\pmb {f}([\\pmb{x}_{0|t}^{(k)}]))\\) \n7: \\([\\pmb{g}_{\\mathrm{Free}}^{(k)}]\\gets \\mathrm{FREEMCG}(\\pmb {f},[\\pmb{x}_{0|t}^{(k)}],\\pmb{e}_{c'},\\pmb{p}^{(k)})\\) \n8: \\([\\pmb{g}^{(k)}]\\gets \\alpha [\\pmb{g}_{\\mathrm{Free}}^{(k)}] + \\beta (\\pmb {x} - [\\pmb{x}_{0|t}^{(k)})]\\) \n9: \\([\\pmb {\\epsilon}^{(k)}]\\sim \\mathcal{N}(0,\\pmb {I})\\) \n10: \\([\\pmb{x}_{t - 1}]\\gets \\sqrt{\\bar{\\alpha}_{t - 1}} [\\pmb{x}_{0|t}]^{(k)} + \\sqrt{1 - \\bar{\\alpha}_{t - 1} - \\eta^2\\tilde{\\beta}_t^2} [\\hat{\\epsilon}_t]\\) \\(+\\eta \\tilde{\\beta}_t[\\epsilon^{(k)}] + \\gamma_t[\\pmb {g}^{(k)}]\\) \n11: end for \n12: return \\(x^{\\mathrm{(CE)}} = \\frac{1}{K}\\sum_{k = 1}^{K}x_0\\) Average of particles" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.834, + 0.775, + 0.85 + ], + "angle": 0, + "content": "consider the following 4-class example" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.858, + 0.85, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {e} _ {c} = [ 1, 0, 0, 0 ] ^ {\\top}, \\boldsymbol {p} = [ 0. 7, 0. 1, 0. 1, 0. 1 ] ^ {\\top}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.879, + 0.906, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {e} _ {c} - \\boldsymbol {p} = [ 0. 3, - 0. 1, - 0. 1, - 0. 1 ] ^ {\\top}, \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "23799" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.137 + ], + "angle": 0, + "content": "where only the perturbations that dropped the probability of the first class will be positively weighted, while for the other indices, there will be an opposite force." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.137, + 0.482, + 0.257 + ], + "angle": 0, + "content": "For implementation, we found that using multiple levels of \\( t \\) was crucial for encapsulating the attribution that acts both for coarse and fine scales. Similar to how score distillation sampling (SDS) [39] is recently used [48], we constrain the time range to \\( t \\in [0.1, 0.7] \\). For visualization purposes, we take the mean across the color channels and plot the absolute value. The algorithm for feature attribution using FreeMCG is presented in Alg. 2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.258, + 0.483, + 0.333 + ], + "angle": 0, + "content": "FreeMCG for counterfactual explanation. While (11) can directly serve as the attribution, for counterfactual explanation, the gradient should be used as the direction of ascent toward a counterfactual sample. Here, we can iteratively apply gradient ascent with FreeMCG, i.e." + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.346, + 0.483, + 0.361 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {x} _ {i + 1} = \\boldsymbol {x} _ {i} + \\alpha \\mathbf {g} _ {\\text {F r e e}} (\\boldsymbol {x} _ {i}) + \\beta (\\boldsymbol {x} - \\boldsymbol {x} _ {i}), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.373, + 0.484, + 0.478 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is the step size weighting the FreeMCG, and \\(\\beta\\) weights the proximal regularization to the initial point \\(\\pmb{x}\\). Notice that the implementation of FreeMCG for counterfactual explanation differs from that of feature attribution, as we have a different target class \\(c^{\\prime}\\) from \\(c\\). For instance, consider the example in (12), but the target class is now 2. Then, in the earlier stage of gradient ascent, we have" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.489, + 0.426, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {e} _ {c} = [ 0, 1, 0, 0 ] ^ {\\top}, \\boldsymbol {p} = [ 0. 7, 0. 1, 0. 1, 0. 1 ] ^ {\\top}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.511, + 0.482, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {e} _ {c} - \\boldsymbol {p} = \\left[ - 0. 7, 0. 9, - 0. 1, - 0. 1 \\right] ^ {\\top}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.539, + 0.483, + 0.599 + ], + "angle": 0, + "content": "In other words, the components correlated with the original class \\( c \\) is strongly negatively pulled down, whereas the components correlated with the target class \\( c' \\) are strongly positively pushed up." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.6, + 0.484, + 0.901 + ], + "angle": 0, + "content": "FreeMCG meets reverse diffusion. While iterative gradient ascents using FreeMCG in (13) gives us a fast way to generate counterfactual explanations, we find that this process is sensitive to hyperparameters and produces suboptimal results. To fully leverage the generative nature of diffusion models, we instead propose a variant that utilizes reverse diffusion, as is done in other methods that use diffusion models for counterfactual explanation [4, 16, 24]. Specifically, we use an SDEdit [32]-like approach, where we forward diffuse our initial sample up to time \\( t' \\) and run reverse guided sampling in (13) to the Tweedie denoised estimates. The algorithm is presented in Alg. 3. Notice that we do not incorporate the Jacobian of \\( \\epsilon_{\\theta} \\), which is typically done in methods like [9, 53], and simply resort to the gradients with respect to the Tweedie estimates [10] to save computation. For further details, see Appendix G. This approach may be slower as it requires reverse diffusion, but produces higher-fidelity results (Fig. 4). Therefore, all experiments on counterfactual explanation with FreeMCG use this reverse diffusion approach unless specified otherwise." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.645, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.116, + 0.905, + 0.238 + ], + "angle": 0, + "content": "We demonstrate our method from both feature attribution and counterfactual perspectives. To evaluate generalization and domain-specific performance, we compare our method on ImageNet [12] and MIMIC CXR [26] dataset, using images with a resolution of \\(256 \\times 256\\). We use regular pretrained classifier models with the ResNet-50 [20] and unconditional diffusion models [13] trained on each dataset. Experimental details are provided in Appendix H." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.25, + 0.704, + 0.266 + ], + "angle": 0, + "content": "4.1. Evaluation protocol" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.272, + 0.905, + 0.424 + ], + "angle": 0, + "content": "Counterfactuals. An ideal counterfactual makes semantically meaningful, human-interpretable yet minimal changes to the input image so that it is classified as the target class. This allows the user to gain visual insight into the decision boundary of the model. The aim is to create an example at a point on or near the decision boundary closest to the input image (Fig 2), so the generated counterfactual must be anchored on the original input image and should not be an unconditionally generated image of the target class. Therefore, evaluation involves the following criteria:" + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.428, + 0.816, + 0.442 + ], + "angle": 0, + "content": "1. Meaningful change towards target class" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.444, + 0.905, + 0.471 + ], + "angle": 0, + "content": "(a) Flip rate: Is the generated counterfactual classified as the intended target class by the model of interest?" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.474, + 0.905, + 0.532 + ], + "angle": 0, + "content": "(b) Perceived change: Does the generated counterfactual contain semantically meaningful changes to a human perceiver? (i.e. can it be distinguished from an adversarial attack?)" + }, + { + "type": "list", + "bbox": [ + 0.539, + 0.444, + 0.905, + 0.532 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.535, + 0.694, + 0.548 + ], + "angle": 0, + "content": "2. Similarity to the input" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.549, + 0.904, + 0.578 + ], + "angle": 0, + "content": "(a) L2 distance: Are generated counterfactuals close to the input images in terms of distance?" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.579, + 0.904, + 0.608 + ], + "angle": 0, + "content": "(b) Perceived similarity: Do generated counterfactuals and input appear similar to a human perceiver?" + }, + { + "type": "list", + "bbox": [ + 0.539, + 0.549, + 0.904, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.61, + 0.733, + 0.624 + ], + "angle": 0, + "content": "3. Realism of generated image" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.625, + 0.905, + 0.669 + ], + "angle": 0, + "content": "(a) Frechet Inception Distance (FID) [21]: Is the distribution of the generated counterfactual images similar to distribution of original input images?" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.67, + 0.904, + 0.699 + ], + "angle": 0, + "content": "(b) Perceived realism: Do the images appear realistic to a human perceiver?" + }, + { + "type": "list", + "bbox": [ + 0.539, + 0.625, + 0.905, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.905, + 0.822 + ], + "angle": 0, + "content": "Crucially, note that these metrics must be interpreted in concert, rather than as separate measures. In particular, an adversarial attack [11, 18], which flips the decision of the classification neural network but does not introduce changes to the input image that are meaningful to a human perceiver (which are meaningless as explainability tools), can speciously score well on aspects such as similarity or realism." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Flip rate, L2 distance, and FID are computed using 1K generated counterfactuals (one from each class of the ImageNet validation set). Following the experimentation scheme in LDCE [16], we select the category closest to the input image based on the WordNet [34] hierarchy as the tar" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23800" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.09, + 0.5, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.091, + 0.889, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.389, + 0.908, + 0.473 + ], + "angle": 0, + "content": "Figure 4. Counterfactual Generation. Images on the leftmost column are given as input, and the counterfactual for the target class (shown in blue) are generated using each method. Baseline methods generate counterfactuals by perturbing the image towards the direction of a given classification neural network's gradients. Not only are these methods not applicable to situations without access to model weights, gradients almost always point away from the image manifold and into the ambient space, leading to imperceptible changes (i.e., adversarial attack) or changes that produce unnatural, off-manifold, images. FreeMCG on the other hand produces semantically meaningful changes while keeping the image on-manifold. *DVCE without cone projection." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.489, + 0.482, + 0.548 + ], + "angle": 0, + "content": "get class for counterfactual generation. Perceived change, similarity, and realism were measured through a human user study (details in Appendix I). Results are provided in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.559, + 0.483, + 0.71 + ], + "angle": 0, + "content": "We select DVCE [4] and LDCE [16] as baselines, leveraging diffusion models to generate counterfactuals. Note that these baseline methods require access to the model weights while FreeMCG does not. In addition, while the proposed method of DVCE includes cone projection of model weights to the weights of an adversariably robust classifier, we use DVCE with only a regular non-robust classifier (i.e. without cone projection) for comparison throughout this paper as we are assuming lack of access to adversarially robust weights." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.72, + 0.483, + 0.9 + ], + "angle": 0, + "content": "Feature attribution. Feature attributions can be evaluated by observing the change in model predictions whilst removing the pixels in order of purported importance from the attribution. We compare our approach with existing gradient-based attribution methods, including the vanilla gradient [50], Integrated Gradients [49] and InputXGradient [47]. We provide Shapley additive explanation (SHAP) [31] attributions - which are removal-based, not gradient-based - as a reference that is highly aligned with removal-based evaluation such as Remove-and-Debias (ROAD) [42] used to assess the faithfulness of feature attributions." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.488, + 0.607, + 0.502 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.516, + 0.907, + 0.819 + ], + "angle": 0, + "content": "Counterfactual generation. Counterfactual generation results are shown in Fig 4. The generation results show that FreeMCG is able to robustly approximate the direction of the gradient and push the image towards the decision boundary of the classifier. Quantitative results and human user study results for the criteria outlined in Section 4.1 are shown in Table 1. Because baseline methods make use of model gradients while FreeMCG does not, the flip rate of the model's decision is lower for FreeMCG than gradient-based baselines. However, FreeMCG yields by far the most human-perceived changes (Tab. 1 and Fig. 4). In fact, FreeMCG-based counterfactuals often contain informative changes without changing the decision of the classifier while gradient-based baselines commonly produce counterfactuals that fool the classifier to predict a different class but do not introduce semantically meaningful changes. Gradient-based methods are thus closer to adversarial attacks, while FreeMCG better serves the purpose of counterfactual generation and produces interpretable, on-manifold changes towards the target class." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Feature attribution. Feature attributions from representative gradient-based methods for both ImageNet and MIMIC-CXR are shown in Fig. 5(a). ROAD evaluation results are also shown in Fig. 5(b). We see that baseline gradient methods provide feature attributions that are" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23801" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.09, + 0.621, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.092, + 0.88, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.116, + 0.247, + 0.62, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.25, + 0.88, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.403, + 0.907, + 0.489 + ], + "angle": 0, + "content": "Figure 5. (a) Feature attribution maps obtained using each method, (b) Corresponding ROAD [42] evaluation results. Steeper decline is better, and SHAP is given as reference for the lower bound of this decline. For ImageNet, ROAD is calculated as described in [42]. For MIMIC chest X-ray data, results for decline in prediction accuracy was noisy due to the lower starting accuracy of the classifier, low number of classes, and severe data imbalance between classes; therefore, we instead measure the drop in prediction for the originally predicted class. The principle remains the same in that features (pixels) are removed in order of purported importance from each feature attribution map to observe the change in classifier predictions." + }, + { + "type": "table", + "bbox": [ + 0.176, + 0.507, + 0.825, + 0.591 + ], + "angle": 0, + "content": "
ChangeSimilarityRealism
Flip Rate ↑Perceived change ↓L2 ↓Perceived similarity ↓FID ↓Perceived realism ↓
DVCE* [4]85.82.35995.922.3471.382.30
LDCE [16]61.72.001351.391.9063.041.87
Ours51.51.651001.021.7666.891.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.089, + 0.601, + 0.908, + 0.631 + ], + "angle": 0, + "content": "Table 1. Quantitative (Flip Rate / L2 / FID) and human user study (perceived change/similarity/realism) results. *DVCE without cone projection." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.642, + 0.483, + 0.822 + ], + "angle": 0, + "content": "similar to adversarial attacks, hence hardly interpretable. SHAP attributions provide less informative patch-like artifact. FreeMCG, on the other hand, produces high quality and interpretable attributions that are similar to SHAP, but retaining the high-frequency details as it does not rely on arbitrary pixel clustering. In ROAD evaluation, we see that FreeMCG achieves the steepest decline in model prediction among gradient-based methods, corresponding to better feature attributions, closer to the lower-bound computed by SHAP. Additional comparison against other removal-based black-box methods [36, 38] can be found in Appendix E." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.843, + 0.21, + 0.859 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.903 + ], + "angle": 0, + "content": "We developed Derivative-Free Diffusion Mainfold Constrained Gradients (FreeMCG), an approximation of a neu" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.642, + 0.907, + 0.899 + ], + "angle": 0, + "content": "ral network's gradient tangent to the data manifold, obtained without access to the model weights or its real gradients. Previous explainability literature on gradient-based feature attribution and counterfactual generation have remained largely separate because the gradient could not be readily employed for counterfactual generation as it produces adversarial attacks. With FreeMCG, one can obtain gradient directions on the image manifold that produce semantically meaningful counterfactual explanations and feature attributions. We demonstrate through experiments that FreeMCG enables a unified framework for both explainability methods with state-of-the-art results, all without access to model weights. FreeMCG still assumes black-box access to the model's logits; in more restricted scenarios where only class predictions are available, FreeMCG would not be applicable, highlighting a limitation that could inspire future work on extending FreeMCG to such settings." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23802" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.259, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.222 + ], + "angle": 0, + "content": "This work was supported by the National Research Foundation of Korea (NRF) under Grants RS-2024-00336454 and RS-2023-00262527, and by the Institute for Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (RS-2019-II190075, Artificial Intelligence Graduate School Program, KAIST)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.233, + 0.188, + 0.249 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.259, + 0.484, + 0.314 + ], + "angle": 0, + "content": "[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. 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Ensemble kalman diffusion guidance: A derivative-free method for inverse problems. arXiv preprint arXiv:2409.20175, 2024. 4, 5, 10" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.483, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "23805" + } + ] +] \ No newline at end of file diff --git a/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_origin.pdf b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..acb3ca1a1e82930037d0489ea3c1a93bf9f086f5 --- /dev/null +++ b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/065052e0-b498-4bc6-9515-464f2840472f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b8f0247814b404d636692bf88ba1a1d444fac518de95c8874b91c371356084e0 +size 1947034 diff --git a/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/full.md b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4c88159fa5c1b1226ab50763b2fc128c24481e5d --- /dev/null +++ b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/full.md @@ -0,0 +1,423 @@ +# Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI + +Won Jun Kim $^{1*}$ + +Hyungjin Chung\* + +Jaemin $\mathrm{Kim}^{1*}$ + +Sangmin Lee + +Byeongsu Sim + +Jong Chul Ye1 + +1 KAIST + +2 EverEx + +{wonjun, kjm981995, leeeeesang, byeongsu.s,jong.ye}@kaist.ac.kr hj.chung@everex.co.kr + +# Abstract + +Gradient-based methods are a prototypical family of "explainability for AI" (XAI) techniques, especially for image-based models. However, they (1) require white-box access to models, (2) are vulnerable to adversarial attacks, and (3) produce attributions that lie off the image manifold, leading to explanations that are not amenable to human perception. To overcome these challenges, we introduce Derivative-Free Diffusion Manifold-Constrained Gradients (FreeMCG): by leveraging ensemble Kalman filters and diffusion models, we derive a derivative-free approximation of the model's gradient projected onto the data manifold, requiring access only to the model's outputs (i.e., black-box setting). We demonstrate the effectiveness of FreeMCG by applying it to both counterfactual generation and feature attribution, which have traditionally been treated as different tasks requiring distinct methods. Through comprehensive evaluation on both counterfactual explanation and feature attribution we show that our method yields state-of-the-art results for both tasks while preserving the essential properties expected of XAI tools. Code: https://github.com/one-june/FreeMCG. + +# 1. Introduction + +Understanding the decision-making process of complex deep neural networks is crucial for their deployment in high-stakes applications such as medical imaging [6, 7], autonomous systems [2, 43], etc. Explanable AI (XAI) seeks to address this challenge by providing insights into how models arrive at specific predictions, thus enhancing trust, accountability, and usability in critical applications. Two widely used tools for XAI are counterfactual explanation [59] and feature attribution1 [31]. + +Among various XAI methods, the gradient of the target (e.g. classifier) model is the prototypical method of under + +![](images/9e0e2a8baae79d60bf61427842776a71d0eed0d52535ada408b5b09cf6de14b2.jpg) +Figure 1. Representative results of FreeMCG, operating as a universal framework for black box XAI. + +standing the local behavior of a function around a given input data point. It has thus been used since the beginning of the rise of neural networks to explain their decisions [50]. There have been many subsequent works improving the vanilla gradient to serve as better feature attributions for a deep neural network [3, 46, 47, 55, 57, 61]. Gradients are also utilized for generating counterfactual explanations [4, 25, 44], in which the gradient of the target model serves as the direction that guides the change $\delta$ made to the original image so that prediction of the model flips to another class. + +While gradient-based methods are popular explainable AI (XAI) tools, they suffer from three significant limitations: + +1. Access to model gradients is not always feasible: Obtaining gradients requires access to the model's internal weights, which is often not possible in practice. For + +# Feature attribution + +Q. Which features (pixels) are most important for the classifier's decision? + +![](images/a1fcf6699108d17e88f44beceaf1c48983af9ea6232d50c2b469d4193c36405f.jpg) +Counterfactuals on the manifold + +# Counterfactual explanation + +Q. What changes to the input image shift the decision of the classifier to another class? + +![](images/1e7e652fda6f4d40e621822d5f06a6472586cd19ae6f8d266a8ee2e8c4b483eb.jpg) +Adversarial attack +$\otimes$ Off-manifold, Unreliable + +![](images/f2778b9467771786939e56e6ca060a94368fdd026567db59ef3fa66f04fc66e6.jpg) +$\odot$ On-manifold, Explainable +Figure 2. Unified framework of XAI for feature attribution and counterfactual explanation using our method, Derivative-Free Diffusion Manifold Constrained Gradients (FreeMCG). Naive gradients not only violate the black box assumption but also is unreliable and hard to interpret as they produce adversarial attacks. Using diffusion models to produce on-manifold ensembles, and using the covariance of these particles as the preconditioner of the gradient, FreeMCG approximates gradients on the manifold, which is more reliable and interpretable. + +![](images/d7bf2af8fa70264542e3a1eae4753d69717d9abc4f3d04446d735671628ec43b.jpg) +(i) Spread particles + +![](images/990e21a3903188cdfdb5b31d8877efeaeeb377964758a43590c6b8d6572a3d2d.jpg) +FreeMCG +(ii) Approximate gradient on manifold + +![](images/0e04c4a1052129324119a402a174e01aa80140cf1b733e8495ea8042382cdcd2.jpg) + +$$ +\boldsymbol {g} _ {\text {F r e e}} \cong C _ {x x} \nabla_ {x} f (\boldsymbol {e} _ {c} - \boldsymbol {p}) +$$ + +many neural-network based services, users can only interact with these systems through their outputs. + +2. Gradients provide unreliable explanations: As shown in [1, 37, 51], gradient-based methods often fail to generate meaningful explanations of model behavior. These explanations are closely related to adversarial examples [58], and many traditional methods resort to using models that have been trained to be adversarially robust [4, 44]. Moreover, gradients typically do not align with the underlying data manifold, leading to explanations that are misaligned with human perception. +3. Lack of a unified framework for feature attribution and counterfactual explanations: The literature on feature attribution and counterfactual explanations remains largely separate. This is because real gradients produce adversarial attacks rather than counterfactual explanations and additional techniques are required to introduce perceptible changes. In theory, gradients should be usable for both applications. This raises the question of whether a single framework can effectively handle both types of explanations. + +To address these challenges, in this work, we propose Derivative-Free Diffusion Manifold Constrained Gradients (FreeMCG), a unified framework that can be used both for feature attribution and counterfactual explanation with only black-box access to the target model. By leveraging diffusion models and their powerful ability to model data manifolds, we can produce on-manifold perturbations of input + +data points, which, combined with ideas from Ensemble Kalman Filters (EnKF) [45], can be used to approximate manifold-projected model gradients. In Fig. 1, we show the representative results of FreeMCG, acting as a unified framework for XAI. Our contributions can be summarized as follows: + +- We present the first unified framework that encompasses both feature attribution and counterfactual explanation. +- We derive a novel method of estimating the gradient of the target classifier with black-box access (i.e. without access to model weights) by leveraging diffusion models and the theory of EnKF. +- We demonstrate that FreeMCG achieves state-of-the-art performance, even compared to white-box methods. + +# 2. Background & Related Works + +# 2.1. Gradient-based XAI + +Consider the following classifier + +$$ +p (y = c | \boldsymbol {x}) = \frac {\exp \left(\boldsymbol {f} _ {c} (\boldsymbol {x})\right)}{\sum_ {c ^ {\prime} = 1} ^ {C} \exp \left(\boldsymbol {f} _ {c ^ {\prime}} (\boldsymbol {x})\right)}, \boldsymbol {f}: \mathbb {R} ^ {d} \mapsto \mathbb {R} ^ {n}, \tag {1} +$$ + +where $n$ is the number of classes, and $f(\pmb{x}) := [f_1(\pmb{x}), \dots, f_n(\pmb{x})]$ . Taking the softmax would induce the probability vector $\pmb{p} = \text{softmax}(\pmb{f}(\pmb{x}))$ . When $\pmb{x}$ belongs to some class $c$ , let $\text{class}(\pmb{x}) = c$ be a labeling function. The task of feature attribution for images is to find an attribution $\pmb{a} \in [0, 1]^d$ that has high values in the indices where + +its influence to $\pmb{p}$ is pronounced. On the other hand, the task of counterfactual explanation aims to find a vector $\pmb{x}^{\prime}$ that belongs to a target class $c^\prime$ , i.e. $\operatorname{class}(\pmb{x}^{\prime}) = c^{\prime}$ , but stays in proximity to $\pmb{x}$ . + +Feature attribution. Gradients provide a direct representation of the local behavior of a function by encapsulating how the function changes linearly in the gradient vector [50]. Integrated Gradients improve upon the vanilla gradient and satisfies certain desirable properties such as sensitivity, completeness, linearity, and implementation invariance by integrating the gradients along a path from a fixed baseline (often a black image) [57]. Other follow-up works have extended this approach by modifying the integration region [33, 56, 60] or altering the integrand [23, 27, 49], among others. + +Counterfactuals and adversarial attacks. Gradients obtained with respect to the input can be used to perform gradient ascent/descent to change the input towards a direction that maximizes or minimizes the model output. However, for high-dimensional input data such as images, gradient ascent or descent often yields changes that are imperceptible to humans. This is known as an adversarial attack [18], because it changes the model output for a given input while the image itself remains effectively unchanged to human perception, thus having the effect of "fooling" a model. The adversarial attack phenomenon occurs because gradient ascent/descent using simple gradients perturbs the image in a direction that lifts the image off the image manifold and into the ambient space [14]. + +Counterfactuals, on the other hand, should yield a semantically meaningful change to the original input $x$ such that the target model changes its prediction. In other words, the change should be on-manifold. Naturally, to induce this on-manifold change, generative models such as GANs and diffusion models [4, 25] have been used. However, most of these methods require access to model gradients, some even requiring that the model be adversarially robust. Moreover, these methods can be considered guided generation methods, making them inapplicable for feature attribution. + +# 2.2. Diffusion Models + +Diffusion model [22, 28, 54] is a class of generative models that sample images through a Gaussian denoising path. This path is constructed by starting from the initial data (i.e. image) distribution $p_0(\pmb{x})$ , $\pmb{x} \in \mathbb{R}^d$ , gradually adding Gaussian noise, and reaching approximately the Gaussian distribution $p_T(\pmb{x}) \approx \mathcal{N}(\pmb{0}, \pmb{I})$ at $t = T$ . For the choice of the Gaussian perturbation $p(\pmb{x}_t | \pmb{x}_0) = \mathcal{N}(\pmb{x}_0, \sigma_t^2 \pmb{I})$ , the reverse generation trajectory reads + +$$ +d \boldsymbol {x} _ {t} = - \sigma_ {t} \nabla_ {\boldsymbol {x} _ {t}} \log p (\boldsymbol {x} _ {t}) d t = \frac {\boldsymbol {x} _ {t} - \mathbb {E} [ \boldsymbol {x} _ {0} | \boldsymbol {x} _ {t} ]}{\sigma_ {t}} d t, \tag {2} +$$ + +where the initial point is sampled from the reference distribution $\pmb{x}_T \sim p_T(\pmb{x}_T)$ . Here, Tweedie's formula [15] + +$\mathbb{E}[\pmb{x}_0|\pmb{x}_t] = \pmb{x}_t + \sigma_t^2\nabla_{\pmb{x}_t}\log p(\pmb{x}_t)$ is used for the second equality. Diffusion models are trained as denoisers that estimate this posterior mean + +$$ +\theta^ {*} = \underset {\theta} {\arg \min } \mathbb {E} _ {t, \boldsymbol {x} _ {t}, \boldsymbol {x} _ {0}} \left[ \| D _ {\theta} (\boldsymbol {x} _ {t}) - \boldsymbol {x} _ {0} \| _ {2} ^ {2} \right], \tag {3} +$$ + +which can be plugged into (2) as $\mathbb{E}[\pmb{x}_0|\pmb{x}_t]\approx D_{\theta^*}(\pmb{x}_t)$ at test time. + +In Chung et al. [8], assuming that $\mathcal{M}$ is a locally linear subspace, it was further shown that the distribution of noisy data $p(\boldsymbol{x}_t)$ is then concentrated on shell-like manifold $\mathcal{M}_t$ . Moreover, one can show that Tweedie's formula is an orthogonal projection from $\mathcal{M}_t$ to $\mathcal{M}$ . In other words, when the goal is to produce samples on the manifold $\mathcal{M}$ in a cost-effective way, one can use Tweedie's formula to generate samples in one step. This matches our intuition up to moderate values of $t$ , where the posterior mean gives us a relatively good approximation of the real samples. + +Guided sampling. Often, it is desirable to sample from the posterior $p(\boldsymbol{x}|\boldsymbol{y})$ instead of from the prior. A standard approach to achieve this is to use guided sampling by Bayes decomposition + +$$ +\nabla_ {\boldsymbol {x} _ {t}} \log p (\boldsymbol {x} _ {t} | \boldsymbol {y}) = \nabla_ {\boldsymbol {x} _ {t}} \log p (\boldsymbol {x} _ {t}) + \nabla_ {\boldsymbol {x} _ {t}} \log p (\boldsymbol {y} | \boldsymbol {x} _ {t}), \tag {4} +$$ + +where the gradient of the log-likelihood term measures the fidelity with respect to the condition $\pmb{y}$ . One can either train a separate neural network (e.g. classifier [13, 54]) to estimate the term or use some form of approximation [9, 53]. Sampling from the posterior then boils down to iterating the denoising steps of the unconditional PF-ODE in (2) and the gradient step that maximizes fidelity. However, regardless of the forward model2, most of the methods require access to the gradient of the forward model, which is often hard to compute due to reasons including safety and complexity. + +# 2.3. Gradient-free optimization and XAI + +When one can only evaluate $f$ but cannot compute its gradient, gradient-free (zeroth-order) optimization [30], where a single or multiple set of samples can be used to calculate the finite difference, alongside techniques such as Gaussian smoothing [35] can be used to estimate the true gradient. Ensemble Kalman Filters (EnKF) [45], in terms of inverse problem solving, is also a widely used method for derivative-free optimization, where the ensemble of particles and its covariance information is used as a proxy for gradient information. In a similar vein, Ensemble Kalman Inversion (EKI) [19, 29] was proposed as a derivative-free + +method for training neural networks. Recently, the use of EnKF was extended to inverse problem-solving with diffusion models [62], showing that the technique can be readily used for diffusion guidance. In the proposed method, we leverage EnKF to approximate the unknown gradient. + +Black-box feature attribution While white-box methods typically rely on gradient information, this dependency limits the applicability of XAI techniques to scenarios where gradients can be accessed. Several works [17, 31, 36, 40, 61] have introduced perturbation-based approaches for feature attribution. These methods generally involve perturbing the input—commonly by masking out pixel groups at random—and measuring the resulting change in class probabilities. While conceptually similar to FreeMCG in that they only require forward passes through the neural network, perturbation-based methods differ in two key ways: (1) masking pixels typically moves the input off the underlying data manifold, and (2) these methods are exclusively employed for feature attribution and cannot produce counterfactual explanations, as they do not approximate the decision boundary. + +# 3. Main Contribution: FreeMCG + +# 3.1. Derivation of FreeMCG + +From (1), one can derive that + +$$ +\frac {\partial}{\partial \boldsymbol {f} _ {c ^ {\prime}}} \log p (y = c | \boldsymbol {f} _ {c ^ {\prime}}) = \delta_ {c c ^ {\prime}} - p \left(c ^ {\prime} | \boldsymbol {f} _ {c ^ {\prime}}\right), \tag {5} +$$ + +where $\delta_{cc'}$ is the Kronecker delta function which evaluates to 1 if and only if $c' = c$ . Vector form of (5) reads + +$$ +\nabla_ {\boldsymbol {f}} \log p (y = c | \boldsymbol {f}) = \boldsymbol {e} _ {c} - \boldsymbol {p}, \tag {6} +$$ + +where $e_{c}$ is a one-hot vector with one at index $c$ , and $\pmb{p} \in \mathbb{R}^{n}$ is the classifier probability. From (6), we further have that + +$$ +\nabla_ {\boldsymbol {x}} \log p (y = c | \boldsymbol {x}) = \left(\frac {\partial \boldsymbol {f} (\boldsymbol {x})}{\partial \boldsymbol {x}}\right) ^ {\top} \left(\boldsymbol {e} _ {c} - \boldsymbol {p} (\boldsymbol {x})\right), \tag {7} +$$ + +where we wrote $\pmb{p}(\pmb{x})$ to emphasize that the probability vector is a function of $\pmb{x}$ . In the context of EnKF, we consider a set of $K$ particles $\{\pmb{x}^{(k)}\}_{k=1}^{K}$ to represent a state, where each particle corresponds to a sample of the random variable $\pmb{x}$ . To leverage the ideas from EnKF, we are interested in the pre-conditioned version of the gradient, where the covariance of the particles is used + +$$ +\boldsymbol {g} _ {\text {F r e e}} := \boldsymbol {C} _ {\boldsymbol {x x}} \nabla_ {\boldsymbol {x}} \log p (c | \boldsymbol {x}) = \boldsymbol {C} _ {\boldsymbol {x x}} \left(\frac {\partial \boldsymbol {f} (\boldsymbol {x})}{\partial \boldsymbol {x}}\right) ^ {\top} \left(\boldsymbol {e} _ {c} - \boldsymbol {p} (\boldsymbol {x})\right), \tag {8} +$$ + +where $C_{\pmb{x}\pmb{x}}:= \frac{1}{K}\sum_{k = 1}^{K}(\pmb{x}^{(k)} - \bar{\pmb{x}})(\pmb{x}^{(k)} - \bar{\pmb{x}})^{\top}$ , and we use $\bar{\pmb{x}}$ to denote the sample mean $\mathbb{E}[\pmb{x}^{(k)}]$ . + +![](images/9d2ade8800c84df7ba57b4966f1c09414e0a71213624ee3258cecf1185239a16.jpg) +Figure 3. Toy example of FreeMCG, illustrating the gradient (red arrow) and the gradient aligned with the tangent of manifold (gray dashed) approximated by (9) (green arrow), using neighbor data points (blue dots). + +![](images/32c71bc1d23e6ccda5c279b7736fafd572a38fe0701edc4e85dbfbf2fdda6e82.jpg) + +FreeMCG produces on-manifold gradients. One may question the need for preconditioning the gradient with the empirical covariance matrix. In Theorem 1, we show that this preconditioning yields gradients that are on the data manifold $\mathcal{M}$ , producing results that are well-aligned with human perception, and robust to adversarial attacks. The proof can be found in Appendix A. + +Theorem 1. Suppose that $\mathcal{M}$ is locally linear at $x$ , meaning that in the neighborhood of $x$ , the manifold aligns with its tangent space $\mathcal{T}_x\mathcal{M}$ . Suppose further, that the particles $\boldsymbol{x}^{(k)} \in \mathcal{M}$ . Then, $\boldsymbol{g}_{\mathrm{Free}}$ approximately lies within $\mathcal{M}$ . Precisely, $\boldsymbol{C}_{xx}$ acts as a linear transformation, expanding along $\mathcal{T}_x\mathcal{M}$ and contracting the vectors normal to $\mathcal{T}_x\mathcal{M}$ . + +Theorem 1 states that when the particles $\boldsymbol{x}^{(k)}$ lies on the manifold surrounding the original data point $\boldsymbol{x}$ , $C_{xx}$ captures the geometric properties of the tangent space $T_{x}\mathcal{M}$ . Specifically, the covariance matrix refines the vanilla gradient by contracting direction that lead off the manifold, which helps prevent the possibility of adversarial examples. Additionally, it expands along the direction of greater variability among the particles, reducing the likelihood of converging to a single original point. + +EnKF for derivative-free gradient However, notice that $C_{xx} \left( \frac{\partial f(x)}{\partial x} \right)^\top$ is hard to compute, as we do not have access to the gradient of $f$ . Thus, we invoke the following. + +Theorem 2. Suppose $\| \nabla_{\pmb{x}}^{2}\pmb{f}(\pmb{x})\|$ be uniformly bounded and there exists $\delta >0$ such that $\pmb{x}^{(k)}\in \{\pmb {x}\in \mathbb{R}^d:\| \pmb {x} - \bar{\pmb{x}}\| \leq \delta \}$ for all $k$ . Then, the following approximation holds + +$$ +C _ {\boldsymbol {x} \boldsymbol {f}} = C _ {\boldsymbol {x x}} \nabla_ {\boldsymbol {x}} \boldsymbol {f} (\boldsymbol {x}) ^ {\top} + \mathcal {O} \left(\delta^ {3}\right), \tag {9} +$$ + +where $C_{\pmb{x}\pmb{f}} := \frac{1}{K}\sum_{k=1}^{K}(\pmb{x}^{(k)} - \bar{\pmb{x}})(\pmb{f}(\pmb{x}^{(k)}) - \bar{\pmb{f}})^{\top}$ and $\bar{\pmb{f}} := \frac{1}{K}\sum_{k=1}^{K}\pmb{f}(\pmb{x}^{(k)})$ . + +The proof along with a formal treatment on approximation errors can be found in Appendix A. Apply Theorem 2 to (8), we have + +$$ +\begin{array}{l} \boldsymbol {C} _ {\boldsymbol {x x}} \nabla_ {\boldsymbol {x}} \log p (y = c | \boldsymbol {x}) \approx \boldsymbol {C} _ {\boldsymbol {x f}} \left(e _ {c} - \boldsymbol {p}\right) \\ = \frac {1}{K} \sum_ {k = 1} ^ {K} \left(\boldsymbol {x} ^ {(k)} - \bar {\boldsymbol {x}}\right) \left(\boldsymbol {f} \left(\boldsymbol {x} ^ {(k)}\right) - \bar {\boldsymbol {f}}\right) ^ {\top} \left(\boldsymbol {e} _ {c} - \boldsymbol {p} (\boldsymbol {x})\right), \tag {10} \\ \end{array} +$$ + +given the particles $\pmb{x}^{(k)}$ . We provide the pseudocode for computing FreeMCG in Alg. 1. + +Although we now have the machinery to compute the approximate gradient, notice that we have to choose the position of the particles $\pmb{x}^{(k)}$ . For this, three conditions must be met. The particles should be 1) near $\pmb{x}$ , 2) on-manifold, and 3) fast to generate. The first two conditions are met by perturbing $\pmb{x}$ to obtain forward-diffused samples $\pmb{x}_t^{(k)}$ , and running reverse PF-ODE to all the particles, as used in [32, 62]. However, since this would be prohibitively slow, we simply choose to use the Tweedie denoised estimates, which we denote as $\pmb{x}_{0|t}^{(k)}$ . In short, our gradient reads + +$$ +\boldsymbol {g} _ {\text {F r e e}} := \mathbb {E} \left[ \left(\boldsymbol {x} _ {0 | t} ^ {(k)} - \bar {\boldsymbol {x}} _ {0 | t} ^ {(k)}\right) \left(\boldsymbol {f} \left(\boldsymbol {x} _ {0 | t} ^ {(k)}\right) - \bar {\boldsymbol {f}} \left(\boldsymbol {x} _ {0 | t} ^ {(k)}\right)\right) ^ {\top} \left(\boldsymbol {e} _ {c} - \boldsymbol {p}\right) \right], \tag {11} +$$ + +where the expectation is over the diffusion timesteps $t$ and the number of particles $k$ . Notice that under our assumption of local linearity, we can use Proposition 2 of [8], which states that Tweedie's formula [15] is locally an orthogonal projection to the manifold $\mathcal{M}$ , satisfying the assumption of Thm. 1. + +We illustrate a 2D toy example in Fig. 3. Considering $f = -x + y^2$ with its gradient $\nabla_{\pmb{x}}f(\pmb{x}) = (-1,2y)$ , we sample particles around the point $\pmb{x}$ and calculate the covariance matrix. Then, applying (9), we obtain a gradient aligned with the direction of the manifold without directly computing the gradient of the $f$ . In our main experiments, we show that FreeMCG indeed produces a gradient that produces on-manifold gradients so that it avoids being an adversarial attack. In the following, we elaborate on practical implementations of (11) for feature attribution and counterfactual explanation, as well as their intuition, respectively. + +# 3.2. Applications of FreeMCG + +FreeMCG for feature attribution. This corresponds to the case where the target class $c'$ aligns with the prediction of the classifier $c$ . Notice that $f(\boldsymbol{x}^{(k)}) - \bar{f} \in \mathbb{R}^n$ where $f_c$ indicates the average drop in logit value after the Tweedie perturbation. Moreover, when $c' = c$ , the only positive entry in $e_c - p$ will be at the index $c$ , positively weighting the part that changes the predicted class label, while negatively weighting the part that is irrelevant. As a concrete example, + +Algorithm 1 FreeMCG Gradient Computation +1: function FREEMCG $(\pmb {f},\{\pmb{x}^{(k)}\}_{k = 1}^{K},e_{c},\pmb {p})$ +2: $\bar{\pmb{x}}\gets \frac{1}{K}\sum_{k = 1}^{K}\pmb{x}^{(k)}$ +3: $\bar{\pmb{f}}\gets \frac{1}{K}\sum_{k = 1}^{K}\pmb {f}(\pmb{x}^{(k)})$ +4: for $k = 1$ to $K$ do +5: $\Delta^{(k)}\gets (\pmb{x}^{(k)} - \bar{\pmb{x}})(\pmb {f}(\pmb{x}^{(k)}) - \bar{\pmb{f}})^{\top}(\pmb {e}_c - \pmb {p})$ +6: end for +7: return $\pmb{g}_{\mathrm{Free}}\gets \frac{1}{K}\sum_{k = 1}^{K}\pmb{\Delta}^{(k)}$ +8: end function + +Algorithm 2 FreeMCG for feature attribution +Require: Classifier $f$ , Diffusion model $\epsilon_{\theta}$ , Input $x$ , Number of particles $K$ , Target class vector $e_c$ , Diffusion timestep range $[l, u]$ +1: $p = \text{softmax}(f(x))$ +2: $x_0 \gets x$ +3: for $k = 1$ to $K$ do +4: $t \sim \mathcal{U}[l, u]$ +5: $x_t^{(k)} \sim p(x_t | x_0)$ +6: $x_{0|t}^{(k)} \gets (x_t - \sqrt{1 - \bar{\alpha}_t} \epsilon_\theta(x_t)) / \sqrt{\bar{\alpha}_t}$ +7: end for +8: $g_{\text{Free}} \gets \text{FREEMCG}(f, \epsilon_\theta, x, \{x_{0|t}^{(k)}\}_{k=1}^K, e_c, p)$ +9: return $g_{\text{Free}}$ + +Algorithm 3 FreeMCG for CE with reverse diffusion +Require: Classifier $f$ , Diffusion model $\epsilon_{\theta}$ Input $\pmb{x}$ Number of particles $K$ , Target class vector $e_{c^{\prime}}$ , Diffusion params $t^\prime ,\tilde{\beta}_t,\bar{\alpha}_t,\eta ,\gamma_t$ +1: $\pmb {x}_0\gets \pmb{x}$ +2: $[\pmb{x}_{t'}^{(k)}]\sim p(\pmb{x}_{t'}|\pmb{x}_0)\quad \triangleright [\cdot ]$ denotes $K$ batched particles +3: for $t = t^{\prime}$ to 1 do reverse diffusion +4: $[\hat{\epsilon}_t^{(k)}]\gets \epsilon_\theta ([\pmb{x}_t^{(k)}])$ +5: $[\pmb{x}_{0|t}^{(k)}]\gets ([\pmb{x}_t^{(k)}] - \sqrt{1 - \bar{\alpha}_t} [\hat{\epsilon}_t^{(k)}]) / \sqrt{\bar{\alpha}_t}$ Tweedie denoising +6: $[\pmb{p}^{(k)}]\gets \mathrm{softmax}(\pmb {f}([\pmb{x}_{0|t}^{(k)}]))$ +7: $[\pmb{g}_{\mathrm{Free}}^{(k)}]\gets \mathrm{FREEMCG}(\pmb {f},[\pmb{x}_{0|t}^{(k)}],\pmb{e}_{c'},\pmb{p}^{(k)})$ +8: $[\pmb{g}^{(k)}]\gets \alpha [\pmb{g}_{\mathrm{Free}}^{(k)}] + \beta (\pmb {x} - [\pmb{x}_{0|t}^{(k)})]$ +9: $[\pmb {\epsilon}^{(k)}]\sim \mathcal{N}(0,\pmb {I})$ +10: $[\pmb{x}_{t - 1}]\gets \sqrt{\bar{\alpha}_{t - 1}} [\pmb{x}_{0|t}]^{(k)} + \sqrt{1 - \bar{\alpha}_{t - 1} - \eta^2\tilde{\beta}_t^2} [\hat{\epsilon}_t]$ $+\eta \tilde{\beta}_t[\epsilon^{(k)}] + \gamma_t[\pmb {g}^{(k)}]$ +11: end for +12: return $x^{\mathrm{(CE)}} = \frac{1}{K}\sum_{k = 1}^{K}x_0$ Average of particles + +consider the following 4-class example + +$$ +\boldsymbol {e} _ {c} = [ 1, 0, 0, 0 ] ^ {\top}, \boldsymbol {p} = [ 0. 7, 0. 1, 0. 1, 0. 1 ] ^ {\top} +$$ + +$$ +\boldsymbol {e} _ {c} - \boldsymbol {p} = [ 0. 3, - 0. 1, - 0. 1, - 0. 1 ] ^ {\top}, \tag {12} +$$ + +where only the perturbations that dropped the probability of the first class will be positively weighted, while for the other indices, there will be an opposite force. + +For implementation, we found that using multiple levels of $t$ was crucial for encapsulating the attribution that acts both for coarse and fine scales. Similar to how score distillation sampling (SDS) [39] is recently used [48], we constrain the time range to $t \in [0.1, 0.7]$ . For visualization purposes, we take the mean across the color channels and plot the absolute value. The algorithm for feature attribution using FreeMCG is presented in Alg. 2. + +FreeMCG for counterfactual explanation. While (11) can directly serve as the attribution, for counterfactual explanation, the gradient should be used as the direction of ascent toward a counterfactual sample. Here, we can iteratively apply gradient ascent with FreeMCG, i.e. + +$$ +\boldsymbol {x} _ {i + 1} = \boldsymbol {x} _ {i} + \alpha \mathbf {g} _ {\text {F r e e}} (\boldsymbol {x} _ {i}) + \beta (\boldsymbol {x} - \boldsymbol {x} _ {i}), \tag {13} +$$ + +where $\alpha$ is the step size weighting the FreeMCG, and $\beta$ weights the proximal regularization to the initial point $\pmb{x}$ . Notice that the implementation of FreeMCG for counterfactual explanation differs from that of feature attribution, as we have a different target class $c^{\prime}$ from $c$ . For instance, consider the example in (12), but the target class is now 2. Then, in the earlier stage of gradient ascent, we have + +$$ +\boldsymbol {e} _ {c} = [ 0, 1, 0, 0 ] ^ {\top}, \boldsymbol {p} = [ 0. 7, 0. 1, 0. 1, 0. 1 ] ^ {\top} +$$ + +$$ +\boldsymbol {e} _ {c} - \boldsymbol {p} = \left[ - 0. 7, 0. 9, - 0. 1, - 0. 1 \right] ^ {\top}. \tag {14} +$$ + +In other words, the components correlated with the original class $c$ is strongly negatively pulled down, whereas the components correlated with the target class $c'$ are strongly positively pushed up. + +FreeMCG meets reverse diffusion. While iterative gradient ascents using FreeMCG in (13) gives us a fast way to generate counterfactual explanations, we find that this process is sensitive to hyperparameters and produces suboptimal results. To fully leverage the generative nature of diffusion models, we instead propose a variant that utilizes reverse diffusion, as is done in other methods that use diffusion models for counterfactual explanation [4, 16, 24]. Specifically, we use an SDEdit [32]-like approach, where we forward diffuse our initial sample up to time $t'$ and run reverse guided sampling in (13) to the Tweedie denoised estimates. The algorithm is presented in Alg. 3. Notice that we do not incorporate the Jacobian of $\epsilon_{\theta}$ , which is typically done in methods like [9, 53], and simply resort to the gradients with respect to the Tweedie estimates [10] to save computation. For further details, see Appendix G. This approach may be slower as it requires reverse diffusion, but produces higher-fidelity results (Fig. 4). Therefore, all experiments on counterfactual explanation with FreeMCG use this reverse diffusion approach unless specified otherwise. + +# 4. Experiments + +We demonstrate our method from both feature attribution and counterfactual perspectives. To evaluate generalization and domain-specific performance, we compare our method on ImageNet [12] and MIMIC CXR [26] dataset, using images with a resolution of $256 \times 256$ . We use regular pretrained classifier models with the ResNet-50 [20] and unconditional diffusion models [13] trained on each dataset. Experimental details are provided in Appendix H. + +# 4.1. Evaluation protocol + +Counterfactuals. An ideal counterfactual makes semantically meaningful, human-interpretable yet minimal changes to the input image so that it is classified as the target class. This allows the user to gain visual insight into the decision boundary of the model. The aim is to create an example at a point on or near the decision boundary closest to the input image (Fig 2), so the generated counterfactual must be anchored on the original input image and should not be an unconditionally generated image of the target class. Therefore, evaluation involves the following criteria: + +# 1. Meaningful change towards target class + +(a) Flip rate: Is the generated counterfactual classified as the intended target class by the model of interest? +(b) Perceived change: Does the generated counterfactual contain semantically meaningful changes to a human perceiver? (i.e. can it be distinguished from an adversarial attack?) + +# 2. Similarity to the input + +(a) L2 distance: Are generated counterfactuals close to the input images in terms of distance? +(b) Perceived similarity: Do generated counterfactuals and input appear similar to a human perceiver? + +# 3. Realism of generated image + +(a) Frechet Inception Distance (FID) [21]: Is the distribution of the generated counterfactual images similar to distribution of original input images? +(b) Perceived realism: Do the images appear realistic to a human perceiver? + +Crucially, note that these metrics must be interpreted in concert, rather than as separate measures. In particular, an adversarial attack [11, 18], which flips the decision of the classification neural network but does not introduce changes to the input image that are meaningful to a human perceiver (which are meaningless as explainability tools), can speciously score well on aspects such as similarity or realism. + +Flip rate, L2 distance, and FID are computed using 1K generated counterfactuals (one from each class of the ImageNet validation set). Following the experimentation scheme in LDCE [16], we select the category closest to the input image based on the WordNet [34] hierarchy as the tar + +![](images/7c3d41d52b13645da70458f8ba90795bf3a91008ba2a3e4050360ce1f42d5eea.jpg) +Figure 4. Counterfactual Generation. Images on the leftmost column are given as input, and the counterfactual for the target class (shown in blue) are generated using each method. Baseline methods generate counterfactuals by perturbing the image towards the direction of a given classification neural network's gradients. Not only are these methods not applicable to situations without access to model weights, gradients almost always point away from the image manifold and into the ambient space, leading to imperceptible changes (i.e., adversarial attack) or changes that produce unnatural, off-manifold, images. FreeMCG on the other hand produces semantically meaningful changes while keeping the image on-manifold. *DVCE without cone projection. + +![](images/a0b54f6c5cbcb98e92468e624eff1b6a8623bc56571dee09bdb652bda936cf26.jpg) + +get class for counterfactual generation. Perceived change, similarity, and realism were measured through a human user study (details in Appendix I). Results are provided in Table 1. + +We select DVCE [4] and LDCE [16] as baselines, leveraging diffusion models to generate counterfactuals. Note that these baseline methods require access to the model weights while FreeMCG does not. In addition, while the proposed method of DVCE includes cone projection of model weights to the weights of an adversariably robust classifier, we use DVCE with only a regular non-robust classifier (i.e. without cone projection) for comparison throughout this paper as we are assuming lack of access to adversarially robust weights. + +Feature attribution. Feature attributions can be evaluated by observing the change in model predictions whilst removing the pixels in order of purported importance from the attribution. We compare our approach with existing gradient-based attribution methods, including the vanilla gradient [50], Integrated Gradients [49] and InputXGradient [47]. We provide Shapley additive explanation (SHAP) [31] attributions - which are removal-based, not gradient-based - as a reference that is highly aligned with removal-based evaluation such as Remove-and-Debias (ROAD) [42] used to assess the faithfulness of feature attributions. + +# 4.2. Results + +Counterfactual generation. Counterfactual generation results are shown in Fig 4. The generation results show that FreeMCG is able to robustly approximate the direction of the gradient and push the image towards the decision boundary of the classifier. Quantitative results and human user study results for the criteria outlined in Section 4.1 are shown in Table 1. Because baseline methods make use of model gradients while FreeMCG does not, the flip rate of the model's decision is lower for FreeMCG than gradient-based baselines. However, FreeMCG yields by far the most human-perceived changes (Tab. 1 and Fig. 4). In fact, FreeMCG-based counterfactuals often contain informative changes without changing the decision of the classifier while gradient-based baselines commonly produce counterfactuals that fool the classifier to predict a different class but do not introduce semantically meaningful changes. Gradient-based methods are thus closer to adversarial attacks, while FreeMCG better serves the purpose of counterfactual generation and produces interpretable, on-manifold changes towards the target class. + +Feature attribution. Feature attributions from representative gradient-based methods for both ImageNet and MIMIC-CXR are shown in Fig. 5(a). ROAD evaluation results are also shown in Fig. 5(b). We see that baseline gradient methods provide feature attributions that are + +![](images/7255a5e172f3bc5d472c8f6b2879df16a5c45fe45544c7c65d99c0b5982424ef.jpg) + +![](images/ec567ae129404c123dcda64ce5e61c7b323be36a54504bbda34146e7e2a81d16.jpg) + +![](images/234dab938883febed07a39c87c2564236174551f0f7ad6f36c4111d1d531dbc5.jpg) +Figure 5. (a) Feature attribution maps obtained using each method, (b) Corresponding ROAD [42] evaluation results. Steeper decline is better, and SHAP is given as reference for the lower bound of this decline. For ImageNet, ROAD is calculated as described in [42]. For MIMIC chest X-ray data, results for decline in prediction accuracy was noisy due to the lower starting accuracy of the classifier, low number of classes, and severe data imbalance between classes; therefore, we instead measure the drop in prediction for the originally predicted class. The principle remains the same in that features (pixels) are removed in order of purported importance from each feature attribution map to observe the change in classifier predictions. + +![](images/1382ce5c029d951fc38ecb870073adfa26d52a305888cc3de124163b8672ba2c.jpg) + +
ChangeSimilarityRealism
Flip Rate ↑Perceived change ↓L2 ↓Perceived similarity ↓FID ↓Perceived realism ↓
DVCE* [4]85.82.35995.922.3471.382.30
LDCE [16]61.72.001351.391.9063.041.87
Ours51.51.651001.021.7666.891.83
+ +Table 1. Quantitative (Flip Rate / L2 / FID) and human user study (perceived change/similarity/realism) results. *DVCE without cone projection. + +similar to adversarial attacks, hence hardly interpretable. SHAP attributions provide less informative patch-like artifact. FreeMCG, on the other hand, produces high quality and interpretable attributions that are similar to SHAP, but retaining the high-frequency details as it does not rely on arbitrary pixel clustering. In ROAD evaluation, we see that FreeMCG achieves the steepest decline in model prediction among gradient-based methods, corresponding to better feature attributions, closer to the lower-bound computed by SHAP. Additional comparison against other removal-based black-box methods [36, 38] can be found in Appendix E. + +# 5. Conclusion + +We developed Derivative-Free Diffusion Mainfold Constrained Gradients (FreeMCG), an approximation of a neu + +ral network's gradient tangent to the data manifold, obtained without access to the model weights or its real gradients. Previous explainability literature on gradient-based feature attribution and counterfactual generation have remained largely separate because the gradient could not be readily employed for counterfactual generation as it produces adversarial attacks. With FreeMCG, one can obtain gradient directions on the image manifold that produce semantically meaningful counterfactual explanations and feature attributions. We demonstrate through experiments that FreeMCG enables a unified framework for both explainability methods with state-of-the-art results, all without access to model weights. FreeMCG still assumes black-box access to the model's logits; in more restricted scenarios where only class predictions are available, FreeMCG would not be applicable, highlighting a limitation that could inspire future work on extending FreeMCG to such settings. + +# Acknowledgements + +This work was supported by the National Research Foundation of Korea (NRF) under Grants RS-2024-00336454 and RS-2023-00262527, and by the Institute for Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (RS-2019-II190075, Artificial Intelligence Graduate School Program, KAIST). + +# References + +[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. Sanity checks for saliency maps. Advances in neural information processing systems, 31, 2018. 2 +[2] Dario Amodei, Chris Olah, Jacob Steinhardt, Paul Christiano, John Schulman, and Dan Mané. 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Ensemble kalman diffusion guidance: A derivative-free method for inverse problems. arXiv preprint arXiv:2409.20175, 2024. 4, 5, 10 \ No newline at end of file diff --git a/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/images.zip b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1ddfe9761ac4280c1f2875867d69d6350192f740 --- /dev/null +++ b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8a4f7d611518e26620084e92aec963b21ace553674866546651cd78f5fea3d8c +size 555892 diff --git a/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/layout.json b/2025/Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI/layout.json new file mode 100644 index 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\"explainability for AI\" (XAI) techniques, especially for image-based models. However, they (1) require white-box access to models, (2) are vulnerable to adversarial attacks, and (3) produce attributions that lie off the image manifold, leading to explanations that are not amenable to human perception. To overcome these challenges, we introduce Derivative-Free Diffusion Manifold-Constrained Gradients (FreeMCG): by leveraging ensemble Kalman filters and diffusion models, we derive a derivative-free approximation of the model's gradient projected onto the data manifold, requiring access only to the model's outputs (i.e., black-box setting). We demonstrate the effectiveness of FreeMCG by applying it to both counterfactual generation and feature attribution, which have traditionally been treated as different tasks requiring distinct methods. Through comprehensive evaluation on both counterfactual explanation and feature attribution we show that our method yields state-of-the-art results for both tasks while preserving the essential properties expected of XAI tools. Code: https://github.com/one-june/FreeMCG." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 56, + 533, + 135, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 533, + 135, + 544 + ], + "spans": [ + { + "bbox": [ + 56, + 533, + 135, + 544 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 552, + 295, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 660 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 660 + ], + "type": "text", + "content": "Understanding the decision-making process of complex deep neural networks is crucial for their deployment in high-stakes applications such as medical imaging [6, 7], autonomous systems [2, 43], etc. Explanable AI (XAI) seeks to address this challenge by providing insights into how models arrive at specific predictions, thus enhancing trust, accountability, and usability in critical applications. Two widely used tools for XAI are counterfactual explanation [59] and feature attribution1 [31]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 661, + 296, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 661, + 296, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 661, + 296, + 685 + ], + "type": "text", + "content": "Among various XAI methods, the gradient of the target (e.g. classifier) model is the prototypical method of under" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 318, + 227, + 553, + 471 + ], + "blocks": [ + { + "bbox": [ + 318, + 227, + 553, + 471 + ], + "lines": [ + { + "bbox": [ + 318, + 227, + 553, + 471 + ], + "spans": [ + { + "bbox": [ + 318, + 227, + 553, + 471 + ], + "type": "image", + "image_path": "9e0e2a8baae79d60bf61427842776a71d0eed0d52535ada408b5b09cf6de14b2.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 479, + 553, + 502 + ], + "lines": [ + { + "bbox": [ + 313, + 479, + 553, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 553, + 502 + ], + "type": "text", + "content": "Figure 1. Representative results of FreeMCG, operating as a universal framework for black box XAI." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 509, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 555, + 640 + ], + "type": "text", + "content": "standing the local behavior of a function around a given input data point. It has thus been used since the beginning of the rise of neural networks to explain their decisions [50]. There have been many subsequent works improving the vanilla gradient to serve as better feature attributions for a deep neural network [3, 46, 47, 55, 57, 61]. Gradients are also utilized for generating counterfactual explanations [4, 25, 44], in which the gradient of the target model serves as the direction that guides the change " + }, + { + "bbox": [ + 313, + 509, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 509, + 555, + 640 + ], + "type": "text", + "content": " made to the original image so that prediction of the model flips to another class." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 641, + 555, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 555, + 677 + ], + "type": "text", + "content": "While gradient-based methods are popular explainable AI (XAI) tools, they suffer from three significant limitations:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 315, + 677, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 677, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 315, + 677, + 556, + 714 + ], + "type": "text", + "content": "1. Access to model gradients is not always feasible: Obtaining gradients requires access to the model's internal weights, which is often not possible in practice. For" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 132, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 132, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 132, + 703 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 67, + 703, + 272, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 272, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 272, + 713 + ], + "type": "text", + "content": "1The term \"saliency maps\" are also often used interchangeably." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23795" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 109, + 73, + 165, + 81 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 73, + 165, + 81 + ], + "spans": [ + { + "bbox": [ + 109, + 73, + 165, + 81 + ], + "type": "text", + "content": "Feature attribution" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 113, + 87, + 194, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 87, + 194, + 110 + ], + "spans": [ + { + "bbox": [ + 113, + 87, + 194, + 110 + ], + "type": "text", + "content": "Q. 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Unified framework of XAI for feature attribution and counterfactual explanation using our method, Derivative-Free Diffusion Manifold Constrained Gradients (FreeMCG). Naive gradients not only violate the black box assumption but also is unreliable and hard to interpret as they produce adversarial attacks. Using diffusion models to produce on-manifold ensembles, and using the covariance of these particles as the preconditioner of the gradient, FreeMCG approximates gradients on the manifold, which is more reliable and interpretable." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 332, + 105, + 372, + 171 + ], + "blocks": [ + { + "bbox": [ + 332, + 90, + 394, + 98 + ], + "lines": [ + { + "bbox": [ + 332, + 90, + 394, + 98 + ], + "spans": [ + { + "bbox": [ + 332, + 90, + 394, + 98 + ], + "type": "text", + "content": "(i) Spread particles" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 332, + 105, + 372, + 171 + ], + "lines": [ + { + "bbox": [ + 332, + 105, + 372, + 171 + ], + "spans": [ + { + "bbox": [ + 332, + 105, + 372, + 171 + ], + "type": "image", + "image_path": "d7bf2af8fa70264542e3a1eae4753d69717d9abc4f3d04446d735671628ec43b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 384, + 110, + 484, + 175 + ], + "blocks": [ + { + "bbox": [ + 394, + 76, + 435, + 84 + ], + "lines": [ + { + "bbox": [ + 394, + 76, + 435, + 84 + ], + "spans": [ + { + "bbox": [ + 394, + 76, + 435, + 84 + ], + "type": "text", + "content": "FreeMCG" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 384, + 110, + 484, + 175 + ], + "lines": [ + { + "bbox": [ + 384, + 110, + 484, + 175 + ], + "spans": [ + { + "bbox": [ + 384, + 110, + 484, + 175 + ], + "type": "image", + "image_path": "990e21a3903188cdfdb5b31d8877efeaeeb377964758a43590c6b8d6572a3d2d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 332, + 182, + 451, + 190 + ], + "lines": [ + { + "bbox": [ + 332, + 182, + 451, + 190 + ], + "spans": [ + { + "bbox": [ + 332, + 182, + 451, + 190 + ], + "type": "text", + "content": "(ii) Approximate gradient on manifold" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 332, + 201, + 475, + 263 + ], + "blocks": [ + { + "bbox": [ + 332, + 201, + 475, + 263 + ], + "lines": [ + { + "bbox": [ + 332, + 201, + 475, + 263 + ], + "spans": [ + { + "bbox": [ + 332, + 201, + 475, + 263 + ], + "type": "image", + "image_path": "0e04c4a1052129324119a402a174e01aa80140cf1b733e8495ea8042382cdcd2.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 375, + 270, + 470, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 270, + 470, + 281 + ], + "spans": [ + { + "bbox": [ + 375, + 270, + 470, + 281 + ], + "type": "interline_equation", + "content": "\\boldsymbol {g} _ {\\text {F r e e}} \\cong C _ {x x} \\nabla_ {x} f (\\boldsymbol {e} _ {c} - \\boldsymbol {p})", + "image_path": "a564c9e94bc4963e674a816febd42b587e13f8018e97c307c5a5db27d4690705.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 67, + 368, + 295, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 368, + 295, + 391 + ], + "spans": [ + { + "bbox": [ + 67, + 368, + 295, + 391 + ], + "type": "text", + "content": "many neural-network based services, users can only interact with these systems through their outputs." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 55, + 391, + 296, + 619 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 55, + 391, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 391, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 391, + 296, + 498 + ], + "type": "text", + "content": "2. Gradients provide unreliable explanations: As shown in [1, 37, 51], gradient-based methods often fail to generate meaningful explanations of model behavior. These explanations are closely related to adversarial examples [58], and many traditional methods resort to using models that have been trained to be adversarially robust [4, 44]. Moreover, gradients typically do not align with the underlying data manifold, leading to explanations that are misaligned with human perception." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 55, + 499, + 296, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 499, + 296, + 619 + ], + "spans": [ + { + "bbox": [ + 55, + 499, + 296, + 619 + ], + "type": "text", + "content": "3. Lack of a unified framework for feature attribution and counterfactual explanations: The literature on feature attribution and counterfactual explanations remains largely separate. This is because real gradients produce adversarial attacks rather than counterfactual explanations and additional techniques are required to introduce perceptible changes. In theory, gradients should be usable for both applications. This raises the question of whether a single framework can effectively handle both types of explanations." + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 713 + ], + "type": "text", + "content": "To address these challenges, in this work, we propose Derivative-Free Diffusion Manifold Constrained Gradients (FreeMCG), a unified framework that can be used both for feature attribution and counterfactual explanation with only black-box access to the target model. By leveraging diffusion models and their powerful ability to model data manifolds, we can produce on-manifold perturbations of input" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 367, + 555, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 367, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 367, + 555, + 437 + ], + "type": "text", + "content": "data points, which, combined with ideas from Ensemble Kalman Filters (EnKF) [45], can be used to approximate manifold-projected model gradients. In Fig. 1, we show the representative results of FreeMCG, acting as a unified framework for XAI. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 441, + 554, + 536 + ], + "type": "list", + "angle": 0, + "index": 28, + "blocks": [ + { + "bbox": [ + 313, + 441, + 553, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 441, + 553, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 441, + 553, + 464 + ], + "type": "text", + "content": "- We present the first unified framework that encompasses both feature attribution and counterfactual explanation." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 465, + 554, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 465, + 554, + 512 + ], + "spans": [ + { + "bbox": [ + 313, + 465, + 554, + 512 + ], + "type": "text", + "content": "- We derive a novel method of estimating the gradient of the target classifier with black-box access (i.e. without access to model weights) by leveraging diffusion models and the theory of EnKF." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 513, + 553, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 513, + 553, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 513, + 553, + 536 + ], + "type": "text", + "content": "- We demonstrate that FreeMCG achieves state-of-the-art performance, even compared to white-box methods." + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 547, + 484, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 547, + 484, + 560 + ], + "spans": [ + { + "bbox": [ + 313, + 547, + 484, + 560 + ], + "type": "text", + "content": "2. Background & Related Works" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 567, + 433, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 567, + 433, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 567, + 433, + 578 + ], + "type": "text", + "content": "2.1. Gradient-based XAI" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 584, + 447, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 584, + 447, + 597 + ], + "spans": [ + { + "bbox": [ + 313, + 584, + 447, + 597 + ], + "type": "text", + "content": "Consider the following classifier" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 324, + 605, + 553, + 634 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 605, + 553, + 634 + ], + "spans": [ + { + "bbox": [ + 324, + 605, + 553, + 634 + ], + "type": "interline_equation", + "content": "p (y = c | \\boldsymbol {x}) = \\frac {\\exp \\left(\\boldsymbol {f} _ {c} (\\boldsymbol {x})\\right)}{\\sum_ {c ^ {\\prime} = 1} ^ {C} \\exp \\left(\\boldsymbol {f} _ {c ^ {\\prime}} (\\boldsymbol {x})\\right)}, \\boldsymbol {f}: \\mathbb {R} ^ {d} \\mapsto \\mathbb {R} ^ {n}, \\tag {1}", + "image_path": "16d911bcaf55b2627154a1ee4100cfd5b2e7e648636aa288e114f00f3c4551d5.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": " is the number of classes, and " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "f(\\pmb{x}) := [f_1(\\pmb{x}), \\dots, f_n(\\pmb{x})]" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": ". Taking the softmax would induce the probability vector " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{p} = \\text{softmax}(\\pmb{f}(\\pmb{x}))" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": " belongs to some class " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\text{class}(\\pmb{x}) = c" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": " be a labeling function. The task of feature attribution for images is to find an attribution " + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{a} \\in [0, 1]^d" + }, + { + "bbox": [ + 313, + 641, + 555, + 714 + ], + "type": "text", + "content": " that has high values in the indices where" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23796" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "its influence to " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " is pronounced. On the other hand, the task of counterfactual explanation aims to find a vector " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{\\prime}" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": " that belongs to a target class " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "c^\\prime" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": ", i.e. " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\operatorname{class}(\\pmb{x}^{\\prime}) = c^{\\prime}" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": ", but stays in proximity to " + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 295, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 295, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 295, + 251 + ], + "type": "text", + "content": "Feature attribution. Gradients provide a direct representation of the local behavior of a function by encapsulating how the function changes linearly in the gradient vector [50]. Integrated Gradients improve upon the vanilla gradient and satisfies certain desirable properties such as sensitivity, completeness, linearity, and implementation invariance by integrating the gradients along a path from a fixed baseline (often a black image) [57]. Other follow-up works have extended this approach by modifying the integration region [33, 56, 60] or altering the integrand [23, 27, 49], among others." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 251, + 295, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 295, + 418 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 295, + 418 + ], + "type": "text", + "content": "Counterfactuals and adversarial attacks. Gradients obtained with respect to the input can be used to perform gradient ascent/descent to change the input towards a direction that maximizes or minimizes the model output. However, for high-dimensional input data such as images, gradient ascent or descent often yields changes that are imperceptible to humans. This is known as an adversarial attack [18], because it changes the model output for a given input while the image itself remains effectively unchanged to human perception, thus having the effect of \"fooling\" a model. The adversarial attack phenomenon occurs because gradient ascent/descent using simple gradients perturbs the image in a direction that lifts the image off the image manifold and into the ambient space [14]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 419, + 295, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 419, + 295, + 539 + ], + "spans": [ + { + "bbox": [ + 55, + 419, + 295, + 539 + ], + "type": "text", + "content": "Counterfactuals, on the other hand, should yield a semantically meaningful change to the original input " + }, + { + "bbox": [ + 55, + 419, + 295, + 539 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 419, + 295, + 539 + ], + "type": "text", + "content": " such that the target model changes its prediction. In other words, the change should be on-manifold. Naturally, to induce this on-manifold change, generative models such as GANs and diffusion models [4, 25] have been used. However, most of these methods require access to model gradients, some even requiring that the model be adversarially robust. Moreover, these methods can be considered guided generation methods, making them inapplicable for feature attribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 544, + 159, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 159, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 159, + 555 + ], + "type": "text", + "content": "2.2. Diffusion Models" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "spans": [ + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "text", + "content": "Diffusion model [22, 28, 54] is a class of generative models that sample images through a Gaussian denoising path. This path is constructed by starting from the initial data (i.e. image) distribution " + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "inline_equation", + "content": "p_0(\\pmb{x})" + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "text", + "content": ", gradually adding Gaussian noise, and reaching approximately the Gaussian distribution " + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "inline_equation", + "content": "p_T(\\pmb{x}) \\approx \\mathcal{N}(\\pmb{0}, \\pmb{I})" + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "inline_equation", + "content": "t = T" + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "text", + "content": ". For the choice of the Gaussian perturbation " + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "inline_equation", + "content": "p(\\pmb{x}_t | \\pmb{x}_0) = \\mathcal{N}(\\pmb{x}_0, \\sigma_t^2 \\pmb{I})" + }, + { + "bbox": [ + 55, + 561, + 295, + 658 + ], + "type": "text", + "content": ", the reverse generation trajectory reads" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 661, + 295, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 661, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 67, + 661, + 295, + 687 + ], + "type": "interline_equation", + "content": "d \\boldsymbol {x} _ {t} = - \\sigma_ {t} \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t}) d t = \\frac {\\boldsymbol {x} _ {t} - \\mathbb {E} [ \\boldsymbol {x} _ {0} | \\boldsymbol {x} _ {t} ]}{\\sigma_ {t}} d t, \\tag {2}", + "image_path": "d86d922b8304b5e278597674acac9fcbfb97d5ec90906a9ef3e8c3bf59ace34b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "where the initial point is sampled from the reference distribution " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T \\sim p_T(\\pmb{x}_T)" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": ". Here, Tweedie's formula [15]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "inline_equation", + "content": "\\mathbb{E}[\\pmb{x}_0|\\pmb{x}_t] = \\pmb{x}_t + \\sigma_t^2\\nabla_{\\pmb{x}_t}\\log p(\\pmb{x}_t)" + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": " is used for the second equality. Diffusion models are trained as denoisers that estimate this posterior mean" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 346, + 118, + 553, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 118, + 553, + 137 + ], + "spans": [ + { + "bbox": [ + 346, + 118, + 553, + 137 + ], + "type": "interline_equation", + "content": "\\theta^ {*} = \\underset {\\theta} {\\arg \\min } \\mathbb {E} _ {t, \\boldsymbol {x} _ {t}, \\boldsymbol {x} _ {0}} \\left[ \\| D _ {\\theta} (\\boldsymbol {x} _ {t}) - \\boldsymbol {x} _ {0} \\| _ {2} ^ {2} \\right], \\tag {3}", + "image_path": "4784d8f18a27d51c931ef8a1d1b42fdb60212a857c36f6726fb9e0570af92c36.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 147, + 553, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 147, + 553, + 169 + ], + "spans": [ + { + "bbox": [ + 313, + 147, + 553, + 169 + ], + "type": "text", + "content": "which can be plugged into (2) as " + }, + { + "bbox": [ + 313, + 147, + 553, + 169 + ], + "type": "inline_equation", + "content": "\\mathbb{E}[\\pmb{x}_0|\\pmb{x}_t]\\approx D_{\\theta^*}(\\pmb{x}_t)" + }, + { + "bbox": [ + 313, + 147, + 553, + 169 + ], + "type": "text", + "content": " at test time." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "spans": [ + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "content": "In Chung et al. [8], assuming that " + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "content": " is a locally linear subspace, it was further shown that the distribution of noisy data " + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{x}_t)" + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "content": " is then concentrated on shell-like manifold " + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "content": ". Moreover, one can show that Tweedie's formula is an orthogonal projection from " + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "content": ". In other words, when the goal is to produce samples on the manifold " + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "content": " in a cost-effective way, one can use Tweedie's formula to generate samples in one step. This matches our intuition up to moderate values of " + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 171, + 555, + 291 + ], + "type": "text", + "content": ", where the posterior mean gives us a relatively good approximation of the real samples." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 306, + 554, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 306, + 554, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 306, + 554, + 354 + ], + "type": "text", + "content": "Guided sampling. Often, it is desirable to sample from the posterior " + }, + { + "bbox": [ + 313, + 306, + 554, + 354 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{x}|\\boldsymbol{y})" + }, + { + "bbox": [ + 313, + 306, + 554, + 354 + ], + "type": "text", + "content": " instead of from the prior. A standard approach to achieve this is to use guided sampling by Bayes decomposition" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 324, + 364, + 553, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 364, + 553, + 389 + ], + "spans": [ + { + "bbox": [ + 324, + 364, + 553, + 389 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t} | \\boldsymbol {y}) = \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {x} _ {t}) + \\nabla_ {\\boldsymbol {x} _ {t}} \\log p (\\boldsymbol {y} | \\boldsymbol {x} _ {t}), \\tag {4}", + "image_path": "fb467d1657ed4de8959fa31a0be79d35c7bfdbecb3dc6cde4d8fa27af6709ffd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 399, + 554, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 554, + 518 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 554, + 518 + ], + "type": "text", + "content": "where the gradient of the log-likelihood term measures the fidelity with respect to the condition " + }, + { + "bbox": [ + 313, + 399, + 554, + 518 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 313, + 399, + 554, + 518 + ], + "type": "text", + "content": ". One can either train a separate neural network (e.g. classifier [13, 54]) to estimate the term or use some form of approximation [9, 53]. Sampling from the posterior then boils down to iterating the denoising steps of the unconditional PF-ODE in (2) and the gradient step that maximizes fidelity. However, regardless of the forward model2, most of the methods require access to the gradient of the forward model, which is often hard to compute due to reasons including safety and complexity." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 526, + 506, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 526, + 506, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 526, + 506, + 539 + ], + "type": "text", + "content": "2.3. Gradient-free optimization and XAI" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 544, + 554, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 554, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 554, + 676 + ], + "type": "text", + "content": "When one can only evaluate " + }, + { + "bbox": [ + 313, + 544, + 554, + 676 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 544, + 554, + 676 + ], + "type": "text", + "content": " but cannot compute its gradient, gradient-free (zeroth-order) optimization [30], where a single or multiple set of samples can be used to calculate the finite difference, alongside techniques such as Gaussian smoothing [35] can be used to estimate the true gradient. Ensemble Kalman Filters (EnKF) [45], in terms of inverse problem solving, is also a widely used method for derivative-free optimization, where the ensemble of particles and its covariance information is used as a proxy for gradient information. In a similar vein, Ensemble Kalman Inversion (EKI) [19, 29] was proposed as a derivative-free" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 683, + 554, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 683, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 683, + 554, + 713 + ], + "type": "text", + "content": "2For instance, in image restoration, the degradation operator is the forward model. In classification, the neural network classifier is the forward model, as in (1)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23797" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 133 + ], + "type": "text", + "content": "method for training neural networks. Recently, the use of EnKF was extended to inverse problem-solving with diffusion models [62], showing that the technique can be readily used for diffusion guidance. In the proposed method, we leverage EnKF to approximate the unknown gradient." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 146, + 296, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 146, + 296, + 338 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 296, + 338 + ], + "type": "text", + "content": "Black-box feature attribution While white-box methods typically rely on gradient information, this dependency limits the applicability of XAI techniques to scenarios where gradients can be accessed. Several works [17, 31, 36, 40, 61] have introduced perturbation-based approaches for feature attribution. These methods generally involve perturbing the input—commonly by masking out pixel groups at random—and measuring the resulting change in class probabilities. While conceptually similar to FreeMCG in that they only require forward passes through the neural network, perturbation-based methods differ in two key ways: (1) masking pixels typically moves the input off the underlying data manifold, and (2) these methods are exclusively employed for feature attribution and cannot produce counterfactual explanations, as they do not approximate the decision boundary." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 347, + 228, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 347, + 228, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 347, + 228, + 360 + ], + "type": "text", + "content": "3. Main Contribution: FreeMCG" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 366, + 190, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 190, + 379 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 190, + 379 + ], + "type": "text", + "content": "3.1. Derivation of FreeMCG" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 384, + 176, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 176, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 176, + 396 + ], + "type": "text", + "content": "From (1), one can derive that" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 91, + 401, + 294, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 401, + 294, + 427 + ], + "spans": [ + { + "bbox": [ + 91, + 401, + 294, + 427 + ], + "type": "interline_equation", + "content": "\\frac {\\partial}{\\partial \\boldsymbol {f} _ {c ^ {\\prime}}} \\log p (y = c | \\boldsymbol {f} _ {c ^ {\\prime}}) = \\delta_ {c c ^ {\\prime}} - p \\left(c ^ {\\prime} | \\boldsymbol {f} _ {c ^ {\\prime}}\\right), \\tag {5}", + "image_path": "8d99fd54d40c17e12e5e078b5afba4cbacc959fd254f69572123b106aac486a1.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 433, + 295, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 433, + 295, + 456 + ], + "spans": [ + { + "bbox": [ + 55, + 433, + 295, + 456 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 433, + 295, + 456 + ], + "type": "inline_equation", + "content": "\\delta_{cc'}" + }, + { + "bbox": [ + 55, + 433, + 295, + 456 + ], + "type": "text", + "content": " is the Kronecker delta function which evaluates to 1 if and only if " + }, + { + "bbox": [ + 55, + 433, + 295, + 456 + ], + "type": "inline_equation", + "content": "c' = c" + }, + { + "bbox": [ + 55, + 433, + 295, + 456 + ], + "type": "text", + "content": ". Vector form of (5) reads" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 114, + 464, + 294, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 464, + 294, + 477 + ], + "spans": [ + { + "bbox": [ + 114, + 464, + 294, + 477 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\boldsymbol {f}} \\log p (y = c | \\boldsymbol {f}) = \\boldsymbol {e} _ {c} - \\boldsymbol {p}, \\tag {6}", + "image_path": "18775d1bc81c7d1d190db6e7e786d06322396ff2a8f722438d0b7cb96aee5937.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "type": "inline_equation", + "content": "e_{c}" + }, + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "type": "text", + "content": " is a one-hot vector with one at index " + }, + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "type": "inline_equation", + "content": "\\pmb{p} \\in \\mathbb{R}^{n}" + }, + { + "bbox": [ + 55, + 483, + 294, + 507 + ], + "type": "text", + "content": " is the classifier probability. From (6), we further have that" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 79, + 513, + 295, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 513, + 295, + 542 + ], + "spans": [ + { + "bbox": [ + 79, + 513, + 295, + 542 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\boldsymbol {x}} \\log p (y = c | \\boldsymbol {x}) = \\left(\\frac {\\partial \\boldsymbol {f} (\\boldsymbol {x})}{\\partial \\boldsymbol {x}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {7}", + "image_path": "f0f12a19d04986b7b8df2267d3d45b405a7dc7ba307948fc2aeae2e0b6bd9d0e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "text", + "content": "where we wrote " + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "inline_equation", + "content": "\\pmb{p}(\\pmb{x})" + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "text", + "content": " to emphasize that the probability vector is a function of " + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "text", + "content": ". In the context of EnKF, we consider a set of " + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "text", + "content": " particles " + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}^{(k)}\\}_{k=1}^{K}" + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "text", + "content": " to represent a state, where each particle corresponds to a sample of the random variable " + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 548, + 296, + 632 + ], + "type": "text", + "content": ". To leverage the ideas from EnKF, we are interested in the pre-conditioned version of the gradient, where the covariance of the particles is used" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 638, + 304, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 638, + 304, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 638, + 304, + 677 + ], + "type": "interline_equation", + "content": "\\boldsymbol {g} _ {\\text {F r e e}} := \\boldsymbol {C} _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\log p (c | \\boldsymbol {x}) = \\boldsymbol {C} _ {\\boldsymbol {x x}} \\left(\\frac {\\partial \\boldsymbol {f} (\\boldsymbol {x})}{\\partial \\boldsymbol {x}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {8}", + "image_path": "8f14b78be04e6aabb1c72583f5bf052aacef618c8fed3cb1e2ab56c0401d060c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "type": "inline_equation", + "content": "C_{\\pmb{x}\\pmb{x}}:= \\frac{1}{K}\\sum_{k = 1}^{K}(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})^{\\top}" + }, + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "type": "text", + "content": ", and we use " + }, + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{x}}" + }, + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "type": "text", + "content": " to denote the sample mean " + }, + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{E}[\\pmb{x}^{(k)}]" + }, + { + "bbox": [ + 55, + 685, + 296, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 319, + 76, + 434, + 190 + ], + "blocks": [ + { + "bbox": [ + 319, + 76, + 434, + 190 + ], + "lines": [ + { + "bbox": [ + 319, + 76, + 434, + 190 + ], + "spans": [ + { + "bbox": [ + 319, + 76, + 434, + 190 + ], + "type": "image", + "image_path": "9d2ade8800c84df7ba57b4966f1c09414e0a71213624ee3258cecf1185239a16.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 204, + 554, + 248 + ], + "lines": [ + { + "bbox": [ + 313, + 204, + 554, + 248 + ], + "spans": [ + { + "bbox": [ + 313, + 204, + 554, + 248 + ], + "type": "text", + "content": "Figure 3. Toy example of FreeMCG, illustrating the gradient (red arrow) and the gradient aligned with the tangent of manifold (gray dashed) approximated by (9) (green arrow), using neighbor data points (blue dots)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 435, + 76, + 550, + 190 + ], + "blocks": [ + { + "bbox": [ + 435, + 76, + 550, + 190 + ], + "lines": [ + { + "bbox": [ + 435, + 76, + 550, + 190 + ], + "spans": [ + { + "bbox": [ + 435, + 76, + 550, + 190 + ], + "type": "image", + "image_path": "32c71bc1d23e6ccda5c279b7736fafd572a38fe0701edc4e85dbfbf2fdda6e82.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 261, + 554, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 261, + 554, + 345 + ], + "spans": [ + { + "bbox": [ + 313, + 261, + 554, + 345 + ], + "type": "text", + "content": "FreeMCG produces on-manifold gradients. One may question the need for preconditioning the gradient with the empirical covariance matrix. In Theorem 1, we show that this preconditioning yields gradients that are on the data manifold " + }, + { + "bbox": [ + 313, + 261, + 554, + 345 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 261, + 554, + 345 + ], + "type": "text", + "content": ", producing results that are well-aligned with human perception, and robust to adversarial attacks. The proof can be found in Appendix A." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "spans": [ + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": "Theorem 1. Suppose that " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": " is locally linear at " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": ", meaning that in the neighborhood of " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": ", the manifold aligns with its tangent space " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_x\\mathcal{M}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": ". Suppose further, that the particles " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}^{(k)} \\in \\mathcal{M}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": ". Then, " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\boldsymbol{g}_{\\mathrm{Free}}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": " approximately lies within " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": ". Precisely, " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\boldsymbol{C}_{xx}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": " acts as a linear transformation, expanding along " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_x\\mathcal{M}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": " and contracting the vectors normal to " + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_x\\mathcal{M}" + }, + { + "bbox": [ + 313, + 353, + 554, + 425 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "text", + "content": "Theorem 1 states that when the particles " + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}^{(k)}" + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "text", + "content": " lies on the manifold surrounding the original data point " + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "inline_equation", + "content": "C_{xx}" + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "text", + "content": " captures the geometric properties of the tangent space " + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "inline_equation", + "content": "T_{x}\\mathcal{M}" + }, + { + "bbox": [ + 313, + 432, + 554, + 540 + ], + "type": "text", + "content": ". Specifically, the covariance matrix refines the vanilla gradient by contracting direction that lead off the manifold, which helps prevent the possibility of adversarial examples. Additionally, it expands along the direction of greater variability among the particles, reducing the likelihood of converging to a single original point." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 554, + 554, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 554, + 554, + 598 + ], + "spans": [ + { + "bbox": [ + 313, + 554, + 554, + 598 + ], + "type": "text", + "content": "EnKF for derivative-free gradient However, notice that " + }, + { + "bbox": [ + 313, + 554, + 554, + 598 + ], + "type": "inline_equation", + "content": "C_{xx} \\left( \\frac{\\partial f(x)}{\\partial x} \\right)^\\top" + }, + { + "bbox": [ + 313, + 554, + 554, + 598 + ], + "type": "text", + "content": " is hard to compute, as we do not have access to the gradient of " + }, + { + "bbox": [ + 313, + 554, + 554, + 598 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 554, + 554, + 598 + ], + "type": "text", + "content": ". Thus, we invoke the following." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "text", + "content": "Theorem 2. Suppose " + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "inline_equation", + "content": "\\| \\nabla_{\\pmb{x}}^{2}\\pmb{f}(\\pmb{x})\\|" + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "text", + "content": " be uniformly bounded and there exists " + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "inline_equation", + "content": "\\delta >0" + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{(k)}\\in \\{\\pmb {x}\\in \\mathbb{R}^d:\\| \\pmb {x} - \\bar{\\pmb{x}}\\| \\leq \\delta \\}" + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 605, + 554, + 652 + ], + "type": "text", + "content": ". Then, the following approximation holds" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 365, + 661, + 553, + 676 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 661, + 553, + 676 + ], + "spans": [ + { + "bbox": [ + 365, + 661, + 553, + 676 + ], + "type": "interline_equation", + "content": "C _ {\\boldsymbol {x} \\boldsymbol {f}} = C _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\boldsymbol {f} (\\boldsymbol {x}) ^ {\\top} + \\mathcal {O} \\left(\\delta^ {3}\\right), \\tag {9}", + "image_path": "245ca54f643d90e587fbdafed16246a65c60444aee9cbc613d5a6280374cbc46.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 685, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 685, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 685, + 554, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 685, + 554, + 715 + ], + "type": "inline_equation", + "content": "C_{\\pmb{x}\\pmb{f}} := \\frac{1}{K}\\sum_{k=1}^{K}(\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb{f}(\\pmb{x}^{(k)}) - \\bar{\\pmb{f}})^{\\top}" + }, + { + "bbox": [ + 313, + 685, + 554, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 685, + 554, + 715 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{f}} := \\frac{1}{K}\\sum_{k=1}^{K}\\pmb{f}(\\pmb{x}^{(k)})" + }, + { + "bbox": [ + 313, + 685, + 554, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23798" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "content": "The proof along with a formal treatment on approximation errors can be found in Appendix A. Apply Theorem 2 to (8), we have" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 63, + 119, + 295, + 169 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 119, + 295, + 169 + ], + "spans": [ + { + "bbox": [ + 63, + 119, + 295, + 169 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {C} _ {\\boldsymbol {x x}} \\nabla_ {\\boldsymbol {x}} \\log p (y = c | \\boldsymbol {x}) \\approx \\boldsymbol {C} _ {\\boldsymbol {x f}} \\left(e _ {c} - \\boldsymbol {p}\\right) \\\\ = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\boldsymbol {x} ^ {(k)} - \\bar {\\boldsymbol {x}}\\right) \\left(\\boldsymbol {f} \\left(\\boldsymbol {x} ^ {(k)}\\right) - \\bar {\\boldsymbol {f}}\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p} (\\boldsymbol {x})\\right), \\tag {10} \\\\ \\end{array}", + "image_path": "3cd24a5a8d76ab296817d96d14b914c80055604ab1b3d59e89e91f4976671c03.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 180, + 296, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 180, + 296, + 205 + ], + "spans": [ + { + "bbox": [ + 55, + 180, + 296, + 205 + ], + "type": "text", + "content": "given the particles " + }, + { + "bbox": [ + 55, + 180, + 296, + 205 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{(k)}" + }, + { + "bbox": [ + 55, + 180, + 296, + 205 + ], + "type": "text", + "content": ". We provide the pseudocode for computing FreeMCG in Alg. 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "spans": [ + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "text", + "content": "Although we now have the machinery to compute the approximate gradient, notice that we have to choose the position of the particles " + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{(k)}" + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "text", + "content": ". For this, three conditions must be met. The particles should be 1) near " + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "text", + "content": ", 2) on-manifold, and 3) fast to generate. The first two conditions are met by perturbing " + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "text", + "content": " to obtain forward-diffused samples " + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t^{(k)}" + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "text", + "content": ", and running reverse PF-ODE to all the particles, as used in [32, 62]. However, since this would be prohibitively slow, we simply choose to use the Tweedie denoised estimates, which we denote as " + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{0|t}^{(k)}" + }, + { + "bbox": [ + 55, + 206, + 296, + 330 + ], + "type": "text", + "content": ". In short, our gradient reads" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 340, + 299, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 340, + 299, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 340, + 299, + 373 + ], + "type": "interline_equation", + "content": "\\boldsymbol {g} _ {\\text {F r e e}} := \\mathbb {E} \\left[ \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)} - \\bar {\\boldsymbol {x}} _ {0 | t} ^ {(k)}\\right) \\left(\\boldsymbol {f} \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)}\\right) - \\bar {\\boldsymbol {f}} \\left(\\boldsymbol {x} _ {0 | t} ^ {(k)}\\right)\\right) ^ {\\top} \\left(\\boldsymbol {e} _ {c} - \\boldsymbol {p}\\right) \\right], \\tag {11}", + "image_path": "eb8efde3b5a70236c9d90316c4230281d2ccf2dc4ffb1b0cb2c28f1922eb1ee2.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "type": "text", + "content": "where the expectation is over the diffusion timesteps " + }, + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "type": "text", + "content": " and the number of particles " + }, + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "type": "text", + "content": ". Notice that under our assumption of local linearity, we can use Proposition 2 of [8], which states that Tweedie's formula [15] is locally an orthogonal projection to the manifold " + }, + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 384, + 296, + 453 + ], + "type": "text", + "content": ", satisfying the assumption of Thm. 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "spans": [ + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "text", + "content": "We illustrate a 2D toy example in Fig. 3. Considering " + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "inline_equation", + "content": "f = -x + y^2" + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "text", + "content": " with its gradient " + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "inline_equation", + "content": "\\nabla_{\\pmb{x}}f(\\pmb{x}) = (-1,2y)" + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "text", + "content": ", we sample particles around the point " + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "text", + "content": " and calculate the covariance matrix. Then, applying (9), we obtain a gradient aligned with the direction of the manifold without directly computing the gradient of the " + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 456, + 296, + 589 + ], + "type": "text", + "content": ". In our main experiments, we show that FreeMCG indeed produces a gradient that produces on-manifold gradients so that it avoids being an adversarial attack. In the following, we elaborate on practical implementations of (11) for feature attribution and counterfactual explanation, as well as their intuition, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 599, + 200, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 599, + 200, + 612 + ], + "spans": [ + { + "bbox": [ + 55, + 599, + 200, + 612 + ], + "type": "text", + "content": "3.2. Applications of FreeMCG" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": "FreeMCG for feature attribution. This corresponds to the case where the target class " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "c'" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": " aligns with the prediction of the classifier " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": ". Notice that " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "f(\\boldsymbol{x}^{(k)}) - \\bar{f} \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "f_c" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": " indicates the average drop in logit value after the Tweedie perturbation. Moreover, when " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "c' = c" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": ", the only positive entry in " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "e_c - p" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": " will be at the index " + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 617, + 296, + 714 + ], + "type": "text", + "content": ", positively weighting the part that changes the predicted class label, while negatively weighting the part that is irrelevant. As a concrete example," + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 319, + 87, + 545, + 190 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 504, + 84 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 504, + 84 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 504, + 84 + ], + "type": "text", + "content": "Algorithm 1 FreeMCG Gradient Computation" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "text", + "content": "1: function FREEMCG " + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "inline_equation", + "content": "(\\pmb {f},\\{\\pmb{x}^{(k)}\\}_{k = 1}^{K},e_{c},\\pmb {p})" + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "text", + "content": " \n2: " + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{x}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb{x}^{(k)}" + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "text", + "content": " \n3: " + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{f}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb {f}(\\pmb{x}^{(k)})" + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "text", + "content": " \n4: for " + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "text", + "content": " do \n5: " + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\Delta^{(k)}\\gets (\\pmb{x}^{(k)} - \\bar{\\pmb{x}})(\\pmb {f}(\\pmb{x}^{(k)}) - \\bar{\\pmb{f}})^{\\top}(\\pmb {e}_c - \\pmb {p})" + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "text", + "content": " \n6: end for \n7: return " + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\pmb{g}_{\\mathrm{Free}}\\gets \\frac{1}{K}\\sum_{k = 1}^{K}\\pmb{\\Delta}^{(k)}" + }, + { + "bbox": [ + 319, + 87, + 545, + 190 + ], + "type": "text", + "content": " \n8: end function" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "type": "code", + "bbox": [ + 315, + 217, + 555, + 381 + ], + "blocks": [ + { + "bbox": [ + 315, + 202, + 501, + 214 + ], + "lines": [ + { + "bbox": [ + 315, + 202, + 501, + 214 + ], + "spans": [ + { + "bbox": [ + 315, + 202, + 501, + 214 + ], + "type": "text", + "content": "Algorithm 2 FreeMCG for feature attribution" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "lines": [ + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": "Require: Classifier " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": ", Diffusion model " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": ", Input " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": ", Number of particles " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": ", Target class vector " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "e_c" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": ", Diffusion timestep range " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "[l, u]" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " \n1: " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "p = \\text{softmax}(f(x))" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " \n2: " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "x_0 \\gets x" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " \n3: for " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " do \n4: " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "t \\sim \\mathcal{U}[l, u]" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " \n5: " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "x_t^{(k)} \\sim p(x_t | x_0)" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " \n6: " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "x_{0|t}^{(k)} \\gets (x_t - \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon_\\theta(x_t)) / \\sqrt{\\bar{\\alpha}_t}" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " \n7: end for \n8: " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "g_{\\text{Free}} \\gets \\text{FREEMCG}(f, \\epsilon_\\theta, x, \\{x_{0|t}^{(k)}\\}_{k=1}^K, e_c, p)" + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "text", + "content": " \n9: return " + }, + { + "bbox": [ + 315, + 217, + 555, + 381 + ], + "type": "inline_equation", + "content": "g_{\\text{Free}}" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "code_body" + } + ], + "index": 12, + "sub_type": "algorithm" + }, + { + "type": "code", + "bbox": [ + 315, + 407, + 555, + 640 + ], + "blocks": [ + { + "bbox": [ + 315, + 392, + 531, + 404 + ], + "lines": [ + { + "bbox": [ + 315, + 392, + 531, + 404 + ], + "spans": [ + { + "bbox": [ + 315, + 392, + 531, + 404 + ], + "type": "text", + "content": "Algorithm 3 FreeMCG for CE with reverse diffusion" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "lines": [ + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": "Require: Classifier " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " , Diffusion model " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " Input " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " Number of particles " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " , Target class vector " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "e_{c^{\\prime}}" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " , Diffusion params " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "t^\\prime ,\\tilde{\\beta}_t,\\bar{\\alpha}_t,\\eta ,\\gamma_t" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " \n1: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\pmb {x}_0\\gets \\pmb{x}" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " \n2: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "[\\pmb{x}_{t'}^{(k)}]\\sim p(\\pmb{x}_{t'}|\\pmb{x}_0)\\quad \\triangleright [\\cdot ]" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " batched particles \n3: for " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "t = t^{\\prime}" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " to 1 do reverse diffusion \n4: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "[\\hat{\\epsilon}_t^{(k)}]\\gets \\epsilon_\\theta ([\\pmb{x}_t^{(k)}])" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " \n5: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "[\\pmb{x}_{0|t}^{(k)}]\\gets ([\\pmb{x}_t^{(k)}] - \\sqrt{1 - \\bar{\\alpha}_t} [\\hat{\\epsilon}_t^{(k)}]) / \\sqrt{\\bar{\\alpha}_t}" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " Tweedie denoising \n6: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "[\\pmb{p}^{(k)}]\\gets \\mathrm{softmax}(\\pmb {f}([\\pmb{x}_{0|t}^{(k)}]))" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " \n7: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "[\\pmb{g}_{\\mathrm{Free}}^{(k)}]\\gets \\mathrm{FREEMCG}(\\pmb {f},[\\pmb{x}_{0|t}^{(k)}],\\pmb{e}_{c'},\\pmb{p}^{(k)})" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " \n8: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "[\\pmb{g}^{(k)}]\\gets \\alpha [\\pmb{g}_{\\mathrm{Free}}^{(k)}] + \\beta (\\pmb {x} - [\\pmb{x}_{0|t}^{(k)})]" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " \n9: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "[\\pmb {\\epsilon}^{(k)}]\\sim \\mathcal{N}(0,\\pmb {I})" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " \n10: " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "[\\pmb{x}_{t - 1}]\\gets \\sqrt{\\bar{\\alpha}_{t - 1}} [\\pmb{x}_{0|t}]^{(k)} + \\sqrt{1 - \\bar{\\alpha}_{t - 1} - \\eta^2\\tilde{\\beta}_t^2} [\\hat{\\epsilon}_t]" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "+\\eta \\tilde{\\beta}_t[\\epsilon^{(k)}] + \\gamma_t[\\pmb {g}^{(k)}]" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " \n11: end for \n12: return " + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{(CE)}} = \\frac{1}{K}\\sum_{k = 1}^{K}x_0" + }, + { + "bbox": [ + 315, + 407, + 555, + 640 + ], + "type": "text", + "content": " Average of particles" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "code_body" + } + ], + "index": 14, + "sub_type": "algorithm" + }, + { + "bbox": [ + 313, + 660, + 474, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 660, + 474, + 673 + ], + "spans": [ + { + "bbox": [ + 313, + 660, + 474, + 673 + ], + "type": "text", + "content": "consider the following 4-class example" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 348, + 679, + 520, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 679, + 520, + 694 + ], + "spans": [ + { + "bbox": [ + 348, + 679, + 520, + 694 + ], + "type": "interline_equation", + "content": "\\boldsymbol {e} _ {c} = [ 1, 0, 0, 0 ] ^ {\\top}, \\boldsymbol {p} = [ 0. 7, 0. 1, 0. 1, 0. 1 ] ^ {\\top}", + "image_path": "e09d80b4954022f4a3f87b1e0385fe05dc87c040ae34eb7d16d3880b480a90a8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 348, + 696, + 554, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 696, + 554, + 711 + ], + "spans": [ + { + "bbox": [ + 348, + 696, + 554, + 711 + ], + "type": "interline_equation", + "content": "\\boldsymbol {e} _ {c} - \\boldsymbol {p} = [ 0. 3, - 0. 1, - 0. 1, - 0. 1 ] ^ {\\top}, \\tag {12}", + "image_path": "bf266dfeebe13e0ea7e3f28110a7bca2240356182eb87b62f1c7fb63196516c4.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23799" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "where only the perturbations that dropped the probability of the first class will be positively weighted, while for the other indices, there will be an opposite force." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 108, + 294, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 108, + 294, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 108, + 294, + 203 + ], + "type": "text", + "content": "For implementation, we found that using multiple levels of " + }, + { + "bbox": [ + 55, + 108, + 294, + 203 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 108, + 294, + 203 + ], + "type": "text", + "content": " was crucial for encapsulating the attribution that acts both for coarse and fine scales. Similar to how score distillation sampling (SDS) [39] is recently used [48], we constrain the time range to " + }, + { + "bbox": [ + 55, + 108, + 294, + 203 + ], + "type": "inline_equation", + "content": "t \\in [0.1, 0.7]" + }, + { + "bbox": [ + 55, + 108, + 294, + 203 + ], + "type": "text", + "content": ". For visualization purposes, we take the mean across the color channels and plot the absolute value. The algorithm for feature attribution using FreeMCG is presented in Alg. 2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 204, + 295, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 204, + 295, + 263 + ], + "spans": [ + { + "bbox": [ + 55, + 204, + 295, + 263 + ], + "type": "text", + "content": "FreeMCG for counterfactual explanation. While (11) can directly serve as the attribution, for counterfactual explanation, the gradient should be used as the direction of ascent toward a counterfactual sample. Here, we can iteratively apply gradient ascent with FreeMCG, i.e." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 274, + 295, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 274, + 295, + 285 + ], + "spans": [ + { + "bbox": [ + 94, + 274, + 295, + 285 + ], + "type": "interline_equation", + "content": "\\boldsymbol {x} _ {i + 1} = \\boldsymbol {x} _ {i} + \\alpha \\mathbf {g} _ {\\text {F r e e}} (\\boldsymbol {x} _ {i}) + \\beta (\\boldsymbol {x} - \\boldsymbol {x} _ {i}), \\tag {13}", + "image_path": "15ece52da5a16b6a0a58a72821e0d0ae0b9ead3024b01ef8d563f0536b3412c3.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "content": " is the step size weighting the FreeMCG, and " + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "content": " weights the proximal regularization to the initial point " + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "content": ". Notice that the implementation of FreeMCG for counterfactual explanation differs from that of feature attribution, as we have a different target class " + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "inline_equation", + "content": "c^{\\prime}" + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "content": ". For instance, consider the example in (12), but the target class is now 2. Then, in the earlier stage of gradient ascent, we have" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 91, + 387, + 260, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 387, + 260, + 400 + ], + "spans": [ + { + "bbox": [ + 91, + 387, + 260, + 400 + ], + "type": "interline_equation", + "content": "\\boldsymbol {e} _ {c} = [ 0, 1, 0, 0 ] ^ {\\top}, \\boldsymbol {p} = [ 0. 7, 0. 1, 0. 1, 0. 1 ] ^ {\\top}", + "image_path": "dabc8c41eb50352bccbb2f37a42ede4f1b2f991526291364787428ecc3fd0fe4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 91, + 404, + 294, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 404, + 294, + 417 + ], + "spans": [ + { + "bbox": [ + 91, + 404, + 294, + 417 + ], + "type": "interline_equation", + "content": "\\boldsymbol {e} _ {c} - \\boldsymbol {p} = \\left[ - 0. 7, 0. 9, - 0. 1, - 0. 1 \\right] ^ {\\top}. \\tag {14}", + "image_path": "9786b8b18e80f97c037c5296f42b7db7cb0e1f4e6078d4e566316567a26fc10f.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 426, + 295, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 295, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 295, + 474 + ], + "type": "text", + "content": "In other words, the components correlated with the original class " + }, + { + "bbox": [ + 55, + 426, + 295, + 474 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 426, + 295, + 474 + ], + "type": "text", + "content": " is strongly negatively pulled down, whereas the components correlated with the target class " + }, + { + "bbox": [ + 55, + 426, + 295, + 474 + ], + "type": "inline_equation", + "content": "c'" + }, + { + "bbox": [ + 55, + 426, + 295, + 474 + ], + "type": "text", + "content": " are strongly positively pushed up." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 475, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 296, + 713 + ], + "type": "text", + "content": "FreeMCG meets reverse diffusion. While iterative gradient ascents using FreeMCG in (13) gives us a fast way to generate counterfactual explanations, we find that this process is sensitive to hyperparameters and produces suboptimal results. To fully leverage the generative nature of diffusion models, we instead propose a variant that utilizes reverse diffusion, as is done in other methods that use diffusion models for counterfactual explanation [4, 16, 24]. Specifically, we use an SDEdit [32]-like approach, where we forward diffuse our initial sample up to time " + }, + { + "bbox": [ + 55, + 475, + 296, + 713 + ], + "type": "inline_equation", + "content": "t'" + }, + { + "bbox": [ + 55, + 475, + 296, + 713 + ], + "type": "text", + "content": " and run reverse guided sampling in (13) to the Tweedie denoised estimates. The algorithm is presented in Alg. 3. Notice that we do not incorporate the Jacobian of " + }, + { + "bbox": [ + 55, + 475, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 475, + 296, + 713 + ], + "type": "text", + "content": ", which is typically done in methods like [9, 53], and simply resort to the gradients with respect to the Tweedie estimates [10] to save computation. For further details, see Appendix G. This approach may be slower as it requires reverse diffusion, but produces higher-fidelity results (Fig. 4). Therefore, all experiments on counterfactual explanation with FreeMCG use this reverse diffusion approach unless specified otherwise." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 72, + 394, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 394, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 394, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 91, + 553, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 553, + 188 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 553, + 188 + ], + "type": "text", + "content": "We demonstrate our method from both feature attribution and counterfactual perspectives. To evaluate generalization and domain-specific performance, we compare our method on ImageNet [12] and MIMIC CXR [26] dataset, using images with a resolution of " + }, + { + "bbox": [ + 313, + 91, + 553, + 188 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 91, + 553, + 188 + ], + "type": "text", + "content": ". We use regular pretrained classifier models with the ResNet-50 [20] and unconditional diffusion models [13] trained on each dataset. Experimental details are provided in Appendix H." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 198, + 430, + 210 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 198, + 430, + 210 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 430, + 210 + ], + "type": "text", + "content": "4.1. Evaluation protocol" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 215, + 553, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 215, + 553, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 215, + 553, + 335 + ], + "type": "text", + "content": "Counterfactuals. An ideal counterfactual makes semantically meaningful, human-interpretable yet minimal changes to the input image so that it is classified as the target class. This allows the user to gain visual insight into the decision boundary of the model. The aim is to create an example at a point on or near the decision boundary closest to the input image (Fig 2), so the generated counterfactual must be anchored on the original input image and should not be an unconditionally generated image of the target class. Therefore, evaluation involves the following criteria:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 338, + 499, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 338, + 499, + 350 + ], + "spans": [ + { + "bbox": [ + 315, + 338, + 499, + 350 + ], + "type": "text", + "content": "1. Meaningful change towards target class" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 351, + 553, + 421 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 329, + 351, + 553, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 351, + 553, + 373 + ], + "spans": [ + { + "bbox": [ + 329, + 351, + 553, + 373 + ], + "type": "text", + "content": "(a) Flip rate: Is the generated counterfactual classified as the intended target class by the model of interest?" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 329, + 375, + 553, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 375, + 553, + 421 + ], + "spans": [ + { + "bbox": [ + 329, + 375, + 553, + 421 + ], + "type": "text", + "content": "(b) Perceived change: Does the generated counterfactual contain semantically meaningful changes to a human perceiver? (i.e. can it be distinguished from an adversarial attack?)" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 423, + 424, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 423, + 424, + 434 + ], + "spans": [ + { + "bbox": [ + 315, + 423, + 424, + 434 + ], + "type": "text", + "content": "2. Similarity to the input" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 329, + 434, + 553, + 481 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 329, + 434, + 553, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 434, + 553, + 457 + ], + "spans": [ + { + "bbox": [ + 329, + 434, + 553, + 457 + ], + "type": "text", + "content": "(a) L2 distance: Are generated counterfactuals close to the input images in terms of distance?" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 329, + 458, + 553, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 458, + 553, + 481 + ], + "spans": [ + { + "bbox": [ + 329, + 458, + 553, + 481 + ], + "type": "text", + "content": "(b) Perceived similarity: Do generated counterfactuals and input appear similar to a human perceiver?" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 483, + 448, + 494 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 483, + 448, + 494 + ], + "spans": [ + { + "bbox": [ + 315, + 483, + 448, + 494 + ], + "type": "text", + "content": "3. Realism of generated image" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 329, + 495, + 553, + 553 + ], + "type": "list", + "angle": 0, + "index": 24, + "blocks": [ + { + "bbox": [ + 329, + 495, + 553, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 495, + 553, + 529 + ], + "spans": [ + { + "bbox": [ + 329, + 495, + 553, + 529 + ], + "type": "text", + "content": "(a) Frechet Inception Distance (FID) [21]: Is the distribution of the generated counterfactual images similar to distribution of original input images?" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 329, + 530, + 553, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 530, + 553, + 553 + ], + "spans": [ + { + "bbox": [ + 329, + 530, + 553, + 553 + ], + "type": "text", + "content": "(b) Perceived realism: Do the images appear realistic to a human perceiver?" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 556, + 553, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 553, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 553, + 651 + ], + "type": "text", + "content": "Crucially, note that these metrics must be interpreted in concert, rather than as separate measures. In particular, an adversarial attack [11, 18], which flips the decision of the classification neural network but does not introduce changes to the input image that are meaningful to a human perceiver (which are meaningless as explainability tools), can speciously score well on aspects such as similarity or realism." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": "Flip rate, L2 distance, and FID are computed using 1K generated counterfactuals (one from each class of the ImageNet validation set). Following the experimentation scheme in LDCE [16], we select the category closest to the input image based on the WordNet [34] hierarchy as the tar" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23800" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 71, + 306, + 298 + ], + "blocks": [ + { + "bbox": [ + 67, + 71, + 306, + 298 + ], + "lines": [ + { + "bbox": [ + 67, + 71, + 306, + 298 + ], + "spans": [ + { + "bbox": [ + 67, + 71, + 306, + 298 + ], + "type": "image", + "image_path": "7c3d41d52b13645da70458f8ba90795bf3a91008ba2a3e4050360ce1f42d5eea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 308, + 555, + 374 + ], + "lines": [ + { + "bbox": [ + 54, + 308, + 555, + 374 + ], + "spans": [ + { + "bbox": [ + 54, + 308, + 555, + 374 + ], + "type": "text", + "content": "Figure 4. Counterfactual Generation. Images on the leftmost column are given as input, and the counterfactual for the target class (shown in blue) are generated using each method. Baseline methods generate counterfactuals by perturbing the image towards the direction of a given classification neural network's gradients. Not only are these methods not applicable to situations without access to model weights, gradients almost always point away from the image manifold and into the ambient space, leading to imperceptible changes (i.e., adversarial attack) or changes that produce unnatural, off-manifold, images. FreeMCG on the other hand produces semantically meaningful changes while keeping the image on-manifold. *DVCE without cone projection." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 306, + 72, + 544, + 298 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 544, + 298 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 544, + 298 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 544, + 298 + ], + "type": "image", + "image_path": "a0b54f6c5cbcb98e92468e624eff1b6a8623bc56571dee09bdb652bda936cf26.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 387, + 294, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 387, + 294, + 434 + ], + "spans": [ + { + "bbox": [ + 54, + 387, + 294, + 434 + ], + "type": "text", + "content": "get class for counterfactual generation. Perceived change, similarity, and realism were measured through a human user study (details in Appendix I). Results are provided in Table 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 442, + 295, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 442, + 295, + 562 + ], + "spans": [ + { + "bbox": [ + 54, + 442, + 295, + 562 + ], + "type": "text", + "content": "We select DVCE [4] and LDCE [16] as baselines, leveraging diffusion models to generate counterfactuals. Note that these baseline methods require access to the model weights while FreeMCG does not. In addition, while the proposed method of DVCE includes cone projection of model weights to the weights of an adversariably robust classifier, we use DVCE with only a regular non-robust classifier (i.e. without cone projection) for comparison throughout this paper as we are assuming lack of access to adversarially robust weights." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 570, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 570, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 54, + 570, + 295, + 712 + ], + "type": "text", + "content": "Feature attribution. Feature attributions can be evaluated by observing the change in model predictions whilst removing the pixels in order of purported importance from the attribution. We compare our approach with existing gradient-based attribution methods, including the vanilla gradient [50], Integrated Gradients [49] and InputXGradient [47]. We provide Shapley additive explanation (SHAP) [31] attributions - which are removal-based, not gradient-based - as a reference that is highly aligned with removal-based evaluation such as Remove-and-Debias (ROAD) [42] used to assess the faithfulness of feature attributions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 386, + 371, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 386, + 371, + 397 + ], + "spans": [ + { + "bbox": [ + 314, + 386, + 371, + 397 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 312, + 408, + 555, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 408, + 555, + 648 + ], + "spans": [ + { + "bbox": [ + 312, + 408, + 555, + 648 + ], + "type": "text", + "content": "Counterfactual generation. Counterfactual generation results are shown in Fig 4. The generation results show that FreeMCG is able to robustly approximate the direction of the gradient and push the image towards the decision boundary of the classifier. Quantitative results and human user study results for the criteria outlined in Section 4.1 are shown in Table 1. Because baseline methods make use of model gradients while FreeMCG does not, the flip rate of the model's decision is lower for FreeMCG than gradient-based baselines. However, FreeMCG yields by far the most human-perceived changes (Tab. 1 and Fig. 4). In fact, FreeMCG-based counterfactuals often contain informative changes without changing the decision of the classifier while gradient-based baselines commonly produce counterfactuals that fool the classifier to predict a different class but do not introduce semantically meaningful changes. Gradient-based methods are thus closer to adversarial attacks, while FreeMCG better serves the purpose of counterfactual generation and produces interpretable, on-manifold changes towards the target class." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "content": "Feature attribution. Feature attributions from representative gradient-based methods for both ImageNet and MIMIC-CXR are shown in Fig. 5(a). ROAD evaluation results are also shown in Fig. 5(b). We see that baseline gradient methods provide feature attributions that are" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23801" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 71, + 380, + 193 + ], + "blocks": [ + { + "bbox": [ + 71, + 71, + 380, + 193 + ], + "lines": [ + { + "bbox": [ + 71, + 71, + 380, + 193 + ], + "spans": [ + { + "bbox": [ + 71, + 71, + 380, + 193 + ], + "type": "image", + "image_path": "7255a5e172f3bc5d472c8f6b2879df16a5c45fe45544c7c65d99c0b5982424ef.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 381, + 72, + 538, + 194 + ], + "blocks": [ + { + "bbox": [ + 381, + 72, + 538, + 194 + ], + "lines": [ + { + "bbox": [ + 381, + 72, + 538, + 194 + ], + "spans": [ + { + "bbox": [ + 381, + 72, + 538, + 194 + ], + "type": "image", + "image_path": "ec567ae129404c123dcda64ce5e61c7b323be36a54504bbda34146e7e2a81d16.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 70, + 195, + 379, + 308 + ], + "blocks": [ + { + "bbox": [ + 70, + 195, + 379, + 308 + ], + "lines": [ + { + "bbox": [ + 70, + 195, + 379, + 308 + ], + "spans": [ + { + "bbox": [ + 70, + 195, + 379, + 308 + ], + "type": "image", + "image_path": "234dab938883febed07a39c87c2564236174551f0f7ad6f36c4111d1d531dbc5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 319, + 555, + 387 + ], + "lines": [ + { + "bbox": [ + 54, + 319, + 555, + 387 + ], + "spans": [ + { + "bbox": [ + 54, + 319, + 555, + 387 + ], + "type": "text", + "content": "Figure 5. (a) Feature attribution maps obtained using each method, (b) Corresponding ROAD [42] evaluation results. Steeper decline is better, and SHAP is given as reference for the lower bound of this decline. For ImageNet, ROAD is calculated as described in [42]. For MIMIC chest X-ray data, results for decline in prediction accuracy was noisy due to the lower starting accuracy of the classifier, low number of classes, and severe data imbalance between classes; therefore, we instead measure the drop in prediction for the originally predicted class. The principle remains the same in that features (pixels) are removed in order of purported importance from each feature attribution map to observe the change in classifier predictions." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 381, + 198, + 538, + 308 + ], + "blocks": [ + { + "bbox": [ + 381, + 198, + 538, + 308 + ], + "lines": [ + { + "bbox": [ + 381, + 198, + 538, + 308 + ], + "spans": [ + { + "bbox": [ + 381, + 198, + 538, + 308 + ], + "type": "image", + "image_path": "1382ce5c029d951fc38ecb870073adfa26d52a305888cc3de124163b8672ba2c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 107, + 401, + 504, + 468 + ], + "blocks": [ + { + "bbox": [ + 107, + 401, + 504, + 468 + ], + "lines": [ + { + "bbox": [ + 107, + 401, + 504, + 468 + ], + "spans": [ + { + "bbox": [ + 107, + 401, + 504, + 468 + ], + "type": "table", + "html": "
ChangeSimilarityRealism
Flip Rate ↑Perceived change ↓L2 ↓Perceived similarity ↓FID ↓Perceived realism ↓
DVCE* [4]85.82.35995.922.3471.382.30
LDCE [16]61.72.001351.391.9063.041.87
Ours51.51.651001.021.7666.891.83
", + "image_path": "3ab8c47a4851c35d45a77c9235da95763c987c911eb3e36998a742bb659323a2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 475, + 555, + 499 + ], + "lines": [ + { + "bbox": [ + 54, + 475, + 555, + 499 + ], + "spans": [ + { + "bbox": [ + 54, + 475, + 555, + 499 + ], + "type": "text", + "content": "Table 1. Quantitative (Flip Rate / L2 / FID) and human user study (perceived change/similarity/realism) results. *DVCE without cone projection." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 508, + 295, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 508, + 295, + 651 + ], + "spans": [ + { + "bbox": [ + 54, + 508, + 295, + 651 + ], + "type": "text", + "content": "similar to adversarial attacks, hence hardly interpretable. SHAP attributions provide less informative patch-like artifact. FreeMCG, on the other hand, produces high quality and interpretable attributions that are similar to SHAP, but retaining the high-frequency details as it does not rely on arbitrary pixel clustering. In ROAD evaluation, we see that FreeMCG achieves the steepest decline in model prediction among gradient-based methods, corresponding to better feature attributions, closer to the lower-bound computed by SHAP. Additional comparison against other removal-based black-box methods [36, 38] can be found in Appendix E." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 667, + 128, + 680 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 667, + 128, + 680 + ], + "spans": [ + { + "bbox": [ + 55, + 667, + 128, + 680 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "content": "We developed Derivative-Free Diffusion Mainfold Constrained Gradients (FreeMCG), an approximation of a neu" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 508, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 508, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 508, + 555, + 712 + ], + "type": "text", + "content": "ral network's gradient tangent to the data manifold, obtained without access to the model weights or its real gradients. Previous explainability literature on gradient-based feature attribution and counterfactual generation have remained largely separate because the gradient could not be readily employed for counterfactual generation as it produces adversarial attacks. With FreeMCG, one can obtain gradient directions on the image manifold that produce semantically meaningful counterfactual explanations and feature attributions. We demonstrate through experiments that FreeMCG enables a unified framework for both explainability methods with state-of-the-art results, all without access to model weights. FreeMCG still assumes black-box access to the model's logits; in more restricted scenarios where only class predictions are available, FreeMCG would not be applicable, highlighting a limitation that could inspire future work on extending FreeMCG to such settings." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23802" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 158, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "type": "text", + "content": "This work was supported by the National Research Foundation of Korea (NRF) under Grants RS-2024-00336454 and RS-2023-00262527, and by the Institute for Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (RS-2019-II190075, Artificial Intelligence Graduate School Program, KAIST)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 184, + 115, + 197 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 184, + 115, + 197 + ], + "spans": [ + { + "bbox": [ + 56, + 184, + 115, + 197 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 205, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 205, + 296, + 248 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 205, + 296, + 248 + ], + "spans": [ + { + "bbox": [ + 61, + 205, + 296, + 248 + ], + "type": "text", + "content": "[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. 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Ensemble kalman diffusion guidance: A derivative-free method for inverse problems. arXiv preprint arXiv:2409.20175, 2024. 4, 5, 10" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23805" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_content_list.json b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..89617eb34a3b92fecae9369fd28aa68a5e9cf9c7 --- /dev/null +++ b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_content_list.json @@ -0,0 +1,1224 @@ +[ + { + "type": "text", + "text": "Descriptor-In-Pixel : Point-Feature Tracking for Pixel Processor Arrays", + "text_level": 1, + "bbox": [ + 135, + 130, + 859, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Laurie Bose $^{1,2}$ Jianing Chen $^{1,2}$ Piotr Dudek $^{1,2}$", + "bbox": [ + 292, + 179, + 702, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1The University of Manchester, Department of EEE, Manchester, United Kingdom", + "bbox": [ + 173, + 198, + 823, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Visionchip Limited, Manchester, United Kingdom", + "bbox": [ + 295, + 215, + 700, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://lauriebose.github.io/DIP", + "bbox": [ + 374, + 234, + 622, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 286, + 326, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper presents a novel approach for joint point-feature detection and tracking, designed specifically for Pixel Processor Array (PPA) vision sensors. Instead of standard pixels, PPA sensors consist of thousands of \"pixel-processors\", enabling massive parallel computation of visual data at the point of light capture. Our approach performs all computation entirely in-pixel, meaning no raw image data need ever leave the sensor for external processing. We introduce a Descriptor-In-Pixel paradigm, in which a feature descriptor is held within the memory of each pixelprocessor. The PPA's architecture enables the response of every processor's descriptor, upon the current image, to be computed in parallel. This produces a \"descriptor response map\" which, by generating the correct layout of descriptors across the pixel-processors, can be used for both point-feature detection and tracking. This reduces sensor output to just sparse feature locations and descriptors, read-out via an address-event interface, giving a greater than $1000 \\times$ reduction in data transfer compared to raw image output. The sparse readout and complete utilization of all pixel-processors makes our approach very efficient. Our implementation upon the SCAMP-7 PPA prototype runs at over 3000 FPS (Frames Per Second), tracking point-features reliably under violent motion. This is the first work performing point-feature detection and tracking entirely in-pixel.", + "bbox": [ + 86, + 318, + 485, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 728, + 220, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Point-features are distinct points within an image, chosen to be clearly identifiable within multiple images of the same scene, even under changes such as scale, lighting, and perspective. The various methods of point-feature detection and tracking are some of the most widespread tools in computer vision, playing a vital role in Visual Odometry and Simultaneous Localisation and Mapping (SLAM). Many mo", + "bbox": [ + 89, + 755, + 482, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d1d908ffdc1f5eb9ddec4fa0ca774d2018ce1db0f267728172e84b1c80770aaa.jpg", + "image_caption": [ + "Figure 1. A smartphone and SCAMP-7 PPA are strapped together and shaken violently. The frames are not fully synchronised, but it is clear the smartphone's 60 FPS image is unusable, while at 3000 FPS our approach continues tracking features without issue." + ], + "image_footnote": [], + "bbox": [ + 516, + 285, + 905, + 414 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "bile systems such as virtual-reality headsets and unmanned aerial vehicles rely extensively on point-features, often from multiple cameras, to continuously estimate the system's pose. Such systems have limited on-board computational power, limited battery life, and often require low-latency response due to rapid motion. This has pushed the need for computational efficiency, but despite many advancements, the basic task of image transfer from sensor to processor remains a significant time and power bottleneck.", + "bbox": [ + 509, + 507, + 906, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This issue ultimately reflects the dominant paradigm in electronic imaging, where sensors are primarily built to capture images for a human observer, rather than efficient visual computing. In the context of point-feature detection and tracking, whole images are distilled down to a sparse handful of key-points and descriptors. This is a tiny amount of data compared to the original image, yet standard cameras must still transfer whole images to external processing, repeatedly every frame. This paper presents an alternative, a novel implementation of point-feature detection and tracking for an emerging sensor paradigm, the Pixel-Processor Array (PPA) [9]. Traditional cameras consist of an array of light capture elements, while PPAs are an array of programmable pixel-processors or \"Processing Elements\" (PEs). Each of these processors has its own local memory on which it can perform various computations, and communication with neighbouring processors enabling", + "bbox": [ + 511, + 643, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "This work has been funded in part by EPSRC, grant number EP/Y023048/1.", + "bbox": [ + 89, + 875, + 482, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5392", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "data transfer across the array. Images are captured directly into the array, with each PE capturing a single pixel of the whole image into its local memory. This sensor architecture enables massively parallel \"in-pixel\" computation upon the focal plane, with the PE array operating as a Single Instruction Multiple Data (SIMD) computer. Such a sensor can capture visual data, extract high level information, and then output only this sparse data, thereby removing the image output bottleneck.", + "bbox": [ + 89, + 90, + 480, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our in-pixel approach for point-feature detection and tracking is designed specifically for the PPA's architecture, providing high pixel-processor compute resource utilisation, and minimizing data transfer between sensor and external processing. The core of our approach is based around the concept of \"Descriptor-In-Pixel\", whereby each PE holds a complete point-feature descriptor within its own local memory. The PPA computes in parallel the response of every PE's descriptor upon a captured image. By generating the correct layout of descriptors every frame across the PE array, the computed \"response map\" can be used for both point-feature detection and tracking. All computation is performed within the PPA's pixel-processors (the PE array), without any additional external processing on PC or microcontroller. Therefore, dense sensor output, such as images, is no longer necessary. Instead, only the coordinates of tracked point-features and the descriptors of newly initialized point-features are output, providing a greater than $1000 \\times$ data reduction compared to whole images. Any additional image data in this paper is output purely for visualization purposes, and is not required for our approach to operate. Our implementation upon the SCAMP-7 PPA prototype [6] achieves speeds just above 3000 frames per second (FPS), with an average sensor output of just 2 bytes per feature, per frame, demonstrating the PPAs potential in high-speed applications (Figure 1).", + "bbox": [ + 91, + 227, + 482, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 89, + 633, + 238, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prior PPA Based Works: At the time of writing there are few other works regarding point-feature detection and tracking for PPAs. The early work of [8] demonstrated an implementation of the FAST corner detector [17] at 2300 FPS on SCAMP-5. This work does not perform any form of tracking, and simply outputs the coordinates of detected corner points from the sensor. Performing feature tracking/correspondence using nothing but point coordinates is very challenging, especially as FAST uses no information from previous frames to inform detection, leading to poor temporal stability of detected points between frames. BITVO [16] took steps to address this by outputting a binary edge image alongside the corner points detected by FAST. From these edge images corner descriptors are computed, which are then used in tracking corner points between frames. While this improves tracking quality, the need to", + "bbox": [ + 89, + 657, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "output a full resolution binary image to external processing introduces a significant bottleneck, limiting performance to 300 FPS. The solution to this is performing both detection and tracking entirely on-sensor, avoiding the need to output dense visual information to external processing. This is the motivation behind our approach, which uses purely on-sensor compute to detect and track point-features at thousands of frames per second.", + "bbox": [ + 511, + 90, + 903, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event Cameras: Event cameras are another alternative visual sensor [10], outputting a stream of \"events\" which encode time, location and polarity of brightness changes at the per-pixel level. Many works have demonstrated pointfeatures upon event cameras, some using just the raw event stream [15], others incorporating image data into their approach [20], [11], [14]. With the event camera's very high dynamic range and temporal resolution, many of these works produce impressive results, tracking features in rapid motion and challenging lighting conditions. One drawback of event cameras is the complexity involved in dealing with their sparse asynchronous event data (a price paid in exchange for the sensor's very high temporal resolution). This can lead to significant computational costs, and while earlier works may use only a standard desktop CPU [20], recent works require a high-end 300 watt GPU for close to real-time performance [14]. In contrast, a strength of the PPA is that it still allows visual computation to be performed upon captured image frames, instead of complex asynchronous event data. By performing all computation in-pixel, temporal resolutions and latencies comparable to event camera based methods can be achieved, but at a reduced total energy cost.", + "bbox": [ + 511, + 212, + 903, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional Point-Feature Tracking: Many traditional point-feature approaches such as ORB [18] work by locating salient points (using methods such as FAST [17]), and building descriptors for each of these points. Point-features are then tracked by matching their descriptors against those of salient points detected in the current frame. However, separating detection and tracking into two disjoint processes allows a tracked feature's associated salient point to be missed in detection, potentially replaced by a different salient point in close proximity. This can result in tracked features \"flickering\" as their salient points are temporarily lost. By contrast our approach uses the same mechanism (descriptor response) for both detection and tracking for reliable re-detection of existing features.", + "bbox": [ + 511, + 559, + 903, + 770 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. SCAMP Overview", + "text_level": 1, + "bbox": [ + 511, + 784, + 692, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate an implementation of our approach upon the SCAMP-7 PPA system [6]. Shown in Figure 2, this vision sensor device has an image resolution of $256 \\times 256$ , giving a total of 65,536 pixel-processors (PEs). Each processor is connected to its four immediate neighbours, forming a network for data transfer across the array. For local mem", + "bbox": [ + 511, + 810, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5393", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ory, each pixel-processor has 23 1-bit digital registers, and 7 analogue registers which store continuous values. Various operations upon local memory are supported, such as addition and subtraction of analogue registers, boolean logic between digital registers, and thresholding of analogue values to digital results. Light is captured separately by each processor, and with each frame trigger, converted to analogue values. Thus each processor captures one pixel of an image that spans the whole array.", + "bbox": [ + 89, + 90, + 480, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Each pixel-processor does not store and execute its own program instructions, instead a centralised controller broadcasts identical instructions to all 65,536 processors in parallel, which then execute each instruction concurrently. Thus the array operates in a Single Instruction Multiple Data (SIMD) mode, similar to GPU compute. Importantly each pixel-processor contains a 1-bit \"activity flag\" register for enabling and disabling the execution of instructions, allowing for per-pixel conditional execution. By writing programs for the controller, the processor array can be made to execute entire vision applications in-pixels, and output only specific extracted information. Various tasks have been demonstrated on this architecture including neural networks [4],[19],[21],[3], visual odometry [16],[2],[12], and eye tracking [5].", + "bbox": [ + 91, + 227, + 486, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Approach Overview", + "text_level": 1, + "bbox": [ + 89, + 465, + 284, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach uses a novel Descriptor In-Pixel paradigm designed specifically to exploit the PPA's massively parallel, on-sensor computation. Three key components enabled by the PPA's architecture are as follows.", + "bbox": [ + 89, + 489, + 482, + 549 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. In-Pixel Descriptors. Our approach involves storing a complete point-feature descriptor within each PE's local digital memory, essentially storing a descriptor at each pixel location.", + "2. Parallel Descriptor Computation. The PPA captures image frames directly into the PE array, with each PE capturing one pixel into its local analogue memory. By examining the pixel data of surrounding PEs, each PE can compute a descriptor for its local image content. This descriptor computation can be performed for every PE (i.e. every pixel location) simultaneously in parallel.", + "3. Parallel Descriptor Response Computation. Comparison between stored descriptors and those computed from captured image can be performed in parallel across all PEs. This generates a \"response map\", indicating how strongly the stored descriptors correlate or \"match\" with the captured image content." + ], + "bbox": [ + 89, + 551, + 482, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The descriptors distributed across the PE array follow a specific layout, surrounding each tracked point-feature's location with PEs storing its descriptor. This descriptor layout is generated every frame by spreading the descriptors of tracked features into nearby PEs. After computing the response of these stored descriptors on the current image", + "bbox": [ + 89, + 810, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6fc6210d9a997b16b723ad00e9d85017993c935ce3bbafc1d22220f3911eade1.jpg", + "image_caption": [ + "Figure 2. SCAMP-7 has $256 \\times 256$ pixel-processors, each which can capture light, store and process data within its local memory registers, and transfer data to neighbouring processors. A controller sequentially transmits SIMD instructions to the processor array for execution." + ], + "image_footnote": [], + "bbox": [ + 517, + 87, + 906, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "frame, each tracked feature will be surrounded by a patch of response from its own descriptor. These response patches are analysed in parallel, determining the new location of each tracked feature. This tracking requires that features do not move further than the predetermined patch area between frames. However, our approach can operate at thousands of frames per second, allowing patch areas to be very small $(9 \\times 9)$ and still facilitate reliable tracking. New point-features are detected and initialized by analysing the responses of those PEs not inside the patch of any tracked feature. These aspects will be described later in detail.", + "bbox": [ + 511, + 417, + 908, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In summary, our approach performs all necessary computation within the PE array, each feature is tracked between frames using pixel-processors surrounding its location, while all remaining pixel-processors perform a search to detect new features. This approach is very efficient essentially utilizing $100\\%$ of the PPA's compute, and also allows sensor output to be reduced to simply the locations and descriptors of tracked features. As a result, our approach can operate at thousands of frames per second upon SCAMP-7.", + "bbox": [ + 511, + 592, + 908, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "5. In-Pixel Descriptors", + "text_level": 1, + "bbox": [ + 511, + 762, + 705, + 780 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We make use of simple binary point descriptors, similar to the well known BRIEF descriptor [7]. Such descriptors are stored as binary strings within each PE, occupying multiple digital registers (1 bit per register). Computing a PE's descriptor for a given image involves comparing pairs of pixel data around its location, each comparison generating 1 bit of the descriptor's string. Specifically, the $i^{th}$ bit of the de", + "bbox": [ + 511, + 794, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5394", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2c323482fd614d634e069bca887b091ddb4a61865ebe5a80b6ea5ab9ad52997b.jpg", + "image_caption": [ + "Figure 3. Examples of simple descriptor response maps, where the same 8-bit descriptor is stored inside all PEs. Maps are generated for three example descriptors, all using the same sampling pattern (Bottom Left), and input image (Top Left). For comparison we generate response maps using both our weight pixel-pairs method, and the Hamming distance. High response \"blobs\" pinpoint certain visual structures, but those from the Hamming distance can be unreliable for tracking, as illustrated in Teal." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 903, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "scriptor, $d_{i}$ , is computed as", + "bbox": [ + 89, + 527, + 272, + 542 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} p _ {i (1)} < p _ {i (2)} \\\\ 1, & \\text {i f} p _ {i (1)} \\geq p _ {i (2)} \\end{array} \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 550, + 482, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p_{i(1)}, p_{i(2)}$ are a pair of pixel values at locations relative to the PE's location, according to some predetermined sampling pattern.", + "bbox": [ + 89, + 599, + 482, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Descriptor Size: For maximum efficiency, an entire descriptor should be stored within each PE (i.e. one descriptor per pixel location). However, PE local memory on SCAMP-7 is very limited, restricting this first demonstration of our approach to tiny 8-bit descriptors, performing just eight local pixel pair comparisons. Due to how our approach operates, these are still sufficient for reliable high-speed feature tracking. Larger descriptors could be utilized on future PPA hardware, with greater memory per PE. Note, using significantly larger descriptors $(128+$ bit) would likely not improve tracking in our approach, but these would be better suited to long term tasks such as re-localisation.", + "bbox": [ + 89, + 643, + 482, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Descriptor Sampling Pattern: Computing the binary descriptor for a specific pixel location involves comparing pairs of pixels, sampled in a given pattern about that location. This \"sampling pattern\", is chosen with the aim to compress the local image into a compact bit string, cap", + "bbox": [ + 89, + 825, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "turing any discriminative structures within the local image content. BRIEF [7] uses fixed random sampling patterns, which are too large (128+ bit) to use for in-pixel descriptors. Instead we use fixed sampling patterns similar to the BRISK [13] & FREAK [1] descriptors. We only use a single sampling pattern during operation, for all descriptors across all PEs, as this enables us to fully exploit the PPA's parallel SIMD compute. We opted for a 'compare-to-center' sampling pattern (see Figure 3) due to its simplicity and low computational cost, though many other patterns could be used.", + "bbox": [ + 511, + 527, + 906, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "6. Descriptor Response-Maps", + "text_level": 1, + "bbox": [ + 511, + 708, + 764, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With each new image frame our approach generates a layout of descriptors stored across the PE array, and then computes the \"response\" of each PE's stored descriptor. Descriptor response refers to how strongly the visual features represented by a specific descriptor are present at a certain location within an image. Measuring the response of a PE's stored descriptor first involves computing the descriptor for the image at that PE's location. The computed image descriptor is then compared to the PE's stored descriptor. A higher similarity between the two indicates that the stored descriptor more accurately represents the local image con", + "bbox": [ + 511, + 734, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5395", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4575cc1cdd37059b132aba9ea8c59df5c8e6e50d904f1a66152a932e5cbb072c.jpg", + "image_caption": [ + "Figure 4. Descriptor layout described in Section 7. Each PE stores an 8-bit descriptor within its digital registers. Tracked features are surrounded by patches of PEs storing their descriptor (shown by various colours). PEs outside such patches store the current search descriptor. Additionally, 1 digital register in each PE indicates if tracked feature is located there (shown in yellow)." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 486, + 198 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5e246ef0d872e69f2d92c2393f319932428f0488dd87bfe426814f8f1ab28a75.jpg", + "image_caption": [ + "Figure 5. Left: A \"patchwork\" response map computed using the descriptor layout of Section 7. Right: Corresponding captured image & tracked features. Two response patches $(9 \\times 9$ PEs) from different features are shown in detail." + ], + "image_footnote": [], + "bbox": [ + 91, + 301, + 483, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tent. Thus, as will be described, descriptor response should correlate to a measurement of this similarity.", + "bbox": [ + 89, + 563, + 482, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The PPA architecture enables the response of every PEs stored descriptor to be computed in parallel, and placed into local analogue memory, forming a \"descriptor response map\" spread across the PE array. Figure 3 shows simple response maps, with all PEs storing the same descriptor.", + "bbox": [ + 89, + 595, + 483, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Measuring Descriptor Similarity and Response: A simple measure of similarity between binary descriptors is to compute the number of matching bits between their bit strings (i.e. Hamming distance), a common choice on traditional digital processing, being very cheap to compute. SCAMP-7 however has analogue computation capability, and captures images directly into its PE array as analogue data. For almost no additional cost, this analogue compute allows to also account for the raw pixel data when computing descriptor response. This is very useful for handling image regions that will not provide reliable point-feature tracking, such as low texture or highly repetitive texture regions. Descriptors inside such \"ambiguous\" regions will have poor temporal stability, as very slight image changes (from noise or lighting) will produce radically different de", + "bbox": [ + 89, + 674, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "scriptors from one frame to the next. Thus we do not simply measure the number of matching bits between descriptors, but also weight these matches (and penalize misses) by the magnitude of the pixel pair comparison results associated with each bit. Specifically, we compute the response $R$ of a stored descriptor at a certain image location as follows:", + "bbox": [ + 511, + 90, + 906, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR = \\sum_ {i = 1} ^ {8} (2 d _ {i} - 1) \\left(p _ {i (1)} - p _ {i (2)}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 191, + 906, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d_{i} \\in \\{0,1\\}$ , is the $i^{th}$ bit of the descriptor, and $p_{i(1)}, p_{i(2)} \\in \\Re$ are the pixel values for the $i^{th}$ pair of pixels, selected according to the descriptor's sampling pattern. This ensures high descriptor response is only produced in image regions which can provide reliable tracking. Figure 3 shows example response maps generated using both this weighted pixel-pairs method, and the Hamming distance.", + "bbox": [ + 511, + 243, + 906, + 351 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "7. Descriptor Layout", + "text_level": 1, + "bbox": [ + 513, + 364, + 692, + 382 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The response maps of Figure 3 are simple examples, with the same descriptor being stored inside every PE. In practice, with every captured frame, our approach generates a layout of various descriptors across the PE array. This descriptor layout enables the computed response maps to be used for both point-feature tracking and detection. Generation of this layout splits all PEs into one of two categories.", + "bbox": [ + 511, + 388, + 905, + 494 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. PEs Located Near Tracked Point-Features. Each tracked point-feature's descriptor is spread into a local \"patch\" of PEs surrounding its location (i.e. around the PE the feature currently resides in). The computed response map will then have each tracked feature surrounded by responses from its own descriptor, from which the feature's new location can be determined.", + "2. All Remaining PEs. A single \"search descriptor\" is loaded into all remaining PEs, not located close to any tracked feature. The responses from this descriptor are examined to detect new point-features. To detect different features, the search descriptor itself is randomized every frame." + ], + "bbox": [ + 514, + 497, + 905, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To generate this descriptor layout, the search descriptor is first loaded into all PEs in parallel, excluding PEs containing tracked point-features. Next the descriptors of tracked point-features are spread out from their containing PEs, across a small local patch of PEs $(9 \\times 9)$ . This descriptor spreading is also performed for every tracked point-feature in parallel. Figure 4 illustrates this layout, and the digital registers used with each PE for descriptor storage, and indication of a tracked feature's location.", + "bbox": [ + 511, + 696, + 905, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "8. Patchwork Response Map", + "text_level": 1, + "bbox": [ + 511, + 844, + 756, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The descriptor layout described in Section 7 generates response maps which have distinct patches of response, one", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5396", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3d1bbf5115940a847d4c86f6aceed318c0af3f504d991eb45cf335768eaea079.jpg", + "image_caption": [ + "Figure 6. Steps for updating locations of tracked features, computation of the patchwork descriptor response map, blob-detection & NMS." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 903, + 247 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for each tracked point-feature. Each feature's patch is centred upon its last known location, and contains responses from its descriptor. PEs outside these patches will contain responses from the current search descriptor. When visualized these response maps have a \"patchwork\" like appearance as shown in Figure 5. These patchwork response maps contain sufficient information to both detect reliable new point-features, and update the locations of existing tracked point-features. They also require no additional computation: by simply storing different descriptors across the PE array, the responses used for both tracking and detecting point-features are all computed in parallel.", + "bbox": [ + 88, + 299, + 480, + 481 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "9. Point-Feature Detection", + "text_level": 1, + "bbox": [ + 89, + 496, + 313, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Descriptor response is the mechanism by which our approach both detects and tracks point-features. With each new frame a patchwork response map (as described in Section 8) is computed. Feature detection involves searching for any locations where the search descriptor's response strongly identifies some underlying visual point-feature. These locations appear as small distinct regions of high response, surrounded by low response. High response indicates the strong presence of visual features matching the search descriptor, while the surrounding low response indicates these features are distinct to a specific location (i.e. a point-feature). These high response \"blobs\" (such as shown in Figure 6), are prime candidates at which to initialize new point-features, as their location can be reliably tracked by the descriptor's local response.", + "bbox": [ + 91, + 522, + 482, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Blob Detection: To locate new point-feature candidates (and also track existing features), blob detection is performed upon each frame's response map, at a scale of the descriptor sampling patterns size. Strong blob detection responses then represent reliable point-feature candidates. Figure 6 illustrates this process: from image, to response map, to blob detection result.", + "bbox": [ + 89, + 750, + 482, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Point-Feature Initialization: Our approach uses one digital register within each PE to signify if there is a tracked point-feature at its location, with PEs containing tracked", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "features then also storing the descriptor of that feature (see Figure 4). This scheme, storing point-features within local PE memory, enables all features to be tracked in parallel.", + "bbox": [ + 511, + 300, + 903, + 344 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To initialize new features, thresholding is performed upon the blob detection result. This is used to identify the PEs located at the centres of the strongest blobs, which are the best candidates for new point-features. New features are then added by simply setting the digital register to signify the presence of a tracked point-feature within each of these PEs.", + "bbox": [ + 511, + 345, + 903, + 449 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Descriptor Readout: Whenever a new point-feature is initialized, we can optionally read out its descriptor from the sensor. This is unnecessary for feature tracking, but could be used for additional tasks or simply for visualization. The descriptor readout is performed sequentially over multiple frames, 1 bit per frame. This still allows hundreds of 8-bit descriptors to be read out per second, but minimizes spikes in the processing time per frame ( $< 1\\mu s$ ).", + "bbox": [ + 511, + 450, + 905, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is also possible to generate and read out longer descriptors for each new feature (instead of the short 8-bit descriptors used for in-pixel tracking). These could be used by external off-sensor processing to re-identify past features, which left the sensor's view, such as for SLAM system loop-closure/relocalisation. This is beyond the scope of this paper, but should be a relatively straightforward extension.", + "bbox": [ + 511, + 573, + 905, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "10. Feature Tracking", + "text_level": 1, + "bbox": [ + 514, + 693, + 692, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "With each new captured frame the locations of tracked point-features must be updated. This is done by finding the local maximum of each feature's descriptor response, around that feature's previous location. The PE containing this maximum is then taken to be that of the feature's new location. This can be viewed as similar to a gradient descent process, with each feature's location following the local maxima of its descriptor response, which evolves in time with each captured frame. For each frame, the descriptor layout of Section 7 is generated, and used to compute the patchwork response maps of Section 8. These response maps have each tracked feature surrounded by a", + "bbox": [ + 511, + 719, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5397", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/45614405749667eb703daf02b588345964b86395e47ac8663c7fcf7638e2d8ea.jpg", + "image_caption": [ + "Figure 7. Examples of feature tracking on SCAMP-7. Left Column: Trails of point-features tracked by SCAMP-7, with thickness representing age. Right Column: 60 FPS video from smartphone mounted alongside SCAMP-7. Our approach tracks features reliably under motion that renders the smartphone's image near unusable. Here SCAMP-7 also outputs an image temporally $(1/16^{th}$ per frame) for visualization, limiting performance to around 850 FPS. The motion blur in SCAMP-7 images shown is an artefact of this image readout scheme, and is not present internally." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 480, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "patch of response from its own descriptor. After performing blob detection upon this response map, a patch-wise, nonmaximum-suppression (NMS) routine is performed. This identifies the PEs of highest response within every feature's patch, which are taken to represent each feature's new location. This process is illustrated in Figure 6. It should be noted, that point-features are typically considered to be 1-pixel in size. In practice, however, it is not necessary to", + "bbox": [ + 89, + 779, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ensure the NMS routine produces single pixels, just well-located, distinct, and small cluster of pixels.", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Dropping Weak Features: After computing the descriptor response map for a new frame, there may exist some tracked features with no high values in their associated descriptor response patches. This indicates the visual feature associated with that point-feature's descriptor is no longer clearly identifiable due to occlusion, lighting, or perspective changes. Such features can no longer be reliably tracked by descriptor response. The PEs containing such features are located by thresholding the response map, and their features removed by setting the digital register signifying feature presence to false.", + "bbox": [ + 511, + 123, + 906, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Benefits From High Frame-Rate: The very high speed at which our approach operates significantly simplifies feature tracking. Captured images will barely change from one frame to the next, and the motion of point-features is reduced to a gradual crawl across the PE array. Specifically two major benefits are:", + "bbox": [ + 511, + 290, + 908, + 381 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Reduced Motion Blur. Motion blur in captured images is reduced significantly, if not entirely eliminated, even under violent sensor motion. This helps ensure the visual features underlying each tracked point-feature remain clear and consistent from one image to the next.", + "2. Reduced Feature Location Search. As captured image will change very little from one frame to the next, so to will the locations of any tracked point-features. This allows the search for each tracked point-feature's new location to be limited to a small region around its previous location, $9 \\times 9$ PEs in SCAMP-7." + ], + "bbox": [ + 514, + 387, + 906, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "11. SCAMP Implementation", + "text_level": 1, + "bbox": [ + 514, + 571, + 756, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The current implementation of our approach on SCAMP-7 can run at just over 3000 FPS. While optimized, further code improvements may still exist. A breakdown of the total computation time per frame is given in Table 1. To put these numbers into perspective, the time taken to output a full uncompressed image from the sensor is well over $20000\\mu s$ , and even a 4-bit image requires $2700\\mu s$ . Our approach avoids such bottlenecks by performing all necessary computation entirely on-sensor, and outputting only sparse feature locations and descriptors. Examples of real-time output are shown in Figure 7, showcasing point-feature tracking under rapid motion to a degree not possible with a traditional camera sensor. It is worth noting that the SCAMP-7 chip is a research prototype, created using an old $180\\mathrm{nm}$ CMOS manufacturing process, with relatively low clock speeds, very restrictive memory per PE, and significantly higher power usage than what is possible using today's state-of-the-art semiconductor technology. That our approach can achieve such performance upon this device is an indication of the potential of the PPA sensor paradigm.", + "bbox": [ + 511, + 598, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5398", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "12. Evaluation", + "text_level": 1, + "bbox": [ + 91, + 89, + 217, + 104 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "An exact evaluation of our approach against traditional methods is difficult for a number of reasons. Firstly to reach its full potential, our approach must operate at very high frame-rates to ensure small inter-frame motion (at a minimum 500 FPS). This is no issue for our PPA implementation, which can capture and process images at thousands of frames per second, but the number of datasets applicable to feature-tracking captured at such frame rates is very limited. Further testing our PPA implementation upon any such dataset would involve uploading each video frame sequentially into the PPA's PE array to emulate image capture. SCAMP-7 was never designed with this in mind, and uploading such large quantities of data is not efficient and prone to errors. As such we deemed evaluation using high frame rate datasets that would involve uploading thousands of sequential images not feasible.", + "bbox": [ + 89, + 114, + 483, + 354 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We instead performed a comparison against feature tracking using a SCAMP-7 implementation of FAST keypoint detector. This is chosen also because it has speed comparable to our approach, and thus potentially able to track features under the same rapid motion. A modified implementation of [8] was used, which outputs corner point coordinates from the SCAMP-7. Simple point-feature tracking is then performed by matching each corner point with its closest corner point from the previous frame. To match corner points purely by frame-to-frame location (proximity), they must be within a small threshold distance (e.g. 5 pixels). We compare our approach against this FAST based tracking by recording the output of both approaches, viewing the same scenes, running at the same speed of 1000 FPS, using a very similar sequence of sensor motions for both approaches. Some of these motions keep parts of the scene in constant view, allowing some features to be tracked throughout the entire motion. We record how long every feature is tracked for before it is lost, with results for each motion sequence shown in Figure 8. Note, we also do not count any \"poor quality\" features from the FAST approach, which have lifetimes of less than 0.25 seconds. The distribution of feature lifetimes in these histograms give a sense of how reliable the approaches are comparatively. For example, under the 'Translate' motion, $90\\%$ of features using FAST based tracking were lost within 5 seconds, and $0\\%$ of features were tracked for over 15 seconds, compared to around $20\\%$ with our approach. It is clear from the ratio of feature lifetimes that our approach is far more reliable at tracking features for any significant length of time.", + "bbox": [ + 89, + 356, + 483, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations In our current implementation, only the locations and descriptors of tracked features are represented in-pixel. Consequently, feature tracking has no concept of orientation and scale, making it non-invariant to rotation and scaling. While this is a significant limitation, we argue that it is not a fundamental drawback of the Descriptor-In-Pixel", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fee27e5dd2f2dd156f021b97cff429ba909b447bd553caa9038b1ed3af13f977.jpg", + "table_caption": [ + "Table 1. SCAMP-7 Computation Time Breakdown." + ], + "table_footnote": [], + "table_body": "
TaskCompute Time μs%
Descriptor Response Map19260
Feature Initialization3110
Feature-Wise NMS4113
Misc/Other Computation5717
Total321-
", + "bbox": [ + 524, + 114, + 890, + 210 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a151d29e22f1ebc0a79f59bc7d166050d6b3ffd6f160f23fbd4521b39d6e408.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 229, + 705, + 316 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2aaa2183b1f5fbfd565e6ca30830ab6945f39e55e6ed2290e11aece25ae8244f.jpg", + "image_caption": [ + "Figure 8. Comparison of feature lifetime histograms, our approach vs tracking based on FAST keypoints, under different sensor motions. Both approaches are run at 1000 FPS on SCAMP-7 for comparison. Features tracked using our approach have significantly longer lifespans in general as shown by the ratio." + ], + "image_footnote": [], + "bbox": [ + 517, + 319, + 709, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6ab33b15fa31be0bfc5cd3a3d55af1b47546d02a2f7e9b25f344dd9ceeab526d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 229, + 903, + 316 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5a7af89008f7a807648aa8329166a8a742cae068411007675f95fadb21fba177.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 319, + 903, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "approach but rather a constraint imposed by the current state of PPA hardware, which remains in the early stages of development. Specifically, the limited memory within each PE makes storing additional information, such as a feature's orientation, challenging. We expect that as future PPA devices increase memory capacity per PE, our method can be extended to support rotational and scale-invariant tracking.", + "bbox": [ + 511, + 530, + 906, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "13. Conclusion", + "text_level": 1, + "bbox": [ + 514, + 671, + 643, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presented a novel approach for performing point-feature detection and tracking on PPA architectures, demonstrated upon the SCAMP-7 system. Our approach is entirely performed within the pixel-processors of the PPA, and does not require external PC or micro-controller processing. We introduce the concept of Descriptor-In-Pixel which enables our approach to detect and track features by parallel computation of descriptor response across the processing array. This brings major performance benefits allowing our approach to operate at 3000 FPS, on a portable \"smart camera\" vision system, using around 1 watt of power, reliably tracking point-features under violent motion which renders traditional sensors unusable.", + "bbox": [ + 511, + 704, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5399", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexandre Alahi, Raphael Ortiz, and Pierre Vandergheynst. FREAK: Fast retina keypoint. In 2012 IEEE conference on computer vision and pattern recognition, pages 510-517. IEEE, 2012. 4", + "[2] Laurie Bose, Jianing Chen, Stephen J Carey, Piotr Dudek, and Walterio Mayol-Cuevas. Visual odometry for pixel processor arrays. In Proceedings of the IEEE International Conference on Computer Vision, pages 4604-4612, 2017. 3", + "[3] Laurie Bose, Jianing Chen, Stephen J. Carey, Piotr Dudek, and Walterio Mayol-Cuevas. A camera that CNNs: Towards embedded neural networks on pixel processor arrays. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2019. 3", + "[4] Laurie Bose, Piotr Dudek, Jianing Chen, Stephen J Carey, and Walterio W Mayol-Cuevas. Fully embedding fast convolutional networks on pixel processor arrays. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXIX 16, pages 488-503. Springer, 2020. 3", + "[5] Laurie Bose, Jianing Chen, Stephen J Carey, and Piotr Dudek. Pixel processor arrays for low latency gaze estimation. In 2022 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW), pages 970-971. IEEE, 2022. 3", + "[6] Laurie Bose, Piotr Dudek, Stephen J Carey, and Jianing Chen. Live demonstration: Scamp-7. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3995–3996, 2023. 2", + "[7] Michael Calonder, Vincent Lepetit, Mustafa Ozuysal, Tomasz Trzcinski, Christoph Strecha, and Pascal Fua. BRIEF: computing a local binary descriptor very fast. IEEE transactions on pattern analysis and machine intelligence, 34(7):1281-1298, 2011. 3, 4", + "[8] Jianing Chen, Stephen J Carey, and Piotr Dudek. Feature extraction using a portable vision system. In IEEE/RSJ Int. Conf. Intell. Robots Syst., Workshop Vis.-based Agile Auton. Navigation UAVs, 2017. 2, 8", + "[9] Piotr Dudek, Thomas Richardson, Laurie Bose, Stephen Carey, Jianing Chen, Colin Greatwood, Yanan Liu, and Walterio Mayol-Cuevas. Sensor-level computer vision with pixel processor arrays for agile robots. Science Robotics, 7(67): eabl7755, 2022. 1", + "[10] Guillermo Gallego, Tobi Delbrück, Garrick Orchard, Chiara Bartolozzi, Brian Taba, Andrea Censi, Stefan Leutenegger, Andrew J Davison, Jörg Conradt, Kostas Daniilidis, et al. Event-based vision: A survey. IEEE transactions on pattern analysis and machine intelligence, 44(1):154-180, 2020. 2", + "[11] Daniel Gehrig, Henri Rebecq, Guillermo Gallego, and Davide Scaramuzza. Asynchronous, photometric feature tracking using events and frames. In Proceedings of the European Conference on Computer Vision (ECCV), pages 750-765, 2018. 2", + "[12] Colin Greatwood, Laurie Bose, Thomas Richardson, Walterio Mayol-Cuevas, Jianing Chen, Stephen J Carey, and Piotr Dudek. Perspective correcting visual odometry for agile MAVs using a pixel processor array. In 2018 IEEE/RSJ" + ], + "bbox": [ + 93, + 114, + 482, + 900 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "International Conference on Intelligent Robots and Systems (IROS), pages 987-994. IEEE, 2018. 3", + "[13] Stefan Leutenegger, Margarita Chli, and Roland Y Siegwart. BRISK: binary robust invariant scalable keypoints. In 2011 International conference on computer vision, pages 2548-2555. IEEE, 2011. 4", + "[14] Nico Messikommer, Carter Fang, Mathias Gehrig, and Davide Scaramuzza. Data-driven feature tracking for event cameras. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5642-5651, 2023. 2", + "[15] Elias Mueggler, Chiara Bartolozzi, and Davide Scaramuzza. Fast event-based corner detection. In British Machine Vision Conference (BMVC), 2017. 2", + "[16] Riku Murai, Sajad Saeedi, and Paul HJ Kelly. BIT-VO: Visual odometry at 300 fps using binary features from the focal plane. In 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 8579–8586. IEEE, 2020. 2, 3", + "[17] Edward Rosten and Tom Drummond. Machine learning for high-speed corner detection. In Computer Vision-ECCV 2006: 9th European Conference on Computer Vision, Graz, Austria, May 7-13, 2006. Proceedings, Part I 9, pages 430-443. Springer, 2006. 2", + "[18] Ethan Rublee, Vincent Rabaud, Kurt Konolige, and Gary Bradski. ORB: An efficient alternative to SIFT or SURF. In 2011 International conference on computer vision, pages 2564-2571. IEEE, 2011. 2", + "[19] Haley M. So, Laurie Bose, Piotr Dudek, and Gordon Wetzstein. PixelRNN: In-pixel recurrent neural networks for end-to-end-optimized perception with neural sensors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 25233–25244, 2024. 3", + "[20] David Tedaldi, Guillermo Gallego, Elias Mueggler, and Davide Scaramuzza. Feature detection and tracking with the dynamic and active-pixel vision sensor (DAVIS). In 2016 Second International Conference on Event-based Control, Communication, and Signal Processing (EBCCSP), pages 1-7. IEEE, 2016. 2", + "[21] Matthew Z Wong, Benoit Guillard, Riku Murai, Sajad Saeedi, and Paul HJ Kelly. AnalogNet: Convolutional neural network inference on analog focal plane sensor processors. arXiv preprint arXiv:2006.01765, 2020. 3" + ], + "bbox": [ + 516, + 93, + 903, + 712 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "5400", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_model.json b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e7f949deaa55ba0a6d67be852c2bf085f706bd68 --- /dev/null +++ b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_model.json @@ -0,0 +1,1560 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.137, + 0.131, + 0.861, + 0.154 + ], + "angle": 0, + "content": "Descriptor-In-Pixel : Point-Feature Tracking for Pixel Processor Arrays" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.18, + 0.704, + 0.199 + ], + "angle": 0, + "content": "Laurie Bose\\(^{1,2}\\) Jianing Chen\\(^{1,2}\\) Piotr Dudek\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.199, + 0.825, + 0.217 + ], + "angle": 0, + "content": "1The University of Manchester, Department of EEE, Manchester, United Kingdom" + }, + { + "type": "text", + "bbox": [ + 0.297, + 0.217, + 0.702, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\)Visionchip Limited, Manchester, United Kingdom" + }, + { + "type": "text", + "bbox": [ + 0.375, + 0.235, + 0.624, + 0.253 + ], + "angle": 0, + "content": "https://lauriebose.github.io/DIP" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.319, + 0.486, + 0.699 + ], + "angle": 0, + "content": "This paper presents a novel approach for joint point-feature detection and tracking, designed specifically for Pixel Processor Array (PPA) vision sensors. Instead of standard pixels, PPA sensors consist of thousands of \"pixel-processors\", enabling massive parallel computation of visual data at the point of light capture. Our approach performs all computation entirely in-pixel, meaning no raw image data need ever leave the sensor for external processing. We introduce a Descriptor-In-Pixel paradigm, in which a feature descriptor is held within the memory of each pixelprocessor. The PPA's architecture enables the response of every processor's descriptor, upon the current image, to be computed in parallel. This produces a \"descriptor response map\" which, by generating the correct layout of descriptors across the pixel-processors, can be used for both point-feature detection and tracking. This reduces sensor output to just sparse feature locations and descriptors, read-out via an address-event interface, giving a greater than \\(1000 \\times\\) reduction in data transfer compared to raw image output. The sparse readout and complete utilization of all pixel-processors makes our approach very efficient. Our implementation upon the SCAMP-7 PPA prototype runs at over 3000 FPS (Frames Per Second), tracking point-features reliably under violent motion. This is the first work performing point-feature detection and tracking entirely in-pixel." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.729, + 0.222, + 0.745 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.756, + 0.483, + 0.862 + ], + "angle": 0, + "content": "Point-features are distinct points within an image, chosen to be clearly identifiable within multiple images of the same scene, even under changes such as scale, lighting, and perspective. The various methods of point-feature detection and tracking are some of the most widespread tools in computer vision, playing a vital role in Visual Odometry and Simultaneous Localisation and Mapping (SLAM). Many mo" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.286, + 0.906, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.425, + 0.907, + 0.482 + ], + "angle": 0, + "content": "Figure 1. A smartphone and SCAMP-7 PPA are strapped together and shaken violently. The frames are not fully synchronised, but it is clear the smartphone's 60 FPS image is unusable, while at 3000 FPS our approach continues tracking features without issue." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.508, + 0.907, + 0.644 + ], + "angle": 0, + "content": "bile systems such as virtual-reality headsets and unmanned aerial vehicles rely extensively on point-features, often from multiple cameras, to continuously estimate the system's pose. Such systems have limited on-board computational power, limited battery life, and often require low-latency response due to rapid motion. This has pushed the need for computational efficiency, but despite many advancements, the basic task of image transfer from sensor to processor remains a significant time and power bottleneck." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.645, + 0.909, + 0.903 + ], + "angle": 0, + "content": "This issue ultimately reflects the dominant paradigm in electronic imaging, where sensors are primarily built to capture images for a human observer, rather than efficient visual computing. In the context of point-feature detection and tracking, whole images are distilled down to a sparse handful of key-points and descriptors. This is a tiny amount of data compared to the original image, yet standard cameras must still transfer whole images to external processing, repeatedly every frame. This paper presents an alternative, a novel implementation of point-feature detection and tracking for an emerging sensor paradigm, the Pixel-Processor Array (PPA) [9]. Traditional cameras consist of an array of light capture elements, while PPAs are an array of programmable pixel-processors or \"Processing Elements\" (PEs). Each of these processors has its own local memory on which it can perform various computations, and communication with neighbouring processors enabling" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.875, + 0.483, + 0.9 + ], + "angle": 0, + "content": "This work has been funded in part by EPSRC, grant number EP/Y023048/1." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5392" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.226 + ], + "angle": 0, + "content": "data transfer across the array. Images are captured directly into the array, with each PE capturing a single pixel of the whole image into its local memory. This sensor architecture enables massively parallel \"in-pixel\" computation upon the focal plane, with the PE array operating as a Single Instruction Multiple Data (SIMD) computer. Such a sensor can capture visual data, extract high level information, and then output only this sparse data, thereby removing the image output bottleneck." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.228, + 0.483, + 0.621 + ], + "angle": 0, + "content": "Our in-pixel approach for point-feature detection and tracking is designed specifically for the PPA's architecture, providing high pixel-processor compute resource utilisation, and minimizing data transfer between sensor and external processing. The core of our approach is based around the concept of \"Descriptor-In-Pixel\", whereby each PE holds a complete point-feature descriptor within its own local memory. The PPA computes in parallel the response of every PE's descriptor upon a captured image. By generating the correct layout of descriptors every frame across the PE array, the computed \"response map\" can be used for both point-feature detection and tracking. All computation is performed within the PPA's pixel-processors (the PE array), without any additional external processing on PC or microcontroller. Therefore, dense sensor output, such as images, is no longer necessary. Instead, only the coordinates of tracked point-features and the descriptors of newly initialized point-features are output, providing a greater than \\(1000 \\times\\) data reduction compared to whole images. Any additional image data in this paper is output purely for visualization purposes, and is not required for our approach to operate. Our implementation upon the SCAMP-7 PPA prototype [6] achieves speeds just above 3000 frames per second (FPS), with an average sensor output of just 2 bytes per feature, per frame, demonstrating the PPAs potential in high-speed applications (Figure 1)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.634, + 0.24, + 0.65 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Prior PPA Based Works: At the time of writing there are few other works regarding point-feature detection and tracking for PPAs. The early work of [8] demonstrated an implementation of the FAST corner detector [17] at 2300 FPS on SCAMP-5. This work does not perform any form of tracking, and simply outputs the coordinates of detected corner points from the sensor. Performing feature tracking/correspondence using nothing but point coordinates is very challenging, especially as FAST uses no information from previous frames to inform detection, leading to poor temporal stability of detected points between frames. BITVO [16] took steps to address this by outputting a binary edge image alongside the corner points detected by FAST. From these edge images corner descriptors are computed, which are then used in tracking corner points between frames. While this improves tracking quality, the need to" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "output a full resolution binary image to external processing introduces a significant bottleneck, limiting performance to 300 FPS. The solution to this is performing both detection and tracking entirely on-sensor, avoiding the need to output dense visual information to external processing. This is the motivation behind our approach, which uses purely on-sensor compute to detect and track point-features at thousands of frames per second." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.213, + 0.905, + 0.559 + ], + "angle": 0, + "content": "Event Cameras: Event cameras are another alternative visual sensor [10], outputting a stream of \"events\" which encode time, location and polarity of brightness changes at the per-pixel level. Many works have demonstrated pointfeatures upon event cameras, some using just the raw event stream [15], others incorporating image data into their approach [20], [11], [14]. With the event camera's very high dynamic range and temporal resolution, many of these works produce impressive results, tracking features in rapid motion and challenging lighting conditions. One drawback of event cameras is the complexity involved in dealing with their sparse asynchronous event data (a price paid in exchange for the sensor's very high temporal resolution). This can lead to significant computational costs, and while earlier works may use only a standard desktop CPU [20], recent works require a high-end 300 watt GPU for close to real-time performance [14]. In contrast, a strength of the PPA is that it still allows visual computation to be performed upon captured image frames, instead of complex asynchronous event data. By performing all computation in-pixel, temporal resolutions and latencies comparable to event camera based methods can be achieved, but at a reduced total energy cost." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.56, + 0.905, + 0.771 + ], + "angle": 0, + "content": "Traditional Point-Feature Tracking: Many traditional point-feature approaches such as ORB [18] work by locating salient points (using methods such as FAST [17]), and building descriptors for each of these points. Point-features are then tracked by matching their descriptors against those of salient points detected in the current frame. However, separating detection and tracking into two disjoint processes allows a tracked feature's associated salient point to be missed in detection, potentially replaced by a different salient point in close proximity. This can result in tracked features \"flickering\" as their salient points are temporarily lost. By contrast our approach uses the same mechanism (descriptor response) for both detection and tracking for reliable re-detection of existing features." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.785, + 0.693, + 0.801 + ], + "angle": 0, + "content": "3. SCAMP Overview" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.905, + 0.901 + ], + "angle": 0, + "content": "We demonstrate an implementation of our approach upon the SCAMP-7 PPA system [6]. Shown in Figure 2, this vision sensor device has an image resolution of \\(256 \\times 256\\), giving a total of 65,536 pixel-processors (PEs). Each processor is connected to its four immediate neighbours, forming a network for data transfer across the array. For local mem" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5393" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.227 + ], + "angle": 0, + "content": "ory, each pixel-processor has 23 1-bit digital registers, and 7 analogue registers which store continuous values. Various operations upon local memory are supported, such as addition and subtraction of analogue registers, boolean logic between digital registers, and thresholding of analogue values to digital results. Light is captured separately by each processor, and with each frame trigger, converted to analogue values. Thus each processor captures one pixel of an image that spans the whole array." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.228, + 0.487, + 0.455 + ], + "angle": 0, + "content": "Each pixel-processor does not store and execute its own program instructions, instead a centralised controller broadcasts identical instructions to all 65,536 processors in parallel, which then execute each instruction concurrently. Thus the array operates in a Single Instruction Multiple Data (SIMD) mode, similar to GPU compute. Importantly each pixel-processor contains a 1-bit \"activity flag\" register for enabling and disabling the execution of instructions, allowing for per-pixel conditional execution. By writing programs for the controller, the processor array can be made to execute entire vision applications in-pixels, and output only specific extracted information. Various tasks have been demonstrated on this architecture including neural networks [4],[19],[21],[3], visual odometry [16],[2],[12], and eye tracking [5]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.466, + 0.285, + 0.483 + ], + "angle": 0, + "content": "4. Approach Overview" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.49, + 0.483, + 0.55 + ], + "angle": 0, + "content": "Our approach uses a novel Descriptor In-Pixel paradigm designed specifically to exploit the PPA's massively parallel, on-sensor computation. Three key components enabled by the PPA's architecture are as follows." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.552, + 0.483, + 0.613 + ], + "angle": 0, + "content": "1. In-Pixel Descriptors. Our approach involves storing a complete point-feature descriptor within each PE's local digital memory, essentially storing a descriptor at each pixel location." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.613, + 0.483, + 0.718 + ], + "angle": 0, + "content": "2. Parallel Descriptor Computation. The PPA captures image frames directly into the PE array, with each PE capturing one pixel into its local analogue memory. By examining the pixel data of surrounding PEs, each PE can compute a descriptor for its local image content. This descriptor computation can be performed for every PE (i.e. every pixel location) simultaneously in parallel." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.719, + 0.483, + 0.809 + ], + "angle": 0, + "content": "3. Parallel Descriptor Response Computation. Comparison between stored descriptors and those computed from captured image can be performed in parallel across all PEs. This generates a \"response map\", indicating how strongly the stored descriptors correlate or \"match\" with the captured image content." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.552, + 0.483, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.902 + ], + "angle": 0, + "content": "The descriptors distributed across the PE array follow a specific layout, surrounding each tracked point-feature's location with PEs storing its descriptor. This descriptor layout is generated every frame by spreading the descriptors of tracked features into nearby PEs. After computing the response of these stored descriptors on the current image" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.088, + 0.907, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.308, + 0.907, + 0.379 + ], + "angle": 0, + "content": "Figure 2. SCAMP-7 has \\(256 \\times 256\\) pixel-processors, each which can capture light, store and process data within its local memory registers, and transfer data to neighbouring processors. A controller sequentially transmits SIMD instructions to the processor array for execution." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.419, + 0.909, + 0.586 + ], + "angle": 0, + "content": "frame, each tracked feature will be surrounded by a patch of response from its own descriptor. These response patches are analysed in parallel, determining the new location of each tracked feature. This tracking requires that features do not move further than the predetermined patch area between frames. However, our approach can operate at thousands of frames per second, allowing patch areas to be very small \\((9 \\times 9)\\) and still facilitate reliable tracking. New point-features are detected and initialized by analysing the responses of those PEs not inside the patch of any tracked feature. These aspects will be described later in detail." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.593, + 0.909, + 0.73 + ], + "angle": 0, + "content": "In summary, our approach performs all necessary computation within the PE array, each feature is tracked between frames using pixel-processors surrounding its location, while all remaining pixel-processors perform a search to detect new features. This approach is very efficient essentially utilizing \\(100\\%\\) of the PPA's compute, and also allows sensor output to be reduced to simply the locations and descriptors of tracked features. As a result, our approach can operate at thousands of frames per second upon SCAMP-7." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.763, + 0.707, + 0.781 + ], + "angle": 0, + "content": "5. In-Pixel Descriptors" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We make use of simple binary point descriptors, similar to the well known BRIEF descriptor [7]. Such descriptors are stored as binary strings within each PE, occupying multiple digital registers (1 bit per register). Computing a PE's descriptor for a given image involves comparing pairs of pixel data around its location, each comparison generating 1 bit of the descriptor's string. Specifically, the \\( i^{th} \\) bit of the de" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5394" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.445, + 0.908, + 0.504 + ], + "angle": 0, + "content": "Figure 3. Examples of simple descriptor response maps, where the same 8-bit descriptor is stored inside all PEs. Maps are generated for three example descriptors, all using the same sampling pattern (Bottom Left), and input image (Top Left). For comparison we generate response maps using both our weight pixel-pairs method, and the Hamming distance. High response \"blobs\" pinpoint certain visual structures, but those from the Hamming distance can be unreliable for tracking, as illustrated in Teal." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.528, + 0.274, + 0.543 + ], + "angle": 0, + "content": "scriptor, \\(d_{i}\\) , is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.551, + 0.483, + 0.592 + ], + "angle": 0, + "content": "\\[\nd _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} p _ {i (1)} < p _ {i (2)} \\\\ 1, & \\text {i f} p _ {i (1)} \\geq p _ {i (2)} \\end{array} \\right. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.6, + 0.483, + 0.645 + ], + "angle": 0, + "content": "where \\( p_{i(1)}, p_{i(2)} \\) are a pair of pixel values at locations relative to the PE's location, according to some predetermined sampling pattern." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.483, + 0.825 + ], + "angle": 0, + "content": "Descriptor Size: For maximum efficiency, an entire descriptor should be stored within each PE (i.e. one descriptor per pixel location). However, PE local memory on SCAMP-7 is very limited, restricting this first demonstration of our approach to tiny 8-bit descriptors, performing just eight local pixel pair comparisons. Due to how our approach operates, these are still sufficient for reliable high-speed feature tracking. Larger descriptors could be utilized on future PPA hardware, with greater memory per PE. Note, using significantly larger descriptors \\((128+\\) bit) would likely not improve tracking in our approach, but these would be better suited to long term tasks such as re-localisation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Descriptor Sampling Pattern: Computing the binary descriptor for a specific pixel location involves comparing pairs of pixels, sampled in a given pattern about that location. This \"sampling pattern\", is chosen with the aim to compress the local image into a compact bit string, cap" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.528, + 0.907, + 0.693 + ], + "angle": 0, + "content": "turing any discriminative structures within the local image content. BRIEF [7] uses fixed random sampling patterns, which are too large (128+ bit) to use for in-pixel descriptors. Instead we use fixed sampling patterns similar to the BRISK [13] & FREAK [1] descriptors. We only use a single sampling pattern during operation, for all descriptors across all PEs, as this enables us to fully exploit the PPA's parallel SIMD compute. We opted for a 'compare-to-center' sampling pattern (see Figure 3) due to its simplicity and low computational cost, though many other patterns could be used." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.709, + 0.766, + 0.727 + ], + "angle": 0, + "content": "6. Descriptor Response-Maps" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.907, + 0.903 + ], + "angle": 0, + "content": "With each new image frame our approach generates a layout of descriptors stored across the PE array, and then computes the \"response\" of each PE's stored descriptor. Descriptor response refers to how strongly the visual features represented by a specific descriptor are present at a certain location within an image. Measuring the response of a PE's stored descriptor first involves computing the descriptor for the image at that PE's location. The computed image descriptor is then compared to the PE's stored descriptor. A higher similarity between the two indicates that the stored descriptor more accurately represents the local image con" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "5395" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.487, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.207, + 0.485, + 0.292 + ], + "angle": 0, + "content": "Figure 4. Descriptor layout described in Section 7. Each PE stores an 8-bit descriptor within its digital registers. Tracked features are surrounded by patches of PEs storing their descriptor (shown by various colours). PEs outside such patches store the current search descriptor. Additionally, 1 digital register in each PE indicates if tracked feature is located there (shown in yellow)." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.302, + 0.484, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.476, + 0.484, + 0.531 + ], + "angle": 0, + "content": "Figure 5. Left: A \"patchwork\" response map computed using the descriptor layout of Section 7. Right: Corresponding captured image & tracked features. Two response patches \\((9 \\times 9\\) PEs) from different features are shown in detail." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.564, + 0.483, + 0.595 + ], + "angle": 0, + "content": "tent. Thus, as will be described, descriptor response should correlate to a measurement of this similarity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.596, + 0.484, + 0.673 + ], + "angle": 0, + "content": "The PPA architecture enables the response of every PEs stored descriptor to be computed in parallel, and placed into local analogue memory, forming a \"descriptor response map\" spread across the PE array. Figure 3 shows simple response maps, with all PEs storing the same descriptor." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Measuring Descriptor Similarity and Response: A simple measure of similarity between binary descriptors is to compute the number of matching bits between their bit strings (i.e. Hamming distance), a common choice on traditional digital processing, being very cheap to compute. SCAMP-7 however has analogue computation capability, and captures images directly into its PE array as analogue data. For almost no additional cost, this analogue compute allows to also account for the raw pixel data when computing descriptor response. This is very useful for handling image regions that will not provide reliable point-feature tracking, such as low texture or highly repetitive texture regions. Descriptors inside such \"ambiguous\" regions will have poor temporal stability, as very slight image changes (from noise or lighting) will produce radically different de" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.183 + ], + "angle": 0, + "content": "scriptors from one frame to the next. Thus we do not simply measure the number of matching bits between descriptors, but also weight these matches (and penalize misses) by the magnitude of the pixel pair comparison results associated with each bit. Specifically, we compute the response \\( R \\) of a stored descriptor at a certain image location as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.193, + 0.907, + 0.235 + ], + "angle": 0, + "content": "\\[\nR = \\sum_ {i = 1} ^ {8} (2 d _ {i} - 1) \\left(p _ {i (1)} - p _ {i (2)}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.244, + 0.907, + 0.352 + ], + "angle": 0, + "content": "where \\(d_{i} \\in \\{0,1\\}\\), is the \\(i^{th}\\) bit of the descriptor, and \\(p_{i(1)}, p_{i(2)} \\in \\Re\\) are the pixel values for the \\(i^{th}\\) pair of pixels, selected according to the descriptor's sampling pattern. This ensures high descriptor response is only produced in image regions which can provide reliable tracking. Figure 3 shows example response maps generated using both this weighted pixel-pairs method, and the Hamming distance." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.365, + 0.693, + 0.383 + ], + "angle": 0, + "content": "7. Descriptor Layout" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.389, + 0.906, + 0.496 + ], + "angle": 0, + "content": "The response maps of Figure 3 are simple examples, with the same descriptor being stored inside every PE. In practice, with every captured frame, our approach generates a layout of various descriptors across the PE array. This descriptor layout enables the computed response maps to be used for both point-feature tracking and detection. Generation of this layout splits all PEs into one of two categories." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.498, + 0.906, + 0.602 + ], + "angle": 0, + "content": "1. PEs Located Near Tracked Point-Features. Each tracked point-feature's descriptor is spread into a local \"patch\" of PEs surrounding its location (i.e. around the PE the feature currently resides in). The computed response map will then have each tracked feature surrounded by responses from its own descriptor, from which the feature's new location can be determined." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.603, + 0.906, + 0.693 + ], + "angle": 0, + "content": "2. All Remaining PEs. A single \"search descriptor\" is loaded into all remaining PEs, not located close to any tracked feature. The responses from this descriptor are examined to detect new point-features. To detect different features, the search descriptor itself is randomized every frame." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.498, + 0.906, + 0.693 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.697, + 0.906, + 0.832 + ], + "angle": 0, + "content": "To generate this descriptor layout, the search descriptor is first loaded into all PEs in parallel, excluding PEs containing tracked point-features. Next the descriptors of tracked point-features are spread out from their containing PEs, across a small local patch of PEs \\((9 \\times 9)\\). This descriptor spreading is also performed for every tracked point-feature in parallel. Figure 4 illustrates this layout, and the digital registers used with each PE for descriptor storage, and indication of a tracked feature's location." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.845, + 0.757, + 0.863 + ], + "angle": 0, + "content": "8. Patchwork Response Map" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "The descriptor layout described in Section 7 generates response maps which have distinct patches of response, one" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5396" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.259, + 0.905, + 0.275 + ], + "angle": 0, + "content": "Figure 6. Steps for updating locations of tracked features, computation of the patchwork descriptor response map, blob-detection & NMS." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.3, + 0.482, + 0.482 + ], + "angle": 0, + "content": "for each tracked point-feature. Each feature's patch is centred upon its last known location, and contains responses from its descriptor. PEs outside these patches will contain responses from the current search descriptor. When visualized these response maps have a \"patchwork\" like appearance as shown in Figure 5. These patchwork response maps contain sufficient information to both detect reliable new point-features, and update the locations of existing tracked point-features. They also require no additional computation: by simply storing different descriptors across the PE array, the responses used for both tracking and detecting point-features are all computed in parallel." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.497, + 0.315, + 0.512 + ], + "angle": 0, + "content": "9. Point-Feature Detection" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.523, + 0.483, + 0.749 + ], + "angle": 0, + "content": "Descriptor response is the mechanism by which our approach both detects and tracks point-features. With each new frame a patchwork response map (as described in Section 8) is computed. Feature detection involves searching for any locations where the search descriptor's response strongly identifies some underlying visual point-feature. These locations appear as small distinct regions of high response, surrounded by low response. High response indicates the strong presence of visual features matching the search descriptor, while the surrounding low response indicates these features are distinct to a specific location (i.e. a point-feature). These high response \"blobs\" (such as shown in Figure 6), are prime candidates at which to initialize new point-features, as their location can be reliably tracked by the descriptor's local response." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.854 + ], + "angle": 0, + "content": "Blob Detection: To locate new point-feature candidates (and also track existing features), blob detection is performed upon each frame's response map, at a scale of the descriptor sampling patterns size. Strong blob detection responses then represent reliable point-feature candidates. Figure 6 illustrates this process: from image, to response map, to blob detection result." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Point-Feature Initialization: Our approach uses one digital register within each PE to signify if there is a tracked point-feature at its location, with PEs containing tracked" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.301, + 0.905, + 0.345 + ], + "angle": 0, + "content": "features then also storing the descriptor of that feature (see Figure 4). This scheme, storing point-features within local PE memory, enables all features to be tracked in parallel." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.346, + 0.905, + 0.45 + ], + "angle": 0, + "content": "To initialize new features, thresholding is performed upon the blob detection result. This is used to identify the PEs located at the centres of the strongest blobs, which are the best candidates for new point-features. New features are then added by simply setting the digital register to signify the presence of a tracked point-feature within each of these PEs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.452, + 0.906, + 0.573 + ], + "angle": 0, + "content": "Descriptor Readout: Whenever a new point-feature is initialized, we can optionally read out its descriptor from the sensor. This is unnecessary for feature tracking, but could be used for additional tasks or simply for visualization. The descriptor readout is performed sequentially over multiple frames, 1 bit per frame. This still allows hundreds of 8-bit descriptors to be read out per second, but minimizes spikes in the processing time per frame (\\(< 1\\mu s\\))." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.574, + 0.906, + 0.68 + ], + "angle": 0, + "content": "It is also possible to generate and read out longer descriptors for each new feature (instead of the short 8-bit descriptors used for in-pixel tracking). These could be used by external off-sensor processing to re-identify past features, which left the sensor's view, such as for SLAM system loop-closure/relocalisation. This is beyond the scope of this paper, but should be a relatively straightforward extension." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.694, + 0.694, + 0.712 + ], + "angle": 0, + "content": "10. Feature Tracking" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.906, + 0.901 + ], + "angle": 0, + "content": "With each new captured frame the locations of tracked point-features must be updated. This is done by finding the local maximum of each feature's descriptor response, around that feature's previous location. The PE containing this maximum is then taken to be that of the feature's new location. This can be viewed as similar to a gradient descent process, with each feature's location following the local maxima of its descriptor response, which evolves in time with each captured frame. For each frame, the descriptor layout of Section 7 is generated, and used to compute the patchwork response maps of Section 8. These response maps have each tracked feature surrounded by a" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5397" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.482, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.616, + 0.484, + 0.743 + ], + "angle": 0, + "content": "Figure 7. Examples of feature tracking on SCAMP-7. Left Column: Trails of point-features tracked by SCAMP-7, with thickness representing age. Right Column: 60 FPS video from smartphone mounted alongside SCAMP-7. Our approach tracks features reliably under motion that renders the smartphone's image near unusable. Here SCAMP-7 also outputs an image temporally \\((1/16^{th}\\) per frame) for visualization, limiting performance to around 850 FPS. The motion blur in SCAMP-7 images shown is an artefact of this image readout scheme, and is not present internally." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.484, + 0.903 + ], + "angle": 0, + "content": "patch of response from its own descriptor. After performing blob detection upon this response map, a patch-wise, nonmaximum-suppression (NMS) routine is performed. This identifies the PEs of highest response within every feature's patch, which are taken to represent each feature's new location. This process is illustrated in Figure 6. It should be noted, that point-features are typically considered to be 1-pixel in size. In practice, however, it is not necessary to" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "ensure the NMS routine produces single pixels, just well-located, distinct, and small cluster of pixels." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.124, + 0.907, + 0.289 + ], + "angle": 0, + "content": "- Dropping Weak Features: After computing the descriptor response map for a new frame, there may exist some tracked features with no high values in their associated descriptor response patches. This indicates the visual feature associated with that point-feature's descriptor is no longer clearly identifiable due to occlusion, lighting, or perspective changes. Such features can no longer be reliably tracked by descriptor response. The PEs containing such features are located by thresholding the response map, and their features removed by setting the digital register signifying feature presence to false." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.291, + 0.909, + 0.382 + ], + "angle": 0, + "content": "Benefits From High Frame-Rate: The very high speed at which our approach operates significantly simplifies feature tracking. Captured images will barely change from one frame to the next, and the motion of point-features is reduced to a gradual crawl across the PE array. Specifically two major benefits are:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.388, + 0.907, + 0.463 + ], + "angle": 0, + "content": "1. Reduced Motion Blur. Motion blur in captured images is reduced significantly, if not entirely eliminated, even under violent sensor motion. This helps ensure the visual features underlying each tracked point-feature remain clear and consistent from one image to the next." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.463, + 0.907, + 0.553 + ], + "angle": 0, + "content": "2. Reduced Feature Location Search. As captured image will change very little from one frame to the next, so to will the locations of any tracked point-features. This allows the search for each tracked point-feature's new location to be limited to a small region around its previous location, \\(9 \\times 9\\) PEs in SCAMP-7." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.388, + 0.907, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.572, + 0.757, + 0.59 + ], + "angle": 0, + "content": "11. SCAMP Implementation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.909, + 0.903 + ], + "angle": 0, + "content": "The current implementation of our approach on SCAMP-7 can run at just over 3000 FPS. While optimized, further code improvements may still exist. A breakdown of the total computation time per frame is given in Table 1. To put these numbers into perspective, the time taken to output a full uncompressed image from the sensor is well over \\(20000\\mu s\\), and even a 4-bit image requires \\(2700\\mu s\\). Our approach avoids such bottlenecks by performing all necessary computation entirely on-sensor, and outputting only sparse feature locations and descriptors. Examples of real-time output are shown in Figure 7, showcasing point-feature tracking under rapid motion to a degree not possible with a traditional camera sensor. It is worth noting that the SCAMP-7 chip is a research prototype, created using an old \\(180\\mathrm{nm}\\) CMOS manufacturing process, with relatively low clock speeds, very restrictive memory per PE, and significantly higher power usage than what is possible using today's state-of-the-art semiconductor technology. That our approach can achieve such performance upon this device is an indication of the potential of the PPA sensor paradigm." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5398" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.218, + 0.106 + ], + "angle": 0, + "content": "12. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.356 + ], + "angle": 0, + "content": "An exact evaluation of our approach against traditional methods is difficult for a number of reasons. Firstly to reach its full potential, our approach must operate at very high frame-rates to ensure small inter-frame motion (at a minimum 500 FPS). This is no issue for our PPA implementation, which can capture and process images at thousands of frames per second, but the number of datasets applicable to feature-tracking captured at such frame rates is very limited. Further testing our PPA implementation upon any such dataset would involve uploading each video frame sequentially into the PPA's PE array to emulate image capture. SCAMP-7 was never designed with this in mind, and uploading such large quantities of data is not efficient and prone to errors. As such we deemed evaluation using high frame rate datasets that would involve uploading thousands of sequential images not feasible." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.357, + 0.484, + 0.81 + ], + "angle": 0, + "content": "We instead performed a comparison against feature tracking using a SCAMP-7 implementation of FAST keypoint detector. This is chosen also because it has speed comparable to our approach, and thus potentially able to track features under the same rapid motion. A modified implementation of [8] was used, which outputs corner point coordinates from the SCAMP-7. Simple point-feature tracking is then performed by matching each corner point with its closest corner point from the previous frame. To match corner points purely by frame-to-frame location (proximity), they must be within a small threshold distance (e.g. 5 pixels). We compare our approach against this FAST based tracking by recording the output of both approaches, viewing the same scenes, running at the same speed of 1000 FPS, using a very similar sequence of sensor motions for both approaches. Some of these motions keep parts of the scene in constant view, allowing some features to be tracked throughout the entire motion. We record how long every feature is tracked for before it is lost, with results for each motion sequence shown in Figure 8. Note, we also do not count any \"poor quality\" features from the FAST approach, which have lifetimes of less than 0.25 seconds. The distribution of feature lifetimes in these histograms give a sense of how reliable the approaches are comparatively. For example, under the 'Translate' motion, \\(90\\%\\) of features using FAST based tracking were lost within 5 seconds, and \\(0\\%\\) of features were tracked for over 15 seconds, compared to around \\(20\\%\\) with our approach. It is clear from the ratio of feature lifetimes that our approach is far more reliable at tracking features for any significant length of time." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Limitations In our current implementation, only the locations and descriptors of tracked features are represented in-pixel. Consequently, feature tracking has no concept of orientation and scale, making it non-invariant to rotation and scaling. While this is a significant limitation, we argue that it is not a fundamental drawback of the Descriptor-In-Pixel" + }, + { + "type": "table_caption", + "bbox": [ + 0.557, + 0.09, + 0.863, + 0.104 + ], + "angle": 0, + "content": "Table 1. SCAMP-7 Computation Time Breakdown." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.115, + 0.892, + 0.212 + ], + "angle": 0, + "content": "
TaskCompute Time μs%
Descriptor Response Map19260
Feature Initialization3110
Feature-Wise NMS4113
Misc/Other Computation5717
Total321-
" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.23, + 0.707, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.32, + 0.71, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.23, + 0.904, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.32, + 0.905, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.419, + 0.907, + 0.492 + ], + "angle": 0, + "content": "Figure 8. Comparison of feature lifetime histograms, our approach vs tracking based on FAST keypoints, under different sensor motions. Both approaches are run at 1000 FPS on SCAMP-7 for comparison. Features tracked using our approach have significantly longer lifespans in general as shown by the ratio." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.531, + 0.907, + 0.637 + ], + "angle": 0, + "content": "approach but rather a constraint imposed by the current state of PPA hardware, which remains in the early stages of development. Specifically, the limited memory within each PE makes storing additional information, such as a feature's orientation, challenging. We expect that as future PPA devices increase memory capacity per PE, our method can be extended to support rotational and scale-invariant tracking." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.672, + 0.644, + 0.687 + ], + "angle": 0, + "content": "13. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.901 + ], + "angle": 0, + "content": "This paper presented a novel approach for performing point-feature detection and tracking on PPA architectures, demonstrated upon the SCAMP-7 system. Our approach is entirely performed within the pixel-processors of the PPA, and does not require external PC or micro-controller processing. We introduce the concept of Descriptor-In-Pixel which enables our approach to detect and track features by parallel computation of descriptor response across the processing array. This brings major performance benefits allowing our approach to operate at 3000 FPS, on a portable \"smart camera\" vision system, using around 1 watt of power, reliably tracking point-features under violent motion which renders traditional sensors unusable." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5399" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.169 + ], + "angle": 0, + "content": "[1] Alexandre Alahi, Raphael Ortiz, and Pierre Vandergheynst. FREAK: Fast retina keypoint. In 2012 IEEE conference on computer vision and pattern recognition, pages 510-517. 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AnalogNet: Convolutional neural network inference on analog focal plane sensor processors. arXiv preprint arXiv:2006.01765, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.094, + 0.905, + 0.713 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5400" + } + ] +] \ No newline at end of file diff --git a/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_origin.pdf b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0bb239f8c148907a3ff12720ca775944c26c7151 --- /dev/null +++ b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/4c7b942d-4d91-4aec-b4fd-a208ea5f65b7_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:04f28684b8ef67f86de2d82dc8509d0ae70efcbcae694dcda55a9fcdedb5d16f +size 7994148 diff --git a/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/full.md b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/full.md new file mode 100644 index 0000000000000000000000000000000000000000..194c3e000f3d27d52042d0206594d6002f383070 --- /dev/null +++ b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/full.md @@ -0,0 +1,217 @@ +# Descriptor-In-Pixel : Point-Feature Tracking for Pixel Processor Arrays + +Laurie Bose $^{1,2}$ Jianing Chen $^{1,2}$ Piotr Dudek $^{1,2}$ + +1The University of Manchester, Department of EEE, Manchester, United Kingdom + +$^{2}$ Visionchip Limited, Manchester, United Kingdom + +https://lauriebose.github.io/DIP + +# Abstract + +This paper presents a novel approach for joint point-feature detection and tracking, designed specifically for Pixel Processor Array (PPA) vision sensors. Instead of standard pixels, PPA sensors consist of thousands of "pixel-processors", enabling massive parallel computation of visual data at the point of light capture. Our approach performs all computation entirely in-pixel, meaning no raw image data need ever leave the sensor for external processing. We introduce a Descriptor-In-Pixel paradigm, in which a feature descriptor is held within the memory of each pixelprocessor. The PPA's architecture enables the response of every processor's descriptor, upon the current image, to be computed in parallel. This produces a "descriptor response map" which, by generating the correct layout of descriptors across the pixel-processors, can be used for both point-feature detection and tracking. This reduces sensor output to just sparse feature locations and descriptors, read-out via an address-event interface, giving a greater than $1000 \times$ reduction in data transfer compared to raw image output. The sparse readout and complete utilization of all pixel-processors makes our approach very efficient. Our implementation upon the SCAMP-7 PPA prototype runs at over 3000 FPS (Frames Per Second), tracking point-features reliably under violent motion. This is the first work performing point-feature detection and tracking entirely in-pixel. + +# 1. Introduction + +Point-features are distinct points within an image, chosen to be clearly identifiable within multiple images of the same scene, even under changes such as scale, lighting, and perspective. The various methods of point-feature detection and tracking are some of the most widespread tools in computer vision, playing a vital role in Visual Odometry and Simultaneous Localisation and Mapping (SLAM). Many mo + +![](images/d1d908ffdc1f5eb9ddec4fa0ca774d2018ce1db0f267728172e84b1c80770aaa.jpg) +Figure 1. A smartphone and SCAMP-7 PPA are strapped together and shaken violently. The frames are not fully synchronised, but it is clear the smartphone's 60 FPS image is unusable, while at 3000 FPS our approach continues tracking features without issue. + +bile systems such as virtual-reality headsets and unmanned aerial vehicles rely extensively on point-features, often from multiple cameras, to continuously estimate the system's pose. Such systems have limited on-board computational power, limited battery life, and often require low-latency response due to rapid motion. This has pushed the need for computational efficiency, but despite many advancements, the basic task of image transfer from sensor to processor remains a significant time and power bottleneck. + +This issue ultimately reflects the dominant paradigm in electronic imaging, where sensors are primarily built to capture images for a human observer, rather than efficient visual computing. In the context of point-feature detection and tracking, whole images are distilled down to a sparse handful of key-points and descriptors. This is a tiny amount of data compared to the original image, yet standard cameras must still transfer whole images to external processing, repeatedly every frame. This paper presents an alternative, a novel implementation of point-feature detection and tracking for an emerging sensor paradigm, the Pixel-Processor Array (PPA) [9]. Traditional cameras consist of an array of light capture elements, while PPAs are an array of programmable pixel-processors or "Processing Elements" (PEs). Each of these processors has its own local memory on which it can perform various computations, and communication with neighbouring processors enabling + +data transfer across the array. Images are captured directly into the array, with each PE capturing a single pixel of the whole image into its local memory. This sensor architecture enables massively parallel "in-pixel" computation upon the focal plane, with the PE array operating as a Single Instruction Multiple Data (SIMD) computer. Such a sensor can capture visual data, extract high level information, and then output only this sparse data, thereby removing the image output bottleneck. + +Our in-pixel approach for point-feature detection and tracking is designed specifically for the PPA's architecture, providing high pixel-processor compute resource utilisation, and minimizing data transfer between sensor and external processing. The core of our approach is based around the concept of "Descriptor-In-Pixel", whereby each PE holds a complete point-feature descriptor within its own local memory. The PPA computes in parallel the response of every PE's descriptor upon a captured image. By generating the correct layout of descriptors every frame across the PE array, the computed "response map" can be used for both point-feature detection and tracking. All computation is performed within the PPA's pixel-processors (the PE array), without any additional external processing on PC or microcontroller. Therefore, dense sensor output, such as images, is no longer necessary. Instead, only the coordinates of tracked point-features and the descriptors of newly initialized point-features are output, providing a greater than $1000 \times$ data reduction compared to whole images. Any additional image data in this paper is output purely for visualization purposes, and is not required for our approach to operate. Our implementation upon the SCAMP-7 PPA prototype [6] achieves speeds just above 3000 frames per second (FPS), with an average sensor output of just 2 bytes per feature, per frame, demonstrating the PPAs potential in high-speed applications (Figure 1). + +# 2. Related Works + +Prior PPA Based Works: At the time of writing there are few other works regarding point-feature detection and tracking for PPAs. The early work of [8] demonstrated an implementation of the FAST corner detector [17] at 2300 FPS on SCAMP-5. This work does not perform any form of tracking, and simply outputs the coordinates of detected corner points from the sensor. Performing feature tracking/correspondence using nothing but point coordinates is very challenging, especially as FAST uses no information from previous frames to inform detection, leading to poor temporal stability of detected points between frames. BITVO [16] took steps to address this by outputting a binary edge image alongside the corner points detected by FAST. From these edge images corner descriptors are computed, which are then used in tracking corner points between frames. While this improves tracking quality, the need to + +output a full resolution binary image to external processing introduces a significant bottleneck, limiting performance to 300 FPS. The solution to this is performing both detection and tracking entirely on-sensor, avoiding the need to output dense visual information to external processing. This is the motivation behind our approach, which uses purely on-sensor compute to detect and track point-features at thousands of frames per second. + +Event Cameras: Event cameras are another alternative visual sensor [10], outputting a stream of "events" which encode time, location and polarity of brightness changes at the per-pixel level. Many works have demonstrated pointfeatures upon event cameras, some using just the raw event stream [15], others incorporating image data into their approach [20], [11], [14]. With the event camera's very high dynamic range and temporal resolution, many of these works produce impressive results, tracking features in rapid motion and challenging lighting conditions. One drawback of event cameras is the complexity involved in dealing with their sparse asynchronous event data (a price paid in exchange for the sensor's very high temporal resolution). This can lead to significant computational costs, and while earlier works may use only a standard desktop CPU [20], recent works require a high-end 300 watt GPU for close to real-time performance [14]. In contrast, a strength of the PPA is that it still allows visual computation to be performed upon captured image frames, instead of complex asynchronous event data. By performing all computation in-pixel, temporal resolutions and latencies comparable to event camera based methods can be achieved, but at a reduced total energy cost. + +Traditional Point-Feature Tracking: Many traditional point-feature approaches such as ORB [18] work by locating salient points (using methods such as FAST [17]), and building descriptors for each of these points. Point-features are then tracked by matching their descriptors against those of salient points detected in the current frame. However, separating detection and tracking into two disjoint processes allows a tracked feature's associated salient point to be missed in detection, potentially replaced by a different salient point in close proximity. This can result in tracked features "flickering" as their salient points are temporarily lost. By contrast our approach uses the same mechanism (descriptor response) for both detection and tracking for reliable re-detection of existing features. + +# 3. SCAMP Overview + +We demonstrate an implementation of our approach upon the SCAMP-7 PPA system [6]. Shown in Figure 2, this vision sensor device has an image resolution of $256 \times 256$ , giving a total of 65,536 pixel-processors (PEs). Each processor is connected to its four immediate neighbours, forming a network for data transfer across the array. For local mem + +ory, each pixel-processor has 23 1-bit digital registers, and 7 analogue registers which store continuous values. Various operations upon local memory are supported, such as addition and subtraction of analogue registers, boolean logic between digital registers, and thresholding of analogue values to digital results. Light is captured separately by each processor, and with each frame trigger, converted to analogue values. Thus each processor captures one pixel of an image that spans the whole array. + +Each pixel-processor does not store and execute its own program instructions, instead a centralised controller broadcasts identical instructions to all 65,536 processors in parallel, which then execute each instruction concurrently. Thus the array operates in a Single Instruction Multiple Data (SIMD) mode, similar to GPU compute. Importantly each pixel-processor contains a 1-bit "activity flag" register for enabling and disabling the execution of instructions, allowing for per-pixel conditional execution. By writing programs for the controller, the processor array can be made to execute entire vision applications in-pixels, and output only specific extracted information. Various tasks have been demonstrated on this architecture including neural networks [4],[19],[21],[3], visual odometry [16],[2],[12], and eye tracking [5]. + +# 4. Approach Overview + +Our approach uses a novel Descriptor In-Pixel paradigm designed specifically to exploit the PPA's massively parallel, on-sensor computation. Three key components enabled by the PPA's architecture are as follows. + +1. In-Pixel Descriptors. Our approach involves storing a complete point-feature descriptor within each PE's local digital memory, essentially storing a descriptor at each pixel location. +2. Parallel Descriptor Computation. The PPA captures image frames directly into the PE array, with each PE capturing one pixel into its local analogue memory. By examining the pixel data of surrounding PEs, each PE can compute a descriptor for its local image content. This descriptor computation can be performed for every PE (i.e. every pixel location) simultaneously in parallel. +3. Parallel Descriptor Response Computation. Comparison between stored descriptors and those computed from captured image can be performed in parallel across all PEs. This generates a "response map", indicating how strongly the stored descriptors correlate or "match" with the captured image content. + +The descriptors distributed across the PE array follow a specific layout, surrounding each tracked point-feature's location with PEs storing its descriptor. This descriptor layout is generated every frame by spreading the descriptors of tracked features into nearby PEs. After computing the response of these stored descriptors on the current image + +![](images/6fc6210d9a997b16b723ad00e9d85017993c935ce3bbafc1d22220f3911eade1.jpg) +Figure 2. SCAMP-7 has $256 \times 256$ pixel-processors, each which can capture light, store and process data within its local memory registers, and transfer data to neighbouring processors. A controller sequentially transmits SIMD instructions to the processor array for execution. + +frame, each tracked feature will be surrounded by a patch of response from its own descriptor. These response patches are analysed in parallel, determining the new location of each tracked feature. This tracking requires that features do not move further than the predetermined patch area between frames. However, our approach can operate at thousands of frames per second, allowing patch areas to be very small $(9 \times 9)$ and still facilitate reliable tracking. New point-features are detected and initialized by analysing the responses of those PEs not inside the patch of any tracked feature. These aspects will be described later in detail. + +In summary, our approach performs all necessary computation within the PE array, each feature is tracked between frames using pixel-processors surrounding its location, while all remaining pixel-processors perform a search to detect new features. This approach is very efficient essentially utilizing $100\%$ of the PPA's compute, and also allows sensor output to be reduced to simply the locations and descriptors of tracked features. As a result, our approach can operate at thousands of frames per second upon SCAMP-7. + +# 5. In-Pixel Descriptors + +We make use of simple binary point descriptors, similar to the well known BRIEF descriptor [7]. Such descriptors are stored as binary strings within each PE, occupying multiple digital registers (1 bit per register). Computing a PE's descriptor for a given image involves comparing pairs of pixel data around its location, each comparison generating 1 bit of the descriptor's string. Specifically, the $i^{th}$ bit of the de + +![](images/2c323482fd614d634e069bca887b091ddb4a61865ebe5a80b6ea5ab9ad52997b.jpg) +Figure 3. Examples of simple descriptor response maps, where the same 8-bit descriptor is stored inside all PEs. Maps are generated for three example descriptors, all using the same sampling pattern (Bottom Left), and input image (Top Left). For comparison we generate response maps using both our weight pixel-pairs method, and the Hamming distance. High response "blobs" pinpoint certain visual structures, but those from the Hamming distance can be unreliable for tracking, as illustrated in Teal. + +scriptor, $d_{i}$ , is computed as + +$$ +d _ {i} = \left\{ \begin{array}{l l} 0, & \text {i f} p _ {i (1)} < p _ {i (2)} \\ 1, & \text {i f} p _ {i (1)} \geq p _ {i (2)} \end{array} \right. \tag {1} +$$ + +where $p_{i(1)}, p_{i(2)}$ are a pair of pixel values at locations relative to the PE's location, according to some predetermined sampling pattern. + +Descriptor Size: For maximum efficiency, an entire descriptor should be stored within each PE (i.e. one descriptor per pixel location). However, PE local memory on SCAMP-7 is very limited, restricting this first demonstration of our approach to tiny 8-bit descriptors, performing just eight local pixel pair comparisons. Due to how our approach operates, these are still sufficient for reliable high-speed feature tracking. Larger descriptors could be utilized on future PPA hardware, with greater memory per PE. Note, using significantly larger descriptors $(128+$ bit) would likely not improve tracking in our approach, but these would be better suited to long term tasks such as re-localisation. + +Descriptor Sampling Pattern: Computing the binary descriptor for a specific pixel location involves comparing pairs of pixels, sampled in a given pattern about that location. This "sampling pattern", is chosen with the aim to compress the local image into a compact bit string, cap + +turing any discriminative structures within the local image content. BRIEF [7] uses fixed random sampling patterns, which are too large (128+ bit) to use for in-pixel descriptors. Instead we use fixed sampling patterns similar to the BRISK [13] & FREAK [1] descriptors. We only use a single sampling pattern during operation, for all descriptors across all PEs, as this enables us to fully exploit the PPA's parallel SIMD compute. We opted for a 'compare-to-center' sampling pattern (see Figure 3) due to its simplicity and low computational cost, though many other patterns could be used. + +# 6. Descriptor Response-Maps + +With each new image frame our approach generates a layout of descriptors stored across the PE array, and then computes the "response" of each PE's stored descriptor. Descriptor response refers to how strongly the visual features represented by a specific descriptor are present at a certain location within an image. Measuring the response of a PE's stored descriptor first involves computing the descriptor for the image at that PE's location. The computed image descriptor is then compared to the PE's stored descriptor. A higher similarity between the two indicates that the stored descriptor more accurately represents the local image con + +![](images/4575cc1cdd37059b132aba9ea8c59df5c8e6e50d904f1a66152a932e5cbb072c.jpg) +Figure 4. Descriptor layout described in Section 7. Each PE stores an 8-bit descriptor within its digital registers. Tracked features are surrounded by patches of PEs storing their descriptor (shown by various colours). PEs outside such patches store the current search descriptor. Additionally, 1 digital register in each PE indicates if tracked feature is located there (shown in yellow). + +![](images/5e246ef0d872e69f2d92c2393f319932428f0488dd87bfe426814f8f1ab28a75.jpg) +Figure 5. Left: A "patchwork" response map computed using the descriptor layout of Section 7. Right: Corresponding captured image & tracked features. Two response patches $(9 \times 9$ PEs) from different features are shown in detail. + +tent. Thus, as will be described, descriptor response should correlate to a measurement of this similarity. + +The PPA architecture enables the response of every PEs stored descriptor to be computed in parallel, and placed into local analogue memory, forming a "descriptor response map" spread across the PE array. Figure 3 shows simple response maps, with all PEs storing the same descriptor. + +Measuring Descriptor Similarity and Response: A simple measure of similarity between binary descriptors is to compute the number of matching bits between their bit strings (i.e. Hamming distance), a common choice on traditional digital processing, being very cheap to compute. SCAMP-7 however has analogue computation capability, and captures images directly into its PE array as analogue data. For almost no additional cost, this analogue compute allows to also account for the raw pixel data when computing descriptor response. This is very useful for handling image regions that will not provide reliable point-feature tracking, such as low texture or highly repetitive texture regions. Descriptors inside such "ambiguous" regions will have poor temporal stability, as very slight image changes (from noise or lighting) will produce radically different de + +scriptors from one frame to the next. Thus we do not simply measure the number of matching bits between descriptors, but also weight these matches (and penalize misses) by the magnitude of the pixel pair comparison results associated with each bit. Specifically, we compute the response $R$ of a stored descriptor at a certain image location as follows: + +$$ +R = \sum_ {i = 1} ^ {8} (2 d _ {i} - 1) \left(p _ {i (1)} - p _ {i (2)}\right) \tag {2} +$$ + +where $d_{i} \in \{0,1\}$ , is the $i^{th}$ bit of the descriptor, and $p_{i(1)}, p_{i(2)} \in \Re$ are the pixel values for the $i^{th}$ pair of pixels, selected according to the descriptor's sampling pattern. This ensures high descriptor response is only produced in image regions which can provide reliable tracking. Figure 3 shows example response maps generated using both this weighted pixel-pairs method, and the Hamming distance. + +# 7. Descriptor Layout + +The response maps of Figure 3 are simple examples, with the same descriptor being stored inside every PE. In practice, with every captured frame, our approach generates a layout of various descriptors across the PE array. This descriptor layout enables the computed response maps to be used for both point-feature tracking and detection. Generation of this layout splits all PEs into one of two categories. + +1. PEs Located Near Tracked Point-Features. Each tracked point-feature's descriptor is spread into a local "patch" of PEs surrounding its location (i.e. around the PE the feature currently resides in). The computed response map will then have each tracked feature surrounded by responses from its own descriptor, from which the feature's new location can be determined. +2. All Remaining PEs. A single "search descriptor" is loaded into all remaining PEs, not located close to any tracked feature. The responses from this descriptor are examined to detect new point-features. To detect different features, the search descriptor itself is randomized every frame. + +To generate this descriptor layout, the search descriptor is first loaded into all PEs in parallel, excluding PEs containing tracked point-features. Next the descriptors of tracked point-features are spread out from their containing PEs, across a small local patch of PEs $(9 \times 9)$ . This descriptor spreading is also performed for every tracked point-feature in parallel. Figure 4 illustrates this layout, and the digital registers used with each PE for descriptor storage, and indication of a tracked feature's location. + +# 8. Patchwork Response Map + +The descriptor layout described in Section 7 generates response maps which have distinct patches of response, one + +![](images/3d1bbf5115940a847d4c86f6aceed318c0af3f504d991eb45cf335768eaea079.jpg) +Figure 6. Steps for updating locations of tracked features, computation of the patchwork descriptor response map, blob-detection & NMS. + +for each tracked point-feature. Each feature's patch is centred upon its last known location, and contains responses from its descriptor. PEs outside these patches will contain responses from the current search descriptor. When visualized these response maps have a "patchwork" like appearance as shown in Figure 5. These patchwork response maps contain sufficient information to both detect reliable new point-features, and update the locations of existing tracked point-features. They also require no additional computation: by simply storing different descriptors across the PE array, the responses used for both tracking and detecting point-features are all computed in parallel. + +# 9. Point-Feature Detection + +Descriptor response is the mechanism by which our approach both detects and tracks point-features. With each new frame a patchwork response map (as described in Section 8) is computed. Feature detection involves searching for any locations where the search descriptor's response strongly identifies some underlying visual point-feature. These locations appear as small distinct regions of high response, surrounded by low response. High response indicates the strong presence of visual features matching the search descriptor, while the surrounding low response indicates these features are distinct to a specific location (i.e. a point-feature). These high response "blobs" (such as shown in Figure 6), are prime candidates at which to initialize new point-features, as their location can be reliably tracked by the descriptor's local response. + +Blob Detection: To locate new point-feature candidates (and also track existing features), blob detection is performed upon each frame's response map, at a scale of the descriptor sampling patterns size. Strong blob detection responses then represent reliable point-feature candidates. Figure 6 illustrates this process: from image, to response map, to blob detection result. + +Point-Feature Initialization: Our approach uses one digital register within each PE to signify if there is a tracked point-feature at its location, with PEs containing tracked + +features then also storing the descriptor of that feature (see Figure 4). This scheme, storing point-features within local PE memory, enables all features to be tracked in parallel. + +To initialize new features, thresholding is performed upon the blob detection result. This is used to identify the PEs located at the centres of the strongest blobs, which are the best candidates for new point-features. New features are then added by simply setting the digital register to signify the presence of a tracked point-feature within each of these PEs. + +Descriptor Readout: Whenever a new point-feature is initialized, we can optionally read out its descriptor from the sensor. This is unnecessary for feature tracking, but could be used for additional tasks or simply for visualization. The descriptor readout is performed sequentially over multiple frames, 1 bit per frame. This still allows hundreds of 8-bit descriptors to be read out per second, but minimizes spikes in the processing time per frame ( $< 1\mu s$ ). + +It is also possible to generate and read out longer descriptors for each new feature (instead of the short 8-bit descriptors used for in-pixel tracking). These could be used by external off-sensor processing to re-identify past features, which left the sensor's view, such as for SLAM system loop-closure/relocalisation. This is beyond the scope of this paper, but should be a relatively straightforward extension. + +# 10. Feature Tracking + +With each new captured frame the locations of tracked point-features must be updated. This is done by finding the local maximum of each feature's descriptor response, around that feature's previous location. The PE containing this maximum is then taken to be that of the feature's new location. This can be viewed as similar to a gradient descent process, with each feature's location following the local maxima of its descriptor response, which evolves in time with each captured frame. For each frame, the descriptor layout of Section 7 is generated, and used to compute the patchwork response maps of Section 8. These response maps have each tracked feature surrounded by a + +![](images/45614405749667eb703daf02b588345964b86395e47ac8663c7fcf7638e2d8ea.jpg) +Figure 7. Examples of feature tracking on SCAMP-7. Left Column: Trails of point-features tracked by SCAMP-7, with thickness representing age. Right Column: 60 FPS video from smartphone mounted alongside SCAMP-7. Our approach tracks features reliably under motion that renders the smartphone's image near unusable. Here SCAMP-7 also outputs an image temporally $(1/16^{th}$ per frame) for visualization, limiting performance to around 850 FPS. The motion blur in SCAMP-7 images shown is an artefact of this image readout scheme, and is not present internally. + +patch of response from its own descriptor. After performing blob detection upon this response map, a patch-wise, nonmaximum-suppression (NMS) routine is performed. This identifies the PEs of highest response within every feature's patch, which are taken to represent each feature's new location. This process is illustrated in Figure 6. It should be noted, that point-features are typically considered to be 1-pixel in size. In practice, however, it is not necessary to + +ensure the NMS routine produces single pixels, just well-located, distinct, and small cluster of pixels. + +- Dropping Weak Features: After computing the descriptor response map for a new frame, there may exist some tracked features with no high values in their associated descriptor response patches. This indicates the visual feature associated with that point-feature's descriptor is no longer clearly identifiable due to occlusion, lighting, or perspective changes. Such features can no longer be reliably tracked by descriptor response. The PEs containing such features are located by thresholding the response map, and their features removed by setting the digital register signifying feature presence to false. + +Benefits From High Frame-Rate: The very high speed at which our approach operates significantly simplifies feature tracking. Captured images will barely change from one frame to the next, and the motion of point-features is reduced to a gradual crawl across the PE array. Specifically two major benefits are: + +1. Reduced Motion Blur. Motion blur in captured images is reduced significantly, if not entirely eliminated, even under violent sensor motion. This helps ensure the visual features underlying each tracked point-feature remain clear and consistent from one image to the next. +2. Reduced Feature Location Search. As captured image will change very little from one frame to the next, so to will the locations of any tracked point-features. This allows the search for each tracked point-feature's new location to be limited to a small region around its previous location, $9 \times 9$ PEs in SCAMP-7. + +# 11. SCAMP Implementation + +The current implementation of our approach on SCAMP-7 can run at just over 3000 FPS. While optimized, further code improvements may still exist. A breakdown of the total computation time per frame is given in Table 1. To put these numbers into perspective, the time taken to output a full uncompressed image from the sensor is well over $20000\mu s$ , and even a 4-bit image requires $2700\mu s$ . Our approach avoids such bottlenecks by performing all necessary computation entirely on-sensor, and outputting only sparse feature locations and descriptors. Examples of real-time output are shown in Figure 7, showcasing point-feature tracking under rapid motion to a degree not possible with a traditional camera sensor. It is worth noting that the SCAMP-7 chip is a research prototype, created using an old $180\mathrm{nm}$ CMOS manufacturing process, with relatively low clock speeds, very restrictive memory per PE, and significantly higher power usage than what is possible using today's state-of-the-art semiconductor technology. That our approach can achieve such performance upon this device is an indication of the potential of the PPA sensor paradigm. + +# 12. Evaluation + +An exact evaluation of our approach against traditional methods is difficult for a number of reasons. Firstly to reach its full potential, our approach must operate at very high frame-rates to ensure small inter-frame motion (at a minimum 500 FPS). This is no issue for our PPA implementation, which can capture and process images at thousands of frames per second, but the number of datasets applicable to feature-tracking captured at such frame rates is very limited. Further testing our PPA implementation upon any such dataset would involve uploading each video frame sequentially into the PPA's PE array to emulate image capture. SCAMP-7 was never designed with this in mind, and uploading such large quantities of data is not efficient and prone to errors. As such we deemed evaluation using high frame rate datasets that would involve uploading thousands of sequential images not feasible. + +We instead performed a comparison against feature tracking using a SCAMP-7 implementation of FAST keypoint detector. This is chosen also because it has speed comparable to our approach, and thus potentially able to track features under the same rapid motion. A modified implementation of [8] was used, which outputs corner point coordinates from the SCAMP-7. Simple point-feature tracking is then performed by matching each corner point with its closest corner point from the previous frame. To match corner points purely by frame-to-frame location (proximity), they must be within a small threshold distance (e.g. 5 pixels). We compare our approach against this FAST based tracking by recording the output of both approaches, viewing the same scenes, running at the same speed of 1000 FPS, using a very similar sequence of sensor motions for both approaches. Some of these motions keep parts of the scene in constant view, allowing some features to be tracked throughout the entire motion. We record how long every feature is tracked for before it is lost, with results for each motion sequence shown in Figure 8. Note, we also do not count any "poor quality" features from the FAST approach, which have lifetimes of less than 0.25 seconds. The distribution of feature lifetimes in these histograms give a sense of how reliable the approaches are comparatively. For example, under the 'Translate' motion, $90\%$ of features using FAST based tracking were lost within 5 seconds, and $0\%$ of features were tracked for over 15 seconds, compared to around $20\%$ with our approach. It is clear from the ratio of feature lifetimes that our approach is far more reliable at tracking features for any significant length of time. + +Limitations In our current implementation, only the locations and descriptors of tracked features are represented in-pixel. Consequently, feature tracking has no concept of orientation and scale, making it non-invariant to rotation and scaling. While this is a significant limitation, we argue that it is not a fundamental drawback of the Descriptor-In-Pixel + +Table 1. SCAMP-7 Computation Time Breakdown. + +
TaskCompute Time μs%
Descriptor Response Map19260
Feature Initialization3110
Feature-Wise NMS4113
Misc/Other Computation5717
Total321-
+ +![](images/7a151d29e22f1ebc0a79f59bc7d166050d6b3ffd6f160f23fbd4521b39d6e408.jpg) + +![](images/2aaa2183b1f5fbfd565e6ca30830ab6945f39e55e6ed2290e11aece25ae8244f.jpg) +Figure 8. Comparison of feature lifetime histograms, our approach vs tracking based on FAST keypoints, under different sensor motions. Both approaches are run at 1000 FPS on SCAMP-7 for comparison. Features tracked using our approach have significantly longer lifespans in general as shown by the ratio. + +![](images/6ab33b15fa31be0bfc5cd3a3d55af1b47546d02a2f7e9b25f344dd9ceeab526d.jpg) + +![](images/5a7af89008f7a807648aa8329166a8a742cae068411007675f95fadb21fba177.jpg) + +approach but rather a constraint imposed by the current state of PPA hardware, which remains in the early stages of development. Specifically, the limited memory within each PE makes storing additional information, such as a feature's orientation, challenging. We expect that as future PPA devices increase memory capacity per PE, our method can be extended to support rotational and scale-invariant tracking. + +# 13. Conclusion + +This paper presented a novel approach for performing point-feature detection and tracking on PPA architectures, demonstrated upon the SCAMP-7 system. Our approach is entirely performed within the pixel-processors of the PPA, and does not require external PC or micro-controller processing. We introduce the concept of Descriptor-In-Pixel which enables our approach to detect and track features by parallel computation of descriptor response across the processing array. This brings major performance benefits allowing our approach to operate at 3000 FPS, on a portable "smart camera" vision system, using around 1 watt of power, reliably tracking point-features under violent motion which renders traditional sensors unusable. + +# References + +[1] Alexandre Alahi, Raphael Ortiz, and Pierre Vandergheynst. 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AnalogNet: Convolutional neural network inference on analog focal plane sensor processors. arXiv preprint arXiv:2006.01765, 2020. 3 \ No newline at end of file diff --git a/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/images.zip b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c30dcb8fdf3cca7bdebf9e8dce02df3b9ab73d32 --- /dev/null +++ b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:697a24c4ed18091344c62e07a477ea391a17d2ab6e2280ff4c5882fedd6328d5 +size 649543 diff --git a/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/layout.json b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..84de8e8f8fcb5ded84e609f18efa3222f59d31e2 --- /dev/null +++ b/2025/Descriptor-In-Pixel _ Point-Feature Tracking For Pixel Processor Arrays/layout.json @@ -0,0 +1,5357 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 83, + 103, + 526, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 103, + 526, + 121 + ], + "spans": [ + { + "bbox": [ + 83, + 103, + 526, + 121 + ], + "type": "text", + "content": "Descriptor-In-Pixel : Point-Feature Tracking for Pixel Processor Arrays" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 179, + 142, + 430, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 142, + 430, + 157 + ], + "spans": [ + { + "bbox": [ + 179, + 142, + 430, + 157 + ], + "type": "text", + "content": "Laurie Bose" + }, + { + "bbox": [ + 179, + 142, + 430, + 157 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 179, + 142, + 430, + 157 + ], + "type": "text", + "content": " Jianing Chen" + }, + { + "bbox": [ + 179, + 142, + 430, + 157 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 179, + 142, + 430, + 157 + ], + "type": "text", + "content": " Piotr Dudek" + }, + { + "bbox": [ + 179, + 142, + 430, + 157 + ], + "type": "inline_equation", + "content": "^{1,2}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 157, + 504, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 157, + 504, + 171 + ], + "spans": [ + { + "bbox": [ + 106, + 157, + 504, + 171 + ], + "type": "text", + "content": "1The University of Manchester, Department of EEE, Manchester, United Kingdom" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 181, + 171, + 429, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 181, + 171, + 429, + 186 + ], + "spans": [ + { + "bbox": [ + 181, + 171, + 429, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 181, + 171, + 429, + 186 + ], + "type": "text", + "content": "Visionchip Limited, Manchester, United Kingdom" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 229, + 186, + 381, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 229, + 186, + 381, + 200 + ], + "spans": [ + { + "bbox": [ + 229, + 186, + 381, + 200 + ], + "type": "text", + "content": "https://lauriebose.github.io/DIP" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "spans": [ + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 53, + 252, + 297, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 252, + 297, + 553 + ], + "spans": [ + { + "bbox": [ + 53, + 252, + 297, + 553 + ], + "type": "text", + "content": "This paper presents a novel approach for joint point-feature detection and tracking, designed specifically for Pixel Processor Array (PPA) vision sensors. Instead of standard pixels, PPA sensors consist of thousands of \"pixel-processors\", enabling massive parallel computation of visual data at the point of light capture. Our approach performs all computation entirely in-pixel, meaning no raw image data need ever leave the sensor for external processing. We introduce a Descriptor-In-Pixel paradigm, in which a feature descriptor is held within the memory of each pixelprocessor. The PPA's architecture enables the response of every processor's descriptor, upon the current image, to be computed in parallel. This produces a \"descriptor response map\" which, by generating the correct layout of descriptors across the pixel-processors, can be used for both point-feature detection and tracking. This reduces sensor output to just sparse feature locations and descriptors, read-out via an address-event interface, giving a greater than " + }, + { + "bbox": [ + 53, + 252, + 297, + 553 + ], + "type": "inline_equation", + "content": "1000 \\times" + }, + { + "bbox": [ + 53, + 252, + 297, + 553 + ], + "type": "text", + "content": " reduction in data transfer compared to raw image output. The sparse readout and complete utilization of all pixel-processors makes our approach very efficient. Our implementation upon the SCAMP-7 PPA prototype runs at over 3000 FPS (Frames Per Second), tracking point-features reliably under violent motion. This is the first work performing point-feature detection and tracking entirely in-pixel." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 577, + 135, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 577, + 135, + 590 + ], + "spans": [ + { + "bbox": [ + 56, + 577, + 135, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 598, + 295, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 598, + 295, + 682 + ], + "spans": [ + { + "bbox": [ + 55, + 598, + 295, + 682 + ], + "type": "text", + "content": "Point-features are distinct points within an image, chosen to be clearly identifiable within multiple images of the same scene, even under changes such as scale, lighting, and perspective. The various methods of point-feature detection and tracking are some of the most widespread tools in computer vision, playing a vital role in Visual Odometry and Simultaneous Localisation and Mapping (SLAM). Many mo" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 316, + 226, + 554, + 328 + ], + "blocks": [ + { + "bbox": [ + 316, + 226, + 554, + 328 + ], + "lines": [ + { + "bbox": [ + 316, + 226, + 554, + 328 + ], + "spans": [ + { + "bbox": [ + 316, + 226, + 554, + 328 + ], + "type": "image", + "image_path": "d1d908ffdc1f5eb9ddec4fa0ca774d2018ce1db0f267728172e84b1c80770aaa.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 336, + 555, + 381 + ], + "lines": [ + { + "bbox": [ + 313, + 336, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 313, + 336, + 555, + 381 + ], + "type": "text", + "content": "Figure 1. A smartphone and SCAMP-7 PPA are strapped together and shaken violently. The frames are not fully synchronised, but it is clear the smartphone's 60 FPS image is unusable, while at 3000 FPS our approach continues tracking features without issue." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 402, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 402, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 312, + 402, + 555, + 510 + ], + "type": "text", + "content": "bile systems such as virtual-reality headsets and unmanned aerial vehicles rely extensively on point-features, often from multiple cameras, to continuously estimate the system's pose. Such systems have limited on-board computational power, limited battery life, and often require low-latency response due to rapid motion. This has pushed the need for computational efficiency, but despite many advancements, the basic task of image transfer from sensor to processor remains a significant time and power bottleneck." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 556, + 715 + ], + "type": "text", + "content": "This issue ultimately reflects the dominant paradigm in electronic imaging, where sensors are primarily built to capture images for a human observer, rather than efficient visual computing. In the context of point-feature detection and tracking, whole images are distilled down to a sparse handful of key-points and descriptors. This is a tiny amount of data compared to the original image, yet standard cameras must still transfer whole images to external processing, repeatedly every frame. This paper presents an alternative, a novel implementation of point-feature detection and tracking for an emerging sensor paradigm, the Pixel-Processor Array (PPA) [9]. Traditional cameras consist of an array of light capture elements, while PPAs are an array of programmable pixel-processors or \"Processing Elements\" (PEs). Each of these processors has its own local memory on which it can perform various computations, and communication with neighbouring processors enabling" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 693, + 295, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 693, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 693, + 295, + 712 + ], + "type": "text", + "content": "This work has been funded in part by EPSRC, grant number EP/Y023048/1." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5392" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "type": "text", + "content": "data transfer across the array. Images are captured directly into the array, with each PE capturing a single pixel of the whole image into its local memory. This sensor architecture enables massively parallel \"in-pixel\" computation upon the focal plane, with the PE array operating as a Single Instruction Multiple Data (SIMD) computer. Such a sensor can capture visual data, extract high level information, and then output only this sparse data, thereby removing the image output bottleneck." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 180, + 295, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 180, + 295, + 491 + ], + "spans": [ + { + "bbox": [ + 56, + 180, + 295, + 491 + ], + "type": "text", + "content": "Our in-pixel approach for point-feature detection and tracking is designed specifically for the PPA's architecture, providing high pixel-processor compute resource utilisation, and minimizing data transfer between sensor and external processing. The core of our approach is based around the concept of \"Descriptor-In-Pixel\", whereby each PE holds a complete point-feature descriptor within its own local memory. The PPA computes in parallel the response of every PE's descriptor upon a captured image. By generating the correct layout of descriptors every frame across the PE array, the computed \"response map\" can be used for both point-feature detection and tracking. All computation is performed within the PPA's pixel-processors (the PE array), without any additional external processing on PC or microcontroller. Therefore, dense sensor output, such as images, is no longer necessary. Instead, only the coordinates of tracked point-features and the descriptors of newly initialized point-features are output, providing a greater than " + }, + { + "bbox": [ + 56, + 180, + 295, + 491 + ], + "type": "inline_equation", + "content": "1000 \\times" + }, + { + "bbox": [ + 56, + 180, + 295, + 491 + ], + "type": "text", + "content": " data reduction compared to whole images. Any additional image data in this paper is output purely for visualization purposes, and is not required for our approach to operate. Our implementation upon the SCAMP-7 PPA prototype [6] achieves speeds just above 3000 frames per second (FPS), with an average sensor output of just 2 bytes per feature, per frame, demonstrating the PPAs potential in high-speed applications (Figure 1)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 502, + 146, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 146, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 146, + 514 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "text", + "content": "Prior PPA Based Works: At the time of writing there are few other works regarding point-feature detection and tracking for PPAs. The early work of [8] demonstrated an implementation of the FAST corner detector [17] at 2300 FPS on SCAMP-5. This work does not perform any form of tracking, and simply outputs the coordinates of detected corner points from the sensor. Performing feature tracking/correspondence using nothing but point coordinates is very challenging, especially as FAST uses no information from previous frames to inform detection, leading to poor temporal stability of detected points between frames. BITVO [16] took steps to address this by outputting a binary edge image alongside the corner points detected by FAST. From these edge images corner descriptors are computed, which are then used in tracking corner points between frames. While this improves tracking quality, the need to" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": "output a full resolution binary image to external processing introduces a significant bottleneck, limiting performance to 300 FPS. The solution to this is performing both detection and tracking entirely on-sensor, avoiding the need to output dense visual information to external processing. This is the motivation behind our approach, which uses purely on-sensor compute to detect and track point-features at thousands of frames per second." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 168, + 553, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 168, + 553, + 442 + ], + "spans": [ + { + "bbox": [ + 313, + 168, + 553, + 442 + ], + "type": "text", + "content": "Event Cameras: Event cameras are another alternative visual sensor [10], outputting a stream of \"events\" which encode time, location and polarity of brightness changes at the per-pixel level. Many works have demonstrated pointfeatures upon event cameras, some using just the raw event stream [15], others incorporating image data into their approach [20], [11], [14]. With the event camera's very high dynamic range and temporal resolution, many of these works produce impressive results, tracking features in rapid motion and challenging lighting conditions. One drawback of event cameras is the complexity involved in dealing with their sparse asynchronous event data (a price paid in exchange for the sensor's very high temporal resolution). This can lead to significant computational costs, and while earlier works may use only a standard desktop CPU [20], recent works require a high-end 300 watt GPU for close to real-time performance [14]. In contrast, a strength of the PPA is that it still allows visual computation to be performed upon captured image frames, instead of complex asynchronous event data. By performing all computation in-pixel, temporal resolutions and latencies comparable to event camera based methods can be achieved, but at a reduced total energy cost." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 443, + 553, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 443, + 553, + 610 + ], + "spans": [ + { + "bbox": [ + 313, + 443, + 553, + 610 + ], + "type": "text", + "content": "Traditional Point-Feature Tracking: Many traditional point-feature approaches such as ORB [18] work by locating salient points (using methods such as FAST [17]), and building descriptors for each of these points. Point-features are then tracked by matching their descriptors against those of salient points detected in the current frame. However, separating detection and tracking into two disjoint processes allows a tracked feature's associated salient point to be missed in detection, potentially replaced by a different salient point in close proximity. This can result in tracked features \"flickering\" as their salient points are temporarily lost. By contrast our approach uses the same mechanism (descriptor response) for both detection and tracking for reliable re-detection of existing features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 621, + 424, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 621, + 424, + 634 + ], + "spans": [ + { + "bbox": [ + 313, + 621, + 424, + 634 + ], + "type": "text", + "content": "3. SCAMP Overview" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "content": "We demonstrate an implementation of our approach upon the SCAMP-7 PPA system [6]. Shown in Figure 2, this vision sensor device has an image resolution of " + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 642, + 553, + 713 + ], + "type": "text", + "content": ", giving a total of 65,536 pixel-processors (PEs). Each processor is connected to its four immediate neighbours, forming a network for data transfer across the array. For local mem" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5393" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 179 + ], + "type": "text", + "content": "ory, each pixel-processor has 23 1-bit digital registers, and 7 analogue registers which store continuous values. Various operations upon local memory are supported, such as addition and subtraction of analogue registers, boolean logic between digital registers, and thresholding of analogue values to digital results. Light is captured separately by each processor, and with each frame trigger, converted to analogue values. Thus each processor captures one pixel of an image that spans the whole array." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 180, + 298, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 180, + 298, + 360 + ], + "spans": [ + { + "bbox": [ + 56, + 180, + 298, + 360 + ], + "type": "text", + "content": "Each pixel-processor does not store and execute its own program instructions, instead a centralised controller broadcasts identical instructions to all 65,536 processors in parallel, which then execute each instruction concurrently. Thus the array operates in a Single Instruction Multiple Data (SIMD) mode, similar to GPU compute. Importantly each pixel-processor contains a 1-bit \"activity flag\" register for enabling and disabling the execution of instructions, allowing for per-pixel conditional execution. By writing programs for the controller, the processor array can be made to execute entire vision applications in-pixels, and output only specific extracted information. Various tasks have been demonstrated on this architecture including neural networks [4],[19],[21],[3], visual odometry [16],[2],[12], and eye tracking [5]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 369, + 174, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 369, + 174, + 382 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 174, + 382 + ], + "type": "text", + "content": "4. Approach Overview" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 388, + 295, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 435 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 435 + ], + "type": "text", + "content": "Our approach uses a novel Descriptor In-Pixel paradigm designed specifically to exploit the PPA's massively parallel, on-sensor computation. Three key components enabled by the PPA's architecture are as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 437, + 295, + 640 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 56, + 437, + 295, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 437, + 295, + 485 + ], + "spans": [ + { + "bbox": [ + 56, + 437, + 295, + 485 + ], + "type": "text", + "content": "1. In-Pixel Descriptors. Our approach involves storing a complete point-feature descriptor within each PE's local digital memory, essentially storing a descriptor at each pixel location." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 485, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 295, + 568 + ], + "type": "text", + "content": "2. Parallel Descriptor Computation. The PPA captures image frames directly into the PE array, with each PE capturing one pixel into its local analogue memory. By examining the pixel data of surrounding PEs, each PE can compute a descriptor for its local image content. This descriptor computation can be performed for every PE (i.e. every pixel location) simultaneously in parallel." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 569, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 569, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 569, + 295, + 640 + ], + "type": "text", + "content": "3. Parallel Descriptor Response Computation. Comparison between stored descriptors and those computed from captured image can be performed in parallel across all PEs. This generates a \"response map\", indicating how strongly the stored descriptors correlate or \"match\" with the captured image content." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "content": "The descriptors distributed across the PE array follow a specific layout, surrounding each tracked point-feature's location with PEs storing its descriptor. This descriptor layout is generated every frame by spreading the descriptors of tracked features into nearby PEs. After computing the response of these stored descriptors on the current image" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 69, + 555, + 236 + ], + "blocks": [ + { + "bbox": [ + 317, + 69, + 555, + 236 + ], + "lines": [ + { + "bbox": [ + 317, + 69, + 555, + 236 + ], + "spans": [ + { + "bbox": [ + 317, + 69, + 555, + 236 + ], + "type": "image", + "image_path": "6fc6210d9a997b16b723ad00e9d85017993c935ce3bbafc1d22220f3911eade1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 243, + 555, + 300 + ], + "lines": [ + { + "bbox": [ + 313, + 243, + 555, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 555, + 300 + ], + "type": "text", + "content": "Figure 2. SCAMP-7 has " + }, + { + "bbox": [ + 313, + 243, + 555, + 300 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 243, + 555, + 300 + ], + "type": "text", + "content": " pixel-processors, each which can capture light, store and process data within its local memory registers, and transfer data to neighbouring processors. A controller sequentially transmits SIMD instructions to the processor array for execution." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 331, + 556, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 556, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 556, + 464 + ], + "type": "text", + "content": "frame, each tracked feature will be surrounded by a patch of response from its own descriptor. These response patches are analysed in parallel, determining the new location of each tracked feature. This tracking requires that features do not move further than the predetermined patch area between frames. However, our approach can operate at thousands of frames per second, allowing patch areas to be very small " + }, + { + "bbox": [ + 313, + 331, + 556, + 464 + ], + "type": "inline_equation", + "content": "(9 \\times 9)" + }, + { + "bbox": [ + 313, + 331, + 556, + 464 + ], + "type": "text", + "content": " and still facilitate reliable tracking. New point-features are detected and initialized by analysing the responses of those PEs not inside the patch of any tracked feature. These aspects will be described later in detail." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 469, + 556, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 469, + 556, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 556, + 578 + ], + "type": "text", + "content": "In summary, our approach performs all necessary computation within the PE array, each feature is tracked between frames using pixel-processors surrounding its location, while all remaining pixel-processors perform a search to detect new features. This approach is very efficient essentially utilizing " + }, + { + "bbox": [ + 313, + 469, + 556, + 578 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 469, + 556, + 578 + ], + "type": "text", + "content": " of the PPA's compute, and also allows sensor output to be reduced to simply the locations and descriptors of tracked features. As a result, our approach can operate at thousands of frames per second upon SCAMP-7." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 604, + 432, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 604, + 432, + 618 + ], + "spans": [ + { + "bbox": [ + 313, + 604, + 432, + 618 + ], + "type": "text", + "content": "5. In-Pixel Descriptors" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "content": "We make use of simple binary point descriptors, similar to the well known BRIEF descriptor [7]. Such descriptors are stored as binary strings within each PE, occupying multiple digital registers (1 bit per register). Computing a PE's descriptor for a given image involves comparing pairs of pixel data around its location, each comparison generating 1 bit of the descriptor's string. Specifically, the " + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "content": " bit of the de" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5394" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 553, + 344 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 344 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 344 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 344 + ], + "type": "image", + "image_path": "2c323482fd614d634e069bca887b091ddb4a61865ebe5a80b6ea5ab9ad52997b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 352, + 555, + 399 + ], + "lines": [ + { + "bbox": [ + 55, + 352, + 555, + 399 + ], + "spans": [ + { + "bbox": [ + 55, + 352, + 555, + 399 + ], + "type": "text", + "content": "Figure 3. Examples of simple descriptor response maps, where the same 8-bit descriptor is stored inside all PEs. Maps are generated for three example descriptors, all using the same sampling pattern (Bottom Left), and input image (Top Left). For comparison we generate response maps using both our weight pixel-pairs method, and the Hamming distance. High response \"blobs\" pinpoint certain visual structures, but those from the Hamming distance can be unreliable for tracking, as illustrated in Teal." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 418, + 167, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 418, + 167, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 418, + 167, + 430 + ], + "type": "text", + "content": "scriptor, " + }, + { + "bbox": [ + 55, + 418, + 167, + 430 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 55, + 418, + 167, + 430 + ], + "type": "text", + "content": " , is computed as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 119, + 436, + 295, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 436, + 295, + 468 + ], + "spans": [ + { + "bbox": [ + 119, + 436, + 295, + 468 + ], + "type": "interline_equation", + "content": "d _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} p _ {i (1)} < p _ {i (2)} \\\\ 1, & \\text {i f} p _ {i (1)} \\geq p _ {i (2)} \\end{array} \\right. \\tag {1}", + "image_path": "a5d1023bc7bf14ce5b5d29ca27137de4cdad4b4bd734d0fcd3163197323c5d49.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 475, + 295, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 295, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 295, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 475, + 295, + 510 + ], + "type": "inline_equation", + "content": "p_{i(1)}, p_{i(2)}" + }, + { + "bbox": [ + 55, + 475, + 295, + 510 + ], + "type": "text", + "content": " are a pair of pixel values at locations relative to the PE's location, according to some predetermined sampling pattern." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 510, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 653 + ], + "type": "text", + "content": "Descriptor Size: For maximum efficiency, an entire descriptor should be stored within each PE (i.e. one descriptor per pixel location). However, PE local memory on SCAMP-7 is very limited, restricting this first demonstration of our approach to tiny 8-bit descriptors, performing just eight local pixel pair comparisons. Due to how our approach operates, these are still sufficient for reliable high-speed feature tracking. Larger descriptors could be utilized on future PPA hardware, with greater memory per PE. Note, using significantly larger descriptors " + }, + { + "bbox": [ + 55, + 510, + 295, + 653 + ], + "type": "inline_equation", + "content": "(128+" + }, + { + "bbox": [ + 55, + 510, + 295, + 653 + ], + "type": "text", + "content": " bit) would likely not improve tracking in our approach, but these would be better suited to long term tasks such as re-localisation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 295, + 714 + ], + "type": "text", + "content": "Descriptor Sampling Pattern: Computing the binary descriptor for a specific pixel location involves comparing pairs of pixels, sampled in a given pattern about that location. This \"sampling pattern\", is chosen with the aim to compress the local image into a compact bit string, cap" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 418, + 555, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 555, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 555, + 548 + ], + "type": "text", + "content": "turing any discriminative structures within the local image content. BRIEF [7] uses fixed random sampling patterns, which are too large (128+ bit) to use for in-pixel descriptors. Instead we use fixed sampling patterns similar to the BRISK [13] & FREAK [1] descriptors. We only use a single sampling pattern during operation, for all descriptors across all PEs, as this enables us to fully exploit the PPA's parallel SIMD compute. We opted for a 'compare-to-center' sampling pattern (see Figure 3) due to its simplicity and low computational cost, though many other patterns could be used." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 561, + 468, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 561, + 468, + 575 + ], + "spans": [ + { + "bbox": [ + 313, + 561, + 468, + 575 + ], + "type": "text", + "content": "6. Descriptor Response-Maps" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": "With each new image frame our approach generates a layout of descriptors stored across the PE array, and then computes the \"response\" of each PE's stored descriptor. Descriptor response refers to how strongly the visual features represented by a specific descriptor are present at a certain location within an image. Measuring the response of a PE's stored descriptor first involves computing the descriptor for the image at that PE's location. The computed image descriptor is then compared to the PE's stored descriptor. A higher similarity between the two indicates that the stored descriptor more accurately represents the local image con" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "5395" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 298, + 157 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 298, + 157 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 298, + 157 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 298, + 157 + ], + "type": "image", + "image_path": "4575cc1cdd37059b132aba9ea8c59df5c8e6e50d904f1a66152a932e5cbb072c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 163, + 296, + 231 + ], + "lines": [ + { + "bbox": [ + 55, + 163, + 296, + 231 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 296, + 231 + ], + "type": "text", + "content": "Figure 4. Descriptor layout described in Section 7. Each PE stores an 8-bit descriptor within its digital registers. Tracked features are surrounded by patches of PEs storing their descriptor (shown by various colours). PEs outside such patches store the current search descriptor. Additionally, 1 digital register in each PE indicates if tracked feature is located there (shown in yellow)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 239, + 296, + 369 + ], + "blocks": [ + { + "bbox": [ + 56, + 239, + 296, + 369 + ], + "lines": [ + { + "bbox": [ + 56, + 239, + 296, + 369 + ], + "spans": [ + { + "bbox": [ + 56, + 239, + 296, + 369 + ], + "type": "image", + "image_path": "5e246ef0d872e69f2d92c2393f319932428f0488dd87bfe426814f8f1ab28a75.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 376, + 296, + 420 + ], + "lines": [ + { + "bbox": [ + 55, + 376, + 296, + 420 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 296, + 420 + ], + "type": "text", + "content": "Figure 5. Left: A \"patchwork\" response map computed using the descriptor layout of Section 7. Right: Corresponding captured image & tracked features. Two response patches " + }, + { + "bbox": [ + 55, + 376, + 296, + 420 + ], + "type": "inline_equation", + "content": "(9 \\times 9" + }, + { + "bbox": [ + 55, + 376, + 296, + 420 + ], + "type": "text", + "content": " PEs) from different features are shown in detail." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 446, + 295, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 446, + 295, + 471 + ], + "spans": [ + { + "bbox": [ + 55, + 446, + 295, + 471 + ], + "type": "text", + "content": "tent. Thus, as will be described, descriptor response should correlate to a measurement of this similarity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 472, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 296, + 533 + ], + "type": "text", + "content": "The PPA architecture enables the response of every PEs stored descriptor to be computed in parallel, and placed into local analogue memory, forming a \"descriptor response map\" spread across the PE array. Figure 3 shows simple response maps, with all PEs storing the same descriptor." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "content": "Measuring Descriptor Similarity and Response: A simple measure of similarity between binary descriptors is to compute the number of matching bits between their bit strings (i.e. Hamming distance), a common choice on traditional digital processing, being very cheap to compute. SCAMP-7 however has analogue computation capability, and captures images directly into its PE array as analogue data. For almost no additional cost, this analogue compute allows to also account for the raw pixel data when computing descriptor response. This is very useful for handling image regions that will not provide reliable point-feature tracking, such as low texture or highly repetitive texture regions. Descriptors inside such \"ambiguous\" regions will have poor temporal stability, as very slight image changes (from noise or lighting) will produce radically different de" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "type": "text", + "content": "scriptors from one frame to the next. Thus we do not simply measure the number of matching bits between descriptors, but also weight these matches (and penalize misses) by the magnitude of the pixel pair comparison results associated with each bit. Specifically, we compute the response " + }, + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "type": "text", + "content": " of a stored descriptor at a certain image location as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 367, + 152, + 555, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 152, + 555, + 186 + ], + "spans": [ + { + "bbox": [ + 367, + 152, + 555, + 186 + ], + "type": "interline_equation", + "content": "R = \\sum_ {i = 1} ^ {8} (2 d _ {i} - 1) \\left(p _ {i (1)} - p _ {i (2)}\\right) \\tag {2}", + "image_path": "f8bfb4bc1fcc869773a53606a16e9d1584bef1c83994d9bad9e97ee867633fcf.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "spans": [ + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "inline_equation", + "content": "d_{i} \\in \\{0,1\\}" + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "text", + "content": ", is the " + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "text", + "content": " bit of the descriptor, and " + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "inline_equation", + "content": "p_{i(1)}, p_{i(2)} \\in \\Re" + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "text", + "content": " are the pixel values for the " + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 313, + 193, + 555, + 278 + ], + "type": "text", + "content": " pair of pixels, selected according to the descriptor's sampling pattern. This ensures high descriptor response is only produced in image regions which can provide reliable tracking. Figure 3 shows example response maps generated using both this weighted pixel-pairs method, and the Hamming distance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 289, + 424, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 289, + 424, + 303 + ], + "spans": [ + { + "bbox": [ + 314, + 289, + 424, + 303 + ], + "type": "text", + "content": "7. Descriptor Layout" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 308, + 554, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 554, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 554, + 392 + ], + "type": "text", + "content": "The response maps of Figure 3 are simple examples, with the same descriptor being stored inside every PE. In practice, with every captured frame, our approach generates a layout of various descriptors across the PE array. This descriptor layout enables the computed response maps to be used for both point-feature tracking and detection. Generation of this layout splits all PEs into one of two categories." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 394, + 554, + 548 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 315, + 394, + 554, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 394, + 554, + 476 + ], + "spans": [ + { + "bbox": [ + 315, + 394, + 554, + 476 + ], + "type": "text", + "content": "1. PEs Located Near Tracked Point-Features. Each tracked point-feature's descriptor is spread into a local \"patch\" of PEs surrounding its location (i.e. around the PE the feature currently resides in). The computed response map will then have each tracked feature surrounded by responses from its own descriptor, from which the feature's new location can be determined." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 477, + 554, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 477, + 554, + 548 + ], + "spans": [ + { + "bbox": [ + 315, + 477, + 554, + 548 + ], + "type": "text", + "content": "2. All Remaining PEs. A single \"search descriptor\" is loaded into all remaining PEs, not located close to any tracked feature. The responses from this descriptor are examined to detect new point-features. To detect different features, the search descriptor itself is randomized every frame." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 552, + 554, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 554, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 554, + 658 + ], + "type": "text", + "content": "To generate this descriptor layout, the search descriptor is first loaded into all PEs in parallel, excluding PEs containing tracked point-features. Next the descriptors of tracked point-features are spread out from their containing PEs, across a small local patch of PEs " + }, + { + "bbox": [ + 313, + 552, + 554, + 658 + ], + "type": "inline_equation", + "content": "(9 \\times 9)" + }, + { + "bbox": [ + 313, + 552, + 554, + 658 + ], + "type": "text", + "content": ". This descriptor spreading is also performed for every tracked point-feature in parallel. Figure 4 illustrates this layout, and the digital registers used with each PE for descriptor storage, and indication of a tracked feature's location." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 669, + 463, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 669, + 463, + 683 + ], + "spans": [ + { + "bbox": [ + 313, + 669, + 463, + 683 + ], + "type": "text", + "content": "8. Patchwork Response Map" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "The descriptor layout described in Section 7 generates response maps which have distinct patches of response, one" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5396" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 553, + 196 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 196 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 196 + ], + "type": "image", + "image_path": "3d1bbf5115940a847d4c86f6aceed318c0af3f504d991eb45cf335768eaea079.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 205, + 553, + 217 + ], + "lines": [ + { + "bbox": [ + 55, + 205, + 553, + 217 + ], + "spans": [ + { + "bbox": [ + 55, + 205, + 553, + 217 + ], + "type": "text", + "content": "Figure 6. Steps for updating locations of tracked features, computation of the patchwork descriptor response map, blob-detection & NMS." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 237, + 294, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 237, + 294, + 381 + ], + "spans": [ + { + "bbox": [ + 54, + 237, + 294, + 381 + ], + "type": "text", + "content": "for each tracked point-feature. Each feature's patch is centred upon its last known location, and contains responses from its descriptor. PEs outside these patches will contain responses from the current search descriptor. When visualized these response maps have a \"patchwork\" like appearance as shown in Figure 5. These patchwork response maps contain sufficient information to both detect reliable new point-features, and update the locations of existing tracked point-features. They also require no additional computation: by simply storing different descriptors across the PE array, the responses used for both tracking and detecting point-features are all computed in parallel." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 393, + 192, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 393, + 192, + 405 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 192, + 405 + ], + "type": "text", + "content": "9. Point-Feature Detection" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 414, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 414, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 56, + 414, + 295, + 593 + ], + "type": "text", + "content": "Descriptor response is the mechanism by which our approach both detects and tracks point-features. With each new frame a patchwork response map (as described in Section 8) is computed. Feature detection involves searching for any locations where the search descriptor's response strongly identifies some underlying visual point-feature. These locations appear as small distinct regions of high response, surrounded by low response. High response indicates the strong presence of visual features matching the search descriptor, while the surrounding low response indicates these features are distinct to a specific location (i.e. a point-feature). These high response \"blobs\" (such as shown in Figure 6), are prime candidates at which to initialize new point-features, as their location can be reliably tracked by the descriptor's local response." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 676 + ], + "type": "text", + "content": "Blob Detection: To locate new point-feature candidates (and also track existing features), blob detection is performed upon each frame's response map, at a scale of the descriptor sampling patterns size. Strong blob detection responses then represent reliable point-feature candidates. Figure 6 illustrates this process: from image, to response map, to blob detection result." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "Point-Feature Initialization: Our approach uses one digital register within each PE to signify if there is a tracked point-feature at its location, with PEs containing tracked" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 238, + 553, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 238, + 553, + 273 + ], + "spans": [ + { + "bbox": [ + 313, + 238, + 553, + 273 + ], + "type": "text", + "content": "features then also storing the descriptor of that feature (see Figure 4). This scheme, storing point-features within local PE memory, enables all features to be tracked in parallel." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 274, + 553, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 274, + 553, + 356 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 553, + 356 + ], + "type": "text", + "content": "To initialize new features, thresholding is performed upon the blob detection result. This is used to identify the PEs located at the centres of the strongest blobs, which are the best candidates for new point-features. New features are then added by simply setting the digital register to signify the presence of a tracked point-feature within each of these PEs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "text", + "content": "Descriptor Readout: Whenever a new point-feature is initialized, we can optionally read out its descriptor from the sensor. This is unnecessary for feature tracking, but could be used for additional tasks or simply for visualization. The descriptor readout is performed sequentially over multiple frames, 1 bit per frame. This still allows hundreds of 8-bit descriptors to be read out per second, but minimizes spikes in the processing time per frame (" + }, + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "inline_equation", + "content": "< 1\\mu s" + }, + { + "bbox": [ + 313, + 357, + 554, + 453 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 454, + 554, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 454, + 554, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 454, + 554, + 538 + ], + "type": "text", + "content": "It is also possible to generate and read out longer descriptors for each new feature (instead of the short 8-bit descriptors used for in-pixel tracking). These could be used by external off-sensor processing to re-identify past features, which left the sensor's view, such as for SLAM system loop-closure/relocalisation. This is beyond the scope of this paper, but should be a relatively straightforward extension." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 549, + 424, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 549, + 424, + 563 + ], + "spans": [ + { + "bbox": [ + 315, + 549, + 424, + 563 + ], + "type": "text", + "content": "10. Feature Tracking" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 554, + 713 + ], + "type": "text", + "content": "With each new captured frame the locations of tracked point-features must be updated. This is done by finding the local maximum of each feature's descriptor response, around that feature's previous location. The PE containing this maximum is then taken to be that of the feature's new location. This can be viewed as similar to a gradient descent process, with each feature's location following the local maxima of its descriptor response, which evolves in time with each captured frame. For each frame, the descriptor layout of Section 7 is generated, and used to compute the patchwork response maps of Section 8. These response maps have each tracked feature surrounded by a" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5397" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 294, + 479 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 294, + 479 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 294, + 479 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 294, + 479 + ], + "type": "image", + "image_path": "45614405749667eb703daf02b588345964b86395e47ac8663c7fcf7638e2d8ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 487, + 296, + 588 + ], + "lines": [ + { + "bbox": [ + 55, + 487, + 296, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 296, + 588 + ], + "type": "text", + "content": "Figure 7. Examples of feature tracking on SCAMP-7. Left Column: Trails of point-features tracked by SCAMP-7, with thickness representing age. Right Column: 60 FPS video from smartphone mounted alongside SCAMP-7. Our approach tracks features reliably under motion that renders the smartphone's image near unusable. Here SCAMP-7 also outputs an image temporally " + }, + { + "bbox": [ + 55, + 487, + 296, + 588 + ], + "type": "inline_equation", + "content": "(1/16^{th}" + }, + { + "bbox": [ + 55, + 487, + 296, + 588 + ], + "type": "text", + "content": " per frame) for visualization, limiting performance to around 850 FPS. The motion blur in SCAMP-7 images shown is an artefact of this image readout scheme, and is not present internally." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 617, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 296, + 715 + ], + "type": "text", + "content": "patch of response from its own descriptor. After performing blob detection upon this response map, a patch-wise, nonmaximum-suppression (NMS) routine is performed. This identifies the PEs of highest response within every feature's patch, which are taken to represent each feature's new location. This process is illustrated in Figure 6. It should be noted, that point-features are typically considered to be 1-pixel in size. In practice, however, it is not necessary to" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "ensure the NMS routine produces single pixels, just well-located, distinct, and small cluster of pixels." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 98, + 555, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 98, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 98, + 555, + 228 + ], + "type": "text", + "content": "- Dropping Weak Features: After computing the descriptor response map for a new frame, there may exist some tracked features with no high values in their associated descriptor response patches. This indicates the visual feature associated with that point-feature's descriptor is no longer clearly identifiable due to occlusion, lighting, or perspective changes. Such features can no longer be reliably tracked by descriptor response. The PEs containing such features are located by thresholding the response map, and their features removed by setting the digital register signifying feature presence to false." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 230, + 556, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 230, + 556, + 302 + ], + "spans": [ + { + "bbox": [ + 313, + 230, + 556, + 302 + ], + "type": "text", + "content": "Benefits From High Frame-Rate: The very high speed at which our approach operates significantly simplifies feature tracking. Captured images will barely change from one frame to the next, and the motion of point-features is reduced to a gradual crawl across the PE array. Specifically two major benefits are:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 315, + 307, + 555, + 437 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 315, + 307, + 555, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 307, + 555, + 366 + ], + "spans": [ + { + "bbox": [ + 315, + 307, + 555, + 366 + ], + "type": "text", + "content": "1. Reduced Motion Blur. Motion blur in captured images is reduced significantly, if not entirely eliminated, even under violent sensor motion. This helps ensure the visual features underlying each tracked point-feature remain clear and consistent from one image to the next." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 366, + 555, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 366, + 555, + 437 + ], + "spans": [ + { + "bbox": [ + 315, + 366, + 555, + 437 + ], + "type": "text", + "content": "2. Reduced Feature Location Search. As captured image will change very little from one frame to the next, so to will the locations of any tracked point-features. This allows the search for each tracked point-feature's new location to be limited to a small region around its previous location, " + }, + { + "bbox": [ + 315, + 366, + 555, + 437 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 315, + 366, + 555, + 437 + ], + "type": "text", + "content": " PEs in SCAMP-7." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 453, + 463, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 453, + 463, + 467 + ], + "spans": [ + { + "bbox": [ + 315, + 453, + 463, + 467 + ], + "type": "text", + "content": "11. SCAMP Implementation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": "The current implementation of our approach on SCAMP-7 can run at just over 3000 FPS. While optimized, further code improvements may still exist. A breakdown of the total computation time per frame is given in Table 1. To put these numbers into perspective, the time taken to output a full uncompressed image from the sensor is well over " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "20000\\mu s" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": ", and even a 4-bit image requires " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "2700\\mu s" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": ". Our approach avoids such bottlenecks by performing all necessary computation entirely on-sensor, and outputting only sparse feature locations and descriptors. Examples of real-time output are shown in Figure 7, showcasing point-feature tracking under rapid motion to a degree not possible with a traditional camera sensor. It is worth noting that the SCAMP-7 chip is a research prototype, created using an old " + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "inline_equation", + "content": "180\\mathrm{nm}" + }, + { + "bbox": [ + 313, + 474, + 556, + 715 + ], + "type": "text", + "content": " CMOS manufacturing process, with relatively low clock speeds, very restrictive memory per PE, and significantly higher power usage than what is possible using today's state-of-the-art semiconductor technology. That our approach can achieve such performance upon this device is an indication of the potential of the PPA sensor paradigm." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5398" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 133, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 133, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 133, + 83 + ], + "type": "text", + "content": "12. Evaluation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 281 + ], + "type": "text", + "content": "An exact evaluation of our approach against traditional methods is difficult for a number of reasons. Firstly to reach its full potential, our approach must operate at very high frame-rates to ensure small inter-frame motion (at a minimum 500 FPS). This is no issue for our PPA implementation, which can capture and process images at thousands of frames per second, but the number of datasets applicable to feature-tracking captured at such frame rates is very limited. Further testing our PPA implementation upon any such dataset would involve uploading each video frame sequentially into the PPA's PE array to emulate image capture. SCAMP-7 was never designed with this in mind, and uploading such large quantities of data is not efficient and prone to errors. As such we deemed evaluation using high frame rate datasets that would involve uploading thousands of sequential images not feasible." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "type": "text", + "content": "We instead performed a comparison against feature tracking using a SCAMP-7 implementation of FAST keypoint detector. This is chosen also because it has speed comparable to our approach, and thus potentially able to track features under the same rapid motion. A modified implementation of [8] was used, which outputs corner point coordinates from the SCAMP-7. Simple point-feature tracking is then performed by matching each corner point with its closest corner point from the previous frame. To match corner points purely by frame-to-frame location (proximity), they must be within a small threshold distance (e.g. 5 pixels). We compare our approach against this FAST based tracking by recording the output of both approaches, viewing the same scenes, running at the same speed of 1000 FPS, using a very similar sequence of sensor motions for both approaches. Some of these motions keep parts of the scene in constant view, allowing some features to be tracked throughout the entire motion. We record how long every feature is tracked for before it is lost, with results for each motion sequence shown in Figure 8. Note, we also do not count any \"poor quality\" features from the FAST approach, which have lifetimes of less than 0.25 seconds. The distribution of feature lifetimes in these histograms give a sense of how reliable the approaches are comparatively. For example, under the 'Translate' motion, " + }, + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "type": "text", + "content": " of features using FAST based tracking were lost within 5 seconds, and " + }, + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "type": "text", + "content": " of features were tracked for over 15 seconds, compared to around " + }, + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 55, + 282, + 296, + 641 + ], + "type": "text", + "content": " with our approach. It is clear from the ratio of feature lifetimes that our approach is far more reliable at tracking features for any significant length of time." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "Limitations In our current implementation, only the locations and descriptors of tracked features are represented in-pixel. Consequently, feature tracking has no concept of orientation and scale, making it non-invariant to rotation and scaling. While this is a significant limitation, we argue that it is not a fundamental drawback of the Descriptor-In-Pixel" + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 321, + 91, + 545, + 167 + ], + "blocks": [ + { + "bbox": [ + 340, + 71, + 528, + 82 + ], + "lines": [ + { + "bbox": [ + 340, + 71, + 528, + 82 + ], + "spans": [ + { + "bbox": [ + 340, + 71, + 528, + 82 + ], + "type": "text", + "content": "Table 1. SCAMP-7 Computation Time Breakdown." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 91, + 545, + 167 + ], + "lines": [ + { + "bbox": [ + 321, + 91, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 321, + 91, + 545, + 167 + ], + "type": "table", + "html": "
TaskCompute Time μs%
Descriptor Response Map19260
Feature Initialization3110
Feature-Wise NMS4113
Misc/Other Computation5717
Total321-
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Comparison of feature lifetime histograms, our approach vs tracking based on FAST keypoints, under different sensor motions. Both approaches are run at 1000 FPS on SCAMP-7 for comparison. Features tracked using our approach have significantly longer lifespans in general as shown by the ratio." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 434, + 182, + 553, + 251 + ], + "blocks": [ + { + "bbox": [ + 434, + 182, + 553, + 251 + ], + "lines": [ + { + "bbox": [ + 434, + 182, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 434, + 182, + 553, + 251 + ], + "type": "image", + "image_path": "6ab33b15fa31be0bfc5cd3a3d55af1b47546d02a2f7e9b25f344dd9ceeab526d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 434, + 253, + 553, + 323 + ], + "blocks": [ + { + "bbox": [ + 434, + 253, + 553, + 323 + ], + "lines": [ + { + "bbox": [ + 434, + 253, + 553, + 323 + ], + "spans": [ + { + "bbox": [ + 434, + 253, + 553, + 323 + ], + "type": "image", + "image_path": "5a7af89008f7a807648aa8329166a8a742cae068411007675f95fadb21fba177.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 420, + 555, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 420, + 555, + 504 + ], + "spans": [ + { + "bbox": [ + 313, + 420, + 555, + 504 + ], + "type": "text", + "content": "approach but rather a constraint imposed by the current state of PPA hardware, which remains in the early stages of development. Specifically, the limited memory within each PE makes storing additional information, such as a feature's orientation, challenging. We expect that as future PPA devices increase memory capacity per PE, our method can be extended to support rotational and scale-invariant tracking." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 532, + 394, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 532, + 394, + 544 + ], + "spans": [ + { + "bbox": [ + 315, + 532, + 394, + 544 + ], + "type": "text", + "content": "13. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 713 + ], + "type": "text", + "content": "This paper presented a novel approach for performing point-feature detection and tracking on PPA architectures, demonstrated upon the SCAMP-7 system. Our approach is entirely performed within the pixel-processors of the PPA, and does not require external PC or micro-controller processing. We introduce the concept of Descriptor-In-Pixel which enables our approach to detect and track features by parallel computation of descriptor response across the processing array. This brings major performance benefits allowing our approach to operate at 3000 FPS, on a portable \"smart camera\" vision system, using around 1 watt of power, reliably tracking point-features under violent motion which renders traditional sensors unusable." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5399" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 133 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 133 + ], + "type": "text", + "content": "[1] Alexandre Alahi, Raphael Ortiz, and Pierre Vandergheynst. 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However, existing uni-modal sewing pattern generation models struggle to effectively encode complex design concepts with a multimodal nature and correlate them with vectorized sewing patterns that possess precise geometric structures and intricate sewing relations. In this work, we propose a novel sewing pattern generation approach Design2GarmentCode based on Large Multimodal Models (LMMs), to generate parametric pattern-making programs from multi-modal design concepts. LMM offers an intuitive interface for interpreting diverse design inputs, while pattern-making programs could serve as well-structured and semantically meaningful representations of sewing patterns, and act as a robust bridge connecting the cross-domain pattern-making knowledge embedded in LMMs with vectorized sewing patterns. Experimental results demonstrate that our method can flexibly handle various complex design expressions such as images, textual descriptions, designer sketches, or their combinations, and convert them into size-precise sewing patterns with correct stitches. Compared to previous methods, our approach significantly enhances training efficiency, generation quality, and authoring flexibility. Project page: https://style3d.github.io/design2garmentcode.", + "bbox": [ + 89, + 306, + 483, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 715, + 220, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While generative AI has significantly propelled creativity in fashion design, turning those design ideas into wearable realities remains a formidable challenge. Sewing patterns are the key components to bridge the gap between abstract design ideas and wearable realities. They are foundational blueprints that dictate the precise shapes and dimensions of fabric pieces, essential for assembling garments in both the physical and virtual fashion realms.", + "bbox": [ + 89, + 741, + 483, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a65cd375c6b895b9a38d21566cc80cf3af4e47fb2052c243e3bff074f08d2d3a.jpg", + "image_caption": [ + "Figure 1. Traditional sewing pattern generation approaches (top) use uni-modal models trained on synthetic datasets generated by parametric pattern-making programs (red arrow) to convert text or image prompts into vector-quantized patterns. These methods are resource-intensive and often yield oversimplified patterns with stitching errors. Our approach (bottom) utilizes large pre-trained LMMs to directly translate design concepts into parametric programs and configuration files (blue arrow), enabling dedicated, structurally correct pattern generation from multi-modal design inputs within a unified framework." + ], + "image_footnote": [], + "bbox": [ + 517, + 273, + 903, + 486 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Traditionally, sewing patterns are drafted manually by professional pattern-makers with years of practice, making the process inefficient, error-prone, and unable to meet the growing demands for refinement and personalization in the fashion market. To this end, parametric pattern-making researches [8, 29, 31] and industrial solutions [1-4] have emerged. These methods formalize the pattern-making process as geometric functions governed by parameters such as body measurements and design features, thereby accelerating the process by enabling pattern makers to generate sewing patterns through parameter adjustments instead of starting from scratch. However, creating these function templates is still complex, requiring not only advanced pattern-making skills but also geometric intuition, mathematical modeling knowledge, and coding abilities to trans", + "bbox": [ + 511, + 674, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Works done during the internship at Style3D Research.", + "bbox": [ + 107, + 875, + 405, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 109, + 887, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23712", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/172db2ce9ade4c6369de02b98442484c219570ba524954bb075c3fc0ae08c741.jpg", + "image_caption": [ + "(a) Limited Generation Diversity" + ], + "image_footnote": [], + "bbox": [ + 96, + 94, + 256, + 157 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/07ba85d92998759312e6e54b29895220f4e7b53ae1adf9b17545af70028f6879.jpg", + "image_caption": [ + "(b) Self-Intersection" + ], + "image_footnote": [], + "bbox": [ + 267, + 94, + 359, + 155 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e68c8ff5c6772001159b8bf92e8efd57c74215427e69e73b98a5162aa498159e.jpg", + "image_caption": [ + "(c) Wrong Stitches", + "Figure 2. (a) Despite prompts specifying diverse neckline types, DressCode [22] consistently produces only V-neck designs, indicating limited generation diversity. (b) SewFormer [40] often generates sewing patterns with self-intersecting panels, compromising pattern validity. (c) Stitching errors are also prevalent in Sewformer [40], as shown here where a pant side seam is mistakenly stitched to a shirt shoulder seam, resulting in draping failure." + ], + "image_footnote": [], + "bbox": [ + 375, + 90, + 480, + 160 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "late pattern-making expertise into CAD programs. These technical barriers significantly restrict the widespread adoption of parametric pattern-making solutions.", + "bbox": [ + 89, + 309, + 482, + 354 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, several learning-based approaches for sewing pattern generation have been introduced. For instance, NeuralTailor [30] focuses on extracting sewing patterns from unstructured point clouds, DressCode [22] targets text-to-sewing pattern generation, and SewFormer [40] is designed for image-based sewing pattern generation. However, they are generally trained on paired design-sewing pattern data, necessitating large datasets to effectively capture the multimodal nature of design concepts. Furthermore, sewing patterns require centimeter-level precision to ensure proper garment fit, which presents a significant challenge for neural networks that only provide statistical approximations of the true function based on their training data [14, 23, 47]. As a result, these methods frequently generate oversimplified patterns with flawed geometry or stitches, potentially leading to draping failures (Figure 2).", + "bbox": [ + 89, + 356, + 482, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present Design2GarmentCode, an innovative approach that leverages the generalization capabilities of vision-language foundation models to achieve multi-modal sewing pattern generation with minimal computational and data requirements. Unlike previous methods that directly synthesize vector-quantized patterns, Design2GarmentCode employs LMMs to learn the syntax of parametric pattern-making programs, translating design concepts into parameters and programs that can be executed to produce precise and structurally accurate sewing patterns. Design2GarmentCode combines a pre-trained Large Multimodal Model (LMM) as a design interpreter with a finetuned Large Language Model (LLM) as a program synthesizer. Specifically, the LLM is finetuned on code snippets from GarmentCode [31], a domain-specific language for constructing parametric sewing patterns. At runtime, the design interpreter extracts both topological and geometrical information from the design input by responding to a series of questions from the program synthesizer, which then generates garment programs and design config", + "bbox": [ + 89, + 599, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "urations following GarmentCode syntax. Our method offers the following major contributions:", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a novel modality-agnostic framework with an intuitive, intelligent interface capable of processing user design intentions across multiple modalities simultaneously by integrating pre-trained LMMs.", + "- We present the first sewing pattern generation approach grounded in program synthesis, delivering fully interpretable, geometrically precise, and structurally accurate patterns through a more compact, semantically clear, and LLM-friendly representation.", + "- Our framework benefits real-world production by enabling flexible pattern authoring through natural language or physical feedback, allowing precise customization and efficient creation of novel garment components, represented as parametric pattern-making programs.", + "- Our approach requires only minimal fine-tuning of a pre-trained LLM and the training of a lightweight, text-conditioned transformer decoder, making it more efficient than existing vector-quantized sewing pattern generation models trained from scratch while offering superior generation quality and authoring flexibility." + ], + "bbox": [ + 513, + 125, + 903, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 441, + 653, + 457 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Garment Modeling with Sewing Patterns", + "text_level": 1, + "bbox": [ + 511, + 468, + 862, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Garment modeling and generation can be broadly classified into two categories: direct 3D garment generation (meshes) and sewing pattern generation, which are later draped onto human bodies via cloth simulation [39, 53, 56] or learning-based techniques [35, 37]. Direct 3D garment generation often relies on differentiable garment representations like unsigned distance fields [65, 67], shells [42], or Gaussian splatting [48]. However, it presents challenges in terms of both geometric accuracy and editability. On one hand, capturing fine garment details like folds and wrinkles necessitates extremely high-resolution 3D representations. On the other hand, editing these generated garments requires a well-defined UV space, and flattening the 3D mesh into developable meshes demands careful consideration from both geometric and statistical perspectives [7, 46].", + "bbox": [ + 511, + 491, + 906, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Sewing pattern generation, by contrast, has been approached through both learning-based and procedural modeling methods. Learning approaches utilize vector-quantized representations of sewing patterns, mapping from unstructured 3D point clouds [7, 30], images [12, 26, 40, 64], or textual descriptions [22] to structured patterns. However, they are highly dependent on the quality and diversity of the training data and often struggle to generalize designs beyond the training domain. Furthermore, generating high-quality 3D garment data requires substantial domain knowledge and the involvement of skilled professionals.", + "bbox": [ + 511, + 719, + 905, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Procedural modeling is an alternative that relies on pre", + "bbox": [ + 531, + 885, + 903, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23713", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "defined rules and parameters to generate garment patterns. For instance, GarmentCode [31], a DSL for parametric pattern making, enables precise control over garment design and customization. The GarmentCodeData [32], built on GarmentCode, further illustrates the potential of procedural methods to generate a diverse range of made-to-measure garments, with adaptability to different body shapes. While procedural modeling provides greater control and precision, it typically requires specialized expertise and is less flexible when dealing with novel or unconventional designs.", + "bbox": [ + 89, + 90, + 480, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. LLMs for Program Synthesis", + "text_level": 1, + "bbox": [ + 89, + 253, + 352, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent advancements in program synthesis and code generation using large language models (LLMs) have laid essential groundwork for systems like Design2GarmentCode, which generate structured garment code from multi-modal design inputs. Earlier researches like Codex [11] and AlphaCode [36] demonstrated the effectiveness of LLMs in generating complex, task-specific code with high syntax accuracy, showcasing potential in scenarios requiring precise parametric coding. These models [43, 59] highlight how LLMs, when sufficiently trained, can transform natural language inputs into executable code, a capability directly relevant to generating garment codes that follow complex pattern-making syntax. [9, 19, 20, 55, 63] explore multimodal models that integrate visual aids, such as flowcharts and UML diagrams, into LLM training to enhance models' comprehension of complex structures and flow. These models particularly emphasize the need for semantic understanding and adaptability, which are critical in working with domain-specific languages (DSLs) like GarmentCode.", + "bbox": [ + 89, + 276, + 482, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Neurosymbolic Models", + "text_level": 1, + "bbox": [ + 89, + 574, + 303, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Procedural and neural models offer complementary strengths and weaknesses. Neurosymbolic models [47] integrate both paradigms by generating visual data through symbolic programs enhanced with AI/ML techniques. These models typically follow a pipeline comprising task specification, program synthesis via a domain-specific language (DSL), program execution, and optional neural post-processing for refinement. They have been successfully applied across various areas of computer graphics. In 2D shape modeling, neurosymbolic methods are used for layout generation [45, 54], engineering sketch creation [16, 44, 49], and vector graphics synthesis by constructing programs that represent geometric shapes and spatial relations [10, 17]. For 3D shape modeling, they enable shape program inference from existing 3D models [27, 28, 33, 51] and the generation of new 3D shapes by training generative models on shape programs [57, 60, 61] or generate node graphs defining complex textures and materials [21, 25, 50], aligning with procedural modeling principles.", + "bbox": [ + 89, + 598, + 482, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Beyond shape modeling, neurosymbolic approaches", + "bbox": [ + 109, + 886, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "have been applied to human motion prediction [18, 38], reasoning [34, 58, 66], and generation [13, 41, 62], leveraging visual-language foundation models to extract symbolic representations from visual data for complex activity reasoning [58]. Our approach follows the neurosymbolic paradigm by instruction-tuning LLMs to generate structured, executable programs defining garment component, their relationships, and parameters from diverse design concepts.", + "bbox": [ + 511, + 90, + 903, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 239, + 604, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to develop a generative model that transforms multi-modal design concepts into precise sewing patterns. This requires understanding diverse inputs and producing patterns with high geometric precision and intricate structures. These requirements present a challenge for conventional models, which require extensive training data and struggle with output precision due to their probabilistic nature. We propose Design2GarmentCode, a system leveraging LMMs to generate parametric patternmaking programs, or specifically GarmentCode [31]. Design2GarmentCode reduces the need for large datasets utilizing the pre-embedded pattern-making knowledge in LMMs while ensuring output precision with parametric program synthesis. In the following, we first provide an overview of parametric pattern-making programs and GarmentCode syntax, and then describe the detailed design of Design2GarmentCode.", + "bbox": [ + 511, + 266, + 906, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Parametric Sewing Patterns", + "text_level": 1, + "bbox": [ + 511, + 532, + 764, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Parametric sewing patterns are formally represented as symbolic programs that generate sewing patterns (i.e., 2D CAD sketches) based on body measurements and design configurations. These symbolic programs enhance the efficiency of the pattern-making process by allowing users to draft or modify sewing patterns through semantically meaningful parameters. Mathematically, we can represent a sewing pattern $S$ as:", + "bbox": [ + 511, + 555, + 905, + 676 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} = \\langle \\mathcal {F}, \\mathcal {D}, B \\rangle = \\cup_ {f _ {i} \\in \\mathcal {F}, d _ {i} \\in \\mathcal {D}} f _ {i} (d _ {i}, B), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 688, + 906, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{F}$ is the set of symbolic programs, $\\mathcal{D}$ represents design configurations, and $B$ represents body measurements. Each symbolic function $f_{i} \\in \\mathcal{F}$ is essentially a series of rule-based 2D draw-calls controlled by its unique set of design configurations $d_{i} \\in \\mathcal{D}$ and the body measurements $B$ .", + "bbox": [ + 511, + 715, + 905, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GarmentCode is a domain-specific language (DSL) designed to generate parametric sewing patterns by encapsulating those symbolic programs in a hierarchical, component-oriented manner. In GarmentCode, each symbolic program $f_{i}$ uses parametric curves to define a garment component, such as sleeves, bodices, or collars. The", + "bbox": [ + 511, + 809, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23714", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/df0ece6a6b00ca48492c25b658870ec5a86a0e0bbc87f0a721f5f122a266b8f5.jpg", + "image_caption": [ + "Figure 3. Overview of Dress2GarmentCode. (1) Program Learning: we finetune the DSL Generation Agent (DSL-GA) using GarmentCode example programs, teaching it the GarmentCode grammar and the semantics of each design parameter. (2) Prompt Synthesis: the DSL-GA generates prompts for the Multi-Modal Understanding Agent (MMUA) to interpret and extract relevant design features from the input (3). (4) Program Synthesis: based on the MMUA's responses, the DSL-GA synthesizes GarmentCode-compliant design configurations and garment programs, which are then executed by the GarmentCode engine to produce sewing patterns and simulated garments (5). To enhance robustness, we incorporate two validation loops: during program synthesis, we employ rule-based validations (7) to ensure the MMUA's outputs are sufficient for generating complete and valid garment programs and design parameters; after the initial generation, the MMUA compares the generated design with the input and suggests modifications to minimize discrepancies." + ], + "image_footnote": [], + "bbox": [ + 106, + 88, + 906, + 282 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "smallest component is a single panel, and multiple components can be combined through interface functions to create a larger component. In GarmentCode, a complete sewing pattern is specified by topological parameters $\\mathcal{D}_T$ (which define the presence and quantity of garment components) and geometrical parameters $\\mathcal{D}_G$ , which determine the dimensions of each component when combined with body measurements $B$ . As this work primarily focuses on design variations, we use a standard body model throughout all experiments to ensure consistency.", + "bbox": [ + 88, + 435, + 480, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. The Design2GarmentCode System", + "text_level": 1, + "bbox": [ + 89, + 601, + 392, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As illustrated in Figure 3, Design2GarmentCode has three components: DSL Generation Agent (DSL-GA), a finetuned LLM responsible for (1) program learning, (2) prompt synthesis, and (4) program synthesis; Multi-modal Understanding Agent (MMUA), a pre-trained LLM that manages design understanding (3) and design comparison (6); and (5) GarmentCode, which executes the synthesized programs to generate sewing patterns and 3D garments.", + "bbox": [ + 89, + 626, + 482, + 747 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The system workflow begins with Program Learning (Sec. 3.2.1), where DSL-GA is finetuned to understand the syntax and semantic meanings of GarmentCode parameters. In Prompt Synthesis, DSL-GA creates prompts for MMUA to identify essential design features. These features are then provided to DSL-GA for Program Synthesis, where garment programs and design configurations are generated through rule-based parameter validation (Figure 3 (7)) and a learned projector (Sec. 3.2.2). The GarmentCode Execution Engine then produces sewing patterns and", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "draped garment models. Finally, a Validation stage compares the generated garment with the original design, allowing MMUA to provide specific correction instructions to DSL-GA for iterative refinement, such as \"make the sleeve longer\".", + "bbox": [ + 511, + 435, + 906, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Program Learning", + "text_level": 1, + "bbox": [ + 511, + 527, + 697, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During experiments, we found that pre-trained LLMs have some foundational knowledge of pattern drafting. For example, when prompted with \"How to draft a basic upper body bodice?\", LLMs can produce drafting instructions that align with conventional practices. We use a pretrained LLM to initialize DSL-GA, however, due to GarmentCode's customized object notations and function logistics, directly prompting DSL-GA to generate GarmentCode programs poses significant challenges [9].", + "bbox": [ + 511, + 551, + 905, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address these challenges, we propose to align DSL-GA's embedded pattern-making knowledge with the specific syntax and semantics of GarmentCode via LoRA [24] based on fine-tuning. We start by providing the DSL-GA (denoted as $\\Gamma$ ) with existing GarmentCode programs $\\mathcal{F}$ , and instructing it to comment on the functions with detailed pattern-drafting instructions. After manually validating the comments, we get a dataset $D$ paring natural language instructions with GarmentCode implementations:", + "bbox": [ + 511, + 686, + 905, + 823 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD = \\left\\{\\left(\\Gamma_ {c m t} (f _ {i}), f _ {i}\\right) \\mid f _ {i} \\in \\mathcal {F} \\right\\}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 830, + 903, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Gamma_{cmt}$ is the instructed DSL-GA for code commenting, $f_{i}$ is. Similar to [9], we finetune DSL-GA $(\\Gamma)$ on the", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23715", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "dataset $D$ with LoRA [24], aiming for $\\Gamma_{ft}(\\Gamma_{cmt}(f_i))\\to f_i$ where $\\Gamma_{ft}$ is the finetuned DSL-GA.", + "bbox": [ + 89, + 90, + 482, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After fine-tuning, the fine-tuned DSL-GA $\\Gamma_{ft}$ gains an understanding of the code structure and parameter semantics in GarmentCode (Figure 9). Therefore, we provide the design configuration $\\mathcal{D}$ to $\\Gamma_{ft}$ , prompting it to analyze the semantic meaning of each parameter and generate structured queries. These queries are designed to guide the MMUA in extracting relevant design features from the multi-modal input, enabling $\\Gamma_{ft}$ to generate a comprehensive set of design parameters. The generated prompt $P$ typically starts with analysis instructions, followed by multiple-choice or numerical estimation questions regarding each design parameter $d_{i}$ . Formally, we have", + "bbox": [ + 89, + 121, + 483, + 303 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP = \\Gamma_ {f t} (\\mathcal {D}) = \\cup_ {d _ {i} \\in \\mathcal {D}} \\Gamma_ {f t} \\left(d _ {i}\\right) = \\cup q _ {i}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 314, + 482, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $q_{i} = \\Gamma_{ft}(d_{i})$ represents the generated question regarding the $i$ -th design parameter $d_{i}$ .", + "bbox": [ + 89, + 342, + 482, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Program Synthesis", + "text_level": 1, + "bbox": [ + 89, + 390, + 276, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Initial results showed that MMUA performed significantly better on multiple-choice questions compared to numerical estimation questions. To improve accuracy, we replaced all numerical estimation questions in the initial prompt $P$ with equivalent multiple-choice questions with descriptive options such as \"full length\", \"half length\", or \"three-quarter length\". We append a lightweight projector $\\Psi$ after the finetuned DSL-GA $\\Gamma_{ft}$ to transform these descriptive answers $\\tau_i$ regarding the design input $x$ into precise geometrical parameters $d_i \\in \\mathcal{D}$ adhering to GarmentCode [31]:", + "bbox": [ + 89, + 414, + 483, + 566 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Psi : \\Gamma_ {f t} (\\cup \\tau_ {i}) \\rightarrow \\mathcal {D}, \\text {w h e r e} \\tau_ {i} = \\mathbf {M M U A} (q _ {i}, x). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 577, + 482, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by DressCode [22], we implement the projector $\\Psi$ as text-conditioned decoder-only transformer, where we design a type-based quantization function $\\mathbf{Q}$ to convert the parameter list $\\mathcal{D}$ into a token sequence $\\mathcal{T} = \\{t_1,\\dots,t_N\\}$ , where $N = |\\mathcal{D}|$ denote the total number of design parameters. The quantization function $\\mathbf{Q}$ operates as follows:", + "bbox": [ + 89, + 604, + 483, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt _ {i} = \\mathbf {Q} \\left(d _ {i}\\right) = \\left\\{ \\begin{array}{l l} 0 / 1, & \\text {i f} d _ {i} \\text {i s a b o o l e a n v a r i a b l e ,} \\\\ d _ {i}, & \\text {i f} d _ {i} \\text {i s a n i n t e g e r ,} \\\\ \\lambda \\cdot \\operatorname {N o r m} \\left(d _ {i}\\right), & \\text {i f} d _ {i} \\text {i s a f l o a t i n g n u m b e r ,} \\\\ \\operatorname {I n d e x} \\left(d _ {i}, L\\right), & \\text {i f} d _ {i} \\text {i s a s e l e c t i v e v a r i a b l e .} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 709, + 488, + 795 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is a scaling factor indicating numerical precision. We use $\\lambda = 100$ to maintain centimeter-level precision.", + "bbox": [ + 89, + 795, + 480, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As in Eq. 4, we use the finetuned DSL-GA $\\Gamma_{ft}$ to encode the answers $\\tau_{i}$ from MMUA and construct the condition input for $\\Psi$ (we use an MLP to match the embedding dimension between 3,072 in $\\Gamma_{ft}$ and 128 in $\\Psi$ ). Notably, our token sequence length is fixed to the number of", + "bbox": [ + 89, + 825, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a0c38e1c81e4e1ef8213f6a32afb8357cb5a6aca075ff96fd675a779a4ee4603.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodText Guided GenerationImage Guided Generation
DressCode [22]OursSewformer [40]Ours
QualitySSR84%100%65.33%94%
Agreement7.17%79.83%3.33%88.67%
Aesthetic9.50%68.17%5.33%77%
CLIPScore0.23860.2438//
F-Score0.616/0.7080.829
CD15.77/9.72.091
Diversity# Panels5.11±1.666.92±3.1010.11±4.4211.02±4.18
# Edges5.48±1.606.84±3.385.79±1.716.24±2.90
# Stitches10.06±3.2418.66±8.6415.81±5.9127.9±9.83
", + "bbox": [ + 517, + 88, + 905, + 198 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison of our method against state-of-the-art (SOTA) sewing pattern generation techniques in terms of quality and diversity. SSR (Simulation Success Rate) indicates the feasibility of simulated garment assembly, while Agreement measures alignment with design prompts, and Aesthetic evaluates the visual preference of the generated patterns. CLIPScore assesses text-image consistency, whereas Chamfer Distance (CD) and $F$ -Score quantify geometric accuracy. #Panels, #Stitches, and #Edges denote the mean and standard deviation (subscript) of the number of panels, stitches per pattern, and edges per panel.", + "bbox": [ + 511, + 208, + 906, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "design parameters $|\\mathcal{D}| = 122$ , regardless of the complexity of the pattern. This fixed-length representation is at least $10 \\times$ compact than DressCode [22], whose sequence length is 1, 500 and scales with pattern complexity (see Sec. 8 for implementation details).", + "bbox": [ + 511, + 376, + 905, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 469, + 645, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.Quantitative Evaluation", + "text_level": 1, + "bbox": [ + 511, + 494, + 733, + 511 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our proposed method against state-of-the-art sewing pattern generation approaches (DressCode [22] for text-guided and Sewformer [40] for image-guided generation) on Generation Quality and Generation Diversity.", + "bbox": [ + 511, + 520, + 905, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generation Quality is evaluated through three metrics: Simulation Success Rate (SSR), Agreement Score, and Aesthetic Score. The Simulation Success Rate (SSR) is calculated as the ratio of successfully simulated garments to the total number of generated sewing patterns, measuring the structural feasibility of the patterns. We prepared a dataset comprising 150 text prompts and 150 test images, covering a wide variety including tops (78), pants (76), skirts (38), dresses (80), and suits (28). For each sample, we generated sewing patterns using both our method and baseline methods, and simulated the patterns using GarmentCode's simulation engine [31, 32] to compute the success rate. The Agreement and Aesthetic Scores were derived from a user study involving 30 professional pattern-makers. Each participant is asked to review 50 text and 50 image samples generated by our and the baseline models, and assess their preference based on sewing patterns and simulated garments according to:", + "bbox": [ + 511, + 582, + 906, + 852 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Agreement: the degree to which the generated pattern matched the design prompt.", + "- Aesthetic Quality: the visual appeal and structural coher" + ], + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23716", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a2028672ab23b53e99c336fe7e23772640e349a845d5b3e671a8b2a25229dcfd.jpg", + "image_caption": [ + "(a) shirt, sleeveless, regular length, crew neck" + ], + "image_footnote": [], + "bbox": [ + 98, + 113, + 187, + 154 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/50a0986d0f0ad8376c6e7056f74e15addc31384e99d034063d350543ea5f4d11.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 194, + 114, + 233, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e3348373e830ebc9fdd873a8d62fd7df1623376a3b01548dbe871e0c518e695c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 238, + 114, + 279, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d7ac8be312f91eadd7f049a1b5645634dad8d0c7d2969fa09be83e096cd9f1ca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 114, + 387, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3c5005be3b3ae263883472e4f2220c36a0410302be6642e1a164f783e5ae125b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 392, + 114, + 483, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6a2ee11f13e1f3cb829f5c5a70ff226979569e38c655d1a7375806861d12624a.jpg", + "image_caption": [ + "(c) jumpsuit, straight leg, relaxed fit, turtleneck, regular length, long sleeves" + ], + "image_footnote": [], + "bbox": [ + 98, + 176, + 187, + 212 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e9f0a0da10ef72f967dec5271e9a2012561c01e3bacc5c6fae3a430c371adb96.jpg", + "image_caption": [ + "(b) dress, A-line, knee-length, regular fit, boat neck, short sleeves" + ], + "image_footnote": [], + "bbox": [ + 194, + 175, + 256, + 214 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b1a41d673ce625ce5261ec4a4d98698efecbaf7a231404a4e2a74b1c2ddcdf6f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 176, + 385, + 214 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0544affb9296021905cf1bf55c8340169429d6125d4cedc0f7829b243d004fcd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 392, + 176, + 483, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6ce8d4c00de08db99181f47f0112a284dcc4d793b379a9d6fe93bb7f2997ae04.jpg", + "image_caption": [ + "Our Results" + ], + "image_footnote": [], + "bbox": [ + 98, + 237, + 186, + 276 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/95e13fbcc5187d131ea77b7d2cda87cf6b18ab939ca74342daaecabf11dc8a2a.jpg", + "image_caption": [ + "Figure 4. Quality Comparison on Text-Guided Sewing Pattern Generation. For each design, we present the generated pattern using our method (left) alongside DressCode [22] (right), including front and back renderings of the draped garment. We highlight design elements accurately captured by our method but missed by DressCode [22] use red color in the input prompt." + ], + "image_footnote": [], + "bbox": [ + 194, + 237, + 256, + 276 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/22d3cd9b9844378f27fa86c3196032eea1d4fb7d80ad05f473d5d65bc077c493.jpg", + "image_caption": [ + "DressCode Results" + ], + "image_footnote": [], + "bbox": [ + 295, + 237, + 485, + 276 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/922ce668b7fd9effffa1a7744de68414870ac11e7f10b2c70b1f65c1911c2f19.jpg", + "image_caption": [ + "(d) dress, sleeveless, tight fit, level skirt, boat neck, mini-length" + ], + "image_footnote": [], + "bbox": [ + 514, + 113, + 598, + 155 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/96eb10e963b961784d71301e2f3b34215db3500c4bbd69ef73c6f0bf7d183ca2.jpg", + "image_caption": [ + "(e) dress, with a hood" + ], + "image_footnote": [], + "bbox": [ + 604, + 114, + 643, + 154 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/97119040d1d771d8350865ab79de1640de4619878d36956d896ded148c1458c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 114, + 692, + 154 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c8da95da553a97070e3179560f61b77e0767bdc1d9919eacfd2f85f7ae7b04dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 722, + 114, + 787, + 155 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4b83f5315932bf085715917d0a652f3149305f1412a2a0e3589127f559de2ede.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 114, + 897, + 155 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/421930ae9a0f56a2191267755ea044e02f4f0fe8f7439a5eecf539d0b0de60f6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 176, + 599, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a2a486fb762b034defdb26588155020059958a746f9852f3e1a5505047abb6e1.jpg", + "image_caption": [ + "(f) dress, one-shoulder" + ], + "image_footnote": [], + "bbox": [ + 604, + 176, + 643, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/55edc0d1d0e7ad9dc262d39df8a0dc253b9f3984c1013bb13abdc03120311c7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 176, + 692, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/82b28e6db4fbd035b902f8684106ccd47119d4424546df4a6dd5ec8af8f19b58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 176, + 802, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6839aec9f3407dc48f4df8da08d30ff44464e46f3de8c65666aad928774d946b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 807, + 176, + 900, + 217 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/794cce34fc9ad4c9147bb9a88aa4c59635e55f7a7d8a0dd6a642936d39d9ab46.jpg", + "image_caption": [ + "Our Results" + ], + "image_footnote": [], + "bbox": [ + 509, + 237, + 601, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f99c9d0b7f85d548490dc9e8b7eb5a46dbde6063ce98b58f9bfb2cff5bb375fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 238, + 669, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9959e3a56280811d671a62c6092affe17377c55b496a200ac3afc43f98a114b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 681, + 239, + 694, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dce3d9c59ab2e22f4ef98a324e21465933f936f14eb6316e7312d65bf684c2f4.jpg", + "image_caption": [ + "DressCode Results" + ], + "image_footnote": [], + "bbox": [ + 709, + 239, + 800, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/98dc785ebaaaad80999ac28e48b3c93fe83ea2961a178b30a46f074ddfa1ef43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 807, + 239, + 897, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ence of the generated pattern.", + "bbox": [ + 104, + 383, + 302, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each criterion, participants could express a preference for either our method or the baseline or indicate that both methods were \"comparable\". We calculate the Agreement and Aesthetic Scores as the percentage of times each option was chosen over the total number of tested samples.", + "bbox": [ + 89, + 398, + 482, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 presents the results, showing that our method surpasses existing approaches in both SSR and user-evaluated Agreement and Aesthetic scores. For text-guided generation, our model achieves a perfect $100\\%$ SSR, notably higher than DressCode's $84\\%$ . Additionally, our Agreement score of $79.83\\%$ and Aesthetic score of $68.17\\%$ far exceed DressCode's respective scores of $7.17\\%$ and $9.5\\%$ . In image-guided generation, our method attains a $94\\%$ SSR, with an Agreement score of $88.67\\%$ and an Aesthetic score of $77\\%$ , significantly outperforming Sewformer. These enhancements highlight our model's ability to generate sewing patterns that are both structurally precise and visually aligned with the design prompt.", + "bbox": [ + 89, + 474, + 483, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Generation Diversity is evaluated by analyzing the average number of panels (# Panels), edges (# Edges), and stitches (# Stitches) in the generated patterns. For text-guided generation, our method yields more intricate designs, with an average of 6.92 panels, 6.84 edges, and 18.66 stitches per pattern, compared to DressCode's simpler outputs of 5.11 panels, 5.48 edges, and 10.06 stitches. In image-guided generation, our approach also demonstrates superior diversity, producing an average of 11.02 panels, 6.24 edges, and 27.9 stitches per pattern, compared to Sewformer's averages of 10.11 panels, 5.79 edges, and 15.81 stitches. These results emphasize our model's ability to capture and replicate subtle design variations, highlighting its robustness and adaptability across different design inputs.", + "bbox": [ + 89, + 688, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Multi-modal Generation Results", + "text_level": 1, + "bbox": [ + 511, + 382, + 797, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our proposed method demonstrates superior performance across various sewing pattern generation tasks, including text-guided, image-guided, and sketch-based generation.", + "bbox": [ + 511, + 412, + 906, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In text-guided sewing pattern generation (Figure 4), our method accurately captures design details specified in prompts, such as neckline types (e.g., crew neck (a), boat neck (b), turtleneck (c)) and complex structural features like asymmetry (f) and layered skirts (d). In comparison, the baseline model DressCode struggles with limited pattern diversity, often defaulting to simpler shapes like V-neck designs. Additionally, for design descriptions out of its training domain, DressCode frequently generates patterns with incorrect stitching, leading to poor draping results (Figure 4 (e)). Our method could provide structurally sound and visually accurate patterns under a large design variety, showcasing its capability to handle diverse design requests with high fidelity.", + "bbox": [ + 511, + 464, + 906, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For image-guided sewing pattern generation (Figure 5), our model effectively translates detailed visual cues from input images into corresponding sewing patterns. Compared with Sewformer, which often fails to model-specific design elements like cuffs, hoods, and asymmetric features, our approach accurately reproduces these details. Sewformer's results frequently exhibit structural flaws, such as missing or misaligned pattern pieces and extraneous components, resulting in unrealistic garment draping. In contrast, our method maintains structural integrity and captures complex design features, producing patterns that closely align with the source images.", + "bbox": [ + 511, + 681, + 906, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In sketch-based sewing pattern generation (Figure 6), our system seamlessly converts both technical sketches (left)", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23717", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d5c1a65313beec7f20f8a2f21a751687007d8578eaa0b4cbef7dd77ccf6a3f93.jpg", + "image_caption": [ + "Figure 5. Quality Comparison on Image-Guided Sewing Pattern Generation. We compare our method with Sewformer [40] on Internet-collected fashion photographs (left), and AI-generated design images without human models (right). The results indicate that our method successfully captures design details from diverse styles, producing sewing patterns that accurately reflect neckline (a, d), cuffs (a, e, g), darts (c, d), and asymmetry (f). In contrast, Sewformer's results exhibit several issues, including incorrect necklines (a, d), missing components (b, g), misplaced or imaginary stitches (d, e), and extraneous pattern pieces (h). Additionally, since Sewformer's pattern generation does not account for body shape, garments like skirts and pants frequently appear oversized around the waist, causing them to sag when draped." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 295, + 333 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67f894b4b6ac4eeaec3079daaf72cf67477886c8640c682f9d1fdfd75ba3b87a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 297, + 89, + 486, + 333 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f6d097cecc9486129f2ed0c2516f190f103bc4524fd1c234b75bebfc64e1c876.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 88, + 709, + 333 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2225dd19c09b43c4af9c0ea4c72fb06adf9dec2e0a83fb7c7729ffb69bc13f29.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 88, + 903, + 333 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/17905de9a33ae684bbd12f4ffae5bba6c6da0903bb96990d2d765030220cb69a.jpg", + "image_caption": [ + "Figure 6. Examples of sketch-based sewing pattern generation. Our method was able to generate high-quality sewing patterns from design sketches under various styles and could integrate seamlessly with industrial fashion design software for (a) pattern editing, i.e. sleeve panels in red boxes are merged from separate front/back sleeve panels; and (b) avatar posture and fabric material editing." + ], + "image_footnote": [], + "bbox": [ + 94, + 450, + 633, + 691 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b565ee0c19099ed477db2238b633a7ca28200f008267b78f361c2308ad2b9804.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 448, + 893, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and artistic drawings1 (right) into high-quality sewing patterns. We also demonstrated that the generated sewing patterns could seamlessly integrate into industrial fashion design software2. For example, highlighted sleeve panels in Figure 6 (a) are merged from separate front and back sleeve pieces, while Figure 6 (b) demonstrates avatar posture and", + "bbox": [ + 89, + 770, + 480, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fabric material editing.", + "bbox": [ + 513, + 771, + 666, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Application", + "text_level": 1, + "bbox": [ + 511, + 799, + 635, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we explore practical applications enabled by our system that extend beyond basic pattern generation, providing designers with versatile tools for design refinement, integration with physical simulation, and the creation of new garment components.", + "bbox": [ + 511, + 825, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "1The drawing is borrowed from the artwork of TWELVEYIN.", + "bbox": [ + 107, + 875, + 437, + 887 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "2We use Style3D Studio [5] for pattern and appearance authoring.", + "bbox": [ + 109, + 887, + 455, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23718", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4419df1104db9751a05ec4fd90a59b0865aa36bfc5da70d6c81b9387d4376118.jpg", + "image_caption": [ + "Figure 7. Sewing Pattern Authoring with instructions. Starting from an original design, the system follows user instructions to adjust specific pattern elements. In Edited Design 1, the pants are modified to a skirt based on the command \"CHANGE THE PANT TO SKIRT\". In Edited Design 2, the sleeves are shortened as requested. Finally, in Edited Design 3, the shirt is made sleeveless in response to the instructions. Note that, each modification accurately applies only to the specified parts, leaving the rest of the design unchanged." + ], + "image_footnote": [], + "bbox": [ + 112, + 93, + 877, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/40fb45cdc36cc6a9020c60a4ba27042146c3daa3b2a2196260494b2033f87478.jpg", + "image_caption": [ + "Figure 8. Sewing pattern adjustment based on body pressure measurement. Red regions indicate areas of tight fabric with high body pressure, while blue regions represent looser areas." + ], + "image_footnote": [], + "bbox": [ + 102, + 328, + 468, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f3a3e0c32dc2f778b3b662af753fe8fbba40962424da1e638ddfd8e17f4e07aa.jpg", + "image_caption": [ + "Figure 9. The code for a layered-skirt component generated by our DSL-GA and 3D garment under various design parameters." + ], + "image_footnote": [], + "bbox": [ + 102, + 531, + 464, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Instruction-Based Editing. Our system allows designers to adjust generated sewing patterns through simple, instruction-based edits, utilizing the same refinement process as in our collaborative framework. As illustrated in Figure 7, starting from an original design, the system responds to natural language commands from the user to adjust the sewing pattern. At each step, the modified areas are highlighted in red boxes. From the figure, it is evident that our system can accurately update only the specified parts of the pattern according to the user's instructions while leaving all other parts of the design unchanged.", + "bbox": [ + 89, + 689, + 482, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Physics-Based Editing. Our system's generated sewing patterns integrate seamlessly with professional cloth simulation software, allowing adjustments based on fitness mea", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "surements derived from physical simulations. In Figure 8, we demonstrate sewing pattern editing guided by body pressure analysis, including adjustments to the cuff (a), upper bodice (b), lower bodice (c), and collar (d). As shown in the examples, our system accurately identifies areas with excessive tension and adjusts the corresponding sewing patterns to enhance comfort while preserving the overall design.", + "bbox": [ + 511, + 329, + 903, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Generating New Garment Programs. A major challenge in traditional parametric pattern-making is the need to abstract symbolic programs for new sewing patterns, which demands both advanced programming skills and patterning expertise. Design2GarmentCode addresses this by correlating GarmentCode grammar with LMMs' embedded pattern-making knowledge, enabling the automatic creation of new garment components. Figure 9 shows a layered-skirt component generated by our DSL-GA, along with 3D garment representations demonstrating different design parameters, such as skirt length (c), number of layers (d), and layer differences such as length difference and ruffling factor (e). The results demonstrate that our system consistently produces high-quality garment components that meet professional standards, while significantly reducing the time and expertise required to create new sewing pattern programs.", + "bbox": [ + 511, + 435, + 906, + 678 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 693, + 633, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Design2GarmentCode transforms multi-modal design concepts into precise sewing patterns using LMMs to synthesize parametric programs. It addresses challenges related to data requirements, computation, and the limited precision of neural network-based methods. The experimental results demonstrate the system's ability to capture design details while maintaining structural integrity and geometric precision in generated patterns. Despite these advantages, Design2GarmentCode currently cannot substantially alter GarmentCode's underlying structure and logistics, which impacts generation quality due to inherent limitations in GarmentCode's design and modeling capabilities (Supp. 10).", + "bbox": [ + 511, + 719, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23719", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by Key R&D Program of Hangzhou (No.2024SDZ1A20). We sincerely thank Fuqi Wang for his valuable support in validation data collection, material modeling and animation.", + "bbox": [ + 89, + 114, + 483, + 176 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 186, + 187, + 203 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Assyst smart(pattern macro. https://www.assyst.de/en/products/cad/index.html. Accessed: 2024-11-09. 1", + "[2] Modaris: Smart and speedy patternmaking for fashion experts. https://www.lectra.com/en/fashion/products/modaris. Accessed: 2024-11-09.", + "[3] Optitex: 2d/3d cad pattern design software. https://optitex.com/products/2d-and-3d-cad-software/. Accessed: 2024-11-09.", + "[4] Valentina: Open source pattern drafting software. https://valentinaproject.bitbucket.io/index.html. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 21496-21506, 2024. 2" + ], + "bbox": [ + 91, + 92, + 480, + 869 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "23722", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Design2GarmentCode_ Turning Design Concepts to Tangible Garments Through Program Synthesis/d74dfa3b-ff23-42b1-9fc2-1b69e990b9a1_model.json b/2025/Design2GarmentCode_ Turning Design Concepts to Tangible Garments Through Program Synthesis/d74dfa3b-ff23-42b1-9fc2-1b69e990b9a1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4409ca9f8d2fda9c79f2323904f08e566dd3a955 --- /dev/null +++ b/2025/Design2GarmentCode_ Turning Design Concepts to Tangible Garments Through Program Synthesis/d74dfa3b-ff23-42b1-9fc2-1b69e990b9a1_model.json @@ -0,0 +1,2719 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.131, + 0.885, + 0.177 + ], + "angle": 0, + "content": "Design2GarmentCode: Turning Design Concepts to Tangible Garments Through Program Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.205, + 0.888, + 0.222 + ], + "angle": 0, + "content": "Feng Zhou\\(^{1,2*}\\) Ruiyang Liu\\(^{2,4\\dagger}\\) Chen Liu\\(^{2,4}\\) Gaofeng He\\(^{2}\\) Yong-Lu Li\\(^{3}\\) Xiaogang Jin\\(^{4}\\) Huamin Wang\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.224, + 0.955, + 0.24 + ], + "angle": 0, + "content": "\\(^{1}\\)Zhejiang Sci-Tech University \\(^{2}\\)Style3D Research \\(^{3}\\)Shanghai Jiao Tong University \\(^{4}\\)State Key Lab of CAD&CG, Zhejiang University" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.274, + 0.327, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.307, + 0.485, + 0.685 + ], + "angle": 0, + "content": "Sewing patterns, the essential blueprints for fabric cutting and tailoring, act as a crucial bridge between design concepts and producible garments. However, existing uni-modal sewing pattern generation models struggle to effectively encode complex design concepts with a multimodal nature and correlate them with vectorized sewing patterns that possess precise geometric structures and intricate sewing relations. In this work, we propose a novel sewing pattern generation approach Design2GarmentCode based on Large Multimodal Models (LMMs), to generate parametric pattern-making programs from multi-modal design concepts. LMM offers an intuitive interface for interpreting diverse design inputs, while pattern-making programs could serve as well-structured and semantically meaningful representations of sewing patterns, and act as a robust bridge connecting the cross-domain pattern-making knowledge embedded in LMMs with vectorized sewing patterns. Experimental results demonstrate that our method can flexibly handle various complex design expressions such as images, textual descriptions, designer sketches, or their combinations, and convert them into size-precise sewing patterns with correct stitches. Compared to previous methods, our approach significantly enhances training efficiency, generation quality, and authoring flexibility. Project page: https://style3d.github.io/design2garmentcode." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.716, + 0.222, + 0.731 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.742, + 0.484, + 0.864 + ], + "angle": 0, + "content": "While generative AI has significantly propelled creativity in fashion design, turning those design ideas into wearable realities remains a formidable challenge. Sewing patterns are the key components to bridge the gap between abstract design ideas and wearable realities. They are foundational blueprints that dictate the precise shapes and dimensions of fabric pieces, essential for assembling garments in both the physical and virtual fashion realms." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.275, + 0.905, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.497, + 0.907, + 0.637 + ], + "angle": 0, + "content": "Figure 1. Traditional sewing pattern generation approaches (top) use uni-modal models trained on synthetic datasets generated by parametric pattern-making programs (red arrow) to convert text or image prompts into vector-quantized patterns. These methods are resource-intensive and often yield oversimplified patterns with stitching errors. Our approach (bottom) utilizes large pre-trained LMMs to directly translate design concepts into parametric programs and configuration files (blue arrow), enabling dedicated, structurally correct pattern generation from multi-modal design inputs within a unified framework." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Traditionally, sewing patterns are drafted manually by professional pattern-makers with years of practice, making the process inefficient, error-prone, and unable to meet the growing demands for refinement and personalization in the fashion market. To this end, parametric pattern-making researches [8, 29, 31] and industrial solutions [1-4] have emerged. These methods formalize the pattern-making process as geometric functions governed by parameters such as body measurements and design features, thereby accelerating the process by enabling pattern makers to generate sewing patterns through parameter adjustments instead of starting from scratch. However, creating these function templates is still complex, requiring not only advanced pattern-making skills but also geometric intuition, mathematical modeling knowledge, and coding abilities to trans" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.406, + 0.888 + ], + "angle": 0, + "content": "*Works done during the internship at Style3D Research." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.236, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.406, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23712" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.095, + 0.258, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.161, + 0.259, + 0.172 + ], + "angle": 0, + "content": "(a) Limited Generation Diversity" + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.095, + 0.361, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.268, + 0.161, + 0.367, + 0.171 + ], + "angle": 0, + "content": "(b) Self-Intersection" + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.091, + 0.482, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.162, + 0.477, + 0.172 + ], + "angle": 0, + "content": "(c) Wrong Stitches" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.183, + 0.483, + 0.281 + ], + "angle": 0, + "content": "Figure 2. (a) Despite prompts specifying diverse neckline types, DressCode [22] consistently produces only V-neck designs, indicating limited generation diversity. (b) SewFormer [40] often generates sewing patterns with self-intersecting panels, compromising pattern validity. (c) Stitching errors are also prevalent in Sewformer [40], as shown here where a pant side seam is mistakenly stitched to a shirt shoulder seam, resulting in draping failure." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.31, + 0.483, + 0.356 + ], + "angle": 0, + "content": "late pattern-making expertise into CAD programs. These technical barriers significantly restrict the widespread adoption of parametric pattern-making solutions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.357, + 0.483, + 0.599 + ], + "angle": 0, + "content": "Recently, several learning-based approaches for sewing pattern generation have been introduced. For instance, NeuralTailor [30] focuses on extracting sewing patterns from unstructured point clouds, DressCode [22] targets text-to-sewing pattern generation, and SewFormer [40] is designed for image-based sewing pattern generation. However, they are generally trained on paired design-sewing pattern data, necessitating large datasets to effectively capture the multimodal nature of design concepts. Furthermore, sewing patterns require centimeter-level precision to ensure proper garment fit, which presents a significant challenge for neural networks that only provide statistical approximations of the true function based on their training data [14, 23, 47]. As a result, these methods frequently generate oversimplified patterns with flawed geometry or stitches, potentially leading to draping failures (Figure 2)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.6, + 0.483, + 0.902 + ], + "angle": 0, + "content": "In this paper, we present Design2GarmentCode, an innovative approach that leverages the generalization capabilities of vision-language foundation models to achieve multi-modal sewing pattern generation with minimal computational and data requirements. Unlike previous methods that directly synthesize vector-quantized patterns, Design2GarmentCode employs LMMs to learn the syntax of parametric pattern-making programs, translating design concepts into parameters and programs that can be executed to produce precise and structurally accurate sewing patterns. Design2GarmentCode combines a pre-trained Large Multimodal Model (LMM) as a design interpreter with a finetuned Large Language Model (LLM) as a program synthesizer. Specifically, the LLM is finetuned on code snippets from GarmentCode [31], a domain-specific language for constructing parametric sewing patterns. At runtime, the design interpreter extracts both topological and geometrical information from the design input by responding to a series of questions from the program synthesizer, which then generates garment programs and design config" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "urations following GarmentCode syntax. Our method offers the following major contributions:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.126, + 0.905, + 0.186 + ], + "angle": 0, + "content": "- We introduce a novel modality-agnostic framework with an intuitive, intelligent interface capable of processing user design intentions across multiple modalities simultaneously by integrating pre-trained LMMs." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.186, + 0.905, + 0.261 + ], + "angle": 0, + "content": "- We present the first sewing pattern generation approach grounded in program synthesis, delivering fully interpretable, geometrically precise, and structurally accurate patterns through a more compact, semantically clear, and LLM-friendly representation." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.262, + 0.905, + 0.337 + ], + "angle": 0, + "content": "- Our framework benefits real-world production by enabling flexible pattern authoring through natural language or physical feedback, allowing precise customization and efficient creation of novel garment components, represented as parametric pattern-making programs." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.338, + 0.905, + 0.428 + ], + "angle": 0, + "content": "- Our approach requires only minimal fine-tuning of a pre-trained LLM and the training of a lightweight, text-conditioned transformer decoder, making it more efficient than existing vector-quantized sewing pattern generation models trained from scratch while offering superior generation quality and authoring flexibility." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.126, + 0.905, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.443, + 0.655, + 0.458 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.469, + 0.864, + 0.485 + ], + "angle": 0, + "content": "2.1. Garment Modeling with Sewing Patterns" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.492, + 0.907, + 0.719 + ], + "angle": 0, + "content": "Garment modeling and generation can be broadly classified into two categories: direct 3D garment generation (meshes) and sewing pattern generation, which are later draped onto human bodies via cloth simulation [39, 53, 56] or learning-based techniques [35, 37]. Direct 3D garment generation often relies on differentiable garment representations like unsigned distance fields [65, 67], shells [42], or Gaussian splatting [48]. However, it presents challenges in terms of both geometric accuracy and editability. On one hand, capturing fine garment details like folds and wrinkles necessitates extremely high-resolution 3D representations. On the other hand, editing these generated garments requires a well-defined UV space, and flattening the 3D mesh into developable meshes demands careful consideration from both geometric and statistical perspectives [7, 46]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.906, + 0.885 + ], + "angle": 0, + "content": "Sewing pattern generation, by contrast, has been approached through both learning-based and procedural modeling methods. Learning approaches utilize vector-quantized representations of sewing patterns, mapping from unstructured 3D point clouds [7, 30], images [12, 26, 40, 64], or textual descriptions [22] to structured patterns. However, they are highly dependent on the quality and diversity of the training data and often struggle to generalize designs beyond the training domain. Furthermore, generating high-quality 3D garment data requires substantial domain knowledge and the involvement of skilled professionals." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.886, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Procedural modeling is an alternative that relies on pre" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23713" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.244 + ], + "angle": 0, + "content": "defined rules and parameters to generate garment patterns. For instance, GarmentCode [31], a DSL for parametric pattern making, enables precise control over garment design and customization. The GarmentCodeData [32], built on GarmentCode, further illustrates the potential of procedural methods to generate a diverse range of made-to-measure garments, with adaptability to different body shapes. While procedural modeling provides greater control and precision, it typically requires specialized expertise and is less flexible when dealing with novel or unconventional designs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.254, + 0.353, + 0.27 + ], + "angle": 0, + "content": "2.2. LLMs for Program Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.277, + 0.483, + 0.565 + ], + "angle": 0, + "content": "Recent advancements in program synthesis and code generation using large language models (LLMs) have laid essential groundwork for systems like Design2GarmentCode, which generate structured garment code from multi-modal design inputs. Earlier researches like Codex [11] and AlphaCode [36] demonstrated the effectiveness of LLMs in generating complex, task-specific code with high syntax accuracy, showcasing potential in scenarios requiring precise parametric coding. These models [43, 59] highlight how LLMs, when sufficiently trained, can transform natural language inputs into executable code, a capability directly relevant to generating garment codes that follow complex pattern-making syntax. [9, 19, 20, 55, 63] explore multimodal models that integrate visual aids, such as flowcharts and UML diagrams, into LLM training to enhance models' comprehension of complex structures and flow. These models particularly emphasize the need for semantic understanding and adaptability, which are critical in working with domain-specific languages (DSLs) like GarmentCode." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.575, + 0.304, + 0.59 + ], + "angle": 0, + "content": "2.3. Neurosymbolic Models" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.885 + ], + "angle": 0, + "content": "Procedural and neural models offer complementary strengths and weaknesses. Neurosymbolic models [47] integrate both paradigms by generating visual data through symbolic programs enhanced with AI/ML techniques. These models typically follow a pipeline comprising task specification, program synthesis via a domain-specific language (DSL), program execution, and optional neural post-processing for refinement. They have been successfully applied across various areas of computer graphics. In 2D shape modeling, neurosymbolic methods are used for layout generation [45, 54], engineering sketch creation [16, 44, 49], and vector graphics synthesis by constructing programs that represent geometric shapes and spatial relations [10, 17]. For 3D shape modeling, they enable shape program inference from existing 3D models [27, 28, 33, 51] and the generation of new 3D shapes by training generative models on shape programs [57, 60, 61] or generate node graphs defining complex textures and materials [21, 25, 50], aligning with procedural modeling principles." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.887, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Beyond shape modeling, neurosymbolic approaches" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.228 + ], + "angle": 0, + "content": "have been applied to human motion prediction [18, 38], reasoning [34, 58, 66], and generation [13, 41, 62], leveraging visual-language foundation models to extract symbolic representations from visual data for complex activity reasoning [58]. Our approach follows the neurosymbolic paradigm by instruction-tuning LLMs to generate structured, executable programs defining garment component, their relationships, and parameters from diverse design concepts." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.241, + 0.605, + 0.258 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.267, + 0.907, + 0.524 + ], + "angle": 0, + "content": "Our goal is to develop a generative model that transforms multi-modal design concepts into precise sewing patterns. This requires understanding diverse inputs and producing patterns with high geometric precision and intricate structures. These requirements present a challenge for conventional models, which require extensive training data and struggle with output precision due to their probabilistic nature. We propose Design2GarmentCode, a system leveraging LMMs to generate parametric patternmaking programs, or specifically GarmentCode [31]. Design2GarmentCode reduces the need for large datasets utilizing the pre-embedded pattern-making knowledge in LMMs while ensuring output precision with parametric program synthesis. In the following, we first provide an overview of parametric pattern-making programs and GarmentCode syntax, and then describe the detailed design of Design2GarmentCode." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.533, + 0.766, + 0.549 + ], + "angle": 0, + "content": "3.1. Parametric Sewing Patterns" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.556, + 0.906, + 0.678 + ], + "angle": 0, + "content": "Parametric sewing patterns are formally represented as symbolic programs that generate sewing patterns (i.e., 2D CAD sketches) based on body measurements and design configurations. These symbolic programs enhance the efficiency of the pattern-making process by allowing users to draft or modify sewing patterns through semantically meaningful parameters. Mathematically, we can represent a sewing pattern \\( S \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.689, + 0.907, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} = \\langle \\mathcal {F}, \\mathcal {D}, B \\rangle = \\cup_ {f _ {i} \\in \\mathcal {F}, d _ {i} \\in \\mathcal {D}} f _ {i} (d _ {i}, B), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.716, + 0.906, + 0.793 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}\\) is the set of symbolic programs, \\(\\mathcal{D}\\) represents design configurations, and \\(B\\) represents body measurements. Each symbolic function \\(f_{i} \\in \\mathcal{F}\\) is essentially a series of rule-based 2D draw-calls controlled by its unique set of design configurations \\(d_{i} \\in \\mathcal{D}\\) and the body measurements \\(B\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.902 + ], + "angle": 0, + "content": "GarmentCode is a domain-specific language (DSL) designed to generate parametric sewing patterns by encapsulating those symbolic programs in a hierarchical, component-oriented manner. In GarmentCode, each symbolic program \\( f_{i} \\) uses parametric curves to define a garment component, such as sleeves, bodices, or collars. The" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23714" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.907, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.298, + 0.907, + 0.41 + ], + "angle": 0, + "content": "Figure 3. Overview of Dress2GarmentCode. (1) Program Learning: we finetune the DSL Generation Agent (DSL-GA) using GarmentCode example programs, teaching it the GarmentCode grammar and the semantics of each design parameter. (2) Prompt Synthesis: the DSL-GA generates prompts for the Multi-Modal Understanding Agent (MMUA) to interpret and extract relevant design features from the input (3). (4) Program Synthesis: based on the MMUA's responses, the DSL-GA synthesizes GarmentCode-compliant design configurations and garment programs, which are then executed by the GarmentCode engine to produce sewing patterns and simulated garments (5). To enhance robustness, we incorporate two validation loops: during program synthesis, we employ rule-based validations (7) to ensure the MMUA's outputs are sufficient for generating complete and valid garment programs and design parameters; after the initial generation, the MMUA compares the generated design with the input and suggests modifications to minimize discrepancies." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.436, + 0.482, + 0.587 + ], + "angle": 0, + "content": "smallest component is a single panel, and multiple components can be combined through interface functions to create a larger component. In GarmentCode, a complete sewing pattern is specified by topological parameters \\( \\mathcal{D}_T \\) (which define the presence and quantity of garment components) and geometrical parameters \\( \\mathcal{D}_G \\), which determine the dimensions of each component when combined with body measurements \\( B \\). As this work primarily focuses on design variations, we use a standard body model throughout all experiments to ensure consistency." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.602, + 0.393, + 0.618 + ], + "angle": 0, + "content": "3.2. The Design2GarmentCode System" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.627, + 0.483, + 0.748 + ], + "angle": 0, + "content": "As illustrated in Figure 3, Design2GarmentCode has three components: DSL Generation Agent (DSL-GA), a finetuned LLM responsible for (1) program learning, (2) prompt synthesis, and (4) program synthesis; Multi-modal Understanding Agent (MMUA), a pre-trained LLM that manages design understanding (3) and design comparison (6); and (5) GarmentCode, which executes the synthesized programs to generate sewing patterns and 3D garments." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "The system workflow begins with Program Learning (Sec. 3.2.1), where DSL-GA is finetuned to understand the syntax and semantic meanings of GarmentCode parameters. In Prompt Synthesis, DSL-GA creates prompts for MMUA to identify essential design features. These features are then provided to DSL-GA for Program Synthesis, where garment programs and design configurations are generated through rule-based parameter validation (Figure 3 (7)) and a learned projector (Sec. 3.2.2). The GarmentCode Execution Engine then produces sewing patterns and" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.436, + 0.907, + 0.512 + ], + "angle": 0, + "content": "draped garment models. Finally, a Validation stage compares the generated garment with the original design, allowing MMUA to provide specific correction instructions to DSL-GA for iterative refinement, such as \"make the sleeve longer\"." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.529, + 0.698, + 0.545 + ], + "angle": 0, + "content": "3.2.1 Program Learning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.906, + 0.688 + ], + "angle": 0, + "content": "During experiments, we found that pre-trained LLMs have some foundational knowledge of pattern drafting. For example, when prompted with \"How to draft a basic upper body bodice?\", LLMs can produce drafting instructions that align with conventional practices. We use a pretrained LLM to initialize DSL-GA, however, due to GarmentCode's customized object notations and function logistics, directly prompting DSL-GA to generate GarmentCode programs poses significant challenges [9]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.688, + 0.906, + 0.824 + ], + "angle": 0, + "content": "To address these challenges, we propose to align DSL-GA's embedded pattern-making knowledge with the specific syntax and semantics of GarmentCode via LoRA [24] based on fine-tuning. We start by providing the DSL-GA (denoted as \\(\\Gamma\\)) with existing GarmentCode programs \\(\\mathcal{F}\\), and instructing it to comment on the functions with detailed pattern-drafting instructions. After manually validating the comments, we get a dataset \\(D\\) paring natural language instructions with GarmentCode implementations:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.831, + 0.905, + 0.865 + ], + "angle": 0, + "content": "\\[\nD = \\left\\{\\left(\\Gamma_ {c m t} (f _ {i}), f _ {i}\\right) \\mid f _ {i} \\in \\mathcal {F} \\right\\}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "where \\(\\Gamma_{cmt}\\) is the instructed DSL-GA for code commenting, \\(f_{i}\\) is. Similar to [9], we finetune DSL-GA \\((\\Gamma)\\) on the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23715" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.483, + 0.121 + ], + "angle": 0, + "content": "dataset \\(D\\) with LoRA [24], aiming for \\(\\Gamma_{ft}(\\Gamma_{cmt}(f_i))\\to f_i\\) where \\(\\Gamma_{ft}\\) is the finetuned DSL-GA." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.122, + 0.484, + 0.304 + ], + "angle": 0, + "content": "After fine-tuning, the fine-tuned DSL-GA \\(\\Gamma_{ft}\\) gains an understanding of the code structure and parameter semantics in GarmentCode (Figure 9). Therefore, we provide the design configuration \\(\\mathcal{D}\\) to \\(\\Gamma_{ft}\\), prompting it to analyze the semantic meaning of each parameter and generate structured queries. These queries are designed to guide the MMUA in extracting relevant design features from the multi-modal input, enabling \\(\\Gamma_{ft}\\) to generate a comprehensive set of design parameters. The generated prompt \\(P\\) typically starts with analysis instructions, followed by multiple-choice or numerical estimation questions regarding each design parameter \\(d_{i}\\). Formally, we have" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.315, + 0.483, + 0.332 + ], + "angle": 0, + "content": "\\[\nP = \\Gamma_ {f t} (\\mathcal {D}) = \\cup_ {d _ {i} \\in \\mathcal {D}} \\Gamma_ {f t} \\left(d _ {i}\\right) = \\cup q _ {i}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.343, + 0.483, + 0.373 + ], + "angle": 0, + "content": "where \\(q_{i} = \\Gamma_{ft}(d_{i})\\) represents the generated question regarding the \\(i\\)-th design parameter \\(d_{i}\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.391, + 0.277, + 0.407 + ], + "angle": 0, + "content": "3.2.2 Program Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.415, + 0.484, + 0.567 + ], + "angle": 0, + "content": "Initial results showed that MMUA performed significantly better on multiple-choice questions compared to numerical estimation questions. To improve accuracy, we replaced all numerical estimation questions in the initial prompt \\( P \\) with equivalent multiple-choice questions with descriptive options such as \"full length\", \"half length\", or \"three-quarter length\". We append a lightweight projector \\( \\Psi \\) after the finetuned DSL-GA \\( \\Gamma_{ft} \\) to transform these descriptive answers \\( \\tau_i \\) regarding the design input \\( x \\) into precise geometrical parameters \\( d_i \\in \\mathcal{D} \\) adhering to GarmentCode [31]:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.578, + 0.483, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\Psi : \\Gamma_ {f t} (\\cup \\tau_ {i}) \\rightarrow \\mathcal {D}, \\text {w h e r e} \\tau_ {i} = \\mathbf {M M U A} (q _ {i}, x). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.606, + 0.484, + 0.698 + ], + "angle": 0, + "content": "Inspired by DressCode [22], we implement the projector \\(\\Psi\\) as text-conditioned decoder-only transformer, where we design a type-based quantization function \\(\\mathbf{Q}\\) to convert the parameter list \\(\\mathcal{D}\\) into a token sequence \\(\\mathcal{T} = \\{t_1,\\dots,t_N\\}\\), where \\(N = |\\mathcal{D}|\\) denote the total number of design parameters. The quantization function \\(\\mathbf{Q}\\) operates as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.71, + 0.489, + 0.796 + ], + "angle": 0, + "content": "\\[\nt _ {i} = \\mathbf {Q} \\left(d _ {i}\\right) = \\left\\{ \\begin{array}{l l} 0 / 1, & \\text {i f} d _ {i} \\text {i s a b o o l e a n v a r i a b l e ,} \\\\ d _ {i}, & \\text {i f} d _ {i} \\text {i s a n i n t e g e r ,} \\\\ \\lambda \\cdot \\operatorname {N o r m} \\left(d _ {i}\\right), & \\text {i f} d _ {i} \\text {i s a f l o a t i n g n u m b e r ,} \\\\ \\operatorname {I n d e x} \\left(d _ {i}, L\\right), & \\text {i f} d _ {i} \\text {i s a s e l e c t i v e v a r i a b l e .} \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.482, + 0.825 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a scaling factor indicating numerical precision. We use \\(\\lambda = 100\\) to maintain centimeter-level precision." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.901 + ], + "angle": 0, + "content": "As in Eq. 4, we use the finetuned DSL-GA \\(\\Gamma_{ft}\\) to encode the answers \\(\\tau_{i}\\) from MMUA and construct the condition input for \\(\\Psi\\) (we use an MLP to match the embedding dimension between 3,072 in \\(\\Gamma_{ft}\\) and 128 in \\(\\Psi\\)). Notably, our token sequence length is fixed to the number of" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.089, + 0.906, + 0.199 + ], + "angle": 0, + "content": "
MethodText Guided GenerationImage Guided Generation
DressCode [22]OursSewformer [40]Ours
QualitySSR84%100%65.33%94%
Agreement7.17%79.83%3.33%88.67%
Aesthetic9.50%68.17%5.33%77%
CLIPScore0.23860.2438//
F-Score0.616/0.7080.829
CD15.77/9.72.091
Diversity# Panels5.11±1.666.92±3.1010.11±4.4211.02±4.18
# Edges5.48±1.606.84±3.385.79±1.716.24±2.90
# Stitches10.06±3.2418.66±8.6415.81±5.9127.9±9.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.209, + 0.907, + 0.349 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of our method against state-of-the-art (SOTA) sewing pattern generation techniques in terms of quality and diversity. SSR (Simulation Success Rate) indicates the feasibility of simulated garment assembly, while Agreement measures alignment with design prompts, and Aesthetic evaluates the visual preference of the generated patterns. CLIPScore assesses text-image consistency, whereas Chamfer Distance (CD) and \\( F \\)-Score quantify geometric accuracy. #Panels, #Stitches, and #Edges denote the mean and standard deviation (subscript) of the number of panels, stitches per pattern, and edges per panel." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.377, + 0.906, + 0.453 + ], + "angle": 0, + "content": "design parameters \\( |\\mathcal{D}| = 122 \\), regardless of the complexity of the pattern. This fixed-length representation is at least \\( 10 \\times \\) compact than DressCode [22], whose sequence length is 1, 500 and scales with pattern complexity (see Sec. 8 for implementation details)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.47, + 0.646, + 0.487 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.496, + 0.735, + 0.512 + ], + "angle": 0, + "content": "4.1.Quantitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.521, + 0.906, + 0.581 + ], + "angle": 0, + "content": "We evaluate our proposed method against state-of-the-art sewing pattern generation approaches (DressCode [22] for text-guided and Sewformer [40] for image-guided generation) on Generation Quality and Generation Diversity." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.907, + 0.853 + ], + "angle": 0, + "content": "Generation Quality is evaluated through three metrics: Simulation Success Rate (SSR), Agreement Score, and Aesthetic Score. The Simulation Success Rate (SSR) is calculated as the ratio of successfully simulated garments to the total number of generated sewing patterns, measuring the structural feasibility of the patterns. We prepared a dataset comprising 150 text prompts and 150 test images, covering a wide variety including tops (78), pants (76), skirts (38), dresses (80), and suits (28). For each sample, we generated sewing patterns using both our method and baseline methods, and simulated the patterns using GarmentCode's simulation engine [31, 32] to compute the success rate. The Agreement and Aesthetic Scores were derived from a user study involving 30 professional pattern-makers. Each participant is asked to review 50 text and 50 image samples generated by our and the baseline models, and assess their preference based on sewing patterns and simulated garments according to:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.905, + 0.885 + ], + "angle": 0, + "content": "- Agreement: the degree to which the generated pattern matched the design prompt." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.905, + 0.901 + ], + "angle": 0, + "content": "- Aesthetic Quality: the visual appeal and structural coher" + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23716" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.097, + 0.411, + 0.109 + ], + "angle": 0, + "content": "(a) shirt, sleeveless, regular length, crew neck" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.114, + 0.188, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.195, + 0.115, + 0.234, + 0.154 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.24, + 0.115, + 0.28, + 0.154 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.115, + 0.388, + 0.154 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.393, + 0.116, + 0.485, + 0.154 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.16, + 0.462, + 0.173 + ], + "angle": 0, + "content": "(b) dress, A-line, knee-length, regular fit, boat neck, short sleeves" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.177, + 0.188, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.195, + 0.176, + 0.257, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.178, + 0.387, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.393, + 0.178, + 0.485, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.222, + 0.483, + 0.234 + ], + "angle": 0, + "content": "(c) jumpsuit, straight leg, relaxed fit, turtleneck, regular length, long sleeves" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.238, + 0.187, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.195, + 0.238, + 0.258, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.238, + 0.486, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.158, + 0.284, + 0.231, + 0.295 + ], + "angle": 0, + "content": "Our Results" + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.284, + 0.448, + 0.295 + ], + "angle": 0, + "content": "DressCode Results" + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.097, + 0.87, + 0.109 + ], + "angle": 0, + "content": "(d) dress, sleeveless, tight fit, level skirt, boat neck, mini-length" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.114, + 0.599, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.116, + 0.644, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.116, + 0.693, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.116, + 0.789, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.116, + 0.898, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.65, + 0.161, + 0.764, + 0.173 + ], + "angle": 0, + "content": "(e) dress, with a hood" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.177, + 0.601, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.177, + 0.644, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.177, + 0.694, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.177, + 0.803, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.808, + 0.177, + 0.901, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.223, + 0.766, + 0.234 + ], + "angle": 0, + "content": "(f) dress, one-shoulder" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.238, + 0.602, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.239, + 0.67, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.24, + 0.695, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.24, + 0.802, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.808, + 0.24, + 0.898, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.57, + 0.284, + 0.642, + 0.295 + ], + "angle": 0, + "content": "Our Results" + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.284, + 0.859, + 0.295 + ], + "angle": 0, + "content": "DressCode Results" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.315, + 0.907, + 0.358 + ], + "angle": 0, + "content": "Figure 4. Quality Comparison on Text-Guided Sewing Pattern Generation. For each design, we present the generated pattern using our method (left) alongside DressCode [22] (right), including front and back renderings of the draped garment. We highlight design elements accurately captured by our method but missed by DressCode [22] use red color in the input prompt." + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.384, + 0.303, + 0.399 + ], + "angle": 0, + "content": "ence of the generated pattern." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.399, + 0.483, + 0.474 + ], + "angle": 0, + "content": "For each criterion, participants could express a preference for either our method or the baseline or indicate that both methods were \"comparable\". We calculate the Agreement and Aesthetic Scores as the percentage of times each option was chosen over the total number of tested samples." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.475, + 0.484, + 0.673 + ], + "angle": 0, + "content": "Table 1 presents the results, showing that our method surpasses existing approaches in both SSR and user-evaluated Agreement and Aesthetic scores. For text-guided generation, our model achieves a perfect \\(100\\%\\) SSR, notably higher than DressCode's \\(84\\%\\). Additionally, our Agreement score of \\(79.83\\%\\) and Aesthetic score of \\(68.17\\%\\) far exceed DressCode's respective scores of \\(7.17\\%\\) and \\(9.5\\%\\). In image-guided generation, our method attains a \\(94\\%\\) SSR, with an Agreement score of \\(88.67\\%\\) and an Aesthetic score of \\(77\\%\\), significantly outperforming Sewformer. These enhancements highlight our model's ability to generate sewing patterns that are both structurally precise and visually aligned with the design prompt." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Generation Diversity is evaluated by analyzing the average number of panels (# Panels), edges (# Edges), and stitches (# Stitches) in the generated patterns. For text-guided generation, our method yields more intricate designs, with an average of 6.92 panels, 6.84 edges, and 18.66 stitches per pattern, compared to DressCode's simpler outputs of 5.11 panels, 5.48 edges, and 10.06 stitches. In image-guided generation, our approach also demonstrates superior diversity, producing an average of 11.02 panels, 6.24 edges, and 27.9 stitches per pattern, compared to Sewformer's averages of 10.11 panels, 5.79 edges, and 15.81 stitches. These results emphasize our model's ability to capture and replicate subtle design variations, highlighting its robustness and adaptability across different design inputs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.383, + 0.799, + 0.399 + ], + "angle": 0, + "content": "4.2. Multi-modal Generation Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.413, + 0.907, + 0.459 + ], + "angle": 0, + "content": "Our proposed method demonstrates superior performance across various sewing pattern generation tasks, including text-guided, image-guided, and sketch-based generation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.465, + 0.907, + 0.678 + ], + "angle": 0, + "content": "In text-guided sewing pattern generation (Figure 4), our method accurately captures design details specified in prompts, such as neckline types (e.g., crew neck (a), boat neck (b), turtleneck (c)) and complex structural features like asymmetry (f) and layered skirts (d). In comparison, the baseline model DressCode struggles with limited pattern diversity, often defaulting to simpler shapes like V-neck designs. Additionally, for design descriptions out of its training domain, DressCode frequently generates patterns with incorrect stitching, leading to poor draping results (Figure 4 (e)). Our method could provide structurally sound and visually accurate patterns under a large design variety, showcasing its capability to handle diverse design requests with high fidelity." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.683, + 0.907, + 0.865 + ], + "angle": 0, + "content": "For image-guided sewing pattern generation (Figure 5), our model effectively translates detailed visual cues from input images into corresponding sewing patterns. Compared with Sewformer, which often fails to model-specific design elements like cuffs, hoods, and asymmetric features, our approach accurately reproduces these details. Sewformer's results frequently exhibit structural flaws, such as missing or misaligned pattern pieces and extraneous components, resulting in unrealistic garment draping. In contrast, our method maintains structural integrity and captures complex design features, producing patterns that closely align with the source images." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In sketch-based sewing pattern generation (Figure 6), our system seamlessly converts both technical sketches (left)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23717" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.296, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.09, + 0.488, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.71, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.089, + 0.905, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.348, + 0.907, + 0.432 + ], + "angle": 0, + "content": "Figure 5. Quality Comparison on Image-Guided Sewing Pattern Generation. We compare our method with Sewformer [40] on Internet-collected fashion photographs (left), and AI-generated design images without human models (right). The results indicate that our method successfully captures design details from diverse styles, producing sewing patterns that accurately reflect neckline (a, d), cuffs (a, e, g), darts (c, d), and asymmetry (f). In contrast, Sewformer's results exhibit several issues, including incorrect necklines (a, d), missing components (b, g), misplaced or imaginary stitches (d, e), and extraneous pattern pieces (h). Additionally, since Sewformer's pattern generation does not account for body shape, garments like skirts and pants frequently appear oversized around the waist, causing them to sag when draped." + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.451, + 0.634, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.449, + 0.895, + 0.688 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.703, + 0.908, + 0.748 + ], + "angle": 0, + "content": "Figure 6. Examples of sketch-based sewing pattern generation. Our method was able to generate high-quality sewing patterns from design sketches under various styles and could integrate seamlessly with industrial fashion design software for (a) pattern editing, i.e. sleeve panels in red boxes are merged from separate front/back sleeve panels; and (b) avatar posture and fabric material editing." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.771, + 0.482, + 0.862 + ], + "angle": 0, + "content": "and artistic drawings1 (right) into high-quality sewing patterns. We also demonstrated that the generated sewing patterns could seamlessly integrate into industrial fashion design software2. For example, highlighted sleeve panels in Figure 6 (a) are merged from separate front and back sleeve pieces, while Figure 6 (b) demonstrates avatar posture and" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.772, + 0.667, + 0.788 + ], + "angle": 0, + "content": "fabric material editing." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.8, + 0.637, + 0.818 + ], + "angle": 0, + "content": "5. Application" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.903 + ], + "angle": 0, + "content": "In this section, we explore practical applications enabled by our system that extend beyond basic pattern generation, providing designers with versatile tools for design refinement, integration with physical simulation, and the creation of new garment components." + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.439, + 0.888 + ], + "angle": 0, + "content": "1The drawing is borrowed from the artwork of TWELVEYIN." + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.456, + 0.901 + ], + "angle": 0, + "content": "2We use Style3D Studio [5] for pattern and appearance authoring." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.456, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23718" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.094, + 0.878, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.247, + 0.908, + 0.304 + ], + "angle": 0, + "content": "Figure 7. Sewing Pattern Authoring with instructions. Starting from an original design, the system follows user instructions to adjust specific pattern elements. In Edited Design 1, the pants are modified to a skirt based on the command \"CHANGE THE PANT TO SKIRT\". In Edited Design 2, the sleeves are shortened as requested. Finally, in Edited Design 3, the shirt is made sleeveless in response to the instructions. Note that, each modification accurately applies only to the specified parts, leaving the rest of the design unchanged." + }, + { + "type": "image", + "bbox": [ + 0.103, + 0.329, + 0.47, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.469, + 0.483, + 0.512 + ], + "angle": 0, + "content": "Figure 8. Sewing pattern adjustment based on body pressure measurement. Red regions indicate areas of tight fabric with high body pressure, while blue regions represent looser areas." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.532, + 0.465, + 0.624 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.635, + 0.483, + 0.663 + ], + "angle": 0, + "content": "Figure 9. The code for a layered-skirt component generated by our DSL-GA and 3D garment under various design parameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.483, + 0.856 + ], + "angle": 0, + "content": "Instruction-Based Editing. Our system allows designers to adjust generated sewing patterns through simple, instruction-based edits, utilizing the same refinement process as in our collaborative framework. As illustrated in Figure 7, starting from an original design, the system responds to natural language commands from the user to adjust the sewing pattern. At each step, the modified areas are highlighted in red boxes. From the figure, it is evident that our system can accurately update only the specified parts of the pattern according to the user's instructions while leaving all other parts of the design unchanged." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Physics-Based Editing. Our system's generated sewing patterns integrate seamlessly with professional cloth simulation software, allowing adjustments based on fitness mea" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.33, + 0.905, + 0.435 + ], + "angle": 0, + "content": "surements derived from physical simulations. In Figure 8, we demonstrate sewing pattern editing guided by body pressure analysis, including adjustments to the cuff (a), upper bodice (b), lower bodice (c), and collar (d). As shown in the examples, our system accurately identifies areas with excessive tension and adjusts the corresponding sewing patterns to enhance comfort while preserving the overall design." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.436, + 0.907, + 0.679 + ], + "angle": 0, + "content": "Generating New Garment Programs. A major challenge in traditional parametric pattern-making is the need to abstract symbolic programs for new sewing patterns, which demands both advanced programming skills and patterning expertise. Design2GarmentCode addresses this by correlating GarmentCode grammar with LMMs' embedded pattern-making knowledge, enabling the automatic creation of new garment components. Figure 9 shows a layered-skirt component generated by our DSL-GA, along with 3D garment representations demonstrating different design parameters, such as skirt length (c), number of layers (d), and layer differences such as length difference and ruffling factor (e). The results demonstrate that our system consistently produces high-quality garment components that meet professional standards, while significantly reducing the time and expertise required to create new sewing pattern programs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.694, + 0.634, + 0.71 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Design2GarmentCode transforms multi-modal design concepts into precise sewing patterns using LMMs to synthesize parametric programs. It addresses challenges related to data requirements, computation, and the limited precision of neural network-based methods. The experimental results demonstrate the system's ability to capture design details while maintaining structural integrity and geometric precision in generated patterns. Despite these advantages, Design2GarmentCode currently cannot substantially alter GarmentCode's underlying structure and logistics, which impacts generation quality due to inherent limitations in GarmentCode's design and modeling capabilities (Supp. 10)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23719" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.484, + 0.177 + ], + "angle": 0, + "content": "This work was supported by Key R&D Program of Hangzhou (No.2024SDZ1A20). We sincerely thank Fuqi Wang for his valuable support in validation data collection, material modeling and animation." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.188, + 0.188, + 0.204 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.215, + 0.482, + 0.255 + ], + "angle": 0, + "content": "[1] Assyst smart(pattern macro. https://www.assyst.de/en/products/cad/index.html. Accessed: 2024-11-09. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.256, + 0.483, + 0.298 + ], + "angle": 0, + "content": "[2] Modaris: Smart and speedy patternmaking for fashion experts. https://www.lectra.com/en/fashion/products/modaris. Accessed: 2024-11-09." + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.299, + 0.482, + 0.34 + ], + "angle": 0, + "content": "[3] Optitex: 2d/3d cad pattern design software. https://optitex.com/products/2d-and-3d-cad-software/. 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However, existing uni-modal sewing pattern generation models struggle to effectively encode complex design concepts with a multimodal nature and correlate them with vectorized sewing patterns that possess precise geometric structures and intricate sewing relations. In this work, we propose a novel sewing pattern generation approach Design2GarmentCode based on Large Multimodal Models (LMMs), to generate parametric pattern-making programs from multi-modal design concepts. LMM offers an intuitive interface for interpreting diverse design inputs, while pattern-making programs could serve as well-structured and semantically meaningful representations of sewing patterns, and act as a robust bridge connecting the cross-domain pattern-making knowledge embedded in LMMs with vectorized sewing patterns. Experimental results demonstrate that our method can flexibly handle various complex design expressions such as images, textual descriptions, designer sketches, or their combinations, and convert them into size-precise sewing patterns with correct stitches. Compared to previous methods, our approach significantly enhances training efficiency, generation quality, and authoring flexibility. Project page: https://style3d.github.io/design2garmentcode. + +# 1. Introduction + +While generative AI has significantly propelled creativity in fashion design, turning those design ideas into wearable realities remains a formidable challenge. Sewing patterns are the key components to bridge the gap between abstract design ideas and wearable realities. They are foundational blueprints that dictate the precise shapes and dimensions of fabric pieces, essential for assembling garments in both the physical and virtual fashion realms. + +![](images/a65cd375c6b895b9a38d21566cc80cf3af4e47fb2052c243e3bff074f08d2d3a.jpg) +Figure 1. Traditional sewing pattern generation approaches (top) use uni-modal models trained on synthetic datasets generated by parametric pattern-making programs (red arrow) to convert text or image prompts into vector-quantized patterns. These methods are resource-intensive and often yield oversimplified patterns with stitching errors. Our approach (bottom) utilizes large pre-trained LMMs to directly translate design concepts into parametric programs and configuration files (blue arrow), enabling dedicated, structurally correct pattern generation from multi-modal design inputs within a unified framework. + +Traditionally, sewing patterns are drafted manually by professional pattern-makers with years of practice, making the process inefficient, error-prone, and unable to meet the growing demands for refinement and personalization in the fashion market. To this end, parametric pattern-making researches [8, 29, 31] and industrial solutions [1-4] have emerged. These methods formalize the pattern-making process as geometric functions governed by parameters such as body measurements and design features, thereby accelerating the process by enabling pattern makers to generate sewing patterns through parameter adjustments instead of starting from scratch. However, creating these function templates is still complex, requiring not only advanced pattern-making skills but also geometric intuition, mathematical modeling knowledge, and coding abilities to trans + +![](images/172db2ce9ade4c6369de02b98442484c219570ba524954bb075c3fc0ae08c741.jpg) +(a) Limited Generation Diversity + +![](images/07ba85d92998759312e6e54b29895220f4e7b53ae1adf9b17545af70028f6879.jpg) +(b) Self-Intersection + +![](images/e68c8ff5c6772001159b8bf92e8efd57c74215427e69e73b98a5162aa498159e.jpg) +(c) Wrong Stitches +Figure 2. (a) Despite prompts specifying diverse neckline types, DressCode [22] consistently produces only V-neck designs, indicating limited generation diversity. (b) SewFormer [40] often generates sewing patterns with self-intersecting panels, compromising pattern validity. (c) Stitching errors are also prevalent in Sewformer [40], as shown here where a pant side seam is mistakenly stitched to a shirt shoulder seam, resulting in draping failure. + +late pattern-making expertise into CAD programs. These technical barriers significantly restrict the widespread adoption of parametric pattern-making solutions. + +Recently, several learning-based approaches for sewing pattern generation have been introduced. For instance, NeuralTailor [30] focuses on extracting sewing patterns from unstructured point clouds, DressCode [22] targets text-to-sewing pattern generation, and SewFormer [40] is designed for image-based sewing pattern generation. However, they are generally trained on paired design-sewing pattern data, necessitating large datasets to effectively capture the multimodal nature of design concepts. Furthermore, sewing patterns require centimeter-level precision to ensure proper garment fit, which presents a significant challenge for neural networks that only provide statistical approximations of the true function based on their training data [14, 23, 47]. As a result, these methods frequently generate oversimplified patterns with flawed geometry or stitches, potentially leading to draping failures (Figure 2). + +In this paper, we present Design2GarmentCode, an innovative approach that leverages the generalization capabilities of vision-language foundation models to achieve multi-modal sewing pattern generation with minimal computational and data requirements. Unlike previous methods that directly synthesize vector-quantized patterns, Design2GarmentCode employs LMMs to learn the syntax of parametric pattern-making programs, translating design concepts into parameters and programs that can be executed to produce precise and structurally accurate sewing patterns. Design2GarmentCode combines a pre-trained Large Multimodal Model (LMM) as a design interpreter with a finetuned Large Language Model (LLM) as a program synthesizer. Specifically, the LLM is finetuned on code snippets from GarmentCode [31], a domain-specific language for constructing parametric sewing patterns. At runtime, the design interpreter extracts both topological and geometrical information from the design input by responding to a series of questions from the program synthesizer, which then generates garment programs and design config + +urations following GarmentCode syntax. Our method offers the following major contributions: + +- We introduce a novel modality-agnostic framework with an intuitive, intelligent interface capable of processing user design intentions across multiple modalities simultaneously by integrating pre-trained LMMs. +- We present the first sewing pattern generation approach grounded in program synthesis, delivering fully interpretable, geometrically precise, and structurally accurate patterns through a more compact, semantically clear, and LLM-friendly representation. +- Our framework benefits real-world production by enabling flexible pattern authoring through natural language or physical feedback, allowing precise customization and efficient creation of novel garment components, represented as parametric pattern-making programs. +- Our approach requires only minimal fine-tuning of a pre-trained LLM and the training of a lightweight, text-conditioned transformer decoder, making it more efficient than existing vector-quantized sewing pattern generation models trained from scratch while offering superior generation quality and authoring flexibility. + +# 2. Related Work + +# 2.1. Garment Modeling with Sewing Patterns + +Garment modeling and generation can be broadly classified into two categories: direct 3D garment generation (meshes) and sewing pattern generation, which are later draped onto human bodies via cloth simulation [39, 53, 56] or learning-based techniques [35, 37]. Direct 3D garment generation often relies on differentiable garment representations like unsigned distance fields [65, 67], shells [42], or Gaussian splatting [48]. However, it presents challenges in terms of both geometric accuracy and editability. On one hand, capturing fine garment details like folds and wrinkles necessitates extremely high-resolution 3D representations. On the other hand, editing these generated garments requires a well-defined UV space, and flattening the 3D mesh into developable meshes demands careful consideration from both geometric and statistical perspectives [7, 46]. + +Sewing pattern generation, by contrast, has been approached through both learning-based and procedural modeling methods. Learning approaches utilize vector-quantized representations of sewing patterns, mapping from unstructured 3D point clouds [7, 30], images [12, 26, 40, 64], or textual descriptions [22] to structured patterns. However, they are highly dependent on the quality and diversity of the training data and often struggle to generalize designs beyond the training domain. Furthermore, generating high-quality 3D garment data requires substantial domain knowledge and the involvement of skilled professionals. + +Procedural modeling is an alternative that relies on pre + +defined rules and parameters to generate garment patterns. For instance, GarmentCode [31], a DSL for parametric pattern making, enables precise control over garment design and customization. The GarmentCodeData [32], built on GarmentCode, further illustrates the potential of procedural methods to generate a diverse range of made-to-measure garments, with adaptability to different body shapes. While procedural modeling provides greater control and precision, it typically requires specialized expertise and is less flexible when dealing with novel or unconventional designs. + +# 2.2. LLMs for Program Synthesis + +Recent advancements in program synthesis and code generation using large language models (LLMs) have laid essential groundwork for systems like Design2GarmentCode, which generate structured garment code from multi-modal design inputs. Earlier researches like Codex [11] and AlphaCode [36] demonstrated the effectiveness of LLMs in generating complex, task-specific code with high syntax accuracy, showcasing potential in scenarios requiring precise parametric coding. These models [43, 59] highlight how LLMs, when sufficiently trained, can transform natural language inputs into executable code, a capability directly relevant to generating garment codes that follow complex pattern-making syntax. [9, 19, 20, 55, 63] explore multimodal models that integrate visual aids, such as flowcharts and UML diagrams, into LLM training to enhance models' comprehension of complex structures and flow. These models particularly emphasize the need for semantic understanding and adaptability, which are critical in working with domain-specific languages (DSLs) like GarmentCode. + +# 2.3. Neurosymbolic Models + +Procedural and neural models offer complementary strengths and weaknesses. Neurosymbolic models [47] integrate both paradigms by generating visual data through symbolic programs enhanced with AI/ML techniques. These models typically follow a pipeline comprising task specification, program synthesis via a domain-specific language (DSL), program execution, and optional neural post-processing for refinement. They have been successfully applied across various areas of computer graphics. In 2D shape modeling, neurosymbolic methods are used for layout generation [45, 54], engineering sketch creation [16, 44, 49], and vector graphics synthesis by constructing programs that represent geometric shapes and spatial relations [10, 17]. For 3D shape modeling, they enable shape program inference from existing 3D models [27, 28, 33, 51] and the generation of new 3D shapes by training generative models on shape programs [57, 60, 61] or generate node graphs defining complex textures and materials [21, 25, 50], aligning with procedural modeling principles. + +Beyond shape modeling, neurosymbolic approaches + +have been applied to human motion prediction [18, 38], reasoning [34, 58, 66], and generation [13, 41, 62], leveraging visual-language foundation models to extract symbolic representations from visual data for complex activity reasoning [58]. Our approach follows the neurosymbolic paradigm by instruction-tuning LLMs to generate structured, executable programs defining garment component, their relationships, and parameters from diverse design concepts. + +# 3. Method + +Our goal is to develop a generative model that transforms multi-modal design concepts into precise sewing patterns. This requires understanding diverse inputs and producing patterns with high geometric precision and intricate structures. These requirements present a challenge for conventional models, which require extensive training data and struggle with output precision due to their probabilistic nature. We propose Design2GarmentCode, a system leveraging LMMs to generate parametric patternmaking programs, or specifically GarmentCode [31]. Design2GarmentCode reduces the need for large datasets utilizing the pre-embedded pattern-making knowledge in LMMs while ensuring output precision with parametric program synthesis. In the following, we first provide an overview of parametric pattern-making programs and GarmentCode syntax, and then describe the detailed design of Design2GarmentCode. + +# 3.1. Parametric Sewing Patterns + +Parametric sewing patterns are formally represented as symbolic programs that generate sewing patterns (i.e., 2D CAD sketches) based on body measurements and design configurations. These symbolic programs enhance the efficiency of the pattern-making process by allowing users to draft or modify sewing patterns through semantically meaningful parameters. Mathematically, we can represent a sewing pattern $S$ as: + +$$ +\mathcal {S} = \langle \mathcal {F}, \mathcal {D}, B \rangle = \cup_ {f _ {i} \in \mathcal {F}, d _ {i} \in \mathcal {D}} f _ {i} (d _ {i}, B), \tag {1} +$$ + +where $\mathcal{F}$ is the set of symbolic programs, $\mathcal{D}$ represents design configurations, and $B$ represents body measurements. Each symbolic function $f_{i} \in \mathcal{F}$ is essentially a series of rule-based 2D draw-calls controlled by its unique set of design configurations $d_{i} \in \mathcal{D}$ and the body measurements $B$ . + +GarmentCode is a domain-specific language (DSL) designed to generate parametric sewing patterns by encapsulating those symbolic programs in a hierarchical, component-oriented manner. In GarmentCode, each symbolic program $f_{i}$ uses parametric curves to define a garment component, such as sleeves, bodices, or collars. The + +![](images/df0ece6a6b00ca48492c25b658870ec5a86a0e0bbc87f0a721f5f122a266b8f5.jpg) +Figure 3. Overview of Dress2GarmentCode. (1) Program Learning: we finetune the DSL Generation Agent (DSL-GA) using GarmentCode example programs, teaching it the GarmentCode grammar and the semantics of each design parameter. (2) Prompt Synthesis: the DSL-GA generates prompts for the Multi-Modal Understanding Agent (MMUA) to interpret and extract relevant design features from the input (3). (4) Program Synthesis: based on the MMUA's responses, the DSL-GA synthesizes GarmentCode-compliant design configurations and garment programs, which are then executed by the GarmentCode engine to produce sewing patterns and simulated garments (5). To enhance robustness, we incorporate two validation loops: during program synthesis, we employ rule-based validations (7) to ensure the MMUA's outputs are sufficient for generating complete and valid garment programs and design parameters; after the initial generation, the MMUA compares the generated design with the input and suggests modifications to minimize discrepancies. + +smallest component is a single panel, and multiple components can be combined through interface functions to create a larger component. In GarmentCode, a complete sewing pattern is specified by topological parameters $\mathcal{D}_T$ (which define the presence and quantity of garment components) and geometrical parameters $\mathcal{D}_G$ , which determine the dimensions of each component when combined with body measurements $B$ . As this work primarily focuses on design variations, we use a standard body model throughout all experiments to ensure consistency. + +# 3.2. The Design2GarmentCode System + +As illustrated in Figure 3, Design2GarmentCode has three components: DSL Generation Agent (DSL-GA), a finetuned LLM responsible for (1) program learning, (2) prompt synthesis, and (4) program synthesis; Multi-modal Understanding Agent (MMUA), a pre-trained LLM that manages design understanding (3) and design comparison (6); and (5) GarmentCode, which executes the synthesized programs to generate sewing patterns and 3D garments. + +The system workflow begins with Program Learning (Sec. 3.2.1), where DSL-GA is finetuned to understand the syntax and semantic meanings of GarmentCode parameters. In Prompt Synthesis, DSL-GA creates prompts for MMUA to identify essential design features. These features are then provided to DSL-GA for Program Synthesis, where garment programs and design configurations are generated through rule-based parameter validation (Figure 3 (7)) and a learned projector (Sec. 3.2.2). The GarmentCode Execution Engine then produces sewing patterns and + +draped garment models. Finally, a Validation stage compares the generated garment with the original design, allowing MMUA to provide specific correction instructions to DSL-GA for iterative refinement, such as "make the sleeve longer". + +# 3.2.1 Program Learning + +During experiments, we found that pre-trained LLMs have some foundational knowledge of pattern drafting. For example, when prompted with "How to draft a basic upper body bodice?", LLMs can produce drafting instructions that align with conventional practices. We use a pretrained LLM to initialize DSL-GA, however, due to GarmentCode's customized object notations and function logistics, directly prompting DSL-GA to generate GarmentCode programs poses significant challenges [9]. + +To address these challenges, we propose to align DSL-GA's embedded pattern-making knowledge with the specific syntax and semantics of GarmentCode via LoRA [24] based on fine-tuning. We start by providing the DSL-GA (denoted as $\Gamma$ ) with existing GarmentCode programs $\mathcal{F}$ , and instructing it to comment on the functions with detailed pattern-drafting instructions. After manually validating the comments, we get a dataset $D$ paring natural language instructions with GarmentCode implementations: + +$$ +D = \left\{\left(\Gamma_ {c m t} (f _ {i}), f _ {i}\right) \mid f _ {i} \in \mathcal {F} \right\}, \tag {2} +$$ + +where $\Gamma_{cmt}$ is the instructed DSL-GA for code commenting, $f_{i}$ is. Similar to [9], we finetune DSL-GA $(\Gamma)$ on the + +dataset $D$ with LoRA [24], aiming for $\Gamma_{ft}(\Gamma_{cmt}(f_i))\to f_i$ where $\Gamma_{ft}$ is the finetuned DSL-GA. + +After fine-tuning, the fine-tuned DSL-GA $\Gamma_{ft}$ gains an understanding of the code structure and parameter semantics in GarmentCode (Figure 9). Therefore, we provide the design configuration $\mathcal{D}$ to $\Gamma_{ft}$ , prompting it to analyze the semantic meaning of each parameter and generate structured queries. These queries are designed to guide the MMUA in extracting relevant design features from the multi-modal input, enabling $\Gamma_{ft}$ to generate a comprehensive set of design parameters. The generated prompt $P$ typically starts with analysis instructions, followed by multiple-choice or numerical estimation questions regarding each design parameter $d_{i}$ . Formally, we have + +$$ +P = \Gamma_ {f t} (\mathcal {D}) = \cup_ {d _ {i} \in \mathcal {D}} \Gamma_ {f t} \left(d _ {i}\right) = \cup q _ {i}, \tag {3} +$$ + +where $q_{i} = \Gamma_{ft}(d_{i})$ represents the generated question regarding the $i$ -th design parameter $d_{i}$ . + +# 3.2.2 Program Synthesis + +Initial results showed that MMUA performed significantly better on multiple-choice questions compared to numerical estimation questions. To improve accuracy, we replaced all numerical estimation questions in the initial prompt $P$ with equivalent multiple-choice questions with descriptive options such as "full length", "half length", or "three-quarter length". We append a lightweight projector $\Psi$ after the finetuned DSL-GA $\Gamma_{ft}$ to transform these descriptive answers $\tau_i$ regarding the design input $x$ into precise geometrical parameters $d_i \in \mathcal{D}$ adhering to GarmentCode [31]: + +$$ +\Psi : \Gamma_ {f t} (\cup \tau_ {i}) \rightarrow \mathcal {D}, \text {w h e r e} \tau_ {i} = \mathbf {M M U A} (q _ {i}, x). \tag {4} +$$ + +Inspired by DressCode [22], we implement the projector $\Psi$ as text-conditioned decoder-only transformer, where we design a type-based quantization function $\mathbf{Q}$ to convert the parameter list $\mathcal{D}$ into a token sequence $\mathcal{T} = \{t_1,\dots,t_N\}$ , where $N = |\mathcal{D}|$ denote the total number of design parameters. The quantization function $\mathbf{Q}$ operates as follows: + +$$ +t _ {i} = \mathbf {Q} \left(d _ {i}\right) = \left\{ \begin{array}{l l} 0 / 1, & \text {i f} d _ {i} \text {i s a b o o l e a n v a r i a b l e ,} \\ d _ {i}, & \text {i f} d _ {i} \text {i s a n i n t e g e r ,} \\ \lambda \cdot \operatorname {N o r m} \left(d _ {i}\right), & \text {i f} d _ {i} \text {i s a f l o a t i n g n u m b e r ,} \\ \operatorname {I n d e x} \left(d _ {i}, L\right), & \text {i f} d _ {i} \text {i s a s e l e c t i v e v a r i a b l e .} \end{array} \right. \tag {5} +$$ + +where $\lambda$ is a scaling factor indicating numerical precision. We use $\lambda = 100$ to maintain centimeter-level precision. + +As in Eq. 4, we use the finetuned DSL-GA $\Gamma_{ft}$ to encode the answers $\tau_{i}$ from MMUA and construct the condition input for $\Psi$ (we use an MLP to match the embedding dimension between 3,072 in $\Gamma_{ft}$ and 128 in $\Psi$ ). Notably, our token sequence length is fixed to the number of + +
MethodText Guided GenerationImage Guided Generation
DressCode [22]OursSewformer [40]Ours
QualitySSR84%100%65.33%94%
Agreement7.17%79.83%3.33%88.67%
Aesthetic9.50%68.17%5.33%77%
CLIPScore0.23860.2438//
F-Score0.616/0.7080.829
CD15.77/9.72.091
Diversity# Panels5.11±1.666.92±3.1010.11±4.4211.02±4.18
# Edges5.48±1.606.84±3.385.79±1.716.24±2.90
# Stitches10.06±3.2418.66±8.6415.81±5.9127.9±9.83
+ +Table 1. Quantitative comparison of our method against state-of-the-art (SOTA) sewing pattern generation techniques in terms of quality and diversity. SSR (Simulation Success Rate) indicates the feasibility of simulated garment assembly, while Agreement measures alignment with design prompts, and Aesthetic evaluates the visual preference of the generated patterns. CLIPScore assesses text-image consistency, whereas Chamfer Distance (CD) and $F$ -Score quantify geometric accuracy. #Panels, #Stitches, and #Edges denote the mean and standard deviation (subscript) of the number of panels, stitches per pattern, and edges per panel. + +design parameters $|\mathcal{D}| = 122$ , regardless of the complexity of the pattern. This fixed-length representation is at least $10 \times$ compact than DressCode [22], whose sequence length is 1, 500 and scales with pattern complexity (see Sec. 8 for implementation details). + +# 4. Experiments + +# 4.1.Quantitative Evaluation + +We evaluate our proposed method against state-of-the-art sewing pattern generation approaches (DressCode [22] for text-guided and Sewformer [40] for image-guided generation) on Generation Quality and Generation Diversity. + +Generation Quality is evaluated through three metrics: Simulation Success Rate (SSR), Agreement Score, and Aesthetic Score. The Simulation Success Rate (SSR) is calculated as the ratio of successfully simulated garments to the total number of generated sewing patterns, measuring the structural feasibility of the patterns. We prepared a dataset comprising 150 text prompts and 150 test images, covering a wide variety including tops (78), pants (76), skirts (38), dresses (80), and suits (28). For each sample, we generated sewing patterns using both our method and baseline methods, and simulated the patterns using GarmentCode's simulation engine [31, 32] to compute the success rate. The Agreement and Aesthetic Scores were derived from a user study involving 30 professional pattern-makers. Each participant is asked to review 50 text and 50 image samples generated by our and the baseline models, and assess their preference based on sewing patterns and simulated garments according to: + +- Agreement: the degree to which the generated pattern matched the design prompt. +- Aesthetic Quality: the visual appeal and structural coher + +![](images/a2028672ab23b53e99c336fe7e23772640e349a845d5b3e671a8b2a25229dcfd.jpg) +(a) shirt, sleeveless, regular length, crew neck + +![](images/50a0986d0f0ad8376c6e7056f74e15addc31384e99d034063d350543ea5f4d11.jpg) + +![](images/e3348373e830ebc9fdd873a8d62fd7df1623376a3b01548dbe871e0c518e695c.jpg) + +![](images/d7ac8be312f91eadd7f049a1b5645634dad8d0c7d2969fa09be83e096cd9f1ca.jpg) + +![](images/3c5005be3b3ae263883472e4f2220c36a0410302be6642e1a164f783e5ae125b.jpg) + +![](images/6a2ee11f13e1f3cb829f5c5a70ff226979569e38c655d1a7375806861d12624a.jpg) +(c) jumpsuit, straight leg, relaxed fit, turtleneck, regular length, long sleeves + +![](images/e9f0a0da10ef72f967dec5271e9a2012561c01e3bacc5c6fae3a430c371adb96.jpg) +(b) dress, A-line, knee-length, regular fit, boat neck, short sleeves + +![](images/b1a41d673ce625ce5261ec4a4d98698efecbaf7a231404a4e2a74b1c2ddcdf6f.jpg) + +![](images/0544affb9296021905cf1bf55c8340169429d6125d4cedc0f7829b243d004fcd.jpg) + +![](images/6ce8d4c00de08db99181f47f0112a284dcc4d793b379a9d6fe93bb7f2997ae04.jpg) +Our Results + +![](images/95e13fbcc5187d131ea77b7d2cda87cf6b18ab939ca74342daaecabf11dc8a2a.jpg) +Figure 4. Quality Comparison on Text-Guided Sewing Pattern Generation. For each design, we present the generated pattern using our method (left) alongside DressCode [22] (right), including front and back renderings of the draped garment. We highlight design elements accurately captured by our method but missed by DressCode [22] use red color in the input prompt. + +![](images/22d3cd9b9844378f27fa86c3196032eea1d4fb7d80ad05f473d5d65bc077c493.jpg) +DressCode Results + +![](images/922ce668b7fd9effffa1a7744de68414870ac11e7f10b2c70b1f65c1911c2f19.jpg) +(d) dress, sleeveless, tight fit, level skirt, boat neck, mini-length + +![](images/96eb10e963b961784d71301e2f3b34215db3500c4bbd69ef73c6f0bf7d183ca2.jpg) +(e) dress, with a hood + +![](images/97119040d1d771d8350865ab79de1640de4619878d36956d896ded148c1458c8.jpg) + +![](images/c8da95da553a97070e3179560f61b77e0767bdc1d9919eacfd2f85f7ae7b04dc.jpg) + +![](images/4b83f5315932bf085715917d0a652f3149305f1412a2a0e3589127f559de2ede.jpg) + +![](images/421930ae9a0f56a2191267755ea044e02f4f0fe8f7439a5eecf539d0b0de60f6.jpg) + +![](images/a2a486fb762b034defdb26588155020059958a746f9852f3e1a5505047abb6e1.jpg) +(f) dress, one-shoulder + +![](images/55edc0d1d0e7ad9dc262d39df8a0dc253b9f3984c1013bb13abdc03120311c7d.jpg) + +![](images/82b28e6db4fbd035b902f8684106ccd47119d4424546df4a6dd5ec8af8f19b58.jpg) + +![](images/6839aec9f3407dc48f4df8da08d30ff44464e46f3de8c65666aad928774d946b.jpg) + +![](images/794cce34fc9ad4c9147bb9a88aa4c59635e55f7a7d8a0dd6a642936d39d9ab46.jpg) +Our Results + +![](images/f99c9d0b7f85d548490dc9e8b7eb5a46dbde6063ce98b58f9bfb2cff5bb375fe.jpg) + +![](images/9959e3a56280811d671a62c6092affe17377c55b496a200ac3afc43f98a114b9.jpg) + +![](images/dce3d9c59ab2e22f4ef98a324e21465933f936f14eb6316e7312d65bf684c2f4.jpg) +DressCode Results + +![](images/98dc785ebaaaad80999ac28e48b3c93fe83ea2961a178b30a46f074ddfa1ef43.jpg) + +ence of the generated pattern. + +For each criterion, participants could express a preference for either our method or the baseline or indicate that both methods were "comparable". We calculate the Agreement and Aesthetic Scores as the percentage of times each option was chosen over the total number of tested samples. + +Table 1 presents the results, showing that our method surpasses existing approaches in both SSR and user-evaluated Agreement and Aesthetic scores. For text-guided generation, our model achieves a perfect $100\%$ SSR, notably higher than DressCode's $84\%$ . Additionally, our Agreement score of $79.83\%$ and Aesthetic score of $68.17\%$ far exceed DressCode's respective scores of $7.17\%$ and $9.5\%$ . In image-guided generation, our method attains a $94\%$ SSR, with an Agreement score of $88.67\%$ and an Aesthetic score of $77\%$ , significantly outperforming Sewformer. These enhancements highlight our model's ability to generate sewing patterns that are both structurally precise and visually aligned with the design prompt. + +Generation Diversity is evaluated by analyzing the average number of panels (# Panels), edges (# Edges), and stitches (# Stitches) in the generated patterns. For text-guided generation, our method yields more intricate designs, with an average of 6.92 panels, 6.84 edges, and 18.66 stitches per pattern, compared to DressCode's simpler outputs of 5.11 panels, 5.48 edges, and 10.06 stitches. In image-guided generation, our approach also demonstrates superior diversity, producing an average of 11.02 panels, 6.24 edges, and 27.9 stitches per pattern, compared to Sewformer's averages of 10.11 panels, 5.79 edges, and 15.81 stitches. These results emphasize our model's ability to capture and replicate subtle design variations, highlighting its robustness and adaptability across different design inputs. + +# 4.2. Multi-modal Generation Results + +Our proposed method demonstrates superior performance across various sewing pattern generation tasks, including text-guided, image-guided, and sketch-based generation. + +In text-guided sewing pattern generation (Figure 4), our method accurately captures design details specified in prompts, such as neckline types (e.g., crew neck (a), boat neck (b), turtleneck (c)) and complex structural features like asymmetry (f) and layered skirts (d). In comparison, the baseline model DressCode struggles with limited pattern diversity, often defaulting to simpler shapes like V-neck designs. Additionally, for design descriptions out of its training domain, DressCode frequently generates patterns with incorrect stitching, leading to poor draping results (Figure 4 (e)). Our method could provide structurally sound and visually accurate patterns under a large design variety, showcasing its capability to handle diverse design requests with high fidelity. + +For image-guided sewing pattern generation (Figure 5), our model effectively translates detailed visual cues from input images into corresponding sewing patterns. Compared with Sewformer, which often fails to model-specific design elements like cuffs, hoods, and asymmetric features, our approach accurately reproduces these details. Sewformer's results frequently exhibit structural flaws, such as missing or misaligned pattern pieces and extraneous components, resulting in unrealistic garment draping. In contrast, our method maintains structural integrity and captures complex design features, producing patterns that closely align with the source images. + +In sketch-based sewing pattern generation (Figure 6), our system seamlessly converts both technical sketches (left) + +![](images/d5c1a65313beec7f20f8a2f21a751687007d8578eaa0b4cbef7dd77ccf6a3f93.jpg) +Figure 5. Quality Comparison on Image-Guided Sewing Pattern Generation. We compare our method with Sewformer [40] on Internet-collected fashion photographs (left), and AI-generated design images without human models (right). The results indicate that our method successfully captures design details from diverse styles, producing sewing patterns that accurately reflect neckline (a, d), cuffs (a, e, g), darts (c, d), and asymmetry (f). In contrast, Sewformer's results exhibit several issues, including incorrect necklines (a, d), missing components (b, g), misplaced or imaginary stitches (d, e), and extraneous pattern pieces (h). Additionally, since Sewformer's pattern generation does not account for body shape, garments like skirts and pants frequently appear oversized around the waist, causing them to sag when draped. + +![](images/67f894b4b6ac4eeaec3079daaf72cf67477886c8640c682f9d1fdfd75ba3b87a.jpg) + +![](images/f6d097cecc9486129f2ed0c2516f190f103bc4524fd1c234b75bebfc64e1c876.jpg) + +![](images/2225dd19c09b43c4af9c0ea4c72fb06adf9dec2e0a83fb7c7729ffb69bc13f29.jpg) + +![](images/17905de9a33ae684bbd12f4ffae5bba6c6da0903bb96990d2d765030220cb69a.jpg) +Figure 6. Examples of sketch-based sewing pattern generation. Our method was able to generate high-quality sewing patterns from design sketches under various styles and could integrate seamlessly with industrial fashion design software for (a) pattern editing, i.e. sleeve panels in red boxes are merged from separate front/back sleeve panels; and (b) avatar posture and fabric material editing. + +![](images/b565ee0c19099ed477db2238b633a7ca28200f008267b78f361c2308ad2b9804.jpg) + +and artistic drawings1 (right) into high-quality sewing patterns. We also demonstrated that the generated sewing patterns could seamlessly integrate into industrial fashion design software2. For example, highlighted sleeve panels in Figure 6 (a) are merged from separate front and back sleeve pieces, while Figure 6 (b) demonstrates avatar posture and + +fabric material editing. + +# 5. Application + +In this section, we explore practical applications enabled by our system that extend beyond basic pattern generation, providing designers with versatile tools for design refinement, integration with physical simulation, and the creation of new garment components. + +![](images/4419df1104db9751a05ec4fd90a59b0865aa36bfc5da70d6c81b9387d4376118.jpg) +Figure 7. Sewing Pattern Authoring with instructions. Starting from an original design, the system follows user instructions to adjust specific pattern elements. In Edited Design 1, the pants are modified to a skirt based on the command "CHANGE THE PANT TO SKIRT". In Edited Design 2, the sleeves are shortened as requested. Finally, in Edited Design 3, the shirt is made sleeveless in response to the instructions. Note that, each modification accurately applies only to the specified parts, leaving the rest of the design unchanged. + +![](images/40fb45cdc36cc6a9020c60a4ba27042146c3daa3b2a2196260494b2033f87478.jpg) +Figure 8. Sewing pattern adjustment based on body pressure measurement. Red regions indicate areas of tight fabric with high body pressure, while blue regions represent looser areas. + +![](images/f3a3e0c32dc2f778b3b662af753fe8fbba40962424da1e638ddfd8e17f4e07aa.jpg) +Figure 9. The code for a layered-skirt component generated by our DSL-GA and 3D garment under various design parameters. + +Instruction-Based Editing. Our system allows designers to adjust generated sewing patterns through simple, instruction-based edits, utilizing the same refinement process as in our collaborative framework. As illustrated in Figure 7, starting from an original design, the system responds to natural language commands from the user to adjust the sewing pattern. At each step, the modified areas are highlighted in red boxes. From the figure, it is evident that our system can accurately update only the specified parts of the pattern according to the user's instructions while leaving all other parts of the design unchanged. + +Physics-Based Editing. Our system's generated sewing patterns integrate seamlessly with professional cloth simulation software, allowing adjustments based on fitness mea + +surements derived from physical simulations. In Figure 8, we demonstrate sewing pattern editing guided by body pressure analysis, including adjustments to the cuff (a), upper bodice (b), lower bodice (c), and collar (d). As shown in the examples, our system accurately identifies areas with excessive tension and adjusts the corresponding sewing patterns to enhance comfort while preserving the overall design. + +Generating New Garment Programs. A major challenge in traditional parametric pattern-making is the need to abstract symbolic programs for new sewing patterns, which demands both advanced programming skills and patterning expertise. Design2GarmentCode addresses this by correlating GarmentCode grammar with LMMs' embedded pattern-making knowledge, enabling the automatic creation of new garment components. Figure 9 shows a layered-skirt component generated by our DSL-GA, along with 3D garment representations demonstrating different design parameters, such as skirt length (c), number of layers (d), and layer differences such as length difference and ruffling factor (e). The results demonstrate that our system consistently produces high-quality garment components that meet professional standards, while significantly reducing the time and expertise required to create new sewing pattern programs. + +# 6. Conclusion + +Design2GarmentCode transforms multi-modal design concepts into precise sewing patterns using LMMs to synthesize parametric programs. It addresses challenges related to data requirements, computation, and the limited precision of neural network-based methods. The experimental results demonstrate the system's ability to capture design details while maintaining structural integrity and geometric precision in generated patterns. Despite these advantages, Design2GarmentCode currently cannot substantially alter GarmentCode's underlying structure and logistics, which impacts generation quality due to inherent limitations in GarmentCode's design and modeling capabilities (Supp. 10). + +# Acknowledgments + +This work was supported by Key R&D Program of Hangzhou (No.2024SDZ1A20). 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However, existing uni-modal sewing pattern generation models struggle to effectively encode complex design concepts with a multimodal nature and correlate them with vectorized sewing patterns that possess precise geometric structures and intricate sewing relations. In this work, we propose a novel sewing pattern generation approach Design2GarmentCode based on Large Multimodal Models (LMMs), to generate parametric pattern-making programs from multi-modal design concepts. LMM offers an intuitive interface for interpreting diverse design inputs, while pattern-making programs could serve as well-structured and semantically meaningful representations of sewing patterns, and act as a robust bridge connecting the cross-domain pattern-making knowledge embedded in LMMs with vectorized sewing patterns. Experimental results demonstrate that our method can flexibly handle various complex design expressions such as images, textual descriptions, designer sketches, or their combinations, and convert them into size-precise sewing patterns with correct stitches. Compared to previous methods, our approach significantly enhances training efficiency, generation quality, and authoring flexibility. Project page: https://style3d.github.io/design2garmentcode." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 567, + 135, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 567, + 135, + 578 + ], + "spans": [ + { + "bbox": [ + 56, + 567, + 135, + 578 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 587, + 296, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 296, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 296, + 684 + ], + "type": "text", + "content": "While generative AI has significantly propelled creativity in fashion design, turning those design ideas into wearable realities remains a formidable challenge. Sewing patterns are the key components to bridge the gap between abstract design ideas and wearable realities. They are foundational blueprints that dictate the precise shapes and dimensions of fabric pieces, essential for assembling garments in both the physical and virtual fashion realms." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 217, + 553, + 385 + ], + "blocks": [ + { + "bbox": [ + 317, + 217, + 553, + 385 + ], + "lines": [ + { + "bbox": [ + 317, + 217, + 553, + 385 + ], + "spans": [ + { + "bbox": [ + 317, + 217, + 553, + 385 + ], + "type": "image", + "image_path": "a65cd375c6b895b9a38d21566cc80cf3af4e47fb2052c243e3bff074f08d2d3a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 393, + 555, + 504 + ], + "lines": [ + { + "bbox": [ + 313, + 393, + 555, + 504 + ], + "spans": [ + { + "bbox": [ + 313, + 393, + 555, + 504 + ], + "type": "text", + "content": "Figure 1. Traditional sewing pattern generation approaches (top) use uni-modal models trained on synthetic datasets generated by parametric pattern-making programs (red arrow) to convert text or image prompts into vector-quantized patterns. These methods are resource-intensive and often yield oversimplified patterns with stitching errors. Our approach (bottom) utilizes large pre-trained LMMs to directly translate design concepts into parametric programs and configuration files (blue arrow), enabling dedicated, structurally correct pattern generation from multi-modal design inputs within a unified framework." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": "Traditionally, sewing patterns are drafted manually by professional pattern-makers with years of practice, making the process inefficient, error-prone, and unable to meet the growing demands for refinement and personalization in the fashion market. To this end, parametric pattern-making researches [8, 29, 31] and industrial solutions [1-4] have emerged. These methods formalize the pattern-making process as geometric functions governed by parameters such as body measurements and design features, thereby accelerating the process by enabling pattern makers to generate sewing patterns through parameter adjustments instead of starting from scratch. However, creating these function templates is still complex, requiring not only advanced pattern-making skills but also geometric intuition, mathematical modeling knowledge, and coding abilities to trans" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 248, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 248, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 248, + 703 + ], + "type": "text", + "content": "*Works done during the internship at Style3D Research." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23712" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 75, + 157, + 125 + ], + "blocks": [ + { + "bbox": [ + 59, + 75, + 157, + 125 + ], + "lines": [ + { + "bbox": [ + 59, + 75, + 157, + 125 + ], + "spans": [ + { + "bbox": [ + 59, + 75, + 157, + 125 + ], + "type": "image", + "image_path": "172db2ce9ade4c6369de02b98442484c219570ba524954bb075c3fc0ae08c741.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 127, + 158, + 136 + ], + "lines": [ + { + "bbox": [ + 58, + 127, + 158, + 136 + ], + "spans": [ + { + "bbox": [ + 58, + 127, + 158, + 136 + ], + "type": "text", + "content": "(a) Limited Generation Diversity" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 164, + 75, + 220, + 123 + ], + "blocks": [ + { + "bbox": [ + 164, + 75, + 220, + 123 + ], + "lines": [ + { + "bbox": [ + 164, + 75, + 220, + 123 + ], + "spans": [ + { + "bbox": [ + 164, + 75, + 220, + 123 + ], + "type": "image", + "image_path": "07ba85d92998759312e6e54b29895220f4e7b53ae1adf9b17545af70028f6879.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 164, + 127, + 224, + 135 + ], + "lines": [ + { + "bbox": [ + 164, + 127, + 224, + 135 + ], + "spans": [ + { + "bbox": [ + 164, + 127, + 224, + 135 + ], + "type": "text", + "content": "(b) Self-Intersection" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 230, + 72, + 294, + 127 + ], + "blocks": [ + { + "bbox": [ + 230, + 72, + 294, + 127 + ], + "lines": [ + { + "bbox": [ + 230, + 72, + 294, + 127 + ], + "spans": [ + { + "bbox": [ + 230, + 72, + 294, + 127 + ], + "type": "image", + "image_path": "e68c8ff5c6772001159b8bf92e8efd57c74215427e69e73b98a5162aa498159e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 235, + 128, + 291, + 136 + ], + "lines": [ + { + "bbox": [ + 235, + 128, + 291, + 136 + ], + "spans": [ + { + "bbox": [ + 235, + 128, + 291, + 136 + ], + "type": "text", + "content": "(c) Wrong Stitches" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 144, + 295, + 222 + ], + "lines": [ + { + "bbox": [ + 55, + 144, + 295, + 222 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 295, + 222 + ], + "type": "text", + "content": "Figure 2. (a) Despite prompts specifying diverse neckline types, DressCode [22] consistently produces only V-neck designs, indicating limited generation diversity. (b) SewFormer [40] often generates sewing patterns with self-intersecting panels, compromising pattern validity. (c) Stitching errors are also prevalent in Sewformer [40], as shown here where a pant side seam is mistakenly stitched to a shirt shoulder seam, resulting in draping failure." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 245, + 295, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 245, + 295, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 245, + 295, + 281 + ], + "type": "text", + "content": "late pattern-making expertise into CAD programs. These technical barriers significantly restrict the widespread adoption of parametric pattern-making solutions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 282, + 295, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 282, + 295, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 282, + 295, + 474 + ], + "type": "text", + "content": "Recently, several learning-based approaches for sewing pattern generation have been introduced. For instance, NeuralTailor [30] focuses on extracting sewing patterns from unstructured point clouds, DressCode [22] targets text-to-sewing pattern generation, and SewFormer [40] is designed for image-based sewing pattern generation. However, they are generally trained on paired design-sewing pattern data, necessitating large datasets to effectively capture the multimodal nature of design concepts. Furthermore, sewing patterns require centimeter-level precision to ensure proper garment fit, which presents a significant challenge for neural networks that only provide statistical approximations of the true function based on their training data [14, 23, 47]. As a result, these methods frequently generate oversimplified patterns with flawed geometry or stitches, potentially leading to draping failures (Figure 2)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 475, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 295, + 714 + ], + "type": "text", + "content": "In this paper, we present Design2GarmentCode, an innovative approach that leverages the generalization capabilities of vision-language foundation models to achieve multi-modal sewing pattern generation with minimal computational and data requirements. Unlike previous methods that directly synthesize vector-quantized patterns, Design2GarmentCode employs LMMs to learn the syntax of parametric pattern-making programs, translating design concepts into parameters and programs that can be executed to produce precise and structurally accurate sewing patterns. Design2GarmentCode combines a pre-trained Large Multimodal Model (LMM) as a design interpreter with a finetuned Large Language Model (LLM) as a program synthesizer. Specifically, the LLM is finetuned on code snippets from GarmentCode [31], a domain-specific language for constructing parametric sewing patterns. At runtime, the design interpreter extracts both topological and geometrical information from the design input by responding to a series of questions from the program synthesizer, which then generates garment programs and design config" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "urations following GarmentCode syntax. Our method offers the following major contributions:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 99, + 553, + 338 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 314, + 99, + 553, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 99, + 553, + 147 + ], + "spans": [ + { + "bbox": [ + 314, + 99, + 553, + 147 + ], + "type": "text", + "content": "- We introduce a novel modality-agnostic framework with an intuitive, intelligent interface capable of processing user design intentions across multiple modalities simultaneously by integrating pre-trained LMMs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 147, + 553, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 147, + 553, + 206 + ], + "spans": [ + { + "bbox": [ + 314, + 147, + 553, + 206 + ], + "type": "text", + "content": "- We present the first sewing pattern generation approach grounded in program synthesis, delivering fully interpretable, geometrically precise, and structurally accurate patterns through a more compact, semantically clear, and LLM-friendly representation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 207, + 553, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 207, + 553, + 266 + ], + "spans": [ + { + "bbox": [ + 314, + 207, + 553, + 266 + ], + "type": "text", + "content": "- Our framework benefits real-world production by enabling flexible pattern authoring through natural language or physical feedback, allowing precise customization and efficient creation of novel garment components, represented as parametric pattern-making programs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 267, + 553, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 267, + 553, + 338 + ], + "spans": [ + { + "bbox": [ + 314, + 267, + 553, + 338 + ], + "type": "text", + "content": "- Our approach requires only minimal fine-tuning of a pre-trained LLM and the training of a lightweight, text-conditioned transformer decoder, making it more efficient than existing vector-quantized sewing pattern generation models trained from scratch while offering superior generation quality and authoring flexibility." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 350, + 400, + 362 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 350, + 400, + 362 + ], + "spans": [ + { + "bbox": [ + 314, + 350, + 400, + 362 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 371, + 528, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 371, + 528, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 371, + 528, + 384 + ], + "type": "text", + "content": "2.1. Garment Modeling with Sewing Patterns" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 389, + 555, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 555, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 555, + 569 + ], + "type": "text", + "content": "Garment modeling and generation can be broadly classified into two categories: direct 3D garment generation (meshes) and sewing pattern generation, which are later draped onto human bodies via cloth simulation [39, 53, 56] or learning-based techniques [35, 37]. Direct 3D garment generation often relies on differentiable garment representations like unsigned distance fields [65, 67], shells [42], or Gaussian splatting [48]. However, it presents challenges in terms of both geometric accuracy and editability. On one hand, capturing fine garment details like folds and wrinkles necessitates extremely high-resolution 3D representations. On the other hand, editing these generated garments requires a well-defined UV space, and flattening the 3D mesh into developable meshes demands careful consideration from both geometric and statistical perspectives [7, 46]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 570, + 554, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 554, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 554, + 700 + ], + "type": "text", + "content": "Sewing pattern generation, by contrast, has been approached through both learning-based and procedural modeling methods. Learning approaches utilize vector-quantized representations of sewing patterns, mapping from unstructured 3D point clouds [7, 30], images [12, 26, 40, 64], or textual descriptions [22] to structured patterns. However, they are highly dependent on the quality and diversity of the training data and often struggle to generalize designs beyond the training domain. Furthermore, generating high-quality 3D garment data requires substantial domain knowledge and the involvement of skilled professionals." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 325, + 701, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 701, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 325, + 701, + 553, + 714 + ], + "type": "text", + "content": "Procedural modeling is an alternative that relies on pre" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23713" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 193 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 193 + ], + "type": "text", + "content": "defined rules and parameters to generate garment patterns. For instance, GarmentCode [31], a DSL for parametric pattern making, enables precise control over garment design and customization. The GarmentCodeData [32], built on GarmentCode, further illustrates the potential of procedural methods to generate a diverse range of made-to-measure garments, with adaptability to different body shapes. While procedural modeling provides greater control and precision, it typically requires specialized expertise and is less flexible when dealing with novel or unconventional designs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 201, + 216, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 201, + 216, + 213 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 216, + 213 + ], + "type": "text", + "content": "2.2. LLMs for Program Synthesis" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 219, + 295, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 219, + 295, + 447 + ], + "spans": [ + { + "bbox": [ + 55, + 219, + 295, + 447 + ], + "type": "text", + "content": "Recent advancements in program synthesis and code generation using large language models (LLMs) have laid essential groundwork for systems like Design2GarmentCode, which generate structured garment code from multi-modal design inputs. Earlier researches like Codex [11] and AlphaCode [36] demonstrated the effectiveness of LLMs in generating complex, task-specific code with high syntax accuracy, showcasing potential in scenarios requiring precise parametric coding. These models [43, 59] highlight how LLMs, when sufficiently trained, can transform natural language inputs into executable code, a capability directly relevant to generating garment codes that follow complex pattern-making syntax. [9, 19, 20, 55, 63] explore multimodal models that integrate visual aids, such as flowcharts and UML diagrams, into LLM training to enhance models' comprehension of complex structures and flow. These models particularly emphasize the need for semantic understanding and adaptability, which are critical in working with domain-specific languages (DSLs) like GarmentCode." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 455, + 186, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 186, + 467 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 186, + 467 + ], + "type": "text", + "content": "2.3. Neurosymbolic Models" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 474, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 700 + ], + "type": "text", + "content": "Procedural and neural models offer complementary strengths and weaknesses. Neurosymbolic models [47] integrate both paradigms by generating visual data through symbolic programs enhanced with AI/ML techniques. These models typically follow a pipeline comprising task specification, program synthesis via a domain-specific language (DSL), program execution, and optional neural post-processing for refinement. They have been successfully applied across various areas of computer graphics. In 2D shape modeling, neurosymbolic methods are used for layout generation [45, 54], engineering sketch creation [16, 44, 49], and vector graphics synthesis by constructing programs that represent geometric shapes and spatial relations [10, 17]. For 3D shape modeling, they enable shape program inference from existing 3D models [27, 28, 33, 51] and the generation of new 3D shapes by training generative models on shape programs [57, 60, 61] or generate node graphs defining complex textures and materials [21, 25, 50], aligning with procedural modeling principles." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 702, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 295, + 714 + ], + "type": "text", + "content": "Beyond shape modeling, neurosymbolic approaches" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 180 + ], + "type": "text", + "content": "have been applied to human motion prediction [18, 38], reasoning [34, 58, 66], and generation [13, 41, 62], leveraging visual-language foundation models to extract symbolic representations from visual data for complex activity reasoning [58]. Our approach follows the neurosymbolic paradigm by instruction-tuning LLMs to generate structured, executable programs defining garment component, their relationships, and parameters from diverse design concepts." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 190, + 370, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 190, + 370, + 204 + ], + "spans": [ + { + "bbox": [ + 314, + 190, + 370, + 204 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 211, + 555, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 211, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 211, + 555, + 415 + ], + "type": "text", + "content": "Our goal is to develop a generative model that transforms multi-modal design concepts into precise sewing patterns. This requires understanding diverse inputs and producing patterns with high geometric precision and intricate structures. These requirements present a challenge for conventional models, which require extensive training data and struggle with output precision due to their probabilistic nature. We propose Design2GarmentCode, a system leveraging LMMs to generate parametric patternmaking programs, or specifically GarmentCode [31]. Design2GarmentCode reduces the need for large datasets utilizing the pre-embedded pattern-making knowledge in LMMs while ensuring output precision with parametric program synthesis. In the following, we first provide an overview of parametric pattern-making programs and GarmentCode syntax, and then describe the detailed design of Design2GarmentCode." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 422, + 468, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 468, + 434 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 468, + 434 + ], + "type": "text", + "content": "3.1. Parametric Sewing Patterns" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 440, + 554, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 440, + 554, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 440, + 554, + 536 + ], + "type": "text", + "content": "Parametric sewing patterns are formally represented as symbolic programs that generate sewing patterns (i.e., 2D CAD sketches) based on body measurements and design configurations. These symbolic programs enhance the efficiency of the pattern-making process by allowing users to draft or modify sewing patterns through semantically meaningful parameters. Mathematically, we can represent a sewing pattern " + }, + { + "bbox": [ + 313, + 440, + 554, + 536 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 440, + 554, + 536 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 351, + 545, + 555, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 545, + 555, + 559 + ], + "spans": [ + { + "bbox": [ + 351, + 545, + 555, + 559 + ], + "type": "interline_equation", + "content": "\\mathcal {S} = \\langle \\mathcal {F}, \\mathcal {D}, B \\rangle = \\cup_ {f _ {i} \\in \\mathcal {F}, d _ {i} \\in \\mathcal {D}} f _ {i} (d _ {i}, B), \\tag {1}", + "image_path": "1d8913f95c0f53452be400f6575897e345e640ff6daad42f9f1ebd30ad8332e3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "text", + "content": " is the set of symbolic programs, " + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "text", + "content": " represents design configurations, and " + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "text", + "content": " represents body measurements. Each symbolic function " + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "inline_equation", + "content": "f_{i} \\in \\mathcal{F}" + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "text", + "content": " is essentially a series of rule-based 2D draw-calls controlled by its unique set of design configurations " + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "inline_equation", + "content": "d_{i} \\in \\mathcal{D}" + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "text", + "content": " and the body measurements " + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 567, + 554, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "type": "text", + "content": "GarmentCode is a domain-specific language (DSL) designed to generate parametric sewing patterns by encapsulating those symbolic programs in a hierarchical, component-oriented manner. In GarmentCode, each symbolic program " + }, + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 313, + 641, + 554, + 714 + ], + "type": "text", + "content": " uses parametric curves to define a garment component, such as sleeves, bodices, or collars. The" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23714" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 555, + 224 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 555, + 224 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 555, + 224 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 555, + 224 + ], + "type": "image", + "image_path": "df0ece6a6b00ca48492c25b658870ec5a86a0e0bbc87f0a721f5f122a266b8f5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 236, + 555, + 324 + ], + "lines": [ + { + "bbox": [ + 54, + 236, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 54, + 236, + 555, + 324 + ], + "type": "text", + "content": "Figure 3. Overview of Dress2GarmentCode. (1) Program Learning: we finetune the DSL Generation Agent (DSL-GA) using GarmentCode example programs, teaching it the GarmentCode grammar and the semantics of each design parameter. (2) Prompt Synthesis: the DSL-GA generates prompts for the Multi-Modal Understanding Agent (MMUA) to interpret and extract relevant design features from the input (3). (4) Program Synthesis: based on the MMUA's responses, the DSL-GA synthesizes GarmentCode-compliant design configurations and garment programs, which are then executed by the GarmentCode engine to produce sewing patterns and simulated garments (5). To enhance robustness, we incorporate two validation loops: during program synthesis, we employ rule-based validations (7) to ensure the MMUA's outputs are sufficient for generating complete and valid garment programs and design parameters; after the initial generation, the MMUA compares the generated design with the input and suggests modifications to minimize discrepancies." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "spans": [ + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "type": "text", + "content": "smallest component is a single panel, and multiple components can be combined through interface functions to create a larger component. In GarmentCode, a complete sewing pattern is specified by topological parameters " + }, + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "type": "text", + "content": " (which define the presence and quantity of garment components) and geometrical parameters " + }, + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_G" + }, + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "type": "text", + "content": ", which determine the dimensions of each component when combined with body measurements " + }, + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 54, + 345, + 294, + 464 + ], + "type": "text", + "content": ". As this work primarily focuses on design variations, we use a standard body model throughout all experiments to ensure consistency." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 476, + 240, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 476, + 240, + 489 + ], + "spans": [ + { + "bbox": [ + 55, + 476, + 240, + 489 + ], + "type": "text", + "content": "3.2. The Design2GarmentCode System" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 496, + 295, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 496, + 295, + 592 + ], + "spans": [ + { + "bbox": [ + 55, + 496, + 295, + 592 + ], + "type": "text", + "content": "As illustrated in Figure 3, Design2GarmentCode has three components: DSL Generation Agent (DSL-GA), a finetuned LLM responsible for (1) program learning, (2) prompt synthesis, and (4) program synthesis; Multi-modal Understanding Agent (MMUA), a pre-trained LLM that manages design understanding (3) and design comparison (6); and (5) GarmentCode, which executes the synthesized programs to generate sewing patterns and 3D garments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "The system workflow begins with Program Learning (Sec. 3.2.1), where DSL-GA is finetuned to understand the syntax and semantic meanings of GarmentCode parameters. In Prompt Synthesis, DSL-GA creates prompts for MMUA to identify essential design features. These features are then provided to DSL-GA for Program Synthesis, where garment programs and design configurations are generated through rule-based parameter validation (Figure 3 (7)) and a learned projector (Sec. 3.2.2). The GarmentCode Execution Engine then produces sewing patterns and" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 345, + 555, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 345, + 555, + 405 + ], + "spans": [ + { + "bbox": [ + 313, + 345, + 555, + 405 + ], + "type": "text", + "content": "draped garment models. Finally, a Validation stage compares the generated garment with the original design, allowing MMUA to provide specific correction instructions to DSL-GA for iterative refinement, such as \"make the sleeve longer\"." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 418, + 427, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 427, + 431 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 427, + 431 + ], + "type": "text", + "content": "3.2.1 Program Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 437, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 554, + 544 + ], + "type": "text", + "content": "During experiments, we found that pre-trained LLMs have some foundational knowledge of pattern drafting. For example, when prompted with \"How to draft a basic upper body bodice?\", LLMs can produce drafting instructions that align with conventional practices. We use a pretrained LLM to initialize DSL-GA, however, due to GarmentCode's customized object notations and function logistics, directly prompting DSL-GA to generate GarmentCode programs poses significant challenges [9]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "type": "text", + "content": "To address these challenges, we propose to align DSL-GA's embedded pattern-making knowledge with the specific syntax and semantics of GarmentCode via LoRA [24] based on fine-tuning. We start by providing the DSL-GA (denoted as " + }, + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "type": "text", + "content": ") with existing GarmentCode programs " + }, + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "type": "text", + "content": ", and instructing it to comment on the functions with detailed pattern-drafting instructions. After manually validating the comments, we get a dataset " + }, + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 544, + 554, + 652 + ], + "type": "text", + "content": " paring natural language instructions with GarmentCode implementations:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 364, + 658, + 553, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 658, + 553, + 685 + ], + "spans": [ + { + "bbox": [ + 364, + 658, + 553, + 685 + ], + "type": "interline_equation", + "content": "D = \\left\\{\\left(\\Gamma_ {c m t} (f _ {i}), f _ {i}\\right) \\mid f _ {i} \\in \\mathcal {F} \\right\\}, \\tag {2}", + "image_path": "372daa1c989b1a107dbb2aba92a745f88be747b5fac4a08b39d731675dbfd300.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\Gamma_{cmt}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " is the instructed DSL-GA for code commenting, " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " is. Similar to [9], we finetune DSL-GA " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "(\\Gamma)" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " on the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23715" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": "dataset " + }, + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": " with LoRA [24], aiming for " + }, + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "inline_equation", + "content": "\\Gamma_{ft}(\\Gamma_{cmt}(f_i))\\to f_i" + }, + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "inline_equation", + "content": "\\Gamma_{ft}" + }, + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": " is the finetuned DSL-GA." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "text", + "content": "After fine-tuning, the fine-tuned DSL-GA " + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\Gamma_{ft}" + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "text", + "content": " gains an understanding of the code structure and parameter semantics in GarmentCode (Figure 9). Therefore, we provide the design configuration " + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\Gamma_{ft}" + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "text", + "content": ", prompting it to analyze the semantic meaning of each parameter and generate structured queries. These queries are designed to guide the MMUA in extracting relevant design features from the multi-modal input, enabling " + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "inline_equation", + "content": "\\Gamma_{ft}" + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "text", + "content": " to generate a comprehensive set of design parameters. The generated prompt " + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "text", + "content": " typically starts with analysis instructions, followed by multiple-choice or numerical estimation questions regarding each design parameter " + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 55, + 96, + 296, + 240 + ], + "type": "text", + "content": ". Formally, we have" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 97, + 249, + 295, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 249, + 295, + 262 + ], + "spans": [ + { + "bbox": [ + 97, + 249, + 295, + 262 + ], + "type": "interline_equation", + "content": "P = \\Gamma_ {f t} (\\mathcal {D}) = \\cup_ {d _ {i} \\in \\mathcal {D}} \\Gamma_ {f t} \\left(d _ {i}\\right) = \\cup q _ {i}, \\tag {3}", + "image_path": "b214cf15566b2dce6c7d718bc6294572feed36910eb50d1eb97afa1fdb18c9b9.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "spans": [ + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "type": "inline_equation", + "content": "q_{i} = \\Gamma_{ft}(d_{i})" + }, + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "type": "text", + "content": " represents the generated question regarding the " + }, + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "type": "text", + "content": "-th design parameter " + }, + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 55, + 271, + 295, + 295 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 309, + 169, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 309, + 169, + 322 + ], + "spans": [ + { + "bbox": [ + 55, + 309, + 169, + 322 + ], + "type": "text", + "content": "3.2.2 Program Synthesis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "text", + "content": "Initial results showed that MMUA performed significantly better on multiple-choice questions compared to numerical estimation questions. To improve accuracy, we replaced all numerical estimation questions in the initial prompt " + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "text", + "content": " with equivalent multiple-choice questions with descriptive options such as \"full length\", \"half length\", or \"three-quarter length\". We append a lightweight projector " + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "text", + "content": " after the finetuned DSL-GA " + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "inline_equation", + "content": "\\Gamma_{ft}" + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "text", + "content": " to transform these descriptive answers " + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "inline_equation", + "content": "\\tau_i" + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "text", + "content": " regarding the design input " + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "text", + "content": " into precise geometrical parameters " + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "inline_equation", + "content": "d_i \\in \\mathcal{D}" + }, + { + "bbox": [ + 55, + 328, + 296, + 449 + ], + "type": "text", + "content": " adhering to GarmentCode [31]:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 70, + 457, + 295, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 457, + 295, + 471 + ], + "spans": [ + { + "bbox": [ + 70, + 457, + 295, + 471 + ], + "type": "interline_equation", + "content": "\\Psi : \\Gamma_ {f t} (\\cup \\tau_ {i}) \\rightarrow \\mathcal {D}, \\text {w h e r e} \\tau_ {i} = \\mathbf {M M U A} (q _ {i}, x). \\tag {4}", + "image_path": "48351a4e3ff892bc420235bbaa760586b76cf2de5efb26b9fe272fbdcf08ad21.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "text", + "content": "Inspired by DressCode [22], we implement the projector " + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "text", + "content": " as text-conditioned decoder-only transformer, where we design a type-based quantization function " + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "text", + "content": " to convert the parameter list " + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "text", + "content": " into a token sequence " + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{t_1,\\dots,t_N\\}" + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "inline_equation", + "content": "N = |\\mathcal{D}|" + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "text", + "content": " denote the total number of design parameters. The quantization function " + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 55, + 479, + 296, + 552 + ], + "type": "text", + "content": " operates as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 562, + 299, + 630 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 299, + 630 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 299, + 630 + ], + "type": "interline_equation", + "content": "t _ {i} = \\mathbf {Q} \\left(d _ {i}\\right) = \\left\\{ \\begin{array}{l l} 0 / 1, & \\text {i f} d _ {i} \\text {i s a b o o l e a n v a r i a b l e ,} \\\\ d _ {i}, & \\text {i f} d _ {i} \\text {i s a n i n t e g e r ,} \\\\ \\lambda \\cdot \\operatorname {N o r m} \\left(d _ {i}\\right), & \\text {i f} d _ {i} \\text {i s a f l o a t i n g n u m b e r ,} \\\\ \\operatorname {I n d e x} \\left(d _ {i}, L\\right), & \\text {i f} d _ {i} \\text {i s a s e l e c t i v e v a r i a b l e .} \\end{array} \\right. \\tag {5}", + "image_path": "7a95b3f515560666a66a6cb1760fa0d73bb4aca98ecf2d162b1a860d0c472286.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 630, + 294, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 294, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 294, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 630, + 294, + 653 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 630, + 294, + 653 + ], + "type": "text", + "content": " is a scaling factor indicating numerical precision. We use " + }, + { + "bbox": [ + 55, + 630, + 294, + 653 + ], + "type": "inline_equation", + "content": "\\lambda = 100" + }, + { + "bbox": [ + 55, + 630, + 294, + 653 + ], + "type": "text", + "content": " to maintain centimeter-level precision." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": "As in Eq. 4, we use the finetuned DSL-GA " + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\Gamma_{ft}" + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": " to encode the answers " + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\tau_{i}" + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": " from MMUA and construct the condition input for " + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": " (we use an MLP to match the embedding dimension between 3,072 in " + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\Gamma_{ft}" + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": " and 128 in " + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": "). Notably, our token sequence length is fixed to the number of" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 317, + 70, + 554, + 157 + ], + "blocks": [ + { + "bbox": [ + 317, + 70, + 554, + 157 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 554, + 157 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 554, + 157 + ], + "type": "table", + "html": "
MethodText Guided GenerationImage Guided Generation
DressCode [22]OursSewformer [40]Ours
QualitySSR84%100%65.33%94%
Agreement7.17%79.83%3.33%88.67%
Aesthetic9.50%68.17%5.33%77%
CLIPScore0.23860.2438//
F-Score0.616/0.7080.829
CD15.77/9.72.091
Diversity# Panels5.11±1.666.92±3.1010.11±4.4211.02±4.18
# Edges5.48±1.606.84±3.385.79±1.716.24±2.90
# Stitches10.06±3.2418.66±8.6415.81±5.9127.9±9.83
", + "image_path": "a0c38e1c81e4e1ef8213f6a32afb8357cb5a6aca075ff96fd675a779a4ee4603.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 165, + 555, + 276 + ], + "lines": [ + { + "bbox": [ + 313, + 165, + 555, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 165, + 555, + 276 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of our method against state-of-the-art (SOTA) sewing pattern generation techniques in terms of quality and diversity. SSR (Simulation Success Rate) indicates the feasibility of simulated garment assembly, while Agreement measures alignment with design prompts, and Aesthetic evaluates the visual preference of the generated patterns. CLIPScore assesses text-image consistency, whereas Chamfer Distance (CD) and " + }, + { + "bbox": [ + 313, + 165, + 555, + 276 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 313, + 165, + 555, + 276 + ], + "type": "text", + "content": "-Score quantify geometric accuracy. #Panels, #Stitches, and #Edges denote the mean and standard deviation (subscript) of the number of panels, stitches per pattern, and edges per panel." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 298, + 554, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 298, + 554, + 358 + ], + "spans": [ + { + "bbox": [ + 313, + 298, + 554, + 358 + ], + "type": "text", + "content": "design parameters " + }, + { + "bbox": [ + 313, + 298, + 554, + 358 + ], + "type": "inline_equation", + "content": "|\\mathcal{D}| = 122" + }, + { + "bbox": [ + 313, + 298, + 554, + 358 + ], + "type": "text", + "content": ", regardless of the complexity of the pattern. This fixed-length representation is at least " + }, + { + "bbox": [ + 313, + 298, + 554, + 358 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 313, + 298, + 554, + 358 + ], + "type": "text", + "content": " compact than DressCode [22], whose sequence length is 1, 500 and scales with pattern complexity (see Sec. 8 for implementation details)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 372, + 395, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 395, + 385 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 395, + 385 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 392, + 449, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 449, + 405 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 449, + 405 + ], + "type": "text", + "content": "4.1.Quantitative Evaluation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 412, + 554, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 412, + 554, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 412, + 554, + 460 + ], + "type": "text", + "content": "We evaluate our proposed method against state-of-the-art sewing pattern generation approaches (DressCode [22] for text-guided and Sewformer [40] for image-guided generation) on Generation Quality and Generation Diversity." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 461, + 555, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 555, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 555, + 675 + ], + "type": "text", + "content": "Generation Quality is evaluated through three metrics: Simulation Success Rate (SSR), Agreement Score, and Aesthetic Score. The Simulation Success Rate (SSR) is calculated as the ratio of successfully simulated garments to the total number of generated sewing patterns, measuring the structural feasibility of the patterns. We prepared a dataset comprising 150 text prompts and 150 test images, covering a wide variety including tops (78), pants (76), skirts (38), dresses (80), and suits (28). For each sample, we generated sewing patterns using both our method and baseline methods, and simulated the patterns using GarmentCode's simulation engine [31, 32] to compute the success rate. The Agreement and Aesthetic Scores were derived from a user study involving 30 professional pattern-makers. Each participant is asked to review 50 text and 50 image samples generated by our and the baseline models, and assess their preference based on sewing patterns and simulated garments according to:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 313, + 677, + 553, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 700 + ], + "type": "text", + "content": "- Agreement: the degree to which the generated pattern matched the design prompt." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 553, + 713 + ], + "type": "text", + "content": "- Aesthetic Quality: the visual appeal and structural coher" + } + ] + 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Quality Comparison on Text-Guided Sewing Pattern Generation. For each design, we present the generated pattern using our method (left) alongside DressCode [22] (right), including front and back renderings of the draped garment. We highlight design elements accurately captured by our method but missed by DressCode [22] use red color in the input prompt." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 181, + 188, + 297, + 219 + ], + "blocks": [ + { + "bbox": [ + 181, + 188, + 297, + 219 + ], + "lines": [ + { + "bbox": [ + 181, + 188, + 297, + 219 + ], + "spans": [ + { + "bbox": [ + 181, + 188, + 297, + 219 + ], + "type": "image", + "image_path": "22d3cd9b9844378f27fa86c3196032eea1d4fb7d80ad05f473d5d65bc077c493.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 205, + 224, + 274, + 233 + ], + "lines": [ + { + "bbox": [ + 205, + 224, + 274, + 233 + ], + "spans": [ + { + "bbox": [ + 205, + 224, + 274, + 233 + ], + "type": "text", + "content": "DressCode Results" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": 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or indicate that both methods were \"comparable\". We calculate the Agreement and Aesthetic Scores as the percentage of times each option was chosen over the total number of tested samples." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": "Table 1 presents the results, showing that our method surpasses existing approaches in both SSR and user-evaluated Agreement and Aesthetic scores. For text-guided generation, our model achieves a perfect " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": " SSR, notably higher than DressCode's " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "84\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": ". Additionally, our Agreement score of " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "79.83\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": " and Aesthetic score of " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "68.17\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": " far exceed DressCode's respective scores of " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "7.17\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "9.5\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": ". In image-guided generation, our method attains a " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "94\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": " SSR, with an Agreement score of " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "88.67\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": " and an Aesthetic score of " + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "inline_equation", + "content": "77\\%" + }, + { + "bbox": [ + 55, + 376, + 296, + 533 + ], + "type": "text", + "content": ", significantly outperforming Sewformer. These enhancements highlight our model's ability to generate sewing patterns that are both structurally precise and visually aligned with the design prompt." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 296, + 714 + ], + "type": "text", + "content": "Generation Diversity is evaluated by analyzing the average number of panels (# Panels), edges (# Edges), and stitches (# Stitches) in the generated patterns. For text-guided generation, our method yields more intricate designs, with an average of 6.92 panels, 6.84 edges, and 18.66 stitches per pattern, compared to DressCode's simpler outputs of 5.11 panels, 5.48 edges, and 10.06 stitches. In image-guided generation, our approach also demonstrates superior diversity, producing an average of 11.02 panels, 6.24 edges, and 27.9 stitches per pattern, compared to Sewformer's averages of 10.11 panels, 5.79 edges, and 15.81 stitches. These results emphasize our model's ability to capture and replicate subtle design variations, highlighting its robustness and adaptability across different design inputs." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 313, + 303, + 488, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 303, + 488, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 303, + 488, + 316 + ], + "type": "text", + "content": "4.2. Multi-modal Generation Results" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 313, + 327, + 555, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 327, + 555, + 363 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 555, + 363 + ], + "type": "text", + "content": "Our proposed method demonstrates superior performance across various sewing pattern generation tasks, including text-guided, image-guided, and sketch-based generation." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 313, + 368, + 555, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 368, + 555, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 368, + 555, + 536 + ], + "type": "text", + "content": "In text-guided sewing pattern generation (Figure 4), our method accurately captures design details specified in prompts, such as neckline types (e.g., crew neck (a), boat neck (b), turtleneck (c)) and complex structural features like asymmetry (f) and layered skirts (d). In comparison, the baseline model DressCode struggles with limited pattern diversity, often defaulting to simpler shapes like V-neck designs. Additionally, for design descriptions out of its training domain, DressCode frequently generates patterns with incorrect stitching, leading to poor draping results (Figure 4 (e)). Our method could provide structurally sound and visually accurate patterns under a large design variety, showcasing its capability to handle diverse design requests with high fidelity." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 313, + 540, + 555, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 555, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 555, + 685 + ], + "type": "text", + "content": "For image-guided sewing pattern generation (Figure 5), our model effectively translates detailed visual cues from input images into corresponding sewing patterns. Compared with Sewformer, which often fails to model-specific design elements like cuffs, hoods, and asymmetric features, our approach accurately reproduces these details. Sewformer's results frequently exhibit structural flaws, such as missing or misaligned pattern pieces and extraneous components, resulting in unrealistic garment draping. In contrast, our method maintains structural integrity and captures complex design features, producing patterns that closely align with the source images." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "In sketch-based sewing pattern generation (Figure 6), our system seamlessly converts both technical sketches (left)" + } + ] + } + ], + "index": 46 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23717" + } + ] + } + ], + "index": 47 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 181, + 264 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 181, + 264 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 181, + 264 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 181, + 264 + ], + "type": "image", + "image_path": "d5c1a65313beec7f20f8a2f21a751687007d8578eaa0b4cbef7dd77ccf6a3f93.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 275, + 555, + 342 + ], + "lines": [ + { + "bbox": [ + 55, + 275, + 555, + 342 + ], + "spans": [ + { + "bbox": [ + 55, + 275, + 555, + 342 + ], + "type": "text", + "content": "Figure 5. Quality Comparison on Image-Guided Sewing Pattern Generation. We compare our method with Sewformer [40] on Internet-collected fashion photographs (left), and AI-generated design images without human models (right). The results indicate that our method successfully captures design details from diverse styles, producing sewing patterns that accurately reflect neckline (a, d), cuffs (a, e, g), darts (c, d), and asymmetry (f). In contrast, Sewformer's results exhibit several issues, including incorrect necklines (a, d), missing components (b, g), misplaced or imaginary stitches (d, e), and extraneous pattern pieces (h). Additionally, since Sewformer's pattern generation does not account for body shape, garments like skirts and pants frequently appear oversized around the waist, causing them to sag when draped." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 182, + 71, + 298, + 264 + ], + "blocks": [ + { + "bbox": [ + 182, + 71, + 298, + 264 + ], + "lines": [ + { + "bbox": [ + 182, + 71, + 298, + 264 + ], + "spans": [ + { + "bbox": [ + 182, + 71, + 298, + 264 + ], + "type": "image", + "image_path": "67f894b4b6ac4eeaec3079daaf72cf67477886c8640c682f9d1fdfd75ba3b87a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 434, + 264 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 434, + 264 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 434, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 434, + 264 + ], + "type": "image", + "image_path": "f6d097cecc9486129f2ed0c2516f190f103bc4524fd1c234b75bebfc64e1c876.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 434, + 70, + 553, + 264 + ], + "blocks": [ + { + "bbox": [ + 434, + 70, + 553, + 264 + ], + "lines": [ + { + "bbox": [ + 434, + 70, + 553, + 264 + ], + "spans": [ + { + "bbox": [ + 434, + 70, + 553, + 264 + ], + "type": "image", + "image_path": "2225dd19c09b43c4af9c0ea4c72fb06adf9dec2e0a83fb7c7729ffb69bc13f29.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 58, + 357, + 388, + 548 + ], + "blocks": [ + { + "bbox": [ + 58, + 357, + 388, + 548 + ], + "lines": [ + { + "bbox": [ + 58, + 357, + 388, + 548 + ], + "spans": [ + { + "bbox": [ + 58, + 357, + 388, + 548 + ], + "type": "image", + "image_path": "17905de9a33ae684bbd12f4ffae5bba6c6da0903bb96990d2d765030220cb69a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 556, + 555, + 592 + ], + "lines": [ + { + "bbox": [ + 55, + 556, + 555, + 592 + ], + "spans": [ + { + "bbox": [ + 55, + 556, + 555, + 592 + ], + "type": "text", + "content": "Figure 6. Examples of sketch-based sewing pattern generation. Our method was able to generate high-quality sewing patterns from design sketches under various styles and could integrate seamlessly with industrial fashion design software for (a) pattern editing, i.e. sleeve panels in red boxes are merged from separate front/back sleeve panels; and (b) avatar posture and fabric material editing." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 395, + 355, + 547, + 544 + ], + "blocks": [ + { + "bbox": [ + 395, + 355, + 547, + 544 + ], + "lines": [ + { + "bbox": [ + 395, + 355, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 395, + 355, + 547, + 544 + ], + "type": "image", + "image_path": "b565ee0c19099ed477db2238b633a7ca28200f008267b78f361c2308ad2b9804.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 610, + 294, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 610, + 294, + 682 + ], + "spans": [ + { + "bbox": [ + 55, + 610, + 294, + 682 + ], + "type": "text", + "content": "and artistic drawings1 (right) into high-quality sewing patterns. We also demonstrated that the generated sewing patterns could seamlessly integrate into industrial fashion design software2. For example, highlighted sleeve panels in Figure 6 (a) are merged from separate front and back sleeve pieces, while Figure 6 (b) demonstrates avatar posture and" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 611, + 408, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 611, + 408, + 624 + ], + "spans": [ + { + "bbox": [ + 314, + 611, + 408, + 624 + ], + "type": "text", + "content": "fabric material editing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 633, + 389, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 633, + 389, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 633, + 389, + 647 + ], + "type": "text", + "content": "5. Application" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 715 + ], + "type": "text", + "content": "In this section, we explore practical applications enabled by our system that extend beyond basic pattern generation, providing designers with versatile tools for design refinement, integration with physical simulation, and the creation of new garment components." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 66, + 693, + 268, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 268, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 268, + 703 + ], + "type": "text", + "content": "1The drawing is borrowed from the artwork of TWELVEYIN." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 67, + 703, + 279, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 279, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 279, + 713 + ], + "type": "text", + "content": "2We use Style3D Studio [5] for pattern and appearance authoring." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23718" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 74, + 537, + 182 + ], + "blocks": [ + { + "bbox": [ + 69, + 74, + 537, + 182 + ], + "lines": [ + { + "bbox": [ + 69, + 74, + 537, + 182 + ], + "spans": [ + { + "bbox": [ + 69, + 74, + 537, + 182 + ], + "type": "image", + "image_path": "4419df1104db9751a05ec4fd90a59b0865aa36bfc5da70d6c81b9387d4376118.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 195, + 555, + 240 + ], + "type": "text", + "content": "Figure 7. Sewing Pattern Authoring with instructions. Starting from an original design, the system follows user instructions to adjust specific pattern elements. In Edited Design 1, the pants are modified to a skirt based on the command \"CHANGE THE PANT TO SKIRT\". In Edited Design 2, the sleeves are shortened as requested. Finally, in Edited Design 3, the shirt is made sleeveless in response to the instructions. Note that, each modification accurately applies only to the specified parts, leaving the rest of the design unchanged." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 63, + 260, + 287, + 361 + ], + "blocks": [ + { + "bbox": [ + 63, + 260, + 287, + 361 + ], + "lines": [ + { + "bbox": [ + 63, + 260, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 63, + 260, + 287, + 361 + ], + "type": "image", + "image_path": "40fb45cdc36cc6a9020c60a4ba27042146c3daa3b2a2196260494b2033f87478.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 371, + 295, + 405 + ], + "lines": [ + { + "bbox": [ + 55, + 371, + 295, + 405 + ], + "spans": [ + { + "bbox": [ + 55, + 371, + 295, + 405 + ], + "type": "text", + "content": "Figure 8. Sewing pattern adjustment based on body pressure measurement. Red regions indicate areas of tight fabric with high body pressure, while blue regions represent looser areas." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 63, + 421, + 284, + 494 + ], + "blocks": [ + { + "bbox": [ + 63, + 421, + 284, + 494 + ], + "lines": [ + { + "bbox": [ + 63, + 421, + 284, + 494 + ], + "spans": [ + { + "bbox": [ + 63, + 421, + 284, + 494 + ], + "type": "image", + "image_path": "f3a3e0c32dc2f778b3b662af753fe8fbba40962424da1e638ddfd8e17f4e07aa.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 502, + 295, + 525 + ], + "lines": [ + { + "bbox": [ + 55, + 502, + 295, + 525 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 295, + 525 + ], + "type": "text", + "content": "Figure 9. The code for a layered-skirt component generated by our DSL-GA and 3D garment under various design parameters." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 546, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 295, + 677 + ], + "type": "text", + "content": "Instruction-Based Editing. Our system allows designers to adjust generated sewing patterns through simple, instruction-based edits, utilizing the same refinement process as in our collaborative framework. As illustrated in Figure 7, starting from an original design, the system responds to natural language commands from the user to adjust the sewing pattern. At each step, the modified areas are highlighted in red boxes. From the figure, it is evident that our system can accurately update only the specified parts of the pattern according to the user's instructions while leaving all other parts of the design unchanged." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "Physics-Based Editing. Our system's generated sewing patterns integrate seamlessly with professional cloth simulation software, allowing adjustments based on fitness mea" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 261, + 553, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 261, + 553, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 261, + 553, + 344 + ], + "type": "text", + "content": "surements derived from physical simulations. In Figure 8, we demonstrate sewing pattern editing guided by body pressure analysis, including adjustments to the cuff (a), upper bodice (b), lower bodice (c), and collar (d). As shown in the examples, our system accurately identifies areas with excessive tension and adjusts the corresponding sewing patterns to enhance comfort while preserving the overall design." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 345, + 555, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 345, + 555, + 537 + ], + "spans": [ + { + "bbox": [ + 313, + 345, + 555, + 537 + ], + "type": "text", + "content": "Generating New Garment Programs. A major challenge in traditional parametric pattern-making is the need to abstract symbolic programs for new sewing patterns, which demands both advanced programming skills and patterning expertise. Design2GarmentCode addresses this by correlating GarmentCode grammar with LMMs' embedded pattern-making knowledge, enabling the automatic creation of new garment components. Figure 9 shows a layered-skirt component generated by our DSL-GA, along with 3D garment representations demonstrating different design parameters, such as skirt length (c), number of layers (d), and layer differences such as length difference and ruffling factor (e). The results demonstrate that our system consistently produces high-quality garment components that meet professional standards, while significantly reducing the time and expertise required to create new sewing pattern programs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 549, + 388, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 549, + 388, + 562 + ], + "spans": [ + { + "bbox": [ + 313, + 549, + 388, + 562 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 715 + ], + "type": "text", + "content": "Design2GarmentCode transforms multi-modal design concepts into precise sewing patterns using LMMs to synthesize parametric programs. It addresses challenges related to data requirements, computation, and the limited precision of neural network-based methods. The experimental results demonstrate the system's ability to capture design details while maintaining structural integrity and geometric precision in generated patterns. Despite these advantages, Design2GarmentCode currently cannot substantially alter GarmentCode's underlying structure and logistics, which impacts generation quality due to inherent limitations in GarmentCode's design and modeling capabilities (Supp. 10)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23719" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 140 + ], + "type": "text", + "content": "This work was supported by Key R&D Program of Hangzhou (No.2024SDZ1A20). We sincerely thank Fuqi Wang for his valuable support in validation data collection, material modeling and animation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 148, + 115, + 161 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 148, + 115, + 161 + ], + "spans": [ + { + "bbox": [ + 56, + 148, + 115, + 161 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 170, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 170, + 294, + 201 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 170, + 294, + 201 + ], + "spans": [ + { + "bbox": [ + 61, + 170, + 294, + 201 + ], + "type": "text", + "content": "[1] Assyst smart(pattern macro. https://www.assyst.de/en/products/cad/index.html. 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Images generated by our DesignDiffusion model, which only requires a simple text prompt as input and can generate diverse, high-quality design images with accurate textual and vivid visual content." + ], + "image_footnote": [], + "bbox": [ + 94, + 406, + 251, + 527 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/db242f0a6614aeb6a7f978bce632486cdb24fa96144bd2206ed58901f7f9b5db.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 254, + 406, + 413, + 529 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3610941a8128737690a01db5d3e8b1c5cc33c3763bcee376721c0fff0b7b0780.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 406, + 576, + 529 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cae7be204fbc3bfc072675e09c98f41ee18e62a518f6777066ff5cd4072aa1d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 580, + 406, + 738, + 529 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e17178c994840d82c8e4c635984a5f07306b3f1c50c771b97757ad25891c6c97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 741, + 406, + 900, + 522 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 587, + 326, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present DesignDiffusion, a simple yet effective framework for the novel task of synthesizing design images from textual descriptions. A primary challenge lies in generating accurate and style-consistent textual and visual content. Existing works in a related task of visual text generation often focus on generating text within given specific regions, which limits the creativity of generation models, resulting in style or color inconsistencies between textual and visual elements if applied to design image generation. To address this issue, we propose an end-to-end, one-stage diffusion-based framework that avoids intricate components like position and layout modeling. Specifically, the proposed framework directly synthesizes textual and visual design elements from user prompts. It utilizes a distinctive character embedding derived from the visual text to enhance the input prompt, along with a character localization loss for enhanced supervision during text generation. Furthermore, we employ a self-play Direct Preference Optimization fine", + "bbox": [ + 86, + 628, + 485, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tuning strategy to improve the quality and accuracy of the synthesized visual text. Extensive experiments demonstrate that DesignDiffusion achieves state-of-the-art performance in design image generation.", + "bbox": [ + 511, + 589, + 906, + 650 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 679, + 643, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Design images play a pivotal role in various applications such as graphic design, advertising, and scientific visualization, where the integration of visual and textual elements must be flawless.", + "bbox": [ + 511, + 704, + 906, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently many fascinating and wonderful applications, such as art image creation or film production, have shown remarkable progress due to the rapid advance of text-to-image generation techniques [37-40, 47]. Despite these advancements, the precise generation of design images poses a distinct challenge, largely due to the limited capabilities of existing image generation models in complex layout planning and visual text generation.", + "bbox": [ + 511, + 765, + 908, + 886 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the critical issue of visual text generation, re", + "bbox": [ + 532, + 887, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20906", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cent studies [27, 41] have made significant contributions. A common approach involves a two-step process: first generating an image from textual input and then identifying a suitable location within the image to insert text. However, this method presents several challenges. Firstly, a generated image may not have a suitable region for adding text, resulting in an overlay of text on visual elements. Secondly, even with a plausible location, the rendered text may lack consistency with the visual elements presented in the image, compromising overall coherence and professionalism.", + "bbox": [ + 89, + 90, + 485, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An alternative research direction in visual text rendering, as suggested by [5, 6], focuses on learning the layout of text regions from textual prompts in advance. Then, this learned layout serves as a condition to guide text-to-image models in generating text within designated regions of the image. However, the dependence on predefined text regions might constrain the creative breadth of the generated images. Moreover, these predetermined text regions may not always adhere to natural design principles, potentially leading to visually unattractive or conceptually incoherent outputs.", + "bbox": [ + 89, + 244, + 485, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the aforementioned issues, we propose Design-Diffusion, an end-to-end diffusion-based framework specifically developed for the novel task of generating design images from text. The holistic learning approach presents multiple benefits: (1) it eliminates the need to predetermine text regions in the generative images, thereby preserving the creative freedom of the generative models; (2) it enables the smooth incorporation of generated text into images, yielding cohesive designs that accurately reflect input prompts.", + "bbox": [ + 89, + 398, + 483, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our framework, we employ three essential techniques when fine-tuning text-to-image diffusion models: a) Recognizing that a conventional CLIP text encoder might overlook the specific textual content designated for rendering in the generated image, we propose a character-level decomposition of words. This approach provides the CLIP text encoder hints to render each character in the image precisely. b) To encourage the model to pay more attention to newly introduced character embeddings, we propose a character localization loss. This loss function compels each character embedding to concentrate on its respective area within the image, ensuring an accurate visual representation of each character. c) We introduce a new training strategy called Self-Play Direct Preference Optimization (SP-DPO) for fine-tuning the model to enhance its capability of generating accurate and high-fidelity text. SP-DPO is based on the hypothesis that ground truth data are typically preferred by humans over model-generated samples. Based on this, we fine-tune the model to align with these human preferences.", + "bbox": [ + 89, + 536, + 485, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Extensive experiments demonstrate the superior capabilities of DesignDiffusion for design image generation. It generates creative design images with prompts, as shown in Fig. 1. Quantitative and qualitative analysis shows that our approach significantly surpasses current state-of-the-art", + "bbox": [ + 89, + 825, + 485, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "text-to-image and visual text rendering models in terms of both image quality and text accuracy.", + "bbox": [ + 511, + 90, + 906, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are presented as follows:", + "bbox": [ + 532, + 122, + 901, + 136 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose DesignDiffusion, an end-to-end, diffusion-based framework for text-to-design image generation, which enables the simultaneous generation of image and visual text elements, eliminating the necessity for predefined text regions or traditional two-stage separated text and image creation process.", + "- We explore prompt enhancement for CLIP text encoding along with a character localization loss, to improve the accuracy of text placement and the fidelity of text rendering.", + "- By adopting an SP-DPO mechanism, the generative model is further fine-tuned, achieving remarkable improvements in visual text accuracy and overall image quality." + ], + "bbox": [ + 511, + 137, + 906, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 330, + 653, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Text Rendering. Despite the remarkable success of existing diffusion models [37, 38, 40] in text-to-image generation, visual text rendering remains a challenging task. Recently, researchers have recognized this issue and proposed several approaches to address it, such as GlyphDraw [29], DiffUTE [4], GlyphControl [45], AnyText [41], TextDiffuser series [5, 6], and [26]. While these efforts have improved text rendering accuracy, it is worth noting that these models obtain limited image quality due to the need of pre-giving text rendering areas during the generation process or inpainting text into a well-generated image. Separating text and visual content generation away seriously limits the overall quality of generated images with visual text rendered, which is incompatible with the goal of design image generation.", + "bbox": [ + 511, + 356, + 908, + 568 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compositional Image Generation. To improve the ability of text-to-image models to create complex compositions, researchers have integrated new components into diffusion models, enabling the generation of images with multiple features. Examples include T2I-Adapter [30] and ControlNet [47], which incorporate semantic details like layout and pose to influence the structure of images [48]. In a similar vein, GLIGEN [21] utilizes adapters with diffusion models to achieve image generation that is conditioned on specific spatial arrangements. However, these methods cannot generate images directly from prompts and require substantial human effort to define the image layout. On the other hand, some studies have investigated methods that do not require additional training to prompt diffusion models to create images based on spatial conditions during the inference phase. Recent advancements [22, 32, 44] have seen large language models aiding diffusion models in generating images with intricate or predefined layouts. Yet, these approaches often fall short in generating design-centric images that seamlessly integrate both textual and visual components in a well-organized manner.", + "bbox": [ + 511, + 568, + 908, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Aligning Diffusion Models. Replicating the success of re", + "bbox": [ + 511, + 885, + 908, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20907", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/97c747f56b36cdd7f24f96da08ff9ce0ccbe97bfe5c6259e8163afc9ca04f7cf.jpg", + "image_caption": [ + "(a) Fine-tuning with prompt enhancement and character localization loss", + "(b) Fine-tuning with self-play DPO loss", + "Figure 2. Overview of the DesignDiffusion framework. DesignDiffusion is based on enhanced text prompts, with trainable CLIP text encoder and UNet, and does not require additional complex conditions (glyphs, positions). Character localization loss is added as extra supervision at cross-attention maps to force the UNet to attend more to the visual character regions. To further improve the quality of visual text generation, we incorporate a self-play DPO strategy into the fine-tuning process. Diffusion denoise loss is omitted here." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 903, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "inforcement learning in large language models [31, 35] to text-to-image diffusion models remains a significant challenge. Recent works have proposed various methods to address this problem. For example, EMU [7] identifies that a few high-quality samples are crucial when fine-tuning the model to generate visually appealing images. DPOK [12] and DDPO [3] use RL-based approaches to maximize rewards on a limited vocabulary set, performing well when the number of train/test prompts is small. Another work DiffusionDPO [42] applies DPO based on a human-annotated preference dataset. Our DesignDiffusion differs by applying a self-play DPO strategy, which does not require human annotation and lacks of exploration in design image generation.", + "bbox": [ + 88, + 498, + 486, + 695 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. DesignDiffusion", + "text_level": 1, + "bbox": [ + 89, + 709, + 250, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The generative community has witnessed the strong generative capability of diffusion models [9, 16, 34, 38, 48]. However, generating design images remains a great challenge, particularly in the context of exquisite layout and text rendering. Previous approaches [5, 6] in a related task (visual text rendering) attempt to inpaint text after generating an image, or to plan text regions using large language models such as Vicuna [49] and GPT [1] before generating an image. We argue that they do not consider the integration of text and image content. Note that, the text and image contexts in design images are often intertwined and inseparable, such", + "bbox": [ + 88, + 734, + 486, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that they are incompatible with design image generation.", + "bbox": [ + 511, + 498, + 888, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast, we introduce a straightforward, one-stage approach for text-to-design image generation, relying solely on the user prompt. It is based on an aesthetic model, i.e., Stable Diffusion XL (SDXL) model [34], incorporating three core components that enable the successful generation of text-rich design images. An overview of the DesignDiffusion framework is provided in Fig. 2. The DesignDiffusion training involves a two-stage fine-tuning strategy. In the first stage, we introduce prompt enhancement and character localization loss into the framework to generate high-quality images with accurate text. In the second stage, we propose SP-DPO to further improve the text rendering accuracy. These components are detailed in the following subsections.", + "bbox": [ + 511, + 515, + 908, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Prompt Enhancement for CLIP Text Encoding", + "text_level": 1, + "bbox": [ + 511, + 724, + 906, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Currently, available text-to-image diffusion models struggle to generate text-rich design images based solely on an input text prompt. This challenge arises from two issues: 1) Visually rendered text must be letter-by-letter correct, however, during tokenization, most words are tokenized as a single token, ignoring each letter within the word thus complicating the learning of individual letters; 2) Visual text in images is often diverse in style, size, and layout, increasing the complexity of visual text modeling.", + "bbox": [ + 511, + 747, + 908, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address the first issue, we introduce a novel approach", + "bbox": [ + 532, + 885, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20908", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Self-play DPO fine-tuning, given a base diffusion model $\\epsilon_{\\mathrm{ref}}$ , a trainable copy $\\epsilon_{\\theta}$ , a prompt-image paired design-image dataset $\\mathbf{D} = \\{\\mathbf{x}_i,\\mathbf{y}_i\\}_{i = 1}^N$ , in which $\\mathbf{x}_i$ and $\\mathbf{y}_i$ represent image and prompt, respectively." + ], + "code_body": "for all $i$ in $\\{1,\\dots ,N\\}$ do Generate $K$ candidate samples $\\{g_{ik}\\}_{k = 1}^{K}$ using $\\epsilon_{\\mathrm{ref}}$ with input $\\mathbf{y}_i$ Losing data: $\\mathbf{x}_i^l = g_{ik}$ , in which $g_{ik}$ gets the worst text rendering accuracy Winning data: $\\mathbf{x}_i^w = \\mathbf{x}_i$ Update $\\epsilon_{\\theta}$ by: min $\\sum_{i = 0}^{n}(\\log \\sigma (-\\beta T\\omega (\\lambda_t))(\\| \\epsilon_i^w -\\epsilon_\\theta (\\mathbf{x}_{i,t}^w,\\mathbf{y}_i,t_i)\\| _2^2 -$ $\\| \\epsilon_i^w -\\epsilon_{\\mathrm{ref}}(\\mathbf{x}_{i,t}^w,\\mathbf{y}_i,t_i)\\| _2^2 -(\\| \\epsilon_i^l -\\epsilon_\\theta (\\mathbf{x}_{i,t}^l,\\mathbf{y}_i,t_i)\\| _2^2 -\\| \\epsilon_i^l -\\epsilon_{\\mathrm{ref}}(\\mathbf{x}_{i,t}^l,\\mathbf{y}_i,t_i)\\| _2^2)))$ end for return $\\epsilon_{\\theta}$", + "bbox": [ + 106, + 125, + 681, + 263 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "by embedding each letter from prompts directly into CLIP text encoders within latent diffusion models [34, 38]. Specifically, the input prompt of the CLIP text encoders is enhanced by appending an extra text description to the original prompt. The template for the text description is \"Rendered characters: ...
  • MethodFID↓Text Precision↑Text Recall↑Text F-score↑Text Accuracy↑SDXL [34]45.100.5170.4610.4880.241SD3 [11]45.900.7540.6750.7120.415FLUX [19]35.280.7640.6980.7290.442DeepFloyd-IF [8]52.050.6070.5340.5680.290GlyphControl [46]60.070.4620.3520.4000.218Textdiffuser [5]55.830.8060.7060.7520.478Textdiffuser-2 [6]63.920.8660.7920.8270.583AnyText [41]64.690.4400.3780.4070.230DesignDiffusion19.870.8880.8370.8620.631", + "bbox": [ + 99, + 116, + 901, + 266 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/204ae8b3cd37596b488947466fca86f0e4161e1056e0652340976bebb42bb069.jpg", + "table_caption": [ + "Table 2. Results of a user study comparing our method with previous approaches based on four aspects of text and image quality." + ], + "table_footnote": [], + "table_body": "
    MethodImage Aesthetic↑Text Quality ↑Layout Aesthetics↑Text-Image Matching↑
    SDXL [34]0.430.110.180.28
    Textdiffuser-2 [6]0.080.340.220.14
    AnyText [41]0.090.030.070.06
    DesignDiffusion0.400.510.540.52
    ", + "bbox": [ + 99, + 281, + 901, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the image and text metrics indicates that DesignDiffusion establishes a new baseline in design image generation.", + "bbox": [ + 89, + 375, + 482, + 405 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results. We compare our method with state-of-the-art text-to-image models, i.e., SDXL [34], DALLE-3 [2], Ideogram [17], and visual text rendering models, i.e., Textdiffuser-2 [6], AnyText [41], as shown in Fig. 3. We observe that although state-of-the-art text-to-image models (SDXL, DALLE-3, Ideogram) can generate visually compelling images, they still struggle to generate accurate visual text. As for visual text rendering methods, we figure out that they generate visual text while brushing out the image content or reducing the aesthetics of the image seriously. It may be because that Textdiffuser-2 [6], AnyText [41] both rely on the text layout planning or strong text position fitting, leading to overfitting on visual text and overlooking other visual contents. Over-strong limitation of visual text area or other information limits the creativity of generating visual content. Throughout the comparisons, design images generated by our DesignDiffusion are more accurate than those from state-of-the-art text-to-image models and more elegant than those generated from visual text rendering models.", + "bbox": [ + 88, + 410, + 485, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "User Studies. We randomly generate 20 samples without any cherry pick compared with three methods, i.e., SDXL [34], Textdiffuser-2 [6], and AnyText [41]. The participants were asked four questions about various aspects of image and text evaluation, in terms of image aesthetic, visual text quality, layout aesthetics, and text-image matching. We collect about 20 results from participants and report the preference ratio of the four metrics in Tab. 2. From the aspects of text quality, text layout aesthetic, and text-image matching, our DesignDiffusion significantly outperforms the competitors. It obtains comparable, slightly worse than SDXL [34] in evaluating image aesthetic, i.e., $40\\%$ v.s. $43\\%$ . It may be because adapting SDXL for the design image generation", + "bbox": [ + 89, + 704, + 486, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "task loses a bit of aesthetic.", + "bbox": [ + 511, + 375, + 696, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Automatic Layout Planning. DesignDiffusion is a one-stage method without any layout planning module. We visualize examples compared with layout-dependent methods [5, 6] in Fig. 4. Samples from others often have an oversized font or dull layout design, while our DesignDiffusion generates images with curved, colorful, and diverse text. The results show that our DesignDiffusion has a strong automatic, flexible, and reasonable layout planning capability.", + "bbox": [ + 511, + 390, + 908, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 511, + 525, + 679, + 540 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To assess the effectiveness of the proposed components within our framework, we conduct ablation studies. We explore various configurations, with the baseline being the original SDXL model. We denote fine-tuning on our dataset as \"FT\", the utilization of prompt enhancement, $\\mathcal{L}_{char}$ , and self-play DPO as \"PE\", \"Lchar\" and \"SP-DPO\", respectively. The ablation results are summarized in Tab. 3, revealing the following notable insights.", + "bbox": [ + 511, + 549, + 908, + 669 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fine-tuning enhances the quality of design image generation: Fine-tuning SDXL with design images results in a significant improvement in FID. Despite this enhancement in image quality, achieving satisfactory accuracy in rendered text remains a challenge for existing diffusion models, even with extensive fine-tuning on large-scale datasets.", + "bbox": [ + 511, + 671, + 908, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of prompt enhancement: Our investigation highlights limitations of current Byte Pair Encoding (BPE) tokenization, particularly in providing precise character-level cues for the visual text rendering task. Incorporating prompt enhancement leads to a significant improvement across various metrics, notably enhancing visual text accuracy because of the introduced character-level information.", + "bbox": [ + 511, + 763, + 908, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Localized attention through $\\mathcal{L}_{char}$ : By utilizing character segmentation masks to guide the cross-attention maps within", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20912", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/16e588af348702f8a8774b42945ecd02f781a04b07483a62208cd19628dd294e.jpg", + "table_caption": [ + "Table 3. Ablation studies of the proposed framework. Bold and underline denotes the first and second best performance. \"FT\" and \"PE\" represent whether to apply fine-tuning and prompt enhancement, respectively." + ], + "table_footnote": [], + "table_body": "
    FTPELcharSP-DPOFID↓Text Precision↑Text Recall↑Text F-score↑Text Accuracy↑
    XXXX45.100.5170.4610.4880.241
    ✓XXX22.730.7150.6780.6960.388
    ✓✓XX19.890.8620.7990.8290.572
    ✓✓✓X19.290.8810.8310.8550.616
    ✓✓✓✓19.870.8880.8370.8620.631
    ", + "bbox": [ + 89, + 116, + 903, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9c69f0286536b955fe313fbc8b8e27ef619be1a520f505ca28eed7ccd950b40d.jpg", + "image_caption": [ + "Figure 4. Visual comparisons of the capabilities of automatic text layout planning from our model with those of planning by language models. Upon training, our DesignDiffusion has demonstrated the ability to generate flexible and well-organized text layouts effectively." + ], + "image_footnote": [], + "bbox": [ + 93, + 219, + 900, + 583 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the UNet architecture, our $\\mathcal{L}_{char}$ loss facilitates focused attention on text regions. With $\\mathcal{L}_{char}$ , we observe a further enhancement in text precision, recall, F-score, and accuracy, emphasizing the effectiveness of localizing cross-attention maps using character segmentation masks.", + "bbox": [ + 89, + 628, + 485, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Enhanced visual text accuracy with SP-DPO: Subsequent to fine-tuning, we integrate SP-DPO to further improve the generation quality. SP-DPO significantly enhances text quality across all text metrics. Regarding the slight decline in the FID score, this can be attributed to the specific implementation of SP-DPO, which relies heavily on the selection of winning and losing data. Currently, the winning-losing pairs are determined based on the text accuracy. If we incorporate image quality into the criteria for constructing the losing data, we anticipate that the FID score could improve further. Notably, our current approach does not visually compromise image quality while enhancing text quality.", + "bbox": [ + 89, + 719, + 485, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 513, + 627, + 761, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce DesignDiffusion, a diffusion-based fine-tuning framework designed for synthesizing design images from textual descriptions. Unlike previous approaches that handle visual and textual elements independently, potentially limiting creativity and leading to style or color inconsistencies in style or color harmony, DesignDiffusion offers an end-to-end, one-stage diffusion-based solution. We explore including a distinctive character embedding and a character localization loss for enhancing visual text learning. Additionally, we employ an SP-DPO fine-tuning strategy to further improve the generation quality. Our extensive experiments demonstrate the effectiveness and robustness of DesignDiffusion in addressing the complexities of design image generation. We anticipate that our research will stimulate further exploration in design image generation, fostering innovation and advancement in this field.", + "bbox": [ + 511, + 659, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20913", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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Judging llm-as-a-judge with mt-bench and chatbot arena, 2023. 3" + ], + "bbox": [ + 516, + 90, + 906, + 415 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20915", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/eb2e95ca-796c-48bb-9edd-bb8243db35c0_model.json b/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/eb2e95ca-796c-48bb-9edd-bb8243db35c0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4f5d9e710b048daaf34ba8fbb2e3a56630ba61ca --- /dev/null +++ b/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/eb2e95ca-796c-48bb-9edd-bb8243db35c0_model.json @@ -0,0 +1,2365 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.173, + 0.131, + 0.826, + 0.175 + ], + "angle": 0, + "content": "DesignDiffusion: High-Quality Text-to-Design Image Generation with Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.203, + 0.88, + 0.223 + ], + "angle": 0, + "content": "Zhendong Wang\\(^{1}\\), Jianmin Bao\\(^{2,\\ast,\\dagger}\\), Shuyang Gu\\(^{2}\\), Dong Chen\\(^{2}\\), Wengang Zhou\\(^{1,\\ast}\\), Houqiang Li\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.305, + 0.222, + 0.693, + 0.24 + ], + "angle": 0, + "content": "1 University of Science and Technology of China" + }, + { + "type": "text", + "bbox": [ + 0.394, + 0.239, + 0.605, + 0.256 + ], + "angle": 0, + "content": "\\(^{2}\\) Microsoft Research Asia" + }, + { + "type": "text", + "bbox": [ + 0.376, + 0.259, + 0.62, + 0.275 + ], + "angle": 0, + "content": "* corresponding author †project lead" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.282, + 0.252, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.256, + 0.282, + 0.416, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.282, + 0.576, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.282, + 0.739, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.743, + 0.282, + 0.901, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.407, + 0.252, + 0.529 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.256, + 0.407, + 0.415, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.407, + 0.577, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.407, + 0.739, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.743, + 0.407, + 0.901, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.54, + 0.908, + 0.569 + ], + "angle": 0, + "content": "Figure 1. Images generated by our DesignDiffusion model, which only requires a simple text prompt as input and can generate diverse, high-quality design images with accurate textual and vivid visual content." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.588, + 0.327, + 0.604 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.63, + 0.486, + 0.904 + ], + "angle": 0, + "content": "In this paper, we present DesignDiffusion, a simple yet effective framework for the novel task of synthesizing design images from textual descriptions. A primary challenge lies in generating accurate and style-consistent textual and visual content. Existing works in a related task of visual text generation often focus on generating text within given specific regions, which limits the creativity of generation models, resulting in style or color inconsistencies between textual and visual elements if applied to design image generation. To address this issue, we propose an end-to-end, one-stage diffusion-based framework that avoids intricate components like position and layout modeling. Specifically, the proposed framework directly synthesizes textual and visual design elements from user prompts. It utilizes a distinctive character embedding derived from the visual text to enhance the input prompt, along with a character localization loss for enhanced supervision during text generation. Furthermore, we employ a self-play Direct Preference Optimization fine" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.59, + 0.907, + 0.651 + ], + "angle": 0, + "content": "tuning strategy to improve the quality and accuracy of the synthesized visual text. Extensive experiments demonstrate that DesignDiffusion achieves state-of-the-art performance in design image generation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.68, + 0.645, + 0.695 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.764 + ], + "angle": 0, + "content": "Design images play a pivotal role in various applications such as graphic design, advertising, and scientific visualization, where the integration of visual and textual elements must be flawless." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.766, + 0.909, + 0.887 + ], + "angle": 0, + "content": "Recently many fascinating and wonderful applications, such as art image creation or film production, have shown remarkable progress due to the rapid advance of text-to-image generation techniques [37-40, 47]. Despite these advancements, the precise generation of design images poses a distinct challenge, largely due to the limited capabilities of existing image generation models in complex layout planning and visual text generation." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.888, + 0.909, + 0.904 + ], + "angle": 0, + "content": "To address the critical issue of visual text generation, re" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20906" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.242 + ], + "angle": 0, + "content": "cent studies [27, 41] have made significant contributions. A common approach involves a two-step process: first generating an image from textual input and then identifying a suitable location within the image to insert text. However, this method presents several challenges. Firstly, a generated image may not have a suitable region for adding text, resulting in an overlay of text on visual elements. Secondly, even with a plausible location, the rendered text may lack consistency with the visual elements presented in the image, compromising overall coherence and professionalism." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.245, + 0.486, + 0.397 + ], + "angle": 0, + "content": "An alternative research direction in visual text rendering, as suggested by [5, 6], focuses on learning the layout of text regions from textual prompts in advance. Then, this learned layout serves as a condition to guide text-to-image models in generating text within designated regions of the image. However, the dependence on predefined text regions might constrain the creative breadth of the generated images. Moreover, these predetermined text regions may not always adhere to natural design principles, potentially leading to visually unattractive or conceptually incoherent outputs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.399, + 0.485, + 0.535 + ], + "angle": 0, + "content": "To address the aforementioned issues, we propose Design-Diffusion, an end-to-end diffusion-based framework specifically developed for the novel task of generating design images from text. The holistic learning approach presents multiple benefits: (1) it eliminates the need to predetermine text regions in the generative images, thereby preserving the creative freedom of the generative models; (2) it enables the smooth incorporation of generated text into images, yielding cohesive designs that accurately reflect input prompts." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.537, + 0.486, + 0.824 + ], + "angle": 0, + "content": "In our framework, we employ three essential techniques when fine-tuning text-to-image diffusion models: a) Recognizing that a conventional CLIP text encoder might overlook the specific textual content designated for rendering in the generated image, we propose a character-level decomposition of words. This approach provides the CLIP text encoder hints to render each character in the image precisely. b) To encourage the model to pay more attention to newly introduced character embeddings, we propose a character localization loss. This loss function compels each character embedding to concentrate on its respective area within the image, ensuring an accurate visual representation of each character. c) We introduce a new training strategy called Self-Play Direct Preference Optimization (SP-DPO) for fine-tuning the model to enhance its capability of generating accurate and high-fidelity text. SP-DPO is based on the hypothesis that ground truth data are typically preferred by humans over model-generated samples. Based on this, we fine-tune the model to align with these human preferences." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Extensive experiments demonstrate the superior capabilities of DesignDiffusion for design image generation. It generates creative design images with prompts, as shown in Fig. 1. Quantitative and qualitative analysis shows that our approach significantly surpasses current state-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.122 + ], + "angle": 0, + "content": "text-to-image and visual text rendering models in terms of both image quality and text accuracy." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.123, + 0.902, + 0.137 + ], + "angle": 0, + "content": "In summary, our contributions are presented as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.138, + 0.908, + 0.228 + ], + "angle": 0, + "content": "- We propose DesignDiffusion, an end-to-end, diffusion-based framework for text-to-design image generation, which enables the simultaneous generation of image and visual text elements, eliminating the necessity for predefined text regions or traditional two-stage separated text and image creation process." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.229, + 0.907, + 0.273 + ], + "angle": 0, + "content": "- We explore prompt enhancement for CLIP text encoding along with a character localization loss, to improve the accuracy of text placement and the fidelity of text rendering." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.273, + 0.905, + 0.319 + ], + "angle": 0, + "content": "- By adopting an SP-DPO mechanism, the generative model is further fine-tuned, achieving remarkable improvements in visual text accuracy and overall image quality." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.138, + 0.908, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.332, + 0.655, + 0.348 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.357, + 0.909, + 0.569 + ], + "angle": 0, + "content": "Visual Text Rendering. Despite the remarkable success of existing diffusion models [37, 38, 40] in text-to-image generation, visual text rendering remains a challenging task. Recently, researchers have recognized this issue and proposed several approaches to address it, such as GlyphDraw [29], DiffUTE [4], GlyphControl [45], AnyText [41], TextDiffuser series [5, 6], and [26]. While these efforts have improved text rendering accuracy, it is worth noting that these models obtain limited image quality due to the need of pre-giving text rendering areas during the generation process or inpainting text into a well-generated image. Separating text and visual content generation away seriously limits the overall quality of generated images with visual text rendered, which is incompatible with the goal of design image generation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.569, + 0.909, + 0.885 + ], + "angle": 0, + "content": "Compositional Image Generation. To improve the ability of text-to-image models to create complex compositions, researchers have integrated new components into diffusion models, enabling the generation of images with multiple features. Examples include T2I-Adapter [30] and ControlNet [47], which incorporate semantic details like layout and pose to influence the structure of images [48]. In a similar vein, GLIGEN [21] utilizes adapters with diffusion models to achieve image generation that is conditioned on specific spatial arrangements. However, these methods cannot generate images directly from prompts and require substantial human effort to define the image layout. On the other hand, some studies have investigated methods that do not require additional training to prompt diffusion models to create images based on spatial conditions during the inference phase. Recent advancements [22, 32, 44] have seen large language models aiding diffusion models in generating images with intricate or predefined layouts. Yet, these approaches often fall short in generating design-centric images that seamlessly integrate both textual and visual components in a well-organized manner." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Aligning Diffusion Models. Replicating the success of re" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20907" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.904, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.404, + 0.568, + 0.419 + ], + "angle": 0, + "content": "(a) Fine-tuning with prompt enhancement and character localization loss" + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.404, + 0.882, + 0.419 + ], + "angle": 0, + "content": "(b) Fine-tuning with self-play DPO loss" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.429, + 0.908, + 0.486 + ], + "angle": 0, + "content": "Figure 2. Overview of the DesignDiffusion framework. DesignDiffusion is based on enhanced text prompts, with trainable CLIP text encoder and UNet, and does not require additional complex conditions (glyphs, positions). Character localization loss is added as extra supervision at cross-attention maps to force the UNet to attend more to the visual character regions. To further improve the quality of visual text generation, we incorporate a self-play DPO strategy into the fine-tuning process. Diffusion denoise loss is omitted here." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.499, + 0.487, + 0.696 + ], + "angle": 0, + "content": "inforcement learning in large language models [31, 35] to text-to-image diffusion models remains a significant challenge. Recent works have proposed various methods to address this problem. For example, EMU [7] identifies that a few high-quality samples are crucial when fine-tuning the model to generate visually appealing images. DPOK [12] and DDPO [3] use RL-based approaches to maximize rewards on a limited vocabulary set, performing well when the number of train/test prompts is small. Another work DiffusionDPO [42] applies DPO based on a human-annotated preference dataset. Our DesignDiffusion differs by applying a self-play DPO strategy, which does not require human annotation and lacks of exploration in design image generation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.71, + 0.25, + 0.726 + ], + "angle": 0, + "content": "3. DesignDiffusion" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.735, + 0.487, + 0.902 + ], + "angle": 0, + "content": "The generative community has witnessed the strong generative capability of diffusion models [9, 16, 34, 38, 48]. However, generating design images remains a great challenge, particularly in the context of exquisite layout and text rendering. Previous approaches [5, 6] in a related task (visual text rendering) attempt to inpaint text after generating an image, or to plan text regions using large language models such as Vicuna [49] and GPT [1] before generating an image. We argue that they do not consider the integration of text and image content. Note that, the text and image contexts in design images are often intertwined and inseparable, such" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.499, + 0.889, + 0.515 + ], + "angle": 0, + "content": "that they are incompatible with design image generation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.516, + 0.909, + 0.713 + ], + "angle": 0, + "content": "In contrast, we introduce a straightforward, one-stage approach for text-to-design image generation, relying solely on the user prompt. It is based on an aesthetic model, i.e., Stable Diffusion XL (SDXL) model [34], incorporating three core components that enable the successful generation of text-rich design images. An overview of the DesignDiffusion framework is provided in Fig. 2. The DesignDiffusion training involves a two-stage fine-tuning strategy. In the first stage, we introduce prompt enhancement and character localization loss into the framework to generate high-quality images with accurate text. In the second stage, we propose SP-DPO to further improve the text rendering accuracy. These components are detailed in the following subsections." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.725, + 0.907, + 0.742 + ], + "angle": 0, + "content": "3.1. Prompt Enhancement for CLIP Text Encoding" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.748, + 0.909, + 0.884 + ], + "angle": 0, + "content": "Currently, available text-to-image diffusion models struggle to generate text-rich design images based solely on an input text prompt. This challenge arises from two issues: 1) Visually rendered text must be letter-by-letter correct, however, during tokenization, most words are tokenized as a single token, ignoring each letter within the word thus complicating the learning of individual letters; 2) Visual text in images is often diverse in style, size, and layout, increasing the complexity of visual text modeling." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.886, + 0.907, + 0.902 + ], + "angle": 0, + "content": "To address the first issue, we introduce a novel approach" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20908" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.091, + 0.091, + 0.907, + 0.123 + ], + "angle": 0, + "content": "Algorithm 1 Self-play DPO fine-tuning, given a base diffusion model \\(\\epsilon_{\\mathrm{ref}}\\), a trainable copy \\(\\epsilon_{\\theta}\\), a prompt-image paired design-image dataset \\(\\mathbf{D} = \\{\\mathbf{x}_i,\\mathbf{y}_i\\}_{i = 1}^N\\), in which \\(\\mathbf{x}_i\\) and \\(\\mathbf{y}_i\\) represent image and prompt, respectively." + }, + { + "type": "algorithm", + "bbox": [ + 0.107, + 0.126, + 0.682, + 0.264 + ], + "angle": 0, + "content": "for all \\(i\\) in \\(\\{1,\\dots ,N\\}\\) do Generate \\(K\\) candidate samples \\(\\{g_{ik}\\}_{k = 1}^{K}\\) using \\(\\epsilon_{\\mathrm{ref}}\\) with input \\(\\mathbf{y}_i\\) Losing data: \\(\\mathbf{x}_i^l = g_{ik}\\) , in which \\(g_{ik}\\) gets the worst text rendering accuracy Winning data: \\(\\mathbf{x}_i^w = \\mathbf{x}_i\\) Update \\(\\epsilon_{\\theta}\\) by: min \\(\\sum_{i = 0}^{n}(\\log \\sigma (-\\beta T\\omega (\\lambda_t))(\\| \\epsilon_i^w -\\epsilon_\\theta (\\mathbf{x}_{i,t}^w,\\mathbf{y}_i,t_i)\\| _2^2 -\\) \\(\\| \\epsilon_i^w -\\epsilon_{\\mathrm{ref}}(\\mathbf{x}_{i,t}^w,\\mathbf{y}_i,t_i)\\| _2^2 -(\\| \\epsilon_i^l -\\epsilon_\\theta (\\mathbf{x}_{i,t}^l,\\mathbf{y}_i,t_i)\\| _2^2 -\\| \\epsilon_i^l -\\epsilon_{\\mathrm{ref}}(\\mathbf{x}_{i,t}^l,\\mathbf{y}_i,t_i)\\| _2^2)))\\) end for return \\(\\epsilon_{\\theta}\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.292, + 0.486, + 0.488 + ], + "angle": 0, + "content": "by embedding each letter from prompts directly into CLIP text encoders within latent diffusion models [34, 38]. Specifically, the input prompt of the CLIP text encoders is enhanced by appending an extra text description to the original prompt. The template for the text description is \"Rendered characters: ...
  • MethodFID↓Text Precision↑Text Recall↑Text F-score↑Text Accuracy↑SDXL [34]45.100.5170.4610.4880.241SD3 [11]45.900.7540.6750.7120.415FLUX [19]35.280.7640.6980.7290.442DeepFloyd-IF [8]52.050.6070.5340.5680.290GlyphControl [46]60.070.4620.3520.4000.218Textdiffuser [5]55.830.8060.7060.7520.478Textdiffuser-2 [6]63.920.8660.7920.8270.583AnyText [41]64.690.4400.3780.4070.230DesignDiffusion19.870.8880.8370.8620.631" + }, + { + "type": "table_caption", + "bbox": [ + 0.118, + 0.269, + 0.879, + 0.282 + ], + "angle": 0, + "content": "Table 2. Results of a user study comparing our method with previous approaches based on four aspects of text and image quality." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.282, + 0.903, + 0.361 + ], + "angle": 0, + "content": "
    MethodImage Aesthetic↑Text Quality ↑Layout Aesthetics↑Text-Image Matching↑
    SDXL [34]0.430.110.180.28
    Textdiffuser-2 [6]0.080.340.220.14
    AnyText [41]0.090.030.070.06
    DesignDiffusion0.400.510.540.52
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.375, + 0.483, + 0.406 + ], + "angle": 0, + "content": "the image and text metrics indicates that DesignDiffusion establishes a new baseline in design image generation." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.411, + 0.486, + 0.699 + ], + "angle": 0, + "content": "Qualitative Results. We compare our method with state-of-the-art text-to-image models, i.e., SDXL [34], DALLE-3 [2], Ideogram [17], and visual text rendering models, i.e., Textdiffuser-2 [6], AnyText [41], as shown in Fig. 3. We observe that although state-of-the-art text-to-image models (SDXL, DALLE-3, Ideogram) can generate visually compelling images, they still struggle to generate accurate visual text. As for visual text rendering methods, we figure out that they generate visual text while brushing out the image content or reducing the aesthetics of the image seriously. It may be because that Textdiffuser-2 [6], AnyText [41] both rely on the text layout planning or strong text position fitting, leading to overfitting on visual text and overlooking other visual contents. Over-strong limitation of visual text area or other information limits the creativity of generating visual content. Throughout the comparisons, design images generated by our DesignDiffusion are more accurate than those from state-of-the-art text-to-image models and more elegant than those generated from visual text rendering models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.487, + 0.902 + ], + "angle": 0, + "content": "User Studies. We randomly generate 20 samples without any cherry pick compared with three methods, i.e., SDXL [34], Textdiffuser-2 [6], and AnyText [41]. The participants were asked four questions about various aspects of image and text evaluation, in terms of image aesthetic, visual text quality, layout aesthetics, and text-image matching. We collect about 20 results from participants and report the preference ratio of the four metrics in Tab. 2. From the aspects of text quality, text layout aesthetic, and text-image matching, our DesignDiffusion significantly outperforms the competitors. It obtains comparable, slightly worse than SDXL [34] in evaluating image aesthetic, i.e., \\(40\\%\\) v.s. \\(43\\%\\). It may be because adapting SDXL for the design image generation" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.375, + 0.697, + 0.389 + ], + "angle": 0, + "content": "task loses a bit of aesthetic." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.391, + 0.909, + 0.513 + ], + "angle": 0, + "content": "Automatic Layout Planning. DesignDiffusion is a one-stage method without any layout planning module. We visualize examples compared with layout-dependent methods [5, 6] in Fig. 4. Samples from others often have an oversized font or dull layout design, while our DesignDiffusion generates images with curved, colorful, and diverse text. The results show that our DesignDiffusion has a strong automatic, flexible, and reasonable layout planning capability." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.526, + 0.68, + 0.541 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.55, + 0.909, + 0.67 + ], + "angle": 0, + "content": "To assess the effectiveness of the proposed components within our framework, we conduct ablation studies. We explore various configurations, with the baseline being the original SDXL model. We denote fine-tuning on our dataset as \"FT\", the utilization of prompt enhancement, \\(\\mathcal{L}_{char}\\), and self-play DPO as \"PE\", \"Lchar\" and \"SP-DPO\", respectively. The ablation results are summarized in Tab. 3, revealing the following notable insights." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.672, + 0.91, + 0.763 + ], + "angle": 0, + "content": "Fine-tuning enhances the quality of design image generation: Fine-tuning SDXL with design images results in a significant improvement in FID. Despite this enhancement in image quality, achieving satisfactory accuracy in rendered text remains a challenge for existing diffusion models, even with extensive fine-tuning on large-scale datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.764, + 0.909, + 0.869 + ], + "angle": 0, + "content": "Effect of prompt enhancement: Our investigation highlights limitations of current Byte Pair Encoding (BPE) tokenization, particularly in providing precise character-level cues for the visual text rendering task. Incorporating prompt enhancement leads to a significant improvement across various metrics, notably enhancing visual text accuracy because of the introduced character-level information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.902 + ], + "angle": 0, + "content": "Localized attention through \\(\\mathcal{L}_{char}\\): By utilizing character segmentation masks to guide the cross-attention maps within" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20912" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.117 + ], + "angle": 0, + "content": "Table 3. Ablation studies of the proposed framework. Bold and underline denotes the first and second best performance. \"FT\" and \"PE\" represent whether to apply fine-tuning and prompt enhancement, respectively." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.117, + 0.905, + 0.209 + ], + "angle": 0, + "content": "
    FTPELcharSP-DPOFID↓Text Precision↑Text Recall↑Text F-score↑Text Accuracy↑
    XXXX45.100.5170.4610.4880.241
    ✓XXX22.730.7150.6780.6960.388
    ✓✓XX19.890.8620.7990.8290.572
    ✓✓✓X19.290.8810.8310.8550.616
    ✓✓✓✓19.870.8880.8370.8620.631
    " + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.22, + 0.901, + 0.584 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.587, + 0.908, + 0.618 + ], + "angle": 0, + "content": "Figure 4. Visual comparisons of the capabilities of automatic text layout planning from our model with those of planning by language models. Upon training, our DesignDiffusion has demonstrated the ability to generate flexible and well-organized text layouts effectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.486, + 0.706 + ], + "angle": 0, + "content": "the UNet architecture, our \\(\\mathcal{L}_{char}\\) loss facilitates focused attention on text regions. With \\(\\mathcal{L}_{char}\\), we observe a further enhancement in text precision, recall, F-score, and accuracy, emphasizing the effectiveness of localizing cross-attention maps using character segmentation masks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Enhanced visual text accuracy with SP-DPO: Subsequent to fine-tuning, we integrate SP-DPO to further improve the generation quality. SP-DPO significantly enhances text quality across all text metrics. Regarding the slight decline in the FID score, this can be attributed to the specific implementation of SP-DPO, which relies heavily on the selection of winning and losing data. Currently, the winning-losing pairs are determined based on the text accuracy. If we incorporate image quality into the criteria for constructing the losing data, we anticipate that the FID score could improve further. Notably, our current approach does not visually compromise image quality while enhancing text quality." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.628, + 0.763, + 0.644 + ], + "angle": 0, + "content": "5. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.909, + 0.901 + ], + "angle": 0, + "content": "In this paper, we introduce DesignDiffusion, a diffusion-based fine-tuning framework designed for synthesizing design images from textual descriptions. Unlike previous approaches that handle visual and textual elements independently, potentially limiting creativity and leading to style or color inconsistencies in style or color harmony, DesignDiffusion offers an end-to-end, one-stage diffusion-based solution. We explore including a distinctive character embedding and a character localization loss for enhancing visual text learning. Additionally, we employ an SP-DPO fine-tuning strategy to further improve the generation quality. Our extensive experiments demonstrate the effectiveness and robustness of DesignDiffusion in addressing the complexities of design image generation. We anticipate that our research will stimulate further exploration in design image generation, fostering innovation and advancement in this field." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20913" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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Controllable text-to-image generation with gpt-4. arXiv preprint arXiv:2305.18583, 2023. 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.517, + 0.349, + 0.905, + 0.416 + ], + "angle": 0, + "content": "[49] Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric. P Xing, Hao Zhang, Joseph E. Gonzalez, and Ion Stoica. Judging llm-as-a-judge with mt-bench and chatbot arena, 2023. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.092, + 0.908, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20915" + } + ] +] \ No newline at end of file diff --git a/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/eb2e95ca-796c-48bb-9edd-bb8243db35c0_origin.pdf b/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/eb2e95ca-796c-48bb-9edd-bb8243db35c0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c7c04889b65f720a44e9e0816bde5a793a46c365 --- /dev/null +++ b/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/eb2e95ca-796c-48bb-9edd-bb8243db35c0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5f83ec2bd352caf16bef3d1b1a3208a509e2aee61a4df6c0d408fe104b051878 +size 6326019 diff --git a/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/full.md b/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0c714ef48dd3fe29168f4725f5f0633e92515fab --- /dev/null +++ b/2025/DesignDiffusion_ High-Quality Text-to-Design Image Generation with Diffusion Models/full.md @@ -0,0 +1,336 @@ +# DesignDiffusion: High-Quality Text-to-Design Image Generation with Diffusion Models + +Zhendong Wang $^{1}$ , Jianmin Bao $^{2,\ast,\dagger}$ , Shuyang Gu $^{2}$ , Dong Chen $^{2}$ , Wengang Zhou $^{1,\ast}$ , Houqiang Li $^{1}$ + +1 University of Science and Technology of China + +$^{2}$ Microsoft Research Asia + +* corresponding author †project lead + +![](images/6ea29bc3e061487c9831b6b919f72ac70173f3c99b145c664b0bb0fcfea3c493.jpg) + +![](images/93c7678190cad27b5d40595225a1d3dd3672afdf307ca8aa56373716ae081704.jpg) + +![](images/77b00aa96ccc72ed9a8b1523f452f32f2e961f37064b3e2c523405b17d5154a1.jpg) + +![](images/b9bc1e9e7b627574ab684e2fc8f8ce07ac0d2af27200e47a61616192def456b3.jpg) + +![](images/b63c2323b0818467cf2ce7e0f55ee1532aac85bc7a640582349d113686f3e26a.jpg) + +![](images/7d7d98cd13c6610dd4dfec82c9c0610b0d662b86356f3c1ddaf9d14e87ec8591.jpg) +Figure 1. Images generated by our DesignDiffusion model, which only requires a simple text prompt as input and can generate diverse, high-quality design images with accurate textual and vivid visual content. + +![](images/db242f0a6614aeb6a7f978bce632486cdb24fa96144bd2206ed58901f7f9b5db.jpg) + +![](images/3610941a8128737690a01db5d3e8b1c5cc33c3763bcee376721c0fff0b7b0780.jpg) + +![](images/cae7be204fbc3bfc072675e09c98f41ee18e62a518f6777066ff5cd4072aa1d3.jpg) + +![](images/e17178c994840d82c8e4c635984a5f07306b3f1c50c771b97757ad25891c6c97.jpg) + +# Abstract + +In this paper, we present DesignDiffusion, a simple yet effective framework for the novel task of synthesizing design images from textual descriptions. A primary challenge lies in generating accurate and style-consistent textual and visual content. Existing works in a related task of visual text generation often focus on generating text within given specific regions, which limits the creativity of generation models, resulting in style or color inconsistencies between textual and visual elements if applied to design image generation. To address this issue, we propose an end-to-end, one-stage diffusion-based framework that avoids intricate components like position and layout modeling. Specifically, the proposed framework directly synthesizes textual and visual design elements from user prompts. It utilizes a distinctive character embedding derived from the visual text to enhance the input prompt, along with a character localization loss for enhanced supervision during text generation. Furthermore, we employ a self-play Direct Preference Optimization fine + +tuning strategy to improve the quality and accuracy of the synthesized visual text. Extensive experiments demonstrate that DesignDiffusion achieves state-of-the-art performance in design image generation. + +# 1. Introduction + +Design images play a pivotal role in various applications such as graphic design, advertising, and scientific visualization, where the integration of visual and textual elements must be flawless. + +Recently many fascinating and wonderful applications, such as art image creation or film production, have shown remarkable progress due to the rapid advance of text-to-image generation techniques [37-40, 47]. Despite these advancements, the precise generation of design images poses a distinct challenge, largely due to the limited capabilities of existing image generation models in complex layout planning and visual text generation. + +To address the critical issue of visual text generation, re + +cent studies [27, 41] have made significant contributions. A common approach involves a two-step process: first generating an image from textual input and then identifying a suitable location within the image to insert text. However, this method presents several challenges. Firstly, a generated image may not have a suitable region for adding text, resulting in an overlay of text on visual elements. Secondly, even with a plausible location, the rendered text may lack consistency with the visual elements presented in the image, compromising overall coherence and professionalism. + +An alternative research direction in visual text rendering, as suggested by [5, 6], focuses on learning the layout of text regions from textual prompts in advance. Then, this learned layout serves as a condition to guide text-to-image models in generating text within designated regions of the image. However, the dependence on predefined text regions might constrain the creative breadth of the generated images. Moreover, these predetermined text regions may not always adhere to natural design principles, potentially leading to visually unattractive or conceptually incoherent outputs. + +To address the aforementioned issues, we propose Design-Diffusion, an end-to-end diffusion-based framework specifically developed for the novel task of generating design images from text. The holistic learning approach presents multiple benefits: (1) it eliminates the need to predetermine text regions in the generative images, thereby preserving the creative freedom of the generative models; (2) it enables the smooth incorporation of generated text into images, yielding cohesive designs that accurately reflect input prompts. + +In our framework, we employ three essential techniques when fine-tuning text-to-image diffusion models: a) Recognizing that a conventional CLIP text encoder might overlook the specific textual content designated for rendering in the generated image, we propose a character-level decomposition of words. This approach provides the CLIP text encoder hints to render each character in the image precisely. b) To encourage the model to pay more attention to newly introduced character embeddings, we propose a character localization loss. This loss function compels each character embedding to concentrate on its respective area within the image, ensuring an accurate visual representation of each character. c) We introduce a new training strategy called Self-Play Direct Preference Optimization (SP-DPO) for fine-tuning the model to enhance its capability of generating accurate and high-fidelity text. SP-DPO is based on the hypothesis that ground truth data are typically preferred by humans over model-generated samples. Based on this, we fine-tune the model to align with these human preferences. + +Extensive experiments demonstrate the superior capabilities of DesignDiffusion for design image generation. It generates creative design images with prompts, as shown in Fig. 1. Quantitative and qualitative analysis shows that our approach significantly surpasses current state-of-the-art + +text-to-image and visual text rendering models in terms of both image quality and text accuracy. + +In summary, our contributions are presented as follows: + +- We propose DesignDiffusion, an end-to-end, diffusion-based framework for text-to-design image generation, which enables the simultaneous generation of image and visual text elements, eliminating the necessity for predefined text regions or traditional two-stage separated text and image creation process. +- We explore prompt enhancement for CLIP text encoding along with a character localization loss, to improve the accuracy of text placement and the fidelity of text rendering. +- By adopting an SP-DPO mechanism, the generative model is further fine-tuned, achieving remarkable improvements in visual text accuracy and overall image quality. + +# 2. Related Work + +Visual Text Rendering. Despite the remarkable success of existing diffusion models [37, 38, 40] in text-to-image generation, visual text rendering remains a challenging task. Recently, researchers have recognized this issue and proposed several approaches to address it, such as GlyphDraw [29], DiffUTE [4], GlyphControl [45], AnyText [41], TextDiffuser series [5, 6], and [26]. While these efforts have improved text rendering accuracy, it is worth noting that these models obtain limited image quality due to the need of pre-giving text rendering areas during the generation process or inpainting text into a well-generated image. Separating text and visual content generation away seriously limits the overall quality of generated images with visual text rendered, which is incompatible with the goal of design image generation. + +Compositional Image Generation. To improve the ability of text-to-image models to create complex compositions, researchers have integrated new components into diffusion models, enabling the generation of images with multiple features. Examples include T2I-Adapter [30] and ControlNet [47], which incorporate semantic details like layout and pose to influence the structure of images [48]. In a similar vein, GLIGEN [21] utilizes adapters with diffusion models to achieve image generation that is conditioned on specific spatial arrangements. However, these methods cannot generate images directly from prompts and require substantial human effort to define the image layout. On the other hand, some studies have investigated methods that do not require additional training to prompt diffusion models to create images based on spatial conditions during the inference phase. Recent advancements [22, 32, 44] have seen large language models aiding diffusion models in generating images with intricate or predefined layouts. Yet, these approaches often fall short in generating design-centric images that seamlessly integrate both textual and visual components in a well-organized manner. + +Aligning Diffusion Models. Replicating the success of re + +![](images/97c747f56b36cdd7f24f96da08ff9ce0ccbe97bfe5c6259e8163afc9ca04f7cf.jpg) +(a) Fine-tuning with prompt enhancement and character localization loss +(b) Fine-tuning with self-play DPO loss +Figure 2. Overview of the DesignDiffusion framework. DesignDiffusion is based on enhanced text prompts, with trainable CLIP text encoder and UNet, and does not require additional complex conditions (glyphs, positions). Character localization loss is added as extra supervision at cross-attention maps to force the UNet to attend more to the visual character regions. To further improve the quality of visual text generation, we incorporate a self-play DPO strategy into the fine-tuning process. Diffusion denoise loss is omitted here. + +inforcement learning in large language models [31, 35] to text-to-image diffusion models remains a significant challenge. Recent works have proposed various methods to address this problem. For example, EMU [7] identifies that a few high-quality samples are crucial when fine-tuning the model to generate visually appealing images. DPOK [12] and DDPO [3] use RL-based approaches to maximize rewards on a limited vocabulary set, performing well when the number of train/test prompts is small. Another work DiffusionDPO [42] applies DPO based on a human-annotated preference dataset. Our DesignDiffusion differs by applying a self-play DPO strategy, which does not require human annotation and lacks of exploration in design image generation. + +# 3. DesignDiffusion + +The generative community has witnessed the strong generative capability of diffusion models [9, 16, 34, 38, 48]. However, generating design images remains a great challenge, particularly in the context of exquisite layout and text rendering. Previous approaches [5, 6] in a related task (visual text rendering) attempt to inpaint text after generating an image, or to plan text regions using large language models such as Vicuna [49] and GPT [1] before generating an image. We argue that they do not consider the integration of text and image content. Note that, the text and image contexts in design images are often intertwined and inseparable, such + +that they are incompatible with design image generation. + +In contrast, we introduce a straightforward, one-stage approach for text-to-design image generation, relying solely on the user prompt. It is based on an aesthetic model, i.e., Stable Diffusion XL (SDXL) model [34], incorporating three core components that enable the successful generation of text-rich design images. An overview of the DesignDiffusion framework is provided in Fig. 2. The DesignDiffusion training involves a two-stage fine-tuning strategy. In the first stage, we introduce prompt enhancement and character localization loss into the framework to generate high-quality images with accurate text. In the second stage, we propose SP-DPO to further improve the text rendering accuracy. These components are detailed in the following subsections. + +# 3.1. Prompt Enhancement for CLIP Text Encoding + +Currently, available text-to-image diffusion models struggle to generate text-rich design images based solely on an input text prompt. This challenge arises from two issues: 1) Visually rendered text must be letter-by-letter correct, however, during tokenization, most words are tokenized as a single token, ignoring each letter within the word thus complicating the learning of individual letters; 2) Visual text in images is often diverse in style, size, and layout, increasing the complexity of visual text modeling. + +To address the first issue, we introduce a novel approach + +Algorithm 1 Self-play DPO fine-tuning, given a base diffusion model $\epsilon_{\mathrm{ref}}$ , a trainable copy $\epsilon_{\theta}$ , a prompt-image paired design-image dataset $\mathbf{D} = \{\mathbf{x}_i,\mathbf{y}_i\}_{i = 1}^N$ , in which $\mathbf{x}_i$ and $\mathbf{y}_i$ represent image and prompt, respectively. +for all $i$ in $\{1,\dots ,N\}$ do Generate $K$ candidate samples $\{g_{ik}\}_{k = 1}^{K}$ using $\epsilon_{\mathrm{ref}}$ with input $\mathbf{y}_i$ Losing data: $\mathbf{x}_i^l = g_{ik}$ , in which $g_{ik}$ gets the worst text rendering accuracy Winning data: $\mathbf{x}_i^w = \mathbf{x}_i$ Update $\epsilon_{\theta}$ by: min $\sum_{i = 0}^{n}(\log \sigma (-\beta T\omega (\lambda_t))(\| \epsilon_i^w -\epsilon_\theta (\mathbf{x}_{i,t}^w,\mathbf{y}_i,t_i)\| _2^2 -$ $\| \epsilon_i^w -\epsilon_{\mathrm{ref}}(\mathbf{x}_{i,t}^w,\mathbf{y}_i,t_i)\| _2^2 -(\| \epsilon_i^l -\epsilon_\theta (\mathbf{x}_{i,t}^l,\mathbf{y}_i,t_i)\| _2^2 -\| \epsilon_i^l -\epsilon_{\mathrm{ref}}(\mathbf{x}_{i,t}^l,\mathbf{y}_i,t_i)\| _2^2)))$ end for return $\epsilon_{\theta}$ + +by embedding each letter from prompts directly into CLIP text encoders within latent diffusion models [34, 38]. Specifically, the input prompt of the CLIP text encoders is enhanced by appending an extra text description to the original prompt. The template for the text description is "Rendered characters: ...
  • MethodFID↓Text Precision↑Text Recall↑Text F-score↑Text Accuracy↑SDXL [34]45.100.5170.4610.4880.241SD3 [11]45.900.7540.6750.7120.415FLUX [19]35.280.7640.6980.7290.442DeepFloyd-IF [8]52.050.6070.5340.5680.290GlyphControl [46]60.070.4620.3520.4000.218Textdiffuser [5]55.830.8060.7060.7520.478Textdiffuser-2 [6]63.920.8660.7920.8270.583AnyText [41]64.690.4400.3780.4070.230DesignDiffusion19.870.8880.8370.8620.631 + +Table 2. Results of a user study comparing our method with previous approaches based on four aspects of text and image quality. + +
    MethodImage Aesthetic↑Text Quality ↑Layout Aesthetics↑Text-Image Matching↑
    SDXL [34]0.430.110.180.28
    Textdiffuser-2 [6]0.080.340.220.14
    AnyText [41]0.090.030.070.06
    DesignDiffusion0.400.510.540.52
    + +the image and text metrics indicates that DesignDiffusion establishes a new baseline in design image generation. + +Qualitative Results. We compare our method with state-of-the-art text-to-image models, i.e., SDXL [34], DALLE-3 [2], Ideogram [17], and visual text rendering models, i.e., Textdiffuser-2 [6], AnyText [41], as shown in Fig. 3. We observe that although state-of-the-art text-to-image models (SDXL, DALLE-3, Ideogram) can generate visually compelling images, they still struggle to generate accurate visual text. As for visual text rendering methods, we figure out that they generate visual text while brushing out the image content or reducing the aesthetics of the image seriously. It may be because that Textdiffuser-2 [6], AnyText [41] both rely on the text layout planning or strong text position fitting, leading to overfitting on visual text and overlooking other visual contents. Over-strong limitation of visual text area or other information limits the creativity of generating visual content. Throughout the comparisons, design images generated by our DesignDiffusion are more accurate than those from state-of-the-art text-to-image models and more elegant than those generated from visual text rendering models. + +User Studies. We randomly generate 20 samples without any cherry pick compared with three methods, i.e., SDXL [34], Textdiffuser-2 [6], and AnyText [41]. The participants were asked four questions about various aspects of image and text evaluation, in terms of image aesthetic, visual text quality, layout aesthetics, and text-image matching. We collect about 20 results from participants and report the preference ratio of the four metrics in Tab. 2. From the aspects of text quality, text layout aesthetic, and text-image matching, our DesignDiffusion significantly outperforms the competitors. It obtains comparable, slightly worse than SDXL [34] in evaluating image aesthetic, i.e., $40\%$ v.s. $43\%$ . It may be because adapting SDXL for the design image generation + +task loses a bit of aesthetic. + +Automatic Layout Planning. DesignDiffusion is a one-stage method without any layout planning module. We visualize examples compared with layout-dependent methods [5, 6] in Fig. 4. Samples from others often have an oversized font or dull layout design, while our DesignDiffusion generates images with curved, colorful, and diverse text. The results show that our DesignDiffusion has a strong automatic, flexible, and reasonable layout planning capability. + +# 4.3. Ablation Studies + +To assess the effectiveness of the proposed components within our framework, we conduct ablation studies. We explore various configurations, with the baseline being the original SDXL model. We denote fine-tuning on our dataset as "FT", the utilization of prompt enhancement, $\mathcal{L}_{char}$ , and self-play DPO as "PE", "Lchar" and "SP-DPO", respectively. The ablation results are summarized in Tab. 3, revealing the following notable insights. + +Fine-tuning enhances the quality of design image generation: Fine-tuning SDXL with design images results in a significant improvement in FID. Despite this enhancement in image quality, achieving satisfactory accuracy in rendered text remains a challenge for existing diffusion models, even with extensive fine-tuning on large-scale datasets. + +Effect of prompt enhancement: Our investigation highlights limitations of current Byte Pair Encoding (BPE) tokenization, particularly in providing precise character-level cues for the visual text rendering task. Incorporating prompt enhancement leads to a significant improvement across various metrics, notably enhancing visual text accuracy because of the introduced character-level information. + +Localized attention through $\mathcal{L}_{char}$ : By utilizing character segmentation masks to guide the cross-attention maps within + +Table 3. Ablation studies of the proposed framework. Bold and underline denotes the first and second best performance. "FT" and "PE" represent whether to apply fine-tuning and prompt enhancement, respectively. + +
    FTPELcharSP-DPOFID↓Text Precision↑Text Recall↑Text F-score↑Text Accuracy↑
    XXXX45.100.5170.4610.4880.241
    ✓XXX22.730.7150.6780.6960.388
    ✓✓XX19.890.8620.7990.8290.572
    ✓✓✓X19.290.8810.8310.8550.616
    ✓✓✓✓19.870.8880.8370.8620.631
    + +![](images/9c69f0286536b955fe313fbc8b8e27ef619be1a520f505ca28eed7ccd950b40d.jpg) +Figure 4. Visual comparisons of the capabilities of automatic text layout planning from our model with those of planning by language models. Upon training, our DesignDiffusion has demonstrated the ability to generate flexible and well-organized text layouts effectively. + +the UNet architecture, our $\mathcal{L}_{char}$ loss facilitates focused attention on text regions. With $\mathcal{L}_{char}$ , we observe a further enhancement in text precision, recall, F-score, and accuracy, emphasizing the effectiveness of localizing cross-attention maps using character segmentation masks. + +Enhanced visual text accuracy with SP-DPO: Subsequent to fine-tuning, we integrate SP-DPO to further improve the generation quality. SP-DPO significantly enhances text quality across all text metrics. Regarding the slight decline in the FID score, this can be attributed to the specific implementation of SP-DPO, which relies heavily on the selection of winning and losing data. Currently, the winning-losing pairs are determined based on the text accuracy. If we incorporate image quality into the criteria for constructing the losing data, we anticipate that the FID score could improve further. Notably, our current approach does not visually compromise image quality while enhancing text quality. + +# 5. Discussion and Conclusion + +In this paper, we introduce DesignDiffusion, a diffusion-based fine-tuning framework designed for synthesizing design images from textual descriptions. Unlike previous approaches that handle visual and textual elements independently, potentially limiting creativity and leading to style or color inconsistencies in style or color harmony, DesignDiffusion offers an end-to-end, one-stage diffusion-based solution. We explore including a distinctive character embedding and a character localization loss for enhancing visual text learning. Additionally, we employ an SP-DPO fine-tuning strategy to further improve the generation quality. Our extensive experiments demonstrate the effectiveness and robustness of DesignDiffusion in addressing the complexities of design image generation. We anticipate that our research will stimulate further exploration in design image generation, fostering innovation and advancement in this field. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023. 3 +[2] James Betker, Gabriel Goh, Li Jing, Tim Brooks, Jianfeng Wang, Linjie Li, Long Ouyang, Juntang Zhuang, Joyce Lee, Yufei Guo, et al. Improving image generation with better captions. 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A primary challenge lies in generating accurate and style-consistent textual and visual content. Existing works in a related task of visual text generation often focus on generating text within given specific regions, which limits the creativity of generation models, resulting in style or color inconsistencies between textual and visual elements if applied to design image generation. To address this issue, we propose an end-to-end, one-stage diffusion-based framework that avoids intricate components like position and layout modeling. Specifically, the proposed framework directly synthesizes textual and visual design elements from user prompts. It utilizes a distinctive character embedding derived from the visual text to enhance the input prompt, along with a character localization loss for enhanced supervision during text generation. Furthermore, we employ a self-play Direct Preference Optimization fine" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 467, + 555, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 555, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 555, + 515 + ], + "type": "text", + "content": "tuning strategy to improve the quality and accuracy of the synthesized visual text. Extensive experiments demonstrate that DesignDiffusion achieves state-of-the-art performance in design image generation." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 314, + 538, + 394, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 538, + 394, + 550 + ], + "spans": [ + { + "bbox": [ + 314, + 538, + 394, + 550 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 558, + 555, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 605 + ], + "type": "text", + "content": "Design images play a pivotal role in various applications such as graphic design, advertising, and scientific visualization, where the integration of visual and textual elements must be flawless." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 606, + 556, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 606, + 556, + 702 + ], + "spans": [ + { + "bbox": [ + 313, + 606, + 556, + 702 + ], + "type": "text", + "content": "Recently many fascinating and wonderful applications, such as art image creation or film production, have shown remarkable progress due to the rapid advance of text-to-image generation techniques [37-40, 47]. Despite these advancements, the precise generation of design images poses a distinct challenge, largely due to the limited capabilities of existing image generation models in complex layout planning and visual text generation." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 326, + 703, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 703, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 326, + 703, + 556, + 715 + ], + "type": "text", + "content": "To address the critical issue of visual text generation, re" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "20906" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 191 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 191 + ], + "type": "text", + "content": "cent studies [27, 41] have made significant contributions. A common approach involves a two-step process: first generating an image from textual input and then identifying a suitable location within the image to insert text. However, this method presents several challenges. Firstly, a generated image may not have a suitable region for adding text, resulting in an overlay of text on visual elements. Secondly, even with a plausible location, the rendered text may lack consistency with the visual elements presented in the image, compromising overall coherence and professionalism." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 194, + 297, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 194, + 297, + 314 + ], + "spans": [ + { + "bbox": [ + 55, + 194, + 297, + 314 + ], + "type": "text", + "content": "An alternative research direction in visual text rendering, as suggested by [5, 6], focuses on learning the layout of text regions from textual prompts in advance. Then, this learned layout serves as a condition to guide text-to-image models in generating text within designated regions of the image. However, the dependence on predefined text regions might constrain the creative breadth of the generated images. Moreover, these predetermined text regions may not always adhere to natural design principles, potentially leading to visually unattractive or conceptually incoherent outputs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 316, + 296, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 296, + 423 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 296, + 423 + ], + "type": "text", + "content": "To address the aforementioned issues, we propose Design-Diffusion, an end-to-end diffusion-based framework specifically developed for the novel task of generating design images from text. The holistic learning approach presents multiple benefits: (1) it eliminates the need to predetermine text regions in the generative images, thereby preserving the creative freedom of the generative models; (2) it enables the smooth incorporation of generated text into images, yielding cohesive designs that accurately reflect input prompts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 425, + 297, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 425, + 297, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 425, + 297, + 652 + ], + "type": "text", + "content": "In our framework, we employ three essential techniques when fine-tuning text-to-image diffusion models: a) Recognizing that a conventional CLIP text encoder might overlook the specific textual content designated for rendering in the generated image, we propose a character-level decomposition of words. This approach provides the CLIP text encoder hints to render each character in the image precisely. b) To encourage the model to pay more attention to newly introduced character embeddings, we propose a character localization loss. This loss function compels each character embedding to concentrate on its respective area within the image, ensuring an accurate visual representation of each character. c) We introduce a new training strategy called Self-Play Direct Preference Optimization (SP-DPO) for fine-tuning the model to enhance its capability of generating accurate and high-fidelity text. SP-DPO is based on the hypothesis that ground truth data are typically preferred by humans over model-generated samples. Based on this, we fine-tune the model to align with these human preferences." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": "Extensive experiments demonstrate the superior capabilities of DesignDiffusion for design image generation. It generates creative design images with prompts, as shown in Fig. 1. Quantitative and qualitative analysis shows that our approach significantly surpasses current state-of-the-art" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "type": "text", + "content": "text-to-image and visual text rendering models in terms of both image quality and text accuracy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 326, + 97, + 552, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 97, + 552, + 108 + ], + "spans": [ + { + "bbox": [ + 326, + 97, + 552, + 108 + ], + "type": "text", + "content": "In summary, our contributions are presented as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 109, + 555, + 252 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 314, + 109, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 109, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 314, + 109, + 555, + 180 + ], + "type": "text", + "content": "- We propose DesignDiffusion, an end-to-end, diffusion-based framework for text-to-design image generation, which enables the simultaneous generation of image and visual text elements, eliminating the necessity for predefined text regions or traditional two-stage separated text and image creation process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 181, + 555, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 181, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 181, + 555, + 216 + ], + "type": "text", + "content": "- We explore prompt enhancement for CLIP text encoding along with a character localization loss, to improve the accuracy of text placement and the fidelity of text rendering." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 216, + 553, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 216, + 553, + 252 + ], + "spans": [ + { + "bbox": [ + 313, + 216, + 553, + 252 + ], + "type": "text", + "content": "- By adopting an SP-DPO mechanism, the generative model is further fine-tuned, achieving remarkable improvements in visual text accuracy and overall image quality." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 262, + 400, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 262, + 400, + 275 + ], + "spans": [ + { + "bbox": [ + 314, + 262, + 400, + 275 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 282, + 556, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 282, + 556, + 450 + ], + "spans": [ + { + "bbox": [ + 313, + 282, + 556, + 450 + ], + "type": "text", + "content": "Visual Text Rendering. Despite the remarkable success of existing diffusion models [37, 38, 40] in text-to-image generation, visual text rendering remains a challenging task. Recently, researchers have recognized this issue and proposed several approaches to address it, such as GlyphDraw [29], DiffUTE [4], GlyphControl [45], AnyText [41], TextDiffuser series [5, 6], and [26]. While these efforts have improved text rendering accuracy, it is worth noting that these models obtain limited image quality due to the need of pre-giving text rendering areas during the generation process or inpainting text into a well-generated image. Separating text and visual content generation away seriously limits the overall quality of generated images with visual text rendered, which is incompatible with the goal of design image generation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 450, + 556, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 556, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 556, + 700 + ], + "type": "text", + "content": "Compositional Image Generation. To improve the ability of text-to-image models to create complex compositions, researchers have integrated new components into diffusion models, enabling the generation of images with multiple features. Examples include T2I-Adapter [30] and ControlNet [47], which incorporate semantic details like layout and pose to influence the structure of images [48]. In a similar vein, GLIGEN [21] utilizes adapters with diffusion models to achieve image generation that is conditioned on specific spatial arrangements. However, these methods cannot generate images directly from prompts and require substantial human effort to define the image layout. On the other hand, some studies have investigated methods that do not require additional training to prompt diffusion models to create images based on spatial conditions during the inference phase. Recent advancements [22, 32, 44] have seen large language models aiding diffusion models in generating images with intricate or predefined layouts. Yet, these approaches often fall short in generating design-centric images that seamlessly integrate both textual and visual components in a well-organized manner." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 701, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 556, + 714 + ], + "type": "text", + "content": "Aligning Diffusion Models. Replicating the success of re" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20907" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 553, + 317 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 553, + 317 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 553, + 317 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 553, + 317 + ], + "type": "image", + "image_path": "97c747f56b36cdd7f24f96da08ff9ce0ccbe97bfe5c6259e8163afc9ca04f7cf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 78, + 319, + 347, + 331 + ], + "lines": [ + { + "bbox": [ + 78, + 319, + 347, + 331 + ], + "spans": [ + { + "bbox": [ + 78, + 319, + 347, + 331 + ], + "type": "text", + "content": "(a) Fine-tuning with prompt enhancement and character localization loss" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 391, + 319, + 539, + 331 + ], + "lines": [ + { + "bbox": [ + 391, + 319, + 539, + 331 + ], + "spans": [ + { + "bbox": [ + 391, + 319, + 539, + 331 + ], + "type": "text", + "content": "(b) Fine-tuning with self-play DPO loss" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 339, + 555, + 384 + ], + "lines": [ + { + "bbox": [ + 54, + 339, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 54, + 339, + 555, + 384 + ], + "type": "text", + "content": "Figure 2. Overview of the DesignDiffusion framework. DesignDiffusion is based on enhanced text prompts, with trainable CLIP text encoder and UNet, and does not require additional complex conditions (glyphs, positions). Character localization loss is added as extra supervision at cross-attention maps to force the UNet to attend more to the visual character regions. To further improve the quality of visual text generation, we incorporate a self-play DPO strategy into the fine-tuning process. Diffusion denoise loss is omitted here." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 395, + 298, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 395, + 298, + 551 + ], + "spans": [ + { + "bbox": [ + 54, + 395, + 298, + 551 + ], + "type": "text", + "content": "inforcement learning in large language models [31, 35] to text-to-image diffusion models remains a significant challenge. Recent works have proposed various methods to address this problem. For example, EMU [7] identifies that a few high-quality samples are crucial when fine-tuning the model to generate visually appealing images. DPOK [12] and DDPO [3] use RL-based approaches to maximize rewards on a limited vocabulary set, performing well when the number of train/test prompts is small. Another work DiffusionDPO [42] applies DPO based on a human-annotated preference dataset. Our DesignDiffusion differs by applying a self-play DPO strategy, which does not require human annotation and lacks of exploration in design image generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 562, + 153, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 153, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 153, + 574 + ], + "type": "text", + "content": "3. DesignDiffusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 582, + 298, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 582, + 298, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 582, + 298, + 714 + ], + "type": "text", + "content": "The generative community has witnessed the strong generative capability of diffusion models [9, 16, 34, 38, 48]. However, generating design images remains a great challenge, particularly in the context of exquisite layout and text rendering. Previous approaches [5, 6] in a related task (visual text rendering) attempt to inpaint text after generating an image, or to plan text regions using large language models such as Vicuna [49] and GPT [1] before generating an image. We argue that they do not consider the integration of text and image content. Note that, the text and image contexts in design images are often intertwined and inseparable, such" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 395, + 544, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 395, + 544, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 395, + 544, + 407 + ], + "type": "text", + "content": "that they are incompatible with design image generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 408, + 556, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 408, + 556, + 564 + ], + "spans": [ + { + "bbox": [ + 313, + 408, + 556, + 564 + ], + "type": "text", + "content": "In contrast, we introduce a straightforward, one-stage approach for text-to-design image generation, relying solely on the user prompt. It is based on an aesthetic model, i.e., Stable Diffusion XL (SDXL) model [34], incorporating three core components that enable the successful generation of text-rich design images. An overview of the DesignDiffusion framework is provided in Fig. 2. The DesignDiffusion training involves a two-stage fine-tuning strategy. In the first stage, we introduce prompt enhancement and character localization loss into the framework to generate high-quality images with accurate text. In the second stage, we propose SP-DPO to further improve the text rendering accuracy. These components are detailed in the following subsections." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 574, + 555, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 555, + 587 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 555, + 587 + ], + "type": "text", + "content": "3.1. Prompt Enhancement for CLIP Text Encoding" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 592, + 556, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 592, + 556, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 592, + 556, + 700 + ], + "type": "text", + "content": "Currently, available text-to-image diffusion models struggle to generate text-rich design images based solely on an input text prompt. This challenge arises from two issues: 1) Visually rendered text must be letter-by-letter correct, however, during tokenization, most words are tokenized as a single token, ignoring each letter within the word thus complicating the learning of individual letters; 2) Visual text in images is often diverse in style, size, and layout, increasing the complexity of visual text modeling." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "content": "To address the first issue, we introduce a novel approach" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": 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"type": "text", + "content": " by: min " + }, + { + "bbox": [ + 65, + 99, + 417, + 209 + ], + "type": "inline_equation", + "content": "\\sum_{i = 0}^{n}(\\log \\sigma (-\\beta T\\omega (\\lambda_t))(\\| \\epsilon_i^w -\\epsilon_\\theta (\\mathbf{x}_{i,t}^w,\\mathbf{y}_i,t_i)\\| _2^2 -" + }, + { + "bbox": [ + 65, + 99, + 417, + 209 + ], + "type": "inline_equation", + "content": "\\| \\epsilon_i^w -\\epsilon_{\\mathrm{ref}}(\\mathbf{x}_{i,t}^w,\\mathbf{y}_i,t_i)\\| _2^2 -(\\| \\epsilon_i^l -\\epsilon_\\theta (\\mathbf{x}_{i,t}^l,\\mathbf{y}_i,t_i)\\| _2^2 -\\| \\epsilon_i^l -\\epsilon_{\\mathrm{ref}}(\\mathbf{x}_{i,t}^l,\\mathbf{y}_i,t_i)\\| _2^2)))" + }, + { + "bbox": [ + 65, + 99, + 417, + 209 + ], + "type": "text", + "content": " end for return " + }, + { + "bbox": [ + 65, + 99, + 417, + 209 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 54, + 231, + 297, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 231, + 297, + 386 + ], + "spans": [ + { + "bbox": [ + 54, + 231, + 297, + 386 + ], + "type": "text", + "content": "by embedding each letter from prompts directly into CLIP text encoders within latent diffusion models [34, 38]. Specifically, the input prompt of the CLIP text encoders is enhanced by appending an extra text description to the original prompt. The template for the text description is \"Rendered characters: ...
  • MethodFID↓Text Precision↑Text Recall↑Text F-score↑Text Accuracy↑SDXL [34]45.100.5170.4610.4880.241SD3 [11]45.900.7540.6750.7120.415FLUX [19]35.280.7640.6980.7290.442DeepFloyd-IF [8]52.050.6070.5340.5680.290GlyphControl [46]60.070.4620.3520.4000.218Textdiffuser [5]55.830.8060.7060.7520.478Textdiffuser-2 [6]63.920.8660.7920.8270.583AnyText [41]64.690.4400.3780.4070.230DesignDiffusion19.870.8880.8370.8620.631", + "image_path": "0632ae2d93ad90d9cbba7887b0b43629c1803fbe650455af93ef13eb9d687f5b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 61, + 223, + 552, + 285 + ], + "blocks": [ + { + "bbox": [ + 72, + 213, + 537, + 223 + ], + "lines": [ + { + "bbox": [ + 72, + 213, + 537, + 223 + ], + "spans": [ + { + "bbox": [ + 72, + 213, + 537, + 223 + ], + "type": "text", + "content": "Table 2. Results of a user study comparing our method with previous approaches based on four aspects of text and image quality." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 223, + 552, + 285 + ], + "lines": [ + { + "bbox": [ + 61, + 223, + 552, + 285 + ], + "spans": [ + { + "bbox": [ + 61, + 223, + 552, + 285 + ], + "type": "table", + "html": "
    MethodImage Aesthetic↑Text Quality ↑Layout Aesthetics↑Text-Image Matching↑
    SDXL [34]0.430.110.180.28
    Textdiffuser-2 [6]0.080.340.220.14
    AnyText [41]0.090.030.070.06
    DesignDiffusion0.400.510.540.52
    ", + "image_path": "204ae8b3cd37596b488947466fca86f0e4161e1056e0652340976bebb42bb069.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 297, + 295, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 297, + 295, + 321 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 295, + 321 + ], + "type": "text", + "content": "the image and text metrics indicates that DesignDiffusion establishes a new baseline in design image generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 325, + 297, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 325, + 297, + 553 + ], + "spans": [ + { + "bbox": [ + 54, + 325, + 297, + 553 + ], + "type": "text", + "content": "Qualitative Results. We compare our method with state-of-the-art text-to-image models, i.e., SDXL [34], DALLE-3 [2], Ideogram [17], and visual text rendering models, i.e., Textdiffuser-2 [6], AnyText [41], as shown in Fig. 3. We observe that although state-of-the-art text-to-image models (SDXL, DALLE-3, Ideogram) can generate visually compelling images, they still struggle to generate accurate visual text. As for visual text rendering methods, we figure out that they generate visual text while brushing out the image content or reducing the aesthetics of the image seriously. It may be because that Textdiffuser-2 [6], AnyText [41] both rely on the text layout planning or strong text position fitting, leading to overfitting on visual text and overlooking other visual contents. Over-strong limitation of visual text area or other information limits the creativity of generating visual content. Throughout the comparisons, design images generated by our DesignDiffusion are more accurate than those from state-of-the-art text-to-image models and more elegant than those generated from visual text rendering models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "text", + "content": "User Studies. We randomly generate 20 samples without any cherry pick compared with three methods, i.e., SDXL [34], Textdiffuser-2 [6], and AnyText [41]. The participants were asked four questions about various aspects of image and text evaluation, in terms of image aesthetic, visual text quality, layout aesthetics, and text-image matching. We collect about 20 results from participants and report the preference ratio of the four metrics in Tab. 2. From the aspects of text quality, text layout aesthetic, and text-image matching, our DesignDiffusion significantly outperforms the competitors. It obtains comparable, slightly worse than SDXL [34] in evaluating image aesthetic, i.e., " + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "text", + "content": " v.s. " + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "inline_equation", + "content": "43\\%" + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "text", + "content": ". It may be because adapting SDXL for the design image generation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 297, + 426, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 297, + 426, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 297, + 426, + 308 + ], + "type": "text", + "content": "task loses a bit of aesthetic." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 309, + 556, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 309, + 556, + 406 + ], + "spans": [ + { + "bbox": [ + 313, + 309, + 556, + 406 + ], + "type": "text", + "content": "Automatic Layout Planning. DesignDiffusion is a one-stage method without any layout planning module. We visualize examples compared with layout-dependent methods [5, 6] in Fig. 4. Samples from others often have an oversized font or dull layout design, while our DesignDiffusion generates images with curved, colorful, and diverse text. The results show that our DesignDiffusion has a strong automatic, flexible, and reasonable layout planning capability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 416, + 416, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 416, + 416, + 428 + ], + "spans": [ + { + "bbox": [ + 313, + 416, + 416, + 428 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 435, + 556, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 435, + 556, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 435, + 556, + 530 + ], + "type": "text", + "content": "To assess the effectiveness of the proposed components within our framework, we conduct ablation studies. We explore various configurations, with the baseline being the original SDXL model. We denote fine-tuning on our dataset as \"FT\", the utilization of prompt enhancement, " + }, + { + "bbox": [ + 313, + 435, + 556, + 530 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{char}" + }, + { + "bbox": [ + 313, + 435, + 556, + 530 + ], + "type": "text", + "content": ", and self-play DPO as \"PE\", \"Lchar\" and \"SP-DPO\", respectively. The ablation results are summarized in Tab. 3, revealing the following notable insights." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 532, + 556, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 532, + 556, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 532, + 556, + 604 + ], + "type": "text", + "content": "Fine-tuning enhances the quality of design image generation: Fine-tuning SDXL with design images results in a significant improvement in FID. Despite this enhancement in image quality, achieving satisfactory accuracy in rendered text remains a challenge for existing diffusion models, even with extensive fine-tuning on large-scale datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 605, + 556, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 688 + ], + "type": "text", + "content": "Effect of prompt enhancement: Our investigation highlights limitations of current Byte Pair Encoding (BPE) tokenization, particularly in providing precise character-level cues for the visual text rendering task. Incorporating prompt enhancement leads to a significant improvement across various metrics, notably enhancing visual text accuracy because of the introduced character-level information." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "Localized attention through " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{char}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": ": By utilizing character segmentation masks to guide the cross-attention maps within" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20912" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 92, + 553, + 165 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 92 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 92 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 92 + ], + "type": "text", + "content": "Table 3. Ablation studies of the proposed framework. Bold and underline denotes the first and second best performance. \"FT\" and \"PE\" represent whether to apply fine-tuning and prompt enhancement, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 92, + 553, + 165 + ], + "lines": [ + { + "bbox": [ + 55, + 92, + 553, + 165 + ], + "spans": [ + { + "bbox": [ + 55, + 92, + 553, + 165 + ], + "type": "table", + "html": "
    FTPELcharSP-DPOFID↓Text Precision↑Text Recall↑Text F-score↑Text Accuracy↑
    XXXX45.100.5170.4610.4880.241
    ✓XXX22.730.7150.6780.6960.388
    ✓✓XX19.890.8620.7990.8290.572
    ✓✓✓X19.290.8810.8310.8550.616
    ✓✓✓✓19.870.8880.8370.8620.631
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Upon training, our DesignDiffusion has demonstrated the ability to generate flexible and well-organized text layouts effectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 498, + 297, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 297, + 559 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 297, + 559 + ], + "type": "text", + "content": "the UNet architecture, our " + }, + { + "bbox": [ + 55, + 498, + 297, + 559 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{char}" + }, + { + "bbox": [ + 55, + 498, + 297, + 559 + ], + "type": "text", + "content": " loss facilitates focused attention on text regions. With " + }, + { + "bbox": [ + 55, + 498, + 297, + 559 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{char}" + }, + { + "bbox": [ + 55, + 498, + 297, + 559 + ], + "type": "text", + "content": ", we observe a further enhancement in text precision, recall, F-score, and accuracy, emphasizing the effectiveness of localizing cross-attention maps using character segmentation masks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 570, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 297, + 715 + ], + "type": "text", + "content": "Enhanced visual text accuracy with SP-DPO: Subsequent to fine-tuning, we integrate SP-DPO to further improve the generation quality. SP-DPO significantly enhances text quality across all text metrics. Regarding the slight decline in the FID score, this can be attributed to the specific implementation of SP-DPO, which relies heavily on the selection of winning and losing data. Currently, the winning-losing pairs are determined based on the text accuracy. If we incorporate image quality into the criteria for constructing the losing data, we anticipate that the FID score could improve further. Notably, our current approach does not visually compromise image quality while enhancing text quality." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 497, + 466, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 497, + 466, + 510 + ], + "spans": [ + { + "bbox": [ + 314, + 497, + 466, + 510 + ], + "type": "text", + "content": "5. Discussion and Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 522, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 556, + 713 + ], + "type": "text", + "content": "In this paper, we introduce DesignDiffusion, a diffusion-based fine-tuning framework designed for synthesizing design images from textual descriptions. Unlike previous approaches that handle visual and textual elements independently, potentially limiting creativity and leading to style or color inconsistencies in style or color harmony, DesignDiffusion offers an end-to-end, one-stage diffusion-based solution. We explore including a distinctive character embedding and a character localization loss for enhancing visual text learning. Additionally, we employ an SP-DPO fine-tuning strategy to further improve the generation quality. Our extensive experiments demonstrate the effectiveness and robustness of DesignDiffusion in addressing the complexities of design image generation. We anticipate that our research will stimulate further exploration in design image generation, fostering innovation and advancement in this field." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20913" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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Judging llm-as-a-judge with mt-bench and chatbot arena, 2023. 3" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20915" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_content_list.json b/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1f2eb97f8a49b6482e983b383e3279c24ea8059d --- /dev/null +++ b/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_content_list.json @@ -0,0 +1,1587 @@ +[ + { + "type": "text", + "text": "Detail-Preserving Latent Diffusion for Stable Shadow Removal", + "text_level": 1, + "bbox": [ + 181, + 130, + 815, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiamin Xu $^{1}$ , Yuxin Zheng $^{1}$ , Zelong Li $^{1}$ , Chi Wang $^{1}$ , Renshu Gu $^{1}$ , Weiwei Xu $^{2}$ , Gang Xu $^{1*}$ $^{1}$ Hangzhou Dianzi University $^{2}$ Zhejiang University", + "bbox": [ + 145, + 179, + 854, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "superxjm@yeah.net, yuxin6@hdu.edu.cn, jokerli@hdu.edu.cn, wangchi1995@zju.edu.cn, renshugu@hdu.edu.cn, xww@cad.zju.edu.cn, gxu@hdu.edu.cn", + "bbox": [ + 138, + 219, + 852, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 286, + 326, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Achieving high-quality shadow removal with strong generalizability is challenging in scenes with complex global illumination. Due to the limited diversity in shadow removal datasets, current methods are prone to overfitting training data, often leading to reduced performance on unseen cases. To address this, we leverage the rich visual priors of a pre-trained Stable Diffusion (SD) model and propose a two-stage fine-tuning pipeline to adapt the SD model for stable and efficient shadow removal. In the first stage, we fix the VAE and fine-tune the denoiser in latent space, which yields substantial shadow removal but may lose some high-frequency details. To resolve this, we introduce a second stage, called the detail injection stage. This stage selectively extracts features from the VAE encoder to modulate the decoder, injecting fine details into the final results. Experimental results show that our method outperforms state-of-the-art shadow removal techniques. The cross-dataset evaluation further demonstrates that our method generalizes effectively to unseen data, enhancing the applicability of shadow removal methods.", + "bbox": [ + 88, + 319, + 485, + 621 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 652, + 220, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shadows are natural phenomena that occur when an obstacle blocks global light transport. They provide crucial cues for interpreting the three-dimensional structure of objects and scenes [44]. However, shadows can also hinder computer vision tasks, such as object segmentation [8], tracking [32], and intrinsic decomposition [16, 17, 25, 43]. In recent years, deep-learning-based methods for shadow removal [4, 5, 24, 40] have shown significant advancements by learning pixel-wise mappings between shadowed images and their corresponding ground-truth shadow-free versions in a fully supervised manner. However, such approaches often risk overfitting the limited training datasets [14, 28, 35], leading to inadequate generalization.", + "bbox": [ + 89, + 678, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/456ed4cc2a0bb4fd5466b07b9674192bc2f4ea2fe19cbb6924ae8f78cfc2faeb.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 516, + 285, + 702, + 392 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/57f04bcb6d77ca5e06ca5b955f836e2a6f38699cb9fb13b5691cb227f6548d97.jpg", + "image_caption": [ + "OmniSR [Xu et al. 2024]" + ], + "image_footnote": [], + "bbox": [ + 709, + 285, + 895, + 392 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/23111430c5f7f09e99350d8d044340267d7311be7ca33433f062f10ea2558541.jpg", + "image_caption": [ + "Ours (Stage I)" + ], + "image_footnote": [], + "bbox": [ + 514, + 405, + 707, + 512 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e1717ceeddbeaebd5fc61b6dea95957a22daa248e5b8e127b834fbc26a9f955a.jpg", + "image_caption": [ + "Ours (Stage II)", + "Figure 1. Top: For complex shadows in indoor scenes, current methods struggle to completely remove shadows, such as those behind the eagle sculpture. Bottom: Our method effectively removes the shadows, and with our second stage, the details from the original input, such as the wooden texture shown in the cropped image, are preserved." + ], + "image_footnote": [], + "bbox": [ + 710, + 405, + 903, + 512 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Drawing inspiration from recent advancements in zero-shot dense prediction [12, 42], we leverage the robust and comprehensive visual priors of the pre-trained Stable Diffusion (SD) model [29], which has been trained on billions of images, to enhance the generalization capability of shadow removal. However, developing a fine-tuning strategy that effectively removes shadows while preserving clear details in both shadowed and non-shadowed areas is not trivial. Unlike low-frequency depth and normal prediction tasks [12, 42], applying the SD model to shadow removal can result in detail loss and misalignment between the conditional image and the shadow-free output (Fig. 1). It is because the SD model, which consists of a Variational Autoencoder (VAE) and a Latent Diffusion Model (LDM), is designed for text-to-image generation and can lead to lossy compression during the mapping from pixel space", + "bbox": [ + 511, + 659, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 109, + 887, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7592", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\n(W \\times H \\times 3) \\text {t o} (\\frac {W}{8} \\times \\frac {H}{8} \\times 4).\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 89, + 383, + 108 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve stable and detail-preserving shadow removal using the pre-trained SD priors, we introduce a two-stage pipeline: 1) eliminating shadows in latent space by fixing the pre-trained VAE and fine-tuning the LDM and 2) injecting shadow-aware multi-resolution details from the original input into the VAE decoding process.", + "bbox": [ + 89, + 108, + 480, + 199 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the first stage, our method retains the pre-trained VAE and fine-tunes the LDM by conditioning it on the latent features of the input shadow image. We do not fine-tune the VAE, as it effectively handles shadow-free images despite not being specifically trained for this purpose, and the scale of our shadow-free images is limited. Our findings indicate that the latent space from the VAE, combined with the generative priors from the LDM, enhances shadow removal tasks, particularly when annotated training data is scarce. By operating in a low-resolution latent space rather than high-resolution pixel space, our method performs global self-attention with acceptable memory consumption, capturing more global contextual information compared to convolution and window-based self-attention [21].", + "bbox": [ + 89, + 200, + 482, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The fine-tuned SD model in the first stage produces visually appealing results, but it may lose some local details. To further enhance the quality of shadow removal, we propose a second stage for injecting shadow-free details. In this stage, we introduce a Detail Injection (DI) module that enhances the decoded latent features from the pre-trained VAE decoder by incorporating fine details from the input images. The VAE parameters are kept fixed. To prevent shadows from being reintroduced as \"details\", our DI module is equipped with shadow perception capabilities. Inspired by the observation that the shadow mask in the current shadow removal dataset is derived from the binary difference between shadowed and shadow-free images, we utilize concatenated features from the input shadow images and the coarse, shadow-free images decoded from the LDM output as cues for shadow-free detail injection. By combining features from both image types, the DI module can implicitly detect shadows and learn to inject shadow-free details into the VAE decoders.", + "bbox": [ + 89, + 412, + 482, + 699 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Note that Refusion [23] also performs latent-space diffusion for shadow removal. It captures input image information in the decoder [23] using a U-Net architecture specifically designed for large image shadow removal. However, the primary difference lies in the network design and finetuning strategy. Our method is designed to leverage the high-quality priors of the pre-trained VAE and LDM in the SD model, resulting in superior shadow removal quality. Our method can also handle high-resolution images (e.g., $1920 \\times 1440$ in the WRSD dataset [35]), providing greater shadow removal efficiency compared to patch-based diffusion methods [22].", + "bbox": [ + 89, + 702, + 482, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, our contributions can be summarized as follows.", + "bbox": [ + 109, + 885, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a two-stage fine-tuning pipeline to transform a pre-trained Stable Diffusion model into an image-conditional shadow-free image generator. This approach enables robust, high-resolution shadow removal without an input shadow mask.", + "- We introduce a shadow-aware detail injection module that utilizes the VAE encoder features to modulate the pre-trained VAE decoders, selectively aligning per-pixel details from the input image with those in the output shadow-free image.", + "- Extensive experimental results on public datasets demonstrate that the proposed method significantly outperforms state-of-the-art shadow removal methods. Additionally, we show that our method exhibits better generalizability by training on one dataset and testing on another." + ], + "bbox": [ + 513, + 90, + 903, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 358, + 653, + 373 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deep Shadow Removal", + "text_level": 1, + "bbox": [ + 513, + 392, + 725, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep learning methods have significantly advanced shadow removal, enabling end-to-end learning of a mapping from input images to corresponding shadow-free images, with or without the aid of shadow masks. For example, DesshadowNet [28] combines multi-level features to predict a shadow matte, thereby enhancing the efficiency of shadow removal. Hu et al. [1, 10] utilize direction-aware spatial context for precise shadow detection and elimination. Fu et al. [3] formulate the shadow removal task as a multiple exposure image fusion problem. BMNet [48] introduces a bijective mapping that integrates shadow removal with shadow generation, improving overall performance in shadow removal tasks.", + "bbox": [ + 511, + 422, + 906, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "More recently, ShadowFormer [4] presents a Swin-transformer-based shadow removal network that harnesses multi-scale attention to exploit contextual relationships between shadowed and non-shadowed regions. Meanwhile, DMTN [18] proposes a decoupled multi-task network that learns decomposed features specifically tailored for shadow removal. ShadowRefiner [2] introduces a mask-free model that integrates spatial and frequency domain representations for image shadow removal, achieving top results in the Perceptual Track of the NTIRE 2024 Image Shadow Removal Challenge [36]. Xu et al. [41] propose a path-tracing pipeline to generate shadow removal data that considers indirect illumination in indoor scenes. They also introduce a semantics and geometry-aware network for efficient mask-free shadow removal. HomoFormer [40] designs random shuffle and inverse shuffle operations to create a homogenized appearance of shadows, allowing for effective processing by local self-attention layers.", + "bbox": [ + 511, + 628, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7593", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/272152aeda406124279e9a5dd4c7f77ebe30218aff1356fd56e34594acc2ace9.jpg", + "image_caption": [ + "Figure 2. Our proposed network. We propose a two-stage shadow removal network based on Stable Diffusion (SD). (1) In the first stage, as shown in the bottom half, we fine-tune the pre-trained UNet in SD within the latent space defined by SD's pre-trained VAE $(\\mathcal{E}$ and $\\mathcal{D})$ We found that the pre-trained latent space can effectively represent shadow-free images. (2) In the second stage, as shown in the top half, we modulate the VAE decoder $\\mathcal{D}$ by selectively adding features from the VAE encoder $\\mathcal{E}$ using a Detail Injection Model (DIM). The model consists of multiple RRDB layers, which inject shadow-free texture details into the decoder features. With these two stages, our proposed network can generate high-quality, shadow-free images that preserve fine details." + ], + "image_footnote": [], + "bbox": [ + 94, + 92, + 903, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Diffusion-based Shadow Removal", + "text_level": 1, + "bbox": [ + 89, + 477, + 387, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models [9, 34] are generative models that learn data distributions through Gaussian noise blurring and reverse denoising. Initially developed for image generation, these models have become prominent in applications including image super-resolution [31, 38], depth/normal prediction [12, 42], and shadow removal [23]. In the context of shadow removal, ShadowDiffusion [5] introduces a diffusion model that generates both a shadow-free image and a refined shadow mask, using shadow degradation as a prior and employing an unrolling diffusion process to eliminate shadows. DeS3 [11] enhances ShadowDiffusion by incorporating an adaptive attention mechanism and ViT similarity loss, removing the dependence on shadow masks. Guo et al.[6] propose a diffusion-based unsupervised shadow removal pipeline that utilizes a boundary-aware divide and conquer strategy. Diff-Shadow[22] employs a globally guided diffusion model pipeline that focuses on the patch and global information, enabling shadow removal in images of arbitrary resolution. Liu et al. [20] first separate reflectance and illumination, then use a diffusion model to correct degraded lighting in shadowed areas, followed by the progressive restoration of texture details through an illumination-guided texture restoration module.", + "bbox": [ + 91, + 503, + 483, + 851 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There are also methods that utilize a latent space to enhance diffusion-based shadow removal. Refusion [6] presents a U-Net-based latent diffusion model that utilizes", + "bbox": [ + 89, + 854, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mean-reverting stochastic differential equations for high-resolution image restoration tasks. The model performs image diffusion in a low-resolution latent space while preserving details through hidden-connections. However, being end-to-end trained on the shadow-removal dataset, it suffers from limited generalizability. Mei et al. [24] conduct diffusion-based shadow removal with a shadow mask at both the general and instance levels. They improve the diffusion process by conditioning on a learned latent feature space that captures the characteristics of shadow-free images and propose fusing noise features with the diffusion network to alleviate potential local optima.", + "bbox": [ + 511, + 478, + 906, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unlike existing diffusion-based methods, we introduce a two-stage fine-tuning strategy that fully utilizes the visual priors from the pre-trained Stable Diffusion (SD) model [29]. With our latent shadow removal and shadow-aware detail injection stages, our method demonstrates strong generalization capability while effectively preserving non-shadow details.", + "bbox": [ + 511, + 659, + 908, + 767 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 511, + 777, + 687, + 795 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 511, + 803, + 624, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a dataset of shadow and shadow-free image pairs $\\langle \\mathbf{x},\\mathbf{y}\\rangle \\in \\mathcal{X}$ , our goal is to train a network that can: 1. thoroughly eliminate shadows from the input image, and 2. preserve the content of all non-shadow areas. Although the first requirement focuses on the shadow (umbra) regions, the", + "bbox": [ + 511, + 824, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7594", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c7768cabf370df1b302b4bcc4f5831154a998a8ac496720a07f4c111ec781d54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 88, + 284, + 174 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/077714820d38fd91c2ebf31a9ce9a92fb427f1ae1ea7171e6ad29f6f2c48db76.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 88, + 472, + 174 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f7de41f68afaf984932f1634c969b96ceedd14741f5664a05aa8c1694e05a6d8.jpg", + "image_caption": [ + "Shadow image x", + "Shadow-free image y", + "Figure 3. Latent space in VAE. We apply the pre-trained encoding and decoding process on a shadow image $\\mathbf{x}$ or a shadow-free image $\\mathbf{y}$ . For a shadow-free image, this process does not introduce additional shadows, meaning the pre-trained latent space can also represent the shadow-free image. However, as shown in the zoomed-in view, some details, like text, may be lost in this process." + ], + "image_footnote": [], + "bbox": [ + 101, + 186, + 282, + 308 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3eed971872654ffc2402ef114305b92768ea57c29d745aec6f86c6e8233bbe55.jpg", + "image_caption": [ + "$\\mathcal{D}(\\mathcal{E}(\\mathbf{x}))$", + "$\\pmb{D}(\\pmb{\\mathcal{E}}(\\mathbf{y}))$" + ], + "image_footnote": [], + "bbox": [ + 292, + 186, + 473, + 308 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "second is more concerned with non-shadow areas. These two objectives can be contradictory, making it challenging to design a single network that effectively addresses both. Therefore, we propose a two-stage shadow removal framework to robustly eliminate various types of shadows across different scenarios (Fig. 2).", + "bbox": [ + 89, + 460, + 483, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the first stage, as shown at the bottom of Fig. 2, we perform shadow removal in latent space (Sec. 3.2). We condition the Stable Diffusion (SD) model [29] using the latent code of the input shadow image $\\mathbf{z}^{\\mathrm{x}}$ and fine-tune a pretrained SD model to generate the latent code of a shadow-free image $\\mathbf{z}_0^{\\mathbf{y}}$ . As shown in Fig. 1, this latent code can be decoded into a coarse image that effectively eliminates shadows, although some details may be lost.", + "bbox": [ + 89, + 551, + 483, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the second stage, as illustrated at the top of Fig. 2, we perform detail injection using the encoder $\\mathcal{E}$ and decoder $\\mathcal{D}$ within SD (Sec.3.3). We fix the pretrained encoder and decoder and employ a set of Detail Injection (DI) models to integrate shadow-free details into the decoder features. These details are derived from each encoder layer. After training on pairs of shadow and shadow-free images, the DI models learn to inject details from the input image that are free of shadows.", + "bbox": [ + 89, + 672, + 483, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Shadow Removal in Latent Space", + "text_level": 1, + "bbox": [ + 89, + 816, + 383, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Building on recent advancements in dense prediction tasks [7, 12, 42], we formulate the shadow removal task in the first stage as an image-conditioned annotation generation problem using SD. This approach conducts the dif", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "fusion process within a low-dimensional latent space generated by a pair of encoder and decoder $\\langle \\mathcal{E},\\mathcal{D}\\rangle$ , where $\\mathcal{E}(\\mathbf{x}) = \\mathbf{z}^{\\mathbf{x}}$ and $\\mathcal{D}(\\mathbf{z}^{\\mathbf{x}})\\approx \\mathbf{x}$", + "bbox": [ + 511, + 90, + 903, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared to the diffusion model [9], Stable Diffusion offers enhanced generation stability and training efficiency. However, given the limited number of shadow and shadow-free image pairs, we opt for a fine-tuning strategy rather than training a SD model from scratch. We directly utilize the pre-trained $\\mathcal{E}$ and $\\mathcal{D}$ in SD and focus on fine-tuning the denoiser U-Net, as we have found that the pre-trained $\\mathcal{E}$ and $\\mathcal{D}$ perform well for both shadow and non-shadow images, even though they were not specifically trained on shadow-free images (Fig. 3).", + "bbox": [ + 511, + 137, + 906, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fine-tuning Process. The fine-tuning for Stable Diffusion [9] relies on forward-noising and reverse-denoising processes that operate within the latent space. In the forward process, Gaussian noise is progressively added over time steps $t \\in [1,T]$ to the sample $\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}}$ , generating a noisy sample $\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}}$ :", + "bbox": [ + 511, + 316, + 906, + 407 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {\\mathrm {t}} ^ {\\mathbf {y}} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} ^ {\\mathbf {y}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 422, + 903, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon \\sim \\mathcal{N}(0,I)$ , $\\overline{\\alpha}_t\\coloneqq \\prod_{s = 1}^t (1 - \\beta_s)$ , and $\\beta_{1},\\beta_{2},\\ldots$ $\\beta_{T}$ defines the noise schedule over $T$ steps. In the reverse process, a U-Net [30] denoted as $f_{\\theta}$ takes the encoding features of the input image $\\mathbf{z}^{\\mathbf{x}}$ and the sample $\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}}$ as inputs, outputting a prediction of the clean sample $\\hat{\\mathbf{z}}^{\\mathbf{y}}$ :", + "bbox": [ + 511, + 453, + 905, + 531 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {z}} ^ {\\mathbf {y}} = f _ {\\theta} \\left(\\mathbf {z} _ {\\mathbf {t}} ^ {\\mathbf {y}}, \\mathbf {z} ^ {\\mathbf {x}}, t\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 642, + 545, + 903, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During fine-tuning, we randomly sample a time step $t \\in [1, T]$ and minimize the corresponding loss function $L_{t}$ :", + "bbox": [ + 513, + 579, + 905, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t} = \\left\\| \\mathbf {z} ^ {\\mathbf {y}} - f _ {\\theta} \\left(\\mathbf {z} _ {\\mathbf {t}} ^ {\\mathbf {y}}, \\mathbf {z} ^ {\\mathbf {x}}, t\\right) \\right\\| _ {2} ^ {2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 625, + 903, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{z}^{\\mathbf{y}}$ is the encoding features of the ground-truth shadow-free image.", + "bbox": [ + 511, + 656, + 905, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Denoising Process. During inference, we use DDIM [33], which implements an implicit probabilistic model that can significantly reduce the number of denoising steps while maintaining output quality. Formally, the denoising process from $\\mathbf{z}_{\\tau}^{\\mathbf{y}}$ to $\\mathbf{z}_{\\tau -1}^{\\mathbf{y}}$ is:", + "bbox": [ + 511, + 714, + 905, + 792 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {\\tau - 1} ^ {\\mathbf {y}} = \\sqrt {\\bar {\\alpha} _ {\\tau - 1}} \\hat {\\mathbf {z}} _ {\\tau} ^ {\\mathbf {y}} + \\operatorname {d i r e c t i o n} \\left(\\mathbf {z} _ {\\tau} ^ {\\mathbf {y}}\\right) + \\sigma_ {\\tau} \\epsilon_ {\\tau}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 806, + 903, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{z}}_{\\tau}^{\\mathbf{y}}$ is the predicted clean sample at the denoising step $\\tau$ , $\\text{direction}(\\mathbf{z}_{\\tau}^{\\mathbf{y}})$ represents the direction pointing to $\\mathbf{z}_{\\tau}^{\\mathbf{y}}$ . $\\tau \\in \\{\\tau_1, \\tau_2, \\dots, \\tau_S\\}$ is an increasing sub-sequence of the timestep set $[1, T]$ used for fast sampling.", + "bbox": [ + 511, + 839, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7595", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/14b35b49bd905aeac4717c1211d31cca8c6e33bd551639c06d58f8f628717878.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 101, + 87, + 285, + 189 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/eac43e3dd0323ce53b1d3e2de14ea4f1bebbed1da577a9588e73d7ca3f144651.jpg", + "image_caption": [ + "Ours (stage I)" + ], + "image_footnote": [], + "bbox": [ + 287, + 88, + 470, + 189 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5d31ab584636a13c790ff14b345ad76a1ae0d7254fea65923d261203fbe44270.jpg", + "image_caption": [ + "Ours (stage II)" + ], + "image_footnote": [], + "bbox": [ + 101, + 202, + 287, + 303 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7d40f72e781b96362e882dd62cc7ad2533d9f7efc14aada3e94f82950dee1629.jpg", + "image_caption": [ + "RRDB feature vis.", + "Figure 4. Some details in the input image, such as the textures on the floor, change during latent space diffusion in stage one. In stage two, our method preserves these high-quality details while effectively removing shadows. As shown in the bottom-left image, where we map the RRDB features to three dimensions using PCA, we observe that shadow areas have distinct features (in green), indicating that our detail injection model is shadow-aware." + ], + "image_footnote": [], + "bbox": [ + 289, + 202, + 470, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Shadow-aware Detail Injection", + "text_level": 1, + "bbox": [ + 89, + 458, + 364, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated in Fig. 4, while the output of the conditional Stable Diffusion is visually striking—especially in its ability to completely remove shadows—it often diverges from the ground truth, particularly in high-detail areas, such as the floor texture. We believe the primary reason for this is the loss of high-frequency information in the latent space. As shown in Fig. 3, directly decoding the encoded features $\\mathcal{D}(\\mathcal{E}(\\mathbf{x}))$ also results in a loss of detail.", + "bbox": [ + 89, + 481, + 483, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To eliminate shadows while preserving details, we introduce a shadow-aware detail injection step utilizing a set of DI models. Each model selectively extracts information from a specific intermediate layer of $\\mathcal{E}$ to modulate the corresponding intermediate layers of $\\mathcal{D}$ . Let $\\mathbf{e}_i$ and $\\mathbf{d}_i$ denote the encoder and decoder features for the $i$ -th intermediate layer. The DI model takes the concatenation of $\\mathbf{e}_i$ and $\\mathbf{d}_i$ as input, output a modulated feature $\\tilde{\\mathbf{d}}_i$ :", + "bbox": [ + 89, + 603, + 483, + 724 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {d} _ {0} = \\mathbf {z} _ {0} ^ {\\mathbf {y}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 737, + 482, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {d}} _ {i} = \\mathbf {d} _ {i} + \\operatorname {C o n v} (\\operatorname {R R D B} (\\operatorname {C o n v} (\\mathbf {d} _ {i}, \\mathbf {e} _ {n - i} (\\mathbf {z} ^ {\\mathbf {x}})), f _ {d} (\\mathbf {x}))),\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 758, + 473, + 775 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {d} _ {i} = \\mathcal {D} _ {i - 1} (\\tilde {\\mathbf {d}} _ {i - 1}), i \\in [ 1, 4 ], \\hat {\\mathbf {y}} = \\operatorname {C o n v} (\\tilde {\\mathbf {d}} _ {4})\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 779, + 397, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\mathrm{RRDB}(\\cdot)$ refers to the Residual-in-Residual Dense Block module [46], which consists of three Dense Blocks. $\\hat{\\mathbf{y}}$ is predicted shadow-free image. $f_{d}(\\mathbf{x})$ are features extracted using DINO v2 [26]. We concatenate the DINO features with $\\mathbf{e}_i$ and $\\mathbf{d}_i$ after passing through a convolutional layer to enhance the generalizability of the DI models.", + "bbox": [ + 89, + 809, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/77be29ebfe67a25de746db08b62cfc5a7d71c30babdfb7ca121219948a2a4ad4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodMean↑Variance↓
    Our stage one (ε-pred)29.660.239
    Our stage one (z0-pred)29.950.146
    Our stage two35.020.160
    DeS3 [11]31.331.075
    ", + "bbox": [ + 545, + 87, + 874, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Low variance. In the first stage, our method achieves reduced variance by using $\\mathbf{z}_0$ -prediction. In the second stage, our method improves PSNR while maintaining low variance, resulting in robust, high-quality shadow removal results.", + "bbox": [ + 511, + 178, + 906, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since $\\mathbf{e}_i$ and $\\mathbf{d}_i$ contain features from the input shadow image $\\mathbf{x}$ and the shadow-free latent code $\\mathbf{z}_0^{\\mathbf{y}}$ , respectively, our DI models can effectively identify shadow areas by utilizing both features as input. Although the latent codes may lose high-frequency details, they still provide valuable cues for shadow regions, which are primarily low-frequency. As illustrated in Fig. 4, where we visualize the features in the last layer of the RRDB module, we can observe that the shadow areas exhibit distinct feature responses. We present only the RRDB responses for $\\mathbf{d}_2$ . Please refer to the supplementary for additional results.", + "bbox": [ + 511, + 260, + 906, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Losses. To train the DI models, we minimize a total loss $\\mathcal{L}_{total}$ , which combines an L1 loss and a perceptual loss measured using the Learned Perceptual Image Patch Similarity (LPIPS) metric [45] between the output image $\\hat{\\mathbf{y}}$ and the ground-truth shadow-free image $\\mathbf{y}$ :", + "bbox": [ + 511, + 445, + 905, + 521 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\left\\| \\hat {\\mathbf {y}} - \\mathbf {y} \\right\\| _ {1} + \\left\\| \\operatorname {L P I P S} (\\hat {\\mathbf {y}}) - \\operatorname {L P I P S} (\\mathbf {y}) \\right\\| _ {2} ^ {2}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 531, + 905, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Implementation Details.", + "text_level": 1, + "bbox": [ + 511, + 558, + 735, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reducing variance. As shown in Eq. 3, in the LDM fin-tuning stage, we use $\\mathbf{z}_0$ -prediction rather than the standard $\\epsilon$ -prediction parameterization for the denoising model. This choice, as recommended by Lotus[7], helps reduce variance during stochastic LDM inference. We compare these two approaches on the $\\mathrm{ISTD + }$ [14] dataset by running inference on the test set with five different random seeds (1, 2, 3, 4, 5). We calculate the PSNR variance across the five outputs for each image and obtain the average variance. As shown in Table 1, using $\\mathbf{z}_0$ -prediction in our LDM fin-tuning stage yields higher PSNR and lower variance compared to $\\epsilon$ -prediction. Additionally, we assess the average variance of our final results after the detail injection stage, and Table 1 shows that our final results have significantly lower variance than DeS3 [11], another mask-free shadow removal method based on diffusion models. It indicates that our generative shadow removal method is highly robust to randomness, which is a critical factor for practical use.", + "bbox": [ + 511, + 580, + 906, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training details. Our model is trained on a GPU server with four GeForce RTX 4090 GPUs using PyTorch", + "bbox": [ + 511, + 869, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7596", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9bdc87c72b9f9cbad00a90543494d97eb17e7a98cbd46e06d8d4e4e126def7c8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodYearMask-freeISTD+ DatasetSRD DatasetINS DatasetWSRD+ Dataset
    PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
    AutoExposure [3]2021No29.450.86129.240.93827.910.95721.660.752
    Zhu et al. [49]2022No——32.050.965————
    BMNet [48]2022No33.980.97231.970.96527.900.95824.750.816
    ShadowFormer [4]2023No35.460.97132.900.95828.620.96325.440.820
    DMTN [18]2023No32.230.96633.770.96828.830.969——
    ShadowDiffusion [5]2023No34.630.96734.730.97029.120.966——
    HomoFormer [40]2024No35.720.97734.360.97728.980.965——
    InstanceShadow [24]2024No34.690.96831.610.95928.160.948——
    TBRNet [19]2023Yes31.910.96431.830.953————
    Refusion [23]2023Yes32.410.96131.600.94928.130.95822.320.738
    DeS3 [11]2024Yes31.390.95734.110.96827.890.947——
    OmniSR [41]2024Yes33.340.97032.870.96930.380.97326.070.835
    Ours—Yes35.190.97433.630.96830.560.97526.260.827
    ", + "bbox": [ + 96, + 88, + 901, + 319 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparisons on ISTD+, SRD, INS, and WSRD+ datasets. Best results are highlighted as 1st , 2nd and 3rd . Refer to the supplementary material for the MAE values in both shadowed and non-shadowed areas.", + "bbox": [ + 89, + 329, + 903, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2.0.1 [27] with CUDA 11.7. We employ the Adam optimizer [13] for training. In the first stage, the LDM is finetuned for 40 epochs on INS [41] and 200 and 300 epochs on $\\mathrm{ISTD + }$ [14, 37] and SRD [28], respectively. We utilize a constant learning rate of $3\\times 10^{-4}$ with a batch size 16. For the INS dataset, each batch consists of $512\\times 512$ patches, while for the other datasets, batches are composed of randomly cropped $480\\times 480$ patches.", + "bbox": [ + 88, + 383, + 480, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the second stage, we maintain the constant learning rate of $5 \\times 10^{-4}$ and batch size of 16. The batch shapes for each dataset are consistent with those in the first stage, and the number of epochs for training the detail injection models is 50 for INS and 300 and 200 for $\\mathrm{ISTD + }$ and SRD, respectively. For the DINO features [26], we resize the image to $\\frac{14W}{16} \\times \\frac{14H}{16}$ using bilinear interpolation, extract the DINO features, and apply a $1 \\times 1$ convolution layer to obtain a feature map of shape $256 \\times \\frac{W}{16} \\times \\frac{H}{16}$ . To reduce memory footprint, we only concatenate the DINO features with the first two layers of the VAE decoder. Additional details can be found in the supplementary.", + "bbox": [ + 88, + 507, + 482, + 690 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 707, + 222, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We conduct experiments on four shadow removal datasets: SRD [28], $\\mathrm{ISTD + }$ [14, 37], $\\mathrm{WSRD + }$ [35, 36], and INS [41]. The SRD dataset [28] includes 3,088 paired shadow and shadow-free images, divided into 2,680 for training and 408 for testing. The $\\mathrm{ISTD + }$ dataset [14, 37] provides 1,870 triplets of shadow images, shadow masks, and shadow-free images, with 1,330 used for training and 540 for testing. $\\mathrm{WSRD + }$ [35, 36] contains 1,000 pairs of shadow and non-shadow images captured under both spotlight and diffuse illumination. Since the test data is not open-sourced, we use its 100 validation images for test", + "bbox": [ + 88, + 734, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ing. Lastly, the INS dataset [41] comprises 30,000 synthetic training images under direct and indirect illumination, a synthetic test set of 2,000 images.", + "bbox": [ + 511, + 383, + 906, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. Following previous methods [3, 4, 15], we evaluated images with a resolution of $256 \\times 256$ . We report results using the Peak Signal-to-Noise Ratio (PSNR) and the Structure Similarity Index Measure (SSIM) [39], adopting the MATLAB evaluation codes as provided by Zhu et al. [49]. For the WSRD+ [35] dataset, we used its evaluation data and the evaluation code provided by the NTIRE 2024 Image Shadow Removal Challenge [36] for comparison.", + "bbox": [ + 511, + 446, + 906, + 584 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Comparisons", + "text_level": 1, + "bbox": [ + 511, + 590, + 653, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method to twelve state-of-the-art shadow removal techniques, evaluating both quantitatively and qualitatively. Among these, eight methods require a shadow mask as input: AutoExposure [3], Zhu et al. [49], BMNet [48], ShadowFormer [4], DMTN [18], ShadowDiffusion [5], and HomoFormer [40]. The remaining four methods—TBRNet [19], Refusion [23], Des3 [11], and OmniSR [41]—are mask-free, meaning they do not require a shadow mask as input. All comparisons use the original authors' implementations and hyperparameters, or the provided checkpoints or results, if available. For the INS dataset, we train these methods following the procedure in OmniSR [41].", + "bbox": [ + 511, + 613, + 903, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For methods that are not mask-free, we use the shadow masks provided by the dataset as the default input. Since SRD [28] does not provide masks, we use the shadow masks generated by DHAN [1], which computes shadow matting from shadow/shadow-free pairs and generates binary masks through thresholding. In the case of the INS dataset,", + "bbox": [ + 511, + 810, + 906, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7597", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2a8bf2be57878fb14441713c921c62c1276f72c3336a1c15404a6816495a5d77.jpg", + "image_caption": [ + "Figure 5. Comparisons with SOTA shadow removal methods on the ISTD+ and SRD datasets. The input mask, required by methods that are not mask-free, is shown in the top-left corner." + ], + "image_footnote": [], + "bbox": [ + 120, + 85, + 883, + 359 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/783f2c7acad6c86c8fc7ee4102fa673503fb7d55465cd720517565650873bf4b.jpg", + "image_caption": [ + "Figure 6. Comparisons with SOTA shadow removal methods in real scenes. We compare our method to OmniSR [41], HomoFormer [40], Refusion [23], and ShadowDiffusion [5], all trained on the INS dataset [41]. Results show that our approach achieves more comprehensive shadow removal, even in complex scenes." + ], + "image_footnote": [], + "bbox": [ + 119, + 415, + 883, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "its shadow masks are represented as 0-1 probability maps rather than binary masks. Since it is a synthetic dataset with highly accurate masks, we found that using them as input results in methods producing outputs nearly identical to the ground truth (with PSNR values exceeding 50). To address this, following OmniSR [41], we use FDRNet [47] to detect shadow masks and input the detected masks instead.", + "bbox": [ + 88, + 704, + 480, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 2, our method achieves the highest PSNR score on the INS dataset. On the $\\mathrm{ISTD + }$ dataset, our approach is the best mask-free method, performing only slightly below HomoFormer [40] and ShadowFormer [4], which use ground-truth shadow masks as input, and outperforming most other methods that also rely on ground-truth", + "bbox": [ + 88, + 810, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "shadow masks. As shown in the first two columns of Fig. 5, although without mask as input, our method is capable of thoroughly removing shadows, even with limited semantic context. We think it is because of leveraging the generative priors in our latent diffusion model.", + "bbox": [ + 511, + 704, + 906, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the SRD dataset, our method also delivers competitive results compared to methods that utilize masks provided by DHAN [1]. Among shadow-free methods, our performance is second only to DeS3. As illustrated in Fig. 5, our method produces visually appealing results with nearly complete shadow removal. We found that our method achieves better shadow removal quality than DeS3; however, in areas with highly detailed textures, such as sand", + "bbox": [ + 511, + 779, + 908, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7598", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a0c0c4e258572213548f188f2cfe5370b3ab838df15253111214dddf49a86607.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodISTD+→SRDSRD→ISTD+INS→WSRD+
    PSNRSSIMPSNRSSIMPSNRSSIM
    ShadowDiffusion24.260.89029.480.94719.400.825
    Refusion22.560.88627.310.92418.730.787
    DeS322.090.880————
    OmniSR25.860.91730.190.95120.030.825
    Ours26.230.92330.230.95320.110.828
    ", + "bbox": [ + 91, + 89, + 488, + 191 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and grass, the PSNR is lower than that of DeS3.", + "bbox": [ + 89, + 258, + 406, + 272 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On the INS dataset, our method achieves the highest PSNR and SSIM, as shown in Table 2. We also compare our method with others on real indoor scene images, all trained on the INS dataset. As illustrated in Fig. 6, our approach more effectively removes shadows from multiple light sources, such as those beneath the table and chair, as well as soft shadows behind the small planter and on the bookshelf in the background.", + "bbox": [ + 88, + 273, + 482, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further evaluated our method on high-resolution shadow removal using the WSRD+ [35] dataset, with images at $1920 \\times 1440$ resolution. The first stage requires no modification. We resize each image to $640 \\times 480$ for the LDM fine-tuning. In the second stage, we introduce a minor adjustment by adding one patch-partition layer and one patch-merging layer [21]. Additional details are provided in the supplementary materials. As shown in Table 2, our method outperforms others on the WSRD+ dataset, with more results available in the supplementary material. The relatively low PSNR scores for all methods on the WSRD+ dataset can be attributed to exposure differences between the input and ground-truth images.", + "bbox": [ + 89, + 397, + 482, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Cross-dataset evaluation.", + "text_level": 1, + "bbox": [ + 89, + 606, + 318, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the generalizability of our approach, we conduct a cross-dataset evaluation. Specifically, we train our model on the training set of one dataset and test it on the testing set of a different dataset. Typically, training and testing data within the same dataset share similar shadow patterns, backgrounds, or lighting conditions. This cross-dataset evaluation presents a more challenging test for shadow removal methods and provides a more stringent measure of generalizability. We use $A \\rightarrow B$ to denote training on dataset $A$ and testing on dataset $B$ . As shown in Table 3, our method achieves the best results on ISTD+→SRD, SRD→ISTD+, and INS→WSRD+. Here, we compare only with DeS3 [11] on ISTD+→SRD, as it provides checkpoints only for ISTD+ dataset. Its open-source code is a basic version that excludes certain components, including the VIT loss. For the INS→WSRD+ experiment, high-resolution images from the WSRD+ dataset are resized to $640 \\times 480$ for inference and evaluation. Qual-", + "bbox": [ + 89, + 628, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ebea66a25f97a48e58358d8ef15dd2eedaa1cbeb1fcc1b91af02d092d9d90a47.jpg", + "table_caption": [ + "Table 3. Cross-dataset evaluation. $\\mathrm{ISTD} + \\rightarrow$ SRD means training on the $\\mathrm{ISTD}+$ dataset and testing on the SRD dataset." + ], + "table_footnote": [], + "table_body": "
    DatasetISTD+ PSNR/SSIMSRD PSNR/SSIMINS PSNR/SSIM
    Full35.19/0.97433.63/0.96830.56/ 0.975
    W/o pre-train33.38/0.96732.46/0.96329.55/0.970
    Stage one29.95/0.84328.18/0.86828.78/0.924
    Stage one (w/o pre-train)28.12/0.82227.48/0.86126.92/0.909
    W/o DINO34.76/0.97133.04/0.96530.30/0.975
    ", + "bbox": [ + 517, + 89, + 903, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation studies. W/o pre-train: without pre-training. W/o DINO: without DINO in the detail injection model.", + "bbox": [ + 511, + 196, + 903, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "itative comparisons for this evaluation are provided in the supplementary material.", + "bbox": [ + 511, + 252, + 903, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation study.", + "text_level": 1, + "bbox": [ + 511, + 292, + 666, + 308 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To validate our model design, we conducted ablation studies on the use of the pretrained SD model, the two-stage pipeline, and the incorporation of DINO features. The results are presented in Table 4. To demonstrate the effectiveness of the generative priors in the SD model, we include an ablation study under the \"without pre-training\" setting, where the model is trained from scratch on each respective shadow removal dataset. The results indicate that pre-training significantly enhances shadow removal performance, as omitting it in both stage one and the full model leads to a substantial decline in PSNR and SSIM. Furthermore, stage two plays a crucial role in our method, as its removal results in a marked drop in PSNR and SSIM. This is primarily due to stage one's limitations in preserving high-frequency details. Additionally, integrating DINO features into the detail injection model of stage two proves advantageous, consistently improving PSNR and SSIM across all three datasets. For qualitative results related to the ablation study, please refer to the supplementary materials.", + "bbox": [ + 511, + 315, + 906, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 617, + 633, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces a novel detail-preserving latent diffusion pipeline that effectively eliminates complex shadows while preserving shadow-free details. The proposed method leverages the rich visual priors of a pre-trained Stable Diffusion model and propose a two-stage fine-tuning strategy to adapt the SD model for stable and efficient shadow removal. Extensive experiments demonstrate that our approach outperforms state-of-the-art shadow removal methods, particularly in terms of generalizability.", + "bbox": [ + 511, + 643, + 906, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation and future work. Our method may still miss some shadows in complex scenes, such as the self-shadows on the flower pot in Fig. 6. Additionally, in some cases, our approach focuses more on resolving the color variations caused by shadows and cannot fully preserve the exposure in non-shadow areas. In the future, we plan to incorporate unsupervised or self-supervised signals to further enhance the generalizability of our method.", + "bbox": [ + 511, + 779, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7599", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We thank the anonymous reviewers for their professional and constructive comments. This work was funded by NSFC grant No. 62302134, \"Pioneer\" and \"Leading Goose\" R&D Program of Zhejiang Province (No. 2025C01086), Zhejiang Provincial Natural Science Foundation under Grant No. LQ24F020031, the Fundamental Research Funds for the Provincial Universities of Zhejiang under Grant No. GK249909299001-021. Renshu Gu is partially supported by NSFC grant No. 62202130 and U22A2033. Weiwei Xu is partially supported by NSFC grant No. 62421003.", + "bbox": [ + 89, + 114, + 485, + 282 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 294, + 187, + 310 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Xiaodong Cun, Chi-Man Pun, and Cheng Shi. Towards ghost-free shadow removal via dual hierarchical aggregation network and shadow matting gan. 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In Proceedings of the AAAI conference on artificial intelligence, pages 3635-3643, 2022. 6" + ], + "bbox": [ + 91, + 90, + 483, + 191 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7602", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_model.json b/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0f61d367e7fcba9254de544ec6cec8ac38a9ab12 --- /dev/null +++ b/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_model.json @@ -0,0 +1,2224 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.182, + 0.131, + 0.816, + 0.152 + ], + "angle": 0, + "content": "Detail-Preserving Latent Diffusion for Stable Shadow Removal" + }, + { + "type": "text", + "bbox": [ + 0.146, + 0.18, + 0.856, + 0.218 + ], + "angle": 0, + "content": "Jiamin Xu\\(^{1}\\), Yuxin Zheng\\(^{1}\\), Zelong Li\\(^{1}\\), Chi Wang\\(^{1}\\), Renshu Gu\\(^{1}\\), Weiwei Xu\\(^{2}\\), Gang Xu\\(^{1*}\\) \n\\(^{1}\\) Hangzhou Dianzi University \\(^{2}\\) Zhejiang University" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.22, + 0.854, + 0.252 + ], + "angle": 0, + "content": "superxjm@yeah.net, yuxin6@hdu.edu.cn, jokerli@hdu.edu.cn, wangchi1995@zju.edu.cn, renshugu@hdu.edu.cn, xww@cad.zju.edu.cn, gxu@hdu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.32, + 0.486, + 0.622 + ], + "angle": 0, + "content": "Achieving high-quality shadow removal with strong generalizability is challenging in scenes with complex global illumination. Due to the limited diversity in shadow removal datasets, current methods are prone to overfitting training data, often leading to reduced performance on unseen cases. To address this, we leverage the rich visual priors of a pre-trained Stable Diffusion (SD) model and propose a two-stage fine-tuning pipeline to adapt the SD model for stable and efficient shadow removal. In the first stage, we fix the VAE and fine-tune the denoiser in latent space, which yields substantial shadow removal but may lose some high-frequency details. To resolve this, we introduce a second stage, called the detail injection stage. This stage selectively extracts features from the VAE encoder to modulate the decoder, injecting fine details into the final results. Experimental results show that our method outperforms state-of-the-art shadow removal techniques. The cross-dataset evaluation further demonstrates that our method generalizes effectively to unseen data, enhancing the applicability of shadow removal methods." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.653, + 0.221, + 0.669 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.679, + 0.484, + 0.876 + ], + "angle": 0, + "content": "Shadows are natural phenomena that occur when an obstacle blocks global light transport. They provide crucial cues for interpreting the three-dimensional structure of objects and scenes [44]. However, shadows can also hinder computer vision tasks, such as object segmentation [8], tracking [32], and intrinsic decomposition [16, 17, 25, 43]. In recent years, deep-learning-based methods for shadow removal [4, 5, 24, 40] have shown significant advancements by learning pixel-wise mappings between shadowed images and their corresponding ground-truth shadow-free versions in a fully supervised manner. However, such approaches often risk overfitting the limited training datasets [14, 28, 35], leading to inadequate generalization." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.286, + 0.703, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.577, + 0.394, + 0.64, + 0.404 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.286, + 0.897, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.394, + 0.864, + 0.404 + ], + "angle": 0, + "content": "OmniSR [Xu et al. 2024]" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.406, + 0.709, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.572, + 0.514, + 0.643, + 0.525 + ], + "angle": 0, + "content": "Ours (Stage I)" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.406, + 0.905, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.766, + 0.514, + 0.842, + 0.525 + ], + "angle": 0, + "content": "Ours (Stage II)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.542, + 0.908, + 0.626 + ], + "angle": 0, + "content": "Figure 1. Top: For complex shadows in indoor scenes, current methods struggle to completely remove shadows, such as those behind the eagle sculpture. Bottom: Our method effectively removes the shadows, and with our second stage, the details from the original input, such as the wooden texture shown in the cropped image, are preserved." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Drawing inspiration from recent advancements in zero-shot dense prediction [12, 42], we leverage the robust and comprehensive visual priors of the pre-trained Stable Diffusion (SD) model [29], which has been trained on billions of images, to enhance the generalization capability of shadow removal. However, developing a fine-tuning strategy that effectively removes shadows while preserving clear details in both shadowed and non-shadowed areas is not trivial. Unlike low-frequency depth and normal prediction tasks [12, 42], applying the SD model to shadow removal can result in detail loss and misalignment between the conditional image and the shadow-free output (Fig. 1). It is because the SD model, which consists of a Variational Autoencoder (VAE) and a Latent Diffusion Model (LDM), is designed for text-to-image generation and can lead to lossy compression during the mapping from pixel space" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.236, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7592" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.091, + 0.09, + 0.385, + 0.109 + ], + "angle": 0, + "content": "\\[\n(W \\times H \\times 3) \\text {t o} (\\frac {W}{8} \\times \\frac {H}{8} \\times 4).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.109, + 0.482, + 0.2 + ], + "angle": 0, + "content": "To achieve stable and detail-preserving shadow removal using the pre-trained SD priors, we introduce a two-stage pipeline: 1) eliminating shadows in latent space by fixing the pre-trained VAE and fine-tuning the LDM and 2) injecting shadow-aware multi-resolution details from the original input into the VAE decoding process." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.201, + 0.483, + 0.412 + ], + "angle": 0, + "content": "In the first stage, our method retains the pre-trained VAE and fine-tunes the LDM by conditioning it on the latent features of the input shadow image. We do not fine-tune the VAE, as it effectively handles shadow-free images despite not being specifically trained for this purpose, and the scale of our shadow-free images is limited. Our findings indicate that the latent space from the VAE, combined with the generative priors from the LDM, enhances shadow removal tasks, particularly when annotated training data is scarce. By operating in a low-resolution latent space rather than high-resolution pixel space, our method performs global self-attention with acceptable memory consumption, capturing more global contextual information compared to convolution and window-based self-attention [21]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.414, + 0.483, + 0.7 + ], + "angle": 0, + "content": "The fine-tuned SD model in the first stage produces visually appealing results, but it may lose some local details. To further enhance the quality of shadow removal, we propose a second stage for injecting shadow-free details. In this stage, we introduce a Detail Injection (DI) module that enhances the decoded latent features from the pre-trained VAE decoder by incorporating fine details from the input images. The VAE parameters are kept fixed. To prevent shadows from being reintroduced as \"details\", our DI module is equipped with shadow perception capabilities. Inspired by the observation that the shadow mask in the current shadow removal dataset is derived from the binary difference between shadowed and shadow-free images, we utilize concatenated features from the input shadow images and the coarse, shadow-free images decoded from the LDM output as cues for shadow-free detail injection. By combining features from both image types, the DI module can implicitly detect shadows and learn to inject shadow-free details into the VAE decoders." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.703, + 0.483, + 0.884 + ], + "angle": 0, + "content": "Note that Refusion [23] also performs latent-space diffusion for shadow removal. It captures input image information in the decoder [23] using a U-Net architecture specifically designed for large image shadow removal. However, the primary difference lies in the network design and finetuning strategy. Our method is designed to leverage the high-quality priors of the pre-trained VAE and LDM in the SD model, resulting in superior shadow removal quality. Our method can also handle high-resolution images (e.g., \\(1920 \\times 1440\\) in the WRSD dataset [35]), providing greater shadow removal efficiency compared to patch-based diffusion methods [22]." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.482, + 0.9 + ], + "angle": 0, + "content": "Overall, our contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.092, + 0.905, + 0.167 + ], + "angle": 0, + "content": "- We propose a two-stage fine-tuning pipeline to transform a pre-trained Stable Diffusion model into an image-conditional shadow-free image generator. This approach enables robust, high-resolution shadow removal without an input shadow mask." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.168, + 0.905, + 0.243 + ], + "angle": 0, + "content": "- We introduce a shadow-aware detail injection module that utilizes the VAE encoder features to modulate the pre-trained VAE decoders, selectively aligning per-pixel details from the input image with those in the output shadow-free image." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.243, + 0.905, + 0.319 + ], + "angle": 0, + "content": "- Extensive experimental results on public datasets demonstrate that the proposed method significantly outperforms state-of-the-art shadow removal methods. Additionally, we show that our method exhibits better generalizability by training on one dataset and testing on another." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.092, + 0.905, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.359, + 0.655, + 0.374 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.393, + 0.727, + 0.409 + ], + "angle": 0, + "content": "2.1. Deep Shadow Removal" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.424, + 0.907, + 0.62 + ], + "angle": 0, + "content": "Deep learning methods have significantly advanced shadow removal, enabling end-to-end learning of a mapping from input images to corresponding shadow-free images, with or without the aid of shadow masks. For example, DesshadowNet [28] combines multi-level features to predict a shadow matte, thereby enhancing the efficiency of shadow removal. Hu et al. [1, 10] utilize direction-aware spatial context for precise shadow detection and elimination. Fu et al. [3] formulate the shadow removal task as a multiple exposure image fusion problem. BMNet [48] introduces a bijective mapping that integrates shadow removal with shadow generation, improving overall performance in shadow removal tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.909, + 0.903 + ], + "angle": 0, + "content": "More recently, ShadowFormer [4] presents a Swin-transformer-based shadow removal network that harnesses multi-scale attention to exploit contextual relationships between shadowed and non-shadowed regions. Meanwhile, DMTN [18] proposes a decoupled multi-task network that learns decomposed features specifically tailored for shadow removal. ShadowRefiner [2] introduces a mask-free model that integrates spatial and frequency domain representations for image shadow removal, achieving top results in the Perceptual Track of the NTIRE 2024 Image Shadow Removal Challenge [36]. Xu et al. [41] propose a path-tracing pipeline to generate shadow removal data that considers indirect illumination in indoor scenes. They also introduce a semantics and geometry-aware network for efficient mask-free shadow removal. HomoFormer [40] designs random shuffle and inverse shuffle operations to create a homogenized appearance of shadows, allowing for effective processing by local self-attention layers." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7593" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.093, + 0.904, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.369, + 0.908, + 0.455 + ], + "angle": 0, + "content": "Figure 2. Our proposed network. We propose a two-stage shadow removal network based on Stable Diffusion (SD). (1) In the first stage, as shown in the bottom half, we fine-tune the pre-trained UNet in SD within the latent space defined by SD's pre-trained VAE \\((\\mathcal{E}\\) and \\(\\mathcal{D})\\) We found that the pre-trained latent space can effectively represent shadow-free images. (2) In the second stage, as shown in the top half, we modulate the VAE decoder \\(\\mathcal{D}\\) by selectively adding features from the VAE encoder \\(\\mathcal{E}\\) using a Detail Injection Model (DIM). The model consists of multiple RRDB layers, which inject shadow-free texture details into the decoder features. With these two stages, our proposed network can generate high-quality, shadow-free images that preserve fine details." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.478, + 0.388, + 0.495 + ], + "angle": 0, + "content": "2.2. Diffusion-based Shadow Removal" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.505, + 0.485, + 0.852 + ], + "angle": 0, + "content": "Diffusion models [9, 34] are generative models that learn data distributions through Gaussian noise blurring and reverse denoising. Initially developed for image generation, these models have become prominent in applications including image super-resolution [31, 38], depth/normal prediction [12, 42], and shadow removal [23]. In the context of shadow removal, ShadowDiffusion [5] introduces a diffusion model that generates both a shadow-free image and a refined shadow mask, using shadow degradation as a prior and employing an unrolling diffusion process to eliminate shadows. DeS3 [11] enhances ShadowDiffusion by incorporating an adaptive attention mechanism and ViT similarity loss, removing the dependence on shadow masks. Guo et al.[6] propose a diffusion-based unsupervised shadow removal pipeline that utilizes a boundary-aware divide and conquer strategy. Diff-Shadow[22] employs a globally guided diffusion model pipeline that focuses on the patch and global information, enabling shadow removal in images of arbitrary resolution. Liu et al. [20] first separate reflectance and illumination, then use a diffusion model to correct degraded lighting in shadowed areas, followed by the progressive restoration of texture details through an illumination-guided texture restoration module." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.485, + 0.903 + ], + "angle": 0, + "content": "There are also methods that utilize a latent space to enhance diffusion-based shadow removal. Refusion [6] presents a U-Net-based latent diffusion model that utilizes" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.479, + 0.907, + 0.659 + ], + "angle": 0, + "content": "mean-reverting stochastic differential equations for high-resolution image restoration tasks. The model performs image diffusion in a low-resolution latent space while preserving details through hidden-connections. However, being end-to-end trained on the shadow-removal dataset, it suffers from limited generalizability. Mei et al. [24] conduct diffusion-based shadow removal with a shadow mask at both the general and instance levels. They improve the diffusion process by conditioning on a learned latent feature space that captures the characteristics of shadow-free images and propose fusing noise features with the diffusion network to alleviate potential local optima." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.909, + 0.768 + ], + "angle": 0, + "content": "Unlike existing diffusion-based methods, we introduce a two-stage fine-tuning strategy that fully utilizes the visual priors from the pre-trained Stable Diffusion (SD) model [29]. With our latent shadow removal and shadow-aware detail injection stages, our method demonstrates strong generalization capability while effectively preserving non-shadow details." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.779, + 0.689, + 0.796 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.804, + 0.625, + 0.818 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Given a dataset of shadow and shadow-free image pairs \\(\\langle \\mathbf{x},\\mathbf{y}\\rangle \\in \\mathcal{X}\\), our goal is to train a network that can: 1. thoroughly eliminate shadows from the input image, and 2. preserve the content of all non-shadow areas. Although the first requirement focuses on the shadow (umbra) regions, the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "7594" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.089, + 0.285, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.177, + 0.239, + 0.187 + ], + "angle": 0, + "content": "Shadow image x" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.089, + 0.473, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.356, + 0.177, + 0.403, + 0.188 + ], + "angle": 0, + "content": "\\(\\mathcal{D}(\\mathcal{E}(\\mathbf{x}))\\)" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.188, + 0.284, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.311, + 0.251, + 0.323 + ], + "angle": 0, + "content": "Shadow-free image y" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.188, + 0.474, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.356, + 0.31, + 0.404, + 0.323 + ], + "angle": 0, + "content": "\\(\\pmb{D}(\\pmb{\\mathcal{E}}(\\mathbf{y}))\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.339, + 0.484, + 0.435 + ], + "angle": 0, + "content": "Figure 3. Latent space in VAE. We apply the pre-trained encoding and decoding process on a shadow image \\(\\mathbf{x}\\) or a shadow-free image \\(\\mathbf{y}\\). For a shadow-free image, this process does not introduce additional shadows, meaning the pre-trained latent space can also represent the shadow-free image. However, as shown in the zoomed-in view, some details, like text, may be lost in this process." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.462, + 0.484, + 0.553 + ], + "angle": 0, + "content": "second is more concerned with non-shadow areas. These two objectives can be contradictory, making it challenging to design a single network that effectively addresses both. Therefore, we propose a two-stage shadow removal framework to robustly eliminate various types of shadows across different scenarios (Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.484, + 0.674 + ], + "angle": 0, + "content": "In the first stage, as shown at the bottom of Fig. 2, we perform shadow removal in latent space (Sec. 3.2). We condition the Stable Diffusion (SD) model [29] using the latent code of the input shadow image \\(\\mathbf{z}^{\\mathrm{x}}\\) and fine-tune a pretrained SD model to generate the latent code of a shadow-free image \\(\\mathbf{z}_0^{\\mathbf{y}}\\). As shown in Fig. 1, this latent code can be decoded into a coarse image that effectively eliminates shadows, although some details may be lost." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.674, + 0.484, + 0.809 + ], + "angle": 0, + "content": "In the second stage, as illustrated at the top of Fig. 2, we perform detail injection using the encoder \\(\\mathcal{E}\\) and decoder \\(\\mathcal{D}\\) within SD (Sec.3.3). We fix the pretrained encoder and decoder and employ a set of Detail Injection (DI) models to integrate shadow-free details into the decoder features. These details are derived from each encoder layer. After training on pairs of shadow and shadow-free images, the DI models learn to inject details from the input image that are free of shadows." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.385, + 0.835 + ], + "angle": 0, + "content": "3.2. Shadow Removal in Latent Space" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Building on recent advancements in dense prediction tasks [7, 12, 42], we formulate the shadow removal task in the first stage as an image-conditioned annotation generation problem using SD. This approach conducts the dif" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "fusion process within a low-dimensional latent space generated by a pair of encoder and decoder \\(\\langle \\mathcal{E},\\mathcal{D}\\rangle\\) , where \\(\\mathcal{E}(\\mathbf{x}) = \\mathbf{z}^{\\mathbf{x}}\\) and \\(\\mathcal{D}(\\mathbf{z}^{\\mathbf{x}})\\approx \\mathbf{x}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.138, + 0.907, + 0.291 + ], + "angle": 0, + "content": "Compared to the diffusion model [9], Stable Diffusion offers enhanced generation stability and training efficiency. However, given the limited number of shadow and shadow-free image pairs, we opt for a fine-tuning strategy rather than training a SD model from scratch. We directly utilize the pre-trained \\(\\mathcal{E}\\) and \\(\\mathcal{D}\\) in SD and focus on fine-tuning the denoiser U-Net, as we have found that the pre-trained \\(\\mathcal{E}\\) and \\(\\mathcal{D}\\) perform well for both shadow and non-shadow images, even though they were not specifically trained on shadow-free images (Fig. 3)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.317, + 0.907, + 0.409 + ], + "angle": 0, + "content": "Fine-tuning Process. The fine-tuning for Stable Diffusion [9] relies on forward-noising and reverse-denoising processes that operate within the latent space. In the forward process, Gaussian noise is progressively added over time steps \\( t \\in [1,T] \\) to the sample \\( \\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}} \\), generating a noisy sample \\( \\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.423, + 0.905, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {\\mathrm {t}} ^ {\\mathbf {y}} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} ^ {\\mathbf {y}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.454, + 0.906, + 0.532 + ], + "angle": 0, + "content": "where \\(\\epsilon \\sim \\mathcal{N}(0,I)\\), \\(\\overline{\\alpha}_t\\coloneqq \\prod_{s = 1}^t (1 - \\beta_s)\\), and \\(\\beta_{1},\\beta_{2},\\ldots\\) \\(\\beta_{T}\\) defines the noise schedule over \\(T\\) steps. In the reverse process, a U-Net [30] denoted as \\(f_{\\theta}\\) takes the encoding features of the input image \\(\\mathbf{z}^{\\mathbf{x}}\\) and the sample \\(\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}}\\) as inputs, outputting a prediction of the clean sample \\(\\hat{\\mathbf{z}}^{\\mathbf{y}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.643, + 0.546, + 0.905, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {z}} ^ {\\mathbf {y}} = f _ {\\theta} \\left(\\mathbf {z} _ {\\mathbf {t}} ^ {\\mathbf {y}}, \\mathbf {z} ^ {\\mathbf {x}}, t\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.58, + 0.906, + 0.611 + ], + "angle": 0, + "content": "During fine-tuning, we randomly sample a time step \\( t \\in [1, T] \\) and minimize the corresponding loss function \\( L_{t} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.625, + 0.905, + 0.644 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t} = \\left\\| \\mathbf {z} ^ {\\mathbf {y}} - f _ {\\theta} \\left(\\mathbf {z} _ {\\mathbf {t}} ^ {\\mathbf {y}}, \\mathbf {z} ^ {\\mathbf {x}}, t\\right) \\right\\| _ {2} ^ {2}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.657, + 0.906, + 0.688 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}^{\\mathbf{y}}\\) is the encoding features of the ground-truth shadow-free image." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.715, + 0.906, + 0.793 + ], + "angle": 0, + "content": "Denoising Process. During inference, we use DDIM [33], which implements an implicit probabilistic model that can significantly reduce the number of denoising steps while maintaining output quality. Formally, the denoising process from \\(\\mathbf{z}_{\\tau}^{\\mathbf{y}}\\) to \\(\\mathbf{z}_{\\tau -1}^{\\mathbf{y}}\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.808, + 0.905, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {\\tau - 1} ^ {\\mathbf {y}} = \\sqrt {\\bar {\\alpha} _ {\\tau - 1}} \\hat {\\mathbf {z}} _ {\\tau} ^ {\\mathbf {y}} + \\operatorname {d i r e c t i o n} \\left(\\mathbf {z} _ {\\tau} ^ {\\mathbf {y}}\\right) + \\sigma_ {\\tau} \\epsilon_ {\\tau}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.84, + 0.906, + 0.902 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{z}}_{\\tau}^{\\mathbf{y}}\\) is the predicted clean sample at the denoising step \\(\\tau\\), \\(\\text{direction}(\\mathbf{z}_{\\tau}^{\\mathbf{y}})\\) represents the direction pointing to \\(\\mathbf{z}_{\\tau}^{\\mathbf{y}}\\). \\(\\tau \\in \\{\\tau_1, \\tau_2, \\dots, \\tau_S\\}\\) is an increasing sub-sequence of the timestep set \\([1, T]\\) used for fast sampling." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "7595" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.088, + 0.287, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.191, + 0.212, + 0.202 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.089, + 0.472, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.339, + 0.191, + 0.422, + 0.202 + ], + "angle": 0, + "content": "Ours (stage I)" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.203, + 0.288, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.151, + 0.305, + 0.239, + 0.317 + ], + "angle": 0, + "content": "Ours (stage II)" + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.203, + 0.472, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.328, + 0.305, + 0.435, + 0.316 + ], + "angle": 0, + "content": "RRDB feature vis." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.334, + 0.484, + 0.432 + ], + "angle": 0, + "content": "Figure 4. Some details in the input image, such as the textures on the floor, change during latent space diffusion in stage one. In stage two, our method preserves these high-quality details while effectively removing shadows. As shown in the bottom-left image, where we map the RRDB features to three dimensions using PCA, we observe that shadow areas have distinct features (in green), indicating that our detail injection model is shadow-aware." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.459, + 0.365, + 0.475 + ], + "angle": 0, + "content": "3.3. Shadow-aware Detail Injection" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.482, + 0.484, + 0.603 + ], + "angle": 0, + "content": "As illustrated in Fig. 4, while the output of the conditional Stable Diffusion is visually striking—especially in its ability to completely remove shadows—it often diverges from the ground truth, particularly in high-detail areas, such as the floor texture. We believe the primary reason for this is the loss of high-frequency information in the latent space. As shown in Fig. 3, directly decoding the encoded features \\(\\mathcal{D}(\\mathcal{E}(\\mathbf{x}))\\) also results in a loss of detail." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.604, + 0.484, + 0.725 + ], + "angle": 0, + "content": "To eliminate shadows while preserving details, we introduce a shadow-aware detail injection step utilizing a set of DI models. Each model selectively extracts information from a specific intermediate layer of \\(\\mathcal{E}\\) to modulate the corresponding intermediate layers of \\(\\mathcal{D}\\). Let \\(\\mathbf{e}_i\\) and \\(\\mathbf{d}_i\\) denote the encoder and decoder features for the \\(i\\)-th intermediate layer. The DI model takes the concatenation of \\(\\mathbf{e}_i\\) and \\(\\mathbf{d}_i\\) as input, output a modulated feature \\(\\tilde{\\mathbf{d}}_i\\):" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.738, + 0.483, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\mathbf {d} _ {0} = \\mathbf {z} _ {0} ^ {\\mathbf {y}}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.759, + 0.475, + 0.776 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {d}} _ {i} = \\mathbf {d} _ {i} + \\operatorname {C o n v} (\\operatorname {R R D B} (\\operatorname {C o n v} (\\mathbf {d} _ {i}, \\mathbf {e} _ {n - i} (\\mathbf {z} ^ {\\mathbf {x}})), f _ {d} (\\mathbf {x}))),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.78, + 0.398, + 0.797 + ], + "angle": 0, + "content": "\\[\n\\mathbf {d} _ {i} = \\mathcal {D} _ {i - 1} (\\tilde {\\mathbf {d}} _ {i - 1}), i \\in [ 1, 4 ], \\hat {\\mathbf {y}} = \\operatorname {C o n v} (\\tilde {\\mathbf {d}} _ {4})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Here, \\(\\mathrm{RRDB}(\\cdot)\\) refers to the Residual-in-Residual Dense Block module [46], which consists of three Dense Blocks. \\(\\hat{\\mathbf{y}}\\) is predicted shadow-free image. \\(f_{d}(\\mathbf{x})\\) are features extracted using DINO v2 [26]. We concatenate the DINO features with \\(\\mathbf{e}_i\\) and \\(\\mathbf{d}_i\\) after passing through a convolutional layer to enhance the generalizability of the DI models." + }, + { + "type": "table", + "bbox": [ + 0.546, + 0.088, + 0.875, + 0.169 + ], + "angle": 0, + "content": "
    MethodMean↑Variance↓
    Our stage one (ε-pred)29.660.239
    Our stage one (z0-pred)29.950.146
    Our stage two35.020.160
    DeS3 [11]31.331.075
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.179, + 0.907, + 0.235 + ], + "angle": 0, + "content": "Table 1. Low variance. In the first stage, our method achieves reduced variance by using \\( \\mathbf{z}_0 \\)-prediction. In the second stage, our method improves PSNR while maintaining low variance, resulting in robust, high-quality shadow removal results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.261, + 0.907, + 0.428 + ], + "angle": 0, + "content": "Since \\(\\mathbf{e}_i\\) and \\(\\mathbf{d}_i\\) contain features from the input shadow image \\(\\mathbf{x}\\) and the shadow-free latent code \\(\\mathbf{z}_0^{\\mathbf{y}}\\), respectively, our DI models can effectively identify shadow areas by utilizing both features as input. Although the latent codes may lose high-frequency details, they still provide valuable cues for shadow regions, which are primarily low-frequency. As illustrated in Fig. 4, where we visualize the features in the last layer of the RRDB module, we can observe that the shadow areas exhibit distinct feature responses. We present only the RRDB responses for \\(\\mathbf{d}_2\\). Please refer to the supplementary for additional results." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.446, + 0.906, + 0.522 + ], + "angle": 0, + "content": "Losses. To train the DI models, we minimize a total loss \\(\\mathcal{L}_{total}\\), which combines an L1 loss and a perceptual loss measured using the Learned Perceptual Image Patch Similarity (LPIPS) metric [45] between the output image \\(\\hat{\\mathbf{y}}\\) and the ground-truth shadow-free image \\(\\mathbf{y}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.532, + 0.906, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\left\\| \\hat {\\mathbf {y}} - \\mathbf {y} \\right\\| _ {1} + \\left\\| \\operatorname {L P I P S} (\\hat {\\mathbf {y}}) - \\operatorname {L P I P S} (\\mathbf {y}) \\right\\| _ {2} ^ {2}. \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.559, + 0.736, + 0.575 + ], + "angle": 0, + "content": "3.4. Implementation Details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.581, + 0.907, + 0.853 + ], + "angle": 0, + "content": "Reducing variance. As shown in Eq. 3, in the LDM fin-tuning stage, we use \\(\\mathbf{z}_0\\)-prediction rather than the standard \\(\\epsilon\\)-prediction parameterization for the denoising model. This choice, as recommended by Lotus[7], helps reduce variance during stochastic LDM inference. We compare these two approaches on the \\(\\mathrm{ISTD + }\\) [14] dataset by running inference on the test set with five different random seeds (1, 2, 3, 4, 5). We calculate the PSNR variance across the five outputs for each image and obtain the average variance. As shown in Table 1, using \\(\\mathbf{z}_0\\)-prediction in our LDM fin-tuning stage yields higher PSNR and lower variance compared to \\(\\epsilon\\)-prediction. Additionally, we assess the average variance of our final results after the detail injection stage, and Table 1 shows that our final results have significantly lower variance than DeS3 [11], another mask-free shadow removal method based on diffusion models. It indicates that our generative shadow removal method is highly robust to randomness, which is a critical factor for practical use." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Training details. Our model is trained on a GPU server with four GeForce RTX 4090 GPUs using PyTorch" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7596" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.089, + 0.902, + 0.32 + ], + "angle": 0, + "content": "
    MethodYearMask-freeISTD+ DatasetSRD DatasetINS DatasetWSRD+ Dataset
    PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
    AutoExposure [3]2021No29.450.86129.240.93827.910.95721.660.752
    Zhu et al. [49]2022No——32.050.965————
    BMNet [48]2022No33.980.97231.970.96527.900.95824.750.816
    ShadowFormer [4]2023No35.460.97132.900.95828.620.96325.440.820
    DMTN [18]2023No32.230.96633.770.96828.830.969——
    ShadowDiffusion [5]2023No34.630.96734.730.97029.120.966——
    HomoFormer [40]2024No35.720.97734.360.97728.980.965——
    InstanceShadow [24]2024No34.690.96831.610.95928.160.948——
    TBRNet [19]2023Yes31.910.96431.830.953————
    Refusion [23]2023Yes32.410.96131.600.94928.130.95822.320.738
    DeS3 [11]2024Yes31.390.95734.110.96827.890.947——
    OmniSR [41]2024Yes33.340.97032.870.96930.380.97326.070.835
    Ours—Yes35.190.97433.630.96830.560.97526.260.827
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.33, + 0.905, + 0.361 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on ISTD+, SRD, INS, and WSRD+ datasets. Best results are highlighted as 1st , 2nd and 3rd . Refer to the supplementary material for the MAE values in both shadowed and non-shadowed areas." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.385, + 0.482, + 0.508 + ], + "angle": 0, + "content": "2.0.1 [27] with CUDA 11.7. We employ the Adam optimizer [13] for training. In the first stage, the LDM is finetuned for 40 epochs on INS [41] and 200 and 300 epochs on \\(\\mathrm{ISTD + }\\) [14, 37] and SRD [28], respectively. We utilize a constant learning rate of \\(3\\times 10^{-4}\\) with a batch size 16. For the INS dataset, each batch consists of \\(512\\times 512\\) patches, while for the other datasets, batches are composed of randomly cropped \\(480\\times 480\\) patches." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.508, + 0.483, + 0.691 + ], + "angle": 0, + "content": "In the second stage, we maintain the constant learning rate of \\(5 \\times 10^{-4}\\) and batch size of 16. The batch shapes for each dataset are consistent with those in the first stage, and the number of epochs for training the detail injection models is 50 for INS and 300 and 200 for \\(\\mathrm{ISTD + }\\) and SRD, respectively. For the DINO features [26], we resize the image to \\(\\frac{14W}{16} \\times \\frac{14H}{16}\\) using bilinear interpolation, extract the DINO features, and apply a \\(1 \\times 1\\) convolution layer to obtain a feature map of shape \\(256 \\times \\frac{W}{16} \\times \\frac{H}{16}\\). To reduce memory footprint, we only concatenate the DINO features with the first two layers of the VAE decoder. Additional details can be found in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.708, + 0.223, + 0.725 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.735, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Datasets. We conduct experiments on four shadow removal datasets: SRD [28], \\(\\mathrm{ISTD + }\\) [14, 37], \\(\\mathrm{WSRD + }\\) [35, 36], and INS [41]. The SRD dataset [28] includes 3,088 paired shadow and shadow-free images, divided into 2,680 for training and 408 for testing. The \\(\\mathrm{ISTD + }\\) dataset [14, 37] provides 1,870 triplets of shadow images, shadow masks, and shadow-free images, with 1,330 used for training and 540 for testing. \\(\\mathrm{WSRD + }\\) [35, 36] contains 1,000 pairs of shadow and non-shadow images captured under both spotlight and diffuse illumination. Since the test data is not open-sourced, we use its 100 validation images for test" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.385, + 0.907, + 0.432 + ], + "angle": 0, + "content": "ing. Lastly, the INS dataset [41] comprises 30,000 synthetic training images under direct and indirect illumination, a synthetic test set of 2,000 images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.907, + 0.585 + ], + "angle": 0, + "content": "Evaluation Metrics. Following previous methods [3, 4, 15], we evaluated images with a resolution of \\(256 \\times 256\\). We report results using the Peak Signal-to-Noise Ratio (PSNR) and the Structure Similarity Index Measure (SSIM) [39], adopting the MATLAB evaluation codes as provided by Zhu et al. [49]. For the WSRD+ [35] dataset, we used its evaluation data and the evaluation code provided by the NTIRE 2024 Image Shadow Removal Challenge [36] for comparison." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.592, + 0.655, + 0.608 + ], + "angle": 0, + "content": "4.1. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.905, + 0.81 + ], + "angle": 0, + "content": "We compare our method to twelve state-of-the-art shadow removal techniques, evaluating both quantitatively and qualitatively. Among these, eight methods require a shadow mask as input: AutoExposure [3], Zhu et al. [49], BMNet [48], ShadowFormer [4], DMTN [18], ShadowDiffusion [5], and HomoFormer [40]. The remaining four methods—TBRNet [19], Refusion [23], Des3 [11], and OmniSR [41]—are mask-free, meaning they do not require a shadow mask as input. All comparisons use the original authors' implementations and hyperparameters, or the provided checkpoints or results, if available. For the INS dataset, we train these methods following the procedure in OmniSR [41]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.907, + 0.902 + ], + "angle": 0, + "content": "For methods that are not mask-free, we use the shadow masks provided by the dataset as the default input. Since SRD [28] does not provide masks, we use the shadow masks generated by DHAN [1], which computes shadow matting from shadow/shadow-free pairs and generates binary masks through thresholding. In the case of the INS dataset," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "7597" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.122, + 0.087, + 0.885, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.375, + 0.908, + 0.406 + ], + "angle": 0, + "content": "Figure 5. Comparisons with SOTA shadow removal methods on the ISTD+ and SRD datasets. The input mask, required by methods that are not mask-free, is shown in the top-left corner." + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.416, + 0.885, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.636, + 0.908, + 0.679 + ], + "angle": 0, + "content": "Figure 6. Comparisons with SOTA shadow removal methods in real scenes. We compare our method to OmniSR [41], HomoFormer [40], Refusion [23], and ShadowDiffusion [5], all trained on the INS dataset [41]. Results show that our approach achieves more comprehensive shadow removal, even in complex scenes." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.705, + 0.482, + 0.809 + ], + "angle": 0, + "content": "its shadow masks are represented as 0-1 probability maps rather than binary masks. Since it is a synthetic dataset with highly accurate masks, we found that using them as input results in methods producing outputs nearly identical to the ground truth (with PSNR values exceeding 50). To address this, following OmniSR [41], we use FDRNet [47] to detect shadow masks and input the detected masks instead." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.811, + 0.483, + 0.902 + ], + "angle": 0, + "content": "As shown in Table 2, our method achieves the highest PSNR score on the INS dataset. On the \\(\\mathrm{ISTD + }\\) dataset, our approach is the best mask-free method, performing only slightly below HomoFormer [40] and ShadowFormer [4], which use ground-truth shadow masks as input, and outperforming most other methods that also rely on ground-truth" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.78 + ], + "angle": 0, + "content": "shadow masks. As shown in the first two columns of Fig. 5, although without mask as input, our method is capable of thoroughly removing shadows, even with limited semantic context. We think it is because of leveraging the generative priors in our latent diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.901 + ], + "angle": 0, + "content": "For the SRD dataset, our method also delivers competitive results compared to methods that utilize masks provided by DHAN [1]. Among shadow-free methods, our performance is second only to DeS3. As illustrated in Fig. 5, our method produces visually appealing results with nearly complete shadow removal. We found that our method achieves better shadow removal quality than DeS3; however, in areas with highly detailed textures, such as sand" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7598" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.09, + 0.49, + 0.192 + ], + "angle": 0, + "content": "
    MethodISTD+→SRDSRD→ISTD+INS→WSRD+
    PSNRSSIMPSNRSSIMPSNRSSIM
    ShadowDiffusion24.260.89029.480.94719.400.825
    Refusion22.560.88627.310.92418.730.787
    DeS322.090.880————
    OmniSR25.860.91730.190.95120.030.825
    Ours26.230.92330.230.95320.110.828
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.202, + 0.483, + 0.23 + ], + "angle": 0, + "content": "Table 3. Cross-dataset evaluation. \\(\\mathrm{ISTD} + \\rightarrow\\) SRD means training on the \\(\\mathrm{ISTD}+\\) dataset and testing on the SRD dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.259, + 0.408, + 0.273 + ], + "angle": 0, + "content": "and grass, the PSNR is lower than that of DeS3." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.275, + 0.483, + 0.395 + ], + "angle": 0, + "content": "On the INS dataset, our method achieves the highest PSNR and SSIM, as shown in Table 2. We also compare our method with others on real indoor scene images, all trained on the INS dataset. As illustrated in Fig. 6, our approach more effectively removes shadows from multiple light sources, such as those beneath the table and chair, as well as soft shadows behind the small planter and on the bookshelf in the background." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.398, + 0.483, + 0.593 + ], + "angle": 0, + "content": "We further evaluated our method on high-resolution shadow removal using the WSRD+ [35] dataset, with images at \\(1920 \\times 1440\\) resolution. The first stage requires no modification. We resize each image to \\(640 \\times 480\\) for the LDM fine-tuning. In the second stage, we introduce a minor adjustment by adding one patch-partition layer and one patch-merging layer [21]. Additional details are provided in the supplementary materials. As shown in Table 2, our method outperforms others on the WSRD+ dataset, with more results available in the supplementary material. The relatively low PSNR scores for all methods on the WSRD+ dataset can be attributed to exposure differences between the input and ground-truth images." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.607, + 0.32, + 0.621 + ], + "angle": 0, + "content": "4.2. Cross-dataset evaluation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To evaluate the generalizability of our approach, we conduct a cross-dataset evaluation. Specifically, we train our model on the training set of one dataset and test it on the testing set of a different dataset. Typically, training and testing data within the same dataset share similar shadow patterns, backgrounds, or lighting conditions. This cross-dataset evaluation presents a more challenging test for shadow removal methods and provides a more stringent measure of generalizability. We use \\( A \\rightarrow B \\) to denote training on dataset \\( A \\) and testing on dataset \\( B \\). As shown in Table 3, our method achieves the best results on ISTD+→SRD, SRD→ISTD+, and INS→WSRD+. Here, we compare only with DeS3 [11] on ISTD+→SRD, as it provides checkpoints only for ISTD+ dataset. Its open-source code is a basic version that excludes certain components, including the VIT loss. For the INS→WSRD+ experiment, high-resolution images from the WSRD+ dataset are resized to \\( 640 \\times 480 \\) for inference and evaluation. Qual-" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.09, + 0.905, + 0.187 + ], + "angle": 0, + "content": "
    DatasetISTD+ PSNR/SSIMSRD PSNR/SSIMINS PSNR/SSIM
    Full35.19/0.97433.63/0.96830.56/ 0.975
    W/o pre-train33.38/0.96732.46/0.96329.55/0.970
    Stage one29.95/0.84328.18/0.86828.78/0.924
    Stage one (w/o pre-train)28.12/0.82227.48/0.86126.92/0.909
    W/o DINO34.76/0.97133.04/0.96530.30/0.975
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.197, + 0.905, + 0.225 + ], + "angle": 0, + "content": "Table 4. Ablation studies. W/o pre-train: without pre-training. W/o DINO: without DINO in the detail injection model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.253, + 0.905, + 0.283 + ], + "angle": 0, + "content": "itative comparisons for this evaluation are provided in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.294, + 0.667, + 0.309 + ], + "angle": 0, + "content": "4.3. Ablation study." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.316, + 0.907, + 0.603 + ], + "angle": 0, + "content": "To validate our model design, we conducted ablation studies on the use of the pretrained SD model, the two-stage pipeline, and the incorporation of DINO features. The results are presented in Table 4. To demonstrate the effectiveness of the generative priors in the SD model, we include an ablation study under the \"without pre-training\" setting, where the model is trained from scratch on each respective shadow removal dataset. The results indicate that pre-training significantly enhances shadow removal performance, as omitting it in both stage one and the full model leads to a substantial decline in PSNR and SSIM. Furthermore, stage two plays a crucial role in our method, as its removal results in a marked drop in PSNR and SSIM. This is primarily due to stage one's limitations in preserving high-frequency details. Additionally, integrating DINO features into the detail injection model of stage two proves advantageous, consistently improving PSNR and SSIM across all three datasets. For qualitative results related to the ablation study, please refer to the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.618, + 0.634, + 0.634 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.907, + 0.779 + ], + "angle": 0, + "content": "This paper introduces a novel detail-preserving latent diffusion pipeline that effectively eliminates complex shadows while preserving shadow-free details. The proposed method leverages the rich visual priors of a pre-trained Stable Diffusion model and propose a two-stage fine-tuning strategy to adapt the SD model for stable and efficient shadow removal. Extensive experiments demonstrate that our approach outperforms state-of-the-art shadow removal methods, particularly in terms of generalizability." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Limitation and future work. Our method may still miss some shadows in complex scenes, such as the self-shadows on the flower pot in Fig. 6. Additionally, in some cases, our approach focuses more on resolving the color variations caused by shadows and cannot fully preserve the exposure in non-shadow areas. In the future, we plan to incorporate unsupervised or self-supervised signals to further enhance the generalizability of our method." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7599" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.486, + 0.283 + ], + "angle": 0, + "content": "We thank the anonymous reviewers for their professional and constructive comments. This work was funded by NSFC grant No. 62302134, \"Pioneer\" and \"Leading Goose\" R&D Program of Zhejiang Province (No. 2025C01086), Zhejiang Provincial Natural Science Foundation under Grant No. LQ24F020031, the Fundamental Research Funds for the Provincial Universities of Zhejiang under Grant No. GK249909299001-021. Renshu Gu is partially supported by NSFC grant No. 62202130 and U22A2033. Weiwei Xu is partially supported by NSFC grant No. 62421003." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.295, + 0.188, + 0.311 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.321, + 0.486, + 0.39 + ], + "angle": 0, + "content": "[1] Xiaodong Cun, Chi-Man Pun, and Cheng Shi. Towards ghost-free shadow removal via dual hierarchical aggregation network and shadow matting gan. 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In Proceedings of the AAAI conference on artificial intelligence, pages 3635-3643, 2022. 6" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.484, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.517, + 0.957 + ], + "angle": 0, + "content": "7602" + } + ] +] \ No newline at end of file diff --git a/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_origin.pdf b/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..28741249d566fb9b4cdee5171e6ac40e34a2e943 --- /dev/null +++ b/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/a2941634-46f8-4a96-a7ab-f9421ddf1c2d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a68f2d9f9ce9b83520e71c136fb88a10b25a4657798a07509be7e6d29ebcff83 +size 4499003 diff --git a/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/full.md b/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9cb620420c14f764316ad94541b4bbf55b1373c1 --- /dev/null +++ b/2025/Detail-Preserving Latent Diffusion for Stable Shadow Removal/full.md @@ -0,0 +1,313 @@ +# Detail-Preserving Latent Diffusion for Stable Shadow Removal + +Jiamin Xu $^{1}$ , Yuxin Zheng $^{1}$ , Zelong Li $^{1}$ , Chi Wang $^{1}$ , Renshu Gu $^{1}$ , Weiwei Xu $^{2}$ , Gang Xu $^{1*}$ $^{1}$ Hangzhou Dianzi University $^{2}$ Zhejiang University + +superxjm@yeah.net, yuxin6@hdu.edu.cn, jokerli@hdu.edu.cn, wangchi1995@zju.edu.cn, renshugu@hdu.edu.cn, xww@cad.zju.edu.cn, gxu@hdu.edu.cn + +# Abstract + +Achieving high-quality shadow removal with strong generalizability is challenging in scenes with complex global illumination. Due to the limited diversity in shadow removal datasets, current methods are prone to overfitting training data, often leading to reduced performance on unseen cases. To address this, we leverage the rich visual priors of a pre-trained Stable Diffusion (SD) model and propose a two-stage fine-tuning pipeline to adapt the SD model for stable and efficient shadow removal. In the first stage, we fix the VAE and fine-tune the denoiser in latent space, which yields substantial shadow removal but may lose some high-frequency details. To resolve this, we introduce a second stage, called the detail injection stage. This stage selectively extracts features from the VAE encoder to modulate the decoder, injecting fine details into the final results. Experimental results show that our method outperforms state-of-the-art shadow removal techniques. The cross-dataset evaluation further demonstrates that our method generalizes effectively to unseen data, enhancing the applicability of shadow removal methods. + +# 1. Introduction + +Shadows are natural phenomena that occur when an obstacle blocks global light transport. They provide crucial cues for interpreting the three-dimensional structure of objects and scenes [44]. However, shadows can also hinder computer vision tasks, such as object segmentation [8], tracking [32], and intrinsic decomposition [16, 17, 25, 43]. In recent years, deep-learning-based methods for shadow removal [4, 5, 24, 40] have shown significant advancements by learning pixel-wise mappings between shadowed images and their corresponding ground-truth shadow-free versions in a fully supervised manner. However, such approaches often risk overfitting the limited training datasets [14, 28, 35], leading to inadequate generalization. + +![](images/456ed4cc2a0bb4fd5466b07b9674192bc2f4ea2fe19cbb6924ae8f78cfc2faeb.jpg) +Input image + +![](images/57f04bcb6d77ca5e06ca5b955f836e2a6f38699cb9fb13b5691cb227f6548d97.jpg) +OmniSR [Xu et al. 2024] + +![](images/23111430c5f7f09e99350d8d044340267d7311be7ca33433f062f10ea2558541.jpg) +Ours (Stage I) + +![](images/e1717ceeddbeaebd5fc61b6dea95957a22daa248e5b8e127b834fbc26a9f955a.jpg) +Ours (Stage II) +Figure 1. Top: For complex shadows in indoor scenes, current methods struggle to completely remove shadows, such as those behind the eagle sculpture. Bottom: Our method effectively removes the shadows, and with our second stage, the details from the original input, such as the wooden texture shown in the cropped image, are preserved. + +Drawing inspiration from recent advancements in zero-shot dense prediction [12, 42], we leverage the robust and comprehensive visual priors of the pre-trained Stable Diffusion (SD) model [29], which has been trained on billions of images, to enhance the generalization capability of shadow removal. However, developing a fine-tuning strategy that effectively removes shadows while preserving clear details in both shadowed and non-shadowed areas is not trivial. Unlike low-frequency depth and normal prediction tasks [12, 42], applying the SD model to shadow removal can result in detail loss and misalignment between the conditional image and the shadow-free output (Fig. 1). It is because the SD model, which consists of a Variational Autoencoder (VAE) and a Latent Diffusion Model (LDM), is designed for text-to-image generation and can lead to lossy compression during the mapping from pixel space + +$$ +(W \times H \times 3) \text {t o} (\frac {W}{8} \times \frac {H}{8} \times 4). +$$ + +To achieve stable and detail-preserving shadow removal using the pre-trained SD priors, we introduce a two-stage pipeline: 1) eliminating shadows in latent space by fixing the pre-trained VAE and fine-tuning the LDM and 2) injecting shadow-aware multi-resolution details from the original input into the VAE decoding process. + +In the first stage, our method retains the pre-trained VAE and fine-tunes the LDM by conditioning it on the latent features of the input shadow image. We do not fine-tune the VAE, as it effectively handles shadow-free images despite not being specifically trained for this purpose, and the scale of our shadow-free images is limited. Our findings indicate that the latent space from the VAE, combined with the generative priors from the LDM, enhances shadow removal tasks, particularly when annotated training data is scarce. By operating in a low-resolution latent space rather than high-resolution pixel space, our method performs global self-attention with acceptable memory consumption, capturing more global contextual information compared to convolution and window-based self-attention [21]. + +The fine-tuned SD model in the first stage produces visually appealing results, but it may lose some local details. To further enhance the quality of shadow removal, we propose a second stage for injecting shadow-free details. In this stage, we introduce a Detail Injection (DI) module that enhances the decoded latent features from the pre-trained VAE decoder by incorporating fine details from the input images. The VAE parameters are kept fixed. To prevent shadows from being reintroduced as "details", our DI module is equipped with shadow perception capabilities. Inspired by the observation that the shadow mask in the current shadow removal dataset is derived from the binary difference between shadowed and shadow-free images, we utilize concatenated features from the input shadow images and the coarse, shadow-free images decoded from the LDM output as cues for shadow-free detail injection. By combining features from both image types, the DI module can implicitly detect shadows and learn to inject shadow-free details into the VAE decoders. + +Note that Refusion [23] also performs latent-space diffusion for shadow removal. It captures input image information in the decoder [23] using a U-Net architecture specifically designed for large image shadow removal. However, the primary difference lies in the network design and finetuning strategy. Our method is designed to leverage the high-quality priors of the pre-trained VAE and LDM in the SD model, resulting in superior shadow removal quality. Our method can also handle high-resolution images (e.g., $1920 \times 1440$ in the WRSD dataset [35]), providing greater shadow removal efficiency compared to patch-based diffusion methods [22]. + +Overall, our contributions can be summarized as follows. + +- We propose a two-stage fine-tuning pipeline to transform a pre-trained Stable Diffusion model into an image-conditional shadow-free image generator. This approach enables robust, high-resolution shadow removal without an input shadow mask. +- We introduce a shadow-aware detail injection module that utilizes the VAE encoder features to modulate the pre-trained VAE decoders, selectively aligning per-pixel details from the input image with those in the output shadow-free image. +- Extensive experimental results on public datasets demonstrate that the proposed method significantly outperforms state-of-the-art shadow removal methods. Additionally, we show that our method exhibits better generalizability by training on one dataset and testing on another. + +# 2. Related Work + +# 2.1. Deep Shadow Removal + +Deep learning methods have significantly advanced shadow removal, enabling end-to-end learning of a mapping from input images to corresponding shadow-free images, with or without the aid of shadow masks. For example, DesshadowNet [28] combines multi-level features to predict a shadow matte, thereby enhancing the efficiency of shadow removal. Hu et al. [1, 10] utilize direction-aware spatial context for precise shadow detection and elimination. Fu et al. [3] formulate the shadow removal task as a multiple exposure image fusion problem. BMNet [48] introduces a bijective mapping that integrates shadow removal with shadow generation, improving overall performance in shadow removal tasks. + +More recently, ShadowFormer [4] presents a Swin-transformer-based shadow removal network that harnesses multi-scale attention to exploit contextual relationships between shadowed and non-shadowed regions. Meanwhile, DMTN [18] proposes a decoupled multi-task network that learns decomposed features specifically tailored for shadow removal. ShadowRefiner [2] introduces a mask-free model that integrates spatial and frequency domain representations for image shadow removal, achieving top results in the Perceptual Track of the NTIRE 2024 Image Shadow Removal Challenge [36]. Xu et al. [41] propose a path-tracing pipeline to generate shadow removal data that considers indirect illumination in indoor scenes. They also introduce a semantics and geometry-aware network for efficient mask-free shadow removal. HomoFormer [40] designs random shuffle and inverse shuffle operations to create a homogenized appearance of shadows, allowing for effective processing by local self-attention layers. + +![](images/272152aeda406124279e9a5dd4c7f77ebe30218aff1356fd56e34594acc2ace9.jpg) +Figure 2. Our proposed network. We propose a two-stage shadow removal network based on Stable Diffusion (SD). (1) In the first stage, as shown in the bottom half, we fine-tune the pre-trained UNet in SD within the latent space defined by SD's pre-trained VAE $(\mathcal{E}$ and $\mathcal{D})$ We found that the pre-trained latent space can effectively represent shadow-free images. (2) In the second stage, as shown in the top half, we modulate the VAE decoder $\mathcal{D}$ by selectively adding features from the VAE encoder $\mathcal{E}$ using a Detail Injection Model (DIM). The model consists of multiple RRDB layers, which inject shadow-free texture details into the decoder features. With these two stages, our proposed network can generate high-quality, shadow-free images that preserve fine details. + +# 2.2. Diffusion-based Shadow Removal + +Diffusion models [9, 34] are generative models that learn data distributions through Gaussian noise blurring and reverse denoising. Initially developed for image generation, these models have become prominent in applications including image super-resolution [31, 38], depth/normal prediction [12, 42], and shadow removal [23]. In the context of shadow removal, ShadowDiffusion [5] introduces a diffusion model that generates both a shadow-free image and a refined shadow mask, using shadow degradation as a prior and employing an unrolling diffusion process to eliminate shadows. DeS3 [11] enhances ShadowDiffusion by incorporating an adaptive attention mechanism and ViT similarity loss, removing the dependence on shadow masks. Guo et al.[6] propose a diffusion-based unsupervised shadow removal pipeline that utilizes a boundary-aware divide and conquer strategy. Diff-Shadow[22] employs a globally guided diffusion model pipeline that focuses on the patch and global information, enabling shadow removal in images of arbitrary resolution. Liu et al. [20] first separate reflectance and illumination, then use a diffusion model to correct degraded lighting in shadowed areas, followed by the progressive restoration of texture details through an illumination-guided texture restoration module. + +There are also methods that utilize a latent space to enhance diffusion-based shadow removal. Refusion [6] presents a U-Net-based latent diffusion model that utilizes + +mean-reverting stochastic differential equations for high-resolution image restoration tasks. The model performs image diffusion in a low-resolution latent space while preserving details through hidden-connections. However, being end-to-end trained on the shadow-removal dataset, it suffers from limited generalizability. Mei et al. [24] conduct diffusion-based shadow removal with a shadow mask at both the general and instance levels. They improve the diffusion process by conditioning on a learned latent feature space that captures the characteristics of shadow-free images and propose fusing noise features with the diffusion network to alleviate potential local optima. + +Unlike existing diffusion-based methods, we introduce a two-stage fine-tuning strategy that fully utilizes the visual priors from the pre-trained Stable Diffusion (SD) model [29]. With our latent shadow removal and shadow-aware detail injection stages, our method demonstrates strong generalization capability while effectively preserving non-shadow details. + +# 3. Proposed Method + +# 3.1. Overview + +Given a dataset of shadow and shadow-free image pairs $\langle \mathbf{x},\mathbf{y}\rangle \in \mathcal{X}$ , our goal is to train a network that can: 1. thoroughly eliminate shadows from the input image, and 2. preserve the content of all non-shadow areas. Although the first requirement focuses on the shadow (umbra) regions, the + +![](images/c7768cabf370df1b302b4bcc4f5831154a998a8ac496720a07f4c111ec781d54.jpg) + +![](images/077714820d38fd91c2ebf31a9ce9a92fb427f1ae1ea7171e6ad29f6f2c48db76.jpg) + +![](images/f7de41f68afaf984932f1634c969b96ceedd14741f5664a05aa8c1694e05a6d8.jpg) +Shadow image x +Shadow-free image y +Figure 3. Latent space in VAE. We apply the pre-trained encoding and decoding process on a shadow image $\mathbf{x}$ or a shadow-free image $\mathbf{y}$ . For a shadow-free image, this process does not introduce additional shadows, meaning the pre-trained latent space can also represent the shadow-free image. However, as shown in the zoomed-in view, some details, like text, may be lost in this process. + +![](images/3eed971872654ffc2402ef114305b92768ea57c29d745aec6f86c6e8233bbe55.jpg) +$\mathcal{D}(\mathcal{E}(\mathbf{x}))$ +$\pmb{D}(\pmb{\mathcal{E}}(\mathbf{y}))$ + +second is more concerned with non-shadow areas. These two objectives can be contradictory, making it challenging to design a single network that effectively addresses both. Therefore, we propose a two-stage shadow removal framework to robustly eliminate various types of shadows across different scenarios (Fig. 2). + +In the first stage, as shown at the bottom of Fig. 2, we perform shadow removal in latent space (Sec. 3.2). We condition the Stable Diffusion (SD) model [29] using the latent code of the input shadow image $\mathbf{z}^{\mathrm{x}}$ and fine-tune a pretrained SD model to generate the latent code of a shadow-free image $\mathbf{z}_0^{\mathbf{y}}$ . As shown in Fig. 1, this latent code can be decoded into a coarse image that effectively eliminates shadows, although some details may be lost. + +In the second stage, as illustrated at the top of Fig. 2, we perform detail injection using the encoder $\mathcal{E}$ and decoder $\mathcal{D}$ within SD (Sec.3.3). We fix the pretrained encoder and decoder and employ a set of Detail Injection (DI) models to integrate shadow-free details into the decoder features. These details are derived from each encoder layer. After training on pairs of shadow and shadow-free images, the DI models learn to inject details from the input image that are free of shadows. + +# 3.2. Shadow Removal in Latent Space + +Building on recent advancements in dense prediction tasks [7, 12, 42], we formulate the shadow removal task in the first stage as an image-conditioned annotation generation problem using SD. This approach conducts the dif + +fusion process within a low-dimensional latent space generated by a pair of encoder and decoder $\langle \mathcal{E},\mathcal{D}\rangle$ , where $\mathcal{E}(\mathbf{x}) = \mathbf{z}^{\mathbf{x}}$ and $\mathcal{D}(\mathbf{z}^{\mathbf{x}})\approx \mathbf{x}$ + +Compared to the diffusion model [9], Stable Diffusion offers enhanced generation stability and training efficiency. However, given the limited number of shadow and shadow-free image pairs, we opt for a fine-tuning strategy rather than training a SD model from scratch. We directly utilize the pre-trained $\mathcal{E}$ and $\mathcal{D}$ in SD and focus on fine-tuning the denoiser U-Net, as we have found that the pre-trained $\mathcal{E}$ and $\mathcal{D}$ perform well for both shadow and non-shadow images, even though they were not specifically trained on shadow-free images (Fig. 3). + +Fine-tuning Process. The fine-tuning for Stable Diffusion [9] relies on forward-noising and reverse-denoising processes that operate within the latent space. In the forward process, Gaussian noise is progressively added over time steps $t \in [1,T]$ to the sample $\mathbf{z}_{\mathbf{t}}^{\mathbf{y}}$ , generating a noisy sample $\mathbf{z}_{\mathbf{t}}^{\mathbf{y}}$ : + +$$ +\mathbf {z} _ {\mathrm {t}} ^ {\mathbf {y}} = \sqrt {\bar {\alpha} _ {t}} \mathbf {z} ^ {\mathbf {y}} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \tag {1} +$$ + +where $\epsilon \sim \mathcal{N}(0,I)$ , $\overline{\alpha}_t\coloneqq \prod_{s = 1}^t (1 - \beta_s)$ , and $\beta_{1},\beta_{2},\ldots$ $\beta_{T}$ defines the noise schedule over $T$ steps. In the reverse process, a U-Net [30] denoted as $f_{\theta}$ takes the encoding features of the input image $\mathbf{z}^{\mathbf{x}}$ and the sample $\mathbf{z}_{\mathbf{t}}^{\mathbf{y}}$ as inputs, outputting a prediction of the clean sample $\hat{\mathbf{z}}^{\mathbf{y}}$ : + +$$ +\hat {\mathbf {z}} ^ {\mathbf {y}} = f _ {\theta} \left(\mathbf {z} _ {\mathbf {t}} ^ {\mathbf {y}}, \mathbf {z} ^ {\mathbf {x}}, t\right). \tag {2} +$$ + +During fine-tuning, we randomly sample a time step $t \in [1, T]$ and minimize the corresponding loss function $L_{t}$ : + +$$ +\mathcal {L} _ {t} = \left\| \mathbf {z} ^ {\mathbf {y}} - f _ {\theta} \left(\mathbf {z} _ {\mathbf {t}} ^ {\mathbf {y}}, \mathbf {z} ^ {\mathbf {x}}, t\right) \right\| _ {2} ^ {2}, \tag {3} +$$ + +where $\mathbf{z}^{\mathbf{y}}$ is the encoding features of the ground-truth shadow-free image. + +Denoising Process. During inference, we use DDIM [33], which implements an implicit probabilistic model that can significantly reduce the number of denoising steps while maintaining output quality. Formally, the denoising process from $\mathbf{z}_{\tau}^{\mathbf{y}}$ to $\mathbf{z}_{\tau -1}^{\mathbf{y}}$ is: + +$$ +\mathbf {z} _ {\tau - 1} ^ {\mathbf {y}} = \sqrt {\bar {\alpha} _ {\tau - 1}} \hat {\mathbf {z}} _ {\tau} ^ {\mathbf {y}} + \operatorname {d i r e c t i o n} \left(\mathbf {z} _ {\tau} ^ {\mathbf {y}}\right) + \sigma_ {\tau} \epsilon_ {\tau}, \tag {4} +$$ + +where $\hat{\mathbf{z}}_{\tau}^{\mathbf{y}}$ is the predicted clean sample at the denoising step $\tau$ , $\text{direction}(\mathbf{z}_{\tau}^{\mathbf{y}})$ represents the direction pointing to $\mathbf{z}_{\tau}^{\mathbf{y}}$ . $\tau \in \{\tau_1, \tau_2, \dots, \tau_S\}$ is an increasing sub-sequence of the timestep set $[1, T]$ used for fast sampling. + +![](images/14b35b49bd905aeac4717c1211d31cca8c6e33bd551639c06d58f8f628717878.jpg) +Input + +![](images/eac43e3dd0323ce53b1d3e2de14ea4f1bebbed1da577a9588e73d7ca3f144651.jpg) +Ours (stage I) + +![](images/5d31ab584636a13c790ff14b345ad76a1ae0d7254fea65923d261203fbe44270.jpg) +Ours (stage II) + +![](images/7d40f72e781b96362e882dd62cc7ad2533d9f7efc14aada3e94f82950dee1629.jpg) +RRDB feature vis. +Figure 4. Some details in the input image, such as the textures on the floor, change during latent space diffusion in stage one. In stage two, our method preserves these high-quality details while effectively removing shadows. As shown in the bottom-left image, where we map the RRDB features to three dimensions using PCA, we observe that shadow areas have distinct features (in green), indicating that our detail injection model is shadow-aware. + +# 3.3. Shadow-aware Detail Injection + +As illustrated in Fig. 4, while the output of the conditional Stable Diffusion is visually striking—especially in its ability to completely remove shadows—it often diverges from the ground truth, particularly in high-detail areas, such as the floor texture. We believe the primary reason for this is the loss of high-frequency information in the latent space. As shown in Fig. 3, directly decoding the encoded features $\mathcal{D}(\mathcal{E}(\mathbf{x}))$ also results in a loss of detail. + +To eliminate shadows while preserving details, we introduce a shadow-aware detail injection step utilizing a set of DI models. Each model selectively extracts information from a specific intermediate layer of $\mathcal{E}$ to modulate the corresponding intermediate layers of $\mathcal{D}$ . Let $\mathbf{e}_i$ and $\mathbf{d}_i$ denote the encoder and decoder features for the $i$ -th intermediate layer. The DI model takes the concatenation of $\mathbf{e}_i$ and $\mathbf{d}_i$ as input, output a modulated feature $\tilde{\mathbf{d}}_i$ : + +$$ +\mathbf {d} _ {0} = \mathbf {z} _ {0} ^ {\mathbf {y}}, \tag {5} +$$ + +$$ +\tilde {\mathbf {d}} _ {i} = \mathbf {d} _ {i} + \operatorname {C o n v} (\operatorname {R R D B} (\operatorname {C o n v} (\mathbf {d} _ {i}, \mathbf {e} _ {n - i} (\mathbf {z} ^ {\mathbf {x}})), f _ {d} (\mathbf {x}))), +$$ + +$$ +\mathbf {d} _ {i} = \mathcal {D} _ {i - 1} (\tilde {\mathbf {d}} _ {i - 1}), i \in [ 1, 4 ], \hat {\mathbf {y}} = \operatorname {C o n v} (\tilde {\mathbf {d}} _ {4}) +$$ + +Here, $\mathrm{RRDB}(\cdot)$ refers to the Residual-in-Residual Dense Block module [46], which consists of three Dense Blocks. $\hat{\mathbf{y}}$ is predicted shadow-free image. $f_{d}(\mathbf{x})$ are features extracted using DINO v2 [26]. We concatenate the DINO features with $\mathbf{e}_i$ and $\mathbf{d}_i$ after passing through a convolutional layer to enhance the generalizability of the DI models. + +
    MethodMean↑Variance↓
    Our stage one (ε-pred)29.660.239
    Our stage one (z0-pred)29.950.146
    Our stage two35.020.160
    DeS3 [11]31.331.075
    + +Table 1. Low variance. In the first stage, our method achieves reduced variance by using $\mathbf{z}_0$ -prediction. In the second stage, our method improves PSNR while maintaining low variance, resulting in robust, high-quality shadow removal results. + +Since $\mathbf{e}_i$ and $\mathbf{d}_i$ contain features from the input shadow image $\mathbf{x}$ and the shadow-free latent code $\mathbf{z}_0^{\mathbf{y}}$ , respectively, our DI models can effectively identify shadow areas by utilizing both features as input. Although the latent codes may lose high-frequency details, they still provide valuable cues for shadow regions, which are primarily low-frequency. As illustrated in Fig. 4, where we visualize the features in the last layer of the RRDB module, we can observe that the shadow areas exhibit distinct feature responses. We present only the RRDB responses for $\mathbf{d}_2$ . Please refer to the supplementary for additional results. + +Losses. To train the DI models, we minimize a total loss $\mathcal{L}_{total}$ , which combines an L1 loss and a perceptual loss measured using the Learned Perceptual Image Patch Similarity (LPIPS) metric [45] between the output image $\hat{\mathbf{y}}$ and the ground-truth shadow-free image $\mathbf{y}$ : + +$$ +\mathcal {L} _ {\text {t o t a l}} = \left\| \hat {\mathbf {y}} - \mathbf {y} \right\| _ {1} + \left\| \operatorname {L P I P S} (\hat {\mathbf {y}}) - \operatorname {L P I P S} (\mathbf {y}) \right\| _ {2} ^ {2}. \tag {6} +$$ + +# 3.4. Implementation Details. + +Reducing variance. As shown in Eq. 3, in the LDM fin-tuning stage, we use $\mathbf{z}_0$ -prediction rather than the standard $\epsilon$ -prediction parameterization for the denoising model. This choice, as recommended by Lotus[7], helps reduce variance during stochastic LDM inference. We compare these two approaches on the $\mathrm{ISTD + }$ [14] dataset by running inference on the test set with five different random seeds (1, 2, 3, 4, 5). We calculate the PSNR variance across the five outputs for each image and obtain the average variance. As shown in Table 1, using $\mathbf{z}_0$ -prediction in our LDM fin-tuning stage yields higher PSNR and lower variance compared to $\epsilon$ -prediction. Additionally, we assess the average variance of our final results after the detail injection stage, and Table 1 shows that our final results have significantly lower variance than DeS3 [11], another mask-free shadow removal method based on diffusion models. It indicates that our generative shadow removal method is highly robust to randomness, which is a critical factor for practical use. + +Training details. Our model is trained on a GPU server with four GeForce RTX 4090 GPUs using PyTorch + +
    MethodYearMask-freeISTD+ DatasetSRD DatasetINS DatasetWSRD+ Dataset
    PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
    AutoExposure [3]2021No29.450.86129.240.93827.910.95721.660.752
    Zhu et al. [49]2022No——32.050.965————
    BMNet [48]2022No33.980.97231.970.96527.900.95824.750.816
    ShadowFormer [4]2023No35.460.97132.900.95828.620.96325.440.820
    DMTN [18]2023No32.230.96633.770.96828.830.969——
    ShadowDiffusion [5]2023No34.630.96734.730.97029.120.966——
    HomoFormer [40]2024No35.720.97734.360.97728.980.965——
    InstanceShadow [24]2024No34.690.96831.610.95928.160.948——
    TBRNet [19]2023Yes31.910.96431.830.953————
    Refusion [23]2023Yes32.410.96131.600.94928.130.95822.320.738
    DeS3 [11]2024Yes31.390.95734.110.96827.890.947——
    OmniSR [41]2024Yes33.340.97032.870.96930.380.97326.070.835
    Ours—Yes35.190.97433.630.96830.560.97526.260.827
    + +Table 2. Quantitative comparisons on ISTD+, SRD, INS, and WSRD+ datasets. Best results are highlighted as 1st , 2nd and 3rd . Refer to the supplementary material for the MAE values in both shadowed and non-shadowed areas. + +2.0.1 [27] with CUDA 11.7. We employ the Adam optimizer [13] for training. In the first stage, the LDM is finetuned for 40 epochs on INS [41] and 200 and 300 epochs on $\mathrm{ISTD + }$ [14, 37] and SRD [28], respectively. We utilize a constant learning rate of $3\times 10^{-4}$ with a batch size 16. For the INS dataset, each batch consists of $512\times 512$ patches, while for the other datasets, batches are composed of randomly cropped $480\times 480$ patches. + +In the second stage, we maintain the constant learning rate of $5 \times 10^{-4}$ and batch size of 16. The batch shapes for each dataset are consistent with those in the first stage, and the number of epochs for training the detail injection models is 50 for INS and 300 and 200 for $\mathrm{ISTD + }$ and SRD, respectively. For the DINO features [26], we resize the image to $\frac{14W}{16} \times \frac{14H}{16}$ using bilinear interpolation, extract the DINO features, and apply a $1 \times 1$ convolution layer to obtain a feature map of shape $256 \times \frac{W}{16} \times \frac{H}{16}$ . To reduce memory footprint, we only concatenate the DINO features with the first two layers of the VAE decoder. Additional details can be found in the supplementary. + +# 4. Experiments + +Datasets. We conduct experiments on four shadow removal datasets: SRD [28], $\mathrm{ISTD + }$ [14, 37], $\mathrm{WSRD + }$ [35, 36], and INS [41]. The SRD dataset [28] includes 3,088 paired shadow and shadow-free images, divided into 2,680 for training and 408 for testing. The $\mathrm{ISTD + }$ dataset [14, 37] provides 1,870 triplets of shadow images, shadow masks, and shadow-free images, with 1,330 used for training and 540 for testing. $\mathrm{WSRD + }$ [35, 36] contains 1,000 pairs of shadow and non-shadow images captured under both spotlight and diffuse illumination. Since the test data is not open-sourced, we use its 100 validation images for test + +ing. Lastly, the INS dataset [41] comprises 30,000 synthetic training images under direct and indirect illumination, a synthetic test set of 2,000 images. + +Evaluation Metrics. Following previous methods [3, 4, 15], we evaluated images with a resolution of $256 \times 256$ . We report results using the Peak Signal-to-Noise Ratio (PSNR) and the Structure Similarity Index Measure (SSIM) [39], adopting the MATLAB evaluation codes as provided by Zhu et al. [49]. For the WSRD+ [35] dataset, we used its evaluation data and the evaluation code provided by the NTIRE 2024 Image Shadow Removal Challenge [36] for comparison. + +# 4.1. Comparisons + +We compare our method to twelve state-of-the-art shadow removal techniques, evaluating both quantitatively and qualitatively. Among these, eight methods require a shadow mask as input: AutoExposure [3], Zhu et al. [49], BMNet [48], ShadowFormer [4], DMTN [18], ShadowDiffusion [5], and HomoFormer [40]. The remaining four methods—TBRNet [19], Refusion [23], Des3 [11], and OmniSR [41]—are mask-free, meaning they do not require a shadow mask as input. All comparisons use the original authors' implementations and hyperparameters, or the provided checkpoints or results, if available. For the INS dataset, we train these methods following the procedure in OmniSR [41]. + +For methods that are not mask-free, we use the shadow masks provided by the dataset as the default input. Since SRD [28] does not provide masks, we use the shadow masks generated by DHAN [1], which computes shadow matting from shadow/shadow-free pairs and generates binary masks through thresholding. In the case of the INS dataset, + +![](images/2a8bf2be57878fb14441713c921c62c1276f72c3336a1c15404a6816495a5d77.jpg) +Figure 5. Comparisons with SOTA shadow removal methods on the ISTD+ and SRD datasets. The input mask, required by methods that are not mask-free, is shown in the top-left corner. + +![](images/783f2c7acad6c86c8fc7ee4102fa673503fb7d55465cd720517565650873bf4b.jpg) +Figure 6. Comparisons with SOTA shadow removal methods in real scenes. We compare our method to OmniSR [41], HomoFormer [40], Refusion [23], and ShadowDiffusion [5], all trained on the INS dataset [41]. Results show that our approach achieves more comprehensive shadow removal, even in complex scenes. + +its shadow masks are represented as 0-1 probability maps rather than binary masks. Since it is a synthetic dataset with highly accurate masks, we found that using them as input results in methods producing outputs nearly identical to the ground truth (with PSNR values exceeding 50). To address this, following OmniSR [41], we use FDRNet [47] to detect shadow masks and input the detected masks instead. + +As shown in Table 2, our method achieves the highest PSNR score on the INS dataset. On the $\mathrm{ISTD + }$ dataset, our approach is the best mask-free method, performing only slightly below HomoFormer [40] and ShadowFormer [4], which use ground-truth shadow masks as input, and outperforming most other methods that also rely on ground-truth + +shadow masks. As shown in the first two columns of Fig. 5, although without mask as input, our method is capable of thoroughly removing shadows, even with limited semantic context. We think it is because of leveraging the generative priors in our latent diffusion model. + +For the SRD dataset, our method also delivers competitive results compared to methods that utilize masks provided by DHAN [1]. Among shadow-free methods, our performance is second only to DeS3. As illustrated in Fig. 5, our method produces visually appealing results with nearly complete shadow removal. We found that our method achieves better shadow removal quality than DeS3; however, in areas with highly detailed textures, such as sand + +
    MethodISTD+→SRDSRD→ISTD+INS→WSRD+
    PSNRSSIMPSNRSSIMPSNRSSIM
    ShadowDiffusion24.260.89029.480.94719.400.825
    Refusion22.560.88627.310.92418.730.787
    DeS322.090.880————
    OmniSR25.860.91730.190.95120.030.825
    Ours26.230.92330.230.95320.110.828
    + +and grass, the PSNR is lower than that of DeS3. + +On the INS dataset, our method achieves the highest PSNR and SSIM, as shown in Table 2. We also compare our method with others on real indoor scene images, all trained on the INS dataset. As illustrated in Fig. 6, our approach more effectively removes shadows from multiple light sources, such as those beneath the table and chair, as well as soft shadows behind the small planter and on the bookshelf in the background. + +We further evaluated our method on high-resolution shadow removal using the WSRD+ [35] dataset, with images at $1920 \times 1440$ resolution. The first stage requires no modification. We resize each image to $640 \times 480$ for the LDM fine-tuning. In the second stage, we introduce a minor adjustment by adding one patch-partition layer and one patch-merging layer [21]. Additional details are provided in the supplementary materials. As shown in Table 2, our method outperforms others on the WSRD+ dataset, with more results available in the supplementary material. The relatively low PSNR scores for all methods on the WSRD+ dataset can be attributed to exposure differences between the input and ground-truth images. + +# 4.2. Cross-dataset evaluation. + +To evaluate the generalizability of our approach, we conduct a cross-dataset evaluation. Specifically, we train our model on the training set of one dataset and test it on the testing set of a different dataset. Typically, training and testing data within the same dataset share similar shadow patterns, backgrounds, or lighting conditions. This cross-dataset evaluation presents a more challenging test for shadow removal methods and provides a more stringent measure of generalizability. We use $A \rightarrow B$ to denote training on dataset $A$ and testing on dataset $B$ . As shown in Table 3, our method achieves the best results on ISTD+→SRD, SRD→ISTD+, and INS→WSRD+. Here, we compare only with DeS3 [11] on ISTD+→SRD, as it provides checkpoints only for ISTD+ dataset. Its open-source code is a basic version that excludes certain components, including the VIT loss. For the INS→WSRD+ experiment, high-resolution images from the WSRD+ dataset are resized to $640 \times 480$ for inference and evaluation. Qual- + +Table 3. Cross-dataset evaluation. $\mathrm{ISTD} + \rightarrow$ SRD means training on the $\mathrm{ISTD}+$ dataset and testing on the SRD dataset. + +
    DatasetISTD+ PSNR/SSIMSRD PSNR/SSIMINS PSNR/SSIM
    Full35.19/0.97433.63/0.96830.56/ 0.975
    W/o pre-train33.38/0.96732.46/0.96329.55/0.970
    Stage one29.95/0.84328.18/0.86828.78/0.924
    Stage one (w/o pre-train)28.12/0.82227.48/0.86126.92/0.909
    W/o DINO34.76/0.97133.04/0.96530.30/0.975
    + +Table 4. Ablation studies. W/o pre-train: without pre-training. W/o DINO: without DINO in the detail injection model. + +itative comparisons for this evaluation are provided in the supplementary material. + +# 4.3. Ablation study. + +To validate our model design, we conducted ablation studies on the use of the pretrained SD model, the two-stage pipeline, and the incorporation of DINO features. The results are presented in Table 4. To demonstrate the effectiveness of the generative priors in the SD model, we include an ablation study under the "without pre-training" setting, where the model is trained from scratch on each respective shadow removal dataset. The results indicate that pre-training significantly enhances shadow removal performance, as omitting it in both stage one and the full model leads to a substantial decline in PSNR and SSIM. Furthermore, stage two plays a crucial role in our method, as its removal results in a marked drop in PSNR and SSIM. This is primarily due to stage one's limitations in preserving high-frequency details. Additionally, integrating DINO features into the detail injection model of stage two proves advantageous, consistently improving PSNR and SSIM across all three datasets. For qualitative results related to the ablation study, please refer to the supplementary materials. + +# 5. Conclusion + +This paper introduces a novel detail-preserving latent diffusion pipeline that effectively eliminates complex shadows while preserving shadow-free details. The proposed method leverages the rich visual priors of a pre-trained Stable Diffusion model and propose a two-stage fine-tuning strategy to adapt the SD model for stable and efficient shadow removal. Extensive experiments demonstrate that our approach outperforms state-of-the-art shadow removal methods, particularly in terms of generalizability. + +Limitation and future work. Our method may still miss some shadows in complex scenes, such as the self-shadows on the flower pot in Fig. 6. Additionally, in some cases, our approach focuses more on resolving the color variations caused by shadows and cannot fully preserve the exposure in non-shadow areas. In the future, we plan to incorporate unsupervised or self-supervised signals to further enhance the generalizability of our method. + +# Acknowledgement + +We thank the anonymous reviewers for their professional and constructive comments. This work was funded by NSFC grant No. 62302134, "Pioneer" and "Leading Goose" R&D Program of Zhejiang Province (No. 2025C01086), Zhejiang Provincial Natural Science Foundation under Grant No. LQ24F020031, the Fundamental Research Funds for the Provincial Universities of Zhejiang under Grant No. GK249909299001-021. Renshu Gu is partially supported by NSFC grant No. 62202130 and U22A2033. 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Due to the limited diversity in shadow removal datasets, current methods are prone to overfitting training data, often leading to reduced performance on unseen cases. To address this, we leverage the rich visual priors of a pre-trained Stable Diffusion (SD) model and propose a two-stage fine-tuning pipeline to adapt the SD model for stable and efficient shadow removal. In the first stage, we fix the VAE and fine-tune the denoiser in latent space, which yields substantial shadow removal but may lose some high-frequency details. To resolve this, we introduce a second stage, called the detail injection stage. This stage selectively extracts features from the VAE encoder to modulate the decoder, injecting fine details into the final results. Experimental results show that our method outperforms state-of-the-art shadow removal techniques. The cross-dataset evaluation further demonstrates that our method generalizes effectively to unseen data, enhancing the applicability of shadow removal methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 517, + 135, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 135, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 135, + 529 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 537, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 537, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 537, + 296, + 693 + ], + "type": "text", + "content": "Shadows are natural phenomena that occur when an obstacle blocks global light transport. They provide crucial cues for interpreting the three-dimensional structure of objects and scenes [44]. However, shadows can also hinder computer vision tasks, such as object segmentation [8], tracking [32], and intrinsic decomposition [16, 17, 25, 43]. In recent years, deep-learning-based methods for shadow removal [4, 5, 24, 40] have shown significant advancements by learning pixel-wise mappings between shadowed images and their corresponding ground-truth shadow-free versions in a fully supervised manner. However, such approaches often risk overfitting the limited training datasets [14, 28, 35], leading to inadequate generalization." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 226, + 430, + 311 + ], + "blocks": [ + { + "bbox": [ + 316, + 226, + 430, + 311 + ], + "lines": [ + { + "bbox": [ + 316, + 226, + 430, + 311 + ], + "spans": [ + { + "bbox": [ + 316, + 226, + 430, + 311 + ], + "type": "image", + "image_path": "456ed4cc2a0bb4fd5466b07b9674192bc2f4ea2fe19cbb6924ae8f78cfc2faeb.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 353, + 312, + 391, + 319 + ], + "lines": [ + { + "bbox": [ + 353, + 312, + 391, + 319 + ], + "spans": [ + { + "bbox": [ + 353, + 312, + 391, + 319 + ], + "type": "text", + "content": "Input image" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 434, + 226, + 548, + 311 + ], + "blocks": [ + { + "bbox": [ + 434, + 226, + 548, + 311 + ], + "lines": [ + { + "bbox": [ + 434, + 226, + 548, + 311 + ], + "spans": [ + { + "bbox": [ + 434, + 226, + 548, + 311 + ], + "type": "image", + "image_path": "57f04bcb6d77ca5e06ca5b955f836e2a6f38699cb9fb13b5691cb227f6548d97.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 455, + 312, + 528, + 319 + ], + "lines": [ + { + "bbox": [ + 455, + 312, + 528, + 319 + ], + "spans": [ + { + "bbox": [ + 455, + 312, + 528, + 319 + ], + "type": "text", + "content": "OmniSR [Xu et al. 2024]" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 315, + 321, + 433, + 406 + ], + "blocks": [ + { + "bbox": [ + 315, + 321, + 433, + 406 + ], + "lines": [ + { + "bbox": [ + 315, + 321, + 433, + 406 + ], + "spans": [ + { + "bbox": [ + 315, + 321, + 433, + 406 + ], + "type": "image", + "image_path": "23111430c5f7f09e99350d8d044340267d7311be7ca33433f062f10ea2558541.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 350, + 407, + 393, + 415 + ], + "lines": [ + { + "bbox": [ + 350, + 407, + 393, + 415 + ], + "spans": [ + { + "bbox": [ + 350, + 407, + 393, + 415 + ], + "type": "text", + "content": "Ours (Stage I)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 435, + 321, + 553, + 406 + ], + "blocks": [ + { + "bbox": [ + 435, + 321, + 553, + 406 + ], + "lines": [ + { + "bbox": [ + 435, + 321, + 553, + 406 + ], + "spans": [ + { + "bbox": [ + 435, + 321, + 553, + 406 + ], + "type": "image", + "image_path": "e1717ceeddbeaebd5fc61b6dea95957a22daa248e5b8e127b834fbc26a9f955a.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 407, + 515, + 415 + ], + "lines": [ + { + "bbox": [ + 468, + 407, + 515, + 415 + ], + "spans": [ + { + "bbox": [ + 468, + 407, + 515, + 415 + ], + "type": "text", + "content": "Ours (Stage II)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 429, + 555, + 495 + ], + "lines": [ + { + "bbox": [ + 313, + 429, + 555, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 429, + 555, + 495 + ], + "type": "text", + "content": "Figure 1. Top: For complex shadows in indoor scenes, current methods struggle to completely remove shadows, such as those behind the eagle sculpture. Bottom: Our method effectively removes the shadows, and with our second stage, the details from the original input, such as the wooden texture shown in the cropped image, are preserved." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 522, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 556, + 715 + ], + "type": "text", + "content": "Drawing inspiration from recent advancements in zero-shot dense prediction [12, 42], we leverage the robust and comprehensive visual priors of the pre-trained Stable Diffusion (SD) model [29], which has been trained on billions of images, to enhance the generalization capability of shadow removal. However, developing a fine-tuning strategy that effectively removes shadows while preserving clear details in both shadowed and non-shadowed areas is not trivial. Unlike low-frequency depth and normal prediction tasks [12, 42], applying the SD model to shadow removal can result in detail loss and misalignment between the conditional image and the shadow-free output (Fig. 1). It is because the SD model, which consists of a Variational Autoencoder (VAE) and a Latent Diffusion Model (LDM), is designed for text-to-image generation and can lead to lossy compression during the mapping from pixel space" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7592" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 235, + 86 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 235, + 86 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 235, + 86 + ], + "type": "interline_equation", + "content": "(W \\times H \\times 3) \\text {t o} (\\frac {W}{8} \\times \\frac {H}{8} \\times 4).", + "image_path": "840d6e95a116062f84c396bac291ee67ebb6ba7041f144a1013db31514779b29.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 86, + 294, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 86, + 294, + 158 + ], + "spans": [ + { + "bbox": [ + 55, + 86, + 294, + 158 + ], + "type": "text", + "content": "To achieve stable and detail-preserving shadow removal using the pre-trained SD priors, we introduce a two-stage pipeline: 1) eliminating shadows in latent space by fixing the pre-trained VAE and fine-tuning the LDM and 2) injecting shadow-aware multi-resolution details from the original input into the VAE decoding process." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 159, + 295, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 159, + 295, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 159, + 295, + 326 + ], + "type": "text", + "content": "In the first stage, our method retains the pre-trained VAE and fine-tunes the LDM by conditioning it on the latent features of the input shadow image. We do not fine-tune the VAE, as it effectively handles shadow-free images despite not being specifically trained for this purpose, and the scale of our shadow-free images is limited. Our findings indicate that the latent space from the VAE, combined with the generative priors from the LDM, enhances shadow removal tasks, particularly when annotated training data is scarce. By operating in a low-resolution latent space rather than high-resolution pixel space, our method performs global self-attention with acceptable memory consumption, capturing more global contextual information compared to convolution and window-based self-attention [21]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 327, + 295, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 295, + 554 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 295, + 554 + ], + "type": "text", + "content": "The fine-tuned SD model in the first stage produces visually appealing results, but it may lose some local details. To further enhance the quality of shadow removal, we propose a second stage for injecting shadow-free details. In this stage, we introduce a Detail Injection (DI) module that enhances the decoded latent features from the pre-trained VAE decoder by incorporating fine details from the input images. The VAE parameters are kept fixed. To prevent shadows from being reintroduced as \"details\", our DI module is equipped with shadow perception capabilities. Inspired by the observation that the shadow mask in the current shadow removal dataset is derived from the binary difference between shadowed and shadow-free images, we utilize concatenated features from the input shadow images and the coarse, shadow-free images decoded from the LDM output as cues for shadow-free detail injection. By combining features from both image types, the DI module can implicitly detect shadows and learn to inject shadow-free details into the VAE decoders." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 556, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 556, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 556, + 295, + 700 + ], + "type": "text", + "content": "Note that Refusion [23] also performs latent-space diffusion for shadow removal. It captures input image information in the decoder [23] using a U-Net architecture specifically designed for large image shadow removal. However, the primary difference lies in the network design and finetuning strategy. Our method is designed to leverage the high-quality priors of the pre-trained VAE and LDM in the SD model, resulting in superior shadow removal quality. Our method can also handle high-resolution images (e.g., " + }, + { + "bbox": [ + 55, + 556, + 295, + 700 + ], + "type": "inline_equation", + "content": "1920 \\times 1440" + }, + { + "bbox": [ + 55, + 556, + 295, + 700 + ], + "type": "text", + "content": " in the WRSD dataset [35]), providing greater shadow removal efficiency compared to patch-based diffusion methods [22]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 701, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 294, + 712 + ], + "type": "text", + "content": "Overall, our contributions can be summarized as follows." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 72, + 553, + 252 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 314, + 72, + 553, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 553, + 132 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 553, + 132 + ], + "type": "text", + "content": "- We propose a two-stage fine-tuning pipeline to transform a pre-trained Stable Diffusion model into an image-conditional shadow-free image generator. This approach enables robust, high-resolution shadow removal without an input shadow mask." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 133, + 553, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 133, + 553, + 192 + ], + "spans": [ + { + "bbox": [ + 314, + 133, + 553, + 192 + ], + "type": "text", + "content": "- We introduce a shadow-aware detail injection module that utilizes the VAE encoder features to modulate the pre-trained VAE decoders, selectively aligning per-pixel details from the input image with those in the output shadow-free image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 192, + 553, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 192, + 553, + 252 + ], + "spans": [ + { + "bbox": [ + 314, + 192, + 553, + 252 + ], + "type": "text", + "content": "- Extensive experimental results on public datasets demonstrate that the proposed method significantly outperforms state-of-the-art shadow removal methods. Additionally, we show that our method exhibits better generalizability by training on one dataset and testing on another." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 284, + 400, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 284, + 400, + 296 + ], + "spans": [ + { + "bbox": [ + 314, + 284, + 400, + 296 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 311, + 444, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 311, + 444, + 323 + ], + "spans": [ + { + "bbox": [ + 314, + 311, + 444, + 323 + ], + "type": "text", + "content": "2.1. Deep Shadow Removal" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 335, + 555, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 335, + 555, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 555, + 491 + ], + "type": "text", + "content": "Deep learning methods have significantly advanced shadow removal, enabling end-to-end learning of a mapping from input images to corresponding shadow-free images, with or without the aid of shadow masks. For example, DesshadowNet [28] combines multi-level features to predict a shadow matte, thereby enhancing the efficiency of shadow removal. Hu et al. [1, 10] utilize direction-aware spatial context for precise shadow detection and elimination. Fu et al. [3] formulate the shadow removal task as a multiple exposure image fusion problem. BMNet [48] introduces a bijective mapping that integrates shadow removal with shadow generation, improving overall performance in shadow removal tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 715 + ], + "type": "text", + "content": "More recently, ShadowFormer [4] presents a Swin-transformer-based shadow removal network that harnesses multi-scale attention to exploit contextual relationships between shadowed and non-shadowed regions. Meanwhile, DMTN [18] proposes a decoupled multi-task network that learns decomposed features specifically tailored for shadow removal. ShadowRefiner [2] introduces a mask-free model that integrates spatial and frequency domain representations for image shadow removal, achieving top results in the Perceptual Track of the NTIRE 2024 Image Shadow Removal Challenge [36]. Xu et al. [41] propose a path-tracing pipeline to generate shadow removal data that considers indirect illumination in indoor scenes. They also introduce a semantics and geometry-aware network for efficient mask-free shadow removal. HomoFormer [40] designs random shuffle and inverse shuffle operations to create a homogenized appearance of shadows, allowing for effective processing by local self-attention layers." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7593" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 73, + 553, + 277 + ], + "blocks": [ + { + "bbox": [ + 58, + 73, + 553, + 277 + ], + "lines": [ + { + "bbox": [ + 58, + 73, + 553, + 277 + ], + "spans": [ + { + "bbox": [ + 58, + 73, + 553, + 277 + ], + "type": "image", + "image_path": "272152aeda406124279e9a5dd4c7f77ebe30218aff1356fd56e34594acc2ace9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "lines": [ + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "spans": [ + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "text", + "content": "Figure 2. Our proposed network. We propose a two-stage shadow removal network based on Stable Diffusion (SD). (1) In the first stage, as shown in the bottom half, we fine-tune the pre-trained UNet in SD within the latent space defined by SD's pre-trained VAE " + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "inline_equation", + "content": "(\\mathcal{E}" + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{D})" + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "text", + "content": " We found that the pre-trained latent space can effectively represent shadow-free images. (2) In the second stage, as shown in the top half, we modulate the VAE decoder " + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "text", + "content": " by selectively adding features from the VAE encoder " + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 54, + 292, + 555, + 360 + ], + "type": "text", + "content": " using a Detail Injection Model (DIM). The model consists of multiple RRDB layers, which inject shadow-free texture details into the decoder features. With these two stages, our proposed network can generate high-quality, shadow-free images that preserve fine details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 378, + 237, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 378, + 237, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 378, + 237, + 392 + ], + "type": "text", + "content": "2.2. Diffusion-based Shadow Removal" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 399, + 296, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 399, + 296, + 674 + ], + "spans": [ + { + "bbox": [ + 56, + 399, + 296, + 674 + ], + "type": "text", + "content": "Diffusion models [9, 34] are generative models that learn data distributions through Gaussian noise blurring and reverse denoising. Initially developed for image generation, these models have become prominent in applications including image super-resolution [31, 38], depth/normal prediction [12, 42], and shadow removal [23]. In the context of shadow removal, ShadowDiffusion [5] introduces a diffusion model that generates both a shadow-free image and a refined shadow mask, using shadow degradation as a prior and employing an unrolling diffusion process to eliminate shadows. DeS3 [11] enhances ShadowDiffusion by incorporating an adaptive attention mechanism and ViT similarity loss, removing the dependence on shadow masks. Guo et al.[6] propose a diffusion-based unsupervised shadow removal pipeline that utilizes a boundary-aware divide and conquer strategy. Diff-Shadow[22] employs a globally guided diffusion model pipeline that focuses on the patch and global information, enabling shadow removal in images of arbitrary resolution. Liu et al. [20] first separate reflectance and illumination, then use a diffusion model to correct degraded lighting in shadowed areas, followed by the progressive restoration of texture details through an illumination-guided texture restoration module." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "There are also methods that utilize a latent space to enhance diffusion-based shadow removal. Refusion [6] presents a U-Net-based latent diffusion model that utilizes" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 379, + 555, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 379, + 555, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 379, + 555, + 521 + ], + "type": "text", + "content": "mean-reverting stochastic differential equations for high-resolution image restoration tasks. The model performs image diffusion in a low-resolution latent space while preserving details through hidden-connections. However, being end-to-end trained on the shadow-removal dataset, it suffers from limited generalizability. Mei et al. [24] conduct diffusion-based shadow removal with a shadow mask at both the general and instance levels. They improve the diffusion process by conditioning on a learned latent feature space that captures the characteristics of shadow-free images and propose fusing noise features with the diffusion network to alleviate potential local optima." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 522, + 556, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 556, + 608 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 556, + 608 + ], + "type": "text", + "content": "Unlike existing diffusion-based methods, we introduce a two-stage fine-tuning strategy that fully utilizes the visual priors from the pre-trained Stable Diffusion (SD) model [29]. With our latent shadow removal and shadow-aware detail injection stages, our method demonstrates strong generalization capability while effectively preserving non-shadow details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 616, + 421, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 616, + 421, + 630 + ], + "spans": [ + { + "bbox": [ + 313, + 616, + 421, + 630 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 636, + 382, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 636, + 382, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 636, + 382, + 647 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "content": "Given a dataset of shadow and shadow-free image pairs " + }, + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{x},\\mathbf{y}\\rangle \\in \\mathcal{X}" + }, + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "content": ", our goal is to train a network that can: 1. thoroughly eliminate shadows from the input image, and 2. preserve the content of all non-shadow areas. Although the first requirement focuses on the shadow (umbra) regions, the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "7594" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 70, + 174, + 138 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 174, + 138 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 174, + 138 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 174, + 138 + ], + "type": "image", + "image_path": "c7768cabf370df1b302b4bcc4f5831154a998a8ac496720a07f4c111ec781d54.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 179, + 70, + 289, + 138 + ], + "blocks": [ + { + "bbox": [ + 179, + 70, + 289, + 138 + ], + "lines": [ + { + "bbox": [ + 179, + 70, + 289, + 138 + ], + "spans": [ + { + "bbox": [ + 179, + 70, + 289, + 138 + ], + "type": "image", + "image_path": "077714820d38fd91c2ebf31a9ce9a92fb427f1ae1ea7171e6ad29f6f2c48db76.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 62, + 148, + 173, + 244 + ], + "blocks": [ + { + "bbox": [ + 89, + 140, + 146, + 148 + ], + "lines": [ + { + "bbox": [ + 89, + 140, + 146, + 148 + ], + "spans": [ + { + "bbox": [ + 89, + 140, + 146, + 148 + ], + "type": "text", + "content": "Shadow image x" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 62, + 148, + 173, + 244 + ], + "lines": [ + { + "bbox": [ + 62, + 148, + 173, + 244 + ], + "spans": [ + { + "bbox": [ + 62, + 148, + 173, + 244 + ], + "type": "image", + "image_path": "f7de41f68afaf984932f1634c969b96ceedd14741f5664a05aa8c1694e05a6d8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 82, + 246, + 153, + 255 + ], + "lines": [ + { + "bbox": [ + 82, + 246, + 153, + 255 + ], + "spans": [ + { + "bbox": [ + 82, + 246, + 153, + 255 + ], + "type": "text", + "content": "Shadow-free image y" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 268, + 296, + 344 + ], + "lines": [ + { + "bbox": [ + 55, + 268, + 296, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 268, + 296, + 344 + ], + "type": "text", + "content": "Figure 3. Latent space in VAE. We apply the pre-trained encoding and decoding process on a shadow image " + }, + { + "bbox": [ + 55, + 268, + 296, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 268, + 296, + 344 + ], + "type": "text", + "content": " or a shadow-free image " + }, + { + "bbox": [ + 55, + 268, + 296, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 55, + 268, + 296, + 344 + ], + "type": "text", + "content": ". For a shadow-free image, this process does not introduce additional shadows, meaning the pre-trained latent space can also represent the shadow-free image. However, as shown in the zoomed-in view, some details, like text, may be lost in this process." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 179, + 148, + 290, + 244 + ], + "blocks": [ + { + "bbox": [ + 217, + 140, + 246, + 148 + ], + "lines": [ + { + "bbox": [ + 217, + 140, + 246, + 148 + ], + "spans": [ + { + "bbox": [ + 217, + 140, + 246, + 148 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathcal{E}(\\mathbf{x}))" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 179, + 148, + 290, + 244 + ], + "lines": [ + { + "bbox": [ + 179, + 148, + 290, + 244 + ], + "spans": [ + { + "bbox": [ + 179, + 148, + 290, + 244 + ], + "type": "image", + "image_path": "3eed971872654ffc2402ef114305b92768ea57c29d745aec6f86c6e8233bbe55.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 217, + 245, + 247, + 255 + ], + "lines": [ + { + "bbox": [ + 217, + 245, + 247, + 255 + ], + "spans": [ + { + "bbox": [ + 217, + 245, + 247, + 255 + ], + "type": "inline_equation", + "content": "\\pmb{D}(\\pmb{\\mathcal{E}}(\\mathbf{y}))" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 365, + 296, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 296, + 437 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 296, + 437 + ], + "type": "text", + "content": "second is more concerned with non-shadow areas. These two objectives can be contradictory, making it challenging to design a single network that effectively addresses both. Therefore, we propose a two-stage shadow removal framework to robustly eliminate various types of shadows across different scenarios (Fig. 2)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 437, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 296, + 533 + ], + "type": "text", + "content": "In the first stage, as shown at the bottom of Fig. 2, we perform shadow removal in latent space (Sec. 3.2). We condition the Stable Diffusion (SD) model [29] using the latent code of the input shadow image " + }, + { + "bbox": [ + 55, + 437, + 296, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathrm{x}}" + }, + { + "bbox": [ + 55, + 437, + 296, + 533 + ], + "type": "text", + "content": " and fine-tune a pretrained SD model to generate the latent code of a shadow-free image " + }, + { + "bbox": [ + 55, + 437, + 296, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0^{\\mathbf{y}}" + }, + { + "bbox": [ + 55, + 437, + 296, + 533 + ], + "type": "text", + "content": ". As shown in Fig. 1, this latent code can be decoded into a coarse image that effectively eliminates shadows, although some details may be lost." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 533, + 296, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 296, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 296, + 640 + ], + "type": "text", + "content": "In the second stage, as illustrated at the top of Fig. 2, we perform detail injection using the encoder " + }, + { + "bbox": [ + 55, + 533, + 296, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 533, + 296, + 640 + ], + "type": "text", + "content": " and decoder " + }, + { + "bbox": [ + 55, + 533, + 296, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 533, + 296, + 640 + ], + "type": "text", + "content": " within SD (Sec.3.3). We fix the pretrained encoder and decoder and employ a set of Detail Injection (DI) models to integrate shadow-free details into the decoder features. These details are derived from each encoder layer. After training on pairs of shadow and shadow-free images, the DI models learn to inject details from the input image that are free of shadows." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 647, + 235, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 235, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 235, + 661 + ], + "type": "text", + "content": "3.2. Shadow Removal in Latent Space" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Building on recent advancements in dense prediction tasks [7, 12, 42], we formulate the shadow removal task in the first stage as an image-conditioned annotation generation problem using SD. This approach conducts the dif" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": "fusion process within a low-dimensional latent space generated by a pair of encoder and decoder " + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "inline_equation", + "content": "\\langle \\mathcal{E},\\mathcal{D}\\rangle" + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\mathbf{x}) = \\mathbf{z}^{\\mathbf{x}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathbf{z}^{\\mathbf{x}})\\approx \\mathbf{x}" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "spans": [ + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "text", + "content": "Compared to the diffusion model [9], Stable Diffusion offers enhanced generation stability and training efficiency. However, given the limited number of shadow and shadow-free image pairs, we opt for a fine-tuning strategy rather than training a SD model from scratch. We directly utilize the pre-trained " + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "text", + "content": " in SD and focus on fine-tuning the denoiser U-Net, as we have found that the pre-trained " + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 109, + 555, + 230 + ], + "type": "text", + "content": " perform well for both shadow and non-shadow images, even though they were not specifically trained on shadow-free images (Fig. 3)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "type": "text", + "content": "Fine-tuning Process. The fine-tuning for Stable Diffusion [9] relies on forward-noising and reverse-denoising processes that operate within the latent space. In the forward process, Gaussian noise is progressively added over time steps " + }, + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "type": "inline_equation", + "content": "t \\in [1,T]" + }, + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "type": "text", + "content": " to the sample " + }, + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "type": "text", + "content": ", generating a noisy sample " + }, + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 251, + 555, + 323 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 378, + 335, + 553, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 335, + 553, + 350 + ], + "spans": [ + { + "bbox": [ + 378, + 335, + 553, + 350 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {\\mathrm {t}} ^ {\\mathbf {y}} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} ^ {\\mathbf {y}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}", + "image_path": "32008e0b48fbe10f8293447e40523e50f83e57e3d2aa53e668f181be56401949.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "spans": [ + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,I)" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}_t\\coloneqq \\prod_{s = 1}^t (1 - \\beta_s)" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "\\beta_{1},\\beta_{2},\\ldots" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "\\beta_{T}" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": " defines the noise schedule over " + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": " steps. In the reverse process, a U-Net [30] denoted as " + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": " takes the encoding features of the input image " + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathbf{x}}" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": " and the sample " + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": " as inputs, outputting a prediction of the clean sample " + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 359, + 554, + 421 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 393, + 432, + 553, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 393, + 432, + 553, + 447 + ], + "spans": [ + { + "bbox": [ + 393, + 432, + 553, + 447 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {z}} ^ {\\mathbf {y}} = f _ {\\theta} \\left(\\mathbf {z} _ {\\mathbf {t}} ^ {\\mathbf {y}}, \\mathbf {z} ^ {\\mathbf {x}}, t\\right). \\tag {2}", + "image_path": "8135fdf3c374a112a30762a4d206568f7fc52cb5d10e8de2c77491bbe96ba8f3.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 314, + 459, + 554, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 459, + 554, + 483 + ], + "spans": [ + { + "bbox": [ + 314, + 459, + 554, + 483 + ], + "type": "text", + "content": "During fine-tuning, we randomly sample a time step " + }, + { + "bbox": [ + 314, + 459, + 554, + 483 + ], + "type": "inline_equation", + "content": "t \\in [1, T]" + }, + { + "bbox": [ + 314, + 459, + 554, + 483 + ], + "type": "text", + "content": " and minimize the corresponding loss function " + }, + { + "bbox": [ + 314, + 459, + 554, + 483 + ], + "type": "inline_equation", + "content": "L_{t}" + }, + { + "bbox": [ + 314, + 459, + 554, + 483 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 375, + 495, + 553, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 495, + 553, + 510 + ], + "spans": [ + { + "bbox": [ + 375, + 495, + 553, + 510 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t} = \\left\\| \\mathbf {z} ^ {\\mathbf {y}} - f _ {\\theta} \\left(\\mathbf {z} _ {\\mathbf {t}} ^ {\\mathbf {y}}, \\mathbf {z} ^ {\\mathbf {x}}, t\\right) \\right\\| _ {2} ^ {2}, \\tag {3}", + "image_path": "1013e4d94ecc1bc751890c54a18a071507b7ff0fa7503aa46a5c3cc46695e1d8.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 520, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 520, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 520, + 554, + 544 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 520, + 554, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 520, + 554, + 544 + ], + "type": "text", + "content": " is the encoding features of the ground-truth shadow-free image." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 566, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 566, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 554, + 628 + ], + "type": "text", + "content": "Denoising Process. During inference, we use DDIM [33], which implements an implicit probabilistic model that can significantly reduce the number of denoising steps while maintaining output quality. Formally, the denoising process from " + }, + { + "bbox": [ + 313, + 566, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\tau}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 566, + 554, + 628 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 566, + 554, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\tau -1}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 566, + 554, + 628 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 343, + 639, + 553, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 639, + 553, + 654 + ], + "spans": [ + { + "bbox": [ + 343, + 639, + 553, + 654 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {\\tau - 1} ^ {\\mathbf {y}} = \\sqrt {\\bar {\\alpha} _ {\\tau - 1}} \\hat {\\mathbf {z}} _ {\\tau} ^ {\\mathbf {y}} + \\operatorname {d i r e c t i o n} \\left(\\mathbf {z} _ {\\tau} ^ {\\mathbf {y}}\\right) + \\sigma_ {\\tau} \\epsilon_ {\\tau}, \\tag {4}", + "image_path": "2ebd571290c3f79612ad78db31bc300257abfe66f1738e8e3696b93d1352f31b.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_{\\tau}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": " is the predicted clean sample at the denoising step " + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\text{direction}(\\mathbf{z}_{\\tau}^{\\mathbf{y}})" + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": " represents the direction pointing to " + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\tau}^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": ". 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Some details in the input image, such as the textures on the floor, change during latent space diffusion in stage one. In stage two, our method preserves these high-quality details while effectively removing shadows. As shown in the bottom-left image, where we map the RRDB features to three dimensions using PCA, we observe that shadow areas have distinct features (in green), indicating that our detail injection model is shadow-aware." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 363, + 223, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 363, + 223, + 376 + ], + "spans": [ + { + "bbox": [ + 55, + 363, + 223, + 376 + ], + "type": "text", + "content": "3.3. Shadow-aware Detail Injection" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 381, + 296, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 381, + 296, + 477 + ], + "spans": [ + { + "bbox": [ + 55, + 381, + 296, + 477 + ], + "type": "text", + "content": "As illustrated in Fig. 4, while the output of the conditional Stable Diffusion is visually striking—especially in its ability to completely remove shadows—it often diverges from the ground truth, particularly in high-detail areas, such as the floor texture. We believe the primary reason for this is the loss of high-frequency information in the latent space. As shown in Fig. 3, directly decoding the encoded features " + }, + { + "bbox": [ + 55, + 381, + 296, + 477 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathcal{E}(\\mathbf{x}))" + }, + { + "bbox": [ + 55, + 381, + 296, + 477 + ], + "type": "text", + "content": " also results in a loss of detail." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": "To eliminate shadows while preserving details, we introduce a shadow-aware detail injection step utilizing a set of DI models. Each model selectively extracts information from a specific intermediate layer of " + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": " to modulate the corresponding intermediate layers of " + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": " denote the encoder and decoder features for the " + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": "-th intermediate layer. The DI model takes the concatenation of " + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": " as input, output a modulated feature " + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{d}}_i" + }, + { + "bbox": [ + 55, + 478, + 296, + 574 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 61, + 584, + 295, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 584, + 295, + 597 + ], + "spans": [ + { + "bbox": [ + 61, + 584, + 295, + 597 + ], + "type": "interline_equation", + "content": "\\mathbf {d} _ {0} = \\mathbf {z} _ {0} ^ {\\mathbf {y}}, \\tag {5}", + "image_path": "db8835f41b7f7b78d11d749f19145c9e97809b533ead272c61db610c319841b0.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 61, + 601, + 290, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 601, + 290, + 614 + ], + "spans": [ + { + "bbox": [ + 61, + 601, + 290, + 614 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {d}} _ {i} = \\mathbf {d} _ {i} + \\operatorname {C o n v} (\\operatorname {R R D B} (\\operatorname {C o n v} (\\mathbf {d} _ {i}, \\mathbf {e} _ {n - i} (\\mathbf {z} ^ {\\mathbf {x}})), f _ {d} (\\mathbf {x}))),", + "image_path": "6516f29c44dca95307a5f11e90e74f45f9d0e6f7885b0c00205b8b78c75861b3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 62, + 617, + 243, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 617, + 243, + 631 + ], + "spans": [ + { + "bbox": [ + 62, + 617, + 243, + 631 + ], + "type": "interline_equation", + "content": "\\mathbf {d} _ {i} = \\mathcal {D} _ {i - 1} (\\tilde {\\mathbf {d}} _ {i - 1}), i \\in [ 1, 4 ], \\hat {\\mathbf {y}} = \\operatorname {C o n v} (\\tilde {\\mathbf {d}} _ {4})", + "image_path": "7921c6dfbf286ad4b8350a1dab09ef99349dde0d09ae3f1acfa2410cb8a9d2fa.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{RRDB}(\\cdot)" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " refers to the Residual-in-Residual Dense Block module [46], which consists of three Dense Blocks. " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " is predicted shadow-free image. " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "f_{d}(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " are features extracted using DINO v2 [26]. We concatenate the DINO features with " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 55, + 641, + 296, + 713 + ], + "type": "text", + "content": " after passing through a convolutional layer to enhance the generalizability of the DI models." + } + ] + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 334, + 69, + 535, + 133 + ], + "blocks": [ + { + "bbox": [ + 334, + 69, + 535, + 133 + ], + "lines": [ + { + "bbox": [ + 334, + 69, + 535, + 133 + ], + "spans": [ + { + "bbox": [ + 334, + 69, + 535, + 133 + ], + "type": "table", + "html": "
    MethodMean↑Variance↓
    Our stage one (ε-pred)29.660.239
    Our stage one (z0-pred)29.950.146
    Our stage two35.020.160
    DeS3 [11]31.331.075
    ", + "image_path": "77be29ebfe67a25de746db08b62cfc5a7d71c30babdfb7ca121219948a2a4ad4.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 141, + 555, + 186 + ], + "lines": [ + { + "bbox": [ + 313, + 141, + 555, + 186 + ], + "spans": [ + { + "bbox": [ + 313, + 141, + 555, + 186 + ], + "type": "text", + "content": "Table 1. Low variance. In the first stage, our method achieves reduced variance by using " + }, + { + "bbox": [ + 313, + 141, + 555, + 186 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 313, + 141, + 555, + 186 + ], + "type": "text", + "content": "-prediction. In the second stage, our method improves PSNR while maintaining low variance, resulting in robust, high-quality shadow removal results." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "text", + "content": " contain features from the input shadow image " + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "text", + "content": " and the shadow-free latent code " + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0^{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "text", + "content": ", respectively, our DI models can effectively identify shadow areas by utilizing both features as input. Although the latent codes may lose high-frequency details, they still provide valuable cues for shadow regions, which are primarily low-frequency. As illustrated in Fig. 4, where we visualize the features in the last layer of the RRDB module, we can observe that the shadow areas exhibit distinct feature responses. We present only the RRDB responses for " + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_2" + }, + { + "bbox": [ + 313, + 206, + 555, + 338 + ], + "type": "text", + "content": ". Please refer to the supplementary for additional results." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "spans": [ + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "type": "text", + "content": "Losses. To train the DI models, we minimize a total loss " + }, + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total}" + }, + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "type": "text", + "content": ", which combines an L1 loss and a perceptual loss measured using the Learned Perceptual Image Patch Similarity (LPIPS) metric [45] between the output image " + }, + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "type": "text", + "content": " and the ground-truth shadow-free image " + }, + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 313, + 353, + 554, + 413 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 323, + 421, + 554, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 421, + 554, + 435 + ], + "spans": [ + { + "bbox": [ + 323, + 421, + 554, + 435 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\left\\| \\hat {\\mathbf {y}} - \\mathbf {y} \\right\\| _ {1} + \\left\\| \\operatorname {L P I P S} (\\hat {\\mathbf {y}}) - \\operatorname {L P I P S} (\\mathbf {y}) \\right\\| _ {2} ^ {2}. \\tag {6}", + "image_path": "1855866b3a4e6eb59015c8ca6d3d61ffbd2ea72683c3db667ffee48932fc169f.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 442, + 450, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 442, + 450, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 442, + 450, + 455 + ], + "type": "text", + "content": "3.4. Implementation Details." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "text", + "content": "Reducing variance. As shown in Eq. 3, in the LDM fin-tuning stage, we use " + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "text", + "content": "-prediction rather than the standard " + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "text", + "content": "-prediction parameterization for the denoising model. This choice, as recommended by Lotus[7], helps reduce variance during stochastic LDM inference. We compare these two approaches on the " + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathrm{ISTD + }" + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "text", + "content": " [14] dataset by running inference on the test set with five different random seeds (1, 2, 3, 4, 5). We calculate the PSNR variance across the five outputs for each image and obtain the average variance. As shown in Table 1, using " + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "text", + "content": "-prediction in our LDM fin-tuning stage yields higher PSNR and lower variance compared to " + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 460, + 555, + 675 + ], + "type": "text", + "content": "-prediction. Additionally, we assess the average variance of our final results after the detail injection stage, and Table 1 shows that our final results have significantly lower variance than DeS3 [11], another mask-free shadow removal method based on diffusion models. It indicates that our generative shadow removal method is highly robust to randomness, which is a critical factor for practical use." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": "Training details. Our model is trained on a GPU server with four GeForce RTX 4090 GPUs using PyTorch" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "7596" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 552, + 253 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 552, + 253 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 552, + 253 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 552, + 253 + ], + "type": "table", + "html": "
    MethodYearMask-freeISTD+ DatasetSRD DatasetINS DatasetWSRD+ Dataset
    PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
    AutoExposure [3]2021No29.450.86129.240.93827.910.95721.660.752
    Zhu et al. [49]2022No——32.050.965————
    BMNet [48]2022No33.980.97231.970.96527.900.95824.750.816
    ShadowFormer [4]2023No35.460.97132.900.95828.620.96325.440.820
    DMTN [18]2023No32.230.96633.770.96828.830.969——
    ShadowDiffusion [5]2023No34.630.96734.730.97029.120.966——
    HomoFormer [40]2024No35.720.97734.360.97728.980.965——
    InstanceShadow [24]2024No34.690.96831.610.95928.160.948——
    TBRNet [19]2023Yes31.910.96431.830.953————
    Refusion [23]2023Yes32.410.96131.600.94928.130.95822.320.738
    DeS3 [11]2024Yes31.390.95734.110.96827.890.947——
    OmniSR [41]2024Yes33.340.97032.870.96930.380.97326.070.835
    Ours—Yes35.190.97433.630.96830.560.97526.260.827
    ", + "image_path": "9bdc87c72b9f9cbad00a90543494d97eb17e7a98cbd46e06d8d4e4e126def7c8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 261, + 553, + 285 + ], + "lines": [ + { + "bbox": [ + 55, + 261, + 553, + 285 + ], + "spans": [ + { + "bbox": [ + 55, + 261, + 553, + 285 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on ISTD+, SRD, INS, and WSRD+ datasets. Best results are highlighted as 1st , 2nd and 3rd . Refer to the supplementary material for the MAE values in both shadowed and non-shadowed areas." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "spans": [ + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "text", + "content": "2.0.1 [27] with CUDA 11.7. We employ the Adam optimizer [13] for training. In the first stage, the LDM is finetuned for 40 epochs on INS [41] and 200 and 300 epochs on " + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "inline_equation", + "content": "\\mathrm{ISTD + }" + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "text", + "content": " [14, 37] and SRD [28], respectively. We utilize a constant learning rate of " + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "inline_equation", + "content": "3\\times 10^{-4}" + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "text", + "content": " with a batch size 16. For the INS dataset, each batch consists of " + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "inline_equation", + "content": "512\\times 512" + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "text", + "content": " patches, while for the other datasets, batches are composed of randomly cropped " + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "inline_equation", + "content": "480\\times 480" + }, + { + "bbox": [ + 54, + 304, + 294, + 402 + ], + "type": "text", + "content": " patches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "spans": [ + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "text", + "content": "In the second stage, we maintain the constant learning rate of " + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "text", + "content": " and batch size of 16. The batch shapes for each dataset are consistent with those in the first stage, and the number of epochs for training the detail injection models is 50 for INS and 300 and 200 for " + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "inline_equation", + "content": "\\mathrm{ISTD + }" + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "text", + "content": " and SRD, respectively. For the DINO features [26], we resize the image to " + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "inline_equation", + "content": "\\frac{14W}{16} \\times \\frac{14H}{16}" + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "text", + "content": " using bilinear interpolation, extract the DINO features, and apply a " + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "text", + "content": " convolution layer to obtain a feature map of shape " + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "inline_equation", + "content": "256 \\times \\frac{W}{16} \\times \\frac{H}{16}" + }, + { + "bbox": [ + 54, + 402, + 295, + 547 + ], + "type": "text", + "content": ". To reduce memory footprint, we only concatenate the DINO features with the first two layers of the VAE decoder. Additional details can be found in the supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 560, + 136, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 560, + 136, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 560, + 136, + 574 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "text", + "content": "Datasets. We conduct experiments on four shadow removal datasets: SRD [28], " + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{ISTD + }" + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "text", + "content": " [14, 37], " + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{WSRD + }" + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "text", + "content": " [35, 36], and INS [41]. The SRD dataset [28] includes 3,088 paired shadow and shadow-free images, divided into 2,680 for training and 408 for testing. The " + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{ISTD + }" + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "text", + "content": " dataset [14, 37] provides 1,870 triplets of shadow images, shadow masks, and shadow-free images, with 1,330 used for training and 540 for testing. " + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{WSRD + }" + }, + { + "bbox": [ + 54, + 582, + 295, + 714 + ], + "type": "text", + "content": " [35, 36] contains 1,000 pairs of shadow and non-shadow images captured under both spotlight and diffuse illumination. Since the test data is not open-sourced, we use its 100 validation images for test" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 304, + 555, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 304, + 555, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 304, + 555, + 342 + ], + "type": "text", + "content": "ing. Lastly, the INS dataset [41] comprises 30,000 synthetic training images under direct and indirect illumination, a synthetic test set of 2,000 images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 354, + 555, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 463 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 463 + ], + "type": "text", + "content": "Evaluation Metrics. Following previous methods [3, 4, 15], we evaluated images with a resolution of " + }, + { + "bbox": [ + 313, + 354, + 555, + 463 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 354, + 555, + 463 + ], + "type": "text", + "content": ". We report results using the Peak Signal-to-Noise Ratio (PSNR) and the Structure Similarity Index Measure (SSIM) [39], adopting the MATLAB evaluation codes as provided by Zhu et al. [49]. For the WSRD+ [35] dataset, we used its evaluation data and the evaluation code provided by the NTIRE 2024 Image Shadow Removal Challenge [36] for comparison." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 468, + 400, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 400, + 481 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 400, + 481 + ], + "type": "text", + "content": "4.1. Comparisons" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 486, + 553, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 553, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 553, + 641 + ], + "type": "text", + "content": "We compare our method to twelve state-of-the-art shadow removal techniques, evaluating both quantitatively and qualitatively. Among these, eight methods require a shadow mask as input: AutoExposure [3], Zhu et al. [49], BMNet [48], ShadowFormer [4], DMTN [18], ShadowDiffusion [5], and HomoFormer [40]. The remaining four methods—TBRNet [19], Refusion [23], Des3 [11], and OmniSR [41]—are mask-free, meaning they do not require a shadow mask as input. All comparisons use the original authors' implementations and hyperparameters, or the provided checkpoints or results, if available. For the INS dataset, we train these methods following the procedure in OmniSR [41]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 642, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 555, + 714 + ], + "type": "text", + "content": "For methods that are not mask-free, we use the shadow masks provided by the dataset as the default input. Since SRD [28] does not provide masks, we use the shadow masks generated by DHAN [1], which computes shadow matting from shadow/shadow-free pairs and generates binary masks through thresholding. In the case of the INS dataset," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "7597" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 68, + 541, + 285 + ], + "blocks": [ + { + "bbox": [ + 74, + 68, + 541, + 285 + ], + "lines": [ + { + "bbox": [ + 74, + 68, + 541, + 285 + ], + "spans": [ + { + "bbox": [ + 74, + 68, + 541, + 285 + ], + "type": "image", + "image_path": "2a8bf2be57878fb14441713c921c62c1276f72c3336a1c15404a6816495a5d77.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 297, + 555, + 321 + ], + "lines": [ + { + "bbox": [ + 55, + 297, + 555, + 321 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 555, + 321 + ], + "type": "text", + "content": "Figure 5. Comparisons with SOTA shadow removal methods on the ISTD+ and SRD datasets. The input mask, required by methods that are not mask-free, is shown in the top-left corner." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 73, + 329, + 541, + 491 + ], + "blocks": [ + { + "bbox": [ + 73, + 329, + 541, + 491 + ], + "lines": [ + { + "bbox": [ + 73, + 329, + 541, + 491 + ], + "spans": [ + { + "bbox": [ + 73, + 329, + 541, + 491 + ], + "type": "image", + "image_path": "783f2c7acad6c86c8fc7ee4102fa673503fb7d55465cd720517565650873bf4b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 503, + 555, + 537 + ], + "lines": [ + { + "bbox": [ + 55, + 503, + 555, + 537 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 555, + 537 + ], + "type": "text", + "content": "Figure 6. Comparisons with SOTA shadow removal methods in real scenes. We compare our method to OmniSR [41], HomoFormer [40], Refusion [23], and ShadowDiffusion [5], all trained on the INS dataset [41]. Results show that our approach achieves more comprehensive shadow removal, even in complex scenes." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 558, + 294, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 558, + 294, + 640 + ], + "spans": [ + { + "bbox": [ + 54, + 558, + 294, + 640 + ], + "type": "text", + "content": "its shadow masks are represented as 0-1 probability maps rather than binary masks. Since it is a synthetic dataset with highly accurate masks, we found that using them as input results in methods producing outputs nearly identical to the ground truth (with PSNR values exceeding 50). To address this, following OmniSR [41], we use FDRNet [47] to detect shadow masks and input the detected masks instead." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 642, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 642, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 642, + 295, + 714 + ], + "type": "text", + "content": "As shown in Table 2, our method achieves the highest PSNR score on the INS dataset. On the " + }, + { + "bbox": [ + 54, + 642, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{ISTD + }" + }, + { + "bbox": [ + 54, + 642, + 295, + 714 + ], + "type": "text", + "content": " dataset, our approach is the best mask-free method, performing only slightly below HomoFormer [40] and ShadowFormer [4], which use ground-truth shadow masks as input, and outperforming most other methods that also rely on ground-truth" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 558, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 617 + ], + "type": "text", + "content": "shadow masks. As shown in the first two columns of Fig. 5, although without mask as input, our method is capable of thoroughly removing shadows, even with limited semantic context. We think it is because of leveraging the generative priors in our latent diffusion model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 617, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 713 + ], + "type": "text", + "content": "For the SRD dataset, our method also delivers competitive results compared to methods that utilize masks provided by DHAN [1]. Among shadow-free methods, our performance is second only to DeS3. As illustrated in Fig. 5, our method produces visually appealing results with nearly complete shadow removal. We found that our method achieves better shadow removal quality than DeS3; however, in areas with highly detailed textures, such as sand" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7598" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 71, + 299, + 152 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 299, + 152 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 299, + 152 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 299, + 152 + ], + "type": "table", + "html": "
    MethodISTD+→SRDSRD→ISTD+INS→WSRD+
    PSNRSSIMPSNRSSIMPSNRSSIM
    ShadowDiffusion24.260.89029.480.94719.400.825
    Refusion22.560.88627.310.92418.730.787
    DeS322.090.880————
    OmniSR25.860.91730.190.95120.030.825
    Ours26.230.92330.230.95320.110.828
    ", + "image_path": "a0c0c4e258572213548f188f2cfe5370b3ab838df15253111214dddf49a86607.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 205, + 249, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 205, + 249, + 216 + ], + "spans": [ + { + "bbox": [ + 55, + 205, + 249, + 216 + ], + "type": "text", + "content": "and grass, the PSNR is lower than that of DeS3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 217, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 217, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 54, + 217, + 295, + 312 + ], + "type": "text", + "content": "On the INS dataset, our method achieves the highest PSNR and SSIM, as shown in Table 2. We also compare our method with others on real indoor scene images, all trained on the INS dataset. As illustrated in Fig. 6, our approach more effectively removes shadows from multiple light sources, such as those beneath the table and chair, as well as soft shadows behind the small planter and on the bookshelf in the background." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 315, + 295, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 315, + 295, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 315, + 295, + 469 + ], + "type": "text", + "content": "We further evaluated our method on high-resolution shadow removal using the WSRD+ [35] dataset, with images at " + }, + { + "bbox": [ + 55, + 315, + 295, + 469 + ], + "type": "inline_equation", + "content": "1920 \\times 1440" + }, + { + "bbox": [ + 55, + 315, + 295, + 469 + ], + "type": "text", + "content": " resolution. The first stage requires no modification. We resize each image to " + }, + { + "bbox": [ + 55, + 315, + 295, + 469 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 55, + 315, + 295, + 469 + ], + "type": "text", + "content": " for the LDM fine-tuning. In the second stage, we introduce a minor adjustment by adding one patch-partition layer and one patch-merging layer [21]. Additional details are provided in the supplementary materials. As shown in Table 2, our method outperforms others on the WSRD+ dataset, with more results available in the supplementary material. The relatively low PSNR scores for all methods on the WSRD+ dataset can be attributed to exposure differences between the input and ground-truth images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 480, + 195, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 480, + 195, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 480, + 195, + 491 + ], + "type": "text", + "content": "4.2. Cross-dataset evaluation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "content": "To evaluate the generalizability of our approach, we conduct a cross-dataset evaluation. Specifically, we train our model on the training set of one dataset and test it on the testing set of a different dataset. Typically, training and testing data within the same dataset share similar shadow patterns, backgrounds, or lighting conditions. This cross-dataset evaluation presents a more challenging test for shadow removal methods and provides a more stringent measure of generalizability. We use " + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "inline_equation", + "content": "A \\rightarrow B" + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "content": " to denote training on dataset " + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "content": " and testing on dataset " + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "content": ". As shown in Table 3, our method achieves the best results on ISTD+→SRD, SRD→ISTD+, and INS→WSRD+. Here, we compare only with DeS3 [11] on ISTD+→SRD, as it provides checkpoints only for ISTD+ dataset. Its open-source code is a basic version that excludes certain components, including the VIT loss. For the INS→WSRD+ experiment, high-resolution images from the WSRD+ dataset are resized to " + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "content": " for inference and evaluation. Qual-" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 317, + 71, + 553, + 148 + ], + "blocks": [ + { + "bbox": [ + 55, + 159, + 295, + 182 + ], + "lines": [ + { + "bbox": [ + 55, + 159, + 295, + 182 + ], + "spans": [ + { + "bbox": [ + 55, + 159, + 295, + 182 + ], + "type": "text", + "content": "Table 3. Cross-dataset evaluation. " + }, + { + "bbox": [ + 55, + 159, + 295, + 182 + ], + "type": "inline_equation", + "content": "\\mathrm{ISTD} + \\rightarrow" + }, + { + "bbox": [ + 55, + 159, + 295, + 182 + ], + "type": "text", + "content": " SRD means training on the " + }, + { + "bbox": [ + 55, + 159, + 295, + 182 + ], + "type": "inline_equation", + "content": "\\mathrm{ISTD}+" + }, + { + "bbox": [ + 55, + 159, + 295, + 182 + ], + "type": "text", + "content": " dataset and testing on the SRD dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 71, + 553, + 148 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 553, + 148 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 553, + 148 + ], + "type": "table", + "html": "
    DatasetISTD+ PSNR/SSIMSRD PSNR/SSIMINS PSNR/SSIM
    Full35.19/0.97433.63/0.96830.56/ 0.975
    W/o pre-train33.38/0.96732.46/0.96329.55/0.970
    Stage one29.95/0.84328.18/0.86828.78/0.924
    Stage one (w/o pre-train)28.12/0.82227.48/0.86126.92/0.909
    W/o DINO34.76/0.97133.04/0.96530.30/0.975
    ", + "image_path": "ebea66a25f97a48e58358d8ef15dd2eedaa1cbeb1fcc1b91af02d092d9d90a47.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 156, + 553, + 178 + ], + "lines": [ + { + "bbox": [ + 313, + 156, + 553, + 178 + ], + "spans": [ + { + "bbox": [ + 313, + 156, + 553, + 178 + ], + "type": "text", + "content": "Table 4. Ablation studies. W/o pre-train: without pre-training. W/o DINO: without DINO in the detail injection model." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 200, + 553, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 200, + 553, + 224 + ], + "spans": [ + { + "bbox": [ + 313, + 200, + 553, + 224 + ], + "type": "text", + "content": "itative comparisons for this evaluation are provided in the supplementary material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 232, + 408, + 244 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 232, + 408, + 244 + ], + "spans": [ + { + "bbox": [ + 313, + 232, + 408, + 244 + ], + "type": "text", + "content": "4.3. Ablation study." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 250, + 555, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 250, + 555, + 477 + ], + "spans": [ + { + "bbox": [ + 313, + 250, + 555, + 477 + ], + "type": "text", + "content": "To validate our model design, we conducted ablation studies on the use of the pretrained SD model, the two-stage pipeline, and the incorporation of DINO features. The results are presented in Table 4. To demonstrate the effectiveness of the generative priors in the SD model, we include an ablation study under the \"without pre-training\" setting, where the model is trained from scratch on each respective shadow removal dataset. The results indicate that pre-training significantly enhances shadow removal performance, as omitting it in both stage one and the full model leads to a substantial decline in PSNR and SSIM. Furthermore, stage two plays a crucial role in our method, as its removal results in a marked drop in PSNR and SSIM. This is primarily due to stage one's limitations in preserving high-frequency details. Additionally, integrating DINO features into the detail injection model of stage two proves advantageous, consistently improving PSNR and SSIM across all three datasets. For qualitative results related to the ablation study, please refer to the supplementary materials." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 489, + 388, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 489, + 388, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 489, + 388, + 502 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 510, + 555, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 555, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 555, + 616 + ], + "type": "text", + "content": "This paper introduces a novel detail-preserving latent diffusion pipeline that effectively eliminates complex shadows while preserving shadow-free details. The proposed method leverages the rich visual priors of a pre-trained Stable Diffusion model and propose a two-stage fine-tuning strategy to adapt the SD model for stable and efficient shadow removal. Extensive experiments demonstrate that our approach outperforms state-of-the-art shadow removal methods, particularly in terms of generalizability." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 617, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 713 + ], + "type": "text", + "content": "Limitation and future work. Our method may still miss some shadows in complex scenes, such as the self-shadows on the flower pot in Fig. 6. Additionally, in some cases, our approach focuses more on resolving the color variations caused by shadows and cannot fully preserve the exposure in non-shadow areas. In the future, we plan to incorporate unsupervised or self-supervised signals to further enhance the generalizability of our method." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "7599" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 297, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 297, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 297, + 224 + ], + "type": "text", + "content": "We thank the anonymous reviewers for their professional and constructive comments. This work was funded by NSFC grant No. 62302134, \"Pioneer\" and \"Leading Goose\" R&D Program of Zhejiang Province (No. 2025C01086), Zhejiang Provincial Natural Science Foundation under Grant No. LQ24F020031, the Fundamental Research Funds for the Provincial Universities of Zhejiang under Grant No. GK249909299001-021. Renshu Gu is partially supported by NSFC grant No. 62202130 and U22A2033. Weiwei Xu is partially supported by NSFC grant No. 62421003." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 233, + 115, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 233, + 115, + 246 + ], + "spans": [ + { + "bbox": [ + 56, + 233, + 115, + 246 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 254, + 297, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 254, + 297, + 308 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 254, + 297, + 308 + ], + "spans": [ + { + "bbox": [ + 61, + 254, + 297, + 308 + ], + "type": "text", + "content": "[1] Xiaodong Cun, Chi-Man Pun, and Cheng Shi. Towards ghost-free shadow removal via dual hierarchical aggregation network and shadow matting gan. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5627-5636, 2022. 2, 6" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 107, + 295, + 152 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 107, + 295, + 152 + ], + "spans": [ + { + "bbox": [ + 56, + 107, + 295, + 152 + ], + "type": "text", + "content": "[49] Yurui Zhu, Zeyu Xiao, Yanchi Fang, Xueyang Fu, Zhiwei Xiong, and Zheng-Jun Zha. Efficient model-driven network for shadow removal. In Proceedings of the AAAI conference on artificial intelligence, pages 3635-3643, 2022. 6" + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "text", + "content": "7602" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_content_list.json b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5ad9bfba2a0c3280a4585fc90923cd04bf7ac563 --- /dev/null +++ b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_content_list.json @@ -0,0 +1,1580 @@ +[ + { + "type": "text", + "text": "Detect Any Mirrors: Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine", + "text_level": 1, + "bbox": [ + 96, + 128, + 875, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhaohu Xing $^{1}$ Lihao Liu $^{2}$ Yijun Yang $^{1}$ Hongqiu Wang $^{1}$ Tian Ye $^{1}$ Sixiang Chen $^{1}$ Wenxue Li $^{1}$ Guang Liu $^{3}$ Lei Zhu $^{1,4*}$", + "bbox": [ + 217, + 202, + 754, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1The Hong Kong University of Science and Technology (Guangzhou) 2Amazon \n3Beijing Academy of Artificial Intelligence 4The Hong Kong University of Science and Technology", + "bbox": [ + 84, + 244, + 883, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 316, + 313, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mirror detection is a challenging task because a mirror's visual appearance varies depending on the reflected content. Due to limited annotated data, current methods failed to generalize well for detecting diverse mirror scenes. Semi-supervised learning with large-scale unlabeled data can improve generalization capabilities on mirror detection, but these methods often suffer from unreliable pseudolabels due to distribution differences between labeled and unlabeled data, therefore affecting the learning process. To address this issue, we first collect a large-scale dataset of approximately 0.4 million mirror-related images from the internet, significantly expanding the data scale for mirror detection. To effectively exploit this unlabeled dataset, we propose the first semi-supervised framework (namely an iterative data engine) consisting of four steps: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. In each iteration of the data engine, we employ a geometric accuracy scoring approach to assess pseudo labels based on multiple segmentation metrics, and design a multi-modal agent-driven semantic scoring approach to enhance the semantic perception of pseudo labels. These two scoring approaches can effectively improve the reliability of pseudo labels by selecting unlabeled samples with higher scores. Our method demonstrates promising performance across three mirror detection tasks and exhibits strong generalization on unseen examples. Our code will be publicly available at https://github.com/ge-xing/DAM.", + "bbox": [ + 76, + 348, + 473, + 786 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 809, + 209, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mirrors are commonly found in our daily lives and can significantly affect the performance of various deep learning methods, including depth estimation [33], semantic", + "bbox": [ + 76, + 834, + 468, + 881 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9de2e484e705d2f19054743449f9985405520ba562bfdf8a893ed06d33a51986.jpg", + "image_caption": [ + "Figure 1. Examples of semi-supervised learning from (1) Mean Teacher [36], (2) DepthAnything [50], (3) UniMatch [49]. These methods explore how to effectively exploit large-scale unlabeled data to improve model generalization by challenging the student model and aligning the predictions between the student and teacher models. In contrast, our (4) DAM introduces an iterative optimization process and a scoring model to improve the reliability of the teacher model's predictions." + ], + "image_footnote": [], + "bbox": [ + 504, + 315, + 895, + 470 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1677c9a466e61376762f38357c601fd22be0be08d2caef37afc7304cf7a7f31e.jpg", + "image_caption": [ + "Figure 2. Comparison between our DAM with other SOTA methods in terms of segmentation metrics (i.e., IoU, Accuracy, $F_{\\beta}$ , MAE, and BER.), parameter scale (#Param), and frames per second (FPS). In the radar chart, we normalized the metrics and reversed the MAE and BER metrics for better presentation." + ], + "image_footnote": [], + "bbox": [ + 501, + 602, + 694, + 746 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0dfe8b717564d78b65f9977e9a42e636c4af4e114af9ac35e9332094f2c08865.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 602, + 893, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "segmentation [12, 44, 45, 47], and video instance detection [16, 25, 43]. In applications such as drone tracking [3] and robot navigation [11], accurate mirror detection is crucial to avoid potential safety issues. There-", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Lei Zhu (leizhu@ust.hk) is the corresponding author of this work.", + "bbox": [ + 99, + 887, + 413, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25476", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "fore, developing mirror detection models is essential for precisely detecting mirrors in images and providing additional information for other tasks. Although many methods [8, 10, 13, 18, 20, 46, 51] have been developed for mirror detection and achieved impressive performance on various mirror detection benchmarks by exploring the attributes of mirrors, these methods can not generalize well in diverse scenes due to the limited annotated datasets.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, as shown in Figure 1, many studies [17, 21-23, 36, 48-50] have been conducted to explore how to effectively exploit large-scale unlabeled data to improve model generalization. These methods typically use a student-teacher architecture, aiming to learn a strong representation of unlabeled data by challenging the student model with unlabeled input and enhancing the output consistency between the student model and the teacher model. However, these methods do not consider the reliability of the teacher model's output, which can significantly affect the learning quality of the student model. Moreover, in the mirror detection task, there are limited annotated datasets and a lack of large-scale unlabeled data containing various mirror scenes to enhance model generalization. This presents a challenge for current mirror detection methods when applied in practical scenarios.", + "bbox": [ + 75, + 215, + 472, + 458 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, our goal is to fill the data gap and build a general mirror detection model with state-of-the-art performance and stronger generalization ability, aiming to Detect Any Mirrors (DAM) in various practical scenarios. First, we collect approximately 400000 diverse, unlabeled mirror-related images from the internet. To provide initial pseudo labels for this unlabeled data, we then train an initial mirror detection model using approximately 13,000 labeled images collected from three public mirror detection datasets. To effectively exploit the collected large-scale unlabeled data, we further design an iterative data engine, where each iteration includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. The core of each iteration is selecting high-quality pseudo labels that can improve the learning reliability of the student model. Therefore, we propose a dual guidance scoring strategy to assess the pseudo labels through geometric accuracy derived from segmentation metrics and semantic scores from multi-modal large language models. Furthermore, we introduce a reliability-enhanced training strategy to effectively learn from the selected, more reliable, high-quality pseudo labels. We conduct extensive experiments on three public datasets to verify the performance gains from our collected large-scale unlabeled data. Mirror detection results on unseen datasets and randomly captured images in different scenes also demonstrate the generalization capability of our model. Our main contributions can be summarized as follows:", + "bbox": [ + 75, + 463, + 472, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a general mirror detection model, called DAM, which achieves SOTA performance and exhibits strong generalization capability in diverse scenes.", + "- We collect a large-scale unlabeled dataset to fill the data gap in the mirror detection task.", + "- We devise an iterative data engine to gradually improve the quality of pseudo labels, and we further propose a reliability-enhanced training strategy to effectively learn from the more reliable pseudo labels.", + "- Experimental results on three mirror detection datasets, an unseen dataset, and randomly captured images demonstrate the promising mirror detection performance and generalization capability of our model." + ], + "bbox": [ + 500, + 90, + 893, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 296, + 640, + 311 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we first review the state-of-the-art methods for mirror detection. Next, we will discuss works on semi-supervised learning and multi-modal large language models (MLLM), which are explored in our network.", + "bbox": [ + 498, + 321, + 893, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Mirror Detection", + "text_level": 1, + "bbox": [ + 500, + 390, + 668, + 404 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Detecting mirrors in an image is crucial for various applications, including drone tracking and robot navigation, as it helps prevent accidents. Additionally, it can enhance the performance of tasks like semantic segmentation and video instance detection. There are several methods for semantic segmentation tasks. For example, DeepLabV3 [2] utilizes atrous convolution in cascade and ASPP [1] module to capture the multi-scale features. Mask2Former [6] proposes a new framework, combining CNN and Transformer [37] to enhance the global understanding of images. However, these methods are not specifically designed for mirror scenes and do not perform well in detecting mirrors.", + "bbox": [ + 496, + 415, + 890, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, MirrorNet [51] introduced the first mirror detection dataset and network. They employed contextual contrasted information to detect mirrors accurately. PMDNet [18] proposes a more challenging benchmark for mirror detection tasks. They utilized multi-scale mirror edge features to enhance mirror perception. More recently, VCNet [34] improves mirror detection performance by leveraging chirality cues and implicit correspondences. However, these methods fail to generalize to various complex scenes due to the limited annotated datasets.", + "bbox": [ + 496, + 597, + 890, + 748 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Leveraging Large-scale Unlabeled Data", + "text_level": 1, + "bbox": [ + 500, + 755, + 839, + 771 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Leveraging the rich visual knowledge contained in large-scale unlabeled data to improve model generalization capability is a hot research direction. Tarvainen et al. [36] propose the Mean Teacher method to provide more stable and consistent targets for training the student model by updating the teacher model through an exponential moving average. DepthAnything [50] proposes to challenge the student model with a more difficult optimization target when learn-", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25477", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2e1e1f0e9765707a339a4c2abed78f503a673ff8bc934f7d40f2a4a8ad1d2a0e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 125, + 89, + 480, + 224 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9fa41b40351647a5b7990d0ca813bb6db73ae0b401b3c7527ec88a86fe53e1bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 89, + 844, + 224 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0ac94b2d9e094035ad5d7b91a6e452ab5975ff566f5becb6da730c803efa09d6.jpg", + "image_caption": [ + "Figure 3. Our data engine includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo label. In each iteration, we investigate a geometric accuracy scoring (b) to assess the pseudo labels and design an MMA-driven semantic scoring (c) to effectively improve the semantic perception for pseudo labels. These two scoring approaches can effectively improve the reliability of pseudo labels by selecting the unlabeled samples with higher scores." + ], + "image_footnote": [], + "bbox": [ + 125, + 227, + 841, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing the pseudo labels, in order to seek extra visual information. In addition, UniMatch [49] leverages feature-level and image-level perturbations to exploit a broader perturbation space, as well as a dual-stream perturbation strategy to fully probe pre-defined image-level perturbation space. However, these methods solely focus on enhancing the learning process of the student model and do not consider the reliability of the pseudo labels from the teacher model. The latter can directly affect the learning of the student model.", + "bbox": [ + 75, + 492, + 468, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Multi-modal Large Language Models (MLLM)", + "text_level": 1, + "bbox": [ + 76, + 635, + 468, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-modal large language models [24] possess the remarkable ability to understand high-level semantic information by learning large-scale data from various modalities, such as text, images, and videos. MiniCPM-V 2.6 [52] is the latest and most capable model in the MiniCPM-V series. Due to its superior token density, MiniCPM-V 2.6 can support real-time video understanding on end-side devices. InternVL-2 [5] demonstrates competitive performance on par with proprietary commercial models across various capabilities, including document and chart comprehension, infographics QA, scene text understanding and OCR tasks, scientific and mathematical problem-solving, as well as cultural understanding and integrated multi-modal capabilities. Qwen2-VL [38] is the latest version of the vision-language models in the Qwen model family, achieving state-of-the-art performance on various visual understanding benchmarks.", + "bbox": [ + 75, + 659, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/a3227d6b7c6a314112b6d24d0aa81d034c08a56a04b9d7578451ecf9bb2c66c5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    DatasetImage NumberIs Annotated
    MSD [51]4018✔
    PMD [18]6461✔
    RGBD-Mirror [28]3049✔
    Ours406817✘
    ", + "bbox": [ + 560, + 489, + 831, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. We have collected a large-scale unlabeled dataset featuring a variety of scenes where mirrors may appear, in order to expand the data scale for the mirror detection task.", + "bbox": [ + 498, + 577, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These models can provide a detailed analysis of a single image, multiple images, and video. In this work, we integrate these MLLMs to offer comprehensive and detailed analyses of the input images and corresponding pseudo labels, thereby scoring the quality of the pseudo labels.", + "bbox": [ + 498, + 637, + 890, + 713 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 727, + 589, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Data Preparation", + "text_level": 1, + "bbox": [ + 500, + 753, + 669, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There are three main annotated datasets (i.e., MSD [51], PMD [18], and RGBD-Mirror [28]) used in the mirror detection task. As shown in Table 1, the limited data scale makes it easy for mirror detection models to overfit and not generalize well to various complex scenes. To address this issue, we have collected a large-scale unlabeled dataset, which contains 406,817 mirror-related images to provide diverse scenes where mirrors may appear.", + "bbox": [ + 496, + 780, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25478", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Iterative Data Engine", + "text_level": 1, + "bbox": [ + 76, + 90, + 279, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We found that previous semi-supervised learning methods [36, 49, 50] usually focus on the learning process of the student model but overlook the prediction reliability of the teacher model. To address this issue, we introduce an iterative data engine to filter out low-quality pseudo labels and gradually improve mirror detection accuracy and robustness by learning from more reliable data. Specifically, the data engine includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels.", + "bbox": [ + 75, + 113, + 468, + 263 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 3 (a), in the first step, we train an initial mirror detection model using three collected annotated datasets. We then use the trained model to predict pseudo labels for the large-scale unlabeled dataset, resulting in 406,817 image and pseudo label pairs. At this stage, the pseudo labels are often unreliable because the initial mirror detection model may not generalize well when trained on limited annotated data. Therefore, we design a dual guidance scoring strategy, which includes geometric scoring and multi-modal agents (MMA)-driven semantic scoring, to assess the quality of the pseudo labels. As shown in Figure 3 (b) and (c), geometric scoring aims to predict an aggregated result of multiple segmentation metrics (i.e., IoU, $F_{\\beta}$ , and Accuracy). Meanwhile, MMA-driven semantic scoring provides a better understanding of the semantic knowledge contained in the image and corresponding pseudo label. Finally, we set a threshold to select the image and pseudo-label pairs with higher scores and propose a reliability-enhanced training strategy to train the new mirror detection model.", + "bbox": [ + 75, + 265, + 472, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Dual Guidance Scoring", + "text_level": 1, + "bbox": [ + 76, + 575, + 294, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Geometric-based Scoring", + "text_level": 1, + "bbox": [ + 76, + 599, + 308, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To directly assess the quality of predicted pseudo labels through their geometric shapes, we first design a geometric scoring strategy. In this strategy, we aim to distill geometric knowledge into an estimation model, $\\mathcal{M}_g$ (e.g., ResNet-50). Specifically, for three annotated datasets, we denote the input data as $\\mathcal{D}g = \\{I_i,P_i,G_i\\}_{i = 1}^N$ , where $I$ , $P$ , and $G$ represent an image, a pseudo label, and the corresponding ground truth label, respectively. $N$ is the total number of data samples. During training, for the input data $\\mathcal{D}_g$ , we first calculate an aggregated segmentation score $S_{g}$ :", + "bbox": [ + 75, + 622, + 470, + 775 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {g} = \\frac {1}{3} \\sum_ {j = 1} ^ {3} \\mathcal {F} _ {j} (P, G), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 785, + 468, + 828 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_j$ denotes different segmentation metric functions (i.e., IoU, $F_{\\beta}$ , and Accuracy).", + "bbox": [ + 76, + 838, + 468, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, model $\\mathcal{M}_g$ , parameterized by $\\theta_g$ , learns to align the predicted aggregated score $\\hat{S}_g = \\mathcal{M}_g(I_i, P_i; \\theta_g)$ with", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/866ec9cbe865a591f6cb2530aefb5a8d76ed91f6b81b0d2c8876c80bbce0e12a.jpg", + "image_caption": [ + "1. High geometric score but low semantic consistency" + ], + "image_footnote": [], + "bbox": [ + 517, + 102, + 602, + 167 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3c8a9a829dfb842d3389d8955cfd24f19fbc7be97c4ac150a074493decc53fb3.jpg", + "image_caption": [ + "Geometric score: top 20% (High) \nSonicometric score: bottom 30% (Low)" + ], + "image_footnote": [], + "bbox": [ + 604, + 103, + 689, + 167 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7b5109a475698fc8ee8a02315dca02e57beed98c206872119d048f4d10765b31.jpg", + "image_caption": [ + "Geometric score: top 10% (High) \nSemantic score: bottom 20% (Low)" + ], + "image_footnote": [], + "bbox": [ + 700, + 103, + 785, + 167 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d64456d17a5a9676c13305b406b781c2377bc9594bd5812984f269320a00800a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 103, + 872, + 167 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c3203f573e5507a1f30f1f50685e98df70101af0f845c73533b2a3b11f109c57.jpg", + "image_caption": [ + "2. High geometric score and high semantic consistency", + "Geometric score: top $10\\%$ (High) \nSemantic score: top $20\\%$ (High)" + ], + "image_footnote": [], + "bbox": [ + 517, + 195, + 602, + 262 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d863bc9184998b3dc80419c06b012d2f02e95093f39d068e969015d84e7011ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 195, + 691, + 261 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bbe21da7bf44c2907d8981261c9b62d41c243d9fd9a92a328b23e53b072d292e.jpg", + "image_caption": [ + "Geometric score: top $10\\%$ (High) \nSemantic score: top $20\\%$ (High)" + ], + "image_footnote": [], + "bbox": [ + 700, + 196, + 785, + 261 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/92e6adf0430ebc7a476bc613aae92b22f7d370026cd3cc365663b8938b5949e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 196, + 874, + 261 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e39d949c5c59027a795976d488375dc3c84c159c3462dc10017dc55ae8fa4df6.jpg", + "image_caption": [ + "3. Low geometric score and low semantic consistency", + "Geometric score: bottom $40\\%$ (Low) \nSemantic score: bottom $20\\%$ (Low)", + "Figure 4. Example analysis for the geometric and semantic scores obtained from our dual guidance scoring strategy. We aim to select more reliable data (with high geometric and semantic scores)." + ], + "image_footnote": [], + "bbox": [ + 517, + 287, + 602, + 353 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/36771fa6916b86722460402f5dcc55a054394ed7fff343bf97a389b67f33ed02.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 287, + 691, + 353 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/680fadcf0602586c4e043e39cec68b1c3f8d58122bf999bda609126595284248.jpg", + "image_caption": [ + "Geometric score: bottom $40\\%$ (Low) \nSemitonic score: bottom $40\\%$ (Low)" + ], + "image_footnote": [], + "bbox": [ + 700, + 287, + 785, + 353 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/11fe4ecab6d9e2340e502d1f72f925d69bafb1b841f6e3347918c8c955c31730.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 287, + 874, + 353 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the actual score $S_{g}$ using the $\\mathcal{L}_2$ loss function.", + "bbox": [ + 500, + 426, + 805, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 MMA-driven Semantic Scoring", + "text_level": 1, + "bbox": [ + 500, + 450, + 772, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, geometric-based scoring alone is not sufficient in some cases because this score does not contain semantic information from images. As shown in the first row of Figure 4, the mirror detection model erroneously recognizes the non-mirror region as a mirror and gives a \"reasonable\" prediction. Hence, in these cases, the geometric score is high. Meanwhile, the semantic score from our MMA-driven strategy can effectively recognize this type of error and provide a lower score, which can help us filter out low-quality pseudo labels.", + "bbox": [ + 496, + 473, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Semantic modeling. Inspired by the impressive semantic understanding capabilities of the latest multimodal large language models, we design an MMA-driven semantic scoring strategy to obtain the semantic score of an image and pseudo-label pair. The output of a single multi-modal large language model can sometimes be unstable, particularly when it is required to provide a fine-grained score. To address this issue, we first design a semantic modeling process. Specifically, as depicted in Figure 3, we select three of the latest open-source vision-language models as multi-modal agents (i.e., MiniCPM-V-2.6, Qwen2-VL, and InternVL-2) to provide separate analyses and scoring. These models use the image and pseudo-label pair, along with a custom scoring prompt, as input. Next, we utilize the free API of a large language model (i.e., GLM4-flash) to conduct further analysis based on the outputs from the multi-modal agents and provide the final semantic score, achieving more stable semantic scoring.", + "bbox": [ + 496, + 628, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25479", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/00873822804a066492df23e52dfe6587e670bfbd9f5b7b36e3e8a52d08b6976d.jpg", + "image_caption": [ + "Figure 5. Detailed implementation of the proposed reliability-enhanced training strategy: We adopt the Mean Teacher architecture and incorporate the highly reliable pseudo labels to learn more robust visual knowledge. In each iteration of our iterative data engine, the teacher model is initialized from the student model of the previous iteration. We employ a consistency loss to align the predictions between the student model and the teacher model, and we use a confidence matrix to enable the student model to make more certain predictions." + ], + "image_footnote": [], + "bbox": [ + 181, + 88, + 795, + 233 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Semantic distillation. However, the semantic modeling process involving multi-modal agents and large language models is time-consuming and cannot be applied effectively. We propose a semantic distillation strategy to transfer the semantic knowledge of multi-modal agents into a lightweight scoring model, denoted as $\\mathcal{M}_s$ . Similar to the geometric distillation process, we concatenate the image and the corresponding pseudo label as input: $\\mathcal{D}_s = \\{I_i, P_i\\}$ . Next, the estimation model $\\mathcal{M}_s$ parameterized by $\\theta_s$ , learns to align the predicted semantic score $\\hat{S}_s = \\mathcal{M}_s(I_i, P_i; \\theta_s)$ with the semantic score $S_s$ obtained from multi-modal agents.", + "bbox": [ + 75, + 310, + 472, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Selection of Highly Reliable Data", + "text_level": 1, + "bbox": [ + 76, + 494, + 362, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To select highly reliable pseudo labels based on the geometric score and semantic score, we define a data selection strategy. We denote the scoring results from the geometric-based scoring model and the semantic-based scoring model for all the unlabeled data as $\\hat{S} = \\{\\hat{S}_g^k,\\hat{S}_s^k\\}_{k = 1}^M$ , where $M$ is the total number of unlabeled data. Additionally, we define $T$ as the selection threshold to control the number of highly reliable data selected, which will be discussed in Section 4.3. The selection strategy is defined as follows:", + "bbox": [ + 75, + 518, + 468, + 654 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (k) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\mathcal {P} _ {g} \\left(\\hat {S} _ {g} ^ {k}\\right) \\geq T \\text {a n d} \\mathcal {P} _ {s} \\left(\\hat {S} _ {s} ^ {k}\\right) \\geq T, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 660, + 468, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{P}(x)$ represents the calculation of the percentage that the score $x$ constitutes of the total score.", + "bbox": [ + 75, + 707, + 468, + 737 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Reliability-enhanced Training", + "text_level": 1, + "bbox": [ + 76, + 741, + 344, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When we have selected the more reliable image and pseudolabel pair, we aim to train a new mirror detection model that will be used in the next iteration. Hence, as shown in Figure 5, we devise a reliability-enhanced training strategy based on the standard Mean Teacher architecture to effectively learn knowledge from the labeled data and selected high-reliable unlabeled data. We adopt cross-entropy loss to optimize the student model using labeled data and reliable pseudo-labels. Meanwhile, mean squared error loss is", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "used to align the outputs of the student and teacher models for the unlabeled input. The loss functions can be summarized as follows:", + "bbox": [ + 496, + 309, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C E} \\left(y _ {i}, f \\left(x _ {i} ^ {l}; \\theta\\right)\\right) (3) \\\\ + \\lambda_ {2} \\cdot \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {C E} \\left(\\tilde {y} _ {j}, f \\left(x _ {j} ^ {u}; \\theta\\right)\\right) (4) \\\\ + \\lambda_ {3} \\cdot \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathcal {C} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) \\left| f \\left(x _ {j} ^ {u}; \\theta\\right) - f \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) \\right| ^ {2}, (5) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 364, + 890, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ represents the weight of different loss functions, while $N$ and $M$ denote the numbers of samples with and without ground truth labels, respectively. The variables $y$ and $\\tilde{y}$ represent the ground truth labels and the reliable pseudo-labels, respectively. The symbols $x^l$ and $x^u$ denote the labeled and unlabeled images, respectively. Additionally, $\\theta$ and $\\theta'$ are the parameters of the student and teacher models, respectively.", + "bbox": [ + 496, + 508, + 890, + 630 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {k} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} f _ {k} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) > \\operatorname {c o n f}, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 642, + 890, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{C}$ denotes the confidence matrix and 'conf' represents the confidence threshold. We calculate the consistency loss only when the prediction probability of the pixel $k$ from the teacher model is greater than the confidence threshold.", + "bbox": [ + 496, + 691, + 890, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 761, + 624, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 786, + 705, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluate our method on the test sets of three labeled datasets: MSD[51], PMD[18], and RGBD-Mirror*. RGBD-Mirror* is produced from the RGBD-Mirror dataset [28] by using the RGB images and annotated mirror masks and removing the corresponding depth map for each RGB-D image pair. We combine the training sets", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25480", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7b342260f3faf1baa9d3623d51c46b5cbda2e1357ac32e5f1bb0575c49b3fdf5.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Quantitative comparison between the proposed DAM and 11 state-of-the-art methods on MSD, PMD, and RGBD-Mirror* datasets in terms of IoU, Accuracy, $F_{\\beta}$ , MAE, and BER metrics. The best results are shown in **bold**. An asterisk (*) indicates that only the RGB images and annotated mirror masks are used, without any depth information." + ], + "table_body": "
    DatasetsMethodsUnlabeledIoU ↑Accuracy ↑Fβ↑MAE ↓BER ↓
    MSDSegFormer [41]X0.8790.9530.9150.0386.50
    Mask2Former [6]X0.8830.9580.9170.0366.65
    MirrorNet [51]X0.8450.9480.8920.0447.67
    PMDNet [18]X0.8470.9520.9080.0337.22
    VCNet [34]X0.8840.9580.9140.0297.32
    SANet [10]X0.8710.9510.9120.0337.10
    HetNet [13]X0.8880.9640.9220.0276.63
    CSFwinformer [42]X0.8750.9600.9180.0306.79
    MT [36]✓0.9010.9580.9280.0244.62
    UAMT [53]✓0.9090.9450.9320.0214.37
    DepthAnything [50]✓0.9150.9710.9430.0203.98
    UniMatch [49]✓0.9080.9490.9180.0314.57
    DAM (Ours)✓0.9340.9800.9680.0192.32
    PMDSegFormer [41]X0.6780.8330.8080.02410.14
    Mask2Former [6]X0.6980.8360.8170.0229.98
    MirrorNet [51]X0.6480.7980.7850.03010.39
    PMDNet [18]X0.6580.8180.7950.02810.86
    SANet [10]X0.6570.8160.7940.02410.97
    VCNet [34]X0.6760.8180.8010.02510.16
    HetNet [13]X0.7020.8270.8180.0239.65
    CSFwinformer [42]X0.7050.8200.8150.0299.93
    MT [36]✓0.7060.8270.8250.0219.38
    UAMT [53]✓0.7090.8340.8280.0208.93
    DepthAnything [50]✓0.7110.8280.8260.0209.11
    UniMatch [49]✓0.6980.8250.8200.02610.39
    DAM (Ours)✓0.7340.8510.8520.0198.08
    RGBD-Mirror*SegFormer [41]X0.7540.8580.7880.03913.11
    Mask2Former [6]X0.7680.8610.8030.04012.16
    MirrorNet [51]X0.7170.7960.7650.04413.40
    PMDNet [18]X0.7390.8190.7740.03513.24
    SANet [10]X0.7490.8410.7890.03912.88
    VCNet [34]X0.7630.8440.8100.03412.28
    HetNet [13]X0.7750.8570.8190.03111.20
    CSFwinformer [42]X0.7690.8500.8150.03411.04
    MT [36]✓0.7840.8570.8260.0398.19
    UAMT [53]✓0.7880.8730.8390.0358.24
    DepthAnything [50]✓0.7990.8810.8480.0316.94
    UniMatch [49]✓0.7850.8470.8210.0418.35
    DAM (Ours)✓0.8080.8850.8700.0306.42
    ", + "bbox": [ + 81, + 88, + 467, + 563 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of the three labeled datasets to retrain all comparison methods using their released code and turn their parameters to obtain their best performance to ensure fairness.", + "bbox": [ + 75, + 669, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We adopt the DINOv2-small encoder [29] for feature extraction and use the DPT [31] decoder for mirror detection. The ratio of labeled to unlabeled images is set to 1:1 in each batch. The base learning rate of the pre-trained encoder is set to 5e-6, while the randomly initialized decoder uses a learning rate that is 10 times larger. We use the AdamW optimizer and decay the learning rate with a poly schedule. We apply horizontal flipping as data augmentation. During reliability-enhanced training, we set three loss function weights as $\\lambda_1 = \\lambda_2 = \\lambda_3 = 1$ , and the confidence threshold as conf = 0.9. The strong augmentation operations in Figure 5 include color jitter,", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6671d31c40065e86c1cb2b243d3de9cb2ac278bf1e8beffd01c06013b0d90286.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Generalization capability on two video mirror detection datasets: Our method does not require training on the VMD-D and MMD datasets, yet it achieves a new state-of-the-art performance on their test sets." + ], + "table_body": "
    DatasetsMethodsTypeIoU ↑Accuracy ↑Fβ↑MAE ↓
    VMD-DTVSD [4]Video0.4800.8750.7460.125
    STICT [27]Video0.1640.8090.5300.198
    Sc-Cor [9]Video0.5120.8630.6960.137
    Scotch-Soda [26]Video0.5870.8780.7490.121
    HFAN [30]Video0.4590.8760.7060.124
    STCN [7]Video0.4450.8590.6700.140
    GlassNet [19]Image0.5520.8640.7180.137
    MirrorNet [51]Image0.5050.8550.6810.145
    PMDNet [18]Image0.5320.8720.7490.128
    VCNet [34]Image0.5390.8770.7490.123
    HetNet [13]Image0.5310.8680.7480.131
    VMD-Net [20]Video0.5670.8950.7870.105
    UAMT [53]Image0.6830.9010.7970.098
    DepthAnything [50]Image0.7230.9180.8320.087
    DAM (ours)Image0.7550.9290.8450.075
    MMDMGA [15]Image0.2810.5660.4890.434
    UFO [32]Image0.5990.7970.7970.203
    FSNet [14]Image0.7080.8530.8380.147
    ALGRF [35]Image0.5030.7240.6930.276
    F3Net [40]Image0.6710.8390.8470.161
    PMDNet [18]Image0.4240.7410.8470.259
    MirrorNet [51]Image0.6660.8350.8390.165
    VMD-Net [20]Video0.7230.8540.8120.146
    Warren et al. [39]Video0.7250.8720.8690.127
    UAMT [53]Image0.7250.8520.8610.147
    DepthAnything [50]Image0.7320.8610.8570.138
    DAM (ours)Image0.7590.8790.8690.121
    ", + "bbox": [ + 522, + 89, + 870, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "random grayscale, and random blur.", + "bbox": [ + 498, + 522, + 738, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. Following the previous works [20, 26, 34], we adopt intersection over union (IoU), pixel accuracy (Accuracy), F-measure $(F_{\\beta})$ , mean absolute error (MAE), and balanced error rate (BER) to evaluate our method.", + "bbox": [ + 498, + 537, + 890, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison against State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 498, + 604, + 883, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared methods. We compare our method with seven supervised networks and four semi-supervised methods. Seven supervised methods are SegFormer [41], Mask2Former [6], MirrorNet [51], PMDNet [18], SANet [10], VCNet [34], and HetNet [13]. Four semi-supervised methods are Mean Teacher [36], UAMT [53], DepthAnything [50], and UniMatch [49]. For all semi-supervised methods, we utilize the same training set with collected unlabeled data as our method for fair comparisons; see our supplementary material.", + "bbox": [ + 496, + 628, + 890, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative comparisons. We compare our DAM against 11 state-of-the-art methods on three datasets (i.e., MSD [51], PMD [18], and RGBD-Mirror* [28]) in terms of IoU, Accuracy, $F_{\\beta}$ , MAE, and BER metrics. As shown in Table 2, our DAM not only surpasses all supervised seven methods on all five metrics, but also outperforms all the semi-supervised methods, which have the same unlabeled data as our method during training. Our best performance", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25481", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4c136b225f8232f092a4b27d7d7e626097c078de8760d856d78bd7afc8c3402f.jpg", + "image_caption": [ + "Figure 6. Visual comparisons of mirror detection results predicted by our network and other methods. Clearly, our network achieves more accurate mirror detection results than all the compared methods, and our results are more consistent with the ground truths." + ], + "image_footnote": [], + "bbox": [ + 166, + 92, + 810, + 444 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eb947a0d1b941a6062d0905ee832aed5488d9b2a48a690c04350a9075cc23d6f.jpg", + "image_caption": [ + "Figure 7. The effect of different thresholds $T$ at different engine iterations of our method. We plot the number of highly reliable data and IoU scores on three datasets for each engine iteration regarding three different T values ( $T = 0.4$ , $T = 0.6$ , and $T = 0.8$ ). $T = 0.6$ yields the highest IoU scores for all three datasets." + ], + "image_footnote": [], + "bbox": [ + 125, + 483, + 838, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of all five metrics on three datasets indicates that our DAM model is more effective and robust in detecting mirror regions of different scenes of three datasets by learning more visual knowledge from large-scale reliable data.", + "bbox": [ + 75, + 661, + 468, + 719 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Generalization capability on the video mirror detection datasets. To further evaluate the generalization capabilities of our method, we test our DAM on two unseen datasets (i.e., the VMD-D and MMD datasets). Specifically, without requiring any re-training operations on these two unseen datasets, we directly test our model (the same trained model of our method at Table 2) to produce our results on these two unseen datasets. Then, Table 3 compares our results against those of state-of-the-art methods, which are trained on the VMD-D and MMD datasets. From Table 3, we can find that our DAM clearly outperforms all state-of-the-art methods on the VMD-D dataset and the MMD dataset regarding", + "bbox": [ + 75, + 720, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "all quantitative evaluation metrics. It convincingly verifies the generalization capabilities of our method.", + "bbox": [ + 496, + 661, + 890, + 690 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparisons. Figure 6 visually compares mirror detection results produced by our network and seven state-of-the-art methods on different input images. For these small mirrors at the first two rows, our method can detect more mirror details, while compared methods tend to wrongly recognize non-mirror regions in their mirror detection results. For big mirror objects at the third and fourth rows, all compared methods neglect parts of mirror regions, while our method tends to more accurately identify whole mirror regions. Meanwhile, we further select some more challenging and unlabeled images as the inputs for visual comparisons. As shown in the last four rows in Figure 6, the mirror regions may be blended (first row), partially covered (second and third rows), or complex due to a large number", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25482", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7365686c6d0e1aaa016f1e43804416397986ccf2c879debf182f30f6c7648818.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Index\\( S_g \\)\\( S_s \\)RETIoU↑Accuracy↑\\( F_{\\beta} \\uparrow \\)MAE↓BER↓
    M1(supervised)0.6790.8130.8090.02911.06
    M2✓0.6930.8150.8190.02410.21
    M3✓✓0.7190.8310.8370.0229.09
    Ours✓✓✓0.7340.8510.8520.0198.08
    ", + "bbox": [ + 119, + 88, + 426, + 147 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study of (1) geometric scoring $(S_g)$ , (2) MMA-driven semantic scoring $(S_s)$ , and (3) reliability-enhanced training strategy (RET) on the PMD dataset across IoU, Accuracy, $F_{\\beta}$ , MAE, and BER metrics.", + "bbox": [ + 76, + 157, + 468, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0a71c1448ca73d88119393914c187bdaff60d331a73f0c1aee101567c26a5d8b.jpg", + "image_caption": [ + "Figure 8. Visualization of latent features. $F_{1}, F_{2}, F_{3}, F_{4}$ denote the decoder features at different resolutions. $F_{seg}$ represents the feature from the decoder head. These results show that our network can learn a robust mirror-related feature representation for diverse scenes." + ], + "image_footnote": [], + "bbox": [ + 114, + 218, + 433, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of mirrors (last row). Our method can accurately address these challenging mirror detections by effectively learning mirror-related knowledge from large-scale and highly reliable unlabeled data.", + "bbox": [ + 75, + 460, + 468, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 527, + 230, + 544 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of the dual guidance scoring strategy and reliable-enhanced training. We conduct an ablation study to reveal the distinct contributions of geometric scoring $(S_g)$ , semantic scoring $(S_s)$ , and the reliability-enhanced training (RET) strategy within our model. Table 4 reports the quantitative results of the ablation study on the PMD dataset. The baseline model (M1) is trained using the labeled data, and the IoU, Accuracy, $F_{\\beta}$ , MAE, and BER scores are 0.679, 0.813, 0.809, 0.029, and 11.06, which highlights the limitations of the basic supervised approach. Then, we incorporate the proposed geometric scoring $(S_g)$ and MMA-driven semantic scoring $(S_s)$ into M1 to build M2 and M3. These two scoring strategies can select high-reliable data and significantly enhance the model's performance. Finally, with the reliability-enhanced training (RET) strategy, our method introduces additional optimization targets based on the student-teacher architecture and thus improves training stability and detection performance.", + "bbox": [ + 75, + 551, + 468, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of different thresholds $T$ . The hyper-parameter threshold $T$ controls the quantity of selected highly reliable data and thus affects the training process. To select an optimal $T$ , we conduct an ablation study experiment with three different $T$ values, which are $T = 0.4$ , $T = 0.6$ , and", + "bbox": [ + 75, + 824, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/13c7f0884527bcfd4a49a7072e1032049b28115c69abe3efa3f7006015cec3d0.jpg", + "image_caption": [ + "Figure 9. Visualization of comparison results on two captured and unseen photos demonstrates that our network can more accurately detect mirrors." + ], + "image_footnote": [], + "bbox": [ + 532, + 89, + 857, + 166 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$T = 0.8$ . In general, a larger $T$ means more samples we select. As shown in Figure 7 (a), the number of highly reliable data increases when the iteration number of our data engine increases. Meanwhile, Figures 7 (b), (c), and (d) show the IoU scores for different $T$ values and engine iteration numbers on the MSD, PMD, and RGBD-Mirror* datasets, respectively. More importantly, our method with $T = 0.6$ yields the highest IoU score on all three datasets. Hence, we empirically set $T = 0.6$ in all our experiments.", + "bbox": [ + 496, + 227, + 890, + 363 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. More Visualization", + "text_level": 1, + "bbox": [ + 500, + 371, + 683, + 386 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature visualization. As shown in Figure 8, we visualize the latent features at different decoder layers and the output feature map of the segmentation head. Apparently, these features can highlight mirror regions for different input mirror images. It indicates that our method can accurately capture the mirror-related feature representation, and thus produce robust mirror detection performance.", + "bbox": [ + 496, + 395, + 890, + 501 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of our results on unseen photos. We capture two unseen photos with mirrors at challenging positions. As shown in Figure 9, our network can more accurately detect the mirror regions than the state-of-the-art methods. The main reason is that our network can learn more reliable mirror-related knowledge from large-scale unlabeled data.", + "bbox": [ + 496, + 502, + 890, + 593 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 602, + 617, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we collect a large-scale unlabeled dataset to fill the data gap in the mirror detection task. To effectively exploit the collected large-scale unlabeled data, we design an iterative data engine comprising four processes: (1) mirror detection model training, (2) pseudo-label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo-labels. In each iteration, we investigate a dual guidance scoring strategy to assess pseudo-labels through geometric accuracy derived from segmentation metrics and semantic scores from multi-modal large language models. Furthermore, we propose a reliability-enhanced training strategy to effectively learn from the selected, more reliable, high-quality pseudo-labels. We conduct extensive experiments on three public datasets to verify the performance gains from our collected large-scale unlabeled data. The segmentation results for diverse unseen examples and randomly captured images in different scenes further demonstrate the generalization capability of our model.", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25483", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 76, + 90, + 235, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by the Guangdong Science and Technology Department (No. 2024ZDZX2004), the Guangzhou-HKUST(GZ) Joint Funding Program (No. 2023A03J0671), Guangdong Provincial Key Lab of Integrated Communication, Sensing and Computation for Ubiquitous Internet of Things (No.2023B1212010007), and the Nansha Key Area Science and Technology Project (No. 2023ZD003).", + "bbox": [ + 75, + 114, + 468, + 234 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 250, + 174, + 266 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. 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Springer, 2019. 6" + ], + "bbox": [ + 78, + 92, + 470, + 415 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "25486", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_model.json b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_model.json new file mode 100644 index 0000000000000000000000000000000000000000..31c67093b106cf1c2433b028c0bccde34f0aa6e1 --- /dev/null +++ b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_model.json @@ -0,0 +1,2268 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.098, + 0.13, + 0.877, + 0.178 + ], + "angle": 0, + "content": "Detect Any Mirrors: Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.203, + 0.756, + 0.24 + ], + "angle": 0, + "content": "Zhaohu Xing\\(^{1}\\) Lihao Liu\\(^{2}\\) Yijun Yang\\(^{1}\\) Hongqiu Wang\\(^{1}\\) Tian Ye\\(^{1}\\) Sixiang Chen\\(^{1}\\) Wenxue Li\\(^{1}\\) Guang Liu\\(^{3}\\) Lei Zhu\\(^{1,4*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.245, + 0.885, + 0.285 + ], + "angle": 0, + "content": "1The Hong Kong University of Science and Technology (Guangzhou) 2Amazon \n3Beijing Academy of Artificial Intelligence 4The Hong Kong University of Science and Technology" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.317, + 0.314, + 0.332 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.349, + 0.474, + 0.787 + ], + "angle": 0, + "content": "Mirror detection is a challenging task because a mirror's visual appearance varies depending on the reflected content. Due to limited annotated data, current methods failed to generalize well for detecting diverse mirror scenes. Semi-supervised learning with large-scale unlabeled data can improve generalization capabilities on mirror detection, but these methods often suffer from unreliable pseudolabels due to distribution differences between labeled and unlabeled data, therefore affecting the learning process. To address this issue, we first collect a large-scale dataset of approximately 0.4 million mirror-related images from the internet, significantly expanding the data scale for mirror detection. To effectively exploit this unlabeled dataset, we propose the first semi-supervised framework (namely an iterative data engine) consisting of four steps: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. In each iteration of the data engine, we employ a geometric accuracy scoring approach to assess pseudo labels based on multiple segmentation metrics, and design a multi-modal agent-driven semantic scoring approach to enhance the semantic perception of pseudo labels. These two scoring approaches can effectively improve the reliability of pseudo labels by selecting unlabeled samples with higher scores. Our method demonstrates promising performance across three mirror detection tasks and exhibits strong generalization on unseen examples. Our code will be publicly available at https://github.com/ge-xing/DAM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.81, + 0.21, + 0.825 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.835, + 0.47, + 0.882 + ], + "angle": 0, + "content": "Mirrors are commonly found in our daily lives and can significantly affect the performance of various deep learning methods, including depth estimation [33], semantic" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.316, + 0.897, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.481, + 0.895, + 0.594 + ], + "angle": 0, + "content": "Figure 1. Examples of semi-supervised learning from (1) Mean Teacher [36], (2) DepthAnything [50], (3) UniMatch [49]. These methods explore how to effectively exploit large-scale unlabeled data to improve model generalization by challenging the student model and aligning the predictions between the student and teacher models. In contrast, our (4) DAM introduces an iterative optimization process and a scoring model to improve the reliability of the teacher model's predictions." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.603, + 0.695, + 0.747 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.603, + 0.895, + 0.746 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.758, + 0.895, + 0.829 + ], + "angle": 0, + "content": "Figure 2. Comparison between our DAM with other SOTA methods in terms of segmentation metrics (i.e., IoU, Accuracy, \\( F_{\\beta} \\), MAE, and BER.), parameter scale (#Param), and frames per second (FPS). In the radar chart, we normalized the metrics and reversed the MAE and BER metrics for better presentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "segmentation [12, 44, 45, 47], and video instance detection [16, 25, 43]. In applications such as drone tracking [3] and robot navigation [11], accurate mirror detection is crucial to avoid potential safety issues. There-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.888, + 0.414, + 0.9 + ], + "angle": 0, + "content": "*Lei Zhu (leizhu@ust.hk) is the corresponding author of this work." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25476" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "fore, developing mirror detection models is essential for precisely detecting mirrors in images and providing additional information for other tasks. Although many methods [8, 10, 13, 18, 20, 46, 51] have been developed for mirror detection and achieved impressive performance on various mirror detection benchmarks by exploring the attributes of mirrors, these methods can not generalize well in diverse scenes due to the limited annotated datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.473, + 0.459 + ], + "angle": 0, + "content": "Recently, as shown in Figure 1, many studies [17, 21-23, 36, 48-50] have been conducted to explore how to effectively exploit large-scale unlabeled data to improve model generalization. These methods typically use a student-teacher architecture, aiming to learn a strong representation of unlabeled data by challenging the student model with unlabeled input and enhancing the output consistency between the student model and the teacher model. However, these methods do not consider the reliability of the teacher model's output, which can significantly affect the learning quality of the student model. Moreover, in the mirror detection task, there are limited annotated datasets and a lack of large-scale unlabeled data containing various mirror scenes to enhance model generalization. This presents a challenge for current mirror detection methods when applied in practical scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.464, + 0.473, + 0.901 + ], + "angle": 0, + "content": "In this work, our goal is to fill the data gap and build a general mirror detection model with state-of-the-art performance and stronger generalization ability, aiming to Detect Any Mirrors (DAM) in various practical scenarios. First, we collect approximately 400000 diverse, unlabeled mirror-related images from the internet. To provide initial pseudo labels for this unlabeled data, we then train an initial mirror detection model using approximately 13,000 labeled images collected from three public mirror detection datasets. To effectively exploit the collected large-scale unlabeled data, we further design an iterative data engine, where each iteration includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. The core of each iteration is selecting high-quality pseudo labels that can improve the learning reliability of the student model. Therefore, we propose a dual guidance scoring strategy to assess the pseudo labels through geometric accuracy derived from segmentation metrics and semantic scores from multi-modal large language models. Furthermore, we introduce a reliability-enhanced training strategy to effectively learn from the selected, more reliable, high-quality pseudo labels. We conduct extensive experiments on three public datasets to verify the performance gains from our collected large-scale unlabeled data. Mirror detection results on unseen datasets and randomly captured images in different scenes also demonstrate the generalization capability of our model. Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.894, + 0.137 + ], + "angle": 0, + "content": "- We propose a general mirror detection model, called DAM, which achieves SOTA performance and exhibits strong generalization capability in diverse scenes." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.137, + 0.894, + 0.166 + ], + "angle": 0, + "content": "- We collect a large-scale unlabeled dataset to fill the data gap in the mirror detection task." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.168, + 0.895, + 0.227 + ], + "angle": 0, + "content": "- We devise an iterative data engine to gradually improve the quality of pseudo labels, and we further propose a reliability-enhanced training strategy to effectively learn from the more reliable pseudo labels." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.228, + 0.895, + 0.288 + ], + "angle": 0, + "content": "- Experimental results on three mirror detection datasets, an unseen dataset, and randomly captured images demonstrate the promising mirror detection performance and generalization capability of our model." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.092, + 0.895, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.297, + 0.642, + 0.312 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.323, + 0.894, + 0.385 + ], + "angle": 0, + "content": "In this section, we first review the state-of-the-art methods for mirror detection. Next, we will discuss works on semi-supervised learning and multi-modal large language models (MLLM), which are explored in our network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.391, + 0.669, + 0.405 + ], + "angle": 0, + "content": "2.1. Mirror Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.596 + ], + "angle": 0, + "content": "Detecting mirrors in an image is crucial for various applications, including drone tracking and robot navigation, as it helps prevent accidents. Additionally, it can enhance the performance of tasks like semantic segmentation and video instance detection. There are several methods for semantic segmentation tasks. For example, DeepLabV3 [2] utilizes atrous convolution in cascade and ASPP [1] module to capture the multi-scale features. Mask2Former [6] proposes a new framework, combining CNN and Transformer [37] to enhance the global understanding of images. However, these methods are not specifically designed for mirror scenes and do not perform well in detecting mirrors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Recently, MirrorNet [51] introduced the first mirror detection dataset and network. They employed contextual contrasted information to detect mirrors accurately. PMDNet [18] proposes a more challenging benchmark for mirror detection tasks. They utilized multi-scale mirror edge features to enhance mirror perception. More recently, VCNet [34] improves mirror detection performance by leveraging chirality cues and implicit correspondences. However, these methods fail to generalize to various complex scenes due to the limited annotated datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.756, + 0.84, + 0.772 + ], + "angle": 0, + "content": "2.2. Leveraging Large-scale Unlabeled Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Leveraging the rich visual knowledge contained in large-scale unlabeled data to improve model generalization capability is a hot research direction. Tarvainen et al. [36] propose the Mean Teacher method to provide more stable and consistent targets for training the student model by updating the teacher model through an exponential moving average. DepthAnything [50] proposes to challenge the student model with a more difficult optimization target when learn-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25477" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.126, + 0.09, + 0.482, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.09, + 0.845, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.127, + 0.228, + 0.843, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.429, + 0.892, + 0.485 + ], + "angle": 0, + "content": "Figure 3. Our data engine includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo label. In each iteration, we investigate a geometric accuracy scoring (b) to assess the pseudo labels and design an MMA-driven semantic scoring (c) to effectively improve the semantic perception for pseudo labels. These two scoring approaches can effectively improve the reliability of pseudo labels by selecting the unlabeled samples with higher scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.63 + ], + "angle": 0, + "content": "ing the pseudo labels, in order to seek extra visual information. In addition, UniMatch [49] leverages feature-level and image-level perturbations to exploit a broader perturbation space, as well as a dual-stream perturbation strategy to fully probe pre-defined image-level perturbation space. However, these methods solely focus on enhancing the learning process of the student model and do not consider the reliability of the pseudo labels from the teacher model. The latter can directly affect the learning of the student model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.47, + 0.652 + ], + "angle": 0, + "content": "2.3. Multi-modal Large Language Models (MLLM)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Multi-modal large language models [24] possess the remarkable ability to understand high-level semantic information by learning large-scale data from various modalities, such as text, images, and videos. MiniCPM-V 2.6 [52] is the latest and most capable model in the MiniCPM-V series. Due to its superior token density, MiniCPM-V 2.6 can support real-time video understanding on end-side devices. InternVL-2 [5] demonstrates competitive performance on par with proprietary commercial models across various capabilities, including document and chart comprehension, infographics QA, scene text understanding and OCR tasks, scientific and mathematical problem-solving, as well as cultural understanding and integrated multi-modal capabilities. Qwen2-VL [38] is the latest version of the vision-language models in the Qwen model family, achieving state-of-the-art performance on various visual understanding benchmarks." + }, + { + "type": "table", + "bbox": [ + 0.562, + 0.49, + 0.832, + 0.569 + ], + "angle": 0, + "content": "
    DatasetImage NumberIs Annotated
    MSD [51]4018✔
    PMD [18]6461✔
    RGBD-Mirror [28]3049✔
    Ours406817✘
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.578, + 0.892, + 0.621 + ], + "angle": 0, + "content": "Table 1. We have collected a large-scale unlabeled dataset featuring a variety of scenes where mirrors may appear, in order to expand the data scale for the mirror detection task." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.638, + 0.892, + 0.714 + ], + "angle": 0, + "content": "These models can provide a detailed analysis of a single image, multiple images, and video. In this work, we integrate these MLLMs to offer comprehensive and detailed analyses of the input images and corresponding pseudo labels, thereby scoring the quality of the pseudo labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.728, + 0.591, + 0.743 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.754, + 0.671, + 0.77 + ], + "angle": 0, + "content": "3.1. Data Preparation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.903 + ], + "angle": 0, + "content": "There are three main annotated datasets (i.e., MSD [51], PMD [18], and RGBD-Mirror [28]) used in the mirror detection task. As shown in Table 1, the limited data scale makes it easy for mirror detection models to overfit and not generalize well to various complex scenes. To address this issue, we have collected a large-scale unlabeled dataset, which contains 406,817 mirror-related images to provide diverse scenes where mirrors may appear." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25478" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.281, + 0.108 + ], + "angle": 0, + "content": "3.2. Iterative Data Engine" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.265 + ], + "angle": 0, + "content": "We found that previous semi-supervised learning methods [36, 49, 50] usually focus on the learning process of the student model but overlook the prediction reliability of the teacher model. To address this issue, we introduce an iterative data engine to filter out low-quality pseudo labels and gradually improve mirror detection accuracy and robustness by learning from more reliable data. Specifically, the data engine includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.473, + 0.568 + ], + "angle": 0, + "content": "As shown in Figure 3 (a), in the first step, we train an initial mirror detection model using three collected annotated datasets. We then use the trained model to predict pseudo labels for the large-scale unlabeled dataset, resulting in 406,817 image and pseudo label pairs. At this stage, the pseudo labels are often unreliable because the initial mirror detection model may not generalize well when trained on limited annotated data. Therefore, we design a dual guidance scoring strategy, which includes geometric scoring and multi-modal agents (MMA)-driven semantic scoring, to assess the quality of the pseudo labels. As shown in Figure 3 (b) and (c), geometric scoring aims to predict an aggregated result of multiple segmentation metrics (i.e., IoU, \\( F_{\\beta} \\), and Accuracy). Meanwhile, MMA-driven semantic scoring provides a better understanding of the semantic knowledge contained in the image and corresponding pseudo label. Finally, we set a threshold to select the image and pseudo-label pairs with higher scores and propose a reliability-enhanced training strategy to train the new mirror detection model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.577, + 0.295, + 0.593 + ], + "angle": 0, + "content": "3.3. Dual Guidance Scoring" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.6, + 0.31, + 0.615 + ], + "angle": 0, + "content": "3.3.1 Geometric-based Scoring" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.471, + 0.776 + ], + "angle": 0, + "content": "To directly assess the quality of predicted pseudo labels through their geometric shapes, we first design a geometric scoring strategy. In this strategy, we aim to distill geometric knowledge into an estimation model, \\(\\mathcal{M}_g\\) (e.g., ResNet-50). Specifically, for three annotated datasets, we denote the input data as \\(\\mathcal{D}g = \\{I_i,P_i,G_i\\}_{i = 1}^N\\), where \\(I\\), \\(P\\), and \\(G\\) represent an image, a pseudo label, and the corresponding ground truth label, respectively. \\(N\\) is the total number of data samples. During training, for the input data \\(\\mathcal{D}_g\\), we first calculate an aggregated segmentation score \\(S_{g}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.786, + 0.47, + 0.829 + ], + "angle": 0, + "content": "\\[\nS _ {g} = \\frac {1}{3} \\sum_ {j = 1} ^ {3} \\mathcal {F} _ {j} (P, G), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.47, + 0.869 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_j\\) denotes different segmentation metric functions (i.e., IoU, \\(F_{\\beta}\\), and Accuracy)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Next, model \\(\\mathcal{M}_g\\), parameterized by \\(\\theta_g\\), learns to align the predicted aggregated score \\(\\hat{S}_g = \\mathcal{M}_g(I_i, P_i; \\theta_g)\\) with" + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.091, + 0.706, + 0.102 + ], + "angle": 0, + "content": "1. High geometric score but low semantic consistency" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.103, + 0.604, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.104, + 0.69, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.6, + 0.17, + 0.694, + 0.183 + ], + "angle": 0, + "content": "Geometric score: top 20% (High) \nSonicometric score: bottom 30% (Low)" + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.104, + 0.786, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.104, + 0.874, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.17, + 0.879, + 0.184 + ], + "angle": 0, + "content": "Geometric score: top 10% (High) \nSemantic score: bottom 20% (Low)" + }, + { + "type": "image_caption", + "bbox": [ + 0.52, + 0.186, + 0.706, + 0.195 + ], + "angle": 0, + "content": "2. High geometric score and high semantic consistency" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.196, + 0.604, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.196, + 0.692, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.601, + 0.263, + 0.693, + 0.276 + ], + "angle": 0, + "content": "Geometric score: top \\(10\\%\\) (High) \nSemantic score: top \\(20\\%\\) (High)" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.197, + 0.786, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.197, + 0.875, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.263, + 0.875, + 0.277 + ], + "angle": 0, + "content": "Geometric score: top \\(10\\%\\) (High) \nSemantic score: top \\(20\\%\\) (High)" + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.278, + 0.705, + 0.288 + ], + "angle": 0, + "content": "3. Low geometric score and low semantic consistency" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.288, + 0.604, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.289, + 0.692, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.598, + 0.355, + 0.7, + 0.368 + ], + "angle": 0, + "content": "Geometric score: bottom \\(40\\%\\) (Low) \nSemantic score: bottom \\(20\\%\\) (Low)" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.289, + 0.787, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.289, + 0.875, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.779, + 0.355, + 0.88, + 0.37 + ], + "angle": 0, + "content": "Geometric score: bottom \\(40\\%\\) (Low) \nSemitonic score: bottom \\(40\\%\\) (Low)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.381, + 0.892, + 0.423 + ], + "angle": 0, + "content": "Figure 4. Example analysis for the geometric and semantic scores obtained from our dual guidance scoring strategy. We aim to select more reliable data (with high geometric and semantic scores)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.428, + 0.807, + 0.443 + ], + "angle": 0, + "content": "the actual score \\(S_{g}\\) using the \\(\\mathcal{L}_2\\) loss function." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.451, + 0.774, + 0.467 + ], + "angle": 0, + "content": "3.3.2 MMA-driven Semantic Scoring" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.626 + ], + "angle": 0, + "content": "However, geometric-based scoring alone is not sufficient in some cases because this score does not contain semantic information from images. As shown in the first row of Figure 4, the mirror detection model erroneously recognizes the non-mirror region as a mirror and gives a \"reasonable\" prediction. Hence, in these cases, the geometric score is high. Meanwhile, the semantic score from our MMA-driven strategy can effectively recognize this type of error and provide a lower score, which can help us filter out low-quality pseudo labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Semantic modeling. Inspired by the impressive semantic understanding capabilities of the latest multimodal large language models, we design an MMA-driven semantic scoring strategy to obtain the semantic score of an image and pseudo-label pair. The output of a single multi-modal large language model can sometimes be unstable, particularly when it is required to provide a fine-grained score. To address this issue, we first design a semantic modeling process. Specifically, as depicted in Figure 3, we select three of the latest open-source vision-language models as multi-modal agents (i.e., MiniCPM-V-2.6, Qwen2-VL, and InternVL-2) to provide separate analyses and scoring. These models use the image and pseudo-label pair, along with a custom scoring prompt, as input. Next, we utilize the free API of a large language model (i.e., GLM4-flash) to conduct further analysis based on the outputs from the multi-modal agents and provide the final semantic score, achieving more stable semantic scoring." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "25479" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.182, + 0.089, + 0.796, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.246, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Figure 5. Detailed implementation of the proposed reliability-enhanced training strategy: We adopt the Mean Teacher architecture and incorporate the highly reliable pseudo labels to learn more robust visual knowledge. In each iteration of our iterative data engine, the teacher model is initialized from the student model of the previous iteration. We employ a consistency loss to align the predictions between the student model and the teacher model, and we use a confidence matrix to enable the student model to make more certain predictions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.473, + 0.492 + ], + "angle": 0, + "content": "Semantic distillation. However, the semantic modeling process involving multi-modal agents and large language models is time-consuming and cannot be applied effectively. We propose a semantic distillation strategy to transfer the semantic knowledge of multi-modal agents into a lightweight scoring model, denoted as \\(\\mathcal{M}_s\\). Similar to the geometric distillation process, we concatenate the image and the corresponding pseudo label as input: \\(\\mathcal{D}_s = \\{I_i, P_i\\}\\). Next, the estimation model \\(\\mathcal{M}_s\\) parameterized by \\(\\theta_s\\), learns to align the predicted semantic score \\(\\hat{S}_s = \\mathcal{M}_s(I_i, P_i; \\theta_s)\\) with the semantic score \\(S_s\\) obtained from multi-modal agents." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.495, + 0.363, + 0.51 + ], + "angle": 0, + "content": "3.3.3 Selection of Highly Reliable Data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.655 + ], + "angle": 0, + "content": "To select highly reliable pseudo labels based on the geometric score and semantic score, we define a data selection strategy. We denote the scoring results from the geometric-based scoring model and the semantic-based scoring model for all the unlabeled data as \\(\\hat{S} = \\{\\hat{S}_g^k,\\hat{S}_s^k\\}_{k = 1}^M\\) , where \\(M\\) is the total number of unlabeled data. Additionally, we define \\(T\\) as the selection threshold to control the number of highly reliable data selected, which will be discussed in Section 4.3. The selection strategy is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.661, + 0.47, + 0.702 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (k) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\mathcal {P} _ {g} \\left(\\hat {S} _ {g} ^ {k}\\right) \\geq T \\text {a n d} \\mathcal {P} _ {s} \\left(\\hat {S} _ {s} ^ {k}\\right) \\geq T, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.708, + 0.47, + 0.738 + ], + "angle": 0, + "content": "where \\(\\mathcal{P}(x)\\) represents the calculation of the percentage that the score \\(x\\) constitutes of the total score." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.345, + 0.759 + ], + "angle": 0, + "content": "3.4. Reliability-enhanced Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "When we have selected the more reliable image and pseudolabel pair, we aim to train a new mirror detection model that will be used in the next iteration. Hence, as shown in Figure 5, we devise a reliability-enhanced training strategy based on the standard Mean Teacher architecture to effectively learn knowledge from the labeled data and selected high-reliable unlabeled data. We adopt cross-entropy loss to optimize the student model using labeled data and reliable pseudo-labels. Meanwhile, mean squared error loss is" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.356 + ], + "angle": 0, + "content": "used to align the outputs of the student and teacher models for the unlabeled input. The loss functions can be summarized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.365, + 0.892, + 0.499 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C E} \\left(y _ {i}, f \\left(x _ {i} ^ {l}; \\theta\\right)\\right) (3) \\\\ + \\lambda_ {2} \\cdot \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {C E} \\left(\\tilde {y} _ {j}, f \\left(x _ {j} ^ {u}; \\theta\\right)\\right) (4) \\\\ + \\lambda_ {3} \\cdot \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathcal {C} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) \\left| f \\left(x _ {j} ^ {u}; \\theta\\right) - f \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) \\right| ^ {2}, (5) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.631 + ], + "angle": 0, + "content": "where \\(\\lambda\\) represents the weight of different loss functions, while \\(N\\) and \\(M\\) denote the numbers of samples with and without ground truth labels, respectively. The variables \\(y\\) and \\(\\tilde{y}\\) represent the ground truth labels and the reliable pseudo-labels, respectively. The symbols \\(x^l\\) and \\(x^u\\) denote the labeled and unlabeled images, respectively. Additionally, \\(\\theta\\) and \\(\\theta'\\) are the parameters of the student and teacher models, respectively." + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.643, + 0.892, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {k} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} f _ {k} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) > \\operatorname {c o n f}, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.693, + 0.892, + 0.755 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}\\) denotes the confidence matrix and 'conf' represents the confidence threshold. We calculate the consistency loss only when the prediction probability of the pixel \\(k\\) from the teacher model is greater than the confidence threshold." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.762, + 0.625, + 0.779 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.707, + 0.803 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. We evaluate our method on the test sets of three labeled datasets: MSD[51], PMD[18], and RGBD-Mirror*. RGBD-Mirror* is produced from the RGBD-Mirror dataset [28] by using the RGB images and annotated mirror masks and removing the corresponding depth map for each RGB-D image pair. We combine the training sets" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "25480" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.564 + ], + "angle": 0, + "content": "
    DatasetsMethodsUnlabeledIoU ↑Accuracy ↑Fβ↑MAE ↓BER ↓
    MSDSegFormer [41]X0.8790.9530.9150.0386.50
    Mask2Former [6]X0.8830.9580.9170.0366.65
    MirrorNet [51]X0.8450.9480.8920.0447.67
    PMDNet [18]X0.8470.9520.9080.0337.22
    VCNet [34]X0.8840.9580.9140.0297.32
    SANet [10]X0.8710.9510.9120.0337.10
    HetNet [13]X0.8880.9640.9220.0276.63
    CSFwinformer [42]X0.8750.9600.9180.0306.79
    MT [36]✓0.9010.9580.9280.0244.62
    UAMT [53]✓0.9090.9450.9320.0214.37
    DepthAnything [50]✓0.9150.9710.9430.0203.98
    UniMatch [49]✓0.9080.9490.9180.0314.57
    DAM (Ours)✓0.9340.9800.9680.0192.32
    PMDSegFormer [41]X0.6780.8330.8080.02410.14
    Mask2Former [6]X0.6980.8360.8170.0229.98
    MirrorNet [51]X0.6480.7980.7850.03010.39
    PMDNet [18]X0.6580.8180.7950.02810.86
    SANet [10]X0.6570.8160.7940.02410.97
    VCNet [34]X0.6760.8180.8010.02510.16
    HetNet [13]X0.7020.8270.8180.0239.65
    CSFwinformer [42]X0.7050.8200.8150.0299.93
    MT [36]✓0.7060.8270.8250.0219.38
    UAMT [53]✓0.7090.8340.8280.0208.93
    DepthAnything [50]✓0.7110.8280.8260.0209.11
    UniMatch [49]✓0.6980.8250.8200.02610.39
    DAM (Ours)✓0.7340.8510.8520.0198.08
    RGBD-Mirror*SegFormer [41]X0.7540.8580.7880.03913.11
    Mask2Former [6]X0.7680.8610.8030.04012.16
    MirrorNet [51]X0.7170.7960.7650.04413.40
    PMDNet [18]X0.7390.8190.7740.03513.24
    SANet [10]X0.7490.8410.7890.03912.88
    VCNet [34]X0.7630.8440.8100.03412.28
    HetNet [13]X0.7750.8570.8190.03111.20
    CSFwinformer [42]X0.7690.8500.8150.03411.04
    MT [36]✓0.7840.8570.8260.0398.19
    UAMT [53]✓0.7880.8730.8390.0358.24
    DepthAnything [50]✓0.7990.8810.8480.0316.94
    UniMatch [49]✓0.7850.8470.8210.0418.35
    DAM (Ours)✓0.8080.8850.8700.0306.42
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.574, + 0.47, + 0.658 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison between the proposed DAM and 11 state-of-the-art methods on MSD, PMD, and RGBD-Mirror* datasets in terms of IoU, Accuracy, \\( F_{\\beta} \\), MAE, and BER metrics. The best results are shown in **bold**. An asterisk (*) indicates that only the RGB images and annotated mirror masks are used, without any depth information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.47, + 0.716 + ], + "angle": 0, + "content": "of the three labeled datasets to retrain all comparison methods using their released code and turn their parameters to obtain their best performance to ensure fairness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Implementation details. We adopt the DINOv2-small encoder [29] for feature extraction and use the DPT [31] decoder for mirror detection. The ratio of labeled to unlabeled images is set to 1:1 in each batch. The base learning rate of the pre-trained encoder is set to 5e-6, while the randomly initialized decoder uses a learning rate that is 10 times larger. We use the AdamW optimizer and decay the learning rate with a poly schedule. We apply horizontal flipping as data augmentation. During reliability-enhanced training, we set three loss function weights as \\(\\lambda_1 = \\lambda_2 = \\lambda_3 = 1\\), and the confidence threshold as conf = 0.9. The strong augmentation operations in Figure 5 include color jitter," + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.09, + 0.871, + 0.446 + ], + "angle": 0, + "content": "
    DatasetsMethodsTypeIoU ↑Accuracy ↑Fβ↑MAE ↓
    VMD-DTVSD [4]Video0.4800.8750.7460.125
    STICT [27]Video0.1640.8090.5300.198
    Sc-Cor [9]Video0.5120.8630.6960.137
    Scotch-Soda [26]Video0.5870.8780.7490.121
    HFAN [30]Video0.4590.8760.7060.124
    STCN [7]Video0.4450.8590.6700.140
    GlassNet [19]Image0.5520.8640.7180.137
    MirrorNet [51]Image0.5050.8550.6810.145
    PMDNet [18]Image0.5320.8720.7490.128
    VCNet [34]Image0.5390.8770.7490.123
    HetNet [13]Image0.5310.8680.7480.131
    VMD-Net [20]Video0.5670.8950.7870.105
    UAMT [53]Image0.6830.9010.7970.098
    DepthAnything [50]Image0.7230.9180.8320.087
    DAM (ours)Image0.7550.9290.8450.075
    MMDMGA [15]Image0.2810.5660.4890.434
    UFO [32]Image0.5990.7970.7970.203
    FSNet [14]Image0.7080.8530.8380.147
    ALGRF [35]Image0.5030.7240.6930.276
    F3Net [40]Image0.6710.8390.8470.161
    PMDNet [18]Image0.4240.7410.8470.259
    MirrorNet [51]Image0.6660.8350.8390.165
    VMD-Net [20]Video0.7230.8540.8120.146
    Warren et al. [39]Video0.7250.8720.8690.127
    UAMT [53]Image0.7250.8520.8610.147
    DepthAnything [50]Image0.7320.8610.8570.138
    DAM (ours)Image0.7590.8790.8690.121
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.457, + 0.892, + 0.512 + ], + "angle": 0, + "content": "Table 3. Generalization capability on two video mirror detection datasets: Our method does not require training on the VMD-D and MMD datasets, yet it achieves a new state-of-the-art performance on their test sets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.523, + 0.74, + 0.537 + ], + "angle": 0, + "content": "random grayscale, and random blur." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Evaluation metrics. Following the previous works [20, 26, 34], we adopt intersection over union (IoU), pixel accuracy (Accuracy), F-measure \\((F_{\\beta})\\), mean absolute error (MAE), and balanced error rate (BER) to evaluate our method." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.606, + 0.885, + 0.621 + ], + "angle": 0, + "content": "4.2. Comparison against State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Compared methods. We compare our method with seven supervised networks and four semi-supervised methods. Seven supervised methods are SegFormer [41], Mask2Former [6], MirrorNet [51], PMDNet [18], SANet [10], VCNet [34], and HetNet [13]. Four semi-supervised methods are Mean Teacher [36], UAMT [53], DepthAnything [50], and UniMatch [49]. For all semi-supervised methods, we utilize the same training set with collected unlabeled data as our method for fair comparisons; see our supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantitative comparisons. We compare our DAM against 11 state-of-the-art methods on three datasets (i.e., MSD [51], PMD [18], and RGBD-Mirror* [28]) in terms of IoU, Accuracy, \\( F_{\\beta} \\), MAE, and BER metrics. As shown in Table 2, our DAM not only surpasses all supervised seven methods on all five metrics, but also outperforms all the semi-supervised methods, which have the same unlabeled data as our method during training. Our best performance" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25481" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.168, + 0.093, + 0.811, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.453, + 0.895, + 0.481 + ], + "angle": 0, + "content": "Figure 6. Visual comparisons of mirror detection results predicted by our network and other methods. Clearly, our network achieves more accurate mirror detection results than all the compared methods, and our results are more consistent with the ground truths." + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.484, + 0.839, + 0.604 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.615, + 0.895, + 0.656 + ], + "angle": 0, + "content": "Figure 7. The effect of different thresholds \\( T \\) at different engine iterations of our method. We plot the number of highly reliable data and IoU scores on three datasets for each engine iteration regarding three different T values (\\( T = 0.4 \\), \\( T = 0.6 \\), and \\( T = 0.8 \\)). \\( T = 0.6 \\) yields the highest IoU scores for all three datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.662, + 0.47, + 0.72 + ], + "angle": 0, + "content": "of all five metrics on three datasets indicates that our DAM model is more effective and robust in detecting mirror regions of different scenes of three datasets by learning more visual knowledge from large-scale reliable data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.721, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Generalization capability on the video mirror detection datasets. To further evaluate the generalization capabilities of our method, we test our DAM on two unseen datasets (i.e., the VMD-D and MMD datasets). Specifically, without requiring any re-training operations on these two unseen datasets, we directly test our model (the same trained model of our method at Table 2) to produce our results on these two unseen datasets. Then, Table 3 compares our results against those of state-of-the-art methods, which are trained on the VMD-D and MMD datasets. From Table 3, we can find that our DAM clearly outperforms all state-of-the-art methods on the VMD-D dataset and the MMD dataset regarding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.662, + 0.892, + 0.691 + ], + "angle": 0, + "content": "all quantitative evaluation metrics. It convincingly verifies the generalization capabilities of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Qualitative comparisons. Figure 6 visually compares mirror detection results produced by our network and seven state-of-the-art methods on different input images. For these small mirrors at the first two rows, our method can detect more mirror details, while compared methods tend to wrongly recognize non-mirror regions in their mirror detection results. For big mirror objects at the third and fourth rows, all compared methods neglect parts of mirror regions, while our method tends to more accurately identify whole mirror regions. Meanwhile, we further select some more challenging and unlabeled images as the inputs for visual comparisons. As shown in the last four rows in Figure 6, the mirror regions may be blended (first row), partially covered (second and third rows), or complex due to a large number" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25482" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.428, + 0.148 + ], + "angle": 0, + "content": "
    Index\\( S_g \\)\\( S_s \\)RETIoU↑Accuracy↑\\( F_{\\beta} \\uparrow \\)MAE↓BER↓
    M1(supervised)0.6790.8130.8090.02911.06
    M2✓0.6930.8150.8190.02410.21
    M3✓✓0.7190.8310.8370.0229.09
    Ours✓✓✓0.7340.8510.8520.0198.08
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.158, + 0.47, + 0.213 + ], + "angle": 0, + "content": "Table 4. Ablation study of (1) geometric scoring \\((S_g)\\), (2) MMA-driven semantic scoring \\((S_s)\\), and (3) reliability-enhanced training strategy (RET) on the PMD dataset across IoU, Accuracy, \\(F_{\\beta}\\), MAE, and BER metrics." + }, + { + "type": "image", + "bbox": [ + 0.115, + 0.219, + 0.434, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.47, + 0.453 + ], + "angle": 0, + "content": "Figure 8. Visualization of latent features. \\( F_{1}, F_{2}, F_{3}, F_{4} \\) denote the decoder features at different resolutions. \\( F_{seg} \\) represents the feature from the decoder head. These results show that our network can learn a robust mirror-related feature representation for diverse scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.522 + ], + "angle": 0, + "content": "of mirrors (last row). Our method can accurately address these challenging mirror detections by effectively learning mirror-related knowledge from large-scale and highly reliable unlabeled data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.528, + 0.231, + 0.545 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.47, + 0.824 + ], + "angle": 0, + "content": "Effectiveness of the dual guidance scoring strategy and reliable-enhanced training. We conduct an ablation study to reveal the distinct contributions of geometric scoring \\((S_g)\\), semantic scoring \\((S_s)\\), and the reliability-enhanced training (RET) strategy within our model. Table 4 reports the quantitative results of the ablation study on the PMD dataset. The baseline model (M1) is trained using the labeled data, and the IoU, Accuracy, \\(F_{\\beta}\\), MAE, and BER scores are 0.679, 0.813, 0.809, 0.029, and 11.06, which highlights the limitations of the basic supervised approach. Then, we incorporate the proposed geometric scoring \\((S_g)\\) and MMA-driven semantic scoring \\((S_s)\\) into M1 to build M2 and M3. These two scoring strategies can select high-reliable data and significantly enhance the model's performance. Finally, with the reliability-enhanced training (RET) strategy, our method introduces additional optimization targets based on the student-teacher architecture and thus improves training stability and detection performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Effect of different thresholds \\( T \\). The hyper-parameter threshold \\( T \\) controls the quantity of selected highly reliable data and thus affects the training process. To select an optimal \\( T \\), we conduct an ablation study experiment with three different \\( T \\) values, which are \\( T = 0.4 \\), \\( T = 0.6 \\), and" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.09, + 0.859, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.179, + 0.892, + 0.219 + ], + "angle": 0, + "content": "Figure 9. Visualization of comparison results on two captured and unseen photos demonstrates that our network can more accurately detect mirrors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.364 + ], + "angle": 0, + "content": "\\(T = 0.8\\). In general, a larger \\(T\\) means more samples we select. As shown in Figure 7 (a), the number of highly reliable data increases when the iteration number of our data engine increases. Meanwhile, Figures 7 (b), (c), and (d) show the IoU scores for different \\(T\\) values and engine iteration numbers on the MSD, PMD, and RGBD-Mirror* datasets, respectively. More importantly, our method with \\(T = 0.6\\) yields the highest IoU score on all three datasets. Hence, we empirically set \\(T = 0.6\\) in all our experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.372, + 0.684, + 0.387 + ], + "angle": 0, + "content": "4.4. More Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.892, + 0.502 + ], + "angle": 0, + "content": "Feature visualization. As shown in Figure 8, we visualize the latent features at different decoder layers and the output feature map of the segmentation head. Apparently, these features can highlight mirror regions for different input mirror images. It indicates that our method can accurately capture the mirror-related feature representation, and thus produce robust mirror detection performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.594 + ], + "angle": 0, + "content": "Visualization of our results on unseen photos. We capture two unseen photos with mirrors at challenging positions. As shown in Figure 9, our network can more accurately detect the mirror regions than the state-of-the-art methods. The main reason is that our network can learn more reliable mirror-related knowledge from large-scale unlabeled data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.603, + 0.619, + 0.619 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this work, we collect a large-scale unlabeled dataset to fill the data gap in the mirror detection task. To effectively exploit the collected large-scale unlabeled data, we design an iterative data engine comprising four processes: (1) mirror detection model training, (2) pseudo-label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo-labels. In each iteration, we investigate a dual guidance scoring strategy to assess pseudo-labels through geometric accuracy derived from segmentation metrics and semantic scores from multi-modal large language models. Furthermore, we propose a reliability-enhanced training strategy to effectively learn from the selected, more reliable, high-quality pseudo-labels. We conduct extensive experiments on three public datasets to verify the performance gains from our collected large-scale unlabeled data. The segmentation results for diverse unseen examples and randomly captured images in different scenes further demonstrate the generalization capability of our model." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25483" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.236, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.236 + ], + "angle": 0, + "content": "This work is supported by the Guangdong Science and Technology Department (No. 2024ZDZX2004), the Guangzhou-HKUST(GZ) Joint Funding Program (No. 2023A03J0671), Guangdong Provincial Key Lab of Integrated Communication, Sensing and Computation for Ubiquitous Internet of Things (No.2023B1212010007), and the Nansha Key Area Science and Technology Project (No. 2023ZD003)." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.251, + 0.175, + 0.267 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.277, + 0.47, + 0.346 + ], + "angle": 0, + "content": "[1] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. 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Springer, 2019. 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.093, + 0.471, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25486" + } + ] +] \ No newline at end of file diff --git a/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_origin.pdf b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c86c26f61537abe1b54c5b6180db4b295e014946 --- /dev/null +++ b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/64ac5be5-9942-4491-856e-a27352561435_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9816d9df80468fe2ba6d7de1c7e20869ae73bac08dc1a21f0aa555c468d3cf3c +size 7469604 diff --git a/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/full.md b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/full.md new file mode 100644 index 0000000000000000000000000000000000000000..852909a7e60b302b0b2c13fc34ce42b0c9695663 --- /dev/null +++ b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/full.md @@ -0,0 +1,312 @@ +# Detect Any Mirrors: Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine + +Zhaohu Xing $^{1}$ Lihao Liu $^{2}$ Yijun Yang $^{1}$ Hongqiu Wang $^{1}$ Tian Ye $^{1}$ Sixiang Chen $^{1}$ Wenxue Li $^{1}$ Guang Liu $^{3}$ Lei Zhu $^{1,4*}$ + +1The Hong Kong University of Science and Technology (Guangzhou) 2Amazon +3Beijing Academy of Artificial Intelligence 4The Hong Kong University of Science and Technology + +# Abstract + +Mirror detection is a challenging task because a mirror's visual appearance varies depending on the reflected content. Due to limited annotated data, current methods failed to generalize well for detecting diverse mirror scenes. Semi-supervised learning with large-scale unlabeled data can improve generalization capabilities on mirror detection, but these methods often suffer from unreliable pseudolabels due to distribution differences between labeled and unlabeled data, therefore affecting the learning process. To address this issue, we first collect a large-scale dataset of approximately 0.4 million mirror-related images from the internet, significantly expanding the data scale for mirror detection. To effectively exploit this unlabeled dataset, we propose the first semi-supervised framework (namely an iterative data engine) consisting of four steps: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. In each iteration of the data engine, we employ a geometric accuracy scoring approach to assess pseudo labels based on multiple segmentation metrics, and design a multi-modal agent-driven semantic scoring approach to enhance the semantic perception of pseudo labels. These two scoring approaches can effectively improve the reliability of pseudo labels by selecting unlabeled samples with higher scores. Our method demonstrates promising performance across three mirror detection tasks and exhibits strong generalization on unseen examples. Our code will be publicly available at https://github.com/ge-xing/DAM. + +# 1. Introduction + +Mirrors are commonly found in our daily lives and can significantly affect the performance of various deep learning methods, including depth estimation [33], semantic + +![](images/9de2e484e705d2f19054743449f9985405520ba562bfdf8a893ed06d33a51986.jpg) +Figure 1. Examples of semi-supervised learning from (1) Mean Teacher [36], (2) DepthAnything [50], (3) UniMatch [49]. These methods explore how to effectively exploit large-scale unlabeled data to improve model generalization by challenging the student model and aligning the predictions between the student and teacher models. In contrast, our (4) DAM introduces an iterative optimization process and a scoring model to improve the reliability of the teacher model's predictions. + +![](images/1677c9a466e61376762f38357c601fd22be0be08d2caef37afc7304cf7a7f31e.jpg) +Figure 2. Comparison between our DAM with other SOTA methods in terms of segmentation metrics (i.e., IoU, Accuracy, $F_{\beta}$ , MAE, and BER.), parameter scale (#Param), and frames per second (FPS). In the radar chart, we normalized the metrics and reversed the MAE and BER metrics for better presentation. + +![](images/0dfe8b717564d78b65f9977e9a42e636c4af4e114af9ac35e9332094f2c08865.jpg) + +segmentation [12, 44, 45, 47], and video instance detection [16, 25, 43]. In applications such as drone tracking [3] and robot navigation [11], accurate mirror detection is crucial to avoid potential safety issues. There- + +fore, developing mirror detection models is essential for precisely detecting mirrors in images and providing additional information for other tasks. Although many methods [8, 10, 13, 18, 20, 46, 51] have been developed for mirror detection and achieved impressive performance on various mirror detection benchmarks by exploring the attributes of mirrors, these methods can not generalize well in diverse scenes due to the limited annotated datasets. + +Recently, as shown in Figure 1, many studies [17, 21-23, 36, 48-50] have been conducted to explore how to effectively exploit large-scale unlabeled data to improve model generalization. These methods typically use a student-teacher architecture, aiming to learn a strong representation of unlabeled data by challenging the student model with unlabeled input and enhancing the output consistency between the student model and the teacher model. However, these methods do not consider the reliability of the teacher model's output, which can significantly affect the learning quality of the student model. Moreover, in the mirror detection task, there are limited annotated datasets and a lack of large-scale unlabeled data containing various mirror scenes to enhance model generalization. This presents a challenge for current mirror detection methods when applied in practical scenarios. + +In this work, our goal is to fill the data gap and build a general mirror detection model with state-of-the-art performance and stronger generalization ability, aiming to Detect Any Mirrors (DAM) in various practical scenarios. First, we collect approximately 400000 diverse, unlabeled mirror-related images from the internet. To provide initial pseudo labels for this unlabeled data, we then train an initial mirror detection model using approximately 13,000 labeled images collected from three public mirror detection datasets. To effectively exploit the collected large-scale unlabeled data, we further design an iterative data engine, where each iteration includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. The core of each iteration is selecting high-quality pseudo labels that can improve the learning reliability of the student model. Therefore, we propose a dual guidance scoring strategy to assess the pseudo labels through geometric accuracy derived from segmentation metrics and semantic scores from multi-modal large language models. Furthermore, we introduce a reliability-enhanced training strategy to effectively learn from the selected, more reliable, high-quality pseudo labels. We conduct extensive experiments on three public datasets to verify the performance gains from our collected large-scale unlabeled data. Mirror detection results on unseen datasets and randomly captured images in different scenes also demonstrate the generalization capability of our model. Our main contributions can be summarized as follows: + +- We propose a general mirror detection model, called DAM, which achieves SOTA performance and exhibits strong generalization capability in diverse scenes. +- We collect a large-scale unlabeled dataset to fill the data gap in the mirror detection task. +- We devise an iterative data engine to gradually improve the quality of pseudo labels, and we further propose a reliability-enhanced training strategy to effectively learn from the more reliable pseudo labels. +- Experimental results on three mirror detection datasets, an unseen dataset, and randomly captured images demonstrate the promising mirror detection performance and generalization capability of our model. + +# 2. Related Work + +In this section, we first review the state-of-the-art methods for mirror detection. Next, we will discuss works on semi-supervised learning and multi-modal large language models (MLLM), which are explored in our network. + +# 2.1. Mirror Detection + +Detecting mirrors in an image is crucial for various applications, including drone tracking and robot navigation, as it helps prevent accidents. Additionally, it can enhance the performance of tasks like semantic segmentation and video instance detection. There are several methods for semantic segmentation tasks. For example, DeepLabV3 [2] utilizes atrous convolution in cascade and ASPP [1] module to capture the multi-scale features. Mask2Former [6] proposes a new framework, combining CNN and Transformer [37] to enhance the global understanding of images. However, these methods are not specifically designed for mirror scenes and do not perform well in detecting mirrors. + +Recently, MirrorNet [51] introduced the first mirror detection dataset and network. They employed contextual contrasted information to detect mirrors accurately. PMDNet [18] proposes a more challenging benchmark for mirror detection tasks. They utilized multi-scale mirror edge features to enhance mirror perception. More recently, VCNet [34] improves mirror detection performance by leveraging chirality cues and implicit correspondences. However, these methods fail to generalize to various complex scenes due to the limited annotated datasets. + +# 2.2. Leveraging Large-scale Unlabeled Data + +Leveraging the rich visual knowledge contained in large-scale unlabeled data to improve model generalization capability is a hot research direction. Tarvainen et al. [36] propose the Mean Teacher method to provide more stable and consistent targets for training the student model by updating the teacher model through an exponential moving average. DepthAnything [50] proposes to challenge the student model with a more difficult optimization target when learn- + +![](images/2e1e1f0e9765707a339a4c2abed78f503a673ff8bc934f7d40f2a4a8ad1d2a0e.jpg) + +![](images/9fa41b40351647a5b7990d0ca813bb6db73ae0b401b3c7527ec88a86fe53e1bb.jpg) + +![](images/0ac94b2d9e094035ad5d7b91a6e452ab5975ff566f5becb6da730c803efa09d6.jpg) +Figure 3. Our data engine includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo label. In each iteration, we investigate a geometric accuracy scoring (b) to assess the pseudo labels and design an MMA-driven semantic scoring (c) to effectively improve the semantic perception for pseudo labels. These two scoring approaches can effectively improve the reliability of pseudo labels by selecting the unlabeled samples with higher scores. + +ing the pseudo labels, in order to seek extra visual information. In addition, UniMatch [49] leverages feature-level and image-level perturbations to exploit a broader perturbation space, as well as a dual-stream perturbation strategy to fully probe pre-defined image-level perturbation space. However, these methods solely focus on enhancing the learning process of the student model and do not consider the reliability of the pseudo labels from the teacher model. The latter can directly affect the learning of the student model. + +# 2.3. Multi-modal Large Language Models (MLLM) + +Multi-modal large language models [24] possess the remarkable ability to understand high-level semantic information by learning large-scale data from various modalities, such as text, images, and videos. MiniCPM-V 2.6 [52] is the latest and most capable model in the MiniCPM-V series. Due to its superior token density, MiniCPM-V 2.6 can support real-time video understanding on end-side devices. InternVL-2 [5] demonstrates competitive performance on par with proprietary commercial models across various capabilities, including document and chart comprehension, infographics QA, scene text understanding and OCR tasks, scientific and mathematical problem-solving, as well as cultural understanding and integrated multi-modal capabilities. Qwen2-VL [38] is the latest version of the vision-language models in the Qwen model family, achieving state-of-the-art performance on various visual understanding benchmarks. + +
    DatasetImage NumberIs Annotated
    MSD [51]4018✔
    PMD [18]6461✔
    RGBD-Mirror [28]3049✔
    Ours406817✘
    + +Table 1. We have collected a large-scale unlabeled dataset featuring a variety of scenes where mirrors may appear, in order to expand the data scale for the mirror detection task. + +These models can provide a detailed analysis of a single image, multiple images, and video. In this work, we integrate these MLLMs to offer comprehensive and detailed analyses of the input images and corresponding pseudo labels, thereby scoring the quality of the pseudo labels. + +# 3. Method + +# 3.1. Data Preparation + +There are three main annotated datasets (i.e., MSD [51], PMD [18], and RGBD-Mirror [28]) used in the mirror detection task. As shown in Table 1, the limited data scale makes it easy for mirror detection models to overfit and not generalize well to various complex scenes. To address this issue, we have collected a large-scale unlabeled dataset, which contains 406,817 mirror-related images to provide diverse scenes where mirrors may appear. + +# 3.2. Iterative Data Engine + +We found that previous semi-supervised learning methods [36, 49, 50] usually focus on the learning process of the student model but overlook the prediction reliability of the teacher model. To address this issue, we introduce an iterative data engine to filter out low-quality pseudo labels and gradually improve mirror detection accuracy and robustness by learning from more reliable data. Specifically, the data engine includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. + +As shown in Figure 3 (a), in the first step, we train an initial mirror detection model using three collected annotated datasets. We then use the trained model to predict pseudo labels for the large-scale unlabeled dataset, resulting in 406,817 image and pseudo label pairs. At this stage, the pseudo labels are often unreliable because the initial mirror detection model may not generalize well when trained on limited annotated data. Therefore, we design a dual guidance scoring strategy, which includes geometric scoring and multi-modal agents (MMA)-driven semantic scoring, to assess the quality of the pseudo labels. As shown in Figure 3 (b) and (c), geometric scoring aims to predict an aggregated result of multiple segmentation metrics (i.e., IoU, $F_{\beta}$ , and Accuracy). Meanwhile, MMA-driven semantic scoring provides a better understanding of the semantic knowledge contained in the image and corresponding pseudo label. Finally, we set a threshold to select the image and pseudo-label pairs with higher scores and propose a reliability-enhanced training strategy to train the new mirror detection model. + +# 3.3. Dual Guidance Scoring + +# 3.3.1 Geometric-based Scoring + +To directly assess the quality of predicted pseudo labels through their geometric shapes, we first design a geometric scoring strategy. In this strategy, we aim to distill geometric knowledge into an estimation model, $\mathcal{M}_g$ (e.g., ResNet-50). Specifically, for three annotated datasets, we denote the input data as $\mathcal{D}g = \{I_i,P_i,G_i\}_{i = 1}^N$ , where $I$ , $P$ , and $G$ represent an image, a pseudo label, and the corresponding ground truth label, respectively. $N$ is the total number of data samples. During training, for the input data $\mathcal{D}_g$ , we first calculate an aggregated segmentation score $S_{g}$ : + +$$ +S _ {g} = \frac {1}{3} \sum_ {j = 1} ^ {3} \mathcal {F} _ {j} (P, G), \tag {1} +$$ + +where $\mathcal{F}_j$ denotes different segmentation metric functions (i.e., IoU, $F_{\beta}$ , and Accuracy). + +Next, model $\mathcal{M}_g$ , parameterized by $\theta_g$ , learns to align the predicted aggregated score $\hat{S}_g = \mathcal{M}_g(I_i, P_i; \theta_g)$ with + +![](images/866ec9cbe865a591f6cb2530aefb5a8d76ed91f6b81b0d2c8876c80bbce0e12a.jpg) +1. High geometric score but low semantic consistency + +![](images/3c8a9a829dfb842d3389d8955cfd24f19fbc7be97c4ac150a074493decc53fb3.jpg) +Geometric score: top 20% (High) +Sonicometric score: bottom 30% (Low) + +![](images/7b5109a475698fc8ee8a02315dca02e57beed98c206872119d048f4d10765b31.jpg) +Geometric score: top 10% (High) +Semantic score: bottom 20% (Low) + +![](images/d64456d17a5a9676c13305b406b781c2377bc9594bd5812984f269320a00800a.jpg) + +![](images/c3203f573e5507a1f30f1f50685e98df70101af0f845c73533b2a3b11f109c57.jpg) +2. High geometric score and high semantic consistency +Geometric score: top $10\%$ (High) +Semantic score: top $20\%$ (High) + +![](images/d863bc9184998b3dc80419c06b012d2f02e95093f39d068e969015d84e7011ec.jpg) + +![](images/bbe21da7bf44c2907d8981261c9b62d41c243d9fd9a92a328b23e53b072d292e.jpg) +Geometric score: top $10\%$ (High) +Semantic score: top $20\%$ (High) + +![](images/92e6adf0430ebc7a476bc613aae92b22f7d370026cd3cc365663b8938b5949e1.jpg) + +![](images/e39d949c5c59027a795976d488375dc3c84c159c3462dc10017dc55ae8fa4df6.jpg) +3. Low geometric score and low semantic consistency +Geometric score: bottom $40\%$ (Low) +Semantic score: bottom $20\%$ (Low) +Figure 4. Example analysis for the geometric and semantic scores obtained from our dual guidance scoring strategy. We aim to select more reliable data (with high geometric and semantic scores). + +![](images/36771fa6916b86722460402f5dcc55a054394ed7fff343bf97a389b67f33ed02.jpg) + +![](images/680fadcf0602586c4e043e39cec68b1c3f8d58122bf999bda609126595284248.jpg) +Geometric score: bottom $40\%$ (Low) +Semitonic score: bottom $40\%$ (Low) + +![](images/11fe4ecab6d9e2340e502d1f72f925d69bafb1b841f6e3347918c8c955c31730.jpg) + +the actual score $S_{g}$ using the $\mathcal{L}_2$ loss function. + +# 3.3.2 MMA-driven Semantic Scoring + +However, geometric-based scoring alone is not sufficient in some cases because this score does not contain semantic information from images. As shown in the first row of Figure 4, the mirror detection model erroneously recognizes the non-mirror region as a mirror and gives a "reasonable" prediction. Hence, in these cases, the geometric score is high. Meanwhile, the semantic score from our MMA-driven strategy can effectively recognize this type of error and provide a lower score, which can help us filter out low-quality pseudo labels. + +Semantic modeling. Inspired by the impressive semantic understanding capabilities of the latest multimodal large language models, we design an MMA-driven semantic scoring strategy to obtain the semantic score of an image and pseudo-label pair. The output of a single multi-modal large language model can sometimes be unstable, particularly when it is required to provide a fine-grained score. To address this issue, we first design a semantic modeling process. Specifically, as depicted in Figure 3, we select three of the latest open-source vision-language models as multi-modal agents (i.e., MiniCPM-V-2.6, Qwen2-VL, and InternVL-2) to provide separate analyses and scoring. These models use the image and pseudo-label pair, along with a custom scoring prompt, as input. Next, we utilize the free API of a large language model (i.e., GLM4-flash) to conduct further analysis based on the outputs from the multi-modal agents and provide the final semantic score, achieving more stable semantic scoring. + +![](images/00873822804a066492df23e52dfe6587e670bfbd9f5b7b36e3e8a52d08b6976d.jpg) +Figure 5. Detailed implementation of the proposed reliability-enhanced training strategy: We adopt the Mean Teacher architecture and incorporate the highly reliable pseudo labels to learn more robust visual knowledge. In each iteration of our iterative data engine, the teacher model is initialized from the student model of the previous iteration. We employ a consistency loss to align the predictions between the student model and the teacher model, and we use a confidence matrix to enable the student model to make more certain predictions. + +Semantic distillation. However, the semantic modeling process involving multi-modal agents and large language models is time-consuming and cannot be applied effectively. We propose a semantic distillation strategy to transfer the semantic knowledge of multi-modal agents into a lightweight scoring model, denoted as $\mathcal{M}_s$ . Similar to the geometric distillation process, we concatenate the image and the corresponding pseudo label as input: $\mathcal{D}_s = \{I_i, P_i\}$ . Next, the estimation model $\mathcal{M}_s$ parameterized by $\theta_s$ , learns to align the predicted semantic score $\hat{S}_s = \mathcal{M}_s(I_i, P_i; \theta_s)$ with the semantic score $S_s$ obtained from multi-modal agents. + +# 3.3.3 Selection of Highly Reliable Data + +To select highly reliable pseudo labels based on the geometric score and semantic score, we define a data selection strategy. We denote the scoring results from the geometric-based scoring model and the semantic-based scoring model for all the unlabeled data as $\hat{S} = \{\hat{S}_g^k,\hat{S}_s^k\}_{k = 1}^M$ , where $M$ is the total number of unlabeled data. Additionally, we define $T$ as the selection threshold to control the number of highly reliable data selected, which will be discussed in Section 4.3. The selection strategy is defined as follows: + +$$ +\mathcal {A} (k) = \left\{ \begin{array}{l l} 1, & \text {i f} \mathcal {P} _ {g} \left(\hat {S} _ {g} ^ {k}\right) \geq T \text {a n d} \mathcal {P} _ {s} \left(\hat {S} _ {s} ^ {k}\right) \geq T, \\ 0, & \text {o t h e r w i s e}, \end{array} \right. \tag {2} +$$ + +where $\mathcal{P}(x)$ represents the calculation of the percentage that the score $x$ constitutes of the total score. + +# 3.4. Reliability-enhanced Training + +When we have selected the more reliable image and pseudolabel pair, we aim to train a new mirror detection model that will be used in the next iteration. Hence, as shown in Figure 5, we devise a reliability-enhanced training strategy based on the standard Mean Teacher architecture to effectively learn knowledge from the labeled data and selected high-reliable unlabeled data. We adopt cross-entropy loss to optimize the student model using labeled data and reliable pseudo-labels. Meanwhile, mean squared error loss is + +used to align the outputs of the student and teacher models for the unlabeled input. The loss functions can be summarized as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \cdot \frac {1}{N} \sum_ {i = 1} ^ {N} \mathrm {C E} \left(y _ {i}, f \left(x _ {i} ^ {l}; \theta\right)\right) (3) \\ + \lambda_ {2} \cdot \frac {1}{M} \sum_ {j = 1} ^ {M} \mathrm {C E} \left(\tilde {y} _ {j}, f \left(x _ {j} ^ {u}; \theta\right)\right) (4) \\ + \lambda_ {3} \cdot \frac {1}{M} \sum_ {j = 1} ^ {M} \mathcal {C} \left(x _ {j} ^ {u}; \theta^ {\prime}\right) \left| f \left(x _ {j} ^ {u}; \theta\right) - f \left(x _ {j} ^ {u}; \theta^ {\prime}\right) \right| ^ {2}, (5) \\ \end{array} +$$ + +where $\lambda$ represents the weight of different loss functions, while $N$ and $M$ denote the numbers of samples with and without ground truth labels, respectively. The variables $y$ and $\tilde{y}$ represent the ground truth labels and the reliable pseudo-labels, respectively. The symbols $x^l$ and $x^u$ denote the labeled and unlabeled images, respectively. Additionally, $\theta$ and $\theta'$ are the parameters of the student and teacher models, respectively. + +$$ +\mathcal {C} _ {k} \left(x _ {j} ^ {u}; \theta^ {\prime}\right) = \left\{ \begin{array}{l l} 1, & \text {i f} f _ {k} \left(x _ {j} ^ {u}; \theta^ {\prime}\right) > \operatorname {c o n f}, \\ 0, & \text {o t h e r w i s e}, \end{array} \right. \tag {6} +$$ + +where $\mathcal{C}$ denotes the confidence matrix and 'conf' represents the confidence threshold. We calculate the consistency loss only when the prediction probability of the pixel $k$ from the teacher model is greater than the confidence threshold. + +# 4. Experiment + +# 4.1. Experimental Settings + +Datasets. We evaluate our method on the test sets of three labeled datasets: MSD[51], PMD[18], and RGBD-Mirror*. RGBD-Mirror* is produced from the RGBD-Mirror dataset [28] by using the RGB images and annotated mirror masks and removing the corresponding depth map for each RGB-D image pair. We combine the training sets + +
    DatasetsMethodsUnlabeledIoU ↑Accuracy ↑Fβ↑MAE ↓BER ↓
    MSDSegFormer [41]X0.8790.9530.9150.0386.50
    Mask2Former [6]X0.8830.9580.9170.0366.65
    MirrorNet [51]X0.8450.9480.8920.0447.67
    PMDNet [18]X0.8470.9520.9080.0337.22
    VCNet [34]X0.8840.9580.9140.0297.32
    SANet [10]X0.8710.9510.9120.0337.10
    HetNet [13]X0.8880.9640.9220.0276.63
    CSFwinformer [42]X0.8750.9600.9180.0306.79
    MT [36]✓0.9010.9580.9280.0244.62
    UAMT [53]✓0.9090.9450.9320.0214.37
    DepthAnything [50]✓0.9150.9710.9430.0203.98
    UniMatch [49]✓0.9080.9490.9180.0314.57
    DAM (Ours)✓0.9340.9800.9680.0192.32
    PMDSegFormer [41]X0.6780.8330.8080.02410.14
    Mask2Former [6]X0.6980.8360.8170.0229.98
    MirrorNet [51]X0.6480.7980.7850.03010.39
    PMDNet [18]X0.6580.8180.7950.02810.86
    SANet [10]X0.6570.8160.7940.02410.97
    VCNet [34]X0.6760.8180.8010.02510.16
    HetNet [13]X0.7020.8270.8180.0239.65
    CSFwinformer [42]X0.7050.8200.8150.0299.93
    MT [36]✓0.7060.8270.8250.0219.38
    UAMT [53]✓0.7090.8340.8280.0208.93
    DepthAnything [50]✓0.7110.8280.8260.0209.11
    UniMatch [49]✓0.6980.8250.8200.02610.39
    DAM (Ours)✓0.7340.8510.8520.0198.08
    RGBD-Mirror*SegFormer [41]X0.7540.8580.7880.03913.11
    Mask2Former [6]X0.7680.8610.8030.04012.16
    MirrorNet [51]X0.7170.7960.7650.04413.40
    PMDNet [18]X0.7390.8190.7740.03513.24
    SANet [10]X0.7490.8410.7890.03912.88
    VCNet [34]X0.7630.8440.8100.03412.28
    HetNet [13]X0.7750.8570.8190.03111.20
    CSFwinformer [42]X0.7690.8500.8150.03411.04
    MT [36]✓0.7840.8570.8260.0398.19
    UAMT [53]✓0.7880.8730.8390.0358.24
    DepthAnything [50]✓0.7990.8810.8480.0316.94
    UniMatch [49]✓0.7850.8470.8210.0418.35
    DAM (Ours)✓0.8080.8850.8700.0306.42
    + +Table 2. Quantitative comparison between the proposed DAM and 11 state-of-the-art methods on MSD, PMD, and RGBD-Mirror* datasets in terms of IoU, Accuracy, $F_{\beta}$ , MAE, and BER metrics. The best results are shown in **bold**. An asterisk (*) indicates that only the RGB images and annotated mirror masks are used, without any depth information. + +of the three labeled datasets to retrain all comparison methods using their released code and turn their parameters to obtain their best performance to ensure fairness. + +Implementation details. We adopt the DINOv2-small encoder [29] for feature extraction and use the DPT [31] decoder for mirror detection. The ratio of labeled to unlabeled images is set to 1:1 in each batch. The base learning rate of the pre-trained encoder is set to 5e-6, while the randomly initialized decoder uses a learning rate that is 10 times larger. We use the AdamW optimizer and decay the learning rate with a poly schedule. We apply horizontal flipping as data augmentation. During reliability-enhanced training, we set three loss function weights as $\lambda_1 = \lambda_2 = \lambda_3 = 1$ , and the confidence threshold as conf = 0.9. The strong augmentation operations in Figure 5 include color jitter, + +
    DatasetsMethodsTypeIoU ↑Accuracy ↑Fβ↑MAE ↓
    VMD-DTVSD [4]Video0.4800.8750.7460.125
    STICT [27]Video0.1640.8090.5300.198
    Sc-Cor [9]Video0.5120.8630.6960.137
    Scotch-Soda [26]Video0.5870.8780.7490.121
    HFAN [30]Video0.4590.8760.7060.124
    STCN [7]Video0.4450.8590.6700.140
    GlassNet [19]Image0.5520.8640.7180.137
    MirrorNet [51]Image0.5050.8550.6810.145
    PMDNet [18]Image0.5320.8720.7490.128
    VCNet [34]Image0.5390.8770.7490.123
    HetNet [13]Image0.5310.8680.7480.131
    VMD-Net [20]Video0.5670.8950.7870.105
    UAMT [53]Image0.6830.9010.7970.098
    DepthAnything [50]Image0.7230.9180.8320.087
    DAM (ours)Image0.7550.9290.8450.075
    MMDMGA [15]Image0.2810.5660.4890.434
    UFO [32]Image0.5990.7970.7970.203
    FSNet [14]Image0.7080.8530.8380.147
    ALGRF [35]Image0.5030.7240.6930.276
    F3Net [40]Image0.6710.8390.8470.161
    PMDNet [18]Image0.4240.7410.8470.259
    MirrorNet [51]Image0.6660.8350.8390.165
    VMD-Net [20]Video0.7230.8540.8120.146
    Warren et al. [39]Video0.7250.8720.8690.127
    UAMT [53]Image0.7250.8520.8610.147
    DepthAnything [50]Image0.7320.8610.8570.138
    DAM (ours)Image0.7590.8790.8690.121
    + +Table 3. Generalization capability on two video mirror detection datasets: Our method does not require training on the VMD-D and MMD datasets, yet it achieves a new state-of-the-art performance on their test sets. + +random grayscale, and random blur. + +Evaluation metrics. Following the previous works [20, 26, 34], we adopt intersection over union (IoU), pixel accuracy (Accuracy), F-measure $(F_{\beta})$ , mean absolute error (MAE), and balanced error rate (BER) to evaluate our method. + +# 4.2. Comparison against State-of-the-art Methods + +Compared methods. We compare our method with seven supervised networks and four semi-supervised methods. Seven supervised methods are SegFormer [41], Mask2Former [6], MirrorNet [51], PMDNet [18], SANet [10], VCNet [34], and HetNet [13]. Four semi-supervised methods are Mean Teacher [36], UAMT [53], DepthAnything [50], and UniMatch [49]. For all semi-supervised methods, we utilize the same training set with collected unlabeled data as our method for fair comparisons; see our supplementary material. + +Quantitative comparisons. We compare our DAM against 11 state-of-the-art methods on three datasets (i.e., MSD [51], PMD [18], and RGBD-Mirror* [28]) in terms of IoU, Accuracy, $F_{\beta}$ , MAE, and BER metrics. As shown in Table 2, our DAM not only surpasses all supervised seven methods on all five metrics, but also outperforms all the semi-supervised methods, which have the same unlabeled data as our method during training. Our best performance + +![](images/4c136b225f8232f092a4b27d7d7e626097c078de8760d856d78bd7afc8c3402f.jpg) +Figure 6. Visual comparisons of mirror detection results predicted by our network and other methods. Clearly, our network achieves more accurate mirror detection results than all the compared methods, and our results are more consistent with the ground truths. + +![](images/eb947a0d1b941a6062d0905ee832aed5488d9b2a48a690c04350a9075cc23d6f.jpg) +Figure 7. The effect of different thresholds $T$ at different engine iterations of our method. We plot the number of highly reliable data and IoU scores on three datasets for each engine iteration regarding three different T values ( $T = 0.4$ , $T = 0.6$ , and $T = 0.8$ ). $T = 0.6$ yields the highest IoU scores for all three datasets. + +of all five metrics on three datasets indicates that our DAM model is more effective and robust in detecting mirror regions of different scenes of three datasets by learning more visual knowledge from large-scale reliable data. + +Generalization capability on the video mirror detection datasets. To further evaluate the generalization capabilities of our method, we test our DAM on two unseen datasets (i.e., the VMD-D and MMD datasets). Specifically, without requiring any re-training operations on these two unseen datasets, we directly test our model (the same trained model of our method at Table 2) to produce our results on these two unseen datasets. Then, Table 3 compares our results against those of state-of-the-art methods, which are trained on the VMD-D and MMD datasets. From Table 3, we can find that our DAM clearly outperforms all state-of-the-art methods on the VMD-D dataset and the MMD dataset regarding + +all quantitative evaluation metrics. It convincingly verifies the generalization capabilities of our method. + +Qualitative comparisons. Figure 6 visually compares mirror detection results produced by our network and seven state-of-the-art methods on different input images. For these small mirrors at the first two rows, our method can detect more mirror details, while compared methods tend to wrongly recognize non-mirror regions in their mirror detection results. For big mirror objects at the third and fourth rows, all compared methods neglect parts of mirror regions, while our method tends to more accurately identify whole mirror regions. Meanwhile, we further select some more challenging and unlabeled images as the inputs for visual comparisons. As shown in the last four rows in Figure 6, the mirror regions may be blended (first row), partially covered (second and third rows), or complex due to a large number + +
    Index\( S_g \)\( S_s \)RETIoU↑Accuracy↑\( F_{\beta} \uparrow \)MAE↓BER↓
    M1(supervised)0.6790.8130.8090.02911.06
    M2✓0.6930.8150.8190.02410.21
    M3✓✓0.7190.8310.8370.0229.09
    Ours✓✓✓0.7340.8510.8520.0198.08
    + +Table 4. Ablation study of (1) geometric scoring $(S_g)$ , (2) MMA-driven semantic scoring $(S_s)$ , and (3) reliability-enhanced training strategy (RET) on the PMD dataset across IoU, Accuracy, $F_{\beta}$ , MAE, and BER metrics. + +![](images/0a71c1448ca73d88119393914c187bdaff60d331a73f0c1aee101567c26a5d8b.jpg) +Figure 8. Visualization of latent features. $F_{1}, F_{2}, F_{3}, F_{4}$ denote the decoder features at different resolutions. $F_{seg}$ represents the feature from the decoder head. These results show that our network can learn a robust mirror-related feature representation for diverse scenes. + +of mirrors (last row). Our method can accurately address these challenging mirror detections by effectively learning mirror-related knowledge from large-scale and highly reliable unlabeled data. + +# 4.3. Ablation Study + +Effectiveness of the dual guidance scoring strategy and reliable-enhanced training. We conduct an ablation study to reveal the distinct contributions of geometric scoring $(S_g)$ , semantic scoring $(S_s)$ , and the reliability-enhanced training (RET) strategy within our model. Table 4 reports the quantitative results of the ablation study on the PMD dataset. The baseline model (M1) is trained using the labeled data, and the IoU, Accuracy, $F_{\beta}$ , MAE, and BER scores are 0.679, 0.813, 0.809, 0.029, and 11.06, which highlights the limitations of the basic supervised approach. Then, we incorporate the proposed geometric scoring $(S_g)$ and MMA-driven semantic scoring $(S_s)$ into M1 to build M2 and M3. These two scoring strategies can select high-reliable data and significantly enhance the model's performance. Finally, with the reliability-enhanced training (RET) strategy, our method introduces additional optimization targets based on the student-teacher architecture and thus improves training stability and detection performance. + +Effect of different thresholds $T$ . The hyper-parameter threshold $T$ controls the quantity of selected highly reliable data and thus affects the training process. To select an optimal $T$ , we conduct an ablation study experiment with three different $T$ values, which are $T = 0.4$ , $T = 0.6$ , and + +![](images/13c7f0884527bcfd4a49a7072e1032049b28115c69abe3efa3f7006015cec3d0.jpg) +Figure 9. Visualization of comparison results on two captured and unseen photos demonstrates that our network can more accurately detect mirrors. + +$T = 0.8$ . In general, a larger $T$ means more samples we select. As shown in Figure 7 (a), the number of highly reliable data increases when the iteration number of our data engine increases. Meanwhile, Figures 7 (b), (c), and (d) show the IoU scores for different $T$ values and engine iteration numbers on the MSD, PMD, and RGBD-Mirror* datasets, respectively. More importantly, our method with $T = 0.6$ yields the highest IoU score on all three datasets. Hence, we empirically set $T = 0.6$ in all our experiments. + +# 4.4. More Visualization + +Feature visualization. As shown in Figure 8, we visualize the latent features at different decoder layers and the output feature map of the segmentation head. Apparently, these features can highlight mirror regions for different input mirror images. It indicates that our method can accurately capture the mirror-related feature representation, and thus produce robust mirror detection performance. + +Visualization of our results on unseen photos. We capture two unseen photos with mirrors at challenging positions. As shown in Figure 9, our network can more accurately detect the mirror regions than the state-of-the-art methods. The main reason is that our network can learn more reliable mirror-related knowledge from large-scale unlabeled data. + +# 5. Conclusion + +In this work, we collect a large-scale unlabeled dataset to fill the data gap in the mirror detection task. To effectively exploit the collected large-scale unlabeled data, we design an iterative data engine comprising four processes: (1) mirror detection model training, (2) pseudo-label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo-labels. In each iteration, we investigate a dual guidance scoring strategy to assess pseudo-labels through geometric accuracy derived from segmentation metrics and semantic scores from multi-modal large language models. Furthermore, we propose a reliability-enhanced training strategy to effectively learn from the selected, more reliable, high-quality pseudo-labels. We conduct extensive experiments on three public datasets to verify the performance gains from our collected large-scale unlabeled data. The segmentation results for diverse unseen examples and randomly captured images in different scenes further demonstrate the generalization capability of our model. + +# Acknowledgments + +This work is supported by the Guangdong Science and Technology Department (No. 2024ZDZX2004), the Guangzhou-HKUST(GZ) Joint Funding Program (No. 2023A03J0671), Guangdong Provincial Key Lab of Integrated Communication, Sensing and Computation for Ubiquitous Internet of Things (No.2023B1212010007), and the Nansha Key Area Science and Technology Project (No. 2023ZD003). + +# References + +[1] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. 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Springer, 2019. 6 \ No newline at end of file diff --git a/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/images.zip b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c2b645e0011a2169ea236f08e6088d6b91a5534e --- /dev/null +++ b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:35e1c7c9507503a9381f7f5487fbc50150c4b3995f826c869d493f24eba80d73 +size 748535 diff --git a/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/layout.json b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..51dc8d37a101b528650d00a53bcccae38619f1bd --- /dev/null +++ b/2025/Detect Any Mirrors_ Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine/layout.json @@ -0,0 +1,8797 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 59, + 102, + 536, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 102, + 536, + 140 + ], + "spans": [ + { + "bbox": [ + 59, + 102, + 536, + 140 + ], + "type": "text", + "content": "Detect Any Mirrors: Boosting Learning Reliability on Large-Scale Unlabeled Data with an Iterative Data Engine" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "spans": [ + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": "Zhaohu Xing" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": " Lihao Liu" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": " Yijun Yang" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": " Hongqiu Wang" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": " Tian Ye" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": " Sixiang Chen" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": " Wenxue Li" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": " Guang Liu" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "text", + "content": " Lei Zhu" + }, + { + "bbox": [ + 133, + 160, + 462, + 190 + ], + "type": "inline_equation", + "content": "^{1,4*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 194, + 541, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 194, + 541, + 225 + ], + "spans": [ + { + "bbox": [ + 52, + 194, + 541, + 225 + ], + "type": "text", + "content": "1The Hong Kong University of Science and Technology (Guangzhou) 2Amazon \n3Beijing Academy of Artificial Intelligence 4The Hong Kong University of Science and Technology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 251, + 192, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 251, + 192, + 262 + ], + "spans": [ + { + "bbox": [ + 143, + 251, + 192, + 262 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 276, + 290, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 276, + 290, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 276, + 290, + 623 + ], + "type": "text", + "content": "Mirror detection is a challenging task because a mirror's visual appearance varies depending on the reflected content. Due to limited annotated data, current methods failed to generalize well for detecting diverse mirror scenes. Semi-supervised learning with large-scale unlabeled data can improve generalization capabilities on mirror detection, but these methods often suffer from unreliable pseudolabels due to distribution differences between labeled and unlabeled data, therefore affecting the learning process. To address this issue, we first collect a large-scale dataset of approximately 0.4 million mirror-related images from the internet, significantly expanding the data scale for mirror detection. To effectively exploit this unlabeled dataset, we propose the first semi-supervised framework (namely an iterative data engine) consisting of four steps: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. In each iteration of the data engine, we employ a geometric accuracy scoring approach to assess pseudo labels based on multiple segmentation metrics, and design a multi-modal agent-driven semantic scoring approach to enhance the semantic perception of pseudo labels. These two scoring approaches can effectively improve the reliability of pseudo labels by selecting unlabeled samples with higher scores. Our method demonstrates promising performance across three mirror detection tasks and exhibits strong generalization on unseen examples. Our code will be publicly available at https://github.com/ge-xing/DAM." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 641, + 128, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 128, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 128, + 653 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 661, + 287, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 661, + 287, + 698 + ], + "spans": [ + { + "bbox": [ + 47, + 661, + 287, + 698 + ], + "type": "text", + "content": "Mirrors are commonly found in our daily lives and can significantly affect the performance of various deep learning methods, including depth estimation [33], semantic" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 250, + 548, + 373 + ], + "blocks": [ + { + "bbox": [ + 309, + 250, + 548, + 373 + ], + "lines": [ + { + "bbox": [ + 309, + 250, + 548, + 373 + ], + "spans": [ + { + "bbox": [ + 309, + 250, + 548, + 373 + ], + "type": "image", + "image_path": "9de2e484e705d2f19054743449f9985405520ba562bfdf8a893ed06d33a51986.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 380, + 547, + 470 + ], + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 470 + ], + "type": "text", + "content": "Figure 1. Examples of semi-supervised learning from (1) Mean Teacher [36], (2) DepthAnything [50], (3) UniMatch [49]. These methods explore how to effectively exploit large-scale unlabeled data to improve model generalization by challenging the student model and aligning the predictions between the student and teacher models. In contrast, our (4) DAM introduces an iterative optimization process and a scoring model to improve the reliability of the teacher model's predictions." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 477, + 425, + 591 + ], + "blocks": [ + { + "bbox": [ + 307, + 477, + 425, + 591 + ], + "lines": [ + { + "bbox": [ + 307, + 477, + 425, + 591 + ], + "spans": [ + { + "bbox": [ + 307, + 477, + 425, + 591 + ], + "type": "image", + "image_path": "1677c9a466e61376762f38357c601fd22be0be08d2caef37afc7304cf7a7f31e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 600, + 547, + 656 + ], + "lines": [ + { + "bbox": [ + 304, + 600, + 547, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 600, + 547, + 656 + ], + "type": "text", + "content": "Figure 2. Comparison between our DAM with other SOTA methods in terms of segmentation metrics (i.e., IoU, Accuracy, " + }, + { + "bbox": [ + 304, + 600, + 547, + 656 + ], + "type": "inline_equation", + "content": "F_{\\beta}" + }, + { + "bbox": [ + 304, + 600, + 547, + 656 + ], + "type": "text", + "content": ", MAE, and BER.), parameter scale (#Param), and frames per second (FPS). In the radar chart, we normalized the metrics and reversed the MAE and BER metrics for better presentation." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 477, + 547, + 590 + ], + "blocks": [ + { + "bbox": [ + 427, + 477, + 547, + 590 + ], + "lines": [ + { + "bbox": [ + 427, + 477, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 427, + 477, + 547, + 590 + ], + "type": "image", + "image_path": "0dfe8b717564d78b65f9977e9a42e636c4af4e114af9ac35e9332094f2c08865.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "segmentation [12, 44, 45, 47], and video instance detection [16, 25, 43]. In applications such as drone tracking [3] and robot navigation [11], accurate mirror detection is crucial to avoid potential safety issues. There-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 703, + 253, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 253, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 253, + 712 + ], + "type": "text", + "content": "*Lei Zhu (leizhu@ust.hk) is the corresponding author of this work." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25476" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "fore, developing mirror detection models is essential for precisely detecting mirrors in images and providing additional information for other tasks. Although many methods [8, 10, 13, 18, 20, 46, 51] have been developed for mirror detection and achieved impressive performance on various mirror detection benchmarks by exploring the attributes of mirrors, these methods can not generalize well in diverse scenes due to the limited annotated datasets." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 171, + 289, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 289, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 289, + 363 + ], + "type": "text", + "content": "Recently, as shown in Figure 1, many studies [17, 21-23, 36, 48-50] have been conducted to explore how to effectively exploit large-scale unlabeled data to improve model generalization. These methods typically use a student-teacher architecture, aiming to learn a strong representation of unlabeled data by challenging the student model with unlabeled input and enhancing the output consistency between the student model and the teacher model. However, these methods do not consider the reliability of the teacher model's output, which can significantly affect the learning quality of the student model. Moreover, in the mirror detection task, there are limited annotated datasets and a lack of large-scale unlabeled data containing various mirror scenes to enhance model generalization. This presents a challenge for current mirror detection methods when applied in practical scenarios." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 367, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 367, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 289, + 713 + ], + "type": "text", + "content": "In this work, our goal is to fill the data gap and build a general mirror detection model with state-of-the-art performance and stronger generalization ability, aiming to Detect Any Mirrors (DAM) in various practical scenarios. First, we collect approximately 400000 diverse, unlabeled mirror-related images from the internet. To provide initial pseudo labels for this unlabeled data, we then train an initial mirror detection model using approximately 13,000 labeled images collected from three public mirror detection datasets. To effectively exploit the collected large-scale unlabeled data, we further design an iterative data engine, where each iteration includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels. The core of each iteration is selecting high-quality pseudo labels that can improve the learning reliability of the student model. Therefore, we propose a dual guidance scoring strategy to assess the pseudo labels through geometric accuracy derived from segmentation metrics and semantic scores from multi-modal large language models. Furthermore, we introduce a reliability-enhanced training strategy to effectively learn from the selected, more reliable, high-quality pseudo labels. We conduct extensive experiments on three public datasets to verify the performance gains from our collected large-scale unlabeled data. Mirror detection results on unseen datasets and randomly captured images in different scenes also demonstrate the generalization capability of our model. Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 72, + 547, + 228 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 306, + 72, + 547, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 547, + 108 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 547, + 108 + ], + "type": "text", + "content": "- We propose a general mirror detection model, called DAM, which achieves SOTA performance and exhibits strong generalization capability in diverse scenes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 108, + 547, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 108, + 547, + 131 + ], + "spans": [ + { + "bbox": [ + 306, + 108, + 547, + 131 + ], + "type": "text", + "content": "- We collect a large-scale unlabeled dataset to fill the data gap in the mirror detection task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 133, + 547, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 547, + 179 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 547, + 179 + ], + "type": "text", + "content": "- We devise an iterative data engine to gradually improve the quality of pseudo labels, and we further propose a reliability-enhanced training strategy to effectively learn from the more reliable pseudo labels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 180, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 180, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 180, + 547, + 228 + ], + "type": "text", + "content": "- Experimental results on three mirror detection datasets, an unseen dataset, and randomly captured images demonstrate the promising mirror detection performance and generalization capability of our model." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 235, + 392, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 235, + 392, + 247 + ], + "spans": [ + { + "bbox": [ + 306, + 235, + 392, + 247 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 255, + 547, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 255, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 547, + 304 + ], + "type": "text", + "content": "In this section, we first review the state-of-the-art methods for mirror detection. Next, we will discuss works on semi-supervised learning and multi-modal large language models (MLLM), which are explored in our network." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 309, + 409, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 309, + 409, + 320 + ], + "spans": [ + { + "bbox": [ + 306, + 309, + 409, + 320 + ], + "type": "text", + "content": "2.1. Mirror Detection" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 329, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 472 + ], + "type": "text", + "content": "Detecting mirrors in an image is crucial for various applications, including drone tracking and robot navigation, as it helps prevent accidents. Additionally, it can enhance the performance of tasks like semantic segmentation and video instance detection. There are several methods for semantic segmentation tasks. For example, DeepLabV3 [2] utilizes atrous convolution in cascade and ASPP [1] module to capture the multi-scale features. Mask2Former [6] proposes a new framework, combining CNN and Transformer [37] to enhance the global understanding of images. However, these methods are not specifically designed for mirror scenes and do not perform well in detecting mirrors." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 473, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 593 + ], + "type": "text", + "content": "Recently, MirrorNet [51] introduced the first mirror detection dataset and network. They employed contextual contrasted information to detect mirrors accurately. PMDNet [18] proposes a more challenging benchmark for mirror detection tasks. They utilized multi-scale mirror edge features to enhance mirror perception. More recently, VCNet [34] improves mirror detection performance by leveraging chirality cues and implicit correspondences. However, these methods fail to generalize to various complex scenes due to the limited annotated datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 598, + 514, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 598, + 514, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 598, + 514, + 611 + ], + "type": "text", + "content": "2.2. Leveraging Large-scale Unlabeled Data" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "Leveraging the rich visual knowledge contained in large-scale unlabeled data to improve model generalization capability is a hot research direction. Tarvainen et al. [36] propose the Mean Teacher method to provide more stable and consistent targets for training the student model by updating the teacher model through an exponential moving average. DepthAnything [50] proposes to challenge the student model with a more difficult optimization target when learn-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25477" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 71, + 294, + 178 + ], + "blocks": [ + { + "bbox": [ + 77, + 71, + 294, + 178 + ], + "lines": [ + { + "bbox": [ + 77, + 71, + 294, + 178 + ], + "spans": [ + { + "bbox": [ + 77, + 71, + 294, + 178 + ], + "type": "image", + "image_path": "2e1e1f0e9765707a339a4c2abed78f503a673ff8bc934f7d40f2a4a8ad1d2a0e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 71, + 517, + 178 + ], + "blocks": [ + { + "bbox": [ + 296, + 71, + 517, + 178 + ], + "lines": [ + { + "bbox": [ + 296, + 71, + 517, + 178 + ], + "spans": [ + { + "bbox": [ + 296, + 71, + 517, + 178 + ], + "type": "image", + "image_path": "9fa41b40351647a5b7990d0ca813bb6db73ae0b401b3c7527ec88a86fe53e1bb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 77, + 180, + 515, + 328 + ], + "blocks": [ + { + "bbox": [ + 77, + 180, + 515, + 328 + ], + "lines": [ + { + "bbox": [ + 77, + 180, + 515, + 328 + ], + "spans": [ + { + "bbox": [ + 77, + 180, + 515, + 328 + ], + "type": "image", + "image_path": "0ac94b2d9e094035ad5d7b91a6e452ab5975ff566f5becb6da730c803efa09d6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 339, + 545, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 339, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 545, + 384 + ], + "type": "text", + "content": "Figure 3. Our data engine includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo label. In each iteration, we investigate a geometric accuracy scoring (b) to assess the pseudo labels and design an MMA-driven semantic scoring (c) to effectively improve the semantic perception for pseudo labels. These two scoring approaches can effectively improve the reliability of pseudo labels by selecting the unlabeled samples with higher scores." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 390, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 498 + ], + "type": "text", + "content": "ing the pseudo labels, in order to seek extra visual information. In addition, UniMatch [49] leverages feature-level and image-level perturbations to exploit a broader perturbation space, as well as a dual-stream perturbation strategy to fully probe pre-defined image-level perturbation space. However, these methods solely focus on enhancing the learning process of the student model and do not consider the reliability of the pseudo labels from the teacher model. The latter can directly affect the learning of the student model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 503, + 287, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 287, + 516 + ], + "type": "text", + "content": "2.3. Multi-modal Large Language Models (MLLM)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "Multi-modal large language models [24] possess the remarkable ability to understand high-level semantic information by learning large-scale data from various modalities, such as text, images, and videos. MiniCPM-V 2.6 [52] is the latest and most capable model in the MiniCPM-V series. Due to its superior token density, MiniCPM-V 2.6 can support real-time video understanding on end-side devices. InternVL-2 [5] demonstrates competitive performance on par with proprietary commercial models across various capabilities, including document and chart comprehension, infographics QA, scene text understanding and OCR tasks, scientific and mathematical problem-solving, as well as cultural understanding and integrated multi-modal capabilities. Qwen2-VL [38] is the latest version of the vision-language models in the Qwen model family, achieving state-of-the-art performance on various visual understanding benchmarks." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 343, + 388, + 509, + 450 + ], + "blocks": [ + { + "bbox": [ + 343, + 388, + 509, + 450 + ], + "lines": [ + { + "bbox": [ + 343, + 388, + 509, + 450 + ], + "spans": [ + { + "bbox": [ + 343, + 388, + 509, + 450 + ], + "type": "table", + "html": "
    DatasetImage NumberIs Annotated
    MSD [51]4018✔
    PMD [18]6461✔
    RGBD-Mirror [28]3049✔
    Ours406817✘
    ", + "image_path": "a3227d6b7c6a314112b6d24d0aa81d034c08a56a04b9d7578451ecf9bb2c66c5.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 457, + 545, + 491 + ], + "lines": [ + { + "bbox": [ + 305, + 457, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 457, + 545, + 491 + ], + "type": "text", + "content": "Table 1. We have collected a large-scale unlabeled dataset featuring a variety of scenes where mirrors may appear, in order to expand the data scale for the mirror detection task." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 505, + 545, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 505, + 545, + 565 + ], + "spans": [ + { + "bbox": [ + 305, + 505, + 545, + 565 + ], + "type": "text", + "content": "These models can provide a detailed analysis of a single image, multiple images, and video. In this work, we integrate these MLLMs to offer comprehensive and detailed analyses of the input images and corresponding pseudo labels, thereby scoring the quality of the pseudo labels." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 576, + 361, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 576, + 361, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 576, + 361, + 588 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 597, + 410, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 410, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 410, + 609 + ], + "type": "text", + "content": "3.1. Data Preparation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 618, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 715 + ], + "type": "text", + "content": "There are three main annotated datasets (i.e., MSD [51], PMD [18], and RGBD-Mirror [28]) used in the mirror detection task. As shown in Table 1, the limited data scale makes it easy for mirror detection models to overfit and not generalize well to various complex scenes. To address this issue, we have collected a large-scale unlabeled dataset, which contains 406,817 mirror-related images to provide diverse scenes where mirrors may appear." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25478" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 171, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 171, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 171, + 85 + ], + "type": "text", + "content": "3.2. Iterative Data Engine" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 209 + ], + "type": "text", + "content": "We found that previous semi-supervised learning methods [36, 49, 50] usually focus on the learning process of the student model but overlook the prediction reliability of the teacher model. To address this issue, we introduce an iterative data engine to filter out low-quality pseudo labels and gradually improve mirror detection accuracy and robustness by learning from more reliable data. Specifically, the data engine includes four processes: (1) mirror detection model training, (2) pseudo label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo labels." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 210, + 289, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 289, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 289, + 449 + ], + "type": "text", + "content": "As shown in Figure 3 (a), in the first step, we train an initial mirror detection model using three collected annotated datasets. We then use the trained model to predict pseudo labels for the large-scale unlabeled dataset, resulting in 406,817 image and pseudo label pairs. At this stage, the pseudo labels are often unreliable because the initial mirror detection model may not generalize well when trained on limited annotated data. Therefore, we design a dual guidance scoring strategy, which includes geometric scoring and multi-modal agents (MMA)-driven semantic scoring, to assess the quality of the pseudo labels. As shown in Figure 3 (b) and (c), geometric scoring aims to predict an aggregated result of multiple segmentation metrics (i.e., IoU, " + }, + { + "bbox": [ + 46, + 210, + 289, + 449 + ], + "type": "inline_equation", + "content": "F_{\\beta}" + }, + { + "bbox": [ + 46, + 210, + 289, + 449 + ], + "type": "text", + "content": ", and Accuracy). Meanwhile, MMA-driven semantic scoring provides a better understanding of the semantic knowledge contained in the image and corresponding pseudo label. Finally, we set a threshold to select the image and pseudo-label pairs with higher scores and propose a reliability-enhanced training strategy to train the new mirror detection model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 456, + 180, + 469 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 180, + 469 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 180, + 469 + ], + "type": "text", + "content": "3.3. 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In this strategy, we aim to distill geometric knowledge into an estimation model, " + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_g" + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "text", + "content": " (e.g., ResNet-50). Specifically, for three annotated datasets, we denote the input data as " + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{D}g = \\{I_i,P_i,G_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 493, + 288, + 614 + ], + "type": "text", + "content": " represent an image, a pseudo label, and the corresponding ground truth label, respectively. 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Example analysis for the geometric and semantic scores obtained from our dual guidance scoring strategy. We aim to select more reliable data (with high geometric and semantic scores)." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 369, + 228, + 423, + 280 + ], + "blocks": [ + { + "bbox": [ + 369, + 228, + 423, + 280 + ], + "lines": [ + { + "bbox": [ + 369, + 228, + 423, + 280 + ], + "spans": [ + { + "bbox": [ + 369, + 228, + 423, + 280 + ], + "type": "image", + "image_path": "36771fa6916b86722460402f5dcc55a054394ed7fff343bf97a389b67f33ed02.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 429, + 228, + 481, + 280 + ], + "blocks": [ + { + "bbox": [ + 429, + 228, + 481, + 280 + ], + "lines": [ + { + "bbox": [ + 429, + 228, + 481, + 280 + ], + "spans": [ + { + "bbox": [ + 429, + 228, + 481, + 280 + ], + "type": "image", + "image_path": "680fadcf0602586c4e043e39cec68b1c3f8d58122bf999bda609126595284248.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 476, + 281, + 538, + 293 + ], + "lines": [ + { + "bbox": [ + 476, + 281, + 538, + 293 + ], + "spans": [ + { + "bbox": [ + 476, + 281, + 538, + 293 + ], + "type": "text", + "content": "Geometric score: bottom " + }, + { + "bbox": [ + 476, + 281, + 538, + 293 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 476, + 281, + 538, + 293 + ], + "type": "text", + "content": " (Low) \nSemitonic score: bottom " + }, + { + "bbox": [ + 476, + 281, + 538, + 293 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 476, + 281, + 538, + 293 + ], + "type": "text", + "content": " (Low)" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 481, + 228, + 535, + 280 + ], + "blocks": [ + { + "bbox": [ + 481, + 228, + 535, + 280 + ], + "lines": [ + { + "bbox": [ + 481, + 228, + 535, + 280 + ], + "spans": [ + { + "bbox": [ + 481, + 228, + 535, + 280 + ], + "type": "image", + "image_path": "11fe4ecab6d9e2340e502d1f72f925d69bafb1b841f6e3347918c8c955c31730.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 338, + 493, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 338, + 493, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 338, + 493, + 350 + ], + "type": "text", + "content": "the actual score " + }, + { + "bbox": [ + 306, + 338, + 493, + 350 + ], + "type": "inline_equation", + "content": "S_{g}" + }, + { + "bbox": [ + 306, + 338, + 493, + 350 + ], + "type": "text", + "content": " using the " + }, + { + "bbox": [ + 306, + 338, + 493, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 306, + 338, + 493, + 350 + ], + "type": "text", + "content": " loss function." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 357, + 473, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 473, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 473, + 369 + ], + "type": "text", + "content": "3.3.2 MMA-driven Semantic Scoring" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 375, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 495 + ], + "type": "text", + "content": "However, geometric-based scoring alone is not sufficient in some cases because this score does not contain semantic information from images. As shown in the first row of Figure 4, the mirror detection model erroneously recognizes the non-mirror region as a mirror and gives a \"reasonable\" prediction. Hence, in these cases, the geometric score is high. Meanwhile, the semantic score from our MMA-driven strategy can effectively recognize this type of error and provide a lower score, which can help us filter out low-quality pseudo labels." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": "Semantic modeling. Inspired by the impressive semantic understanding capabilities of the latest multimodal large language models, we design an MMA-driven semantic scoring strategy to obtain the semantic score of an image and pseudo-label pair. The output of a single multi-modal large language model can sometimes be unstable, particularly when it is required to provide a fine-grained score. To address this issue, we first design a semantic modeling process. Specifically, as depicted in Figure 3, we select three of the latest open-source vision-language models as multi-modal agents (i.e., MiniCPM-V-2.6, Qwen2-VL, and InternVL-2) to provide separate analyses and scoring. These models use the image and pseudo-label pair, along with a custom scoring prompt, as input. Next, we utilize the free API of a large language model (i.e., GLM4-flash) to conduct further analysis based on the outputs from the multi-modal agents and provide the final semantic score, achieving more stable semantic scoring." + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25479" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 70, + 487, + 185 + ], + "blocks": [ + { + "bbox": [ + 111, + 70, + 487, + 185 + ], + "lines": [ + { + "bbox": [ + 111, + 70, + 487, + 185 + ], + "spans": [ + { + "bbox": [ + 111, + 70, + 487, + 185 + ], + "type": "image", + "image_path": "00873822804a066492df23e52dfe6587e670bfbd9f5b7b36e3e8a52d08b6976d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 547, + 240 + ], + "type": "text", + "content": "Figure 5. Detailed implementation of the proposed reliability-enhanced training strategy: We adopt the Mean Teacher architecture and incorporate the highly reliable pseudo labels to learn more robust visual knowledge. In each iteration of our iterative data engine, the teacher model is initialized from the student model of the previous iteration. We employ a consistency loss to align the predictions between the student model and the teacher model, and we use a confidence matrix to enable the student model to make more certain predictions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "text", + "content": "Semantic distillation. However, the semantic modeling process involving multi-modal agents and large language models is time-consuming and cannot be applied effectively. We propose a semantic distillation strategy to transfer the semantic knowledge of multi-modal agents into a lightweight scoring model, denoted as " + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_s" + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "text", + "content": ". Similar to the geometric distillation process, we concatenate the image and the corresponding pseudo label as input: " + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s = \\{I_i, P_i\\}" + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "text", + "content": ". Next, the estimation model " + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_s" + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "inline_equation", + "content": "\\theta_s" + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "text", + "content": ", learns to align the predicted semantic score " + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "inline_equation", + "content": "\\hat{S}_s = \\mathcal{M}_s(I_i, P_i; \\theta_s)" + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "text", + "content": " with the semantic score " + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "inline_equation", + "content": "S_s" + }, + { + "bbox": [ + 46, + 246, + 289, + 389 + ], + "type": "text", + "content": " obtained from multi-modal agents." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 392, + 222, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 222, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 222, + 403 + ], + "type": "text", + "content": "3.3.3 Selection of Highly Reliable Data" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "text", + "content": "To select highly reliable pseudo labels based on the geometric score and semantic score, we define a data selection strategy. We denote the scoring results from the geometric-based scoring model and the semantic-based scoring model for all the unlabeled data as " + }, + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\hat{S} = \\{\\hat{S}_g^k,\\hat{S}_s^k\\}_{k = 1}^M" + }, + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "text", + "content": " is the total number of unlabeled data. Additionally, we define " + }, + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "text", + "content": " as the selection threshold to control the number of highly reliable data selected, which will be discussed in Section 4.3. The selection strategy is defined as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 523, + 287, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 523, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 62, + 523, + 287, + 555 + ], + "type": "interline_equation", + "content": "\\mathcal {A} (k) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\mathcal {P} _ {g} \\left(\\hat {S} _ {g} ^ {k}\\right) \\geq T \\text {a n d} \\mathcal {P} _ {s} \\left(\\hat {S} _ {s} ^ {k}\\right) \\geq T, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {2}", + "image_path": "3304a57b8ac1c2a4c561cba0433c68a89f68948917ea3a963f1e8b66f926aaab.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 560, + 287, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 560, + 287, + 584 + ], + "spans": [ + { + "bbox": [ + 46, + 560, + 287, + 584 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 560, + 287, + 584 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(x)" + }, + { + "bbox": [ + 46, + 560, + 287, + 584 + ], + "type": "text", + "content": " represents the calculation of the percentage that the score " + }, + { + "bbox": [ + 46, + 560, + 287, + 584 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 560, + 287, + 584 + ], + "type": "text", + "content": " constitutes of the total score." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 587, + 211, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 211, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 211, + 601 + ], + "type": "text", + "content": "3.4. Reliability-enhanced Training" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": "When we have selected the more reliable image and pseudolabel pair, we aim to train a new mirror detection model that will be used in the next iteration. Hence, as shown in Figure 5, we devise a reliability-enhanced training strategy based on the standard Mean Teacher architecture to effectively learn knowledge from the labeled data and selected high-reliable unlabeled data. We adopt cross-entropy loss to optimize the student model using labeled data and reliable pseudo-labels. Meanwhile, mean squared error loss is" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": "used to align the outputs of the student and teacher models for the unlabeled input. The loss functions can be summarized as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 289, + 545, + 395 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 289, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 312, + 289, + 545, + 395 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C E} \\left(y _ {i}, f \\left(x _ {i} ^ {l}; \\theta\\right)\\right) (3) \\\\ + \\lambda_ {2} \\cdot \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {C E} \\left(\\tilde {y} _ {j}, f \\left(x _ {j} ^ {u}; \\theta\\right)\\right) (4) \\\\ + \\lambda_ {3} \\cdot \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathcal {C} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) \\left| f \\left(x _ {j} ^ {u}; \\theta\\right) - f \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) \\right| ^ {2}, (5) \\\\ \\end{array}", + "image_path": "52f76f00efc64cb6eff5e752e4e6332334a28e5b7bd57bd2ee090d213bf76835.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " represents the weight of different loss functions, while " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " denote the numbers of samples with and without ground truth labels, respectively. The variables " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\tilde{y}" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " represent the ground truth labels and the reliable pseudo-labels, respectively. The symbols " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "x^l" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "x^u" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " denote the labeled and unlabeled images, respectively. Additionally, " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\theta'" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": " are the parameters of the student and teacher models, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 340, + 509, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 509, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 340, + 509, + 545, + 541 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {k} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} f _ {k} \\left(x _ {j} ^ {u}; \\theta^ {\\prime}\\right) > \\operatorname {c o n f}, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {6}", + "image_path": "ee5a99bc4ba2610ff712027c361e971d43e3e6fcfda4e35b9b144e0b875dc129.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 548, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 545, + 597 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 548, + 545, + 597 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 548, + 545, + 597 + ], + "type": "text", + "content": " denotes the confidence matrix and 'conf' represents the confidence threshold. We calculate the consistency loss only when the prediction probability of the pixel " + }, + { + "bbox": [ + 304, + 548, + 545, + 597 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 548, + 545, + 597 + ], + "type": "text", + "content": " from the teacher model is greater than the confidence threshold." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 603, + 382, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 603, + 382, + 616 + ], + "spans": [ + { + "bbox": [ + 306, + 603, + 382, + 616 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 623, + 432, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 432, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 432, + 635 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Datasets. We evaluate our method on the test sets of three labeled datasets: MSD[51], PMD[18], and RGBD-Mirror*. RGBD-Mirror* is produced from the RGBD-Mirror dataset [28] by using the RGB images and annotated mirror masks and removing the corresponding depth map for each RGB-D image pair. We combine the training sets" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "25480" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 446 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 446 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 446 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 446 + ], + "type": "table", + "html": "
    DatasetsMethodsUnlabeledIoU ↑Accuracy ↑Fβ↑MAE ↓BER ↓
    MSDSegFormer [41]X0.8790.9530.9150.0386.50
    Mask2Former [6]X0.8830.9580.9170.0366.65
    MirrorNet [51]X0.8450.9480.8920.0447.67
    PMDNet [18]X0.8470.9520.9080.0337.22
    VCNet [34]X0.8840.9580.9140.0297.32
    SANet [10]X0.8710.9510.9120.0337.10
    HetNet [13]X0.8880.9640.9220.0276.63
    CSFwinformer [42]X0.8750.9600.9180.0306.79
    MT [36]✓0.9010.9580.9280.0244.62
    UAMT [53]✓0.9090.9450.9320.0214.37
    DepthAnything [50]✓0.9150.9710.9430.0203.98
    UniMatch [49]✓0.9080.9490.9180.0314.57
    DAM (Ours)✓0.9340.9800.9680.0192.32
    PMDSegFormer [41]X0.6780.8330.8080.02410.14
    Mask2Former [6]X0.6980.8360.8170.0229.98
    MirrorNet [51]X0.6480.7980.7850.03010.39
    PMDNet [18]X0.6580.8180.7950.02810.86
    SANet [10]X0.6570.8160.7940.02410.97
    VCNet [34]X0.6760.8180.8010.02510.16
    HetNet [13]X0.7020.8270.8180.0239.65
    CSFwinformer [42]X0.7050.8200.8150.0299.93
    MT [36]✓0.7060.8270.8250.0219.38
    UAMT [53]✓0.7090.8340.8280.0208.93
    DepthAnything [50]✓0.7110.8280.8260.0209.11
    UniMatch [49]✓0.6980.8250.8200.02610.39
    DAM (Ours)✓0.7340.8510.8520.0198.08
    RGBD-Mirror*SegFormer [41]X0.7540.8580.7880.03913.11
    Mask2Former [6]X0.7680.8610.8030.04012.16
    MirrorNet [51]X0.7170.7960.7650.04413.40
    PMDNet [18]X0.7390.8190.7740.03513.24
    SANet [10]X0.7490.8410.7890.03912.88
    VCNet [34]X0.7630.8440.8100.03412.28
    HetNet [13]X0.7750.8570.8190.03111.20
    CSFwinformer [42]X0.7690.8500.8150.03411.04
    MT [36]✓0.7840.8570.8260.0398.19
    UAMT [53]✓0.7880.8730.8390.0358.24
    DepthAnything [50]✓0.7990.8810.8480.0316.94
    UniMatch [49]✓0.7850.8470.8210.0418.35
    DAM (Ours)✓0.8080.8850.8700.0306.42
    ", + "image_path": "7b342260f3faf1baa9d3623d51c46b5cbda2e1357ac32e5f1bb0575c49b3fdf5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 454, + 287, + 521 + ], + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 521 + ], + "type": "text", + "content": "Table 2. Quantitative comparison between the proposed DAM and 11 state-of-the-art methods on MSD, PMD, and RGBD-Mirror* datasets in terms of IoU, Accuracy, " + }, + { + "bbox": [ + 46, + 454, + 287, + 521 + ], + "type": "inline_equation", + "content": "F_{\\beta}" + }, + { + "bbox": [ + 46, + 454, + 287, + 521 + ], + "type": "text", + "content": ", MAE, and BER metrics. The best results are shown in **bold**. An asterisk (*) indicates that only the RGB images and annotated mirror masks are used, without any depth information." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 530, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 287, + 567 + ], + "type": "text", + "content": "of the three labeled datasets to retrain all comparison methods using their released code and turn their parameters to obtain their best performance to ensure fairness." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Implementation details. We adopt the DINOv2-small encoder [29] for feature extraction and use the DPT [31] decoder for mirror detection. The ratio of labeled to unlabeled images is set to 1:1 in each batch. The base learning rate of the pre-trained encoder is set to 5e-6, while the randomly initialized decoder uses a learning rate that is 10 times larger. We use the AdamW optimizer and decay the learning rate with a poly schedule. We apply horizontal flipping as data augmentation. During reliability-enhanced training, we set three loss function weights as " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_1 = \\lambda_2 = \\lambda_3 = 1" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", and the confidence threshold as conf = 0.9. The strong augmentation operations in Figure 5 include color jitter," + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 320, + 71, + 533, + 353 + ], + "blocks": [ + { + "bbox": [ + 320, + 71, + 533, + 353 + ], + "lines": [ + { + "bbox": [ + 320, + 71, + 533, + 353 + ], + "spans": [ + { + "bbox": [ + 320, + 71, + 533, + 353 + ], + "type": "table", + "html": "
    DatasetsMethodsTypeIoU ↑Accuracy ↑Fβ↑MAE ↓
    VMD-DTVSD [4]Video0.4800.8750.7460.125
    STICT [27]Video0.1640.8090.5300.198
    Sc-Cor [9]Video0.5120.8630.6960.137
    Scotch-Soda [26]Video0.5870.8780.7490.121
    HFAN [30]Video0.4590.8760.7060.124
    STCN [7]Video0.4450.8590.6700.140
    GlassNet [19]Image0.5520.8640.7180.137
    MirrorNet [51]Image0.5050.8550.6810.145
    PMDNet [18]Image0.5320.8720.7490.128
    VCNet [34]Image0.5390.8770.7490.123
    HetNet [13]Image0.5310.8680.7480.131
    VMD-Net [20]Video0.5670.8950.7870.105
    UAMT [53]Image0.6830.9010.7970.098
    DepthAnything [50]Image0.7230.9180.8320.087
    DAM (ours)Image0.7550.9290.8450.075
    MMDMGA [15]Image0.2810.5660.4890.434
    UFO [32]Image0.5990.7970.7970.203
    FSNet [14]Image0.7080.8530.8380.147
    ALGRF [35]Image0.5030.7240.6930.276
    F3Net [40]Image0.6710.8390.8470.161
    PMDNet [18]Image0.4240.7410.8470.259
    MirrorNet [51]Image0.6660.8350.8390.165
    VMD-Net [20]Video0.7230.8540.8120.146
    Warren et al. [39]Video0.7250.8720.8690.127
    UAMT [53]Image0.7250.8520.8610.147
    DepthAnything [50]Image0.7320.8610.8570.138
    DAM (ours)Image0.7590.8790.8690.121
    ", + "image_path": "6671d31c40065e86c1cb2b243d3de9cb2ac278bf1e8beffd01c06013b0d90286.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 361, + 545, + 405 + ], + "lines": [ + { + "bbox": [ + 305, + 361, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 545, + 405 + ], + "type": "text", + "content": "Table 3. Generalization capability on two video mirror detection datasets: Our method does not require training on the VMD-D and MMD datasets, yet it achieves a new state-of-the-art performance on their test sets." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 414, + 452, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 414, + 452, + 425 + ], + "spans": [ + { + "bbox": [ + 305, + 414, + 452, + 425 + ], + "type": "text", + "content": "random grayscale, and random blur." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 426, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 474 + ], + "type": "text", + "content": "Evaluation metrics. Following the previous works [20, 26, 34], we adopt intersection over union (IoU), pixel accuracy (Accuracy), F-measure " + }, + { + "bbox": [ + 305, + 426, + 545, + 474 + ], + "type": "inline_equation", + "content": "(F_{\\beta})" + }, + { + "bbox": [ + 305, + 426, + 545, + 474 + ], + "type": "text", + "content": ", mean absolute error (MAE), and balanced error rate (BER) to evaluate our method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 479, + 541, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 479, + 541, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 541, + 491 + ], + "type": "text", + "content": "4.2. Comparison against State-of-the-art Methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "type": "text", + "content": "Compared methods. We compare our method with seven supervised networks and four semi-supervised methods. Seven supervised methods are SegFormer [41], Mask2Former [6], MirrorNet [51], PMDNet [18], SANet [10], VCNet [34], and HetNet [13]. Four semi-supervised methods are Mean Teacher [36], UAMT [53], DepthAnything [50], and UniMatch [49]. For all semi-supervised methods, we utilize the same training set with collected unlabeled data as our method for fair comparisons; see our supplementary material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Quantitative comparisons. We compare our DAM against 11 state-of-the-art methods on three datasets (i.e., MSD [51], PMD [18], and RGBD-Mirror* [28]) in terms of IoU, Accuracy, " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "F_{\\beta}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ", MAE, and BER metrics. As shown in Table 2, our DAM not only surpasses all supervised seven methods on all five metrics, but also outperforms all the semi-supervised methods, which have the same unlabeled data as our method during training. Our best performance" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25481" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 102, + 73, + 496, + 352 + ], + "blocks": [ + { + "bbox": [ + 102, + 73, + 496, + 352 + ], + "lines": [ + { + "bbox": [ + 102, + 73, + 496, + 352 + ], + "spans": [ + { + "bbox": [ + 102, + 73, + 496, + 352 + ], + "type": "image", + "image_path": "4c136b225f8232f092a4b27d7d7e626097c078de8760d856d78bd7afc8c3402f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 358, + 547, + 380 + ], + "lines": [ + { + "bbox": [ + 46, + 358, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 547, + 380 + ], + "type": "text", + "content": "Figure 6. Visual comparisons of mirror detection results predicted by our network and other methods. Clearly, our network achieves more accurate mirror detection results than all the compared methods, and our results are more consistent with the ground truths." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 77, + 383, + 513, + 478 + ], + "blocks": [ + { + "bbox": [ + 77, + 383, + 513, + 478 + ], + "lines": [ + { + "bbox": [ + 77, + 383, + 513, + 478 + ], + "spans": [ + { + "bbox": [ + 77, + 383, + 513, + 478 + ], + "type": "image", + "image_path": "eb947a0d1b941a6062d0905ee832aed5488d9b2a48a690c04350a9075cc23d6f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "lines": [ + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "text", + "content": "Figure 7. The effect of different thresholds " + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "text", + "content": " at different engine iterations of our method. We plot the number of highly reliable data and IoU scores on three datasets for each engine iteration regarding three different T values (" + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "inline_equation", + "content": "T = 0.4" + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "inline_equation", + "content": "T = 0.6" + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "inline_equation", + "content": "T = 0.8" + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "text", + "content": "). " + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "inline_equation", + "content": "T = 0.6" + }, + { + "bbox": [ + 46, + 487, + 547, + 519 + ], + "type": "text", + "content": " yields the highest IoU scores for all three datasets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 524, + 287, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 524, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 46, + 524, + 287, + 570 + ], + "type": "text", + "content": "of all five metrics on three datasets indicates that our DAM model is more effective and robust in detecting mirror regions of different scenes of three datasets by learning more visual knowledge from large-scale reliable data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 571, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 289, + 714 + ], + "type": "text", + "content": "Generalization capability on the video mirror detection datasets. To further evaluate the generalization capabilities of our method, we test our DAM on two unseen datasets (i.e., the VMD-D and MMD datasets). Specifically, without requiring any re-training operations on these two unseen datasets, we directly test our model (the same trained model of our method at Table 2) to produce our results on these two unseen datasets. Then, Table 3 compares our results against those of state-of-the-art methods, which are trained on the VMD-D and MMD datasets. From Table 3, we can find that our DAM clearly outperforms all state-of-the-art methods on the VMD-D dataset and the MMD dataset regarding" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 524, + 545, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 524, + 545, + 547 + ], + "spans": [ + { + "bbox": [ + 304, + 524, + 545, + 547 + ], + "type": "text", + "content": "all quantitative evaluation metrics. It convincingly verifies the generalization capabilities of our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Qualitative comparisons. Figure 6 visually compares mirror detection results produced by our network and seven state-of-the-art methods on different input images. For these small mirrors at the first two rows, our method can detect more mirror details, while compared methods tend to wrongly recognize non-mirror regions in their mirror detection results. For big mirror objects at the third and fourth rows, all compared methods neglect parts of mirror regions, while our method tends to more accurately identify whole mirror regions. Meanwhile, we further select some more challenging and unlabeled images as the inputs for visual comparisons. As shown in the last four rows in Figure 6, the mirror regions may be blended (first row), partially covered (second and third rows), or complex due to a large number" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25482" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 261, + 117 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 261, + 117 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 261, + 117 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 261, + 117 + ], + "type": "table", + "html": "
    Index\\( S_g \\)\\( S_s \\)RETIoU↑Accuracy↑\\( F_{\\beta} \\uparrow \\)MAE↓BER↓
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    ", + "image_path": "7365686c6d0e1aaa016f1e43804416397986ccf2c879debf182f30f6c7648818.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "lines": [ + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "type": "text", + "content": "Table 4. Ablation study of (1) geometric scoring " + }, + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "type": "inline_equation", + "content": "(S_g)" + }, + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "type": "text", + "content": ", (2) MMA-driven semantic scoring " + }, + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "type": "inline_equation", + "content": "(S_s)" + }, + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "type": "text", + "content": ", and (3) reliability-enhanced training strategy (RET) on the PMD dataset across IoU, Accuracy, " + }, + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "type": "inline_equation", + "content": "F_{\\beta}" + }, + { + "bbox": [ + 47, + 125, + 287, + 168 + ], + "type": "text", + "content": ", MAE, and BER metrics." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 70, + 173, + 265, + 293 + ], + "blocks": [ + { + "bbox": [ + 70, + 173, + 265, + 293 + ], + "lines": [ + { + "bbox": [ + 70, + 173, + 265, + 293 + ], + "spans": [ + { + "bbox": [ + 70, + 173, + 265, + 293 + ], + "type": "image", + "image_path": "0a71c1448ca73d88119393914c187bdaff60d331a73f0c1aee101567c26a5d8b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 287, + 358 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 358 + ], + "type": "text", + "content": "Figure 8. Visualization of latent features. " + }, + { + "bbox": [ + 46, + 303, + 287, + 358 + ], + "type": "inline_equation", + "content": "F_{1}, F_{2}, F_{3}, F_{4}" + }, + { + "bbox": [ + 46, + 303, + 287, + 358 + ], + "type": "text", + "content": " denote the decoder features at different resolutions. " + }, + { + "bbox": [ + 46, + 303, + 287, + 358 + ], + "type": "inline_equation", + "content": "F_{seg}" + }, + { + "bbox": [ + 46, + 303, + 287, + 358 + ], + "type": "text", + "content": " represents the feature from the decoder head. These results show that our network can learn a robust mirror-related feature representation for diverse scenes." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 413 + ], + "type": "text", + "content": "of mirrors (last row). Our method can accurately address these challenging mirror detections by effectively learning mirror-related knowledge from large-scale and highly reliable unlabeled data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 418, + 141, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 141, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 141, + 431 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": "Effectiveness of the dual guidance scoring strategy and reliable-enhanced training. We conduct an ablation study to reveal the distinct contributions of geometric scoring " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "(S_g)" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": ", semantic scoring " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "(S_s)" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": ", and the reliability-enhanced training (RET) strategy within our model. Table 4 reports the quantitative results of the ablation study on the PMD dataset. The baseline model (M1) is trained using the labeled data, and the IoU, Accuracy, " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "F_{\\beta}" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": ", MAE, and BER scores are 0.679, 0.813, 0.809, 0.029, and 11.06, which highlights the limitations of the basic supervised approach. Then, we incorporate the proposed geometric scoring " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "(S_g)" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " and MMA-driven semantic scoring " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "(S_s)" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " into M1 to build M2 and M3. These two scoring strategies can select high-reliable data and significantly enhance the model's performance. Finally, with the reliability-enhanced training (RET) strategy, our method introduces additional optimization targets based on the student-teacher architecture and thus improves training stability and detection performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": "Effect of different thresholds " + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": ". The hyper-parameter threshold " + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": " controls the quantity of selected highly reliable data and thus affects the training process. To select an optimal " + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": ", we conduct an ablation study experiment with three different " + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": " values, which are " + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "inline_equation", + "content": "T = 0.4" + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "inline_equation", + "content": "T = 0.6" + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": ", and" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 326, + 71, + 525, + 132 + ], + "blocks": [ + { + "bbox": [ + 326, + 71, + 525, + 132 + ], + "lines": [ + { + "bbox": [ + 326, + 71, + 525, + 132 + ], + "spans": [ + { + "bbox": [ + 326, + 71, + 525, + 132 + ], + "type": "image", + "image_path": "13c7f0884527bcfd4a49a7072e1032049b28115c69abe3efa3f7006015cec3d0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 141, + 545, + 173 + ], + "lines": [ + { + "bbox": [ + 304, + 141, + 545, + 173 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 545, + 173 + ], + "type": "text", + "content": "Figure 9. Visualization of comparison results on two captured and unseen photos demonstrates that our network can more accurately detect mirrors." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "inline_equation", + "content": "T = 0.8" + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "text", + "content": ". In general, a larger " + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "text", + "content": " means more samples we select. As shown in Figure 7 (a), the number of highly reliable data increases when the iteration number of our data engine increases. Meanwhile, Figures 7 (b), (c), and (d) show the IoU scores for different " + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "text", + "content": " values and engine iteration numbers on the MSD, PMD, and RGBD-Mirror* datasets, respectively. More importantly, our method with " + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "inline_equation", + "content": "T = 0.6" + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "text", + "content": " yields the highest IoU score on all three datasets. Hence, we empirically set " + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "inline_equation", + "content": "T = 0.6" + }, + { + "bbox": [ + 304, + 180, + 545, + 288 + ], + "type": "text", + "content": " in all our experiments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 294, + 418, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 294, + 418, + 306 + ], + "spans": [ + { + "bbox": [ + 306, + 294, + 418, + 306 + ], + "type": "text", + "content": "4.4. More Visualization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 313, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 545, + 397 + ], + "type": "text", + "content": "Feature visualization. As shown in Figure 8, we visualize the latent features at different decoder layers and the output feature map of the segmentation head. Apparently, these features can highlight mirror regions for different input mirror images. It indicates that our method can accurately capture the mirror-related feature representation, and thus produce robust mirror detection performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 398, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 470 + ], + "type": "text", + "content": "Visualization of our results on unseen photos. We capture two unseen photos with mirrors at challenging positions. As shown in Figure 9, our network can more accurately detect the mirror regions than the state-of-the-art methods. The main reason is that our network can learn more reliable mirror-related knowledge from large-scale unlabeled data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "In this work, we collect a large-scale unlabeled dataset to fill the data gap in the mirror detection task. To effectively exploit the collected large-scale unlabeled data, we design an iterative data engine comprising four processes: (1) mirror detection model training, (2) pseudo-label prediction, (3) dual guidance scoring, and (4) selection of highly reliable pseudo-labels. In each iteration, we investigate a dual guidance scoring strategy to assess pseudo-labels through geometric accuracy derived from segmentation metrics and semantic scores from multi-modal large language models. Furthermore, we propose a reliability-enhanced training strategy to effectively learn from the selected, more reliable, high-quality pseudo-labels. We conduct extensive experiments on three public datasets to verify the performance gains from our collected large-scale unlabeled data. The segmentation results for diverse unseen examples and randomly captured images in different scenes further demonstrate the generalization capability of our model." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25483" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 144, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 144, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 144, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 186 + ], + "type": "text", + "content": "This work is supported by the Guangdong Science and Technology Department (No. 2024ZDZX2004), the Guangzhou-HKUST(GZ) Joint Funding Program (No. 2023A03J0671), Guangdong Provincial Key Lab of Integrated Communication, Sensing and Computation for Ubiquitous Internet of Things (No.2023B1212010007), and the Nansha Key Area Science and Technology Project (No. 2023ZD003)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 198, + 107, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 198, + 107, + 211 + ], + "spans": [ + { + "bbox": [ + 48, + 198, + 107, + 211 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 219, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 219, + 287, + 274 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 219, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 53, + 219, + 287, + 274 + ], + "type": "text", + "content": "[1] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. 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To mitigate these risks, post-hoc model intervention techniques, such as concept unlearning and safety guidance, have been developed. However, fine-tuning model weights or adapting the hidden states of the diffusion model operates in an uninterpretable way, making it unclear which part of the intermediate variables is responsible for unsafe generation. These interventions severely affect the sampling trajectory when erasing harmful concepts from complex, multi-concept prompts, thus hindering their practical use in real-world settings. In this work, we propose the safe generation framework Detect-and-Guide (DAG), leveraging the internal knowledge of diffusion models to perform self-diagnosis and fine-grained self-regulation during the sampling process. DAG first detects harmful concepts from noisy latents using refined cross-attention maps of optimized tokens, then applies safety", + "bbox": [ + 75, + 323, + 473, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "guidance with adaptive strength and editing regions to negate unsafe generation. The optimization only requires a small annotated dataset and can provide precise detection maps with generalizability and concept specificity. Moreover, DAG does not require fine-tuning of diffusion models, and therefore introduces no loss to their generation diversity. Experiments on erasing sexual content show that DAG achieves state-of-the-art safe generation performance, balancing harmfulness mitigation and text-following performance on multi-concept real-world prompts.", + "bbox": [ + 500, + 292, + 893, + 444 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 473, + 632, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent advancements, text-to-image diffusion models (DM) have exhibited remarkable capabilities in generating high-resolution images based on textual prompts that outperform GANs and VAEs [4]. Notably, models such as DALL-E [2, 36], MidJourney [31], and Stable Diffusion [6, 39] have achieved commercial standards, enabling a wide range of applications designed for end-users. However, growing regulatory concerns about the safety of generated images and their social impacts, such as the gen", + "bbox": [ + 496, + 500, + 893, + 636 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d6df31427c38b58f85a0acc3085b2385e1ba74b9c098131cf196ed222eefeba8.jpg", + "image_caption": [ + "Figure 1. Results of safe generation with sexual content erased, masks are applied for censorship purposes. Our proposed method, DAG, can leverage the internal knowledge of pretrained Text-to-Image Diffusion Models to perform fine-grained erasure of unsafe visual concepts to avoid modifying other concepts in the same image. It effectively preserves the composition of unsafe images and the appearance of objects in benign regions, achieving a favorable balance between harm mitigation and text alignment for partially harmful prompts. This approach underscores concerns about practical usability in developing safe generation methods and reveals the self-regulation capability of text-to-image diffusion models, shedding light on scalable safety alignment for image generation." + ], + "image_footnote": [], + "bbox": [ + 86, + 645, + 880, + 814 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 94, + 619, + 227, + 635 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13252", + "bbox": [ + 478, + 950, + 519, + 962 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "eration of unauthorized and Not-Safe-for-Work (NSFW) content [20, 34, 37], primarily arise from the weakness of unfiltered pretraining datasets sourced from the real world [40, 43, 45].", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, post-hoc model intervention methods for safe generation have emerged as a promising approach, enabling safe generation without the need for expensive retraining on a curated clean dataset. Unlike text or image filters that passively block unsafe content, these methods improve practical usability by directly guiding the generation process toward safe outputs. Depending on how they handle unsafe concepts, these techniques can be categorized into two types: Unlearning-based methods modify the model's distribution by aligning its internal understanding of unsafe concepts with corresponding safe ones. In contrast, guiding-based methods require no additional training; they rely on extra negative or safety prompts to define unsafe concepts and adjust the estimated noises from U-Net denoisers during the generation process, offering greater scalability potential.", + "bbox": [ + 75, + 154, + 470, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, some of existing unlearning methods are inherently text-centric [33, 46] and unreliable when unsafe visual concepts emerge from harmful knowledge recalled by benign prompts, which represents a form of blacklist shortcut arising from the manually crafted datasets used for fine-tuning. Moreover, as demonstrated in Figure 1-(b), methods designed to erase unsafe concepts from single-concept prompts, like \"A photo of $[c_{\\mathrm{unsafe}}]$ ,\" are inadequate for real-world prompts containing multiple co-existing concepts. The lack of control in distinguishing and retaining safe concepts leads to significant mode shift between original generation and erased safe generation. Hence come our research questions: Can we design an image-centric safe generation framework to minimize the mode shift of safe generation and surmount the challenge of blacklist shortcuts?", + "bbox": [ + 75, + 398, + 470, + 641 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by the understanding of cross-attention layers in diffusion models [25], as well as the token optimization methods for accurate cross-attention maps (CAM) [16, 30, 49], we propose our safe generation framework Detect-and-Guide that leverages internal knowledge of diffusion models to negate sexual content guided using detecting CAMs. The detection target for sexual content can be coarsely described by the combination of attributes $a \\in \\mathcal{A}$ and specific object categories $o \\in \\mathcal{O}$ (e.g., 'nude' and 'human'). The desired criteria include: (1) Generalizability to different styles, scenes, and poses. (2) Specificity to the combination of $(a,o) \\in \\mathcal{A} \\times \\mathcal{O}$ that should be detected; in contrast, a bare wall or a clothed human is unnecessarily to be detected. (3) Fine-grained detection with precise region mask, which excludes the background and covered part of human body. We investigate the role of cross-attention layers and manage to extract CAMs from high-level U-Net layers that", + "bbox": [ + 75, + 643, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "meet all the criteria by their characteristics of entangling relations of objects together with attributes [25]. The entanglement makes it possible to directly extract the CAMs only for paired $(a,o)$ and enables fine-grained guidance applied accordingly.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Starting with the guideline tokens that need to be optimized and a small annotated dataset created using grounded segmentation models, we incorporate (1) background leakage loss [49] and (2) negative sample loss [16] to optimize the embeddings for precisely extracting CAMs that aligns with the ground truth mask. During the sampling process, the optimized token embedding $c^*$ is capable of detecting unsafe concepts at each timestep with generalizability and concept specificity across different scenarios, which can be competitive with supervised semantic segmentation methods at image level [30] and is naturally robust to different levels of noise, without accumulating the CAM over all timesteps. With the detection mask, we can then incorporate latent-level safety guidance to address the limitations of heavily relying on hyperparameters choices (e.g., guidance scale, guidance steps) by using CAM magnitude together with adaptive unsafe area rescaling.", + "bbox": [ + 496, + 167, + 892, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The proposed method is evaluated with sexual concept erased. We propose to evaluate the safe generation performance of erased models comprehensively on three evaluation dimensions: (i) Erasing effectiveness and robustness, (ii) fine-grained erasing performance with unsafe concepts excluded and safe concept retrained, and (iii) the utility of models in benign dataset. We use NudeNet [32] score as the safety metrics, and conduct experiments in real-world sexual prompts dataset I2P [41]. We additionally introduce a novel vision-language alignment metrics VQA-score [24] to flexibly measure the text-to-image safety alignment on unsafe prompts. The utility of erased models can be evaluated by image quality (FID score) and prompt-following performance on MS-COCO [23]. Our qualitative and quantitative results show that DAG can successfully erase sexual content from generated images, achieving optimal generation performance that balancing harmful mitigation and generation quality.", + "bbox": [ + 496, + 424, + 892, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Disclaimer. The manuscript contains discussions and visual representation of NSFW content. We censor Not-Safe-for-Work (NSFW) imagery. Reader discretion is advised.", + "bbox": [ + 496, + 696, + 890, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background", + "text_level": 1, + "bbox": [ + 500, + 753, + 629, + 771 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-Image Diffusion Models. Our paper mainly implemented with Stable Diffusion (SD) [39], one of the most popular and influential latent diffusion models (LDM), with an active community and numerous variations. LDM comprises a VAE [5, 47] that maps high-dimensional images $x_0$ into a latent space $z_0 = \\operatorname{E}(x_0)$ and reconstructs them back with vector quantization $x_0' \\approx \\mathrm{D}(z_0)$ , and a denoiser $\\epsilon_{\\theta}$ samples noise backward. The denoiser is trained using the", + "bbox": [ + 496, + 779, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13253", + "bbox": [ + 480, + 950, + 517, + 962 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "following mean squared error (MSE) loss objective:", + "bbox": [ + 76, + 90, + 421, + 107 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {L D M}} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathrm {E} (\\mathbf {x}), \\mathbf {c}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ | | \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\mathbf {c}) | | _ {2} ^ {2} ], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 114, + 468, + 132 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}(\\cdot)$ is the estimated noise conditioned on the noisy latent $z_{t}$ at timestep $t$ . SD introduces text condition $c$ from input prompt $p$ into diffusion models through a pretrained CLIP text encoder $c = \\tau_{\\theta}(p)$ [35], and incorporates cross-attention layers [48] in a U-Net denoiser that project $c$ through key and value layers.", + "bbox": [ + 75, + 140, + 468, + 231 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Delving into Cross-attention Layers. Each block in U-Net denoiser is composed of self-attention, cross-attention and convolution layers. Recent works have presented causal analyses attributing generated elements to layers or neurons in the U-Net, revealing the function of cross-attention layers at different levels [1, 13, 25]. In conclusion, cross-attention layers play an important role in controlling generation in specific regions, guided by token-wise cross-attention maps (CAMs) [13]. However, CAMs that entangle both attributes (such as colors) and object category information may hinder single-concept editing [25]. Also, knowledge of different types of elements (colors, actions/poses, styles, and objects) is distributed across all layers of the U-Net [1], but with varying degrees of causal effects considering the dimension level. Moreover, by leveraging the flexibility of condition $c$ , the potential of diffusion models can be extended beyond image synthesis. T2I diffusion models can be used for discriminative tasks such as classification [15] ( $\\arg \\max_i \\mathcal{L}_{\\mathrm{LDM}}(c = \\tau_\\theta(y_i))$ ) for all labels $y_i \\in \\mathcal{Y}$ ) and semantic segmentation [30], achieving comparable capabilities to supervised models. These findings have inspired us to leverage the power of CAMs to detect the presence of sexual concepts at each timestep and provide a precise guidance map at pixel level for $z_t$ .", + "bbox": [ + 75, + 248, + 472, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Safe Generation of Diffusion Models. The unlearning methods show promise in providing insights into functions of DM components and how they affect unsafe concept generation. For example, cross-attention refinement in the U-Net denoiser aims to reduce harmful semantics from conditional prompts [11, 27, 28, 51], while fine-tuning unconditional components (self-attention and convolutions) is aimed at erasing global concepts that arise from word combinations rather than specific individual concepts [10]. Other works provide evidence that fine-tuning the CLIP text encoder can be as effective as fine-tuning cross-attention layers [18], and that it benefits more from adversarial training than other components [52]. The refinement and fine-tuning rely on manually defined paired concepts of $(c_{\\mathrm{unsafe}}, c_{\\mathrm{safe}} / c_{\\emptyset})$ to supervise the unlearning. Methods that leverage the internal knowledge of diffusion models are centered around generating paired image datasets for manually crafted paired concepts [17], with the exception of the", + "bbox": [ + 75, + 628, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/edd69fa5282a27286c222546c2ffdba81b487f415f432698b4912d08345e8421.jpg", + "image_caption": [ + "Figure 2. Token optimization for sexual content detection." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "method that leverages the self-discovered disentangled unsafe direction in the $h$ -space (the middle bottleneck of U-Net with the highest levels of semantics) [19, 21]. However, in our work, we find that sexual content detection should fully leverage the entanglement of attributes and category information in lower-level latents, beyond the $h$ -space.", + "bbox": [ + 498, + 367, + 893, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Detect-and-Guide", + "text_level": 1, + "bbox": [ + 500, + 484, + 674, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DAG comprises two key operations for safe generation:", + "bbox": [ + 500, + 513, + 867, + 529 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) Guideline detection: We first collect a small dataset to optimize embeddings of guideline tokens with novel losses to align their semantics with specific concepts, which enhances unsafe region detection (Sec. 3.1). These optimized embeddings to extract cross-attention maps (CAMs), which are capable of providing pixel-level magnitudes of sexual content that highlights the nude region, specifically for the presence of co-existing $(a,o) =$ (nude, human), and are generalizable when $(a,o)$ is further combined with non-targeted attributes such as styles, scenes, and poses. The self-diagnostic detections will then be used for self-regulation to negate unsafe generation.", + "(2) Safe Self-regulation: We follow the implementations of safety guidance [3, 34] to refine the estimated noise $\\epsilon_{\\theta}(\\mathbf{z}_t,t,\\mathbf{c})$ applied to denoise the noisy latent $\\mathbf{z}_t\\rightarrow \\mathbf{z}_{t - 1}$ in a classifier-free style [14] (Sec. 3.2). We identify and inherit the advantages of safety guidance, which automatically explores a safe mode that is close to the generated unsafe mode during sampling dynamics. We overcome shortcomings such as unnecessary global changes, lack of specificity, and heavy dependence on the appropriate choice of guidance strength by (a) restricting the guided region to the detected region and (b) applying an adaptive scalar based on CAM magnitude and the area of unsafe region." + ], + "bbox": [ + 496, + 534, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13254", + "bbox": [ + 480, + 950, + 519, + 963 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/40fcf966ce85d68cd5dfe836638f032a3f2c9a4609992283acc6b349209d1149.jpg", + "image_caption": [ + "Figure 3. CAMs from non-optimized $c$ generate a detection region of nudity that diffuses into the irrelevant background and highlight the non-target concept 'cat'. We optimize the embedding to address background leakage and lack of specificity, using pixel-level CE loss w.r.t ground truth masks. The refined CAMs are demonstrated in (a). The learned refined semantics of $c^*$ generalize well to unseen test samples, as demonstrated in (b). The presence of nudity can easily be measured by CAM values greater than 0.5." + ], + "image_footnote": [], + "bbox": [ + 86, + 94, + 460, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. CAM-based Guideline Detection", + "text_level": 1, + "bbox": [ + 76, + 334, + 362, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we describe the way of deriving detection maps from cross-attention layers in the U-net. As demonstrated in Figure 2, the noisy latent $z_{t}$ and conditional embedding from prompt $c_{p}$ are fed forward the U-Net, and we cache all hidden states in cross-attention layers, which is denoted as $h_{t}^{l}$ . The original CA operation during sampling process will project visual latents $h_{t}^{l}$ to queries $Q = W_{Q}^{l} \\cdot h_{t}^{l}$ , and project original condition $c_{p}$ to keys and values. In our work, we use the static hidden states and projection weights $W_{Q}^{l}, W_{K}^{l}$ to calculate cross-attention between guideline embeddings $c$ and $h_{t}^{l}$ .", + "bbox": [ + 75, + 358, + 468, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Limitations of Non-optimized Guideline Tokens. We initialize $c$ with token embeddings of 'nude person', which is desired to give high attention scores on the concept that match the description. However, as shown in Figure 3-(a), $\\mathrm{CAM}(c)$ premises to the background and detects nudity concepts on a cat. The first phenomenon is identified as cross-attention leakage problem. In previous work, for the CAM which is extracted using original prompts, the text encoder that apply self-attention layers on token sequences make the embeddings $c_{p}$ contain rich semantic information of the context, as well as the special tokens, therefore causing the leakage to the background [49]. The second problem of unexpectedly highlighting the cat which is unrelated to 'nude person' mainly arises from the rich semantics of 'nude', as the cat is sometimes considered to be unclothed.", + "bbox": [ + 75, + 547, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Token Optimization. To address these problems, we suggest the token optimization approach [30] that can effectively refine the resulting CAMs with semantics generalizability and specificity on the target combination of attribute and object category. A small dataset contains safe images and annotated unsafe images is required for optimizing the embedding. We first instruct LLM to generate text-to-image", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "prompts with nude concepts, then generate images using T2I diffusion models. We select five unsafe and three safe images with various styles (e.g., sculpture, painting, and photograph) and with several non-target concepts (dogs and cats) to help distinguish the nudity of human. Noted that unsafe annotations can be constructed easily with GroundedSAM [26, 38]. We detail the annotating pipeline in Figure 2-(a): By incorporating positive textual labels and negative textual labels, we can exclude non-sexual part of human like hair or face from the body segmentation results and give precise GT masks. For safe images, their annotations are simply initialized as zero masks indicating no nude concepts should be detected. We denoted the small dataset of generated images and annotations as $\\mathcal{D} = \\{\\mathcal{X},\\mathcal{Y}\\}$ .", + "bbox": [ + 496, + 90, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the dataset, we cache their intermediate hidden states before cross-attention layers over all sampling timesteps $\\{h_t^l [i]|i\\in \\mathcal{X},t\\sim [1,50]\\}$ . Resulting maps for the embedding $c$ can then be derived as $\\mathrm{CAM}(h_t^l [i],c)$ and interpolated to the size of images (i.e., $\\hat{A}\\in \\mathbb{R}^{K\\times H\\times W}$ ). We define the CAM loss for detecting regions with specific target concepts as follows:", + "bbox": [ + 496, + 301, + 890, + 407 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C A M}} = \\mathbb {E} _ {(i, y) \\sim (\\mathcal {X}, \\mathcal {Y})} \\mathbb {E} _ {t \\sim \\mathcal {T}, l \\sim \\mathcal {L}} \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\sum_ {h = 1} ^ {H} \\sum_ {w = 1} ^ {W} [ \\\\ - \\operatorname {O n e - h o t} \\left(y ^ {G T}\\right) _ {h, w} \\cdot \\log \\left(\\hat {A} _ {k, h, w} \\left(h _ {t} ^ {l} [ i ], c\\right)\\right), \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 417, + 890, + 483 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{T}$ is a set of all sampling timesteps, $K$ is the number of guideline tokens, and $\\mathcal{L}$ denotes the chosen layers to extract the CAMs. We average the loss of each CAM over tokens, and the values of $\\hat{A}$ are normalized to [0,1] with min-max scalar for calculating the logits.", + "bbox": [ + 496, + 491, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Noted that hidden states in the U-Net of SD model have three size dimensions $[16^2, 32^2, 64^2]$ with difference levels of semantics. We assign layer-wise learnable weights initialized by all ones and find that weights of larger CAMs are monotonic decreasing. This means that the hidden state with resolution of 64 contains the lowest level of semantics, and is too noisy for token optimization. Thus we choose $\\mathcal{L} = \\{l|h_t^l.\\mathrm{size}\\in [16^2,32^2]\\}$ to extract CAM layers.", + "bbox": [ + 496, + 566, + 890, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To summary, our optimizing objective can be formalized as follows:", + "bbox": [ + 498, + 688, + 890, + 717 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc ^ {*} = \\min _ {c} \\left[ \\mathbb {E} _ {(i, y) \\sim (\\mathcal {X}, \\mathcal {Y})} \\mathcal {L} _ {\\mathrm {C A M}} \\right] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 729, + 890, + 751 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and we use a mini-batch of size two where one sample from unsafe subset and another from the safe subset.", + "bbox": [ + 498, + 761, + 890, + 790 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Improved Guideline Detection. The detection map of optimized guideline token embeddings, $\\hat{A}(c^{*})$ , on trained samples is demonstrated in Figure 3-(a), and that on randomly chosen samples from unseen datasets is shown in Figure 3-(b). The CA leakage to the background is significantly mitigated and target-concept specificity is improved.", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13255", + "bbox": [ + 480, + 950, + 517, + 962 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a467c3ba33eeac6286a8f13f134e42393a7e0ed8a7da6b7909eb1fbe61ebc251.jpg", + "image_caption": [ + "Figure 4. Overview of Our Proposed Safe Generation Framework, Detect-and-Guide (DAG). The notations for (a) Original Generation can be found in Sec. 2. In (b), DAG utilizes guideline token embeddings $c^*$ to perform self-diagnostics by calculating cross-attention maps (CAM) at higher-level hidden states of the U-Net. The $c^*$ is optimized in advance on a small annotated dataset for precisely segmenting unsafe regions, addressing the problem of cross-attention leakage [49]. In (c), DAG achieves safe self-regulation by editing the detected unsafe regions. This editing process uses pixel-level magnitudes that are adaptively determined based on region area and CAM values." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 883, + 328 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As further illustrated in Figure 5, CAMs for non-target concepts, such as 'a nude wall', will contain only a few values larger than 0.5 (i.e., they will not be detected), which can serve as an indicator of the presence of unsafe content. We analyze the distribution of CAM values in Sec. 3.2 to develop an adaptive scaling strategy that best balancing sexual content erasure and mode preservation.", + "bbox": [ + 75, + 421, + 470, + 526 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bfd3d59b63df80ba481a511282c670b80e5398697d5728f8fe65cd96b72a87bf.jpg", + "image_caption": [ + "Figure 5. The comparison of cross-attention map with non-optimized token embeddings and their effect on performing the self-regulation." + ], + "image_footnote": [], + "bbox": [ + 122, + 535, + 419, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Safe Self-regulation", + "text_level": 1, + "bbox": [ + 76, + 710, + 264, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the attention maps of guideline detection, we then utilize the idea of classifier-free guidance [14] to adjust a noisy latent in an unsafe mode to a nearby safe mode during sampling following the implementation of safety guidance [3, 41].", + "bbox": [ + 75, + 734, + 468, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The classifier-free guidance introduces a null-text embedding $\\varnothing = \\tau_{\\theta}({}^{\\prime \\prime \\prime \\prime})$ as the unconditional generative probability beyond the conditional probability to estimate the gradient of an implicit classifier. We denote unconditional estimated noise as $\\epsilon^{\\emptyset}$ , conditional estimated noise as $\\epsilon^{p}$ and the scale of guidance as $s_g$ (default as 7.5 for SDv1.4).", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarly, safety guidance [41] introduces a safety condition $c_{s} = \\tau_{\\theta}(p_{s})$ and the corresponding estimated noise $\\epsilon^{c_s}$ that reuses the implicit Bayesian classifier for conditional probability [14] to adjust the estimated gradient with selective pixel-level scale map $\\mathbf{S}_{c_s}\\cdot \\mathbf{M}_{c_s}$ :", + "bbox": [ + 498, + 421, + 890, + 498 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\epsilon} _ {\\theta} (x _ {t}, t, c _ {p}) ^ {\\mathrm {C F}} = (1 - s _ {g}) \\underbrace {\\epsilon_ {\\theta} (x _ {t} , t , \\varnothing)} _ {\\epsilon^ {\\emptyset}} + s _ {g} \\underbrace {\\epsilon_ {\\theta} (x _ {t} , t , c _ {p})} _ {\\epsilon^ {p}} \\\\ = \\epsilon^ {\\varnothing} + s _ {g} \\underbrace {\\left(\\epsilon^ {\\varnothing} - \\epsilon^ {p}\\right)} _ {\\tilde {\\epsilon} ^ {p}} \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 505, + 890, + 575 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, t, c _ {p}, c _ {s}\\right) ^ {\\text {S a f e}} = \\left(1 - s _ {g}\\right) \\epsilon^ {\\varnothing} + s _ {g} \\left(\\epsilon^ {p} - \\mathbf {S} _ {c _ {s}} \\cdot \\mathbf {M} _ {c _ {s}} \\epsilon^ {c _ {s}}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 579, + 888, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the purpose of safe generation, guidance-based methods are advanced in the capability of discovering the direction of a nearby safe mode given an existing unsafe mode. However, the safety guidance applied in an early stage will introduce severe mode shift that affect the generation quality, with necessity of warm-up steps $\\underline{t}_{c_s}$ to regulate the mode change. Therefore, we leverage detection maps $\\hat{A}(c^*)$ as a gate function to enable adaptive guidance scale (stronger when detected with higher confidence) that also works at higher noise level and prevent severe mode shift. The overall comparison of how our method apply safety guidance is different from existing methods is shown in Table 1.", + "bbox": [ + 496, + 607, + 890, + 790 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The safety scale map $\\mathbf{S}_{c_s}$ used in DAG depends on (i) a scalar denoted as $\\mathrm{Area}_{0.5}(\\hat{A})$ , which highlights the area of detected unsafe region with a confidence no less than 0.5, as the yellow region shown in Figure 4-(b), along with a base weight of 5 for pixel editing $\\overline{s}_c = \\frac{5}{H\\times W}$ ; and (ii) a magnitude scalar $T_{0.01}(\\hat{A})$ based on confidence value of attention map $\\hat{A} = \\{a\\}_{:h,w}$ , which assigns an appropri", + "bbox": [ + 496, + 791, + 892, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13256", + "bbox": [ + 480, + 950, + 517, + 962 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4b06e0203af54cbb3727bc8909b61668823cfbc8b764834912ffdb3506dbc0f8.jpg", + "table_caption": [ + "Table 1. Notations for classifier-free guidance and safety guidance." + ], + "table_footnote": [], + "table_body": "
    CF [14]SLD [41]SEGA [3]DAG (Ours)
    ε∅1 - sg1 - sg + sg · Scs · Mcs
    εpsgsg
    εcs--sg · Scs · Mcs
    Scs-max(εp - εcs, 1)scs(¯¯¯¯sc · Area0.5(Â)) ⊙ T0.01(Â)
    Mcs-I(εcschw + λ > εpchw)chwI[¯¯¯¯epsilonchw ∈ top-p(¯¯¯¯epsiloncs)]chwI[ ≥ 0.01]:hw ⊙ McsSEGA/SLD
    tcs-7 (strong), 10 (medium), 15 (weak)105
    ", + "bbox": [ + 165, + 106, + 797, + 214 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ate editing scale only for pixels whose confidence satisfies $0.01 \\leq a \\leq 1$ by rescaling their attention values to range $1 \\leq T_{0.01}(a) \\leq 5$ . Besides the scale map, we simply set a gate function $\\hat{A} \\geq 0.01$ to the safety selective mask of existing methods, as the green region demonstrated in Figure 4-(b). We use $\\mathbf{M}_{c_s}^{\\mathrm{SEGA}}$ in main experiments and compare different safety guidance methods in Supp. B.", + "bbox": [ + 75, + 232, + 472, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 352, + 209, + 369 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation Setting", + "text_level": 1, + "bbox": [ + 76, + 377, + 256, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we comprehensively evaluate the effectiveness of DAG in erasing sexual content from three perspectives:", + "bbox": [ + 75, + 401, + 468, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Erasing Effectiveness and Robustness. We utilize 931 sexual prompts from real-world harmful prompts benchmark Inappropriate Image Prompts (I2P) [41] to evaluate effectiveness, denoted as I2P-sexual. Additionally, we filter a subset of complex prompts containing terms, resulting in a 439-prompt subset, denoted as I2P-sexual-complex. To assess robustness, we further leverage two black-box adversarial prompt datasets, Ring-A-Bell (RAB)[46] and MMA[50]. We use 1,000 released adversarial prompts from MMA focused on sexual content generation, and we implement RAB attacks on I2P-sexual-complex, resulting in 439 adversarial prompts.", + "bbox": [ + 75, + 446, + 468, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We employ a YOLO-based nudity detector NudeNet [32] to evaluate unsafe content in generated images from I2P-sexual, RAB and MMA, where each prompt generates four images using fixed seeds, producing a total of 9480 images per method. We apply NudeNet's five unsafe classes and a confidence threshold of 0.6 to calculate the evaluation results. We report the number of detected unsafe classes as NudeNet Number (N3), and calculate the Erase Rate (ER) compared to undefended SDv1.4 as follows: $\\mathrm{ER} = 1 - \\frac{\\mathrm{N3}_{\\mathrm{defense}}}{\\mathrm{N3}_{\\mathrm{SDv1.4}}}$ , where all unsafe concepts erased will give a $100\\%$ ER.", + "bbox": [ + 75, + 628, + 468, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fine-grained erase performance. We consider that a harmful prompt may contain multiple concepts, and thus the design principle of safe generation should account for prompt-following performance on the remaining safe concepts. To assess this, we introduce an advanced metric, VQA Score [24], which evaluates text-to-image alignment using pre-trained large VLMs (CLIP-FlanT5-XL). We eval", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "uate the alignment capability of the erased models on I2Psexual dataset by prepending a short task description 'Safe Generation:' to the prompt before feeding the (prompt, image) pair into the VLM evaluator. This metric, denoted as VQA Score-SG, reflects the self-regulation capability of safely following the harmful prompt. We use VQA Score as a sanity check to ensure safety methods 018 do not degrade normal generation", + "bbox": [ + 496, + 232, + 890, + 352 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model Utility. We resample 1000 prompts from the MS-COCO validation dataset [23] as benign prompts to evaluate model utility, denoted as COCO-1K. Image quality metrics include $FID_{\\mathrm{real}}$ , which measures the similarity between generated images generated by erased models and real images from MS-COCO, and $FID_{\\mathrm{SDv1.4}}$ , which assesses the mode shift introduced by erasing methods. We also calculate the VQA Score on resampled data to evaluate generation capability.", + "bbox": [ + 496, + 353, + 890, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. In our experiments, we compare against nine popular unlearning methods under different settings, resulting in a total of eleven erasing baselines (ESD [9], SLD-(weak, medium, strong) [42], SPM [29], SA [12], SalUn [8], Self-Dis [22], SEGA [3], MACE [27], AdvUnlearn [52]). The baseline model with no defense is SDv1.4, and we also conduct experiments on SDv2.1, which training data is filtered by an NSFW detector, to serve as a retraining baseline. For the fine-tuning-based erasing methods, we download their official checkpoints for erasing the concept of nudity. For the safety guidance-based methods, we run their official generating scripts with hyper-parameters from their paper. For SEGA, we set the scale of semantic guidance to 10 (default as 5) and reverse the guidance for effectively removing nudity from generation.", + "bbox": [ + 496, + 489, + 892, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Erase Performance", + "text_level": 1, + "bbox": [ + 500, + 726, + 684, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Erase Effectiveness and Model Utility Perservation We generate 9840 images for each method, and report the NudeNet detection results of five unsafe classes. The erasure effectiveness of the proposed method compared with baselines are demonstrate in Table 2. Our method, DAG, outperforms all guidance-based methods (three variants of SLD and SEGA) and achieves competitive erasure performance compared to fine-tuning-based methods (SA, SPM) and SDID. Fine-tuning-based methods with strong erasure performance come at the cost of lower generation quality on", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13257", + "bbox": [ + 480, + 950, + 517, + 962 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7a4630282cffc9717ff56d45b720c1d1b575ab3ac313b838e76aaeee7fca98bb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodsGeneration Quality (COCO-1K)Erase Effectiveness (I2P-sexual)
    VQA Score\\( FID_{\\text{real}} \\downarrow \\)\\( FID_{\\text{SDv1.4}} \\downarrow \\)Total↓ButtocksChest(F)Genitalia(F)Chest(M)Genitalia(M)
    SDv1.4 [39]0.7058.03010708383854914
    SLD-weak [41]0.6859.3823.348566267148723
    SLD-medium [41]0.7061.1531.736605550633615
    SLD-strong [41]0.6462.8741.14207271447272
    SEGA [3]0.7058.9533.4715511873513
    SDID [21]0.7357.931.521812512212166
    ESD-u [10]0.6358.0150.55631492110
    SA [12]0.6763.8353.9711411841450
    SalUn [7]0.4280.2787.68000000
    SPM [29]0.7157.6235.372083813917131
    MACE [27]0.5955.9951.01565363102
    AdvUnlearn [52]0.5460.0244.561018001
    DAG (ours)0.7258.2223.67861471325
    ", + "bbox": [ + 81, + 90, + 686, + 282 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Assessment of Unsafe Concept Erase: Evaluation of FIDs and VQA scores on COCO-1K and the count of unsafe concepts detected by NudeNet on I2P-sexual. We use best, second-best and third-best to highlight the top-3 results, respectively. Italicized methods are fine-tuning-based.", + "bbox": [ + 75, + 289, + 689, + 333 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eb05d808fa60bd3b880e2a67d57542ca34bf8de5f16edf2e49340a520fca1b98.jpg", + "image_caption": [ + "Figure 6. Erase rate $(\\%)$ on I2P-sexual, measuring the relative deduction of unsafe concepts compared to SDv1.4." + ], + "image_footnote": [], + "bbox": [ + 705, + 90, + 885, + 273 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "woman with shiny skin lying on the grass dressed in roman clothes, ultra detailed, Guido Reni style", + "bbox": [ + 183, + 376, + 290, + 436 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "'high resolution $8k_{\\mathrm{e}}$ close up portrait photograph of Selena Gomez, dressed in bikini, standing near the beach, vogue photoshoot", + "bbox": [ + 184, + 478, + 284, + 561 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f7c20188561e86f9c57dce8228c44b4813a3cb034d015451f41ee1f4c41bac76.jpg", + "image_caption": [ + "Figure 7. Qualitative Experiments. The examples are randomly sampled from I2P-sexual. Note that not all prompts in I2P-sexual can generate harmful images, and the regional specification advantages of DAG can be observed." + ], + "image_footnote": [], + "bbox": [ + 299, + 345, + 787, + 564 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the benign dataset COCO-1K. For example, the strongest defense methods suffer from severe distribution shifts when generating non-target concepts and fail to achieve text-to-image alignment, as quantitatively observed by a significantly lower VQA Score (0.42) compared to ours (0.72) and SDv1.4 (0.70). We visualize the trade-off between generation quality and erasure performance in Figure 1 (right), showing that our method, without expensive retraining or fine-tuning, achieves the optimal balance by incorporating optimized token-based detection maps.", + "bbox": [ + 75, + 612, + 470, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Erase Robustness. We conduct robustness experiments using two black-box adversarial prompt attacks: Ring-A-Bell and MMA. Ring-A-Bell is based on CLIP-embedding inversion to reconstruct the token sequence with similar semantics to an unsafe embedding. MMA conducts a sensitive word replacement attack and generates adversarial prompts in natural language. We present the results in Ta", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ble 3. Note that our results align with fine-tuning-based methods in robustness evaluations, without any weight tuning or modifications.", + "bbox": [ + 498, + 612, + 890, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fine-grained Erase Performance. We demonstrate the VQA Score-SG in Figure 8 to measure the text-to-image alignment degree of erased methods on the datasets I2P-sexual. DAG ranks the second in the results, and primarily benefit from the restriction of guidance in detected unsafe region, which introduce slightly background modification as demonstrated in Figure 7.", + "bbox": [ + 496, + 681, + 890, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Parameters Study", + "text_level": 1, + "bbox": [ + 500, + 800, + 674, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Although the optimized embeddings can meet both generalizability and specificity, one remaining question is how the detection performance varies across different noise levels and whether it can be aggregated using a smaller number of maps, such as one. We visualize the detection map at dif", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13258", + "bbox": [ + 480, + 950, + 517, + 962 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b87518c8197e013de732957bba802d12fab68a351ddf1deb9a3f3ecd1972ba22.jpg", + "table_caption": [ + "Table 3. Erasure Robustness for Nudity: Best, Second-best and Third-best highlight top-3 results. Italicized methods are fine-tuning-based." + ], + "table_footnote": [], + "table_body": "
    Defense MethodsRing-a-bell Adversarial PromptsMMA Adversarial Prompts
    Erase Rate↑ (%)Total↓ButtocksChest (F)Genitalia (F)Chest (M)Genitalia (M)Erase Rate↑ (%)Total↓ButtocksChest (F)Genitalia (F)Chest (M)Genitalia (M)
    SDv1.40.003279115249€342266600.002732413154€83301391
    SLD-weak(7.44)3523107266543526848(1.57)2775433151782336407
    SLD-medium(7.11)3512742725433246341.542690410142095360405
    SLD-strong43.15186433163810090348.43140928369233174227
    SEGA66.54109723768452511065.419452333007248157
    SDID87.6840434309124547.142537373144474306340
    ESD-u87.74402143271346297.806020222214
    SA48.031704431393146122089.602846219012011
    SalUn100.0000000099.93202000
    SPM87.07424293172255149.34138430866639208163
    MACE99.57142921099.411654016
    AdvUnlearn100.0000000099.491428022
    DAG (ours)88.14389102067166077.601276121854183113
    ", + "bbox": [ + 99, + 108, + 867, + 323 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e95ef35fb4ed816db851535c45f09716b098e5ea53d4203b38118a862e53143f.jpg", + "image_caption": [ + "Figure 8. The VQA Score-SG (prepend 'Safe Generation:' to the prompt for text-to-image alignment evaluation) $(\\%)$ on I2P-sexual datasets." + ], + "image_footnote": [], + "bbox": [ + 81, + 343, + 459, + 460 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/79dd37a9565ee692b34043b1cf98de026bad26020384f0673688ad0a5fc7f7f2.jpg", + "image_caption": [ + "Figure 9. Comparisons of single-step attention map and multi-step attention map." + ], + "image_footnote": [], + "bbox": [ + 84, + 510, + 467, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ferent steps stacked using different number of maps in Figure 9, and observe that single-step CAM can be sufficient for the detection.", + "bbox": [ + 75, + 723, + 468, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 782, + 194, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our proposed methods, DAG, offers a fine-grained approach to sexual concept erasure for safe generation. DAG leverages specific internal knowledge of diffusion models that can be activated through cross-attention layers to detect unsafe concepts. We apply fine control to the cross-attention maps by optimizing guideline token embeddings,", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "enabling the attention map to provide information about unsafe intensity and regions. This allows us to improve erasure methods based on safety guidance, addressing the limitations of unbounded guidance regions that may cause unnecessary mode shifts.", + "bbox": [ + 496, + 349, + 890, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Though Detect-and-Guide is effective at erasing nude visual content and achieves both safe and high-quality generation, some unsafe concepts may still be generated by then models. We investigate the failure cases and categorize the generation of nudity concepts into two trajectory types: The first type, easy-to-erase nudity, typically appears in the later stage of denoising. For example, a nude mark for a person in a painting emerges later than for a person in the gallery, as shown in Figure 4. This phenomenon recurs in Figure 3-(a), where three marble sculptures of different sizes require varying degrees of scaling strength to ensure they are all reliably removed. This observation motivates the design of a CAM area-basedScaler in Sec. 3.2. The second type, hard-to-erase nudity, occurs when prompts trigger memorized unsafe images, straying significantly from other safe modes that make it challenging to adjust towards a safe mode effectively. In these cases, the sampling mode collapses rapidly within the first few steps (e.g., $< 5$ sampling times), making guidance on this collapsed latent less effective. We leave the identification and mitigation of memorized unsafe images to future work.", + "bbox": [ + 496, + 436, + 892, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While the contradiction between generation performance (including prompt-following capability, generation diversity, and image quality) and erasure effectiveness is currently complex and difficult to reconcile, our work takes an initial step toward fine-grained self-regulation of T2I diffusion models that mitigates this issue to some extent. We also suggest that safety mechanisms for generative models should integrate these advancements to enhance both interpretability and usability.", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13259", + "bbox": [ + 480, + 950, + 517, + 962 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 76, + 90, + 236, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We are thankful to the shepherd and reviewers for their careful assessment and valuable suggestions, which have helped us improve this paper. This work was supported in part by the National Natural Science Foundation of China (62472096, 62172104, 62172105, 62102093, 62102091, 62302101, 62202106). Min Yang is a faculty of the Shanghai Institute of Intelligent Electronics & Systems and Engineering Research Center of Cyber Security Auditing and Monitoring, Ministry of Education, China.", + "bbox": [ + 75, + 114, + 472, + 252 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 263, + 174, + 277 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Samyadeep Basu, Nanxuan Zhao, Vlad I Morariu, Soheil Feizi, and Varun Manjunatha. Localizing and editing knowledge in text-to-image generative models. In The Twelfth International Conference on Learning Representations, 2023. 3", + "[2] James Betker, Gabriel Goh, Li Jing, Tim Brooks, Jianfeng Wang, Linjie Li, Long Ouyang, Juntang Zhuang, Joyce Lee, Yufei Guo, et al. Improving image generation with better captions. 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Defensive unlearning with adversarial training for robust concept erasure in diffusion models. arXiv preprint arXiv:2405.15234, 2024. 3, 6, 7" + ], + "bbox": [ + 78, + 90, + 468, + 486 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "13262", + "bbox": [ + 480, + 950, + 519, + 963 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/2a9b10bf-47cd-4616-ab01-1e841be5bccf_model.json b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/2a9b10bf-47cd-4616-ab01-1e841be5bccf_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cc4e1a591e819a247ed26fd9033867036ee1939e --- /dev/null +++ b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/2a9b10bf-47cd-4616-ab01-1e841be5bccf_model.json @@ -0,0 +1,1993 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.096, + 0.13, + 0.877, + 0.177 + ], + "angle": 0, + "content": "Detect-and-Guide: Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization" + }, + { + "type": "text", + "bbox": [ + 0.286, + 0.203, + 0.689, + 0.223 + ], + "angle": 0, + "content": "Feifei Li Mi Zhang† Yiming Sun Min Yang†" + }, + { + "type": "text", + "bbox": [ + 0.272, + 0.223, + 0.699, + 0.24 + ], + "angle": 0, + "content": "School of Computer Science, Fudan University, China" + }, + { + "type": "text", + "bbox": [ + 0.244, + 0.242, + 0.695, + 0.256 + ], + "angle": 0, + "content": "{ffli23@m.,mi_zhang@,ymsun24@m.,m_yang@}fudan.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.613 + ], + "angle": 0, + "content": "Text-to-image diffusion models have achieved state-of-the-art results in synthesis tasks; however, there is a growing concern about their potential misuse in creating harmful content. To mitigate these risks, post-hoc model intervention techniques, such as concept unlearning and safety guidance, have been developed. However, fine-tuning model weights or adapting the hidden states of the diffusion model operates in an uninterpretable way, making it unclear which part of the intermediate variables is responsible for unsafe generation. These interventions severely affect the sampling trajectory when erasing harmful concepts from complex, multi-concept prompts, thus hindering their practical use in real-world settings. In this work, we propose the safe generation framework Detect-and-Guide (DAG), leveraging the internal knowledge of diffusion models to perform self-diagnosis and fine-grained self-regulation during the sampling process. DAG first detects harmful concepts from noisy latents using refined cross-attention maps of optimized tokens, then applies safety" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.293, + 0.895, + 0.445 + ], + "angle": 0, + "content": "guidance with adaptive strength and editing regions to negate unsafe generation. The optimization only requires a small annotated dataset and can provide precise detection maps with generalizability and concept specificity. Moreover, DAG does not require fine-tuning of diffusion models, and therefore introduces no loss to their generation diversity. Experiments on erasing sexual content show that DAG achieves state-of-the-art safe generation performance, balancing harmfulness mitigation and text-following performance on multi-concept real-world prompts." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.474, + 0.633, + 0.49 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.895, + 0.637 + ], + "angle": 0, + "content": "In recent advancements, text-to-image diffusion models (DM) have exhibited remarkable capabilities in generating high-resolution images based on textual prompts that outperform GANs and VAEs [4]. Notably, models such as DALL-E [2, 36], MidJourney [31], and Stable Diffusion [6, 39] have achieved commercial standards, enabling a wide range of applications designed for end-users. However, growing regulatory concerns about the safety of generated images and their social impacts, such as the gen" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.621, + 0.228, + 0.636 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.646, + 0.881, + 0.815 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.831, + 0.897, + 0.916 + ], + "angle": 0, + "content": "Figure 1. Results of safe generation with sexual content erased, masks are applied for censorship purposes. Our proposed method, DAG, can leverage the internal knowledge of pretrained Text-to-Image Diffusion Models to perform fine-grained erasure of unsafe visual concepts to avoid modifying other concepts in the same image. It effectively preserves the composition of unsafe images and the appearance of objects in benign regions, achieving a favorable balance between harm mitigation and text alignment for partially harmful prompts. This approach underscores concerns about practical usability in developing safe generation methods and reveals the self-regulation capability of text-to-image diffusion models, shedding light on scalable safety alignment for image generation." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.951, + 0.52, + 0.963 + ], + "angle": 0, + "content": "13252" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.152 + ], + "angle": 0, + "content": "eration of unauthorized and Not-Safe-for-Work (NSFW) content [20, 34, 37], primarily arise from the weakness of unfiltered pretraining datasets sourced from the real world [40, 43, 45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.155, + 0.471, + 0.397 + ], + "angle": 0, + "content": "Recently, post-hoc model intervention methods for safe generation have emerged as a promising approach, enabling safe generation without the need for expensive retraining on a curated clean dataset. Unlike text or image filters that passively block unsafe content, these methods improve practical usability by directly guiding the generation process toward safe outputs. Depending on how they handle unsafe concepts, these techniques can be categorized into two types: Unlearning-based methods modify the model's distribution by aligning its internal understanding of unsafe concepts with corresponding safe ones. In contrast, guiding-based methods require no additional training; they rely on extra negative or safety prompts to define unsafe concepts and adjust the estimated noises from U-Net denoisers during the generation process, offering greater scalability potential." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.471, + 0.642 + ], + "angle": 0, + "content": "However, some of existing unlearning methods are inherently text-centric [33, 46] and unreliable when unsafe visual concepts emerge from harmful knowledge recalled by benign prompts, which represents a form of blacklist shortcut arising from the manually crafted datasets used for fine-tuning. Moreover, as demonstrated in Figure 1-(b), methods designed to erase unsafe concepts from single-concept prompts, like \"A photo of \\([c_{\\mathrm{unsafe}}]\\),\" are inadequate for real-world prompts containing multiple co-existing concepts. The lack of control in distinguishing and retaining safe concepts leads to significant mode shift between original generation and erased safe generation. Hence come our research questions: Can we design an image-centric safe generation framework to minimize the mode shift of safe generation and surmount the challenge of blacklist shortcuts?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Inspired by the understanding of cross-attention layers in diffusion models [25], as well as the token optimization methods for accurate cross-attention maps (CAM) [16, 30, 49], we propose our safe generation framework Detect-and-Guide that leverages internal knowledge of diffusion models to negate sexual content guided using detecting CAMs. The detection target for sexual content can be coarsely described by the combination of attributes \\(a \\in \\mathcal{A}\\) and specific object categories \\(o \\in \\mathcal{O}\\) (e.g., 'nude' and 'human'). The desired criteria include: (1) Generalizability to different styles, scenes, and poses. (2) Specificity to the combination of \\((a,o) \\in \\mathcal{A} \\times \\mathcal{O}\\) that should be detected; in contrast, a bare wall or a clothed human is unnecessarily to be detected. (3) Fine-grained detection with precise region mask, which excludes the background and covered part of human body. We investigate the role of cross-attention layers and manage to extract CAMs from high-level U-Net layers that" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "meet all the criteria by their characteristics of entangling relations of objects together with attributes [25]. The entanglement makes it possible to directly extract the CAMs only for paired \\((a,o)\\) and enables fine-grained guidance applied accordingly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.893, + 0.424 + ], + "angle": 0, + "content": "Starting with the guideline tokens that need to be optimized and a small annotated dataset created using grounded segmentation models, we incorporate (1) background leakage loss [49] and (2) negative sample loss [16] to optimize the embeddings for precisely extracting CAMs that aligns with the ground truth mask. During the sampling process, the optimized token embedding \\( c^* \\) is capable of detecting unsafe concepts at each timestep with generalizability and concept specificity across different scenarios, which can be competitive with supervised semantic segmentation methods at image level [30] and is naturally robust to different levels of noise, without accumulating the CAM over all timesteps. With the detection mask, we can then incorporate latent-level safety guidance to address the limitations of heavily relying on hyperparameters choices (e.g., guidance scale, guidance steps) by using CAM magnitude together with adaptive unsafe area rescaling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.893, + 0.697 + ], + "angle": 0, + "content": "The proposed method is evaluated with sexual concept erased. We propose to evaluate the safe generation performance of erased models comprehensively on three evaluation dimensions: (i) Erasing effectiveness and robustness, (ii) fine-grained erasing performance with unsafe concepts excluded and safe concept retrained, and (iii) the utility of models in benign dataset. We use NudeNet [32] score as the safety metrics, and conduct experiments in real-world sexual prompts dataset I2P [41]. We additionally introduce a novel vision-language alignment metrics VQA-score [24] to flexibly measure the text-to-image safety alignment on unsafe prompts. The utility of erased models can be evaluated by image quality (FID score) and prompt-following performance on MS-COCO [23]. Our qualitative and quantitative results show that DAG can successfully erase sexual content from generated images, achieving optimal generation performance that balancing harmful mitigation and generation quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.741 + ], + "angle": 0, + "content": "Disclaimer. The manuscript contains discussions and visual representation of NSFW content. We censor Not-Safe-for-Work (NSFW) imagery. Reader discretion is advised." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.63, + 0.772 + ], + "angle": 0, + "content": "2. Background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Text-to-Image Diffusion Models. Our paper mainly implemented with Stable Diffusion (SD) [39], one of the most popular and influential latent diffusion models (LDM), with an active community and numerous variations. LDM comprises a VAE [5, 47] that maps high-dimensional images \\( x_0 \\) into a latent space \\( z_0 = \\operatorname{E}(x_0) \\) and reconstructs them back with vector quantization \\( x_0' \\approx \\mathrm{D}(z_0) \\), and a denoiser \\( \\epsilon_{\\theta} \\) samples noise backward. The denoiser is trained using the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.952, + 0.519, + 0.963 + ], + "angle": 0, + "content": "13253" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.423, + 0.108 + ], + "angle": 0, + "content": "following mean squared error (MSE) loss objective:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.115, + 0.47, + 0.133 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {L D M}} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathrm {E} (\\mathbf {x}), \\mathbf {c}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ | | \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\mathbf {c}) | | _ {2} ^ {2} ], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.141, + 0.47, + 0.232 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}(\\cdot)\\) is the estimated noise conditioned on the noisy latent \\(z_{t}\\) at timestep \\(t\\). SD introduces text condition \\(c\\) from input prompt \\(p\\) into diffusion models through a pretrained CLIP text encoder \\(c = \\tau_{\\theta}(p)\\) [35], and incorporates cross-attention layers [48] in a U-Net denoiser that project \\(c\\) through key and value layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.249, + 0.473, + 0.613 + ], + "angle": 0, + "content": "Delving into Cross-attention Layers. Each block in U-Net denoiser is composed of self-attention, cross-attention and convolution layers. Recent works have presented causal analyses attributing generated elements to layers or neurons in the U-Net, revealing the function of cross-attention layers at different levels [1, 13, 25]. In conclusion, cross-attention layers play an important role in controlling generation in specific regions, guided by token-wise cross-attention maps (CAMs) [13]. However, CAMs that entangle both attributes (such as colors) and object category information may hinder single-concept editing [25]. Also, knowledge of different types of elements (colors, actions/poses, styles, and objects) is distributed across all layers of the U-Net [1], but with varying degrees of causal effects considering the dimension level. Moreover, by leveraging the flexibility of condition \\( c \\), the potential of diffusion models can be extended beyond image synthesis. T2I diffusion models can be used for discriminative tasks such as classification [15] (\\( \\arg \\max_i \\mathcal{L}_{\\mathrm{LDM}}(c = \\tau_\\theta(y_i)) \\)) for all labels \\( y_i \\in \\mathcal{Y} \\)) and semantic segmentation [30], achieving comparable capabilities to supervised models. These findings have inspired us to leverage the power of CAMs to detect the presence of sexual concepts at each timestep and provide a precise guidance map at pixel level for \\( z_t \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Safe Generation of Diffusion Models. The unlearning methods show promise in providing insights into functions of DM components and how they affect unsafe concept generation. For example, cross-attention refinement in the U-Net denoiser aims to reduce harmful semantics from conditional prompts [11, 27, 28, 51], while fine-tuning unconditional components (self-attention and convolutions) is aimed at erasing global concepts that arise from word combinations rather than specific individual concepts [10]. Other works provide evidence that fine-tuning the CLIP text encoder can be as effective as fine-tuning cross-attention layers [18], and that it benefits more from adversarial training than other components [52]. The refinement and fine-tuning rely on manually defined paired concepts of \\((c_{\\mathrm{unsafe}}, c_{\\mathrm{safe}} / c_{\\emptyset})\\) to supervise the unlearning. Methods that leverage the internal knowledge of diffusion models are centered around generating paired image datasets for manually crafted paired concepts [17], with the exception of the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.318, + 0.871, + 0.333 + ], + "angle": 0, + "content": "Figure 2. Token optimization for sexual content detection." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.368, + 0.895, + 0.46 + ], + "angle": 0, + "content": "method that leverages the self-discovered disentangled unsafe direction in the \\( h \\)-space (the middle bottleneck of U-Net with the highest levels of semantics) [19, 21]. However, in our work, we find that sexual content detection should fully leverage the entanglement of attributes and category information in lower-level latents, beyond the \\( h \\)-space." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.676, + 0.501 + ], + "angle": 0, + "content": "3. Detect-and-Guide" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.515, + 0.868, + 0.53 + ], + "angle": 0, + "content": "DAG comprises two key operations for safe generation:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.716 + ], + "angle": 0, + "content": "(1) Guideline detection: We first collect a small dataset to optimize embeddings of guideline tokens with novel losses to align their semantics with specific concepts, which enhances unsafe region detection (Sec. 3.1). These optimized embeddings to extract cross-attention maps (CAMs), which are capable of providing pixel-level magnitudes of sexual content that highlights the nude region, specifically for the presence of co-existing \\((a,o) =\\) (nude, human), and are generalizable when \\((a,o)\\) is further combined with non-targeted attributes such as styles, scenes, and poses. The self-diagnostic detections will then be used for self-regulation to negate unsafe generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "(2) Safe Self-regulation: We follow the implementations of safety guidance [3, 34] to refine the estimated noise \\(\\epsilon_{\\theta}(\\mathbf{z}_t,t,\\mathbf{c})\\) applied to denoise the noisy latent \\(\\mathbf{z}_t\\rightarrow \\mathbf{z}_{t - 1}\\) in a classifier-free style [14] (Sec. 3.2). We identify and inherit the advantages of safety guidance, which automatically explores a safe mode that is close to the generated unsafe mode during sampling dynamics. We overcome shortcomings such as unnecessary global changes, lack of specificity, and heavy dependence on the appropriate choice of guidance strength by (a) restricting the guided region to the detected region and (b) applying an adaptive scalar based on CAM magnitude and the area of unsafe region." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.535, + 0.895, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.952, + 0.52, + 0.964 + ], + "angle": 0, + "content": "13254" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.095, + 0.462, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.208, + 0.47, + 0.32 + ], + "angle": 0, + "content": "Figure 3. CAMs from non-optimized \\( c \\) generate a detection region of nudity that diffuses into the irrelevant background and highlight the non-target concept 'cat'. We optimize the embedding to address background leakage and lack of specificity, using pixel-level CE loss w.r.t ground truth masks. The refined CAMs are demonstrated in (a). The learned refined semantics of \\( c^* \\) generalize well to unseen test samples, as demonstrated in (b). The presence of nudity can easily be measured by CAM values greater than 0.5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.335, + 0.364, + 0.35 + ], + "angle": 0, + "content": "3.1. CAM-based Guideline Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.47, + 0.527 + ], + "angle": 0, + "content": "In this section, we describe the way of deriving detection maps from cross-attention layers in the U-net. As demonstrated in Figure 2, the noisy latent \\( z_{t} \\) and conditional embedding from prompt \\( c_{p} \\) are fed forward the U-Net, and we cache all hidden states in cross-attention layers, which is denoted as \\( h_{t}^{l} \\). The original CA operation during sampling process will project visual latents \\( h_{t}^{l} \\) to queries \\( Q = W_{Q}^{l} \\cdot h_{t}^{l} \\), and project original condition \\( c_{p} \\) to keys and values. In our work, we use the static hidden states and projection weights \\( W_{Q}^{l}, W_{K}^{l} \\) to calculate cross-attention between guideline embeddings \\( c \\) and \\( h_{t}^{l} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.47, + 0.775 + ], + "angle": 0, + "content": "Limitations of Non-optimized Guideline Tokens. We initialize \\( c \\) with token embeddings of 'nude person', which is desired to give high attention scores on the concept that match the description. However, as shown in Figure 3-(a), \\( \\mathrm{CAM}(c) \\) premises to the background and detects nudity concepts on a cat. The first phenomenon is identified as cross-attention leakage problem. In previous work, for the CAM which is extracted using original prompts, the text encoder that apply self-attention layers on token sequences make the embeddings \\( c_{p} \\) contain rich semantic information of the context, as well as the special tokens, therefore causing the leakage to the background [49]. The second problem of unexpectedly highlighting the cat which is unrelated to 'nude person' mainly arises from the rich semantics of 'nude', as the cat is sometimes considered to be unclothed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Token Optimization. To address these problems, we suggest the token optimization approach [30] that can effectively refine the resulting CAMs with semantics generalizability and specificity on the target combination of attribute and object category. A small dataset contains safe images and annotated unsafe images is required for optimizing the embedding. We first instruct LLM to generate text-to-image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.303 + ], + "angle": 0, + "content": "prompts with nude concepts, then generate images using T2I diffusion models. We select five unsafe and three safe images with various styles (e.g., sculpture, painting, and photograph) and with several non-target concepts (dogs and cats) to help distinguish the nudity of human. Noted that unsafe annotations can be constructed easily with GroundedSAM [26, 38]. We detail the annotating pipeline in Figure 2-(a): By incorporating positive textual labels and negative textual labels, we can exclude non-sexual part of human like hair or face from the body segmentation results and give precise GT masks. For safe images, their annotations are simply initialized as zero masks indicating no nude concepts should be detected. We denoted the small dataset of generated images and annotations as \\(\\mathcal{D} = \\{\\mathcal{X},\\mathcal{Y}\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.409 + ], + "angle": 0, + "content": "Given the dataset, we cache their intermediate hidden states before cross-attention layers over all sampling timesteps \\(\\{h_t^l [i]|i\\in \\mathcal{X},t\\sim [1,50]\\}\\). Resulting maps for the embedding \\(c\\) can then be derived as \\(\\mathrm{CAM}(h_t^l [i],c)\\) and interpolated to the size of images (i.e., \\(\\hat{A}\\in \\mathbb{R}^{K\\times H\\times W}\\)). We define the CAM loss for detecting regions with specific target concepts as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.419, + 0.892, + 0.484 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C A M}} = \\mathbb {E} _ {(i, y) \\sim (\\mathcal {X}, \\mathcal {Y})} \\mathbb {E} _ {t \\sim \\mathcal {T}, l \\sim \\mathcal {L}} \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\sum_ {h = 1} ^ {H} \\sum_ {w = 1} ^ {W} [ \\\\ - \\operatorname {O n e - h o t} \\left(y ^ {G T}\\right) _ {h, w} \\cdot \\log \\left(\\hat {A} _ {k, h, w} \\left(h _ {t} ^ {l} [ i ], c\\right)\\right), \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.568 + ], + "angle": 0, + "content": "where \\(\\mathcal{T}\\) is a set of all sampling timesteps, \\(K\\) is the number of guideline tokens, and \\(\\mathcal{L}\\) denotes the chosen layers to extract the CAMs. We average the loss of each CAM over tokens, and the values of \\(\\hat{A}\\) are normalized to [0,1] with min-max scalar for calculating the logits." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.689 + ], + "angle": 0, + "content": "Noted that hidden states in the U-Net of SD model have three size dimensions \\([16^2, 32^2, 64^2]\\) with difference levels of semantics. We assign layer-wise learnable weights initialized by all ones and find that weights of larger CAMs are monotonic decreasing. This means that the hidden state with resolution of 64 contains the lowest level of semantics, and is too noisy for token optimization. Thus we choose \\(\\mathcal{L} = \\{l|h_t^l.\\mathrm{size}\\in [16^2,32^2]\\}\\) to extract CAM layers." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.689, + 0.892, + 0.718 + ], + "angle": 0, + "content": "To summary, our optimizing objective can be formalized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.731, + 0.891, + 0.752 + ], + "angle": 0, + "content": "\\[\nc ^ {*} = \\min _ {c} \\left[ \\mathbb {E} _ {(i, y) \\sim (\\mathcal {X}, \\mathcal {Y})} \\mathcal {L} _ {\\mathrm {C A M}} \\right] \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.762, + 0.892, + 0.791 + ], + "angle": 0, + "content": "and we use a mini-batch of size two where one sample from unsafe subset and another from the safe subset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Improved Guideline Detection. The detection map of optimized guideline token embeddings, \\(\\hat{A}(c^{*})\\), on trained samples is demonstrated in Figure 3-(a), and that on randomly chosen samples from unseen datasets is shown in Figure 3-(b). The CA leakage to the background is significantly mitigated and target-concept specificity is improved." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.951, + 0.518, + 0.963 + ], + "angle": 0, + "content": "13255" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.885, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.336, + 0.895, + 0.407 + ], + "angle": 0, + "content": "Figure 4. Overview of Our Proposed Safe Generation Framework, Detect-and-Guide (DAG). The notations for (a) Original Generation can be found in Sec. 2. In (b), DAG utilizes guideline token embeddings \\( c^* \\) to perform self-diagnostics by calculating cross-attention maps (CAM) at higher-level hidden states of the U-Net. The \\( c^* \\) is optimized in advance on a small annotated dataset for precisely segmenting unsafe regions, addressing the problem of cross-attention leakage [49]. In (c), DAG achieves safe self-regulation by editing the detected unsafe regions. This editing process uses pixel-level magnitudes that are adaptively determined based on region area and CAM values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.471, + 0.527 + ], + "angle": 0, + "content": "As further illustrated in Figure 5, CAMs for non-target concepts, such as 'a nude wall', will contain only a few values larger than 0.5 (i.e., they will not be detected), which can serve as an indicator of the presence of unsafe content. We analyze the distribution of CAM values in Sec. 3.2 to develop an adaptive scaling strategy that best balancing sexual content erasure and mode preservation." + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.536, + 0.42, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.699 + ], + "angle": 0, + "content": "Figure 5. The comparison of cross-attention map with non-optimized token embeddings and their effect on performing the self-regulation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.265, + 0.728 + ], + "angle": 0, + "content": "3.2. Safe Self-regulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.81 + ], + "angle": 0, + "content": "With the attention maps of guideline detection, we then utilize the idea of classifier-free guidance [14] to adjust a noisy latent in an unsafe mode to a nearby safe mode during sampling following the implementation of safety guidance [3, 41]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.902 + ], + "angle": 0, + "content": "The classifier-free guidance introduces a null-text embedding \\(\\varnothing = \\tau_{\\theta}({}^{\\prime \\prime \\prime \\prime})\\) as the unconditional generative probability beyond the conditional probability to estimate the gradient of an implicit classifier. We denote unconditional estimated noise as \\(\\epsilon^{\\emptyset}\\), conditional estimated noise as \\(\\epsilon^{p}\\) and the scale of guidance as \\(s_g\\) (default as 7.5 for SDv1.4)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.422, + 0.892, + 0.499 + ], + "angle": 0, + "content": "Similarly, safety guidance [41] introduces a safety condition \\( c_{s} = \\tau_{\\theta}(p_{s}) \\) and the corresponding estimated noise \\( \\epsilon^{c_s} \\) that reuses the implicit Bayesian classifier for conditional probability [14] to adjust the estimated gradient with selective pixel-level scale map \\( \\mathbf{S}_{c_s}\\cdot \\mathbf{M}_{c_s} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.506, + 0.891, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\epsilon} _ {\\theta} (x _ {t}, t, c _ {p}) ^ {\\mathrm {C F}} = (1 - s _ {g}) \\underbrace {\\epsilon_ {\\theta} (x _ {t} , t , \\varnothing)} _ {\\epsilon^ {\\emptyset}} + s _ {g} \\underbrace {\\epsilon_ {\\theta} (x _ {t} , t , c _ {p})} _ {\\epsilon^ {p}} \\\\ = \\epsilon^ {\\varnothing} + s _ {g} \\underbrace {\\left(\\epsilon^ {\\varnothing} - \\epsilon^ {p}\\right)} _ {\\tilde {\\epsilon} ^ {p}} \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.503, + 0.58, + 0.889, + 0.599 + ], + "angle": 0, + "content": "\\[\n\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, t, c _ {p}, c _ {s}\\right) ^ {\\text {S a f e}} = \\left(1 - s _ {g}\\right) \\epsilon^ {\\varnothing} + s _ {g} \\left(\\epsilon^ {p} - \\mathbf {S} _ {c _ {s}} \\cdot \\mathbf {M} _ {c _ {s}} \\epsilon^ {c _ {s}}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.791 + ], + "angle": 0, + "content": "For the purpose of safe generation, guidance-based methods are advanced in the capability of discovering the direction of a nearby safe mode given an existing unsafe mode. However, the safety guidance applied in an early stage will introduce severe mode shift that affect the generation quality, with necessity of warm-up steps \\(\\underline{t}_{c_s}\\) to regulate the mode change. Therefore, we leverage detection maps \\(\\hat{A}(c^*)\\) as a gate function to enable adaptive guidance scale (stronger when detected with higher confidence) that also works at higher noise level and prevent severe mode shift. The overall comparison of how our method apply safety guidance is different from existing methods is shown in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.792, + 0.893, + 0.902 + ], + "angle": 0, + "content": "The safety scale map \\(\\mathbf{S}_{c_s}\\) used in DAG depends on (i) a scalar denoted as \\(\\mathrm{Area}_{0.5}(\\hat{A})\\), which highlights the area of detected unsafe region with a confidence no less than 0.5, as the yellow region shown in Figure 4-(b), along with a base weight of 5 for pixel editing \\(\\overline{s}_c = \\frac{5}{H\\times W}\\); and (ii) a magnitude scalar \\(T_{0.01}(\\hat{A})\\) based on confidence value of attention map \\(\\hat{A} = \\{a\\}_{:h,w}\\), which assigns an appropri" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.952, + 0.519, + 0.963 + ], + "angle": 0, + "content": "13256" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.286, + 0.09, + 0.683, + 0.104 + ], + "angle": 0, + "content": "Table 1. Notations for classifier-free guidance and safety guidance." + }, + { + "type": "table", + "bbox": [ + 0.166, + 0.107, + 0.798, + 0.215 + ], + "angle": 0, + "content": "
    CF [14]SLD [41]SEGA [3]DAG (Ours)
    ε∅1 - sg1 - sg + sg · Scs · Mcs
    εpsgsg
    εcs--sg · Scs · Mcs
    Scs-max(εp - εcs, 1)scs(¯¯¯¯sc · Area0.5(Â)) ⊙ T0.01(Â)
    Mcs-I(εcschw + λ > εpchw)chwI[¯¯¯¯epsilonchw ∈ top-p(¯¯¯¯epsiloncs)]chwI[ ≥ 0.01]:hw ⊙ McsSEGA/SLD
    tcs-7 (strong), 10 (medium), 15 (weak)105
    " + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.233, + 0.473, + 0.34 + ], + "angle": 0, + "content": "ate editing scale only for pixels whose confidence satisfies \\(0.01 \\leq a \\leq 1\\) by rescaling their attention values to range \\(1 \\leq T_{0.01}(a) \\leq 5\\). Besides the scale map, we simply set a gate function \\(\\hat{A} \\geq 0.01\\) to the safety selective mask of existing methods, as the green region demonstrated in Figure 4-(b). We use \\(\\mathbf{M}_{c_s}^{\\mathrm{SEGA}}\\) in main experiments and compare different safety guidance methods in Supp. B." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.353, + 0.21, + 0.37 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.378, + 0.257, + 0.394 + ], + "angle": 0, + "content": "4.1. Evaluation Setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.47, + 0.446 + ], + "angle": 0, + "content": "In this section, we comprehensively evaluate the effectiveness of DAG in erasing sexual content from three perspectives:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.47, + 0.629 + ], + "angle": 0, + "content": "Erasing Effectiveness and Robustness. We utilize 931 sexual prompts from real-world harmful prompts benchmark Inappropriate Image Prompts (I2P) [41] to evaluate effectiveness, denoted as I2P-sexual. Additionally, we filter a subset of complex prompts containing terms, resulting in a 439-prompt subset, denoted as I2P-sexual-complex. To assess robustness, we further leverage two black-box adversarial prompt datasets, Ring-A-Bell (RAB)[46] and MMA[50]. We use 1,000 released adversarial prompts from MMA focused on sexual content generation, and we implement RAB attacks on I2P-sexual-complex, resulting in 439 adversarial prompts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.795 + ], + "angle": 0, + "content": "We employ a YOLO-based nudity detector NudeNet [32] to evaluate unsafe content in generated images from I2P-sexual, RAB and MMA, where each prompt generates four images using fixed seeds, producing a total of 9480 images per method. We apply NudeNet's five unsafe classes and a confidence threshold of 0.6 to calculate the evaluation results. We report the number of detected unsafe classes as NudeNet Number (N3), and calculate the Erase Rate (ER) compared to undefended SDv1.4 as follows: \\(\\mathrm{ER} = 1 - \\frac{\\mathrm{N3}_{\\mathrm{defense}}}{\\mathrm{N3}_{\\mathrm{SDv1.4}}}\\), where all unsafe concepts erased will give a \\(100\\%\\) ER." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Fine-grained erase performance. We consider that a harmful prompt may contain multiple concepts, and thus the design principle of safe generation should account for prompt-following performance on the remaining safe concepts. To assess this, we introduce an advanced metric, VQA Score [24], which evaluates text-to-image alignment using pre-trained large VLMs (CLIP-FlanT5-XL). We eval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.233, + 0.892, + 0.353 + ], + "angle": 0, + "content": "uate the alignment capability of the erased models on I2Psexual dataset by prepending a short task description 'Safe Generation:' to the prompt before feeding the (prompt, image) pair into the VLM evaluator. This metric, denoted as VQA Score-SG, reflects the self-regulation capability of safely following the harmful prompt. We use VQA Score as a sanity check to ensure safety methods 018 do not degrade normal generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.354, + 0.892, + 0.49 + ], + "angle": 0, + "content": "Model Utility. We resample 1000 prompts from the MS-COCO validation dataset [23] as benign prompts to evaluate model utility, denoted as COCO-1K. Image quality metrics include \\( FID_{\\mathrm{real}} \\), which measures the similarity between generated images generated by erased models and real images from MS-COCO, and \\( FID_{\\mathrm{SDv1.4}} \\), which assesses the mode shift introduced by erasing methods. We also calculate the VQA Score on resampled data to evaluate generation capability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.893, + 0.717 + ], + "angle": 0, + "content": "Baselines. In our experiments, we compare against nine popular unlearning methods under different settings, resulting in a total of eleven erasing baselines (ESD [9], SLD-(weak, medium, strong) [42], SPM [29], SA [12], SalUn [8], Self-Dis [22], SEGA [3], MACE [27], AdvUnlearn [52]). The baseline model with no defense is SDv1.4, and we also conduct experiments on SDv2.1, which training data is filtered by an NSFW detector, to serve as a retraining baseline. For the fine-tuning-based erasing methods, we download their official checkpoints for erasing the concept of nudity. For the safety guidance-based methods, we run their official generating scripts with hyper-parameters from their paper. For SEGA, we set the scale of semantic guidance to 10 (default as 5) and reverse the guidance for effectively removing nudity from generation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.685, + 0.741 + ], + "angle": 0, + "content": "4.2. Erase Performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Erase Effectiveness and Model Utility Perservation We generate 9840 images for each method, and report the NudeNet detection results of five unsafe classes. The erasure effectiveness of the proposed method compared with baselines are demonstrate in Table 2. Our method, DAG, outperforms all guidance-based methods (three variants of SLD and SEGA) and achieves competitive erasure performance compared to fine-tuning-based methods (SA, SPM) and SDID. Fine-tuning-based methods with strong erasure performance come at the cost of lower generation quality on" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.952, + 0.519, + 0.963 + ], + "angle": 0, + "content": "13257" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.091, + 0.687, + 0.284 + ], + "angle": 0, + "content": "
    MethodsGeneration Quality (COCO-1K)Erase Effectiveness (I2P-sexual)
    VQA Score\\( FID_{\\text{real}} \\downarrow \\)\\( FID_{\\text{SDv1.4}} \\downarrow \\)Total↓ButtocksChest(F)Genitalia(F)Chest(M)Genitalia(M)
    SDv1.4 [39]0.7058.03010708383854914
    SLD-weak [41]0.6859.3823.348566267148723
    SLD-medium [41]0.7061.1531.736605550633615
    SLD-strong [41]0.6462.8741.14207271447272
    SEGA [3]0.7058.9533.4715511873513
    SDID [21]0.7357.931.521812512212166
    ESD-u [10]0.6358.0150.55631492110
    SA [12]0.6763.8353.9711411841450
    SalUn [7]0.4280.2787.68000000
    SPM [29]0.7157.6235.372083813917131
    MACE [27]0.5955.9951.01565363102
    AdvUnlearn [52]0.5460.0244.561018001
    DAG (ours)0.7258.2223.67861471325
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.29, + 0.69, + 0.334 + ], + "angle": 0, + "content": "Table 2. Assessment of Unsafe Concept Erase: Evaluation of FIDs and VQA scores on COCO-1K and the count of unsafe concepts detected by NudeNet on I2P-sexual. We use best, second-best and third-best to highlight the top-3 results, respectively. Italicized methods are fine-tuning-based." + }, + { + "type": "image", + "bbox": [ + 0.707, + 0.091, + 0.887, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.703, + 0.277, + 0.892, + 0.333 + ], + "angle": 0, + "content": "Figure 6. Erase rate \\((\\%)\\) on I2P-sexual, measuring the relative deduction of unsafe concepts compared to SDv1.4." + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.377, + 0.291, + 0.437 + ], + "angle": 0, + "content": "woman with shiny skin lying on the grass dressed in roman clothes, ultra detailed, Guido Reni style" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.479, + 0.285, + 0.563 + ], + "angle": 0, + "content": "'high resolution \\(8k_{\\mathrm{e}}\\) close up portrait photograph of Selena Gomez, dressed in bikini, standing near the beach, vogue photoshoot" + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.347, + 0.788, + 0.565 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.569, + 0.89, + 0.598 + ], + "angle": 0, + "content": "Figure 7. Qualitative Experiments. The examples are randomly sampled from I2P-sexual. Note that not all prompts in I2P-sexual can generate harmful images, and the regional specification advantages of DAG can be observed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.471, + 0.765 + ], + "angle": 0, + "content": "the benign dataset COCO-1K. For example, the strongest defense methods suffer from severe distribution shifts when generating non-target concepts and fail to achieve text-to-image alignment, as quantitatively observed by a significantly lower VQA Score (0.42) compared to ours (0.72) and SDv1.4 (0.70). We visualize the trade-off between generation quality and erasure performance in Figure 1 (right), showing that our method, without expensive retraining or fine-tuning, achieves the optimal balance by incorporating optimized token-based detection maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Erase Robustness. We conduct robustness experiments using two black-box adversarial prompt attacks: Ring-A-Bell and MMA. Ring-A-Bell is based on CLIP-embedding inversion to reconstruct the token sequence with similar semantics to an unsafe embedding. MMA conducts a sensitive word replacement attack and generates adversarial prompts in natural language. We present the results in Ta" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.613, + 0.892, + 0.659 + ], + "angle": 0, + "content": "ble 3. Note that our results align with fine-tuning-based methods in robustness evaluations, without any weight tuning or modifications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Fine-grained Erase Performance. We demonstrate the VQA Score-SG in Figure 8 to measure the text-to-image alignment degree of erased methods on the datasets I2P-sexual. DAG ranks the second in the results, and primarily benefit from the restriction of guidance in detected unsafe region, which introduce slightly background modification as demonstrated in Figure 7." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.676, + 0.817 + ], + "angle": 0, + "content": "4.3. Parameters Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Although the optimized embeddings can meet both generalizability and specificity, one remaining question is how the detection performance varies across different noise levels and whether it can be aggregated using a smaller number of maps, such as one. We visualize the detection map at dif" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.952, + 0.519, + 0.963 + ], + "angle": 0, + "content": "13258" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.09, + 0.891, + 0.104 + ], + "angle": 0, + "content": "Table 3. Erasure Robustness for Nudity: Best, Second-best and Third-best highlight top-3 results. Italicized methods are fine-tuning-based." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.109, + 0.868, + 0.324 + ], + "angle": 0, + "content": "
    Defense MethodsRing-a-bell Adversarial PromptsMMA Adversarial Prompts
    Erase Rate↑ (%)Total↓ButtocksChest (F)Genitalia (F)Chest (M)Genitalia (M)Erase Rate↑ (%)Total↓ButtocksChest (F)Genitalia (F)Chest (M)Genitalia (M)
    SDv1.40.003279115249€342266600.002732413154€83301391
    SLD-weak(7.44)3523107266543526848(1.57)2775433151782336407
    SLD-medium(7.11)3512742725433246341.542690410142095360405
    SLD-strong43.15186433163810090348.43140928369233174227
    SEGA66.54109723768452511065.419452333007248157
    SDID87.6840434309124547.142537373144474306340
    ESD-u87.74402143271346297.806020222214
    SA48.031704431393146122089.602846219012011
    SalUn100.0000000099.93202000
    SPM87.07424293172255149.34138430866639208163
    MACE99.57142921099.411654016
    AdvUnlearn100.0000000099.491428022
    DAG (ours)88.14389102067166077.601276121854183113
    " + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.344, + 0.46, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.464, + 0.47, + 0.504 + ], + "angle": 0, + "content": "Figure 8. The VQA Score-SG (prepend 'Safe Generation:' to the prompt for text-to-image alignment evaluation) \\((\\%)\\) on I2P-sexual datasets." + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.511, + 0.468, + 0.667 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.682, + 0.47, + 0.71 + ], + "angle": 0, + "content": "Figure 9. Comparisons of single-step attention map and multi-step attention map." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.724, + 0.47, + 0.768 + ], + "angle": 0, + "content": "ferent steps stacked using different number of maps in Figure 9, and observe that single-step CAM can be sufficient for the detection." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.784, + 0.196, + 0.8 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our proposed methods, DAG, offers a fine-grained approach to sexual concept erasure for safe generation. DAG leverages specific internal knowledge of diffusion models that can be activated through cross-attention layers to detect unsafe concepts. We apply fine control to the cross-attention maps by optimizing guideline token embeddings," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.892, + 0.426 + ], + "angle": 0, + "content": "enabling the attention map to provide information about unsafe intensity and regions. This allows us to improve erasure methods based on safety guidance, addressing the limitations of unbounded guidance regions that may cause unnecessary mode shifts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.893, + 0.754 + ], + "angle": 0, + "content": "Though Detect-and-Guide is effective at erasing nude visual content and achieves both safe and high-quality generation, some unsafe concepts may still be generated by then models. We investigate the failure cases and categorize the generation of nudity concepts into two trajectory types: The first type, easy-to-erase nudity, typically appears in the later stage of denoising. For example, a nude mark for a person in a painting emerges later than for a person in the gallery, as shown in Figure 4. This phenomenon recurs in Figure 3-(a), where three marble sculptures of different sizes require varying degrees of scaling strength to ensure they are all reliably removed. This observation motivates the design of a CAM area-basedScaler in Sec. 3.2. The second type, hard-to-erase nudity, occurs when prompts trigger memorized unsafe images, straying significantly from other safe modes that make it challenging to adjust towards a safe mode effectively. In these cases, the sampling mode collapses rapidly within the first few steps (e.g., \\(< 5\\) sampling times), making guidance on this collapsed latent less effective. We leave the identification and mitigation of memorized unsafe images to future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "While the contradiction between generation performance (including prompt-following capability, generation diversity, and image quality) and erasure effectiveness is currently complex and difficult to reconcile, our work takes an initial step toward fine-grained self-regulation of T2I diffusion models that mitigates this issue to some extent. We also suggest that safety mechanisms for generative models should integrate these advancements to enhance both interpretability and usability." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.952, + 0.519, + 0.963 + ], + "angle": 0, + "content": "13259" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.238, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.473, + 0.253 + ], + "angle": 0, + "content": "We are thankful to the shepherd and reviewers for their careful assessment and valuable suggestions, which have helped us improve this paper. This work was supported in part by the National Natural Science Foundation of China (62472096, 62172104, 62172105, 62102093, 62102091, 62302101, 62202106). Min Yang is a faculty of the Shanghai Institute of Intelligent Electronics & Systems and Engineering Research Center of Cyber Security Auditing and Monitoring, Ministry of Education, China." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.264, + 0.175, + 0.279 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.288, + 0.47, + 0.356 + ], + "angle": 0, + "content": "[1] Samyadeep Basu, Nanxuan Zhao, Vlad I Morariu, Soheil Feizi, and Varun Manjunatha. Localizing and editing knowledge in text-to-image generative models. In The Twelfth International Conference on Learning Representations, 2023. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.359, + 0.47, + 0.427 + ], + "angle": 0, + "content": "[2] James Betker, Gabriel Goh, Li Jing, Tim Brooks, Jianfeng Wang, Linjie Li, Long Ouyang, Juntang Zhuang, Joyce Lee, Yufei Guo, et al. Improving image generation with better captions. 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Defensive unlearning with adversarial training for robust concept erasure in diffusion models. arXiv preprint arXiv:2405.15234, 2024. 3, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.952, + 0.52, + 0.964 + ], + "angle": 0, + "content": "13262" + } + ] +] \ No newline at end of file diff --git a/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/2a9b10bf-47cd-4616-ab01-1e841be5bccf_origin.pdf b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/2a9b10bf-47cd-4616-ab01-1e841be5bccf_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3fdcf3bd5071fc55bb8b2155483a713210678169 --- /dev/null +++ b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/2a9b10bf-47cd-4616-ab01-1e841be5bccf_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f10749ae24883a614e6a0eb8bcb48dd74aaba172f28cbf9c72e665e3fe99880e +size 6110757 diff --git a/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/full.md b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c3a51661e2536a2943413873716dd8e965afb6ee --- /dev/null +++ b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/full.md @@ -0,0 +1,267 @@ +# Detect-and-Guide: Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization + +Feifei Li Mi Zhang† Yiming Sun Min Yang† + +School of Computer Science, Fudan University, China + +{ffli23@m.,mi_zhang@,ymsun24@m.,m_yang@}fudan.edu.cn + +# Abstract + +Text-to-image diffusion models have achieved state-of-the-art results in synthesis tasks; however, there is a growing concern about their potential misuse in creating harmful content. To mitigate these risks, post-hoc model intervention techniques, such as concept unlearning and safety guidance, have been developed. However, fine-tuning model weights or adapting the hidden states of the diffusion model operates in an uninterpretable way, making it unclear which part of the intermediate variables is responsible for unsafe generation. These interventions severely affect the sampling trajectory when erasing harmful concepts from complex, multi-concept prompts, thus hindering their practical use in real-world settings. In this work, we propose the safe generation framework Detect-and-Guide (DAG), leveraging the internal knowledge of diffusion models to perform self-diagnosis and fine-grained self-regulation during the sampling process. DAG first detects harmful concepts from noisy latents using refined cross-attention maps of optimized tokens, then applies safety + +guidance with adaptive strength and editing regions to negate unsafe generation. The optimization only requires a small annotated dataset and can provide precise detection maps with generalizability and concept specificity. Moreover, DAG does not require fine-tuning of diffusion models, and therefore introduces no loss to their generation diversity. Experiments on erasing sexual content show that DAG achieves state-of-the-art safe generation performance, balancing harmfulness mitigation and text-following performance on multi-concept real-world prompts. + +# 1. Introduction + +In recent advancements, text-to-image diffusion models (DM) have exhibited remarkable capabilities in generating high-resolution images based on textual prompts that outperform GANs and VAEs [4]. Notably, models such as DALL-E [2, 36], MidJourney [31], and Stable Diffusion [6, 39] have achieved commercial standards, enabling a wide range of applications designed for end-users. However, growing regulatory concerns about the safety of generated images and their social impacts, such as the gen + +![](images/d6df31427c38b58f85a0acc3085b2385e1ba74b9c098131cf196ed222eefeba8.jpg) +Figure 1. Results of safe generation with sexual content erased, masks are applied for censorship purposes. Our proposed method, DAG, can leverage the internal knowledge of pretrained Text-to-Image Diffusion Models to perform fine-grained erasure of unsafe visual concepts to avoid modifying other concepts in the same image. It effectively preserves the composition of unsafe images and the appearance of objects in benign regions, achieving a favorable balance between harm mitigation and text alignment for partially harmful prompts. This approach underscores concerns about practical usability in developing safe generation methods and reveals the self-regulation capability of text-to-image diffusion models, shedding light on scalable safety alignment for image generation. + +eration of unauthorized and Not-Safe-for-Work (NSFW) content [20, 34, 37], primarily arise from the weakness of unfiltered pretraining datasets sourced from the real world [40, 43, 45]. + +Recently, post-hoc model intervention methods for safe generation have emerged as a promising approach, enabling safe generation without the need for expensive retraining on a curated clean dataset. Unlike text or image filters that passively block unsafe content, these methods improve practical usability by directly guiding the generation process toward safe outputs. Depending on how they handle unsafe concepts, these techniques can be categorized into two types: Unlearning-based methods modify the model's distribution by aligning its internal understanding of unsafe concepts with corresponding safe ones. In contrast, guiding-based methods require no additional training; they rely on extra negative or safety prompts to define unsafe concepts and adjust the estimated noises from U-Net denoisers during the generation process, offering greater scalability potential. + +However, some of existing unlearning methods are inherently text-centric [33, 46] and unreliable when unsafe visual concepts emerge from harmful knowledge recalled by benign prompts, which represents a form of blacklist shortcut arising from the manually crafted datasets used for fine-tuning. Moreover, as demonstrated in Figure 1-(b), methods designed to erase unsafe concepts from single-concept prompts, like "A photo of $[c_{\mathrm{unsafe}}]$ ," are inadequate for real-world prompts containing multiple co-existing concepts. The lack of control in distinguishing and retaining safe concepts leads to significant mode shift between original generation and erased safe generation. Hence come our research questions: Can we design an image-centric safe generation framework to minimize the mode shift of safe generation and surmount the challenge of blacklist shortcuts? + +Inspired by the understanding of cross-attention layers in diffusion models [25], as well as the token optimization methods for accurate cross-attention maps (CAM) [16, 30, 49], we propose our safe generation framework Detect-and-Guide that leverages internal knowledge of diffusion models to negate sexual content guided using detecting CAMs. The detection target for sexual content can be coarsely described by the combination of attributes $a \in \mathcal{A}$ and specific object categories $o \in \mathcal{O}$ (e.g., 'nude' and 'human'). The desired criteria include: (1) Generalizability to different styles, scenes, and poses. (2) Specificity to the combination of $(a,o) \in \mathcal{A} \times \mathcal{O}$ that should be detected; in contrast, a bare wall or a clothed human is unnecessarily to be detected. (3) Fine-grained detection with precise region mask, which excludes the background and covered part of human body. We investigate the role of cross-attention layers and manage to extract CAMs from high-level U-Net layers that + +meet all the criteria by their characteristics of entangling relations of objects together with attributes [25]. The entanglement makes it possible to directly extract the CAMs only for paired $(a,o)$ and enables fine-grained guidance applied accordingly. + +Starting with the guideline tokens that need to be optimized and a small annotated dataset created using grounded segmentation models, we incorporate (1) background leakage loss [49] and (2) negative sample loss [16] to optimize the embeddings for precisely extracting CAMs that aligns with the ground truth mask. During the sampling process, the optimized token embedding $c^*$ is capable of detecting unsafe concepts at each timestep with generalizability and concept specificity across different scenarios, which can be competitive with supervised semantic segmentation methods at image level [30] and is naturally robust to different levels of noise, without accumulating the CAM over all timesteps. With the detection mask, we can then incorporate latent-level safety guidance to address the limitations of heavily relying on hyperparameters choices (e.g., guidance scale, guidance steps) by using CAM magnitude together with adaptive unsafe area rescaling. + +The proposed method is evaluated with sexual concept erased. We propose to evaluate the safe generation performance of erased models comprehensively on three evaluation dimensions: (i) Erasing effectiveness and robustness, (ii) fine-grained erasing performance with unsafe concepts excluded and safe concept retrained, and (iii) the utility of models in benign dataset. We use NudeNet [32] score as the safety metrics, and conduct experiments in real-world sexual prompts dataset I2P [41]. We additionally introduce a novel vision-language alignment metrics VQA-score [24] to flexibly measure the text-to-image safety alignment on unsafe prompts. The utility of erased models can be evaluated by image quality (FID score) and prompt-following performance on MS-COCO [23]. Our qualitative and quantitative results show that DAG can successfully erase sexual content from generated images, achieving optimal generation performance that balancing harmful mitigation and generation quality. + +Disclaimer. The manuscript contains discussions and visual representation of NSFW content. We censor Not-Safe-for-Work (NSFW) imagery. Reader discretion is advised. + +# 2. Background + +Text-to-Image Diffusion Models. Our paper mainly implemented with Stable Diffusion (SD) [39], one of the most popular and influential latent diffusion models (LDM), with an active community and numerous variations. LDM comprises a VAE [5, 47] that maps high-dimensional images $x_0$ into a latent space $z_0 = \operatorname{E}(x_0)$ and reconstructs them back with vector quantization $x_0' \approx \mathrm{D}(z_0)$ , and a denoiser $\epsilon_{\theta}$ samples noise backward. The denoiser is trained using the + +following mean squared error (MSE) loss objective: + +$$ +\mathcal {L} _ {\mathrm {L D M}} = \mathbb {E} _ {\mathbf {z} \sim \mathrm {E} (\mathbf {x}), \mathbf {c}, \epsilon \sim \mathcal {N} (0, 1), t} [ | | \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {t}, t, \mathbf {c}) | | _ {2} ^ {2} ], \tag {1} +$$ + +where $\epsilon_{\theta}(\cdot)$ is the estimated noise conditioned on the noisy latent $z_{t}$ at timestep $t$ . SD introduces text condition $c$ from input prompt $p$ into diffusion models through a pretrained CLIP text encoder $c = \tau_{\theta}(p)$ [35], and incorporates cross-attention layers [48] in a U-Net denoiser that project $c$ through key and value layers. + +Delving into Cross-attention Layers. Each block in U-Net denoiser is composed of self-attention, cross-attention and convolution layers. Recent works have presented causal analyses attributing generated elements to layers or neurons in the U-Net, revealing the function of cross-attention layers at different levels [1, 13, 25]. In conclusion, cross-attention layers play an important role in controlling generation in specific regions, guided by token-wise cross-attention maps (CAMs) [13]. However, CAMs that entangle both attributes (such as colors) and object category information may hinder single-concept editing [25]. Also, knowledge of different types of elements (colors, actions/poses, styles, and objects) is distributed across all layers of the U-Net [1], but with varying degrees of causal effects considering the dimension level. Moreover, by leveraging the flexibility of condition $c$ , the potential of diffusion models can be extended beyond image synthesis. T2I diffusion models can be used for discriminative tasks such as classification [15] ( $\arg \max_i \mathcal{L}_{\mathrm{LDM}}(c = \tau_\theta(y_i))$ ) for all labels $y_i \in \mathcal{Y}$ ) and semantic segmentation [30], achieving comparable capabilities to supervised models. These findings have inspired us to leverage the power of CAMs to detect the presence of sexual concepts at each timestep and provide a precise guidance map at pixel level for $z_t$ . + +Safe Generation of Diffusion Models. The unlearning methods show promise in providing insights into functions of DM components and how they affect unsafe concept generation. For example, cross-attention refinement in the U-Net denoiser aims to reduce harmful semantics from conditional prompts [11, 27, 28, 51], while fine-tuning unconditional components (self-attention and convolutions) is aimed at erasing global concepts that arise from word combinations rather than specific individual concepts [10]. Other works provide evidence that fine-tuning the CLIP text encoder can be as effective as fine-tuning cross-attention layers [18], and that it benefits more from adversarial training than other components [52]. The refinement and fine-tuning rely on manually defined paired concepts of $(c_{\mathrm{unsafe}}, c_{\mathrm{safe}} / c_{\emptyset})$ to supervise the unlearning. Methods that leverage the internal knowledge of diffusion models are centered around generating paired image datasets for manually crafted paired concepts [17], with the exception of the + +![](images/edd69fa5282a27286c222546c2ffdba81b487f415f432698b4912d08345e8421.jpg) +Figure 2. Token optimization for sexual content detection. + +method that leverages the self-discovered disentangled unsafe direction in the $h$ -space (the middle bottleneck of U-Net with the highest levels of semantics) [19, 21]. However, in our work, we find that sexual content detection should fully leverage the entanglement of attributes and category information in lower-level latents, beyond the $h$ -space. + +# 3. Detect-and-Guide + +DAG comprises two key operations for safe generation: + +(1) Guideline detection: We first collect a small dataset to optimize embeddings of guideline tokens with novel losses to align their semantics with specific concepts, which enhances unsafe region detection (Sec. 3.1). These optimized embeddings to extract cross-attention maps (CAMs), which are capable of providing pixel-level magnitudes of sexual content that highlights the nude region, specifically for the presence of co-existing $(a,o) =$ (nude, human), and are generalizable when $(a,o)$ is further combined with non-targeted attributes such as styles, scenes, and poses. The self-diagnostic detections will then be used for self-regulation to negate unsafe generation. +(2) Safe Self-regulation: We follow the implementations of safety guidance [3, 34] to refine the estimated noise $\epsilon_{\theta}(\mathbf{z}_t,t,\mathbf{c})$ applied to denoise the noisy latent $\mathbf{z}_t\rightarrow \mathbf{z}_{t - 1}$ in a classifier-free style [14] (Sec. 3.2). We identify and inherit the advantages of safety guidance, which automatically explores a safe mode that is close to the generated unsafe mode during sampling dynamics. We overcome shortcomings such as unnecessary global changes, lack of specificity, and heavy dependence on the appropriate choice of guidance strength by (a) restricting the guided region to the detected region and (b) applying an adaptive scalar based on CAM magnitude and the area of unsafe region. + +![](images/40fcf966ce85d68cd5dfe836638f032a3f2c9a4609992283acc6b349209d1149.jpg) +Figure 3. CAMs from non-optimized $c$ generate a detection region of nudity that diffuses into the irrelevant background and highlight the non-target concept 'cat'. We optimize the embedding to address background leakage and lack of specificity, using pixel-level CE loss w.r.t ground truth masks. The refined CAMs are demonstrated in (a). The learned refined semantics of $c^*$ generalize well to unseen test samples, as demonstrated in (b). The presence of nudity can easily be measured by CAM values greater than 0.5. + +# 3.1. CAM-based Guideline Detection + +In this section, we describe the way of deriving detection maps from cross-attention layers in the U-net. As demonstrated in Figure 2, the noisy latent $z_{t}$ and conditional embedding from prompt $c_{p}$ are fed forward the U-Net, and we cache all hidden states in cross-attention layers, which is denoted as $h_{t}^{l}$ . The original CA operation during sampling process will project visual latents $h_{t}^{l}$ to queries $Q = W_{Q}^{l} \cdot h_{t}^{l}$ , and project original condition $c_{p}$ to keys and values. In our work, we use the static hidden states and projection weights $W_{Q}^{l}, W_{K}^{l}$ to calculate cross-attention between guideline embeddings $c$ and $h_{t}^{l}$ . + +Limitations of Non-optimized Guideline Tokens. We initialize $c$ with token embeddings of 'nude person', which is desired to give high attention scores on the concept that match the description. However, as shown in Figure 3-(a), $\mathrm{CAM}(c)$ premises to the background and detects nudity concepts on a cat. The first phenomenon is identified as cross-attention leakage problem. In previous work, for the CAM which is extracted using original prompts, the text encoder that apply self-attention layers on token sequences make the embeddings $c_{p}$ contain rich semantic information of the context, as well as the special tokens, therefore causing the leakage to the background [49]. The second problem of unexpectedly highlighting the cat which is unrelated to 'nude person' mainly arises from the rich semantics of 'nude', as the cat is sometimes considered to be unclothed. + +Token Optimization. To address these problems, we suggest the token optimization approach [30] that can effectively refine the resulting CAMs with semantics generalizability and specificity on the target combination of attribute and object category. A small dataset contains safe images and annotated unsafe images is required for optimizing the embedding. We first instruct LLM to generate text-to-image + +prompts with nude concepts, then generate images using T2I diffusion models. We select five unsafe and three safe images with various styles (e.g., sculpture, painting, and photograph) and with several non-target concepts (dogs and cats) to help distinguish the nudity of human. Noted that unsafe annotations can be constructed easily with GroundedSAM [26, 38]. We detail the annotating pipeline in Figure 2-(a): By incorporating positive textual labels and negative textual labels, we can exclude non-sexual part of human like hair or face from the body segmentation results and give precise GT masks. For safe images, their annotations are simply initialized as zero masks indicating no nude concepts should be detected. We denoted the small dataset of generated images and annotations as $\mathcal{D} = \{\mathcal{X},\mathcal{Y}\}$ . + +Given the dataset, we cache their intermediate hidden states before cross-attention layers over all sampling timesteps $\{h_t^l [i]|i\in \mathcal{X},t\sim [1,50]\}$ . Resulting maps for the embedding $c$ can then be derived as $\mathrm{CAM}(h_t^l [i],c)$ and interpolated to the size of images (i.e., $\hat{A}\in \mathbb{R}^{K\times H\times W}$ ). We define the CAM loss for detecting regions with specific target concepts as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {C A M}} = \mathbb {E} _ {(i, y) \sim (\mathcal {X}, \mathcal {Y})} \mathbb {E} _ {t \sim \mathcal {T}, l \sim \mathcal {L}} \frac {1}{K} \sum_ {k = 1} ^ {K} \sum_ {h = 1} ^ {H} \sum_ {w = 1} ^ {W} [ \\ - \operatorname {O n e - h o t} \left(y ^ {G T}\right) _ {h, w} \cdot \log \left(\hat {A} _ {k, h, w} \left(h _ {t} ^ {l} [ i ], c\right)\right), \tag {2} \\ \end{array} +$$ + +where $\mathcal{T}$ is a set of all sampling timesteps, $K$ is the number of guideline tokens, and $\mathcal{L}$ denotes the chosen layers to extract the CAMs. We average the loss of each CAM over tokens, and the values of $\hat{A}$ are normalized to [0,1] with min-max scalar for calculating the logits. + +Noted that hidden states in the U-Net of SD model have three size dimensions $[16^2, 32^2, 64^2]$ with difference levels of semantics. We assign layer-wise learnable weights initialized by all ones and find that weights of larger CAMs are monotonic decreasing. This means that the hidden state with resolution of 64 contains the lowest level of semantics, and is too noisy for token optimization. Thus we choose $\mathcal{L} = \{l|h_t^l.\mathrm{size}\in [16^2,32^2]\}$ to extract CAM layers. + +To summary, our optimizing objective can be formalized as follows: + +$$ +c ^ {*} = \min _ {c} \left[ \mathbb {E} _ {(i, y) \sim (\mathcal {X}, \mathcal {Y})} \mathcal {L} _ {\mathrm {C A M}} \right] \tag {3} +$$ + +and we use a mini-batch of size two where one sample from unsafe subset and another from the safe subset. + +Improved Guideline Detection. The detection map of optimized guideline token embeddings, $\hat{A}(c^{*})$ , on trained samples is demonstrated in Figure 3-(a), and that on randomly chosen samples from unseen datasets is shown in Figure 3-(b). The CA leakage to the background is significantly mitigated and target-concept specificity is improved. + +![](images/a467c3ba33eeac6286a8f13f134e42393a7e0ed8a7da6b7909eb1fbe61ebc251.jpg) +Figure 4. Overview of Our Proposed Safe Generation Framework, Detect-and-Guide (DAG). The notations for (a) Original Generation can be found in Sec. 2. In (b), DAG utilizes guideline token embeddings $c^*$ to perform self-diagnostics by calculating cross-attention maps (CAM) at higher-level hidden states of the U-Net. The $c^*$ is optimized in advance on a small annotated dataset for precisely segmenting unsafe regions, addressing the problem of cross-attention leakage [49]. In (c), DAG achieves safe self-regulation by editing the detected unsafe regions. This editing process uses pixel-level magnitudes that are adaptively determined based on region area and CAM values. + +As further illustrated in Figure 5, CAMs for non-target concepts, such as 'a nude wall', will contain only a few values larger than 0.5 (i.e., they will not be detected), which can serve as an indicator of the presence of unsafe content. We analyze the distribution of CAM values in Sec. 3.2 to develop an adaptive scaling strategy that best balancing sexual content erasure and mode preservation. + +![](images/bfd3d59b63df80ba481a511282c670b80e5398697d5728f8fe65cd96b72a87bf.jpg) +Figure 5. The comparison of cross-attention map with non-optimized token embeddings and their effect on performing the self-regulation. + +# 3.2. Safe Self-regulation + +With the attention maps of guideline detection, we then utilize the idea of classifier-free guidance [14] to adjust a noisy latent in an unsafe mode to a nearby safe mode during sampling following the implementation of safety guidance [3, 41]. + +The classifier-free guidance introduces a null-text embedding $\varnothing = \tau_{\theta}({}^{\prime \prime \prime \prime})$ as the unconditional generative probability beyond the conditional probability to estimate the gradient of an implicit classifier. We denote unconditional estimated noise as $\epsilon^{\emptyset}$ , conditional estimated noise as $\epsilon^{p}$ and the scale of guidance as $s_g$ (default as 7.5 for SDv1.4). + +Similarly, safety guidance [41] introduces a safety condition $c_{s} = \tau_{\theta}(p_{s})$ and the corresponding estimated noise $\epsilon^{c_s}$ that reuses the implicit Bayesian classifier for conditional probability [14] to adjust the estimated gradient with selective pixel-level scale map $\mathbf{S}_{c_s}\cdot \mathbf{M}_{c_s}$ : + +$$ +\begin{array}{l} \hat {\epsilon} _ {\theta} (x _ {t}, t, c _ {p}) ^ {\mathrm {C F}} = (1 - s _ {g}) \underbrace {\epsilon_ {\theta} (x _ {t} , t , \varnothing)} _ {\epsilon^ {\emptyset}} + s _ {g} \underbrace {\epsilon_ {\theta} (x _ {t} , t , c _ {p})} _ {\epsilon^ {p}} \\ = \epsilon^ {\varnothing} + s _ {g} \underbrace {\left(\epsilon^ {\varnothing} - \epsilon^ {p}\right)} _ {\tilde {\epsilon} ^ {p}} \tag {4} \\ \end{array} +$$ + +$$ +\hat {\epsilon} _ {\theta} \left(x _ {t}, t, c _ {p}, c _ {s}\right) ^ {\text {S a f e}} = \left(1 - s _ {g}\right) \epsilon^ {\varnothing} + s _ {g} \left(\epsilon^ {p} - \mathbf {S} _ {c _ {s}} \cdot \mathbf {M} _ {c _ {s}} \epsilon^ {c _ {s}}\right). +$$ + +For the purpose of safe generation, guidance-based methods are advanced in the capability of discovering the direction of a nearby safe mode given an existing unsafe mode. However, the safety guidance applied in an early stage will introduce severe mode shift that affect the generation quality, with necessity of warm-up steps $\underline{t}_{c_s}$ to regulate the mode change. Therefore, we leverage detection maps $\hat{A}(c^*)$ as a gate function to enable adaptive guidance scale (stronger when detected with higher confidence) that also works at higher noise level and prevent severe mode shift. The overall comparison of how our method apply safety guidance is different from existing methods is shown in Table 1. + +The safety scale map $\mathbf{S}_{c_s}$ used in DAG depends on (i) a scalar denoted as $\mathrm{Area}_{0.5}(\hat{A})$ , which highlights the area of detected unsafe region with a confidence no less than 0.5, as the yellow region shown in Figure 4-(b), along with a base weight of 5 for pixel editing $\overline{s}_c = \frac{5}{H\times W}$ ; and (ii) a magnitude scalar $T_{0.01}(\hat{A})$ based on confidence value of attention map $\hat{A} = \{a\}_{:h,w}$ , which assigns an appropri + +Table 1. Notations for classifier-free guidance and safety guidance. + +
    CF [14]SLD [41]SEGA [3]DAG (Ours)
    ε∅1 - sg1 - sg + sg · Scs · Mcs
    εpsgsg
    εcs--sg · Scs · Mcs
    Scs-max(εp - εcs, 1)scs(¯¯¯¯sc · Area0.5(Â)) ⊙ T0.01(Â)
    Mcs-I(εcschw + λ > εpchw)chwI[¯¯¯¯epsilonchw ∈ top-p(¯¯¯¯epsiloncs)]chwI[ ≥ 0.01]:hw ⊙ McsSEGA/SLD
    tcs-7 (strong), 10 (medium), 15 (weak)105
    + +ate editing scale only for pixels whose confidence satisfies $0.01 \leq a \leq 1$ by rescaling their attention values to range $1 \leq T_{0.01}(a) \leq 5$ . Besides the scale map, we simply set a gate function $\hat{A} \geq 0.01$ to the safety selective mask of existing methods, as the green region demonstrated in Figure 4-(b). We use $\mathbf{M}_{c_s}^{\mathrm{SEGA}}$ in main experiments and compare different safety guidance methods in Supp. B. + +# 4. Experiments + +# 4.1. Evaluation Setting + +In this section, we comprehensively evaluate the effectiveness of DAG in erasing sexual content from three perspectives: + +Erasing Effectiveness and Robustness. We utilize 931 sexual prompts from real-world harmful prompts benchmark Inappropriate Image Prompts (I2P) [41] to evaluate effectiveness, denoted as I2P-sexual. Additionally, we filter a subset of complex prompts containing terms, resulting in a 439-prompt subset, denoted as I2P-sexual-complex. To assess robustness, we further leverage two black-box adversarial prompt datasets, Ring-A-Bell (RAB)[46] and MMA[50]. We use 1,000 released adversarial prompts from MMA focused on sexual content generation, and we implement RAB attacks on I2P-sexual-complex, resulting in 439 adversarial prompts. + +We employ a YOLO-based nudity detector NudeNet [32] to evaluate unsafe content in generated images from I2P-sexual, RAB and MMA, where each prompt generates four images using fixed seeds, producing a total of 9480 images per method. We apply NudeNet's five unsafe classes and a confidence threshold of 0.6 to calculate the evaluation results. We report the number of detected unsafe classes as NudeNet Number (N3), and calculate the Erase Rate (ER) compared to undefended SDv1.4 as follows: $\mathrm{ER} = 1 - \frac{\mathrm{N3}_{\mathrm{defense}}}{\mathrm{N3}_{\mathrm{SDv1.4}}}$ , where all unsafe concepts erased will give a $100\%$ ER. + +Fine-grained erase performance. We consider that a harmful prompt may contain multiple concepts, and thus the design principle of safe generation should account for prompt-following performance on the remaining safe concepts. To assess this, we introduce an advanced metric, VQA Score [24], which evaluates text-to-image alignment using pre-trained large VLMs (CLIP-FlanT5-XL). We eval + +uate the alignment capability of the erased models on I2Psexual dataset by prepending a short task description 'Safe Generation:' to the prompt before feeding the (prompt, image) pair into the VLM evaluator. This metric, denoted as VQA Score-SG, reflects the self-regulation capability of safely following the harmful prompt. We use VQA Score as a sanity check to ensure safety methods 018 do not degrade normal generation + +Model Utility. We resample 1000 prompts from the MS-COCO validation dataset [23] as benign prompts to evaluate model utility, denoted as COCO-1K. Image quality metrics include $FID_{\mathrm{real}}$ , which measures the similarity between generated images generated by erased models and real images from MS-COCO, and $FID_{\mathrm{SDv1.4}}$ , which assesses the mode shift introduced by erasing methods. We also calculate the VQA Score on resampled data to evaluate generation capability. + +Baselines. In our experiments, we compare against nine popular unlearning methods under different settings, resulting in a total of eleven erasing baselines (ESD [9], SLD-(weak, medium, strong) [42], SPM [29], SA [12], SalUn [8], Self-Dis [22], SEGA [3], MACE [27], AdvUnlearn [52]). The baseline model with no defense is SDv1.4, and we also conduct experiments on SDv2.1, which training data is filtered by an NSFW detector, to serve as a retraining baseline. For the fine-tuning-based erasing methods, we download their official checkpoints for erasing the concept of nudity. For the safety guidance-based methods, we run their official generating scripts with hyper-parameters from their paper. For SEGA, we set the scale of semantic guidance to 10 (default as 5) and reverse the guidance for effectively removing nudity from generation. + +# 4.2. Erase Performance + +Erase Effectiveness and Model Utility Perservation We generate 9840 images for each method, and report the NudeNet detection results of five unsafe classes. The erasure effectiveness of the proposed method compared with baselines are demonstrate in Table 2. Our method, DAG, outperforms all guidance-based methods (three variants of SLD and SEGA) and achieves competitive erasure performance compared to fine-tuning-based methods (SA, SPM) and SDID. Fine-tuning-based methods with strong erasure performance come at the cost of lower generation quality on + +
    MethodsGeneration Quality (COCO-1K)Erase Effectiveness (I2P-sexual)
    VQA Score\( FID_{\text{real}} \downarrow \)\( FID_{\text{SDv1.4}} \downarrow \)Total↓ButtocksChest(F)Genitalia(F)Chest(M)Genitalia(M)
    SDv1.4 [39]0.7058.03010708383854914
    SLD-weak [41]0.6859.3823.348566267148723
    SLD-medium [41]0.7061.1531.736605550633615
    SLD-strong [41]0.6462.8741.14207271447272
    SEGA [3]0.7058.9533.4715511873513
    SDID [21]0.7357.931.521812512212166
    ESD-u [10]0.6358.0150.55631492110
    SA [12]0.6763.8353.9711411841450
    SalUn [7]0.4280.2787.68000000
    SPM [29]0.7157.6235.372083813917131
    MACE [27]0.5955.9951.01565363102
    AdvUnlearn [52]0.5460.0244.561018001
    DAG (ours)0.7258.2223.67861471325
    + +Table 2. Assessment of Unsafe Concept Erase: Evaluation of FIDs and VQA scores on COCO-1K and the count of unsafe concepts detected by NudeNet on I2P-sexual. We use best, second-best and third-best to highlight the top-3 results, respectively. Italicized methods are fine-tuning-based. + +![](images/eb05d808fa60bd3b880e2a67d57542ca34bf8de5f16edf2e49340a520fca1b98.jpg) +Figure 6. Erase rate $(\%)$ on I2P-sexual, measuring the relative deduction of unsafe concepts compared to SDv1.4. + +woman with shiny skin lying on the grass dressed in roman clothes, ultra detailed, Guido Reni style + +'high resolution $8k_{\mathrm{e}}$ close up portrait photograph of Selena Gomez, dressed in bikini, standing near the beach, vogue photoshoot + +![](images/f7c20188561e86f9c57dce8228c44b4813a3cb034d015451f41ee1f4c41bac76.jpg) +Figure 7. Qualitative Experiments. The examples are randomly sampled from I2P-sexual. Note that not all prompts in I2P-sexual can generate harmful images, and the regional specification advantages of DAG can be observed. + +the benign dataset COCO-1K. For example, the strongest defense methods suffer from severe distribution shifts when generating non-target concepts and fail to achieve text-to-image alignment, as quantitatively observed by a significantly lower VQA Score (0.42) compared to ours (0.72) and SDv1.4 (0.70). We visualize the trade-off between generation quality and erasure performance in Figure 1 (right), showing that our method, without expensive retraining or fine-tuning, achieves the optimal balance by incorporating optimized token-based detection maps. + +Erase Robustness. We conduct robustness experiments using two black-box adversarial prompt attacks: Ring-A-Bell and MMA. Ring-A-Bell is based on CLIP-embedding inversion to reconstruct the token sequence with similar semantics to an unsafe embedding. MMA conducts a sensitive word replacement attack and generates adversarial prompts in natural language. We present the results in Ta + +ble 3. Note that our results align with fine-tuning-based methods in robustness evaluations, without any weight tuning or modifications. + +Fine-grained Erase Performance. We demonstrate the VQA Score-SG in Figure 8 to measure the text-to-image alignment degree of erased methods on the datasets I2P-sexual. DAG ranks the second in the results, and primarily benefit from the restriction of guidance in detected unsafe region, which introduce slightly background modification as demonstrated in Figure 7. + +# 4.3. Parameters Study + +Although the optimized embeddings can meet both generalizability and specificity, one remaining question is how the detection performance varies across different noise levels and whether it can be aggregated using a smaller number of maps, such as one. We visualize the detection map at dif + +Table 3. Erasure Robustness for Nudity: Best, Second-best and Third-best highlight top-3 results. Italicized methods are fine-tuning-based. + +
    Defense MethodsRing-a-bell Adversarial PromptsMMA Adversarial Prompts
    Erase Rate↑ (%)Total↓ButtocksChest (F)Genitalia (F)Chest (M)Genitalia (M)Erase Rate↑ (%)Total↓ButtocksChest (F)Genitalia (F)Chest (M)Genitalia (M)
    SDv1.40.003279115249€342266600.002732413154€83301391
    SLD-weak(7.44)3523107266543526848(1.57)2775433151782336407
    SLD-medium(7.11)3512742725433246341.542690410142095360405
    SLD-strong43.15186433163810090348.43140928369233174227
    SEGA66.54109723768452511065.419452333007248157
    SDID87.6840434309124547.142537373144474306340
    ESD-u87.74402143271346297.806020222214
    SA48.031704431393146122089.602846219012011
    SalUn100.0000000099.93202000
    SPM87.07424293172255149.34138430866639208163
    MACE99.57142921099.411654016
    AdvUnlearn100.0000000099.491428022
    DAG (ours)88.14389102067166077.601276121854183113
    + +![](images/e95ef35fb4ed816db851535c45f09716b098e5ea53d4203b38118a862e53143f.jpg) +Figure 8. The VQA Score-SG (prepend 'Safe Generation:' to the prompt for text-to-image alignment evaluation) $(\%)$ on I2P-sexual datasets. + +![](images/79dd37a9565ee692b34043b1cf98de026bad26020384f0673688ad0a5fc7f7f2.jpg) +Figure 9. Comparisons of single-step attention map and multi-step attention map. + +ferent steps stacked using different number of maps in Figure 9, and observe that single-step CAM can be sufficient for the detection. + +# 5. Conclusion + +Our proposed methods, DAG, offers a fine-grained approach to sexual concept erasure for safe generation. DAG leverages specific internal knowledge of diffusion models that can be activated through cross-attention layers to detect unsafe concepts. We apply fine control to the cross-attention maps by optimizing guideline token embeddings, + +enabling the attention map to provide information about unsafe intensity and regions. This allows us to improve erasure methods based on safety guidance, addressing the limitations of unbounded guidance regions that may cause unnecessary mode shifts. + +Though Detect-and-Guide is effective at erasing nude visual content and achieves both safe and high-quality generation, some unsafe concepts may still be generated by then models. We investigate the failure cases and categorize the generation of nudity concepts into two trajectory types: The first type, easy-to-erase nudity, typically appears in the later stage of denoising. For example, a nude mark for a person in a painting emerges later than for a person in the gallery, as shown in Figure 4. This phenomenon recurs in Figure 3-(a), where three marble sculptures of different sizes require varying degrees of scaling strength to ensure they are all reliably removed. This observation motivates the design of a CAM area-basedScaler in Sec. 3.2. The second type, hard-to-erase nudity, occurs when prompts trigger memorized unsafe images, straying significantly from other safe modes that make it challenging to adjust towards a safe mode effectively. In these cases, the sampling mode collapses rapidly within the first few steps (e.g., $< 5$ sampling times), making guidance on this collapsed latent less effective. We leave the identification and mitigation of memorized unsafe images to future work. + +While the contradiction between generation performance (including prompt-following capability, generation diversity, and image quality) and erasure effectiveness is currently complex and difficult to reconcile, our work takes an initial step toward fine-grained self-regulation of T2I diffusion models that mitigates this issue to some extent. We also suggest that safety mechanisms for generative models should integrate these advancements to enhance both interpretability and usability. + +# Acknowledgement + +We are thankful to the shepherd and reviewers for their careful assessment and valuable suggestions, which have helped us improve this paper. This work was supported in part by the National Natural Science Foundation of China (62472096, 62172104, 62172105, 62102093, 62102091, 62302101, 62202106). Min Yang is a faculty of the Shanghai Institute of Intelligent Electronics & Systems and Engineering Research Center of Cyber Security Auditing and Monitoring, Ministry of Education, China. + +# References + +[1] Samyadeep Basu, Nanxuan Zhao, Vlad I Morariu, Soheil Feizi, and Varun Manjunatha. Localizing and editing knowledge in text-to-image generative models. 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Defensive unlearning with adversarial training for robust concept erasure in diffusion models. arXiv preprint arXiv:2405.15234, 2024. 3, 6, 7 \ No newline at end of file diff --git a/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/images.zip b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..113e0d4d722b158b912de45f563548ed48fb12dc --- /dev/null +++ b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5bf569ca453996d19a98217feb6449689620dfaaaad5915b4dbd47b562537652 +size 793826 diff --git a/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/layout.json b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1b5c0a5f35e55e3948917049a09423dc4c47c8ad --- /dev/null +++ b/2025/Detect-and-Guide_ Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization/layout.json @@ -0,0 +1,7712 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 58, + 102, + 536, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 102, + 536, + 140 + ], + "spans": [ + { + "bbox": [ + 58, + 102, + 536, + 140 + ], + "type": "text", + "content": "Detect-and-Guide: Self-regulation of Diffusion Models for Safe Text-to-Image Generation via Guideline Token Optimization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 175, + 160, + 421, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 160, + 421, + 176 + ], + "spans": [ + { + "bbox": [ + 175, + 160, + 421, + 176 + ], + "type": "text", + "content": "Feifei Li Mi Zhang† Yiming Sun Min Yang†" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 166, + 176, + 427, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 166, + 176, + 427, + 190 + ], + "spans": [ + { + "bbox": [ + 166, + 176, + 427, + 190 + ], + "type": "text", + "content": "School of Computer Science, Fudan University, China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 149, + 191, + 425, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 191, + 425, + 202 + ], + "spans": [ + { + "bbox": [ + 149, + 191, + 425, + 202 + ], + "type": "text", + "content": "{ffli23@m.,mi_zhang@,ymsun24@m.,m_yang@}fudan.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 256, + 290, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 485 + ], + "type": "text", + "content": "Text-to-image diffusion models have achieved state-of-the-art results in synthesis tasks; however, there is a growing concern about their potential misuse in creating harmful content. To mitigate these risks, post-hoc model intervention techniques, such as concept unlearning and safety guidance, have been developed. However, fine-tuning model weights or adapting the hidden states of the diffusion model operates in an uninterpretable way, making it unclear which part of the intermediate variables is responsible for unsafe generation. These interventions severely affect the sampling trajectory when erasing harmful concepts from complex, multi-concept prompts, thus hindering their practical use in real-world settings. In this work, we propose the safe generation framework Detect-and-Guide (DAG), leveraging the internal knowledge of diffusion models to perform self-diagnosis and fine-grained self-regulation during the sampling process. DAG first detects harmful concepts from noisy latents using refined cross-attention maps of optimized tokens, then applies safety" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 232, + 547, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 547, + 352 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 547, + 352 + ], + "type": "text", + "content": "guidance with adaptive strength and editing regions to negate unsafe generation. The optimization only requires a small annotated dataset and can provide precise detection maps with generalizability and concept specificity. Moreover, DAG does not require fine-tuning of diffusion models, and therefore introduces no loss to their generation diversity. Experiments on erasing sexual content show that DAG achieves state-of-the-art safe generation performance, balancing harmfulness mitigation and text-following performance on multi-concept real-world prompts." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 375, + 387, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 375, + 387, + 388 + ], + "spans": [ + { + "bbox": [ + 306, + 375, + 387, + 388 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 396, + 547, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 547, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 547, + 504 + ], + "type": "text", + "content": "In recent advancements, text-to-image diffusion models (DM) have exhibited remarkable capabilities in generating high-resolution images based on textual prompts that outperform GANs and VAEs [4]. Notably, models such as DALL-E [2, 36], MidJourney [31], and Stable Diffusion [6, 39] have achieved commercial standards, enabling a wide range of applications designed for end-users. However, growing regulatory concerns about the safety of generated images and their social impacts, such as the gen" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 53, + 511, + 539, + 645 + ], + "blocks": [ + { + "bbox": [ + 53, + 511, + 539, + 645 + ], + "lines": [ + { + "bbox": [ + 53, + 511, + 539, + 645 + ], + "spans": [ + { + "bbox": [ + 53, + 511, + 539, + 645 + ], + "type": "image", + "image_path": "d6df31427c38b58f85a0acc3085b2385e1ba74b9c098131cf196ed222eefeba8.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 658, + 548, + 725 + ], + "lines": [ + { + "bbox": [ + 45, + 658, + 548, + 725 + ], + "spans": [ + { + "bbox": [ + 45, + 658, + 548, + 725 + ], + "type": "text", + "content": "Figure 1. Results of safe generation with sexual content erased, masks are applied for censorship purposes. Our proposed method, DAG, can leverage the internal knowledge of pretrained Text-to-Image Diffusion Models to perform fine-grained erasure of unsafe visual concepts to avoid modifying other concepts in the same image. It effectively preserves the composition of unsafe images and the appearance of objects in benign regions, achieving a favorable balance between harm mitigation and text alignment for partially harmful prompts. This approach underscores concerns about practical usability in developing safe generation methods and reveals the self-regulation capability of text-to-image diffusion models, shedding light on scalable safety alignment for image generation." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 491, + 139, + 503 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 491, + 139, + 503 + ], + "spans": [ + { + "bbox": [ + 58, + 491, + 139, + 503 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 293, + 753, + 318, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 318, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 318, + 762 + ], + "type": "text", + "content": "13252" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "eration of unauthorized and Not-Safe-for-Work (NSFW) content [20, 34, 37], primarily arise from the weakness of unfiltered pretraining datasets sourced from the real world [40, 43, 45]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 122, + 288, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 122, + 288, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 122, + 288, + 314 + ], + "type": "text", + "content": "Recently, post-hoc model intervention methods for safe generation have emerged as a promising approach, enabling safe generation without the need for expensive retraining on a curated clean dataset. Unlike text or image filters that passively block unsafe content, these methods improve practical usability by directly guiding the generation process toward safe outputs. Depending on how they handle unsafe concepts, these techniques can be categorized into two types: Unlearning-based methods modify the model's distribution by aligning its internal understanding of unsafe concepts with corresponding safe ones. In contrast, guiding-based methods require no additional training; they rely on extra negative or safety prompts to define unsafe concepts and adjust the estimated noises from U-Net denoisers during the generation process, offering greater scalability potential." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 316, + 288, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 288, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 288, + 508 + ], + "type": "text", + "content": "However, some of existing unlearning methods are inherently text-centric [33, 46] and unreliable when unsafe visual concepts emerge from harmful knowledge recalled by benign prompts, which represents a form of blacklist shortcut arising from the manually crafted datasets used for fine-tuning. Moreover, as demonstrated in Figure 1-(b), methods designed to erase unsafe concepts from single-concept prompts, like \"A photo of " + }, + { + "bbox": [ + 46, + 316, + 288, + 508 + ], + "type": "inline_equation", + "content": "[c_{\\mathrm{unsafe}}]" + }, + { + "bbox": [ + 46, + 316, + 288, + 508 + ], + "type": "text", + "content": ",\" are inadequate for real-world prompts containing multiple co-existing concepts. The lack of control in distinguishing and retaining safe concepts leads to significant mode shift between original generation and erased safe generation. Hence come our research questions: Can we design an image-centric safe generation framework to minimize the mode shift of safe generation and surmount the challenge of blacklist shortcuts?" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": "Inspired by the understanding of cross-attention layers in diffusion models [25], as well as the token optimization methods for accurate cross-attention maps (CAM) [16, 30, 49], we propose our safe generation framework Detect-and-Guide that leverages internal knowledge of diffusion models to negate sexual content guided using detecting CAMs. The detection target for sexual content can be coarsely described by the combination of attributes " + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "inline_equation", + "content": "a \\in \\mathcal{A}" + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": " and specific object categories " + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "inline_equation", + "content": "o \\in \\mathcal{O}" + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": " (e.g., 'nude' and 'human'). The desired criteria include: (1) Generalizability to different styles, scenes, and poses. (2) Specificity to the combination of " + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "inline_equation", + "content": "(a,o) \\in \\mathcal{A} \\times \\mathcal{O}" + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": " that should be detected; in contrast, a bare wall or a clothed human is unnecessarily to be detected. (3) Fine-grained detection with precise region mask, which excludes the background and covered part of human body. We investigate the role of cross-attention layers and manage to extract CAMs from high-level U-Net layers that" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "meet all the criteria by their characteristics of entangling relations of objects together with attributes [25]. The entanglement makes it possible to directly extract the CAMs only for paired " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "(a,o)" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " and enables fine-grained guidance applied accordingly." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 133, + 546, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 546, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 546, + 335 + ], + "type": "text", + "content": "Starting with the guideline tokens that need to be optimized and a small annotated dataset created using grounded segmentation models, we incorporate (1) background leakage loss [49] and (2) negative sample loss [16] to optimize the embeddings for precisely extracting CAMs that aligns with the ground truth mask. During the sampling process, the optimized token embedding " + }, + { + "bbox": [ + 304, + 133, + 546, + 335 + ], + "type": "inline_equation", + "content": "c^*" + }, + { + "bbox": [ + 304, + 133, + 546, + 335 + ], + "type": "text", + "content": " is capable of detecting unsafe concepts at each timestep with generalizability and concept specificity across different scenarios, which can be competitive with supervised semantic segmentation methods at image level [30] and is naturally robust to different levels of noise, without accumulating the CAM over all timesteps. With the detection mask, we can then incorporate latent-level safety guidance to address the limitations of heavily relying on hyperparameters choices (e.g., guidance scale, guidance steps) by using CAM magnitude together with adaptive unsafe area rescaling." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 336, + 546, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 546, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 546, + 552 + ], + "type": "text", + "content": "The proposed method is evaluated with sexual concept erased. We propose to evaluate the safe generation performance of erased models comprehensively on three evaluation dimensions: (i) Erasing effectiveness and robustness, (ii) fine-grained erasing performance with unsafe concepts excluded and safe concept retrained, and (iii) the utility of models in benign dataset. We use NudeNet [32] score as the safety metrics, and conduct experiments in real-world sexual prompts dataset I2P [41]. We additionally introduce a novel vision-language alignment metrics VQA-score [24] to flexibly measure the text-to-image safety alignment on unsafe prompts. The utility of erased models can be evaluated by image quality (FID score) and prompt-following performance on MS-COCO [23]. Our qualitative and quantitative results show that DAG can successfully erase sexual content from generated images, achieving optimal generation performance that balancing harmful mitigation and generation quality." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 552, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 586 + ], + "type": "text", + "content": "Disclaimer. The manuscript contains discussions and visual representation of NSFW content. We censor Not-Safe-for-Work (NSFW) imagery. Reader discretion is advised." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 597, + 385, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 385, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 385, + 611 + ], + "type": "text", + "content": "2. Background" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "content": "Text-to-Image Diffusion Models. Our paper mainly implemented with Stable Diffusion (SD) [39], one of the most popular and influential latent diffusion models (LDM), with an active community and numerous variations. LDM comprises a VAE [5, 47] that maps high-dimensional images " + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "content": " into a latent space " + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "inline_equation", + "content": "z_0 = \\operatorname{E}(x_0)" + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "content": " and reconstructs them back with vector quantization " + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "inline_equation", + "content": "x_0' \\approx \\mathrm{D}(z_0)" + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "content": ", and a denoiser " + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "content": " samples noise backward. The denoiser is trained using the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "text", + "content": "13253" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 258, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 258, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 258, + 85 + ], + "type": "text", + "content": "following mean squared error (MSE) loss objective:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 91, + 287, + 105 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 91, + 287, + 105 + ], + "spans": [ + { + "bbox": [ + 59, + 91, + 287, + 105 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {L D M}} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathrm {E} (\\mathbf {x}), \\mathbf {c}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ | | \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\mathbf {c}) | | _ {2} ^ {2} ], \\tag {1}", + "image_path": "e1e1b3f5598e941d794d49d5cea66eac855088eae1dfa016f8417be2bba9f1ce.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "spans": [ + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "content": " is the estimated noise conditioned on the noisy latent " + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "content": ". SD introduces text condition " + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "content": " from input prompt " + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "content": " into diffusion models through a pretrained CLIP text encoder " + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "inline_equation", + "content": "c = \\tau_{\\theta}(p)" + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "content": " [35], and incorporates cross-attention layers [48] in a U-Net denoiser that project " + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 111, + 287, + 183 + ], + "type": "text", + "content": " through key and value layers." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "text", + "content": "Delving into Cross-attention Layers. Each block in U-Net denoiser is composed of self-attention, cross-attention and convolution layers. Recent works have presented causal analyses attributing generated elements to layers or neurons in the U-Net, revealing the function of cross-attention layers at different levels [1, 13, 25]. In conclusion, cross-attention layers play an important role in controlling generation in specific regions, guided by token-wise cross-attention maps (CAMs) [13]. However, CAMs that entangle both attributes (such as colors) and object category information may hinder single-concept editing [25]. Also, knowledge of different types of elements (colors, actions/poses, styles, and objects) is distributed across all layers of the U-Net [1], but with varying degrees of causal effects considering the dimension level. Moreover, by leveraging the flexibility of condition " + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "text", + "content": ", the potential of diffusion models can be extended beyond image synthesis. T2I diffusion models can be used for discriminative tasks such as classification [15] (" + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "inline_equation", + "content": "\\arg \\max_i \\mathcal{L}_{\\mathrm{LDM}}(c = \\tau_\\theta(y_i))" + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "text", + "content": ") for all labels " + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "inline_equation", + "content": "y_i \\in \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "text", + "content": ") and semantic segmentation [30], achieving comparable capabilities to supervised models. These findings have inspired us to leverage the power of CAMs to detect the presence of sexual concepts at each timestep and provide a precise guidance map at pixel level for " + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "inline_equation", + "content": "z_t" + }, + { + "bbox": [ + 46, + 197, + 289, + 485 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": "Safe Generation of Diffusion Models. The unlearning methods show promise in providing insights into functions of DM components and how they affect unsafe concept generation. For example, cross-attention refinement in the U-Net denoiser aims to reduce harmful semantics from conditional prompts [11, 27, 28, 51], while fine-tuning unconditional components (self-attention and convolutions) is aimed at erasing global concepts that arise from word combinations rather than specific individual concepts [10]. Other works provide evidence that fine-tuning the CLIP text encoder can be as effective as fine-tuning cross-attention layers [18], and that it benefits more from adversarial training than other components [52]. The refinement and fine-tuning rely on manually defined paired concepts of " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "(c_{\\mathrm{unsafe}}, c_{\\mathrm{safe}} / c_{\\emptyset})" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " to supervise the unlearning. Methods that leverage the internal knowledge of diffusion models are centered around generating paired image datasets for manually crafted paired concepts [17], with the exception of the" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 243 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 243 + ], + "type": "image", + "image_path": "edd69fa5282a27286c222546c2ffdba81b487f415f432698b4912d08345e8421.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 251, + 533, + 263 + ], + "lines": [ + { + "bbox": [ + 320, + 251, + 533, + 263 + ], + "spans": [ + { + "bbox": [ + 320, + 251, + 533, + 263 + ], + "type": "text", + "content": "Figure 2. Token optimization for sexual content detection." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 291, + 547, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 291, + 547, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 291, + 547, + 364 + ], + "type": "text", + "content": "method that leverages the self-discovered disentangled unsafe direction in the " + }, + { + "bbox": [ + 305, + 291, + 547, + 364 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 291, + 547, + 364 + ], + "type": "text", + "content": "-space (the middle bottleneck of U-Net with the highest levels of semantics) [19, 21]. However, in our work, we find that sexual content detection should fully leverage the entanglement of attributes and category information in lower-level latents, beyond the " + }, + { + "bbox": [ + 305, + 291, + 547, + 364 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 291, + 547, + 364 + ], + "type": "text", + "content": "-space." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 384, + 413, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 413, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 413, + 396 + ], + "type": "text", + "content": "3. Detect-and-Guide" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 407, + 531, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 407, + 531, + 419 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 531, + 419 + ], + "type": "text", + "content": "DAG comprises two key operations for safe generation:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 423, + 547, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 304, + 423, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 567 + ], + "type": "text", + "content": "(1) Guideline detection: We first collect a small dataset to optimize embeddings of guideline tokens with novel losses to align their semantics with specific concepts, which enhances unsafe region detection (Sec. 3.1). These optimized embeddings to extract cross-attention maps (CAMs), which are capable of providing pixel-level magnitudes of sexual content that highlights the nude region, specifically for the presence of co-existing " + }, + { + "bbox": [ + 304, + 423, + 545, + 567 + ], + "type": "inline_equation", + "content": "(a,o) =" + }, + { + "bbox": [ + 304, + 423, + 545, + 567 + ], + "type": "text", + "content": " (nude, human), and are generalizable when " + }, + { + "bbox": [ + 304, + 423, + 545, + 567 + ], + "type": "inline_equation", + "content": "(a,o)" + }, + { + "bbox": [ + 304, + 423, + 545, + 567 + ], + "type": "text", + "content": " is further combined with non-targeted attributes such as styles, scenes, and poses. The self-diagnostic detections will then be used for self-regulation to negate unsafe generation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "(2) Safe Self-regulation: We follow the implementations of safety guidance [3, 34] to refine the estimated noise " + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t,t,\\mathbf{c})" + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": " applied to denoise the noisy latent " + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t\\rightarrow \\mathbf{z}_{t - 1}" + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": " in a classifier-free style [14] (Sec. 3.2). We identify and inherit the advantages of safety guidance, which automatically explores a safe mode that is close to the generated unsafe mode during sampling dynamics. We overcome shortcomings such as unnecessary global changes, lack of specificity, and heavy dependence on the appropriate choice of guidance strength by (a) restricting the guided region to the detected region and (b) applying an adaptive scalar based on CAM magnitude and the area of unsafe region." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 753, + 318, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 753, + 318, + 763 + ], + "spans": [ + { + "bbox": [ + 294, + 753, + 318, + 763 + ], + "type": "text", + "content": "13254" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 75, + 282, + 159 + ], + "blocks": [ + { + "bbox": [ + 53, + 75, + 282, + 159 + ], + "lines": [ + { + "bbox": [ + 53, + 75, + 282, + 159 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 282, + 159 + ], + "type": "image", + "image_path": "40fcf966ce85d68cd5dfe836638f032a3f2c9a4609992283acc6b349209d1149.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 164, + 287, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 164, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 287, + 253 + ], + "type": "text", + "content": "Figure 3. CAMs from non-optimized " + }, + { + "bbox": [ + 46, + 164, + 287, + 253 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 164, + 287, + 253 + ], + "type": "text", + "content": " generate a detection region of nudity that diffuses into the irrelevant background and highlight the non-target concept 'cat'. We optimize the embedding to address background leakage and lack of specificity, using pixel-level CE loss w.r.t ground truth masks. The refined CAMs are demonstrated in (a). The learned refined semantics of " + }, + { + "bbox": [ + 46, + 164, + 287, + 253 + ], + "type": "inline_equation", + "content": "c^*" + }, + { + "bbox": [ + 46, + 164, + 287, + 253 + ], + "type": "text", + "content": " generalize well to unseen test samples, as demonstrated in (b). The presence of nudity can easily be measured by CAM values greater than 0.5." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 265, + 222, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 222, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 222, + 277 + ], + "type": "text", + "content": "3.1. CAM-based Guideline Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": "In this section, we describe the way of deriving detection maps from cross-attention layers in the U-net. As demonstrated in Figure 2, the noisy latent " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": " and conditional embedding from prompt " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "c_{p}" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": " are fed forward the U-Net, and we cache all hidden states in cross-attention layers, which is denoted as " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "h_{t}^{l}" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": ". The original CA operation during sampling process will project visual latents " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "h_{t}^{l}" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": " to queries " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "Q = W_{Q}^{l} \\cdot h_{t}^{l}" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": ", and project original condition " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "c_{p}" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": " to keys and values. In our work, we use the static hidden states and projection weights " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "W_{Q}^{l}, W_{K}^{l}" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": " to calculate cross-attention between guideline embeddings " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "inline_equation", + "content": "h_{t}^{l}" + }, + { + "bbox": [ + 46, + 284, + 287, + 417 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "text", + "content": "Limitations of Non-optimized Guideline Tokens. We initialize " + }, + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "text", + "content": " with token embeddings of 'nude person', which is desired to give high attention scores on the concept that match the description. However, as shown in Figure 3-(a), " + }, + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathrm{CAM}(c)" + }, + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "text", + "content": " premises to the background and detects nudity concepts on a cat. The first phenomenon is identified as cross-attention leakage problem. In previous work, for the CAM which is extracted using original prompts, the text encoder that apply self-attention layers on token sequences make the embeddings " + }, + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "inline_equation", + "content": "c_{p}" + }, + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "text", + "content": " contain rich semantic information of the context, as well as the special tokens, therefore causing the leakage to the background [49]. The second problem of unexpectedly highlighting the cat which is unrelated to 'nude person' mainly arises from the rich semantics of 'nude', as the cat is sometimes considered to be unclothed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "Token Optimization. To address these problems, we suggest the token optimization approach [30] that can effectively refine the resulting CAMs with semantics generalizability and specificity on the target combination of attribute and object category. A small dataset contains safe images and annotated unsafe images is required for optimizing the embedding. We first instruct LLM to generate text-to-image" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": "prompts with nude concepts, then generate images using T2I diffusion models. We select five unsafe and three safe images with various styles (e.g., sculpture, painting, and photograph) and with several non-target concepts (dogs and cats) to help distinguish the nudity of human. Noted that unsafe annotations can be constructed easily with GroundedSAM [26, 38]. We detail the annotating pipeline in Figure 2-(a): By incorporating positive textual labels and negative textual labels, we can exclude non-sexual part of human like hair or face from the body segmentation results and give precise GT masks. For safe images, their annotations are simply initialized as zero masks indicating no nude concepts should be detected. We denoted the small dataset of generated images and annotations as " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{\\mathcal{X},\\mathcal{Y}\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "text", + "content": "Given the dataset, we cache their intermediate hidden states before cross-attention layers over all sampling timesteps " + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\{h_t^l [i]|i\\in \\mathcal{X},t\\sim [1,50]\\}" + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "text", + "content": ". Resulting maps for the embedding " + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "text", + "content": " can then be derived as " + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\mathrm{CAM}(h_t^l [i],c)" + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "text", + "content": " and interpolated to the size of images (i.e., " + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\hat{A}\\in \\mathbb{R}^{K\\times H\\times W}" + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "text", + "content": "). We define the CAM loss for detecting regions with specific target concepts as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 322, + 331, + 545, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 331, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 322, + 331, + 545, + 383 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C A M}} = \\mathbb {E} _ {(i, y) \\sim (\\mathcal {X}, \\mathcal {Y})} \\mathbb {E} _ {t \\sim \\mathcal {T}, l \\sim \\mathcal {L}} \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\sum_ {h = 1} ^ {H} \\sum_ {w = 1} ^ {W} [ \\\\ - \\operatorname {O n e - h o t} \\left(y ^ {G T}\\right) _ {h, w} \\cdot \\log \\left(\\hat {A} _ {k, h, w} \\left(h _ {t} ^ {l} [ i ], c\\right)\\right), \\tag {2} \\\\ \\end{array}", + "image_path": "5d26d20ce9d6f99fb1c88284deb08395ec8f8065f0555cdffe126acdf3e492c2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "text", + "content": " is a set of all sampling timesteps, " + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "text", + "content": " is the number of guideline tokens, and " + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "text", + "content": " denotes the chosen layers to extract the CAMs. We average the loss of each CAM over tokens, and the values of " + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\hat{A}" + }, + { + "bbox": [ + 304, + 389, + 545, + 449 + ], + "type": "text", + "content": " are normalized to [0,1] with min-max scalar for calculating the logits." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 449, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 545 + ], + "type": "text", + "content": "Noted that hidden states in the U-Net of SD model have three size dimensions " + }, + { + "bbox": [ + 304, + 449, + 545, + 545 + ], + "type": "inline_equation", + "content": "[16^2, 32^2, 64^2]" + }, + { + "bbox": [ + 304, + 449, + 545, + 545 + ], + "type": "text", + "content": " with difference levels of semantics. We assign layer-wise learnable weights initialized by all ones and find that weights of larger CAMs are monotonic decreasing. This means that the hidden state with resolution of 64 contains the lowest level of semantics, and is too noisy for token optimization. Thus we choose " + }, + { + "bbox": [ + 304, + 449, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\{l|h_t^l.\\mathrm{size}\\in [16^2,32^2]\\}" + }, + { + "bbox": [ + 304, + 449, + 545, + 545 + ], + "type": "text", + "content": " to extract CAM layers." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 545, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 545, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 545, + 545, + 568 + ], + "type": "text", + "content": "To summary, our optimizing objective can be formalized as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 365, + 578, + 545, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 578, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 365, + 578, + 545, + 595 + ], + "type": "interline_equation", + "content": "c ^ {*} = \\min _ {c} \\left[ \\mathbb {E} _ {(i, y) \\sim (\\mathcal {X}, \\mathcal {Y})} \\mathcal {L} _ {\\mathrm {C A M}} \\right] \\tag {3}", + "image_path": "0c2273f09e8f780532a213b684fe00d171782841fac38437861cccb6afb5dbbd.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 603, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 603, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 305, + 603, + 545, + 626 + ], + "type": "text", + "content": "and we use a mini-batch of size two where one sample from unsafe subset and another from the safe subset." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Improved Guideline Detection. The detection map of optimized guideline token embeddings, " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{A}(c^{*})" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": ", on trained samples is demonstrated in Figure 3-(a), and that on randomly chosen samples from unseen datasets is shown in Figure 3-(b). The CA leakage to the background is significantly mitigated and target-concept specificity is improved." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "text", + "content": "13255" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 541, + 260 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 541, + 260 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 541, + 260 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 541, + 260 + ], + "type": "image", + "image_path": "a467c3ba33eeac6286a8f13f134e42393a7e0ed8a7da6b7909eb1fbe61ebc251.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 266, + 547, + 322 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 547, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 547, + 322 + ], + "type": "text", + "content": "Figure 4. Overview of Our Proposed Safe Generation Framework, Detect-and-Guide (DAG). The notations for (a) Original Generation can be found in Sec. 2. In (b), DAG utilizes guideline token embeddings " + }, + { + "bbox": [ + 46, + 266, + 547, + 322 + ], + "type": "inline_equation", + "content": "c^*" + }, + { + "bbox": [ + 46, + 266, + 547, + 322 + ], + "type": "text", + "content": " to perform self-diagnostics by calculating cross-attention maps (CAM) at higher-level hidden states of the U-Net. The " + }, + { + "bbox": [ + 46, + 266, + 547, + 322 + ], + "type": "inline_equation", + "content": "c^*" + }, + { + "bbox": [ + 46, + 266, + 547, + 322 + ], + "type": "text", + "content": " is optimized in advance on a small annotated dataset for precisely segmenting unsafe regions, addressing the problem of cross-attention leakage [49]. In (c), DAG achieves safe self-regulation by editing the detected unsafe regions. This editing process uses pixel-level magnitudes that are adaptively determined based on region area and CAM values." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 334, + 288, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 288, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 288, + 417 + ], + "type": "text", + "content": "As further illustrated in Figure 5, CAMs for non-target concepts, such as 'a nude wall', will contain only a few values larger than 0.5 (i.e., they will not be detected), which can serve as an indicator of the presence of unsafe content. We analyze the distribution of CAM values in Sec. 3.2 to develop an adaptive scaling strategy that best balancing sexual content erasure and mode preservation." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 75, + 424, + 257, + 517 + ], + "blocks": [ + { + "bbox": [ + 75, + 424, + 257, + 517 + ], + "lines": [ + { + "bbox": [ + 75, + 424, + 257, + 517 + ], + "spans": [ + { + "bbox": [ + 75, + 424, + 257, + 517 + ], + "type": "image", + "image_path": "bfd3d59b63df80ba481a511282c670b80e5398697d5728f8fe65cd96b72a87bf.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 521, + 287, + 553 + ], + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 553 + ], + "type": "text", + "content": "Figure 5. The comparison of cross-attention map with non-optimized token embeddings and their effect on performing the self-regulation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 563, + 162, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 162, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 162, + 576 + ], + "type": "text", + "content": "3.2. Safe Self-regulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "text", + "content": "With the attention maps of guideline detection, we then utilize the idea of classifier-free guidance [14] to adjust a noisy latent in an unsafe mode to a nearby safe mode during sampling following the implementation of safety guidance [3, 41]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "The classifier-free guidance introduces a null-text embedding " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\varnothing = \\tau_{\\theta}({}^{\\prime \\prime \\prime \\prime})" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": " as the unconditional generative probability beyond the conditional probability to estimate the gradient of an implicit classifier. We denote unconditional estimated noise as " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon^{\\emptyset}" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": ", conditional estimated noise as " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon^{p}" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": " and the scale of guidance as " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "s_g" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": " (default as 7.5 for SDv1.4)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "type": "text", + "content": "Similarly, safety guidance [41] introduces a safety condition " + }, + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "type": "inline_equation", + "content": "c_{s} = \\tau_{\\theta}(p_{s})" + }, + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "type": "text", + "content": " and the corresponding estimated noise " + }, + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\epsilon^{c_s}" + }, + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "type": "text", + "content": " that reuses the implicit Bayesian classifier for conditional probability [14] to adjust the estimated gradient with selective pixel-level scale map " + }, + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{c_s}\\cdot \\mathbf{M}_{c_s}" + }, + { + "bbox": [ + 305, + 334, + 545, + 395 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 323, + 400, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 400, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 323, + 400, + 545, + 456 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\epsilon} _ {\\theta} (x _ {t}, t, c _ {p}) ^ {\\mathrm {C F}} = (1 - s _ {g}) \\underbrace {\\epsilon_ {\\theta} (x _ {t} , t , \\varnothing)} _ {\\epsilon^ {\\emptyset}} + s _ {g} \\underbrace {\\epsilon_ {\\theta} (x _ {t} , t , c _ {p})} _ {\\epsilon^ {p}} \\\\ = \\epsilon^ {\\varnothing} + s _ {g} \\underbrace {\\left(\\epsilon^ {\\varnothing} - \\epsilon^ {p}\\right)} _ {\\tilde {\\epsilon} ^ {p}} \\tag {4} \\\\ \\end{array}", + "image_path": "62f4013abc47b982e6c7495f8ed721845ca0b6f36beedd42cffb9f7fe68b7265.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 459, + 544, + 474 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 459, + 544, + 474 + ], + "spans": [ + { + "bbox": [ + 307, + 459, + 544, + 474 + ], + "type": "interline_equation", + "content": "\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, t, c _ {p}, c _ {s}\\right) ^ {\\text {S a f e}} = \\left(1 - s _ {g}\\right) \\epsilon^ {\\varnothing} + s _ {g} \\left(\\epsilon^ {p} - \\mathbf {S} _ {c _ {s}} \\cdot \\mathbf {M} _ {c _ {s}} \\epsilon^ {c _ {s}}\\right).", + "image_path": "036fd3bb05d407a5c4b958ee118c758a416430295d769327cf41e12b443c5a96.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 481, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 626 + ], + "type": "text", + "content": "For the purpose of safe generation, guidance-based methods are advanced in the capability of discovering the direction of a nearby safe mode given an existing unsafe mode. However, the safety guidance applied in an early stage will introduce severe mode shift that affect the generation quality, with necessity of warm-up steps " + }, + { + "bbox": [ + 304, + 481, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\underline{t}_{c_s}" + }, + { + "bbox": [ + 304, + 481, + 545, + 626 + ], + "type": "text", + "content": " to regulate the mode change. Therefore, we leverage detection maps " + }, + { + "bbox": [ + 304, + 481, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\hat{A}(c^*)" + }, + { + "bbox": [ + 304, + 481, + 545, + 626 + ], + "type": "text", + "content": " as a gate function to enable adaptive guidance scale (stronger when detected with higher confidence) that also works at higher noise level and prevent severe mode shift. The overall comparison of how our method apply safety guidance is different from existing methods is shown in Table 1." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "text", + "content": "The safety scale map " + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{c_s}" + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "text", + "content": " used in DAG depends on (i) a scalar denoted as " + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{Area}_{0.5}(\\hat{A})" + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "text", + "content": ", which highlights the area of detected unsafe region with a confidence no less than 0.5, as the yellow region shown in Figure 4-(b), along with a base weight of 5 for pixel editing " + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\overline{s}_c = \\frac{5}{H\\times W}" + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "text", + "content": "; and (ii) a magnitude scalar " + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "inline_equation", + "content": "T_{0.01}(\\hat{A})" + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "text", + "content": " based on confidence value of attention map " + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\hat{A} = \\{a\\}_{:h,w}" + }, + { + "bbox": [ + 304, + 627, + 546, + 714 + ], + "type": "text", + "content": ", which assigns an appropri" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "text", + "content": "13256" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 101, + 84, + 488, + 170 + ], + "blocks": [ + { + "bbox": [ + 175, + 71, + 417, + 82 + ], + "lines": [ + { + "bbox": [ + 175, + 71, + 417, + 82 + ], + "spans": [ + { + "bbox": [ + 175, + 71, + 417, + 82 + ], + "type": "text", + "content": "Table 1. Notations for classifier-free guidance and safety guidance." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 101, + 84, + 488, + 170 + ], + "lines": [ + { + "bbox": [ + 101, + 84, + 488, + 170 + ], + "spans": [ + { + "bbox": [ + 101, + 84, + 488, + 170 + ], + "type": "table", + "html": "
    CF [14]SLD [41]SEGA [3]DAG (Ours)
    ε∅1 - sg1 - sg + sg · Scs · Mcs
    εpsgsg
    εcs--sg · Scs · Mcs
    Scs-max(εp - εcs, 1)scs(¯¯¯¯sc · Area0.5(Â)) ⊙ T0.01(Â)
    Mcs-I(εcschw + λ > εpchw)chwI[¯¯¯¯epsilonchw ∈ top-p(¯¯¯¯epsiloncs)]chwI[ ≥ 0.01]:hw ⊙ McsSEGA/SLD
    tcs-7 (strong), 10 (medium), 15 (weak)105
    ", + "image_path": "4b06e0203af54cbb3727bc8909b61668823cfbc8b764834912ffdb3506dbc0f8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "text", + "content": "ate editing scale only for pixels whose confidence satisfies " + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "inline_equation", + "content": "0.01 \\leq a \\leq 1" + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "text", + "content": " by rescaling their attention values to range " + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "inline_equation", + "content": "1 \\leq T_{0.01}(a) \\leq 5" + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "text", + "content": ". Besides the scale map, we simply set a gate function " + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "inline_equation", + "content": "\\hat{A} \\geq 0.01" + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "text", + "content": " to the safety selective mask of existing methods, as the green region demonstrated in Figure 4-(b). We use " + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{c_s}^{\\mathrm{SEGA}}" + }, + { + "bbox": [ + 46, + 184, + 289, + 269 + ], + "type": "text", + "content": " in main experiments and compare different safety guidance methods in Supp. B." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 279, + 128, + 293 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 128, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 128, + 293 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 299, + 157, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 299, + 157, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 299, + 157, + 312 + ], + "type": "text", + "content": "4.1. Evaluation Setting" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 318, + 287, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 287, + 353 + ], + "type": "text", + "content": "In this section, we comprehensively evaluate the effectiveness of DAG in erasing sexual content from three perspectives:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "text", + "content": "Erasing Effectiveness and Robustness. We utilize 931 sexual prompts from real-world harmful prompts benchmark Inappropriate Image Prompts (I2P) [41] to evaluate effectiveness, denoted as I2P-sexual. Additionally, we filter a subset of complex prompts containing terms, resulting in a 439-prompt subset, denoted as I2P-sexual-complex. To assess robustness, we further leverage two black-box adversarial prompt datasets, Ring-A-Bell (RAB)[46] and MMA[50]. We use 1,000 released adversarial prompts from MMA focused on sexual content generation, and we implement RAB attacks on I2P-sexual-complex, resulting in 439 adversarial prompts." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": "We employ a YOLO-based nudity detector NudeNet [32] to evaluate unsafe content in generated images from I2P-sexual, RAB and MMA, where each prompt generates four images using fixed seeds, producing a total of 9480 images per method. We apply NudeNet's five unsafe classes and a confidence threshold of 0.6 to calculate the evaluation results. We report the number of detected unsafe classes as NudeNet Number (N3), and calculate the Erase Rate (ER) compared to undefended SDv1.4 as follows: " + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{ER} = 1 - \\frac{\\mathrm{N3}_{\\mathrm{defense}}}{\\mathrm{N3}_{\\mathrm{SDv1.4}}}" + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": ", where all unsafe concepts erased will give a " + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": " ER." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Fine-grained erase performance. We consider that a harmful prompt may contain multiple concepts, and thus the design principle of safe generation should account for prompt-following performance on the remaining safe concepts. To assess this, we introduce an advanced metric, VQA Score [24], which evaluates text-to-image alignment using pre-trained large VLMs (CLIP-FlanT5-XL). We eval" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 184, + 545, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 184, + 545, + 279 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 545, + 279 + ], + "type": "text", + "content": "uate the alignment capability of the erased models on I2Psexual dataset by prepending a short task description 'Safe Generation:' to the prompt before feeding the (prompt, image) pair into the VLM evaluator. This metric, denoted as VQA Score-SG, reflects the self-regulation capability of safely following the harmful prompt. We use VQA Score as a sanity check to ensure safety methods 018 do not degrade normal generation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 280, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 280, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 280, + 545, + 388 + ], + "type": "text", + "content": "Model Utility. We resample 1000 prompts from the MS-COCO validation dataset [23] as benign prompts to evaluate model utility, denoted as COCO-1K. Image quality metrics include " + }, + { + "bbox": [ + 304, + 280, + 545, + 388 + ], + "type": "inline_equation", + "content": "FID_{\\mathrm{real}}" + }, + { + "bbox": [ + 304, + 280, + 545, + 388 + ], + "type": "text", + "content": ", which measures the similarity between generated images generated by erased models and real images from MS-COCO, and " + }, + { + "bbox": [ + 304, + 280, + 545, + 388 + ], + "type": "inline_equation", + "content": "FID_{\\mathrm{SDv1.4}}" + }, + { + "bbox": [ + 304, + 280, + 545, + 388 + ], + "type": "text", + "content": ", which assesses the mode shift introduced by erasing methods. We also calculate the VQA Score on resampled data to evaluate generation capability." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 388, + 546, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 567 + ], + "type": "text", + "content": "Baselines. In our experiments, we compare against nine popular unlearning methods under different settings, resulting in a total of eleven erasing baselines (ESD [9], SLD-(weak, medium, strong) [42], SPM [29], SA [12], SalUn [8], Self-Dis [22], SEGA [3], MACE [27], AdvUnlearn [52]). The baseline model with no defense is SDv1.4, and we also conduct experiments on SDv2.1, which training data is filtered by an NSFW detector, to serve as a retraining baseline. For the fine-tuning-based erasing methods, we download their official checkpoints for erasing the concept of nudity. For the safety guidance-based methods, we run their official generating scripts with hyper-parameters from their paper. For SEGA, we set the scale of semantic guidance to 10 (default as 5) and reverse the guidance for effectively removing nudity from generation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 575, + 419, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 419, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 419, + 586 + ], + "type": "text", + "content": "4.2. Erase Performance" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Erase Effectiveness and Model Utility Perservation We generate 9840 images for each method, and report the NudeNet detection results of five unsafe classes. The erasure effectiveness of the proposed method compared with baselines are demonstrate in Table 2. Our method, DAG, outperforms all guidance-based methods (three variants of SLD and SEGA) and achieves competitive erasure performance compared to fine-tuning-based methods (SA, SPM) and SDID. Fine-tuning-based methods with strong erasure performance come at the cost of lower generation quality on" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "text", + "content": "13257" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 72, + 420, + 224 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 420, + 224 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 420, + 224 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 420, + 224 + ], + "type": "table", + "html": "
    MethodsGeneration Quality (COCO-1K)Erase Effectiveness (I2P-sexual)
    VQA Score\\( FID_{\\text{real}} \\downarrow \\)\\( FID_{\\text{SDv1.4}} \\downarrow \\)Total↓ButtocksChest(F)Genitalia(F)Chest(M)Genitalia(M)
    SDv1.4 [39]0.7058.03010708383854914
    SLD-weak [41]0.6859.3823.348566267148723
    SLD-medium [41]0.7061.1531.736605550633615
    SLD-strong [41]0.6462.8741.14207271447272
    SEGA [3]0.7058.9533.4715511873513
    SDID [21]0.7357.931.521812512212166
    ESD-u [10]0.6358.0150.55631492110
    SA [12]0.6763.8353.9711411841450
    SalUn [7]0.4280.2787.68000000
    SPM [29]0.7157.6235.372083813917131
    MACE [27]0.5955.9951.01565363102
    AdvUnlearn [52]0.5460.0244.561018001
    DAG (ours)0.7258.2223.67861471325
    ", + "image_path": "7a4630282cffc9717ff56d45b720c1d1b575ab3ac313b838e76aaeee7fca98bb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 229, + 422, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 422, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 422, + 264 + ], + "type": "text", + "content": "Table 2. Assessment of Unsafe Concept Erase: Evaluation of FIDs and VQA scores on COCO-1K and the count of unsafe concepts detected by NudeNet on I2P-sexual. We use best, second-best and third-best to highlight the top-3 results, respectively. Italicized methods are fine-tuning-based." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 432, + 72, + 542, + 217 + ], + "blocks": [ + { + "bbox": [ + 432, + 72, + 542, + 217 + ], + "lines": [ + { + "bbox": [ + 432, + 72, + 542, + 217 + ], + "spans": [ + { + "bbox": [ + 432, + 72, + 542, + 217 + ], + "type": "image", + "image_path": "eb05d808fa60bd3b880e2a67d57542ca34bf8de5f16edf2e49340a520fca1b98.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 430, + 219, + 545, + 263 + ], + "lines": [ + { + "bbox": [ + 430, + 219, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 430, + 219, + 545, + 263 + ], + "type": "text", + "content": "Figure 6. Erase rate " + }, + { + "bbox": [ + 430, + 219, + 545, + 263 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 430, + 219, + 545, + 263 + ], + "type": "text", + "content": " on I2P-sexual, measuring the relative deduction of unsafe concepts compared to SDv1.4." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 112, + 298, + 178, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 298, + 178, + 346 + ], + "spans": [ + { + "bbox": [ + 112, + 298, + 178, + 346 + ], + "type": "text", + "content": "woman with shiny skin lying on the grass dressed in roman clothes, ultra detailed, Guido Reni style" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 113, + 379, + 174, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 379, + 174, + 445 + ], + "spans": [ + { + "bbox": [ + 113, + 379, + 174, + 445 + ], + "type": "text", + "content": "'high resolution " + }, + { + "bbox": [ + 113, + 379, + 174, + 445 + ], + "type": "inline_equation", + "content": "8k_{\\mathrm{e}}" + }, + { + "bbox": [ + 113, + 379, + 174, + 445 + ], + "type": "text", + "content": " close up portrait photograph of Selena Gomez, dressed in bikini, standing near the beach, vogue photoshoot" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 183, + 274, + 482, + 447 + ], + "blocks": [ + { + "bbox": [ + 183, + 274, + 482, + 447 + ], + "lines": [ + { + "bbox": [ + 183, + 274, + 482, + 447 + ], + "spans": [ + { + "bbox": [ + 183, + 274, + 482, + 447 + ], + "type": "image", + "image_path": "f7c20188561e86f9c57dce8228c44b4813a3cb034d015451f41ee1f4c41bac76.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 450, + 544, + 473 + ], + "lines": [ + { + "bbox": [ + 46, + 450, + 544, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 544, + 473 + ], + "type": "text", + "content": "Figure 7. Qualitative Experiments. The examples are randomly sampled from I2P-sexual. Note that not all prompts in I2P-sexual can generate harmful images, and the regional specification advantages of DAG can be observed." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 485, + 288, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 288, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 288, + 605 + ], + "type": "text", + "content": "the benign dataset COCO-1K. For example, the strongest defense methods suffer from severe distribution shifts when generating non-target concepts and fail to achieve text-to-image alignment, as quantitatively observed by a significantly lower VQA Score (0.42) compared to ours (0.72) and SDv1.4 (0.70). We visualize the trade-off between generation quality and erasure performance in Figure 1 (right), showing that our method, without expensive retraining or fine-tuning, achieves the optimal balance by incorporating optimized token-based detection maps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Erase Robustness. We conduct robustness experiments using two black-box adversarial prompt attacks: Ring-A-Bell and MMA. Ring-A-Bell is based on CLIP-embedding inversion to reconstruct the token sequence with similar semantics to an unsafe embedding. MMA conducts a sensitive word replacement attack and generates adversarial prompts in natural language. We present the results in Ta" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 485, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 485, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 485, + 545, + 521 + ], + "type": "text", + "content": "ble 3. Note that our results align with fine-tuning-based methods in robustness evaluations, without any weight tuning or modifications." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": "Fine-grained Erase Performance. We demonstrate the VQA Score-SG in Figure 8 to measure the text-to-image alignment degree of erased methods on the datasets I2P-sexual. DAG ranks the second in the results, and primarily benefit from the restriction of guidance in detected unsafe region, which introduce slightly background modification as demonstrated in Figure 7." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 634, + 413, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 413, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 413, + 647 + ], + "type": "text", + "content": "4.3. Parameters Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Although the optimized embeddings can meet both generalizability and specificity, one remaining question is how the detection performance varies across different noise levels and whether it can be aggregated using a smaller number of maps, such as one. We visualize the detection map at dif" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "text", + "content": "13258" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 86, + 531, + 256 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 545, + 82 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 545, + 82 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 545, + 82 + ], + "type": "text", + "content": "Table 3. Erasure Robustness for Nudity: Best, Second-best and Third-best highlight top-3 results. Italicized methods are fine-tuning-based." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 86, + 531, + 256 + ], + "lines": [ + { + "bbox": [ + 61, + 86, + 531, + 256 + ], + "spans": [ + { + "bbox": [ + 61, + 86, + 531, + 256 + ], + "type": "table", + "html": "
    Defense MethodsRing-a-bell Adversarial PromptsMMA Adversarial Prompts
    Erase Rate↑ (%)Total↓ButtocksChest (F)Genitalia (F)Chest (M)Genitalia (M)Erase Rate↑ (%)Total↓ButtocksChest (F)Genitalia (F)Chest (M)Genitalia (M)
    SDv1.40.003279115249€342266600.002732413154€83301391
    SLD-weak(7.44)3523107266543526848(1.57)2775433151782336407
    SLD-medium(7.11)3512742725433246341.542690410142095360405
    SLD-strong43.15186433163810090348.43140928369233174227
    SEGA66.54109723768452511065.419452333007248157
    SDID87.6840434309124547.142537373144474306340
    ESD-u87.74402143271346297.806020222214
    SA48.031704431393146122089.602846219012011
    SalUn100.0000000099.93202000
    SPM87.07424293172255149.34138430866639208163
    MACE99.57142921099.411654016
    AdvUnlearn100.0000000099.491428022
    DAG (ours)88.14389102067166077.601276121854183113
    ", + "image_path": "b87518c8197e013de732957bba802d12fab68a351ddf1deb9a3f3ecd1972ba22.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 272, + 281, + 365 + ], + "blocks": [ + { + "bbox": [ + 50, + 272, + 281, + 365 + ], + "lines": [ + { + "bbox": [ + 50, + 272, + 281, + 365 + ], + "spans": [ + { + "bbox": [ + 50, + 272, + 281, + 365 + ], + "type": "image", + "image_path": "e95ef35fb4ed816db851535c45f09716b098e5ea53d4203b38118a862e53143f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 367, + 287, + 399 + ], + "lines": [ + { + "bbox": [ + 46, + 367, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 287, + 399 + ], + "type": "text", + "content": "Figure 8. The VQA Score-SG (prepend 'Safe Generation:' to the prompt for text-to-image alignment evaluation) " + }, + { + "bbox": [ + 46, + 367, + 287, + 399 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 367, + 287, + 399 + ], + "type": "text", + "content": " on I2P-sexual datasets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 52, + 404, + 286, + 528 + ], + "blocks": [ + { + "bbox": [ + 52, + 404, + 286, + 528 + ], + "lines": [ + { + "bbox": [ + 52, + 404, + 286, + 528 + ], + "spans": [ + { + "bbox": [ + 52, + 404, + 286, + 528 + ], + "type": "image", + "image_path": "79dd37a9565ee692b34043b1cf98de026bad26020384f0673688ad0a5fc7f7f2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 540, + 287, + 562 + ], + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 562 + ], + "type": "text", + "content": "Figure 9. Comparisons of single-step attention map and multi-step attention map." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 573, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 573, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 573, + 287, + 608 + ], + "type": "text", + "content": "ferent steps stacked using different number of maps in Figure 9, and observe that single-step CAM can be sufficient for the detection." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 620, + 119, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 119, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 119, + 633 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Our proposed methods, DAG, offers a fine-grained approach to sexual concept erasure for safe generation. DAG leverages specific internal knowledge of diffusion models that can be activated through cross-attention layers to detect unsafe concepts. We apply fine control to the cross-attention maps by optimizing guideline token embeddings," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 277, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 337 + ], + "type": "text", + "content": "enabling the attention map to provide information about unsafe intensity and regions. This allows us to improve erasure methods based on safety guidance, addressing the limitations of unbounded guidance regions that may cause unnecessary mode shifts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 346, + 546, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 546, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 546, + 597 + ], + "type": "text", + "content": "Though Detect-and-Guide is effective at erasing nude visual content and achieves both safe and high-quality generation, some unsafe concepts may still be generated by then models. We investigate the failure cases and categorize the generation of nudity concepts into two trajectory types: The first type, easy-to-erase nudity, typically appears in the later stage of denoising. For example, a nude mark for a person in a painting emerges later than for a person in the gallery, as shown in Figure 4. This phenomenon recurs in Figure 3-(a), where three marble sculptures of different sizes require varying degrees of scaling strength to ensure they are all reliably removed. This observation motivates the design of a CAM area-basedScaler in Sec. 3.2. The second type, hard-to-erase nudity, occurs when prompts trigger memorized unsafe images, straying significantly from other safe modes that make it challenging to adjust towards a safe mode effectively. In these cases, the sampling mode collapses rapidly within the first few steps (e.g., " + }, + { + "bbox": [ + 304, + 346, + 546, + 597 + ], + "type": "inline_equation", + "content": "< 5" + }, + { + "bbox": [ + 304, + 346, + 546, + 597 + ], + "type": "text", + "content": " sampling times), making guidance on this collapsed latent less effective. We leave the identification and mitigation of memorized unsafe images to future work." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "While the contradiction between generation performance (including prompt-following capability, generation diversity, and image quality) and erasure effectiveness is currently complex and difficult to reconcile, our work takes an initial step toward fine-grained self-regulation of T2I diffusion models that mitigates this issue to some extent. We also suggest that safety mechanisms for generative models should integrate these advancements to enhance both interpretability and usability." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 294, + 753, + 317, + 762 + ], + "type": "text", + "content": "13259" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 145, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 145, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 145, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 289, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 289, + 200 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 289, + 200 + ], + "type": "text", + "content": "We are thankful to the shepherd and reviewers for their careful assessment and valuable suggestions, which have helped us improve this paper. This work was supported in part by the National Natural Science Foundation of China (62472096, 62172104, 62172105, 62102093, 62102091, 62302101, 62202106). Min Yang is a faculty of the Shanghai Institute of Intelligent Electronics & Systems and Engineering Research Center of Cyber Security Auditing and Monitoring, Ministry of Education, China." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 209, + 107, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 209, + 107, + 220 + ], + "spans": [ + { + "bbox": [ + 48, + 209, + 107, + 220 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 228, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 228, + 287, + 281 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 228, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 53, + 228, + 287, + 281 + ], + "type": "text", + "content": "[1] Samyadeep Basu, Nanxuan Zhao, Vlad I Morariu, Soheil Feizi, and Varun Manjunatha. 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Although previous detection methods achieve high performance in detecting gradient-based adversarial attacks, new attacks based on generative models with imbalanced and anisotropic noise patterns evade detection. Even worse, the significant inference time overhead and limited performance against unseen attacks make existing techniques impractical for real-world use. In this paper, we explore the proximity relationship among adversarial noise distributions and demonstrate the existence of an open covering for these distributions. By training on the open covering of adversarial noise distributions, a detector with strong generalization performance against various types of unseen attacks can be developed. Based on this insight, we heuristically propose Perturbation Forgery, which includes noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production, to train an adversarial detector capable of detecting any unseen gradient-based, generative-based, and physical adversarial attacks. Comprehensive experiments conducted on multiple general and facial datasets, with a wide spectrum of attacks, validate the strong generalization of our method.", + "bbox": [ + 89, + 335, + 485, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 744, + 220, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Numerous studies have demonstrated the effectiveness of deep neural networks (DNNs) in various tasks [36]. However, it is also well-known that DNNs are vulnerable to adversarial attacks, which generate adversarial data by adding imperceptible perturbations to natural images, potentially causing the model to make abnormal predictions. This vul", + "bbox": [ + 89, + 771, + 483, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "nerability reduces the reliability of deep learning systems, highlighting the urgent need for defense techniques. Some approaches employ adversarial training techniques [48], which incorporate adversarial data into the training process to inherently bolster the model's immunity against adversarial noise (adv-noise). Other methods utilize adversarial purification [47] to cleanse the input data of adv-noise before model inference. Unfortunately, adversarial training often results in diminished classification accuracy on adversarial data and may sacrifice performance on natural data [1]. While purification techniques may seem more reliable, the denoising process can inadvertently smooth the high-frequency texture of clean images, leading to suboptimal accuracy on both natural and adversarial images.", + "bbox": [ + 511, + 305, + 906, + 517 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Another branch of adversarial defense is adversarial detection [12, 28], which aims to filter out adversarial data before they are fed into target systems. These methods rely on discerning the discrepancies between adversarial and natural distributions, thereby maintaining the integrity of target systems while achieving high performance in defending against adversarial attacks. However, existing adversarial detection approaches primarily train specialized detectors tailored for specific attacks or classifiers [8], which may not generalize well to unseen advanced attacks [2, 39].", + "bbox": [ + 511, + 518, + 908, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some recent approaches [40, 49] have attempted to enhance the generalization of adversarial detectors by leveraging diffusion models and manually designed pseudo-noise. Nevertheless, as shown in Table 1, this improvement often comes at the expense of increased inference overhead, and even well-trained detectors still struggle with adversarial data produced by generative models such as generative adversarial networks (GANs) and diffusion models. Specifically, generative-based adversarial attacks, such as M3D [51] and Diff-PGD [44], are recently developed techniques designed to generate more natural adversarial data. Unlike traditional gradient-based attacks like PGD [29], generative-based attacks tend to create imbalanced and anisotropic perturbations that are intense in high-frequency and salient areas but mild in low-frequency and background", + "bbox": [ + 511, + 674, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author\n1Code at https://github.com/cc13qq/PFD", + "bbox": [ + 107, + 875, + 326, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13917", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/a6b37e916f4ead15a851cab4e3e7913e55c12fb59390d923aefa7b3b58b0851a.jpg", + "table_caption": [ + "Table 1. Properties of our method vs Other Adversarial Detection: We summarize four metrics for adversarial detection. \"Detect Attacks\" specifies the types of attacks each method is designed to detect. \"Model-Agnostic\" indicates whether the detection method operates independently of the protected model. \"Unseen-Attack Detection\" assesses the method's generalization to detect previously unseen attacks, with the reported value representing the AUROC score for detecting the MIFGSM attack on the ImageNet dataset. Lastly, \"Time Overhead\" quantifies the time required for the detector to process 100 samples from the ImageNet dataset." + ], + "table_footnote": [], + "table_body": "
    MethodsDetect AttacksModel-AgnosticUnseen-Attack DetectionTime Overhead
    LID [28]Gradient×0.91461.80s
    LiBRe [8]Gradient×0.87252.56s
    SPAD [40]Gradient + GAN✓0.98204.56s
    EPSAD [49]Gradient✓0.9918396.81s
    OursGradient + GAN + Diffusion✓0.99314.85
    ", + "bbox": [ + 129, + 169, + 869, + 284 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "areas. These perturbations make them harder to detect with current methods, posing a new challenge to the field of adversarial detection. Therefore, there is an urgent need for a low-time-cost detection method with strong generalization performance against both unseen gradient-based attacks and unseen generative-based attacks.", + "bbox": [ + 88, + 308, + 480, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we investigate the association between the distributions of different adv-noises. As shown in Figure 1, by modeling noise as multivariate Gaussian distributions, we define the proximity relationship of the noise distributions in a metric space and establish a perturbation method to construct the proximal distributions. Based on the assumption and definition, we demonstrate that all adv-noise distributions are proximal using the Wasserstein distance, and we deduce a corollary that an open covering of the adv-noise distributions exists. We then propose the core idea of this paper: by training on the open covering, we obtain a detector with strong generalization performance against various types of unseen attacks.", + "bbox": [ + 88, + 400, + 482, + 597 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on this idea, we propose Perturbation Forgery, a pseudo-adversarial data (pseudo-adv-data) generation method designed to train a detector with strong generalization capabilities for detecting various types of adversarial attacks. As shown in Figure 2, Perturbation Forgery comprises noise distribution perturbation, sparse mask generation, and pseudo-adversarial data (pseudo-adv-data) production. By continuously perturbing the noise distribution of a commonly used attack, such as FGSM [15], we obtain a nearly complete family of distributions that form the aforementioned open covering. Simultaneously, sparse masks are generated using attention maps and saliency maps of the natural data, converting the sampled global noises into local forms to help the detector focus on local noise patterns so as to detect generative-based adv-noise. By sampling noise from the perturbed noise distributions, we sparsify it using sparse masks and inject it into natural data. This process converts half of the natural data into pseudo-adv-data, replacing actual adversarial data. The pseudo-adv-data is then combined with the remaining uncontaminated data to train", + "bbox": [ + 91, + 599, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the binary adversarial detector.", + "bbox": [ + 511, + 309, + 718, + 323 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To the best of our knowledge, we are the first to empower a detector with the robust ability to detect various types of adversarial attacks, including gradient-based, GAN-based, diffusion-based, and physical attacks, with minor inference time overhead.", + "bbox": [ + 511, + 324, + 906, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized in four thrusts:", + "bbox": [ + 532, + 398, + 861, + 414 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- By modeling adversarial noise as Gaussian distributions, we investigate the association between different adversarial noise distributions and demonstrate their proximity in a metric space.", + "- Based on our assumption and definition, we deduce the existence of an open covering for adversarial noise distributions and propose training a detector to distinguish this open covering from the natural data distribution, thereby achieving strong generalization in detection.", + "- Building on our deductions, we propose Perturbation Forgery, which includes noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production. This method is designed to train a binary detector with strong generalization performance against various types of unseen attacks, including gradient-based, GAN-based, diffusion-based, and physical adversarial data, with minor inference time overhead.", + "- We conduct evaluations on multiple general and facial datasets across a wide spectrum of gradient-based, generative-based, and physical attacks, demonstrating the consistently strong performance of our method in adversarial detection tasks." + ], + "bbox": [ + 511, + 415, + 905, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 762, + 653, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Adversarial Attack", + "text_level": 1, + "bbox": [ + 511, + 787, + 697, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gradient-based adversarial attack Adversarial attacks [15] attempt to fool a classifier into changing prediction results by injecting subtle perturbations to the input data while maintaining imperceptibility from human eyes. By introducing iterative perturbation, PGD [29] and BIM [24] generate adversarial data with significantly im", + "bbox": [ + 511, + 809, + 906, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13918", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/126b929994d65958e289f67770158a3c2b5aecfdc5d1b59a60749148b1a3254d.jpg", + "image_caption": [ + "Figure 1. Illustration of the proximity of adversarial noise distributions and perturbed noise distributions. Left: all the distributions of adversarial noise and the perturbed distributions are in a $\\varepsilon$ -ball centered on a given adversarial noise distribution. Right: by continuously perturbing the given adversarial noise distribution, we obtain an open covering of distributions of adversarial noise." + ], + "image_footnote": [], + "bbox": [ + 109, + 88, + 890, + 277 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "proved attack performance, while DIM [43], NIM [26], and MIM [9] improve the transferability under the black-box setting. Besides, adaptive attacks [6, 13, 18] are proposed to exploit the weak points of each defense, achieving a high attack rate against several defense techniques.", + "bbox": [ + 89, + 354, + 483, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generative-based Adversarial Attacks Recently, another branch of attacks uses generative models to produce adversarial data with a more natural style and imbalanced noise compared to gradient-based attacks. Among them, CDA [31], TTP [30], and M3D [51] utilize GAN to craft adversarial data and achieve higher efficiency when attacking large-scale datasets. Diff-Attack [4] and Diff-PGD [44] employ the diffusion model as a strong prior to better ensure the realism of generated data. Designed for perturbing facial recognition systems, AdvMakeup [46] and AMTGAN [19] are presented to generate imperceptible adversarial images of the face.", + "bbox": [ + 89, + 448, + 483, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, a wide spectrum of gradient-based, generative-based, and physical adversarial attacks on ImageNet and facial datasets is used to evaluate the detection performance of our method.", + "bbox": [ + 89, + 628, + 483, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Adversarial Detection", + "text_level": 1, + "bbox": [ + 89, + 696, + 294, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As one of the technical solutions to ensure the safety of DNNs, there has been a significant amount of exploration in the field of adversarial detection [28].", + "bbox": [ + 89, + 719, + 482, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LiBRe [8] leverages Bayesian neural networks to endow pre-trained DNNs with the ability to defend against unseen adversarial attacks, SPAD [40] leverages a data augmentation method to detect adversarial face images from unseen attack, while EPSAD [49] incorporates a diffusion model to detect adversarial data with minimal attack intensity, albeit at the cost of inference time.", + "bbox": [ + 89, + 763, + 482, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While current methods have achieved remarkable improvements in adversarial detection, generative-based ad", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "versarial attacks are harder to detect, posing a new challenge. To address the problems above, our method is proposed to detect various types of unseen attacks, including gradient-based, generative-based, and physical attacks.", + "bbox": [ + 511, + 354, + 906, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proximity of Adversarial Noise Distribution", + "text_level": 1, + "bbox": [ + 511, + 429, + 903, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we provide an overview of preliminary concepts related to adversarial data generation and explore the relationship between adversarial noise distributions. We define the proximity of noise distributions and present the core idea of this paper: by training on the open covering of adversarial noise distributions, we obtain a detector with strong generalization performance against various types of unseen attacks.", + "bbox": [ + 511, + 454, + 906, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Adversarial data generation", + "text_level": 1, + "bbox": [ + 511, + 585, + 764, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a DNN $f$ that works on dataset $\\mathcal{D} = \\{(\\mathbf{x}_i, y_i)\\}_{i=1}^n$ with $(\\mathbf{x}_i \\in \\mathcal{X}, y_i \\in \\mathcal{C})$ being (sample, ground-truth) pair, an adversarial example $\\hat{\\mathbf{x}}$ regarding sample $\\mathbf{x}$ with attack intensity $\\epsilon$ is calculated as:", + "bbox": [ + 511, + 606, + 905, + 667 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} = \\underset {\\hat {\\mathbf {x}} \\in \\mathcal {B} (\\mathbf {x}, \\epsilon)} {\\operatorname {a r g m a x}} \\mathcal {L} (f (\\hat {\\mathbf {x}}), y), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 679, + 906, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}$ is some loss function and $\\mathcal{B}(\\mathbf{x},\\epsilon) = \\{\\mathbf{x}'|\\ell^p (\\mathbf{x},\\mathbf{x}') < \\epsilon \\}$ restricts the perturbation under $\\ell^p$ norm. Following [15], we simply denote adversarial sample as $\\hat{\\mathbf{x}} = \\mathbf{x} + \\boldsymbol{\\eta}$ .", + "bbox": [ + 511, + 717, + 906, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Proximity of noise distribution", + "text_level": 1, + "bbox": [ + 511, + 787, + 784, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the subtle and imperceptible nature of adv-noise, adversarial data and natural data appear visually similar. Thus, we assume that this similarity also exists between the noises of different adversarial attacks. To investigate the similarity of these noises, we provide the following definition, which depicts a close relationship between two noise distributions.", + "bbox": [ + 511, + 810, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13919", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6373eca2d893772aa2f4d84ff3004f1b98ba9fe2471440f6ca6368ce9e973a00.jpg", + "image_caption": [ + "Figure 2. Illustration of Perturbation Forgery. Before training, we estimate the noise distribution from a commonly used attack, then continuously perturb it in each batch to create an open covering of the adversarial noise distributions. Next, noises sampled from these perturbed distributions are converted into localized noise by applying sparse masks. Finally, pseudo-adversarial data is generated by adding these localized noises to natural samples." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 890, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 1 (Proximal Noise Distribution). Let $P$ and $Q$ be the distribution functions of two independent noise samples $\\mathbf{x}_1$ and $\\mathbf{x}_2$ . We call them proximal noise distributions under $\\varepsilon$ if we have a metric $d(\\cdot, \\cdot)$ and $\\exists \\varepsilon > 0$ , s.t. $d(P, Q) < \\varepsilon$ .", + "bbox": [ + 88, + 366, + 480, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A common assumption for instance feature distribution is to model it as a Gaussian distribution [10]. Obtained by subtracting from natural data and adversarial data, adv-noises naturally form a Gaussian distribution. Therefore, we assume that noise r.v $\\pmb{\\eta} \\in \\mathbb{R}^d$ satisfies truncated Gaussian distribution $\\mathcal{N}(\\pmb{\\mu}, \\sigma^2\\mathbf{I}_d)$ with its truncated interval is $[- \\epsilon, \\epsilon]^d$ . Built upon Definition 1, we derive the following theorem about the association between the distributions of different adv-noises:", + "bbox": [ + 89, + 453, + 483, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1. Let $\\mathcal{P}_a$ be the distribution set composed of all the adversarial noise distributions. Given independent noise distributions $Q_{i}, i \\in N^{+}$ . For $\\forall i \\neq j$ , $Q_{i}$ and $Q_{j}$ are proximal noise distributions if the following conditions are met.", + "bbox": [ + 88, + 599, + 483, + 674 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) $Q_{i},Q_{j}\\in \\mathcal{P}_{a}$", + "2) $\\exists \\epsilon_{\\mu}, \\epsilon_{\\sigma} > 0$ s.t. $\\|\\pmb{\\mu}_i - \\pmb{\\mu}_j\\| < \\epsilon_{\\mu}$ and $|\\sigma_i - \\sigma_j| < \\epsilon_{\\sigma}$ where the $\\|\\cdot\\|$ is a Euclidean norm on $\\mathbb{R}^n$ ." + ], + "bbox": [ + 89, + 676, + 482, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 tells us: 1) All the adversarial noise distributions under the same $\\ell^p$ norm are proximal noise distributions. 2) If the parameters of two noise distributions are sufficiently close to those of a given distribution, we can regard these two distributions as proximal noise distributions.", + "bbox": [ + 89, + 733, + 482, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can further deduce several corollaries of the theorem. 1) All noise distributions proximal to the known adversarial distribution $p(\\pmb {\\eta})$ form an open $\\varepsilon$ -ball centered on $p(\\pmb {\\eta})$ ,denoting as $\\mathcal{P}_{\\varepsilon} = \\{p(\\pmb {\\eta}_i)|d(p(\\pmb {\\eta}_i),p(\\pmb {\\eta})) < \\varepsilon \\}$ , and also form a metric space $(\\mathcal{P}_{\\varepsilon},d)$ .2) The adv-noise distribution set is also located in this ball: $\\mathcal{P}_a\\subset \\mathcal{P}_{\\varepsilon}$ .3) Based on the prop", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "erties of the metric space $(\\mathcal{P}_{\\varepsilon},d)$ , for all subset $\\mathcal{P}_i\\subset \\mathcal{P}_\\varepsilon$ there exists an open covering of the subset: $\\mathcal{P}_i\\subset \\{G_c\\}_{c\\in \\mathbb{I}}$", + "bbox": [ + 511, + 366, + 903, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the corollaries, we deduce the core idea of this paper: Let $p(\\hat{\\eta}_i|\\boldsymbol {\\eta}) = \\mathcal{N}(\\boldsymbol {\\mu} + \\epsilon_{\\mu i},(\\sigma +\\epsilon_{\\sigma i})^2\\mathbf{I}_d),i = 1,2,\\ldots ,n$ denote generated proximal noise distributions of the given adv-noise distribution $p(\\pmb {\\eta}) = \\mathcal{N}(\\pmb {\\mu},\\sigma^2\\mathbf{I}_d)$ , where $\\epsilon_{\\mu i},\\epsilon_{\\sigma i}$ are randomly sampled from uniform distributions and restricted by $\\epsilon_{\\mu i},\\epsilon_{\\sigma i} < \\varepsilon$ . As shown in Figure 1, when $n\\to \\infty$ , we can always obtain a distribution set $\\mathcal{P}_c = \\{p(\\hat{\\eta}_i|\\boldsymbol {\\eta})\\}_{i = 1}^\\infty$ that forms an open covering of the adversarial distribution set $\\mathcal{P}_a$ . By training on the open covering, the detector learns to distinguish between the distributions of natural and adversarial data, enabling it to effectively detect unseen adversarial attacks.", + "bbox": [ + 511, + 398, + 905, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Analysis of distribution assumption, proofs of theorem, and corollaries are provided in the supplementary materials.", + "bbox": [ + 511, + 580, + 905, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Perturbation Forgery", + "text_level": 1, + "bbox": [ + 511, + 630, + 718, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the theory in the last section, we heuristically propose Perturbation Forgery to train a detector with strong generalization against various types of unseen attacks.", + "bbox": [ + 511, + 657, + 905, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As illustrated in Figure 2, Perturbation Forgery encompasses three elements: noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production. At first, the noise distribution of a commonly used attack is continuously perturbed using noise distribution perturbation into numerous noise distributions that remain proximal to the original, thereby forming the open covering. After that, we sample noises from the perturbed distribution and convert them into sparse local noise using sparse mask generation. Subsequently, we convert half of the natural data into pseudo-adv-data using pseudo-adversarial data production. This pseudo-adv data replaces actual adversarial data and is combined with the remaining natural data to", + "bbox": [ + 509, + 704, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13920", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "train a binary detector.", + "bbox": [ + 89, + 90, + 243, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Noise Distribution Perturbation", + "text_level": 1, + "bbox": [ + 89, + 114, + 372, + 128 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the training dataset $\\{(\\mathbf{x}_k,y_k)\\}_{k = 1}^n$ composed by natural data, we add adv-noise on it using a commonly used attack (such as FGSM) and generate adversarial noise features $\\mathcal{D}_{\\mathrm{noise}}\\coloneqq \\{\\mathbf{z}_k = h(\\pmb {\\eta}_k)\\}_{k = 1}^n$ by", + "bbox": [ + 89, + 135, + 483, + 199 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\eta} _ {k} = \\operatorname {A t t a c k} (\\mathbf {x}) - \\mathbf {x}, k \\in [ 1, n ], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 205, + 482, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $h:\\mathcal{X}\\to \\mathbb{R}^d$ is the flattening operation that converts multidimensional data into vectors.", + "bbox": [ + 89, + 229, + 482, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assuming the noise features form a multivariate Gaussian distribution $p(\\mathbf{z}) = \\mathcal{N}(\\boldsymbol {\\mu},\\boldsymbol {\\Sigma})$ [10], we estimate the parameters mean $\\pmb{\\mu}$ and covariance $\\pmb{\\Sigma}$ of $\\mathcal{D}_{\\mathrm{noise}}$ by", + "bbox": [ + 89, + 261, + 483, + 306 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\boldsymbol {\\mu}} = \\frac {1}{N} \\sum_ {k} \\mathbf {z} _ {k}, \\quad \\widehat {\\boldsymbol {\\Sigma}} = \\frac {1}{N} \\sum_ {k} \\left(\\mathbf {z} _ {k} - \\widehat {\\boldsymbol {\\mu}}\\right) \\left(\\mathbf {z} _ {k} - \\widehat {\\boldsymbol {\\mu}}\\right) ^ {\\top}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 313, + 482, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the $i^{\\mathrm{th}}$ batch of training, we perturb the estimated distribution to a proximal noise distribution by", + "bbox": [ + 89, + 357, + 483, + 388 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\boldsymbol {\\mu}} _ {i} = \\widehat {\\boldsymbol {\\mu}} + \\alpha_ {i} \\cdot \\boldsymbol {m} _ {i}, \\quad \\widehat {\\boldsymbol {\\Sigma}} _ {i} = \\widehat {\\boldsymbol {\\Sigma}} + \\beta_ {i} \\cdot \\boldsymbol {V} _ {i}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 393, + 482, + 414 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{m}_i\\sim \\mathcal{N}(0,\\mathbf{I}_d)$ and $\\pmb {V}_i\\sim \\mathcal{N}(0,\\mathbf{I}_{d\\times d})$ are vector and matrix of perturbation. $\\alpha_{i}\\sim U(-\\epsilon_{\\mu},\\epsilon_{\\mu})$ and $\\beta_{i}\\sim$ $U(0,\\epsilon_{\\sigma})$ are scale parameters. After $n$ batches of training, we have a perturbed distribution set $\\{\\mathcal{N}(\\widehat{\\pmb{\\mu}}_i,\\widehat{\\pmb{\\Sigma}}_i)\\}$ , thereby forming the approximate open covering $\\mathcal{P}_c$ . Trained with $\\mathcal{P}_c$ , the detector can distinguish the distributions of natural and adversarial data.", + "bbox": [ + 89, + 421, + 483, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Sparse Mask Generation", + "text_level": 1, + "bbox": [ + 89, + 537, + 318, + 553 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unlike gradient-based adversarial attacks, generative-based attacks tend to generate imbalanced and anisotropic perturbations, showing much intensity in high-frequency and salient areas and mild in low-frequency and background areas. Besides, in physical scenarios, adversarial attacks also tend to add patches to local areas. Noticing this, we propose sparse masks to perturbation forgery to assist the detector in detecting local adv-noises. Previous research has demonstrated that the spectra of real and fake images differ significantly in high-frequency regions [27]. Additionally, generative-based adversarial data manipulate characteristics, such as abnormal color aberrations, in these high-frequency regions [40]. To augment the detection performance on generative-based adversarial data, we need to sparse the pseudo-noise sampled from perturbed noise distribution and highlight the noise in high-frequency regions to mimic the style of generative-based attacks.", + "bbox": [ + 88, + 558, + 482, + 815 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given this, for a natural sample $\\mathbf{x}_{i,k}$ in the $i^{th}$ batch, we first mask the high-frequency area using saliency detection [33] and GradCAM [34]:", + "bbox": [ + 89, + 815, + 483, + 861 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {M a s k} _ {1} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a p} \\left(f _ {s} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {s}\\right) \\cup \\operatorname {M a p} \\left(f _ {c} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {c}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 869, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Training Procedure with Perturbation Forgery \nInput: Training dataset, a commonly used attack, saliency detection model $f_{s}$ , and GradCAM model $f_{c}$ .", + "bbox": [ + 513, + 90, + 906, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: A detector with strong generalization capabilities against various types of unseen attacks.", + "bbox": [ + 513, + 137, + 906, + 167 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Generate adversarial noise using the commonly used attack in Eq. 2.", + "2: Estimate a multivariate Gaussian distribution $p(\\mathbf{z}) = \\mathcal{N}(\\hat{\\mu},\\hat{\\Sigma})$ of adv-noise using Eq. 3.", + "3: for batch $i$ in $1, \\dots, n$ do", + "4: Generate a perturbed noise distribution $p(\\mathbf{z}_i) = \\mathcal{N}(\\hat{\\boldsymbol{\\mu}}_i, \\hat{\\boldsymbol{\\Sigma}}_i)$ using Eq. 4.", + "5: for sample $\\mathbf{x}_{i,k}$ in half of batch $i$ do", + "6: Generate sparse masks $\\mathrm{Mask}(\\mathbf{x}_{i,k})$ using Eq. 8.", + "7: Sample pseudo-adv noise $\\widehat{\\eta}_{i,k}$ using Eq. 9.", + "8: Generate pseudo-adv data $\\widehat{\\mathbf{x}}_{i,k}$ using Eq. 11 and replace $\\mathbf{x}_{i,k}$ .", + "9: end for", + "10: Train the detector on batch $i$ .", + "11: end for" + ], + "bbox": [ + 519, + 170, + 906, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{s}$ and $f_{c}$ are the saliency detection model and Grad-CAM model respectively. $\\operatorname{Map}(\\mathbf{x};\\gamma)$ is a binary indicator function parameterized by $\\gamma$ :", + "bbox": [ + 511, + 428, + 906, + 474 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {M a p} \\left(\\mathbf {x} _ {i, k}; \\gamma\\right) = \\operatorname {C l i p} _ {[ 0, 1 ]} \\left(\\mathbf {x} _ {i, k} - \\gamma \\mathbf {I} _ {\\mathcal {X}}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 487, + 905, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The adv-noise that occurs in the high-frequency region tends to occupy only a small part of the region. Therefore, we select the high-frequency point from the gradient map obtained by Sobel operator [11] to sparsify the mask of sample $\\mathbf{x}_{i,k}$ :", + "bbox": [ + 511, + 516, + 905, + 592 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {M a s k} _ {2} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a p} (\\operatorname {S o b e l} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {l}), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 604, + 903, + 621 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {M a s k} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a s k} _ {1} \\left(\\mathbf {x} _ {i, k}\\right) \\cap \\operatorname {M a s k} _ {2} \\left(\\mathbf {x} _ {i, k}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 623, + 903, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Pseudo-Adversarial Data Production", + "text_level": 1, + "bbox": [ + 511, + 652, + 833, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the $i^{\\mathrm{th}}$ batch of training, we sample pseudo-adv noise from the perturbed distribution by:", + "bbox": [ + 511, + 674, + 905, + 705 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\boldsymbol {\\eta}} _ {i, k} = h ^ {- 1} \\left(\\mathbf {z} _ {i, k}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 715, + 903, + 734 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {i, k} \\in \\left\\{\\mathbf {z} _ {k} \\mid \\mathbf {z} _ {k} \\sim \\mathcal {N} \\left(\\widehat {\\boldsymbol {\\mu}} _ {i}, \\widehat {\\boldsymbol {\\Sigma}} _ {i}\\right) \\text {a n d} p \\left(\\mathbf {z} _ {k}\\right) < \\gamma_ {p} \\right\\} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 737, + 903, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $h^{-1}:\\mathbb{R}^d\\to \\mathcal{X}$ is an inverse function of $h$ to unflatten noise features, and $\\gamma_{p}$ is a threshold that excludes data with a low likelihood. Note that $\\eta_{i}$ is a global noise and needs to be localized by a sparse mask. The pseudo-adv data $\\widehat{\\mathbf{x}}_{i,k}$ is produced by adding the masked local noise to $\\mathbf{x}_{i,k}$ :", + "bbox": [ + 511, + 768, + 905, + 845 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathbf {x}} _ {i, k} = \\mathbf {x} _ {i, k} + \\widehat {\\boldsymbol {\\eta}} _ {i, k} \\otimes \\operatorname {M a s k} \\left(\\mathbf {x} _ {\\mathbf {i}, \\mathbf {k}}\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 861, + 903, + 878 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\otimes$ is Hadamard product.", + "bbox": [ + 511, + 885, + 720, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13921", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/cd3c431dbaa087f115b0d246d1895e117012e7ca69a8a62fddda400dc89da29b.jpg", + "table_caption": [ + "Table 2. Comparison of AUROC scores of detecting gradient-based and adaptive attacks on ImageNet100 under $\\epsilon = 4/{255}$ ." + ], + "table_footnote": [], + "table_body": "
    DetectorBIMPGDDIMMIMNIMAABPDA+EOTMM
    LID [28]0.97820.97500.89420.91460.89770.91240.92020.9227
    LiBRe [8]0.92590.95480.92430.87250.90130.86530.87140.8573
    SPAD [40]0.98460.98510.98150.98200.98230.98900.98850.9811
    EPSAD [49]0.99980.99890.99230.99180.99720.99980.99850.9923
    ours0.99110.99120.98630.99310.99340.99410.99270.9944
    ", + "bbox": [ + 107, + 114, + 885, + 218 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each batch, we convert half of the natural data to pseudo-adv data by Perturbation Forgery and train a binary detector using the Cross-Entropy classification loss [50]. The overall training procedure with Perturbation Forgery is presented in Algorithm 1.", + "bbox": [ + 89, + 242, + 480, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 332, + 225, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate the detection performance of our approach against various adversarial attack methods, we conduct extensive experiments on multiple general and facial datasets. For additional experiments, analyses, and a discussion of limitations, please refer to the supplementary material.", + "bbox": [ + 89, + 358, + 483, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 89, + 444, + 284, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets The datasets used for evaluation include: 1) general datasets: ImageNet100 [7] and CIFAR-10 [23] for evaluate gradient-based and generative-based attacks, and 2) face datasets: Makeup [16] for Adv-Makeup [46], CelebAHQ [21] for AMT-GAN [19], and LFW [14] for TIPIM [45] and physical attacks.", + "bbox": [ + 89, + 465, + 483, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Adversarial Attacks We adopt 5 gradient-based attacks, 3 adaptive attacks, 5 generative-based attacks, and 6 face attacks to evaluate our method. For gradient-based attacks, BIM [24], PGD [29], MIM [9], DIM [43], and NIM [26] are used as the unseen attacks. For adaptive attacks, we adopt AutoAttack (AA) [6], BPDA+EOT [18], and Minimum-Margin Attack (MM) [13]. For generative-based attacks, we adopt 3 GAN-based attacks including CDA [31], TTP [30], and M3D [51], and 2 Diffusion-based attacks including Diff-Attack [4] and Diff-PGD [44]. For face attacks, we adopt 1 gradient-based attack TIPIM [45], 2 GAN-based attacks including AdvMakeup [46] and AMT-GAN [19], and 3 physical attacks including Adv-Sticker [38], Adv-Glasses [35], and Adv-Mask [38]. For each of the above attack methods, adversarial data is generated with the attack intensity of $\\epsilon = 4 / 255$ (except for the unrestricted attacks), and iterative attacks run for 10 steps using step size 2.", + "bbox": [ + 89, + 578, + 482, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines To evaluate our method across various types of adversarial attacks, we compare it with state-of-the-art detection methods from three related research domains:", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "adversarial detection, synthetic image detection, and face forgery detection. For gradient-based attacks, we benchmark against four adversarial detection methods: LID [28], LiBRe [8], SPAD [40], and EPSAD [49]. Since most adversarial detection methods are not designed to address generative-based adversarial attacks, we include a comparison with four synthetic image detection techniques: CNN-Detection [41], LGrad [37], Universal-Detector [32], and DIRE [42]. For detecting GAN-based face attacks, we also compare against two face forgery detection methods, Luo et al.[27] and He et al.[17], as well as ODIN [25].", + "bbox": [ + 511, + 242, + 906, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics Following previous adversarial detection works [49], we employ the Area Under the Receiver Operating Characteristic Curve (AUROC) [20] as the primary evaluation metric to assess the performance of our classification models. The AUROC is a widely recognized metric in the field of machine learning and is particularly useful for evaluating binary classification problems. For fair comparisons, the number of natural data and adversarial data in the experiments remained consistent.", + "bbox": [ + 511, + 426, + 908, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details XceptionNet [5] is selected as our backbone model and is trained on all the above datasets. For adversarial noise distribution estimation, we utilize Torchattacks [22] to generate 1000 noise images for each dataset. The uniform distribution parameters are set as $\\epsilon_{\\mu} = 3$ and $\\epsilon_{\\sigma} = 0.005$ . The threshold of the sample control is set as $\\gamma_{s} = 0.05$ . The thresholds of the binary indicator function are set as $\\gamma_{s} = 0$ , $\\gamma_{c} = 125$ and $\\gamma_{l} = 100$ . FGSM [15] is used as the initial attack, i.e. the commonly used attack, for Perturbation Forgery. Training epochs are set to 10 and convergence is witnessed.", + "bbox": [ + 511, + 580, + 908, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Detecting Gradient-based Attacks", + "text_level": 1, + "bbox": [ + 511, + 757, + 810, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We begin by comparing our method with state-of-the-art techniques in detecting gradient-based attacks on ImageNet100. All the attacks are unseen by both the baseline methods and our method. For each attack, 1,000 adversarial images are generated in the gray-box setting, where the attacker has access to the victim model but is blind to the detection model. All baseline methods are sourced from existing adversarial detection research.", + "bbox": [ + 511, + 780, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13922", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/82ab80270c2d31443a08eb4d08f5a9bc65e03fcc87a674dec15528b5ef3cd280.jpg", + "table_caption": [ + "Table 3. Comparison of AUROC scores of detecting generative-based attacks on ImageNet100." + ], + "table_footnote": [], + "table_body": "
    DetectorCDATTPM3DDiff-AttackDiff-PGD
    CNN-Detection [41]0.70510.67430.69170.39630.5260
    LGrad [37]0.61440.60770.60680.55860.5835
    Universal-Detector [32]0.79450.81700.83120.92020.5531
    DIRE [42]0.89760.90970.91290.90970.9143
    SPAD0.93850.90640.89840.88620.8879
    EPSAD0.96740.69970.72650.47000.1507
    ours0.98780.96780.93640.92230.9223
    ", + "bbox": [ + 107, + 114, + 885, + 247 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/335f14845d7b7f5402c6e6bb38ebaa40bffecba909025025542af1e3234c3bb9.jpg", + "table_caption": [ + "Table 4. Comparison of AUROC scores for detecting various adversarial attacks on the face dataset." + ], + "table_footnote": [], + "table_body": "
    DetectorTIPIIMAdv-StickerAdv-GlassesAdv-MaskDetectorAdv-MakeupAMT-GAN
    LID0.69740.51030.64720.5319He et al. [17]0.52520.8823
    LiBRe0.53450.97390.81400.9993Luo et al. [27]0.61780.6511
    EPSAD0.96470.94620.92600.9578ODIN[25]0.63250.6970
    SPAD0.92560.99750.92440.9863SPAD0.96570.8969
    ours0.98850.99990.99990.9999ours0.97620.9216
    ", + "bbox": [ + 104, + 286, + 888, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As reported in Table 2, although EPSAD performs well, our method demonstrates effective detection (achieving an AUROC score of 0.9931 against MIM and 0.9944 against MM) across a variety of attack methods. These results validate our assumptions about the proximity of the noise distribution. By continuously perturbing the estimated noise distribution of a given attack (FGSM), we obtain an open covering noise of distributions from all the attacks. Given one seen attack, we are able to detect all the unseen attacks. The consistent detection performance verifies the effectiveness of our core idea of training a detector to distinguish the open covering of adv-noise distributions from natural ones and demonstrates the strong generalization capability of our method against gradient-based attacks.", + "bbox": [ + 89, + 412, + 483, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Detecting Generative-based Attacks", + "text_level": 1, + "bbox": [ + 89, + 635, + 401, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To investigate our method's advantage in detecting generative-based attacks, we compared it with state-of-the-art synthetic image detection and adversarial detection methods on ImageNet100. As shown in Table 3, our method significantly outperforms the baseline methods, demonstrating highly effective detection capabilities.", + "bbox": [ + 89, + 657, + 482, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For adversarial detection baselines, the imbalanced noise generated by GAN and diffusion models makes it difficult for these methods, which are typically designed for gradient-based attacks, to detect effectively. In contrast, our sparse mask approach enables effective detection of such localized noise.", + "bbox": [ + 89, + 750, + 482, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Most synthetic image detection methods are less effective in detecting adversarial data crafted from natural samples, with the exception of DIRE[42]. This effectiveness may stem from DIRE's use of reconstruction error from im", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ages generated by diffusion models, which maintains its robustness in this setting.", + "bbox": [ + 511, + 412, + 903, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Detecting Face Adversarial Examples", + "text_level": 1, + "bbox": [ + 511, + 454, + 836, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Adversarial attacks targeting face recognition models represent an important branch of adversarial example research. Therefore, the detection ability of adversarial face examples is an important indicator of the performance of the detector. We perform various adversarial face attacks and compare our approach with state-of-the-art methods from adversarial face detection and face forgery detection.", + "bbox": [ + 511, + 476, + 905, + 582 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 4, our method shows excellent performance against a variety of adversarial attacks targeting faces and surpasses many existing adversarial face detection techniques. It further indicates the ability of the sparse mask to capture the essential characteristics of face adversarial examples and the strong generalization capability of our method.", + "bbox": [ + 511, + 583, + 905, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Ablation Study and Analysis", + "text_level": 1, + "bbox": [ + 511, + 699, + 769, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To further evaluate our method, we report an ablation study on the sparse mask, white-box attack detection results, the impact of the initial attack and the data size for distribution estimation, and the functionality of Perturbation Forgery through visualizations. The impact of hyper-parameters and other analyses are reported in the supplementary materials.", + "bbox": [ + 511, + 720, + 903, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5.1. Impact of each mask", + "text_level": 1, + "bbox": [ + 511, + 821, + 705, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As argued, the sparse mask is proposed to assist the detector in identifying local adversarial noises in generative-based adversarial data. As shown in Table 5, the absence of the saliency detection model $f_{s}$ or the GradCAM model $f_{c}$ has", + "bbox": [ + 511, + 840, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13923", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/67c8fcdb8510f448fcbd9a29f6cdc34a2dff0f8bc00928795dd40f2de4cc396e.jpg", + "table_caption": [ + "Table 5. Ablation study on masks (AUROC score), where $f_{s}$ denotes saliency detection model and $f_{c}$ represents the CAM model." + ], + "table_footnote": [], + "table_body": "
    AblationCDATTPM3DDiff-AttackDiff-PGD
    w/o fs0.97550.95850.93200.91970.9135
    w/o f_c0.98640.95100.92620.90310.9062
    w/o Sobel0.98680.72350.69840.52310.5547
    ", + "bbox": [ + 91, + 128, + 478, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8c1edc90dfaf934c259a7c916e8e932b2d899bd7758a44d6bb19cec997f11aab.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 96, + 213, + 287, + 340 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/42ed1c5d54b7d85134b044e544dd86119c84911ee66cae6d4566e4e0775de8fc.jpg", + "image_caption": [ + "(b)", + "Figure 3. 2D T-SNE visualizations. (a) ImageNet100 flattened noises of adversarial data and Perturbation Forgery-generated data. (b) ImageNet100 features extracted by the backbone model trained with Perturbation Forgery." + ], + "image_footnote": [], + "bbox": [ + 292, + 213, + 478, + 342 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9e9f3e9f3f01778f5e26f7f271ad1174462d7779408edc52af1d0eec8d10cf45.jpg", + "table_caption": [ + "Table 6. AUROC scores against white-box attacks under $\\epsilon = 4/255$ on CIFAR-10." + ], + "table_footnote": [], + "table_body": "
    AttackBIMPGDDIMMIMAA
    AUROC0.91800.91680.90620.90310.9019
    ", + "bbox": [ + 91, + 483, + 483, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "little effect on the overall system. This is because the regions masked by $f_{s}$ and $f_{c}$ are somewhat complementary. However, without the Sobel operation to sparsify the mask, the detector fails to detect most attacks, except for CDA. This is because generative-based adversarial noise tends to be imbalanced and localized, while CDA's noise is more global. The generated pseudo-adversarial noise without Sobel becomes too dense, preventing the detector from effectively focusing on localized noise.", + "bbox": [ + 89, + 551, + 483, + 690 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5.2. Functionality Visualization", + "text_level": 1, + "bbox": [ + 89, + 699, + 326, + 714 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To validate the functionality of our method, we extract features and flattened noise from adversarial data and Perturbation Forgery-generated data, then visualize them using 2D t-SNE projections. All adversarial data originate from unseen attacks. As shown in Figure 3(a), Perturbation Forgery continuously perturbs the adv-noise distribution of the initial attack, thereby forming an open covering for noises from unseen attacks. Individual samples appear as outliers, floating outside the collective noise distribution. As shown in Figure 3(b), by learning to separate natural data from those generated by Perturbation Forgery, the trained detector can effectively distinguish between natural and adversarial data.", + "bbox": [ + 89, + 719, + 485, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/68c5d5d083fea5ddb3a49c3391683c3fae37afd568a0f044db263fdd52e3348d.jpg", + "table_caption": [ + "Table 7. Impact of data size on distribution estimation: AUROC score against PGD under $\\epsilon = 4 / 255$ on CIFAR-10." + ], + "table_footnote": [], + "table_body": "
    Data size10025050075010002000
    AUROC0.82780.93680.98660.99210.99650.9948
    ", + "bbox": [ + 514, + 128, + 903, + 170 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5.3. Detecting White-box Attack", + "text_level": 1, + "bbox": [ + 511, + 202, + 756, + 217 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To verify the robustness of our approach to white-box attacks, i.e., both the victim model and the detector are available to the attacker, we conduct the experiment on CIFAR-10. Following [3], a modified objective of attacks is:", + "bbox": [ + 511, + 224, + 906, + 287 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {\\boldsymbol {\\eta}} \\mathcal {L} (f (\\hat {\\mathbf {x}}), y) + \\alpha \\cdot \\mathcal {L} (f _ {d} (\\hat {\\mathbf {x}}), y _ {d}), s. t. | | \\boldsymbol {\\eta} | | \\leq \\epsilon \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 301, + 906, + 327 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $y$ is the ground-truth label, $y_{d} = 0$ indicates that $\\hat{\\mathbf{x}}$ is an adversarial example, and $\\alpha = 1$ is a constant balancing between the attack of the classifier $f$ and detector $f_{d}$ . As shown in Table 6, our method achieves a high average AUROC of 0.9092, demonstrating its robustness against white-box attacks. This may be attributed to the comprehensive open covering formed by perturbation forgery, which effectively encompasses adversarial data from white-box attacks, making it harder to mislead the trained detector.", + "bbox": [ + 511, + 342, + 906, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5.4. Data size for Distribution Estimation", + "text_level": 1, + "bbox": [ + 511, + 494, + 812, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To assess the influence of data size for distribution estimation, we train detectors using distributions estimated from various data sizes and test them against PGD on CIFAR-10. As shown in Table 7, our method only requires a small amount of data ( $\\geq 500$ samples) to estimate the adversarial noise distribution so as to train an effective detector. Notably, using fewer than 500 samples leads to a significant decrease in detection performance.", + "bbox": [ + 511, + 517, + 908, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 660, + 633, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we explore and define the proximity relationship between adversarial noise distributions. Based on our assumption and definition, we develop a perturbation method to craft proximal distributions and demonstrate an open covering of adversarial noise spaces. Building on this, we propose training detectors on the open coverings to achieve strong generalization against diverse adversarial attacks. We introduce Perturbation Forgery, which combines noise perturbation, sparse mask generation, and pseudo-adversarial data synthesis, enabling detection of unseen gradient-based, generative, and physical attacks, independent of specific models. Extensive experiments validate our approach's effectiveness and generalization with minimal inference overhead.", + "bbox": [ + 511, + 689, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13924", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 269, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported in part by the Natural Science Foundation of China under Grant 62372203 and 62302186, in part by the Major Scientific and Technological Project of Shenzhen (202316021), in part by the National key research and development program of China(2022YFB2601802), in part by the Major Scientific and Technological Project of Hubei Province (2022BAA046, 2022BAA042).", + "bbox": [ + 89, + 114, + 483, + 220 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 232, + 187, + 248 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples. In ICML, pages 274-283. 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In CVPR, pages 8153-8162, 2023. 1, 3, 6" + ], + "bbox": [ + 516, + 92, + 903, + 415 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13926", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Detecting Adversarial Data Using Perturbation Forgery/a87e2166-e7a0-46b8-94b2-0c0c61135018_model.json b/2025/Detecting Adversarial Data Using Perturbation Forgery/a87e2166-e7a0-46b8-94b2-0c0c61135018_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b8c36c5cd8ade0281a9d46dd22a9c4ac80149133 --- /dev/null +++ b/2025/Detecting Adversarial Data Using Perturbation Forgery/a87e2166-e7a0-46b8-94b2-0c0c61135018_model.json @@ -0,0 +1,2475 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.218, + 0.131, + 0.78, + 0.154 + ], + "angle": 0, + "content": "Detecting Adversarial Data Using Perturbation Forgery" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.18, + 0.862, + 0.27 + ], + "angle": 0, + "content": "Qian Wang\\(^{1}\\), Chen Li\\(^{1}\\), Yuchen Luo\\(^{2}\\), Hefei Ling\\(^{1*}\\), Shijuan Huang\\(^{1}\\), Ruoxi Jia\\(^{3}\\), Ning Yu\\(^{4}\\) \n\\(^{1}\\)Huazhong University of Science and Technology, China \\(^{2}\\)Wuhan University, China \n\\(^{3}\\)Virginia Tech, USA \\(^{4}\\)Netflix Eyeline, USA \n{yqwq1996, lhefei, llichen, shijuan_huang} @hust.edu.cn, {yuchenluo} @whu.edu.cn, ruoxijia@vt.edu, ningyu.hust@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.304, + 0.327, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.337, + 0.486, + 0.715 + ], + "angle": 0, + "content": "As a defense strategy against adversarial attacks, adversarial detection aims to identify and filter out adversarial data from the data flow based on discrepancies in distribution and noise patterns between natural and adversarial data. Although previous detection methods achieve high performance in detecting gradient-based adversarial attacks, new attacks based on generative models with imbalanced and anisotropic noise patterns evade detection. Even worse, the significant inference time overhead and limited performance against unseen attacks make existing techniques impractical for real-world use. In this paper, we explore the proximity relationship among adversarial noise distributions and demonstrate the existence of an open covering for these distributions. By training on the open covering of adversarial noise distributions, a detector with strong generalization performance against various types of unseen attacks can be developed. Based on this insight, we heuristically propose Perturbation Forgery, which includes noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production, to train an adversarial detector capable of detecting any unseen gradient-based, generative-based, and physical adversarial attacks. Comprehensive experiments conducted on multiple general and facial datasets, with a wide spectrum of attacks, validate the strong generalization of our method." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.746, + 0.222, + 0.761 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.772, + 0.484, + 0.864 + ], + "angle": 0, + "content": "Numerous studies have demonstrated the effectiveness of deep neural networks (DNNs) in various tasks [36]. However, it is also well-known that DNNs are vulnerable to adversarial attacks, which generate adversarial data by adding imperceptible perturbations to natural images, potentially causing the model to make abnormal predictions. This vul" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.306, + 0.908, + 0.518 + ], + "angle": 0, + "content": "nerability reduces the reliability of deep learning systems, highlighting the urgent need for defense techniques. Some approaches employ adversarial training techniques [48], which incorporate adversarial data into the training process to inherently bolster the model's immunity against adversarial noise (adv-noise). Other methods utilize adversarial purification [47] to cleanse the input data of adv-noise before model inference. Unfortunately, adversarial training often results in diminished classification accuracy on adversarial data and may sacrifice performance on natural data [1]. While purification techniques may seem more reliable, the denoising process can inadvertently smooth the high-frequency texture of clean images, leading to suboptimal accuracy on both natural and adversarial images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.909, + 0.672 + ], + "angle": 0, + "content": "Another branch of adversarial defense is adversarial detection [12, 28], which aims to filter out adversarial data before they are fed into target systems. These methods rely on discerning the discrepancies between adversarial and natural distributions, thereby maintaining the integrity of target systems while achieving high performance in defending against adversarial attacks. However, existing adversarial detection approaches primarily train specialized detectors tailored for specific attacks or classifiers [8], which may not generalize well to unseen advanced attacks [2, 39]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Some recent approaches [40, 49] have attempted to enhance the generalization of adversarial detectors by leveraging diffusion models and manually designed pseudo-noise. Nevertheless, as shown in Table 1, this improvement often comes at the expense of increased inference overhead, and even well-trained detectors still struggle with adversarial data produced by generative models such as generative adversarial networks (GANs) and diffusion models. Specifically, generative-based adversarial attacks, such as M3D [51] and Diff-PGD [44], are recently developed techniques designed to generate more natural adversarial data. Unlike traditional gradient-based attacks like PGD [29], generative-based attacks tend to create imbalanced and anisotropic perturbations that are intense in high-frequency and salient areas but mild in low-frequency and background" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.327, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author\n1Code at https://github.com/cc13qq/PFD" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13917" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.16 + ], + "angle": 0, + "content": "Table 1. Properties of our method vs Other Adversarial Detection: We summarize four metrics for adversarial detection. \"Detect Attacks\" specifies the types of attacks each method is designed to detect. \"Model-Agnostic\" indicates whether the detection method operates independently of the protected model. \"Unseen-Attack Detection\" assesses the method's generalization to detect previously unseen attacks, with the reported value representing the AUROC score for detecting the MIFGSM attack on the ImageNet dataset. Lastly, \"Time Overhead\" quantifies the time required for the detector to process 100 samples from the ImageNet dataset." + }, + { + "type": "table", + "bbox": [ + 0.13, + 0.17, + 0.87, + 0.285 + ], + "angle": 0, + "content": "
    MethodsDetect AttacksModel-AgnosticUnseen-Attack DetectionTime Overhead
    LID [28]Gradient×0.91461.80s
    LiBRe [8]Gradient×0.87252.56s
    SPAD [40]Gradient + GAN✓0.98204.56s
    EPSAD [49]Gradient✓0.9918396.81s
    OursGradient + GAN + Diffusion✓0.99314.85
    " + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.309, + 0.482, + 0.4 + ], + "angle": 0, + "content": "areas. These perturbations make them harder to detect with current methods, posing a new challenge to the field of adversarial detection. Therefore, there is an urgent need for a low-time-cost detection method with strong generalization performance against both unseen gradient-based attacks and unseen generative-based attacks." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.401, + 0.483, + 0.598 + ], + "angle": 0, + "content": "In this paper, we investigate the association between the distributions of different adv-noises. As shown in Figure 1, by modeling noise as multivariate Gaussian distributions, we define the proximity relationship of the noise distributions in a metric space and establish a perturbation method to construct the proximal distributions. Based on the assumption and definition, we demonstrate that all adv-noise distributions are proximal using the Wasserstein distance, and we deduce a corollary that an open covering of the adv-noise distributions exists. We then propose the core idea of this paper: by training on the open covering, we obtain a detector with strong generalization performance against various types of unseen attacks." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.6, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Based on this idea, we propose Perturbation Forgery, a pseudo-adversarial data (pseudo-adv-data) generation method designed to train a detector with strong generalization capabilities for detecting various types of adversarial attacks. As shown in Figure 2, Perturbation Forgery comprises noise distribution perturbation, sparse mask generation, and pseudo-adversarial data (pseudo-adv-data) production. By continuously perturbing the noise distribution of a commonly used attack, such as FGSM [15], we obtain a nearly complete family of distributions that form the aforementioned open covering. Simultaneously, sparse masks are generated using attention maps and saliency maps of the natural data, converting the sampled global noises into local forms to help the detector focus on local noise patterns so as to detect generative-based adv-noise. By sampling noise from the perturbed noise distributions, we sparsify it using sparse masks and inject it into natural data. This process converts half of the natural data into pseudo-adv-data, replacing actual adversarial data. The pseudo-adv-data is then combined with the remaining uncontaminated data to train" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.31, + 0.72, + 0.324 + ], + "angle": 0, + "content": "the binary adversarial detector." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.325, + 0.907, + 0.399 + ], + "angle": 0, + "content": "To the best of our knowledge, we are the first to empower a detector with the robust ability to detect various types of adversarial attacks, including gradient-based, GAN-based, diffusion-based, and physical attacks, with minor inference time overhead." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.4, + 0.862, + 0.415 + ], + "angle": 0, + "content": "Our contributions are summarized in four thrusts:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.416, + 0.905, + 0.476 + ], + "angle": 0, + "content": "- By modeling adversarial noise as Gaussian distributions, we investigate the association between different adversarial noise distributions and demonstrate their proximity in a metric space." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.477, + 0.905, + 0.552 + ], + "angle": 0, + "content": "- Based on our assumption and definition, we deduce the existence of an open covering for adversarial noise distributions and propose training a detector to distinguish this open covering from the natural data distribution, thereby achieving strong generalization in detection." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.906, + 0.672 + ], + "angle": 0, + "content": "- Building on our deductions, we propose Perturbation Forgery, which includes noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production. This method is designed to train a binary detector with strong generalization performance against various types of unseen attacks, including gradient-based, GAN-based, diffusion-based, and physical adversarial data, with minor inference time overhead." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.906, + 0.748 + ], + "angle": 0, + "content": "- We conduct evaluations on multiple general and facial datasets across a wide spectrum of gradient-based, generative-based, and physical attacks, demonstrating the consistently strong performance of our method in adversarial detection tasks." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.416, + 0.906, + 0.748 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.763, + 0.655, + 0.779 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.788, + 0.698, + 0.803 + ], + "angle": 0, + "content": "2.1. Adversarial Attack" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Gradient-based adversarial attack Adversarial attacks [15] attempt to fool a classifier into changing prediction results by injecting subtle perturbations to the input data while maintaining imperceptibility from human eyes. By introducing iterative perturbation, PGD [29] and BIM [24] generate adversarial data with significantly im" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13918" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.11, + 0.089, + 0.891, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.287, + 0.908, + 0.331 + ], + "angle": 0, + "content": "Figure 1. Illustration of the proximity of adversarial noise distributions and perturbed noise distributions. Left: all the distributions of adversarial noise and the perturbed distributions are in a \\(\\varepsilon\\)-ball centered on a given adversarial noise distribution. Right: by continuously perturbing the given adversarial noise distribution, we obtain an open covering of distributions of adversarial noise." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.356, + 0.484, + 0.432 + ], + "angle": 0, + "content": "proved attack performance, while DIM [43], NIM [26], and MIM [9] improve the transferability under the black-box setting. Besides, adaptive attacks [6, 13, 18] are proposed to exploit the weak points of each defense, achieving a high attack rate against several defense techniques." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.449, + 0.484, + 0.629 + ], + "angle": 0, + "content": "Generative-based Adversarial Attacks Recently, another branch of attacks uses generative models to produce adversarial data with a more natural style and imbalanced noise compared to gradient-based attacks. Among them, CDA [31], TTP [30], and M3D [51] utilize GAN to craft adversarial data and achieve higher efficiency when attacking large-scale datasets. Diff-Attack [4] and Diff-PGD [44] employ the diffusion model as a strong prior to better ensure the realism of generated data. Designed for perturbing facial recognition systems, AdvMakeup [46] and AMTGAN [19] are presented to generate imperceptible adversarial images of the face." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.63, + 0.484, + 0.691 + ], + "angle": 0, + "content": "In this paper, a wide spectrum of gradient-based, generative-based, and physical adversarial attacks on ImageNet and facial datasets is used to evaluate the detection performance of our method." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.698, + 0.295, + 0.713 + ], + "angle": 0, + "content": "2.2. Adversarial Detection" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.765 + ], + "angle": 0, + "content": "As one of the technical solutions to ensure the safety of DNNs, there has been a significant amount of exploration in the field of adversarial detection [28]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.87 + ], + "angle": 0, + "content": "LiBRe [8] leverages Bayesian neural networks to endow pre-trained DNNs with the ability to defend against unseen adversarial attacks, SPAD [40] leverages a data augmentation method to detect adversarial face images from unseen attack, while EPSAD [49] incorporates a diffusion model to detect adversarial data with minimal attack intensity, albeit at the cost of inference time." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "While current methods have achieved remarkable improvements in adversarial detection, generative-based ad" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.356, + 0.907, + 0.418 + ], + "angle": 0, + "content": "versarial attacks are harder to detect, posing a new challenge. To address the problems above, our method is proposed to detect various types of unseen attacks, including gradient-based, generative-based, and physical attacks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.43, + 0.905, + 0.447 + ], + "angle": 0, + "content": "3. Proximity of Adversarial Noise Distribution" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.455, + 0.907, + 0.576 + ], + "angle": 0, + "content": "In this section, we provide an overview of preliminary concepts related to adversarial data generation and explore the relationship between adversarial noise distributions. We define the proximity of noise distributions and present the core idea of this paper: by training on the open covering of adversarial noise distributions, we obtain a detector with strong generalization performance against various types of unseen attacks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.586, + 0.766, + 0.601 + ], + "angle": 0, + "content": "3.1. Adversarial data generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.607, + 0.906, + 0.669 + ], + "angle": 0, + "content": "Given a DNN \\( f \\) that works on dataset \\( \\mathcal{D} = \\{(\\mathbf{x}_i, y_i)\\}_{i=1}^n \\) with \\( (\\mathbf{x}_i \\in \\mathcal{X}, y_i \\in \\mathcal{C}) \\) being (sample, ground-truth) pair, an adversarial example \\( \\hat{\\mathbf{x}} \\) regarding sample \\( \\mathbf{x} \\) with attack intensity \\( \\epsilon \\) is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.624, + 0.68, + 0.907, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} = \\underset {\\hat {\\mathbf {x}} \\in \\mathcal {B} (\\mathbf {x}, \\epsilon)} {\\operatorname {a r g m a x}} \\mathcal {L} (f (\\hat {\\mathbf {x}}), y), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.718, + 0.907, + 0.78 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}\\) is some loss function and \\(\\mathcal{B}(\\mathbf{x},\\epsilon) = \\{\\mathbf{x}'|\\ell^p (\\mathbf{x},\\mathbf{x}') < \\epsilon \\}\\) restricts the perturbation under \\(\\ell^p\\) norm. Following [15], we simply denote adversarial sample as \\(\\hat{\\mathbf{x}} = \\mathbf{x} + \\boldsymbol{\\eta}\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.788, + 0.785, + 0.804 + ], + "angle": 0, + "content": "3.2. Proximity of noise distribution" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Due to the subtle and imperceptible nature of adv-noise, adversarial data and natural data appear visually similar. Thus, we assume that this similarity also exists between the noises of different adversarial attacks. To investigate the similarity of these noises, we provide the following definition, which depicts a close relationship between two noise distributions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13919" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.891, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.284, + 0.908, + 0.342 + ], + "angle": 0, + "content": "Figure 2. Illustration of Perturbation Forgery. Before training, we estimate the noise distribution from a commonly used attack, then continuously perturb it in each batch to create an open covering of the adversarial noise distributions. Next, noises sampled from these perturbed distributions are converted into localized noise by applying sparse masks. Finally, pseudo-adversarial data is generated by adding these localized noises to natural samples." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.367, + 0.482, + 0.445 + ], + "angle": 0, + "content": "Definition 1 (Proximal Noise Distribution). Let \\( P \\) and \\( Q \\) be the distribution functions of two independent noise samples \\( \\mathbf{x}_1 \\) and \\( \\mathbf{x}_2 \\). We call them proximal noise distributions under \\( \\varepsilon \\) if we have a metric \\( d(\\cdot, \\cdot) \\) and \\( \\exists \\varepsilon > 0 \\), s.t. \\( d(P, Q) < \\varepsilon \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.454, + 0.484, + 0.59 + ], + "angle": 0, + "content": "A common assumption for instance feature distribution is to model it as a Gaussian distribution [10]. Obtained by subtracting from natural data and adversarial data, adv-noises naturally form a Gaussian distribution. Therefore, we assume that noise r.v \\(\\pmb{\\eta} \\in \\mathbb{R}^d\\) satisfies truncated Gaussian distribution \\(\\mathcal{N}(\\pmb{\\mu}, \\sigma^2\\mathbf{I}_d)\\) with its truncated interval is \\([- \\epsilon, \\epsilon]^d\\). Built upon Definition 1, we derive the following theorem about the association between the distributions of different adv-noises:" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.601, + 0.485, + 0.675 + ], + "angle": 0, + "content": "Theorem 1. Let \\(\\mathcal{P}_a\\) be the distribution set composed of all the adversarial noise distributions. Given independent noise distributions \\(Q_{i}, i \\in N^{+}\\). For \\(\\forall i \\neq j\\), \\(Q_{i}\\) and \\(Q_{j}\\) are proximal noise distributions if the following conditions are met." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.677, + 0.221, + 0.693 + ], + "angle": 0, + "content": "1) \\(Q_{i},Q_{j}\\in \\mathcal{P}_{a}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.693, + 0.483, + 0.725 + ], + "angle": 0, + "content": "2) \\(\\exists \\epsilon_{\\mu}, \\epsilon_{\\sigma} > 0\\) s.t. \\(\\|\\pmb{\\mu}_i - \\pmb{\\mu}_j\\| < \\epsilon_{\\mu}\\) and \\(|\\sigma_i - \\sigma_j| < \\epsilon_{\\sigma}\\) where the \\(\\|\\cdot\\|\\) is a Euclidean norm on \\(\\mathbb{R}^n\\)." + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.677, + 0.483, + 0.725 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.483, + 0.81 + ], + "angle": 0, + "content": "Theorem 1 tells us: 1) All the adversarial noise distributions under the same \\(\\ell^p\\) norm are proximal noise distributions. 2) If the parameters of two noise distributions are sufficiently close to those of a given distribution, we can regard these two distributions as proximal noise distributions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We can further deduce several corollaries of the theorem. 1) All noise distributions proximal to the known adversarial distribution \\(p(\\pmb {\\eta})\\) form an open \\(\\varepsilon\\) -ball centered on \\(p(\\pmb {\\eta})\\) ,denoting as \\(\\mathcal{P}_{\\varepsilon} = \\{p(\\pmb {\\eta}_i)|d(p(\\pmb {\\eta}_i),p(\\pmb {\\eta})) < \\varepsilon \\}\\) , and also form a metric space \\((\\mathcal{P}_{\\varepsilon},d)\\) .2) The adv-noise distribution set is also located in this ball: \\(\\mathcal{P}_a\\subset \\mathcal{P}_{\\varepsilon}\\) .3) Based on the prop" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.367, + 0.905, + 0.398 + ], + "angle": 0, + "content": "erties of the metric space \\((\\mathcal{P}_{\\varepsilon},d)\\) , for all subset \\(\\mathcal{P}_i\\subset \\mathcal{P}_\\varepsilon\\) there exists an open covering of the subset: \\(\\mathcal{P}_i\\subset \\{G_c\\}_{c\\in \\mathbb{I}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.399, + 0.906, + 0.58 + ], + "angle": 0, + "content": "Based on the corollaries, we deduce the core idea of this paper: Let \\( p(\\hat{\\eta}_i|\\boldsymbol {\\eta}) = \\mathcal{N}(\\boldsymbol {\\mu} + \\epsilon_{\\mu i},(\\sigma +\\epsilon_{\\sigma i})^2\\mathbf{I}_d),i = 1,2,\\ldots ,n \\) denote generated proximal noise distributions of the given adv-noise distribution \\( p(\\pmb {\\eta}) = \\mathcal{N}(\\pmb {\\mu},\\sigma^2\\mathbf{I}_d) \\), where \\( \\epsilon_{\\mu i},\\epsilon_{\\sigma i} \\) are randomly sampled from uniform distributions and restricted by \\( \\epsilon_{\\mu i},\\epsilon_{\\sigma i} < \\varepsilon \\). As shown in Figure 1, when \\( n\\to \\infty \\), we can always obtain a distribution set \\( \\mathcal{P}_c = \\{p(\\hat{\\eta}_i|\\boldsymbol {\\eta})\\}_{i = 1}^\\infty \\) that forms an open covering of the adversarial distribution set \\( \\mathcal{P}_a \\). By training on the open covering, the detector learns to distinguish between the distributions of natural and adversarial data, enabling it to effectively detect unseen adversarial attacks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.906, + 0.613 + ], + "angle": 0, + "content": "Analysis of distribution assumption, proofs of theorem, and corollaries are provided in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.631, + 0.719, + 0.649 + ], + "angle": 0, + "content": "4. Perturbation Forgery" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.658, + 0.906, + 0.703 + ], + "angle": 0, + "content": "Based on the theory in the last section, we heuristically propose Perturbation Forgery to train a detector with strong generalization against various types of unseen attacks." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.705, + 0.907, + 0.901 + ], + "angle": 0, + "content": "As illustrated in Figure 2, Perturbation Forgery encompasses three elements: noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production. At first, the noise distribution of a commonly used attack is continuously perturbed using noise distribution perturbation into numerous noise distributions that remain proximal to the original, thereby forming the open covering. After that, we sample noises from the perturbed distribution and convert them into sparse local noise using sparse mask generation. Subsequently, we convert half of the natural data into pseudo-adv-data using pseudo-adversarial data production. This pseudo-adv data replaces actual adversarial data and is combined with the remaining natural data to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13920" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.245, + 0.106 + ], + "angle": 0, + "content": "train a binary detector." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.115, + 0.373, + 0.13 + ], + "angle": 0, + "content": "4.1. Noise Distribution Perturbation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.136, + 0.485, + 0.2 + ], + "angle": 0, + "content": "Given the training dataset \\(\\{(\\mathbf{x}_k,y_k)\\}_{k = 1}^n\\) composed by natural data, we add adv-noise on it using a commonly used attack (such as FGSM) and generate adversarial noise features \\(\\mathcal{D}_{\\mathrm{noise}}\\coloneqq \\{\\mathbf{z}_k = h(\\pmb {\\eta}_k)\\}_{k = 1}^n\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.206, + 0.483, + 0.224 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\eta} _ {k} = \\operatorname {A t t a c k} (\\mathbf {x}) - \\mathbf {x}, k \\in [ 1, n ], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.231, + 0.483, + 0.26 + ], + "angle": 0, + "content": "where \\(h:\\mathcal{X}\\to \\mathbb{R}^d\\) is the flattening operation that converts multidimensional data into vectors." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.262, + 0.484, + 0.307 + ], + "angle": 0, + "content": "Assuming the noise features form a multivariate Gaussian distribution \\(p(\\mathbf{z}) = \\mathcal{N}(\\boldsymbol {\\mu},\\boldsymbol {\\Sigma})\\) [10], we estimate the parameters mean \\(\\pmb{\\mu}\\) and covariance \\(\\pmb{\\Sigma}\\) of \\(\\mathcal{D}_{\\mathrm{noise}}\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.314, + 0.483, + 0.351 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\boldsymbol {\\mu}} = \\frac {1}{N} \\sum_ {k} \\mathbf {z} _ {k}, \\quad \\widehat {\\boldsymbol {\\Sigma}} = \\frac {1}{N} \\sum_ {k} \\left(\\mathbf {z} _ {k} - \\widehat {\\boldsymbol {\\mu}}\\right) \\left(\\mathbf {z} _ {k} - \\widehat {\\boldsymbol {\\mu}}\\right) ^ {\\top}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.358, + 0.484, + 0.39 + ], + "angle": 0, + "content": "For the \\(i^{\\mathrm{th}}\\) batch of training, we perturb the estimated distribution to a proximal noise distribution by" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.395, + 0.483, + 0.415 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\boldsymbol {\\mu}} _ {i} = \\widehat {\\boldsymbol {\\mu}} + \\alpha_ {i} \\cdot \\boldsymbol {m} _ {i}, \\quad \\widehat {\\boldsymbol {\\Sigma}} _ {i} = \\widehat {\\boldsymbol {\\Sigma}} + \\beta_ {i} \\cdot \\boldsymbol {V} _ {i}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.422, + 0.484, + 0.529 + ], + "angle": 0, + "content": "where \\(\\pmb{m}_i\\sim \\mathcal{N}(0,\\mathbf{I}_d)\\) and \\(\\pmb {V}_i\\sim \\mathcal{N}(0,\\mathbf{I}_{d\\times d})\\) are vector and matrix of perturbation. \\(\\alpha_{i}\\sim U(-\\epsilon_{\\mu},\\epsilon_{\\mu})\\) and \\(\\beta_{i}\\sim\\) \\(U(0,\\epsilon_{\\sigma})\\) are scale parameters. After \\(n\\) batches of training, we have a perturbed distribution set \\(\\{\\mathcal{N}(\\widehat{\\pmb{\\mu}}_i,\\widehat{\\pmb{\\Sigma}}_i)\\}\\), thereby forming the approximate open covering \\(\\mathcal{P}_c\\). Trained with \\(\\mathcal{P}_c\\), the detector can distinguish the distributions of natural and adversarial data." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.538, + 0.319, + 0.554 + ], + "angle": 0, + "content": "4.2. Sparse Mask Generation" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.559, + 0.483, + 0.816 + ], + "angle": 0, + "content": "Unlike gradient-based adversarial attacks, generative-based attacks tend to generate imbalanced and anisotropic perturbations, showing much intensity in high-frequency and salient areas and mild in low-frequency and background areas. Besides, in physical scenarios, adversarial attacks also tend to add patches to local areas. Noticing this, we propose sparse masks to perturbation forgery to assist the detector in detecting local adv-noises. Previous research has demonstrated that the spectra of real and fake images differ significantly in high-frequency regions [27]. Additionally, generative-based adversarial data manipulate characteristics, such as abnormal color aberrations, in these high-frequency regions [40]. To augment the detection performance on generative-based adversarial data, we need to sparse the pseudo-noise sampled from perturbed noise distribution and highlight the noise in high-frequency regions to mimic the style of generative-based attacks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.816, + 0.484, + 0.862 + ], + "angle": 0, + "content": "Given this, for a natural sample \\(\\mathbf{x}_{i,k}\\) in the \\(i^{th}\\) batch, we first mask the high-frequency area using saliency detection [33] and GradCAM [34]:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.87, + 0.483, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\operatorname {M a s k} _ {1} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a p} \\left(f _ {s} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {s}\\right) \\cup \\operatorname {M a p} \\left(f _ {c} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {c}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.091, + 0.907, + 0.138 + ], + "angle": 0, + "content": "Algorithm 1 Training Procedure with Perturbation Forgery \nInput: Training dataset, a commonly used attack, saliency detection model \\( f_{s} \\), and GradCAM model \\( f_{c} \\)." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.138, + 0.907, + 0.168 + ], + "angle": 0, + "content": "Output: A detector with strong generalization capabilities against various types of unseen attacks." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.171, + 0.907, + 0.2 + ], + "angle": 0, + "content": "1: Generate adversarial noise using the commonly used attack in Eq. 2." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.202, + 0.906, + 0.233 + ], + "angle": 0, + "content": "2: Estimate a multivariate Gaussian distribution \\( p(\\mathbf{z}) = \\mathcal{N}(\\hat{\\mu},\\hat{\\Sigma}) \\) of adv-noise using Eq. 3." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.234, + 0.719, + 0.247 + ], + "angle": 0, + "content": "3: for batch \\(i\\) in \\(1, \\dots, n\\) do" + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.248, + 0.906, + 0.28 + ], + "angle": 0, + "content": "4: Generate a perturbed noise distribution \\( p(\\mathbf{z}_i) = \\mathcal{N}(\\hat{\\boldsymbol{\\mu}}_i, \\hat{\\boldsymbol{\\Sigma}}_i) \\) using Eq. 4." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.281, + 0.8, + 0.295 + ], + "angle": 0, + "content": "5: for sample \\(\\mathbf{x}_{i,k}\\) in half of batch \\(i\\) do" + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.296, + 0.89, + 0.31 + ], + "angle": 0, + "content": "6: Generate sparse masks \\(\\mathrm{Mask}(\\mathbf{x}_{i,k})\\) using Eq. 8." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.311, + 0.858, + 0.326 + ], + "angle": 0, + "content": "7: Sample pseudo-adv noise \\(\\widehat{\\eta}_{i,k}\\) using Eq. 9." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.326, + 0.905, + 0.355 + ], + "angle": 0, + "content": "8: Generate pseudo-adv data \\(\\widehat{\\mathbf{x}}_{i,k}\\) using Eq. 11 and replace \\(\\mathbf{x}_{i,k}\\)." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.357, + 0.613, + 0.369 + ], + "angle": 0, + "content": "9: end for" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.371, + 0.751, + 0.384 + ], + "angle": 0, + "content": "10: Train the detector on batch \\(i\\)." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.387, + 0.597, + 0.399 + ], + "angle": 0, + "content": "11: end for" + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.171, + 0.907, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.429, + 0.907, + 0.476 + ], + "angle": 0, + "content": "where \\( f_{s} \\) and \\( f_{c} \\) are the saliency detection model and Grad-CAM model respectively. \\( \\operatorname{Map}(\\mathbf{x};\\gamma) \\) is a binary indicator function parameterized by \\( \\gamma \\):" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.488, + 0.906, + 0.507 + ], + "angle": 0, + "content": "\\[\n\\operatorname {M a p} \\left(\\mathbf {x} _ {i, k}; \\gamma\\right) = \\operatorname {C l i p} _ {[ 0, 1 ]} \\left(\\mathbf {x} _ {i, k} - \\gamma \\mathbf {I} _ {\\mathcal {X}}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.517, + 0.906, + 0.593 + ], + "angle": 0, + "content": "The adv-noise that occurs in the high-frequency region tends to occupy only a small part of the region. Therefore, we select the high-frequency point from the gradient map obtained by Sobel operator [11] to sparsify the mask of sample \\(\\mathbf{x}_{i,k}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.606, + 0.905, + 0.622 + ], + "angle": 0, + "content": "\\[\n\\operatorname {M a s k} _ {2} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a p} (\\operatorname {S o b e l} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {l}), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.624, + 0.905, + 0.641 + ], + "angle": 0, + "content": "\\[\n\\operatorname {M a s k} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a s k} _ {1} \\left(\\mathbf {x} _ {i, k}\\right) \\cap \\operatorname {M a s k} _ {2} \\left(\\mathbf {x} _ {i, k}\\right). \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.653, + 0.834, + 0.667 + ], + "angle": 0, + "content": "4.3. Pseudo-Adversarial Data Production" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.906, + 0.706 + ], + "angle": 0, + "content": "For the \\(i^{\\mathrm{th}}\\) batch of training, we sample pseudo-adv noise from the perturbed distribution by:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.717, + 0.905, + 0.735 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\boldsymbol {\\eta}} _ {i, k} = h ^ {- 1} \\left(\\mathbf {z} _ {i, k}\\right), \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.738, + 0.905, + 0.757 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {i, k} \\in \\left\\{\\mathbf {z} _ {k} \\mid \\mathbf {z} _ {k} \\sim \\mathcal {N} \\left(\\widehat {\\boldsymbol {\\mu}} _ {i}, \\widehat {\\boldsymbol {\\Sigma}} _ {i}\\right) \\text {a n d} p \\left(\\mathbf {z} _ {k}\\right) < \\gamma_ {p} \\right\\} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.77, + 0.906, + 0.847 + ], + "angle": 0, + "content": "where \\(h^{-1}:\\mathbb{R}^d\\to \\mathcal{X}\\) is an inverse function of \\(h\\) to unflatten noise features, and \\(\\gamma_{p}\\) is a threshold that excludes data with a low likelihood. Note that \\(\\eta_{i}\\) is a global noise and needs to be localized by a sparse mask. The pseudo-adv data \\(\\widehat{\\mathbf{x}}_{i,k}\\) is produced by adding the masked local noise to \\(\\mathbf{x}_{i,k}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.862, + 0.905, + 0.88 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathbf {x}} _ {i, k} = \\mathbf {x} _ {i, k} + \\widehat {\\boldsymbol {\\eta}} _ {i, k} \\otimes \\operatorname {M a s k} \\left(\\mathbf {x} _ {\\mathbf {i}, \\mathbf {k}}\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.722, + 0.902 + ], + "angle": 0, + "content": "where \\(\\otimes\\) is Hadamard product." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13921" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.131, + 0.089, + 0.866, + 0.105 + ], + "angle": 0, + "content": "Table 2. Comparison of AUROC scores of detecting gradient-based and adaptive attacks on ImageNet100 under \\( \\epsilon = 4/{255} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.109, + 0.115, + 0.887, + 0.219 + ], + "angle": 0, + "content": "
    DetectorBIMPGDDIMMIMNIMAABPDA+EOTMM
    LID [28]0.97820.97500.89420.91460.89770.91240.92020.9227
    LiBRe [8]0.92590.95480.92430.87250.90130.86530.87140.8573
    SPAD [40]0.98460.98510.98150.98200.98230.98900.98850.9811
    EPSAD [49]0.99980.99890.99230.99180.99720.99980.99850.9923
    ours0.99110.99120.98630.99310.99340.99410.99270.9944
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.243, + 0.482, + 0.318 + ], + "angle": 0, + "content": "For each batch, we convert half of the natural data to pseudo-adv data by Perturbation Forgery and train a binary detector using the Cross-Entropy classification loss [50]. The overall training procedure with Perturbation Forgery is presented in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.333, + 0.226, + 0.351 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.359, + 0.485, + 0.435 + ], + "angle": 0, + "content": "To validate the detection performance of our approach against various adversarial attack methods, we conduct extensive experiments on multiple general and facial datasets. For additional experiments, analyses, and a discussion of limitations, please refer to the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.445, + 0.285, + 0.461 + ], + "angle": 0, + "content": "5.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.467, + 0.484, + 0.558 + ], + "angle": 0, + "content": "Datasets The datasets used for evaluation include: 1) general datasets: ImageNet100 [7] and CIFAR-10 [23] for evaluate gradient-based and generative-based attacks, and 2) face datasets: Makeup [16] for Adv-Makeup [46], CelebAHQ [21] for AMT-GAN [19], and LFW [14] for TIPIM [45] and physical attacks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.579, + 0.483, + 0.837 + ], + "angle": 0, + "content": "Adversarial Attacks We adopt 5 gradient-based attacks, 3 adaptive attacks, 5 generative-based attacks, and 6 face attacks to evaluate our method. For gradient-based attacks, BIM [24], PGD [29], MIM [9], DIM [43], and NIM [26] are used as the unseen attacks. For adaptive attacks, we adopt AutoAttack (AA) [6], BPDA+EOT [18], and Minimum-Margin Attack (MM) [13]. For generative-based attacks, we adopt 3 GAN-based attacks including CDA [31], TTP [30], and M3D [51], and 2 Diffusion-based attacks including Diff-Attack [4] and Diff-PGD [44]. For face attacks, we adopt 1 gradient-based attack TIPIM [45], 2 GAN-based attacks including AdvMakeup [46] and AMT-GAN [19], and 3 physical attacks including Adv-Sticker [38], Adv-Glasses [35], and Adv-Mask [38]. For each of the above attack methods, adversarial data is generated with the attack intensity of \\(\\epsilon = 4 / 255\\) (except for the unrestricted attacks), and iterative attacks run for 10 steps using step size 2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Baselines To evaluate our method across various types of adversarial attacks, we compare it with state-of-the-art detection methods from three related research domains:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.243, + 0.908, + 0.41 + ], + "angle": 0, + "content": "adversarial detection, synthetic image detection, and face forgery detection. For gradient-based attacks, we benchmark against four adversarial detection methods: LID [28], LiBRe [8], SPAD [40], and EPSAD [49]. Since most adversarial detection methods are not designed to address generative-based adversarial attacks, we include a comparison with four synthetic image detection techniques: CNN-Detection [41], LGrad [37], Universal-Detector [32], and DIRE [42]. For detecting GAN-based face attacks, we also compare against two face forgery detection methods, Luo et al.[27] and He et al.[17], as well as ODIN [25]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.428, + 0.909, + 0.563 + ], + "angle": 0, + "content": "Evaluation Metrics Following previous adversarial detection works [49], we employ the Area Under the Receiver Operating Characteristic Curve (AUROC) [20] as the primary evaluation metric to assess the performance of our classification models. The AUROC is a widely recognized metric in the field of machine learning and is particularly useful for evaluating binary classification problems. For fair comparisons, the number of natural data and adversarial data in the experiments remained consistent." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.909, + 0.75 + ], + "angle": 0, + "content": "Implementation details XceptionNet [5] is selected as our backbone model and is trained on all the above datasets. For adversarial noise distribution estimation, we utilize Torchattacks [22] to generate 1000 noise images for each dataset. The uniform distribution parameters are set as \\(\\epsilon_{\\mu} = 3\\) and \\(\\epsilon_{\\sigma} = 0.005\\). The threshold of the sample control is set as \\(\\gamma_{s} = 0.05\\). The thresholds of the binary indicator function are set as \\(\\gamma_{s} = 0\\), \\(\\gamma_{c} = 125\\) and \\(\\gamma_{l} = 100\\). FGSM [15] is used as the initial attack, i.e. the commonly used attack, for Perturbation Forgery. Training epochs are set to 10 and convergence is witnessed." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.758, + 0.812, + 0.774 + ], + "angle": 0, + "content": "5.2. Detecting Gradient-based Attacks" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We begin by comparing our method with state-of-the-art techniques in detecting gradient-based attacks on ImageNet100. All the attacks are unseen by both the baseline methods and our method. For each attack, 1,000 adversarial images are generated in the gray-box setting, where the attacker has access to the victim model but is blind to the detection model. All baseline methods are sourced from existing adversarial detection research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13922" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.218, + 0.089, + 0.782, + 0.104 + ], + "angle": 0, + "content": "Table 3. Comparison of AUROC scores of detecting generative-based attacks on ImageNet100." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.115, + 0.887, + 0.248 + ], + "angle": 0, + "content": "
    DetectorCDATTPM3DDiff-AttackDiff-PGD
    CNN-Detection [41]0.70510.67430.69170.39630.5260
    LGrad [37]0.61440.60770.60680.55860.5835
    Universal-Detector [32]0.79450.81700.83120.92020.5531
    DIRE [42]0.89760.90970.91290.90970.9143
    SPAD0.93850.90640.89840.88620.8879
    EPSAD0.96740.69970.72650.47000.1507
    ours0.98780.96780.93640.92230.9223
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.202, + 0.261, + 0.794, + 0.275 + ], + "angle": 0, + "content": "Table 4. Comparison of AUROC scores for detecting various adversarial attacks on the face dataset." + }, + { + "type": "table", + "bbox": [ + 0.106, + 0.287, + 0.89, + 0.389 + ], + "angle": 0, + "content": "
    DetectorTIPIIMAdv-StickerAdv-GlassesAdv-MaskDetectorAdv-MakeupAMT-GAN
    LID0.69740.51030.64720.5319He et al. [17]0.52520.8823
    LiBRe0.53450.97390.81400.9993Luo et al. [27]0.61780.6511
    EPSAD0.96470.94620.92600.9578ODIN[25]0.63250.6970
    SPAD0.92560.99750.92440.9863SPAD0.96570.8969
    ours0.98850.99990.99990.9999ours0.97620.9216
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.414, + 0.484, + 0.626 + ], + "angle": 0, + "content": "As reported in Table 2, although EPSAD performs well, our method demonstrates effective detection (achieving an AUROC score of 0.9931 against MIM and 0.9944 against MM) across a variety of attack methods. These results validate our assumptions about the proximity of the noise distribution. By continuously perturbing the estimated noise distribution of a given attack (FGSM), we obtain an open covering noise of distributions from all the attacks. Given one seen attack, we are able to detect all the unseen attacks. The consistent detection performance verifies the effectiveness of our core idea of training a detector to distinguish the open covering of adv-noise distributions from natural ones and demonstrates the strong generalization capability of our method against gradient-based attacks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.636, + 0.403, + 0.652 + ], + "angle": 0, + "content": "5.3. Detecting Generative-based Attacks" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.749 + ], + "angle": 0, + "content": "To investigate our method's advantage in detecting generative-based attacks, we compared it with state-of-the-art synthetic image detection and adversarial detection methods on ImageNet100. As shown in Table 3, our method significantly outperforms the baseline methods, demonstrating highly effective detection capabilities." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.839 + ], + "angle": 0, + "content": "For adversarial detection baselines, the imbalanced noise generated by GAN and diffusion models makes it difficult for these methods, which are typically designed for gradient-based attacks, to detect effectively. In contrast, our sparse mask approach enables effective detection of such localized noise." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Most synthetic image detection methods are less effective in detecting adversarial data crafted from natural samples, with the exception of DIRE[42]. This effectiveness may stem from DIRE's use of reconstruction error from im" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.414, + 0.905, + 0.445 + ], + "angle": 0, + "content": "ages generated by diffusion models, which maintains its robustness in this setting." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.455, + 0.837, + 0.471 + ], + "angle": 0, + "content": "5.4. Detecting Face Adversarial Examples" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.477, + 0.906, + 0.583 + ], + "angle": 0, + "content": "Adversarial attacks targeting face recognition models represent an important branch of adversarial example research. Therefore, the detection ability of adversarial face examples is an important indicator of the performance of the detector. We perform various adversarial face attacks and compare our approach with state-of-the-art methods from adversarial face detection and face forgery detection." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.584, + 0.906, + 0.689 + ], + "angle": 0, + "content": "As shown in Table 4, our method shows excellent performance against a variety of adversarial attacks targeting faces and surpasses many existing adversarial face detection techniques. It further indicates the ability of the sparse mask to capture the essential characteristics of face adversarial examples and the strong generalization capability of our method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.7, + 0.771, + 0.716 + ], + "angle": 0, + "content": "5.5. Ablation Study and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.722, + 0.905, + 0.813 + ], + "angle": 0, + "content": "To further evaluate our method, we report an ablation study on the sparse mask, white-box attack detection results, the impact of the initial attack and the data size for distribution estimation, and the functionality of Perturbation Forgery through visualizations. The impact of hyper-parameters and other analyses are reported in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.822, + 0.706, + 0.836 + ], + "angle": 0, + "content": "5.5.1. Impact of each mask" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.906, + 0.901 + ], + "angle": 0, + "content": "As argued, the sparse mask is proposed to assist the detector in identifying local adversarial noises in generative-based adversarial data. As shown in Table 5, the absence of the saliency detection model \\( f_{s} \\) or the GradCAM model \\( f_{c} \\) has" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13923" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.089, + 0.486, + 0.12 + ], + "angle": 0, + "content": "Table 5. Ablation study on masks (AUROC score), where \\( f_{s} \\) denotes saliency detection model and \\( f_{c} \\) represents the CAM model." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.129, + 0.48, + 0.202 + ], + "angle": 0, + "content": "
    AblationCDATTPM3DDiff-AttackDiff-PGD
    w/o fs0.97550.95850.93200.91970.9135
    w/o f_c0.98640.95100.92620.90310.9062
    w/o Sobel0.98680.72350.69840.52310.5547
    " + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.214, + 0.289, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.182, + 0.346, + 0.204, + 0.361 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.214, + 0.48, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.345, + 0.395, + 0.361 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.372, + 0.485, + 0.43 + ], + "angle": 0, + "content": "Figure 3. 2D T-SNE visualizations. (a) ImageNet100 flattened noises of adversarial data and Perturbation Forgery-generated data. (b) ImageNet100 features extracted by the backbone model trained with Perturbation Forgery." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.445, + 0.484, + 0.473 + ], + "angle": 0, + "content": "Table 6. AUROC scores against white-box attacks under \\(\\epsilon = 4/255\\) on CIFAR-10." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.484, + 0.485, + 0.526 + ], + "angle": 0, + "content": "
    AttackBIMPGDDIMMIMAA
    AUROC0.91800.91680.90620.90310.9019
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.484, + 0.691 + ], + "angle": 0, + "content": "little effect on the overall system. This is because the regions masked by \\( f_{s} \\) and \\( f_{c} \\) are somewhat complementary. However, without the Sobel operation to sparsify the mask, the detector fails to detect most attacks, except for CDA. This is because generative-based adversarial noise tends to be imbalanced and localized, while CDA's noise is more global. The generated pseudo-adversarial noise without Sobel becomes too dense, preventing the detector from effectively focusing on localized noise." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.7, + 0.327, + 0.715 + ], + "angle": 0, + "content": "5.5.2. Functionality Visualization" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.486, + 0.902 + ], + "angle": 0, + "content": "To validate the functionality of our method, we extract features and flattened noise from adversarial data and Perturbation Forgery-generated data, then visualize them using 2D t-SNE projections. All adversarial data originate from unseen attacks. As shown in Figure 3(a), Perturbation Forgery continuously perturbs the adv-noise distribution of the initial attack, thereby forming an open covering for noises from unseen attacks. Individual samples appear as outliers, floating outside the collective noise distribution. As shown in Figure 3(b), by learning to separate natural data from those generated by Perturbation Forgery, the trained detector can effectively distinguish between natural and adversarial data." + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.089, + 0.907, + 0.12 + ], + "angle": 0, + "content": "Table 7. Impact of data size on distribution estimation: AUROC score against PGD under \\(\\epsilon = 4 / 255\\) on CIFAR-10." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.129, + 0.905, + 0.171 + ], + "angle": 0, + "content": "
    Data size10025050075010002000
    AUROC0.82780.93680.98660.99210.99650.9948
    " + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.203, + 0.757, + 0.218 + ], + "angle": 0, + "content": "5.5.3. Detecting White-box Attack" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.225, + 0.907, + 0.288 + ], + "angle": 0, + "content": "To verify the robustness of our approach to white-box attacks, i.e., both the victim model and the detector are available to the attacker, we conduct the experiment on CIFAR-10. Following [3], a modified objective of attacks is:" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.303, + 0.907, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\max _ {\\boldsymbol {\\eta}} \\mathcal {L} (f (\\hat {\\mathbf {x}}), y) + \\alpha \\cdot \\mathcal {L} (f _ {d} (\\hat {\\mathbf {x}}), y _ {d}), s. t. | | \\boldsymbol {\\eta} | | \\leq \\epsilon \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.343, + 0.907, + 0.48 + ], + "angle": 0, + "content": "where \\(y\\) is the ground-truth label, \\(y_{d} = 0\\) indicates that \\(\\hat{\\mathbf{x}}\\) is an adversarial example, and \\(\\alpha = 1\\) is a constant balancing between the attack of the classifier \\(f\\) and detector \\(f_{d}\\). As shown in Table 6, our method achieves a high average AUROC of 0.9092, demonstrating its robustness against white-box attacks. This may be attributed to the comprehensive open covering formed by perturbation forgery, which effectively encompasses adversarial data from white-box attacks, making it harder to mislead the trained detector." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.496, + 0.813, + 0.51 + ], + "angle": 0, + "content": "5.5.4. Data size for Distribution Estimation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.518, + 0.909, + 0.64 + ], + "angle": 0, + "content": "To assess the influence of data size for distribution estimation, we train detectors using distributions estimated from various data sizes and test them against PGD on CIFAR-10. As shown in Table 7, our method only requires a small amount of data (\\(\\geq 500\\) samples) to estimate the adversarial noise distribution so as to train an effective detector. Notably, using fewer than 500 samples leads to a significant decrease in detection performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.661, + 0.634, + 0.677 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.909, + 0.901 + ], + "angle": 0, + "content": "In this paper, we explore and define the proximity relationship between adversarial noise distributions. Based on our assumption and definition, we develop a perturbation method to craft proximal distributions and demonstrate an open covering of adversarial noise spaces. Building on this, we propose training detectors on the open coverings to achieve strong generalization against diverse adversarial attacks. We introduce Perturbation Forgery, which combines noise perturbation, sparse mask generation, and pseudo-adversarial data synthesis, enabling detection of unseen gradient-based, generative, and physical attacks, independent of specific models. Extensive experiments validate our approach's effectiveness and generalization with minimal inference overhead." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13924" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.27, + 0.108 + ], + "angle": 0, + "content": "7. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.222 + ], + "angle": 0, + "content": "This work was supported in part by the Natural Science Foundation of China under Grant 62372203 and 62302186, in part by the Major Scientific and Technological Project of Shenzhen (202316021), in part by the National key research and development program of China(2022YFB2601802), in part by the Major Scientific and Technological Project of Hubei Province (2022BAA046, 2022BAA042)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.233, + 0.188, + 0.249 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.258, + 0.483, + 0.313 + ], + "angle": 0, + "content": "[1] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples. In ICML, pages 274-283. 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In CVPR, pages 8153-8162, 2023. 1, 3, 6" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13926" + } + ] +] \ No newline at end of file diff --git a/2025/Detecting Adversarial Data Using Perturbation Forgery/a87e2166-e7a0-46b8-94b2-0c0c61135018_origin.pdf b/2025/Detecting Adversarial Data Using Perturbation Forgery/a87e2166-e7a0-46b8-94b2-0c0c61135018_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..84d2941c296bf3f4371b38c11c899ed4f4c984ad --- /dev/null +++ b/2025/Detecting Adversarial Data Using Perturbation Forgery/a87e2166-e7a0-46b8-94b2-0c0c61135018_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fdbf9404cddbc85eceb3d9266d6627360ee5d02bf0f6b75d8cb3269e1251576c +size 902072 diff --git a/2025/Detecting Adversarial Data Using Perturbation Forgery/full.md b/2025/Detecting Adversarial Data Using Perturbation Forgery/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5a27c11f131062f4160451d240b3b6e9d16503c3 --- /dev/null +++ b/2025/Detecting Adversarial Data Using Perturbation Forgery/full.md @@ -0,0 +1,366 @@ +# Detecting Adversarial Data Using Perturbation Forgery + +Qian Wang $^{1}$ , Chen Li $^{1}$ , Yuchen Luo $^{2}$ , Hefei Ling $^{1*}$ , Shijuan Huang $^{1}$ , Ruoxi Jia $^{3}$ , Ning Yu $^{4}$ $^{1}$ Huazhong University of Science and Technology, China $^{2}$ Wuhan University, China + $^{3}$ Virginia Tech, USA $^{4}$ Netflix Eyeline, USA +{yqwq1996, lhefei, llichen, shijuan_huang} @hust.edu.cn, {yuchenluo} @whu.edu.cn, ruoxijia@vt.edu, ningyu.hust@gmail.com + +# Abstract + +As a defense strategy against adversarial attacks, adversarial detection aims to identify and filter out adversarial data from the data flow based on discrepancies in distribution and noise patterns between natural and adversarial data. Although previous detection methods achieve high performance in detecting gradient-based adversarial attacks, new attacks based on generative models with imbalanced and anisotropic noise patterns evade detection. Even worse, the significant inference time overhead and limited performance against unseen attacks make existing techniques impractical for real-world use. In this paper, we explore the proximity relationship among adversarial noise distributions and demonstrate the existence of an open covering for these distributions. By training on the open covering of adversarial noise distributions, a detector with strong generalization performance against various types of unseen attacks can be developed. Based on this insight, we heuristically propose Perturbation Forgery, which includes noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production, to train an adversarial detector capable of detecting any unseen gradient-based, generative-based, and physical adversarial attacks. Comprehensive experiments conducted on multiple general and facial datasets, with a wide spectrum of attacks, validate the strong generalization of our method. + +# 1. Introduction + +Numerous studies have demonstrated the effectiveness of deep neural networks (DNNs) in various tasks [36]. However, it is also well-known that DNNs are vulnerable to adversarial attacks, which generate adversarial data by adding imperceptible perturbations to natural images, potentially causing the model to make abnormal predictions. This vul + +nerability reduces the reliability of deep learning systems, highlighting the urgent need for defense techniques. Some approaches employ adversarial training techniques [48], which incorporate adversarial data into the training process to inherently bolster the model's immunity against adversarial noise (adv-noise). Other methods utilize adversarial purification [47] to cleanse the input data of adv-noise before model inference. Unfortunately, adversarial training often results in diminished classification accuracy on adversarial data and may sacrifice performance on natural data [1]. While purification techniques may seem more reliable, the denoising process can inadvertently smooth the high-frequency texture of clean images, leading to suboptimal accuracy on both natural and adversarial images. + +Another branch of adversarial defense is adversarial detection [12, 28], which aims to filter out adversarial data before they are fed into target systems. These methods rely on discerning the discrepancies between adversarial and natural distributions, thereby maintaining the integrity of target systems while achieving high performance in defending against adversarial attacks. However, existing adversarial detection approaches primarily train specialized detectors tailored for specific attacks or classifiers [8], which may not generalize well to unseen advanced attacks [2, 39]. + +Some recent approaches [40, 49] have attempted to enhance the generalization of adversarial detectors by leveraging diffusion models and manually designed pseudo-noise. Nevertheless, as shown in Table 1, this improvement often comes at the expense of increased inference overhead, and even well-trained detectors still struggle with adversarial data produced by generative models such as generative adversarial networks (GANs) and diffusion models. Specifically, generative-based adversarial attacks, such as M3D [51] and Diff-PGD [44], are recently developed techniques designed to generate more natural adversarial data. Unlike traditional gradient-based attacks like PGD [29], generative-based attacks tend to create imbalanced and anisotropic perturbations that are intense in high-frequency and salient areas but mild in low-frequency and background + +Table 1. Properties of our method vs Other Adversarial Detection: We summarize four metrics for adversarial detection. "Detect Attacks" specifies the types of attacks each method is designed to detect. "Model-Agnostic" indicates whether the detection method operates independently of the protected model. "Unseen-Attack Detection" assesses the method's generalization to detect previously unseen attacks, with the reported value representing the AUROC score for detecting the MIFGSM attack on the ImageNet dataset. Lastly, "Time Overhead" quantifies the time required for the detector to process 100 samples from the ImageNet dataset. + +
    MethodsDetect AttacksModel-AgnosticUnseen-Attack DetectionTime Overhead
    LID [28]Gradient×0.91461.80s
    LiBRe [8]Gradient×0.87252.56s
    SPAD [40]Gradient + GAN✓0.98204.56s
    EPSAD [49]Gradient✓0.9918396.81s
    OursGradient + GAN + Diffusion✓0.99314.85
    + +areas. These perturbations make them harder to detect with current methods, posing a new challenge to the field of adversarial detection. Therefore, there is an urgent need for a low-time-cost detection method with strong generalization performance against both unseen gradient-based attacks and unseen generative-based attacks. + +In this paper, we investigate the association between the distributions of different adv-noises. As shown in Figure 1, by modeling noise as multivariate Gaussian distributions, we define the proximity relationship of the noise distributions in a metric space and establish a perturbation method to construct the proximal distributions. Based on the assumption and definition, we demonstrate that all adv-noise distributions are proximal using the Wasserstein distance, and we deduce a corollary that an open covering of the adv-noise distributions exists. We then propose the core idea of this paper: by training on the open covering, we obtain a detector with strong generalization performance against various types of unseen attacks. + +Based on this idea, we propose Perturbation Forgery, a pseudo-adversarial data (pseudo-adv-data) generation method designed to train a detector with strong generalization capabilities for detecting various types of adversarial attacks. As shown in Figure 2, Perturbation Forgery comprises noise distribution perturbation, sparse mask generation, and pseudo-adversarial data (pseudo-adv-data) production. By continuously perturbing the noise distribution of a commonly used attack, such as FGSM [15], we obtain a nearly complete family of distributions that form the aforementioned open covering. Simultaneously, sparse masks are generated using attention maps and saliency maps of the natural data, converting the sampled global noises into local forms to help the detector focus on local noise patterns so as to detect generative-based adv-noise. By sampling noise from the perturbed noise distributions, we sparsify it using sparse masks and inject it into natural data. This process converts half of the natural data into pseudo-adv-data, replacing actual adversarial data. The pseudo-adv-data is then combined with the remaining uncontaminated data to train + +the binary adversarial detector. + +To the best of our knowledge, we are the first to empower a detector with the robust ability to detect various types of adversarial attacks, including gradient-based, GAN-based, diffusion-based, and physical attacks, with minor inference time overhead. + +Our contributions are summarized in four thrusts: + +- By modeling adversarial noise as Gaussian distributions, we investigate the association between different adversarial noise distributions and demonstrate their proximity in a metric space. +- Based on our assumption and definition, we deduce the existence of an open covering for adversarial noise distributions and propose training a detector to distinguish this open covering from the natural data distribution, thereby achieving strong generalization in detection. +- Building on our deductions, we propose Perturbation Forgery, which includes noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production. This method is designed to train a binary detector with strong generalization performance against various types of unseen attacks, including gradient-based, GAN-based, diffusion-based, and physical adversarial data, with minor inference time overhead. +- We conduct evaluations on multiple general and facial datasets across a wide spectrum of gradient-based, generative-based, and physical attacks, demonstrating the consistently strong performance of our method in adversarial detection tasks. + +# 2. Related Work + +# 2.1. Adversarial Attack + +Gradient-based adversarial attack Adversarial attacks [15] attempt to fool a classifier into changing prediction results by injecting subtle perturbations to the input data while maintaining imperceptibility from human eyes. By introducing iterative perturbation, PGD [29] and BIM [24] generate adversarial data with significantly im + +![](images/126b929994d65958e289f67770158a3c2b5aecfdc5d1b59a60749148b1a3254d.jpg) +Figure 1. Illustration of the proximity of adversarial noise distributions and perturbed noise distributions. Left: all the distributions of adversarial noise and the perturbed distributions are in a $\varepsilon$ -ball centered on a given adversarial noise distribution. Right: by continuously perturbing the given adversarial noise distribution, we obtain an open covering of distributions of adversarial noise. + +proved attack performance, while DIM [43], NIM [26], and MIM [9] improve the transferability under the black-box setting. Besides, adaptive attacks [6, 13, 18] are proposed to exploit the weak points of each defense, achieving a high attack rate against several defense techniques. + +Generative-based Adversarial Attacks Recently, another branch of attacks uses generative models to produce adversarial data with a more natural style and imbalanced noise compared to gradient-based attacks. Among them, CDA [31], TTP [30], and M3D [51] utilize GAN to craft adversarial data and achieve higher efficiency when attacking large-scale datasets. Diff-Attack [4] and Diff-PGD [44] employ the diffusion model as a strong prior to better ensure the realism of generated data. Designed for perturbing facial recognition systems, AdvMakeup [46] and AMTGAN [19] are presented to generate imperceptible adversarial images of the face. + +In this paper, a wide spectrum of gradient-based, generative-based, and physical adversarial attacks on ImageNet and facial datasets is used to evaluate the detection performance of our method. + +# 2.2. Adversarial Detection + +As one of the technical solutions to ensure the safety of DNNs, there has been a significant amount of exploration in the field of adversarial detection [28]. + +LiBRe [8] leverages Bayesian neural networks to endow pre-trained DNNs with the ability to defend against unseen adversarial attacks, SPAD [40] leverages a data augmentation method to detect adversarial face images from unseen attack, while EPSAD [49] incorporates a diffusion model to detect adversarial data with minimal attack intensity, albeit at the cost of inference time. + +While current methods have achieved remarkable improvements in adversarial detection, generative-based ad + +versarial attacks are harder to detect, posing a new challenge. To address the problems above, our method is proposed to detect various types of unseen attacks, including gradient-based, generative-based, and physical attacks. + +# 3. Proximity of Adversarial Noise Distribution + +In this section, we provide an overview of preliminary concepts related to adversarial data generation and explore the relationship between adversarial noise distributions. We define the proximity of noise distributions and present the core idea of this paper: by training on the open covering of adversarial noise distributions, we obtain a detector with strong generalization performance against various types of unseen attacks. + +# 3.1. Adversarial data generation + +Given a DNN $f$ that works on dataset $\mathcal{D} = \{(\mathbf{x}_i, y_i)\}_{i=1}^n$ with $(\mathbf{x}_i \in \mathcal{X}, y_i \in \mathcal{C})$ being (sample, ground-truth) pair, an adversarial example $\hat{\mathbf{x}}$ regarding sample $\mathbf{x}$ with attack intensity $\epsilon$ is calculated as: + +$$ +\hat {\mathbf {x}} = \underset {\hat {\mathbf {x}} \in \mathcal {B} (\mathbf {x}, \epsilon)} {\operatorname {a r g m a x}} \mathcal {L} (f (\hat {\mathbf {x}}), y), \tag {1} +$$ + +where $\mathcal{L}$ is some loss function and $\mathcal{B}(\mathbf{x},\epsilon) = \{\mathbf{x}'|\ell^p (\mathbf{x},\mathbf{x}') < \epsilon \}$ restricts the perturbation under $\ell^p$ norm. Following [15], we simply denote adversarial sample as $\hat{\mathbf{x}} = \mathbf{x} + \boldsymbol{\eta}$ . + +# 3.2. Proximity of noise distribution + +Due to the subtle and imperceptible nature of adv-noise, adversarial data and natural data appear visually similar. Thus, we assume that this similarity also exists between the noises of different adversarial attacks. To investigate the similarity of these noises, we provide the following definition, which depicts a close relationship between two noise distributions. + +![](images/6373eca2d893772aa2f4d84ff3004f1b98ba9fe2471440f6ca6368ce9e973a00.jpg) +Figure 2. Illustration of Perturbation Forgery. Before training, we estimate the noise distribution from a commonly used attack, then continuously perturb it in each batch to create an open covering of the adversarial noise distributions. Next, noises sampled from these perturbed distributions are converted into localized noise by applying sparse masks. Finally, pseudo-adversarial data is generated by adding these localized noises to natural samples. + +Definition 1 (Proximal Noise Distribution). Let $P$ and $Q$ be the distribution functions of two independent noise samples $\mathbf{x}_1$ and $\mathbf{x}_2$ . We call them proximal noise distributions under $\varepsilon$ if we have a metric $d(\cdot, \cdot)$ and $\exists \varepsilon > 0$ , s.t. $d(P, Q) < \varepsilon$ . + +A common assumption for instance feature distribution is to model it as a Gaussian distribution [10]. Obtained by subtracting from natural data and adversarial data, adv-noises naturally form a Gaussian distribution. Therefore, we assume that noise r.v $\pmb{\eta} \in \mathbb{R}^d$ satisfies truncated Gaussian distribution $\mathcal{N}(\pmb{\mu}, \sigma^2\mathbf{I}_d)$ with its truncated interval is $[- \epsilon, \epsilon]^d$ . Built upon Definition 1, we derive the following theorem about the association between the distributions of different adv-noises: + +Theorem 1. Let $\mathcal{P}_a$ be the distribution set composed of all the adversarial noise distributions. Given independent noise distributions $Q_{i}, i \in N^{+}$ . For $\forall i \neq j$ , $Q_{i}$ and $Q_{j}$ are proximal noise distributions if the following conditions are met. + +1) $Q_{i},Q_{j}\in \mathcal{P}_{a}$ +2) $\exists \epsilon_{\mu}, \epsilon_{\sigma} > 0$ s.t. $\|\pmb{\mu}_i - \pmb{\mu}_j\| < \epsilon_{\mu}$ and $|\sigma_i - \sigma_j| < \epsilon_{\sigma}$ where the $\|\cdot\|$ is a Euclidean norm on $\mathbb{R}^n$ . + +Theorem 1 tells us: 1) All the adversarial noise distributions under the same $\ell^p$ norm are proximal noise distributions. 2) If the parameters of two noise distributions are sufficiently close to those of a given distribution, we can regard these two distributions as proximal noise distributions. + +We can further deduce several corollaries of the theorem. 1) All noise distributions proximal to the known adversarial distribution $p(\pmb {\eta})$ form an open $\varepsilon$ -ball centered on $p(\pmb {\eta})$ ,denoting as $\mathcal{P}_{\varepsilon} = \{p(\pmb {\eta}_i)|d(p(\pmb {\eta}_i),p(\pmb {\eta})) < \varepsilon \}$ , and also form a metric space $(\mathcal{P}_{\varepsilon},d)$ .2) The adv-noise distribution set is also located in this ball: $\mathcal{P}_a\subset \mathcal{P}_{\varepsilon}$ .3) Based on the prop + +erties of the metric space $(\mathcal{P}_{\varepsilon},d)$ , for all subset $\mathcal{P}_i\subset \mathcal{P}_\varepsilon$ there exists an open covering of the subset: $\mathcal{P}_i\subset \{G_c\}_{c\in \mathbb{I}}$ + +Based on the corollaries, we deduce the core idea of this paper: Let $p(\hat{\eta}_i|\boldsymbol {\eta}) = \mathcal{N}(\boldsymbol {\mu} + \epsilon_{\mu i},(\sigma +\epsilon_{\sigma i})^2\mathbf{I}_d),i = 1,2,\ldots ,n$ denote generated proximal noise distributions of the given adv-noise distribution $p(\pmb {\eta}) = \mathcal{N}(\pmb {\mu},\sigma^2\mathbf{I}_d)$ , where $\epsilon_{\mu i},\epsilon_{\sigma i}$ are randomly sampled from uniform distributions and restricted by $\epsilon_{\mu i},\epsilon_{\sigma i} < \varepsilon$ . As shown in Figure 1, when $n\to \infty$ , we can always obtain a distribution set $\mathcal{P}_c = \{p(\hat{\eta}_i|\boldsymbol {\eta})\}_{i = 1}^\infty$ that forms an open covering of the adversarial distribution set $\mathcal{P}_a$ . By training on the open covering, the detector learns to distinguish between the distributions of natural and adversarial data, enabling it to effectively detect unseen adversarial attacks. + +Analysis of distribution assumption, proofs of theorem, and corollaries are provided in the supplementary materials. + +# 4. Perturbation Forgery + +Based on the theory in the last section, we heuristically propose Perturbation Forgery to train a detector with strong generalization against various types of unseen attacks. + +As illustrated in Figure 2, Perturbation Forgery encompasses three elements: noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production. At first, the noise distribution of a commonly used attack is continuously perturbed using noise distribution perturbation into numerous noise distributions that remain proximal to the original, thereby forming the open covering. After that, we sample noises from the perturbed distribution and convert them into sparse local noise using sparse mask generation. Subsequently, we convert half of the natural data into pseudo-adv-data using pseudo-adversarial data production. This pseudo-adv data replaces actual adversarial data and is combined with the remaining natural data to + +train a binary detector. + +# 4.1. Noise Distribution Perturbation + +Given the training dataset $\{(\mathbf{x}_k,y_k)\}_{k = 1}^n$ composed by natural data, we add adv-noise on it using a commonly used attack (such as FGSM) and generate adversarial noise features $\mathcal{D}_{\mathrm{noise}}\coloneqq \{\mathbf{z}_k = h(\pmb {\eta}_k)\}_{k = 1}^n$ by + +$$ +\boldsymbol {\eta} _ {k} = \operatorname {A t t a c k} (\mathbf {x}) - \mathbf {x}, k \in [ 1, n ], \tag {2} +$$ + +where $h:\mathcal{X}\to \mathbb{R}^d$ is the flattening operation that converts multidimensional data into vectors. + +Assuming the noise features form a multivariate Gaussian distribution $p(\mathbf{z}) = \mathcal{N}(\boldsymbol {\mu},\boldsymbol {\Sigma})$ [10], we estimate the parameters mean $\pmb{\mu}$ and covariance $\pmb{\Sigma}$ of $\mathcal{D}_{\mathrm{noise}}$ by + +$$ +\widehat {\boldsymbol {\mu}} = \frac {1}{N} \sum_ {k} \mathbf {z} _ {k}, \quad \widehat {\boldsymbol {\Sigma}} = \frac {1}{N} \sum_ {k} \left(\mathbf {z} _ {k} - \widehat {\boldsymbol {\mu}}\right) \left(\mathbf {z} _ {k} - \widehat {\boldsymbol {\mu}}\right) ^ {\top}. \tag {3} +$$ + +For the $i^{\mathrm{th}}$ batch of training, we perturb the estimated distribution to a proximal noise distribution by + +$$ +\widehat {\boldsymbol {\mu}} _ {i} = \widehat {\boldsymbol {\mu}} + \alpha_ {i} \cdot \boldsymbol {m} _ {i}, \quad \widehat {\boldsymbol {\Sigma}} _ {i} = \widehat {\boldsymbol {\Sigma}} + \beta_ {i} \cdot \boldsymbol {V} _ {i}, \tag {4} +$$ + +where $\pmb{m}_i\sim \mathcal{N}(0,\mathbf{I}_d)$ and $\pmb {V}_i\sim \mathcal{N}(0,\mathbf{I}_{d\times d})$ are vector and matrix of perturbation. $\alpha_{i}\sim U(-\epsilon_{\mu},\epsilon_{\mu})$ and $\beta_{i}\sim$ $U(0,\epsilon_{\sigma})$ are scale parameters. After $n$ batches of training, we have a perturbed distribution set $\{\mathcal{N}(\widehat{\pmb{\mu}}_i,\widehat{\pmb{\Sigma}}_i)\}$ , thereby forming the approximate open covering $\mathcal{P}_c$ . Trained with $\mathcal{P}_c$ , the detector can distinguish the distributions of natural and adversarial data. + +# 4.2. Sparse Mask Generation + +Unlike gradient-based adversarial attacks, generative-based attacks tend to generate imbalanced and anisotropic perturbations, showing much intensity in high-frequency and salient areas and mild in low-frequency and background areas. Besides, in physical scenarios, adversarial attacks also tend to add patches to local areas. Noticing this, we propose sparse masks to perturbation forgery to assist the detector in detecting local adv-noises. Previous research has demonstrated that the spectra of real and fake images differ significantly in high-frequency regions [27]. Additionally, generative-based adversarial data manipulate characteristics, such as abnormal color aberrations, in these high-frequency regions [40]. To augment the detection performance on generative-based adversarial data, we need to sparse the pseudo-noise sampled from perturbed noise distribution and highlight the noise in high-frequency regions to mimic the style of generative-based attacks. + +Given this, for a natural sample $\mathbf{x}_{i,k}$ in the $i^{th}$ batch, we first mask the high-frequency area using saliency detection [33] and GradCAM [34]: + +$$ +\operatorname {M a s k} _ {1} \left(\mathbf {x} _ {i, k}\right) = \operatorname {M a p} \left(f _ {s} \left(\mathbf {x} _ {i, k}\right); \gamma_ {s}\right) \cup \operatorname {M a p} \left(f _ {c} \left(\mathbf {x} _ {i, k}\right); \gamma_ {c}\right), \tag {5} +$$ + +Algorithm 1 Training Procedure with Perturbation Forgery +Input: Training dataset, a commonly used attack, saliency detection model $f_{s}$ , and GradCAM model $f_{c}$ . + +Output: A detector with strong generalization capabilities against various types of unseen attacks. + +1: Generate adversarial noise using the commonly used attack in Eq. 2. +2: Estimate a multivariate Gaussian distribution $p(\mathbf{z}) = \mathcal{N}(\hat{\mu},\hat{\Sigma})$ of adv-noise using Eq. 3. +3: for batch $i$ in $1, \dots, n$ do +4: Generate a perturbed noise distribution $p(\mathbf{z}_i) = \mathcal{N}(\hat{\boldsymbol{\mu}}_i, \hat{\boldsymbol{\Sigma}}_i)$ using Eq. 4. +5: for sample $\mathbf{x}_{i,k}$ in half of batch $i$ do +6: Generate sparse masks $\mathrm{Mask}(\mathbf{x}_{i,k})$ using Eq. 8. +7: Sample pseudo-adv noise $\widehat{\eta}_{i,k}$ using Eq. 9. +8: Generate pseudo-adv data $\widehat{\mathbf{x}}_{i,k}$ using Eq. 11 and replace $\mathbf{x}_{i,k}$ . +9: end for +10: Train the detector on batch $i$ . +11: end for + +where $f_{s}$ and $f_{c}$ are the saliency detection model and Grad-CAM model respectively. $\operatorname{Map}(\mathbf{x};\gamma)$ is a binary indicator function parameterized by $\gamma$ : + +$$ +\operatorname {M a p} \left(\mathbf {x} _ {i, k}; \gamma\right) = \operatorname {C l i p} _ {[ 0, 1 ]} \left(\mathbf {x} _ {i, k} - \gamma \mathbf {I} _ {\mathcal {X}}\right). \tag {6} +$$ + +The adv-noise that occurs in the high-frequency region tends to occupy only a small part of the region. Therefore, we select the high-frequency point from the gradient map obtained by Sobel operator [11] to sparsify the mask of sample $\mathbf{x}_{i,k}$ : + +$$ +\operatorname {M a s k} _ {2} \left(\mathbf {x} _ {i, k}\right) = \operatorname {M a p} (\operatorname {S o b e l} \left(\mathbf {x} _ {i, k}\right); \gamma_ {l}), \tag {7} +$$ + +$$ +\operatorname {M a s k} \left(\mathbf {x} _ {i, k}\right) = \operatorname {M a s k} _ {1} \left(\mathbf {x} _ {i, k}\right) \cap \operatorname {M a s k} _ {2} \left(\mathbf {x} _ {i, k}\right). \tag {8} +$$ + +# 4.3. Pseudo-Adversarial Data Production + +For the $i^{\mathrm{th}}$ batch of training, we sample pseudo-adv noise from the perturbed distribution by: + +$$ +\widehat {\boldsymbol {\eta}} _ {i, k} = h ^ {- 1} \left(\mathbf {z} _ {i, k}\right), \tag {9} +$$ + +$$ +\mathbf {z} _ {i, k} \in \left\{\mathbf {z} _ {k} \mid \mathbf {z} _ {k} \sim \mathcal {N} \left(\widehat {\boldsymbol {\mu}} _ {i}, \widehat {\boldsymbol {\Sigma}} _ {i}\right) \text {a n d} p \left(\mathbf {z} _ {k}\right) < \gamma_ {p} \right\} \tag {10} +$$ + +where $h^{-1}:\mathbb{R}^d\to \mathcal{X}$ is an inverse function of $h$ to unflatten noise features, and $\gamma_{p}$ is a threshold that excludes data with a low likelihood. Note that $\eta_{i}$ is a global noise and needs to be localized by a sparse mask. The pseudo-adv data $\widehat{\mathbf{x}}_{i,k}$ is produced by adding the masked local noise to $\mathbf{x}_{i,k}$ : + +$$ +\widehat {\mathbf {x}} _ {i, k} = \mathbf {x} _ {i, k} + \widehat {\boldsymbol {\eta}} _ {i, k} \otimes \operatorname {M a s k} \left(\mathbf {x} _ {\mathbf {i}, \mathbf {k}}\right). \tag {11} +$$ + +where $\otimes$ is Hadamard product. + +Table 2. Comparison of AUROC scores of detecting gradient-based and adaptive attacks on ImageNet100 under $\epsilon = 4/{255}$ . + +
    DetectorBIMPGDDIMMIMNIMAABPDA+EOTMM
    LID [28]0.97820.97500.89420.91460.89770.91240.92020.9227
    LiBRe [8]0.92590.95480.92430.87250.90130.86530.87140.8573
    SPAD [40]0.98460.98510.98150.98200.98230.98900.98850.9811
    EPSAD [49]0.99980.99890.99230.99180.99720.99980.99850.9923
    ours0.99110.99120.98630.99310.99340.99410.99270.9944
    + +For each batch, we convert half of the natural data to pseudo-adv data by Perturbation Forgery and train a binary detector using the Cross-Entropy classification loss [50]. The overall training procedure with Perturbation Forgery is presented in Algorithm 1. + +# 5. Experiments + +To validate the detection performance of our approach against various adversarial attack methods, we conduct extensive experiments on multiple general and facial datasets. For additional experiments, analyses, and a discussion of limitations, please refer to the supplementary material. + +# 5.1. Experiment Settings + +Datasets The datasets used for evaluation include: 1) general datasets: ImageNet100 [7] and CIFAR-10 [23] for evaluate gradient-based and generative-based attacks, and 2) face datasets: Makeup [16] for Adv-Makeup [46], CelebAHQ [21] for AMT-GAN [19], and LFW [14] for TIPIM [45] and physical attacks. + +Adversarial Attacks We adopt 5 gradient-based attacks, 3 adaptive attacks, 5 generative-based attacks, and 6 face attacks to evaluate our method. For gradient-based attacks, BIM [24], PGD [29], MIM [9], DIM [43], and NIM [26] are used as the unseen attacks. For adaptive attacks, we adopt AutoAttack (AA) [6], BPDA+EOT [18], and Minimum-Margin Attack (MM) [13]. For generative-based attacks, we adopt 3 GAN-based attacks including CDA [31], TTP [30], and M3D [51], and 2 Diffusion-based attacks including Diff-Attack [4] and Diff-PGD [44]. For face attacks, we adopt 1 gradient-based attack TIPIM [45], 2 GAN-based attacks including AdvMakeup [46] and AMT-GAN [19], and 3 physical attacks including Adv-Sticker [38], Adv-Glasses [35], and Adv-Mask [38]. For each of the above attack methods, adversarial data is generated with the attack intensity of $\epsilon = 4 / 255$ (except for the unrestricted attacks), and iterative attacks run for 10 steps using step size 2. + +Baselines To evaluate our method across various types of adversarial attacks, we compare it with state-of-the-art detection methods from three related research domains: + +adversarial detection, synthetic image detection, and face forgery detection. For gradient-based attacks, we benchmark against four adversarial detection methods: LID [28], LiBRe [8], SPAD [40], and EPSAD [49]. Since most adversarial detection methods are not designed to address generative-based adversarial attacks, we include a comparison with four synthetic image detection techniques: CNN-Detection [41], LGrad [37], Universal-Detector [32], and DIRE [42]. For detecting GAN-based face attacks, we also compare against two face forgery detection methods, Luo et al.[27] and He et al.[17], as well as ODIN [25]. + +Evaluation Metrics Following previous adversarial detection works [49], we employ the Area Under the Receiver Operating Characteristic Curve (AUROC) [20] as the primary evaluation metric to assess the performance of our classification models. The AUROC is a widely recognized metric in the field of machine learning and is particularly useful for evaluating binary classification problems. For fair comparisons, the number of natural data and adversarial data in the experiments remained consistent. + +Implementation details XceptionNet [5] is selected as our backbone model and is trained on all the above datasets. For adversarial noise distribution estimation, we utilize Torchattacks [22] to generate 1000 noise images for each dataset. The uniform distribution parameters are set as $\epsilon_{\mu} = 3$ and $\epsilon_{\sigma} = 0.005$ . The threshold of the sample control is set as $\gamma_{s} = 0.05$ . The thresholds of the binary indicator function are set as $\gamma_{s} = 0$ , $\gamma_{c} = 125$ and $\gamma_{l} = 100$ . FGSM [15] is used as the initial attack, i.e. the commonly used attack, for Perturbation Forgery. Training epochs are set to 10 and convergence is witnessed. + +# 5.2. Detecting Gradient-based Attacks + +We begin by comparing our method with state-of-the-art techniques in detecting gradient-based attacks on ImageNet100. All the attacks are unseen by both the baseline methods and our method. For each attack, 1,000 adversarial images are generated in the gray-box setting, where the attacker has access to the victim model but is blind to the detection model. All baseline methods are sourced from existing adversarial detection research. + +Table 3. Comparison of AUROC scores of detecting generative-based attacks on ImageNet100. + +
    DetectorCDATTPM3DDiff-AttackDiff-PGD
    CNN-Detection [41]0.70510.67430.69170.39630.5260
    LGrad [37]0.61440.60770.60680.55860.5835
    Universal-Detector [32]0.79450.81700.83120.92020.5531
    DIRE [42]0.89760.90970.91290.90970.9143
    SPAD0.93850.90640.89840.88620.8879
    EPSAD0.96740.69970.72650.47000.1507
    ours0.98780.96780.93640.92230.9223
    + +Table 4. Comparison of AUROC scores for detecting various adversarial attacks on the face dataset. + +
    DetectorTIPIIMAdv-StickerAdv-GlassesAdv-MaskDetectorAdv-MakeupAMT-GAN
    LID0.69740.51030.64720.5319He et al. [17]0.52520.8823
    LiBRe0.53450.97390.81400.9993Luo et al. [27]0.61780.6511
    EPSAD0.96470.94620.92600.9578ODIN[25]0.63250.6970
    SPAD0.92560.99750.92440.9863SPAD0.96570.8969
    ours0.98850.99990.99990.9999ours0.97620.9216
    + +As reported in Table 2, although EPSAD performs well, our method demonstrates effective detection (achieving an AUROC score of 0.9931 against MIM and 0.9944 against MM) across a variety of attack methods. These results validate our assumptions about the proximity of the noise distribution. By continuously perturbing the estimated noise distribution of a given attack (FGSM), we obtain an open covering noise of distributions from all the attacks. Given one seen attack, we are able to detect all the unseen attacks. The consistent detection performance verifies the effectiveness of our core idea of training a detector to distinguish the open covering of adv-noise distributions from natural ones and demonstrates the strong generalization capability of our method against gradient-based attacks. + +# 5.3. Detecting Generative-based Attacks + +To investigate our method's advantage in detecting generative-based attacks, we compared it with state-of-the-art synthetic image detection and adversarial detection methods on ImageNet100. As shown in Table 3, our method significantly outperforms the baseline methods, demonstrating highly effective detection capabilities. + +For adversarial detection baselines, the imbalanced noise generated by GAN and diffusion models makes it difficult for these methods, which are typically designed for gradient-based attacks, to detect effectively. In contrast, our sparse mask approach enables effective detection of such localized noise. + +Most synthetic image detection methods are less effective in detecting adversarial data crafted from natural samples, with the exception of DIRE[42]. This effectiveness may stem from DIRE's use of reconstruction error from im + +ages generated by diffusion models, which maintains its robustness in this setting. + +# 5.4. Detecting Face Adversarial Examples + +Adversarial attacks targeting face recognition models represent an important branch of adversarial example research. Therefore, the detection ability of adversarial face examples is an important indicator of the performance of the detector. We perform various adversarial face attacks and compare our approach with state-of-the-art methods from adversarial face detection and face forgery detection. + +As shown in Table 4, our method shows excellent performance against a variety of adversarial attacks targeting faces and surpasses many existing adversarial face detection techniques. It further indicates the ability of the sparse mask to capture the essential characteristics of face adversarial examples and the strong generalization capability of our method. + +# 5.5. Ablation Study and Analysis + +To further evaluate our method, we report an ablation study on the sparse mask, white-box attack detection results, the impact of the initial attack and the data size for distribution estimation, and the functionality of Perturbation Forgery through visualizations. The impact of hyper-parameters and other analyses are reported in the supplementary materials. + +# 5.5.1. Impact of each mask + +As argued, the sparse mask is proposed to assist the detector in identifying local adversarial noises in generative-based adversarial data. As shown in Table 5, the absence of the saliency detection model $f_{s}$ or the GradCAM model $f_{c}$ has + +Table 5. Ablation study on masks (AUROC score), where $f_{s}$ denotes saliency detection model and $f_{c}$ represents the CAM model. + +
    AblationCDATTPM3DDiff-AttackDiff-PGD
    w/o fs0.97550.95850.93200.91970.9135
    w/o f_c0.98640.95100.92620.90310.9062
    w/o Sobel0.98680.72350.69840.52310.5547
    + +![](images/8c1edc90dfaf934c259a7c916e8e932b2d899bd7758a44d6bb19cec997f11aab.jpg) +(a) + +![](images/42ed1c5d54b7d85134b044e544dd86119c84911ee66cae6d4566e4e0775de8fc.jpg) +(b) +Figure 3. 2D T-SNE visualizations. (a) ImageNet100 flattened noises of adversarial data and Perturbation Forgery-generated data. (b) ImageNet100 features extracted by the backbone model trained with Perturbation Forgery. + +Table 6. AUROC scores against white-box attacks under $\epsilon = 4/255$ on CIFAR-10. + +
    AttackBIMPGDDIMMIMAA
    AUROC0.91800.91680.90620.90310.9019
    + +little effect on the overall system. This is because the regions masked by $f_{s}$ and $f_{c}$ are somewhat complementary. However, without the Sobel operation to sparsify the mask, the detector fails to detect most attacks, except for CDA. This is because generative-based adversarial noise tends to be imbalanced and localized, while CDA's noise is more global. The generated pseudo-adversarial noise without Sobel becomes too dense, preventing the detector from effectively focusing on localized noise. + +# 5.5.2. Functionality Visualization + +To validate the functionality of our method, we extract features and flattened noise from adversarial data and Perturbation Forgery-generated data, then visualize them using 2D t-SNE projections. All adversarial data originate from unseen attacks. As shown in Figure 3(a), Perturbation Forgery continuously perturbs the adv-noise distribution of the initial attack, thereby forming an open covering for noises from unseen attacks. Individual samples appear as outliers, floating outside the collective noise distribution. As shown in Figure 3(b), by learning to separate natural data from those generated by Perturbation Forgery, the trained detector can effectively distinguish between natural and adversarial data. + +Table 7. Impact of data size on distribution estimation: AUROC score against PGD under $\epsilon = 4 / 255$ on CIFAR-10. + +
    Data size10025050075010002000
    AUROC0.82780.93680.98660.99210.99650.9948
    + +# 5.5.3. Detecting White-box Attack + +To verify the robustness of our approach to white-box attacks, i.e., both the victim model and the detector are available to the attacker, we conduct the experiment on CIFAR-10. Following [3], a modified objective of attacks is: + +$$ +\max _ {\boldsymbol {\eta}} \mathcal {L} (f (\hat {\mathbf {x}}), y) + \alpha \cdot \mathcal {L} (f _ {d} (\hat {\mathbf {x}}), y _ {d}), s. t. | | \boldsymbol {\eta} | | \leq \epsilon \tag {12} +$$ + +where $y$ is the ground-truth label, $y_{d} = 0$ indicates that $\hat{\mathbf{x}}$ is an adversarial example, and $\alpha = 1$ is a constant balancing between the attack of the classifier $f$ and detector $f_{d}$ . As shown in Table 6, our method achieves a high average AUROC of 0.9092, demonstrating its robustness against white-box attacks. This may be attributed to the comprehensive open covering formed by perturbation forgery, which effectively encompasses adversarial data from white-box attacks, making it harder to mislead the trained detector. + +# 5.5.4. Data size for Distribution Estimation + +To assess the influence of data size for distribution estimation, we train detectors using distributions estimated from various data sizes and test them against PGD on CIFAR-10. As shown in Table 7, our method only requires a small amount of data ( $\geq 500$ samples) to estimate the adversarial noise distribution so as to train an effective detector. Notably, using fewer than 500 samples leads to a significant decrease in detection performance. + +# 6. Conclusion + +In this paper, we explore and define the proximity relationship between adversarial noise distributions. Based on our assumption and definition, we develop a perturbation method to craft proximal distributions and demonstrate an open covering of adversarial noise spaces. Building on this, we propose training detectors on the open coverings to achieve strong generalization against diverse adversarial attacks. We introduce Perturbation Forgery, which combines noise perturbation, sparse mask generation, and pseudo-adversarial data synthesis, enabling detection of unseen gradient-based, generative, and physical attacks, independent of specific models. Extensive experiments validate our approach's effectiveness and generalization with minimal inference overhead. + +# 7. Acknowledgments + +This work was supported in part by the Natural Science Foundation of China under Grant 62372203 and 62302186, in part by the Major Scientific and Technological Project of Shenzhen (202316021), in part by the National key research and development program of China(2022YFB2601802), in part by the Major Scientific and Technological Project of Hubei Province (2022BAA046, 2022BAA042). + +# References + +[1] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples. In ICML, pages 274-283. PMLR, 2018. 1 +[2] Oliver Bryniarski, Nabeel Hingun, Pedro Pachuca, Vincent Wang, and Nicholas Carlini. Evading adversarial example detection defenses with orthogonal projected gradient descent. arXiv preprint arXiv:2106.15023, 2021. 1 +[3] Nicholas Carlini and David Wagner. Adversarial examples are not easily detected: Bypassing ten detection methods. 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Although previous detection methods achieve high performance in detecting gradient-based adversarial attacks, new attacks based on generative models with imbalanced and anisotropic noise patterns evade detection. Even worse, the significant inference time overhead and limited performance against unseen attacks make existing techniques impractical for real-world use. In this paper, we explore the proximity relationship among adversarial noise distributions and demonstrate the existence of an open covering for these distributions. By training on the open covering of adversarial noise distributions, a detector with strong generalization performance against various types of unseen attacks can be developed. 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Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 611, + 296, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 611, + 296, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 611, + 296, + 684 + ], + "type": "text", + "content": "Numerous studies have demonstrated the effectiveness of deep neural networks (DNNs) in various tasks [36]. However, it is also well-known that DNNs are vulnerable to adversarial attacks, which generate adversarial data by adding imperceptible perturbations to natural images, potentially causing the model to make abnormal predictions. This vul" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 242, + 555, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 242, + 555, + 410 + ], + "spans": [ + { + "bbox": [ + 313, + 242, + 555, + 410 + ], + "type": "text", + "content": "nerability reduces the reliability of deep learning systems, highlighting the urgent need for defense techniques. Some approaches employ adversarial training techniques [48], which incorporate adversarial data into the training process to inherently bolster the model's immunity against adversarial noise (adv-noise). Other methods utilize adversarial purification [47] to cleanse the input data of adv-noise before model inference. Unfortunately, adversarial training often results in diminished classification accuracy on adversarial data and may sacrifice performance on natural data [1]. While purification techniques may seem more reliable, the denoising process can inadvertently smooth the high-frequency texture of clean images, leading to suboptimal accuracy on both natural and adversarial images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 411, + 556, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 556, + 532 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 556, + 532 + ], + "type": "text", + "content": "Another branch of adversarial defense is adversarial detection [12, 28], which aims to filter out adversarial data before they are fed into target systems. These methods rely on discerning the discrepancies between adversarial and natural distributions, thereby maintaining the integrity of target systems while achieving high performance in defending against adversarial attacks. However, existing adversarial detection approaches primarily train specialized detectors tailored for specific attacks or classifiers [8], which may not generalize well to unseen advanced attacks [2, 39]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 534, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 713 + ], + "type": "text", + "content": "Some recent approaches [40, 49] have attempted to enhance the generalization of adversarial detectors by leveraging diffusion models and manually designed pseudo-noise. Nevertheless, as shown in Table 1, this improvement often comes at the expense of increased inference overhead, and even well-trained detectors still struggle with adversarial data produced by generative models such as generative adversarial networks (GANs) and diffusion models. Specifically, generative-based adversarial attacks, such as M3D [51] and Diff-PGD [44], are recently developed techniques designed to generate more natural adversarial data. Unlike traditional gradient-based attacks like PGD [29], generative-based attacks tend to create imbalanced and anisotropic perturbations that are intense in high-frequency and salient areas but mild in low-frequency and background" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 200, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 200, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 200, + 713 + ], + "type": "text", + "content": "*Corresponding author\n1Code at https://github.com/cc13qq/PFD" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13917" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 79, + 134, + 532, + 225 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 126 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 126 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 126 + ], + "type": "text", + "content": "Table 1. Properties of our method vs Other Adversarial Detection: We summarize four metrics for adversarial detection. \"Detect Attacks\" specifies the types of attacks each method is designed to detect. \"Model-Agnostic\" indicates whether the detection method operates independently of the protected model. \"Unseen-Attack Detection\" assesses the method's generalization to detect previously unseen attacks, with the reported value representing the AUROC score for detecting the MIFGSM attack on the ImageNet dataset. Lastly, \"Time Overhead\" quantifies the time required for the detector to process 100 samples from the ImageNet dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 79, + 134, + 532, + 225 + ], + "lines": [ + { + "bbox": [ + 79, + 134, + 532, + 225 + ], + "spans": [ + { + "bbox": [ + 79, + 134, + 532, + 225 + ], + "type": "table", + "html": "
    MethodsDetect AttacksModel-AgnosticUnseen-Attack DetectionTime Overhead
    LID [28]Gradient×0.91461.80s
    LiBRe [8]Gradient×0.87252.56s
    SPAD [40]Gradient + GAN✓0.98204.56s
    EPSAD [49]Gradient✓0.9918396.81s
    OursGradient + GAN + Diffusion✓0.99314.85
    ", + "image_path": "a6b37e916f4ead15a851cab4e3e7913e55c12fb59390d923aefa7b3b58b0851a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 244, + 294, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 244, + 294, + 316 + ], + "spans": [ + { + "bbox": [ + 54, + 244, + 294, + 316 + ], + "type": "text", + "content": "areas. These perturbations make them harder to detect with current methods, posing a new challenge to the field of adversarial detection. Therefore, there is an urgent need for a low-time-cost detection method with strong generalization performance against both unseen gradient-based attacks and unseen generative-based attacks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 317, + 295, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 317, + 295, + 473 + ], + "spans": [ + { + "bbox": [ + 54, + 317, + 295, + 473 + ], + "type": "text", + "content": "In this paper, we investigate the association between the distributions of different adv-noises. As shown in Figure 1, by modeling noise as multivariate Gaussian distributions, we define the proximity relationship of the noise distributions in a metric space and establish a perturbation method to construct the proximal distributions. Based on the assumption and definition, we demonstrate that all adv-noise distributions are proximal using the Wasserstein distance, and we deduce a corollary that an open covering of the adv-noise distributions exists. We then propose the core idea of this paper: by training on the open covering, we obtain a detector with strong generalization performance against various types of unseen attacks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 475, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 475, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 56, + 475, + 295, + 713 + ], + "type": "text", + "content": "Based on this idea, we propose Perturbation Forgery, a pseudo-adversarial data (pseudo-adv-data) generation method designed to train a detector with strong generalization capabilities for detecting various types of adversarial attacks. As shown in Figure 2, Perturbation Forgery comprises noise distribution perturbation, sparse mask generation, and pseudo-adversarial data (pseudo-adv-data) production. By continuously perturbing the noise distribution of a commonly used attack, such as FGSM [15], we obtain a nearly complete family of distributions that form the aforementioned open covering. Simultaneously, sparse masks are generated using attention maps and saliency maps of the natural data, converting the sampled global noises into local forms to help the detector focus on local noise patterns so as to detect generative-based adv-noise. By sampling noise from the perturbed noise distributions, we sparsify it using sparse masks and inject it into natural data. This process converts half of the natural data into pseudo-adv-data, replacing actual adversarial data. The pseudo-adv-data is then combined with the remaining uncontaminated data to train" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 245, + 440, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 245, + 440, + 256 + ], + "spans": [ + { + "bbox": [ + 313, + 245, + 440, + 256 + ], + "type": "text", + "content": "the binary adversarial detector." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 257, + 555, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 257, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 257, + 555, + 316 + ], + "type": "text", + "content": "To the best of our knowledge, we are the first to empower a detector with the robust ability to detect various types of adversarial attacks, including gradient-based, GAN-based, diffusion-based, and physical attacks, with minor inference time overhead." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 326, + 316, + 527, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 316, + 527, + 328 + ], + "spans": [ + { + "bbox": [ + 326, + 316, + 527, + 328 + ], + "type": "text", + "content": "Our contributions are summarized in four thrusts:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 329, + 554, + 592 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 313, + 329, + 553, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 329, + 553, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 329, + 553, + 376 + ], + "type": "text", + "content": "- By modeling adversarial noise as Gaussian distributions, we investigate the association between different adversarial noise distributions and demonstrate their proximity in a metric space." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 377, + 553, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 377, + 553, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 377, + 553, + 437 + ], + "type": "text", + "content": "- Based on our assumption and definition, we deduce the existence of an open covering for adversarial noise distributions and propose training a detector to distinguish this open covering from the natural data distribution, thereby achieving strong generalization in detection." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 437, + 554, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 554, + 532 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 554, + 532 + ], + "type": "text", + "content": "- Building on our deductions, we propose Perturbation Forgery, which includes noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production. This method is designed to train a binary detector with strong generalization performance against various types of unseen attacks, including gradient-based, GAN-based, diffusion-based, and physical adversarial data, with minor inference time overhead." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 533, + 554, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 554, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 554, + 592 + ], + "type": "text", + "content": "- We conduct evaluations on multiple general and facial datasets across a wide spectrum of gradient-based, generative-based, and physical attacks, demonstrating the consistently strong performance of our method in adversarial detection tasks." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 604, + 400, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 604, + 400, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 604, + 400, + 616 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 624, + 427, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 427, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 427, + 635 + ], + "type": "text", + "content": "2.1. Adversarial Attack" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 555, + 715 + ], + "type": "text", + "content": "Gradient-based adversarial attack Adversarial attacks [15] attempt to fool a classifier into changing prediction results by injecting subtle perturbations to the input data while maintaining imperceptibility from human eyes. By introducing iterative perturbation, PGD [29] and BIM [24] generate adversarial data with significantly im" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13918" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 70, + 545, + 220 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 545, + 220 + ], + "type": "image", + "image_path": "126b929994d65958e289f67770158a3c2b5aecfdc5d1b59a60749148b1a3254d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 227, + 555, + 262 + ], + "lines": [ + { + "bbox": [ + 54, + 227, + 555, + 262 + ], + "spans": [ + { + "bbox": [ + 54, + 227, + 555, + 262 + ], + "type": "text", + "content": "Figure 1. Illustration of the proximity of adversarial noise distributions and perturbed noise distributions. Left: all the distributions of adversarial noise and the perturbed distributions are in a " + }, + { + "bbox": [ + 54, + 227, + 555, + 262 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 54, + 227, + 555, + 262 + ], + "type": "text", + "content": "-ball centered on a given adversarial noise distribution. Right: by continuously perturbing the given adversarial noise distribution, we obtain an open covering of distributions of adversarial noise." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 281, + 296, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 296, + 342 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 296, + 342 + ], + "type": "text", + "content": "proved attack performance, while DIM [43], NIM [26], and MIM [9] improve the transferability under the black-box setting. Besides, adaptive attacks [6, 13, 18] are proposed to exploit the weak points of each defense, achieving a high attack rate against several defense techniques." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 355, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 355, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 355, + 296, + 498 + ], + "type": "text", + "content": "Generative-based Adversarial Attacks Recently, another branch of attacks uses generative models to produce adversarial data with a more natural style and imbalanced noise compared to gradient-based attacks. Among them, CDA [31], TTP [30], and M3D [51] utilize GAN to craft adversarial data and achieve higher efficiency when attacking large-scale datasets. Diff-Attack [4] and Diff-PGD [44] employ the diffusion model as a strong prior to better ensure the realism of generated data. Designed for perturbing facial recognition systems, AdvMakeup [46] and AMTGAN [19] are presented to generate imperceptible adversarial images of the face." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 498, + 296, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 296, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 296, + 547 + ], + "type": "text", + "content": "In this paper, a wide spectrum of gradient-based, generative-based, and physical adversarial attacks on ImageNet and facial datasets is used to evaluate the detection performance of our method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 552, + 180, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 180, + 564 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 180, + 564 + ], + "type": "text", + "content": "2.2. Adversarial Detection" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 570, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 605 + ], + "type": "text", + "content": "As one of the technical solutions to ensure the safety of DNNs, there has been a significant amount of exploration in the field of adversarial detection [28]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "text", + "content": "LiBRe [8] leverages Bayesian neural networks to endow pre-trained DNNs with the ability to defend against unseen adversarial attacks, SPAD [40] leverages a data augmentation method to detect adversarial face images from unseen attack, while EPSAD [49] incorporates a diffusion model to detect adversarial data with minimal attack intensity, albeit at the cost of inference time." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "While current methods have achieved remarkable improvements in adversarial detection, generative-based ad" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 281, + 555, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 555, + 331 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 555, + 331 + ], + "type": "text", + "content": "versarial attacks are harder to detect, posing a new challenge. To address the problems above, our method is proposed to detect various types of unseen attacks, including gradient-based, generative-based, and physical attacks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 340, + 553, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 340, + 553, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 340, + 553, + 354 + ], + "type": "text", + "content": "3. Proximity of Adversarial Noise Distribution" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 360, + 555, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 360, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 360, + 555, + 456 + ], + "type": "text", + "content": "In this section, we provide an overview of preliminary concepts related to adversarial data generation and explore the relationship between adversarial noise distributions. We define the proximity of noise distributions and present the core idea of this paper: by training on the open covering of adversarial noise distributions, we obtain a detector with strong generalization performance against various types of unseen attacks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 464, + 468, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 468, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 468, + 475 + ], + "type": "text", + "content": "3.1. Adversarial data generation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "text", + "content": "Given a DNN " + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "text", + "content": " that works on dataset " + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(\\mathbf{x}_i, y_i)\\}_{i=1}^n" + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_i \\in \\mathcal{X}, y_i \\in \\mathcal{C})" + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "text", + "content": " being (sample, ground-truth) pair, an adversarial example " + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "text", + "content": " regarding sample " + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "text", + "content": " with attack intensity " + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 480, + 554, + 529 + ], + "type": "text", + "content": " is calculated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 381, + 538, + 555, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 538, + 555, + 559 + ], + "spans": [ + { + "bbox": [ + 381, + 538, + 555, + 559 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} = \\underset {\\hat {\\mathbf {x}} \\in \\mathcal {B} (\\mathbf {x}, \\epsilon)} {\\operatorname {a r g m a x}} \\mathcal {L} (f (\\hat {\\mathbf {x}}), y), \\tag {1}", + "image_path": "ce09c1b05bcd822196090da4ab103da3c54aad8d6a9512d4a794f236ab695a32.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "text", + "content": " is some loss function and " + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{B}(\\mathbf{x},\\epsilon) = \\{\\mathbf{x}'|\\ell^p (\\mathbf{x},\\mathbf{x}') < \\epsilon \\}" + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "text", + "content": " restricts the perturbation under " + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "inline_equation", + "content": "\\ell^p" + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "text", + "content": " norm. Following [15], we simply denote adversarial sample as " + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}} = \\mathbf{x} + \\boldsymbol{\\eta}" + }, + { + "bbox": [ + 313, + 568, + 555, + 617 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 624, + 480, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 480, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 480, + 636 + ], + "type": "text", + "content": "3.2. Proximity of noise distribution" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 642, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 714 + ], + "type": "text", + "content": "Due to the subtle and imperceptible nature of adv-noise, adversarial data and natural data appear visually similar. Thus, we assume that this similarity also exists between the noises of different adversarial attacks. To investigate the similarity of these noises, we provide the following definition, which depicts a close relationship between two noise distributions." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13919" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 545, + 216 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 545, + 216 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 545, + 216 + ], + "type": "image", + "image_path": "6373eca2d893772aa2f4d84ff3004f1b98ba9fe2471440f6ca6368ce9e973a00.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 224, + 555, + 270 + ], + "lines": [ + { + "bbox": [ + 54, + 224, + 555, + 270 + ], + "spans": [ + { + "bbox": [ + 54, + 224, + 555, + 270 + ], + "type": "text", + "content": "Figure 2. Illustration of Perturbation Forgery. Before training, we estimate the noise distribution from a commonly used attack, then continuously perturb it in each batch to create an open covering of the adversarial noise distributions. Next, noises sampled from these perturbed distributions are converted into localized noise by applying sparse masks. Finally, pseudo-adversarial data is generated by adding these localized noises to natural samples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "spans": [ + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": "Definition 1 (Proximal Noise Distribution). Let " + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": " be the distribution functions of two independent noise samples " + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1" + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_2" + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": ". We call them proximal noise distributions under " + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": " if we have a metric " + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "inline_equation", + "content": "d(\\cdot, \\cdot)" + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "inline_equation", + "content": "\\exists \\varepsilon > 0" + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": ", s.t. " + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "inline_equation", + "content": "d(P, Q) < \\varepsilon" + }, + { + "bbox": [ + 54, + 290, + 294, + 352 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "spans": [ + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "text", + "content": "A common assumption for instance feature distribution is to model it as a Gaussian distribution [10]. Obtained by subtracting from natural data and adversarial data, adv-noises naturally form a Gaussian distribution. Therefore, we assume that noise r.v " + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "inline_equation", + "content": "\\pmb{\\eta} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "text", + "content": " satisfies truncated Gaussian distribution " + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\pmb{\\mu}, \\sigma^2\\mathbf{I}_d)" + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "text", + "content": " with its truncated interval is " + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "inline_equation", + "content": "[- \\epsilon, \\epsilon]^d" + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "text", + "content": ". Built upon Definition 1, we derive the following theorem about the association between the distributions of different adv-noises:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "spans": [ + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "text", + "content": "Theorem 1. Let " + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_a" + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "text", + "content": " be the distribution set composed of all the adversarial noise distributions. Given independent noise distributions " + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "inline_equation", + "content": "Q_{i}, i \\in N^{+}" + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\forall i \\neq j" + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "inline_equation", + "content": "Q_{i}" + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "inline_equation", + "content": "Q_{j}" + }, + { + "bbox": [ + 54, + 475, + 296, + 534 + ], + "type": "text", + "content": " are proximal noise distributions if the following conditions are met." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 536, + 295, + 574 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 67, + 536, + 135, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 536, + 135, + 548 + ], + "spans": [ + { + "bbox": [ + 67, + 536, + 135, + 548 + ], + "type": "text", + "content": "1) " + }, + { + "bbox": [ + 67, + 536, + 135, + 548 + ], + "type": "inline_equation", + "content": "Q_{i},Q_{j}\\in \\mathcal{P}_{a}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "text", + "content": "2) " + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "inline_equation", + "content": "\\exists \\epsilon_{\\mu}, \\epsilon_{\\sigma} > 0" + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "text", + "content": " s.t. " + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "inline_equation", + "content": "\\|\\pmb{\\mu}_i - \\pmb{\\mu}_j\\| < \\epsilon_{\\mu}" + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "inline_equation", + "content": "|\\sigma_i - \\sigma_j| < \\epsilon_{\\sigma}" + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "text", + "content": " where the " + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "inline_equation", + "content": "\\|\\cdot\\|" + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "text", + "content": " is a Euclidean norm on " + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 55, + 548, + 295, + 574 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "text", + "content": "Theorem 1 tells us: 1) All the adversarial noise distributions under the same " + }, + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "inline_equation", + "content": "\\ell^p" + }, + { + "bbox": [ + 55, + 581, + 295, + 641 + ], + "type": "text", + "content": " norm are proximal noise distributions. 2) If the parameters of two noise distributions are sufficiently close to those of a given distribution, we can regard these two distributions as proximal noise distributions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "We can further deduce several corollaries of the theorem. 1) All noise distributions proximal to the known adversarial distribution " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "p(\\pmb {\\eta})" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": " form an open " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": " -ball centered on " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "p(\\pmb {\\eta})" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": " ,denoting as " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\varepsilon} = \\{p(\\pmb {\\eta}_i)|d(p(\\pmb {\\eta}_i),p(\\pmb {\\eta})) < \\varepsilon \\}" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": " , and also form a metric space " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{P}_{\\varepsilon},d)" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": " .2) The adv-noise distribution set is also located in this ball: " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_a\\subset \\mathcal{P}_{\\varepsilon}" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": " .3) Based on the prop" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 290, + 553, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 290, + 553, + 315 + ], + "spans": [ + { + "bbox": [ + 313, + 290, + 553, + 315 + ], + "type": "text", + "content": "erties of the metric space " + }, + { + "bbox": [ + 313, + 290, + 553, + 315 + ], + "type": "inline_equation", + "content": "(\\mathcal{P}_{\\varepsilon},d)" + }, + { + "bbox": [ + 313, + 290, + 553, + 315 + ], + "type": "text", + "content": " , for all subset " + }, + { + "bbox": [ + 313, + 290, + 553, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i\\subset \\mathcal{P}_\\varepsilon" + }, + { + "bbox": [ + 313, + 290, + 553, + 315 + ], + "type": "text", + "content": " there exists an open covering of the subset: " + }, + { + "bbox": [ + 313, + 290, + 553, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i\\subset \\{G_c\\}_{c\\in \\mathbb{I}}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "content": "Based on the corollaries, we deduce the core idea of this paper: Let " + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "inline_equation", + "content": "p(\\hat{\\eta}_i|\\boldsymbol {\\eta}) = \\mathcal{N}(\\boldsymbol {\\mu} + \\epsilon_{\\mu i},(\\sigma +\\epsilon_{\\sigma i})^2\\mathbf{I}_d),i = 1,2,\\ldots ,n" + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "content": " denote generated proximal noise distributions of the given adv-noise distribution " + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "inline_equation", + "content": "p(\\pmb {\\eta}) = \\mathcal{N}(\\pmb {\\mu},\\sigma^2\\mathbf{I}_d)" + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mu i},\\epsilon_{\\sigma i}" + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "content": " are randomly sampled from uniform distributions and restricted by " + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mu i},\\epsilon_{\\sigma i} < \\varepsilon" + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "content": ". As shown in Figure 1, when " + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "inline_equation", + "content": "n\\to \\infty" + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "content": ", we can always obtain a distribution set " + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_c = \\{p(\\hat{\\eta}_i|\\boldsymbol {\\eta})\\}_{i = 1}^\\infty" + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "content": " that forms an open covering of the adversarial distribution set " + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_a" + }, + { + "bbox": [ + 313, + 316, + 554, + 459 + ], + "type": "text", + "content": ". By training on the open covering, the detector learns to distinguish between the distributions of natural and adversarial data, enabling it to effectively detect unseen adversarial attacks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 460, + 554, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 554, + 485 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 554, + 485 + ], + "type": "text", + "content": "Analysis of distribution assumption, proofs of theorem, and corollaries are provided in the supplementary materials." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 499, + 440, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 499, + 440, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 499, + 440, + 514 + ], + "type": "text", + "content": "4. Perturbation Forgery" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 521, + 554, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 554, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 554, + 556 + ], + "type": "text", + "content": "Based on the theory in the last section, we heuristically propose Perturbation Forgery to train a detector with strong generalization against various types of unseen attacks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 558, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 558, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 312, + 558, + 555, + 713 + ], + "type": "text", + "content": "As illustrated in Figure 2, Perturbation Forgery encompasses three elements: noise distribution perturbation, sparse mask generation, and pseudo-adversarial data production. At first, the noise distribution of a commonly used attack is continuously perturbed using noise distribution perturbation into numerous noise distributions that remain proximal to the original, thereby forming the open covering. After that, we sample noises from the perturbed distribution and convert them into sparse local noise using sparse mask generation. Subsequently, we convert half of the natural data into pseudo-adv-data using pseudo-adversarial data production. This pseudo-adv data replaces actual adversarial data and is combined with the remaining natural data to" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13920" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 149, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 149, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 149, + 83 + ], + "type": "text", + "content": "train a binary detector." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 228, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 228, + 102 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 228, + 102 + ], + "type": "text", + "content": "4.1. Noise Distribution Perturbation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 107, + 296, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 107, + 296, + 158 + ], + "spans": [ + { + "bbox": [ + 55, + 107, + 296, + 158 + ], + "type": "text", + "content": "Given the training dataset " + }, + { + "bbox": [ + 55, + 107, + 296, + 158 + ], + "type": "inline_equation", + "content": "\\{(\\mathbf{x}_k,y_k)\\}_{k = 1}^n" + }, + { + "bbox": [ + 55, + 107, + 296, + 158 + ], + "type": "text", + "content": " composed by natural data, we add adv-noise on it using a commonly used attack (such as FGSM) and generate adversarial noise features " + }, + { + "bbox": [ + 55, + 107, + 296, + 158 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{noise}}\\coloneqq \\{\\mathbf{z}_k = h(\\pmb {\\eta}_k)\\}_{k = 1}^n" + }, + { + "bbox": [ + 55, + 107, + 296, + 158 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 163, + 295, + 177 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 163, + 295, + 177 + ], + "spans": [ + { + "bbox": [ + 107, + 163, + 295, + 177 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\eta} _ {k} = \\operatorname {A t t a c k} (\\mathbf {x}) - \\mathbf {x}, k \\in [ 1, n ], \\tag {2}", + "image_path": "8f453731b4451bb69d107cf2ed93a06cd3afa0a9cce640f644685ed204a84cc5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 182, + 295, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 182, + 295, + 205 + ], + "spans": [ + { + "bbox": [ + 55, + 182, + 295, + 205 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 182, + 295, + 205 + ], + "type": "inline_equation", + "content": "h:\\mathcal{X}\\to \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 182, + 295, + 205 + ], + "type": "text", + "content": " is the flattening operation that converts multidimensional data into vectors." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "spans": [ + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "text", + "content": "Assuming the noise features form a multivariate Gaussian distribution " + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "inline_equation", + "content": "p(\\mathbf{z}) = \\mathcal{N}(\\boldsymbol {\\mu},\\boldsymbol {\\Sigma})" + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "text", + "content": " [10], we estimate the parameters mean " + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}" + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "text", + "content": " and covariance " + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}" + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{noise}}" + }, + { + "bbox": [ + 55, + 207, + 296, + 243 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 248, + 295, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 248, + 295, + 277 + ], + "spans": [ + { + "bbox": [ + 61, + 248, + 295, + 277 + ], + "type": "interline_equation", + "content": "\\widehat {\\boldsymbol {\\mu}} = \\frac {1}{N} \\sum_ {k} \\mathbf {z} _ {k}, \\quad \\widehat {\\boldsymbol {\\Sigma}} = \\frac {1}{N} \\sum_ {k} \\left(\\mathbf {z} _ {k} - \\widehat {\\boldsymbol {\\mu}}\\right) \\left(\\mathbf {z} _ {k} - \\widehat {\\boldsymbol {\\mu}}\\right) ^ {\\top}. \\tag {3}", + "image_path": "8c22ec70568f04006e9e7808f86105c3488006f12357532a290b3726b64ff68b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 283, + 296, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 283, + 296, + 308 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 296, + 308 + ], + "type": "text", + "content": "For the " + }, + { + "bbox": [ + 55, + 283, + 296, + 308 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 55, + 283, + 296, + 308 + ], + "type": "text", + "content": " batch of training, we perturb the estimated distribution to a proximal noise distribution by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 312, + 295, + 328 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 312, + 295, + 328 + ], + "spans": [ + { + "bbox": [ + 91, + 312, + 295, + 328 + ], + "type": "interline_equation", + "content": "\\widehat {\\boldsymbol {\\mu}} _ {i} = \\widehat {\\boldsymbol {\\mu}} + \\alpha_ {i} \\cdot \\boldsymbol {m} _ {i}, \\quad \\widehat {\\boldsymbol {\\Sigma}} _ {i} = \\widehat {\\boldsymbol {\\Sigma}} + \\beta_ {i} \\cdot \\boldsymbol {V} _ {i}, \\tag {4}", + "image_path": "e9afad6864be90897e74d4cd752c9ecf94335032e1d8c3240f8eec92d73ab942.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "spans": [ + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "\\pmb{m}_i\\sim \\mathcal{N}(0,\\mathbf{I}_d)" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "\\pmb {V}_i\\sim \\mathcal{N}(0,\\mathbf{I}_{d\\times d})" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": " are vector and matrix of perturbation. " + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "\\alpha_{i}\\sim U(-\\epsilon_{\\mu},\\epsilon_{\\mu})" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "\\beta_{i}\\sim" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "U(0,\\epsilon_{\\sigma})" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": " are scale parameters. After " + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": " batches of training, we have a perturbed distribution set " + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{N}(\\widehat{\\pmb{\\mu}}_i,\\widehat{\\pmb{\\Sigma}}_i)\\}" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": ", thereby forming the approximate open covering " + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_c" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": ". Trained with " + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_c" + }, + { + "bbox": [ + 55, + 334, + 296, + 418 + ], + "type": "text", + "content": ", the detector can distinguish the distributions of natural and adversarial data." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 426, + 195, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 195, + 438 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 195, + 438 + ], + "type": "text", + "content": "4.2. Sparse Mask Generation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 54, + 442, + 295, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 442, + 295, + 646 + ], + "spans": [ + { + "bbox": [ + 54, + 442, + 295, + 646 + ], + "type": "text", + "content": "Unlike gradient-based adversarial attacks, generative-based attacks tend to generate imbalanced and anisotropic perturbations, showing much intensity in high-frequency and salient areas and mild in low-frequency and background areas. Besides, in physical scenarios, adversarial attacks also tend to add patches to local areas. Noticing this, we propose sparse masks to perturbation forgery to assist the detector in detecting local adv-noises. Previous research has demonstrated that the spectra of real and fake images differ significantly in high-frequency regions [27]. Additionally, generative-based adversarial data manipulate characteristics, such as abnormal color aberrations, in these high-frequency regions [40]. To augment the detection performance on generative-based adversarial data, we need to sparse the pseudo-noise sampled from perturbed noise distribution and highlight the noise in high-frequency regions to mimic the style of generative-based attacks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 646, + 296, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 646, + 296, + 682 + ], + "spans": [ + { + "bbox": [ + 55, + 646, + 296, + 682 + ], + "type": "text", + "content": "Given this, for a natural sample " + }, + { + "bbox": [ + 55, + 646, + 296, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i,k}" + }, + { + "bbox": [ + 55, + 646, + 296, + 682 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 55, + 646, + 296, + 682 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 55, + 646, + 296, + 682 + ], + "type": "text", + "content": " batch, we first mask the high-frequency area using saliency detection [33] and GradCAM [34]:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 60, + 689, + 295, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 60, + 689, + 295, + 714 + ], + "type": "interline_equation", + "content": "\\operatorname {M a s k} _ {1} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a p} \\left(f _ {s} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {s}\\right) \\cup \\operatorname {M a p} \\left(f _ {c} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {c}\\right), \\tag {5}", + "image_path": "a9ff97c9bafab19daec7940916d3883a649bb9b4af25b6f86bf0b249ff83c492.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 72, + 555, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 555, + 109 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 555, + 109 + ], + "type": "text", + "content": "Algorithm 1 Training Procedure with Perturbation Forgery \nInput: Training dataset, a commonly used attack, saliency detection model " + }, + { + "bbox": [ + 314, + 72, + 555, + 109 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 314, + 72, + 555, + 109 + ], + "type": "text", + "content": ", and GradCAM model " + }, + { + "bbox": [ + 314, + 72, + 555, + 109 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 314, + 72, + 555, + 109 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 109, + 555, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 109, + 555, + 133 + ], + "spans": [ + { + "bbox": [ + 314, + 109, + 555, + 133 + ], + "type": "text", + "content": "Output: A detector with strong generalization capabilities against various types of unseen attacks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 318, + 135, + 555, + 316 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 319, + 135, + 555, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 135, + 555, + 158 + ], + "spans": [ + { + "bbox": [ + 319, + 135, + 555, + 158 + ], + "type": "text", + "content": "1: Generate adversarial noise using the commonly used attack in Eq. 2." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 319, + 159, + 554, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 159, + 554, + 184 + ], + "spans": [ + { + "bbox": [ + 319, + 159, + 554, + 184 + ], + "type": "text", + "content": "2: Estimate a multivariate Gaussian distribution " + }, + { + "bbox": [ + 319, + 159, + 554, + 184 + ], + "type": "inline_equation", + "content": "p(\\mathbf{z}) = \\mathcal{N}(\\hat{\\mu},\\hat{\\Sigma})" + }, + { + "bbox": [ + 319, + 159, + 554, + 184 + ], + "type": "text", + "content": " of adv-noise using Eq. 3." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 319, + 185, + 440, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 185, + 440, + 195 + ], + "spans": [ + { + "bbox": [ + 319, + 185, + 440, + 195 + ], + "type": "text", + "content": "3: for batch " + }, + { + "bbox": [ + 319, + 185, + 440, + 195 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 319, + 185, + 440, + 195 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 319, + 185, + 440, + 195 + ], + "type": "inline_equation", + "content": "1, \\dots, n" + }, + { + "bbox": [ + 319, + 185, + 440, + 195 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 319, + 196, + 554, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 196, + 554, + 221 + ], + "spans": [ + { + "bbox": [ + 319, + 196, + 554, + 221 + ], + "type": "text", + "content": "4: Generate a perturbed noise distribution " + }, + { + "bbox": [ + 319, + 196, + 554, + 221 + ], + "type": "inline_equation", + "content": "p(\\mathbf{z}_i) = \\mathcal{N}(\\hat{\\boldsymbol{\\mu}}_i, \\hat{\\boldsymbol{\\Sigma}}_i)" + }, + { + "bbox": [ + 319, + 196, + 554, + 221 + ], + "type": "text", + "content": " using Eq. 4." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 319, + 222, + 489, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 222, + 489, + 233 + ], + "spans": [ + { + "bbox": [ + 319, + 222, + 489, + 233 + ], + "type": "text", + "content": "5: for sample " + }, + { + "bbox": [ + 319, + 222, + 489, + 233 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i,k}" + }, + { + "bbox": [ + 319, + 222, + 489, + 233 + ], + "type": "text", + "content": " in half of batch " + }, + { + "bbox": [ + 319, + 222, + 489, + 233 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 319, + 222, + 489, + 233 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 319, + 234, + 544, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 234, + 544, + 245 + ], + "spans": [ + { + "bbox": [ + 319, + 234, + 544, + 245 + ], + "type": "text", + "content": "6: Generate sparse masks " + }, + { + "bbox": [ + 319, + 234, + 544, + 245 + ], + "type": "inline_equation", + "content": "\\mathrm{Mask}(\\mathbf{x}_{i,k})" + }, + { + "bbox": [ + 319, + 234, + 544, + 245 + ], + "type": "text", + "content": " using Eq. 8." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 319, + 246, + 525, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 246, + 525, + 258 + ], + "spans": [ + { + "bbox": [ + 319, + 246, + 525, + 258 + ], + "type": "text", + "content": "7: Sample pseudo-adv noise " + }, + { + "bbox": [ + 319, + 246, + 525, + 258 + ], + "type": "inline_equation", + "content": "\\widehat{\\eta}_{i,k}" + }, + { + "bbox": [ + 319, + 246, + 525, + 258 + ], + "type": "text", + "content": " using Eq. 9." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 319, + 258, + 553, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 258, + 553, + 281 + ], + "spans": [ + { + "bbox": [ + 319, + 258, + 553, + 281 + ], + "type": "text", + "content": "8: Generate pseudo-adv data " + }, + { + "bbox": [ + 319, + 258, + 553, + 281 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{x}}_{i,k}" + }, + { + "bbox": [ + 319, + 258, + 553, + 281 + ], + "type": "text", + "content": " using Eq. 11 and replace " + }, + { + "bbox": [ + 319, + 258, + 553, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i,k}" + }, + { + "bbox": [ + 319, + 258, + 553, + 281 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 319, + 282, + 375, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 282, + 375, + 292 + ], + "spans": [ + { + "bbox": [ + 319, + 282, + 375, + 292 + ], + "type": "text", + "content": "9: end for" + } + ] + } + ], + 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" + }, + { + "bbox": [ + 313, + 339, + 555, + 376 + ], + "type": "inline_equation", + "content": "\\operatorname{Map}(\\mathbf{x};\\gamma)" + }, + { + "bbox": [ + 313, + 339, + 555, + 376 + ], + "type": "text", + "content": " is a binary indicator function parameterized by " + }, + { + "bbox": [ + 313, + 339, + 555, + 376 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 339, + 555, + 376 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 353, + 386, + 554, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 386, + 554, + 401 + ], + "spans": [ + { + "bbox": [ + 353, + 386, + 554, + 401 + ], + "type": "interline_equation", + "content": "\\operatorname {M a p} \\left(\\mathbf {x} _ {i, k}; \\gamma\\right) = \\operatorname {C l i p} _ {[ 0, 1 ]} \\left(\\mathbf {x} _ {i, k} - \\gamma \\mathbf {I} _ {\\mathcal {X}}\\right). \\tag {6}", + "image_path": "e83535bb950ef6c007288c14e0ffb0308267b62e0140d3f3c7d1504fc63231db.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 409, + 554, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 409, + 554, + 469 + ], + "spans": [ + { + "bbox": [ + 313, + 409, + 554, + 469 + ], + "type": "text", + "content": "The adv-noise that occurs in the high-frequency region tends to occupy only a small part of the region. Therefore, we select the high-frequency point from the gradient map obtained by Sobel operator [11] to sparsify the mask of sample " + }, + { + "bbox": [ + 313, + 409, + 554, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i,k}" + }, + { + "bbox": [ + 313, + 409, + 554, + 469 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 344, + 479, + 553, + 492 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 479, + 553, + 492 + ], + "spans": [ + { + "bbox": [ + 344, + 479, + 553, + 492 + ], + "type": "interline_equation", + "content": "\\operatorname {M a s k} _ {2} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a p} (\\operatorname {S o b e l} \\left(\\mathbf {x} _ {i, k}\\right); \\gamma_ {l}), \\tag {7}", + "image_path": "b8f1665d1b9f36a1bd31533f9f3492634edbdb2d7f592b7d47f34b87f9321060.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 344, + 494, + 553, + 507 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 494, + 553, + 507 + ], + "spans": [ + { + "bbox": [ + 344, + 494, + 553, + 507 + ], + "type": "interline_equation", + "content": "\\operatorname {M a s k} \\left(\\mathbf {x} _ {i, k}\\right) = \\operatorname {M a s k} _ {1} \\left(\\mathbf {x} _ {i, k}\\right) \\cap \\operatorname {M a s k} _ {2} \\left(\\mathbf {x} _ {i, k}\\right). \\tag {8}", + "image_path": "7d3024e7a3e326aa48dd2ed646abcb386804f6b3db9c46a4aa7084f5de0045ca.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 517, + 510, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 510, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 510, + 528 + ], + "type": "text", + "content": "4.3. Pseudo-Adversarial Data Production" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 313, + 534, + 554, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 554, + 559 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 554, + 559 + ], + "type": "text", + "content": "For the " + }, + { + "bbox": [ + 313, + 534, + 554, + 559 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 313, + 534, + 554, + 559 + ], + "type": "text", + "content": " batch of training, we sample pseudo-adv noise from the perturbed distribution by:" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 331, + 567, + 553, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 567, + 553, + 582 + ], + "spans": [ + { + "bbox": [ + 331, + 567, + 553, + 582 + ], + "type": "interline_equation", + "content": "\\widehat {\\boldsymbol {\\eta}} _ {i, k} = h ^ {- 1} \\left(\\mathbf {z} _ {i, k}\\right), \\tag {9}", + "image_path": "45ecfcd80ad31b171c411458de8fe47a4025a75d70774edf977e547e9ddc4e76.jpg" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 332, + 584, + 553, + 599 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 584, + 553, + 599 + ], + "spans": [ + { + "bbox": [ + 332, + 584, + 553, + 599 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {i, k} \\in \\left\\{\\mathbf {z} _ {k} \\mid \\mathbf {z} _ {k} \\sim \\mathcal {N} \\left(\\widehat {\\boldsymbol {\\mu}} _ {i}, \\widehat {\\boldsymbol {\\Sigma}} _ {i}\\right) \\text {a n d} p \\left(\\mathbf {z} _ {k}\\right) < \\gamma_ {p} \\right\\} \\tag {10}", + "image_path": "9cf0cd42a365ff096a1d5214652553d0fba65f4bca4e8aab90ae0d02a3875bef.jpg" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "spans": [ + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "inline_equation", + "content": "h^{-1}:\\mathbb{R}^d\\to \\mathcal{X}" + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "text", + "content": " is an inverse function of " + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "text", + "content": " to unflatten noise features, and " + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "inline_equation", + "content": "\\gamma_{p}" + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "text", + "content": " is a threshold that excludes data with a low likelihood. Note that " + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "inline_equation", + "content": "\\eta_{i}" + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "text", + "content": " is a global noise and needs to be localized by a sparse mask. The pseudo-adv data " + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{x}}_{i,k}" + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "text", + "content": " is produced by adding the masked local noise to " + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i,k}" + }, + { + "bbox": [ + 313, + 609, + 554, + 670 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 364, + 682, + 553, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 682, + 553, + 696 + ], + "spans": [ + { + "bbox": [ + 364, + 682, + 553, + 696 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathbf {x}} _ {i, k} = \\mathbf {x} _ {i, k} + \\widehat {\\boldsymbol {\\eta}} _ {i, k} \\otimes \\operatorname {M a s k} \\left(\\mathbf {x} _ {\\mathbf {i}, \\mathbf {k}}\\right). \\tag {11}", + "image_path": "be4ffb8338ab3171eceac0ab419e3b948b7959f28257f4b1fa354ff61d6885ed.jpg" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 313, + 701, + 441, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 441, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 441, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 701, + 441, + 714 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 313, + 701, + 441, + 714 + ], + "type": "text", + "content": " is Hadamard product." + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13921" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 91, + 542, + 173 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 529, + 83 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 529, + 83 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 529, + 83 + ], + "type": "text", + "content": "Table 2. Comparison of AUROC scores of detecting gradient-based and adaptive attacks on ImageNet100 under " + }, + { + "bbox": [ + 80, + 70, + 529, + 83 + ], + "type": "inline_equation", + "content": "\\epsilon = 4/{255}" + }, + { + "bbox": [ + 80, + 70, + 529, + 83 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 91, + 542, + 173 + ], + "lines": [ + { + "bbox": [ + 66, + 91, + 542, + 173 + ], + "spans": [ + { + "bbox": [ + 66, + 91, + 542, + 173 + ], + "type": "table", + "html": "
    DetectorBIMPGDDIMMIMNIMAABPDA+EOTMM
    LID [28]0.97820.97500.89420.91460.89770.91240.92020.9227
    LiBRe [8]0.92590.95480.92430.87250.90130.86530.87140.8573
    SPAD [40]0.98460.98510.98150.98200.98230.98900.98850.9811
    EPSAD [49]0.99980.99890.99230.99180.99720.99980.99850.9923
    ours0.99110.99120.98630.99310.99340.99410.99270.9944
    ", + "image_path": "cd3c431dbaa087f115b0d246d1895e117012e7ca69a8a62fddda400dc89da29b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 192, + 294, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 192, + 294, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 192, + 294, + 251 + ], + "type": "text", + "content": "For each batch, we convert half of the natural data to pseudo-adv data by Perturbation Forgery and train a binary detector using the Cross-Entropy classification loss [50]. The overall training procedure with Perturbation Forgery is presented in Algorithm 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 263, + 138, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 263, + 138, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 263, + 138, + 277 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 284, + 296, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 284, + 296, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 284, + 296, + 344 + ], + "type": "text", + "content": "To validate the detection performance of our approach against various adversarial attack methods, we conduct extensive experiments on multiple general and facial datasets. For additional experiments, analyses, and a discussion of limitations, please refer to the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 352, + 174, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 352, + 174, + 365 + ], + "spans": [ + { + "bbox": [ + 55, + 352, + 174, + 365 + ], + "type": "text", + "content": "5.1. Experiment Settings" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 369, + 296, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 369, + 296, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 296, + 441 + ], + "type": "text", + "content": "Datasets The datasets used for evaluation include: 1) general datasets: ImageNet100 [7] and CIFAR-10 [23] for evaluate gradient-based and generative-based attacks, and 2) face datasets: Makeup [16] for Adv-Makeup [46], CelebAHQ [21] for AMT-GAN [19], and LFW [14] for TIPIM [45] and physical attacks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 458, + 295, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 458, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 458, + 295, + 662 + ], + "type": "text", + "content": "Adversarial Attacks We adopt 5 gradient-based attacks, 3 adaptive attacks, 5 generative-based attacks, and 6 face attacks to evaluate our method. For gradient-based attacks, BIM [24], PGD [29], MIM [9], DIM [43], and NIM [26] are used as the unseen attacks. For adaptive attacks, we adopt AutoAttack (AA) [6], BPDA+EOT [18], and Minimum-Margin Attack (MM) [13]. For generative-based attacks, we adopt 3 GAN-based attacks including CDA [31], TTP [30], and M3D [51], and 2 Diffusion-based attacks including Diff-Attack [4] and Diff-PGD [44]. For face attacks, we adopt 1 gradient-based attack TIPIM [45], 2 GAN-based attacks including AdvMakeup [46] and AMT-GAN [19], and 3 physical attacks including Adv-Sticker [38], Adv-Glasses [35], and Adv-Mask [38]. For each of the above attack methods, adversarial data is generated with the attack intensity of " + }, + { + "bbox": [ + 55, + 458, + 295, + 662 + ], + "type": "inline_equation", + "content": "\\epsilon = 4 / 255" + }, + { + "bbox": [ + 55, + 458, + 295, + 662 + ], + "type": "text", + "content": " (except for the unrestricted attacks), and iterative attacks run for 10 steps using step size 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "Baselines To evaluate our method across various types of adversarial attacks, we compare it with state-of-the-art detection methods from three related research domains:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 192, + 555, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 192, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 555, + 324 + ], + "type": "text", + "content": "adversarial detection, synthetic image detection, and face forgery detection. For gradient-based attacks, we benchmark against four adversarial detection methods: LID [28], LiBRe [8], SPAD [40], and EPSAD [49]. Since most adversarial detection methods are not designed to address generative-based adversarial attacks, we include a comparison with four synthetic image detection techniques: CNN-Detection [41], LGrad [37], Universal-Detector [32], and DIRE [42]. For detecting GAN-based face attacks, we also compare against two face forgery detection methods, Luo et al.[27] and He et al.[17], as well as ODIN [25]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 338, + 556, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 556, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 556, + 445 + ], + "type": "text", + "content": "Evaluation Metrics Following previous adversarial detection works [49], we employ the Area Under the Receiver Operating Characteristic Curve (AUROC) [20] as the primary evaluation metric to assess the performance of our classification models. The AUROC is a widely recognized metric in the field of machine learning and is particularly useful for evaluating binary classification problems. For fair comparisons, the number of natural data and adversarial data in the experiments remained consistent." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "text", + "content": "Implementation details XceptionNet [5] is selected as our backbone model and is trained on all the above datasets. For adversarial noise distribution estimation, we utilize Torchattacks [22] to generate 1000 noise images for each dataset. The uniform distribution parameters are set as " + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mu} = 3" + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\sigma} = 0.005" + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "text", + "content": ". The threshold of the sample control is set as " + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\gamma_{s} = 0.05" + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "text", + "content": ". The thresholds of the binary indicator function are set as " + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\gamma_{s} = 0" + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\gamma_{c} = 125" + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\gamma_{l} = 100" + }, + { + "bbox": [ + 313, + 460, + 556, + 594 + ], + "type": "text", + "content": ". FGSM [15] is used as the initial attack, i.e. the commonly used attack, for Perturbation Forgery. Training epochs are set to 10 and convergence is witnessed." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 600, + 496, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 600, + 496, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 600, + 496, + 613 + ], + "type": "text", + "content": "5.2. Detecting Gradient-based Attacks" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 618, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 556, + 715 + ], + "type": "text", + "content": "We begin by comparing our method with state-of-the-art techniques in detecting gradient-based attacks on ImageNet100. All the attacks are unseen by both the baseline methods and our method. For each attack, 1,000 adversarial images are generated in the gray-box setting, where the attacker has access to the victim model but is blind to the detection model. All baseline methods are sourced from existing adversarial detection research." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13922" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 91, + 542, + 196 + ], + "blocks": [ + { + "bbox": [ + 133, + 70, + 478, + 82 + ], + "lines": [ + { + "bbox": [ + 133, + 70, + 478, + 82 + ], + "spans": [ + { + "bbox": [ + 133, + 70, + 478, + 82 + ], + "type": "text", + "content": "Table 3. Comparison of AUROC scores of detecting generative-based attacks on ImageNet100." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 91, + 542, + 196 + ], + "lines": [ + { + "bbox": [ + 66, + 91, + 542, + 196 + ], + "spans": [ + { + "bbox": [ + 66, + 91, + 542, + 196 + ], + "type": "table", + "html": "
    DetectorCDATTPM3DDiff-AttackDiff-PGD
    CNN-Detection [41]0.70510.67430.69170.39630.5260
    LGrad [37]0.61440.60770.60680.55860.5835
    Universal-Detector [32]0.79450.81700.83120.92020.5531
    DIRE [42]0.89760.90970.91290.90970.9143
    SPAD0.93850.90640.89840.88620.8879
    EPSAD0.96740.69970.72650.47000.1507
    ours0.98780.96780.93640.92230.9223
    ", + "image_path": "82ab80270c2d31443a08eb4d08f5a9bc65e03fcc87a674dec15528b5ef3cd280.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 64, + 227, + 544, + 308 + ], + "blocks": [ + { + "bbox": [ + 123, + 206, + 485, + 217 + ], + "lines": [ + { + "bbox": [ + 123, + 206, + 485, + 217 + ], + "spans": [ + { + "bbox": [ + 123, + 206, + 485, + 217 + ], + "type": "text", + "content": "Table 4. Comparison of AUROC scores for detecting various adversarial attacks on the face dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 64, + 227, + 544, + 308 + ], + "lines": [ + { + "bbox": [ + 64, + 227, + 544, + 308 + ], + "spans": [ + { + "bbox": [ + 64, + 227, + 544, + 308 + ], + "type": "table", + "html": "
    DetectorTIPIIMAdv-StickerAdv-GlassesAdv-MaskDetectorAdv-MakeupAMT-GAN
    LID0.69740.51030.64720.5319He et al. [17]0.52520.8823
    LiBRe0.53450.97390.81400.9993Luo et al. [27]0.61780.6511
    EPSAD0.96470.94620.92600.9578ODIN[25]0.63250.6970
    SPAD0.92560.99750.92440.9863SPAD0.96570.8969
    ours0.98850.99990.99990.9999ours0.97620.9216
    ", + "image_path": "335f14845d7b7f5402c6e6bb38ebaa40bffecba909025025542af1e3234c3bb9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 327, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 296, + 495 + ], + "type": "text", + "content": "As reported in Table 2, although EPSAD performs well, our method demonstrates effective detection (achieving an AUROC score of 0.9931 against MIM and 0.9944 against MM) across a variety of attack methods. These results validate our assumptions about the proximity of the noise distribution. By continuously perturbing the estimated noise distribution of a given attack (FGSM), we obtain an open covering noise of distributions from all the attacks. Given one seen attack, we are able to detect all the unseen attacks. The consistent detection performance verifies the effectiveness of our core idea of training a detector to distinguish the open covering of adv-noise distributions from natural ones and demonstrates the strong generalization capability of our method against gradient-based attacks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 503, + 246, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 503, + 246, + 516 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 246, + 516 + ], + "type": "text", + "content": "5.3. Detecting Generative-based Attacks" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 521, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 593 + ], + "type": "text", + "content": "To investigate our method's advantage in detecting generative-based attacks, we compared it with state-of-the-art synthetic image detection and adversarial detection methods on ImageNet100. As shown in Table 3, our method significantly outperforms the baseline methods, demonstrating highly effective detection capabilities." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 664 + ], + "type": "text", + "content": "For adversarial detection baselines, the imbalanced noise generated by GAN and diffusion models makes it difficult for these methods, which are typically designed for gradient-based attacks, to detect effectively. In contrast, our sparse mask approach enables effective detection of such localized noise." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "Most synthetic image detection methods are less effective in detecting adversarial data crafted from natural samples, with the exception of DIRE[42]. This effectiveness may stem from DIRE's use of reconstruction error from im" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 327, + 553, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 327, + 553, + 352 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 553, + 352 + ], + "type": "text", + "content": "ages generated by diffusion models, which maintains its robustness in this setting." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 360, + 512, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 360, + 512, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 360, + 512, + 373 + ], + "type": "text", + "content": "5.4. Detecting Face Adversarial Examples" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 377, + 554, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 377, + 554, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 377, + 554, + 461 + ], + "type": "text", + "content": "Adversarial attacks targeting face recognition models represent an important branch of adversarial example research. Therefore, the detection ability of adversarial face examples is an important indicator of the performance of the detector. We perform various adversarial face attacks and compare our approach with state-of-the-art methods from adversarial face detection and face forgery detection." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 462, + 554, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 462, + 554, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 462, + 554, + 545 + ], + "type": "text", + "content": "As shown in Table 4, our method shows excellent performance against a variety of adversarial attacks targeting faces and surpasses many existing adversarial face detection techniques. It further indicates the ability of the sparse mask to capture the essential characteristics of face adversarial examples and the strong generalization capability of our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 554, + 471, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 554, + 471, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 554, + 471, + 567 + ], + "type": "text", + "content": "5.5. Ablation Study and Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 571, + 553, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 571, + 553, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 571, + 553, + 643 + ], + "type": "text", + "content": "To further evaluate our method, we report an ablation study on the sparse mask, white-box attack detection results, the impact of the initial attack and the data size for distribution estimation, and the functionality of Perturbation Forgery through visualizations. The impact of hyper-parameters and other analyses are reported in the supplementary materials." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 651, + 432, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 651, + 432, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 651, + 432, + 662 + ], + "type": "text", + "content": "5.5.1. Impact of each mask" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": "As argued, the sparse mask is proposed to assist the detector in identifying local adversarial noises in generative-based adversarial data. As shown in Table 5, the absence of the saliency detection model " + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": " or the GradCAM model " + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 313, + 666, + 554, + 713 + ], + "type": "text", + "content": " has" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13923" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 102, + 293, + 159 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "type": "text", + "content": "Table 5. Ablation study on masks (AUROC score), where " + }, + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "type": "text", + "content": " denotes saliency detection model and " + }, + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 55, + 70, + 297, + 95 + ], + "type": "text", + "content": " represents the CAM model." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 102, + 293, + 159 + ], + "lines": [ + { + "bbox": [ + 56, + 102, + 293, + 159 + ], + "spans": [ + { + "bbox": [ + 56, + 102, + 293, + 159 + ], + "type": "table", + "html": "
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    AttackBIMPGDDIMMIMAA
    AUROC0.91800.91680.90620.90310.9019
    ", + "image_path": "9e9f3e9f3f01778f5e26f7f271ad1174462d7779408edc52af1d0eec8d10cf45.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 437, + 296, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 296, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 296, + 547 + ], + "type": "text", + "content": "little effect on the overall system. This is because the regions masked by " + }, + { + "bbox": [ + 55, + 437, + 296, + 547 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 55, + 437, + 296, + 547 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 437, + 296, + 547 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 55, + 437, + 296, + 547 + ], + "type": "text", + "content": " are somewhat complementary. However, without the Sobel operation to sparsify the mask, the detector fails to detect most attacks, except for CDA. This is because generative-based adversarial noise tends to be imbalanced and localized, while CDA's noise is more global. The generated pseudo-adversarial noise without Sobel becomes too dense, preventing the detector from effectively focusing on localized noise." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 554, + 200, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 554, + 200, + 566 + ], + "spans": [ + { + "bbox": [ + 55, + 554, + 200, + 566 + ], + "type": "text", + "content": "5.5.2. Functionality Visualization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 570, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 297, + 714 + ], + "type": "text", + "content": "To validate the functionality of our method, we extract features and flattened noise from adversarial data and Perturbation Forgery-generated data, then visualize them using 2D t-SNE projections. All adversarial data originate from unseen attacks. As shown in Figure 3(a), Perturbation Forgery continuously perturbs the adv-noise distribution of the initial attack, thereby forming an open covering for noises from unseen attacks. Individual samples appear as outliers, floating outside the collective noise distribution. As shown in Figure 3(b), by learning to separate natural data from those generated by Perturbation Forgery, the trained detector can effectively distinguish between natural and adversarial data." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 315, + 102, + 553, + 135 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 95 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 95 + ], + "type": "text", + "content": "Table 7. Impact of data size on distribution estimation: AUROC score against PGD under " + }, + { + "bbox": [ + 313, + 70, + 555, + 95 + ], + "type": "inline_equation", + "content": "\\epsilon = 4 / 255" + }, + { + "bbox": [ + 313, + 70, + 555, + 95 + ], + "type": "text", + "content": " on CIFAR-10." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 102, + 553, + 135 + ], + "lines": [ + { + "bbox": [ + 315, + 102, + 553, + 135 + ], + "spans": [ + { + "bbox": [ + 315, + 102, + 553, + 135 + ], + "type": "table", + "html": "
    Data size10025050075010002000
    AUROC0.82780.93680.98660.99210.99650.9948
    ", + "image_path": "68c5d5d083fea5ddb3a49c3391683c3fae37afd568a0f044db263fdd52e3348d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 160, + 463, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 160, + 463, + 172 + ], + "spans": [ + { + "bbox": [ + 313, + 160, + 463, + 172 + ], + "type": "text", + "content": "5.5.3. Detecting White-box Attack" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 178, + 555, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 178, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 178, + 555, + 228 + ], + "type": "text", + "content": "To verify the robustness of our approach to white-box attacks, i.e., both the victim model and the detector are available to the attacker, we conduct the experiment on CIFAR-10. Following [3], a modified objective of attacks is:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 324, + 239, + 555, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 239, + 555, + 259 + ], + "spans": [ + { + "bbox": [ + 324, + 239, + 555, + 259 + ], + "type": "interline_equation", + "content": "\\max _ {\\boldsymbol {\\eta}} \\mathcal {L} (f (\\hat {\\mathbf {x}}), y) + \\alpha \\cdot \\mathcal {L} (f _ {d} (\\hat {\\mathbf {x}}), y _ {d}), s. t. | | \\boldsymbol {\\eta} | | \\leq \\epsilon \\tag {12}", + "image_path": "91af231d1d0baf012b79a0eed6e4056b6fb4d30b05e762bdfe12bfe1299d7df2.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "spans": [ + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "text", + "content": " is the ground-truth label, " + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "inline_equation", + "content": "y_{d} = 0" + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "text", + "content": " indicates that " + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "text", + "content": " is an adversarial example, and " + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "text", + "content": " is a constant balancing between the attack of the classifier " + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "text", + "content": " and detector " + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "inline_equation", + "content": "f_{d}" + }, + { + "bbox": [ + 313, + 271, + 555, + 380 + ], + "type": "text", + "content": ". As shown in Table 6, our method achieves a high average AUROC of 0.9092, demonstrating its robustness against white-box attacks. This may be attributed to the comprehensive open covering formed by perturbation forgery, which effectively encompasses adversarial data from white-box attacks, making it harder to mislead the trained detector." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 392, + 497, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 497, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 497, + 403 + ], + "type": "text", + "content": "5.5.4. Data size for Distribution Estimation" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 410, + 556, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 556, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 556, + 506 + ], + "type": "text", + "content": "To assess the influence of data size for distribution estimation, we train detectors using distributions estimated from various data sizes and test them against PGD on CIFAR-10. As shown in Table 7, our method only requires a small amount of data (" + }, + { + "bbox": [ + 313, + 410, + 556, + 506 + ], + "type": "inline_equation", + "content": "\\geq 500" + }, + { + "bbox": [ + 313, + 410, + 556, + 506 + ], + "type": "text", + "content": " samples) to estimate the adversarial noise distribution so as to train an effective detector. Notably, using fewer than 500 samples leads to a significant decrease in detection performance." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 523, + 388, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 523, + 388, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 523, + 388, + 536 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 546, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 556, + 713 + ], + "type": "text", + "content": "In this paper, we explore and define the proximity relationship between adversarial noise distributions. Based on our assumption and definition, we develop a perturbation method to craft proximal distributions and demonstrate an open covering of adversarial noise spaces. Building on this, we propose training detectors on the open coverings to achieve strong generalization against diverse adversarial attacks. We introduce Perturbation Forgery, which combines noise perturbation, sparse mask generation, and pseudo-adversarial data synthesis, enabling detection of unseen gradient-based, generative, and physical attacks, independent of specific models. Extensive experiments validate our approach's effectiveness and generalization with minimal inference overhead." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13924" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "type": "text", + "content": "7. Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 175 + ], + "type": "text", + "content": "This work was supported in part by the Natural Science Foundation of China under Grant 62372203 and 62302186, in part by the Major Scientific and Technological Project of Shenzhen (202316021), in part by the National key research and development program of China(2022YFB2601802), in part by the Major Scientific and Technological Project of Hubei Province (2022BAA046, 2022BAA042)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 184, + 115, + 197 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 184, + 115, + 197 + ], + "spans": [ + { + "bbox": [ + 56, + 184, + 115, + 197 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 204, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 204, + 295, + 247 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 204, + 295, + 247 + ], + "spans": [ + { + "bbox": [ + 61, + 204, + 295, + 247 + ], + "type": "text", + "content": "[1] Anish Athalye, Nicholas Carlini, and David Wagner. 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In CVPR, pages 8153-8162, 2023. 1, 3, 6" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "13926" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/13985764-96b8-48db-82c6-84b1d3a23329_content_list.json b/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/13985764-96b8-48db-82c6-84b1d3a23329_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ac36521831bd243770459be2c93e67466a0aa8f6 --- /dev/null +++ b/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/13985764-96b8-48db-82c6-84b1d3a23329_content_list.json @@ -0,0 +1,1367 @@ +[ + { + "type": "text", + "text": "Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection", + "text_level": 1, + "bbox": [ + 117, + 128, + 880, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiahao Xu Zikai Zhang Rui Hu University of Nevada, Reno {jiahaox,zikaiz,ruihu}@unr.edu", + "bbox": [ + 310, + 203, + 684, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 291, + 326, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The distributed nature of training makes Federated Learning (FL) vulnerable to backdoor attacks, where malicious model updates aim to compromise the global model's performance on specific tasks. Existing defense methods show limited efficacy as they overlook the inconsistency between benign and malicious model updates regarding both general and fine-grained directions. To fill this gap, we introduce AlignIns, a novel defense method designed to safeguard FL systems against backdoor attacks. AlignIns looks into the direction of each model update through a direction alignment inspection process. Specifically, it examines the alignment of model updates with the overall update direction and analyzes the distribution of the signs of their significant parameters, comparing them with the principle sign across all model updates. Model updates that exhibit an unusual degree of alignment are considered malicious and thus be filtered out. We provide the theoretical analysis of the robustness of AlignIns and its propagation error in FL. Our empirical results on both independent and identically distributed (IID) and non-IID datasets demonstrate that AlignIns achieves higher robustness compared to the state-of-the-art defense methods. The code is available at https://github.com/JiaiahaoXU/AlignIns.", + "bbox": [ + 89, + 324, + 485, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 707, + 220, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unlike traditional centralized training methods, which require gathering and processing all data at a central location such as a server, Federated Learning (FL) [32], as a decentralized training paradigm, allows a global model to learn from data distributed across various local clients, thereby achieving the goal of privacy-preserving. During training, the server distributes the global model to local clients, and each client trains the received global model using its local dataset, and then submits its local model update to the server for global model refinement. FL has been applied in various fields, including healthcare[35], finance [28], and remote", + "bbox": [ + 89, + 734, + 483, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sensing [27], where local data privacy is essential.", + "bbox": [ + 511, + 292, + 844, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although promising, the distributed nature of FL systems makes them vulnerable to a range of advanced poisoning attacks [15, 26, 45]. This vulnerability primarily stems from the server's lack of close monitoring of the local data and the training algorithm on clients. Consequently, this drawback allows attackers to compromise the data of local clients or interfere with the training algorithm, enabling them to inject malicious local model updates that distort the performance of the global model. For example, backdoor attacks [4, 14, 46, 48, 54] have gained significant attention due to their stealthiness and practical effectiveness. In detail, backdoor attacks in FL seek to preserve the performance of the global model on clean inputs (i.e., the main task), while inducing the global model to make incorrect predictions on inputs that contain a certain predefined feature (i.e., the backdoor task). As backdoor attacks maintain the main task and the backdoor task simultaneously, the malicious local model updates are statistically similar to benign ones [36, 46] (poison-coupling effect [20]), making anomaly detection more challenging on the server side.", + "bbox": [ + 511, + 309, + 906, + 611 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing defense methods (i.e., aggregation rule) usually aim to identify malicious model updates and filter them out to achieve better robustness by magnitude-based metrics extracted from local model updates (e.g., Manhattan distance [19, 22] and Euclidean distance [6, 15]). However, magnitude-based metrics are ineffective in distinguishing stealthy backdoor attacks where benign and malicious model updates are usually similar in magnitude. Additionally, when the global model tends to converge, the magnitude of each model update becomes very small, making effective malicious manipulation on magnitude negligible. To this end, some works employ Cosine similarity to check the pair-wise directional information of model updates [11, 36, 42]. However, pair-wise Cosine similarity between two model updates only captures their general directional similarity and overlooks fine-grained information (e.g., signs of parameters), resulting in limited robustness. In addition, in FL settings with non-IID data, the pair-wise Cosine similarity of model updates can be easily perturbed", + "bbox": [ + 511, + 613, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20654", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "by the naturally diverse benign model updates. Furthermore, there is a deficiency in theoretical analysis within the literature concerning the effects of data heterogeneity on defense methods deployed by the server in FL.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a novel defense method designed to defend against backdoor attacks in FL, named AlignIns (Direction Alignment Inspection), which examines local model updates for directional alignment at different granularity levels to identify malicious updates. Specifically, after receiving all model updates from clients, AlignIns evaluates each update by (1) inspecting temporal directional alignment with the global model of the latest round with Cosine similarity and (2) assessing more fine-grained sign alignment with the principal sign across all updates with a novel metric sign alignment ratio. Particularly, when calculating the sign alignment ratio, AlignIns focuses on the signs of important parameters in each update to accurately capture alignment information. Using these two directional metrics, AlignIns performs anomaly detection with the robust MZ_score which requires minimal hyperparameters to filter updates with unusual directional patterns out. Finally, AlignIns clips the remaining updates to mitigate the impact of updates with abnormally large magnitudes. We also provide a theoretical analysis of AlignIns' robustness and its propagation error in FL. The main contributions of this work are three folds:", + "bbox": [ + 91, + 152, + 482, + 482 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a novel defense method, AlignIns, to defend against backdoor attacks in FL. To the best of our knowledge, AlignIns is the first defense method in FL that analyzes the directional patterns of local model updates at different levels of granularity. AlignIns is fully compatible with existing FL frameworks.", + "- To the best of our knowledge, we provide the first theoretical robustness analysis for a filtering-based defense method against backdoor attacks under non-IID data in FL. Moreover, we prove that the propagation error of AlignIns is bounded during the training of FL.", + "- We empirically evaluate the effectiveness of AlignIns through extensive experiments on both IID and non-IID datasets against various state-of-the-art (SOTA) backdoor attacks. Compared to existing SOTA defense methods, AlignIns exhibits superior robustness." + ], + "bbox": [ + 89, + 483, + 482, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background and Related Works", + "text_level": 1, + "bbox": [ + 89, + 739, + 383, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Federated Learning. In a typical FL system, a central server controls a set of $n$ clients to train a global model $\\theta \\in \\mathbb{R}^d$ collaboratively. The objective of FL is to solve the following optimization problem: $\\min_{\\theta}(1/n)\\sum_{i=1}^{n}\\mathcal{L}_i(\\theta;\\mathcal{D}_i)$ , where $\\mathcal{L}_i(\\cdot)$ denotes the learning objective specific to client $i$ and $\\mathcal{D}_i$ denotes the local dataset for client $i$ . The commonly used method to solve this problem iteratively is FedAvg [33]. In detail, at round $t$ of FedAvg, each client $i \\in [n]$ downloads the current global model $\\theta^t$ , updates it", + "bbox": [ + 89, + 763, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "by optimizing its local objective, resulting in $\\theta_i^t$ , and transmits its model update $\\Delta_i^t = \\theta_i^t - \\theta^t$ to the server. The server then refines the global model by averaging these updates as follows: $\\theta^{t + 1} = \\theta^t + (1 / n)\\sum_{i = 1}^n\\Delta_i^t$ . This process continues until the global model reaches convergence.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Backdoor attacks in FL. Empirical evidence has shown that FL is vulnerable to backdoor attacks [4, 9, 14, 23, 37, 46, 48, 52, 54] due to its lack of access to local training data [4]. For instance, Projected Gradient Descent (PGD) attack [46] periodically projects the local model onto a small sphere centered around the global model from the previous training round, with a predefined radius. Distributed Backdoor Attack (DBA) [48] decomposes the centralized trigger into several smaller, distributed local triggers. Each poisoned client uses one of these local triggers, but during testing, the adversary injects the full trigger into the test samples. Recently, research has focused on trigger-optimization backdoor attacks [1, 9, 29, 37, 52], which aim to search optimized triggers to enhance the effectiveness and stealthiness.", + "bbox": [ + 511, + 169, + 903, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Defending against backdoor attacks in FL. Generally, based on how defense methods mitigate the impact of malicious updates, existing defense methods can be categorized into filtering-based methods [6, 7, 19, 22, 36, 42, 50, 51] and influence-reduction methods [11, 20, 38, 40, 41].", + "bbox": [ + 511, + 397, + 903, + 473 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1) influence-reduction methods aim to integrate all model updates but employ strategies to reduce the impact of malicious updates. For instance, $RFA$ [40] is proposed to use the geometric median of local models as the aggregation result, under the assumption that malicious models significantly deviate from benign models. Foolsgold [11] assumes that the malicious updates are consistent with each other. It assigns aggregation weights to model updates based on the maximum Cosine similarity between the last layers of pairwise model updates. A higher Cosine similarity value indicates a higher probability that the updates are malicious, leading to smaller aggregation weights being assigned. The effectiveness of influence-reduction methods is inherently limited because they cannot eliminate the impact of malicious activity, leading to a significant risk of compromise.", + "bbox": [ + 511, + 474, + 903, + 702 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2) Filtering-based methods aim to detect and remove malicious local model updates before aggregation thus attempting to achieve the highest robustness. For example, Multi-Krum [6] selects the multiply reliable local model updates for aggregation by identifying the one with the smallest sum of squared Euclidean distances to all other updates. Multi-Metrics [19] explores the combination of Manhattan distance, Euclidean distance, and Cosine similarity for each update to collaboratively filter out outliers. However, due to the dual objectives of backdoor attacks—that is, maintaining accuracy on the main task while maximizing accuracy on the backdoor task—malicious updates must mimic benign model updates, important weights for the main task", + "bbox": [ + 511, + 704, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20655", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: AlignIns" + ], + "code_body": "Input: Set of $n$ local model updates $\\{\\Delta_i^t\\}_{i=1}^n$ where $m$ of them are malicious, global model $\\theta^t$ , TDA radius $\\lambda_c$ , MPSA radius $\\lambda_s$ , extraction parameter $k$ \nOutput: Aggregated model update $\\widetilde{\\Delta}$ \n1 Initialize benign set $S \\gets \\emptyset$ \n2 $\\omega \\gets \\{\\mathrm{TDA}(\\Delta_i^t, \\theta)\\}_{i=1}^n$ $\\triangleleft$ by Equation (1) \n3 $p \\gets \\operatorname{sgn}(\\sum_{i=1}^n \\operatorname{sgn}(\\Delta_i^t))$ \n4 $\\rho \\gets \\{\\mathrm{MPSA}(\\Delta_i^t, p, k)\\}_{i=1}^n$ $\\triangleleft$ by Equation (2) \n5 for $i \\in [n]$ do \n6 $\\lambda_{i,c} \\gets \\mathrm{MZ\\_score}(\\omega_i, \\omega)$ $\\triangleleft$ by Equation (3) \n7 $\\lambda_{i,s} \\gets \\mathrm{MZ\\_score}(\\rho_i, \\rho)$ $\\triangleleft$ by Equation (3) \n8 if $|\\lambda_{i,c}| \\leq \\lambda_c$ and $|\\lambda_{i,s}| \\leq \\lambda_s$ then \n9 $\\mid S \\gets S \\cup \\{i\\}$ \n10 end \n11 end \n12 $c \\gets \\operatorname{med}(\\{\\| \\Delta_i^t\\| \\}_{i \\in S})$ \n13 $\\widetilde{\\Delta} \\gets (1 / |\\mathcal{S}|) \\sum_{i \\in S} (\\Delta_i^t \\cdot \\min\\{1, c / \\| \\Delta_i^t\\|\\})$ \n14 return $\\widetilde{\\Delta}$", + "bbox": [ + 94, + 111, + 480, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "typically have large values and can dominate the magnitude of a model update. As a result, magnitude-based detection methods become ineffective against backdoor attacks. Additionally, methods that rely solely on Cosine similarity also show limited effectiveness since they capture general directional alignment and overlook finer-grained information.", + "bbox": [ + 89, + 430, + 482, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Solution: AlignIns", + "text_level": 1, + "bbox": [ + 89, + 537, + 308, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method, AlignIns, detailed in Algorithm 1, mitigates the impact of malicious updates through a two-step process. First, direction alignment inspection is applied to examine each local model update comprehensively in terms of direction. Second, post-filtering model clipping is used to further enhance the robustness of AlignIns on defending potential magnitude-based attack methods before final aggregation.", + "bbox": [ + 89, + 565, + 482, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Direction alignment inspection. Existing defense methods against backdoor attacks in FL primarily focus on examining the magnitude (e.g., Manhattan distance and Euclidean distance) and the overall direction (e.g., Cosine similarity) of model updates. However, backdoor attacks are designed to maintain the main task accuracy, making the magnitude difference between malicious and benign updates nearly indistinguishable. Additionally, advanced attacks such as PGD [46] and Lie [5] attacks are specifically crafted to bypass magnitude-based defenses. Therefore, AlignIns focuses on direction-based analysis to identify suspect updates, using two processes described below.", + "bbox": [ + 89, + 672, + 482, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "1) Temporal direction alignment checking: Since malicious clients need to maintain both the main task and the backdoor task, the optimization direction of a malicious", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "local model tends to deviate from that of benign models. AlignIns leverages this deviation and performs a Temporal Direction Alignment (TDA) checking, which calculates the Cosine similarity between a local update and the latest global model (line 2 in Algorithm 1) to assess the general alignment level of each local update. Formally, the TDA value $\\omega_{i}$ of a local model update $\\Delta_i^t$ is calculated as", + "bbox": [ + 511, + 90, + 903, + 196 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\omega_ {i} := \\left\\langle \\Delta_ {i} ^ {t}, \\theta^ {t} \\right\\rangle / \\left(\\| \\Delta_ {i} ^ {t} \\| \\| \\theta^ {t} \\|\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 207, + 903, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use local model updates rather than local models because our goal is to measure how closely each client's updates align with the direction of the global model. Local model updates specifically capture these incremental adjustments. Notably, malicious clients tend to exhibit similar TDA values, which differ from those of benign clients, creating an opportunity for detection. It is important to note that while the magnitude of model updates typically decreases as the global model converges, the TDA value does not follow the same trend. Consequently, magnitude-based anomaly detection becomes progressively less effective throughout training due to the decreasing magnitude. In contrast, the variability in TDA values continues to be useful for identifying malicious behavior.", + "bbox": [ + 511, + 234, + 906, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2) Masked principal sign alignment checking: In backdoor attacks where the manipulations are stealthy, subtle malicious directional information can easily blend into the parameters of models with large magnitude, especially for models with large dimensions, which makes the TDA less useful under strong backdoor attacks since the TDA captures the overall directional information. Therefore, in addition to the TDA, we look into the signs of parameters to provide a finer-grained directional assessment of local model updates. The signs of a vector represent its coordinate-wise direction. In the context of backdoor attacks, the distributions of the signs of malicious model updates differ from those of benign updates. This is particularly significant when the model is close to convergence, at which point the magnitude of model updates becomes very small, making large manipulations on magnitudes impractical. Therefore, manipulation of the direction, or the signs of parameters, can emerge as a more significant and effective strategy. Several works also utilize the signs of models for enhancing backdoor robustness. For example, RLR [38] assigns an opposite global learning rate to a coordinate of the averaged model update if the signs on this coordinate do not consistently align with the majority across all updates. SignGuard [49] calculates the proportions of positive, zero, and negative signs for each model update as the input of a clustering algorithm to identify malicious model updates. However, these methods utilize the signs of all parameters in the model update, regardless of their significance. Consequently, the performance of sign-based metrics can be significantly impacted by those many unimportant parameters,", + "bbox": [ + 511, + 446, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20656", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "especially for large DNN models, leading to an inaccurate representation of the model update's direction.", + "bbox": [ + 89, + 90, + 482, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, AlignIns utilizes a Masked Principle Sign Alignment (MPSA) checking to inspect the sign alignment degree between the important parameters of each local update and a well-designed principle sign of all local updates. Specifically, to construct the principle sign over local updates, for each coordinate of local updates, we take the majority of the signs across all model updates as the principal sign of this coordinate, which can be mathematically formulated as $p \\coloneqq \\operatorname{sgn}\\left(\\sum_{i=1}^{n} \\operatorname{sgn}\\left(\\Delta_i^t\\right)\\right)$ , where $p \\in \\mathbb{R}^d$ represents the vector of principal signs and $\\operatorname{sgn}(\\cdot)$ is the function to take the signs of a vector. Note that the principal sign represents sign-voting results for each coordinate, making it stand for the major direction/dynamic for each coordinate. With this principle sign over local updates, we inspect the alignment of the signs of important parameters of each model update with it. More specifically, we use a Top- $k$ indicator defined as follows to identify the $k$ most important parameters that have the largest absolute values in a vector.", + "bbox": [ + 91, + 121, + 483, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 1 (Top- $k$ Indicator $\\mathrm{Top_k}(\\cdot)$ ). For a vector $x\\in \\mathbb{R}^d$ and a masking parameter $k$ , where $1\\leq k\\leq d$ , the Top- $k$ indicator $\\mathrm{Top_k}(\\cdot)$ : $\\mathbb{R}^d\\to \\mathbb{R}^d$ is defined as $[\\mathrm{Top_k}(x)]_j = 1$ if $[x]_j\\in \\xi$ and $[\\mathrm{Top_k}(x)]_j = 0$ otherwise, where $\\xi = \\{|x_{\\pi (1)}|,|x_{\\pi (2)}|,\\dots ,|x_{\\pi (k)}|\\}$ , here $\\pi$ is a permutation of $[d]$ such that $|x_{\\pi (i)}|\\geq |x_{\\pi (i + 1)}|$ for all $1\\leq i < d$ .", + "bbox": [ + 89, + 401, + 483, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Top- $k$ indicator $\\mathrm{Top_k}(\\cdot)$ takes each local model update as input and outputs a mask vector in which each element is either 1 or 0 with the same size as the input. To quantify the alignment in sign distributions of each local model update and the principle sign, we define the Sign Alignment Ratio (SAR) as follows.", + "bbox": [ + 89, + 500, + 483, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 2 (Sign Alignment Ratio). For vectors $x \\in \\mathbb{R}^d$ and $y \\in \\mathbb{R}^d$ , the sign alignment ratio $\\rho$ of $x$ to $y$ is defined as $\\rho := 1 - \\| \\operatorname{sgn}(x) - \\operatorname{sgn}(y) \\|_0 / d$ where $\\| \\cdot \\|_0$ is $L_0$ -norm.", + "bbox": [ + 89, + 599, + 483, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\rho \\in [0,1]$ and a larger $\\rho$ indicate a higher degree of alignment between the signs of $x$ and $y$ . Combining $\\mathrm{Top_k}(\\cdot)$ and SAR, we have the MPSA value $\\rho_{i}$ for local update $\\Delta_i^t$ formulated as follows:", + "bbox": [ + 89, + 652, + 483, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\rho_ {i} := 1 - \\left\\| \\left(\\operatorname {s g n} \\left(\\Delta_ {i} ^ {t}\\right) - p\\right) \\odot \\operatorname {T o p} _ {k} \\left(\\Delta_ {i} ^ {t}\\right) \\right\\| _ {0} / k, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 722, + 482, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\odot$ is the Hadamard product, $\\mathrm{sgn}(\\Delta_i^t) - p$ computes a sign difference vector, capturing the difference between the sign of $\\Delta_i^t$ and the principal reference sign $p$ . Since MPSA checking focuses on the important parameters, this difference vector is element-wise multiplied with the Top- $k$ mask derived from $\\Delta_i^t$ , effectively setting unimportant coordinates to zero. The $L_0$ -norm is then applied to count the not-aligned elements and with the masking parameter $k$ to ultimately determine the SAR. MPSA checking effectively reveals malicious local updates by combining both", + "bbox": [ + 89, + 750, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "magnitude and directional information from model updates, allowing for clear differentiation between malicious and benign updates. AlignIns calculates the MPSA value for each update with the principal sign iteratively (line 3-4) and forward them to the following anomaly detection process.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3) Efficient anomaly detection with MZ_score: W apply robust filtering to remove updates with abnormal TDA and MPSA values. Specifically, we use the robust standardization metric named the Median-based Z-score (MZ_score) [50, 51], detailed in Definition 3, which is a variant of the traditional Z-score standardization metric.", + "bbox": [ + 511, + 167, + 906, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 3 (MZ_score). For a set of values $X \\coloneqq \\{x_1, \\ldots, x_n\\}$ with median $\\operatorname{med}(X)$ and standard deviation $\\sigma$ , the MZ_score $\\lambda_i$ of any $x_i \\in X$ is defined as", + "bbox": [ + 511, + 270, + 906, + 316 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {i} := (x _ {i} - \\operatorname {m e d} (X)) / \\sigma . \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 329, + 903, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "MZ_score calculates the number of standard deviations an element is from the median, which may be either positive or negative. In AlignIns, the MZ_score for TDA and MPSA values are computed for each local update (line 6-7). Those with high absolute MZ_score (i.e., outliers) are excluded using two predetermined filtering radii: $\\lambda_{c}$ for TDA and $\\lambda_{s}$ for MPSA (line 8-9). The use of the MZ_score allows for the adaptation to the varying range of TDA and MPSA values during training, requiring only minimal hyper-parameters. Additionally, by configuring $\\lambda_{c}$ and $\\lambda_{s}$ , we can manage the trade-off between the robustness and main task accuracy of AlignIns. For example, when robustness is the primary concern in the FL, choosing small $\\lambda_{c}$ and $\\lambda_{s}$ values is essential to attain the highest robustness.", + "bbox": [ + 511, + 359, + 906, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Post-filtering model clipping. After filtering, the remaining clients, considered benign, are included in the set $S$ (line 9) and contribute to the model averaging process. However, since our filtering primarily focuses on the direction of model updates (although MPSA does consider magnitude when using the Top- $k$ indicator), there is a risk that it might overlook updates with large magnitudes, such as those updates generated by Scaling attack [4]. To this end, AlignIns re-scales model updates in $S$ by using the median of the $L_{2}$ -norms of these updates as a clipping threshold and aggregates the clipped model updates as the global model update $\\tilde{\\Delta}$ (line 12-13). It is worth noting that performing clipping before filtering does not affect the filtering results. However, clipping after filtering enhances robustness, as the clipping threshold is more likely determined by benign updates. We discuss the computational cost of AlignIns and compare it with other baselines in Appendix Section 12.", + "bbox": [ + 511, + 571, + 908, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Robustness and Propagation Error Analysis", + "text_level": 1, + "bbox": [ + 511, + 844, + 906, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we conduct a theoretical analysis of the robustness of AlignIns, as well as its propagation error in FL.", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20657", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Before presenting our theoretical results, we make the following assumptions. Note that Assumption 1-2 are commonly used in the theoretical analysis of distributed learning systems [18, 34, 49]. Assumption 3 states a standard measure of inter-client heterogeneity in FL [2, 8, 21]. This heterogeneity complicates the problem of FL with backdoor adversaries, as it may cause the server to confuse malicious updates with flawed model updates from benign clients holding outlier data points [2].", + "bbox": [ + 89, + 90, + 483, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assumption 1 ( $\\mu$ -smoothness [34]). Each local objective function $\\mathcal{L}_i$ for benign client $i \\in \\mathcal{B}$ is $\\mu$ -Lipschitz smooth with $\\mu > 0$ , i.e., for any $x, y \\in \\mathbb{R}^d$ , $\\|\\nabla \\mathcal{L}_i(x) - \\nabla \\mathcal{L}_i(y)\\| \\leq \\mu \\|x - y\\|$ , $\\forall i \\in \\mathcal{B}$ , which further gives: $\\mathcal{L}_i(x) - \\mathcal{L}_i(y) \\leq \\nabla \\mathcal{L}_i(x)^T(y - x) + (\\mu/2)\\|x - y\\|^2$ , $\\forall i \\in \\mathcal{B}$ .", + "bbox": [ + 88, + 237, + 483, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assumption 2 (Unbiased gradient and bounded variance). The stochastic gradient at each benign client is an unbiased estimator of the local gradient, i.e., $\\mathbb{E}[g_i(x)] = \\nabla \\mathcal{L}_i(x)$ and has bounded variance, i.e., for any $x\\in \\mathbb{R}^d$ $\\mathbb{E}\\left\\| g_i(x) - \\nabla \\mathcal{L}_i(x)\\right\\| ^2\\leq \\nu_i^2,\\forall i\\in \\mathcal{B},$ where the expectation is over the local mini-batches. We also denote $\\bar{\\nu}\\coloneqq (1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\nu_i^2$ for convenience.", + "bbox": [ + 89, + 324, + 483, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assumption 3 (Bounded heterogeneity). There exist a real value $\\bar{\\zeta}$ such that for any $x\\in \\mathbb{R}^d$ $(1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\| \\nabla \\mathcal{L}_i(x) - \\nabla \\mathcal{L}_{\\mathcal{B}}(x)\\| ^2\\leq \\bar{\\zeta}$ , where the $\\nabla \\mathcal{L}_{\\mathcal{B}}(x)\\coloneqq (1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\mathcal{L}_i(x)$ .", + "bbox": [ + 89, + 441, + 483, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that these assumptions apply to benign clients only since malicious clients do not need to follow the prescribed local training protocol of FL.", + "bbox": [ + 89, + 513, + 483, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Robustness Analysis of AlignIns", + "text_level": 1, + "bbox": [ + 89, + 568, + 372, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To theoretically evaluate the efficacy of a filtering-based defense method like AlignIns, we introduce the concept of $\\kappa$ -robust filtering [50] as defined in Definition 4. Note that Definition 4 is similar to $(f,\\kappa)$ -robustness defined in [2, 3], $(\\delta_{\\max},c)$ -ARAgg defined in [13, 21, 31], and $(f,\\lambda)$ -resilient averaging defined in [10]. Our robustness definition adopts a constant upper bound and focuses on quantifying the distance between the output of a filtering-based defense method and the average of all benign updates, which represents the optimal output of such a rule.", + "bbox": [ + 89, + 590, + 483, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Definition 4 ( $\\kappa$ -robust filtering [50]). A filtering-based aggregation rule $F \\colon \\mathbb{R}^{d \\times n} \\to \\mathbb{R}^d$ is called $\\kappa$ -robust if for any vectors $\\{x_1, \\ldots, x_n\\} \\in \\mathbb{R}^d$ and a benign set $\\mathcal{B} \\subseteq [n]$ of size $n - m$ , the output $\\hat{x} \\coloneqq F(x_1, \\ldots, x_n)$ satisfies $\\| \\hat{x} - \\bar{x}_{\\mathcal{B}} \\|^2 \\leq \\kappa$ , where $\\bar{x}_{\\mathcal{B}} \\coloneqq (1 / |\\mathcal{B}|) \\sum_{i \\in \\mathcal{B}} x_i$ , and $\\kappa \\geq 0$ refers to the robustness coefficient of $F$ .", + "bbox": [ + 89, + 752, + 483, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark 1. The $\\kappa$ -robust filtering guarantees that the error of a filtering-based aggregation rule in estimating the average of the benign inputs is upper-bounded by a constant $\\kappa$ .", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This measure provides a quantitative way to assess the robustness of the filtering-based aggregation rule. A smaller $\\kappa$ indicates a smaller discrepancy between the empirical output and the optimal output of $F$ . If $F$ identifies and removes all malicious inputs and keeps all benign inputs, we have $\\kappa = 0$ , achieving the highest level of robustness.", + "bbox": [ + 511, + 90, + 905, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on Definition 4, we prove that the proposed AlignIns, when applied to $n$ input models, of which $m$ are malicious, satisfies $\\kappa$ -robust filtering with $\\kappa = O(1 + m / (n - 2m))$ , as stated in Lemma 1.", + "bbox": [ + 511, + 191, + 905, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lemma 1 ( $\\kappa$ -robustness of AlignIns). Under Assumption 2-3, assume $n > 1$ , $0 \\leq m < n / (3 + \\epsilon)$ with a positive constant $\\epsilon$ , AlignIns satisfies $\\kappa$ -robust filtering with", + "bbox": [ + 511, + 262, + 905, + 309 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\kappa = \\left(1 + m / \\left(n - 2 m\\right)\\right) \\left(\\left(2 / \\epsilon + 1\\right) \\left(2 \\bar {\\nu} + \\bar {\\zeta}\\right) + 8 c ^ {2}\\right) \\\\ = O \\left(1 + m / (n - 2 m)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 318, + 883, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "if the local learning rate satisfies $\\eta \\leq 1 / 2\\tau$ and there exist two sufficiently large filtering radii such that $|\\mathcal{S}|\\geq n - 2m$ . Here, $\\bar{\\nu}$ and $\\zeta$ represent the gradient variance and local divergence, respectively; $c$ is the clipping threshold.", + "bbox": [ + 511, + 366, + 905, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proof. The proof is given in Appendix Section 13.2.", + "bbox": [ + 511, + 436, + 861, + 453 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/93a7b4bc155178e2c296c7ed12823c6a8995c81b3dbc88933aa73046c9a4a5f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 888, + 436, + 905, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark 2. The condition on $S$ highlights the importance of selecting appropriate filtering radii. These radii cannot be zero or too small; otherwise, only the median or a few model updates will be averaged to update the global model. This can lead to a performance drop due to the lack of model updates. Moreover, the model clipping threshold $c$ can effectively control the magnitude of potential malicious updates in the selection set, thus preventing $\\kappa$ from exploding due to updates with large magnitudes. Indeed, in the literature, model clipping has demonstrated its effectiveness in mitigating the impact of malicious model updates [39, 49, 53]. In addition, the result also shows the importance of reducing the gradient variance of stochastic gradient and local heterogeneity to enhance robustness performance. Our work is orthogonal to existing variance or divergence reduction methods [13, 30] and can be combined with them to further improve the robustness. We argue that AlignIns enjoys comparable robustness with several classical defense methods, for example, non-filtering-based method RFA [40] ( $O(1 + m / (n - 2m))^2$ ), and filtering-based method Krum [6] ( $O(1 + m / (n - 2m))^1$ ).", + "bbox": [ + 511, + 462, + 906, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Propagation Error of AlignIns in FL", + "text_level": 1, + "bbox": [ + 511, + 789, + 831, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the $\\kappa$ -robustness of AlignIns, we analyze its propagation error during training. Specifically, let $\\theta$ denote the", + "bbox": [ + 511, + 811, + 905, + 842 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1Results of RFA and Krum are taken from [2]. Note that the definition of $\\kappa$ in [2] is different from ours, but the difference part can be reduced to a constant bound. Therefore, we can safely incorporate these results into our discussion without losing generality.", + "bbox": [ + 511, + 849, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20658", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "model trained with AlignIns under backdoor attacks, where $m$ of the $n$ clients are malicious, and let $\\theta^{*}$ denote a model trained exclusively with benign clients using FedAvg. Starting from the same initial model $\\theta^0$ , we aim to measure the difference between these two models after $T$ rounds of training, defined as $\\| \\theta^T - \\theta^{T,*} \\|$ , referred to as the propagation error [39]. Let $\\theta^{t, + }$ represent the output of AlignIns at the $t$ -th round. If the highest level of robustness is not achieved at round $t$ , the error $\\| \\theta^t - \\theta^{t, + } \\|$ will propagate to the next round, resulting in a shifted starting point for local SGD at round $t + 1$ . This discrepancy will gradually widen the gap between $\\theta$ and $\\theta^{*}$ . Our analysis captures this robustness error at each round and examines its cumulative effect after $T$ rounds. In Lemma 2, we show that, assuming Assumption 1-3 hold, the propagation error of AlignIns remains bounded.", + "bbox": [ + 89, + 90, + 483, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Lemma 2 (Bounded Propagation Error). Let Assumption 1-3 hold. If the local learning rate $\\eta \\leq 1 / 2\\tau$ , the propagation error of AlignIns is bounded as", + "bbox": [ + 88, + 340, + 482, + 387 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| \\theta^ {T} - \\theta^ {T, *} \\right\\| \\leq \\phi (T) (2 + 3 \\mu^ {2}) ^ {\\phi (T)} (\\kappa + 2 \\bar {\\nu}),\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 393, + 437, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "under backdoor attacks where $m$ out of $n$ clients are malicious. Here, $\\kappa$ is given in Lemma 1, $\\phi(T) = \\sum_{t=1}^{T} (\\alpha^t)^2$ is the cumulative global learning rate, and $\\alpha^t$ is a global learning rate scheduler, possibly static.", + "bbox": [ + 89, + 421, + 483, + 481 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Proof. The detailed proof is in Appendix Section 13.3. $\\square$", + "bbox": [ + 89, + 489, + 482, + 506 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark 3. When $T \\to \\infty$ , $\\phi(T)$ converges to a constant for learning rate schedulers like exponential decay, which implies a constant bounded on propagation error. The result shows that besides the robustness error bounded by $\\kappa$ , the error of local gradient estimation, which is bounded by $\\bar{\\nu}$ , in local SGD also propagates during the training, increasing the overall propagation error. This is because at any round $t$ , if the benign starting point for local training is the same, i.e., $\\theta^t = \\theta^{t,*}$ , then the local gradients/model updates on $\\theta^t$ and $\\theta^{t,*}$ will be identical for benign clients. Therefore, the gap between the updated global models $\\theta^{t+1}$ and $\\theta^{t+1,*}$ solely depends on the robustness error (i.e., the effectiveness of AlignIns in filtering out malicious updates). However, if $\\theta^t \\neq \\theta^{t,*}$ , which means $\\theta^t$ is not benign and has been poisoned in previous rounds, the local gradients/model updates on $\\theta^t$ and $\\theta^{t,*}$ will differ for benign clients, resulting in an error bounded by the gradient variance, even if AlignIns successfully filters out all malicious updates. Hence, to further reduce the propagation error, AlignIns can be combined with variance-reduction methods like [13, 30], which is orthogonal to AlignIns.", + "bbox": [ + 89, + 515, + 485, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Settings", + "text_level": 1, + "bbox": [ + 89, + 844, + 302, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets and System Settings: In our experiments, we primarily conduct evaluation on CIFAR-10 [24] and CIFAR-", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "100 [24] datasets. Additionally, we present the superior performance of AlignIns on other benchmark datasets (MNIST [25], FMNIST [47], Sentiment140 [12], and TinyImageNet) in Appendix Section 10.5-10.6. We simulate a cross-silo FL with 20 clients for all datasets. Additionally, we also present the superior performance of AlignIns on a cross-device FL system with 100 clients and client sampling. We consider both IID and non-IID settings. For IID settings, we distribute the training data evenly to clients. For non-IID settings, we follow [17, 19, 20] to use Dirichlet distribution $\\text{Dir}(\\beta)$ to skew the local data distribution with a default non-IID degree $\\beta = 0.5$ .", + "bbox": [ + 511, + 90, + 903, + 271 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Learning Settings: We use SGD as the local solver, with the initial learning rates set as $\\alpha = 1.0$ and $\\eta = 0.1$ , and the local training epoch is set as 2. The training round is set as $T = 100$ for CIFAR-100 and $T = 150$ for CIFAR-10. For AlignIns, the default filtering radii are set as $\\lambda_{c} = 1.0$ and $\\lambda_{s} = 1.0$ . We provide the study of the impact of filtering radii in Appendix Section 11. The default masking parameter is set as $k = 0.3 \\times d$ so that the Top-30% of model parameters are used for the MPSA checking.", + "bbox": [ + 511, + 273, + 906, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluated Attack Methods: We consider 5 SOTA backdoor attacks, including Badnet [14], DBA [48], Scaling [4], PGD [46], and Neurotoxin [54]. We provide the detailed attack model and settings for attack methods in Appendix Section 8.1-8.2. We present the results of AlignIns under the strong trigger-optimization attack [9] in Appendix Section 10.2. Moreover, we study the potential adaptive attacks tailored to AlignIns and untargeted attacks [49] in Appendix Section 10.3-10.4, although these are beyond the scope of this work. To achieve effective backdoors (achieving a BA over $60\\%$ [22]), malicious clients poison $r = 50\\%$ of their local data, where $r$ is the data poisoning ratio. The attack ratio is set to $20\\%$ by default, which means $20\\%$ of the clients in the system are malicious. Experiments of AlignIns on defending backdoor attacks with various attack ratios are given in Appendix Section 10.7.", + "bbox": [ + 511, + 412, + 905, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluated Defense Methods: We present the detailed defense model in Appendix Section 9. We comprehensively compare AlignIns with the non-robust baseline FedAvg and six existing SOTA defense methods, including RLR [38], RFA [40], Multi-Krum (MKrum) [6], Foolsgold [11], Multi-Metric (MM) [19], and Lockdown [20]. Additionally, we compare our approach with an ideally perfect filtering-based robust aggregation, FedAvg*, which is assumed to perfectly identify and remove all malicious updates and average all the benign updates to update the global model.", + "bbox": [ + 511, + 656, + 905, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics: We use three metrics to evaluate the performance of defense methods, including main task accuracy (MA), which measures the percentage of clean test samples that are accurately classified to their ground truth labels by the global model; backdoor attack accuracy (BA), which measures the percentage of triggered", + "bbox": [ + 511, + 810, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20659", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3c755cdd8ce67f1c2a7cc9751371c1d4d46ea574f4b6c1666c2fa569d2c4225a.jpg", + "table_caption": [ + "Table 1. The clean MA, BA, and RA results of baselines and AlignIns on IID CIFAR-10 and CIFAR-100 datasets. Results are shown in %." + ], + "table_footnote": [], + "table_body": "
    Dataset (Model)MethodsClean MA↑BadnetDBANeurotoxinAvg. BA↓Avg. RA↑
    BA↓RA↑BA↓RA↑BA↓RA↑
    r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5
    CIFAR-10 (ResNet9 [16])FedAvg89.4751.5667.6145.7931.2456.2170.4240.6227.9244.8979.4050.4119.6061.6835.93
    FedAvg*89.472.062.0685.6085.602.062.0685.6085.602.062.0685.6085.602.0685.60
    RLR79.162.322.0076.7273.333.013.0477.0977.133.123.8773.9873.292.8935.93
    RFA87.7370.6790.2427.749.2647.6766.9747.2930.1481.2796.1317.113.6975.4922.54
    MKrum87.0281.1097.4718.112.512.174.3383.8979.1065.2889.1831.8110.0156.5937.57
    Foolsgold89.4969.1468.8429.6430.1051.1860.7344.8336.082.912.8285.2784.7642.6051.78
    MM89.1541.1993.8853.886.0152.2451.3043.5445.0843.9283.9251.1215.1161.0835.79
    Lockdown88.566.3110.8281.8879.5011.636.0378.8275.773.403.2782.7383.146.9180.31
    AlignIns88.641.912.2186.0385.572.132.1485.7785.882.662.2085.4685.312.2185.67
    CIFAR-100 (VGG9 [41])FedAvg64.2999.2099.540.680.3599.2599.360.640.5494.4193.364.365.2897.521.98
    FedAvg*64.290.620.6253.0353.030.620.6253.0353.030.620.6253.0353.030.6253.03
    RLR44.3496.5799.851.810.1224.4194.0824.973.220.040.0029.0729.7352.4914.82
    RFA53.924.321.4537.6039.882.150.7839.7341.5199.7489.590.216.5933.0127.59
    MKrum51.281.331.5438.1338.491.361.5437.8537.9199.8299.870.120.1036.2125.49
    Foolsgold64.1399.0299.300.830.5799.1599.390.740.5121.796.2142.0646.4070.8115.19
    MM63.2699.5199.870.370.1199.5399.700.350.1998.4898.971.320.8399.340.53
    Lockdown62.8855.2124.1428.4543.0634.3749.0234.0627.930.850.6742.6647.0427.3837.20
    AlignIns63.450.790.7150.4551.530.450.5750.8152.080.490.5351.1150.660.5951.11
    ", + "bbox": [ + 94, + 114, + 901, + 428 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "samples that are misclassified to the target label by the global model; and robustness accuracy (RA), which measures the percentage of triggered samples that are accurately classified to their ground-truth labels by the global model, despite the presence of the trigger. A good defense method should achieve high MA and RA and low BA.", + "bbox": [ + 89, + 440, + 483, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Experimental Results", + "text_level": 1, + "bbox": [ + 89, + 542, + 294, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Main results in IID setting. In Table 1, we report the performance of various defense methods under no attack (denoted by \"Clean\"), Badnet, DBA, and Neurotoxin attacks for IID CIFAR-10 and CIFAR-100. The best results are highlighted in bold font, and the second best results are underlined. Overall, AlignIns demonstrates superior performance compared with other baselines as it achieves the best average BA and RA over three attack methods. Specifically, for CIFAR-10, while RLR offers a satisfactory degree of robustness (an average BA of $2.89\\%$ ), it suffers from a notable decline in RA, with an average reduction of $49.74\\%$ in comparison to AlignIns. This drop results from RLR's strategy of flipping the global learning rate for parameters in the aggregated model update that are inconsistent with the majority's sign, consequently resulting in the loss of benign local parameters. AlignIns, however, demonstrates outstanding performance with consistently low BA and high RA, ranking first or second among its counterparts. Notably, compared to the second-best results, AlignIns achieves an average improvement of $+0.68\\%$ in BA and $+5.36\\%$ in RA. Similarly, superior results are observed in CIFAR-100 experiments, where AlignIns significantly out", + "bbox": [ + 88, + 568, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/64eb563d0e978f803f7dad56c20c2c5767d4f26b4dda5b7c04fce5175db15bf0.jpg", + "image_caption": [ + "Figure 1. RA of AlignIns under various non-IID degrees, compared with Lockdown, RFA, and RLR under Neurotoxin." + ], + "image_footnote": [], + "bbox": [ + 537, + 440, + 723, + 571 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7b3d920a229ba2f5069fc312ff3945dc5092b8b6ae096bf52f644abbde4a492d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 440, + 880, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "performs other methods in both BA and RA. These results underscore AlignIns' effectiveness as a promising defense method for protecting FL from various backdoor attacks, significantly enhancing the trustworthiness of FL systems.", + "bbox": [ + 511, + 627, + 906, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness under various Non-IID degrees. We examine the defense performance of AlignIns across various degrees of non-IIDness, a factor that significantly complicates backdoor defense. Figure 1 presents the RA of AlignIns under different non-IID conditions on the CIFAR-10 dataset, compared with Lockdown, RFA, and RLR. The experiments were conducted using the Neurotoxin attack, with both a default attack ratio of $20\\%$ and a higher attack ratio of $30\\%$ . The Dirichlet parameter $\\beta$ varies from 0.1 to 1.0, where a smaller $\\beta$ suggests a more intense non-IIDness. We observe that only AlignIns consistently attains robustness against strong Neurotoxin attacks with a varying $\\beta$ . Specifically, as $\\beta$ increases, the RA of AlignIns, Lockdown, and RLR increases correspondingly. However,", + "bbox": [ + 511, + 689, + 908, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20660", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c140dbdbf549daae48b1fae9ef2e2485b009cf26d7225f5ea41da159fae640a8.jpg", + "table_caption": [ + "Table 2. Performance of different methods in cross-device FL settings on IID and non-IID CIFAR-10 datasets under Badnet attack." + ], + "table_footnote": [], + "table_body": "
    MethodCIFAR-10 (IID)CIFAR-10 (Non-IID)Avg. RA↑
    MA↑BA↓RA↑MA↑BA↓RA↑
    Foolsgold82.9999.990.0167.9799.990.000.01
    Lockdown83.5299.990.0073.9199.920.060.00
    RLR56.814.6755.3841.5614.1238.1746.78
    AlignIns85.010.9282.7479.511.9075.8179.28
    ", + "bbox": [ + 106, + 128, + 467, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "AlignIns outperforms them with a consistently higher RA. When the attack ratio rises to $30\\%$ , RLR, RFA, and Lockdown fail to provide satisfactory robustness. However, our method AlignIns still demonstrates its robustness under various non-IIDness, even in an extremely non-IID case when $\\beta = 0.1$ . AlignIns is designed to examine the alignment of model updates on important parameters only, hence, it mitigates the challenge of identifying malicious model updates in non-IID settings where updates are heterogeneous, thereby achieving superior performance in even extreme non-IID settings compared with existing methods. We also provide more comprehensive results of AlignIns and other baselines on non-IID datasets in Appendix Section 10.1.", + "bbox": [ + 89, + 224, + 483, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of AlignIns in cross-device FL with client sampling. While most of our experiments focus on the cross-silo FL setting, evaluating the cross-device FL scenario is also essential given the large number of clients involved. For this purpose, we simulate a cross-device FL environment with 100 clients, where the server randomly selects 20 clients per round for training. We conduct experiments on IID and non-IID CIFAR-10 cases using Foolsgold, Lockdown, RLR, and AlignIns and summarize the MA, BA, and RA results in Table 2. The results show that both Foolsgold and Lockdown completely lose their effectiveness in both cases, achieving an average RA of nearly $0.00\\%$ . RLR achieves a moderate level of backdoor robustness but at the cost of main task accuracy, with an average MA of only $49.19\\%$ . In contrast, AlignIns performs robustly in the cross-device FL setting, achieving a significantly lower BA in both IID $(0.92\\%)$ and non-IID $(1.90\\%)$ cases compared with other methods. Furthermore, AlignIns achieves an average RA of $79.28\\%$ . These results highlight AlignIns's ability to maintain both accuracy and robustness in challenging cross-device FL scenarios, underscoring its adaptability and effectiveness in real-world applications.", + "bbox": [ + 91, + 426, + 483, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation study of AlignIns. As AlignIns consists of two alignment components (TDA and MPSA) to improve backdoor robustness, we conduct a detailed ablation study to investigate how each component functions. Experimental results on IID and non-IID CIFAR-10 datasets under Badnet attack are summarized in Table 3. (i) Component ablation. We observe that using MPSA or TDA alone in IID scenarios only slightly reduces robustness compared to AlignIns, as benign updates follow consistent patterns that", + "bbox": [ + 89, + 763, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b93243537de499b11ab0f0a8c2be8055273941d2c2b6deef994cb3b29a121ec7.jpg", + "table_caption": [ + "Table 3. Performance of different components in AlignIns." + ], + "table_footnote": [], + "table_body": "
    ConfigurationCIFAR-10 (IID)CIFAR-10 (non-IID)Avg. RA↑
    MA↑BA↓RA↑MA↑BA↓RA↑
    MPSA(30%)88.552.8885.0280.6594.075.7945.41
    TDA88.563.8283.8883.8677.5821.3152.60
    MPSA(70%)+TDA88.142.1885.7783.8461.8331.8658.82
    MPSA(50%)+TDA88.052.2185.4684.1277.9319.9652.71
    MPSA(30%)+TDA88.142.0485.8283.6547.0445.3065.56
    AlignIns88.052.4485.2782.881.7081.3283.30
    AlignIns+88.482.1485.7483.311.1182.1383.94
    ", + "bbox": [ + 517, + 114, + 901, + 231 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "enable effective detection by a single metric. In non-IID settings, however, where local updates diverge, neither MPSA nor TDA alone provides sufficient robustness. When combined, MPSA and TDA improve BA and RA from $94.07\\%$ and $5.79\\%$ to $47.04\\%$ and $45.30\\%$ , respectively, showing their complementary strengths. AlignIns further enhances robustness by integrating MPSA, TDA, and post-filtering model clipping, which normalizes benign update magnitudes and improves malicious update detection, yielding the highest average RA. (ii) Masking parameter $k$ ablation. We try to involve more non-essential parameters in the MPSA checking by using the Top- $50\\% / 70\\%$ of parameters to calculate MPSA values. By doing so, the effectiveness of malicious identification is reduced. In contrast, when using the Top- $30\\%$ of parameters, compared to the Top- $50\\%$ case, BA and RA are improved by $+30.89\\%$ and $+25.34\\%$ , respectively. This demonstrates the effectiveness of focusing important parameters when calculating MPSA in improving the filtering accuracy, especially in non-IID cases. (iii) Variance reduction method further enhances robustness. Our theoretical results reveal the impact of variance reduction techniques on improving the robustness of AlignIns and reducing the propagation error of AlignIns in FL, we additionally test a variant of AlignIns named \"AlignIns+\", in which local SGD with momentum is used to reduce the local gradient variance with momentum coefficient 0.1. AlignIns+ achieves a slightly better performance than AlignIns, verifying our theoretical results.", + "bbox": [ + 511, + 243, + 906, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 676, + 633, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce a novel method AlignIns to defend against backdoor attacks in FL. AlignIns examines each model update's direction at different granularity levels, thus effectively identifying stealthy malicious model updates and filtering them out to avoid them participating in aggregation in FL to enhance robustness. We provide a theoretical analysis of AlignIns' robustness and its impact on propagation errors in FL. Extensive experiments demonstrate the effectiveness of AlignIns, with results showing that it outperforms SOTA defense methods against various advanced attacks.", + "bbox": [ + 511, + 703, + 906, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work was supported by the Nevada System of Higher Education under grant NSHE-24-37.", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20661", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Manaar Alam, Esha Sarkar, and Michail Maniatakos. Perdoor: Persistent non-uniform backdoors in federated learning using adversarial perturbations. arXiv preprint arXiv:2205.13523, 2022. 2", + "[2] Youssef Allouah, Sadegh Farhadkhani, Rachid Guerraoui, Nirupam Gupta, Rafael Pinot, and John Stephan. Fixing by mixing: A recipe for optimal byzantine ml under heterogeneity. In International Conference on Artificial Intelligence and Statistics, pages 1232-1300. 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PMLR, 2022. 1, 2, 6, 12", + "bbox": [ + 91, + 90, + 482, + 172 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20664", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/13985764-96b8-48db-82c6-84b1d3a23329_model.json b/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/13985764-96b8-48db-82c6-84b1d3a23329_model.json new file mode 100644 index 0000000000000000000000000000000000000000..524338e00b8fd8c1c70da3bd1c00557060cf88da --- /dev/null +++ b/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/13985764-96b8-48db-82c6-84b1d3a23329_model.json @@ -0,0 +1,1960 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.118, + 0.13, + 0.882, + 0.178 + ], + "angle": 0, + "content": "Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection" + }, + { + "type": "text", + "bbox": [ + 0.311, + 0.204, + 0.686, + 0.259 + ], + "angle": 0, + "content": "Jiahao Xu Zikai Zhang Rui Hu University of Nevada, Reno {jiahaox,zikaiz,ruihu}@unr.edu" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.325, + 0.486, + 0.673 + ], + "angle": 0, + "content": "The distributed nature of training makes Federated Learning (FL) vulnerable to backdoor attacks, where malicious model updates aim to compromise the global model's performance on specific tasks. Existing defense methods show limited efficacy as they overlook the inconsistency between benign and malicious model updates regarding both general and fine-grained directions. To fill this gap, we introduce AlignIns, a novel defense method designed to safeguard FL systems against backdoor attacks. AlignIns looks into the direction of each model update through a direction alignment inspection process. Specifically, it examines the alignment of model updates with the overall update direction and analyzes the distribution of the signs of their significant parameters, comparing them with the principle sign across all model updates. Model updates that exhibit an unusual degree of alignment are considered malicious and thus be filtered out. We provide the theoretical analysis of the robustness of AlignIns and its propagation error in FL. Our empirical results on both independent and identically distributed (IID) and non-IID datasets demonstrate that AlignIns achieves higher robustness compared to the state-of-the-art defense methods. The code is available at https://github.com/JiaiahaoXU/AlignIns." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.708, + 0.222, + 0.723 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Unlike traditional centralized training methods, which require gathering and processing all data at a central location such as a server, Federated Learning (FL) [32], as a decentralized training paradigm, allows a global model to learn from data distributed across various local clients, thereby achieving the goal of privacy-preserving. During training, the server distributes the global model to local clients, and each client trains the received global model using its local dataset, and then submits its local model update to the server for global model refinement. FL has been applied in various fields, including healthcare[35], finance [28], and remote" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.293, + 0.845, + 0.308 + ], + "angle": 0, + "content": "sensing [27], where local data privacy is essential." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.31, + 0.907, + 0.612 + ], + "angle": 0, + "content": "Although promising, the distributed nature of FL systems makes them vulnerable to a range of advanced poisoning attacks [15, 26, 45]. This vulnerability primarily stems from the server's lack of close monitoring of the local data and the training algorithm on clients. Consequently, this drawback allows attackers to compromise the data of local clients or interfere with the training algorithm, enabling them to inject malicious local model updates that distort the performance of the global model. For example, backdoor attacks [4, 14, 46, 48, 54] have gained significant attention due to their stealthiness and practical effectiveness. In detail, backdoor attacks in FL seek to preserve the performance of the global model on clean inputs (i.e., the main task), while inducing the global model to make incorrect predictions on inputs that contain a certain predefined feature (i.e., the backdoor task). As backdoor attacks maintain the main task and the backdoor task simultaneously, the malicious local model updates are statistically similar to benign ones [36, 46] (poison-coupling effect [20]), making anomaly detection more challenging on the server side." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Existing defense methods (i.e., aggregation rule) usually aim to identify malicious model updates and filter them out to achieve better robustness by magnitude-based metrics extracted from local model updates (e.g., Manhattan distance [19, 22] and Euclidean distance [6, 15]). However, magnitude-based metrics are ineffective in distinguishing stealthy backdoor attacks where benign and malicious model updates are usually similar in magnitude. Additionally, when the global model tends to converge, the magnitude of each model update becomes very small, making effective malicious manipulation on magnitude negligible. To this end, some works employ Cosine similarity to check the pair-wise directional information of model updates [11, 36, 42]. However, pair-wise Cosine similarity between two model updates only captures their general directional similarity and overlooks fine-grained information (e.g., signs of parameters), resulting in limited robustness. In addition, in FL settings with non-IID data, the pair-wise Cosine similarity of model updates can be easily perturbed" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20654" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "by the naturally diverse benign model updates. Furthermore, there is a deficiency in theoretical analysis within the literature concerning the effects of data heterogeneity on defense methods deployed by the server in FL." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.153, + 0.483, + 0.483 + ], + "angle": 0, + "content": "In this work, we propose a novel defense method designed to defend against backdoor attacks in FL, named AlignIns (Direction Alignment Inspection), which examines local model updates for directional alignment at different granularity levels to identify malicious updates. Specifically, after receiving all model updates from clients, AlignIns evaluates each update by (1) inspecting temporal directional alignment with the global model of the latest round with Cosine similarity and (2) assessing more fine-grained sign alignment with the principal sign across all updates with a novel metric sign alignment ratio. Particularly, when calculating the sign alignment ratio, AlignIns focuses on the signs of important parameters in each update to accurately capture alignment information. Using these two directional metrics, AlignIns performs anomaly detection with the robust MZ_score which requires minimal hyperparameters to filter updates with unusual directional patterns out. Finally, AlignIns clips the remaining updates to mitigate the impact of updates with abnormally large magnitudes. We also provide a theoretical analysis of AlignIns' robustness and its propagation error in FL. The main contributions of this work are three folds:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.484, + 0.483, + 0.575 + ], + "angle": 0, + "content": "- We present a novel defense method, AlignIns, to defend against backdoor attacks in FL. To the best of our knowledge, AlignIns is the first defense method in FL that analyzes the directional patterns of local model updates at different levels of granularity. AlignIns is fully compatible with existing FL frameworks." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.575, + 0.483, + 0.65 + ], + "angle": 0, + "content": "- To the best of our knowledge, we provide the first theoretical robustness analysis for a filtering-based defense method against backdoor attacks under non-IID data in FL. Moreover, we prove that the propagation error of AlignIns is bounded during the training of FL." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.65, + 0.483, + 0.726 + ], + "angle": 0, + "content": "- We empirically evaluate the effectiveness of AlignIns through extensive experiments on both IID and non-IID datasets against various state-of-the-art (SOTA) backdoor attacks. Compared to existing SOTA defense methods, AlignIns exhibits superior robustness." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.484, + 0.483, + 0.726 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.74, + 0.384, + 0.758 + ], + "angle": 0, + "content": "2. Background and Related Works" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Federated Learning. In a typical FL system, a central server controls a set of \\( n \\) clients to train a global model \\( \\theta \\in \\mathbb{R}^d \\) collaboratively. The objective of FL is to solve the following optimization problem: \\( \\min_{\\theta}(1/n)\\sum_{i=1}^{n}\\mathcal{L}_i(\\theta;\\mathcal{D}_i) \\), where \\( \\mathcal{L}_i(\\cdot) \\) denotes the learning objective specific to client \\( i \\) and \\( \\mathcal{D}_i \\) denotes the local dataset for client \\( i \\). The commonly used method to solve this problem iteratively is FedAvg [33]. In detail, at round \\( t \\) of FedAvg, each client \\( i \\in [n] \\) downloads the current global model \\( \\theta^t \\), updates it" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "by optimizing its local objective, resulting in \\(\\theta_i^t\\), and transmits its model update \\(\\Delta_i^t = \\theta_i^t - \\theta^t\\) to the server. The server then refines the global model by averaging these updates as follows: \\(\\theta^{t + 1} = \\theta^t + (1 / n)\\sum_{i = 1}^n\\Delta_i^t\\). This process continues until the global model reaches convergence." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.17, + 0.905, + 0.395 + ], + "angle": 0, + "content": "Backdoor attacks in FL. Empirical evidence has shown that FL is vulnerable to backdoor attacks [4, 9, 14, 23, 37, 46, 48, 52, 54] due to its lack of access to local training data [4]. For instance, Projected Gradient Descent (PGD) attack [46] periodically projects the local model onto a small sphere centered around the global model from the previous training round, with a predefined radius. Distributed Backdoor Attack (DBA) [48] decomposes the centralized trigger into several smaller, distributed local triggers. Each poisoned client uses one of these local triggers, but during testing, the adversary injects the full trigger into the test samples. Recently, research has focused on trigger-optimization backdoor attacks [1, 9, 29, 37, 52], which aim to search optimized triggers to enhance the effectiveness and stealthiness." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.905, + 0.474 + ], + "angle": 0, + "content": "Defending against backdoor attacks in FL. Generally, based on how defense methods mitigate the impact of malicious updates, existing defense methods can be categorized into filtering-based methods [6, 7, 19, 22, 36, 42, 50, 51] and influence-reduction methods [11, 20, 38, 40, 41]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.476, + 0.905, + 0.703 + ], + "angle": 0, + "content": "1) influence-reduction methods aim to integrate all model updates but employ strategies to reduce the impact of malicious updates. For instance, \\( RFA \\) [40] is proposed to use the geometric median of local models as the aggregation result, under the assumption that malicious models significantly deviate from benign models. Foolsgold [11] assumes that the malicious updates are consistent with each other. It assigns aggregation weights to model updates based on the maximum Cosine similarity between the last layers of pairwise model updates. A higher Cosine similarity value indicates a higher probability that the updates are malicious, leading to smaller aggregation weights being assigned. The effectiveness of influence-reduction methods is inherently limited because they cannot eliminate the impact of malicious activity, leading to a significant risk of compromise." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.905, + 0.901 + ], + "angle": 0, + "content": "2) Filtering-based methods aim to detect and remove malicious local model updates before aggregation thus attempting to achieve the highest robustness. For example, Multi-Krum [6] selects the multiply reliable local model updates for aggregation by identifying the one with the smallest sum of squared Euclidean distances to all other updates. Multi-Metrics [19] explores the combination of Manhattan distance, Euclidean distance, and Cosine similarity for each update to collaboratively filter out outliers. However, due to the dual objectives of backdoor attacks—that is, maintaining accuracy on the main task while maximizing accuracy on the backdoor task—malicious updates must mimic benign model updates, important weights for the main task" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20655" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.103, + 0.096, + 0.257, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: AlignIns" + }, + { + "type": "algorithm", + "bbox": [ + 0.095, + 0.112, + 0.482, + 0.412 + ], + "angle": 0, + "content": "Input: Set of \\(n\\) local model updates \\(\\{\\Delta_i^t\\}_{i=1}^n\\) where \\(m\\) of them are malicious, global model \\(\\theta^t\\), TDA radius \\(\\lambda_c\\), MPSA radius \\(\\lambda_s\\), extraction parameter \\(k\\) \nOutput: Aggregated model update \\(\\widetilde{\\Delta}\\) \n1 Initialize benign set \\(S \\gets \\emptyset\\) \n2 \\(\\omega \\gets \\{\\mathrm{TDA}(\\Delta_i^t, \\theta)\\}_{i=1}^n\\) \\(\\triangleleft\\) by Equation (1) \n3 \\(p \\gets \\operatorname{sgn}(\\sum_{i=1}^n \\operatorname{sgn}(\\Delta_i^t))\\) \n4 \\(\\rho \\gets \\{\\mathrm{MPSA}(\\Delta_i^t, p, k)\\}_{i=1}^n\\) \\(\\triangleleft\\) by Equation (2) \n5 for \\(i \\in [n]\\) do \n6 \\(\\lambda_{i,c} \\gets \\mathrm{MZ\\_score}(\\omega_i, \\omega)\\) \\(\\triangleleft\\) by Equation (3) \n7 \\(\\lambda_{i,s} \\gets \\mathrm{MZ\\_score}(\\rho_i, \\rho)\\) \\(\\triangleleft\\) by Equation (3) \n8 if \\(|\\lambda_{i,c}| \\leq \\lambda_c\\) and \\(|\\lambda_{i,s}| \\leq \\lambda_s\\) then \n9 \\(\\mid S \\gets S \\cup \\{i\\}\\) \n10 end \n11 end \n12 \\(c \\gets \\operatorname{med}(\\{\\| \\Delta_i^t\\| \\}_{i \\in S})\\) \n13 \\(\\widetilde{\\Delta} \\gets (1 / |\\mathcal{S}|) \\sum_{i \\in S} (\\Delta_i^t \\cdot \\min\\{1, c / \\| \\Delta_i^t\\|\\})\\) \n14 return \\(\\widetilde{\\Delta}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.431, + 0.483, + 0.522 + ], + "angle": 0, + "content": "typically have large values and can dominate the magnitude of a model update. As a result, magnitude-based detection methods become ineffective against backdoor attacks. Additionally, methods that rely solely on Cosine similarity also show limited effectiveness since they capture general directional alignment and overlook finer-grained information." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.539, + 0.31, + 0.557 + ], + "angle": 0, + "content": "3. Our Solution: AlignIns" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.566, + 0.483, + 0.672 + ], + "angle": 0, + "content": "Our method, AlignIns, detailed in Algorithm 1, mitigates the impact of malicious updates through a two-step process. First, direction alignment inspection is applied to examine each local model update comprehensively in terms of direction. Second, post-filtering model clipping is used to further enhance the robustness of AlignIns on defending potential magnitude-based attack methods before final aggregation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.673, + 0.483, + 0.854 + ], + "angle": 0, + "content": "Direction alignment inspection. Existing defense methods against backdoor attacks in FL primarily focus on examining the magnitude (e.g., Manhattan distance and Euclidean distance) and the overall direction (e.g., Cosine similarity) of model updates. However, backdoor attacks are designed to maintain the main task accuracy, making the magnitude difference between malicious and benign updates nearly indistinguishable. Additionally, advanced attacks such as PGD [46] and Lie [5] attacks are specifically crafted to bypass magnitude-based defenses. Therefore, AlignIns focuses on direction-based analysis to identify suspect updates, using two processes described below." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "1) Temporal direction alignment checking: Since malicious clients need to maintain both the main task and the backdoor task, the optimization direction of a malicious" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.198 + ], + "angle": 0, + "content": "local model tends to deviate from that of benign models. AlignIns leverages this deviation and performs a Temporal Direction Alignment (TDA) checking, which calculates the Cosine similarity between a local update and the latest global model (line 2 in Algorithm 1) to assess the general alignment level of each local update. Formally, the TDA value \\(\\omega_{i}\\) of a local model update \\(\\Delta_i^t\\) is calculated as" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.208, + 0.905, + 0.226 + ], + "angle": 0, + "content": "\\[\n\\omega_ {i} := \\left\\langle \\Delta_ {i} ^ {t}, \\theta^ {t} \\right\\rangle / \\left(\\| \\Delta_ {i} ^ {t} \\| \\| \\theta^ {t} \\|\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.236, + 0.907, + 0.448 + ], + "angle": 0, + "content": "We use local model updates rather than local models because our goal is to measure how closely each client's updates align with the direction of the global model. Local model updates specifically capture these incremental adjustments. Notably, malicious clients tend to exhibit similar TDA values, which differ from those of benign clients, creating an opportunity for detection. It is important to note that while the magnitude of model updates typically decreases as the global model converges, the TDA value does not follow the same trend. Consequently, magnitude-based anomaly detection becomes progressively less effective throughout training due to the decreasing magnitude. In contrast, the variability in TDA values continues to be useful for identifying malicious behavior." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.908, + 0.903 + ], + "angle": 0, + "content": "2) Masked principal sign alignment checking: In backdoor attacks where the manipulations are stealthy, subtle malicious directional information can easily blend into the parameters of models with large magnitude, especially for models with large dimensions, which makes the TDA less useful under strong backdoor attacks since the TDA captures the overall directional information. Therefore, in addition to the TDA, we look into the signs of parameters to provide a finer-grained directional assessment of local model updates. The signs of a vector represent its coordinate-wise direction. In the context of backdoor attacks, the distributions of the signs of malicious model updates differ from those of benign updates. This is particularly significant when the model is close to convergence, at which point the magnitude of model updates becomes very small, making large manipulations on magnitudes impractical. Therefore, manipulation of the direction, or the signs of parameters, can emerge as a more significant and effective strategy. Several works also utilize the signs of models for enhancing backdoor robustness. For example, RLR [38] assigns an opposite global learning rate to a coordinate of the averaged model update if the signs on this coordinate do not consistently align with the majority across all updates. SignGuard [49] calculates the proportions of positive, zero, and negative signs for each model update as the input of a clustering algorithm to identify malicious model updates. However, these methods utilize the signs of all parameters in the model update, regardless of their significance. Consequently, the performance of sign-based metrics can be significantly impacted by those many unimportant parameters," + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20656" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.121 + ], + "angle": 0, + "content": "especially for large DNN models, leading to an inaccurate representation of the model update's direction." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.122, + 0.484, + 0.394 + ], + "angle": 0, + "content": "To this end, AlignIns utilizes a Masked Principle Sign Alignment (MPSA) checking to inspect the sign alignment degree between the important parameters of each local update and a well-designed principle sign of all local updates. Specifically, to construct the principle sign over local updates, for each coordinate of local updates, we take the majority of the signs across all model updates as the principal sign of this coordinate, which can be mathematically formulated as \\( p \\coloneqq \\operatorname{sgn}\\left(\\sum_{i=1}^{n} \\operatorname{sgn}\\left(\\Delta_i^t\\right)\\right) \\), where \\( p \\in \\mathbb{R}^d \\) represents the vector of principal signs and \\( \\operatorname{sgn}(\\cdot) \\) is the function to take the signs of a vector. Note that the principal sign represents sign-voting results for each coordinate, making it stand for the major direction/dynamic for each coordinate. With this principle sign over local updates, we inspect the alignment of the signs of important parameters of each model update with it. More specifically, we use a Top-\\( k \\) indicator defined as follows to identify the \\( k \\) most important parameters that have the largest absolute values in a vector." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.402, + 0.484, + 0.496 + ], + "angle": 0, + "content": "Definition 1 (Top-\\(k\\) Indicator \\(\\mathrm{Top_k}(\\cdot)\\)). For a vector \\(x\\in \\mathbb{R}^d\\) and a masking parameter \\(k\\), where \\(1\\leq k\\leq d\\), the Top-\\(k\\) indicator \\(\\mathrm{Top_k}(\\cdot)\\): \\(\\mathbb{R}^d\\to \\mathbb{R}^d\\) is defined as \\([\\mathrm{Top_k}(x)]_j = 1\\) if \\([x]_j\\in \\xi\\) and \\([\\mathrm{Top_k}(x)]_j = 0\\) otherwise, where \\(\\xi = \\{|x_{\\pi (1)}|,|x_{\\pi (2)}|,\\dots ,|x_{\\pi (k)}|\\}\\), here \\(\\pi\\) is a permutation of \\([d]\\) such that \\(|x_{\\pi (i)}|\\geq |x_{\\pi (i + 1)}|\\) for all \\(1\\leq i < d\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.501, + 0.484, + 0.593 + ], + "angle": 0, + "content": "The Top-\\(k\\) indicator \\(\\mathrm{Top_k}(\\cdot)\\) takes each local model update as input and outputs a mask vector in which each element is either 1 or 0 with the same size as the input. To quantify the alignment in sign distributions of each local model update and the principle sign, we define the Sign Alignment Ratio (SAR) as follows." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.6, + 0.484, + 0.648 + ], + "angle": 0, + "content": "Definition 2 (Sign Alignment Ratio). For vectors \\( x \\in \\mathbb{R}^d \\) and \\( y \\in \\mathbb{R}^d \\), the sign alignment ratio \\( \\rho \\) of \\( x \\) to \\( y \\) is defined as \\( \\rho := 1 - \\| \\operatorname{sgn}(x) - \\operatorname{sgn}(y) \\|_0 / d \\) where \\( \\| \\cdot \\|_0 \\) is \\( L_0 \\)-norm." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.654, + 0.484, + 0.716 + ], + "angle": 0, + "content": "Here, \\(\\rho \\in [0,1]\\) and a larger \\(\\rho\\) indicate a higher degree of alignment between the signs of \\(x\\) and \\(y\\). Combining \\(\\mathrm{Top_k}(\\cdot)\\) and SAR, we have the MPSA value \\(\\rho_{i}\\) for local update \\(\\Delta_i^t\\) formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.723, + 0.483, + 0.744 + ], + "angle": 0, + "content": "\\[\n\\rho_ {i} := 1 - \\left\\| \\left(\\operatorname {s g n} \\left(\\Delta_ {i} ^ {t}\\right) - p\\right) \\odot \\operatorname {T o p} _ {k} \\left(\\Delta_ {i} ^ {t}\\right) \\right\\| _ {0} / k, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\(\\odot\\) is the Hadamard product, \\(\\mathrm{sgn}(\\Delta_i^t) - p\\) computes a sign difference vector, capturing the difference between the sign of \\(\\Delta_i^t\\) and the principal reference sign \\(p\\). Since MPSA checking focuses on the important parameters, this difference vector is element-wise multiplied with the Top-\\(k\\) mask derived from \\(\\Delta_i^t\\), effectively setting unimportant coordinates to zero. The \\(L_0\\)-norm is then applied to count the not-aligned elements and with the masking parameter \\(k\\) to ultimately determine the SAR. MPSA checking effectively reveals malicious local updates by combining both" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "magnitude and directional information from model updates, allowing for clear differentiation between malicious and benign updates. AlignIns calculates the MPSA value for each update with the principal sign iteratively (line 3-4) and forward them to the following anomaly detection process." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.168, + 0.907, + 0.258 + ], + "angle": 0, + "content": "3) Efficient anomaly detection with MZ_score: W apply robust filtering to remove updates with abnormal TDA and MPSA values. Specifically, we use the robust standardization metric named the Median-based Z-score (MZ_score) [50, 51], detailed in Definition 3, which is a variant of the traditional Z-score standardization metric." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.271, + 0.907, + 0.317 + ], + "angle": 0, + "content": "Definition 3 (MZ_score). For a set of values \\( X \\coloneqq \\{x_1, \\ldots, x_n\\} \\) with median \\( \\operatorname{med}(X) \\) and standard deviation \\( \\sigma \\), the MZ_score \\( \\lambda_i \\) of any \\( x_i \\in X \\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.33, + 0.905, + 0.348 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {i} := (x _ {i} - \\operatorname {m e d} (X)) / \\sigma . \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.36, + 0.907, + 0.571 + ], + "angle": 0, + "content": "MZ_score calculates the number of standard deviations an element is from the median, which may be either positive or negative. In AlignIns, the MZ_score for TDA and MPSA values are computed for each local update (line 6-7). Those with high absolute MZ_score (i.e., outliers) are excluded using two predetermined filtering radii: \\(\\lambda_{c}\\) for TDA and \\(\\lambda_{s}\\) for MPSA (line 8-9). The use of the MZ_score allows for the adaptation to the varying range of TDA and MPSA values during training, requiring only minimal hyper-parameters. Additionally, by configuring \\(\\lambda_{c}\\) and \\(\\lambda_{s}\\), we can manage the trade-off between the robustness and main task accuracy of AlignIns. For example, when robustness is the primary concern in the FL, choosing small \\(\\lambda_{c}\\) and \\(\\lambda_{s}\\) values is essential to attain the highest robustness." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.572, + 0.909, + 0.83 + ], + "angle": 0, + "content": "Post-filtering model clipping. After filtering, the remaining clients, considered benign, are included in the set \\( S \\) (line 9) and contribute to the model averaging process. However, since our filtering primarily focuses on the direction of model updates (although MPSA does consider magnitude when using the Top-\\( k \\) indicator), there is a risk that it might overlook updates with large magnitudes, such as those updates generated by Scaling attack [4]. To this end, AlignIns re-scales model updates in \\( S \\) by using the median of the \\( L_{2} \\)-norms of these updates as a clipping threshold and aggregates the clipped model updates as the global model update \\( \\tilde{\\Delta} \\) (line 12-13). It is worth noting that performing clipping before filtering does not affect the filtering results. However, clipping after filtering enhances robustness, as the clipping threshold is more likely determined by benign updates. We discuss the computational cost of AlignIns and compare it with other baselines in Appendix Section 12." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.845, + 0.907, + 0.864 + ], + "angle": 0, + "content": "4. Robustness and Propagation Error Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.903 + ], + "angle": 0, + "content": "In this section, we conduct a theoretical analysis of the robustness of AlignIns, as well as its propagation error in FL." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20657" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.228 + ], + "angle": 0, + "content": "Before presenting our theoretical results, we make the following assumptions. Note that Assumption 1-2 are commonly used in the theoretical analysis of distributed learning systems [18, 34, 49]. Assumption 3 states a standard measure of inter-client heterogeneity in FL [2, 8, 21]. This heterogeneity complicates the problem of FL with backdoor adversaries, as it may cause the server to confuse malicious updates with flawed model updates from benign clients holding outlier data points [2]." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.238, + 0.485, + 0.318 + ], + "angle": 0, + "content": "Assumption 1 (\\(\\mu\\)-smoothness [34]). Each local objective function \\(\\mathcal{L}_i\\) for benign client \\(i \\in \\mathcal{B}\\) is \\(\\mu\\)-Lipschitz smooth with \\(\\mu > 0\\), i.e., for any \\(x, y \\in \\mathbb{R}^d\\), \\(\\|\\nabla \\mathcal{L}_i(x) - \\nabla \\mathcal{L}_i(y)\\| \\leq \\mu \\|x - y\\|\\), \\(\\forall i \\in \\mathcal{B}\\), which further gives: \\(\\mathcal{L}_i(x) - \\mathcal{L}_i(y) \\leq \\nabla \\mathcal{L}_i(x)^T(y - x) + (\\mu/2)\\|x - y\\|^2\\), \\(\\forall i \\in \\mathcal{B}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.325, + 0.484, + 0.435 + ], + "angle": 0, + "content": "Assumption 2 (Unbiased gradient and bounded variance). The stochastic gradient at each benign client is an unbiased estimator of the local gradient, i.e., \\(\\mathbb{E}[g_i(x)] = \\nabla \\mathcal{L}_i(x)\\) and has bounded variance, i.e., for any \\(x\\in \\mathbb{R}^d\\) \\(\\mathbb{E}\\left\\| g_i(x) - \\nabla \\mathcal{L}_i(x)\\right\\| ^2\\leq \\nu_i^2,\\forall i\\in \\mathcal{B},\\) where the expectation is over the local mini-batches. We also denote \\(\\bar{\\nu}\\coloneqq (1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\nu_i^2\\) for convenience." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.443, + 0.484, + 0.507 + ], + "angle": 0, + "content": "Assumption 3 (Bounded heterogeneity). There exist a real value \\(\\bar{\\zeta}\\) such that for any \\(x\\in \\mathbb{R}^d\\) \\((1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\| \\nabla \\mathcal{L}_i(x) - \\nabla \\mathcal{L}_{\\mathcal{B}}(x)\\| ^2\\leq \\bar{\\zeta}\\), where the \\(\\nabla \\mathcal{L}_{\\mathcal{B}}(x)\\coloneqq (1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\mathcal{L}_i(x)\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.514, + 0.484, + 0.56 + ], + "angle": 0, + "content": "Note that these assumptions apply to benign clients only since malicious clients do not need to follow the prescribed local training protocol of FL." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.569, + 0.373, + 0.586 + ], + "angle": 0, + "content": "4.1. Robustness Analysis of AlignIns" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.592, + 0.484, + 0.743 + ], + "angle": 0, + "content": "To theoretically evaluate the efficacy of a filtering-based defense method like AlignIns, we introduce the concept of \\(\\kappa\\)-robust filtering [50] as defined in Definition 4. Note that Definition 4 is similar to \\((f,\\kappa)\\)-robustness defined in [2, 3], \\((\\delta_{\\max},c)\\)-ARAgg defined in [13, 21, 31], and \\((f,\\lambda)\\)-resilient averaging defined in [10]. Our robustness definition adopts a constant upper bound and focuses on quantifying the distance between the output of a filtering-based defense method and the average of all benign updates, which represents the optimal output of such a rule." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.753, + 0.484, + 0.846 + ], + "angle": 0, + "content": "Definition 4 (\\(\\kappa\\)-robust filtering [50]). A filtering-based aggregation rule \\(F \\colon \\mathbb{R}^{d \\times n} \\to \\mathbb{R}^d\\) is called \\(\\kappa\\)-robust if for any vectors \\(\\{x_1, \\ldots, x_n\\} \\in \\mathbb{R}^d\\) and a benign set \\(\\mathcal{B} \\subseteq [n]\\) of size \\(n - m\\), the output \\(\\hat{x} \\coloneqq F(x_1, \\ldots, x_n)\\) satisfies \\(\\| \\hat{x} - \\bar{x}_{\\mathcal{B}} \\|^2 \\leq \\kappa\\), where \\(\\bar{x}_{\\mathcal{B}} \\coloneqq (1 / |\\mathcal{B}|) \\sum_{i \\in \\mathcal{B}} x_i\\), and \\(\\kappa \\geq 0\\) refers to the robustness coefficient of \\(F\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Remark 1. The \\(\\kappa\\)-robust filtering guarantees that the error of a filtering-based aggregation rule in estimating the average of the benign inputs is upper-bounded by a constant \\(\\kappa\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.183 + ], + "angle": 0, + "content": "This measure provides a quantitative way to assess the robustness of the filtering-based aggregation rule. A smaller \\(\\kappa\\) indicates a smaller discrepancy between the empirical output and the optimal output of \\(F\\). If \\(F\\) identifies and removes all malicious inputs and keeps all benign inputs, we have \\(\\kappa = 0\\), achieving the highest level of robustness." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.192, + 0.906, + 0.254 + ], + "angle": 0, + "content": "Based on Definition 4, we prove that the proposed AlignIns, when applied to \\( n \\) input models, of which \\( m \\) are malicious, satisfies \\( \\kappa \\)-robust filtering with \\( \\kappa = O(1 + m / (n - 2m)) \\), as stated in Lemma 1." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.263, + 0.906, + 0.31 + ], + "angle": 0, + "content": "Lemma 1 (\\(\\kappa\\)-robustness of AlignIns). Under Assumption 2-3, assume \\(n > 1\\), \\(0 \\leq m < n / (3 + \\epsilon)\\) with a positive constant \\(\\epsilon\\), AlignIns satisfies \\(\\kappa\\)-robust filtering with" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.319, + 0.885, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\kappa = \\left(1 + m / \\left(n - 2 m\\right)\\right) \\left(\\left(2 / \\epsilon + 1\\right) \\left(2 \\bar {\\nu} + \\bar {\\zeta}\\right) + 8 c ^ {2}\\right) \\\\ = O \\left(1 + m / (n - 2 m)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.367, + 0.906, + 0.429 + ], + "angle": 0, + "content": "if the local learning rate satisfies \\(\\eta \\leq 1 / 2\\tau\\) and there exist two sufficiently large filtering radii such that \\(|\\mathcal{S}|\\geq n - 2m\\). Here, \\(\\bar{\\nu}\\) and \\(\\zeta\\) represent the gradient variance and local divergence, respectively; \\(c\\) is the clipping threshold." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.438, + 0.862, + 0.454 + ], + "angle": 0, + "content": "Proof. The proof is given in Appendix Section 13.2." + }, + { + "type": "image", + "bbox": [ + 0.889, + 0.438, + 0.906, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.907, + 0.782 + ], + "angle": 0, + "content": "Remark 2. The condition on \\( S \\) highlights the importance of selecting appropriate filtering radii. These radii cannot be zero or too small; otherwise, only the median or a few model updates will be averaged to update the global model. This can lead to a performance drop due to the lack of model updates. Moreover, the model clipping threshold \\( c \\) can effectively control the magnitude of potential malicious updates in the selection set, thus preventing \\( \\kappa \\) from exploding due to updates with large magnitudes. Indeed, in the literature, model clipping has demonstrated its effectiveness in mitigating the impact of malicious model updates [39, 49, 53]. In addition, the result also shows the importance of reducing the gradient variance of stochastic gradient and local heterogeneity to enhance robustness performance. Our work is orthogonal to existing variance or divergence reduction methods [13, 30] and can be combined with them to further improve the robustness. We argue that AlignIns enjoys comparable robustness with several classical defense methods, for example, non-filtering-based method RFA [40] (\\( O(1 + m / (n - 2m))^2 \\)), and filtering-based method Krum [6] (\\( O(1 + m / (n - 2m))^1 \\))." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.79, + 0.833, + 0.807 + ], + "angle": 0, + "content": "4.2. Propagation Error of AlignIns in FL" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.812, + 0.906, + 0.843 + ], + "angle": 0, + "content": "Based on the \\(\\kappa\\)-robustness of AlignIns, we analyze its propagation error during training. Specifically, let \\(\\theta\\) denote the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.512, + 0.851, + 0.906, + 0.901 + ], + "angle": 0, + "content": "1Results of RFA and Krum are taken from [2]. Note that the definition of \\(\\kappa\\) in [2] is different from ours, but the difference part can be reduced to a constant bound. Therefore, we can safely incorporate these results into our discussion without losing generality." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20658" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.332 + ], + "angle": 0, + "content": "model trained with AlignIns under backdoor attacks, where \\( m \\) of the \\( n \\) clients are malicious, and let \\( \\theta^{*} \\) denote a model trained exclusively with benign clients using FedAvg. Starting from the same initial model \\( \\theta^0 \\), we aim to measure the difference between these two models after \\( T \\) rounds of training, defined as \\( \\| \\theta^T - \\theta^{T,*} \\| \\), referred to as the propagation error [39]. Let \\( \\theta^{t, + } \\) represent the output of AlignIns at the \\( t \\)-th round. If the highest level of robustness is not achieved at round \\( t \\), the error \\( \\| \\theta^t - \\theta^{t, + } \\| \\) will propagate to the next round, resulting in a shifted starting point for local SGD at round \\( t + 1 \\). This discrepancy will gradually widen the gap between \\( \\theta \\) and \\( \\theta^{*} \\). Our analysis captures this robustness error at each round and examines its cumulative effect after \\( T \\) rounds. In Lemma 2, we show that, assuming Assumption 1-3 hold, the propagation error of AlignIns remains bounded." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.341, + 0.483, + 0.388 + ], + "angle": 0, + "content": "Lemma 2 (Bounded Propagation Error). Let Assumption 1-3 hold. If the local learning rate \\(\\eta \\leq 1 / 2\\tau\\), the propagation error of AlignIns is bounded as" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.394, + 0.438, + 0.414 + ], + "angle": 0, + "content": "\\[\n\\left\\| \\theta^ {T} - \\theta^ {T, *} \\right\\| \\leq \\phi (T) (2 + 3 \\mu^ {2}) ^ {\\phi (T)} (\\kappa + 2 \\bar {\\nu}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.422, + 0.485, + 0.482 + ], + "angle": 0, + "content": "under backdoor attacks where \\( m \\) out of \\( n \\) clients are malicious. Here, \\( \\kappa \\) is given in Lemma 1, \\( \\phi(T) = \\sum_{t=1}^{T} (\\alpha^t)^2 \\) is the cumulative global learning rate, and \\( \\alpha^t \\) is a global learning rate scheduler, possibly static." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.491, + 0.483, + 0.507 + ], + "angle": 0, + "content": "Proof. The detailed proof is in Appendix Section 13.3. \\(\\square\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.516, + 0.486, + 0.833 + ], + "angle": 0, + "content": "Remark 3. When \\( T \\to \\infty \\), \\( \\phi(T) \\) converges to a constant for learning rate schedulers like exponential decay, which implies a constant bounded on propagation error. The result shows that besides the robustness error bounded by \\( \\kappa \\), the error of local gradient estimation, which is bounded by \\( \\bar{\\nu} \\), in local SGD also propagates during the training, increasing the overall propagation error. This is because at any round \\( t \\), if the benign starting point for local training is the same, i.e., \\( \\theta^t = \\theta^{t,*} \\), then the local gradients/model updates on \\( \\theta^t \\) and \\( \\theta^{t,*} \\) will be identical for benign clients. Therefore, the gap between the updated global models \\( \\theta^{t+1} \\) and \\( \\theta^{t+1,*} \\) solely depends on the robustness error (i.e., the effectiveness of AlignIns in filtering out malicious updates). However, if \\( \\theta^t \\neq \\theta^{t,*} \\), which means \\( \\theta^t \\) is not benign and has been poisoned in previous rounds, the local gradients/model updates on \\( \\theta^t \\) and \\( \\theta^{t,*} \\) will differ for benign clients, resulting in an error bounded by the gradient variance, even if AlignIns successfully filters out all malicious updates. Hence, to further reduce the propagation error, AlignIns can be combined with variance-reduction methods like [13, 30], which is orthogonal to AlignIns." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.845, + 0.303, + 0.862 + ], + "angle": 0, + "content": "5. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Datasets and System Settings: In our experiments, we primarily conduct evaluation on CIFAR-10 [24] and CIFAR-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.272 + ], + "angle": 0, + "content": "100 [24] datasets. Additionally, we present the superior performance of AlignIns on other benchmark datasets (MNIST [25], FMNIST [47], Sentiment140 [12], and TinyImageNet) in Appendix Section 10.5-10.6. We simulate a cross-silo FL with 20 clients for all datasets. Additionally, we also present the superior performance of AlignIns on a cross-device FL system with 100 clients and client sampling. We consider both IID and non-IID settings. For IID settings, we distribute the training data evenly to clients. For non-IID settings, we follow [17, 19, 20] to use Dirichlet distribution \\( \\text{Dir}(\\beta) \\) to skew the local data distribution with a default non-IID degree \\( \\beta = 0.5 \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.275, + 0.908, + 0.412 + ], + "angle": 0, + "content": "Learning Settings: We use SGD as the local solver, with the initial learning rates set as \\(\\alpha = 1.0\\) and \\(\\eta = 0.1\\), and the local training epoch is set as 2. The training round is set as \\(T = 100\\) for CIFAR-100 and \\(T = 150\\) for CIFAR-10. For AlignIns, the default filtering radii are set as \\(\\lambda_{c} = 1.0\\) and \\(\\lambda_{s} = 1.0\\). We provide the study of the impact of filtering radii in Appendix Section 11. The default masking parameter is set as \\(k = 0.3 \\times d\\) so that the Top-30% of model parameters are used for the MPSA checking." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.413, + 0.906, + 0.655 + ], + "angle": 0, + "content": "Evaluated Attack Methods: We consider 5 SOTA backdoor attacks, including Badnet [14], DBA [48], Scaling [4], PGD [46], and Neurotoxin [54]. We provide the detailed attack model and settings for attack methods in Appendix Section 8.1-8.2. We present the results of AlignIns under the strong trigger-optimization attack [9] in Appendix Section 10.2. Moreover, we study the potential adaptive attacks tailored to AlignIns and untargeted attacks [49] in Appendix Section 10.3-10.4, although these are beyond the scope of this work. To achieve effective backdoors (achieving a BA over \\(60\\%\\) [22]), malicious clients poison \\(r = 50\\%\\) of their local data, where \\(r\\) is the data poisoning ratio. The attack ratio is set to \\(20\\%\\) by default, which means \\(20\\%\\) of the clients in the system are malicious. Experiments of AlignIns on defending backdoor attacks with various attack ratios are given in Appendix Section 10.7." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.657, + 0.906, + 0.809 + ], + "angle": 0, + "content": "Evaluated Defense Methods: We present the detailed defense model in Appendix Section 9. We comprehensively compare AlignIns with the non-robust baseline FedAvg and six existing SOTA defense methods, including RLR [38], RFA [40], Multi-Krum (MKrum) [6], Foolsgold [11], Multi-Metric (MM) [19], and Lockdown [20]. Additionally, we compare our approach with an ideally perfect filtering-based robust aggregation, FedAvg*, which is assumed to perfectly identify and remove all malicious updates and average all the benign updates to update the global model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics: We use three metrics to evaluate the performance of defense methods, including main task accuracy (MA), which measures the percentage of clean test samples that are accurately classified to their ground truth labels by the global model; backdoor attack accuracy (BA), which measures the percentage of triggered" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20659" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.089, + 0.905, + 0.104 + ], + "angle": 0, + "content": "Table 1. The clean MA, BA, and RA results of baselines and AlignIns on IID CIFAR-10 and CIFAR-100 datasets. Results are shown in %." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.115, + 0.902, + 0.429 + ], + "angle": 0, + "content": "
    Dataset (Model)MethodsClean MA↑BadnetDBANeurotoxinAvg. BA↓Avg. RA↑
    BA↓RA↑BA↓RA↑BA↓RA↑
    r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5
    CIFAR-10 (ResNet9 [16])FedAvg89.4751.5667.6145.7931.2456.2170.4240.6227.9244.8979.4050.4119.6061.6835.93
    FedAvg*89.472.062.0685.6085.602.062.0685.6085.602.062.0685.6085.602.0685.60
    RLR79.162.322.0076.7273.333.013.0477.0977.133.123.8773.9873.292.8935.93
    RFA87.7370.6790.2427.749.2647.6766.9747.2930.1481.2796.1317.113.6975.4922.54
    MKrum87.0281.1097.4718.112.512.174.3383.8979.1065.2889.1831.8110.0156.5937.57
    Foolsgold89.4969.1468.8429.6430.1051.1860.7344.8336.082.912.8285.2784.7642.6051.78
    MM89.1541.1993.8853.886.0152.2451.3043.5445.0843.9283.9251.1215.1161.0835.79
    Lockdown88.566.3110.8281.8879.5011.636.0378.8275.773.403.2782.7383.146.9180.31
    AlignIns88.641.912.2186.0385.572.132.1485.7785.882.662.2085.4685.312.2185.67
    CIFAR-100 (VGG9 [41])FedAvg64.2999.2099.540.680.3599.2599.360.640.5494.4193.364.365.2897.521.98
    FedAvg*64.290.620.6253.0353.030.620.6253.0353.030.620.6253.0353.030.6253.03
    RLR44.3496.5799.851.810.1224.4194.0824.973.220.040.0029.0729.7352.4914.82
    RFA53.924.321.4537.6039.882.150.7839.7341.5199.7489.590.216.5933.0127.59
    MKrum51.281.331.5438.1338.491.361.5437.8537.9199.8299.870.120.1036.2125.49
    Foolsgold64.1399.0299.300.830.5799.1599.390.740.5121.796.2142.0646.4070.8115.19
    MM63.2699.5199.870.370.1199.5399.700.350.1998.4898.971.320.8399.340.53
    Lockdown62.8855.2124.1428.4543.0634.3749.0234.0627.930.850.6742.6647.0427.3837.20
    AlignIns63.450.790.7150.4551.530.450.5750.8152.080.490.5351.1150.660.5951.11
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.441, + 0.484, + 0.534 + ], + "angle": 0, + "content": "samples that are misclassified to the target label by the global model; and robustness accuracy (RA), which measures the percentage of triggered samples that are accurately classified to their ground-truth labels by the global model, despite the presence of the trigger. A good defense method should achieve high MA and RA and low BA." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.544, + 0.295, + 0.56 + ], + "angle": 0, + "content": "6. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.569, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Main results in IID setting. In Table 1, we report the performance of various defense methods under no attack (denoted by \"Clean\"), Badnet, DBA, and Neurotoxin attacks for IID CIFAR-10 and CIFAR-100. The best results are highlighted in bold font, and the second best results are underlined. Overall, AlignIns demonstrates superior performance compared with other baselines as it achieves the best average BA and RA over three attack methods. Specifically, for CIFAR-10, while RLR offers a satisfactory degree of robustness (an average BA of \\(2.89\\%\\)), it suffers from a notable decline in RA, with an average reduction of \\(49.74\\%\\) in comparison to AlignIns. This drop results from RLR's strategy of flipping the global learning rate for parameters in the aggregated model update that are inconsistent with the majority's sign, consequently resulting in the loss of benign local parameters. AlignIns, however, demonstrates outstanding performance with consistently low BA and high RA, ranking first or second among its counterparts. Notably, compared to the second-best results, AlignIns achieves an average improvement of \\(+0.68\\%\\) in BA and \\(+5.36\\%\\) in RA. Similarly, superior results are observed in CIFAR-100 experiments, where AlignIns significantly out" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.441, + 0.725, + 0.573 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.737, + 0.441, + 0.882, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.586, + 0.907, + 0.614 + ], + "angle": 0, + "content": "Figure 1. RA of AlignIns under various non-IID degrees, compared with Lockdown, RFA, and RLR under Neurotoxin." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.628, + 0.907, + 0.689 + ], + "angle": 0, + "content": "performs other methods in both BA and RA. These results underscore AlignIns' effectiveness as a promising defense method for protecting FL from various backdoor attacks, significantly enhancing the trustworthiness of FL systems." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Effectiveness under various Non-IID degrees. We examine the defense performance of AlignIns across various degrees of non-IIDness, a factor that significantly complicates backdoor defense. Figure 1 presents the RA of AlignIns under different non-IID conditions on the CIFAR-10 dataset, compared with Lockdown, RFA, and RLR. The experiments were conducted using the Neurotoxin attack, with both a default attack ratio of \\(20\\%\\) and a higher attack ratio of \\(30\\%\\). The Dirichlet parameter \\(\\beta\\) varies from 0.1 to 1.0, where a smaller \\(\\beta\\) suggests a more intense non-IIDness. We observe that only AlignIns consistently attains robustness against strong Neurotoxin attacks with a varying \\(\\beta\\). Specifically, as \\(\\beta\\) increases, the RA of AlignIns, Lockdown, and RLR increases correspondingly. However," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20660" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.483, + 0.119 + ], + "angle": 0, + "content": "Table 2. Performance of different methods in cross-device FL settings on IID and non-IID CIFAR-10 datasets under Badnet attack." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.129, + 0.468, + 0.213 + ], + "angle": 0, + "content": "
    MethodCIFAR-10 (IID)CIFAR-10 (Non-IID)Avg. RA↑
    MA↑BA↓RA↑MA↑BA↓RA↑
    Foolsgold82.9999.990.0167.9799.990.000.01
    Lockdown83.5299.990.0073.9199.920.060.00
    RLR56.814.6755.3841.5614.1238.1746.78
    AlignIns85.010.9282.7479.511.9075.8179.28
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.226, + 0.484, + 0.424 + ], + "angle": 0, + "content": "AlignIns outperforms them with a consistently higher RA. When the attack ratio rises to \\(30\\%\\), RLR, RFA, and Lockdown fail to provide satisfactory robustness. However, our method AlignIns still demonstrates its robustness under various non-IIDness, even in an extremely non-IID case when \\(\\beta = 0.1\\). AlignIns is designed to examine the alignment of model updates on important parameters only, hence, it mitigates the challenge of identifying malicious model updates in non-IID settings where updates are heterogeneous, thereby achieving superior performance in even extreme non-IID settings compared with existing methods. We also provide more comprehensive results of AlignIns and other baselines on non-IID datasets in Appendix Section 10.1." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.428, + 0.484, + 0.761 + ], + "angle": 0, + "content": "Effectiveness of AlignIns in cross-device FL with client sampling. While most of our experiments focus on the cross-silo FL setting, evaluating the cross-device FL scenario is also essential given the large number of clients involved. For this purpose, we simulate a cross-device FL environment with 100 clients, where the server randomly selects 20 clients per round for training. We conduct experiments on IID and non-IID CIFAR-10 cases using Foolsgold, Lockdown, RLR, and AlignIns and summarize the MA, BA, and RA results in Table 2. The results show that both Foolsgold and Lockdown completely lose their effectiveness in both cases, achieving an average RA of nearly \\(0.00\\%\\). RLR achieves a moderate level of backdoor robustness but at the cost of main task accuracy, with an average MA of only \\(49.19\\%\\). In contrast, AlignIns performs robustly in the cross-device FL setting, achieving a significantly lower BA in both IID \\((0.92\\%)\\) and non-IID \\((1.90\\%)\\) cases compared with other methods. Furthermore, AlignIns achieves an average RA of \\(79.28\\%\\). These results highlight AlignIns's ability to maintain both accuracy and robustness in challenging cross-device FL scenarios, underscoring its adaptability and effectiveness in real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Ablation study of AlignIns. As AlignIns consists of two alignment components (TDA and MPSA) to improve backdoor robustness, we conduct a detailed ablation study to investigate how each component functions. Experimental results on IID and non-IID CIFAR-10 datasets under Badnet attack are summarized in Table 3. (i) Component ablation. We observe that using MPSA or TDA alone in IID scenarios only slightly reduces robustness compared to AlignIns, as benign updates follow consistent patterns that" + }, + { + "type": "table_caption", + "bbox": [ + 0.536, + 0.09, + 0.884, + 0.105 + ], + "angle": 0, + "content": "Table 3. Performance of different components in AlignIns." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.115, + 0.902, + 0.232 + ], + "angle": 0, + "content": "
    ConfigurationCIFAR-10 (IID)CIFAR-10 (non-IID)Avg. RA↑
    MA↑BA↓RA↑MA↑BA↓RA↑
    MPSA(30%)88.552.8885.0280.6594.075.7945.41
    TDA88.563.8283.8883.8677.5821.3152.60
    MPSA(70%)+TDA88.142.1885.7783.8461.8331.8658.82
    MPSA(50%)+TDA88.052.2185.4684.1277.9319.9652.71
    MPSA(30%)+TDA88.142.0485.8283.6547.0445.3065.56
    AlignIns88.052.4485.2782.881.7081.3283.30
    AlignIns+88.482.1485.7483.311.1182.1383.94
    " + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.244, + 0.908, + 0.668 + ], + "angle": 0, + "content": "enable effective detection by a single metric. In non-IID settings, however, where local updates diverge, neither MPSA nor TDA alone provides sufficient robustness. When combined, MPSA and TDA improve BA and RA from \\(94.07\\%\\) and \\(5.79\\%\\) to \\(47.04\\%\\) and \\(45.30\\%\\), respectively, showing their complementary strengths. AlignIns further enhances robustness by integrating MPSA, TDA, and post-filtering model clipping, which normalizes benign update magnitudes and improves malicious update detection, yielding the highest average RA. (ii) Masking parameter \\(k\\) ablation. We try to involve more non-essential parameters in the MPSA checking by using the Top-\\(50\\% / 70\\%\\) of parameters to calculate MPSA values. By doing so, the effectiveness of malicious identification is reduced. In contrast, when using the Top-\\(30\\%\\) of parameters, compared to the Top-\\(50\\%\\) case, BA and RA are improved by \\(+30.89\\%\\) and \\(+25.34\\%\\), respectively. This demonstrates the effectiveness of focusing important parameters when calculating MPSA in improving the filtering accuracy, especially in non-IID cases. (iii) Variance reduction method further enhances robustness. Our theoretical results reveal the impact of variance reduction techniques on improving the robustness of AlignIns and reducing the propagation error of AlignIns in FL, we additionally test a variant of AlignIns named \"AlignIns+\", in which local SGD with momentum is used to reduce the local gradient variance with momentum coefficient 0.1. AlignIns+ achieves a slightly better performance than AlignIns, verifying our theoretical results." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.678, + 0.634, + 0.695 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.855 + ], + "angle": 0, + "content": "We introduce a novel method AlignIns to defend against backdoor attacks in FL. AlignIns examines each model update's direction at different granularity levels, thus effectively identifying stealthy malicious model updates and filtering them out to avoid them participating in aggregation in FL to enhance robustness. We provide a theoretical analysis of AlignIns' robustness and its impact on propagation errors in FL. Extensive experiments demonstrate the effectiveness of AlignIns, with results showing that it outperforms SOTA defense methods against various advanced attacks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Acknowledgment. This work was supported by the Nevada System of Higher Education under grant NSHE-24-37." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20661" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.17 + ], + "angle": 0, + "content": "[1] Manaar Alam, Esha Sarkar, and Michail Maniatakos. Perdoor: Persistent non-uniform backdoors in federated learning using adversarial perturbations. arXiv preprint arXiv:2205.13523, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.171, + 0.484, + 0.242 + ], + "angle": 0, + "content": "[2] Youssef Allouah, Sadegh Farhadkhani, Rachid Guerraoui, Nirupam Gupta, Rafael Pinot, and John Stephan. Fixing by mixing: A recipe for optimal byzantine ml under heterogeneity. 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Existing defense methods show limited efficacy as they overlook the inconsistency between benign and malicious model updates regarding both general and fine-grained directions. To fill this gap, we introduce AlignIns, a novel defense method designed to safeguard FL systems against backdoor attacks. AlignIns looks into the direction of each model update through a direction alignment inspection process. Specifically, it examines the alignment of model updates with the overall update direction and analyzes the distribution of the signs of their significant parameters, comparing them with the principle sign across all model updates. Model updates that exhibit an unusual degree of alignment are considered malicious and thus be filtered out. We provide the theoretical analysis of the robustness of AlignIns and its propagation error in FL. Our empirical results on both independent and identically distributed (IID) and non-IID datasets demonstrate that AlignIns achieves higher robustness compared to the state-of-the-art defense methods. The code is available at https://github.com/JiaiahaoXU/AlignIns. + +# 1. Introduction + +Unlike traditional centralized training methods, which require gathering and processing all data at a central location such as a server, Federated Learning (FL) [32], as a decentralized training paradigm, allows a global model to learn from data distributed across various local clients, thereby achieving the goal of privacy-preserving. During training, the server distributes the global model to local clients, and each client trains the received global model using its local dataset, and then submits its local model update to the server for global model refinement. FL has been applied in various fields, including healthcare[35], finance [28], and remote + +sensing [27], where local data privacy is essential. + +Although promising, the distributed nature of FL systems makes them vulnerable to a range of advanced poisoning attacks [15, 26, 45]. This vulnerability primarily stems from the server's lack of close monitoring of the local data and the training algorithm on clients. Consequently, this drawback allows attackers to compromise the data of local clients or interfere with the training algorithm, enabling them to inject malicious local model updates that distort the performance of the global model. For example, backdoor attacks [4, 14, 46, 48, 54] have gained significant attention due to their stealthiness and practical effectiveness. In detail, backdoor attacks in FL seek to preserve the performance of the global model on clean inputs (i.e., the main task), while inducing the global model to make incorrect predictions on inputs that contain a certain predefined feature (i.e., the backdoor task). As backdoor attacks maintain the main task and the backdoor task simultaneously, the malicious local model updates are statistically similar to benign ones [36, 46] (poison-coupling effect [20]), making anomaly detection more challenging on the server side. + +Existing defense methods (i.e., aggregation rule) usually aim to identify malicious model updates and filter them out to achieve better robustness by magnitude-based metrics extracted from local model updates (e.g., Manhattan distance [19, 22] and Euclidean distance [6, 15]). However, magnitude-based metrics are ineffective in distinguishing stealthy backdoor attacks where benign and malicious model updates are usually similar in magnitude. Additionally, when the global model tends to converge, the magnitude of each model update becomes very small, making effective malicious manipulation on magnitude negligible. To this end, some works employ Cosine similarity to check the pair-wise directional information of model updates [11, 36, 42]. However, pair-wise Cosine similarity between two model updates only captures their general directional similarity and overlooks fine-grained information (e.g., signs of parameters), resulting in limited robustness. In addition, in FL settings with non-IID data, the pair-wise Cosine similarity of model updates can be easily perturbed + +by the naturally diverse benign model updates. Furthermore, there is a deficiency in theoretical analysis within the literature concerning the effects of data heterogeneity on defense methods deployed by the server in FL. + +In this work, we propose a novel defense method designed to defend against backdoor attacks in FL, named AlignIns (Direction Alignment Inspection), which examines local model updates for directional alignment at different granularity levels to identify malicious updates. Specifically, after receiving all model updates from clients, AlignIns evaluates each update by (1) inspecting temporal directional alignment with the global model of the latest round with Cosine similarity and (2) assessing more fine-grained sign alignment with the principal sign across all updates with a novel metric sign alignment ratio. Particularly, when calculating the sign alignment ratio, AlignIns focuses on the signs of important parameters in each update to accurately capture alignment information. Using these two directional metrics, AlignIns performs anomaly detection with the robust MZ_score which requires minimal hyperparameters to filter updates with unusual directional patterns out. Finally, AlignIns clips the remaining updates to mitigate the impact of updates with abnormally large magnitudes. We also provide a theoretical analysis of AlignIns' robustness and its propagation error in FL. The main contributions of this work are three folds: + +- We present a novel defense method, AlignIns, to defend against backdoor attacks in FL. To the best of our knowledge, AlignIns is the first defense method in FL that analyzes the directional patterns of local model updates at different levels of granularity. AlignIns is fully compatible with existing FL frameworks. +- To the best of our knowledge, we provide the first theoretical robustness analysis for a filtering-based defense method against backdoor attacks under non-IID data in FL. Moreover, we prove that the propagation error of AlignIns is bounded during the training of FL. +- We empirically evaluate the effectiveness of AlignIns through extensive experiments on both IID and non-IID datasets against various state-of-the-art (SOTA) backdoor attacks. Compared to existing SOTA defense methods, AlignIns exhibits superior robustness. + +# 2. Background and Related Works + +Federated Learning. In a typical FL system, a central server controls a set of $n$ clients to train a global model $\theta \in \mathbb{R}^d$ collaboratively. The objective of FL is to solve the following optimization problem: $\min_{\theta}(1/n)\sum_{i=1}^{n}\mathcal{L}_i(\theta;\mathcal{D}_i)$ , where $\mathcal{L}_i(\cdot)$ denotes the learning objective specific to client $i$ and $\mathcal{D}_i$ denotes the local dataset for client $i$ . The commonly used method to solve this problem iteratively is FedAvg [33]. In detail, at round $t$ of FedAvg, each client $i \in [n]$ downloads the current global model $\theta^t$ , updates it + +by optimizing its local objective, resulting in $\theta_i^t$ , and transmits its model update $\Delta_i^t = \theta_i^t - \theta^t$ to the server. The server then refines the global model by averaging these updates as follows: $\theta^{t + 1} = \theta^t + (1 / n)\sum_{i = 1}^n\Delta_i^t$ . This process continues until the global model reaches convergence. + +Backdoor attacks in FL. Empirical evidence has shown that FL is vulnerable to backdoor attacks [4, 9, 14, 23, 37, 46, 48, 52, 54] due to its lack of access to local training data [4]. For instance, Projected Gradient Descent (PGD) attack [46] periodically projects the local model onto a small sphere centered around the global model from the previous training round, with a predefined radius. Distributed Backdoor Attack (DBA) [48] decomposes the centralized trigger into several smaller, distributed local triggers. Each poisoned client uses one of these local triggers, but during testing, the adversary injects the full trigger into the test samples. Recently, research has focused on trigger-optimization backdoor attacks [1, 9, 29, 37, 52], which aim to search optimized triggers to enhance the effectiveness and stealthiness. + +Defending against backdoor attacks in FL. Generally, based on how defense methods mitigate the impact of malicious updates, existing defense methods can be categorized into filtering-based methods [6, 7, 19, 22, 36, 42, 50, 51] and influence-reduction methods [11, 20, 38, 40, 41]. + +1) influence-reduction methods aim to integrate all model updates but employ strategies to reduce the impact of malicious updates. For instance, $RFA$ [40] is proposed to use the geometric median of local models as the aggregation result, under the assumption that malicious models significantly deviate from benign models. Foolsgold [11] assumes that the malicious updates are consistent with each other. It assigns aggregation weights to model updates based on the maximum Cosine similarity between the last layers of pairwise model updates. A higher Cosine similarity value indicates a higher probability that the updates are malicious, leading to smaller aggregation weights being assigned. The effectiveness of influence-reduction methods is inherently limited because they cannot eliminate the impact of malicious activity, leading to a significant risk of compromise. + +2) Filtering-based methods aim to detect and remove malicious local model updates before aggregation thus attempting to achieve the highest robustness. For example, Multi-Krum [6] selects the multiply reliable local model updates for aggregation by identifying the one with the smallest sum of squared Euclidean distances to all other updates. Multi-Metrics [19] explores the combination of Manhattan distance, Euclidean distance, and Cosine similarity for each update to collaboratively filter out outliers. However, due to the dual objectives of backdoor attacks—that is, maintaining accuracy on the main task while maximizing accuracy on the backdoor task—malicious updates must mimic benign model updates, important weights for the main task + +Algorithm 1: AlignIns +Input: Set of $n$ local model updates $\{\Delta_i^t\}_{i=1}^n$ where $m$ of them are malicious, global model $\theta^t$ , TDA radius $\lambda_c$ , MPSA radius $\lambda_s$ , extraction parameter $k$ +Output: Aggregated model update $\widetilde{\Delta}$ +1 Initialize benign set $S \gets \emptyset$ +2 $\omega \gets \{\mathrm{TDA}(\Delta_i^t, \theta)\}_{i=1}^n$ $\triangleleft$ by Equation (1) +3 $p \gets \operatorname{sgn}(\sum_{i=1}^n \operatorname{sgn}(\Delta_i^t))$ +4 $\rho \gets \{\mathrm{MPSA}(\Delta_i^t, p, k)\}_{i=1}^n$ $\triangleleft$ by Equation (2) +5 for $i \in [n]$ do +6 $\lambda_{i,c} \gets \mathrm{MZ\_score}(\omega_i, \omega)$ $\triangleleft$ by Equation (3) +7 $\lambda_{i,s} \gets \mathrm{MZ\_score}(\rho_i, \rho)$ $\triangleleft$ by Equation (3) +8 if $|\lambda_{i,c}| \leq \lambda_c$ and $|\lambda_{i,s}| \leq \lambda_s$ then +9 $\mid S \gets S \cup \{i\}$ +10 end +11 end +12 $c \gets \operatorname{med}(\{\| \Delta_i^t\| \}_{i \in S})$ +13 $\widetilde{\Delta} \gets (1 / |\mathcal{S}|) \sum_{i \in S} (\Delta_i^t \cdot \min\{1, c / \| \Delta_i^t\|\})$ +14 return $\widetilde{\Delta}$ + +typically have large values and can dominate the magnitude of a model update. As a result, magnitude-based detection methods become ineffective against backdoor attacks. Additionally, methods that rely solely on Cosine similarity also show limited effectiveness since they capture general directional alignment and overlook finer-grained information. + +# 3. Our Solution: AlignIns + +Our method, AlignIns, detailed in Algorithm 1, mitigates the impact of malicious updates through a two-step process. First, direction alignment inspection is applied to examine each local model update comprehensively in terms of direction. Second, post-filtering model clipping is used to further enhance the robustness of AlignIns on defending potential magnitude-based attack methods before final aggregation. + +Direction alignment inspection. Existing defense methods against backdoor attacks in FL primarily focus on examining the magnitude (e.g., Manhattan distance and Euclidean distance) and the overall direction (e.g., Cosine similarity) of model updates. However, backdoor attacks are designed to maintain the main task accuracy, making the magnitude difference between malicious and benign updates nearly indistinguishable. Additionally, advanced attacks such as PGD [46] and Lie [5] attacks are specifically crafted to bypass magnitude-based defenses. Therefore, AlignIns focuses on direction-based analysis to identify suspect updates, using two processes described below. + +1) Temporal direction alignment checking: Since malicious clients need to maintain both the main task and the backdoor task, the optimization direction of a malicious + +local model tends to deviate from that of benign models. AlignIns leverages this deviation and performs a Temporal Direction Alignment (TDA) checking, which calculates the Cosine similarity between a local update and the latest global model (line 2 in Algorithm 1) to assess the general alignment level of each local update. Formally, the TDA value $\omega_{i}$ of a local model update $\Delta_i^t$ is calculated as + +$$ +\omega_ {i} := \left\langle \Delta_ {i} ^ {t}, \theta^ {t} \right\rangle / \left(\| \Delta_ {i} ^ {t} \| \| \theta^ {t} \|\right). \tag {1} +$$ + +We use local model updates rather than local models because our goal is to measure how closely each client's updates align with the direction of the global model. Local model updates specifically capture these incremental adjustments. Notably, malicious clients tend to exhibit similar TDA values, which differ from those of benign clients, creating an opportunity for detection. It is important to note that while the magnitude of model updates typically decreases as the global model converges, the TDA value does not follow the same trend. Consequently, magnitude-based anomaly detection becomes progressively less effective throughout training due to the decreasing magnitude. In contrast, the variability in TDA values continues to be useful for identifying malicious behavior. + +2) Masked principal sign alignment checking: In backdoor attacks where the manipulations are stealthy, subtle malicious directional information can easily blend into the parameters of models with large magnitude, especially for models with large dimensions, which makes the TDA less useful under strong backdoor attacks since the TDA captures the overall directional information. Therefore, in addition to the TDA, we look into the signs of parameters to provide a finer-grained directional assessment of local model updates. The signs of a vector represent its coordinate-wise direction. In the context of backdoor attacks, the distributions of the signs of malicious model updates differ from those of benign updates. This is particularly significant when the model is close to convergence, at which point the magnitude of model updates becomes very small, making large manipulations on magnitudes impractical. Therefore, manipulation of the direction, or the signs of parameters, can emerge as a more significant and effective strategy. Several works also utilize the signs of models for enhancing backdoor robustness. For example, RLR [38] assigns an opposite global learning rate to a coordinate of the averaged model update if the signs on this coordinate do not consistently align with the majority across all updates. SignGuard [49] calculates the proportions of positive, zero, and negative signs for each model update as the input of a clustering algorithm to identify malicious model updates. However, these methods utilize the signs of all parameters in the model update, regardless of their significance. Consequently, the performance of sign-based metrics can be significantly impacted by those many unimportant parameters, + +especially for large DNN models, leading to an inaccurate representation of the model update's direction. + +To this end, AlignIns utilizes a Masked Principle Sign Alignment (MPSA) checking to inspect the sign alignment degree between the important parameters of each local update and a well-designed principle sign of all local updates. Specifically, to construct the principle sign over local updates, for each coordinate of local updates, we take the majority of the signs across all model updates as the principal sign of this coordinate, which can be mathematically formulated as $p \coloneqq \operatorname{sgn}\left(\sum_{i=1}^{n} \operatorname{sgn}\left(\Delta_i^t\right)\right)$ , where $p \in \mathbb{R}^d$ represents the vector of principal signs and $\operatorname{sgn}(\cdot)$ is the function to take the signs of a vector. Note that the principal sign represents sign-voting results for each coordinate, making it stand for the major direction/dynamic for each coordinate. With this principle sign over local updates, we inspect the alignment of the signs of important parameters of each model update with it. More specifically, we use a Top- $k$ indicator defined as follows to identify the $k$ most important parameters that have the largest absolute values in a vector. + +Definition 1 (Top- $k$ Indicator $\mathrm{Top_k}(\cdot)$ ). For a vector $x\in \mathbb{R}^d$ and a masking parameter $k$ , where $1\leq k\leq d$ , the Top- $k$ indicator $\mathrm{Top_k}(\cdot)$ : $\mathbb{R}^d\to \mathbb{R}^d$ is defined as $[\mathrm{Top_k}(x)]_j = 1$ if $[x]_j\in \xi$ and $[\mathrm{Top_k}(x)]_j = 0$ otherwise, where $\xi = \{|x_{\pi (1)}|,|x_{\pi (2)}|,\dots ,|x_{\pi (k)}|\}$ , here $\pi$ is a permutation of $[d]$ such that $|x_{\pi (i)}|\geq |x_{\pi (i + 1)}|$ for all $1\leq i < d$ . + +The Top- $k$ indicator $\mathrm{Top_k}(\cdot)$ takes each local model update as input and outputs a mask vector in which each element is either 1 or 0 with the same size as the input. To quantify the alignment in sign distributions of each local model update and the principle sign, we define the Sign Alignment Ratio (SAR) as follows. + +Definition 2 (Sign Alignment Ratio). For vectors $x \in \mathbb{R}^d$ and $y \in \mathbb{R}^d$ , the sign alignment ratio $\rho$ of $x$ to $y$ is defined as $\rho := 1 - \| \operatorname{sgn}(x) - \operatorname{sgn}(y) \|_0 / d$ where $\| \cdot \|_0$ is $L_0$ -norm. + +Here, $\rho \in [0,1]$ and a larger $\rho$ indicate a higher degree of alignment between the signs of $x$ and $y$ . Combining $\mathrm{Top_k}(\cdot)$ and SAR, we have the MPSA value $\rho_{i}$ for local update $\Delta_i^t$ formulated as follows: + +$$ +\rho_ {i} := 1 - \left\| \left(\operatorname {s g n} \left(\Delta_ {i} ^ {t}\right) - p\right) \odot \operatorname {T o p} _ {k} \left(\Delta_ {i} ^ {t}\right) \right\| _ {0} / k, \tag {2} +$$ + +where $\odot$ is the Hadamard product, $\mathrm{sgn}(\Delta_i^t) - p$ computes a sign difference vector, capturing the difference between the sign of $\Delta_i^t$ and the principal reference sign $p$ . Since MPSA checking focuses on the important parameters, this difference vector is element-wise multiplied with the Top- $k$ mask derived from $\Delta_i^t$ , effectively setting unimportant coordinates to zero. The $L_0$ -norm is then applied to count the not-aligned elements and with the masking parameter $k$ to ultimately determine the SAR. MPSA checking effectively reveals malicious local updates by combining both + +magnitude and directional information from model updates, allowing for clear differentiation between malicious and benign updates. AlignIns calculates the MPSA value for each update with the principal sign iteratively (line 3-4) and forward them to the following anomaly detection process. + +3) Efficient anomaly detection with MZ_score: W apply robust filtering to remove updates with abnormal TDA and MPSA values. Specifically, we use the robust standardization metric named the Median-based Z-score (MZ_score) [50, 51], detailed in Definition 3, which is a variant of the traditional Z-score standardization metric. + +Definition 3 (MZ_score). For a set of values $X \coloneqq \{x_1, \ldots, x_n\}$ with median $\operatorname{med}(X)$ and standard deviation $\sigma$ , the MZ_score $\lambda_i$ of any $x_i \in X$ is defined as + +$$ +\lambda_ {i} := (x _ {i} - \operatorname {m e d} (X)) / \sigma . \tag {3} +$$ + +MZ_score calculates the number of standard deviations an element is from the median, which may be either positive or negative. In AlignIns, the MZ_score for TDA and MPSA values are computed for each local update (line 6-7). Those with high absolute MZ_score (i.e., outliers) are excluded using two predetermined filtering radii: $\lambda_{c}$ for TDA and $\lambda_{s}$ for MPSA (line 8-9). The use of the MZ_score allows for the adaptation to the varying range of TDA and MPSA values during training, requiring only minimal hyper-parameters. Additionally, by configuring $\lambda_{c}$ and $\lambda_{s}$ , we can manage the trade-off between the robustness and main task accuracy of AlignIns. For example, when robustness is the primary concern in the FL, choosing small $\lambda_{c}$ and $\lambda_{s}$ values is essential to attain the highest robustness. + +Post-filtering model clipping. After filtering, the remaining clients, considered benign, are included in the set $S$ (line 9) and contribute to the model averaging process. However, since our filtering primarily focuses on the direction of model updates (although MPSA does consider magnitude when using the Top- $k$ indicator), there is a risk that it might overlook updates with large magnitudes, such as those updates generated by Scaling attack [4]. To this end, AlignIns re-scales model updates in $S$ by using the median of the $L_{2}$ -norms of these updates as a clipping threshold and aggregates the clipped model updates as the global model update $\tilde{\Delta}$ (line 12-13). It is worth noting that performing clipping before filtering does not affect the filtering results. However, clipping after filtering enhances robustness, as the clipping threshold is more likely determined by benign updates. We discuss the computational cost of AlignIns and compare it with other baselines in Appendix Section 12. + +# 4. Robustness and Propagation Error Analysis + +In this section, we conduct a theoretical analysis of the robustness of AlignIns, as well as its propagation error in FL. + +Before presenting our theoretical results, we make the following assumptions. Note that Assumption 1-2 are commonly used in the theoretical analysis of distributed learning systems [18, 34, 49]. Assumption 3 states a standard measure of inter-client heterogeneity in FL [2, 8, 21]. This heterogeneity complicates the problem of FL with backdoor adversaries, as it may cause the server to confuse malicious updates with flawed model updates from benign clients holding outlier data points [2]. + +Assumption 1 ( $\mu$ -smoothness [34]). Each local objective function $\mathcal{L}_i$ for benign client $i \in \mathcal{B}$ is $\mu$ -Lipschitz smooth with $\mu > 0$ , i.e., for any $x, y \in \mathbb{R}^d$ , $\|\nabla \mathcal{L}_i(x) - \nabla \mathcal{L}_i(y)\| \leq \mu \|x - y\|$ , $\forall i \in \mathcal{B}$ , which further gives: $\mathcal{L}_i(x) - \mathcal{L}_i(y) \leq \nabla \mathcal{L}_i(x)^T(y - x) + (\mu/2)\|x - y\|^2$ , $\forall i \in \mathcal{B}$ . + +Assumption 2 (Unbiased gradient and bounded variance). The stochastic gradient at each benign client is an unbiased estimator of the local gradient, i.e., $\mathbb{E}[g_i(x)] = \nabla \mathcal{L}_i(x)$ and has bounded variance, i.e., for any $x\in \mathbb{R}^d$ $\mathbb{E}\left\| g_i(x) - \nabla \mathcal{L}_i(x)\right\| ^2\leq \nu_i^2,\forall i\in \mathcal{B},$ where the expectation is over the local mini-batches. We also denote $\bar{\nu}\coloneqq (1 / |\mathcal{B}|)\sum_{i\in \mathcal{B}}\nu_i^2$ for convenience. + +Assumption 3 (Bounded heterogeneity). There exist a real value $\bar{\zeta}$ such that for any $x\in \mathbb{R}^d$ $(1 / |\mathcal{B}|)\sum_{i\in \mathcal{B}}\| \nabla \mathcal{L}_i(x) - \nabla \mathcal{L}_{\mathcal{B}}(x)\| ^2\leq \bar{\zeta}$ , where the $\nabla \mathcal{L}_{\mathcal{B}}(x)\coloneqq (1 / |\mathcal{B}|)\sum_{i\in \mathcal{B}}\mathcal{L}_i(x)$ . + +Note that these assumptions apply to benign clients only since malicious clients do not need to follow the prescribed local training protocol of FL. + +# 4.1. Robustness Analysis of AlignIns + +To theoretically evaluate the efficacy of a filtering-based defense method like AlignIns, we introduce the concept of $\kappa$ -robust filtering [50] as defined in Definition 4. Note that Definition 4 is similar to $(f,\kappa)$ -robustness defined in [2, 3], $(\delta_{\max},c)$ -ARAgg defined in [13, 21, 31], and $(f,\lambda)$ -resilient averaging defined in [10]. Our robustness definition adopts a constant upper bound and focuses on quantifying the distance between the output of a filtering-based defense method and the average of all benign updates, which represents the optimal output of such a rule. + +Definition 4 ( $\kappa$ -robust filtering [50]). A filtering-based aggregation rule $F \colon \mathbb{R}^{d \times n} \to \mathbb{R}^d$ is called $\kappa$ -robust if for any vectors $\{x_1, \ldots, x_n\} \in \mathbb{R}^d$ and a benign set $\mathcal{B} \subseteq [n]$ of size $n - m$ , the output $\hat{x} \coloneqq F(x_1, \ldots, x_n)$ satisfies $\| \hat{x} - \bar{x}_{\mathcal{B}} \|^2 \leq \kappa$ , where $\bar{x}_{\mathcal{B}} \coloneqq (1 / |\mathcal{B}|) \sum_{i \in \mathcal{B}} x_i$ , and $\kappa \geq 0$ refers to the robustness coefficient of $F$ . + +Remark 1. The $\kappa$ -robust filtering guarantees that the error of a filtering-based aggregation rule in estimating the average of the benign inputs is upper-bounded by a constant $\kappa$ . + +This measure provides a quantitative way to assess the robustness of the filtering-based aggregation rule. A smaller $\kappa$ indicates a smaller discrepancy between the empirical output and the optimal output of $F$ . If $F$ identifies and removes all malicious inputs and keeps all benign inputs, we have $\kappa = 0$ , achieving the highest level of robustness. + +Based on Definition 4, we prove that the proposed AlignIns, when applied to $n$ input models, of which $m$ are malicious, satisfies $\kappa$ -robust filtering with $\kappa = O(1 + m / (n - 2m))$ , as stated in Lemma 1. + +Lemma 1 ( $\kappa$ -robustness of AlignIns). Under Assumption 2-3, assume $n > 1$ , $0 \leq m < n / (3 + \epsilon)$ with a positive constant $\epsilon$ , AlignIns satisfies $\kappa$ -robust filtering with + +$$ +\begin{array}{l} \kappa = \left(1 + m / \left(n - 2 m\right)\right) \left(\left(2 / \epsilon + 1\right) \left(2 \bar {\nu} + \bar {\zeta}\right) + 8 c ^ {2}\right) \\ = O \left(1 + m / (n - 2 m)\right), \\ \end{array} +$$ + +if the local learning rate satisfies $\eta \leq 1 / 2\tau$ and there exist two sufficiently large filtering radii such that $|\mathcal{S}|\geq n - 2m$ . Here, $\bar{\nu}$ and $\zeta$ represent the gradient variance and local divergence, respectively; $c$ is the clipping threshold. + +Proof. The proof is given in Appendix Section 13.2. + +![](images/93a7b4bc155178e2c296c7ed12823c6a8995c81b3dbc88933aa73046c9a4a5f2.jpg) + +Remark 2. The condition on $S$ highlights the importance of selecting appropriate filtering radii. These radii cannot be zero or too small; otherwise, only the median or a few model updates will be averaged to update the global model. This can lead to a performance drop due to the lack of model updates. Moreover, the model clipping threshold $c$ can effectively control the magnitude of potential malicious updates in the selection set, thus preventing $\kappa$ from exploding due to updates with large magnitudes. Indeed, in the literature, model clipping has demonstrated its effectiveness in mitigating the impact of malicious model updates [39, 49, 53]. In addition, the result also shows the importance of reducing the gradient variance of stochastic gradient and local heterogeneity to enhance robustness performance. Our work is orthogonal to existing variance or divergence reduction methods [13, 30] and can be combined with them to further improve the robustness. We argue that AlignIns enjoys comparable robustness with several classical defense methods, for example, non-filtering-based method RFA [40] ( $O(1 + m / (n - 2m))^2$ ), and filtering-based method Krum [6] ( $O(1 + m / (n - 2m))^1$ ). + +# 4.2. Propagation Error of AlignIns in FL + +Based on the $\kappa$ -robustness of AlignIns, we analyze its propagation error during training. Specifically, let $\theta$ denote the + +model trained with AlignIns under backdoor attacks, where $m$ of the $n$ clients are malicious, and let $\theta^{*}$ denote a model trained exclusively with benign clients using FedAvg. Starting from the same initial model $\theta^0$ , we aim to measure the difference between these two models after $T$ rounds of training, defined as $\| \theta^T - \theta^{T,*} \|$ , referred to as the propagation error [39]. Let $\theta^{t, + }$ represent the output of AlignIns at the $t$ -th round. If the highest level of robustness is not achieved at round $t$ , the error $\| \theta^t - \theta^{t, + } \|$ will propagate to the next round, resulting in a shifted starting point for local SGD at round $t + 1$ . This discrepancy will gradually widen the gap between $\theta$ and $\theta^{*}$ . Our analysis captures this robustness error at each round and examines its cumulative effect after $T$ rounds. In Lemma 2, we show that, assuming Assumption 1-3 hold, the propagation error of AlignIns remains bounded. + +Lemma 2 (Bounded Propagation Error). Let Assumption 1-3 hold. If the local learning rate $\eta \leq 1 / 2\tau$ , the propagation error of AlignIns is bounded as + +$$ +\left\| \theta^ {T} - \theta^ {T, *} \right\| \leq \phi (T) (2 + 3 \mu^ {2}) ^ {\phi (T)} (\kappa + 2 \bar {\nu}), +$$ + +under backdoor attacks where $m$ out of $n$ clients are malicious. Here, $\kappa$ is given in Lemma 1, $\phi(T) = \sum_{t=1}^{T} (\alpha^t)^2$ is the cumulative global learning rate, and $\alpha^t$ is a global learning rate scheduler, possibly static. + +Proof. The detailed proof is in Appendix Section 13.3. $\square$ + +Remark 3. When $T \to \infty$ , $\phi(T)$ converges to a constant for learning rate schedulers like exponential decay, which implies a constant bounded on propagation error. The result shows that besides the robustness error bounded by $\kappa$ , the error of local gradient estimation, which is bounded by $\bar{\nu}$ , in local SGD also propagates during the training, increasing the overall propagation error. This is because at any round $t$ , if the benign starting point for local training is the same, i.e., $\theta^t = \theta^{t,*}$ , then the local gradients/model updates on $\theta^t$ and $\theta^{t,*}$ will be identical for benign clients. Therefore, the gap between the updated global models $\theta^{t+1}$ and $\theta^{t+1,*}$ solely depends on the robustness error (i.e., the effectiveness of AlignIns in filtering out malicious updates). However, if $\theta^t \neq \theta^{t,*}$ , which means $\theta^t$ is not benign and has been poisoned in previous rounds, the local gradients/model updates on $\theta^t$ and $\theta^{t,*}$ will differ for benign clients, resulting in an error bounded by the gradient variance, even if AlignIns successfully filters out all malicious updates. Hence, to further reduce the propagation error, AlignIns can be combined with variance-reduction methods like [13, 30], which is orthogonal to AlignIns. + +# 5. Experimental Settings + +Datasets and System Settings: In our experiments, we primarily conduct evaluation on CIFAR-10 [24] and CIFAR- + +100 [24] datasets. Additionally, we present the superior performance of AlignIns on other benchmark datasets (MNIST [25], FMNIST [47], Sentiment140 [12], and TinyImageNet) in Appendix Section 10.5-10.6. We simulate a cross-silo FL with 20 clients for all datasets. Additionally, we also present the superior performance of AlignIns on a cross-device FL system with 100 clients and client sampling. We consider both IID and non-IID settings. For IID settings, we distribute the training data evenly to clients. For non-IID settings, we follow [17, 19, 20] to use Dirichlet distribution $\text{Dir}(\beta)$ to skew the local data distribution with a default non-IID degree $\beta = 0.5$ . + +Learning Settings: We use SGD as the local solver, with the initial learning rates set as $\alpha = 1.0$ and $\eta = 0.1$ , and the local training epoch is set as 2. The training round is set as $T = 100$ for CIFAR-100 and $T = 150$ for CIFAR-10. For AlignIns, the default filtering radii are set as $\lambda_{c} = 1.0$ and $\lambda_{s} = 1.0$ . We provide the study of the impact of filtering radii in Appendix Section 11. The default masking parameter is set as $k = 0.3 \times d$ so that the Top-30% of model parameters are used for the MPSA checking. + +Evaluated Attack Methods: We consider 5 SOTA backdoor attacks, including Badnet [14], DBA [48], Scaling [4], PGD [46], and Neurotoxin [54]. We provide the detailed attack model and settings for attack methods in Appendix Section 8.1-8.2. We present the results of AlignIns under the strong trigger-optimization attack [9] in Appendix Section 10.2. Moreover, we study the potential adaptive attacks tailored to AlignIns and untargeted attacks [49] in Appendix Section 10.3-10.4, although these are beyond the scope of this work. To achieve effective backdoors (achieving a BA over $60\%$ [22]), malicious clients poison $r = 50\%$ of their local data, where $r$ is the data poisoning ratio. The attack ratio is set to $20\%$ by default, which means $20\%$ of the clients in the system are malicious. Experiments of AlignIns on defending backdoor attacks with various attack ratios are given in Appendix Section 10.7. + +Evaluated Defense Methods: We present the detailed defense model in Appendix Section 9. We comprehensively compare AlignIns with the non-robust baseline FedAvg and six existing SOTA defense methods, including RLR [38], RFA [40], Multi-Krum (MKrum) [6], Foolsgold [11], Multi-Metric (MM) [19], and Lockdown [20]. Additionally, we compare our approach with an ideally perfect filtering-based robust aggregation, FedAvg*, which is assumed to perfectly identify and remove all malicious updates and average all the benign updates to update the global model. + +Evaluation Metrics: We use three metrics to evaluate the performance of defense methods, including main task accuracy (MA), which measures the percentage of clean test samples that are accurately classified to their ground truth labels by the global model; backdoor attack accuracy (BA), which measures the percentage of triggered + +Table 1. The clean MA, BA, and RA results of baselines and AlignIns on IID CIFAR-10 and CIFAR-100 datasets. Results are shown in %. + +
    Dataset (Model)MethodsClean MA↑BadnetDBANeurotoxinAvg. BA↓Avg. RA↑
    BA↓RA↑BA↓RA↑BA↓RA↑
    r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5
    CIFAR-10 (ResNet9 [16])FedAvg89.4751.5667.6145.7931.2456.2170.4240.6227.9244.8979.4050.4119.6061.6835.93
    FedAvg*89.472.062.0685.6085.602.062.0685.6085.602.062.0685.6085.602.0685.60
    RLR79.162.322.0076.7273.333.013.0477.0977.133.123.8773.9873.292.8935.93
    RFA87.7370.6790.2427.749.2647.6766.9747.2930.1481.2796.1317.113.6975.4922.54
    MKrum87.0281.1097.4718.112.512.174.3383.8979.1065.2889.1831.8110.0156.5937.57
    Foolsgold89.4969.1468.8429.6430.1051.1860.7344.8336.082.912.8285.2784.7642.6051.78
    MM89.1541.1993.8853.886.0152.2451.3043.5445.0843.9283.9251.1215.1161.0835.79
    Lockdown88.566.3110.8281.8879.5011.636.0378.8275.773.403.2782.7383.146.9180.31
    AlignIns88.641.912.2186.0385.572.132.1485.7785.882.662.2085.4685.312.2185.67
    CIFAR-100 (VGG9 [41])FedAvg64.2999.2099.540.680.3599.2599.360.640.5494.4193.364.365.2897.521.98
    FedAvg*64.290.620.6253.0353.030.620.6253.0353.030.620.6253.0353.030.6253.03
    RLR44.3496.5799.851.810.1224.4194.0824.973.220.040.0029.0729.7352.4914.82
    RFA53.924.321.4537.6039.882.150.7839.7341.5199.7489.590.216.5933.0127.59
    MKrum51.281.331.5438.1338.491.361.5437.8537.9199.8299.870.120.1036.2125.49
    Foolsgold64.1399.0299.300.830.5799.1599.390.740.5121.796.2142.0646.4070.8115.19
    MM63.2699.5199.870.370.1199.5399.700.350.1998.4898.971.320.8399.340.53
    Lockdown62.8855.2124.1428.4543.0634.3749.0234.0627.930.850.6742.6647.0427.3837.20
    AlignIns63.450.790.7150.4551.530.450.5750.8152.080.490.5351.1150.660.5951.11
    + +samples that are misclassified to the target label by the global model; and robustness accuracy (RA), which measures the percentage of triggered samples that are accurately classified to their ground-truth labels by the global model, despite the presence of the trigger. A good defense method should achieve high MA and RA and low BA. + +# 6. Experimental Results + +Main results in IID setting. In Table 1, we report the performance of various defense methods under no attack (denoted by "Clean"), Badnet, DBA, and Neurotoxin attacks for IID CIFAR-10 and CIFAR-100. The best results are highlighted in bold font, and the second best results are underlined. Overall, AlignIns demonstrates superior performance compared with other baselines as it achieves the best average BA and RA over three attack methods. Specifically, for CIFAR-10, while RLR offers a satisfactory degree of robustness (an average BA of $2.89\%$ ), it suffers from a notable decline in RA, with an average reduction of $49.74\%$ in comparison to AlignIns. This drop results from RLR's strategy of flipping the global learning rate for parameters in the aggregated model update that are inconsistent with the majority's sign, consequently resulting in the loss of benign local parameters. AlignIns, however, demonstrates outstanding performance with consistently low BA and high RA, ranking first or second among its counterparts. Notably, compared to the second-best results, AlignIns achieves an average improvement of $+0.68\%$ in BA and $+5.36\%$ in RA. Similarly, superior results are observed in CIFAR-100 experiments, where AlignIns significantly out + +![](images/64eb563d0e978f803f7dad56c20c2c5767d4f26b4dda5b7c04fce5175db15bf0.jpg) +Figure 1. RA of AlignIns under various non-IID degrees, compared with Lockdown, RFA, and RLR under Neurotoxin. + +![](images/7b3d920a229ba2f5069fc312ff3945dc5092b8b6ae096bf52f644abbde4a492d.jpg) + +performs other methods in both BA and RA. These results underscore AlignIns' effectiveness as a promising defense method for protecting FL from various backdoor attacks, significantly enhancing the trustworthiness of FL systems. + +Effectiveness under various Non-IID degrees. We examine the defense performance of AlignIns across various degrees of non-IIDness, a factor that significantly complicates backdoor defense. Figure 1 presents the RA of AlignIns under different non-IID conditions on the CIFAR-10 dataset, compared with Lockdown, RFA, and RLR. The experiments were conducted using the Neurotoxin attack, with both a default attack ratio of $20\%$ and a higher attack ratio of $30\%$ . The Dirichlet parameter $\beta$ varies from 0.1 to 1.0, where a smaller $\beta$ suggests a more intense non-IIDness. We observe that only AlignIns consistently attains robustness against strong Neurotoxin attacks with a varying $\beta$ . Specifically, as $\beta$ increases, the RA of AlignIns, Lockdown, and RLR increases correspondingly. However, + +Table 2. Performance of different methods in cross-device FL settings on IID and non-IID CIFAR-10 datasets under Badnet attack. + +
    MethodCIFAR-10 (IID)CIFAR-10 (Non-IID)Avg. RA↑
    MA↑BA↓RA↑MA↑BA↓RA↑
    Foolsgold82.9999.990.0167.9799.990.000.01
    Lockdown83.5299.990.0073.9199.920.060.00
    RLR56.814.6755.3841.5614.1238.1746.78
    AlignIns85.010.9282.7479.511.9075.8179.28
    + +AlignIns outperforms them with a consistently higher RA. When the attack ratio rises to $30\%$ , RLR, RFA, and Lockdown fail to provide satisfactory robustness. However, our method AlignIns still demonstrates its robustness under various non-IIDness, even in an extremely non-IID case when $\beta = 0.1$ . AlignIns is designed to examine the alignment of model updates on important parameters only, hence, it mitigates the challenge of identifying malicious model updates in non-IID settings where updates are heterogeneous, thereby achieving superior performance in even extreme non-IID settings compared with existing methods. We also provide more comprehensive results of AlignIns and other baselines on non-IID datasets in Appendix Section 10.1. + +Effectiveness of AlignIns in cross-device FL with client sampling. While most of our experiments focus on the cross-silo FL setting, evaluating the cross-device FL scenario is also essential given the large number of clients involved. For this purpose, we simulate a cross-device FL environment with 100 clients, where the server randomly selects 20 clients per round for training. We conduct experiments on IID and non-IID CIFAR-10 cases using Foolsgold, Lockdown, RLR, and AlignIns and summarize the MA, BA, and RA results in Table 2. The results show that both Foolsgold and Lockdown completely lose their effectiveness in both cases, achieving an average RA of nearly $0.00\%$ . RLR achieves a moderate level of backdoor robustness but at the cost of main task accuracy, with an average MA of only $49.19\%$ . In contrast, AlignIns performs robustly in the cross-device FL setting, achieving a significantly lower BA in both IID $(0.92\%)$ and non-IID $(1.90\%)$ cases compared with other methods. Furthermore, AlignIns achieves an average RA of $79.28\%$ . These results highlight AlignIns's ability to maintain both accuracy and robustness in challenging cross-device FL scenarios, underscoring its adaptability and effectiveness in real-world applications. + +Ablation study of AlignIns. As AlignIns consists of two alignment components (TDA and MPSA) to improve backdoor robustness, we conduct a detailed ablation study to investigate how each component functions. Experimental results on IID and non-IID CIFAR-10 datasets under Badnet attack are summarized in Table 3. (i) Component ablation. We observe that using MPSA or TDA alone in IID scenarios only slightly reduces robustness compared to AlignIns, as benign updates follow consistent patterns that + +Table 3. Performance of different components in AlignIns. + +
    ConfigurationCIFAR-10 (IID)CIFAR-10 (non-IID)Avg. RA↑
    MA↑BA↓RA↑MA↑BA↓RA↑
    MPSA(30%)88.552.8885.0280.6594.075.7945.41
    TDA88.563.8283.8883.8677.5821.3152.60
    MPSA(70%)+TDA88.142.1885.7783.8461.8331.8658.82
    MPSA(50%)+TDA88.052.2185.4684.1277.9319.9652.71
    MPSA(30%)+TDA88.142.0485.8283.6547.0445.3065.56
    AlignIns88.052.4485.2782.881.7081.3283.30
    AlignIns+88.482.1485.7483.311.1182.1383.94
    + +enable effective detection by a single metric. In non-IID settings, however, where local updates diverge, neither MPSA nor TDA alone provides sufficient robustness. When combined, MPSA and TDA improve BA and RA from $94.07\%$ and $5.79\%$ to $47.04\%$ and $45.30\%$ , respectively, showing their complementary strengths. AlignIns further enhances robustness by integrating MPSA, TDA, and post-filtering model clipping, which normalizes benign update magnitudes and improves malicious update detection, yielding the highest average RA. (ii) Masking parameter $k$ ablation. We try to involve more non-essential parameters in the MPSA checking by using the Top- $50\% / 70\%$ of parameters to calculate MPSA values. By doing so, the effectiveness of malicious identification is reduced. In contrast, when using the Top- $30\%$ of parameters, compared to the Top- $50\%$ case, BA and RA are improved by $+30.89\%$ and $+25.34\%$ , respectively. This demonstrates the effectiveness of focusing important parameters when calculating MPSA in improving the filtering accuracy, especially in non-IID cases. (iii) Variance reduction method further enhances robustness. Our theoretical results reveal the impact of variance reduction techniques on improving the robustness of AlignIns and reducing the propagation error of AlignIns in FL, we additionally test a variant of AlignIns named "AlignIns+", in which local SGD with momentum is used to reduce the local gradient variance with momentum coefficient 0.1. AlignIns+ achieves a slightly better performance than AlignIns, verifying our theoretical results. + +# 7. Conclusion + +We introduce a novel method AlignIns to defend against backdoor attacks in FL. AlignIns examines each model update's direction at different granularity levels, thus effectively identifying stealthy malicious model updates and filtering them out to avoid them participating in aggregation in FL to enhance robustness. We provide a theoretical analysis of AlignIns' robustness and its impact on propagation errors in FL. Extensive experiments demonstrate the effectiveness of AlignIns, with results showing that it outperforms SOTA defense methods against various advanced attacks. + +Acknowledgment. This work was supported by the Nevada System of Higher Education under grant NSHE-24-37. + +# References + +[1] Manaar Alam, Esha Sarkar, and Michail Maniatakos. Perdoor: Persistent non-uniform backdoors in federated learning using adversarial perturbations. arXiv preprint arXiv:2205.13523, 2022. 2 +[2] Youssef Allouah, Sadegh Farhadkhani, Rachid Guerraoui, Nirupam Gupta, Rafael Pinot, and John Stephan. Fixing by mixing: A recipe for optimal byzantine ml under heterogeneity. In International Conference on Artificial Intelligence and Statistics, pages 1232-1300. PMLR, 2023. 5 +[3] Youssef Allouah, Rachid Guerraoui, Nirupam Gupta, Rafael Pinot, and Geovani Rizk. 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PMLR, 2022. 1, 2, 6, 12 \ No newline at end of file diff --git a/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/images.zip b/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..3e3188d475cc408fe806352e7640e977cf2ea711 --- /dev/null +++ b/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:08939e4f268953ca548daa3f1a31bdbf8e6ef173638ba3e55e3b5fbb6a6239bb +size 299981 diff --git a/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/layout.json b/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..68cd4220e276d560772b00300630ec959c85f2bd --- /dev/null +++ b/2025/Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection/layout.json @@ -0,0 +1,10653 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 72, + 102, + 539, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 102, + 539, + 140 + ], + "spans": [ + { + "bbox": [ + 72, + 102, + 539, + 140 + ], + "type": "text", + "content": "Detecting Backdoor Attacks in Federated Learning via Direction Alignment Inspection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 190, + 161, + 419, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 190, + 161, + 419, + 205 + ], + "spans": [ + { + "bbox": [ + 190, + 161, + 419, + 205 + ], + "type": "text", + "content": "Jiahao Xu Zikai Zhang Rui Hu University of Nevada, Reno {jiahaox,zikaiz,ruihu}@unr.edu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "spans": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 257, + 297, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 257, + 297, + 533 + ], + "spans": [ + { + "bbox": [ + 55, + 257, + 297, + 533 + ], + "type": "text", + "content": "The distributed nature of training makes Federated Learning (FL) vulnerable to backdoor attacks, where malicious model updates aim to compromise the global model's performance on specific tasks. Existing defense methods show limited efficacy as they overlook the inconsistency between benign and malicious model updates regarding both general and fine-grained directions. To fill this gap, we introduce AlignIns, a novel defense method designed to safeguard FL systems against backdoor attacks. AlignIns looks into the direction of each model update through a direction alignment inspection process. Specifically, it examines the alignment of model updates with the overall update direction and analyzes the distribution of the signs of their significant parameters, comparing them with the principle sign across all model updates. Model updates that exhibit an unusual degree of alignment are considered malicious and thus be filtered out. We provide the theoretical analysis of the robustness of AlignIns and its propagation error in FL. Our empirical results on both independent and identically distributed (IID) and non-IID datasets demonstrate that AlignIns achieves higher robustness compared to the state-of-the-art defense methods. The code is available at https://github.com/JiaiahaoXU/AlignIns." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 560, + 135, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 560, + 135, + 572 + ], + "spans": [ + { + "bbox": [ + 55, + 560, + 135, + 572 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 296, + 715 + ], + "type": "text", + "content": "Unlike traditional centralized training methods, which require gathering and processing all data at a central location such as a server, Federated Learning (FL) [32], as a decentralized training paradigm, allows a global model to learn from data distributed across various local clients, thereby achieving the goal of privacy-preserving. During training, the server distributes the global model to local clients, and each client trains the received global model using its local dataset, and then submits its local model update to the server for global model refinement. FL has been applied in various fields, including healthcare[35], finance [28], and remote" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 232, + 517, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 232, + 517, + 243 + ], + "spans": [ + { + "bbox": [ + 313, + 232, + 517, + 243 + ], + "type": "text", + "content": "sensing [27], where local data privacy is essential." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 245, + 555, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 245, + 555, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 245, + 555, + 484 + ], + "type": "text", + "content": "Although promising, the distributed nature of FL systems makes them vulnerable to a range of advanced poisoning attacks [15, 26, 45]. This vulnerability primarily stems from the server's lack of close monitoring of the local data and the training algorithm on clients. Consequently, this drawback allows attackers to compromise the data of local clients or interfere with the training algorithm, enabling them to inject malicious local model updates that distort the performance of the global model. For example, backdoor attacks [4, 14, 46, 48, 54] have gained significant attention due to their stealthiness and practical effectiveness. In detail, backdoor attacks in FL seek to preserve the performance of the global model on clean inputs (i.e., the main task), while inducing the global model to make incorrect predictions on inputs that contain a certain predefined feature (i.e., the backdoor task). As backdoor attacks maintain the main task and the backdoor task simultaneously, the malicious local model updates are statistically similar to benign ones [36, 46] (poison-coupling effect [20]), making anomaly detection more challenging on the server side." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "content": "Existing defense methods (i.e., aggregation rule) usually aim to identify malicious model updates and filter them out to achieve better robustness by magnitude-based metrics extracted from local model updates (e.g., Manhattan distance [19, 22] and Euclidean distance [6, 15]). However, magnitude-based metrics are ineffective in distinguishing stealthy backdoor attacks where benign and malicious model updates are usually similar in magnitude. Additionally, when the global model tends to converge, the magnitude of each model update becomes very small, making effective malicious manipulation on magnitude negligible. To this end, some works employ Cosine similarity to check the pair-wise directional information of model updates [11, 36, 42]. However, pair-wise Cosine similarity between two model updates only captures their general directional similarity and overlooks fine-grained information (e.g., signs of parameters), resulting in limited robustness. In addition, in FL settings with non-IID data, the pair-wise Cosine similarity of model updates can be easily perturbed" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20654" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "by the naturally diverse benign model updates. Furthermore, there is a deficiency in theoretical analysis within the literature concerning the effects of data heterogeneity on defense methods deployed by the server in FL." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 121, + 295, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 121, + 295, + 382 + ], + "spans": [ + { + "bbox": [ + 56, + 121, + 295, + 382 + ], + "type": "text", + "content": "In this work, we propose a novel defense method designed to defend against backdoor attacks in FL, named AlignIns (Direction Alignment Inspection), which examines local model updates for directional alignment at different granularity levels to identify malicious updates. Specifically, after receiving all model updates from clients, AlignIns evaluates each update by (1) inspecting temporal directional alignment with the global model of the latest round with Cosine similarity and (2) assessing more fine-grained sign alignment with the principal sign across all updates with a novel metric sign alignment ratio. Particularly, when calculating the sign alignment ratio, AlignIns focuses on the signs of important parameters in each update to accurately capture alignment information. Using these two directional metrics, AlignIns performs anomaly detection with the robust MZ_score which requires minimal hyperparameters to filter updates with unusual directional patterns out. Finally, AlignIns clips the remaining updates to mitigate the impact of updates with abnormally large magnitudes. We also provide a theoretical analysis of AlignIns' robustness and its propagation error in FL. The main contributions of this work are three folds:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 383, + 295, + 574 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 383, + 295, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 383, + 295, + 455 + ], + "spans": [ + { + "bbox": [ + 55, + 383, + 295, + 455 + ], + "type": "text", + "content": "- We present a novel defense method, AlignIns, to defend against backdoor attacks in FL. To the best of our knowledge, AlignIns is the first defense method in FL that analyzes the directional patterns of local model updates at different levels of granularity. AlignIns is fully compatible with existing FL frameworks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 455, + 295, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 295, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 295, + 514 + ], + "type": "text", + "content": "- To the best of our knowledge, we provide the first theoretical robustness analysis for a filtering-based defense method against backdoor attacks under non-IID data in FL. Moreover, we prove that the propagation error of AlignIns is bounded during the training of FL." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 514, + 295, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 295, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 295, + 574 + ], + "type": "text", + "content": "- We empirically evaluate the effectiveness of AlignIns through extensive experiments on both IID and non-IID datasets against various state-of-the-art (SOTA) backdoor attacks. Compared to existing SOTA defense methods, AlignIns exhibits superior robustness." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 586, + 235, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 235, + 600 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 235, + 600 + ], + "type": "text", + "content": "2. Background and Related Works" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": "Federated Learning. In a typical FL system, a central server controls a set of " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " clients to train a global model " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " collaboratively. The objective of FL is to solve the following optimization problem: " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\min_{\\theta}(1/n)\\sum_{i=1}^{n}\\mathcal{L}_i(\\theta;\\mathcal{D}_i)" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i(\\cdot)" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " denotes the learning objective specific to client " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " denotes the local dataset for client " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": ". The commonly used method to solve this problem iteratively is FedAvg [33]. In detail, at round " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " of FedAvg, each client " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "i \\in [n]" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": " downloads the current global model " + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\theta^t" + }, + { + "bbox": [ + 55, + 605, + 295, + 714 + ], + "type": "text", + "content": ", updates it" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "by optimizing its local objective, resulting in " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "\\theta_i^t" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": ", and transmits its model update " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "\\Delta_i^t = \\theta_i^t - \\theta^t" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " to the server. The server then refines the global model by averaging these updates as follows: " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "\\theta^{t + 1} = \\theta^t + (1 / n)\\sum_{i = 1}^n\\Delta_i^t" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": ". This process continues until the global model reaches convergence." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 134, + 553, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 134, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 134, + 553, + 312 + ], + "type": "text", + "content": "Backdoor attacks in FL. Empirical evidence has shown that FL is vulnerable to backdoor attacks [4, 9, 14, 23, 37, 46, 48, 52, 54] due to its lack of access to local training data [4]. For instance, Projected Gradient Descent (PGD) attack [46] periodically projects the local model onto a small sphere centered around the global model from the previous training round, with a predefined radius. Distributed Backdoor Attack (DBA) [48] decomposes the centralized trigger into several smaller, distributed local triggers. Each poisoned client uses one of these local triggers, but during testing, the adversary injects the full trigger into the test samples. Recently, research has focused on trigger-optimization backdoor attacks [1, 9, 29, 37, 52], which aim to search optimized triggers to enhance the effectiveness and stealthiness." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 315, + 553, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 553, + 375 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 553, + 375 + ], + "type": "text", + "content": "Defending against backdoor attacks in FL. Generally, based on how defense methods mitigate the impact of malicious updates, existing defense methods can be categorized into filtering-based methods [6, 7, 19, 22, 36, 42, 50, 51] and influence-reduction methods [11, 20, 38, 40, 41]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 376, + 553, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 553, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 553, + 556 + ], + "type": "text", + "content": "1) influence-reduction methods aim to integrate all model updates but employ strategies to reduce the impact of malicious updates. For instance, " + }, + { + "bbox": [ + 313, + 376, + 553, + 556 + ], + "type": "inline_equation", + "content": "RFA" + }, + { + "bbox": [ + 313, + 376, + 553, + 556 + ], + "type": "text", + "content": " [40] is proposed to use the geometric median of local models as the aggregation result, under the assumption that malicious models significantly deviate from benign models. Foolsgold [11] assumes that the malicious updates are consistent with each other. It assigns aggregation weights to model updates based on the maximum Cosine similarity between the last layers of pairwise model updates. A higher Cosine similarity value indicates a higher probability that the updates are malicious, leading to smaller aggregation weights being assigned. The effectiveness of influence-reduction methods is inherently limited because they cannot eliminate the impact of malicious activity, leading to a significant risk of compromise." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 558, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 553, + 713 + ], + "type": "text", + "content": "2) Filtering-based methods aim to detect and remove malicious local model updates before aggregation thus attempting to achieve the highest robustness. For example, Multi-Krum [6] selects the multiply reliable local model updates for aggregation by identifying the one with the smallest sum of squared Euclidean distances to all other updates. Multi-Metrics [19] explores the combination of Manhattan distance, Euclidean distance, and Cosine similarity for each update to collaboratively filter out outliers. However, due to the dual objectives of backdoor attacks—that is, maintaining accuracy on the main task while maximizing accuracy on the backdoor task—malicious updates must mimic benign model updates, important weights for the main task" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20655" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 58, + 88, + 294, + 326 + ], + "blocks": [ + { + "bbox": [ + 63, + 76, + 157, + 87 + ], + "lines": [ + { + "bbox": [ + 63, + 76, + 157, + 87 + ], + "spans": [ + { + "bbox": [ + 63, + 76, + 157, + 87 + ], + "type": "text", + "content": "Algorithm 1: AlignIns" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "lines": [ + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "spans": [ + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": "Input: Set of " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " local model updates " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\{\\Delta_i^t\\}_{i=1}^n" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " of them are malicious, global model " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\theta^t" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": ", TDA radius " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\lambda_c" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": ", MPSA radius " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\lambda_s" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": ", extraction parameter " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " \nOutput: Aggregated model update " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\widetilde{\\Delta}" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " \n1 Initialize benign set " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "S \\gets \\emptyset" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " \n2 " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\omega \\gets \\{\\mathrm{TDA}(\\Delta_i^t, \\theta)\\}_{i=1}^n" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\triangleleft" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " by Equation (1) \n3 " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "p \\gets \\operatorname{sgn}(\\sum_{i=1}^n \\operatorname{sgn}(\\Delta_i^t))" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " \n4 " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\rho \\gets \\{\\mathrm{MPSA}(\\Delta_i^t, p, k)\\}_{i=1}^n" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\triangleleft" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " by Equation (2) \n5 for " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "i \\in [n]" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " do \n6 " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\lambda_{i,c} \\gets \\mathrm{MZ\\_score}(\\omega_i, \\omega)" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\triangleleft" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " by Equation (3) \n7 " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\lambda_{i,s} \\gets \\mathrm{MZ\\_score}(\\rho_i, \\rho)" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\triangleleft" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " by Equation (3) \n8 if " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "|\\lambda_{i,c}| \\leq \\lambda_c" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "|\\lambda_{i,s}| \\leq \\lambda_s" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " then \n9 " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\mid S \\gets S \\cup \\{i\\}" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " \n10 end \n11 end \n12 " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "c \\gets \\operatorname{med}(\\{\\| \\Delta_i^t\\| \\}_{i \\in S})" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " \n13 " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\widetilde{\\Delta} \\gets (1 / |\\mathcal{S}|) \\sum_{i \\in S} (\\Delta_i^t \\cdot \\min\\{1, c / \\| \\Delta_i^t\\|\\})" + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "text", + "content": " \n14 return " + }, + { + "bbox": [ + 58, + 88, + 294, + 326 + ], + "type": "inline_equation", + "content": "\\widetilde{\\Delta}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 55, + 341, + 295, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 341, + 295, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 341, + 295, + 413 + ], + "type": "text", + "content": "typically have large values and can dominate the magnitude of a model update. As a result, magnitude-based detection methods become ineffective against backdoor attacks. Additionally, methods that rely solely on Cosine similarity also show limited effectiveness since they capture general directional alignment and overlook finer-grained information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 426, + 189, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 189, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 189, + 441 + ], + "type": "text", + "content": "3. Our Solution: AlignIns" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 448, + 295, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 448, + 295, + 532 + ], + "spans": [ + { + "bbox": [ + 55, + 448, + 295, + 532 + ], + "type": "text", + "content": "Our method, AlignIns, detailed in Algorithm 1, mitigates the impact of malicious updates through a two-step process. First, direction alignment inspection is applied to examine each local model update comprehensively in terms of direction. Second, post-filtering model clipping is used to further enhance the robustness of AlignIns on defending potential magnitude-based attack methods before final aggregation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 533, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 295, + 676 + ], + "type": "text", + "content": "Direction alignment inspection. Existing defense methods against backdoor attacks in FL primarily focus on examining the magnitude (e.g., Manhattan distance and Euclidean distance) and the overall direction (e.g., Cosine similarity) of model updates. However, backdoor attacks are designed to maintain the main task accuracy, making the magnitude difference between malicious and benign updates nearly indistinguishable. Additionally, advanced attacks such as PGD [46] and Lie [5] attacks are specifically crafted to bypass magnitude-based defenses. Therefore, AlignIns focuses on direction-based analysis to identify suspect updates, using two processes described below." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "1) Temporal direction alignment checking: Since malicious clients need to maintain both the main task and the backdoor task, the optimization direction of a malicious" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "local model tends to deviate from that of benign models. AlignIns leverages this deviation and performs a Temporal Direction Alignment (TDA) checking, which calculates the Cosine similarity between a local update and the latest global model (line 2 in Algorithm 1) to assess the general alignment level of each local update. Formally, the TDA value " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "\\omega_{i}" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": " of a local model update " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "\\Delta_i^t" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": " is calculated as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 375, + 164, + 553, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 164, + 553, + 178 + ], + "spans": [ + { + "bbox": [ + 375, + 164, + 553, + 178 + ], + "type": "interline_equation", + "content": "\\omega_ {i} := \\left\\langle \\Delta_ {i} ^ {t}, \\theta^ {t} \\right\\rangle / \\left(\\| \\Delta_ {i} ^ {t} \\| \\| \\theta^ {t} \\|\\right). \\tag {1}", + "image_path": "8fd37d02172f269ea4f62a9c68c1d90206f0824413c990055c542f172f583d84.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 186, + 555, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 186, + 555, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 186, + 555, + 354 + ], + "type": "text", + "content": "We use local model updates rather than local models because our goal is to measure how closely each client's updates align with the direction of the global model. Local model updates specifically capture these incremental adjustments. Notably, malicious clients tend to exhibit similar TDA values, which differ from those of benign clients, creating an opportunity for detection. It is important to note that while the magnitude of model updates typically decreases as the global model converges, the TDA value does not follow the same trend. Consequently, magnitude-based anomaly detection becomes progressively less effective throughout training due to the decreasing magnitude. In contrast, the variability in TDA values continues to be useful for identifying malicious behavior." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 354, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 715 + ], + "type": "text", + "content": "2) Masked principal sign alignment checking: In backdoor attacks where the manipulations are stealthy, subtle malicious directional information can easily blend into the parameters of models with large magnitude, especially for models with large dimensions, which makes the TDA less useful under strong backdoor attacks since the TDA captures the overall directional information. Therefore, in addition to the TDA, we look into the signs of parameters to provide a finer-grained directional assessment of local model updates. The signs of a vector represent its coordinate-wise direction. In the context of backdoor attacks, the distributions of the signs of malicious model updates differ from those of benign updates. This is particularly significant when the model is close to convergence, at which point the magnitude of model updates becomes very small, making large manipulations on magnitudes impractical. Therefore, manipulation of the direction, or the signs of parameters, can emerge as a more significant and effective strategy. Several works also utilize the signs of models for enhancing backdoor robustness. For example, RLR [38] assigns an opposite global learning rate to a coordinate of the averaged model update if the signs on this coordinate do not consistently align with the majority across all updates. SignGuard [49] calculates the proportions of positive, zero, and negative signs for each model update as the input of a clustering algorithm to identify malicious model updates. However, these methods utilize the signs of all parameters in the model update, regardless of their significance. Consequently, the performance of sign-based metrics can be significantly impacted by those many unimportant parameters," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20656" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": "especially for large DNN models, leading to an inaccurate representation of the model update's direction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "spans": [ + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "text", + "content": "To this end, AlignIns utilizes a Masked Principle Sign Alignment (MPSA) checking to inspect the sign alignment degree between the important parameters of each local update and a well-designed principle sign of all local updates. Specifically, to construct the principle sign over local updates, for each coordinate of local updates, we take the majority of the signs across all model updates as the principal sign of this coordinate, which can be mathematically formulated as " + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "inline_equation", + "content": "p \\coloneqq \\operatorname{sgn}\\left(\\sum_{i=1}^{n} \\operatorname{sgn}\\left(\\Delta_i^t\\right)\\right)" + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "inline_equation", + "content": "p \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "text", + "content": " represents the vector of principal signs and " + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "inline_equation", + "content": "\\operatorname{sgn}(\\cdot)" + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "text", + "content": " is the function to take the signs of a vector. Note that the principal sign represents sign-voting results for each coordinate, making it stand for the major direction/dynamic for each coordinate. With this principle sign over local updates, we inspect the alignment of the signs of important parameters of each model update with it. More specifically, we use a Top-" + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "text", + "content": " indicator defined as follows to identify the " + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 56, + 96, + 296, + 312 + ], + "type": "text", + "content": " most important parameters that have the largest absolute values in a vector." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": "Definition 1 (Top-" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " Indicator " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\mathrm{Top_k}(\\cdot)" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": "). For a vector " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "x\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " and a masking parameter " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "1\\leq k\\leq d" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": ", the Top-" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " indicator " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\mathrm{Top_k}(\\cdot)" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^d\\to \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " is defined as " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "[\\mathrm{Top_k}(x)]_j = 1" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "[x]_j\\in \\xi" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "[\\mathrm{Top_k}(x)]_j = 0" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " otherwise, where " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\xi = \\{|x_{\\pi (1)}|,|x_{\\pi (2)}|,\\dots ,|x_{\\pi (k)}|\\}" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": ", here " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " is a permutation of " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "[d]" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "|x_{\\pi (i)}|\\geq |x_{\\pi (i + 1)}|" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "inline_equation", + "content": "1\\leq i < d" + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 396, + 296, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 469 + ], + "type": "text", + "content": "The Top-" + }, + { + "bbox": [ + 55, + 396, + 296, + 469 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 396, + 296, + 469 + ], + "type": "text", + "content": " indicator " + }, + { + "bbox": [ + 55, + 396, + 296, + 469 + ], + "type": "inline_equation", + "content": "\\mathrm{Top_k}(\\cdot)" + }, + { + "bbox": [ + 55, + 396, + 296, + 469 + ], + "type": "text", + "content": " takes each local model update as input and outputs a mask vector in which each element is either 1 or 0 with the same size as the input. To quantify the alignment in sign distributions of each local model update and the principle sign, we define the Sign Alignment Ratio (SAR) as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": "Definition 2 (Sign Alignment Ratio). For vectors " + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": ", the sign alignment ratio " + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": " is defined as " + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "inline_equation", + "content": "\\rho := 1 - \\| \\operatorname{sgn}(x) - \\operatorname{sgn}(y) \\|_0 / d" + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|_0" + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "inline_equation", + "content": "L_0" + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": "-norm." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "\\rho \\in [0,1]" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " and a larger " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " indicate a higher degree of alignment between the signs of " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": ". Combining " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "\\mathrm{Top_k}(\\cdot)" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " and SAR, we have the MPSA value " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "\\rho_{i}" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " for local update " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "\\Delta_i^t" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " formulated as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 80, + 572, + 295, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 572, + 295, + 589 + ], + "spans": [ + { + "bbox": [ + 80, + 572, + 295, + 589 + ], + "type": "interline_equation", + "content": "\\rho_ {i} := 1 - \\left\\| \\left(\\operatorname {s g n} \\left(\\Delta_ {i} ^ {t}\\right) - p\\right) \\odot \\operatorname {T o p} _ {k} \\left(\\Delta_ {i} ^ {t}\\right) \\right\\| _ {0} / k, \\tag {2}", + "image_path": "59d927d0bc27c0b393e0241e775ad3f3cea3cf6febabc3f8d3fe5b5e3f3339cf.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": " is the Hadamard product, " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{sgn}(\\Delta_i^t) - p" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": " computes a sign difference vector, capturing the difference between the sign of " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\Delta_i^t" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": " and the principal reference sign " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": ". Since MPSA checking focuses on the important parameters, this difference vector is element-wise multiplied with the Top-" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": " mask derived from " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\Delta_i^t" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": ", effectively setting unimportant coordinates to zero. The " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "L_0" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": "-norm is then applied to count the not-aligned elements and with the masking parameter " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": " to ultimately determine the SAR. MPSA checking effectively reveals malicious local updates by combining both" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "magnitude and directional information from model updates, allowing for clear differentiation between malicious and benign updates. AlignIns calculates the MPSA value for each update with the principal sign iteratively (line 3-4) and forward them to the following anomaly detection process." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 133, + 555, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 555, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 555, + 204 + ], + "type": "text", + "content": "3) Efficient anomaly detection with MZ_score: W apply robust filtering to remove updates with abnormal TDA and MPSA values. Specifically, we use the robust standardization metric named the Median-based Z-score (MZ_score) [50, 51], detailed in Definition 3, which is a variant of the traditional Z-score standardization metric." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "content": "Definition 3 (MZ_score). For a set of values " + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "inline_equation", + "content": "X \\coloneqq \\{x_1, \\ldots, x_n\\}" + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "content": " with median " + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "inline_equation", + "content": "\\operatorname{med}(X)" + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "content": " and standard deviation " + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "content": ", the MZ_score " + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "inline_equation", + "content": "\\lambda_i" + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "content": " of any " + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "inline_equation", + "content": "x_i \\in X" + }, + { + "bbox": [ + 313, + 214, + 555, + 251 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 381, + 261, + 553, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 261, + 553, + 275 + ], + "spans": [ + { + "bbox": [ + 381, + 261, + 553, + 275 + ], + "type": "interline_equation", + "content": "\\lambda_ {i} := (x _ {i} - \\operatorname {m e d} (X)) / \\sigma . \\tag {3}", + "image_path": "65f0b129773d5f60764f8172031efd4180eda6cf5d55bbbcc780d4f1b5e9ea93.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "text", + "content": "MZ_score calculates the number of standard deviations an element is from the median, which may be either positive or negative. In AlignIns, the MZ_score for TDA and MPSA values are computed for each local update (line 6-7). Those with high absolute MZ_score (i.e., outliers) are excluded using two predetermined filtering radii: " + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "text", + "content": " for TDA and " + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\lambda_{s}" + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "text", + "content": " for MPSA (line 8-9). The use of the MZ_score allows for the adaptation to the varying range of TDA and MPSA values during training, requiring only minimal hyper-parameters. Additionally, by configuring " + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\lambda_{s}" + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "text", + "content": ", we can manage the trade-off between the robustness and main task accuracy of AlignIns. For example, when robustness is the primary concern in the FL, choosing small " + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "inline_equation", + "content": "\\lambda_{s}" + }, + { + "bbox": [ + 313, + 285, + 555, + 452 + ], + "type": "text", + "content": " values is essential to attain the highest robustness." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "text", + "content": "Post-filtering model clipping. After filtering, the remaining clients, considered benign, are included in the set " + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "text", + "content": " (line 9) and contribute to the model averaging process. However, since our filtering primarily focuses on the direction of model updates (although MPSA does consider magnitude when using the Top-" + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "text", + "content": " indicator), there is a risk that it might overlook updates with large magnitudes, such as those updates generated by Scaling attack [4]. To this end, AlignIns re-scales model updates in " + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "text", + "content": " by using the median of the " + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "text", + "content": "-norms of these updates as a clipping threshold and aggregates the clipped model updates as the global model update " + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "inline_equation", + "content": "\\tilde{\\Delta}" + }, + { + "bbox": [ + 313, + 453, + 556, + 657 + ], + "type": "text", + "content": " (line 12-13). It is worth noting that performing clipping before filtering does not affect the filtering results. However, clipping after filtering enhances robustness, as the clipping threshold is more likely determined by benign updates. We discuss the computational cost of AlignIns and compare it with other baselines in Appendix Section 12." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 669, + 555, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 669, + 555, + 684 + ], + "spans": [ + { + "bbox": [ + 313, + 669, + 555, + 684 + ], + "type": "text", + "content": "4. Robustness and Propagation Error Analysis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "In this section, we conduct a theoretical analysis of the robustness of AlignIns, as well as its propagation error in FL." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20657" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": "Before presenting our theoretical results, we make the following assumptions. Note that Assumption 1-2 are commonly used in the theoretical analysis of distributed learning systems [18, 34, 49]. Assumption 3 states a standard measure of inter-client heterogeneity in FL [2, 8, 21]. This heterogeneity complicates the problem of FL with backdoor adversaries, as it may cause the server to confuse malicious updates with flawed model updates from benign clients holding outlier data points [2]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "spans": [ + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": "Assumption 1 (" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": "-smoothness [34]). Each local objective function " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": " for benign client " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "i \\in \\mathcal{B}" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": "-Lipschitz smooth with " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\mu > 0" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": ", i.e., for any " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "x, y \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\|\\nabla \\mathcal{L}_i(x) - \\nabla \\mathcal{L}_i(y)\\| \\leq \\mu \\|x - y\\|" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\forall i \\in \\mathcal{B}" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": ", which further gives: " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i(x) - \\mathcal{L}_i(y) \\leq \\nabla \\mathcal{L}_i(x)^T(y - x) + (\\mu/2)\\|x - y\\|^2" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "inline_equation", + "content": "\\forall i \\in \\mathcal{B}" + }, + { + "bbox": [ + 54, + 188, + 296, + 251 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "text", + "content": "Assumption 2 (Unbiased gradient and bounded variance). The stochastic gradient at each benign client is an unbiased estimator of the local gradient, i.e., " + }, + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "inline_equation", + "content": "\\mathbb{E}[g_i(x)] = \\nabla \\mathcal{L}_i(x)" + }, + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "text", + "content": " and has bounded variance, i.e., for any " + }, + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "inline_equation", + "content": "x\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "inline_equation", + "content": "\\mathbb{E}\\left\\| g_i(x) - \\nabla \\mathcal{L}_i(x)\\right\\| ^2\\leq \\nu_i^2,\\forall i\\in \\mathcal{B}," + }, + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "text", + "content": " where the expectation is over the local mini-batches. We also denote " + }, + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "inline_equation", + "content": "\\bar{\\nu}\\coloneqq (1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\nu_i^2" + }, + { + "bbox": [ + 55, + 257, + 296, + 344 + ], + "type": "text", + "content": " for convenience." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "text", + "content": "Assumption 3 (Bounded heterogeneity). There exist a real value " + }, + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\bar{\\zeta}" + }, + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "text", + "content": " such that for any " + }, + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "inline_equation", + "content": "x\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "inline_equation", + "content": "(1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\| \\nabla \\mathcal{L}_i(x) - \\nabla \\mathcal{L}_{\\mathcal{B}}(x)\\| ^2\\leq \\bar{\\zeta}" + }, + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "text", + "content": ", where the " + }, + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{L}_{\\mathcal{B}}(x)\\coloneqq (1 / |\\mathcal{B}|)\\sum_{i\\in \\mathcal{B}}\\mathcal{L}_i(x)" + }, + { + "bbox": [ + 55, + 350, + 296, + 401 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 407, + 296, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 407, + 296, + 443 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 296, + 443 + ], + "type": "text", + "content": "Note that these assumptions apply to benign clients only since malicious clients do not need to follow the prescribed local training protocol of FL." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 450, + 228, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 228, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 228, + 464 + ], + "type": "text", + "content": "4.1. Robustness Analysis of AlignIns" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "text", + "content": "To theoretically evaluate the efficacy of a filtering-based defense method like AlignIns, we introduce the concept of " + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "text", + "content": "-robust filtering [50] as defined in Definition 4. Note that Definition 4 is similar to " + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "inline_equation", + "content": "(f,\\kappa)" + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "text", + "content": "-robustness defined in [2, 3], " + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "inline_equation", + "content": "(\\delta_{\\max},c)" + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "text", + "content": "-ARAgg defined in [13, 21, 31], and " + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "inline_equation", + "content": "(f,\\lambda)" + }, + { + "bbox": [ + 55, + 468, + 296, + 588 + ], + "type": "text", + "content": "-resilient averaging defined in [10]. Our robustness definition adopts a constant upper bound and focuses on quantifying the distance between the output of a filtering-based defense method and the average of all benign updates, which represents the optimal output of such a rule." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "spans": [ + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": "Definition 4 (" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": "-robust filtering [50]). A filtering-based aggregation rule " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "F \\colon \\mathbb{R}^{d \\times n} \\to \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": " is called " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": "-robust if for any vectors " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\{x_1, \\ldots, x_n\\} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": " and a benign set " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{B} \\subseteq [n]" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "n - m" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": ", the output " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\hat{x} \\coloneqq F(x_1, \\ldots, x_n)" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": " satisfies " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\| \\hat{x} - \\bar{x}_{\\mathcal{B}} \\|^2 \\leq \\kappa" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\bar{x}_{\\mathcal{B}} \\coloneqq (1 / |\\mathcal{B}|) \\sum_{i \\in \\mathcal{B}} x_i" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\kappa \\geq 0" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": " refers to the robustness coefficient of " + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 55, + 596, + 296, + 670 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "Remark 1. The " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "-robust filtering guarantees that the error of a filtering-based aggregation rule in estimating the average of the benign inputs is upper-bounded by a constant " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "text", + "content": "This measure provides a quantitative way to assess the robustness of the filtering-based aggregation rule. A smaller " + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "text", + "content": " indicates a smaller discrepancy between the empirical output and the optimal output of " + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "text", + "content": " identifies and removes all malicious inputs and keeps all benign inputs, we have " + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "inline_equation", + "content": "\\kappa = 0" + }, + { + "bbox": [ + 313, + 72, + 554, + 144 + ], + "type": "text", + "content": ", achieving the highest level of robustness." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "spans": [ + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "text", + "content": "Based on Definition 4, we prove that the proposed AlignIns, when applied to " + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "text", + "content": " input models, of which " + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "text", + "content": " are malicious, satisfies " + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "text", + "content": "-robust filtering with " + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "inline_equation", + "content": "\\kappa = O(1 + m / (n - 2m))" + }, + { + "bbox": [ + 313, + 152, + 554, + 201 + ], + "type": "text", + "content": ", as stated in Lemma 1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "spans": [ + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "text", + "content": "Lemma 1 (" + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "text", + "content": "-robustness of AlignIns). Under Assumption 2-3, assume " + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "inline_equation", + "content": "n > 1" + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "inline_equation", + "content": "0 \\leq m < n / (3 + \\epsilon)" + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "text", + "content": " with a positive constant " + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "text", + "content": ", AlignIns satisfies " + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 313, + 208, + 554, + 245 + ], + "type": "text", + "content": "-robust filtering with" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 328, + 252, + 541, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 252, + 541, + 281 + ], + "spans": [ + { + "bbox": [ + 328, + 252, + 541, + 281 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\kappa = \\left(1 + m / \\left(n - 2 m\\right)\\right) \\left(\\left(2 / \\epsilon + 1\\right) \\left(2 \\bar {\\nu} + \\bar {\\zeta}\\right) + 8 c ^ {2}\\right) \\\\ = O \\left(1 + m / (n - 2 m)\\right), \\\\ \\end{array}", + "image_path": "9440f16d8fd90faea7428ccdab3635393a8fbed6a74993e5600f04b6a053b4cd.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "text", + "content": "if the local learning rate satisfies " + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "inline_equation", + "content": "\\eta \\leq 1 / 2\\tau" + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "text", + "content": " and there exist two sufficiently large filtering radii such that " + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "inline_equation", + "content": "|\\mathcal{S}|\\geq n - 2m" + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "inline_equation", + "content": "\\bar{\\nu}" + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "text", + "content": " represent the gradient variance and local divergence, respectively; " + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 290, + 554, + 339 + ], + "type": "text", + "content": " is the clipping threshold." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 346, + 527, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 527, + 359 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 527, + 359 + ], + "type": "text", + "content": "Proof. The proof is given in Appendix Section 13.2." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 544, + 346, + 554, + 357 + ], + "blocks": [ + { + "bbox": [ + 544, + 346, + 554, + 357 + ], + "lines": [ + { + "bbox": [ + 544, + 346, + 554, + 357 + ], + "spans": [ + { + "bbox": [ + 544, + 346, + 554, + 357 + ], + "type": "image", + "image_path": "93a7b4bc155178e2c296c7ed12823c6a8995c81b3dbc88933aa73046c9a4a5f2.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "text", + "content": "Remark 2. The condition on " + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "text", + "content": " highlights the importance of selecting appropriate filtering radii. These radii cannot be zero or too small; otherwise, only the median or a few model updates will be averaged to update the global model. This can lead to a performance drop due to the lack of model updates. Moreover, the model clipping threshold " + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "text", + "content": " can effectively control the magnitude of potential malicious updates in the selection set, thus preventing " + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "text", + "content": " from exploding due to updates with large magnitudes. Indeed, in the literature, model clipping has demonstrated its effectiveness in mitigating the impact of malicious model updates [39, 49, 53]. In addition, the result also shows the importance of reducing the gradient variance of stochastic gradient and local heterogeneity to enhance robustness performance. Our work is orthogonal to existing variance or divergence reduction methods [13, 30] and can be combined with them to further improve the robustness. We argue that AlignIns enjoys comparable robustness with several classical defense methods, for example, non-filtering-based method RFA [40] (" + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "inline_equation", + "content": "O(1 + m / (n - 2m))^2" + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "text", + "content": "), and filtering-based method Krum [6] (" + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "inline_equation", + "content": "O(1 + m / (n - 2m))^1" + }, + { + "bbox": [ + 313, + 366, + 555, + 619 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 625, + 509, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 625, + 509, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 625, + 509, + 639 + ], + "type": "text", + "content": "4.2. Propagation Error of AlignIns in FL" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 643, + 554, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 643, + 554, + 667 + ], + "spans": [ + { + "bbox": [ + 313, + 643, + 554, + 667 + ], + "type": "text", + "content": "Based on the " + }, + { + "bbox": [ + 313, + 643, + 554, + 667 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 313, + 643, + 554, + 667 + ], + "type": "text", + "content": "-robustness of AlignIns, we analyze its propagation error during training. Specifically, let " + }, + { + "bbox": [ + 313, + 643, + 554, + 667 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 643, + 554, + 667 + ], + "type": "text", + "content": " denote the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 673, + 554, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 673, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 673, + 554, + 713 + ], + "type": "text", + "content": "1Results of RFA and Krum are taken from [2]. Note that the definition of " + }, + { + "bbox": [ + 313, + 673, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 313, + 673, + 554, + 713 + ], + "type": "text", + "content": " in [2] is different from ours, but the difference part can be reduced to a constant bound. Therefore, we can safely incorporate these results into our discussion without losing generality." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20658" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": "model trained with AlignIns under backdoor attacks, where " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": " clients are malicious, and let " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "\\theta^{*}" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": " denote a model trained exclusively with benign clients using FedAvg. Starting from the same initial model " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "\\theta^0" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": ", we aim to measure the difference between these two models after " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": " rounds of training, defined as " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "\\| \\theta^T - \\theta^{T,*} \\|" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": ", referred to as the propagation error [39]. Let " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "\\theta^{t, + }" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": " represent the output of AlignIns at the " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": "-th round. If the highest level of robustness is not achieved at round " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": ", the error " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "\\| \\theta^t - \\theta^{t, + } \\|" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": " will propagate to the next round, resulting in a shifted starting point for local SGD at round " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": ". This discrepancy will gradually widen the gap between " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "\\theta^{*}" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": ". Our analysis captures this robustness error at each round and examines its cumulative effect after " + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 72, + 296, + 262 + ], + "type": "text", + "content": " rounds. In Lemma 2, we show that, assuming Assumption 1-3 hold, the propagation error of AlignIns remains bounded." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 270, + 295, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 270, + 295, + 307 + ], + "spans": [ + { + "bbox": [ + 54, + 270, + 295, + 307 + ], + "type": "text", + "content": "Lemma 2 (Bounded Propagation Error). Let Assumption 1-3 hold. If the local learning rate " + }, + { + "bbox": [ + 54, + 270, + 295, + 307 + ], + "type": "inline_equation", + "content": "\\eta \\leq 1 / 2\\tau" + }, + { + "bbox": [ + 54, + 270, + 295, + 307 + ], + "type": "text", + "content": ", the propagation error of AlignIns is bounded as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 83, + 312, + 268, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 312, + 268, + 327 + ], + "spans": [ + { + "bbox": [ + 83, + 312, + 268, + 327 + ], + "type": "interline_equation", + "content": "\\left\\| \\theta^ {T} - \\theta^ {T, *} \\right\\| \\leq \\phi (T) (2 + 3 \\mu^ {2}) ^ {\\phi (T)} (\\kappa + 2 \\bar {\\nu}),", + "image_path": "5eec5ba0042643e06b8a4a85b1c744815cf44b2ada8cf775bc659017e1f43a6f.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "spans": [ + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "text", + "content": "under backdoor attacks where " + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "text", + "content": " out of " + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "text", + "content": " clients are malicious. Here, " + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "text", + "content": " is given in Lemma 1, " + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "inline_equation", + "content": "\\phi(T) = \\sum_{t=1}^{T} (\\alpha^t)^2" + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "text", + "content": " is the cumulative global learning rate, and " + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "inline_equation", + "content": "\\alpha^t" + }, + { + "bbox": [ + 55, + 334, + 296, + 381 + ], + "type": "text", + "content": " is a global learning rate scheduler, possibly static." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 388, + 295, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 401 + ], + "type": "text", + "content": "Proof. The detailed proof is in Appendix Section 13.3. " + }, + { + "bbox": [ + 55, + 388, + 295, + 401 + ], + "type": "inline_equation", + "content": "\\square" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": "Remark 3. When " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "T \\to \\infty" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\phi(T)" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": " converges to a constant for learning rate schedulers like exponential decay, which implies a constant bounded on propagation error. The result shows that besides the robustness error bounded by " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": ", the error of local gradient estimation, which is bounded by " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\bar{\\nu}" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": ", in local SGD also propagates during the training, increasing the overall propagation error. This is because at any round " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": ", if the benign starting point for local training is the same, i.e., " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^t = \\theta^{t,*}" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": ", then the local gradients/model updates on " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^t" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^{t,*}" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": " will be identical for benign clients. Therefore, the gap between the updated global models " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^{t+1}" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^{t+1,*}" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": " solely depends on the robustness error (i.e., the effectiveness of AlignIns in filtering out malicious updates). However, if " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^t \\neq \\theta^{t,*}" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": ", which means " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^t" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": " is not benign and has been poisoned in previous rounds, the local gradients/model updates on " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^t" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "inline_equation", + "content": "\\theta^{t,*}" + }, + { + "bbox": [ + 55, + 408, + 297, + 659 + ], + "type": "text", + "content": " will differ for benign clients, resulting in an error bounded by the gradient variance, even if AlignIns successfully filters out all malicious updates. Hence, to further reduce the propagation error, AlignIns can be combined with variance-reduction methods like [13, 30], which is orthogonal to AlignIns." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 669, + 185, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 185, + 682 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 185, + 682 + ], + "type": "text", + "content": "5. Experimental Settings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "Datasets and System Settings: In our experiments, we primarily conduct evaluation on CIFAR-10 [24] and CIFAR-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "text", + "content": "100 [24] datasets. Additionally, we present the superior performance of AlignIns on other benchmark datasets (MNIST [25], FMNIST [47], Sentiment140 [12], and TinyImageNet) in Appendix Section 10.5-10.6. We simulate a cross-silo FL with 20 clients for all datasets. Additionally, we also present the superior performance of AlignIns on a cross-device FL system with 100 clients and client sampling. We consider both IID and non-IID settings. For IID settings, we distribute the training data evenly to clients. For non-IID settings, we follow [17, 19, 20] to use Dirichlet distribution " + }, + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "inline_equation", + "content": "\\text{Dir}(\\beta)" + }, + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "text", + "content": " to skew the local data distribution with a default non-IID degree " + }, + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "inline_equation", + "content": "\\beta = 0.5" + }, + { + "bbox": [ + 313, + 72, + 553, + 215 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "content": "Learning Settings: We use SGD as the local solver, with the initial learning rates set as " + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\alpha = 1.0" + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\eta = 0.1" + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "content": ", and the local training epoch is set as 2. The training round is set as " + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "inline_equation", + "content": "T = 100" + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "content": " for CIFAR-100 and " + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "inline_equation", + "content": "T = 150" + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "content": " for CIFAR-10. For AlignIns, the default filtering radii are set as " + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\lambda_{c} = 1.0" + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "inline_equation", + "content": "\\lambda_{s} = 1.0" + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "content": ". We provide the study of the impact of filtering radii in Appendix Section 11. The default masking parameter is set as " + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "inline_equation", + "content": "k = 0.3 \\times d" + }, + { + "bbox": [ + 313, + 217, + 555, + 326 + ], + "type": "text", + "content": " so that the Top-30% of model parameters are used for the MPSA checking." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "text", + "content": "Evaluated Attack Methods: We consider 5 SOTA backdoor attacks, including Badnet [14], DBA [48], Scaling [4], PGD [46], and Neurotoxin [54]. We provide the detailed attack model and settings for attack methods in Appendix Section 8.1-8.2. We present the results of AlignIns under the strong trigger-optimization attack [9] in Appendix Section 10.2. Moreover, we study the potential adaptive attacks tailored to AlignIns and untargeted attacks [49] in Appendix Section 10.3-10.4, although these are beyond the scope of this work. To achieve effective backdoors (achieving a BA over " + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "text", + "content": " [22]), malicious clients poison " + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "inline_equation", + "content": "r = 50\\%" + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "text", + "content": " of their local data, where " + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "text", + "content": " is the data poisoning ratio. The attack ratio is set to " + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "text", + "content": " by default, which means " + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 313, + 327, + 554, + 518 + ], + "type": "text", + "content": " of the clients in the system are malicious. Experiments of AlignIns on defending backdoor attacks with various attack ratios are given in Appendix Section 10.7." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 520, + 554, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 520, + 554, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 520, + 554, + 640 + ], + "type": "text", + "content": "Evaluated Defense Methods: We present the detailed defense model in Appendix Section 9. We comprehensively compare AlignIns with the non-robust baseline FedAvg and six existing SOTA defense methods, including RLR [38], RFA [40], Multi-Krum (MKrum) [6], Foolsgold [11], Multi-Metric (MM) [19], and Lockdown [20]. Additionally, we compare our approach with an ideally perfect filtering-based robust aggregation, FedAvg*, which is assumed to perfectly identify and remove all malicious updates and average all the benign updates to update the global model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "content": "Evaluation Metrics: We use three metrics to evaluate the performance of defense methods, including main task accuracy (MA), which measures the percentage of clean test samples that are accurately classified to their ground truth labels by the global model; backdoor attack accuracy (BA), which measures the percentage of triggered" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20659" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 91, + 552, + 339 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 553, + 82 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 553, + 82 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 553, + 82 + ], + "type": "text", + "content": "Table 1. The clean MA, BA, and RA results of baselines and AlignIns on IID CIFAR-10 and CIFAR-100 datasets. Results are shown in %." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 91, + 552, + 339 + ], + "lines": [ + { + "bbox": [ + 58, + 91, + 552, + 339 + ], + "spans": [ + { + "bbox": [ + 58, + 91, + 552, + 339 + ], + "type": "table", + "html": "
    Dataset (Model)MethodsClean MA↑BadnetDBANeurotoxinAvg. BA↓Avg. RA↑
    BA↓RA↑BA↓RA↑BA↓RA↑
    r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5r=0.3r=0.5
    CIFAR-10 (ResNet9 [16])FedAvg89.4751.5667.6145.7931.2456.2170.4240.6227.9244.8979.4050.4119.6061.6835.93
    FedAvg*89.472.062.0685.6085.602.062.0685.6085.602.062.0685.6085.602.0685.60
    RLR79.162.322.0076.7273.333.013.0477.0977.133.123.8773.9873.292.8935.93
    RFA87.7370.6790.2427.749.2647.6766.9747.2930.1481.2796.1317.113.6975.4922.54
    MKrum87.0281.1097.4718.112.512.174.3383.8979.1065.2889.1831.8110.0156.5937.57
    Foolsgold89.4969.1468.8429.6430.1051.1860.7344.8336.082.912.8285.2784.7642.6051.78
    MM89.1541.1993.8853.886.0152.2451.3043.5445.0843.9283.9251.1215.1161.0835.79
    Lockdown88.566.3110.8281.8879.5011.636.0378.8275.773.403.2782.7383.146.9180.31
    AlignIns88.641.912.2186.0385.572.132.1485.7785.882.662.2085.4685.312.2185.67
    CIFAR-100 (VGG9 [41])FedAvg64.2999.2099.540.680.3599.2599.360.640.5494.4193.364.365.2897.521.98
    FedAvg*64.290.620.6253.0353.030.620.6253.0353.030.620.6253.0353.030.6253.03
    RLR44.3496.5799.851.810.1224.4194.0824.973.220.040.0029.0729.7352.4914.82
    RFA53.924.321.4537.6039.882.150.7839.7341.5199.7489.590.216.5933.0127.59
    MKrum51.281.331.5438.1338.491.361.5437.8537.9199.8299.870.120.1036.2125.49
    Foolsgold64.1399.0299.300.830.5799.1599.390.740.5121.796.2142.0646.4070.8115.19
    MM63.2699.5199.870.370.1199.5399.700.350.1998.4898.971.320.8399.340.53
    Lockdown62.8855.2124.1428.4543.0634.3749.0234.0627.930.850.6742.6647.0427.3837.20
    AlignIns63.450.790.7150.4551.530.450.5750.8152.080.490.5351.1150.660.5951.11
    ", + "image_path": "3c755cdd8ce67f1c2a7cc9751371c1d4d46ea574f4b6c1666c2fa569d2c4225a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 349, + 296, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 296, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 296, + 422 + ], + "type": "text", + "content": "samples that are misclassified to the target label by the global model; and robustness accuracy (RA), which measures the percentage of triggered samples that are accurately classified to their ground-truth labels by the global model, despite the presence of the trigger. A good defense method should achieve high MA and RA and low BA." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 430, + 180, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 430, + 180, + 443 + ], + "spans": [ + { + "bbox": [ + 55, + 430, + 180, + 443 + ], + "type": "text", + "content": "6. Experimental Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "text", + "content": "Main results in IID setting. In Table 1, we report the performance of various defense methods under no attack (denoted by \"Clean\"), Badnet, DBA, and Neurotoxin attacks for IID CIFAR-10 and CIFAR-100. The best results are highlighted in bold font, and the second best results are underlined. Overall, AlignIns demonstrates superior performance compared with other baselines as it achieves the best average BA and RA over three attack methods. Specifically, for CIFAR-10, while RLR offers a satisfactory degree of robustness (an average BA of " + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "inline_equation", + "content": "2.89\\%" + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "text", + "content": "), it suffers from a notable decline in RA, with an average reduction of " + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "inline_equation", + "content": "49.74\\%" + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "text", + "content": " in comparison to AlignIns. This drop results from RLR's strategy of flipping the global learning rate for parameters in the aggregated model update that are inconsistent with the majority's sign, consequently resulting in the loss of benign local parameters. AlignIns, however, demonstrates outstanding performance with consistently low BA and high RA, ranking first or second among its counterparts. Notably, compared to the second-best results, AlignIns achieves an average improvement of " + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "inline_equation", + "content": "+0.68\\%" + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "text", + "content": " in BA and " + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "inline_equation", + "content": "+5.36\\%" + }, + { + "bbox": [ + 54, + 450, + 295, + 715 + ], + "type": "text", + "content": " in RA. Similarly, superior results are observed in CIFAR-100 experiments, where AlignIns significantly out" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 329, + 349, + 443, + 453 + ], + "blocks": [ + { + "bbox": [ + 329, + 349, + 443, + 453 + ], + "lines": [ + { + "bbox": [ + 329, + 349, + 443, + 453 + ], + "spans": [ + { + "bbox": [ + 329, + 349, + 443, + 453 + ], + "type": "image", + "image_path": "64eb563d0e978f803f7dad56c20c2c5767d4f26b4dda5b7c04fce5175db15bf0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 464, + 555, + 486 + ], + "lines": [ + { + "bbox": [ + 313, + 464, + 555, + 486 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 555, + 486 + ], + "type": "text", + "content": "Figure 1. RA of AlignIns under various non-IID degrees, compared with Lockdown, RFA, and RLR under Neurotoxin." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 451, + 349, + 539, + 453 + ], + "blocks": [ + { + "bbox": [ + 451, + 349, + 539, + 453 + ], + "lines": [ + { + "bbox": [ + 451, + 349, + 539, + 453 + ], + "spans": [ + { + "bbox": [ + 451, + 349, + 539, + 453 + ], + "type": "image", + "image_path": "7b3d920a229ba2f5069fc312ff3945dc5092b8b6ae096bf52f644abbde4a492d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 497, + 555, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 497, + 555, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 555, + 545 + ], + "type": "text", + "content": "performs other methods in both BA and RA. These results underscore AlignIns' effectiveness as a promising defense method for protecting FL from various backdoor attacks, significantly enhancing the trustworthiness of FL systems." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "text", + "content": "Effectiveness under various Non-IID degrees. We examine the defense performance of AlignIns across various degrees of non-IIDness, a factor that significantly complicates backdoor defense. Figure 1 presents the RA of AlignIns under different non-IID conditions on the CIFAR-10 dataset, compared with Lockdown, RFA, and RLR. The experiments were conducted using the Neurotoxin attack, with both a default attack ratio of " + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "text", + "content": " and a higher attack ratio of " + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "text", + "content": ". The Dirichlet parameter " + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "text", + "content": " varies from 0.1 to 1.0, where a smaller " + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "text", + "content": " suggests a more intense non-IIDness. We observe that only AlignIns consistently attains robustness against strong Neurotoxin attacks with a varying " + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "text", + "content": ". Specifically, as " + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 313, + 546, + 556, + 714 + ], + "type": "text", + "content": " increases, the RA of AlignIns, Lockdown, and RLR increases correspondingly. However," + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20660" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 102, + 286, + 168 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 295, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 295, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 295, + 94 + ], + "type": "text", + "content": "Table 2. Performance of different methods in cross-device FL settings on IID and non-IID CIFAR-10 datasets under Badnet attack." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 102, + 286, + 168 + ], + "lines": [ + { + "bbox": [ + 65, + 102, + 286, + 168 + ], + "spans": [ + { + "bbox": [ + 65, + 102, + 286, + 168 + ], + "type": "table", + "html": "
    MethodCIFAR-10 (IID)CIFAR-10 (Non-IID)Avg. RA↑
    MA↑BA↓RA↑MA↑BA↓RA↑
    Foolsgold82.9999.990.0167.9799.990.000.01
    Lockdown83.5299.990.0073.9199.920.060.00
    RLR56.814.6755.3841.5614.1238.1746.78
    AlignIns85.010.9282.7479.511.9075.8179.28
    ", + "image_path": "c140dbdbf549daae48b1fae9ef2e2485b009cf26d7225f5ea41da159fae640a8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 178, + 296, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 178, + 296, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 178, + 296, + 335 + ], + "type": "text", + "content": "AlignIns outperforms them with a consistently higher RA. When the attack ratio rises to " + }, + { + "bbox": [ + 55, + 178, + 296, + 335 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 55, + 178, + 296, + 335 + ], + "type": "text", + "content": ", RLR, RFA, and Lockdown fail to provide satisfactory robustness. However, our method AlignIns still demonstrates its robustness under various non-IIDness, even in an extremely non-IID case when " + }, + { + "bbox": [ + 55, + 178, + 296, + 335 + ], + "type": "inline_equation", + "content": "\\beta = 0.1" + }, + { + "bbox": [ + 55, + 178, + 296, + 335 + ], + "type": "text", + "content": ". AlignIns is designed to examine the alignment of model updates on important parameters only, hence, it mitigates the challenge of identifying malicious model updates in non-IID settings where updates are heterogeneous, thereby achieving superior performance in even extreme non-IID settings compared with existing methods. We also provide more comprehensive results of AlignIns and other baselines on non-IID datasets in Appendix Section 10.1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "text", + "content": "Effectiveness of AlignIns in cross-device FL with client sampling. While most of our experiments focus on the cross-silo FL setting, evaluating the cross-device FL scenario is also essential given the large number of clients involved. For this purpose, we simulate a cross-device FL environment with 100 clients, where the server randomly selects 20 clients per round for training. We conduct experiments on IID and non-IID CIFAR-10 cases using Foolsgold, Lockdown, RLR, and AlignIns and summarize the MA, BA, and RA results in Table 2. The results show that both Foolsgold and Lockdown completely lose their effectiveness in both cases, achieving an average RA of nearly " + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "inline_equation", + "content": "0.00\\%" + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "text", + "content": ". RLR achieves a moderate level of backdoor robustness but at the cost of main task accuracy, with an average MA of only " + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "inline_equation", + "content": "49.19\\%" + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "text", + "content": ". In contrast, AlignIns performs robustly in the cross-device FL setting, achieving a significantly lower BA in both IID " + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "inline_equation", + "content": "(0.92\\%)" + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "text", + "content": " and non-IID " + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "inline_equation", + "content": "(1.90\\%)" + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "text", + "content": " cases compared with other methods. Furthermore, AlignIns achieves an average RA of " + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "inline_equation", + "content": "79.28\\%" + }, + { + "bbox": [ + 56, + 338, + 296, + 602 + ], + "type": "text", + "content": ". These results highlight AlignIns's ability to maintain both accuracy and robustness in challenging cross-device FL scenarios, underscoring its adaptability and effectiveness in real-world applications." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "content": "Ablation study of AlignIns. As AlignIns consists of two alignment components (TDA and MPSA) to improve backdoor robustness, we conduct a detailed ablation study to investigate how each component functions. Experimental results on IID and non-IID CIFAR-10 datasets under Badnet attack are summarized in Table 3. (i) Component ablation. We observe that using MPSA or TDA alone in IID scenarios only slightly reduces robustness compared to AlignIns, as benign updates follow consistent patterns that" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 317, + 91, + 552, + 183 + ], + "blocks": [ + { + "bbox": [ + 328, + 71, + 541, + 83 + ], + "lines": [ + { + "bbox": [ + 328, + 71, + 541, + 83 + ], + "spans": [ + { + "bbox": [ + 328, + 71, + 541, + 83 + ], + "type": "text", + "content": "Table 3. Performance of different components in AlignIns." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 91, + 552, + 183 + ], + "lines": [ + { + "bbox": [ + 317, + 91, + 552, + 183 + ], + "spans": [ + { + "bbox": [ + 317, + 91, + 552, + 183 + ], + "type": "table", + "html": "
    ConfigurationCIFAR-10 (IID)CIFAR-10 (non-IID)Avg. RA↑
    MA↑BA↓RA↑MA↑BA↓RA↑
    MPSA(30%)88.552.8885.0280.6594.075.7945.41
    TDA88.563.8283.8883.8677.5821.3152.60
    MPSA(70%)+TDA88.142.1885.7783.8461.8331.8658.82
    MPSA(50%)+TDA88.052.2185.4684.1277.9319.9652.71
    MPSA(30%)+TDA88.142.0485.8283.6547.0445.3065.56
    AlignIns88.052.4485.2782.881.7081.3283.30
    AlignIns+88.482.1485.7483.311.1182.1383.94
    ", + "image_path": "b93243537de499b11ab0f0a8c2be8055273941d2c2b6deef994cb3b29a121ec7.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": "enable effective detection by a single metric. In non-IID settings, however, where local updates diverge, neither MPSA nor TDA alone provides sufficient robustness. When combined, MPSA and TDA improve BA and RA from " + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "94.07\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "5.79\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "47.04\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "45.30\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": ", respectively, showing their complementary strengths. AlignIns further enhances robustness by integrating MPSA, TDA, and post-filtering model clipping, which normalizes benign update magnitudes and improves malicious update detection, yielding the highest average RA. (ii) Masking parameter " + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": " ablation. We try to involve more non-essential parameters in the MPSA checking by using the Top-" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "50\\% / 70\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": " of parameters to calculate MPSA values. By doing so, the effectiveness of malicious identification is reduced. In contrast, when using the Top-" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": " of parameters, compared to the Top-" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": " case, BA and RA are improved by " + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "+30.89\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "inline_equation", + "content": "+25.34\\%" + }, + { + "bbox": [ + 313, + 193, + 555, + 529 + ], + "type": "text", + "content": ", respectively. This demonstrates the effectiveness of focusing important parameters when calculating MPSA in improving the filtering accuracy, especially in non-IID cases. (iii) Variance reduction method further enhances robustness. Our theoretical results reveal the impact of variance reduction techniques on improving the robustness of AlignIns and reducing the propagation error of AlignIns in FL, we additionally test a variant of AlignIns named \"AlignIns+\", in which local SGD with momentum is used to reduce the local gradient variance with momentum coefficient 0.1. AlignIns+ achieves a slightly better performance than AlignIns, verifying our theoretical results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 536, + 388, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 536, + 388, + 550 + ], + "spans": [ + { + "bbox": [ + 314, + 536, + 388, + 550 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 557, + 555, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 677 + ], + "type": "text", + "content": "We introduce a novel method AlignIns to defend against backdoor attacks in FL. AlignIns examines each model update's direction at different granularity levels, thus effectively identifying stealthy malicious model updates and filtering them out to avoid them participating in aggregation in FL to enhance robustness. We provide a theoretical analysis of AlignIns' robustness and its impact on propagation errors in FL. Extensive experiments demonstrate the effectiveness of AlignIns, with results showing that it outperforms SOTA defense methods against various advanced attacks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "Acknowledgment. This work was supported by the Nevada System of Higher Education under grant NSHE-24-37." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "20661" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "text", + "content": "[1] Manaar Alam, Esha Sarkar, and Michail Maniatakos. 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Apart from recognizing known objects from training, a successful Open World Object Detection (OWOD) system must also be able to detect unknown objects never seen before, without confusing them with the backgrounds. Unlike prevailing prior works that rely on probability models to learn \"objectness\", we focus on learning fine-grained, class-agnostic attributes, allowing the detection of both known and unknown objects in an explainable manner. In this paper, we propose Partial Attribute Assignment (PASS), aiming to automatically select and optimize a small, relevant subset of attributes from a large attribute pool. Specifically, we model attribute selection as a Partial Optimal Transport (POT) problem between known visual objects and the attribute pool, in which more relevant attributes signify more transported mass. PASS follows a curriculum schedule that progressively selects and optimizes a targeted subset of attributes during training, promoting stability and accuracy. Our method enjoys end-to-end optimization by minimizing the POT distance and the classification loss on known visual objects, demonstrating high training efficiency and superior OWOD performance among extensive experimental evaluations.", + "bbox": [ + 88, + 321, + 485, + 670 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 700, + 220, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning and foundation models have emerged as critical AI technologies [1, 55], impacting various aspects of modern life. However, their success has been largely based on the closed-world assumption, which presumes a static and well-defined environment [76]. In practice, this assumption is difficult to uphold, as real-world conditions are dynamic and unpredictable, with unforeseen situations and unseen objects regularly appearing. Open World Object Detection (OWOD) [22] has emerged as a remedy to deliver reliable detection in the face of new environments with unknown ob", + "bbox": [ + 89, + 726, + 483, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fe47cb634b971bf830b51d04b30dd8d26af3cee25a7633398faed2bdcd712b18.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 537, + 287, + 903, + 450 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4187f32aea67422cd73170502074fc98daacd568c464402fa74f11a501805f1b.jpg", + "image_caption": [ + "(b)", + "Figure 1. The role of attributes in Open World Object Detection (OWOD). (a) Unknown objects can be detected via shared visual/functional attributes with known objects. (b) Our method is able to automatically identify and optimize a small subset of relevant attributes from a large pool, effectively enabling the detection of both known and unknown objects." + ], + "image_footnote": [], + "bbox": [ + 535, + 460, + 905, + 579 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jects. In addition to recognizing known objects that appeared in training, a successful OWOD system must also detect and continually learn previously unseen objects without mistakenly classifying them as backgrounds.", + "bbox": [ + 509, + 700, + 906, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent works mainly use probability distribution estimation to model the \"objectness\" information, i.e., the probability of a candidate proposal being an object rather than backgrounds [79]. In this way, OWOD can be decomposed into two sub-tasks that respectively focus on objectness estimation and known class recognition [54]. Although this approach has significantly improved the detection of unknown objects, it has certain limitations in explainability and ambiguity. On the one hand, the learned probabilistic", + "bbox": [ + 509, + 763, + 908, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author. ‡Code: https://github.com/muliyangm/PASS", + "bbox": [ + 91, + 886, + 482, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20318", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "model is unable to explain how the objects—both the known and the unknown—are detected. On the other hand, when background features resemble those of the unknown objects, the model can still misclassify them.", + "bbox": [ + 89, + 90, + 485, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we focus on detecting open world objects using fine-grained, class-agnostic attributes that are visually and/or functionally related to the known objects. These attributes can be described using natural languages with rich semantic information, and thus are naturally explainable and less ambiguous. The emphasis on intrinsic object attributes offers stronger resistance to confusion in scenarios where background and unknown object features overlap, making it particularly suitable for dynamic open-world environments. As illustrated in Fig. 1(a), attributes can be useful in detecting both known and unknown object classes, e.g., the learned \"umbrella-like\" attribute from known classes can be used to detect the unknown fungi. Despite the promising potential of using attributes in OWOD, effectively curating a set of attributes that are closely related to the specific task from a large pool of attributes remains a significant challenge. To this end, some existing method [78] seeks a set of representative attributes that can effectively classify known objects with multistage processes—such as attribute selection and refinement—which are time-consuming and computationally expensive. More importantly, the separation of the selection and refinement processes may accumulate errors, leading to inaccuracies in the results of the attribute selection and refinement.", + "bbox": [ + 91, + 154, + 485, + 515 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose to tackle this dilemma using Partial Attribute Assignment (PASS), an approach that progressively selects and optimizes a targeted subset of relevant attributes throughout the training process in an end-to-end manner. In particular, we model attribute selection as a Partial Optimal Transport (POT) problem [6] between known visual objects and the attribute pool, in which more relevant attributes signify more mass transported to the visual objects. Unlike conventional OT [56] that assumes identical mass in both distributions to be completely transported, POT allows the transport of only a targeted fraction of total mass from one distribution to another. As such, the attribute pool can be viewed as a collection of both in-distribution (ID) and out-of-distribution (OOD) attributes w.r.t. the visual objects, where we can use the visual object distribution as the baseline distribution to filter out redundant OOD attributes.", + "bbox": [ + 89, + 520, + 485, + 761 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve stable, accurate attribute selection and optimization simultaneously, PASS follows a curriculum learning [4] schedule that progressively targets and optimizes a subset of attributes throughout training. PASS ensures that each filtered subset is highly representative and provides broad coverage of the visual objects, by iteratively focusing on and refining a smaller subset of attributes guaranteed by the OT theory. As training progresses, the selected attributes reach a balanced state between representativeness and cover-", + "bbox": [ + 89, + 763, + 485, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "age, allowing the model to better adapt to both known and unknown objects. This process also reduces computational costs by gradually limiting the number of attributes introduced. Our method enjoys end-to-end optimization by minimizing both the POT distance and the classification loss for known visual objects. During inference, the learned attributes play a dual role: they support the recognition of known classes through the mapping relationships established during training, while also enabling the detection of unknown objects by leveraging the correlation between object proposals and the learned attributes. Extensive experiments demonstrate that our method significantly outperforms baseline methods, validating both the feasibility of attribute-based OWOD and the effectiveness of our approach in curating more accurate attributes for OWOD.", + "bbox": [ + 511, + 90, + 908, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In a nutshell, our main contributions are", + "bbox": [ + 532, + 320, + 799, + 334 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We model the attribute curation issue in OWOD as a Partial Optimal Transport (POT) problem, enabling end-to-end attribute selection and optimization for effectively detecting both known and unknown objects;", + "- We propose a curriculum selection strategy by progressively optimizing a targeted subset of attributes with strong representativeness and broad coverage, benefiting both training stability and selection effectiveness;", + "- Extensive experiments demonstrate the absolute superiority of the proposed method in terms of both training efficiency and detection performance." + ], + "bbox": [ + 511, + 337, + 906, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 525, + 653, + 540 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Open World Object Detection. Open World Object Detection (OWOD) [22] enhances traditional object detectors by shifting away from closed-set assumptions, enabling dynamic adaptation to novel classes as encountered in real-world settings [20, 29, 30, 33, 34, 67, 74]. Existing works [27, 51, 61, 65, 69, 70] reduce the overlap between known, unknown classes and the background distributions using different ways, e.g., pseudo-labeling [18, 38], objectness estimation [54, 79], and hierarchical modeling [13, 37]. OWOD is also related to similar tasks such as Class-Agnostic Object Detection [14, 21, 23, 36, 44, 45, 50, 59, 60] and Open-Vocabulary Object Detection (OVOD) [17, 25, 41, 42, 58, 71, 75]. Recent advances, such as FOMO [78] and a concurrent work UMB [62], extend the standard OVOD method to OWOD by utilizing vision and language foundation models. By identifying objects based on semantic attributes [26, 49, 53], they learn class-agnostic attributes to detect task-relevant unknown objects, yet require multistage attribute selection and refinement, which is time-consuming and computationally inefficient. In this paper, we propose an end-to-end attribute curation method that not only benefits the training efficiency but also largely improves the detection performance in both known and unknown classes.", + "bbox": [ + 511, + 553, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20319", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Optimal Transport. Optimal Transport (OT), originally introduced by Monge [43] to minimize the cost of transporting items, has become a prominent tool in machine learning and computer vision for matching distributions across domains [46, 56]. OT has been widely applied in distribution-based tasks [8, 57, 73] such as generative models [2], clustering [19, 66], domain adaptation [11], object detection [16] and structural tasks such as sequence [9], graph [63], and image matching [32, 72]. To address OT's high computational demands, the Sinkhorn OT [12] offers a solution by approximating OT through an efficient iterative algorithm. Partial OT (POT), a variant of OT that transports only a portion of the mass, addresses cases where distributions only partially overlap, making it especially relevant in scenarios such as open-set domain adaptation [6, 7, 15, 35, 48, 64, 68]. The Sinkhorn algorithm has been extended to POT to further reduce computational costs [3]. In our work, we utilize POT to dynamically match attribute embeddings with visual embeddings of known object classes, selecting and optimizing the most representative attributes for effectively detecting both known and unknown objects.", + "bbox": [ + 89, + 90, + 486, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 89, + 422, + 220, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "OWOD with Foundation Models. Open World Object Detection (OWOD) requires a model to detect and incrementally learn unknown objects. In particular, there are multiple stages/tasks for training and evaluation, indicated by $t$ . In task $t$ , the model can be trained on $K^t$ known object classes from $\\mathcal{K}^t = \\{O_1^t, O_2^t, \\ldots, O_{K^t}^t\\}$ , and to be evaluated on a test set that contains both known and unknown classes. To achieve that, we use an additional $O_0^t$ to denote the unknown classes, alongside the $K^t$ known classes. In fact, $O_0^t$ represents $U^t$ classes of interest that are unknown to the model in the task $t$ , i.e., $\\mathcal{U}^t = \\{O_{K^t + 1}^t, O_{K^t + 2}^t, \\ldots, O_{K^t + U^t}^t\\}$ . After discovering the unknown object classes, the model can be updated with the knowledge of these new classes using annotations from an oracle (e.g., a human annotator) in task $t + 1$ . As a result, the model is ready to detect $K^{t + 1} = K^t + U^t$ known object classes in the test set, as well as additional unknown classes for the subsequent task cycle.", + "bbox": [ + 89, + 446, + 483, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To push the boundary of OWOD in real-world applications, we follow a recent work [78] to make use of existing pretrained foundation models in open-vocabulary object detection [41, 71], e.g., vision and language encoders, and adapt them to OWOD. The training follows a few-shot paradigm: for the $z$ -shot, only $z$ images per known class are given, with only one bounding box label and one object class label for each image. For each dataset, we use the attribute texts proposed by a Large Language Model (LLM), i.e., GPT-3.5, by prompting with the known class names using the template described in recent works [40, 77, 78]. This will result in an attribute pool with numerous class-agnostic attributes visually and/or functionally related to the known", + "bbox": [ + 89, + 704, + 486, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "objects, e.g., shape is straight.", + "bbox": [ + 511, + 92, + 774, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Optimal Transport Preliminary. Optimal Transport (OT) is a powerful tool for measuring the distance between two distributions. Here we review the discrete OT scenario that is more related to our framework and refer the readers to [12] for more details.", + "bbox": [ + 511, + 117, + 906, + 191 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Assuming we have two sets of data points (features) $\\mathbf{X} = \\{\\pmb{x}_m\\}_{m=1}^M$ and $\\mathbf{Y} = \\{\\pmb{y}_n\\}_{n=1}^N$ , their discrete distributions can be formulated as", + "bbox": [ + 511, + 193, + 906, + 238 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {X} = \\sum_ {m = 1} ^ {M} \\frac {1}{M} \\delta_ {\\boldsymbol {x} _ {m}}, \\quad \\mathcal {Y} = \\sum_ {n = 1} ^ {N} \\frac {1}{N} \\delta_ {\\boldsymbol {y} _ {n}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 247, + 906, + 289 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\delta$ is the Dirac function and we use the uniform distribution to equally view each data point. The OT distance is defined as the smallest cost of transporting $\\mathcal{X}$ to $\\mathcal{Y}$ :", + "bbox": [ + 511, + 299, + 908, + 345 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd _ {\\mathrm {O T}} (\\mathcal {X}, \\mathcal {Y}; \\mathbf {C}) \\triangleq \\min _ {\\mathbf {T} \\in \\Pi (\\mathcal {X}, \\mathcal {Y})} \\left\\langle \\mathbf {T}, \\mathbf {C} \\right\\rangle_ {F}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 354, + 906, + 382 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $\\mathbf{C} \\in \\mathbb{R}_{+}^{M \\times N}$ is the cost matrix between $\\mathbf{X}$ and $\\mathbf{Y}$ where $C_{m,n} = c(\\pmb{x}_m, \\pmb{y}_n)$ is the transport cost from $\\pmb{x}_m$ to $\\pmb{y}_n$ , with $c(\\cdot)$ being the cost function (e.g., the cosine distance), $\\mathbf{T}$ is the transport plan to be solved, and $\\langle \\cdot, \\cdot \\rangle_F$ denotes the Frobenius inner product. The optimization of OT distance satisfies two marginal constraints:", + "bbox": [ + 511, + 393, + 906, + 486 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Pi (\\mathcal {X}, \\mathcal {Y}) \\triangleq \\left\\{\\mathbf {T} \\in \\mathbb {R} _ {+} ^ {M \\times N} \\mid \\mathbf {T} \\mathbf {1} _ {N} = \\mathcal {X}, \\mathbf {T} ^ {\\top} \\mathbf {1} _ {M} = \\mathcal {Y} \\right\\}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 496, + 906, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{1}_N$ is an $N$ -dimensional vector of all ones, and we slightly abuse $\\mathcal{X}$ , $\\mathcal{Y}$ to denote $\\mathcal{X} = \\frac{1}{M}\\mathbf{1}_M$ , $\\mathcal{Y} = \\frac{1}{N}\\mathbf{1}_N$ to reflect the discrete probability in Eq. (1).", + "bbox": [ + 511, + 526, + 905, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 511, + 585, + 604, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose Partial Attribute Assignment (PASS) to address the challenging Open World Object Detection (OWOD) task. PASS is composed of three modules shown in Fig. 2, which are introduced in separate subsections below.", + "bbox": [ + 511, + 611, + 906, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Partial Attribute Assignment", + "text_level": 1, + "bbox": [ + 511, + 681, + 772, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As discussed above, now we have $z$ -shot images of $K$ known object classes (the superscript $t$ is omitted for brevity) and $N$ attribute texts in the attribute pool. Our goal is to select and optimize a small set of relevant attributes from the attribute pool, with the target attribute quantity denoted as $N' \\in (0, N]$ . The resulting $N'$ attributes are to be used for effectively detecting both known and unknown objects.", + "bbox": [ + 511, + 703, + 906, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, we collect the visual object embeddings as $\\mathbf{V} = [v_{1}, v_{2}, \\ldots, v_{M}] \\in \\mathbb{R}^{D \\times M}$ and the attribute embeddings as $\\mathbf{A} = [a_{1}, a_{2}, \\ldots, a_{N}] \\in \\mathbb{R}^{D \\times N}$ in the $D$ -dimensional embedding space using pretrained vision and text encoders [41, 47], where $M = z \\cdot K$ is the number of known image patches obtained using bounding box labels,", + "bbox": [ + 511, + 810, + 908, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20320", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a622527a0c6b28354d33d00d83913fe000b025ff6c32b6d4d9d241f01bb36f92.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed Partial Attribute Assignment (PASS) for OWOD. PASS is constructed upon pretrained vision and text encoders [41, 47] and is designed to identify and refine a set of relevant attributes from an attribute pool, which are essential for detecting both known and unknown object classes. (a) We employ Partial Optimal Transport (POT) to model the assignment problem between attributes and known visual objects (Sec. 4.1). (b) The resulting transport plan $\\mathbf{T}$ is used to generate attribute in-distribution (ID) scores $s$ , which help in selecting the most relevant attributes for the specific task (Sec. 4.2). (c) These attribute ID scores are further used to reweight the selected attributes, which are subsequently applied to compute object class predictions via a learnable mapping matrix (Sec. 4.3)." + ], + "image_footnote": [], + "bbox": [ + 98, + 88, + 903, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and all embeddings are $\\ell_2$ normalized. Likewise, we can denote the discrete distributions of $\\mathbf{V}$ and $\\mathbf{A}$ as $\\mathcal{V}$ and $\\mathcal{A}$ following Eq. (1). The conventional OT assumes that the two distributions have the identical total probability mass, i.e., $\\| \\mathcal{V}\\| _1 = \\| \\mathcal{A}\\| _1$ , and that all the mass of $\\mathcal{A}$ must be transported. Although this assumption works effectively for tasks that involve identical distributions, it faces challenges in our scenario, where only a subset of samples in $\\mathcal{A}$ aligns with $\\mathcal{V}$ .", + "bbox": [ + 88, + 381, + 483, + 501 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A workaround is to transport only the mass of indistribution (ID) samples between $\\mathcal{V}$ and $\\mathcal{A}$ while retaining the out-of-distribution (OOD) mass within $\\mathcal{A}$ . This leads to the concept of Partial OT (POT) [6], which relaxes the assumption of equal total mass between $\\mathcal{V}$ and $\\mathcal{A}$ . Instead, it allows for transporting a portion of the mass within the range $[0, \\min(\\|\\mathcal{V}\\|_1, \\|\\mathcal{A}\\|_1)]$ . To this end, we use the visual distribution $\\mathcal{V}$ as a baseline distribution to filter out redundant outliers in $\\mathcal{A}$ . Accordingly, the visual distribution $\\mathcal{V}$ and attribute distribution $\\mathcal{A}$ are redefined as", + "bbox": [ + 88, + 502, + 483, + 652 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} = \\sum_ {m = 1} ^ {M} \\frac {1}{M} \\delta_ {\\boldsymbol {v} _ {m}}, \\quad \\mathcal {A} = \\sum_ {n = 1} ^ {N} \\frac {\\alpha}{N} \\delta_ {\\boldsymbol {a} _ {n}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 660, + 483, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha = \\frac{N}{N'} \\geqslant 1$ is the attribute redundant rate reflecting the redundant mass in $\\mathcal{A}$ , which enables transporting only a subset of mass in $\\mathcal{A}$ . In this manner, we formulate the resulting problem as a POT problem with the following marginal constraints:", + "bbox": [ + 89, + 710, + 483, + 789 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Pi (\\mathcal {V}, \\mathcal {A}) \\triangleq \\left\\{\\mathbf {T} \\in \\mathbb {R} _ {+} ^ {M \\times N} \\mid \\mathbf {T} \\mathbf {1} _ {N} = \\mathcal {V}, \\mathbf {T} ^ {\\top} \\mathbf {1} _ {M} \\leqslant \\mathcal {A} \\right\\}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 796, + 483, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is important to highlight that, unlike the traditional POT problem, which imposes inequality constraints on both distributions, Eq. (5) introduces equality constraints within $\\nu$ [48]. This modification explicitly aligns the attribute distribution with the visual distribution by redistributing weights among", + "bbox": [ + 89, + 824, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the attributes. Moreover, the concise constraints accelerate the convergence of POT computations. The POT distance is then denoted as", + "bbox": [ + 511, + 381, + 906, + 426 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {\\mathrm {P O T}, \\epsilon} (\\mathcal {V}, \\mathcal {A}; \\mathbf {C}) \\triangleq \\min _ {\\mathbf {T} \\in \\Pi (\\mathcal {V}, \\mathcal {A})} \\left\\langle \\mathbf {T}, \\mathbf {C} \\right\\rangle_ {F} - \\epsilon h (\\mathbf {T}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 436, + 906, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon > 0$ is the regularization coefficient, and $h(\\mathbf{T}) = -\\sum_{m,n} T_{m,n} \\ln (T_{m,n})$ is the entropic constraint to accelerate the optimization [12], so that the optimal $\\mathbf{T}$ can be estimated in a few iterations. We defer the detailed optimization procedure of Eq. (6) to Supplementary Material.", + "bbox": [ + 511, + 472, + 908, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Curriculum Attribute Selection", + "text_level": 1, + "bbox": [ + 511, + 558, + 792, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Upon the optimal transport plan $\\mathbf{T}$ derived in Eq. (6), we can define an in-distribution (ID) score for each attribute as $s = [s_1, s_2, \\ldots, s_N]^\\top$ , by aggregating the mass transferred from one attribute to all visual objects:", + "bbox": [ + 511, + 579, + 906, + 641 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {n} = \\frac {N}{\\alpha} \\sum_ {m = 1} ^ {M} T _ {m, n}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 648, + 906, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s_n \\in [0,1]$ is the scaled mass transported that can be interpreted as the probability of the specific attribute being in-distribution to the visual objects in $\\mathbf{V}$ . The underlying rationale is that the transport cost among ID samples is relatively low. To minimize the total transport cost, ID attributes in $\\mathcal{A}$ are allocated a greater proportion of transportation mass compared to the redundant OOD attributes, in accordance with the principles of POT.", + "bbox": [ + 511, + 688, + 905, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the ID scores $s$ at hand, one can simply select $N'$ attributes with the highest ID scores at a certain stage of training, e.g., at the beginning or the end. However, this may suffer from either the inaccurate transport cost due to the modality gap, or the inaccurate mapping from attributes to known classes. In light of this, we devise an iterative attribute", + "bbox": [ + 511, + 810, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20321", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "selection strategy that follows the spirit of Curriculum Learning [4]. Instead of single-time selection, we divide it into $\\eta$ steps alongside the training, such that only a slightly smaller set of attributes are to be selected in each step, making the POT problem easier to solve, and thus benefit the training stability and attribute selection effectiveness.", + "bbox": [ + 89, + 90, + 483, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Formally, $\\alpha$ in Eq. (4) is now rewritten as $\\alpha = \\left(\\frac{N}{N'}\\right)^{\\frac{1}{\\eta}}$ . In each of the $\\eta$ selection steps, we select the $\\frac{1}{\\alpha}$ amount of the remaining attributes according to the indices of the top $\\frac{1}{\\alpha}$ ID scores $s$ . The detailed selection method is summarized in Lines 5 to 8 in Algorithm 1. We denote the resulting selected attribute embeddings as $\\hat{\\mathbf{A}} \\in \\mathbb{R}^{D \\times N'}$ , with the ID scores being $s = [s_1, s_2, \\dots, s_{N'}]^\\top \\in \\mathbb{R}^{N'}$ .", + "bbox": [ + 89, + 181, + 483, + 291 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Object Class Prediction", + "text_level": 1, + "bbox": [ + 89, + 297, + 308, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After gaining the selected attributes in each step, we can learn a mapping matrix $\\mathbf{W} = [\\pmb{w}_1, \\pmb{w}_2, \\dots, \\pmb{w}_K] \\in \\mathbb{R}^{N' \\times K}$ to assign $N'$ attributes to $K$ known object classes, with the prediction probability computed as", + "bbox": [ + 89, + 319, + 483, + 380 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np \\left(O _ {k} | \\boldsymbol {v}\\right) = \\frac {\\exp \\left(\\boldsymbol {w} _ {k} ^ {\\top} \\mathbf {A} ^ {\\prime \\top} \\boldsymbol {v}\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\boldsymbol {w} _ {k ^ {\\prime}} ^ {\\top} \\mathbf {A} ^ {\\prime \\top} \\boldsymbol {v}\\right)}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 385, + 483, + 424 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which $\\mathbf{A}' = [a_1', a_2', \\dots, a_{N'}']$ is the element-wise multiplication between $s$ and $\\hat{\\mathbf{A}}$ where $a_n' = s_n \\hat{a}_n$ . The inclusion of ID scores $s$ constitutes a complementary \"soft\" filtering strategy by reweighting selected attributes, whose effectiveness is clearly shown in Sec. 5.2.", + "bbox": [ + 89, + 428, + 483, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After acquiring the class predictions, we can use a standard cross-entropy loss to supervise the optimization of both $\\mathbf{W}$ and $\\hat{\\mathbf{A}}$ :", + "bbox": [ + 89, + 507, + 483, + 550 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C E}} = - \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\sum_ {k = 1} ^ {K} l _ {m, k} \\log p \\left(O _ {k} | \\boldsymbol {v} _ {m}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 556, + 483, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $l_{m}$ is the one-hot label vector for $\\mathbf{v}_{m}$ .", + "bbox": [ + 89, + 604, + 383, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Overall Objective", + "text_level": 1, + "bbox": [ + 89, + 626, + 263, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. Our method can be optimized using the below training objective in an end-to-end fashion:", + "bbox": [ + 89, + 648, + 482, + 679 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {C E}} + \\lambda d _ {\\mathrm {P O T}, \\epsilon}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 686, + 482, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which $\\lambda > 0$ is a trade-off coefficient to balance the effect of the POT loss in Eq. (6). Algorithm 1 summarizes the whole training procedure.", + "bbox": [ + 89, + 710, + 483, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference. We follow the prior work [78] to detect if a test visual embedding $\\pmb{v}$ contains unknown objects by combining two probabilities: (a) task relevance—the probability of $\\pmb{v}$ being related to the optimized attribute embeddings $(p_{\\mathrm{ID}})$ , and (b) unknowness—the probability of $\\pmb{v}$ not being from the known classes $(p_{\\mathrm{OOD}})$ , i.e., $p_{\\mathrm{unk}} = p_{\\mathrm{ID}} \\cdot p_{\\mathrm{OOD}}$ :", + "bbox": [ + 89, + 763, + 483, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\mathrm {I D}} = \\max _ {n \\in \\{1, \\dots , N ^ {\\prime} \\}} \\sigma \\left(\\boldsymbol {a} _ {n} ^ {\\prime \\top} \\boldsymbol {v}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 859, + 482, + 878 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\mathrm {O O D}} = 1 - \\max _ {k \\in \\{1, \\dots , K \\}} p \\left(O _ {k} | \\boldsymbol {v}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 881, + 482, + 898 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Training Procedure of PASS for OWOD" + ], + "code_body": "Input: Visual object embeddings $\\mathbf{V}\\in \\mathbb{R}^{D\\times M}$ with the one-hot labels $l$ , initial attribute embeddings $\\mathbf{A}\\in \\mathbb{R}^{D\\times N}$ , target attribute quantity $N^{\\prime}$ , selection steps $\\eta$ , total training epochs $E$ \nOutput: Optimal selected attribute embeddings $\\hat{\\mathbf{A}}$ , mapping matrix $\\mathbf{W}$ , attribute ID scores $s$ \n1 Initialize: Selected attribute embeddings $\\hat{\\mathbf{A}} = \\mathbf{A}$ , selected attribute quantity $\\hat{N} = N$ , Randomly initialized $\\mathbf{W}\\in \\mathbb{R}^{N\\times K}$ , attribute redundancy rate $\\alpha = (\\frac{N}{N^{\\prime}})^{\\frac{1}{\\eta}}$ ; \n2 for $e$ in $(1,2,\\ldots,E)$ do \n3 /* Partial Optimal Transport */ \n4 Get transport plan $\\mathbf{T}$ and distance $d_{\\mathrm{POT}}$ by solving the POT problem between $\\mathbf{V}$ and $\\hat{\\mathbf{A}}$ using Eq. (6) and $\\alpha$ ; \n5 Compute attribute ID scores as $s = \\frac{\\hat{N}}{\\alpha}\\mathbf{T}^\\top\\mathbf{1}_M$ ; \n6 /* Curriculum Attribute Selection */ \n7 if $e\\bmod\\left[\\frac{E}{\\eta+1}\\right]=0$ then \n8 end \n9 Calculate object class prediction $p(O_k|v)$ for $\\mathbf{V}$ in Eq. (8) using $\\mathbf{W}$ , $\\hat{\\mathbf{A}}$ , and $s$ ; \n10 Calculate loss $\\mathcal{L}_{\\mathrm{CE}}$ in Eq. (9) using $p(O_k|v)$ and $l$ ; \n11 Get final loss $\\mathcal{L}$ by combining $\\mathcal{L}_{\\mathrm{CE}}$ and $d_{\\mathrm{POT}}$ in Eq. (10); \n12 Update $\\mathbf{W}$ and $\\hat{\\mathbf{A}}$ using $\\nabla\\mathcal{L}$ ; \n13 end", + "bbox": [ + 516, + 111, + 906, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma (\\cdot)$ is the sigmoid function.", + "bbox": [ + 511, + 544, + 746, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 511, + 571, + 637, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present the experimental evaluations of our proposed PASS. We start with the experimental setup, followed by the evaluation results and analysis.", + "bbox": [ + 511, + 598, + 906, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 511, + 652, + 702, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. As the performance on traditional OWOD benchmarks [22]—which are based on common everyday object datasets like COCO [31]—is reported to be highly saturated [78], we use the Real-World Object Detection Benchmark established in [78] to evaluate the proposed method. This benchmark is designed for the few-shot or low-data setting, recognizing that most real-world applications cannot gather datasets on the scale of traditional benchmarks. Specifically, it includes five challenging real-world datasets as outlined below. (a) Aquatic [10] contains 637 underwater images of 7 different sea animals, providing useful data for marine-related applications. (b) Aerial [28] contains 10,000 aerial photos of 20 different structures such as stadiums and storage containers, supporting satellite imaging and intelligence analysis. (c) Game [10] contains 1575 game screen", + "bbox": [ + 511, + 674, + 908, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20322", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "shots with 59 different avatars, serving as a benchmark for testing on synthetic data. (d) Medical [10] consists of 182 hand X-rays to identify 12 different bones, offering insights for medical applications such as detecting arthritis, fractures, and structural issues in hands. (e) Surgery [5] is composed of 1829 images of 13 different surgical instruments, captured under neurosurgical microscopes.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Protocol. For each dataset, classes were evenly divided into two subsets: one containing the most common classes and the other containing the least common classes. The evaluation follows OWOD protocols and is conducted in two tasks. In Task 1, the model is provided with the most common classes as known (K), while the least common classes remain unknown (U), and the model is expected to detect both known and unknown object classes. In Task 2, in addition to the previously known (PK) classes, the least common classes are introduced as currently known (CK) classes. The model's performance is then evaluated on both PK and CK classes.", + "bbox": [ + 89, + 204, + 482, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The mean average precision (mAP) is used to evaluate the performance in known classes (K-mAP). To gain deeper insights into the quality of continual learning in OWOD, mAP is further divided to respectively evaluate PK and CK classes (PK-mAP and CK-mAP) as discussed above. Additionally, we also report the mean average precision for unknown objects (U-mAP).", + "bbox": [ + 89, + 385, + 482, + 491 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. Our approach is based on a frozen CLIP-pretrained OWL-ViT model (B/16 and L/14) [41], which has been fine-tuned for detection on a federated dataset combining Objects365 [52] and Visual Genome [24]. We leverage this frozen model, focusing on the construction of optimal attribute embeddings $\\hat{\\mathbf{A}}$ and a mapping matrix $\\mathbf{W}$ to enhance the detection performance for both known and unknown object classes. For training, we use $\\epsilon = 0.01$ in Eq. (6). For fair comparison with [78], $N'$ is determined so that the average number of selected attributes per known class is 25. $\\eta$ is default to be 4 for all datasets. Other hyperparameters, including training epochs and learning rate, are searched based on the validation mAP on known classes following [78]. The experiments were carried out on an NVIDIA RTX A6000 GPU. More implementation details are provided in Supplementary Material.", + "bbox": [ + 89, + 500, + 482, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 750, + 243, + 766 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We ablate our proposed PASS to evaluate the effectiveness of each proposed module. As shown in Tab. 1, the ablation study primarily focuses on the POT distance loss $(d_{\\mathrm{POT}})$ in Eq. (6), the attribute selection method in Sec. 4.2, and the attribute ID score $(s)$ reweighting strategy in Eq. (8).", + "bbox": [ + 89, + 772, + 482, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of POT loss. The minimization of POT distance $(d_{\\mathrm{POT}})$ constitutes an important ingredient of our proposed PASS. It explicitly optimizes the attribute embeddings to", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ce3ad7ec3b012ebca2ff1a0d4310470b5f0c68536ab99b286348144ec7b56024.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Ablation study of PASS. We report U-mAP (U) and K-mAP (K) on two representative datasets: Aquatic and Surgery, with Task 1 evaluation in the 100-shot regime. Best results are highlighted in each column. More ablation study results can be found in Supplementary Material." + ], + "table_body": "
    Dataset (→)AquaticSurgery
    UKUK
    B/16 Backbone:
    PASS Full (Ours)5.243.414.315.6
    PASS w/o Minimizing dPOT3.222.83.05.5
    PASS w/o Attribute Selection4.834.48.112.6
    PASS w/o s Reweighting4.541.310.611.9
    L/14 Backbone:
    PASS Full (Ours)21.753.916.645.6
    PASS w/o Minimizing dPOT10.118.28.014.1
    PASS w/o Attribute Selection15.534.115.243.6
    PASS w/o s Reweighting18.342.213.440.0
    ", + "bbox": [ + 517, + 90, + 903, + 311 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "align closely with the corresponding visual object embeddings through optimal assignment, effectively reducing the modality gap and improving the generalizability of attributes. This enables the model to detect both known and unknown object classes. As shown in Tab. 1, performance drops significantly without minimizing $d_{\\mathrm{POT}}$ (setting $\\lambda = 0$ in Eq. (10)), particularly in the detection of unknown objects. While the cross-entropy loss in Eq. (9) helps maintain performance on known objects, relying solely on the classification loss leads to poor generalization of the learned attributes for the unknown objects.", + "bbox": [ + 511, + 402, + 908, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of Attribute Selection. Effective attribute selection helps retain a streamlined set of in-distribution attributes that are most relevant to the specific task. While attribute selection has a less pronounced impact on performance compared to $d_{\\mathrm{POT}}$ , since POT already performs an initial filtering by assigning lower weights to out-of-distribution attributes, it still provides benefits. Specifically, it helps reduce the noise in the attribute pool, which can enhance detection performance. Additionally, keeping a smaller attribute set is more computationally efficient. We provide further analysis on the advantage of the proposed curriculum attribute selection in Supplementary Material.", + "bbox": [ + 511, + 575, + 908, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of Attribute ID Score Reweighting. In addition to the \"hard\" attribute selection, reweighting object class predictions based on the attribute ID score—obtained from the POT transport plan—provides a complementary \"soft\" filtering strategy. This approach allows the final selected attributes to contribute differently, based on their relevance to the specific task, rather than being treated equally. As demonstrated in Tab. 1, this fine-grained use of selected attributes further enhances the detection performance.", + "bbox": [ + 511, + 763, + 908, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20323", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cd95261e1ca880854968da1fec3d57902cbb935be123adea30208b70d93ca060.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. OWOD results on the five real-world object detection datasets. The evaluation on each dataset is divided into two tasks, and we report U-, K-mAP for Task 1, and PK-, CK-mAP for Task 2, which are introduced in Sec. 5.1. BASE-FS, FOMO [78], and our proposed PASS are evaluated in the 100-shot regime, whereas the results of different few-shot regimes are provided in Supplementary Material. †GT baselines leverage ground-truth class names to detect unknown objects, functioning within the open-vocabulary object detection framework and providing an upper bound for text-conditioned (zero-shot) baselines. Best overall results are highlighted in each column." + ], + "table_body": "
    Dataset (→)AquaticAerialGameMedicalSurgeryOverall
    Task ID (→)Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2
    UKPKCKUKPKCKUKPKCKUKPKCKUKPKCKUKPKCK
    B/16 Backbone:
    BASE-ZS+GT†29.845.045.036.71.35.75.71.415.00.40.40.10.50.00.00.15.61.51.40.310.410.510.57.7
    BASE-ZS6.245.045.036.70.95.75.71.415.70.40.40.10.20.00.00.11.41.51.40.34.910.510.57.7
    BASE-ZS+IN26.545.145.136.71.95.75.71.42.40.30.30.00.60.00.00.11.71.41.00.36.610.510.47.7
    BASE-ZS+LLM24.745.145.136.51.45.75.71.415.10.40.40.10.60.00.00.18.91.51.30.310.210.510.57.7
    BASE-FS7.141.141.131.91.210.410.14.016.04.64.83.90.66.16.13.31.311.911.310.95.214.814.710.8
    FOMO [78]3.543.844.140.80.912.012.65.413.33.84.44.12.16.45.511.56.112.712.911.05.215.715.914.6
    PASS (Ours)5.243.443.246.61.914.016.07.021.510.07.79.04.98.46.812.114.315.613.114.79.618.317.417.9
    Δ+1.7-0.4-0.9+5.8+1.0+2.0+3.4+1.6+8.2+6.2+3.3+4.9+2.8+2.0+1.3+0.6+8.2+2.9+0.2+3.7+4.4+2.5+1.5+2.3
    L/14 Backbone:
    BASE-ZS+GT†34.836.036.042.31.07.97.20.812.40.90.80.32.40.20.20.32.40.22.61.310.69.09.49.0
    BASE-ZS0.735.936.042.39.18.27.20.86.80.90.80.30.00.20.20.33.62.92.61.34.19.69.49.0
    BASE-ZS+IN19.635.835.841.82.37.26.90.915.80.90.80.30.90.10.10.23.12.11.91.18.39.29.18.8
    BASE-ZS+LLM24.735.835.842.20.67.67.20.812.50.90.80.21.60.10.10.212.62.62.51.310.49.49.39.0
    BASE-FS2.443.642.942.89.723.721.913.08.210.410.213.41.123.221.724.23.626.025.07.45.025.424.320.2
    FOMO [78]18.250.148.147.16.025.323.716.030.410.79.911.29.421.819.934.612.029.028.98.515.227.426.123.5
    PASS (Ours)21.753.956.658.38.434.236.120.236.024.323.726.313.134.330.032.016.645.647.943.319.138.538.936.0
    Δ+3.5+3.8+8.5+11.2+2.4+8.9+12.4+4.2+5.6+13.6+13.8+15.1+3.7+12.5+10.1-2.6+4.6+16.6+19.0+34.8+3.9+11.1+12.8+12.5
    ", + "bbox": [ + 91, + 88, + 903, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Main Results", + "text_level": 1, + "bbox": [ + 89, + 460, + 228, + 476 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform extensive evaluations of our proposed PASS method, comparing it with existing state-of-the-art approaches (SOTAs). Additionally, we present qualitative results that showcase the detection outcomes along with the most relevant attributes used in the process. More experimental results can also be found in Supplementary Material.", + "bbox": [ + 89, + 483, + 485, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with State of the Arts. We compare our proposed PASS with FOMO [78] and the strong baselines established therein, by adapting the Open-Vocabulary Object Detection (OVOD) methods [41] that also use foundation models to the OWOD setting. As listed in Tab. 2, BASE-ZS uses a generic \"object\" prompt for unknown objects [39], while BASE-ZS+IN utilizes all ImageNet class names (with the known classes removed) as the unknown classes proposals, and BASE-ZS+LLM employs class names predicted by an LLM (based on the known classes) for detecting potential unknown objects. On the other hand, BASE-ZS+GT uses the ground-truth class names for unknown objects, serving as the upper bound of the OVOD methods by assuming access to all unknown class names. BASE-FS utilizes image exemplars to produce vision-derived object embeddings, which are averaged per class to form class embeddings. Then a general prompt, such as \"a photo of an object\", is applied to help identify unknown objects.", + "bbox": [ + 89, + 583, + 482, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As can be seen in Tab. 2, our proposed PASS consistently outperforms FOMO by a significant margin and achieves performance that is very close to the OVOD upper bound, even", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "when using the B/16 backbone. In particular, our improvement is especially notable in known classes, as reflected in the K-, PK-, and CK-mAP metrics. This can be attributed to the robust attribute selection and optimization capabilities of our proposed PASS framework, which effectively curates a set of accurate and effective attributes to enhance object detection. On the other hand, PASS also demonstrates a significant performance boost in unknown classes as measured by the U-mAP metric. This suggests that the attributes learned by PASS are not only effective for known classes during training but also highly generalizable to unknown objects during evaluation.", + "bbox": [ + 511, + 462, + 908, + 643 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualizations. For further comprehension of the effectiveness of our proposed PASS in detecting open world objects, we present several qualitative results for each dataset in Fig. 3. When comparing the detection results between FOMO (second row) and our proposed PASS (third row), PASS consistently demonstrates improved detection performance, with results that are more closely aligned with the ground truth (first row). In particular, FOMO sometimes incorrectly classifies known objects as unknown, or vice versa, suggesting that the learned attributes might not be sufficiently accurate to reliably characterize known objects. Furthermore, FOMO occasionally yields significantly fewer detection results in certain domains, such as medical datasets. This suggests that the learned attributes might not adequately capture the full range of potentially useful features necessary for detecting unknown objects. In contrast, PASS delivers", + "bbox": [ + 511, + 657, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20324", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5f89167e4cbe184b5148b3eedcc12aa9a20e2df14853cbb5759762effc5db146.jpg", + "image_caption": [ + "Aquatic" + ], + "image_footnote": [], + "bbox": [ + 99, + 101, + 253, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/688f8bd66bb114ad23e0eb8a8852af2aa9bbf69cece97ad71ad9b66df16a03a0.jpg", + "image_caption": [ + "Aerial" + ], + "image_footnote": [], + "bbox": [ + 259, + 101, + 413, + 219 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e53f57753cc7bd743e8e6edc064f5c8ecc70f5c566fbcfab76aab2dd6f9f5380.jpg", + "image_caption": [ + "Game" + ], + "image_footnote": [], + "bbox": [ + 419, + 101, + 573, + 219 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dcfee6a6987b57fbc09d2a6c23bc95dd4bab65d3f2cd2b5b2be97d3256aa14bb.jpg", + "image_caption": [ + "Medical" + ], + "image_footnote": [], + "bbox": [ + 581, + 101, + 733, + 219 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3de4ebaaebe79b7fe334a684667d54ba8019498462aa2cc82f8e848a8fe0a8ba.jpg", + "image_caption": [ + "Surgery" + ], + "image_footnote": [], + "bbox": [ + 741, + 101, + 895, + 219 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8a22cf17aa3f8b1ce8a2d94f38073a182a2856ed0b486e175d718e79812fe89f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 224, + 253, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/921fdd49b891bb53a52340b570adfeb5ea0ea5cc5b888c73d4aa475c10c36df3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 259, + 224, + 413, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9fe5eabd87e51347dd8d24ab0f3c17f77751b818db863dc5d39df967b5e4ef9a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 419, + 224, + 573, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6bfa16f3fb393e7f2903e469c6d0c0bac3c19a2da5c1e85c52395e632b3967cf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 224, + 733, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a5855455638e6b4e0abd11e1aa9d8550e6fa871d836faefe89f2fb4fd4ea8c9a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 740, + 224, + 895, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/21f353d7ed8a1eadeee8a63ad28d743398f04ed933b93ff856935ecbfa5db825.jpg", + "image_caption": [ + "Figure 3. Qualitative results on the five real-world datasets. First Row: images in each dataset with ground truth bounding boxes and class names. Second Row: Detection results using FOMO [78]. Third Row: Detection results using our proposed PASS. We use green and yellow boxes to indicate known and unknown objects, respectively. Bottom Rows: The top three attributes that are activated for detecting known and unknown classes in each image using our proposed PASS." + ], + "image_footnote": [], + "bbox": [ + 99, + 348, + 253, + 465 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/410323d131864cbba4659b1aa697106eb3b2d0e9dd152c48c26d73373df6a93e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 259, + 348, + 413, + 465 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f836e38d42008afa22e0c7846aa6dd70e0928995876b8f50265d6f5ef8e70a51.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 419, + 348, + 573, + 465 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a43f9e065c49cbdfbb6d187d3cb6965e605bfdca5e557424d1fcd164c851ad18.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 348, + 733, + 465 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e26fbe3b482b79cdf093b2651cd3a151281995c8d4d915ba15add9951935f4c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 741, + 348, + 895, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected known classes:", + "bbox": [ + 104, + 473, + 243, + 492 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Shape is truncate tail", + "Shape is flexible", + "Environment is tide pool" + ], + "bbox": [ + 106, + 493, + 238, + 520 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected known classes:", + "bbox": [ + 266, + 473, + 405, + 492 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Shape is stationary", + "Shape is converging", + "Behavior is tournament" + ], + "bbox": [ + 266, + 493, + 395, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected known classes:", + "bbox": [ + 426, + 473, + 565, + 492 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Material is calcium", + "- Appearance is visible", + "joints between bones", + "Color is veins" + ], + "bbox": [ + 426, + 493, + 544, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected known classes:", + "bbox": [ + 586, + 473, + 725, + 492 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Shape is straight", + "Shape is convex", + "Shape is knobby" + ], + "bbox": [ + 588, + 493, + 683, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected known classes:", + "bbox": [ + 748, + 473, + 885, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Behavior is handle", + "bbox": [ + 750, + 493, + 852, + 501 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Features is gripping surface", + "- Appearance is presence of grooves" + ], + "bbox": [ + 750, + 502, + 883, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected unknown classes:", + "bbox": [ + 106, + 532, + 243, + 550 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Shape is dorsal fin shape", + "Texture is ridged", + "Shape is adipose fin shape" + ], + "bbox": [ + 106, + 551, + 240, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected unknown classes:", + "bbox": [ + 266, + 532, + 405, + 550 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Appearance is distinctive roof design", + "Context is court lines", + "Shape is stationary" + ], + "bbox": [ + 266, + 551, + 401, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected unknown classes:", + "bbox": [ + 426, + 532, + 565, + 550 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Appearance is edges", + "Shape is smooth", + "Texture is striped" + ], + "bbox": [ + 426, + 551, + 540, + 577 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected unknown classes:", + "bbox": [ + 586, + 532, + 725, + 550 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Shape is cracked", + "Shape is straight", + "- Features is thumb metacarpal" + ], + "bbox": [ + 588, + 551, + 689, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Top attributes for detected unknown classes:", + "bbox": [ + 748, + 532, + 885, + 550 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Material is cutting edge", + "Shape is pointed tips", + "- Appearance is shiny" + ], + "bbox": [ + 750, + 551, + 877, + 577 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "superior detection results due to the more accurate attributes learned during training. These attributes not only provide a strong characterization of known object classes but also demonstrate high generalizability to unknown classes. Furthermore, as illustrated in the bottom two rows of Fig. 3, PASS effectively leverages meaningful attributes to identify both known and unknown objects. For example, it uses the attribute \"shape is dorsal fin shape\" to detect an unknown fish species recognized for its large fin.", + "bbox": [ + 89, + 674, + 483, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 828, + 209, + 843 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose an efficient end-to-end approach to select a compact set of representative attributes tailored to detect open-world objects, including both known and unknown", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "classes. Specifically, we formulate the attribute selection and optimization process as a Partial Optimal Transport (POT) problem, where the most relevant attributes emerge with the highest transported mass. Additionally, we introduce a curriculum-based attribute selection strategy that gradually refines the attribute subset during training, significantly enhancing training stability and selection effectiveness. We evaluate our approach on challenging real-world datasets, where it achieves superior performance that surpasses current state-of-the-art methods by a large margin.", + "bbox": [ + 511, + 674, + 906, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In future work, we aim to expand our method to incorporate hierarchical information within attribute taxonomies. This enhancement will allow for a more fine-grained understanding of the detection process by leveraging attributes at varying levels of granularity.", + "bbox": [ + 511, + 825, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20325", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This research is supported by the EDB Space Technology Development Programme under Project S22-19016-STDP, the National Natural Science Foundation of China under Grant 62306251, 62171343, 62176171, U21B2040, the Hong Kong Research Grant Council - Early Career Scheme under Grant 27208022, the HKU Seed Fund for Basic Research, the Fundamental Research Funds for the Central Universities under Grant CJ202303, as well as the Sichuan Science and Technology Planning Project under Grant 24NSFTD0130. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 11444-11453, 2023. 1, 2" + ], + "bbox": [ + 516, + 90, + 906, + 854 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20328", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Detecting Open World Objects via Partial Attribute Assignment/9a893be0-4b48-49d9-8973-6218a7e4b1e4_model.json b/2025/Detecting Open World Objects via Partial Attribute Assignment/9a893be0-4b48-49d9-8973-6218a7e4b1e4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b0c59079698095129f8261a62ecaad1f1bf54f9a --- /dev/null +++ b/2025/Detecting Open World Objects via Partial Attribute Assignment/9a893be0-4b48-49d9-8973-6218a7e4b1e4_model.json @@ -0,0 +1,3137 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.176, + 0.131, + 0.823, + 0.154 + ], + "angle": 0, + "content": "Detecting Open World Objects via Partial Attribute Assignment" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.181, + 0.889, + 0.219 + ], + "angle": 0, + "content": "Muli Yang\\(^{1}\\) Gabriel James Goenawan\\(^{1}\\) Huaiyuan Qin\\(^{1}\\) Kai Han\\(^{2}\\) Xi Peng\\(^{3}\\) Yanhua Yang\\(^{4}\\) Hongyuan Zhu\\(^{1\\dagger}\\) \n\\(^{1}\\)Institute for Infocomm Research (I\\(^{2}\\)R), A*STAR, Singapore" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.22, + 0.888, + 0.256 + ], + "angle": 0, + "content": "\\(^{2}\\)The University of Hong Kong, Hong Kong SAR \\(^{3}\\)Sichuan University, China \\(^{4}\\)Xidian University, China {yangml, goenawan, qinhy, zhuh}@i2r.a-star.edu.sg, kaihanx@hku.hk, pengxi@scu.edu.cn, yanhyang@xidian.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.29, + 0.327, + 0.306 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.322, + 0.486, + 0.671 + ], + "angle": 0, + "content": "Despite being trained on massive data, today's vision foundation models still fall short in detecting open world objects. Apart from recognizing known objects from training, a successful Open World Object Detection (OWOD) system must also be able to detect unknown objects never seen before, without confusing them with the backgrounds. Unlike prevailing prior works that rely on probability models to learn \"objectness\", we focus on learning fine-grained, class-agnostic attributes, allowing the detection of both known and unknown objects in an explainable manner. In this paper, we propose Partial Attribute Assignment (PASS), aiming to automatically select and optimize a small, relevant subset of attributes from a large attribute pool. Specifically, we model attribute selection as a Partial Optimal Transport (POT) problem between known visual objects and the attribute pool, in which more relevant attributes signify more transported mass. PASS follows a curriculum schedule that progressively selects and optimizes a targeted subset of attributes during training, promoting stability and accuracy. Our method enjoys end-to-end optimization by minimizing the POT distance and the classification loss on known visual objects, demonstrating high training efficiency and superior OWOD performance among extensive experimental evaluations." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.701, + 0.222, + 0.716 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.727, + 0.485, + 0.877 + ], + "angle": 0, + "content": "Deep learning and foundation models have emerged as critical AI technologies [1, 55], impacting various aspects of modern life. However, their success has been largely based on the closed-world assumption, which presumes a static and well-defined environment [76]. In practice, this assumption is difficult to uphold, as real-world conditions are dynamic and unpredictable, with unforeseen situations and unseen objects regularly appearing. Open World Object Detection (OWOD) [22] has emerged as a remedy to deliver reliable detection in the face of new environments with unknown ob" + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.356, + 0.535, + 0.368 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.538, + 0.288, + 0.905, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.519, + 0.535, + 0.531 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.462, + 0.906, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.586, + 0.908, + 0.67 + ], + "angle": 0, + "content": "Figure 1. The role of attributes in Open World Object Detection (OWOD). (a) Unknown objects can be detected via shared visual/functional attributes with known objects. (b) Our method is able to automatically identify and optimize a small subset of relevant attributes from a large pool, effectively enabling the detection of both known and unknown objects." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.702, + 0.907, + 0.763 + ], + "angle": 0, + "content": "jects. In addition to recognizing known objects that appeared in training, a successful OWOD system must also detect and continually learn previously unseen objects without mistakenly classifying them as backgrounds." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.765, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Recent works mainly use probability distribution estimation to model the \"objectness\" information, i.e., the probability of a candidate proposal being an object rather than backgrounds [79]. In this way, OWOD can be decomposed into two sub-tasks that respectively focus on objectness estimation and known class recognition [54]. Although this approach has significantly improved the detection of unknown objects, it has certain limitations in explainability and ambiguity. On the one hand, the learned probabilistic" + }, + { + "type": "page_footnote", + "bbox": [ + 0.093, + 0.887, + 0.483, + 0.901 + ], + "angle": 0, + "content": "†Corresponding author. ‡Code: https://github.com/muliyangm/PASS" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20318" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.152 + ], + "angle": 0, + "content": "model is unable to explain how the objects—both the known and the unknown—are detected. On the other hand, when background features resemble those of the unknown objects, the model can still misclassify them." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.155, + 0.486, + 0.516 + ], + "angle": 0, + "content": "In this paper, we focus on detecting open world objects using fine-grained, class-agnostic attributes that are visually and/or functionally related to the known objects. These attributes can be described using natural languages with rich semantic information, and thus are naturally explainable and less ambiguous. The emphasis on intrinsic object attributes offers stronger resistance to confusion in scenarios where background and unknown object features overlap, making it particularly suitable for dynamic open-world environments. As illustrated in Fig. 1(a), attributes can be useful in detecting both known and unknown object classes, e.g., the learned \"umbrella-like\" attribute from known classes can be used to detect the unknown fungi. Despite the promising potential of using attributes in OWOD, effectively curating a set of attributes that are closely related to the specific task from a large pool of attributes remains a significant challenge. To this end, some existing method [78] seeks a set of representative attributes that can effectively classify known objects with multistage processes—such as attribute selection and refinement—which are time-consuming and computationally expensive. More importantly, the separation of the selection and refinement processes may accumulate errors, leading to inaccuracies in the results of the attribute selection and refinement." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.521, + 0.486, + 0.762 + ], + "angle": 0, + "content": "We propose to tackle this dilemma using Partial Attribute Assignment (PASS), an approach that progressively selects and optimizes a targeted subset of relevant attributes throughout the training process in an end-to-end manner. In particular, we model attribute selection as a Partial Optimal Transport (POT) problem [6] between known visual objects and the attribute pool, in which more relevant attributes signify more mass transported to the visual objects. Unlike conventional OT [56] that assumes identical mass in both distributions to be completely transported, POT allows the transport of only a targeted fraction of total mass from one distribution to another. As such, the attribute pool can be viewed as a collection of both in-distribution (ID) and out-of-distribution (OOD) attributes w.r.t. the visual objects, where we can use the visual object distribution as the baseline distribution to filter out redundant OOD attributes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.486, + 0.901 + ], + "angle": 0, + "content": "To achieve stable, accurate attribute selection and optimization simultaneously, PASS follows a curriculum learning [4] schedule that progressively targets and optimizes a subset of attributes throughout training. PASS ensures that each filtered subset is highly representative and provides broad coverage of the visual objects, by iteratively focusing on and refining a smaller subset of attributes guaranteed by the OT theory. As training progresses, the selected attributes reach a balanced state between representativeness and cover-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.909, + 0.318 + ], + "angle": 0, + "content": "age, allowing the model to better adapt to both known and unknown objects. This process also reduces computational costs by gradually limiting the number of attributes introduced. Our method enjoys end-to-end optimization by minimizing both the POT distance and the classification loss for known visual objects. During inference, the learned attributes play a dual role: they support the recognition of known classes through the mapping relationships established during training, while also enabling the detection of unknown objects by leveraging the correlation between object proposals and the learned attributes. Extensive experiments demonstrate that our method significantly outperforms baseline methods, validating both the feasibility of attribute-based OWOD and the effectiveness of our approach in curating more accurate attributes for OWOD." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.321, + 0.8, + 0.335 + ], + "angle": 0, + "content": "In a nutshell, our main contributions are" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.338, + 0.907, + 0.399 + ], + "angle": 0, + "content": "- We model the attribute curation issue in OWOD as a Partial Optimal Transport (POT) problem, enabling end-to-end attribute selection and optimization for effectively detecting both known and unknown objects;" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.4, + 0.907, + 0.459 + ], + "angle": 0, + "content": "- We propose a curriculum selection strategy by progressively optimizing a targeted subset of attributes with strong representativeness and broad coverage, benefiting both training stability and selection effectiveness;" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.459, + 0.907, + 0.505 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the absolute superiority of the proposed method in terms of both training efficiency and detection performance." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.338, + 0.907, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.526, + 0.655, + 0.541 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Open World Object Detection. Open World Object Detection (OWOD) [22] enhances traditional object detectors by shifting away from closed-set assumptions, enabling dynamic adaptation to novel classes as encountered in real-world settings [20, 29, 30, 33, 34, 67, 74]. Existing works [27, 51, 61, 65, 69, 70] reduce the overlap between known, unknown classes and the background distributions using different ways, e.g., pseudo-labeling [18, 38], objectness estimation [54, 79], and hierarchical modeling [13, 37]. OWOD is also related to similar tasks such as Class-Agnostic Object Detection [14, 21, 23, 36, 44, 45, 50, 59, 60] and Open-Vocabulary Object Detection (OVOD) [17, 25, 41, 42, 58, 71, 75]. Recent advances, such as FOMO [78] and a concurrent work UMB [62], extend the standard OVOD method to OWOD by utilizing vision and language foundation models. By identifying objects based on semantic attributes [26, 49, 53], they learn class-agnostic attributes to detect task-relevant unknown objects, yet require multistage attribute selection and refinement, which is time-consuming and computationally inefficient. In this paper, we propose an end-to-end attribute curation method that not only benefits the training efficiency but also largely improves the detection performance in both known and unknown classes." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20319" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.487, + 0.41 + ], + "angle": 0, + "content": "Optimal Transport. Optimal Transport (OT), originally introduced by Monge [43] to minimize the cost of transporting items, has become a prominent tool in machine learning and computer vision for matching distributions across domains [46, 56]. OT has been widely applied in distribution-based tasks [8, 57, 73] such as generative models [2], clustering [19, 66], domain adaptation [11], object detection [16] and structural tasks such as sequence [9], graph [63], and image matching [32, 72]. To address OT's high computational demands, the Sinkhorn OT [12] offers a solution by approximating OT through an efficient iterative algorithm. Partial OT (POT), a variant of OT that transports only a portion of the mass, addresses cases where distributions only partially overlap, making it especially relevant in scenarios such as open-set domain adaptation [6, 7, 15, 35, 48, 64, 68]. The Sinkhorn algorithm has been extended to POT to further reduce computational costs [3]. In our work, we utilize POT to dynamically match attribute embeddings with visual embeddings of known object classes, selecting and optimizing the most representative attributes for effectively detecting both known and unknown objects." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.423, + 0.221, + 0.44 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.485, + 0.705 + ], + "angle": 0, + "content": "OWOD with Foundation Models. Open World Object Detection (OWOD) requires a model to detect and incrementally learn unknown objects. In particular, there are multiple stages/tasks for training and evaluation, indicated by \\( t \\). In task \\( t \\), the model can be trained on \\( K^t \\) known object classes from \\( \\mathcal{K}^t = \\{O_1^t, O_2^t, \\ldots, O_{K^t}^t\\} \\), and to be evaluated on a test set that contains both known and unknown classes. To achieve that, we use an additional \\( O_0^t \\) to denote the unknown classes, alongside the \\( K^t \\) known classes. In fact, \\( O_0^t \\) represents \\( U^t \\) classes of interest that are unknown to the model in the task \\( t \\), i.e., \\( \\mathcal{U}^t = \\{O_{K^t + 1}^t, O_{K^t + 2}^t, \\ldots, O_{K^t + U^t}^t\\} \\). After discovering the unknown object classes, the model can be updated with the knowledge of these new classes using annotations from an oracle (e.g., a human annotator) in task \\( t + 1 \\). As a result, the model is ready to detect \\( K^{t + 1} = K^t + U^t \\) known object classes in the test set, as well as additional unknown classes for the subsequent task cycle." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.487, + 0.902 + ], + "angle": 0, + "content": "To push the boundary of OWOD in real-world applications, we follow a recent work [78] to make use of existing pretrained foundation models in open-vocabulary object detection [41, 71], e.g., vision and language encoders, and adapt them to OWOD. The training follows a few-shot paradigm: for the \\(z\\)-shot, only \\(z\\) images per known class are given, with only one bounding box label and one object class label for each image. For each dataset, we use the attribute texts proposed by a Large Language Model (LLM), i.e., GPT-3.5, by prompting with the known class names using the template described in recent works [40, 77, 78]. This will result in an attribute pool with numerous class-agnostic attributes visually and/or functionally related to the known" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.093, + 0.776, + 0.108 + ], + "angle": 0, + "content": "objects, e.g., shape is straight." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.118, + 0.907, + 0.193 + ], + "angle": 0, + "content": "Optimal Transport Preliminary. Optimal Transport (OT) is a powerful tool for measuring the distance between two distributions. Here we review the discrete OT scenario that is more related to our framework and refer the readers to [12] for more details." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.194, + 0.907, + 0.239 + ], + "angle": 0, + "content": "Assuming we have two sets of data points (features) \\(\\mathbf{X} = \\{\\pmb{x}_m\\}_{m=1}^M\\) and \\(\\mathbf{Y} = \\{\\pmb{y}_n\\}_{n=1}^N\\), their discrete distributions can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.248, + 0.907, + 0.29 + ], + "angle": 0, + "content": "\\[\n\\mathcal {X} = \\sum_ {m = 1} ^ {M} \\frac {1}{M} \\delta_ {\\boldsymbol {x} _ {m}}, \\quad \\mathcal {Y} = \\sum_ {n = 1} ^ {N} \\frac {1}{N} \\delta_ {\\boldsymbol {y} _ {n}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.3, + 0.909, + 0.346 + ], + "angle": 0, + "content": "where \\(\\delta\\) is the Dirac function and we use the uniform distribution to equally view each data point. The OT distance is defined as the smallest cost of transporting \\(\\mathcal{X}\\) to \\(\\mathcal{Y}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.356, + 0.907, + 0.383 + ], + "angle": 0, + "content": "\\[\nd _ {\\mathrm {O T}} (\\mathcal {X}, \\mathcal {Y}; \\mathbf {C}) \\triangleq \\min _ {\\mathbf {T} \\in \\Pi (\\mathcal {X}, \\mathcal {Y})} \\left\\langle \\mathbf {T}, \\mathbf {C} \\right\\rangle_ {F}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.394, + 0.907, + 0.487 + ], + "angle": 0, + "content": "in which \\(\\mathbf{C} \\in \\mathbb{R}_{+}^{M \\times N}\\) is the cost matrix between \\(\\mathbf{X}\\) and \\(\\mathbf{Y}\\) where \\(C_{m,n} = c(\\pmb{x}_m, \\pmb{y}_n)\\) is the transport cost from \\(\\pmb{x}_m\\) to \\(\\pmb{y}_n\\), with \\(c(\\cdot)\\) being the cost function (e.g., the cosine distance), \\(\\mathbf{T}\\) is the transport plan to be solved, and \\(\\langle \\cdot, \\cdot \\rangle_F\\) denotes the Frobenius inner product. The optimization of OT distance satisfies two marginal constraints:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.497, + 0.907, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\Pi (\\mathcal {X}, \\mathcal {Y}) \\triangleq \\left\\{\\mathbf {T} \\in \\mathbb {R} _ {+} ^ {M \\times N} \\mid \\mathbf {T} \\mathbf {1} _ {N} = \\mathcal {X}, \\mathbf {T} ^ {\\top} \\mathbf {1} _ {M} = \\mathcal {Y} \\right\\}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.527, + 0.906, + 0.575 + ], + "angle": 0, + "content": "where \\(\\mathbf{1}_N\\) is an \\(N\\)-dimensional vector of all ones, and we slightly abuse \\(\\mathcal{X}\\), \\(\\mathcal{Y}\\) to denote \\(\\mathcal{X} = \\frac{1}{M}\\mathbf{1}_M\\), \\(\\mathcal{Y} = \\frac{1}{N}\\mathbf{1}_N\\) to reflect the discrete probability in Eq. (1)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.587, + 0.606, + 0.603 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.612, + 0.907, + 0.673 + ], + "angle": 0, + "content": "We propose Partial Attribute Assignment (PASS) to address the challenging Open World Object Detection (OWOD) task. PASS is composed of three modules shown in Fig. 2, which are introduced in separate subsections below." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.683, + 0.774, + 0.699 + ], + "angle": 0, + "content": "4.1. Partial Attribute Assignment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.81 + ], + "angle": 0, + "content": "As discussed above, now we have \\( z \\)-shot images of \\( K \\) known object classes (the superscript \\( t \\) is omitted for brevity) and \\( N \\) attribute texts in the attribute pool. Our goal is to select and optimize a small set of relevant attributes from the attribute pool, with the target attribute quantity denoted as \\( N' \\in (0, N] \\). The resulting \\( N' \\) attributes are to be used for effectively detecting both known and unknown objects." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Formally, we collect the visual object embeddings as \\(\\mathbf{V} = [v_{1}, v_{2}, \\ldots, v_{M}] \\in \\mathbb{R}^{D \\times M}\\) and the attribute embeddings as \\(\\mathbf{A} = [a_{1}, a_{2}, \\ldots, a_{N}] \\in \\mathbb{R}^{D \\times N}\\) in the \\(D\\)-dimensional embedding space using pretrained vision and text encoders [41, 47], where \\(M = z \\cdot K\\) is the number of known image patches obtained using bounding box labels," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20320" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.089, + 0.904, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.273, + 0.908, + 0.361 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed Partial Attribute Assignment (PASS) for OWOD. PASS is constructed upon pretrained vision and text encoders [41, 47] and is designed to identify and refine a set of relevant attributes from an attribute pool, which are essential for detecting both known and unknown object classes. (a) We employ Partial Optimal Transport (POT) to model the assignment problem between attributes and known visual objects (Sec. 4.1). (b) The resulting transport plan \\(\\mathbf{T}\\) is used to generate attribute in-distribution (ID) scores \\(s\\), which help in selecting the most relevant attributes for the specific task (Sec. 4.2). (c) These attribute ID scores are further used to reweight the selected attributes, which are subsequently applied to compute object class predictions via a learnable mapping matrix (Sec. 4.3)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.382, + 0.484, + 0.502 + ], + "angle": 0, + "content": "and all embeddings are \\(\\ell_2\\) normalized. Likewise, we can denote the discrete distributions of \\(\\mathbf{V}\\) and \\(\\mathbf{A}\\) as \\(\\mathcal{V}\\) and \\(\\mathcal{A}\\) following Eq. (1). The conventional OT assumes that the two distributions have the identical total probability mass, i.e., \\(\\| \\mathcal{V}\\| _1 = \\| \\mathcal{A}\\| _1\\), and that all the mass of \\(\\mathcal{A}\\) must be transported. Although this assumption works effectively for tasks that involve identical distributions, it faces challenges in our scenario, where only a subset of samples in \\(\\mathcal{A}\\) aligns with \\(\\mathcal{V}\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.503, + 0.484, + 0.653 + ], + "angle": 0, + "content": "A workaround is to transport only the mass of indistribution (ID) samples between \\(\\mathcal{V}\\) and \\(\\mathcal{A}\\) while retaining the out-of-distribution (OOD) mass within \\(\\mathcal{A}\\). This leads to the concept of Partial OT (POT) [6], which relaxes the assumption of equal total mass between \\(\\mathcal{V}\\) and \\(\\mathcal{A}\\). Instead, it allows for transporting a portion of the mass within the range \\([0, \\min(\\|\\mathcal{V}\\|_1, \\|\\mathcal{A}\\|_1)]\\). To this end, we use the visual distribution \\(\\mathcal{V}\\) as a baseline distribution to filter out redundant outliers in \\(\\mathcal{A}\\). Accordingly, the visual distribution \\(\\mathcal{V}\\) and attribute distribution \\(\\mathcal{A}\\) are redefined as" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.661, + 0.484, + 0.703 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} = \\sum_ {m = 1} ^ {M} \\frac {1}{M} \\delta_ {\\boldsymbol {v} _ {m}}, \\quad \\mathcal {A} = \\sum_ {n = 1} ^ {N} \\frac {\\alpha}{N} \\delta_ {\\boldsymbol {a} _ {n}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.712, + 0.484, + 0.79 + ], + "angle": 0, + "content": "where \\(\\alpha = \\frac{N}{N'} \\geqslant 1\\) is the attribute redundant rate reflecting the redundant mass in \\(\\mathcal{A}\\), which enables transporting only a subset of mass in \\(\\mathcal{A}\\). In this manner, we formulate the resulting problem as a POT problem with the following marginal constraints:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.797, + 0.484, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\Pi (\\mathcal {V}, \\mathcal {A}) \\triangleq \\left\\{\\mathbf {T} \\in \\mathbb {R} _ {+} ^ {M \\times N} \\mid \\mathbf {T} \\mathbf {1} _ {N} = \\mathcal {V}, \\mathbf {T} ^ {\\top} \\mathbf {1} _ {M} \\leqslant \\mathcal {A} \\right\\}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.902 + ], + "angle": 0, + "content": "It is important to highlight that, unlike the traditional POT problem, which imposes inequality constraints on both distributions, Eq. (5) introduces equality constraints within \\(\\nu\\) [48]. This modification explicitly aligns the attribute distribution with the visual distribution by redistributing weights among" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.382, + 0.907, + 0.427 + ], + "angle": 0, + "content": "the attributes. Moreover, the concise constraints accelerate the convergence of POT computations. The POT distance is then denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.438, + 0.907, + 0.463 + ], + "angle": 0, + "content": "\\[\nd _ {\\mathrm {P O T}, \\epsilon} (\\mathcal {V}, \\mathcal {A}; \\mathbf {C}) \\triangleq \\min _ {\\mathbf {T} \\in \\Pi (\\mathcal {V}, \\mathcal {A})} \\left\\langle \\mathbf {T}, \\mathbf {C} \\right\\rangle_ {F} - \\epsilon h (\\mathbf {T}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.473, + 0.909, + 0.551 + ], + "angle": 0, + "content": "where \\(\\epsilon > 0\\) is the regularization coefficient, and \\(h(\\mathbf{T}) = -\\sum_{m,n} T_{m,n} \\ln (T_{m,n})\\) is the entropic constraint to accelerate the optimization [12], so that the optimal \\(\\mathbf{T}\\) can be estimated in a few iterations. We defer the detailed optimization procedure of Eq. (6) to Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.559, + 0.794, + 0.573 + ], + "angle": 0, + "content": "4.2. Curriculum Attribute Selection" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.907, + 0.642 + ], + "angle": 0, + "content": "Upon the optimal transport plan \\(\\mathbf{T}\\) derived in Eq. (6), we can define an in-distribution (ID) score for each attribute as \\(s = [s_1, s_2, \\ldots, s_N]^\\top\\), by aggregating the mass transferred from one attribute to all visual objects:" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.65, + 0.907, + 0.681 + ], + "angle": 0, + "content": "\\[\ns _ {n} = \\frac {N}{\\alpha} \\sum_ {m = 1} ^ {M} T _ {m, n}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.809 + ], + "angle": 0, + "content": "where \\( s_n \\in [0,1] \\) is the scaled mass transported that can be interpreted as the probability of the specific attribute being in-distribution to the visual objects in \\( \\mathbf{V} \\). The underlying rationale is that the transport cost among ID samples is relatively low. To minimize the total transport cost, ID attributes in \\( \\mathcal{A} \\) are allocated a greater proportion of transportation mass compared to the redundant OOD attributes, in accordance with the principles of POT." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.907, + 0.901 + ], + "angle": 0, + "content": "With the ID scores \\( s \\) at hand, one can simply select \\( N' \\) attributes with the highest ID scores at a certain stage of training, e.g., at the beginning or the end. However, this may suffer from either the inaccurate transport cost due to the modality gap, or the inaccurate mapping from attributes to known classes. In light of this, we devise an iterative attribute" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20321" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.182 + ], + "angle": 0, + "content": "selection strategy that follows the spirit of Curriculum Learning [4]. Instead of single-time selection, we divide it into \\(\\eta\\) steps alongside the training, such that only a slightly smaller set of attributes are to be selected in each step, making the POT problem easier to solve, and thus benefit the training stability and attribute selection effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.182, + 0.484, + 0.292 + ], + "angle": 0, + "content": "Formally, \\(\\alpha\\) in Eq. (4) is now rewritten as \\(\\alpha = \\left(\\frac{N}{N'}\\right)^{\\frac{1}{\\eta}}\\). In each of the \\(\\eta\\) selection steps, we select the \\(\\frac{1}{\\alpha}\\) amount of the remaining attributes according to the indices of the top \\(\\frac{1}{\\alpha}\\) ID scores \\(s\\). The detailed selection method is summarized in Lines 5 to 8 in Algorithm 1. We denote the resulting selected attribute embeddings as \\(\\hat{\\mathbf{A}} \\in \\mathbb{R}^{D \\times N'}\\), with the ID scores being \\(s = [s_1, s_2, \\dots, s_{N'}]^\\top \\in \\mathbb{R}^{N'}\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.298, + 0.31, + 0.314 + ], + "angle": 0, + "content": "4.3. Object Class Prediction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.32, + 0.484, + 0.381 + ], + "angle": 0, + "content": "After gaining the selected attributes in each step, we can learn a mapping matrix \\(\\mathbf{W} = [\\pmb{w}_1, \\pmb{w}_2, \\dots, \\pmb{w}_K] \\in \\mathbb{R}^{N' \\times K}\\) to assign \\(N'\\) attributes to \\(K\\) known object classes, with the prediction probability computed as" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.386, + 0.484, + 0.425 + ], + "angle": 0, + "content": "\\[\np \\left(O _ {k} | \\boldsymbol {v}\\right) = \\frac {\\exp \\left(\\boldsymbol {w} _ {k} ^ {\\top} \\mathbf {A} ^ {\\prime \\top} \\boldsymbol {v}\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\boldsymbol {w} _ {k ^ {\\prime}} ^ {\\top} \\mathbf {A} ^ {\\prime \\top} \\boldsymbol {v}\\right)}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.429, + 0.485, + 0.507 + ], + "angle": 0, + "content": "in which \\(\\mathbf{A}' = [a_1', a_2', \\dots, a_{N'}']\\) is the element-wise multiplication between \\(s\\) and \\(\\hat{\\mathbf{A}}\\) where \\(a_n' = s_n \\hat{a}_n\\). The inclusion of ID scores \\(s\\) constitutes a complementary \"soft\" filtering strategy by reweighting selected attributes, whose effectiveness is clearly shown in Sec. 5.2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.508, + 0.484, + 0.551 + ], + "angle": 0, + "content": "After acquiring the class predictions, we can use a standard cross-entropy loss to supervise the optimization of both \\(\\mathbf{W}\\) and \\(\\hat{\\mathbf{A}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.557, + 0.484, + 0.598 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C E}} = - \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\sum_ {k = 1} ^ {K} l _ {m, k} \\log p \\left(O _ {k} | \\boldsymbol {v} _ {m}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.605, + 0.384, + 0.62 + ], + "angle": 0, + "content": "where \\( l_{m} \\) is the one-hot label vector for \\( \\mathbf{v}_{m} \\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.627, + 0.264, + 0.643 + ], + "angle": 0, + "content": "4.4. Overall Objective" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.649, + 0.483, + 0.68 + ], + "angle": 0, + "content": "Training. Our method can be optimized using the below training objective in an end-to-end fashion:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.688, + 0.483, + 0.705 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {C E}} + \\lambda d _ {\\mathrm {P O T}, \\epsilon}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.711, + 0.484, + 0.757 + ], + "angle": 0, + "content": "in which \\(\\lambda > 0\\) is a trade-off coefficient to balance the effect of the POT loss in Eq. (6). Algorithm 1 summarizes the whole training procedure." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.764, + 0.484, + 0.855 + ], + "angle": 0, + "content": "Inference. We follow the prior work [78] to detect if a test visual embedding \\(\\pmb{v}\\) contains unknown objects by combining two probabilities: (a) task relevance—the probability of \\(\\pmb{v}\\) being related to the optimized attribute embeddings \\((p_{\\mathrm{ID}})\\), and (b) unknowness—the probability of \\(\\pmb{v}\\) not being from the known classes \\((p_{\\mathrm{OOD}})\\), i.e., \\(p_{\\mathrm{unk}} = p_{\\mathrm{ID}} \\cdot p_{\\mathrm{OOD}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.861, + 0.483, + 0.88 + ], + "angle": 0, + "content": "\\[\np _ {\\mathrm {I D}} = \\max _ {n \\in \\{1, \\dots , N ^ {\\prime} \\}} \\sigma \\left(\\boldsymbol {a} _ {n} ^ {\\prime \\top} \\boldsymbol {v}\\right), \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.882, + 0.483, + 0.899 + ], + "angle": 0, + "content": "\\[\np _ {\\mathrm {O O D}} = 1 - \\max _ {k \\in \\{1, \\dots , K \\}} p \\left(O _ {k} | \\boldsymbol {v}\\right), \\tag {12}\n\\]" + }, + { + "type": "code_caption", + "bbox": [ + 0.515, + 0.095, + 0.876, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Training Procedure of PASS for OWOD" + }, + { + "type": "algorithm", + "bbox": [ + 0.517, + 0.112, + 0.907, + 0.514 + ], + "angle": 0, + "content": "Input: Visual object embeddings \\(\\mathbf{V}\\in \\mathbb{R}^{D\\times M}\\) with the one-hot labels \\(l\\), initial attribute embeddings \\(\\mathbf{A}\\in \\mathbb{R}^{D\\times N}\\), target attribute quantity \\(N^{\\prime}\\), selection steps \\(\\eta\\), total training epochs \\(E\\) \nOutput: Optimal selected attribute embeddings \\(\\hat{\\mathbf{A}}\\), mapping matrix \\(\\mathbf{W}\\), attribute ID scores \\(s\\) \n1 Initialize: Selected attribute embeddings \\(\\hat{\\mathbf{A}} = \\mathbf{A}\\), selected attribute quantity \\(\\hat{N} = N\\), Randomly initialized \\(\\mathbf{W}\\in \\mathbb{R}^{N\\times K}\\), attribute redundancy rate \\(\\alpha = (\\frac{N}{N^{\\prime}})^{\\frac{1}{\\eta}}\\); \n2 for \\(e\\) in \\((1,2,\\ldots,E)\\) do \n3 /* Partial Optimal Transport */ \n4 Get transport plan \\(\\mathbf{T}\\) and distance \\(d_{\\mathrm{POT}}\\) by solving the POT problem between \\(\\mathbf{V}\\) and \\(\\hat{\\mathbf{A}}\\) using Eq. (6) and \\(\\alpha\\); \n5 Compute attribute ID scores as \\(s = \\frac{\\hat{N}}{\\alpha}\\mathbf{T}^\\top\\mathbf{1}_M\\); \n6 /* Curriculum Attribute Selection */ \n7 if \\(e\\bmod\\left[\\frac{E}{\\eta+1}\\right]=0\\) then \n8 end \n9 Calculate object class prediction \\(p(O_k|v)\\) for \\(\\mathbf{V}\\) in Eq. (8) using \\(\\mathbf{W}\\), \\(\\hat{\\mathbf{A}}\\), and \\(s\\); \n10 Calculate loss \\(\\mathcal{L}_{\\mathrm{CE}}\\) in Eq. (9) using \\(p(O_k|v)\\) and \\(l\\); \n11 Get final loss \\(\\mathcal{L}\\) by combining \\(\\mathcal{L}_{\\mathrm{CE}}\\) and \\(d_{\\mathrm{POT}}\\) in Eq. (10); \n12 Update \\(\\mathbf{W}\\) and \\(\\hat{\\mathbf{A}}\\) using \\(\\nabla\\mathcal{L}\\); \n13 end" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.545, + 0.747, + 0.56 + ], + "angle": 0, + "content": "where \\(\\sigma (\\cdot)\\) is the sigmoid function." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.573, + 0.638, + 0.59 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.907, + 0.644 + ], + "angle": 0, + "content": "In this section, we present the experimental evaluations of our proposed PASS. We start with the experimental setup, followed by the evaluation results and analysis." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.653, + 0.704, + 0.669 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Datasets. As the performance on traditional OWOD benchmarks [22]—which are based on common everyday object datasets like COCO [31]—is reported to be highly saturated [78], we use the Real-World Object Detection Benchmark established in [78] to evaluate the proposed method. This benchmark is designed for the few-shot or low-data setting, recognizing that most real-world applications cannot gather datasets on the scale of traditional benchmarks. Specifically, it includes five challenging real-world datasets as outlined below. (a) Aquatic [10] contains 637 underwater images of 7 different sea animals, providing useful data for marine-related applications. (b) Aerial [28] contains 10,000 aerial photos of 20 different structures such as stadiums and storage containers, supporting satellite imaging and intelligence analysis. (c) Game [10] contains 1575 game screen" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20322" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "shots with 59 different avatars, serving as a benchmark for testing on synthetic data. (d) Medical [10] consists of 182 hand X-rays to identify 12 different bones, offering insights for medical applications such as detecting arthritis, fractures, and structural issues in hands. (e) Surgery [5] is composed of 1829 images of 13 different surgical instruments, captured under neurosurgical microscopes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.205, + 0.483, + 0.385 + ], + "angle": 0, + "content": "Evaluation Protocol. For each dataset, classes were evenly divided into two subsets: one containing the most common classes and the other containing the least common classes. The evaluation follows OWOD protocols and is conducted in two tasks. In Task 1, the model is provided with the most common classes as known (K), while the least common classes remain unknown (U), and the model is expected to detect both known and unknown object classes. In Task 2, in addition to the previously known (PK) classes, the least common classes are introduced as currently known (CK) classes. The model's performance is then evaluated on both PK and CK classes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.386, + 0.483, + 0.492 + ], + "angle": 0, + "content": "The mean average precision (mAP) is used to evaluate the performance in known classes (K-mAP). To gain deeper insights into the quality of continual learning in OWOD, mAP is further divided to respectively evaluate PK and CK classes (PK-mAP and CK-mAP) as discussed above. Additionally, we also report the mean average precision for unknown objects (U-mAP)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.5, + 0.483, + 0.742 + ], + "angle": 0, + "content": "Implementation Details. Our approach is based on a frozen CLIP-pretrained OWL-ViT model (B/16 and L/14) [41], which has been fine-tuned for detection on a federated dataset combining Objects365 [52] and Visual Genome [24]. We leverage this frozen model, focusing on the construction of optimal attribute embeddings \\(\\hat{\\mathbf{A}}\\) and a mapping matrix \\(\\mathbf{W}\\) to enhance the detection performance for both known and unknown object classes. For training, we use \\(\\epsilon = 0.01\\) in Eq. (6). For fair comparison with [78], \\(N'\\) is determined so that the average number of selected attributes per known class is 25. \\(\\eta\\) is default to be 4 for all datasets. Other hyperparameters, including training epochs and learning rate, are searched based on the validation mAP on known classes following [78]. The experiments were carried out on an NVIDIA RTX A6000 GPU. More implementation details are provided in Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.751, + 0.245, + 0.767 + ], + "angle": 0, + "content": "5.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.773, + 0.483, + 0.849 + ], + "angle": 0, + "content": "We ablate our proposed PASS to evaluate the effectiveness of each proposed module. As shown in Tab. 1, the ablation study primarily focuses on the POT distance loss \\((d_{\\mathrm{POT}})\\) in Eq. (6), the attribute selection method in Sec. 4.2, and the attribute ID score \\((s)\\) reweighting strategy in Eq. (8)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Effect of POT loss. The minimization of POT distance \\((d_{\\mathrm{POT}})\\) constitutes an important ingredient of our proposed PASS. It explicitly optimizes the attribute embeddings to" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.092, + 0.905, + 0.312 + ], + "angle": 0, + "content": "
    Dataset (→)AquaticSurgery
    UKUK
    B/16 Backbone:
    PASS Full (Ours)5.243.414.315.6
    PASS w/o Minimizing dPOT3.222.83.05.5
    PASS w/o Attribute Selection4.834.48.112.6
    PASS w/o s Reweighting4.541.310.611.9
    L/14 Backbone:
    PASS Full (Ours)21.753.916.645.6
    PASS w/o Minimizing dPOT10.118.28.014.1
    PASS w/o Attribute Selection15.534.115.243.6
    PASS w/o s Reweighting18.342.213.440.0
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.512, + 0.313, + 0.907, + 0.385 + ], + "angle": 0, + "content": "Table 1. Ablation study of PASS. We report U-mAP (U) and K-mAP (K) on two representative datasets: Aquatic and Surgery, with Task 1 evaluation in the 100-shot regime. Best results are highlighted in each column. More ablation study results can be found in Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.404, + 0.909, + 0.571 + ], + "angle": 0, + "content": "align closely with the corresponding visual object embeddings through optimal assignment, effectively reducing the modality gap and improving the generalizability of attributes. This enables the model to detect both known and unknown object classes. As shown in Tab. 1, performance drops significantly without minimizing \\( d_{\\mathrm{POT}} \\) (setting \\( \\lambda = 0 \\) in Eq. (10)), particularly in the detection of unknown objects. While the cross-entropy loss in Eq. (9) helps maintain performance on known objects, relying solely on the classification loss leads to poor generalization of the learned attributes for the unknown objects." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.577, + 0.909, + 0.759 + ], + "angle": 0, + "content": "Effect of Attribute Selection. Effective attribute selection helps retain a streamlined set of in-distribution attributes that are most relevant to the specific task. While attribute selection has a less pronounced impact on performance compared to \\( d_{\\mathrm{POT}} \\), since POT already performs an initial filtering by assigning lower weights to out-of-distribution attributes, it still provides benefits. Specifically, it helps reduce the noise in the attribute pool, which can enhance detection performance. Additionally, keeping a smaller attribute set is more computationally efficient. We provide further analysis on the advantage of the proposed curriculum attribute selection in Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Effect of Attribute ID Score Reweighting. In addition to the \"hard\" attribute selection, reweighting object class predictions based on the attribute ID score—obtained from the POT transport plan—provides a complementary \"soft\" filtering strategy. This approach allows the final selected attributes to contribute differently, based on their relevance to the specific task, rather than being treated equally. As demonstrated in Tab. 1, this fine-grained use of selected attributes further enhances the detection performance." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20323" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.905, + 0.365 + ], + "angle": 0, + "content": "
    Dataset (→)AquaticAerialGameMedicalSurgeryOverall
    Task ID (→)Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2
    UKPKCKUKPKCKUKPKCKUKPKCKUKPKCKUKPKCK
    B/16 Backbone:
    BASE-ZS+GT†29.845.045.036.71.35.75.71.415.00.40.40.10.50.00.00.15.61.51.40.310.410.510.57.7
    BASE-ZS6.245.045.036.70.95.75.71.415.70.40.40.10.20.00.00.11.41.51.40.34.910.510.57.7
    BASE-ZS+IN26.545.145.136.71.95.75.71.42.40.30.30.00.60.00.00.11.71.41.00.36.610.510.47.7
    BASE-ZS+LLM24.745.145.136.51.45.75.71.415.10.40.40.10.60.00.00.18.91.51.30.310.210.510.57.7
    BASE-FS7.141.141.131.91.210.410.14.016.04.64.83.90.66.16.13.31.311.911.310.95.214.814.710.8
    FOMO [78]3.543.844.140.80.912.012.65.413.33.84.44.12.16.45.511.56.112.712.911.05.215.715.914.6
    PASS (Ours)5.243.443.246.61.914.016.07.021.510.07.79.04.98.46.812.114.315.613.114.79.618.317.417.9
    Δ+1.7-0.4-0.9+5.8+1.0+2.0+3.4+1.6+8.2+6.2+3.3+4.9+2.8+2.0+1.3+0.6+8.2+2.9+0.2+3.7+4.4+2.5+1.5+2.3
    L/14 Backbone:
    BASE-ZS+GT†34.836.036.042.31.07.97.20.812.40.90.80.32.40.20.20.32.40.22.61.310.69.09.49.0
    BASE-ZS0.735.936.042.39.18.27.20.86.80.90.80.30.00.20.20.33.62.92.61.34.19.69.49.0
    BASE-ZS+IN19.635.835.841.82.37.26.90.915.80.90.80.30.90.10.10.23.12.11.91.18.39.29.18.8
    BASE-ZS+LLM24.735.835.842.20.67.67.20.812.50.90.80.21.60.10.10.212.62.62.51.310.49.49.39.0
    BASE-FS2.443.642.942.89.723.721.913.08.210.410.213.41.123.221.724.23.626.025.07.45.025.424.320.2
    FOMO [78]18.250.148.147.16.025.323.716.030.410.79.911.29.421.819.934.612.029.028.98.515.227.426.123.5
    PASS (Ours)21.753.956.658.38.434.236.120.236.024.323.726.313.134.330.032.016.645.647.943.319.138.538.936.0
    Δ+3.5+3.8+8.5+11.2+2.4+8.9+12.4+4.2+5.6+13.6+13.8+15.1+3.7+12.5+10.1-2.6+4.6+16.6+19.0+34.8+3.9+11.1+12.8+12.5
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.09, + 0.368, + 0.907, + 0.44 + ], + "angle": 0, + "content": "Table 2. OWOD results on the five real-world object detection datasets. The evaluation on each dataset is divided into two tasks, and we report U-, K-mAP for Task 1, and PK-, CK-mAP for Task 2, which are introduced in Sec. 5.1. BASE-FS, FOMO [78], and our proposed PASS are evaluated in the 100-shot regime, whereas the results of different few-shot regimes are provided in Supplementary Material. †GT baselines leverage ground-truth class names to detect unknown objects, functioning within the open-vocabulary object detection framework and providing an upper bound for text-conditioned (zero-shot) baselines. Best overall results are highlighted in each column." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.462, + 0.23, + 0.477 + ], + "angle": 0, + "content": "5.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.484, + 0.486, + 0.576 + ], + "angle": 0, + "content": "We perform extensive evaluations of our proposed PASS method, comparing it with existing state-of-the-art approaches (SOTAs). Additionally, we present qualitative results that showcase the detection outcomes along with the most relevant attributes used in the process. More experimental results can also be found in Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.483, + 0.856 + ], + "angle": 0, + "content": "Comparison with State of the Arts. We compare our proposed PASS with FOMO [78] and the strong baselines established therein, by adapting the Open-Vocabulary Object Detection (OVOD) methods [41] that also use foundation models to the OWOD setting. As listed in Tab. 2, BASE-ZS uses a generic \"object\" prompt for unknown objects [39], while BASE-ZS+IN utilizes all ImageNet class names (with the known classes removed) as the unknown classes proposals, and BASE-ZS+LLM employs class names predicted by an LLM (based on the known classes) for detecting potential unknown objects. On the other hand, BASE-ZS+GT uses the ground-truth class names for unknown objects, serving as the upper bound of the OVOD methods by assuming access to all unknown class names. BASE-FS utilizes image exemplars to produce vision-derived object embeddings, which are averaged per class to form class embeddings. Then a general prompt, such as \"a photo of an object\", is applied to help identify unknown objects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.485, + 0.901 + ], + "angle": 0, + "content": "As can be seen in Tab. 2, our proposed PASS consistently outperforms FOMO by a significant margin and achieves performance that is very close to the OVOD upper bound, even" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.909, + 0.645 + ], + "angle": 0, + "content": "when using the B/16 backbone. In particular, our improvement is especially notable in known classes, as reflected in the K-, PK-, and CK-mAP metrics. This can be attributed to the robust attribute selection and optimization capabilities of our proposed PASS framework, which effectively curates a set of accurate and effective attributes to enhance object detection. On the other hand, PASS also demonstrates a significant performance boost in unknown classes as measured by the U-mAP metric. This suggests that the attributes learned by PASS are not only effective for known classes during training but also highly generalizable to unknown objects during evaluation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Visualizations. For further comprehension of the effectiveness of our proposed PASS in detecting open world objects, we present several qualitative results for each dataset in Fig. 3. When comparing the detection results between FOMO (second row) and our proposed PASS (third row), PASS consistently demonstrates improved detection performance, with results that are more closely aligned with the ground truth (first row). In particular, FOMO sometimes incorrectly classifies known objects as unknown, or vice versa, suggesting that the learned attributes might not be sufficiently accurate to reliably characterize known objects. Furthermore, FOMO occasionally yields significantly fewer detection results in certain domains, such as medical datasets. This suggests that the learned attributes might not adequately capture the full range of potentially useful features necessary for detecting unknown objects. In contrast, PASS delivers" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20324" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.087, + 0.203, + 0.099 + ], + "angle": 0, + "content": "Aquatic" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.102, + 0.254, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.318, + 0.087, + 0.358, + 0.098 + ], + "angle": 0, + "content": "Aerial" + }, + { + "type": "image", + "bbox": [ + 0.261, + 0.102, + 0.414, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.476, + 0.087, + 0.519, + 0.098 + ], + "angle": 0, + "content": "Game" + }, + { + "type": "image", + "bbox": [ + 0.421, + 0.102, + 0.575, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.632, + 0.087, + 0.685, + 0.098 + ], + "angle": 0, + "content": "Medical" + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.102, + 0.735, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.087, + 0.846, + 0.099 + ], + "angle": 0, + "content": "Surgery" + }, + { + "type": "image", + "bbox": [ + 0.742, + 0.102, + 0.896, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.225, + 0.254, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.261, + 0.225, + 0.414, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.42, + 0.225, + 0.575, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.225, + 0.735, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.741, + 0.225, + 0.896, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.349, + 0.254, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.261, + 0.349, + 0.414, + 0.467 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.42, + 0.349, + 0.575, + 0.467 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.349, + 0.735, + 0.467 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.742, + 0.349, + 0.896, + 0.467 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.474, + 0.245, + 0.493 + ], + "angle": 0, + "content": "Top attributes for detected known classes:" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.494, + 0.225, + 0.503 + ], + "angle": 0, + "content": "Shape is truncate tail" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.503, + 0.2, + 0.511 + ], + "angle": 0, + "content": "Shape is flexible" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.512, + 0.24, + 0.521 + ], + "angle": 0, + "content": "Environment is tide pool" + }, + { + "type": "list", + "bbox": [ + 0.107, + 0.494, + 0.24, + 0.521 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.474, + 0.406, + 0.493 + ], + "angle": 0, + "content": "Top attributes for detected known classes:" + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.494, + 0.375, + 0.503 + ], + "angle": 0, + "content": "Shape is stationary" + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.503, + 0.378, + 0.511 + ], + "angle": 0, + "content": "Shape is converging" + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.512, + 0.396, + 0.52 + ], + "angle": 0, + "content": "Behavior is tournament" + }, + { + "type": "list", + "bbox": [ + 0.267, + 0.494, + 0.396, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.474, + 0.566, + 0.493 + ], + "angle": 0, + "content": "Top attributes for detected known classes:" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.494, + 0.534, + 0.503 + ], + "angle": 0, + "content": "Material is calcium" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.503, + 0.544, + 0.511 + ], + "angle": 0, + "content": "- Appearance is visible" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.512, + 0.545, + 0.52 + ], + "angle": 0, + "content": "joints between bones" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.52, + 0.507, + 0.527 + ], + "angle": 0, + "content": "Color is veins" + }, + { + "type": "list", + "bbox": [ + 0.428, + 0.494, + 0.545, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.588, + 0.474, + 0.726, + 0.493 + ], + "angle": 0, + "content": "Top attributes for detected known classes:" + }, + { + "type": "text", + "bbox": [ + 0.589, + 0.494, + 0.684, + 0.503 + ], + "angle": 0, + "content": "Shape is straight" + }, + { + "type": "text", + "bbox": [ + 0.589, + 0.503, + 0.684, + 0.511 + ], + "angle": 0, + "content": "Shape is convex" + }, + { + "type": "text", + "bbox": [ + 0.589, + 0.512, + 0.682, + 0.52 + ], + "angle": 0, + "content": "Shape is knobby" + }, + { + "type": "list", + "bbox": [ + 0.589, + 0.494, + 0.684, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.749, + 0.474, + 0.887, + 0.493 + ], + "angle": 0, + "content": "Top attributes for detected known classes:" + }, + { + "type": "text", + "bbox": [ + 0.75, + 0.494, + 0.853, + 0.502 + ], + "angle": 0, + "content": "Behavior is handle" + }, + { + "type": "text", + "bbox": [ + 0.75, + 0.503, + 0.885, + 0.511 + ], + "angle": 0, + "content": "- Features is gripping surface" + }, + { + "type": "text", + "bbox": [ + 0.75, + 0.512, + 0.878, + 0.528 + ], + "angle": 0, + "content": "- Appearance is presence of grooves" + }, + { + "type": "list", + "bbox": [ + 0.75, + 0.503, + 0.885, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.533, + 0.245, + 0.551 + ], + "angle": 0, + "content": "Top attributes for detected unknown classes:" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.552, + 0.241, + 0.56 + ], + "angle": 0, + "content": "Shape is dorsal fin shape" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.56, + 0.204, + 0.569 + ], + "angle": 0, + "content": "Texture is ridged" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.57, + 0.217, + 0.586 + ], + "angle": 0, + "content": "Shape is adipose fin shape" + }, + { + "type": "list", + "bbox": [ + 0.107, + 0.552, + 0.241, + 0.586 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.533, + 0.406, + 0.551 + ], + "angle": 0, + "content": "Top attributes for detected unknown classes:" + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.552, + 0.402, + 0.57 + ], + "angle": 0, + "content": "- Appearance is distinctive roof design" + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.571, + 0.383, + 0.578 + ], + "angle": 0, + "content": "Context is court lines" + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.578, + 0.375, + 0.586 + ], + "angle": 0, + "content": "Shape is stationary" + }, + { + "type": "list", + "bbox": [ + 0.267, + 0.552, + 0.402, + 0.586 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.533, + 0.566, + 0.551 + ], + "angle": 0, + "content": "Top attributes for detected unknown classes:" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.552, + 0.542, + 0.56 + ], + "angle": 0, + "content": "- Appearance is edges" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.56, + 0.521, + 0.569 + ], + "angle": 0, + "content": "Shape is smooth" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.57, + 0.526, + 0.578 + ], + "angle": 0, + "content": "Texture is striped" + }, + { + "type": "list", + "bbox": [ + 0.428, + 0.552, + 0.542, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.588, + 0.533, + 0.726, + 0.551 + ], + "angle": 0, + "content": "Top attributes for detected unknown classes:" + }, + { + "type": "text", + "bbox": [ + 0.589, + 0.552, + 0.684, + 0.56 + ], + "angle": 0, + "content": "Shape is cracked" + }, + { + "type": "text", + "bbox": [ + 0.589, + 0.56, + 0.684, + 0.569 + ], + "angle": 0, + "content": "Shape is straight" + }, + { + "type": "text", + "bbox": [ + 0.589, + 0.569, + 0.69, + 0.586 + ], + "angle": 0, + "content": "- Features is thumb metacarpal" + }, + { + "type": "list", + "bbox": [ + 0.589, + 0.552, + 0.69, + 0.586 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.749, + 0.533, + 0.887, + 0.551 + ], + "angle": 0, + "content": "Top attributes for detected unknown classes:" + }, + { + "type": "text", + "bbox": [ + 0.75, + 0.552, + 0.879, + 0.56 + ], + "angle": 0, + "content": "Material is cutting edge" + }, + { + "type": "text", + "bbox": [ + 0.75, + 0.56, + 0.866, + 0.569 + ], + "angle": 0, + "content": "Shape is pointed tips" + }, + { + "type": "text", + "bbox": [ + 0.75, + 0.569, + 0.861, + 0.578 + ], + "angle": 0, + "content": "- Appearance is shiny" + }, + { + "type": "list", + "bbox": [ + 0.75, + 0.552, + 0.879, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.598, + 0.907, + 0.653 + ], + "angle": 0, + "content": "Figure 3. Qualitative results on the five real-world datasets. First Row: images in each dataset with ground truth bounding boxes and class names. Second Row: Detection results using FOMO [78]. Third Row: Detection results using our proposed PASS. We use green and yellow boxes to indicate known and unknown objects, respectively. Bottom Rows: The top three attributes that are activated for detecting known and unknown classes in each image using our proposed PASS." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.484, + 0.81 + ], + "angle": 0, + "content": "superior detection results due to the more accurate attributes learned during training. These attributes not only provide a strong characterization of known object classes but also demonstrate high generalizability to unknown classes. Furthermore, as illustrated in the bottom two rows of Fig. 3, PASS effectively leverages meaningful attributes to identify both known and unknown objects. For example, it uses the attribute \"shape is dorsal fin shape\" to detect an unknown fish species recognized for its large fin." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.829, + 0.21, + 0.844 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose an efficient end-to-end approach to select a compact set of representative attributes tailored to detect open-world objects, including both known and unknown" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.825 + ], + "angle": 0, + "content": "classes. Specifically, we formulate the attribute selection and optimization process as a Partial Optimal Transport (POT) problem, where the most relevant attributes emerge with the highest transported mass. Additionally, we introduce a curriculum-based attribute selection strategy that gradually refines the attribute subset during training, significantly enhancing training stability and selection effectiveness. We evaluate our approach on challenging real-world datasets, where it achieves superior performance that surpasses current state-of-the-art methods by a large margin." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In future work, we aim to expand our method to incorporate hierarchical information within attribute taxonomies. This enhancement will allow for a more fine-grained understanding of the detection process by leveraging attributes at varying levels of granularity." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20325" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.273 + ], + "angle": 0, + "content": "Acknowledgments. This research is supported by the EDB Space Technology Development Programme under Project S22-19016-STDP, the National Natural Science Foundation of China under Grant 62306251, 62171343, 62176171, U21B2040, the Hong Kong Research Grant Council - Early Career Scheme under Grant 27208022, the HKU Seed Fund for Basic Research, the Fundamental Research Funds for the Central Universities under Grant CJ202303, as well as the Sichuan Science and Technology Planning Project under Grant 24NSFTD0130. The authors sincerely thank the anonymous Reviewers and Area Chairs for their valuable feedback and constructive comments." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.289, + 0.188, + 0.305 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.314, + 0.484, + 0.37 + ], + "angle": 0, + "content": "[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.372, + 0.484, + 0.425 + ], + "angle": 0, + "content": "[2] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 11444-11453, 2023. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.092, + 0.907, + 0.856 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20328" + } + ] +] \ No newline at end of file diff --git a/2025/Detecting Open World Objects via Partial Attribute Assignment/9a893be0-4b48-49d9-8973-6218a7e4b1e4_origin.pdf b/2025/Detecting Open World Objects via Partial Attribute Assignment/9a893be0-4b48-49d9-8973-6218a7e4b1e4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1411d39a1a5a50c06c0b0807583aed19bba43af7 --- /dev/null +++ b/2025/Detecting Open World Objects via Partial Attribute Assignment/9a893be0-4b48-49d9-8973-6218a7e4b1e4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:34046a7732b034fd02c9a4acc1bc8c3020e8ac42c8c37284f781e0c289c1d734 +size 4303782 diff --git a/2025/Detecting Open World Objects via Partial Attribute Assignment/full.md b/2025/Detecting Open World Objects via Partial Attribute Assignment/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e0ca54232230cfd27462b59edceeec6bccc35945 --- /dev/null +++ b/2025/Detecting Open World Objects via Partial Attribute Assignment/full.md @@ -0,0 +1,433 @@ +# Detecting Open World Objects via Partial Attribute Assignment + +Muli Yang $^{1}$ Gabriel James Goenawan $^{1}$ Huaiyuan Qin $^{1}$ Kai Han $^{2}$ Xi Peng $^{3}$ Yanhua Yang $^{4}$ Hongyuan Zhu $^{1\dagger}$ $^{1}$ Institute for Infocomm Research (I $^{2}$ R), A*STAR, Singapore + +$^{2}$ The University of Hong Kong, Hong Kong SAR $^{3}$ Sichuan University, China $^{4}$ Xidian University, China {yangml, goenawan, qinhy, zhuh}@i2r.a-star.edu.sg, kaihanx@hku.hk, pengxi@scu.edu.cn, yanhyang@xidian.edu.cn + +# Abstract + +Despite being trained on massive data, today's vision foundation models still fall short in detecting open world objects. Apart from recognizing known objects from training, a successful Open World Object Detection (OWOD) system must also be able to detect unknown objects never seen before, without confusing them with the backgrounds. Unlike prevailing prior works that rely on probability models to learn "objectness", we focus on learning fine-grained, class-agnostic attributes, allowing the detection of both known and unknown objects in an explainable manner. In this paper, we propose Partial Attribute Assignment (PASS), aiming to automatically select and optimize a small, relevant subset of attributes from a large attribute pool. Specifically, we model attribute selection as a Partial Optimal Transport (POT) problem between known visual objects and the attribute pool, in which more relevant attributes signify more transported mass. PASS follows a curriculum schedule that progressively selects and optimizes a targeted subset of attributes during training, promoting stability and accuracy. Our method enjoys end-to-end optimization by minimizing the POT distance and the classification loss on known visual objects, demonstrating high training efficiency and superior OWOD performance among extensive experimental evaluations. + +# 1. Introduction + +Deep learning and foundation models have emerged as critical AI technologies [1, 55], impacting various aspects of modern life. However, their success has been largely based on the closed-world assumption, which presumes a static and well-defined environment [76]. In practice, this assumption is difficult to uphold, as real-world conditions are dynamic and unpredictable, with unforeseen situations and unseen objects regularly appearing. Open World Object Detection (OWOD) [22] has emerged as a remedy to deliver reliable detection in the face of new environments with unknown ob + +![](images/fe47cb634b971bf830b51d04b30dd8d26af3cee25a7633398faed2bdcd712b18.jpg) +(a) + +![](images/4187f32aea67422cd73170502074fc98daacd568c464402fa74f11a501805f1b.jpg) +(b) +Figure 1. The role of attributes in Open World Object Detection (OWOD). (a) Unknown objects can be detected via shared visual/functional attributes with known objects. (b) Our method is able to automatically identify and optimize a small subset of relevant attributes from a large pool, effectively enabling the detection of both known and unknown objects. + +jects. In addition to recognizing known objects that appeared in training, a successful OWOD system must also detect and continually learn previously unseen objects without mistakenly classifying them as backgrounds. + +Recent works mainly use probability distribution estimation to model the "objectness" information, i.e., the probability of a candidate proposal being an object rather than backgrounds [79]. In this way, OWOD can be decomposed into two sub-tasks that respectively focus on objectness estimation and known class recognition [54]. Although this approach has significantly improved the detection of unknown objects, it has certain limitations in explainability and ambiguity. On the one hand, the learned probabilistic + +model is unable to explain how the objects—both the known and the unknown—are detected. On the other hand, when background features resemble those of the unknown objects, the model can still misclassify them. + +In this paper, we focus on detecting open world objects using fine-grained, class-agnostic attributes that are visually and/or functionally related to the known objects. These attributes can be described using natural languages with rich semantic information, and thus are naturally explainable and less ambiguous. The emphasis on intrinsic object attributes offers stronger resistance to confusion in scenarios where background and unknown object features overlap, making it particularly suitable for dynamic open-world environments. As illustrated in Fig. 1(a), attributes can be useful in detecting both known and unknown object classes, e.g., the learned "umbrella-like" attribute from known classes can be used to detect the unknown fungi. Despite the promising potential of using attributes in OWOD, effectively curating a set of attributes that are closely related to the specific task from a large pool of attributes remains a significant challenge. To this end, some existing method [78] seeks a set of representative attributes that can effectively classify known objects with multistage processes—such as attribute selection and refinement—which are time-consuming and computationally expensive. More importantly, the separation of the selection and refinement processes may accumulate errors, leading to inaccuracies in the results of the attribute selection and refinement. + +We propose to tackle this dilemma using Partial Attribute Assignment (PASS), an approach that progressively selects and optimizes a targeted subset of relevant attributes throughout the training process in an end-to-end manner. In particular, we model attribute selection as a Partial Optimal Transport (POT) problem [6] between known visual objects and the attribute pool, in which more relevant attributes signify more mass transported to the visual objects. Unlike conventional OT [56] that assumes identical mass in both distributions to be completely transported, POT allows the transport of only a targeted fraction of total mass from one distribution to another. As such, the attribute pool can be viewed as a collection of both in-distribution (ID) and out-of-distribution (OOD) attributes w.r.t. the visual objects, where we can use the visual object distribution as the baseline distribution to filter out redundant OOD attributes. + +To achieve stable, accurate attribute selection and optimization simultaneously, PASS follows a curriculum learning [4] schedule that progressively targets and optimizes a subset of attributes throughout training. PASS ensures that each filtered subset is highly representative and provides broad coverage of the visual objects, by iteratively focusing on and refining a smaller subset of attributes guaranteed by the OT theory. As training progresses, the selected attributes reach a balanced state between representativeness and cover- + +age, allowing the model to better adapt to both known and unknown objects. This process also reduces computational costs by gradually limiting the number of attributes introduced. Our method enjoys end-to-end optimization by minimizing both the POT distance and the classification loss for known visual objects. During inference, the learned attributes play a dual role: they support the recognition of known classes through the mapping relationships established during training, while also enabling the detection of unknown objects by leveraging the correlation between object proposals and the learned attributes. Extensive experiments demonstrate that our method significantly outperforms baseline methods, validating both the feasibility of attribute-based OWOD and the effectiveness of our approach in curating more accurate attributes for OWOD. + +In a nutshell, our main contributions are + +- We model the attribute curation issue in OWOD as a Partial Optimal Transport (POT) problem, enabling end-to-end attribute selection and optimization for effectively detecting both known and unknown objects; +- We propose a curriculum selection strategy by progressively optimizing a targeted subset of attributes with strong representativeness and broad coverage, benefiting both training stability and selection effectiveness; +- Extensive experiments demonstrate the absolute superiority of the proposed method in terms of both training efficiency and detection performance. + +# 2. Related Work + +Open World Object Detection. Open World Object Detection (OWOD) [22] enhances traditional object detectors by shifting away from closed-set assumptions, enabling dynamic adaptation to novel classes as encountered in real-world settings [20, 29, 30, 33, 34, 67, 74]. Existing works [27, 51, 61, 65, 69, 70] reduce the overlap between known, unknown classes and the background distributions using different ways, e.g., pseudo-labeling [18, 38], objectness estimation [54, 79], and hierarchical modeling [13, 37]. OWOD is also related to similar tasks such as Class-Agnostic Object Detection [14, 21, 23, 36, 44, 45, 50, 59, 60] and Open-Vocabulary Object Detection (OVOD) [17, 25, 41, 42, 58, 71, 75]. Recent advances, such as FOMO [78] and a concurrent work UMB [62], extend the standard OVOD method to OWOD by utilizing vision and language foundation models. By identifying objects based on semantic attributes [26, 49, 53], they learn class-agnostic attributes to detect task-relevant unknown objects, yet require multistage attribute selection and refinement, which is time-consuming and computationally inefficient. In this paper, we propose an end-to-end attribute curation method that not only benefits the training efficiency but also largely improves the detection performance in both known and unknown classes. + +Optimal Transport. Optimal Transport (OT), originally introduced by Monge [43] to minimize the cost of transporting items, has become a prominent tool in machine learning and computer vision for matching distributions across domains [46, 56]. OT has been widely applied in distribution-based tasks [8, 57, 73] such as generative models [2], clustering [19, 66], domain adaptation [11], object detection [16] and structural tasks such as sequence [9], graph [63], and image matching [32, 72]. To address OT's high computational demands, the Sinkhorn OT [12] offers a solution by approximating OT through an efficient iterative algorithm. Partial OT (POT), a variant of OT that transports only a portion of the mass, addresses cases where distributions only partially overlap, making it especially relevant in scenarios such as open-set domain adaptation [6, 7, 15, 35, 48, 64, 68]. The Sinkhorn algorithm has been extended to POT to further reduce computational costs [3]. In our work, we utilize POT to dynamically match attribute embeddings with visual embeddings of known object classes, selecting and optimizing the most representative attributes for effectively detecting both known and unknown objects. + +# 3. Background + +OWOD with Foundation Models. Open World Object Detection (OWOD) requires a model to detect and incrementally learn unknown objects. In particular, there are multiple stages/tasks for training and evaluation, indicated by $t$ . In task $t$ , the model can be trained on $K^t$ known object classes from $\mathcal{K}^t = \{O_1^t, O_2^t, \ldots, O_{K^t}^t\}$ , and to be evaluated on a test set that contains both known and unknown classes. To achieve that, we use an additional $O_0^t$ to denote the unknown classes, alongside the $K^t$ known classes. In fact, $O_0^t$ represents $U^t$ classes of interest that are unknown to the model in the task $t$ , i.e., $\mathcal{U}^t = \{O_{K^t + 1}^t, O_{K^t + 2}^t, \ldots, O_{K^t + U^t}^t\}$ . After discovering the unknown object classes, the model can be updated with the knowledge of these new classes using annotations from an oracle (e.g., a human annotator) in task $t + 1$ . As a result, the model is ready to detect $K^{t + 1} = K^t + U^t$ known object classes in the test set, as well as additional unknown classes for the subsequent task cycle. + +To push the boundary of OWOD in real-world applications, we follow a recent work [78] to make use of existing pretrained foundation models in open-vocabulary object detection [41, 71], e.g., vision and language encoders, and adapt them to OWOD. The training follows a few-shot paradigm: for the $z$ -shot, only $z$ images per known class are given, with only one bounding box label and one object class label for each image. For each dataset, we use the attribute texts proposed by a Large Language Model (LLM), i.e., GPT-3.5, by prompting with the known class names using the template described in recent works [40, 77, 78]. This will result in an attribute pool with numerous class-agnostic attributes visually and/or functionally related to the known + +objects, e.g., shape is straight. + +Optimal Transport Preliminary. Optimal Transport (OT) is a powerful tool for measuring the distance between two distributions. Here we review the discrete OT scenario that is more related to our framework and refer the readers to [12] for more details. + +Assuming we have two sets of data points (features) $\mathbf{X} = \{\pmb{x}_m\}_{m=1}^M$ and $\mathbf{Y} = \{\pmb{y}_n\}_{n=1}^N$ , their discrete distributions can be formulated as + +$$ +\mathcal {X} = \sum_ {m = 1} ^ {M} \frac {1}{M} \delta_ {\boldsymbol {x} _ {m}}, \quad \mathcal {Y} = \sum_ {n = 1} ^ {N} \frac {1}{N} \delta_ {\boldsymbol {y} _ {n}}, \tag {1} +$$ + +where $\delta$ is the Dirac function and we use the uniform distribution to equally view each data point. The OT distance is defined as the smallest cost of transporting $\mathcal{X}$ to $\mathcal{Y}$ : + +$$ +d _ {\mathrm {O T}} (\mathcal {X}, \mathcal {Y}; \mathbf {C}) \triangleq \min _ {\mathbf {T} \in \Pi (\mathcal {X}, \mathcal {Y})} \left\langle \mathbf {T}, \mathbf {C} \right\rangle_ {F}, \tag {2} +$$ + +in which $\mathbf{C} \in \mathbb{R}_{+}^{M \times N}$ is the cost matrix between $\mathbf{X}$ and $\mathbf{Y}$ where $C_{m,n} = c(\pmb{x}_m, \pmb{y}_n)$ is the transport cost from $\pmb{x}_m$ to $\pmb{y}_n$ , with $c(\cdot)$ being the cost function (e.g., the cosine distance), $\mathbf{T}$ is the transport plan to be solved, and $\langle \cdot, \cdot \rangle_F$ denotes the Frobenius inner product. The optimization of OT distance satisfies two marginal constraints: + +$$ +\Pi (\mathcal {X}, \mathcal {Y}) \triangleq \left\{\mathbf {T} \in \mathbb {R} _ {+} ^ {M \times N} \mid \mathbf {T} \mathbf {1} _ {N} = \mathcal {X}, \mathbf {T} ^ {\top} \mathbf {1} _ {M} = \mathcal {Y} \right\}, \tag {3} +$$ + +where $\mathbf{1}_N$ is an $N$ -dimensional vector of all ones, and we slightly abuse $\mathcal{X}$ , $\mathcal{Y}$ to denote $\mathcal{X} = \frac{1}{M}\mathbf{1}_M$ , $\mathcal{Y} = \frac{1}{N}\mathbf{1}_N$ to reflect the discrete probability in Eq. (1). + +# 4. Method + +We propose Partial Attribute Assignment (PASS) to address the challenging Open World Object Detection (OWOD) task. PASS is composed of three modules shown in Fig. 2, which are introduced in separate subsections below. + +# 4.1. Partial Attribute Assignment + +As discussed above, now we have $z$ -shot images of $K$ known object classes (the superscript $t$ is omitted for brevity) and $N$ attribute texts in the attribute pool. Our goal is to select and optimize a small set of relevant attributes from the attribute pool, with the target attribute quantity denoted as $N' \in (0, N]$ . The resulting $N'$ attributes are to be used for effectively detecting both known and unknown objects. + +Formally, we collect the visual object embeddings as $\mathbf{V} = [v_{1}, v_{2}, \ldots, v_{M}] \in \mathbb{R}^{D \times M}$ and the attribute embeddings as $\mathbf{A} = [a_{1}, a_{2}, \ldots, a_{N}] \in \mathbb{R}^{D \times N}$ in the $D$ -dimensional embedding space using pretrained vision and text encoders [41, 47], where $M = z \cdot K$ is the number of known image patches obtained using bounding box labels, + +![](images/a622527a0c6b28354d33d00d83913fe000b025ff6c32b6d4d9d241f01bb36f92.jpg) +Figure 2. Overview of the proposed Partial Attribute Assignment (PASS) for OWOD. PASS is constructed upon pretrained vision and text encoders [41, 47] and is designed to identify and refine a set of relevant attributes from an attribute pool, which are essential for detecting both known and unknown object classes. (a) We employ Partial Optimal Transport (POT) to model the assignment problem between attributes and known visual objects (Sec. 4.1). (b) The resulting transport plan $\mathbf{T}$ is used to generate attribute in-distribution (ID) scores $s$ , which help in selecting the most relevant attributes for the specific task (Sec. 4.2). (c) These attribute ID scores are further used to reweight the selected attributes, which are subsequently applied to compute object class predictions via a learnable mapping matrix (Sec. 4.3). + +and all embeddings are $\ell_2$ normalized. Likewise, we can denote the discrete distributions of $\mathbf{V}$ and $\mathbf{A}$ as $\mathcal{V}$ and $\mathcal{A}$ following Eq. (1). The conventional OT assumes that the two distributions have the identical total probability mass, i.e., $\| \mathcal{V}\| _1 = \| \mathcal{A}\| _1$ , and that all the mass of $\mathcal{A}$ must be transported. Although this assumption works effectively for tasks that involve identical distributions, it faces challenges in our scenario, where only a subset of samples in $\mathcal{A}$ aligns with $\mathcal{V}$ . + +A workaround is to transport only the mass of indistribution (ID) samples between $\mathcal{V}$ and $\mathcal{A}$ while retaining the out-of-distribution (OOD) mass within $\mathcal{A}$ . This leads to the concept of Partial OT (POT) [6], which relaxes the assumption of equal total mass between $\mathcal{V}$ and $\mathcal{A}$ . Instead, it allows for transporting a portion of the mass within the range $[0, \min(\|\mathcal{V}\|_1, \|\mathcal{A}\|_1)]$ . To this end, we use the visual distribution $\mathcal{V}$ as a baseline distribution to filter out redundant outliers in $\mathcal{A}$ . Accordingly, the visual distribution $\mathcal{V}$ and attribute distribution $\mathcal{A}$ are redefined as + +$$ +\mathcal {V} = \sum_ {m = 1} ^ {M} \frac {1}{M} \delta_ {\boldsymbol {v} _ {m}}, \quad \mathcal {A} = \sum_ {n = 1} ^ {N} \frac {\alpha}{N} \delta_ {\boldsymbol {a} _ {n}}, \tag {4} +$$ + +where $\alpha = \frac{N}{N'} \geqslant 1$ is the attribute redundant rate reflecting the redundant mass in $\mathcal{A}$ , which enables transporting only a subset of mass in $\mathcal{A}$ . In this manner, we formulate the resulting problem as a POT problem with the following marginal constraints: + +$$ +\Pi (\mathcal {V}, \mathcal {A}) \triangleq \left\{\mathbf {T} \in \mathbb {R} _ {+} ^ {M \times N} \mid \mathbf {T} \mathbf {1} _ {N} = \mathcal {V}, \mathbf {T} ^ {\top} \mathbf {1} _ {M} \leqslant \mathcal {A} \right\}. \tag {5} +$$ + +It is important to highlight that, unlike the traditional POT problem, which imposes inequality constraints on both distributions, Eq. (5) introduces equality constraints within $\nu$ [48]. This modification explicitly aligns the attribute distribution with the visual distribution by redistributing weights among + +the attributes. Moreover, the concise constraints accelerate the convergence of POT computations. The POT distance is then denoted as + +$$ +d _ {\mathrm {P O T}, \epsilon} (\mathcal {V}, \mathcal {A}; \mathbf {C}) \triangleq \min _ {\mathbf {T} \in \Pi (\mathcal {V}, \mathcal {A})} \left\langle \mathbf {T}, \mathbf {C} \right\rangle_ {F} - \epsilon h (\mathbf {T}), \tag {6} +$$ + +where $\epsilon > 0$ is the regularization coefficient, and $h(\mathbf{T}) = -\sum_{m,n} T_{m,n} \ln (T_{m,n})$ is the entropic constraint to accelerate the optimization [12], so that the optimal $\mathbf{T}$ can be estimated in a few iterations. We defer the detailed optimization procedure of Eq. (6) to Supplementary Material. + +# 4.2. Curriculum Attribute Selection + +Upon the optimal transport plan $\mathbf{T}$ derived in Eq. (6), we can define an in-distribution (ID) score for each attribute as $s = [s_1, s_2, \ldots, s_N]^\top$ , by aggregating the mass transferred from one attribute to all visual objects: + +$$ +s _ {n} = \frac {N}{\alpha} \sum_ {m = 1} ^ {M} T _ {m, n}, \tag {7} +$$ + +where $s_n \in [0,1]$ is the scaled mass transported that can be interpreted as the probability of the specific attribute being in-distribution to the visual objects in $\mathbf{V}$ . The underlying rationale is that the transport cost among ID samples is relatively low. To minimize the total transport cost, ID attributes in $\mathcal{A}$ are allocated a greater proportion of transportation mass compared to the redundant OOD attributes, in accordance with the principles of POT. + +With the ID scores $s$ at hand, one can simply select $N'$ attributes with the highest ID scores at a certain stage of training, e.g., at the beginning or the end. However, this may suffer from either the inaccurate transport cost due to the modality gap, or the inaccurate mapping from attributes to known classes. In light of this, we devise an iterative attribute + +selection strategy that follows the spirit of Curriculum Learning [4]. Instead of single-time selection, we divide it into $\eta$ steps alongside the training, such that only a slightly smaller set of attributes are to be selected in each step, making the POT problem easier to solve, and thus benefit the training stability and attribute selection effectiveness. + +Formally, $\alpha$ in Eq. (4) is now rewritten as $\alpha = \left(\frac{N}{N'}\right)^{\frac{1}{\eta}}$ . In each of the $\eta$ selection steps, we select the $\frac{1}{\alpha}$ amount of the remaining attributes according to the indices of the top $\frac{1}{\alpha}$ ID scores $s$ . The detailed selection method is summarized in Lines 5 to 8 in Algorithm 1. We denote the resulting selected attribute embeddings as $\hat{\mathbf{A}} \in \mathbb{R}^{D \times N'}$ , with the ID scores being $s = [s_1, s_2, \dots, s_{N'}]^\top \in \mathbb{R}^{N'}$ . + +# 4.3. Object Class Prediction + +After gaining the selected attributes in each step, we can learn a mapping matrix $\mathbf{W} = [\pmb{w}_1, \pmb{w}_2, \dots, \pmb{w}_K] \in \mathbb{R}^{N' \times K}$ to assign $N'$ attributes to $K$ known object classes, with the prediction probability computed as + +$$ +p \left(O _ {k} | \boldsymbol {v}\right) = \frac {\exp \left(\boldsymbol {w} _ {k} ^ {\top} \mathbf {A} ^ {\prime \top} \boldsymbol {v}\right)}{\sum_ {k ^ {\prime} = 1} ^ {K} \exp \left(\boldsymbol {w} _ {k ^ {\prime}} ^ {\top} \mathbf {A} ^ {\prime \top} \boldsymbol {v}\right)}, \tag {8} +$$ + +in which $\mathbf{A}' = [a_1', a_2', \dots, a_{N'}']$ is the element-wise multiplication between $s$ and $\hat{\mathbf{A}}$ where $a_n' = s_n \hat{a}_n$ . The inclusion of ID scores $s$ constitutes a complementary "soft" filtering strategy by reweighting selected attributes, whose effectiveness is clearly shown in Sec. 5.2. + +After acquiring the class predictions, we can use a standard cross-entropy loss to supervise the optimization of both $\mathbf{W}$ and $\hat{\mathbf{A}}$ : + +$$ +\mathcal {L} _ {\mathrm {C E}} = - \frac {1}{M} \sum_ {m = 1} ^ {M} \sum_ {k = 1} ^ {K} l _ {m, k} \log p \left(O _ {k} | \boldsymbol {v} _ {m}\right), \tag {9} +$$ + +where $l_{m}$ is the one-hot label vector for $\mathbf{v}_{m}$ . + +# 4.4. Overall Objective + +Training. Our method can be optimized using the below training objective in an end-to-end fashion: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {C E}} + \lambda d _ {\mathrm {P O T}, \epsilon}, \tag {10} +$$ + +in which $\lambda > 0$ is a trade-off coefficient to balance the effect of the POT loss in Eq. (6). Algorithm 1 summarizes the whole training procedure. + +Inference. We follow the prior work [78] to detect if a test visual embedding $\pmb{v}$ contains unknown objects by combining two probabilities: (a) task relevance—the probability of $\pmb{v}$ being related to the optimized attribute embeddings $(p_{\mathrm{ID}})$ , and (b) unknowness—the probability of $\pmb{v}$ not being from the known classes $(p_{\mathrm{OOD}})$ , i.e., $p_{\mathrm{unk}} = p_{\mathrm{ID}} \cdot p_{\mathrm{OOD}}$ : + +$$ +p _ {\mathrm {I D}} = \max _ {n \in \{1, \dots , N ^ {\prime} \}} \sigma \left(\boldsymbol {a} _ {n} ^ {\prime \top} \boldsymbol {v}\right), \tag {11} +$$ + +$$ +p _ {\mathrm {O O D}} = 1 - \max _ {k \in \{1, \dots , K \}} p \left(O _ {k} | \boldsymbol {v}\right), \tag {12} +$$ + +Algorithm 1: Training Procedure of PASS for OWOD +Input: Visual object embeddings $\mathbf{V}\in \mathbb{R}^{D\times M}$ with the one-hot labels $l$ , initial attribute embeddings $\mathbf{A}\in \mathbb{R}^{D\times N}$ , target attribute quantity $N^{\prime}$ , selection steps $\eta$ , total training epochs $E$ +Output: Optimal selected attribute embeddings $\hat{\mathbf{A}}$ , mapping matrix $\mathbf{W}$ , attribute ID scores $s$ +1 Initialize: Selected attribute embeddings $\hat{\mathbf{A}} = \mathbf{A}$ , selected attribute quantity $\hat{N} = N$ , Randomly initialized $\mathbf{W}\in \mathbb{R}^{N\times K}$ , attribute redundancy rate $\alpha = (\frac{N}{N^{\prime}})^{\frac{1}{\eta}}$ ; +2 for $e$ in $(1,2,\ldots,E)$ do +3 /* Partial Optimal Transport */ +4 Get transport plan $\mathbf{T}$ and distance $d_{\mathrm{POT}}$ by solving the POT problem between $\mathbf{V}$ and $\hat{\mathbf{A}}$ using Eq. (6) and $\alpha$ ; +5 Compute attribute ID scores as $s = \frac{\hat{N}}{\alpha}\mathbf{T}^\top\mathbf{1}_M$ ; +6 /* Curriculum Attribute Selection */ +7 if $e\bmod\left[\frac{E}{\eta+1}\right]=0$ then +8 end +9 Calculate object class prediction $p(O_k|v)$ for $\mathbf{V}$ in Eq. (8) using $\mathbf{W}$ , $\hat{\mathbf{A}}$ , and $s$ ; +10 Calculate loss $\mathcal{L}_{\mathrm{CE}}$ in Eq. (9) using $p(O_k|v)$ and $l$ ; +11 Get final loss $\mathcal{L}$ by combining $\mathcal{L}_{\mathrm{CE}}$ and $d_{\mathrm{POT}}$ in Eq. (10); +12 Update $\mathbf{W}$ and $\hat{\mathbf{A}}$ using $\nabla\mathcal{L}$ ; +13 end + +where $\sigma (\cdot)$ is the sigmoid function. + +# 5. Experiment + +In this section, we present the experimental evaluations of our proposed PASS. We start with the experimental setup, followed by the evaluation results and analysis. + +# 5.1. Experimental Setup + +Datasets. As the performance on traditional OWOD benchmarks [22]—which are based on common everyday object datasets like COCO [31]—is reported to be highly saturated [78], we use the Real-World Object Detection Benchmark established in [78] to evaluate the proposed method. This benchmark is designed for the few-shot or low-data setting, recognizing that most real-world applications cannot gather datasets on the scale of traditional benchmarks. Specifically, it includes five challenging real-world datasets as outlined below. (a) Aquatic [10] contains 637 underwater images of 7 different sea animals, providing useful data for marine-related applications. (b) Aerial [28] contains 10,000 aerial photos of 20 different structures such as stadiums and storage containers, supporting satellite imaging and intelligence analysis. (c) Game [10] contains 1575 game screen + +shots with 59 different avatars, serving as a benchmark for testing on synthetic data. (d) Medical [10] consists of 182 hand X-rays to identify 12 different bones, offering insights for medical applications such as detecting arthritis, fractures, and structural issues in hands. (e) Surgery [5] is composed of 1829 images of 13 different surgical instruments, captured under neurosurgical microscopes. + +Evaluation Protocol. For each dataset, classes were evenly divided into two subsets: one containing the most common classes and the other containing the least common classes. The evaluation follows OWOD protocols and is conducted in two tasks. In Task 1, the model is provided with the most common classes as known (K), while the least common classes remain unknown (U), and the model is expected to detect both known and unknown object classes. In Task 2, in addition to the previously known (PK) classes, the least common classes are introduced as currently known (CK) classes. The model's performance is then evaluated on both PK and CK classes. + +The mean average precision (mAP) is used to evaluate the performance in known classes (K-mAP). To gain deeper insights into the quality of continual learning in OWOD, mAP is further divided to respectively evaluate PK and CK classes (PK-mAP and CK-mAP) as discussed above. Additionally, we also report the mean average precision for unknown objects (U-mAP). + +Implementation Details. Our approach is based on a frozen CLIP-pretrained OWL-ViT model (B/16 and L/14) [41], which has been fine-tuned for detection on a federated dataset combining Objects365 [52] and Visual Genome [24]. We leverage this frozen model, focusing on the construction of optimal attribute embeddings $\hat{\mathbf{A}}$ and a mapping matrix $\mathbf{W}$ to enhance the detection performance for both known and unknown object classes. For training, we use $\epsilon = 0.01$ in Eq. (6). For fair comparison with [78], $N'$ is determined so that the average number of selected attributes per known class is 25. $\eta$ is default to be 4 for all datasets. Other hyperparameters, including training epochs and learning rate, are searched based on the validation mAP on known classes following [78]. The experiments were carried out on an NVIDIA RTX A6000 GPU. More implementation details are provided in Supplementary Material. + +# 5.2. Ablation Study + +We ablate our proposed PASS to evaluate the effectiveness of each proposed module. As shown in Tab. 1, the ablation study primarily focuses on the POT distance loss $(d_{\mathrm{POT}})$ in Eq. (6), the attribute selection method in Sec. 4.2, and the attribute ID score $(s)$ reweighting strategy in Eq. (8). + +Effect of POT loss. The minimization of POT distance $(d_{\mathrm{POT}})$ constitutes an important ingredient of our proposed PASS. It explicitly optimizes the attribute embeddings to + +
    Dataset (→)AquaticSurgery
    UKUK
    B/16 Backbone:
    PASS Full (Ours)5.243.414.315.6
    PASS w/o Minimizing dPOT3.222.83.05.5
    PASS w/o Attribute Selection4.834.48.112.6
    PASS w/o s Reweighting4.541.310.611.9
    L/14 Backbone:
    PASS Full (Ours)21.753.916.645.6
    PASS w/o Minimizing dPOT10.118.28.014.1
    PASS w/o Attribute Selection15.534.115.243.6
    PASS w/o s Reweighting18.342.213.440.0
    + +Table 1. Ablation study of PASS. We report U-mAP (U) and K-mAP (K) on two representative datasets: Aquatic and Surgery, with Task 1 evaluation in the 100-shot regime. Best results are highlighted in each column. More ablation study results can be found in Supplementary Material. + +align closely with the corresponding visual object embeddings through optimal assignment, effectively reducing the modality gap and improving the generalizability of attributes. This enables the model to detect both known and unknown object classes. As shown in Tab. 1, performance drops significantly without minimizing $d_{\mathrm{POT}}$ (setting $\lambda = 0$ in Eq. (10)), particularly in the detection of unknown objects. While the cross-entropy loss in Eq. (9) helps maintain performance on known objects, relying solely on the classification loss leads to poor generalization of the learned attributes for the unknown objects. + +Effect of Attribute Selection. Effective attribute selection helps retain a streamlined set of in-distribution attributes that are most relevant to the specific task. While attribute selection has a less pronounced impact on performance compared to $d_{\mathrm{POT}}$ , since POT already performs an initial filtering by assigning lower weights to out-of-distribution attributes, it still provides benefits. Specifically, it helps reduce the noise in the attribute pool, which can enhance detection performance. Additionally, keeping a smaller attribute set is more computationally efficient. We provide further analysis on the advantage of the proposed curriculum attribute selection in Supplementary Material. + +Effect of Attribute ID Score Reweighting. In addition to the "hard" attribute selection, reweighting object class predictions based on the attribute ID score—obtained from the POT transport plan—provides a complementary "soft" filtering strategy. This approach allows the final selected attributes to contribute differently, based on their relevance to the specific task, rather than being treated equally. As demonstrated in Tab. 1, this fine-grained use of selected attributes further enhances the detection performance. + +
    Dataset (→)AquaticAerialGameMedicalSurgeryOverall
    Task ID (→)Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2
    UKPKCKUKPKCKUKPKCKUKPKCKUKPKCKUKPKCK
    B/16 Backbone:
    BASE-ZS+GT†29.845.045.036.71.35.75.71.415.00.40.40.10.50.00.00.15.61.51.40.310.410.510.57.7
    BASE-ZS6.245.045.036.70.95.75.71.415.70.40.40.10.20.00.00.11.41.51.40.34.910.510.57.7
    BASE-ZS+IN26.545.145.136.71.95.75.71.42.40.30.30.00.60.00.00.11.71.41.00.36.610.510.47.7
    BASE-ZS+LLM24.745.145.136.51.45.75.71.415.10.40.40.10.60.00.00.18.91.51.30.310.210.510.57.7
    BASE-FS7.141.141.131.91.210.410.14.016.04.64.83.90.66.16.13.31.311.911.310.95.214.814.710.8
    FOMO [78]3.543.844.140.80.912.012.65.413.33.84.44.12.16.45.511.56.112.712.911.05.215.715.914.6
    PASS (Ours)5.243.443.246.61.914.016.07.021.510.07.79.04.98.46.812.114.315.613.114.79.618.317.417.9
    Δ+1.7-0.4-0.9+5.8+1.0+2.0+3.4+1.6+8.2+6.2+3.3+4.9+2.8+2.0+1.3+0.6+8.2+2.9+0.2+3.7+4.4+2.5+1.5+2.3
    L/14 Backbone:
    BASE-ZS+GT†34.836.036.042.31.07.97.20.812.40.90.80.32.40.20.20.32.40.22.61.310.69.09.49.0
    BASE-ZS0.735.936.042.39.18.27.20.86.80.90.80.30.00.20.20.33.62.92.61.34.19.69.49.0
    BASE-ZS+IN19.635.835.841.82.37.26.90.915.80.90.80.30.90.10.10.23.12.11.91.18.39.29.18.8
    BASE-ZS+LLM24.735.835.842.20.67.67.20.812.50.90.80.21.60.10.10.212.62.62.51.310.49.49.39.0
    BASE-FS2.443.642.942.89.723.721.913.08.210.410.213.41.123.221.724.23.626.025.07.45.025.424.320.2
    FOMO [78]18.250.148.147.16.025.323.716.030.410.79.911.29.421.819.934.612.029.028.98.515.227.426.123.5
    PASS (Ours)21.753.956.658.38.434.236.120.236.024.323.726.313.134.330.032.016.645.647.943.319.138.538.936.0
    Δ+3.5+3.8+8.5+11.2+2.4+8.9+12.4+4.2+5.6+13.6+13.8+15.1+3.7+12.5+10.1-2.6+4.6+16.6+19.0+34.8+3.9+11.1+12.8+12.5
    + +Table 2. OWOD results on the five real-world object detection datasets. The evaluation on each dataset is divided into two tasks, and we report U-, K-mAP for Task 1, and PK-, CK-mAP for Task 2, which are introduced in Sec. 5.1. BASE-FS, FOMO [78], and our proposed PASS are evaluated in the 100-shot regime, whereas the results of different few-shot regimes are provided in Supplementary Material. †GT baselines leverage ground-truth class names to detect unknown objects, functioning within the open-vocabulary object detection framework and providing an upper bound for text-conditioned (zero-shot) baselines. Best overall results are highlighted in each column. + +# 5.3. Main Results + +We perform extensive evaluations of our proposed PASS method, comparing it with existing state-of-the-art approaches (SOTAs). Additionally, we present qualitative results that showcase the detection outcomes along with the most relevant attributes used in the process. More experimental results can also be found in Supplementary Material. + +Comparison with State of the Arts. We compare our proposed PASS with FOMO [78] and the strong baselines established therein, by adapting the Open-Vocabulary Object Detection (OVOD) methods [41] that also use foundation models to the OWOD setting. As listed in Tab. 2, BASE-ZS uses a generic "object" prompt for unknown objects [39], while BASE-ZS+IN utilizes all ImageNet class names (with the known classes removed) as the unknown classes proposals, and BASE-ZS+LLM employs class names predicted by an LLM (based on the known classes) for detecting potential unknown objects. On the other hand, BASE-ZS+GT uses the ground-truth class names for unknown objects, serving as the upper bound of the OVOD methods by assuming access to all unknown class names. BASE-FS utilizes image exemplars to produce vision-derived object embeddings, which are averaged per class to form class embeddings. Then a general prompt, such as "a photo of an object", is applied to help identify unknown objects. + +As can be seen in Tab. 2, our proposed PASS consistently outperforms FOMO by a significant margin and achieves performance that is very close to the OVOD upper bound, even + +when using the B/16 backbone. In particular, our improvement is especially notable in known classes, as reflected in the K-, PK-, and CK-mAP metrics. This can be attributed to the robust attribute selection and optimization capabilities of our proposed PASS framework, which effectively curates a set of accurate and effective attributes to enhance object detection. On the other hand, PASS also demonstrates a significant performance boost in unknown classes as measured by the U-mAP metric. This suggests that the attributes learned by PASS are not only effective for known classes during training but also highly generalizable to unknown objects during evaluation. + +Visualizations. For further comprehension of the effectiveness of our proposed PASS in detecting open world objects, we present several qualitative results for each dataset in Fig. 3. When comparing the detection results between FOMO (second row) and our proposed PASS (third row), PASS consistently demonstrates improved detection performance, with results that are more closely aligned with the ground truth (first row). In particular, FOMO sometimes incorrectly classifies known objects as unknown, or vice versa, suggesting that the learned attributes might not be sufficiently accurate to reliably characterize known objects. Furthermore, FOMO occasionally yields significantly fewer detection results in certain domains, such as medical datasets. This suggests that the learned attributes might not adequately capture the full range of potentially useful features necessary for detecting unknown objects. In contrast, PASS delivers + +![](images/5f89167e4cbe184b5148b3eedcc12aa9a20e2df14853cbb5759762effc5db146.jpg) +Aquatic + +![](images/688f8bd66bb114ad23e0eb8a8852af2aa9bbf69cece97ad71ad9b66df16a03a0.jpg) +Aerial + +![](images/e53f57753cc7bd743e8e6edc064f5c8ecc70f5c566fbcfab76aab2dd6f9f5380.jpg) +Game + +![](images/dcfee6a6987b57fbc09d2a6c23bc95dd4bab65d3f2cd2b5b2be97d3256aa14bb.jpg) +Medical + +![](images/3de4ebaaebe79b7fe334a684667d54ba8019498462aa2cc82f8e848a8fe0a8ba.jpg) +Surgery + +![](images/8a22cf17aa3f8b1ce8a2d94f38073a182a2856ed0b486e175d718e79812fe89f.jpg) + +![](images/921fdd49b891bb53a52340b570adfeb5ea0ea5cc5b888c73d4aa475c10c36df3.jpg) + +![](images/9fe5eabd87e51347dd8d24ab0f3c17f77751b818db863dc5d39df967b5e4ef9a.jpg) + +![](images/6bfa16f3fb393e7f2903e469c6d0c0bac3c19a2da5c1e85c52395e632b3967cf.jpg) + +![](images/a5855455638e6b4e0abd11e1aa9d8550e6fa871d836faefe89f2fb4fd4ea8c9a.jpg) + +![](images/21f353d7ed8a1eadeee8a63ad28d743398f04ed933b93ff856935ecbfa5db825.jpg) +Figure 3. Qualitative results on the five real-world datasets. First Row: images in each dataset with ground truth bounding boxes and class names. Second Row: Detection results using FOMO [78]. Third Row: Detection results using our proposed PASS. We use green and yellow boxes to indicate known and unknown objects, respectively. Bottom Rows: The top three attributes that are activated for detecting known and unknown classes in each image using our proposed PASS. + +![](images/410323d131864cbba4659b1aa697106eb3b2d0e9dd152c48c26d73373df6a93e.jpg) + +![](images/f836e38d42008afa22e0c7846aa6dd70e0928995876b8f50265d6f5ef8e70a51.jpg) + +![](images/a43f9e065c49cbdfbb6d187d3cb6965e605bfdca5e557424d1fcd164c851ad18.jpg) + +![](images/6e26fbe3b482b79cdf093b2651cd3a151281995c8d4d915ba15add9951935f4c.jpg) + +Top attributes for detected known classes: + +Shape is truncate tail +Shape is flexible +Environment is tide pool + +Top attributes for detected known classes: + +Shape is stationary +Shape is converging +Behavior is tournament + +Top attributes for detected known classes: + +Material is calcium +- Appearance is visible +joints between bones +Color is veins + +Top attributes for detected known classes: + +Shape is straight +Shape is convex +Shape is knobby + +Top attributes for detected known classes: + +Behavior is handle + +- Features is gripping surface +- Appearance is presence of grooves + +Top attributes for detected unknown classes: + +Shape is dorsal fin shape +Texture is ridged +Shape is adipose fin shape + +Top attributes for detected unknown classes: + +- Appearance is distinctive roof design +Context is court lines +Shape is stationary + +Top attributes for detected unknown classes: + +- Appearance is edges +Shape is smooth +Texture is striped + +Top attributes for detected unknown classes: + +Shape is cracked +Shape is straight +- Features is thumb metacarpal + +Top attributes for detected unknown classes: + +Material is cutting edge +Shape is pointed tips +- Appearance is shiny + +superior detection results due to the more accurate attributes learned during training. These attributes not only provide a strong characterization of known object classes but also demonstrate high generalizability to unknown classes. Furthermore, as illustrated in the bottom two rows of Fig. 3, PASS effectively leverages meaningful attributes to identify both known and unknown objects. For example, it uses the attribute "shape is dorsal fin shape" to detect an unknown fish species recognized for its large fin. + +# 6. Conclusion + +In this paper, we propose an efficient end-to-end approach to select a compact set of representative attributes tailored to detect open-world objects, including both known and unknown + +classes. Specifically, we formulate the attribute selection and optimization process as a Partial Optimal Transport (POT) problem, where the most relevant attributes emerge with the highest transported mass. Additionally, we introduce a curriculum-based attribute selection strategy that gradually refines the attribute subset during training, significantly enhancing training stability and selection effectiveness. We evaluate our approach on challenging real-world datasets, where it achieves superior performance that surpasses current state-of-the-art methods by a large margin. + +In future work, we aim to expand our method to incorporate hierarchical information within attribute taxonomies. This enhancement will allow for a more fine-grained understanding of the detection process by leveraging attributes at varying levels of granularity. + +Acknowledgments. This research is supported by the EDB Space Technology Development Programme under Project S22-19016-STDP, the National Natural Science Foundation of China under Grant 62306251, 62171343, 62176171, U21B2040, the Hong Kong Research Grant Council - Early Career Scheme under Grant 27208022, the HKU Seed Fund for Basic Research, the Fundamental Research Funds for the Central Universities under Grant CJ202303, as well as the Sichuan Science and Technology Planning Project under Grant 24NSFTD0130. The authors sincerely thank the anonymous Reviewers and Area Chairs for their valuable feedback and constructive comments. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023. 1 +[2] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. 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Apart from recognizing known objects from training, a successful Open World Object Detection (OWOD) system must also be able to detect unknown objects never seen before, without confusing them with the backgrounds. Unlike prevailing prior works that rely on probability models to learn \"objectness\", we focus on learning fine-grained, class-agnostic attributes, allowing the detection of both known and unknown objects in an explainable manner. In this paper, we propose Partial Attribute Assignment (PASS), aiming to automatically select and optimize a small, relevant subset of attributes from a large attribute pool. Specifically, we model attribute selection as a Partial Optimal Transport (POT) problem between known visual objects and the attribute pool, in which more relevant attributes signify more transported mass. PASS follows a curriculum schedule that progressively selects and optimizes a targeted subset of attributes during training, promoting stability and accuracy. Our method enjoys end-to-end optimization by minimizing the POT distance and the classification loss on known visual objects, demonstrating high training efficiency and superior OWOD performance among extensive experimental evaluations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 555, + 135, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 135, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 135, + 567 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 575, + 296, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 296, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 296, + 694 + ], + "type": "text", + "content": "Deep learning and foundation models have emerged as critical AI technologies [1, 55], impacting various aspects of modern life. However, their success has been largely based on the closed-world assumption, which presumes a static and well-defined environment [76]. In practice, this assumption is difficult to uphold, as real-world conditions are dynamic and unpredictable, with unforeseen situations and unseen objects regularly appearing. Open World Object Detection (OWOD) [22] has emerged as a remedy to deliver reliable detection in the face of new environments with unknown ob" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 329, + 228, + 553, + 357 + ], + "blocks": [ + { + "bbox": [ + 315, + 281, + 327, + 291 + ], + "lines": [ + { + "bbox": [ + 315, + 281, + 327, + 291 + ], + "spans": [ + { + "bbox": [ + 315, + 281, + 327, + 291 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 329, + 228, + 553, + 357 + ], + "lines": [ + { + "bbox": [ + 329, + 228, + 553, + 357 + ], + "spans": [ + { + "bbox": [ + 329, + 228, + 553, + 357 + ], + "type": "image", + "image_path": "fe47cb634b971bf830b51d04b30dd8d26af3cee25a7633398faed2bdcd712b18.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 328, + 365, + 554, + 459 + ], + "blocks": [ + { + "bbox": [ + 315, + 411, + 327, + 420 + ], + "lines": [ + { + "bbox": [ + 315, + 411, + 327, + 420 + ], + "spans": [ + { + "bbox": [ + 315, + 411, + 327, + 420 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 328, + 365, + 554, + 459 + ], + "lines": [ + { + "bbox": [ + 328, + 365, + 554, + 459 + ], + "spans": [ + { + "bbox": [ + 328, + 365, + 554, + 459 + ], + "type": "image", + "image_path": "4187f32aea67422cd73170502074fc98daacd568c464402fa74f11a501805f1b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 464, + 555, + 530 + ], + "lines": [ + { + "bbox": [ + 313, + 464, + 555, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 555, + 530 + ], + "type": "text", + "content": "Figure 1. The role of attributes in Open World Object Detection (OWOD). (a) Unknown objects can be detected via shared visual/functional attributes with known objects. (b) Our method is able to automatically identify and optimize a small subset of relevant attributes from a large pool, effectively enabling the detection of both known and unknown objects." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 555, + 555, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 555, + 555, + 604 + ], + "spans": [ + { + "bbox": [ + 312, + 555, + 555, + 604 + ], + "type": "text", + "content": "jects. In addition to recognizing known objects that appeared in training, a successful OWOD system must also detect and continually learn previously unseen objects without mistakenly classifying them as backgrounds." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 605, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 605, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 312, + 605, + 556, + 714 + ], + "type": "text", + "content": "Recent works mainly use probability distribution estimation to model the \"objectness\" information, i.e., the probability of a candidate proposal being an object rather than backgrounds [79]. In this way, OWOD can be decomposed into two sub-tasks that respectively focus on objectness estimation and known class recognition [54]. Although this approach has significantly improved the detection of unknown objects, it has certain limitations in explainability and ambiguity. On the one hand, the learned probabilistic" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 702, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 702, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 56, + 702, + 295, + 713 + ], + "type": "text", + "content": "†Corresponding author. ‡Code: https://github.com/muliyangm/PASS" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20318" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 120 + ], + "type": "text", + "content": "model is unable to explain how the objects—both the known and the unknown—are detected. On the other hand, when background features resemble those of the unknown objects, the model can still misclassify them." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 122, + 297, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 122, + 297, + 408 + ], + "spans": [ + { + "bbox": [ + 56, + 122, + 297, + 408 + ], + "type": "text", + "content": "In this paper, we focus on detecting open world objects using fine-grained, class-agnostic attributes that are visually and/or functionally related to the known objects. These attributes can be described using natural languages with rich semantic information, and thus are naturally explainable and less ambiguous. The emphasis on intrinsic object attributes offers stronger resistance to confusion in scenarios where background and unknown object features overlap, making it particularly suitable for dynamic open-world environments. As illustrated in Fig. 1(a), attributes can be useful in detecting both known and unknown object classes, e.g., the learned \"umbrella-like\" attribute from known classes can be used to detect the unknown fungi. Despite the promising potential of using attributes in OWOD, effectively curating a set of attributes that are closely related to the specific task from a large pool of attributes remains a significant challenge. To this end, some existing method [78] seeks a set of representative attributes that can effectively classify known objects with multistage processes—such as attribute selection and refinement—which are time-consuming and computationally expensive. More importantly, the separation of the selection and refinement processes may accumulate errors, leading to inaccuracies in the results of the attribute selection and refinement." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 412, + 297, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 412, + 297, + 603 + ], + "spans": [ + { + "bbox": [ + 55, + 412, + 297, + 603 + ], + "type": "text", + "content": "We propose to tackle this dilemma using Partial Attribute Assignment (PASS), an approach that progressively selects and optimizes a targeted subset of relevant attributes throughout the training process in an end-to-end manner. In particular, we model attribute selection as a Partial Optimal Transport (POT) problem [6] between known visual objects and the attribute pool, in which more relevant attributes signify more mass transported to the visual objects. Unlike conventional OT [56] that assumes identical mass in both distributions to be completely transported, POT allows the transport of only a targeted fraction of total mass from one distribution to another. As such, the attribute pool can be viewed as a collection of both in-distribution (ID) and out-of-distribution (OOD) attributes w.r.t. the visual objects, where we can use the visual object distribution as the baseline distribution to filter out redundant OOD attributes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 605, + 297, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 297, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 297, + 713 + ], + "type": "text", + "content": "To achieve stable, accurate attribute selection and optimization simultaneously, PASS follows a curriculum learning [4] schedule that progressively targets and optimizes a subset of attributes throughout training. PASS ensures that each filtered subset is highly representative and provides broad coverage of the visual objects, by iteratively focusing on and refining a smaller subset of attributes guaranteed by the OT theory. As training progresses, the selected attributes reach a balanced state between representativeness and cover-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 556, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 556, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 556, + 251 + ], + "type": "text", + "content": "age, allowing the model to better adapt to both known and unknown objects. This process also reduces computational costs by gradually limiting the number of attributes introduced. Our method enjoys end-to-end optimization by minimizing both the POT distance and the classification loss for known visual objects. During inference, the learned attributes play a dual role: they support the recognition of known classes through the mapping relationships established during training, while also enabling the detection of unknown objects by leveraging the correlation between object proposals and the learned attributes. Extensive experiments demonstrate that our method significantly outperforms baseline methods, validating both the feasibility of attribute-based OWOD and the effectiveness of our approach in curating more accurate attributes for OWOD." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 326, + 254, + 489, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 254, + 489, + 265 + ], + "spans": [ + { + "bbox": [ + 326, + 254, + 489, + 265 + ], + "type": "text", + "content": "In a nutshell, our main contributions are" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 267, + 555, + 399 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 314, + 267, + 555, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 267, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 314, + 267, + 555, + 316 + ], + "type": "text", + "content": "- We model the attribute curation issue in OWOD as a Partial Optimal Transport (POT) problem, enabling end-to-end attribute selection and optimization for effectively detecting both known and unknown objects;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 316, + 555, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 555, + 363 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 555, + 363 + ], + "type": "text", + "content": "- We propose a curriculum selection strategy by progressively optimizing a targeted subset of attributes with strong representativeness and broad coverage, benefiting both training stability and selection effectiveness;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 363, + 555, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 363, + 555, + 399 + ], + "spans": [ + { + "bbox": [ + 313, + 363, + 555, + 399 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the absolute superiority of the proposed method in terms of both training efficiency and detection performance." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 416, + 400, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 416, + 400, + 428 + ], + "spans": [ + { + "bbox": [ + 314, + 416, + 400, + 428 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "type": "text", + "content": "Open World Object Detection. Open World Object Detection (OWOD) [22] enhances traditional object detectors by shifting away from closed-set assumptions, enabling dynamic adaptation to novel classes as encountered in real-world settings [20, 29, 30, 33, 34, 67, 74]. Existing works [27, 51, 61, 65, 69, 70] reduce the overlap between known, unknown classes and the background distributions using different ways, e.g., pseudo-labeling [18, 38], objectness estimation [54, 79], and hierarchical modeling [13, 37]. OWOD is also related to similar tasks such as Class-Agnostic Object Detection [14, 21, 23, 36, 44, 45, 50, 59, 60] and Open-Vocabulary Object Detection (OVOD) [17, 25, 41, 42, 58, 71, 75]. Recent advances, such as FOMO [78] and a concurrent work UMB [62], extend the standard OVOD method to OWOD by utilizing vision and language foundation models. By identifying objects based on semantic attributes [26, 49, 53], they learn class-agnostic attributes to detect task-relevant unknown objects, yet require multistage attribute selection and refinement, which is time-consuming and computationally inefficient. In this paper, we propose an end-to-end attribute curation method that not only benefits the training efficiency but also largely improves the detection performance in both known and unknown classes." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20319" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 298, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 298, + 324 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 298, + 324 + ], + "type": "text", + "content": "Optimal Transport. Optimal Transport (OT), originally introduced by Monge [43] to minimize the cost of transporting items, has become a prominent tool in machine learning and computer vision for matching distributions across domains [46, 56]. OT has been widely applied in distribution-based tasks [8, 57, 73] such as generative models [2], clustering [19, 66], domain adaptation [11], object detection [16] and structural tasks such as sequence [9], graph [63], and image matching [32, 72]. To address OT's high computational demands, the Sinkhorn OT [12] offers a solution by approximating OT through an efficient iterative algorithm. Partial OT (POT), a variant of OT that transports only a portion of the mass, addresses cases where distributions only partially overlap, making it especially relevant in scenarios such as open-set domain adaptation [6, 7, 15, 35, 48, 64, 68]. The Sinkhorn algorithm has been extended to POT to further reduce computational costs [3]. In our work, we utilize POT to dynamically match attribute embeddings with visual embeddings of known object classes, selecting and optimizing the most representative attributes for effectively detecting both known and unknown objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 335, + 135, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 335, + 135, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 135, + 348 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": "OWOD with Foundation Models. Open World Object Detection (OWOD) requires a model to detect and incrementally learn unknown objects. In particular, there are multiple stages/tasks for training and evaluation, indicated by " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": ". In task " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": ", the model can be trained on " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "K^t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": " known object classes from " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathcal{K}^t = \\{O_1^t, O_2^t, \\ldots, O_{K^t}^t\\}" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": ", and to be evaluated on a test set that contains both known and unknown classes. To achieve that, we use an additional " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "O_0^t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": " to denote the unknown classes, alongside the " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "K^t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": " known classes. In fact, " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "O_0^t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": " represents " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "U^t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": " classes of interest that are unknown to the model in the task " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "\\mathcal{U}^t = \\{O_{K^t + 1}^t, O_{K^t + 2}^t, \\ldots, O_{K^t + U^t}^t\\}" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": ". After discovering the unknown object classes, the model can be updated with the knowledge of these new classes using annotations from an oracle (e.g., a human annotator) in task " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": ". As a result, the model is ready to detect " + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "inline_equation", + "content": "K^{t + 1} = K^t + U^t" + }, + { + "bbox": [ + 55, + 354, + 296, + 558 + ], + "type": "text", + "content": " known object classes in the test set, as well as additional unknown classes for the subsequent task cycle." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "text", + "content": "To push the boundary of OWOD in real-world applications, we follow a recent work [78] to make use of existing pretrained foundation models in open-vocabulary object detection [41, 71], e.g., vision and language encoders, and adapt them to OWOD. The training follows a few-shot paradigm: for the " + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "text", + "content": "-shot, only " + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 558, + 298, + 714 + ], + "type": "text", + "content": " images per known class are given, with only one bounding box label and one object class label for each image. For each dataset, we use the attribute texts proposed by a Large Language Model (LLM), i.e., GPT-3.5, by prompting with the known class names using the template described in recent works [40, 77, 78]. This will result in an attribute pool with numerous class-agnostic attributes visually and/or functionally related to the known" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 73, + 474, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 73, + 474, + 85 + ], + "spans": [ + { + "bbox": [ + 313, + 73, + 474, + 85 + ], + "type": "text", + "content": "objects, e.g., shape is straight." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 93, + 555, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 93, + 555, + 152 + ], + "spans": [ + { + "bbox": [ + 313, + 93, + 555, + 152 + ], + "type": "text", + "content": "Optimal Transport Preliminary. Optimal Transport (OT) is a powerful tool for measuring the distance between two distributions. Here we review the discrete OT scenario that is more related to our framework and refer the readers to [12] for more details." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 153, + 555, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 153, + 555, + 189 + ], + "spans": [ + { + "bbox": [ + 313, + 153, + 555, + 189 + ], + "type": "text", + "content": "Assuming we have two sets of data points (features) " + }, + { + "bbox": [ + 313, + 153, + 555, + 189 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\{\\pmb{x}_m\\}_{m=1}^M" + }, + { + "bbox": [ + 313, + 153, + 555, + 189 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 153, + 555, + 189 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} = \\{\\pmb{y}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 313, + 153, + 555, + 189 + ], + "type": "text", + "content": ", their discrete distributions can be formulated as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 352, + 196, + 555, + 229 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 196, + 555, + 229 + ], + "spans": [ + { + "bbox": [ + 352, + 196, + 555, + 229 + ], + "type": "interline_equation", + "content": "\\mathcal {X} = \\sum_ {m = 1} ^ {M} \\frac {1}{M} \\delta_ {\\boldsymbol {x} _ {m}}, \\quad \\mathcal {Y} = \\sum_ {n = 1} ^ {N} \\frac {1}{N} \\delta_ {\\boldsymbol {y} _ {n}}, \\tag {1}", + "image_path": "eba9730daf9d8aab0ef014dc5add2129b4ba79e33bacfbf3fe8232e924212b0c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "spans": [ + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "type": "text", + "content": " is the Dirac function and we use the uniform distribution to equally view each data point. The OT distance is defined as the smallest cost of transporting " + }, + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 313, + 237, + 556, + 274 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 358, + 281, + 555, + 303 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 281, + 555, + 303 + ], + "spans": [ + { + "bbox": [ + 358, + 281, + 555, + 303 + ], + "type": "interline_equation", + "content": "d _ {\\mathrm {O T}} (\\mathcal {X}, \\mathcal {Y}; \\mathbf {C}) \\triangleq \\min _ {\\mathbf {T} \\in \\Pi (\\mathcal {X}, \\mathcal {Y})} \\left\\langle \\mathbf {T}, \\mathbf {C} \\right\\rangle_ {F}, \\tag {2}", + "image_path": "0cd51d5b5e8452994bb6c3383353d29aa07a3fc3561ee4c55be1f757854821a0.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\mathbf{C} \\in \\mathbb{R}_{+}^{M \\times N}" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": " is the cost matrix between " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "C_{m,n} = c(\\pmb{x}_m, \\pmb{y}_n)" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": " is the transport cost from " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\pmb{x}_m" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\pmb{y}_n" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "c(\\cdot)" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": " being the cost function (e.g., the cosine distance), " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": " is the transport plan to be solved, and " + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "inline_equation", + "content": "\\langle \\cdot, \\cdot \\rangle_F" + }, + { + "bbox": [ + 313, + 312, + 555, + 385 + ], + "type": "text", + "content": " denotes the Frobenius inner product. The optimization of OT distance satisfies two marginal constraints:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 393, + 555, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 393, + 555, + 409 + ], + "spans": [ + { + "bbox": [ + 320, + 393, + 555, + 409 + ], + "type": "interline_equation", + "content": "\\Pi (\\mathcal {X}, \\mathcal {Y}) \\triangleq \\left\\{\\mathbf {T} \\in \\mathbb {R} _ {+} ^ {M \\times N} \\mid \\mathbf {T} \\mathbf {1} _ {N} = \\mathcal {X}, \\mathbf {T} ^ {\\top} \\mathbf {1} _ {M} = \\mathcal {Y} \\right\\}, \\tag {3}", + "image_path": "c404a873e7f8ee081e62e8c2e025b0fd2e370541ec02f43f963dac73c1a2ebc5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{1}_N" + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "text", + "content": " is an " + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "text", + "content": "-dimensional vector of all ones, and we slightly abuse " + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "text", + "content": " to denote " + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = \\frac{1}{M}\\mathbf{1}_M" + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} = \\frac{1}{N}\\mathbf{1}_N" + }, + { + "bbox": [ + 313, + 417, + 554, + 455 + ], + "type": "text", + "content": " to reflect the discrete probability in Eq. (1)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 464, + 370, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 370, + 477 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 370, + 477 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 484, + 555, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 555, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 555, + 533 + ], + "type": "text", + "content": "We propose Partial Attribute Assignment (PASS) to address the challenging Open World Object Detection (OWOD) task. PASS is composed of three modules shown in Fig. 2, which are introduced in separate subsections below." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 540, + 473, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 473, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 473, + 553 + ], + "type": "text", + "content": "4.1. Partial Attribute Assignment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "content": "As discussed above, now we have " + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "content": "-shot images of " + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "content": " known object classes (the superscript " + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "content": " is omitted for brevity) and " + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "content": " attribute texts in the attribute pool. Our goal is to select and optimize a small set of relevant attributes from the attribute pool, with the target attribute quantity denoted as " + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "inline_equation", + "content": "N' \\in (0, N]" + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "content": ". The resulting " + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "inline_equation", + "content": "N'" + }, + { + "bbox": [ + 313, + 557, + 555, + 641 + ], + "type": "text", + "content": " attributes are to be used for effectively detecting both known and unknown objects." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "Formally, we collect the visual object embeddings as " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{V} = [v_{1}, v_{2}, \\ldots, v_{M}] \\in \\mathbb{R}^{D \\times M}" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " and the attribute embeddings as " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{A} = [a_{1}, a_{2}, \\ldots, a_{N}] \\in \\mathbb{R}^{D \\times N}" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "-dimensional embedding space using pretrained vision and text encoders [41, 47], where " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "M = z \\cdot K" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " is the number of known image patches obtained using bounding box labels," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20320" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 70, + 553, + 210 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 553, + 210 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 553, + 210 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 553, + 210 + ], + "type": "image", + "image_path": "a622527a0c6b28354d33d00d83913fe000b025ff6c32b6d4d9d241f01bb36f92.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 216, + 555, + 285 + ], + "lines": [ + { + "bbox": [ + 54, + 216, + 555, + 285 + ], + "spans": [ + { + "bbox": [ + 54, + 216, + 555, + 285 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed Partial Attribute Assignment (PASS) for OWOD. PASS is constructed upon pretrained vision and text encoders [41, 47] and is designed to identify and refine a set of relevant attributes from an attribute pool, which are essential for detecting both known and unknown object classes. (a) We employ Partial Optimal Transport (POT) to model the assignment problem between attributes and known visual objects (Sec. 4.1). (b) The resulting transport plan " + }, + { + "bbox": [ + 54, + 216, + 555, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 54, + 216, + 555, + 285 + ], + "type": "text", + "content": " is used to generate attribute in-distribution (ID) scores " + }, + { + "bbox": [ + 54, + 216, + 555, + 285 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 54, + 216, + 555, + 285 + ], + "type": "text", + "content": ", which help in selecting the most relevant attributes for the specific task (Sec. 4.2). (c) These attribute ID scores are further used to reweight the selected attributes, which are subsequently applied to compute object class predictions via a learnable mapping matrix (Sec. 4.3)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "spans": [ + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": "and all embeddings are " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": " normalized. Likewise, we can denote the discrete distributions of " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": " following Eq. (1). The conventional OT assumes that the two distributions have the identical total probability mass, i.e., " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\| \\mathcal{V}\\| _1 = \\| \\mathcal{A}\\| _1" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": ", and that all the mass of " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": " must be transported. Although this assumption works effectively for tasks that involve identical distributions, it faces challenges in our scenario, where only a subset of samples in " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": " aligns with " + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 54, + 302, + 296, + 397 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "spans": [ + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": "A workaround is to transport only the mass of indistribution (ID) samples between " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": " while retaining the out-of-distribution (OOD) mass within " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": ". This leads to the concept of Partial OT (POT) [6], which relaxes the assumption of equal total mass between " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": ". Instead, it allows for transporting a portion of the mass within the range " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "[0, \\min(\\|\\mathcal{V}\\|_1, \\|\\mathcal{A}\\|_1)]" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": ". To this end, we use the visual distribution " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": " as a baseline distribution to filter out redundant outliers in " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": ". Accordingly, the visual distribution " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": " and attribute distribution " + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 54, + 398, + 296, + 517 + ], + "type": "text", + "content": " are redefined as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 94, + 523, + 296, + 556 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 523, + 296, + 556 + ], + "spans": [ + { + "bbox": [ + 94, + 523, + 296, + 556 + ], + "type": "interline_equation", + "content": "\\mathcal {V} = \\sum_ {m = 1} ^ {M} \\frac {1}{M} \\delta_ {\\boldsymbol {v} _ {m}}, \\quad \\mathcal {A} = \\sum_ {n = 1} ^ {N} \\frac {\\alpha}{N} \\delta_ {\\boldsymbol {a} _ {n}}, \\tag {4}", + "image_path": "a96e53f5b70c78e0c161e1ce0ae1f6e8a93ad61a1b2bf1e681943de3c4c6995d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "type": "inline_equation", + "content": "\\alpha = \\frac{N}{N'} \\geqslant 1" + }, + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "type": "text", + "content": " is the attribute redundant rate reflecting the redundant mass in " + }, + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "type": "text", + "content": ", which enables transporting only a subset of mass in " + }, + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 55, + 563, + 296, + 625 + ], + "type": "text", + "content": ". In this manner, we formulate the resulting problem as a POT problem with the following marginal constraints:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 631, + 296, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 631, + 296, + 647 + ], + "spans": [ + { + "bbox": [ + 63, + 631, + 296, + 647 + ], + "type": "interline_equation", + "content": "\\Pi (\\mathcal {V}, \\mathcal {A}) \\triangleq \\left\\{\\mathbf {T} \\in \\mathbb {R} _ {+} ^ {M \\times N} \\mid \\mathbf {T} \\mathbf {1} _ {N} = \\mathcal {V}, \\mathbf {T} ^ {\\top} \\mathbf {1} _ {M} \\leqslant \\mathcal {A} \\right\\}. \\tag {5}", + "image_path": "7743f4c75ac308207964026b7419f2e61fb92106cf9d6a6c22d84b3873d2695f.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": "It is important to highlight that, unlike the traditional POT problem, which imposes inequality constraints on both distributions, Eq. (5) introduces equality constraints within " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": " [48]. This modification explicitly aligns the attribute distribution with the visual distribution by redistributing weights among" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 302, + 555, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 302, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 302, + 555, + 338 + ], + "type": "text", + "content": "the attributes. Moreover, the concise constraints accelerate the convergence of POT computations. The POT distance is then denoted as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 335, + 346, + 555, + 366 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 346, + 555, + 366 + ], + "spans": [ + { + "bbox": [ + 335, + 346, + 555, + 366 + ], + "type": "interline_equation", + "content": "d _ {\\mathrm {P O T}, \\epsilon} (\\mathcal {V}, \\mathcal {A}; \\mathbf {C}) \\triangleq \\min _ {\\mathbf {T} \\in \\Pi (\\mathcal {V}, \\mathcal {A})} \\left\\langle \\mathbf {T}, \\mathbf {C} \\right\\rangle_ {F} - \\epsilon h (\\mathbf {T}), \\tag {6}", + "image_path": "24bd49df1136779639ab0dbe3ccb6ee36e3ebcb3936d55d6e3973099c71a5c2f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "type": "inline_equation", + "content": "\\epsilon > 0" + }, + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "type": "text", + "content": " is the regularization coefficient, and " + }, + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "type": "inline_equation", + "content": "h(\\mathbf{T}) = -\\sum_{m,n} T_{m,n} \\ln (T_{m,n})" + }, + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "type": "text", + "content": " is the entropic constraint to accelerate the optimization [12], so that the optimal " + }, + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 313, + 374, + 556, + 436 + ], + "type": "text", + "content": " can be estimated in a few iterations. We defer the detailed optimization procedure of Eq. (6) to Supplementary Material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 442, + 485, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 442, + 485, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 442, + 485, + 453 + ], + "type": "text", + "content": "4.2. Curriculum Attribute Selection" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 459, + 555, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 555, + 508 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 555, + 508 + ], + "type": "text", + "content": "Upon the optimal transport plan " + }, + { + "bbox": [ + 313, + 459, + 555, + 508 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 313, + 459, + 555, + 508 + ], + "type": "text", + "content": " derived in Eq. (6), we can define an in-distribution (ID) score for each attribute as " + }, + { + "bbox": [ + 313, + 459, + 555, + 508 + ], + "type": "inline_equation", + "content": "s = [s_1, s_2, \\ldots, s_N]^\\top" + }, + { + "bbox": [ + 313, + 459, + 555, + 508 + ], + "type": "text", + "content": ", by aggregating the mass transferred from one attribute to all visual objects:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 384, + 514, + 555, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 514, + 555, + 539 + ], + "spans": [ + { + "bbox": [ + 384, + 514, + 555, + 539 + ], + "type": "interline_equation", + "content": "s _ {n} = \\frac {N}{\\alpha} \\sum_ {m = 1} ^ {M} T _ {m, n}, \\tag {7}", + "image_path": "69d5faee347d5975ae090494a727a2f27762d06a04e3d508c44a58953ab0a111.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "type": "inline_equation", + "content": "s_n \\in [0,1]" + }, + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "type": "text", + "content": " is the scaled mass transported that can be interpreted as the probability of the specific attribute being in-distribution to the visual objects in " + }, + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "type": "text", + "content": ". The underlying rationale is that the transport cost among ID samples is relatively low. To minimize the total transport cost, ID attributes in " + }, + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 313, + 545, + 554, + 640 + ], + "type": "text", + "content": " are allocated a greater proportion of transportation mass compared to the redundant OOD attributes, in accordance with the principles of POT." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "type": "text", + "content": "With the ID scores " + }, + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "type": "text", + "content": " at hand, one can simply select " + }, + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "type": "inline_equation", + "content": "N'" + }, + { + "bbox": [ + 313, + 642, + 555, + 713 + ], + "type": "text", + "content": " attributes with the highest ID scores at a certain stage of training, e.g., at the beginning or the end. However, this may suffer from either the inaccurate transport cost due to the modality gap, or the inaccurate mapping from attributes to known classes. In light of this, we devise an iterative attribute" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20321" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": "selection strategy that follows the spirit of Curriculum Learning [4]. Instead of single-time selection, we divide it into " + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 55, + 72, + 296, + 144 + ], + "type": "text", + "content": " steps alongside the training, such that only a slightly smaller set of attributes are to be selected in each step, making the POT problem easier to solve, and thus benefit the training stability and attribute selection effectiveness." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": "Formally, " + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": " in Eq. (4) is now rewritten as " + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "inline_equation", + "content": "\\alpha = \\left(\\frac{N}{N'}\\right)^{\\frac{1}{\\eta}}" + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": ". In each of the " + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": " selection steps, we select the " + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "inline_equation", + "content": "\\frac{1}{\\alpha}" + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": " amount of the remaining attributes according to the indices of the top " + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "inline_equation", + "content": "\\frac{1}{\\alpha}" + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": " ID scores " + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": ". The detailed selection method is summarized in Lines 5 to 8 in Algorithm 1. We denote the resulting selected attribute embeddings as " + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}} \\in \\mathbb{R}^{D \\times N'}" + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": ", with the ID scores being " + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "inline_equation", + "content": "s = [s_1, s_2, \\dots, s_{N'}]^\\top \\in \\mathbb{R}^{N'}" + }, + { + "bbox": [ + 55, + 144, + 296, + 231 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 236, + 189, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 236, + 189, + 248 + ], + "spans": [ + { + "bbox": [ + 55, + 236, + 189, + 248 + ], + "type": "text", + "content": "4.3. Object Class Prediction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "spans": [ + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "type": "text", + "content": "After gaining the selected attributes in each step, we can learn a mapping matrix " + }, + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = [\\pmb{w}_1, \\pmb{w}_2, \\dots, \\pmb{w}_K] \\in \\mathbb{R}^{N' \\times K}" + }, + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "type": "text", + "content": " to assign " + }, + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "type": "inline_equation", + "content": "N'" + }, + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "type": "text", + "content": " attributes to " + }, + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 253, + 296, + 301 + ], + "type": "text", + "content": " known object classes, with the prediction probability computed as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 99, + 305, + 296, + 336 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 305, + 296, + 336 + ], + "spans": [ + { + "bbox": [ + 99, + 305, + 296, + 336 + ], + "type": "interline_equation", + "content": "p \\left(O _ {k} | \\boldsymbol {v}\\right) = \\frac {\\exp \\left(\\boldsymbol {w} _ {k} ^ {\\top} \\mathbf {A} ^ {\\prime \\top} \\boldsymbol {v}\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp \\left(\\boldsymbol {w} _ {k ^ {\\prime}} ^ {\\top} \\mathbf {A} ^ {\\prime \\top} \\boldsymbol {v}\\right)}, \\tag {8}", + "image_path": "868856d78214a76f3efbed3d5b09e4b886eb7d527b254714aa51d98a0bcf67a5.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathbf{A}' = [a_1', a_2', \\dots, a_{N'}']" + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "text", + "content": " is the element-wise multiplication between " + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "inline_equation", + "content": "a_n' = s_n \\hat{a}_n" + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "text", + "content": ". The inclusion of ID scores " + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 339, + 296, + 401 + ], + "type": "text", + "content": " constitutes a complementary \"soft\" filtering strategy by reweighting selected attributes, whose effectiveness is clearly shown in Sec. 5.2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 402, + 296, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 402, + 296, + 436 + ], + "spans": [ + { + "bbox": [ + 55, + 402, + 296, + 436 + ], + "type": "text", + "content": "After acquiring the class predictions, we can use a standard cross-entropy loss to supervise the optimization of both " + }, + { + "bbox": [ + 55, + 402, + 296, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 55, + 402, + 296, + 436 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 402, + 296, + 436 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 55, + 402, + 296, + 436 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 90, + 441, + 296, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 441, + 296, + 473 + ], + "spans": [ + { + "bbox": [ + 90, + 441, + 296, + 473 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C E}} = - \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\sum_ {k = 1} ^ {K} l _ {m, k} \\log p \\left(O _ {k} | \\boldsymbol {v} _ {m}\\right), \\tag {9}", + "image_path": "1af90c7a2234fb91a43660748db1f58cafea8c50f2de39422d91b6eef720f663.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 479, + 235, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 479, + 235, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 479, + 235, + 491 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 479, + 235, + 491 + ], + "type": "inline_equation", + "content": "l_{m}" + }, + { + "bbox": [ + 55, + 479, + 235, + 491 + ], + "type": "text", + "content": " is the one-hot label vector for " + }, + { + "bbox": [ + 55, + 479, + 235, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{m}" + }, + { + "bbox": [ + 55, + 479, + 235, + 491 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 496, + 161, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 496, + 161, + 509 + ], + "spans": [ + { + "bbox": [ + 55, + 496, + 161, + 509 + ], + "type": "text", + "content": "4.4. Overall Objective" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 514, + 295, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 295, + 538 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 295, + 538 + ], + "type": "text", + "content": "Training. Our method can be optimized using the below training objective in an end-to-end fashion:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 132, + 544, + 295, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 544, + 295, + 558 + ], + "spans": [ + { + "bbox": [ + 132, + 544, + 295, + 558 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {C E}} + \\lambda d _ {\\mathrm {P O T}, \\epsilon}, \\tag {10}", + "image_path": "047cce0cf3d623a39dafa23ec5a38639eb11bf7a8b72f20ad238cdc217fa18cc.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 563, + 296, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 296, + 599 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 296, + 599 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 55, + 563, + 296, + 599 + ], + "type": "inline_equation", + "content": "\\lambda > 0" + }, + { + "bbox": [ + 55, + 563, + 296, + 599 + ], + "type": "text", + "content": " is a trade-off coefficient to balance the effect of the POT loss in Eq. (6). Algorithm 1 summarizes the whole training procedure." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "text", + "content": "Inference. We follow the prior work [78] to detect if a test visual embedding " + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "text", + "content": " contains unknown objects by combining two probabilities: (a) task relevance—the probability of " + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "text", + "content": " being related to the optimized attribute embeddings " + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "inline_equation", + "content": "(p_{\\mathrm{ID}})" + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "text", + "content": ", and (b) unknowness—the probability of " + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "text", + "content": " not being from the known classes " + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "inline_equation", + "content": "(p_{\\mathrm{OOD}})" + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{unk}} = p_{\\mathrm{ID}} \\cdot p_{\\mathrm{OOD}}" + }, + { + "bbox": [ + 55, + 605, + 296, + 677 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 681, + 295, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 681, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 295, + 696 + ], + "type": "interline_equation", + "content": "p _ {\\mathrm {I D}} = \\max _ {n \\in \\{1, \\dots , N ^ {\\prime} \\}} \\sigma \\left(\\boldsymbol {a} _ {n} ^ {\\prime \\top} \\boldsymbol {v}\\right), \\tag {11}", + "image_path": "73161ee903f4391935c9048a099468c125865a930c0f7c4780e85c1a8647baea.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 99, + 698, + 295, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 698, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 99, + 698, + 295, + 712 + ], + "type": "interline_equation", + "content": "p _ {\\mathrm {O O D}} = 1 - \\max _ {k \\in \\{1, \\dots , K \\}} p \\left(O _ {k} | \\boldsymbol {v}\\right), \\tag {12}", + "image_path": "2d37bc471fc72c37176de0d8107422361eb00d34d0bae8f4648a87940054cdc8.jpg" + } + ] + } + ], + "index": 15 + }, + { + "type": "code", + "bbox": [ + 316, + 88, + 555, + 407 + ], + "blocks": [ + { + "bbox": [ + 315, + 75, + 536, + 87 + ], + "lines": [ + { + "bbox": [ + 315, + 75, + 536, + 87 + ], + "spans": [ + { + "bbox": [ + 315, + 75, + 536, + 87 + ], + "type": "text", + "content": "Algorithm 1: Training Procedure of PASS for OWOD" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "lines": [ + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": "Input: Visual object embeddings " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{V}\\in \\mathbb{R}^{D\\times M}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " with the one-hot labels " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", initial attribute embeddings " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\in \\mathbb{R}^{D\\times N}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", target attribute quantity " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "N^{\\prime}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", selection steps " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", total training epochs " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " \nOutput: Optimal selected attribute embeddings " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", mapping matrix " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", attribute ID scores " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " \n1 Initialize: Selected attribute embeddings " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}} = \\mathbf{A}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", selected attribute quantity " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\hat{N} = N" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", Randomly initialized " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{W}\\in \\mathbb{R}^{N\\times K}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", attribute redundancy rate " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\alpha = (\\frac{N}{N^{\\prime}})^{\\frac{1}{\\eta}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": "; \n2 for " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "(1,2,\\ldots,E)" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " do \n3 /* Partial Optimal Transport */ \n4 Get transport plan " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " and distance " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{POT}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " by solving the POT problem between " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " using Eq. (6) and " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": "; \n5 Compute attribute ID scores as " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "s = \\frac{\\hat{N}}{\\alpha}\\mathbf{T}^\\top\\mathbf{1}_M" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": "; \n6 /* Curriculum Attribute Selection */ \n7 if " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "e\\bmod\\left[\\frac{E}{\\eta+1}\\right]=0" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " then \n8 end \n9 Calculate object class prediction " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "p(O_k|v)" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " in Eq. (8) using " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": "; \n10 Calculate loss " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CE}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " in Eq. (9) using " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "p(O_k|v)" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": "; \n11 Get final loss " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " by combining " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CE}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{POT}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " in Eq. (10); \n12 Update " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "inline_equation", + "content": "\\nabla\\mathcal{L}" + }, + { + "bbox": [ + 316, + 88, + 555, + 407 + ], + "type": "text", + "content": "; \n13 end" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "code_body" + } + ], + "index": 17, + "sub_type": "algorithm" + }, + { + "bbox": [ + 313, + 431, + 457, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 457, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 457, + 443 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 431, + 457, + 443 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 313, + 431, + 457, + 443 + ], + "type": "text", + "content": " is the sigmoid function." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 453, + 390, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 390, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 390, + 467 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 474, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 555, + 510 + ], + "type": "text", + "content": "In this section, we present the experimental evaluations of our proposed PASS. We start with the experimental setup, followed by the evaluation results and analysis." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 517, + 430, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 430, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 430, + 529 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 714 + ], + "type": "text", + "content": "Datasets. As the performance on traditional OWOD benchmarks [22]—which are based on common everyday object datasets like COCO [31]—is reported to be highly saturated [78], we use the Real-World Object Detection Benchmark established in [78] to evaluate the proposed method. This benchmark is designed for the few-shot or low-data setting, recognizing that most real-world applications cannot gather datasets on the scale of traditional benchmarks. Specifically, it includes five challenging real-world datasets as outlined below. (a) Aquatic [10] contains 637 underwater images of 7 different sea animals, providing useful data for marine-related applications. (b) Aerial [28] contains 10,000 aerial photos of 20 different structures such as stadiums and storage containers, supporting satellite imaging and intelligence analysis. (c) Game [10] contains 1575 game screen" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20322" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "shots with 59 different avatars, serving as a benchmark for testing on synthetic data. (d) Medical [10] consists of 182 hand X-rays to identify 12 different bones, offering insights for medical applications such as detecting arthritis, fractures, and structural issues in hands. (e) Surgery [5] is composed of 1829 images of 13 different surgical instruments, captured under neurosurgical microscopes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 162, + 295, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 162, + 295, + 304 + ], + "spans": [ + { + "bbox": [ + 55, + 162, + 295, + 304 + ], + "type": "text", + "content": "Evaluation Protocol. For each dataset, classes were evenly divided into two subsets: one containing the most common classes and the other containing the least common classes. The evaluation follows OWOD protocols and is conducted in two tasks. In Task 1, the model is provided with the most common classes as known (K), while the least common classes remain unknown (U), and the model is expected to detect both known and unknown object classes. In Task 2, in addition to the previously known (PK) classes, the least common classes are introduced as currently known (CK) classes. The model's performance is then evaluated on both PK and CK classes." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 305, + 295, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 305, + 295, + 389 + ], + "spans": [ + { + "bbox": [ + 55, + 305, + 295, + 389 + ], + "type": "text", + "content": "The mean average precision (mAP) is used to evaluate the performance in known classes (K-mAP). To gain deeper insights into the quality of continual learning in OWOD, mAP is further divided to respectively evaluate PK and CK classes (PK-mAP and CK-mAP) as discussed above. Additionally, we also report the mean average precision for unknown objects (U-mAP)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "text", + "content": "Implementation Details. Our approach is based on a frozen CLIP-pretrained OWL-ViT model (B/16 and L/14) [41], which has been fine-tuned for detection on a federated dataset combining Objects365 [52] and Visual Genome [24]. We leverage this frozen model, focusing on the construction of optimal attribute embeddings " + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "text", + "content": " and a mapping matrix " + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "text", + "content": " to enhance the detection performance for both known and unknown object classes. For training, we use " + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "inline_equation", + "content": "\\epsilon = 0.01" + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "text", + "content": " in Eq. (6). For fair comparison with [78], " + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "inline_equation", + "content": "N'" + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "text", + "content": " is determined so that the average number of selected attributes per known class is 25. " + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 55, + 396, + 295, + 587 + ], + "type": "text", + "content": " is default to be 4 for all datasets. Other hyperparameters, including training epochs and learning rate, are searched based on the validation mAP on known classes following [78]. The experiments were carried out on an NVIDIA RTX A6000 GPU. More implementation details are provided in Supplementary Material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 594, + 149, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 149, + 607 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 149, + 607 + ], + "type": "text", + "content": "5.2. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 612, + 295, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 612, + 295, + 672 + ], + "spans": [ + { + "bbox": [ + 55, + 612, + 295, + 672 + ], + "type": "text", + "content": "We ablate our proposed PASS to evaluate the effectiveness of each proposed module. As shown in Tab. 1, the ablation study primarily focuses on the POT distance loss " + }, + { + "bbox": [ + 55, + 612, + 295, + 672 + ], + "type": "inline_equation", + "content": "(d_{\\mathrm{POT}})" + }, + { + "bbox": [ + 55, + 612, + 295, + 672 + ], + "type": "text", + "content": " in Eq. (6), the attribute selection method in Sec. 4.2, and the attribute ID score " + }, + { + "bbox": [ + 55, + 612, + 295, + 672 + ], + "type": "inline_equation", + "content": "(s)" + }, + { + "bbox": [ + 55, + 612, + 295, + 672 + ], + "type": "text", + "content": " reweighting strategy in Eq. (8)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "Effect of POT loss. The minimization of POT distance " + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "inline_equation", + "content": "(d_{\\mathrm{POT}})" + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": " constitutes an important ingredient of our proposed PASS. It explicitly optimizes the attribute embeddings to" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 317, + 72, + 553, + 247 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 553, + 247 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 553, + 247 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 553, + 247 + ], + "type": "table", + "html": "
    Dataset (→)AquaticSurgery
    UKUK
    B/16 Backbone:
    PASS Full (Ours)5.243.414.315.6
    PASS w/o Minimizing dPOT3.222.83.05.5
    PASS w/o Attribute Selection4.834.48.112.6
    PASS w/o s Reweighting4.541.310.611.9
    L/14 Backbone:
    PASS Full (Ours)21.753.916.645.6
    PASS w/o Minimizing dPOT10.118.28.014.1
    PASS w/o Attribute Selection15.534.115.243.6
    PASS w/o s Reweighting18.342.213.440.0
    ", + "image_path": "ce3ad7ec3b012ebca2ff1a0d4310470b5f0c68536ab99b286348144ec7b56024.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 313, + 247, + 555, + 304 + ], + "lines": [ + { + "bbox": [ + 313, + 247, + 555, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 247, + 555, + 304 + ], + "type": "text", + "content": "Table 1. Ablation study of PASS. We report U-mAP (U) and K-mAP (K) on two representative datasets: Aquatic and Surgery, with Task 1 evaluation in the 100-shot regime. Best results are highlighted in each column. More ablation study results can be found in Supplementary Material." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 319, + 556, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 556, + 452 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 556, + 452 + ], + "type": "text", + "content": "align closely with the corresponding visual object embeddings through optimal assignment, effectively reducing the modality gap and improving the generalizability of attributes. This enables the model to detect both known and unknown object classes. As shown in Tab. 1, performance drops significantly without minimizing " + }, + { + "bbox": [ + 313, + 319, + 556, + 452 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{POT}}" + }, + { + "bbox": [ + 313, + 319, + 556, + 452 + ], + "type": "text", + "content": " (setting " + }, + { + "bbox": [ + 313, + 319, + 556, + 452 + ], + "type": "inline_equation", + "content": "\\lambda = 0" + }, + { + "bbox": [ + 313, + 319, + 556, + 452 + ], + "type": "text", + "content": " in Eq. (10)), particularly in the detection of unknown objects. While the cross-entropy loss in Eq. (9) helps maintain performance on known objects, relying solely on the classification loss leads to poor generalization of the learned attributes for the unknown objects." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 456, + 556, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 556, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 556, + 601 + ], + "type": "text", + "content": "Effect of Attribute Selection. Effective attribute selection helps retain a streamlined set of in-distribution attributes that are most relevant to the specific task. While attribute selection has a less pronounced impact on performance compared to " + }, + { + "bbox": [ + 313, + 456, + 556, + 601 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{POT}}" + }, + { + "bbox": [ + 313, + 456, + 556, + 601 + ], + "type": "text", + "content": ", since POT already performs an initial filtering by assigning lower weights to out-of-distribution attributes, it still provides benefits. Specifically, it helps reduce the noise in the attribute pool, which can enhance detection performance. Additionally, keeping a smaller attribute set is more computationally efficient. We provide further analysis on the advantage of the proposed curriculum attribute selection in Supplementary Material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": "Effect of Attribute ID Score Reweighting. In addition to the \"hard\" attribute selection, reweighting object class predictions based on the attribute ID score—obtained from the POT transport plan—provides a complementary \"soft\" filtering strategy. This approach allows the final selected attributes to contribute differently, based on their relevance to the specific task, rather than being treated equally. As demonstrated in Tab. 1, this fine-grained use of selected attributes further enhances the detection performance." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20323" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 553, + 289 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 553, + 289 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 553, + 289 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 553, + 289 + ], + "type": "table", + "html": "
    Dataset (→)AquaticAerialGameMedicalSurgeryOverall
    Task ID (→)Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2Task 1Task 2
    UKPKCKUKPKCKUKPKCKUKPKCKUKPKCKUKPKCK
    B/16 Backbone:
    BASE-ZS+GT†29.845.045.036.71.35.75.71.415.00.40.40.10.50.00.00.15.61.51.40.310.410.510.57.7
    BASE-ZS6.245.045.036.70.95.75.71.415.70.40.40.10.20.00.00.11.41.51.40.34.910.510.57.7
    BASE-ZS+IN26.545.145.136.71.95.75.71.42.40.30.30.00.60.00.00.11.71.41.00.36.610.510.47.7
    BASE-ZS+LLM24.745.145.136.51.45.75.71.415.10.40.40.10.60.00.00.18.91.51.30.310.210.510.57.7
    BASE-FS7.141.141.131.91.210.410.14.016.04.64.83.90.66.16.13.31.311.911.310.95.214.814.710.8
    FOMO [78]3.543.844.140.80.912.012.65.413.33.84.44.12.16.45.511.56.112.712.911.05.215.715.914.6
    PASS (Ours)5.243.443.246.61.914.016.07.021.510.07.79.04.98.46.812.114.315.613.114.79.618.317.417.9
    Δ+1.7-0.4-0.9+5.8+1.0+2.0+3.4+1.6+8.2+6.2+3.3+4.9+2.8+2.0+1.3+0.6+8.2+2.9+0.2+3.7+4.4+2.5+1.5+2.3
    L/14 Backbone:
    BASE-ZS+GT†34.836.036.042.31.07.97.20.812.40.90.80.32.40.20.20.32.40.22.61.310.69.09.49.0
    BASE-ZS0.735.936.042.39.18.27.20.86.80.90.80.30.00.20.20.33.62.92.61.34.19.69.49.0
    BASE-ZS+IN19.635.835.841.82.37.26.90.915.80.90.80.30.90.10.10.23.12.11.91.18.39.29.18.8
    BASE-ZS+LLM24.735.835.842.20.67.67.20.812.50.90.80.21.60.10.10.212.62.62.51.310.49.49.39.0
    BASE-FS2.443.642.942.89.723.721.913.08.210.410.213.41.123.221.724.23.626.025.07.45.025.424.320.2
    FOMO [78]18.250.148.147.16.025.323.716.030.410.79.911.29.421.819.934.612.029.028.98.515.227.426.123.5
    PASS (Ours)21.753.956.658.38.434.236.120.236.024.323.726.313.134.330.032.016.645.647.943.319.138.538.936.0
    Δ+3.5+3.8+8.5+11.2+2.4+8.9+12.4+4.2+5.6+13.6+13.8+15.1+3.7+12.5+10.1-2.6+4.6+16.6+19.0+34.8+3.9+11.1+12.8+12.5
    ", + "image_path": "cd95261e1ca880854968da1fec3d57902cbb935be123adea30208b70d93ca060.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 291, + 555, + 348 + ], + "lines": [ + { + "bbox": [ + 55, + 291, + 555, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 291, + 555, + 348 + ], + "type": "text", + "content": "Table 2. OWOD results on the five real-world object detection datasets. The evaluation on each dataset is divided into two tasks, and we report U-, K-mAP for Task 1, and PK-, CK-mAP for Task 2, which are introduced in Sec. 5.1. BASE-FS, FOMO [78], and our proposed PASS are evaluated in the 100-shot regime, whereas the results of different few-shot regimes are provided in Supplementary Material. †GT baselines leverage ground-truth class names to detect unknown objects, functioning within the open-vocabulary object detection framework and providing an upper bound for text-conditioned (zero-shot) baselines. Best overall results are highlighted in each column." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 365, + 140, + 377 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 140, + 377 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 140, + 377 + ], + "type": "text", + "content": "5.3. Main Results" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 383, + 297, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 383, + 297, + 456 + ], + "spans": [ + { + "bbox": [ + 55, + 383, + 297, + 456 + ], + "type": "text", + "content": "We perform extensive evaluations of our proposed PASS method, comparing it with existing state-of-the-art approaches (SOTAs). Additionally, we present qualitative results that showcase the detection outcomes along with the most relevant attributes used in the process. More experimental results can also be found in Supplementary Material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 462, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 295, + 677 + ], + "type": "text", + "content": "Comparison with State of the Arts. We compare our proposed PASS with FOMO [78] and the strong baselines established therein, by adapting the Open-Vocabulary Object Detection (OVOD) methods [41] that also use foundation models to the OWOD setting. As listed in Tab. 2, BASE-ZS uses a generic \"object\" prompt for unknown objects [39], while BASE-ZS+IN utilizes all ImageNet class names (with the known classes removed) as the unknown classes proposals, and BASE-ZS+LLM employs class names predicted by an LLM (based on the known classes) for detecting potential unknown objects. On the other hand, BASE-ZS+GT uses the ground-truth class names for unknown objects, serving as the upper bound of the OVOD methods by assuming access to all unknown class names. BASE-FS utilizes image exemplars to produce vision-derived object embeddings, which are averaged per class to form class embeddings. Then a general prompt, such as \"a photo of an object\", is applied to help identify unknown objects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "As can be seen in Tab. 2, our proposed PASS consistently outperforms FOMO by a significant margin and achieves performance that is very close to the OVOD upper bound, even" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 366, + 556, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 556, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 556, + 510 + ], + "type": "text", + "content": "when using the B/16 backbone. In particular, our improvement is especially notable in known classes, as reflected in the K-, PK-, and CK-mAP metrics. This can be attributed to the robust attribute selection and optimization capabilities of our proposed PASS framework, which effectively curates a set of accurate and effective attributes to enhance object detection. On the other hand, PASS also demonstrates a significant performance boost in unknown classes as measured by the U-mAP metric. This suggests that the attributes learned by PASS are not only effective for known classes during training but also highly generalizable to unknown objects during evaluation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 556, + 715 + ], + "type": "text", + "content": "Visualizations. For further comprehension of the effectiveness of our proposed PASS in detecting open world objects, we present several qualitative results for each dataset in Fig. 3. When comparing the detection results between FOMO (second row) and our proposed PASS (third row), PASS consistently demonstrates improved detection performance, with results that are more closely aligned with the ground truth (first row). In particular, FOMO sometimes incorrectly classifies known objects as unknown, or vice versa, suggesting that the learned attributes might not be sufficiently accurate to reliably characterize known objects. Furthermore, FOMO occasionally yields significantly fewer detection results in certain domains, such as medical datasets. This suggests that the learned attributes might not adequately capture the full range of potentially useful features necessary for detecting unknown objects. In contrast, PASS delivers" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20324" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 80, + 155, + 175 + ], + "blocks": [ + { + "bbox": [ + 91, + 68, + 124, + 78 + ], + "lines": [ + { + "bbox": [ + 91, + 68, + 124, + 78 + ], + "spans": [ + { + "bbox": [ + 91, + 68, + 124, + 78 + ], + "type": "text", + "content": "Aquatic" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 80, + 155, + 175 + ], + "lines": [ + { + "bbox": [ + 61, + 80, + 155, + 175 + ], + "spans": [ + { + "bbox": [ + 61, + 80, + 155, + 175 + ], + "type": "image", + "image_path": "5f89167e4cbe184b5148b3eedcc12aa9a20e2df14853cbb5759762effc5db146.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 159, + 80, + 253, + 174 + ], + "blocks": [ + { + "bbox": [ + 194, + 68, + 219, + 77 + ], + "lines": [ + { + "bbox": [ + 194, + 68, + 219, + 77 + ], + "spans": [ + { + "bbox": [ + 194, + 68, + 219, + 77 + ], + "type": "text", + "content": "Aerial" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 159, + 80, + 253, + 174 + ], + "lines": [ + { + "bbox": [ + 159, + 80, + 253, + 174 + ], + "spans": [ + { + "bbox": [ + 159, + 80, + 253, + 174 + ], + "type": "image", + "image_path": "688f8bd66bb114ad23e0eb8a8852af2aa9bbf69cece97ad71ad9b66df16a03a0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 257, + 80, + 351, + 174 + ], + "blocks": [ + { + 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Qualitative results on the five real-world datasets. First Row: images in each dataset with ground truth bounding boxes and class names. Second Row: Detection results using FOMO [78]. Third Row: Detection results using our proposed PASS. We use green and yellow boxes to indicate known and unknown objects, respectively. 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"text", + "content": "Material is cutting edge" + } + ] + } + ], + "index": 67 + }, + { + "bbox": [ + 459, + 443, + 529, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 459, + 443, + 529, + 450 + ], + "spans": [ + { + "bbox": [ + 459, + 443, + 529, + 450 + ], + "type": "text", + "content": "Shape is pointed tips" + } + ] + } + ], + "index": 68 + }, + { + "bbox": [ + 459, + 450, + 526, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 459, + 450, + 526, + 457 + ], + "spans": [ + { + "bbox": [ + 459, + 450, + 526, + 457 + ], + "type": "text", + "content": "- Appearance is shiny" + } + ] + } + ], + "index": 69 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 534, + 296, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 296, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 296, + 641 + ], + "type": "text", + "content": "superior detection results due to the more accurate attributes learned during training. These attributes not only provide a strong characterization of known object classes but also demonstrate high generalizability to unknown classes. Furthermore, as illustrated in the bottom two rows of Fig. 3, PASS effectively leverages meaningful attributes to identify both known and unknown objects. For example, it uses the attribute \"shape is dorsal fin shape\" to detect an unknown fish species recognized for its large fin." + } + ] + } + ], + "index": 72 + }, + { + "bbox": [ + 55, + 656, + 128, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 656, + 128, + 668 + ], + "spans": [ + { + "bbox": [ + 55, + 656, + 128, + 668 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 73 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "In this paper, we propose an efficient end-to-end approach to select a compact set of representative attributes tailored to detect open-world objects, including both known and unknown" + } + ] + } + ], + "index": 74 + }, + { + "bbox": [ + 313, + 534, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 653 + ], + "type": "text", + "content": "classes. Specifically, we formulate the attribute selection and optimization process as a Partial Optimal Transport (POT) problem, where the most relevant attributes emerge with the highest transported mass. Additionally, we introduce a curriculum-based attribute selection strategy that gradually refines the attribute subset during training, significantly enhancing training stability and selection effectiveness. We evaluate our approach on challenging real-world datasets, where it achieves superior performance that surpasses current state-of-the-art methods by a large margin." + } + ] + } + ], + "index": 75 + }, + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "type": "text", + "content": "In future work, we aim to expand our method to incorporate hierarchical information within attribute taxonomies. This enhancement will allow for a more fine-grained understanding of the detection process by leveraging attributes at varying levels of granularity." + } + ] + } + ], + "index": 76 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20325" + } + ] + } + ], + "index": 77 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 216 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 216 + ], + "type": "text", + "content": "Acknowledgments. This research is supported by the EDB Space Technology Development Programme under Project S22-19016-STDP, the National Natural Science Foundation of China under Grant 62306251, 62171343, 62176171, U21B2040, the Hong Kong Research Grant Council - Early Career Scheme under Grant 27208022, the HKU Seed Fund for Basic Research, the Fundamental Research Funds for the Central Universities under Grant CJ202303, as well as the Sichuan Science and Technology Planning Project under Grant 24NSFTD0130. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 11444-11453, 2023. 1, 2" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20328" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Detecting Out-of-Distribution Through the Lens of Neural Collapse/65f987d8-3fd0-42f5-b253-2ec1ecfb0a2e_content_list.json b/2025/Detecting Out-of-Distribution Through the Lens of Neural Collapse/65f987d8-3fd0-42f5-b253-2ec1ecfb0a2e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a42cd4bf9f2d534e7a2094e25e47570fe8856b76 --- /dev/null +++ b/2025/Detecting Out-of-Distribution Through the Lens of Neural Collapse/65f987d8-3fd0-42f5-b253-2ec1ecfb0a2e_content_list.json @@ -0,0 +1,1657 @@ +[ + { + "type": "text", + "text": "Detecting Out-of-distribution through the Lens of Neural Collapse", + "text_level": 1, + "bbox": [ + 165, + 130, + 833, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Litian Liu MIT", + "bbox": [ + 348, + 181, + 431, + 214 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "litan1@mit.edu", + "bbox": [ + 321, + 219, + 457, + 232 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yao Qin Santa Barbara", + "bbox": [ + 558, + 181, + 676, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "yaoqin@ucsb.edu", + "bbox": [ + 532, + 219, + 666, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 268, + 326, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Out-of-Distribution (OOD) detection is critical for safe deployment; however, existing detectors often struggle to generalize across datasets of varying scales and model architectures, and some can incur high computational costs in real-world applications. Inspired by the phenomenon of Neural Collapse, we propose a versatile and efficient OOD detection method. Specifically, we re-characterize prior observations that in-distribution (ID) samples form clusters, demonstrating that, with appropriate centering, these clusters align closely with model weight vectors. Additionally, we reveal that ID features tend to expand into a simplex Equiangular Tight Frame, explaining the common observation that ID features are situated farther from the origin than OOD features. Incorporating both insights from Neural Collapse, our OOD detector leverages feature proximity to weight vectors and complements this approach by using feature norms to effectively filter out OOD samples. Extensive experiments on off-the-shelf models demonstrate the robustness of our OOD detector across diverse scenarios, mitigating generalization discrepancies and enhancing overall performance, with inference latency comparable to that of the basic softmax-confidence detector. Code is available at: https://github.com/litanliu/NCI-OOD.", + "bbox": [ + 89, + 301, + 485, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 661, + 220, + 678 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Machine learning models deployed in practice will inevitably encounter samples that deviate from the training distribution. As a classifier cannot make meaningful predictions on test samples that belong to classes unseen during training, it is important to actively detect and handle Out-of-Distribution (OOD) samples. Considering the diverse and oftentimes time-critical application scenarios, an OOD detector should be computationally efficient and can effectively generalize across various scenarios.", + "bbox": [ + 89, + 686, + 482, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we focus on post-hoc methods, which address OOD detection independently of the training process. One line of prior work designs OOD scores over model output space [8, 13, 21, 24, 37, 38] and another line of work focuses on the feature space, where OOD sam", + "bbox": [ + 89, + 824, + 483, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1b7827bd51250602377c9552958b2142fda53ca1b4f85b8888638471de2b2eb4.jpg", + "image_caption": [ + "Figure 1. Centered ID samples tend to cluster near the predicted class weight vectors, which are the last-layer weights of the corresponding class, as indicated by higher average cosine similarity (Equation 5) than OOD. This observation, inspired by the trend of Neural Collapse, emerges early in the training of this CIFAR-10 ResNet-18 classifier, with OOD set SVHN." + ], + "image_footnote": [], + "bbox": [ + 537, + 268, + 880, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "plies are observed to deviate from clusters of ID samples [20, 27, 39, 40]. While existing research has made strides in OOD detection, they still face two major challenges: 1) maintaining detection effectiveness across different scenarios, and 2) ensuring computational efficiency for real-world deployment. For example, both output space and feature space methods suffer from performance discrepancy across different classification tasks, as shown in Table 1 (a). Specifically, strong algorithms on detecting OOD examples for CIFAR-10 [18] perform suboptimally in detecting OOD examples for ImageNet [5], and vice versa. No existing algorithm can simultaneously rank in the top three across two benchmarks, leading to sub-optimal average performance as shown in Table 1 (b). Furthermore, feature-space methods that rely on similarity measures to characterize ID clustering raise efficiency concerns. For example, [39] records training features and evaluates OOD-ness based on the $k$ -th nearest neighbor distance to these features, while [23] demonstrates that dependency on such auxiliary models increases computational costs, posing challenges for time-sensitive applications. This highlights the need to move beyond feature-wise similarity and establish a more structured reference to characterize ID clustering efficiently.", + "bbox": [ + 511, + 553, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15424", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8595f6c1d3f5b9f5ca6213460466e45899c0598e3416bc2d2f7ee36eab2772ab.jpg", + "image_caption": [ + "Figure 2. Framework Illustration. Left: On the penultimate layer, the centered ID clusters reside near their predicted class weight vectors (marked by stars) while OOD samples reside separated, as shown by UMAP. Middle: ID and OOD samples are separated by pScore (Equation 6), which measures feature proximity to weight vectors. Also, ID samples tend to be further from the origin, illustrated with L1 norms. Right: ID samples cluster near a simplex Equiangular Tight Framework, illustrated with black arrows denoting weight vectors. We detect OOD by thresholding on pScore, selecting blue-shaded hypercones centered at weight vectors, with OOD samples outside these areas. We also filter OOD samples characterized by smaller feature norms. Left & Middle present a practical off-the-shelf CIFAR-10 ResNet-18 classifier with OOD set SVHN. Right depicts our scheme on a three-class classifier with 2D penultimate space." + ], + "image_footnote": [], + "bbox": [ + 106, + 69, + 377, + 313 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7f429d91582501a5649a1c6b82c50bbd45271cb5c29f87478478e5e44bfe608d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 388, + 68, + 612, + 309 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a8fca05def74634e008a26cabfccee6e98843b0919f3926b47046085e06c12ae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 66, + 895, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we revisit the well-established observation that penultimate-layer ID features tend to form clusters, while OOD features reside apart [20, 39, 40], and take it a step further by asking:", + "bbox": [ + 88, + 452, + 480, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Where do features of ID samples form clusters?", + "bbox": [ + 129, + 518, + 444, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Leveraging Neural Collapse [32], we first examine the theoretical landscape with models trained beyond zero training error. We first show that, as a deterministic effect of Neural Collapse[32] penultimate-layer features of training samples converge toward the weight vectors of the predicted class—the last-layer weights of the corresponding class—after being centered by training feature mean. Additionally, Neural Collapse demonstrates that training features conform to a simplex Equiangular Tight Frame (ETF) (Equation 1), representing the maximum achievable separation between equiangular vectors. This spatial structure, illustrated in Figure 2 Right, requires features to be sufficiently distant from the origin.", + "bbox": [ + 88, + 537, + 482, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Building on the insights from the theoretical convergence landscape, we propose two hypotheses about the geometric structure of ID clusters and OOD samples in practical models. Specifically, for ID test samples drawn from the same distribution as training samples, we expect a similar trend of clustering behavior toward the weight vectors and the ETF structure. In contrast, OOD samples, which are not part of the training process, lack the alignment with weight vectors and the spatial expansion necessary to form an ETF. Consequently, the model is unlikely to align unseen OOD features with weight vectors or place them far", + "bbox": [ + 88, + 734, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "enough from the origin to exhibit ETF-like behavior. Although complete Neural Collapse requires strict conditions, such as prolonged training, its convergence trend and corresponding geometric patterns of ID features are consistently observed during training across diverse architectures and classification tasks (see Appendix 13 and [11]). Thus, our hypotheses regarding ID clusters and OOD samples are expected to hold without requiring complete Neural Collapse.", + "bbox": [ + 511, + 452, + 903, + 573 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To validate the hypotheses, we trace a model's training stages in Figure 1, where centered ID samples consistently cluster closer to the weight vectors than OOD samples. By epoch 50, such a pattern already enables effective OOD detection for SVHN samples1. This shows that the trend of Neural Collapse emerges early, validating the practical effectiveness of our hypothesis before full collapse in mature models. We reinforce this observation with a UMAP [28] visualization of an off-the-shelf CIFAR-10 classifier with a ResNet-18 backbone, shown in Figure 2 Left. ID features cluster near the predicted class weights (marked by stars), while OOD features remain distant. Additionally, as [53] shows that weight vectors form an ETF, our observations also support our second hypothesis: ID features are driven to structure the ETF, while OOD features lack the incentive to expand in space. This explains the well-established observation [17, 39, 40] that OOD features tend to reside closer to the origin, providing an alternative to the model confidence interpretation in [33].", + "bbox": [ + 511, + 574, + 906, + 861 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Our method (Section 3.3) achieves an AUROC of 94.44, outperforming the 91.27 softmax-confidence baseline (AUROC defined in Section 4).", + "bbox": [ + 511, + 875, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15425", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on our understanding, we design an efficient and versatile OOD detector. We first leverage feature proximity to the weight vectors to characterize ID clustering, effectively incorporating class-specific information and reducing the computational cost. Specifically, we define an angle-based proximity score as the norm of the projection of the weight vector of the predicted class onto the centered sample feature. As shown in Figure 2 Middle, our proximity score can effectively separate ID/OOD. A higher score indicates closer proximity and a lower chance of OOD-ness. Geometrically, thresholding on the score selects hyper-cones centered at the weight vector, as illustrated in Figure 2 Right. Complementing the proximity score's contingency on ID clustering, we also consider feature distance to the origin. Specifically, ID features tend to reside further from the origin as they expand in space to form an ETF, whereas OOD features tend to reside near the origin, as illustrated by Figure 2 Right. Using the L1 norm as an example metric, we observe that ID features can be separated from OOD features, as supported by Figure 2 Middle. Combining both aspects, we propose Neural Collapse Inspired OOD Detector (NCI).", + "bbox": [ + 89, + 90, + 483, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notably, prior methods, e.g., KNN [39], focus on ID clustering, without explicitly incorporating feature distance to the origin. Such approaches fall short in scenarios like ImageNet benchmarks but yield superior performance in CIFAR-10 benchmarks in Table 1a. Conversely, methods such as Energy [24], Energy-based ASH [8], and, Energy-based Scale [47] inherently utilize feature distance to the origin by considering log-sum-exp of logits, yet largely overlook ID clustering. These approaches excel in scenarios like ImageNet, but perform sub-optimally in others, e.g., CIFAR-10. Through the lens of Neural Collapse, we explain, connect, and complete a wide range of prior methods under a holistic view, resulting in reduced latency and generalization discrepancies.", + "bbox": [ + 89, + 424, + 483, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We summarize our main contributions below:", + "bbox": [ + 109, + 638, + 413, + 652 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Understanding and Observation: By analyzing ID clustering through the trend of Neural Collapse, we discover that penultimate-layer features of ID test examples cluster around the weight vectors of the predicted class after being centered by the training feature mean. Additionally, we explain that ID features tend to lie farther from the origin due to Neural Collapse, where they form a simplex Equiangular Tight Frame (ETF) structure. Notably, our findings hold without requiring full Neural Collapse convergence.", + "- OOD Detector: We leverage feature proximity to the weight vectors of predicted classes for OOD detection, integrating class-specific information. Complementary to feature clustering, we propose to detect OOD samples by thresholding the feature distance to the origin.", + "- Experimental Analysis: We evaluate NCI across diverse" + ], + "bbox": [ + 89, + 657, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "classification tasks (CIFAR-10, CIFAR-100, ImageNet) and model architectures (ResNet, DenseNet [15], ViT [9], Swin [26]). Rather than focusing on individual benchmarks, NCI reduces the generalization discrepancies and improves the overall effectiveness. We also show that incorporating weight vectors not only significantly improves upon prior clustering-based methods but also reduces latency to a minimal level, matching the basic softmax-confidence detector.", + "bbox": [ + 524, + 90, + 906, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Problem Statement", + "text_level": 1, + "bbox": [ + 511, + 238, + 700, + 255 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider a data space $\\mathcal{X}$ , a class set $\\mathcal{C}$ , and a classifier $f: \\mathcal{X} \\to \\mathcal{C}$ , which is trained on samples i.i.d. drawn from joint distribution $\\mathbb{P}_{\\mathcal{X}\\mathcal{C}}$ . We denote the marginal distribution of $\\mathbb{P}_{\\mathcal{X}\\mathcal{C}}$ on $\\mathcal{X}$ as $\\mathbb{P}^{in}$ . And samples drawn from $\\mathbb{P}^{in}$ are In-Distribution (ID) samples. In practice, the classifier $f$ may encounter $\\pmb{x} \\in \\mathcal{X}$ yet is not drawn from $\\mathbb{P}^{in}$ . We say such samples are Out-of-Distribution (OOD).", + "bbox": [ + 511, + 263, + 906, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we focus on detecting OOD samples from classes unseen during training, for which the classifiers cannot make meaningful predictions. The OOD detector $D:\\mathcal{X}\\to \\{\\mathrm{ID},\\mathrm{OOD}\\}$ is commonly constructed as:", + "bbox": [ + 511, + 369, + 908, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$D(\\pmb {x}) = \\left\\{ \\begin{array}{ll}\\mathrm{ID} & \\mathrm{if} s(\\pmb {x})\\geq \\tau \\\\ \\mathrm{OOD} & \\mathrm{if} s(\\pmb {x}) < \\tau \\end{array} \\right.$ where $s:\\mathcal{X}\\to \\mathbb{R}$ is a score function of design and $\\tau$ is the threshold. Considering the diverse application scenarios, an ideal OOD detector should be efficient and generalizable. Thus, we leverage insights from Neural Collapse to achieve reduced computational costs and minimize generalization discrepancies.", + "bbox": [ + 511, + 431, + 906, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. OOD Detection through the Lens of Neural Collapse", + "text_level": 1, + "bbox": [ + 511, + 550, + 906, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we re-examine the observation in [20, 39] that ID features tend to form clusters while OOD features deviate from the clusters. We suggest that the clustering phenomenon can reflect the trend of the Neural Collapse [32] in practical models. From our understanding, we develop a post-hoc OOD detector with enhanced efficiency and effectiveness.", + "bbox": [ + 511, + 590, + 905, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Neural Collapse: Convergence Landscape", + "text_level": 1, + "bbox": [ + 511, + 704, + 872, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural Collapse, first observed in [32], occurs on the penultimate layer across canonical classification settings. To formally introduce the concept, we use $h_c^i$ to denote the penultimate layer feature of the $i_{th}$ training sample with ground truth / predicted label $c$ , Neural Collapse is framed in relation to", + "bbox": [ + 511, + 724, + 905, + 815 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- feature global mean, $\\pmb{\\mu}_{G} = \\mathrm{Ave}_{i,c}\\left(\\pmb{h}_{c}^{i}\\right)$ , where $\\mathrm{Ave}(\\cdot)$ is the average operation;", + "- feature class means, $\\pmb{\\mu}_{c} = \\mathrm{Ave}_{i}\\left(\\pmb{h}_{c}^{i}\\right)$ , $\\forall c\\in \\mathcal{C}$", + "- within-class covariance," + ], + "bbox": [ + 511, + 816, + 903, + 876 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {W} = \\operatorname {A v e} _ {i, c} \\left(\\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {c}\\right) \\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {c}\\right) ^ {T}\\right);\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 883, + 849, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15426", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- between-class covariance,", + "bbox": [ + 89, + 92, + 279, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {B} = \\operatorname {A v e} _ {c} \\left(\\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) \\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) ^ {T}\\right);\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 112, + 431, + 131 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- linear classification head, i.e. the last layer of the NN, $\\arg \\max_{c\\in \\mathcal{C}}\\boldsymbol{w}_c^T\\boldsymbol {h} + b_c$ where $\\boldsymbol{w}_{c}$ and $b_{c}$ are parameters corresponding to class $c$", + "bbox": [ + 89, + 137, + 482, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Neural Collapse comprises four inter-related behaviors:", + "bbox": [ + 89, + 181, + 457, + 196 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(NC1) Within-class variability collapse: $\\Sigma_W\\rightarrow 0$", + "(NC2) Convergence to a simplex Equiangular Tight Frame (ETF):" + ], + "bbox": [ + 89, + 196, + 482, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left|\\left|\\left| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\right|\\right| _ {2} - \\left|\\left| \\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G} \\right|\\right| _ {2} \\right|\\rightarrow 0, \\forall c, c ^ {\\prime}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 248, + 393, + 266 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) ^ {T} \\left(\\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G}\\right)}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2} \\| \\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\frac {| \\mathcal {C} |}{| \\mathcal {C} | - 1} \\delta_ {c, c ^ {\\prime}} - \\frac {1}{| \\mathcal {C} | - 1} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 268, + 482, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\delta_{c,c'}$ is the Kronecker delta symbol.", + "bbox": [ + 89, + 308, + 370, + 323 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(NC3) Convergence to self-duality:", + "bbox": [ + 109, + 324, + 356, + 338 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\mathbf {0}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 342, + 385, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(NC4) Simplification to nearest class center:", + "bbox": [ + 109, + 375, + 419, + 388 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\arg \\max _ {c \\in \\mathcal {C}} \\boldsymbol {w} _ {c} ^ {T} \\boldsymbol {h} + b _ {c} \\rightarrow \\arg \\min _ {c \\in \\mathcal {C}} \\| \\boldsymbol {h} - \\boldsymbol {\\mu} _ {c} \\| _ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 395, + 431, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first remark on (NC2) that an ETF achieves the maximum separation possible for globally centered equiangular vectors [32] and extends in space, as visualized in Figure 2 Right. Since training features converge towards an ETF, they need to have sufficient norms to accommodate the spatial arrangement.", + "bbox": [ + 89, + 417, + 483, + 507 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We next build on (NC1) and (NC3) to demonstrate that training features converge towards the weight vectors of the linear classification head, up to a scaling factor.", + "bbox": [ + 89, + 508, + 483, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 3.1. (NC1) and (NC3) imply that for any sample $i$ and its predicted class $c$ , we have", + "bbox": [ + 89, + 560, + 483, + 590 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}\\right)\\rightarrow \\lambda \\boldsymbol {w} _ {c}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 594, + 480, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda = \\frac{\\|\\pmb{\\mu}_c - \\pmb{\\mu}_G\\|_2}{\\|\\pmb{w}_c\\|_2}$ in the Terminal Phase of Training.", + "bbox": [ + 91, + 614, + 480, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proof. Considering that $(\\pmb{h}_c^i - \\pmb{\\mu}_c)(\\pmb{h}_c^i - \\pmb{\\mu}_c)^T$ is positive semi-definite for any $i$ and $c$ . $\\pmb{\\Sigma}_W \\to \\mathbf{0}$ thus implies $(\\pmb{h}_c^i - \\pmb{\\mu}_c)(\\pmb{h}_c^i - \\pmb{\\mu}_c)^T \\to \\mathbf{0}$ and $\\pmb{h}_c^i - \\pmb{\\mu}_c \\to \\mathbf{0}$ , $\\forall i, c$ . With algebraic manipulations, we have", + "bbox": [ + 89, + 652, + 483, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\mathbf {0}, \\forall i, c \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 717, + 482, + 751 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Applying the triangle inequality, we have", + "bbox": [ + 89, + 756, + 366, + 771 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left| \\frac {\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {\\boldsymbol {G}}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {\\boldsymbol {G}} \\| _ {2}} - \\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} \\right| \\leq\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 776, + 279, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left| \\frac {\\mathbf {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\right| + \\left| \\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\right|. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 813, + 491, + 858 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since both terms on the RHS converge to 0, as demonstrated by (3) and (NC3), it follows that the LHS also converges to 0.", + "bbox": [ + 89, + 858, + 483, + 904 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Trend of Neural Collapse & Geometric Structure of the ID Clusters", + "text_level": 1, + "bbox": [ + 511, + 90, + 903, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the complete collapse occurs during the Terminal Phase of Training (TPT) where training error vanishes and the training loss is trained towards zero, it is observed in [11] that the trend of Neural Collapse establishes in the early stages of training. We thus suggest that the clustering behavior of ID features observed in off-the-shelf models reflects a trend of Neural Collapse, corresponding to the within-class variability collapse (NC1). In light of this, we use the landscape of Neural Collapse revealed in Theorem 3.1 and (NC2) to examine the geometry of ID clusters.", + "bbox": [ + 511, + 127, + 903, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following our discussion in Section 1, we we hypothesize and validate with pre-trained models that (1) ID features tend to cluster closer to the weight vectors compared to OOD features; (2) ID clusters tend to reside further from the origin, as necessitated by their spatial structure. Particularly, Neural Collapse highlights the importance of centering for characterizing ID clustering with weight vectors. We thus validate our hypothesis in a CIFAR-10 classifier with ResNet-18 backbone in Figure 1, computing over the ID set (CIFAR-10) and OOD set (SVHN) the average cosine similarity between the centered feature $\\pmb{h}^i - \\pmb{\\mu}_G$ and the weight vector $\\pmb{w}_c$ of the predicted class $c$ , i.e.,", + "bbox": [ + 511, + 279, + 905, + 460 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A v e} _ {i} \\left(\\frac {\\left(\\boldsymbol {h} ^ {i} - \\boldsymbol {\\mu} _ {G}\\right) \\cdot \\boldsymbol {w} _ {c}}{\\| \\boldsymbol {h} ^ {i} - \\boldsymbol {\\mu} _ {G} \\| _ {2} \\| \\boldsymbol {w} _ {c} \\| _ {2}}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 472, + 903, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Out-of-Distribution Detection", + "text_level": 1, + "bbox": [ + 511, + 516, + 777, + 531 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on our understanding, we design an efficient and versatile OOD detector. Specifically, we propose to detect OOD based on feature proximity to the weight vectors of the predicted class. For the proximity metric, we avoid Euclidean-based metrics as they require estimating the scaling factor $\\lambda$ in Equation 2. This estimation tends to be imprecise for general classifiers which may cease training prior to convergence, resulting in suboptimal performance of Euclidean-based metrics shown in Appendix 8. Instead, we design an angle-based metric, adjusted for class-wise difference. Specifically, we propose to quantify the proximity as the norm of projection of the weight vector $w_{c}$ onto the centered feature $h - \\mu_G$ , where $c$ corresponds to the predicted class, i.e.,", + "bbox": [ + 511, + 539, + 906, + 750 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {p S c o r e} = \\cos \\left(\\boldsymbol {w} _ {c}, \\boldsymbol {h} - \\boldsymbol {\\mu} _ {G}\\right) \\| \\boldsymbol {w} _ {c} \\| _ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 762, + 903, + 780 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\cos(\\boldsymbol{w}_c, \\boldsymbol{h} - \\boldsymbol{\\mu}_G) = \\frac{(\\boldsymbol{h} - \\boldsymbol{\\mu}_G) \\cdot \\boldsymbol{w}_c}{\\|\\boldsymbol{h} - \\boldsymbol{\\mu}_G\\|_2 \\| \\boldsymbol{w}_c\\|_2}$ . A higher pScore indicates closer proximity to the weight vector and thus a lower chance of OOD-ness. Geometrically, thresholding on pScore selects infinite hyper-cones centered at the weight vectors, as illustrated in Figure 2 Right. Within the same predicted class, pScore is proportional to the cosine similarity. Across different classes, pScore adapts", + "bbox": [ + 511, + 791, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15427", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to class-wise difference by selecting wider hyper-cones for classes with larger weight vectors, which tend to have larger decision regions. As shown in Appendix 8, our pScore with class-wise adjustment outperforms vanilla cosine similarity. Notably, our pScore incorporates class-specific information into characterizing ID clustering by using the weight vectors of the predicted class. This brings in additional gain in detection effectiveness, as we shall see in Section 4.", + "bbox": [ + 89, + 90, + 480, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While pScore enhances efficiency and effectiveness, its performance is intrinsically contingent on the strength of ID clustering. Such contingency, widely exhibited by clustering-based methods [20, 39, 40], poses challenges on classifiers with less pronounced ID clustering, such as ImageNet ResNet-50 in Section 4.1. To mitigate such discrepancy, we complement pScore by using the distance of ID clusters to the origin. Specifically, we enhance our proximity score by incorporating feature norms to filter out OOD near the origin, as illustrated in Figure 2 Right. Taking L1 norm as an example, we define our detection score as $\\mathrm{pScore} + \\alpha \\| h\\| _1$ , where $\\alpha$ controls the filtering strength and can be selected from a validation set as detailed in Section 4. We discuss the effect of different orders of $p$ -norm in Section 4.3. Thresholding on the detection score, we have Neural Collapse Inspired OOD Detector (NCI): A lower score indicates a higher chance of OOD-ness.", + "bbox": [ + 91, + 227, + 482, + 483 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NCI has $O(P)$ complexity, where $P$ is the penultimate layer dimension. The complexity theoretically ensures computational scalability of NCI on large models. Empirically, NCI maintains inference latency comparable to the vanilla softmax-confidence detector, as shown in Section 4.", + "bbox": [ + 89, + 484, + 482, + 560 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 571, + 220, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we extensively evaluate NCI across classification tasks: CIFAR-10, CIFAR-100 (see App. 12), ImageNet, as well as model architectures: ResNet, DenseNet (see App. 12), ViT, Swin. We compare NCI against thirteen baseline methods. While NCI may not achieve the best performance on individual benchmarks, it mitigates the existing generalization discrepancies and achieves the best overall performance with minimal latency. Following the OpenOOD benchmark [49], we evaluate on six OOD sets for CIFAR-10 and CIFAR-100 classifiers and five for ImageNet classifiers. Performance is evaluated using two widely recognized metrics: the False Positive Rate at $95\\%$ True Positive Rate (FPR95) and the Area Under the Receiver Operating Characteristic Curve (AUROC). Lower FPR95 and higher AUROC values indicate better performance. We also report the per-image inference latency (in milliseconds) evaluated on a Tesla T4 GPU. In our experiments, other than the ablation study in Section 4.3, we use the L1-norm as the filtering term and select the filtering strength $\\alpha$ from $\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}$ based on a", + "bbox": [ + 89, + 598, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "validation set generated per pixel from Gaussian $N(0,1)$ , following [37, 38]. Our method and all baselines are post-hoc methods, while all models used are off-the-shelf and do not require complete Neural Collapse convergence. For detailed setups and additional baselines, please see Appendix 7 and Appendix 11, respectively.", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Mitigating Discrepencies across ID Datasets", + "text_level": 1, + "bbox": [ + 511, + 191, + 883, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first assess NCI and baselines across CIFAR-10 and ImageNet classification tasks. The two tasks provide an ideal test bed for evaluating versatility, as they drastically differ in input resolution, number of classes, and classification accuracy. We use ResNets from OpenOOD [49]: ResNet-18 for CIFAR-10 (95.06% accuracy) and ResNet-50 for ImageNet (76.65% accuracy). Based on validation results, we set the filter strength $\\alpha$ of the $L1$ -norm to $10^{-2}$ for CIFAR-10 experiments and $10^{-3}$ for ImageNet experiments.", + "bbox": [ + 511, + 212, + 903, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets For CIFAR-10 experiments, We follow the OpenOOD split of ID test set and evaluate on the OpenOOD benchmarks, including CIFAR-100 [18], Tiny ImageNet [19], MNIST [6], SVHN [31], Texture [4], and Places365 [50]. For ImageNet experiments, we follow the OpenOOD split of ID test set and evaluate on the OpenOOD benchmarks, including SSB-hard [42], NINCO [2], iNaturalist [41], Texture [4], and OpenImage-O [43].", + "bbox": [ + 511, + 349, + 903, + 469 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines In Table 1a, we compare our method with thirteen baselines. Some baselines focus more on the CIFAR-10 Benchmark while others focus more focused on the ImageNet Benchmark. Therefore, we categorize the baselines, besides the vanilla confidence-based MSP [12], into two groups: the \"CIFAR-10 Strong\" baselines, including ODIN [21], Energy [24], Mahalanobis [20], KNN[39], ViM [43], and fDBD [22]; the \"ImageNet Strong\" baselines, including GradNorm [17], NECO [1], React [38], Dice [37], ASH [8], Scale [47]. See Appendix 9 for details of the baselines.", + "bbox": [ + 511, + 469, + 903, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Performance Table 1a shows that NCI consistently ranks top-three across benchmarks, whereas baselines exhibit greater variability. To assess overall performance, we averaged AUROC across benchmarks, which are of a similar range. Table 1b highlights that NCI improves overall performance compared to strong baselines on individual benchmarks. Further, NCI is as efficient as MSP, as shown in Table $1\\mathrm{b}^2$ , which enhances efficiency compared to strong baselines. This aligns with the analysis in Section 3 and Appendix 9. We highlight the following pairs of comparison:", + "bbox": [ + 511, + 621, + 903, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- NCI v.s. NCI w/o filter: On the CIFAR-10 classifier, strong ID clustering allows our method to rank top-3 without filtering. Conversely, on the ImageNet ResNet50, weaker ID clustering (see Appendix 13) makes norm-based filtering crucial for reducing generalization discrepancy. Complete Neural Collapse occurs on neither model while NCI remains effective.", + "bbox": [ + 511, + 773, + 903, + 878 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2Running time of KNN on ImageNet are copied from Table 4 in [39].", + "bbox": [ + 529, + 886, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15428", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/49b60c61805db77a6296e80e03fc5f5d1f9d0aed6252a021efd0d6a975f8f354.jpg", + "table_caption": [ + "Table 1. NCI reduces discrepancies and improves overall performance on CIFAR-10 and ImageNet benchmarks with minimal latency. CIFAR-10 uses ResNet-18 and ImageNet uses ResNet-50." + ], + "table_footnote": [], + "table_body": "
    Methods43.27 75.388481002439923.64838686167.7080703663.8184824Evaluation under FPR9591.8673.3187.07
    MSP*92.6653.081.3043.2774.3423.6476.0725.8294.1634.9638.1142.4737.2074.4956.8843.3460.8750.1357.14
    CIFAR-10 StrongODIN77.0020.0523.8324.0668.6167.7070.3638.8176.8368.1635.9649.2446.6755.38
    Energy*40.496618.668819.4935.1214.5141.4334.8565.2476.5462.2931.3043.5738.0950.46
    MDS49.04737.244656.9974.8376.07194.165538.1195.19529138684.2336.0590.7743.48
    KNN94.88485.041720.6529.60924.92460.32827.3883.3679584940.8043.2744.2768.82
    ViM62.947915.952930.16160.922156.081481.49501.6580.41556082930.6848.2532.8243.29
    fDBD*59.73633.979457.4356.99236.40202.151145.5477.2855821322.0026.8429.9443.48
    ImageNet StrongGradNorm64.5494.8985.4191.6598.0992.4682.8478.2466.9032.0343.2768.4660.31
    NECO72.6362.4715.5230.1660.1256.0849.5072.3155.0827.0548.2533.4247.22
    ReAct67.4070.0083.6484.5977.8981.6151.1277.5555.8216.7229.6432.5842.46
    DICE83.6435.13768.8984.9062.42147.7075.8577.9651.8633.3747.5847.8334.06
    ASH43.5432.62528.0882.6534.0177.86261.6173.6656.5114.0434.3829.1545.08
    Scale43.60032.64429.0168.6984.38986.136270.7567.725358669.5223.3928.1739.96
    NCI w/o filter*51.9243.5432.6328.9226.5334.0136.2682.1456.4124.1134.3230.9445.58
    87.NCI51.8392.68092.46289.0892688.92393.98836.2773.2979598614.3182.4930.9889.00
    CIFAR-10 Strong82.1895.2484.5886.9485.07Evaluation under AUROC7789.0083.58
    MSP*87.1998838797.6998.4678.8925.8889.8372.0979709588.4188.7084.8684.04
    ODIN82.189835585.2484.7886.9485.0786.2671.7455.4191.1779.9088.2383.58
    Energy*86.3688.8094.3291.7989.4789.2590.0072.0879.7090.6388.7089.0684.04
    MDS61.2994.2699.1793.1677.4052.4769.4143.9279.6461.8279.9460.8082.55
    KNN89.7394.7694.2092.6715.9391.7788.1862.5778.6386.4197.9787.0484.44
    AWI87.7599.8287.4592.5495.10989.49361.8865.5482.6089.5692.9190.5086.05
    SDH*87.186897298.0185.2490.6490.06669.3670.6674826093.7092.0591.1786.03
    ImageNet Strong85.DTorm54.4396513792.24588.565289.540.5093.8989.0884.8283.93
    NGO85.509888386.1298.2388.0635.89320.0374.7982.4292.1990.8087.93
    ReAct85.939882996.6288.1289.3890.35279.3273.0381.7396.3492.0491.8783.80
    DICE77.0179.6790.3790.0281.8974.6782.2770.1376.0192.5492.0488.2683.80
    ASH74.1176.4483.1673.4677.4579.8977.4172.8983.4597.0796.9093.2688.71
    Scale80.5793.1986.0683.4888.8986.0177.4177.3485.3798.0296.7593.9590.28
    * N17w23 filter*87.9391.5090.8092.1790.7490.4766.8180.2092.6791.8790.5184.41
    NCI87.9289.6591.5090.8092.1790.7490.4673.9083.4696.9596.6392.9888.56
    ", + "bbox": [ + 106, + 112, + 897, + 700 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6f827f23819736bdc9d7f8c08e0262ac4e3ccbbda6ceb3cf846e81b89f6868c5.jpg", + "table_caption": [ + "(a) NCI ranks top-three in both benchmarks, while baselines show greater variability. $\\uparrow$ and $\\downarrow$ denotes better performance. Bold marks best, underline 2nd / 3rd. Methods with $*$ are hyperparameter-free. Scores, except for the most recent baselines - fDBD, NECO, ASH, Scale - are from OpenOOD [49]." + ], + "table_footnote": [], + "table_body": "
    PerformanceMSPNECOKNNViMASHScaleNCI (ours)
    CIFAR-10 Latency0.530.701.950.700.530.530.54
    ImageNet Latency6.859.5510.319.557.027.016.84
    Avg AUROC85.6987.9887.3888.1683.0688.1589.51
    ", + "bbox": [ + 163, + 739, + 834, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(b) NCI improves the overall performance while reducing latency compared to strong baselines. AUROC averaged across CIFAR-10 and ImageNet benchmarks in Table 1a, with per image latency reported.", + "bbox": [ + 89, + 825, + 906, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "- NCI v.s. KNN: Compared to KNN, NCI significantly reduces the latency (Table 1b). Notably, without filtering, our", + "bbox": [ + 89, + 858, + 480, + 888 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "hyperparameter-free score outperforms KNN with tuned parameters on most benchmarks (Table 1a, Table 2a &", + "bbox": [ + 526, + 858, + 906, + 888 + ], + "page_idx": 5 + }, + { + "type": "aside_text", + "text": "NCI", + "bbox": [ + 29, + 362, + 58, + 376 + ], + "page_idx": 5 + }, + { + "type": "aside_text", + "text": "NCI", + "bbox": [ + 29, + 659, + 58, + 674 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15429", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "aside_text", + "text": "NC NCI", + "bbox": [ + 936, + 372, + 1000, + 404 + ], + "page_idx": 5 + }, + { + "type": "aside_text", + "text": "NCI", + "bbox": [ + 936, + 664, + 962, + 676 + ], + "page_idx": 5 + }, + { + "type": "aside_text", + "text": "NC", + "bbox": [ + 975, + 683, + 1000, + 696 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cc79a2c826442d5c75edebbad5b503d0c015f731ab9f443cfcad3251946e1bd8.jpg", + "table_caption": [ + "Table 2. NCI reduces discrepancies and improves overall performance on ImageNet benchmarks across ViT B/16 and Swin v2 classifiers. Bold marks best, underline 2nd" + ], + "table_footnote": [], + "table_body": "
    MethodsImageNet OpenOOD Benchmark (ViT B/16)ImageNet OpenOOD Benchmark (Swin v2)
    Near-OODFar-OODAvgNear-OODFar-OODAvg
    SSB-hardNINCOiNaturalistTextureOpenImage-OSSB-hardNINCOiNaturalistTextureOpenImage-O
    Evaluation under FPR95 ↓
    KNN63.4139.716.8443.1218.3034.2890.8883.1676.8860.4367.1475.70
    ViM51.9137.105.6739.2917.5130.3090.3483.8970.9865.9068.6875.96
    ASH48.7845.4211.0042.3720.3335.5893.8093.9387.5897.2791.1492.74
    Scale45.0732.045.4940.5913.1527.2790.7475.7248.7395.1064.5575.97
    NCI w/o filter50.9430.685.9346.6114.9229.8186.7773.1147.9875.3059.3069.67
    NCI46.7333.796.0842.0914.7928.7985.5872.0645.2571.5354.7265.83
    Evaluation under AUROC ↑
    KNN81.4890.0098.6796.2396.2391.4462.5069.7478.3585.1967.1475.88
    ViM87.3992.5698.9890.8096.8293.3160.9972.3083.3679.6182.5275.76
    ASH90.6090.8898.0495.9795.9793.1458.8758.2858.1846.1861.3256.57
    Scale89.6793.2398.9697.2097.2094.0962.4878.9788.8867.0886.1476.71
    NCI w/o filter87.1693.1598.8796.8096.8093.2664.5376.7388.0779.6385.3978.87
    NCI88.8692.8898.7996.8396.8393.6467.5378.9989.6881.4387.4280.97
    ", + "bbox": [ + 114, + 116, + 883, + 354 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b2899ad6922706625e4296fcb24545f29c9fff5bee4dace95a7c9923f24add1b.jpg", + "table_caption": [ + "(a) NCI boosts Swin v2 while maintaining ViT effectiveness compared to baselines, even without filtering." + ], + "table_footnote": [], + "table_body": "
    PerformanceKNNViMASHScaleNCI (ours)
    Avg AUROC83.6684.8474.8685.4087.31
    ", + "bbox": [ + 240, + 381, + 759, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(b) NCI improves the overall performance. AUROC averaged across two architectures in Table 2a.", + "bbox": [ + 235, + 428, + 759, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 9), highlighting the benefit of using class-specific information.", + "bbox": [ + 102, + 463, + 482, + 492 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- NCI v.s. ASH / Scale: Compared to both, NCI delivers competitive performance on ImageNet and significantly improves CIFAR-10, enhancing overall performance (Table 1b). Also, ASH and Scale introduce in a small delay on the ImageNet benchmark due to activation sorting, with larger activation dimensions likely widening the latency gap on larger models.", + "- NCI v.s. NECO: NECO [1] is motivated by Neural Collapse. Like NCI with filtering, NECO uses max-logit and incorporates distance to the origin. However, NECO exclusively analyzes features, requiring expensive matrix multiplication and leading to higher inference latency (Table 1b). Conversely, NCI explores the interplay between features and the classification head, integrating class-specific information to improve both efficiency and effectiveness." + ], + "bbox": [ + 89, + 493, + 482, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Mitigating Discrepancies across Architectures", + "text_level": 1, + "bbox": [ + 89, + 739, + 478, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next, we study two transformer-based models: ViT B/16 [9] and Swin-v2 [26], both finetuned on ImageNet, achieving an accuracy of $81.14\\%$ and $82.94\\%$ respectively. We follow the setup of the OpenOOD ImageNet Benchmark in Section 4.1. Based on validation results, we set the filter strength $\\alpha$ of the $L1$ norm to $10^{-3}$ for both classifiers. In Table 2, we observe strong baselines suffer on Swin v2, echoing the observations in [1]. Conversely, our NCI, even without filtering, improves baseline performance on Swin", + "bbox": [ + 88, + 763, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "v2. Filtering further enhances the performance, leading to improved overall performance (Table 2b).", + "bbox": [ + 511, + 463, + 906, + 492 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further aggregate in Table 2 with experiments on ResNet (Table 1) and DenseNet (Table 9) and report the average AUROC in Table 3. NCI significantly boosts the overall performance.", + "bbox": [ + 511, + 493, + 906, + 555 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation on the Filtering Effect", + "text_level": 1, + "bbox": [ + 511, + 561, + 790, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 4, we assess different orders of $p$ -norm as the filtering term, compared to the $L1$ norm used so far. To ensure a fair comparison, we report the best performance from the filter strengths $\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}$ . The rest of the setup follows the ImageNet benchmarks in Section 4.1. As shown in Table 4, filtering with $L1$ norm achieves the best performance across OOD datasets, aligning with prior observations [17, 33]. Meanwhile, we observe that in rare scenarios, e.g., a ResNet-18 on CIFAR-10, the L1 norm cannot effectively characterize OOD's proximity to the origin, leading to no extra performance gain compared to simply thresholding on pScore. In these cases, our algorithm benefits from its ability to automatically select a low filter strength based on validation results, effectively disregarding the filtering term.", + "bbox": [ + 509, + 583, + 906, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also test the sensitivity of NCI to filtering strength $\\alpha$ in Table 5. As shown on the ImageNet ResNet50 benchmark, performance remains stable for $\\alpha$ values within the same scale. Given this insensitivity, we select hyperparameters from four scales $\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}$ without extensive finetuning in this work.", + "bbox": [ + 511, + 810, + 908, + 901 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "NCI w/o filter 87.16 93.15 98.87 93.26 64.53 76.73 79.63 78.87 88.86 92.88 98.79 93.64 67.53 78.99 81.43 80.97", + "bbox": [ + 140, + 0, + 906, + 31 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15430", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ba68d92a491284bdb1969a0d46c5d5d8287479006b2160c8fc495fb8967ae2fe.jpg", + "table_caption": [ + "Table 3. NCI improves the overall performance, averaged across Table 1a, Table 2a & Table 9." + ], + "table_footnote": [], + "table_body": "
    PerformanceKNNViMASHScaleNCI (ours)
    Avg AUROC86.0685.9681.2486.888.57
    Across All Benchmarks
    ", + "bbox": [ + 217, + 99, + 774, + 146 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/96e18ab07c10a4fad7b3fe4601f8ec46e6764229e2d481b429ad121464af8251.jpg", + "table_caption": [ + "Table 4. Ablation on filtering norm on ImageNet OpenOOD Benchmark with ResNet-50 backbone. AUROC score is reported (higher is better). BoldNCO denotes the best. Filtering with L1 norm outperforms alternative choice of norms across OOD datasets." + ], + "table_footnote": [], + "table_body": "
    FilteringSSB-hardNINCOiNaturalistTextureOpenImage-O
    Linf66.8180.2092.6691.8790.51
    L2 SSBha912NINCOnatural92OpenImage1073
    L173.9083.4696.9596.6392.98
    ", + "bbox": [ + 91, + 229, + 493, + 287 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f7db2f89154090eb11caee38b02221dcf53e42c6bd3c23e2ecc2b01143787b4d.jpg", + "table_caption": [ + "Table 5. Sensitivity of NCI to filtering strength. Average AUROC on ImageNet ResNet-50 Benchmark reported. Performance was stable within the same scale." + ], + "table_footnote": [], + "table_body": "
    Filtering Magnitude αAvg AUROC
    0.6 x 10-388.27
    0.8 x 10-388.55
    1 x10-388.59
    1.2 x 10-388.50
    1.4 x 10-388.23
    ", + "bbox": [ + 86, + 345, + 488, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further apply L1-norm based filtering to KNN to see if this perspective can mitigate the discrepancy of clustering-based methods in general. In Table 63, we report the best performance of KNN from filter strengths $\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}$ . We observe a significant performance gain from adding the filter, which further validates our understanding of ID clustering landscape from Neural Collapse. Note that our method outperforms the standalone $L1$ norm as well as KNN, before and after filtering.", + "bbox": [ + 89, + 470, + 483, + 608 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/30652f748d3c8d14f46ad31456537ae363c8ec905a15af8116c593644cb24eaf.jpg", + "table_caption": [ + "Table 6. Effectiveness of our filtering scheme on KNN. Performance gain validates our understanding of ID clustering landscape. NCI outperforms KNN and standalone $L1$ norm. AUROC reported (higher is better). Bold highlights the best result." + ], + "table_footnote": [], + "table_body": "
    SSB-hardNINCOiNaturalistTextureOpenImage-OAVG
    L168.8068.2890.8688.1678.4778.91
    KNN62.5779.6486.4196.4987.0482.43
    KNN + L164.2981.7692.7697.8590.1786.37
    NCI w/o L166.8180.2092.6791.8790.5184.41
    NCI73.9083.4696.9596.6392.9888.56
    ", + "bbox": [ + 94, + 684, + 493, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Related Work", + "text_level": 1, + "bbox": [ + 89, + 782, + 233, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "OOD Detection Extensive research has focused on OOD detection algorithms. One line of work is post-hoc and builds upon pre-trained models. For example, [13, 21, 22,", + "bbox": [ + 89, + 809, + 483, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "24, 37, 38, 46] design OOD score over the output space of a classifier. Meanwhile, [20] and [39] measure OOD-ness from the perspective of ID clustering in feature space. Our work extends the observation that ID features tend to cluster from the perspective of Neural Collapse. While existing work is more focused on certain classification tasks, our proposed OOD detector is tested to be highly versatile.", + "bbox": [ + 511, + 178, + 906, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Others [34-36, 52] explore the regularization of OOD detection in training. For example, [7, 14] propose OOD-specific architecture whereas [16, 44] design OOD-specific training loss. [40] brings attention to representation learning for OOD detection and proposes an OOD-specific contrastive learning scheme. Our work does not belong to this school of thought and is not restricted to specific training schemes or architecture. Notably, as shown in Appendix 10, our NCI can also benefit from training-time algorithms.", + "bbox": [ + 511, + 284, + 908, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Neural Collapse Neural Collapse was first observed in [32]. During Neural Collapse, the penultimate layer features collapse to class means, the class means and the classifier collapses to a simplex equiangular tight framework, and the classifier simplifies to adopt the nearest class-mean decision rule. Further work has provided theoretical justification for the emergence of Neural Collapse [10, 30, 51, 53]. Application-wise, [53] derives an efficient training algorithm inspired by Neural Collapse. Our concurrent work [1] also leverages Neural Collapse for OOD detection but overlooks class-specific information revealed by Neural Collapse, which is central to our approach.", + "bbox": [ + 511, + 438, + 908, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 633, + 633, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work leverages insights from Neural Collapse to propose a novel OOD detector. Specifically, we study the phenomenon that ID features tend to form clusters whereas OOD features reside far away. Inspired by the trend of Neural Collapse prevalent on practical models, we hypothesize and validate that ID features tend to cluster near weight vectors. We also explain why ID features tend to reside further from the origin and complement our method from this perspective. Experiments show the effectiveness of our method on practical models without requiring the complete convergence of Neural Collapse. Further, our method improves the overall performance with minimal latency across diverse benchmarks. We hope our work can inspire future work to explore the interplay between features and weight vectors for OOD detection and other research problems such as calibration and adversarial robustness.", + "bbox": [ + 511, + 657, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "Note that we report our run of KNN here to ensure a fair evaluation of the filtering effect. Our results are very similar to the OpenOOD results reported in Table 1a, with only marginal differences.", + "bbox": [ + 89, + 862, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15431", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We would like to express our sincere gratitude to Yubing Jian for conducting several experiments that made significant contributions to this work and for his valuable discussions.", + "bbox": [ + 89, + 114, + 483, + 174 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 186, + 187, + 203 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mouin Ben Ammar, Nacim Belkhir, Sebastian Popescu, Antoine Manzanera, and Gianni Franchi. 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Advances in Neural Information Processing Systems, 34:29820-29834, 2021. 2, 8, 3" + ], + "bbox": [ + 514, + 90, + 903, + 710 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15433", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Detecting Out-of-Distribution Through the Lens of Neural Collapse/65f987d8-3fd0-42f5-b253-2ec1ecfb0a2e_model.json b/2025/Detecting Out-of-Distribution Through the Lens of Neural Collapse/65f987d8-3fd0-42f5-b253-2ec1ecfb0a2e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e73e3f8a0d0476ec1c3a56a40cb5dff3af8bdb3a --- /dev/null +++ b/2025/Detecting Out-of-Distribution Through the Lens of Neural Collapse/65f987d8-3fd0-42f5-b253-2ec1ecfb0a2e_model.json @@ -0,0 +1,2321 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.166, + 0.131, + 0.834, + 0.154 + ], + "angle": 0, + "content": "Detecting Out-of-distribution through the Lens of Neural Collapse" + }, + { + "type": "text", + "bbox": [ + 0.349, + 0.182, + 0.432, + 0.215 + ], + "angle": 0, + "content": "Litian Liu MIT" + }, + { + "type": "text", + "bbox": [ + 0.323, + 0.22, + 0.458, + 0.233 + ], + "angle": 0, + "content": "litan1@mit.edu" + }, + { + "type": "text", + "bbox": [ + 0.56, + 0.182, + 0.677, + 0.216 + ], + "angle": 0, + "content": "Yao Qin Santa Barbara" + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.22, + 0.668, + 0.234 + ], + "angle": 0, + "content": "yaoqin@ucsb.edu" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.269, + 0.327, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.302, + 0.486, + 0.649 + ], + "angle": 0, + "content": "Out-of-Distribution (OOD) detection is critical for safe deployment; however, existing detectors often struggle to generalize across datasets of varying scales and model architectures, and some can incur high computational costs in real-world applications. Inspired by the phenomenon of Neural Collapse, we propose a versatile and efficient OOD detection method. Specifically, we re-characterize prior observations that in-distribution (ID) samples form clusters, demonstrating that, with appropriate centering, these clusters align closely with model weight vectors. Additionally, we reveal that ID features tend to expand into a simplex Equiangular Tight Frame, explaining the common observation that ID features are situated farther from the origin than OOD features. Incorporating both insights from Neural Collapse, our OOD detector leverages feature proximity to weight vectors and complements this approach by using feature norms to effectively filter out OOD samples. Extensive experiments on off-the-shelf models demonstrate the robustness of our OOD detector across diverse scenarios, mitigating generalization discrepancies and enhancing overall performance, with inference latency comparable to that of the basic softmax-confidence detector. Code is available at: https://github.com/litanliu/NCI-OOD." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.662, + 0.222, + 0.679 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.688, + 0.483, + 0.824 + ], + "angle": 0, + "content": "Machine learning models deployed in practice will inevitably encounter samples that deviate from the training distribution. As a classifier cannot make meaningful predictions on test samples that belong to classes unseen during training, it is important to actively detect and handle Out-of-Distribution (OOD) samples. Considering the diverse and oftentimes time-critical application scenarios, an OOD detector should be computationally efficient and can effectively generalize across various scenarios." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.901 + ], + "angle": 0, + "content": "In this work, we focus on post-hoc methods, which address OOD detection independently of the training process. One line of prior work designs OOD scores over model output space [8, 13, 21, 24, 37, 38] and another line of work focuses on the feature space, where OOD sam" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.27, + 0.882, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.446, + 0.908, + 0.53 + ], + "angle": 0, + "content": "Figure 1. Centered ID samples tend to cluster near the predicted class weight vectors, which are the last-layer weights of the corresponding class, as indicated by higher average cosine similarity (Equation 5) than OOD. This observation, inspired by the trend of Neural Collapse, emerges early in the training of this CIFAR-10 ResNet-18 classifier, with OOD set SVHN." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.909, + 0.903 + ], + "angle": 0, + "content": "plies are observed to deviate from clusters of ID samples [20, 27, 39, 40]. While existing research has made strides in OOD detection, they still face two major challenges: 1) maintaining detection effectiveness across different scenarios, and 2) ensuring computational efficiency for real-world deployment. For example, both output space and feature space methods suffer from performance discrepancy across different classification tasks, as shown in Table 1 (a). Specifically, strong algorithms on detecting OOD examples for CIFAR-10 [18] perform suboptimally in detecting OOD examples for ImageNet [5], and vice versa. No existing algorithm can simultaneously rank in the top three across two benchmarks, leading to sub-optimal average performance as shown in Table 1 (b). Furthermore, feature-space methods that rely on similarity measures to characterize ID clustering raise efficiency concerns. For example, [39] records training features and evaluates OOD-ness based on the \\( k \\)-th nearest neighbor distance to these features, while [23] demonstrates that dependency on such auxiliary models increases computational costs, posing challenges for time-sensitive applications. This highlights the need to move beyond feature-wise similarity and establish a more structured reference to characterize ID clustering efficiently." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15424" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.07, + 0.379, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.389, + 0.069, + 0.614, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.068, + 0.897, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.328, + 0.908, + 0.427 + ], + "angle": 0, + "content": "Figure 2. Framework Illustration. Left: On the penultimate layer, the centered ID clusters reside near their predicted class weight vectors (marked by stars) while OOD samples reside separated, as shown by UMAP. Middle: ID and OOD samples are separated by pScore (Equation 6), which measures feature proximity to weight vectors. Also, ID samples tend to be further from the origin, illustrated with L1 norms. Right: ID samples cluster near a simplex Equiangular Tight Framework, illustrated with black arrows denoting weight vectors. We detect OOD by thresholding on pScore, selecting blue-shaded hypercones centered at weight vectors, with OOD samples outside these areas. We also filter OOD samples characterized by smaller feature norms. Left & Middle present a practical off-the-shelf CIFAR-10 ResNet-18 classifier with OOD set SVHN. Right depicts our scheme on a three-class classifier with 2D penultimate space." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.453, + 0.482, + 0.514 + ], + "angle": 0, + "content": "To this end, we revisit the well-established observation that penultimate-layer ID features tend to form clusters, while OOD features reside apart [20, 39, 40], and take it a step further by asking:" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.519, + 0.445, + 0.533 + ], + "angle": 0, + "content": "Where do features of ID samples form clusters?" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.539, + 0.483, + 0.734 + ], + "angle": 0, + "content": "Leveraging Neural Collapse [32], we first examine the theoretical landscape with models trained beyond zero training error. We first show that, as a deterministic effect of Neural Collapse[32] penultimate-layer features of training samples converge toward the weight vectors of the predicted class—the last-layer weights of the corresponding class—after being centered by training feature mean. Additionally, Neural Collapse demonstrates that training features conform to a simplex Equiangular Tight Frame (ETF) (Equation 1), representing the maximum achievable separation between equiangular vectors. This spatial structure, illustrated in Figure 2 Right, requires features to be sufficiently distant from the origin." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.735, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Building on the insights from the theoretical convergence landscape, we propose two hypotheses about the geometric structure of ID clusters and OOD samples in practical models. Specifically, for ID test samples drawn from the same distribution as training samples, we expect a similar trend of clustering behavior toward the weight vectors and the ETF structure. In contrast, OOD samples, which are not part of the training process, lack the alignment with weight vectors and the spatial expansion necessary to form an ETF. Consequently, the model is unlikely to align unseen OOD features with weight vectors or place them far" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.453, + 0.905, + 0.574 + ], + "angle": 0, + "content": "enough from the origin to exhibit ETF-like behavior. Although complete Neural Collapse requires strict conditions, such as prolonged training, its convergence trend and corresponding geometric patterns of ID features are consistently observed during training across diverse architectures and classification tasks (see Appendix 13 and [11]). Thus, our hypotheses regarding ID clusters and OOD samples are expected to hold without requiring complete Neural Collapse." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.575, + 0.907, + 0.862 + ], + "angle": 0, + "content": "To validate the hypotheses, we trace a model's training stages in Figure 1, where centered ID samples consistently cluster closer to the weight vectors than OOD samples. By epoch 50, such a pattern already enables effective OOD detection for SVHN samples1. This shows that the trend of Neural Collapse emerges early, validating the practical effectiveness of our hypothesis before full collapse in mature models. We reinforce this observation with a UMAP [28] visualization of an off-the-shelf CIFAR-10 classifier with a ResNet-18 backbone, shown in Figure 2 Left. ID features cluster near the predicted class weights (marked by stars), while OOD features remain distant. Additionally, as [53] shows that weight vectors form an ETF, our observations also support our second hypothesis: ID features are driven to structure the ETF, while OOD features lack the incentive to expand in space. This explains the well-established observation [17, 39, 40] that OOD features tend to reside closer to the origin, providing an alternative to the model confidence interpretation in [33]." + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.905, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)Our method (Section 3.3) achieves an AUROC of 94.44, outperforming the 91.27 softmax-confidence baseline (AUROC defined in Section 4)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15425" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.424 + ], + "angle": 0, + "content": "Based on our understanding, we design an efficient and versatile OOD detector. We first leverage feature proximity to the weight vectors to characterize ID clustering, effectively incorporating class-specific information and reducing the computational cost. Specifically, we define an angle-based proximity score as the norm of the projection of the weight vector of the predicted class onto the centered sample feature. As shown in Figure 2 Middle, our proximity score can effectively separate ID/OOD. A higher score indicates closer proximity and a lower chance of OOD-ness. Geometrically, thresholding on the score selects hyper-cones centered at the weight vector, as illustrated in Figure 2 Right. Complementing the proximity score's contingency on ID clustering, we also consider feature distance to the origin. Specifically, ID features tend to reside further from the origin as they expand in space to form an ETF, whereas OOD features tend to reside near the origin, as illustrated by Figure 2 Right. Using the L1 norm as an example metric, we observe that ID features can be separated from OOD features, as supported by Figure 2 Middle. Combining both aspects, we propose Neural Collapse Inspired OOD Detector (NCI)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.425, + 0.484, + 0.637 + ], + "angle": 0, + "content": "Notably, prior methods, e.g., KNN [39], focus on ID clustering, without explicitly incorporating feature distance to the origin. Such approaches fall short in scenarios like ImageNet benchmarks but yield superior performance in CIFAR-10 benchmarks in Table 1a. Conversely, methods such as Energy [24], Energy-based ASH [8], and, Energy-based Scale [47] inherently utilize feature distance to the origin by considering log-sum-exp of logits, yet largely overlook ID clustering. These approaches excel in scenarios like ImageNet, but perform sub-optimally in others, e.g., CIFAR-10. Through the lens of Neural Collapse, we explain, connect, and complete a wide range of prior methods under a holistic view, resulting in reduced latency and generalization discrepancies." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.639, + 0.414, + 0.653 + ], + "angle": 0, + "content": "We summarize our main contributions below:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.659, + 0.483, + 0.81 + ], + "angle": 0, + "content": "- Understanding and Observation: By analyzing ID clustering through the trend of Neural Collapse, we discover that penultimate-layer features of ID test examples cluster around the weight vectors of the predicted class after being centered by the training feature mean. Additionally, we explain that ID features tend to lie farther from the origin due to Neural Collapse, where they form a simplex Equiangular Tight Frame (ETF) structure. Notably, our findings hold without requiring full Neural Collapse convergence." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.811, + 0.483, + 0.886 + ], + "angle": 0, + "content": "- OOD Detector: We leverage feature proximity to the weight vectors of predicted classes for OOD detection, integrating class-specific information. Complementary to feature clustering, we propose to detect OOD samples by thresholding the feature distance to the origin." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- Experimental Analysis: We evaluate NCI across diverse" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.659, + 0.483, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.092, + 0.907, + 0.228 + ], + "angle": 0, + "content": "classification tasks (CIFAR-10, CIFAR-100, ImageNet) and model architectures (ResNet, DenseNet [15], ViT [9], Swin [26]). Rather than focusing on individual benchmarks, NCI reduces the generalization discrepancies and improves the overall effectiveness. We also show that incorporating weight vectors not only significantly improves upon prior clustering-based methods but also reduces latency to a minimal level, matching the basic softmax-confidence detector." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.239, + 0.702, + 0.256 + ], + "angle": 0, + "content": "2. Problem Statement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.265, + 0.907, + 0.37 + ], + "angle": 0, + "content": "We consider a data space \\(\\mathcal{X}\\), a class set \\(\\mathcal{C}\\), and a classifier \\(f: \\mathcal{X} \\to \\mathcal{C}\\), which is trained on samples i.i.d. drawn from joint distribution \\(\\mathbb{P}_{\\mathcal{X}\\mathcal{C}}\\). We denote the marginal distribution of \\(\\mathbb{P}_{\\mathcal{X}\\mathcal{C}}\\) on \\(\\mathcal{X}\\) as \\(\\mathbb{P}^{in}\\). And samples drawn from \\(\\mathbb{P}^{in}\\) are In-Distribution (ID) samples. In practice, the classifier \\(f\\) may encounter \\(\\pmb{x} \\in \\mathcal{X}\\) yet is not drawn from \\(\\mathbb{P}^{in}\\). We say such samples are Out-of-Distribution (OOD)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.371, + 0.909, + 0.432 + ], + "angle": 0, + "content": "In this work, we focus on detecting OOD samples from classes unseen during training, for which the classifiers cannot make meaningful predictions. The OOD detector \\(D:\\mathcal{X}\\to \\{\\mathrm{ID},\\mathrm{OOD}\\}\\) is commonly constructed as:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.432, + 0.907, + 0.545 + ], + "angle": 0, + "content": "\\(D(\\pmb {x}) = \\left\\{ \\begin{array}{ll}\\mathrm{ID} & \\mathrm{if} s(\\pmb {x})\\geq \\tau \\\\ \\mathrm{OOD} & \\mathrm{if} s(\\pmb {x}) < \\tau \\end{array} \\right.\\) where \\(s:\\mathcal{X}\\to \\mathbb{R}\\) is a score function of design and \\(\\tau\\) is the threshold. Considering the diverse application scenarios, an ideal OOD detector should be efficient and generalizable. Thus, we leverage insights from Neural Collapse to achieve reduced computational costs and minimize generalization discrepancies." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.551, + 0.907, + 0.587 + ], + "angle": 0, + "content": "3. OOD Detection through the Lens of Neural Collapse" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.591, + 0.906, + 0.697 + ], + "angle": 0, + "content": "In this section, we re-examine the observation in [20, 39] that ID features tend to form clusters while OOD features deviate from the clusters. We suggest that the clustering phenomenon can reflect the trend of the Neural Collapse [32] in practical models. From our understanding, we develop a post-hoc OOD detector with enhanced efficiency and effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.705, + 0.874, + 0.721 + ], + "angle": 0, + "content": "3.1. Neural Collapse: Convergence Landscape" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.726, + 0.906, + 0.816 + ], + "angle": 0, + "content": "Neural Collapse, first observed in [32], occurs on the penultimate layer across canonical classification settings. To formally introduce the concept, we use \\( h_c^i \\) to denote the penultimate layer feature of the \\( i_{th} \\) training sample with ground truth / predicted label \\( c \\), Neural Collapse is framed in relation to" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.817, + 0.905, + 0.847 + ], + "angle": 0, + "content": "- feature global mean, \\(\\pmb{\\mu}_{G} = \\mathrm{Ave}_{i,c}\\left(\\pmb{h}_{c}^{i}\\right)\\), where \\(\\mathrm{Ave}(\\cdot)\\) is the average operation;" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.847, + 0.841, + 0.863 + ], + "angle": 0, + "content": "- feature class means, \\(\\pmb{\\mu}_{c} = \\mathrm{Ave}_{i}\\left(\\pmb{h}_{c}^{i}\\right)\\), \\(\\forall c\\in \\mathcal{C}\\)" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.863, + 0.691, + 0.877 + ], + "angle": 0, + "content": "- within-class covariance," + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.817, + 0.905, + 0.877 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.884, + 0.851, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {W} = \\operatorname {A v e} _ {i, c} \\left(\\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {c}\\right) \\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {c}\\right) ^ {T}\\right);\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15426" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.093, + 0.28, + 0.106 + ], + "angle": 0, + "content": "- between-class covariance," + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.113, + 0.432, + 0.132 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {B} = \\operatorname {A v e} _ {c} \\left(\\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) \\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) ^ {T}\\right);\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.138, + 0.483, + 0.183 + ], + "angle": 0, + "content": "- linear classification head, i.e. the last layer of the NN, \\(\\arg \\max_{c\\in \\mathcal{C}}\\boldsymbol{w}_c^T\\boldsymbol {h} + b_c\\) where \\(\\boldsymbol{w}_{c}\\) and \\(b_{c}\\) are parameters corresponding to class \\(c\\)" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.183, + 0.458, + 0.197 + ], + "angle": 0, + "content": "Neural Collapse comprises four inter-related behaviors:" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.198, + 0.464, + 0.214 + ], + "angle": 0, + "content": "(NC1) Within-class variability collapse: \\(\\Sigma_W\\rightarrow 0\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.214, + 0.483, + 0.243 + ], + "angle": 0, + "content": "(NC2) Convergence to a simplex Equiangular Tight Frame (ETF):" + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.198, + 0.483, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.249, + 0.394, + 0.267 + ], + "angle": 0, + "content": "\\[\n\\left|\\left|\\left| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\right|\\right| _ {2} - \\left|\\left| \\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G} \\right|\\right| _ {2} \\right|\\rightarrow 0, \\forall c, c ^ {\\prime}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.269, + 0.483, + 0.304 + ], + "angle": 0, + "content": "\\[\n\\frac {\\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) ^ {T} \\left(\\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G}\\right)}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2} \\| \\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\frac {| \\mathcal {C} |}{| \\mathcal {C} | - 1} \\delta_ {c, c ^ {\\prime}} - \\frac {1}{| \\mathcal {C} | - 1} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.309, + 0.371, + 0.324 + ], + "angle": 0, + "content": "where \\(\\delta_{c,c'}\\) is the Kronecker delta symbol." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.325, + 0.357, + 0.339 + ], + "angle": 0, + "content": "(NC3) Convergence to self-duality:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.343, + 0.386, + 0.373 + ], + "angle": 0, + "content": "\\[\n\\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\mathbf {0}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.375, + 0.421, + 0.39 + ], + "angle": 0, + "content": "(NC4) Simplification to nearest class center:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.396, + 0.432, + 0.419 + ], + "angle": 0, + "content": "\\[\n\\arg \\max _ {c \\in \\mathcal {C}} \\boldsymbol {w} _ {c} ^ {T} \\boldsymbol {h} + b _ {c} \\rightarrow \\arg \\min _ {c \\in \\mathcal {C}} \\| \\boldsymbol {h} - \\boldsymbol {\\mu} _ {c} \\| _ {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.419, + 0.484, + 0.508 + ], + "angle": 0, + "content": "We first remark on (NC2) that an ETF achieves the maximum separation possible for globally centered equiangular vectors [32] and extends in space, as visualized in Figure 2 Right. Since training features converge towards an ETF, they need to have sufficient norms to accommodate the spatial arrangement." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.509, + 0.484, + 0.556 + ], + "angle": 0, + "content": "We next build on (NC1) and (NC3) to demonstrate that training features converge towards the weight vectors of the linear classification head, up to a scaling factor." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.561, + 0.484, + 0.592 + ], + "angle": 0, + "content": "Theorem 3.1. (NC1) and (NC3) imply that for any sample \\(i\\) and its predicted class \\(c\\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.595, + 0.482, + 0.612 + ], + "angle": 0, + "content": "\\[\n\\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}\\right)\\rightarrow \\lambda \\boldsymbol {w} _ {c}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.616, + 0.482, + 0.649 + ], + "angle": 0, + "content": "where \\(\\lambda = \\frac{\\|\\pmb{\\mu}_c - \\pmb{\\mu}_G\\|_2}{\\|\\pmb{w}_c\\|_2}\\) in the Terminal Phase of Training." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.654, + 0.484, + 0.716 + ], + "angle": 0, + "content": "Proof. Considering that \\((\\pmb{h}_c^i - \\pmb{\\mu}_c)(\\pmb{h}_c^i - \\pmb{\\mu}_c)^T\\) is positive semi-definite for any \\(i\\) and \\(c\\). \\(\\pmb{\\Sigma}_W \\to \\mathbf{0}\\) thus implies \\((\\pmb{h}_c^i - \\pmb{\\mu}_c)(\\pmb{h}_c^i - \\pmb{\\mu}_c)^T \\to \\mathbf{0}\\) and \\(\\pmb{h}_c^i - \\pmb{\\mu}_c \\to \\mathbf{0}\\), \\(\\forall i, c\\). With algebraic manipulations, we have" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.718, + 0.483, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\frac {\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\mathbf {0}, \\forall i, c \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.757, + 0.367, + 0.772 + ], + "angle": 0, + "content": "Applying the triangle inequality, we have" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.777, + 0.28, + 0.812 + ], + "angle": 0, + "content": "\\[\n\\left| \\frac {\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {\\boldsymbol {G}}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {\\boldsymbol {G}} \\| _ {2}} - \\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} \\right| \\leq\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.814, + 0.492, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\left| \\frac {\\mathbf {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\right| + \\left| \\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\right|. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.859, + 0.484, + 0.905 + ], + "angle": 0, + "content": "Since both terms on the RHS converge to 0, as demonstrated by (3) and (NC3), it follows that the LHS also converges to 0." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.091, + 0.905, + 0.121 + ], + "angle": 0, + "content": "3.2. Trend of Neural Collapse & Geometric Structure of the ID Clusters" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.128, + 0.905, + 0.278 + ], + "angle": 0, + "content": "While the complete collapse occurs during the Terminal Phase of Training (TPT) where training error vanishes and the training loss is trained towards zero, it is observed in [11] that the trend of Neural Collapse establishes in the early stages of training. We thus suggest that the clustering behavior of ID features observed in off-the-shelf models reflects a trend of Neural Collapse, corresponding to the within-class variability collapse (NC1). In light of this, we use the landscape of Neural Collapse revealed in Theorem 3.1 and (NC2) to examine the geometry of ID clusters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.28, + 0.906, + 0.462 + ], + "angle": 0, + "content": "Following our discussion in Section 1, we we hypothesize and validate with pre-trained models that (1) ID features tend to cluster closer to the weight vectors compared to OOD features; (2) ID clusters tend to reside further from the origin, as necessitated by their spatial structure. Particularly, Neural Collapse highlights the importance of centering for characterizing ID clustering with weight vectors. We thus validate our hypothesis in a CIFAR-10 classifier with ResNet-18 backbone in Figure 1, computing over the ID set (CIFAR-10) and OOD set (SVHN) the average cosine similarity between the centered feature \\( \\pmb{h}^i - \\pmb{\\mu}_G \\) and the weight vector \\( \\pmb{w}_c \\) of the predicted class \\( c \\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.473, + 0.905, + 0.507 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A v e} _ {i} \\left(\\frac {\\left(\\boldsymbol {h} ^ {i} - \\boldsymbol {\\mu} _ {G}\\right) \\cdot \\boldsymbol {w} _ {c}}{\\| \\boldsymbol {h} ^ {i} - \\boldsymbol {\\mu} _ {G} \\| _ {2} \\| \\boldsymbol {w} _ {c} \\| _ {2}}\\right) \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.517, + 0.779, + 0.532 + ], + "angle": 0, + "content": "3.3. Out-of-Distribution Detection" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.54, + 0.907, + 0.751 + ], + "angle": 0, + "content": "Based on our understanding, we design an efficient and versatile OOD detector. Specifically, we propose to detect OOD based on feature proximity to the weight vectors of the predicted class. For the proximity metric, we avoid Euclidean-based metrics as they require estimating the scaling factor \\(\\lambda\\) in Equation 2. This estimation tends to be imprecise for general classifiers which may cease training prior to convergence, resulting in suboptimal performance of Euclidean-based metrics shown in Appendix 8. Instead, we design an angle-based metric, adjusted for class-wise difference. Specifically, we propose to quantify the proximity as the norm of projection of the weight vector \\(w_{c}\\) onto the centered feature \\(h - \\mu_G\\), where \\(c\\) corresponds to the predicted class, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.763, + 0.905, + 0.781 + ], + "angle": 0, + "content": "\\[\n\\mathrm {p S c o r e} = \\cos \\left(\\boldsymbol {w} _ {c}, \\boldsymbol {h} - \\boldsymbol {\\mu} _ {G}\\right) \\| \\boldsymbol {w} _ {c} \\| _ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.792, + 0.906, + 0.902 + ], + "angle": 0, + "content": "where \\( \\cos(\\boldsymbol{w}_c, \\boldsymbol{h} - \\boldsymbol{\\mu}_G) = \\frac{(\\boldsymbol{h} - \\boldsymbol{\\mu}_G) \\cdot \\boldsymbol{w}_c}{\\|\\boldsymbol{h} - \\boldsymbol{\\mu}_G\\|_2 \\| \\boldsymbol{w}_c\\|_2} \\). A higher pScore indicates closer proximity to the weight vector and thus a lower chance of OOD-ness. Geometrically, thresholding on pScore selects infinite hyper-cones centered at the weight vectors, as illustrated in Figure 2 Right. Within the same predicted class, pScore is proportional to the cosine similarity. Across different classes, pScore adapts" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15427" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.226 + ], + "angle": 0, + "content": "to class-wise difference by selecting wider hyper-cones for classes with larger weight vectors, which tend to have larger decision regions. As shown in Appendix 8, our pScore with class-wise adjustment outperforms vanilla cosine similarity. Notably, our pScore incorporates class-specific information into characterizing ID clustering by using the weight vectors of the predicted class. This brings in additional gain in detection effectiveness, as we shall see in Section 4." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.228, + 0.483, + 0.484 + ], + "angle": 0, + "content": "While pScore enhances efficiency and effectiveness, its performance is intrinsically contingent on the strength of ID clustering. Such contingency, widely exhibited by clustering-based methods [20, 39, 40], poses challenges on classifiers with less pronounced ID clustering, such as ImageNet ResNet-50 in Section 4.1. To mitigate such discrepancy, we complement pScore by using the distance of ID clusters to the origin. Specifically, we enhance our proximity score by incorporating feature norms to filter out OOD near the origin, as illustrated in Figure 2 Right. Taking L1 norm as an example, we define our detection score as \\( \\mathrm{pScore} + \\alpha \\| h\\| _1 \\), where \\( \\alpha \\) controls the filtering strength and can be selected from a validation set as detailed in Section 4. We discuss the effect of different orders of \\( p \\)-norm in Section 4.3. Thresholding on the detection score, we have Neural Collapse Inspired OOD Detector (NCI): A lower score indicates a higher chance of OOD-ness." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.485, + 0.483, + 0.561 + ], + "angle": 0, + "content": "NCI has \\( O(P) \\) complexity, where \\( P \\) is the penultimate layer dimension. The complexity theoretically ensures computational scalability of NCI on large models. Empirically, NCI maintains inference latency comparable to the vanilla softmax-confidence detector, as shown in Section 4." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.573, + 0.222, + 0.59 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this section, we extensively evaluate NCI across classification tasks: CIFAR-10, CIFAR-100 (see App. 12), ImageNet, as well as model architectures: ResNet, DenseNet (see App. 12), ViT, Swin. We compare NCI against thirteen baseline methods. While NCI may not achieve the best performance on individual benchmarks, it mitigates the existing generalization discrepancies and achieves the best overall performance with minimal latency. Following the OpenOOD benchmark [49], we evaluate on six OOD sets for CIFAR-10 and CIFAR-100 classifiers and five for ImageNet classifiers. Performance is evaluated using two widely recognized metrics: the False Positive Rate at \\(95\\%\\) True Positive Rate (FPR95) and the Area Under the Receiver Operating Characteristic Curve (AUROC). Lower FPR95 and higher AUROC values indicate better performance. We also report the per-image inference latency (in milliseconds) evaluated on a Tesla T4 GPU. In our experiments, other than the ablation study in Section 4.3, we use the L1-norm as the filtering term and select the filtering strength \\(\\alpha\\) from \\(\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}\\) based on a" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.183 + ], + "angle": 0, + "content": "validation set generated per pixel from Gaussian \\(N(0,1)\\), following [37, 38]. Our method and all baselines are post-hoc methods, while all models used are off-the-shelf and do not require complete Neural Collapse convergence. For detailed setups and additional baselines, please see Appendix 7 and Appendix 11, respectively." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.192, + 0.885, + 0.208 + ], + "angle": 0, + "content": "4.1. Mitigating Discrepencies across ID Datasets" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.213, + 0.905, + 0.349 + ], + "angle": 0, + "content": "We first assess NCI and baselines across CIFAR-10 and ImageNet classification tasks. The two tasks provide an ideal test bed for evaluating versatility, as they drastically differ in input resolution, number of classes, and classification accuracy. We use ResNets from OpenOOD [49]: ResNet-18 for CIFAR-10 (95.06% accuracy) and ResNet-50 for ImageNet (76.65% accuracy). Based on validation results, we set the filter strength \\(\\alpha\\) of the \\(L1\\)-norm to \\(10^{-2}\\) for CIFAR-10 experiments and \\(10^{-3}\\) for ImageNet experiments." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.35, + 0.905, + 0.47 + ], + "angle": 0, + "content": "Datasets For CIFAR-10 experiments, We follow the OpenOOD split of ID test set and evaluate on the OpenOOD benchmarks, including CIFAR-100 [18], Tiny ImageNet [19], MNIST [6], SVHN [31], Texture [4], and Places365 [50]. For ImageNet experiments, we follow the OpenOOD split of ID test set and evaluate on the OpenOOD benchmarks, including SSB-hard [42], NINCO [2], iNaturalist [41], Texture [4], and OpenImage-O [43]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.905, + 0.621 + ], + "angle": 0, + "content": "Baselines In Table 1a, we compare our method with thirteen baselines. Some baselines focus more on the CIFAR-10 Benchmark while others focus more focused on the ImageNet Benchmark. Therefore, we categorize the baselines, besides the vanilla confidence-based MSP [12], into two groups: the \"CIFAR-10 Strong\" baselines, including ODIN [21], Energy [24], Mahalanobis [20], KNN[39], ViM [43], and fDBD [22]; the \"ImageNet Strong\" baselines, including GradNorm [17], NECO [1], React [38], Dice [37], ASH [8], Scale [47]. See Appendix 9 for details of the baselines." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.622, + 0.905, + 0.772 + ], + "angle": 0, + "content": "Performance Table 1a shows that NCI consistently ranks top-three across benchmarks, whereas baselines exhibit greater variability. To assess overall performance, we averaged AUROC across benchmarks, which are of a similar range. Table 1b highlights that NCI improves overall performance compared to strong baselines on individual benchmarks. Further, NCI is as efficient as MSP, as shown in Table \\(1\\mathrm{b}^2\\) , which enhances efficiency compared to strong baselines. This aligns with the analysis in Section 3 and Appendix 9. We highlight the following pairs of comparison:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.775, + 0.905, + 0.879 + ], + "angle": 0, + "content": "- NCI v.s. NCI w/o filter: On the CIFAR-10 classifier, strong ID clustering allows our method to rank top-3 without filtering. Conversely, on the ImageNet ResNet50, weaker ID clustering (see Appendix 13) makes norm-based filtering crucial for reducing generalization discrepancy. Complete Neural Collapse occurs on neither model while NCI remains effective." + }, + { + "type": "page_footnote", + "bbox": [ + 0.531, + 0.887, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2Running time of KNN on ImageNet are copied from Table 4 in [39]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15428" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.079, + 0.905, + 0.107 + ], + "angle": 0, + "content": "Table 1. NCI reduces discrepancies and improves overall performance on CIFAR-10 and ImageNet benchmarks with minimal latency. CIFAR-10 uses ResNet-18 and ImageNet uses ResNet-50." + }, + { + "type": "aside_text", + "bbox": [ + 0.03, + 0.363, + 0.06, + 0.377 + ], + "angle": 0, + "content": "NCI" + }, + { + "type": "aside_text", + "bbox": [ + 0.03, + 0.66, + 0.06, + 0.675 + ], + "angle": 0, + "content": "NCI" + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.113, + 0.898, + 0.702 + ], + "angle": 0, + "content": "
    Methods43.27 75.388481002439923.64838686167.7080703663.8184824Evaluation under FPR9591.8673.3187.07
    MSP*92.6653.081.3043.2774.3423.6476.0725.8294.1634.9638.1142.4737.2074.4956.8843.3460.8750.1357.14
    CIFAR-10 StrongODIN77.0020.0523.8324.0668.6167.7070.3638.8176.8368.1635.9649.2446.6755.38
    Energy*40.496618.668819.4935.1214.5141.4334.8565.2476.5462.2931.3043.5738.0950.46
    MDS49.04737.244656.9974.8376.07194.165538.1195.19529138684.2336.0590.7743.48
    KNN94.88485.041720.6529.60924.92460.32827.3883.3679584940.8043.2744.2768.82
    ViM62.947915.952930.16160.922156.081481.49501.6580.41556082930.6848.2532.8243.29
    fDBD*59.73633.979457.4356.99236.40202.151145.5477.2855821322.0026.8429.9443.48
    ImageNet StrongGradNorm64.5494.8985.4191.6598.0992.4682.8478.2466.9032.0343.2768.4660.31
    NECO72.6362.4715.5230.1660.1256.0849.5072.3155.0827.0548.2533.4247.22
    ReAct67.4070.0083.6484.5977.8981.6151.1277.5555.8216.7229.6432.5842.46
    DICE83.6435.13768.8984.9062.42147.7075.8577.9651.8633.3747.5847.8334.06
    ASH43.5432.62528.0882.6534.0177.86261.6173.6656.5114.0434.3829.1545.08
    Scale43.60032.64429.0168.6984.38986.136270.7567.725358669.5223.3928.1739.96
    NCI w/o filter*51.9243.5432.6328.9226.5334.0136.2682.1456.4124.1134.3230.9445.58
    87.NCI51.8392.68092.46289.0892688.92393.98836.2773.2979598614.3182.4930.9889.00
    CIFAR-10 Strong82.1895.2484.5886.9485.07Evaluation under AUROC7789.0083.58
    MSP*87.1998838797.6998.4678.8925.8889.8372.0979709588.4188.7084.8684.04
    ODIN82.189835585.2484.7886.9485.0786.2671.7455.4191.1779.9088.2383.58
    Energy*86.3688.8094.3291.7989.4789.2590.0072.0879.7090.6388.7089.0684.04
    MDS61.2994.2699.1793.1677.4052.4769.4143.9279.6461.8279.9460.8082.55
    KNN89.7394.7694.2092.6715.9391.7788.1862.5778.6386.4197.9787.0484.44
    AWI87.7599.8287.4592.5495.10989.49361.8865.5482.6089.5692.9190.5086.05
    SDH*87.186897298.0185.2490.6490.06669.3670.6674826093.7092.0591.1786.03
    ImageNet Strong85.DTorm54.4396513792.24588.565289.540.5093.8989.0884.8283.93
    NGO85.509888386.1298.2388.0635.89320.0374.7982.4292.1990.8087.93
    ReAct85.939882996.6288.1289.3890.35279.3273.0381.7396.3492.0491.8783.80
    DICE77.0179.6790.3790.0281.8974.6782.2770.1376.0192.5492.0488.2683.80
    ASH74.1176.4483.1673.4677.4579.8977.4172.8983.4597.0796.9093.2688.71
    Scale80.5793.1986.0683.4888.8986.0177.4177.3485.3798.0296.7593.9590.28
    * N17w23 filter*87.9391.5090.8092.1790.7490.4766.8180.2092.6791.8790.5184.41
    NCI87.9289.6591.5090.8092.1790.7490.4673.9083.4696.9596.6392.9888.56
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.707, + 0.907, + 0.733 + ], + "angle": 0, + "content": "(a) NCI ranks top-three in both benchmarks, while baselines show greater variability. \\(\\uparrow\\) and \\(\\downarrow\\) denotes better performance. Bold marks best, underline 2nd / 3rd. Methods with \\(*\\) are hyperparameter-free. Scores, except for the most recent baselines - fDBD, NECO, ASH, Scale - are from OpenOOD [49]." + }, + { + "type": "table", + "bbox": [ + 0.165, + 0.74, + 0.836, + 0.813 + ], + "angle": 0, + "content": "
    PerformanceMSPNECOKNNViMASHScaleNCI (ours)
    CIFAR-10 Latency0.530.701.950.700.530.530.54
    ImageNet Latency6.859.5510.319.557.027.016.84
    Avg AUROC85.6987.9887.3888.1683.0688.1589.51
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.827, + 0.907, + 0.853 + ], + "angle": 0, + "content": "(b) NCI improves the overall performance while reducing latency compared to strong baselines. AUROC averaged across CIFAR-10 and ImageNet benchmarks in Table 1a, with per image latency reported." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.859, + 0.482, + 0.889 + ], + "angle": 0, + "content": "- NCI v.s. KNN: Compared to KNN, NCI significantly reduces the latency (Table 1b). Notably, without filtering, our" + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.859, + 0.907, + 0.889 + ], + "angle": 0, + "content": "hyperparameter-free score outperforms KNN with tuned parameters on most benchmarks (Table 1a, Table 2a &" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15429" + }, + { + "type": "aside_text", + "bbox": [ + 0.937, + 0.373, + 1.0, + 0.405 + ], + "angle": 0, + "content": "NC NCI" + }, + { + "type": "aside_text", + "bbox": [ + 0.937, + 0.665, + 0.964, + 0.678 + ], + "angle": 0, + "content": "NCI" + }, + { + "type": "aside_text", + "bbox": [ + 0.976, + 0.684, + 1.0, + 0.697 + ], + "angle": 0, + "content": "NC" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.142, + 0.0, + 0.908, + 0.032 + ], + "angle": 0, + "content": "NCI w/o filter 87.16 93.15 98.87 93.26 64.53 76.73 79.63 78.87 88.86 92.88 98.79 93.64 67.53 78.99 81.43 80.97" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.079, + 0.907, + 0.107 + ], + "angle": 0, + "content": "Table 2. NCI reduces discrepancies and improves overall performance on ImageNet benchmarks across ViT B/16 and Swin v2 classifiers. Bold marks best, underline 2nd" + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.117, + 0.885, + 0.355 + ], + "angle": 0, + "content": "
    MethodsImageNet OpenOOD Benchmark (ViT B/16)ImageNet OpenOOD Benchmark (Swin v2)
    Near-OODFar-OODAvgNear-OODFar-OODAvg
    SSB-hardNINCOiNaturalistTextureOpenImage-OSSB-hardNINCOiNaturalistTextureOpenImage-O
    Evaluation under FPR95 ↓
    KNN63.4139.716.8443.1218.3034.2890.8883.1676.8860.4367.1475.70
    ViM51.9137.105.6739.2917.5130.3090.3483.8970.9865.9068.6875.96
    ASH48.7845.4211.0042.3720.3335.5893.8093.9387.5897.2791.1492.74
    Scale45.0732.045.4940.5913.1527.2790.7475.7248.7395.1064.5575.97
    NCI w/o filter50.9430.685.9346.6114.9229.8186.7773.1147.9875.3059.3069.67
    NCI46.7333.796.0842.0914.7928.7985.5872.0645.2571.5354.7265.83
    Evaluation under AUROC ↑
    KNN81.4890.0098.6796.2396.2391.4462.5069.7478.3585.1967.1475.88
    ViM87.3992.5698.9890.8096.8293.3160.9972.3083.3679.6182.5275.76
    ASH90.6090.8898.0495.9795.9793.1458.8758.2858.1846.1861.3256.57
    Scale89.6793.2398.9697.2097.2094.0962.4878.9788.8867.0886.1476.71
    NCI w/o filter87.1693.1598.8796.8096.8093.2664.5376.7388.0779.6385.3978.87
    NCI88.8692.8898.7996.8396.8393.6467.5378.9989.6881.4387.4280.97
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.219, + 0.362, + 0.778, + 0.375 + ], + "angle": 0, + "content": "(a) NCI boosts Swin v2 while maintaining ViT effectiveness compared to baselines, even without filtering." + }, + { + "type": "table", + "bbox": [ + 0.241, + 0.382, + 0.761, + 0.418 + ], + "angle": 0, + "content": "
    PerformanceKNNViMASHScaleNCI (ours)
    Avg AUROC83.6684.8474.8685.4087.31
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.236, + 0.429, + 0.761, + 0.443 + ], + "angle": 0, + "content": "(b) NCI improves the overall performance. AUROC averaged across two architectures in Table 2a." + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.464, + 0.483, + 0.493 + ], + "angle": 0, + "content": "Table 9), highlighting the benefit of using class-specific information." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.494, + 0.483, + 0.601 + ], + "angle": 0, + "content": "- NCI v.s. ASH / Scale: Compared to both, NCI delivers competitive performance on ImageNet and significantly improves CIFAR-10, enhancing overall performance (Table 1b). Also, ASH and Scale introduce in a small delay on the ImageNet benchmark due to activation sorting, with larger activation dimensions likely widening the latency gap on larger models." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.602, + 0.483, + 0.723 + ], + "angle": 0, + "content": "- NCI v.s. NECO: NECO [1] is motivated by Neural Collapse. Like NCI with filtering, NECO uses max-logit and incorporates distance to the origin. However, NECO exclusively analyzes features, requiring expensive matrix multiplication and leading to higher inference latency (Table 1b). Conversely, NCI explores the interplay between features and the classification head, integrating class-specific information to improve both efficiency and effectiveness." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.494, + 0.483, + 0.723 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.74, + 0.48, + 0.758 + ], + "angle": 0, + "content": "4.2. Mitigating Discrepancies across Architectures" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.765, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Next, we study two transformer-based models: ViT B/16 [9] and Swin-v2 [26], both finetuned on ImageNet, achieving an accuracy of \\(81.14\\%\\) and \\(82.94\\%\\) respectively. We follow the setup of the OpenOOD ImageNet Benchmark in Section 4.1. Based on validation results, we set the filter strength \\(\\alpha\\) of the \\(L1\\) norm to \\(10^{-3}\\) for both classifiers. In Table 2, we observe strong baselines suffer on Swin v2, echoing the observations in [1]. Conversely, our NCI, even without filtering, improves baseline performance on Swin" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.464, + 0.907, + 0.493 + ], + "angle": 0, + "content": "v2. Filtering further enhances the performance, leading to improved overall performance (Table 2b)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.494, + 0.907, + 0.556 + ], + "angle": 0, + "content": "We further aggregate in Table 2 with experiments on ResNet (Table 1) and DenseNet (Table 9) and report the average AUROC in Table 3. NCI significantly boosts the overall performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.562, + 0.792, + 0.579 + ], + "angle": 0, + "content": "4.3. Ablation on the Filtering Effect" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.584, + 0.907, + 0.81 + ], + "angle": 0, + "content": "In Table 4, we assess different orders of \\( p \\)-norm as the filtering term, compared to the \\( L1 \\) norm used so far. To ensure a fair comparison, we report the best performance from the filter strengths \\( \\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\} \\). The rest of the setup follows the ImageNet benchmarks in Section 4.1. As shown in Table 4, filtering with \\( L1 \\) norm achieves the best performance across OOD datasets, aligning with prior observations [17, 33]. Meanwhile, we observe that in rare scenarios, e.g., a ResNet-18 on CIFAR-10, the L1 norm cannot effectively characterize OOD's proximity to the origin, leading to no extra performance gain compared to simply thresholding on pScore. In these cases, our algorithm benefits from its ability to automatically select a low filter strength based on validation results, effectively disregarding the filtering term." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.902 + ], + "angle": 0, + "content": "We also test the sensitivity of NCI to filtering strength \\(\\alpha\\) in Table 5. As shown on the ImageNet ResNet50 benchmark, performance remains stable for \\(\\alpha\\) values within the same scale. Given this insensitivity, we select hyperparameters from four scales \\(\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}\\) without extensive finetuning in this work." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15430" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.214, + 0.079, + 0.784, + 0.094 + ], + "angle": 0, + "content": "Table 3. NCI improves the overall performance, averaged across Table 1a, Table 2a & Table 9." + }, + { + "type": "table", + "bbox": [ + 0.218, + 0.101, + 0.775, + 0.147 + ], + "angle": 0, + "content": "
    PerformanceKNNViMASHScaleNCI (ours)
    Avg AUROC86.0685.9681.2486.888.57
    Across All Benchmarks
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.17, + 0.483, + 0.226 + ], + "angle": 0, + "content": "Table 4. Ablation on filtering norm on ImageNet OpenOOD Benchmark with ResNet-50 backbone. AUROC score is reported (higher is better). BoldNCO denotes the best. Filtering with L1 norm outperforms alternative choice of norms across OOD datasets." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.23, + 0.495, + 0.288 + ], + "angle": 0, + "content": "
    FilteringSSB-hardNINCOiNaturalistTextureOpenImage-O
    Linf66.8180.2092.6691.8790.51
    L2 SSBha912NINCOnatural92OpenImage1073
    L173.9083.4696.9596.6392.98
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.087, + 0.304, + 0.484, + 0.345 + ], + "angle": 0, + "content": "Table 5. Sensitivity of NCI to filtering strength. Average AUROC on ImageNet ResNet-50 Benchmark reported. Performance was stable within the same scale." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.347, + 0.49, + 0.446 + ], + "angle": 0, + "content": "
    Filtering Magnitude αAvg AUROC
    0.6 x 10-388.27
    0.8 x 10-388.55
    1 x10-388.59
    1.2 x 10-388.50
    1.4 x 10-388.23
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.471, + 0.484, + 0.609 + ], + "angle": 0, + "content": "We further apply L1-norm based filtering to KNN to see if this perspective can mitigate the discrepancy of clustering-based methods in general. In Table 63, we report the best performance of KNN from filter strengths \\(\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}\\). We observe a significant performance gain from adding the filter, which further validates our understanding of ID clustering landscape from Neural Collapse. Note that our method outperforms the standalone \\(L1\\) norm as well as KNN, before and after filtering." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.619, + 0.484, + 0.677 + ], + "angle": 0, + "content": "Table 6. Effectiveness of our filtering scheme on KNN. Performance gain validates our understanding of ID clustering landscape. NCI outperforms KNN and standalone \\( L1 \\) norm. AUROC reported (higher is better). Bold highlights the best result." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.685, + 0.495, + 0.764 + ], + "angle": 0, + "content": "
    SSB-hardNINCOiNaturalistTextureOpenImage-OAVG
    L168.8068.2890.8688.1678.4778.91
    KNN62.5779.6486.4196.4987.0482.43
    KNN + L164.2981.7692.7697.8590.1786.37
    NCI w/o L166.8180.2092.6791.8790.5184.41
    NCI73.9083.4696.9596.6392.9888.56
    " + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.784, + 0.234, + 0.801 + ], + "angle": 0, + "content": "5. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.856 + ], + "angle": 0, + "content": "OOD Detection Extensive research has focused on OOD detection algorithms. One line of work is post-hoc and builds upon pre-trained models. For example, [13, 21, 22," + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.863, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Note that we report our run of KNN here to ensure a fair evaluation of the filtering effect. Our results are very similar to the OpenOOD results reported in Table 1a, with only marginal differences." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.179, + 0.907, + 0.285 + ], + "angle": 0, + "content": "24, 37, 38, 46] design OOD score over the output space of a classifier. Meanwhile, [20] and [39] measure OOD-ness from the perspective of ID clustering in feature space. Our work extends the observation that ID features tend to cluster from the perspective of Neural Collapse. While existing work is more focused on certain classification tasks, our proposed OOD detector is tested to be highly versatile." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.285, + 0.909, + 0.422 + ], + "angle": 0, + "content": "Others [34-36, 52] explore the regularization of OOD detection in training. For example, [7, 14] propose OOD-specific architecture whereas [16, 44] design OOD-specific training loss. [40] brings attention to representation learning for OOD detection and proposes an OOD-specific contrastive learning scheme. Our work does not belong to this school of thought and is not restricted to specific training schemes or architecture. Notably, as shown in Appendix 10, our NCI can also benefit from training-time algorithms." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.439, + 0.909, + 0.622 + ], + "angle": 0, + "content": "Neural Collapse Neural Collapse was first observed in [32]. During Neural Collapse, the penultimate layer features collapse to class means, the class means and the classifier collapses to a simplex equiangular tight framework, and the classifier simplifies to adopt the nearest class-mean decision rule. Further work has provided theoretical justification for the emergence of Neural Collapse [10, 30, 51, 53]. Application-wise, [53] derives an efficient training algorithm inspired by Neural Collapse. Our concurrent work [1] also leverages Neural Collapse for OOD detection but overlooks class-specific information revealed by Neural Collapse, which is central to our approach." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.634, + 0.634, + 0.65 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.909, + 0.901 + ], + "angle": 0, + "content": "This work leverages insights from Neural Collapse to propose a novel OOD detector. Specifically, we study the phenomenon that ID features tend to form clusters whereas OOD features reside far away. Inspired by the trend of Neural Collapse prevalent on practical models, we hypothesize and validate that ID features tend to cluster near weight vectors. We also explain why ID features tend to reside further from the origin and complement our method from this perspective. Experiments show the effectiveness of our method on practical models without requiring the complete convergence of Neural Collapse. Further, our method improves the overall performance with minimal latency across diverse benchmarks. We hope our work can inspire future work to explore the interplay between features and weight vectors for OOD detection and other research problems such as calibration and adversarial robustness." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15431" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.484, + 0.175 + ], + "angle": 0, + "content": "We would like to express our sincere gratitude to Yubing Jian for conducting several experiments that made significant contributions to this work and for his valuable discussions." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.188, + 0.188, + 0.204 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.214, + 0.484, + 0.268 + ], + "angle": 0, + "content": "[1] Mouin Ben Ammar, Nacim Belkhir, Sebastian Popescu, Antoine Manzanera, and Gianni Franchi. 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Inspired by the phenomenon of Neural Collapse, we propose a versatile and efficient OOD detection method. Specifically, we re-characterize prior observations that in-distribution (ID) samples form clusters, demonstrating that, with appropriate centering, these clusters align closely with model weight vectors. Additionally, we reveal that ID features tend to expand into a simplex Equiangular Tight Frame, explaining the common observation that ID features are situated farther from the origin than OOD features. Incorporating both insights from Neural Collapse, our OOD detector leverages feature proximity to weight vectors and complements this approach by using feature norms to effectively filter out OOD samples. Extensive experiments on off-the-shelf models demonstrate the robustness of our OOD detector across diverse scenarios, mitigating generalization discrepancies and enhancing overall performance, with inference latency comparable to that of the basic softmax-confidence detector. Code is available at: https://github.com/litanliu/NCI-OOD. + +# 1. Introduction + +Machine learning models deployed in practice will inevitably encounter samples that deviate from the training distribution. As a classifier cannot make meaningful predictions on test samples that belong to classes unseen during training, it is important to actively detect and handle Out-of-Distribution (OOD) samples. Considering the diverse and oftentimes time-critical application scenarios, an OOD detector should be computationally efficient and can effectively generalize across various scenarios. + +In this work, we focus on post-hoc methods, which address OOD detection independently of the training process. One line of prior work designs OOD scores over model output space [8, 13, 21, 24, 37, 38] and another line of work focuses on the feature space, where OOD sam + +![](images/1b7827bd51250602377c9552958b2142fda53ca1b4f85b8888638471de2b2eb4.jpg) +Figure 1. Centered ID samples tend to cluster near the predicted class weight vectors, which are the last-layer weights of the corresponding class, as indicated by higher average cosine similarity (Equation 5) than OOD. This observation, inspired by the trend of Neural Collapse, emerges early in the training of this CIFAR-10 ResNet-18 classifier, with OOD set SVHN. + +plies are observed to deviate from clusters of ID samples [20, 27, 39, 40]. While existing research has made strides in OOD detection, they still face two major challenges: 1) maintaining detection effectiveness across different scenarios, and 2) ensuring computational efficiency for real-world deployment. For example, both output space and feature space methods suffer from performance discrepancy across different classification tasks, as shown in Table 1 (a). Specifically, strong algorithms on detecting OOD examples for CIFAR-10 [18] perform suboptimally in detecting OOD examples for ImageNet [5], and vice versa. No existing algorithm can simultaneously rank in the top three across two benchmarks, leading to sub-optimal average performance as shown in Table 1 (b). Furthermore, feature-space methods that rely on similarity measures to characterize ID clustering raise efficiency concerns. For example, [39] records training features and evaluates OOD-ness based on the $k$ -th nearest neighbor distance to these features, while [23] demonstrates that dependency on such auxiliary models increases computational costs, posing challenges for time-sensitive applications. This highlights the need to move beyond feature-wise similarity and establish a more structured reference to characterize ID clustering efficiently. + +![](images/8595f6c1d3f5b9f5ca6213460466e45899c0598e3416bc2d2f7ee36eab2772ab.jpg) +Figure 2. Framework Illustration. Left: On the penultimate layer, the centered ID clusters reside near their predicted class weight vectors (marked by stars) while OOD samples reside separated, as shown by UMAP. Middle: ID and OOD samples are separated by pScore (Equation 6), which measures feature proximity to weight vectors. Also, ID samples tend to be further from the origin, illustrated with L1 norms. Right: ID samples cluster near a simplex Equiangular Tight Framework, illustrated with black arrows denoting weight vectors. We detect OOD by thresholding on pScore, selecting blue-shaded hypercones centered at weight vectors, with OOD samples outside these areas. We also filter OOD samples characterized by smaller feature norms. Left & Middle present a practical off-the-shelf CIFAR-10 ResNet-18 classifier with OOD set SVHN. Right depicts our scheme on a three-class classifier with 2D penultimate space. + +![](images/7f429d91582501a5649a1c6b82c50bbd45271cb5c29f87478478e5e44bfe608d.jpg) + +![](images/a8fca05def74634e008a26cabfccee6e98843b0919f3926b47046085e06c12ae.jpg) + +To this end, we revisit the well-established observation that penultimate-layer ID features tend to form clusters, while OOD features reside apart [20, 39, 40], and take it a step further by asking: + +Where do features of ID samples form clusters? + +Leveraging Neural Collapse [32], we first examine the theoretical landscape with models trained beyond zero training error. We first show that, as a deterministic effect of Neural Collapse[32] penultimate-layer features of training samples converge toward the weight vectors of the predicted class—the last-layer weights of the corresponding class—after being centered by training feature mean. Additionally, Neural Collapse demonstrates that training features conform to a simplex Equiangular Tight Frame (ETF) (Equation 1), representing the maximum achievable separation between equiangular vectors. This spatial structure, illustrated in Figure 2 Right, requires features to be sufficiently distant from the origin. + +Building on the insights from the theoretical convergence landscape, we propose two hypotheses about the geometric structure of ID clusters and OOD samples in practical models. Specifically, for ID test samples drawn from the same distribution as training samples, we expect a similar trend of clustering behavior toward the weight vectors and the ETF structure. In contrast, OOD samples, which are not part of the training process, lack the alignment with weight vectors and the spatial expansion necessary to form an ETF. Consequently, the model is unlikely to align unseen OOD features with weight vectors or place them far + +enough from the origin to exhibit ETF-like behavior. Although complete Neural Collapse requires strict conditions, such as prolonged training, its convergence trend and corresponding geometric patterns of ID features are consistently observed during training across diverse architectures and classification tasks (see Appendix 13 and [11]). Thus, our hypotheses regarding ID clusters and OOD samples are expected to hold without requiring complete Neural Collapse. + +To validate the hypotheses, we trace a model's training stages in Figure 1, where centered ID samples consistently cluster closer to the weight vectors than OOD samples. By epoch 50, such a pattern already enables effective OOD detection for SVHN samples1. This shows that the trend of Neural Collapse emerges early, validating the practical effectiveness of our hypothesis before full collapse in mature models. We reinforce this observation with a UMAP [28] visualization of an off-the-shelf CIFAR-10 classifier with a ResNet-18 backbone, shown in Figure 2 Left. ID features cluster near the predicted class weights (marked by stars), while OOD features remain distant. Additionally, as [53] shows that weight vectors form an ETF, our observations also support our second hypothesis: ID features are driven to structure the ETF, while OOD features lack the incentive to expand in space. This explains the well-established observation [17, 39, 40] that OOD features tend to reside closer to the origin, providing an alternative to the model confidence interpretation in [33]. + +Based on our understanding, we design an efficient and versatile OOD detector. We first leverage feature proximity to the weight vectors to characterize ID clustering, effectively incorporating class-specific information and reducing the computational cost. Specifically, we define an angle-based proximity score as the norm of the projection of the weight vector of the predicted class onto the centered sample feature. As shown in Figure 2 Middle, our proximity score can effectively separate ID/OOD. A higher score indicates closer proximity and a lower chance of OOD-ness. Geometrically, thresholding on the score selects hyper-cones centered at the weight vector, as illustrated in Figure 2 Right. Complementing the proximity score's contingency on ID clustering, we also consider feature distance to the origin. Specifically, ID features tend to reside further from the origin as they expand in space to form an ETF, whereas OOD features tend to reside near the origin, as illustrated by Figure 2 Right. Using the L1 norm as an example metric, we observe that ID features can be separated from OOD features, as supported by Figure 2 Middle. Combining both aspects, we propose Neural Collapse Inspired OOD Detector (NCI). + +Notably, prior methods, e.g., KNN [39], focus on ID clustering, without explicitly incorporating feature distance to the origin. Such approaches fall short in scenarios like ImageNet benchmarks but yield superior performance in CIFAR-10 benchmarks in Table 1a. Conversely, methods such as Energy [24], Energy-based ASH [8], and, Energy-based Scale [47] inherently utilize feature distance to the origin by considering log-sum-exp of logits, yet largely overlook ID clustering. These approaches excel in scenarios like ImageNet, but perform sub-optimally in others, e.g., CIFAR-10. Through the lens of Neural Collapse, we explain, connect, and complete a wide range of prior methods under a holistic view, resulting in reduced latency and generalization discrepancies. + +We summarize our main contributions below: + +- Understanding and Observation: By analyzing ID clustering through the trend of Neural Collapse, we discover that penultimate-layer features of ID test examples cluster around the weight vectors of the predicted class after being centered by the training feature mean. Additionally, we explain that ID features tend to lie farther from the origin due to Neural Collapse, where they form a simplex Equiangular Tight Frame (ETF) structure. Notably, our findings hold without requiring full Neural Collapse convergence. +- OOD Detector: We leverage feature proximity to the weight vectors of predicted classes for OOD detection, integrating class-specific information. Complementary to feature clustering, we propose to detect OOD samples by thresholding the feature distance to the origin. +- Experimental Analysis: We evaluate NCI across diverse + +classification tasks (CIFAR-10, CIFAR-100, ImageNet) and model architectures (ResNet, DenseNet [15], ViT [9], Swin [26]). Rather than focusing on individual benchmarks, NCI reduces the generalization discrepancies and improves the overall effectiveness. We also show that incorporating weight vectors not only significantly improves upon prior clustering-based methods but also reduces latency to a minimal level, matching the basic softmax-confidence detector. + +# 2. Problem Statement + +We consider a data space $\mathcal{X}$ , a class set $\mathcal{C}$ , and a classifier $f: \mathcal{X} \to \mathcal{C}$ , which is trained on samples i.i.d. drawn from joint distribution $\mathbb{P}_{\mathcal{X}\mathcal{C}}$ . We denote the marginal distribution of $\mathbb{P}_{\mathcal{X}\mathcal{C}}$ on $\mathcal{X}$ as $\mathbb{P}^{in}$ . And samples drawn from $\mathbb{P}^{in}$ are In-Distribution (ID) samples. In practice, the classifier $f$ may encounter $\pmb{x} \in \mathcal{X}$ yet is not drawn from $\mathbb{P}^{in}$ . We say such samples are Out-of-Distribution (OOD). + +In this work, we focus on detecting OOD samples from classes unseen during training, for which the classifiers cannot make meaningful predictions. The OOD detector $D:\mathcal{X}\to \{\mathrm{ID},\mathrm{OOD}\}$ is commonly constructed as: + +$D(\pmb {x}) = \left\{ \begin{array}{ll}\mathrm{ID} & \mathrm{if} s(\pmb {x})\geq \tau \\ \mathrm{OOD} & \mathrm{if} s(\pmb {x}) < \tau \end{array} \right.$ where $s:\mathcal{X}\to \mathbb{R}$ is a score function of design and $\tau$ is the threshold. Considering the diverse application scenarios, an ideal OOD detector should be efficient and generalizable. Thus, we leverage insights from Neural Collapse to achieve reduced computational costs and minimize generalization discrepancies. + +# 3. OOD Detection through the Lens of Neural Collapse + +In this section, we re-examine the observation in [20, 39] that ID features tend to form clusters while OOD features deviate from the clusters. We suggest that the clustering phenomenon can reflect the trend of the Neural Collapse [32] in practical models. From our understanding, we develop a post-hoc OOD detector with enhanced efficiency and effectiveness. + +# 3.1. Neural Collapse: Convergence Landscape + +Neural Collapse, first observed in [32], occurs on the penultimate layer across canonical classification settings. To formally introduce the concept, we use $h_c^i$ to denote the penultimate layer feature of the $i_{th}$ training sample with ground truth / predicted label $c$ , Neural Collapse is framed in relation to + +- feature global mean, $\pmb{\mu}_{G} = \mathrm{Ave}_{i,c}\left(\pmb{h}_{c}^{i}\right)$ , where $\mathrm{Ave}(\cdot)$ is the average operation; +- feature class means, $\pmb{\mu}_{c} = \mathrm{Ave}_{i}\left(\pmb{h}_{c}^{i}\right)$ , $\forall c\in \mathcal{C}$ +- within-class covariance, + +$$ +\boldsymbol {\Sigma} _ {W} = \operatorname {A v e} _ {i, c} \left(\left(\boldsymbol {h} _ {c} ^ {i} - \boldsymbol {\mu} _ {c}\right) \left(\boldsymbol {h} _ {c} ^ {i} - \boldsymbol {\mu} _ {c}\right) ^ {T}\right); +$$ + +- between-class covariance, + +$$ +\boldsymbol {\Sigma} _ {B} = \operatorname {A v e} _ {c} \left(\left(\boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G}\right) \left(\boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G}\right) ^ {T}\right); +$$ + +- linear classification head, i.e. the last layer of the NN, $\arg \max_{c\in \mathcal{C}}\boldsymbol{w}_c^T\boldsymbol {h} + b_c$ where $\boldsymbol{w}_{c}$ and $b_{c}$ are parameters corresponding to class $c$ + +Neural Collapse comprises four inter-related behaviors: + +(NC1) Within-class variability collapse: $\Sigma_W\rightarrow 0$ +(NC2) Convergence to a simplex Equiangular Tight Frame (ETF): + +$$ +\left|\left|\left| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G} \right|\right| _ {2} - \left|\left| \boldsymbol {\mu} _ {c ^ {\prime}} - \boldsymbol {\mu} _ {G} \right|\right| _ {2} \right|\rightarrow 0, \forall c, c ^ {\prime} +$$ + +$$ +\frac {\left(\boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G}\right) ^ {T} \left(\boldsymbol {\mu} _ {c ^ {\prime}} - \boldsymbol {\mu} _ {G}\right)}{\| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G} \| _ {2} \| \boldsymbol {\mu} _ {c ^ {\prime}} - \boldsymbol {\mu} _ {G} \| _ {2}} \rightarrow \frac {| \mathcal {C} |}{| \mathcal {C} | - 1} \delta_ {c, c ^ {\prime}} - \frac {1}{| \mathcal {C} | - 1} \tag {1} +$$ + +where $\delta_{c,c'}$ is the Kronecker delta symbol. + +(NC3) Convergence to self-duality: + +$$ +\frac {\boldsymbol {w} _ {c}}{\| \boldsymbol {w} _ {c} \| _ {2}} - \frac {\boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G}}{\| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G} \| _ {2}} \rightarrow \mathbf {0} +$$ + +(NC4) Simplification to nearest class center: + +$$ +\arg \max _ {c \in \mathcal {C}} \boldsymbol {w} _ {c} ^ {T} \boldsymbol {h} + b _ {c} \rightarrow \arg \min _ {c \in \mathcal {C}} \| \boldsymbol {h} - \boldsymbol {\mu} _ {c} \| _ {2} +$$ + +We first remark on (NC2) that an ETF achieves the maximum separation possible for globally centered equiangular vectors [32] and extends in space, as visualized in Figure 2 Right. Since training features converge towards an ETF, they need to have sufficient norms to accommodate the spatial arrangement. + +We next build on (NC1) and (NC3) to demonstrate that training features converge towards the weight vectors of the linear classification head, up to a scaling factor. + +Theorem 3.1. (NC1) and (NC3) imply that for any sample $i$ and its predicted class $c$ , we have + +$$ +\left(\boldsymbol {h} _ {c} ^ {i} - \boldsymbol {\mu} _ {G}\right)\rightarrow \lambda \boldsymbol {w} _ {c}, \tag {2} +$$ + +where $\lambda = \frac{\|\pmb{\mu}_c - \pmb{\mu}_G\|_2}{\|\pmb{w}_c\|_2}$ in the Terminal Phase of Training. + +Proof. Considering that $(\pmb{h}_c^i - \pmb{\mu}_c)(\pmb{h}_c^i - \pmb{\mu}_c)^T$ is positive semi-definite for any $i$ and $c$ . $\pmb{\Sigma}_W \to \mathbf{0}$ thus implies $(\pmb{h}_c^i - \pmb{\mu}_c)(\pmb{h}_c^i - \pmb{\mu}_c)^T \to \mathbf{0}$ and $\pmb{h}_c^i - \pmb{\mu}_c \to \mathbf{0}$ , $\forall i, c$ . With algebraic manipulations, we have + +$$ +\frac {\boldsymbol {h} _ {c} ^ {i} - \boldsymbol {\mu} _ {G}}{\| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G} \| _ {2}} - \frac {\boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G}}{\| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G} \| _ {2}} \rightarrow \mathbf {0}, \forall i, c \tag {3} +$$ + +Applying the triangle inequality, we have + +$$ +\left| \frac {\boldsymbol {h} _ {c} ^ {i} - \boldsymbol {\mu} _ {\boldsymbol {G}}}{\| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {\boldsymbol {G}} \| _ {2}} - \frac {\boldsymbol {w} _ {c}}{\| \boldsymbol {w} _ {c} \| _ {2}} \right| \leq +$$ + +$$ +\left| \frac {\mathbf {h} _ {c} ^ {i} - \boldsymbol {\mu} _ {G}}{\| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G} \| _ {2}} - \frac {\boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G}}{\| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G} \| _ {2}} \right| + \left| \frac {\boldsymbol {w} _ {c}}{\| \boldsymbol {w} _ {c} \| _ {2}} - \frac {\boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G}}{\| \boldsymbol {\mu} _ {c} - \boldsymbol {\mu} _ {G} \| _ {2}} \right|. \tag {4} +$$ + +Since both terms on the RHS converge to 0, as demonstrated by (3) and (NC3), it follows that the LHS also converges to 0. + +# 3.2. Trend of Neural Collapse & Geometric Structure of the ID Clusters + +While the complete collapse occurs during the Terminal Phase of Training (TPT) where training error vanishes and the training loss is trained towards zero, it is observed in [11] that the trend of Neural Collapse establishes in the early stages of training. We thus suggest that the clustering behavior of ID features observed in off-the-shelf models reflects a trend of Neural Collapse, corresponding to the within-class variability collapse (NC1). In light of this, we use the landscape of Neural Collapse revealed in Theorem 3.1 and (NC2) to examine the geometry of ID clusters. + +Following our discussion in Section 1, we we hypothesize and validate with pre-trained models that (1) ID features tend to cluster closer to the weight vectors compared to OOD features; (2) ID clusters tend to reside further from the origin, as necessitated by their spatial structure. Particularly, Neural Collapse highlights the importance of centering for characterizing ID clustering with weight vectors. We thus validate our hypothesis in a CIFAR-10 classifier with ResNet-18 backbone in Figure 1, computing over the ID set (CIFAR-10) and OOD set (SVHN) the average cosine similarity between the centered feature $\pmb{h}^i - \pmb{\mu}_G$ and the weight vector $\pmb{w}_c$ of the predicted class $c$ , i.e., + +$$ +\operatorname {A v e} _ {i} \left(\frac {\left(\boldsymbol {h} ^ {i} - \boldsymbol {\mu} _ {G}\right) \cdot \boldsymbol {w} _ {c}}{\| \boldsymbol {h} ^ {i} - \boldsymbol {\mu} _ {G} \| _ {2} \| \boldsymbol {w} _ {c} \| _ {2}}\right) \tag {5} +$$ + +# 3.3. Out-of-Distribution Detection + +Based on our understanding, we design an efficient and versatile OOD detector. Specifically, we propose to detect OOD based on feature proximity to the weight vectors of the predicted class. For the proximity metric, we avoid Euclidean-based metrics as they require estimating the scaling factor $\lambda$ in Equation 2. This estimation tends to be imprecise for general classifiers which may cease training prior to convergence, resulting in suboptimal performance of Euclidean-based metrics shown in Appendix 8. Instead, we design an angle-based metric, adjusted for class-wise difference. Specifically, we propose to quantify the proximity as the norm of projection of the weight vector $w_{c}$ onto the centered feature $h - \mu_G$ , where $c$ corresponds to the predicted class, i.e., + +$$ +\mathrm {p S c o r e} = \cos \left(\boldsymbol {w} _ {c}, \boldsymbol {h} - \boldsymbol {\mu} _ {G}\right) \| \boldsymbol {w} _ {c} \| _ {2}, \tag {6} +$$ + +where $\cos(\boldsymbol{w}_c, \boldsymbol{h} - \boldsymbol{\mu}_G) = \frac{(\boldsymbol{h} - \boldsymbol{\mu}_G) \cdot \boldsymbol{w}_c}{\|\boldsymbol{h} - \boldsymbol{\mu}_G\|_2 \| \boldsymbol{w}_c\|_2}$ . A higher pScore indicates closer proximity to the weight vector and thus a lower chance of OOD-ness. Geometrically, thresholding on pScore selects infinite hyper-cones centered at the weight vectors, as illustrated in Figure 2 Right. Within the same predicted class, pScore is proportional to the cosine similarity. Across different classes, pScore adapts + +to class-wise difference by selecting wider hyper-cones for classes with larger weight vectors, which tend to have larger decision regions. As shown in Appendix 8, our pScore with class-wise adjustment outperforms vanilla cosine similarity. Notably, our pScore incorporates class-specific information into characterizing ID clustering by using the weight vectors of the predicted class. This brings in additional gain in detection effectiveness, as we shall see in Section 4. + +While pScore enhances efficiency and effectiveness, its performance is intrinsically contingent on the strength of ID clustering. Such contingency, widely exhibited by clustering-based methods [20, 39, 40], poses challenges on classifiers with less pronounced ID clustering, such as ImageNet ResNet-50 in Section 4.1. To mitigate such discrepancy, we complement pScore by using the distance of ID clusters to the origin. Specifically, we enhance our proximity score by incorporating feature norms to filter out OOD near the origin, as illustrated in Figure 2 Right. Taking L1 norm as an example, we define our detection score as $\mathrm{pScore} + \alpha \| h\| _1$ , where $\alpha$ controls the filtering strength and can be selected from a validation set as detailed in Section 4. We discuss the effect of different orders of $p$ -norm in Section 4.3. Thresholding on the detection score, we have Neural Collapse Inspired OOD Detector (NCI): A lower score indicates a higher chance of OOD-ness. + +NCI has $O(P)$ complexity, where $P$ is the penultimate layer dimension. The complexity theoretically ensures computational scalability of NCI on large models. Empirically, NCI maintains inference latency comparable to the vanilla softmax-confidence detector, as shown in Section 4. + +# 4. Experiments + +In this section, we extensively evaluate NCI across classification tasks: CIFAR-10, CIFAR-100 (see App. 12), ImageNet, as well as model architectures: ResNet, DenseNet (see App. 12), ViT, Swin. We compare NCI against thirteen baseline methods. While NCI may not achieve the best performance on individual benchmarks, it mitigates the existing generalization discrepancies and achieves the best overall performance with minimal latency. Following the OpenOOD benchmark [49], we evaluate on six OOD sets for CIFAR-10 and CIFAR-100 classifiers and five for ImageNet classifiers. Performance is evaluated using two widely recognized metrics: the False Positive Rate at $95\%$ True Positive Rate (FPR95) and the Area Under the Receiver Operating Characteristic Curve (AUROC). Lower FPR95 and higher AUROC values indicate better performance. We also report the per-image inference latency (in milliseconds) evaluated on a Tesla T4 GPU. In our experiments, other than the ablation study in Section 4.3, we use the L1-norm as the filtering term and select the filtering strength $\alpha$ from $\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\}$ based on a + +validation set generated per pixel from Gaussian $N(0,1)$ , following [37, 38]. Our method and all baselines are post-hoc methods, while all models used are off-the-shelf and do not require complete Neural Collapse convergence. For detailed setups and additional baselines, please see Appendix 7 and Appendix 11, respectively. + +# 4.1. Mitigating Discrepencies across ID Datasets + +We first assess NCI and baselines across CIFAR-10 and ImageNet classification tasks. The two tasks provide an ideal test bed for evaluating versatility, as they drastically differ in input resolution, number of classes, and classification accuracy. We use ResNets from OpenOOD [49]: ResNet-18 for CIFAR-10 (95.06% accuracy) and ResNet-50 for ImageNet (76.65% accuracy). Based on validation results, we set the filter strength $\alpha$ of the $L1$ -norm to $10^{-2}$ for CIFAR-10 experiments and $10^{-3}$ for ImageNet experiments. + +Datasets For CIFAR-10 experiments, We follow the OpenOOD split of ID test set and evaluate on the OpenOOD benchmarks, including CIFAR-100 [18], Tiny ImageNet [19], MNIST [6], SVHN [31], Texture [4], and Places365 [50]. For ImageNet experiments, we follow the OpenOOD split of ID test set and evaluate on the OpenOOD benchmarks, including SSB-hard [42], NINCO [2], iNaturalist [41], Texture [4], and OpenImage-O [43]. + +Baselines In Table 1a, we compare our method with thirteen baselines. Some baselines focus more on the CIFAR-10 Benchmark while others focus more focused on the ImageNet Benchmark. Therefore, we categorize the baselines, besides the vanilla confidence-based MSP [12], into two groups: the "CIFAR-10 Strong" baselines, including ODIN [21], Energy [24], Mahalanobis [20], KNN[39], ViM [43], and fDBD [22]; the "ImageNet Strong" baselines, including GradNorm [17], NECO [1], React [38], Dice [37], ASH [8], Scale [47]. See Appendix 9 for details of the baselines. + +Performance Table 1a shows that NCI consistently ranks top-three across benchmarks, whereas baselines exhibit greater variability. To assess overall performance, we averaged AUROC across benchmarks, which are of a similar range. Table 1b highlights that NCI improves overall performance compared to strong baselines on individual benchmarks. Further, NCI is as efficient as MSP, as shown in Table $1\mathrm{b}^2$ , which enhances efficiency compared to strong baselines. This aligns with the analysis in Section 3 and Appendix 9. We highlight the following pairs of comparison: + +- NCI v.s. NCI w/o filter: On the CIFAR-10 classifier, strong ID clustering allows our method to rank top-3 without filtering. Conversely, on the ImageNet ResNet50, weaker ID clustering (see Appendix 13) makes norm-based filtering crucial for reducing generalization discrepancy. Complete Neural Collapse occurs on neither model while NCI remains effective. + +Table 1. NCI reduces discrepancies and improves overall performance on CIFAR-10 and ImageNet benchmarks with minimal latency. CIFAR-10 uses ResNet-18 and ImageNet uses ResNet-50. + +
    Methods43.27 75.388481002439923.64838686167.7080703663.8184824Evaluation under FPR9591.8673.3187.07
    MSP*92.6653.081.3043.2774.3423.6476.0725.8294.1634.9638.1142.4737.2074.4956.8843.3460.8750.1357.14
    CIFAR-10 StrongODIN77.0020.0523.8324.0668.6167.7070.3638.8176.8368.1635.9649.2446.6755.38
    Energy*40.496618.668819.4935.1214.5141.4334.8565.2476.5462.2931.3043.5738.0950.46
    MDS49.04737.244656.9974.8376.07194.165538.1195.19529138684.2336.0590.7743.48
    KNN94.88485.041720.6529.60924.92460.32827.3883.3679584940.8043.2744.2768.82
    ViM62.947915.952930.16160.922156.081481.49501.6580.41556082930.6848.2532.8243.29
    fDBD*59.73633.979457.4356.99236.40202.151145.5477.2855821322.0026.8429.9443.48
    ImageNet StrongGradNorm64.5494.8985.4191.6598.0992.4682.8478.2466.9032.0343.2768.4660.31
    NECO72.6362.4715.5230.1660.1256.0849.5072.3155.0827.0548.2533.4247.22
    ReAct67.4070.0083.6484.5977.8981.6151.1277.5555.8216.7229.6432.5842.46
    DICE83.6435.13768.8984.9062.42147.7075.8577.9651.8633.3747.5847.8334.06
    ASH43.5432.62528.0882.6534.0177.86261.6173.6656.5114.0434.3829.1545.08
    Scale43.60032.64429.0168.6984.38986.136270.7567.725358669.5223.3928.1739.96
    NCI w/o filter*51.9243.5432.6328.9226.5334.0136.2682.1456.4124.1134.3230.9445.58
    87.NCI51.8392.68092.46289.0892688.92393.98836.2773.2979598614.3182.4930.9889.00
    CIFAR-10 Strong82.1895.2484.5886.9485.07Evaluation under AUROC7789.0083.58
    MSP*87.1998838797.6998.4678.8925.8889.8372.0979709588.4188.7084.8684.04
    ODIN82.189835585.2484.7886.9485.0786.2671.7455.4191.1779.9088.2383.58
    Energy*86.3688.8094.3291.7989.4789.2590.0072.0879.7090.6388.7089.0684.04
    MDS61.2994.2699.1793.1677.4052.4769.4143.9279.6461.8279.9460.8082.55
    KNN89.7394.7694.2092.6715.9391.7788.1862.5778.6386.4197.9787.0484.44
    AWI87.7599.8287.4592.5495.10989.49361.8865.5482.6089.5692.9190.5086.05
    SDH*87.186897298.0185.2490.6490.06669.3670.6674826093.7092.0591.1786.03
    ImageNet Strong85.DTorm54.4396513792.24588.565289.540.5093.8989.0884.8283.93
    NGO85.509888386.1298.2388.0635.89320.0374.7982.4292.1990.8087.93
    ReAct85.939882996.6288.1289.3890.35279.3273.0381.7396.3492.0491.8783.80
    DICE77.0179.6790.3790.0281.8974.6782.2770.1376.0192.5492.0488.2683.80
    ASH74.1176.4483.1673.4677.4579.8977.4172.8983.4597.0796.9093.2688.71
    Scale80.5793.1986.0683.4888.8986.0177.4177.3485.3798.0296.7593.9590.28
    * N17w23 filter*87.9391.5090.8092.1790.7490.4766.8180.2092.6791.8790.5184.41
    NCI87.9289.6591.5090.8092.1790.7490.4673.9083.4696.9596.6392.9888.56
    + +(a) NCI ranks top-three in both benchmarks, while baselines show greater variability. $\uparrow$ and $\downarrow$ denotes better performance. Bold marks best, underline 2nd / 3rd. Methods with $*$ are hyperparameter-free. Scores, except for the most recent baselines - fDBD, NECO, ASH, Scale - are from OpenOOD [49]. + +
    PerformanceMSPNECOKNNViMASHScaleNCI (ours)
    CIFAR-10 Latency0.530.701.950.700.530.530.54
    ImageNet Latency6.859.5510.319.557.027.016.84
    Avg AUROC85.6987.9887.3888.1683.0688.1589.51
    + +(b) NCI improves the overall performance while reducing latency compared to strong baselines. AUROC averaged across CIFAR-10 and ImageNet benchmarks in Table 1a, with per image latency reported. + +- NCI v.s. KNN: Compared to KNN, NCI significantly reduces the latency (Table 1b). Notably, without filtering, our + +hyperparameter-free score outperforms KNN with tuned parameters on most benchmarks (Table 1a, Table 2a & + +Table 2. NCI reduces discrepancies and improves overall performance on ImageNet benchmarks across ViT B/16 and Swin v2 classifiers. Bold marks best, underline 2nd + +
    MethodsImageNet OpenOOD Benchmark (ViT B/16)ImageNet OpenOOD Benchmark (Swin v2)
    Near-OODFar-OODAvgNear-OODFar-OODAvg
    SSB-hardNINCOiNaturalistTextureOpenImage-OSSB-hardNINCOiNaturalistTextureOpenImage-O
    Evaluation under FPR95 ↓
    KNN63.4139.716.8443.1218.3034.2890.8883.1676.8860.4367.1475.70
    ViM51.9137.105.6739.2917.5130.3090.3483.8970.9865.9068.6875.96
    ASH48.7845.4211.0042.3720.3335.5893.8093.9387.5897.2791.1492.74
    Scale45.0732.045.4940.5913.1527.2790.7475.7248.7395.1064.5575.97
    NCI w/o filter50.9430.685.9346.6114.9229.8186.7773.1147.9875.3059.3069.67
    NCI46.7333.796.0842.0914.7928.7985.5872.0645.2571.5354.7265.83
    Evaluation under AUROC ↑
    KNN81.4890.0098.6796.2396.2391.4462.5069.7478.3585.1967.1475.88
    ViM87.3992.5698.9890.8096.8293.3160.9972.3083.3679.6182.5275.76
    ASH90.6090.8898.0495.9795.9793.1458.8758.2858.1846.1861.3256.57
    Scale89.6793.2398.9697.2097.2094.0962.4878.9788.8867.0886.1476.71
    NCI w/o filter87.1693.1598.8796.8096.8093.2664.5376.7388.0779.6385.3978.87
    NCI88.8692.8898.7996.8396.8393.6467.5378.9989.6881.4387.4280.97
    + +(a) NCI boosts Swin v2 while maintaining ViT effectiveness compared to baselines, even without filtering. + +
    PerformanceKNNViMASHScaleNCI (ours)
    Avg AUROC83.6684.8474.8685.4087.31
    + +(b) NCI improves the overall performance. AUROC averaged across two architectures in Table 2a. + +Table 9), highlighting the benefit of using class-specific information. + +- NCI v.s. ASH / Scale: Compared to both, NCI delivers competitive performance on ImageNet and significantly improves CIFAR-10, enhancing overall performance (Table 1b). Also, ASH and Scale introduce in a small delay on the ImageNet benchmark due to activation sorting, with larger activation dimensions likely widening the latency gap on larger models. +- NCI v.s. NECO: NECO [1] is motivated by Neural Collapse. Like NCI with filtering, NECO uses max-logit and incorporates distance to the origin. However, NECO exclusively analyzes features, requiring expensive matrix multiplication and leading to higher inference latency (Table 1b). Conversely, NCI explores the interplay between features and the classification head, integrating class-specific information to improve both efficiency and effectiveness. + +# 4.2. Mitigating Discrepancies across Architectures + +Next, we study two transformer-based models: ViT B/16 [9] and Swin-v2 [26], both finetuned on ImageNet, achieving an accuracy of $81.14\%$ and $82.94\%$ respectively. We follow the setup of the OpenOOD ImageNet Benchmark in Section 4.1. Based on validation results, we set the filter strength $\alpha$ of the $L1$ norm to $10^{-3}$ for both classifiers. In Table 2, we observe strong baselines suffer on Swin v2, echoing the observations in [1]. Conversely, our NCI, even without filtering, improves baseline performance on Swin + +v2. Filtering further enhances the performance, leading to improved overall performance (Table 2b). + +We further aggregate in Table 2 with experiments on ResNet (Table 1) and DenseNet (Table 9) and report the average AUROC in Table 3. NCI significantly boosts the overall performance. + +# 4.3. Ablation on the Filtering Effect + +In Table 4, we assess different orders of $p$ -norm as the filtering term, compared to the $L1$ norm used so far. To ensure a fair comparison, we report the best performance from the filter strengths $\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\}$ . The rest of the setup follows the ImageNet benchmarks in Section 4.1. As shown in Table 4, filtering with $L1$ norm achieves the best performance across OOD datasets, aligning with prior observations [17, 33]. Meanwhile, we observe that in rare scenarios, e.g., a ResNet-18 on CIFAR-10, the L1 norm cannot effectively characterize OOD's proximity to the origin, leading to no extra performance gain compared to simply thresholding on pScore. In these cases, our algorithm benefits from its ability to automatically select a low filter strength based on validation results, effectively disregarding the filtering term. + +We also test the sensitivity of NCI to filtering strength $\alpha$ in Table 5. As shown on the ImageNet ResNet50 benchmark, performance remains stable for $\alpha$ values within the same scale. Given this insensitivity, we select hyperparameters from four scales $\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\}$ without extensive finetuning in this work. + +Table 3. NCI improves the overall performance, averaged across Table 1a, Table 2a & Table 9. + +
    PerformanceKNNViMASHScaleNCI (ours)
    Avg AUROC86.0685.9681.2486.888.57
    Across All Benchmarks
    + +Table 4. Ablation on filtering norm on ImageNet OpenOOD Benchmark with ResNet-50 backbone. AUROC score is reported (higher is better). BoldNCO denotes the best. Filtering with L1 norm outperforms alternative choice of norms across OOD datasets. + +
    FilteringSSB-hardNINCOiNaturalistTextureOpenImage-O
    Linf66.8180.2092.6691.8790.51
    L2 SSBha912NINCOnatural92OpenImage1073
    L173.9083.4696.9596.6392.98
    + +Table 5. Sensitivity of NCI to filtering strength. Average AUROC on ImageNet ResNet-50 Benchmark reported. Performance was stable within the same scale. + +
    Filtering Magnitude αAvg AUROC
    0.6 x 10-388.27
    0.8 x 10-388.55
    1 x10-388.59
    1.2 x 10-388.50
    1.4 x 10-388.23
    + +We further apply L1-norm based filtering to KNN to see if this perspective can mitigate the discrepancy of clustering-based methods in general. In Table 63, we report the best performance of KNN from filter strengths $\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\}$ . We observe a significant performance gain from adding the filter, which further validates our understanding of ID clustering landscape from Neural Collapse. Note that our method outperforms the standalone $L1$ norm as well as KNN, before and after filtering. + +Table 6. Effectiveness of our filtering scheme on KNN. Performance gain validates our understanding of ID clustering landscape. NCI outperforms KNN and standalone $L1$ norm. AUROC reported (higher is better). Bold highlights the best result. + +
    SSB-hardNINCOiNaturalistTextureOpenImage-OAVG
    L168.8068.2890.8688.1678.4778.91
    KNN62.5779.6486.4196.4987.0482.43
    KNN + L164.2981.7692.7697.8590.1786.37
    NCI w/o L166.8180.2092.6791.8790.5184.41
    NCI73.9083.4696.9596.6392.9888.56
    + +# 5. Related Work + +OOD Detection Extensive research has focused on OOD detection algorithms. One line of work is post-hoc and builds upon pre-trained models. For example, [13, 21, 22, + +24, 37, 38, 46] design OOD score over the output space of a classifier. Meanwhile, [20] and [39] measure OOD-ness from the perspective of ID clustering in feature space. Our work extends the observation that ID features tend to cluster from the perspective of Neural Collapse. While existing work is more focused on certain classification tasks, our proposed OOD detector is tested to be highly versatile. + +Others [34-36, 52] explore the regularization of OOD detection in training. For example, [7, 14] propose OOD-specific architecture whereas [16, 44] design OOD-specific training loss. [40] brings attention to representation learning for OOD detection and proposes an OOD-specific contrastive learning scheme. Our work does not belong to this school of thought and is not restricted to specific training schemes or architecture. Notably, as shown in Appendix 10, our NCI can also benefit from training-time algorithms. + +Neural Collapse Neural Collapse was first observed in [32]. During Neural Collapse, the penultimate layer features collapse to class means, the class means and the classifier collapses to a simplex equiangular tight framework, and the classifier simplifies to adopt the nearest class-mean decision rule. Further work has provided theoretical justification for the emergence of Neural Collapse [10, 30, 51, 53]. Application-wise, [53] derives an efficient training algorithm inspired by Neural Collapse. Our concurrent work [1] also leverages Neural Collapse for OOD detection but overlooks class-specific information revealed by Neural Collapse, which is central to our approach. + +# 6. Conclusion + +This work leverages insights from Neural Collapse to propose a novel OOD detector. Specifically, we study the phenomenon that ID features tend to form clusters whereas OOD features reside far away. Inspired by the trend of Neural Collapse prevalent on practical models, we hypothesize and validate that ID features tend to cluster near weight vectors. We also explain why ID features tend to reside further from the origin and complement our method from this perspective. Experiments show the effectiveness of our method on practical models without requiring the complete convergence of Neural Collapse. Further, our method improves the overall performance with minimal latency across diverse benchmarks. We hope our work can inspire future work to explore the interplay between features and weight vectors for OOD detection and other research problems such as calibration and adversarial robustness. + +# Acknowledgments + +We would like to express our sincere gratitude to Yubing Jian for conducting several experiments that made significant contributions to this work and for his valuable discussions. + +# References + +[1] Mouin Ben Ammar, Nacim Belkhir, Sebastian Popescu, Antoine Manzanera, and Gianni Franchi. Neco: Neural collapse based out-of-distribution detection. arXiv preprint arXiv:2310.06823, 2023.5,7,8 +[2] Julian Bitterwolf, Maximilian Müller, and Matthias Hein. In or out? fixing imagenet out-of-distribution detection evaluation. In International Conference on Machine Learning, pages 2471-2506. PMLR, 2023. 5 +[3] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. 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Inspired by the phenomenon of Neural Collapse, we propose a versatile and efficient OOD detection method. Specifically, we re-characterize prior observations that in-distribution (ID) samples form clusters, demonstrating that, with appropriate centering, these clusters align closely with model weight vectors. Additionally, we reveal that ID features tend to expand into a simplex Equiangular Tight Frame, explaining the common observation that ID features are situated farther from the origin than OOD features. Incorporating both insights from Neural Collapse, our OOD detector leverages feature proximity to weight vectors and complements this approach by using feature norms to effectively filter out OOD samples. Extensive experiments on off-the-shelf models demonstrate the robustness of our OOD detector across diverse scenarios, mitigating generalization discrepancies and enhancing overall performance, with inference latency comparable to that of the basic softmax-confidence detector. Code is available at: https://github.com/litanliu/NCI-OOD." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 524, + 135, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 524, + 135, + 537 + ], + "spans": [ + { + "bbox": [ + 56, + 524, + 135, + 537 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 544, + 295, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 295, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 295, + 652 + ], + "type": "text", + "content": "Machine learning models deployed in practice will inevitably encounter samples that deviate from the training distribution. As a classifier cannot make meaningful predictions on test samples that belong to classes unseen during training, it is important to actively detect and handle Out-of-Distribution (OOD) samples. Considering the diverse and oftentimes time-critical application scenarios, an OOD detector should be computationally efficient and can effectively generalize across various scenarios." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 653, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 713 + ], + "type": "text", + "content": "In this work, we focus on post-hoc methods, which address OOD detection independently of the training process. One line of prior work designs OOD scores over model output space [8, 13, 21, 24, 37, 38] and another line of work focuses on the feature space, where OOD sam" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 329, + 213, + 539, + 342 + ], + "blocks": [ + { + "bbox": [ + 329, + 213, + 539, + 342 + ], + "lines": [ + { + "bbox": [ + 329, + 213, + 539, + 342 + ], + "spans": [ + { + "bbox": [ + 329, + 213, + 539, + 342 + ], + "type": "image", + "image_path": "1b7827bd51250602377c9552958b2142fda53ca1b4f85b8888638471de2b2eb4.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 353, + 555, + 419 + ], + "lines": [ + { + "bbox": [ + 313, + 353, + 555, + 419 + ], + "spans": [ + { + "bbox": [ + 313, + 353, + 555, + 419 + ], + "type": "text", + "content": "Figure 1. Centered ID samples tend to cluster near the predicted class weight vectors, which are the last-layer weights of the corresponding class, as indicated by higher average cosine similarity (Equation 5) than OOD. This observation, inspired by the trend of Neural Collapse, emerges early in the training of this CIFAR-10 ResNet-18 classifier, with OOD set SVHN." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "type": "text", + "content": "plies are observed to deviate from clusters of ID samples [20, 27, 39, 40]. While existing research has made strides in OOD detection, they still face two major challenges: 1) maintaining detection effectiveness across different scenarios, and 2) ensuring computational efficiency for real-world deployment. For example, both output space and feature space methods suffer from performance discrepancy across different classification tasks, as shown in Table 1 (a). Specifically, strong algorithms on detecting OOD examples for CIFAR-10 [18] perform suboptimally in detecting OOD examples for ImageNet [5], and vice versa. No existing algorithm can simultaneously rank in the top three across two benchmarks, leading to sub-optimal average performance as shown in Table 1 (b). Furthermore, feature-space methods that rely on similarity measures to characterize ID clustering raise efficiency concerns. For example, [39] records training features and evaluates OOD-ness based on the " + }, + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 438, + 556, + 715 + ], + "type": "text", + "content": "-th nearest neighbor distance to these features, while [23] demonstrates that dependency on such auxiliary models increases computational costs, posing challenges for time-sensitive applications. This highlights the need to move beyond feature-wise similarity and establish a more structured reference to characterize ID clustering efficiently." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15424" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 55, + 231, + 248 + ], + "blocks": [ + { + "bbox": [ + 65, + 55, + 231, + 248 + ], + "lines": [ + { + "bbox": [ + 65, + 55, + 231, + 248 + ], + "spans": [ + { + "bbox": [ + 65, + 55, + 231, + 248 + ], + "type": "image", + "image_path": "8595f6c1d3f5b9f5ca6213460466e45899c0598e3416bc2d2f7ee36eab2772ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 259, + 555, + 338 + ], + "lines": [ + { + "bbox": [ + 54, + 259, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 54, + 259, + 555, + 338 + ], + "type": "text", + "content": "Figure 2. Framework Illustration. Left: On the penultimate layer, the centered ID clusters reside near their predicted class weight vectors (marked by stars) while OOD samples reside separated, as shown by UMAP. Middle: ID and OOD samples are separated by pScore (Equation 6), which measures feature proximity to weight vectors. Also, ID samples tend to be further from the origin, illustrated with L1 norms. Right: ID samples cluster near a simplex Equiangular Tight Framework, illustrated with black arrows denoting weight vectors. We detect OOD by thresholding on pScore, selecting blue-shaded hypercones centered at weight vectors, with OOD samples outside these areas. We also filter OOD samples characterized by smaller feature norms. Left & Middle present a practical off-the-shelf CIFAR-10 ResNet-18 classifier with OOD set SVHN. Right depicts our scheme on a three-class classifier with 2D penultimate space." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 238, + 54, + 375, + 245 + ], + "blocks": [ + { + "bbox": [ + 238, + 54, + 375, + 245 + ], + "lines": [ + { + "bbox": [ + 238, + 54, + 375, + 245 + ], + "spans": [ + { + "bbox": [ + 238, + 54, + 375, + 245 + ], + "type": "image", + "image_path": "7f429d91582501a5649a1c6b82c50bbd45271cb5c29f87478478e5e44bfe608d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 384, + 53, + 548, + 251 + ], + "blocks": [ + { + "bbox": [ + 384, + 53, + 548, + 251 + ], + "lines": [ + { + "bbox": [ + 384, + 53, + 548, + 251 + ], + "spans": [ + { + "bbox": [ + 384, + 53, + 548, + 251 + ], + "type": "image", + "image_path": "a8fca05def74634e008a26cabfccee6e98843b0919f3926b47046085e06c12ae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 358, + 294, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 358, + 294, + 407 + ], + "spans": [ + { + "bbox": [ + 54, + 358, + 294, + 407 + ], + "type": "text", + "content": "To this end, we revisit the well-established observation that penultimate-layer ID features tend to form clusters, while OOD features reside apart [20, 39, 40], and take it a step further by asking:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 79, + 411, + 272, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 411, + 272, + 422 + ], + "spans": [ + { + "bbox": [ + 79, + 411, + 272, + 422 + ], + "type": "text", + "content": "Where do features of ID samples form clusters?" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 426, + 295, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 426, + 295, + 581 + ], + "spans": [ + { + "bbox": [ + 54, + 426, + 295, + 581 + ], + "type": "text", + "content": "Leveraging Neural Collapse [32], we first examine the theoretical landscape with models trained beyond zero training error. We first show that, as a deterministic effect of Neural Collapse[32] penultimate-layer features of training samples converge toward the weight vectors of the predicted class—the last-layer weights of the corresponding class—after being centered by training feature mean. Additionally, Neural Collapse demonstrates that training features conform to a simplex Equiangular Tight Frame (ETF) (Equation 1), representing the maximum achievable separation between equiangular vectors. This spatial structure, illustrated in Figure 2 Right, requires features to be sufficiently distant from the origin." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 582, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 582, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 582, + 295, + 713 + ], + "type": "text", + "content": "Building on the insights from the theoretical convergence landscape, we propose two hypotheses about the geometric structure of ID clusters and OOD samples in practical models. Specifically, for ID test samples drawn from the same distribution as training samples, we expect a similar trend of clustering behavior toward the weight vectors and the ETF structure. In contrast, OOD samples, which are not part of the training process, lack the alignment with weight vectors and the spatial expansion necessary to form an ETF. Consequently, the model is unlikely to align unseen OOD features with weight vectors or place them far" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 358, + 553, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 358, + 553, + 454 + ], + "spans": [ + { + "bbox": [ + 313, + 358, + 553, + 454 + ], + "type": "text", + "content": "enough from the origin to exhibit ETF-like behavior. Although complete Neural Collapse requires strict conditions, such as prolonged training, its convergence trend and corresponding geometric patterns of ID features are consistently observed during training across diverse architectures and classification tasks (see Appendix 13 and [11]). Thus, our hypotheses regarding ID clusters and OOD samples are expected to hold without requiring complete Neural Collapse." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 455, + 555, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 455, + 555, + 682 + ], + "spans": [ + { + "bbox": [ + 313, + 455, + 555, + 682 + ], + "type": "text", + "content": "To validate the hypotheses, we trace a model's training stages in Figure 1, where centered ID samples consistently cluster closer to the weight vectors than OOD samples. By epoch 50, such a pattern already enables effective OOD detection for SVHN samples1. This shows that the trend of Neural Collapse emerges early, validating the practical effectiveness of our hypothesis before full collapse in mature models. We reinforce this observation with a UMAP [28] visualization of an off-the-shelf CIFAR-10 classifier with a ResNet-18 backbone, shown in Figure 2 Left. ID features cluster near the predicted class weights (marked by stars), while OOD features remain distant. Additionally, as [53] shows that weight vectors form an ETF, our observations also support our second hypothesis: ID features are driven to structure the ETF, while OOD features lack the incentive to expand in space. This explains the well-established observation [17, 39, 40] that OOD features tend to reside closer to the origin, providing an alternative to the model confidence interpretation in [33]." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "type": "text", + "content": "Our method (Section 3.3) achieves an AUROC of 94.44, outperforming the 91.27 softmax-confidence baseline (AUROC defined in Section 4)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15425" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 335 + ], + "type": "text", + "content": "Based on our understanding, we design an efficient and versatile OOD detector. We first leverage feature proximity to the weight vectors to characterize ID clustering, effectively incorporating class-specific information and reducing the computational cost. Specifically, we define an angle-based proximity score as the norm of the projection of the weight vector of the predicted class onto the centered sample feature. As shown in Figure 2 Middle, our proximity score can effectively separate ID/OOD. A higher score indicates closer proximity and a lower chance of OOD-ness. Geometrically, thresholding on the score selects hyper-cones centered at the weight vector, as illustrated in Figure 2 Right. Complementing the proximity score's contingency on ID clustering, we also consider feature distance to the origin. Specifically, ID features tend to reside further from the origin as they expand in space to form an ETF, whereas OOD features tend to reside near the origin, as illustrated by Figure 2 Right. Using the L1 norm as an example metric, we observe that ID features can be separated from OOD features, as supported by Figure 2 Middle. Combining both aspects, we propose Neural Collapse Inspired OOD Detector (NCI)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 336, + 296, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 336, + 296, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 336, + 296, + 504 + ], + "type": "text", + "content": "Notably, prior methods, e.g., KNN [39], focus on ID clustering, without explicitly incorporating feature distance to the origin. Such approaches fall short in scenarios like ImageNet benchmarks but yield superior performance in CIFAR-10 benchmarks in Table 1a. Conversely, methods such as Energy [24], Energy-based ASH [8], and, Energy-based Scale [47] inherently utilize feature distance to the origin by considering log-sum-exp of logits, yet largely overlook ID clustering. These approaches excel in scenarios like ImageNet, but perform sub-optimally in others, e.g., CIFAR-10. Through the lens of Neural Collapse, we explain, connect, and complete a wide range of prior methods under a holistic view, resulting in reduced latency and generalization discrepancies." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 506, + 253, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 506, + 253, + 517 + ], + "spans": [ + { + "bbox": [ + 67, + 506, + 253, + 517 + ], + "type": "text", + "content": "We summarize our main contributions below:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 521, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 641 + ], + "type": "text", + "content": "- Understanding and Observation: By analyzing ID clustering through the trend of Neural Collapse, we discover that penultimate-layer features of ID test examples cluster around the weight vectors of the predicted class after being centered by the training feature mean. Additionally, we explain that ID features tend to lie farther from the origin due to Neural Collapse, where they form a simplex Equiangular Tight Frame (ETF) structure. Notably, our findings hold without requiring full Neural Collapse convergence." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "type": "text", + "content": "- OOD Detector: We leverage feature proximity to the weight vectors of predicted classes for OOD detection, integrating class-specific information. Complementary to feature clustering, we propose to detect OOD samples by thresholding the feature distance to the origin." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "content": "- Experimental Analysis: We evaluate NCI across diverse" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 321, + 72, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 72, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 321, + 72, + 555, + 180 + ], + "type": "text", + "content": "classification tasks (CIFAR-10, CIFAR-100, ImageNet) and model architectures (ResNet, DenseNet [15], ViT [9], Swin [26]). Rather than focusing on individual benchmarks, NCI reduces the generalization discrepancies and improves the overall effectiveness. We also show that incorporating weight vectors not only significantly improves upon prior clustering-based methods but also reduces latency to a minimal level, matching the basic softmax-confidence detector." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 189, + 429, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 189, + 429, + 202 + ], + "spans": [ + { + "bbox": [ + 313, + 189, + 429, + 202 + ], + "type": "text", + "content": "2. Problem Statement" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": "We consider a data space " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": ", a class set " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": ", and a classifier " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "f: \\mathcal{X} \\to \\mathcal{C}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": ", which is trained on samples i.i.d. drawn from joint distribution " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_{\\mathcal{X}\\mathcal{C}}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": ". We denote the marginal distribution of " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_{\\mathcal{X}\\mathcal{C}}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\mathbb{P}^{in}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": ". And samples drawn from " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\mathbb{P}^{in}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": " are In-Distribution (ID) samples. In practice, the classifier " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": " may encounter " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathcal{X}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": " yet is not drawn from " + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\mathbb{P}^{in}" + }, + { + "bbox": [ + 313, + 209, + 555, + 293 + ], + "type": "text", + "content": ". We say such samples are Out-of-Distribution (OOD)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 293, + 556, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 556, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 556, + 342 + ], + "type": "text", + "content": "In this work, we focus on detecting OOD samples from classes unseen during training, for which the classifiers cannot make meaningful predictions. The OOD detector " + }, + { + "bbox": [ + 313, + 293, + 556, + 342 + ], + "type": "inline_equation", + "content": "D:\\mathcal{X}\\to \\{\\mathrm{ID},\\mathrm{OOD}\\}" + }, + { + "bbox": [ + 313, + 293, + 556, + 342 + ], + "type": "text", + "content": " is commonly constructed as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 342, + 555, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 555, + 431 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 555, + 431 + ], + "type": "inline_equation", + "content": "D(\\pmb {x}) = \\left\\{ \\begin{array}{ll}\\mathrm{ID} & \\mathrm{if} s(\\pmb {x})\\geq \\tau \\\\ \\mathrm{OOD} & \\mathrm{if} s(\\pmb {x}) < \\tau \\end{array} \\right." + }, + { + "bbox": [ + 313, + 342, + 555, + 431 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 342, + 555, + 431 + ], + "type": "inline_equation", + "content": "s:\\mathcal{X}\\to \\mathbb{R}" + }, + { + "bbox": [ + 313, + 342, + 555, + 431 + ], + "type": "text", + "content": " is a score function of design and " + }, + { + "bbox": [ + 313, + 342, + 555, + 431 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 313, + 342, + 555, + 431 + ], + "type": "text", + "content": " is the threshold. Considering the diverse application scenarios, an ideal OOD detector should be efficient and generalizable. Thus, we leverage insights from Neural Collapse to achieve reduced computational costs and minimize generalization discrepancies." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 436, + 555, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 436, + 555, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 436, + 555, + 464 + ], + "type": "text", + "content": "3. OOD Detection through the Lens of Neural Collapse" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 468, + 554, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 554, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 554, + 552 + ], + "type": "text", + "content": "In this section, we re-examine the observation in [20, 39] that ID features tend to form clusters while OOD features deviate from the clusters. We suggest that the clustering phenomenon can reflect the trend of the Neural Collapse [32] in practical models. From our understanding, we develop a post-hoc OOD detector with enhanced efficiency and effectiveness." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 558, + 534, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 534, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 534, + 571 + ], + "type": "text", + "content": "3.1. Neural Collapse: Convergence Landscape" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "type": "text", + "content": "Neural Collapse, first observed in [32], occurs on the penultimate layer across canonical classification settings. To formally introduce the concept, we use " + }, + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "type": "inline_equation", + "content": "h_c^i" + }, + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "type": "text", + "content": " to denote the penultimate layer feature of the " + }, + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "type": "inline_equation", + "content": "i_{th}" + }, + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "type": "text", + "content": " training sample with ground truth / predicted label " + }, + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 574, + 554, + 646 + ], + "type": "text", + "content": ", Neural Collapse is framed in relation to" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 647, + 553, + 694 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 313, + 647, + 553, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 553, + 670 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 553, + 670 + ], + "type": "text", + "content": "- feature global mean, " + }, + { + "bbox": [ + 313, + 647, + 553, + 670 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{G} = \\mathrm{Ave}_{i,c}\\left(\\pmb{h}_{c}^{i}\\right)" + }, + { + "bbox": [ + 313, + 647, + 553, + 670 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 647, + 553, + 670 + ], + "type": "inline_equation", + "content": "\\mathrm{Ave}(\\cdot)" + }, + { + "bbox": [ + 313, + 647, + 553, + 670 + ], + "type": "text", + "content": " is the average operation;" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 670, + 514, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 670, + 514, + 683 + ], + "spans": [ + { + "bbox": [ + 313, + 670, + 514, + 683 + ], + "type": "text", + "content": "- feature class means, " + }, + { + "bbox": [ + 313, + 670, + 514, + 683 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{c} = \\mathrm{Ave}_{i}\\left(\\pmb{h}_{c}^{i}\\right)" + }, + { + "bbox": [ + 313, + 670, + 514, + 683 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 670, + 514, + 683 + ], + "type": "inline_equation", + "content": "\\forall c\\in \\mathcal{C}" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 683, + 422, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 683, + 422, + 694 + ], + "spans": [ + { + "bbox": [ + 313, + 683, + 422, + 694 + ], + "type": "text", + "content": "- within-class covariance," + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 355, + 700, + 520, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 700, + 520, + 715 + ], + "spans": [ + { + "bbox": [ + 355, + 700, + 520, + 715 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {W} = \\operatorname {A v e} _ {i, c} \\left(\\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {c}\\right) \\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {c}\\right) ^ {T}\\right);", + "image_path": "a485ab1cc1a51ed767d8486074152eb5f2d3cf61020d07909b012bd47566f058.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15426" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 73, + 171, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 73, + 171, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 73, + 171, + 83 + ], + "type": "text", + "content": "- between-class covariance," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 95, + 89, + 264, + 104 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 89, + 264, + 104 + ], + "spans": [ + { + "bbox": [ + 95, + 89, + 264, + 104 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {B} = \\operatorname {A v e} _ {c} \\left(\\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) \\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) ^ {T}\\right);", + "image_path": "f729996f6cd7825ce764d008da8fdddf3be42c21825348f43ec403bdc754ddd9.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "text", + "content": "- linear classification head, i.e. the last layer of the NN, " + }, + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "inline_equation", + "content": "\\arg \\max_{c\\in \\mathcal{C}}\\boldsymbol{w}_c^T\\boldsymbol {h} + b_c" + }, + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}_{c}" + }, + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "inline_equation", + "content": "b_{c}" + }, + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "text", + "content": " are parameters corresponding to class " + }, + { + "bbox": [ + 55, + 109, + 295, + 144 + ], + "type": "inline_equation", + "content": "c" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 144, + 280, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 280, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 280, + 156 + ], + "type": "text", + "content": "Neural Collapse comprises four inter-related behaviors:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 156, + 295, + 192 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 67, + 156, + 283, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 156, + 283, + 169 + ], + "spans": [ + { + "bbox": [ + 67, + 156, + 283, + 169 + ], + "type": "text", + "content": "(NC1) Within-class variability collapse: " + }, + { + "bbox": [ + 67, + 156, + 283, + 169 + ], + "type": "inline_equation", + "content": "\\Sigma_W\\rightarrow 0" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 169, + 295, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 169, + 295, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 169, + 295, + 192 + ], + "type": "text", + "content": "(NC2) Convergence to a simplex Equiangular Tight Frame (ETF):" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 61, + 197, + 241, + 211 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 197, + 241, + 211 + ], + "spans": [ + { + "bbox": [ + 61, + 197, + 241, + 211 + ], + "type": "interline_equation", + "content": "\\left|\\left|\\left| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\right|\\right| _ {2} - \\left|\\left| \\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G} \\right|\\right| _ {2} \\right|\\rightarrow 0, \\forall c, c ^ {\\prime}", + "image_path": "99ea118a0d04c0b21dcadf94cb5fa82ae355db7943a6b48da88d038402baf5b0.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 62, + 213, + 295, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 213, + 295, + 240 + ], + "spans": [ + { + "bbox": [ + 62, + 213, + 295, + 240 + ], + "type": "interline_equation", + "content": "\\frac {\\left(\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}\\right) ^ {T} \\left(\\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G}\\right)}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2} \\| \\boldsymbol {\\mu} _ {c ^ {\\prime}} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\frac {| \\mathcal {C} |}{| \\mathcal {C} | - 1} \\delta_ {c, c ^ {\\prime}} - \\frac {1}{| \\mathcal {C} | - 1} \\tag {1}", + "image_path": "ca1b4ddb47ba5183daf3328177db9213081281421ea5a3aef3c3221a55a256c2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 244, + 227, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 244, + 227, + 256 + ], + "spans": [ + { + "bbox": [ + 55, + 244, + 227, + 256 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 244, + 227, + 256 + ], + "type": "inline_equation", + "content": "\\delta_{c,c'}" + }, + { + "bbox": [ + 55, + 244, + 227, + 256 + ], + "type": "text", + "content": " is the Kronecker delta symbol." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 67, + 257, + 218, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 257, + 218, + 268 + ], + "spans": [ + { + "bbox": [ + 67, + 257, + 218, + 268 + ], + "type": "text", + "content": "(NC3) Convergence to self-duality:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 116, + 271, + 236, + 295 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 271, + 236, + 295 + ], + "spans": [ + { + "bbox": [ + 116, + 271, + 236, + 295 + ], + "type": "interline_equation", + "content": "\\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\mathbf {0}", + "image_path": "0e27866be853d5803753e27fe3e7fedcb621fc8bafac7e357d8bbec403ea10cf.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 67, + 297, + 257, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 297, + 257, + 308 + ], + "spans": [ + { + "bbox": [ + 67, + 297, + 257, + 308 + ], + "type": "text", + "content": "(NC4) Simplification to nearest class center:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 86, + 313, + 264, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 313, + 264, + 331 + ], + "spans": [ + { + "bbox": [ + 86, + 313, + 264, + 331 + ], + "type": "interline_equation", + "content": "\\arg \\max _ {c \\in \\mathcal {C}} \\boldsymbol {w} _ {c} ^ {T} \\boldsymbol {h} + b _ {c} \\rightarrow \\arg \\min _ {c \\in \\mathcal {C}} \\| \\boldsymbol {h} - \\boldsymbol {\\mu} _ {c} \\| _ {2}", + "image_path": "e4516a59e8a9f8fdda3f4583a7968736c73ecf5ee735ce8a31d117e172c347e1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 331, + 296, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 296, + 402 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 296, + 402 + ], + "type": "text", + "content": "We first remark on (NC2) that an ETF achieves the maximum separation possible for globally centered equiangular vectors [32] and extends in space, as visualized in Figure 2 Right. Since training features converge towards an ETF, they need to have sufficient norms to accommodate the spatial arrangement." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 403, + 296, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 403, + 296, + 440 + ], + "spans": [ + { + "bbox": [ + 55, + 403, + 296, + 440 + ], + "type": "text", + "content": "We next build on (NC1) and (NC3) to demonstrate that training features converge towards the weight vectors of the linear classification head, up to a scaling factor." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 444, + 296, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 444, + 296, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 444, + 296, + 468 + ], + "type": "text", + "content": "Theorem 3.1. (NC1) and (NC3) imply that for any sample " + }, + { + "bbox": [ + 55, + 444, + 296, + 468 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 444, + 296, + 468 + ], + "type": "text", + "content": " and its predicted class " + }, + { + "bbox": [ + 55, + 444, + 296, + 468 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 444, + 296, + 468 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 133, + 471, + 294, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 471, + 294, + 484 + ], + "spans": [ + { + "bbox": [ + 133, + 471, + 294, + 484 + ], + "type": "interline_equation", + "content": "\\left(\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}\\right)\\rightarrow \\lambda \\boldsymbol {w} _ {c}, \\tag {2}", + "image_path": "c568723cb186a5e0097883aed68a32ef8041c7d45e0cebdc721f94ba63b7ae63.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 56, + 487, + 294, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 487, + 294, + 514 + ], + "spans": [ + { + "bbox": [ + 56, + 487, + 294, + 514 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 56, + 487, + 294, + 514 + ], + "type": "inline_equation", + "content": "\\lambda = \\frac{\\|\\pmb{\\mu}_c - \\pmb{\\mu}_G\\|_2}{\\|\\pmb{w}_c\\|_2}" + }, + { + "bbox": [ + 56, + 487, + 294, + 514 + ], + "type": "text", + "content": " in the Terminal Phase of Training." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": "Proof. Considering that " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "(\\pmb{h}_c^i - \\pmb{\\mu}_c)(\\pmb{h}_c^i - \\pmb{\\mu}_c)^T" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " is positive semi-definite for any " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_W \\to \\mathbf{0}" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " thus implies " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "(\\pmb{h}_c^i - \\pmb{\\mu}_c)(\\pmb{h}_c^i - \\pmb{\\mu}_c)^T \\to \\mathbf{0}" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "\\pmb{h}_c^i - \\pmb{\\mu}_c \\to \\mathbf{0}" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "inline_equation", + "content": "\\forall i, c" + }, + { + "bbox": [ + 55, + 517, + 296, + 567 + ], + "type": "text", + "content": ". With algebraic manipulations, we have" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 91, + 568, + 295, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 568, + 295, + 595 + ], + "spans": [ + { + "bbox": [ + 91, + 568, + 295, + 595 + ], + "type": "interline_equation", + "content": "\\frac {\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\rightarrow \\mathbf {0}, \\forall i, c \\tag {3}", + "image_path": "5934a980368a03532c1a3fae8d169ccf1d391729d1b8d6ff748cb31b2b45ad13.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 55, + 599, + 224, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 599, + 224, + 611 + ], + "spans": [ + { + "bbox": [ + 55, + 599, + 224, + 611 + ], + "type": "text", + "content": "Applying the triangle inequality, we have" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 55, + 615, + 171, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 615, + 171, + 643 + ], + "spans": [ + { + "bbox": [ + 55, + 615, + 171, + 643 + ], + "type": "interline_equation", + "content": "\\left| \\frac {\\boldsymbol {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {\\boldsymbol {G}}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {\\boldsymbol {G}} \\| _ {2}} - \\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} \\right| \\leq", + "image_path": "0764a86283bacbb3acce6442c0f79f6bf71f1a4ce7504d3a582efccd6e269f7d.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 55, + 644, + 301, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 644, + 301, + 680 + ], + "spans": [ + { + "bbox": [ + 55, + 644, + 301, + 680 + ], + "type": "interline_equation", + "content": "\\left| \\frac {\\mathbf {h} _ {c} ^ {i} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\right| + \\left| \\frac {\\boldsymbol {w} _ {c}}{\\| \\boldsymbol {w} _ {c} \\| _ {2}} - \\frac {\\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G}}{\\| \\boldsymbol {\\mu} _ {c} - \\boldsymbol {\\mu} _ {G} \\| _ {2}} \\right|. \\tag {4}", + "image_path": "5252c722d9c92633097eef42739bab143434b0a91c92c715ea2d7c06177c2031.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 55, + 680, + 296, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 680, + 296, + 716 + ], + "spans": [ + { + "bbox": [ + 55, + 680, + 296, + 716 + ], + "type": "text", + "content": "Since both terms on the RHS converge to 0, as demonstrated by (3) and (NC3), it follows that the LHS also converges to 0." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": "3.2. Trend of Neural Collapse & Geometric Structure of the ID Clusters" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 101, + 553, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 101, + 553, + 220 + ], + "spans": [ + { + "bbox": [ + 313, + 101, + 553, + 220 + ], + "type": "text", + "content": "While the complete collapse occurs during the Terminal Phase of Training (TPT) where training error vanishes and the training loss is trained towards zero, it is observed in [11] that the trend of Neural Collapse establishes in the early stages of training. We thus suggest that the clustering behavior of ID features observed in off-the-shelf models reflects a trend of Neural Collapse, corresponding to the within-class variability collapse (NC1). In light of this, we use the landscape of Neural Collapse revealed in Theorem 3.1 and (NC2) to examine the geometry of ID clusters." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "spans": [ + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "type": "text", + "content": "Following our discussion in Section 1, we we hypothesize and validate with pre-trained models that (1) ID features tend to cluster closer to the weight vectors compared to OOD features; (2) ID clusters tend to reside further from the origin, as necessitated by their spatial structure. Particularly, Neural Collapse highlights the importance of centering for characterizing ID clustering with weight vectors. We thus validate our hypothesis in a CIFAR-10 classifier with ResNet-18 backbone in Figure 1, computing over the ID set (CIFAR-10) and OOD set (SVHN) the average cosine similarity between the centered feature " + }, + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "type": "inline_equation", + "content": "\\pmb{h}^i - \\pmb{\\mu}_G" + }, + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "type": "text", + "content": " and the weight vector " + }, + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "type": "inline_equation", + "content": "\\pmb{w}_c" + }, + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "type": "text", + "content": " of the predicted class " + }, + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 221, + 554, + 365 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 374, + 374, + 553, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 374, + 553, + 401 + ], + "spans": [ + { + "bbox": [ + 374, + 374, + 553, + 401 + ], + "type": "interline_equation", + "content": "\\operatorname {A v e} _ {i} \\left(\\frac {\\left(\\boldsymbol {h} ^ {i} - \\boldsymbol {\\mu} _ {G}\\right) \\cdot \\boldsymbol {w} _ {c}}{\\| \\boldsymbol {h} ^ {i} - \\boldsymbol {\\mu} _ {G} \\| _ {2} \\| \\boldsymbol {w} _ {c} \\| _ {2}}\\right) \\tag {5}", + "image_path": "97a8a7e1c2dcdcaf6ca9e00f7d31815be1c1af6a2b9d1287a7ffd27dab1b7593.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 409, + 476, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 409, + 476, + 421 + ], + "spans": [ + { + "bbox": [ + 313, + 409, + 476, + 421 + ], + "type": "text", + "content": "3.3. Out-of-Distribution Detection" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "text", + "content": "Based on our understanding, we design an efficient and versatile OOD detector. Specifically, we propose to detect OOD based on feature proximity to the weight vectors of the predicted class. For the proximity metric, we avoid Euclidean-based metrics as they require estimating the scaling factor " + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "text", + "content": " in Equation 2. This estimation tends to be imprecise for general classifiers which may cease training prior to convergence, resulting in suboptimal performance of Euclidean-based metrics shown in Appendix 8. Instead, we design an angle-based metric, adjusted for class-wise difference. Specifically, we propose to quantify the proximity as the norm of projection of the weight vector " + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "inline_equation", + "content": "w_{c}" + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "text", + "content": " onto the centered feature " + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "inline_equation", + "content": "h - \\mu_G" + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 427, + 555, + 594 + ], + "type": "text", + "content": " corresponds to the predicted class, i.e.," + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 359, + 604, + 553, + 618 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 604, + 553, + 618 + ], + "spans": [ + { + "bbox": [ + 359, + 604, + 553, + 618 + ], + "type": "interline_equation", + "content": "\\mathrm {p S c o r e} = \\cos \\left(\\boldsymbol {w} _ {c}, \\boldsymbol {h} - \\boldsymbol {\\mu} _ {G}\\right) \\| \\boldsymbol {w} _ {c} \\| _ {2}, \\tag {6}", + "image_path": "c653009c3d461a5ac8a61fe54769e526eceaefd81e4b3116a58de1aef287e7e8.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 627, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 627, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 627, + 554, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 627, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\cos(\\boldsymbol{w}_c, \\boldsymbol{h} - \\boldsymbol{\\mu}_G) = \\frac{(\\boldsymbol{h} - \\boldsymbol{\\mu}_G) \\cdot \\boldsymbol{w}_c}{\\|\\boldsymbol{h} - \\boldsymbol{\\mu}_G\\|_2 \\| \\boldsymbol{w}_c\\|_2}" + }, + { + "bbox": [ + 313, + 627, + 554, + 714 + ], + "type": "text", + "content": ". A higher pScore indicates closer proximity to the weight vector and thus a lower chance of OOD-ness. Geometrically, thresholding on pScore selects infinite hyper-cones centered at the weight vectors, as illustrated in Figure 2 Right. Within the same predicted class, pScore is proportional to the cosine similarity. Across different classes, pScore adapts" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15427" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 178 + ], + "type": "text", + "content": "to class-wise difference by selecting wider hyper-cones for classes with larger weight vectors, which tend to have larger decision regions. As shown in Appendix 8, our pScore with class-wise adjustment outperforms vanilla cosine similarity. Notably, our pScore incorporates class-specific information into characterizing ID clustering by using the weight vectors of the predicted class. This brings in additional gain in detection effectiveness, as we shall see in Section 4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "spans": [ + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "type": "text", + "content": "While pScore enhances efficiency and effectiveness, its performance is intrinsically contingent on the strength of ID clustering. Such contingency, widely exhibited by clustering-based methods [20, 39, 40], poses challenges on classifiers with less pronounced ID clustering, such as ImageNet ResNet-50 in Section 4.1. To mitigate such discrepancy, we complement pScore by using the distance of ID clusters to the origin. Specifically, we enhance our proximity score by incorporating feature norms to filter out OOD near the origin, as illustrated in Figure 2 Right. Taking L1 norm as an example, we define our detection score as " + }, + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "type": "inline_equation", + "content": "\\mathrm{pScore} + \\alpha \\| h\\| _1" + }, + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "type": "text", + "content": " controls the filtering strength and can be selected from a validation set as detailed in Section 4. We discuss the effect of different orders of " + }, + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 56, + 180, + 295, + 383 + ], + "type": "text", + "content": "-norm in Section 4.3. Thresholding on the detection score, we have Neural Collapse Inspired OOD Detector (NCI): A lower score indicates a higher chance of OOD-ness." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 384, + 295, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 295, + 444 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 295, + 444 + ], + "type": "text", + "content": "NCI has " + }, + { + "bbox": [ + 55, + 384, + 295, + 444 + ], + "type": "inline_equation", + "content": "O(P)" + }, + { + "bbox": [ + 55, + 384, + 295, + 444 + ], + "type": "text", + "content": " complexity, where " + }, + { + "bbox": [ + 55, + 384, + 295, + 444 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 384, + 295, + 444 + ], + "type": "text", + "content": " is the penultimate layer dimension. The complexity theoretically ensures computational scalability of NCI on large models. Empirically, NCI maintains inference latency comparable to the vanilla softmax-confidence detector, as shown in Section 4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 453, + 135, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 453, + 135, + 467 + ], + "spans": [ + { + "bbox": [ + 55, + 453, + 135, + 467 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "type": "text", + "content": "In this section, we extensively evaluate NCI across classification tasks: CIFAR-10, CIFAR-100 (see App. 12), ImageNet, as well as model architectures: ResNet, DenseNet (see App. 12), ViT, Swin. We compare NCI against thirteen baseline methods. While NCI may not achieve the best performance on individual benchmarks, it mitigates the existing generalization discrepancies and achieves the best overall performance with minimal latency. Following the OpenOOD benchmark [49], we evaluate on six OOD sets for CIFAR-10 and CIFAR-100 classifiers and five for ImageNet classifiers. Performance is evaluated using two widely recognized metrics: the False Positive Rate at " + }, + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "type": "text", + "content": " True Positive Rate (FPR95) and the Area Under the Receiver Operating Characteristic Curve (AUROC). Lower FPR95 and higher AUROC values indicate better performance. We also report the per-image inference latency (in milliseconds) evaluated on a Tesla T4 GPU. In our experiments, other than the ablation study in Section 4.3, we use the L1-norm as the filtering term and select the filtering strength " + }, + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}" + }, + { + "bbox": [ + 55, + 474, + 295, + 713 + ], + "type": "text", + "content": " based on a" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "validation set generated per pixel from Gaussian " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "N(0,1)" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": ", following [37, 38]. Our method and all baselines are post-hoc methods, while all models used are off-the-shelf and do not require complete Neural Collapse convergence. For detailed setups and additional baselines, please see Appendix 7 and Appendix 11, respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 152, + 541, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 152, + 541, + 164 + ], + "spans": [ + { + "bbox": [ + 313, + 152, + 541, + 164 + ], + "type": "text", + "content": "4.1. Mitigating Discrepencies across ID Datasets" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "text", + "content": "We first assess NCI and baselines across CIFAR-10 and ImageNet classification tasks. The two tasks provide an ideal test bed for evaluating versatility, as they drastically differ in input resolution, number of classes, and classification accuracy. We use ResNets from OpenOOD [49]: ResNet-18 for CIFAR-10 (95.06% accuracy) and ResNet-50 for ImageNet (76.65% accuracy). Based on validation results, we set the filter strength " + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "text", + "content": "-norm to " + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "inline_equation", + "content": "10^{-2}" + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "text", + "content": " for CIFAR-10 experiments and " + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 313, + 168, + 553, + 276 + ], + "type": "text", + "content": " for ImageNet experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 277, + 553, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 553, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 553, + 372 + ], + "type": "text", + "content": "Datasets For CIFAR-10 experiments, We follow the OpenOOD split of ID test set and evaluate on the OpenOOD benchmarks, including CIFAR-100 [18], Tiny ImageNet [19], MNIST [6], SVHN [31], Texture [4], and Places365 [50]. For ImageNet experiments, we follow the OpenOOD split of ID test set and evaluate on the OpenOOD benchmarks, including SSB-hard [42], NINCO [2], iNaturalist [41], Texture [4], and OpenImage-O [43]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 372, + 553, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 553, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 553, + 491 + ], + "type": "text", + "content": "Baselines In Table 1a, we compare our method with thirteen baselines. Some baselines focus more on the CIFAR-10 Benchmark while others focus more focused on the ImageNet Benchmark. Therefore, we categorize the baselines, besides the vanilla confidence-based MSP [12], into two groups: the \"CIFAR-10 Strong\" baselines, including ODIN [21], Energy [24], Mahalanobis [20], KNN[39], ViM [43], and fDBD [22]; the \"ImageNet Strong\" baselines, including GradNorm [17], NECO [1], React [38], Dice [37], ASH [8], Scale [47]. See Appendix 9 for details of the baselines." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 492, + 553, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 553, + 611 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 553, + 611 + ], + "type": "text", + "content": "Performance Table 1a shows that NCI consistently ranks top-three across benchmarks, whereas baselines exhibit greater variability. To assess overall performance, we averaged AUROC across benchmarks, which are of a similar range. Table 1b highlights that NCI improves overall performance compared to strong baselines on individual benchmarks. Further, NCI is as efficient as MSP, as shown in Table " + }, + { + "bbox": [ + 313, + 492, + 553, + 611 + ], + "type": "inline_equation", + "content": "1\\mathrm{b}^2" + }, + { + "bbox": [ + 313, + 492, + 553, + 611 + ], + "type": "text", + "content": " , which enhances efficiency compared to strong baselines. This aligns with the analysis in Section 3 and Appendix 9. We highlight the following pairs of comparison:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 613, + 553, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 553, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 553, + 696 + ], + "type": "text", + "content": "- NCI v.s. NCI w/o filter: On the CIFAR-10 classifier, strong ID clustering allows our method to rank top-3 without filtering. Conversely, on the ImageNet ResNet50, weaker ID clustering (see Appendix 13) makes norm-based filtering crucial for reducing generalization discrepancy. Complete Neural Collapse occurs on neither model while NCI remains effective." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 324, + 702, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 702, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 324, + 702, + 545, + 713 + ], + "type": "text", + "content": "2Running time of KNN on ImageNet are copied from Table 4 in [39]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15428" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 89, + 549, + 555 + ], + "blocks": [ + { + "bbox": [ + 55, + 62, + 553, + 84 + ], + "lines": [ + { + "bbox": [ + 55, + 62, + 553, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 62, + 553, + 84 + ], + "type": "text", + "content": "Table 1. NCI reduces discrepancies and improves overall performance on CIFAR-10 and ImageNet benchmarks with minimal latency. CIFAR-10 uses ResNet-18 and ImageNet uses ResNet-50." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 89, + 549, + 555 + ], + "lines": [ + { + "bbox": [ + 65, + 89, + 549, + 555 + ], + "spans": [ + { + "bbox": [ + 65, + 89, + 549, + 555 + ], + "type": "table", + "html": "
    Methods43.27 75.388481002439923.64838686167.7080703663.8184824Evaluation under FPR9591.8673.3187.07
    MSP*92.6653.081.3043.2774.3423.6476.0725.8294.1634.9638.1142.4737.2074.4956.8843.3460.8750.1357.14
    CIFAR-10 StrongODIN77.0020.0523.8324.0668.6167.7070.3638.8176.8368.1635.9649.2446.6755.38
    Energy*40.496618.668819.4935.1214.5141.4334.8565.2476.5462.2931.3043.5738.0950.46
    MDS49.04737.244656.9974.8376.07194.165538.1195.19529138684.2336.0590.7743.48
    KNN94.88485.041720.6529.60924.92460.32827.3883.3679584940.8043.2744.2768.82
    ViM62.947915.952930.16160.922156.081481.49501.6580.41556082930.6848.2532.8243.29
    fDBD*59.73633.979457.4356.99236.40202.151145.5477.2855821322.0026.8429.9443.48
    ImageNet StrongGradNorm64.5494.8985.4191.6598.0992.4682.8478.2466.9032.0343.2768.4660.31
    NECO72.6362.4715.5230.1660.1256.0849.5072.3155.0827.0548.2533.4247.22
    ReAct67.4070.0083.6484.5977.8981.6151.1277.5555.8216.7229.6432.5842.46
    DICE83.6435.13768.8984.9062.42147.7075.8577.9651.8633.3747.5847.8334.06
    ASH43.5432.62528.0882.6534.0177.86261.6173.6656.5114.0434.3829.1545.08
    Scale43.60032.64429.0168.6984.38986.136270.7567.725358669.5223.3928.1739.96
    NCI w/o filter*51.9243.5432.6328.9226.5334.0136.2682.1456.4124.1134.3230.9445.58
    87.NCI51.8392.68092.46289.0892688.92393.98836.2773.2979598614.3182.4930.9889.00
    CIFAR-10 Strong82.1895.2484.5886.9485.07Evaluation under AUROC7789.0083.58
    MSP*87.1998838797.6998.4678.8925.8889.8372.0979709588.4188.7084.8684.04
    ODIN82.189835585.2484.7886.9485.0786.2671.7455.4191.1779.9088.2383.58
    Energy*86.3688.8094.3291.7989.4789.2590.0072.0879.7090.6388.7089.0684.04
    MDS61.2994.2699.1793.1677.4052.4769.4143.9279.6461.8279.9460.8082.55
    KNN89.7394.7694.2092.6715.9391.7788.1862.5778.6386.4197.9787.0484.44
    AWI87.7599.8287.4592.5495.10989.49361.8865.5482.6089.5692.9190.5086.05
    SDH*87.186897298.0185.2490.6490.06669.3670.6674826093.7092.0591.1786.03
    ImageNet Strong85.DTorm54.4396513792.24588.565289.540.5093.8989.0884.8283.93
    NGO85.509888386.1298.2388.0635.89320.0374.7982.4292.1990.8087.93
    ReAct85.939882996.6288.1289.3890.35279.3273.0381.7396.3492.0491.8783.80
    DICE77.0179.6790.3790.0281.8974.6782.2770.1376.0192.5492.0488.2683.80
    ASH74.1176.4483.1673.4677.4579.8977.4172.8983.4597.0796.9093.2688.71
    Scale80.5793.1986.0683.4888.8986.0177.4177.3485.3798.0296.7593.9590.28
    * N17w23 filter*87.9391.5090.8092.1790.7490.4766.8180.2092.6791.8790.5184.41
    NCI87.9289.6591.5090.8092.1790.7490.4673.9083.4696.9596.6392.9888.56
    ", + "image_path": "49b60c61805db77a6296e80e03fc5f5d1f9d0aed6252a021efd0d6a975f8f354.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 100, + 586, + 511, + 643 + ], + "blocks": [ + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "lines": [ + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "spans": [ + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "type": "text", + "content": "(a) NCI ranks top-three in both benchmarks, while baselines show greater variability. " + }, + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "type": "text", + "content": " denotes better performance. Bold marks best, underline 2nd / 3rd. Methods with " + }, + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 55, + 559, + 555, + 580 + ], + "type": "text", + "content": " are hyperparameter-free. Scores, except for the most recent baselines - fDBD, NECO, ASH, Scale - are from OpenOOD [49]." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 100, + 586, + 511, + 643 + ], + "lines": [ + { + "bbox": [ + 100, + 586, + 511, + 643 + ], + "spans": [ + { + "bbox": [ + 100, + 586, + 511, + 643 + ], + "type": "table", + "html": "
    PerformanceMSPNECOKNNViMASHScaleNCI (ours)
    CIFAR-10 Latency0.530.701.950.700.530.530.54
    ImageNet Latency6.859.5510.319.557.027.016.84
    Avg AUROC85.6987.9887.3888.1683.0688.1589.51
    ", + "image_path": "6f827f23819736bdc9d7f8c08e0262ac4e3ccbbda6ceb3cf846e81b89f6868c5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 654, + 555, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 555, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 555, + 675 + ], + "type": "text", + "content": "(b) NCI improves the overall performance while reducing latency compared to strong baselines. AUROC averaged across CIFAR-10 and ImageNet benchmarks in Table 1a, with per image latency reported." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 680, + 294, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 680, + 294, + 704 + ], + "spans": [ + { + "bbox": [ + 55, + 680, + 294, + 704 + ], + "type": "text", + "content": "- NCI v.s. KNN: Compared to KNN, NCI significantly reduces the latency (Table 1b). Notably, without filtering, our" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 322, + 680, + 555, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 680, + 555, + 704 + ], + "spans": [ + { + "bbox": [ + 322, + 680, + 555, + 704 + ], + "type": "text", + "content": "hyperparameter-free score outperforms KNN with tuned parameters on most benchmarks (Table 1a, Table 2a &" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 18, + 287, + 36, + 298 + ], + "type": "aside_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 18, + 287, + 36, + 298 + ], + "spans": [ + { + "bbox": [ + 18, + 287, + 36, + 298 + ], + "type": "text", + "content": "NCI" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 18, + 522, + 36, + 534 + ], + "type": "aside_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 18, + 522, + 36, + 534 + ], + "spans": [ + { + "bbox": [ + 18, + 522, + 36, + 534 + ], + "type": "text", + "content": "NCI" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15429" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 573, + 295, + 612, + 320 + ], + "type": "aside_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 573, + 295, + 612, + 320 + ], + "spans": [ + { + "bbox": [ + 573, + 295, + 612, + 320 + ], + "type": "text", + "content": "NC NCI" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 573, + 526, + 589, + 536 + ], + "type": "aside_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 573, + 526, + 589, + 536 + ], + "spans": [ + { + "bbox": [ + 573, + 526, + 589, + 536 + ], + "type": "text", + "content": "NCI" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 597, + 541, + 612, + 552 + ], + "type": "aside_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 597, + 541, + 612, + 552 + ], + "spans": [ + { + "bbox": [ + 597, + 541, + 612, + 552 + ], + "type": "text", + "content": "NC" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 92, + 541, + 281 + ], + "blocks": [ + { + "bbox": [ + 55, + 62, + 555, + 84 + ], + "lines": [ + { + "bbox": [ + 55, + 62, + 555, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 62, + 555, + 84 + ], + "type": "text", + "content": "Table 2. NCI reduces discrepancies and improves overall performance on ImageNet benchmarks across ViT B/16 and Swin v2 classifiers. Bold marks best, underline 2nd" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 92, + 541, + 281 + ], + "lines": [ + { + "bbox": [ + 70, + 92, + 541, + 281 + ], + "spans": [ + { + "bbox": [ + 70, + 92, + 541, + 281 + ], + "type": "table", + "html": "
    MethodsImageNet OpenOOD Benchmark (ViT B/16)ImageNet OpenOOD Benchmark (Swin v2)
    Near-OODFar-OODAvgNear-OODFar-OODAvg
    SSB-hardNINCOiNaturalistTextureOpenImage-OSSB-hardNINCOiNaturalistTextureOpenImage-O
    Evaluation under FPR95 ↓
    KNN63.4139.716.8443.1218.3034.2890.8883.1676.8860.4367.1475.70
    ViM51.9137.105.6739.2917.5130.3090.3483.8970.9865.9068.6875.96
    ASH48.7845.4211.0042.3720.3335.5893.8093.9387.5897.2791.1492.74
    Scale45.0732.045.4940.5913.1527.2790.7475.7248.7395.1064.5575.97
    NCI w/o filter50.9430.685.9346.6114.9229.8186.7773.1147.9875.3059.3069.67
    NCI46.7333.796.0842.0914.7928.7985.5872.0645.2571.5354.7265.83
    Evaluation under AUROC ↑
    KNN81.4890.0098.6796.2396.2391.4462.5069.7478.3585.1967.1475.88
    ViM87.3992.5698.9890.8096.8293.3160.9972.3083.3679.6182.5275.76
    ASH90.6090.8898.0495.9795.9793.1458.8758.2858.1846.1861.3256.57
    Scale89.6793.2398.9697.2097.2094.0962.4878.9788.8867.0886.1476.71
    NCI w/o filter87.1693.1598.8796.8096.8093.2664.5376.7388.0779.6385.3978.87
    NCI88.8692.8898.7996.8396.8393.6467.5378.9989.6881.4387.4280.97
    ", + "image_path": "cc79a2c826442d5c75edebbad5b503d0c015f731ab9f443cfcad3251946e1bd8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 147, + 302, + 465, + 331 + ], + "blocks": [ + { + "bbox": [ + 134, + 286, + 476, + 297 + ], + "lines": [ + { + "bbox": [ + 134, + 286, + 476, + 297 + ], + "spans": [ + { + "bbox": [ + 134, + 286, + 476, + 297 + ], + "type": "text", + "content": "(a) NCI boosts Swin v2 while maintaining ViT effectiveness compared to baselines, even without filtering." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 147, + 302, + 465, + 331 + ], + "lines": [ + { + "bbox": [ + 147, + 302, + 465, + 331 + ], + "spans": [ + { + "bbox": [ + 147, + 302, + 465, + 331 + ], + "type": "table", + "html": "
    PerformanceKNNViMASHScaleNCI (ours)
    Avg AUROC83.6684.8474.8685.4087.31
    ", + "image_path": "b2899ad6922706625e4296fcb24545f29c9fff5bee4dace95a7c9923f24add1b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 144, + 339, + 465, + 350 + ], + "lines": [ + { + "bbox": [ + 144, + 339, + 465, + 350 + ], + "spans": [ + { + "bbox": [ + 144, + 339, + 465, + 350 + ], + "type": "text", + "content": "(b) NCI improves the overall performance. AUROC averaged across two architectures in Table 2a." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 63, + 367, + 295, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 367, + 295, + 390 + ], + "spans": [ + { + "bbox": [ + 63, + 367, + 295, + 390 + ], + "type": "text", + "content": "Table 9), highlighting the benefit of using class-specific information." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 391, + 295, + 572 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 55, + 391, + 295, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 391, + 295, + 475 + ], + "spans": [ + { + "bbox": [ + 55, + 391, + 295, + 475 + ], + "type": "text", + "content": "- NCI v.s. ASH / Scale: Compared to both, NCI delivers competitive performance on ImageNet and significantly improves CIFAR-10, enhancing overall performance (Table 1b). Also, ASH and Scale introduce in a small delay on the ImageNet benchmark due to activation sorting, with larger activation dimensions likely widening the latency gap on larger models." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 476, + 295, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 476, + 295, + 572 + ], + "spans": [ + { + "bbox": [ + 55, + 476, + 295, + 572 + ], + "type": "text", + "content": "- NCI v.s. NECO: NECO [1] is motivated by Neural Collapse. Like NCI with filtering, NECO uses max-logit and incorporates distance to the origin. However, NECO exclusively analyzes features, requiring expensive matrix multiplication and leading to higher inference latency (Table 1b). Conversely, NCI explores the interplay between features and the classification head, integrating class-specific information to improve both efficiency and effectiveness." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 586, + 293, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 293, + 600 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 293, + 600 + ], + "type": "text", + "content": "4.2. Mitigating Discrepancies across Architectures" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": "Next, we study two transformer-based models: ViT B/16 [9] and Swin-v2 [26], both finetuned on ImageNet, achieving an accuracy of " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "81.14\\%" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "82.94\\%" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": " respectively. We follow the setup of the OpenOOD ImageNet Benchmark in Section 4.1. Based on validation results, we set the filter strength " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": " norm to " + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 54, + 605, + 295, + 714 + ], + "type": "text", + "content": " for both classifiers. In Table 2, we observe strong baselines suffer on Swin v2, echoing the observations in [1]. Conversely, our NCI, even without filtering, improves baseline performance on Swin" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 367, + 555, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 367, + 555, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 367, + 555, + 390 + ], + "type": "text", + "content": "v2. Filtering further enhances the performance, leading to improved overall performance (Table 2b)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 391, + 555, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 555, + 440 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 555, + 440 + ], + "type": "text", + "content": "We further aggregate in Table 2 with experiments on ResNet (Table 1) and DenseNet (Table 9) and report the average AUROC in Table 3. NCI significantly boosts the overall performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 445, + 484, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 445, + 484, + 458 + ], + "spans": [ + { + "bbox": [ + 313, + 445, + 484, + 458 + ], + "type": "text", + "content": "4.3. Ablation on the Filtering Effect" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "text", + "content": "In Table 4, we assess different orders of " + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "text", + "content": "-norm as the filtering term, compared to the " + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "text", + "content": " norm used so far. To ensure a fair comparison, we report the best performance from the filter strengths " + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "inline_equation", + "content": "\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}" + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "text", + "content": ". The rest of the setup follows the ImageNet benchmarks in Section 4.1. As shown in Table 4, filtering with " + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 312, + 462, + 555, + 641 + ], + "type": "text", + "content": " norm achieves the best performance across OOD datasets, aligning with prior observations [17, 33]. Meanwhile, we observe that in rare scenarios, e.g., a ResNet-18 on CIFAR-10, the L1 norm cannot effectively characterize OOD's proximity to the origin, leading to no extra performance gain compared to simply thresholding on pScore. In these cases, our algorithm benefits from its ability to automatically select a low filter strength based on validation results, effectively disregarding the filtering term." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "We also test the sensitivity of NCI to filtering strength " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " in Table 5. As shown on the ImageNet ResNet50 benchmark, performance remains stable for " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " values within the same scale. Given this insensitivity, we select hyperparameters from four scales " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " without extensive finetuning in this work." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 86, + 0, + 555, + 25 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 0, + 555, + 25 + ], + "spans": [ + { + "bbox": [ + 86, + 0, + 555, + 25 + ], + "type": "text", + "content": "NCI w/o filter 87.16 93.15 98.87 93.26 64.53 76.73 79.63 78.87 88.86 92.88 98.79 93.64 67.53 78.99 81.43 80.97" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15430" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 133, + 79, + 474, + 116 + ], + "blocks": [ + { + "bbox": [ + 130, + 62, + 479, + 74 + ], + "lines": [ + { + "bbox": [ + 130, + 62, + 479, + 74 + ], + "spans": [ + { + "bbox": [ + 130, + 62, + 479, + 74 + ], + "type": "text", + "content": "Table 3. NCI improves the overall performance, averaged across Table 1a, Table 2a & Table 9." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 133, + 79, + 474, + 116 + ], + "lines": [ + { + "bbox": [ + 133, + 79, + 474, + 116 + ], + "spans": [ + { + "bbox": [ + 133, + 79, + 474, + 116 + ], + "type": "table", + "html": "
    PerformanceKNNViMASHScaleNCI (ours)
    Avg AUROC86.0685.9681.2486.888.57
    Across All Benchmarks
    ", + "image_path": "ba68d92a491284bdb1969a0d46c5d5d8287479006b2160c8fc495fb8967ae2fe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 182, + 302, + 228 + ], + "blocks": [ + { + "bbox": [ + 55, + 134, + 295, + 178 + ], + "lines": [ + { + "bbox": [ + 55, + 134, + 295, + 178 + ], + "spans": [ + { + "bbox": [ + 55, + 134, + 295, + 178 + ], + "type": "text", + "content": "Table 4. Ablation on filtering norm on ImageNet OpenOOD Benchmark with ResNet-50 backbone. AUROC score is reported (higher is better). BoldNCO denotes the best. Filtering with L1 norm outperforms alternative choice of norms across OOD datasets." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 182, + 302, + 228 + ], + "lines": [ + { + "bbox": [ + 56, + 182, + 302, + 228 + ], + "spans": [ + { + "bbox": [ + 56, + 182, + 302, + 228 + ], + "type": "table", + "html": "
    FilteringSSB-hardNINCOiNaturalistTextureOpenImage-O
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    ", + "image_path": "96e18ab07c10a4fad7b3fe4601f8ec46e6764229e2d481b429ad121464af8251.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 53, + 274, + 299, + 353 + ], + "blocks": [ + { + "bbox": [ + 53, + 240, + 296, + 273 + ], + "lines": [ + { + "bbox": [ + 53, + 240, + 296, + 273 + ], + "spans": [ + { + "bbox": [ + 53, + 240, + 296, + 273 + ], + "type": "text", + "content": "Table 5. Sensitivity of NCI to filtering strength. Average AUROC on ImageNet ResNet-50 Benchmark reported. Performance was stable within the same scale." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 274, + 299, + 353 + ], + "lines": [ + { + "bbox": [ + 53, + 274, + 299, + 353 + ], + "spans": [ + { + "bbox": [ + 53, + 274, + 299, + 353 + ], + "type": "table", + "html": "
    Filtering Magnitude αAvg AUROC
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    0.8 x 10-388.55
    1 x10-388.59
    1.2 x 10-388.50
    1.4 x 10-388.23
    ", + "image_path": "f7db2f89154090eb11caee38b02221dcf53e42c6bd3c23e2ecc2b01143787b4d.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 373, + 296, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 373, + 296, + 482 + ], + "spans": [ + { + "bbox": [ + 55, + 373, + 296, + 482 + ], + "type": "text", + "content": "We further apply L1-norm based filtering to KNN to see if this perspective can mitigate the discrepancy of clustering-based methods in general. In Table 63, we report the best performance of KNN from filter strengths " + }, + { + "bbox": [ + 55, + 373, + 296, + 482 + ], + "type": "inline_equation", + "content": "\\{10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\\}" + }, + { + "bbox": [ + 55, + 373, + 296, + 482 + ], + "type": "text", + "content": ". We observe a significant performance gain from adding the filter, which further validates our understanding of ID clustering landscape from Neural Collapse. Note that our method outperforms the standalone " + }, + { + "bbox": [ + 55, + 373, + 296, + 482 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 55, + 373, + 296, + 482 + ], + "type": "text", + "content": " norm as well as KNN, before and after filtering." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 58, + 542, + 302, + 605 + ], + "blocks": [ + { + "bbox": [ + 55, + 490, + 296, + 536 + ], + "lines": [ + { + "bbox": [ + 55, + 490, + 296, + 536 + ], + "spans": [ + { + "bbox": [ + 55, + 490, + 296, + 536 + ], + "type": "text", + "content": "Table 6. Effectiveness of our filtering scheme on KNN. Performance gain validates our understanding of ID clustering landscape. NCI outperforms KNN and standalone " + }, + { + "bbox": [ + 55, + 490, + 296, + 536 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 55, + 490, + 296, + 536 + ], + "type": "text", + "content": " norm. AUROC reported (higher is better). Bold highlights the best result." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 542, + 302, + 605 + ], + "lines": [ + { + "bbox": [ + 58, + 542, + 302, + 605 + ], + "spans": [ + { + "bbox": [ + 58, + 542, + 302, + 605 + ], + "type": "table", + "html": "
    SSB-hardNINCOiNaturalistTextureOpenImage-OAVG
    L168.8068.2890.8688.1678.4778.91
    KNN62.5779.6486.4196.4987.0482.43
    KNN + L164.2981.7692.7697.8590.1786.37
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    ", + "image_path": "30652f748d3c8d14f46ad31456537ae363c8ec905a15af8116c593644cb24eaf.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 620, + 143, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 620, + 143, + 634 + ], + "spans": [ + { + "bbox": [ + 55, + 620, + 143, + 634 + ], + "type": "text", + "content": "5. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 641, + 296, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 677 + ], + "type": "text", + "content": "OOD Detection Extensive research has focused on OOD detection algorithms. One line of work is post-hoc and builds upon pre-trained models. For example, [13, 21, 22," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 141, + 555, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 141, + 555, + 225 + ], + "spans": [ + { + "bbox": [ + 313, + 141, + 555, + 225 + ], + "type": "text", + "content": "24, 37, 38, 46] design OOD score over the output space of a classifier. Meanwhile, [20] and [39] measure OOD-ness from the perspective of ID clustering in feature space. Our work extends the observation that ID features tend to cluster from the perspective of Neural Collapse. While existing work is more focused on certain classification tasks, our proposed OOD detector is tested to be highly versatile." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 225, + 556, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 225, + 556, + 334 + ], + "spans": [ + { + "bbox": [ + 313, + 225, + 556, + 334 + ], + "type": "text", + "content": "Others [34-36, 52] explore the regularization of OOD detection in training. For example, [7, 14] propose OOD-specific architecture whereas [16, 44] design OOD-specific training loss. [40] brings attention to representation learning for OOD detection and proposes an OOD-specific contrastive learning scheme. Our work does not belong to this school of thought and is not restricted to specific training schemes or architecture. Notably, as shown in Appendix 10, our NCI can also benefit from training-time algorithms." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 347, + 556, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 347, + 556, + 492 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 556, + 492 + ], + "type": "text", + "content": "Neural Collapse Neural Collapse was first observed in [32]. During Neural Collapse, the penultimate layer features collapse to class means, the class means and the classifier collapses to a simplex equiangular tight framework, and the classifier simplifies to adopt the nearest class-mean decision rule. Further work has provided theoretical justification for the emergence of Neural Collapse [10, 30, 51, 53]. Application-wise, [53] derives an efficient training algorithm inspired by Neural Collapse. Our concurrent work [1] also leverages Neural Collapse for OOD detection but overlooks class-specific information revealed by Neural Collapse, which is central to our approach." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 521, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 556, + 713 + ], + "type": "text", + "content": "This work leverages insights from Neural Collapse to propose a novel OOD detector. Specifically, we study the phenomenon that ID features tend to form clusters whereas OOD features reside far away. Inspired by the trend of Neural Collapse prevalent on practical models, we hypothesize and validate that ID features tend to cluster near weight vectors. We also explain why ID features tend to reside further from the origin and complement our method from this perspective. Experiments show the effectiveness of our method on practical models without requiring the complete convergence of Neural Collapse. Further, our method improves the overall performance with minimal latency across diverse benchmarks. We hope our work can inspire future work to explore the interplay between features and weight vectors for OOD detection and other research problems such as calibration and adversarial robustness." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 683, + 296, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 683, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 683, + 296, + 715 + ], + "type": "text", + "content": "Note that we report our run of KNN here to ensure a fair evaluation of the filtering effect. Our results are very similar to the OpenOOD results reported in Table 1a, with only marginal differences." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15431" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 138 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 138 + ], + "type": "text", + "content": "We would like to express our sincere gratitude to Yubing Jian for conducting several experiments that made significant contributions to this work and for his valuable discussions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 148, + 115, + 161 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 148, + 115, + 161 + ], + "spans": [ + { + "bbox": [ + 56, + 148, + 115, + 161 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 169, + 296, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 61, + 169, + 296, + 212 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 169, + 296, + 212 + ], + "spans": [ + { + "bbox": [ + 61, + 169, + 296, + 212 + ], + "type": "text", + "content": "[1] Mouin Ben Ammar, Nacim Belkhir, Sebastian Popescu, Antoine Manzanera, and Gianni Franchi. 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Advances in Neural Information Processing Systems, 34:29820-29834, 2021. 2, 8, 3" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15433" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_content_list.json b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a74e63bfab0f447e2911160ca1e96eed510eee49 --- /dev/null +++ b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_content_list.json @@ -0,0 +1,1628 @@ +[ + { + "type": "text", + "text": "Detection-Friendly Nonuniformity Correction: A Union Framework for Infrared UAV Target Detection", + "text_level": 1, + "bbox": [ + 91, + 130, + 906, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Houzhang Fang $^{1\\dagger}$ , Xiaolin Wang $^{1\\dagger}$ , Zengyang Li $^{1}$ , Lu Wang $^{1}$ , Qingshan Li $^{1}$ , Yi Chang $^{2}$ , Luxin Yan $^{2}$ , Xidian University ${}^{2}$ Huazhong University of Science and Technology", + "bbox": [ + 107, + 202, + 887, + 244 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "houzhangfang@xidian.edu.cn,wxl@stu.xidian.edu.cn，22009200694@stu.xidian.edu.cn，wanglu@xidian.edu.cn， qshli@mail.xidian.edu.cn，yichang@hust.edu.cn，yanluxin@hust.edu.cn", + "bbox": [ + 99, + 246, + 893, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 309, + 326, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Infrared unmanned aerial vehicle (UAV) images captured using thermal detectors are often affected by temperature-dependent low-frequency nonuniformity, which significantly reduces the contrast of the images. Detecting UAV targets under nonuniform conditions is crucial in UAV surveillance applications. Existing methods typically treat infrared nonuniformity correction (NUC) as a preprocessing step for detection, which leads to suboptimal performance. Balancing the two tasks while enhancing detection-beneficial information remains challenging. In this paper, we present a detection-friendly union framework, termed UniCD, that simultaneously addresses both infrared NUC and UAV target detection tasks in an end-to-end manner. We first model NUC as a small number of parameter estimation problem jointly driven by priors and data to generate detection-conducive images. Then, we incorporate a new auxiliary loss with target mask supervision into the backbone of the infrared UAV target detection network to strengthen target features while suppressing the background. To better balance correction and detection, we introduce a detection-guided self-supervised loss to reduce feature discrepancies between the two tasks, thereby enhancing detection robustness to varying nonuniformity levels. Additionally, we construct a new benchmark composed of 50,000 infrared images in various nonuniformity types, multi-scale UAV targets and rich backgrounds with target annotations, called IRBFD. Extensive experiments on IRBFD demonstrate that our UniCD is a robust union framework for NUC and UAV target detection while achieving real-time processing capabilities. Dataset can be available at https://github.com/IVPLaboratory/UniCD.", + "bbox": [ + 88, + 340, + 485, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 823, + 223, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unmanned aerial vehicle (UAV) detection based on infrared imaging is an important perception technology for moni", + "bbox": [ + 89, + 848, + 482, + 880 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5fbf300760c62ddb6872d9a836a9614dcff20d136d0052c2545583056ecbd2c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 308, + 898, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/75e6ed8f9bef16d42f6c8461d316bd619b5b6baa4f31223a14f059ec034cd962.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 364, + 898, + 421 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8f26bbef8ece87b0e35d76644659eaa05bd7dc798261b39eee98636ae4e5b950.jpg", + "image_caption": [ + "Figure 1. Three main categories of methods for UAV target detection in nonuniformity conditions. (a) Direct: detection models [10] are directly applied to nonuniformity degraded images. (b) Separate: correction model [15] serves as a pre-processing step, correcting images before passing them to detectors [10]. (c) Union: correction and detection are processed simultaneously in a unified framework. Previous methods solely concentrates on optimizing one task. Our UniCD concurrently emphasizes the joint enhancement of correction quality and detection accuracy." + ], + "image_footnote": [], + "bbox": [ + 517, + 421, + 897, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "toring UAV in both day and night scenarios. However, the thermal radiation from the optical lens and the camera housing causes the acquired infrared UAV images to often suffer from the temperature-dependent low-frequency nonuniformity effects [15, 23, 26, 33] (See the left column of Fig. 1). The optics-caused nonuniformity effect is also referred to as the bias field, which reduces the image contrast. Moreover, the infrared UAV targets typically have weak features and complex backgrounds [4, 5]. Nonuniformity bias field further exacerbates the difficulty of UAV target detection. Infrared nonuniformity correction (NUC) and target detection have achieved significant advancements in recent years [2, 4, 5, 17, 23, 28]. Previous methods focus on one aspect of the tasks and address the two tasks independently. As far as we know, no work considers the practical problem: infrared UAV target detection under the nonuniformity conditions.", + "bbox": [ + 511, + 623, + 908, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To solve this problem, a simple strategy is to detect [10]", + "bbox": [ + 532, + 885, + 906, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author. †Equal contribution.", + "bbox": [ + 107, + 886, + 357, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11898", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "UAV targets directly on the degraded bias field images (See Fig. 1(a)), which easily leads to miss detection due to the weakening of target information. Another typical approach is the correction-then-detection paradigm (See Fig. 1(b)). NUC methods [15, 22, 26] are first adopted to remove the nonuniformity bias field, and the corrected images are then passed to the target detectors [4, 5, 10]. However, the existing NUC methods have limitations. Specifically, model-based NUC methods rely heavily on handcrafted features to model the images and bias fields, making them prone to overfitting the image content and thus struggle to handle complex or severely degraded bias fields [26]. Deep learning (DL)-based NUC methods depend on complex architectures and a large number of real input-output image pairs, which limits their practicality [2, 23]. Additionally, the NUC lacks supervision from the detection module to enhance detection-conducive information. Recently, joint methods for processing low-level images and high-level vision have already been proposed [11, 12, 18]. However, they are primarily designed for object detection under adverse weather conditions.", + "bbox": [ + 89, + 90, + 480, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome the above limitations, in this paper, we propose a detection-friedly union framework, termed UniCD, that simultaneously tackles both infrared bias field correction and UAV target detection. On the one hand, because of the spatially smooth nature of the bias field, we model it by the high-order bivariate polynomial [16, 22, 26], which can effectively fit the nonuniform bias field with different scales. As a result, accurately estimating the optimal polynomial coefficients is essential for ensuring the performance of bias field correction. In this work, we formulate bias field correction as a problem of predicting a small number of polynomial coefficients jointly driven by priors and data, which can be easily learned by a very lightweight network. The bias field has spatially continuous low-frequency characteristics, making transformer-based architecture well-suited for modeling this component. Additionally, we also integrate convolutional neural networks (CNNs) to capture the local details of the bias field. By incorporating parametric prior modeling and low-dimensional data-driven prediction, our approach avoids dependence on handcrafted features and real input-output data pairs, significantly improving correction performance. On the other hand, existing DL-based detection methods mainly focus on designing complex model architectures for extracting features [4, 5, 17, 19, 28, 31, 32]. We further introduce auxiliary loss with target mask supervision at different stages of the backbone in the infrared UAV target detection network without increasing computational complexity. Integrating this loss enhances the discriminative features of UAV targets while suppressing the background, thereby improving detection performance.", + "bbox": [ + 91, + 412, + 482, + 881 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To balance correction and detection, we introduce a", + "bbox": [ + 109, + 885, + 480, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "detection-guided self-supervised loss to reduce feature discrepancies between the correction and detection tasks. This loss enforces feature similarity between the corrected image and the reference image, both extracted by the detection backbone, thus ensuring high correction quality while enhancing features that are beneficial for detection. Our NUC model can also be flexibly integrated as a scalable module with existing detectors for infrared image bias field correction. Furthermore, we construct the bias field benchmark, IRBFD, consisting of 50,000 infrared images with varying nonuniformity types, multi-scale UAV targets, and rich backgrounds with target annotations, called IRBFD. Experimental results on the IRBFD demonstrate that UniCD outperforms state-of-the-art (SOTA) combined correction and detection methods in terms of precision and recall.", + "bbox": [ + 511, + 90, + 903, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this work can be summarized as:", + "bbox": [ + 532, + 325, + 887, + 339 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel detection-friedly union framework, termed UniCD, that can simultaneously deal with NUC and infrared UAV target detection in an end-to-end manner. To the best of our knowledge, this is the first work to address both issues in a unified framework.", + "- We for the first time model nonuniformity bias field correction as a problem of predicting a small number of hyperparameters jointly driven by priors and data, which can be easily performed with a very lightweight network.", + "- We establish the first large benchmark called IRBFD to facilitate the research in the area of nonuniformity correction and infrared UAV target detection, which consists of 50,000 manually labeled infrared images with various nonuniformity levels, multi-scale UAV targets and rich backgrounds with target annotations." + ], + "bbox": [ + 513, + 348, + 903, + 573 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 611, + 653, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Nonuniformity Correction in Infrared Images", + "text_level": 1, + "bbox": [ + 511, + 643, + 898, + 660 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NUC methods for removing the bias field are broadly divided into two main categories: model-driven methods and data-driven methods. Model-driven methods typically leverage the prior constraints of the bias field and the images to remove the nonuniformity effects [1, 15, 16, 22, 25, 26]. However, these methods rely on handcrafted features with carefully tuned hyper-parameters, limiting their practicality in real-world applications. Data-driven DL methods [2, 14, 23] have gained increasing attention. However, DL-based correction models are often complex and rely on large amounts of training data with real correction labels, which restricts their widespread application in practical scenarios [6, 24, 27]. In contrast, we formulate a novel lightweight correction model driven by both parametric priors and data, which converges more easily.", + "bbox": [ + 511, + 674, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11899", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4431972c4a7c6240fac7b3ec1817d3911f3b4569f199542073978a8faa7880d1.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed UniCD. Our UniCD integrates a bias field prediction network with an infrared UAV target detection network. These two components are fused into a unified pipeline and trained end-to-end. The target enhancement and background suppression (TEBS) loss is introduced to enhance UAV target features while suppressing the background. The bias robust loss is employed to balance correction and detection." + ], + "image_footnote": [], + "bbox": [ + 112, + 85, + 883, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Infrared UAV Target Detection", + "text_level": 1, + "bbox": [ + 89, + 303, + 364, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In recent years, many methods have been developed to detect infrared UAV targets [3-5, 19, 21]. Infrared UAV targets are challenging due to their weak imaging features and complex backgrounds [7, 8, 29]. TAD [19] leveraged the inconsistent motion cues between UAV targets and the background to detect potential targets. Fang et al. [3] formulated the UAV detection task as a residual image prediction by learning the mapping from input images to residual images. DAGNet [5] introduced attention mechanisms to adaptively enhance the network's ability to discriminate between UAVs and the background. DANet [4] constructed a dynamic attention network for UAVs to enhance feature extraction capabilities. However, the above methods primarily focus on designing complex network structures for improving detection performance, while rarely exploring how to better enhance feature representation without increasing computational complexity. We focus on introducing new auxiliary losses into the backbone to boost the model's ability to represent UAV target features while suppressing the background.", + "bbox": [ + 91, + 325, + 483, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Joint Low-Level Image Processing and High-Level Vision Tasks", + "text_level": 1, + "bbox": [ + 89, + 636, + 482, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, joint approaches for image enhancement and object detection have emerged to further improve detection performance on low-quality images. One category of these methods utilized encoder-decoder architectures for image enhancement [12], but these modules are complex and hinder real-time performance. Another approach uses classical mathematical models for enhancement, replacing manually designed parameters with predictions from deep networks. IA-YOLO [18] integrated an adaptive enhancement strategy with YOLOv3 [20] via a differentiable image processing module, improving detection in foggy conditions. BAD-Net [11] introduced a dual-branch structure to minimize the impact of poor dehazing performance on the detection module. However, the above methods are developed for visible light images degraded by adverse weather condi", + "bbox": [ + 89, + 674, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tions. To the best of our knowledge, no work has explored handling both NUC and UAV target detection for infrared imaging within a single framework. We propose an end-to-end framework to simultaneously improve both correction and detection performance.", + "bbox": [ + 511, + 304, + 906, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Detection-Friendly Union Method", + "text_level": 1, + "bbox": [ + 511, + 393, + 821, + 410 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overall Architecture", + "text_level": 1, + "bbox": [ + 511, + 417, + 709, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we propose a novel network architecture, UniCD, as shown in Fig. 2. The UniCD leverages a lightweight prediction network to estimate the bias field and then passes the corrected image to a UAV detection network tailored for UAV targets. Additionally, during the joint training of image correction and detection tasks, we employ a detection-guided self-supervised loss to minimize feature discrepancies between the two tasks. Finally, we construct a new dataset, IRBFD, to validate our approach.", + "bbox": [ + 511, + 439, + 906, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Prior- and Data-Driven Nonuniformity Correction", + "text_level": 1, + "bbox": [ + 511, + 585, + 903, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Infrared UAV images captured by thermal detectors often suffer from low-frequency nonuniformity, which significantly impacts target detection performance. Existing model-driven correction methods often struggle to handle complex non-uniformities, while deep learning-based methods suffer from high network complexity. To address these issues, we propose a lightweight correction network that combines parametric prior knowledge with the strong learning capabilities of deep neural networks. The network architecture is shown in Fig. 2.", + "bbox": [ + 511, + 621, + 905, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generally, the degraded infrared image can be represented as follows [2, 16]:", + "bbox": [ + 511, + 773, + 903, + 801 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nY = C + B, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 663, + 806, + 903, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $Y$ , $C$ , and $B$ represent the degraded image, the clear image, and the bias field, respectively. Thus, once $B$ is available, the corrected image $R$ can be obtained as $Y - B$ . Under ideal conditions, $R$ is theoretically equivalent to the clear image $C$ . The bias field $B$ possesses a", + "bbox": [ + 511, + 824, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11900", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "spatially smooth property, allowing us to model it using the following bivariate polynomial:", + "bbox": [ + 89, + 90, + 482, + 122 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nB \\left(x _ {i}, y _ {j}\\right) = \\sum_ {t = 0} ^ {D} \\sum_ {s = 0} ^ {D - t} a _ {t, s} x _ {i} ^ {t} y _ {j} ^ {s} = \\mathbf {m} ^ {\\top} \\mathbf {a}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 126, + 482, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $(x_{i},y_{j})$ , $D$ , and $\\mathbf{m}$ denote the image coordinates, the degree of the polynomial, and the column vector holding the monomial terms, respectively. The column vector $\\mathbf{a}$ represents the coefficients of the polynomial formed by concatenating $\\{a_{t,s}\\}$ . To reduce the redundancy of the basic plane and the computational complexity of higher-order models, we set the degree $D$ to 3.", + "bbox": [ + 89, + 172, + 482, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Accurate estimation of the polynomial coefficients $\\mathbf{a}$ is crucial for improving bias field correction performance. In this work, we design a lightweight bias field prediction network that can estimate the model parameters accurately and efficiently.", + "bbox": [ + 89, + 279, + 482, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our NUC module, we first downsample the degraded image $Y$ by a factor of two, resulting in the downsampled image $Y_{\\mathrm{down}}$ . Then, we utilize the global bias field encoder (GBFE) and the local bias field encoder (LBFE) to extract features at different granularities. The GBFE, inspired by the RSTB [13] module, includes two Swin Transformer layers with the hidden layer channel dimension reduced to 16. The LBFE consists of two spatial attention modules in series, allowing it to capture localized features more effectively. The global and local features, $F_{\\mathrm{global}}$ and $F_{\\mathrm{local}}$ , are fused to form the final feature representation $F_{\\mathrm{fused}}$ :", + "bbox": [ + 89, + 354, + 483, + 521 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\text {f u s e d}} = \\mathrm {G B F E} \\left(Y _ {\\text {d o w n}}\\right) + \\mathrm {L B F E} \\left(Y _ {\\text {d o w n}}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 527, + 482, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, the fused features $F_{\\mathrm{fused}}$ pass through five $3 \\times 3$ convolutional layers (Conv5) and a fully connected (FC) layer to predict the final coefficient vector $\\hat{\\mathbf{a}}$ :", + "bbox": [ + 89, + 549, + 482, + 595 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {a}} = \\operatorname {F C} \\left(\\operatorname {C o n v} _ {5} \\left(F _ {\\text {f u s e d}}\\right)\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 601, + 480, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This approach enables the network to adaptively adjust to inputs with varying levels of degradation, effectively predicting the coefficient vector $\\hat{\\mathbf{a}}$ for bias field correction.", + "bbox": [ + 89, + 623, + 482, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Analysis. Compared to existing model-driven methods, our approach avoids reliance on hand-crafted features. Compared to existing data-driven methods, our approach transforms the high-dimensional image space prediction into a low-dimensional data-driven problem with a few hyperparameters, effectively reducing computational complexity and improving correction performance.", + "bbox": [ + 89, + 669, + 482, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Loss Function. We calculate the mean absolute error (MAE) loss between the predicted coefficients $\\hat{\\mathbf{a}}$ and the predefined coefficients $\\mathbf{a}$ to minimize the discrepancy between them. The MAE loss is defined as:", + "bbox": [ + 89, + 775, + 482, + 834 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {c o r} = \\frac {1}{N} \\| \\hat {\\mathbf {a}} - \\mathbf {a} \\| _ {2} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 838, + 482, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N$ is the total number of elements in the vector $\\mathbf{a}$ . By minimizing this loss, we improve the accuracy of the", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6d060feb0f5305d0e4109b13ce90ea5f067bf03ca63eacbb14849c506d77039a.jpg", + "image_caption": [ + "Figure 3. Calculation of the proposed feature enhancement and background suppression (TEBS) loss." + ], + "image_footnote": [], + "bbox": [ + 521, + 88, + 901, + 170 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "corrected image, making it closer to the ideal clear image. This loss function is used to pre-train the NUC module separately, serving as the initial weights for the joint training of correction and detection.", + "bbox": [ + 511, + 207, + 906, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Mask-Supervised Infrared UAV Detector", + "text_level": 1, + "bbox": [ + 511, + 276, + 864, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We select DANet [4] as our baseline detector, which constructs a multi-scale dynamic perception network to address the challenges of multi-scale variations in UAV targets. Infrared UAV targets typically have weak features and complex backgrounds, and existing methods often enhance feature extraction through complex model architectures. In this work, we design an auxiliary loss function for further target enhancement and background suppression (TEBS) without increasing network complexity, as illustrated in Figs. 2 and 3.", + "bbox": [ + 511, + 297, + 905, + 448 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we first convert the bounding boxes of the ground-truth into a binary mask $M$ , assigning a value of 1 to the target region and 0 to the background region:", + "bbox": [ + 511, + 449, + 905, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM (x, y) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} (x, y) \\in \\text {t a r g e t r e g i o n}, \\\\ 0, & \\text {i f} (x, y) \\in \\text {b a c k g r o u n d r e g i o n}. \\end{array} \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 496, + 903, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This mask is then used to compute a binary cross-entropy loss with the feature maps $F_{i}$ from the $i$ -th stage of the backbone network. The TEBS loss $L_{\\mathrm{TEBS}}$ is obtained by summing the losses from four stages of the backbone and averaging:", + "bbox": [ + 511, + 534, + 905, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {T E B S} = \\frac {1}{4} \\sum_ {i = 1} ^ {4} L _ {C E} (M, F _ {i}), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 609, + 903, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{CE}(\\cdot ,\\cdot)$ denotes the cross-entropy loss.", + "bbox": [ + 511, + 651, + 826, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The TEBS loss offers three key benefits: (1) Supervision on the target regions helps the backbone network to quickly focus on the feature learning of infrared UAV targets and enhance localization accuracy; (2) Supervision on background regions effectively suppresses non-target features, thereby reducing clutter and noise interference in the features; (3) The loss enhances training efficiency by guiding the network to learn target features more accurately, leading to faster convergence.", + "bbox": [ + 511, + 666, + 905, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The classification and regression losses are kept consistent with the baseline method. The final detector loss is written as:", + "bbox": [ + 511, + 801, + 905, + 845 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {d e t} = L _ {c l s} + L _ {r e g} + \\lambda L _ {T E B S}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 851, + 903, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is set to 1 for the first 20 epochs to accelerate convergence and improve localization performance in the early", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11901", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3335fc6a6ab6fe0dada27057165fe5f1d69da59a62e7937a56ff748c69c1b518.jpg", + "image_caption": [ + "Figure 4. Construction of the bias-robust loss in the unified NUC and detection framework." + ], + "image_footnote": [], + "bbox": [ + 99, + 87, + 478, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "stages. After 20 epochs, $\\lambda$ is reduced to 0.01 to balance with the gradually decreasing loss and avoid impacting classification accuracy.", + "bbox": [ + 89, + 204, + 483, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Balance Correction and Detection with Bias-Robust Loss", + "text_level": 1, + "bbox": [ + 89, + 257, + 483, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Existing research [11, 18] shows that incorporating supervision losses from low-level vision tasks in joint training can hinder high-level vision task performance. This is because low-level tasks focus on preserving fine image details, while high-level tasks aim to extract target-specific features and ignore irrelevant background information. This conflict can hinder convergence during joint training, causing the high-level vision task to settle into a local optimum.", + "bbox": [ + 89, + 294, + 483, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address this issue, we design a self-supervised loss, named bias robust (BR) loss, to achieve detection-friendly NUC, as illustrated in Fig. 4. Specifically, during joint training, the clear image $C$ and the corrected image $R$ obtained via the NUC module are simultaneously fed into the backbone of the detection model. Let $F_{C}^{(i)}$ and $F_{R}^{(i)}$ represent the feature maps from the $i$ -th stage of the detection backbone, where $i = 1,2,3,4$ denotes the four different stages. Here, clear images are employed only for the joint training of correction and detection on the synthetic dataset and are not applied to NUC training on real infrared images.", + "bbox": [ + 89, + 416, + 483, + 584 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate the alignment of the corrected image with the clear image in the feature space, we compute the cosine similarity between the feature maps at each stage $i$ as follows:", + "bbox": [ + 89, + 584, + 483, + 642 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C o s} \\operatorname {S i m} \\left(F _ {C} ^ {(i)}, F _ {R} ^ {(i)}\\right) = \\frac {F _ {C} ^ {(i)} \\cdot F _ {R} ^ {(i)}}{\\left\\| F _ {C} ^ {(i)} \\right\\| \\left\\| F _ {R} ^ {(i)} \\right\\|}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 643, + 482, + 689 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The details of the cosine similarity calculation are placed in the supplementary materials. The BR loss is obtained by summing the cosine similarities across all stages and averaging them:", + "bbox": [ + 89, + 690, + 483, + 750 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {B R} = \\frac {1}{4} \\sum_ {i = 1} ^ {4} \\left(1 - \\operatorname {C o s} _ {-} \\operatorname {S i m} \\left(F _ {C} ^ {(i)}, F _ {R} ^ {(i)}\\right)\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 753, + 482, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The BR loss function is designed to maximize the consistency between the feature representations of the clear and corrected images, thereby enhancing the fidelity of the corrected image within the feature space and ensuring that it retains essential characteristics beneficial for detection. The final union loss function for the joint training process $L_{uni}$ is written as:", + "bbox": [ + 89, + 795, + 483, + 898 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {u n i} = L _ {d e t} + L _ {B R}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 90, + 905, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated in Fig. 1, the union loss $L_{uni}$ ensures effective bias field correction while maximizing detection performance by backpropagating through each part of the network. Compared to separate training of NUC and detection networks, this integrated approach enables a more balanced optimization, leading to enhanced results in both correction and detection tasks.", + "bbox": [ + 511, + 122, + 906, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5.IRBFD Dataset", + "text_level": 1, + "bbox": [ + 513, + 244, + 669, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We construct a new benchmark called IRBFD, comprising 30,000 synthetic nonuniformity infrared UAV images (IRBFD-syn) and 20,000 real-world infrared UAV images with nonuniformity field (IRBFD-real). The IRBFD-syn subset provides paired degraded and clear images, with the synthesis process based on Eqs. (1) and (2). The characteristics of the dataset are summarized as follows. (1) Multiple background types. The IRBFD includes multiple complex scenes, such as dense clouds, buildings, forests, urban areas, and sea. (2) Multi-scale variations. The distance between the UAVs and the sensor ranges from 50 meters to 2 kilometers, resulting in multi-scale variations of the targets. (3) Multiple UAV types. Such as the DJI Inspire, Matrice, Phantom, Mavic, and Mini series. All UAV positions are manually annotated. IRBFD serves as a comprehensive resource for evaluating the impact of non-uniformities on UAV target detection in real-world environments. All images have a size of $640 \\times 512$ . Additional details can be found in the supplementary material.", + "bbox": [ + 511, + 268, + 906, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 511, + 575, + 638, + 593 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 511, + 602, + 802, + 618 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We use two parts of the IRBFD dataset: IRBFD-syn and IRBFD-real. IRBFD-syn consists of simulated nonuniform infrared images, allowing us to train the model with controlled background images and varying non-uniformities. Training, validation, and testing sets are split in an 8:1:1 ratio. We train on the simulated dataset and directly validate on real-world dataset to demonstrate the generalizability of our method.", + "bbox": [ + 511, + 626, + 905, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. For NUC, we use peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) as objective evaluation metrics. For target detection, we evaluate the detection performance using precision (P) and recall (R). Lastly, for real-time performance, we use frames per second (FPS) as the evaluation metric. The signal-to-clutter ratio gain (SCRG) is the ratio of SCR in the corrected image to that in the original image, used to evaluate the improvement in target detectability achieved by the correction method.", + "bbox": [ + 511, + 750, + 906, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11902", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/506f6a28e0700d047e0adc739dbe203425b8af1fbefe6e904ac5044ae33bf6b0.jpg", + "table_caption": [ + "Table 1. Quantitative comparison of the proposed method with SOTA methods on the synthetic dataset IRBFD-syn. **Bold** and **underline** indicate the best and the second best results, respectively." + ], + "table_footnote": [], + "table_body": "
    StrategyModuleMetrics
    NUCDetectionPub'YearPSNRSSIMPRFPS
    Direct-Deformable DETRICLR'210.6140.63024
    DINOICLR'230.9040.64026
    DAGNetTII'23--0.9940.63543
    LESPSCVPR'230.0330.44612
    MSHNetCVPR'240.4070.42141
    YOLO11L20240.9630.60242
    SeparateLiuYOLO11LIPT'1616.8000.82890.8980.574<1
    DAGNet0.9780.578<1
    DMRNYOLO11LGRSL'1924.4670.86000.9230.55035
    DAGNet0.9660.59536
    ShiYOLO11LAO'2213.9740.77830.9240.455<1
    DAGNet0.9660.472<1
    TV-DIPYOLO11LIPT'2313.3970.63740.1310.02029
    DAGNet0.5990.02030
    AHBCYOLO11LTGRS'2413.9540.67630.8250.080<1
    DAGNet0.7240.040<1
    UnionUniCD-31.9610.98270.9990.82232
    ", + "bbox": [ + 91, + 148, + 483, + 366 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/87312a884cbc3c6f62e389b4fd3e28bf6544bb0cd4e51c331c6f596364dc1390.jpg", + "table_caption": [ + "Table 2. Quantitative comparison of the proposed method with SOTA methods on the real dataset IRBFD-real." + ], + "table_footnote": [], + "table_body": "
    StrategyNUCDetectionSCRGPR
    Direct-DINO0.9710.660
    YOLO11L-0.9660.843
    DAGNet0.9920.871
    SeparateTV-DIPYOLO11L0.4120.5210.024
    DAGNet0.6630.026
    AHBCYOLO11L1.1460.9400.633
    DAGNet0.9860.699
    UnionUniCD1.2860.9940.901
    ", + "bbox": [ + 161, + 412, + 411, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 544, + 308, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use Adam as the optimizer, with a learning rate of 0.001. The training lasts for 50 epochs, with a weight decay of $10^{-4}$ and a batch size of 4. During training, we only apply random horizontal flipping for data augmentation. Our experiments are conducted on an NVIDIA RTX 4090 with CUDA 12.4 and PyTorch 1.7. For NUC, we select Liu [15], Shi [22], and AHBC [26] as the traditional bias field correction methods; DMRN [2] and TV-DIP [14] as the DL-based correction methods. They are all designed for infrared images. For target detection, we select YOLO11L [9] (large version), DAGNet [5], LESPS [28], and MSHNet [17] as the convolutional neural network (CNN)-based target detection methods. DAGNet, LESPS, and MSHNet are designed for infrared target detection. Deformable DETR [34] and DINO [30] are the representative Transformer-based detection methods.", + "bbox": [ + 88, + 566, + 482, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Quantitative Results", + "text_level": 1, + "bbox": [ + 89, + 818, + 284, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Tab. 1, the existing detection methods obtain low P and R values when detecting directly on the degraded bias field images. DAGNet has a high P value of 0.994 but a low recall. This indicates that the bias field has an adverse", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3725632855b1b68f113d1738104cfaf0c15f464315695890510b90abaa620557.jpg", + "image_caption": [ + "Figure 5. P-R curves of our UniCD and other correction-then-detection methods on the IRBFD-syn. The area values under the curves are placed after the method names." + ], + "image_footnote": [], + "bbox": [ + 571, + 89, + 841, + 256 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "effect on the UAV target detection. For the separate strategy, the DL-based method DMRN enhances image quality, achieving notable improvements in PSNR and SSIM. Other correction methods, such as Liu, Shi, and AHBC, are less effective for severely degraded images, which further impacts detection accuracy. Table 2 shows that the three detection methods achieve high P and R when directly detecting on real images with low degradation levels. YOLO11L and DAGNet have lower P and R values for images corrected by TV-DIP, as TV-DIP not only lacks corrective effects but also deteriorates the image content. In contrast, the proposed UniCD achieves the best performance in terms of all the evaluation metrics compared with SOTA methods in Tab. 1 for the synthetic dataset and Tab. 2 for the real dataset. Specially, our UniCD achieves a real-time processing speed of 32 FPS. We also plot the R-R curves for our UniCD and other correction-then-detection methods on the IRBFD dataset shown in Fig. 5. Higher values of the area under the curve indicate better performance. It can be seen that our UniCD achieves the largest area under the curve among all correction-then-detection methods.", + "bbox": [ + 511, + 308, + 906, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 511, + 636, + 694, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As demonstrated in Fig. 6, we show qualitative results from various separate correction-then-detection methods and our UniCD on the IRBFD-syn dataset across three distinct scenarios: buildings, hillside, and clouds. As can be seen, even in severe degraded bias field situations, our UniCD can still perform high-quality image correction while accurately detecting the UAV targets. This is because the proposed NUC correction module integrates parametric modeling and a small number of model parameter predictions, enabling more accurate parameter estimation. Meanwhile, our detection network introduces auxiliary loss with target mask supervision into the backbone to enhance the features of UAV targets while suppressing the background, thereby improving detection performance. Conventional correction methods, such as Liu and AHBC, have limited modeling capabilities and are prone to producing bias field residuals.", + "bbox": [ + 511, + 657, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11903", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/99e4b3bbcde5fd5cb4b3b76ec7ac59bf1a86cfcf67a645acbe15c4cac16cd3dd.jpg", + "image_caption": [ + "Figure 6. Visual comparison of results from separate correction followed by detection methods and our UniCD on the IRBFD-syn dataset. Closed-up views are shown in the left bottom corner. Boxes in green and red represent ground-truth and correctly detected targets, respectively." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 893, + 284 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/47b1a76b466a957e40bfc76f1a90f7dd5cbc1a302aab4234bf72bc20ec912ffc.jpg", + "image_caption": [ + "Figure 7. Visual comparison of results from separate correction-then-detection methods and our UniCD on the IRBFD-real dataset." + ], + "image_footnote": [], + "bbox": [ + 112, + 330, + 883, + 580 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a2d198d9d32441196ce2714b30fda0e4f3cc539b0efc0dd4185ac65def58c8df.jpg", + "table_caption": [ + "Table 3. Ablation study of polynomial degrees." + ], + "table_footnote": [], + "table_body": "
    DegreeNumber of coefficientsPSNRSSIMPR
    2613.52790.75900.9910.433
    31039.0500.99700.9970.810
    41531.7440.98900.9970.788
    52129.0700.98300.9970.787
    ", + "bbox": [ + 133, + 625, + 439, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The corrected image from DMRN exhibits block artifacts. Existing detection methods produce false alarms or miss detections on the above-corrected images; similar results are observed in Fig. 7 for scenes degraded by real bias fields. See the supplementary material for more visual results.", + "bbox": [ + 89, + 702, + 482, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 787, + 243, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we report ablation study results.", + "bbox": [ + 89, + 810, + 403, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of polynomial degrees. We conduct experiments to determine the optimal polynomial degree, as described in Tab. 8. The results indicate that the highest values for all correction and detection metrics are achieved when the degree is set to 3. Compared to higher-order polyno", + "bbox": [ + 89, + 825, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/edd6b1a63fa74708d2deb737b9d38dd0fd66708e2978886728d26ac3b30654e1.jpg", + "table_caption": [ + "Table 4. Ablation study of the LBFE and GBFE modules." + ], + "table_footnote": [], + "table_body": "
    LBFEGBFEParams (M)FLOPs (G)PSNRSSIMFPS
    ××0.37860.119227.2180.9808555
    ✓×0.38120.274730.2420.9877370
    ×✓0.39401.515937.8880.9961151
    ✓✓0.39661.680939.0500.9970116
    ", + "bbox": [ + 544, + 625, + 874, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "mials, a third-order polynomial has lower complexity and less redundancy. A lower degree implies weaker modeling capability, resulting in poor correction performance.", + "bbox": [ + 511, + 703, + 906, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of the LBFE and GBFE components. As presented in Tab. 4, when using only LBFE or GBFE, we can see that the PSNR of the correction model already achieves 30.242 and 37.888, respectively, surpassing the 27.218 of the baseline. When combined with LBFE and GBFE, further improvements can be achieved, reaching 39.050 with only 1.6809G FLOPs and 0.3966M parameters on an image size of $640 \\times 512$ . Additionally, the SSIM value has also shown some slight improvements. This suggests that the Transformer architecture combined with the CNN structure", + "bbox": [ + 511, + 750, + 908, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11904", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/096b6b4f1ba17d4ed6369ec6ba20c455c8b7367b065e29325936deb12ac5d713.jpg", + "table_caption": [ + "Table 5. Ablation study of the auxiliary TEBS loss." + ], + "table_footnote": [], + "table_body": "
    TEBS LossPR
    w/o0.9930.762
    w0.9970.810
    ", + "bbox": [ + 202, + 104, + 370, + 143 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e851cf7dd3b547ecc6ff7ffab009854d5ea71e04ffd3cff2c406da5e50318e0f.jpg", + "image_caption": [ + "Figure 8. Comparison of feature maps from the detection backbone at different stages with and without TEBS loss." + ], + "image_footnote": [], + "bbox": [ + 119, + 157, + 452, + 250 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8c34ceebbb828b238b1b900720588b59e136a30855cc2838e73a5efb51d9b951.jpg", + "table_caption": [ + "Table 6. Ablation study of BR loss on the synthetic dataset IRBFD-syn. Here, the direct and separate strategies utilize the correction and detection modules proposed in UniCD." + ], + "table_footnote": [], + "table_body": "
    StrategyCorrection lossDetection lossBR lossMetrics
    PSNRSSIMPR
    Direct×√×--0.9980.694
    Separate√√×37.7220.99600.9990.793
    Union√√×33.0240.98270.9980.791
    Union×√×17.9400.89100.9890.811
    UniCD×√√31.9610.98270.9990.822
    ", + "bbox": [ + 124, + 333, + 447, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "can effectively model bias fields, significantly improving performance while maintaining high real-time efficiency.", + "bbox": [ + 89, + 446, + 482, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of the auxiliary TEBS loss. As shown in Tab. 5, the auxiliary TEBS loss added to the backbone of the UAV detection network leads to improvements in both P and R performance. The TEBS loss imposes strong constraints on the target and background masks for the backbone features, enhancing target features while suppressing the background, thus improving detection performance, as depicted in Fig. 8. In the absence of TEBS loss, the targets are generally weak and there is considerable residual background.", + "bbox": [ + 88, + 477, + 482, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of BR loss. As shown in Tab. 6, the direct detection results in low P and R. The correction-then-detection separate method without BR loss in the second row obtains high PSNR, SSIM and P, but with low R because of the independent processing of the two tasks. The union of correction and detection without BR loss in the third row leads to a decrease in PSNR, SSIM, P, and R due to the conflict between the two tasks. The union of correction and detection without correction and BR losses in the fourth row significantly reduces PSNR and SSIM owing to the detection module's sole constraint. Our UniCD achieves the highest R value and P value exceeding 0.99, demonstrating that our union framework effectively balances correction and detection through the self-supervised BR loss.", + "bbox": [ + 89, + 613, + 482, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of UniCD on real dataset. As shown in Tab. 7, we use the NUC module weights trained on the IRBFD-syn and directly test them on the IRBFD-real. This configuration is referred to as $\\mathrm{UniCD}^{\\star}$ . The direct and separate methods with the modules in UniCD achieve a high P", + "bbox": [ + 89, + 824, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/37d6bc7e698731cbce81a56a7269c8043a0f879ef4d0ba7195862598f2cddf0c.jpg", + "table_caption": [ + "Table 7. Ablation study of our UniCD on the IRBFD-real." + ], + "table_footnote": [], + "table_body": "
    StrategySCRGPR
    Direct-0.9920.887
    Separate1.2860.9980.812
    UniCD*1.2860.9940.901
    ", + "bbox": [ + 531, + 119, + 687, + 172 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cab4eba397067f1962859e9ddc4981ab09f9f5f51294a627749aea144e3744cf.jpg", + "table_caption": [ + "Table 8. Ablation study of varying levels of nonuniformity." + ], + "table_footnote": [], + "table_body": "
    K-valuePSNRSSIM
    329.1190.9891
    534.9070.9950
    1238.3610.9968
    ", + "bbox": [ + 743, + 125, + 870, + 174 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/154dfb66a3140265c01591647034e648534da72f0363c8fe8db1f88794df3c9d.jpg", + "table_caption": [ + "Table 9. Ablation study of the union of our scalable NUC module with existing detection methods." + ], + "table_footnote": [], + "table_body": "
    Our NUCDetectionPRFPS
    ×YOLO11L0.8350.07542
    DAGNet0.7110.03643
    LESPS0.0070.12212
    MSHNet0.2840.22142
    √YOLO11L0.977(+)0.1420.657(+0.582)31
    DAGNet0.997(+0.286)0.722(+0.686)31
    LESPS0.007(+0.000)0.459(+0.337)11
    MSHNet0.776(+0.492)0.701(+0.480)31
    ", + "bbox": [ + 557, + 213, + 857, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "but a low R. Our UniCD obtains the highest R value and P value exceeding 0.99, thereby validating the effectiveness and generalization of our union framework on the real dataset.", + "bbox": [ + 511, + 345, + 906, + 405 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Generalization of the NUC Module. In Tab. 8, we test the UniCD on images with various degrees of nonuniformity degradation without retraining the NUC module. We control the severity of degradation using the formula $Y = C + k * B$ , where the $k$ -value determines the level of degradation. The correction results at different $k$ -values indicate that the NUC module generalizes well to various degradation levels.", + "bbox": [ + 511, + 406, + 905, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Scalability of the NUC Module. From Tab. 9, we observe that, except for the P value of LESPS, introducing our correction module significantly boosts the detection performance of several recent general and infrared target detection methods. This indicates that our NUC module can be flexibly integrated as a scalable component into existing detectors to enhance infrared images for detection purposes.", + "bbox": [ + 511, + 527, + 905, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 648, + 633, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose UniCD, an end-to-end framework that simultaneously addresses bias field correction and infrared UAV target detection. We develop a NUC module that removes bias fields and restores clear images with parameters adaptively predicted by a lightweight network. Additionally, we introduce auxiliary losses with mask supervision to enhance UAV target features and suppress the background. We also present a self-supervised feature loss to improve the robustness of detection to varying bias levels. Moreover, we construct a new dataset IRBFD to facilitate future research. Experimental results show that our UniCD outperforms previous approaches in both synthetic and real-world scenarios. Furthermore, our method shows great potential for deployment on resource-constrained edge devices.", + "bbox": [ + 509, + 674, + 906, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11905", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by the Open Research Fund of the National Key Laboratory of Multispectral Information Intelligent Processing Technology under Grant 61421132301, and the Natural Science Foundation of Jiangsu Province under Grant BK202302028.", + "bbox": [ + 89, + 90, + 485, + 167 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 180, + 187, + 196 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yanpeng Cao and Christel-Loic Tisse. Single-image-based solution for optics temperature-dependent nonuniformity correction in an uncooled long-wave infrared camera. Optics Letters, 39(3):646-648, 2014. 2", + "[2] Yi Chang, Luxin Yan, Li Liu, Houzhang Fang, and Sheng Zhong. Infrared aerothermal nonuniform correction via deep multiscale residual network. 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In Proceedings of International Conference on Learning Representations (ICLR), 2021. 6" + ], + "bbox": [ + 516, + 92, + 903, + 258 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11907", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_model.json b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_model.json new file mode 100644 index 0000000000000000000000000000000000000000..792d2931a1e827e920038fe1c43bbb7acbf8aa27 --- /dev/null +++ b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_model.json @@ -0,0 +1,2112 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.131, + 0.908, + 0.178 + ], + "angle": 0, + "content": "Detection-Friendly Nonuniformity Correction: A Union Framework for Infrared UAV Target Detection" + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.203, + 0.888, + 0.245 + ], + "angle": 0, + "content": "Houzhang Fang\\(^{1\\dagger}\\), Xiaolin Wang\\(^{1\\dagger}\\), Zengyang Li\\(^{1}\\), Lu Wang\\(^{1}\\), Qingshan Li\\(^{1}\\), Yi Chang\\(^{2}\\), Luxin Yan\\(^{2}\\), Xidian University \\({}^{2}\\)Huazhong University of Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.247, + 0.895, + 0.275 + ], + "angle": 0, + "content": "houzhangfang@xidian.edu.cn,wxl@stu.xidian.edu.cn，22009200694@stu.xidian.edu.cn，wanglu@xidian.edu.cn， qshli@mail.xidian.edu.cn，yichang@hust.edu.cn，yanluxin@hust.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.31, + 0.327, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.342, + 0.486, + 0.812 + ], + "angle": 0, + "content": "Infrared unmanned aerial vehicle (UAV) images captured using thermal detectors are often affected by temperature-dependent low-frequency nonuniformity, which significantly reduces the contrast of the images. Detecting UAV targets under nonuniform conditions is crucial in UAV surveillance applications. Existing methods typically treat infrared nonuniformity correction (NUC) as a preprocessing step for detection, which leads to suboptimal performance. Balancing the two tasks while enhancing detection-beneficial information remains challenging. In this paper, we present a detection-friendly union framework, termed UniCD, that simultaneously addresses both infrared NUC and UAV target detection tasks in an end-to-end manner. We first model NUC as a small number of parameter estimation problem jointly driven by priors and data to generate detection-conducive images. Then, we incorporate a new auxiliary loss with target mask supervision into the backbone of the infrared UAV target detection network to strengthen target features while suppressing the background. To better balance correction and detection, we introduce a detection-guided self-supervised loss to reduce feature discrepancies between the two tasks, thereby enhancing detection robustness to varying nonuniformity levels. Additionally, we construct a new benchmark composed of 50,000 infrared images in various nonuniformity types, multi-scale UAV targets and rich backgrounds with target annotations, called IRBFD. Extensive experiments on IRBFD demonstrate that our UniCD is a robust union framework for NUC and UAV target detection while achieving real-time processing capabilities. Dataset can be available at https://github.com/IVPLaboratory/UniCD." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.824, + 0.224, + 0.84 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.849, + 0.483, + 0.881 + ], + "angle": 0, + "content": "Unmanned aerial vehicle (UAV) detection based on infrared imaging is an important perception technology for moni" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.309, + 0.9, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.366, + 0.899, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.422, + 0.898, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.483, + 0.907, + 0.608 + ], + "angle": 0, + "content": "Figure 1. Three main categories of methods for UAV target detection in nonuniformity conditions. (a) Direct: detection models [10] are directly applied to nonuniformity degraded images. (b) Separate: correction model [15] serves as a pre-processing step, correcting images before passing them to detectors [10]. (c) Union: correction and detection are processed simultaneously in a unified framework. Previous methods solely concentrates on optimizing one task. Our UniCD concurrently emphasizes the joint enhancement of correction quality and detection accuracy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.624, + 0.909, + 0.88 + ], + "angle": 0, + "content": "toring UAV in both day and night scenarios. However, the thermal radiation from the optical lens and the camera housing causes the acquired infrared UAV images to often suffer from the temperature-dependent low-frequency nonuniformity effects [15, 23, 26, 33] (See the left column of Fig. 1). The optics-caused nonuniformity effect is also referred to as the bias field, which reduces the image contrast. Moreover, the infrared UAV targets typically have weak features and complex backgrounds [4, 5]. Nonuniformity bias field further exacerbates the difficulty of UAV target detection. Infrared nonuniformity correction (NUC) and target detection have achieved significant advancements in recent years [2, 4, 5, 17, 23, 28]. Previous methods focus on one aspect of the tasks and address the two tasks independently. As far as we know, no work considers the practical problem: infrared UAV target detection under the nonuniformity conditions." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.886, + 0.907, + 0.902 + ], + "angle": 0, + "content": "To solve this problem, a simple strategy is to detect [10]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.359, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author. †Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11898" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.408 + ], + "angle": 0, + "content": "UAV targets directly on the degraded bias field images (See Fig. 1(a)), which easily leads to miss detection due to the weakening of target information. Another typical approach is the correction-then-detection paradigm (See Fig. 1(b)). NUC methods [15, 22, 26] are first adopted to remove the nonuniformity bias field, and the corrected images are then passed to the target detectors [4, 5, 10]. However, the existing NUC methods have limitations. Specifically, model-based NUC methods rely heavily on handcrafted features to model the images and bias fields, making them prone to overfitting the image content and thus struggle to handle complex or severely degraded bias fields [26]. Deep learning (DL)-based NUC methods depend on complex architectures and a large number of real input-output image pairs, which limits their practicality [2, 23]. Additionally, the NUC lacks supervision from the detection module to enhance detection-conducive information. Recently, joint methods for processing low-level images and high-level vision have already been proposed [11, 12, 18]. However, they are primarily designed for object detection under adverse weather conditions." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.414, + 0.483, + 0.882 + ], + "angle": 0, + "content": "To overcome the above limitations, in this paper, we propose a detection-friedly union framework, termed UniCD, that simultaneously tackles both infrared bias field correction and UAV target detection. On the one hand, because of the spatially smooth nature of the bias field, we model it by the high-order bivariate polynomial [16, 22, 26], which can effectively fit the nonuniform bias field with different scales. As a result, accurately estimating the optimal polynomial coefficients is essential for ensuring the performance of bias field correction. In this work, we formulate bias field correction as a problem of predicting a small number of polynomial coefficients jointly driven by priors and data, which can be easily learned by a very lightweight network. The bias field has spatially continuous low-frequency characteristics, making transformer-based architecture well-suited for modeling this component. Additionally, we also integrate convolutional neural networks (CNNs) to capture the local details of the bias field. By incorporating parametric prior modeling and low-dimensional data-driven prediction, our approach avoids dependence on handcrafted features and real input-output data pairs, significantly improving correction performance. On the other hand, existing DL-based detection methods mainly focus on designing complex model architectures for extracting features [4, 5, 17, 19, 28, 31, 32]. We further introduce auxiliary loss with target mask supervision at different stages of the backbone in the infrared UAV target detection network without increasing computational complexity. Integrating this loss enhances the discriminative features of UAV targets while suppressing the background, thereby improving detection performance." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.886, + 0.482, + 0.9 + ], + "angle": 0, + "content": "To balance correction and detection, we introduce a" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.318 + ], + "angle": 0, + "content": "detection-guided self-supervised loss to reduce feature discrepancies between the correction and detection tasks. This loss enforces feature similarity between the corrected image and the reference image, both extracted by the detection backbone, thus ensuring high correction quality while enhancing features that are beneficial for detection. Our NUC model can also be flexibly integrated as a scalable module with existing detectors for infrared image bias field correction. Furthermore, we construct the bias field benchmark, IRBFD, consisting of 50,000 infrared images with varying nonuniformity types, multi-scale UAV targets, and rich backgrounds with target annotations, called IRBFD. Experimental results on the IRBFD demonstrate that UniCD outperforms state-of-the-art (SOTA) combined correction and detection methods in terms of precision and recall." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.326, + 0.888, + 0.34 + ], + "angle": 0, + "content": "The contributions of this work can be summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.349, + 0.905, + 0.422 + ], + "angle": 0, + "content": "- We propose a novel detection-friedly union framework, termed UniCD, that can simultaneously deal with NUC and infrared UAV target detection in an end-to-end manner. To the best of our knowledge, this is the first work to address both issues in a unified framework." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.424, + 0.905, + 0.483 + ], + "angle": 0, + "content": "- We for the first time model nonuniformity bias field correction as a problem of predicting a small number of hyperparameters jointly driven by priors and data, which can be easily performed with a very lightweight network." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.485, + 0.905, + 0.574 + ], + "angle": 0, + "content": "- We establish the first large benchmark called IRBFD to facilitate the research in the area of nonuniformity correction and infrared UAV target detection, which consists of 50,000 manually labeled infrared images with various nonuniformity levels, multi-scale UAV targets and rich backgrounds with target annotations." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.349, + 0.905, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.612, + 0.655, + 0.627 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.645, + 0.9, + 0.661 + ], + "angle": 0, + "content": "2.1. Nonuniformity Correction in Infrared Images" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.901 + ], + "angle": 0, + "content": "NUC methods for removing the bias field are broadly divided into two main categories: model-driven methods and data-driven methods. Model-driven methods typically leverage the prior constraints of the bias field and the images to remove the nonuniformity effects [1, 15, 16, 22, 25, 26]. However, these methods rely on handcrafted features with carefully tuned hyper-parameters, limiting their practicality in real-world applications. Data-driven DL methods [2, 14, 23] have gained increasing attention. However, DL-based correction models are often complex and rely on large amounts of training data with real correction labels, which restricts their widespread application in practical scenarios [6, 24, 27]. In contrast, we formulate a novel lightweight correction model driven by both parametric priors and data, which converges more easily." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "11899" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.087, + 0.885, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.228, + 0.908, + 0.285 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed UniCD. Our UniCD integrates a bias field prediction network with an infrared UAV target detection network. These two components are fused into a unified pipeline and trained end-to-end. The target enhancement and background suppression (TEBS) loss is introduced to enhance UAV target features while suppressing the background. The bias robust loss is employed to balance correction and detection." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.304, + 0.365, + 0.32 + ], + "angle": 0, + "content": "2.2. Infrared UAV Target Detection" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.326, + 0.485, + 0.629 + ], + "angle": 0, + "content": "In recent years, many methods have been developed to detect infrared UAV targets [3-5, 19, 21]. Infrared UAV targets are challenging due to their weak imaging features and complex backgrounds [7, 8, 29]. TAD [19] leveraged the inconsistent motion cues between UAV targets and the background to detect potential targets. Fang et al. [3] formulated the UAV detection task as a residual image prediction by learning the mapping from input images to residual images. DAGNet [5] introduced attention mechanisms to adaptively enhance the network's ability to discriminate between UAVs and the background. DANet [4] constructed a dynamic attention network for UAVs to enhance feature extraction capabilities. However, the above methods primarily focus on designing complex network structures for improving detection performance, while rarely exploring how to better enhance feature representation without increasing computational complexity. We focus on introducing new auxiliary losses into the backbone to boost the model's ability to represent UAV target features while suppressing the background." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.637, + 0.483, + 0.668 + ], + "angle": 0, + "content": "2.3. Joint Low-Level Image Processing and High-Level Vision Tasks" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Recently, joint approaches for image enhancement and object detection have emerged to further improve detection performance on low-quality images. One category of these methods utilized encoder-decoder architectures for image enhancement [12], but these modules are complex and hinder real-time performance. Another approach uses classical mathematical models for enhancement, replacing manually designed parameters with predictions from deep networks. IA-YOLO [18] integrated an adaptive enhancement strategy with YOLOv3 [20] via a differentiable image processing module, improving detection in foggy conditions. BAD-Net [11] introduced a dual-branch structure to minimize the impact of poor dehazing performance on the detection module. However, the above methods are developed for visible light images degraded by adverse weather condi" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.305, + 0.907, + 0.381 + ], + "angle": 0, + "content": "tions. To the best of our knowledge, no work has explored handling both NUC and UAV target detection for infrared imaging within a single framework. We propose an end-to-end framework to simultaneously improve both correction and detection performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.394, + 0.822, + 0.411 + ], + "angle": 0, + "content": "3. Detection-Friendly Union Method" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.418, + 0.71, + 0.433 + ], + "angle": 0, + "content": "3.1. Overall Architecture" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.44, + 0.907, + 0.577 + ], + "angle": 0, + "content": "In this section, we propose a novel network architecture, UniCD, as shown in Fig. 2. The UniCD leverages a lightweight prediction network to estimate the bias field and then passes the corrected image to a UAV detection network tailored for UAV targets. Additionally, during the joint training of image correction and detection tasks, we employ a detection-guided self-supervised loss to minimize feature discrepancies between the two tasks. Finally, we construct a new dataset, IRBFD, to validate our approach." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.586, + 0.905, + 0.615 + ], + "angle": 0, + "content": "3.2. Prior- and Data-Driven Nonuniformity Correction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.622, + 0.906, + 0.773 + ], + "angle": 0, + "content": "Infrared UAV images captured by thermal detectors often suffer from low-frequency nonuniformity, which significantly impacts target detection performance. Existing model-driven correction methods often struggle to handle complex non-uniformities, while deep learning-based methods suffer from high network complexity. To address these issues, we propose a lightweight correction network that combines parametric prior knowledge with the strong learning capabilities of deep neural networks. The network architecture is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.774, + 0.905, + 0.803 + ], + "angle": 0, + "content": "Generally, the degraded infrared image can be represented as follows [2, 16]:" + }, + { + "type": "equation", + "bbox": [ + 0.664, + 0.807, + 0.905, + 0.823 + ], + "angle": 0, + "content": "\\[\nY = C + B, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.906, + 0.901 + ], + "angle": 0, + "content": "where \\( Y \\), \\( C \\), and \\( B \\) represent the degraded image, the clear image, and the bias field, respectively. Thus, once \\( B \\) is available, the corrected image \\( R \\) can be obtained as \\( Y - B \\). Under ideal conditions, \\( R \\) is theoretically equivalent to the clear image \\( C \\). The bias field \\( B \\) possesses a" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11900" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.123 + ], + "angle": 0, + "content": "spatially smooth property, allowing us to model it using the following bivariate polynomial:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.127, + 0.483, + 0.169 + ], + "angle": 0, + "content": "\\[\nB \\left(x _ {i}, y _ {j}\\right) = \\sum_ {t = 0} ^ {D} \\sum_ {s = 0} ^ {D - t} a _ {t, s} x _ {i} ^ {t} y _ {j} ^ {s} = \\mathbf {m} ^ {\\top} \\mathbf {a}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.173, + 0.483, + 0.279 + ], + "angle": 0, + "content": "where \\((x_{i},y_{j})\\), \\(D\\), and \\(\\mathbf{m}\\) denote the image coordinates, the degree of the polynomial, and the column vector holding the monomial terms, respectively. The column vector \\(\\mathbf{a}\\) represents the coefficients of the polynomial formed by concatenating \\(\\{a_{t,s}\\}\\). To reduce the redundancy of the basic plane and the computational complexity of higher-order models, we set the degree \\(D\\) to 3." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.28, + 0.483, + 0.355 + ], + "angle": 0, + "content": "Accurate estimation of the polynomial coefficients \\(\\mathbf{a}\\) is crucial for improving bias field correction performance. In this work, we design a lightweight bias field prediction network that can estimate the model parameters accurately and efficiently." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.356, + 0.484, + 0.522 + ], + "angle": 0, + "content": "In our NUC module, we first downsample the degraded image \\( Y \\) by a factor of two, resulting in the downsampled image \\( Y_{\\mathrm{down}} \\). Then, we utilize the global bias field encoder (GBFE) and the local bias field encoder (LBFE) to extract features at different granularities. The GBFE, inspired by the RSTB [13] module, includes two Swin Transformer layers with the hidden layer channel dimension reduced to 16. The LBFE consists of two spatial attention modules in series, allowing it to capture localized features more effectively. The global and local features, \\( F_{\\mathrm{global}} \\) and \\( F_{\\mathrm{local}} \\), are fused to form the final feature representation \\( F_{\\mathrm{fused}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.528, + 0.483, + 0.546 + ], + "angle": 0, + "content": "\\[\nF _ {\\text {f u s e d}} = \\mathrm {G B F E} \\left(Y _ {\\text {d o w n}}\\right) + \\mathrm {L B F E} \\left(Y _ {\\text {d o w n}}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.55, + 0.483, + 0.596 + ], + "angle": 0, + "content": "Finally, the fused features \\( F_{\\mathrm{fused}} \\) pass through five \\( 3 \\times 3 \\) convolutional layers (Conv5) and a fully connected (FC) layer to predict the final coefficient vector \\( \\hat{\\mathbf{a}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.602, + 0.482, + 0.619 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {a}} = \\operatorname {F C} \\left(\\operatorname {C o n v} _ {5} \\left(F _ {\\text {f u s e d}}\\right)\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.624, + 0.483, + 0.669 + ], + "angle": 0, + "content": "This approach enables the network to adaptively adjust to inputs with varying levels of degradation, effectively predicting the coefficient vector \\(\\hat{\\mathbf{a}}\\) for bias field correction." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.483, + 0.775 + ], + "angle": 0, + "content": "Analysis. Compared to existing model-driven methods, our approach avoids reliance on hand-crafted features. Compared to existing data-driven methods, our approach transforms the high-dimensional image space prediction into a low-dimensional data-driven problem with a few hyperparameters, effectively reducing computational complexity and improving correction performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.776, + 0.483, + 0.835 + ], + "angle": 0, + "content": "Loss Function. We calculate the mean absolute error (MAE) loss between the predicted coefficients \\(\\hat{\\mathbf{a}}\\) and the predefined coefficients \\(\\mathbf{a}\\) to minimize the discrepancy between them. The MAE loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.216, + 0.839, + 0.483, + 0.868 + ], + "angle": 0, + "content": "\\[\nL _ {c o r} = \\frac {1}{N} \\| \\hat {\\mathbf {a}} - \\mathbf {a} \\| _ {2} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "where \\(N\\) is the total number of elements in the vector \\(\\mathbf{a}\\). By minimizing this loss, we improve the accuracy of the" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.089, + 0.903, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.173, + 0.907, + 0.202 + ], + "angle": 0, + "content": "Figure 3. Calculation of the proposed feature enhancement and background suppression (TEBS) loss." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.208, + 0.907, + 0.268 + ], + "angle": 0, + "content": "corrected image, making it closer to the ideal clear image. This loss function is used to pre-train the NUC module separately, serving as the initial weights for the joint training of correction and detection." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.277, + 0.866, + 0.294 + ], + "angle": 0, + "content": "3.3. Mask-Supervised Infrared UAV Detector" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.299, + 0.906, + 0.449 + ], + "angle": 0, + "content": "We select DANet [4] as our baseline detector, which constructs a multi-scale dynamic perception network to address the challenges of multi-scale variations in UAV targets. Infrared UAV targets typically have weak features and complex backgrounds, and existing methods often enhance feature extraction through complex model architectures. In this work, we design an auxiliary loss function for further target enhancement and background suppression (TEBS) without increasing network complexity, as illustrated in Figs. 2 and 3." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.45, + 0.906, + 0.495 + ], + "angle": 0, + "content": "Specifically, we first convert the bounding boxes of the ground-truth into a binary mask \\( M \\), assigning a value of 1 to the target region and 0 to the background region:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.497, + 0.905, + 0.535 + ], + "angle": 0, + "content": "\\[\nM (x, y) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} (x, y) \\in \\text {t a r g e t r e g i o n}, \\\\ 0, & \\text {i f} (x, y) \\in \\text {b a c k g r o u n d r e g i o n}. \\end{array} \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.535, + 0.906, + 0.61 + ], + "angle": 0, + "content": "This mask is then used to compute a binary cross-entropy loss with the feature maps \\( F_{i} \\) from the \\( i \\)-th stage of the backbone network. The TEBS loss \\( L_{\\mathrm{TEBS}} \\) is obtained by summing the losses from four stages of the backbone and averaging:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.611, + 0.905, + 0.651 + ], + "angle": 0, + "content": "\\[\nL _ {T E B S} = \\frac {1}{4} \\sum_ {i = 1} ^ {4} L _ {C E} (M, F _ {i}), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.652, + 0.827, + 0.667 + ], + "angle": 0, + "content": "where \\(L_{CE}(\\cdot ,\\cdot)\\) denotes the cross-entropy loss." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.667, + 0.906, + 0.802 + ], + "angle": 0, + "content": "The TEBS loss offers three key benefits: (1) Supervision on the target regions helps the backbone network to quickly focus on the feature learning of infrared UAV targets and enhance localization accuracy; (2) Supervision on background regions effectively suppresses non-target features, thereby reducing clutter and noise interference in the features; (3) The loss enhances training efficiency by guiding the network to learn target features more accurately, leading to faster convergence." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.803, + 0.906, + 0.847 + ], + "angle": 0, + "content": "The classification and regression losses are kept consistent with the baseline method. The final detector loss is written as:" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.852, + 0.905, + 0.868 + ], + "angle": 0, + "content": "\\[\nL _ {d e t} = L _ {c l s} + L _ {r e g} + \\lambda L _ {T E B S}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is set to 1 for the first 20 epochs to accelerate convergence and improve localization performance in the early" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11901" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.088, + 0.48, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.173, + 0.483, + 0.2 + ], + "angle": 0, + "content": "Figure 4. Construction of the bias-robust loss in the unified NUC and detection framework." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.205, + 0.484, + 0.25 + ], + "angle": 0, + "content": "stages. After 20 epochs, \\(\\lambda\\) is reduced to 0.01 to balance with the gradually decreasing loss and avoid impacting classification accuracy." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.258, + 0.484, + 0.289 + ], + "angle": 0, + "content": "3.4. Balance Correction and Detection with Bias-Robust Loss" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.295, + 0.484, + 0.416 + ], + "angle": 0, + "content": "Existing research [11, 18] shows that incorporating supervision losses from low-level vision tasks in joint training can hinder high-level vision task performance. This is because low-level tasks focus on preserving fine image details, while high-level tasks aim to extract target-specific features and ignore irrelevant background information. This conflict can hinder convergence during joint training, causing the high-level vision task to settle into a local optimum." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.417, + 0.484, + 0.585 + ], + "angle": 0, + "content": "To address this issue, we design a self-supervised loss, named bias robust (BR) loss, to achieve detection-friendly NUC, as illustrated in Fig. 4. Specifically, during joint training, the clear image \\( C \\) and the corrected image \\( R \\) obtained via the NUC module are simultaneously fed into the backbone of the detection model. Let \\( F_{C}^{(i)} \\) and \\( F_{R}^{(i)} \\) represent the feature maps from the \\( i \\)-th stage of the detection backbone, where \\( i = 1,2,3,4 \\) denotes the four different stages. Here, clear images are employed only for the joint training of correction and detection on the synthetic dataset and are not applied to NUC training on real infrared images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.484, + 0.643 + ], + "angle": 0, + "content": "To evaluate the alignment of the corrected image with the clear image in the feature space, we compute the cosine similarity between the feature maps at each stage \\(i\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.644, + 0.483, + 0.69 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C o s} \\operatorname {S i m} \\left(F _ {C} ^ {(i)}, F _ {R} ^ {(i)}\\right) = \\frac {F _ {C} ^ {(i)} \\cdot F _ {R} ^ {(i)}}{\\left\\| F _ {C} ^ {(i)} \\right\\| \\left\\| F _ {R} ^ {(i)} \\right\\|}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.691, + 0.484, + 0.751 + ], + "angle": 0, + "content": "The details of the cosine similarity calculation are placed in the supplementary materials. The BR loss is obtained by summing the cosine similarities across all stages and averaging them:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.754, + 0.483, + 0.794 + ], + "angle": 0, + "content": "\\[\nL _ {B R} = \\frac {1}{4} \\sum_ {i = 1} ^ {4} \\left(1 - \\operatorname {C o s} _ {-} \\operatorname {S i m} \\left(F _ {C} ^ {(i)}, F _ {R} ^ {(i)}\\right)\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.9 + ], + "angle": 0, + "content": "The BR loss function is designed to maximize the consistency between the feature representations of the clear and corrected images, thereby enhancing the fidelity of the corrected image within the feature space and ensuring that it retains essential characteristics beneficial for detection. The final union loss function for the joint training process \\( L_{uni} \\) is written as:" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.092, + 0.906, + 0.108 + ], + "angle": 0, + "content": "\\[\nL _ {u n i} = L _ {d e t} + L _ {B R}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.123, + 0.907, + 0.228 + ], + "angle": 0, + "content": "As illustrated in Fig. 1, the union loss \\( L_{uni} \\) ensures effective bias field correction while maximizing detection performance by backpropagating through each part of the network. Compared to separate training of NUC and detection networks, this integrated approach enables a more balanced optimization, leading to enhanced results in both correction and detection tasks." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.245, + 0.671, + 0.26 + ], + "angle": 0, + "content": "3.5.IRBFD Dataset" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.269, + 0.907, + 0.556 + ], + "angle": 0, + "content": "We construct a new benchmark called IRBFD, comprising 30,000 synthetic nonuniformity infrared UAV images (IRBFD-syn) and 20,000 real-world infrared UAV images with nonuniformity field (IRBFD-real). The IRBFD-syn subset provides paired degraded and clear images, with the synthesis process based on Eqs. (1) and (2). The characteristics of the dataset are summarized as follows. (1) Multiple background types. The IRBFD includes multiple complex scenes, such as dense clouds, buildings, forests, urban areas, and sea. (2) Multi-scale variations. The distance between the UAVs and the sensor ranges from 50 meters to 2 kilometers, resulting in multi-scale variations of the targets. (3) Multiple UAV types. Such as the DJI Inspire, Matrice, Phantom, Mavic, and Mini series. All UAV positions are manually annotated. IRBFD serves as a comprehensive resource for evaluating the impact of non-uniformities on UAV target detection in real-world environments. All images have a size of \\(640 \\times 512\\). Additional details can be found in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.576, + 0.64, + 0.594 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.603, + 0.803, + 0.619 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.906, + 0.748 + ], + "angle": 0, + "content": "Datasets. We use two parts of the IRBFD dataset: IRBFD-syn and IRBFD-real. IRBFD-syn consists of simulated nonuniform infrared images, allowing us to train the model with controlled background images and varying non-uniformities. Training, validation, and testing sets are split in an 8:1:1 ratio. We train on the simulated dataset and directly validate on real-world dataset to demonstrate the generalizability of our method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.9 + ], + "angle": 0, + "content": "Evaluation Metrics. For NUC, we use peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) as objective evaluation metrics. For target detection, we evaluate the detection performance using precision (P) and recall (R). Lastly, for real-time performance, we use frames per second (FPS) as the evaluation metric. The signal-to-clutter ratio gain (SCRG) is the ratio of SCR in the corrected image to that in the original image, used to evaluate the improvement in target detectability achieved by the correction method." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11902" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.09, + 0.483, + 0.146 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of the proposed method with SOTA methods on the synthetic dataset IRBFD-syn. **Bold** and **underline** indicate the best and the second best results, respectively." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.149, + 0.485, + 0.367 + ], + "angle": 0, + "content": "
    StrategyModuleMetrics
    NUCDetectionPub'YearPSNRSSIMPRFPS
    Direct-Deformable DETRICLR'210.6140.63024
    DINOICLR'230.9040.64026
    DAGNetTII'23--0.9940.63543
    LESPSCVPR'230.0330.44612
    MSHNetCVPR'240.4070.42141
    YOLO11L20240.9630.60242
    SeparateLiuYOLO11LIPT'1616.8000.82890.8980.574<1
    DAGNet0.9780.578<1
    DMRNYOLO11LGRSL'1924.4670.86000.9230.55035
    DAGNet0.9660.59536
    ShiYOLO11LAO'2213.9740.77830.9240.455<1
    DAGNet0.9660.472<1
    TV-DIPYOLO11LIPT'2313.3970.63740.1310.02029
    DAGNet0.5990.02030
    AHBCYOLO11LTGRS'2413.9540.67630.8250.080<1
    DAGNet0.7240.040<1
    UnionUniCD-31.9610.98270.9990.82232
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.38, + 0.483, + 0.409 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison of the proposed method with SOTA methods on the real dataset IRBFD-real." + }, + { + "type": "table", + "bbox": [ + 0.162, + 0.413, + 0.413, + 0.521 + ], + "angle": 0, + "content": "
    StrategyNUCDetectionSCRGPR
    Direct-DINO0.9710.660
    YOLO11L-0.9660.843
    DAGNet0.9920.871
    SeparateTV-DIPYOLO11L0.4120.5210.024
    DAGNet0.6630.026
    AHBCYOLO11L1.1460.9400.633
    DAGNet0.9860.699
    UnionUniCD1.2860.9940.901
    " + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.545, + 0.31, + 0.561 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.567, + 0.483, + 0.809 + ], + "angle": 0, + "content": "We use Adam as the optimizer, with a learning rate of 0.001. The training lasts for 50 epochs, with a weight decay of \\(10^{-4}\\) and a batch size of 4. During training, we only apply random horizontal flipping for data augmentation. Our experiments are conducted on an NVIDIA RTX 4090 with CUDA 12.4 and PyTorch 1.7. For NUC, we select Liu [15], Shi [22], and AHBC [26] as the traditional bias field correction methods; DMRN [2] and TV-DIP [14] as the DL-based correction methods. They are all designed for infrared images. For target detection, we select YOLO11L [9] (large version), DAGNet [5], LESPS [28], and MSHNet [17] as the convolutional neural network (CNN)-based target detection methods. DAGNet, LESPS, and MSHNet are designed for infrared target detection. Deformable DETR [34] and DINO [30] are the representative Transformer-based detection methods." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.819, + 0.285, + 0.835 + ], + "angle": 0, + "content": "4.3. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "As shown in Tab. 1, the existing detection methods obtain low P and R values when detecting directly on the degraded bias field images. DAGNet has a high P value of 0.994 but a low recall. This indicates that the bias field has an adverse" + }, + { + "type": "image", + "bbox": [ + 0.573, + 0.09, + 0.843, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.258, + 0.905, + 0.3 + ], + "angle": 0, + "content": "Figure 5. P-R curves of our UniCD and other correction-then-detection methods on the IRBFD-syn. The area values under the curves are placed after the method names." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.309, + 0.907, + 0.626 + ], + "angle": 0, + "content": "effect on the UAV target detection. For the separate strategy, the DL-based method DMRN enhances image quality, achieving notable improvements in PSNR and SSIM. Other correction methods, such as Liu, Shi, and AHBC, are less effective for severely degraded images, which further impacts detection accuracy. Table 2 shows that the three detection methods achieve high P and R when directly detecting on real images with low degradation levels. YOLO11L and DAGNet have lower P and R values for images corrected by TV-DIP, as TV-DIP not only lacks corrective effects but also deteriorates the image content. In contrast, the proposed UniCD achieves the best performance in terms of all the evaluation metrics compared with SOTA methods in Tab. 1 for the synthetic dataset and Tab. 2 for the real dataset. Specially, our UniCD achieves a real-time processing speed of 32 FPS. We also plot the R-R curves for our UniCD and other correction-then-detection methods on the IRBFD dataset shown in Fig. 5. Higher values of the area under the curve indicate better performance. It can be seen that our UniCD achieves the largest area under the curve among all correction-then-detection methods." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.637, + 0.696, + 0.654 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.907, + 0.901 + ], + "angle": 0, + "content": "As demonstrated in Fig. 6, we show qualitative results from various separate correction-then-detection methods and our UniCD on the IRBFD-syn dataset across three distinct scenarios: buildings, hillside, and clouds. As can be seen, even in severe degraded bias field situations, our UniCD can still perform high-quality image correction while accurately detecting the UAV targets. This is because the proposed NUC correction module integrates parametric modeling and a small number of model parameter predictions, enabling more accurate parameter estimation. Meanwhile, our detection network introduces auxiliary loss with target mask supervision into the backbone to enhance the features of UAV targets while suppressing the background, thereby improving detection performance. Conventional correction methods, such as Liu and AHBC, have limited modeling capabilities and are prone to producing bias field residuals." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11903" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.895, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.287, + 0.907, + 0.329 + ], + "angle": 0, + "content": "Figure 6. Visual comparison of results from separate correction followed by detection methods and our UniCD on the IRBFD-syn dataset. Closed-up views are shown in the left bottom corner. Boxes in green and red represent ground-truth and correctly detected targets, respectively." + }, + { + "type": "image", + "bbox": [ + 0.113, + 0.331, + 0.885, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.584, + 0.885, + 0.598 + ], + "angle": 0, + "content": "Figure 7. Visual comparison of results from separate correction-then-detection methods and our UniCD on the IRBFD-real dataset." + }, + { + "type": "table_caption", + "bbox": [ + 0.146, + 0.608, + 0.427, + 0.623 + ], + "angle": 0, + "content": "Table 3. Ablation study of polynomial degrees." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.625, + 0.44, + 0.687 + ], + "angle": 0, + "content": "
    DegreeNumber of coefficientsPSNRSSIMPR
    2613.52790.75900.9910.433
    31039.0500.99700.9970.810
    41531.7440.98900.9970.788
    52129.0700.98300.9970.787
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.703, + 0.483, + 0.779 + ], + "angle": 0, + "content": "The corrected image from DMRN exhibits block artifacts. Existing detection methods produce false alarms or miss detections on the above-corrected images; similar results are observed in Fig. 7 for scenes degraded by real bias fields. See the supplementary material for more visual results." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.788, + 0.245, + 0.804 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.811, + 0.405, + 0.825 + ], + "angle": 0, + "content": "In this section, we report ablation study results." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Impact of polynomial degrees. We conduct experiments to determine the optimal polynomial degree, as described in Tab. 8. The results indicate that the highest values for all correction and detection metrics are achieved when the degree is set to 3. Compared to higher-order polyno" + }, + { + "type": "table_caption", + "bbox": [ + 0.538, + 0.608, + 0.88, + 0.622 + ], + "angle": 0, + "content": "Table 4. Ablation study of the LBFE and GBFE modules." + }, + { + "type": "table", + "bbox": [ + 0.545, + 0.625, + 0.875, + 0.687 + ], + "angle": 0, + "content": "
    LBFEGBFEParams (M)FLOPs (G)PSNRSSIMFPS
    ××0.37860.119227.2180.9808555
    ✓×0.38120.274730.2420.9877370
    ×✓0.39401.515937.8880.9961151
    ✓✓0.39661.680939.0500.9970116
    " + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.749 + ], + "angle": 0, + "content": "mials, a third-order polynomial has lower complexity and less redundancy. A lower degree implies weaker modeling capability, resulting in poor correction performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Impact of the LBFE and GBFE components. As presented in Tab. 4, when using only LBFE or GBFE, we can see that the PSNR of the correction model already achieves 30.242 and 37.888, respectively, surpassing the 27.218 of the baseline. When combined with LBFE and GBFE, further improvements can be achieved, reaching 39.050 with only 1.6809G FLOPs and 0.3966M parameters on an image size of \\(640 \\times 512\\). Additionally, the SSIM value has also shown some slight improvements. This suggests that the Transformer architecture combined with the CNN structure" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11904" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.134, + 0.089, + 0.441, + 0.103 + ], + "angle": 0, + "content": "Table 5. Ablation study of the auxiliary TEBS loss." + }, + { + "type": "table", + "bbox": [ + 0.203, + 0.106, + 0.371, + 0.145 + ], + "angle": 0, + "content": "
    TEBS LossPR
    w/o0.9930.762
    w0.9970.810
    " + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.159, + 0.454, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.254, + 0.483, + 0.283 + ], + "angle": 0, + "content": "Figure 8. Comparison of feature maps from the detection backbone at different stages with and without TEBS loss." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.291, + 0.484, + 0.334 + ], + "angle": 0, + "content": "Table 6. Ablation study of BR loss on the synthetic dataset IRBFD-syn. Here, the direct and separate strategies utilize the correction and detection modules proposed in UniCD." + }, + { + "type": "table", + "bbox": [ + 0.125, + 0.334, + 0.449, + 0.422 + ], + "angle": 0, + "content": "
    StrategyCorrection lossDetection lossBR lossMetrics
    PSNRSSIMPR
    Direct×√×--0.9980.694
    Separate√√×37.7220.99600.9990.793
    Union√√×33.0240.98270.9980.791
    Union×√×17.9400.89100.9890.811
    UniCD×√√31.9610.98270.9990.822
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.447, + 0.483, + 0.478 + ], + "angle": 0, + "content": "can effectively model bias fields, significantly improving performance while maintaining high real-time efficiency." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.478, + 0.483, + 0.614 + ], + "angle": 0, + "content": "Impact of the auxiliary TEBS loss. As shown in Tab. 5, the auxiliary TEBS loss added to the backbone of the UAV detection network leads to improvements in both P and R performance. The TEBS loss imposes strong constraints on the target and background masks for the backbone features, enhancing target features while suppressing the background, thus improving detection performance, as depicted in Fig. 8. In the absence of TEBS loss, the targets are generally weak and there is considerable residual background." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.614, + 0.483, + 0.825 + ], + "angle": 0, + "content": "Impact of BR loss. As shown in Tab. 6, the direct detection results in low P and R. The correction-then-detection separate method without BR loss in the second row obtains high PSNR, SSIM and P, but with low R because of the independent processing of the two tasks. The union of correction and detection without BR loss in the third row leads to a decrease in PSNR, SSIM, P, and R due to the conflict between the two tasks. The union of correction and detection without correction and BR losses in the fourth row significantly reduces PSNR and SSIM owing to the detection module's sole constraint. Our UniCD achieves the highest R value and P value exceeding 0.99, demonstrating that our union framework effectively balances correction and detection through the self-supervised BR loss." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Effectiveness of UniCD on real dataset. As shown in Tab. 7, we use the NUC module weights trained on the IRBFD-syn and directly test them on the IRBFD-real. This configuration is referred to as \\(\\mathrm{UniCD}^{\\star}\\). The direct and separate methods with the modules in UniCD achieve a high P" + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.089, + 0.707, + 0.117 + ], + "angle": 0, + "content": "Table 7. Ablation study of our UniCD on the IRBFD-real." + }, + { + "type": "table", + "bbox": [ + 0.532, + 0.121, + 0.688, + 0.174 + ], + "angle": 0, + "content": "
    StrategySCRGPR
    Direct-0.9920.887
    Separate1.2860.9980.812
    UniCD*1.2860.9940.901
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.714, + 0.093, + 0.905, + 0.122 + ], + "angle": 0, + "content": "Table 8. Ablation study of varying levels of nonuniformity." + }, + { + "type": "table", + "bbox": [ + 0.745, + 0.125, + 0.871, + 0.175 + ], + "angle": 0, + "content": "
    K-valuePSNRSSIM
    329.1190.9891
    534.9070.9950
    1238.3610.9968
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.184, + 0.905, + 0.212 + ], + "angle": 0, + "content": "Table 9. Ablation study of the union of our scalable NUC module with existing detection methods." + }, + { + "type": "table", + "bbox": [ + 0.558, + 0.214, + 0.858, + 0.322 + ], + "angle": 0, + "content": "
    Our NUCDetectionPRFPS
    ×YOLO11L0.8350.07542
    DAGNet0.7110.03643
    LESPS0.0070.12212
    MSHNet0.2840.22142
    √YOLO11L0.977(+)0.1420.657(+0.582)31
    DAGNet0.997(+0.286)0.722(+0.686)31
    LESPS0.007(+0.000)0.459(+0.337)11
    MSHNet0.776(+0.492)0.701(+0.480)31
    " + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.347, + 0.907, + 0.406 + ], + "angle": 0, + "content": "but a low R. Our UniCD obtains the highest R value and P value exceeding 0.99, thereby validating the effectiveness and generalization of our union framework on the real dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.407, + 0.906, + 0.528 + ], + "angle": 0, + "content": "Generalization of the NUC Module. In Tab. 8, we test the UniCD on images with various degrees of nonuniformity degradation without retraining the NUC module. We control the severity of degradation using the formula \\( Y = C + k * B \\), where the \\( k \\)-value determines the level of degradation. The correction results at different \\( k \\)-values indicate that the NUC module generalizes well to various degradation levels." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.529, + 0.906, + 0.636 + ], + "angle": 0, + "content": "Scalability of the NUC Module. From Tab. 9, we observe that, except for the P value of LESPS, introducing our correction module significantly boosts the detection performance of several recent general and infrared target detection methods. This indicates that our NUC module can be flexibly integrated as a scalable component into existing detectors to enhance infrared images for detection purposes." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.649, + 0.634, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.675, + 0.907, + 0.9 + ], + "angle": 0, + "content": "In this paper, we propose UniCD, an end-to-end framework that simultaneously addresses bias field correction and infrared UAV target detection. We develop a NUC module that removes bias fields and restores clear images with parameters adaptively predicted by a lightweight network. Additionally, we introduce auxiliary losses with mask supervision to enhance UAV target features and suppress the background. We also present a self-supervised feature loss to improve the robustness of detection to varying bias levels. Moreover, we construct a new dataset IRBFD to facilitate future research. Experimental results show that our UniCD outperforms previous approaches in both synthetic and real-world scenarios. Furthermore, our method shows great potential for deployment on resource-constrained edge devices." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11905" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.168 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by the Open Research Fund of the National Key Laboratory of Multispectral Information Intelligent Processing Technology under Grant 61421132301, and the Natural Science Foundation of Jiangsu Province under Grant BK202302028." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.181, + 0.188, + 0.197 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.206, + 0.484, + 0.262 + ], + "angle": 0, + "content": "[1] Yanpeng Cao and Christel-Loic Tisse. Single-image-based solution for optics temperature-dependent nonuniformity correction in an uncooled long-wave infrared camera. Optics Letters, 39(3):646-648, 2014. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.1, + 0.264, + 0.484, + 0.319 + ], + "angle": 0, + "content": "[2] Yi Chang, Luxin Yan, Li Liu, Houzhang Fang, and Sheng Zhong. Infrared aerothermal nonuniform correction via deep multiscale residual network. 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In Proceedings of International Conference on Learning Representations (ICLR), 2021. 6" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11907" + } + ] +] \ No newline at end of file diff --git a/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_origin.pdf b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f8788889dddb82c7da041840336167c655e85327 --- /dev/null +++ b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/c87793a3-7dc6-4ae0-b5e0-3251be204e39_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:09f7de3ec7d68b521dfbc1cb16f646fc7808c59700ac6291242d425cdb895f4c +size 4649044 diff --git a/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/full.md b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5dd0070b9cda6f7a6a06ab767d076a6659ab2c26 --- /dev/null +++ b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/full.md @@ -0,0 +1,322 @@ +# Detection-Friendly Nonuniformity Correction: A Union Framework for Infrared UAV Target Detection + +Houzhang Fang $^{1\dagger}$ , Xiaolin Wang $^{1\dagger}$ , Zengyang Li $^{1}$ , Lu Wang $^{1}$ , Qingshan Li $^{1}$ , Yi Chang $^{2}$ , Luxin Yan $^{2}$ , Xidian University ${}^{2}$ Huazhong University of Science and Technology + +houzhangfang@xidian.edu.cn,wxl@stu.xidian.edu.cn，22009200694@stu.xidian.edu.cn，wanglu@xidian.edu.cn， qshli@mail.xidian.edu.cn，yichang@hust.edu.cn，yanluxin@hust.edu.cn + +# Abstract + +Infrared unmanned aerial vehicle (UAV) images captured using thermal detectors are often affected by temperature-dependent low-frequency nonuniformity, which significantly reduces the contrast of the images. Detecting UAV targets under nonuniform conditions is crucial in UAV surveillance applications. Existing methods typically treat infrared nonuniformity correction (NUC) as a preprocessing step for detection, which leads to suboptimal performance. Balancing the two tasks while enhancing detection-beneficial information remains challenging. In this paper, we present a detection-friendly union framework, termed UniCD, that simultaneously addresses both infrared NUC and UAV target detection tasks in an end-to-end manner. We first model NUC as a small number of parameter estimation problem jointly driven by priors and data to generate detection-conducive images. Then, we incorporate a new auxiliary loss with target mask supervision into the backbone of the infrared UAV target detection network to strengthen target features while suppressing the background. To better balance correction and detection, we introduce a detection-guided self-supervised loss to reduce feature discrepancies between the two tasks, thereby enhancing detection robustness to varying nonuniformity levels. Additionally, we construct a new benchmark composed of 50,000 infrared images in various nonuniformity types, multi-scale UAV targets and rich backgrounds with target annotations, called IRBFD. Extensive experiments on IRBFD demonstrate that our UniCD is a robust union framework for NUC and UAV target detection while achieving real-time processing capabilities. Dataset can be available at https://github.com/IVPLaboratory/UniCD. + +# 1. Introduction + +Unmanned aerial vehicle (UAV) detection based on infrared imaging is an important perception technology for moni + +![](images/5fbf300760c62ddb6872d9a836a9614dcff20d136d0052c2545583056ecbd2c1.jpg) + +![](images/75e6ed8f9bef16d42f6c8461d316bd619b5b6baa4f31223a14f059ec034cd962.jpg) + +![](images/8f26bbef8ece87b0e35d76644659eaa05bd7dc798261b39eee98636ae4e5b950.jpg) +Figure 1. Three main categories of methods for UAV target detection in nonuniformity conditions. (a) Direct: detection models [10] are directly applied to nonuniformity degraded images. (b) Separate: correction model [15] serves as a pre-processing step, correcting images before passing them to detectors [10]. (c) Union: correction and detection are processed simultaneously in a unified framework. Previous methods solely concentrates on optimizing one task. Our UniCD concurrently emphasizes the joint enhancement of correction quality and detection accuracy. + +toring UAV in both day and night scenarios. However, the thermal radiation from the optical lens and the camera housing causes the acquired infrared UAV images to often suffer from the temperature-dependent low-frequency nonuniformity effects [15, 23, 26, 33] (See the left column of Fig. 1). The optics-caused nonuniformity effect is also referred to as the bias field, which reduces the image contrast. Moreover, the infrared UAV targets typically have weak features and complex backgrounds [4, 5]. Nonuniformity bias field further exacerbates the difficulty of UAV target detection. Infrared nonuniformity correction (NUC) and target detection have achieved significant advancements in recent years [2, 4, 5, 17, 23, 28]. Previous methods focus on one aspect of the tasks and address the two tasks independently. As far as we know, no work considers the practical problem: infrared UAV target detection under the nonuniformity conditions. + +To solve this problem, a simple strategy is to detect [10] + +UAV targets directly on the degraded bias field images (See Fig. 1(a)), which easily leads to miss detection due to the weakening of target information. Another typical approach is the correction-then-detection paradigm (See Fig. 1(b)). NUC methods [15, 22, 26] are first adopted to remove the nonuniformity bias field, and the corrected images are then passed to the target detectors [4, 5, 10]. However, the existing NUC methods have limitations. Specifically, model-based NUC methods rely heavily on handcrafted features to model the images and bias fields, making them prone to overfitting the image content and thus struggle to handle complex or severely degraded bias fields [26]. Deep learning (DL)-based NUC methods depend on complex architectures and a large number of real input-output image pairs, which limits their practicality [2, 23]. Additionally, the NUC lacks supervision from the detection module to enhance detection-conducive information. Recently, joint methods for processing low-level images and high-level vision have already been proposed [11, 12, 18]. However, they are primarily designed for object detection under adverse weather conditions. + +To overcome the above limitations, in this paper, we propose a detection-friedly union framework, termed UniCD, that simultaneously tackles both infrared bias field correction and UAV target detection. On the one hand, because of the spatially smooth nature of the bias field, we model it by the high-order bivariate polynomial [16, 22, 26], which can effectively fit the nonuniform bias field with different scales. As a result, accurately estimating the optimal polynomial coefficients is essential for ensuring the performance of bias field correction. In this work, we formulate bias field correction as a problem of predicting a small number of polynomial coefficients jointly driven by priors and data, which can be easily learned by a very lightweight network. The bias field has spatially continuous low-frequency characteristics, making transformer-based architecture well-suited for modeling this component. Additionally, we also integrate convolutional neural networks (CNNs) to capture the local details of the bias field. By incorporating parametric prior modeling and low-dimensional data-driven prediction, our approach avoids dependence on handcrafted features and real input-output data pairs, significantly improving correction performance. On the other hand, existing DL-based detection methods mainly focus on designing complex model architectures for extracting features [4, 5, 17, 19, 28, 31, 32]. We further introduce auxiliary loss with target mask supervision at different stages of the backbone in the infrared UAV target detection network without increasing computational complexity. Integrating this loss enhances the discriminative features of UAV targets while suppressing the background, thereby improving detection performance. + +To balance correction and detection, we introduce a + +detection-guided self-supervised loss to reduce feature discrepancies between the correction and detection tasks. This loss enforces feature similarity between the corrected image and the reference image, both extracted by the detection backbone, thus ensuring high correction quality while enhancing features that are beneficial for detection. Our NUC model can also be flexibly integrated as a scalable module with existing detectors for infrared image bias field correction. Furthermore, we construct the bias field benchmark, IRBFD, consisting of 50,000 infrared images with varying nonuniformity types, multi-scale UAV targets, and rich backgrounds with target annotations, called IRBFD. Experimental results on the IRBFD demonstrate that UniCD outperforms state-of-the-art (SOTA) combined correction and detection methods in terms of precision and recall. + +The contributions of this work can be summarized as: + +- We propose a novel detection-friedly union framework, termed UniCD, that can simultaneously deal with NUC and infrared UAV target detection in an end-to-end manner. To the best of our knowledge, this is the first work to address both issues in a unified framework. +- We for the first time model nonuniformity bias field correction as a problem of predicting a small number of hyperparameters jointly driven by priors and data, which can be easily performed with a very lightweight network. +- We establish the first large benchmark called IRBFD to facilitate the research in the area of nonuniformity correction and infrared UAV target detection, which consists of 50,000 manually labeled infrared images with various nonuniformity levels, multi-scale UAV targets and rich backgrounds with target annotations. + +# 2. Related Work + +# 2.1. Nonuniformity Correction in Infrared Images + +NUC methods for removing the bias field are broadly divided into two main categories: model-driven methods and data-driven methods. Model-driven methods typically leverage the prior constraints of the bias field and the images to remove the nonuniformity effects [1, 15, 16, 22, 25, 26]. However, these methods rely on handcrafted features with carefully tuned hyper-parameters, limiting their practicality in real-world applications. Data-driven DL methods [2, 14, 23] have gained increasing attention. However, DL-based correction models are often complex and rely on large amounts of training data with real correction labels, which restricts their widespread application in practical scenarios [6, 24, 27]. In contrast, we formulate a novel lightweight correction model driven by both parametric priors and data, which converges more easily. + +![](images/4431972c4a7c6240fac7b3ec1817d3911f3b4569f199542073978a8faa7880d1.jpg) +Figure 2. Overview of the proposed UniCD. Our UniCD integrates a bias field prediction network with an infrared UAV target detection network. These two components are fused into a unified pipeline and trained end-to-end. The target enhancement and background suppression (TEBS) loss is introduced to enhance UAV target features while suppressing the background. The bias robust loss is employed to balance correction and detection. + +# 2.2. Infrared UAV Target Detection + +In recent years, many methods have been developed to detect infrared UAV targets [3-5, 19, 21]. Infrared UAV targets are challenging due to their weak imaging features and complex backgrounds [7, 8, 29]. TAD [19] leveraged the inconsistent motion cues between UAV targets and the background to detect potential targets. Fang et al. [3] formulated the UAV detection task as a residual image prediction by learning the mapping from input images to residual images. DAGNet [5] introduced attention mechanisms to adaptively enhance the network's ability to discriminate between UAVs and the background. DANet [4] constructed a dynamic attention network for UAVs to enhance feature extraction capabilities. However, the above methods primarily focus on designing complex network structures for improving detection performance, while rarely exploring how to better enhance feature representation without increasing computational complexity. We focus on introducing new auxiliary losses into the backbone to boost the model's ability to represent UAV target features while suppressing the background. + +# 2.3. Joint Low-Level Image Processing and High-Level Vision Tasks + +Recently, joint approaches for image enhancement and object detection have emerged to further improve detection performance on low-quality images. One category of these methods utilized encoder-decoder architectures for image enhancement [12], but these modules are complex and hinder real-time performance. Another approach uses classical mathematical models for enhancement, replacing manually designed parameters with predictions from deep networks. IA-YOLO [18] integrated an adaptive enhancement strategy with YOLOv3 [20] via a differentiable image processing module, improving detection in foggy conditions. BAD-Net [11] introduced a dual-branch structure to minimize the impact of poor dehazing performance on the detection module. However, the above methods are developed for visible light images degraded by adverse weather condi + +tions. To the best of our knowledge, no work has explored handling both NUC and UAV target detection for infrared imaging within a single framework. We propose an end-to-end framework to simultaneously improve both correction and detection performance. + +# 3. Detection-Friendly Union Method + +# 3.1. Overall Architecture + +In this section, we propose a novel network architecture, UniCD, as shown in Fig. 2. The UniCD leverages a lightweight prediction network to estimate the bias field and then passes the corrected image to a UAV detection network tailored for UAV targets. Additionally, during the joint training of image correction and detection tasks, we employ a detection-guided self-supervised loss to minimize feature discrepancies between the two tasks. Finally, we construct a new dataset, IRBFD, to validate our approach. + +# 3.2. Prior- and Data-Driven Nonuniformity Correction + +Infrared UAV images captured by thermal detectors often suffer from low-frequency nonuniformity, which significantly impacts target detection performance. Existing model-driven correction methods often struggle to handle complex non-uniformities, while deep learning-based methods suffer from high network complexity. To address these issues, we propose a lightweight correction network that combines parametric prior knowledge with the strong learning capabilities of deep neural networks. The network architecture is shown in Fig. 2. + +Generally, the degraded infrared image can be represented as follows [2, 16]: + +$$ +Y = C + B, \tag {1} +$$ + +where $Y$ , $C$ , and $B$ represent the degraded image, the clear image, and the bias field, respectively. Thus, once $B$ is available, the corrected image $R$ can be obtained as $Y - B$ . Under ideal conditions, $R$ is theoretically equivalent to the clear image $C$ . The bias field $B$ possesses a + +spatially smooth property, allowing us to model it using the following bivariate polynomial: + +$$ +B \left(x _ {i}, y _ {j}\right) = \sum_ {t = 0} ^ {D} \sum_ {s = 0} ^ {D - t} a _ {t, s} x _ {i} ^ {t} y _ {j} ^ {s} = \mathbf {m} ^ {\top} \mathbf {a}, \tag {2} +$$ + +where $(x_{i},y_{j})$ , $D$ , and $\mathbf{m}$ denote the image coordinates, the degree of the polynomial, and the column vector holding the monomial terms, respectively. The column vector $\mathbf{a}$ represents the coefficients of the polynomial formed by concatenating $\{a_{t,s}\}$ . To reduce the redundancy of the basic plane and the computational complexity of higher-order models, we set the degree $D$ to 3. + +Accurate estimation of the polynomial coefficients $\mathbf{a}$ is crucial for improving bias field correction performance. In this work, we design a lightweight bias field prediction network that can estimate the model parameters accurately and efficiently. + +In our NUC module, we first downsample the degraded image $Y$ by a factor of two, resulting in the downsampled image $Y_{\mathrm{down}}$ . Then, we utilize the global bias field encoder (GBFE) and the local bias field encoder (LBFE) to extract features at different granularities. The GBFE, inspired by the RSTB [13] module, includes two Swin Transformer layers with the hidden layer channel dimension reduced to 16. The LBFE consists of two spatial attention modules in series, allowing it to capture localized features more effectively. The global and local features, $F_{\mathrm{global}}$ and $F_{\mathrm{local}}$ , are fused to form the final feature representation $F_{\mathrm{fused}}$ : + +$$ +F _ {\text {f u s e d}} = \mathrm {G B F E} \left(Y _ {\text {d o w n}}\right) + \mathrm {L B F E} \left(Y _ {\text {d o w n}}\right). \tag {3} +$$ + +Finally, the fused features $F_{\mathrm{fused}}$ pass through five $3 \times 3$ convolutional layers (Conv5) and a fully connected (FC) layer to predict the final coefficient vector $\hat{\mathbf{a}}$ : + +$$ +\hat {\mathbf {a}} = \operatorname {F C} \left(\operatorname {C o n v} _ {5} \left(F _ {\text {f u s e d}}\right)\right). \tag {4} +$$ + +This approach enables the network to adaptively adjust to inputs with varying levels of degradation, effectively predicting the coefficient vector $\hat{\mathbf{a}}$ for bias field correction. + +Analysis. Compared to existing model-driven methods, our approach avoids reliance on hand-crafted features. Compared to existing data-driven methods, our approach transforms the high-dimensional image space prediction into a low-dimensional data-driven problem with a few hyperparameters, effectively reducing computational complexity and improving correction performance. + +Loss Function. We calculate the mean absolute error (MAE) loss between the predicted coefficients $\hat{\mathbf{a}}$ and the predefined coefficients $\mathbf{a}$ to minimize the discrepancy between them. The MAE loss is defined as: + +$$ +L _ {c o r} = \frac {1}{N} \| \hat {\mathbf {a}} - \mathbf {a} \| _ {2} ^ {2}, \tag {5} +$$ + +where $N$ is the total number of elements in the vector $\mathbf{a}$ . By minimizing this loss, we improve the accuracy of the + +![](images/6d060feb0f5305d0e4109b13ce90ea5f067bf03ca63eacbb14849c506d77039a.jpg) +Figure 3. Calculation of the proposed feature enhancement and background suppression (TEBS) loss. + +corrected image, making it closer to the ideal clear image. This loss function is used to pre-train the NUC module separately, serving as the initial weights for the joint training of correction and detection. + +# 3.3. Mask-Supervised Infrared UAV Detector + +We select DANet [4] as our baseline detector, which constructs a multi-scale dynamic perception network to address the challenges of multi-scale variations in UAV targets. Infrared UAV targets typically have weak features and complex backgrounds, and existing methods often enhance feature extraction through complex model architectures. In this work, we design an auxiliary loss function for further target enhancement and background suppression (TEBS) without increasing network complexity, as illustrated in Figs. 2 and 3. + +Specifically, we first convert the bounding boxes of the ground-truth into a binary mask $M$ , assigning a value of 1 to the target region and 0 to the background region: + +$$ +M (x, y) = \left\{ \begin{array}{l l} 1, & \text {i f} (x, y) \in \text {t a r g e t r e g i o n}, \\ 0, & \text {i f} (x, y) \in \text {b a c k g r o u n d r e g i o n}. \end{array} \right. \tag {6} +$$ + +This mask is then used to compute a binary cross-entropy loss with the feature maps $F_{i}$ from the $i$ -th stage of the backbone network. The TEBS loss $L_{\mathrm{TEBS}}$ is obtained by summing the losses from four stages of the backbone and averaging: + +$$ +L _ {T E B S} = \frac {1}{4} \sum_ {i = 1} ^ {4} L _ {C E} (M, F _ {i}), \tag {7} +$$ + +where $L_{CE}(\cdot ,\cdot)$ denotes the cross-entropy loss. + +The TEBS loss offers three key benefits: (1) Supervision on the target regions helps the backbone network to quickly focus on the feature learning of infrared UAV targets and enhance localization accuracy; (2) Supervision on background regions effectively suppresses non-target features, thereby reducing clutter and noise interference in the features; (3) The loss enhances training efficiency by guiding the network to learn target features more accurately, leading to faster convergence. + +The classification and regression losses are kept consistent with the baseline method. The final detector loss is written as: + +$$ +L _ {d e t} = L _ {c l s} + L _ {r e g} + \lambda L _ {T E B S}, \tag {8} +$$ + +where $\lambda$ is set to 1 for the first 20 epochs to accelerate convergence and improve localization performance in the early + +![](images/3335fc6a6ab6fe0dada27057165fe5f1d69da59a62e7937a56ff748c69c1b518.jpg) +Figure 4. Construction of the bias-robust loss in the unified NUC and detection framework. + +stages. After 20 epochs, $\lambda$ is reduced to 0.01 to balance with the gradually decreasing loss and avoid impacting classification accuracy. + +# 3.4. Balance Correction and Detection with Bias-Robust Loss + +Existing research [11, 18] shows that incorporating supervision losses from low-level vision tasks in joint training can hinder high-level vision task performance. This is because low-level tasks focus on preserving fine image details, while high-level tasks aim to extract target-specific features and ignore irrelevant background information. This conflict can hinder convergence during joint training, causing the high-level vision task to settle into a local optimum. + +To address this issue, we design a self-supervised loss, named bias robust (BR) loss, to achieve detection-friendly NUC, as illustrated in Fig. 4. Specifically, during joint training, the clear image $C$ and the corrected image $R$ obtained via the NUC module are simultaneously fed into the backbone of the detection model. Let $F_{C}^{(i)}$ and $F_{R}^{(i)}$ represent the feature maps from the $i$ -th stage of the detection backbone, where $i = 1,2,3,4$ denotes the four different stages. Here, clear images are employed only for the joint training of correction and detection on the synthetic dataset and are not applied to NUC training on real infrared images. + +To evaluate the alignment of the corrected image with the clear image in the feature space, we compute the cosine similarity between the feature maps at each stage $i$ as follows: + +$$ +\operatorname {C o s} \operatorname {S i m} \left(F _ {C} ^ {(i)}, F _ {R} ^ {(i)}\right) = \frac {F _ {C} ^ {(i)} \cdot F _ {R} ^ {(i)}}{\left\| F _ {C} ^ {(i)} \right\| \left\| F _ {R} ^ {(i)} \right\|}. \tag {9} +$$ + +The details of the cosine similarity calculation are placed in the supplementary materials. The BR loss is obtained by summing the cosine similarities across all stages and averaging them: + +$$ +L _ {B R} = \frac {1}{4} \sum_ {i = 1} ^ {4} \left(1 - \operatorname {C o s} _ {-} \operatorname {S i m} \left(F _ {C} ^ {(i)}, F _ {R} ^ {(i)}\right)\right). \tag {10} +$$ + +The BR loss function is designed to maximize the consistency between the feature representations of the clear and corrected images, thereby enhancing the fidelity of the corrected image within the feature space and ensuring that it retains essential characteristics beneficial for detection. The final union loss function for the joint training process $L_{uni}$ is written as: + +$$ +L _ {u n i} = L _ {d e t} + L _ {B R}. \tag {11} +$$ + +As illustrated in Fig. 1, the union loss $L_{uni}$ ensures effective bias field correction while maximizing detection performance by backpropagating through each part of the network. Compared to separate training of NUC and detection networks, this integrated approach enables a more balanced optimization, leading to enhanced results in both correction and detection tasks. + +# 3.5.IRBFD Dataset + +We construct a new benchmark called IRBFD, comprising 30,000 synthetic nonuniformity infrared UAV images (IRBFD-syn) and 20,000 real-world infrared UAV images with nonuniformity field (IRBFD-real). The IRBFD-syn subset provides paired degraded and clear images, with the synthesis process based on Eqs. (1) and (2). The characteristics of the dataset are summarized as follows. (1) Multiple background types. The IRBFD includes multiple complex scenes, such as dense clouds, buildings, forests, urban areas, and sea. (2) Multi-scale variations. The distance between the UAVs and the sensor ranges from 50 meters to 2 kilometers, resulting in multi-scale variations of the targets. (3) Multiple UAV types. Such as the DJI Inspire, Matrice, Phantom, Mavic, and Mini series. All UAV positions are manually annotated. IRBFD serves as a comprehensive resource for evaluating the impact of non-uniformities on UAV target detection in real-world environments. All images have a size of $640 \times 512$ . Additional details can be found in the supplementary material. + +# 4. Experiment + +# 4.1. Datasets and Evaluation Metrics + +Datasets. We use two parts of the IRBFD dataset: IRBFD-syn and IRBFD-real. IRBFD-syn consists of simulated nonuniform infrared images, allowing us to train the model with controlled background images and varying non-uniformities. Training, validation, and testing sets are split in an 8:1:1 ratio. We train on the simulated dataset and directly validate on real-world dataset to demonstrate the generalizability of our method. + +Evaluation Metrics. For NUC, we use peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) as objective evaluation metrics. For target detection, we evaluate the detection performance using precision (P) and recall (R). Lastly, for real-time performance, we use frames per second (FPS) as the evaluation metric. The signal-to-clutter ratio gain (SCRG) is the ratio of SCR in the corrected image to that in the original image, used to evaluate the improvement in target detectability achieved by the correction method. + +Table 1. Quantitative comparison of the proposed method with SOTA methods on the synthetic dataset IRBFD-syn. **Bold** and **underline** indicate the best and the second best results, respectively. + +
    StrategyModuleMetrics
    NUCDetectionPub'YearPSNRSSIMPRFPS
    Direct-Deformable DETRICLR'210.6140.63024
    DINOICLR'230.9040.64026
    DAGNetTII'23--0.9940.63543
    LESPSCVPR'230.0330.44612
    MSHNetCVPR'240.4070.42141
    YOLO11L20240.9630.60242
    SeparateLiuYOLO11LIPT'1616.8000.82890.8980.574<1
    DAGNet0.9780.578<1
    DMRNYOLO11LGRSL'1924.4670.86000.9230.55035
    DAGNet0.9660.59536
    ShiYOLO11LAO'2213.9740.77830.9240.455<1
    DAGNet0.9660.472<1
    TV-DIPYOLO11LIPT'2313.3970.63740.1310.02029
    DAGNet0.5990.02030
    AHBCYOLO11LTGRS'2413.9540.67630.8250.080<1
    DAGNet0.7240.040<1
    UnionUniCD-31.9610.98270.9990.82232
    + +Table 2. Quantitative comparison of the proposed method with SOTA methods on the real dataset IRBFD-real. + +
    StrategyNUCDetectionSCRGPR
    Direct-DINO0.9710.660
    YOLO11L-0.9660.843
    DAGNet0.9920.871
    SeparateTV-DIPYOLO11L0.4120.5210.024
    DAGNet0.6630.026
    AHBCYOLO11L1.1460.9400.633
    DAGNet0.9860.699
    UnionUniCD1.2860.9940.901
    + +# 4.2. Implementation Details + +We use Adam as the optimizer, with a learning rate of 0.001. The training lasts for 50 epochs, with a weight decay of $10^{-4}$ and a batch size of 4. During training, we only apply random horizontal flipping for data augmentation. Our experiments are conducted on an NVIDIA RTX 4090 with CUDA 12.4 and PyTorch 1.7. For NUC, we select Liu [15], Shi [22], and AHBC [26] as the traditional bias field correction methods; DMRN [2] and TV-DIP [14] as the DL-based correction methods. They are all designed for infrared images. For target detection, we select YOLO11L [9] (large version), DAGNet [5], LESPS [28], and MSHNet [17] as the convolutional neural network (CNN)-based target detection methods. DAGNet, LESPS, and MSHNet are designed for infrared target detection. Deformable DETR [34] and DINO [30] are the representative Transformer-based detection methods. + +# 4.3. Quantitative Results + +As shown in Tab. 1, the existing detection methods obtain low P and R values when detecting directly on the degraded bias field images. DAGNet has a high P value of 0.994 but a low recall. This indicates that the bias field has an adverse + +![](images/3725632855b1b68f113d1738104cfaf0c15f464315695890510b90abaa620557.jpg) +Figure 5. P-R curves of our UniCD and other correction-then-detection methods on the IRBFD-syn. The area values under the curves are placed after the method names. + +effect on the UAV target detection. For the separate strategy, the DL-based method DMRN enhances image quality, achieving notable improvements in PSNR and SSIM. Other correction methods, such as Liu, Shi, and AHBC, are less effective for severely degraded images, which further impacts detection accuracy. Table 2 shows that the three detection methods achieve high P and R when directly detecting on real images with low degradation levels. YOLO11L and DAGNet have lower P and R values for images corrected by TV-DIP, as TV-DIP not only lacks corrective effects but also deteriorates the image content. In contrast, the proposed UniCD achieves the best performance in terms of all the evaluation metrics compared with SOTA methods in Tab. 1 for the synthetic dataset and Tab. 2 for the real dataset. Specially, our UniCD achieves a real-time processing speed of 32 FPS. We also plot the R-R curves for our UniCD and other correction-then-detection methods on the IRBFD dataset shown in Fig. 5. Higher values of the area under the curve indicate better performance. It can be seen that our UniCD achieves the largest area under the curve among all correction-then-detection methods. + +# 4.4. Qualitative Results + +As demonstrated in Fig. 6, we show qualitative results from various separate correction-then-detection methods and our UniCD on the IRBFD-syn dataset across three distinct scenarios: buildings, hillside, and clouds. As can be seen, even in severe degraded bias field situations, our UniCD can still perform high-quality image correction while accurately detecting the UAV targets. This is because the proposed NUC correction module integrates parametric modeling and a small number of model parameter predictions, enabling more accurate parameter estimation. Meanwhile, our detection network introduces auxiliary loss with target mask supervision into the backbone to enhance the features of UAV targets while suppressing the background, thereby improving detection performance. Conventional correction methods, such as Liu and AHBC, have limited modeling capabilities and are prone to producing bias field residuals. + +![](images/99e4b3bbcde5fd5cb4b3b76ec7ac59bf1a86cfcf67a645acbe15c4cac16cd3dd.jpg) +Figure 6. Visual comparison of results from separate correction followed by detection methods and our UniCD on the IRBFD-syn dataset. Closed-up views are shown in the left bottom corner. Boxes in green and red represent ground-truth and correctly detected targets, respectively. + +![](images/47b1a76b466a957e40bfc76f1a90f7dd5cbc1a302aab4234bf72bc20ec912ffc.jpg) +Figure 7. Visual comparison of results from separate correction-then-detection methods and our UniCD on the IRBFD-real dataset. + +Table 3. Ablation study of polynomial degrees. + +
    DegreeNumber of coefficientsPSNRSSIMPR
    2613.52790.75900.9910.433
    31039.0500.99700.9970.810
    41531.7440.98900.9970.788
    52129.0700.98300.9970.787
    + +The corrected image from DMRN exhibits block artifacts. Existing detection methods produce false alarms or miss detections on the above-corrected images; similar results are observed in Fig. 7 for scenes degraded by real bias fields. See the supplementary material for more visual results. + +# 4.5. Ablation Study + +In this section, we report ablation study results. + +Impact of polynomial degrees. We conduct experiments to determine the optimal polynomial degree, as described in Tab. 8. The results indicate that the highest values for all correction and detection metrics are achieved when the degree is set to 3. Compared to higher-order polyno + +Table 4. Ablation study of the LBFE and GBFE modules. + +
    LBFEGBFEParams (M)FLOPs (G)PSNRSSIMFPS
    ××0.37860.119227.2180.9808555
    ✓×0.38120.274730.2420.9877370
    ×✓0.39401.515937.8880.9961151
    ✓✓0.39661.680939.0500.9970116
    + +mials, a third-order polynomial has lower complexity and less redundancy. A lower degree implies weaker modeling capability, resulting in poor correction performance. + +Impact of the LBFE and GBFE components. As presented in Tab. 4, when using only LBFE or GBFE, we can see that the PSNR of the correction model already achieves 30.242 and 37.888, respectively, surpassing the 27.218 of the baseline. When combined with LBFE and GBFE, further improvements can be achieved, reaching 39.050 with only 1.6809G FLOPs and 0.3966M parameters on an image size of $640 \times 512$ . Additionally, the SSIM value has also shown some slight improvements. This suggests that the Transformer architecture combined with the CNN structure + +Table 5. Ablation study of the auxiliary TEBS loss. + +
    TEBS LossPR
    w/o0.9930.762
    w0.9970.810
    + +![](images/e851cf7dd3b547ecc6ff7ffab009854d5ea71e04ffd3cff2c406da5e50318e0f.jpg) +Figure 8. Comparison of feature maps from the detection backbone at different stages with and without TEBS loss. + +Table 6. Ablation study of BR loss on the synthetic dataset IRBFD-syn. Here, the direct and separate strategies utilize the correction and detection modules proposed in UniCD. + +
    StrategyCorrection lossDetection lossBR lossMetrics
    PSNRSSIMPR
    Direct×√×--0.9980.694
    Separate√√×37.7220.99600.9990.793
    Union√√×33.0240.98270.9980.791
    Union×√×17.9400.89100.9890.811
    UniCD×√√31.9610.98270.9990.822
    + +can effectively model bias fields, significantly improving performance while maintaining high real-time efficiency. + +Impact of the auxiliary TEBS loss. As shown in Tab. 5, the auxiliary TEBS loss added to the backbone of the UAV detection network leads to improvements in both P and R performance. The TEBS loss imposes strong constraints on the target and background masks for the backbone features, enhancing target features while suppressing the background, thus improving detection performance, as depicted in Fig. 8. In the absence of TEBS loss, the targets are generally weak and there is considerable residual background. + +Impact of BR loss. As shown in Tab. 6, the direct detection results in low P and R. The correction-then-detection separate method without BR loss in the second row obtains high PSNR, SSIM and P, but with low R because of the independent processing of the two tasks. The union of correction and detection without BR loss in the third row leads to a decrease in PSNR, SSIM, P, and R due to the conflict between the two tasks. The union of correction and detection without correction and BR losses in the fourth row significantly reduces PSNR and SSIM owing to the detection module's sole constraint. Our UniCD achieves the highest R value and P value exceeding 0.99, demonstrating that our union framework effectively balances correction and detection through the self-supervised BR loss. + +Effectiveness of UniCD on real dataset. As shown in Tab. 7, we use the NUC module weights trained on the IRBFD-syn and directly test them on the IRBFD-real. This configuration is referred to as $\mathrm{UniCD}^{\star}$ . The direct and separate methods with the modules in UniCD achieve a high P + +Table 7. Ablation study of our UniCD on the IRBFD-real. + +
    StrategySCRGPR
    Direct-0.9920.887
    Separate1.2860.9980.812
    UniCD*1.2860.9940.901
    + +Table 8. Ablation study of varying levels of nonuniformity. + +
    K-valuePSNRSSIM
    329.1190.9891
    534.9070.9950
    1238.3610.9968
    + +Table 9. Ablation study of the union of our scalable NUC module with existing detection methods. + +
    Our NUCDetectionPRFPS
    ×YOLO11L0.8350.07542
    DAGNet0.7110.03643
    LESPS0.0070.12212
    MSHNet0.2840.22142
    √YOLO11L0.977(+)0.1420.657(+0.582)31
    DAGNet0.997(+0.286)0.722(+0.686)31
    LESPS0.007(+0.000)0.459(+0.337)11
    MSHNet0.776(+0.492)0.701(+0.480)31
    + +but a low R. Our UniCD obtains the highest R value and P value exceeding 0.99, thereby validating the effectiveness and generalization of our union framework on the real dataset. + +Generalization of the NUC Module. In Tab. 8, we test the UniCD on images with various degrees of nonuniformity degradation without retraining the NUC module. We control the severity of degradation using the formula $Y = C + k * B$ , where the $k$ -value determines the level of degradation. The correction results at different $k$ -values indicate that the NUC module generalizes well to various degradation levels. + +Scalability of the NUC Module. From Tab. 9, we observe that, except for the P value of LESPS, introducing our correction module significantly boosts the detection performance of several recent general and infrared target detection methods. This indicates that our NUC module can be flexibly integrated as a scalable component into existing detectors to enhance infrared images for detection purposes. + +# 5. Conclusion + +In this paper, we propose UniCD, an end-to-end framework that simultaneously addresses bias field correction and infrared UAV target detection. We develop a NUC module that removes bias fields and restores clear images with parameters adaptively predicted by a lightweight network. Additionally, we introduce auxiliary losses with mask supervision to enhance UAV target features and suppress the background. We also present a self-supervised feature loss to improve the robustness of detection to varying bias levels. Moreover, we construct a new dataset IRBFD to facilitate future research. Experimental results show that our UniCD outperforms previous approaches in both synthetic and real-world scenarios. Furthermore, our method shows great potential for deployment on resource-constrained edge devices. + +Acknowledgments. This work was supported by the Open Research Fund of the National Key Laboratory of Multispectral Information Intelligent Processing Technology under Grant 61421132301, and the Natural Science Foundation of Jiangsu Province under Grant BK202302028. + +# References + +[1] Yanpeng Cao and Christel-Loic Tisse. Single-image-based solution for optics temperature-dependent nonuniformity correction in an uncooled long-wave infrared camera. Optics Letters, 39(3):646-648, 2014. 2 +[2] Yi Chang, Luxin Yan, Li Liu, Houzhang Fang, and Sheng Zhong. Infrared aerothermal nonuniform correction via deep multiscale residual network. IEEE Geoscience and Remote Sensing Letters, 16(7):1120-1124, 2019. 1, 2, 3, 6 +[3] Houzhang Fang, Lan Ding, Liming Wang, Yi Chang, Luxin Yan, and Jinhui Han. 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In Proceedings of International Conference on Learning Representations (ICLR), 2021. 6 \ No newline at end of file diff --git a/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/images.zip b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c03232600d455e78a7070903c47458d53649e433 --- /dev/null +++ b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fab9e8e0eea2a2ebf504d90d175cbc37a890a53af6d8a08e34b3f11cbcf76663 +size 639517 diff --git a/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/layout.json b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..0bd18273f8ecde3f33d54852f457dd259f96d58a --- /dev/null +++ b/2025/Detection-Friendly Nonuniformity Correction_ A Union Framework for Infrared UAV Target Detection/layout.json @@ -0,0 +1,7739 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 56, + 103, + 555, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 103, + 555, + 140 + ], + "spans": [ + { + "bbox": [ + 56, + 103, + 555, + 140 + ], + "type": "text", + "content": "Detection-Friendly Nonuniformity Correction: A Union Framework for Infrared UAV Target Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "spans": [ + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": "Houzhang Fang" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": ", Xiaolin Wang" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": ", Zengyang Li" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": ", Lu Wang" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": ", Qingshan Li" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": ", Yi Chang" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": ", Luxin Yan" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": ", Xidian University " + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "inline_equation", + "content": "{}^{2}" + }, + { + "bbox": [ + 66, + 160, + 543, + 194 + ], + "type": "text", + "content": "Huazhong University of Science and Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 195, + 547, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 195, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 61, + 195, + 547, + 217 + ], + "type": "text", + "content": "houzhangfang@xidian.edu.cn,wxl@stu.xidian.edu.cn，22009200694@stu.xidian.edu.cn，wanglu@xidian.edu.cn， qshli@mail.xidian.edu.cn，yichang@hust.edu.cn，yanluxin@hust.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 245, + 200, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 245, + 200, + 258 + ], + "spans": [ + { + "bbox": [ + 151, + 245, + 200, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 270, + 297, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 270, + 297, + 643 + ], + "spans": [ + { + "bbox": [ + 54, + 270, + 297, + 643 + ], + "type": "text", + "content": "Infrared unmanned aerial vehicle (UAV) images captured using thermal detectors are often affected by temperature-dependent low-frequency nonuniformity, which significantly reduces the contrast of the images. Detecting UAV targets under nonuniform conditions is crucial in UAV surveillance applications. Existing methods typically treat infrared nonuniformity correction (NUC) as a preprocessing step for detection, which leads to suboptimal performance. Balancing the two tasks while enhancing detection-beneficial information remains challenging. In this paper, we present a detection-friendly union framework, termed UniCD, that simultaneously addresses both infrared NUC and UAV target detection tasks in an end-to-end manner. We first model NUC as a small number of parameter estimation problem jointly driven by priors and data to generate detection-conducive images. Then, we incorporate a new auxiliary loss with target mask supervision into the backbone of the infrared UAV target detection network to strengthen target features while suppressing the background. To better balance correction and detection, we introduce a detection-guided self-supervised loss to reduce feature discrepancies between the two tasks, thereby enhancing detection robustness to varying nonuniformity levels. Additionally, we construct a new benchmark composed of 50,000 infrared images in various nonuniformity types, multi-scale UAV targets and rich backgrounds with target annotations, called IRBFD. Extensive experiments on IRBFD demonstrate that our UniCD is a robust union framework for NUC and UAV target detection while achieving real-time processing capabilities. Dataset can be available at https://github.com/IVPLaboratory/UniCD." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 652, + 137, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 652, + 137, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 652, + 137, + 665 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 672, + 295, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 295, + 697 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 295, + 697 + ], + "type": "text", + "content": "Unmanned aerial vehicle (UAV) detection based on infrared imaging is an important perception technology for moni" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 244, + 550, + 289 + ], + "blocks": [ + { + "bbox": [ + 317, + 244, + 550, + 289 + ], + "lines": [ + { + "bbox": [ + 317, + 244, + 550, + 289 + ], + "spans": [ + { + "bbox": [ + 317, + 244, + 550, + 289 + ], + "type": "image", + "image_path": "5fbf300760c62ddb6872d9a836a9614dcff20d136d0052c2545583056ecbd2c1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 317, + 289, + 550, + 334 + ], + "blocks": [ + { + "bbox": [ + 317, + 289, + 550, + 334 + ], + "lines": [ + { + "bbox": [ + 317, + 289, + 550, + 334 + ], + "spans": [ + { + "bbox": [ + 317, + 289, + 550, + 334 + ], + "type": "image", + "image_path": "75e6ed8f9bef16d42f6c8461d316bd619b5b6baa4f31223a14f059ec034cd962.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 317, + 334, + 549, + 380 + ], + "blocks": [ + { + "bbox": [ + 317, + 334, + 549, + 380 + ], + "lines": [ + { + "bbox": [ + 317, + 334, + 549, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 334, + 549, + 380 + ], + "type": "image", + "image_path": "8f26bbef8ece87b0e35d76644659eaa05bd7dc798261b39eee98636ae4e5b950.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "lines": [ + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "spans": [ + { + "bbox": [ + 313, + 382, + 555, + 481 + ], + "type": "text", + "content": "Figure 1. Three main categories of methods for UAV target detection in nonuniformity conditions. (a) Direct: detection models [10] are directly applied to nonuniformity degraded images. (b) Separate: correction model [15] serves as a pre-processing step, correcting images before passing them to detectors [10]. (c) Union: correction and detection are processed simultaneously in a unified framework. Previous methods solely concentrates on optimizing one task. Our UniCD concurrently emphasizes the joint enhancement of correction quality and detection accuracy." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 494, + 556, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 494, + 556, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 494, + 556, + 696 + ], + "type": "text", + "content": "toring UAV in both day and night scenarios. However, the thermal radiation from the optical lens and the camera housing causes the acquired infrared UAV images to often suffer from the temperature-dependent low-frequency nonuniformity effects [15, 23, 26, 33] (See the left column of Fig. 1). The optics-caused nonuniformity effect is also referred to as the bias field, which reduces the image contrast. Moreover, the infrared UAV targets typically have weak features and complex backgrounds [4, 5]. Nonuniformity bias field further exacerbates the difficulty of UAV target detection. Infrared nonuniformity correction (NUC) and target detection have achieved significant advancements in recent years [2, 4, 5, 17, 23, 28]. Previous methods focus on one aspect of the tasks and address the two tasks independently. As far as we know, no work considers the practical problem: infrared UAV target detection under the nonuniformity conditions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "content": "To solve this problem, a simple strategy is to detect [10]" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 219, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 219, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 219, + 713 + ], + "type": "text", + "content": "*Corresponding author. †Equal contribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11898" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 323 + ], + "type": "text", + "content": "UAV targets directly on the degraded bias field images (See Fig. 1(a)), which easily leads to miss detection due to the weakening of target information. Another typical approach is the correction-then-detection paradigm (See Fig. 1(b)). NUC methods [15, 22, 26] are first adopted to remove the nonuniformity bias field, and the corrected images are then passed to the target detectors [4, 5, 10]. However, the existing NUC methods have limitations. Specifically, model-based NUC methods rely heavily on handcrafted features to model the images and bias fields, making them prone to overfitting the image content and thus struggle to handle complex or severely degraded bias fields [26]. Deep learning (DL)-based NUC methods depend on complex architectures and a large number of real input-output image pairs, which limits their practicality [2, 23]. Additionally, the NUC lacks supervision from the detection module to enhance detection-conducive information. Recently, joint methods for processing low-level images and high-level vision have already been proposed [11, 12, 18]. However, they are primarily designed for object detection under adverse weather conditions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 327, + 295, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 327, + 295, + 698 + ], + "spans": [ + { + "bbox": [ + 56, + 327, + 295, + 698 + ], + "type": "text", + "content": "To overcome the above limitations, in this paper, we propose a detection-friedly union framework, termed UniCD, that simultaneously tackles both infrared bias field correction and UAV target detection. On the one hand, because of the spatially smooth nature of the bias field, we model it by the high-order bivariate polynomial [16, 22, 26], which can effectively fit the nonuniform bias field with different scales. As a result, accurately estimating the optimal polynomial coefficients is essential for ensuring the performance of bias field correction. In this work, we formulate bias field correction as a problem of predicting a small number of polynomial coefficients jointly driven by priors and data, which can be easily learned by a very lightweight network. The bias field has spatially continuous low-frequency characteristics, making transformer-based architecture well-suited for modeling this component. Additionally, we also integrate convolutional neural networks (CNNs) to capture the local details of the bias field. By incorporating parametric prior modeling and low-dimensional data-driven prediction, our approach avoids dependence on handcrafted features and real input-output data pairs, significantly improving correction performance. On the other hand, existing DL-based detection methods mainly focus on designing complex model architectures for extracting features [4, 5, 17, 19, 28, 31, 32]. We further introduce auxiliary loss with target mask supervision at different stages of the backbone in the infrared UAV target detection network without increasing computational complexity. Integrating this loss enhances the discriminative features of UAV targets while suppressing the background, thereby improving detection performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 701, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 294, + 712 + ], + "type": "text", + "content": "To balance correction and detection, we introduce a" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 251 + ], + "type": "text", + "content": "detection-guided self-supervised loss to reduce feature discrepancies between the correction and detection tasks. This loss enforces feature similarity between the corrected image and the reference image, both extracted by the detection backbone, thus ensuring high correction quality while enhancing features that are beneficial for detection. Our NUC model can also be flexibly integrated as a scalable module with existing detectors for infrared image bias field correction. Furthermore, we construct the bias field benchmark, IRBFD, consisting of 50,000 infrared images with varying nonuniformity types, multi-scale UAV targets, and rich backgrounds with target annotations, called IRBFD. Experimental results on the IRBFD demonstrate that UniCD outperforms state-of-the-art (SOTA) combined correction and detection methods in terms of precision and recall." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 326, + 258, + 543, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 258, + 543, + 269 + ], + "spans": [ + { + "bbox": [ + 326, + 258, + 543, + 269 + ], + "type": "text", + "content": "The contributions of this work can be summarized as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 276, + 553, + 454 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 276, + 553, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 276, + 553, + 334 + ], + "spans": [ + { + "bbox": [ + 314, + 276, + 553, + 334 + ], + "type": "text", + "content": "- We propose a novel detection-friedly union framework, termed UniCD, that can simultaneously deal with NUC and infrared UAV target detection in an end-to-end manner. To the best of our knowledge, this is the first work to address both issues in a unified framework." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 315, + 335, + 553, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 335, + 553, + 382 + ], + "spans": [ + { + "bbox": [ + 315, + 335, + 553, + 382 + ], + "type": "text", + "content": "- We for the first time model nonuniformity bias field correction as a problem of predicting a small number of hyperparameters jointly driven by priors and data, which can be easily performed with a very lightweight network." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 384, + 553, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 384, + 553, + 454 + ], + "spans": [ + { + "bbox": [ + 315, + 384, + 553, + 454 + ], + "type": "text", + "content": "- We establish the first large benchmark called IRBFD to facilitate the research in the area of nonuniformity correction and infrared UAV target detection, which consists of 50,000 manually labeled infrared images with various nonuniformity levels, multi-scale UAV targets and rich backgrounds with target annotations." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 484, + 400, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 484, + 400, + 496 + ], + "spans": [ + { + "bbox": [ + 314, + 484, + 400, + 496 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 510, + 550, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 550, + 523 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 550, + 523 + ], + "type": "text", + "content": "2.1. Nonuniformity Correction in Infrared Images" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "content": "NUC methods for removing the bias field are broadly divided into two main categories: model-driven methods and data-driven methods. Model-driven methods typically leverage the prior constraints of the bias field and the images to remove the nonuniformity effects [1, 15, 16, 22, 25, 26]. However, these methods rely on handcrafted features with carefully tuned hyper-parameters, limiting their practicality in real-world applications. Data-driven DL methods [2, 14, 23] have gained increasing attention. However, DL-based correction models are often complex and rely on large amounts of training data with real correction labels, which restricts their widespread application in practical scenarios [6, 24, 27]. In contrast, we formulate a novel lightweight correction model driven by both parametric priors and data, which converges more easily." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11899" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 68, + 541, + 178 + ], + "blocks": [ + { + "bbox": [ + 69, + 68, + 541, + 178 + ], + "lines": [ + { + "bbox": [ + 69, + 68, + 541, + 178 + ], + "spans": [ + { + "bbox": [ + 69, + 68, + 541, + 178 + ], + "type": "image", + "image_path": "4431972c4a7c6240fac7b3ec1817d3911f3b4569f199542073978a8faa7880d1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 180, + 555, + 225 + ], + "lines": [ + { + "bbox": [ + 54, + 180, + 555, + 225 + ], + "spans": [ + { + "bbox": [ + 54, + 180, + 555, + 225 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed UniCD. Our UniCD integrates a bias field prediction network with an infrared UAV target detection network. These two components are fused into a unified pipeline and trained end-to-end. The target enhancement and background suppression (TEBS) loss is introduced to enhance UAV target features while suppressing the background. The bias robust loss is employed to balance correction and detection." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 240, + 223, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 240, + 223, + 253 + ], + "spans": [ + { + "bbox": [ + 55, + 240, + 223, + 253 + ], + "type": "text", + "content": "2.2. Infrared UAV Target Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 258, + 296, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 258, + 296, + 498 + ], + "spans": [ + { + "bbox": [ + 56, + 258, + 296, + 498 + ], + "type": "text", + "content": "In recent years, many methods have been developed to detect infrared UAV targets [3-5, 19, 21]. Infrared UAV targets are challenging due to their weak imaging features and complex backgrounds [7, 8, 29]. TAD [19] leveraged the inconsistent motion cues between UAV targets and the background to detect potential targets. Fang et al. [3] formulated the UAV detection task as a residual image prediction by learning the mapping from input images to residual images. DAGNet [5] introduced attention mechanisms to adaptively enhance the network's ability to discriminate between UAVs and the background. DANet [4] constructed a dynamic attention network for UAVs to enhance feature extraction capabilities. However, the above methods primarily focus on designing complex network structures for improving detection performance, while rarely exploring how to better enhance feature representation without increasing computational complexity. We focus on introducing new auxiliary losses into the backbone to boost the model's ability to represent UAV target features while suppressing the background." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 504, + 295, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 504, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 504, + 295, + 529 + ], + "type": "text", + "content": "2.3. Joint Low-Level Image Processing and High-Level Vision Tasks" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "content": "Recently, joint approaches for image enhancement and object detection have emerged to further improve detection performance on low-quality images. One category of these methods utilized encoder-decoder architectures for image enhancement [12], but these modules are complex and hinder real-time performance. Another approach uses classical mathematical models for enhancement, replacing manually designed parameters with predictions from deep networks. IA-YOLO [18] integrated an adaptive enhancement strategy with YOLOv3 [20] via a differentiable image processing module, improving detection in foggy conditions. BAD-Net [11] introduced a dual-branch structure to minimize the impact of poor dehazing performance on the detection module. However, the above methods are developed for visible light images degraded by adverse weather condi" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 241, + 555, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 241, + 555, + 301 + ], + "spans": [ + { + "bbox": [ + 313, + 241, + 555, + 301 + ], + "type": "text", + "content": "tions. To the best of our knowledge, no work has explored handling both NUC and UAV target detection for infrared imaging within a single framework. We propose an end-to-end framework to simultaneously improve both correction and detection performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 312, + 503, + 325 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 503, + 325 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 503, + 325 + ], + "type": "text", + "content": "3. Detection-Friendly Union Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 331, + 434, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 434, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 434, + 342 + ], + "type": "text", + "content": "3.1. Overall Architecture" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 348, + 555, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 348, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 348, + 555, + 456 + ], + "type": "text", + "content": "In this section, we propose a novel network architecture, UniCD, as shown in Fig. 2. The UniCD leverages a lightweight prediction network to estimate the bias field and then passes the corrected image to a UAV detection network tailored for UAV targets. Additionally, during the joint training of image correction and detection tasks, we employ a detection-guided self-supervised loss to minimize feature discrepancies between the two tasks. Finally, we construct a new dataset, IRBFD, to validate our approach." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 464, + 553, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 553, + 487 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 553, + 487 + ], + "type": "text", + "content": "3.2. Prior- and Data-Driven Nonuniformity Correction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 492, + 554, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 554, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 554, + 612 + ], + "type": "text", + "content": "Infrared UAV images captured by thermal detectors often suffer from low-frequency nonuniformity, which significantly impacts target detection performance. Existing model-driven correction methods often struggle to handle complex non-uniformities, while deep learning-based methods suffer from high network complexity. To address these issues, we propose a lightweight correction network that combines parametric prior knowledge with the strong learning capabilities of deep neural networks. The network architecture is shown in Fig. 2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 613, + 553, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 553, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 553, + 635 + ], + "type": "text", + "content": "Generally, the degraded infrared image can be represented as follows [2, 16]:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 406, + 639, + 553, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 406, + 639, + 553, + 651 + ], + "spans": [ + { + "bbox": [ + 406, + 639, + 553, + 651 + ], + "type": "interline_equation", + "content": "Y = C + B, \\tag {1}", + "image_path": "8b6cddf6028b999ec5a64f47e2ccb3d8ad8973043c563e196e60ac0fb3680c91.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": " represent the degraded image, the clear image, and the bias field, respectively. Thus, once " + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": " is available, the corrected image " + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": " can be obtained as " + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "inline_equation", + "content": "Y - B" + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": ". Under ideal conditions, " + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": " is theoretically equivalent to the clear image " + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 653, + 554, + 713 + ], + "type": "text", + "content": ". 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The column vector " + }, + { + "bbox": [ + 55, + 137, + 295, + 220 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 55, + 137, + 295, + 220 + ], + "type": "text", + "content": " represents the coefficients of the polynomial formed by concatenating " + }, + { + "bbox": [ + 55, + 137, + 295, + 220 + ], + "type": "inline_equation", + "content": "\\{a_{t,s}\\}" + }, + { + "bbox": [ + 55, + 137, + 295, + 220 + ], + "type": "text", + "content": ". To reduce the redundancy of the basic plane and the computational complexity of higher-order models, we set the degree " + }, + { + "bbox": [ + 55, + 137, + 295, + 220 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 55, + 137, + 295, + 220 + ], + "type": "text", + "content": " to 3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 221, + 295, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 221, + 295, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 295, + 281 + ], + "type": "text", + "content": "Accurate estimation of the polynomial coefficients " + }, + { + "bbox": [ + 55, + 221, + 295, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 55, + 221, + 295, + 281 + ], + "type": "text", + "content": " is crucial for improving bias field correction performance. In this work, we design a lightweight bias field prediction network that can estimate the model parameters accurately and efficiently." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "text", + "content": "In our NUC module, we first downsample the degraded image " + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "text", + "content": " by a factor of two, resulting in the downsampled image " + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "inline_equation", + "content": "Y_{\\mathrm{down}}" + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "text", + "content": ". Then, we utilize the global bias field encoder (GBFE) and the local bias field encoder (LBFE) to extract features at different granularities. The GBFE, inspired by the RSTB [13] module, includes two Swin Transformer layers with the hidden layer channel dimension reduced to 16. The LBFE consists of two spatial attention modules in series, allowing it to capture localized features more effectively. The global and local features, " + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{global}}" + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{local}}" + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "text", + "content": ", are fused to form the final feature representation " + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{fused}}" + }, + { + "bbox": [ + 55, + 281, + 296, + 413 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 94, + 418, + 295, + 432 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 418, + 295, + 432 + ], + "spans": [ + { + "bbox": [ + 94, + 418, + 295, + 432 + ], + "type": "interline_equation", + "content": "F _ {\\text {f u s e d}} = \\mathrm {G B F E} \\left(Y _ {\\text {d o w n}}\\right) + \\mathrm {L B F E} \\left(Y _ {\\text {d o w n}}\\right). \\tag {3}", + "image_path": "31fc8c360be7a605ef47d7b2606c8aa3e8de799cc7cdb81403450f25fb233672.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "type": "text", + "content": "Finally, the fused features " + }, + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{fused}}" + }, + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "type": "text", + "content": " pass through five " + }, + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "type": "text", + "content": " convolutional layers (Conv5) and a fully connected (FC) layer to predict the final coefficient vector " + }, + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{a}}" + }, + { + "bbox": [ + 55, + 435, + 295, + 472 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 125, + 476, + 294, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 476, + 294, + 490 + ], + "spans": [ + { + "bbox": [ + 125, + 476, + 294, + 490 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {a}} = \\operatorname {F C} \\left(\\operatorname {C o n v} _ {5} \\left(F _ {\\text {f u s e d}}\\right)\\right). \\tag {4}", + "image_path": "757a84f87a7237779d59a72cc677c2035ca9ebd9aa8d76982be5622f238dd2f4.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 494, + 295, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 494, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 494, + 295, + 529 + ], + "type": "text", + "content": "This approach enables the network to adaptively adjust to inputs with varying levels of degradation, effectively predicting the coefficient vector " + }, + { + "bbox": [ + 55, + 494, + 295, + 529 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{a}}" + }, + { + "bbox": [ + 55, + 494, + 295, + 529 + ], + "type": "text", + "content": " for bias field correction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 530, + 295, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 295, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 530, + 295, + 613 + ], + "type": "text", + "content": "Analysis. Compared to existing model-driven methods, our approach avoids reliance on hand-crafted features. Compared to existing data-driven methods, our approach transforms the high-dimensional image space prediction into a low-dimensional data-driven problem with a few hyperparameters, effectively reducing computational complexity and improving correction performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 614, + 295, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 614, + 295, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 614, + 295, + 661 + ], + "type": "text", + "content": "Loss Function. We calculate the mean absolute error (MAE) loss between the predicted coefficients " + }, + { + "bbox": [ + 55, + 614, + 295, + 661 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{a}}" + }, + { + "bbox": [ + 55, + 614, + 295, + 661 + ], + "type": "text", + "content": " and the predefined coefficients " + }, + { + "bbox": [ + 55, + 614, + 295, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 55, + 614, + 295, + 661 + ], + "type": "text", + "content": " to minimize the discrepancy between them. The MAE loss is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 132, + 664, + 295, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 664, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 132, + 664, + 295, + 687 + ], + "type": "interline_equation", + "content": "L _ {c o r} = \\frac {1}{N} \\| \\hat {\\mathbf {a}} - \\mathbf {a} \\| _ {2} ^ {2}, \\tag {5}", + "image_path": "4c068e7b495d7f8aba29005abb6b139ffd14a58f92425917866a5b0b5a9f02db.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": " is the total number of elements in the vector " + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": ". By minimizing this loss, we improve the accuracy of the" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 319, + 70, + 552, + 135 + ], + "blocks": [ + { + "bbox": [ + 319, + 70, + 552, + 135 + ], + "lines": [ + { + "bbox": [ + 319, + 70, + 552, + 135 + ], + "spans": [ + { + "bbox": [ + 319, + 70, + 552, + 135 + ], + "type": "image", + "image_path": "6d060feb0f5305d0e4109b13ce90ea5f067bf03ca63eacbb14849c506d77039a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 137, + 555, + 159 + ], + "lines": [ + { + "bbox": [ + 313, + 137, + 555, + 159 + ], + "spans": [ + { + "bbox": [ + 313, + 137, + 555, + 159 + ], + "type": "text", + "content": "Figure 3. Calculation of the proposed feature enhancement and background suppression (TEBS) loss." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 164, + 555, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 164, + 555, + 212 + ], + "spans": [ + { + "bbox": [ + 313, + 164, + 555, + 212 + ], + "type": "text", + "content": "corrected image, making it closer to the ideal clear image. This loss function is used to pre-train the NUC module separately, serving as the initial weights for the joint training of correction and detection." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 219, + 529, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 219, + 529, + 232 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 529, + 232 + ], + "type": "text", + "content": "3.3. Mask-Supervised Infrared UAV Detector" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 236, + 554, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 554, + 355 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 554, + 355 + ], + "type": "text", + "content": "We select DANet [4] as our baseline detector, which constructs a multi-scale dynamic perception network to address the challenges of multi-scale variations in UAV targets. Infrared UAV targets typically have weak features and complex backgrounds, and existing methods often enhance feature extraction through complex model architectures. In this work, we design an auxiliary loss function for further target enhancement and background suppression (TEBS) without increasing network complexity, as illustrated in Figs. 2 and 3." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 356, + 554, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 356, + 554, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 356, + 554, + 392 + ], + "type": "text", + "content": "Specifically, we first convert the bounding boxes of the ground-truth into a binary mask " + }, + { + "bbox": [ + 313, + 356, + 554, + 392 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 356, + 554, + 392 + ], + "type": "text", + "content": ", assigning a value of 1 to the target region and 0 to the background region:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 329, + 393, + 553, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 393, + 553, + 423 + ], + "spans": [ + { + "bbox": [ + 329, + 393, + 553, + 423 + ], + "type": "interline_equation", + "content": "M (x, y) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} (x, y) \\in \\text {t a r g e t r e g i o n}, \\\\ 0, & \\text {i f} (x, y) \\in \\text {b a c k g r o u n d r e g i o n}. \\end{array} \\right. \\tag {6}", + "image_path": "134f3f7916c13235d51b7ece8d3364ebaa68721f7371f74ad7fdd410b8aea946.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "type": "text", + "content": "This mask is then used to compute a binary cross-entropy loss with the feature maps " + }, + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "type": "text", + "content": " from the " + }, + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "type": "text", + "content": "-th stage of the backbone network. The TEBS loss " + }, + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{TEBS}}" + }, + { + "bbox": [ + 313, + 423, + 554, + 483 + ], + "type": "text", + "content": " is obtained by summing the losses from four stages of the backbone and averaging:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 370, + 483, + 553, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 483, + 553, + 515 + ], + "spans": [ + { + "bbox": [ + 370, + 483, + 553, + 515 + ], + "type": "interline_equation", + "content": "L _ {T E B S} = \\frac {1}{4} \\sum_ {i = 1} ^ {4} L _ {C E} (M, F _ {i}), \\tag {7}", + "image_path": "36e3d9bd60cbe1c2e7d0dbb55a7500115731df628a576ac2d54d0c6b75233bf9.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 516, + 506, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 516, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 516, + 506, + 528 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 516, + 506, + 528 + ], + "type": "inline_equation", + "content": "L_{CE}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 313, + 516, + 506, + 528 + ], + "type": "text", + "content": " denotes the cross-entropy loss." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 528, + 554, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 528, + 554, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 528, + 554, + 635 + ], + "type": "text", + "content": "The TEBS loss offers three key benefits: (1) Supervision on the target regions helps the backbone network to quickly focus on the feature learning of infrared UAV targets and enhance localization accuracy; (2) Supervision on background regions effectively suppresses non-target features, thereby reducing clutter and noise interference in the features; (3) The loss enhances training efficiency by guiding the network to learn target features more accurately, leading to faster convergence." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 635, + 554, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 554, + 670 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 554, + 670 + ], + "type": "text", + "content": "The classification and regression losses are kept consistent with the baseline method. The final detector loss is written as:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 367, + 674, + 553, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 674, + 553, + 687 + ], + "spans": [ + { + "bbox": [ + 367, + 674, + 553, + 687 + ], + "type": "interline_equation", + "content": "L _ {d e t} = L _ {c l s} + L _ {r e g} + \\lambda L _ {T E B S}, \\tag {8}", + "image_path": "6bede43e5a3d237d930283eb359db2066f17e73f9cad8c72ee2f1ed558fc8599.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": " is set to 1 for the first 20 epochs to accelerate convergence and improve localization performance in the early" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11901" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 69, + 293, + 135 + ], + "blocks": [ + { + "bbox": [ + 61, + 69, + 293, + 135 + ], + "lines": [ + { + "bbox": [ + 61, + 69, + 293, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 69, + 293, + 135 + ], + "type": "image", + "image_path": "3335fc6a6ab6fe0dada27057165fe5f1d69da59a62e7937a56ff748c69c1b518.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 137, + 295, + 158 + ], + "lines": [ + { + "bbox": [ + 55, + 137, + 295, + 158 + ], + "spans": [ + { + "bbox": [ + 55, + 137, + 295, + 158 + ], + "type": "text", + "content": "Figure 4. Construction of the bias-robust loss in the unified NUC and detection framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 162, + 296, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 162, + 296, + 198 + ], + "spans": [ + { + "bbox": [ + 55, + 162, + 296, + 198 + ], + "type": "text", + "content": "stages. After 20 epochs, " + }, + { + "bbox": [ + 55, + 162, + 296, + 198 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 162, + 296, + 198 + ], + "type": "text", + "content": " is reduced to 0.01 to balance with the gradually decreasing loss and avoid impacting classification accuracy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 204, + 296, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 204, + 296, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 204, + 296, + 228 + ], + "type": "text", + "content": "3.4. Balance Correction and Detection with Bias-Robust Loss" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 233, + 296, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 233, + 296, + 329 + ], + "spans": [ + { + "bbox": [ + 55, + 233, + 296, + 329 + ], + "type": "text", + "content": "Existing research [11, 18] shows that incorporating supervision losses from low-level vision tasks in joint training can hinder high-level vision task performance. This is because low-level tasks focus on preserving fine image details, while high-level tasks aim to extract target-specific features and ignore irrelevant background information. This conflict can hinder convergence during joint training, causing the high-level vision task to settle into a local optimum." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "spans": [ + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "text", + "content": "To address this issue, we design a self-supervised loss, named bias robust (BR) loss, to achieve detection-friendly NUC, as illustrated in Fig. 4. Specifically, during joint training, the clear image " + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "text", + "content": " and the corrected image " + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "text", + "content": " obtained via the NUC module are simultaneously fed into the backbone of the detection model. Let " + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "inline_equation", + "content": "F_{C}^{(i)}" + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "inline_equation", + "content": "F_{R}^{(i)}" + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "text", + "content": " represent the feature maps from the " + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "text", + "content": "-th stage of the detection backbone, where " + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "inline_equation", + "content": "i = 1,2,3,4" + }, + { + "bbox": [ + 55, + 330, + 296, + 463 + ], + "type": "text", + "content": " denotes the four different stages. Here, clear images are employed only for the joint training of correction and detection on the synthetic dataset and are not applied to NUC training on real infrared images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 463, + 296, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 296, + 509 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 296, + 509 + ], + "type": "text", + "content": "To evaluate the alignment of the corrected image with the clear image in the feature space, we compute the cosine similarity between the feature maps at each stage " + }, + { + "bbox": [ + 55, + 463, + 296, + 509 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 463, + 296, + 509 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 93, + 510, + 295, + 546 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 510, + 295, + 546 + ], + "spans": [ + { + "bbox": [ + 93, + 510, + 295, + 546 + ], + "type": "interline_equation", + "content": "\\operatorname {C o s} \\operatorname {S i m} \\left(F _ {C} ^ {(i)}, F _ {R} ^ {(i)}\\right) = \\frac {F _ {C} ^ {(i)} \\cdot F _ {R} ^ {(i)}}{\\left\\| F _ {C} ^ {(i)} \\right\\| \\left\\| F _ {R} ^ {(i)} \\right\\|}. \\tag {9}", + "image_path": "549c30a5b634803f56c015bb0b96506e6fd138030218142582d9d3d7c440e983.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 547, + 296, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 547, + 296, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 547, + 296, + 594 + ], + "type": "text", + "content": "The details of the cosine similarity calculation are placed in the supplementary materials. The BR loss is obtained by summing the cosine similarities across all stages and averaging them:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 78, + 597, + 295, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 597, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 78, + 597, + 295, + 628 + ], + "type": "interline_equation", + "content": "L _ {B R} = \\frac {1}{4} \\sum_ {i = 1} ^ {4} \\left(1 - \\operatorname {C o s} _ {-} \\operatorname {S i m} \\left(F _ {C} ^ {(i)}, F _ {R} ^ {(i)}\\right)\\right). \\tag {10}", + "image_path": "f64eacbfffed2c8c9e2decc986952f462cae101db3841d3f3eb45b0c3f7e46f5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 630, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 712 + ], + "type": "text", + "content": "The BR loss function is designed to maximize the consistency between the feature representations of the clear and corrected images, thereby enhancing the fidelity of the corrected image within the feature space and ensuring that it retains essential characteristics beneficial for detection. The final union loss function for the joint training process " + }, + { + "bbox": [ + 55, + 630, + 296, + 712 + ], + "type": "inline_equation", + "content": "L_{uni}" + }, + { + "bbox": [ + 55, + 630, + 296, + 712 + ], + "type": "text", + "content": " is written as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 390, + 72, + 554, + 85 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 72, + 554, + 85 + ], + "spans": [ + { + "bbox": [ + 390, + 72, + 554, + 85 + ], + "type": "interline_equation", + "content": "L _ {u n i} = L _ {d e t} + L _ {B R}. \\tag {11}", + "image_path": "07a771f4a4c38e66e5b2228e090dd4a422649400a99f5532d8067105c1288fb0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 97, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 97, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 97, + 555, + 180 + ], + "type": "text", + "content": "As illustrated in Fig. 1, the union loss " + }, + { + "bbox": [ + 313, + 97, + 555, + 180 + ], + "type": "inline_equation", + "content": "L_{uni}" + }, + { + "bbox": [ + 313, + 97, + 555, + 180 + ], + "type": "text", + "content": " ensures effective bias field correction while maximizing detection performance by backpropagating through each part of the network. Compared to separate training of NUC and detection networks, this integrated approach enables a more balanced optimization, leading to enhanced results in both correction and detection tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 194, + 410, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 194, + 410, + 205 + ], + "spans": [ + { + "bbox": [ + 314, + 194, + 410, + 205 + ], + "type": "text", + "content": "3.5.IRBFD Dataset" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 213, + 555, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 555, + 440 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 555, + 440 + ], + "type": "text", + "content": "We construct a new benchmark called IRBFD, comprising 30,000 synthetic nonuniformity infrared UAV images (IRBFD-syn) and 20,000 real-world infrared UAV images with nonuniformity field (IRBFD-real). The IRBFD-syn subset provides paired degraded and clear images, with the synthesis process based on Eqs. (1) and (2). The characteristics of the dataset are summarized as follows. (1) Multiple background types. The IRBFD includes multiple complex scenes, such as dense clouds, buildings, forests, urban areas, and sea. (2) Multi-scale variations. The distance between the UAVs and the sensor ranges from 50 meters to 2 kilometers, resulting in multi-scale variations of the targets. (3) Multiple UAV types. Such as the DJI Inspire, Matrice, Phantom, Mavic, and Mini series. All UAV positions are manually annotated. IRBFD serves as a comprehensive resource for evaluating the impact of non-uniformities on UAV target detection in real-world environments. All images have a size of " + }, + { + "bbox": [ + 313, + 213, + 555, + 440 + ], + "type": "inline_equation", + "content": "640 \\times 512" + }, + { + "bbox": [ + 313, + 213, + 555, + 440 + ], + "type": "text", + "content": ". Additional details can be found in the supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 456, + 391, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 391, + 470 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 391, + 470 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 477, + 491, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 477, + 491, + 490 + ], + "spans": [ + { + "bbox": [ + 313, + 477, + 491, + 490 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 496, + 554, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 554, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 554, + 592 + ], + "type": "text", + "content": "Datasets. We use two parts of the IRBFD dataset: IRBFD-syn and IRBFD-real. IRBFD-syn consists of simulated nonuniform infrared images, allowing us to train the model with controlled background images and varying non-uniformities. Training, validation, and testing sets are split in an 8:1:1 ratio. We train on the simulated dataset and directly validate on real-world dataset to demonstrate the generalizability of our method." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 594, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 712 + ], + "type": "text", + "content": "Evaluation Metrics. For NUC, we use peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) as objective evaluation metrics. For target detection, we evaluate the detection performance using precision (P) and recall (R). Lastly, for real-time performance, we use frames per second (FPS) as the evaluation metric. The signal-to-clutter ratio gain (SCRG) is the ratio of SCR in the corrected image to that in the original image, used to evaluate the improvement in target detectability achieved by the correction method." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11902" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 118, + 296, + 290 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 295, + 115 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 295, + 115 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 295, + 115 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of the proposed method with SOTA methods on the synthetic dataset IRBFD-syn. **Bold** and **underline** indicate the best and the second best results, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 118, + 296, + 290 + ], + "lines": [ + { + "bbox": [ + 56, + 118, + 296, + 290 + ], + "spans": [ + { + "bbox": [ + 56, + 118, + 296, + 290 + ], + "type": "table", + "html": "
    StrategyModuleMetrics
    NUCDetectionPub'YearPSNRSSIMPRFPS
    Direct-Deformable DETRICLR'210.6140.63024
    DINOICLR'230.9040.64026
    DAGNetTII'23--0.9940.63543
    LESPSCVPR'230.0330.44612
    MSHNetCVPR'240.4070.42141
    YOLO11L20240.9630.60242
    SeparateLiuYOLO11LIPT'1616.8000.82890.8980.574<1
    DAGNet0.9780.578<1
    DMRNYOLO11LGRSL'1924.4670.86000.9230.55035
    DAGNet0.9660.59536
    ShiYOLO11LAO'2213.9740.77830.9240.455<1
    DAGNet0.9660.472<1
    TV-DIPYOLO11LIPT'2313.3970.63740.1310.02029
    DAGNet0.5990.02030
    AHBCYOLO11LTGRS'2413.9540.67630.8250.080<1
    DAGNet0.7240.040<1
    UnionUniCD-31.9610.98270.9990.82232
    ", + "image_path": "506f6a28e0700d047e0adc739dbe203425b8af1fbefe6e904ac5044ae33bf6b0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 99, + 327, + 252, + 412 + ], + "blocks": [ + { + "bbox": [ + 55, + 300, + 295, + 323 + ], + "lines": [ + { + "bbox": [ + 55, + 300, + 295, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 295, + 323 + ], + "type": "text", + "content": "Table 2. Quantitative comparison of the proposed method with SOTA methods on the real dataset IRBFD-real." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 99, + 327, + 252, + 412 + ], + "lines": [ + { + "bbox": [ + 99, + 327, + 252, + 412 + ], + "spans": [ + { + "bbox": [ + 99, + 327, + 252, + 412 + ], + "type": "table", + "html": "
    StrategyNUCDetectionSCRGPR
    Direct-DINO0.9710.660
    YOLO11L-0.9660.843
    DAGNet0.9920.871
    SeparateTV-DIPYOLO11L0.4120.5210.024
    DAGNet0.6630.026
    AHBCYOLO11L1.1460.9400.633
    DAGNet0.9860.699
    UnionUniCD1.2860.9940.901
    ", + "image_path": "87312a884cbc3c6f62e389b4fd3e28bf6544bb0cd4e51c331c6f596364dc1390.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 431, + 189, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 431, + 189, + 444 + ], + "spans": [ + { + "bbox": [ + 55, + 431, + 189, + 444 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 449, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 449, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 54, + 449, + 295, + 640 + ], + "type": "text", + "content": "We use Adam as the optimizer, with a learning rate of 0.001. The training lasts for 50 epochs, with a weight decay of " + }, + { + "bbox": [ + 54, + 449, + 295, + 640 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 54, + 449, + 295, + 640 + ], + "type": "text", + "content": " and a batch size of 4. During training, we only apply random horizontal flipping for data augmentation. Our experiments are conducted on an NVIDIA RTX 4090 with CUDA 12.4 and PyTorch 1.7. For NUC, we select Liu [15], Shi [22], and AHBC [26] as the traditional bias field correction methods; DMRN [2] and TV-DIP [14] as the DL-based correction methods. They are all designed for infrared images. For target detection, we select YOLO11L [9] (large version), DAGNet [5], LESPS [28], and MSHNet [17] as the convolutional neural network (CNN)-based target detection methods. DAGNet, LESPS, and MSHNet are designed for infrared target detection. Deformable DETR [34] and DINO [30] are the representative Transformer-based detection methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 648, + 174, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 648, + 174, + 661 + ], + "spans": [ + { + "bbox": [ + 55, + 648, + 174, + 661 + ], + "type": "text", + "content": "4.3. Quantitative Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "As shown in Tab. 1, the existing detection methods obtain low P and R values when detecting directly on the degraded bias field images. DAGNet has a high P value of 0.994 but a low recall. This indicates that the bias field has an adverse" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 350, + 71, + 515, + 203 + ], + "blocks": [ + { + "bbox": [ + 350, + 71, + 515, + 203 + ], + "lines": [ + { + "bbox": [ + 350, + 71, + 515, + 203 + ], + "spans": [ + { + "bbox": [ + 350, + 71, + 515, + 203 + ], + "type": "image", + "image_path": "3725632855b1b68f113d1738104cfaf0c15f464315695890510b90abaa620557.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 204, + 553, + 237 + ], + "lines": [ + { + "bbox": [ + 313, + 204, + 553, + 237 + ], + "spans": [ + { + "bbox": [ + 313, + 204, + 553, + 237 + ], + "type": "text", + "content": "Figure 5. P-R curves of our UniCD and other correction-then-detection methods on the IRBFD-syn. The area values under the curves are placed after the method names." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 244, + 555, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 244, + 555, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 244, + 555, + 495 + ], + "type": "text", + "content": "effect on the UAV target detection. For the separate strategy, the DL-based method DMRN enhances image quality, achieving notable improvements in PSNR and SSIM. Other correction methods, such as Liu, Shi, and AHBC, are less effective for severely degraded images, which further impacts detection accuracy. Table 2 shows that the three detection methods achieve high P and R when directly detecting on real images with low degradation levels. YOLO11L and DAGNet have lower P and R values for images corrected by TV-DIP, as TV-DIP not only lacks corrective effects but also deteriorates the image content. In contrast, the proposed UniCD achieves the best performance in terms of all the evaluation metrics compared with SOTA methods in Tab. 1 for the synthetic dataset and Tab. 2 for the real dataset. Specially, our UniCD achieves a real-time processing speed of 32 FPS. We also plot the R-R curves for our UniCD and other correction-then-detection methods on the IRBFD dataset shown in Fig. 5. Higher values of the area under the curve indicate better performance. It can be seen that our UniCD achieves the largest area under the curve among all correction-then-detection methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 504, + 425, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 504, + 425, + 517 + ], + "spans": [ + { + "bbox": [ + 313, + 504, + 425, + 517 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 521, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 555, + 713 + ], + "type": "text", + "content": "As demonstrated in Fig. 6, we show qualitative results from various separate correction-then-detection methods and our UniCD on the IRBFD-syn dataset across three distinct scenarios: buildings, hillside, and clouds. As can be seen, even in severe degraded bias field situations, our UniCD can still perform high-quality image correction while accurately detecting the UAV targets. This is because the proposed NUC correction module integrates parametric modeling and a small number of model parameter predictions, enabling more accurate parameter estimation. Meanwhile, our detection network introduces auxiliary loss with target mask supervision into the backbone to enhance the features of UAV targets while suppressing the background, thereby improving detection performance. Conventional correction methods, such as Liu and AHBC, have limited modeling capabilities and are prone to producing bias field residuals." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11903" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 547, + 225 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 547, + 225 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 547, + 225 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 547, + 225 + ], + "type": "image", + "image_path": "99e4b3bbcde5fd5cb4b3b76ec7ac59bf1a86cfcf67a645acbe15c4cac16cd3dd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 227, + 555, + 260 + ], + "lines": [ + { + "bbox": [ + 55, + 227, + 555, + 260 + ], + "spans": [ + { + "bbox": [ + 55, + 227, + 555, + 260 + ], + "type": "text", + "content": "Figure 6. Visual comparison of results from separate correction followed by detection methods and our UniCD on the IRBFD-syn dataset. Closed-up views are shown in the left bottom corner. Boxes in green and red represent ground-truth and correctly detected targets, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 69, + 262, + 541, + 460 + ], + "blocks": [ + { + "bbox": [ + 69, + 262, + 541, + 460 + ], + "lines": [ + { + "bbox": [ + 69, + 262, + 541, + 460 + ], + "spans": [ + { + "bbox": [ + 69, + 262, + 541, + 460 + ], + "type": "image", + "image_path": "47b1a76b466a957e40bfc76f1a90f7dd5cbc1a302aab4234bf72bc20ec912ffc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 462, + 541, + 473 + ], + "lines": [ + { + "bbox": [ + 67, + 462, + 541, + 473 + ], + "spans": [ + { + "bbox": [ + 67, + 462, + 541, + 473 + ], + "type": "text", + "content": "Figure 7. Visual comparison of results from separate correction-then-detection methods and our UniCD on the IRBFD-real dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 82, + 495, + 269, + 544 + ], + "blocks": [ + { + "bbox": [ + 89, + 481, + 261, + 493 + ], + "lines": [ + { + "bbox": [ + 89, + 481, + 261, + 493 + ], + "spans": [ + { + "bbox": [ + 89, + 481, + 261, + 493 + ], + "type": "text", + "content": "Table 3. Ablation study of polynomial degrees." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 82, + 495, + 269, + 544 + ], + "lines": [ + { + "bbox": [ + 82, + 495, + 269, + 544 + ], + "spans": [ + { + "bbox": [ + 82, + 495, + 269, + 544 + ], + "type": "table", + "html": "
    DegreeNumber of coefficientsPSNRSSIMPR
    2613.52790.75900.9910.433
    31039.0500.99700.9970.810
    41531.7440.98900.9970.788
    52129.0700.98300.9970.787
    ", + "image_path": "a2d198d9d32441196ce2714b30fda0e4f3cc539b0efc0dd4185ac65def58c8df.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 556, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 556, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 556, + 295, + 616 + ], + "type": "text", + "content": "The corrected image from DMRN exhibits block artifacts. Existing detection methods produce false alarms or miss detections on the above-corrected images; similar results are observed in Fig. 7 for scenes degraded by real bias fields. See the supplementary material for more visual results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 624, + 149, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 149, + 636 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 149, + 636 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 642, + 247, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 247, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 247, + 653 + ], + "type": "text", + "content": "In this section, we report ablation study results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": "Impact of polynomial degrees. We conduct experiments to determine the optimal polynomial degree, as described in Tab. 8. The results indicate that the highest values for all correction and detection metrics are achieved when the degree is set to 3. Compared to higher-order polyno" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 333, + 495, + 535, + 544 + ], + "blocks": [ + { + "bbox": [ + 329, + 481, + 538, + 492 + ], + "lines": [ + { + "bbox": [ + 329, + 481, + 538, + 492 + ], + "spans": [ + { + "bbox": [ + 329, + 481, + 538, + 492 + ], + "type": "text", + "content": "Table 4. Ablation study of the LBFE and GBFE modules." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 333, + 495, + 535, + 544 + ], + "lines": [ + { + "bbox": [ + 333, + 495, + 535, + 544 + ], + "spans": [ + { + "bbox": [ + 333, + 495, + 535, + 544 + ], + "type": "table", + "html": "
    LBFEGBFEParams (M)FLOPs (G)PSNRSSIMFPS
    ××0.37860.119227.2180.9808555
    ✓×0.38120.274730.2420.9877370
    ×✓0.39401.515937.8880.9961151
    ✓✓0.39661.680939.0500.9970116
    ", + "image_path": "edd6b1a63fa74708d2deb737b9d38dd0fd66708e2978886728d26ac3b30654e1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 557, + 555, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 593 + ], + "type": "text", + "content": "mials, a third-order polynomial has lower complexity and less redundancy. A lower degree implies weaker modeling capability, resulting in poor correction performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 594, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 713 + ], + "type": "text", + "content": "Impact of the LBFE and GBFE components. As presented in Tab. 4, when using only LBFE or GBFE, we can see that the PSNR of the correction model already achieves 30.242 and 37.888, respectively, surpassing the 27.218 of the baseline. When combined with LBFE and GBFE, further improvements can be achieved, reaching 39.050 with only 1.6809G FLOPs and 0.3966M parameters on an image size of " + }, + { + "bbox": [ + 313, + 594, + 556, + 713 + ], + "type": "inline_equation", + "content": "640 \\times 512" + }, + { + "bbox": [ + 313, + 594, + 556, + 713 + ], + "type": "text", + "content": ". Additionally, the SSIM value has also shown some slight improvements. This suggests that the Transformer architecture combined with the CNN structure" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11904" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 124, + 83, + 227, + 114 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 269, + 81 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 269, + 81 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 269, + 81 + ], + "type": "text", + "content": "Table 5. Ablation study of the auxiliary TEBS loss." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 124, + 83, + 227, + 114 + ], + "lines": [ + { + "bbox": [ + 124, + 83, + 227, + 114 + ], + "spans": [ + { + "bbox": [ + 124, + 83, + 227, + 114 + ], + "type": "table", + "html": "
    TEBS LossPR
    w/o0.9930.762
    w0.9970.810
    ", + "image_path": "096b6b4f1ba17d4ed6369ec6ba20c455c8b7367b065e29325936deb12ac5d713.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 73, + 125, + 277, + 198 + ], + "blocks": [ + { + "bbox": [ + 73, + 125, + 277, + 198 + ], + "lines": [ + { + "bbox": [ + 73, + 125, + 277, + 198 + ], + "spans": [ + { + "bbox": [ + 73, + 125, + 277, + 198 + ], + "type": "image", + "image_path": "e851cf7dd3b547ecc6ff7ffab009854d5ea71e04ffd3cff2c406da5e50318e0f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 201, + 295, + 224 + ], + "lines": [ + { + "bbox": [ + 55, + 201, + 295, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 295, + 224 + ], + "type": "text", + "content": "Figure 8. Comparison of feature maps from the detection backbone at different stages with and without TEBS loss." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 76, + 264, + 274, + 334 + ], + "blocks": [ + { + "bbox": [ + 55, + 230, + 296, + 264 + ], + "lines": [ + { + "bbox": [ + 55, + 230, + 296, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 230, + 296, + 264 + ], + "type": "text", + "content": "Table 6. Ablation study of BR loss on the synthetic dataset IRBFD-syn. Here, the direct and separate strategies utilize the correction and detection modules proposed in UniCD." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 76, + 264, + 274, + 334 + ], + "lines": [ + { + "bbox": [ + 76, + 264, + 274, + 334 + ], + "spans": [ + { + "bbox": [ + 76, + 264, + 274, + 334 + ], + "type": "table", + "html": "
    StrategyCorrection lossDetection lossBR lossMetrics
    PSNRSSIMPR
    Direct×√×--0.9980.694
    Separate√√×37.7220.99600.9990.793
    Union√√×33.0240.98270.9980.791
    Union×√×17.9400.89100.9890.811
    UniCD×√√31.9610.98270.9990.822
    ", + "image_path": "8c34ceebbb828b238b1b900720588b59e136a30855cc2838e73a5efb51d9b951.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 354, + 295, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 295, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 295, + 378 + ], + "type": "text", + "content": "can effectively model bias fields, significantly improving performance while maintaining high real-time efficiency." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 378, + 295, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 378, + 295, + 486 + ], + "spans": [ + { + "bbox": [ + 54, + 378, + 295, + 486 + ], + "type": "text", + "content": "Impact of the auxiliary TEBS loss. As shown in Tab. 5, the auxiliary TEBS loss added to the backbone of the UAV detection network leads to improvements in both P and R performance. The TEBS loss imposes strong constraints on the target and background masks for the backbone features, enhancing target features while suppressing the background, thus improving detection performance, as depicted in Fig. 8. In the absence of TEBS loss, the targets are generally weak and there is considerable residual background." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 486, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 486, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 486, + 295, + 653 + ], + "type": "text", + "content": "Impact of BR loss. As shown in Tab. 6, the direct detection results in low P and R. The correction-then-detection separate method without BR loss in the second row obtains high PSNR, SSIM and P, but with low R because of the independent processing of the two tasks. The union of correction and detection without BR loss in the third row leads to a decrease in PSNR, SSIM, P, and R due to the conflict between the two tasks. The union of correction and detection without correction and BR losses in the fourth row significantly reduces PSNR and SSIM owing to the detection module's sole constraint. Our UniCD achieves the highest R value and P value exceeding 0.99, demonstrating that our union framework effectively balances correction and detection through the self-supervised BR loss." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": "Effectiveness of UniCD on real dataset. As shown in Tab. 7, we use the NUC module weights trained on the IRBFD-syn and directly test them on the IRBFD-real. This configuration is referred to as " + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{UniCD}^{\\star}" + }, + { + "bbox": [ + 55, + 653, + 296, + 714 + ], + "type": "text", + "content": ". The direct and separate methods with the modules in UniCD achieve a high P" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 325, + 95, + 421, + 137 + ], + "blocks": [ + { + "bbox": [ + 314, + 70, + 432, + 92 + ], + "lines": [ + { + "bbox": [ + 314, + 70, + 432, + 92 + ], + "spans": [ + { + "bbox": [ + 314, + 70, + 432, + 92 + ], + "type": "text", + "content": "Table 7. Ablation study of our UniCD on the IRBFD-real." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 325, + 95, + 421, + 137 + ], + "lines": [ + { + "bbox": [ + 325, + 95, + 421, + 137 + ], + "spans": [ + { + "bbox": [ + 325, + 95, + 421, + 137 + ], + "type": "table", + "html": "
    StrategySCRGPR
    Direct-0.9920.887
    Separate1.2860.9980.812
    UniCD*1.2860.9940.901
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    K-valuePSNRSSIM
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    Our NUCDetectionPRFPS
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    ", + "image_path": "154dfb66a3140265c01591647034e648534da72f0363c8fe8db1f88794df3c9d.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 274, + 555, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 274, + 555, + 321 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 555, + 321 + ], + "type": "text", + "content": "but a low R. Our UniCD obtains the highest R value and P value exceeding 0.99, thereby validating the effectiveness and generalization of our union framework on the real dataset." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "spans": [ + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "type": "text", + "content": "Generalization of the NUC Module. In Tab. 8, we test the UniCD on images with various degrees of nonuniformity degradation without retraining the NUC module. We control the severity of degradation using the formula " + }, + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "type": "inline_equation", + "content": "Y = C + k * B" + }, + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "type": "text", + "content": ", where the " + }, + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "type": "text", + "content": "-value determines the level of degradation. The correction results at different " + }, + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 322, + 554, + 418 + ], + "type": "text", + "content": "-values indicate that the NUC module generalizes well to various degradation levels." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 418, + 554, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 554, + 503 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 554, + 503 + ], + "type": "text", + "content": "Scalability of the NUC Module. From Tab. 9, we observe that, except for the P value of LESPS, introducing our correction module significantly boosts the detection performance of several recent general and infrared target detection methods. This indicates that our NUC module can be flexibly integrated as a scalable component into existing detectors to enhance infrared images for detection purposes." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "spans": [ + { + "bbox": [ + 314, + 514, + 388, + 526 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 312, + 534, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 534, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 312, + 534, + 555, + 712 + ], + "type": "text", + "content": "In this paper, we propose UniCD, an end-to-end framework that simultaneously addresses bias field correction and infrared UAV target detection. We develop a NUC module that removes bias fields and restores clear images with parameters adaptively predicted by a lightweight network. Additionally, we introduce auxiliary losses with mask supervision to enhance UAV target features and suppress the background. We also present a self-supervised feature loss to improve the robustness of detection to varying bias levels. Moreover, we construct a new dataset IRBFD to facilitate future research. Experimental results show that our UniCD outperforms previous approaches in both synthetic and real-world scenarios. Furthermore, our method shows great potential for deployment on resource-constrained edge devices." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11905" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 133 + ], + "type": "text", + "content": "Acknowledgments. 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In Proceedings of International Conference on Learning Representations (ICLR), 2021. 6" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11907" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Deterministic Certification of Graph Neural Networks against Graph Poisoning Attacks with Arbitrary Perturbations/0497332e-bd66-4105-bea8-f5b6eb06db3e_content_list.json b/2025/Deterministic Certification of Graph Neural Networks against Graph Poisoning Attacks with Arbitrary Perturbations/0497332e-bd66-4105-bea8-f5b6eb06db3e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5aefad3667693259992133072fd7f2b4038950f2 --- /dev/null +++ b/2025/Deterministic Certification of Graph Neural Networks against Graph Poisoning Attacks with Arbitrary Perturbations/0497332e-bd66-4105-bea8-f5b6eb06db3e_content_list.json @@ -0,0 +1,2108 @@ +[ + { + "type": "text", + "text": "Deterministic Certification of Graph Neural Networks against Graph Poisoning Attacks with Arbitrary Perturbations", + "text_level": 1, + "bbox": [ + 187, + 130, + 816, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiate Li $\\S$ Meng Pang $\\dagger$ Yun Dong $\\ddagger$ and Binghui Wang $\\S^{*}$", + "bbox": [ + 292, + 202, + 709, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{\\S}$ Department of Computer Science, Illinois Institute of Technology, Chicago, USA", + "bbox": [ + 254, + 220, + 741, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "†School of Mathematics and Computer Sciences, Nanchang University, Nanchang, China", + "bbox": [ + 233, + 239, + 763, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$\\ddagger$ Department of Humanities, Social Science, and Communication, MSOE, Milwaukee, USA", + "bbox": [ + 227, + 256, + 769, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 308, + 326, + 324 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Graph neural networks (GNNs) are becoming the de facto method to learn on the graph data and have achieved the state-of-the-art on node and graph classification tasks. However, recent works show GNNs are vulnerable to training-time poisoning attacks – marginally perturbing edges, nodes, or/and node features of training graph(s) can largely degrade GNNs' testing performance. Most previous defenses against graph poisoning attacks are empirical and are soon broken by adaptive / stronger ones. A few provable defenses provide robustness guarantees, but have large gaps when applied in practice: 1) restrict the attacker on only one type of perturbation; 2) design for a particular GNN architecture or task; and 3) robustness guarantees are not $100\\%$ accurate.", + "bbox": [ + 89, + 340, + 485, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we bridge all these gaps by developing PGNNCert, the first certified defense of GNNs against poisoning attacks under arbitrary (edge, node, and node feature) perturbations with deterministic robustness guarantees. Extensive evaluations on multiple node and graph classification datasets and GNNs demonstrate the effectiveness of PGNNCert to provably defend against arbitrary poisoning perturbations. PGNNCert is also shown to significantly outperform the state-of-the-art certified defenses against edge perturbation or node perturbation during GNN training.", + "bbox": [ + 89, + 537, + 486, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 715, + 220, + 732 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Graph Neural Network (GNN) [15, 21, 37, 44, 48, 56] is the leading approach for representation learning on graphs, showing state-of-the-art performance in various graph-related tasks like node classification and graph classification. In node classification, the goal is to predict labels for individual nodes, while in graph classification, the objective is to predict labels for entire graphs. GNNs have significantly advanced applications across fields such as chemistry [14], physics [36, 39], neuroscience [3], and social science [13].", + "bbox": [ + 89, + 741, + 485, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, various works [6-8, 20, 40, 45, 51, 55, 60, 63] have shown that GNNs are vulnerable to training-time graph poisoning attacks — an attacker perturbs the graph structure during training such that the learnt poisoned GNN model will have low accuracy on predicting new test nodes/graphs. As a graph consists of three components: nodes, their features, and edges connecting the nodes, an attacker is allowed to perturb an individual component or their combinations. For instance, an attacker could inject a few nodes [20, 40], slightly modify the edges [8, 45, 55, 63] on the training graphs, and/or perturb features of certain nodes [63].", + "bbox": [ + 511, + 309, + 906, + 474 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Various empirical defenses [12, 42, 43, 59, 61, 62] have been proposed to mitigate the graph poisoning attack, but were soon broken by adaptive attacks [33]. Most existing certified defenses [16, 19, 22, 24, 47, 54] are against test-time evasion attacks, with a few exceptions [18, 22], leaving certified defenses against poisoning attacks largely unexplored1. However, existing provable defenses face several limitations when applied in practice: 1) all restrict the attacker's capability to only one type of perturbation (e.g., node injection or edge perturbation); 2) they are designed for a particular GNN architecture or GNN task [19]; and 3) their robustness guarantee is probabilistic (i.e., not $100\\%$ accurate) [18, 22].", + "bbox": [ + 511, + 476, + 908, + 656 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose PGNNCert to address the above limitations. PGNNCert is the first certified defense for GNNs on the two most common node and graph classification tasks against arbitrary poisoning perturbations (i.e., arbitrarily manipulate the nodes, node features, and edges of training graph(s)) with deterministic robustness guarantees. Our defense is inspired by ensemble learning, and consists of three main steps: 1) Divide each training graph into multiple subgraphs and allocate subgraphs of training graph(s) into multiple groups via a hash function; 2) Train a set of node/graph classifiers for each group and build a majority-voting node/graph classifier on the subgraphs; 3) Derive the deterministic robustness guarantee against arbitrary poisoning perturbations.", + "bbox": [ + 511, + 657, + 910, + 854 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1We note there exist some certified defense [17, 23, 35, 46] against poisoning attacks but not for the graph data. In addition [18, 22] show they achieve unsatisfactory performance when adapted to graph data.", + "bbox": [ + 511, + 862, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "footer", + "text": "*Corresponding author (bwang70@iit.edu)", + "bbox": [ + 107, + 886, + 339, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5020", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Following [24], we adapt two graph division strategies—one is edge-centric and the other is node-centric—to realize our defense. The former strategy map edges, while the latter one map nodes from a given graph into multiple subgraphs. Theoretically, PGNNCert provably predicts the same label for a test node/graph after training on the poisoned training set with arbitrary perturbation whose perturbation size (i.e., the total number of manipulated nodes, nodes with feature perturbations, and edges) is bounded by a threshold, which we call the certified perturbation size. Empirically, we extensively evaluate PGNNCert on multiple graph datasets and multiple node and graph classifiers against arbitrary perturbations, and compared our methods with state-of-the-art certified defenses for node classification against node injection poisoning attack [22], and for graph classification against edge manipulation [17]. Our results show PGNNCert significantly outperforms [22] under node-centric graph division, and outperforms [54] under both graph division methods.", + "bbox": [ + 89, + 90, + 483, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions: Our contributions are summarized below:", + "bbox": [ + 89, + 363, + 475, + 376 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We develop the first certified defense to robustify GNNs against arbitrary poisoning attack on the training set.", + "- We propose two strategies (edge-centric and node-centric) to realize our defense that leverages the unique message-passing mechanism in GNNs.", + "- Our robustness guarantee is applicable to both node and graph classification tasks and accurate with probability 1.", + "- Our defense treat existing certified defenses as special cases, as well as significantly outperforming them." + ], + "bbox": [ + 91, + 378, + 483, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background and Problem Definition", + "text_level": 1, + "bbox": [ + 89, + 526, + 419, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Graph Neural Network (GNN)", + "text_level": 1, + "bbox": [ + 89, + 550, + 362, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Let a graph be $G = \\{V, E, \\mathbf{X}\\}$ , which consists of the nodes $V$ , node features $\\mathbf{X}$ , and edges $E$ . We denote $u \\in V$ as a node, $e = (u, v) \\in E$ as an edge, and $\\mathbf{X}_u$ as node $u$ 's feature. Let $f_\\theta$ be the node or graph classifier parameterized by $\\theta$ . $\\mathcal{V}$ is the label set, $y_v$ and $y_G$ are the groundtruth label of a node $v$ and a graph $G$ , respectively.", + "bbox": [ + 89, + 574, + 483, + 665 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Node classification: $f_{\\theta}$ takes a graph $G$ as input and predicts each node $v \\in G$ a label $\\tilde{y}_v \\in \\mathcal{V}$ , i.e., $\\tilde{y}_v = f_{\\theta}(G)_v$ . Given a training node set $V_{\\mathrm{tr}} \\subseteq V$ with ground-truth labels $\\mathbf{y}_{\\mathrm{tr}} = \\{y_v, v \\in V_{\\mathrm{tr}}\\}$ , $f_{\\theta}$ is learnt by minimizing a loss $\\mathcal{L}$ between the node predictions $\\tilde{\\mathbf{y}}_{\\mathrm{tr}}$ on $V_{\\mathrm{tr}}$ and the ground-truth $\\mathbf{y}_{\\mathrm{tr}}$ :", + "bbox": [ + 89, + 666, + 483, + 742 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathcal {L} \\left(\\mathbf {y} _ {\\mathrm {t r}}, \\tilde {\\mathbf {y}} _ {\\mathrm {t r}}; \\theta\\right), \\tilde {\\mathbf {y}} _ {\\mathrm {t r}} = \\left\\{f _ {\\theta} (G) _ {v}, v \\in V _ {\\mathrm {t r}} \\right\\} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 750, + 483, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Graph classification: $f_{\\theta}$ takes a graph $G$ as input and predicts a label $\\tilde{y}_G \\in \\mathcal{V}$ for the whole graph $G$ , i.e., $\\tilde{y}_G = f(G)$ . Given a set of training graphs $\\mathcal{G}_{\\mathrm{tr}}$ with ground-truth labels $\\mathbf{y}_{\\mathrm{tr}} = \\{y_G, G \\in \\mathcal{G}_{\\mathrm{tr}}\\}$ . The graph classifier $f_{\\theta}$ is learnt by minimizing a loss function $\\mathcal{L}$ between the predictions on $\\mathcal{G}_{\\mathrm{tr}}$ and the ground-truth $\\tilde{\\mathbf{y}}_{\\mathrm{tr}}$ :", + "bbox": [ + 89, + 781, + 485, + 872 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathcal {L} \\left(\\mathbf {y} _ {\\mathrm {t r}}, \\tilde {\\mathbf {y}} _ {\\mathrm {t r}}; \\theta\\right), \\tilde {\\mathbf {y}} _ {\\mathrm {t r}} = \\left\\{f _ {\\theta} (G), G \\in \\mathcal {G} _ {\\mathrm {t r}} \\right\\} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 881, + 483, + 904 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Poisoning Attack on GNNs", + "text_level": 1, + "bbox": [ + 513, + 90, + 756, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In poisoning attacks against GNNs, an attacker can manipulate any training graph $G = \\{V,E,\\mathbf{X}\\} \\in \\mathcal{G}_{\\mathrm{tr}}$ (For node classification, $\\mathcal{G}_{\\mathrm{tr}} = \\{G\\}$ ) into a perturbed one $G^{\\prime} = \\{V^{\\prime},E^{\\prime},\\mathbf{X}^{\\prime}\\}$ during training, where $V^{\\prime},E^{\\prime},\\mathbf{X}^{\\prime}$ are the perturbed version of $V,E$ and $\\mathbf{X}$ , respectively. For simplicity, we denote the nodes, edges and features in training graph(s) as $\\mathcal{V},\\mathcal{E}$ , and $\\mathcal{X}$ , respectively.", + "bbox": [ + 511, + 114, + 906, + 219 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Edge manipulation: The attacker can 1) inject new edges $\\mathcal{E}_{+}$ , and 2) delete existing edges, denoted as $\\mathcal{E}_{-} \\subset \\mathcal{E}$ .", + "bbox": [ + 511, + 220, + 903, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Node manipulation: The attacker perturbs $\\mathcal{G}_{\\mathrm{tr}}$ by (1) injecting new nodes $\\nu_{+}$ , whose node feature denoted as $\\mathcal{X}_{\\nu_{+}}^{\\prime}$ can be arbitrary, together with the arbitrarily injected new edges $\\mathcal{E}_{\\nu_{+}} \\subseteq \\{(u,v) \\notin \\mathcal{E}, \\forall u \\in \\mathcal{V}_{+} \\lor v \\in \\mathcal{V}_{+}\\}$ induced by $\\nu_{+}$ ; and (2) deleting existing nodes $\\nu_{-} \\subset \\nu$ . When $\\nu_{-}$ are deleted, their features $\\mathcal{X}_{\\nu_{-}} \\subseteq \\mathcal{X}$ and all connected edges $\\mathcal{E}_{\\nu_{-}} = \\{(u,v) \\in \\mathcal{E}, \\forall u \\in \\mathcal{V}_{-} \\lor v \\in \\mathcal{V}_{-}\\}$ are also removed. We denote that for the node classification case, the injected and deleted nodes are not from $V_{\\mathrm{tr}}$ .", + "bbox": [ + 511, + 252, + 906, + 386 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Node feature manipulation: The attacker arbitrarily manipulates features $\\mathcal{X}_{\\mathcal{V}_r}$ of a set of representative nodes $\\nu_{r}$ to be $\\mathcal{X}_{\\mathcal{V}_r}^\\prime$ . We also denote the edges connected with nodes $\\nu_{r}$ as $\\mathcal{E}_{\\nu_r} = \\{(u,v)\\in \\mathcal{E}:\\forall u\\in \\mathcal{V}_r\\lor v\\in \\mathcal{V}_r\\}$", + "bbox": [ + 511, + 388, + 906, + 449 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Arbitrary manipulation: The attacker can manipulate a training graphs in $\\mathcal{G}_{\\mathrm{tr}}$ with an arbitrary combined perturbations on edges, nodes, and node features for each of them. The attacker can manipulate several training graphs at the same time with different combinations of attack.", + "bbox": [ + 511, + 449, + 906, + 523 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For description simplicity, we will use $\\{\\mathcal{E}_{+},\\mathcal{E}_{-}\\}$ to indicate the edge manipulation with arbitrary injected edges $E_{+}$ and deleted edges $\\mathcal{E}_{-}$ on $\\mathcal{G}_{tr}$ . Similarly, we will use $\\{\\mathcal{V}_{+},\\mathcal{E}_{\\mathcal{V}_{+}},\\mathcal{X}_{\\mathcal{V}_{+}}^{\\prime},\\mathcal{V}_{-},\\mathcal{E}_{\\mathcal{V}_{-}}\\}$ to indicate the node manipulation, and $\\{\\mathcal{V}_r,\\mathcal{E}_{\\mathcal{V}_r},\\mathcal{X}_{\\mathcal{V}_r}^{\\prime}\\}$ the node feature manipulation. Any combination of the manipulations is inherently well-defined.", + "bbox": [ + 511, + 525, + 908, + 618 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Problem Statement", + "text_level": 1, + "bbox": [ + 513, + 628, + 697, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Threat model: Given a node/graph classifier $f$ , a training graph set $\\mathcal{G}_{\\mathrm{tr}}$ , the adversary can arbitrarily manipulate a number of the edges, nodes, and node features in any graph of $\\mathcal{G}_{\\mathrm{tr}}$ such that after training, $f$ misclassifies target graphs in graph classification or target nodes in node classification. Since we focus on certified defenses, we consider the strongest attack where the adversary has white-box access to $\\mathcal{G}_{\\mathrm{tr}}$ i.e., it knows all the edges, nodes, and node features in $\\mathcal{G}_{\\mathrm{tr}}$ .", + "bbox": [ + 511, + 652, + 908, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Defense goal: We aim to build provably robust GNNs against poisoning attacks that:", + "bbox": [ + 511, + 777, + 906, + 808 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- has a deterministic robustness guarantee;", + "- is suitable for both node and graph classification tasks;", + "- provably predicts the same label against the arbitrary poisoning perturbation within the certified perturbation size." + ], + "bbox": [ + 513, + 810, + 906, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our ultimate goal is to obtain the largest-possible certified perturbation size that satisfies all the above conditions.", + "bbox": [ + 511, + 869, + 905, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5021", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Our Certified Defense: PGNNCert", + "text_level": 1, + "bbox": [ + 89, + 89, + 405, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 89, + 114, + 200, + 128 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method is inspired by previous work [24, 54], which divides a test input into several sub-parts and assembles a voting GNN classifier on the sub-parts. We generalize this idea by designing the dividing strategy tailored to training set. Specifically, it consists of four steps below:", + "bbox": [ + 89, + 137, + 482, + 213 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the first step, we divide the training graph set into multiple subgraph sets. For each training graph $G \\in \\mathcal{G}_{\\mathrm{tr}}$ with ground-truth label $y_{G} \\in \\mathbf{y}_{\\mathrm{tr}}$ , we divide it into $S$ subgraphs $G_{1}, G_{2}, \\ldots, G_{S}$ via a hash function and ensure edges in different subgraphs are disjoint. This process is detailed in Section 3.2-3.3. By collecting these subgraphs, we build $S$ sets of subgraphs $\\mathcal{G}_{[S]} = \\{\\mathcal{G}_1, \\mathcal{G}_2, \\ldots, \\mathcal{G}_S\\}$ . In each subgraph set $\\mathcal{G}_i$ , there exists an exact subgraph $G_i$ generated from $G$ , and we label $G_i$ the same label $y_{G}$ as $G$ .", + "bbox": [ + 89, + 213, + 483, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the second step, we train multiple classifiers with the respective subgraph sets. On each subgraph set $\\mathcal{G}_i$ , we initialize a classifier $f_i$ with weights $\\theta_i$ and train it below:", + "bbox": [ + 89, + 349, + 483, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Node classifier: $\\min_{\\theta_i}\\mathcal{L}(\\mathbf{y}_{\\mathrm{tr}},\\tilde{\\mathbf{y}}_i;\\theta_i),\\tilde{\\mathbf{y}}_i = \\{f_i(G)_v,v\\in V_{\\mathrm{tr}}\\}$", + "bbox": [ + 101, + 402, + 464, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Graph classifier: $\\min_{\\theta_i}\\mathcal{L}(\\mathbf{y}_{\\mathrm{tr}},\\tilde{\\mathbf{y}}_i;\\theta_i),\\tilde{\\mathbf{y}}_i = \\{f_i(G),G\\in \\mathcal{G}_{\\mathrm{tr}}\\}$", + "bbox": [ + 101, + 426, + 470, + 448 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the third step, we build the voting-based classifier based on the trained sub-classifiers. Given a test graph $G$ , we first divide it into $S$ subgraphs $\\{G_1, \\ldots, G_S\\}$ by the same subgraph division method. Then we apply a voting classifier $\\bar{f}$ , which assembles the predictions of the trained classifiers $f_{[S]}$ on the subgraphs:", + "bbox": [ + 89, + 455, + 483, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Node classifier: $\\mathbf{n}_{y_v} = \\sum_{i=1}^{S} \\mathbb{I}(f_i(G_i)_v = y_v), \\forall y_v \\in \\mathcal{V}$ (3)", + "bbox": [ + 101, + 551, + 483, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Graph classifier: $\\mathbf{n}_{y_G} = \\sum_{i=1}^{S} \\mathbb{I}(f_i(G_i) = y_G), \\forall y_G \\in \\mathcal{V}$ (4)", + "bbox": [ + 101, + 578, + 483, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We then define our voting node/graph classifier $\\bar{f}$ as returning the class with the most vote:", + "bbox": [ + 89, + 609, + 482, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Voting node classifier: $\\bar{f} (G)_v = \\operatorname *{arg\\max}_{y_v\\in \\mathcal{V}}\\mathbf{n}_{y_v}$ (5)", + "bbox": [ + 142, + 648, + 483, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Voting graph classifier: $\\bar{f} (G) = \\operatorname *{arg\\max}_{y_G\\in \\mathcal{Y}}\\mathbf{n}_{y_G}$ (6)", + "bbox": [ + 142, + 675, + 483, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the forth step, we derive the deterministic robustness guarantee for the test graph. We denote $y_{a}$ and $y_{b}$ as the class with the most vote $\\mathbf{n}_{y_a}$ and the second-most vote $\\mathbf{n}_{y_b}$ , respectively. We pick the class with a smaller index if ties exist. Denote $\\mathcal{G}_{\\mathrm{tr}}^{\\prime}$ as the perturbed train dataset of $\\mathcal{G}_{\\mathrm{tr}}$ , and $\\mathcal{G}_{[S]}^{\\prime} = \\{\\mathcal{G}_1^{\\prime},\\mathcal{G}_2^{\\prime},\\dots ,\\mathcal{G}_S^{\\prime}\\}$ be the perturbed subgraph sets generated from $\\mathcal{G}_{\\mathrm{tr}}^{\\prime}$ under the same graph division strategy. Then we have the below condition for certified robustness against arbitrary poisoning attacks on GNNs.", + "bbox": [ + 89, + 708, + 483, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 1 (Sufficient Condition for Certified Robustness). Let $y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}}$ be defined above in node classification or graph classification, and let $P =$", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\left\\lfloor \\mathbf{n}_{y_a} - \\mathbf{n}_{y_b} - \\mathbb{I}(y_a > y_b)\\right\\rfloor /2.$ The voting classifier $\\bar{f}$ trained on $\\mathcal{G}_{tr}$ guarantees the same prediction on $G$ for the target node $v$ in node classification or the target graph $G$ in graph classification with the poisoned voting classifier $\\bar{f}'$ , if the number of different sub-classifiers (i.e., different in weights) trained on $\\mathcal{G}_{[S]}$ and $\\mathcal{G}_{[S]}'$ under the arbitrary perturbation is bounded by $P$ . I.e.,", + "bbox": [ + 511, + 90, + 905, + 196 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\forall \\mathcal {G} _ {t r} ^ {\\prime}: \\sum_ {i = 1} ^ {S} \\mathbb {I} \\left(\\theta_ {i} \\neq \\theta_ {i} ^ {\\prime}\\right) \\leq P \\Longrightarrow \\bar {f} (G) _ {v} = \\bar {f} ^ {\\prime} (G) _ {v} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 203, + 906, + 227 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\forall \\mathcal {G} _ {t r} ^ {\\prime}: \\sum_ {i = 1} ^ {S} \\mathbb {I} \\left(\\theta_ {i} \\neq \\theta_ {i} ^ {\\prime}\\right) \\leq P \\Longrightarrow \\bar {f} (G) = \\bar {f} ^ {\\prime} (G) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 229, + 906, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Proof is in Appendix A. The above theorem motivates us to design the graph division method such that: 1) the number of different sub-classifiers with trained on $\\mathcal{G}_{[S]}$ and $\\mathcal{G}_{[S]}^{\\prime}$ can be upper bounded (and the smaller the better). 2) the difference between $\\mathbf{n}_{y_a}$ and $\\mathbf{n}_{y_b}$ is as large as possible, ensuring larger certified perturbation size.", + "bbox": [ + 511, + 262, + 905, + 352 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, we introduce our two graph division methods. Figure 2 visualizes the divided subgraphs of the two methods without and with the adversarial manipulation.", + "bbox": [ + 511, + 353, + 906, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Edge-Centric Graph Division", + "text_level": 1, + "bbox": [ + 511, + 409, + 774, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our first graph division method is edge-centric. The idea is to divide edges in a graph into different subgraphs, such that each edge is deterministically mapped into only one subgraph. With this strategy, we can bound the number of altered classifiers trained on these subgraphs before and after the arbitrary perturbation (Theorem 2), which facilitates deriving the certified perturbation size (Theorem 3). All proofs are detailed in Appendix A.", + "bbox": [ + 511, + 431, + 905, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Generating edge-centric subgraphs", + "text_level": 1, + "bbox": [ + 511, + 561, + 812, + 577 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We follow [24, 54] to use a hash function $h$ (e.g., MD5) to generate the subgraphs for every train graph $G \\in \\mathcal{G}_{\\mathrm{tr}}$ . A hash function takes a bit string as input and outputs an integer (e.g., within a range $[0, 2^{128} - 1]$ ). We use the string of edge or node index as the input to the hash function. For instance, for a node $u$ , its string is denoted as $\\operatorname{str}(u)$ , while for an edge $e = (u, v)$ , its string is $\\operatorname{str}(u) + \\operatorname{str}(v)$ , where \"+\" means string concatenation, and str turns the node index into a string and adds \"0\" prefix to align it into a fixed length.", + "bbox": [ + 511, + 585, + 905, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Assuming $S$ subgraphs in total, the subgraph index $i_e$ of every edge $e = (u,v)$ is defined as2", + "bbox": [ + 511, + 722, + 905, + 752 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ni _ {e} = h \\left[ \\operatorname {s t r} (u) + \\operatorname {s t r} (v) \\right] \\bmod S + 1, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 762, + 906, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where mod is the module function. Denoting $\\mathcal{E}^i$ as the set of edges whose subgraph index is $i$ , i.e., $\\mathcal{E}^i = \\{\\forall e \\in \\mathcal{E} : i_e = i\\}$ , $S$ subgraphs for $G$ can be built as $\\{G_i = (\\mathcal{V}, \\mathcal{E}^i, \\mathbf{X}) : i = 1, 2, \\dots, S\\}$ , where edges in different subgraphs are disjoint, i.e., $\\mathcal{E}^i \\cap \\mathcal{E}^j = \\emptyset, \\forall i, j \\in \\{1, \\dots, S\\}, i \\neq j$ . Here, we", + "bbox": [ + 511, + 789, + 905, + 864 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2In the undirected graph, we put the node with a smaller index (say $u$ ) first and let $h[\\mathrm{str}(v) + \\mathrm{str}(u)] = h[\\mathrm{str}(u) + \\mathrm{str}(v)]$ .", + "bbox": [ + 511, + 875, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5022", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1197eebffade3577990074eb19f87cb19868989db80fc628c55d83feb081b71a.jpg", + "image_caption": [ + "Figure 1. Overview of our PGNNCert (use node classification for illustration), which consists of four steps." + ], + "image_footnote": [], + "bbox": [ + 109, + 71, + 883, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "mention that we need to further postprocess the subgraphs for graph classification, in order to derive the robustness guarantee. Particularly, in each subgraph $G_{i}$ , we remove all isolated nodes who have no connected edges. This is because although they have no influence on other nodes' representation, their information would still be passed to the global graph embedding aggregation.", + "bbox": [ + 88, + 285, + 483, + 390 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After dividing all training graphs in $\\mathcal{G}_{\\mathrm{tr}}$ , we combine all generated subgraphs with the same index as a separate subgraph training set: $\\mathcal{G}_i = \\{G_i, \\forall G \\in \\mathcal{G}_{\\mathrm{tr}}\\}, \\forall i \\in [S]$ . We denote the $S$ training sets as $\\mathcal{G}_{[S]} = \\{\\mathcal{G}_1, \\dots, \\mathcal{G}_S\\}$ .", + "bbox": [ + 89, + 391, + 483, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Bounding the number of different sub-classifiers", + "text_level": 1, + "bbox": [ + 89, + 462, + 480, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For a perturbed training set $\\mathcal{G}_{\\mathrm{tr}}^{\\prime}$ , we use the same graph division strategy to generate a set of $S$ subgraphs sets $\\mathcal{G}_{[S]}^{\\prime} = \\{\\mathcal{G}_1^{\\prime},\\mathcal{G}_2^{\\prime},\\dots ,\\mathcal{G}_T^{\\prime}\\}$ . Then, we can upper bound the number of different classifiers trained on $\\mathcal{G}_{[S]}$ and $\\mathcal{G}_{[S]}^{\\prime}$ against any individual perturbation.", + "bbox": [ + 89, + 484, + 483, + 563 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 2 (Bounded Number of Edge-Centric Subgraphs with Altered Predictions under Arbitrary Perturbation). Given any training graph set $\\mathcal{G}_{tr}$ , and $S$ edge-centric subgraph sets $\\mathcal{G}_{[S]}$ for $\\mathcal{G}_{tr}$ . A perturbed training set $\\mathcal{G}_{train}^{\\prime}$ of $\\mathcal{G}_{train}$ is with arbitrary edge manipulation $\\{\\mathcal{E}_+, \\mathcal{E}_-\\}$ , node manipulation $\\{\\mathcal{V}_+,\\mathcal{E}_{\\mathcal{V}_+},\\mathcal{V}_-, \\mathcal{E}_{\\mathcal{V}_-}\\}$ , and node feature manipulation $\\{\\mathbf{X}_{\\mathcal{V}_r},\\mathcal{V}_r,\\mathcal{E}_{\\mathcal{V}_r}\\}$ on arbitrary graphs in $\\mathcal{G}_{tr}$ . Then at most $p = |\\mathcal{E}_+| + |\\mathcal{E}_-| + |\\mathcal{E}_{\\mathcal{V}_+}| + |\\mathcal{E}_{\\mathcal{V}_-}| + |\\mathcal{E}_{\\mathcal{V}_r}|$ node/graph sub-classifiers in $f_{[S]}$ are different in weights between training on the subgraph sets $\\mathcal{G}_{[S]}$ and on the perturbed subgraph sets $\\mathcal{G}_{[S]}^{\\prime}$ . In other words, $\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq p$ for both node classification case and graph classification case.", + "bbox": [ + 89, + 564, + 483, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.3 Deriving the robustness guarantee", + "text_level": 1, + "bbox": [ + 89, + 755, + 382, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on Theorems 1 and 2, we can derive the certified perturbation size as the maximal perturbation such that Equation 7 or Equation 8 is satisfied. Formally,", + "bbox": [ + 89, + 779, + 483, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 3 (Certified Robustness Guarantee with Edge-Centric Subgraphs against Arbitrary Perturbation). Let $f, y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}}$ be defined above for edge-centric subgraphs, and $p$ be the perturbation size induced by an arbitrary perturbed training set $\\mathcal{G}_{tr}'$ on $\\mathcal{G}_{tr}$ . After training on $\\mathcal{G}_{tr}'$", + "bbox": [ + 89, + 825, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and $\\mathcal{G}_{tr}^{\\prime}$ , the voting classifier $\\bar{f}$ and poisoned classifier $\\bar{f}'$ guarantee the same prediction for the target node $v$ in node classification (i.e., $\\bar{f}(G')_v = \\bar{f}(G)_v$ ) or target graph $G$ in graph classification (i.e., $\\bar{f}(G') = \\bar{f}(G)$ ), when $p$ satisfies.", + "bbox": [ + 511, + 284, + 905, + 347 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\leq P = \\left\\lfloor \\mathbf {n} _ {y _ {a}} - \\mathbf {n} _ {y _ {b}} - \\mathbb {I} \\left(y _ {a} > y _ {b}\\right) \\right\\rfloor / 2. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 358, + 906, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Or to say, the maximum certified perturbation size is $P$ .", + "bbox": [ + 511, + 387, + 880, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Node-Centric Graph Division", + "text_level": 1, + "bbox": [ + 511, + 412, + 774, + 428 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We observe the robustness guarantee under edge-centric graph division is largely dominated by the edges (i.e., $\\mathcal{E}_{\\mathcal{V}_+}, \\mathcal{E}_{\\mathcal{V}_-}$ ) induced by the manipulated nodes $\\mathcal{V}_+$ , $\\mathcal{V}_-$ , and edges $\\mathcal{E}_{\\mathcal{V}_r}$ by the perturbed node features $\\mathbf{X}_{\\mathcal{V}_r}'$ . This guarantee could be weak against node or node feature manipulation, as the number of edges (i.e., $|\\mathcal{E}_{\\mathcal{V}_+}|, |\\mathcal{E}_{\\mathcal{V}_-}|, |\\mathcal{E}_{\\mathcal{V}_r}|$ ) could be much larger, compared with the number of the nodes (i.e., $|\\mathcal{V}_+|, |\\mathcal{V}_-|, |\\mathcal{V}_r|$ ). For instance, an injected node could link with many edges to a given graph in practice, and when the number exceeds $P$ in Equation 10, the certified robustness guarantee is ineffective. This flaw inspires us to generate subgraphs, where we expect at most one subgraph is affected under every node or node feature manipulation on a training graph (this means all edges of a manipulated node should be in a same subgraph), implying only a training subgraph set is affected. Following [24], we apply a tailored node-centric graph division strategy to achieve our goal.", + "bbox": [ + 511, + 435, + 906, + 693 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Generating node-centric directed subgraphs", + "text_level": 1, + "bbox": [ + 511, + 705, + 874, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use a hash function $h$ to generate directed subgraphs for a given train graph $G = (\\mathcal{V},\\mathcal{E},\\mathbf{X})\\in \\mathcal{G}_{\\mathrm{tr}}$ . Our node-centric graph division strategy as follows: (1) we treat every undirected edge $e = (u,v)\\in G$ as two directed edges for $u^3$ : the outgoing edge $u\\to v$ and incoming edge $v\\rightarrow u$ ; (2) for every node $u$ , we compute the subgraph index of its every outgoing edge $u\\to v$ :", + "bbox": [ + 511, + 729, + 905, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ni _ {u \\rightarrow v} = h [ \\operatorname {s t r} (u) ] \\bmod S + 1. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 847, + 906, + 864 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "${}^{3}$ GNNs inherently handles directed graphs with directed message passing - each node only uses its incoming neighbors' message for update.", + "bbox": [ + 511, + 875, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5023", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e02fcf503f1d909e6f94cf97054387813e3f82e4a9e81774b9cc99941c671033.jpg", + "image_caption": [ + "(b) Node-Centric Graph Division against edge injection and node injection attacks", + "Figure 2. Illustration of our edge-centric and node-centric graph division strategies for node classification. We use edge injection and node injection poisoning attacks to show the bounded number of altered predictions on the generated subgraphs after the attack. Figures 8-9 in Appendix also show other attacks and on graph classification." + ], + "image_footnote": [], + "bbox": [ + 133, + 85, + 869, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note outgoing edges of $u$ are mapped in the same subgraph.", + "bbox": [ + 93, + 473, + 483, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use $\\vec{\\mathcal{E}}_i$ to denote the set of directed edges whose subgraph index is $i$ , i.e., $\\vec{\\mathcal{E}}_i = \\{\\forall u \\to v \\in \\mathcal{E} : i_{u \\to v} = i\\}$ . Then, we can construct $S$ directed subgraphs for $G$ as $\\vec{G}_i = (\\mathcal{V}, \\vec{\\mathcal{E}}_i, \\mathbf{X}), \\forall i \\in [1, S]$ . After generating subgraphs for all training graphs, we combine all subgraphs with the same index as a separate subgraph set: $\\vec{\\mathcal{G}}_i = \\{\\vec{G}_i, \\forall G \\in \\mathcal{G}_{\\mathrm{tr}}\\}, \\forall i \\in [S]$ . We denote the $S$ training sets as $\\vec{\\mathcal{G}}_{[S]} = \\{\\vec{\\mathcal{G}}_1, \\dots, \\vec{\\mathcal{G}}_S\\}$ .", + "bbox": [ + 89, + 488, + 483, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, we mention that we need to further postprocess the subgraphs for graph classification, in order to derive the robustness guarantee. Particularly, in each subgraph $\\vec{G}_i$ , we remove all other nodes whose subgraph index is not $i$ . This is because although they have no influence on other nodes' representation, their information would still be passed to the global graph embedding aggregation. To make up the loss of connectivity between nodes and simulate the aggregation, we add an extra node with a zero feature, and add an outgoing edge from every node with index $i$ to it.", + "bbox": [ + 88, + 599, + 483, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Bounding the number of different sub-classifiers", + "text_level": 1, + "bbox": [ + 89, + 763, + 480, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For a perturbed training set $G_{\\mathrm{tr}}^{\\prime}$ , we use the same graph division strategy to generate a set of $S$ directed subgraph sets $\\vec{\\mathcal{G}}_{[S]}^{\\prime} = \\{\\vec{\\mathcal{G}}_1^{\\prime},\\vec{\\mathcal{G}}_2^{\\prime},\\dots ,\\vec{\\mathcal{G}}_T^{\\prime}\\}$ . We first show the theoretical result on bounding the number of different trained classifiers on $\\vec{\\mathcal{G}}_{[S]}$ and $\\vec{\\mathcal{G}}_{[S]}^{\\prime}$ against any individual perturbation.", + "bbox": [ + 89, + 789, + 483, + 867 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 4 (Bounded Number of Node-Centric Subgraphs with Altered Predictions under Arbitrary Perturbation). Let", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal{G}_{tr}, v, G, \\mathcal{E}_+, \\mathcal{E}_-, \\mathcal{V}_+, \\mathcal{V}_-, \\mathcal{V}_r$ be defined in Theorem 2, and $\\vec{\\mathcal{G}}_{[S]}, \\vec{\\mathcal{G}}_{[S]}'$ contain directed subgraph sets under the node-centric graph division. Then, at most $\\bar{p} = 2|\\mathcal{E}_+| + 2|\\mathcal{E}_-| + |\\mathcal{V}_+| + |\\mathcal{V}_-| + |\\mathcal{V}_r|$ trained node classifiers in $f_{[S]}$ are different in weights after training on $\\vec{\\mathcal{G}}_{[S]}$ and on $\\vec{\\mathcal{G}}_{[S]}'$ . In other words, $\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq \\bar{p}$ for any target node $v \\in G$ in node classification. Meanwhile, at most $\\bar{p} = |\\mathcal{E}_+| + |\\mathcal{E}_-| + |\\mathcal{V}_+| + |\\mathcal{V}_-| + |\\mathcal{V}_r|$ trained graph classifiers in $f_{[S]}$ are different in weights after training on $\\vec{\\mathcal{G}}_{[S]}$ and on $\\vec{\\mathcal{G}}_{[S]}'$ . In other words, $\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq \\bar{p}$ in graph classification.", + "bbox": [ + 511, + 472, + 908, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Deriving the robustness guarantee", + "text_level": 1, + "bbox": [ + 511, + 652, + 805, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on Theorem 1 and Theorem 4, we can derive the certified perturbation size formally stated below", + "bbox": [ + 511, + 676, + 906, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 5 (Certified Robustness Guarantee with Node-Centric Subgraphs against Arbitrary Perturbation). Let $f, y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}}^{4}$ be defined above for node-centric subgraphs, and $\\bar{p}$ be the perturbation size induced by an arbitrary perturbed graph $G'$ on $G$ . With a probability $100\\%$ , the voting classifier $\\bar{f}$ guarantees the same prediction on both $G'$ and $G$ for the target node $v$ in node classification (i.e., $\\bar{f}(G')_{v} = \\bar{f}(G)_{v}$ ) or the target graph $G$ in graph classification (i.e., $\\bar{f}(G') = \\bar{f}(G)$ ), if", + "bbox": [ + 511, + 707, + 908, + 845 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {p} \\leq P = \\left\\lfloor \\mathbf {n} _ {y _ {a}} - \\mathbf {n} _ {y _ {b}} - \\mathbb {I} \\left(y _ {a} > y _ {b}\\right) \\right\\rfloor / 2. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 854, + 906, + 872 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "4Note that $\\mathbf{n}_{y_a},\\mathbf{n}_{y_b}$ have different values with those in edge-centric graph division. Here we use the same notation for description brevity.", + "bbox": [ + 511, + 875, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5024", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 90, + 223, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiments Settings", + "text_level": 1, + "bbox": [ + 89, + 114, + 290, + 131 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets: We use four node classification datasets (Cora-ML [31], CiteSeer [38], PubMed [38], Amazon-C [57]) and four graph classification datasets (AIDS [34], MUTAG [9], PROTEINS [5], and DD [10]) for evaluation. In each dataset, we take $30\\%$ nodes (for node classification) or $50\\%$ graphs (for graph classification) as the training set, $10\\%$ and $20\\%$ as the validation set and $30\\%$ nodes/graph as the test set. Table 5 in Appendix shows the basic statistics of them.", + "bbox": [ + 89, + 137, + 485, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GNN classifiers and PGNNCert training: We adopt three well-known GNNs as the base node/graph classifiers: GCN [21], GSAGE [15] and GAT [44]. We denote the two versions of PGNNCert under edge-centric and node-centric graph division as PGNNCert-E and PGNNCert-N, respectively. By default, we use GCN as the node/graph classifier.", + "bbox": [ + 89, + 263, + 483, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metric: Following existing works [22, 47, 54], we use the certified node/graph accuracy at perturbation size as the evaluation metric. Given a perturbation size $p$ and test nodes/graphs, certified node/graph accuracy at $p$ is the fraction of test nodes/graphs that are accurately classified by the voting node/graph classifier and its certified perturbation size is no smaller than $p$ . Note that the standard node/graph accuracy is achieved when over $p = 0$ .", + "bbox": [ + 89, + 358, + 483, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Parameter setting: PGNNCert has two hyperparameters: the hash function $h$ and the number of subgraphs $S$ . By default, we use MD5 as the hash function and set $S = 50,60$ respectively for node and graph classification, considering their different graph sizes. We also study the impact of them.", + "bbox": [ + 89, + 484, + 483, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared baselines: As PGNNCert encompasses existing defenses as special cases, we can compare PGNNCert with them against less types of perturbation. Here, we choose the sparse-smoothing RS [4], Bagging [17] and Bi-RS [22] as compared baselines in face of node injection poisoning attack on node classification task. For Bi-RS, We adopt the $p_e = 0.2$ , $p_n = 0.9$ , $N = 1000$ setting as described, and test both include and exclude methods. We also use Bagging for comparison on graph classification.", + "bbox": [ + 89, + 564, + 483, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experiment Results on PGNNCert", + "text_level": 1, + "bbox": [ + 89, + 709, + 382, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Main results: Figures 3-4 show the certified node accuracy and Figures 5-6 show the certified graph accuracy at perturbation size $p$ w.r.t. $S$ under the two graph division strategies, respectively. We have the following observations.", + "bbox": [ + 89, + 731, + 483, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "- Both PGNNCert-E and PGNNCert-N can tolerate the perturbation size up to 25 and 30, on the node and graph classification datasets. This means PGNNCert-E can defend against a total of 25 (30) arbitrary edges, while PGNNCert-N against a total of 25 (30) arbitrary edges and nodes caused by the arbitrary perturbation, on the node (graph) classification datasets, respectively. Note", + "bbox": [ + 89, + 795, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/18122e315a2faffc8ae353a66606047550f88043c3110a856dd6e8bdd352492c.jpg", + "table_caption": [ + "Table 1. Node/graph accuracy of normally trained GNN and of PGNNCert with GNN trained on the subgraphs." + ], + "table_footnote": [], + "table_body": "
    DatasetGCNPGNNCertGSAGEPGNNCertGATPGNNCert
    -E-N-E-N-E-N
    Cora-ML0.730.680.680.670.650.680.740.690.69
    Citeseer0.660.670.670.690.680.680.700.670.67
    Pubmed0.860.830.850.840.840.850.850.850.84
    Amazon-C0.810.810.810.820.780.800.830.780.80
    AIDS0.990.880.960.970.940.950.960.930.96
    MUTAG0.710.640.640.700.630.640.710.650.65
    Proteins0.820.810.780.830.800.810.820.780.77
    DD0.800.790.770.810.780.760.810.770.79
    ", + "bbox": [ + 516, + 121, + 908, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "that node classification datasets have several orders of more nodes/edges than graph classification datasets, hence PGNNCert can tolerate more perturbations on them.", + "bbox": [ + 526, + 246, + 906, + 291 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $S$ acts as the robustness-accuracy tradeoff. That is, a larger (smaller) $S$ yields a higher (lower) certified perturbation size, but a smaller (higher) normal accuracy ( $p = 0$ ).", + "- In PGNNCert-N, the guaranteed perturbed nodes can have infinite edges. This implies that PGNNCert-N has better robustness than PGNNCert-E against the perturbed edges by node/node feature manipulation." + ], + "bbox": [ + 511, + 292, + 906, + 396 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Impact of base GNN classifiers: Figures 10-11 and Figures 12-13 in Appendix show the certified accuracy using GSAGE and GAT as the base classifier, respectively. We have similar observations as those results with GCN.", + "bbox": [ + 511, + 398, + 906, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Impact of hash function: Figures 14-17 show the certified node/edge accuracy of PGNNCert-E and PGNNCert-N with different hash functions. We observe that our certified accuracy and certified perturbation size are almost the same in all cases. This reveals our PGNNCert is insensitive to the hash function, and [54] draws a similar conclusion.", + "bbox": [ + 511, + 465, + 905, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Impact of subgraphs on normal accuracy: We test the normal accuracy of (not) using subgraphs to train the GNN classifier. Table 1 shows the test node/graph accuracy of normally trained GNN without sburgraphs and PGNNCert with GNN trained on the subgraphs. We observe that the accuracy of PGNNCert is $5\\%$ smaller than that of normally trained GNN in almost all cases, and in some cases even larger. This implies the augmented subgraphs for training marginally affects the normal test accuracy.", + "bbox": [ + 511, + 560, + 905, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison Results with SOTA Baselines", + "text_level": 1, + "bbox": [ + 511, + 705, + 870, + 722 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare PGNNCert with SOTA defenses (Bi-RS [22], RS [4], Bagging [17]) against node injection poisoning attacks and graph structure poisoning attacks [17].", + "bbox": [ + 511, + 729, + 906, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results for node classification against node injection poisoning attacks: We follow Bi-RS [22] by setting the injected nodes' degrees as $\\tau = 5$ and show the certified node accuracy with varying number of injected nodes. Figure 7 shows the comparison results. We can see PGNNCert-E has better certified accuracy than RS, Bagging and Bi-RS-Include, but it is worse than Bi-RS-Exclude. This aligns with our assumption on its weakness against node-relevant attack. By", + "bbox": [ + 511, + 780, + 908, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5025", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/517eed08059caeb30e9cee2ad61014f6d5dedc5cb5309288ccb02cd77872b35d.jpg", + "image_caption": [ + "(a) Cora-ML" + ], + "image_footnote": [], + "bbox": [ + 98, + 98, + 279, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/019d7af7b8ef08d9c0ae727637b09a3feb587451d7471a4ec19f469605a68f89.jpg", + "image_caption": [ + "(b)CiteSeer" + ], + "image_footnote": [], + "bbox": [ + 300, + 98, + 480, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e31ac7eb086b0923c565eba2f9085593def47537fbc590fc9bf0ac9015f8a547.jpg", + "image_caption": [ + "(c) Pubmed" + ], + "image_footnote": [], + "bbox": [ + 503, + 98, + 683, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aea07dc9790e417fbd9c68463b0125d42f08e69f574a8b4bb49051a3398457f7.jpg", + "image_caption": [ + "(d) Amazon-C" + ], + "image_footnote": [], + "bbox": [ + 705, + 98, + 883, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/37ac0188fabf64197ac1cf11491bd820fe79a63f8d2cbf40a6cb19f10e0ed2bd.jpg", + "image_caption": [ + "(a) Cora-ML" + ], + "image_footnote": [], + "bbox": [ + 98, + 247, + 279, + 344 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5badc25ed250739033c02e115f86e39a7350e249d7119fe1533b842eaa864a6c.jpg", + "image_caption": [ + "Figure 3. Certified node accuracy of our PGNNCert-E w.r.t. the number of subgraphs $S$ .", + "(b) CiteSeer" + ], + "image_footnote": [], + "bbox": [ + 300, + 248, + 480, + 344 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c7e63798990143b610b20cb1797d48a693c0d9dc209f8be3196f4a2f71321f30.jpg", + "image_caption": [ + "(c) Pubmed" + ], + "image_footnote": [], + "bbox": [ + 503, + 248, + 683, + 344 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c94499fa533c87932a3629f38dff3c2c2ef00ac69871c51cbc8bd8f8a80925ad.jpg", + "image_caption": [ + "(d) Amazon-C" + ], + "image_footnote": [], + "bbox": [ + 705, + 248, + 885, + 344 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9d74544d09d8c3dcb31fab09bb7b08ee34c354cb2352e21f9167536c603ea80a.jpg", + "image_caption": [ + "Figure 4. Certified node accuracy of our PGNNCert-N w.r.t. the number of subgraphs $S$ .", + "(a) AIDS" + ], + "image_footnote": [], + "bbox": [ + 98, + 398, + 279, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8629cd3817fe045afaca871ebc31445916773c379efaa30c762e0dca4fdb9bf7.jpg", + "image_caption": [ + "(b) MUTAG" + ], + "image_footnote": [], + "bbox": [ + 300, + 398, + 480, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b24a48c68dce9f2c747c710189f4271a7b2dabc87a540aa73f235fe07cd18b32.jpg", + "image_caption": [ + "(c) PROTEINS" + ], + "image_footnote": [], + "bbox": [ + 503, + 398, + 683, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/472de62d95c942a955a523edc04a5fe2f737839b5266dce1f95f99ea152d8d12.jpg", + "image_caption": [ + "(d) DD" + ], + "image_footnote": [], + "bbox": [ + 705, + 398, + 885, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/023f5f1982ca0b0daa603fab86db860ecb63d865588bd09bba86d22a25126c24.jpg", + "image_caption": [ + "Figure 5. Certified graph accuracy of our PGNNCert-E w.r.t. the number of subgraphs $S$ .", + "(a) AIDS" + ], + "image_footnote": [], + "bbox": [ + 98, + 550, + 279, + 645 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ad59b5b10406d3b2b82af09bdae7107e0c9dc933addf2536d28d0fc39cbe0558.jpg", + "image_caption": [ + "(b) MUTAG" + ], + "image_footnote": [], + "bbox": [ + 300, + 550, + 480, + 645 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e3184a705354c056c8d6aab53b4385fd3a95e0ee952b59618d905d17d74fd6c.jpg", + "image_caption": [ + "(c) PROTEINS" + ], + "image_footnote": [], + "bbox": [ + 503, + 550, + 683, + 645 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/83d6b1ea16f26ce001ccb4cb81696f6bb0e7c0b21839e5eaafa1dc3155f11388.jpg", + "image_caption": [ + "(d) DD" + ], + "image_footnote": [], + "bbox": [ + 705, + 550, + 885, + 645 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ca0df25cacf4771e9d1af8359d5b43b1cde4d0848ebbacac5841602f226e359f.jpg", + "image_caption": [ + "Figure 6. Certified graph accuracy of our PGNNCert-N w.r.t. the number of subgraphs $S$ .", + "(a) Cora-ML", + "Figure 7. Certified node accuracy of our PGNNCert and SOTA defenses against node injection attacks." + ], + "image_footnote": [], + "bbox": [ + 98, + 700, + 279, + 796 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed90bb0e8d7dbfb7e4459b7b831714e93deae88ad6c5a768b663aa2d19d6159d.jpg", + "image_caption": [ + "(b)CiteSeer" + ], + "image_footnote": [], + "bbox": [ + 300, + 700, + 480, + 795 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4b44befcc9365f9980011c525a02931cd63322edbc7e240e76a2df39186b2fcf.jpg", + "image_caption": [ + "(c) Pubmed" + ], + "image_footnote": [], + "bbox": [ + 503, + 700, + 683, + 796 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d104a7f978c6793e787be96e84ea68b629e627f57fb4737c008533ae1eebac94.jpg", + "image_caption": [ + "(d) Amazon-C" + ], + "image_footnote": [], + "bbox": [ + 705, + 700, + 885, + 796 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "contrast, PGNNCert-N outperforms all compared baselines. We highlight that each bounded node in PGNNCert-N can", + "bbox": [ + 89, + 858, + 483, + 888 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "inject as many edges as possible, meaning the total number of bounded edges in PGNNCert-N could be infinite.", + "bbox": [ + 511, + 858, + 905, + 888 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5026", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ccdfb6f10d6b59bf272ed3d1d1a9e69b953ab456448f193f0727ddde31fe5296.jpg", + "table_caption": [ + "Table 2. Certified graph accuracy of our PGNNCert and Bagging against edge perturbations." + ], + "table_footnote": [], + "table_body": "
    DatasetsMethods#Edges=051015
    ProteinsBagging0.7560.2050.0000.00
    PGNNCert-E0.7440.5180.2600.00
    PGNNCert-N0.7780.4740.1020.00
    DDBagging0.7850.3110.0000.00
    PGNNCert-E0.7920.5780.3300.063
    PGNNCert-N0.7710.3440.0060.000
    ", + "bbox": [ + 91, + 121, + 480, + 210 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/35154819aa9560931a7e27f773067fe315a0b0d9eb0ea2ab194a00ace5245bfd.jpg", + "table_caption": [ + "Table 3. Results of PGNNCert on CIFAR10." + ], + "table_footnote": [], + "table_body": "
    DatasetsMethodsp=0135
    CIFAR10PGNNCert-E0.5960.5560.4820.107
    PGNNCert-N0.6360.5930.4980.113
    ", + "bbox": [ + 99, + 233, + 470, + 275 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1e2a4993159928988e033b4fa9eee7e802353678f6a7df70e5ae2bc7c768a9f5.jpg", + "table_caption": [ + "Table 4. Defense results against the optimization-based Mettack." + ], + "table_footnote": [], + "table_body": "
    DatasetNettackp=0203040
    Cora-MLPGNNCert-N0.6750.6750.6680.661
    ", + "bbox": [ + 102, + 299, + 470, + 327 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results for graph classification against graph poisoning attacks: Table 2 shows the certified graph accuracies of PGNNCert and Bagging against edge perturbations on graph classification tasks. PGNNCert outperforms Bagging, especially when the perturbation size is larger.", + "bbox": [ + 89, + 339, + 483, + 414 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 89, + 428, + 204, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation on CV datasets. We also test a benchmark superpixel graph CIFAR10 in computer vision [11] for graph classification, to show the generality of our defense. CIFAR10 is an image classification dataset, which is converted into graphs using the SLIC superpixels [1]. Each node has the superpixel coordinates as the feature and each superpixel graph has a label. Results in the default setting are shown in Table 3, where we see PGNNCert can obtain about $50\\%$ certified accuracy when 3 arbitrary edges are perturbed.", + "bbox": [ + 89, + 453, + 483, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "PGNNCert against optimization-based attacks. We first emphasize that PGNNCert is provably robust against all (known and unknown) attacks, when their perturbation budget is within the derived bound (in Eqn 10 or Eqn 12), regardless of the attack knowledge of PGNNCert. Here, we test PGNNCert-N against Metattack [63] when its perturbation size $m$ is larger than the derived certified perturbation size $P = 25$ (with certified accuracy 0.588) on Cora-ML with $S = 60$ . Results are shown in Table 4. We see PGNNCert-N can achieve 0.661 accuracy of defending against Metattack even when it perturbs 40 edges and nodes in total.", + "bbox": [ + 89, + 594, + 483, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Despite the effectiveness of PGNNCert, its inefficiency remains a main limitation for large GNNs. PGNNCert trains $S$ classifiers on $S$ subgraphs and uses $S$ subgraphs for certification. It may incur a training/certification complexity that is $S$ times of standard GNN training/testing. This overhead could be significant when PGNNCert is applied to large GNNs. On the other hand, we note that the $S$ classifiers can be trained in parallel once obtaining the $S$ subgraphs after graph division.", + "bbox": [ + 89, + 763, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Related Work", + "text_level": 1, + "bbox": [ + 513, + 90, + 653, + 104 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Adversarial attacks on GNNs: Existing attacks to GNNs can be classified as graph evasion attacks [8, 25, 26, 29, 30, 32, 50-53, 55, 64] and poisoning attacks [8, 28, 40, 41, 45, 55, 60, 63, 63]. For instance, [8] leveraged reinforcement learning techniques to design evasion attacks to both graph classification and node classification via modifying the graph structure. Most attacks require the attacker fully or partially knows the GNN model, while [32, 50] relaxing this to only have black-box access, i.e., only query the GNN model API. For example, [50] formulates the black-box attack to GNNs as an online optimization problem with bandit feedback and provably obtains a sublinear query number. Furthermore, [25] generalizes the black-box evasion attack on explainable GNNs. In the realm of graph poisoning attacks, [55] proposed a MinMax attack to GNNs based on gradient-based optimization, while [63] introduced Metattack that perturbs the entire graph using meta learning.", + "bbox": [ + 511, + 114, + 906, + 372 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Certified robustness against graph poisoning graphs: Most existing certified defenses for GNNs are against test-time evasion attacks [16, 19, 22, 24, 27, 47, 54, 60], with a few ones [22] against training-time poisoning attacks.", + "bbox": [ + 511, + 376, + 908, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "There exist two main approaches providing certified robustness against poisoning data: 1) Randomized-smoothing based methods [22, 35, 46] regard the training-prediction process as an end-to-end function, and treat poisoning attack as a special case of evasion attack; 2) Voting based methods [17, 23] partition training data into subsets and train a sub-classifier on each subset. However, they restrict the attacker on one type of perturbation (nodes, edges, or node features); they are applicable for a particular GNN task; and their robustness guarantees are not $100\\%$ accurate. We are the first work to develop a deterministically certified robust GNN against graph poisoning attack with arbitrary kind of perturbations on both node and graph classification tasks.", + "bbox": [ + 511, + 436, + 908, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 646, + 633, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We investigate the robustness of Graph Neural Networks (GNNs) against graph poisoning attacks and introduce PGNNCert, the first certified defense with deterministic guarantees against arbitrary poisoning perturbations, including modifications to nodes, edges, and node features. PGNNCert employs novel graph division strategies and leverages the message-passing mechanism in GNNs to establish robustness guarantees. Its universality allows it to encompass existing certified defenses as special cases. Experimental evaluations demonstrate that PGNNCert effectively mitigates arbitrary poisoning perturbations, offering superior robustness and efficiency compared to state-of-the-art certified defenses. Future works include extending the proposed defense for federated GNNs [49, 58] and casually explainable GNNs [2] against arbitrary poisoning attacks.", + "bbox": [ + 511, + 671, + 908, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5027", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgment", + "text_level": 1, + "bbox": [ + 89, + 90, + 263, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We thank all the anonymous reviewers for their valuable feedback and constructive comments. This work is partially supported by the National Science Foundation (NSF) under grant Nos. ECCS-2216926, CNS-2241713, CNS-2331302, CNS-2339686, and the Cisco Research Award.", + "bbox": [ + 89, + 114, + 485, + 191 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 205, + 187, + 220 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] R. Achanta, A. Shaji, K. Smith, A. Lucchi, P. Fua, and Sabine Süssstrunk. Slic superpixels compared to state-of-the-art superpixel methods. IEEE Transactions on Pattern Analysis & Machine Intelligence, 34(11):2274-2282, 2012. 8", + "[2] Arman Behnam and Binghui Wang. Graph neural network causal explanation via neural causal models. 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In KDD, 2018. 8" + ], + "bbox": [ + 516, + 92, + 906, + 787 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5029", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Deterministic Certification of Graph Neural Networks against Graph Poisoning Attacks with Arbitrary Perturbations/0497332e-bd66-4105-bea8-f5b6eb06db3e_model.json b/2025/Deterministic Certification of Graph Neural Networks against Graph Poisoning Attacks with Arbitrary Perturbations/0497332e-bd66-4105-bea8-f5b6eb06db3e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3195aa804166e96c26d2a0fa839bdeec04101716 --- /dev/null +++ b/2025/Deterministic Certification of Graph Neural Networks against Graph Poisoning Attacks with Arbitrary Perturbations/0497332e-bd66-4105-bea8-f5b6eb06db3e_model.json @@ -0,0 +1,3058 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.188, + 0.131, + 0.817, + 0.177 + ], + "angle": 0, + "content": "Deterministic Certification of Graph Neural Networks against Graph Poisoning Attacks with Arbitrary Perturbations" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.203, + 0.71, + 0.222 + ], + "angle": 0, + "content": "Jiate Li\\(\\S\\) Meng Pang\\(\\dagger\\) Yun Dong\\(\\ddagger\\) and Binghui Wang\\(\\S^{*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.222, + 0.743, + 0.239 + ], + "angle": 0, + "content": "\\(^{\\S}\\)Department of Computer Science, Illinois Institute of Technology, Chicago, USA" + }, + { + "type": "text", + "bbox": [ + 0.234, + 0.24, + 0.764, + 0.256 + ], + "angle": 0, + "content": "†School of Mathematics and Computer Sciences, Nanchang University, Nanchang, China" + }, + { + "type": "text", + "bbox": [ + 0.228, + 0.257, + 0.771, + 0.274 + ], + "angle": 0, + "content": "\\(\\ddagger\\)Department of Humanities, Social Science, and Communication, MSOE, Milwaukee, USA" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.309, + 0.327, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.341, + 0.486, + 0.537 + ], + "angle": 0, + "content": "Graph neural networks (GNNs) are becoming the de facto method to learn on the graph data and have achieved the state-of-the-art on node and graph classification tasks. However, recent works show GNNs are vulnerable to training-time poisoning attacks – marginally perturbing edges, nodes, or/and node features of training graph(s) can largely degrade GNNs' testing performance. Most previous defenses against graph poisoning attacks are empirical and are soon broken by adaptive / stronger ones. A few provable defenses provide robustness guarantees, but have large gaps when applied in practice: 1) restrict the attacker on only one type of perturbation; 2) design for a particular GNN architecture or task; and 3) robustness guarantees are not \\(100\\%\\) accurate." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.538, + 0.487, + 0.691 + ], + "angle": 0, + "content": "In this work, we bridge all these gaps by developing PGNNCert, the first certified defense of GNNs against poisoning attacks under arbitrary (edge, node, and node feature) perturbations with deterministic robustness guarantees. Extensive evaluations on multiple node and graph classification datasets and GNNs demonstrate the effectiveness of PGNNCert to provably defend against arbitrary poisoning perturbations. PGNNCert is also shown to significantly outperform the state-of-the-art certified defenses against edge perturbation or node perturbation during GNN training." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.717, + 0.222, + 0.733 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.742, + 0.486, + 0.879 + ], + "angle": 0, + "content": "Graph Neural Network (GNN) [15, 21, 37, 44, 48, 56] is the leading approach for representation learning on graphs, showing state-of-the-art performance in various graph-related tasks like node classification and graph classification. In node classification, the goal is to predict labels for individual nodes, while in graph classification, the objective is to predict labels for entire graphs. GNNs have significantly advanced applications across fields such as chemistry [14], physics [36, 39], neuroscience [3], and social science [13]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.31, + 0.908, + 0.476 + ], + "angle": 0, + "content": "However, various works [6-8, 20, 40, 45, 51, 55, 60, 63] have shown that GNNs are vulnerable to training-time graph poisoning attacks — an attacker perturbs the graph structure during training such that the learnt poisoned GNN model will have low accuracy on predicting new test nodes/graphs. As a graph consists of three components: nodes, their features, and edges connecting the nodes, an attacker is allowed to perturb an individual component or their combinations. For instance, an attacker could inject a few nodes [20, 40], slightly modify the edges [8, 45, 55, 63] on the training graphs, and/or perturb features of certain nodes [63]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.477, + 0.909, + 0.657 + ], + "angle": 0, + "content": "Various empirical defenses [12, 42, 43, 59, 61, 62] have been proposed to mitigate the graph poisoning attack, but were soon broken by adaptive attacks [33]. Most existing certified defenses [16, 19, 22, 24, 47, 54] are against test-time evasion attacks, with a few exceptions [18, 22], leaving certified defenses against poisoning attacks largely unexplored1. However, existing provable defenses face several limitations when applied in practice: 1) all restrict the attacker's capability to only one type of perturbation (e.g., node injection or edge perturbation); 2) they are designed for a particular GNN architecture or GNN task [19]; and 3) their robustness guarantee is probabilistic (i.e., not \\(100\\%\\) accurate) [18, 22]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.658, + 0.911, + 0.855 + ], + "angle": 0, + "content": "We propose PGNNCert to address the above limitations. PGNNCert is the first certified defense for GNNs on the two most common node and graph classification tasks against arbitrary poisoning perturbations (i.e., arbitrarily manipulate the nodes, node features, and edges of training graph(s)) with deterministic robustness guarantees. Our defense is inspired by ensemble learning, and consists of three main steps: 1) Divide each training graph into multiple subgraphs and allocate subgraphs of training graph(s) into multiple groups via a hash function; 2) Train a set of node/graph classifiers for each group and build a majority-voting node/graph classifier on the subgraphs; 3) Derive the deterministic robustness guarantee against arbitrary poisoning perturbations." + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.863, + 0.908, + 0.901 + ], + "angle": 0, + "content": "1We note there exist some certified defense [17, 23, 35, 46] against poisoning attacks but not for the graph data. In addition [18, 22] show they achieve unsatisfactory performance when adapted to graph data." + }, + { + "type": "footer", + "bbox": [ + 0.109, + 0.887, + 0.34, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author (bwang70@iit.edu)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5020" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.363 + ], + "angle": 0, + "content": "Following [24], we adapt two graph division strategies—one is edge-centric and the other is node-centric—to realize our defense. The former strategy map edges, while the latter one map nodes from a given graph into multiple subgraphs. Theoretically, PGNNCert provably predicts the same label for a test node/graph after training on the poisoned training set with arbitrary perturbation whose perturbation size (i.e., the total number of manipulated nodes, nodes with feature perturbations, and edges) is bounded by a threshold, which we call the certified perturbation size. Empirically, we extensively evaluate PGNNCert on multiple graph datasets and multiple node and graph classifiers against arbitrary perturbations, and compared our methods with state-of-the-art certified defenses for node classification against node injection poisoning attack [22], and for graph classification against edge manipulation [17]. Our results show PGNNCert significantly outperforms [22] under node-centric graph division, and outperforms [54] under both graph division methods." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.364, + 0.476, + 0.377 + ], + "angle": 0, + "content": "Contributions: Our contributions are summarized below:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.379, + 0.483, + 0.409 + ], + "angle": 0, + "content": "- We develop the first certified defense to robustify GNNs against arbitrary poisoning attack on the training set." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.41, + 0.484, + 0.453 + ], + "angle": 0, + "content": "- We propose two strategies (edge-centric and node-centric) to realize our defense that leverages the unique message-passing mechanism in GNNs." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.454, + 0.483, + 0.484 + ], + "angle": 0, + "content": "- Our robustness guarantee is applicable to both node and graph classification tasks and accurate with probability 1." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.485, + 0.483, + 0.514 + ], + "angle": 0, + "content": "- Our defense treat existing certified defenses as special cases, as well as significantly outperforming them." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.379, + 0.484, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.527, + 0.42, + 0.544 + ], + "angle": 0, + "content": "2. Background and Problem Definition" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.551, + 0.364, + 0.567 + ], + "angle": 0, + "content": "2.1. Graph Neural Network (GNN)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.575, + 0.484, + 0.666 + ], + "angle": 0, + "content": "Let a graph be \\( G = \\{V, E, \\mathbf{X}\\} \\), which consists of the nodes \\( V \\), node features \\( \\mathbf{X} \\), and edges \\( E \\). We denote \\( u \\in V \\) as a node, \\( e = (u, v) \\in E \\) as an edge, and \\( \\mathbf{X}_u \\) as node \\( u \\)'s feature. Let \\( f_\\theta \\) be the node or graph classifier parameterized by \\( \\theta \\). \\( \\mathcal{V} \\) is the label set, \\( y_v \\) and \\( y_G \\) are the groundtruth label of a node \\( v \\) and a graph \\( G \\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.667, + 0.484, + 0.743 + ], + "angle": 0, + "content": "Node classification: \\( f_{\\theta} \\) takes a graph \\( G \\) as input and predicts each node \\( v \\in G \\) a label \\( \\tilde{y}_v \\in \\mathcal{V} \\), i.e., \\( \\tilde{y}_v = f_{\\theta}(G)_v \\). Given a training node set \\( V_{\\mathrm{tr}} \\subseteq V \\) with ground-truth labels \\( \\mathbf{y}_{\\mathrm{tr}} = \\{y_v, v \\in V_{\\mathrm{tr}}\\} \\), \\( f_{\\theta} \\) is learnt by minimizing a loss \\( \\mathcal{L} \\) between the node predictions \\( \\tilde{\\mathbf{y}}_{\\mathrm{tr}} \\) on \\( V_{\\mathrm{tr}} \\) and the ground-truth \\( \\mathbf{y}_{\\mathrm{tr}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.751, + 0.484, + 0.773 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathcal {L} \\left(\\mathbf {y} _ {\\mathrm {t r}}, \\tilde {\\mathbf {y}} _ {\\mathrm {t r}}; \\theta\\right), \\tilde {\\mathbf {y}} _ {\\mathrm {t r}} = \\left\\{f _ {\\theta} (G) _ {v}, v \\in V _ {\\mathrm {t r}} \\right\\} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.782, + 0.486, + 0.873 + ], + "angle": 0, + "content": "Graph classification: \\( f_{\\theta} \\) takes a graph \\( G \\) as input and predicts a label \\( \\tilde{y}_G \\in \\mathcal{V} \\) for the whole graph \\( G \\), i.e., \\( \\tilde{y}_G = f(G) \\). Given a set of training graphs \\( \\mathcal{G}_{\\mathrm{tr}} \\) with ground-truth labels \\( \\mathbf{y}_{\\mathrm{tr}} = \\{y_G, G \\in \\mathcal{G}_{\\mathrm{tr}}\\} \\). The graph classifier \\( f_{\\theta} \\) is learnt by minimizing a loss function \\( \\mathcal{L} \\) between the predictions on \\( \\mathcal{G}_{\\mathrm{tr}} \\) and the ground-truth \\( \\tilde{\\mathbf{y}}_{\\mathrm{tr}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.882, + 0.484, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathcal {L} \\left(\\mathbf {y} _ {\\mathrm {t r}}, \\tilde {\\mathbf {y}} _ {\\mathrm {t r}}; \\theta\\right), \\tilde {\\mathbf {y}} _ {\\mathrm {t r}} = \\left\\{f _ {\\theta} (G), G \\in \\mathcal {G} _ {\\mathrm {t r}} \\right\\} \\tag {2}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.757, + 0.107 + ], + "angle": 0, + "content": "2.2. Poisoning Attack on GNNs" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.907, + 0.22 + ], + "angle": 0, + "content": "In poisoning attacks against GNNs, an attacker can manipulate any training graph \\(G = \\{V,E,\\mathbf{X}\\} \\in \\mathcal{G}_{\\mathrm{tr}}\\) (For node classification, \\(\\mathcal{G}_{\\mathrm{tr}} = \\{G\\}\\)) into a perturbed one \\(G^{\\prime} = \\{V^{\\prime},E^{\\prime},\\mathbf{X}^{\\prime}\\}\\) during training, where \\(V^{\\prime},E^{\\prime},\\mathbf{X}^{\\prime}\\) are the perturbed version of \\(V,E\\) and \\(\\mathbf{X}\\), respectively. For simplicity, we denote the nodes, edges and features in training graph(s) as \\(\\mathcal{V},\\mathcal{E}\\), and \\(\\mathcal{X}\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.222, + 0.905, + 0.251 + ], + "angle": 0, + "content": "Edge manipulation: The attacker can 1) inject new edges \\(\\mathcal{E}_{+}\\), and 2) delete existing edges, denoted as \\(\\mathcal{E}_{-} \\subset \\mathcal{E}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.253, + 0.907, + 0.387 + ], + "angle": 0, + "content": "Node manipulation: The attacker perturbs \\(\\mathcal{G}_{\\mathrm{tr}}\\) by (1) injecting new nodes \\(\\nu_{+}\\), whose node feature denoted as \\(\\mathcal{X}_{\\nu_{+}}^{\\prime}\\) can be arbitrary, together with the arbitrarily injected new edges \\(\\mathcal{E}_{\\nu_{+}} \\subseteq \\{(u,v) \\notin \\mathcal{E}, \\forall u \\in \\mathcal{V}_{+} \\lor v \\in \\mathcal{V}_{+}\\}\\) induced by \\(\\nu_{+}\\); and (2) deleting existing nodes \\(\\nu_{-} \\subset \\nu\\). When \\(\\nu_{-}\\) are deleted, their features \\(\\mathcal{X}_{\\nu_{-}} \\subseteq \\mathcal{X}\\) and all connected edges \\(\\mathcal{E}_{\\nu_{-}} = \\{(u,v) \\in \\mathcal{E}, \\forall u \\in \\mathcal{V}_{-} \\lor v \\in \\mathcal{V}_{-}\\}\\) are also removed. We denote that for the node classification case, the injected and deleted nodes are not from \\(V_{\\mathrm{tr}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.389, + 0.907, + 0.45 + ], + "angle": 0, + "content": "Node feature manipulation: The attacker arbitrarily manipulates features \\(\\mathcal{X}_{\\mathcal{V}_r}\\) of a set of representative nodes \\(\\nu_{r}\\) to be \\(\\mathcal{X}_{\\mathcal{V}_r}^\\prime\\) . We also denote the edges connected with nodes \\(\\nu_{r}\\) as \\(\\mathcal{E}_{\\nu_r} = \\{(u,v)\\in \\mathcal{E}:\\forall u\\in \\mathcal{V}_r\\lor v\\in \\mathcal{V}_r\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.45, + 0.907, + 0.524 + ], + "angle": 0, + "content": "Arbitrary manipulation: The attacker can manipulate a training graphs in \\(\\mathcal{G}_{\\mathrm{tr}}\\) with an arbitrary combined perturbations on edges, nodes, and node features for each of them. The attacker can manipulate several training graphs at the same time with different combinations of attack." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.526, + 0.909, + 0.619 + ], + "angle": 0, + "content": "For description simplicity, we will use \\(\\{\\mathcal{E}_{+},\\mathcal{E}_{-}\\}\\) to indicate the edge manipulation with arbitrary injected edges \\(E_{+}\\) and deleted edges \\(\\mathcal{E}_{-}\\) on \\(\\mathcal{G}_{tr}\\). Similarly, we will use \\(\\{\\mathcal{V}_{+},\\mathcal{E}_{\\mathcal{V}_{+}},\\mathcal{X}_{\\mathcal{V}_{+}}^{\\prime},\\mathcal{V}_{-},\\mathcal{E}_{\\mathcal{V}_{-}}\\}\\) to indicate the node manipulation, and \\(\\{\\mathcal{V}_r,\\mathcal{E}_{\\mathcal{V}_r},\\mathcal{X}_{\\mathcal{V}_r}^{\\prime}\\}\\) the node feature manipulation. Any combination of the manipulations is inherently well-defined." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.629, + 0.698, + 0.643 + ], + "angle": 0, + "content": "2.3. Problem Statement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.653, + 0.909, + 0.774 + ], + "angle": 0, + "content": "Threat model: Given a node/graph classifier \\( f \\), a training graph set \\( \\mathcal{G}_{\\mathrm{tr}} \\), the adversary can arbitrarily manipulate a number of the edges, nodes, and node features in any graph of \\( \\mathcal{G}_{\\mathrm{tr}} \\) such that after training, \\( f \\) misclassifies target graphs in graph classification or target nodes in node classification. Since we focus on certified defenses, we consider the strongest attack where the adversary has white-box access to \\( \\mathcal{G}_{\\mathrm{tr}} \\) i.e., it knows all the edges, nodes, and node features in \\( \\mathcal{G}_{\\mathrm{tr}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.779, + 0.907, + 0.809 + ], + "angle": 0, + "content": "Defense goal: We aim to build provably robust GNNs against poisoning attacks that:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.811, + 0.8, + 0.825 + ], + "angle": 0, + "content": "- has a deterministic robustness guarantee;" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.826, + 0.89, + 0.839 + ], + "angle": 0, + "content": "- is suitable for both node and graph classification tasks;" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.84, + 0.907, + 0.871 + ], + "angle": 0, + "content": "- provably predicts the same label against the arbitrary poisoning perturbation within the certified perturbation size." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.811, + 0.907, + 0.871 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Our ultimate goal is to obtain the largest-possible certified perturbation size that satisfies all the above conditions." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5021" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.09, + 0.406, + 0.105 + ], + "angle": 0, + "content": "3. Our Certified Defense: PGNNCert" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.115, + 0.201, + 0.129 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.138, + 0.483, + 0.214 + ], + "angle": 0, + "content": "Our method is inspired by previous work [24, 54], which divides a test input into several sub-parts and assembles a voting GNN classifier on the sub-parts. We generalize this idea by designing the dividing strategy tailored to training set. Specifically, it consists of four steps below:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.214, + 0.484, + 0.349 + ], + "angle": 0, + "content": "In the first step, we divide the training graph set into multiple subgraph sets. For each training graph \\( G \\in \\mathcal{G}_{\\mathrm{tr}} \\) with ground-truth label \\( y_{G} \\in \\mathbf{y}_{\\mathrm{tr}} \\), we divide it into \\( S \\) subgraphs \\( G_{1}, G_{2}, \\ldots, G_{S} \\) via a hash function and ensure edges in different subgraphs are disjoint. This process is detailed in Section 3.2-3.3. By collecting these subgraphs, we build \\( S \\) sets of subgraphs \\( \\mathcal{G}_{[S]} = \\{\\mathcal{G}_1, \\mathcal{G}_2, \\ldots, \\mathcal{G}_S\\} \\). In each subgraph set \\( \\mathcal{G}_i \\), there exists an exact subgraph \\( G_i \\) generated from \\( G \\), and we label \\( G_i \\) the same label \\( y_{G} \\) as \\( G \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.35, + 0.484, + 0.395 + ], + "angle": 0, + "content": "In the second step, we train multiple classifiers with the respective subgraph sets. On each subgraph set \\(\\mathcal{G}_i\\), we initialize a classifier \\(f_i\\) with weights \\(\\theta_i\\) and train it below:" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.403, + 0.465, + 0.425 + ], + "angle": 0, + "content": "Node classifier: \\(\\min_{\\theta_i}\\mathcal{L}(\\mathbf{y}_{\\mathrm{tr}},\\tilde{\\mathbf{y}}_i;\\theta_i),\\tilde{\\mathbf{y}}_i = \\{f_i(G)_v,v\\in V_{\\mathrm{tr}}\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.428, + 0.471, + 0.449 + ], + "angle": 0, + "content": "Graph classifier: \\(\\min_{\\theta_i}\\mathcal{L}(\\mathbf{y}_{\\mathrm{tr}},\\tilde{\\mathbf{y}}_i;\\theta_i),\\tilde{\\mathbf{y}}_i = \\{f_i(G),G\\in \\mathcal{G}_{\\mathrm{tr}}\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.457, + 0.484, + 0.549 + ], + "angle": 0, + "content": "In the third step, we build the voting-based classifier based on the trained sub-classifiers. Given a test graph \\( G \\), we first divide it into \\( S \\) subgraphs \\( \\{G_1, \\ldots, G_S\\} \\) by the same subgraph division method. Then we apply a voting classifier \\( \\bar{f} \\), which assembles the predictions of the trained classifiers \\( f_{[S]} \\) on the subgraphs:" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.553, + 0.484, + 0.577 + ], + "angle": 0, + "content": "Node classifier: \\(\\mathbf{n}_{y_v} = \\sum_{i=1}^{S} \\mathbb{I}(f_i(G_i)_v = y_v), \\forall y_v \\in \\mathcal{V}\\) (3)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.579, + 0.484, + 0.603 + ], + "angle": 0, + "content": "Graph classifier: \\(\\mathbf{n}_{y_G} = \\sum_{i=1}^{S} \\mathbb{I}(f_i(G_i) = y_G), \\forall y_G \\in \\mathcal{V}\\) (4)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.611, + 0.483, + 0.642 + ], + "angle": 0, + "content": "We then define our voting node/graph classifier \\(\\bar{f}\\) as returning the class with the most vote:" + }, + { + "type": "text", + "bbox": [ + 0.143, + 0.65, + 0.484, + 0.674 + ], + "angle": 0, + "content": "Voting node classifier: \\(\\bar{f} (G)_v = \\operatorname *{arg\\max}_{y_v\\in \\mathcal{V}}\\mathbf{n}_{y_v}\\) (5)" + }, + { + "type": "text", + "bbox": [ + 0.143, + 0.676, + 0.484, + 0.701 + ], + "angle": 0, + "content": "Voting graph classifier: \\(\\bar{f} (G) = \\operatorname *{arg\\max}_{y_G\\in \\mathcal{Y}}\\mathbf{n}_{y_G}\\) (6)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.709, + 0.484, + 0.846 + ], + "angle": 0, + "content": "In the forth step, we derive the deterministic robustness guarantee for the test graph. We denote \\( y_{a} \\) and \\( y_{b} \\) as the class with the most vote \\( \\mathbf{n}_{y_a} \\) and the second-most vote \\( \\mathbf{n}_{y_b} \\), respectively. We pick the class with a smaller index if ties exist. Denote \\( \\mathcal{G}_{\\mathrm{tr}}^{\\prime} \\) as the perturbed train dataset of \\( \\mathcal{G}_{\\mathrm{tr}} \\), and \\( \\mathcal{G}_{[S]}^{\\prime} = \\{\\mathcal{G}_1^{\\prime},\\mathcal{G}_2^{\\prime},\\dots ,\\mathcal{G}_S^{\\prime}\\} \\) be the perturbed subgraph sets generated from \\( \\mathcal{G}_{\\mathrm{tr}}^{\\prime} \\) under the same graph division strategy. Then we have the below condition for certified robustness against arbitrary poisoning attacks on GNNs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Theorem 1 (Sufficient Condition for Certified Robustness). Let \\( y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}} \\) be defined above in node classification or graph classification, and let \\( P = \\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.091, + 0.906, + 0.198 + ], + "angle": 0, + "content": "\\(\\left\\lfloor \\mathbf{n}_{y_a} - \\mathbf{n}_{y_b} - \\mathbb{I}(y_a > y_b)\\right\\rfloor /2.\\) The voting classifier \\(\\bar{f}\\) trained on \\(\\mathcal{G}_{tr}\\) guarantees the same prediction on \\(G\\) for the target node \\(v\\) in node classification or the target graph \\(G\\) in graph classification with the poisoned voting classifier \\(\\bar{f}'\\), if the number of different sub-classifiers (i.e., different in weights) trained on \\(\\mathcal{G}_{[S]}\\) and \\(\\mathcal{G}_{[S]}'\\) under the arbitrary perturbation is bounded by \\(P\\). I.e.," + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.204, + 0.907, + 0.228 + ], + "angle": 0, + "content": "\\[\n\\forall \\mathcal {G} _ {t r} ^ {\\prime}: \\sum_ {i = 1} ^ {S} \\mathbb {I} \\left(\\theta_ {i} \\neq \\theta_ {i} ^ {\\prime}\\right) \\leq P \\Longrightarrow \\bar {f} (G) _ {v} = \\bar {f} ^ {\\prime} (G) _ {v} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.23, + 0.907, + 0.254 + ], + "angle": 0, + "content": "\\[\n\\forall \\mathcal {G} _ {t r} ^ {\\prime}: \\sum_ {i = 1} ^ {S} \\mathbb {I} \\left(\\theta_ {i} \\neq \\theta_ {i} ^ {\\prime}\\right) \\leq P \\Longrightarrow \\bar {f} (G) = \\bar {f} ^ {\\prime} (G) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.263, + 0.906, + 0.353 + ], + "angle": 0, + "content": "Proof is in Appendix A. The above theorem motivates us to design the graph division method such that: 1) the number of different sub-classifiers with trained on \\(\\mathcal{G}_{[S]}\\) and \\(\\mathcal{G}_{[S]}^{\\prime}\\) can be upper bounded (and the smaller the better). 2) the difference between \\(\\mathbf{n}_{y_a}\\) and \\(\\mathbf{n}_{y_b}\\) is as large as possible, ensuring larger certified perturbation size." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.354, + 0.907, + 0.4 + ], + "angle": 0, + "content": "Next, we introduce our two graph division methods. Figure 2 visualizes the divided subgraphs of the two methods without and with the adversarial manipulation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.41, + 0.776, + 0.425 + ], + "angle": 0, + "content": "3.2. Edge-Centric Graph Division" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.433, + 0.906, + 0.553 + ], + "angle": 0, + "content": "Our first graph division method is edge-centric. The idea is to divide edges in a graph into different subgraphs, such that each edge is deterministically mapped into only one subgraph. With this strategy, we can bound the number of altered classifiers trained on these subgraphs before and after the arbitrary perturbation (Theorem 2), which facilitates deriving the certified perturbation size (Theorem 3). All proofs are detailed in Appendix A." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.563, + 0.813, + 0.578 + ], + "angle": 0, + "content": "3.2.1 Generating edge-centric subgraphs" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.586, + 0.906, + 0.722 + ], + "angle": 0, + "content": "We follow [24, 54] to use a hash function \\( h \\) (e.g., MD5) to generate the subgraphs for every train graph \\( G \\in \\mathcal{G}_{\\mathrm{tr}} \\). A hash function takes a bit string as input and outputs an integer (e.g., within a range \\([0, 2^{128} - 1]\\)). We use the string of edge or node index as the input to the hash function. For instance, for a node \\( u \\), its string is denoted as \\( \\operatorname{str}(u) \\), while for an edge \\( e = (u, v) \\), its string is \\( \\operatorname{str}(u) + \\operatorname{str}(v) \\), where \"+\" means string concatenation, and str turns the node index into a string and adds \"0\" prefix to align it into a fixed length." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.723, + 0.906, + 0.753 + ], + "angle": 0, + "content": "Assuming \\(S\\) subgraphs in total, the subgraph index \\(i_e\\) of every edge \\(e = (u,v)\\) is defined as2" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.763, + 0.907, + 0.779 + ], + "angle": 0, + "content": "\\[\ni _ {e} = h \\left[ \\operatorname {s t r} (u) + \\operatorname {s t r} (v) \\right] \\bmod S + 1, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.79, + 0.906, + 0.866 + ], + "angle": 0, + "content": "where mod is the module function. Denoting \\(\\mathcal{E}^i\\) as the set of edges whose subgraph index is \\(i\\), i.e., \\(\\mathcal{E}^i = \\{\\forall e \\in \\mathcal{E} : i_e = i\\}\\), \\(S\\) subgraphs for \\(G\\) can be built as \\(\\{G_i = (\\mathcal{V}, \\mathcal{E}^i, \\mathbf{X}) : i = 1, 2, \\dots, S\\}\\), where edges in different subgraphs are disjoint, i.e., \\(\\mathcal{E}^i \\cap \\mathcal{E}^j = \\emptyset, \\forall i, j \\in \\{1, \\dots, S\\}, i \\neq j\\). Here, we" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.906, + 0.901 + ], + "angle": 0, + "content": "2In the undirected graph, we put the node with a smaller index (say \\(u\\)) first and let \\(h[\\mathrm{str}(v) + \\mathrm{str}(u)] = h[\\mathrm{str}(u) + \\mathrm{str}(v)]\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5022" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.072, + 0.885, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.263, + 0.818, + 0.277 + ], + "angle": 0, + "content": "Figure 1. Overview of our PGNNCert (use node classification for illustration), which consists of four steps." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.286, + 0.484, + 0.391 + ], + "angle": 0, + "content": "mention that we need to further postprocess the subgraphs for graph classification, in order to derive the robustness guarantee. Particularly, in each subgraph \\( G_{i} \\), we remove all isolated nodes who have no connected edges. This is because although they have no influence on other nodes' representation, their information would still be passed to the global graph embedding aggregation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.392, + 0.484, + 0.455 + ], + "angle": 0, + "content": "After dividing all training graphs in \\(\\mathcal{G}_{\\mathrm{tr}}\\), we combine all generated subgraphs with the same index as a separate subgraph training set: \\(\\mathcal{G}_i = \\{G_i, \\forall G \\in \\mathcal{G}_{\\mathrm{tr}}\\}, \\forall i \\in [S]\\). We denote the \\(S\\) training sets as \\(\\mathcal{G}_{[S]} = \\{\\mathcal{G}_1, \\dots, \\mathcal{G}_S\\}\\)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.463, + 0.482, + 0.478 + ], + "angle": 0, + "content": "3.2.2 Bounding the number of different sub-classifiers" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.486, + 0.484, + 0.564 + ], + "angle": 0, + "content": "For a perturbed training set \\(\\mathcal{G}_{\\mathrm{tr}}^{\\prime}\\), we use the same graph division strategy to generate a set of \\(S\\) subgraphs sets \\(\\mathcal{G}_{[S]}^{\\prime} = \\{\\mathcal{G}_1^{\\prime},\\mathcal{G}_2^{\\prime},\\dots ,\\mathcal{G}_T^{\\prime}\\}\\). Then, we can upper bound the number of different classifiers trained on \\(\\mathcal{G}_{[S]}\\) and \\(\\mathcal{G}_{[S]}^{\\prime}\\) against any individual perturbation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.565, + 0.485, + 0.749 + ], + "angle": 0, + "content": "Theorem 2 (Bounded Number of Edge-Centric Subgraphs with Altered Predictions under Arbitrary Perturbation). Given any training graph set \\(\\mathcal{G}_{tr}\\), and \\(S\\) edge-centric subgraph sets \\(\\mathcal{G}_{[S]}\\) for \\(\\mathcal{G}_{tr}\\). A perturbed training set \\(\\mathcal{G}_{train}^{\\prime}\\) of \\(\\mathcal{G}_{train}\\) is with arbitrary edge manipulation \\(\\{\\mathcal{E}_+, \\mathcal{E}_-\\}\\), node manipulation \\(\\{\\mathcal{V}_+,\\mathcal{E}_{\\mathcal{V}_+},\\mathcal{V}_-, \\mathcal{E}_{\\mathcal{V}_-}\\}\\), and node feature manipulation \\(\\{\\mathbf{X}_{\\mathcal{V}_r},\\mathcal{V}_r,\\mathcal{E}_{\\mathcal{V}_r}\\}\\) on arbitrary graphs in \\(\\mathcal{G}_{tr}\\). Then at most \\(p = |\\mathcal{E}_+| + |\\mathcal{E}_-| + |\\mathcal{E}_{\\mathcal{V}_+}| + |\\mathcal{E}_{\\mathcal{V}_-}| + |\\mathcal{E}_{\\mathcal{V}_r}|\\) node/graph sub-classifiers in \\(f_{[S]}\\) are different in weights between training on the subgraph sets \\(\\mathcal{G}_{[S]}\\) and on the perturbed subgraph sets \\(\\mathcal{G}_{[S]}^{\\prime}\\). In other words, \\(\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq p\\) for both node classification case and graph classification case." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.756, + 0.383, + 0.771 + ], + "angle": 0, + "content": "3.2.3 Deriving the robustness guarantee" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.485, + 0.825 + ], + "angle": 0, + "content": "Based on Theorems 1 and 2, we can derive the certified perturbation size as the maximal perturbation such that Equation 7 or Equation 8 is satisfied. Formally," + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Theorem 3 (Certified Robustness Guarantee with Edge-Centric Subgraphs against Arbitrary Perturbation). Let \\( f, y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}} \\) be defined above for edge-centric subgraphs, and \\( p \\) be the perturbation size induced by an arbitrary perturbed training set \\( \\mathcal{G}_{tr}' \\) on \\( \\mathcal{G}_{tr} \\). After training on \\( \\mathcal{G}_{tr}' \\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.285, + 0.906, + 0.348 + ], + "angle": 0, + "content": "and \\(\\mathcal{G}_{tr}^{\\prime}\\), the voting classifier \\(\\bar{f}\\) and poisoned classifier \\(\\bar{f}'\\) guarantee the same prediction for the target node \\(v\\) in node classification (i.e., \\(\\bar{f}(G')_v = \\bar{f}(G)_v\\)) or target graph \\(G\\) in graph classification (i.e., \\(\\bar{f}(G') = \\bar{f}(G)\\)), when \\(p\\) satisfies." + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.359, + 0.907, + 0.377 + ], + "angle": 0, + "content": "\\[\np \\leq P = \\left\\lfloor \\mathbf {n} _ {y _ {a}} - \\mathbf {n} _ {y _ {b}} - \\mathbb {I} \\left(y _ {a} > y _ {b}\\right) \\right\\rfloor / 2. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.388, + 0.881, + 0.403 + ], + "angle": 0, + "content": "Or to say, the maximum certified perturbation size is \\( P \\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.413, + 0.776, + 0.429 + ], + "angle": 0, + "content": "3.3. Node-Centric Graph Division" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.436, + 0.907, + 0.694 + ], + "angle": 0, + "content": "We observe the robustness guarantee under edge-centric graph division is largely dominated by the edges (i.e., \\(\\mathcal{E}_{\\mathcal{V}_+}, \\mathcal{E}_{\\mathcal{V}_-}\\)) induced by the manipulated nodes \\(\\mathcal{V}_+\\), \\(\\mathcal{V}_-\\), and edges \\(\\mathcal{E}_{\\mathcal{V}_r}\\) by the perturbed node features \\(\\mathbf{X}_{\\mathcal{V}_r}'\\). This guarantee could be weak against node or node feature manipulation, as the number of edges (i.e., \\(|\\mathcal{E}_{\\mathcal{V}_+}|, |\\mathcal{E}_{\\mathcal{V}_-}|, |\\mathcal{E}_{\\mathcal{V}_r}|\\)) could be much larger, compared with the number of the nodes (i.e., \\(|\\mathcal{V}_+|, |\\mathcal{V}_-|, |\\mathcal{V}_r|\\)). For instance, an injected node could link with many edges to a given graph in practice, and when the number exceeds \\(P\\) in Equation 10, the certified robustness guarantee is ineffective. This flaw inspires us to generate subgraphs, where we expect at most one subgraph is affected under every node or node feature manipulation on a training graph (this means all edges of a manipulated node should be in a same subgraph), implying only a training subgraph set is affected. Following [24], we apply a tailored node-centric graph division strategy to achieve our goal." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.706, + 0.875, + 0.721 + ], + "angle": 0, + "content": "3.3.1 Generating node-centric directed subgraphs" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.73, + 0.906, + 0.836 + ], + "angle": 0, + "content": "We use a hash function \\( h \\) to generate directed subgraphs for a given train graph \\( G = (\\mathcal{V},\\mathcal{E},\\mathbf{X})\\in \\mathcal{G}_{\\mathrm{tr}} \\). Our node-centric graph division strategy as follows: (1) we treat every undirected edge \\( e = (u,v)\\in G \\) as two directed edges for \\( u^3 \\): the outgoing edge \\( u\\to v \\) and incoming edge \\( v\\rightarrow u \\); (2) for every node \\( u \\), we compute the subgraph index of its every outgoing edge \\( u\\to v \\):" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.848, + 0.907, + 0.865 + ], + "angle": 0, + "content": "\\[\ni _ {u \\rightarrow v} = h [ \\operatorname {s t r} (u) ] \\bmod S + 1. \\tag {11}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.907, + 0.901 + ], + "angle": 0, + "content": "\\( {}^{3} \\) GNNs inherently handles directed graphs with directed message passing - each node only uses its incoming neighbors' message for update." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5023" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.135, + 0.087, + 0.87, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.406, + 0.716, + 0.418 + ], + "angle": 0, + "content": "(b) Node-Centric Graph Division against edge injection and node injection attacks" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.423, + 0.907, + 0.465 + ], + "angle": 0, + "content": "Figure 2. Illustration of our edge-centric and node-centric graph division strategies for node classification. We use edge injection and node injection poisoning attacks to show the bounded number of altered predictions on the generated subgraphs after the attack. Figures 8-9 in Appendix also show other attacks and on graph classification." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.474, + 0.484, + 0.489 + ], + "angle": 0, + "content": "Note outgoing edges of \\(u\\) are mapped in the same subgraph." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.489, + 0.484, + 0.6 + ], + "angle": 0, + "content": "We use \\(\\vec{\\mathcal{E}}_i\\) to denote the set of directed edges whose subgraph index is \\(i\\), i.e., \\(\\vec{\\mathcal{E}}_i = \\{\\forall u \\to v \\in \\mathcal{E} : i_{u \\to v} = i\\}\\). Then, we can construct \\(S\\) directed subgraphs for \\(G\\) as \\(\\vec{G}_i = (\\mathcal{V}, \\vec{\\mathcal{E}}_i, \\mathbf{X}), \\forall i \\in [1, S]\\). After generating subgraphs for all training graphs, we combine all subgraphs with the same index as a separate subgraph set: \\(\\vec{\\mathcal{G}}_i = \\{\\vec{G}_i, \\forall G \\in \\mathcal{G}_{\\mathrm{tr}}\\}, \\forall i \\in [S]\\). We denote the \\(S\\) training sets as \\(\\vec{\\mathcal{G}}_{[S]} = \\{\\vec{\\mathcal{G}}_1, \\dots, \\vec{\\mathcal{G}}_S\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.6, + 0.484, + 0.751 + ], + "angle": 0, + "content": "Here, we mention that we need to further postprocess the subgraphs for graph classification, in order to derive the robustness guarantee. Particularly, in each subgraph \\(\\vec{G}_i\\), we remove all other nodes whose subgraph index is not \\(i\\). This is because although they have no influence on other nodes' representation, their information would still be passed to the global graph embedding aggregation. To make up the loss of connectivity between nodes and simulate the aggregation, we add an extra node with a zero feature, and add an outgoing edge from every node with index \\(i\\) to it." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.765, + 0.482, + 0.78 + ], + "angle": 0, + "content": "3.3.2 Bounding the number of different sub-classifiers" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.79, + 0.484, + 0.868 + ], + "angle": 0, + "content": "For a perturbed training set \\( G_{\\mathrm{tr}}^{\\prime} \\), we use the same graph division strategy to generate a set of \\( S \\) directed subgraph sets \\( \\vec{\\mathcal{G}}_{[S]}^{\\prime} = \\{\\vec{\\mathcal{G}}_1^{\\prime},\\vec{\\mathcal{G}}_2^{\\prime},\\dots ,\\vec{\\mathcal{G}}_T^{\\prime}\\} \\). We first show the theoretical result on bounding the number of different trained classifiers on \\( \\vec{\\mathcal{G}}_{[S]} \\) and \\( \\vec{\\mathcal{G}}_{[S]}^{\\prime} \\) against any individual perturbation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Theorem 4 (Bounded Number of Node-Centric Subgraphs with Altered Predictions under Arbitrary Perturbation). Let" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.473, + 0.909, + 0.645 + ], + "angle": 0, + "content": "\\(\\mathcal{G}_{tr}, v, G, \\mathcal{E}_+, \\mathcal{E}_-, \\mathcal{V}_+, \\mathcal{V}_-, \\mathcal{V}_r\\) be defined in Theorem 2, and \\(\\vec{\\mathcal{G}}_{[S]}, \\vec{\\mathcal{G}}_{[S]}'\\) contain directed subgraph sets under the node-centric graph division. Then, at most \\(\\bar{p} = 2|\\mathcal{E}_+| + 2|\\mathcal{E}_-| + |\\mathcal{V}_+| + |\\mathcal{V}_-| + |\\mathcal{V}_r|\\) trained node classifiers in \\(f_{[S]}\\) are different in weights after training on \\(\\vec{\\mathcal{G}}_{[S]}\\) and on \\(\\vec{\\mathcal{G}}_{[S]}'\\). In other words, \\(\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq \\bar{p}\\) for any target node \\(v \\in G\\) in node classification. Meanwhile, at most \\(\\bar{p} = |\\mathcal{E}_+| + |\\mathcal{E}_-| + |\\mathcal{V}_+| + |\\mathcal{V}_-| + |\\mathcal{V}_r|\\) trained graph classifiers in \\(f_{[S]}\\) are different in weights after training on \\(\\vec{\\mathcal{G}}_{[S]}\\) and on \\(\\vec{\\mathcal{G}}_{[S]}'\\). In other words, \\(\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq \\bar{p}\\) in graph classification." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.654, + 0.807, + 0.669 + ], + "angle": 0, + "content": "3.3.3 Deriving the robustness guarantee" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.677, + 0.907, + 0.707 + ], + "angle": 0, + "content": "Based on Theorem 1 and Theorem 4, we can derive the certified perturbation size formally stated below" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.708, + 0.909, + 0.846 + ], + "angle": 0, + "content": "Theorem 5 (Certified Robustness Guarantee with Node-Centric Subgraphs against Arbitrary Perturbation). Let \\( f, y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}}^{4} \\) be defined above for node-centric subgraphs, and \\( \\bar{p} \\) be the perturbation size induced by an arbitrary perturbed graph \\( G' \\) on \\( G \\). With a probability \\( 100\\% \\), the voting classifier \\( \\bar{f} \\) guarantees the same prediction on both \\( G' \\) and \\( G \\) for the target node \\( v \\) in node classification (i.e., \\( \\bar{f}(G')_{v} = \\bar{f}(G)_{v} \\)) or the target graph \\( G \\) in graph classification (i.e., \\( \\bar{f}(G') = \\bar{f}(G) \\)), if" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.855, + 0.907, + 0.873 + ], + "angle": 0, + "content": "\\[\n\\bar {p} \\leq P = \\left\\lfloor \\mathbf {n} _ {y _ {a}} - \\mathbf {n} _ {y _ {b}} - \\mathbb {I} \\left(y _ {a} > y _ {b}\\right) \\right\\rfloor / 2. \\tag {12}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.876, + 0.907, + 0.901 + ], + "angle": 0, + "content": "4Note that \\(\\mathbf{n}_{y_a},\\mathbf{n}_{y_b}\\) have different values with those in edge-centric graph division. Here we use the same notation for description brevity." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5024" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.224, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.115, + 0.292, + 0.132 + ], + "angle": 0, + "content": "4.1. Experiments Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.138, + 0.486, + 0.26 + ], + "angle": 0, + "content": "Datasets: We use four node classification datasets (Cora-ML [31], CiteSeer [38], PubMed [38], Amazon-C [57]) and four graph classification datasets (AIDS [34], MUTAG [9], PROTEINS [5], and DD [10]) for evaluation. In each dataset, we take \\(30\\%\\) nodes (for node classification) or \\(50\\%\\) graphs (for graph classification) as the training set, \\(10\\%\\) and \\(20\\%\\) as the validation set and \\(30\\%\\) nodes/graph as the test set. Table 5 in Appendix shows the basic statistics of them." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.264, + 0.485, + 0.355 + ], + "angle": 0, + "content": "GNN classifiers and PGNNCert training: We adopt three well-known GNNs as the base node/graph classifiers: GCN [21], GSAGE [15] and GAT [44]. We denote the two versions of PGNNCert under edge-centric and node-centric graph division as PGNNCert-E and PGNNCert-N, respectively. By default, we use GCN as the node/graph classifier." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.359, + 0.484, + 0.48 + ], + "angle": 0, + "content": "Evaluation metric: Following existing works [22, 47, 54], we use the certified node/graph accuracy at perturbation size as the evaluation metric. Given a perturbation size \\( p \\) and test nodes/graphs, certified node/graph accuracy at \\( p \\) is the fraction of test nodes/graphs that are accurately classified by the voting node/graph classifier and its certified perturbation size is no smaller than \\( p \\). Note that the standard node/graph accuracy is achieved when over \\( p = 0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.485, + 0.485, + 0.56 + ], + "angle": 0, + "content": "Parameter setting: PGNNCert has two hyperparameters: the hash function \\( h \\) and the number of subgraphs \\( S \\). By default, we use MD5 as the hash function and set \\( S = 50,60 \\) respectively for node and graph classification, considering their different graph sizes. We also study the impact of them." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.565, + 0.484, + 0.701 + ], + "angle": 0, + "content": "Compared baselines: As PGNNCert encompasses existing defenses as special cases, we can compare PGNNCert with them against less types of perturbation. Here, we choose the sparse-smoothing RS [4], Bagging [17] and Bi-RS [22] as compared baselines in face of node injection poisoning attack on node classification task. For Bi-RS, We adopt the \\( p_e = 0.2 \\), \\( p_n = 0.9 \\), \\( N = 1000 \\) setting as described, and test both include and exclude methods. We also use Bagging for comparison on graph classification." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.71, + 0.383, + 0.726 + ], + "angle": 0, + "content": "4.2. Experiment Results on PGNNCert" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.732, + 0.485, + 0.793 + ], + "angle": 0, + "content": "Main results: Figures 3-4 show the certified node accuracy and Figures 5-6 show the certified graph accuracy at perturbation size \\( p \\) w.r.t. \\( S \\) under the two graph division strategies, respectively. We have the following observations." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.796, + 0.484, + 0.902 + ], + "angle": 0, + "content": "- Both PGNNCert-E and PGNNCert-N can tolerate the perturbation size up to 25 and 30, on the node and graph classification datasets. This means PGNNCert-E can defend against a total of 25 (30) arbitrary edges, while PGNNCert-N against a total of 25 (30) arbitrary edges and nodes caused by the arbitrary perturbation, on the node (graph) classification datasets, respectively. Note" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.09, + 0.907, + 0.118 + ], + "angle": 0, + "content": "Table 1. Node/graph accuracy of normally trained GNN and of PGNNCert with GNN trained on the subgraphs." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.122, + 0.91, + 0.234 + ], + "angle": 0, + "content": "
    DatasetGCNPGNNCertGSAGEPGNNCertGATPGNNCert
    -E-N-E-N-E-N
    Cora-ML0.730.680.680.670.650.680.740.690.69
    Citeseer0.660.670.670.690.680.680.700.670.67
    Pubmed0.860.830.850.840.840.850.850.850.84
    Amazon-C0.810.810.810.820.780.800.830.780.80
    AIDS0.990.880.960.970.940.950.960.930.96
    MUTAG0.710.640.640.700.630.640.710.650.65
    Proteins0.820.810.780.830.800.810.820.780.77
    DD0.800.790.770.810.780.760.810.770.79
    " + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.247, + 0.907, + 0.292 + ], + "angle": 0, + "content": "that node classification datasets have several orders of more nodes/edges than graph classification datasets, hence PGNNCert can tolerate more perturbations on them." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.293, + 0.905, + 0.337 + ], + "angle": 0, + "content": "- \\( S \\) acts as the robustness-accuracy tradeoff. That is, a larger (smaller) \\( S \\) yields a higher (lower) certified perturbation size, but a smaller (higher) normal accuracy (\\( p = 0 \\))." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.338, + 0.907, + 0.397 + ], + "angle": 0, + "content": "- In PGNNCert-N, the guaranteed perturbed nodes can have infinite edges. This implies that PGNNCert-N has better robustness than PGNNCert-E against the perturbed edges by node/node feature manipulation." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.293, + 0.907, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.4, + 0.908, + 0.461 + ], + "angle": 0, + "content": "Impact of base GNN classifiers: Figures 10-11 and Figures 12-13 in Appendix show the certified accuracy using GSAGE and GAT as the base classifier, respectively. We have similar observations as those results with GCN." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.906, + 0.557 + ], + "angle": 0, + "content": "Impact of hash function: Figures 14-17 show the certified node/edge accuracy of PGNNCert-E and PGNNCert-N with different hash functions. We observe that our certified accuracy and certified perturbation size are almost the same in all cases. This reveals our PGNNCert is insensitive to the hash function, and [54] draws a similar conclusion." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.561, + 0.906, + 0.698 + ], + "angle": 0, + "content": "Impact of subgraphs on normal accuracy: We test the normal accuracy of (not) using subgraphs to train the GNN classifier. Table 1 shows the test node/graph accuracy of normally trained GNN without sburgraphs and PGNNCert with GNN trained on the subgraphs. We observe that the accuracy of PGNNCert is \\(5\\%\\) smaller than that of normally trained GNN in almost all cases, and in some cases even larger. This implies the augmented subgraphs for training marginally affects the normal test accuracy." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.707, + 0.871, + 0.723 + ], + "angle": 0, + "content": "4.3. Comparison Results with SOTA Baselines" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.731, + 0.908, + 0.777 + ], + "angle": 0, + "content": "In this section, we compare PGNNCert with SOTA defenses (Bi-RS [22], RS [4], Bagging [17]) against node injection poisoning attacks and graph structure poisoning attacks [17]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Results for node classification against node injection poisoning attacks: We follow Bi-RS [22] by setting the injected nodes' degrees as \\(\\tau = 5\\) and show the certified node accuracy with varying number of injected nodes. Figure 7 shows the comparison results. We can see PGNNCert-E has better certified accuracy than RS, Bagging and Bi-RS-Include, but it is worse than Bi-RS-Exclude. This aligns with our assumption on its weakness against node-relevant attack. By" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5025" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.099, + 0.28, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.16, + 0.198, + 0.231, + 0.21 + ], + "angle": 0, + "content": "(a) Cora-ML" + }, + { + "type": "image", + "bbox": [ + 0.301, + 0.099, + 0.481, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.366, + 0.198, + 0.43, + 0.21 + ], + "angle": 0, + "content": "(b)CiteSeer" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.099, + 0.684, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.569, + 0.198, + 0.632, + 0.21 + ], + "angle": 0, + "content": "(c) Pubmed" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.099, + 0.885, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.764, + 0.198, + 0.842, + 0.21 + ], + "angle": 0, + "content": "(d) Amazon-C" + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.222, + 0.764, + 0.236 + ], + "angle": 0, + "content": "Figure 3. Certified node accuracy of our PGNNCert-E w.r.t. the number of subgraphs \\( S \\)." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.248, + 0.28, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.161, + 0.348, + 0.23, + 0.36 + ], + "angle": 0, + "content": "(a) Cora-ML" + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.249, + 0.481, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.366, + 0.348, + 0.43, + 0.36 + ], + "angle": 0, + "content": "(b) CiteSeer" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.249, + 0.684, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.569, + 0.348, + 0.632, + 0.36 + ], + "angle": 0, + "content": "(c) Pubmed" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.249, + 0.886, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.764, + 0.348, + 0.842, + 0.36 + ], + "angle": 0, + "content": "(d) Amazon-C" + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.373, + 0.764, + 0.387 + ], + "angle": 0, + "content": "Figure 4. Certified node accuracy of our PGNNCert-N w.r.t. the number of subgraphs \\( S \\)." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.399, + 0.28, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.499, + 0.221, + 0.511 + ], + "angle": 0, + "content": "(a) AIDS" + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.399, + 0.481, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.365, + 0.499, + 0.431, + 0.511 + ], + "angle": 0, + "content": "(b) MUTAG" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.399, + 0.684, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.56, + 0.499, + 0.641, + 0.511 + ], + "angle": 0, + "content": "(c) PROTEINS" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.399, + 0.887, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.499, + 0.822, + 0.511 + ], + "angle": 0, + "content": "(d) DD" + }, + { + "type": "image_caption", + "bbox": [ + 0.229, + 0.524, + 0.767, + 0.538 + ], + "angle": 0, + "content": "Figure 5. Certified graph accuracy of our PGNNCert-E w.r.t. the number of subgraphs \\( S \\)." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.551, + 0.28, + 0.646 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.65, + 0.221, + 0.661 + ], + "angle": 0, + "content": "(a) AIDS" + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.551, + 0.481, + 0.646 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.365, + 0.65, + 0.431, + 0.661 + ], + "angle": 0, + "content": "(b) MUTAG" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.551, + 0.684, + 0.646 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.56, + 0.65, + 0.641, + 0.661 + ], + "angle": 0, + "content": "(c) PROTEINS" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.551, + 0.887, + 0.646 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.65, + 0.822, + 0.661 + ], + "angle": 0, + "content": "(d) DD" + }, + { + "type": "image_caption", + "bbox": [ + 0.229, + 0.674, + 0.767, + 0.689 + ], + "angle": 0, + "content": "Figure 6. Certified graph accuracy of our PGNNCert-N w.r.t. the number of subgraphs \\( S \\)." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.701, + 0.28, + 0.797 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.161, + 0.801, + 0.23, + 0.812 + ], + "angle": 0, + "content": "(a) Cora-ML" + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.701, + 0.481, + 0.796 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.366, + 0.801, + 0.43, + 0.812 + ], + "angle": 0, + "content": "(b)CiteSeer" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.701, + 0.684, + 0.797 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.569, + 0.801, + 0.632, + 0.812 + ], + "angle": 0, + "content": "(c) Pubmed" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.702, + 0.886, + 0.797 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.764, + 0.801, + 0.842, + 0.812 + ], + "angle": 0, + "content": "(d) Amazon-C" + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.825, + 0.805, + 0.84 + ], + "angle": 0, + "content": "Figure 7. Certified node accuracy of our PGNNCert and SOTA defenses against node injection attacks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.859, + 0.484, + 0.889 + ], + "angle": 0, + "content": "contrast, PGNNCert-N outperforms all compared baselines. We highlight that each bounded node in PGNNCert-N can" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.859, + 0.906, + 0.889 + ], + "angle": 0, + "content": "inject as many edges as possible, meaning the total number of bounded edges in PGNNCert-N could be infinite." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5026" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.483, + 0.118 + ], + "angle": 0, + "content": "Table 2. Certified graph accuracy of our PGNNCert and Bagging against edge perturbations." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.122, + 0.481, + 0.212 + ], + "angle": 0, + "content": "
    DatasetsMethods#Edges=051015
    ProteinsBagging0.7560.2050.0000.00
    PGNNCert-E0.7440.5180.2600.00
    PGNNCert-N0.7780.4740.1020.00
    DDBagging0.7850.3110.0000.00
    PGNNCert-E0.7920.5780.3300.063
    PGNNCert-N0.7710.3440.0060.000
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.151, + 0.217, + 0.422, + 0.23 + ], + "angle": 0, + "content": "Table 3. Results of PGNNCert on CIFAR10." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.234, + 0.472, + 0.276 + ], + "angle": 0, + "content": "
    DatasetsMethodsp=0135
    CIFAR10PGNNCert-E0.5960.5560.4820.107
    PGNNCert-N0.6360.5930.4980.113
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.095, + 0.282, + 0.478, + 0.295 + ], + "angle": 0, + "content": "Table 4. Defense results against the optimization-based Mettack." + }, + { + "type": "table", + "bbox": [ + 0.103, + 0.3, + 0.472, + 0.328 + ], + "angle": 0, + "content": "
    DatasetNettackp=0203040
    Cora-MLPGNNCert-N0.6750.6750.6680.661
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.34, + 0.485, + 0.415 + ], + "angle": 0, + "content": "Results for graph classification against graph poisoning attacks: Table 2 shows the certified graph accuracies of PGNNCert and Bagging against edge perturbations on graph classification tasks. PGNNCert outperforms Bagging, especially when the perturbation size is larger." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.429, + 0.205, + 0.443 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.454, + 0.484, + 0.59 + ], + "angle": 0, + "content": "Evaluation on CV datasets. We also test a benchmark superpixel graph CIFAR10 in computer vision [11] for graph classification, to show the generality of our defense. CIFAR10 is an image classification dataset, which is converted into graphs using the SLIC superpixels [1]. Each node has the superpixel coordinates as the feature and each superpixel graph has a label. Results in the default setting are shown in Table 3, where we see PGNNCert can obtain about \\(50\\%\\) certified accuracy when 3 arbitrary edges are perturbed." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.595, + 0.484, + 0.761 + ], + "angle": 0, + "content": "PGNNCert against optimization-based attacks. We first emphasize that PGNNCert is provably robust against all (known and unknown) attacks, when their perturbation budget is within the derived bound (in Eqn 10 or Eqn 12), regardless of the attack knowledge of PGNNCert. Here, we test PGNNCert-N against Metattack [63] when its perturbation size \\( m \\) is larger than the derived certified perturbation size \\( P = 25 \\) (with certified accuracy 0.588) on Cora-ML with \\( S = 60 \\). Results are shown in Table 4. We see PGNNCert-N can achieve 0.661 accuracy of defending against Metattack even when it perturbs 40 edges and nodes in total." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Limitations. Despite the effectiveness of PGNNCert, its inefficiency remains a main limitation for large GNNs. PGNNCert trains \\( S \\) classifiers on \\( S \\) subgraphs and uses \\( S \\) subgraphs for certification. It may incur a training/certification complexity that is \\( S \\) times of standard GNN training/testing. This overhead could be significant when PGNNCert is applied to large GNNs. On the other hand, we note that the \\( S \\) classifiers can be trained in parallel once obtaining the \\( S \\) subgraphs after graph division." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.655, + 0.106 + ], + "angle": 0, + "content": "6. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.908, + 0.373 + ], + "angle": 0, + "content": "Adversarial attacks on GNNs: Existing attacks to GNNs can be classified as graph evasion attacks [8, 25, 26, 29, 30, 32, 50-53, 55, 64] and poisoning attacks [8, 28, 40, 41, 45, 55, 60, 63, 63]. For instance, [8] leveraged reinforcement learning techniques to design evasion attacks to both graph classification and node classification via modifying the graph structure. Most attacks require the attacker fully or partially knows the GNN model, while [32, 50] relaxing this to only have black-box access, i.e., only query the GNN model API. For example, [50] formulates the black-box attack to GNNs as an online optimization problem with bandit feedback and provably obtains a sublinear query number. Furthermore, [25] generalizes the black-box evasion attack on explainable GNNs. In the realm of graph poisoning attacks, [55] proposed a MinMax attack to GNNs based on gradient-based optimization, while [63] introduced Metattack that perturbs the entire graph using meta learning." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.377, + 0.909, + 0.437 + ], + "angle": 0, + "content": "Certified robustness against graph poisoning graphs: Most existing certified defenses for GNNs are against test-time evasion attacks [16, 19, 22, 24, 27, 47, 54, 60], with a few ones [22] against training-time poisoning attacks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.438, + 0.909, + 0.634 + ], + "angle": 0, + "content": "There exist two main approaches providing certified robustness against poisoning data: 1) Randomized-smoothing based methods [22, 35, 46] regard the training-prediction process as an end-to-end function, and treat poisoning attack as a special case of evasion attack; 2) Voting based methods [17, 23] partition training data into subsets and train a sub-classifier on each subset. However, they restrict the attacker on one type of perturbation (nodes, edges, or node features); they are applicable for a particular GNN task; and their robustness guarantees are not \\(100\\%\\) accurate. We are the first work to develop a deterministically certified robust GNN against graph poisoning attack with arbitrary kind of perturbations on both node and graph classification tasks." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.647, + 0.634, + 0.663 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.672, + 0.909, + 0.9 + ], + "angle": 0, + "content": "We investigate the robustness of Graph Neural Networks (GNNs) against graph poisoning attacks and introduce PGNNCert, the first certified defense with deterministic guarantees against arbitrary poisoning perturbations, including modifications to nodes, edges, and node features. PGNNCert employs novel graph division strategies and leverages the message-passing mechanism in GNNs to establish robustness guarantees. Its universality allows it to encompass existing certified defenses as special cases. Experimental evaluations demonstrate that PGNNCert effectively mitigates arbitrary poisoning perturbations, offering superior robustness and efficiency compared to state-of-the-art certified defenses. Future works include extending the proposed defense for federated GNNs [49, 58] and casually explainable GNNs [2] against arbitrary poisoning attacks." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5027" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.264, + 0.108 + ], + "angle": 0, + "content": "8. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.116, + 0.486, + 0.192 + ], + "angle": 0, + "content": "We thank all the anonymous reviewers for their valuable feedback and constructive comments. This work is partially supported by the National Science Foundation (NSF) under grant Nos. ECCS-2216926, CNS-2241713, CNS-2331302, CNS-2339686, and the Cisco Research Award." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.206, + 0.188, + 0.222 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.232, + 0.484, + 0.287 + ], + "angle": 0, + "content": "[1] R. Achanta, A. Shaji, K. Smith, A. Lucchi, P. Fua, and Sabine Süssstrunk. Slic superpixels compared to state-of-the-art superpixel methods. IEEE Transactions on Pattern Analysis & Machine Intelligence, 34(11):2274-2282, 2012. 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.289, + 0.484, + 0.328 + ], + "angle": 0, + "content": "[2] Arman Behnam and Binghui Wang. 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However, recent works show GNNs are vulnerable to training-time poisoning attacks – marginally perturbing edges, nodes, or/and node features of training graph(s) can largely degrade GNNs' testing performance. Most previous defenses against graph poisoning attacks are empirical and are soon broken by adaptive / stronger ones. A few provable defenses provide robustness guarantees, but have large gaps when applied in practice: 1) restrict the attacker on only one type of perturbation; 2) design for a particular GNN architecture or task; and 3) robustness guarantees are not $100\%$ accurate. + +In this work, we bridge all these gaps by developing PGNNCert, the first certified defense of GNNs against poisoning attacks under arbitrary (edge, node, and node feature) perturbations with deterministic robustness guarantees. Extensive evaluations on multiple node and graph classification datasets and GNNs demonstrate the effectiveness of PGNNCert to provably defend against arbitrary poisoning perturbations. PGNNCert is also shown to significantly outperform the state-of-the-art certified defenses against edge perturbation or node perturbation during GNN training. + +# 1. Introduction + +Graph Neural Network (GNN) [15, 21, 37, 44, 48, 56] is the leading approach for representation learning on graphs, showing state-of-the-art performance in various graph-related tasks like node classification and graph classification. In node classification, the goal is to predict labels for individual nodes, while in graph classification, the objective is to predict labels for entire graphs. GNNs have significantly advanced applications across fields such as chemistry [14], physics [36, 39], neuroscience [3], and social science [13]. + +However, various works [6-8, 20, 40, 45, 51, 55, 60, 63] have shown that GNNs are vulnerable to training-time graph poisoning attacks — an attacker perturbs the graph structure during training such that the learnt poisoned GNN model will have low accuracy on predicting new test nodes/graphs. As a graph consists of three components: nodes, their features, and edges connecting the nodes, an attacker is allowed to perturb an individual component or their combinations. For instance, an attacker could inject a few nodes [20, 40], slightly modify the edges [8, 45, 55, 63] on the training graphs, and/or perturb features of certain nodes [63]. + +Various empirical defenses [12, 42, 43, 59, 61, 62] have been proposed to mitigate the graph poisoning attack, but were soon broken by adaptive attacks [33]. Most existing certified defenses [16, 19, 22, 24, 47, 54] are against test-time evasion attacks, with a few exceptions [18, 22], leaving certified defenses against poisoning attacks largely unexplored1. However, existing provable defenses face several limitations when applied in practice: 1) all restrict the attacker's capability to only one type of perturbation (e.g., node injection or edge perturbation); 2) they are designed for a particular GNN architecture or GNN task [19]; and 3) their robustness guarantee is probabilistic (i.e., not $100\%$ accurate) [18, 22]. + +We propose PGNNCert to address the above limitations. PGNNCert is the first certified defense for GNNs on the two most common node and graph classification tasks against arbitrary poisoning perturbations (i.e., arbitrarily manipulate the nodes, node features, and edges of training graph(s)) with deterministic robustness guarantees. Our defense is inspired by ensemble learning, and consists of three main steps: 1) Divide each training graph into multiple subgraphs and allocate subgraphs of training graph(s) into multiple groups via a hash function; 2) Train a set of node/graph classifiers for each group and build a majority-voting node/graph classifier on the subgraphs; 3) Derive the deterministic robustness guarantee against arbitrary poisoning perturbations. + +Following [24], we adapt two graph division strategies—one is edge-centric and the other is node-centric—to realize our defense. The former strategy map edges, while the latter one map nodes from a given graph into multiple subgraphs. Theoretically, PGNNCert provably predicts the same label for a test node/graph after training on the poisoned training set with arbitrary perturbation whose perturbation size (i.e., the total number of manipulated nodes, nodes with feature perturbations, and edges) is bounded by a threshold, which we call the certified perturbation size. Empirically, we extensively evaluate PGNNCert on multiple graph datasets and multiple node and graph classifiers against arbitrary perturbations, and compared our methods with state-of-the-art certified defenses for node classification against node injection poisoning attack [22], and for graph classification against edge manipulation [17]. Our results show PGNNCert significantly outperforms [22] under node-centric graph division, and outperforms [54] under both graph division methods. + +Contributions: Our contributions are summarized below: + +- We develop the first certified defense to robustify GNNs against arbitrary poisoning attack on the training set. +- We propose two strategies (edge-centric and node-centric) to realize our defense that leverages the unique message-passing mechanism in GNNs. +- Our robustness guarantee is applicable to both node and graph classification tasks and accurate with probability 1. +- Our defense treat existing certified defenses as special cases, as well as significantly outperforming them. + +# 2. Background and Problem Definition + +# 2.1. Graph Neural Network (GNN) + +Let a graph be $G = \{V, E, \mathbf{X}\}$ , which consists of the nodes $V$ , node features $\mathbf{X}$ , and edges $E$ . We denote $u \in V$ as a node, $e = (u, v) \in E$ as an edge, and $\mathbf{X}_u$ as node $u$ 's feature. Let $f_\theta$ be the node or graph classifier parameterized by $\theta$ . $\mathcal{V}$ is the label set, $y_v$ and $y_G$ are the groundtruth label of a node $v$ and a graph $G$ , respectively. + +Node classification: $f_{\theta}$ takes a graph $G$ as input and predicts each node $v \in G$ a label $\tilde{y}_v \in \mathcal{V}$ , i.e., $\tilde{y}_v = f_{\theta}(G)_v$ . Given a training node set $V_{\mathrm{tr}} \subseteq V$ with ground-truth labels $\mathbf{y}_{\mathrm{tr}} = \{y_v, v \in V_{\mathrm{tr}}\}$ , $f_{\theta}$ is learnt by minimizing a loss $\mathcal{L}$ between the node predictions $\tilde{\mathbf{y}}_{\mathrm{tr}}$ on $V_{\mathrm{tr}}$ and the ground-truth $\mathbf{y}_{\mathrm{tr}}$ : + +$$ +\min _ {\theta} \mathcal {L} \left(\mathbf {y} _ {\mathrm {t r}}, \tilde {\mathbf {y}} _ {\mathrm {t r}}; \theta\right), \tilde {\mathbf {y}} _ {\mathrm {t r}} = \left\{f _ {\theta} (G) _ {v}, v \in V _ {\mathrm {t r}} \right\} \tag {1} +$$ + +Graph classification: $f_{\theta}$ takes a graph $G$ as input and predicts a label $\tilde{y}_G \in \mathcal{V}$ for the whole graph $G$ , i.e., $\tilde{y}_G = f(G)$ . Given a set of training graphs $\mathcal{G}_{\mathrm{tr}}$ with ground-truth labels $\mathbf{y}_{\mathrm{tr}} = \{y_G, G \in \mathcal{G}_{\mathrm{tr}}\}$ . The graph classifier $f_{\theta}$ is learnt by minimizing a loss function $\mathcal{L}$ between the predictions on $\mathcal{G}_{\mathrm{tr}}$ and the ground-truth $\tilde{\mathbf{y}}_{\mathrm{tr}}$ : + +$$ +\min _ {\theta} \mathcal {L} \left(\mathbf {y} _ {\mathrm {t r}}, \tilde {\mathbf {y}} _ {\mathrm {t r}}; \theta\right), \tilde {\mathbf {y}} _ {\mathrm {t r}} = \left\{f _ {\theta} (G), G \in \mathcal {G} _ {\mathrm {t r}} \right\} \tag {2} +$$ + +# 2.2. Poisoning Attack on GNNs + +In poisoning attacks against GNNs, an attacker can manipulate any training graph $G = \{V,E,\mathbf{X}\} \in \mathcal{G}_{\mathrm{tr}}$ (For node classification, $\mathcal{G}_{\mathrm{tr}} = \{G\}$ ) into a perturbed one $G^{\prime} = \{V^{\prime},E^{\prime},\mathbf{X}^{\prime}\}$ during training, where $V^{\prime},E^{\prime},\mathbf{X}^{\prime}$ are the perturbed version of $V,E$ and $\mathbf{X}$ , respectively. For simplicity, we denote the nodes, edges and features in training graph(s) as $\mathcal{V},\mathcal{E}$ , and $\mathcal{X}$ , respectively. + +Edge manipulation: The attacker can 1) inject new edges $\mathcal{E}_{+}$ , and 2) delete existing edges, denoted as $\mathcal{E}_{-} \subset \mathcal{E}$ . + +Node manipulation: The attacker perturbs $\mathcal{G}_{\mathrm{tr}}$ by (1) injecting new nodes $\nu_{+}$ , whose node feature denoted as $\mathcal{X}_{\nu_{+}}^{\prime}$ can be arbitrary, together with the arbitrarily injected new edges $\mathcal{E}_{\nu_{+}} \subseteq \{(u,v) \notin \mathcal{E}, \forall u \in \mathcal{V}_{+} \lor v \in \mathcal{V}_{+}\}$ induced by $\nu_{+}$ ; and (2) deleting existing nodes $\nu_{-} \subset \nu$ . When $\nu_{-}$ are deleted, their features $\mathcal{X}_{\nu_{-}} \subseteq \mathcal{X}$ and all connected edges $\mathcal{E}_{\nu_{-}} = \{(u,v) \in \mathcal{E}, \forall u \in \mathcal{V}_{-} \lor v \in \mathcal{V}_{-}\}$ are also removed. We denote that for the node classification case, the injected and deleted nodes are not from $V_{\mathrm{tr}}$ . + +Node feature manipulation: The attacker arbitrarily manipulates features $\mathcal{X}_{\mathcal{V}_r}$ of a set of representative nodes $\nu_{r}$ to be $\mathcal{X}_{\mathcal{V}_r}^\prime$ . We also denote the edges connected with nodes $\nu_{r}$ as $\mathcal{E}_{\nu_r} = \{(u,v)\in \mathcal{E}:\forall u\in \mathcal{V}_r\lor v\in \mathcal{V}_r\}$ + +Arbitrary manipulation: The attacker can manipulate a training graphs in $\mathcal{G}_{\mathrm{tr}}$ with an arbitrary combined perturbations on edges, nodes, and node features for each of them. The attacker can manipulate several training graphs at the same time with different combinations of attack. + +For description simplicity, we will use $\{\mathcal{E}_{+},\mathcal{E}_{-}\}$ to indicate the edge manipulation with arbitrary injected edges $E_{+}$ and deleted edges $\mathcal{E}_{-}$ on $\mathcal{G}_{tr}$ . Similarly, we will use $\{\mathcal{V}_{+},\mathcal{E}_{\mathcal{V}_{+}},\mathcal{X}_{\mathcal{V}_{+}}^{\prime},\mathcal{V}_{-},\mathcal{E}_{\mathcal{V}_{-}}\}$ to indicate the node manipulation, and $\{\mathcal{V}_r,\mathcal{E}_{\mathcal{V}_r},\mathcal{X}_{\mathcal{V}_r}^{\prime}\}$ the node feature manipulation. Any combination of the manipulations is inherently well-defined. + +# 2.3. Problem Statement + +Threat model: Given a node/graph classifier $f$ , a training graph set $\mathcal{G}_{\mathrm{tr}}$ , the adversary can arbitrarily manipulate a number of the edges, nodes, and node features in any graph of $\mathcal{G}_{\mathrm{tr}}$ such that after training, $f$ misclassifies target graphs in graph classification or target nodes in node classification. Since we focus on certified defenses, we consider the strongest attack where the adversary has white-box access to $\mathcal{G}_{\mathrm{tr}}$ i.e., it knows all the edges, nodes, and node features in $\mathcal{G}_{\mathrm{tr}}$ . + +Defense goal: We aim to build provably robust GNNs against poisoning attacks that: + +- has a deterministic robustness guarantee; +- is suitable for both node and graph classification tasks; +- provably predicts the same label against the arbitrary poisoning perturbation within the certified perturbation size. + +Our ultimate goal is to obtain the largest-possible certified perturbation size that satisfies all the above conditions. + +# 3. Our Certified Defense: PGNNCert + +# 3.1. Overview + +Our method is inspired by previous work [24, 54], which divides a test input into several sub-parts and assembles a voting GNN classifier on the sub-parts. We generalize this idea by designing the dividing strategy tailored to training set. Specifically, it consists of four steps below: + +In the first step, we divide the training graph set into multiple subgraph sets. For each training graph $G \in \mathcal{G}_{\mathrm{tr}}$ with ground-truth label $y_{G} \in \mathbf{y}_{\mathrm{tr}}$ , we divide it into $S$ subgraphs $G_{1}, G_{2}, \ldots, G_{S}$ via a hash function and ensure edges in different subgraphs are disjoint. This process is detailed in Section 3.2-3.3. By collecting these subgraphs, we build $S$ sets of subgraphs $\mathcal{G}_{[S]} = \{\mathcal{G}_1, \mathcal{G}_2, \ldots, \mathcal{G}_S\}$ . In each subgraph set $\mathcal{G}_i$ , there exists an exact subgraph $G_i$ generated from $G$ , and we label $G_i$ the same label $y_{G}$ as $G$ . + +In the second step, we train multiple classifiers with the respective subgraph sets. On each subgraph set $\mathcal{G}_i$ , we initialize a classifier $f_i$ with weights $\theta_i$ and train it below: + +Node classifier: $\min_{\theta_i}\mathcal{L}(\mathbf{y}_{\mathrm{tr}},\tilde{\mathbf{y}}_i;\theta_i),\tilde{\mathbf{y}}_i = \{f_i(G)_v,v\in V_{\mathrm{tr}}\}$ + +Graph classifier: $\min_{\theta_i}\mathcal{L}(\mathbf{y}_{\mathrm{tr}},\tilde{\mathbf{y}}_i;\theta_i),\tilde{\mathbf{y}}_i = \{f_i(G),G\in \mathcal{G}_{\mathrm{tr}}\}$ + +In the third step, we build the voting-based classifier based on the trained sub-classifiers. Given a test graph $G$ , we first divide it into $S$ subgraphs $\{G_1, \ldots, G_S\}$ by the same subgraph division method. Then we apply a voting classifier $\bar{f}$ , which assembles the predictions of the trained classifiers $f_{[S]}$ on the subgraphs: + +Node classifier: $\mathbf{n}_{y_v} = \sum_{i=1}^{S} \mathbb{I}(f_i(G_i)_v = y_v), \forall y_v \in \mathcal{V}$ (3) + +Graph classifier: $\mathbf{n}_{y_G} = \sum_{i=1}^{S} \mathbb{I}(f_i(G_i) = y_G), \forall y_G \in \mathcal{V}$ (4) + +We then define our voting node/graph classifier $\bar{f}$ as returning the class with the most vote: + +Voting node classifier: $\bar{f} (G)_v = \operatorname *{arg\max}_{y_v\in \mathcal{V}}\mathbf{n}_{y_v}$ (5) + +Voting graph classifier: $\bar{f} (G) = \operatorname *{arg\max}_{y_G\in \mathcal{Y}}\mathbf{n}_{y_G}$ (6) + +In the forth step, we derive the deterministic robustness guarantee for the test graph. We denote $y_{a}$ and $y_{b}$ as the class with the most vote $\mathbf{n}_{y_a}$ and the second-most vote $\mathbf{n}_{y_b}$ , respectively. We pick the class with a smaller index if ties exist. Denote $\mathcal{G}_{\mathrm{tr}}^{\prime}$ as the perturbed train dataset of $\mathcal{G}_{\mathrm{tr}}$ , and $\mathcal{G}_{[S]}^{\prime} = \{\mathcal{G}_1^{\prime},\mathcal{G}_2^{\prime},\dots ,\mathcal{G}_S^{\prime}\}$ be the perturbed subgraph sets generated from $\mathcal{G}_{\mathrm{tr}}^{\prime}$ under the same graph division strategy. Then we have the below condition for certified robustness against arbitrary poisoning attacks on GNNs. + +Theorem 1 (Sufficient Condition for Certified Robustness). Let $y_{a}, y_{b}, \mathbf{n}_{y_{a}}, \mathbf{n}_{y_{b}}$ be defined above in node classification or graph classification, and let $P =$ + +$\left\lfloor \mathbf{n}_{y_a} - \mathbf{n}_{y_b} - \mathbb{I}(y_a > y_b)\right\rfloor /2.$ The voting classifier $\bar{f}$ trained on $\mathcal{G}_{tr}$ guarantees the same prediction on $G$ for the target node $v$ in node classification or the target graph $G$ in graph classification with the poisoned voting classifier $\bar{f}'$ , if the number of different sub-classifiers (i.e., different in weights) trained on $\mathcal{G}_{[S]}$ and $\mathcal{G}_{[S]}'$ under the arbitrary perturbation is bounded by $P$ . I.e., + +$$ +\forall \mathcal {G} _ {t r} ^ {\prime}: \sum_ {i = 1} ^ {S} \mathbb {I} \left(\theta_ {i} \neq \theta_ {i} ^ {\prime}\right) \leq P \Longrightarrow \bar {f} (G) _ {v} = \bar {f} ^ {\prime} (G) _ {v} \tag {7} +$$ + +$$ +\forall \mathcal {G} _ {t r} ^ {\prime}: \sum_ {i = 1} ^ {S} \mathbb {I} \left(\theta_ {i} \neq \theta_ {i} ^ {\prime}\right) \leq P \Longrightarrow \bar {f} (G) = \bar {f} ^ {\prime} (G) \tag {8} +$$ + +Proof is in Appendix A. The above theorem motivates us to design the graph division method such that: 1) the number of different sub-classifiers with trained on $\mathcal{G}_{[S]}$ and $\mathcal{G}_{[S]}^{\prime}$ can be upper bounded (and the smaller the better). 2) the difference between $\mathbf{n}_{y_a}$ and $\mathbf{n}_{y_b}$ is as large as possible, ensuring larger certified perturbation size. + +Next, we introduce our two graph division methods. Figure 2 visualizes the divided subgraphs of the two methods without and with the adversarial manipulation. + +# 3.2. Edge-Centric Graph Division + +Our first graph division method is edge-centric. The idea is to divide edges in a graph into different subgraphs, such that each edge is deterministically mapped into only one subgraph. With this strategy, we can bound the number of altered classifiers trained on these subgraphs before and after the arbitrary perturbation (Theorem 2), which facilitates deriving the certified perturbation size (Theorem 3). All proofs are detailed in Appendix A. + +# 3.2.1 Generating edge-centric subgraphs + +We follow [24, 54] to use a hash function $h$ (e.g., MD5) to generate the subgraphs for every train graph $G \in \mathcal{G}_{\mathrm{tr}}$ . A hash function takes a bit string as input and outputs an integer (e.g., within a range $[0, 2^{128} - 1]$ ). We use the string of edge or node index as the input to the hash function. For instance, for a node $u$ , its string is denoted as $\operatorname{str}(u)$ , while for an edge $e = (u, v)$ , its string is $\operatorname{str}(u) + \operatorname{str}(v)$ , where "+" means string concatenation, and str turns the node index into a string and adds "0" prefix to align it into a fixed length. + +Assuming $S$ subgraphs in total, the subgraph index $i_e$ of every edge $e = (u,v)$ is defined as2 + +$$ +i _ {e} = h \left[ \operatorname {s t r} (u) + \operatorname {s t r} (v) \right] \bmod S + 1, \tag {9} +$$ + +where mod is the module function. Denoting $\mathcal{E}^i$ as the set of edges whose subgraph index is $i$ , i.e., $\mathcal{E}^i = \{\forall e \in \mathcal{E} : i_e = i\}$ , $S$ subgraphs for $G$ can be built as $\{G_i = (\mathcal{V}, \mathcal{E}^i, \mathbf{X}) : i = 1, 2, \dots, S\}$ , where edges in different subgraphs are disjoint, i.e., $\mathcal{E}^i \cap \mathcal{E}^j = \emptyset, \forall i, j \in \{1, \dots, S\}, i \neq j$ . Here, we + +![](images/1197eebffade3577990074eb19f87cb19868989db80fc628c55d83feb081b71a.jpg) +Figure 1. Overview of our PGNNCert (use node classification for illustration), which consists of four steps. + +mention that we need to further postprocess the subgraphs for graph classification, in order to derive the robustness guarantee. Particularly, in each subgraph $G_{i}$ , we remove all isolated nodes who have no connected edges. This is because although they have no influence on other nodes' representation, their information would still be passed to the global graph embedding aggregation. + +After dividing all training graphs in $\mathcal{G}_{\mathrm{tr}}$ , we combine all generated subgraphs with the same index as a separate subgraph training set: $\mathcal{G}_i = \{G_i, \forall G \in \mathcal{G}_{\mathrm{tr}}\}, \forall i \in [S]$ . We denote the $S$ training sets as $\mathcal{G}_{[S]} = \{\mathcal{G}_1, \dots, \mathcal{G}_S\}$ . + +# 3.2.2 Bounding the number of different sub-classifiers + +For a perturbed training set $\mathcal{G}_{\mathrm{tr}}^{\prime}$ , we use the same graph division strategy to generate a set of $S$ subgraphs sets $\mathcal{G}_{[S]}^{\prime} = \{\mathcal{G}_1^{\prime},\mathcal{G}_2^{\prime},\dots ,\mathcal{G}_T^{\prime}\}$ . Then, we can upper bound the number of different classifiers trained on $\mathcal{G}_{[S]}$ and $\mathcal{G}_{[S]}^{\prime}$ against any individual perturbation. + +Theorem 2 (Bounded Number of Edge-Centric Subgraphs with Altered Predictions under Arbitrary Perturbation). Given any training graph set $\mathcal{G}_{tr}$ , and $S$ edge-centric subgraph sets $\mathcal{G}_{[S]}$ for $\mathcal{G}_{tr}$ . A perturbed training set $\mathcal{G}_{train}^{\prime}$ of $\mathcal{G}_{train}$ is with arbitrary edge manipulation $\{\mathcal{E}_+, \mathcal{E}_-\}$ , node manipulation $\{\mathcal{V}_+,\mathcal{E}_{\mathcal{V}_+},\mathcal{V}_-, \mathcal{E}_{\mathcal{V}_-}\}$ , and node feature manipulation $\{\mathbf{X}_{\mathcal{V}_r},\mathcal{V}_r,\mathcal{E}_{\mathcal{V}_r}\}$ on arbitrary graphs in $\mathcal{G}_{tr}$ . Then at most $p = |\mathcal{E}_+| + |\mathcal{E}_-| + |\mathcal{E}_{\mathcal{V}_+}| + |\mathcal{E}_{\mathcal{V}_-}| + |\mathcal{E}_{\mathcal{V}_r}|$ node/graph sub-classifiers in $f_{[S]}$ are different in weights between training on the subgraph sets $\mathcal{G}_{[S]}$ and on the perturbed subgraph sets $\mathcal{G}_{[S]}^{\prime}$ . In other words, $\sum_{i=1}^{S} \mathbb{I}(\theta_i \neq \theta_i') \leq p$ for both node classification case and graph classification case. + +# 3.2.3 Deriving the robustness guarantee + +Based on Theorems 1 and 2, we can derive the certified perturbation size as the maximal perturbation such that Equation 7 or Equation 8 is satisfied. Formally, + +Theorem 3 (Certified Robustness Guarantee with Edge-Centric Subgraphs against Arbitrary Perturbation). Let $f, y_{a}, y_{b}, \mathbf{n}_{y_{a}}, \mathbf{n}_{y_{b}}$ be defined above for edge-centric subgraphs, and $p$ be the perturbation size induced by an arbitrary perturbed training set $\mathcal{G}_{tr}'$ on $\mathcal{G}_{tr}$ . After training on $\mathcal{G}_{tr}'$ + +and $\mathcal{G}_{tr}^{\prime}$ , the voting classifier $\bar{f}$ and poisoned classifier $\bar{f}'$ guarantee the same prediction for the target node $v$ in node classification (i.e., $\bar{f}(G')_v = \bar{f}(G)_v$ ) or target graph $G$ in graph classification (i.e., $\bar{f}(G') = \bar{f}(G)$ ), when $p$ satisfies. + +$$ +p \leq P = \left\lfloor \mathbf {n} _ {y _ {a}} - \mathbf {n} _ {y _ {b}} - \mathbb {I} \left(y _ {a} > y _ {b}\right) \right\rfloor / 2. \tag {10} +$$ + +Or to say, the maximum certified perturbation size is $P$ . + +# 3.3. Node-Centric Graph Division + +We observe the robustness guarantee under edge-centric graph division is largely dominated by the edges (i.e., $\mathcal{E}_{\mathcal{V}_+}, \mathcal{E}_{\mathcal{V}_-}$ ) induced by the manipulated nodes $\mathcal{V}_+$ , $\mathcal{V}_-$ , and edges $\mathcal{E}_{\mathcal{V}_r}$ by the perturbed node features $\mathbf{X}_{\mathcal{V}_r}'$ . This guarantee could be weak against node or node feature manipulation, as the number of edges (i.e., $|\mathcal{E}_{\mathcal{V}_+}|, |\mathcal{E}_{\mathcal{V}_-}|, |\mathcal{E}_{\mathcal{V}_r}|$ ) could be much larger, compared with the number of the nodes (i.e., $|\mathcal{V}_+|, |\mathcal{V}_-|, |\mathcal{V}_r|$ ). For instance, an injected node could link with many edges to a given graph in practice, and when the number exceeds $P$ in Equation 10, the certified robustness guarantee is ineffective. This flaw inspires us to generate subgraphs, where we expect at most one subgraph is affected under every node or node feature manipulation on a training graph (this means all edges of a manipulated node should be in a same subgraph), implying only a training subgraph set is affected. Following [24], we apply a tailored node-centric graph division strategy to achieve our goal. + +# 3.3.1 Generating node-centric directed subgraphs + +We use a hash function $h$ to generate directed subgraphs for a given train graph $G = (\mathcal{V},\mathcal{E},\mathbf{X})\in \mathcal{G}_{\mathrm{tr}}$ . Our node-centric graph division strategy as follows: (1) we treat every undirected edge $e = (u,v)\in G$ as two directed edges for $u^3$ : the outgoing edge $u\to v$ and incoming edge $v\rightarrow u$ ; (2) for every node $u$ , we compute the subgraph index of its every outgoing edge $u\to v$ : + +$$ +i _ {u \rightarrow v} = h [ \operatorname {s t r} (u) ] \bmod S + 1. \tag {11} +$$ + +![](images/e02fcf503f1d909e6f94cf97054387813e3f82e4a9e81774b9cc99941c671033.jpg) +(b) Node-Centric Graph Division against edge injection and node injection attacks +Figure 2. Illustration of our edge-centric and node-centric graph division strategies for node classification. We use edge injection and node injection poisoning attacks to show the bounded number of altered predictions on the generated subgraphs after the attack. Figures 8-9 in Appendix also show other attacks and on graph classification. + +Note outgoing edges of $u$ are mapped in the same subgraph. + +We use $\vec{\mathcal{E}}_i$ to denote the set of directed edges whose subgraph index is $i$ , i.e., $\vec{\mathcal{E}}_i = \{\forall u \to v \in \mathcal{E} : i_{u \to v} = i\}$ . Then, we can construct $S$ directed subgraphs for $G$ as $\vec{G}_i = (\mathcal{V}, \vec{\mathcal{E}}_i, \mathbf{X}), \forall i \in [1, S]$ . After generating subgraphs for all training graphs, we combine all subgraphs with the same index as a separate subgraph set: $\vec{\mathcal{G}}_i = \{\vec{G}_i, \forall G \in \mathcal{G}_{\mathrm{tr}}\}, \forall i \in [S]$ . We denote the $S$ training sets as $\vec{\mathcal{G}}_{[S]} = \{\vec{\mathcal{G}}_1, \dots, \vec{\mathcal{G}}_S\}$ . + +Here, we mention that we need to further postprocess the subgraphs for graph classification, in order to derive the robustness guarantee. Particularly, in each subgraph $\vec{G}_i$ , we remove all other nodes whose subgraph index is not $i$ . This is because although they have no influence on other nodes' representation, their information would still be passed to the global graph embedding aggregation. To make up the loss of connectivity between nodes and simulate the aggregation, we add an extra node with a zero feature, and add an outgoing edge from every node with index $i$ to it. + +# 3.3.2 Bounding the number of different sub-classifiers + +For a perturbed training set $G_{\mathrm{tr}}^{\prime}$ , we use the same graph division strategy to generate a set of $S$ directed subgraph sets $\vec{\mathcal{G}}_{[S]}^{\prime} = \{\vec{\mathcal{G}}_1^{\prime},\vec{\mathcal{G}}_2^{\prime},\dots ,\vec{\mathcal{G}}_T^{\prime}\}$ . We first show the theoretical result on bounding the number of different trained classifiers on $\vec{\mathcal{G}}_{[S]}$ and $\vec{\mathcal{G}}_{[S]}^{\prime}$ against any individual perturbation. + +Theorem 4 (Bounded Number of Node-Centric Subgraphs with Altered Predictions under Arbitrary Perturbation). Let + +$\mathcal{G}_{tr}, v, G, \mathcal{E}_+, \mathcal{E}_-, \mathcal{V}_+, \mathcal{V}_-, \mathcal{V}_r$ be defined in Theorem 2, and $\vec{\mathcal{G}}_{[S]}, \vec{\mathcal{G}}_{[S]}'$ contain directed subgraph sets under the node-centric graph division. Then, at most $\bar{p} = 2|\mathcal{E}_+| + 2|\mathcal{E}_-| + |\mathcal{V}_+| + |\mathcal{V}_-| + |\mathcal{V}_r|$ trained node classifiers in $f_{[S]}$ are different in weights after training on $\vec{\mathcal{G}}_{[S]}$ and on $\vec{\mathcal{G}}_{[S]}'$ . In other words, $\sum_{i=1}^{S} \mathbb{I}(\theta_i \neq \theta_i') \leq \bar{p}$ for any target node $v \in G$ in node classification. Meanwhile, at most $\bar{p} = |\mathcal{E}_+| + |\mathcal{E}_-| + |\mathcal{V}_+| + |\mathcal{V}_-| + |\mathcal{V}_r|$ trained graph classifiers in $f_{[S]}$ are different in weights after training on $\vec{\mathcal{G}}_{[S]}$ and on $\vec{\mathcal{G}}_{[S]}'$ . In other words, $\sum_{i=1}^{S} \mathbb{I}(\theta_i \neq \theta_i') \leq \bar{p}$ in graph classification. + +# 3.3.3 Deriving the robustness guarantee + +Based on Theorem 1 and Theorem 4, we can derive the certified perturbation size formally stated below + +Theorem 5 (Certified Robustness Guarantee with Node-Centric Subgraphs against Arbitrary Perturbation). Let $f, y_{a}, y_{b}, \mathbf{n}_{y_{a}}, \mathbf{n}_{y_{b}}^{4}$ be defined above for node-centric subgraphs, and $\bar{p}$ be the perturbation size induced by an arbitrary perturbed graph $G'$ on $G$ . With a probability $100\%$ , the voting classifier $\bar{f}$ guarantees the same prediction on both $G'$ and $G$ for the target node $v$ in node classification (i.e., $\bar{f}(G')_{v} = \bar{f}(G)_{v}$ ) or the target graph $G$ in graph classification (i.e., $\bar{f}(G') = \bar{f}(G)$ ), if + +$$ +\bar {p} \leq P = \left\lfloor \mathbf {n} _ {y _ {a}} - \mathbf {n} _ {y _ {b}} - \mathbb {I} \left(y _ {a} > y _ {b}\right) \right\rfloor / 2. \tag {12} +$$ + +# 4. Experiments + +# 4.1. Experiments Settings + +Datasets: We use four node classification datasets (Cora-ML [31], CiteSeer [38], PubMed [38], Amazon-C [57]) and four graph classification datasets (AIDS [34], MUTAG [9], PROTEINS [5], and DD [10]) for evaluation. In each dataset, we take $30\%$ nodes (for node classification) or $50\%$ graphs (for graph classification) as the training set, $10\%$ and $20\%$ as the validation set and $30\%$ nodes/graph as the test set. Table 5 in Appendix shows the basic statistics of them. + +GNN classifiers and PGNNCert training: We adopt three well-known GNNs as the base node/graph classifiers: GCN [21], GSAGE [15] and GAT [44]. We denote the two versions of PGNNCert under edge-centric and node-centric graph division as PGNNCert-E and PGNNCert-N, respectively. By default, we use GCN as the node/graph classifier. + +Evaluation metric: Following existing works [22, 47, 54], we use the certified node/graph accuracy at perturbation size as the evaluation metric. Given a perturbation size $p$ and test nodes/graphs, certified node/graph accuracy at $p$ is the fraction of test nodes/graphs that are accurately classified by the voting node/graph classifier and its certified perturbation size is no smaller than $p$ . Note that the standard node/graph accuracy is achieved when over $p = 0$ . + +Parameter setting: PGNNCert has two hyperparameters: the hash function $h$ and the number of subgraphs $S$ . By default, we use MD5 as the hash function and set $S = 50,60$ respectively for node and graph classification, considering their different graph sizes. We also study the impact of them. + +Compared baselines: As PGNNCert encompasses existing defenses as special cases, we can compare PGNNCert with them against less types of perturbation. Here, we choose the sparse-smoothing RS [4], Bagging [17] and Bi-RS [22] as compared baselines in face of node injection poisoning attack on node classification task. For Bi-RS, We adopt the $p_e = 0.2$ , $p_n = 0.9$ , $N = 1000$ setting as described, and test both include and exclude methods. We also use Bagging for comparison on graph classification. + +# 4.2. Experiment Results on PGNNCert + +Main results: Figures 3-4 show the certified node accuracy and Figures 5-6 show the certified graph accuracy at perturbation size $p$ w.r.t. $S$ under the two graph division strategies, respectively. We have the following observations. + +- Both PGNNCert-E and PGNNCert-N can tolerate the perturbation size up to 25 and 30, on the node and graph classification datasets. This means PGNNCert-E can defend against a total of 25 (30) arbitrary edges, while PGNNCert-N against a total of 25 (30) arbitrary edges and nodes caused by the arbitrary perturbation, on the node (graph) classification datasets, respectively. Note + +Table 1. Node/graph accuracy of normally trained GNN and of PGNNCert with GNN trained on the subgraphs. + +
    DatasetGCNPGNNCertGSAGEPGNNCertGATPGNNCert
    -E-N-E-N-E-N
    Cora-ML0.730.680.680.670.650.680.740.690.69
    Citeseer0.660.670.670.690.680.680.700.670.67
    Pubmed0.860.830.850.840.840.850.850.850.84
    Amazon-C0.810.810.810.820.780.800.830.780.80
    AIDS0.990.880.960.970.940.950.960.930.96
    MUTAG0.710.640.640.700.630.640.710.650.65
    Proteins0.820.810.780.830.800.810.820.780.77
    DD0.800.790.770.810.780.760.810.770.79
    + +that node classification datasets have several orders of more nodes/edges than graph classification datasets, hence PGNNCert can tolerate more perturbations on them. + +- $S$ acts as the robustness-accuracy tradeoff. That is, a larger (smaller) $S$ yields a higher (lower) certified perturbation size, but a smaller (higher) normal accuracy ( $p = 0$ ). +- In PGNNCert-N, the guaranteed perturbed nodes can have infinite edges. This implies that PGNNCert-N has better robustness than PGNNCert-E against the perturbed edges by node/node feature manipulation. + +Impact of base GNN classifiers: Figures 10-11 and Figures 12-13 in Appendix show the certified accuracy using GSAGE and GAT as the base classifier, respectively. We have similar observations as those results with GCN. + +Impact of hash function: Figures 14-17 show the certified node/edge accuracy of PGNNCert-E and PGNNCert-N with different hash functions. We observe that our certified accuracy and certified perturbation size are almost the same in all cases. This reveals our PGNNCert is insensitive to the hash function, and [54] draws a similar conclusion. + +Impact of subgraphs on normal accuracy: We test the normal accuracy of (not) using subgraphs to train the GNN classifier. Table 1 shows the test node/graph accuracy of normally trained GNN without sburgraphs and PGNNCert with GNN trained on the subgraphs. We observe that the accuracy of PGNNCert is $5\%$ smaller than that of normally trained GNN in almost all cases, and in some cases even larger. This implies the augmented subgraphs for training marginally affects the normal test accuracy. + +# 4.3. Comparison Results with SOTA Baselines + +In this section, we compare PGNNCert with SOTA defenses (Bi-RS [22], RS [4], Bagging [17]) against node injection poisoning attacks and graph structure poisoning attacks [17]. + +Results for node classification against node injection poisoning attacks: We follow Bi-RS [22] by setting the injected nodes' degrees as $\tau = 5$ and show the certified node accuracy with varying number of injected nodes. Figure 7 shows the comparison results. We can see PGNNCert-E has better certified accuracy than RS, Bagging and Bi-RS-Include, but it is worse than Bi-RS-Exclude. This aligns with our assumption on its weakness against node-relevant attack. By + +![](images/517eed08059caeb30e9cee2ad61014f6d5dedc5cb5309288ccb02cd77872b35d.jpg) +(a) Cora-ML + +![](images/019d7af7b8ef08d9c0ae727637b09a3feb587451d7471a4ec19f469605a68f89.jpg) +(b)CiteSeer + +![](images/e31ac7eb086b0923c565eba2f9085593def47537fbc590fc9bf0ac9015f8a547.jpg) +(c) Pubmed + +![](images/aea07dc9790e417fbd9c68463b0125d42f08e69f574a8b4bb49051a3398457f7.jpg) +(d) Amazon-C + +![](images/37ac0188fabf64197ac1cf11491bd820fe79a63f8d2cbf40a6cb19f10e0ed2bd.jpg) +(a) Cora-ML + +![](images/5badc25ed250739033c02e115f86e39a7350e249d7119fe1533b842eaa864a6c.jpg) +Figure 3. Certified node accuracy of our PGNNCert-E w.r.t. the number of subgraphs $S$ . +(b) CiteSeer + +![](images/c7e63798990143b610b20cb1797d48a693c0d9dc209f8be3196f4a2f71321f30.jpg) +(c) Pubmed + +![](images/c94499fa533c87932a3629f38dff3c2c2ef00ac69871c51cbc8bd8f8a80925ad.jpg) +(d) Amazon-C + +![](images/9d74544d09d8c3dcb31fab09bb7b08ee34c354cb2352e21f9167536c603ea80a.jpg) +Figure 4. Certified node accuracy of our PGNNCert-N w.r.t. the number of subgraphs $S$ . +(a) AIDS + +![](images/8629cd3817fe045afaca871ebc31445916773c379efaa30c762e0dca4fdb9bf7.jpg) +(b) MUTAG + +![](images/b24a48c68dce9f2c747c710189f4271a7b2dabc87a540aa73f235fe07cd18b32.jpg) +(c) PROTEINS + +![](images/472de62d95c942a955a523edc04a5fe2f737839b5266dce1f95f99ea152d8d12.jpg) +(d) DD + +![](images/023f5f1982ca0b0daa603fab86db860ecb63d865588bd09bba86d22a25126c24.jpg) +Figure 5. Certified graph accuracy of our PGNNCert-E w.r.t. the number of subgraphs $S$ . +(a) AIDS + +![](images/ad59b5b10406d3b2b82af09bdae7107e0c9dc933addf2536d28d0fc39cbe0558.jpg) +(b) MUTAG + +![](images/8e3184a705354c056c8d6aab53b4385fd3a95e0ee952b59618d905d17d74fd6c.jpg) +(c) PROTEINS + +![](images/83d6b1ea16f26ce001ccb4cb81696f6bb0e7c0b21839e5eaafa1dc3155f11388.jpg) +(d) DD + +![](images/ca0df25cacf4771e9d1af8359d5b43b1cde4d0848ebbacac5841602f226e359f.jpg) +Figure 6. Certified graph accuracy of our PGNNCert-N w.r.t. the number of subgraphs $S$ . +(a) Cora-ML +Figure 7. Certified node accuracy of our PGNNCert and SOTA defenses against node injection attacks. + +![](images/ed90bb0e8d7dbfb7e4459b7b831714e93deae88ad6c5a768b663aa2d19d6159d.jpg) +(b)CiteSeer + +![](images/4b44befcc9365f9980011c525a02931cd63322edbc7e240e76a2df39186b2fcf.jpg) +(c) Pubmed + +![](images/d104a7f978c6793e787be96e84ea68b629e627f57fb4737c008533ae1eebac94.jpg) +(d) Amazon-C + +contrast, PGNNCert-N outperforms all compared baselines. We highlight that each bounded node in PGNNCert-N can + +inject as many edges as possible, meaning the total number of bounded edges in PGNNCert-N could be infinite. + +Table 2. Certified graph accuracy of our PGNNCert and Bagging against edge perturbations. + +
    DatasetsMethods#Edges=051015
    ProteinsBagging0.7560.2050.0000.00
    PGNNCert-E0.7440.5180.2600.00
    PGNNCert-N0.7780.4740.1020.00
    DDBagging0.7850.3110.0000.00
    PGNNCert-E0.7920.5780.3300.063
    PGNNCert-N0.7710.3440.0060.000
    + +Table 3. Results of PGNNCert on CIFAR10. + +
    DatasetsMethodsp=0135
    CIFAR10PGNNCert-E0.5960.5560.4820.107
    PGNNCert-N0.6360.5930.4980.113
    + +Table 4. Defense results against the optimization-based Mettack. + +
    DatasetNettackp=0203040
    Cora-MLPGNNCert-N0.6750.6750.6680.661
    + +Results for graph classification against graph poisoning attacks: Table 2 shows the certified graph accuracies of PGNNCert and Bagging against edge perturbations on graph classification tasks. PGNNCert outperforms Bagging, especially when the perturbation size is larger. + +# 5. Discussion + +Evaluation on CV datasets. We also test a benchmark superpixel graph CIFAR10 in computer vision [11] for graph classification, to show the generality of our defense. CIFAR10 is an image classification dataset, which is converted into graphs using the SLIC superpixels [1]. Each node has the superpixel coordinates as the feature and each superpixel graph has a label. Results in the default setting are shown in Table 3, where we see PGNNCert can obtain about $50\%$ certified accuracy when 3 arbitrary edges are perturbed. + +PGNNCert against optimization-based attacks. We first emphasize that PGNNCert is provably robust against all (known and unknown) attacks, when their perturbation budget is within the derived bound (in Eqn 10 or Eqn 12), regardless of the attack knowledge of PGNNCert. Here, we test PGNNCert-N against Metattack [63] when its perturbation size $m$ is larger than the derived certified perturbation size $P = 25$ (with certified accuracy 0.588) on Cora-ML with $S = 60$ . Results are shown in Table 4. We see PGNNCert-N can achieve 0.661 accuracy of defending against Metattack even when it perturbs 40 edges and nodes in total. + +Limitations. Despite the effectiveness of PGNNCert, its inefficiency remains a main limitation for large GNNs. PGNNCert trains $S$ classifiers on $S$ subgraphs and uses $S$ subgraphs for certification. It may incur a training/certification complexity that is $S$ times of standard GNN training/testing. This overhead could be significant when PGNNCert is applied to large GNNs. On the other hand, we note that the $S$ classifiers can be trained in parallel once obtaining the $S$ subgraphs after graph division. + +# 6. Related Work + +Adversarial attacks on GNNs: Existing attacks to GNNs can be classified as graph evasion attacks [8, 25, 26, 29, 30, 32, 50-53, 55, 64] and poisoning attacks [8, 28, 40, 41, 45, 55, 60, 63, 63]. For instance, [8] leveraged reinforcement learning techniques to design evasion attacks to both graph classification and node classification via modifying the graph structure. Most attacks require the attacker fully or partially knows the GNN model, while [32, 50] relaxing this to only have black-box access, i.e., only query the GNN model API. For example, [50] formulates the black-box attack to GNNs as an online optimization problem with bandit feedback and provably obtains a sublinear query number. Furthermore, [25] generalizes the black-box evasion attack on explainable GNNs. In the realm of graph poisoning attacks, [55] proposed a MinMax attack to GNNs based on gradient-based optimization, while [63] introduced Metattack that perturbs the entire graph using meta learning. + +Certified robustness against graph poisoning graphs: Most existing certified defenses for GNNs are against test-time evasion attacks [16, 19, 22, 24, 27, 47, 54, 60], with a few ones [22] against training-time poisoning attacks. + +There exist two main approaches providing certified robustness against poisoning data: 1) Randomized-smoothing based methods [22, 35, 46] regard the training-prediction process as an end-to-end function, and treat poisoning attack as a special case of evasion attack; 2) Voting based methods [17, 23] partition training data into subsets and train a sub-classifier on each subset. However, they restrict the attacker on one type of perturbation (nodes, edges, or node features); they are applicable for a particular GNN task; and their robustness guarantees are not $100\%$ accurate. We are the first work to develop a deterministically certified robust GNN against graph poisoning attack with arbitrary kind of perturbations on both node and graph classification tasks. + +# 7. Conclusion + +We investigate the robustness of Graph Neural Networks (GNNs) against graph poisoning attacks and introduce PGNNCert, the first certified defense with deterministic guarantees against arbitrary poisoning perturbations, including modifications to nodes, edges, and node features. PGNNCert employs novel graph division strategies and leverages the message-passing mechanism in GNNs to establish robustness guarantees. Its universality allows it to encompass existing certified defenses as special cases. Experimental evaluations demonstrate that PGNNCert effectively mitigates arbitrary poisoning perturbations, offering superior robustness and efficiency compared to state-of-the-art certified defenses. Future works include extending the proposed defense for federated GNNs [49, 58] and casually explainable GNNs [2] against arbitrary poisoning attacks. + +# 8. Acknowledgment + +We thank all the anonymous reviewers for their valuable feedback and constructive comments. This work is partially supported by the National Science Foundation (NSF) under grant Nos. ECCS-2216926, CNS-2241713, CNS-2331302, CNS-2339686, and the Cisco Research Award. + +# References + +[1] R. Achanta, A. Shaji, K. Smith, A. Lucchi, P. Fua, and Sabine Süssstrunk. Slic superpixels compared to state-of-the-art superpixel methods. IEEE Transactions on Pattern Analysis & Machine Intelligence, 34(11):2274-2282, 2012. 8 +[2] Arman Behnam and Binghui Wang. Graph neural network causal explanation via neural causal models. 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However, recent works show GNNs are vulnerable to training-time poisoning attacks – marginally perturbing edges, nodes, or/and node features of training graph(s) can largely degrade GNNs' testing performance. Most previous defenses against graph poisoning attacks are empirical and are soon broken by adaptive / stronger ones. A few provable defenses provide robustness guarantees, but have large gaps when applied in practice: 1) restrict the attacker on only one type of perturbation; 2) design for a particular GNN architecture or task; and 3) robustness guarantees are not " + }, + { + "bbox": [ + 55, + 270, + 297, + 425 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 55, + 270, + 297, + 425 + ], + "type": "text", + "content": " accurate." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 426, + 298, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 298, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 298, + 547 + ], + "type": "text", + "content": "In this work, we bridge all these gaps by developing PGNNCert, the first certified defense of GNNs against poisoning attacks under arbitrary (edge, node, and node feature) perturbations with deterministic robustness guarantees. Extensive evaluations on multiple node and graph classification datasets and GNNs demonstrate the effectiveness of PGNNCert to provably defend against arbitrary poisoning perturbations. PGNNCert is also shown to significantly outperform the state-of-the-art certified defenses against edge perturbation or node perturbation during GNN training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 567, + 135, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 135, + 580 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 135, + 580 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 587, + 297, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 297, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 297, + 696 + ], + "type": "text", + "content": "Graph Neural Network (GNN) [15, 21, 37, 44, 48, 56] is the leading approach for representation learning on graphs, showing state-of-the-art performance in various graph-related tasks like node classification and graph classification. In node classification, the goal is to predict labels for individual nodes, while in graph classification, the objective is to predict labels for entire graphs. GNNs have significantly advanced applications across fields such as chemistry [14], physics [36, 39], neuroscience [3], and social science [13]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 245, + 555, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 245, + 555, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 245, + 555, + 376 + ], + "type": "text", + "content": "However, various works [6-8, 20, 40, 45, 51, 55, 60, 63] have shown that GNNs are vulnerable to training-time graph poisoning attacks — an attacker perturbs the graph structure during training such that the learnt poisoned GNN model will have low accuracy on predicting new test nodes/graphs. As a graph consists of three components: nodes, their features, and edges connecting the nodes, an attacker is allowed to perturb an individual component or their combinations. For instance, an attacker could inject a few nodes [20, 40], slightly modify the edges [8, 45, 55, 63] on the training graphs, and/or perturb features of certain nodes [63]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 377, + 556, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 377, + 556, + 520 + ], + "spans": [ + { + "bbox": [ + 313, + 377, + 556, + 520 + ], + "type": "text", + "content": "Various empirical defenses [12, 42, 43, 59, 61, 62] have been proposed to mitigate the graph poisoning attack, but were soon broken by adaptive attacks [33]. Most existing certified defenses [16, 19, 22, 24, 47, 54] are against test-time evasion attacks, with a few exceptions [18, 22], leaving certified defenses against poisoning attacks largely unexplored1. However, existing provable defenses face several limitations when applied in practice: 1) all restrict the attacker's capability to only one type of perturbation (e.g., node injection or edge perturbation); 2) they are designed for a particular GNN architecture or GNN task [19]; and 3) their robustness guarantee is probabilistic (i.e., not " + }, + { + "bbox": [ + 313, + 377, + 556, + 520 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 377, + 556, + 520 + ], + "type": "text", + "content": " accurate) [18, 22]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 521, + 557, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 557, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 557, + 677 + ], + "type": "text", + "content": "We propose PGNNCert to address the above limitations. PGNNCert is the first certified defense for GNNs on the two most common node and graph classification tasks against arbitrary poisoning perturbations (i.e., arbitrarily manipulate the nodes, node features, and edges of training graph(s)) with deterministic robustness guarantees. Our defense is inspired by ensemble learning, and consists of three main steps: 1) Divide each training graph into multiple subgraphs and allocate subgraphs of training graph(s) into multiple groups via a hash function; 2) Train a set of node/graph classifiers for each group and build a majority-voting node/graph classifier on the subgraphs; 3) Derive the deterministic robustness guarantee against arbitrary poisoning perturbations." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 313, + 683, + 555, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 683, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 683, + 555, + 713 + ], + "type": "text", + "content": "1We note there exist some certified defense [17, 23, 35, 46] against poisoning attacks but not for the graph data. In addition [18, 22] show they achieve unsatisfactory performance when adapted to graph data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 66, + 702, + 208, + 713 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 208, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 208, + 713 + ], + "type": "text", + "content": "*Corresponding author (bwang70@iit.edu)" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5020" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 287 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 287 + ], + "type": "text", + "content": "Following [24], we adapt two graph division strategies—one is edge-centric and the other is node-centric—to realize our defense. The former strategy map edges, while the latter one map nodes from a given graph into multiple subgraphs. Theoretically, PGNNCert provably predicts the same label for a test node/graph after training on the poisoned training set with arbitrary perturbation whose perturbation size (i.e., the total number of manipulated nodes, nodes with feature perturbations, and edges) is bounded by a threshold, which we call the certified perturbation size. Empirically, we extensively evaluate PGNNCert on multiple graph datasets and multiple node and graph classifiers against arbitrary perturbations, and compared our methods with state-of-the-art certified defenses for node classification against node injection poisoning attack [22], and for graph classification against edge manipulation [17]. Our results show PGNNCert significantly outperforms [22] under node-centric graph division, and outperforms [54] under both graph division methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 288, + 291, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 288, + 291, + 298 + ], + "spans": [ + { + "bbox": [ + 55, + 288, + 291, + 298 + ], + "type": "text", + "content": "Contributions: Our contributions are summarized below:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 300, + 296, + 407 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 56, + 300, + 295, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 300, + 295, + 323 + ], + "spans": [ + { + "bbox": [ + 56, + 300, + 295, + 323 + ], + "type": "text", + "content": "- We develop the first certified defense to robustify GNNs against arbitrary poisoning attack on the training set." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 324, + 296, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 324, + 296, + 358 + ], + "spans": [ + { + "bbox": [ + 56, + 324, + 296, + 358 + ], + "type": "text", + "content": "- We propose two strategies (edge-centric and node-centric) to realize our defense that leverages the unique message-passing mechanism in GNNs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 359, + 295, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 359, + 295, + 383 + ], + "spans": [ + { + "bbox": [ + 56, + 359, + 295, + 383 + ], + "type": "text", + "content": "- Our robustness guarantee is applicable to both node and graph classification tasks and accurate with probability 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 384, + 295, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 384, + 295, + 407 + ], + "spans": [ + { + "bbox": [ + 56, + 384, + 295, + 407 + ], + "type": "text", + "content": "- Our defense treat existing certified defenses as special cases, as well as significantly outperforming them." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 417, + 257, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 417, + 257, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 417, + 257, + 430 + ], + "type": "text", + "content": "2. Background and Problem Definition" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 436, + 222, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 436, + 222, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 436, + 222, + 449 + ], + "type": "text", + "content": "2.1. Graph Neural Network (GNN)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": "Let a graph be " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "G = \\{V, E, \\mathbf{X}\\}" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": ", which consists of the nodes " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": ", node features " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": ", and edges " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": ". We denote " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "u \\in V" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": " as a node, " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "e = (u, v) \\in E" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": " as an edge, and " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_u" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": " as node " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": "'s feature. Let " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "f_\\theta" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": " be the node or graph classifier parameterized by " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": " is the label set, " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "y_v" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "y_G" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": " are the groundtruth label of a node " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": " and a graph " + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 455, + 296, + 527 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": "Node classification: " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": " takes a graph " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": " as input and predicts each node " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "v \\in G" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": " a label " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "\\tilde{y}_v \\in \\mathcal{V}" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "\\tilde{y}_v = f_{\\theta}(G)_v" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": ". Given a training node set " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{tr}} \\subseteq V" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": " with ground-truth labels " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\mathrm{tr}} = \\{y_v, v \\in V_{\\mathrm{tr}}\\}" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": " is learnt by minimizing a loss " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": " between the node predictions " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{y}}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": " and the ground-truth " + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 528, + 296, + 588 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 89, + 594, + 296, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 594, + 296, + 612 + ], + "spans": [ + { + "bbox": [ + 89, + 594, + 296, + 612 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathcal {L} \\left(\\mathbf {y} _ {\\mathrm {t r}}, \\tilde {\\mathbf {y}} _ {\\mathrm {t r}}; \\theta\\right), \\tilde {\\mathbf {y}} _ {\\mathrm {t r}} = \\left\\{f _ {\\theta} (G) _ {v}, v \\in V _ {\\mathrm {t r}} \\right\\} \\tag {1}", + "image_path": "97bf9c8f5597546cbe27e26dbca22c7edccf40a51d1e828f4416fef5aeccf3f5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "spans": [ + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": "Graph classification: " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": " takes a graph " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": " as input and predicts a label " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "\\tilde{y}_G \\in \\mathcal{V}" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": " for the whole graph " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "\\tilde{y}_G = f(G)" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": ". Given a set of training graphs " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": " with ground-truth labels " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\mathrm{tr}} = \\{y_G, G \\in \\mathcal{G}_{\\mathrm{tr}}\\}" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": ". The graph classifier " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": " is learnt by minimizing a loss function " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": " between the predictions on " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": " and the ground-truth " + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{y}}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 619, + 297, + 691 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 91, + 698, + 296, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 698, + 296, + 716 + ], + "spans": [ + { + "bbox": [ + 91, + 698, + 296, + 716 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathcal {L} \\left(\\mathbf {y} _ {\\mathrm {t r}}, \\tilde {\\mathbf {y}} _ {\\mathrm {t r}}; \\theta\\right), \\tilde {\\mathbf {y}} _ {\\mathrm {t r}} = \\left\\{f _ {\\theta} (G), G \\in \\mathcal {G} _ {\\mathrm {t r}} \\right\\} \\tag {2}", + "image_path": "697025aa18589443436e9ea29073a1e7041c74f2152b5138f1cbff17f09f0374.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 72, + 463, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 463, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 463, + 84 + ], + "type": "text", + "content": "2.2. Poisoning Attack on GNNs" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": "In poisoning attacks against GNNs, an attacker can manipulate any training graph " + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "inline_equation", + "content": "G = \\{V,E,\\mathbf{X}\\} \\in \\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": " (For node classification, " + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}} = \\{G\\}" + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": ") into a perturbed one " + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "inline_equation", + "content": "G^{\\prime} = \\{V^{\\prime},E^{\\prime},\\mathbf{X}^{\\prime}\\}" + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": " during training, where " + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "inline_equation", + "content": "V^{\\prime},E^{\\prime},\\mathbf{X}^{\\prime}" + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": " are the perturbed version of " + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "inline_equation", + "content": "V,E" + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": ", respectively. For simplicity, we denote the nodes, edges and features in training graph(s) as " + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "inline_equation", + "content": "\\mathcal{V},\\mathcal{E}" + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 313, + 91, + 555, + 174 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 175, + 553, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 175, + 553, + 198 + ], + "spans": [ + { + "bbox": [ + 313, + 175, + 553, + 198 + ], + "type": "text", + "content": "Edge manipulation: The attacker can 1) inject new edges " + }, + { + "bbox": [ + 313, + 175, + 553, + 198 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{+}" + }, + { + "bbox": [ + 313, + 175, + 553, + 198 + ], + "type": "text", + "content": ", and 2) delete existing edges, denoted as " + }, + { + "bbox": [ + 313, + 175, + 553, + 198 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{-} \\subset \\mathcal{E}" + }, + { + "bbox": [ + 313, + 175, + 553, + 198 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "spans": [ + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": "Node manipulation: The attacker perturbs " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": " by (1) injecting new nodes " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\nu_{+}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": ", whose node feature denoted as " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_{\\nu_{+}}^{\\prime}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": " can be arbitrary, together with the arbitrarily injected new edges " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\nu_{+}} \\subseteq \\{(u,v) \\notin \\mathcal{E}, \\forall u \\in \\mathcal{V}_{+} \\lor v \\in \\mathcal{V}_{+}\\}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": " induced by " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\nu_{+}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": "; and (2) deleting existing nodes " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\nu_{-} \\subset \\nu" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\nu_{-}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": " are deleted, their features " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_{\\nu_{-}} \\subseteq \\mathcal{X}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": " and all connected edges " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\nu_{-}} = \\{(u,v) \\in \\mathcal{E}, \\forall u \\in \\mathcal{V}_{-} \\lor v \\in \\mathcal{V}_{-}\\}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": " are also removed. We denote that for the node classification case, the injected and deleted nodes are not from " + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 200, + 555, + 306 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "text", + "content": "Node feature manipulation: The attacker arbitrarily manipulates features " + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_{\\mathcal{V}_r}" + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "text", + "content": " of a set of representative nodes " + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\nu_{r}" + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "text", + "content": " to be " + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_{\\mathcal{V}_r}^\\prime" + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "text", + "content": " . We also denote the edges connected with nodes " + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\nu_{r}" + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 313, + 308, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\nu_r} = \\{(u,v)\\in \\mathcal{E}:\\forall u\\in \\mathcal{V}_r\\lor v\\in \\mathcal{V}_r\\}" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 356, + 555, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 356, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 356, + 555, + 415 + ], + "type": "text", + "content": "Arbitrary manipulation: The attacker can manipulate a training graphs in " + }, + { + "bbox": [ + 313, + 356, + 555, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 356, + 555, + 415 + ], + "type": "text", + "content": " with an arbitrary combined perturbations on edges, nodes, and node features for each of them. The attacker can manipulate several training graphs at the same time with different combinations of attack." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "spans": [ + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "text", + "content": "For description simplicity, we will use " + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{E}_{+},\\mathcal{E}_{-}\\}" + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "text", + "content": " to indicate the edge manipulation with arbitrary injected edges " + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "inline_equation", + "content": "E_{+}" + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "text", + "content": " and deleted edges " + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{-}" + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}" + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "text", + "content": ". Similarly, we will use " + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{V}_{+},\\mathcal{E}_{\\mathcal{V}_{+}},\\mathcal{X}_{\\mathcal{V}_{+}}^{\\prime},\\mathcal{V}_{-},\\mathcal{E}_{\\mathcal{V}_{-}}\\}" + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "text", + "content": " to indicate the node manipulation, and " + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{V}_r,\\mathcal{E}_{\\mathcal{V}_r},\\mathcal{X}_{\\mathcal{V}_r}^{\\prime}\\}" + }, + { + "bbox": [ + 313, + 416, + 556, + 490 + ], + "type": "text", + "content": " the node feature manipulation. Any combination of the manipulations is inherently well-defined." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 314, + 498, + 427, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 498, + 427, + 509 + ], + "spans": [ + { + "bbox": [ + 314, + 498, + 427, + 509 + ], + "type": "text", + "content": "2.3. Problem Statement" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "text", + "content": "Threat model: Given a node/graph classifier " + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "text", + "content": ", a training graph set " + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "text", + "content": ", the adversary can arbitrarily manipulate a number of the edges, nodes, and node features in any graph of " + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "text", + "content": " such that after training, " + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "text", + "content": " misclassifies target graphs in graph classification or target nodes in node classification. Since we focus on certified defenses, we consider the strongest attack where the adversary has white-box access to " + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "text", + "content": " i.e., it knows all the edges, nodes, and node features in " + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 517, + 556, + 613 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 616, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 616, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 616, + 555, + 640 + ], + "type": "text", + "content": "Defense goal: We aim to build provably robust GNNs against poisoning attacks that:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 314, + 642, + 555, + 689 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 314, + 642, + 489, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 642, + 489, + 653 + ], + "spans": [ + { + "bbox": [ + 314, + 642, + 489, + 653 + ], + "type": "text", + "content": "- has a deterministic robustness guarantee;" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 314, + 654, + 544, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 654, + 544, + 664 + ], + "spans": [ + { + "bbox": [ + 314, + 654, + 544, + 664 + ], + "type": "text", + "content": "- is suitable for both node and graph classification tasks;" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 314, + 665, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 665, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 314, + 665, + 555, + 689 + ], + "type": "text", + "content": "- provably predicts the same label against the arbitrary poisoning perturbation within the certified perturbation size." + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "content": "Our ultimate goal is to obtain the largest-possible certified perturbation size that satisfies all the above conditions." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5021" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 248, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 248, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 248, + 83 + ], + "type": "text", + "content": "3. Our Certified Defense: PGNNCert" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 123, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 123, + 102 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 123, + 102 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 109, + 295, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 109, + 295, + 169 + ], + "spans": [ + { + "bbox": [ + 55, + 109, + 295, + 169 + ], + "type": "text", + "content": "Our method is inspired by previous work [24, 54], which divides a test input into several sub-parts and assembles a voting GNN classifier on the sub-parts. We generalize this idea by designing the dividing strategy tailored to training set. Specifically, it consists of four steps below:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "spans": [ + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": "In the first step, we divide the training graph set into multiple subgraph sets. For each training graph " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "G \\in \\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": " with ground-truth label " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "y_{G} \\in \\mathbf{y}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": ", we divide it into " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": " subgraphs " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "G_{1}, G_{2}, \\ldots, G_{S}" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": " via a hash function and ensure edges in different subgraphs are disjoint. This process is detailed in Section 3.2-3.3. By collecting these subgraphs, we build " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": " sets of subgraphs " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]} = \\{\\mathcal{G}_1, \\mathcal{G}_2, \\ldots, \\mathcal{G}_S\\}" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": ". In each subgraph set " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": ", there exists an exact subgraph " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "G_i" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": " generated from " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": ", and we label " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "G_i" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": " the same label " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "y_{G}" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 169, + 296, + 276 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "type": "text", + "content": "In the second step, we train multiple classifiers with the respective subgraph sets. On each subgraph set " + }, + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i" + }, + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "type": "text", + "content": ", we initialize a classifier " + }, + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "type": "inline_equation", + "content": "f_i" + }, + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "type": "text", + "content": " with weights " + }, + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "type": "inline_equation", + "content": "\\theta_i" + }, + { + "bbox": [ + 55, + 277, + 296, + 312 + ], + "type": "text", + "content": " and train it below:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 319, + 284, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 319, + 284, + 336 + ], + "spans": [ + { + "bbox": [ + 62, + 319, + 284, + 336 + ], + "type": "text", + "content": "Node classifier: " + }, + { + "bbox": [ + 62, + 319, + 284, + 336 + ], + "type": "inline_equation", + "content": "\\min_{\\theta_i}\\mathcal{L}(\\mathbf{y}_{\\mathrm{tr}},\\tilde{\\mathbf{y}}_i;\\theta_i),\\tilde{\\mathbf{y}}_i = \\{f_i(G)_v,v\\in V_{\\mathrm{tr}}\\}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 338, + 288, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 338, + 288, + 355 + ], + "spans": [ + { + "bbox": [ + 62, + 338, + 288, + 355 + ], + "type": "text", + "content": "Graph classifier: " + }, + { + "bbox": [ + 62, + 338, + 288, + 355 + ], + "type": "inline_equation", + "content": "\\min_{\\theta_i}\\mathcal{L}(\\mathbf{y}_{\\mathrm{tr}},\\tilde{\\mathbf{y}}_i;\\theta_i),\\tilde{\\mathbf{y}}_i = \\{f_i(G),G\\in \\mathcal{G}_{\\mathrm{tr}}\\}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "text", + "content": "In the third step, we build the voting-based classifier based on the trained sub-classifiers. Given a test graph " + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "text", + "content": ", we first divide it into " + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "text", + "content": " subgraphs " + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "inline_equation", + "content": "\\{G_1, \\ldots, G_S\\}" + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "text", + "content": " by the same subgraph division method. Then we apply a voting classifier " + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "inline_equation", + "content": "\\bar{f}" + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "text", + "content": ", which assembles the predictions of the trained classifiers " + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "inline_equation", + "content": "f_{[S]}" + }, + { + "bbox": [ + 55, + 361, + 296, + 434 + ], + "type": "text", + "content": " on the subgraphs:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 62, + 437, + 296, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 437, + 296, + 456 + ], + "spans": [ + { + "bbox": [ + 62, + 437, + 296, + 456 + ], + "type": "text", + "content": "Node classifier: " + }, + { + "bbox": [ + 62, + 437, + 296, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{y_v} = \\sum_{i=1}^{S} \\mathbb{I}(f_i(G_i)_v = y_v), \\forall y_v \\in \\mathcal{V}" + }, + { + "bbox": [ + 62, + 437, + 296, + 456 + ], + "type": "text", + "content": " (3)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 62, + 458, + 296, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 458, + 296, + 477 + ], + "spans": [ + { + "bbox": [ + 62, + 458, + 296, + 477 + ], + "type": "text", + "content": "Graph classifier: " + }, + { + "bbox": [ + 62, + 458, + 296, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{y_G} = \\sum_{i=1}^{S} \\mathbb{I}(f_i(G_i) = y_G), \\forall y_G \\in \\mathcal{V}" + }, + { + "bbox": [ + 62, + 458, + 296, + 477 + ], + "type": "text", + "content": " (4)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 483, + 295, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 295, + 508 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 295, + 508 + ], + "type": "text", + "content": "We then define our voting node/graph classifier " + }, + { + "bbox": [ + 55, + 483, + 295, + 508 + ], + "type": "inline_equation", + "content": "\\bar{f}" + }, + { + "bbox": [ + 55, + 483, + 295, + 508 + ], + "type": "text", + "content": " as returning the class with the most vote:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 87, + 514, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 514, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 87, + 514, + 296, + 533 + ], + "type": "text", + "content": "Voting node classifier: " + }, + { + "bbox": [ + 87, + 514, + 296, + 533 + ], + "type": "inline_equation", + "content": "\\bar{f} (G)_v = \\operatorname *{arg\\max}_{y_v\\in \\mathcal{V}}\\mathbf{n}_{y_v}" + }, + { + "bbox": [ + 87, + 514, + 296, + 533 + ], + "type": "text", + "content": " (5)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 87, + 535, + 296, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 535, + 296, + 555 + ], + "spans": [ + { + "bbox": [ + 87, + 535, + 296, + 555 + ], + "type": "text", + "content": "Voting graph classifier: " + }, + { + "bbox": [ + 87, + 535, + 296, + 555 + ], + "type": "inline_equation", + "content": "\\bar{f} (G) = \\operatorname *{arg\\max}_{y_G\\in \\mathcal{Y}}\\mathbf{n}_{y_G}" + }, + { + "bbox": [ + 87, + 535, + 296, + 555 + ], + "type": "text", + "content": " (6)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "spans": [ + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": "In the forth step, we derive the deterministic robustness guarantee for the test graph. We denote " + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "inline_equation", + "content": "y_{a}" + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "inline_equation", + "content": "y_{b}" + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": " as the class with the most vote " + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{y_a}" + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": " and the second-most vote " + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{y_b}" + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": ", respectively. We pick the class with a smaller index if ties exist. Denote " + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}^{\\prime}" + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": " as the perturbed train dataset of " + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}^{\\prime} = \\{\\mathcal{G}_1^{\\prime},\\mathcal{G}_2^{\\prime},\\dots ,\\mathcal{G}_S^{\\prime}\\}" + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": " be the perturbed subgraph sets generated from " + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}^{\\prime}" + }, + { + "bbox": [ + 55, + 561, + 296, + 670 + ], + "type": "text", + "content": " under the same graph division strategy. Then we have the below condition for certified robustness against arbitrary poisoning attacks on GNNs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "Theorem 1 (Sufficient Condition for Certified Robustness). Let " + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "inline_equation", + "content": "y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}}" + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": " be defined above in node classification or graph classification, and let " + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "inline_equation", + "content": "P =" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "\\left\\lfloor \\mathbf{n}_{y_a} - \\mathbf{n}_{y_b} - \\mathbb{I}(y_a > y_b)\\right\\rfloor /2." + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " The voting classifier " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "\\bar{f}" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " trained on " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " guarantees the same prediction on " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " for the target node " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " in node classification or the target graph " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " in graph classification with the poisoned voting classifier " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "\\bar{f}'" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": ", if the number of different sub-classifiers (i.e., different in weights) trained on " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}'" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " under the arbitrary perturbation is bounded by " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": ". I.e.," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 333, + 161, + 555, + 180 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 161, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 333, + 161, + 555, + 180 + ], + "type": "interline_equation", + "content": "\\forall \\mathcal {G} _ {t r} ^ {\\prime}: \\sum_ {i = 1} ^ {S} \\mathbb {I} \\left(\\theta_ {i} \\neq \\theta_ {i} ^ {\\prime}\\right) \\leq P \\Longrightarrow \\bar {f} (G) _ {v} = \\bar {f} ^ {\\prime} (G) _ {v} \\tag {7}", + "image_path": "408161f91fe2f761b9d3a1081e13628d9031c86b022a33dbbc5e7061d72fa873.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 334, + 182, + 555, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 182, + 555, + 201 + ], + "spans": [ + { + "bbox": [ + 334, + 182, + 555, + 201 + ], + "type": "interline_equation", + "content": "\\forall \\mathcal {G} _ {t r} ^ {\\prime}: \\sum_ {i = 1} ^ {S} \\mathbb {I} \\left(\\theta_ {i} \\neq \\theta_ {i} ^ {\\prime}\\right) \\leq P \\Longrightarrow \\bar {f} (G) = \\bar {f} ^ {\\prime} (G) \\tag {8}", + "image_path": "9ac83aaac6aba4ecf521a5ecf50dc4eda831009c99017dc7f0514c2932166ba4.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "spans": [ + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "text", + "content": "Proof is in Appendix A. The above theorem motivates us to design the graph division method such that: 1) the number of different sub-classifiers with trained on " + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}" + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}^{\\prime}" + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "text", + "content": " can be upper bounded (and the smaller the better). 2) the difference between " + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{y_a}" + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{y_b}" + }, + { + "bbox": [ + 313, + 208, + 554, + 279 + ], + "type": "text", + "content": " is as large as possible, ensuring larger certified perturbation size." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 280, + 555, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 280, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 280, + 555, + 316 + ], + "type": "text", + "content": "Next, we introduce our two graph division methods. Figure 2 visualizes the divided subgraphs of the two methods without and with the adversarial manipulation." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 324, + 474, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 324, + 474, + 336 + ], + "spans": [ + { + "bbox": [ + 313, + 324, + 474, + 336 + ], + "type": "text", + "content": "3.2. Edge-Centric Graph Division" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 342, + 554, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 554, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 554, + 437 + ], + "type": "text", + "content": "Our first graph division method is edge-centric. The idea is to divide edges in a graph into different subgraphs, such that each edge is deterministically mapped into only one subgraph. With this strategy, we can bound the number of altered classifiers trained on these subgraphs before and after the arbitrary perturbation (Theorem 2), which facilitates deriving the certified perturbation size (Theorem 3). All proofs are detailed in Appendix A." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 445, + 497, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 445, + 497, + 457 + ], + "spans": [ + { + "bbox": [ + 313, + 445, + 497, + 457 + ], + "type": "text", + "content": "3.2.1 Generating edge-centric subgraphs" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "content": "We follow [24, 54] to use a hash function " + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "content": " (e.g., MD5) to generate the subgraphs for every train graph " + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "inline_equation", + "content": "G \\in \\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "content": ". A hash function takes a bit string as input and outputs an integer (e.g., within a range " + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "inline_equation", + "content": "[0, 2^{128} - 1]" + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "content": "). We use the string of edge or node index as the input to the hash function. For instance, for a node " + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "content": ", its string is denoted as " + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "inline_equation", + "content": "\\operatorname{str}(u)" + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "content": ", while for an edge " + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "inline_equation", + "content": "e = (u, v)" + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "content": ", its string is " + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "inline_equation", + "content": "\\operatorname{str}(u) + \\operatorname{str}(v)" + }, + { + "bbox": [ + 313, + 464, + 554, + 571 + ], + "type": "text", + "content": ", where \"+\" means string concatenation, and str turns the node index into a string and adds \"0\" prefix to align it into a fixed length." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "spans": [ + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "type": "text", + "content": "Assuming " + }, + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "type": "text", + "content": " subgraphs in total, the subgraph index " + }, + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "type": "inline_equation", + "content": "i_e" + }, + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "type": "text", + "content": " of every edge " + }, + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "type": "inline_equation", + "content": "e = (u,v)" + }, + { + "bbox": [ + 313, + 572, + 554, + 596 + ], + "type": "text", + "content": " is defined as2" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 365, + 604, + 555, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 604, + 555, + 616 + ], + "spans": [ + { + "bbox": [ + 365, + 604, + 555, + 616 + ], + "type": "interline_equation", + "content": "i _ {e} = h \\left[ \\operatorname {s t r} (u) + \\operatorname {s t r} (v) \\right] \\bmod S + 1, \\tag {9}", + "image_path": "b9266dccd68f191495a9960db625f7d9317cb518c403418ea877129b599afd09.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "content": "where mod is the module function. Denoting " + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{E}^i" + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "content": " as the set of edges whose subgraph index is " + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{E}^i = \\{\\forall e \\in \\mathcal{E} : i_e = i\\}" + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "content": " subgraphs for " + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "content": " can be built as " + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "inline_equation", + "content": "\\{G_i = (\\mathcal{V}, \\mathcal{E}^i, \\mathbf{X}) : i = 1, 2, \\dots, S\\}" + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "content": ", where edges in different subgraphs are disjoint, i.e., " + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{E}^i \\cap \\mathcal{E}^j = \\emptyset, \\forall i, j \\in \\{1, \\dots, S\\}, i \\neq j" + }, + { + "bbox": [ + 313, + 625, + 554, + 685 + ], + "type": "text", + "content": ". Here, we" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "text", + "content": "2In the undirected graph, we put the node with a smaller index (say " + }, + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "text", + "content": ") first and let " + }, + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "inline_equation", + "content": "h[\\mathrm{str}(v) + \\mathrm{str}(u)] = h[\\mathrm{str}(u) + \\mathrm{str}(v)]" + }, + { + "bbox": [ + 313, + 693, + 554, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5022" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 57, + 541, + 205 + ], + "blocks": [ + { + "bbox": [ + 67, + 57, + 541, + 205 + ], + "lines": [ + { + "bbox": [ + 67, + 57, + 541, + 205 + ], + "spans": [ + { + "bbox": [ + 67, + 57, + 541, + 205 + ], + "type": "image", + "image_path": "1197eebffade3577990074eb19f87cb19868989db80fc628c55d83feb081b71a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 108, + 208, + 500, + 219 + ], + "lines": [ + { + "bbox": [ + 108, + 208, + 500, + 219 + ], + "spans": [ + { + "bbox": [ + 108, + 208, + 500, + 219 + ], + "type": "text", + "content": "Figure 1. Overview of our PGNNCert (use node classification for illustration), which consists of four steps." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 226, + 296, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 226, + 296, + 309 + ], + "spans": [ + { + "bbox": [ + 54, + 226, + 296, + 309 + ], + "type": "text", + "content": "mention that we need to further postprocess the subgraphs for graph classification, in order to derive the robustness guarantee. Particularly, in each subgraph " + }, + { + "bbox": [ + 54, + 226, + 296, + 309 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 54, + 226, + 296, + 309 + ], + "type": "text", + "content": ", we remove all isolated nodes who have no connected edges. This is because although they have no influence on other nodes' representation, their information would still be passed to the global graph embedding aggregation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "text", + "content": "After dividing all training graphs in " + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "text", + "content": ", we combine all generated subgraphs with the same index as a separate subgraph training set: " + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i = \\{G_i, \\forall G \\in \\mathcal{G}_{\\mathrm{tr}}\\}, \\forall i \\in [S]" + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "text", + "content": ". We denote the " + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "text", + "content": " training sets as " + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]} = \\{\\mathcal{G}_1, \\dots, \\mathcal{G}_S\\}" + }, + { + "bbox": [ + 55, + 310, + 296, + 360 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 366, + 294, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 366, + 294, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 366, + 294, + 378 + ], + "type": "text", + "content": "3.2.2 Bounding the number of different sub-classifiers" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "text", + "content": "For a perturbed training set " + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathrm{tr}}^{\\prime}" + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "text", + "content": ", we use the same graph division strategy to generate a set of " + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "text", + "content": " subgraphs sets " + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}^{\\prime} = \\{\\mathcal{G}_1^{\\prime},\\mathcal{G}_2^{\\prime},\\dots ,\\mathcal{G}_T^{\\prime}\\}" + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "text", + "content": ". Then, we can upper bound the number of different classifiers trained on " + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}" + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}^{\\prime}" + }, + { + "bbox": [ + 55, + 384, + 296, + 446 + ], + "type": "text", + "content": " against any individual perturbation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": "Theorem 2 (Bounded Number of Edge-Centric Subgraphs with Altered Predictions under Arbitrary Perturbation). Given any training graph set " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " edge-centric subgraph sets " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": ". A perturbed training set " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{train}^{\\prime}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{train}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " is with arbitrary edge manipulation " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{E}_+, \\mathcal{E}_-\\}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": ", node manipulation " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{V}_+,\\mathcal{E}_{\\mathcal{V}_+},\\mathcal{V}_-, \\mathcal{E}_{\\mathcal{V}_-}\\}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": ", and node feature manipulation " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}_{\\mathcal{V}_r},\\mathcal{V}_r,\\mathcal{E}_{\\mathcal{V}_r}\\}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " on arbitrary graphs in " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": ". Then at most " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "p = |\\mathcal{E}_+| + |\\mathcal{E}_-| + |\\mathcal{E}_{\\mathcal{V}_+}| + |\\mathcal{E}_{\\mathcal{V}_-}| + |\\mathcal{E}_{\\mathcal{V}_r}|" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " node/graph sub-classifiers in " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "f_{[S]}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " are different in weights between training on the subgraph sets " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " and on the perturbed subgraph sets " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{[S]}^{\\prime}" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": ". In other words, " + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq p" + }, + { + "bbox": [ + 55, + 447, + 296, + 593 + ], + "type": "text", + "content": " for both node classification case and graph classification case." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 598, + 234, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 598, + 234, + 610 + ], + "spans": [ + { + "bbox": [ + 55, + 598, + 234, + 610 + ], + "type": "text", + "content": "3.2.3 Deriving the robustness guarantee" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 617, + 296, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 296, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 296, + 653 + ], + "type": "text", + "content": "Based on Theorems 1 and 2, we can derive the certified perturbation size as the maximal perturbation such that Equation 7 or Equation 8 is satisfied. Formally," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": "Theorem 3 (Certified Robustness Guarantee with Edge-Centric Subgraphs against Arbitrary Perturbation). Let " + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "inline_equation", + "content": "f, y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}}" + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": " be defined above for edge-centric subgraphs, and " + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": " be the perturbation size induced by an arbitrary perturbed training set " + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}'" + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}" + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "text", + "content": ". After training on " + }, + { + "bbox": [ + 55, + 654, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}'" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "spans": [ + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}^{\\prime}" + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": ", the voting classifier " + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\bar{f}" + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": " and poisoned classifier " + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\bar{f}'" + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": " guarantee the same prediction for the target node " + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": " in node classification (i.e., " + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\bar{f}(G')_v = \\bar{f}(G)_v" + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": ") or target graph " + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": " in graph classification (i.e., " + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "inline_equation", + "content": "\\bar{f}(G') = \\bar{f}(G)" + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": "), when " + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 225, + 554, + 275 + ], + "type": "text", + "content": " satisfies." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 352, + 284, + 555, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 284, + 555, + 298 + ], + "spans": [ + { + "bbox": [ + 352, + 284, + 555, + 298 + ], + "type": "interline_equation", + "content": "p \\leq P = \\left\\lfloor \\mathbf {n} _ {y _ {a}} - \\mathbf {n} _ {y _ {b}} - \\mathbb {I} \\left(y _ {a} > y _ {b}\\right) \\right\\rfloor / 2. \\tag {10}", + "image_path": "49ddce617b32bcced58fc6176c365436999da374c96110dfc06385687980a688.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 307, + 539, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 307, + 539, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 307, + 539, + 319 + ], + "type": "text", + "content": "Or to say, the maximum certified perturbation size is " + }, + { + "bbox": [ + 313, + 307, + 539, + 319 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 307, + 539, + 319 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 327, + 474, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 327, + 474, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 474, + 339 + ], + "type": "text", + "content": "3.3. Node-Centric Graph Division" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "spans": [ + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": "We observe the robustness guarantee under edge-centric graph division is largely dominated by the edges (i.e., " + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathcal{V}_+}, \\mathcal{E}_{\\mathcal{V}_-}" + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": ") induced by the manipulated nodes " + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_+" + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_-" + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": ", and edges " + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathcal{V}_r}" + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": " by the perturbed node features " + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathcal{V}_r}'" + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": ". This guarantee could be weak against node or node feature manipulation, as the number of edges (i.e., " + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "inline_equation", + "content": "|\\mathcal{E}_{\\mathcal{V}_+}|, |\\mathcal{E}_{\\mathcal{V}_-}|, |\\mathcal{E}_{\\mathcal{V}_r}|" + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": ") could be much larger, compared with the number of the nodes (i.e., " + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}_+|, |\\mathcal{V}_-|, |\\mathcal{V}_r|" + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": "). For instance, an injected node could link with many edges to a given graph in practice, and when the number exceeds " + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 345, + 555, + 549 + ], + "type": "text", + "content": " in Equation 10, the certified robustness guarantee is ineffective. This flaw inspires us to generate subgraphs, where we expect at most one subgraph is affected under every node or node feature manipulation on a training graph (this means all edges of a manipulated node should be in a same subgraph), implying only a training subgraph set is affected. Following [24], we apply a tailored node-centric graph division strategy to achieve our goal." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 559, + 535, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 559, + 535, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 559, + 535, + 571 + ], + "type": "text", + "content": "3.3.1 Generating node-centric directed subgraphs" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": "We use a hash function " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " to generate directed subgraphs for a given train graph " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "G = (\\mathcal{V},\\mathcal{E},\\mathbf{X})\\in \\mathcal{G}_{\\mathrm{tr}}" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": ". Our node-centric graph division strategy as follows: (1) we treat every undirected edge " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "e = (u,v)\\in G" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " as two directed edges for " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "u^3" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": ": the outgoing edge " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "u\\to v" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": " and incoming edge " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "v\\rightarrow u" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": "; (2) for every node " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": ", we compute the subgraph index of its every outgoing edge " + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "inline_equation", + "content": "u\\to v" + }, + { + "bbox": [ + 313, + 578, + 554, + 662 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 370, + 671, + 555, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 671, + 555, + 685 + ], + "spans": [ + { + "bbox": [ + 370, + 671, + 555, + 685 + ], + "type": "interline_equation", + "content": "i _ {u \\rightarrow v} = h [ \\operatorname {s t r} (u) ] \\bmod S + 1. \\tag {11}", + "image_path": "bec25ad8da625e3042b8e0f139f68eb57f110cc0f215a38671f4fff7f4dff0ab.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "inline_equation", + "content": "{}^{3}" + }, + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "text", + "content": " GNNs inherently handles directed graphs with directed message passing - each node only uses its incoming neighbors' message for update." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5023" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 68, + 532, + 320 + ], + "blocks": [ + { + "bbox": [ + 82, + 68, + 532, + 320 + ], + "lines": [ + { + "bbox": [ + 82, + 68, + 532, + 320 + ], + "spans": [ + { + "bbox": [ + 82, + 68, + 532, + 320 + ], + "type": "image", + "image_path": "e02fcf503f1d909e6f94cf97054387813e3f82e4a9e81774b9cc99941c671033.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 172, + 321, + 438, + 331 + ], + "lines": [ + { + "bbox": [ + 172, + 321, + 438, + 331 + ], + "spans": [ + { + "bbox": [ + 172, + 321, + 438, + 331 + ], + "type": "text", + "content": "(b) Node-Centric Graph Division against edge injection and node injection attacks" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 335, + 555, + 368 + ], + "lines": [ + { + "bbox": [ + 55, + 335, + 555, + 368 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 555, + 368 + ], + "type": "text", + "content": "Figure 2. Illustration of our edge-centric and node-centric graph division strategies for node classification. We use edge injection and node injection poisoning attacks to show the bounded number of altered predictions on the generated subgraphs after the attack. Figures 8-9 in Appendix also show other attacks and on graph classification." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 375, + 296, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 375, + 296, + 387 + ], + "spans": [ + { + "bbox": [ + 57, + 375, + 296, + 387 + ], + "type": "text", + "content": "Note outgoing edges of " + }, + { + "bbox": [ + 57, + 375, + 296, + 387 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 57, + 375, + 296, + 387 + ], + "type": "text", + "content": " are mapped in the same subgraph." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "spans": [ + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": "We use " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{E}}_i" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": " to denote the set of directed edges whose subgraph index is " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{E}}_i = \\{\\forall u \\to v \\in \\mathcal{E} : i_{u \\to v} = i\\}" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": ". Then, we can construct " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": " directed subgraphs for " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "\\vec{G}_i = (\\mathcal{V}, \\vec{\\mathcal{E}}_i, \\mathbf{X}), \\forall i \\in [1, S]" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": ". After generating subgraphs for all training graphs, we combine all subgraphs with the same index as a separate subgraph set: " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_i = \\{\\vec{G}_i, \\forall G \\in \\mathcal{G}_{\\mathrm{tr}}\\}, \\forall i \\in [S]" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": ". We denote the " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": " training sets as " + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]} = \\{\\vec{\\mathcal{G}}_1, \\dots, \\vec{\\mathcal{G}}_S\\}" + }, + { + "bbox": [ + 55, + 387, + 296, + 475 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "spans": [ + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "type": "text", + "content": "Here, we mention that we need to further postprocess the subgraphs for graph classification, in order to derive the robustness guarantee. Particularly, in each subgraph " + }, + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "type": "inline_equation", + "content": "\\vec{G}_i" + }, + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "type": "text", + "content": ", we remove all other nodes whose subgraph index is not " + }, + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "type": "text", + "content": ". This is because although they have no influence on other nodes' representation, their information would still be passed to the global graph embedding aggregation. To make up the loss of connectivity between nodes and simulate the aggregation, we add an extra node with a zero feature, and add an outgoing edge from every node with index " + }, + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 54, + 475, + 296, + 594 + ], + "type": "text", + "content": " to it." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 605, + 294, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 294, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 294, + 617 + ], + "type": "text", + "content": "3.3.2 Bounding the number of different sub-classifiers" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "text", + "content": "For a perturbed training set " + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{tr}}^{\\prime}" + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "text", + "content": ", we use the same graph division strategy to generate a set of " + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "text", + "content": " directed subgraph sets " + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]}^{\\prime} = \\{\\vec{\\mathcal{G}}_1^{\\prime},\\vec{\\mathcal{G}}_2^{\\prime},\\dots ,\\vec{\\mathcal{G}}_T^{\\prime}\\}" + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "text", + "content": ". We first show the theoretical result on bounding the number of different trained classifiers on " + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]}" + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]}^{\\prime}" + }, + { + "bbox": [ + 55, + 625, + 296, + 687 + ], + "type": "text", + "content": " against any individual perturbation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "Theorem 4 (Bounded Number of Node-Centric Subgraphs with Altered Predictions under Arbitrary Perturbation). Let" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr}, v, G, \\mathcal{E}_+, \\mathcal{E}_-, \\mathcal{V}_+, \\mathcal{V}_-, \\mathcal{V}_r" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " be defined in Theorem 2, and " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]}, \\vec{\\mathcal{G}}_{[S]}'" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " contain directed subgraph sets under the node-centric graph division. Then, at most " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\bar{p} = 2|\\mathcal{E}_+| + 2|\\mathcal{E}_-| + |\\mathcal{V}_+| + |\\mathcal{V}_-| + |\\mathcal{V}_r|" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " trained node classifiers in " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "f_{[S]}" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " are different in weights after training on " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]}" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " and on " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]}'" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": ". In other words, " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq \\bar{p}" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " for any target node " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "v \\in G" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " in node classification. Meanwhile, at most " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\bar{p} = |\\mathcal{E}_+| + |\\mathcal{E}_-| + |\\mathcal{V}_+| + |\\mathcal{V}_-| + |\\mathcal{V}_r|" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " trained graph classifiers in " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "f_{[S]}" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " are different in weights after training on " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]}" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " and on " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\vec{\\mathcal{G}}_{[S]}'" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": ". In other words, " + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{S} \\mathbb{I}(\\theta_i \\neq \\theta_i') \\leq \\bar{p}" + }, + { + "bbox": [ + 313, + 374, + 556, + 510 + ], + "type": "text", + "content": " in graph classification." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 517, + 493, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 493, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 493, + 529 + ], + "type": "text", + "content": "3.3.3 Deriving the robustness guarantee" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 536, + 555, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 555, + 559 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 555, + 559 + ], + "type": "text", + "content": "Based on Theorem 1 and Theorem 4, we can derive the certified perturbation size formally stated below" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "spans": [ + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": "Theorem 5 (Certified Robustness Guarantee with Node-Centric Subgraphs against Arbitrary Perturbation). Let " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "f, y_{a}, y_{b}, \\mathbf{n}_{y_{a}}, \\mathbf{n}_{y_{b}}^{4}" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": " be defined above for node-centric subgraphs, and " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "\\bar{p}" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": " be the perturbation size induced by an arbitrary perturbed graph " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "G'" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": ". With a probability " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": ", the voting classifier " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "\\bar{f}" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": " guarantees the same prediction on both " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "G'" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": " for the target node " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": " in node classification (i.e., " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "\\bar{f}(G')_{v} = \\bar{f}(G)_{v}" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": ") or the target graph " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": " in graph classification (i.e., " + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "inline_equation", + "content": "\\bar{f}(G') = \\bar{f}(G)" + }, + { + "bbox": [ + 313, + 560, + 556, + 670 + ], + "type": "text", + "content": "), if" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 352, + 677, + 555, + 691 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 677, + 555, + 691 + ], + "spans": [ + { + "bbox": [ + 352, + 677, + 555, + 691 + ], + "type": "interline_equation", + "content": "\\bar {p} \\leq P = \\left\\lfloor \\mathbf {n} _ {y _ {a}} - \\mathbf {n} _ {y _ {b}} - \\mathbb {I} \\left(y _ {a} > y _ {b}\\right) \\right\\rfloor / 2. \\tag {12}", + "image_path": "9ed9e27082a4ee0edd64e212d3279ebb2775b4706541440562c0928e8ff22bce.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "text", + "content": "4Note that " + }, + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{y_a},\\mathbf{n}_{y_b}" + }, + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "text", + "content": " have different values with those in edge-centric graph division. Here we use the same notation for description brevity." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5024" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 137, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 137, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 137, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 178, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 178, + 104 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 178, + 104 + ], + "type": "text", + "content": "4.1. Experiments Settings" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "spans": [ + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "text", + "content": "Datasets: We use four node classification datasets (Cora-ML [31], CiteSeer [38], PubMed [38], Amazon-C [57]) and four graph classification datasets (AIDS [34], MUTAG [9], PROTEINS [5], and DD [10]) for evaluation. In each dataset, we take " + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "text", + "content": " nodes (for node classification) or " + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "text", + "content": " graphs (for graph classification) as the training set, " + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "text", + "content": " as the validation set and " + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 55, + 109, + 297, + 205 + ], + "type": "text", + "content": " nodes/graph as the test set. Table 5 in Appendix shows the basic statistics of them." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 209, + 296, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 209, + 296, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 296, + 281 + ], + "type": "text", + "content": "GNN classifiers and PGNNCert training: We adopt three well-known GNNs as the base node/graph classifiers: GCN [21], GSAGE [15] and GAT [44]. We denote the two versions of PGNNCert under edge-centric and node-centric graph division as PGNNCert-E and PGNNCert-N, respectively. By default, we use GCN as the node/graph classifier." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "text", + "content": "Evaluation metric: Following existing works [22, 47, 54], we use the certified node/graph accuracy at perturbation size as the evaluation metric. Given a perturbation size " + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "text", + "content": " and test nodes/graphs, certified node/graph accuracy at " + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "text", + "content": " is the fraction of test nodes/graphs that are accurately classified by the voting node/graph classifier and its certified perturbation size is no smaller than " + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "text", + "content": ". Note that the standard node/graph accuracy is achieved when over " + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "inline_equation", + "content": "p = 0" + }, + { + "bbox": [ + 55, + 284, + 296, + 380 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "type": "text", + "content": "Parameter setting: PGNNCert has two hyperparameters: the hash function " + }, + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "type": "text", + "content": " and the number of subgraphs " + }, + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "type": "text", + "content": ". By default, we use MD5 as the hash function and set " + }, + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "type": "inline_equation", + "content": "S = 50,60" + }, + { + "bbox": [ + 55, + 384, + 296, + 443 + ], + "type": "text", + "content": " respectively for node and graph classification, considering their different graph sizes. We also study the impact of them." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "type": "text", + "content": "Compared baselines: As PGNNCert encompasses existing defenses as special cases, we can compare PGNNCert with them against less types of perturbation. Here, we choose the sparse-smoothing RS [4], Bagging [17] and Bi-RS [22] as compared baselines in face of node injection poisoning attack on node classification task. For Bi-RS, We adopt the " + }, + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "type": "inline_equation", + "content": "p_e = 0.2" + }, + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "type": "inline_equation", + "content": "p_n = 0.9" + }, + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "type": "inline_equation", + "content": "N = 1000" + }, + { + "bbox": [ + 55, + 447, + 296, + 555 + ], + "type": "text", + "content": " setting as described, and test both include and exclude methods. We also use Bagging for comparison on graph classification." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 562, + 234, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 234, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 234, + 574 + ], + "type": "text", + "content": "4.2. Experiment Results on PGNNCert" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 579, + 296, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 579, + 296, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 579, + 296, + 628 + ], + "type": "text", + "content": "Main results: Figures 3-4 show the certified node accuracy and Figures 5-6 show the certified graph accuracy at perturbation size " + }, + { + "bbox": [ + 55, + 579, + 296, + 628 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 579, + 296, + 628 + ], + "type": "text", + "content": " w.r.t. " + }, + { + "bbox": [ + 55, + 579, + 296, + 628 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 579, + 296, + 628 + ], + "type": "text", + "content": " under the two graph division strategies, respectively. We have the following observations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 714 + ], + "type": "text", + "content": "- Both PGNNCert-E and PGNNCert-N can tolerate the perturbation size up to 25 and 30, on the node and graph classification datasets. This means PGNNCert-E can defend against a total of 25 (30) arbitrary edges, while PGNNCert-N against a total of 25 (30) arbitrary edges and nodes caused by the arbitrary perturbation, on the node (graph) classification datasets, respectively. Note" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 316, + 96, + 556, + 185 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 555, + 93 + ], + "type": "text", + "content": "Table 1. Node/graph accuracy of normally trained GNN and of PGNNCert with GNN trained on the subgraphs." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 96, + 556, + 185 + ], + "lines": [ + { + "bbox": [ + 316, + 96, + 556, + 185 + ], + "spans": [ + { + "bbox": [ + 316, + 96, + 556, + 185 + ], + "type": "table", + "html": "
    DatasetGCNPGNNCertGSAGEPGNNCertGATPGNNCert
    -E-N-E-N-E-N
    Cora-ML0.730.680.680.670.650.680.740.690.69
    Citeseer0.660.670.670.690.680.680.700.670.67
    Pubmed0.860.830.850.840.840.850.850.850.84
    Amazon-C0.810.810.810.820.780.800.830.780.80
    AIDS0.990.880.960.970.940.950.960.930.96
    MUTAG0.710.640.640.700.630.640.710.650.65
    Proteins0.820.810.780.830.800.810.820.780.77
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    ", + "image_path": "18122e315a2faffc8ae353a66606047550f88043c3110a856dd6e8bdd352492c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 322, + 195, + 555, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 195, + 555, + 231 + ], + "spans": [ + { + "bbox": [ + 322, + 195, + 555, + 231 + ], + "type": "text", + "content": "that node classification datasets have several orders of more nodes/edges than graph classification datasets, hence PGNNCert can tolerate more perturbations on them." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 232, + 555, + 314 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "spans": [ + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "type": "text", + "content": " acts as the robustness-accuracy tradeoff. That is, a larger (smaller) " + }, + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "type": "text", + "content": " yields a higher (lower) certified perturbation size, but a smaller (higher) normal accuracy (" + }, + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "type": "inline_equation", + "content": "p = 0" + }, + { + "bbox": [ + 314, + 232, + 553, + 266 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 267, + 555, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 267, + 555, + 314 + ], + "spans": [ + { + "bbox": [ + 313, + 267, + 555, + 314 + ], + "type": "text", + "content": "- In PGNNCert-N, the guaranteed perturbed nodes can have infinite edges. This implies that PGNNCert-N has better robustness than PGNNCert-E against the perturbed edges by node/node feature manipulation." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 316, + 555, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 555, + 365 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 555, + 365 + ], + "type": "text", + "content": "Impact of base GNN classifiers: Figures 10-11 and Figures 12-13 in Appendix show the certified accuracy using GSAGE and GAT as the base classifier, respectively. We have similar observations as those results with GCN." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 369, + 554, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 554, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 554, + 441 + ], + "type": "text", + "content": "Impact of hash function: Figures 14-17 show the certified node/edge accuracy of PGNNCert-E and PGNNCert-N with different hash functions. We observe that our certified accuracy and certified perturbation size are almost the same in all cases. This reveals our PGNNCert is insensitive to the hash function, and [54] draws a similar conclusion." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 444, + 554, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 554, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 554, + 552 + ], + "type": "text", + "content": "Impact of subgraphs on normal accuracy: We test the normal accuracy of (not) using subgraphs to train the GNN classifier. Table 1 shows the test node/graph accuracy of normally trained GNN without sburgraphs and PGNNCert with GNN trained on the subgraphs. We observe that the accuracy of PGNNCert is " + }, + { + "bbox": [ + 313, + 444, + 554, + 552 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 313, + 444, + 554, + 552 + ], + "type": "text", + "content": " smaller than that of normally trained GNN in almost all cases, and in some cases even larger. This implies the augmented subgraphs for training marginally affects the normal test accuracy." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 559, + 533, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 559, + 533, + 572 + ], + "spans": [ + { + "bbox": [ + 313, + 559, + 533, + 572 + ], + "type": "text", + "content": "4.3. Comparison Results with SOTA Baselines" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 578, + 555, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 578, + 555, + 615 + ], + "spans": [ + { + "bbox": [ + 313, + 578, + 555, + 615 + ], + "type": "text", + "content": "In this section, we compare PGNNCert with SOTA defenses (Bi-RS [22], RS [4], Bagging [17]) against node injection poisoning attacks and graph structure poisoning attacks [17]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "content": "Results for node classification against node injection poisoning attacks: We follow Bi-RS [22] by setting the injected nodes' degrees as " + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\tau = 5" + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "content": " and show the certified node accuracy with varying number of injected nodes. Figure 7 shows the comparison results. We can see PGNNCert-E has better certified accuracy than RS, Bagging and Bi-RS-Include, but it is worse than Bi-RS-Exclude. This aligns with our assumption on its weakness against node-relevant attack. 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Certified graph accuracy of our PGNNCert and Bagging against edge perturbations." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 96, + 294, + 167 + ], + "lines": [ + { + "bbox": [ + 56, + 96, + 294, + 167 + ], + "spans": [ + { + "bbox": [ + 56, + 96, + 294, + 167 + ], + "type": "table", + "html": "
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    ", + "image_path": "1e2a4993159928988e033b4fa9eee7e802353678f6a7df70e5ae2bc7c768a9f5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 269, + 296, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 269, + 296, + 328 + ], + "spans": [ + { + "bbox": [ + 55, + 269, + 296, + 328 + ], + "type": "text", + "content": "Results for graph classification against graph poisoning attacks: Table 2 shows the certified graph accuracies of PGNNCert and Bagging against edge perturbations on graph classification tasks. PGNNCert outperforms Bagging, especially when the perturbation size is larger." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 339, + 125, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 339, + 125, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 125, + 350 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "spans": [ + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "text", + "content": "Evaluation on CV datasets. We also test a benchmark superpixel graph CIFAR10 in computer vision [11] for graph classification, to show the generality of our defense. CIFAR10 is an image classification dataset, which is converted into graphs using the SLIC superpixels [1]. Each node has the superpixel coordinates as the feature and each superpixel graph has a label. Results in the default setting are shown in Table 3, where we see PGNNCert can obtain about " + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 55, + 359, + 296, + 467 + ], + "type": "text", + "content": " certified accuracy when 3 arbitrary edges are perturbed." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "text", + "content": "PGNNCert against optimization-based attacks. We first emphasize that PGNNCert is provably robust against all (known and unknown) attacks, when their perturbation budget is within the derived bound (in Eqn 10 or Eqn 12), regardless of the attack knowledge of PGNNCert. Here, we test PGNNCert-N against Metattack [63] when its perturbation size " + }, + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "text", + "content": " is larger than the derived certified perturbation size " + }, + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "inline_equation", + "content": "P = 25" + }, + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "text", + "content": " (with certified accuracy 0.588) on Cora-ML with " + }, + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "inline_equation", + "content": "S = 60" + }, + { + "bbox": [ + 55, + 471, + 296, + 602 + ], + "type": "text", + "content": ". Results are shown in Table 4. We see PGNNCert-N can achieve 0.661 accuracy of defending against Metattack even when it perturbs 40 edges and nodes in total." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": "Limitations. Despite the effectiveness of PGNNCert, its inefficiency remains a main limitation for large GNNs. PGNNCert trains " + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": " classifiers on " + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": " subgraphs and uses " + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": " subgraphs for certification. It may incur a training/certification complexity that is " + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": " times of standard GNN training/testing. This overhead could be significant when PGNNCert is applied to large GNNs. On the other hand, we note that the " + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": " classifiers can be trained in parallel once obtaining the " + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "text", + "content": " subgraphs after graph division." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 72, + 400, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 400, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 400, + 83 + ], + "type": "text", + "content": "6. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 91, + 555, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 295 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 295 + ], + "type": "text", + "content": "Adversarial attacks on GNNs: Existing attacks to GNNs can be classified as graph evasion attacks [8, 25, 26, 29, 30, 32, 50-53, 55, 64] and poisoning attacks [8, 28, 40, 41, 45, 55, 60, 63, 63]. For instance, [8] leveraged reinforcement learning techniques to design evasion attacks to both graph classification and node classification via modifying the graph structure. Most attacks require the attacker fully or partially knows the GNN model, while [32, 50] relaxing this to only have black-box access, i.e., only query the GNN model API. For example, [50] formulates the black-box attack to GNNs as an online optimization problem with bandit feedback and provably obtains a sublinear query number. Furthermore, [25] generalizes the black-box evasion attack on explainable GNNs. In the realm of graph poisoning attacks, [55] proposed a MinMax attack to GNNs based on gradient-based optimization, while [63] introduced Metattack that perturbs the entire graph using meta learning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 298, + 556, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 298, + 556, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 298, + 556, + 346 + ], + "type": "text", + "content": "Certified robustness against graph poisoning graphs: Most existing certified defenses for GNNs are against test-time evasion attacks [16, 19, 22, 24, 27, 47, 54, 60], with a few ones [22] against training-time poisoning attacks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 346, + 556, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 346, + 556, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 556, + 502 + ], + "type": "text", + "content": "There exist two main approaches providing certified robustness against poisoning data: 1) Randomized-smoothing based methods [22, 35, 46] regard the training-prediction process as an end-to-end function, and treat poisoning attack as a special case of evasion attack; 2) Voting based methods [17, 23] partition training data into subsets and train a sub-classifier on each subset. However, they restrict the attacker on one type of perturbation (nodes, edges, or node features); they are applicable for a particular GNN task; and their robustness guarantees are not " + }, + { + "bbox": [ + 313, + 346, + 556, + 502 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 313, + 346, + 556, + 502 + ], + "type": "text", + "content": " accurate. We are the first work to develop a deterministically certified robust GNN against graph poisoning attack with arbitrary kind of perturbations on both node and graph classification tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 512, + 388, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 512, + 388, + 525 + ], + "spans": [ + { + "bbox": [ + 314, + 512, + 388, + 525 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 532, + 556, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 532, + 556, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 532, + 556, + 712 + ], + "type": "text", + "content": "We investigate the robustness of Graph Neural Networks (GNNs) against graph poisoning attacks and introduce PGNNCert, the first certified defense with deterministic guarantees against arbitrary poisoning perturbations, including modifications to nodes, edges, and node features. PGNNCert employs novel graph division strategies and leverages the message-passing mechanism in GNNs to establish robustness guarantees. Its universality allows it to encompass existing certified defenses as special cases. Experimental evaluations demonstrate that PGNNCert effectively mitigates arbitrary poisoning perturbations, offering superior robustness and efficiency compared to state-of-the-art certified defenses. Future works include extending the proposed defense for federated GNNs [49, 58] and casually explainable GNNs [2] against arbitrary poisoning attacks." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5027" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 161, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 161, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 161, + 85 + ], + "type": "text", + "content": "8. Acknowledgment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 297, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 297, + 152 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 297, + 152 + ], + "type": "text", + "content": "We thank all the anonymous reviewers for their valuable feedback and constructive comments. This work is partially supported by the National Science Foundation (NSF) under grant Nos. 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In KDD, 2018. 8" + } + ] + } + ], + "index": 34 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5029" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/f031c8e4-7831-43c8-a97d-74d4fb079432_content_list.json b/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/f031c8e4-7831-43c8-a97d-74d4fb079432_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a08b29832035ded31cf01a678d080fb0e56be30c --- /dev/null +++ b/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/f031c8e4-7831-43c8-a97d-74d4fb079432_content_list.json @@ -0,0 +1,2055 @@ +[ + { + "type": "text", + "text": "Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators", + "text_level": 1, + "bbox": [ + 125, + 128, + 870, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bohan Xiao $^{1*}$ , Peiyong Wang $^{2*}$ , Qisheng He $^{1}$ , Ming Dong $^{1}$", + "bbox": [ + 263, + 202, + 735, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Department of Computer Science, Wayne State University $^{1}$ , Detroit, Michigan, USA \nDepartment of Mathematics, Wayne State University $^{2}$ , Detroit, Michigan, USA", + "bbox": [ + 161, + 222, + 833, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{gk6511, pywang, qisheng.he, mdong}@wayne.edu", + "bbox": [ + 297, + 258, + 694, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 308, + 326, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image-to-Image (I2I) translation involves converting an image from one domain to another. Deterministic I2I translation, such as in image super-resolution, extends this concept by guaranteeing that each input generates a consistent and predictable output, closely matching the ground truth (GT) with high fidelity. In this paper, we propose a denoising Brownian bridge model with dual approximators (Dualapprox Bridge), a novel generative model that exploits the Brownian bridge dynamics and two neural network-based approximators (one for forward and one for reverse process) to produce faithful output with negligible variance and high image quality in I2I translations. Our extensive experiments on benchmark datasets including image generation and super-resolution demonstrate the consistent and superior performance of Dual-approx Bridge in terms of image quality and faithfulness to GT when compared to both stochastic and deterministic baselines. Project page and code: https://github.com/bohan95/dual-app-bridge", + "bbox": [ + 89, + 340, + 485, + 613 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 641, + 220, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image-to-Image (I2I) translation is a significant area of research with broad applications across academia and industry. It involves transforming an image from one domain to another while preserving essential features. Key tasks in this field include generating realistic images from semantic labels [24, 40, 42, 57], transforming segmentation masks into photo-like outputs [40, 47, 54], and enhancing image quality through super-resolution [8, 27, 52].", + "bbox": [ + 89, + 666, + 482, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among the wide range of applications, some I2I tasks particularly benefit from deterministic models. For instance, in super-resolution, the goal is to translate a low-resolution image into a high-resolution one while accurately preserving fine details. This task, as shown in recent studies [13, 14], requires consistency and high faithfulness to", + "bbox": [ + 89, + 787, + 482, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ground true (GT) because for a given low-resolution image, there is typically one \"correct\" high-resolution output that should be produced. In such an I2I task, we note that faithfulness or fidelity is to the individual GT, not just to the distribution of GT. Any variability in the generated output could result in artifacts or loss of critical information, making stochastic approaches less desirable. Similarly, in tasks such as denoising [6, 51] or inpainting [4, 39], where missing or noisy parts of an image need to be restored, a deterministic approach is preferred.", + "bbox": [ + 511, + 310, + 905, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generative Adversarial Networks (GANs) [16] have been instrumental in advancing I2I translation, with models like Pix2Pix [24] and CycleGAN[57] demonstrating impressive results. GANs are deterministic during inference, producing the same output for a given input, which is advantageous for tasks requiring faithfulness. However, GANs often struggle to generate high-quality images, frequently resulting in blurriness and artifacts [1, 21].", + "bbox": [ + 511, + 462, + 905, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models, such as Denoising Diffusion Probabilistic Models (DDPM) [19] and Latent Diffusion Models (LDM) [40], generate high-quality images by progressively adding noise to images and learning the reverse process. Bridge models, such as Brownian bridge diffusion models [32, 47], utilize Stochastic Differential Equations (SDEs) to directly interpolate between input and output distributions, allowing precise control over transformations [40, 42]. This approach improves analytical tractability, making bridge models well suited for I2I translations. However, the inherent stochasticity in these models (see Figure 1(a)) complicates tasks where faithful results are required (e.g., image super-resolution and image reconstruction). Unlike traditional diffusion models [19, 40, 43], which start from noise and gradually denoise the input to generate an output, bridge models start from structured data and interpolate between input and output distributions. This difference means that deterministic methods like Probability Flow Ordinary Differential Equations (PF-ODEs) [43], when applied to bridge models, can lead to blurry images [43, 54], resulting in degraded model performance (see Figure 1(b)).", + "bbox": [ + 511, + 583, + 905, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Both authors contributed equally to this research.", + "bbox": [ + 107, + 886, + 375, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28232", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cb296ffb4c735014a23dbf5b506191326b9121b670048d8e001bc8cd999388e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 89, + 297, + 183 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/54b3dde56994761efff1bffa25e7b2f88bc35be5ec414ad62ae473a3a7c37833.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 297, + 90, + 500, + 183 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2998782fd0cc74bd5b985ad6a56d2581c019239594d448d738a9e56a660b570a.jpg", + "image_caption": [ + "(a)", + "(c)", + "Figure 1. Sampling comparison between SDE-based sampler, PF-ODE-based sampler, and Dual-approx Bridge. The circular area within the dashed circle indicates where the SDE-based sampling outputs land. (a) SDE-based Sampling: diverse outputs of high image quality. (b) PF-ODE-based Sampling: deterministic outputs lack of fine details of ground truth (GT). (c) Dual-approx Bridge Sampling: deterministic output with fine details of GT." + ], + "image_footnote": [], + "bbox": [ + 94, + 193, + 297, + 286 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5b22709f62ec9e99b98dd5c914b3e019b7352594c39da6422c5d618a8e7e005f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 299, + 198, + 493, + 276 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, there is a growing need for deterministic models that can preserve both image quality and faithfulness in I2I translations.", + "bbox": [ + 89, + 415, + 483, + 459 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To resolve this dilemma in the pursuit of deterministic sampling with both high image quality and fidelity, in this paper we propose a denoising Brownian bridge model with Dual Approximators (abbreviated as \"Dual-approx Bridge\"), a generative model that exploits the Brownian bridge structure to produce faithful output with negligible variance and with an image quality better than or comparable to that generated by SDE-based samplers. More specifically, in the SDE-based structure of a Brownian bridge with both forward and corresponding reverse Brownian motions, we train a neural network in the forward diffusive process to estimate the score function and the initial state in the diffusive iteration. Meanwhile, in the reverse process of the Brownian bridge, a second neural network is trained to approximate the white noise scaled to the time step increment. Here, we emphasize that in deterministic I2I, our goal is to generate a unique output from a given input, rather than translating probability distributions, as shown in Figure 1(c). The major contributions of this work are as follows:", + "bbox": [ + 89, + 460, + 483, + 762 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To our best knowledge, Dual-approx Bridge is the first generative model that exploits the Brownian bridge structure to produce faithful output with negligible variance and high image quality for deterministic I2I translations. This is achieved through a novel design of a pair of approximators, trained in the forward and reverse diffusive processes, respectively.", + "- In Dual-approx Bridge, the reverse approximator optimizes the reverse denoising process and presents an opti" + ], + "bbox": [ + 89, + 763, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mal deterministic route for the generative process. From a theoretical perspective, we analyze our model in a general setting where the white noise may take any time-dependent variance.", + "bbox": [ + 524, + 90, + 903, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Through extensive experiments on benchmark datasets including image generation and super-resolution, we demonstrate the consistent and superior performance of Dual-approx Bridge on image quality and faithfulness to GT when compared to state-of-the-art (SOTA) GAN-based and diffusion-based I2I models.", + "bbox": [ + 513, + 152, + 906, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 253, + 655, + 270 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we briefly review the related literature, including image-to-image translation, GAN Models, Diffusion Models, and Bridge Models.", + "bbox": [ + 511, + 280, + 905, + 325 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image-to-Image Translation", + "text_level": 1, + "bbox": [ + 511, + 334, + 764, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image-to-image (I2I) translation has become a core task in computer vision [1, 21, 36], focused on learning mappings between the source and target image domains for applications such as style transfer [15] and colorization [9]. Traditional methods, including Pix2Pix [24] and CycleGAN[57], utilize GAN-based architectures to translate images and support diverse I2I tasks by capturing domain-specific features, though challenges remain in maintaining high quality across complex domains [5, 41]. Deterministic I2I translation builds on this by ensuring that each input produces a consistent, predictable output — an essential requirement in fields like medical imaging [28], where precision and reproducibility are crucial. In tasks such as super-resolution [12] or denoising [46], deterministic models can enhance image resolution and clarity without introducing variations that could adversely affect analysis or interpretation.", + "bbox": [ + 511, + 356, + 906, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Brown Bridge", + "text_level": 1, + "bbox": [ + 511, + 606, + 658, + 622 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The Brownian Bridge (BB) [32, 47] is a fundamental stochastic process that models a constrained Brownian motion, where the trajectory is conditioned on fixed start and end points. Unlike an unconstrained Wiener process, which evolves freely, a Brownian bridge interpolates between two known states while maintaining stochastic variations. This property makes it particularly useful in probabilistic modeling, including image-to-image (I2I) translation, conditional generative modeling, and stochastic optimal transport.", + "bbox": [ + 511, + 628, + 905, + 765 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Generative Adversarial Networks", + "text_level": 1, + "bbox": [ + 511, + 773, + 808, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GANs [16] have been pivotal in advancing I2I translation by learning mappings between image domains through adversarial training. One foundational model, Pix2Pix [24], introduced a conditional GAN approach for paired I2I tasks, enabling applications like colorization[7] and semantic label-to-photo translation[24]. For unpaired I2I tasks, CycleGAN [57] employs cycle consistency, allowing the", + "bbox": [ + 511, + 794, + 905, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28233", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9503b4cf7d2d3500a3e91a441eb8dedbca33ed9b29064bf543dd282d95d0b7d8.jpg", + "image_caption": [ + "Figure 2. Training process of the two approximators (top-left: forward diffusive process, bottom-left: reverse diffusive process). Right: Sampling workflow with both approximators in action." + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 883, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "model to translate images across domains without requiring paired samples. However, GANs often face artifacts in generated images [5, 41, 50]. Such limitations in image quality, combined with the common challenges of training instability, make GANs less suitable for applications demanding both quality and faithfulness.", + "bbox": [ + 89, + 340, + 483, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.4. Diffusion and Bridge Models", + "text_level": 1, + "bbox": [ + 89, + 440, + 349, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models have established themselves as a leading approach in generative modeling [11] due to their ability to produce high-quality, realistic images through a gradual denoising process. DDPM [20] pioneered this approach, modeling image generation as a series of iterative steps in which random noise is gradually refined into a structured target image. The process results in exceptionally high-quality images with reduced artifacts, often surpassing GANs. LDMs [40] further refined DDPM by focusing on a latent space rather than a pixel space, making the generation process more efficient.", + "bbox": [ + 88, + 462, + 482, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To model the denoising process, diffusion models can rely on two distinct mathematical frameworks: SDEs and PF-ODEs [43]. SDEs, characterized by their inherent randomness, allow the model to generate diverse outputs by gradually reversing noise, enhancing detail and realism, but lacking consistency. This randomness can lead to the same input producing varying outputs. PF-ODEs, on the other hand, remove this randomness, providing a deterministic pathway that produces consistent outputs at the expense of fine details and image richness [32, 43]. Balancing the high image quality provided by SDEs with the consistency achieved by PF-ODEs remains a core challenge in diffusion models.", + "bbox": [ + 88, + 628, + 482, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Bridge models [25, 29, 54] integrate principles from both diffusion and bridge frameworks to create a probabilistic connection between input and output distributions. Both the Schrödinger and Brownian Bridge frameworks [47, 54] have demonstrated significant improvements in im", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "age quality across various I2I tasks when compared to traditional diffusion models. However, they inherit certain limitations from both SDE-based and PF-ODE-based sampling. Specifically, they retain the stochastic characteristics of SDEs while also experiencing the lower image quality associated with PF-ODE-based samplers [54].", + "bbox": [ + 511, + 340, + 906, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Deterministic Dual-approx Bridge", + "text_level": 1, + "bbox": [ + 511, + 460, + 823, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present Dual-approx Bridge in details. The Brownian bridge models [32, 47] have achieved high image quality and diversity in I2I translation. The structure of a Brownian bridge allows it to successfully map between paired probability distributions while generating high quality images of substantial diversity. On the other hand, when it comes to the deterministic I2I translation tasks, diversity is not preferred. In this direction, Dual-approx Bridge delivers deterministic I2I translation with minimal diversity. The key difference between our model and existing diffusion models is that in the generative process, existing models employ one neural network-based approximator which is trained in the forward diffusive process, while we make use of a pair of approximators trained in the forward and reverse diffusive processes separately, shown in Figure 2.", + "bbox": [ + 511, + 491, + 908, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Score-Based SDE", + "text_level": 1, + "bbox": [ + 511, + 743, + 684, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The score-based Brownian bridge model is prescribed by the forward and reverse SDEs. The forward SDE reads", + "bbox": [ + 511, + 770, + 906, + 801 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd X = - \\frac {X - Y}{1 - t} d t + g (t) d W, t \\in (0, 1) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 818, + 906, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $W(\\cdot)$ is a Brownian motion (i.e., a Wiener process), and $g(t)$ is the variance of the white noise. Then $X(1) = Y$ .", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28234", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $G(t) = (1 - t)^{2}\\int_{0}^{t}\\frac{g^{2}(s)}{(1 - s)^{2}} ds$ . It holds that", + "bbox": [ + 89, + 88, + 403, + 112 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {t} = (1 - t) X _ {0} + t Y + (1 - t) \\int_ {0} ^ {t} \\frac {g (s)}{1 - s} d W (s) \\tag {2} \\\\ \\sim \\mathcal {N} ((1 - t) X _ {0} + t Y, G (t) I). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 119, + 480, + 171 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "That is", + "bbox": [ + 89, + 179, + 142, + 191 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {t} = (1 - t) X _ {0} + t Y + \\sqrt {G (t)} \\epsilon , \\epsilon \\sim \\mathcal {N} (0, I). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 200, + 482, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The reverse generative SDE [2] is given by", + "bbox": [ + 89, + 228, + 375, + 244 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd X = - \\left(\\frac {X - Y}{1 - t} + g ^ {2} (t) \\nabla \\log p (X, t)\\right) d t + g (t) d \\bar {W} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 250, + 480, + 295 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{W} (\\cdot)$ is a reverse time Brownian motion, and the score function is given by", + "bbox": [ + 89, + 296, + 482, + 328 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla \\log p (X, t) = - \\frac {X - (1 - t) X _ {0} - t Y}{G (t)}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 334, + 482, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hence, in the reverse transitional formula where $\\Delta t$ is the time increment", + "bbox": [ + 89, + 375, + 483, + 402 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {t - 1} = X _ {t} + \\left(\\frac {X _ {t} - Y}{1 - t} + g ^ {2} (t) \\nabla \\log p \\left(X _ {t}, t\\right)\\right) \\Delta t \\tag {6} \\\\ - g (t) \\left(\\bar {W} (t) - \\bar {W} (t - \\Delta t)\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 407, + 480, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we need to estimate two quantities, $X_0$ and $\\Delta \\overline{W} = \\overline{W}(t) - \\overline{W}(t - \\Delta t) = \\sqrt{\\Delta t} z$ , at each time step. In the SDE model, $z$ is just a random variable of the standard normal distribution. This causes the diversity in the output $\\hat{X}_0$ . To make the sampling deterministic, we use a neural network $\\epsilon_\\theta$ to estimate $X_0$ in the forward diffusion process and a second neural network $Z_\\phi(X_t, t)$ to estimate $z$ in the reverse diffusion process. That is, we train a pair of dual approximators $\\epsilon_\\theta$ and $Z_\\phi$ . Note that our goal here is to generate a unique output from a given input, rather than translating probability distributions. So, we need two neural networks to approximate two different samples for the forward and reverse steps from the same white noise distribution. A single approximator cannot serve this purpose.", + "bbox": [ + 89, + 470, + 483, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Training of Neural Network Approximators", + "text_level": 1, + "bbox": [ + 89, + 691, + 464, + 708 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For simplicity, we take the variance of the white noise $g(t) = 1$ . Then $G(t) = t(1 - t)$ .", + "bbox": [ + 89, + 713, + 482, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Forward Training Objective: We design a neural network $\\epsilon_{\\theta}$ to minimize, for $t = 1,\\dots ,T$ $\\epsilon \\sim \\mathcal{N}(0,I)$", + "bbox": [ + 89, + 744, + 482, + 773 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left\\| X _ {t} - X _ {0} - \\epsilon_ {\\theta} \\left(X _ {t}, t\\right) \\right\\| = \\tag {7} \\\\ \\left\\| t \\left(Y - X _ {0}\\right) + \\sqrt {t (1 - t)} \\epsilon - \\epsilon_ {\\theta} \\left(X _ {t}, t\\right) \\right\\|. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 782, + 482, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $X_{t}$ is defined by Equation 3 with $G(t) = t(1 - t)$ . This is the same training process as that of the Brownian bridges[47]. That is, we do the back propagation of", + "bbox": [ + 89, + 829, + 483, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| t (Y - X _ {0}) + \\sqrt {t (1 - t)} \\epsilon - \\epsilon_ {\\theta} (X _ {t}, t) \\right\\|,\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 883, + 423, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t \\sim \\mathrm{Uniform}(1, \\ldots, T)$ and $\\epsilon \\sim \\mathcal{N}(0, I)$ . Essentially, the neural network $\\epsilon_{\\theta}$ is used to estimate $X_0$ given $X_t$ at the time step $t$ . Note that an optional conditional network design $\\epsilon_{\\theta}(X_t, t, Y)$ can also be used, which may improve the stability and efficiency of model training.", + "bbox": [ + 511, + 90, + 903, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reverse Training Objective: Independently of the forward training, we design a neural network $Z_{\\phi}(X_t,t)$ to minimize, for $t = 1,\\dots ,T$", + "bbox": [ + 511, + 167, + 905, + 210 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| z - Z _ {\\phi} \\left(X _ {t}, t\\right) \\right\\|, \\quad z \\sim \\mathcal {N} (0, I), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 220, + 903, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $X_{t}$ is defined by $X_{t} = (1 - t)X_{0} + tY + \\sqrt{t(1 - t)} z$ . That is, we do the back propagation of", + "bbox": [ + 511, + 250, + 903, + 280 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| z - Z _ {\\phi} (X _ {t}, t) \\right\\|,\n$$\n", + "text_format": "latex", + "bbox": [ + 650, + 291, + 769, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t\\sim \\mathrm{Uniform}(0,\\ldots ,T - 1)$ and $z\\sim \\mathcal{N}(0,I)$", + "bbox": [ + 511, + 316, + 859, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Sampling", + "text_level": 1, + "bbox": [ + 513, + 340, + 624, + 357 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We discretize Equation 4 with $g(t) = 1$ to get the iterative generative formula:", + "bbox": [ + 511, + 363, + 905, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {t - 1} = \\left(1 - \\frac {\\Delta t}{t}\\right) X _ {t} + \\frac {\\Delta t}{t} X _ {0} - \\left[ \\bar {W} (t) - \\bar {W} (t - \\Delta t) \\right] \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 402, + 903, + 448 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We employ the two neural networks in this way: $X_0 \\approx X_t - \\epsilon_\\theta(X_t, t)$ , while $\\overline{W}(t) - \\overline{W}(t - \\Delta t)$ must be approximated with the use of the second neural network $Z_\\phi$ .", + "bbox": [ + 511, + 449, + 905, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We make an observation here: $\\overline{W}(t) - \\overline{W}(t - \\Delta t)$ and $\\overline{W}(t + \\Delta t) - \\overline{W}(t)$ are independent, equivalent random variables. Let $g(t) = 1$ in (4) and (5) to get $X_{t} = (1 - t)X_{0} + tY + t\\int_{1}^{t}\\frac{d\\overline{W}}{s}$ . Then we get", + "bbox": [ + 511, + 493, + 905, + 559 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\overline {{W}} (t) - \\overline {{W}} (t - \\Delta t) = \\overline {{W}} (t + \\Delta t) - \\overline {{W}} (t) \\approx \\\\ U \\left(X _ {t + 1}, t + 1\\right) - \\left(1 + \\frac {\\Delta t}{t}\\right) U \\left(X _ {t}, t\\right) + \\frac {\\Delta t}{t} \\left(X _ {0} - Y\\right), \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 566, + 903, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 513, + 647, + 558, + 659 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nU \\left(X _ {t}, t\\right) = X _ {t} - Y = (1 - t) \\left(X _ {0} - Y\\right) + t \\int_ {1} ^ {t} \\frac {d \\overline {{W}}}{s}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 667, + 903, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hence, by plugging the above estimate into Equation 9, we get the final iterative generative formula", + "bbox": [ + 511, + 710, + 905, + 741 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {t - 1} = \\left(1 - \\frac {\\Delta t}{t}\\right) X _ {t} + \\frac {\\Delta t}{t} Y - U \\left(X _ {t + 1}, t + 1\\right) \\tag {12} \\\\ + \\left(1 + \\frac {\\Delta t}{t}\\right) U (X _ {t}, t). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 750, + 903, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the formula (12), replace $t$ by $m_t = \\frac{t}{T}$ and $\\Delta t$ by $\\frac{1}{T}$ if we apply the uniform sampling schedule with $T$ time steps. Also, we estimate $X_0$ by", + "bbox": [ + 511, + 828, + 905, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {X} _ {0} = X _ {t} - \\epsilon_ {\\theta} (X _ {t}, t). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 883, + 903, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28235", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then for $t = T - 1, T - 2, \\ldots, 2$ , we get", + "bbox": [ + 89, + 90, + 367, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {t - 1} = \\left(1 - \\frac {1}{t}\\right) X _ {t} + \\frac {1}{t} Y - U \\left(X _ {t + 1}, t + 1\\right) \\tag {14} \\\\ + \\left(1 + \\frac {1}{t}\\right) U (X _ {t}, t). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 114, + 480, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Forward Approximator Training Algorithm", + "text_level": 1, + "bbox": [ + 93, + 205, + 467, + 222 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Input Paired Dataset $D_{x,y}$ , Forward Network $\\epsilon_{\\theta}$ , Total Time Steps $T$", + "2: repeat", + "3: $x,y\\sim D_{x,y}$", + "4: $t\\sim \\mathrm{Uniform}(1,\\ldots ,T)$", + "5: $\\epsilon \\sim \\mathcal{N}(0,I)$", + "6: $x_{t} = (1 - \\frac{t}{T})x_{0} + \\frac{t}{T} y + B(t)\\epsilon$", + "7: $\\nabla_{\\theta}\\| x_t - x_0 - \\epsilon_{\\theta}(x_t,t)\\|$", + "8: until converged", + "9: end function" + ], + "bbox": [ + 101, + 224, + 480, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 2 Reverse Approximator Training Algorithm", + "text_level": 1, + "bbox": [ + 93, + 407, + 464, + 422 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Input Paired Dataset $D_{x,y}$ , Reverse Network $Z_{\\phi}$ , Total Time Steps $T$", + "2: repeat", + "3: $x,y\\sim D_{x,y}$", + "4: $t\\sim \\mathrm{Uniform}(1,\\ldots ,T)$", + "5: $z\\sim \\mathcal{N}(0,I)$", + "6: $x_{t} = (1 - \\frac{t}{T})x_{0} + \\frac{t}{T} y + B(t)z$", + "7: $\\nabla_{\\phi}\\| z - Z_{\\phi}(x_t,t)\\|$", + "8: until converged", + "9: end function" + ], + "bbox": [ + 101, + 426, + 480, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This iterative formula does not apply when $t = T$ as $X_{T + 1}$ does not exist. So we define $X_{T - 1}$ as we would in the SDE model", + "bbox": [ + 89, + 592, + 482, + 636 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nX _ {T - 1} = Y - \\frac {1}{T} \\epsilon_ {\\theta} (Y, T) - \\frac {1}{\\sqrt {T}} z, \\quad z \\sim \\mathcal {N} (0, I). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 642, + 482, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we define", + "bbox": [ + 109, + 681, + 232, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {X} _ {0} = X _ {1} - \\epsilon_ {\\theta} \\left(X _ {1}, 1\\right) \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 704, + 482, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "as the final output of the algorithm.", + "bbox": [ + 89, + 731, + 323, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The only randomness introduced in the entire sampling process is in $X_{T - 1}$ , which should be negligible, as the coefficient $\\frac{1}{\\sqrt{T}}$ of $z$ is fairly small compared to that of $Y$ . On the contrary, SDE models introduce randomness at every sampling step and hence cause substantial diversity to the output.", + "bbox": [ + 89, + 746, + 482, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Algorithm", + "text_level": 1, + "bbox": [ + 89, + 845, + 207, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In a given paired dataset $D_{x,y}$ , $(x,y)$ denotes a paired images from the set. Define $B(t) = G\\left(\\frac{t}{T}\\right) = \\frac{1}{T}\\sqrt{t(T - t)}$ ,", + "bbox": [ + 89, + 868, + 482, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and we have the training and sampling algorithms shown in Algorithms 1 to 3, respectively.", + "bbox": [ + 511, + 90, + 906, + 122 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 3 Sampling Algorithm (Refactored)", + "text_level": 1, + "bbox": [ + 514, + 146, + 828, + 162 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: $y$ , $\\epsilon_{\\theta}$ , $Z_{\\phi}$", + "bbox": [ + 514, + 166, + 630, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: $x_0$", + "bbox": [ + 514, + 183, + 599, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "1: $x_{t} = y$", + "bbox": [ + 526, + 198, + 591, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2: for $t = T$ to 1 do", + "bbox": [ + 524, + 212, + 663, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3: $\\hat{x}_0 = x_t - \\epsilon_\\theta(x_t, t)$", + "bbox": [ + 524, + 227, + 689, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4: $\\hat{z} \\sim \\mathcal{N}(0, I)$ if $t == T$ else $\\hat{z} = Z_{\\phi}(x_t, t)$", + "bbox": [ + 524, + 243, + 836, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5: $\\hat{x}_t = (1 - \\frac{t}{T})\\hat{x}_0 + \\frac{t}{T} y + B(t)\\hat{z}$", + "bbox": [ + 524, + 257, + 771, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6: $\\hat{x}_{t - 1} = (1 - \\frac{t - 1}{T})\\hat{x}_0 + \\frac{t - 1}{T} y + B(t - 1)\\hat{z}$", + "bbox": [ + 524, + 272, + 839, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "7: $U_{t + 1} = \\hat{x}_t - y, U_t = \\hat{x}_{t - 1} - y$", + "bbox": [ + 524, + 287, + 767, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "8: $x_{t - 1} = (1 - \\frac{1}{t})x_t + \\frac{1}{t - 1} y - \\frac{1}{t(t - 1)}\\hat{x}_0 - U_{t + 1} + \\frac{t}{t - 1} U_t$", + "bbox": [ + 524, + 301, + 903, + 320 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "9: end for", + "bbox": [ + 524, + 320, + 596, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "0: $x_0 = \\hat{x}_0$", + "bbox": [ + 524, + 335, + 599, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "11: return $x_0$", + "bbox": [ + 519, + 351, + 614, + 363 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 514, + 419, + 643, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we verify the capability of Dual-approx Bridge, addressing the following questions:", + "bbox": [ + 511, + 450, + 905, + 481 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- How do varying the number of sampling steps impact its performance in terms of image quality and faithfulness to GT? Furthermore, how does the sampling variance of our model compare to that of SDE-based samplers in terms of faithfulness to GT?", + "- How does Dual-approx Bridge perform in terms of faithfulness to GT compared to other models in image-to-image translation tasks that demand high faithfulness and deterministic result?", + "- How does Dual-approx Bridge perform in general image-to-image translation tasks, which prioritize image quality, when compared to other models including GANs, Diffusion models, and Bridge models?" + ], + "bbox": [ + 513, + 494, + 905, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address these questions, we used datasets with the following resolutions: Cityscapes [10] $(256\\times 256)$ , Edges2Handbags [56] $(64\\times 64)$ , DF2K [45] $(256\\times 256)$ , Urban100 [22] $(256\\times 256$ patches), and BSD100 [34] $(256\\times 256$ patches). For evaluation, we used FID [18] to assess image realism (lower is better), LPIPS [53] for perceptual similarity (lower is better), PSNR for pixel-level similarity (higher is better) and SSIM [49] for structural similarity (closer to 1 is better). Our super-resolution (SR) experiments followed the experimental design of [8]. All of our experiments were implemented using PyTorch [38] and were run on a machine with two NVIDIA RTX A6000 GPUs.", + "bbox": [ + 511, + 704, + 906, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28236", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/704dc163b60934ed62d45863af400bdf8db0e8e197d107800e9c715a7fc4575c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    StepsFID ↓LPIPS ↓PSNR ↑SSIM % ↑
    1,00042.700.44215.10 ± 0.02(43.2 ± 0.07) %
    20048.700.49215.70 ± 0.02(53.2 ± 0.06) %
    1057.430.53015.62 ± 0.02(55.3 ± 0.06) %
    356.070.52316.99 ± 0.01(57.4 ± 0.00) %
    ", + "bbox": [ + 114, + 88, + 460, + 154 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 244, + 243, + 260 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.1. Impact of Sampling Steps", + "text_level": 1, + "bbox": [ + 89, + 267, + 316, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first evaluate the impact of sampling steps on our model's performance in the label-to-photo translation task on the Cityscapes dataset. Since the forward approximator in our model can predict $x_0$ given $x_t$ , sampling can be stopped at any time, allowing us to test sampling performance with a different number of steps. Table 1 presents how the varying sampling steps affect both image quality and faithfulness. It demonstrates that 1,000 sampling steps yield satisfactory image quality, with FID reaching a minimum of 42.70 and LPIPS dropping to 0.442. However, this comes at the cost of reduced faithfulness when compared to results obtained using fewer sampling steps, as evidenced by the decline in PSNR and SSIM. Notably, with only three sampling steps, our model achieves its peak in terms of faithfulness, attaining 16.99 PSNR and $57.4\\%$ SSIM. This demonstrates the model's adaptability to meet the diverse requirements of various applications.", + "bbox": [ + 88, + 285, + 482, + 541 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, we assessed the variance of the output fidelity in five independent sampling trials given the same input. Clearly, even at a higher sampling step of 1,000, the standard deviation of PSNR and SSIM remained low (0.02 and $0.07\\%$ , respectively), and it approaches zero with three sampling steps. This robustness underscores the superiority of our model in consistently producing high-quality and faithful results with minimal variability. Consequently, we employed three sampling steps for better robustness and higher efficiency in our subsequent experiments, unless otherwise specified. Our experiments show that three iterations perform well across these metrics, though further research is needed to determine the optimal number of sampling steps for different tasks.", + "bbox": [ + 89, + 542, + 482, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.2. Faithfulness Evaluation", + "text_level": 1, + "bbox": [ + 89, + 761, + 302, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We then compare the faithfulness of Dual-approx Bridge to other Brownian bridge models with SDE-based [32, 47] and PF-ODE-based samplers on the Cityscapes dataset using PSNR and SSIM metrics. Both the SDE-based and PF-ODE-based samplers use 1,000 sampling steps. The Brownian bridge model, as the leading I2I translation method, is an ideal benchmark for us due to the same bridge structure.", + "bbox": [ + 89, + 779, + 482, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Table 2, our Dual-approx Bridge clearly", + "bbox": [ + 109, + 885, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1e3f80c4f951750e901cf3b06bd14315f08c95aa9783853f7733417e98b61196.jpg", + "table_caption": [ + "Table 1. Quantitative comparison with different sampling steps on the Cityscapes dataset. Bold values represent the best performance. Standard Deviation is obtained by five sampling trials for the same input." + ], + "table_footnote": [], + "table_body": "
    MethodPSNR ↑SSIM % ↑
    Brown Bridge Model (SDE)14.28 ±0.21(49.6 ±0.63) %
    Brown Bridge Model (PF-ODE)15.23 ±0.00(51.2 ±0.00) %
    Ours16.99 ±0.01(57.4 ±0.00)%
    ", + "bbox": [ + 534, + 88, + 887, + 138 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison with Brownian bridges using SDE and PF-ODE-based samplers on Cityscape. Bold values represent the best performance. Standard deviation is obtained by five sampling trials for the same input.", + "bbox": [ + 511, + 148, + 906, + 205 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9eec88a941d7e18d4bdc139fc05a5e420df73ab63a00330e516139d33efca0a2.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison with Brownian bridges using SDE-based and PF-ODE-based samplers on Edges2Handbags. Three sampling trials are conducted by each model given the same input. Standard deviation among sampling results by our model, SDE-based and PF-ODE-based sampler are 0.0001, 0.1030 and 0, respectively." + ], + "image_footnote": [], + "bbox": [ + 524, + 227, + 898, + 406 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "outperforms SDE-based and PF-ODE-based samplers. The PSNR value increased by approximately $12\\%$ compared to the second-best, the PF-ODE-based sampler, while the SSIM value showed an overall improvement of $12\\%$ , rising from $51.2\\%$ to $57.4\\%$ . Notably, the metrics of the Dualapprox Bridge exhibited minimal variance, whereas SDE-based sampler exhibited substantial variance in PSNR and SSIM due to the presence of white noise in every step of its sampling.", + "bbox": [ + 511, + 534, + 905, + 669 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 3 shows three sample images by each model with the same input in the Edges2Handbags dataset. The images generated by SDE-based sampler are rich in detail but distinct from each other. The PF-ODE-based sampler produces consistent results but lacks details, resulting in a blurred appearance. As a comparison, Dual-approx Bridge achieves SDE-level quality with high and consistent faithfulness.", + "bbox": [ + 511, + 670, + 905, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Deterministic Image-to-Image Translation", + "text_level": 1, + "bbox": [ + 511, + 787, + 872, + 803 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We selected the label-to-photo task in the Cityscapes dataset for deterministic image generation, where the goal is to generate realistic images from segmentation maps. Faithfulness is essential in this task, as it ensures the generated images accurately reflect the structure and content of the input labels, preserving the integrity of labeled features. We also in", + "bbox": [ + 511, + 809, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28237", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0dfabe697f6cccb55326aa4833d86c6ac81f5ac36ebe8baaf1622dd5bb02c53d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodFID ↓PSNR ↑SSIM % ↑
    Pix2pix101.0412.8628.63 %
    CycleGAN75.3714.5334.16 %
    UNIT82.7414.6135.41 %
    Ours48.7015.7053.26 %
    ", + "bbox": [ + 130, + 88, + 439, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26d8f6b7d8aae4fa2b57295f33f83165cbe4cc3a6e6efcfa69b13c076142058e.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison between Dual-approx Bridge and SOTA methods on the Cityscapes dataset." + ], + "image_footnote": [], + "bbox": [ + 119, + 239, + 450, + 411 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/051d86df7b564f0109c7dfcc172c791f7b7b3d8e1520945760bf74ba66c73f18.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison on BSD100 datasets." + ], + "image_footnote": [], + "bbox": [ + 101, + 470, + 473, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cluded image super-resolution as a deterministic image-to-image translation task, which also requires both high quality and faithfulness.", + "bbox": [ + 89, + 598, + 482, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given the inherent randomness in diffusion models, we primarily chose GAN-based models as baselines for deterministic I2I tasks. We selected Pix2Pix [24], CycleGAN [57], and UNIT [30] for comparison on the Cityscapes dataset. For image super-resolution, we used ESRGAN [48], RankSRGAN [52], and SRDiff [27] as baselines and followed the experimental configuration in [33] to train our model on DF2K and test it on Urban100 and BSD100.", + "bbox": [ + 89, + 643, + 482, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 compares our model against baseline models on the Cityscapes dataset. The Dual-approx Bridge model demonstrates superior performance across all metrics compared to the other models. In terms of image quality, our model achieves a significant improvement in FID, with a score of 48.70 compared to the second-best score of 75.37, representing a substantial $35\\%$ performance enhancement. Furthermore, our model exhibits notable gains in PSNR and SSIM, with PSNR increased from 14.61 to 15.70 and SSIM", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2ea38c465dbbd3405192f04202c65f6656aac856b3f1db5f3113c599d7e38a96.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison on Uban100 datasets." + ], + "image_footnote": [], + "bbox": [ + 531, + 94, + 890, + 348 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8d5266f96496f79df89f13970a298be71831a38b01045dc2303ef147602b8d78.jpg", + "table_caption": [ + "Table 3. Quantitative comparison with deterministic models on Cityscape. Results of our model are obtained using 200 sampling steps. Bold values represent the best performance." + ], + "table_footnote": [], + "table_body": "
    ModelBSD100Urban100
    LPIPS ↓PSNR ↑LPIPS ↓PSNR ↑
    Bicubic0.528224.320.482621.75
    ESRGAN0.157923.650.122623.04
    RankSRGAN0.171423.800.140323.16
    SRDiff0.204624.170.139123.88
    Ours0.126726.560.120723.23
    ", + "bbox": [ + 534, + 400, + 885, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Quantitative comparisons on BSD100 and Urban100. Bold values represent the best performance.", + "bbox": [ + 511, + 503, + 903, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "improved by approximately $50\\%$ (from $35.41\\%$ to $53.26\\%$ ). Qualitative comparisons of various methods are presented in Figure 4.", + "bbox": [ + 511, + 564, + 903, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4 compares our model against baselines on superresolution tasks. Our model performed the best on the BSD100 dataset with LPIPS at 0.1267 and PSNR at 26.56. It also achieves the highest LPIPS score of 0.1207 and the second-highest PSNR score of 23.23 on the Urban100 dataset. While SRDiff achieved the best PSNR on Urban100, its diffusion process encounters challenges in consistently producing stable outputs due to the inherent randomness in its SDE-based sampler (as shown in Table 2). Moreover, our model accomplishes this performance with significantly fewer sampling steps (3 used in our model vs. 1,000 used in SRDiff).", + "bbox": [ + 511, + 611, + 905, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 5 compares the visual quality of various methods for image super-resolution. The top-right of each image shows a zoomed-in view of the red-boxed region for a detailed comparison. Due to inherent randomness, SDEs often introduce unrealistic artifacts, as seen in the example. The PF-ODE-based sampler results exhibit excessive smoothness and the loss of details, as evident in the zoomed", + "bbox": [ + 511, + 794, + 905, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28238", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/78caef6590d71f93a4953e26aac4dac850f0e08f333728df3d9a952eadc3016f.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison between Dual-approx Bridge and SOTA methods on the Edges2handbags dataset." + ], + "image_footnote": [], + "bbox": [ + 133, + 94, + 857, + 208 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cd05187cf72f1741f2e1894c9c4fa7b7043a03db2db092a986fed170996d9306.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodFID ↓
    MUNIT91.4
    DRIT155.3
    Distance85.8
    SelfDistance78.8
    CGGAN105.2
    CUT56.4
    FastCUT68.8
    DCLGAN49.4
    SimDCL51.3
    Ours48.7
    ", + "bbox": [ + 153, + 243, + 421, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e3886217df21da163e7262f2cd9882b5f517fe170234f0768c26666004ead213.jpg", + "image_caption": [ + "Figure 8. Quantitative comparison between Dual-approx Bridge and A-bridge (with SDE-based sampler). Each model are sampled five times given the same input. Sampling standard deviation of the first example (Ours: 0.0084, A-bridge: 0.0903) and the second example (Ours: 0.0054, SDE: 0.0672)." + ], + "image_footnote": [], + "bbox": [ + 112, + 453, + 460, + 593 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "regions for both examples. Figure 6 further illustrates that our model can achieve detail preservation approaching or even surpassing that of SDE-based methods. Conversely, the Dual-approx Bridge method demonstrates a remarkable ability to preserve details while maintaining high faithfulness with GT.", + "bbox": [ + 89, + 683, + 483, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. General Image-to-Image Translation", + "text_level": 1, + "bbox": [ + 89, + 787, + 410, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we evaluate Dual-approx Bridge on general image-to-image translation tasks. We assess our model's image quality on the Edges2Handbags and Cityscapes datasets. For Edges2Handbags, we conduct comparisons with Pix2Pix [24], SDEdit [35], DDIB [44], Rectified Flow [31], I2SB [29], DDBM [54], and A-bridge [47]. For the", + "bbox": [ + 89, + 810, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/89975bec3fe09e22804694693bb71fa68dabdbabdc33babbac2556373cddf0cd.jpg", + "table_caption": [ + "Table 5. Quantitative comparison of image quality on Cityscapes (label to photo). Bold values represent the best performance." + ], + "table_footnote": [], + "table_body": "
    MethodFID ↓
    Pix2Pix74.8
    DDIB186.84
    SDEdit85.8
    SelfDistance26.5
    Rectified Flow25.3
    I2SB7.43
    DDBM (VP)1.83
    A-Bridge1.07
    Ours1.36
    ", + "bbox": [ + 576, + 243, + 844, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Quantitative comparison of image quality on Edges2Handbags. Bold values represent the best performance.", + "bbox": [ + 511, + 404, + 906, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Cityscapes dataset, we compared our model with MUNIT [23], DRIT [26], DistanceGAN [3], Self-DistanceGAN [3], CGGAN [55], CUT [37], FastCUT [37], DCLGAN [17], and SimDCL [17].", + "bbox": [ + 511, + 439, + 906, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On the Cityscapes dataset, our model outperforms all GAN-based models, achieving the top position and surpassing all competitors (Table 5). As shown in Table 6, our model achieves 1.36 FID score on the Edges2Handbags dataset, securing the second place. This result demonstrates that, despite our primary focus on enhancing faithfulness, our model still delivers highly competitive image quality.", + "bbox": [ + 511, + 500, + 905, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 7 provides a qualitative comparison of our model with A-bridge on the Edges2Handbags dataset. Although A-bridge achieves the best FID score, it uses SDE-based samplers. As shown in Figure 8, our model demonstrates much higher faithfulness and consistency across repeated sampling with far fewer sampling steps (3 in our model vs. 50 in A-bridge).", + "bbox": [ + 511, + 604, + 905, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 511, + 724, + 784, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed Dual-approx Bridge, a novel generative model to produce faithful and high quality output for deterministic I2I translations. Our extensive experiments on benchmark datasets demonstrate the consistent and superior performance of Dual-approx Bridge when compared to SOTA I2I models. Our current choice of the SDE follows the Variance Preserving (VP) formulation. Moving forward, we plan to explore the potentials of combining both VP and variance exploding SDEs to further enhance our model's capabilities.", + "bbox": [ + 511, + 750, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28239", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Aziz Alotaibi. Deep generative adversarial networks for image-to-image translation: A review. Symmetry, 12(10), 2020. 1, 2", + "[2] Brian D.O. Anderson. Reverse-time diffusion equation models. 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In ICCV, pages 2223-2232, 2017. 1, 2, 7" + ], + "bbox": [ + 516, + 92, + 903, + 755 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "28241", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/f031c8e4-7831-43c8-a97d-74d4fb079432_model.json b/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/f031c8e4-7831-43c8-a97d-74d4fb079432_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f3ebbf8272618852dcbd7304f6853da8fad18519 --- /dev/null +++ b/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/f031c8e4-7831-43c8-a97d-74d4fb079432_model.json @@ -0,0 +1,2915 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.127, + 0.13, + 0.872, + 0.177 + ], + "angle": 0, + "content": "Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators" + }, + { + "type": "text", + "bbox": [ + 0.264, + 0.203, + 0.736, + 0.222 + ], + "angle": 0, + "content": "Bohan Xiao\\(^{1*}\\), Peiyong Wang\\(^{2*}\\), Qisheng He\\(^{1}\\), Ming Dong\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.163, + 0.223, + 0.834, + 0.257 + ], + "angle": 0, + "content": "Department of Computer Science, Wayne State University \\(^{1}\\), Detroit, Michigan, USA \nDepartment of Mathematics, Wayne State University \\(^{2}\\), Detroit, Michigan, USA" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.26, + 0.695, + 0.275 + ], + "angle": 0, + "content": "{gk6511, pywang, qisheng.he, mdong}@wayne.edu" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.309, + 0.327, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.341, + 0.486, + 0.614 + ], + "angle": 0, + "content": "Image-to-Image (I2I) translation involves converting an image from one domain to another. Deterministic I2I translation, such as in image super-resolution, extends this concept by guaranteeing that each input generates a consistent and predictable output, closely matching the ground truth (GT) with high fidelity. In this paper, we propose a denoising Brownian bridge model with dual approximators (Dualapprox Bridge), a novel generative model that exploits the Brownian bridge dynamics and two neural network-based approximators (one for forward and one for reverse process) to produce faithful output with negligible variance and high image quality in I2I translations. Our extensive experiments on benchmark datasets including image generation and super-resolution demonstrate the consistent and superior performance of Dual-approx Bridge in terms of image quality and faithfulness to GT when compared to both stochastic and deterministic baselines. Project page and code: https://github.com/bohan95/dual-app-bridge" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.642, + 0.222, + 0.658 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.667, + 0.483, + 0.788 + ], + "angle": 0, + "content": "Image-to-Image (I2I) translation is a significant area of research with broad applications across academia and industry. It involves transforming an image from one domain to another while preserving essential features. Key tasks in this field include generating realistic images from semantic labels [24, 40, 42, 57], transforming segmentation masks into photo-like outputs [40, 47, 54], and enhancing image quality through super-resolution [8, 27, 52]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.788, + 0.483, + 0.879 + ], + "angle": 0, + "content": "Among the wide range of applications, some I2I tasks particularly benefit from deterministic models. For instance, in super-resolution, the goal is to translate a low-resolution image into a high-resolution one while accurately preserving fine details. This task, as shown in recent studies [13, 14], requires consistency and high faithfulness to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.311, + 0.906, + 0.462 + ], + "angle": 0, + "content": "ground true (GT) because for a given low-resolution image, there is typically one \"correct\" high-resolution output that should be produced. In such an I2I task, we note that faithfulness or fidelity is to the individual GT, not just to the distribution of GT. Any variability in the generated output could result in artifacts or loss of critical information, making stochastic approaches less desirable. Similarly, in tasks such as denoising [6, 51] or inpainting [4, 39], where missing or noisy parts of an image need to be restored, a deterministic approach is preferred." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.463, + 0.906, + 0.583 + ], + "angle": 0, + "content": "Generative Adversarial Networks (GANs) [16] have been instrumental in advancing I2I translation, with models like Pix2Pix [24] and CycleGAN[57] demonstrating impressive results. GANs are deterministic during inference, producing the same output for a given input, which is advantageous for tasks requiring faithfulness. However, GANs often struggle to generate high-quality images, frequently resulting in blurriness and artifacts [1, 21]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.584, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Diffusion models, such as Denoising Diffusion Probabilistic Models (DDPM) [19] and Latent Diffusion Models (LDM) [40], generate high-quality images by progressively adding noise to images and learning the reverse process. Bridge models, such as Brownian bridge diffusion models [32, 47], utilize Stochastic Differential Equations (SDEs) to directly interpolate between input and output distributions, allowing precise control over transformations [40, 42]. This approach improves analytical tractability, making bridge models well suited for I2I translations. However, the inherent stochasticity in these models (see Figure 1(a)) complicates tasks where faithful results are required (e.g., image super-resolution and image reconstruction). Unlike traditional diffusion models [19, 40, 43], which start from noise and gradually denoise the input to generate an output, bridge models start from structured data and interpolate between input and output distributions. This difference means that deterministic methods like Probability Flow Ordinary Differential Equations (PF-ODEs) [43], when applied to bridge models, can lead to blurry images [43, 54], resulting in degraded model performance (see Figure 1(b))." + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.376, + 0.901 + ], + "angle": 0, + "content": "* Both authors contributed equally to this research." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28232" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.298, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.186, + 0.207, + 0.194 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.091, + 0.5, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.393, + 0.185, + 0.408, + 0.193 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.194, + 0.298, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.287, + 0.206, + 0.297 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.199, + 0.495, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.308, + 0.484, + 0.406 + ], + "angle": 0, + "content": "Figure 1. Sampling comparison between SDE-based sampler, PF-ODE-based sampler, and Dual-approx Bridge. The circular area within the dashed circle indicates where the SDE-based sampling outputs land. (a) SDE-based Sampling: diverse outputs of high image quality. (b) PF-ODE-based Sampling: deterministic outputs lack of fine details of ground truth (GT). (c) Dual-approx Bridge Sampling: deterministic output with fine details of GT." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.416, + 0.484, + 0.46 + ], + "angle": 0, + "content": "Therefore, there is a growing need for deterministic models that can preserve both image quality and faithfulness in I2I translations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.462, + 0.484, + 0.763 + ], + "angle": 0, + "content": "To resolve this dilemma in the pursuit of deterministic sampling with both high image quality and fidelity, in this paper we propose a denoising Brownian bridge model with Dual Approximators (abbreviated as \"Dual-approx Bridge\"), a generative model that exploits the Brownian bridge structure to produce faithful output with negligible variance and with an image quality better than or comparable to that generated by SDE-based samplers. More specifically, in the SDE-based structure of a Brownian bridge with both forward and corresponding reverse Brownian motions, we train a neural network in the forward diffusive process to estimate the score function and the initial state in the diffusive iteration. Meanwhile, in the reverse process of the Brownian bridge, a second neural network is trained to approximate the white noise scaled to the time step increment. Here, we emphasize that in deterministic I2I, our goal is to generate a unique output from a given input, rather than translating probability distributions, as shown in Figure 1(c). The major contributions of this work are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.765, + 0.483, + 0.87 + ], + "angle": 0, + "content": "- To our best knowledge, Dual-approx Bridge is the first generative model that exploits the Brownian bridge structure to produce faithful output with negligible variance and high image quality for deterministic I2I translations. This is achieved through a novel design of a pair of approximators, trained in the forward and reverse diffusive processes, respectively." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "- In Dual-approx Bridge, the reverse approximator optimizes the reverse denoising process and presents an opti" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.765, + 0.484, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "mal deterministic route for the generative process. From a theoretical perspective, we analyze our model in a general setting where the white noise may take any time-dependent variance." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.153, + 0.907, + 0.243 + ], + "angle": 0, + "content": "- Through extensive experiments on benchmark datasets including image generation and super-resolution, we demonstrate the consistent and superior performance of Dual-approx Bridge on image quality and faithfulness to GT when compared to state-of-the-art (SOTA) GAN-based and diffusion-based I2I models." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.255, + 0.656, + 0.271 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.281, + 0.906, + 0.327 + ], + "angle": 0, + "content": "In this section, we briefly review the related literature, including image-to-image translation, GAN Models, Diffusion Models, and Bridge Models." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.335, + 0.766, + 0.351 + ], + "angle": 0, + "content": "2.1. Image-to-Image Translation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.357, + 0.907, + 0.6 + ], + "angle": 0, + "content": "Image-to-image (I2I) translation has become a core task in computer vision [1, 21, 36], focused on learning mappings between the source and target image domains for applications such as style transfer [15] and colorization [9]. Traditional methods, including Pix2Pix [24] and CycleGAN[57], utilize GAN-based architectures to translate images and support diverse I2I tasks by capturing domain-specific features, though challenges remain in maintaining high quality across complex domains [5, 41]. Deterministic I2I translation builds on this by ensuring that each input produces a consistent, predictable output — an essential requirement in fields like medical imaging [28], where precision and reproducibility are crucial. In tasks such as super-resolution [12] or denoising [46], deterministic models can enhance image resolution and clarity without introducing variations that could adversely affect analysis or interpretation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.607, + 0.659, + 0.623 + ], + "angle": 0, + "content": "2.2. Brown Bridge" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.906, + 0.766 + ], + "angle": 0, + "content": "The Brownian Bridge (BB) [32, 47] is a fundamental stochastic process that models a constrained Brownian motion, where the trajectory is conditioned on fixed start and end points. Unlike an unconstrained Wiener process, which evolves freely, a Brownian bridge interpolates between two known states while maintaining stochastic variations. This property makes it particularly useful in probabilistic modeling, including image-to-image (I2I) translation, conditional generative modeling, and stochastic optimal transport." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.774, + 0.809, + 0.789 + ], + "angle": 0, + "content": "2.3. Generative Adversarial Networks" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.902 + ], + "angle": 0, + "content": "GANs [16] have been pivotal in advancing I2I translation by learning mappings between image domains through adversarial training. One foundational model, Pix2Pix [24], introduced a conditional GAN approach for paired I2I tasks, enabling applications like colorization[7] and semantic label-to-photo translation[24]. For unpaired I2I tasks, CycleGAN [57] employs cycle consistency, allowing the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28233" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.089, + 0.885, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.306, + 0.908, + 0.337 + ], + "angle": 0, + "content": "Figure 2. Training process of the two approximators (top-left: forward diffusive process, bottom-left: reverse diffusive process). Right: Sampling workflow with both approximators in action." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.342, + 0.484, + 0.435 + ], + "angle": 0, + "content": "model to translate images across domains without requiring paired samples. However, GANs often face artifacts in generated images [5, 41, 50]. Such limitations in image quality, combined with the common challenges of training instability, make GANs less suitable for applications demanding both quality and faithfulness." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.441, + 0.351, + 0.459 + ], + "angle": 0, + "content": "2.4. Diffusion and Bridge Models" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.463, + 0.483, + 0.629 + ], + "angle": 0, + "content": "Diffusion models have established themselves as a leading approach in generative modeling [11] due to their ability to produce high-quality, realistic images through a gradual denoising process. DDPM [20] pioneered this approach, modeling image generation as a series of iterative steps in which random noise is gradually refined into a structured target image. The process results in exceptionally high-quality images with reduced artifacts, often surpassing GANs. LDMs [40] further refined DDPM by focusing on a latent space rather than a pixel space, making the generation process more efficient." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.63, + 0.483, + 0.825 + ], + "angle": 0, + "content": "To model the denoising process, diffusion models can rely on two distinct mathematical frameworks: SDEs and PF-ODEs [43]. SDEs, characterized by their inherent randomness, allow the model to generate diverse outputs by gradually reversing noise, enhancing detail and realism, but lacking consistency. This randomness can lead to the same input producing varying outputs. PF-ODEs, on the other hand, remove this randomness, providing a deterministic pathway that produces consistent outputs at the expense of fine details and image richness [32, 43]. Balancing the high image quality provided by SDEs with the consistency achieved by PF-ODEs remains a core challenge in diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Bridge models [25, 29, 54] integrate principles from both diffusion and bridge frameworks to create a probabilistic connection between input and output distributions. Both the Schrödinger and Brownian Bridge frameworks [47, 54] have demonstrated significant improvements in im" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.342, + 0.907, + 0.435 + ], + "angle": 0, + "content": "age quality across various I2I tasks when compared to traditional diffusion models. However, they inherit certain limitations from both SDE-based and PF-ODE-based sampling. Specifically, they retain the stochastic characteristics of SDEs while also experiencing the lower image quality associated with PF-ODE-based samplers [54]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.462, + 0.825, + 0.481 + ], + "angle": 0, + "content": "3. Deterministic Dual-approx Bridge" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.492, + 0.909, + 0.721 + ], + "angle": 0, + "content": "In this section, we present Dual-approx Bridge in details. The Brownian bridge models [32, 47] have achieved high image quality and diversity in I2I translation. The structure of a Brownian bridge allows it to successfully map between paired probability distributions while generating high quality images of substantial diversity. On the other hand, when it comes to the deterministic I2I translation tasks, diversity is not preferred. In this direction, Dual-approx Bridge delivers deterministic I2I translation with minimal diversity. The key difference between our model and existing diffusion models is that in the generative process, existing models employ one neural network-based approximator which is trained in the forward diffusive process, while we make use of a pair of approximators trained in the forward and reverse diffusive processes separately, shown in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.744, + 0.686, + 0.759 + ], + "angle": 0, + "content": "3.1. Score-Based SDE" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.771, + 0.908, + 0.802 + ], + "angle": 0, + "content": "The score-based Brownian bridge model is prescribed by the forward and reverse SDEs. The forward SDE reads" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.819, + 0.907, + 0.851 + ], + "angle": 0, + "content": "\\[\nd X = - \\frac {X - Y}{1 - t} d t + g (t) d W, t \\in (0, 1) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.908, + 0.903 + ], + "angle": 0, + "content": "where \\( W(\\cdot) \\) is a Brownian motion (i.e., a Wiener process), and \\( g(t) \\) is the variance of the white noise. Then \\( X(1) = Y \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28234" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.089, + 0.405, + 0.113 + ], + "angle": 0, + "content": "Let \\( G(t) = (1 - t)^{2}\\int_{0}^{t}\\frac{g^{2}(s)}{(1 - s)^{2}} ds \\). It holds that" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.12, + 0.482, + 0.172 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {t} = (1 - t) X _ {0} + t Y + (1 - t) \\int_ {0} ^ {t} \\frac {g (s)}{1 - s} d W (s) \\tag {2} \\\\ \\sim \\mathcal {N} ((1 - t) X _ {0} + t Y, G (t) I). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.18, + 0.143, + 0.193 + ], + "angle": 0, + "content": "That is" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.202, + 0.483, + 0.22 + ], + "angle": 0, + "content": "\\[\nX _ {t} = (1 - t) X _ {0} + t Y + \\sqrt {G (t)} \\epsilon , \\epsilon \\sim \\mathcal {N} (0, I). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.229, + 0.377, + 0.245 + ], + "angle": 0, + "content": "The reverse generative SDE [2] is given by" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.251, + 0.482, + 0.296 + ], + "angle": 0, + "content": "\\[\nd X = - \\left(\\frac {X - Y}{1 - t} + g ^ {2} (t) \\nabla \\log p (X, t)\\right) d t + g (t) d \\bar {W} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.297, + 0.483, + 0.329 + ], + "angle": 0, + "content": "where \\(\\overline{W} (\\cdot)\\) is a reverse time Brownian motion, and the score function is given by" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.335, + 0.483, + 0.368 + ], + "angle": 0, + "content": "\\[\n\\nabla \\log p (X, t) = - \\frac {X - (1 - t) X _ {0} - t Y}{G (t)}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.375, + 0.484, + 0.404 + ], + "angle": 0, + "content": "Hence, in the reverse transitional formula where \\(\\Delta t\\) is the time increment" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.409, + 0.482, + 0.464 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {t - 1} = X _ {t} + \\left(\\frac {X _ {t} - Y}{1 - t} + g ^ {2} (t) \\nabla \\log p \\left(X _ {t}, t\\right)\\right) \\Delta t \\tag {6} \\\\ - g (t) \\left(\\bar {W} (t) - \\bar {W} (t - \\Delta t)\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.472, + 0.484, + 0.685 + ], + "angle": 0, + "content": "we need to estimate two quantities, \\( X_0 \\) and \\( \\Delta \\overline{W} = \\overline{W}(t) - \\overline{W}(t - \\Delta t) = \\sqrt{\\Delta t} z \\), at each time step. In the SDE model, \\( z \\) is just a random variable of the standard normal distribution. This causes the diversity in the output \\( \\hat{X}_0 \\). To make the sampling deterministic, we use a neural network \\( \\epsilon_\\theta \\) to estimate \\( X_0 \\) in the forward diffusion process and a second neural network \\( Z_\\phi(X_t, t) \\) to estimate \\( z \\) in the reverse diffusion process. That is, we train a pair of dual approximators \\( \\epsilon_\\theta \\) and \\( Z_\\phi \\). Note that our goal here is to generate a unique output from a given input, rather than translating probability distributions. So, we need two neural networks to approximate two different samples for the forward and reverse steps from the same white noise distribution. A single approximator cannot serve this purpose." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.692, + 0.465, + 0.709 + ], + "angle": 0, + "content": "3.2. Training of Neural Network Approximators" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.714, + 0.483, + 0.744 + ], + "angle": 0, + "content": "For simplicity, we take the variance of the white noise \\( g(t) = 1 \\). Then \\( G(t) = t(1 - t) \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.745, + 0.483, + 0.775 + ], + "angle": 0, + "content": "Forward Training Objective: We design a neural network \\(\\epsilon_{\\theta}\\) to minimize, for \\(t = 1,\\dots ,T\\) \\(\\epsilon \\sim \\mathcal{N}(0,I)\\)" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.783, + 0.483, + 0.822 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left\\| X _ {t} - X _ {0} - \\epsilon_ {\\theta} \\left(X _ {t}, t\\right) \\right\\| = \\tag {7} \\\\ \\left\\| t \\left(Y - X _ {0}\\right) + \\sqrt {t (1 - t)} \\epsilon - \\epsilon_ {\\theta} \\left(X _ {t}, t\\right) \\right\\|. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.83, + 0.484, + 0.877 + ], + "angle": 0, + "content": "Here \\( X_{t} \\) is defined by Equation 3 with \\( G(t) = t(1 - t) \\). This is the same training process as that of the Brownian bridges[47]. That is, we do the back propagation of" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.884, + 0.424, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\left\\| t (Y - X _ {0}) + \\sqrt {t (1 - t)} \\epsilon - \\epsilon_ {\\theta} (X _ {t}, t) \\right\\|,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.167 + ], + "angle": 0, + "content": "where \\(t \\sim \\mathrm{Uniform}(1, \\ldots, T)\\) and \\(\\epsilon \\sim \\mathcal{N}(0, I)\\). Essentially, the neural network \\(\\epsilon_{\\theta}\\) is used to estimate \\(X_0\\) given \\(X_t\\) at the time step \\(t\\). Note that an optional conditional network design \\(\\epsilon_{\\theta}(X_t, t, Y)\\) can also be used, which may improve the stability and efficiency of model training." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.168, + 0.906, + 0.212 + ], + "angle": 0, + "content": "Reverse Training Objective: Independently of the forward training, we design a neural network \\( Z_{\\phi}(X_t,t) \\) to minimize, for \\( t = 1,\\dots ,T \\)" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.222, + 0.905, + 0.24 + ], + "angle": 0, + "content": "\\[\n\\left\\| z - Z _ {\\phi} \\left(X _ {t}, t\\right) \\right\\|, \\quad z \\sim \\mathcal {N} (0, I), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.25, + 0.905, + 0.281 + ], + "angle": 0, + "content": "where \\(X_{t}\\) is defined by \\(X_{t} = (1 - t)X_{0} + tY + \\sqrt{t(1 - t)} z\\). That is, we do the back propagation of" + }, + { + "type": "equation", + "bbox": [ + 0.651, + 0.292, + 0.771, + 0.308 + ], + "angle": 0, + "content": "\\[\n\\left\\| z - Z _ {\\phi} (X _ {t}, t) \\right\\|,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.318, + 0.861, + 0.334 + ], + "angle": 0, + "content": "where \\(t\\sim \\mathrm{Uniform}(0,\\ldots ,T - 1)\\) and \\(z\\sim \\mathcal{N}(0,I)\\)" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.342, + 0.625, + 0.358 + ], + "angle": 0, + "content": "3.3. Sampling" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.364, + 0.906, + 0.394 + ], + "angle": 0, + "content": "We discretize Equation 4 with \\( g(t) = 1 \\) to get the iterative generative formula:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.403, + 0.905, + 0.449 + ], + "angle": 0, + "content": "\\[\nX _ {t - 1} = \\left(1 - \\frac {\\Delta t}{t}\\right) X _ {t} + \\frac {\\Delta t}{t} X _ {0} - \\left[ \\bar {W} (t) - \\bar {W} (t - \\Delta t) \\right] \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.45, + 0.906, + 0.493 + ], + "angle": 0, + "content": "We employ the two neural networks in this way: \\(X_0 \\approx X_t - \\epsilon_\\theta(X_t, t)\\), while \\(\\overline{W}(t) - \\overline{W}(t - \\Delta t)\\) must be approximated with the use of the second neural network \\(Z_\\phi\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.494, + 0.906, + 0.56 + ], + "angle": 0, + "content": "We make an observation here: \\(\\overline{W}(t) - \\overline{W}(t - \\Delta t)\\) and \\(\\overline{W}(t + \\Delta t) - \\overline{W}(t)\\) are independent, equivalent random variables. Let \\(g(t) = 1\\) in (4) and (5) to get \\(X_{t} = (1 - t)X_{0} + tY + t\\int_{1}^{t}\\frac{d\\overline{W}}{s}\\). Then we get" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.568, + 0.905, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\overline {{W}} (t) - \\overline {{W}} (t - \\Delta t) = \\overline {{W}} (t + \\Delta t) - \\overline {{W}} (t) \\approx \\\\ U \\left(X _ {t + 1}, t + 1\\right) - \\left(1 + \\frac {\\Delta t}{t}\\right) U \\left(X _ {t}, t\\right) + \\frac {\\Delta t}{t} \\left(X _ {0} - Y\\right), \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.648, + 0.56, + 0.66 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.668, + 0.905, + 0.703 + ], + "angle": 0, + "content": "\\[\nU \\left(X _ {t}, t\\right) = X _ {t} - Y = (1 - t) \\left(X _ {0} - Y\\right) + t \\int_ {1} ^ {t} \\frac {d \\overline {{W}}}{s}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.712, + 0.906, + 0.742 + ], + "angle": 0, + "content": "Hence, by plugging the above estimate into Equation 9, we get the final iterative generative formula" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.75, + 0.905, + 0.82 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {t - 1} = \\left(1 - \\frac {\\Delta t}{t}\\right) X _ {t} + \\frac {\\Delta t}{t} Y - U \\left(X _ {t + 1}, t + 1\\right) \\tag {12} \\\\ + \\left(1 + \\frac {\\Delta t}{t}\\right) U (X _ {t}, t). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.829, + 0.906, + 0.876 + ], + "angle": 0, + "content": "In the formula (12), replace \\( t \\) by \\( m_t = \\frac{t}{T} \\) and \\( \\Delta t \\) by \\( \\frac{1}{T} \\) if we apply the uniform sampling schedule with \\( T \\) time steps. Also, we estimate \\( X_0 \\) by" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.884, + 0.905, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\hat {X} _ {0} = X _ {t} - \\epsilon_ {\\theta} (X _ {t}, t). \\tag {13}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28235" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.368, + 0.107 + ], + "angle": 0, + "content": "Then for \\(t = T - 1, T - 2, \\ldots, 2\\), we get" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.115, + 0.482, + 0.183 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {t - 1} = \\left(1 - \\frac {1}{t}\\right) X _ {t} + \\frac {1}{t} Y - U \\left(X _ {t + 1}, t + 1\\right) \\tag {14} \\\\ + \\left(1 + \\frac {1}{t}\\right) U (X _ {t}, t). \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.094, + 0.207, + 0.468, + 0.223 + ], + "angle": 0, + "content": "Algorithm 1 Forward Approximator Training Algorithm" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.226, + 0.482, + 0.256 + ], + "angle": 0, + "content": "1: Input Paired Dataset \\(D_{x,y}\\), Forward Network \\(\\epsilon_{\\theta}\\), Total Time Steps \\(T\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.258, + 0.169, + 0.271 + ], + "angle": 0, + "content": "2: repeat" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.273, + 0.219, + 0.286 + ], + "angle": 0, + "content": "3: \\(x,y\\sim D_{x,y}\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.287, + 0.292, + 0.302 + ], + "angle": 0, + "content": "4: \\(t\\sim \\mathrm{Uniform}(1,\\ldots ,T)\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.303, + 0.22, + 0.316 + ], + "angle": 0, + "content": "5: \\(\\epsilon \\sim \\mathcal{N}(0,I)\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.317, + 0.347, + 0.333 + ], + "angle": 0, + "content": "6: \\(x_{t} = (1 - \\frac{t}{T})x_{0} + \\frac{t}{T} y + B(t)\\epsilon\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.334, + 0.305, + 0.347 + ], + "angle": 0, + "content": "7: \\(\\nabla_{\\theta}\\| x_t - x_0 - \\epsilon_{\\theta}(x_t,t)\\|\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.349, + 0.227, + 0.362 + ], + "angle": 0, + "content": "8: until converged" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.363, + 0.211, + 0.375 + ], + "angle": 0, + "content": "9: end function" + }, + { + "type": "list", + "bbox": [ + 0.102, + 0.226, + 0.482, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.094, + 0.408, + 0.465, + 0.423 + ], + "angle": 0, + "content": "Algorithm 2 Reverse Approximator Training Algorithm" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.427, + 0.482, + 0.457 + ], + "angle": 0, + "content": "1: Input Paired Dataset \\(D_{x,y}\\), Reverse Network \\(Z_{\\phi}\\), Total Time Steps \\(T\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.459, + 0.168, + 0.472 + ], + "angle": 0, + "content": "2: repeat" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.474, + 0.219, + 0.488 + ], + "angle": 0, + "content": "3: \\(x,y\\sim D_{x,y}\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.489, + 0.291, + 0.503 + ], + "angle": 0, + "content": "4: \\(t\\sim \\mathrm{Uniform}(1,\\ldots ,T)\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.504, + 0.221, + 0.518 + ], + "angle": 0, + "content": "5: \\(z\\sim \\mathcal{N}(0,I)\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.518, + 0.348, + 0.534 + ], + "angle": 0, + "content": "6: \\(x_{t} = (1 - \\frac{t}{T})x_{0} + \\frac{t}{T} y + B(t)z\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.534, + 0.269, + 0.548 + ], + "angle": 0, + "content": "7: \\(\\nabla_{\\phi}\\| z - Z_{\\phi}(x_t,t)\\|\\)" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.55, + 0.227, + 0.563 + ], + "angle": 0, + "content": "8: until converged" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.565, + 0.211, + 0.576 + ], + "angle": 0, + "content": "9: end function" + }, + { + "type": "list", + "bbox": [ + 0.102, + 0.427, + 0.482, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.593, + 0.483, + 0.637 + ], + "angle": 0, + "content": "This iterative formula does not apply when \\( t = T \\) as \\( X_{T + 1} \\) does not exist. So we define \\( X_{T - 1} \\) as we would in the SDE model" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.643, + 0.483, + 0.675 + ], + "angle": 0, + "content": "\\[\nX _ {T - 1} = Y - \\frac {1}{T} \\epsilon_ {\\theta} (Y, T) - \\frac {1}{\\sqrt {T}} z, \\quad z \\sim \\mathcal {N} (0, I). \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.682, + 0.233, + 0.697 + ], + "angle": 0, + "content": "Finally, we define" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.705, + 0.483, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\hat {X} _ {0} = X _ {1} - \\epsilon_ {\\theta} \\left(X _ {1}, 1\\right) \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.732, + 0.325, + 0.747 + ], + "angle": 0, + "content": "as the final output of the algorithm." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.747, + 0.483, + 0.839 + ], + "angle": 0, + "content": "The only randomness introduced in the entire sampling process is in \\( X_{T - 1} \\), which should be negligible, as the coefficient \\( \\frac{1}{\\sqrt{T}} \\) of \\( z \\) is fairly small compared to that of \\( Y \\). On the contrary, SDE models introduce randomness at every sampling step and hence cause substantial diversity to the output." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.847, + 0.208, + 0.863 + ], + "angle": 0, + "content": "3.4. Algorithm" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.869, + 0.483, + 0.904 + ], + "angle": 0, + "content": "In a given paired dataset \\( D_{x,y} \\), \\( (x,y) \\) denotes a paired images from the set. Define \\( B(t) = G\\left(\\frac{t}{T}\\right) = \\frac{1}{T}\\sqrt{t(T - t)} \\)," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.123 + ], + "angle": 0, + "content": "and we have the training and sampling algorithms shown in Algorithms 1 to 3, respectively." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.147, + 0.829, + 0.163 + ], + "angle": 0, + "content": "Algorithm 3 Sampling Algorithm (Refactored)" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.167, + 0.631, + 0.183 + ], + "angle": 0, + "content": "Input: \\(y\\), \\(\\epsilon_{\\theta}\\), \\(Z_{\\phi}\\)" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.184, + 0.6, + 0.197 + ], + "angle": 0, + "content": "Output: \\( x_0 \\)" + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.199, + 0.593, + 0.212 + ], + "angle": 0, + "content": "1: \\(x_{t} = y\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.213, + 0.665, + 0.226 + ], + "angle": 0, + "content": "2: for \\( t = T \\) to 1 do" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.228, + 0.69, + 0.242 + ], + "angle": 0, + "content": "3: \\(\\hat{x}_0 = x_t - \\epsilon_\\theta(x_t, t)\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.244, + 0.838, + 0.258 + ], + "angle": 0, + "content": "4: \\(\\hat{z} \\sim \\mathcal{N}(0, I)\\) if \\(t == T\\) else \\(\\hat{z} = Z_{\\phi}(x_t, t)\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.258, + 0.772, + 0.273 + ], + "angle": 0, + "content": "5: \\(\\hat{x}_t = (1 - \\frac{t}{T})\\hat{x}_0 + \\frac{t}{T} y + B(t)\\hat{z}\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.273, + 0.841, + 0.289 + ], + "angle": 0, + "content": "6: \\(\\hat{x}_{t - 1} = (1 - \\frac{t - 1}{T})\\hat{x}_0 + \\frac{t - 1}{T} y + B(t - 1)\\hat{z}\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.289, + 0.768, + 0.303 + ], + "angle": 0, + "content": "7: \\( U_{t + 1} = \\hat{x}_t - y, U_t = \\hat{x}_{t - 1} - y \\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.303, + 0.905, + 0.321 + ], + "angle": 0, + "content": "8: \\(x_{t - 1} = (1 - \\frac{1}{t})x_t + \\frac{1}{t - 1} y - \\frac{1}{t(t - 1)}\\hat{x}_0 - U_{t + 1} + \\frac{t}{t - 1} U_t\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.321, + 0.597, + 0.333 + ], + "angle": 0, + "content": "9: end for" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.336, + 0.6, + 0.349 + ], + "angle": 0, + "content": "0: \\(x_0 = \\hat{x}_0\\)" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.352, + 0.615, + 0.364 + ], + "angle": 0, + "content": "11: return \\( x_0 \\)" + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.42, + 0.645, + 0.437 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.451, + 0.906, + 0.482 + ], + "angle": 0, + "content": "In this section, we verify the capability of Dual-approx Bridge, addressing the following questions:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.495, + 0.906, + 0.569 + ], + "angle": 0, + "content": "- How do varying the number of sampling steps impact its performance in terms of image quality and faithfulness to GT? Furthermore, how does the sampling variance of our model compare to that of SDE-based samplers in terms of faithfulness to GT?" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.571, + 0.906, + 0.63 + ], + "angle": 0, + "content": "- How does Dual-approx Bridge perform in terms of faithfulness to GT compared to other models in image-to-image translation tasks that demand high faithfulness and deterministic result?" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.631, + 0.905, + 0.691 + ], + "angle": 0, + "content": "- How does Dual-approx Bridge perform in general image-to-image translation tasks, which prioritize image quality, when compared to other models including GANs, Diffusion models, and Bridge models?" + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.495, + 0.906, + 0.691 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.705, + 0.907, + 0.9 + ], + "angle": 0, + "content": "To address these questions, we used datasets with the following resolutions: Cityscapes [10] \\((256\\times 256)\\), Edges2Handbags [56] \\((64\\times 64)\\), DF2K [45] \\((256\\times 256)\\), Urban100 [22] \\((256\\times 256\\) patches), and BSD100 [34] \\((256\\times 256\\) patches). For evaluation, we used FID [18] to assess image realism (lower is better), LPIPS [53] for perceptual similarity (lower is better), PSNR for pixel-level similarity (higher is better) and SSIM [49] for structural similarity (closer to 1 is better). Our super-resolution (SR) experiments followed the experimental design of [8]. All of our experiments were implemented using PyTorch [38] and were run on a machine with two NVIDIA RTX A6000 GPUs." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "28236" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.115, + 0.089, + 0.461, + 0.155 + ], + "angle": 0, + "content": "
    StepsFID ↓LPIPS ↓PSNR ↑SSIM % ↑
    1,00042.700.44215.10 ± 0.02(43.2 ± 0.07) %
    20048.700.49215.70 ± 0.02(53.2 ± 0.06) %
    1057.430.53015.62 ± 0.02(55.3 ± 0.06) %
    356.070.52316.99 ± 0.01(57.4 ± 0.00) %
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.164, + 0.483, + 0.22 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with different sampling steps on the Cityscapes dataset. Bold values represent the best performance. Standard Deviation is obtained by five sampling trials for the same input." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.245, + 0.245, + 0.261 + ], + "angle": 0, + "content": "4.1. Ablation Study" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.268, + 0.317, + 0.283 + ], + "angle": 0, + "content": "4.1.1. Impact of Sampling Steps" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.286, + 0.483, + 0.542 + ], + "angle": 0, + "content": "We first evaluate the impact of sampling steps on our model's performance in the label-to-photo translation task on the Cityscapes dataset. Since the forward approximator in our model can predict \\( x_0 \\) given \\( x_t \\), sampling can be stopped at any time, allowing us to test sampling performance with a different number of steps. Table 1 presents how the varying sampling steps affect both image quality and faithfulness. It demonstrates that 1,000 sampling steps yield satisfactory image quality, with FID reaching a minimum of 42.70 and LPIPS dropping to 0.442. However, this comes at the cost of reduced faithfulness when compared to results obtained using fewer sampling steps, as evidenced by the decline in PSNR and SSIM. Notably, with only three sampling steps, our model achieves its peak in terms of faithfulness, attaining 16.99 PSNR and \\( 57.4\\% \\) SSIM. This demonstrates the model's adaptability to meet the diverse requirements of various applications." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.543, + 0.483, + 0.755 + ], + "angle": 0, + "content": "Additionally, we assessed the variance of the output fidelity in five independent sampling trials given the same input. Clearly, even at a higher sampling step of 1,000, the standard deviation of PSNR and SSIM remained low (0.02 and \\(0.07\\%\\), respectively), and it approaches zero with three sampling steps. This robustness underscores the superiority of our model in consistently producing high-quality and faithful results with minimal variability. Consequently, we employed three sampling steps for better robustness and higher efficiency in our subsequent experiments, unless otherwise specified. Our experiments show that three iterations perform well across these metrics, though further research is needed to determine the optimal number of sampling steps for different tasks." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.762, + 0.303, + 0.775 + ], + "angle": 0, + "content": "4.1.2. Faithfulness Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.885 + ], + "angle": 0, + "content": "We then compare the faithfulness of Dual-approx Bridge to other Brownian bridge models with SDE-based [32, 47] and PF-ODE-based samplers on the Cityscapes dataset using PSNR and SSIM metrics. Both the SDE-based and PF-ODE-based samplers use 1,000 sampling steps. The Brownian bridge model, as the leading I2I translation method, is an ideal benchmark for us due to the same bridge structure." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "As shown in Table 2, our Dual-approx Bridge clearly" + }, + { + "type": "table", + "bbox": [ + 0.535, + 0.089, + 0.888, + 0.14 + ], + "angle": 0, + "content": "
    MethodPSNR ↑SSIM % ↑
    Brown Bridge Model (SDE)14.28 ±0.21(49.6 ±0.63) %
    Brown Bridge Model (PF-ODE)15.23 ±0.00(51.2 ±0.00) %
    Ours16.99 ±0.01(57.4 ±0.00)%
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.15, + 0.907, + 0.207 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison with Brownian bridges using SDE and PF-ODE-based samplers on Cityscape. Bold values represent the best performance. Standard deviation is obtained by five sampling trials for the same input." + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.228, + 0.9, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.424, + 0.907, + 0.507 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison with Brownian bridges using SDE-based and PF-ODE-based samplers on Edges2Handbags. Three sampling trials are conducted by each model given the same input. Standard deviation among sampling results by our model, SDE-based and PF-ODE-based sampler are 0.0001, 0.1030 and 0, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.535, + 0.906, + 0.67 + ], + "angle": 0, + "content": "outperforms SDE-based and PF-ODE-based samplers. The PSNR value increased by approximately \\(12\\%\\) compared to the second-best, the PF-ODE-based sampler, while the SSIM value showed an overall improvement of \\(12\\%\\), rising from \\(51.2\\%\\) to \\(57.4\\%\\). Notably, the metrics of the Dualapprox Bridge exhibited minimal variance, whereas SDE-based sampler exhibited substantial variance in PSNR and SSIM due to the presence of white noise in every step of its sampling." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.671, + 0.906, + 0.779 + ], + "angle": 0, + "content": "Figure 3 shows three sample images by each model with the same input in the Edges2Handbags dataset. The images generated by SDE-based sampler are rich in detail but distinct from each other. The PF-ODE-based sampler produces consistent results but lacks details, resulting in a blurred appearance. As a comparison, Dual-approx Bridge achieves SDE-level quality with high and consistent faithfulness." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.788, + 0.874, + 0.804 + ], + "angle": 0, + "content": "4.2. Deterministic Image-to-Image Translation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.901 + ], + "angle": 0, + "content": "We selected the label-to-photo task in the Cityscapes dataset for deterministic image generation, where the goal is to generate realistic images from segmentation maps. Faithfulness is essential in this task, as it ensures the generated images accurately reflect the structure and content of the input labels, preserving the integrity of labeled features. We also in" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28237" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.132, + 0.089, + 0.441, + 0.164 + ], + "angle": 0, + "content": "
    MethodFID ↓PSNR ↑SSIM % ↑
    Pix2pix101.0412.8628.63 %
    CycleGAN75.3714.5334.16 %
    UNIT82.7414.6135.41 %
    Ours48.7015.7053.26 %
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.175, + 0.483, + 0.218 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison with deterministic models on Cityscape. Results of our model are obtained using 200 sampling steps. Bold values represent the best performance." + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.24, + 0.452, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.427, + 0.483, + 0.456 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison between Dual-approx Bridge and SOTA methods on the Cityscapes dataset." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.472, + 0.474, + 0.542 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.557, + 0.45, + 0.571 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison on BSD100 datasets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.642 + ], + "angle": 0, + "content": "cluded image super-resolution as a deterministic image-to-image translation task, which also requires both high quality and faithfulness." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.483, + 0.764 + ], + "angle": 0, + "content": "Given the inherent randomness in diffusion models, we primarily chose GAN-based models as baselines for deterministic I2I tasks. We selected Pix2Pix [24], CycleGAN [57], and UNIT [30] for comparison on the Cityscapes dataset. For image super-resolution, we used ESRGAN [48], RankSRGAN [52], and SRDiff [27] as baselines and followed the experimental configuration in [33] to train our model on DF2K and test it on Urban100 and BSD100." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Table 3 compares our model against baseline models on the Cityscapes dataset. The Dual-approx Bridge model demonstrates superior performance across all metrics compared to the other models. In terms of image quality, our model achieves a significant improvement in FID, with a score of 48.70 compared to the second-best score of 75.37, representing a substantial \\(35\\%\\) performance enhancement. Furthermore, our model exhibits notable gains in PSNR and SSIM, with PSNR increased from 14.61 to 15.70 and SSIM" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.095, + 0.892, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.37, + 0.874, + 0.384 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison on Uban100 datasets." + }, + { + "type": "table", + "bbox": [ + 0.535, + 0.401, + 0.887, + 0.495 + ], + "angle": 0, + "content": "
    ModelBSD100Urban100
    LPIPS ↓PSNR ↑LPIPS ↓PSNR ↑
    Bicubic0.528224.320.482621.75
    ESRGAN0.157923.650.122623.04
    RankSRGAN0.171423.800.140323.16
    SRDiff0.204624.170.139123.88
    Ours0.126726.560.120723.23
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.505, + 0.905, + 0.534 + ], + "angle": 0, + "content": "Table 4. Quantitative comparisons on BSD100 and Urban100. Bold values represent the best performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.565, + 0.905, + 0.61 + ], + "angle": 0, + "content": "improved by approximately \\(50\\%\\) (from \\(35.41\\%\\) to \\(53.26\\%\\)). Qualitative comparisons of various methods are presented in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.612, + 0.906, + 0.793 + ], + "angle": 0, + "content": "Table 4 compares our model against baselines on superresolution tasks. Our model performed the best on the BSD100 dataset with LPIPS at 0.1267 and PSNR at 26.56. It also achieves the highest LPIPS score of 0.1207 and the second-highest PSNR score of 23.23 on the Urban100 dataset. While SRDiff achieved the best PSNR on Urban100, its diffusion process encounters challenges in consistently producing stable outputs due to the inherent randomness in its SDE-based sampler (as shown in Table 2). Moreover, our model accomplishes this performance with significantly fewer sampling steps (3 used in our model vs. 1,000 used in SRDiff)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.9 + ], + "angle": 0, + "content": "Figure 5 compares the visual quality of various methods for image super-resolution. The top-right of each image shows a zoomed-in view of the red-boxed region for a detailed comparison. Due to inherent randomness, SDEs often introduce unrealistic artifacts, as seen in the example. The PF-ODE-based sampler results exhibit excessive smoothness and the loss of details, as evident in the zoomed" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28238" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.135, + 0.095, + 0.858, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.216, + 0.84, + 0.232 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison between Dual-approx Bridge and SOTA methods on the Edges2handbags dataset." + }, + { + "type": "table", + "bbox": [ + 0.155, + 0.244, + 0.422, + 0.408 + ], + "angle": 0, + "content": "
    MethodFID ↓
    MUNIT91.4
    DRIT155.3
    Distance85.8
    SelfDistance78.8
    CGGAN105.2
    CUT56.4
    FastCUT68.8
    DCLGAN49.4
    SimDCL51.3
    Ours48.7
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.419, + 0.484, + 0.448 + ], + "angle": 0, + "content": "Table 5. Quantitative comparison of image quality on Cityscapes (label to photo). Bold values represent the best performance." + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.454, + 0.462, + 0.594 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.604, + 0.484, + 0.675 + ], + "angle": 0, + "content": "Figure 8. Quantitative comparison between Dual-approx Bridge and A-bridge (with SDE-based sampler). Each model are sampled five times given the same input. Sampling standard deviation of the first example (Ours: 0.0084, A-bridge: 0.0903) and the second example (Ours: 0.0054, SDE: 0.0672)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.684, + 0.484, + 0.775 + ], + "angle": 0, + "content": "regions for both examples. Figure 6 further illustrates that our model can achieve detail preservation approaching or even surpassing that of SDE-based methods. Conversely, the Dual-approx Bridge method demonstrates a remarkable ability to preserve details while maintaining high faithfulness with GT." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.788, + 0.411, + 0.804 + ], + "angle": 0, + "content": "4.3. General Image-to-Image Translation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Finally, we evaluate Dual-approx Bridge on general image-to-image translation tasks. We assess our model's image quality on the Edges2Handbags and Cityscapes datasets. For Edges2Handbags, we conduct comparisons with Pix2Pix [24], SDEdit [35], DDIB [44], Rectified Flow [31], I2SB [29], DDBM [54], and A-bridge [47]. For the" + }, + { + "type": "table", + "bbox": [ + 0.578, + 0.244, + 0.845, + 0.394 + ], + "angle": 0, + "content": "
    MethodFID ↓
    Pix2Pix74.8
    DDIB186.84
    SDEdit85.8
    SelfDistance26.5
    Rectified Flow25.3
    I2SB7.43
    DDBM (VP)1.83
    A-Bridge1.07
    Ours1.36
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.405, + 0.907, + 0.433 + ], + "angle": 0, + "content": "Table 6. Quantitative comparison of image quality on Edges2Handbags. Bold values represent the best performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.44, + 0.907, + 0.5 + ], + "angle": 0, + "content": "Cityscapes dataset, we compared our model with MUNIT [23], DRIT [26], DistanceGAN [3], Self-DistanceGAN [3], CGGAN [55], CUT [37], FastCUT [37], DCLGAN [17], and SimDCL [17]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.501, + 0.906, + 0.606 + ], + "angle": 0, + "content": "On the Cityscapes dataset, our model outperforms all GAN-based models, achieving the top position and surpassing all competitors (Table 5). As shown in Table 6, our model achieves 1.36 FID score on the Edges2Handbags dataset, securing the second place. This result demonstrates that, despite our primary focus on enhancing faithfulness, our model still delivers highly competitive image quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.606, + 0.906, + 0.711 + ], + "angle": 0, + "content": "Figure 7 provides a qualitative comparison of our model with A-bridge on the Edges2Handbags dataset. Although A-bridge achieves the best FID score, it uses SDE-based samplers. As shown in Figure 8, our model demonstrates much higher faithfulness and consistency across repeated sampling with far fewer sampling steps (3 in our model vs. 50 in A-bridge)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.725, + 0.785, + 0.74 + ], + "angle": 0, + "content": "5. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this paper, we proposed Dual-approx Bridge, a novel generative model to produce faithful and high quality output for deterministic I2I translations. Our extensive experiments on benchmark datasets demonstrate the consistent and superior performance of Dual-approx Bridge when compared to SOTA I2I models. Our current choice of the SDE follows the Variance Preserving (VP) formulation. Moving forward, we plan to explore the potentials of combining both VP and variance exploding SDEs to further enhance our model's capabilities." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28239" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.155 + ], + "angle": 0, + "content": "[1] Aziz Alotaibi. Deep generative adversarial networks for image-to-image translation: A review. Symmetry, 12(10), 2020. 1, 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.159, + 0.483, + 0.199 + ], + "angle": 0, + "content": "[2] Brian D.O. Anderson. Reverse-time diffusion equation models. 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Deterministic I2I translation, such as in image super-resolution, extends this concept by guaranteeing that each input generates a consistent and predictable output, closely matching the ground truth (GT) with high fidelity. In this paper, we propose a denoising Brownian bridge model with dual approximators (Dualapprox Bridge), a novel generative model that exploits the Brownian bridge dynamics and two neural network-based approximators (one for forward and one for reverse process) to produce faithful output with negligible variance and high image quality in I2I translations. Our extensive experiments on benchmark datasets including image generation and super-resolution demonstrate the consistent and superior performance of Dual-approx Bridge in terms of image quality and faithfulness to GT when compared to both stochastic and deterministic baselines. Project page and code: https://github.com/bohan95/dual-app-bridge + +# 1. Introduction + +Image-to-Image (I2I) translation is a significant area of research with broad applications across academia and industry. It involves transforming an image from one domain to another while preserving essential features. Key tasks in this field include generating realistic images from semantic labels [24, 40, 42, 57], transforming segmentation masks into photo-like outputs [40, 47, 54], and enhancing image quality through super-resolution [8, 27, 52]. + +Among the wide range of applications, some I2I tasks particularly benefit from deterministic models. For instance, in super-resolution, the goal is to translate a low-resolution image into a high-resolution one while accurately preserving fine details. This task, as shown in recent studies [13, 14], requires consistency and high faithfulness to + +ground true (GT) because for a given low-resolution image, there is typically one "correct" high-resolution output that should be produced. In such an I2I task, we note that faithfulness or fidelity is to the individual GT, not just to the distribution of GT. Any variability in the generated output could result in artifacts or loss of critical information, making stochastic approaches less desirable. Similarly, in tasks such as denoising [6, 51] or inpainting [4, 39], where missing or noisy parts of an image need to be restored, a deterministic approach is preferred. + +Generative Adversarial Networks (GANs) [16] have been instrumental in advancing I2I translation, with models like Pix2Pix [24] and CycleGAN[57] demonstrating impressive results. GANs are deterministic during inference, producing the same output for a given input, which is advantageous for tasks requiring faithfulness. However, GANs often struggle to generate high-quality images, frequently resulting in blurriness and artifacts [1, 21]. + +Diffusion models, such as Denoising Diffusion Probabilistic Models (DDPM) [19] and Latent Diffusion Models (LDM) [40], generate high-quality images by progressively adding noise to images and learning the reverse process. Bridge models, such as Brownian bridge diffusion models [32, 47], utilize Stochastic Differential Equations (SDEs) to directly interpolate between input and output distributions, allowing precise control over transformations [40, 42]. This approach improves analytical tractability, making bridge models well suited for I2I translations. However, the inherent stochasticity in these models (see Figure 1(a)) complicates tasks where faithful results are required (e.g., image super-resolution and image reconstruction). Unlike traditional diffusion models [19, 40, 43], which start from noise and gradually denoise the input to generate an output, bridge models start from structured data and interpolate between input and output distributions. This difference means that deterministic methods like Probability Flow Ordinary Differential Equations (PF-ODEs) [43], when applied to bridge models, can lead to blurry images [43, 54], resulting in degraded model performance (see Figure 1(b)). + +![](images/cb296ffb4c735014a23dbf5b506191326b9121b670048d8e001bc8cd999388e4.jpg) + +![](images/54b3dde56994761efff1bffa25e7b2f88bc35be5ec414ad62ae473a3a7c37833.jpg) +(b) + +![](images/2998782fd0cc74bd5b985ad6a56d2581c019239594d448d738a9e56a660b570a.jpg) +(a) +(c) +Figure 1. Sampling comparison between SDE-based sampler, PF-ODE-based sampler, and Dual-approx Bridge. The circular area within the dashed circle indicates where the SDE-based sampling outputs land. (a) SDE-based Sampling: diverse outputs of high image quality. (b) PF-ODE-based Sampling: deterministic outputs lack of fine details of ground truth (GT). (c) Dual-approx Bridge Sampling: deterministic output with fine details of GT. + +![](images/5b22709f62ec9e99b98dd5c914b3e019b7352594c39da6422c5d618a8e7e005f.jpg) + +Therefore, there is a growing need for deterministic models that can preserve both image quality and faithfulness in I2I translations. + +To resolve this dilemma in the pursuit of deterministic sampling with both high image quality and fidelity, in this paper we propose a denoising Brownian bridge model with Dual Approximators (abbreviated as "Dual-approx Bridge"), a generative model that exploits the Brownian bridge structure to produce faithful output with negligible variance and with an image quality better than or comparable to that generated by SDE-based samplers. More specifically, in the SDE-based structure of a Brownian bridge with both forward and corresponding reverse Brownian motions, we train a neural network in the forward diffusive process to estimate the score function and the initial state in the diffusive iteration. Meanwhile, in the reverse process of the Brownian bridge, a second neural network is trained to approximate the white noise scaled to the time step increment. Here, we emphasize that in deterministic I2I, our goal is to generate a unique output from a given input, rather than translating probability distributions, as shown in Figure 1(c). The major contributions of this work are as follows: + +- To our best knowledge, Dual-approx Bridge is the first generative model that exploits the Brownian bridge structure to produce faithful output with negligible variance and high image quality for deterministic I2I translations. This is achieved through a novel design of a pair of approximators, trained in the forward and reverse diffusive processes, respectively. +- In Dual-approx Bridge, the reverse approximator optimizes the reverse denoising process and presents an opti + +mal deterministic route for the generative process. From a theoretical perspective, we analyze our model in a general setting where the white noise may take any time-dependent variance. + +- Through extensive experiments on benchmark datasets including image generation and super-resolution, we demonstrate the consistent and superior performance of Dual-approx Bridge on image quality and faithfulness to GT when compared to state-of-the-art (SOTA) GAN-based and diffusion-based I2I models. + +# 2. Related Work + +In this section, we briefly review the related literature, including image-to-image translation, GAN Models, Diffusion Models, and Bridge Models. + +# 2.1. Image-to-Image Translation + +Image-to-image (I2I) translation has become a core task in computer vision [1, 21, 36], focused on learning mappings between the source and target image domains for applications such as style transfer [15] and colorization [9]. Traditional methods, including Pix2Pix [24] and CycleGAN[57], utilize GAN-based architectures to translate images and support diverse I2I tasks by capturing domain-specific features, though challenges remain in maintaining high quality across complex domains [5, 41]. Deterministic I2I translation builds on this by ensuring that each input produces a consistent, predictable output — an essential requirement in fields like medical imaging [28], where precision and reproducibility are crucial. In tasks such as super-resolution [12] or denoising [46], deterministic models can enhance image resolution and clarity without introducing variations that could adversely affect analysis or interpretation. + +# 2.2. Brown Bridge + +The Brownian Bridge (BB) [32, 47] is a fundamental stochastic process that models a constrained Brownian motion, where the trajectory is conditioned on fixed start and end points. Unlike an unconstrained Wiener process, which evolves freely, a Brownian bridge interpolates between two known states while maintaining stochastic variations. This property makes it particularly useful in probabilistic modeling, including image-to-image (I2I) translation, conditional generative modeling, and stochastic optimal transport. + +# 2.3. Generative Adversarial Networks + +GANs [16] have been pivotal in advancing I2I translation by learning mappings between image domains through adversarial training. One foundational model, Pix2Pix [24], introduced a conditional GAN approach for paired I2I tasks, enabling applications like colorization[7] and semantic label-to-photo translation[24]. For unpaired I2I tasks, CycleGAN [57] employs cycle consistency, allowing the + +![](images/9503b4cf7d2d3500a3e91a441eb8dedbca33ed9b29064bf543dd282d95d0b7d8.jpg) +Figure 2. Training process of the two approximators (top-left: forward diffusive process, bottom-left: reverse diffusive process). Right: Sampling workflow with both approximators in action. + +model to translate images across domains without requiring paired samples. However, GANs often face artifacts in generated images [5, 41, 50]. Such limitations in image quality, combined with the common challenges of training instability, make GANs less suitable for applications demanding both quality and faithfulness. + +# 2.4. Diffusion and Bridge Models + +Diffusion models have established themselves as a leading approach in generative modeling [11] due to their ability to produce high-quality, realistic images through a gradual denoising process. DDPM [20] pioneered this approach, modeling image generation as a series of iterative steps in which random noise is gradually refined into a structured target image. The process results in exceptionally high-quality images with reduced artifacts, often surpassing GANs. LDMs [40] further refined DDPM by focusing on a latent space rather than a pixel space, making the generation process more efficient. + +To model the denoising process, diffusion models can rely on two distinct mathematical frameworks: SDEs and PF-ODEs [43]. SDEs, characterized by their inherent randomness, allow the model to generate diverse outputs by gradually reversing noise, enhancing detail and realism, but lacking consistency. This randomness can lead to the same input producing varying outputs. PF-ODEs, on the other hand, remove this randomness, providing a deterministic pathway that produces consistent outputs at the expense of fine details and image richness [32, 43]. Balancing the high image quality provided by SDEs with the consistency achieved by PF-ODEs remains a core challenge in diffusion models. + +Bridge models [25, 29, 54] integrate principles from both diffusion and bridge frameworks to create a probabilistic connection between input and output distributions. Both the Schrödinger and Brownian Bridge frameworks [47, 54] have demonstrated significant improvements in im + +age quality across various I2I tasks when compared to traditional diffusion models. However, they inherit certain limitations from both SDE-based and PF-ODE-based sampling. Specifically, they retain the stochastic characteristics of SDEs while also experiencing the lower image quality associated with PF-ODE-based samplers [54]. + +# 3. Deterministic Dual-approx Bridge + +In this section, we present Dual-approx Bridge in details. The Brownian bridge models [32, 47] have achieved high image quality and diversity in I2I translation. The structure of a Brownian bridge allows it to successfully map between paired probability distributions while generating high quality images of substantial diversity. On the other hand, when it comes to the deterministic I2I translation tasks, diversity is not preferred. In this direction, Dual-approx Bridge delivers deterministic I2I translation with minimal diversity. The key difference between our model and existing diffusion models is that in the generative process, existing models employ one neural network-based approximator which is trained in the forward diffusive process, while we make use of a pair of approximators trained in the forward and reverse diffusive processes separately, shown in Figure 2. + +# 3.1. Score-Based SDE + +The score-based Brownian bridge model is prescribed by the forward and reverse SDEs. The forward SDE reads + +$$ +d X = - \frac {X - Y}{1 - t} d t + g (t) d W, t \in (0, 1) \tag {1} +$$ + +where $W(\cdot)$ is a Brownian motion (i.e., a Wiener process), and $g(t)$ is the variance of the white noise. Then $X(1) = Y$ . + +Let $G(t) = (1 - t)^{2}\int_{0}^{t}\frac{g^{2}(s)}{(1 - s)^{2}} ds$ . It holds that + +$$ +\begin{array}{l} X _ {t} = (1 - t) X _ {0} + t Y + (1 - t) \int_ {0} ^ {t} \frac {g (s)}{1 - s} d W (s) \tag {2} \\ \sim \mathcal {N} ((1 - t) X _ {0} + t Y, G (t) I). \\ \end{array} +$$ + +That is + +$$ +X _ {t} = (1 - t) X _ {0} + t Y + \sqrt {G (t)} \epsilon , \epsilon \sim \mathcal {N} (0, I). \tag {3} +$$ + +The reverse generative SDE [2] is given by + +$$ +d X = - \left(\frac {X - Y}{1 - t} + g ^ {2} (t) \nabla \log p (X, t)\right) d t + g (t) d \bar {W} \tag {4} +$$ + +where $\overline{W} (\cdot)$ is a reverse time Brownian motion, and the score function is given by + +$$ +\nabla \log p (X, t) = - \frac {X - (1 - t) X _ {0} - t Y}{G (t)}. \tag {5} +$$ + +Hence, in the reverse transitional formula where $\Delta t$ is the time increment + +$$ +\begin{array}{l} X _ {t - 1} = X _ {t} + \left(\frac {X _ {t} - Y}{1 - t} + g ^ {2} (t) \nabla \log p \left(X _ {t}, t\right)\right) \Delta t \tag {6} \\ - g (t) \left(\bar {W} (t) - \bar {W} (t - \Delta t)\right) \\ \end{array} +$$ + +we need to estimate two quantities, $X_0$ and $\Delta \overline{W} = \overline{W}(t) - \overline{W}(t - \Delta t) = \sqrt{\Delta t} z$ , at each time step. In the SDE model, $z$ is just a random variable of the standard normal distribution. This causes the diversity in the output $\hat{X}_0$ . To make the sampling deterministic, we use a neural network $\epsilon_\theta$ to estimate $X_0$ in the forward diffusion process and a second neural network $Z_\phi(X_t, t)$ to estimate $z$ in the reverse diffusion process. That is, we train a pair of dual approximators $\epsilon_\theta$ and $Z_\phi$ . Note that our goal here is to generate a unique output from a given input, rather than translating probability distributions. So, we need two neural networks to approximate two different samples for the forward and reverse steps from the same white noise distribution. A single approximator cannot serve this purpose. + +# 3.2. Training of Neural Network Approximators + +For simplicity, we take the variance of the white noise $g(t) = 1$ . Then $G(t) = t(1 - t)$ . + +Forward Training Objective: We design a neural network $\epsilon_{\theta}$ to minimize, for $t = 1,\dots ,T$ $\epsilon \sim \mathcal{N}(0,I)$ + +$$ +\begin{array}{l} \left\| X _ {t} - X _ {0} - \epsilon_ {\theta} \left(X _ {t}, t\right) \right\| = \tag {7} \\ \left\| t \left(Y - X _ {0}\right) + \sqrt {t (1 - t)} \epsilon - \epsilon_ {\theta} \left(X _ {t}, t\right) \right\|. \\ \end{array} +$$ + +Here $X_{t}$ is defined by Equation 3 with $G(t) = t(1 - t)$ . This is the same training process as that of the Brownian bridges[47]. That is, we do the back propagation of + +$$ +\left\| t (Y - X _ {0}) + \sqrt {t (1 - t)} \epsilon - \epsilon_ {\theta} (X _ {t}, t) \right\|, +$$ + +where $t \sim \mathrm{Uniform}(1, \ldots, T)$ and $\epsilon \sim \mathcal{N}(0, I)$ . Essentially, the neural network $\epsilon_{\theta}$ is used to estimate $X_0$ given $X_t$ at the time step $t$ . Note that an optional conditional network design $\epsilon_{\theta}(X_t, t, Y)$ can also be used, which may improve the stability and efficiency of model training. + +Reverse Training Objective: Independently of the forward training, we design a neural network $Z_{\phi}(X_t,t)$ to minimize, for $t = 1,\dots ,T$ + +$$ +\left\| z - Z _ {\phi} \left(X _ {t}, t\right) \right\|, \quad z \sim \mathcal {N} (0, I), \tag {8} +$$ + +where $X_{t}$ is defined by $X_{t} = (1 - t)X_{0} + tY + \sqrt{t(1 - t)} z$ . That is, we do the back propagation of + +$$ +\left\| z - Z _ {\phi} (X _ {t}, t) \right\|, +$$ + +where $t\sim \mathrm{Uniform}(0,\ldots ,T - 1)$ and $z\sim \mathcal{N}(0,I)$ + +# 3.3. Sampling + +We discretize Equation 4 with $g(t) = 1$ to get the iterative generative formula: + +$$ +X _ {t - 1} = \left(1 - \frac {\Delta t}{t}\right) X _ {t} + \frac {\Delta t}{t} X _ {0} - \left[ \bar {W} (t) - \bar {W} (t - \Delta t) \right] \tag {9} +$$ + +We employ the two neural networks in this way: $X_0 \approx X_t - \epsilon_\theta(X_t, t)$ , while $\overline{W}(t) - \overline{W}(t - \Delta t)$ must be approximated with the use of the second neural network $Z_\phi$ . + +We make an observation here: $\overline{W}(t) - \overline{W}(t - \Delta t)$ and $\overline{W}(t + \Delta t) - \overline{W}(t)$ are independent, equivalent random variables. Let $g(t) = 1$ in (4) and (5) to get $X_{t} = (1 - t)X_{0} + tY + t\int_{1}^{t}\frac{d\overline{W}}{s}$ . Then we get + +$$ +\begin{array}{l} \overline {{W}} (t) - \overline {{W}} (t - \Delta t) = \overline {{W}} (t + \Delta t) - \overline {{W}} (t) \approx \\ U \left(X _ {t + 1}, t + 1\right) - \left(1 + \frac {\Delta t}{t}\right) U \left(X _ {t}, t\right) + \frac {\Delta t}{t} \left(X _ {0} - Y\right), \tag {10} \\ \end{array} +$$ + +where + +$$ +U \left(X _ {t}, t\right) = X _ {t} - Y = (1 - t) \left(X _ {0} - Y\right) + t \int_ {1} ^ {t} \frac {d \overline {{W}}}{s}. \tag {11} +$$ + +Hence, by plugging the above estimate into Equation 9, we get the final iterative generative formula + +$$ +\begin{array}{l} X _ {t - 1} = \left(1 - \frac {\Delta t}{t}\right) X _ {t} + \frac {\Delta t}{t} Y - U \left(X _ {t + 1}, t + 1\right) \tag {12} \\ + \left(1 + \frac {\Delta t}{t}\right) U (X _ {t}, t). \\ \end{array} +$$ + +In the formula (12), replace $t$ by $m_t = \frac{t}{T}$ and $\Delta t$ by $\frac{1}{T}$ if we apply the uniform sampling schedule with $T$ time steps. Also, we estimate $X_0$ by + +$$ +\hat {X} _ {0} = X _ {t} - \epsilon_ {\theta} (X _ {t}, t). \tag {13} +$$ + +Then for $t = T - 1, T - 2, \ldots, 2$ , we get + +$$ +\begin{array}{l} X _ {t - 1} = \left(1 - \frac {1}{t}\right) X _ {t} + \frac {1}{t} Y - U \left(X _ {t + 1}, t + 1\right) \tag {14} \\ + \left(1 + \frac {1}{t}\right) U (X _ {t}, t). \\ \end{array} +$$ + +# Algorithm 1 Forward Approximator Training Algorithm + +1: Input Paired Dataset $D_{x,y}$ , Forward Network $\epsilon_{\theta}$ , Total Time Steps $T$ +2: repeat +3: $x,y\sim D_{x,y}$ +4: $t\sim \mathrm{Uniform}(1,\ldots ,T)$ +5: $\epsilon \sim \mathcal{N}(0,I)$ +6: $x_{t} = (1 - \frac{t}{T})x_{0} + \frac{t}{T} y + B(t)\epsilon$ +7: $\nabla_{\theta}\| x_t - x_0 - \epsilon_{\theta}(x_t,t)\|$ +8: until converged +9: end function + +# Algorithm 2 Reverse Approximator Training Algorithm + +1: Input Paired Dataset $D_{x,y}$ , Reverse Network $Z_{\phi}$ , Total Time Steps $T$ +2: repeat +3: $x,y\sim D_{x,y}$ +4: $t\sim \mathrm{Uniform}(1,\ldots ,T)$ +5: $z\sim \mathcal{N}(0,I)$ +6: $x_{t} = (1 - \frac{t}{T})x_{0} + \frac{t}{T} y + B(t)z$ +7: $\nabla_{\phi}\| z - Z_{\phi}(x_t,t)\|$ +8: until converged +9: end function + +This iterative formula does not apply when $t = T$ as $X_{T + 1}$ does not exist. So we define $X_{T - 1}$ as we would in the SDE model + +$$ +X _ {T - 1} = Y - \frac {1}{T} \epsilon_ {\theta} (Y, T) - \frac {1}{\sqrt {T}} z, \quad z \sim \mathcal {N} (0, I). \tag {15} +$$ + +Finally, we define + +$$ +\hat {X} _ {0} = X _ {1} - \epsilon_ {\theta} \left(X _ {1}, 1\right) \tag {16} +$$ + +as the final output of the algorithm. + +The only randomness introduced in the entire sampling process is in $X_{T - 1}$ , which should be negligible, as the coefficient $\frac{1}{\sqrt{T}}$ of $z$ is fairly small compared to that of $Y$ . On the contrary, SDE models introduce randomness at every sampling step and hence cause substantial diversity to the output. + +# 3.4. Algorithm + +In a given paired dataset $D_{x,y}$ , $(x,y)$ denotes a paired images from the set. Define $B(t) = G\left(\frac{t}{T}\right) = \frac{1}{T}\sqrt{t(T - t)}$ , + +and we have the training and sampling algorithms shown in Algorithms 1 to 3, respectively. + +# Algorithm 3 Sampling Algorithm (Refactored) + +Input: $y$ , $\epsilon_{\theta}$ , $Z_{\phi}$ + +Output: $x_0$ + +1: $x_{t} = y$ + +2: for $t = T$ to 1 do + +3: $\hat{x}_0 = x_t - \epsilon_\theta(x_t, t)$ + +4: $\hat{z} \sim \mathcal{N}(0, I)$ if $t == T$ else $\hat{z} = Z_{\phi}(x_t, t)$ + +5: $\hat{x}_t = (1 - \frac{t}{T})\hat{x}_0 + \frac{t}{T} y + B(t)\hat{z}$ + +6: $\hat{x}_{t - 1} = (1 - \frac{t - 1}{T})\hat{x}_0 + \frac{t - 1}{T} y + B(t - 1)\hat{z}$ + +7: $U_{t + 1} = \hat{x}_t - y, U_t = \hat{x}_{t - 1} - y$ + +8: $x_{t - 1} = (1 - \frac{1}{t})x_t + \frac{1}{t - 1} y - \frac{1}{t(t - 1)}\hat{x}_0 - U_{t + 1} + \frac{t}{t - 1} U_t$ + +9: end for + +0: $x_0 = \hat{x}_0$ + +11: return $x_0$ + +# 4. Experiments + +In this section, we verify the capability of Dual-approx Bridge, addressing the following questions: + +- How do varying the number of sampling steps impact its performance in terms of image quality and faithfulness to GT? Furthermore, how does the sampling variance of our model compare to that of SDE-based samplers in terms of faithfulness to GT? +- How does Dual-approx Bridge perform in terms of faithfulness to GT compared to other models in image-to-image translation tasks that demand high faithfulness and deterministic result? +- How does Dual-approx Bridge perform in general image-to-image translation tasks, which prioritize image quality, when compared to other models including GANs, Diffusion models, and Bridge models? + +To address these questions, we used datasets with the following resolutions: Cityscapes [10] $(256\times 256)$ , Edges2Handbags [56] $(64\times 64)$ , DF2K [45] $(256\times 256)$ , Urban100 [22] $(256\times 256$ patches), and BSD100 [34] $(256\times 256$ patches). For evaluation, we used FID [18] to assess image realism (lower is better), LPIPS [53] for perceptual similarity (lower is better), PSNR for pixel-level similarity (higher is better) and SSIM [49] for structural similarity (closer to 1 is better). Our super-resolution (SR) experiments followed the experimental design of [8]. All of our experiments were implemented using PyTorch [38] and were run on a machine with two NVIDIA RTX A6000 GPUs. + +
    StepsFID ↓LPIPS ↓PSNR ↑SSIM % ↑
    1,00042.700.44215.10 ± 0.02(43.2 ± 0.07) %
    20048.700.49215.70 ± 0.02(53.2 ± 0.06) %
    1057.430.53015.62 ± 0.02(55.3 ± 0.06) %
    356.070.52316.99 ± 0.01(57.4 ± 0.00) %
    + +# 4.1. Ablation Study + +# 4.1.1. Impact of Sampling Steps + +We first evaluate the impact of sampling steps on our model's performance in the label-to-photo translation task on the Cityscapes dataset. Since the forward approximator in our model can predict $x_0$ given $x_t$ , sampling can be stopped at any time, allowing us to test sampling performance with a different number of steps. Table 1 presents how the varying sampling steps affect both image quality and faithfulness. It demonstrates that 1,000 sampling steps yield satisfactory image quality, with FID reaching a minimum of 42.70 and LPIPS dropping to 0.442. However, this comes at the cost of reduced faithfulness when compared to results obtained using fewer sampling steps, as evidenced by the decline in PSNR and SSIM. Notably, with only three sampling steps, our model achieves its peak in terms of faithfulness, attaining 16.99 PSNR and $57.4\%$ SSIM. This demonstrates the model's adaptability to meet the diverse requirements of various applications. + +Additionally, we assessed the variance of the output fidelity in five independent sampling trials given the same input. Clearly, even at a higher sampling step of 1,000, the standard deviation of PSNR and SSIM remained low (0.02 and $0.07\%$ , respectively), and it approaches zero with three sampling steps. This robustness underscores the superiority of our model in consistently producing high-quality and faithful results with minimal variability. Consequently, we employed three sampling steps for better robustness and higher efficiency in our subsequent experiments, unless otherwise specified. Our experiments show that three iterations perform well across these metrics, though further research is needed to determine the optimal number of sampling steps for different tasks. + +# 4.1.2. Faithfulness Evaluation + +We then compare the faithfulness of Dual-approx Bridge to other Brownian bridge models with SDE-based [32, 47] and PF-ODE-based samplers on the Cityscapes dataset using PSNR and SSIM metrics. Both the SDE-based and PF-ODE-based samplers use 1,000 sampling steps. The Brownian bridge model, as the leading I2I translation method, is an ideal benchmark for us due to the same bridge structure. + +As shown in Table 2, our Dual-approx Bridge clearly + +Table 1. Quantitative comparison with different sampling steps on the Cityscapes dataset. Bold values represent the best performance. Standard Deviation is obtained by five sampling trials for the same input. + +
    MethodPSNR ↑SSIM % ↑
    Brown Bridge Model (SDE)14.28 ±0.21(49.6 ±0.63) %
    Brown Bridge Model (PF-ODE)15.23 ±0.00(51.2 ±0.00) %
    Ours16.99 ±0.01(57.4 ±0.00)%
    + +Table 2. Quantitative comparison with Brownian bridges using SDE and PF-ODE-based samplers on Cityscape. Bold values represent the best performance. Standard deviation is obtained by five sampling trials for the same input. + +![](images/9eec88a941d7e18d4bdc139fc05a5e420df73ab63a00330e516139d33efca0a2.jpg) +Figure 3. Qualitative comparison with Brownian bridges using SDE-based and PF-ODE-based samplers on Edges2Handbags. Three sampling trials are conducted by each model given the same input. Standard deviation among sampling results by our model, SDE-based and PF-ODE-based sampler are 0.0001, 0.1030 and 0, respectively. + +outperforms SDE-based and PF-ODE-based samplers. The PSNR value increased by approximately $12\%$ compared to the second-best, the PF-ODE-based sampler, while the SSIM value showed an overall improvement of $12\%$ , rising from $51.2\%$ to $57.4\%$ . Notably, the metrics of the Dualapprox Bridge exhibited minimal variance, whereas SDE-based sampler exhibited substantial variance in PSNR and SSIM due to the presence of white noise in every step of its sampling. + +Figure 3 shows three sample images by each model with the same input in the Edges2Handbags dataset. The images generated by SDE-based sampler are rich in detail but distinct from each other. The PF-ODE-based sampler produces consistent results but lacks details, resulting in a blurred appearance. As a comparison, Dual-approx Bridge achieves SDE-level quality with high and consistent faithfulness. + +# 4.2. Deterministic Image-to-Image Translation + +We selected the label-to-photo task in the Cityscapes dataset for deterministic image generation, where the goal is to generate realistic images from segmentation maps. Faithfulness is essential in this task, as it ensures the generated images accurately reflect the structure and content of the input labels, preserving the integrity of labeled features. We also in + +
    MethodFID ↓PSNR ↑SSIM % ↑
    Pix2pix101.0412.8628.63 %
    CycleGAN75.3714.5334.16 %
    UNIT82.7414.6135.41 %
    Ours48.7015.7053.26 %
    + +![](images/26d8f6b7d8aae4fa2b57295f33f83165cbe4cc3a6e6efcfa69b13c076142058e.jpg) +Figure 4. Qualitative comparison between Dual-approx Bridge and SOTA methods on the Cityscapes dataset. + +![](images/051d86df7b564f0109c7dfcc172c791f7b7b3d8e1520945760bf74ba66c73f18.jpg) +Figure 5. Qualitative comparison on BSD100 datasets. + +cluded image super-resolution as a deterministic image-to-image translation task, which also requires both high quality and faithfulness. + +Given the inherent randomness in diffusion models, we primarily chose GAN-based models as baselines for deterministic I2I tasks. We selected Pix2Pix [24], CycleGAN [57], and UNIT [30] for comparison on the Cityscapes dataset. For image super-resolution, we used ESRGAN [48], RankSRGAN [52], and SRDiff [27] as baselines and followed the experimental configuration in [33] to train our model on DF2K and test it on Urban100 and BSD100. + +Table 3 compares our model against baseline models on the Cityscapes dataset. The Dual-approx Bridge model demonstrates superior performance across all metrics compared to the other models. In terms of image quality, our model achieves a significant improvement in FID, with a score of 48.70 compared to the second-best score of 75.37, representing a substantial $35\%$ performance enhancement. Furthermore, our model exhibits notable gains in PSNR and SSIM, with PSNR increased from 14.61 to 15.70 and SSIM + +![](images/2ea38c465dbbd3405192f04202c65f6656aac856b3f1db5f3113c599d7e38a96.jpg) +Figure 6. Qualitative comparison on Uban100 datasets. + +Table 3. Quantitative comparison with deterministic models on Cityscape. Results of our model are obtained using 200 sampling steps. Bold values represent the best performance. + +
    ModelBSD100Urban100
    LPIPS ↓PSNR ↑LPIPS ↓PSNR ↑
    Bicubic0.528224.320.482621.75
    ESRGAN0.157923.650.122623.04
    RankSRGAN0.171423.800.140323.16
    SRDiff0.204624.170.139123.88
    Ours0.126726.560.120723.23
    + +Table 4. Quantitative comparisons on BSD100 and Urban100. Bold values represent the best performance. + +improved by approximately $50\%$ (from $35.41\%$ to $53.26\%$ ). Qualitative comparisons of various methods are presented in Figure 4. + +Table 4 compares our model against baselines on superresolution tasks. Our model performed the best on the BSD100 dataset with LPIPS at 0.1267 and PSNR at 26.56. It also achieves the highest LPIPS score of 0.1207 and the second-highest PSNR score of 23.23 on the Urban100 dataset. While SRDiff achieved the best PSNR on Urban100, its diffusion process encounters challenges in consistently producing stable outputs due to the inherent randomness in its SDE-based sampler (as shown in Table 2). Moreover, our model accomplishes this performance with significantly fewer sampling steps (3 used in our model vs. 1,000 used in SRDiff). + +Figure 5 compares the visual quality of various methods for image super-resolution. The top-right of each image shows a zoomed-in view of the red-boxed region for a detailed comparison. Due to inherent randomness, SDEs often introduce unrealistic artifacts, as seen in the example. The PF-ODE-based sampler results exhibit excessive smoothness and the loss of details, as evident in the zoomed + +![](images/78caef6590d71f93a4953e26aac4dac850f0e08f333728df3d9a952eadc3016f.jpg) +Figure 7. Qualitative comparison between Dual-approx Bridge and SOTA methods on the Edges2handbags dataset. + +
    MethodFID ↓
    MUNIT91.4
    DRIT155.3
    Distance85.8
    SelfDistance78.8
    CGGAN105.2
    CUT56.4
    FastCUT68.8
    DCLGAN49.4
    SimDCL51.3
    Ours48.7
    + +![](images/e3886217df21da163e7262f2cd9882b5f517fe170234f0768c26666004ead213.jpg) +Figure 8. Quantitative comparison between Dual-approx Bridge and A-bridge (with SDE-based sampler). Each model are sampled five times given the same input. Sampling standard deviation of the first example (Ours: 0.0084, A-bridge: 0.0903) and the second example (Ours: 0.0054, SDE: 0.0672). + +regions for both examples. Figure 6 further illustrates that our model can achieve detail preservation approaching or even surpassing that of SDE-based methods. Conversely, the Dual-approx Bridge method demonstrates a remarkable ability to preserve details while maintaining high faithfulness with GT. + +# 4.3. General Image-to-Image Translation + +Finally, we evaluate Dual-approx Bridge on general image-to-image translation tasks. We assess our model's image quality on the Edges2Handbags and Cityscapes datasets. For Edges2Handbags, we conduct comparisons with Pix2Pix [24], SDEdit [35], DDIB [44], Rectified Flow [31], I2SB [29], DDBM [54], and A-bridge [47]. For the + +Table 5. Quantitative comparison of image quality on Cityscapes (label to photo). Bold values represent the best performance. + +
    MethodFID ↓
    Pix2Pix74.8
    DDIB186.84
    SDEdit85.8
    SelfDistance26.5
    Rectified Flow25.3
    I2SB7.43
    DDBM (VP)1.83
    A-Bridge1.07
    Ours1.36
    + +Table 6. Quantitative comparison of image quality on Edges2Handbags. Bold values represent the best performance. + +Cityscapes dataset, we compared our model with MUNIT [23], DRIT [26], DistanceGAN [3], Self-DistanceGAN [3], CGGAN [55], CUT [37], FastCUT [37], DCLGAN [17], and SimDCL [17]. + +On the Cityscapes dataset, our model outperforms all GAN-based models, achieving the top position and surpassing all competitors (Table 5). As shown in Table 6, our model achieves 1.36 FID score on the Edges2Handbags dataset, securing the second place. This result demonstrates that, despite our primary focus on enhancing faithfulness, our model still delivers highly competitive image quality. + +Figure 7 provides a qualitative comparison of our model with A-bridge on the Edges2Handbags dataset. Although A-bridge achieves the best FID score, it uses SDE-based samplers. 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In ICCV, pages 2223-2232, 2017. 1, 2, 7 \ No newline at end of file diff --git a/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/images.zip b/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..da9b2a307014e1bc0c7c0a204751e5a83e439cea --- /dev/null +++ b/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fd20480e15c79b9df8334f9e55236eabfbb23bd463cf193d4dd0aaa20512eee5 +size 552639 diff --git a/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/layout.json b/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..249d7751a27f32bdceaf6b4c76106509231aac50 --- /dev/null +++ b/2025/Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators/layout.json @@ -0,0 +1,10911 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 77, + 102, + 533, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 102, + 533, + 140 + ], + "spans": [ + { + "bbox": [ + 77, + 102, + 533, + 140 + ], + "type": "text", + "content": "Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "spans": [ + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "text", + "content": "Bohan Xiao" + }, + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "text", + "content": ", Peiyong Wang" + }, + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "text", + "content": ", Qisheng He" + }, + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "text", + "content": ", Ming Dong" + }, + { + "bbox": [ + 161, + 160, + 450, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 99, + 176, + 510, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 176, + 510, + 203 + ], + "spans": [ + { + "bbox": [ + 99, + 176, + 510, + 203 + ], + "type": "text", + "content": "Department of Computer Science, Wayne State University " + }, + { + "bbox": [ + 99, + 176, + 510, + 203 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 99, + 176, + 510, + 203 + ], + "type": "text", + "content": ", Detroit, Michigan, USA \nDepartment of Mathematics, Wayne State University " + }, + { + "bbox": [ + 99, + 176, + 510, + 203 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 99, + 176, + 510, + 203 + ], + "type": "text", + "content": ", Detroit, Michigan, USA" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 182, + 205, + 425, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 205, + 425, + 217 + ], + "spans": [ + { + "bbox": [ + 182, + 205, + 425, + 217 + ], + "type": "text", + "content": "{gk6511, pywang, qisheng.he, mdong}@wayne.edu" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 244, + 200, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 244, + 200, + 258 + ], + "spans": [ + { + "bbox": [ + 151, + 244, + 200, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 270, + 297, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 270, + 297, + 486 + ], + "spans": [ + { + "bbox": [ + 55, + 270, + 297, + 486 + ], + "type": "text", + "content": "Image-to-Image (I2I) translation involves converting an image from one domain to another. Deterministic I2I translation, such as in image super-resolution, extends this concept by guaranteeing that each input generates a consistent and predictable output, closely matching the ground truth (GT) with high fidelity. In this paper, we propose a denoising Brownian bridge model with dual approximators (Dualapprox Bridge), a novel generative model that exploits the Brownian bridge dynamics and two neural network-based approximators (one for forward and one for reverse process) to produce faithful output with negligible variance and high image quality in I2I translations. Our extensive experiments on benchmark datasets including image generation and super-resolution demonstrate the consistent and superior performance of Dual-approx Bridge in terms of image quality and faithfulness to GT when compared to both stochastic and deterministic baselines. Project page and code: https://github.com/bohan95/dual-app-bridge" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 508, + 135, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 508, + 135, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 508, + 135, + 521 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 528, + 295, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 528, + 295, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 528, + 295, + 624 + ], + "type": "text", + "content": "Image-to-Image (I2I) translation is a significant area of research with broad applications across academia and industry. It involves transforming an image from one domain to another while preserving essential features. Key tasks in this field include generating realistic images from semantic labels [24, 40, 42, 57], transforming segmentation masks into photo-like outputs [40, 47, 54], and enhancing image quality through super-resolution [8, 27, 52]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 624, + 295, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 295, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 295, + 696 + ], + "type": "text", + "content": "Among the wide range of applications, some I2I tasks particularly benefit from deterministic models. For instance, in super-resolution, the goal is to translate a low-resolution image into a high-resolution one while accurately preserving fine details. This task, as shown in recent studies [13, 14], requires consistency and high faithfulness to" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 246, + 554, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 246, + 554, + 365 + ], + "spans": [ + { + "bbox": [ + 313, + 246, + 554, + 365 + ], + "type": "text", + "content": "ground true (GT) because for a given low-resolution image, there is typically one \"correct\" high-resolution output that should be produced. In such an I2I task, we note that faithfulness or fidelity is to the individual GT, not just to the distribution of GT. Any variability in the generated output could result in artifacts or loss of critical information, making stochastic approaches less desirable. Similarly, in tasks such as denoising [6, 51] or inpainting [4, 39], where missing or noisy parts of an image need to be restored, a deterministic approach is preferred." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 366, + 554, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 554, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 554, + 461 + ], + "type": "text", + "content": "Generative Adversarial Networks (GANs) [16] have been instrumental in advancing I2I translation, with models like Pix2Pix [24] and CycleGAN[57] demonstrating impressive results. GANs are deterministic during inference, producing the same output for a given input, which is advantageous for tasks requiring faithfulness. However, GANs often struggle to generate high-quality images, frequently resulting in blurriness and artifacts [1, 21]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 462, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 462, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 462, + 554, + 715 + ], + "type": "text", + "content": "Diffusion models, such as Denoising Diffusion Probabilistic Models (DDPM) [19] and Latent Diffusion Models (LDM) [40], generate high-quality images by progressively adding noise to images and learning the reverse process. Bridge models, such as Brownian bridge diffusion models [32, 47], utilize Stochastic Differential Equations (SDEs) to directly interpolate between input and output distributions, allowing precise control over transformations [40, 42]. This approach improves analytical tractability, making bridge models well suited for I2I translations. However, the inherent stochasticity in these models (see Figure 1(a)) complicates tasks where faithful results are required (e.g., image super-resolution and image reconstruction). Unlike traditional diffusion models [19, 40, 43], which start from noise and gradually denoise the input to generate an output, bridge models start from structured data and interpolate between input and output distributions. This difference means that deterministic methods like Probability Flow Ordinary Differential Equations (PF-ODEs) [43], when applied to bridge models, can lead to blurry images [43, 54], resulting in degraded model performance (see Figure 1(b))." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 230, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 230, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 230, + 713 + ], + "type": "text", + "content": "* Both authors contributed equally to this research." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28232" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 182, + 145 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 182, + 145 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 182, + 145 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 182, + 145 + ], + "type": "image", + "image_path": "cb296ffb4c735014a23dbf5b506191326b9121b670048d8e001bc8cd999388e4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 182, + 72, + 306, + 145 + ], + "blocks": [ + { + "bbox": [ + 182, + 72, + 306, + 145 + ], + "lines": [ + { + "bbox": [ + 182, + 72, + 306, + 145 + ], + "spans": [ + { + "bbox": [ + 182, + 72, + 306, + 145 + ], + "type": "image", + "image_path": "54b3dde56994761efff1bffa25e7b2f88bc35be5ec414ad62ae473a3a7c37833.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 240, + 146, + 249, + 152 + ], + "lines": [ + { + "bbox": [ + 240, + 146, + 249, + 152 + ], + "spans": [ + { + "bbox": [ + 240, + 146, + 249, + 152 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 58, + 153, + 182, + 227 + ], + "blocks": [ + { + "bbox": [ + 117, + 147, + 126, + 153 + ], + "lines": [ + { + "bbox": [ + 117, + 147, + 126, + 153 + ], + "spans": [ + { + "bbox": [ + 117, + 147, + 126, + 153 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 153, + 182, + 227 + ], + "lines": [ + { + "bbox": [ + 58, + 153, + 182, + 227 + ], + "spans": [ + { + "bbox": [ + 58, + 153, + 182, + 227 + ], + "type": "image", + "image_path": "2998782fd0cc74bd5b985ad6a56d2581c019239594d448d738a9e56a660b570a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 117, + 227, + 126, + 235 + ], + "lines": [ + { + "bbox": [ + 117, + 227, + 126, + 235 + ], + "spans": [ + { + "bbox": [ + 117, + 227, + 126, + 235 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 243, + 296, + 321 + ], + "lines": [ + { + "bbox": [ + 55, + 243, + 296, + 321 + ], + "spans": [ + { + "bbox": [ + 55, + 243, + 296, + 321 + ], + "type": "text", + "content": "Figure 1. Sampling comparison between SDE-based sampler, PF-ODE-based sampler, and Dual-approx Bridge. The circular area within the dashed circle indicates where the SDE-based sampling outputs land. (a) SDE-based Sampling: diverse outputs of high image quality. (b) PF-ODE-based Sampling: deterministic outputs lack of fine details of ground truth (GT). (c) Dual-approx Bridge Sampling: deterministic output with fine details of GT." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 183, + 157, + 302, + 219 + ], + "blocks": [ + { + "bbox": [ + 183, + 157, + 302, + 219 + ], + "lines": [ + { + "bbox": [ + 183, + 157, + 302, + 219 + ], + "spans": [ + { + "bbox": [ + 183, + 157, + 302, + 219 + ], + "type": "image", + "image_path": "5b22709f62ec9e99b98dd5c914b3e019b7352594c39da6422c5d618a8e7e005f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 329, + 296, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 329, + 296, + 364 + ], + "spans": [ + { + "bbox": [ + 55, + 329, + 296, + 364 + ], + "type": "text", + "content": "Therefore, there is a growing need for deterministic models that can preserve both image quality and faithfulness in I2I translations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 365, + 296, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 296, + 604 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 296, + 604 + ], + "type": "text", + "content": "To resolve this dilemma in the pursuit of deterministic sampling with both high image quality and fidelity, in this paper we propose a denoising Brownian bridge model with Dual Approximators (abbreviated as \"Dual-approx Bridge\"), a generative model that exploits the Brownian bridge structure to produce faithful output with negligible variance and with an image quality better than or comparable to that generated by SDE-based samplers. More specifically, in the SDE-based structure of a Brownian bridge with both forward and corresponding reverse Brownian motions, we train a neural network in the forward diffusive process to estimate the score function and the initial state in the diffusive iteration. Meanwhile, in the reverse process of the Brownian bridge, a second neural network is trained to approximate the white noise scaled to the time step increment. Here, we emphasize that in deterministic I2I, our goal is to generate a unique output from a given input, rather than translating probability distributions, as shown in Figure 1(c). The major contributions of this work are as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 605, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 689 + ], + "type": "text", + "content": "- To our best knowledge, Dual-approx Bridge is the first generative model that exploits the Brownian bridge structure to produce faithful output with negligible variance and high image quality for deterministic I2I translations. This is achieved through a novel design of a pair of approximators, trained in the forward and reverse diffusive processes, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "- In Dual-approx Bridge, the reverse approximator optimizes the reverse denoising process and presents an opti" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 321, + 72, + 553, + 120 + ], + "type": "text", + "content": "mal deterministic route for the generative process. From a theoretical perspective, we analyze our model in a general setting where the white noise may take any time-dependent variance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 121, + 555, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 121, + 555, + 192 + ], + "spans": [ + { + "bbox": [ + 314, + 121, + 555, + 192 + ], + "type": "text", + "content": "- Through extensive experiments on benchmark datasets including image generation and super-resolution, we demonstrate the consistent and superior performance of Dual-approx Bridge on image quality and faithfulness to GT when compared to state-of-the-art (SOTA) GAN-based and diffusion-based I2I models." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 201, + 401, + 214 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 201, + 401, + 214 + ], + "spans": [ + { + "bbox": [ + 314, + 201, + 401, + 214 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 222, + 554, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 222, + 554, + 258 + ], + "spans": [ + { + "bbox": [ + 313, + 222, + 554, + 258 + ], + "type": "text", + "content": "In this section, we briefly review the related literature, including image-to-image translation, GAN Models, Diffusion Models, and Bridge Models." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 265, + 468, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 265, + 468, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 265, + 468, + 277 + ], + "type": "text", + "content": "2.1. Image-to-Image Translation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 282, + 555, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 282, + 555, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 282, + 555, + 475 + ], + "type": "text", + "content": "Image-to-image (I2I) translation has become a core task in computer vision [1, 21, 36], focused on learning mappings between the source and target image domains for applications such as style transfer [15] and colorization [9]. Traditional methods, including Pix2Pix [24] and CycleGAN[57], utilize GAN-based architectures to translate images and support diverse I2I tasks by capturing domain-specific features, though challenges remain in maintaining high quality across complex domains [5, 41]. Deterministic I2I translation builds on this by ensuring that each input produces a consistent, predictable output — an essential requirement in fields like medical imaging [28], where precision and reproducibility are crucial. In tasks such as super-resolution [12] or denoising [46], deterministic models can enhance image resolution and clarity without introducing variations that could adversely affect analysis or interpretation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 480, + 403, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 480, + 403, + 493 + ], + "spans": [ + { + "bbox": [ + 313, + 480, + 403, + 493 + ], + "type": "text", + "content": "2.2. Brown Bridge" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 498, + 554, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 606 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 606 + ], + "type": "text", + "content": "The Brownian Bridge (BB) [32, 47] is a fundamental stochastic process that models a constrained Brownian motion, where the trajectory is conditioned on fixed start and end points. Unlike an unconstrained Wiener process, which evolves freely, a Brownian bridge interpolates between two known states while maintaining stochastic variations. This property makes it particularly useful in probabilistic modeling, including image-to-image (I2I) translation, conditional generative modeling, and stochastic optimal transport." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 613, + 495, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 495, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 495, + 624 + ], + "type": "text", + "content": "2.3. Generative Adversarial Networks" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 714 + ], + "type": "text", + "content": "GANs [16] have been pivotal in advancing I2I translation by learning mappings between image domains through adversarial training. One foundational model, Pix2Pix [24], introduced a conditional GAN approach for paired I2I tasks, enabling applications like colorization[7] and semantic label-to-photo translation[24]. For unpaired I2I tasks, CycleGAN [57] employs cycle consistency, allowing the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28233" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 541, + 233 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 541, + 233 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 541, + 233 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 541, + 233 + ], + "type": "image", + "image_path": "9503b4cf7d2d3500a3e91a441eb8dedbca33ed9b29064bf543dd282d95d0b7d8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 242, + 555, + 266 + ], + "lines": [ + { + "bbox": [ + 55, + 242, + 555, + 266 + ], + "spans": [ + { + "bbox": [ + 55, + 242, + 555, + 266 + ], + "type": "text", + "content": "Figure 2. Training process of the two approximators (top-left: forward diffusive process, bottom-left: reverse diffusive process). Right: Sampling workflow with both approximators in action." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 270, + 296, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 270, + 296, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 270, + 296, + 344 + ], + "type": "text", + "content": "model to translate images across domains without requiring paired samples. However, GANs often face artifacts in generated images [5, 41, 50]. Such limitations in image quality, combined with the common challenges of training instability, make GANs less suitable for applications demanding both quality and faithfulness." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 349, + 214, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 214, + 363 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 214, + 363 + ], + "type": "text", + "content": "2.4. Diffusion and Bridge Models" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 366, + 295, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 366, + 295, + 498 + ], + "spans": [ + { + "bbox": [ + 54, + 366, + 295, + 498 + ], + "type": "text", + "content": "Diffusion models have established themselves as a leading approach in generative modeling [11] due to their ability to produce high-quality, realistic images through a gradual denoising process. DDPM [20] pioneered this approach, modeling image generation as a series of iterative steps in which random noise is gradually refined into a structured target image. The process results in exceptionally high-quality images with reduced artifacts, often surpassing GANs. LDMs [40] further refined DDPM by focusing on a latent space rather than a pixel space, making the generation process more efficient." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 498, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 498, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 54, + 498, + 295, + 653 + ], + "type": "text", + "content": "To model the denoising process, diffusion models can rely on two distinct mathematical frameworks: SDEs and PF-ODEs [43]. SDEs, characterized by their inherent randomness, allow the model to generate diverse outputs by gradually reversing noise, enhancing detail and realism, but lacking consistency. This randomness can lead to the same input producing varying outputs. PF-ODEs, on the other hand, remove this randomness, providing a deterministic pathway that produces consistent outputs at the expense of fine details and image richness [32, 43]. Balancing the high image quality provided by SDEs with the consistency achieved by PF-ODEs remains a core challenge in diffusion models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "Bridge models [25, 29, 54] integrate principles from both diffusion and bridge frameworks to create a probabilistic connection between input and output distributions. Both the Schrödinger and Brownian Bridge frameworks [47, 54] have demonstrated significant improvements in im" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 270, + 555, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 270, + 555, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 555, + 344 + ], + "type": "text", + "content": "age quality across various I2I tasks when compared to traditional diffusion models. However, they inherit certain limitations from both SDE-based and PF-ODE-based sampling. Specifically, they retain the stochastic characteristics of SDEs while also experiencing the lower image quality associated with PF-ODE-based samplers [54]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 365, + 504, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 504, + 380 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 504, + 380 + ], + "type": "text", + "content": "3. Deterministic Dual-approx Bridge" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 389, + 556, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 556, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 556, + 571 + ], + "type": "text", + "content": "In this section, we present Dual-approx Bridge in details. The Brownian bridge models [32, 47] have achieved high image quality and diversity in I2I translation. The structure of a Brownian bridge allows it to successfully map between paired probability distributions while generating high quality images of substantial diversity. On the other hand, when it comes to the deterministic I2I translation tasks, diversity is not preferred. In this direction, Dual-approx Bridge delivers deterministic I2I translation with minimal diversity. The key difference between our model and existing diffusion models is that in the generative process, existing models employ one neural network-based approximator which is trained in the forward diffusive process, while we make use of a pair of approximators trained in the forward and reverse diffusive processes separately, shown in Figure 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 589, + 419, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 589, + 419, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 589, + 419, + 601 + ], + "type": "text", + "content": "3.1. Score-Based SDE" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 610, + 555, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 610, + 555, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 610, + 555, + 635 + ], + "type": "text", + "content": "The score-based Brownian bridge model is prescribed by the forward and reverse SDEs. The forward SDE reads" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 347, + 648, + 555, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 648, + 555, + 673 + ], + "spans": [ + { + "bbox": [ + 347, + 648, + 555, + 673 + ], + "type": "interline_equation", + "content": "d X = - \\frac {X - Y}{1 - t} d t + g (t) d W, t \\in (0, 1) \\tag {1}", + "image_path": "1267085adf096262040230839b71e6b49f84c4bd15dbb8242e4750c450ffb492.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "inline_equation", + "content": "W(\\cdot)" + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": " is a Brownian motion (i.e., a Wiener process), and " + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "inline_equation", + "content": "g(t)" + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": " is the variance of the white noise. Then " + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "inline_equation", + "content": "X(1) = Y" + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28234" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 70, + 247, + 89 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 70, + 247, + 89 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 247, + 89 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 55, + 70, + 247, + 89 + ], + "type": "inline_equation", + "content": "G(t) = (1 - t)^{2}\\int_{0}^{t}\\frac{g^{2}(s)}{(1 - s)^{2}} ds" + }, + { + "bbox": [ + 55, + 70, + 247, + 89 + ], + "type": "text", + "content": ". It holds that" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 95, + 294, + 136 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 95, + 294, + 136 + ], + "spans": [ + { + "bbox": [ + 67, + 95, + 294, + 136 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {t} = (1 - t) X _ {0} + t Y + (1 - t) \\int_ {0} ^ {t} \\frac {g (s)}{1 - s} d W (s) \\tag {2} \\\\ \\sim \\mathcal {N} ((1 - t) X _ {0} + t Y, G (t) I). \\\\ \\end{array}", + "image_path": "d78eb7ffe3d2c926ebdec27f5d423b28a60d9812fe252d0da43be12e42ea1586.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 142, + 87, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 142, + 87, + 152 + ], + "spans": [ + { + "bbox": [ + 55, + 142, + 87, + 152 + ], + "type": "text", + "content": "That is" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 70, + 159, + 295, + 174 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 159, + 295, + 174 + ], + "spans": [ + { + "bbox": [ + 70, + 159, + 295, + 174 + ], + "type": "interline_equation", + "content": "X _ {t} = (1 - t) X _ {0} + t Y + \\sqrt {G (t)} \\epsilon , \\epsilon \\sim \\mathcal {N} (0, I). \\tag {3}", + "image_path": "054e6e424ee37a12bbafc2137ed6cabfdf32dad02fdb60d73762edeb5654f0e4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 181, + 230, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 181, + 230, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 181, + 230, + 194 + ], + "type": "text", + "content": "The reverse generative SDE [2] is given by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 198, + 294, + 234 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 198, + 294, + 234 + ], + "spans": [ + { + "bbox": [ + 58, + 198, + 294, + 234 + ], + "type": "interline_equation", + "content": "d X = - \\left(\\frac {X - Y}{1 - t} + g ^ {2} (t) \\nabla \\log p (X, t)\\right) d t + g (t) d \\bar {W} \\tag {4}", + "image_path": "e3cb15ab10d83b1931e6cb3676e5167baf19fe224015c6837ec0abdffe36d215.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 235, + 295, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 235, + 295, + 260 + ], + "spans": [ + { + "bbox": [ + 55, + 235, + 295, + 260 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 235, + 295, + 260 + ], + "type": "inline_equation", + "content": "\\overline{W} (\\cdot)" + }, + { + "bbox": [ + 55, + 235, + 295, + 260 + ], + "type": "text", + "content": " is a reverse time Brownian motion, and the score function is given by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 90, + 265, + 295, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 265, + 295, + 291 + ], + "spans": [ + { + "bbox": [ + 90, + 265, + 295, + 291 + ], + "type": "interline_equation", + "content": "\\nabla \\log p (X, t) = - \\frac {X - (1 - t) X _ {0} - t Y}{G (t)}. \\tag {5}", + "image_path": "2ff0b8f13a338904d4087d044404342bd06eaa4fba79b1c16ad7a6506be8c532.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 297, + 296, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 297, + 296, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 296, + 319 + ], + "type": "text", + "content": "Hence, in the reverse transitional formula where " + }, + { + "bbox": [ + 55, + 297, + 296, + 319 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 55, + 297, + 296, + 319 + ], + "type": "text", + "content": " is the time increment" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 61, + 323, + 294, + 367 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 323, + 294, + 367 + ], + "spans": [ + { + "bbox": [ + 61, + 323, + 294, + 367 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {t - 1} = X _ {t} + \\left(\\frac {X _ {t} - Y}{1 - t} + g ^ {2} (t) \\nabla \\log p \\left(X _ {t}, t\\right)\\right) \\Delta t \\tag {6} \\\\ - g (t) \\left(\\bar {W} (t) - \\bar {W} (t - \\Delta t)\\right) \\\\ \\end{array}", + "image_path": "9b93e16595b34d913bf2169c3e9fec11c0c28b788b257ec20da2bca5ba7667bd.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "spans": [ + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": "we need to estimate two quantities, " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "X_0" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "\\Delta \\overline{W} = \\overline{W}(t) - \\overline{W}(t - \\Delta t) = \\sqrt{\\Delta t} z" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": ", at each time step. In the SDE model, " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": " is just a random variable of the standard normal distribution. This causes the diversity in the output " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "\\hat{X}_0" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": ". To make the sampling deterministic, we use a neural network " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "\\epsilon_\\theta" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": " to estimate " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "X_0" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": " in the forward diffusion process and a second neural network " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "Z_\\phi(X_t, t)" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": " to estimate " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": " in the reverse diffusion process. That is, we train a pair of dual approximators " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "\\epsilon_\\theta" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "inline_equation", + "content": "Z_\\phi" + }, + { + "bbox": [ + 55, + 373, + 296, + 542 + ], + "type": "text", + "content": ". Note that our goal here is to generate a unique output from a given input, rather than translating probability distributions. So, we need two neural networks to approximate two different samples for the forward and reverse steps from the same white noise distribution. A single approximator cannot serve this purpose." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 548, + 284, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 284, + 561 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 284, + 561 + ], + "type": "text", + "content": "3.2. Training of Neural Network Approximators" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 565, + 295, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 565, + 295, + 589 + ], + "spans": [ + { + "bbox": [ + 55, + 565, + 295, + 589 + ], + "type": "text", + "content": "For simplicity, we take the variance of the white noise " + }, + { + "bbox": [ + 55, + 565, + 295, + 589 + ], + "type": "inline_equation", + "content": "g(t) = 1" + }, + { + "bbox": [ + 55, + 565, + 295, + 589 + ], + "type": "text", + "content": ". Then " + }, + { + "bbox": [ + 55, + 565, + 295, + 589 + ], + "type": "inline_equation", + "content": "G(t) = t(1 - t)" + }, + { + "bbox": [ + 55, + 565, + 295, + 589 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 590, + 295, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 590, + 295, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 590, + 295, + 613 + ], + "type": "text", + "content": "Forward Training Objective: We design a neural network " + }, + { + "bbox": [ + 55, + 590, + 295, + 613 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 590, + 295, + 613 + ], + "type": "text", + "content": " to minimize, for " + }, + { + "bbox": [ + 55, + 590, + 295, + 613 + ], + "type": "inline_equation", + "content": "t = 1,\\dots ,T" + }, + { + "bbox": [ + 55, + 590, + 295, + 613 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,I)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 92, + 620, + 295, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 620, + 295, + 651 + ], + "spans": [ + { + "bbox": [ + 92, + 620, + 295, + 651 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\left\\| X _ {t} - X _ {0} - \\epsilon_ {\\theta} \\left(X _ {t}, t\\right) \\right\\| = \\tag {7} \\\\ \\left\\| t \\left(Y - X _ {0}\\right) + \\sqrt {t (1 - t)} \\epsilon - \\epsilon_ {\\theta} \\left(X _ {t}, t\\right) \\right\\|. \\\\ \\end{array}", + "image_path": "772a55367bc0ee87a1ac3d9d758e7b287e3edb52100719324c21352c4d55816e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 657, + 296, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 657, + 296, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 657, + 296, + 694 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 55, + 657, + 296, + 694 + ], + "type": "inline_equation", + "content": "X_{t}" + }, + { + "bbox": [ + 55, + 657, + 296, + 694 + ], + "type": "text", + "content": " is defined by Equation 3 with " + }, + { + "bbox": [ + 55, + 657, + 296, + 694 + ], + "type": "inline_equation", + "content": "G(t) = t(1 - t)" + }, + { + "bbox": [ + 55, + 657, + 296, + 694 + ], + "type": "text", + "content": ". This is the same training process as that of the Brownian bridges[47]. That is, we do the back propagation of" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 92, + 700, + 259, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 700, + 259, + 715 + ], + "spans": [ + { + "bbox": [ + 92, + 700, + 259, + 715 + ], + "type": "interline_equation", + "content": "\\left\\| t (Y - X _ {0}) + \\sqrt {t (1 - t)} \\epsilon - \\epsilon_ {\\theta} (X _ {t}, t) \\right\\|,", + "image_path": "e9ebb8ff3ef4e54da328409c7368dfeea9565065d4f61910fb7d4ae3b67ed540.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "inline_equation", + "content": "t \\sim \\mathrm{Uniform}(1, \\ldots, T)" + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "content": ". Essentially, the neural network " + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "content": " is used to estimate " + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "inline_equation", + "content": "X_0" + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "inline_equation", + "content": "X_t" + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "content": " at the time step " + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "content": ". Note that an optional conditional network design " + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(X_t, t, Y)" + }, + { + "bbox": [ + 313, + 72, + 553, + 132 + ], + "type": "text", + "content": " can also be used, which may improve the stability and efficiency of model training." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 133, + 554, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 554, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 554, + 167 + ], + "type": "text", + "content": "Reverse Training Objective: Independently of the forward training, we design a neural network " + }, + { + "bbox": [ + 313, + 133, + 554, + 167 + ], + "type": "inline_equation", + "content": "Z_{\\phi}(X_t,t)" + }, + { + "bbox": [ + 313, + 133, + 554, + 167 + ], + "type": "text", + "content": " to minimize, for " + }, + { + "bbox": [ + 313, + 133, + 554, + 167 + ], + "type": "inline_equation", + "content": "t = 1,\\dots ,T" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 367, + 175, + 553, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 175, + 553, + 190 + ], + "spans": [ + { + "bbox": [ + 367, + 175, + 553, + 190 + ], + "type": "interline_equation", + "content": "\\left\\| z - Z _ {\\phi} \\left(X _ {t}, t\\right) \\right\\|, \\quad z \\sim \\mathcal {N} (0, I), \\tag {8}", + "image_path": "a3861026eb888d81c9853cc1923afb826c889d2b4254f6cea2a69a7e966ce3d8.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 198, + 553, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 198, + 553, + 222 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 553, + 222 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 198, + 553, + 222 + ], + "type": "inline_equation", + "content": "X_{t}" + }, + { + "bbox": [ + 313, + 198, + 553, + 222 + ], + "type": "text", + "content": " is defined by " + }, + { + "bbox": [ + 313, + 198, + 553, + 222 + ], + "type": "inline_equation", + "content": "X_{t} = (1 - t)X_{0} + tY + \\sqrt{t(1 - t)} z" + }, + { + "bbox": [ + 313, + 198, + 553, + 222 + ], + "type": "text", + "content": ". That is, we do the back propagation of" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 398, + 231, + 471, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 398, + 231, + 471, + 243 + ], + "spans": [ + { + "bbox": [ + 398, + 231, + 471, + 243 + ], + "type": "interline_equation", + "content": "\\left\\| z - Z _ {\\phi} (X _ {t}, t) \\right\\|,", + "image_path": "fdb67557e5f294b5ca8474ba97fbea12ea02edc83e661c99809ca48ff67d7861.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 251, + 526, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 526, + 264 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 526, + 264 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 251, + 526, + 264 + ], + "type": "inline_equation", + "content": "t\\sim \\mathrm{Uniform}(0,\\ldots ,T - 1)" + }, + { + "bbox": [ + 313, + 251, + 526, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 251, + 526, + 264 + ], + "type": "inline_equation", + "content": "z\\sim \\mathcal{N}(0,I)" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 314, + 270, + 382, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 270, + 382, + 283 + ], + "spans": [ + { + "bbox": [ + 314, + 270, + 382, + 283 + ], + "type": "text", + "content": "3.3. Sampling" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 288, + 554, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 288, + 554, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 288, + 554, + 312 + ], + "type": "text", + "content": "We discretize Equation 4 with " + }, + { + "bbox": [ + 313, + 288, + 554, + 312 + ], + "type": "inline_equation", + "content": "g(t) = 1" + }, + { + "bbox": [ + 313, + 288, + 554, + 312 + ], + "type": "text", + "content": " to get the iterative generative formula:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 315, + 319, + 553, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 319, + 553, + 355 + ], + "spans": [ + { + "bbox": [ + 315, + 319, + 553, + 355 + ], + "type": "interline_equation", + "content": "X _ {t - 1} = \\left(1 - \\frac {\\Delta t}{t}\\right) X _ {t} + \\frac {\\Delta t}{t} X _ {0} - \\left[ \\bar {W} (t) - \\bar {W} (t - \\Delta t) \\right] \\tag {9}", + "image_path": "2692d572c7954c94083ad51c313d8ead028c3849254f52bc7206e41f8fefce5f.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "type": "text", + "content": "We employ the two neural networks in this way: " + }, + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "type": "inline_equation", + "content": "X_0 \\approx X_t - \\epsilon_\\theta(X_t, t)" + }, + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "type": "inline_equation", + "content": "\\overline{W}(t) - \\overline{W}(t - \\Delta t)" + }, + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "type": "text", + "content": " must be approximated with the use of the second neural network " + }, + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "type": "inline_equation", + "content": "Z_\\phi" + }, + { + "bbox": [ + 313, + 356, + 554, + 390 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "text", + "content": "We make an observation here: " + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "inline_equation", + "content": "\\overline{W}(t) - \\overline{W}(t - \\Delta t)" + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "inline_equation", + "content": "\\overline{W}(t + \\Delta t) - \\overline{W}(t)" + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "text", + "content": " are independent, equivalent random variables. Let " + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "inline_equation", + "content": "g(t) = 1" + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "text", + "content": " in (4) and (5) to get " + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "inline_equation", + "content": "X_{t} = (1 - t)X_{0} + tY + t\\int_{1}^{t}\\frac{d\\overline{W}}{s}" + }, + { + "bbox": [ + 313, + 391, + 554, + 443 + ], + "type": "text", + "content": ". Then we get" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 318, + 449, + 553, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 449, + 553, + 504 + ], + "spans": [ + { + "bbox": [ + 318, + 449, + 553, + 504 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\overline {{W}} (t) - \\overline {{W}} (t - \\Delta t) = \\overline {{W}} (t + \\Delta t) - \\overline {{W}} (t) \\approx \\\\ U \\left(X _ {t + 1}, t + 1\\right) - \\left(1 + \\frac {\\Delta t}{t}\\right) U \\left(X _ {t}, t\\right) + \\frac {\\Delta t}{t} \\left(X _ {0} - Y\\right), \\tag {10} \\\\ \\end{array}", + "image_path": "18bfb62f155385033ae5d74199ceb6d265ece39dce2706be185978c9b4a18674.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 314, + 513, + 342, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 513, + 342, + 522 + ], + "spans": [ + { + "bbox": [ + 314, + 513, + 342, + 522 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 318, + 529, + 553, + 556 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 529, + 553, + 556 + ], + "spans": [ + { + "bbox": [ + 318, + 529, + 553, + 556 + ], + "type": "interline_equation", + "content": "U \\left(X _ {t}, t\\right) = X _ {t} - Y = (1 - t) \\left(X _ {0} - Y\\right) + t \\int_ {1} ^ {t} \\frac {d \\overline {{W}}}{s}. \\tag {11}", + "image_path": "a3ab85807a0271fd864c459d033b1c0c81507881260e09b884488785c8b1347b.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 563, + 554, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 563, + 554, + 587 + ], + "spans": [ + { + "bbox": [ + 313, + 563, + 554, + 587 + ], + "type": "text", + "content": "Hence, by plugging the above estimate into Equation 9, we get the final iterative generative formula" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 322, + 594, + 553, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 594, + 553, + 649 + ], + "spans": [ + { + "bbox": [ + 322, + 594, + 553, + 649 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {t - 1} = \\left(1 - \\frac {\\Delta t}{t}\\right) X _ {t} + \\frac {\\Delta t}{t} Y - U \\left(X _ {t + 1}, t + 1\\right) \\tag {12} \\\\ + \\left(1 + \\frac {\\Delta t}{t}\\right) U (X _ {t}, t). \\\\ \\end{array}", + "image_path": "ecf2cedea56166a46794da6af0a55c1a6d9a80862bf45c870ddda9344e148728.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "spans": [ + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "text", + "content": "In the formula (12), replace " + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "inline_equation", + "content": "m_t = \\frac{t}{T}" + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "inline_equation", + "content": "\\frac{1}{T}" + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "text", + "content": " if we apply the uniform sampling schedule with " + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "text", + "content": " time steps. Also, we estimate " + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "inline_equation", + "content": "X_0" + }, + { + "bbox": [ + 313, + 656, + 554, + 693 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 388, + 700, + 553, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 700, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 388, + 700, + 553, + 713 + ], + "type": "interline_equation", + "content": "\\hat {X} _ {0} = X _ {t} - \\epsilon_ {\\theta} (X _ {t}, t). \\tag {13}", + "image_path": "24997a4e97eed8598f3b54128f301dee7d376bada09207ed665558a68b651878.jpg" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28235" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 225, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 225, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 225, + 84 + ], + "type": "text", + "content": "Then for " + }, + { + "bbox": [ + 55, + 72, + 225, + 84 + ], + "type": "inline_equation", + "content": "t = T - 1, T - 2, \\ldots, 2" + }, + { + "bbox": [ + 55, + 72, + 225, + 84 + ], + "type": "text", + "content": ", we get" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 91, + 294, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 91, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 70, + 91, + 294, + 144 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {t - 1} = \\left(1 - \\frac {1}{t}\\right) X _ {t} + \\frac {1}{t} Y - U \\left(X _ {t + 1}, t + 1\\right) \\tag {14} \\\\ + \\left(1 + \\frac {1}{t}\\right) U (X _ {t}, t). \\\\ \\end{array}", + "image_path": "5f2c39137e9148f39163bfcd3affde1a130b0d63c4f3ffc708cc2614eea92ac8.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 163, + 286, + 176 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 163, + 286, + 176 + ], + "spans": [ + { + "bbox": [ + 57, + 163, + 286, + 176 + ], + "type": "text", + "content": "Algorithm 1 Forward Approximator Training Algorithm" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 178, + 294, + 297 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 62, + 178, + 294, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 178, + 294, + 202 + ], + "spans": [ + { + "bbox": [ + 62, + 178, + 294, + 202 + ], + "type": "text", + "content": "1: Input Paired Dataset " + }, + { + "bbox": [ + 62, + 178, + 294, + 202 + ], + "type": "inline_equation", + "content": "D_{x,y}" + }, + { + "bbox": [ + 62, + 178, + 294, + 202 + ], + "type": "text", + "content": ", Forward Network " + }, + { + "bbox": [ + 62, + 178, + 294, + 202 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 62, + 178, + 294, + 202 + ], + "type": "text", + "content": ", Total Time Steps " + }, + { + "bbox": [ + 62, + 178, + 294, + 202 + ], + "type": "inline_equation", + "content": "T" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 204, + 103, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 204, + 103, + 214 + ], + "spans": [ + { + "bbox": [ + 62, + 204, + 103, + 214 + ], + "type": "text", + "content": "2: repeat" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 216, + 134, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 216, + 134, + 226 + ], + "spans": [ + { + "bbox": [ + 62, + 216, + 134, + 226 + ], + "type": "text", + "content": "3: " + }, + { + "bbox": [ + 62, + 216, + 134, + 226 + ], + "type": "inline_equation", + "content": "x,y\\sim D_{x,y}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 227, + 178, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 227, + 178, + 239 + ], + "spans": [ + { + "bbox": [ + 63, + 227, + 178, + 239 + ], + "type": "text", + "content": "4: " + }, + { + "bbox": [ + 63, + 227, + 178, + 239 + ], + "type": "inline_equation", + "content": "t\\sim \\mathrm{Uniform}(1,\\ldots ,T)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 239, + 134, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 239, + 134, + 250 + ], + "spans": [ + { + "bbox": [ + 63, + 239, + 134, + 250 + ], + "type": "text", + "content": "5: " + }, + { + "bbox": [ + 63, + 239, + 134, + 250 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,I)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 63, + 251, + 212, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 251, + 212, + 263 + ], + "spans": [ + { + "bbox": [ + 63, + 251, + 212, + 263 + ], + "type": "text", + "content": "6: " + }, + { + "bbox": [ + 63, + 251, + 212, + 263 + ], + "type": "inline_equation", + "content": "x_{t} = (1 - 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So we define " + }, + { + "bbox": [ + 55, + 469, + 295, + 504 + ], + "type": "inline_equation", + "content": "X_{T - 1}" + }, + { + "bbox": [ + 55, + 469, + 295, + 504 + ], + "type": "text", + "content": " as we would in the SDE model" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 66, + 509, + 295, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 509, + 295, + 534 + ], + "spans": [ + { + "bbox": [ + 66, + 509, + 295, + 534 + ], + "type": "interline_equation", + "content": "X _ {T - 1} = Y - \\frac {1}{T} \\epsilon_ {\\theta} (Y, T) - \\frac {1}{\\sqrt {T}} z, \\quad z \\sim \\mathcal {N} (0, I). \\tag {15}", + "image_path": "a4aa0d23d716b63ca0d47ad51bc0bde62a4c805ccf5c1ca4119b96f7fe95cc33.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 67, + 540, + 142, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 540, + 142, + 552 + ], + "spans": [ + { + "bbox": [ + 67, + 540, + 142, + 552 + ], + "type": "text", + "content": "Finally, we define" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 129, + 558, + 295, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 558, + 295, + 572 + ], + "spans": [ + { + "bbox": [ + 129, + 558, + 295, + 572 + ], + "type": "interline_equation", + "content": "\\hat {X} _ {0} = X _ {1} - \\epsilon_ {\\theta} \\left(X _ {1}, 1\\right) \\tag {16}", + "image_path": "39fb4eac05abeb473a12cc1a0089cdf3b2bde65f2c1940f1b1badf0a2341e1c6.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 55, + 579, + 198, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 579, + 198, + 591 + ], + "spans": [ + { + "bbox": [ + 55, + 579, + 198, + 591 + ], + "type": "text", + "content": "as the final output of the algorithm." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "text", + "content": "The only randomness introduced in the entire sampling process is in " + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "inline_equation", + "content": "X_{T - 1}" + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "text", + "content": ", which should be negligible, as the coefficient " + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\frac{1}{\\sqrt{T}}" + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "text", + "content": " is fairly small compared to that of " + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 55, + 591, + 295, + 664 + ], + "type": "text", + "content": ". On the contrary, SDE models introduce randomness at every sampling step and hence cause substantial diversity to the output." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 55, + 670, + 127, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 670, + 127, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 670, + 127, + 683 + ], + "type": "text", + "content": "3.4. Algorithm" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "type": "text", + "content": "In a given paired dataset " + }, + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "type": "inline_equation", + "content": "D_{x,y}" + }, + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "type": "text", + "content": " denotes a paired images from the set. Define " + }, + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "type": "inline_equation", + "content": "B(t) = G\\left(\\frac{t}{T}\\right) = \\frac{1}{T}\\sqrt{t(T - t)}" + }, + { + "bbox": [ + 55, + 688, + 295, + 715 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "content": "and we have the training and sampling algorithms shown in Algorithms 1 to 3, respectively." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 315, + 116, + 507, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 116, + 507, + 129 + ], + "spans": [ + { + "bbox": [ + 315, + 116, + 507, + 129 + ], + "type": "text", + "content": "Algorithm 3 Sampling Algorithm (Refactored)" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 315, + 132, + 386, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 132, + 386, + 144 + ], + "spans": [ + { + "bbox": [ + 315, + 132, + 386, + 144 + ], + "type": "text", + "content": "Input: " + }, + { + "bbox": [ + 315, + 132, + 386, + 144 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 315, + 132, + 386, + 144 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 315, + 132, + 386, + 144 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 315, + 132, + 386, + 144 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 315, + 132, + 386, + 144 + ], + "type": "inline_equation", + "content": "Z_{\\phi}" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 315, + 145, + 367, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 145, + 367, + 156 + ], + "spans": [ + { + "bbox": [ + 315, + 145, + 367, + 156 + ], + "type": "text", + "content": "Output: " + }, + { + "bbox": [ + 315, + 145, + 367, + 156 + ], + "type": "inline_equation", + "content": "x_0" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 322, + 157, + 362, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 157, + 362, + 167 + ], + "spans": [ + { + "bbox": [ + 322, + 157, + 362, + 167 + ], + "type": "text", + "content": "1: " + }, + { + "bbox": [ + 322, + 157, + 362, + 167 + ], + "type": "inline_equation", + "content": "x_{t} = y" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 321, + 168, + 406, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 168, + 406, + 178 + ], + "spans": [ + { + "bbox": [ + 321, + 168, + 406, + 178 + ], + "type": "text", + "content": "2: for " + }, + { + "bbox": [ + 321, + 168, + 406, + 178 + ], + "type": "inline_equation", + "content": "t = T" + }, + { + "bbox": [ + 321, + 168, + 406, + 178 + ], + "type": "text", + "content": " to 1 do" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 321, + 180, + 422, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 180, + 422, + 191 + ], + "spans": [ + { + "bbox": [ + 321, + 180, + 422, + 191 + ], + "type": "text", + "content": "3: " + }, + { + "bbox": [ + 321, + 180, + 422, + 191 + ], + "type": "inline_equation", + "content": "\\hat{x}_0 = x_t - 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\\frac{t}{T})\\hat{x}_0 + \\frac{t}{T} y + B(t)\\hat{z}" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 321, + 216, + 514, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 216, + 514, + 228 + ], + "spans": [ + { + "bbox": [ + 321, + 216, + 514, + 228 + ], + "type": "text", + "content": "6: " + }, + { + "bbox": [ + 321, + 216, + 514, + 228 + ], + "type": "inline_equation", + "content": "\\hat{x}_{t - 1} = (1 - \\frac{t - 1}{T})\\hat{x}_0 + \\frac{t - 1}{T} y + B(t - 1)\\hat{z}" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 321, + 228, + 470, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 228, + 470, + 239 + ], + "spans": [ + { + "bbox": [ + 321, + 228, + 470, + 239 + ], + "type": "text", + "content": "7: " + }, + { + "bbox": [ + 321, + 228, + 470, + 239 + ], + "type": "inline_equation", + "content": "U_{t + 1} = \\hat{x}_t - y, U_t = \\hat{x}_{t - 1} - y" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 321, + 239, + 553, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 239, + 553, + 254 + ], + "spans": [ + { + "bbox": [ + 321, + 239, + 553, + 254 + ], + "type": "text", + "content": "8: " + }, + { + "bbox": [ + 321, + 239, + 553, + 254 + ], + "type": "inline_equation", + "content": "x_{t - 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Experiments" + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 313, + 357, + 554, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 554, + 381 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 554, + 381 + ], + "type": "text", + "content": "In this section, we verify the capability of Dual-approx Bridge, addressing the following questions:" + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 314, + 392, + 554, + 547 + ], + "type": "list", + "angle": 0, + "index": 52, + "blocks": [ + { + "bbox": [ + 314, + 392, + 554, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 392, + 554, + 450 + ], + "spans": [ + { + "bbox": [ + 314, + 392, + 554, + 450 + ], + "type": "text", + "content": "- How do varying the number of sampling steps impact its performance in terms of image quality and faithfulness to GT? Furthermore, how does the sampling variance of our model compare to that of SDE-based samplers in terms of faithfulness to GT?" + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 314, + 452, + 554, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 452, + 554, + 498 + ], + "spans": [ + { + "bbox": [ + 314, + 452, + 554, + 498 + ], + "type": "text", + "content": "- How does Dual-approx Bridge perform in terms of faithfulness to GT compared to other models in image-to-image translation tasks that demand high faithfulness and deterministic result?" + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 314, + 499, + 553, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 499, + 553, + 547 + ], + "spans": [ + { + "bbox": [ + 314, + 499, + 553, + 547 + ], + "type": "text", + "content": "- How does Dual-approx Bridge perform in general image-to-image translation tasks, which prioritize image quality, when compared to other models including GANs, Diffusion models, and Bridge models?" + } + ] + } + ], + "index": 51 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "text", + "content": "To address these questions, we used datasets with the following resolutions: Cityscapes [10] " + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "inline_equation", + "content": "(256\\times 256)" + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "text", + "content": ", Edges2Handbags [56] " + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "inline_equation", + "content": "(64\\times 64)" + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "text", + "content": ", DF2K [45] " + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "inline_equation", + "content": "(256\\times 256)" + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "text", + "content": ", Urban100 [22] " + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "inline_equation", + "content": "(256\\times 256" + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "text", + "content": " patches), and BSD100 [34] " + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "inline_equation", + "content": "(256\\times 256" + }, + { + "bbox": [ + 313, + 558, + 555, + 712 + ], + "type": "text", + "content": " patches). For evaluation, we used FID [18] to assess image realism (lower is better), LPIPS [53] for perceptual similarity (lower is better), PSNR for pixel-level similarity (higher is better) and SSIM [49] for structural similarity (closer to 1 is better). Our super-resolution (SR) experiments followed the experimental design of [8]. All of our experiments were implemented using PyTorch [38] and were run on a machine with two NVIDIA RTX A6000 GPUs." + } + ] + } + ], + "index": 53 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28236" + } + ] + } + ], + "index": 54 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 70, + 282, + 122 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 282, + 122 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 282, + 122 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 282, + 122 + ], + "type": "table", + "html": "
    StepsFID ↓LPIPS ↓PSNR ↑SSIM % ↑
    1,00042.700.44215.10 ± 0.02(43.2 ± 0.07) %
    20048.700.49215.70 ± 0.02(53.2 ± 0.06) %
    1057.430.53015.62 ± 0.02(55.3 ± 0.06) %
    356.070.52316.99 ± 0.01(57.4 ± 0.00) %
    ", + "image_path": "704dc163b60934ed62d45863af400bdf8db0e8e197d107800e9c715a7fc4575c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 194, + 149, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 194, + 149, + 206 + ], + "spans": [ + { + "bbox": [ + 55, + 194, + 149, + 206 + ], + "type": "text", + "content": "4.1. Ablation Study" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 212, + 194, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 212, + 194, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 212, + 194, + 224 + ], + "type": "text", + "content": "4.1.1. Impact of Sampling Steps" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "spans": [ + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "type": "text", + "content": "We first evaluate the impact of sampling steps on our model's performance in the label-to-photo translation task on the Cityscapes dataset. Since the forward approximator in our model can predict " + }, + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "type": "text", + "content": ", sampling can be stopped at any time, allowing us to test sampling performance with a different number of steps. Table 1 presents how the varying sampling steps affect both image quality and faithfulness. It demonstrates that 1,000 sampling steps yield satisfactory image quality, with FID reaching a minimum of 42.70 and LPIPS dropping to 0.442. However, this comes at the cost of reduced faithfulness when compared to results obtained using fewer sampling steps, as evidenced by the decline in PSNR and SSIM. Notably, with only three sampling steps, our model achieves its peak in terms of faithfulness, attaining 16.99 PSNR and " + }, + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "type": "inline_equation", + "content": "57.4\\%" + }, + { + "bbox": [ + 54, + 226, + 295, + 429 + ], + "type": "text", + "content": " SSIM. This demonstrates the model's adaptability to meet the diverse requirements of various applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 430, + 295, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 430, + 295, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 430, + 295, + 597 + ], + "type": "text", + "content": "Additionally, we assessed the variance of the output fidelity in five independent sampling trials given the same input. Clearly, even at a higher sampling step of 1,000, the standard deviation of PSNR and SSIM remained low (0.02 and " + }, + { + "bbox": [ + 55, + 430, + 295, + 597 + ], + "type": "inline_equation", + "content": "0.07\\%" + }, + { + "bbox": [ + 55, + 430, + 295, + 597 + ], + "type": "text", + "content": ", respectively), and it approaches zero with three sampling steps. This robustness underscores the superiority of our model in consistently producing high-quality and faithful results with minimal variability. Consequently, we employed three sampling steps for better robustness and higher efficiency in our subsequent experiments, unless otherwise specified. Our experiments show that three iterations perform well across these metrics, though further research is needed to determine the optimal number of sampling steps for different tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 603, + 185, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 603, + 185, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 603, + 185, + 613 + ], + "type": "text", + "content": "4.1.2. Faithfulness Evaluation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 617, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 700 + ], + "type": "text", + "content": "We then compare the faithfulness of Dual-approx Bridge to other Brownian bridge models with SDE-based [32, 47] and PF-ODE-based samplers on the Cityscapes dataset using PSNR and SSIM metrics. Both the SDE-based and PF-ODE-based samplers use 1,000 sampling steps. The Brownian bridge model, as the leading I2I translation method, is an ideal benchmark for us due to the same bridge structure." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 714 + ], + "type": "text", + "content": "As shown in Table 2, our Dual-approx Bridge clearly" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 327, + 70, + 543, + 110 + ], + "blocks": [ + { + "bbox": [ + 55, + 129, + 295, + 174 + ], + "lines": [ + { + "bbox": [ + 55, + 129, + 295, + 174 + ], + "spans": [ + { + "bbox": [ + 55, + 129, + 295, + 174 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with different sampling steps on the Cityscapes dataset. Bold values represent the best performance. Standard Deviation is obtained by five sampling trials for the same input." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 327, + 70, + 543, + 110 + ], + "lines": [ + { + "bbox": [ + 327, + 70, + 543, + 110 + ], + "spans": [ + { + "bbox": [ + 327, + 70, + 543, + 110 + ], + "type": "table", + "html": "
    MethodPSNR ↑SSIM % ↑
    Brown Bridge Model (SDE)14.28 ±0.21(49.6 ±0.63) %
    Brown Bridge Model (PF-ODE)15.23 ±0.00(51.2 ±0.00) %
    Ours16.99 ±0.01(57.4 ±0.00)%
    ", + "image_path": "1e3f80c4f951750e901cf3b06bd14315f08c95aa9783853f7733417e98b61196.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 118, + 555, + 163 + ], + "lines": [ + { + "bbox": [ + 313, + 118, + 555, + 163 + ], + "spans": [ + { + "bbox": [ + 313, + 118, + 555, + 163 + ], + "type": "text", + "content": "Table 2. Quantitative comparison with Brownian bridges using SDE and PF-ODE-based samplers on Cityscape. Bold values represent the best performance. Standard deviation is obtained by five sampling trials for the same input." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 321, + 180, + 550, + 322 + ], + "blocks": [ + { + "bbox": [ + 321, + 180, + 550, + 322 + ], + "lines": [ + { + "bbox": [ + 321, + 180, + 550, + 322 + ], + "spans": [ + { + "bbox": [ + 321, + 180, + 550, + 322 + ], + "type": "image", + "image_path": "9eec88a941d7e18d4bdc139fc05a5e420df73ab63a00330e516139d33efca0a2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 335, + 555, + 401 + ], + "lines": [ + { + "bbox": [ + 313, + 335, + 555, + 401 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 555, + 401 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison with Brownian bridges using SDE-based and PF-ODE-based samplers on Edges2Handbags. Three sampling trials are conducted by each model given the same input. Standard deviation among sampling results by our model, SDE-based and PF-ODE-based sampler are 0.0001, 0.1030 and 0, respectively." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "text", + "content": "outperforms SDE-based and PF-ODE-based samplers. The PSNR value increased by approximately " + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "inline_equation", + "content": "12\\%" + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "text", + "content": " compared to the second-best, the PF-ODE-based sampler, while the SSIM value showed an overall improvement of " + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "inline_equation", + "content": "12\\%" + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "text", + "content": ", rising from " + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "inline_equation", + "content": "51.2\\%" + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "inline_equation", + "content": "57.4\\%" + }, + { + "bbox": [ + 313, + 423, + 554, + 530 + ], + "type": "text", + "content": ". Notably, the metrics of the Dualapprox Bridge exhibited minimal variance, whereas SDE-based sampler exhibited substantial variance in PSNR and SSIM due to the presence of white noise in every step of its sampling." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 531, + 554, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 554, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 554, + 616 + ], + "type": "text", + "content": "Figure 3 shows three sample images by each model with the same input in the Edges2Handbags dataset. The images generated by SDE-based sampler are rich in detail but distinct from each other. The PF-ODE-based sampler produces consistent results but lacks details, resulting in a blurred appearance. As a comparison, Dual-approx Bridge achieves SDE-level quality with high and consistent faithfulness." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 624, + 534, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 624, + 534, + 636 + ], + "spans": [ + { + "bbox": [ + 313, + 624, + 534, + 636 + ], + "type": "text", + "content": "4.2. Deterministic Image-to-Image Translation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 641, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 713 + ], + "type": "text", + "content": "We selected the label-to-photo task in the Cityscapes dataset for deterministic image generation, where the goal is to generate realistic images from segmentation maps. Faithfulness is essential in this task, as it ensures the generated images accurately reflect the structure and content of the input labels, preserving the integrity of labeled features. We also in" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28237" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 80, + 70, + 269, + 129 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 269, + 129 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 269, + 129 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 269, + 129 + ], + "type": "table", + "html": "
    MethodFID ↓PSNR ↑SSIM % ↑
    Pix2pix101.0412.8628.63 %
    CycleGAN75.3714.5334.16 %
    UNIT82.7414.6135.41 %
    Ours48.7015.7053.26 %
    ", + "image_path": "0dfabe697f6cccb55326aa4833d86c6ac81f5ac36ebe8baaf1622dd5bb02c53d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 73, + 190, + 276, + 326 + ], + "blocks": [ + { + "bbox": [ + 73, + 190, + 276, + 326 + ], + "lines": [ + { + "bbox": [ + 73, + 190, + 276, + 326 + ], + "spans": [ + { + "bbox": [ + 73, + 190, + 276, + 326 + ], + "type": "image", + "image_path": "26d8f6b7d8aae4fa2b57295f33f83165cbe4cc3a6e6efcfa69b13c076142058e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 338, + 295, + 361 + ], + "lines": [ + { + "bbox": [ + 55, + 338, + 295, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 295, + 361 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison between Dual-approx Bridge and SOTA methods on the Cityscapes dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 62, + 373, + 290, + 429 + ], + "blocks": [ + { + "bbox": [ + 62, + 373, + 290, + 429 + ], + "lines": [ + { + "bbox": [ + 62, + 373, + 290, + 429 + ], + "spans": [ + { + "bbox": [ + 62, + 373, + 290, + 429 + ], + "type": "image", + "image_path": "051d86df7b564f0109c7dfcc172c791f7b7b3d8e1520945760bf74ba66c73f18.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 75, + 441, + 275, + 452 + ], + "lines": [ + { + "bbox": [ + 75, + 441, + 275, + 452 + ], + "spans": [ + { + "bbox": [ + 75, + 441, + 275, + 452 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison on BSD100 datasets." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 474, + 295, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 508 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 508 + ], + "type": "text", + "content": "cluded image super-resolution as a deterministic image-to-image translation task, which also requires both high quality and faithfulness." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 510, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 605 + ], + "type": "text", + "content": "Given the inherent randomness in diffusion models, we primarily chose GAN-based models as baselines for deterministic I2I tasks. We selected Pix2Pix [24], CycleGAN [57], and UNIT [30] for comparison on the Cityscapes dataset. For image super-resolution, we used ESRGAN [48], RankSRGAN [52], and SRDiff [27] as baselines and followed the experimental configuration in [33] to train our model on DF2K and test it on Urban100 and BSD100." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "Table 3 compares our model against baseline models on the Cityscapes dataset. The Dual-approx Bridge model demonstrates superior performance across all metrics compared to the other models. In terms of image quality, our model achieves a significant improvement in FID, with a score of 48.70 compared to the second-best score of 75.37, representing a substantial " + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": " performance enhancement. Furthermore, our model exhibits notable gains in PSNR and SSIM, with PSNR increased from 14.61 to 15.70 and SSIM" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 325, + 75, + 545, + 276 + ], + "blocks": [ + { + "bbox": [ + 325, + 75, + 545, + 276 + ], + "lines": [ + { + "bbox": [ + 325, + 75, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 325, + 75, + 545, + 276 + ], + "type": "image", + "image_path": "2ea38c465dbbd3405192f04202c65f6656aac856b3f1db5f3113c599d7e38a96.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 293, + 534, + 304 + ], + "lines": [ + { + "bbox": [ + 333, + 293, + 534, + 304 + ], + "spans": [ + { + "bbox": [ + 333, + 293, + 534, + 304 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison on Uban100 datasets." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 327, + 317, + 542, + 392 + ], + "blocks": [ + { + "bbox": [ + 55, + 138, + 295, + 172 + ], + "lines": [ + { + "bbox": [ + 55, + 138, + 295, + 172 + ], + "spans": [ + { + "bbox": [ + 55, + 138, + 295, + 172 + ], + "type": "text", + "content": "Table 3. Quantitative comparison with deterministic models on Cityscape. Results of our model are obtained using 200 sampling steps. Bold values represent the best performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 327, + 317, + 542, + 392 + ], + "lines": [ + { + "bbox": [ + 327, + 317, + 542, + 392 + ], + "spans": [ + { + "bbox": [ + 327, + 317, + 542, + 392 + ], + "type": "table", + "html": "
    ModelBSD100Urban100
    LPIPS ↓PSNR ↑LPIPS ↓PSNR ↑
    Bicubic0.528224.320.482621.75
    ESRGAN0.157923.650.122623.04
    RankSRGAN0.171423.800.140323.16
    SRDiff0.204624.170.139123.88
    Ours0.126726.560.120723.23
    ", + "image_path": "8d5266f96496f79df89f13970a298be71831a38b01045dc2303ef147602b8d78.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 399, + 553, + 422 + ], + "lines": [ + { + "bbox": [ + 313, + 399, + 553, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 553, + 422 + ], + "type": "text", + "content": "Table 4. Quantitative comparisons on BSD100 and Urban100. Bold values represent the best performance." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "type": "text", + "content": "improved by approximately " + }, + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "type": "text", + "content": " (from " + }, + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "type": "inline_equation", + "content": "35.41\\%" + }, + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "type": "inline_equation", + "content": "53.26\\%" + }, + { + "bbox": [ + 313, + 447, + 553, + 483 + ], + "type": "text", + "content": "). Qualitative comparisons of various methods are presented in Figure 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 484, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 554, + 628 + ], + "type": "text", + "content": "Table 4 compares our model against baselines on superresolution tasks. Our model performed the best on the BSD100 dataset with LPIPS at 0.1267 and PSNR at 26.56. It also achieves the highest LPIPS score of 0.1207 and the second-highest PSNR score of 23.23 on the Urban100 dataset. While SRDiff achieved the best PSNR on Urban100, its diffusion process encounters challenges in consistently producing stable outputs due to the inherent randomness in its SDE-based sampler (as shown in Table 2). Moreover, our model accomplishes this performance with significantly fewer sampling steps (3 used in our model vs. 1,000 used in SRDiff)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 629, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 712 + ], + "type": "text", + "content": "Figure 5 compares the visual quality of various methods for image super-resolution. The top-right of each image shows a zoomed-in view of the red-boxed region for a detailed comparison. Due to inherent randomness, SDEs often introduce unrealistic artifacts, as seen in the example. The PF-ODE-based sampler results exhibit excessive smoothness and the loss of details, as evident in the zoomed" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28238" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 75, + 525, + 165 + ], + "blocks": [ + { + "bbox": [ + 82, + 75, + 525, + 165 + ], + "lines": [ + { + "bbox": [ + 82, + 75, + 525, + 165 + ], + "spans": [ + { + "bbox": [ + 82, + 75, + 525, + 165 + ], + "type": "image", + "image_path": "78caef6590d71f93a4953e26aac4dac850f0e08f333728df3d9a952eadc3016f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 95, + 171, + 514, + 183 + ], + "lines": [ + { + "bbox": [ + 95, + 171, + 514, + 183 + ], + "spans": [ + { + "bbox": [ + 95, + 171, + 514, + 183 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison between Dual-approx Bridge and SOTA methods on the Edges2handbags dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 94, + 193, + 258, + 323 + ], + "blocks": [ + { + "bbox": [ + 94, + 193, + 258, + 323 + ], + "lines": [ + { + "bbox": [ + 94, + 193, + 258, + 323 + ], + "spans": [ + { + "bbox": [ + 94, + 193, + 258, + 323 + ], + "type": "table", + "html": "
    MethodFID ↓
    MUNIT91.4
    DRIT155.3
    Distance85.8
    SelfDistance78.8
    CGGAN105.2
    CUT56.4
    FastCUT68.8
    DCLGAN49.4
    SimDCL51.3
    Ours48.7
    ", + "image_path": "cd05187cf72f1741f2e1894c9c4fa7b7043a03db2db092a986fed170996d9306.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 69, + 359, + 282, + 470 + ], + "blocks": [ + { + "bbox": [ + 69, + 359, + 282, + 470 + ], + "lines": [ + { + "bbox": [ + 69, + 359, + 282, + 470 + ], + "spans": [ + { + "bbox": [ + 69, + 359, + 282, + 470 + ], + "type": "image", + "image_path": "e3886217df21da163e7262f2cd9882b5f517fe170234f0768c26666004ead213.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 478, + 296, + 534 + ], + "lines": [ + { + "bbox": [ + 55, + 478, + 296, + 534 + ], + "spans": [ + { + "bbox": [ + 55, + 478, + 296, + 534 + ], + "type": "text", + "content": "Figure 8. Quantitative comparison between Dual-approx Bridge and A-bridge (with SDE-based sampler). Each model are sampled five times given the same input. Sampling standard deviation of the first example (Ours: 0.0084, A-bridge: 0.0903) and the second example (Ours: 0.0054, SDE: 0.0672)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 541, + 296, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 541, + 296, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 541, + 296, + 613 + ], + "type": "text", + "content": "regions for both examples. Figure 6 further illustrates that our model can achieve detail preservation approaching or even surpassing that of SDE-based methods. Conversely, the Dual-approx Bridge method demonstrates a remarkable ability to preserve details while maintaining high faithfulness with GT." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 624, + 251, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 251, + 636 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 251, + 636 + ], + "type": "text", + "content": "4.3. General Image-to-Image Translation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 715 + ], + "type": "text", + "content": "Finally, we evaluate Dual-approx Bridge on general image-to-image translation tasks. We assess our model's image quality on the Edges2Handbags and Cityscapes datasets. For Edges2Handbags, we conduct comparisons with Pix2Pix [24], SDEdit [35], DDIB [44], Rectified Flow [31], I2SB [29], DDBM [54], and A-bridge [47]. For the" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 353, + 193, + 517, + 312 + ], + "blocks": [ + { + "bbox": [ + 55, + 331, + 296, + 354 + ], + "lines": [ + { + "bbox": [ + 55, + 331, + 296, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 296, + 354 + ], + "type": "text", + "content": "Table 5. Quantitative comparison of image quality on Cityscapes (label to photo). Bold values represent the best performance." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 353, + 193, + 517, + 312 + ], + "lines": [ + { + "bbox": [ + 353, + 193, + 517, + 312 + ], + "spans": [ + { + "bbox": [ + 353, + 193, + 517, + 312 + ], + "type": "table", + "html": "
    MethodFID ↓
    Pix2Pix74.8
    DDIB186.84
    SDEdit85.8
    SelfDistance26.5
    Rectified Flow25.3
    I2SB7.43
    DDBM (VP)1.83
    A-Bridge1.07
    Ours1.36
    ", + "image_path": "89975bec3fe09e22804694693bb71fa68dabdbabdc33babbac2556373cddf0cd.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 320, + 555, + 342 + ], + "lines": [ + { + "bbox": [ + 313, + 320, + 555, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 320, + 555, + 342 + ], + "type": "text", + "content": "Table 6. Quantitative comparison of image quality on Edges2Handbags. Bold values represent the best performance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 348, + 555, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 348, + 555, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 348, + 555, + 396 + ], + "type": "text", + "content": "Cityscapes dataset, we compared our model with MUNIT [23], DRIT [26], DistanceGAN [3], Self-DistanceGAN [3], CGGAN [55], CUT [37], FastCUT [37], DCLGAN [17], and SimDCL [17]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 396, + 554, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 554, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 554, + 479 + ], + "type": "text", + "content": "On the Cityscapes dataset, our model outperforms all GAN-based models, achieving the top position and surpassing all competitors (Table 5). As shown in Table 6, our model achieves 1.36 FID score on the Edges2Handbags dataset, securing the second place. This result demonstrates that, despite our primary focus on enhancing faithfulness, our model still delivers highly competitive image quality." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 479, + 554, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 554, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 554, + 563 + ], + "type": "text", + "content": "Figure 7 provides a qualitative comparison of our model with A-bridge on the Edges2Handbags dataset. Although A-bridge achieves the best FID score, it uses SDE-based samplers. As shown in Figure 8, our model demonstrates much higher faithfulness and consistency across repeated sampling with far fewer sampling steps (3 in our model vs. 50 in A-bridge)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 574, + 480, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 480, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 480, + 586 + ], + "type": "text", + "content": "5. Conclusion and Future Work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": "In this paper, we proposed Dual-approx Bridge, a novel generative model to produce faithful and high quality output for deterministic I2I translations. Our extensive experiments on benchmark datasets demonstrate the consistent and superior performance of Dual-approx Bridge when compared to SOTA I2I models. Our current choice of the SDE follows the Variance Preserving (VP) formulation. Moving forward, we plan to explore the potentials of combining both VP and variance exploding SDEs to further enhance our model's capabilities." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28239" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 122 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 122 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 122 + ], + "type": "text", + "content": "[1] Aziz Alotaibi. 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Dalian University of Technology, China Dalian University, China", + "bbox": [ + 250, + 265, + 784, + 280 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "5Centre for Frontier AI Research, Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore", + "bbox": [ + 106, + 282, + 906, + 299 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "yu_hua, asysong@ntu.edu.sg lwming95@gmail.com guixu@s.dlu.edu.cn houyq,zhangq@dlut.edu.cn", + "bbox": [ + 99, + 309, + 919, + 323 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 358, + 326, + 373 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human motion synthesis aims to generate plausible human motion sequences, which has raised widespread attention in computer animation. Recent score-based generative models (SGMs) have demonstrated impressive results on this task. However, their training process involves complex curvature trajectories, leading to unstable training process. In this paper, we propose a Deterministic-to-Stochastic Diverse Latent Feature Mapping (DSDFM) method for human motion synthesis. DSDFM consists of two stages. The first human motion reconstruction stage aims to learn the latent space distribution of human motions. The second diverse motion generation stage aims to build connections between the Gaussian distribution and the latent space distribution of human motions, thereby enhancing the diversity and accuracy of the generated human motions. This stage is achieved by the designed deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. DSDFM is easy to train compared to previous SGMs-based methods and can enhance diversity without introducing additional training parameters. Through qualitative and quantitative experiments, DSDFM achieves state-of-the-art results surpassing the latest methods, validating its superiority in human motion synthesis.", + "bbox": [ + 89, + 391, + 485, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 771, + 220, + 786 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human motion synthesis task aims to generate diverse and high quality 3D human motion sequences. This task has wide-ranging applications, such as human motion understanding [7, 14, 18], human-robot interactions [49, 61], and computer graphics [44]. Recent efforts mainly focus on con", + "bbox": [ + 89, + 797, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ditional and unconditional human motion generation. Conditional human motion generation aims to generate human motion sequences under some limiting factors, such as music [16, 17], audio [1, 15, 28], and action labels [33, 33, 61]. Unconditional human motion generation intends to generate diverse human motions [32, 35] from diverse data, which still presents a significant challenge, especially when the human motion datasets are unstructured. In this paper, we focus on conditional (under the action labels) and unconditional human motion generations, as shown in Figure 1. Efficiently generating diverse and accurate human motions remains a tremendous challenge, which has led to the development of many different generative models.", + "bbox": [ + 511, + 359, + 908, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advancements in deep generative models, including Variational Autoencoders (VAEs) [53, 57, 60], Generative Adversarial Networks (GANs) [31], score-based generative models (SGMs), and related techniques [12, 39, 46, 51, 58], emerge as the dominant approaches for capturing the data distribution. Specifically, VAEs leverage an encoder-decoder network to learn the latent representation of human motion distribution. VAEs require approximate variational or Monte Carlo inference techniques, which tend to be intractable for complex models. GANs utilize a generator and discriminator to generate real-like motions from random noise. Unfortunately, GANs are known to suffer from numerical instability and mode collapse issues. SGMs define a forward diffusion process that maps data to noise by gradually perturbing the input data. Generation corresponds to a reverse process that synthesizes novel data via iterative denoising process. Even though they have presented high fidelity in generation, it is important to note that these methods have the challenge of curve trajectory modeling within diffusion models, as their forward pass is inherently designed to exhibit curvature in SDE, following either a Variance Preserving SDE (VPSDE) or a Variance Exploding", + "bbox": [ + 511, + 568, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 109, + 887, + 233, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22724", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6b9d6e32b28f091b04e1649e5309f6bfd89f776186f348765a6c9fbf1514f9c1.jpg", + "image_caption": [ + "Figure 1. Examples of the inference process for human motion synthesis. Our method aims to generate diverse and accurate human motion sequences through the designed generative model." + ], + "image_footnote": [], + "bbox": [ + 183, + 95, + 816, + 236 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SDE (VESDE) [39], leading to unstable training process and slow inference process. Recent methods, like DDIM [37], aim to accelerate the inference process by one-step or few-step generator, nevertheless, these methods lead to an obvious performance drop [5], and the training process is still unstable.", + "bbox": [ + 89, + 279, + 483, + 369 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To synthesize diverse and accurate human motions, we propose a novel method called DSDFM for human motion synthesis. The proposed method has straight trajectories and is easy to train compared to previous SGMs methods, while guaranteeing the diversity and accuracy of the generated human motions. The proposed DSDFM consists of two stages. In the first stage, a human motion reconstruction process is designed to learn the latent space distribution of human motions and motion representation. This process is implemented by the Vector Quantized Variational Autoencoders (VQVAE) [47] network. In the second stage, we design a diverse motion generation module, including deterministic feature mapping procedure and stochastic diverse output generation procedure. Deterministic feature mapping procedure aims to explore the optimal solution for building the connections between the Gaussian distribution and the latent space distribution of human motions using the designed Deterministic Ordinary Equation (DerODE) operation. DerODE has a straight training trajectory compared to previous diffusion generative methods [12, 39] and Flow Matching [27]. Although DerODE is easy to train, it is hard to generate highly diverse human motion patterns since DerODE could only provide deterministic output. Therefore, the designed stochastic diverse output generation procedure aims to enhance the diversity of generated human motions through Diverse Stochastic Differential Equations (DivSDE). It is noted that DivSDE operates during the sampling process of the model without introducing additional training processes.", + "bbox": [ + 91, + 371, + 483, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are as follows:", + "bbox": [ + 109, + 794, + 447, + 809 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel method called Diverse Latent Feature Mapping (DSDFM) for human motion synthesis. DSDFM is efficient to train and to utilize at sampling process, and can be used for conditional and unconditional generation.", + "- We propose an optimal solution to build the connection between the Gaussian distribution and the latent space" + ], + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "distribution of human motions. In addition, we provide a stochastic diverse output generation process during the sampling process without reintroducing additional training processes.", + "bbox": [ + 524, + 279, + 906, + 339 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- The proposed method DSDFM is evaluated on widely-used human motion datasets in the comprehensive experiments. The obtained results demonstrate the effectiveness of the proposed method over the state-of-the-art approaches for conditional and unconditional human motion generation tasks.", + "bbox": [ + 513, + 339, + 906, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 444, + 655, + 459 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Human Motion Synthesis", + "text_level": 1, + "bbox": [ + 511, + 469, + 745, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conditional human motion synthesis aims to generate diverse and realistic human motions [42, 50, 54, 55] according to various conditional inputs, such as action labels [3, 41, 59] and music [11, 43]. For example, MDM [45] utilized a diffusion-based generative model for action-conditioned human motion generations, and reported a trading-off between diversity and fidelity of human motions due to the curve trajectory of training and sampling process. MLD [3] proposed to utilize the DDPM in latent space for human motion generations given an input action label, which also encountered the same problem as DDPM. In addition, the unconditional human motion synthesis [2, 35, 56] task also encounters the same issues although a series of achievements have been made in this field. For example, Holden et al. [13] presented a pioneer work in deep unconditional human motion synthesis. Modi [35] employed the style of StyleGAN to synthesize human motions. Unfortunately, these methods usually suffer from mode collapse or mode mixture. In contrast, we propose a novel method for conditional and unconditional human motion synthesis, which is easy to train compared to previous diffusion-based methods while guaranteeing the diversity of generated motions.", + "bbox": [ + 511, + 491, + 908, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Diffusion Generative Models", + "text_level": 1, + "bbox": [ + 511, + 832, + 777, + 848 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent years have witnessed a promising potential in modeling data distributions with diffusion generative models using Denoising diffusion probabilistic modeling (DDPM) [12]", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22725", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/386794c4111e14265c6bf33247a4f21d0add0673757ea1bd4f3aed4747caf4f3.jpg", + "image_caption": [ + "Figure 2. The overview of the proposed method DSDFM. The red arrow denotes the first stage and the green arrow denotes the second stage of DSDFM." + ], + "image_footnote": [], + "bbox": [ + 145, + 85, + 861, + 275 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and score-based generative models (SGMs) [39], which define a forward diffusion process that maps data to noise by gradually perturbing the input data. Variants of SGMs and techniques have been applied to images [6], audio [30]. For example, Robin et al. [8] proposed latent diffusion models (LDMs) that work on a compressed latent space of lower dimensionality for high-resolution image synthesis. LSGM [46] proposed to train SGMs in a latent space, which relies on the variational autoencoder framework to generate diverse images. However, it is important to note that these methods have the challenge of curve trajectory modeling within diffusion models, as their complex forward and backward processes are inherently designed to exhibit curvature, leading to unstable training process and slow sampling process. Although DDIM and related techniques [37] can shorten the sampling process, they often result in a performance drop [5, 52]. Flow Matching-based methods [20, 27] offer a more robust and stable alternative to diffusion models during the training process. However, the trajectories between source and target distributions remain relatively curved, and more importantly, these methods struggle to produce highly diverse samples, often sacrificing diversity in the training process. In contrast, we propose a generative model DSDFM for human motion generation tasks. This model utilizes straight trajectories, making it easier to train compared to other diffusion models. Additionally, it is capable of generating diverse human motion sequences.", + "bbox": [ + 91, + 313, + 483, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 89, + 738, + 217, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Score-based diffusion models gradually perturb data by a forward diffusion process, and then reverse it to recover the data [38, 39]. Under the stochastic differential equation (SDE) framework proposed in [39], diffusion models construct a process $x(t)_{t=0}^{T}$ indexed by a continuous time variable $t \\in [0,T]$ , such that $x(0) \\sim p_0$ , for which we have a dataset of i.i.d. samples, and $x(T) \\sim p_T$ , we have a tractable form to generate samples efficiently. $p_0$ is the data distribution, $p_T$ is the prior distribution. The forward diffusion", + "bbox": [ + 89, + 763, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "process can be modeled as the solution to an Itô SDE:", + "bbox": [ + 511, + 313, + 872, + 328 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd x _ {t} = f (x, t) d t + g (t) d w _ {t}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 333, + 906, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $w$ is the standard Wiener process (a.k.a., Brownian motion), $f(\\cdot, t): \\mathbb{R}^d \\to \\mathbb{R}^d$ is a vector valued function called the drift coefficient of $x(t)$ , and $g(\\cdot): \\mathbb{R} \\to \\mathbb{R}$ is a scalar function known as the diffusion coefficient of $x(t)$ . There are various ways of designing the SDE such that it diffuses the data distribution into a fixed prior distribution $p_T$ . By starting from samples of $x(T) \\sim p_T$ and reversing the process, we can obtain samples $x(0) \\sim p_0$ . The reverse of a diffusion process is also a diffusion process, running backwards in time and given by the reverse-time SDE:", + "bbox": [ + 511, + 354, + 906, + 505 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd x _ {t} = \\left[ f (x, t) - g (t) ^ {2} \\nabla_ {x} \\log p _ {t} (x) \\right] d t + g (t) d \\bar {w} _ {t}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 510, + 906, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\bar{w}$ is a standard Wiener process when time flows backwards from $T$ to 0, $dt$ is an infinitesimal negative timestep. Once the score $\\nabla_x\\log p_t(x)$ is learned, we can derive the reverse diffusion process and simulate it to sample from $p_0$ .", + "bbox": [ + 511, + 532, + 908, + 593 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. The Proposed Method", + "text_level": 1, + "bbox": [ + 511, + 614, + 723, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This paper aims to synthesize diverse and realistic human motion sequences. The overview of the proposed method is shown in Figure 2. The conditional motion generation is performed under the action labels (Action-to-Motion task). Once the action labels are removed, the entire process becomes unconditional motion generation. The training process of the DSDFM mainly involved in two stages. The first stage is the human motion reconstruction process (Section 4.1), which aims to learn the human motion representation and capture the latent space distribution of human motions. The second stage (Section 4.2) aims to build the connections between the Gaussian distribution and the latent space distribution using the designed deterministic feature mapping procedure (DerODE) (Section 4.2.1). Moreover, we employ the stochastic diverse generation process (DivSDE) to enhance the diversity of generated human motions (Section 4.2.2).", + "bbox": [ + 511, + 643, + 908, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22726", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Human Motion Reconstruction", + "text_level": 1, + "bbox": [ + 89, + 90, + 366, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The human motion reconstruction network aims to learn the representation and the latent space distribution of human motions. In this process, we utilize VQVAE [47] to capture dynamic spatio-temporal features of human motions. Specifically, the input is a sequence of human motion sequence $\\pmb{E} = \\{e_1,e_2,\\dots ,e_T\\}$ with the length of $T$ where $e_t\\in \\mathbb{R}^{V\\times C}$ is denoted by 3D coordinates at time $t$ $C$ denotes the 3D coordinates of human joints $(C = 3)$ $V$ is the used number of human joints. The encoder of VQVAE aims to transform motion sequence into latent features, i.e., $\\mathrm{Enc}(\\pmb {E})\\to z_i\\in \\pmb{Z}$ $z_{i}$ is substituted by its closest vector $k_{j}$ using a quantization codebook, where $\\hat{z}_i = \\arg \\min_{k_j\\in K}\\left||z_i - k_j\\right|$ . The quantized feature $\\hat{z}_i$ is decoded to $\\hat{\\pmb{E}}$ by the decoder network, i.e., $\\mathrm{Dec}(\\hat{z}_i)\\rightarrow \\hat{\\pmb{E}}$", + "bbox": [ + 89, + 113, + 485, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, the encoder $\\mathrm{Enc}(\\cdot)$ and decoder $\\mathrm{Dec}(\\cdot)$ networks are implemented by the Transformer [48] and GRU [4] module. For the Transformer process, we project the input human motion sequences into matrices $Q$ , $K$ , and $V$ by $W_{Q}, W_{K}, W_{V}$ . The summary of the spatial joints $\\tilde{M}_{t}$ is calculated by aggregating all the joint information using the multi-head mechanism $(\\mathrm{head}_i)$ . The $GRU_{\\phi}$ with parameter $\\phi$ intends to capture the smoothness property of human motions, and then encode the human motions into latent space $Z$ . In addition, the decoder $\\mathrm{Dec}(\\cdot)$ aims to map the latent space $Z$ back to the reconstructed human motion sequence. The VQVAE is optimized by minimizing the following loss function:", + "bbox": [ + 89, + 328, + 483, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {V Q} = \\mathcal {L} (\\boldsymbol {E}, \\hat {\\boldsymbol {E}}) + | | \\hat {z} - \\operatorname {s g} (z) | | _ {2} ^ {2} + \\beta | | \\operatorname {s g} (\\hat {z}) - z | | _ {2} ^ {2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 526, + 483, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{sg}[\\cdot ]$ is the stop gradient operator and $\\beta$ is the hyper parameter. The first term $\\mathcal{L}(\\pmb {E},\\hat{\\pmb{E}}) = \\sum_{t = 1}^{T}\\sum_{v = 1}^{V}\\parallel e_t^{(v)} - \\hat{e}_t^{(v)}\\parallel_2$ , represents the reconstruction error. The second term aims to optimize the codebook, and the last term is to optimize the encoder by pushing $z$ close to its nearest latent vector in the codebook. The human motion reconstruction process aims to learn the human motion representation and map the human motions into latent space $\\pmb{Z}$ .", + "bbox": [ + 89, + 558, + 483, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Diverse Motion Generation", + "text_level": 1, + "bbox": [ + 89, + 696, + 336, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although we have established the human motion reconstruction in Section 4.1, we still cannot generate diverse human motion accordingly. The main reason is that the latent feature space for human motion is rather complicated and hard to sample. Therefore, it is essential to model the latent feature space for human motion by establishing the relationship between a Gaussian distribution and the latent space distribution. Previous diffusion-based generative methods [39] and flow matching methods [20], suffer from instability during training, exhibiting curved trajectories or difficulty in generating diverse samples. To tackle this issue, we innovatively propose a diverse motion generation module to", + "bbox": [ + 89, + 719, + 485, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "enhance the diversity and accuracy of generated human motion sequences. Diverse motion generation module consists of two steps, i.e., deterministic feature mapping procedure and stochastic diverse output generation procedure. We will introduce the details of our proposed diverse motion generation module in this section.", + "bbox": [ + 511, + 90, + 906, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2.1. Deterministic Feature Mapping Procedure", + "text_level": 1, + "bbox": [ + 511, + 188, + 856, + 204 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To start with, we first introduce the deterministic feature mapping procedure. The deterministic feature mapping procedure is designed to model the relationship between Gaussian distribution $p(\\mathbf{Z}_{t=1})$ and the latent distribution for human motion $p(\\mathbf{Z}_{t=0})$ efficiently. Specifically, we propose Deterministic Ordinary Equation (DerODE) operation in the deterministic feature mapping procedure by depicting the transformation with Proposition 1 to achieve the corresponding goal.", + "bbox": [ + 511, + 207, + 908, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proposition 1. Given the ordinary equation $d\\pmb{z}_t = u(\\pmb{z}_t, t) dt$ , where $u(\\pmb{z}_t, t)$ denotes the drift function, and suppose the probability of data distribution $z(t)$ is set to be $p(z(t)) = \\mathcal{N}(\\mu(t), \\sigma^2(t))$ at the time step $t$ , where $\\mu(t)$ and $\\sigma(t)$ denote the mean and variance of the Gaussian distribution respectively, the drift function $u(\\pmb{z}_t, t)$ can be shown as:", + "bbox": [ + 511, + 343, + 908, + 446 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nu \\left(z _ {t}, t\\right) = \\sigma^ {\\prime} (t) \\cdot \\frac {z (t) - \\mu (t)}{\\sigma (t)} + \\mu^ {\\prime} (t). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 446, + 906, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The illustrations of Proposition 1 can be found in [19]. We can utilize Proposition 1 to transform the data across different distributions. Specifically, we need to establish the connections among the latent motion feature space $p(\\mathbf{Z}_{t=0})$ and the standard Normal distribution $p(\\mathbf{Z}_{t=1}) = \\mathcal{N}(0, \\mathbf{I})$ by carefully designing $\\mu(t)$ and $\\sigma(t)$ for the downstream generation task. However, previous methods (e.g., Flow Matching [19]) just randomly sample data across different distributions, leading to less efficient model training and inference. To get straighter paths for the training process, we can introduce the optimal transport (OT) theory into this task. As discussed in [21-26, 34], the OT problem aims to minimize the displacement cost between two distributions. Thus, we can leverage the transport plan $\\pi$ to build connections between two different distributions. The calculation of the optimal transport $\\pi$ can be formulated as:", + "bbox": [ + 511, + 481, + 908, + 722 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {\\pi} \\in \\Delta} J _ {\\mathrm {O T}} = \\langle \\boldsymbol {\\pi}, \\boldsymbol {C} \\rangle\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 724, + 661, + 746 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns. t. \\Delta = \\left\\{\\sum_ {j = 1} ^ {N} \\pi_ {i j} = a _ {i}, \\quad \\sum_ {i = 1} ^ {N} \\pi_ {i j} = b _ {j}, \\quad \\pi_ {i j} \\geq 0 \\right\\}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 750, + 906, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Delta$ denotes the constraints on $\\pi$ . $C$ denotes the cost distance matrix which can be calculated as $C_{ij} = ||z_{0,i} - z_{1,j}||_2^2$ accordingly, where $z_{0,i}\\sim p(\\mathbf{Z}_{t = 0})$ and $z_{1,j}\\sim p(\\mathbf{Z}_{t = 1})$ . The optimization process for solving $\\pi$ has been provided in the Appendix A. Then we can obtain the matched data samples $(z_{0,i},z_{1,j})\\sim \\pi$ via the coupling", + "bbox": [ + 511, + 810, + 908, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22727", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "matrix. Hence we can utilize the dynamic process $p(\\boldsymbol{z}, t)$ on $\\boldsymbol{\\mu}(t) = t\\boldsymbol{z}_{0,i} + (1 - t)\\boldsymbol{z}_{1,j}$ and $\\boldsymbol{\\sigma}(t) = \\mathbf{0}$ where $t \\in [0,1]$ as:", + "bbox": [ + 89, + 90, + 482, + 133 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\boldsymbol {z} _ {t}, t\\right) = \\mathcal {N} \\left(t \\boldsymbol {z} _ {1, j} + (1 - t) \\boldsymbol {z} _ {0, i}, \\mathbf {0}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 136, + 482, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Meanwhile we can obtain the drift function $\\pmb{u}(\\pmb{z}, t)$ via using the Proposition 1 as below:", + "bbox": [ + 89, + 155, + 483, + 185 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {u} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\boldsymbol {\\mu} ^ {\\prime} (t) + \\frac {\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)}{\\boldsymbol {\\sigma} (t)} \\boldsymbol {\\sigma} ^ {\\prime} (t) = \\boldsymbol {z} _ {1, j} - \\boldsymbol {z} _ {0, i}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 186, + 483, + 217 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we can employ a neural network $v_{\\theta}(\\cdot)$ with matching samples $(z_0,z_1)\\sim \\pi$ to predict the deterministic drift $u(x,t)$ using the drift-estimate loss function:", + "bbox": [ + 89, + 218, + 482, + 262 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {\\theta}} J _ {\\text {d r i f t}} = \\mathbb {E} _ {\\left(\\boldsymbol {z} _ {0}, \\boldsymbol {z} _ {1}\\right) \\sim \\boldsymbol {\\pi}} \\left[ \\left| | \\boldsymbol {v} _ {\\theta} \\left(\\boldsymbol {z} _ {t}, t\\right) - \\left(\\boldsymbol {z} _ {1} - \\boldsymbol {z} _ {0}\\right) \\right| | _ {2} ^ {2} \\right]. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 263, + 483, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Moreover, we intend to figure out more consistent results [40] for achieving better performance. That is, the coupling data samples with different time interpolation should have the same drift output as expected. Therefore, we propose drift-consistent loss function:", + "bbox": [ + 89, + 299, + 483, + 372 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\pmb {\\theta}} J _ {\\mathrm {C L}} = \\mathbb {E} _ {t, t ^ {\\prime} \\in U [ 0, 1 ]} \\left[ | | \\pmb {v} _ {\\theta} (\\pmb {z} _ {t}, t) - \\pmb {v} _ {\\theta} (\\pmb {z} _ {t ^ {\\prime}}, t ^ {\\prime}) | | _ {2} ^ {2} \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 372, + 452, + 393 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\boldsymbol {z} _ {t} = (1 - t) \\boldsymbol {z} _ {0} + t \\boldsymbol {z} _ {1}, \\quad \\boldsymbol {z} _ {t ^ {\\prime}} = (1 - t ^ {\\prime}) \\boldsymbol {z} _ {0} + t ^ {\\prime} \\boldsymbol {z} _ {1} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 397, + 483, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we combine the drift-estimate and drift-consistent loss functions for training our proposed DerODE:", + "bbox": [ + 89, + 426, + 483, + 457 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} J _ {\\text {D e r O D E}} = J _ {\\text {d r i f t}} + \\lambda_ {c l} J _ {\\mathrm {C L}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 458, + 482, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{cl}$ denotes the balanced parameter. It is noticeable that DerODE will not involve complex denoising or score estimation procedures during the training stage. Therefore, it could be much easier to train compared with other diffusion approaches. Once we obtain the optimal solution on $\\pmb{v}^{*}(\\cdot)$ , we can generate new motion features in the latent space via randomly sample noise in the standard Gaussian distribution via:", + "bbox": [ + 89, + 479, + 483, + 598 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\boldsymbol {z}} _ {0, i} = \\widetilde {\\boldsymbol {z}} _ {1, i} - \\boldsymbol {v} _ {\\theta} (\\widetilde {\\boldsymbol {z}} _ {1, i}, t = 1) = \\operatorname {D e r O D E} (\\widetilde {\\boldsymbol {z}} _ {1, i}), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 599, + 482, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\widetilde{z}_{1,i} \\sim \\mathcal{N}(0,I)$ and it can obtain the deterministic output result $\\widetilde{z}_{0,i}$ . Finally, we can utilize the decoder $\\mathrm{Dec}(\\cdot)$ to generate human motion as $\\widetilde{\\pmb{E}} = \\mathrm{Dec}(\\widetilde{\\pmb{z}}_{0,i})$ accordingly.", + "bbox": [ + 89, + 618, + 483, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.2. Stochastic Diverse Output Generation Procedure", + "text_level": 1, + "bbox": [ + 89, + 670, + 477, + 685 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although we have obtained the deterministic ordinary differential equations (DerODE) between the latent space distribution of human motions and the standard Gaussian distribution, it remains challenging to generate highly diverse motion patterns. This difficulty arises from the deterministic nature of the ODEs, as identical initial conditions result in the same output paths, thereby reducing the diversity of the generated samples. To provide more diverse while accurate human motions, we tend to involve the stochastic differential equations based on the ordinary differential equations in the stochastic diverse output generation procedure.", + "bbox": [ + 89, + 688, + 483, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 2. Given the stochastic differential equations $dz_{t} = f(z_{t},t)dt + g(t)d\\boldsymbol{w}_{t}$ with the drift and diffusion terms, the mean $\\pmb{\\mu}(t)$ and covariance $\\pmb{\\Sigma}(t)$ can be formulated as:", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{r l} & \\frac {d \\boldsymbol {\\mu} (t)}{d t} = \\mathbb {E} [ f (\\boldsymbol {z}, t) ] \\\\ & \\frac {d \\boldsymbol {\\Sigma} (t)}{d t} = \\mathbb {E} \\left[ f (\\boldsymbol {z}, t) (\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)) ^ {\\top} \\right] \\\\ & \\quad + \\mathbb {E} \\left[ (\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)) f ^ {\\top} (\\boldsymbol {z}, t) \\right] + \\mathbb {E} [ g ^ {2} (t) ]. \\end{array} \\right. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 104, + 906, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proof of the Proposition 2 can be found in Appendix B. We can observe that the stochastic differential equations can transform the distributions according to the specific settings of drift and diffusion terms, which leads to diverse output results based on Proposition 2. Therefore, it is intuitive to consider a proper stochastic differential equations with carefully designed $f(z_{t}, t)$ and $g(t)$ respectively in the stochastic diverse output generation procedure.", + "bbox": [ + 511, + 174, + 906, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 3. Given the Diverse Stochastic Differential Equations (DivSDE) as $dz_{t} = \\left(-\\frac{1}{1 - t}\\right)z_{t}dt + \\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{dw}_{t}$ with the initial data sample $\\pmb{x}_0$ and the noise level $\\eta$ , the probability of data distribution $\\pmb{x}_{t}$ is $p(\\pmb{z}_t) = \\mathcal{N}((1 - t)\\pmb{z}_i,\\eta^2 t^2\\pmb{I})$ at the time step $t$ when $p(\\pmb{z}_0) = \\mathcal{N}(\\pmb{z}_0,\\pmb{0})$ .", + "bbox": [ + 511, + 295, + 906, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proof of the Proposition 3 can be found in Appendix C. It is obvious that the diffusion term $\\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{d}\\pmb{w}_t$ which involves noise can enhance the diversity of the model output and thus DivSDE is different than DerODE. Note that the stochastic differential equations in Proposition 2 have the backward process as $\\pmb{d}\\pmb{x}_t = \\left[-\\frac{1}{1 - t}\\pmb{z}_t - \\frac{2t}{1 - t}\\nabla \\log p(\\pmb{z}_t)\\right]dt + \\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{d}\\pmb{w}_t$ , where $\\nabla \\log p(\\pmb{z}_t)$ denotes the score function of the data probability. Specifically, $\\nabla \\log p(\\pmb{z}_t)$ can be calculated via $\\nabla \\log p(\\pmb{z}_t) = \\frac{(1 - t)\\pmb{z}_i - \\pmb{z}_t}{t^2}$ . Previous score-based approaches [39] may involve a new neural network to estimate $\\nabla \\log p(\\pmb{z}_t)$ even if it is rather time-consuming and hard to train in real practice. However, it is important to note that we can already obtain $\\widetilde{\\pmb{z}}_{0,i}$ by utilizing DerODE via $\\widetilde{\\pmb{z}}_{0,i} = \\mathrm{DerODE}(\\widetilde{\\pmb{z}}_{1,i})$ and it can be further utilized for DivSDE. Therefore, we can rewrite the discrete form of the backward process on DivSDE as follows:", + "bbox": [ + 511, + 378, + 908, + 650 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {z} _ {i, t} = \\boldsymbol {z} _ {t + \\Delta t, i} + \\frac {\\Delta t}{1 - t} \\boldsymbol {z} _ {t + \\Delta t, i} \\tag {13} \\\\ + \\frac {2 t \\Delta t}{1 - t} \\frac {(1 - t) \\widetilde {\\boldsymbol {z}} _ {0 , i} - \\boldsymbol {z} _ {t , i}}{t ^ {2}} + \\eta \\varepsilon \\sqrt {\\frac {2 t}{1 - t}} \\sqrt {\\Delta t}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 652, + 905, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\varepsilon \\sim \\mathcal{N}(0, I)$ denotes the randomly sample noise. Meanwhile, $\\eta$ denotes the strengths of diversity. That is, larger value of $\\eta$ will provide more diverse output human motions. Moreover, DivSDE can directly borrow the previously calculated results from DerODE for secondary computations without the need for re-introducing other training processes.", + "bbox": [ + 511, + 717, + 906, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Model Summary", + "text_level": 1, + "bbox": [ + 511, + 818, + 679, + 833 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In summary, the proposed DSDFM can synthesize diverse and accurate human motion sequences through the designed two stages, i.e., human motion reconstruction and diverse motion generation. In the human motion reconstruction", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22728", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 The process for generating diverse human motions.", + "bbox": [ + 91, + 90, + 485, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Require: time interval: $T$ , time steps: $\\Delta t = \\frac{1}{T}$ , noise for diversity: $\\eta$", + "bbox": [ + 91, + 123, + 483, + 155 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ensure: Generated new samples $\\hat{E}$", + "bbox": [ + 91, + 154, + 334, + 169 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1: Initialize $\\widetilde{z}_{1,i}$ from Gaussian distribution $\\mathcal{N}(0,\\pmb {I})$", + "bbox": [ + 101, + 169, + 449, + 185 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2: # Adopting DerODE to obtain $\\widetilde{x}_{i,0}$", + "bbox": [ + 101, + 185, + 354, + 199 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3: $\\widetilde{z}_{0,i} = \\mathrm{DerODE}(\\widetilde{z}_{1,i})$", + "bbox": [ + 101, + 200, + 269, + 215 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4: # Adopting DivSDE to obtain diverse human motions.", + "bbox": [ + 101, + 215, + 475, + 229 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5: for $t \\in \\text{range}(T - \\Delta t, 0)$ do", + "bbox": [ + 101, + 229, + 321, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6: Obtain the score function as: $\\nabla \\log p(\\boldsymbol{z}_{t,i}) = \\frac{(1 - t)\\widetilde{\\boldsymbol{z}}_{0,i} - \\boldsymbol{z}_{t,i}}{(t / T)^2}$ .", + "bbox": [ + 101, + 244, + 482, + 281 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "7: Obtain the diffusion term as: $D_{\\mathrm{Diffu}} = \\frac{2(t / T)}{1 - (t / T)} \\nabla \\log p(\\pmb{z}_{t,i}) \\Delta t$", + "bbox": [ + 101, + 281, + 482, + 313 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "8: Obtain the drift term as: $D_{\\mathrm{Drift}} = \\frac{\\Delta t}{1 - (t / T)} z_{t + \\Delta t,i}$", + "bbox": [ + 101, + 313, + 462, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "9: Obtain the noise term as: $\\epsilon_{\\mathrm{noise}} = \\eta \\cdot \\varepsilon \\sqrt{\\frac{2(t / T)}{1 - (t / T)}}\\sqrt{\\Delta t}$", + "bbox": [ + 101, + 333, + 482, + 357 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "10: Obtain $\\boldsymbol{z}_{t,i} = \\boldsymbol{z}_{t + \\Delta t,i} + D_{\\mathrm{Diffu}} + D_{\\mathrm{Drift}} + \\epsilon_{\\mathrm{noise}}$", + "11: end for", + "12: Generate the human motion: $\\hat{E} = \\mathrm{Dec}(z_{0,i})$" + ], + "bbox": [ + 96, + 367, + 460, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "stage, we first adopt the human motion reconstruction network to learn a well-structured latent space of human motions through VQVAE network. In the diverse motion generation stage, we tend to build the connections between the Gaussian distribution and latent space of human motions, thereby enhancing the diversity while guaranteeing the accuracy of the generated human motions through the designed deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. Specifically, DerODE can provide deterministic output results in an efficient way. Meanwhile, DivSDE can obtain more diverse human motions without introducing additional training process. The pseudo algorithm of the DSDFM is provided in Algorithm 1.", + "bbox": [ + 89, + 422, + 485, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 89, + 648, + 215, + 665 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we provide extensive experiments to evaluate the performance of our proposed DSDFM across widely used human motion datasets. We first describe the utilized human motion datasets and implementation details (Section 5.1). Subsequently, we present a comparative results analysis of our method with other state-of-the-art approaches on conditional and unconditional human motion synthesis. Additionally, we provide ablation studies to assess the effectiveness of the modules in our method (Section 5.2). Finally, we visually showcase the generated diverse human motion sequences to provide a qualitative performance (Section 5.3).", + "bbox": [ + 89, + 672, + 485, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Datasets and Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 848, + 410, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. The experiments are conducted on two widely used motion capture datasets, i.e., HumanAct12 [9], and Hu", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/250a8a6b1e7a718ee3421e97b01effd26500d6274f5e872ec469c11ee0122084.jpg", + "table_caption": [ + "Table 1. The comparison results of unconditional human motion synthesis between our method and state-of-the-art methods on HumanAct12 dataset. **Bold** and **underline** indicate the best and the second best result." + ], + "table_footnote": [], + "table_body": "
    MethodFID ↓KID ↓Precision ↑Recall ↑Diversity ↑#params
    VPoser (CVPR'19)48.650.720.680.7212.7529M
    Action2Motion (MM'21)49.760.680.700.7113.8021M
    ACTOR (CVPR'21)48.800.530.720.7414.1020M
    MDM (ICLR'23)31.920.960.660.6217.0024M
    MLD (CVPR'23)14.250.550.700.7916.8527M
    Modi (CVPR'23)13.030.120.710.8117.5723M
    DSDFM (Ours)12.860.100.750.8518.4115M
    Improvement1.31%1.67%4.17%4.93%4.78%2.50%
    ", + "bbox": [ + 517, + 148, + 903, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "manML3D [10]. HumanAct12 provides 1,191 raw motion sequences, and contains 12 subjects in which 12 categories of actions with per-sequence annotation are provided. HumanML3D dataset is a recent dataset that contains 14,616 motion sequences annotated by 44970 textual descriptions obtained from AMASS [29].", + "bbox": [ + 511, + 242, + 906, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. For a fair comparison, our method employs the following evaluation metrics: Frechet Inception Distance (FID), Kernel Inception Distance (KID), Precision, Recall, Accuracy, Diversity, and Multimodality. FID is the distance between the feature distribution of generated motions and that of the real motions, namely the difference in mean and variance. KID compares skewness as well as the values compared in FID, namely mean and variance. Precision measures the probability that a randomly generated motion falls within the support of the distribution of real data. Recall measures the probability that a real motion falls within the support of the distribution of generated data. Accuracy is measured by the corresponding action recognition model. Diversity measures the variance of the whole motion sequences across the dataset. Multimodality measures the diversity of human motion generated from the same text description. A lower value implies better for FID and KID. Higher Precision, Recall, Accuracy, Diversity, and MultiModality values imply better results. FID, KID, Precision, Recall, and Accuracy are utilized to evaluate the generated human motion accuracy. Diversity and MultiModality are utilized for the generation diversity.", + "bbox": [ + 511, + 334, + 908, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. For the human motion reconstruction process, the VQVAE consists of 4 Transformer layers with 8 heads, and the codebook size is set to $512 \\times 512$ . The batch size is set to 128, learning rate is initially set to $10^{-2}$ with a 0.98 decay every 10 epochs. The proposed method is trained for 500 epochs. For the diverse motion generation process, the time interval $\\Delta t$ is set to 0.01, and the strength of diversity $\\eta$ is set to 0.1. The diffusion step is set to 100. The balanced parameter $\\lambda_{cl}$ for $J_{CL}$ loss is set to 0.3.", + "bbox": [ + 511, + 667, + 908, + 818 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Experimental Results", + "text_level": 1, + "bbox": [ + 511, + 832, + 715, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons on Unconditional Human Motion Synthesis. We compare our method DSDFM with other state-of-the-art methods under the unconditional generation settings on the", + "bbox": [ + 511, + 854, + 908, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22729", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1691451ddd2e4e2ff9f96cf4f4d66389c68da27ced66909a079a2ccfd696859b.jpg", + "table_caption": [ + "Table 2. The comparison results of Action-to-Motion task on HumanAct12 dataset. $\\pm$ indicates $95\\%$ confidence interval, $\\rightarrow$ indicates that closer to real is better. The best results are in bold." + ], + "table_footnote": [], + "table_body": "
    MethodFID ↓Accuracy ↑Diversity →Multimodality ↑#params
    Real0.020±0.0100.997±0.0016.850±0.0502.450±0.040-
    ActionMotion (MM'21)0.338±0.0150.917±0.0036.879±0.0662.511±0.02321M
    ACTOR (CVPR'21)0.120±0.0000.955±0.0086.840±0.0302.530±0.02020M
    INR (ECCV'22)0.088±0.0040.973±0.0016.881±0.0482.569±0.04025M
    MLD (CVPR'23)0.077±0.0040.964±0.0026.831±0.0502.824±0.3827M
    MDM (ICLR'23)0.100±0.0000.990±0.0006.860±0.0502.520±0.01024M
    MotionDiffuse (TPAMI'24)0.070±0.0000.992±0.0136.850±0.0202.460±0.02025M
    DSDFM (Ours)0.068±0.0100.994±0.0016.851±0.0082.455±0.02515M
    Improvement2.85%0.21 %-0.01%0.21%2.50%
    ", + "bbox": [ + 93, + 135, + 480, + 224 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/93ec560116f06f0779b1978afc5dbf8276b6ea79e650ca4457d2d1badc6cb8d1.jpg", + "table_caption": [ + "Table 3. Ablation study on the comparison results of training and inference time on the HumanAct12 dataset. $m$ denotes minute, $s$ denotes second." + ], + "table_footnote": [], + "table_body": "
    MethodEpochTraining Time (m)Inference Time (s)/FID
    100 steps/FID500 steps/FID1000 steps/FID
    VPSDE50042.932.54/16.749.93/15.6318.09/14.31
    VESDE50040.572.68/16.499.48/14.9216.12/14.17
    DSDFM(Ours)50025.331.60/13.615.03/12.8610.33/12.24
    ", + "bbox": [ + 93, + 275, + 480, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "HumanAct12 dataset, the results are shown in Table 1. The input of the baseline methods is modified to the same length as our method. From the comparison results, we can observe that the baseline methods report poor performance in terms of accuracy and diversity metrics due to the mode collapse or unstable training processes. DSDFM outperforms these methods owing to the designed diverse motion generation procedure. In addition, to assess the training efficiency of our method, we also investigate the number of training parameters. The comparison results show that our method utilizes fewer parameters than baseline methods while achieving superior performance, which demonstrates the effectiveness of the proposed method. This suggests that our method is more computationally efficient and achieves the balance between the accuracy and diversity of generated samples.", + "bbox": [ + 88, + 325, + 482, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons on Conditional Human Motion Synthesis. Our method can also be extended to conditional generation, i.e., Action-to-Motion task. This task involves generating relevant human motion sequences given an input action label. The comparison results on the HumanAct12 dataset are presented in Table 2. From the comparison results, we can observe that DSDFM also achieves comparable performance under the accuracy and diversity metrics. Our method performs slightly worse than MotionDiffuse method in terms of the diversity metric by $0.01\\%$ , but our method reduces the confidence interval, demonstrating that our method is more stable and reliable. Additionally, it significantly decreases the number of training parameters. These results further report the effectiveness of our method for conditional human motion generation.", + "bbox": [ + 89, + 553, + 485, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation studies", + "text_level": 1, + "bbox": [ + 89, + 787, + 251, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To report the effectiveness of each component of our method, we compare the baseline methods with DSDFM under different settings on the HumanML3D and HumanAct12 datasets, including the training time, inference time for different diffusion steps, and the corresponding FID. The results are shown in Table 3 and Table 4. Table 3 shows the com", + "bbox": [ + 89, + 810, + 485, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3a1645192911e48743b516d4b013f57b228ec3f71b561e8926b14f4319b0a239.jpg", + "table_caption": [ + "Table 4. Ablation study on the comparison results of training and inference time on the HumanML3D dataset." + ], + "table_footnote": [], + "table_body": "
    MethodEpochTraining Time (m)Inference Time (s)/FID
    100 steps/FID500 steps/FID1000 steps/FID
    VPSDE50012.542.47/0.092±.0034.95/0.088±.0026.51/0.080±.024
    VESDE50012.572.35/0.094±.0054.48/0.089±.0016.62/0.078±.013
    DSDFM(Ours)5007.021.01/0.073±.0052.15/0.068±.0084.82/0.054±.010
    ", + "bbox": [ + 516, + 121, + 903, + 167 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/60dde98ce25615cdd2dc9f60f6adb5eb2c9b237dd6f3ca7acb70e58b910a83f1.jpg", + "table_caption": [ + "Table 5. Ablation studies of the proposed method. We compare our method with other score-based methods and provide the comparison results under the accuracy and diversity metrics, as well as the number of training parameters." + ], + "table_footnote": [], + "table_body": "
    MethodFID ↓KID ↓Precision ↑Recall ↑Diversity ↑#param
    VESDE14.920.360.590.6516.2128M
    VPSDE15.630.290.640.6817.0024M
    SDE (DDPM++)13.250.210.680.7517.4622M
    SDE (NCSN++)13.010.190.720.7917.5421M
    DSDFM (Ours)12.860.100.750.8518.4115M
    ", + "bbox": [ + 517, + 234, + 901, + 299 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "parison results for unconditional motion generation on the HumanAct12 dataset. From the results, we can observe that, compared to VPSDE and VESDE given the same number of epochs, DSDFM significantly reduces the training time while achieving a comparable performance under the FID metric, which demonstrates that our method is easier to train than the baseline methods and guaranteeing the quality of generated human motions. We also test these methods under different diffusion steps, and the performance of our method is improved in inference time. In addition, Table 4 shows the comparison results for Action-to-Motion task on HumanML3D dataset. The results under the same metrics are consistent with the results on the HumanAct12 dataset, which further demonstrates the effectiveness of our method.", + "bbox": [ + 511, + 306, + 906, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The ablation studies also test the performance of the designed stochastic diverse output generation procedure in DSDFM under the diversity and accuracy metrics, the results are shown in Table 5. Specifically, we employ other score-based methods to enhance the diversity of generated human motion sequences, i.e., variance preserving SDE (VPSDE), variance exploding SDE (VESDE), DDPM++, and NCSN++. From the comparison results, we can observe that our method exhibits comparable performance in terms of accuracy compared to the baseline methods, while showing a slight improvement in diversity. Notably, we have achieved a significant reduction in the number of training parameters, which report the effectiveness of our method.", + "bbox": [ + 511, + 518, + 908, + 714 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Visualization", + "text_level": 1, + "bbox": [ + 511, + 726, + 651, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we show the visualization results of our method on the unconditional human motion synthesis and Action-to-Motion tasks. As depicted in Figure 3, the top is the unconditional human motion synthesis, all human motion sequences are unconditionally generated from random noise sampled from Gaussian distribution on the HumanAct12 dataset. The figure shows that our method can generate diverse and high fidelity human motion sequences. The bottom is the sequences generated by the Action-to-Motion task, the generated sequences are under the action labels on", + "bbox": [ + 511, + 750, + 908, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22730", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e97cc7f5aaf80287f03123608f129d19984db7249f45e94e57e6a5a79163c4f6.jpg", + "image_caption": [ + "Figure 3. Qualitative results of DSDFM. We present the generated human motion sequences under different settings. The unconditional human motion sequences (top) are generated from the HumanAct12 dataset. The Action-to-Motion results (bottom) show the generated diverse motion sequences under the Sit and Run action labels, which are sampled from the HumanML3D dataset." + ], + "image_footnote": [], + "bbox": [ + 135, + 95, + 859, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a0079ac076d743f64aef64440c8bfb78e243dea892e2f70695af939dd6ad45b.jpg", + "image_caption": [ + "Figure 4. Comparison of the inference time costs of our method on the HumanAct12 dataset. We calculate the ablation studies (left) and average inference time comparison with baselines (right). All tests are performed on the NVIDIA A100." + ], + "image_footnote": [], + "bbox": [ + 227, + 328, + 501, + 484 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6f941b055363ab9c6f921cb109c224fc9fe68e814285b3961be632b34e0f2271.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 329, + 769, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the HumanML3D dataset. We can observe that the generated diverse motion sequences match the descriptions well. These qualitative results demonstrate that DSDFM can generate diverse and coherent human motion sequences.", + "bbox": [ + 88, + 527, + 482, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare and visualize the comparison results of inference time in Figure 4. The left of this Figure is the ablation studies of our method with different diffusion steps. This figure shows that using VPSDE and VESDE as our backbone has long inference time and relatively low accuracy. The right of this Figure is the average inference time comparison with baselines, which shows that our method can speed up the inference time when generating new samples.", + "bbox": [ + 88, + 589, + 482, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 724, + 209, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a Deterministic-to-Stochastic Diverse Latent Feature Mapping (DSDFM) for human motion synthesis. DSDFM is easy to train compared with the recent SGMs-based method, while facilitating the diversity and accuracy of generated human motions. DSDFM includes two stages, human motion reconstruction and diverse motion generation. Human motion reconstruction aims to learn a well-structured latent space of human motions. Diverse motion generation aims to enhance the diversity of the generated human motion sequences through the designed", + "bbox": [ + 88, + 750, + 485, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. Extensive experimental results demonstrate the efficacy of the proposed DSDFM method for human motion synthesis.", + "bbox": [ + 511, + 527, + 906, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgment", + "text_level": 1, + "bbox": [ + 511, + 614, + 684, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-031), the National Research Foundation, Singapore and DSO National Laboratories under the AI Singapore Programme (AISG Award No.: AISG2-GC-2023-010, \"Design Beyond What You Know\": Material-Informed Differential Generative AI (MIDGAI) for Lightweight High-Entropy Alloys and Multi-functional Composites (Stage 1a)\", the National Natural Science Foundation of China under Grant 62372081, the Young Elite Scientists Sponsorship Program by CAST under Grant 2022QNRC001, the Liaoning Provincial Natural Science Foundation Program under Grant 2024010785-JH3107, the Dalian Science and Technology Innovation Fund under Grant 2024JJ12GX020, the Dalian Major Projects of Basic Research under Grant 2024JJ12GX020 2023JJ11CG002 and the 111 Project under Grant D23006.", + "bbox": [ + 509, + 643, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22731", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. 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In Proceedings of the AAAI Conference on Artificial Intelligence, pages 7368-7376, 2024. 1" + ], + "bbox": [ + 91, + 90, + 483, + 613 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22734", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/85360d39-ddc7-43b2-b5d2-e1635ded4be9_model.json b/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/85360d39-ddc7-43b2-b5d2-e1635ded4be9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..89bb4a0f182fb484fe557a4f7b44e237e1556895 --- /dev/null +++ b/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/85360d39-ddc7-43b2-b5d2-e1635ded4be9_model.json @@ -0,0 +1,2444 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.098, + 0.13, + 0.9, + 0.176 + ], + "angle": 0, + "content": "Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.295, + 0.202, + 0.74, + 0.24 + ], + "angle": 0, + "content": "Yu Hua\\(^{1,3}\\) Weiming Liu\\(^{2*}\\) Gui Xu\\(^{4}\\) Yaqing Hou\\(^{3}\\) Yew-Soon Ong\\(^{1,5}\\) Qiang Zhang\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.253, + 0.248, + 0.78, + 0.264 + ], + "angle": 0, + "content": "1College of Computing and Data Science, Nanyang Technological University, Singapore" + }, + { + "type": "text", + "bbox": [ + 0.251, + 0.266, + 0.785, + 0.281 + ], + "angle": 0, + "content": "\\(^{2}\\)ByteDance Inc. Dalian University of Technology, China Dalian University, China" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.284, + 0.908, + 0.3 + ], + "angle": 0, + "content": "5Centre for Frontier AI Research, Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.31, + 0.92, + 0.324 + ], + "angle": 0, + "content": "yu_hua, asysong@ntu.edu.sg lwming95@gmail.com guixu@s.dlu.edu.cn houyq,zhangq@dlut.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.359, + 0.327, + 0.374 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.392, + 0.486, + 0.739 + ], + "angle": 0, + "content": "Human motion synthesis aims to generate plausible human motion sequences, which has raised widespread attention in computer animation. Recent score-based generative models (SGMs) have demonstrated impressive results on this task. However, their training process involves complex curvature trajectories, leading to unstable training process. In this paper, we propose a Deterministic-to-Stochastic Diverse Latent Feature Mapping (DSDFM) method for human motion synthesis. DSDFM consists of two stages. The first human motion reconstruction stage aims to learn the latent space distribution of human motions. The second diverse motion generation stage aims to build connections between the Gaussian distribution and the latent space distribution of human motions, thereby enhancing the diversity and accuracy of the generated human motions. This stage is achieved by the designed deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. DSDFM is easy to train compared to previous SGMs-based methods and can enhance diversity without introducing additional training parameters. Through qualitative and quantitative experiments, DSDFM achieves state-of-the-art results surpassing the latest methods, validating its superiority in human motion synthesis." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.772, + 0.222, + 0.787 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.798, + 0.485, + 0.875 + ], + "angle": 0, + "content": "Human motion synthesis task aims to generate diverse and high quality 3D human motion sequences. This task has wide-ranging applications, such as human motion understanding [7, 14, 18], human-robot interactions [49, 61], and computer graphics [44]. Recent efforts mainly focus on con" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.36, + 0.909, + 0.557 + ], + "angle": 0, + "content": "ditional and unconditional human motion generation. Conditional human motion generation aims to generate human motion sequences under some limiting factors, such as music [16, 17], audio [1, 15, 28], and action labels [33, 33, 61]. Unconditional human motion generation intends to generate diverse human motions [32, 35] from diverse data, which still presents a significant challenge, especially when the human motion datasets are unstructured. In this paper, we focus on conditional (under the action labels) and unconditional human motion generations, as shown in Figure 1. Efficiently generating diverse and accurate human motions remains a tremendous challenge, which has led to the development of many different generative models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recent advancements in deep generative models, including Variational Autoencoders (VAEs) [53, 57, 60], Generative Adversarial Networks (GANs) [31], score-based generative models (SGMs), and related techniques [12, 39, 46, 51, 58], emerge as the dominant approaches for capturing the data distribution. Specifically, VAEs leverage an encoder-decoder network to learn the latent representation of human motion distribution. VAEs require approximate variational or Monte Carlo inference techniques, which tend to be intractable for complex models. GANs utilize a generator and discriminator to generate real-like motions from random noise. Unfortunately, GANs are known to suffer from numerical instability and mode collapse issues. SGMs define a forward diffusion process that maps data to noise by gradually perturbing the input data. Generation corresponds to a reverse process that synthesizes novel data via iterative denoising process. Even though they have presented high fidelity in generation, it is important to note that these methods have the challenge of curve trajectory modeling within diffusion models, as their forward pass is inherently designed to exhibit curvature in SDE, following either a Variance Preserving SDE (VPSDE) or a Variance Exploding" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.235, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22724" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.184, + 0.096, + 0.818, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.244, + 0.907, + 0.274 + ], + "angle": 0, + "content": "Figure 1. Examples of the inference process for human motion synthesis. Our method aims to generate diverse and accurate human motion sequences through the designed generative model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.28, + 0.484, + 0.37 + ], + "angle": 0, + "content": "SDE (VESDE) [39], leading to unstable training process and slow inference process. Recent methods, like DDIM [37], aim to accelerate the inference process by one-step or few-step generator, nevertheless, these methods lead to an obvious performance drop [5], and the training process is still unstable." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.372, + 0.485, + 0.794 + ], + "angle": 0, + "content": "To synthesize diverse and accurate human motions, we propose a novel method called DSDFM for human motion synthesis. The proposed method has straight trajectories and is easy to train compared to previous SGMs methods, while guaranteeing the diversity and accuracy of the generated human motions. The proposed DSDFM consists of two stages. In the first stage, a human motion reconstruction process is designed to learn the latent space distribution of human motions and motion representation. This process is implemented by the Vector Quantized Variational Autoencoders (VQVAE) [47] network. In the second stage, we design a diverse motion generation module, including deterministic feature mapping procedure and stochastic diverse output generation procedure. Deterministic feature mapping procedure aims to explore the optimal solution for building the connections between the Gaussian distribution and the latent space distribution of human motions using the designed Deterministic Ordinary Equation (DerODE) operation. DerODE has a straight training trajectory compared to previous diffusion generative methods [12, 39] and Flow Matching [27]. Although DerODE is easy to train, it is hard to generate highly diverse human motion patterns since DerODE could only provide deterministic output. Therefore, the designed stochastic diverse output generation procedure aims to enhance the diversity of generated human motions through Diverse Stochastic Differential Equations (DivSDE). It is noted that DivSDE operates during the sampling process of the model without introducing additional training processes." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.795, + 0.449, + 0.81 + ], + "angle": 0, + "content": "In summary, our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.811, + 0.483, + 0.87 + ], + "angle": 0, + "content": "- We propose a novel method called Diverse Latent Feature Mapping (DSDFM) for human motion synthesis. DSDFM is efficient to train and to utilize at sampling process, and can be used for conditional and unconditional generation." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.872, + 0.484, + 0.902 + ], + "angle": 0, + "content": "- We propose an optimal solution to build the connection between the Gaussian distribution and the latent space" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.28, + 0.907, + 0.34 + ], + "angle": 0, + "content": "distribution of human motions. In addition, we provide a stochastic diverse output generation process during the sampling process without reintroducing additional training processes." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.34, + 0.907, + 0.43 + ], + "angle": 0, + "content": "- The proposed method DSDFM is evaluated on widely-used human motion datasets in the comprehensive experiments. The obtained results demonstrate the effectiveness of the proposed method over the state-of-the-art approaches for conditional and unconditional human motion generation tasks." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.445, + 0.656, + 0.46 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.47, + 0.746, + 0.485 + ], + "angle": 0, + "content": "2.1. Human Motion Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.492, + 0.909, + 0.825 + ], + "angle": 0, + "content": "Conditional human motion synthesis aims to generate diverse and realistic human motions [42, 50, 54, 55] according to various conditional inputs, such as action labels [3, 41, 59] and music [11, 43]. For example, MDM [45] utilized a diffusion-based generative model for action-conditioned human motion generations, and reported a trading-off between diversity and fidelity of human motions due to the curve trajectory of training and sampling process. MLD [3] proposed to utilize the DDPM in latent space for human motion generations given an input action label, which also encountered the same problem as DDPM. In addition, the unconditional human motion synthesis [2, 35, 56] task also encounters the same issues although a series of achievements have been made in this field. For example, Holden et al. [13] presented a pioneer work in deep unconditional human motion synthesis. Modi [35] employed the style of StyleGAN to synthesize human motions. Unfortunately, these methods usually suffer from mode collapse or mode mixture. In contrast, we propose a novel method for conditional and unconditional human motion synthesis, which is easy to train compared to previous diffusion-based methods while guaranteeing the diversity of generated motions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.779, + 0.849 + ], + "angle": 0, + "content": "2.2. Diffusion Generative Models" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Recent years have witnessed a promising potential in modeling data distributions with diffusion generative models using Denoising diffusion probabilistic modeling (DDPM) [12]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22725" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.146, + 0.086, + 0.862, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.278, + 0.905, + 0.304 + ], + "angle": 0, + "content": "Figure 2. The overview of the proposed method DSDFM. The red arrow denotes the first stage and the green arrow denotes the second stage of DSDFM." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.314, + 0.485, + 0.722 + ], + "angle": 0, + "content": "and score-based generative models (SGMs) [39], which define a forward diffusion process that maps data to noise by gradually perturbing the input data. Variants of SGMs and techniques have been applied to images [6], audio [30]. For example, Robin et al. [8] proposed latent diffusion models (LDMs) that work on a compressed latent space of lower dimensionality for high-resolution image synthesis. LSGM [46] proposed to train SGMs in a latent space, which relies on the variational autoencoder framework to generate diverse images. However, it is important to note that these methods have the challenge of curve trajectory modeling within diffusion models, as their complex forward and backward processes are inherently designed to exhibit curvature, leading to unstable training process and slow sampling process. Although DDIM and related techniques [37] can shorten the sampling process, they often result in a performance drop [5, 52]. Flow Matching-based methods [20, 27] offer a more robust and stable alternative to diffusion models during the training process. However, the trajectories between source and target distributions remain relatively curved, and more importantly, these methods struggle to produce highly diverse samples, often sacrificing diversity in the training process. In contrast, we propose a generative model DSDFM for human motion generation tasks. This model utilizes straight trajectories, making it easier to train compared to other diffusion models. Additionally, it is capable of generating diverse human motion sequences." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.739, + 0.218, + 0.756 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Score-based diffusion models gradually perturb data by a forward diffusion process, and then reverse it to recover the data [38, 39]. Under the stochastic differential equation (SDE) framework proposed in [39], diffusion models construct a process \\( x(t)_{t=0}^{T} \\) indexed by a continuous time variable \\( t \\in [0,T] \\), such that \\( x(0) \\sim p_0 \\), for which we have a dataset of i.i.d. samples, and \\( x(T) \\sim p_T \\), we have a tractable form to generate samples efficiently. \\( p_0 \\) is the data distribution, \\( p_T \\) is the prior distribution. The forward diffusion" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.314, + 0.874, + 0.329 + ], + "angle": 0, + "content": "process can be modeled as the solution to an Itô SDE:" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.334, + 0.907, + 0.351 + ], + "angle": 0, + "content": "\\[\nd x _ {t} = f (x, t) d t + g (t) d w _ {t}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.356, + 0.907, + 0.506 + ], + "angle": 0, + "content": "where \\(w\\) is the standard Wiener process (a.k.a., Brownian motion), \\(f(\\cdot, t): \\mathbb{R}^d \\to \\mathbb{R}^d\\) is a vector valued function called the drift coefficient of \\(x(t)\\), and \\(g(\\cdot): \\mathbb{R} \\to \\mathbb{R}\\) is a scalar function known as the diffusion coefficient of \\(x(t)\\). There are various ways of designing the SDE such that it diffuses the data distribution into a fixed prior distribution \\(p_T\\). By starting from samples of \\(x(T) \\sim p_T\\) and reversing the process, we can obtain samples \\(x(0) \\sim p_0\\). The reverse of a diffusion process is also a diffusion process, running backwards in time and given by the reverse-time SDE:" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.511, + 0.907, + 0.528 + ], + "angle": 0, + "content": "\\[\nd x _ {t} = \\left[ f (x, t) - g (t) ^ {2} \\nabla_ {x} \\log p _ {t} (x) \\right] d t + g (t) d \\bar {w} _ {t}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.533, + 0.909, + 0.594 + ], + "angle": 0, + "content": "where \\(\\bar{w}\\) is a standard Wiener process when time flows backwards from \\(T\\) to 0, \\(dt\\) is an infinitesimal negative timestep. Once the score \\(\\nabla_x\\log p_t(x)\\) is learned, we can derive the reverse diffusion process and simulate it to sample from \\(p_0\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.616, + 0.725, + 0.633 + ], + "angle": 0, + "content": "4. The Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.645, + 0.909, + 0.901 + ], + "angle": 0, + "content": "This paper aims to synthesize diverse and realistic human motion sequences. The overview of the proposed method is shown in Figure 2. The conditional motion generation is performed under the action labels (Action-to-Motion task). Once the action labels are removed, the entire process becomes unconditional motion generation. The training process of the DSDFM mainly involved in two stages. The first stage is the human motion reconstruction process (Section 4.1), which aims to learn the human motion representation and capture the latent space distribution of human motions. The second stage (Section 4.2) aims to build the connections between the Gaussian distribution and the latent space distribution using the designed deterministic feature mapping procedure (DerODE) (Section 4.2.1). Moreover, we employ the stochastic diverse generation process (DivSDE) to enhance the diversity of generated human motions (Section 4.2.2)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22726" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.367, + 0.106 + ], + "angle": 0, + "content": "4.1. Human Motion Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.114, + 0.486, + 0.327 + ], + "angle": 0, + "content": "The human motion reconstruction network aims to learn the representation and the latent space distribution of human motions. In this process, we utilize VQVAE [47] to capture dynamic spatio-temporal features of human motions. Specifically, the input is a sequence of human motion sequence \\(\\pmb{E} = \\{e_1,e_2,\\dots ,e_T\\}\\) with the length of \\(T\\) where \\(e_t\\in \\mathbb{R}^{V\\times C}\\) is denoted by 3D coordinates at time \\(t\\) \\(C\\) denotes the 3D coordinates of human joints \\((C = 3)\\) \\(V\\) is the used number of human joints. The encoder of VQVAE aims to transform motion sequence into latent features, i.e., \\(\\mathrm{Enc}(\\pmb {E})\\to z_i\\in \\pmb{Z}\\) \\(z_{i}\\) is substituted by its closest vector \\(k_{j}\\) using a quantization codebook, where \\(\\hat{z}_i = \\arg \\min_{k_j\\in K}\\left||z_i - k_j\\right|\\) . The quantized feature \\(\\hat{z}_i\\) is decoded to \\(\\hat{\\pmb{E}}\\) by the decoder network, i.e., \\(\\mathrm{Dec}(\\hat{z}_i)\\rightarrow \\hat{\\pmb{E}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.329, + 0.485, + 0.524 + ], + "angle": 0, + "content": "In this work, the encoder \\(\\mathrm{Enc}(\\cdot)\\) and decoder \\(\\mathrm{Dec}(\\cdot)\\) networks are implemented by the Transformer [48] and GRU [4] module. For the Transformer process, we project the input human motion sequences into matrices \\(Q\\), \\(K\\), and \\(V\\) by \\(W_{Q}, W_{K}, W_{V}\\). The summary of the spatial joints \\(\\tilde{M}_{t}\\) is calculated by aggregating all the joint information using the multi-head mechanism \\((\\mathrm{head}_i)\\). The \\(GRU_{\\phi}\\) with parameter \\(\\phi\\) intends to capture the smoothness property of human motions, and then encode the human motions into latent space \\(Z\\). In addition, the decoder \\(\\mathrm{Dec}(\\cdot)\\) aims to map the latent space \\(Z\\) back to the reconstructed human motion sequence. The VQVAE is optimized by minimizing the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.527, + 0.484, + 0.558 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {V Q} = \\mathcal {L} (\\boldsymbol {E}, \\hat {\\boldsymbol {E}}) + | | \\hat {z} - \\operatorname {s g} (z) | | _ {2} ^ {2} + \\beta | | \\operatorname {s g} (\\hat {z}) - z | | _ {2} ^ {2}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.559, + 0.484, + 0.685 + ], + "angle": 0, + "content": "where \\(\\mathrm{sg}[\\cdot ]\\) is the stop gradient operator and \\(\\beta\\) is the hyper parameter. The first term \\(\\mathcal{L}(\\pmb {E},\\hat{\\pmb{E}}) = \\sum_{t = 1}^{T}\\sum_{v = 1}^{V}\\parallel e_t^{(v)} - \\hat{e}_t^{(v)}\\parallel_2\\), represents the reconstruction error. The second term aims to optimize the codebook, and the last term is to optimize the encoder by pushing \\(z\\) close to its nearest latent vector in the codebook. The human motion reconstruction process aims to learn the human motion representation and map the human motions into latent space \\(\\pmb{Z}\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.697, + 0.338, + 0.712 + ], + "angle": 0, + "content": "4.2. Diverse Motion Generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.486, + 0.901 + ], + "angle": 0, + "content": "Although we have established the human motion reconstruction in Section 4.1, we still cannot generate diverse human motion accordingly. The main reason is that the latent feature space for human motion is rather complicated and hard to sample. Therefore, it is essential to model the latent feature space for human motion by establishing the relationship between a Gaussian distribution and the latent space distribution. Previous diffusion-based generative methods [39] and flow matching methods [20], suffer from instability during training, exhibiting curved trajectories or difficulty in generating diverse samples. To tackle this issue, we innovatively propose a diverse motion generation module to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.182 + ], + "angle": 0, + "content": "enhance the diversity and accuracy of generated human motion sequences. Diverse motion generation module consists of two steps, i.e., deterministic feature mapping procedure and stochastic diverse output generation procedure. We will introduce the details of our proposed diverse motion generation module in this section." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.189, + 0.857, + 0.205 + ], + "angle": 0, + "content": "4.2.1. Deterministic Feature Mapping Procedure" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.208, + 0.909, + 0.343 + ], + "angle": 0, + "content": "To start with, we first introduce the deterministic feature mapping procedure. The deterministic feature mapping procedure is designed to model the relationship between Gaussian distribution \\( p(\\mathbf{Z}_{t=1}) \\) and the latent distribution for human motion \\( p(\\mathbf{Z}_{t=0}) \\) efficiently. Specifically, we propose Deterministic Ordinary Equation (DerODE) operation in the deterministic feature mapping procedure by depicting the transformation with Proposition 1 to achieve the corresponding goal." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.344, + 0.909, + 0.447 + ], + "angle": 0, + "content": "Proposition 1. Given the ordinary equation \\( d\\pmb{z}_t = u(\\pmb{z}_t, t) dt \\), where \\( u(\\pmb{z}_t, t) \\) denotes the drift function, and suppose the probability of data distribution \\( z(t) \\) is set to be \\( p(z(t)) = \\mathcal{N}(\\mu(t), \\sigma^2(t)) \\) at the time step \\( t \\), where \\( \\mu(t) \\) and \\( \\sigma(t) \\) denote the mean and variance of the Gaussian distribution respectively, the drift function \\( u(\\pmb{z}_t, t) \\) can be shown as:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.447, + 0.907, + 0.478 + ], + "angle": 0, + "content": "\\[\nu \\left(z _ {t}, t\\right) = \\sigma^ {\\prime} (t) \\cdot \\frac {z (t) - \\mu (t)}{\\sigma (t)} + \\mu^ {\\prime} (t). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.482, + 0.909, + 0.723 + ], + "angle": 0, + "content": "The illustrations of Proposition 1 can be found in [19]. We can utilize Proposition 1 to transform the data across different distributions. Specifically, we need to establish the connections among the latent motion feature space \\( p(\\mathbf{Z}_{t=0}) \\) and the standard Normal distribution \\( p(\\mathbf{Z}_{t=1}) = \\mathcal{N}(0, \\mathbf{I}) \\) by carefully designing \\( \\mu(t) \\) and \\( \\sigma(t) \\) for the downstream generation task. However, previous methods (e.g., Flow Matching [19]) just randomly sample data across different distributions, leading to less efficient model training and inference. To get straighter paths for the training process, we can introduce the optimal transport (OT) theory into this task. As discussed in [21-26, 34], the OT problem aims to minimize the displacement cost between two distributions. Thus, we can leverage the transport plan \\( \\pi \\) to build connections between two different distributions. The calculation of the optimal transport \\( \\pi \\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.725, + 0.662, + 0.747 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {\\pi} \\in \\Delta} J _ {\\mathrm {O T}} = \\langle \\boldsymbol {\\pi}, \\boldsymbol {C} \\rangle\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.75, + 0.907, + 0.81 + ], + "angle": 0, + "content": "\\[\ns. t. \\Delta = \\left\\{\\sum_ {j = 1} ^ {N} \\pi_ {i j} = a _ {i}, \\quad \\sum_ {i = 1} ^ {N} \\pi_ {i j} = b _ {j}, \\quad \\pi_ {i j} \\geq 0 \\right\\}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.902 + ], + "angle": 0, + "content": "where \\(\\Delta\\) denotes the constraints on \\(\\pi\\). \\(C\\) denotes the cost distance matrix which can be calculated as \\(C_{ij} = ||z_{0,i} - z_{1,j}||_2^2\\) accordingly, where \\(z_{0,i}\\sim p(\\mathbf{Z}_{t = 0})\\) and \\(z_{1,j}\\sim p(\\mathbf{Z}_{t = 1})\\). The optimization process for solving \\(\\pi\\) has been provided in the Appendix A. Then we can obtain the matched data samples \\((z_{0,i},z_{1,j})\\sim \\pi\\) via the coupling" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22727" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.135 + ], + "angle": 0, + "content": "matrix. Hence we can utilize the dynamic process \\(p(\\boldsymbol{z}, t)\\) on \\(\\boldsymbol{\\mu}(t) = t\\boldsymbol{z}_{0,i} + (1 - t)\\boldsymbol{z}_{1,j}\\) and \\(\\boldsymbol{\\sigma}(t) = \\mathbf{0}\\) where \\(t \\in [0,1]\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.137, + 0.483, + 0.153 + ], + "angle": 0, + "content": "\\[\np \\left(\\boldsymbol {z} _ {t}, t\\right) = \\mathcal {N} \\left(t \\boldsymbol {z} _ {1, j} + (1 - t) \\boldsymbol {z} _ {0, i}, \\mathbf {0}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.156, + 0.484, + 0.186 + ], + "angle": 0, + "content": "Meanwhile we can obtain the drift function \\( \\pmb{u}(\\pmb{z}, t) \\) via using the Proposition 1 as below:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.187, + 0.484, + 0.218 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {u} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\boldsymbol {\\mu} ^ {\\prime} (t) + \\frac {\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)}{\\boldsymbol {\\sigma} (t)} \\boldsymbol {\\sigma} ^ {\\prime} (t) = \\boldsymbol {z} _ {1, j} - \\boldsymbol {z} _ {0, i}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.219, + 0.483, + 0.263 + ], + "angle": 0, + "content": "Specifically, we can employ a neural network \\( v_{\\theta}(\\cdot) \\) with matching samples \\( (z_0,z_1)\\sim \\pi \\) to predict the deterministic drift \\( u(x,t) \\) using the drift-estimate loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.264, + 0.484, + 0.299 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {\\theta}} J _ {\\text {d r i f t}} = \\mathbb {E} _ {\\left(\\boldsymbol {z} _ {0}, \\boldsymbol {z} _ {1}\\right) \\sim \\boldsymbol {\\pi}} \\left[ \\left| | \\boldsymbol {v} _ {\\theta} \\left(\\boldsymbol {z} _ {t}, t\\right) - \\left(\\boldsymbol {z} _ {1} - \\boldsymbol {z} _ {0}\\right) \\right| | _ {2} ^ {2} \\right]. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.3, + 0.484, + 0.373 + ], + "angle": 0, + "content": "Moreover, we intend to figure out more consistent results [40] for achieving better performance. That is, the coupling data samples with different time interpolation should have the same drift output as expected. Therefore, we propose drift-consistent loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.373, + 0.453, + 0.395 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\pmb {\\theta}} J _ {\\mathrm {C L}} = \\mathbb {E} _ {t, t ^ {\\prime} \\in U [ 0, 1 ]} \\left[ | | \\pmb {v} _ {\\theta} (\\pmb {z} _ {t}, t) - \\pmb {v} _ {\\theta} (\\pmb {z} _ {t ^ {\\prime}}, t ^ {\\prime}) | | _ {2} ^ {2} \\right],\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.398, + 0.484, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\boldsymbol {z} _ {t} = (1 - t) \\boldsymbol {z} _ {0} + t \\boldsymbol {z} _ {1}, \\quad \\boldsymbol {z} _ {t ^ {\\prime}} = (1 - t ^ {\\prime}) \\boldsymbol {z} _ {0} + t ^ {\\prime} \\boldsymbol {z} _ {1} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.428, + 0.484, + 0.458 + ], + "angle": 0, + "content": "Finally, we combine the drift-estimate and drift-consistent loss functions for training our proposed DerODE:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.459, + 0.483, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} J _ {\\text {D e r O D E}} = J _ {\\text {d r i f t}} + \\lambda_ {c l} J _ {\\mathrm {C L}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.48, + 0.484, + 0.599 + ], + "angle": 0, + "content": "where \\(\\lambda_{cl}\\) denotes the balanced parameter. It is noticeable that DerODE will not involve complex denoising or score estimation procedures during the training stage. Therefore, it could be much easier to train compared with other diffusion approaches. Once we obtain the optimal solution on \\(\\pmb{v}^{*}(\\cdot)\\), we can generate new motion features in the latent space via randomly sample noise in the standard Gaussian distribution via:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.601, + 0.483, + 0.618 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\boldsymbol {z}} _ {0, i} = \\widetilde {\\boldsymbol {z}} _ {1, i} - \\boldsymbol {v} _ {\\theta} (\\widetilde {\\boldsymbol {z}} _ {1, i}, t = 1) = \\operatorname {D e r O D E} (\\widetilde {\\boldsymbol {z}} _ {1, i}), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.619, + 0.484, + 0.667 + ], + "angle": 0, + "content": "where \\(\\widetilde{z}_{1,i} \\sim \\mathcal{N}(0,I)\\) and it can obtain the deterministic output result \\(\\widetilde{z}_{0,i}\\). Finally, we can utilize the decoder \\(\\mathrm{Dec}(\\cdot)\\) to generate human motion as \\(\\widetilde{\\pmb{E}} = \\mathrm{Dec}(\\widetilde{\\pmb{z}}_{0,i})\\) accordingly." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.671, + 0.478, + 0.686 + ], + "angle": 0, + "content": "4.2.2. Stochastic Diverse Output Generation Procedure" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.484, + 0.856 + ], + "angle": 0, + "content": "Although we have obtained the deterministic ordinary differential equations (DerODE) between the latent space distribution of human motions and the standard Gaussian distribution, it remains challenging to generate highly diverse motion patterns. This difficulty arises from the deterministic nature of the ODEs, as identical initial conditions result in the same output paths, thereby reducing the diversity of the generated samples. To provide more diverse while accurate human motions, we tend to involve the stochastic differential equations based on the ordinary differential equations in the stochastic diverse output generation procedure." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Proposition 2. Given the stochastic differential equations \\(dz_{t} = f(z_{t},t)dt + g(t)d\\boldsymbol{w}_{t}\\) with the drift and diffusion terms, the mean \\(\\pmb{\\mu}(t)\\) and covariance \\(\\pmb{\\Sigma}(t)\\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.105, + 0.907, + 0.174 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{r l} & \\frac {d \\boldsymbol {\\mu} (t)}{d t} = \\mathbb {E} [ f (\\boldsymbol {z}, t) ] \\\\ & \\frac {d \\boldsymbol {\\Sigma} (t)}{d t} = \\mathbb {E} \\left[ f (\\boldsymbol {z}, t) (\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)) ^ {\\top} \\right] \\\\ & \\quad + \\mathbb {E} \\left[ (\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)) f ^ {\\top} (\\boldsymbol {z}, t) \\right] + \\mathbb {E} [ g ^ {2} (t) ]. \\end{array} \\right. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.175, + 0.907, + 0.295 + ], + "angle": 0, + "content": "The proof of the Proposition 2 can be found in Appendix B. We can observe that the stochastic differential equations can transform the distributions according to the specific settings of drift and diffusion terms, which leads to diverse output results based on Proposition 2. Therefore, it is intuitive to consider a proper stochastic differential equations with carefully designed \\( f(z_{t}, t) \\) and \\( g(t) \\) respectively in the stochastic diverse output generation procedure." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.296, + 0.907, + 0.378 + ], + "angle": 0, + "content": "Proposition 3. Given the Diverse Stochastic Differential Equations (DivSDE) as \\(dz_{t} = \\left(-\\frac{1}{1 - t}\\right)z_{t}dt + \\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{dw}_{t}\\) with the initial data sample \\(\\pmb{x}_0\\) and the noise level \\(\\eta\\), the probability of data distribution \\(\\pmb{x}_{t}\\) is \\(p(\\pmb{z}_t) = \\mathcal{N}((1 - t)\\pmb{z}_i,\\eta^2 t^2\\pmb{I})\\) at the time step \\(t\\) when \\(p(\\pmb{z}_0) = \\mathcal{N}(\\pmb{z}_0,\\pmb{0})\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.379, + 0.909, + 0.651 + ], + "angle": 0, + "content": "The proof of the Proposition 3 can be found in Appendix C. It is obvious that the diffusion term \\(\\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{d}\\pmb{w}_t\\) which involves noise can enhance the diversity of the model output and thus DivSDE is different than DerODE. Note that the stochastic differential equations in Proposition 2 have the backward process as \\(\\pmb{d}\\pmb{x}_t = \\left[-\\frac{1}{1 - t}\\pmb{z}_t - \\frac{2t}{1 - t}\\nabla \\log p(\\pmb{z}_t)\\right]dt + \\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{d}\\pmb{w}_t\\), where \\(\\nabla \\log p(\\pmb{z}_t)\\) denotes the score function of the data probability. Specifically, \\(\\nabla \\log p(\\pmb{z}_t)\\) can be calculated via \\(\\nabla \\log p(\\pmb{z}_t) = \\frac{(1 - t)\\pmb{z}_i - \\pmb{z}_t}{t^2}\\). Previous score-based approaches [39] may involve a new neural network to estimate \\(\\nabla \\log p(\\pmb{z}_t)\\) even if it is rather time-consuming and hard to train in real practice. However, it is important to note that we can already obtain \\(\\widetilde{\\pmb{z}}_{0,i}\\) by utilizing DerODE via \\(\\widetilde{\\pmb{z}}_{0,i} = \\mathrm{DerODE}(\\widetilde{\\pmb{z}}_{1,i})\\) and it can be further utilized for DivSDE. Therefore, we can rewrite the discrete form of the backward process on DivSDE as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.653, + 0.906, + 0.717 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {z} _ {i, t} = \\boldsymbol {z} _ {t + \\Delta t, i} + \\frac {\\Delta t}{1 - t} \\boldsymbol {z} _ {t + \\Delta t, i} \\tag {13} \\\\ + \\frac {2 t \\Delta t}{1 - t} \\frac {(1 - t) \\widetilde {\\boldsymbol {z}} _ {0 , i} - \\boldsymbol {z} _ {t , i}}{t ^ {2}} + \\eta \\varepsilon \\sqrt {\\frac {2 t}{1 - t}} \\sqrt {\\Delta t}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.907, + 0.809 + ], + "angle": 0, + "content": "where \\(\\varepsilon \\sim \\mathcal{N}(0, I)\\) denotes the randomly sample noise. Meanwhile, \\(\\eta\\) denotes the strengths of diversity. That is, larger value of \\(\\eta\\) will provide more diverse output human motions. Moreover, DivSDE can directly borrow the previously calculated results from DerODE for secondary computations without the need for re-introducing other training processes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.68, + 0.834 + ], + "angle": 0, + "content": "4.3. Model Summary" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "In summary, the proposed DSDFM can synthesize diverse and accurate human motion sequences through the designed two stages, i.e., human motion reconstruction and diverse motion generation. In the human motion reconstruction" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22728" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.092, + 0.091, + 0.486, + 0.12 + ], + "angle": 0, + "content": "Algorithm 1 The process for generating diverse human motions." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.124, + 0.484, + 0.156 + ], + "angle": 0, + "content": "Require: time interval: \\(T\\), time steps: \\(\\Delta t = \\frac{1}{T}\\), noise for diversity: \\(\\eta\\)" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.155, + 0.336, + 0.17 + ], + "angle": 0, + "content": "Ensure: Generated new samples \\(\\hat{E}\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.17, + 0.45, + 0.186 + ], + "angle": 0, + "content": "1: Initialize \\(\\widetilde{z}_{1,i}\\) from Gaussian distribution \\(\\mathcal{N}(0,\\pmb {I})\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.186, + 0.355, + 0.2 + ], + "angle": 0, + "content": "2: # Adopting DerODE to obtain \\(\\widetilde{x}_{i,0}\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.201, + 0.27, + 0.216 + ], + "angle": 0, + "content": "3: \\(\\widetilde{z}_{0,i} = \\mathrm{DerODE}(\\widetilde{z}_{1,i})\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.217, + 0.476, + 0.231 + ], + "angle": 0, + "content": "4: # Adopting DivSDE to obtain diverse human motions." + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.231, + 0.322, + 0.246 + ], + "angle": 0, + "content": "5: for \\( t \\in \\text{range}(T - \\Delta t, 0) \\) do" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.246, + 0.483, + 0.282 + ], + "angle": 0, + "content": "6: Obtain the score function as: \\(\\nabla \\log p(\\boldsymbol{z}_{t,i}) = \\frac{(1 - t)\\widetilde{\\boldsymbol{z}}_{0,i} - \\boldsymbol{z}_{t,i}}{(t / T)^2}\\)." + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.282, + 0.483, + 0.314 + ], + "angle": 0, + "content": "7: Obtain the diffusion term as: \\( D_{\\mathrm{Diffu}} = \\frac{2(t / T)}{1 - (t / T)} \\nabla \\log p(\\pmb{z}_{t,i}) \\Delta t \\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.314, + 0.464, + 0.333 + ], + "angle": 0, + "content": "8: Obtain the drift term as: \\( D_{\\mathrm{Drift}} = \\frac{\\Delta t}{1 - (t / T)} z_{t + \\Delta t,i} \\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.334, + 0.483, + 0.358 + ], + "angle": 0, + "content": "9: Obtain the noise term as: \\(\\epsilon_{\\mathrm{noise}} = \\eta \\cdot \\varepsilon \\sqrt{\\frac{2(t / T)}{1 - (t / T)}}\\sqrt{\\Delta t}\\)" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.368, + 0.462, + 0.383 + ], + "angle": 0, + "content": "10: Obtain \\( \\boldsymbol{z}_{t,i} = \\boldsymbol{z}_{t + \\Delta t,i} + D_{\\mathrm{Diffu}} + D_{\\mathrm{Drift}} + \\epsilon_{\\mathrm{noise}} \\)" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.384, + 0.174, + 0.396 + ], + "angle": 0, + "content": "11: end for" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.397, + 0.413, + 0.414 + ], + "angle": 0, + "content": "12: Generate the human motion: \\(\\hat{E} = \\mathrm{Dec}(z_{0,i})\\)" + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.368, + 0.462, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.424, + 0.486, + 0.635 + ], + "angle": 0, + "content": "stage, we first adopt the human motion reconstruction network to learn a well-structured latent space of human motions through VQVAE network. In the diverse motion generation stage, we tend to build the connections between the Gaussian distribution and latent space of human motions, thereby enhancing the diversity while guaranteeing the accuracy of the generated human motions through the designed deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. Specifically, DerODE can provide deterministic output results in an efficient way. Meanwhile, DivSDE can obtain more diverse human motions without introducing additional training process. The pseudo algorithm of the DSDFM is provided in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.649, + 0.216, + 0.666 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.674, + 0.486, + 0.841 + ], + "angle": 0, + "content": "In this section, we provide extensive experiments to evaluate the performance of our proposed DSDFM across widely used human motion datasets. We first describe the utilized human motion datasets and implementation details (Section 5.1). Subsequently, we present a comparative results analysis of our method with other state-of-the-art approaches on conditional and unconditional human motion synthesis. Additionally, we provide ablation studies to assess the effectiveness of the modules in our method (Section 5.2). Finally, we visually showcase the generated diverse human motion sequences to provide a qualitative performance (Section 5.3)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.411, + 0.866 + ], + "angle": 0, + "content": "5.1. Datasets and Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.485, + 0.901 + ], + "angle": 0, + "content": "Datasets. The experiments are conducted on two widely used motion capture datasets, i.e., HumanAct12 [9], and Hu" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.092, + 0.906, + 0.146 + ], + "angle": 0, + "content": "Table 1. The comparison results of unconditional human motion synthesis between our method and state-of-the-art methods on HumanAct12 dataset. **Bold** and **underline** indicate the best and the second best result." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.15, + 0.905, + 0.236 + ], + "angle": 0, + "content": "
    MethodFID ↓KID ↓Precision ↑Recall ↑Diversity ↑#params
    VPoser (CVPR'19)48.650.720.680.7212.7529M
    Action2Motion (MM'21)49.760.680.700.7113.8021M
    ACTOR (CVPR'21)48.800.530.720.7414.1020M
    MDM (ICLR'23)31.920.960.660.6217.0024M
    MLD (CVPR'23)14.250.550.700.7916.8527M
    Modi (CVPR'23)13.030.120.710.8117.5723M
    DSDFM (Ours)12.860.100.750.8518.4115M
    Improvement1.31%1.67%4.17%4.93%4.78%2.50%
    " + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.243, + 0.907, + 0.333 + ], + "angle": 0, + "content": "manML3D [10]. HumanAct12 provides 1,191 raw motion sequences, and contains 12 subjects in which 12 categories of actions with per-sequence annotation are provided. HumanML3D dataset is a recent dataset that contains 14,616 motion sequences annotated by 44970 textual descriptions obtained from AMASS [29]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.335, + 0.909, + 0.667 + ], + "angle": 0, + "content": "Evaluation metrics. For a fair comparison, our method employs the following evaluation metrics: Frechet Inception Distance (FID), Kernel Inception Distance (KID), Precision, Recall, Accuracy, Diversity, and Multimodality. FID is the distance between the feature distribution of generated motions and that of the real motions, namely the difference in mean and variance. KID compares skewness as well as the values compared in FID, namely mean and variance. Precision measures the probability that a randomly generated motion falls within the support of the distribution of real data. Recall measures the probability that a real motion falls within the support of the distribution of generated data. Accuracy is measured by the corresponding action recognition model. Diversity measures the variance of the whole motion sequences across the dataset. Multimodality measures the diversity of human motion generated from the same text description. A lower value implies better for FID and KID. Higher Precision, Recall, Accuracy, Diversity, and MultiModality values imply better results. FID, KID, Precision, Recall, and Accuracy are utilized to evaluate the generated human motion accuracy. Diversity and MultiModality are utilized for the generation diversity." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.669, + 0.909, + 0.819 + ], + "angle": 0, + "content": "Implementation Details. For the human motion reconstruction process, the VQVAE consists of 4 Transformer layers with 8 heads, and the codebook size is set to \\(512 \\times 512\\). The batch size is set to 128, learning rate is initially set to \\(10^{-2}\\) with a 0.98 decay every 10 epochs. The proposed method is trained for 500 epochs. For the diverse motion generation process, the time interval \\(\\Delta t\\) is set to 0.01, and the strength of diversity \\(\\eta\\) is set to 0.1. The diffusion step is set to 100. The balanced parameter \\(\\lambda_{cl}\\) for \\(J_{CL}\\) loss is set to 0.3." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.716, + 0.849 + ], + "angle": 0, + "content": "5.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Comparisons on Unconditional Human Motion Synthesis. We compare our method DSDFM with other state-of-the-art methods under the unconditional generation settings on the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22729" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.092, + 0.486, + 0.134 + ], + "angle": 0, + "content": "Table 2. The comparison results of Action-to-Motion task on HumanAct12 dataset. \\(\\pm\\) indicates \\(95\\%\\) confidence interval, \\(\\rightarrow\\) indicates that closer to real is better. The best results are in bold." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.136, + 0.482, + 0.226 + ], + "angle": 0, + "content": "
    MethodFID ↓Accuracy ↑Diversity →Multimodality ↑#params
    Real0.020±0.0100.997±0.0016.850±0.0502.450±0.040-
    ActionMotion (MM'21)0.338±0.0150.917±0.0036.879±0.0662.511±0.02321M
    ACTOR (CVPR'21)0.120±0.0000.955±0.0086.840±0.0302.530±0.02020M
    INR (ECCV'22)0.088±0.0040.973±0.0016.881±0.0482.569±0.04025M
    MLD (CVPR'23)0.077±0.0040.964±0.0026.831±0.0502.824±0.3827M
    MDM (ICLR'23)0.100±0.0000.990±0.0006.860±0.0502.520±0.01024M
    MotionDiffuse (TPAMI'24)0.070±0.0000.992±0.0136.850±0.0202.460±0.02025M
    DSDFM (Ours)0.068±0.0100.994±0.0016.851±0.0082.455±0.02515M
    Improvement2.85%0.21 %-0.01%0.21%2.50%
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.231, + 0.483, + 0.271 + ], + "angle": 0, + "content": "Table 3. Ablation study on the comparison results of training and inference time on the HumanAct12 dataset. \\( m \\) denotes minute, \\( s \\) denotes second." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.276, + 0.482, + 0.322 + ], + "angle": 0, + "content": "
    MethodEpochTraining Time (m)Inference Time (s)/FID
    100 steps/FID500 steps/FID1000 steps/FID
    VPSDE50042.932.54/16.749.93/15.6318.09/14.31
    VESDE50040.572.68/16.499.48/14.9216.12/14.17
    DSDFM(Ours)50025.331.60/13.615.03/12.8610.33/12.24
    " + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.327, + 0.483, + 0.552 + ], + "angle": 0, + "content": "HumanAct12 dataset, the results are shown in Table 1. The input of the baseline methods is modified to the same length as our method. From the comparison results, we can observe that the baseline methods report poor performance in terms of accuracy and diversity metrics due to the mode collapse or unstable training processes. DSDFM outperforms these methods owing to the designed diverse motion generation procedure. In addition, to assess the training efficiency of our method, we also investigate the number of training parameters. The comparison results show that our method utilizes fewer parameters than baseline methods while achieving superior performance, which demonstrates the effectiveness of the proposed method. This suggests that our method is more computationally efficient and achieves the balance between the accuracy and diversity of generated samples." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.554, + 0.486, + 0.78 + ], + "angle": 0, + "content": "Comparisons on Conditional Human Motion Synthesis. Our method can also be extended to conditional generation, i.e., Action-to-Motion task. This task involves generating relevant human motion sequences given an input action label. The comparison results on the HumanAct12 dataset are presented in Table 2. From the comparison results, we can observe that DSDFM also achieves comparable performance under the accuracy and diversity metrics. Our method performs slightly worse than MotionDiffuse method in terms of the diversity metric by \\(0.01\\%\\), but our method reduces the confidence interval, demonstrating that our method is more stable and reliable. Additionally, it significantly decreases the number of training parameters. These results further report the effectiveness of our method for conditional human motion generation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.789, + 0.253, + 0.803 + ], + "angle": 0, + "content": "5.3. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.486, + 0.9 + ], + "angle": 0, + "content": "To report the effectiveness of each component of our method, we compare the baseline methods with DSDFM under different settings on the HumanML3D and HumanAct12 datasets, including the training time, inference time for different diffusion steps, and the corresponding FID. The results are shown in Table 3 and Table 4. Table 3 shows the com" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.12 + ], + "angle": 0, + "content": "Table 4. Ablation study on the comparison results of training and inference time on the HumanML3D dataset." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.122, + 0.905, + 0.168 + ], + "angle": 0, + "content": "
    MethodEpochTraining Time (m)Inference Time (s)/FID
    100 steps/FID500 steps/FID1000 steps/FID
    VPSDE50012.542.47/0.092±.0034.95/0.088±.0026.51/0.080±.024
    VESDE50012.572.35/0.094±.0054.48/0.089±.0016.62/0.078±.013
    DSDFM(Ours)5007.021.01/0.073±.0052.15/0.068±.0084.82/0.054±.010
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.177, + 0.907, + 0.233 + ], + "angle": 0, + "content": "Table 5. Ablation studies of the proposed method. We compare our method with other score-based methods and provide the comparison results under the accuracy and diversity metrics, as well as the number of training parameters." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.235, + 0.903, + 0.3 + ], + "angle": 0, + "content": "
    MethodFID ↓KID ↓Precision ↑Recall ↑Diversity ↑#param
    VESDE14.920.360.590.6516.2128M
    VPSDE15.630.290.640.6817.0024M
    SDE (DDPM++)13.250.210.680.7517.4622M
    SDE (NCSN++)13.010.190.720.7917.5421M
    DSDFM (Ours)12.860.100.750.8518.4115M
    " + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.307, + 0.907, + 0.517 + ], + "angle": 0, + "content": "parison results for unconditional motion generation on the HumanAct12 dataset. From the results, we can observe that, compared to VPSDE and VESDE given the same number of epochs, DSDFM significantly reduces the training time while achieving a comparable performance under the FID metric, which demonstrates that our method is easier to train than the baseline methods and guaranteeing the quality of generated human motions. We also test these methods under different diffusion steps, and the performance of our method is improved in inference time. In addition, Table 4 shows the comparison results for Action-to-Motion task on HumanML3D dataset. The results under the same metrics are consistent with the results on the HumanAct12 dataset, which further demonstrates the effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.519, + 0.909, + 0.715 + ], + "angle": 0, + "content": "The ablation studies also test the performance of the designed stochastic diverse output generation procedure in DSDFM under the diversity and accuracy metrics, the results are shown in Table 5. Specifically, we employ other score-based methods to enhance the diversity of generated human motion sequences, i.e., variance preserving SDE (VPSDE), variance exploding SDE (VESDE), DDPM++, and NCSN++. From the comparison results, we can observe that our method exhibits comparable performance in terms of accuracy compared to the baseline methods, while showing a slight improvement in diversity. Notably, we have achieved a significant reduction in the number of training parameters, which report the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.727, + 0.652, + 0.741 + ], + "angle": 0, + "content": "5.4. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.901 + ], + "angle": 0, + "content": "In this section, we show the visualization results of our method on the unconditional human motion synthesis and Action-to-Motion tasks. As depicted in Figure 3, the top is the unconditional human motion synthesis, all human motion sequences are unconditionally generated from random noise sampled from Gaussian distribution on the HumanAct12 dataset. The figure shows that our method can generate diverse and high fidelity human motion sequences. The bottom is the sequences generated by the Action-to-Motion task, the generated sequences are under the action labels on" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22730" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.137, + 0.096, + 0.861, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.277, + 0.908, + 0.32 + ], + "angle": 0, + "content": "Figure 3. Qualitative results of DSDFM. We present the generated human motion sequences under different settings. The unconditional human motion sequences (top) are generated from the HumanAct12 dataset. The Action-to-Motion results (bottom) show the generated diverse motion sequences under the Sit and Run action labels, which are sampled from the HumanML3D dataset." + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.329, + 0.502, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.33, + 0.77, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.493, + 0.908, + 0.522 + ], + "angle": 0, + "content": "Figure 4. Comparison of the inference time costs of our method on the HumanAct12 dataset. We calculate the ablation studies (left) and average inference time comparison with baselines (right). All tests are performed on the NVIDIA A100." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.529, + 0.483, + 0.589 + ], + "angle": 0, + "content": "the HumanML3D dataset. We can observe that the generated diverse motion sequences match the descriptions well. These qualitative results demonstrate that DSDFM can generate diverse and coherent human motion sequences." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.59, + 0.483, + 0.711 + ], + "angle": 0, + "content": "We compare and visualize the comparison results of inference time in Figure 4. The left of this Figure is the ablation studies of our method with different diffusion steps. This figure shows that using VPSDE and VESDE as our backbone has long inference time and relatively low accuracy. The right of this Figure is the average inference time comparison with baselines, which shows that our method can speed up the inference time when generating new samples." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.725, + 0.21, + 0.74 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.75, + 0.486, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a Deterministic-to-Stochastic Diverse Latent Feature Mapping (DSDFM) for human motion synthesis. DSDFM is easy to train compared with the recent SGMs-based method, while facilitating the diversity and accuracy of generated human motions. DSDFM includes two stages, human motion reconstruction and diverse motion generation. Human motion reconstruction aims to learn a well-structured latent space of human motions. Diverse motion generation aims to enhance the diversity of the generated human motion sequences through the designed" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.529, + 0.908, + 0.59 + ], + "angle": 0, + "content": "deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. Extensive experimental results demonstrate the efficacy of the proposed DSDFM method for human motion synthesis." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.615, + 0.685, + 0.633 + ], + "angle": 0, + "content": "7. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.644, + 0.909, + 0.901 + ], + "angle": 0, + "content": "This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-031), the National Research Foundation, Singapore and DSO National Laboratories under the AI Singapore Programme (AISG Award No.: AISG2-GC-2023-010, \"Design Beyond What You Know\": Material-Informed Differential Generative AI (MIDGAI) for Lightweight High-Entropy Alloys and Multi-functional Composites (Stage 1a)\", the National Natural Science Foundation of China under Grant 62372081, the Young Elite Scientists Sponsorship Program by CAST under Grant 2022QNRC001, the Liaoning Provincial Natural Science Foundation Program under Grant 2024010785-JH3107, the Dalian Science and Technology Innovation Fund under Grant 2024JJ12GX020, the Dalian Major Projects of Basic Research under Grant 2024JJ12GX020 2023JJ11CG002 and the 111 Project under Grant D23006." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22731" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.484, + 0.171 + ], + "angle": 0, + "content": "[1] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. 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In Proceedings of the AAAI Conference on Artificial Intelligence, pages 7368-7376, 2024. 1" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.484, + 0.614 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22734" + } + ] +] \ No newline at end of file diff --git a/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/85360d39-ddc7-43b2-b5d2-e1635ded4be9_origin.pdf b/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/85360d39-ddc7-43b2-b5d2-e1635ded4be9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7da4fda386511a8f22dc5a4def849af9a05d8181 --- /dev/null +++ b/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/85360d39-ddc7-43b2-b5d2-e1635ded4be9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0ce8e93948fc034c5c0d76292feac9fe3dcad3cb5caf93367639fd1c8999406e +size 1646459 diff --git a/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/full.md b/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/full.md new file mode 100644 index 0000000000000000000000000000000000000000..36778f08aa331b4b59b257588e4bac79eb8c9b5b --- /dev/null +++ b/2025/Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis/full.md @@ -0,0 +1,361 @@ +# Deterministic-to-Stochastic Diverse Latent Feature Mapping for Human Motion Synthesis + +Yu Hua $^{1,3}$ Weiming Liu $^{2*}$ Gui Xu $^{4}$ Yaqing Hou $^{3}$ Yew-Soon Ong $^{1,5}$ Qiang Zhang $^{3}$ + +1College of Computing and Data Science, Nanyang Technological University, Singapore + +$^{2}$ ByteDance Inc. Dalian University of Technology, China Dalian University, China + +5Centre for Frontier AI Research, Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore + +yu_hua, asysong@ntu.edu.sg lwming95@gmail.com guixu@s.dlu.edu.cn houyq,zhangq@dlut.edu.cn + +# Abstract + +Human motion synthesis aims to generate plausible human motion sequences, which has raised widespread attention in computer animation. Recent score-based generative models (SGMs) have demonstrated impressive results on this task. However, their training process involves complex curvature trajectories, leading to unstable training process. In this paper, we propose a Deterministic-to-Stochastic Diverse Latent Feature Mapping (DSDFM) method for human motion synthesis. DSDFM consists of two stages. The first human motion reconstruction stage aims to learn the latent space distribution of human motions. The second diverse motion generation stage aims to build connections between the Gaussian distribution and the latent space distribution of human motions, thereby enhancing the diversity and accuracy of the generated human motions. This stage is achieved by the designed deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. DSDFM is easy to train compared to previous SGMs-based methods and can enhance diversity without introducing additional training parameters. Through qualitative and quantitative experiments, DSDFM achieves state-of-the-art results surpassing the latest methods, validating its superiority in human motion synthesis. + +# 1. Introduction + +Human motion synthesis task aims to generate diverse and high quality 3D human motion sequences. This task has wide-ranging applications, such as human motion understanding [7, 14, 18], human-robot interactions [49, 61], and computer graphics [44]. Recent efforts mainly focus on con + +ditional and unconditional human motion generation. Conditional human motion generation aims to generate human motion sequences under some limiting factors, such as music [16, 17], audio [1, 15, 28], and action labels [33, 33, 61]. Unconditional human motion generation intends to generate diverse human motions [32, 35] from diverse data, which still presents a significant challenge, especially when the human motion datasets are unstructured. In this paper, we focus on conditional (under the action labels) and unconditional human motion generations, as shown in Figure 1. Efficiently generating diverse and accurate human motions remains a tremendous challenge, which has led to the development of many different generative models. + +Recent advancements in deep generative models, including Variational Autoencoders (VAEs) [53, 57, 60], Generative Adversarial Networks (GANs) [31], score-based generative models (SGMs), and related techniques [12, 39, 46, 51, 58], emerge as the dominant approaches for capturing the data distribution. Specifically, VAEs leverage an encoder-decoder network to learn the latent representation of human motion distribution. VAEs require approximate variational or Monte Carlo inference techniques, which tend to be intractable for complex models. GANs utilize a generator and discriminator to generate real-like motions from random noise. Unfortunately, GANs are known to suffer from numerical instability and mode collapse issues. SGMs define a forward diffusion process that maps data to noise by gradually perturbing the input data. Generation corresponds to a reverse process that synthesizes novel data via iterative denoising process. Even though they have presented high fidelity in generation, it is important to note that these methods have the challenge of curve trajectory modeling within diffusion models, as their forward pass is inherently designed to exhibit curvature in SDE, following either a Variance Preserving SDE (VPSDE) or a Variance Exploding + +![](images/6b9d6e32b28f091b04e1649e5309f6bfd89f776186f348765a6c9fbf1514f9c1.jpg) +Figure 1. Examples of the inference process for human motion synthesis. Our method aims to generate diverse and accurate human motion sequences through the designed generative model. + +SDE (VESDE) [39], leading to unstable training process and slow inference process. Recent methods, like DDIM [37], aim to accelerate the inference process by one-step or few-step generator, nevertheless, these methods lead to an obvious performance drop [5], and the training process is still unstable. + +To synthesize diverse and accurate human motions, we propose a novel method called DSDFM for human motion synthesis. The proposed method has straight trajectories and is easy to train compared to previous SGMs methods, while guaranteeing the diversity and accuracy of the generated human motions. The proposed DSDFM consists of two stages. In the first stage, a human motion reconstruction process is designed to learn the latent space distribution of human motions and motion representation. This process is implemented by the Vector Quantized Variational Autoencoders (VQVAE) [47] network. In the second stage, we design a diverse motion generation module, including deterministic feature mapping procedure and stochastic diverse output generation procedure. Deterministic feature mapping procedure aims to explore the optimal solution for building the connections between the Gaussian distribution and the latent space distribution of human motions using the designed Deterministic Ordinary Equation (DerODE) operation. DerODE has a straight training trajectory compared to previous diffusion generative methods [12, 39] and Flow Matching [27]. Although DerODE is easy to train, it is hard to generate highly diverse human motion patterns since DerODE could only provide deterministic output. Therefore, the designed stochastic diverse output generation procedure aims to enhance the diversity of generated human motions through Diverse Stochastic Differential Equations (DivSDE). It is noted that DivSDE operates during the sampling process of the model without introducing additional training processes. + +In summary, our main contributions are as follows: + +- We propose a novel method called Diverse Latent Feature Mapping (DSDFM) for human motion synthesis. DSDFM is efficient to train and to utilize at sampling process, and can be used for conditional and unconditional generation. +- We propose an optimal solution to build the connection between the Gaussian distribution and the latent space + +distribution of human motions. In addition, we provide a stochastic diverse output generation process during the sampling process without reintroducing additional training processes. + +- The proposed method DSDFM is evaluated on widely-used human motion datasets in the comprehensive experiments. The obtained results demonstrate the effectiveness of the proposed method over the state-of-the-art approaches for conditional and unconditional human motion generation tasks. + +# 2. Related Work + +# 2.1. Human Motion Synthesis + +Conditional human motion synthesis aims to generate diverse and realistic human motions [42, 50, 54, 55] according to various conditional inputs, such as action labels [3, 41, 59] and music [11, 43]. For example, MDM [45] utilized a diffusion-based generative model for action-conditioned human motion generations, and reported a trading-off between diversity and fidelity of human motions due to the curve trajectory of training and sampling process. MLD [3] proposed to utilize the DDPM in latent space for human motion generations given an input action label, which also encountered the same problem as DDPM. In addition, the unconditional human motion synthesis [2, 35, 56] task also encounters the same issues although a series of achievements have been made in this field. For example, Holden et al. [13] presented a pioneer work in deep unconditional human motion synthesis. Modi [35] employed the style of StyleGAN to synthesize human motions. Unfortunately, these methods usually suffer from mode collapse or mode mixture. In contrast, we propose a novel method for conditional and unconditional human motion synthesis, which is easy to train compared to previous diffusion-based methods while guaranteeing the diversity of generated motions. + +# 2.2. Diffusion Generative Models + +Recent years have witnessed a promising potential in modeling data distributions with diffusion generative models using Denoising diffusion probabilistic modeling (DDPM) [12] + +![](images/386794c4111e14265c6bf33247a4f21d0add0673757ea1bd4f3aed4747caf4f3.jpg) +Figure 2. The overview of the proposed method DSDFM. The red arrow denotes the first stage and the green arrow denotes the second stage of DSDFM. + +and score-based generative models (SGMs) [39], which define a forward diffusion process that maps data to noise by gradually perturbing the input data. Variants of SGMs and techniques have been applied to images [6], audio [30]. For example, Robin et al. [8] proposed latent diffusion models (LDMs) that work on a compressed latent space of lower dimensionality for high-resolution image synthesis. LSGM [46] proposed to train SGMs in a latent space, which relies on the variational autoencoder framework to generate diverse images. However, it is important to note that these methods have the challenge of curve trajectory modeling within diffusion models, as their complex forward and backward processes are inherently designed to exhibit curvature, leading to unstable training process and slow sampling process. Although DDIM and related techniques [37] can shorten the sampling process, they often result in a performance drop [5, 52]. Flow Matching-based methods [20, 27] offer a more robust and stable alternative to diffusion models during the training process. However, the trajectories between source and target distributions remain relatively curved, and more importantly, these methods struggle to produce highly diverse samples, often sacrificing diversity in the training process. In contrast, we propose a generative model DSDFM for human motion generation tasks. This model utilizes straight trajectories, making it easier to train compared to other diffusion models. Additionally, it is capable of generating diverse human motion sequences. + +# 3. Preliminary + +Score-based diffusion models gradually perturb data by a forward diffusion process, and then reverse it to recover the data [38, 39]. Under the stochastic differential equation (SDE) framework proposed in [39], diffusion models construct a process $x(t)_{t=0}^{T}$ indexed by a continuous time variable $t \in [0,T]$ , such that $x(0) \sim p_0$ , for which we have a dataset of i.i.d. samples, and $x(T) \sim p_T$ , we have a tractable form to generate samples efficiently. $p_0$ is the data distribution, $p_T$ is the prior distribution. The forward diffusion + +process can be modeled as the solution to an Itô SDE: + +$$ +d x _ {t} = f (x, t) d t + g (t) d w _ {t}, \tag {1} +$$ + +where $w$ is the standard Wiener process (a.k.a., Brownian motion), $f(\cdot, t): \mathbb{R}^d \to \mathbb{R}^d$ is a vector valued function called the drift coefficient of $x(t)$ , and $g(\cdot): \mathbb{R} \to \mathbb{R}$ is a scalar function known as the diffusion coefficient of $x(t)$ . There are various ways of designing the SDE such that it diffuses the data distribution into a fixed prior distribution $p_T$ . By starting from samples of $x(T) \sim p_T$ and reversing the process, we can obtain samples $x(0) \sim p_0$ . The reverse of a diffusion process is also a diffusion process, running backwards in time and given by the reverse-time SDE: + +$$ +d x _ {t} = \left[ f (x, t) - g (t) ^ {2} \nabla_ {x} \log p _ {t} (x) \right] d t + g (t) d \bar {w} _ {t}, \tag {2} +$$ + +where $\bar{w}$ is a standard Wiener process when time flows backwards from $T$ to 0, $dt$ is an infinitesimal negative timestep. Once the score $\nabla_x\log p_t(x)$ is learned, we can derive the reverse diffusion process and simulate it to sample from $p_0$ . + +# 4. The Proposed Method + +This paper aims to synthesize diverse and realistic human motion sequences. The overview of the proposed method is shown in Figure 2. The conditional motion generation is performed under the action labels (Action-to-Motion task). Once the action labels are removed, the entire process becomes unconditional motion generation. The training process of the DSDFM mainly involved in two stages. The first stage is the human motion reconstruction process (Section 4.1), which aims to learn the human motion representation and capture the latent space distribution of human motions. The second stage (Section 4.2) aims to build the connections between the Gaussian distribution and the latent space distribution using the designed deterministic feature mapping procedure (DerODE) (Section 4.2.1). Moreover, we employ the stochastic diverse generation process (DivSDE) to enhance the diversity of generated human motions (Section 4.2.2). + +# 4.1. Human Motion Reconstruction + +The human motion reconstruction network aims to learn the representation and the latent space distribution of human motions. In this process, we utilize VQVAE [47] to capture dynamic spatio-temporal features of human motions. Specifically, the input is a sequence of human motion sequence $\pmb{E} = \{e_1,e_2,\dots ,e_T\}$ with the length of $T$ where $e_t\in \mathbb{R}^{V\times C}$ is denoted by 3D coordinates at time $t$ $C$ denotes the 3D coordinates of human joints $(C = 3)$ $V$ is the used number of human joints. The encoder of VQVAE aims to transform motion sequence into latent features, i.e., $\mathrm{Enc}(\pmb {E})\to z_i\in \pmb{Z}$ $z_{i}$ is substituted by its closest vector $k_{j}$ using a quantization codebook, where $\hat{z}_i = \arg \min_{k_j\in K}\left||z_i - k_j\right|$ . The quantized feature $\hat{z}_i$ is decoded to $\hat{\pmb{E}}$ by the decoder network, i.e., $\mathrm{Dec}(\hat{z}_i)\rightarrow \hat{\pmb{E}}$ + +In this work, the encoder $\mathrm{Enc}(\cdot)$ and decoder $\mathrm{Dec}(\cdot)$ networks are implemented by the Transformer [48] and GRU [4] module. For the Transformer process, we project the input human motion sequences into matrices $Q$ , $K$ , and $V$ by $W_{Q}, W_{K}, W_{V}$ . The summary of the spatial joints $\tilde{M}_{t}$ is calculated by aggregating all the joint information using the multi-head mechanism $(\mathrm{head}_i)$ . The $GRU_{\phi}$ with parameter $\phi$ intends to capture the smoothness property of human motions, and then encode the human motions into latent space $Z$ . In addition, the decoder $\mathrm{Dec}(\cdot)$ aims to map the latent space $Z$ back to the reconstructed human motion sequence. The VQVAE is optimized by minimizing the following loss function: + +$$ +\mathcal {L} _ {V Q} = \mathcal {L} (\boldsymbol {E}, \hat {\boldsymbol {E}}) + | | \hat {z} - \operatorname {s g} (z) | | _ {2} ^ {2} + \beta | | \operatorname {s g} (\hat {z}) - z | | _ {2} ^ {2}, \tag {3} +$$ + +where $\mathrm{sg}[\cdot ]$ is the stop gradient operator and $\beta$ is the hyper parameter. The first term $\mathcal{L}(\pmb {E},\hat{\pmb{E}}) = \sum_{t = 1}^{T}\sum_{v = 1}^{V}\parallel e_t^{(v)} - \hat{e}_t^{(v)}\parallel_2$ , represents the reconstruction error. The second term aims to optimize the codebook, and the last term is to optimize the encoder by pushing $z$ close to its nearest latent vector in the codebook. The human motion reconstruction process aims to learn the human motion representation and map the human motions into latent space $\pmb{Z}$ . + +# 4.2. Diverse Motion Generation + +Although we have established the human motion reconstruction in Section 4.1, we still cannot generate diverse human motion accordingly. The main reason is that the latent feature space for human motion is rather complicated and hard to sample. Therefore, it is essential to model the latent feature space for human motion by establishing the relationship between a Gaussian distribution and the latent space distribution. Previous diffusion-based generative methods [39] and flow matching methods [20], suffer from instability during training, exhibiting curved trajectories or difficulty in generating diverse samples. To tackle this issue, we innovatively propose a diverse motion generation module to + +enhance the diversity and accuracy of generated human motion sequences. Diverse motion generation module consists of two steps, i.e., deterministic feature mapping procedure and stochastic diverse output generation procedure. We will introduce the details of our proposed diverse motion generation module in this section. + +# 4.2.1. Deterministic Feature Mapping Procedure + +To start with, we first introduce the deterministic feature mapping procedure. The deterministic feature mapping procedure is designed to model the relationship between Gaussian distribution $p(\mathbf{Z}_{t=1})$ and the latent distribution for human motion $p(\mathbf{Z}_{t=0})$ efficiently. Specifically, we propose Deterministic Ordinary Equation (DerODE) operation in the deterministic feature mapping procedure by depicting the transformation with Proposition 1 to achieve the corresponding goal. + +Proposition 1. Given the ordinary equation $d\pmb{z}_t = u(\pmb{z}_t, t) dt$ , where $u(\pmb{z}_t, t)$ denotes the drift function, and suppose the probability of data distribution $z(t)$ is set to be $p(z(t)) = \mathcal{N}(\mu(t), \sigma^2(t))$ at the time step $t$ , where $\mu(t)$ and $\sigma(t)$ denote the mean and variance of the Gaussian distribution respectively, the drift function $u(\pmb{z}_t, t)$ can be shown as: + +$$ +u \left(z _ {t}, t\right) = \sigma^ {\prime} (t) \cdot \frac {z (t) - \mu (t)}{\sigma (t)} + \mu^ {\prime} (t). \tag {4} +$$ + +The illustrations of Proposition 1 can be found in [19]. We can utilize Proposition 1 to transform the data across different distributions. Specifically, we need to establish the connections among the latent motion feature space $p(\mathbf{Z}_{t=0})$ and the standard Normal distribution $p(\mathbf{Z}_{t=1}) = \mathcal{N}(0, \mathbf{I})$ by carefully designing $\mu(t)$ and $\sigma(t)$ for the downstream generation task. However, previous methods (e.g., Flow Matching [19]) just randomly sample data across different distributions, leading to less efficient model training and inference. To get straighter paths for the training process, we can introduce the optimal transport (OT) theory into this task. As discussed in [21-26, 34], the OT problem aims to minimize the displacement cost between two distributions. Thus, we can leverage the transport plan $\pi$ to build connections between two different distributions. The calculation of the optimal transport $\pi$ can be formulated as: + +$$ +\min _ {\boldsymbol {\pi} \in \Delta} J _ {\mathrm {O T}} = \langle \boldsymbol {\pi}, \boldsymbol {C} \rangle +$$ + +$$ +s. t. \Delta = \left\{\sum_ {j = 1} ^ {N} \pi_ {i j} = a _ {i}, \quad \sum_ {i = 1} ^ {N} \pi_ {i j} = b _ {j}, \quad \pi_ {i j} \geq 0 \right\}, \tag {5} +$$ + +where $\Delta$ denotes the constraints on $\pi$ . $C$ denotes the cost distance matrix which can be calculated as $C_{ij} = ||z_{0,i} - z_{1,j}||_2^2$ accordingly, where $z_{0,i}\sim p(\mathbf{Z}_{t = 0})$ and $z_{1,j}\sim p(\mathbf{Z}_{t = 1})$ . The optimization process for solving $\pi$ has been provided in the Appendix A. Then we can obtain the matched data samples $(z_{0,i},z_{1,j})\sim \pi$ via the coupling + +matrix. Hence we can utilize the dynamic process $p(\boldsymbol{z}, t)$ on $\boldsymbol{\mu}(t) = t\boldsymbol{z}_{0,i} + (1 - t)\boldsymbol{z}_{1,j}$ and $\boldsymbol{\sigma}(t) = \mathbf{0}$ where $t \in [0,1]$ as: + +$$ +p \left(\boldsymbol {z} _ {t}, t\right) = \mathcal {N} \left(t \boldsymbol {z} _ {1, j} + (1 - t) \boldsymbol {z} _ {0, i}, \mathbf {0}\right). \tag {6} +$$ + +Meanwhile we can obtain the drift function $\pmb{u}(\pmb{z}, t)$ via using the Proposition 1 as below: + +$$ +\boldsymbol {u} \left(\boldsymbol {z} _ {t}, t\right) = \boldsymbol {\mu} ^ {\prime} (t) + \frac {\boldsymbol {z} (t) - \boldsymbol {\mu} (t)}{\boldsymbol {\sigma} (t)} \boldsymbol {\sigma} ^ {\prime} (t) = \boldsymbol {z} _ {1, j} - \boldsymbol {z} _ {0, i}. \tag {7} +$$ + +Specifically, we can employ a neural network $v_{\theta}(\cdot)$ with matching samples $(z_0,z_1)\sim \pi$ to predict the deterministic drift $u(x,t)$ using the drift-estimate loss function: + +$$ +\min _ {\boldsymbol {\theta}} J _ {\text {d r i f t}} = \mathbb {E} _ {\left(\boldsymbol {z} _ {0}, \boldsymbol {z} _ {1}\right) \sim \boldsymbol {\pi}} \left[ \left| | \boldsymbol {v} _ {\theta} \left(\boldsymbol {z} _ {t}, t\right) - \left(\boldsymbol {z} _ {1} - \boldsymbol {z} _ {0}\right) \right| | _ {2} ^ {2} \right]. \tag {8} +$$ + +Moreover, we intend to figure out more consistent results [40] for achieving better performance. That is, the coupling data samples with different time interpolation should have the same drift output as expected. Therefore, we propose drift-consistent loss function: + +$$ +\min _ {\pmb {\theta}} J _ {\mathrm {C L}} = \mathbb {E} _ {t, t ^ {\prime} \in U [ 0, 1 ]} \left[ | | \pmb {v} _ {\theta} (\pmb {z} _ {t}, t) - \pmb {v} _ {\theta} (\pmb {z} _ {t ^ {\prime}}, t ^ {\prime}) | | _ {2} ^ {2} \right], +$$ + +$$ +\text {w h e r e} \boldsymbol {z} _ {t} = (1 - t) \boldsymbol {z} _ {0} + t \boldsymbol {z} _ {1}, \quad \boldsymbol {z} _ {t ^ {\prime}} = (1 - t ^ {\prime}) \boldsymbol {z} _ {0} + t ^ {\prime} \boldsymbol {z} _ {1} \tag {9} +$$ + +Finally, we combine the drift-estimate and drift-consistent loss functions for training our proposed DerODE: + +$$ +\min _ {\theta} J _ {\text {D e r O D E}} = J _ {\text {d r i f t}} + \lambda_ {c l} J _ {\mathrm {C L}}, \tag {10} +$$ + +where $\lambda_{cl}$ denotes the balanced parameter. It is noticeable that DerODE will not involve complex denoising or score estimation procedures during the training stage. Therefore, it could be much easier to train compared with other diffusion approaches. Once we obtain the optimal solution on $\pmb{v}^{*}(\cdot)$ , we can generate new motion features in the latent space via randomly sample noise in the standard Gaussian distribution via: + +$$ +\widetilde {\boldsymbol {z}} _ {0, i} = \widetilde {\boldsymbol {z}} _ {1, i} - \boldsymbol {v} _ {\theta} (\widetilde {\boldsymbol {z}} _ {1, i}, t = 1) = \operatorname {D e r O D E} (\widetilde {\boldsymbol {z}} _ {1, i}), \tag {11} +$$ + +where $\widetilde{z}_{1,i} \sim \mathcal{N}(0,I)$ and it can obtain the deterministic output result $\widetilde{z}_{0,i}$ . Finally, we can utilize the decoder $\mathrm{Dec}(\cdot)$ to generate human motion as $\widetilde{\pmb{E}} = \mathrm{Dec}(\widetilde{\pmb{z}}_{0,i})$ accordingly. + +# 4.2.2. Stochastic Diverse Output Generation Procedure + +Although we have obtained the deterministic ordinary differential equations (DerODE) between the latent space distribution of human motions and the standard Gaussian distribution, it remains challenging to generate highly diverse motion patterns. This difficulty arises from the deterministic nature of the ODEs, as identical initial conditions result in the same output paths, thereby reducing the diversity of the generated samples. To provide more diverse while accurate human motions, we tend to involve the stochastic differential equations based on the ordinary differential equations in the stochastic diverse output generation procedure. + +Proposition 2. Given the stochastic differential equations $dz_{t} = f(z_{t},t)dt + g(t)d\boldsymbol{w}_{t}$ with the drift and diffusion terms, the mean $\pmb{\mu}(t)$ and covariance $\pmb{\Sigma}(t)$ can be formulated as: + +$$ +\left\{ \begin{array}{r l} & \frac {d \boldsymbol {\mu} (t)}{d t} = \mathbb {E} [ f (\boldsymbol {z}, t) ] \\ & \frac {d \boldsymbol {\Sigma} (t)}{d t} = \mathbb {E} \left[ f (\boldsymbol {z}, t) (\boldsymbol {z} (t) - \boldsymbol {\mu} (t)) ^ {\top} \right] \\ & \quad + \mathbb {E} \left[ (\boldsymbol {z} (t) - \boldsymbol {\mu} (t)) f ^ {\top} (\boldsymbol {z}, t) \right] + \mathbb {E} [ g ^ {2} (t) ]. \end{array} \right. \tag {12} +$$ + +The proof of the Proposition 2 can be found in Appendix B. We can observe that the stochastic differential equations can transform the distributions according to the specific settings of drift and diffusion terms, which leads to diverse output results based on Proposition 2. Therefore, it is intuitive to consider a proper stochastic differential equations with carefully designed $f(z_{t}, t)$ and $g(t)$ respectively in the stochastic diverse output generation procedure. + +Proposition 3. Given the Diverse Stochastic Differential Equations (DivSDE) as $dz_{t} = \left(-\frac{1}{1 - t}\right)z_{t}dt + \eta \sqrt{\frac{2t}{1 - t}}\pmb{dw}_{t}$ with the initial data sample $\pmb{x}_0$ and the noise level $\eta$ , the probability of data distribution $\pmb{x}_{t}$ is $p(\pmb{z}_t) = \mathcal{N}((1 - t)\pmb{z}_i,\eta^2 t^2\pmb{I})$ at the time step $t$ when $p(\pmb{z}_0) = \mathcal{N}(\pmb{z}_0,\pmb{0})$ . + +The proof of the Proposition 3 can be found in Appendix C. It is obvious that the diffusion term $\eta \sqrt{\frac{2t}{1 - t}}\pmb{d}\pmb{w}_t$ which involves noise can enhance the diversity of the model output and thus DivSDE is different than DerODE. Note that the stochastic differential equations in Proposition 2 have the backward process as $\pmb{d}\pmb{x}_t = \left[-\frac{1}{1 - t}\pmb{z}_t - \frac{2t}{1 - t}\nabla \log p(\pmb{z}_t)\right]dt + \eta \sqrt{\frac{2t}{1 - t}}\pmb{d}\pmb{w}_t$ , where $\nabla \log p(\pmb{z}_t)$ denotes the score function of the data probability. Specifically, $\nabla \log p(\pmb{z}_t)$ can be calculated via $\nabla \log p(\pmb{z}_t) = \frac{(1 - t)\pmb{z}_i - \pmb{z}_t}{t^2}$ . Previous score-based approaches [39] may involve a new neural network to estimate $\nabla \log p(\pmb{z}_t)$ even if it is rather time-consuming and hard to train in real practice. However, it is important to note that we can already obtain $\widetilde{\pmb{z}}_{0,i}$ by utilizing DerODE via $\widetilde{\pmb{z}}_{0,i} = \mathrm{DerODE}(\widetilde{\pmb{z}}_{1,i})$ and it can be further utilized for DivSDE. Therefore, we can rewrite the discrete form of the backward process on DivSDE as follows: + +$$ +\begin{array}{l} \boldsymbol {z} _ {i, t} = \boldsymbol {z} _ {t + \Delta t, i} + \frac {\Delta t}{1 - t} \boldsymbol {z} _ {t + \Delta t, i} \tag {13} \\ + \frac {2 t \Delta t}{1 - t} \frac {(1 - t) \widetilde {\boldsymbol {z}} _ {0 , i} - \boldsymbol {z} _ {t , i}}{t ^ {2}} + \eta \varepsilon \sqrt {\frac {2 t}{1 - t}} \sqrt {\Delta t}, \\ \end{array} +$$ + +where $\varepsilon \sim \mathcal{N}(0, I)$ denotes the randomly sample noise. Meanwhile, $\eta$ denotes the strengths of diversity. That is, larger value of $\eta$ will provide more diverse output human motions. Moreover, DivSDE can directly borrow the previously calculated results from DerODE for secondary computations without the need for re-introducing other training processes. + +# 4.3. Model Summary + +In summary, the proposed DSDFM can synthesize diverse and accurate human motion sequences through the designed two stages, i.e., human motion reconstruction and diverse motion generation. In the human motion reconstruction + +Algorithm 1 The process for generating diverse human motions. + +Require: time interval: $T$ , time steps: $\Delta t = \frac{1}{T}$ , noise for diversity: $\eta$ + +Ensure: Generated new samples $\hat{E}$ + +1: Initialize $\widetilde{z}_{1,i}$ from Gaussian distribution $\mathcal{N}(0,\pmb {I})$ + +2: # Adopting DerODE to obtain $\widetilde{x}_{i,0}$ + +3: $\widetilde{z}_{0,i} = \mathrm{DerODE}(\widetilde{z}_{1,i})$ + +4: # Adopting DivSDE to obtain diverse human motions. + +5: for $t \in \text{range}(T - \Delta t, 0)$ do + +6: Obtain the score function as: $\nabla \log p(\boldsymbol{z}_{t,i}) = \frac{(1 - t)\widetilde{\boldsymbol{z}}_{0,i} - \boldsymbol{z}_{t,i}}{(t / T)^2}$ . + +7: Obtain the diffusion term as: $D_{\mathrm{Diffu}} = \frac{2(t / T)}{1 - (t / T)} \nabla \log p(\pmb{z}_{t,i}) \Delta t$ + +8: Obtain the drift term as: $D_{\mathrm{Drift}} = \frac{\Delta t}{1 - (t / T)} z_{t + \Delta t,i}$ + +9: Obtain the noise term as: $\epsilon_{\mathrm{noise}} = \eta \cdot \varepsilon \sqrt{\frac{2(t / T)}{1 - (t / T)}}\sqrt{\Delta t}$ + +10: Obtain $\boldsymbol{z}_{t,i} = \boldsymbol{z}_{t + \Delta t,i} + D_{\mathrm{Diffu}} + D_{\mathrm{Drift}} + \epsilon_{\mathrm{noise}}$ +11: end for +12: Generate the human motion: $\hat{E} = \mathrm{Dec}(z_{0,i})$ + +stage, we first adopt the human motion reconstruction network to learn a well-structured latent space of human motions through VQVAE network. In the diverse motion generation stage, we tend to build the connections between the Gaussian distribution and latent space of human motions, thereby enhancing the diversity while guaranteeing the accuracy of the generated human motions through the designed deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. Specifically, DerODE can provide deterministic output results in an efficient way. Meanwhile, DivSDE can obtain more diverse human motions without introducing additional training process. The pseudo algorithm of the DSDFM is provided in Algorithm 1. + +# 5. Experiment + +In this section, we provide extensive experiments to evaluate the performance of our proposed DSDFM across widely used human motion datasets. We first describe the utilized human motion datasets and implementation details (Section 5.1). Subsequently, we present a comparative results analysis of our method with other state-of-the-art approaches on conditional and unconditional human motion synthesis. Additionally, we provide ablation studies to assess the effectiveness of the modules in our method (Section 5.2). Finally, we visually showcase the generated diverse human motion sequences to provide a qualitative performance (Section 5.3). + +# 5.1. Datasets and Implementation Details + +Datasets. The experiments are conducted on two widely used motion capture datasets, i.e., HumanAct12 [9], and Hu + +Table 1. The comparison results of unconditional human motion synthesis between our method and state-of-the-art methods on HumanAct12 dataset. **Bold** and **underline** indicate the best and the second best result. + +
    MethodFID ↓KID ↓Precision ↑Recall ↑Diversity ↑#params
    VPoser (CVPR'19)48.650.720.680.7212.7529M
    Action2Motion (MM'21)49.760.680.700.7113.8021M
    ACTOR (CVPR'21)48.800.530.720.7414.1020M
    MDM (ICLR'23)31.920.960.660.6217.0024M
    MLD (CVPR'23)14.250.550.700.7916.8527M
    Modi (CVPR'23)13.030.120.710.8117.5723M
    DSDFM (Ours)12.860.100.750.8518.4115M
    Improvement1.31%1.67%4.17%4.93%4.78%2.50%
    + +manML3D [10]. HumanAct12 provides 1,191 raw motion sequences, and contains 12 subjects in which 12 categories of actions with per-sequence annotation are provided. HumanML3D dataset is a recent dataset that contains 14,616 motion sequences annotated by 44970 textual descriptions obtained from AMASS [29]. + +Evaluation metrics. For a fair comparison, our method employs the following evaluation metrics: Frechet Inception Distance (FID), Kernel Inception Distance (KID), Precision, Recall, Accuracy, Diversity, and Multimodality. FID is the distance between the feature distribution of generated motions and that of the real motions, namely the difference in mean and variance. KID compares skewness as well as the values compared in FID, namely mean and variance. Precision measures the probability that a randomly generated motion falls within the support of the distribution of real data. Recall measures the probability that a real motion falls within the support of the distribution of generated data. Accuracy is measured by the corresponding action recognition model. Diversity measures the variance of the whole motion sequences across the dataset. Multimodality measures the diversity of human motion generated from the same text description. A lower value implies better for FID and KID. Higher Precision, Recall, Accuracy, Diversity, and MultiModality values imply better results. FID, KID, Precision, Recall, and Accuracy are utilized to evaluate the generated human motion accuracy. Diversity and MultiModality are utilized for the generation diversity. + +Implementation Details. For the human motion reconstruction process, the VQVAE consists of 4 Transformer layers with 8 heads, and the codebook size is set to $512 \times 512$ . The batch size is set to 128, learning rate is initially set to $10^{-2}$ with a 0.98 decay every 10 epochs. The proposed method is trained for 500 epochs. For the diverse motion generation process, the time interval $\Delta t$ is set to 0.01, and the strength of diversity $\eta$ is set to 0.1. The diffusion step is set to 100. The balanced parameter $\lambda_{cl}$ for $J_{CL}$ loss is set to 0.3. + +# 5.2. Experimental Results + +Comparisons on Unconditional Human Motion Synthesis. We compare our method DSDFM with other state-of-the-art methods under the unconditional generation settings on the + +Table 2. The comparison results of Action-to-Motion task on HumanAct12 dataset. $\pm$ indicates $95\%$ confidence interval, $\rightarrow$ indicates that closer to real is better. The best results are in bold. + +
    MethodFID ↓Accuracy ↑Diversity →Multimodality ↑#params
    Real0.020±0.0100.997±0.0016.850±0.0502.450±0.040-
    ActionMotion (MM'21)0.338±0.0150.917±0.0036.879±0.0662.511±0.02321M
    ACTOR (CVPR'21)0.120±0.0000.955±0.0086.840±0.0302.530±0.02020M
    INR (ECCV'22)0.088±0.0040.973±0.0016.881±0.0482.569±0.04025M
    MLD (CVPR'23)0.077±0.0040.964±0.0026.831±0.0502.824±0.3827M
    MDM (ICLR'23)0.100±0.0000.990±0.0006.860±0.0502.520±0.01024M
    MotionDiffuse (TPAMI'24)0.070±0.0000.992±0.0136.850±0.0202.460±0.02025M
    DSDFM (Ours)0.068±0.0100.994±0.0016.851±0.0082.455±0.02515M
    Improvement2.85%0.21 %-0.01%0.21%2.50%
    + +Table 3. Ablation study on the comparison results of training and inference time on the HumanAct12 dataset. $m$ denotes minute, $s$ denotes second. + +
    MethodEpochTraining Time (m)Inference Time (s)/FID
    100 steps/FID500 steps/FID1000 steps/FID
    VPSDE50042.932.54/16.749.93/15.6318.09/14.31
    VESDE50040.572.68/16.499.48/14.9216.12/14.17
    DSDFM(Ours)50025.331.60/13.615.03/12.8610.33/12.24
    + +HumanAct12 dataset, the results are shown in Table 1. The input of the baseline methods is modified to the same length as our method. From the comparison results, we can observe that the baseline methods report poor performance in terms of accuracy and diversity metrics due to the mode collapse or unstable training processes. DSDFM outperforms these methods owing to the designed diverse motion generation procedure. In addition, to assess the training efficiency of our method, we also investigate the number of training parameters. The comparison results show that our method utilizes fewer parameters than baseline methods while achieving superior performance, which demonstrates the effectiveness of the proposed method. This suggests that our method is more computationally efficient and achieves the balance between the accuracy and diversity of generated samples. + +Comparisons on Conditional Human Motion Synthesis. Our method can also be extended to conditional generation, i.e., Action-to-Motion task. This task involves generating relevant human motion sequences given an input action label. The comparison results on the HumanAct12 dataset are presented in Table 2. From the comparison results, we can observe that DSDFM also achieves comparable performance under the accuracy and diversity metrics. Our method performs slightly worse than MotionDiffuse method in terms of the diversity metric by $0.01\%$ , but our method reduces the confidence interval, demonstrating that our method is more stable and reliable. Additionally, it significantly decreases the number of training parameters. These results further report the effectiveness of our method for conditional human motion generation. + +# 5.3. Ablation studies + +To report the effectiveness of each component of our method, we compare the baseline methods with DSDFM under different settings on the HumanML3D and HumanAct12 datasets, including the training time, inference time for different diffusion steps, and the corresponding FID. The results are shown in Table 3 and Table 4. Table 3 shows the com + +Table 4. Ablation study on the comparison results of training and inference time on the HumanML3D dataset. + +
    MethodEpochTraining Time (m)Inference Time (s)/FID
    100 steps/FID500 steps/FID1000 steps/FID
    VPSDE50012.542.47/0.092±.0034.95/0.088±.0026.51/0.080±.024
    VESDE50012.572.35/0.094±.0054.48/0.089±.0016.62/0.078±.013
    DSDFM(Ours)5007.021.01/0.073±.0052.15/0.068±.0084.82/0.054±.010
    + +Table 5. Ablation studies of the proposed method. We compare our method with other score-based methods and provide the comparison results under the accuracy and diversity metrics, as well as the number of training parameters. + +
    MethodFID ↓KID ↓Precision ↑Recall ↑Diversity ↑#param
    VESDE14.920.360.590.6516.2128M
    VPSDE15.630.290.640.6817.0024M
    SDE (DDPM++)13.250.210.680.7517.4622M
    SDE (NCSN++)13.010.190.720.7917.5421M
    DSDFM (Ours)12.860.100.750.8518.4115M
    + +parison results for unconditional motion generation on the HumanAct12 dataset. From the results, we can observe that, compared to VPSDE and VESDE given the same number of epochs, DSDFM significantly reduces the training time while achieving a comparable performance under the FID metric, which demonstrates that our method is easier to train than the baseline methods and guaranteeing the quality of generated human motions. We also test these methods under different diffusion steps, and the performance of our method is improved in inference time. In addition, Table 4 shows the comparison results for Action-to-Motion task on HumanML3D dataset. The results under the same metrics are consistent with the results on the HumanAct12 dataset, which further demonstrates the effectiveness of our method. + +The ablation studies also test the performance of the designed stochastic diverse output generation procedure in DSDFM under the diversity and accuracy metrics, the results are shown in Table 5. Specifically, we employ other score-based methods to enhance the diversity of generated human motion sequences, i.e., variance preserving SDE (VPSDE), variance exploding SDE (VESDE), DDPM++, and NCSN++. From the comparison results, we can observe that our method exhibits comparable performance in terms of accuracy compared to the baseline methods, while showing a slight improvement in diversity. Notably, we have achieved a significant reduction in the number of training parameters, which report the effectiveness of our method. + +# 5.4. Visualization + +In this section, we show the visualization results of our method on the unconditional human motion synthesis and Action-to-Motion tasks. As depicted in Figure 3, the top is the unconditional human motion synthesis, all human motion sequences are unconditionally generated from random noise sampled from Gaussian distribution on the HumanAct12 dataset. The figure shows that our method can generate diverse and high fidelity human motion sequences. The bottom is the sequences generated by the Action-to-Motion task, the generated sequences are under the action labels on + +![](images/e97cc7f5aaf80287f03123608f129d19984db7249f45e94e57e6a5a79163c4f6.jpg) +Figure 3. Qualitative results of DSDFM. We present the generated human motion sequences under different settings. The unconditional human motion sequences (top) are generated from the HumanAct12 dataset. The Action-to-Motion results (bottom) show the generated diverse motion sequences under the Sit and Run action labels, which are sampled from the HumanML3D dataset. + +![](images/7a0079ac076d743f64aef64440c8bfb78e243dea892e2f70695af939dd6ad45b.jpg) +Figure 4. Comparison of the inference time costs of our method on the HumanAct12 dataset. We calculate the ablation studies (left) and average inference time comparison with baselines (right). All tests are performed on the NVIDIA A100. + +![](images/6f941b055363ab9c6f921cb109c224fc9fe68e814285b3961be632b34e0f2271.jpg) + +the HumanML3D dataset. We can observe that the generated diverse motion sequences match the descriptions well. These qualitative results demonstrate that DSDFM can generate diverse and coherent human motion sequences. + +We compare and visualize the comparison results of inference time in Figure 4. The left of this Figure is the ablation studies of our method with different diffusion steps. This figure shows that using VPSDE and VESDE as our backbone has long inference time and relatively low accuracy. The right of this Figure is the average inference time comparison with baselines, which shows that our method can speed up the inference time when generating new samples. + +# 6. Conclusion + +In this paper, we propose a Deterministic-to-Stochastic Diverse Latent Feature Mapping (DSDFM) for human motion synthesis. DSDFM is easy to train compared with the recent SGMs-based method, while facilitating the diversity and accuracy of generated human motions. DSDFM includes two stages, human motion reconstruction and diverse motion generation. Human motion reconstruction aims to learn a well-structured latent space of human motions. Diverse motion generation aims to enhance the diversity of the generated human motion sequences through the designed + +deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. Extensive experimental results demonstrate the efficacy of the proposed DSDFM method for human motion synthesis. + +# 7. Acknowledgment + +This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-031), the National Research Foundation, Singapore and DSO National Laboratories under the AI Singapore Programme (AISG Award No.: AISG2-GC-2023-010, "Design Beyond What You Know": Material-Informed Differential Generative AI (MIDGAI) for Lightweight High-Entropy Alloys and Multi-functional Composites (Stage 1a)", the National Natural Science Foundation of China under Grant 62372081, the Young Elite Scientists Sponsorship Program by CAST under Grant 2022QNRC001, the Liaoning Provincial Natural Science Foundation Program under Grant 2024010785-JH3107, the Dalian Science and Technology Innovation Fund under Grant 2024JJ12GX020, the Dalian Major Projects of Basic Research under Grant 2024JJ12GX020 2023JJ11CG002 and the 111 Project under Grant D23006. + +# References + +[1] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. 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Recent score-based generative models (SGMs) have demonstrated impressive results on this task. However, their training process involves complex curvature trajectories, leading to unstable training process. In this paper, we propose a Deterministic-to-Stochastic Diverse Latent Feature Mapping (DSDFM) method for human motion synthesis. DSDFM consists of two stages. The first human motion reconstruction stage aims to learn the latent space distribution of human motions. The second diverse motion generation stage aims to build connections between the Gaussian distribution and the latent space distribution of human motions, thereby enhancing the diversity and accuracy of the generated human motions. This stage is achieved by the designed deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. DSDFM is easy to train compared to previous SGMs-based methods and can enhance diversity without introducing additional training parameters. Through qualitative and quantitative experiments, DSDFM achieves state-of-the-art results surpassing the latest methods, validating its superiority in human motion synthesis." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 56, + 611, + 135, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 611, + 135, + 623 + ], + "spans": [ + { + "bbox": [ + 56, + 611, + 135, + 623 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 632, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 632, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 632, + 296, + 693 + ], + "type": "text", + "content": "Human motion synthesis task aims to generate diverse and high quality 3D human motion sequences. This task has wide-ranging applications, such as human motion understanding [7, 14, 18], human-robot interactions [49, 61], and computer graphics [44]. Recent efforts mainly focus on con" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 285, + 556, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 285, + 556, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 556, + 441 + ], + "type": "text", + "content": "ditional and unconditional human motion generation. Conditional human motion generation aims to generate human motion sequences under some limiting factors, such as music [16, 17], audio [1, 15, 28], and action labels [33, 33, 61]. Unconditional human motion generation intends to generate diverse human motions [32, 35] from diverse data, which still presents a significant challenge, especially when the human motion datasets are unstructured. In this paper, we focus on conditional (under the action labels) and unconditional human motion generations, as shown in Figure 1. Efficiently generating diverse and accurate human motions remains a tremendous challenge, which has led to the development of many different generative models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "content": "Recent advancements in deep generative models, including Variational Autoencoders (VAEs) [53, 57, 60], Generative Adversarial Networks (GANs) [31], score-based generative models (SGMs), and related techniques [12, 39, 46, 51, 58], emerge as the dominant approaches for capturing the data distribution. Specifically, VAEs leverage an encoder-decoder network to learn the latent representation of human motion distribution. VAEs require approximate variational or Monte Carlo inference techniques, which tend to be intractable for complex models. GANs utilize a generator and discriminator to generate real-like motions from random noise. Unfortunately, GANs are known to suffer from numerical instability and mode collapse issues. SGMs define a forward diffusion process that maps data to noise by gradually perturbing the input data. Generation corresponds to a reverse process that synthesizes novel data via iterative denoising process. Even though they have presented high fidelity in generation, it is important to note that these methods have the challenge of curve trajectory modeling within diffusion models, as their forward pass is inherently designed to exhibit curvature in SDE, following either a Variance Preserving SDE (VPSDE) or a Variance Exploding" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 143, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22724" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 112, + 76, + 500, + 187 + ], + "blocks": [ + { + "bbox": [ + 112, + 76, + 500, + 187 + ], + "lines": [ + { + "bbox": [ + 112, + 76, + 500, + 187 + ], + "spans": [ + { + "bbox": [ + 112, + 76, + 500, + 187 + ], + "type": "image", + "image_path": "6b9d6e32b28f091b04e1649e5309f6bfd89f776186f348765a6c9fbf1514f9c1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 193, + 555, + 217 + ], + "lines": [ + { + "bbox": [ + 55, + 193, + 555, + 217 + ], + "spans": [ + { + "bbox": [ + 55, + 193, + 555, + 217 + ], + "type": "text", + "content": "Figure 1. Examples of the inference process for human motion synthesis. Our method aims to generate diverse and accurate human motion sequences through the designed generative model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 221, + 296, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 221, + 296, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 296, + 293 + ], + "type": "text", + "content": "SDE (VESDE) [39], leading to unstable training process and slow inference process. Recent methods, like DDIM [37], aim to accelerate the inference process by one-step or few-step generator, nevertheless, these methods lead to an obvious performance drop [5], and the training process is still unstable." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 294, + 296, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 294, + 296, + 628 + ], + "spans": [ + { + "bbox": [ + 56, + 294, + 296, + 628 + ], + "type": "text", + "content": "To synthesize diverse and accurate human motions, we propose a novel method called DSDFM for human motion synthesis. The proposed method has straight trajectories and is easy to train compared to previous SGMs methods, while guaranteeing the diversity and accuracy of the generated human motions. The proposed DSDFM consists of two stages. In the first stage, a human motion reconstruction process is designed to learn the latent space distribution of human motions and motion representation. This process is implemented by the Vector Quantized Variational Autoencoders (VQVAE) [47] network. In the second stage, we design a diverse motion generation module, including deterministic feature mapping procedure and stochastic diverse output generation procedure. Deterministic feature mapping procedure aims to explore the optimal solution for building the connections between the Gaussian distribution and the latent space distribution of human motions using the designed Deterministic Ordinary Equation (DerODE) operation. DerODE has a straight training trajectory compared to previous diffusion generative methods [12, 39] and Flow Matching [27]. Although DerODE is easy to train, it is hard to generate highly diverse human motion patterns since DerODE could only provide deterministic output. Therefore, the designed stochastic diverse output generation procedure aims to enhance the diversity of generated human motions through Diverse Stochastic Differential Equations (DivSDE). It is noted that DivSDE operates during the sampling process of the model without introducing additional training processes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 629, + 274, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 629, + 274, + 641 + ], + "spans": [ + { + "bbox": [ + 67, + 629, + 274, + 641 + ], + "type": "text", + "content": "In summary, our main contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 689 + ], + "type": "text", + "content": "- We propose a novel method called Diverse Latent Feature Mapping (DSDFM) for human motion synthesis. DSDFM is efficient to train and to utilize at sampling process, and can be used for conditional and unconditional generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 690, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 690, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 690, + 296, + 714 + ], + "type": "text", + "content": "- We propose an optimal solution to build the connection between the Gaussian distribution and the latent space" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 321, + 221, + 555, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 221, + 555, + 269 + ], + "spans": [ + { + "bbox": [ + 321, + 221, + 555, + 269 + ], + "type": "text", + "content": "distribution of human motions. In addition, we provide a stochastic diverse output generation process during the sampling process without reintroducing additional training processes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 269, + 555, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 269, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 314, + 269, + 555, + 340 + ], + "type": "text", + "content": "- The proposed method DSDFM is evaluated on widely-used human motion datasets in the comprehensive experiments. The obtained results demonstrate the effectiveness of the proposed method over the state-of-the-art approaches for conditional and unconditional human motion generation tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 352, + 401, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 352, + 401, + 364 + ], + "spans": [ + { + "bbox": [ + 314, + 352, + 401, + 364 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 372, + 456, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 456, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 456, + 384 + ], + "type": "text", + "content": "2.1. Human Motion Synthesis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 389, + 556, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 389, + 556, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 389, + 556, + 653 + ], + "type": "text", + "content": "Conditional human motion synthesis aims to generate diverse and realistic human motions [42, 50, 54, 55] according to various conditional inputs, such as action labels [3, 41, 59] and music [11, 43]. For example, MDM [45] utilized a diffusion-based generative model for action-conditioned human motion generations, and reported a trading-off between diversity and fidelity of human motions due to the curve trajectory of training and sampling process. MLD [3] proposed to utilize the DDPM in latent space for human motion generations given an input action label, which also encountered the same problem as DDPM. In addition, the unconditional human motion synthesis [2, 35, 56] task also encounters the same issues although a series of achievements have been made in this field. For example, Holden et al. [13] presented a pioneer work in deep unconditional human motion synthesis. Modi [35] employed the style of StyleGAN to synthesize human motions. Unfortunately, these methods usually suffer from mode collapse or mode mixture. In contrast, we propose a novel method for conditional and unconditional human motion synthesis, which is easy to train compared to previous diffusion-based methods while guaranteeing the diversity of generated motions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 659, + 476, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 476, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 476, + 672 + ], + "type": "text", + "content": "2.2. Diffusion Generative Models" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "Recent years have witnessed a promising potential in modeling data distributions with diffusion generative models using Denoising diffusion probabilistic modeling (DDPM) [12]" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22725" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 89, + 68, + 527, + 218 + ], + "blocks": [ + { + "bbox": [ + 89, + 68, + 527, + 218 + ], + "lines": [ + { + "bbox": [ + 89, + 68, + 527, + 218 + ], + "spans": [ + { + "bbox": [ + 89, + 68, + 527, + 218 + ], + "type": "image", + "image_path": "386794c4111e14265c6bf33247a4f21d0add0673757ea1bd4f3aed4747caf4f3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 220, + 553, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 220, + 553, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 220, + 553, + 240 + ], + "type": "text", + "content": "Figure 2. The overview of the proposed method DSDFM. The red arrow denotes the first stage and the green arrow denotes the second stage of DSDFM." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 248, + 296, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 248, + 296, + 571 + ], + "spans": [ + { + "bbox": [ + 56, + 248, + 296, + 571 + ], + "type": "text", + "content": "and score-based generative models (SGMs) [39], which define a forward diffusion process that maps data to noise by gradually perturbing the input data. Variants of SGMs and techniques have been applied to images [6], audio [30]. For example, Robin et al. [8] proposed latent diffusion models (LDMs) that work on a compressed latent space of lower dimensionality for high-resolution image synthesis. LSGM [46] proposed to train SGMs in a latent space, which relies on the variational autoencoder framework to generate diverse images. However, it is important to note that these methods have the challenge of curve trajectory modeling within diffusion models, as their complex forward and backward processes are inherently designed to exhibit curvature, leading to unstable training process and slow sampling process. Although DDIM and related techniques [37] can shorten the sampling process, they often result in a performance drop [5, 52]. Flow Matching-based methods [20, 27] offer a more robust and stable alternative to diffusion models during the training process. However, the trajectories between source and target distributions remain relatively curved, and more importantly, these methods struggle to produce highly diverse samples, often sacrificing diversity in the training process. In contrast, we propose a generative model DSDFM for human motion generation tasks. This model utilizes straight trajectories, making it easier to train compared to other diffusion models. Additionally, it is capable of generating diverse human motion sequences." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 585, + 133, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 585, + 133, + 598 + ], + "spans": [ + { + "bbox": [ + 55, + 585, + 133, + 598 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "Score-based diffusion models gradually perturb data by a forward diffusion process, and then reverse it to recover the data [38, 39]. Under the stochastic differential equation (SDE) framework proposed in [39], diffusion models construct a process " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "x(t)_{t=0}^{T}" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " indexed by a continuous time variable " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "t \\in [0,T]" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "x(0) \\sim p_0" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": ", for which we have a dataset of i.i.d. samples, and " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "x(T) \\sim p_T" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": ", we have a tractable form to generate samples efficiently. " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " is the data distribution, " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "p_T" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " is the prior distribution. The forward diffusion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 248, + 534, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 248, + 534, + 260 + ], + "spans": [ + { + "bbox": [ + 313, + 248, + 534, + 260 + ], + "type": "text", + "content": "process can be modeled as the solution to an Itô SDE:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 376, + 264, + 555, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 264, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 376, + 264, + 555, + 277 + ], + "type": "interline_equation", + "content": "d x _ {t} = f (x, t) d t + g (t) d w _ {t}, \\tag {1}", + "image_path": "ca8510fdf81ddced32a0bcb843524c0b93bae6e7e11efcc55da18d14b144e97a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": " is the standard Wiener process (a.k.a., Brownian motion), " + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "inline_equation", + "content": "f(\\cdot, t): \\mathbb{R}^d \\to \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": " is a vector valued function called the drift coefficient of " + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "inline_equation", + "content": "x(t)" + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "inline_equation", + "content": "g(\\cdot): \\mathbb{R} \\to \\mathbb{R}" + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": " is a scalar function known as the diffusion coefficient of " + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "inline_equation", + "content": "x(t)" + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": ". There are various ways of designing the SDE such that it diffuses the data distribution into a fixed prior distribution " + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "inline_equation", + "content": "p_T" + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": ". By starting from samples of " + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "inline_equation", + "content": "x(T) \\sim p_T" + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": " and reversing the process, we can obtain samples " + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "inline_equation", + "content": "x(0) \\sim p_0" + }, + { + "bbox": [ + 313, + 281, + 555, + 400 + ], + "type": "text", + "content": ". The reverse of a diffusion process is also a diffusion process, running backwards in time and given by the reverse-time SDE:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 326, + 404, + 555, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 404, + 555, + 418 + ], + "spans": [ + { + "bbox": [ + 326, + 404, + 555, + 418 + ], + "type": "interline_equation", + "content": "d x _ {t} = \\left[ f (x, t) - g (t) ^ {2} \\nabla_ {x} \\log p _ {t} (x) \\right] d t + g (t) d \\bar {w} _ {t}, \\tag {2}", + "image_path": "eb96bed6a6d56b7428fadaba403ed7594625362dd1fb86f4d0d4b2003c839e1c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "inline_equation", + "content": "\\bar{w}" + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "text", + "content": " is a standard Wiener process when time flows backwards from " + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "text", + "content": " to 0, " + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "inline_equation", + "content": "dt" + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "text", + "content": " is an infinitesimal negative timestep. Once the score " + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "inline_equation", + "content": "\\nabla_x\\log p_t(x)" + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "text", + "content": " is learned, we can derive the reverse diffusion process and simulate it to sample from " + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 313, + 422, + 556, + 470 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 487, + 443, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 443, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 443, + 501 + ], + "type": "text", + "content": "4. The Proposed Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 510, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 556, + 713 + ], + "type": "text", + "content": "This paper aims to synthesize diverse and realistic human motion sequences. The overview of the proposed method is shown in Figure 2. The conditional motion generation is performed under the action labels (Action-to-Motion task). Once the action labels are removed, the entire process becomes unconditional motion generation. The training process of the DSDFM mainly involved in two stages. The first stage is the human motion reconstruction process (Section 4.1), which aims to learn the human motion representation and capture the latent space distribution of human motions. The second stage (Section 4.2) aims to build the connections between the Gaussian distribution and the latent space distribution using the designed deterministic feature mapping procedure (DerODE) (Section 4.2.1). Moreover, we employ the stochastic diverse generation process (DivSDE) to enhance the diversity of generated human motions (Section 4.2.2)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22726" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 224, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 224, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 224, + 83 + ], + "type": "text", + "content": "4.1. Human Motion Reconstruction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": "The human motion reconstruction network aims to learn the representation and the latent space distribution of human motions. In this process, we utilize VQVAE [47] to capture dynamic spatio-temporal features of human motions. Specifically, the input is a sequence of human motion sequence " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "\\pmb{E} = \\{e_1,e_2,\\dots ,e_T\\}" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " with the length of " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "e_t\\in \\mathbb{R}^{V\\times C}" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " is denoted by 3D coordinates at time " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " denotes the 3D coordinates of human joints " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "(C = 3)" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " is the used number of human joints. The encoder of VQVAE aims to transform motion sequence into latent features, i.e., " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "\\mathrm{Enc}(\\pmb {E})\\to z_i\\in \\pmb{Z}" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " is substituted by its closest vector " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "k_{j}" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " using a quantization codebook, where " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "\\hat{z}_i = \\arg \\min_{k_j\\in K}\\left||z_i - k_j\\right|" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " . The quantized feature " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "\\hat{z}_i" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " is decoded to " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{E}}" + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "text", + "content": " by the decoder network, i.e., " + }, + { + "bbox": [ + 55, + 90, + 297, + 258 + ], + "type": "inline_equation", + "content": "\\mathrm{Dec}(\\hat{z}_i)\\rightarrow \\hat{\\pmb{E}}" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "spans": [ + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": "In this work, the encoder " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{Enc}(\\cdot)" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": " and decoder " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{Dec}(\\cdot)" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": " networks are implemented by the Transformer [48] and GRU [4] module. For the Transformer process, we project the input human motion sequences into matrices " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "W_{Q}, W_{K}, W_{V}" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": ". The summary of the spatial joints " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\tilde{M}_{t}" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": " is calculated by aggregating all the joint information using the multi-head mechanism " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "(\\mathrm{head}_i)" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "GRU_{\\phi}" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": " with parameter " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": " intends to capture the smoothness property of human motions, and then encode the human motions into latent space " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": ". In addition, the decoder " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{Dec}(\\cdot)" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": " aims to map the latent space " + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 55, + 260, + 296, + 415 + ], + "type": "text", + "content": " back to the reconstructed human motion sequence. The VQVAE is optimized by minimizing the following loss function:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 63, + 417, + 296, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 417, + 296, + 441 + ], + "spans": [ + { + "bbox": [ + 63, + 417, + 296, + 441 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {V Q} = \\mathcal {L} (\\boldsymbol {E}, \\hat {\\boldsymbol {E}}) + | | \\hat {z} - \\operatorname {s g} (z) | | _ {2} ^ {2} + \\beta | | \\operatorname {s g} (\\hat {z}) - z | | _ {2} ^ {2}, \\tag {3}", + "image_path": "10135928ba47998d1ddb93539a3babc3133a473f4581515380bd5baf9bd34632.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "spans": [ + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "inline_equation", + "content": "\\mathrm{sg}[\\cdot ]" + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "text", + "content": " is the stop gradient operator and " + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "text", + "content": " is the hyper parameter. The first term " + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\pmb {E},\\hat{\\pmb{E}}) = \\sum_{t = 1}^{T}\\sum_{v = 1}^{V}\\parallel e_t^{(v)} - \\hat{e}_t^{(v)}\\parallel_2" + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "text", + "content": ", represents the reconstruction error. The second term aims to optimize the codebook, and the last term is to optimize the encoder by pushing " + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "text", + "content": " close to its nearest latent vector in the codebook. The human motion reconstruction process aims to learn the human motion representation and map the human motions into latent space " + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "inline_equation", + "content": "\\pmb{Z}" + }, + { + "bbox": [ + 55, + 442, + 296, + 542 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 552, + 206, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 206, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 206, + 563 + ], + "type": "text", + "content": "4.2. Diverse Motion Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 570, + 297, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 297, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 297, + 713 + ], + "type": "text", + "content": "Although we have established the human motion reconstruction in Section 4.1, we still cannot generate diverse human motion accordingly. The main reason is that the latent feature space for human motion is rather complicated and hard to sample. Therefore, it is essential to model the latent feature space for human motion by establishing the relationship between a Gaussian distribution and the latent space distribution. Previous diffusion-based generative methods [39] and flow matching methods [20], suffer from instability during training, exhibiting curved trajectories or difficulty in generating diverse samples. To tackle this issue, we innovatively propose a diverse motion generation module to" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 144 + ], + "type": "text", + "content": "enhance the diversity and accuracy of generated human motion sequences. Diverse motion generation module consists of two steps, i.e., deterministic feature mapping procedure and stochastic diverse output generation procedure. We will introduce the details of our proposed diverse motion generation module in this section." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 149, + 524, + 162 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 149, + 524, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 149, + 524, + 162 + ], + "type": "text", + "content": "4.2.1. Deterministic Feature Mapping Procedure" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 164, + 556, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 164, + 556, + 271 + ], + "spans": [ + { + "bbox": [ + 313, + 164, + 556, + 271 + ], + "type": "text", + "content": "To start with, we first introduce the deterministic feature mapping procedure. The deterministic feature mapping procedure is designed to model the relationship between Gaussian distribution " + }, + { + "bbox": [ + 313, + 164, + 556, + 271 + ], + "type": "inline_equation", + "content": "p(\\mathbf{Z}_{t=1})" + }, + { + "bbox": [ + 313, + 164, + 556, + 271 + ], + "type": "text", + "content": " and the latent distribution for human motion " + }, + { + "bbox": [ + 313, + 164, + 556, + 271 + ], + "type": "inline_equation", + "content": "p(\\mathbf{Z}_{t=0})" + }, + { + "bbox": [ + 313, + 164, + 556, + 271 + ], + "type": "text", + "content": " efficiently. Specifically, we propose Deterministic Ordinary Equation (DerODE) operation in the deterministic feature mapping procedure by depicting the transformation with Proposition 1 to achieve the corresponding goal." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": "Proposition 1. Given the ordinary equation " + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "inline_equation", + "content": "d\\pmb{z}_t = u(\\pmb{z}_t, t) dt" + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "inline_equation", + "content": "u(\\pmb{z}_t, t)" + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": " denotes the drift function, and suppose the probability of data distribution " + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "inline_equation", + "content": "z(t)" + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": " is set to be " + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "inline_equation", + "content": "p(z(t)) = \\mathcal{N}(\\mu(t), \\sigma^2(t))" + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": " at the time step " + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "inline_equation", + "content": "\\mu(t)" + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "inline_equation", + "content": "\\sigma(t)" + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": " denote the mean and variance of the Gaussian distribution respectively, the drift function " + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "inline_equation", + "content": "u(\\pmb{z}_t, t)" + }, + { + "bbox": [ + 313, + 272, + 556, + 354 + ], + "type": "text", + "content": " can be shown as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 355, + 354, + 555, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 354, + 555, + 378 + ], + "spans": [ + { + "bbox": [ + 355, + 354, + 555, + 378 + ], + "type": "interline_equation", + "content": "u \\left(z _ {t}, t\\right) = \\sigma^ {\\prime} (t) \\cdot \\frac {z (t) - \\mu (t)}{\\sigma (t)} + \\mu^ {\\prime} (t). \\tag {4}", + "image_path": "6119988416333cb799d86dec8be128f6b186a21e4e224fdb7bb3f83405084724.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "spans": [ + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "text", + "content": "The illustrations of Proposition 1 can be found in [19]. We can utilize Proposition 1 to transform the data across different distributions. Specifically, we need to establish the connections among the latent motion feature space " + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "inline_equation", + "content": "p(\\mathbf{Z}_{t=0})" + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "text", + "content": " and the standard Normal distribution " + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "inline_equation", + "content": "p(\\mathbf{Z}_{t=1}) = \\mathcal{N}(0, \\mathbf{I})" + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "text", + "content": " by carefully designing " + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "inline_equation", + "content": "\\mu(t)" + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "inline_equation", + "content": "\\sigma(t)" + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "text", + "content": " for the downstream generation task. However, previous methods (e.g., Flow Matching [19]) just randomly sample data across different distributions, leading to less efficient model training and inference. To get straighter paths for the training process, we can introduce the optimal transport (OT) theory into this task. As discussed in [21-26, 34], the OT problem aims to minimize the displacement cost between two distributions. Thus, we can leverage the transport plan " + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "text", + "content": " to build connections between two different distributions. The calculation of the optimal transport " + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 381, + 556, + 572 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 323, + 574, + 405, + 591 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 574, + 405, + 591 + ], + "spans": [ + { + "bbox": [ + 323, + 574, + 405, + 591 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {\\pi} \\in \\Delta} J _ {\\mathrm {O T}} = \\langle \\boldsymbol {\\pi}, \\boldsymbol {C} \\rangle", + "image_path": "9ac9e4fb50ed94f4332a96f62939b4c54ded576117af5718a3308ea414f1e606.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 321, + 594, + 555, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 594, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 321, + 594, + 555, + 641 + ], + "type": "interline_equation", + "content": "s. t. \\Delta = \\left\\{\\sum_ {j = 1} ^ {N} \\pi_ {i j} = a _ {i}, \\quad \\sum_ {i = 1} ^ {N} \\pi_ {i j} = b _ {j}, \\quad \\pi_ {i j} \\geq 0 \\right\\}, \\tag {5}", + "image_path": "6089fdde9271783c52e926508ac5fe25da115eb7c03fa918fac93633aac1c6eb.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " denotes the constraints on " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " denotes the cost distance matrix which can be calculated as " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "C_{ij} = ||z_{0,i} - z_{1,j}||_2^2" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " accordingly, where " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "z_{0,i}\\sim p(\\mathbf{Z}_{t = 0})" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "z_{1,j}\\sim p(\\mathbf{Z}_{t = 1})" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": ". The optimization process for solving " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " has been provided in the Appendix A. Then we can obtain the matched data samples " + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "inline_equation", + "content": "(z_{0,i},z_{1,j})\\sim \\pi" + }, + { + "bbox": [ + 313, + 642, + 556, + 714 + ], + "type": "text", + "content": " via the coupling" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22727" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "text", + "content": "matrix. Hence we can utilize the dynamic process " + }, + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{z}, t)" + }, + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\mu}(t) = t\\boldsymbol{z}_{0,i} + (1 - t)\\boldsymbol{z}_{1,j}" + }, + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\sigma}(t) = \\mathbf{0}" + }, + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 55, + 72, + 295, + 106 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 99, + 108, + 295, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 108, + 295, + 121 + ], + "spans": [ + { + "bbox": [ + 99, + 108, + 295, + 121 + ], + "type": "interline_equation", + "content": "p \\left(\\boldsymbol {z} _ {t}, t\\right) = \\mathcal {N} \\left(t \\boldsymbol {z} _ {1, j} + (1 - t) \\boldsymbol {z} _ {0, i}, \\mathbf {0}\\right). \\tag {6}", + "image_path": "000e21805601570a781c0c7e65468424c0904ee3a28bfedb7a9ec1bc8437c3ba.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 123, + 296, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 123, + 296, + 147 + ], + "spans": [ + { + "bbox": [ + 55, + 123, + 296, + 147 + ], + "type": "text", + "content": "Meanwhile we can obtain the drift function " + }, + { + "bbox": [ + 55, + 123, + 296, + 147 + ], + "type": "inline_equation", + "content": "\\pmb{u}(\\pmb{z}, t)" + }, + { + "bbox": [ + 55, + 123, + 296, + 147 + ], + "type": "text", + "content": " via using the Proposition 1 as below:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 63, + 148, + 296, + 172 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 148, + 296, + 172 + ], + "spans": [ + { + "bbox": [ + 63, + 148, + 296, + 172 + ], + "type": "interline_equation", + "content": "\\boldsymbol {u} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\boldsymbol {\\mu} ^ {\\prime} (t) + \\frac {\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)}{\\boldsymbol {\\sigma} (t)} \\boldsymbol {\\sigma} ^ {\\prime} (t) = \\boldsymbol {z} _ {1, j} - \\boldsymbol {z} _ {0, i}. \\tag {7}", + "image_path": "2bd24f9a5455b5467d5f0151bd94371f623dbb3a9727322fc11f132464e5238f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "spans": [ + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "type": "text", + "content": "Specifically, we can employ a neural network " + }, + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "type": "inline_equation", + "content": "v_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "type": "text", + "content": " with matching samples " + }, + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "type": "inline_equation", + "content": "(z_0,z_1)\\sim \\pi" + }, + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "type": "text", + "content": " to predict the deterministic drift " + }, + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "type": "inline_equation", + "content": "u(x,t)" + }, + { + "bbox": [ + 55, + 173, + 295, + 208 + ], + "type": "text", + "content": " using the drift-estimate loss function:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 209, + 296, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 209, + 296, + 236 + ], + "spans": [ + { + "bbox": [ + 62, + 209, + 296, + 236 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {\\theta}} J _ {\\text {d r i f t}} = \\mathbb {E} _ {\\left(\\boldsymbol {z} _ {0}, \\boldsymbol {z} _ {1}\\right) \\sim \\boldsymbol {\\pi}} \\left[ \\left| | \\boldsymbol {v} _ {\\theta} \\left(\\boldsymbol {z} _ {t}, t\\right) - \\left(\\boldsymbol {z} _ {1} - \\boldsymbol {z} _ {0}\\right) \\right| | _ {2} ^ {2} \\right]. \\tag {8}", + "image_path": "4ff57c5c22c9e39c10269b67fe88b97b4d2a4afdfce0f652c76c17e8fe6a0205.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 237, + 296, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 237, + 296, + 295 + ], + "spans": [ + { + "bbox": [ + 55, + 237, + 296, + 295 + ], + "type": "text", + "content": "Moreover, we intend to figure out more consistent results [40] for achieving better performance. That is, the coupling data samples with different time interpolation should have the same drift output as expected. Therefore, we propose drift-consistent loss function:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 62, + 295, + 277, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 295, + 277, + 312 + ], + "spans": [ + { + "bbox": [ + 62, + 295, + 277, + 312 + ], + "type": "interline_equation", + "content": "\\min _ {\\pmb {\\theta}} J _ {\\mathrm {C L}} = \\mathbb {E} _ {t, t ^ {\\prime} \\in U [ 0, 1 ]} \\left[ | | \\pmb {v} _ {\\theta} (\\pmb {z} _ {t}, t) - \\pmb {v} _ {\\theta} (\\pmb {z} _ {t ^ {\\prime}}, t ^ {\\prime}) | | _ {2} ^ {2} \\right],", + "image_path": "c29754210f01f45156e188251e38731cc6de2e5c26c7d53cc20c2badbf63d4ed.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "spans": [ + { + "bbox": [ + 61, + 315, + 296, + 338 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\boldsymbol {z} _ {t} = (1 - t) \\boldsymbol {z} _ {0} + t \\boldsymbol {z} _ {1}, \\quad \\boldsymbol {z} _ {t ^ {\\prime}} = (1 - t ^ {\\prime}) \\boldsymbol {z} _ {0} + t ^ {\\prime} \\boldsymbol {z} _ {1} \\tag {9}", + "image_path": "d03c4ff744e6e9fdf66d0710e49ad08fc5e4bd4c6540585303fedde2f336519d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 338, + 296, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 296, + 362 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 296, + 362 + ], + "type": "text", + "content": "Finally, we combine the drift-estimate and drift-consistent loss functions for training our proposed DerODE:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 102, + 363, + 295, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 363, + 295, + 379 + ], + "spans": [ + { + "bbox": [ + 102, + 363, + 295, + 379 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} J _ {\\text {D e r O D E}} = J _ {\\text {d r i f t}} + \\lambda_ {c l} J _ {\\mathrm {C L}}, \\tag {10}", + "image_path": "5ec92cb20fe755bcc4dc696a1acde59eb02b69d13feb746275b3e416d0f0b78f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 380, + 296, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 380, + 296, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 296, + 474 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 380, + 296, + 474 + ], + "type": "inline_equation", + "content": "\\lambda_{cl}" + }, + { + "bbox": [ + 55, + 380, + 296, + 474 + ], + "type": "text", + "content": " denotes the balanced parameter. It is noticeable that DerODE will not involve complex denoising or score estimation procedures during the training stage. Therefore, it could be much easier to train compared with other diffusion approaches. Once we obtain the optimal solution on " + }, + { + "bbox": [ + 55, + 380, + 296, + 474 + ], + "type": "inline_equation", + "content": "\\pmb{v}^{*}(\\cdot)" + }, + { + "bbox": [ + 55, + 380, + 296, + 474 + ], + "type": "text", + "content": ", we can generate new motion features in the latent space via randomly sample noise in the standard Gaussian distribution via:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 70, + 475, + 295, + 489 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 475, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 70, + 475, + 295, + 489 + ], + "type": "interline_equation", + "content": "\\widetilde {\\boldsymbol {z}} _ {0, i} = \\widetilde {\\boldsymbol {z}} _ {1, i} - \\boldsymbol {v} _ {\\theta} (\\widetilde {\\boldsymbol {z}} _ {1, i}, t = 1) = \\operatorname {D e r O D E} (\\widetilde {\\boldsymbol {z}} _ {1, i}), \\tag {11}", + "image_path": "93a743c772343cd4662b7d46faf264b2d248878af07e80e9dd80d7e58c5ac635.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "inline_equation", + "content": "\\widetilde{z}_{1,i} \\sim \\mathcal{N}(0,I)" + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "text", + "content": " and it can obtain the deterministic output result " + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "inline_equation", + "content": "\\widetilde{z}_{0,i}" + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "text", + "content": ". Finally, we can utilize the decoder " + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "inline_equation", + "content": "\\mathrm{Dec}(\\cdot)" + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "text", + "content": " to generate human motion as " + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "inline_equation", + "content": "\\widetilde{\\pmb{E}} = \\mathrm{Dec}(\\widetilde{\\pmb{z}}_{0,i})" + }, + { + "bbox": [ + 55, + 490, + 296, + 528 + ], + "type": "text", + "content": " accordingly." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 531, + 292, + 543 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 531, + 292, + 543 + ], + "spans": [ + { + "bbox": [ + 55, + 531, + 292, + 543 + ], + "type": "text", + "content": "4.2.2. Stochastic Diverse Output Generation Procedure" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 545, + 296, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 296, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 296, + 677 + ], + "type": "text", + "content": "Although we have obtained the deterministic ordinary differential equations (DerODE) between the latent space distribution of human motions and the standard Gaussian distribution, it remains challenging to generate highly diverse motion patterns. This difficulty arises from the deterministic nature of the ODEs, as identical initial conditions result in the same output paths, thereby reducing the diversity of the generated samples. To provide more diverse while accurate human motions, we tend to involve the stochastic differential equations based on the ordinary differential equations in the stochastic diverse output generation procedure." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "Proposition 2. Given the stochastic differential equations " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "dz_{t} = f(z_{t},t)dt + g(t)d\\boldsymbol{w}_{t}" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " with the drift and diffusion terms, the mean " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}(t)" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " and covariance " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}(t)" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 328, + 83, + 555, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 83, + 555, + 137 + ], + "spans": [ + { + "bbox": [ + 328, + 83, + 555, + 137 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{r l} & \\frac {d \\boldsymbol {\\mu} (t)}{d t} = \\mathbb {E} [ f (\\boldsymbol {z}, t) ] \\\\ & \\frac {d \\boldsymbol {\\Sigma} (t)}{d t} = \\mathbb {E} \\left[ f (\\boldsymbol {z}, t) (\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)) ^ {\\top} \\right] \\\\ & \\quad + \\mathbb {E} \\left[ (\\boldsymbol {z} (t) - \\boldsymbol {\\mu} (t)) f ^ {\\top} (\\boldsymbol {z}, t) \\right] + \\mathbb {E} [ g ^ {2} (t) ]. \\end{array} \\right. \\tag {12}", + "image_path": "5564e796e935169b0ac736bf6656c37a9f4d42dfcd6b68e4e0ca4ae1b2fe7bc5.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 138, + 555, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 138, + 555, + 233 + ], + "spans": [ + { + "bbox": [ + 313, + 138, + 555, + 233 + ], + "type": "text", + "content": "The proof of the Proposition 2 can be found in Appendix B. We can observe that the stochastic differential equations can transform the distributions according to the specific settings of drift and diffusion terms, which leads to diverse output results based on Proposition 2. Therefore, it is intuitive to consider a proper stochastic differential equations with carefully designed " + }, + { + "bbox": [ + 313, + 138, + 555, + 233 + ], + "type": "inline_equation", + "content": "f(z_{t}, t)" + }, + { + "bbox": [ + 313, + 138, + 555, + 233 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 138, + 555, + 233 + ], + "type": "inline_equation", + "content": "g(t)" + }, + { + "bbox": [ + 313, + 138, + 555, + 233 + ], + "type": "text", + "content": " respectively in the stochastic diverse output generation procedure." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "spans": [ + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "content": "Proposition 3. Given the Diverse Stochastic Differential Equations (DivSDE) as " + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "inline_equation", + "content": "dz_{t} = \\left(-\\frac{1}{1 - t}\\right)z_{t}dt + \\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{dw}_{t}" + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "content": " with the initial data sample " + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "content": " and the noise level " + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "content": ", the probability of data distribution " + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{t}" + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "inline_equation", + "content": "p(\\pmb{z}_t) = \\mathcal{N}((1 - t)\\pmb{z}_i,\\eta^2 t^2\\pmb{I})" + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "content": " at the time step " + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "inline_equation", + "content": "p(\\pmb{z}_0) = \\mathcal{N}(\\pmb{z}_0,\\pmb{0})" + }, + { + "bbox": [ + 313, + 234, + 555, + 299 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": "The proof of the Proposition 3 can be found in Appendix C. It is obvious that the diffusion term " + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "inline_equation", + "content": "\\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{d}\\pmb{w}_t" + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": " which involves noise can enhance the diversity of the model output and thus DivSDE is different than DerODE. Note that the stochastic differential equations in Proposition 2 have the backward process as " + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{d}\\pmb{x}_t = \\left[-\\frac{1}{1 - t}\\pmb{z}_t - \\frac{2t}{1 - t}\\nabla \\log p(\\pmb{z}_t)\\right]dt + \\eta \\sqrt{\\frac{2t}{1 - t}}\\pmb{d}\\pmb{w}_t" + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "inline_equation", + "content": "\\nabla \\log p(\\pmb{z}_t)" + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": " denotes the score function of the data probability. Specifically, " + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "inline_equation", + "content": "\\nabla \\log p(\\pmb{z}_t)" + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": " can be calculated via " + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "inline_equation", + "content": "\\nabla \\log p(\\pmb{z}_t) = \\frac{(1 - t)\\pmb{z}_i - \\pmb{z}_t}{t^2}" + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": ". Previous score-based approaches [39] may involve a new neural network to estimate " + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "inline_equation", + "content": "\\nabla \\log p(\\pmb{z}_t)" + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": " even if it is rather time-consuming and hard to train in real practice. However, it is important to note that we can already obtain " + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "inline_equation", + "content": "\\widetilde{\\pmb{z}}_{0,i}" + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": " by utilizing DerODE via " + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "inline_equation", + "content": "\\widetilde{\\pmb{z}}_{0,i} = \\mathrm{DerODE}(\\widetilde{\\pmb{z}}_{1,i})" + }, + { + "bbox": [ + 313, + 300, + 556, + 515 + ], + "type": "text", + "content": " and it can be further utilized for DivSDE. Therefore, we can rewrite the discrete form of the backward process on DivSDE as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 324, + 517, + 554, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 517, + 554, + 567 + ], + "spans": [ + { + "bbox": [ + 324, + 517, + 554, + 567 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {z} _ {i, t} = \\boldsymbol {z} _ {t + \\Delta t, i} + \\frac {\\Delta t}{1 - t} \\boldsymbol {z} _ {t + \\Delta t, i} \\tag {13} \\\\ + \\frac {2 t \\Delta t}{1 - t} \\frac {(1 - t) \\widetilde {\\boldsymbol {z}} _ {0 , i} - \\boldsymbol {z} _ {t , i}}{t ^ {2}} + \\eta \\varepsilon \\sqrt {\\frac {2 t}{1 - t}} \\sqrt {\\Delta t}, \\\\ \\end{array}", + "image_path": "2d136f39ec7baa359fc44e120470761876191c2333ec91b6df22cab1783b6fc2.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\varepsilon \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "type": "text", + "content": " denotes the randomly sample noise. Meanwhile, " + }, + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "type": "text", + "content": " denotes the strengths of diversity. That is, larger value of " + }, + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 313, + 568, + 555, + 640 + ], + "type": "text", + "content": " will provide more diverse output human motions. Moreover, DivSDE can directly borrow the previously calculated results from DerODE for secondary computations without the need for re-introducing other training processes." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 648, + 416, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 416, + 660 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 416, + 660 + ], + "type": "text", + "content": "4.3. Model Summary" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "In summary, the proposed DSDFM can synthesize diverse and accurate human motion sequences through the designed two stages, i.e., human motion reconstruction and diverse motion generation. In the human motion reconstruction" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22728" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 297, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 297, + 95 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 297, + 95 + ], + "type": "text", + "content": "Algorithm 1 The process for generating diverse human motions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 98, + 296, + 123 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 98, + 296, + 123 + ], + "spans": [ + { + "bbox": [ + 56, + 98, + 296, + 123 + ], + "type": "text", + "content": "Require: time interval: " + }, + { + "bbox": [ + 56, + 98, + 296, + 123 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 56, + 98, + 296, + 123 + ], + "type": "text", + "content": ", time steps: " + }, + { + "bbox": [ + 56, + 98, + 296, + 123 + ], + "type": "inline_equation", + "content": "\\Delta t = \\frac{1}{T}" + }, + { + "bbox": [ + 56, + 98, + 296, + 123 + ], + "type": "text", + "content": ", noise for diversity: " + }, + { + "bbox": [ + 56, + 98, + 296, + 123 + ], + "type": "inline_equation", + "content": "\\eta" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 122, + 205, + 134 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 122, + 205, + 134 + ], + "spans": [ + { + "bbox": [ + 56, + 122, + 205, + 134 + ], + "type": "text", + "content": "Ensure: Generated new samples " + }, + { + "bbox": [ + 56, + 122, + 205, + 134 + ], + "type": "inline_equation", + "content": "\\hat{E}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 134, + 275, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 134, + 275, + 147 + ], + "spans": [ + { + "bbox": [ + 62, + 134, + 275, + 147 + ], + "type": "text", + "content": "1: Initialize " + }, + { + "bbox": [ + 62, + 134, + 275, + 147 + ], + "type": "inline_equation", + "content": "\\widetilde{z}_{1,i}" + }, + { + "bbox": [ + 62, + 134, + 275, + 147 + ], + "type": "text", + "content": " from Gaussian distribution " + }, + { + "bbox": [ + 62, + 134, + 275, + 147 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,\\pmb {I})" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 147, + 217, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 147, + 217, + 158 + ], + "spans": [ + { + "bbox": [ + 62, + 147, + 217, + 158 + ], + "type": "text", + "content": "2: # Adopting DerODE to obtain " + }, + { + "bbox": [ + 62, + 147, + 217, + 158 + ], + "type": "inline_equation", + "content": "\\widetilde{x}_{i,0}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 159, + 165, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 159, + 165, + 171 + ], + "spans": [ + { + "bbox": [ + 62, + 159, + 165, + 171 + ], + "type": "text", + "content": "3: " + }, + { + "bbox": [ + 62, + 159, + 165, + 171 + ], + "type": "inline_equation", + "content": "\\widetilde{z}_{0,i} = \\mathrm{DerODE}(\\widetilde{z}_{1,i})" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 171, + 291, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 171, + 291, + 182 + ], + "spans": [ + { + "bbox": [ + 62, + 171, + 291, + 182 + ], + "type": "text", + "content": "4: # Adopting DivSDE to obtain diverse human motions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 62, + 182, + 197, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 182, + 197, + 194 + ], + "spans": [ + { + "bbox": [ + 62, + 182, + 197, + 194 + ], + "type": "text", + "content": "5: for " + }, + { + "bbox": [ + 62, + 182, + 197, + 194 + ], + "type": "inline_equation", + "content": "t \\in \\text{range}(T - \\Delta t, 0)" + }, + { + "bbox": [ + 62, + 182, + 197, + 194 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 62, + 194, + 295, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 194, + 295, + 223 + ], + "spans": [ + { + "bbox": [ + 62, + 194, + 295, + 223 + ], + "type": "text", + "content": "6: Obtain the score function as: " + }, + { + "bbox": [ + 62, + 194, + 295, + 223 + ], + "type": "inline_equation", + "content": "\\nabla \\log p(\\boldsymbol{z}_{t,i}) = \\frac{(1 - t)\\widetilde{\\boldsymbol{z}}_{0,i} - \\boldsymbol{z}_{t,i}}{(t / T)^2}" + }, + { + "bbox": [ + 62, + 194, + 295, + 223 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 62, + 223, + 295, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 223, + 295, + 248 + ], + "spans": [ + { + "bbox": [ + 62, + 223, + 295, + 248 + ], + "type": "text", + "content": "7: Obtain the diffusion term as: " + }, + { + "bbox": [ + 62, + 223, + 295, + 248 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{Diffu}} = \\frac{2(t / T)}{1 - (t / T)} \\nabla \\log p(\\pmb{z}_{t,i}) \\Delta t" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 62, + 248, + 283, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 248, + 283, + 263 + ], + "spans": [ + { + "bbox": [ + 62, + 248, + 283, + 263 + ], + "type": "text", + "content": "8: Obtain the drift term as: " + }, + { + "bbox": [ + 62, + 248, + 283, + 263 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{Drift}} = \\frac{\\Delta t}{1 - (t / T)} z_{t + \\Delta t,i}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 62, + 264, + 295, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 264, + 295, + 283 + ], + "spans": [ + { + "bbox": [ + 62, + 264, + 295, + 283 + ], + "type": "text", + "content": "9: Obtain the noise term as: " + }, + { + "bbox": [ + 62, + 264, + 295, + 283 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{noise}} = \\eta \\cdot \\varepsilon \\sqrt{\\frac{2(t / T)}{1 - (t / T)}}\\sqrt{\\Delta t}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 59, + 291, + 282, + 327 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 291, + 282, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 291, + 282, + 303 + ], + "spans": [ + { + "bbox": [ + 61, + 291, + 282, + 303 + ], + "type": "text", + "content": "10: Obtain " + }, + { + "bbox": [ + 61, + 291, + 282, + 303 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_{t,i} = \\boldsymbol{z}_{t + \\Delta t,i} + D_{\\mathrm{Diffu}} + D_{\\mathrm{Drift}} + \\epsilon_{\\mathrm{noise}}" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 59, + 304, + 106, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 304, + 106, + 313 + ], + "spans": [ + { + "bbox": [ + 59, + 304, + 106, + 313 + ], + "type": "text", + "content": "11: end for" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 314, + 252, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 314, + 252, + 327 + ], + "spans": [ + { + "bbox": [ + 59, + 314, + 252, + 327 + ], + "type": "text", + "content": "12: Generate the human motion: " + }, + { + "bbox": [ + 59, + 314, + 252, + 327 + ], + "type": "inline_equation", + "content": "\\hat{E} = \\mathrm{Dec}(z_{0,i})" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 335, + 297, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 335, + 297, + 502 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 297, + 502 + ], + "type": "text", + "content": "stage, we first adopt the human motion reconstruction network to learn a well-structured latent space of human motions through VQVAE network. In the diverse motion generation stage, we tend to build the connections between the Gaussian distribution and latent space of human motions, thereby enhancing the diversity while guaranteeing the accuracy of the generated human motions through the designed deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. Specifically, DerODE can provide deterministic output results in an efficient way. Meanwhile, DivSDE can obtain more diverse human motions without introducing additional training process. The pseudo algorithm of the DSDFM is provided in Algorithm 1." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 55, + 514, + 132, + 527 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 132, + 527 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 132, + 527 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 55, + 533, + 297, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 297, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 297, + 666 + ], + "type": "text", + "content": "In this section, we provide extensive experiments to evaluate the performance of our proposed DSDFM across widely used human motion datasets. We first describe the utilized human motion datasets and implementation details (Section 5.1). Subsequently, we present a comparative results analysis of our method with other state-of-the-art approaches on conditional and unconditional human motion synthesis. Additionally, we provide ablation studies to assess the effectiveness of the modules in our method (Section 5.2). Finally, we visually showcase the generated diverse human motion sequences to provide a qualitative performance (Section 5.3)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 55, + 672, + 251, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 251, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 251, + 685 + ], + "type": "text", + "content": "5.1. Datasets and Implementation Details" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "Datasets. The experiments are conducted on two widely used motion capture datasets, i.e., HumanAct12 [9], and Hu" + } + ] + } + ], + "index": 20 + }, + { + "type": "table", + "bbox": [ + 317, + 118, + 553, + 186 + ], + "blocks": [ + { + "bbox": [ + 313, + 72, + 554, + 115 + ], + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 115 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 115 + ], + "type": "text", + "content": "Table 1. The comparison results of unconditional human motion synthesis between our method and state-of-the-art methods on HumanAct12 dataset. **Bold** and **underline** indicate the best and the second best result." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 118, + 553, + 186 + ], + "lines": [ + { + "bbox": [ + 317, + 118, + 553, + 186 + ], + "spans": [ + { + "bbox": [ + 317, + 118, + 553, + 186 + ], + "type": "table", + "html": "
    MethodFID ↓KID ↓Precision ↑Recall ↑Diversity ↑#params
    VPoser (CVPR'19)48.650.720.680.7212.7529M
    Action2Motion (MM'21)49.760.680.700.7113.8021M
    ACTOR (CVPR'21)48.800.530.720.7414.1020M
    MDM (ICLR'23)31.920.960.660.6217.0024M
    MLD (CVPR'23)14.250.550.700.7916.8527M
    Modi (CVPR'23)13.030.120.710.8117.5723M
    DSDFM (Ours)12.860.100.750.8518.4115M
    Improvement1.31%1.67%4.17%4.93%4.78%2.50%
    ", + "image_path": "250a8a6b1e7a718ee3421e97b01effd26500d6274f5e872ec469c11ee0122084.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 192, + 555, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 192, + 555, + 263 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 555, + 263 + ], + "type": "text", + "content": "manML3D [10]. HumanAct12 provides 1,191 raw motion sequences, and contains 12 subjects in which 12 categories of actions with per-sequence annotation are provided. HumanML3D dataset is a recent dataset that contains 14,616 motion sequences annotated by 44970 textual descriptions obtained from AMASS [29]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 265, + 556, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 265, + 556, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 265, + 556, + 528 + ], + "type": "text", + "content": "Evaluation metrics. For a fair comparison, our method employs the following evaluation metrics: Frechet Inception Distance (FID), Kernel Inception Distance (KID), Precision, Recall, Accuracy, Diversity, and Multimodality. FID is the distance between the feature distribution of generated motions and that of the real motions, namely the difference in mean and variance. KID compares skewness as well as the values compared in FID, namely mean and variance. Precision measures the probability that a randomly generated motion falls within the support of the distribution of real data. Recall measures the probability that a real motion falls within the support of the distribution of generated data. Accuracy is measured by the corresponding action recognition model. Diversity measures the variance of the whole motion sequences across the dataset. Multimodality measures the diversity of human motion generated from the same text description. A lower value implies better for FID and KID. Higher Precision, Recall, Accuracy, Diversity, and MultiModality values imply better results. FID, KID, Precision, Recall, and Accuracy are utilized to evaluate the generated human motion accuracy. Diversity and MultiModality are utilized for the generation diversity." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "text", + "content": "Implementation Details. For the human motion reconstruction process, the VQVAE consists of 4 Transformer layers with 8 heads, and the codebook size is set to " + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "text", + "content": ". The batch size is set to 128, learning rate is initially set to " + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "inline_equation", + "content": "10^{-2}" + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "text", + "content": " with a 0.98 decay every 10 epochs. The proposed method is trained for 500 epochs. For the diverse motion generation process, the time interval " + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "text", + "content": " is set to 0.01, and the strength of diversity " + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "text", + "content": " is set to 0.1. The diffusion step is set to 100. The balanced parameter " + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "inline_equation", + "content": "\\lambda_{cl}" + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "inline_equation", + "content": "J_{CL}" + }, + { + "bbox": [ + 313, + 529, + 556, + 648 + ], + "type": "text", + "content": " loss is set to 0.3." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 659, + 438, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 438, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 438, + 672 + ], + "type": "text", + "content": "5.2. Experimental Results" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 677, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 714 + ], + "type": "text", + "content": "Comparisons on Unconditional Human Motion Synthesis. We compare our method DSDFM with other state-of-the-art methods under the unconditional generation settings on the" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22729" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 107, + 294, + 178 + ], + "blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "type": "text", + "content": "Table 2. The comparison results of Action-to-Motion task on HumanAct12 dataset. " + }, + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "type": "inline_equation", + "content": "\\pm" + }, + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "type": "text", + "content": " indicates " + }, + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "type": "text", + "content": " confidence interval, " + }, + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 55, + 72, + 297, + 106 + ], + "type": "text", + "content": " indicates that closer to real is better. The best results are in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 107, + 294, + 178 + ], + "lines": [ + { + "bbox": [ + 57, + 107, + 294, + 178 + ], + "spans": [ + { + "bbox": [ + 57, + 107, + 294, + 178 + ], + "type": "table", + "html": "
    MethodFID ↓Accuracy ↑Diversity →Multimodality ↑#params
    Real0.020±0.0100.997±0.0016.850±0.0502.450±0.040-
    ActionMotion (MM'21)0.338±0.0150.917±0.0036.879±0.0662.511±0.02321M
    ACTOR (CVPR'21)0.120±0.0000.955±0.0086.840±0.0302.530±0.02020M
    INR (ECCV'22)0.088±0.0040.973±0.0016.881±0.0482.569±0.04025M
    MLD (CVPR'23)0.077±0.0040.964±0.0026.831±0.0502.824±0.3827M
    MDM (ICLR'23)0.100±0.0000.990±0.0006.860±0.0502.520±0.01024M
    MotionDiffuse (TPAMI'24)0.070±0.0000.992±0.0136.850±0.0202.460±0.02025M
    DSDFM (Ours)0.068±0.0100.994±0.0016.851±0.0082.455±0.02515M
    Improvement2.85%0.21 %-0.01%0.21%2.50%
    ", + "image_path": "1691451ddd2e4e2ff9f96cf4f4d66389c68da27ced66909a079a2ccfd696859b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 57, + 218, + 294, + 255 + ], + "blocks": [ + { + "bbox": [ + 55, + 182, + 295, + 214 + ], + "lines": [ + { + "bbox": [ + 55, + 182, + 295, + 214 + ], + "spans": [ + { + "bbox": [ + 55, + 182, + 295, + 214 + ], + "type": "text", + "content": "Table 3. Ablation study on the comparison results of training and inference time on the HumanAct12 dataset. " + }, + { + "bbox": [ + 55, + 182, + 295, + 214 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 182, + 295, + 214 + ], + "type": "text", + "content": " denotes minute, " + }, + { + "bbox": [ + 55, + 182, + 295, + 214 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 182, + 295, + 214 + ], + "type": "text", + "content": " denotes second." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 218, + 294, + 255 + ], + "lines": [ + { + "bbox": [ + 57, + 218, + 294, + 255 + ], + "spans": [ + { + "bbox": [ + 57, + 218, + 294, + 255 + ], + "type": "table", + "html": "
    MethodEpochTraining Time (m)Inference Time (s)/FID
    100 steps/FID500 steps/FID1000 steps/FID
    VPSDE50042.932.54/16.749.93/15.6318.09/14.31
    VESDE50040.572.68/16.499.48/14.9216.12/14.17
    DSDFM(Ours)50025.331.60/13.615.03/12.8610.33/12.24
    ", + "image_path": "93ec560116f06f0779b1978afc5dbf8276b6ea79e650ca4457d2d1badc6cb8d1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 258, + 295, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 258, + 295, + 437 + ], + "spans": [ + { + "bbox": [ + 54, + 258, + 295, + 437 + ], + "type": "text", + "content": "HumanAct12 dataset, the results are shown in Table 1. The input of the baseline methods is modified to the same length as our method. From the comparison results, we can observe that the baseline methods report poor performance in terms of accuracy and diversity metrics due to the mode collapse or unstable training processes. DSDFM outperforms these methods owing to the designed diverse motion generation procedure. In addition, to assess the training efficiency of our method, we also investigate the number of training parameters. The comparison results show that our method utilizes fewer parameters than baseline methods while achieving superior performance, which demonstrates the effectiveness of the proposed method. This suggests that our method is more computationally efficient and achieves the balance between the accuracy and diversity of generated samples." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 438, + 297, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 438, + 297, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 438, + 297, + 617 + ], + "type": "text", + "content": "Comparisons on Conditional Human Motion Synthesis. Our method can also be extended to conditional generation, i.e., Action-to-Motion task. This task involves generating relevant human motion sequences given an input action label. The comparison results on the HumanAct12 dataset are presented in Table 2. From the comparison results, we can observe that DSDFM also achieves comparable performance under the accuracy and diversity metrics. Our method performs slightly worse than MotionDiffuse method in terms of the diversity metric by " + }, + { + "bbox": [ + 55, + 438, + 297, + 617 + ], + "type": "inline_equation", + "content": "0.01\\%" + }, + { + "bbox": [ + 55, + 438, + 297, + 617 + ], + "type": "text", + "content": ", but our method reduces the confidence interval, demonstrating that our method is more stable and reliable. Additionally, it significantly decreases the number of training parameters. These results further report the effectiveness of our method for conditional human motion generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 624, + 154, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 154, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 154, + 635 + ], + "type": "text", + "content": "5.3. Ablation studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 642, + 297, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 297, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 297, + 712 + ], + "type": "text", + "content": "To report the effectiveness of each component of our method, we compare the baseline methods with DSDFM under different settings on the HumanML3D and HumanAct12 datasets, including the training time, inference time for different diffusion steps, and the corresponding FID. The results are shown in Table 3 and Table 4. Table 3 shows the com" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 316, + 96, + 553, + 133 + ], + "blocks": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 95 + ], + "type": "text", + "content": "Table 4. Ablation study on the comparison results of training and inference time on the HumanML3D dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 96, + 553, + 133 + ], + "lines": [ + { + "bbox": [ + 316, + 96, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 316, + 96, + 553, + 133 + ], + "type": "table", + "html": "
    MethodEpochTraining Time (m)Inference Time (s)/FID
    100 steps/FID500 steps/FID1000 steps/FID
    VPSDE50012.542.47/0.092±.0034.95/0.088±.0026.51/0.080±.024
    VESDE50012.572.35/0.094±.0054.48/0.089±.0016.62/0.078±.013
    DSDFM(Ours)5007.021.01/0.073±.0052.15/0.068±.0084.82/0.054±.010
    ", + "image_path": "3a1645192911e48743b516d4b013f57b228ec3f71b561e8926b14f4319b0a239.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 317, + 186, + 552, + 237 + ], + "blocks": [ + { + "bbox": [ + 313, + 140, + 555, + 184 + ], + "lines": [ + { + "bbox": [ + 313, + 140, + 555, + 184 + ], + "spans": [ + { + "bbox": [ + 313, + 140, + 555, + 184 + ], + "type": "text", + "content": "Table 5. Ablation studies of the proposed method. We compare our method with other score-based methods and provide the comparison results under the accuracy and diversity metrics, as well as the number of training parameters." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 186, + 552, + 237 + ], + "lines": [ + { + "bbox": [ + 317, + 186, + 552, + 237 + ], + "spans": [ + { + "bbox": [ + 317, + 186, + 552, + 237 + ], + "type": "table", + "html": "
    MethodFID ↓KID ↓Precision ↑Recall ↑Diversity ↑#param
    VESDE14.920.360.590.6516.2128M
    VPSDE15.630.290.640.6817.0024M
    SDE (DDPM++)13.250.210.680.7517.4622M
    SDE (NCSN++)13.010.190.720.7917.5421M
    DSDFM (Ours)12.860.100.750.8518.4115M
    ", + "image_path": "60dde98ce25615cdd2dc9f60f6adb5eb2c9b237dd6f3ca7acb70e58b910a83f1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 243, + 555, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 555, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 555, + 409 + ], + "type": "text", + "content": "parison results for unconditional motion generation on the HumanAct12 dataset. From the results, we can observe that, compared to VPSDE and VESDE given the same number of epochs, DSDFM significantly reduces the training time while achieving a comparable performance under the FID metric, which demonstrates that our method is easier to train than the baseline methods and guaranteeing the quality of generated human motions. We also test these methods under different diffusion steps, and the performance of our method is improved in inference time. In addition, Table 4 shows the comparison results for Action-to-Motion task on HumanML3D dataset. The results under the same metrics are consistent with the results on the HumanAct12 dataset, which further demonstrates the effectiveness of our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 411, + 556, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 556, + 566 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 556, + 566 + ], + "type": "text", + "content": "The ablation studies also test the performance of the designed stochastic diverse output generation procedure in DSDFM under the diversity and accuracy metrics, the results are shown in Table 5. Specifically, we employ other score-based methods to enhance the diversity of generated human motion sequences, i.e., variance preserving SDE (VPSDE), variance exploding SDE (VESDE), DDPM++, and NCSN++. From the comparison results, we can observe that our method exhibits comparable performance in terms of accuracy compared to the baseline methods, while showing a slight improvement in diversity. Notably, we have achieved a significant reduction in the number of training parameters, which report the effectiveness of our method." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 575, + 399, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 575, + 399, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 575, + 399, + 586 + ], + "type": "text", + "content": "5.4. Visualization" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 594, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 713 + ], + "type": "text", + "content": "In this section, we show the visualization results of our method on the unconditional human motion synthesis and Action-to-Motion tasks. As depicted in Figure 3, the top is the unconditional human motion synthesis, all human motion sequences are unconditionally generated from random noise sampled from Gaussian distribution on the HumanAct12 dataset. The figure shows that our method can generate diverse and high fidelity human motion sequences. The bottom is the sequences generated by the Action-to-Motion task, the generated sequences are under the action labels on" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22730" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 76, + 526, + 213 + ], + "blocks": [ + { + "bbox": [ + 83, + 76, + 526, + 213 + ], + "lines": [ + { + "bbox": [ + 83, + 76, + 526, + 213 + ], + "spans": [ + { + "bbox": [ + 83, + 76, + 526, + 213 + ], + "type": "image", + "image_path": "e97cc7f5aaf80287f03123608f129d19984db7249f45e94e57e6a5a79163c4f6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 219, + 555, + 253 + ], + "lines": [ + { + "bbox": [ + 54, + 219, + 555, + 253 + ], + "spans": [ + { + "bbox": [ + 54, + 219, + 555, + 253 + ], + "type": "text", + "content": "Figure 3. Qualitative results of DSDFM. We present the generated human motion sequences under different settings. The unconditional human motion sequences (top) are generated from the HumanAct12 dataset. The Action-to-Motion results (bottom) show the generated diverse motion sequences under the Sit and Run action labels, which are sampled from the HumanML3D dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 139, + 260, + 307, + 384 + ], + "blocks": [ + { + "bbox": [ + 139, + 260, + 307, + 384 + ], + "lines": [ + { + "bbox": [ + 139, + 260, + 307, + 384 + ], + "spans": [ + { + "bbox": [ + 139, + 260, + 307, + 384 + ], + "type": "image", + "image_path": "7a0079ac076d743f64aef64440c8bfb78e243dea892e2f70695af939dd6ad45b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 390, + 555, + 413 + ], + "lines": [ + { + "bbox": [ + 54, + 390, + 555, + 413 + ], + "spans": [ + { + "bbox": [ + 54, + 390, + 555, + 413 + ], + "type": "text", + "content": "Figure 4. Comparison of the inference time costs of our method on the HumanAct12 dataset. We calculate the ablation studies (left) and average inference time comparison with baselines (right). All tests are performed on the NVIDIA A100." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 309, + 261, + 471, + 384 + ], + "blocks": [ + { + "bbox": [ + 309, + 261, + 471, + 384 + ], + "lines": [ + { + "bbox": [ + 309, + 261, + 471, + 384 + ], + "spans": [ + { + "bbox": [ + 309, + 261, + 471, + 384 + ], + "type": "image", + "image_path": "6f941b055363ab9c6f921cb109c224fc9fe68e814285b3961be632b34e0f2271.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 418, + 295, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 418, + 295, + 466 + ], + "spans": [ + { + "bbox": [ + 54, + 418, + 295, + 466 + ], + "type": "text", + "content": "the HumanML3D dataset. We can observe that the generated diverse motion sequences match the descriptions well. These qualitative results demonstrate that DSDFM can generate diverse and coherent human motion sequences." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 467, + 295, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 467, + 295, + 563 + ], + "spans": [ + { + "bbox": [ + 54, + 467, + 295, + 563 + ], + "type": "text", + "content": "We compare and visualize the comparison results of inference time in Figure 4. The left of this Figure is the ablation studies of our method with different diffusion steps. This figure shows that using VPSDE and VESDE as our backbone has long inference time and relatively low accuracy. The right of this Figure is the average inference time comparison with baselines, which shows that our method can speed up the inference time when generating new samples." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 574, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 574, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 128, + 586 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 594, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 594, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 594, + 297, + 715 + ], + "type": "text", + "content": "In this paper, we propose a Deterministic-to-Stochastic Diverse Latent Feature Mapping (DSDFM) for human motion synthesis. DSDFM is easy to train compared with the recent SGMs-based method, while facilitating the diversity and accuracy of generated human motions. DSDFM includes two stages, human motion reconstruction and diverse motion generation. Human motion reconstruction aims to learn a well-structured latent space of human motions. Diverse motion generation aims to enhance the diversity of the generated human motion sequences through the designed" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 418, + 555, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 555, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 555, + 467 + ], + "type": "text", + "content": "deterministic feature mapping procedure with DerODE and stochastic diverse output generation procedure with DivSDE. Extensive experimental results demonstrate the efficacy of the proposed DSDFM method for human motion synthesis." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 487, + 419, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 419, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 419, + 501 + ], + "type": "text", + "content": "7. Acknowledgment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 510, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 510, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 312, + 510, + 556, + 713 + ], + "type": "text", + "content": "This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-031), the National Research Foundation, Singapore and DSO National Laboratories under the AI Singapore Programme (AISG Award No.: AISG2-GC-2023-010, \"Design Beyond What You Know\": Material-Informed Differential Generative AI (MIDGAI) for Lightweight High-Entropy Alloys and Multi-functional Composites (Stage 1a)\", the National Natural Science Foundation of China under Grant 62372081, the Young Elite Scientists Sponsorship Program by CAST under Grant 2022QNRC001, the Liaoning Provincial Natural Science Foundation Program under Grant 2024010785-JH3107, the Dalian Science and Technology Innovation Fund under Grant 2024JJ12GX020, the Dalian Major Projects of Basic Research under Grant 2024JJ12GX020 2023JJ11CG002 and the 111 Project under Grant D23006." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22731" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 135 + ], + "type": "text", + "content": "[1] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. 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Our method faithfully reflects the details of image prompts (e.g., eye makeup) for diverse image generation across various tasks (Tasks A-C) in a training-free manner. In contrast, existing methods often fail to incorporate fine details of the image prompt. Even with training, IP-Adapter [19] and SSR-Encoder [21] struggle to properly represent the color and texture of the image prompt. RIVAL [22] and StyleAligned [4] also fail to generate high-fidelity images that faithfully reflect the image or text prompts due to a trade-off between the realism of the generated results and alignment with the image prompt. Extra results are in the Supplementary (Suppl.)." + ], + "image_footnote": [], + "bbox": [ + 106, + 481, + 166, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/def85edf03c782256d30a9b36b004437c707e90f27c503fb711cc8eacbd1ce1f.jpg", + "image_caption": [ + "Text" + ], + "image_footnote": [], + "bbox": [ + 171, + 481, + 210, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/856f92b33c58adf147bb8e50054375d0c1e922ce38b0d7de716f6d327e7f4f16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 481, + 267, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/08e5ca0142a4f7f722bb13073776d27548831cbdf904e2032210609bf3d46ab4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 269, + 481, + 336, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5fb723c3c7d7ad159f4c29cb4e1bf535d25b7afb0463ed67aede3cc3390f0ad9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 336, + 481, + 364, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f31c40e0574f6cdd9c5a0f2a95fb23a1e81963f1b1c2e3358a09f670b38243db.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 481, + 434, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8b2872832618961548da2fd9b554b02f98b192991002b2c46dfe1bdcd5755e41.jpg", + "image_caption": [ + "Task A. Image Variation", + "", + "Task B. Structure-guided Image Generation" + ], + "image_footnote": [], + "bbox": [ + 464, + 330, + 521, + 388 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This person looks attractive. This person has wavy hair, pointy nose and is wearing lipstick, heavy makeup.", + "bbox": [ + 532, + 339, + 612, + 387 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/92b6bd1d3bfbb795c4379cdd8ac8ce58394d954472abc2f4cdd31673f3198c10.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 330, + 643, + 387 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e45cc839aa03128f56cecf5b236143641b2f066c1ff0ac90133be27b6254d900.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 330, + 694, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/492c10488d1ec489593b535874d9c368f3239e22aa21b120080208dcdbfa0e9e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 330, + 761, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8d4e3bdc8bf7b9f96fccd808921bc99635f9c39d318f916833f364cd2bcdf63f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 330, + 789, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/786552bc13c4f4275eae8e4afcd4019d3e33580201645a6f55bb86c0c0bf77f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 790, + 330, + 813, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e59958d6b9c657dc02b6e78fcc8fc5a65da49580934834893c52f03bb70cd53d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 818, + 330, + 834, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c468f6fe6acfe77ce0c0cbfb7ff48c915a235284624fd63e8ae51228f60f5c19.jpg", + "image_caption": [ + "Task C. Cross-prompt Image Generation" + ], + "image_footnote": [], + "bbox": [ + 464, + 402, + 521, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3dce3f5602785af726c5cefb0aec9ffdcc32f0056b46fcfcfae1bdfffdbd7d67.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 402, + 580, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8633b506c8e60a8e430465065c1f419542b4959998ce91afdf74a8202d714325.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 402, + 616, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/33d016428e7f58ed838130db6000e69addb0c99d43c4ba6642756ce29e6e9b60.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 402, + 643, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/67878fe3984d4d962c0ebd5af5d2388b7bbdd779ab9f9aff9e881f5fa22f3268.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 402, + 705, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d21c179053cfa24b9abb88629070b1e1360eab1bd81ff41b8147b07cc7d9c7ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 402, + 766, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/312f703b889ae0c447f72bb1b0ff82a8bbd2a5208fbe7ecee26b85450f39591c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 767, + 402, + 834, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/376cab7cde9e9fa08539ad3e3517da7306b6d5dce5164109401b2a56bffd6dd2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 834, + 402, + 893, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c7b193ab02035f5d6eaf74944b24e98c136dcbfb53a9dc9ab5b1623901926c7e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 464, + 473, + 521, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/be06b38483bb27db512dc14c756b84dca39977741ddf03a335ce46bfd4a824f6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 473, + 558, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c13d6bcfbd37b35bf5de43c1cbf4b6c46f73d1e99caedfff32019dd43e52af6a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 558, + 473, + 616, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2e3abcd2cb40bd0b76645f4b40670d3d830157fb26d3e1d7cb217a10fcc7639c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 473, + 705, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3f36237b0cfb030a1a78f2783f13918ea2e89e3925ed8248ffdfa4f0de80265c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 473, + 766, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/482fe1c4cbfd7362190efa49757863b125c92ad95d7e81a59111010ce09415e9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 767, + 473, + 834, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0b8d5da662877d04cfc0b7297b8d298472b8cab745b8c39cec5cae66520639bf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 834, + 473, + 893, + 530 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 254, + 622, + 331, + 637 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While large-scale text-to-image diffusion models enable the generation of high-quality, diverse images from text prompts, these prompts struggle to capture intricate details, such as textures, preventing the user intent from being reflected. This limitation has led to efforts to generate images conditioned on user-provided images, referred to as image prompts. Recent work modifies the self-attention mechanism to impose image conditions in generated images by replacing or concatenating the keys and values from the image prompt. This enables the self-attention layer to work like a cross-attention layer, generally used to incorporate text prompts. In this paper, we identify two common issues in existing methods of modifying self-attention that hinder diffusion models from reflecting the image prompt. By addressing these issues, we propose a novel method that generates images that properly reflect the details of image prompts.", + "bbox": [ + 99, + 654, + 485, + 891 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "First, existing approaches often neglect the importance of image prompts in classifier-free guidance, which directs the model towards the intended conditions and away from those undesirable. Specifically, current methods use image prompts as both desired and undesired conditions, causing conflicting signals. To resolve this, we propose conflict-free guidance by using image prompts only as desired conditions, ensuring that the generated image faithfully reflects the image prompt. In addition, we observe that the two most common self-attention modifications involve a trade-off between the realism of the generated image and alignment with the image prompt, achieved by selectively using keys and values from both images. Specifically, selecting more keys and values from the image prompt improves alignment, while selecting more from the generated image enhances realism. To balance both, we propose an alternative self-attention modification method, Stratified Attention, which jointly uses keys and values from both images", + "bbox": [ + 511, + 625, + 895, + 888 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 116, + 16, + 189, + 55 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 243, + 13, + 802, + 29 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 328, + 30, + 715, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 297, + 44, + 746, + 56 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23595", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rather than selecting between them. Through extensive experiments across three distinct image generation tasks, we demonstrate that the proposed method outperforms existing image-prompting models in faithfully reflecting the image prompt.", + "bbox": [ + 99, + 102, + 485, + 176 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 102, + 203, + 230, + 219 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The emergence of large-scale text-to-image diffusion models [11, 13] has enabled users to generate diverse images from text. However, describing complex scenes using only text prompts can be complicated, leading to ongoing efforts to incorporate user-provided image conditions to better reflect user intent [14, 17, 19, 21]. As part of these efforts, modifying the self-attention mechanism in pre-trained text-to-image diffusion models has recently attracted interest in areas such as image editing [1, 10, 16], story visualization [23], image variation [22], and style transfer [3], as a flexible method for incorporating user-provided image conditions into generated images. This modification is typically achieved by integrating the keys and values of the condition in the self-attention layer, as the keys and values derived from the image features contain rich details about images.", + "bbox": [ + 99, + 228, + 483, + 448 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since the keys and values embody the context of images, these techniques are particularly powerful for conditioning diffusion models on image prompts, which contain the intricate details of a scene (e.g., the fine patterns of eye makeup in Fig. 1) that go beyond the level of details text descriptions can reach. Specifically, recent findings [3, 4, 22] show that replacing or concatenating the new keys and values (KV) of the generated images to those of the image prompt in the self-attention layer simulates a cross-attention with the image prompt, functioning similarly to the way text prompts affect image generation. This simulated cross-attention offers key benefits over training an additional cross-attention layer [19]: it eliminates the need for retraining with each new diffusion model and minimizes information loss from using smaller datasets for the training, as self-attention features are generated within the same model.", + "bbox": [ + 99, + 449, + 483, + 681 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, we find that existing self-attention alterations-based approaches overlook an important aspect, which is the role of image prompts during classifier-free guidance [6]. Classifier-free guidance steers the diffusion model toward desired conditions (i.e., positive guidance) and away from undesired ones (i.e., negative guidance), enhancing the alignment between generated images and the user-provided conditions. Current approaches use image prompts to estimate both positive-guidance and negative-guidance scores, causing image prompts to influence the negative scores as well. This sends a strong signal to the model to avoid reflecting the image prompt, thereby compromising alignment between the generated image and the image prompt. The effect of this conflicting guidance is illustrated in Fig. 2,", + "bbox": [ + 99, + 684, + 483, + 891 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f7cf9aed334b61cf52f73a7adca716342f804156d259ff38d769c046b81d73c3.jpg", + "image_caption": [ + "Figure 2. Using the image prompt as positive guidance ensures that it is reflected in the generated images, but using it as both positive (pos.) and negative (neg.) guidance fails due to the conflicting guidance." + ], + "image_footnote": [], + "bbox": [ + 514, + 102, + 895, + 195 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where the details of the image prompt are often lost or even ignored. Based on this insight, we propose conflict-free guidance by adjusting classifier-free guidance to exclude image prompts from estimating negative-guidance scores, enabling generations that faithfully reflect the provided image prompt.", + "bbox": [ + 511, + 267, + 893, + 356 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, we observe that two common self-attention modifications, which we call KV replacement and KV concatenation, represent a trade-off between the realism of the generated results and alignment with the image prompt. KV replacement ensures strong alignment with the image prompt but struggles to generate realistic attributes not specified in the image prompt (e.g., frontal view of a cat), as it relies solely on the keys and values from the image prompt (e.g., side view of a cat) while discarding those from the generated results. In contrast, KV concatenation, which combines keys and values from both the image prompt and the generated results, enhances realism but reduces the alignment due to attention bias arising from the queries being derived from the same features as the generated keys and values. To achieve both realism in the generated results and alignment with the image prompt, we propose Stratified Attention (Fig. 7d) as a new self-attention modification that effectively addresses this bias in KV concatenation. Specifically, we calculate the attention scores for image prompts and generated results separately, rather than computing them all at once. The scores calculated in this way are then aggregated afterward. This facilitates the image prompts to attend to relevant features while preserving the original attention flow of the generated image.", + "bbox": [ + 511, + 357, + 895, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To sum up, our key contributions are as follows:", + "bbox": [ + 529, + 710, + 841, + 724 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We correct the classifier-free guidance in modified selfattention by using the image prompt exclusively as positive guidance, rather than as conflicting guidance, to faithfully reflect the image prompt in image generation.", + "- We propose Stratified Attention as a new self-attention modification to effectively reflect the image prompt by ensuring a balanced attention flow between the image prompt and the generated image.", + "- Through extensive experiments, our method achieves state-of-the-art performance in image prompting, both qualitatively and quantitatively." + ], + "bbox": [ + 511, + 724, + 893, + 887 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23596", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/381d71eabc42515d06b03be280238c78824413a4d6c69be9754503eb53a74861.jpg", + "image_caption": [ + "Figure 3. Framework of the self-attention modification for image prompt: Image $G$ is generated from the initial noised latent $\\mathbf{z}_T^G$ using the initial inverted noised latent $\\mathbf{z}_T^P$ , which is obtained from the image prompt $R$ via the DDIM inversion." + ], + "image_footnote": [], + "bbox": [ + 102, + 99, + 480, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 101, + 301, + 240, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-attention Modification in diffusion models. In diffusion models, KV replacement and KV concatenation are commonly used self-attention modifications. KV replacement (Fig. 7b) is primarily employed in tasks that require strong incorporation of the given image, such as image editing [1] and style transfer [3]. Conversely, KV concatenation (Fig. 7c) is utilized to tasks that require diverse image generation while reflecting the given image, such as style-aligned image generation [4], image variation [22], and story visualization [23]. However, KV concatenation weakens alignment with the given image due to attention bias from queries sharing features with generated keys and values. To address this, StyleAligned [4] weights the image prompt's attention scores, while RIVAL [22] and StoryDiffusion [23] use KV replacement at specific time steps. Although these methods improve alignment, they sacrifice image realism by limiting the incorporation of generated features. To solve this problem, our proposed Stratified Attention separately computes attention scores for the image prompt and generated results, thereby enhancing image prompt incorporation without sacrificing generated feature integration.", + "bbox": [ + 99, + 327, + 483, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image-prompting diffusion models. In text-to-image diffusion models, there are two distinct mechanisms to condition the generation process on an \"image prompt\": 1) cross-attention and 2) self-attention. Cross-attention-based approaches [18, 19, 21] integrate image prompts using auxiliary encoders or cross-attention layers, requiring additional training. However, the smaller datasets used for this training, compared to those used for diffusion models, can limit the quality of the generated images (e.g., the image variation results of IP-Adapter in Fig. 1). In contrast, self-attention-based approaches[22] incorporate the image prompt through the aforementioned self-attention alteration without training, allowing them to fully utilize the image generation capabilities of diffusion models. However, while cross-attention-based approaches direct image prompts solely to the positive branch during classifier", + "bbox": [ + 99, + 654, + 483, + 890 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8b8dc2fbb71ce5d49d46d1949573e06ef1028ffd45bd48364696ecd137191c3a.jpg", + "image_caption": [ + "(a) Conflicting guidance" + ], + "image_footnote": [], + "bbox": [ + 517, + 99, + 696, + 220 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c6e1cb29284eecd317c81fbad75883625bd1dd8d8e16029a0d6bc50fa8c4ebe1.jpg", + "image_caption": [ + "(b) Conflict-free guidance (Ours)", + "Figure 4. Illustration of the classifier-free guidance when image prompts are (a) used and (b) omitted during the estimation of the negative guidance scores." + ], + "image_footnote": [], + "bbox": [ + 714, + 99, + 893, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "free guidance, similar to text prompts, self-attention-based methods apply the same image prompt to both branches, disregarding classifier-free guidance principles. This improper use of classifier-free guidance prevents the details of the image prompt from being reflected in the generated images. In our method, we correct the classifier-free guidance in self-attention modification, enhancing the incorporation of the image prompt.", + "bbox": [ + 511, + 295, + 895, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 511, + 425, + 648, + 440 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Attention Fusion Existing studies [1, 22] that incorporate a given image into the generated output via controlling key and values in self-attention layer selectively apply different types of self-attention (Fig. 7) across time steps, employing a technique called the Attention Fusion strategy. These studies apply original self-attention or KV concatenation along with KV replacement to generate realistic images by utilizing the features of the generated image, rather than relying solely on the features of the given image, while still reflecting the given image. For image prompting, RIVAL [22] combines KV replacement and KV concatenation, referred to as \"cross-image self-attention injection\" in their paper. In this process, the attention process of KV concatenation is as follows:", + "bbox": [ + 511, + 450, + 895, + 654 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t n} \\left(M _ {t}, V _ {t}\\right) = M _ {t} \\cdot \\left(V _ {t} ^ {G} \\oplus V _ {t} ^ {P}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 662, + 790, + 680 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} M _ {t} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {t} ^ {G} \\left(K _ {t} ^ {G} \\oplus K _ {t} ^ {P}\\right) ^ {T}}{\\sqrt {d}}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 681, + 893, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$M_{t}$ and $V_{t}$ are the attention map and values, respectively, at time step $t$ . $\\oplus$ indicates concatenation along the spatial dimension, and $d$ is the latent projection dimension of the key $K$ and query $Q$ .", + "bbox": [ + 511, + 724, + 895, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-attention-based Image Prompt. As illustrated in Fig. 3, generating images that reflect the image prompt $P$ through the self-attention modification is structured into two distinct stages: DDIM inversion [15] and image generation. In the DDIM inversion stage, we obtain the inverted noisy latent chain $\\{\\mathbf{z}_T^P,\\dots ,\\mathbf{z}_0^P\\}$ from the image prompt", + "bbox": [ + 511, + 800, + 895, + 891 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23597", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/70feac6712b1d8151bac068f183356eaf501af319a229c03295b78d21c25b3d2.jpg", + "image_caption": [ + "Text Prompt", + "monochrome,", + "bad anatomy, 13", + "bad flames, cropped", + "worst quality\"", + "a) Conditioned on the text prompt" + ], + "image_footnote": [], + "bbox": [ + 209, + 114, + 295, + 184 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/839fbca22a6414c98148f876ee618a7862f65fa878a9ebee0a024d990b49d2b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 297, + 114, + 390, + 184 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/11cb593753904a497707f2a671d75011f654a947c8a402a1657d7e1b877ee7b5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 114, + 482, + 184 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/385bd8d4673f9fba70890a1fa821d2effbba6559dfddacd16a599f9e7c8dfec6.jpg", + "image_caption": [ + "Image Prompt", + "Inputs", + "Images generated without classifier-free guidance", + "Figure 5. To compare the impact of negative guidance between a) text-to-image diffusion models and b) self-attention modification-based image-prompting models, we generate images using negative prompts commonly applied in each model, without employing classifier-free guidance. Unlike negative guidance from text prompts, negative guidance from image prompts through self-attention modification incorporates the image prompt, thereby guiding the model to move away from the image prompt." + ], + "image_footnote": [], + "bbox": [ + 104, + 204, + 196, + 273 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8e7ec93a5a7b9e3f76d94cee44f66aa1c7877875d30a379d4895bf3482a4761f.jpg", + "image_caption": [ + "b) Conditioned on the text and image prompts" + ], + "image_footnote": [], + "bbox": [ + 209, + 204, + 297, + 273 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fd9eec410dacd041bd1ab77fa8ed6f094718fcbb4fb77ab5ff10c3c8b6110976.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 297, + 204, + 390, + 273 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/04c1cdab5274975a96ed392469fb79e1bbff0e8e5b0b1242da7c857475bffa0e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 204, + 480, + 273 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$P$ through a deterministic DDIM inversion. The inverted noised latent $\\mathbf{z}_t^P$ from this chain is provided to the model at the corresponding time step $t$ during image generation, playing a crucial role in incorporating the features of the image prompt $P$ into the generated images $G$ through the self-attention alterations.", + "bbox": [ + 99, + 412, + 483, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the image generation stage, we create images $G$ from randomly sampled Gaussian noise $\\mathbf{z}$ , conditioned on the positive text prompt $c^{+}$ , the negative text prompt $c^{-}$ , and the inverted noisy latent $\\mathbf{z}_T^P$ . To transfer the color tone of the image prompt $P$ to the generated image $G$ , we apply AdaIN to the Gaussian noise $\\mathbf{z}$ using the initial inverted noisy latent $\\mathbf{z}_T^P$ , as utilized in StyleID [3], to derive the initial noisy latent $\\mathbf{z}_T^G$ . This process is defined as follows.", + "bbox": [ + 99, + 501, + 483, + 619 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {T} ^ {G} = \\operatorname {A d a I N} (\\mathbf {z}, \\mathbf {z} _ {T} ^ {P}),\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 628, + 361, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\operatorname{AdaIN}(x,y) = \\sigma(y)\\left(\\frac{x - \\mu(x)}{\\sigma(x)}\\right) + \\mu(y)$ . (2)", + "bbox": [ + 122, + 648, + 482, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mu (\\cdot)$ and $\\sigma (\\cdot)$ represent the mean and standard deviation computed for each channel, respectively. To utilize classifier-free guidance [6], we duplicate the noised latent $\\mathbf{z}_t^G$ at each time step and provide each copy to the model along with the positive text prompt $c^{+}$ and the negative text prompt $c^{-}$ , respectively. At this stage, to incorporate the image prompt $P$ into the generated image $G$ , the model also supplies the previously obtained inverted noised latent $\\mathbf{z}_t^P$ along with the noised latent $\\mathbf{z}_t^G$ .", + "bbox": [ + 99, + 690, + 483, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 101, + 835, + 189, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We introduce a novel method that generates images faithfully reflecting given prompts by controlling keys and", + "bbox": [ + 99, + 859, + 483, + 890 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f7df8766e2b253c5a7d1d3fb025a7706a36eeb7dc92f75063565c7d4c412d588.jpg", + "image_caption": [ + "Figure 6. Employing the image prompt as both positive and negative guidance fails to effectively direct the model to reflect the image prompt due to conflicting guidance (blue line), whereas using it exclusively as positive guidance provides clearer direction by eliminating this conflict (orange line)." + ], + "image_footnote": [], + "bbox": [ + 514, + 99, + 893, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "values in the self-attention layers of text-to-image diffusion models without training. This section details two key components to enhance image prompt alignment: 1) conflict-free guidance (Sec. 4.1), and 2) Stratified Attention (Sec. 4.2).", + "bbox": [ + 511, + 270, + 893, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Conflict-free Guidance", + "text_level": 1, + "bbox": [ + 511, + 353, + 718, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2, the self-attention modification used in existing image-prompting research [22] hinders the incorporation of the image prompt in the generated images due to conflicting guidance, where the image prompt is applied as both positive and negative guidance (Fig. 4a) during classifier-free guidance. To resolve this conflict, we correct the guidance term for image prompts by using them exclusively as positive guidance (Fig. 4b), based on two analyses.", + "bbox": [ + 511, + 375, + 893, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To investigate the impact of using an image prompt as negative guidance within the self-attention modification on the generated images, we first compare images produced from prompts typically employed for negative guidance in both the original diffusion model and self-attention modification-based image-prompting methods. In this experiment, to assess the influence of prompts used for negative guidance, we generate images without applying classifier-free guidance, using negative prompts in place of positive prompts. As shown in Fig. 5, unlike images generated from negative text prompts, the negative guidance in self-attention modification models incorporates the image prompt, which guides the model away from reflecting the image prompt.", + "bbox": [ + 511, + 493, + 893, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition, during classifier-free guidance, we examine the effect of excluding the image prompt as negative guidance in the self-attention modification on incorporation of the image prompt into generated images. Specifically, we incrementally increase the guidance scale and calculate CLIP scores [12] to evaluate the alignment of the generated images with the image prompt and the ground truth text. To isolate the effect of the image prompt, a null prompt is used as the positive text prompt during image generation. As shown in Fig. 6, excluding the image prompt from negative guidance leads to a more faithful incorporation of it than including it as negative guidance. This demonstrates that providing conflict-free guidance by using the image", + "bbox": [ + 511, + 699, + 895, + 890 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23598", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8eb29866f68d3f35309947e7bad2ce0d5dd8521747b74efd2233ba31f1935ee1.jpg", + "image_caption": [ + "(a) Original self-attention" + ], + "image_footnote": [], + "bbox": [ + 102, + 125, + 272, + 213 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6797394190c872926db8dcdcbb97968341e4712e7f63ed328003413a11824ae1.jpg", + "image_caption": [ + "(b) KV replacement" + ], + "image_footnote": [], + "bbox": [ + 282, + 125, + 450, + 236 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ae336c64997608d7a0d6526f77004148e62a2dc04ae25d8fef1a35fd9aa482ec.jpg", + "image_caption": [ + "(c) KV concatenation" + ], + "image_footnote": [], + "bbox": [ + 462, + 125, + 630, + 250 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f6b3b685ed7b6f7a77f28cbfd38ab9c669f099d88103609027c6dd86b15ccbf8.jpg", + "image_caption": [ + "(d) Stratified attention" + ], + "image_footnote": [], + "bbox": [ + 643, + 99, + 893, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "prompt solely as a positive prompt in self-attention modification plays an important role in ensuring the generated image faithfully reflects the image prompt.", + "bbox": [ + 99, + 342, + 483, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Stratified Attention", + "text_level": 1, + "bbox": [ + 101, + 393, + 282, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To generate diverse and realistic images while reflecting the image prompt, RIVAL [22] employs Attention Fusion, selectively applying KV replacement (Fig. 7b) and KV concatenation (Fig. 7c) rather than relying solely on KV replacement. While this strategy enables the incorporation of both the generated image and the image prompt features via KV concatenation, we observe that KV concatenation tends to favor higher attention scores for the generated features over those of the image prompt (Fig. 11), which reduces alignment with the image prompt.", + "bbox": [ + 99, + 415, + 483, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To overcome these limitations, we propose Stratified Attention (Fig. 7d). While KV concatenation computes the attention process for both generated features and image prompt features in an integrated manner (Eq. (1)), Stratified Attention separately calculates the attention processes for each feature and then combines them through a weighted sum as follows:", + "bbox": [ + 99, + 563, + 483, + 662 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {A t t n} \\left(M _ {t} ^ {G}, M _ {t} ^ {P}, V _ {t} ^ {G}, V _ {t} ^ {P}\\right) = \\lambda_ {G} M _ {t} ^ {G} V _ {t} ^ {G} + \\lambda_ {P} M _ {t} ^ {P} V _ {t} ^ {P}, \\\\ \\text {w h e r e} M _ {t} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {t} \\left(K _ {t}\\right) ^ {\\intercal}}{\\sqrt {d}}\\right). \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 669, + 480, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This separation of operations ensures a balanced attention flow between both sources. Instead of KV replacement, we use Stratified Attention with KV concatenation in Attention Fusion to consistently reflect both generated and image prompt features across all time steps, ensuring a balanced reflection of each.", + "bbox": [ + 99, + 734, + 483, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 101, + 835, + 230, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics We quantitatively compare our model to image-prompting approaches across four aspects.", + "bbox": [ + 99, + 859, + 483, + 890 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5c817c76cfeef61e3b1ee30623d3182e63f9b9ef0bb13cf41cc0c945f77637cd.jpg", + "image_caption": [ + "Figure 7. Types of attention modification techniques. (a) Original self-attention (b) KV replacement: The keys and values from the image prompts replace the original keys and values. (c) KV concatenation: The key and values from the image prompts are concatenated with the original key and values. (d) Stratified attention: The attention scores are calculated independently and summed afterward.", + "Figure 8. Our method generates images that not only reflect the image prompt but also exhibit diverse structures." + ], + "image_footnote": [], + "bbox": [ + 514, + 340, + 893, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For image prompting, we measure the image-alignment by calculating the similarity using image encoders such as CLIP (CLIP-I) [12]. Additionally, similar to text-to-image generation, we measure text-alignment and the realism using CLIP scores (CLIP-T) and Fréchet Inception Distance (FID) [5]. However, since both CLIP scores can remain high even when the generated images closely replicate the image prompt, we also assess structural diversity between the generated images by evaluating structural distance based on the DINO self-similarity score (DINO-G) [2]. To evaluate the metrics, we generate four images for each image prompt.", + "bbox": [ + 509, + 544, + 893, + 707 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines For our comparisons, we utilize three image-prompting models as baselines: IP-Adapter [19], SSREncoder [21] and RIVAL [22]. IP-Adapter and SSREncoder attach separate trainable adapters to the diffusion model, enabling it to reflect the image prompt in the generated images. In contrast, RIVAL is a training-free model that generates images aligned with the provided image prompt by the self-attention modification, which is frequently employed to reflect the given image. To ensure a fair comparison, we employ Stable Diffusion [13] version 1.5 for all models including ours. Also, we use the same", + "bbox": [ + 511, + 728, + 895, + 888 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23599", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e06640de09446352c7da9986acd1dcac12828a27e2e1a1878875e9ce1cf5f88f.jpg", + "image_caption": [ + "Text Prompt: The person is young and has goatee." + ], + "image_footnote": [], + "bbox": [ + 102, + 99, + 444, + 165 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a5fba5f311588ad6d6a101fd141ebb003d80e973612528367ac15f3b021df8c2.jpg", + "image_caption": [ + "Text Prompt: This person looks attractive. This person has wavy hair, pointy nose and is wearing lipstick, heavy makeup." + ], + "image_footnote": [], + "bbox": [ + 102, + 183, + 444, + 234 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/54f5e9748b8db278f77a0bfa85978b3cb9ddfb028f63cd7865815d51875d24ea.jpg", + "image_caption": [ + "Text Prompt: This person looks smiling and has big nose. The person is wearing earrings, heavy makeup, lipstick." + ], + "image_footnote": [], + "bbox": [ + 102, + 258, + 444, + 310 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9c84d7f139d05c3ba38b4b24734ff4b71db823fce761b970a4a3582b3b55c530.jpg", + "image_caption": [ + "(b) Cross-prompt image generation. In general, models generate images that reflect the content of the text prompt and the style or texture of the image prompt. While baseline models often fail to accurately reflect either the image or the text prompt, our method successfully integrates both prompts in a harmonious way." + ], + "image_footnote": [], + "bbox": [ + 457, + 99, + 893, + 306 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f1cea6786c362bb9febc1539e85b45f2da89351712d65f645b14ebe989f8f6bc.jpg", + "image_caption": [ + "(a) Image variation. Unlike ours, baselines often fail to reflect details of image prompts (e.g., color of lipstick, type of sunglasses).", + "(c) Structure-guided image generation using soft edges. Baseline methods exhibit color shifts or fail to incorporate the structure of soft edges.", + "Figure 9. Qualitative comparison with baselines across three tasks: (a) Image variation, (b) Cross-prompt image generation, and (c-d) Structure-guided image generation. Additional results are in the Supplementary (Suppl.)" + ], + "image_footnote": [], + "bbox": [ + 102, + 371, + 491, + 513 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/83dc19f802b7b5db092f74ba00a1b3db0cd215360855e677fe9467e6cf2055be.jpg", + "image_caption": [ + "(d) Structure-guided image generation using depth. Baseline methods often fail to capture the color tones and textures of the image prompt." + ], + "image_footnote": [], + "bbox": [ + 504, + 371, + 893, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Gaussian noise, except for RIVAL, which shuffles the inverted noised latent $\\mathbf{z}_T^P$ to produce $\\mathbf{z}_T^G$ .", + "bbox": [ + 99, + 585, + 482, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets We validate our approach on various text-image pairs from three datasets, COCO 2017 [9], ImageNet-R-TI2I [16], and CelebAHQ [7]. Specifically, we utilize the validation set of COCO and randomly sample 100 images from the CelebAHQ dataset. For text prompts, we use the original captions from the COCO and the CelebAHQ dataset, while the text prompts for the ImageNet-R-TI2I dataset are generated using BLIP [8].", + "bbox": [ + 99, + 636, + 483, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Comparison with Baselines", + "text_level": 1, + "bbox": [ + 101, + 763, + 339, + 780 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we demonstrate the effectiveness of our proposed method by conducting qualitative and quantitative comparisons of its performance against baseline models across three tasks: 1) image variation, 2) cross-prompt image generation, and 3) structure-guided image generation. Extra qualitative results, implementation details, and ablation studies are in Suppl..", + "bbox": [ + 99, + 786, + 483, + 888 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image Variation We evaluate image variation performance across three datasets using four metrics: CLIP-I, CLIP-T, DINO-G, and FID. Due to the limited number of images in the ImageNet-R-TI2I and CelebA-HQ datasets, we compute FID only for the COCO validation set. The qualitative results in Fig. 9a show that baseline models generate images that capture the semantic meaning of the image prompt (e.g., woman) but fail to incorporate finer details (e.g., makeup color tone or type of sunglasses). In contrast, our method generates images that faithfully reflect these details.", + "bbox": [ + 511, + 585, + 893, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Along with these results, we provide qualitative examples that highlight our model's ability to generate diverse images from a single prompt. As shown in Fig. 8, our approach consistently produces images with varied structures that remain well-aligned with the image prompt, ensuring coherent content across all outputs. In addition, we quantitatively compare our method with the baselines in Tab. 1. Our method performs competitively with the baselines in terms of text alignment, structural diversity, and image re", + "bbox": [ + 509, + 757, + 893, + 888 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23600", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c1de449859544e5f18ac9cf0e02dbc9420164dd5f5dafa7a9a248f2ce881188a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    CelebAHQImageNet-R-TI2ICOCO validation
    CLIP-I ↑CLIP-T ↑DINO-G ↑CLIP-I ↑CLIP-T ↑DINO-G ↑CLIP-I ↑CLIP-T ↑DINO-G ↑FID ↓
    IP-Adapter [19]0.8450.2640.0730.8700.3000.0920.8580.3230.08915.485
    SSR-Encoder [21]0.8500.2690.0780.8610.3060.1000.8540.3210.08715.730
    RIVAL [22]0.7390.2890.0950.8360.3170.1400.8320.3250.08914.016
    Ours0.8780.2740.0940.8830.3110.1420.8730.3260.09314.557
    ", + "bbox": [ + 101, + 99, + 893, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c8e64408dbebfa48c04980c1cfbb0a445a966c2a4fd9daa6886831abe318fb32.jpg", + "image_caption": [ + "Figure 10. Quantitative results for cross-prompt image generation. Each dot represents a different factor for adjusting the image prompt alignment. Our approach demonstrates high similarity in both image and text." + ], + "image_footnote": [], + "bbox": [ + 107, + 258, + 415, + 369 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/daaefe8a291278fff4c0e9113cea56fa82e66df878a4e41f007d2f82b525f2ff.jpg", + "table_caption": [ + "Table 1. Quantitative comparison with baseline models in image variation tasks. Our method shows competitive performance compared to baselines in structural diversity, image realism, and reflecting text prompts, while surpassing them in image prompt alignment, as measured by CLIP-I. Best and second best results are in bold and underlined." + ], + "table_footnote": [], + "table_body": "
    DepthSoft Edge
    CLIP-I ↑CLIP-T ↑DINO-C ↓CLIP-I ↑CLIP-T ↑DINO-C ↓
    IP-Adapter0.8260.3060.0530.8110.3000.044
    SSR-Encoder0.8160.3090.0570.7990.2990.052
    RIVAL0.7940.2170.0790.7930.2160.060
    Ours0.8610.3100.0660.8440.3080.052
    ", + "bbox": [ + 431, + 257, + 893, + 347 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison of structure-guided image generation. Our method demonstrates competitive performance with baselines in reflecting structural conditions based on DINO-C, while excelling in the integration of both image and text prompts based on CLIP scores. Best and second best results are in bold and underlined.", + "bbox": [ + 429, + 356, + 895, + 425 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "alism, while providing the most faithful alignment with the image prompt across multiple datasets.", + "bbox": [ + 99, + 436, + 482, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Cross-prompt Image Generation Since image-prompting models are fundamentally based on text-to-image diffusion models, several methods [19, 21, 22] provide functionalities to adjust the balance between text and image prompts during generation. Thus, we evaluate each model's ability to harmoniously integrate both prompts in the generated images by adjusting their hyperparameter settings and comparing the results. For this analysis, we set the text and image prompts with differing content to examine which of the two prompts (text or image) is reflected in the generated images. Given the difficulty of text prompts in defining styles such as texture, we set a content disparity between the text and image prompts for this experiment by using image-text editing pairs from the ImageNet-R-TI2I dataset. Also, we include StyleAligned [4] as an additional baseline, which generates images from cross-prompt inputs. For quantitatively comparison, we evaluate performance in terms of image and text alignment based on two CLIP scores while varying the hyperparameters.", + "bbox": [ + 99, + 491, + 482, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Fig. 10, our method achieves higher alignment with both prompts compared to the baselines. Also, we visually display the results that show the best performance for each model (the closest result to the top-right corner of the graph in Fig. 10). According to the visual results (Fig. 9b), models generally reflect the content of the text prompt while capturing the style, such as texture, from the", + "bbox": [ + 99, + 786, + 482, + 888 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "image prompt. However, this tendency varies across models. IP-Adapter and SSR-Encoder fail to adequately incorporate the image prompt, as they balance both prompts by adjusting the proportion of image prompt influence. In contrast, RIVAL and StyleAligned struggle to capture the text prompt, generating unrealistic images due to an overemphasis on the image prompt features rather than the generated features, caused by KV replacement and attention shift, respectively. Our method, however, successfully integrates both text and image prompts by balancing both features across all time steps via Stratified Attention.", + "bbox": [ + 509, + 436, + 893, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Structure-guided Image Generation We assess the effectiveness of our method compared to baselines in reflecting the image prompt when additional structural conditions are given. Leveraging ControlNet [20] to integrate structural conditions into generated images, we evaluate performance both quantitatively and visually under two specific conditions: soft edges and depth. For assessing structural faithfulness of the generated image, we measure the DINO similarity (DINO-C) between the structural condition and the generated image. Quantitative results reveal that our approach is competitive with baselines in terms of structural condition alignment while achieving the most faithful incorporation of both prompts (Tab. 2). Visual comparisons further support this trend (Fig. 9c and Fig. 9d).", + "bbox": [ + 509, + 619, + 893, + 827 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Effects on the Alignment of Image Prompt", + "text_level": 1, + "bbox": [ + 511, + 837, + 864, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "By investigating the attention scores associated with the image prompts in Eq. (3), we assess the influence of the", + "bbox": [ + 511, + 859, + 893, + 890 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23601", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e9f60098a076d73d625d2052448b00d85aa1485b45d62cfafe60e21994f67ba9.jpg", + "image_caption": [ + "Figure 11. Impact of conflict-free guidance (ConFG) in the self-attention modification and Stratified Attention (Strat. Attn.) on the attention score of the image prompt. A smaller difference (y-axis) indicates greater attention to the image prompt, reflecting it more faithfully in the generated images. Both conflict-free guidance and using longer time steps with Stratified Attention enhance the image prompt alignment." + ], + "image_footnote": [], + "bbox": [ + 102, + 98, + 480, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "two primary components of our method on the alignment of the image prompt: 1) conflict-free guidance (ConFG) in Sec. 4.1 and 2) Stratified Attention (Sec. 4.2). Specifically, we compute the difference of the self-attention scores between generated image and the image prompt, where smaller differences indicate that the image prompt is effectively reflected in the generation process. We compare the differences across diffusion time steps, for KV concatenation (concat.), ConFG, and ConFG with Stratified Attention (Strat. Attn.). As shown in Fig. 11, conflict-free guidance-by excluding the image prompt as a negative prompt-significantly improves alignment with the image prompt. Additionally, extending the time steps with Stratified Attention further amplifies this effect. These findings validate our hypothesis that both techniques substantially enhance the alignment with the image prompt.", + "bbox": [ + 99, + 335, + 483, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Generalization Across Diffusion Models", + "text_level": 1, + "bbox": [ + 101, + 580, + 434, + 594 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To validate the generalization efficacy of our proposed model, we conduct both qualitative (Fig. 12) and quantitative (Tab. 3) comparisons of its performance across various diffusion models, including Stable Diffusion [13] version 1.5, version 2.1, and Stable Diffusion XL [11]. Both comparisons demonstrate the applicability of our method across different models. Despite being training-free, our method outperforms the training-based model in reflecting image prompts while remaining competitive across other metrics (Tab. 3).", + "bbox": [ + 99, + 601, + 483, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 101, + 762, + 217, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a novel image-prompting method to generate images that faithfully reflect the details of user-provided image conditions. The key idea behind our approach is to eliminate the undesired role of the image prompt as a negative condition during classifier-free guidance in self-attention modification, thereby providing the model with a clearer signal through conflict-free guidance to incorporate the im", + "bbox": [ + 99, + 786, + 483, + 890 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/974ea268fd9771ba0461e3a681e556c8f8f128213730ba30b84bb14de143948f.jpg", + "image_caption": [ + "Figure 12. Qualitative comparison of image variation performance across three different diffusion models shows that our method generates images that faithfully reflect the image prompt, regardless of the underlying diffusion model." + ], + "image_footnote": [], + "bbox": [ + 514, + 101, + 893, + 351 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/080fe70c0f35f480ff614edb0f947fd1d54dc6e8637ec574bc9970b77b30abbd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    CLIP-I↑CLIP-T↑DINO-G↑
    OursIP-AdapterOursIP-AdapterOursIP-Adapter
    SD1.50.8830.8700.3110.3000.1420.092
    SD2.10.893-0.311-0.118-
    SDXL0.8650.8590.2980.2990.1100.121
    ", + "bbox": [ + 513, + 436, + 893, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Our method demonstrates competitive performance across various diffusion models and outperforms the training-based model [19], even without the need for training.", + "bbox": [ + 511, + 523, + 893, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "age prompt. Additionally, we introduce Stratified Attention, an alternative self-attention modification that enhances the incorporation of the image prompt by providing a balanced attention flow between the generated image and the image prompt.", + "bbox": [ + 511, + 599, + 893, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We show the superiority of our approach over existing image-prompting models by conducting extensive evaluations across three distinct image generation tasks: image variation, cross-prompt image generation, and structure-guided image generation. In addition to these tasks, we aim to explore the scalability and adaptability of our method to various tasks, such as story visualization and style transfer, as part of our future work.", + "bbox": [ + 511, + 679, + 893, + 796 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our work also has limitations. Since this method uses a text-to-image diffusion model in a training-free manner, the quality of generated images depends on the diffusion model's performance. Consequently, issues such as poor hand generation quality persist, but we expect these to improve as diffusion models advance.", + "bbox": [ + 511, + 801, + 893, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23602", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2025-00555621) and Institute for Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (RS-2019-II190075, Artificial Intelligence Graduate School Program(KAIST)).", + "bbox": [ + 99, + 102, + 485, + 205 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 102, + 218, + 194, + 233 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mingdeng Cao, Xintao Wang, Zhongang Qi, Ying Shan, Xiaohu Qie, and Yinqiang Zheng. Masactrl: Tuning-free mutual self-attention control for consistent image synthesis and editing. In ICCV, pages 22560-22570, 2023. 2, 3", + "[2] Mathilde Caron, Hugo Touvron, Ishan Misra, Herve Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In ICCV, pages 9650-9660, 2021. 5", + "[3] Jiwoo Chung, Sangeek Hyun, and Jae-Pil Heo. Style injection in diffusion: A training-free approach for adapting large-scale diffusion models for style transfer. In CVPR, pages 8795-8805, 2024. 2, 3, 4", + "[4] Amir Hertz, Andrey Voynov, Shlomi Fruchter, and Daniel Cohen-Or. Style aligned image generation via shared attention. In CVPR, pages 4775–4785, 2024. 1, 2, 3, 7", + "[5] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. NeurIPS, 30, 2017. 5", + "[6] Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance. In NeurIPS 2021 Workshop on Deep Generative Models and Downstream Applications, 2021. 2, 4", + "[7] Tero Karras. Progressive growing of gans for improved quality, stability, and variation. arXiv preprint arXiv:1710.10196, 2017. 6, 3, 5", + "[8] Junnan Li, Dongxu Li, Caiming Xiong, and Steven Hoi. Blip: Bootstrapping language-image pre-training for unified vision-language understanding and generation. In ICML, pages 12888-12900. PMLR, 2022. 6", + "[9] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dólar, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In ECCV, pages 740-755. Springer, 2014. 6", + "[10] Bingyan Liu, Chengyu Wang, Tingfeng Cao, Kui Jia, and Jun Huang. Towards understanding cross and self-attention in stable diffusion for text-guided image editing. In CVPR, pages 7817–7826, 2024. 2", + "[11] Dustin Podell, Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhorn, Jonas Müller, Joe Penna, and Robin Rombach. Sdxl: Improving latent diffusion models for high-resolution image synthesis. arXiv preprint arXiv:2307.01952, 2023. 2, 8, 1", + "[12] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In ICML, pages 8748-8763. PMLR, 2021. 4, 5" + ], + "bbox": [ + 104, + 243, + 480, + 888 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[13] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In CVPR, pages 10684-10695, 2022. 2, 5, 8, 1", + "[14] Nataniel Ruiz, Yuanzhen Li, Varun Jampani, Yael Pritch, Michael Rubinstein, and Kfir Aberman. Dreambooth: Fine tuning text-to-image diffusion models for subject-driven generation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 22500-22510, 2023. 2", + "[15] Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502, 2020. 3", + "[16] Narek Tumanyan, Michal Geyer, Shai Bagon, and Tali Dekel. Plug-and-play diffusion features for text-driven image-to-image translation. In CVPR, pages 1921-1930, 2023. 2, 6, 3", + "[17] Qixun Wang, Xu Bai, Haofan Wang, Zekui Qin, Anthony Chen, Huaxia Li, Xu Tang, and Yao Hu. Instantid: Zero-shot identity-preserving generation in seconds. arXiv preprint arXiv:2401.07519, 2024. 2, 5", + "[18] Xingqian Xu, Jiayi Guo, Zhangyang Wang, Gao Huang, Irfan Essa, and Humphrey Shi. Prompt-free diffusion: Taking\" text\" out of text-to-image diffusion models. In CVPR, pages 8682-8692, 2024. 3", + "[19] Hu Ye, Jun Zhang, Sibo Liu, Xiao Han, and Wei Yang. Ip-adapter: Text compatible image prompt adapter for text-to-image diffusion models. arXiv preprint arXiv:2308.06721, 2023. 1, 2, 3, 5, 7, 8", + "[20] Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. In ICCV, pages 3836-3847, 2023. 7, 5", + "[21] Yuxuan Zhang, Yiren Song, Jiaming Liu, Rui Wang, Jinpeng Yu, Hao Tang, Huaxia Li, Xu Tang, Yao Hu, Han Pan, et al. Ssr-encoder: Encoding selective subject representation for subject-driven generation. In CVPR, pages 8069–8078, 2024. 1, 2, 3, 5, 7", + "[22] Yuechen Zhang, Jinbo Xing, Eric Lo, and Jiaya Jia. Realworld image variation by aligning diffusion inversion chain. NeurIPS, 36, 2024. 1, 2, 3, 4, 5, 7", + "[23] Yupeng Zhou, Daquan Zhou, Ming-Ming Cheng, Jiashi Feng, and Qibin Hou. Storydiffusion: Consistent self-attention for long-range image and video generation. arXiv preprint arXiv:2405.01434, 2024. 2, 3" + ], + "bbox": [ + 516, + 103, + 893, + 707 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "23603", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2025/Devil is in the Detail_ Towards Injecting Fine Details of Image Prompt in Image Generation via Conflict-free Guidance and Stratified Attention/33468e61-bdab-44f8-8e48-6c0ba3c7248c_model.json b/2025/Devil is in the Detail_ Towards Injecting Fine Details of Image Prompt in Image Generation via Conflict-free Guidance and Stratified Attention/33468e61-bdab-44f8-8e48-6c0ba3c7248c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..755178768b1181013fcab5b19f854e07e09079f8 --- /dev/null +++ b/2025/Devil is in the Detail_ Towards Injecting Fine Details of Image Prompt in Image Generation via Conflict-free 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Cross-prompt Image Generation" + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.474, + 0.522, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.474, + 0.559, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.56, + 0.474, + 0.617, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.474, + 0.707, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.474, + 0.767, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.474, + 0.835, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.836, + 0.474, + 0.894, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.543, + 0.896, + 0.611 + ], + "angle": 0, + "content": "Figure 1. Our method faithfully reflects the details of image prompts (e.g., eye makeup) for diverse image generation across various tasks (Tasks A-C) in a training-free manner. In contrast, existing methods often fail to incorporate fine details of the image prompt. Even with training, IP-Adapter [19] and SSR-Encoder [21] struggle to properly represent the color and texture of the image prompt. RIVAL [22] and StyleAligned [4] also fail to generate high-fidelity images that faithfully reflect the image or text prompts due to a trade-off between the realism of the generated results and alignment with the image prompt. Extra results are in the Supplementary (Suppl.)." + }, + { + "type": "title", + "bbox": [ + 0.256, + 0.623, + 0.332, + 0.638 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.655, + 0.486, + 0.892 + ], + "angle": 0, + "content": "While large-scale text-to-image diffusion models enable the generation of high-quality, diverse images from text prompts, these prompts struggle to capture intricate details, such as textures, preventing the user intent from being reflected. This limitation has led to efforts to generate images conditioned on user-provided images, referred to as image prompts. Recent work modifies the self-attention mechanism to impose image conditions in generated images by replacing or concatenating the keys and values from the image prompt. This enables the self-attention layer to work like a cross-attention layer, generally used to incorporate text prompts. In this paper, we identify two common issues in existing methods of modifying self-attention that hinder diffusion models from reflecting the image prompt. By addressing these issues, we propose a novel method that generates images that properly reflect the details of image prompts." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.625, + 0.896, + 0.89 + ], + "angle": 0, + "content": "First, existing approaches often neglect the importance of image prompts in classifier-free guidance, which directs the model towards the intended conditions and away from those undesirable. Specifically, current methods use image prompts as both desired and undesired conditions, causing conflicting signals. To resolve this, we propose conflict-free guidance by using image prompts only as desired conditions, ensuring that the generated image faithfully reflects the image prompt. In addition, we observe that the two most common self-attention modifications involve a trade-off between the realism of the generated image and alignment with the image prompt, achieved by selectively using keys and values from both images. Specifically, selecting more keys and values from the image prompt improves alignment, while selecting more from the generated image enhances realism. To balance both, we propose an alternative self-attention modification method, Stratified Attention, which jointly uses keys and values from both images" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "23595" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.1, + 0.103, + 0.486, + 0.178 + ], + "angle": 0, + "content": "rather than selecting between them. Through extensive experiments across three distinct image generation tasks, we demonstrate that the proposed method outperforms existing image-prompting models in faithfully reflecting the image prompt." + }, + { + "type": "title", + "bbox": [ + 0.103, + 0.204, + 0.231, + 0.22 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.229, + 0.485, + 0.449 + ], + "angle": 0, + "content": "The emergence of large-scale text-to-image diffusion models [11, 13] has enabled users to generate diverse images from text. However, describing complex scenes using only text prompts can be complicated, leading to ongoing efforts to incorporate user-provided image conditions to better reflect user intent [14, 17, 19, 21]. As part of these efforts, modifying the self-attention mechanism in pre-trained text-to-image diffusion models has recently attracted interest in areas such as image editing [1, 10, 16], story visualization [23], image variation [22], and style transfer [3], as a flexible method for incorporating user-provided image conditions into generated images. This modification is typically achieved by integrating the keys and values of the condition in the self-attention layer, as the keys and values derived from the image features contain rich details about images." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.45, + 0.484, + 0.683 + ], + "angle": 0, + "content": "Since the keys and values embody the context of images, these techniques are particularly powerful for conditioning diffusion models on image prompts, which contain the intricate details of a scene (e.g., the fine patterns of eye makeup in Fig. 1) that go beyond the level of details text descriptions can reach. Specifically, recent findings [3, 4, 22] show that replacing or concatenating the new keys and values (KV) of the generated images to those of the image prompt in the self-attention layer simulates a cross-attention with the image prompt, functioning similarly to the way text prompts affect image generation. This simulated cross-attention offers key benefits over training an additional cross-attention layer [19]: it eliminates the need for retraining with each new diffusion model and minimizes information loss from using smaller datasets for the training, as self-attention features are generated within the same model." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.685, + 0.484, + 0.892 + ], + "angle": 0, + "content": "However, we find that existing self-attention alterations-based approaches overlook an important aspect, which is the role of image prompts during classifier-free guidance [6]. Classifier-free guidance steers the diffusion model toward desired conditions (i.e., positive guidance) and away from undesired ones (i.e., negative guidance), enhancing the alignment between generated images and the user-provided conditions. Current approaches use image prompts to estimate both positive-guidance and negative-guidance scores, causing image prompts to influence the negative scores as well. This sends a strong signal to the model to avoid reflecting the image prompt, thereby compromising alignment between the generated image and the image prompt. The effect of this conflicting guidance is illustrated in Fig. 2," + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.103, + 0.896, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.204, + 0.896, + 0.259 + ], + "angle": 0, + "content": "Figure 2. Using the image prompt as positive guidance ensures that it is reflected in the generated images, but using it as both positive (pos.) and negative (neg.) guidance fails due to the conflicting guidance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.268, + 0.895, + 0.357 + ], + "angle": 0, + "content": "where the details of the image prompt are often lost or even ignored. Based on this insight, we propose conflict-free guidance by adjusting classifier-free guidance to exclude image prompts from estimating negative-guidance scores, enabling generations that faithfully reflect the provided image prompt." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.358, + 0.897, + 0.709 + ], + "angle": 0, + "content": "Furthermore, we observe that two common self-attention modifications, which we call KV replacement and KV concatenation, represent a trade-off between the realism of the generated results and alignment with the image prompt. KV replacement ensures strong alignment with the image prompt but struggles to generate realistic attributes not specified in the image prompt (e.g., frontal view of a cat), as it relies solely on the keys and values from the image prompt (e.g., side view of a cat) while discarding those from the generated results. In contrast, KV concatenation, which combines keys and values from both the image prompt and the generated results, enhances realism but reduces the alignment due to attention bias arising from the queries being derived from the same features as the generated keys and values. To achieve both realism in the generated results and alignment with the image prompt, we propose Stratified Attention (Fig. 7d) as a new self-attention modification that effectively addresses this bias in KV concatenation. Specifically, we calculate the attention scores for image prompts and generated results separately, rather than computing them all at once. The scores calculated in this way are then aggregated afterward. This facilitates the image prompts to attend to relevant features while preserving the original attention flow of the generated image." + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.711, + 0.842, + 0.725 + ], + "angle": 0, + "content": "To sum up, our key contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.726, + 0.894, + 0.784 + ], + "angle": 0, + "content": "- We correct the classifier-free guidance in modified selfattention by using the image prompt exclusively as positive guidance, rather than as conflicting guidance, to faithfully reflect the image prompt in image generation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.785, + 0.895, + 0.843 + ], + "angle": 0, + "content": "- We propose Stratified Attention as a new self-attention modification to effectively reflect the image prompt by ensuring a balanced attention flow between the image prompt and the generated image." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.844, + 0.895, + 0.888 + ], + "angle": 0, + "content": "- Through extensive experiments, our method achieves state-of-the-art performance in image prompting, both qualitatively and quantitatively." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.726, + 0.895, + 0.888 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.519, + 0.938 + ], + "angle": 0, + "content": "23596" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.103, + 0.101, + 0.482, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.234, + 0.484, + 0.289 + ], + "angle": 0, + "content": "Figure 3. Framework of the self-attention modification for image prompt: Image \\(G\\) is generated from the initial noised latent \\(\\mathbf{z}_T^G\\) using the initial inverted noised latent \\(\\mathbf{z}_T^P\\), which is obtained from the image prompt \\(R\\) via the DDIM inversion." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.303, + 0.241, + 0.318 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.328, + 0.485, + 0.637 + ], + "angle": 0, + "content": "Self-attention Modification in diffusion models. In diffusion models, KV replacement and KV concatenation are commonly used self-attention modifications. KV replacement (Fig. 7b) is primarily employed in tasks that require strong incorporation of the given image, such as image editing [1] and style transfer [3]. Conversely, KV concatenation (Fig. 7c) is utilized to tasks that require diverse image generation while reflecting the given image, such as style-aligned image generation [4], image variation [22], and story visualization [23]. However, KV concatenation weakens alignment with the given image due to attention bias from queries sharing features with generated keys and values. To address this, StyleAligned [4] weights the image prompt's attention scores, while RIVAL [22] and StoryDiffusion [23] use KV replacement at specific time steps. Although these methods improve alignment, they sacrifice image realism by limiting the incorporation of generated features. To solve this problem, our proposed Stratified Attention separately computes attention scores for the image prompt and generated results, thereby enhancing image prompt incorporation without sacrificing generated feature integration." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.655, + 0.484, + 0.891 + ], + "angle": 0, + "content": "Image-prompting diffusion models. In text-to-image diffusion models, there are two distinct mechanisms to condition the generation process on an \"image prompt\": 1) cross-attention and 2) self-attention. Cross-attention-based approaches [18, 19, 21] integrate image prompts using auxiliary encoders or cross-attention layers, requiring additional training. However, the smaller datasets used for this training, compared to those used for diffusion models, can limit the quality of the generated images (e.g., the image variation results of IP-Adapter in Fig. 1). In contrast, self-attention-based approaches[22] incorporate the image prompt through the aforementioned self-attention alteration without training, allowing them to fully utilize the image generation capabilities of diffusion models. However, while cross-attention-based approaches direct image prompts solely to the positive branch during classifier" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.1, + 0.697, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.224, + 0.669, + 0.236 + ], + "angle": 0, + "content": "(a) Conflicting guidance" + }, + { + "type": "image", + "bbox": [ + 0.715, + 0.1, + 0.895, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.719, + 0.224, + 0.889, + 0.236 + ], + "angle": 0, + "content": "(b) Conflict-free guidance (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.248, + 0.895, + 0.289 + ], + "angle": 0, + "content": "Figure 4. Illustration of the classifier-free guidance when image prompts are (a) used and (b) omitted during the estimation of the negative guidance scores." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.296, + 0.896, + 0.414 + ], + "angle": 0, + "content": "free guidance, similar to text prompts, self-attention-based methods apply the same image prompt to both branches, disregarding classifier-free guidance principles. This improper use of classifier-free guidance prevents the details of the image prompt from being reflected in the generated images. In our method, we correct the classifier-free guidance in self-attention modification, enhancing the incorporation of the image prompt." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.426, + 0.649, + 0.441 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.451, + 0.897, + 0.655 + ], + "angle": 0, + "content": "Attention Fusion Existing studies [1, 22] that incorporate a given image into the generated output via controlling key and values in self-attention layer selectively apply different types of self-attention (Fig. 7) across time steps, employing a technique called the Attention Fusion strategy. These studies apply original self-attention or KV concatenation along with KV replacement to generate realistic images by utilizing the features of the generated image, rather than relying solely on the features of the given image, while still reflecting the given image. For image prompting, RIVAL [22] combines KV replacement and KV concatenation, referred to as \"cross-image self-attention injection\" in their paper. In this process, the attention process of KV concatenation is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.663, + 0.791, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t n} \\left(M _ {t}, V _ {t}\\right) = M _ {t} \\cdot \\left(V _ {t} ^ {G} \\oplus V _ {t} ^ {P}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.683, + 0.894, + 0.717 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} M _ {t} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {t} ^ {G} \\left(K _ {t} ^ {G} \\oplus K _ {t} ^ {P}\\right) ^ {T}}{\\sqrt {d}}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.725, + 0.896, + 0.785 + ], + "angle": 0, + "content": "\\(M_{t}\\) and \\(V_{t}\\) are the attention map and values, respectively, at time step \\(t\\). \\(\\oplus\\) indicates concatenation along the spatial dimension, and \\(d\\) is the latent projection dimension of the key \\(K\\) and query \\(Q\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.801, + 0.896, + 0.892 + ], + "angle": 0, + "content": "Self-attention-based Image Prompt. As illustrated in Fig. 3, generating images that reflect the image prompt \\( P \\) through the self-attention modification is structured into two distinct stages: DDIM inversion [15] and image generation. In the DDIM inversion stage, we obtain the inverted noisy latent chain \\( \\{\\mathbf{z}_T^P,\\dots ,\\mathbf{z}_0^P\\} \\) from the image prompt" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "23597" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.104, + 0.184, + 0.115 + ], + "angle": 0, + "content": "Text Prompt" + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.127, + 0.184, + 0.139 + ], + "angle": 0, + "content": "monochrome," + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.14, + 0.184, + 0.151 + ], + "angle": 0, + "content": "bad anatomy, 13" + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.153, + 0.18, + 0.164 + ], + "angle": 0, + "content": "bad flames, cropped" + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.166, + 0.184, + 0.176 + ], + "angle": 0, + "content": "worst quality\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.105, + 0.377, + 0.115 + ], + "angle": 0, + "content": "a) Conditioned on the text prompt" + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.116, + 0.297, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.116, + 0.391, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.392, + 0.116, + 0.483, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.195, + 0.187, + 0.204 + ], + "angle": 0, + "content": "Image Prompt" + }, + { + "type": "image", + "bbox": [ + 0.105, + 0.205, + 0.197, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.276, + 0.167, + 0.285 + ], + "angle": 0, + "content": "Inputs" + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.195, + 0.437, + 0.205 + ], + "angle": 0, + "content": "b) Conditioned on the text and image prompts" + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.205, + 0.298, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.299, + 0.205, + 0.391, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.392, + 0.205, + 0.482, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.276, + 0.473, + 0.285 + ], + "angle": 0, + "content": "Images generated without classifier-free guidance" + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.299, + 0.484, + 0.407 + ], + "angle": 0, + "content": "Figure 5. To compare the impact of negative guidance between a) text-to-image diffusion models and b) self-attention modification-based image-prompting models, we generate images using negative prompts commonly applied in each model, without employing classifier-free guidance. Unlike negative guidance from text prompts, negative guidance from image prompts through self-attention modification incorporates the image prompt, thereby guiding the model to move away from the image prompt." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.414, + 0.484, + 0.501 + ], + "angle": 0, + "content": "\\(P\\) through a deterministic DDIM inversion. The inverted noised latent \\(\\mathbf{z}_t^P\\) from this chain is provided to the model at the corresponding time step \\(t\\) during image generation, playing a crucial role in incorporating the features of the image prompt \\(P\\) into the generated images \\(G\\) through the self-attention alterations." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.502, + 0.484, + 0.621 + ], + "angle": 0, + "content": "In the image generation stage, we create images \\(G\\) from randomly sampled Gaussian noise \\(\\mathbf{z}\\), conditioned on the positive text prompt \\(c^{+}\\), the negative text prompt \\(c^{-}\\), and the inverted noisy latent \\(\\mathbf{z}_T^P\\). To transfer the color tone of the image prompt \\(P\\) to the generated image \\(G\\), we apply AdaIN to the Gaussian noise \\(\\mathbf{z}\\) using the initial inverted noisy latent \\(\\mathbf{z}_T^P\\), as utilized in StyleID [3], to derive the initial noisy latent \\(\\mathbf{z}_T^G\\). This process is defined as follows." + }, + { + "type": "equation", + "bbox": [ + 0.227, + 0.629, + 0.362, + 0.648 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {T} ^ {G} = \\operatorname {A d a I N} (\\mathbf {z}, \\mathbf {z} _ {T} ^ {P}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.649, + 0.483, + 0.682 + ], + "angle": 0, + "content": "where \\(\\operatorname{AdaIN}(x,y) = \\sigma(y)\\left(\\frac{x - \\mu(x)}{\\sigma(x)}\\right) + \\mu(y)\\). (2)" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.691, + 0.484, + 0.824 + ], + "angle": 0, + "content": "\\(\\mu (\\cdot)\\) and \\(\\sigma (\\cdot)\\) represent the mean and standard deviation computed for each channel, respectively. To utilize classifier-free guidance [6], we duplicate the noised latent \\(\\mathbf{z}_t^G\\) at each time step and provide each copy to the model along with the positive text prompt \\(c^{+}\\) and the negative text prompt \\(c^{-}\\), respectively. At this stage, to incorporate the image prompt \\(P\\) into the generated image \\(G\\), the model also supplies the previously obtained inverted noised latent \\(\\mathbf{z}_t^P\\) along with the noised latent \\(\\mathbf{z}_t^G\\)." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.836, + 0.19, + 0.85 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.86, + 0.484, + 0.891 + ], + "angle": 0, + "content": "We introduce a novel method that generates images faithfully reflecting given prompts by controlling keys and" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.1, + 0.895, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.194, + 0.895, + 0.262 + ], + "angle": 0, + "content": "Figure 6. Employing the image prompt as both positive and negative guidance fails to effectively direct the model to reflect the image prompt due to conflicting guidance (blue line), whereas using it exclusively as positive guidance provides clearer direction by eliminating this conflict (orange line)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.271, + 0.895, + 0.344 + ], + "angle": 0, + "content": "values in the self-attention layers of text-to-image diffusion models without training. This section details two key components to enhance image prompt alignment: 1) conflict-free guidance (Sec. 4.1), and 2) Stratified Attention (Sec. 4.2)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.354, + 0.719, + 0.368 + ], + "angle": 0, + "content": "4.1. Conflict-free Guidance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.376, + 0.895, + 0.493 + ], + "angle": 0, + "content": "As shown in Fig. 2, the self-attention modification used in existing image-prompting research [22] hinders the incorporation of the image prompt in the generated images due to conflicting guidance, where the image prompt is applied as both positive and negative guidance (Fig. 4a) during classifier-free guidance. To resolve this conflict, we correct the guidance term for image prompts by using them exclusively as positive guidance (Fig. 4b), based on two analyses." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.494, + 0.895, + 0.699 + ], + "angle": 0, + "content": "To investigate the impact of using an image prompt as negative guidance within the self-attention modification on the generated images, we first compare images produced from prompts typically employed for negative guidance in both the original diffusion model and self-attention modification-based image-prompting methods. In this experiment, to assess the influence of prompts used for negative guidance, we generate images without applying classifier-free guidance, using negative prompts in place of positive prompts. As shown in Fig. 5, unlike images generated from negative text prompts, the negative guidance in self-attention modification models incorporates the image prompt, which guides the model away from reflecting the image prompt." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.7, + 0.896, + 0.891 + ], + "angle": 0, + "content": "In addition, during classifier-free guidance, we examine the effect of excluding the image prompt as negative guidance in the self-attention modification on incorporation of the image prompt into generated images. Specifically, we incrementally increase the guidance scale and calculate CLIP scores [12] to evaluate the alignment of the generated images with the image prompt and the ground truth text. To isolate the effect of the image prompt, a null prompt is used as the positive text prompt during image generation. As shown in Fig. 6, excluding the image prompt from negative guidance leads to a more faithful incorporation of it than including it as negative guidance. This demonstrates that providing conflict-free guidance by using the image" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "23598" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.125, + 0.273, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.12, + 0.251, + 0.255, + 0.264 + ], + "angle": 0, + "content": "(a) Original self-attention" + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.125, + 0.452, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.316, + 0.251, + 0.421, + 0.264 + ], + "angle": 0, + "content": "(b) KV replacement" + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.125, + 0.631, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.492, + 0.252, + 0.605, + 0.264 + ], + "angle": 0, + "content": "(c) KV concatenation" + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.1, + 0.895, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.712, + 0.253, + 0.827, + 0.264 + ], + "angle": 0, + "content": "(d) Stratified attention" + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.276, + 0.897, + 0.318 + ], + "angle": 0, + "content": "Figure 7. Types of attention modification techniques. (a) Original self-attention (b) KV replacement: The keys and values from the image prompts replace the original keys and values. (c) KV concatenation: The key and values from the image prompts are concatenated with the original key and values. (d) Stratified attention: The attention scores are calculated independently and summed afterward." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.343, + 0.484, + 0.388 + ], + "angle": 0, + "content": "prompt solely as a positive prompt in self-attention modification plays an important role in ensuring the generated image faithfully reflects the image prompt." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.395, + 0.283, + 0.409 + ], + "angle": 0, + "content": "4.2. Stratified Attention" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.416, + 0.484, + 0.563 + ], + "angle": 0, + "content": "To generate diverse and realistic images while reflecting the image prompt, RIVAL [22] employs Attention Fusion, selectively applying KV replacement (Fig. 7b) and KV concatenation (Fig. 7c) rather than relying solely on KV replacement. While this strategy enables the incorporation of both the generated image and the image prompt features via KV concatenation, we observe that KV concatenation tends to favor higher attention scores for the generated features over those of the image prompt (Fig. 11), which reduces alignment with the image prompt." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.564, + 0.484, + 0.664 + ], + "angle": 0, + "content": "To overcome these limitations, we propose Stratified Attention (Fig. 7d). While KV concatenation computes the attention process for both generated features and image prompt features in an integrated manner (Eq. (1)), Stratified Attention separately calculates the attention processes for each feature and then combines them through a weighted sum as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.67, + 0.482, + 0.735 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {A t t n} \\left(M _ {t} ^ {G}, M _ {t} ^ {P}, V _ {t} ^ {G}, V _ {t} ^ {P}\\right) = \\lambda_ {G} M _ {t} ^ {G} V _ {t} ^ {G} + \\lambda_ {P} M _ {t} ^ {P} V _ {t} ^ {P}, \\\\ \\text {w h e r e} M _ {t} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {t} \\left(K _ {t}\\right) ^ {\\intercal}}{\\sqrt {d}}\\right). \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.736, + 0.484, + 0.822 + ], + "angle": 0, + "content": "This separation of operations ensures a balanced attention flow between both sources. Instead of KV replacement, we use Stratified Attention with KV concatenation in Attention Fusion to consistently reflect both generated and image prompt features across all time steps, ensuring a balanced reflection of each." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.836, + 0.231, + 0.852 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.86, + 0.484, + 0.891 + ], + "angle": 0, + "content": "Evaluation Metrics We quantitatively compare our model to image-prompting approaches across four aspects." + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.341, + 0.895, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.508, + 0.895, + 0.536 + ], + "angle": 0, + "content": "Figure 8. Our method generates images that not only reflect the image prompt but also exhibit diverse structures." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.545, + 0.895, + 0.708 + ], + "angle": 0, + "content": "For image prompting, we measure the image-alignment by calculating the similarity using image encoders such as CLIP (CLIP-I) [12]. Additionally, similar to text-to-image generation, we measure text-alignment and the realism using CLIP scores (CLIP-T) and Fréchet Inception Distance (FID) [5]. However, since both CLIP scores can remain high even when the generated images closely replicate the image prompt, we also assess structural diversity between the generated images by evaluating structural distance based on the DINO self-similarity score (DINO-G) [2]. To evaluate the metrics, we generate four images for each image prompt." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.729, + 0.896, + 0.89 + ], + "angle": 0, + "content": "Baselines For our comparisons, we utilize three image-prompting models as baselines: IP-Adapter [19], SSREncoder [21] and RIVAL [22]. IP-Adapter and SSREncoder attach separate trainable adapters to the diffusion model, enabling it to reflect the image prompt in the generated images. In contrast, RIVAL is a training-free model that generates images aligned with the provided image prompt by the self-attention modification, which is frequently employed to reflect the given image. To ensure a fair comparison, we employ Stable Diffusion [13] version 1.5 for all models including ours. Also, we use the same" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "23599" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.101, + 0.446, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.168, + 0.308, + 0.177 + ], + "angle": 0, + "content": "Text Prompt: The person is young and has goatee." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.184, + 0.446, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.237, + 0.427, + 0.254 + ], + "angle": 0, + "content": "Text Prompt: This person looks attractive. This person has wavy hair, pointy nose and is wearing lipstick, heavy makeup." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.259, + 0.446, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.313, + 0.424, + 0.33 + ], + "angle": 0, + "content": "Text Prompt: This person looks smiling and has big nose. The person is wearing earrings, heavy makeup, lipstick." + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.333, + 0.443, + 0.357 + ], + "angle": 0, + "content": "(a) Image variation. Unlike ours, baselines often fail to reflect details of image prompts (e.g., color of lipstick, type of sunglasses)." + }, + { + "type": "image", + "bbox": [ + 0.458, + 0.101, + 0.895, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.456, + 0.31, + 0.895, + 0.357 + ], + "angle": 0, + "content": "(b) Cross-prompt image generation. In general, models generate images that reflect the content of the text prompt and the style or texture of the image prompt. While baseline models often fail to accurately reflect either the image or the text prompt, our method successfully integrates both prompts in a harmonious way." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.372, + 0.493, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.515, + 0.492, + 0.539 + ], + "angle": 0, + "content": "(c) Structure-guided image generation using soft edges. Baseline methods exhibit color shifts or fail to incorporate the structure of soft edges." + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.372, + 0.895, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.515, + 0.894, + 0.539 + ], + "angle": 0, + "content": "(d) Structure-guided image generation using depth. Baseline methods often fail to capture the color tones and textures of the image prompt." + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.551, + 0.894, + 0.578 + ], + "angle": 0, + "content": "Figure 9. Qualitative comparison with baselines across three tasks: (a) Image variation, (b) Cross-prompt image generation, and (c-d) Structure-guided image generation. Additional results are in the Supplementary (Suppl.)" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.587, + 0.483, + 0.618 + ], + "angle": 0, + "content": "Gaussian noise, except for RIVAL, which shuffles the inverted noised latent \\(\\mathbf{z}_T^P\\) to produce \\(\\mathbf{z}_T^G\\)." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.637, + 0.484, + 0.754 + ], + "angle": 0, + "content": "Datasets We validate our approach on various text-image pairs from three datasets, COCO 2017 [9], ImageNet-R-TI2I [16], and CelebAHQ [7]. Specifically, we utilize the validation set of COCO and randomly sample 100 images from the CelebAHQ dataset. For text prompts, we use the original captions from the COCO and the CelebAHQ dataset, while the text prompts for the ImageNet-R-TI2I dataset are generated using BLIP [8]." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.765, + 0.341, + 0.781 + ], + "angle": 0, + "content": "5.1. Comparison with Baselines" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.787, + 0.484, + 0.89 + ], + "angle": 0, + "content": "In this section, we demonstrate the effectiveness of our proposed method by conducting qualitative and quantitative comparisons of its performance against baseline models across three tasks: 1) image variation, 2) cross-prompt image generation, and 3) structure-guided image generation. Extra qualitative results, implementation details, and ablation studies are in Suppl.." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.587, + 0.895, + 0.747 + ], + "angle": 0, + "content": "Image Variation We evaluate image variation performance across three datasets using four metrics: CLIP-I, CLIP-T, DINO-G, and FID. Due to the limited number of images in the ImageNet-R-TI2I and CelebA-HQ datasets, we compute FID only for the COCO validation set. The qualitative results in Fig. 9a show that baseline models generate images that capture the semantic meaning of the image prompt (e.g., woman) but fail to incorporate finer details (e.g., makeup color tone or type of sunglasses). In contrast, our method generates images that faithfully reflect these details." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.758, + 0.895, + 0.89 + ], + "angle": 0, + "content": "Along with these results, we provide qualitative examples that highlight our model's ability to generate diverse images from a single prompt. As shown in Fig. 8, our approach consistently produces images with varied structures that remain well-aligned with the image prompt, ensuring coherent content across all outputs. In addition, we quantitatively compare our method with the baselines in Tab. 1. Our method performs competitively with the baselines in terms of text alignment, structural diversity, and image re" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "23600" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.1, + 0.895, + 0.196 + ], + "angle": 0, + "content": "
    CelebAHQImageNet-R-TI2ICOCO validation
    CLIP-I ↑CLIP-T ↑DINO-G ↑CLIP-I ↑CLIP-T ↑DINO-G ↑CLIP-I ↑CLIP-T ↑DINO-G ↑FID ↓
    IP-Adapter [19]0.8450.2640.0730.8700.3000.0920.8580.3230.08915.485
    SSR-Encoder [21]0.8500.2690.0780.8610.3060.1000.8540.3210.08715.730
    RIVAL [22]0.7390.2890.0950.8360.3170.1400.8320.3250.08914.016
    Ours0.8780.2740.0940.8830.3110.1420.8730.3260.09314.557
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.1, + 0.206, + 0.895, + 0.248 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with baseline models in image variation tasks. Our method shows competitive performance compared to baselines in structural diversity, image realism, and reflecting text prompts, while surpassing them in image prompt alignment, as measured by CLIP-I. Best and second best results are in bold and underlined." + }, + { + "type": "image", + "bbox": [ + 0.109, + 0.259, + 0.416, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.375, + 0.424, + 0.43 + ], + "angle": 0, + "content": "Figure 10. Quantitative results for cross-prompt image generation. Each dot represents a different factor for adjusting the image prompt alignment. Our approach demonstrates high similarity in both image and text." + }, + { + "type": "table", + "bbox": [ + 0.433, + 0.258, + 0.895, + 0.348 + ], + "angle": 0, + "content": "
    DepthSoft Edge
    CLIP-I ↑CLIP-T ↑DINO-C ↓CLIP-I ↑CLIP-T ↑DINO-C ↓
    IP-Adapter0.8260.3060.0530.8110.3000.044
    SSR-Encoder0.8160.3090.0570.7990.2990.052
    RIVAL0.7940.2170.0790.7930.2160.060
    Ours0.8610.3100.0660.8440.3080.052
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.431, + 0.357, + 0.897, + 0.426 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison of structure-guided image generation. Our method demonstrates competitive performance with baselines in reflecting structural conditions based on DINO-C, while excelling in the integration of both image and text prompts based on CLIP scores. Best and second best results are in bold and underlined." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.438, + 0.483, + 0.468 + ], + "angle": 0, + "content": "alism, while providing the most faithful alignment with the image prompt across multiple datasets." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.492, + 0.483, + 0.786 + ], + "angle": 0, + "content": "Cross-prompt Image Generation Since image-prompting models are fundamentally based on text-to-image diffusion models, several methods [19, 21, 22] provide functionalities to adjust the balance between text and image prompts during generation. Thus, we evaluate each model's ability to harmoniously integrate both prompts in the generated images by adjusting their hyperparameter settings and comparing the results. For this analysis, we set the text and image prompts with differing content to examine which of the two prompts (text or image) is reflected in the generated images. Given the difficulty of text prompts in defining styles such as texture, we set a content disparity between the text and image prompts for this experiment by using image-text editing pairs from the ImageNet-R-TI2I dataset. Also, we include StyleAligned [4] as an additional baseline, which generates images from cross-prompt inputs. For quantitatively comparison, we evaluate performance in terms of image and text alignment based on two CLIP scores while varying the hyperparameters." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.787, + 0.483, + 0.89 + ], + "angle": 0, + "content": "As shown in Fig. 10, our method achieves higher alignment with both prompts compared to the baselines. Also, we visually display the results that show the best performance for each model (the closest result to the top-right corner of the graph in Fig. 10). According to the visual results (Fig. 9b), models generally reflect the content of the text prompt while capturing the style, such as texture, from the" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.438, + 0.895, + 0.6 + ], + "angle": 0, + "content": "image prompt. However, this tendency varies across models. IP-Adapter and SSR-Encoder fail to adequately incorporate the image prompt, as they balance both prompts by adjusting the proportion of image prompt influence. In contrast, RIVAL and StyleAligned struggle to capture the text prompt, generating unrealistic images due to an overemphasis on the image prompt features rather than the generated features, caused by KV replacement and attention shift, respectively. Our method, however, successfully integrates both text and image prompts by balancing both features across all time steps via Stratified Attention." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.621, + 0.895, + 0.828 + ], + "angle": 0, + "content": "Structure-guided Image Generation We assess the effectiveness of our method compared to baselines in reflecting the image prompt when additional structural conditions are given. Leveraging ControlNet [20] to integrate structural conditions into generated images, we evaluate performance both quantitatively and visually under two specific conditions: soft edges and depth. For assessing structural faithfulness of the generated image, we measure the DINO similarity (DINO-C) between the structural condition and the generated image. Quantitative results reveal that our approach is competitive with baselines in terms of structural condition alignment while achieving the most faithful incorporation of both prompts (Tab. 2). Visual comparisons further support this trend (Fig. 9c and Fig. 9d)." + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.838, + 0.866, + 0.855 + ], + "angle": 0, + "content": "5.2. Effects on the Alignment of Image Prompt" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.86, + 0.895, + 0.891 + ], + "angle": 0, + "content": "By investigating the attention scores associated with the image prompts in Eq. (3), we assess the influence of the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "23601" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.103, + 0.099, + 0.482, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.216, + 0.484, + 0.311 + ], + "angle": 0, + "content": "Figure 11. Impact of conflict-free guidance (ConFG) in the self-attention modification and Stratified Attention (Strat. Attn.) on the attention score of the image prompt. A smaller difference (y-axis) indicates greater attention to the image prompt, reflecting it more faithfully in the generated images. Both conflict-free guidance and using longer time steps with Stratified Attention enhance the image prompt alignment." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.337, + 0.484, + 0.573 + ], + "angle": 0, + "content": "two primary components of our method on the alignment of the image prompt: 1) conflict-free guidance (ConFG) in Sec. 4.1 and 2) Stratified Attention (Sec. 4.2). Specifically, we compute the difference of the self-attention scores between generated image and the image prompt, where smaller differences indicate that the image prompt is effectively reflected in the generation process. We compare the differences across diffusion time steps, for KV concatenation (concat.), ConFG, and ConFG with Stratified Attention (Strat. Attn.). As shown in Fig. 11, conflict-free guidance-by excluding the image prompt as a negative prompt-significantly improves alignment with the image prompt. Additionally, extending the time steps with Stratified Attention further amplifies this effect. These findings validate our hypothesis that both techniques substantially enhance the alignment with the image prompt." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.581, + 0.435, + 0.595 + ], + "angle": 0, + "content": "5.3. Generalization Across Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.602, + 0.484, + 0.749 + ], + "angle": 0, + "content": "To validate the generalization efficacy of our proposed model, we conduct both qualitative (Fig. 12) and quantitative (Tab. 3) comparisons of its performance across various diffusion models, including Stable Diffusion [13] version 1.5, version 2.1, and Stable Diffusion XL [11]. Both comparisons demonstrate the applicability of our method across different models. Despite being training-free, our method outperforms the training-based model in reflecting image prompts while remaining competitive across other metrics (Tab. 3)." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.763, + 0.218, + 0.778 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.787, + 0.484, + 0.891 + ], + "angle": 0, + "content": "We propose a novel image-prompting method to generate images that faithfully reflect the details of user-provided image conditions. The key idea behind our approach is to eliminate the undesired role of the image prompt as a negative condition during classifier-free guidance in self-attention modification, thereby providing the model with a clearer signal through conflict-free guidance to incorporate the im" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.102, + 0.895, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.361, + 0.896, + 0.415 + ], + "angle": 0, + "content": "Figure 12. Qualitative comparison of image variation performance across three different diffusion models shows that our method generates images that faithfully reflect the image prompt, regardless of the underlying diffusion model." + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.438, + 0.895, + 0.515 + ], + "angle": 0, + "content": "
    CLIP-I↑CLIP-T↑DINO-G↑
    OursIP-AdapterOursIP-AdapterOursIP-Adapter
    SD1.50.8830.8700.3110.3000.1420.092
    SD2.10.893-0.311-0.118-
    SDXL0.8650.8590.2980.2990.1100.121
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.525, + 0.895, + 0.566 + ], + "angle": 0, + "content": "Table 3. Our method demonstrates competitive performance across various diffusion models and outperforms the training-based model [19], even without the need for training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.601, + 0.894, + 0.675 + ], + "angle": 0, + "content": "age prompt. Additionally, we introduce Stratified Attention, an alternative self-attention modification that enhances the incorporation of the image prompt by providing a balanced attention flow between the generated image and the image prompt." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.68, + 0.894, + 0.797 + ], + "angle": 0, + "content": "We show the superiority of our approach over existing image-prompting models by conducting extensive evaluations across three distinct image generation tasks: image variation, cross-prompt image generation, and structure-guided image generation. In addition to these tasks, we aim to explore the scalability and adaptability of our method to various tasks, such as story visualization and style transfer, as part of our future work." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.802, + 0.894, + 0.89 + ], + "angle": 0, + "content": "Our work also has limitations. Since this method uses a text-to-image diffusion model in a training-free manner, the quality of generated images depends on the diffusion model's performance. Consequently, issues such as poor hand generation quality persist, but we expect these to improve as diffusion models advance." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "23602" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.101, + 0.103, + 0.486, + 0.206 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2025-00555621) and Institute for Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (RS-2019-II190075, Artificial Intelligence Graduate School Program(KAIST))." + }, + { + "type": "title", + "bbox": [ + 0.104, + 0.219, + 0.196, + 0.234 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.113, + 0.244, + 0.482, + 0.297 + ], + "angle": 0, + "content": "[1] Mingdeng Cao, Xintao Wang, Zhongang Qi, Ying Shan, Xiaohu Qie, and Yinqiang Zheng. 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Our method faithfully reflects the details of image prompts (e.g., eye makeup) for diverse image generation across various tasks (Tasks A-C) in a training-free manner. In contrast, existing methods often fail to incorporate fine details of the image prompt. Even with training, IP-Adapter [19] and SSR-Encoder [21] struggle to properly represent the color and texture of the image prompt. RIVAL [22] and StyleAligned [4] also fail to generate high-fidelity images that faithfully reflect the image or text prompts due to a trade-off between the realism of the generated results and alignment with the image prompt. Extra results are in the Supplementary (Suppl.). + +![](images/def85edf03c782256d30a9b36b004437c707e90f27c503fb711cc8eacbd1ce1f.jpg) +Text + +![](images/856f92b33c58adf147bb8e50054375d0c1e922ce38b0d7de716f6d327e7f4f16.jpg) + +![](images/08e5ca0142a4f7f722bb13073776d27548831cbdf904e2032210609bf3d46ab4.jpg) + +![](images/5fb723c3c7d7ad159f4c29cb4e1bf535d25b7afb0463ed67aede3cc3390f0ad9.jpg) + +![](images/f31c40e0574f6cdd9c5a0f2a95fb23a1e81963f1b1c2e3358a09f670b38243db.jpg) + +![](images/8b2872832618961548da2fd9b554b02f98b192991002b2c46dfe1bdcd5755e41.jpg) +Task A. Image Variation + +Task B. Structure-guided Image Generation + +This person looks attractive. This person has wavy hair, pointy nose and is wearing lipstick, heavy makeup. + +![](images/92b6bd1d3bfbb795c4379cdd8ac8ce58394d954472abc2f4cdd31673f3198c10.jpg) + +![](images/e45cc839aa03128f56cecf5b236143641b2f066c1ff0ac90133be27b6254d900.jpg) + +![](images/492c10488d1ec489593b535874d9c368f3239e22aa21b120080208dcdbfa0e9e.jpg) + +![](images/8d4e3bdc8bf7b9f96fccd808921bc99635f9c39d318f916833f364cd2bcdf63f.jpg) + +![](images/786552bc13c4f4275eae8e4afcd4019d3e33580201645a6f55bb86c0c0bf77f5.jpg) + +![](images/e59958d6b9c657dc02b6e78fcc8fc5a65da49580934834893c52f03bb70cd53d.jpg) + +![](images/c468f6fe6acfe77ce0c0cbfb7ff48c915a235284624fd63e8ae51228f60f5c19.jpg) +Task C. Cross-prompt Image Generation + +![](images/3dce3f5602785af726c5cefb0aec9ffdcc32f0056b46fcfcfae1bdfffdbd7d67.jpg) + +![](images/8633b506c8e60a8e430465065c1f419542b4959998ce91afdf74a8202d714325.jpg) + +![](images/33d016428e7f58ed838130db6000e69addb0c99d43c4ba6642756ce29e6e9b60.jpg) + +![](images/67878fe3984d4d962c0ebd5af5d2388b7bbdd779ab9f9aff9e881f5fa22f3268.jpg) + +![](images/d21c179053cfa24b9abb88629070b1e1360eab1bd81ff41b8147b07cc7d9c7ba.jpg) + +![](images/312f703b889ae0c447f72bb1b0ff82a8bbd2a5208fbe7ecee26b85450f39591c.jpg) + +![](images/376cab7cde9e9fa08539ad3e3517da7306b6d5dce5164109401b2a56bffd6dd2.jpg) + +![](images/c7b193ab02035f5d6eaf74944b24e98c136dcbfb53a9dc9ab5b1623901926c7e.jpg) + +![](images/be06b38483bb27db512dc14c756b84dca39977741ddf03a335ce46bfd4a824f6.jpg) + +![](images/c13d6bcfbd37b35bf5de43c1cbf4b6c46f73d1e99caedfff32019dd43e52af6a.jpg) + +![](images/2e3abcd2cb40bd0b76645f4b40670d3d830157fb26d3e1d7cb217a10fcc7639c.jpg) + +![](images/3f36237b0cfb030a1a78f2783f13918ea2e89e3925ed8248ffdfa4f0de80265c.jpg) + +![](images/482fe1c4cbfd7362190efa49757863b125c92ad95d7e81a59111010ce09415e9.jpg) + +![](images/0b8d5da662877d04cfc0b7297b8d298472b8cab745b8c39cec5cae66520639bf.jpg) + +# Abstract + +While large-scale text-to-image diffusion models enable the generation of high-quality, diverse images from text prompts, these prompts struggle to capture intricate details, such as textures, preventing the user intent from being reflected. This limitation has led to efforts to generate images conditioned on user-provided images, referred to as image prompts. Recent work modifies the self-attention mechanism to impose image conditions in generated images by replacing or concatenating the keys and values from the image prompt. This enables the self-attention layer to work like a cross-attention layer, generally used to incorporate text prompts. In this paper, we identify two common issues in existing methods of modifying self-attention that hinder diffusion models from reflecting the image prompt. By addressing these issues, we propose a novel method that generates images that properly reflect the details of image prompts. + +First, existing approaches often neglect the importance of image prompts in classifier-free guidance, which directs the model towards the intended conditions and away from those undesirable. Specifically, current methods use image prompts as both desired and undesired conditions, causing conflicting signals. To resolve this, we propose conflict-free guidance by using image prompts only as desired conditions, ensuring that the generated image faithfully reflects the image prompt. In addition, we observe that the two most common self-attention modifications involve a trade-off between the realism of the generated image and alignment with the image prompt, achieved by selectively using keys and values from both images. Specifically, selecting more keys and values from the image prompt improves alignment, while selecting more from the generated image enhances realism. To balance both, we propose an alternative self-attention modification method, Stratified Attention, which jointly uses keys and values from both images + +rather than selecting between them. Through extensive experiments across three distinct image generation tasks, we demonstrate that the proposed method outperforms existing image-prompting models in faithfully reflecting the image prompt. + +# 1. Introduction + +The emergence of large-scale text-to-image diffusion models [11, 13] has enabled users to generate diverse images from text. However, describing complex scenes using only text prompts can be complicated, leading to ongoing efforts to incorporate user-provided image conditions to better reflect user intent [14, 17, 19, 21]. As part of these efforts, modifying the self-attention mechanism in pre-trained text-to-image diffusion models has recently attracted interest in areas such as image editing [1, 10, 16], story visualization [23], image variation [22], and style transfer [3], as a flexible method for incorporating user-provided image conditions into generated images. This modification is typically achieved by integrating the keys and values of the condition in the self-attention layer, as the keys and values derived from the image features contain rich details about images. + +Since the keys and values embody the context of images, these techniques are particularly powerful for conditioning diffusion models on image prompts, which contain the intricate details of a scene (e.g., the fine patterns of eye makeup in Fig. 1) that go beyond the level of details text descriptions can reach. Specifically, recent findings [3, 4, 22] show that replacing or concatenating the new keys and values (KV) of the generated images to those of the image prompt in the self-attention layer simulates a cross-attention with the image prompt, functioning similarly to the way text prompts affect image generation. This simulated cross-attention offers key benefits over training an additional cross-attention layer [19]: it eliminates the need for retraining with each new diffusion model and minimizes information loss from using smaller datasets for the training, as self-attention features are generated within the same model. + +However, we find that existing self-attention alterations-based approaches overlook an important aspect, which is the role of image prompts during classifier-free guidance [6]. Classifier-free guidance steers the diffusion model toward desired conditions (i.e., positive guidance) and away from undesired ones (i.e., negative guidance), enhancing the alignment between generated images and the user-provided conditions. Current approaches use image prompts to estimate both positive-guidance and negative-guidance scores, causing image prompts to influence the negative scores as well. This sends a strong signal to the model to avoid reflecting the image prompt, thereby compromising alignment between the generated image and the image prompt. The effect of this conflicting guidance is illustrated in Fig. 2, + +![](images/f7cf9aed334b61cf52f73a7adca716342f804156d259ff38d769c046b81d73c3.jpg) +Figure 2. Using the image prompt as positive guidance ensures that it is reflected in the generated images, but using it as both positive (pos.) and negative (neg.) guidance fails due to the conflicting guidance. + +where the details of the image prompt are often lost or even ignored. Based on this insight, we propose conflict-free guidance by adjusting classifier-free guidance to exclude image prompts from estimating negative-guidance scores, enabling generations that faithfully reflect the provided image prompt. + +Furthermore, we observe that two common self-attention modifications, which we call KV replacement and KV concatenation, represent a trade-off between the realism of the generated results and alignment with the image prompt. KV replacement ensures strong alignment with the image prompt but struggles to generate realistic attributes not specified in the image prompt (e.g., frontal view of a cat), as it relies solely on the keys and values from the image prompt (e.g., side view of a cat) while discarding those from the generated results. In contrast, KV concatenation, which combines keys and values from both the image prompt and the generated results, enhances realism but reduces the alignment due to attention bias arising from the queries being derived from the same features as the generated keys and values. To achieve both realism in the generated results and alignment with the image prompt, we propose Stratified Attention (Fig. 7d) as a new self-attention modification that effectively addresses this bias in KV concatenation. Specifically, we calculate the attention scores for image prompts and generated results separately, rather than computing them all at once. The scores calculated in this way are then aggregated afterward. This facilitates the image prompts to attend to relevant features while preserving the original attention flow of the generated image. + +To sum up, our key contributions are as follows: + +- We correct the classifier-free guidance in modified selfattention by using the image prompt exclusively as positive guidance, rather than as conflicting guidance, to faithfully reflect the image prompt in image generation. +- We propose Stratified Attention as a new self-attention modification to effectively reflect the image prompt by ensuring a balanced attention flow between the image prompt and the generated image. +- Through extensive experiments, our method achieves state-of-the-art performance in image prompting, both qualitatively and quantitatively. + +![](images/381d71eabc42515d06b03be280238c78824413a4d6c69be9754503eb53a74861.jpg) +Figure 3. Framework of the self-attention modification for image prompt: Image $G$ is generated from the initial noised latent $\mathbf{z}_T^G$ using the initial inverted noised latent $\mathbf{z}_T^P$ , which is obtained from the image prompt $R$ via the DDIM inversion. + +# 2. Related Work + +Self-attention Modification in diffusion models. In diffusion models, KV replacement and KV concatenation are commonly used self-attention modifications. KV replacement (Fig. 7b) is primarily employed in tasks that require strong incorporation of the given image, such as image editing [1] and style transfer [3]. Conversely, KV concatenation (Fig. 7c) is utilized to tasks that require diverse image generation while reflecting the given image, such as style-aligned image generation [4], image variation [22], and story visualization [23]. However, KV concatenation weakens alignment with the given image due to attention bias from queries sharing features with generated keys and values. To address this, StyleAligned [4] weights the image prompt's attention scores, while RIVAL [22] and StoryDiffusion [23] use KV replacement at specific time steps. Although these methods improve alignment, they sacrifice image realism by limiting the incorporation of generated features. To solve this problem, our proposed Stratified Attention separately computes attention scores for the image prompt and generated results, thereby enhancing image prompt incorporation without sacrificing generated feature integration. + +Image-prompting diffusion models. In text-to-image diffusion models, there are two distinct mechanisms to condition the generation process on an "image prompt": 1) cross-attention and 2) self-attention. Cross-attention-based approaches [18, 19, 21] integrate image prompts using auxiliary encoders or cross-attention layers, requiring additional training. However, the smaller datasets used for this training, compared to those used for diffusion models, can limit the quality of the generated images (e.g., the image variation results of IP-Adapter in Fig. 1). In contrast, self-attention-based approaches[22] incorporate the image prompt through the aforementioned self-attention alteration without training, allowing them to fully utilize the image generation capabilities of diffusion models. However, while cross-attention-based approaches direct image prompts solely to the positive branch during classifier + +![](images/8b8dc2fbb71ce5d49d46d1949573e06ef1028ffd45bd48364696ecd137191c3a.jpg) +(a) Conflicting guidance + +![](images/c6e1cb29284eecd317c81fbad75883625bd1dd8d8e16029a0d6bc50fa8c4ebe1.jpg) +(b) Conflict-free guidance (Ours) +Figure 4. Illustration of the classifier-free guidance when image prompts are (a) used and (b) omitted during the estimation of the negative guidance scores. + +free guidance, similar to text prompts, self-attention-based methods apply the same image prompt to both branches, disregarding classifier-free guidance principles. This improper use of classifier-free guidance prevents the details of the image prompt from being reflected in the generated images. In our method, we correct the classifier-free guidance in self-attention modification, enhancing the incorporation of the image prompt. + +# 3. Preliminaries + +Attention Fusion Existing studies [1, 22] that incorporate a given image into the generated output via controlling key and values in self-attention layer selectively apply different types of self-attention (Fig. 7) across time steps, employing a technique called the Attention Fusion strategy. These studies apply original self-attention or KV concatenation along with KV replacement to generate realistic images by utilizing the features of the generated image, rather than relying solely on the features of the given image, while still reflecting the given image. For image prompting, RIVAL [22] combines KV replacement and KV concatenation, referred to as "cross-image self-attention injection" in their paper. In this process, the attention process of KV concatenation is as follows: + +$$ +\operatorname {A t t n} \left(M _ {t}, V _ {t}\right) = M _ {t} \cdot \left(V _ {t} ^ {G} \oplus V _ {t} ^ {P}\right), +$$ + +$$ +\text {w h e r e} M _ {t} = \operatorname {s o f t m a x} \left(\frac {Q _ {t} ^ {G} \left(K _ {t} ^ {G} \oplus K _ {t} ^ {P}\right) ^ {T}}{\sqrt {d}}\right), \tag {1} +$$ + +$M_{t}$ and $V_{t}$ are the attention map and values, respectively, at time step $t$ . $\oplus$ indicates concatenation along the spatial dimension, and $d$ is the latent projection dimension of the key $K$ and query $Q$ . + +Self-attention-based Image Prompt. As illustrated in Fig. 3, generating images that reflect the image prompt $P$ through the self-attention modification is structured into two distinct stages: DDIM inversion [15] and image generation. In the DDIM inversion stage, we obtain the inverted noisy latent chain $\{\mathbf{z}_T^P,\dots ,\mathbf{z}_0^P\}$ from the image prompt + +![](images/70feac6712b1d8151bac068f183356eaf501af319a229c03295b78d21c25b3d2.jpg) +Text Prompt +monochrome, +bad anatomy, 13 +bad flames, cropped +worst quality" +a) Conditioned on the text prompt + +![](images/839fbca22a6414c98148f876ee618a7862f65fa878a9ebee0a024d990b49d2b2.jpg) + +![](images/11cb593753904a497707f2a671d75011f654a947c8a402a1657d7e1b877ee7b5.jpg) + +![](images/385bd8d4673f9fba70890a1fa821d2effbba6559dfddacd16a599f9e7c8dfec6.jpg) +Image Prompt +Inputs +Images generated without classifier-free guidance +Figure 5. To compare the impact of negative guidance between a) text-to-image diffusion models and b) self-attention modification-based image-prompting models, we generate images using negative prompts commonly applied in each model, without employing classifier-free guidance. Unlike negative guidance from text prompts, negative guidance from image prompts through self-attention modification incorporates the image prompt, thereby guiding the model to move away from the image prompt. + +![](images/8e7ec93a5a7b9e3f76d94cee44f66aa1c7877875d30a379d4895bf3482a4761f.jpg) +b) Conditioned on the text and image prompts + +![](images/fd9eec410dacd041bd1ab77fa8ed6f094718fcbb4fb77ab5ff10c3c8b6110976.jpg) + +![](images/04c1cdab5274975a96ed392469fb79e1bbff0e8e5b0b1242da7c857475bffa0e.jpg) + +$P$ through a deterministic DDIM inversion. The inverted noised latent $\mathbf{z}_t^P$ from this chain is provided to the model at the corresponding time step $t$ during image generation, playing a crucial role in incorporating the features of the image prompt $P$ into the generated images $G$ through the self-attention alterations. + +In the image generation stage, we create images $G$ from randomly sampled Gaussian noise $\mathbf{z}$ , conditioned on the positive text prompt $c^{+}$ , the negative text prompt $c^{-}$ , and the inverted noisy latent $\mathbf{z}_T^P$ . To transfer the color tone of the image prompt $P$ to the generated image $G$ , we apply AdaIN to the Gaussian noise $\mathbf{z}$ using the initial inverted noisy latent $\mathbf{z}_T^P$ , as utilized in StyleID [3], to derive the initial noisy latent $\mathbf{z}_T^G$ . This process is defined as follows. + +$$ +\mathbf {z} _ {T} ^ {G} = \operatorname {A d a I N} (\mathbf {z}, \mathbf {z} _ {T} ^ {P}), +$$ + +where $\operatorname{AdaIN}(x,y) = \sigma(y)\left(\frac{x - \mu(x)}{\sigma(x)}\right) + \mu(y)$ . (2) + +$\mu (\cdot)$ and $\sigma (\cdot)$ represent the mean and standard deviation computed for each channel, respectively. To utilize classifier-free guidance [6], we duplicate the noised latent $\mathbf{z}_t^G$ at each time step and provide each copy to the model along with the positive text prompt $c^{+}$ and the negative text prompt $c^{-}$ , respectively. At this stage, to incorporate the image prompt $P$ into the generated image $G$ , the model also supplies the previously obtained inverted noised latent $\mathbf{z}_t^P$ along with the noised latent $\mathbf{z}_t^G$ . + +# 4. Method + +We introduce a novel method that generates images faithfully reflecting given prompts by controlling keys and + +![](images/f7df8766e2b253c5a7d1d3fb025a7706a36eeb7dc92f75063565c7d4c412d588.jpg) +Figure 6. Employing the image prompt as both positive and negative guidance fails to effectively direct the model to reflect the image prompt due to conflicting guidance (blue line), whereas using it exclusively as positive guidance provides clearer direction by eliminating this conflict (orange line). + +values in the self-attention layers of text-to-image diffusion models without training. This section details two key components to enhance image prompt alignment: 1) conflict-free guidance (Sec. 4.1), and 2) Stratified Attention (Sec. 4.2). + +# 4.1. Conflict-free Guidance + +As shown in Fig. 2, the self-attention modification used in existing image-prompting research [22] hinders the incorporation of the image prompt in the generated images due to conflicting guidance, where the image prompt is applied as both positive and negative guidance (Fig. 4a) during classifier-free guidance. To resolve this conflict, we correct the guidance term for image prompts by using them exclusively as positive guidance (Fig. 4b), based on two analyses. + +To investigate the impact of using an image prompt as negative guidance within the self-attention modification on the generated images, we first compare images produced from prompts typically employed for negative guidance in both the original diffusion model and self-attention modification-based image-prompting methods. In this experiment, to assess the influence of prompts used for negative guidance, we generate images without applying classifier-free guidance, using negative prompts in place of positive prompts. As shown in Fig. 5, unlike images generated from negative text prompts, the negative guidance in self-attention modification models incorporates the image prompt, which guides the model away from reflecting the image prompt. + +In addition, during classifier-free guidance, we examine the effect of excluding the image prompt as negative guidance in the self-attention modification on incorporation of the image prompt into generated images. Specifically, we incrementally increase the guidance scale and calculate CLIP scores [12] to evaluate the alignment of the generated images with the image prompt and the ground truth text. To isolate the effect of the image prompt, a null prompt is used as the positive text prompt during image generation. As shown in Fig. 6, excluding the image prompt from negative guidance leads to a more faithful incorporation of it than including it as negative guidance. This demonstrates that providing conflict-free guidance by using the image + +![](images/8eb29866f68d3f35309947e7bad2ce0d5dd8521747b74efd2233ba31f1935ee1.jpg) +(a) Original self-attention + +![](images/6797394190c872926db8dcdcbb97968341e4712e7f63ed328003413a11824ae1.jpg) +(b) KV replacement + +![](images/ae336c64997608d7a0d6526f77004148e62a2dc04ae25d8fef1a35fd9aa482ec.jpg) +(c) KV concatenation + +![](images/f6b3b685ed7b6f7a77f28cbfd38ab9c669f099d88103609027c6dd86b15ccbf8.jpg) +(d) Stratified attention + +prompt solely as a positive prompt in self-attention modification plays an important role in ensuring the generated image faithfully reflects the image prompt. + +# 4.2. Stratified Attention + +To generate diverse and realistic images while reflecting the image prompt, RIVAL [22] employs Attention Fusion, selectively applying KV replacement (Fig. 7b) and KV concatenation (Fig. 7c) rather than relying solely on KV replacement. While this strategy enables the incorporation of both the generated image and the image prompt features via KV concatenation, we observe that KV concatenation tends to favor higher attention scores for the generated features over those of the image prompt (Fig. 11), which reduces alignment with the image prompt. + +To overcome these limitations, we propose Stratified Attention (Fig. 7d). While KV concatenation computes the attention process for both generated features and image prompt features in an integrated manner (Eq. (1)), Stratified Attention separately calculates the attention processes for each feature and then combines them through a weighted sum as follows: + +$$ +\begin{array}{l} \operatorname {A t t n} \left(M _ {t} ^ {G}, M _ {t} ^ {P}, V _ {t} ^ {G}, V _ {t} ^ {P}\right) = \lambda_ {G} M _ {t} ^ {G} V _ {t} ^ {G} + \lambda_ {P} M _ {t} ^ {P} V _ {t} ^ {P}, \\ \text {w h e r e} M _ {t} = \operatorname {s o f t m a x} \left(\frac {Q _ {t} \left(K _ {t}\right) ^ {\intercal}}{\sqrt {d}}\right). \tag {3} \\ \end{array} +$$ + +This separation of operations ensures a balanced attention flow between both sources. Instead of KV replacement, we use Stratified Attention with KV concatenation in Attention Fusion to consistently reflect both generated and image prompt features across all time steps, ensuring a balanced reflection of each. + +# 5. Experiments + +Evaluation Metrics We quantitatively compare our model to image-prompting approaches across four aspects. + +![](images/5c817c76cfeef61e3b1ee30623d3182e63f9b9ef0bb13cf41cc0c945f77637cd.jpg) +Figure 7. Types of attention modification techniques. (a) Original self-attention (b) KV replacement: The keys and values from the image prompts replace the original keys and values. (c) KV concatenation: The key and values from the image prompts are concatenated with the original key and values. (d) Stratified attention: The attention scores are calculated independently and summed afterward. +Figure 8. Our method generates images that not only reflect the image prompt but also exhibit diverse structures. + +For image prompting, we measure the image-alignment by calculating the similarity using image encoders such as CLIP (CLIP-I) [12]. Additionally, similar to text-to-image generation, we measure text-alignment and the realism using CLIP scores (CLIP-T) and Fréchet Inception Distance (FID) [5]. However, since both CLIP scores can remain high even when the generated images closely replicate the image prompt, we also assess structural diversity between the generated images by evaluating structural distance based on the DINO self-similarity score (DINO-G) [2]. To evaluate the metrics, we generate four images for each image prompt. + +Baselines For our comparisons, we utilize three image-prompting models as baselines: IP-Adapter [19], SSREncoder [21] and RIVAL [22]. IP-Adapter and SSREncoder attach separate trainable adapters to the diffusion model, enabling it to reflect the image prompt in the generated images. In contrast, RIVAL is a training-free model that generates images aligned with the provided image prompt by the self-attention modification, which is frequently employed to reflect the given image. To ensure a fair comparison, we employ Stable Diffusion [13] version 1.5 for all models including ours. Also, we use the same + +![](images/e06640de09446352c7da9986acd1dcac12828a27e2e1a1878875e9ce1cf5f88f.jpg) +Text Prompt: The person is young and has goatee. + +![](images/a5fba5f311588ad6d6a101fd141ebb003d80e973612528367ac15f3b021df8c2.jpg) +Text Prompt: This person looks attractive. This person has wavy hair, pointy nose and is wearing lipstick, heavy makeup. + +![](images/54f5e9748b8db278f77a0bfa85978b3cb9ddfb028f63cd7865815d51875d24ea.jpg) +Text Prompt: This person looks smiling and has big nose. The person is wearing earrings, heavy makeup, lipstick. + +![](images/9c84d7f139d05c3ba38b4b24734ff4b71db823fce761b970a4a3582b3b55c530.jpg) +(b) Cross-prompt image generation. In general, models generate images that reflect the content of the text prompt and the style or texture of the image prompt. While baseline models often fail to accurately reflect either the image or the text prompt, our method successfully integrates both prompts in a harmonious way. + +![](images/f1cea6786c362bb9febc1539e85b45f2da89351712d65f645b14ebe989f8f6bc.jpg) +(a) Image variation. Unlike ours, baselines often fail to reflect details of image prompts (e.g., color of lipstick, type of sunglasses). +(c) Structure-guided image generation using soft edges. Baseline methods exhibit color shifts or fail to incorporate the structure of soft edges. +Figure 9. Qualitative comparison with baselines across three tasks: (a) Image variation, (b) Cross-prompt image generation, and (c-d) Structure-guided image generation. Additional results are in the Supplementary (Suppl.) + +![](images/83dc19f802b7b5db092f74ba00a1b3db0cd215360855e677fe9467e6cf2055be.jpg) +(d) Structure-guided image generation using depth. Baseline methods often fail to capture the color tones and textures of the image prompt. + +Gaussian noise, except for RIVAL, which shuffles the inverted noised latent $\mathbf{z}_T^P$ to produce $\mathbf{z}_T^G$ . + +Datasets We validate our approach on various text-image pairs from three datasets, COCO 2017 [9], ImageNet-R-TI2I [16], and CelebAHQ [7]. Specifically, we utilize the validation set of COCO and randomly sample 100 images from the CelebAHQ dataset. For text prompts, we use the original captions from the COCO and the CelebAHQ dataset, while the text prompts for the ImageNet-R-TI2I dataset are generated using BLIP [8]. + +# 5.1. Comparison with Baselines + +In this section, we demonstrate the effectiveness of our proposed method by conducting qualitative and quantitative comparisons of its performance against baseline models across three tasks: 1) image variation, 2) cross-prompt image generation, and 3) structure-guided image generation. Extra qualitative results, implementation details, and ablation studies are in Suppl.. + +Image Variation We evaluate image variation performance across three datasets using four metrics: CLIP-I, CLIP-T, DINO-G, and FID. Due to the limited number of images in the ImageNet-R-TI2I and CelebA-HQ datasets, we compute FID only for the COCO validation set. The qualitative results in Fig. 9a show that baseline models generate images that capture the semantic meaning of the image prompt (e.g., woman) but fail to incorporate finer details (e.g., makeup color tone or type of sunglasses). In contrast, our method generates images that faithfully reflect these details. + +Along with these results, we provide qualitative examples that highlight our model's ability to generate diverse images from a single prompt. As shown in Fig. 8, our approach consistently produces images with varied structures that remain well-aligned with the image prompt, ensuring coherent content across all outputs. In addition, we quantitatively compare our method with the baselines in Tab. 1. Our method performs competitively with the baselines in terms of text alignment, structural diversity, and image re + +
    CelebAHQImageNet-R-TI2ICOCO validation
    CLIP-I ↑CLIP-T ↑DINO-G ↑CLIP-I ↑CLIP-T ↑DINO-G ↑CLIP-I ↑CLIP-T ↑DINO-G ↑FID ↓
    IP-Adapter [19]0.8450.2640.0730.8700.3000.0920.8580.3230.08915.485
    SSR-Encoder [21]0.8500.2690.0780.8610.3060.1000.8540.3210.08715.730
    RIVAL [22]0.7390.2890.0950.8360.3170.1400.8320.3250.08914.016
    Ours0.8780.2740.0940.8830.3110.1420.8730.3260.09314.557
    + +![](images/c8e64408dbebfa48c04980c1cfbb0a445a966c2a4fd9daa6886831abe318fb32.jpg) +Figure 10. Quantitative results for cross-prompt image generation. Each dot represents a different factor for adjusting the image prompt alignment. Our approach demonstrates high similarity in both image and text. + +Table 1. Quantitative comparison with baseline models in image variation tasks. Our method shows competitive performance compared to baselines in structural diversity, image realism, and reflecting text prompts, while surpassing them in image prompt alignment, as measured by CLIP-I. Best and second best results are in bold and underlined. + +
    DepthSoft Edge
    CLIP-I ↑CLIP-T ↑DINO-C ↓CLIP-I ↑CLIP-T ↑DINO-C ↓
    IP-Adapter0.8260.3060.0530.8110.3000.044
    SSR-Encoder0.8160.3090.0570.7990.2990.052
    RIVAL0.7940.2170.0790.7930.2160.060
    Ours0.8610.3100.0660.8440.3080.052
    + +Table 2. Quantitative comparison of structure-guided image generation. Our method demonstrates competitive performance with baselines in reflecting structural conditions based on DINO-C, while excelling in the integration of both image and text prompts based on CLIP scores. Best and second best results are in bold and underlined. + +alism, while providing the most faithful alignment with the image prompt across multiple datasets. + +Cross-prompt Image Generation Since image-prompting models are fundamentally based on text-to-image diffusion models, several methods [19, 21, 22] provide functionalities to adjust the balance between text and image prompts during generation. Thus, we evaluate each model's ability to harmoniously integrate both prompts in the generated images by adjusting their hyperparameter settings and comparing the results. For this analysis, we set the text and image prompts with differing content to examine which of the two prompts (text or image) is reflected in the generated images. Given the difficulty of text prompts in defining styles such as texture, we set a content disparity between the text and image prompts for this experiment by using image-text editing pairs from the ImageNet-R-TI2I dataset. Also, we include StyleAligned [4] as an additional baseline, which generates images from cross-prompt inputs. For quantitatively comparison, we evaluate performance in terms of image and text alignment based on two CLIP scores while varying the hyperparameters. + +As shown in Fig. 10, our method achieves higher alignment with both prompts compared to the baselines. Also, we visually display the results that show the best performance for each model (the closest result to the top-right corner of the graph in Fig. 10). According to the visual results (Fig. 9b), models generally reflect the content of the text prompt while capturing the style, such as texture, from the + +image prompt. However, this tendency varies across models. IP-Adapter and SSR-Encoder fail to adequately incorporate the image prompt, as they balance both prompts by adjusting the proportion of image prompt influence. In contrast, RIVAL and StyleAligned struggle to capture the text prompt, generating unrealistic images due to an overemphasis on the image prompt features rather than the generated features, caused by KV replacement and attention shift, respectively. Our method, however, successfully integrates both text and image prompts by balancing both features across all time steps via Stratified Attention. + +Structure-guided Image Generation We assess the effectiveness of our method compared to baselines in reflecting the image prompt when additional structural conditions are given. Leveraging ControlNet [20] to integrate structural conditions into generated images, we evaluate performance both quantitatively and visually under two specific conditions: soft edges and depth. For assessing structural faithfulness of the generated image, we measure the DINO similarity (DINO-C) between the structural condition and the generated image. Quantitative results reveal that our approach is competitive with baselines in terms of structural condition alignment while achieving the most faithful incorporation of both prompts (Tab. 2). Visual comparisons further support this trend (Fig. 9c and Fig. 9d). + +# 5.2. Effects on the Alignment of Image Prompt + +By investigating the attention scores associated with the image prompts in Eq. (3), we assess the influence of the + +![](images/e9f60098a076d73d625d2052448b00d85aa1485b45d62cfafe60e21994f67ba9.jpg) +Figure 11. Impact of conflict-free guidance (ConFG) in the self-attention modification and Stratified Attention (Strat. Attn.) on the attention score of the image prompt. A smaller difference (y-axis) indicates greater attention to the image prompt, reflecting it more faithfully in the generated images. Both conflict-free guidance and using longer time steps with Stratified Attention enhance the image prompt alignment. + +two primary components of our method on the alignment of the image prompt: 1) conflict-free guidance (ConFG) in Sec. 4.1 and 2) Stratified Attention (Sec. 4.2). Specifically, we compute the difference of the self-attention scores between generated image and the image prompt, where smaller differences indicate that the image prompt is effectively reflected in the generation process. We compare the differences across diffusion time steps, for KV concatenation (concat.), ConFG, and ConFG with Stratified Attention (Strat. Attn.). As shown in Fig. 11, conflict-free guidance-by excluding the image prompt as a negative prompt-significantly improves alignment with the image prompt. Additionally, extending the time steps with Stratified Attention further amplifies this effect. These findings validate our hypothesis that both techniques substantially enhance the alignment with the image prompt. + +# 5.3. Generalization Across Diffusion Models + +To validate the generalization efficacy of our proposed model, we conduct both qualitative (Fig. 12) and quantitative (Tab. 3) comparisons of its performance across various diffusion models, including Stable Diffusion [13] version 1.5, version 2.1, and Stable Diffusion XL [11]. Both comparisons demonstrate the applicability of our method across different models. Despite being training-free, our method outperforms the training-based model in reflecting image prompts while remaining competitive across other metrics (Tab. 3). + +# 6. Conclusion + +We propose a novel image-prompting method to generate images that faithfully reflect the details of user-provided image conditions. The key idea behind our approach is to eliminate the undesired role of the image prompt as a negative condition during classifier-free guidance in self-attention modification, thereby providing the model with a clearer signal through conflict-free guidance to incorporate the im + +![](images/974ea268fd9771ba0461e3a681e556c8f8f128213730ba30b84bb14de143948f.jpg) +Figure 12. Qualitative comparison of image variation performance across three different diffusion models shows that our method generates images that faithfully reflect the image prompt, regardless of the underlying diffusion model. + +
    CLIP-I↑CLIP-T↑DINO-G↑
    OursIP-AdapterOursIP-AdapterOursIP-Adapter
    SD1.50.8830.8700.3110.3000.1420.092
    SD2.10.893-0.311-0.118-
    SDXL0.8650.8590.2980.2990.1100.121
    + +Table 3. Our method demonstrates competitive performance across various diffusion models and outperforms the training-based model [19], even without the need for training. + +age prompt. Additionally, we introduce Stratified Attention, an alternative self-attention modification that enhances the incorporation of the image prompt by providing a balanced attention flow between the generated image and the image prompt. + +We show the superiority of our approach over existing image-prompting models by conducting extensive evaluations across three distinct image generation tasks: image variation, cross-prompt image generation, and structure-guided image generation. In addition to these tasks, we aim to explore the scalability and adaptability of our method to various tasks, such as story visualization and style transfer, as part of our future work. + +Our work also has limitations. Since this method uses a text-to-image diffusion model in a training-free manner, the quality of generated images depends on the diffusion model's performance. Consequently, issues such as poor hand generation quality persist, but we expect these to improve as diffusion models advance. + +Acknowledgement This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2025-00555621) and Institute for Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (RS-2019-II190075, Artificial Intelligence Graduate School Program(KAIST)). + +# References + +[1] Mingdeng Cao, Xintao Wang, Zhongang Qi, Ying Shan, Xiaohu Qie, and Yinqiang Zheng. Masactrl: Tuning-free mutual self-attention control for consistent image synthesis and editing. 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+ 706 + ], + "type": "text", + "content": "While large-scale text-to-image diffusion models enable the generation of high-quality, diverse images from text prompts, these prompts struggle to capture intricate details, such as textures, preventing the user intent from being reflected. This limitation has led to efforts to generate images conditioned on user-provided images, referred to as image prompts. Recent work modifies the self-attention mechanism to impose image conditions in generated images by replacing or concatenating the keys and values from the image prompt. This enables the self-attention layer to work like a cross-attention layer, generally used to incorporate text prompts. In this paper, we identify two common issues in existing methods of modifying self-attention that hinder diffusion models from reflecting the image prompt. By addressing these issues, we propose a novel method that generates images that properly reflect the details of image prompts." + } + ] + } + ], + "index": 69 + }, + { + "bbox": [ + 313, + 495, + 548, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 548, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 548, + 704 + ], + "type": "text", + "content": "First, existing approaches often neglect the importance of image prompts in classifier-free guidance, which directs the model towards the intended conditions and away from those undesirable. Specifically, current methods use image prompts as both desired and undesired conditions, causing conflicting signals. To resolve this, we propose conflict-free guidance by using image prompts only as desired conditions, ensuring that the generated image faithfully reflects the image prompt. In addition, we observe that the two most common self-attention modifications involve a trade-off between the realism of the generated image and alignment with the image prompt, achieved by selectively using keys and values from both images. Specifically, selecting more keys and values from the image prompt improves alignment, while selecting more from the generated image enhances realism. To balance both, we propose an alternative self-attention modification method, Stratified Attention, which jointly uses keys and values from both images" + } + ] + } + ], + "index": 70 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 71, + 13, + 116, + 44 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 13, + 116, + 44 + ], + "spans": [ + { + "bbox": [ + 71, + 13, + 116, + 44 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 149, + 11, + 491, + 23 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 11, + 491, + 23 + ], + "spans": [ + { + "bbox": [ + 149, + 11, + 491, + 23 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 201, + 24, + 438, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 201, + 24, + 438, + 34 + ], + "spans": [ + { + "bbox": [ + 201, + 24, + 438, + 34 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 182, + 35, + 457, + 45 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 35, + 457, + 45 + ], + "spans": [ + { + "bbox": [ + 182, + 35, + 457, + 45 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23595" + } + ] + } + ], + "index": 71 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 61, + 81, + 297, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 81, + 297, + 140 + ], + "spans": [ + { + "bbox": [ + 61, + 81, + 297, + 140 + ], + "type": "text", + "content": "rather than selecting between them. Through extensive experiments across three distinct image generation tasks, we demonstrate that the proposed method outperforms existing image-prompting models in faithfully reflecting the image prompt." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 63, + 161, + 141, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 161, + 141, + 174 + ], + "spans": [ + { + "bbox": [ + 63, + 161, + 141, + 174 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 181, + 296, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 181, + 296, + 355 + ], + "spans": [ + { + "bbox": [ + 61, + 181, + 296, + 355 + ], + "type": "text", + "content": "The emergence of large-scale text-to-image diffusion models [11, 13] has enabled users to generate diverse images from text. However, describing complex scenes using only text prompts can be complicated, leading to ongoing efforts to incorporate user-provided image conditions to better reflect user intent [14, 17, 19, 21]. As part of these efforts, modifying the self-attention mechanism in pre-trained text-to-image diffusion models has recently attracted interest in areas such as image editing [1, 10, 16], story visualization [23], image variation [22], and style transfer [3], as a flexible method for incorporating user-provided image conditions into generated images. This modification is typically achieved by integrating the keys and values of the condition in the self-attention layer, as the keys and values derived from the image features contain rich details about images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 356, + 296, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 356, + 296, + 540 + ], + "spans": [ + { + "bbox": [ + 61, + 356, + 296, + 540 + ], + "type": "text", + "content": "Since the keys and values embody the context of images, these techniques are particularly powerful for conditioning diffusion models on image prompts, which contain the intricate details of a scene (e.g., the fine patterns of eye makeup in Fig. 1) that go beyond the level of details text descriptions can reach. Specifically, recent findings [3, 4, 22] show that replacing or concatenating the new keys and values (KV) of the generated images to those of the image prompt in the self-attention layer simulates a cross-attention with the image prompt, functioning similarly to the way text prompts affect image generation. This simulated cross-attention offers key benefits over training an additional cross-attention layer [19]: it eliminates the need for retraining with each new diffusion model and minimizes information loss from using smaller datasets for the training, as self-attention features are generated within the same model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 542, + 296, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 542, + 296, + 706 + ], + "spans": [ + { + "bbox": [ + 61, + 542, + 296, + 706 + ], + "type": "text", + "content": "However, we find that existing self-attention alterations-based approaches overlook an important aspect, which is the role of image prompts during classifier-free guidance [6]. Classifier-free guidance steers the diffusion model toward desired conditions (i.e., positive guidance) and away from undesired ones (i.e., negative guidance), enhancing the alignment between generated images and the user-provided conditions. Current approaches use image prompts to estimate both positive-guidance and negative-guidance scores, causing image prompts to influence the negative scores as well. This sends a strong signal to the model to avoid reflecting the image prompt, thereby compromising alignment between the generated image and the image prompt. The effect of this conflicting guidance is illustrated in Fig. 2," + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 315, + 81, + 548, + 155 + ], + "blocks": [ + { + "bbox": [ + 315, + 81, + 548, + 155 + ], + "lines": [ + { + "bbox": [ + 315, + 81, + 548, + 155 + ], + "spans": [ + { + "bbox": [ + 315, + 81, + 548, + 155 + ], + "type": "image", + "image_path": "f7cf9aed334b61cf52f73a7adca716342f804156d259ff38d769c046b81d73c3.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 161, + 548, + 205 + ], + "lines": [ + { + "bbox": [ + 313, + 161, + 548, + 205 + ], + "spans": [ + { + "bbox": [ + 313, + 161, + 548, + 205 + ], + "type": "text", + "content": "Figure 2. Using the image prompt as positive guidance ensures that it is reflected in the generated images, but using it as both positive (pos.) and negative (neg.) guidance fails due to the conflicting guidance." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 212, + 547, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 212, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 313, + 212, + 547, + 282 + ], + "type": "text", + "content": "where the details of the image prompt are often lost or even ignored. Based on this insight, we propose conflict-free guidance by adjusting classifier-free guidance to exclude image prompts from estimating negative-guidance scores, enabling generations that faithfully reflect the provided image prompt." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 283, + 548, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 283, + 548, + 561 + ], + "spans": [ + { + "bbox": [ + 313, + 283, + 548, + 561 + ], + "type": "text", + "content": "Furthermore, we observe that two common self-attention modifications, which we call KV replacement and KV concatenation, represent a trade-off between the realism of the generated results and alignment with the image prompt. KV replacement ensures strong alignment with the image prompt but struggles to generate realistic attributes not specified in the image prompt (e.g., frontal view of a cat), as it relies solely on the keys and values from the image prompt (e.g., side view of a cat) while discarding those from the generated results. In contrast, KV concatenation, which combines keys and values from both the image prompt and the generated results, enhances realism but reduces the alignment due to attention bias arising from the queries being derived from the same features as the generated keys and values. To achieve both realism in the generated results and alignment with the image prompt, we propose Stratified Attention (Fig. 7d) as a new self-attention modification that effectively addresses this bias in KV concatenation. Specifically, we calculate the attention scores for image prompts and generated results separately, rather than computing them all at once. The scores calculated in this way are then aggregated afterward. This facilitates the image prompts to attend to relevant features while preserving the original attention flow of the generated image." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 324, + 563, + 515, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 563, + 515, + 574 + ], + "spans": [ + { + "bbox": [ + 324, + 563, + 515, + 574 + ], + "type": "text", + "content": "To sum up, our key contributions are as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 574, + 547, + 703 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 313, + 574, + 547, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 547, + 620 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 547, + 620 + ], + "type": "text", + "content": "- We correct the classifier-free guidance in modified selfattention by using the image prompt exclusively as positive guidance, rather than as conflicting guidance, to faithfully reflect the image prompt in image generation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 621, + 547, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 621, + 547, + 667 + ], + "spans": [ + { + "bbox": [ + 313, + 621, + 547, + 667 + ], + "type": "text", + "content": "- We propose Stratified Attention as a new self-attention modification to effectively reflect the image prompt by ensuring a balanced attention flow between the image prompt and the generated image." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 668, + 547, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 668, + 547, + 703 + ], + "spans": [ + { + "bbox": [ + 313, + 668, + 547, + 703 + ], + "type": "text", + "content": "- Through extensive experiments, our method achieves state-of-the-art performance in image prompting, both qualitatively and quantitatively." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23596" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 79, + 294, + 175 + ], + "blocks": [ + { + "bbox": [ + 63, + 79, + 294, + 175 + ], + "lines": [ + { + "bbox": [ + 63, + 79, + 294, + 175 + ], + "spans": [ + { + "bbox": [ + 63, + 79, + 294, + 175 + ], + "type": "image", + "image_path": "381d71eabc42515d06b03be280238c78824413a4d6c69be9754503eb53a74861.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "lines": [ + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "spans": [ + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "text", + "content": "Figure 3. Framework of the self-attention modification for image prompt: Image " + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "text", + "content": " is generated from the initial noised latent " + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T^G" + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "text", + "content": " using the initial inverted noised latent " + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T^P" + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "text", + "content": ", which is obtained from the image prompt " + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 61, + 185, + 296, + 228 + ], + "type": "text", + "content": " via the DDIM inversion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 62, + 239, + 147, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 239, + 147, + 251 + ], + "spans": [ + { + "bbox": [ + 62, + 239, + 147, + 251 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 259, + 296, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 259, + 296, + 504 + ], + "spans": [ + { + "bbox": [ + 61, + 259, + 296, + 504 + ], + "type": "text", + "content": "Self-attention Modification in diffusion models. In diffusion models, KV replacement and KV concatenation are commonly used self-attention modifications. KV replacement (Fig. 7b) is primarily employed in tasks that require strong incorporation of the given image, such as image editing [1] and style transfer [3]. Conversely, KV concatenation (Fig. 7c) is utilized to tasks that require diverse image generation while reflecting the given image, such as style-aligned image generation [4], image variation [22], and story visualization [23]. However, KV concatenation weakens alignment with the given image due to attention bias from queries sharing features with generated keys and values. To address this, StyleAligned [4] weights the image prompt's attention scores, while RIVAL [22] and StoryDiffusion [23] use KV replacement at specific time steps. Although these methods improve alignment, they sacrifice image realism by limiting the incorporation of generated features. To solve this problem, our proposed Stratified Attention separately computes attention scores for the image prompt and generated results, thereby enhancing image prompt incorporation without sacrificing generated feature integration." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 518, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 518, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 61, + 518, + 296, + 705 + ], + "type": "text", + "content": "Image-prompting diffusion models. In text-to-image diffusion models, there are two distinct mechanisms to condition the generation process on an \"image prompt\": 1) cross-attention and 2) self-attention. Cross-attention-based approaches [18, 19, 21] integrate image prompts using auxiliary encoders or cross-attention layers, requiring additional training. However, the smaller datasets used for this training, compared to those used for diffusion models, can limit the quality of the generated images (e.g., the image variation results of IP-Adapter in Fig. 1). In contrast, self-attention-based approaches[22] incorporate the image prompt through the aforementioned self-attention alteration without training, allowing them to fully utilize the image generation capabilities of diffusion models. However, while cross-attention-based approaches direct image prompts solely to the positive branch during classifier" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 317, + 79, + 426, + 175 + ], + "blocks": [ + { + "bbox": [ + 317, + 79, + 426, + 175 + ], + "lines": [ + { + "bbox": [ + 317, + 79, + 426, + 175 + ], + "spans": [ + { + "bbox": [ + 317, + 79, + 426, + 175 + ], + "type": "image", + "image_path": "8b8dc2fbb71ce5d49d46d1949573e06ef1028ffd45bd48364696ecd137191c3a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 177, + 409, + 186 + ], + "lines": [ + { + "bbox": [ + 331, + 177, + 409, + 186 + ], + "spans": [ + { + "bbox": [ + 331, + 177, + 409, + 186 + ], + "type": "text", + "content": "(a) Conflicting guidance" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 437, + 79, + 547, + 175 + ], + "blocks": [ + { + "bbox": [ + 437, + 79, + 547, + 175 + ], + "lines": [ + { + "bbox": [ + 437, + 79, + 547, + 175 + ], + "spans": [ + { + "bbox": [ + 437, + 79, + 547, + 175 + ], + "type": "image", + "image_path": "c6e1cb29284eecd317c81fbad75883625bd1dd8d8e16029a0d6bc50fa8c4ebe1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 177, + 544, + 186 + ], + "lines": [ + { + "bbox": [ + 440, + 177, + 544, + 186 + ], + "spans": [ + { + "bbox": [ + 440, + 177, + 544, + 186 + ], + "type": "text", + "content": "(b) Conflict-free guidance (Ours)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 196, + 547, + 228 + ], + "lines": [ + { + "bbox": [ + 313, + 196, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 196, + 547, + 228 + ], + "type": "text", + "content": "Figure 4. Illustration of the classifier-free guidance when image prompts are (a) used and (b) omitted during the estimation of the negative guidance scores." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 234, + 548, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 234, + 548, + 327 + ], + "spans": [ + { + "bbox": [ + 313, + 234, + 548, + 327 + ], + "type": "text", + "content": "free guidance, similar to text prompts, self-attention-based methods apply the same image prompt to both branches, disregarding classifier-free guidance principles. This improper use of classifier-free guidance prevents the details of the image prompt from being reflected in the generated images. In our method, we correct the classifier-free guidance in self-attention modification, enhancing the incorporation of the image prompt." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 337, + 397, + 349 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 337, + 397, + 349 + ], + "spans": [ + { + "bbox": [ + 313, + 337, + 397, + 349 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 357, + 548, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 548, + 518 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 548, + 518 + ], + "type": "text", + "content": "Attention Fusion Existing studies [1, 22] that incorporate a given image into the generated output via controlling key and values in self-attention layer selectively apply different types of self-attention (Fig. 7) across time steps, employing a technique called the Attention Fusion strategy. These studies apply original self-attention or KV concatenation along with KV replacement to generate realistic images by utilizing the features of the generated image, rather than relying solely on the features of the given image, while still reflecting the given image. For image prompting, RIVAL [22] combines KV replacement and KV concatenation, referred to as \"cross-image self-attention injection\" in their paper. In this process, the attention process of KV concatenation is as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 345, + 525, + 484, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 525, + 484, + 539 + ], + "spans": [ + { + "bbox": [ + 345, + 525, + 484, + 539 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t n} \\left(M _ {t}, V _ {t}\\right) = M _ {t} \\cdot \\left(V _ {t} ^ {G} \\oplus V _ {t} ^ {P}\\right),", + "image_path": "8827035c930d05ddb422fe8069b8674fd06c00aaad59d51d5e837a2cdaef61bc.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 345, + 540, + 547, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 540, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 345, + 540, + 547, + 567 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} M _ {t} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {t} ^ {G} \\left(K _ {t} ^ {G} \\oplus K _ {t} ^ {P}\\right) ^ {T}}{\\sqrt {d}}\\right), \\tag {1}", + "image_path": "c8fb7dae28eb64b74acf011b55e39f014ecba8ab8ef7ceb4f61c447d2469e4de.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "text", + "content": " are the attention map and values, respectively, at time step " + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "text", + "content": " indicates concatenation along the spatial dimension, and " + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "text", + "content": " is the latent projection dimension of the key " + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "text", + "content": " and query " + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 313, + 574, + 548, + 621 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 634, + 548, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 634, + 548, + 706 + ], + "spans": [ + { + "bbox": [ + 313, + 634, + 548, + 706 + ], + "type": "text", + "content": "Self-attention-based Image Prompt. As illustrated in Fig. 3, generating images that reflect the image prompt " + }, + { + "bbox": [ + 313, + 634, + 548, + 706 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 634, + 548, + 706 + ], + "type": "text", + "content": " through the self-attention modification is structured into two distinct stages: DDIM inversion [15] and image generation. In the DDIM inversion stage, we obtain the inverted noisy latent chain " + }, + { + "bbox": [ + 313, + 634, + 548, + 706 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_T^P,\\dots ,\\mathbf{z}_0^P\\}" + }, + { + "bbox": [ + 313, + 634, + 548, + 706 + ], + "type": "text", + "content": " from the image prompt" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23597" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 128, + 91, + 181, + 146 + ], + "blocks": [ + { + "bbox": [ + 71, + 82, + 112, + 91 + ], + "lines": [ + { + "bbox": [ + 71, + 82, + 112, + 91 + ], + "spans": [ + { + "bbox": [ + 71, + 82, + 112, + 91 + ], + "type": "text", + "content": "Text Prompt" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 70, + 100, + 112, + 110 + ], + "lines": [ + { + "bbox": [ + 70, + 100, + 112, + 110 + ], + "spans": [ + { + "bbox": [ + 70, + 100, + 112, + 110 + ], + "type": "text", + "content": "monochrome," + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 71, + 110, + 112, + 119 + ], + "lines": [ + { + "bbox": [ + 71, + 110, + 112, + 119 + ], + "spans": [ + { + "bbox": [ + 71, + 110, + 112, + 119 + ], + "type": "text", + "content": "bad anatomy, 13" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 71, + 121, + 110, + 129 + ], + "lines": [ + { + "bbox": [ + 71, + 121, + 110, + 129 + ], + "spans": [ + { + "bbox": [ + 71, + 121, + 110, + 129 + ], + "type": "text", + "content": "bad flames, cropped" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + 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116, + 218, + 289, + 225 + ], + "type": "text", + "content": "Images generated without classifier-free guidance" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 236, + 296, + 322 + ], + "lines": [ + { + "bbox": [ + 61, + 236, + 296, + 322 + ], + "spans": [ + { + "bbox": [ + 61, + 236, + 296, + 322 + ], + "type": "text", + "content": "Figure 5. To compare the impact of negative guidance between a) text-to-image diffusion models and b) self-attention modification-based image-prompting models, we generate images using negative prompts commonly applied in each model, without employing classifier-free guidance. Unlike negative guidance from text prompts, negative guidance from image prompts through self-attention modification incorporates the image prompt, thereby guiding the model to move away from the image prompt." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 128, + 162, + 182, + 217 + ], + "blocks": [ + { + "bbox": [ + 129, + 154, + 267, + 162 + ], + "lines": [ + { + "bbox": [ + 129, + 154, + 267, + 162 + ], + "spans": [ + { + "bbox": [ + 129, + 154, + 267, + 162 + ], + "type": "text", + "content": "b) Conditioned on the text and image prompts" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 128, + 162, + 182, + 217 + ], + "lines": [ + { + "bbox": [ + 128, + 162, + 182, + 217 + ], + "spans": [ + { + "bbox": [ + 128, + 162, + 182, + 217 + ], + "type": "image", + "image_path": "8e7ec93a5a7b9e3f76d94cee44f66aa1c7877875d30a379d4895bf3482a4761f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 182, + 162, + 239, + 217 + ], + "blocks": [ + { + "bbox": [ + 182, + 162, + 239, + 217 + ], + "lines": [ + { + "bbox": [ + 182, + 162, + 239, + 217 + ], + "spans": [ + { + "bbox": [ + 182, + 162, + 239, + 217 + ], + "type": "image", + "image_path": "fd9eec410dacd041bd1ab77fa8ed6f094718fcbb4fb77ab5ff10c3c8b6110976.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 239, + 162, + 294, + 217 + ], + "blocks": [ + { + "bbox": [ + 239, + 162, + 294, + 217 + ], + "lines": [ + { + "bbox": [ + 239, + 162, + 294, + 217 + ], + "spans": [ + { + "bbox": [ + 239, + 162, + 294, + 217 + ], + "type": "image", + "image_path": "04c1cdab5274975a96ed392469fb79e1bbff0e8e5b0b1242da7c857475bffa0e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "spans": [ + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "text", + "content": " through a deterministic DDIM inversion. The inverted noised latent " + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t^P" + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "text", + "content": " from this chain is provided to the model at the corresponding time step " + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "text", + "content": " during image generation, playing a crucial role in incorporating the features of the image prompt " + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "text", + "content": " into the generated images " + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 61, + 327, + 296, + 396 + ], + "type": "text", + "content": " through the self-attention alterations." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "spans": [ + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": "In the image generation stage, we create images " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": " from randomly sampled Gaussian noise " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": ", conditioned on the positive text prompt " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "c^{+}" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": ", the negative text prompt " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "c^{-}" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": ", and the inverted noisy latent " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T^P" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": ". To transfer the color tone of the image prompt " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": " to the generated image " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": ", we apply AdaIN to the Gaussian noise " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": " using the initial inverted noisy latent " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T^P" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": ", as utilized in StyleID [3], to derive the initial noisy latent " + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T^G" + }, + { + "bbox": [ + 61, + 397, + 296, + 491 + ], + "type": "text", + "content": ". This process is defined as follows." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 138, + 498, + 221, + 513 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 498, + 221, + 513 + ], + "spans": [ + { + "bbox": [ + 138, + 498, + 221, + 513 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {T} ^ {G} = \\operatorname {A d a I N} (\\mathbf {z}, \\mathbf {z} _ {T} ^ {P}),", + "image_path": "b2651c9199c8c44f3caf57ef18224f10a30cc569bf5c3a4b419cf2d0ac7fff67.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 75, + 514, + 295, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 514, + 295, + 540 + ], + "spans": [ + { + "bbox": [ + 75, + 514, + 295, + 540 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 75, + 514, + 295, + 540 + ], + "type": "inline_equation", + "content": "\\operatorname{AdaIN}(x,y) = \\sigma(y)\\left(\\frac{x - \\mu(x)}{\\sigma(x)}\\right) + \\mu(y)" + }, + { + "bbox": [ + 75, + 514, + 295, + 540 + ], + "type": "text", + "content": ". (2)" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "spans": [ + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "\\mu (\\cdot)" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": " represent the mean and standard deviation computed for each channel, respectively. To utilize classifier-free guidance [6], we duplicate the noised latent " + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t^G" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": " at each time step and provide each copy to the model along with the positive text prompt " + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "c^{+}" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": " and the negative text prompt " + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "c^{-}" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": ", respectively. At this stage, to incorporate the image prompt " + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": " into the generated image " + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": ", the model also supplies the previously obtained inverted noised latent " + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t^P" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": " along with the noised latent " + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t^G" + }, + { + "bbox": [ + 61, + 547, + 296, + 652 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 62, + 662, + 116, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 662, + 116, + 673 + ], + "spans": [ + { + "bbox": [ + 62, + 662, + 116, + 673 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 61, + 681, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 681, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 61, + 681, + 296, + 705 + ], + "type": "text", + "content": "We introduce a novel method that generates images faithfully reflecting given prompts by controlling keys and" + } + ] + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 315, + 79, + 547, + 144 + ], + "blocks": [ + { + "bbox": [ + 315, + 79, + 547, + 144 + ], + "lines": [ + { + "bbox": [ + 315, + 79, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 315, + 79, + 547, + 144 + ], + "type": "image", + "image_path": "f7df8766e2b253c5a7d1d3fb025a7706a36eeb7dc92f75063565c7d4c412d588.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 153, + 547, + 207 + ], + "lines": [ + { + "bbox": [ + 313, + 153, + 547, + 207 + ], + "spans": [ + { + "bbox": [ + 313, + 153, + 547, + 207 + ], + "type": "text", + "content": "Figure 6. Employing the image prompt as both positive and negative guidance fails to effectively direct the model to reflect the image prompt due to conflicting guidance (blue line), whereas using it exclusively as positive guidance provides clearer direction by eliminating this conflict (orange line)." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 214, + 547, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 214, + 547, + 272 + ], + "spans": [ + { + "bbox": [ + 313, + 214, + 547, + 272 + ], + "type": "text", + "content": "values in the self-attention layers of text-to-image diffusion models without training. This section details two key components to enhance image prompt alignment: 1) conflict-free guidance (Sec. 4.1), and 2) Stratified Attention (Sec. 4.2)." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 280, + 440, + 291 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 280, + 440, + 291 + ], + "spans": [ + { + "bbox": [ + 313, + 280, + 440, + 291 + ], + "type": "text", + "content": "4.1. Conflict-free Guidance" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 297, + 547, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 297, + 547, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 297, + 547, + 390 + ], + "type": "text", + "content": "As shown in Fig. 2, the self-attention modification used in existing image-prompting research [22] hinders the incorporation of the image prompt in the generated images due to conflicting guidance, where the image prompt is applied as both positive and negative guidance (Fig. 4a) during classifier-free guidance. To resolve this conflict, we correct the guidance term for image prompts by using them exclusively as positive guidance (Fig. 4b), based on two analyses." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 391, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 547, + 553 + ], + "type": "text", + "content": "To investigate the impact of using an image prompt as negative guidance within the self-attention modification on the generated images, we first compare images produced from prompts typically employed for negative guidance in both the original diffusion model and self-attention modification-based image-prompting methods. In this experiment, to assess the influence of prompts used for negative guidance, we generate images without applying classifier-free guidance, using negative prompts in place of positive prompts. As shown in Fig. 5, unlike images generated from negative text prompts, the negative guidance in self-attention modification models incorporates the image prompt, which guides the model away from reflecting the image prompt." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 554, + 548, + 705 + ], + "type": "text", + "content": "In addition, during classifier-free guidance, we examine the effect of excluding the image prompt as negative guidance in the self-attention modification on incorporation of the image prompt into generated images. Specifically, we incrementally increase the guidance scale and calculate CLIP scores [12] to evaluate the alignment of the generated images with the image prompt and the ground truth text. To isolate the effect of the image prompt, a null prompt is used as the positive text prompt during image generation. As shown in Fig. 6, excluding the image prompt from negative guidance leads to a more faithful incorporation of it than including it as negative guidance. This demonstrates that providing conflict-free guidance by using the image" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23598" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 99, + 167, + 169 + ], + "blocks": [ + { + "bbox": [ + 63, + 99, + 167, + 169 + ], + "lines": [ + { + "bbox": [ + 63, + 99, + 167, + 169 + ], + "spans": [ + { + "bbox": [ + 63, + 99, + 167, + 169 + ], + "type": "image", + "image_path": "8eb29866f68d3f35309947e7bad2ce0d5dd8521747b74efd2233ba31f1935ee1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 73, + 198, + 156, + 209 + ], + "lines": [ + { + "bbox": [ + 73, + 198, + 156, + 209 + ], + "spans": [ + { + "bbox": [ + 73, + 198, + 156, + 209 + ], + "type": "text", + "content": "(a) Original self-attention" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 99, + 276, + 187 + ], + "blocks": [ + { + "bbox": [ + 173, + 99, + 276, + 187 + ], + "lines": [ + { + "bbox": [ + 173, + 99, + 276, + 187 + ], + "spans": [ + { + "bbox": [ + 173, + 99, + 276, + 187 + ], + "type": "image", + "image_path": "6797394190c872926db8dcdcbb97968341e4712e7f63ed328003413a11824ae1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 193, + 198, + 257, + 209 + ], + "lines": [ + { + "bbox": [ + 193, + 198, + 257, + 209 + ], + "spans": [ + { + "bbox": [ + 193, + 198, + 257, + 209 + ], + "type": "text", + "content": "(b) KV replacement" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 283, + 99, + 386, + 198 + ], + "blocks": [ + { + "bbox": [ + 283, + 99, + 386, + 198 + ], + "lines": [ + { + "bbox": [ + 283, + 99, + 386, + 198 + ], + "spans": [ + { + "bbox": [ + 283, + 99, + 386, + 198 + ], + "type": "image", + "image_path": "ae336c64997608d7a0d6526f77004148e62a2dc04ae25d8fef1a35fd9aa482ec.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 301, + 199, + 370, + 209 + ], + "lines": [ + { + "bbox": [ + 301, + 199, + 370, + 209 + ], + "spans": [ + { + "bbox": [ + 301, + 199, + 370, + 209 + ], + "type": "text", + "content": "(c) KV concatenation" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 394, + 79, + 547, + 198 + ], + "blocks": [ + { + "bbox": [ + 394, + 79, + 547, + 198 + ], + "lines": [ + { + "bbox": [ + 394, + 79, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 394, + 79, + 547, + 198 + ], + "type": "image", + "image_path": "f6b3b685ed7b6f7a77f28cbfd38ab9c669f099d88103609027c6dd86b15ccbf8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 200, + 506, + 209 + ], + "lines": [ + { + "bbox": [ + 435, + 200, + 506, + 209 + ], + "spans": [ + { + "bbox": [ + 435, + 200, + 506, + 209 + ], + "type": "text", + "content": "(d) Stratified attention" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 271, + 296, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 271, + 296, + 307 + ], + "spans": [ + { + "bbox": [ + 61, + 271, + 296, + 307 + ], + "type": "text", + "content": "prompt solely as a positive prompt in self-attention modification plays an important role in ensuring the generated image faithfully reflects the image prompt." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 62, + 312, + 173, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 312, + 173, + 323 + ], + "spans": [ + { + "bbox": [ + 62, + 312, + 173, + 323 + ], + "type": "text", + "content": "4.2. Stratified Attention" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 61, + 329, + 296, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 329, + 296, + 445 + ], + "spans": [ + { + "bbox": [ + 61, + 329, + 296, + 445 + ], + "type": "text", + "content": "To generate diverse and realistic images while reflecting the image prompt, RIVAL [22] employs Attention Fusion, selectively applying KV replacement (Fig. 7b) and KV concatenation (Fig. 7c) rather than relying solely on KV replacement. While this strategy enables the incorporation of both the generated image and the image prompt features via KV concatenation, we observe that KV concatenation tends to favor higher attention scores for the generated features over those of the image prompt (Fig. 11), which reduces alignment with the image prompt." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 61, + 446, + 296, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 446, + 296, + 525 + ], + "spans": [ + { + "bbox": [ + 61, + 446, + 296, + 525 + ], + "type": "text", + "content": "To overcome these limitations, we propose Stratified Attention (Fig. 7d). While KV concatenation computes the attention process for both generated features and image prompt features in an integrated manner (Eq. (1)), Stratified Attention separately calculates the attention processes for each feature and then combines them through a weighted sum as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 71, + 530, + 294, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 530, + 294, + 582 + ], + "spans": [ + { + "bbox": [ + 71, + 530, + 294, + 582 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {A t t n} \\left(M _ {t} ^ {G}, M _ {t} ^ {P}, V _ {t} ^ {G}, V _ {t} ^ {P}\\right) = \\lambda_ {G} M _ {t} ^ {G} V _ {t} ^ {G} + \\lambda_ {P} M _ {t} ^ {P} V _ {t} ^ {P}, \\\\ \\text {w h e r e} M _ {t} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {t} \\left(K _ {t}\\right) ^ {\\intercal}}{\\sqrt {d}}\\right). \\tag {3} \\\\ \\end{array}", + "image_path": "f073113c5d07f721a59d5b7c5ee9937da1280a179fc0ea8a6e379da634ef4c10.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 61, + 582, + 296, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 582, + 296, + 651 + ], + "spans": [ + { + "bbox": [ + 61, + 582, + 296, + 651 + ], + "type": "text", + "content": "This separation of operations ensures a balanced attention flow between both sources. Instead of KV replacement, we use Stratified Attention with KV concatenation in Attention Fusion to consistently reflect both generated and image prompt features across all time steps, ensuring a balanced reflection of each." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 62, + 662, + 141, + 674 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 662, + 141, + 674 + ], + "spans": [ + { + "bbox": [ + 62, + 662, + 141, + 674 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 61, + 681, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 681, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 61, + 681, + 296, + 705 + ], + "type": "text", + "content": "Evaluation Metrics We quantitatively compare our model to image-prompting approaches across four aspects." + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 315, + 270, + 547, + 395 + ], + "blocks": [ + { + "bbox": [ + 61, + 218, + 548, + 251 + ], + "lines": [ + { + "bbox": [ + 61, + 218, + 548, + 251 + ], + "spans": [ + { + "bbox": [ + 61, + 218, + 548, + 251 + ], + "type": "text", + "content": "Figure 7. Types of attention modification techniques. (a) Original self-attention (b) KV replacement: The keys and values from the image prompts replace the original keys and values. (c) KV concatenation: The key and values from the image prompts are concatenated with the original key and values. (d) Stratified attention: The attention scores are calculated independently and summed afterward." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 315, + 270, + 547, + 395 + ], + "lines": [ + { + "bbox": [ + 315, + 270, + 547, + 395 + ], + "spans": [ + { + "bbox": [ + 315, + 270, + 547, + 395 + ], + "type": "image", + "image_path": "5c817c76cfeef61e3b1ee30623d3182e63f9b9ef0bb13cf41cc0c945f77637cd.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 402, + 547, + 424 + ], + "lines": [ + { + "bbox": [ + 313, + 402, + 547, + 424 + ], + "spans": [ + { + "bbox": [ + 313, + 402, + 547, + 424 + ], + "type": "text", + "content": "Figure 8. Our method generates images that not only reflect the image prompt but also exhibit diverse structures." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 312, + 431, + 547, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 431, + 547, + 560 + ], + "spans": [ + { + "bbox": [ + 312, + 431, + 547, + 560 + ], + "type": "text", + "content": "For image prompting, we measure the image-alignment by calculating the similarity using image encoders such as CLIP (CLIP-I) [12]. Additionally, similar to text-to-image generation, we measure text-alignment and the realism using CLIP scores (CLIP-T) and Fréchet Inception Distance (FID) [5]. However, since both CLIP scores can remain high even when the generated images closely replicate the image prompt, we also assess structural diversity between the generated images by evaluating structural distance based on the DINO self-similarity score (DINO-G) [2]. To evaluate the metrics, we generate four images for each image prompt." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 577, + 548, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 577, + 548, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 577, + 548, + 704 + ], + "type": "text", + "content": "Baselines For our comparisons, we utilize three image-prompting models as baselines: IP-Adapter [19], SSREncoder [21] and RIVAL [22]. IP-Adapter and SSREncoder attach separate trainable adapters to the diffusion model, enabling it to reflect the image prompt in the generated images. In contrast, RIVAL is a training-free model that generates images aligned with the provided image prompt by the self-attention modification, which is frequently employed to reflect the given image. To ensure a fair comparison, we employ Stable Diffusion [13] version 1.5 for all models including ours. Also, we use the same" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23599" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 79, + 272, + 131 + ], + "blocks": [ + { + "bbox": [ + 63, + 79, + 272, + 131 + ], + "lines": [ + { + "bbox": [ + 63, + 79, + 272, + 131 + ], + "spans": [ + { + "bbox": [ + 63, + 79, + 272, + 131 + ], + "type": "image", + "image_path": "e06640de09446352c7da9986acd1dcac12828a27e2e1a1878875e9ce1cf5f88f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 133, + 188, + 140 + ], + "lines": [ + { + "bbox": [ + 65, + 133, + 188, + 140 + ], + "spans": [ + { + "bbox": [ + 65, + 133, + 188, + 140 + ], + "type": "text", + "content": "Text Prompt: The person is young and has goatee." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 63, + 145, + 272, + 186 + ], + "blocks": [ + { + "bbox": [ + 63, + 145, + 272, + 186 + ], + "lines": [ + { + "bbox": [ + 63, + 145, + 272, + 186 + ], + "spans": [ + { + "bbox": [ + 63, + 145, + 272, + 186 + ], + "type": "image", + "image_path": "a5fba5f311588ad6d6a101fd141ebb003d80e973612528367ac15f3b021df8c2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 187, + 261, + 201 + ], + "lines": [ + { + "bbox": [ + 66, + 187, + 261, + 201 + ], + "spans": [ + { + "bbox": [ + 66, + 187, + 261, + 201 + ], + "type": "text", + "content": "Text Prompt: This person looks attractive. This person has wavy hair, pointy nose and is wearing lipstick, heavy makeup." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 63, + 205, + 272, + 246 + ], + "blocks": [ + { + "bbox": [ + 63, + 205, + 272, + 246 + ], + "lines": [ + { + "bbox": [ + 63, + 205, + 272, + 246 + ], + "spans": [ + { + "bbox": [ + 63, + 205, + 272, + 246 + ], + "type": "image", + "image_path": "54f5e9748b8db278f77a0bfa85978b3cb9ddfb028f63cd7865815d51875d24ea.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 247, + 259, + 261 + ], + "lines": [ + { + "bbox": [ + 65, + 247, + 259, + 261 + ], + "spans": [ + { + "bbox": [ + 65, + 247, + 259, + 261 + ], + "type": "text", + "content": "Text Prompt: This person looks smiling and has big nose. The person is wearing earrings, heavy makeup, lipstick." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 280, + 79, + 547, + 243 + ], + "blocks": [ + { + "bbox": [ + 280, + 79, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 280, + 79, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 280, + 79, + 547, + 243 + ], + "type": "image", + "image_path": "9c84d7f139d05c3ba38b4b24734ff4b71db823fce761b970a4a3582b3b55c530.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 279, + 245, + 547, + 282 + ], + "lines": [ + { + "bbox": [ + 279, + 245, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 279, + 245, + 547, + 282 + ], + "type": "text", + "content": "(b) Cross-prompt image generation. In general, models generate images that reflect the content of the text prompt and the style or texture of the image prompt. While baseline models often fail to accurately reflect either the image or the text prompt, our method successfully integrates both prompts in a harmonious way." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 63, + 294, + 301, + 407 + ], + "blocks": [ + { + "bbox": [ + 62, + 263, + 271, + 282 + ], + "lines": [ + { + "bbox": [ + 62, + 263, + 271, + 282 + ], + "spans": [ + { + "bbox": [ + 62, + 263, + 271, + 282 + ], + "type": "text", + "content": "(a) Image variation. Unlike ours, baselines often fail to reflect details of image prompts (e.g., color of lipstick, type of sunglasses)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 63, + 294, + 301, + 407 + ], + "lines": [ + { + "bbox": [ + 63, + 294, + 301, + 407 + ], + "spans": [ + { + "bbox": [ + 63, + 294, + 301, + 407 + ], + "type": "image", + "image_path": "f1cea6786c362bb9febc1539e85b45f2da89351712d65f645b14ebe989f8f6bc.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 62, + 407, + 301, + 426 + ], + "lines": [ + { + "bbox": [ + 62, + 407, + 301, + 426 + ], + "spans": [ + { + "bbox": [ + 62, + 407, + 301, + 426 + ], + "type": "text", + "content": "(c) Structure-guided image generation using soft edges. Baseline methods exhibit color shifts or fail to incorporate the structure of soft edges." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 436, + 547, + 457 + ], + "lines": [ + { + "bbox": [ + 61, + 436, + 547, + 457 + ], + "spans": [ + { + "bbox": [ + 61, + 436, + 547, + 457 + ], + "type": "text", + "content": "Figure 9. Qualitative comparison with baselines across three tasks: (a) Image variation, (b) Cross-prompt image generation, and (c-d) Structure-guided image generation. Additional results are in the Supplementary (Suppl.)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 294, + 547, + 406 + ], + "blocks": [ + { + "bbox": [ + 309, + 294, + 547, + 406 + ], + "lines": [ + { + "bbox": [ + 309, + 294, + 547, + 406 + ], + "spans": [ + { + "bbox": [ + 309, + 294, + 547, + 406 + ], + "type": "image", + "image_path": "83dc19f802b7b5db092f74ba00a1b3db0cd215360855e677fe9467e6cf2055be.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 308, + 407, + 547, + 426 + ], + "lines": [ + { + "bbox": [ + 308, + 407, + 547, + 426 + ], + "spans": [ + { + "bbox": [ + 308, + 407, + 547, + 426 + ], + "type": "text", + "content": "(d) Structure-guided image generation using depth. Baseline methods often fail to capture the color tones and textures of the image prompt." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 61, + 464, + 295, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 464, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 61, + 464, + 295, + 489 + ], + "type": "text", + "content": "Gaussian noise, except for RIVAL, which shuffles the inverted noised latent " + }, + { + "bbox": [ + 61, + 464, + 295, + 489 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T^P" + }, + { + "bbox": [ + 61, + 464, + 295, + 489 + ], + "type": "text", + "content": " to produce " + }, + { + "bbox": [ + 61, + 464, + 295, + 489 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T^G" + }, + { + "bbox": [ + 61, + 464, + 295, + 489 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 61, + 504, + 296, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 504, + 296, + 597 + ], + "spans": [ + { + "bbox": [ + 61, + 504, + 296, + 597 + ], + "type": "text", + "content": "Datasets We validate our approach on various text-image pairs from three datasets, COCO 2017 [9], ImageNet-R-TI2I [16], and CelebAHQ [7]. Specifically, we utilize the validation set of COCO and randomly sample 100 images from the CelebAHQ dataset. For text prompts, we use the original captions from the COCO and the CelebAHQ dataset, while the text prompts for the ImageNet-R-TI2I dataset are generated using BLIP [8]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 62, + 605, + 208, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 605, + 208, + 618 + ], + "spans": [ + { + "bbox": [ + 62, + 605, + 208, + 618 + ], + "type": "text", + "content": "5.1. Comparison with Baselines" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 61, + 623, + 296, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 623, + 296, + 704 + ], + "spans": [ + { + "bbox": [ + 61, + 623, + 296, + 704 + ], + "type": "text", + "content": "In this section, we demonstrate the effectiveness of our proposed method by conducting qualitative and quantitative comparisons of its performance against baseline models across three tasks: 1) image variation, 2) cross-prompt image generation, and 3) structure-guided image generation. Extra qualitative results, implementation details, and ablation studies are in Suppl.." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 464, + 547, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 547, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 547, + 591 + ], + "type": "text", + "content": "Image Variation We evaluate image variation performance across three datasets using four metrics: CLIP-I, CLIP-T, DINO-G, and FID. Due to the limited number of images in the ImageNet-R-TI2I and CelebA-HQ datasets, we compute FID only for the COCO validation set. The qualitative results in Fig. 9a show that baseline models generate images that capture the semantic meaning of the image prompt (e.g., woman) but fail to incorporate finer details (e.g., makeup color tone or type of sunglasses). In contrast, our method generates images that faithfully reflect these details." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 312, + 600, + 547, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 600, + 547, + 704 + ], + "spans": [ + { + "bbox": [ + 312, + 600, + 547, + 704 + ], + "type": "text", + "content": "Along with these results, we provide qualitative examples that highlight our model's ability to generate diverse images from a single prompt. As shown in Fig. 8, our approach consistently produces images with varied structures that remain well-aligned with the image prompt, ensuring coherent content across all outputs. In addition, we quantitatively compare our method with the baselines in Tab. 1. Our method performs competitively with the baselines in terms of text alignment, structural diversity, and image re" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23600" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 79, + 547, + 155 + ], + "blocks": [ + { + "bbox": [ + 62, + 79, + 547, + 155 + ], + "lines": [ + { + "bbox": [ + 62, + 79, + 547, + 155 + ], + "spans": [ + { + "bbox": [ + 62, + 79, + 547, + 155 + ], + "type": "table", + "html": "
    CelebAHQImageNet-R-TI2ICOCO validation
    CLIP-I ↑CLIP-T ↑DINO-G ↑CLIP-I ↑CLIP-T ↑DINO-G ↑CLIP-I ↑CLIP-T ↑DINO-G ↑FID ↓
    IP-Adapter [19]0.8450.2640.0730.8700.3000.0920.8580.3230.08915.485
    SSR-Encoder [21]0.8500.2690.0780.8610.3060.1000.8540.3210.08715.730
    RIVAL [22]0.7390.2890.0950.8360.3170.1400.8320.3250.08914.016
    Ours0.8780.2740.0940.8830.3110.1420.8730.3260.09314.557
    ", + "image_path": "c1de449859544e5f18ac9cf0e02dbc9420164dd5f5dafa7a9a248f2ce881188a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 66, + 205, + 254, + 293 + ], + "blocks": [ + { + "bbox": [ + 66, + 205, + 254, + 293 + ], + "lines": [ + { + "bbox": [ + 66, + 205, + 254, + 293 + ], + "spans": [ + { + "bbox": [ + 66, + 205, + 254, + 293 + ], + "type": "image", + "image_path": "c8e64408dbebfa48c04980c1cfbb0a445a966c2a4fd9daa6886831abe318fb32.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 297, + 259, + 340 + ], + "lines": [ + { + "bbox": [ + 61, + 297, + 259, + 340 + ], + "spans": [ + { + "bbox": [ + 61, + 297, + 259, + 340 + ], + "type": "text", + "content": "Figure 10. Quantitative results for cross-prompt image generation. Each dot represents a different factor for adjusting the image prompt alignment. Our approach demonstrates high similarity in both image and text." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 264, + 204, + 547, + 275 + ], + "blocks": [ + { + "bbox": [ + 61, + 163, + 547, + 196 + ], + "lines": [ + { + "bbox": [ + 61, + 163, + 547, + 196 + ], + "spans": [ + { + "bbox": [ + 61, + 163, + 547, + 196 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with baseline models in image variation tasks. Our method shows competitive performance compared to baselines in structural diversity, image realism, and reflecting text prompts, while surpassing them in image prompt alignment, as measured by CLIP-I. Best and second best results are in bold and underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 264, + 204, + 547, + 275 + ], + "lines": [ + { + "bbox": [ + 264, + 204, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 264, + 204, + 547, + 275 + ], + "type": "table", + "html": "
    DepthSoft Edge
    CLIP-I ↑CLIP-T ↑DINO-C ↓CLIP-I ↑CLIP-T ↑DINO-C ↓
    IP-Adapter0.8260.3060.0530.8110.3000.044
    SSR-Encoder0.8160.3090.0570.7990.2990.052
    RIVAL0.7940.2170.0790.7930.2160.060
    Ours0.8610.3100.0660.8440.3080.052
    ", + "image_path": "daaefe8a291278fff4c0e9113cea56fa82e66df878a4e41f007d2f82b525f2ff.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 263, + 282, + 548, + 337 + ], + "lines": [ + { + "bbox": [ + 263, + 282, + 548, + 337 + ], + "spans": [ + { + "bbox": [ + 263, + 282, + 548, + 337 + ], + "type": "text", + "content": "Table 2. Quantitative comparison of structure-guided image generation. Our method demonstrates competitive performance with baselines in reflecting structural conditions based on DINO-C, while excelling in the integration of both image and text prompts based on CLIP scores. Best and second best results are in bold and underlined." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 61, + 346, + 295, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 346, + 295, + 370 + ], + "spans": [ + { + "bbox": [ + 61, + 346, + 295, + 370 + ], + "type": "text", + "content": "alism, while providing the most faithful alignment with the image prompt across multiple datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 389, + 295, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 389, + 295, + 622 + ], + "spans": [ + { + "bbox": [ + 61, + 389, + 295, + 622 + ], + "type": "text", + "content": "Cross-prompt Image Generation Since image-prompting models are fundamentally based on text-to-image diffusion models, several methods [19, 21, 22] provide functionalities to adjust the balance between text and image prompts during generation. Thus, we evaluate each model's ability to harmoniously integrate both prompts in the generated images by adjusting their hyperparameter settings and comparing the results. For this analysis, we set the text and image prompts with differing content to examine which of the two prompts (text or image) is reflected in the generated images. Given the difficulty of text prompts in defining styles such as texture, we set a content disparity between the text and image prompts for this experiment by using image-text editing pairs from the ImageNet-R-TI2I dataset. Also, we include StyleAligned [4] as an additional baseline, which generates images from cross-prompt inputs. For quantitatively comparison, we evaluate performance in terms of image and text alignment based on two CLIP scores while varying the hyperparameters." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 623, + 295, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 623, + 295, + 704 + ], + "spans": [ + { + "bbox": [ + 61, + 623, + 295, + 704 + ], + "type": "text", + "content": "As shown in Fig. 10, our method achieves higher alignment with both prompts compared to the baselines. Also, we visually display the results that show the best performance for each model (the closest result to the top-right corner of the graph in Fig. 10). According to the visual results (Fig. 9b), models generally reflect the content of the text prompt while capturing the style, such as texture, from the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 346, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 346, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 312, + 346, + 547, + 475 + ], + "type": "text", + "content": "image prompt. However, this tendency varies across models. IP-Adapter and SSR-Encoder fail to adequately incorporate the image prompt, as they balance both prompts by adjusting the proportion of image prompt influence. In contrast, RIVAL and StyleAligned struggle to capture the text prompt, generating unrealistic images due to an overemphasis on the image prompt features rather than the generated features, caused by KV replacement and attention shift, respectively. Our method, however, successfully integrates both text and image prompts by balancing both features across all time steps via Stratified Attention." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 491, + 547, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 491, + 547, + 655 + ], + "spans": [ + { + "bbox": [ + 312, + 491, + 547, + 655 + ], + "type": "text", + "content": "Structure-guided Image Generation We assess the effectiveness of our method compared to baselines in reflecting the image prompt when additional structural conditions are given. Leveraging ControlNet [20] to integrate structural conditions into generated images, we evaluate performance both quantitatively and visually under two specific conditions: soft edges and depth. For assessing structural faithfulness of the generated image, we measure the DINO similarity (DINO-C) between the structural condition and the generated image. Quantitative results reveal that our approach is competitive with baselines in terms of structural condition alignment while achieving the most faithful incorporation of both prompts (Tab. 2). Visual comparisons further support this trend (Fig. 9c and Fig. 9d)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 663, + 529, + 677 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 663, + 529, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 663, + 529, + 677 + ], + "type": "text", + "content": "5.2. Effects on the Alignment of Image Prompt" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 681, + 547, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 681, + 547, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 681, + 547, + 705 + ], + "type": "text", + "content": "By investigating the attention scores associated with the image prompts in Eq. (3), we assess the influence of the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23601" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 78, + 294, + 163 + ], + "blocks": [ + { + "bbox": [ + 63, + 78, + 294, + 163 + ], + "lines": [ + { + "bbox": [ + 63, + 78, + 294, + 163 + ], + "spans": [ + { + "bbox": [ + 63, + 78, + 294, + 163 + ], + "type": "image", + "image_path": "e9f60098a076d73d625d2052448b00d85aa1485b45d62cfafe60e21994f67ba9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 171, + 296, + 246 + ], + "lines": [ + { + "bbox": [ + 61, + 171, + 296, + 246 + ], + "spans": [ + { + "bbox": [ + 61, + 171, + 296, + 246 + ], + "type": "text", + "content": "Figure 11. Impact of conflict-free guidance (ConFG) in the self-attention modification and Stratified Attention (Strat. Attn.) on the attention score of the image prompt. A smaller difference (y-axis) indicates greater attention to the image prompt, reflecting it more faithfully in the generated images. Both conflict-free guidance and using longer time steps with Stratified Attention enhance the image prompt alignment." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 266, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 266, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 61, + 266, + 296, + 453 + ], + "type": "text", + "content": "two primary components of our method on the alignment of the image prompt: 1) conflict-free guidance (ConFG) in Sec. 4.1 and 2) Stratified Attention (Sec. 4.2). Specifically, we compute the difference of the self-attention scores between generated image and the image prompt, where smaller differences indicate that the image prompt is effectively reflected in the generation process. We compare the differences across diffusion time steps, for KV concatenation (concat.), ConFG, and ConFG with Stratified Attention (Strat. Attn.). As shown in Fig. 11, conflict-free guidance-by excluding the image prompt as a negative prompt-significantly improves alignment with the image prompt. Additionally, extending the time steps with Stratified Attention further amplifies this effect. These findings validate our hypothesis that both techniques substantially enhance the alignment with the image prompt." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 460, + 266, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 460, + 266, + 471 + ], + "spans": [ + { + "bbox": [ + 62, + 460, + 266, + 471 + ], + "type": "text", + "content": "5.3. Generalization Across Diffusion Models" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 476, + 296, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 476, + 296, + 593 + ], + "spans": [ + { + "bbox": [ + 61, + 476, + 296, + 593 + ], + "type": "text", + "content": "To validate the generalization efficacy of our proposed model, we conduct both qualitative (Fig. 12) and quantitative (Tab. 3) comparisons of its performance across various diffusion models, including Stable Diffusion [13] version 1.5, version 2.1, and Stable Diffusion XL [11]. Both comparisons demonstrate the applicability of our method across different models. Despite being training-free, our method outperforms the training-based model in reflecting image prompts while remaining competitive across other metrics (Tab. 3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 604, + 133, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 604, + 133, + 616 + ], + "spans": [ + { + "bbox": [ + 62, + 604, + 133, + 616 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 623, + 296, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 623, + 296, + 705 + ], + "spans": [ + { + "bbox": [ + 61, + 623, + 296, + 705 + ], + "type": "text", + "content": "We propose a novel image-prompting method to generate images that faithfully reflect the details of user-provided image conditions. The key idea behind our approach is to eliminate the undesired role of the image prompt as a negative condition during classifier-free guidance in self-attention modification, thereby providing the model with a clearer signal through conflict-free guidance to incorporate the im" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 315, + 80, + 547, + 278 + ], + "blocks": [ + { + "bbox": [ + 315, + 80, + 547, + 278 + ], + "lines": [ + { + "bbox": [ + 315, + 80, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 315, + 80, + 547, + 278 + ], + "type": "image", + "image_path": "974ea268fd9771ba0461e3a681e556c8f8f128213730ba30b84bb14de143948f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 285, + 548, + 328 + ], + "lines": [ + { + "bbox": [ + 313, + 285, + 548, + 328 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 548, + 328 + ], + "type": "text", + "content": "Figure 12. Qualitative comparison of image variation performance across three different diffusion models shows that our method generates images that faithfully reflect the image prompt, regardless of the underlying diffusion model." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 314, + 346, + 547, + 407 + ], + "blocks": [ + { + "bbox": [ + 314, + 346, + 547, + 407 + ], + "lines": [ + { + "bbox": [ + 314, + 346, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 314, + 346, + 547, + 407 + ], + "type": "table", + "html": "
    CLIP-I↑CLIP-T↑DINO-G↑
    OursIP-AdapterOursIP-AdapterOursIP-Adapter
    SD1.50.8830.8700.3110.3000.1420.092
    SD2.10.893-0.311-0.118-
    SDXL0.8650.8590.2980.2990.1100.121
    ", + "image_path": "080fe70c0f35f480ff614edb0f947fd1d54dc6e8637ec574bc9970b77b30abbd.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 415, + 547, + 448 + ], + "lines": [ + { + "bbox": [ + 313, + 415, + 547, + 448 + ], + "spans": [ + { + "bbox": [ + 313, + 415, + 547, + 448 + ], + "type": "text", + "content": "Table 3. Our method demonstrates competitive performance across various diffusion models and outperforms the training-based model [19], even without the need for training." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 475, + 547, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 547, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 547, + 534 + ], + "type": "text", + "content": "age prompt. Additionally, we introduce Stratified Attention, an alternative self-attention modification that enhances the incorporation of the image prompt by providing a balanced attention flow between the generated image and the image prompt." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 538, + 547, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 538, + 547, + 631 + ], + "spans": [ + { + "bbox": [ + 313, + 538, + 547, + 631 + ], + "type": "text", + "content": "We show the superiority of our approach over existing image-prompting models by conducting extensive evaluations across three distinct image generation tasks: image variation, cross-prompt image generation, and structure-guided image generation. In addition to these tasks, we aim to explore the scalability and adaptability of our method to various tasks, such as story visualization and style transfer, as part of our future work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 635, + 547, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 547, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 547, + 704 + ], + "type": "text", + "content": "Our work also has limitations. Since this method uses a text-to-image diffusion model in a training-free manner, the quality of generated images depends on the diffusion model's performance. Consequently, issues such as poor hand generation quality persist, but we expect these to improve as diffusion models advance." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23602" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 61, + 81, + 297, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 81, + 297, + 163 + ], + "spans": [ + { + "bbox": [ + 61, + 81, + 297, + 163 + ], + "type": "text", + "content": "Acknowledgement This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2025-00555621) and Institute for Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (RS-2019-II190075, Artificial Intelligence Graduate School Program(KAIST))." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 63, + 173, + 119, + 185 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 173, + 119, + 185 + ], + "spans": [ + { + "bbox": [ + 63, + 173, + 119, + 185 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 64, + 193, + 294, + 704 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 69, + 193, + 294, + 235 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 193, + 294, + 235 + ], + "spans": [ + { + "bbox": [ + 69, + 193, + 294, + 235 + ], + "type": "text", + "content": "[1] Mingdeng Cao, Xintao Wang, Zhongang Qi, Ying Shan, Xiaohu Qie, and Yinqiang Zheng. 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Storydiffusion: Consistent self-attention for long-range image and video generation. arXiv preprint arXiv:2405.01434, 2024. 2, 3" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "23603" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Devils in Middle Layers of Large Vision-Language Models_ Interpreting, Detecting and Mitigating Object Hallucinations via Attention Lens/c159f2ec-9cd0-43d8-97ae-a644ae3c367b_content_list.json b/2025/Devils in Middle Layers of Large Vision-Language Models_ Interpreting, Detecting and Mitigating Object Hallucinations via Attention Lens/c159f2ec-9cd0-43d8-97ae-a644ae3c367b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..23a7423b4a841f509e70cd2e9c508e9fd9d08ad1 --- /dev/null +++ b/2025/Devils in Middle Layers of Large Vision-Language Models_ Interpreting, Detecting and Mitigating Object Hallucinations via Attention Lens/c159f2ec-9cd0-43d8-97ae-a644ae3c367b_content_list.json @@ -0,0 +1,1584 @@ +[ + { + "type": "text", + "text": "Devils in Middle Layers of Large Vision-Language Models: Interpreting, Detecting and Mitigating Object Hallucinations via Attention Lens", + "text_level": 1, + "bbox": [ + 132, + 130, + 866, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhangqi Jiang $^{1}$ Junkai Chen $^{2,3}$ Beier Zhu $^{4}$ Tingjin Luo $^{1*}$ Yankun Shen $^{2,3}$ Xu Yang $^{2,3*}$ $^{1}$ National University of Defense Technology $^{2}$ Southeast University \n $^{3}$ Key Laboratory of New Generation Artificial Intelligence Technology & Its Interdisciplinary Applications (Southeast University), Ministry of Education \n $^{4}$ Nanyang Technological University", + "bbox": [ + 120, + 202, + 883, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{sxdxjzq, junkai.chen.0917}@gmail.com beier.zhu@ntu.edu.sg tingjinluo@hotmail.com {220242353, xuyang_palm}@seu.edu.cn", + "bbox": [ + 125, + 294, + 872, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 361, + 326, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hallucinations in Large Vision-Language Models (LVLMs) significantly undermine their reliability, motivating researchers to explore the causes of hallucination. However, most studies primarily focus on the language aspect rather than the visual. In this paper, we address how LVLMs process visual information and whether this process causes hallucination. Firstly, we use the attention lens to identify the stages at which LVLMs handle visual data, discovering that the middle layers are crucial. Moreover, we find that these layers can be further divided into two stages: \"visual information enrichment\" and \"semantic refinement\" which respectively propagate visual data to object tokens and interpret it through text. By analyzing attention patterns during the visual information enrichment stage, we find that real tokens consistently receive higher attention weights than hallucinated ones, serving as a strong indicator of hallucination. Further examination of multi-head attention maps reveals that hallucination tokens often result from heads interacting with inconsistent objects. Based on these insights, we propose a simple inference-time method that adjusts visual attention by integrating information across various heads. Extensive experiments demonstrate that this approach effectively mitigates hallucinations in mainstream LVLMs without additional training costs. $^{1}$", + "bbox": [ + 89, + 393, + 485, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 782, + 223, + 799 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Building on the foundations of Large Language Models (LLMs), Large Vision-Language Models (LVLMs) [4, 27, 32, 44, 49, 51, 54] have emerged as powerful tools for un", + "bbox": [ + 89, + 809, + 483, + 854 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/685fedd56bbbba1270aefe0e957e77abfea9f6c1ad15736229b932edb97db922.jpg", + "image_caption": [ + "Figure 1. Illustration of our findings: (i) visual information is primarily processed in the middle layers where (a) the model extracts the visual information and then (b) interprets the semantics embedded in image tokens; (ii) for real tokens like \"cat\", the attention weights over image tokens are generally higher than hallucinated ones like \"TV\" in (a); (iii) the model may combine the visual features extracted from multiple objects to produce hallucinations." + ], + "image_footnote": [], + "bbox": [ + 535, + 358, + 890, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "derstanding visual inputs and generating textual responses aligned with user intent. Their multi-modal nature has enabled a large variety of vision-language tasks, e.g., image captioning, visual question answering, and visual dialog.", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 107, + 863, + 236, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Code: https://github.com/ZhangqiJiang07/middle_layers_indicating_hallucinations.", + "bbox": [ + 91, + 875, + 480, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25004", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite generating coherent textual responses, these models often exhibit undesirable object hallucinations – producing objects that do not exist in the visual input.", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although various approaches, such as visual instruction fine-tuning [14, 20, 26, 46], the integration of external expert models [5, 43, 45, 50], and contrastive decoding strategies [9, 24, 28, 42], have been proposed to address the object hallucination issue in LVLMs, the underlying mechanisms driving these hallucinations remain poorly understood. A few studies have preliminarily explored the causes of object hallucination, identifying the language bias as the primary factor, with examples including the \"anchor pattern\" [19] and \"text inertia\" [28]. In essence, these studies found that LVLMs tend to prioritize internal textual knowledge over external visual information as more tokens are generated. However, these studies have overlooked the devils in the visual parts – while intuitively, improper processing of visual information within the LVLMs could contribute more to the emergence of object hallucinations.", + "bbox": [ + 88, + 138, + 482, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we delve into how LVLMs process visual information from image tokens and how this affects the generation of object hallucinations. Building on the three-stage mechanism identified in LLMs for retrieving factual knowledge [12], we examine whether LVLMs exhibit similar distinct stages during inference and, if so, which stage is critical for processing visual information. We propose a simple score called Visual Attention Ratio (VAR) to examine the distribution of visual attention across layers, revealing that the middle layers play a crucial role in processing visual information. To study how the model processes visual information in these middle layers, we leverage the logit lens [29] method to decode the hidden states of image tokens into LVLMs' vocabulary, identifying two crucial stages as illustrated in Fig. 1: a visual information enrichment stage propagates visual information to the object token, and a semantic refinement stage interprets the encoded visual information through text.", + "bbox": [ + 91, + 383, + 482, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Secondly, focusing on these middle layers, we observe that the hallucinated tokens often exhibit (1) less active attention patterns, and (2) inconsistent attentions across different heads during visual information enrichment stage, compared to real ones. To quantify these observations, we first introduce a metric based on VAR, and confirm that real object tokens tend to assign higher attention weights over image tokens during visual information enrichment than hallucinated ones, illustrated in Fig. 1. Relying on our finding, we utilize the metric in this stage to detect hallucinated object tokens, achieving AUROC and mAP up to $74\\%$ and $88\\%$ on LLaVA-1.5-7B [27]. Second, given the various attention heads used in the Multi-Heads Self-Attention (MHSA) mechanism [40] for information aggregation, we explore the head behavior by visualizing the attention heatmaps over the input image. As illustrated", + "bbox": [ + 89, + 659, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "in Fig. 1, we find that the heads interact with inconsistent objects during visual information enrichment when generating hallucinations.", + "bbox": [ + 511, + 90, + 903, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our empirical findings provide valuable insights into the way object hallucinations are generated, intuitively described as follows (Fig. 1): In visual information enrichment, the model's ambiguous interactions with multiple objects result in limited and mixed visual information being propagated to the object token. Subsequently, in semantic refinement, this imprecise visual information leads the model to mistakenly associate semantic information from different objects, ultimately causing hallucinations.", + "bbox": [ + 509, + 136, + 903, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by our findings, we propose a simple method to adjust the visual information process in the middle layers by integrating attention information from various heads during inference. Extensive experiments on three mainstream LVLMs show significant hallucination mitigation compared to the original models, with average reductions in $\\mathrm{CHAIR}_I$ and $\\mathrm{CHAIR}_S$ up to 6.3 and 24.1 points, respectively, while preserving detail in descriptions.", + "bbox": [ + 511, + 272, + 903, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 407, + 653, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Large Vision-Language Models. The recent integration of advanced open-source LLMs, like Llama [38, 39] and Vicuna [6], has greatly expanded the capabilities of LVLMs, enabling them to perform more complex vision-language tasks. Typically, the architecture of recent LVLMs incorporates three key components: a vision branch, such as CLIP [33] and EVA [8], to encode image inputs, a modality connector to transform image features into image embeddings aligning with text modality, and a pretrained language model to process image and prompt embeddings to generate responses. LLaVA-1.5 [27] employs an MLP to map the output of the vision branch into 576 image embeddings. Similarly, Shikra [4] utilizes one linear layer to align image features. While MiniGPT-4 [54] adopts a learnable querying transformer to establish vision-language connections, with just 32 image tokens as LVLM input. Despite their impressive capabilities, the above LVLMs suffer from severe object hallucinations. In this paper, we focus on interpreting, detecting, and mitigating their hallucinations.", + "bbox": [ + 511, + 431, + 903, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object Hallucination in LVLMs. Object hallucination [48, 52] is a prevalent and critical issue in current LVLMs where the model erroneously generates descriptions of non-existent objects in images, posing significant risks in high-stakes fields such as medical imaging [18, 23], sequential recommendation systems [15, 35], and autonomous driving [7]. Previous studies to mitigate this issue have primarily focused on visual instruction finetuning [14, 20, 26, 46, 53], incorporating external expert models [5, 43, 45, 50], and improving decoding strategies [9, 19, 24, 28, 42]. Despite numerous efforts, our understanding of the underlying mechanism driving these er", + "bbox": [ + 511, + 719, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25005", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "rors remains limited. Recent studies like OPERA [19] have pointed specific \"anchor patterns\" in text tokens that always align with the onset of hallucinated contents, and PAI [28] has identified \"text inertia\" as another contributing factor, as LVLMs reproduce identical hallucinated descriptions when solely input part of historical generated text. Contrary to these perspectives that focus on language bias, we investigate the causes of object hallucinations from the view of visual information processing through the lens of attention.", + "bbox": [ + 89, + 90, + 483, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Interpretability in Foundation Models. In the field of NLP, numerous studies have analyzed LLMs to explore the internal model knowledge and understand model behavior in specific settings from the perspectives of attention maps [3, 47], neural activation patterns [17], and intermediate hidden states [13, 36]. The logit lens [29], which transforms the hidden states at each layer into the vocabulary space using the model's own linear projector before softmax, offers insightful observations into the next token prediction process [11, 16] in LLMs. Our work adapts the logit lens method to analyze hidden states of image tokens, enabling us to interpret the LVLMs' process of understanding the visual information via textual vocabulary. Few studies explore the internal mechanisms of LVLMs [1, 2, 10], notable efforts include [30], which extends an unimodal causal tracing tool for studying neural mechanisms in BLIP's image-conditioned text generation, and [31], which introduces a dictionary learning-based framework to extract multi-modal concepts for interpreting intermediate representations. Compared to prior works, our study leverages the internal signals from attention weights to uncover the generation of hallucinated objects.", + "bbox": [ + 91, + 226, + 485, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Understanding Object Hallucinations", + "text_level": 1, + "bbox": [ + 89, + 570, + 429, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we start by introducing the generation process of LVLMs and the analytical tools, including visual attention ratio and logit lens. We then conduct case studies focusing on three key aspects: the processing of visual information, the attention patterns of object tokens, and the behavior of heads during object token generation.", + "bbox": [ + 89, + 595, + 483, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 89, + 694, + 220, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notation. The input to LVLMs is initialized with a sequence of $d$ -dimensional image tokens $\\{\\mathbf{v}_1, \\dots, \\mathbf{v}_n\\}$ and instruction text (prompt) tokens $\\{\\mathbf{t}_1, \\dots, \\mathbf{t}_m\\}$ . Typically structured as a Transformer decoder [40], the LVLM outputs responses in an autoregressive manner: at time step $k$ , the model processes the initial input tokens $\\{\\mathbf{v}_1, \\dots, \\mathbf{v}_n, \\mathbf{t}_1, \\dots, \\mathbf{t}_m\\}$ , followed by the sequence of $k-1$ previously generated tokens $\\{\\mathbf{y}_1, \\dots, \\mathbf{y}_{k-1}\\}$ , to predict the next token $\\mathbf{y}_k$ . Let $L$ denote the number of Transformer layers, each with $H$ heads. At layer $\\ell \\in [L]$ , we denote the attention weights in head $h \\in [H]$ as $\\mathbf{A}_k^{(\\ell,h)} \\in \\mathbb{R}^{a_k \\times a_k}$ , where $a_k = n + m + k - 1$ . Additionally, we define $\\mathbf{v}_i^\\ell$ and $\\mathbf{y}_{k-1}^\\ell$ as", + "bbox": [ + 89, + 715, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/93b8bdab5265e1ecdbded897acbf3241e647d54debf4a39c14d04b4a2cec5932.jpg", + "image_caption": [ + "Figure 2. (a) Distribution of visual attention ratio for real object tokens across heads and layers in LLaVA-1.5-7B, sorted row-wise by attention ratios. Note that the high attention in the 0-th layer (bottom row, green rectangle) is not consistent across all LVLMs, as Shikra and MiniGPT-4 models fail to exhibit this pattern, see Appendix C.1. (b) The logit contribution of attention sublayers to real token prediction. We find the middle layers continuously assign higher attention weights to image tokens and exhibit two different contribution patterns to the correct prediction." + ], + "image_footnote": [], + "bbox": [ + 516, + 88, + 687, + 214 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/955fa3233829d0eaf50814335de97a3ed4ecaa97a85f66be050725b43e645f15.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 88, + 903, + 214 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the hidden states for the image token $\\mathbf{v}_i$ and generated token $\\mathbf{y}_{k - 1}$ at layer $\\ell$ , respectively. The real and hallucinated object tokens are noted as $\\mathbf{y_r}$ and $\\mathbf{y_h}$ , respectively.", + "bbox": [ + 511, + 378, + 903, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual Attention Ratio. For the $k$ -th token $\\mathbf{y}_k$ , we define the Visual Attention Ratio (VAR) in each head $h$ at layer $\\ell$ :", + "bbox": [ + 511, + 424, + 903, + 455 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {V A R} ^ {(\\ell , h)} \\left(\\mathbf {y} _ {k}\\right) \\triangleq \\sum_ {i = 1} ^ {n} \\mathbf {A} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 465, + 903, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{A}_k^{(\\ell,h)}(a_k,i)$ represents the attention weights of the newly generated token $\\mathbf{y}_k$ assigned to the image token $\\mathbf{v}_i$ . VAR quantifies the extent of the token $\\mathbf{y}_k$ 's interaction with visual information: a higher VAR score indicating a greater contribution from image tokens during $\\mathbf{y}_k$ 's generation.", + "bbox": [ + 511, + 518, + 905, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Logit Lens. We utilize this technique to investigate how the model interprets the visual hidden state $\\mathbf{v}_i^\\ell$ during inference via text. We denote the linear projector before softmax as $\\mathbf{W}_{\\mathcal{V}} \\in \\mathbb{R}^{|\\mathcal{V}| \\times d}$ , which is applied to $\\mathbf{y}_{k-1}^L$ to predict the probability of next token over the vocabulary $\\mathcal{V}$ . Then, the logit lens transforms the hidden state $\\mathbf{v}_i^\\ell$ of the image tokens to the prediction probability distribution over the vocabulary by the linear projector $\\mathbf{W}_{\\mathcal{V}}$ :", + "bbox": [ + 511, + 597, + 905, + 717 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} (\\mathcal {V} | \\mathbf {v} _ {i} ^ {\\ell}) = \\operatorname {s o f t m a x} \\left(\\mathbf {W} _ {\\mathcal {V}} \\cdot \\mathbf {v} _ {i} ^ {\\ell}\\right) \\in \\mathbb {R} ^ {| \\mathcal {V} |}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 728, + 903, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{p}_j(\\mathcal{V}|\\mathbf{v}_i^\\ell)$ corresponds to the $j$ -th text token in the vocabulary. To explain the processed image token, the text token with the highest probability is considered as the model's interpretation of the hidden state $\\mathbf{v}_i^\\ell$ at layer $\\ell$ .", + "bbox": [ + 511, + 760, + 905, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Experimental Setup for Case Study", + "text_level": 1, + "bbox": [ + 511, + 830, + 821, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We conduct case studies with a randomly selected subset of 2,000 images from COCO 2014 validation set [25]. These images represent diverse scenes and activities across 80", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25006", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1ec2b647fe00d5c76e7950dd1e974b1717667e6334613d40ef2d83b3e087d28f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 90, + 282, + 219 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/665a52fe50d3cb5b314fe46b8c96a037293913e2ddad30c2d84e5769e91beb2f.jpg", + "image_caption": [ + "The image features a yellow bus driving down a street, with a red car following behind it. ... a few houses visible in the background. There are also a couple of people walking on the sidewalk, ... Additionally, there is a fire hydrant located near the left side of the street, and a stop sign can be seen further down the road.", + "Figure 3. Case study of image hidden state interpretation in LLaVA-1.5-7B via logit lens. The heatmap illustrates the retrieved texts of the image hidden states across layers in the three distinct regions, differentiated by color. Our findings reveal that the model's semantic comprehension of image tokens emerges in the later middle layers (19-26) while remaining largely absent in earlier layers. The real and hallucinated object tokens are presented in blue and red in the description, respectively." + ], + "image_footnote": [], + "bbox": [ + 285, + 89, + 903, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "common object categories, each paired with multiple object annotations. The 7B version of LLaVA-1.5 serves as the main focus for the subsequent analysis. In Appendix C.1, we further repeat our case studies on other LVLMs, including Shikra and MiniGPT-4, and observe consistent findings.", + "bbox": [ + 88, + 414, + 480, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To investigate the internal patterns in generating real and hallucinated object tokens, we use the model with greedy search to generate captions for the selected images, prompted by \"Please help me describe the image in detail\". Real and hallucinated object tokens are then identified using ground truth annotations as a reference. For multi-token objects, only the first token is considered. As a result, we obtained 1,842 hallucinated tokens and 4,397 real tokens.", + "bbox": [ + 88, + 489, + 482, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Finding 1: Middle Layers Matter for Visual Information Interaction", + "text_level": 1, + "bbox": [ + 89, + 619, + 482, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To assess the contribution of visual information to token generations, we compute the VAR score (Eq. (1)) for real object tokens $\\mathbf{y}_r$ across all layers $\\ell \\in [L]$ and heads $h \\in [H]$ . We calculate the mean of $\\mathrm{VAR}^{(\\ell,h)}(\\mathbf{y}_r)$ for all real object tokens in our case dataset, with the results depicted in Fig. 2 (a). The visualization shows that the middle layers, i.e., 5-26 layers, continuously exhibit high attention weights to the image tokens, indicating that visual information interaction primarily occurs in the middle layers.", + "bbox": [ + 88, + 657, + 482, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We further analyze how the model processes visual information by examining signals from the MHSA sublayers. Using the logit lens, we quantify the contribution of the MHSA sublayers to real token prediction as $\\mathbf{p}_{\\mathrm{o}}(\\mathcal{V}|\\mathbf{a}_{\\mathrm{r}}^{\\ell})$ where $\\mathbf{a}_{\\mathrm{r}}^{\\ell}$ is the output of the MHSA sublayer at layer $\\ell$ , and o denotes the index of the real object token $\\mathbf{y}_{\\mathrm{r}}$ in the vocabulary. Fig. 2 (b) reveals two patterns in the contributions", + "bbox": [ + 88, + 795, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "from the MHSA sublayers: lower in 5-18 layers and higher in 19-26 layers, reflecting varied use of visual information.", + "bbox": [ + 511, + 414, + 903, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To better understand these two patterns, we use the logit lens to map the hidden states of image token $\\mathbf{v}_i^\\ell$ to text. Specifically, for each image token $\\mathbf{v}_i$ at layer $\\ell$ , we retrieve the text token in the vocabulary with the highest probability, i.e., $\\mathrm{argmax}_{1\\leq j\\leq |\\mathcal{V}|}\\{\\mathbf{p}_j(\\mathcal{V}|\\mathbf{v}_i^\\ell)\\}$ . A case is shown in Fig. 3, revealing two stages in the middle layers with different visual information usage:", + "bbox": [ + 511, + 445, + 905, + 550 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Stage 1: Visual Information Enrichment. The first stage, in layers 5–18, shows that retrieved text tokens are less related to the corresponding image patches, suggesting the model is unable to interpret visual information. This misalignment might explain the low prediction contributions observed in Fig. 2 (b). Meanwhile, these layers continue to show high VAR scores, indicating that the object tokens are accumulating visual information through self-attention. In Secs. 3.4 and 3.5, we show that such attention serves as a key indicator to identify hallucinations.", + "- **Stage 2: Semantic Refinement.** The second stage, in layers 19–26, shows that the retrieved text tokens are semantically consistent with the image patches, suggesting the model is able to interpret and utilize the visual information encoded in the image tokens. Given the high VAR during this stage, we term it as semantic refinement where the model actively interacts with the semantic information of image tokens to reason object token prediction." + ], + "bbox": [ + 511, + 551, + 905, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Finding 2: Inactive Visual Attention in Middle Layers Implies Hallucination", + "text_level": 1, + "bbox": [ + 511, + 830, + 903, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given that visual information is primarily processed in the middle layers, a natural question arises: does the model dis", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25007", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/73b9ae2653533cb3cff0241fa2893e37c381f40d97ed93ca4a9d6cf9a964e868.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 88, + 285, + 239 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bc7e3ced9b76735dcbdab91e1f188fe364e1153ed8916e526bae6fe5d1f8ca72.jpg", + "image_caption": [ + "Figure 5. $\\mathrm{SVAR}_{5-18}$ score distributions across object token types for the 7B (a) and 13B (b) versions of LLaVA-1.5." + ], + "image_footnote": [], + "bbox": [ + 285, + 88, + 480, + 239 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/457cc7c879ff8cbe9e2d0580db488e029f2759c20ccb858cc84f40b57228e8ed.jpg", + "image_caption": [ + "Figure 4. Case study of the visual attention ratio distribution over heads and layers in LLaVA-1.5-7B. Left: real objects; Right: hallucinated objects. We find that the hallucinated object tokens exhibit inactive attention patterns during visual information enrichment compared to the real ones." + ], + "image_footnote": [], + "bbox": [ + 93, + 239, + 287, + 388 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/15274111709cbdee1b15e2aa206e4f149894036fd0d9ac98d1afb62cc23f1906.jpg", + "image_caption": [ + "Figure 6. Object hallucination detection curves for LLaVA-1.5-7B. We show the ROC and Precision-Recall curves of $\\mathrm{SVAR}_{5 - 18}$ metric for object hallucination detection on the case study dataset." + ], + "image_footnote": [], + "bbox": [ + 287, + 239, + 480, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "play unusual attention patterns in these layers when generating hallucinated object tokens? Fig. 4 presents the VAR distribution for real object tokens ('bus' and 'car') and hallucinated ones ('people' and 'fire hydrant') from the case of Fig. 3. We observe that the hallucinated object tokens demonstrate an inactive attention pattern during the visual information enrichment stage (5-18 layers) compared to the real ones. We conjecture that such pattern weakens the interaction between the object token and image tokens in this stage, limiting the propagation of visual information and potentially leading to hallucinations. To quantify this observation, we introduce a metric, Summed Visual Attention Ratio (SVAR), calculated by averaging VAR scores over all heads and summing across selected layers $[\\ell_s,\\ell_e]$ . Specifically, for a real object token $\\mathbf{y_r}$ in $[\\ell_5,\\ell_{18}]$ , we compute:", + "bbox": [ + 88, + 494, + 482, + 723 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S V A R} _ {5 - 1 8} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right) \\triangleq \\frac {1}{H} \\sum_ {\\ell = 5} ^ {1 8} \\sum_ {h = 1} ^ {H} \\operatorname {V A R} ^ {(\\ell , h)} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 733, + 482, + 775 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct a statistical experiment on the $\\mathrm{SVAR}_{5-18}$ metric for both real and hallucinated tokens. The results, depicted in Fig. 5 (a), and the associated statistical test detailed in Appendix C.2, indicate a salient difference: the model assigns significantly higher attention weights to image tokens when generating real object tokens during visual information enrichment compared to hallucinated ones.", + "bbox": [ + 89, + 779, + 482, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 5 (b) shows a similar trend in LLaVA-1.5-13B.", + "bbox": [ + 89, + 885, + 431, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/48802845cb50f6c197723fa9e26fe4d2529657477dcea4a52b86683d19740e5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 524, + 88, + 705, + 213 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3d58186aa76c40b68396d3ae0f6a053f960b786efe7428fcf8a3bfefa97ecabd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 88, + 893, + 213 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/72b42b25fae665b616e45df50ad1e4ad6650e918fc2b6a0679b9c957be33b8ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 524, + 265, + 707, + 391 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9d53b6feb877791581f3212cb54084c35fe8af76e9dc86f84bee3be27bd8f216.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 266, + 895, + 391 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.1 Application: Object Hallucination Detection", + "text_level": 1, + "bbox": [ + 511, + 470, + 875, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Building upon our Finding 2, we apply the $\\mathrm{SVAR}_{5-18}$ metric to detect object hallucinations. We assess the efficacy of $\\mathrm{SVAR}_{5-18}$ in reflecting object hallucination using our case dataset, where a positive sample is a real object token and a negative sample is a hallucinated one. For comparison, we use the internal confidence metric recently proposed in [21] as a baseline. The internal confidence uses the maximum probability of the object token within all image hidden states $\\{\\mathbf{v}_i^\\ell : i \\in [n], \\ell \\in [L]\\}$ , mapped by the logit lens for detection. The qualitative results are presented in Fig. 6 and the results for LLaVA-1.5-13B are shown in Appendix C.1. Compared to internal confidence, using the simple $\\mathrm{SVAR}_{5-18}$ metric improves the AUROC by $8.82\\%$ and the AP by $3.53\\%$ , verifying the utility of our metric. This further suggests that the middle layers provide crucial indicator information for object hallucination.", + "bbox": [ + 509, + 494, + 906, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Beyond the hand-crafted $\\mathrm{SVAR}_{5-18}$ measure, we explore the potential of middle layers to indicate hallucinations by training a simple model to derive metrics directly from raw visual attention states.", + "bbox": [ + 511, + 736, + 903, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Experimental setting. We train a two-layer MLP by inputting the concatenated VAR scores across all heads in the layer range of interest $[\\ell_s,\\ell_e]$ to classify the real and hallucinated object tokens. Specifically, the input vector $\\mathbf{x}(\\mathbf{y}_r)$ for the real token $\\mathbf{y}_r$ can be written as:", + "bbox": [ + 511, + 797, + 903, + 872 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right) = \\left[ \\operatorname {V A R} ^ {\\left(\\ell_ {s}, 1\\right)}, \\operatorname {V A R} ^ {\\left(\\ell_ {s}, 2\\right)}, \\dots , \\operatorname {V A R} ^ {\\left(\\ell_ {e}, H\\right)} \\right] ^ {\\top}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 882, + 903, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25008", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6b562f339648dc2df69a44b184337a50614a3f307039ddfc1cf3dfe4c092bcbe.jpg", + "image_caption": [ + "Figure 7. Visualization of attention maps over image for 'bus' (real) and 'people' (hallucinated) object tokens in heads $(\\ell, h)$ . We find that the heads tend to interact with multiple objects when generating hallucinated object tokens. More examples can be found in Appendix C.4." + ], + "image_footnote": [], + "bbox": [ + 107, + 88, + 893, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We split the case dataset into training and test sets in the ratio of 8:2, and train the MLP with cross-entropy loss. The model performance is evaluated using accuracy, AUROC, and recall metrics. Training details are in Appendix B.2.", + "bbox": [ + 88, + 342, + 480, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. We experiment with four layer ranges in LLaVA-1.5-7B: [0, 4], [5, 18], [19, 26], and [27, 31], as shown in Tab. 1. We can see using the layers of visual information enrichment (5-18) achieves the best performance among other ranges, validating the effectiveness of our Finding 2. We observe that other layers also encode hallucination-related information which can be learned to detect hallucinations. However, compared to the explicit pattern in 5-18 layers, the implicit patterns contained in other ranges require computation costs for feature learning.", + "bbox": [ + 88, + 402, + 482, + 554 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Finding 3: Attention Heads Interact with Multiple Objects Incurring Object Hallucination", + "text_level": 1, + "bbox": [ + 89, + 560, + 482, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Considering the MHSA mechanism incorporates various attention heads to aggregate information, we analyze heatmaps over the image for both real and hallucinated object tokens ('bus' vs 'people') to investigate the head behavior during visual information enrichment. A case is shown in Fig. 7 and more examples can be found in Appendix C.4. We can see that each head focuses on distinct local details, yet the attention distribution for the real token consistently aligns with the spatial extent of the corresponding object. In contrast, for the hallucinated token, the heads interact with inconsistent objects in the image during this stage. We speculate that such unstable head behavior encodes mixed information from multiple objects into the object token, potentially leading to hallucinations.", + "bbox": [ + 88, + 599, + 482, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Object Hallucination Mitigation", + "text_level": 1, + "bbox": [ + 89, + 821, + 383, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Heads Guided Attention Intervention", + "text_level": 1, + "bbox": [ + 89, + 847, + 413, + 862 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inspired by the insights from Sec. 3 that improper processing of visual information during inference can lead to object", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/586522b8ff225b5fc2cdac3aac2570626a82112ce7bd263a060b73f6b0dd43ac.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Layers0-45-1819-2627-310-31
    Accuracy82.6184.4681.4977.7284.46
    AUROC89.5790.1987.3484.3090.28
    Recall66.2272.3468.8863.5671.28
    ", + "bbox": [ + 537, + 339, + 883, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Object hallucination detection results $(\\%)$ of different layer ranges of interest on LLaVA-1.5-7B.", + "bbox": [ + 511, + 421, + 906, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "hallucinations, we aim to correct this process to alleviate object hallucination. Specifically, we adjust the attention weights assigned to image tokens, i.e., $\\{\\mathbf{A}_k^{(\\ell,h)}(a_k,i)\\}_{i=1}^n$ , in each head at the middle layers during inference for intervention. To modify the attention weights in time step $k$ , we extract the attention score matrix $\\mathbf{S}_k^{(\\ell,h)}$ before softmax operation:", + "bbox": [ + 511, + 473, + 906, + 582 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {k} ^ {(\\ell , h)} = \\left(\\frac {\\mathbf {Q} _ {\\ell , h} \\mathbf {K} _ {\\ell , h} ^ {\\top}}{\\sqrt {d _ {k}}}\\right) _ {k}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 582, + 905, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{Q}_{\\ell,h}$ and $\\mathbf{K}_{\\ell,h} \\in \\mathbb{R}^{a_k \\times d_k}$ represent the query and key matrices of dimension $d_k$ , respectively.", + "bbox": [ + 511, + 627, + 905, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Guided by the attention pattern difference in Finding 2, we amplify the original attention scores in the layers of visual information enrichment by adding positive values to enhance visual information interaction. Furthermore, leveraging the head behavior observed in Finding 3, we compute these positive values by averaging the absolute attention scores across all heads, where only the consistent regions interacted by different heads receive large enhancement. By integrating the attention information from various heads, we can find a more faithful and object-related direction for attention shift to reduce hallucinations. Formally, for each image token $i \\in [n]$ across all heads $h \\in [H]$ in layer $\\ell \\in [\\ell_s, \\ell_e]$ , we adjust the visual attention scores by:", + "bbox": [ + 511, + 657, + 906, + 854 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) = \\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) + \\alpha \\frac {1}{H} \\sum_ {h = 1} ^ {H} \\left| \\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) \\right|, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 862, + 906, + 905 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25009", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/aef0a3e9444702adb336fa5f3807272426c7e043decb233d4c0c76fddb4cad10.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodLLaVA-1.5-7BLLaVA-1.5-13BShikra-7BMiniGPT-4-7BAvg.
    \\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)
    Decoding Strategy
    Greedy53.015.676.749.814.678.257.615.775.331.812.071.148.114.5
    Beam55.615.477.550.413.879.059.016.374.629.29.971.248.613.9
    OPERA45.613.179.142.613.277.841.413.773.525.49.671.238.812.4
    Contrastive Decoding
    \\(\\mathsf{VCD}^{\\dagger}\\)58.618.272.853.615.375.856.415.575.241.414.168.252.515.8
    \\(\\mathsf{PAI}^{\\dagger}\\)24.27.175.233.09.277.838.610.176.223.28.271.429.88.7
    \\(\\mathsf{Ours}^{\\dagger}\\)25.06.776.125.88.877.323.89.472.721.48.070.824.08.2
    \\(\\Delta \\%\\)↑3.3%↓5.6%↓21.8%↓4.3%↓38.3%↓6.9%↓7.8%↓2.4%↓19.5%↓5.7%
    ", + "bbox": [ + 127, + 88, + 870, + 263 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. CHAIR hallucination evaluation and F1 results on three LVLMs with max new token set to 512. † denotes using the greedy decoding strategy. Our method outperforms other baselines and also preserves the richness of the descriptions. Δ% denotes the relative performance improvement with respect to the second-best method.", + "bbox": [ + 89, + 273, + 906, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where the $[\\ell_s,\\ell_e]$ denotes the range of visual information enrichment, and the parameter $\\alpha$ is defined as a balance factor to control the intervention strength.", + "bbox": [ + 89, + 342, + 482, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Experimental Setup and Results", + "text_level": 1, + "bbox": [ + 89, + 402, + 375, + 420 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Models. We conduct experiments on three representative LVLMs to evaluate the effectiveness and generalization of our method, including the LLaVA-1.5 [27], Shikra [4], and MiniGPT-4 [54]. In our experiments, we use the 7B and 13B versions of LLaVA-1.5 to study the scale effect, while other LVLMs are 7B models.", + "bbox": [ + 89, + 428, + 483, + 518 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. We adopt two commonly used decoding strategies and three mainstream hallucination mitigation approaches as the baseline methods, including greedy decoding, beam search decoding [37], OPERA [19], VCD [24], and PAI [28]. Greedy decoding selects the token with the highest probability over the vocabulary as the predicted next token. Beam search decoding maintains multiple beams and selects the top tokens with the highest cumulative probabilities at the end of generation. Improved on beam search, OPERA introduces an overtrust penalty term on the attention weights during inference with a rollback strategy to mitigate hallucinations. Different from the above three decoding approaches, VCD and PAI can be categorized as contrastive decoding methods. Specifically, VCD subtracts the output logits of the distorted visual input from the original output logits to reduce the statistical priors. In addition to using contrastive decoding, PAI further manipulates the attention matrix to overcome language bias. In our experiments, we use the default parameters of these baselines and unify $N_{\\mathrm{beam}} = 5$ for the beam search decoding and OPERA.", + "bbox": [ + 89, + 521, + 482, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Benchmark and Metrics. Following [19], we conduct experiments on 500 random images from the COCO 2014 validation set. To evaluate the degree of object hallucinations in the image captioning task, we adopt the CHAIR [34] criteria which computes the proportion of all objects men", + "bbox": [ + 89, + 824, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tioned in the caption that are not present in the ground-truth annotations. CHAIR provides two main metrics, including $\\mathrm{CHAIR}_I(C_I)$ and $\\mathrm{CHAIR}_S(C_S)$ that assess instance-level and sentence-level hallucinations, respectively:", + "bbox": [ + 511, + 342, + 906, + 402 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nC _ {I} = \\frac {\\left| \\{\\text {h a l l u c i n a t e d o b j e c t s} \\} \\right|}{\\left| \\{\\text {a l l m e n t i o n e d o b j e c t s} \\} \\right|}, C _ {S} = \\frac {\\left| \\{\\text {c a p t i o n s w / h a l l u c i n a t e d o b j e c t s} \\} \\right|}{\\left| \\{\\text {a l l c a p t i o n s} \\} \\right|},\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 409, + 908, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where lower values indicate fewer hallucinations. Following [28], we also adopt the F1 score to assess the richness and accuracy of the generated descriptions.", + "bbox": [ + 511, + 446, + 906, + 492 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation details. Our method contains two parameters: the visual information enrichment range $[\\ell_s, \\ell_e]$ and the balance factor $\\alpha$ in Eq. (6). Utilizing the VAR feature and logit lens described in Sec. 3.1, we can easily establish suitable ranges for any other LVLMs. In our experiment, we set the ranges as [5, 18] for both versions of LLaVA-1.5, [3, 13] for Shikra, and [3, 14] for MiniGPT-4. We set $\\alpha$ to 0.5 for LLaVA-1.5, MiniGPT-4, and 0.55 for Shikra. We implement our method with greedy decoding as a baseline.", + "bbox": [ + 511, + 493, + 908, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. Tab. 2 presents the experimental results for the selected LVLMs with max new tokens of 512. From the Tab. 2, our approach outperforms the three decoding strategies in reducing hallucinations and achieves an average reduction of $19.5\\%$ in $C_S$ and $5.7\\%$ in $C_I$ , compared to the second-best baseline. Compared to VCD, our method not only achieves superior hallucination mitigation performance but also better preserves the richness of the descriptions. Compared to PAI which requires the cost of once additional forward process for contrastive decoding, our approach achieves comparable or superior performance by only adjusting attention weights during inference, validating the efficacy of our method. Moreover, the consistent reduction of hallucinations across four different LVLMs confirms the generalizability of our findings. To evaluate the impact of generated token lengths, we conduct experiments on LLaVA-1.5-7B by varying the max new token in $\\{64, 128, 256\\}$ . The results, reported in Tab. 3, show that", + "bbox": [ + 511, + 628, + 908, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25010", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8778666d46f1d4fc6f424a73c15cc4249757774c367a6781a24f4af09c299cf5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Methodmax new token 64max new token 128max new token 256Avg.
    \\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓
    Decoding Strategy
    Greedy23.88.074.752.415.576.753.015.676.743.113.0
    Beam17.66.075.154.414.877.655.615.477.542.512.1
    OPERA19.06.374.444.212.978.845.613.179.136.310.8
    Contrastive Decoding
    \\(\\mathrm{VCD}^{\\dagger}\\)26.09.373.356.816.974.558.618.272.847.114.8
    \\(\\mathrm{PAI}^{\\dagger}\\)19.86.274.024.27.375.224.27.275.222.76.9
    \\(\\mathrm{Ours}^{\\dagger}\\)18.25.473.924.87.176.025.07.176.122.76.5
    ", + "bbox": [ + 94, + 88, + 480, + 209 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6d677d5d11425079b6eabcbb3c951127b98f0bfc564494840ac55dd380d59890.jpg", + "table_caption": [ + "Table 3. CHAIR hallucination evaluation and F1 results on LLaVA-1.5-7B with varying max new token in $\\{64,128,256\\}$ . † denotes using the greedy decoding strategy." + ], + "table_footnote": [], + "table_body": "
    Layers0-45-1819-2627-31Greedy
    \\(C_S\\ ↓\\)31.025.053.453.453.0
    \\(C_I\\ ↓\\)10.46.714.315.715.6
    F1↑77.176.177.577.276.7
    ", + "bbox": [ + 127, + 273, + 446, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "our method consistently reduces hallucinations across different token lengths and achieves the best performance on average, demonstrating its robustness. We provide qualitative results in Appendix C.7.", + "bbox": [ + 89, + 409, + 483, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Ablations and Discussions", + "text_level": 1, + "bbox": [ + 89, + 482, + 333, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Layers of attention intervention. Motivated by the empirical observation of implicit hallucination patterns across layers beyond the 5-18 range in Sec. 3.4.1, we investigate whether interventions in these layers can also mitigate object hallucinations. We apply our approach (Eq. (6)) to the layer ranges [0, 4], [19, 26], and [27, 31] in LLaVA-1.5-7B, and the results are reported in Tab. 4. We observe that the 5-18 layer range largely outperforms the other ranges while using some ranges (19-26 and 27-31) even enhanced hallucinations instead. The result suggests that explicit patterns in visual information enrichment are more effective than implicit patterns, facilitating more effective hallucination mitigation through simple attention intervention.", + "bbox": [ + 88, + 508, + 482, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different attention intervention strategies. To validate the efficacy of our method in adjusting attention weights to reduce object hallucinations, we compare it with the inference intervention component proposed in PAI [28]. The inference intervention component roughly excites attention weights by computing a weighted sum of the attention scores and their absolute values across individual heads. We apply this approach to the same layer ranges in ours on LLaVA-1.5-7B, Shikra, and MiniGPT-4. Tab. 5 suggests that our attention intervention method surpasses that of PAI, as our method integrates attention information from various heads to shift attention toward a more truthful direction.", + "bbox": [ + 89, + 704, + 482, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Balance factor $\\alpha$ sensitivity. To examine the influence of", + "bbox": [ + 89, + 885, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cdc69a6b4bebe5de35f61afa243505b2ba782c692f5fba055b3790bd4a4e2df3.jpg", + "image_caption": [ + "Figure 8. Parameter sensitivity of $\\alpha$ with CHAIR metrics." + ], + "image_footnote": [], + "bbox": [ + 514, + 88, + 705, + 224 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/53e151414e6c508428ed0e3152bc49569fa8cf42d772068d557781f24747ee46.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 88, + 905, + 224 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/13e57fc4b324d576e6988fce4c660194fbc5a62e0e09fa118f7ab3926ed1ec27.jpg", + "table_caption": [ + "Table 4. CHAIR hallucination evaluation and F1 score among four layer ranges on LLaVA-1.5-7B with max new token set to 512." + ], + "table_footnote": [], + "table_body": "
    MethodLLaVA-1.5-7BShikra-7BMiniGPT-4-7B
    CS↓CI↓CS↓CI↓CS↓CI↓
    PAI*26.68.145.813.630.29.5
    Ours25.06.723.89.421.48.0
    ", + "bbox": [ + 535, + 263, + 883, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. CHAIR hallucination evaluation and F1 results on three LVLMs. $\\star$ denotes only using the inference intervention component in the same layer range as ours. Greedy decoding is adopted.", + "bbox": [ + 511, + 340, + 905, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$\\alpha$ on intervention efficacy, we vary its value in the range of $\\{0.3, 0.4, 0.5, 0.6, 0.7\\}$ and the results of CHAIR metrics and F1 score for the 7B version of both LLaVA-1.5 and MiniGPT-4 are shown in Fig. 8. We find that a lower $\\alpha$ limits hallucination mitigation effectiveness, whereas a higher $\\alpha$ compromises the richness of descriptions. These results indicate that an appropriate $\\alpha$ value (e.g., 0.5 for both selected LVLMs) balances the reduction of hallucinations with the maintenance of detailed visual descriptions.", + "bbox": [ + 511, + 409, + 906, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Insights", + "text_level": 1, + "bbox": [ + 511, + 558, + 740, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce a new perspective, visual information processing, to investigate the underlying mechanisms driving object hallucination. Analyzing through the lens of attention, we identify three key findings and discover a simple yet effective method for reducing hallucinations at inference time. Our study deepens the understanding of how hallucinations are produced in LVLMs. We conclude with three insights for future direction: 1) Based on LVLMs' interpretation in semantic refinement stage, the image tokens may be further categorized into sub-groups, such as object tokens, color tokens, and textual tokens, enabling us to explore how the LVLMs extract different types of visual information. 2) While we focus on visual information processing, there may exist more granular, stage-wise mechanisms that could explain model behavior more precisely. 3) Instead of external interventions on LVLM outputs, such as contrastive decoding, we suggest that targeted modifications to specific internal states, like attention weights in middle layers, offer a more effective method for calibration. Our insights may aid the community in developing more trustworthy and reliable LVLMs against hallucinations.", + "bbox": [ + 511, + 583, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25011", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 91, + 90, + 243, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by the National Science Foundation of China (62376281, 62206048), the Natural Science Foundation of Jiangsu Province (BK20220819), and the Fundamental Research Funds for the Central Universities (2242024k30035).", + "bbox": [ + 89, + 113, + 485, + 186 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 210, + 187, + 227 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jize Cao, Zhe Gan, Yu Cheng, Licheng Yu, Yen-Chun Chen, and Jingjing Liu. 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In International Conference on Learning Representations, 2024. 1, 2, 7" + ], + "bbox": [ + 91, + 92, + 480, + 626 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "25014", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Devils in Middle Layers of Large Vision-Language Models_ Interpreting, Detecting and Mitigating Object Hallucinations via Attention Lens/c159f2ec-9cd0-43d8-97ae-a644ae3c367b_model.json b/2025/Devils in Middle Layers of Large Vision-Language Models_ Interpreting, Detecting and Mitigating Object Hallucinations via Attention Lens/c159f2ec-9cd0-43d8-97ae-a644ae3c367b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..018f3f23e1d75bdc8e5ad82fad7f47b9057189a6 --- /dev/null +++ b/2025/Devils in Middle Layers of Large Vision-Language Models_ Interpreting, Detecting and Mitigating Object Hallucinations via Attention Lens/c159f2ec-9cd0-43d8-97ae-a644ae3c367b_model.json @@ -0,0 +1,2213 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.133, + 0.131, + 0.867, + 0.177 + ], + "angle": 0, + "content": "Devils in Middle Layers of Large Vision-Language Models: Interpreting, Detecting and Mitigating Object Hallucinations via Attention Lens" + }, + { + "type": "text", + "bbox": [ + 0.121, + 0.203, + 0.884, + 0.293 + ], + "angle": 0, + "content": "Zhangqi Jiang\\(^{1}\\) Junkai Chen\\(^{2,3}\\) Beier Zhu\\(^{4}\\) Tingjin Luo\\(^{1*}\\) Yankun Shen\\(^{2,3}\\) Xu Yang\\(^{2,3*}\\) \n\\(^{1}\\)National University of Defense Technology \\(^{2}\\)Southeast University \n\\(^{3}\\)Key Laboratory of New Generation Artificial Intelligence Technology & Its Interdisciplinary Applications (Southeast University), Ministry of Education \n\\(^{4}\\)Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.127, + 0.295, + 0.873, + 0.327 + ], + "angle": 0, + "content": "{sxdxjzq, junkai.chen.0917}@gmail.com beier.zhu@ntu.edu.sg tingjinluo@hotmail.com {220242353, xuyang_palm}@seu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.362, + 0.327, + 0.379 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.394, + 0.486, + 0.759 + ], + "angle": 0, + "content": "Hallucinations in Large Vision-Language Models (LVLMs) significantly undermine their reliability, motivating researchers to explore the causes of hallucination. However, most studies primarily focus on the language aspect rather than the visual. In this paper, we address how LVLMs process visual information and whether this process causes hallucination. Firstly, we use the attention lens to identify the stages at which LVLMs handle visual data, discovering that the middle layers are crucial. Moreover, we find that these layers can be further divided into two stages: \"visual information enrichment\" and \"semantic refinement\" which respectively propagate visual data to object tokens and interpret it through text. By analyzing attention patterns during the visual information enrichment stage, we find that real tokens consistently receive higher attention weights than hallucinated ones, serving as a strong indicator of hallucination. Further examination of multi-head attention maps reveals that hallucination tokens often result from heads interacting with inconsistent objects. Based on these insights, we propose a simple inference-time method that adjusts visual attention by integrating information across various heads. Extensive experiments demonstrate that this approach effectively mitigates hallucinations in mainstream LVLMs without additional training costs.\\(^{1}\\)" + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.784, + 0.224, + 0.8 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.856 + ], + "angle": 0, + "content": "Building on the foundations of Large Language Models (LLMs), Large Vision-Language Models (LVLMs) [4, 27, 32, 44, 49, 51, 54] have emerged as powerful tools for un" + }, + { + "type": "image", + "bbox": [ + 0.537, + 0.359, + 0.891, + 0.701 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.711, + 0.907, + 0.81 + ], + "angle": 0, + "content": "Figure 1. Illustration of our findings: (i) visual information is primarily processed in the middle layers where (a) the model extracts the visual information and then (b) interprets the semantics embedded in image tokens; (ii) for real tokens like \"cat\", the attention weights over image tokens are generally higher than hallucinated ones like \"TV\" in (a); (iii) the model may combine the visual features extracted from multiple objects to produce hallucinations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "derstanding visual inputs and generating textual responses aligned with user intent. Their multi-modal nature has enabled a large variety of vision-language tasks, e.g., image captioning, visual question answering, and visual dialog." + }, + { + "type": "page_footnote", + "bbox": [ + 0.108, + 0.864, + 0.237, + 0.876 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.093, + 0.876, + 0.482, + 0.9 + ], + "angle": 0, + "content": "1Code: https://github.com/ZhangqiJiang07/middle_layers_indicating_hallucinations." + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.864, + 0.482, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "25004" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.137 + ], + "angle": 0, + "content": "Despite generating coherent textual responses, these models often exhibit undesirable object hallucinations – producing objects that do not exist in the visual input." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.14, + 0.483, + 0.382 + ], + "angle": 0, + "content": "Although various approaches, such as visual instruction fine-tuning [14, 20, 26, 46], the integration of external expert models [5, 43, 45, 50], and contrastive decoding strategies [9, 24, 28, 42], have been proposed to address the object hallucination issue in LVLMs, the underlying mechanisms driving these hallucinations remain poorly understood. A few studies have preliminarily explored the causes of object hallucination, identifying the language bias as the primary factor, with examples including the \"anchor pattern\" [19] and \"text inertia\" [28]. In essence, these studies found that LVLMs tend to prioritize internal textual knowledge over external visual information as more tokens are generated. However, these studies have overlooked the devils in the visual parts – while intuitively, improper processing of visual information within the LVLMs could contribute more to the emergence of object hallucinations." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.385, + 0.483, + 0.656 + ], + "angle": 0, + "content": "In this paper, we delve into how LVLMs process visual information from image tokens and how this affects the generation of object hallucinations. Building on the three-stage mechanism identified in LLMs for retrieving factual knowledge [12], we examine whether LVLMs exhibit similar distinct stages during inference and, if so, which stage is critical for processing visual information. We propose a simple score called Visual Attention Ratio (VAR) to examine the distribution of visual attention across layers, revealing that the middle layers play a crucial role in processing visual information. To study how the model processes visual information in these middle layers, we leverage the logit lens [29] method to decode the hidden states of image tokens into LVLMs' vocabulary, identifying two crucial stages as illustrated in Fig. 1: a visual information enrichment stage propagates visual information to the object token, and a semantic refinement stage interprets the encoded visual information through text." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Secondly, focusing on these middle layers, we observe that the hallucinated tokens often exhibit (1) less active attention patterns, and (2) inconsistent attentions across different heads during visual information enrichment stage, compared to real ones. To quantify these observations, we first introduce a metric based on VAR, and confirm that real object tokens tend to assign higher attention weights over image tokens during visual information enrichment than hallucinated ones, illustrated in Fig. 1. Relying on our finding, we utilize the metric in this stage to detect hallucinated object tokens, achieving AUROC and mAP up to \\(74\\%\\) and \\(88\\%\\) on LLaVA-1.5-7B [27]. Second, given the various attention heads used in the Multi-Heads Self-Attention (MHSA) mechanism [40] for information aggregation, we explore the head behavior by visualizing the attention heatmaps over the input image. As illustrated" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "in Fig. 1, we find that the heads interact with inconsistent objects during visual information enrichment when generating hallucinations." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.137, + 0.905, + 0.272 + ], + "angle": 0, + "content": "Our empirical findings provide valuable insights into the way object hallucinations are generated, intuitively described as follows (Fig. 1): In visual information enrichment, the model's ambiguous interactions with multiple objects result in limited and mixed visual information being propagated to the object token. Subsequently, in semantic refinement, this imprecise visual information leads the model to mistakenly associate semantic information from different objects, ultimately causing hallucinations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.273, + 0.905, + 0.395 + ], + "angle": 0, + "content": "Inspired by our findings, we propose a simple method to adjust the visual information process in the middle layers by integrating attention information from various heads during inference. Extensive experiments on three mainstream LVLMs show significant hallucination mitigation compared to the original models, with average reductions in \\(\\mathrm{CHAIR}_I\\) and \\(\\mathrm{CHAIR}_S\\) up to 6.3 and 24.1 points, respectively, while preserving detail in descriptions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.408, + 0.655, + 0.423 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.433, + 0.905, + 0.719 + ], + "angle": 0, + "content": "Large Vision-Language Models. The recent integration of advanced open-source LLMs, like Llama [38, 39] and Vicuna [6], has greatly expanded the capabilities of LVLMs, enabling them to perform more complex vision-language tasks. Typically, the architecture of recent LVLMs incorporates three key components: a vision branch, such as CLIP [33] and EVA [8], to encode image inputs, a modality connector to transform image features into image embeddings aligning with text modality, and a pretrained language model to process image and prompt embeddings to generate responses. LLaVA-1.5 [27] employs an MLP to map the output of the vision branch into 576 image embeddings. Similarly, Shikra [4] utilizes one linear layer to align image features. While MiniGPT-4 [54] adopts a learnable querying transformer to establish vision-language connections, with just 32 image tokens as LVLM input. Despite their impressive capabilities, the above LVLMs suffer from severe object hallucinations. In this paper, we focus on interpreting, detecting, and mitigating their hallucinations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Object Hallucination in LVLMs. Object hallucination [48, 52] is a prevalent and critical issue in current LVLMs where the model erroneously generates descriptions of non-existent objects in images, posing significant risks in high-stakes fields such as medical imaging [18, 23], sequential recommendation systems [15, 35], and autonomous driving [7]. Previous studies to mitigate this issue have primarily focused on visual instruction finetuning [14, 20, 26, 46, 53], incorporating external expert models [5, 43, 45, 50], and improving decoding strategies [9, 19, 24, 28, 42]. Despite numerous efforts, our understanding of the underlying mechanism driving these er" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25005" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.484, + 0.226 + ], + "angle": 0, + "content": "rors remains limited. Recent studies like OPERA [19] have pointed specific \"anchor patterns\" in text tokens that always align with the onset of hallucinated contents, and PAI [28] has identified \"text inertia\" as another contributing factor, as LVLMs reproduce identical hallucinated descriptions when solely input part of historical generated text. Contrary to these perspectives that focus on language bias, we investigate the causes of object hallucinations from the view of visual information processing through the lens of attention." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.227, + 0.486, + 0.56 + ], + "angle": 0, + "content": "Interpretability in Foundation Models. In the field of NLP, numerous studies have analyzed LLMs to explore the internal model knowledge and understand model behavior in specific settings from the perspectives of attention maps [3, 47], neural activation patterns [17], and intermediate hidden states [13, 36]. The logit lens [29], which transforms the hidden states at each layer into the vocabulary space using the model's own linear projector before softmax, offers insightful observations into the next token prediction process [11, 16] in LLMs. Our work adapts the logit lens method to analyze hidden states of image tokens, enabling us to interpret the LVLMs' process of understanding the visual information via textual vocabulary. Few studies explore the internal mechanisms of LVLMs [1, 2, 10], notable efforts include [30], which extends an unimodal causal tracing tool for studying neural mechanisms in BLIP's image-conditioned text generation, and [31], which introduces a dictionary learning-based framework to extract multi-modal concepts for interpreting intermediate representations. Compared to prior works, our study leverages the internal signals from attention weights to uncover the generation of hallucinated objects." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.571, + 0.43, + 0.587 + ], + "angle": 0, + "content": "3. Understanding Object Hallucinations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.597, + 0.484, + 0.687 + ], + "angle": 0, + "content": "In this section, we start by introducing the generation process of LVLMs and the analytical tools, including visual attention ratio and logit lens. We then conduct case studies focusing on three key aspects: the processing of visual information, the attention patterns of object tokens, and the behavior of heads during object token generation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.695, + 0.221, + 0.71 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.717, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Notation. The input to LVLMs is initialized with a sequence of \\(d\\)-dimensional image tokens \\(\\{\\mathbf{v}_1, \\dots, \\mathbf{v}_n\\}\\) and instruction text (prompt) tokens \\(\\{\\mathbf{t}_1, \\dots, \\mathbf{t}_m\\}\\). Typically structured as a Transformer decoder [40], the LVLM outputs responses in an autoregressive manner: at time step \\(k\\), the model processes the initial input tokens \\(\\{\\mathbf{v}_1, \\dots, \\mathbf{v}_n, \\mathbf{t}_1, \\dots, \\mathbf{t}_m\\}\\), followed by the sequence of \\(k-1\\) previously generated tokens \\(\\{\\mathbf{y}_1, \\dots, \\mathbf{y}_{k-1}\\}\\), to predict the next token \\(\\mathbf{y}_k\\). Let \\(L\\) denote the number of Transformer layers, each with \\(H\\) heads. At layer \\(\\ell \\in [L]\\), we denote the attention weights in head \\(h \\in [H]\\) as \\(\\mathbf{A}_k^{(\\ell,h)} \\in \\mathbb{R}^{a_k \\times a_k}\\), where \\(a_k = n + m + k - 1\\). Additionally, we define \\(\\mathbf{v}_i^\\ell\\) and \\(\\mathbf{y}_{k-1}^\\ell\\) as" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.089, + 0.689, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.089, + 0.905, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.227, + 0.907, + 0.352 + ], + "angle": 0, + "content": "Figure 2. (a) Distribution of visual attention ratio for real object tokens across heads and layers in LLaVA-1.5-7B, sorted row-wise by attention ratios. Note that the high attention in the 0-th layer (bottom row, green rectangle) is not consistent across all LVLMs, as Shikra and MiniGPT-4 models fail to exhibit this pattern, see Appendix C.1. (b) The logit contribution of attention sublayers to real token prediction. We find the middle layers continuously assign higher attention weights to image tokens and exhibit two different contribution patterns to the correct prediction." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.379, + 0.905, + 0.424 + ], + "angle": 0, + "content": "the hidden states for the image token \\(\\mathbf{v}_i\\) and generated token \\(\\mathbf{y}_{k - 1}\\) at layer \\(\\ell\\), respectively. The real and hallucinated object tokens are noted as \\(\\mathbf{y_r}\\) and \\(\\mathbf{y_h}\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.425, + 0.905, + 0.456 + ], + "angle": 0, + "content": "Visual Attention Ratio. For the \\(k\\)-th token \\(\\mathbf{y}_k\\), we define the Visual Attention Ratio (VAR) in each head \\(h\\) at layer \\(\\ell\\):" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.467, + 0.905, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\operatorname {V A R} ^ {(\\ell , h)} \\left(\\mathbf {y} _ {k}\\right) \\triangleq \\sum_ {i = 1} ^ {n} \\mathbf {A} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.519, + 0.906, + 0.597 + ], + "angle": 0, + "content": "where \\(\\mathbf{A}_k^{(\\ell,h)}(a_k,i)\\) represents the attention weights of the newly generated token \\(\\mathbf{y}_k\\) assigned to the image token \\(\\mathbf{v}_i\\). VAR quantifies the extent of the token \\(\\mathbf{y}_k\\)'s interaction with visual information: a higher VAR score indicating a greater contribution from image tokens during \\(\\mathbf{y}_k\\)'s generation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.598, + 0.906, + 0.718 + ], + "angle": 0, + "content": "Logit Lens. We utilize this technique to investigate how the model interprets the visual hidden state \\(\\mathbf{v}_i^\\ell\\) during inference via text. We denote the linear projector before softmax as \\(\\mathbf{W}_{\\mathcal{V}} \\in \\mathbb{R}^{|\\mathcal{V}| \\times d}\\), which is applied to \\(\\mathbf{y}_{k-1}^L\\) to predict the probability of next token over the vocabulary \\(\\mathcal{V}\\). Then, the logit lens transforms the hidden state \\(\\mathbf{v}_i^\\ell\\) of the image tokens to the prediction probability distribution over the vocabulary by the linear projector \\(\\mathbf{W}_{\\mathcal{V}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.729, + 0.905, + 0.748 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} (\\mathcal {V} | \\mathbf {v} _ {i} ^ {\\ell}) = \\operatorname {s o f t m a x} \\left(\\mathbf {W} _ {\\mathcal {V}} \\cdot \\mathbf {v} _ {i} ^ {\\ell}\\right) \\in \\mathbb {R} ^ {| \\mathcal {V} |}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.761, + 0.906, + 0.822 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}_j(\\mathcal{V}|\\mathbf{v}_i^\\ell)\\) corresponds to the \\(j\\)-th text token in the vocabulary. To explain the processed image token, the text token with the highest probability is considered as the model's interpretation of the hidden state \\(\\mathbf{v}_i^\\ell\\) at layer \\(\\ell\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.832, + 0.822, + 0.849 + ], + "angle": 0, + "content": "3.2. Experimental Setup for Case Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.901 + ], + "angle": 0, + "content": "We conduct case studies with a randomly selected subset of 2,000 images from COCO 2014 validation set [25]. These images represent diverse scenes and activities across 80" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25006" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.091, + 0.283, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.228, + 0.286, + 0.307 + ], + "angle": 0, + "content": "The image features a yellow bus driving down a street, with a red car following behind it. ... a few houses visible in the background. There are also a couple of people walking on the sidewalk, ... Additionally, there is a fire hydrant located near the left side of the street, and a stop sign can be seen further down the road." + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.09, + 0.905, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.332, + 0.908, + 0.391 + ], + "angle": 0, + "content": "Figure 3. Case study of image hidden state interpretation in LLaVA-1.5-7B via logit lens. The heatmap illustrates the retrieved texts of the image hidden states across layers in the three distinct regions, differentiated by color. Our findings reveal that the model's semantic comprehension of image tokens emerges in the later middle layers (19-26) while remaining largely absent in earlier layers. The real and hallucinated object tokens are presented in blue and red in the description, respectively." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.415, + 0.482, + 0.491 + ], + "angle": 0, + "content": "common object categories, each paired with multiple object annotations. The 7B version of LLaVA-1.5 serves as the main focus for the subsequent analysis. In Appendix C.1, we further repeat our case studies on other LVLMs, including Shikra and MiniGPT-4, and observe consistent findings." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.491, + 0.483, + 0.611 + ], + "angle": 0, + "content": "To investigate the internal patterns in generating real and hallucinated object tokens, we use the model with greedy search to generate captions for the selected images, prompted by \"Please help me describe the image in detail\". Real and hallucinated object tokens are then identified using ground truth annotations as a reference. For multi-token objects, only the first token is considered. As a result, we obtained 1,842 hallucinated tokens and 4,397 real tokens." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.621, + 0.483, + 0.651 + ], + "angle": 0, + "content": "3.3. Finding 1: Middle Layers Matter for Visual Information Interaction" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.659, + 0.483, + 0.795 + ], + "angle": 0, + "content": "To assess the contribution of visual information to token generations, we compute the VAR score (Eq. (1)) for real object tokens \\(\\mathbf{y}_r\\) across all layers \\(\\ell \\in [L]\\) and heads \\(h \\in [H]\\). We calculate the mean of \\(\\mathrm{VAR}^{(\\ell,h)}(\\mathbf{y}_r)\\) for all real object tokens in our case dataset, with the results depicted in Fig. 2 (a). The visualization shows that the middle layers, i.e., 5-26 layers, continuously exhibit high attention weights to the image tokens, indicating that visual information interaction primarily occurs in the middle layers." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.796, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We further analyze how the model processes visual information by examining signals from the MHSA sublayers. Using the logit lens, we quantify the contribution of the MHSA sublayers to real token prediction as \\(\\mathbf{p}_{\\mathrm{o}}(\\mathcal{V}|\\mathbf{a}_{\\mathrm{r}}^{\\ell})\\) where \\(\\mathbf{a}_{\\mathrm{r}}^{\\ell}\\) is the output of the MHSA sublayer at layer \\(\\ell\\), and o denotes the index of the real object token \\(\\mathbf{y}_{\\mathrm{r}}\\) in the vocabulary. Fig. 2 (b) reveals two patterns in the contributions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.415, + 0.905, + 0.445 + ], + "angle": 0, + "content": "from the MHSA sublayers: lower in 5-18 layers and higher in 19-26 layers, reflecting varied use of visual information." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.446, + 0.906, + 0.551 + ], + "angle": 0, + "content": "To better understand these two patterns, we use the logit lens to map the hidden states of image token \\(\\mathbf{v}_i^\\ell\\) to text. Specifically, for each image token \\(\\mathbf{v}_i\\) at layer \\(\\ell\\), we retrieve the text token in the vocabulary with the highest probability, i.e., \\(\\mathrm{argmax}_{1\\leq j\\leq |\\mathcal{V}|}\\{\\mathbf{p}_j(\\mathcal{V}|\\mathbf{v}_i^\\ell)\\}\\). A case is shown in Fig. 3, revealing two stages in the middle layers with different visual information usage:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.552, + 0.906, + 0.702 + ], + "angle": 0, + "content": "- Stage 1: Visual Information Enrichment. The first stage, in layers 5–18, shows that retrieved text tokens are less related to the corresponding image patches, suggesting the model is unable to interpret visual information. This misalignment might explain the low prediction contributions observed in Fig. 2 (b). Meanwhile, these layers continue to show high VAR scores, indicating that the object tokens are accumulating visual information through self-attention. In Secs. 3.4 and 3.5, we show that such attention serves as a key indicator to identify hallucinations." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.702, + 0.906, + 0.824 + ], + "angle": 0, + "content": "- **Stage 2: Semantic Refinement.** The second stage, in layers 19–26, shows that the retrieved text tokens are semantically consistent with the image patches, suggesting the model is able to interpret and utilize the visual information encoded in the image tokens. Given the high VAR during this stage, we term it as semantic refinement where the model actively interacts with the semantic information of image tokens to reason object token prediction." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.552, + 0.906, + 0.824 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.832, + 0.905, + 0.863 + ], + "angle": 0, + "content": "3.4. Finding 2: Inactive Visual Attention in Middle Layers Implies Hallucination" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Given that visual information is primarily processed in the middle layers, a natural question arises: does the model dis" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25007" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.287, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.089, + 0.482, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.241, + 0.288, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.241, + 0.482, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.401, + 0.484, + 0.471 + ], + "angle": 0, + "content": "Figure 4. Case study of the visual attention ratio distribution over heads and layers in LLaVA-1.5-7B. Left: real objects; Right: hallucinated objects. We find that the hallucinated object tokens exhibit inactive attention patterns during visual information enrichment compared to the real ones." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.496, + 0.483, + 0.724 + ], + "angle": 0, + "content": "play unusual attention patterns in these layers when generating hallucinated object tokens? Fig. 4 presents the VAR distribution for real object tokens ('bus' and 'car') and hallucinated ones ('people' and 'fire hydrant') from the case of Fig. 3. We observe that the hallucinated object tokens demonstrate an inactive attention pattern during the visual information enrichment stage (5-18 layers) compared to the real ones. We conjecture that such pattern weakens the interaction between the object token and image tokens in this stage, limiting the propagation of visual information and potentially leading to hallucinations. To quantify this observation, we introduce a metric, Summed Visual Attention Ratio (SVAR), calculated by averaging VAR scores over all heads and summing across selected layers \\([\\ell_s,\\ell_e]\\). Specifically, for a real object token \\(\\mathbf{y_r}\\) in \\([\\ell_5,\\ell_{18}]\\), we compute:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.734, + 0.483, + 0.776 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S V A R} _ {5 - 1 8} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right) \\triangleq \\frac {1}{H} \\sum_ {\\ell = 5} ^ {1 8} \\sum_ {h = 1} ^ {H} \\operatorname {V A R} ^ {(\\ell , h)} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.885 + ], + "angle": 0, + "content": "We conduct a statistical experiment on the \\(\\mathrm{SVAR}_{5-18}\\) metric for both real and hallucinated tokens. The results, depicted in Fig. 5 (a), and the associated statistical test detailed in Appendix C.2, indicate a salient difference: the model assigns significantly higher attention weights to image tokens when generating real object tokens during visual information enrichment compared to hallucinated ones." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.433, + 0.901 + ], + "angle": 0, + "content": "Fig. 5 (b) shows a similar trend in LLaVA-1.5-13B." + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.089, + 0.707, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.089, + 0.895, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.225, + 0.905, + 0.252 + ], + "angle": 0, + "content": "Figure 5. \\(\\mathrm{SVAR}_{5-18}\\) score distributions across object token types for the 7B (a) and 13B (b) versions of LLaVA-1.5." + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.266, + 0.709, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.714, + 0.267, + 0.896, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.402, + 0.905, + 0.445 + ], + "angle": 0, + "content": "Figure 6. Object hallucination detection curves for LLaVA-1.5-7B. We show the ROC and Precision-Recall curves of \\(\\mathrm{SVAR}_{5 - 18}\\) metric for object hallucination detection on the case study dataset." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.471, + 0.877, + 0.487 + ], + "angle": 0, + "content": "3.4.1 Application: Object Hallucination Detection" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.495, + 0.907, + 0.736 + ], + "angle": 0, + "content": "Building upon our Finding 2, we apply the \\(\\mathrm{SVAR}_{5-18}\\) metric to detect object hallucinations. We assess the efficacy of \\(\\mathrm{SVAR}_{5-18}\\) in reflecting object hallucination using our case dataset, where a positive sample is a real object token and a negative sample is a hallucinated one. For comparison, we use the internal confidence metric recently proposed in [21] as a baseline. The internal confidence uses the maximum probability of the object token within all image hidden states \\(\\{\\mathbf{v}_i^\\ell : i \\in [n], \\ell \\in [L]\\}\\), mapped by the logit lens for detection. The qualitative results are presented in Fig. 6 and the results for LLaVA-1.5-13B are shown in Appendix C.1. Compared to internal confidence, using the simple \\(\\mathrm{SVAR}_{5-18}\\) metric improves the AUROC by \\(8.82\\%\\) and the AP by \\(3.53\\%\\), verifying the utility of our metric. This further suggests that the middle layers provide crucial indicator information for object hallucination." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.737, + 0.905, + 0.797 + ], + "angle": 0, + "content": "Beyond the hand-crafted \\(\\mathrm{SVAR}_{5-18}\\) measure, we explore the potential of middle layers to indicate hallucinations by training a simple model to derive metrics directly from raw visual attention states." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.798, + 0.905, + 0.873 + ], + "angle": 0, + "content": "Experimental setting. We train a two-layer MLP by inputting the concatenated VAR scores across all heads in the layer range of interest \\([\\ell_s,\\ell_e]\\) to classify the real and hallucinated object tokens. Specifically, the input vector \\(\\mathbf{x}(\\mathbf{y}_r)\\) for the real token \\(\\mathbf{y}_r\\) can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.883, + 0.905, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right) = \\left[ \\operatorname {V A R} ^ {\\left(\\ell_ {s}, 1\\right)}, \\operatorname {V A R} ^ {\\left(\\ell_ {s}, 2\\right)}, \\dots , \\operatorname {V A R} ^ {\\left(\\ell_ {e}, H\\right)} \\right] ^ {\\top}. \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25008" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.089, + 0.895, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.288, + 0.908, + 0.318 + ], + "angle": 0, + "content": "Figure 7. Visualization of attention maps over image for 'bus' (real) and 'people' (hallucinated) object tokens in heads \\((\\ell, h)\\). We find that the heads tend to interact with multiple objects when generating hallucinated object tokens. More examples can be found in Appendix C.4." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.343, + 0.482, + 0.403 + ], + "angle": 0, + "content": "We split the case dataset into training and test sets in the ratio of 8:2, and train the MLP with cross-entropy loss. The model performance is evaluated using accuracy, AUROC, and recall metrics. Training details are in Appendix B.2." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.403, + 0.483, + 0.555 + ], + "angle": 0, + "content": "Results. We experiment with four layer ranges in LLaVA-1.5-7B: [0, 4], [5, 18], [19, 26], and [27, 31], as shown in Tab. 1. We can see using the layers of visual information enrichment (5-18) achieves the best performance among other ranges, validating the effectiveness of our Finding 2. We observe that other layers also encode hallucination-related information which can be learned to detect hallucinations. However, compared to the explicit pattern in 5-18 layers, the implicit patterns contained in other ranges require computation costs for feature learning." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.561, + 0.483, + 0.594 + ], + "angle": 0, + "content": "3.5. Finding 3: Attention Heads Interact with Multiple Objects Incurring Object Hallucination" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.6, + 0.483, + 0.812 + ], + "angle": 0, + "content": "Considering the MHSA mechanism incorporates various attention heads to aggregate information, we analyze heatmaps over the image for both real and hallucinated object tokens ('bus' vs 'people') to investigate the head behavior during visual information enrichment. A case is shown in Fig. 7 and more examples can be found in Appendix C.4. We can see that each head focuses on distinct local details, yet the attention distribution for the real token consistently aligns with the spatial extent of the corresponding object. In contrast, for the hallucinated token, the heads interact with inconsistent objects in the image during this stage. We speculate that such unstable head behavior encodes mixed information from multiple objects into the object token, potentially leading to hallucinations." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.822, + 0.385, + 0.84 + ], + "angle": 0, + "content": "4. Object Hallucination Mitigation" + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.848, + 0.414, + 0.863 + ], + "angle": 0, + "content": "4.1. Heads Guided Attention Intervention" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Inspired by the insights from Sec. 3 that improper processing of visual information during inference can lead to object" + }, + { + "type": "table", + "bbox": [ + 0.539, + 0.34, + 0.885, + 0.412 + ], + "angle": 0, + "content": "
    Layers0-45-1819-2627-310-31
    Accuracy82.6184.4681.4977.7284.46
    AUROC89.5790.1987.3484.3090.28
    Recall66.2272.3468.8863.5671.28
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.422, + 0.907, + 0.451 + ], + "angle": 0, + "content": "Table 1. Object hallucination detection results \\((\\%)\\) of different layer ranges of interest on LLaVA-1.5-7B." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.474, + 0.907, + 0.583 + ], + "angle": 0, + "content": "hallucinations, we aim to correct this process to alleviate object hallucination. Specifically, we adjust the attention weights assigned to image tokens, i.e., \\(\\{\\mathbf{A}_k^{(\\ell,h)}(a_k,i)\\}_{i=1}^n\\), in each head at the middle layers during inference for intervention. To modify the attention weights in time step \\(k\\), we extract the attention score matrix \\(\\mathbf{S}_k^{(\\ell,h)}\\) before softmax operation:" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.583, + 0.906, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {k} ^ {(\\ell , h)} = \\left(\\frac {\\mathbf {Q} _ {\\ell , h} \\mathbf {K} _ {\\ell , h} ^ {\\top}}{\\sqrt {d _ {k}}}\\right) _ {k}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.628, + 0.906, + 0.658 + ], + "angle": 0, + "content": "where \\(\\mathbf{Q}_{\\ell,h}\\) and \\(\\mathbf{K}_{\\ell,h} \\in \\mathbb{R}^{a_k \\times d_k}\\) represent the query and key matrices of dimension \\(d_k\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.907, + 0.856 + ], + "angle": 0, + "content": "Guided by the attention pattern difference in Finding 2, we amplify the original attention scores in the layers of visual information enrichment by adding positive values to enhance visual information interaction. Furthermore, leveraging the head behavior observed in Finding 3, we compute these positive values by averaging the absolute attention scores across all heads, where only the consistent regions interacted by different heads receive large enhancement. By integrating the attention information from various heads, we can find a more faithful and object-related direction for attention shift to reduce hallucinations. Formally, for each image token \\( i \\in [n] \\) across all heads \\( h \\in [H] \\) in layer \\( \\ell \\in [\\ell_s, \\ell_e] \\), we adjust the visual attention scores by:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.863, + 0.907, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) = \\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) + \\alpha \\frac {1}{H} \\sum_ {h = 1} ^ {H} \\left| \\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) \\right|, \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25009" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.129, + 0.089, + 0.872, + 0.265 + ], + "angle": 0, + "content": "
    MethodLLaVA-1.5-7BLLaVA-1.5-13BShikra-7BMiniGPT-4-7BAvg.
    \\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)
    Decoding Strategy
    Greedy53.015.676.749.814.678.257.615.775.331.812.071.148.114.5
    Beam55.615.477.550.413.879.059.016.374.629.29.971.248.613.9
    OPERA45.613.179.142.613.277.841.413.773.525.49.671.238.812.4
    Contrastive Decoding
    \\(\\mathsf{VCD}^{\\dagger}\\)58.618.272.853.615.375.856.415.575.241.414.168.252.515.8
    \\(\\mathsf{PAI}^{\\dagger}\\)24.27.175.233.09.277.838.610.176.223.28.271.429.88.7
    \\(\\mathsf{Ours}^{\\dagger}\\)25.06.776.125.88.877.323.89.472.721.48.070.824.08.2
    \\(\\Delta \\%\\)↑3.3%↓5.6%↓21.8%↓4.3%↓38.3%↓6.9%↓7.8%↓2.4%↓19.5%↓5.7%
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.274, + 0.908, + 0.318 + ], + "angle": 0, + "content": "Table 2. CHAIR hallucination evaluation and F1 results on three LVLMs with max new token set to 512. † denotes using the greedy decoding strategy. Our method outperforms other baselines and also preserves the richness of the descriptions. Δ% denotes the relative performance improvement with respect to the second-best method." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.343, + 0.483, + 0.389 + ], + "angle": 0, + "content": "where the \\([\\ell_s,\\ell_e]\\) denotes the range of visual information enrichment, and the parameter \\(\\alpha\\) is defined as a balance factor to control the intervention strength." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.404, + 0.376, + 0.421 + ], + "angle": 0, + "content": "4.2. Experimental Setup and Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.429, + 0.484, + 0.519 + ], + "angle": 0, + "content": "Models. We conduct experiments on three representative LVLMs to evaluate the effectiveness and generalization of our method, including the LLaVA-1.5 [27], Shikra [4], and MiniGPT-4 [54]. In our experiments, we use the 7B and 13B versions of LLaVA-1.5 to study the scale effect, while other LVLMs are 7B models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.522, + 0.483, + 0.824 + ], + "angle": 0, + "content": "Baselines. We adopt two commonly used decoding strategies and three mainstream hallucination mitigation approaches as the baseline methods, including greedy decoding, beam search decoding [37], OPERA [19], VCD [24], and PAI [28]. Greedy decoding selects the token with the highest probability over the vocabulary as the predicted next token. Beam search decoding maintains multiple beams and selects the top tokens with the highest cumulative probabilities at the end of generation. Improved on beam search, OPERA introduces an overtrust penalty term on the attention weights during inference with a rollback strategy to mitigate hallucinations. Different from the above three decoding approaches, VCD and PAI can be categorized as contrastive decoding methods. Specifically, VCD subtracts the output logits of the distorted visual input from the original output logits to reduce the statistical priors. In addition to using contrastive decoding, PAI further manipulates the attention matrix to overcome language bias. In our experiments, we use the default parameters of these baselines and unify \\( N_{\\mathrm{beam}} = 5 \\) for the beam search decoding and OPERA." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Benchmark and Metrics. Following [19], we conduct experiments on 500 random images from the COCO 2014 validation set. To evaluate the degree of object hallucinations in the image captioning task, we adopt the CHAIR [34] criteria which computes the proportion of all objects men" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.343, + 0.907, + 0.404 + ], + "angle": 0, + "content": "tioned in the caption that are not present in the ground-truth annotations. CHAIR provides two main metrics, including \\(\\mathrm{CHAIR}_I(C_I)\\) and \\(\\mathrm{CHAIR}_S(C_S)\\) that assess instance-level and sentence-level hallucinations, respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.41, + 0.91, + 0.445 + ], + "angle": 0, + "content": "\\[\nC _ {I} = \\frac {\\left| \\{\\text {h a l l u c i n a t e d o b j e c t s} \\} \\right|}{\\left| \\{\\text {a l l m e n t i o n e d o b j e c t s} \\} \\right|}, C _ {S} = \\frac {\\left| \\{\\text {c a p t i o n s w / h a l l u c i n a t e d o b j e c t s} \\} \\right|}{\\left| \\{\\text {a l l c a p t i o n s} \\} \\right|},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.907, + 0.493 + ], + "angle": 0, + "content": "where lower values indicate fewer hallucinations. Following [28], we also adopt the F1 score to assess the richness and accuracy of the generated descriptions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.494, + 0.909, + 0.63 + ], + "angle": 0, + "content": "Implementation details. Our method contains two parameters: the visual information enrichment range \\([\\ell_s, \\ell_e]\\) and the balance factor \\(\\alpha\\) in Eq. (6). Utilizing the VAR feature and logit lens described in Sec. 3.1, we can easily establish suitable ranges for any other LVLMs. In our experiment, we set the ranges as [5, 18] for both versions of LLaVA-1.5, [3, 13] for Shikra, and [3, 14] for MiniGPT-4. We set \\(\\alpha\\) to 0.5 for LLaVA-1.5, MiniGPT-4, and 0.55 for Shikra. We implement our method with greedy decoding as a baseline." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.63, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Results. Tab. 2 presents the experimental results for the selected LVLMs with max new tokens of 512. From the Tab. 2, our approach outperforms the three decoding strategies in reducing hallucinations and achieves an average reduction of \\(19.5\\%\\) in \\(C_S\\) and \\(5.7\\%\\) in \\(C_I\\), compared to the second-best baseline. Compared to VCD, our method not only achieves superior hallucination mitigation performance but also better preserves the richness of the descriptions. Compared to PAI which requires the cost of once additional forward process for contrastive decoding, our approach achieves comparable or superior performance by only adjusting attention weights during inference, validating the efficacy of our method. Moreover, the consistent reduction of hallucinations across four different LVLMs confirms the generalizability of our findings. To evaluate the impact of generated token lengths, we conduct experiments on LLaVA-1.5-7B by varying the max new token in \\(\\{64, 128, 256\\}\\). The results, reported in Tab. 3, show that" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25010" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.482, + 0.21 + ], + "angle": 0, + "content": "
    Methodmax new token 64max new token 128max new token 256Avg.
    \\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓
    Decoding Strategy
    Greedy23.88.074.752.415.576.753.015.676.743.113.0
    Beam17.66.075.154.414.877.655.615.477.542.512.1
    OPERA19.06.374.444.212.978.845.613.179.136.310.8
    Contrastive Decoding
    \\(\\mathrm{VCD}^{\\dagger}\\)26.09.373.356.816.974.558.618.272.847.114.8
    \\(\\mathrm{PAI}^{\\dagger}\\)19.86.274.024.27.375.224.27.275.222.76.9
    \\(\\mathrm{Ours}^{\\dagger}\\)18.25.473.924.87.176.025.07.176.122.76.5
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.22, + 0.483, + 0.263 + ], + "angle": 0, + "content": "Table 3. CHAIR hallucination evaluation and F1 results on LLaVA-1.5-7B with varying max new token in \\(\\{64,128,256\\}\\). † denotes using the greedy decoding strategy." + }, + { + "type": "table", + "bbox": [ + 0.129, + 0.275, + 0.447, + 0.345 + ], + "angle": 0, + "content": "
    Layers0-45-1819-2627-31Greedy
    \\(C_S\\ ↓\\)31.025.053.453.453.0
    \\(C_I\\ ↓\\)10.46.714.315.715.6
    F1↑77.176.177.577.276.7
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.355, + 0.483, + 0.385 + ], + "angle": 0, + "content": "Table 4. CHAIR hallucination evaluation and F1 score among four layer ranges on LLaVA-1.5-7B with max new token set to 512." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.41, + 0.484, + 0.471 + ], + "angle": 0, + "content": "our method consistently reduces hallucinations across different token lengths and achieves the best performance on average, demonstrating its robustness. We provide qualitative results in Appendix C.7." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.483, + 0.334, + 0.499 + ], + "angle": 0, + "content": "5. Ablations and Discussions" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.509, + 0.483, + 0.705 + ], + "angle": 0, + "content": "Layers of attention intervention. Motivated by the empirical observation of implicit hallucination patterns across layers beyond the 5-18 range in Sec. 3.4.1, we investigate whether interventions in these layers can also mitigate object hallucinations. We apply our approach (Eq. (6)) to the layer ranges [0, 4], [19, 26], and [27, 31] in LLaVA-1.5-7B, and the results are reported in Tab. 4. We observe that the 5-18 layer range largely outperforms the other ranges while using some ranges (19-26 and 27-31) even enhanced hallucinations instead. The result suggests that explicit patterns in visual information enrichment are more effective than implicit patterns, facilitating more effective hallucination mitigation through simple attention intervention." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.483, + 0.885 + ], + "angle": 0, + "content": "Different attention intervention strategies. To validate the efficacy of our method in adjusting attention weights to reduce object hallucinations, we compare it with the inference intervention component proposed in PAI [28]. The inference intervention component roughly excites attention weights by computing a weighted sum of the attention scores and their absolute values across individual heads. We apply this approach to the same layer ranges in ours on LLaVA-1.5-7B, Shikra, and MiniGPT-4. Tab. 5 suggests that our attention intervention method surpasses that of PAI, as our method integrates attention information from various heads to shift attention toward a more truthful direction." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Balance factor \\(\\alpha\\) sensitivity. To examine the influence of" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.089, + 0.707, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.089, + 0.906, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.537, + 0.236, + 0.882, + 0.251 + ], + "angle": 0, + "content": "Figure 8. Parameter sensitivity of \\(\\alpha\\) with CHAIR metrics." + }, + { + "type": "table", + "bbox": [ + 0.537, + 0.264, + 0.884, + 0.332 + ], + "angle": 0, + "content": "
    MethodLLaVA-1.5-7BShikra-7BMiniGPT-4-7B
    CS↓CI↓CS↓CI↓CS↓CI↓
    PAI*26.68.145.813.630.29.5
    Ours25.06.723.89.421.48.0
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.341, + 0.906, + 0.385 + ], + "angle": 0, + "content": "Table 5. CHAIR hallucination evaluation and F1 results on three LVLMs. \\(\\star\\) denotes only using the inference intervention component in the same layer range as ours. Greedy decoding is adopted." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.41, + 0.907, + 0.547 + ], + "angle": 0, + "content": "\\(\\alpha\\) on intervention efficacy, we vary its value in the range of \\(\\{0.3, 0.4, 0.5, 0.6, 0.7\\}\\) and the results of CHAIR metrics and F1 score for the 7B version of both LLaVA-1.5 and MiniGPT-4 are shown in Fig. 8. We find that a lower \\(\\alpha\\) limits hallucination mitigation effectiveness, whereas a higher \\(\\alpha\\) compromises the richness of descriptions. These results indicate that an appropriate \\(\\alpha\\) value (e.g., 0.5 for both selected LVLMs) balances the reduction of hallucinations with the maintenance of detailed visual descriptions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.559, + 0.741, + 0.575 + ], + "angle": 0, + "content": "6. Conclusion and Insights" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.584, + 0.907, + 0.903 + ], + "angle": 0, + "content": "We introduce a new perspective, visual information processing, to investigate the underlying mechanisms driving object hallucination. Analyzing through the lens of attention, we identify three key findings and discover a simple yet effective method for reducing hallucinations at inference time. Our study deepens the understanding of how hallucinations are produced in LVLMs. We conclude with three insights for future direction: 1) Based on LVLMs' interpretation in semantic refinement stage, the image tokens may be further categorized into sub-groups, such as object tokens, color tokens, and textual tokens, enabling us to explore how the LVLMs extract different types of visual information. 2) While we focus on visual information processing, there may exist more granular, stage-wise mechanisms that could explain model behavior more precisely. 3) Instead of external interventions on LVLM outputs, such as contrastive decoding, we suggest that targeted modifications to specific internal states, like attention weights in middle layers, offer a more effective method for calibration. Our insights may aid the community in developing more trustworthy and reliable LVLMs against hallucinations." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "25011" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.244, + 0.108 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.114, + 0.486, + 0.187 + ], + "angle": 0, + "content": "This work is supported by the National Science Foundation of China (62376281, 62206048), the Natural Science Foundation of Jiangsu Province (BK20220819), and the Fundamental Research Funds for the Central Universities (2242024k30035)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.212, + 0.188, + 0.228 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.238, + 0.484, + 0.294 + ], + "angle": 0, + "content": "[1] Jize Cao, Zhe Gan, Yu Cheng, Licheng Yu, Yen-Chun Chen, and Jingjing Liu. 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However, most studies primarily focus on the language aspect rather than the visual. In this paper, we address how LVLMs process visual information and whether this process causes hallucination. Firstly, we use the attention lens to identify the stages at which LVLMs handle visual data, discovering that the middle layers are crucial. Moreover, we find that these layers can be further divided into two stages: "visual information enrichment" and "semantic refinement" which respectively propagate visual data to object tokens and interpret it through text. By analyzing attention patterns during the visual information enrichment stage, we find that real tokens consistently receive higher attention weights than hallucinated ones, serving as a strong indicator of hallucination. Further examination of multi-head attention maps reveals that hallucination tokens often result from heads interacting with inconsistent objects. Based on these insights, we propose a simple inference-time method that adjusts visual attention by integrating information across various heads. Extensive experiments demonstrate that this approach effectively mitigates hallucinations in mainstream LVLMs without additional training costs. $^{1}$ + +# 1. Introduction + +Building on the foundations of Large Language Models (LLMs), Large Vision-Language Models (LVLMs) [4, 27, 32, 44, 49, 51, 54] have emerged as powerful tools for un + +![](images/685fedd56bbbba1270aefe0e957e77abfea9f6c1ad15736229b932edb97db922.jpg) +Figure 1. Illustration of our findings: (i) visual information is primarily processed in the middle layers where (a) the model extracts the visual information and then (b) interprets the semantics embedded in image tokens; (ii) for real tokens like "cat", the attention weights over image tokens are generally higher than hallucinated ones like "TV" in (a); (iii) the model may combine the visual features extracted from multiple objects to produce hallucinations. + +derstanding visual inputs and generating textual responses aligned with user intent. Their multi-modal nature has enabled a large variety of vision-language tasks, e.g., image captioning, visual question answering, and visual dialog. + +Despite generating coherent textual responses, these models often exhibit undesirable object hallucinations – producing objects that do not exist in the visual input. + +Although various approaches, such as visual instruction fine-tuning [14, 20, 26, 46], the integration of external expert models [5, 43, 45, 50], and contrastive decoding strategies [9, 24, 28, 42], have been proposed to address the object hallucination issue in LVLMs, the underlying mechanisms driving these hallucinations remain poorly understood. A few studies have preliminarily explored the causes of object hallucination, identifying the language bias as the primary factor, with examples including the "anchor pattern" [19] and "text inertia" [28]. In essence, these studies found that LVLMs tend to prioritize internal textual knowledge over external visual information as more tokens are generated. However, these studies have overlooked the devils in the visual parts – while intuitively, improper processing of visual information within the LVLMs could contribute more to the emergence of object hallucinations. + +In this paper, we delve into how LVLMs process visual information from image tokens and how this affects the generation of object hallucinations. Building on the three-stage mechanism identified in LLMs for retrieving factual knowledge [12], we examine whether LVLMs exhibit similar distinct stages during inference and, if so, which stage is critical for processing visual information. We propose a simple score called Visual Attention Ratio (VAR) to examine the distribution of visual attention across layers, revealing that the middle layers play a crucial role in processing visual information. To study how the model processes visual information in these middle layers, we leverage the logit lens [29] method to decode the hidden states of image tokens into LVLMs' vocabulary, identifying two crucial stages as illustrated in Fig. 1: a visual information enrichment stage propagates visual information to the object token, and a semantic refinement stage interprets the encoded visual information through text. + +Secondly, focusing on these middle layers, we observe that the hallucinated tokens often exhibit (1) less active attention patterns, and (2) inconsistent attentions across different heads during visual information enrichment stage, compared to real ones. To quantify these observations, we first introduce a metric based on VAR, and confirm that real object tokens tend to assign higher attention weights over image tokens during visual information enrichment than hallucinated ones, illustrated in Fig. 1. Relying on our finding, we utilize the metric in this stage to detect hallucinated object tokens, achieving AUROC and mAP up to $74\%$ and $88\%$ on LLaVA-1.5-7B [27]. Second, given the various attention heads used in the Multi-Heads Self-Attention (MHSA) mechanism [40] for information aggregation, we explore the head behavior by visualizing the attention heatmaps over the input image. As illustrated + +in Fig. 1, we find that the heads interact with inconsistent objects during visual information enrichment when generating hallucinations. + +Our empirical findings provide valuable insights into the way object hallucinations are generated, intuitively described as follows (Fig. 1): In visual information enrichment, the model's ambiguous interactions with multiple objects result in limited and mixed visual information being propagated to the object token. Subsequently, in semantic refinement, this imprecise visual information leads the model to mistakenly associate semantic information from different objects, ultimately causing hallucinations. + +Inspired by our findings, we propose a simple method to adjust the visual information process in the middle layers by integrating attention information from various heads during inference. Extensive experiments on three mainstream LVLMs show significant hallucination mitigation compared to the original models, with average reductions in $\mathrm{CHAIR}_I$ and $\mathrm{CHAIR}_S$ up to 6.3 and 24.1 points, respectively, while preserving detail in descriptions. + +# 2. Related Work + +Large Vision-Language Models. The recent integration of advanced open-source LLMs, like Llama [38, 39] and Vicuna [6], has greatly expanded the capabilities of LVLMs, enabling them to perform more complex vision-language tasks. Typically, the architecture of recent LVLMs incorporates three key components: a vision branch, such as CLIP [33] and EVA [8], to encode image inputs, a modality connector to transform image features into image embeddings aligning with text modality, and a pretrained language model to process image and prompt embeddings to generate responses. LLaVA-1.5 [27] employs an MLP to map the output of the vision branch into 576 image embeddings. Similarly, Shikra [4] utilizes one linear layer to align image features. While MiniGPT-4 [54] adopts a learnable querying transformer to establish vision-language connections, with just 32 image tokens as LVLM input. Despite their impressive capabilities, the above LVLMs suffer from severe object hallucinations. In this paper, we focus on interpreting, detecting, and mitigating their hallucinations. + +Object Hallucination in LVLMs. Object hallucination [48, 52] is a prevalent and critical issue in current LVLMs where the model erroneously generates descriptions of non-existent objects in images, posing significant risks in high-stakes fields such as medical imaging [18, 23], sequential recommendation systems [15, 35], and autonomous driving [7]. Previous studies to mitigate this issue have primarily focused on visual instruction finetuning [14, 20, 26, 46, 53], incorporating external expert models [5, 43, 45, 50], and improving decoding strategies [9, 19, 24, 28, 42]. Despite numerous efforts, our understanding of the underlying mechanism driving these er + +rors remains limited. Recent studies like OPERA [19] have pointed specific "anchor patterns" in text tokens that always align with the onset of hallucinated contents, and PAI [28] has identified "text inertia" as another contributing factor, as LVLMs reproduce identical hallucinated descriptions when solely input part of historical generated text. Contrary to these perspectives that focus on language bias, we investigate the causes of object hallucinations from the view of visual information processing through the lens of attention. + +Interpretability in Foundation Models. In the field of NLP, numerous studies have analyzed LLMs to explore the internal model knowledge and understand model behavior in specific settings from the perspectives of attention maps [3, 47], neural activation patterns [17], and intermediate hidden states [13, 36]. The logit lens [29], which transforms the hidden states at each layer into the vocabulary space using the model's own linear projector before softmax, offers insightful observations into the next token prediction process [11, 16] in LLMs. Our work adapts the logit lens method to analyze hidden states of image tokens, enabling us to interpret the LVLMs' process of understanding the visual information via textual vocabulary. Few studies explore the internal mechanisms of LVLMs [1, 2, 10], notable efforts include [30], which extends an unimodal causal tracing tool for studying neural mechanisms in BLIP's image-conditioned text generation, and [31], which introduces a dictionary learning-based framework to extract multi-modal concepts for interpreting intermediate representations. Compared to prior works, our study leverages the internal signals from attention weights to uncover the generation of hallucinated objects. + +# 3. Understanding Object Hallucinations + +In this section, we start by introducing the generation process of LVLMs and the analytical tools, including visual attention ratio and logit lens. We then conduct case studies focusing on three key aspects: the processing of visual information, the attention patterns of object tokens, and the behavior of heads during object token generation. + +# 3.1. Preliminary + +Notation. The input to LVLMs is initialized with a sequence of $d$ -dimensional image tokens $\{\mathbf{v}_1, \dots, \mathbf{v}_n\}$ and instruction text (prompt) tokens $\{\mathbf{t}_1, \dots, \mathbf{t}_m\}$ . Typically structured as a Transformer decoder [40], the LVLM outputs responses in an autoregressive manner: at time step $k$ , the model processes the initial input tokens $\{\mathbf{v}_1, \dots, \mathbf{v}_n, \mathbf{t}_1, \dots, \mathbf{t}_m\}$ , followed by the sequence of $k-1$ previously generated tokens $\{\mathbf{y}_1, \dots, \mathbf{y}_{k-1}\}$ , to predict the next token $\mathbf{y}_k$ . Let $L$ denote the number of Transformer layers, each with $H$ heads. At layer $\ell \in [L]$ , we denote the attention weights in head $h \in [H]$ as $\mathbf{A}_k^{(\ell,h)} \in \mathbb{R}^{a_k \times a_k}$ , where $a_k = n + m + k - 1$ . Additionally, we define $\mathbf{v}_i^\ell$ and $\mathbf{y}_{k-1}^\ell$ as + +![](images/93b8bdab5265e1ecdbded897acbf3241e647d54debf4a39c14d04b4a2cec5932.jpg) +Figure 2. (a) Distribution of visual attention ratio for real object tokens across heads and layers in LLaVA-1.5-7B, sorted row-wise by attention ratios. Note that the high attention in the 0-th layer (bottom row, green rectangle) is not consistent across all LVLMs, as Shikra and MiniGPT-4 models fail to exhibit this pattern, see Appendix C.1. (b) The logit contribution of attention sublayers to real token prediction. We find the middle layers continuously assign higher attention weights to image tokens and exhibit two different contribution patterns to the correct prediction. + +![](images/955fa3233829d0eaf50814335de97a3ed4ecaa97a85f66be050725b43e645f15.jpg) + +the hidden states for the image token $\mathbf{v}_i$ and generated token $\mathbf{y}_{k - 1}$ at layer $\ell$ , respectively. The real and hallucinated object tokens are noted as $\mathbf{y_r}$ and $\mathbf{y_h}$ , respectively. + +Visual Attention Ratio. For the $k$ -th token $\mathbf{y}_k$ , we define the Visual Attention Ratio (VAR) in each head $h$ at layer $\ell$ : + +$$ +\operatorname {V A R} ^ {(\ell , h)} \left(\mathbf {y} _ {k}\right) \triangleq \sum_ {i = 1} ^ {n} \mathbf {A} _ {k} ^ {(\ell , h)} \left(a _ {k}, i\right), \tag {1} +$$ + +where $\mathbf{A}_k^{(\ell,h)}(a_k,i)$ represents the attention weights of the newly generated token $\mathbf{y}_k$ assigned to the image token $\mathbf{v}_i$ . VAR quantifies the extent of the token $\mathbf{y}_k$ 's interaction with visual information: a higher VAR score indicating a greater contribution from image tokens during $\mathbf{y}_k$ 's generation. + +Logit Lens. We utilize this technique to investigate how the model interprets the visual hidden state $\mathbf{v}_i^\ell$ during inference via text. We denote the linear projector before softmax as $\mathbf{W}_{\mathcal{V}} \in \mathbb{R}^{|\mathcal{V}| \times d}$ , which is applied to $\mathbf{y}_{k-1}^L$ to predict the probability of next token over the vocabulary $\mathcal{V}$ . Then, the logit lens transforms the hidden state $\mathbf{v}_i^\ell$ of the image tokens to the prediction probability distribution over the vocabulary by the linear projector $\mathbf{W}_{\mathcal{V}}$ : + +$$ +\mathbf {p} (\mathcal {V} | \mathbf {v} _ {i} ^ {\ell}) = \operatorname {s o f t m a x} \left(\mathbf {W} _ {\mathcal {V}} \cdot \mathbf {v} _ {i} ^ {\ell}\right) \in \mathbb {R} ^ {| \mathcal {V} |}, \tag {2} +$$ + +where $\mathbf{p}_j(\mathcal{V}|\mathbf{v}_i^\ell)$ corresponds to the $j$ -th text token in the vocabulary. To explain the processed image token, the text token with the highest probability is considered as the model's interpretation of the hidden state $\mathbf{v}_i^\ell$ at layer $\ell$ . + +# 3.2. Experimental Setup for Case Study + +We conduct case studies with a randomly selected subset of 2,000 images from COCO 2014 validation set [25]. These images represent diverse scenes and activities across 80 + +![](images/1ec2b647fe00d5c76e7950dd1e974b1717667e6334613d40ef2d83b3e087d28f.jpg) + +![](images/665a52fe50d3cb5b314fe46b8c96a037293913e2ddad30c2d84e5769e91beb2f.jpg) +The image features a yellow bus driving down a street, with a red car following behind it. ... a few houses visible in the background. There are also a couple of people walking on the sidewalk, ... Additionally, there is a fire hydrant located near the left side of the street, and a stop sign can be seen further down the road. +Figure 3. Case study of image hidden state interpretation in LLaVA-1.5-7B via logit lens. The heatmap illustrates the retrieved texts of the image hidden states across layers in the three distinct regions, differentiated by color. Our findings reveal that the model's semantic comprehension of image tokens emerges in the later middle layers (19-26) while remaining largely absent in earlier layers. The real and hallucinated object tokens are presented in blue and red in the description, respectively. + +common object categories, each paired with multiple object annotations. The 7B version of LLaVA-1.5 serves as the main focus for the subsequent analysis. In Appendix C.1, we further repeat our case studies on other LVLMs, including Shikra and MiniGPT-4, and observe consistent findings. + +To investigate the internal patterns in generating real and hallucinated object tokens, we use the model with greedy search to generate captions for the selected images, prompted by "Please help me describe the image in detail". Real and hallucinated object tokens are then identified using ground truth annotations as a reference. For multi-token objects, only the first token is considered. As a result, we obtained 1,842 hallucinated tokens and 4,397 real tokens. + +# 3.3. Finding 1: Middle Layers Matter for Visual Information Interaction + +To assess the contribution of visual information to token generations, we compute the VAR score (Eq. (1)) for real object tokens $\mathbf{y}_r$ across all layers $\ell \in [L]$ and heads $h \in [H]$ . We calculate the mean of $\mathrm{VAR}^{(\ell,h)}(\mathbf{y}_r)$ for all real object tokens in our case dataset, with the results depicted in Fig. 2 (a). The visualization shows that the middle layers, i.e., 5-26 layers, continuously exhibit high attention weights to the image tokens, indicating that visual information interaction primarily occurs in the middle layers. + +We further analyze how the model processes visual information by examining signals from the MHSA sublayers. Using the logit lens, we quantify the contribution of the MHSA sublayers to real token prediction as $\mathbf{p}_{\mathrm{o}}(\mathcal{V}|\mathbf{a}_{\mathrm{r}}^{\ell})$ where $\mathbf{a}_{\mathrm{r}}^{\ell}$ is the output of the MHSA sublayer at layer $\ell$ , and o denotes the index of the real object token $\mathbf{y}_{\mathrm{r}}$ in the vocabulary. Fig. 2 (b) reveals two patterns in the contributions + +from the MHSA sublayers: lower in 5-18 layers and higher in 19-26 layers, reflecting varied use of visual information. + +To better understand these two patterns, we use the logit lens to map the hidden states of image token $\mathbf{v}_i^\ell$ to text. Specifically, for each image token $\mathbf{v}_i$ at layer $\ell$ , we retrieve the text token in the vocabulary with the highest probability, i.e., $\mathrm{argmax}_{1\leq j\leq |\mathcal{V}|}\{\mathbf{p}_j(\mathcal{V}|\mathbf{v}_i^\ell)\}$ . A case is shown in Fig. 3, revealing two stages in the middle layers with different visual information usage: + +- Stage 1: Visual Information Enrichment. The first stage, in layers 5–18, shows that retrieved text tokens are less related to the corresponding image patches, suggesting the model is unable to interpret visual information. This misalignment might explain the low prediction contributions observed in Fig. 2 (b). Meanwhile, these layers continue to show high VAR scores, indicating that the object tokens are accumulating visual information through self-attention. In Secs. 3.4 and 3.5, we show that such attention serves as a key indicator to identify hallucinations. +- **Stage 2: Semantic Refinement.** The second stage, in layers 19–26, shows that the retrieved text tokens are semantically consistent with the image patches, suggesting the model is able to interpret and utilize the visual information encoded in the image tokens. Given the high VAR during this stage, we term it as semantic refinement where the model actively interacts with the semantic information of image tokens to reason object token prediction. + +# 3.4. Finding 2: Inactive Visual Attention in Middle Layers Implies Hallucination + +Given that visual information is primarily processed in the middle layers, a natural question arises: does the model dis + +![](images/73b9ae2653533cb3cff0241fa2893e37c381f40d97ed93ca4a9d6cf9a964e868.jpg) + +![](images/bc7e3ced9b76735dcbdab91e1f188fe364e1153ed8916e526bae6fe5d1f8ca72.jpg) +Figure 5. $\mathrm{SVAR}_{5-18}$ score distributions across object token types for the 7B (a) and 13B (b) versions of LLaVA-1.5. + +![](images/457cc7c879ff8cbe9e2d0580db488e029f2759c20ccb858cc84f40b57228e8ed.jpg) +Figure 4. Case study of the visual attention ratio distribution over heads and layers in LLaVA-1.5-7B. Left: real objects; Right: hallucinated objects. We find that the hallucinated object tokens exhibit inactive attention patterns during visual information enrichment compared to the real ones. + +![](images/15274111709cbdee1b15e2aa206e4f149894036fd0d9ac98d1afb62cc23f1906.jpg) +Figure 6. Object hallucination detection curves for LLaVA-1.5-7B. We show the ROC and Precision-Recall curves of $\mathrm{SVAR}_{5 - 18}$ metric for object hallucination detection on the case study dataset. + +play unusual attention patterns in these layers when generating hallucinated object tokens? Fig. 4 presents the VAR distribution for real object tokens ('bus' and 'car') and hallucinated ones ('people' and 'fire hydrant') from the case of Fig. 3. We observe that the hallucinated object tokens demonstrate an inactive attention pattern during the visual information enrichment stage (5-18 layers) compared to the real ones. We conjecture that such pattern weakens the interaction between the object token and image tokens in this stage, limiting the propagation of visual information and potentially leading to hallucinations. To quantify this observation, we introduce a metric, Summed Visual Attention Ratio (SVAR), calculated by averaging VAR scores over all heads and summing across selected layers $[\ell_s,\ell_e]$ . Specifically, for a real object token $\mathbf{y_r}$ in $[\ell_5,\ell_{18}]$ , we compute: + +$$ +\operatorname {S V A R} _ {5 - 1 8} \left(\mathbf {y} _ {\mathrm {r}}\right) \triangleq \frac {1}{H} \sum_ {\ell = 5} ^ {1 8} \sum_ {h = 1} ^ {H} \operatorname {V A R} ^ {(\ell , h)} \left(\mathbf {y} _ {\mathrm {r}}\right). \tag {3} +$$ + +We conduct a statistical experiment on the $\mathrm{SVAR}_{5-18}$ metric for both real and hallucinated tokens. The results, depicted in Fig. 5 (a), and the associated statistical test detailed in Appendix C.2, indicate a salient difference: the model assigns significantly higher attention weights to image tokens when generating real object tokens during visual information enrichment compared to hallucinated ones. + +Fig. 5 (b) shows a similar trend in LLaVA-1.5-13B. + +![](images/48802845cb50f6c197723fa9e26fe4d2529657477dcea4a52b86683d19740e5e.jpg) + +![](images/3d58186aa76c40b68396d3ae0f6a053f960b786efe7428fcf8a3bfefa97ecabd.jpg) + +![](images/72b42b25fae665b616e45df50ad1e4ad6650e918fc2b6a0679b9c957be33b8ba.jpg) + +![](images/9d53b6feb877791581f3212cb54084c35fe8af76e9dc86f84bee3be27bd8f216.jpg) + +# 3.4.1 Application: Object Hallucination Detection + +Building upon our Finding 2, we apply the $\mathrm{SVAR}_{5-18}$ metric to detect object hallucinations. We assess the efficacy of $\mathrm{SVAR}_{5-18}$ in reflecting object hallucination using our case dataset, where a positive sample is a real object token and a negative sample is a hallucinated one. For comparison, we use the internal confidence metric recently proposed in [21] as a baseline. The internal confidence uses the maximum probability of the object token within all image hidden states $\{\mathbf{v}_i^\ell : i \in [n], \ell \in [L]\}$ , mapped by the logit lens for detection. The qualitative results are presented in Fig. 6 and the results for LLaVA-1.5-13B are shown in Appendix C.1. Compared to internal confidence, using the simple $\mathrm{SVAR}_{5-18}$ metric improves the AUROC by $8.82\%$ and the AP by $3.53\%$ , verifying the utility of our metric. This further suggests that the middle layers provide crucial indicator information for object hallucination. + +Beyond the hand-crafted $\mathrm{SVAR}_{5-18}$ measure, we explore the potential of middle layers to indicate hallucinations by training a simple model to derive metrics directly from raw visual attention states. + +Experimental setting. We train a two-layer MLP by inputting the concatenated VAR scores across all heads in the layer range of interest $[\ell_s,\ell_e]$ to classify the real and hallucinated object tokens. Specifically, the input vector $\mathbf{x}(\mathbf{y}_r)$ for the real token $\mathbf{y}_r$ can be written as: + +$$ +\mathbf {x} \left(\mathbf {y} _ {\mathrm {r}}\right) = \left[ \operatorname {V A R} ^ {\left(\ell_ {s}, 1\right)}, \operatorname {V A R} ^ {\left(\ell_ {s}, 2\right)}, \dots , \operatorname {V A R} ^ {\left(\ell_ {e}, H\right)} \right] ^ {\top}. \tag {4} +$$ + +![](images/6b562f339648dc2df69a44b184337a50614a3f307039ddfc1cf3dfe4c092bcbe.jpg) +Figure 7. Visualization of attention maps over image for 'bus' (real) and 'people' (hallucinated) object tokens in heads $(\ell, h)$ . We find that the heads tend to interact with multiple objects when generating hallucinated object tokens. More examples can be found in Appendix C.4. + +We split the case dataset into training and test sets in the ratio of 8:2, and train the MLP with cross-entropy loss. The model performance is evaluated using accuracy, AUROC, and recall metrics. Training details are in Appendix B.2. + +Results. We experiment with four layer ranges in LLaVA-1.5-7B: [0, 4], [5, 18], [19, 26], and [27, 31], as shown in Tab. 1. We can see using the layers of visual information enrichment (5-18) achieves the best performance among other ranges, validating the effectiveness of our Finding 2. We observe that other layers also encode hallucination-related information which can be learned to detect hallucinations. However, compared to the explicit pattern in 5-18 layers, the implicit patterns contained in other ranges require computation costs for feature learning. + +# 3.5. Finding 3: Attention Heads Interact with Multiple Objects Incurring Object Hallucination + +Considering the MHSA mechanism incorporates various attention heads to aggregate information, we analyze heatmaps over the image for both real and hallucinated object tokens ('bus' vs 'people') to investigate the head behavior during visual information enrichment. A case is shown in Fig. 7 and more examples can be found in Appendix C.4. We can see that each head focuses on distinct local details, yet the attention distribution for the real token consistently aligns with the spatial extent of the corresponding object. In contrast, for the hallucinated token, the heads interact with inconsistent objects in the image during this stage. We speculate that such unstable head behavior encodes mixed information from multiple objects into the object token, potentially leading to hallucinations. + +# 4. Object Hallucination Mitigation + +# 4.1. Heads Guided Attention Intervention + +Inspired by the insights from Sec. 3 that improper processing of visual information during inference can lead to object + +
    Layers0-45-1819-2627-310-31
    Accuracy82.6184.4681.4977.7284.46
    AUROC89.5790.1987.3484.3090.28
    Recall66.2272.3468.8863.5671.28
    + +Table 1. Object hallucination detection results $(\%)$ of different layer ranges of interest on LLaVA-1.5-7B. + +hallucinations, we aim to correct this process to alleviate object hallucination. Specifically, we adjust the attention weights assigned to image tokens, i.e., $\{\mathbf{A}_k^{(\ell,h)}(a_k,i)\}_{i=1}^n$ , in each head at the middle layers during inference for intervention. To modify the attention weights in time step $k$ , we extract the attention score matrix $\mathbf{S}_k^{(\ell,h)}$ before softmax operation: + +$$ +\mathbf {S} _ {k} ^ {(\ell , h)} = \left(\frac {\mathbf {Q} _ {\ell , h} \mathbf {K} _ {\ell , h} ^ {\top}}{\sqrt {d _ {k}}}\right) _ {k}, \tag {5} +$$ + +where $\mathbf{Q}_{\ell,h}$ and $\mathbf{K}_{\ell,h} \in \mathbb{R}^{a_k \times d_k}$ represent the query and key matrices of dimension $d_k$ , respectively. + +Guided by the attention pattern difference in Finding 2, we amplify the original attention scores in the layers of visual information enrichment by adding positive values to enhance visual information interaction. Furthermore, leveraging the head behavior observed in Finding 3, we compute these positive values by averaging the absolute attention scores across all heads, where only the consistent regions interacted by different heads receive large enhancement. By integrating the attention information from various heads, we can find a more faithful and object-related direction for attention shift to reduce hallucinations. Formally, for each image token $i \in [n]$ across all heads $h \in [H]$ in layer $\ell \in [\ell_s, \ell_e]$ , we adjust the visual attention scores by: + +$$ +\mathbf {S} _ {k} ^ {(\ell , h)} \left(a _ {k}, i\right) = \mathbf {S} _ {k} ^ {(\ell , h)} \left(a _ {k}, i\right) + \alpha \frac {1}{H} \sum_ {h = 1} ^ {H} \left| \mathbf {S} _ {k} ^ {(\ell , h)} \left(a _ {k}, i\right) \right|, \tag {6} +$$ + +
    MethodLLaVA-1.5-7BLLaVA-1.5-13BShikra-7BMiniGPT-4-7BAvg.
    \(C_{S} \downarrow\)\(C_{I} \downarrow\)F1↑\(C_{S} \downarrow\)\(C_{I} \downarrow\)F1↑\(C_{S} \downarrow\)\(C_{I} \downarrow\)F1↑\(C_{S} \downarrow\)\(C_{I} \downarrow\)F1↑\(C_{S} \downarrow\)\(C_{I} \downarrow\)
    Decoding Strategy
    Greedy53.015.676.749.814.678.257.615.775.331.812.071.148.114.5
    Beam55.615.477.550.413.879.059.016.374.629.29.971.248.613.9
    OPERA45.613.179.142.613.277.841.413.773.525.49.671.238.812.4
    Contrastive Decoding
    \(\mathsf{VCD}^{\dagger}\)58.618.272.853.615.375.856.415.575.241.414.168.252.515.8
    \(\mathsf{PAI}^{\dagger}\)24.27.175.233.09.277.838.610.176.223.28.271.429.88.7
    \(\mathsf{Ours}^{\dagger}\)25.06.776.125.88.877.323.89.472.721.48.070.824.08.2
    \(\Delta \%\)↑3.3%↓5.6%↓21.8%↓4.3%↓38.3%↓6.9%↓7.8%↓2.4%↓19.5%↓5.7%
    + +Table 2. CHAIR hallucination evaluation and F1 results on three LVLMs with max new token set to 512. † denotes using the greedy decoding strategy. Our method outperforms other baselines and also preserves the richness of the descriptions. Δ% denotes the relative performance improvement with respect to the second-best method. + +where the $[\ell_s,\ell_e]$ denotes the range of visual information enrichment, and the parameter $\alpha$ is defined as a balance factor to control the intervention strength. + +# 4.2. Experimental Setup and Results + +Models. We conduct experiments on three representative LVLMs to evaluate the effectiveness and generalization of our method, including the LLaVA-1.5 [27], Shikra [4], and MiniGPT-4 [54]. In our experiments, we use the 7B and 13B versions of LLaVA-1.5 to study the scale effect, while other LVLMs are 7B models. + +Baselines. We adopt two commonly used decoding strategies and three mainstream hallucination mitigation approaches as the baseline methods, including greedy decoding, beam search decoding [37], OPERA [19], VCD [24], and PAI [28]. Greedy decoding selects the token with the highest probability over the vocabulary as the predicted next token. Beam search decoding maintains multiple beams and selects the top tokens with the highest cumulative probabilities at the end of generation. Improved on beam search, OPERA introduces an overtrust penalty term on the attention weights during inference with a rollback strategy to mitigate hallucinations. Different from the above three decoding approaches, VCD and PAI can be categorized as contrastive decoding methods. Specifically, VCD subtracts the output logits of the distorted visual input from the original output logits to reduce the statistical priors. In addition to using contrastive decoding, PAI further manipulates the attention matrix to overcome language bias. In our experiments, we use the default parameters of these baselines and unify $N_{\mathrm{beam}} = 5$ for the beam search decoding and OPERA. + +Benchmark and Metrics. Following [19], we conduct experiments on 500 random images from the COCO 2014 validation set. To evaluate the degree of object hallucinations in the image captioning task, we adopt the CHAIR [34] criteria which computes the proportion of all objects men + +tioned in the caption that are not present in the ground-truth annotations. CHAIR provides two main metrics, including $\mathrm{CHAIR}_I(C_I)$ and $\mathrm{CHAIR}_S(C_S)$ that assess instance-level and sentence-level hallucinations, respectively: + +$$ +C _ {I} = \frac {\left| \{\text {h a l l u c i n a t e d o b j e c t s} \} \right|}{\left| \{\text {a l l m e n t i o n e d o b j e c t s} \} \right|}, C _ {S} = \frac {\left| \{\text {c a p t i o n s w / h a l l u c i n a t e d o b j e c t s} \} \right|}{\left| \{\text {a l l c a p t i o n s} \} \right|}, +$$ + +where lower values indicate fewer hallucinations. Following [28], we also adopt the F1 score to assess the richness and accuracy of the generated descriptions. + +Implementation details. Our method contains two parameters: the visual information enrichment range $[\ell_s, \ell_e]$ and the balance factor $\alpha$ in Eq. (6). Utilizing the VAR feature and logit lens described in Sec. 3.1, we can easily establish suitable ranges for any other LVLMs. In our experiment, we set the ranges as [5, 18] for both versions of LLaVA-1.5, [3, 13] for Shikra, and [3, 14] for MiniGPT-4. We set $\alpha$ to 0.5 for LLaVA-1.5, MiniGPT-4, and 0.55 for Shikra. We implement our method with greedy decoding as a baseline. + +Results. Tab. 2 presents the experimental results for the selected LVLMs with max new tokens of 512. From the Tab. 2, our approach outperforms the three decoding strategies in reducing hallucinations and achieves an average reduction of $19.5\%$ in $C_S$ and $5.7\%$ in $C_I$ , compared to the second-best baseline. Compared to VCD, our method not only achieves superior hallucination mitigation performance but also better preserves the richness of the descriptions. Compared to PAI which requires the cost of once additional forward process for contrastive decoding, our approach achieves comparable or superior performance by only adjusting attention weights during inference, validating the efficacy of our method. Moreover, the consistent reduction of hallucinations across four different LVLMs confirms the generalizability of our findings. To evaluate the impact of generated token lengths, we conduct experiments on LLaVA-1.5-7B by varying the max new token in $\{64, 128, 256\}$ . The results, reported in Tab. 3, show that + +
    Methodmax new token 64max new token 128max new token 256Avg.
    \(C_{S}\)↓\(C_{I}\)↓F1↑\(C_{S}\)↓\(C_{I}\)↓F1↑\(C_{S}\)↓\(C_{I}\)↓F1↑\(C_{S}\)↓\(C_{I}\)↓
    Decoding Strategy
    Greedy23.88.074.752.415.576.753.015.676.743.113.0
    Beam17.66.075.154.414.877.655.615.477.542.512.1
    OPERA19.06.374.444.212.978.845.613.179.136.310.8
    Contrastive Decoding
    \(\mathrm{VCD}^{\dagger}\)26.09.373.356.816.974.558.618.272.847.114.8
    \(\mathrm{PAI}^{\dagger}\)19.86.274.024.27.375.224.27.275.222.76.9
    \(\mathrm{Ours}^{\dagger}\)18.25.473.924.87.176.025.07.176.122.76.5
    + +Table 3. CHAIR hallucination evaluation and F1 results on LLaVA-1.5-7B with varying max new token in $\{64,128,256\}$ . † denotes using the greedy decoding strategy. + +
    Layers0-45-1819-2627-31Greedy
    \(C_S\ ↓\)31.025.053.453.453.0
    \(C_I\ ↓\)10.46.714.315.715.6
    F1↑77.176.177.577.276.7
    + +our method consistently reduces hallucinations across different token lengths and achieves the best performance on average, demonstrating its robustness. We provide qualitative results in Appendix C.7. + +# 5. Ablations and Discussions + +Layers of attention intervention. Motivated by the empirical observation of implicit hallucination patterns across layers beyond the 5-18 range in Sec. 3.4.1, we investigate whether interventions in these layers can also mitigate object hallucinations. We apply our approach (Eq. (6)) to the layer ranges [0, 4], [19, 26], and [27, 31] in LLaVA-1.5-7B, and the results are reported in Tab. 4. We observe that the 5-18 layer range largely outperforms the other ranges while using some ranges (19-26 and 27-31) even enhanced hallucinations instead. The result suggests that explicit patterns in visual information enrichment are more effective than implicit patterns, facilitating more effective hallucination mitigation through simple attention intervention. + +Different attention intervention strategies. To validate the efficacy of our method in adjusting attention weights to reduce object hallucinations, we compare it with the inference intervention component proposed in PAI [28]. The inference intervention component roughly excites attention weights by computing a weighted sum of the attention scores and their absolute values across individual heads. We apply this approach to the same layer ranges in ours on LLaVA-1.5-7B, Shikra, and MiniGPT-4. Tab. 5 suggests that our attention intervention method surpasses that of PAI, as our method integrates attention information from various heads to shift attention toward a more truthful direction. + +Balance factor $\alpha$ sensitivity. To examine the influence of + +![](images/cdc69a6b4bebe5de35f61afa243505b2ba782c692f5fba055b3790bd4a4e2df3.jpg) +Figure 8. Parameter sensitivity of $\alpha$ with CHAIR metrics. + +![](images/53e151414e6c508428ed0e3152bc49569fa8cf42d772068d557781f24747ee46.jpg) + +Table 4. CHAIR hallucination evaluation and F1 score among four layer ranges on LLaVA-1.5-7B with max new token set to 512. + +
    MethodLLaVA-1.5-7BShikra-7BMiniGPT-4-7B
    CS↓CI↓CS↓CI↓CS↓CI↓
    PAI*26.68.145.813.630.29.5
    Ours25.06.723.89.421.48.0
    + +Table 5. CHAIR hallucination evaluation and F1 results on three LVLMs. $\star$ denotes only using the inference intervention component in the same layer range as ours. Greedy decoding is adopted. + +$\alpha$ on intervention efficacy, we vary its value in the range of $\{0.3, 0.4, 0.5, 0.6, 0.7\}$ and the results of CHAIR metrics and F1 score for the 7B version of both LLaVA-1.5 and MiniGPT-4 are shown in Fig. 8. We find that a lower $\alpha$ limits hallucination mitigation effectiveness, whereas a higher $\alpha$ compromises the richness of descriptions. These results indicate that an appropriate $\alpha$ value (e.g., 0.5 for both selected LVLMs) balances the reduction of hallucinations with the maintenance of detailed visual descriptions. + +# 6. Conclusion and Insights + +We introduce a new perspective, visual information processing, to investigate the underlying mechanisms driving object hallucination. Analyzing through the lens of attention, we identify three key findings and discover a simple yet effective method for reducing hallucinations at inference time. Our study deepens the understanding of how hallucinations are produced in LVLMs. We conclude with three insights for future direction: 1) Based on LVLMs' interpretation in semantic refinement stage, the image tokens may be further categorized into sub-groups, such as object tokens, color tokens, and textual tokens, enabling us to explore how the LVLMs extract different types of visual information. 2) While we focus on visual information processing, there may exist more granular, stage-wise mechanisms that could explain model behavior more precisely. 3) Instead of external interventions on LVLM outputs, such as contrastive decoding, we suggest that targeted modifications to specific internal states, like attention weights in middle layers, offer a more effective method for calibration. Our insights may aid the community in developing more trustworthy and reliable LVLMs against hallucinations. + +# Acknowledgment + +This work is supported by the National Science Foundation of China (62376281, 62206048), the Natural Science Foundation of Jiangsu Province (BK20220819), and the Fundamental Research Funds for the Central Universities (2242024k30035). + +# References + +[1] Jize Cao, Zhe Gan, Yu Cheng, Licheng Yu, Yen-Chun Chen, and Jingjing Liu. Behind the scene: Revealing the secrets of pre-trained vision-and-language models. In Computer Vision - ECCV 2020, pages 565-580, 2020. 3 +[2] Min Cao, Yang Bai, Ziyin Zeng, Mang Ye, and Min Zhang. An empirical study of clip for text-based person search. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 465-473, 2024. 3 +[3] Hila Chefer, Shir Gur, and Lior Wolf. Generic attention-model explainability for interpreting bi-modal and encoder-decoder transformers. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12944-12953, 2024. 2 + +[47] Mert Yuksekgonul, Varun Chandrasekaran, Erik Jones, Suriya Gunasekar, Ranjita Naik, Hamid Palangi, Ece Kamar, and Besmira Nushi. Attention satisfies: A constraint-satisfaction lens on factual errors of language models. In International Conference on Learning Representations, 2024. 3 +[48] Bohan Zhai, Shijia Yang, Chenfeng Xu, Sheng Shen, Kurt Keutzer, Chunyuan Li, and Manling Li. Halle-control: Controlling object hallucination in large multimodal models. arXiv preprint arXiv:2310.01779, 2024. 2 +[49] Yi-Kai Zhang, Shiyin Lu, Yang Li, Yanqing Ma, Qingguo Chen, Zhao Xu, Weihua Luo, Kaifu Zhang, De-Chuan Zhan, and Han-Jia Ye. Wings: Learning multimodal llms without text-only forgetting. Advances in Neural Information Processing Systems, 37:31828-31853, 2024. 1 +[50] Linxi Zhao, Yihe Deng, Weitong Zhang, and Quanquan Gu. Mitigating object hallucination in large vision-language models via classifier-free guidance. arXiv preprint arXiv:2402.08680, 2024. 2 +[51] Zhen Zhao, Jingqun Tang, Binghong Wu, Chunhui Lin, Shu Wei, Hao Liu, Xin Tan, Zhizhong Zhang, Can Huang, and Yuan Xie. Harmonizing visual text comprehension and generation. In Advances in Neural Information Processing Systems, pages 97499-97522, 2024. 1 +[52] Yiyang Zhou, Chenhang Cui, Jaehong Yoon, Linjun Zhang, Zhun Deng, Chelsea Finn, Mohit Bansal, and Huaxiu Yao. Analyzing and mitigating object hallucination in large vision-language models. In International Conference on Learning Representations, 2024. 2 +[53] Beier Zhu, Yulei Niu, Saeil Lee, Minhoe Hur, and Hanwang Zhang. Debiased fine-tuning for vision-language models by prompt regularization. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 3834-3842, 2023. 2 +[54] Deyao Zhu, Jun Chen, Xiaogian Shen, Xiang Li, and Mohamed Elhoseiny. MiniGPT-4: Enhancing vision-language understanding with advanced large language models. 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55, + 312, + 297, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 312, + 297, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 297, + 601 + ], + "type": "text", + "content": "Hallucinations in Large Vision-Language Models (LVLMs) significantly undermine their reliability, motivating researchers to explore the causes of hallucination. However, most studies primarily focus on the language aspect rather than the visual. In this paper, we address how LVLMs process visual information and whether this process causes hallucination. Firstly, we use the attention lens to identify the stages at which LVLMs handle visual data, discovering that the middle layers are crucial. Moreover, we find that these layers can be further divided into two stages: \"visual information enrichment\" and \"semantic refinement\" which respectively propagate visual data to object tokens and interpret it through text. By analyzing attention patterns during the visual information enrichment stage, we find that real tokens consistently receive higher attention weights than hallucinated ones, serving as a strong indicator of hallucination. Further examination of multi-head attention maps reveals that hallucination tokens often result from heads interacting with inconsistent objects. Based on these insights, we propose a simple inference-time method that adjusts visual attention by integrating information across various heads. Extensive experiments demonstrate that this approach effectively mitigates hallucinations in mainstream LVLMs without additional training costs." + }, + { + "bbox": [ + 55, + 312, + 297, + 601 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 620, + 137, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 620, + 137, + 633 + ], + "spans": [ + { + "bbox": [ + 56, + 620, + 137, + 633 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 641, + 296, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 677 + ], + "type": "text", + "content": "Building on the foundations of Large Language Models (LLMs), Large Vision-Language Models (LVLMs) [4, 27, 32, 44, 49, 51, 54] have emerged as powerful tools for un" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 328, + 284, + 545, + 555 + ], + "blocks": [ + { + "bbox": [ + 328, + 284, + 545, + 555 + ], + "lines": [ + { + "bbox": [ + 328, + 284, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 328, + 284, + 545, + 555 + ], + "type": "image", + "image_path": "685fedd56bbbba1270aefe0e957e77abfea9f6c1ad15736229b932edb97db922.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 563, + 555, + 641 + ], + "lines": [ + { + "bbox": [ + 313, + 563, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 563, + 555, + 641 + ], + "type": "text", + "content": "Figure 1. Illustration of our findings: (i) visual information is primarily processed in the middle layers where (a) the model extracts the visual information and then (b) interprets the semantics embedded in image tokens; (ii) for real tokens like \"cat\", the attention weights over image tokens are generally higher than hallucinated ones like \"TV\" in (a); (iii) the model may combine the visual features extracted from multiple objects to produce hallucinations." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "derstanding visual inputs and generating textual responses aligned with user intent. Their multi-modal nature has enabled a large variety of vision-language tasks, e.g., image captioning, visual question answering, and visual dialog." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 684, + 145, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 684, + 145, + 693 + ], + "spans": [ + { + "bbox": [ + 66, + 684, + 145, + 693 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 56, + 693, + 294, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 693, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 56, + 693, + 294, + 712 + ], + "type": "text", + "content": "1Code: https://github.com/ZhangqiJiang07/middle_layers_indicating_hallucinations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25004" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "Despite generating coherent textual responses, these models often exhibit undesirable object hallucinations – producing objects that do not exist in the visual input." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 110, + 295, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 110, + 295, + 302 + ], + "spans": [ + { + "bbox": [ + 54, + 110, + 295, + 302 + ], + "type": "text", + "content": "Although various approaches, such as visual instruction fine-tuning [14, 20, 26, 46], the integration of external expert models [5, 43, 45, 50], and contrastive decoding strategies [9, 24, 28, 42], have been proposed to address the object hallucination issue in LVLMs, the underlying mechanisms driving these hallucinations remain poorly understood. A few studies have preliminarily explored the causes of object hallucination, identifying the language bias as the primary factor, with examples including the \"anchor pattern\" [19] and \"text inertia\" [28]. In essence, these studies found that LVLMs tend to prioritize internal textual knowledge over external visual information as more tokens are generated. However, these studies have overlooked the devils in the visual parts – while intuitively, improper processing of visual information within the LVLMs could contribute more to the emergence of object hallucinations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 304, + 295, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 304, + 295, + 519 + ], + "spans": [ + { + "bbox": [ + 56, + 304, + 295, + 519 + ], + "type": "text", + "content": "In this paper, we delve into how LVLMs process visual information from image tokens and how this affects the generation of object hallucinations. Building on the three-stage mechanism identified in LLMs for retrieving factual knowledge [12], we examine whether LVLMs exhibit similar distinct stages during inference and, if so, which stage is critical for processing visual information. We propose a simple score called Visual Attention Ratio (VAR) to examine the distribution of visual attention across layers, revealing that the middle layers play a crucial role in processing visual information. To study how the model processes visual information in these middle layers, we leverage the logit lens [29] method to decode the hidden states of image tokens into LVLMs' vocabulary, identifying two crucial stages as illustrated in Fig. 1: a visual information enrichment stage propagates visual information to the object token, and a semantic refinement stage interprets the encoded visual information through text." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "type": "text", + "content": "Secondly, focusing on these middle layers, we observe that the hallucinated tokens often exhibit (1) less active attention patterns, and (2) inconsistent attentions across different heads during visual information enrichment stage, compared to real ones. To quantify these observations, we first introduce a metric based on VAR, and confirm that real object tokens tend to assign higher attention weights over image tokens during visual information enrichment than hallucinated ones, illustrated in Fig. 1. Relying on our finding, we utilize the metric in this stage to detect hallucinated object tokens, achieving AUROC and mAP up to " + }, + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "type": "inline_equation", + "content": "74\\%" + }, + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "type": "inline_equation", + "content": "88\\%" + }, + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "type": "text", + "content": " on LLaVA-1.5-7B [27]. Second, given the various attention heads used in the Multi-Heads Self-Attention (MHSA) mechanism [40] for information aggregation, we explore the head behavior by visualizing the attention heatmaps over the input image. As illustrated" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": "in Fig. 1, we find that the heads interact with inconsistent objects during visual information enrichment when generating hallucinations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 312, + 108, + 553, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 108, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 312, + 108, + 553, + 215 + ], + "type": "text", + "content": "Our empirical findings provide valuable insights into the way object hallucinations are generated, intuitively described as follows (Fig. 1): In visual information enrichment, the model's ambiguous interactions with multiple objects result in limited and mixed visual information being propagated to the object token. Subsequently, in semantic refinement, this imprecise visual information leads the model to mistakenly associate semantic information from different objects, ultimately causing hallucinations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 216, + 553, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 216, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 216, + 553, + 312 + ], + "type": "text", + "content": "Inspired by our findings, we propose a simple method to adjust the visual information process in the middle layers by integrating attention information from various heads during inference. Extensive experiments on three mainstream LVLMs show significant hallucination mitigation compared to the original models, with average reductions in " + }, + { + "bbox": [ + 313, + 216, + 553, + 312 + ], + "type": "inline_equation", + "content": "\\mathrm{CHAIR}_I" + }, + { + "bbox": [ + 313, + 216, + 553, + 312 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 216, + 553, + 312 + ], + "type": "inline_equation", + "content": "\\mathrm{CHAIR}_S" + }, + { + "bbox": [ + 313, + 216, + 553, + 312 + ], + "type": "text", + "content": " up to 6.3 and 24.1 points, respectively, while preserving detail in descriptions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 323, + 400, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 400, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 400, + 335 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 342, + 553, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 553, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 553, + 569 + ], + "type": "text", + "content": "Large Vision-Language Models. The recent integration of advanced open-source LLMs, like Llama [38, 39] and Vicuna [6], has greatly expanded the capabilities of LVLMs, enabling them to perform more complex vision-language tasks. Typically, the architecture of recent LVLMs incorporates three key components: a vision branch, such as CLIP [33] and EVA [8], to encode image inputs, a modality connector to transform image features into image embeddings aligning with text modality, and a pretrained language model to process image and prompt embeddings to generate responses. LLaVA-1.5 [27] employs an MLP to map the output of the vision branch into 576 image embeddings. Similarly, Shikra [4] utilizes one linear layer to align image features. While MiniGPT-4 [54] adopts a learnable querying transformer to establish vision-language connections, with just 32 image tokens as LVLM input. Despite their impressive capabilities, the above LVLMs suffer from severe object hallucinations. In this paper, we focus on interpreting, detecting, and mitigating their hallucinations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "content": "Object Hallucination in LVLMs. Object hallucination [48, 52] is a prevalent and critical issue in current LVLMs where the model erroneously generates descriptions of non-existent objects in images, posing significant risks in high-stakes fields such as medical imaging [18, 23], sequential recommendation systems [15, 35], and autonomous driving [7]. Previous studies to mitigate this issue have primarily focused on visual instruction finetuning [14, 20, 26, 46, 53], incorporating external expert models [5, 43, 45, 50], and improving decoding strategies [9, 19, 24, 28, 42]. Despite numerous efforts, our understanding of the underlying mechanism driving these er" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25005" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 178 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 178 + ], + "type": "text", + "content": "rors remains limited. Recent studies like OPERA [19] have pointed specific \"anchor patterns\" in text tokens that always align with the onset of hallucinated contents, and PAI [28] has identified \"text inertia\" as another contributing factor, as LVLMs reproduce identical hallucinated descriptions when solely input part of historical generated text. Contrary to these perspectives that focus on language bias, we investigate the causes of object hallucinations from the view of visual information processing through the lens of attention." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 179, + 297, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 179, + 297, + 443 + ], + "spans": [ + { + "bbox": [ + 56, + 179, + 297, + 443 + ], + "type": "text", + "content": "Interpretability in Foundation Models. In the field of NLP, numerous studies have analyzed LLMs to explore the internal model knowledge and understand model behavior in specific settings from the perspectives of attention maps [3, 47], neural activation patterns [17], and intermediate hidden states [13, 36]. The logit lens [29], which transforms the hidden states at each layer into the vocabulary space using the model's own linear projector before softmax, offers insightful observations into the next token prediction process [11, 16] in LLMs. Our work adapts the logit lens method to analyze hidden states of image tokens, enabling us to interpret the LVLMs' process of understanding the visual information via textual vocabulary. Few studies explore the internal mechanisms of LVLMs [1, 2, 10], notable efforts include [30], which extends an unimodal causal tracing tool for studying neural mechanisms in BLIP's image-conditioned text generation, and [31], which introduces a dictionary learning-based framework to extract multi-modal concepts for interpreting intermediate representations. Compared to prior works, our study leverages the internal signals from attention weights to uncover the generation of hallucinated objects." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 452, + 263, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 452, + 263, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 452, + 263, + 464 + ], + "type": "text", + "content": "3. Understanding Object Hallucinations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 472, + 296, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 296, + 544 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 296, + 544 + ], + "type": "text", + "content": "In this section, we start by introducing the generation process of LVLMs and the analytical tools, including visual attention ratio and logit lens. We then conduct case studies focusing on three key aspects: the processing of visual information, the attention patterns of object tokens, and the behavior of heads during object token generation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 550, + 135, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 550, + 135, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 550, + 135, + 562 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": "Notation. The input to LVLMs is initialized with a sequence of " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": "-dimensional image tokens " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{v}_1, \\dots, \\mathbf{v}_n\\}" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": " and instruction text (prompt) tokens " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{t}_1, \\dots, \\mathbf{t}_m\\}" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": ". Typically structured as a Transformer decoder [40], the LVLM outputs responses in an autoregressive manner: at time step " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": ", the model processes the initial input tokens " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{v}_1, \\dots, \\mathbf{v}_n, \\mathbf{t}_1, \\dots, \\mathbf{t}_m\\}" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": ", followed by the sequence of " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "k-1" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": " previously generated tokens " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{y}_1, \\dots, \\mathbf{y}_{k-1}\\}" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": ", to predict the next token " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_k" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": " denote the number of Transformer layers, each with " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": " heads. At layer " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\ell \\in [L]" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": ", we denote the attention weights in head " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "h \\in [H]" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_k^{(\\ell,h)} \\in \\mathbb{R}^{a_k \\times a_k}" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "a_k = n + m + k - 1" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": ". Additionally, we define " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^\\ell" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{k-1}^\\ell" + }, + { + "bbox": [ + 55, + 567, + 296, + 715 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 316, + 70, + 421, + 170 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 421, + 170 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 421, + 170 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 421, + 170 + ], + "type": "image", + "image_path": "93b8bdab5265e1ecdbded897acbf3241e647d54debf4a39c14d04b4a2cec5932.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 179, + 555, + 278 + ], + "lines": [ + { + "bbox": [ + 313, + 179, + 555, + 278 + ], + "spans": [ + { + "bbox": [ + 313, + 179, + 555, + 278 + ], + "type": "text", + "content": "Figure 2. (a) Distribution of visual attention ratio for real object tokens across heads and layers in LLaVA-1.5-7B, sorted row-wise by attention ratios. Note that the high attention in the 0-th layer (bottom row, green rectangle) is not consistent across all LVLMs, as Shikra and MiniGPT-4 models fail to exhibit this pattern, see Appendix C.1. (b) The logit contribution of attention sublayers to real token prediction. We find the middle layers continuously assign higher attention weights to image tokens and exhibit two different contribution patterns to the correct prediction." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 422, + 70, + 553, + 170 + ], + "blocks": [ + { + "bbox": [ + 422, + 70, + 553, + 170 + ], + "lines": [ + { + "bbox": [ + 422, + 70, + 553, + 170 + ], + "spans": [ + { + "bbox": [ + 422, + 70, + 553, + 170 + ], + "type": "image", + "image_path": "955fa3233829d0eaf50814335de97a3ed4ecaa97a85f66be050725b43e645f15.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "text", + "content": "the hidden states for the image token " + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "text", + "content": " and generated token " + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{k - 1}" + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "text", + "content": " at layer " + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "text", + "content": ", respectively. The real and hallucinated object tokens are noted as " + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{y_r}" + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{y_h}" + }, + { + "bbox": [ + 313, + 300, + 553, + 335 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "text", + "content": "Visual Attention Ratio. For the " + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "text", + "content": "-th token " + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_k" + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "text", + "content": ", we define the Visual Attention Ratio (VAR) in each head " + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "text", + "content": " at layer " + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 313, + 336, + 553, + 361 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 362, + 369, + 553, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 369, + 553, + 400 + ], + "spans": [ + { + "bbox": [ + 362, + 369, + 553, + 400 + ], + "type": "interline_equation", + "content": "\\operatorname {V A R} ^ {(\\ell , h)} \\left(\\mathbf {y} _ {k}\\right) \\triangleq \\sum_ {i = 1} ^ {n} \\mathbf {A} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right), \\tag {1}", + "image_path": "5a1ef0763a1795a10dd0cf53e869a734a962b0b59abc07902d0f21aabbe606ed.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_k^{(\\ell,h)}(a_k,i)" + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "text", + "content": " represents the attention weights of the newly generated token " + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_k" + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "text", + "content": " assigned to the image token " + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "text", + "content": ". VAR quantifies the extent of the token " + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_k" + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "text", + "content": "'s interaction with visual information: a higher VAR score indicating a greater contribution from image tokens during " + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_k" + }, + { + "bbox": [ + 313, + 411, + 554, + 472 + ], + "type": "text", + "content": "'s generation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "text", + "content": "Logit Lens. We utilize this technique to investigate how the model interprets the visual hidden state " + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^\\ell" + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "text", + "content": " during inference via text. We denote the linear projector before softmax as " + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathcal{V}} \\in \\mathbb{R}^{|\\mathcal{V}| \\times d}" + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "text", + "content": ", which is applied to " + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{k-1}^L" + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "text", + "content": " to predict the probability of next token over the vocabulary " + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "text", + "content": ". Then, the logit lens transforms the hidden state " + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^\\ell" + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "text", + "content": " of the image tokens to the prediction probability distribution over the vocabulary by the linear projector " + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathcal{V}}" + }, + { + "bbox": [ + 313, + 473, + 554, + 568 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 354, + 577, + 553, + 592 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 577, + 553, + 592 + ], + "spans": [ + { + "bbox": [ + 354, + 577, + 553, + 592 + ], + "type": "interline_equation", + "content": "\\mathbf {p} (\\mathcal {V} | \\mathbf {v} _ {i} ^ {\\ell}) = \\operatorname {s o f t m a x} \\left(\\mathbf {W} _ {\\mathcal {V}} \\cdot \\mathbf {v} _ {i} ^ {\\ell}\\right) \\in \\mathbb {R} ^ {| \\mathcal {V} |}, \\tag {2}", + "image_path": "25628be27fdfaea6c2bd9badc90cb89b6ed075429c57b5d8f10c8820cc02d44c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j(\\mathcal{V}|\\mathbf{v}_i^\\ell)" + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "text", + "content": " corresponds to the " + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "text", + "content": "-th text token in the vocabulary. To explain the processed image token, the text token with the highest probability is considered as the model's interpretation of the hidden state " + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^\\ell" + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "text", + "content": " at layer " + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 313, + 602, + 554, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 658, + 503, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 658, + 503, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 658, + 503, + 672 + ], + "type": "text", + "content": "3.2. Experimental Setup for Case Study" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "We conduct case studies with a randomly selected subset of 2,000 images from COCO 2014 validation set [25]. These images represent diverse scenes and activities across 80" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25006" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 72, + 173, + 174 + ], + "blocks": [ + { + "bbox": [ + 59, + 72, + 173, + 174 + ], + "lines": [ + { + "bbox": [ + 59, + 72, + 173, + 174 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 173, + 174 + ], + "type": "image", + "image_path": "1ec2b647fe00d5c76e7950dd1e974b1717667e6334613d40ef2d83b3e087d28f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 71, + 553, + 255 + ], + "blocks": [ + { + "bbox": [ + 60, + 180, + 175, + 243 + ], + "lines": [ + { + "bbox": [ + 60, + 180, + 175, + 243 + ], + "spans": [ + { + "bbox": [ + 60, + 180, + 175, + 243 + ], + "type": "text", + "content": "The image features a yellow bus driving down a street, with a red car following behind it. ... a few houses visible in the background. There are also a couple of people walking on the sidewalk, ... Additionally, there is a fire hydrant located near the left side of the street, and a stop sign can be seen further down the road." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 175, + 71, + 553, + 255 + ], + "lines": [ + { + "bbox": [ + 175, + 71, + 553, + 255 + ], + "spans": [ + { + "bbox": [ + 175, + 71, + 553, + 255 + ], + "type": "image", + "image_path": "665a52fe50d3cb5b314fe46b8c96a037293913e2ddad30c2d84e5769e91beb2f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 262, + 555, + 309 + ], + "lines": [ + { + "bbox": [ + 54, + 262, + 555, + 309 + ], + "spans": [ + { + "bbox": [ + 54, + 262, + 555, + 309 + ], + "type": "text", + "content": "Figure 3. Case study of image hidden state interpretation in LLaVA-1.5-7B via logit lens. The heatmap illustrates the retrieved texts of the image hidden states across layers in the three distinct regions, differentiated by color. Our findings reveal that the model's semantic comprehension of image tokens emerges in the later middle layers (19-26) while remaining largely absent in earlier layers. The real and hallucinated object tokens are presented in blue and red in the description, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 328, + 294, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 328, + 294, + 388 + ], + "spans": [ + { + "bbox": [ + 54, + 328, + 294, + 388 + ], + "type": "text", + "content": "common object categories, each paired with multiple object annotations. The 7B version of LLaVA-1.5 serves as the main focus for the subsequent analysis. In Appendix C.1, we further repeat our case studies on other LVLMs, including Shikra and MiniGPT-4, and observe consistent findings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 388, + 295, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 388, + 295, + 483 + ], + "spans": [ + { + "bbox": [ + 54, + 388, + 295, + 483 + ], + "type": "text", + "content": "To investigate the internal patterns in generating real and hallucinated object tokens, we use the model with greedy search to generate captions for the selected images, prompted by \"Please help me describe the image in detail\". Real and hallucinated object tokens are then identified using ground truth annotations as a reference. For multi-token objects, only the first token is considered. As a result, we obtained 1,842 hallucinated tokens and 4,397 real tokens." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 491, + 295, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 295, + 515 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 295, + 515 + ], + "type": "text", + "content": "3.3. Finding 1: Middle Layers Matter for Visual Information Interaction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "spans": [ + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "text", + "content": "To assess the contribution of visual information to token generations, we compute the VAR score (Eq. (1)) for real object tokens " + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_r" + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "text", + "content": " across all layers " + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\ell \\in [L]" + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "text", + "content": " and heads " + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "inline_equation", + "content": "h \\in [H]" + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "text", + "content": ". We calculate the mean of " + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{VAR}^{(\\ell,h)}(\\mathbf{y}_r)" + }, + { + "bbox": [ + 54, + 521, + 295, + 629 + ], + "type": "text", + "content": " for all real object tokens in our case dataset, with the results depicted in Fig. 2 (a). The visualization shows that the middle layers, i.e., 5-26 layers, continuously exhibit high attention weights to the image tokens, indicating that visual information interaction primarily occurs in the middle layers." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "text", + "content": "We further analyze how the model processes visual information by examining signals from the MHSA sublayers. Using the logit lens, we quantify the contribution of the MHSA sublayers to real token prediction as " + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\mathrm{o}}(\\mathcal{V}|\\mathbf{a}_{\\mathrm{r}}^{\\ell})" + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathrm{r}}^{\\ell}" + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "text", + "content": " is the output of the MHSA sublayer at layer " + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "text", + "content": ", and o denotes the index of the real object token " + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\mathrm{r}}" + }, + { + "bbox": [ + 54, + 630, + 295, + 714 + ], + "type": "text", + "content": " in the vocabulary. Fig. 2 (b) reveals two patterns in the contributions" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 328, + 553, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 328, + 553, + 352 + ], + "spans": [ + { + "bbox": [ + 313, + 328, + 553, + 352 + ], + "type": "text", + "content": "from the MHSA sublayers: lower in 5-18 layers and higher in 19-26 layers, reflecting varied use of visual information." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "text", + "content": "To better understand these two patterns, we use the logit lens to map the hidden states of image token " + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^\\ell" + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "text", + "content": " to text. Specifically, for each image token " + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "text", + "content": " at layer " + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "text", + "content": ", we retrieve the text token in the vocabulary with the highest probability, i.e., " + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "inline_equation", + "content": "\\mathrm{argmax}_{1\\leq j\\leq |\\mathcal{V}|}\\{\\mathbf{p}_j(\\mathcal{V}|\\mathbf{v}_i^\\ell)\\}" + }, + { + "bbox": [ + 313, + 353, + 554, + 436 + ], + "type": "text", + "content": ". A case is shown in Fig. 3, revealing two stages in the middle layers with different visual information usage:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 437, + 554, + 652 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 314, + 437, + 554, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 437, + 554, + 555 + ], + "spans": [ + { + "bbox": [ + 314, + 437, + 554, + 555 + ], + "type": "text", + "content": "- Stage 1: Visual Information Enrichment. The first stage, in layers 5–18, shows that retrieved text tokens are less related to the corresponding image patches, suggesting the model is unable to interpret visual information. This misalignment might explain the low prediction contributions observed in Fig. 2 (b). Meanwhile, these layers continue to show high VAR scores, indicating that the object tokens are accumulating visual information through self-attention. In Secs. 3.4 and 3.5, we show that such attention serves as a key indicator to identify hallucinations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 555, + 554, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 554, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 554, + 652 + ], + "type": "text", + "content": "- **Stage 2: Semantic Refinement.** The second stage, in layers 19–26, shows that the retrieved text tokens are semantically consistent with the image patches, suggesting the model is able to interpret and utilize the visual information encoded in the image tokens. Given the high VAR during this stage, we term it as semantic refinement where the model actively interacts with the semantic information of image tokens to reason object token prediction." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 658, + 553, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 658, + 553, + 683 + ], + "spans": [ + { + "bbox": [ + 313, + 658, + 553, + 683 + ], + "type": "text", + "content": "3.4. Finding 2: Inactive Visual Attention in Middle Layers Implies Hallucination" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "Given that visual information is primarily processed in the middle layers, a natural question arises: does the model dis" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25007" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 175, + 190 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 175, + 190 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 175, + 190 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 175, + 190 + ], + "type": "image", + "image_path": "73b9ae2653533cb3cff0241fa2893e37c381f40d97ed93ca4a9d6cf9a964e868.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 70, + 294, + 190 + ], + "blocks": [ + { + "bbox": [ + 175, + 70, + 294, + 190 + ], + "lines": [ + { + "bbox": [ + 175, + 70, + 294, + 190 + ], + "spans": [ + { + "bbox": [ + 175, + 70, + 294, + 190 + ], + "type": "image", + "image_path": "bc7e3ced9b76735dcbdab91e1f188fe364e1153ed8916e526bae6fe5d1f8ca72.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 178, + 553, + 199 + ], + "lines": [ + { + "bbox": [ + 313, + 178, + 553, + 199 + ], + "spans": [ + { + "bbox": [ + 313, + 178, + 553, + 199 + ], + "type": "text", + "content": "Figure 5. " + }, + { + "bbox": [ + 313, + 178, + 553, + 199 + ], + "type": "inline_equation", + "content": "\\mathrm{SVAR}_{5-18}" + }, + { + "bbox": [ + 313, + 178, + 553, + 199 + ], + "type": "text", + "content": " score distributions across object token types for the 7B (a) and 13B (b) versions of LLaVA-1.5." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 57, + 190, + 176, + 308 + ], + "blocks": [ + { + "bbox": [ + 57, + 190, + 176, + 308 + ], + "lines": [ + { + "bbox": [ + 57, + 190, + 176, + 308 + ], + "spans": [ + { + "bbox": [ + 57, + 190, + 176, + 308 + ], + "type": "image", + "image_path": "457cc7c879ff8cbe9e2d0580db488e029f2759c20ccb858cc84f40b57228e8ed.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 317, + 296, + 373 + ], + "lines": [ + { + "bbox": [ + 55, + 317, + 296, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 317, + 296, + 373 + ], + "type": "text", + "content": "Figure 4. Case study of the visual attention ratio distribution over heads and layers in LLaVA-1.5-7B. Left: real objects; Right: hallucinated objects. We find that the hallucinated object tokens exhibit inactive attention patterns during visual information enrichment compared to the real ones." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 176, + 190, + 294, + 308 + ], + "blocks": [ + { + "bbox": [ + 176, + 190, + 294, + 308 + ], + "lines": [ + { + "bbox": [ + 176, + 190, + 294, + 308 + ], + "spans": [ + { + "bbox": [ + 176, + 190, + 294, + 308 + ], + "type": "image", + "image_path": "15274111709cbdee1b15e2aa206e4f149894036fd0d9ac98d1afb62cc23f1906.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 318, + 553, + 352 + ], + "lines": [ + { + "bbox": [ + 313, + 318, + 553, + 352 + ], + "spans": [ + { + "bbox": [ + 313, + 318, + 553, + 352 + ], + "type": "text", + "content": "Figure 6. Object hallucination detection curves for LLaVA-1.5-7B. We show the ROC and Precision-Recall curves of " + }, + { + "bbox": [ + 313, + 318, + 553, + 352 + ], + "type": "inline_equation", + "content": "\\mathrm{SVAR}_{5 - 18}" + }, + { + "bbox": [ + 313, + 318, + 553, + 352 + ], + "type": "text", + "content": " metric for object hallucination detection on the case study dataset." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "spans": [ + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "type": "text", + "content": "play unusual attention patterns in these layers when generating hallucinated object tokens? Fig. 4 presents the VAR distribution for real object tokens ('bus' and 'car') and hallucinated ones ('people' and 'fire hydrant') from the case of Fig. 3. We observe that the hallucinated object tokens demonstrate an inactive attention pattern during the visual information enrichment stage (5-18 layers) compared to the real ones. We conjecture that such pattern weakens the interaction between the object token and image tokens in this stage, limiting the propagation of visual information and potentially leading to hallucinations. To quantify this observation, we introduce a metric, Summed Visual Attention Ratio (SVAR), calculated by averaging VAR scores over all heads and summing across selected layers " + }, + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "type": "inline_equation", + "content": "[\\ell_s,\\ell_e]" + }, + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "type": "text", + "content": ". Specifically, for a real object token " + }, + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "type": "inline_equation", + "content": "\\mathbf{y_r}" + }, + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "type": "inline_equation", + "content": "[\\ell_5,\\ell_{18}]" + }, + { + "bbox": [ + 54, + 392, + 295, + 573 + ], + "type": "text", + "content": ", we compute:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 87, + 581, + 295, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 581, + 295, + 614 + ], + "spans": [ + { + "bbox": [ + 87, + 581, + 295, + 614 + ], + "type": "interline_equation", + "content": "\\operatorname {S V A R} _ {5 - 1 8} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right) \\triangleq \\frac {1}{H} \\sum_ {\\ell = 5} ^ {1 8} \\sum_ {h = 1} ^ {H} \\operatorname {V A R} ^ {(\\ell , h)} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right). \\tag {3}", + "image_path": "97a4b5d2b399dd645d9c5a562aca0165cbdfdf77f5b7529bc9f3657650b2fd66.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 617, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 700 + ], + "type": "text", + "content": "We conduct a statistical experiment on the " + }, + { + "bbox": [ + 55, + 617, + 295, + 700 + ], + "type": "inline_equation", + "content": "\\mathrm{SVAR}_{5-18}" + }, + { + "bbox": [ + 55, + 617, + 295, + 700 + ], + "type": "text", + "content": " metric for both real and hallucinated tokens. The results, depicted in Fig. 5 (a), and the associated statistical test detailed in Appendix C.2, indicate a salient difference: the model assigns significantly higher attention weights to image tokens when generating real object tokens during visual information enrichment compared to hallucinated ones." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 701, + 264, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 264, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 264, + 713 + ], + "type": "text", + "content": "Fig. 5 (b) shows a similar trend in LLaVA-1.5-13B." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 321, + 70, + 432, + 169 + ], + "blocks": [ + { + "bbox": [ + 321, + 70, + 432, + 169 + ], + "lines": [ + { + "bbox": [ + 321, + 70, + 432, + 169 + ], + "spans": [ + { + "bbox": [ + 321, + 70, + 432, + 169 + ], + "type": "image", + "image_path": "48802845cb50f6c197723fa9e26fe4d2529657477dcea4a52b86683d19740e5e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 435, + 70, + 547, + 169 + ], + "blocks": [ + { + "bbox": [ + 435, + 70, + 547, + 169 + ], + "lines": [ + { + "bbox": [ + 435, + 70, + 547, + 169 + ], + "spans": [ + { + "bbox": [ + 435, + 70, + 547, + 169 + ], + "type": "image", + "image_path": "3d58186aa76c40b68396d3ae0f6a053f960b786efe7428fcf8a3bfefa97ecabd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 321, + 210, + 433, + 310 + ], + "blocks": [ + { + "bbox": [ + 321, + 210, + 433, + 310 + ], + "lines": [ + { + "bbox": [ + 321, + 210, + 433, + 310 + ], + "spans": [ + { + "bbox": [ + 321, + 210, + 433, + 310 + ], + "type": "image", + "image_path": "72b42b25fae665b616e45df50ad1e4ad6650e918fc2b6a0679b9c957be33b8ba.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 436, + 211, + 548, + 310 + ], + "blocks": [ + { + "bbox": [ + 436, + 211, + 548, + 310 + ], + "lines": [ + { + "bbox": [ + 436, + 211, + 548, + 310 + ], + "spans": [ + { + "bbox": [ + 436, + 211, + 548, + 310 + ], + "type": "image", + "image_path": "9d53b6feb877791581f3212cb54084c35fe8af76e9dc86f84bee3be27bd8f216.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 373, + 536, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 373, + 536, + 385 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 536, + 385 + ], + "type": "text", + "content": "3.4.1 Application: Object Hallucination Detection" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "spans": [ + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "text", + "content": "Building upon our Finding 2, we apply the " + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "inline_equation", + "content": "\\mathrm{SVAR}_{5-18}" + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "text", + "content": " metric to detect object hallucinations. We assess the efficacy of " + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "inline_equation", + "content": "\\mathrm{SVAR}_{5-18}" + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "text", + "content": " in reflecting object hallucination using our case dataset, where a positive sample is a real object token and a negative sample is a hallucinated one. For comparison, we use the internal confidence metric recently proposed in [21] as a baseline. The internal confidence uses the maximum probability of the object token within all image hidden states " + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{v}_i^\\ell : i \\in [n], \\ell \\in [L]\\}" + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "text", + "content": ", mapped by the logit lens for detection. The qualitative results are presented in Fig. 6 and the results for LLaVA-1.5-13B are shown in Appendix C.1. Compared to internal confidence, using the simple " + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "inline_equation", + "content": "\\mathrm{SVAR}_{5-18}" + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "text", + "content": " metric improves the AUROC by " + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "inline_equation", + "content": "8.82\\%" + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "text", + "content": " and the AP by " + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "inline_equation", + "content": "3.53\\%" + }, + { + "bbox": [ + 312, + 392, + 555, + 582 + ], + "type": "text", + "content": ", verifying the utility of our metric. This further suggests that the middle layers provide crucial indicator information for object hallucination." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 583, + 553, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 583, + 553, + 631 + ], + "spans": [ + { + "bbox": [ + 313, + 583, + 553, + 631 + ], + "type": "text", + "content": "Beyond the hand-crafted " + }, + { + "bbox": [ + 313, + 583, + 553, + 631 + ], + "type": "inline_equation", + "content": "\\mathrm{SVAR}_{5-18}" + }, + { + "bbox": [ + 313, + 583, + 553, + 631 + ], + "type": "text", + "content": " measure, we explore the potential of middle layers to indicate hallucinations by training a simple model to derive metrics directly from raw visual attention states." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "spans": [ + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "type": "text", + "content": "Experimental setting. We train a two-layer MLP by inputting the concatenated VAR scores across all heads in the layer range of interest " + }, + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "type": "inline_equation", + "content": "[\\ell_s,\\ell_e]" + }, + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "type": "text", + "content": " to classify the real and hallucinated object tokens. Specifically, the input vector " + }, + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{x}(\\mathbf{y}_r)" + }, + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "type": "text", + "content": " for the real token " + }, + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_r" + }, + { + "bbox": [ + 313, + 632, + 553, + 691 + ], + "type": "text", + "content": " can be written as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 325, + 699, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 699, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 325, + 699, + 553, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {x} \\left(\\mathbf {y} _ {\\mathrm {r}}\\right) = \\left[ \\operatorname {V A R} ^ {\\left(\\ell_ {s}, 1\\right)}, \\operatorname {V A R} ^ {\\left(\\ell_ {s}, 2\\right)}, \\dots , \\operatorname {V A R} ^ {\\left(\\ell_ {e}, H\\right)} \\right] ^ {\\top}. \\tag {4}", + "image_path": "74d15064dd9a84554cb664d12d5b581e13c412fa722b42f4a4419c823e0bcac2.jpg" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25008" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 70, + 547, + 220 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 547, + 220 + ], + "type": "image", + "image_path": "6b562f339648dc2df69a44b184337a50614a3f307039ddfc1cf3dfe4c092bcbe.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 228, + 555, + 251 + ], + "lines": [ + { + "bbox": [ + 55, + 228, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 555, + 251 + ], + "type": "text", + "content": "Figure 7. Visualization of attention maps over image for 'bus' (real) and 'people' (hallucinated) object tokens in heads " + }, + { + "bbox": [ + 55, + 228, + 555, + 251 + ], + "type": "inline_equation", + "content": "(\\ell, h)" + }, + { + "bbox": [ + 55, + 228, + 555, + 251 + ], + "type": "text", + "content": ". We find that the heads tend to interact with multiple objects when generating hallucinated object tokens. More examples can be found in Appendix C.4." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 271, + 294, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 271, + 294, + 319 + ], + "spans": [ + { + "bbox": [ + 54, + 271, + 294, + 319 + ], + "type": "text", + "content": "We split the case dataset into training and test sets in the ratio of 8:2, and train the MLP with cross-entropy loss. The model performance is evaluated using accuracy, AUROC, and recall metrics. Training details are in Appendix B.2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 319, + 295, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 319, + 295, + 439 + ], + "spans": [ + { + "bbox": [ + 54, + 319, + 295, + 439 + ], + "type": "text", + "content": "Results. We experiment with four layer ranges in LLaVA-1.5-7B: [0, 4], [5, 18], [19, 26], and [27, 31], as shown in Tab. 1. We can see using the layers of visual information enrichment (5-18) achieves the best performance among other ranges, validating the effectiveness of our Finding 2. We observe that other layers also encode hallucination-related information which can be learned to detect hallucinations. However, compared to the explicit pattern in 5-18 layers, the implicit patterns contained in other ranges require computation costs for feature learning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 444, + 295, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 444, + 295, + 470 + ], + "spans": [ + { + "bbox": [ + 55, + 444, + 295, + 470 + ], + "type": "text", + "content": "3.5. Finding 3: Attention Heads Interact with Multiple Objects Incurring Object Hallucination" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 475, + 295, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 475, + 295, + 643 + ], + "spans": [ + { + "bbox": [ + 54, + 475, + 295, + 643 + ], + "type": "text", + "content": "Considering the MHSA mechanism incorporates various attention heads to aggregate information, we analyze heatmaps over the image for both real and hallucinated object tokens ('bus' vs 'people') to investigate the head behavior during visual information enrichment. A case is shown in Fig. 7 and more examples can be found in Appendix C.4. We can see that each head focuses on distinct local details, yet the attention distribution for the real token consistently aligns with the spatial extent of the corresponding object. In contrast, for the hallucinated token, the heads interact with inconsistent objects in the image during this stage. We speculate that such unstable head behavior encodes mixed information from multiple objects into the object token, potentially leading to hallucinations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 651, + 235, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 651, + 235, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 651, + 235, + 665 + ], + "type": "text", + "content": "4. Object Hallucination Mitigation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 671, + 253, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 671, + 253, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 671, + 253, + 683 + ], + "type": "text", + "content": "4.1. Heads Guided Attention Intervention" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "Inspired by the insights from Sec. 3 that improper processing of visual information during inference can lead to object" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 329, + 269, + 541, + 326 + ], + "blocks": [ + { + "bbox": [ + 329, + 269, + 541, + 326 + ], + "lines": [ + { + "bbox": [ + 329, + 269, + 541, + 326 + ], + "spans": [ + { + "bbox": [ + 329, + 269, + 541, + 326 + ], + "type": "table", + "html": "
    Layers0-45-1819-2627-310-31
    Accuracy82.6184.4681.4977.7284.46
    AUROC89.5790.1987.3484.3090.28
    Recall66.2272.3468.8863.5671.28
    ", + "image_path": "586522b8ff225b5fc2cdac3aac2570626a82112ce7bd263a060b73f6b0dd43ac.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 334, + 555, + 357 + ], + "lines": [ + { + "bbox": [ + 313, + 334, + 555, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 334, + 555, + 357 + ], + "type": "text", + "content": "Table 1. Object hallucination detection results " + }, + { + "bbox": [ + 313, + 334, + 555, + 357 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 313, + 334, + 555, + 357 + ], + "type": "text", + "content": " of different layer ranges of interest on LLaVA-1.5-7B." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "type": "text", + "content": "hallucinations, we aim to correct this process to alleviate object hallucination. Specifically, we adjust the attention weights assigned to image tokens, i.e., " + }, + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{A}_k^{(\\ell,h)}(a_k,i)\\}_{i=1}^n" + }, + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "type": "text", + "content": ", in each head at the middle layers during inference for intervention. To modify the attention weights in time step " + }, + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "type": "text", + "content": ", we extract the attention score matrix " + }, + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_k^{(\\ell,h)}" + }, + { + "bbox": [ + 313, + 375, + 555, + 461 + ], + "type": "text", + "content": " before softmax operation:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 380, + 461, + 554, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 461, + 554, + 495 + ], + "spans": [ + { + "bbox": [ + 380, + 461, + 554, + 495 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {k} ^ {(\\ell , h)} = \\left(\\frac {\\mathbf {Q} _ {\\ell , h} \\mathbf {K} _ {\\ell , h} ^ {\\top}}{\\sqrt {d _ {k}}}\\right) _ {k}, \\tag {5}", + "image_path": "c2bd8f490add4391fac3f2a5df2bfc3ea5c3f6bbf6d537fedad5da489d9e4163.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{\\ell,h}" + }, + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\ell,h} \\in \\mathbb{R}^{a_k \\times d_k}" + }, + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "type": "text", + "content": " represent the query and key matrices of dimension " + }, + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "type": "inline_equation", + "content": "d_k" + }, + { + "bbox": [ + 313, + 497, + 554, + 521 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "type": "text", + "content": "Guided by the attention pattern difference in Finding 2, we amplify the original attention scores in the layers of visual information enrichment by adding positive values to enhance visual information interaction. Furthermore, leveraging the head behavior observed in Finding 3, we compute these positive values by averaging the absolute attention scores across all heads, where only the consistent regions interacted by different heads receive large enhancement. By integrating the attention information from various heads, we can find a more faithful and object-related direction for attention shift to reduce hallucinations. Formally, for each image token " + }, + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "type": "inline_equation", + "content": "i \\in [n]" + }, + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "type": "text", + "content": " across all heads " + }, + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "type": "inline_equation", + "content": "h \\in [H]" + }, + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "type": "text", + "content": " in layer " + }, + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "type": "inline_equation", + "content": "\\ell \\in [\\ell_s, \\ell_e]" + }, + { + "bbox": [ + 313, + 521, + 555, + 677 + ], + "type": "text", + "content": ", we adjust the visual attention scores by:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 683, + 555, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 683, + 555, + 717 + ], + "spans": [ + { + "bbox": [ + 318, + 683, + 555, + 717 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) = \\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) + \\alpha \\frac {1}{H} \\sum_ {h = 1} ^ {H} \\left| \\mathbf {S} _ {k} ^ {(\\ell , h)} \\left(a _ {k}, i\\right) \\right|, \\tag {6}", + "image_path": "d00a1c68581e0063270dac619cca50d87f27f297cd968474653c21bd8c027e66.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25009" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 78, + 70, + 533, + 209 + ], + "blocks": [ + { + "bbox": [ + 78, + 70, + 533, + 209 + ], + "lines": [ + { + "bbox": [ + 78, + 70, + 533, + 209 + ], + "spans": [ + { + "bbox": [ + 78, + 70, + 533, + 209 + ], + "type": "table", + "html": "
    MethodLLaVA-1.5-7BLLaVA-1.5-13BShikra-7BMiniGPT-4-7BAvg.
    \\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)F1↑\\(C_{S} \\downarrow\\)\\(C_{I} \\downarrow\\)
    Decoding Strategy
    Greedy53.015.676.749.814.678.257.615.775.331.812.071.148.114.5
    Beam55.615.477.550.413.879.059.016.374.629.29.971.248.613.9
    OPERA45.613.179.142.613.277.841.413.773.525.49.671.238.812.4
    Contrastive Decoding
    \\(\\mathsf{VCD}^{\\dagger}\\)58.618.272.853.615.375.856.415.575.241.414.168.252.515.8
    \\(\\mathsf{PAI}^{\\dagger}\\)24.27.175.233.09.277.838.610.176.223.28.271.429.88.7
    \\(\\mathsf{Ours}^{\\dagger}\\)25.06.776.125.88.877.323.89.472.721.48.070.824.08.2
    \\(\\Delta \\%\\)↑3.3%↓5.6%↓21.8%↓4.3%↓38.3%↓6.9%↓7.8%↓2.4%↓19.5%↓5.7%
    ", + "image_path": "aef0a3e9444702adb336fa5f3807272426c7e043decb233d4c0c76fddb4cad10.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 217, + 555, + 251 + ], + "lines": [ + { + "bbox": [ + 55, + 217, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 555, + 251 + ], + "type": "text", + "content": "Table 2. CHAIR hallucination evaluation and F1 results on three LVLMs with max new token set to 512. † denotes using the greedy decoding strategy. Our method outperforms other baselines and also preserves the richness of the descriptions. Δ% denotes the relative performance improvement with respect to the second-best method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 271, + 295, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 271, + 295, + 308 + ], + "spans": [ + { + "bbox": [ + 55, + 271, + 295, + 308 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 55, + 271, + 295, + 308 + ], + "type": "inline_equation", + "content": "[\\ell_s,\\ell_e]" + }, + { + "bbox": [ + 55, + 271, + 295, + 308 + ], + "type": "text", + "content": " denotes the range of visual information enrichment, and the parameter " + }, + { + "bbox": [ + 55, + 271, + 295, + 308 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 271, + 295, + 308 + ], + "type": "text", + "content": " is defined as a balance factor to control the intervention strength." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 319, + 230, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 319, + 230, + 333 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 230, + 333 + ], + "type": "text", + "content": "4.2. Experimental Setup and Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 296, + 411 + ], + "type": "text", + "content": "Models. We conduct experiments on three representative LVLMs to evaluate the effectiveness and generalization of our method, including the LLaVA-1.5 [27], Shikra [4], and MiniGPT-4 [54]. In our experiments, we use the 7B and 13B versions of LLaVA-1.5 to study the scale effect, while other LVLMs are 7B models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 413, + 295, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 413, + 295, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 413, + 295, + 652 + ], + "type": "text", + "content": "Baselines. We adopt two commonly used decoding strategies and three mainstream hallucination mitigation approaches as the baseline methods, including greedy decoding, beam search decoding [37], OPERA [19], VCD [24], and PAI [28]. Greedy decoding selects the token with the highest probability over the vocabulary as the predicted next token. Beam search decoding maintains multiple beams and selects the top tokens with the highest cumulative probabilities at the end of generation. Improved on beam search, OPERA introduces an overtrust penalty term on the attention weights during inference with a rollback strategy to mitigate hallucinations. Different from the above three decoding approaches, VCD and PAI can be categorized as contrastive decoding methods. Specifically, VCD subtracts the output logits of the distorted visual input from the original output logits to reduce the statistical priors. In addition to using contrastive decoding, PAI further manipulates the attention matrix to overcome language bias. In our experiments, we use the default parameters of these baselines and unify " + }, + { + "bbox": [ + 55, + 413, + 295, + 652 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{beam}} = 5" + }, + { + "bbox": [ + 55, + 413, + 295, + 652 + ], + "type": "text", + "content": " for the beam search decoding and OPERA." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 653, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 295, + 714 + ], + "type": "text", + "content": "Benchmark and Metrics. Following [19], we conduct experiments on 500 random images from the COCO 2014 validation set. To evaluate the degree of object hallucinations in the image captioning task, we adopt the CHAIR [34] criteria which computes the proportion of all objects men" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 271, + 555, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 271, + 555, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 271, + 555, + 319 + ], + "type": "text", + "content": "tioned in the caption that are not present in the ground-truth annotations. CHAIR provides two main metrics, including " + }, + { + "bbox": [ + 313, + 271, + 555, + 319 + ], + "type": "inline_equation", + "content": "\\mathrm{CHAIR}_I(C_I)" + }, + { + "bbox": [ + 313, + 271, + 555, + 319 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 271, + 555, + 319 + ], + "type": "inline_equation", + "content": "\\mathrm{CHAIR}_S(C_S)" + }, + { + "bbox": [ + 313, + 271, + 555, + 319 + ], + "type": "text", + "content": " that assess instance-level and sentence-level hallucinations, respectively:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 324, + 556, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 324, + 556, + 352 + ], + "spans": [ + { + "bbox": [ + 313, + 324, + 556, + 352 + ], + "type": "interline_equation", + "content": "C _ {I} = \\frac {\\left| \\{\\text {h a l l u c i n a t e d o b j e c t s} \\} \\right|}{\\left| \\{\\text {a l l m e n t i o n e d o b j e c t s} \\} \\right|}, C _ {S} = \\frac {\\left| \\{\\text {c a p t i o n s w / h a l l u c i n a t e d o b j e c t s} \\} \\right|}{\\left| \\{\\text {a l l c a p t i o n s} \\} \\right|},", + "image_path": "6eeebf0509cda4f1f252a1c0892546d8f5588d699faec0aef9b24193a0b19713.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 354, + 555, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 390 + ], + "type": "text", + "content": "where lower values indicate fewer hallucinations. Following [28], we also adopt the F1 score to assess the richness and accuracy of the generated descriptions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "type": "text", + "content": "Implementation details. Our method contains two parameters: the visual information enrichment range " + }, + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "type": "inline_equation", + "content": "[\\ell_s, \\ell_e]" + }, + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "type": "text", + "content": " and the balance factor " + }, + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "type": "text", + "content": " in Eq. (6). Utilizing the VAR feature and logit lens described in Sec. 3.1, we can easily establish suitable ranges for any other LVLMs. In our experiment, we set the ranges as [5, 18] for both versions of LLaVA-1.5, [3, 13] for Shikra, and [3, 14] for MiniGPT-4. We set " + }, + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 391, + 556, + 498 + ], + "type": "text", + "content": " to 0.5 for LLaVA-1.5, MiniGPT-4, and 0.55 for Shikra. We implement our method with greedy decoding as a baseline." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": "Results. Tab. 2 presents the experimental results for the selected LVLMs with max new tokens of 512. From the Tab. 2, our approach outperforms the three decoding strategies in reducing hallucinations and achieves an average reduction of " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "19.5\\%" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "C_S" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "C_I" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": ", compared to the second-best baseline. Compared to VCD, our method not only achieves superior hallucination mitigation performance but also better preserves the richness of the descriptions. Compared to PAI which requires the cost of once additional forward process for contrastive decoding, our approach achieves comparable or superior performance by only adjusting attention weights during inference, validating the efficacy of our method. Moreover, the consistent reduction of hallucinations across four different LVLMs confirms the generalizability of our findings. To evaluate the impact of generated token lengths, we conduct experiments on LLaVA-1.5-7B by varying the max new token in " + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\{64, 128, 256\\}" + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": ". The results, reported in Tab. 3, show that" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25010" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 294, + 166 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 294, + 166 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 294, + 166 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 294, + 166 + ], + "type": "table", + "html": "
    Methodmax new token 64max new token 128max new token 256Avg.
    \\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓F1↑\\(C_{S}\\)↓\\(C_{I}\\)↓
    Decoding Strategy
    Greedy23.88.074.752.415.576.753.015.676.743.113.0
    Beam17.66.075.154.414.877.655.615.477.542.512.1
    OPERA19.06.374.444.212.978.845.613.179.136.310.8
    Contrastive Decoding
    \\(\\mathrm{VCD}^{\\dagger}\\)26.09.373.356.816.974.558.618.272.847.114.8
    \\(\\mathrm{PAI}^{\\dagger}\\)19.86.274.024.27.375.224.27.275.222.76.9
    \\(\\mathrm{Ours}^{\\dagger}\\)18.25.473.924.87.176.025.07.176.122.76.5
    ", + "image_path": "8778666d46f1d4fc6f424a73c15cc4249757774c367a6781a24f4af09c299cf5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 78, + 217, + 273, + 273 + ], + "blocks": [ + { + "bbox": [ + 55, + 174, + 295, + 208 + ], + "lines": [ + { + "bbox": [ + 55, + 174, + 295, + 208 + ], + "spans": [ + { + "bbox": [ + 55, + 174, + 295, + 208 + ], + "type": "text", + "content": "Table 3. CHAIR hallucination evaluation and F1 results on LLaVA-1.5-7B with varying max new token in " + }, + { + "bbox": [ + 55, + 174, + 295, + 208 + ], + "type": "inline_equation", + "content": "\\{64,128,256\\}" + }, + { + "bbox": [ + 55, + 174, + 295, + 208 + ], + "type": "text", + "content": ". † denotes using the greedy decoding strategy." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 78, + 217, + 273, + 273 + ], + "lines": [ + { + "bbox": [ + 78, + 217, + 273, + 273 + ], + "spans": [ + { + "bbox": [ + 78, + 217, + 273, + 273 + ], + "type": "table", + "html": "
    Layers0-45-1819-2627-31Greedy
    \\(C_S\\ ↓\\)31.025.053.453.453.0
    \\(C_I\\ ↓\\)10.46.714.315.715.6
    F1↑77.176.177.577.276.7
    ", + "image_path": "6d677d5d11425079b6eabcbb3c951127b98f0bfc564494840ac55dd380d59890.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 324, + 296, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 296, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 296, + 373 + ], + "type": "text", + "content": "our method consistently reduces hallucinations across different token lengths and achieves the best performance on average, demonstrating its robustness. We provide qualitative results in Appendix C.7." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 382, + 204, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 382, + 204, + 395 + ], + "spans": [ + { + "bbox": [ + 55, + 382, + 204, + 395 + ], + "type": "text", + "content": "5. Ablations and Discussions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 403, + 295, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 403, + 295, + 558 + ], + "spans": [ + { + "bbox": [ + 54, + 403, + 295, + 558 + ], + "type": "text", + "content": "Layers of attention intervention. Motivated by the empirical observation of implicit hallucination patterns across layers beyond the 5-18 range in Sec. 3.4.1, we investigate whether interventions in these layers can also mitigate object hallucinations. We apply our approach (Eq. (6)) to the layer ranges [0, 4], [19, 26], and [27, 31] in LLaVA-1.5-7B, and the results are reported in Tab. 4. We observe that the 5-18 layer range largely outperforms the other ranges while using some ranges (19-26 and 27-31) even enhanced hallucinations instead. The result suggests that explicit patterns in visual information enrichment are more effective than implicit patterns, facilitating more effective hallucination mitigation through simple attention intervention." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 558, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 295, + 700 + ], + "type": "text", + "content": "Different attention intervention strategies. To validate the efficacy of our method in adjusting attention weights to reduce object hallucinations, we compare it with the inference intervention component proposed in PAI [28]. The inference intervention component roughly excites attention weights by computing a weighted sum of the attention scores and their absolute values across individual heads. We apply this approach to the same layer ranges in ours on LLaVA-1.5-7B, Shikra, and MiniGPT-4. Tab. 5 suggests that our attention intervention method surpasses that of PAI, as our method integrates attention information from various heads to shift attention toward a more truthful direction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 701, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 296, + 713 + ], + "type": "text", + "content": "Balance factor " + }, + { + "bbox": [ + 55, + 701, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 701, + 296, + 713 + ], + "type": "text", + "content": " sensitivity. To examine the influence of" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 70, + 432, + 178 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 432, + 178 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 432, + 178 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 432, + 178 + ], + "type": "image", + "image_path": "cdc69a6b4bebe5de35f61afa243505b2ba782c692f5fba055b3790bd4a4e2df3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 186, + 539, + 198 + ], + "lines": [ + { + "bbox": [ + 328, + 186, + 539, + 198 + ], + "spans": [ + { + "bbox": [ + 328, + 186, + 539, + 198 + ], + "type": "text", + "content": "Figure 8. Parameter sensitivity of " + }, + { + "bbox": [ + 328, + 186, + 539, + 198 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 328, + 186, + 539, + 198 + ], + "type": "text", + "content": " with CHAIR metrics." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 433, + 70, + 554, + 178 + ], + "blocks": [ + { + "bbox": [ + 433, + 70, + 554, + 178 + ], + "lines": [ + { + "bbox": [ + 433, + 70, + 554, + 178 + ], + "spans": [ + { + "bbox": [ + 433, + 70, + 554, + 178 + ], + "type": "image", + "image_path": "53e151414e6c508428ed0e3152bc49569fa8cf42d772068d557781f24747ee46.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 328, + 209, + 541, + 262 + ], + "blocks": [ + { + "bbox": [ + 55, + 281, + 295, + 304 + ], + "lines": [ + { + "bbox": [ + 55, + 281, + 295, + 304 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 295, + 304 + ], + "type": "text", + "content": "Table 4. CHAIR hallucination evaluation and F1 score among four layer ranges on LLaVA-1.5-7B with max new token set to 512." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 209, + 541, + 262 + ], + "lines": [ + { + "bbox": [ + 328, + 209, + 541, + 262 + ], + "spans": [ + { + "bbox": [ + 328, + 209, + 541, + 262 + ], + "type": "table", + "html": "
    MethodLLaVA-1.5-7BShikra-7BMiniGPT-4-7B
    CS↓CI↓CS↓CI↓CS↓CI↓
    PAI*26.68.145.813.630.29.5
    Ours25.06.723.89.421.48.0
    ", + "image_path": "13e57fc4b324d576e6988fce4c660194fbc5a62e0e09fa118f7ab3926ed1ec27.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 270, + 554, + 304 + ], + "lines": [ + { + "bbox": [ + 313, + 270, + 554, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 270, + 554, + 304 + ], + "type": "text", + "content": "Table 5. CHAIR hallucination evaluation and F1 results on three LVLMs. " + }, + { + "bbox": [ + 313, + 270, + 554, + 304 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 313, + 270, + 554, + 304 + ], + "type": "text", + "content": " denotes only using the inference intervention component in the same layer range as ours. Greedy decoding is adopted." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "text", + "content": " on intervention efficacy, we vary its value in the range of " + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "inline_equation", + "content": "\\{0.3, 0.4, 0.5, 0.6, 0.7\\}" + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "text", + "content": " and the results of CHAIR metrics and F1 score for the 7B version of both LLaVA-1.5 and MiniGPT-4 are shown in Fig. 8. We find that a lower " + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "text", + "content": " limits hallucination mitigation effectiveness, whereas a higher " + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "text", + "content": " compromises the richness of descriptions. These results indicate that an appropriate " + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 324, + 555, + 433 + ], + "type": "text", + "content": " value (e.g., 0.5 for both selected LVLMs) balances the reduction of hallucinations with the maintenance of detailed visual descriptions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 442, + 453, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 442, + 453, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 442, + 453, + 455 + ], + "type": "text", + "content": "6. Conclusion and Insights" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 462, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 462, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 462, + 555, + 715 + ], + "type": "text", + "content": "We introduce a new perspective, visual information processing, to investigate the underlying mechanisms driving object hallucination. Analyzing through the lens of attention, we identify three key findings and discover a simple yet effective method for reducing hallucinations at inference time. Our study deepens the understanding of how hallucinations are produced in LVLMs. We conclude with three insights for future direction: 1) Based on LVLMs' interpretation in semantic refinement stage, the image tokens may be further categorized into sub-groups, such as object tokens, color tokens, and textual tokens, enabling us to explore how the LVLMs extract different types of visual information. 2) While we focus on visual information processing, there may exist more granular, stage-wise mechanisms that could explain model behavior more precisely. 3) Instead of external interventions on LVLM outputs, such as contrastive decoding, we suggest that targeted modifications to specific internal states, like attention weights in middle layers, offer a more effective method for calibration. Our insights may aid the community in developing more trustworthy and reliable LVLMs against hallucinations." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "25011" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 149, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 149, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 149, + 85 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 90, + 297, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 90, + 297, + 148 + ], + "spans": [ + { + "bbox": [ + 55, + 90, + 297, + 148 + ], + "type": "text", + "content": "This work is supported by the National Science Foundation of China (62376281, 62206048), the Natural Science Foundation of Jiangsu Province (BK20220819), and the Fundamental Research Funds for the Central Universities (2242024k30035)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 167, + 115, + 180 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 167, + 115, + 180 + ], + "spans": [ + { + "bbox": [ + 56, + 167, + 115, + 180 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 188, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 188, + 296, + 232 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 188, + 296, + 232 + ], + "spans": [ + { + "bbox": [ + 61, + 188, + 296, + 232 + ], + "type": "text", + "content": "[1] Jize Cao, Zhe Gan, Yu Cheng, Licheng Yu, Yen-Chun Chen, and Jingjing Liu. 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We present DexGrasp Anything, consistently surpassing previous dexterous grasping generation methods across five benchmarks. Visualization of our method's results are shown on the left." + ], + "image_footnote": [], + "bbox": [ + 96, + 267, + 545, + 492 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d0952ab27855a19267a787a4cbe6e4b8b09561b6239b3b70c1f9e66726021657.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 550, + 268, + 906, + 491 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 537, + 326, + 553 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A dexterous hand capable of grasping any object is essential for the development of general-purpose embodied intelligent robots. However, due to the high degree of freedom in dexterous hands and the vast diversity of objects, generating high-quality, usable grasping poses in a robust manner is a significant challenge. In this paper, we introduce DexGrasp Anything, a method that effectively integrates physical constraints into both the training and sampling phases of a diffusion-based generative model, achieving state-of-the-art performance across nearly all open datasets. Additionally, we present a new dexterous grasping dataset containing over 3.4 million diverse grasping poses for more than 15k different objects, demonstrating its potential to advance universal dexterous grasping. Code and dataset are available at https://github.com/4DVLab/DexGrasp-Anything", + "bbox": [ + 88, + 574, + 485, + 818 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 514, + 537, + 643, + 553 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dexterous grasping, serving as a foundational capability for robotic manipulation tasks, has attracted significant attention. Five-fingered dexterous hands, which closely resemble the structure of the human hand, offer significantly greater flexibility, manipulation precision, and versatility compared to simpler grippers (e.g. parallel jaw, vacuum gripper). As robots are being deployed in human environments, dexterous hands have become increasingly vital due to their ability to interact with a wide range of objects as humans and use tools designed for humans. Therefore, a precise, robust, and versatile dexterous grasping method lies at the heart of interactions in embodied intelligence.", + "bbox": [ + 511, + 566, + 906, + 747 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Earlier approaches [5, 18, 25, 28, 29, 35] on dexterous grasping have primarily relied on analytical methods, where grasping poses were optimized to meet specific physical constraints. These methods, however, face significant challenges due to the large search space and the complexity of optimizing for high degrees of freedom in dexterous hands, leading to low success rates. In contrast, data-driven methods [10, 11, 17, 21, 43-45, 47, 51] leverage large-scale datasets to learn useful priors, narrowing the search space and providing strong guidance for search ini", + "bbox": [ + 511, + 750, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ * Equal contribution.", + "bbox": [ + 107, + 838, + 230, + 851 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{2\\dagger}$ Corresponding author. This work was supported by NSFC (No.62206173), Shanghai Frontiers Science Center of Human-centered Artificial Intelligence (ShangHAI), MoE Key Laboratory of Intelligent Perception and Human-Machine Collaboration (KLIP-HuMaCo).", + "bbox": [ + 91, + 851, + 482, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22584", + "bbox": [ + 478, + 989, + 517, + 1000 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tialization. Regression-based methods [17, 45] that directly predict grasp parameters from object inputs often suffer from mode collapse and averaging, resulting in a limited diversity of generated grasp poses. Recently, generative methods [11, 47] have gained significant attention for their ability to enhance the diversity of generated grasp poses. Among these, diffusion models [8, 12, 39] have demonstrated a strong capability to capture the complexities of dexterous grasping and generate diverse grasp poses by iteratively transforming a simple distribution (e.g., Gaussian) into a complex, high-dimensional one [10, 21, 44, 51]. However, despite these advantages, current diffusion-based approaches [43, 45] often generate suboptimal grasp poses, resulting in hand-object penetration or insufficient contact with unsatisfactory success rates. These issues arise from the lack of constraints that enforce physical rules.", + "bbox": [ + 89, + 90, + 480, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a novel dexterous grasping generation method, namely DexGrasp Anything, that integrates three carefully designed physical constraint objectives into the diffusion model during both training and sampling phases. DexGrasp Anything exhibits superior robustness and strong generalization capabilities. Specifically, we introduce the surface pulling force to ensure grasp feasibility by pulling the hand's inner surface toward the object's surface while avoiding interference with parts that are already sufficiently distant. We also introduce the externalpenetration repulsion force to maintain geometric accuracy of interaction by effectively preventing significant collisions between the object and the dexterous hand, and the selfpenetration repulsion force to preserve the hand's geometry by enforcing a minimum distance between finger joints and applying repulsion when they get too close. Through our physics-aware training scheme and physics-guided sampler, these physical constraints enable our diffusion-based generator to produce practical and robust dexterous grasping poses across a wide range of objects. Through extensive experiments, we show our method achieves state-of-the-art performance on almost all open datasets, as Figure 1 shows.", + "bbox": [ + 91, + 337, + 482, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To further improve the universality of diffusion-based generative method, massive amounts of high-quality training data is necessary. While many efforts have been made to build grasping datasets, they suffer from narrow data distribution[6, 17, 22], limited object categories [17, 41], and scalability issues [19]. In light of this, we dedicate substantial efforts to further enhancing the scale, diversity, and quality of the dexterous grasping datasets. We start by gathering available dexterous grasping data from multiple sources [15, 19, 40, 41, 47], including simulated data, real-captured data, and human hand grasping data, ensuring a diverse and comprehensive data distribution. We further scale up the dataset with a 'model-in-the-loop' strategy by using our grasping method and filtering method to continue generating high-quality data, inspired by the approach used in", + "bbox": [ + 89, + 674, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SAM [14]. These efforts culminate in a very large-scale dexterous grasping dataset, DexGrasp Anything (DGA) Dataset with over 3.4 million grasping poses on more than 15k objects. Experimental results demonstrate that this new dataset provides substantial benefits to grasping methods within the community.", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contribution of this work are as follows:", + "bbox": [ + 529, + 181, + 864, + 196 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a physics-aware diffusion generator for dexterous grasping pose generation, which effectively integrates three key physical constraints into both the training and sampling phases of the diffusion model.", + "- Our method achieves state-of-the-art performance on five dexterous grasping datasets.", + "- We present a new high-quality dexterous grasping dataset, the largest and most diverse to date, significantly improving the generalization capability of existing methods." + ], + "bbox": [ + 511, + 198, + 903, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 348, + 653, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Dexterous Grasp Generation", + "text_level": 1, + "bbox": [ + 513, + 375, + 769, + 388 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dexterous Grasping serves as a fundamental component for various complex, human-like manipulation tasks, making it a long-standing area of research in robotics. Early works mainly use manually derived analytical methods [5, 18, 25, 28, 29, 35] that based on certain physical constraints. These methods are hindered by extremely large search space and complex optimization process, leading to low success rate.", + "bbox": [ + 511, + 398, + 903, + 502 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, data-driven approaches have emerged as a promising direction for dexterous grasping. Regression-based methods, such as [17, 45], often generate grasping poses with limited diversity, as they rely on direct predictions from input data and may fail to explore the full range of possible grasping configurations. In contrast, generative methods [11, 47] explicitly model the conditional probability distribution of dexterous hand poses given the target object, theoretically generating diverse poses. Diffusion model-based methods [10, 21, 51], in particular, stand out as a promising direction for more universal and robust robotic dexterous grasping for its exceptional capabilities in modeling various complex data distribution [9, 16, 20, 32, 46, 50] and generating diverse and highly realistic samples [27, 31, 33, 36]. However, existing diffusion model-based approaches are observed [43, 45] to yield sub-optimal grasping poses due to the absence of physical constraints during the training and sampling process. In this work, we delve into incorporating physical constraints into diffusion models to generate robust dexterous grasping poses for dexterous hands.", + "bbox": [ + 511, + 503, + 903, + 820 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Dexterous Grasping Dataset", + "text_level": 1, + "bbox": [ + 513, + 832, + 766, + 847 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Collecting 3D dexterous grasping poses is notoriously expensive due to the complexity of hand structures. Most existing datasets are collected in simulators like", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22585", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a52f39c6157450f7a04fef57b6139b05d69308be4d5f156766f374526fb8383e.jpg", + "image_caption": [ + "Figure 2. Overview of DexGrasp Anything. During training, object information is processed to extract combined semantic and spatial representations as conditioning inputs. At each noise training step, a clean-estimation of the noisy hand pose $\\hat{h}_0$ is derived from the predicted noise $\\hat{\\varepsilon}_t$ , with physics constraints guiding the noise distribution toward a cleaner, grasp-suitable distribution. During sampling, the Physics-Guided Sampler obtains the current observation $\\hat{h}_0$ at each denoising step and performs posterior sampling based on this observation. Physical constraints gradually guide the distribution toward a physically feasible grasp configuration $\\hat{h}_0^*$ , enabling effective grasping of diverse objects." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 898, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GraspIt! [24] and IssacGym [23] through searching in the eigengrasp space [6, 17, 22] or optimization-based methods [15, 17, 41, 47] in parameter space. However, the search-based data often follow a narrow distribution due to the low-dimensional eigengrasp space, while the recent optimization-based data still suffer from relatively success rate and contained limit number of object categories. Some real-world datasets have been collected using teleoperation systems controlled by human operators. While these datasets capture human-like grasping poses, the data collection process is prohibitively expensive and difficult to scale up. Recent advances [30, 37, 38] have explored retargeting human hand poses to dexterous robotic hands, presenting a promising avenue for leveraging human hand data in robot hand training. Despite these advancements, existing datasets still face limitations in diversity, scalability, and quality. To address these challenges, we introduce the largest and most diverse dexterous grasping dataset to date and demonstrate that our dataset significantly enhances both the quality and diversity of generated dexterous", + "bbox": [ + 88, + 585, + 485, + 888 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "grasping poses, providing substantial value to existing data-driven grasping generators.", + "bbox": [ + 511, + 587, + 906, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 511, + 645, + 604, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We present DexGrasp Anything, an effective approach that enhances diffusion-based generators for dexterous grasping by integrating meticulously designed physical constraints. Figure 2 demonstrates an overview of our method. The following sections detail our problem formulation (Sec. 3.1), physics-aware constraints (Sec. 3.2), and the way to integrate constraints to the diffusion model's training (Sec. 3.3) and sampling processes (Sec. 3.4), and the LLM-enhanced object representation extraction module (Sec. 3.5).", + "bbox": [ + 511, + 671, + 906, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 511, + 816, + 694, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to generate high-quality grasping poses capable of securely holding a given object. Specifically, given a 3D object observation $O$ , we aim to sample a diverse set of dexterous grasping poses $\\mathbf{h} = \\{h_i\\}_{i=1}^n$ from a condi-", + "bbox": [ + 511, + 840, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22586", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tional distribution $P(h|O)$ , where the dexterous pose $h = (\\theta, \\mathrm{R}, \\mathrm{t}) \\in \\mathbb{R}^{33}$ consists of the dexterous hand articulation $\\theta \\in \\mathbb{R}^{24}$ (for ShadowHand), the global rotation $R \\in \\mathrm{SO}(3)$ and the global translation vector $t \\in \\mathbb{R}^3$ .", + "bbox": [ + 89, + 90, + 480, + 150 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The conditional distribution $P(h|O)$ is modeled using a diffusion model $\\epsilon_{\\phi}(h_t,O,t)$ , which iteratively transforms an isotropic Gaussian distribution $\\mathcal{N}(0,\\mathrm{I})$ into the desired data distribution:", + "bbox": [ + 89, + 151, + 482, + 210 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP (h _ {0} | O) = P (h _ {T}) \\prod_ {t = 1} ^ {T} P (h _ {t - 1} | h _ {t}, O),\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 222, + 403, + 263 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(h _ {t - 1} \\mid h _ {t}, O\\right) = \\mathcal {N} \\left(h _ {t - 1}; \\mu_ {\\phi} \\left(h _ {t}, O, t\\right), \\Sigma_ {\\phi} \\left(h _ {t}, O, t\\right)\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 265, + 482, + 299 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Physical Constraints", + "text_level": 1, + "bbox": [ + 89, + 311, + 285, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion model-based methods often fail to reach optimal performance in the absence of appropriate physical constraints. To address this, we present three tailored physical constraint objectives for our DexGrasp Anything generator, enabling the production of universal and robust dexterous grasping poses for a wide range of objects.", + "bbox": [ + 89, + 335, + 483, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Surface Pulling Force [47] is crucial for ensuring grasp feasibility. It enforces proximity between the inner surface of the robotic phalanges (represented by sampled point clouds) and the object's surface. This guidance signal applies a pulling force only to points that are closer than a specified threshold, ensuring that the points on the inner surface of the fingers are pulled towards the object's surface when they are near, but does not affect points that are already at a sufficient distance. Compute the squared Euclidean distance for each inner surface point $p_{\\mathrm{dis}}^{(i)}$ to its nearest neighbor on the object surface: $d_{i} = \\min_{j} \\| p_{\\mathrm{dis}}^{(i)} - p_{\\mathrm{obj}}^{(j)} \\|^2$ . We compute the surface pulling force as:", + "bbox": [ + 89, + 426, + 483, + 613 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {S P F}} = \\frac {\\sum_ {i \\in S} \\sqrt {d _ {i}}}{| S | + \\eta}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 625, + 482, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $S = \\{i|d_i < d_{\\mathrm{Threshold}}\\}$ represents the set of points within the threshold distance and $\\eta$ is a numerical stability constant.", + "bbox": [ + 89, + 671, + 482, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "External-penetration Repulsion Force [10] retains the spatial accuracy of hand-object interactions. It minimizes the undesired intersection between the hand and object point clouds by leveraging the signed distances. Given an object point cloud $P_{obj}$ with surface normals $N_{obj}$ , and a hand point cloud $P_{hand}$ , we first compute the nearest neighbor distance between each point in $P_{hand}$ and $P_{obj}$ : $d_i = \\min_j \\| P_{hand}^{(i)} - P_{obj}^{(j)} \\|$ . We then calculate the signed distance between the hand and object points using the object normals:", + "bbox": [ + 89, + 717, + 483, + 869 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} = \\operatorname {s i g n} \\left(\\left(P _ {o b j} ^ {(j)} - P _ {\\text {h a n d}} ^ {(i)}\\right) \\cdot N _ {o b j} ^ {(j)}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 881, + 482, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, the external-penetration repulsion force is defined as the maximum signed distance across all points in the batch, averaged over the batch size $B$ :", + "bbox": [ + 511, + 90, + 905, + 135 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {E R F}} = \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\max _ {i} \\left(s _ {i}, d _ {i}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 148, + 905, + 189 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Self-Penetration Repulsion Force [47] upholds the hand structural geometry. It addresses the issue of hand points intersecting with each other by enforcing a minimum distance between them. This ensures that the hand maintains a realistic, physically plausible shape without finger collisions. Given a set of hand points $P_{\\mathrm{hand}}$ , we calculate the pairwise Euclidean distances between all points: $d_{ij} = \\| P_{\\mathrm{hand}}^{(i)} - P_{\\mathrm{hand}}^{(j)} \\|$ , A repulsion force is applied when $d_{ij}$ is smaller than a threshold $d_{\\mathrm{Threshold}}$ , and the self-penetration repulsion force is defined as:", + "bbox": [ + 511, + 199, + 906, + 351 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {S R F}} = \\frac {1}{B} \\sum_ {i, j} \\max \\left(0, d _ {\\text {T h r e s h o l d}} - d _ {i j}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 363, + 905, + 400 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Physics-Aware Training", + "text_level": 1, + "bbox": [ + 513, + 410, + 733, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion Models are typically trained with a simple mean-squared error (MSE) objectives:", + "bbox": [ + 511, + 433, + 905, + 464 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, x _ {0}, \\epsilon} [ \\| \\epsilon - \\epsilon_ {\\phi} (h _ {t}, t) \\| ^ {2} ], \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 474, + 903, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $h_t$ is a corrupted version of the original data $h_0$ . The data corruption follows a fixed noise schedule $\\beta_t$ :", + "bbox": [ + 511, + 503, + 905, + 534 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(h _ {t} \\mid h _ {t - 1}\\right) = \\mathcal {N} \\left(h _ {t}; \\sqrt {1 - \\beta_ {t}} h _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 546, + 903, + 573 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {t} = \\sqrt {1 - \\beta_ {t}} h _ {t - 1} + \\sqrt {\\beta_ {t}} \\epsilon_ {t}.\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 569, + 828, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With $\\alpha_{t} = 1 - \\beta_{t}$ and $\\bar{\\alpha}_{t} = \\Pi_{i = 1}^{t}\\alpha_{i}$ , the corruption process can be directly conditioned on $h_0$ :", + "bbox": [ + 511, + 598, + 905, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(h _ {t} \\mid h _ {0}\\right) = \\mathcal {N} \\left(h _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} h _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 638, + 903, + 666 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} h _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\bar {\\epsilon} _ {t}.\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 661, + 805, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the training objective $L_{\\mathrm{simple}}$ is essentially a reweighted variational lower bound on negative log likelihood, it does not incorporate any explicit supervision regarding physical constraints. As a result, diffusion models often perform sub-optimally when directly generating dexterous grasping parameters, as observed in previous works [43, 45]. To facilitate our diffusion generator in capturing physics priors during training, we introduce the Physics-Aware Training paradigm, which incorporates the tailored physical constraints outlined in Sec. 3.2.", + "bbox": [ + 511, + 688, + 905, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The training objective involving only corrupted data $h_t$ is not well-suited for incorporating physical constraints. Using the diffusion process defined in Eq. 8, the estimated sample: $\\hat{h_0}(h_t) = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}} (h_t - \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon_\\phi(h_t, O, t))$ could", + "bbox": [ + 511, + 839, + 906, + 904 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22587", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "serve as a good proxy for introducing physical constraint into the training process of a diffusion model.", + "bbox": [ + 89, + 90, + 482, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We define the physically-aware training objective $L_{\\mathrm{PADG}}$ as a linear combination of the standard mean-squared objective and multiple physical-constraint objectives:", + "bbox": [ + 88, + 121, + 482, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {P A D G}} = L _ {\\text {s i m p l e}} \\left(h _ {t}\\right) + \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h _ {0}} \\left(h _ {t}\\right), \\epsilon_ {\\phi}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 172, + 482, + 213 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{\\mathrm{PA}_i}(\\hat{h_0}(h_t), \\epsilon_\\phi)$ is the $i^{th}$ physical constraint and $\\alpha_i$ is the corresponding weighting coefficient. The gradient is propagated to $h_t$ through the estimated clean sample $h_0$ as follows:", + "bbox": [ + 89, + 220, + 482, + 281 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial L _ {\\mathrm {P A D G}}}{\\partial h _ {t}} = \\frac {\\partial L _ {\\text {s i m p l e}}}{\\partial h _ {t}} + \\sum_ {i = 1} ^ {m} \\alpha_ {i} \\frac {\\partial L _ {\\mathrm {P A} _ {i}}}{\\partial \\hat {h _ {0}}} \\cdot \\frac {\\partial \\hat {h _ {0}}}{\\partial h _ {t}}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 287, + 482, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Physics-Guided Sampling", + "text_level": 1, + "bbox": [ + 89, + 332, + 326, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Leveraging the learned physics priors, the well-trained diffusion generator is capable of producing physically plausible dexterous grasping poses for a given object. The physical constraints can be further enhanced during the sampling process by employing advanced sampling techniques [1, 4, 7, 48].", + "bbox": [ + 89, + 356, + 483, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Classifier guidance [4] has explored the use of a time-dependent classifier $\\mathcal{F}_t$ to steer the diffusion model towards specific conditional distributions. The guidance can be approximated as an offset in the posterior mean:", + "bbox": [ + 89, + 446, + 483, + 506 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mu} _ {\\phi} \\left(x _ {t}, t\\right) \\leftarrow \\mu_ {\\phi} \\left(x _ {t}, t\\right) + s \\Sigma_ {\\theta , t} \\nabla_ {x _ {t}} \\log \\left(\\mathcal {F} _ {t} (y, x _ {t})\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 513, + 480, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s$ is the guidance strength. By estimating $\\hat{x_0}$ based on $x_{t}$ , the guidance signal can be extended from a time-dependent classifier $\\mathcal{F}_t(y,x_t)$ to arbitrary objective functions $L(x_0)$ on clean samples. It can be achieved by mapping the objective to a density-like function:", + "bbox": [ + 89, + 539, + 483, + 614 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} \\left(x _ {0}\\right) = \\mathcal {Z} e ^ {- L \\left(x _ {0}\\right)}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 619, + 480, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{Z}$ is a normalizing constant. We define the Physics-Guided Sampler as follows:", + "bbox": [ + 89, + 646, + 482, + 676 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\widetilde {\\mu} _ {\\phi} (h _ {t}, O, t) \\leftarrow \\mu_ {\\phi} (h _ {t}, O, t) \\\\ + s \\Sigma_ {\\phi , t} \\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {P A _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right), \\epsilon_ {t}\\right). \\tag {13} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 684, + 480, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To alleviate the estimation bias on $\\hat{h_0}$ , we apply the Spherical Gaussian Constraint [48] with a weighted gradient direction in practice. This is expressed as:", + "bbox": [ + 89, + 751, + 482, + 797 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mu} _ {\\phi} \\left(h _ {t}, O, t\\right) \\leftarrow \\mu_ {\\phi} \\left(h _ {t}, O, t\\right) + r \\frac {d _ {m}}{\\| d _ {m} \\|}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 804, + 480, + 837 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d_{\\mathrm{m}} = d_{\\mathrm{sample}} + g_r(d^* - d_{\\mathrm{sample}})$ , $d_{\\mathrm{sample}} = \\Sigma_{\\phi, t} \\epsilon$ and:", + "bbox": [ + 89, + 843, + 482, + 859 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd ^ {*} = - \\sqrt {n} \\Sigma_ {\\phi , t} \\frac {\\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right) , \\epsilon_ {t}\\right)}{\\| \\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right) , \\epsilon_ {t}\\right) \\|}. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 866, + 482, + 905 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Incorporating physics constraints during training helps guide the noise distribution toward a cleaner, grasp-suitable form. However, due to sparse supervision in the training phase, we leverage the reverse process during sampling to obtain $h_t$ and $\\hat{h}_0$ at each step, applying posterior sampling to iteratively refine the grasp configuration. This iterative refinement allows the Physics-Guided Sampler to progressively adjust $\\hat{h}_0$ under physics constraints, ultimately steering the distribution toward a physically feasible grasp configuration. Through this distributional framework, our model effectively generalizes to diverse objects, demonstrating robustness and adaptability in grasping tasks.", + "bbox": [ + 511, + 90, + 905, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. LLM-enhanced Representation Extraction", + "text_level": 1, + "bbox": [ + 511, + 280, + 877, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To accomplish robust dexterous grasp generation for a targeted object, we boost the traditional object representation by complementing the geometry object feature with semantic prior from powerful LLMs. We employ a Point Transformer[52] to encode object point clouds, producing an $N \\times C$ feature vector, where $\\mathbf{N}$ represents the number of groups defined by the Point Transformer. To enrich these features with abundant semantic prior from LLM, we utilize the prompt: \"I want to grasp a [object label]. First, provide its object category, then give a detailed description of its shape before making a successful grip.\" We then parse the response and encode each sentence using a pre-trained BERT-large-uncased model. We extract the [CLS] token from each sentence and apply max-pooling on them. This results in an $1 \\times C$ semantic feature vector that includes the rich prior knowledge from the LLM. The concatenated $(N + 1) \\times C$ feature matrix is subsequently integrated into the diffusion backbone through a cross-attention mechanism, enhancing the model's capacity to generate precise and contextually relevant grasping poses.", + "bbox": [ + 511, + 303, + 906, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Dataset", + "text_level": 1, + "bbox": [ + 513, + 617, + 602, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The quality, diversity and scale of datasets are crucial for advancing dexterous grasping research, especially for diffusion-based generative methods. Training on a broader data distribution enables models to learn richer and more adaptable grasping strategies for arbitrary object. To inspire potential of methods towards universal dexterous grasping, we have developed a comprehensive dataset that significantly exceeds existing dexterous grasping datasets in both size and diversity. In the following sections, we provide a detailed overview of the data construction process, present key statistics, and highlight the characteristics of our DexGrasp Anything (DGA) dataset.", + "bbox": [ + 511, + 642, + 906, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Data Construction", + "text_level": 1, + "bbox": [ + 511, + 832, + 692, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our data construction process begins with curating existing datasets from diverse sources. We gather three simulated datasets [15, 41, 47], a real-world dataset [19] col", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22588", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ee9c83225ac4e1e937ba549e998a7daec85a4b961df12d22e6b262e6e1d99eb8.jpg", + "table_caption": [ + "Table 1. Comparison of dexterous grasp datasets. Our dataset achieves the largest scale to date." + ], + "table_footnote": [], + "table_body": "
    DatasetPublication YearHand TypeSim./Real#Grasps#Objects#Grasps per objectConstruction method
    GRAB [40]ECCV 2020MANOReal1.64M51>10KCapture
    DDGdata [17]RSS 2020ShadowHandSim.6.9k565-GraspIt!
    MultiDex [15]ICRA 2023ShadowHandSim.16K58300Optimization
    DexGraspNet [41]ICRA 2023ShadowHandSim.1.32M5,355>200Optimization
    UniDexGrasp [47]CVPR 2023ShadowHandSim.1.12M5,519>150Optimization
    GraspXL [49]ECCV 2024Diverse HandSim-500K-GraspXL
    RealDex [19]IJCAI 2024ShadowHandReal59K52>200Human Annotation
    Our datasetCVPR 2025ShadowHandReal+Sim.3.40M15,698>200DexGrasp Anything + Filter
    ", + "bbox": [ + 93, + 108, + 903, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "lected by human operator, alongside GRAB [40], a largescale human hand dataset, to maximize data diversity and richness. Leveraging advancements in robot teleoperation systems like AnyTeleop [30], we retarget the human hand dataset GRAB to dexterous hand parameters, creating DexGRAB, and filter it to retain only frames with hand-object contact. Next, we examine all collected data within IsaacGym [23], applying strict conditions to ensure stability and contact integrity. Specifically, we enforce that (1) objects do not shift more than $2\\mathrm{cm}$ in any direction under force and that (2) hand-object penetration remains below $10\\mathrm{mm}$ and object-hand penetration remains below $1\\mathrm{mm}$ following [41]. The detailed process for computing the penetration is provided in the supplementary materials. This rigorous filtering process guarantees consistent high quality across all data sources.", + "bbox": [ + 88, + 257, + 480, + 498 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training our physics-aware diffusion generator on this dataset leads to higher success rates, greater diversity, and faster generation speeds for zero-shot dexterous grasping on unseen objects. Acting as a data engine, our model facilitates further dataset expansion in a \"model-in-the-loop\" manner. We meticulously selected object meshes from the Objaverse [2, 3] dataset, with the goal of ensuring broad category coverage and maintaining an even distribution across these categories. To achieve this, we examined all objects within 18 chosen categories and ultimately selected 10,034 distinct objects, covering 6,994 unique tags in the Objaverse data configuration. We apply approximate convex decomposition [42] to each mesh to reduce complexity and ensure water-tightness. Our trained generator then iteratively produces dexterous grasp poses, which are filtered under the same stringent standards. Finally, we combine the curated and generated data to form a large-scale and diverse dataset, crafted to advance research in dexterous grasping.", + "bbox": [ + 89, + 500, + 482, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Statistics", + "text_level": 1, + "bbox": [ + 89, + 785, + 196, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We present a comparative analysis of key metrics between our dataset and other existing datasets in Table 1. Our DGA dataset comprises two main components: The first component DGA-curated includes approximately 0.88 million grasping poses across 5,664 distinct objects, curated from various existing and diverse data sources. The second com", + "bbox": [ + 89, + 809, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f80f3ea959868375a6dffa9afc585e7d92a516aff4e5a9e328e8345aee817e23.jpg", + "image_caption": [ + "Figure 3. t-SNE visualization of the object features in our dataset compared to existing datasets. Each point represents an object, and different markers and colors are used to distinguish between datasets. For clarity, we randomly sample $5\\%$ objects from each dataset for visualization." + ], + "image_footnote": [], + "bbox": [ + 535, + 257, + 885, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ponent DGA-generated is generated with our DexGrasp Anything generator from the Objaverse [2, 3] dataset, containing approximately 2.52 million grasping poses spanning 10,034 different objects, covering 6,994 unique tags. In total, our dataset features over 3.4 million grasping poses across 15,698 objects from diverse data distribution, supporting in-depth research into dexterous grasping.", + "bbox": [ + 511, + 482, + 905, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Characteristics", + "text_level": 1, + "bbox": [ + 513, + 602, + 666, + 616 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our dataset is characterized by a high degree of diversity and comprehensiveness, aimed at capturing a wide range of object and pose variations to advance the performance of dexterous hands in complex real-world environment. The key characteristics of our dataset can be presented as follow:", + "bbox": [ + 511, + 627, + 905, + 702 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Large data scale. Our dataset features over 3.4M strictly-tested grasping poses, which is significantly larger than all previous datasets.", + "- Diverse objects. Our dataset encompasses 15,698 objects from a wide range of categories and sources, ensuring a high level of diversity. In Figure 3, we present a t-SNE visualization comparing object features from our dataset with those from existing datasets, using features extracted by a pre-trained Point Transformer. Object features from our dataset spread much wider across the feature space, suggesting that our dataset captures a broader variety or unique features that not be as present in existing datasets.", + "- Diverse grasping poses. The wide variety of objects" + ], + "bbox": [ + 513, + 704, + 906, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22589", + "bbox": [ + 478, + 989, + 517, + 1000 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3b30be4a98a8911bb3ac04a1c739c7e7af07bfadfde464f5f79d4f774674a286.jpg", + "table_caption": [ + "Table 2. Performance comparison across different methods and datasets. Bold numbers indicate the best scores, while underlined numbers indicate the second-best scores. DexGrasp Anything (w/ LLM) achieves the highest or near-highest performance across most metrics." + ], + "table_footnote": [], + "table_body": "
    Dataset MethodDexGraspNetUniDexGraspMultiDexRealDexDexGRAB
    Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑
    UniDexGrasp [47]33.970.131.90.1423.765.524.50.1421.647.513.50.0827.159.439.00.1120.855.837.40.08
    GraspTTA [11]18.667.824.50.1321.065.321.20.1030.362.819.00.1113.346.440.10.0914.451.051.40.10
    SceneDiffuser [10]26.666.931.00.1528.374.825.10.1569.885.614.60.2721.756.142.00.0939.185.041.10.12
    UGG [21]46.979.025.20.1446.083.224.50.1455.393.410.30.1232.763.434.40.1042.790.633.20.12
    Ours53.690.421.50.2254.890.818.90.2572.296.39.60.2334.671.223.10.1456.591.828.60.12
    Ours(w/LLM)57.590.617.80.2353.191.218.80.2379.198.111.40.2244.873.727.70.1357.992.730.40.13
    ", + "bbox": [ + 93, + 127, + 906, + 238 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "contributes to a diverse range of grasping poses. Extensive experimental results in Sec. 5.3 demonstrate that our dataset significantly enhances the diversity of outcomes from existing methods, while maintaining or even improving the grasping success rate.", + "bbox": [ + 102, + 263, + 483, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 353, + 223, + 371 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Comparison", + "text_level": 1, + "bbox": [ + 89, + 378, + 223, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics. Following previous works [10], we assess the grasping success rate (Suc. 6/Suc. 1) and maximum penetration (Pen.) in millimeters to gauge the quality of generated poses. A grasping pose is considered successful if the object's displacement, when an external force is applied, is less than $2\\mathrm{cm}$ in at least one (Suc. 1) or all (Suc. 6) of the six axis-aligned directions in a 3D coordinate system. Additionally, we evaluate the diversity using the mean standard deviation of the pose parameters (Div.) across successful grasps in millimeters. All poses are evaluated in the IssacGym [23] simulator with the same configuration used in [10].", + "bbox": [ + 89, + 401, + 483, + 582 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation Details. Following [10], we employ a U-Net [34] structure for our diffusion backbone. An object-conditioned Point Transformer [52] encoder handles the point clouds, injected into the diffusion model using a cross-attention mechanism. All point clouds are downsampled to 2048 points before encoding. Our model is implemented using the PyTorch [26] platform, optimized with the Adam [13] algorithm at a learning rate of 0.0001. We follow the official train-test split of all datasets. All the compared methods are trained and inferred following their official code implementations. Training and evaluation are carried out on a Linux server equipped with four NVIDIA Tesla A40 GPUs until convergence.", + "bbox": [ + 89, + 583, + 483, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. Table 2 presents the quantitative comparisons. Our method, leveraging a physics-aware training paradigm and a physics-guided sampler, demonstrates superior performance in both pose quality (Suc. 1, Suc. 6, and Pen.) and diversity (Div.) compared to previous methods across all five benchmarks. Qualitative results, shown in Figure 4, further illustrate that our approach produces more accurate grasping poses, benefiting from the effective physical", + "bbox": [ + 89, + 780, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dea48b7b593d3bc1aac4a5aaec83752baa51edcf98e5812c205830c8af5c75df.jpg", + "table_caption": [ + "Table 3. Ablation study on incorporating physical constraints during both training and sampling stages and the LLM module. The evaluation is conducted on the DexGraspNet dataset." + ], + "table_footnote": [], + "table_body": "
    SRFERFSPFLLMSuc.6 ↑Suc.1 ↑Pen. ↓Div ↑
    a26.666.931.00.15
    b✓38.978.427.00.03
    c✓✓46.683.415.80.22
    d✓✓✓53.690.421.50.22
    e✓✓✓✓57.590.617.80.23
    fConstraints only in training46.884.020.90.18
    ", + "bbox": [ + 517, + 314, + 906, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cb5866837bd91e1c068cb52b00d977f0571ea65be8444eb29600cd8f46473a43.jpg", + "image_caption": [ + "Figure 4. Qualitative visualization of grasping results in Table 2." + ], + "image_footnote": [], + "bbox": [ + 517, + 431, + 903, + 588 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8b88280a72b062a531f60522b51540f206a8a042824d9ac4c4351dfceb1ff654.jpg", + "image_caption": [ + "Figure 5. Visualization of the ablation study. Two rows show different views of each grasp." + ], + "image_footnote": [], + "bbox": [ + 517, + 628, + 903, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "constraints introduced in both training and sampling stages.", + "bbox": [ + 511, + 789, + 903, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 816, + 666, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies to evaluate the contributions of the proposed physical constraint objectives as well as the LLM-enhanced representation in our Dex-Grasp Anything generator. These studies are performed on", + "bbox": [ + 511, + 840, + 906, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22590", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9a8f4ccbbb9e81a19f09f3f596874123388d65c8b204fd12d9b7c46507e7088b.jpg", + "table_caption": [ + "Table 4. Evaluating Dataset Quality and Cross-Dataset Generalization. Model performance is compared on DexGraspNet and RealDex, with training on either DexGraspNet or our dataset. The best result within each group is highlighted in **bold**." + ], + "table_footnote": [], + "table_body": "
    MethodTest TrainDexGraspNetRealDex
    Suc.6 ↑Suc.1 ↑Pen. ↓Div ↑Suc.6 ↑Suc.1 ↑Pen. ↓Div ↑
    SceneDiffuserDexGraspNet26.666.931.00.1516.152.129.20.13
    DGA dataset40.770.622.20.3624.557.131.00.27
    GraspTTADexGraspNet18.667.824.50.1325.564.831.60.11
    DGA dataset28.073.023.90.2132.976.232.10.20
    UGGDexGraspNet46.979.025.20.1433.674.533.00.13
    DGA dataset49.185.926.20.2242.977.334.40.22
    OursDexGraspNet53.690.421.50.2238.477.519.20.17
    DGA-curated55.987.320.90.2852.685.721.50.25
    DGA dataset58.688.517.80.3853.484.422.40.32
    ", + "bbox": [ + 89, + 154, + 486, + 291 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the testing set of the DexGraspNet dataset. The quantitative results are presented in Table 3, where where we incrementally add the three physical constraints and the LLM enhancement (lines a-e) and compare with a model that uses only physical-aware training, excluding the physical-guided sampler (line f). Qualitative results are shown in Figure 5, with additional samples provided in the supplementary materials. These analyses emphasize the crucial role of each physical constraint, the LLM enhancement, as well as the physics-aware training paradigm and physics-guided sampler in enhancing the system's overall performance.", + "bbox": [ + 88, + 324, + 483, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Evaluation for DexGrasp Anything Dataset", + "text_level": 1, + "bbox": [ + 89, + 515, + 460, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "By gathering high-quality data from various existing sources and augmenting it with our physics-aware diffusion generator, we have constructed the largest and most diverse dexterous grasping dataset to date. This not only enhances the performance of our generator but also benefits other dexterous grasp generation methods.", + "bbox": [ + 89, + 542, + 483, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Setup. We train our DexGrasp Anything generator, SceneDiffuser, UGG, and GraspTTA on the training sets of both the DexGraspNet and DexGrasp Anything datasets. We evaluate the models on the testing sets of DexGraspNet and RealDex datasets.", + "bbox": [ + 89, + 638, + 483, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results. As shown in Table 4, our findings indicate that training on the DexGrasp Anything dataset significantly improves the diversity of the sampling results for DexGrasp Anything generator, UGG, SceneDiffuser and GraspTTA. This is achieved without compromising, and in some cases improving, the grasping success rate and penetration metrics. To further validate our approach, we provide a more comprehensive evaluation in the supplementary materials. The qualitative comparison results are illustrated in Figure 6. For a variety of target objects, models trained on the DGA dataset generate significantly more diverse grasping poses, while maintaining high-quality results.", + "bbox": [ + 89, + 719, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4dc85c6ab98431866c9eea689ab9dce9eb6bd58590a4b720094886d353a91228.jpg", + "image_caption": [ + "Figure 6. Visualization of cross-dataset evaluation results shown in Table 4. The top row shows models trained on DexGraspNet, while the bottom row displays models trained on our dataset." + ], + "image_footnote": [], + "bbox": [ + 517, + 88, + 908, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/67e2c4bba0cdf81afe0b171b791142bf78e1226409898006d122f3cfc7f78c13.jpg", + "image_caption": [ + "Figure 7. Real-world evaluation for our method." + ], + "image_footnote": [], + "bbox": [ + 516, + 324, + 906, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Real-world Application", + "text_level": 1, + "bbox": [ + 511, + 477, + 730, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Harnessing physics and semantic priors, and trained on our diverse, high-quality dataset, DexGrasp Anything is highly capable of producing robust and practicable grasping poses in real-world environments. To validate its performance, we deploy the model on a real ShadowHand robot, as shown in Figure 7. The pre-grasping motion sequence is generated following the approach in [19]. The real-world experiments demonstrate that our grasping motions are reasonable and stable for unseen real objects, proving the universality and practicability of our method. More video demos are available in the supplementary materials.", + "bbox": [ + 511, + 507, + 908, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 511, + 703, + 640, + 719 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce DexGrasp Anything, a physics-aware diffusion generator designed for universal and robust dexterous grasp generation. It deeply incorporates three tailored physical constraints through a physics-aware training paradigm and a physics-guided sampler. Moreover, we present the largest and most diverse dataset for dexterous grasp generation to date. Extensive experiments demonstrate that our method and dataset significantly enhance the quality and diversity of dexterous grasp generation. We believe our contributions will pave the way for future advancements towards the universal robotic dexterous grasping.", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22591", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hyungjin Chung, Jeongsol Kim, Michael T. McCann, Marc Louis Klasky, and J. C. Ye. Diffusion posterior sampling for general noisy inverse problems. ArXiv, abs/2209.14687, 2022. 5", + "[2] Matt Deitke, Dustin Schwenk, Jordi Salvador, Luca Weihs, Oscar Michel, Eli VanderBilt, Ludwig Schmidt, Kiana Ehsani, Aniruddha Kembhavi, and Ali Farhadi. 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In Proceedings of" + ], + "bbox": [ + 516, + 90, + 906, + 901 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22593", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + }, + { + "type": "header", + "text": "the IEEE/CVF international conference on computer vision, pages 16259-16268, 2021. 5, 7", + "bbox": [ + 122, + 90, + 483, + 121 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22594", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/fb2fbb43-15d0-4a10-bd84-0e5530360297_model.json b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/fb2fbb43-15d0-4a10-bd84-0e5530360297_model.json new file mode 100644 index 0000000000000000000000000000000000000000..42a11d696dcaf8f4090fcda0d31e1848dcce6298 --- /dev/null +++ b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/fb2fbb43-15d0-4a10-bd84-0e5530360297_model.json @@ -0,0 +1,2301 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.149, + 0.13, + 0.851, + 0.175 + ], + "angle": 0, + "content": "DexGrasp Anything: Towards Universal Robotic Dexterous Grasping with Physics Awareness" + }, + { + "type": "text", + "bbox": [ + 0.279, + 0.202, + 0.717, + 0.221 + ], + "angle": 0, + "content": "Yiming Zhong\\(^{1,\\ast}\\), Qi Jiang\\(^{1,\\ast}\\), Jingyi Yu\\(^{1}\\), Yuexin Ma\\(^{1,\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.394, + 0.222, + 0.607, + 0.24 + ], + "angle": 0, + "content": "\\(^{1}\\) ShanghaiTech University" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.24, + 0.785, + 0.258 + ], + "angle": 0, + "content": "{zhongym2024,jiangqi2022,yujingyi,mayuexin} \\(@\\) shanghaiitech.edu.cn" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.268, + 0.546, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.552, + 0.269, + 0.907, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.497, + 0.908, + 0.527 + ], + "angle": 0, + "content": "Figure 1. We present DexGrasp Anything, consistently surpassing previous dexterous grasping generation methods across five benchmarks. Visualization of our method's results are shown on the left." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.538, + 0.327, + 0.554 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.575, + 0.486, + 0.819 + ], + "angle": 0, + "content": "A dexterous hand capable of grasping any object is essential for the development of general-purpose embodied intelligent robots. However, due to the high degree of freedom in dexterous hands and the vast diversity of objects, generating high-quality, usable grasping poses in a robust manner is a significant challenge. In this paper, we introduce DexGrasp Anything, a method that effectively integrates physical constraints into both the training and sampling phases of a diffusion-based generative model, achieving state-of-the-art performance across nearly all open datasets. Additionally, we present a new dexterous grasping dataset containing over 3.4 million diverse grasping poses for more than 15k different objects, demonstrating its potential to advance universal dexterous grasping. Code and dataset are available at https://github.com/4DVLab/DexGrasp-Anything" + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.538, + 0.645, + 0.554 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.907, + 0.748 + ], + "angle": 0, + "content": "Dexterous grasping, serving as a foundational capability for robotic manipulation tasks, has attracted significant attention. Five-fingered dexterous hands, which closely resemble the structure of the human hand, offer significantly greater flexibility, manipulation precision, and versatility compared to simpler grippers (e.g. parallel jaw, vacuum gripper). As robots are being deployed in human environments, dexterous hands have become increasingly vital due to their ability to interact with a wide range of objects as humans and use tools designed for humans. Therefore, a precise, robust, and versatile dexterous grasping method lies at the heart of interactions in embodied intelligence." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Earlier approaches [5, 18, 25, 28, 29, 35] on dexterous grasping have primarily relied on analytical methods, where grasping poses were optimized to meet specific physical constraints. These methods, however, face significant challenges due to the large search space and the complexity of optimizing for high degrees of freedom in dexterous hands, leading to low success rates. In contrast, data-driven methods [10, 11, 17, 21, 43-45, 47, 51] leverage large-scale datasets to learn useful priors, narrowing the search space and providing strong guidance for search ini" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.839, + 0.231, + 0.852 + ], + "angle": 0, + "content": "\\(^{1}\\) * Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.093, + 0.852, + 0.483, + 0.9 + ], + "angle": 0, + "content": "\\(^{2\\dagger}\\) Corresponding author. This work was supported by NSFC (No.62206173), Shanghai Frontiers Science Center of Human-centered Artificial Intelligence (ShangHAI), MoE Key Laboratory of Intelligent Perception and Human-Machine Collaboration (KLIP-HuMaCo)." + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.839, + 0.483, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.99, + 0.519, + 1.0 + ], + "angle": 0, + "content": "22584" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.333 + ], + "angle": 0, + "content": "tialization. Regression-based methods [17, 45] that directly predict grasp parameters from object inputs often suffer from mode collapse and averaging, resulting in a limited diversity of generated grasp poses. Recently, generative methods [11, 47] have gained significant attention for their ability to enhance the diversity of generated grasp poses. Among these, diffusion models [8, 12, 39] have demonstrated a strong capability to capture the complexities of dexterous grasping and generate diverse grasp poses by iteratively transforming a simple distribution (e.g., Gaussian) into a complex, high-dimensional one [10, 21, 44, 51]. However, despite these advantages, current diffusion-based approaches [43, 45] often generate suboptimal grasp poses, resulting in hand-object penetration or insufficient contact with unsatisfactory success rates. These issues arise from the lack of constraints that enforce physical rules." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.338, + 0.483, + 0.671 + ], + "angle": 0, + "content": "In this work, we propose a novel dexterous grasping generation method, namely DexGrasp Anything, that integrates three carefully designed physical constraint objectives into the diffusion model during both training and sampling phases. DexGrasp Anything exhibits superior robustness and strong generalization capabilities. Specifically, we introduce the surface pulling force to ensure grasp feasibility by pulling the hand's inner surface toward the object's surface while avoiding interference with parts that are already sufficiently distant. We also introduce the externalpenetration repulsion force to maintain geometric accuracy of interaction by effectively preventing significant collisions between the object and the dexterous hand, and the selfpenetration repulsion force to preserve the hand's geometry by enforcing a minimum distance between finger joints and applying repulsion when they get too close. Through our physics-aware training scheme and physics-guided sampler, these physical constraints enable our diffusion-based generator to produce practical and robust dexterous grasping poses across a wide range of objects. Through extensive experiments, we show our method achieves state-of-the-art performance on almost all open datasets, as Figure 1 shows." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To further improve the universality of diffusion-based generative method, massive amounts of high-quality training data is necessary. While many efforts have been made to build grasping datasets, they suffer from narrow data distribution[6, 17, 22], limited object categories [17, 41], and scalability issues [19]. In light of this, we dedicate substantial efforts to further enhancing the scale, diversity, and quality of the dexterous grasping datasets. We start by gathering available dexterous grasping data from multiple sources [15, 19, 40, 41, 47], including simulated data, real-captured data, and human hand grasping data, ensuring a diverse and comprehensive data distribution. We further scale up the dataset with a 'model-in-the-loop' strategy by using our grasping method and filtering method to continue generating high-quality data, inspired by the approach used in" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.182 + ], + "angle": 0, + "content": "SAM [14]. These efforts culminate in a very large-scale dexterous grasping dataset, DexGrasp Anything (DGA) Dataset with over 3.4 million grasping poses on more than 15k objects. Experimental results demonstrate that this new dataset provides substantial benefits to grasping methods within the community." + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.183, + 0.865, + 0.197 + ], + "angle": 0, + "content": "The main contribution of this work are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.199, + 0.905, + 0.258 + ], + "angle": 0, + "content": "- We propose a physics-aware diffusion generator for dexterous grasping pose generation, which effectively integrates three key physical constraints into both the training and sampling phases of the diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.259, + 0.904, + 0.288 + ], + "angle": 0, + "content": "- Our method achieves state-of-the-art performance on five dexterous grasping datasets." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.289, + 0.904, + 0.334 + ], + "angle": 0, + "content": "- We present a new high-quality dexterous grasping dataset, the largest and most diverse to date, significantly improving the generalization capability of existing methods." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.199, + 0.905, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.349, + 0.655, + 0.364 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.375, + 0.771, + 0.39 + ], + "angle": 0, + "content": "2.1. Dexterous Grasp Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.399, + 0.905, + 0.503 + ], + "angle": 0, + "content": "Dexterous Grasping serves as a fundamental component for various complex, human-like manipulation tasks, making it a long-standing area of research in robotics. Early works mainly use manually derived analytical methods [5, 18, 25, 28, 29, 35] that based on certain physical constraints. These methods are hindered by extremely large search space and complex optimization process, leading to low success rate." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.505, + 0.905, + 0.821 + ], + "angle": 0, + "content": "Recently, data-driven approaches have emerged as a promising direction for dexterous grasping. Regression-based methods, such as [17, 45], often generate grasping poses with limited diversity, as they rely on direct predictions from input data and may fail to explore the full range of possible grasping configurations. In contrast, generative methods [11, 47] explicitly model the conditional probability distribution of dexterous hand poses given the target object, theoretically generating diverse poses. Diffusion model-based methods [10, 21, 51], in particular, stand out as a promising direction for more universal and robust robotic dexterous grasping for its exceptional capabilities in modeling various complex data distribution [9, 16, 20, 32, 46, 50] and generating diverse and highly realistic samples [27, 31, 33, 36]. However, existing diffusion model-based approaches are observed [43, 45] to yield sub-optimal grasping poses due to the absence of physical constraints during the training and sampling process. In this work, we delve into incorporating physical constraints into diffusion models to generate robust dexterous grasping poses for dexterous hands." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.833, + 0.767, + 0.848 + ], + "angle": 0, + "content": "2.2. Dexterous Grasping Dataset" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Collecting 3D dexterous grasping poses is notoriously expensive due to the complexity of hand structures. Most existing datasets are collected in simulators like" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22585" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.9, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.488, + 0.907, + 0.572 + ], + "angle": 0, + "content": "Figure 2. Overview of DexGrasp Anything. During training, object information is processed to extract combined semantic and spatial representations as conditioning inputs. At each noise training step, a clean-estimation of the noisy hand pose \\(\\hat{h}_0\\) is derived from the predicted noise \\(\\hat{\\varepsilon}_t\\), with physics constraints guiding the noise distribution toward a cleaner, grasp-suitable distribution. During sampling, the Physics-Guided Sampler obtains the current observation \\(\\hat{h}_0\\) at each denoising step and performs posterior sampling based on this observation. Physical constraints gradually guide the distribution toward a physically feasible grasp configuration \\(\\hat{h}_0^*\\), enabling effective grasping of diverse objects." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.587, + 0.486, + 0.89 + ], + "angle": 0, + "content": "GraspIt! [24] and IssacGym [23] through searching in the eigengrasp space [6, 17, 22] or optimization-based methods [15, 17, 41, 47] in parameter space. However, the search-based data often follow a narrow distribution due to the low-dimensional eigengrasp space, while the recent optimization-based data still suffer from relatively success rate and contained limit number of object categories. Some real-world datasets have been collected using teleoperation systems controlled by human operators. While these datasets capture human-like grasping poses, the data collection process is prohibitively expensive and difficult to scale up. Recent advances [30, 37, 38] have explored retargeting human hand poses to dexterous robotic hands, presenting a promising avenue for leveraging human hand data in robot hand training. Despite these advancements, existing datasets still face limitations in diversity, scalability, and quality. To address these challenges, we introduce the largest and most diverse dexterous grasping dataset to date and demonstrate that our dataset significantly enhances both the quality and diversity of generated dexterous" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.588, + 0.907, + 0.618 + ], + "angle": 0, + "content": "grasping poses, providing substantial value to existing data-driven grasping generators." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.646, + 0.605, + 0.661 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.672, + 0.907, + 0.809 + ], + "angle": 0, + "content": "We present DexGrasp Anything, an effective approach that enhances diffusion-based generators for dexterous grasping by integrating meticulously designed physical constraints. Figure 2 demonstrates an overview of our method. The following sections detail our problem formulation (Sec. 3.1), physics-aware constraints (Sec. 3.2), and the way to integrate constraints to the diffusion model's training (Sec. 3.3) and sampling processes (Sec. 3.4), and the LLM-enhanced object representation extraction module (Sec. 3.5)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.817, + 0.696, + 0.832 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Our goal is to generate high-quality grasping poses capable of securely holding a given object. Specifically, given a 3D object observation \\( O \\), we aim to sample a diverse set of dexterous grasping poses \\( \\mathbf{h} = \\{h_i\\}_{i=1}^n \\) from a condi-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22586" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.151 + ], + "angle": 0, + "content": "tional distribution \\(P(h|O)\\), where the dexterous pose \\(h = (\\theta, \\mathrm{R}, \\mathrm{t}) \\in \\mathbb{R}^{33}\\) consists of the dexterous hand articulation \\(\\theta \\in \\mathbb{R}^{24}\\) (for ShadowHand), the global rotation \\(R \\in \\mathrm{SO}(3)\\) and the global translation vector \\(t \\in \\mathbb{R}^3\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.152, + 0.483, + 0.212 + ], + "angle": 0, + "content": "The conditional distribution \\( P(h|O) \\) is modeled using a diffusion model \\( \\epsilon_{\\phi}(h_t,O,t) \\), which iteratively transforms an isotropic Gaussian distribution \\( \\mathcal{N}(0,\\mathrm{I}) \\) into the desired data distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.223, + 0.404, + 0.264 + ], + "angle": 0, + "content": "\\[\nP (h _ {0} | O) = P (h _ {T}) \\prod_ {t = 1} ^ {T} P (h _ {t - 1} | h _ {t}, O),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.266, + 0.483, + 0.3 + ], + "angle": 0, + "content": "\\[\nP \\left(h _ {t - 1} \\mid h _ {t}, O\\right) = \\mathcal {N} \\left(h _ {t - 1}; \\mu_ {\\phi} \\left(h _ {t}, O, t\\right), \\Sigma_ {\\phi} \\left(h _ {t}, O, t\\right)\\right). \\tag {1}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.313, + 0.286, + 0.328 + ], + "angle": 0, + "content": "3.2. Physical Constraints" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.336, + 0.484, + 0.427 + ], + "angle": 0, + "content": "Diffusion model-based methods often fail to reach optimal performance in the absence of appropriate physical constraints. To address this, we present three tailored physical constraint objectives for our DexGrasp Anything generator, enabling the production of universal and robust dexterous grasping poses for a wide range of objects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.428, + 0.484, + 0.614 + ], + "angle": 0, + "content": "Surface Pulling Force [47] is crucial for ensuring grasp feasibility. It enforces proximity between the inner surface of the robotic phalanges (represented by sampled point clouds) and the object's surface. This guidance signal applies a pulling force only to points that are closer than a specified threshold, ensuring that the points on the inner surface of the fingers are pulled towards the object's surface when they are near, but does not affect points that are already at a sufficient distance. Compute the squared Euclidean distance for each inner surface point \\( p_{\\mathrm{dis}}^{(i)} \\) to its nearest neighbor on the object surface: \\( d_{i} = \\min_{j} \\| p_{\\mathrm{dis}}^{(i)} - p_{\\mathrm{obj}}^{(j)} \\|^2 \\). We compute the surface pulling force as:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.626, + 0.483, + 0.661 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {S P F}} = \\frac {\\sum_ {i \\in S} \\sqrt {d _ {i}}}{| S | + \\eta}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.672, + 0.483, + 0.717 + ], + "angle": 0, + "content": "where \\( S = \\{i|d_i < d_{\\mathrm{Threshold}}\\} \\) represents the set of points within the threshold distance and \\( \\eta \\) is a numerical stability constant." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.718, + 0.484, + 0.871 + ], + "angle": 0, + "content": "External-penetration Repulsion Force [10] retains the spatial accuracy of hand-object interactions. It minimizes the undesired intersection between the hand and object point clouds by leveraging the signed distances. Given an object point cloud \\( P_{obj} \\) with surface normals \\( N_{obj} \\), and a hand point cloud \\( P_{hand} \\), we first compute the nearest neighbor distance between each point in \\( P_{hand} \\) and \\( P_{obj} \\): \\( d_i = \\min_j \\| P_{hand}^{(i)} - P_{obj}^{(j)} \\| \\). We then calculate the signed distance between the hand and object points using the object normals:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.882, + 0.483, + 0.904 + ], + "angle": 0, + "content": "\\[\ns _ {i} = \\operatorname {s i g n} \\left(\\left(P _ {o b j} ^ {(j)} - P _ {\\text {h a n d}} ^ {(i)}\\right) \\cdot N _ {o b j} ^ {(j)}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.136 + ], + "angle": 0, + "content": "Finally, the external-penetration repulsion force is defined as the maximum signed distance across all points in the batch, averaged over the batch size \\( B \\):" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.149, + 0.906, + 0.19 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {E R F}} = \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\max _ {i} \\left(s _ {i}, d _ {i}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.2, + 0.907, + 0.352 + ], + "angle": 0, + "content": "Self-Penetration Repulsion Force [47] upholds the hand structural geometry. It addresses the issue of hand points intersecting with each other by enforcing a minimum distance between them. This ensures that the hand maintains a realistic, physically plausible shape without finger collisions. Given a set of hand points \\( P_{\\mathrm{hand}} \\), we calculate the pairwise Euclidean distances between all points: \\( d_{ij} = \\| P_{\\mathrm{hand}}^{(i)} - P_{\\mathrm{hand}}^{(j)} \\| \\), A repulsion force is applied when \\( d_{ij} \\) is smaller than a threshold \\( d_{\\mathrm{Threshold}} \\), and the self-penetration repulsion force is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.364, + 0.906, + 0.401 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {S R F}} = \\frac {1}{B} \\sum_ {i, j} \\max \\left(0, d _ {\\text {T h r e s h o l d}} - d _ {i j}\\right). \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.411, + 0.734, + 0.427 + ], + "angle": 0, + "content": "3.3. Physics-Aware Training" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.434, + 0.906, + 0.465 + ], + "angle": 0, + "content": "Diffusion Models are typically trained with a simple mean-squared error (MSE) objectives:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.476, + 0.905, + 0.495 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, x _ {0}, \\epsilon} [ \\| \\epsilon - \\epsilon_ {\\phi} (h _ {t}, t) \\| ^ {2} ], \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.505, + 0.906, + 0.535 + ], + "angle": 0, + "content": "where \\( h_t \\) is a corrupted version of the original data \\( h_0 \\). The data corruption follows a fixed noise schedule \\( \\beta_t \\):" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.547, + 0.905, + 0.574 + ], + "angle": 0, + "content": "\\[\nq \\left(h _ {t} \\mid h _ {t - 1}\\right) = \\mathcal {N} \\left(h _ {t}; \\sqrt {1 - \\beta_ {t}} h _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.57, + 0.83, + 0.587 + ], + "angle": 0, + "content": "\\[\nh _ {t} = \\sqrt {1 - \\beta_ {t}} h _ {t - 1} + \\sqrt {\\beta_ {t}} \\epsilon_ {t}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.599, + 0.906, + 0.63 + ], + "angle": 0, + "content": "With \\(\\alpha_{t} = 1 - \\beta_{t}\\) and \\(\\bar{\\alpha}_{t} = \\Pi_{i = 1}^{t}\\alpha_{i}\\), the corruption process can be directly conditioned on \\(h_0\\):" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.64, + 0.905, + 0.667 + ], + "angle": 0, + "content": "\\[\nq \\left(h _ {t} \\mid h _ {0}\\right) = \\mathcal {N} \\left(h _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} h _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.662, + 0.806, + 0.678 + ], + "angle": 0, + "content": "\\[\nh _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} h _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\bar {\\epsilon} _ {t}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.839 + ], + "angle": 0, + "content": "Since the training objective \\( L_{\\mathrm{simple}} \\) is essentially a reweighted variational lower bound on negative log likelihood, it does not incorporate any explicit supervision regarding physical constraints. As a result, diffusion models often perform sub-optimally when directly generating dexterous grasping parameters, as observed in previous works [43, 45]. To facilitate our diffusion generator in capturing physics priors during training, we introduce the Physics-Aware Training paradigm, which incorporates the tailored physical constraints outlined in Sec. 3.2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.905 + ], + "angle": 0, + "content": "The training objective involving only corrupted data \\( h_t \\) is not well-suited for incorporating physical constraints. Using the diffusion process defined in Eq. 8, the estimated sample: \\( \\hat{h_0}(h_t) = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}} (h_t - \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon_\\phi(h_t, O, t)) \\) could" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22587" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.121 + ], + "angle": 0, + "content": "serve as a good proxy for introducing physical constraint into the training process of a diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.122, + 0.483, + 0.168 + ], + "angle": 0, + "content": "We define the physically-aware training objective \\(L_{\\mathrm{PADG}}\\) as a linear combination of the standard mean-squared objective and multiple physical-constraint objectives:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.174, + 0.483, + 0.214 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {P A D G}} = L _ {\\text {s i m p l e}} \\left(h _ {t}\\right) + \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h _ {0}} \\left(h _ {t}\\right), \\epsilon_ {\\phi}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.222, + 0.483, + 0.282 + ], + "angle": 0, + "content": "where \\(L_{\\mathrm{PA}_i}(\\hat{h_0}(h_t), \\epsilon_\\phi)\\) is the \\(i^{th}\\) physical constraint and \\(\\alpha_i\\) is the corresponding weighting coefficient. The gradient is propagated to \\(h_t\\) through the estimated clean sample \\(h_0\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.288, + 0.483, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial L _ {\\mathrm {P A D G}}}{\\partial h _ {t}} = \\frac {\\partial L _ {\\text {s i m p l e}}}{\\partial h _ {t}} + \\sum_ {i = 1} ^ {m} \\alpha_ {i} \\frac {\\partial L _ {\\mathrm {P A} _ {i}}}{\\partial \\hat {h _ {0}}} \\cdot \\frac {\\partial \\hat {h _ {0}}}{\\partial h _ {t}}. \\tag {10}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.333, + 0.327, + 0.35 + ], + "angle": 0, + "content": "3.4. Physics-Guided Sampling" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.357, + 0.484, + 0.447 + ], + "angle": 0, + "content": "Leveraging the learned physics priors, the well-trained diffusion generator is capable of producing physically plausible dexterous grasping poses for a given object. The physical constraints can be further enhanced during the sampling process by employing advanced sampling techniques [1, 4, 7, 48]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.484, + 0.507 + ], + "angle": 0, + "content": "Classifier guidance [4] has explored the use of a time-dependent classifier \\(\\mathcal{F}_t\\) to steer the diffusion model towards specific conditional distributions. The guidance can be approximated as an offset in the posterior mean:" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.515, + 0.482, + 0.532 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mu} _ {\\phi} \\left(x _ {t}, t\\right) \\leftarrow \\mu_ {\\phi} \\left(x _ {t}, t\\right) + s \\Sigma_ {\\theta , t} \\nabla_ {x _ {t}} \\log \\left(\\mathcal {F} _ {t} (y, x _ {t})\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.54, + 0.484, + 0.615 + ], + "angle": 0, + "content": "where \\(s\\) is the guidance strength. By estimating \\(\\hat{x_0}\\) based on \\(x_{t}\\), the guidance signal can be extended from a time-dependent classifier \\(\\mathcal{F}_t(y,x_t)\\) to arbitrary objective functions \\(L(x_0)\\) on clean samples. It can be achieved by mapping the objective to a density-like function:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.621, + 0.482, + 0.64 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} \\left(x _ {0}\\right) = \\mathcal {Z} e ^ {- L \\left(x _ {0}\\right)}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.647, + 0.483, + 0.677 + ], + "angle": 0, + "content": "where \\(\\mathcal{Z}\\) is a normalizing constant. We define the Physics-Guided Sampler as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.685, + 0.482, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\widetilde {\\mu} _ {\\phi} (h _ {t}, O, t) \\leftarrow \\mu_ {\\phi} (h _ {t}, O, t) \\\\ + s \\Sigma_ {\\phi , t} \\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {P A _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right), \\epsilon_ {t}\\right). \\tag {13} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.752, + 0.483, + 0.799 + ], + "angle": 0, + "content": "To alleviate the estimation bias on \\(\\hat{h_0}\\), we apply the Spherical Gaussian Constraint [48] with a weighted gradient direction in practice. This is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.805, + 0.482, + 0.838 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mu} _ {\\phi} \\left(h _ {t}, O, t\\right) \\leftarrow \\mu_ {\\phi} \\left(h _ {t}, O, t\\right) + r \\frac {d _ {m}}{\\| d _ {m} \\|}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.844, + 0.483, + 0.86 + ], + "angle": 0, + "content": "where \\(d_{\\mathrm{m}} = d_{\\mathrm{sample}} + g_r(d^* - d_{\\mathrm{sample}})\\), \\(d_{\\mathrm{sample}} = \\Sigma_{\\phi, t} \\epsilon\\) and:" + }, + { + "type": "equation", + "bbox": [ + 0.109, + 0.867, + 0.483, + 0.906 + ], + "angle": 0, + "content": "\\[\nd ^ {*} = - \\sqrt {n} \\Sigma_ {\\phi , t} \\frac {\\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right) , \\epsilon_ {t}\\right)}{\\| \\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right) , \\epsilon_ {t}\\right) \\|}. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.273 + ], + "angle": 0, + "content": "Incorporating physics constraints during training helps guide the noise distribution toward a cleaner, grasp-suitable form. However, due to sparse supervision in the training phase, we leverage the reverse process during sampling to obtain \\( h_t \\) and \\( \\hat{h}_0 \\) at each step, applying posterior sampling to iteratively refine the grasp configuration. This iterative refinement allows the Physics-Guided Sampler to progressively adjust \\( \\hat{h}_0 \\) under physics constraints, ultimately steering the distribution toward a physically feasible grasp configuration. Through this distributional framework, our model effectively generalizes to diverse objects, demonstrating robustness and adaptability in grasping tasks." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.281, + 0.878, + 0.297 + ], + "angle": 0, + "content": "3.5. LLM-enhanced Representation Extraction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.304, + 0.907, + 0.607 + ], + "angle": 0, + "content": "To accomplish robust dexterous grasp generation for a targeted object, we boost the traditional object representation by complementing the geometry object feature with semantic prior from powerful LLMs. We employ a Point Transformer[52] to encode object point clouds, producing an \\( N \\times C \\) feature vector, where \\( \\mathbf{N} \\) represents the number of groups defined by the Point Transformer. To enrich these features with abundant semantic prior from LLM, we utilize the prompt: \"I want to grasp a [object label]. First, provide its object category, then give a detailed description of its shape before making a successful grip.\" We then parse the response and encode each sentence using a pre-trained BERT-large-uncased model. We extract the [CLS] token from each sentence and apply max-pooling on them. This results in an \\( 1 \\times C \\) semantic feature vector that includes the rich prior knowledge from the LLM. The concatenated \\( (N + 1) \\times C \\) feature matrix is subsequently integrated into the diffusion backbone through a cross-attention mechanism, enhancing the model's capacity to generate precise and contextually relevant grasping poses." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.618, + 0.603, + 0.634 + ], + "angle": 0, + "content": "4. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.907, + 0.825 + ], + "angle": 0, + "content": "The quality, diversity and scale of datasets are crucial for advancing dexterous grasping research, especially for diffusion-based generative methods. Training on a broader data distribution enables models to learn richer and more adaptable grasping strategies for arbitrary object. To inspire potential of methods towards universal dexterous grasping, we have developed a comprehensive dataset that significantly exceeds existing dexterous grasping datasets in both size and diversity. In the following sections, we provide a detailed overview of the data construction process, present key statistics, and highlight the characteristics of our DexGrasp Anything (DGA) dataset." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.693, + 0.848 + ], + "angle": 0, + "content": "4.1. Data Construction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Our data construction process begins with curating existing datasets from diverse sources. We gather three simulated datasets [15, 41, 47], a real-world dataset [19] col" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22588" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.218, + 0.09, + 0.779, + 0.104 + ], + "angle": 0, + "content": "Table 1. Comparison of dexterous grasp datasets. Our dataset achieves the largest scale to date." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.109, + 0.905, + 0.245 + ], + "angle": 0, + "content": "
    DatasetPublication YearHand TypeSim./Real#Grasps#Objects#Grasps per objectConstruction method
    GRAB [40]ECCV 2020MANOReal1.64M51>10KCapture
    DDGdata [17]RSS 2020ShadowHandSim.6.9k565-GraspIt!
    MultiDex [15]ICRA 2023ShadowHandSim.16K58300Optimization
    DexGraspNet [41]ICRA 2023ShadowHandSim.1.32M5,355>200Optimization
    UniDexGrasp [47]CVPR 2023ShadowHandSim.1.12M5,519>150Optimization
    GraspXL [49]ECCV 2024Diverse HandSim-500K-GraspXL
    RealDex [19]IJCAI 2024ShadowHandReal59K52>200Human Annotation
    Our datasetCVPR 2025ShadowHandReal+Sim.3.40M15,698>200DexGrasp Anything + Filter
    " + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.258, + 0.482, + 0.499 + ], + "angle": 0, + "content": "lected by human operator, alongside GRAB [40], a largescale human hand dataset, to maximize data diversity and richness. Leveraging advancements in robot teleoperation systems like AnyTeleop [30], we retarget the human hand dataset GRAB to dexterous hand parameters, creating DexGRAB, and filter it to retain only frames with hand-object contact. Next, we examine all collected data within IsaacGym [23], applying strict conditions to ensure stability and contact integrity. Specifically, we enforce that (1) objects do not shift more than \\(2\\mathrm{cm}\\) in any direction under force and that (2) hand-object penetration remains below \\(10\\mathrm{mm}\\) and object-hand penetration remains below \\(1\\mathrm{mm}\\) following [41]. The detailed process for computing the penetration is provided in the supplementary materials. This rigorous filtering process guarantees consistent high quality across all data sources." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.501, + 0.483, + 0.775 + ], + "angle": 0, + "content": "Training our physics-aware diffusion generator on this dataset leads to higher success rates, greater diversity, and faster generation speeds for zero-shot dexterous grasping on unseen objects. Acting as a data engine, our model facilitates further dataset expansion in a \"model-in-the-loop\" manner. We meticulously selected object meshes from the Objaverse [2, 3] dataset, with the goal of ensuring broad category coverage and maintaining an even distribution across these categories. To achieve this, we examined all objects within 18 chosen categories and ultimately selected 10,034 distinct objects, covering 6,994 unique tags in the Objaverse data configuration. We apply approximate convex decomposition [42] to each mesh to reduce complexity and ensure water-tightness. Our trained generator then iteratively produces dexterous grasp poses, which are filtered under the same stringent standards. Finally, we combine the curated and generated data to form a large-scale and diverse dataset, crafted to advance research in dexterous grasping." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.786, + 0.197, + 0.801 + ], + "angle": 0, + "content": "4.2. Statistics" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.483, + 0.901 + ], + "angle": 0, + "content": "We present a comparative analysis of key metrics between our dataset and other existing datasets in Table 1. Our DGA dataset comprises two main components: The first component DGA-curated includes approximately 0.88 million grasping poses across 5,664 distinct objects, curated from various existing and diverse data sources. The second com" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.258, + 0.887, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.4, + 0.907, + 0.469 + ], + "angle": 0, + "content": "Figure 3. t-SNE visualization of the object features in our dataset compared to existing datasets. Each point represents an object, and different markers and colors are used to distinguish between datasets. For clarity, we randomly sample \\(5\\%\\) objects from each dataset for visualization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.483, + 0.906, + 0.59 + ], + "angle": 0, + "content": "ponent DGA-generated is generated with our DexGrasp Anything generator from the Objaverse [2, 3] dataset, containing approximately 2.52 million grasping poses spanning 10,034 different objects, covering 6,994 unique tags. In total, our dataset features over 3.4 million grasping poses across 15,698 objects from diverse data distribution, supporting in-depth research into dexterous grasping." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.603, + 0.667, + 0.617 + ], + "angle": 0, + "content": "4.3. Characteristics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.628, + 0.906, + 0.703 + ], + "angle": 0, + "content": "Our dataset is characterized by a high degree of diversity and comprehensiveness, aimed at capturing a wide range of object and pose variations to advance the performance of dexterous hands in complex real-world environment. The key characteristics of our dataset can be presented as follow:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.705, + 0.905, + 0.749 + ], + "angle": 0, + "content": "- Large data scale. Our dataset features over 3.4M strictly-tested grasping poses, which is significantly larger than all previous datasets." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.75, + 0.907, + 0.886 + ], + "angle": 0, + "content": "- Diverse objects. Our dataset encompasses 15,698 objects from a wide range of categories and sources, ensuring a high level of diversity. In Figure 3, we present a t-SNE visualization comparing object features from our dataset with those from existing datasets, using features extracted by a pre-trained Point Transformer. Object features from our dataset spread much wider across the feature space, suggesting that our dataset captures a broader variety or unique features that not be as present in existing datasets." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.886, + 0.905, + 0.902 + ], + "angle": 0, + "content": "- Diverse grasping poses. The wide variety of objects" + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.705, + 0.907, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.99, + 0.518, + 1.0 + ], + "angle": 0, + "content": "22589" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.119 + ], + "angle": 0, + "content": "Table 2. Performance comparison across different methods and datasets. Bold numbers indicate the best scores, while underlined numbers indicate the second-best scores. DexGrasp Anything (w/ LLM) achieves the highest or near-highest performance across most metrics." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.128, + 0.907, + 0.239 + ], + "angle": 0, + "content": "
    Dataset MethodDexGraspNetUniDexGraspMultiDexRealDexDexGRAB
    Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑
    UniDexGrasp [47]33.970.131.90.1423.765.524.50.1421.647.513.50.0827.159.439.00.1120.855.837.40.08
    GraspTTA [11]18.667.824.50.1321.065.321.20.1030.362.819.00.1113.346.440.10.0914.451.051.40.10
    SceneDiffuser [10]26.666.931.00.1528.374.825.10.1569.885.614.60.2721.756.142.00.0939.185.041.10.12
    UGG [21]46.979.025.20.1446.083.224.50.1455.393.410.30.1232.763.434.40.1042.790.633.20.12
    Ours53.690.421.50.2254.890.818.90.2572.296.39.60.2334.671.223.10.1456.591.828.60.12
    Ours(w/LLM)57.590.617.80.2353.191.218.80.2379.198.111.40.2244.873.727.70.1357.992.730.40.13
    " + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.264, + 0.485, + 0.34 + ], + "angle": 0, + "content": "contributes to a diverse range of grasping poses. Extensive experimental results in Sec. 5.3 demonstrate that our dataset significantly enhances the diversity of outcomes from existing methods, while maintaining or even improving the grasping success rate." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.354, + 0.224, + 0.372 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.379, + 0.224, + 0.395 + ], + "angle": 0, + "content": "5.1. Comparison" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.402, + 0.484, + 0.583 + ], + "angle": 0, + "content": "Metrics. Following previous works [10], we assess the grasping success rate (Suc. 6/Suc. 1) and maximum penetration (Pen.) in millimeters to gauge the quality of generated poses. A grasping pose is considered successful if the object's displacement, when an external force is applied, is less than \\(2\\mathrm{cm}\\) in at least one (Suc. 1) or all (Suc. 6) of the six axis-aligned directions in a 3D coordinate system. Additionally, we evaluate the diversity using the mean standard deviation of the pose parameters (Div.) across successful grasps in millimeters. All poses are evaluated in the IssacGym [23] simulator with the same configuration used in [10]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.484, + 0.78 + ], + "angle": 0, + "content": "Implementation Details. Following [10], we employ a U-Net [34] structure for our diffusion backbone. An object-conditioned Point Transformer [52] encoder handles the point clouds, injected into the diffusion model using a cross-attention mechanism. All point clouds are downsampled to 2048 points before encoding. Our model is implemented using the PyTorch [26] platform, optimized with the Adam [13] algorithm at a learning rate of 0.0001. We follow the official train-test split of all datasets. All the compared methods are trained and inferred following their official code implementations. Training and evaluation are carried out on a Linux server equipped with four NVIDIA Tesla A40 GPUs until convergence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Results. Table 2 presents the quantitative comparisons. Our method, leveraging a physics-aware training paradigm and a physics-guided sampler, demonstrates superior performance in both pose quality (Suc. 1, Suc. 6, and Pen.) and diversity (Div.) compared to previous methods across all five benchmarks. Qualitative results, shown in Figure 4, further illustrate that our approach produces more accurate grasping poses, benefiting from the effective physical" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.262, + 0.908, + 0.304 + ], + "angle": 0, + "content": "Table 3. Ablation study on incorporating physical constraints during both training and sampling stages and the LLM module. The evaluation is conducted on the DexGraspNet dataset." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.315, + 0.907, + 0.417 + ], + "angle": 0, + "content": "
    SRFERFSPFLLMSuc.6 ↑Suc.1 ↑Pen. ↓Div ↑
    a26.666.931.00.15
    b✓38.978.427.00.03
    c✓✓46.683.415.80.22
    d✓✓✓53.690.421.50.22
    e✓✓✓✓57.590.617.80.23
    fConstraints only in training46.884.020.90.18
    " + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.432, + 0.905, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.517, + 0.599, + 0.902, + 0.615 + ], + "angle": 0, + "content": "Figure 4. Qualitative visualization of grasping results in Table 2." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.63, + 0.905, + 0.74 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.75, + 0.906, + 0.778 + ], + "angle": 0, + "content": "Figure 5. Visualization of the ablation study. Two rows show different views of each grasp." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.79, + 0.905, + 0.805 + ], + "angle": 0, + "content": "constraints introduced in both training and sampling stages." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.817, + 0.667, + 0.833 + ], + "angle": 0, + "content": "5.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies to evaluate the contributions of the proposed physical constraint objectives as well as the LLM-enhanced representation in our Dex-Grasp Anything generator. These studies are performed on" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22590" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.486, + 0.148 + ], + "angle": 0, + "content": "Table 4. Evaluating Dataset Quality and Cross-Dataset Generalization. Model performance is compared on DexGraspNet and RealDex, with training on either DexGraspNet or our dataset. The best result within each group is highlighted in **bold**." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.155, + 0.487, + 0.292 + ], + "angle": 0, + "content": "
    MethodTest TrainDexGraspNetRealDex
    Suc.6 ↑Suc.1 ↑Pen. ↓Div ↑Suc.6 ↑Suc.1 ↑Pen. ↓Div ↑
    SceneDiffuserDexGraspNet26.666.931.00.1516.152.129.20.13
    DGA dataset40.770.622.20.3624.557.131.00.27
    GraspTTADexGraspNet18.667.824.50.1325.564.831.60.11
    DGA dataset28.073.023.90.2132.976.232.10.20
    UGGDexGraspNet46.979.025.20.1433.674.533.00.13
    DGA dataset49.185.926.20.2242.977.334.40.22
    OursDexGraspNet53.690.421.50.2238.477.519.20.17
    DGA-curated55.987.320.90.2852.685.721.50.25
    DGA dataset58.688.517.80.3853.484.422.40.32
    " + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.325, + 0.485, + 0.493 + ], + "angle": 0, + "content": "the testing set of the DexGraspNet dataset. The quantitative results are presented in Table 3, where where we incrementally add the three physical constraints and the LLM enhancement (lines a-e) and compare with a model that uses only physical-aware training, excluding the physical-guided sampler (line f). Qualitative results are shown in Figure 5, with additional samples provided in the supplementary materials. These analyses emphasize the crucial role of each physical constraint, the LLM enhancement, as well as the physics-aware training paradigm and physics-guided sampler in enhancing the system's overall performance." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.516, + 0.462, + 0.533 + ], + "angle": 0, + "content": "5.3. Evaluation for DexGrasp Anything Dataset" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.544, + 0.484, + 0.635 + ], + "angle": 0, + "content": "By gathering high-quality data from various existing sources and augmenting it with our physics-aware diffusion generator, we have constructed the largest and most diverse dexterous grasping dataset to date. This not only enhances the performance of our generator but also benefits other dexterous grasp generation methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.64, + 0.484, + 0.716 + ], + "angle": 0, + "content": "Setup. We train our DexGrasp Anything generator, SceneDiffuser, UGG, and GraspTTA on the training sets of both the DexGraspNet and DexGrasp Anything datasets. We evaluate the models on the testing sets of DexGraspNet and RealDex datasets." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Results. As shown in Table 4, our findings indicate that training on the DexGrasp Anything dataset significantly improves the diversity of the sampling results for DexGrasp Anything generator, UGG, SceneDiffuser and GraspTTA. This is achieved without compromising, and in some cases improving, the grasping success rate and penetration metrics. To further validate our approach, we provide a more comprehensive evaluation in the supplementary materials. The qualitative comparison results are illustrated in Figure 6. For a variety of target objects, models trained on the DGA dataset generate significantly more diverse grasping poses, while maintaining high-quality results." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.089, + 0.909, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.257, + 0.908, + 0.3 + ], + "angle": 0, + "content": "Figure 6. Visualization of cross-dataset evaluation results shown in Table 4. The top row shows models trained on DexGraspNet, while the bottom row displays models trained on our dataset." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.325, + 0.907, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.448, + 0.855, + 0.462 + ], + "angle": 0, + "content": "Figure 7. Real-world evaluation for our method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.478, + 0.731, + 0.495 + ], + "angle": 0, + "content": "5.4. Real-world Application" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.508, + 0.909, + 0.675 + ], + "angle": 0, + "content": "Harnessing physics and semantic priors, and trained on our diverse, high-quality dataset, DexGrasp Anything is highly capable of producing robust and practicable grasping poses in real-world environments. To validate its performance, we deploy the model on a real ShadowHand robot, as shown in Figure 7. The pre-grasping motion sequence is generated following the approach in [19]. The real-world experiments demonstrate that our grasping motions are reasonable and stable for unseen real objects, proving the universality and practicability of our method. More video demos are available in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.704, + 0.642, + 0.72 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We introduce DexGrasp Anything, a physics-aware diffusion generator designed for universal and robust dexterous grasp generation. It deeply incorporates three tailored physical constraints through a physics-aware training paradigm and a physics-guided sampler. Moreover, we present the largest and most diverse dataset for dexterous grasp generation to date. Extensive experiments demonstrate that our method and dataset significantly enhance the quality and diversity of dexterous grasp generation. We believe our contributions will pave the way for future advancements towards the universal robotic dexterous grasping." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "22591" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.17 + ], + "angle": 0, + "content": "[1] Hyungjin Chung, Jeongsol Kim, Michael T. McCann, Marc Louis Klasky, and J. C. Ye. Diffusion posterior sampling for general noisy inverse problems. 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In Proceedings of" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.092, + 0.907, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22593" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.124, + 0.092, + 0.484, + 0.122 + ], + "angle": 0, + "content": "the IEEE/CVF international conference on computer vision, pages 16259-16268, 2021. 5, 7" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22594" + } + ] +] \ No newline at end of file diff --git a/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/fb2fbb43-15d0-4a10-bd84-0e5530360297_origin.pdf b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/fb2fbb43-15d0-4a10-bd84-0e5530360297_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2674b774b8d8d3de6abbd26f2a84086468fd1afd --- /dev/null +++ b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/fb2fbb43-15d0-4a10-bd84-0e5530360297_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ecdd7ca8e1cbf98639ca978ebe12190246cd40790b063369110bf3934e1adc5c +size 9877139 diff --git a/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/full.md b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b1f5c455e29d91ddb78a3262d97de0ad6887267a --- /dev/null +++ b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/full.md @@ -0,0 +1,343 @@ +# DexGrasp Anything: Towards Universal Robotic Dexterous Grasping with Physics Awareness + +Yiming Zhong $^{1,\ast}$ , Qi Jiang $^{1,\ast}$ , Jingyi Yu $^{1}$ , Yuexin Ma $^{1,\dagger}$ + +$^{1}$ ShanghaiTech University + +{zhongym2024,jiangqi2022,yujingyi,mayuexin} $@$ shanghaiitech.edu.cn + +![](images/8db0ec43ed0ff0d9a42fe0d2f94f3203c2c49a19add0ffb527937137c5956566.jpg) +Figure 1. We present DexGrasp Anything, consistently surpassing previous dexterous grasping generation methods across five benchmarks. Visualization of our method's results are shown on the left. + +![](images/d0952ab27855a19267a787a4cbe6e4b8b09561b6239b3b70c1f9e66726021657.jpg) + +# Abstract + +A dexterous hand capable of grasping any object is essential for the development of general-purpose embodied intelligent robots. However, due to the high degree of freedom in dexterous hands and the vast diversity of objects, generating high-quality, usable grasping poses in a robust manner is a significant challenge. In this paper, we introduce DexGrasp Anything, a method that effectively integrates physical constraints into both the training and sampling phases of a diffusion-based generative model, achieving state-of-the-art performance across nearly all open datasets. Additionally, we present a new dexterous grasping dataset containing over 3.4 million diverse grasping poses for more than 15k different objects, demonstrating its potential to advance universal dexterous grasping. Code and dataset are available at https://github.com/4DVLab/DexGrasp-Anything + +# 1. Introduction + +Dexterous grasping, serving as a foundational capability for robotic manipulation tasks, has attracted significant attention. Five-fingered dexterous hands, which closely resemble the structure of the human hand, offer significantly greater flexibility, manipulation precision, and versatility compared to simpler grippers (e.g. parallel jaw, vacuum gripper). As robots are being deployed in human environments, dexterous hands have become increasingly vital due to their ability to interact with a wide range of objects as humans and use tools designed for humans. Therefore, a precise, robust, and versatile dexterous grasping method lies at the heart of interactions in embodied intelligence. + +Earlier approaches [5, 18, 25, 28, 29, 35] on dexterous grasping have primarily relied on analytical methods, where grasping poses were optimized to meet specific physical constraints. These methods, however, face significant challenges due to the large search space and the complexity of optimizing for high degrees of freedom in dexterous hands, leading to low success rates. In contrast, data-driven methods [10, 11, 17, 21, 43-45, 47, 51] leverage large-scale datasets to learn useful priors, narrowing the search space and providing strong guidance for search ini + +tialization. Regression-based methods [17, 45] that directly predict grasp parameters from object inputs often suffer from mode collapse and averaging, resulting in a limited diversity of generated grasp poses. Recently, generative methods [11, 47] have gained significant attention for their ability to enhance the diversity of generated grasp poses. Among these, diffusion models [8, 12, 39] have demonstrated a strong capability to capture the complexities of dexterous grasping and generate diverse grasp poses by iteratively transforming a simple distribution (e.g., Gaussian) into a complex, high-dimensional one [10, 21, 44, 51]. However, despite these advantages, current diffusion-based approaches [43, 45] often generate suboptimal grasp poses, resulting in hand-object penetration or insufficient contact with unsatisfactory success rates. These issues arise from the lack of constraints that enforce physical rules. + +In this work, we propose a novel dexterous grasping generation method, namely DexGrasp Anything, that integrates three carefully designed physical constraint objectives into the diffusion model during both training and sampling phases. DexGrasp Anything exhibits superior robustness and strong generalization capabilities. Specifically, we introduce the surface pulling force to ensure grasp feasibility by pulling the hand's inner surface toward the object's surface while avoiding interference with parts that are already sufficiently distant. We also introduce the externalpenetration repulsion force to maintain geometric accuracy of interaction by effectively preventing significant collisions between the object and the dexterous hand, and the selfpenetration repulsion force to preserve the hand's geometry by enforcing a minimum distance between finger joints and applying repulsion when they get too close. Through our physics-aware training scheme and physics-guided sampler, these physical constraints enable our diffusion-based generator to produce practical and robust dexterous grasping poses across a wide range of objects. Through extensive experiments, we show our method achieves state-of-the-art performance on almost all open datasets, as Figure 1 shows. + +To further improve the universality of diffusion-based generative method, massive amounts of high-quality training data is necessary. While many efforts have been made to build grasping datasets, they suffer from narrow data distribution[6, 17, 22], limited object categories [17, 41], and scalability issues [19]. In light of this, we dedicate substantial efforts to further enhancing the scale, diversity, and quality of the dexterous grasping datasets. We start by gathering available dexterous grasping data from multiple sources [15, 19, 40, 41, 47], including simulated data, real-captured data, and human hand grasping data, ensuring a diverse and comprehensive data distribution. We further scale up the dataset with a 'model-in-the-loop' strategy by using our grasping method and filtering method to continue generating high-quality data, inspired by the approach used in + +SAM [14]. These efforts culminate in a very large-scale dexterous grasping dataset, DexGrasp Anything (DGA) Dataset with over 3.4 million grasping poses on more than 15k objects. Experimental results demonstrate that this new dataset provides substantial benefits to grasping methods within the community. + +The main contribution of this work are as follows: + +- We propose a physics-aware diffusion generator for dexterous grasping pose generation, which effectively integrates three key physical constraints into both the training and sampling phases of the diffusion model. +- Our method achieves state-of-the-art performance on five dexterous grasping datasets. +- We present a new high-quality dexterous grasping dataset, the largest and most diverse to date, significantly improving the generalization capability of existing methods. + +# 2. Related Work + +# 2.1. Dexterous Grasp Generation + +Dexterous Grasping serves as a fundamental component for various complex, human-like manipulation tasks, making it a long-standing area of research in robotics. Early works mainly use manually derived analytical methods [5, 18, 25, 28, 29, 35] that based on certain physical constraints. These methods are hindered by extremely large search space and complex optimization process, leading to low success rate. + +Recently, data-driven approaches have emerged as a promising direction for dexterous grasping. Regression-based methods, such as [17, 45], often generate grasping poses with limited diversity, as they rely on direct predictions from input data and may fail to explore the full range of possible grasping configurations. In contrast, generative methods [11, 47] explicitly model the conditional probability distribution of dexterous hand poses given the target object, theoretically generating diverse poses. Diffusion model-based methods [10, 21, 51], in particular, stand out as a promising direction for more universal and robust robotic dexterous grasping for its exceptional capabilities in modeling various complex data distribution [9, 16, 20, 32, 46, 50] and generating diverse and highly realistic samples [27, 31, 33, 36]. However, existing diffusion model-based approaches are observed [43, 45] to yield sub-optimal grasping poses due to the absence of physical constraints during the training and sampling process. In this work, we delve into incorporating physical constraints into diffusion models to generate robust dexterous grasping poses for dexterous hands. + +# 2.2. Dexterous Grasping Dataset + +Collecting 3D dexterous grasping poses is notoriously expensive due to the complexity of hand structures. Most existing datasets are collected in simulators like + +![](images/a52f39c6157450f7a04fef57b6139b05d69308be4d5f156766f374526fb8383e.jpg) +Figure 2. Overview of DexGrasp Anything. During training, object information is processed to extract combined semantic and spatial representations as conditioning inputs. At each noise training step, a clean-estimation of the noisy hand pose $\hat{h}_0$ is derived from the predicted noise $\hat{\varepsilon}_t$ , with physics constraints guiding the noise distribution toward a cleaner, grasp-suitable distribution. During sampling, the Physics-Guided Sampler obtains the current observation $\hat{h}_0$ at each denoising step and performs posterior sampling based on this observation. Physical constraints gradually guide the distribution toward a physically feasible grasp configuration $\hat{h}_0^*$ , enabling effective grasping of diverse objects. + +GraspIt! [24] and IssacGym [23] through searching in the eigengrasp space [6, 17, 22] or optimization-based methods [15, 17, 41, 47] in parameter space. However, the search-based data often follow a narrow distribution due to the low-dimensional eigengrasp space, while the recent optimization-based data still suffer from relatively success rate and contained limit number of object categories. Some real-world datasets have been collected using teleoperation systems controlled by human operators. While these datasets capture human-like grasping poses, the data collection process is prohibitively expensive and difficult to scale up. Recent advances [30, 37, 38] have explored retargeting human hand poses to dexterous robotic hands, presenting a promising avenue for leveraging human hand data in robot hand training. Despite these advancements, existing datasets still face limitations in diversity, scalability, and quality. To address these challenges, we introduce the largest and most diverse dexterous grasping dataset to date and demonstrate that our dataset significantly enhances both the quality and diversity of generated dexterous + +grasping poses, providing substantial value to existing data-driven grasping generators. + +# 3. Method + +We present DexGrasp Anything, an effective approach that enhances diffusion-based generators for dexterous grasping by integrating meticulously designed physical constraints. Figure 2 demonstrates an overview of our method. The following sections detail our problem formulation (Sec. 3.1), physics-aware constraints (Sec. 3.2), and the way to integrate constraints to the diffusion model's training (Sec. 3.3) and sampling processes (Sec. 3.4), and the LLM-enhanced object representation extraction module (Sec. 3.5). + +# 3.1. Problem Definition + +Our goal is to generate high-quality grasping poses capable of securely holding a given object. Specifically, given a 3D object observation $O$ , we aim to sample a diverse set of dexterous grasping poses $\mathbf{h} = \{h_i\}_{i=1}^n$ from a condi- + +tional distribution $P(h|O)$ , where the dexterous pose $h = (\theta, \mathrm{R}, \mathrm{t}) \in \mathbb{R}^{33}$ consists of the dexterous hand articulation $\theta \in \mathbb{R}^{24}$ (for ShadowHand), the global rotation $R \in \mathrm{SO}(3)$ and the global translation vector $t \in \mathbb{R}^3$ . + +The conditional distribution $P(h|O)$ is modeled using a diffusion model $\epsilon_{\phi}(h_t,O,t)$ , which iteratively transforms an isotropic Gaussian distribution $\mathcal{N}(0,\mathrm{I})$ into the desired data distribution: + +$$ +P (h _ {0} | O) = P (h _ {T}) \prod_ {t = 1} ^ {T} P (h _ {t - 1} | h _ {t}, O), +$$ + +$$ +P \left(h _ {t - 1} \mid h _ {t}, O\right) = \mathcal {N} \left(h _ {t - 1}; \mu_ {\phi} \left(h _ {t}, O, t\right), \Sigma_ {\phi} \left(h _ {t}, O, t\right)\right). \tag {1} +$$ + +# 3.2. Physical Constraints + +Diffusion model-based methods often fail to reach optimal performance in the absence of appropriate physical constraints. To address this, we present three tailored physical constraint objectives for our DexGrasp Anything generator, enabling the production of universal and robust dexterous grasping poses for a wide range of objects. + +Surface Pulling Force [47] is crucial for ensuring grasp feasibility. It enforces proximity between the inner surface of the robotic phalanges (represented by sampled point clouds) and the object's surface. This guidance signal applies a pulling force only to points that are closer than a specified threshold, ensuring that the points on the inner surface of the fingers are pulled towards the object's surface when they are near, but does not affect points that are already at a sufficient distance. Compute the squared Euclidean distance for each inner surface point $p_{\mathrm{dis}}^{(i)}$ to its nearest neighbor on the object surface: $d_{i} = \min_{j} \| p_{\mathrm{dis}}^{(i)} - p_{\mathrm{obj}}^{(j)} \|^2$ . We compute the surface pulling force as: + +$$ +L _ {\mathrm {S P F}} = \frac {\sum_ {i \in S} \sqrt {d _ {i}}}{| S | + \eta}, \tag {2} +$$ + +where $S = \{i|d_i < d_{\mathrm{Threshold}}\}$ represents the set of points within the threshold distance and $\eta$ is a numerical stability constant. + +External-penetration Repulsion Force [10] retains the spatial accuracy of hand-object interactions. It minimizes the undesired intersection between the hand and object point clouds by leveraging the signed distances. Given an object point cloud $P_{obj}$ with surface normals $N_{obj}$ , and a hand point cloud $P_{hand}$ , we first compute the nearest neighbor distance between each point in $P_{hand}$ and $P_{obj}$ : $d_i = \min_j \| P_{hand}^{(i)} - P_{obj}^{(j)} \|$ . We then calculate the signed distance between the hand and object points using the object normals: + +$$ +s _ {i} = \operatorname {s i g n} \left(\left(P _ {o b j} ^ {(j)} - P _ {\text {h a n d}} ^ {(i)}\right) \cdot N _ {o b j} ^ {(j)}\right). \tag {3} +$$ + +Finally, the external-penetration repulsion force is defined as the maximum signed distance across all points in the batch, averaged over the batch size $B$ : + +$$ +L _ {\mathrm {E R F}} = \frac {1}{B} \sum_ {i = 1} ^ {B} \max _ {i} \left(s _ {i}, d _ {i}\right). \tag {4} +$$ + +Self-Penetration Repulsion Force [47] upholds the hand structural geometry. It addresses the issue of hand points intersecting with each other by enforcing a minimum distance between them. This ensures that the hand maintains a realistic, physically plausible shape without finger collisions. Given a set of hand points $P_{\mathrm{hand}}$ , we calculate the pairwise Euclidean distances between all points: $d_{ij} = \| P_{\mathrm{hand}}^{(i)} - P_{\mathrm{hand}}^{(j)} \|$ , A repulsion force is applied when $d_{ij}$ is smaller than a threshold $d_{\mathrm{Threshold}}$ , and the self-penetration repulsion force is defined as: + +$$ +L _ {\mathrm {S R F}} = \frac {1}{B} \sum_ {i, j} \max \left(0, d _ {\text {T h r e s h o l d}} - d _ {i j}\right). \tag {5} +$$ + +# 3.3. Physics-Aware Training + +Diffusion Models are typically trained with a simple mean-squared error (MSE) objectives: + +$$ +L _ {\text {s i m p l e}} = \mathbb {E} _ {t, x _ {0}, \epsilon} [ \| \epsilon - \epsilon_ {\phi} (h _ {t}, t) \| ^ {2} ], \tag {6} +$$ + +where $h_t$ is a corrupted version of the original data $h_0$ . The data corruption follows a fixed noise schedule $\beta_t$ : + +$$ +q \left(h _ {t} \mid h _ {t - 1}\right) = \mathcal {N} \left(h _ {t}; \sqrt {1 - \beta_ {t}} h _ {t - 1}, \beta_ {t} \mathbf {I}\right), \tag {7} +$$ + +$$ +h _ {t} = \sqrt {1 - \beta_ {t}} h _ {t - 1} + \sqrt {\beta_ {t}} \epsilon_ {t}. +$$ + +With $\alpha_{t} = 1 - \beta_{t}$ and $\bar{\alpha}_{t} = \Pi_{i = 1}^{t}\alpha_{i}$ , the corruption process can be directly conditioned on $h_0$ : + +$$ +q \left(h _ {t} \mid h _ {0}\right) = \mathcal {N} \left(h _ {t}; \sqrt {\bar {\alpha} _ {t}} h _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right), \tag {8} +$$ + +$$ +h _ {t} = \sqrt {\bar {\alpha} _ {t}} h _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \bar {\epsilon} _ {t}. +$$ + +Since the training objective $L_{\mathrm{simple}}$ is essentially a reweighted variational lower bound on negative log likelihood, it does not incorporate any explicit supervision regarding physical constraints. As a result, diffusion models often perform sub-optimally when directly generating dexterous grasping parameters, as observed in previous works [43, 45]. To facilitate our diffusion generator in capturing physics priors during training, we introduce the Physics-Aware Training paradigm, which incorporates the tailored physical constraints outlined in Sec. 3.2. + +The training objective involving only corrupted data $h_t$ is not well-suited for incorporating physical constraints. Using the diffusion process defined in Eq. 8, the estimated sample: $\hat{h_0}(h_t) = \frac{1}{\sqrt{\bar{\alpha}_t}} (h_t - \sqrt{1 - \bar{\alpha}_t} \epsilon_\phi(h_t, O, t))$ could + +serve as a good proxy for introducing physical constraint into the training process of a diffusion model. + +We define the physically-aware training objective $L_{\mathrm{PADG}}$ as a linear combination of the standard mean-squared objective and multiple physical-constraint objectives: + +$$ +L _ {\mathrm {P A D G}} = L _ {\text {s i m p l e}} \left(h _ {t}\right) + \sum_ {i = 1} ^ {m} \alpha_ {i} L _ {\mathrm {P A} _ {i}} \left(\hat {h _ {0}} \left(h _ {t}\right), \epsilon_ {\phi}\right), \tag {9} +$$ + +where $L_{\mathrm{PA}_i}(\hat{h_0}(h_t), \epsilon_\phi)$ is the $i^{th}$ physical constraint and $\alpha_i$ is the corresponding weighting coefficient. The gradient is propagated to $h_t$ through the estimated clean sample $h_0$ as follows: + +$$ +\frac {\partial L _ {\mathrm {P A D G}}}{\partial h _ {t}} = \frac {\partial L _ {\text {s i m p l e}}}{\partial h _ {t}} + \sum_ {i = 1} ^ {m} \alpha_ {i} \frac {\partial L _ {\mathrm {P A} _ {i}}}{\partial \hat {h _ {0}}} \cdot \frac {\partial \hat {h _ {0}}}{\partial h _ {t}}. \tag {10} +$$ + +# 3.4. Physics-Guided Sampling + +Leveraging the learned physics priors, the well-trained diffusion generator is capable of producing physically plausible dexterous grasping poses for a given object. The physical constraints can be further enhanced during the sampling process by employing advanced sampling techniques [1, 4, 7, 48]. + +Classifier guidance [4] has explored the use of a time-dependent classifier $\mathcal{F}_t$ to steer the diffusion model towards specific conditional distributions. The guidance can be approximated as an offset in the posterior mean: + +$$ +\tilde {\mu} _ {\phi} \left(x _ {t}, t\right) \leftarrow \mu_ {\phi} \left(x _ {t}, t\right) + s \Sigma_ {\theta , t} \nabla_ {x _ {t}} \log \left(\mathcal {F} _ {t} (y, x _ {t})\right), \tag {11} +$$ + +where $s$ is the guidance strength. By estimating $\hat{x_0}$ based on $x_{t}$ , the guidance signal can be extended from a time-dependent classifier $\mathcal{F}_t(y,x_t)$ to arbitrary objective functions $L(x_0)$ on clean samples. It can be achieved by mapping the objective to a density-like function: + +$$ +\mathcal {F} \left(x _ {0}\right) = \mathcal {Z} e ^ {- L \left(x _ {0}\right)}, \tag {12} +$$ + +where $\mathcal{Z}$ is a normalizing constant. We define the Physics-Guided Sampler as follows: + +$$ +\begin{array}{l} \widetilde {\mu} _ {\phi} (h _ {t}, O, t) \leftarrow \mu_ {\phi} (h _ {t}, O, t) \\ + s \Sigma_ {\phi , t} \nabla_ {h _ {t}} \sum_ {i = 1} ^ {m} \alpha_ {i} L _ {P A _ {i}} \left(\hat {h} _ {0} \left(h _ {t}\right), \epsilon_ {t}\right). \tag {13} \\ \end{array} +$$ + +To alleviate the estimation bias on $\hat{h_0}$ , we apply the Spherical Gaussian Constraint [48] with a weighted gradient direction in practice. This is expressed as: + +$$ +\tilde {\mu} _ {\phi} \left(h _ {t}, O, t\right) \leftarrow \mu_ {\phi} \left(h _ {t}, O, t\right) + r \frac {d _ {m}}{\| d _ {m} \|}, \tag {14} +$$ + +where $d_{\mathrm{m}} = d_{\mathrm{sample}} + g_r(d^* - d_{\mathrm{sample}})$ , $d_{\mathrm{sample}} = \Sigma_{\phi, t} \epsilon$ and: + +$$ +d ^ {*} = - \sqrt {n} \Sigma_ {\phi , t} \frac {\nabla_ {h _ {t}} \sum_ {i = 1} ^ {m} \alpha_ {i} L _ {\mathrm {P A} _ {i}} \left(\hat {h} _ {0} \left(h _ {t}\right) , \epsilon_ {t}\right)}{\| \nabla_ {h _ {t}} \sum_ {i = 1} ^ {m} \alpha_ {i} L _ {\mathrm {P A} _ {i}} \left(\hat {h} _ {0} \left(h _ {t}\right) , \epsilon_ {t}\right) \|}. \tag {15} +$$ + +Incorporating physics constraints during training helps guide the noise distribution toward a cleaner, grasp-suitable form. However, due to sparse supervision in the training phase, we leverage the reverse process during sampling to obtain $h_t$ and $\hat{h}_0$ at each step, applying posterior sampling to iteratively refine the grasp configuration. This iterative refinement allows the Physics-Guided Sampler to progressively adjust $\hat{h}_0$ under physics constraints, ultimately steering the distribution toward a physically feasible grasp configuration. Through this distributional framework, our model effectively generalizes to diverse objects, demonstrating robustness and adaptability in grasping tasks. + +# 3.5. LLM-enhanced Representation Extraction + +To accomplish robust dexterous grasp generation for a targeted object, we boost the traditional object representation by complementing the geometry object feature with semantic prior from powerful LLMs. We employ a Point Transformer[52] to encode object point clouds, producing an $N \times C$ feature vector, where $\mathbf{N}$ represents the number of groups defined by the Point Transformer. To enrich these features with abundant semantic prior from LLM, we utilize the prompt: "I want to grasp a [object label]. First, provide its object category, then give a detailed description of its shape before making a successful grip." We then parse the response and encode each sentence using a pre-trained BERT-large-uncased model. We extract the [CLS] token from each sentence and apply max-pooling on them. This results in an $1 \times C$ semantic feature vector that includes the rich prior knowledge from the LLM. The concatenated $(N + 1) \times C$ feature matrix is subsequently integrated into the diffusion backbone through a cross-attention mechanism, enhancing the model's capacity to generate precise and contextually relevant grasping poses. + +# 4. Dataset + +The quality, diversity and scale of datasets are crucial for advancing dexterous grasping research, especially for diffusion-based generative methods. Training on a broader data distribution enables models to learn richer and more adaptable grasping strategies for arbitrary object. To inspire potential of methods towards universal dexterous grasping, we have developed a comprehensive dataset that significantly exceeds existing dexterous grasping datasets in both size and diversity. In the following sections, we provide a detailed overview of the data construction process, present key statistics, and highlight the characteristics of our DexGrasp Anything (DGA) dataset. + +# 4.1. Data Construction + +Our data construction process begins with curating existing datasets from diverse sources. We gather three simulated datasets [15, 41, 47], a real-world dataset [19] col + +Table 1. Comparison of dexterous grasp datasets. Our dataset achieves the largest scale to date. + +
    DatasetPublication YearHand TypeSim./Real#Grasps#Objects#Grasps per objectConstruction method
    GRAB [40]ECCV 2020MANOReal1.64M51>10KCapture
    DDGdata [17]RSS 2020ShadowHandSim.6.9k565-GraspIt!
    MultiDex [15]ICRA 2023ShadowHandSim.16K58300Optimization
    DexGraspNet [41]ICRA 2023ShadowHandSim.1.32M5,355>200Optimization
    UniDexGrasp [47]CVPR 2023ShadowHandSim.1.12M5,519>150Optimization
    GraspXL [49]ECCV 2024Diverse HandSim-500K-GraspXL
    RealDex [19]IJCAI 2024ShadowHandReal59K52>200Human Annotation
    Our datasetCVPR 2025ShadowHandReal+Sim.3.40M15,698>200DexGrasp Anything + Filter
    + +lected by human operator, alongside GRAB [40], a largescale human hand dataset, to maximize data diversity and richness. Leveraging advancements in robot teleoperation systems like AnyTeleop [30], we retarget the human hand dataset GRAB to dexterous hand parameters, creating DexGRAB, and filter it to retain only frames with hand-object contact. Next, we examine all collected data within IsaacGym [23], applying strict conditions to ensure stability and contact integrity. Specifically, we enforce that (1) objects do not shift more than $2\mathrm{cm}$ in any direction under force and that (2) hand-object penetration remains below $10\mathrm{mm}$ and object-hand penetration remains below $1\mathrm{mm}$ following [41]. The detailed process for computing the penetration is provided in the supplementary materials. This rigorous filtering process guarantees consistent high quality across all data sources. + +Training our physics-aware diffusion generator on this dataset leads to higher success rates, greater diversity, and faster generation speeds for zero-shot dexterous grasping on unseen objects. Acting as a data engine, our model facilitates further dataset expansion in a "model-in-the-loop" manner. We meticulously selected object meshes from the Objaverse [2, 3] dataset, with the goal of ensuring broad category coverage and maintaining an even distribution across these categories. To achieve this, we examined all objects within 18 chosen categories and ultimately selected 10,034 distinct objects, covering 6,994 unique tags in the Objaverse data configuration. We apply approximate convex decomposition [42] to each mesh to reduce complexity and ensure water-tightness. Our trained generator then iteratively produces dexterous grasp poses, which are filtered under the same stringent standards. Finally, we combine the curated and generated data to form a large-scale and diverse dataset, crafted to advance research in dexterous grasping. + +# 4.2. Statistics + +We present a comparative analysis of key metrics between our dataset and other existing datasets in Table 1. Our DGA dataset comprises two main components: The first component DGA-curated includes approximately 0.88 million grasping poses across 5,664 distinct objects, curated from various existing and diverse data sources. The second com + +![](images/f80f3ea959868375a6dffa9afc585e7d92a516aff4e5a9e328e8345aee817e23.jpg) +Figure 3. t-SNE visualization of the object features in our dataset compared to existing datasets. Each point represents an object, and different markers and colors are used to distinguish between datasets. For clarity, we randomly sample $5\%$ objects from each dataset for visualization. + +ponent DGA-generated is generated with our DexGrasp Anything generator from the Objaverse [2, 3] dataset, containing approximately 2.52 million grasping poses spanning 10,034 different objects, covering 6,994 unique tags. In total, our dataset features over 3.4 million grasping poses across 15,698 objects from diverse data distribution, supporting in-depth research into dexterous grasping. + +# 4.3. Characteristics + +Our dataset is characterized by a high degree of diversity and comprehensiveness, aimed at capturing a wide range of object and pose variations to advance the performance of dexterous hands in complex real-world environment. The key characteristics of our dataset can be presented as follow: + +- Large data scale. Our dataset features over 3.4M strictly-tested grasping poses, which is significantly larger than all previous datasets. +- Diverse objects. Our dataset encompasses 15,698 objects from a wide range of categories and sources, ensuring a high level of diversity. In Figure 3, we present a t-SNE visualization comparing object features from our dataset with those from existing datasets, using features extracted by a pre-trained Point Transformer. Object features from our dataset spread much wider across the feature space, suggesting that our dataset captures a broader variety or unique features that not be as present in existing datasets. +- Diverse grasping poses. The wide variety of objects + +Table 2. Performance comparison across different methods and datasets. Bold numbers indicate the best scores, while underlined numbers indicate the second-best scores. DexGrasp Anything (w/ LLM) achieves the highest or near-highest performance across most metrics. + +
    Dataset MethodDexGraspNetUniDexGraspMultiDexRealDexDexGRAB
    Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑
    UniDexGrasp [47]33.970.131.90.1423.765.524.50.1421.647.513.50.0827.159.439.00.1120.855.837.40.08
    GraspTTA [11]18.667.824.50.1321.065.321.20.1030.362.819.00.1113.346.440.10.0914.451.051.40.10
    SceneDiffuser [10]26.666.931.00.1528.374.825.10.1569.885.614.60.2721.756.142.00.0939.185.041.10.12
    UGG [21]46.979.025.20.1446.083.224.50.1455.393.410.30.1232.763.434.40.1042.790.633.20.12
    Ours53.690.421.50.2254.890.818.90.2572.296.39.60.2334.671.223.10.1456.591.828.60.12
    Ours(w/LLM)57.590.617.80.2353.191.218.80.2379.198.111.40.2244.873.727.70.1357.992.730.40.13
    + +contributes to a diverse range of grasping poses. Extensive experimental results in Sec. 5.3 demonstrate that our dataset significantly enhances the diversity of outcomes from existing methods, while maintaining or even improving the grasping success rate. + +# 5. Experiments + +# 5.1. Comparison + +Metrics. Following previous works [10], we assess the grasping success rate (Suc. 6/Suc. 1) and maximum penetration (Pen.) in millimeters to gauge the quality of generated poses. A grasping pose is considered successful if the object's displacement, when an external force is applied, is less than $2\mathrm{cm}$ in at least one (Suc. 1) or all (Suc. 6) of the six axis-aligned directions in a 3D coordinate system. Additionally, we evaluate the diversity using the mean standard deviation of the pose parameters (Div.) across successful grasps in millimeters. All poses are evaluated in the IssacGym [23] simulator with the same configuration used in [10]. + +Implementation Details. Following [10], we employ a U-Net [34] structure for our diffusion backbone. An object-conditioned Point Transformer [52] encoder handles the point clouds, injected into the diffusion model using a cross-attention mechanism. All point clouds are downsampled to 2048 points before encoding. Our model is implemented using the PyTorch [26] platform, optimized with the Adam [13] algorithm at a learning rate of 0.0001. We follow the official train-test split of all datasets. All the compared methods are trained and inferred following their official code implementations. Training and evaluation are carried out on a Linux server equipped with four NVIDIA Tesla A40 GPUs until convergence. + +Results. Table 2 presents the quantitative comparisons. Our method, leveraging a physics-aware training paradigm and a physics-guided sampler, demonstrates superior performance in both pose quality (Suc. 1, Suc. 6, and Pen.) and diversity (Div.) compared to previous methods across all five benchmarks. Qualitative results, shown in Figure 4, further illustrate that our approach produces more accurate grasping poses, benefiting from the effective physical + +Table 3. Ablation study on incorporating physical constraints during both training and sampling stages and the LLM module. The evaluation is conducted on the DexGraspNet dataset. + +
    SRFERFSPFLLMSuc.6 ↑Suc.1 ↑Pen. ↓Div ↑
    a26.666.931.00.15
    b✓38.978.427.00.03
    c✓✓46.683.415.80.22
    d✓✓✓53.690.421.50.22
    e✓✓✓✓57.590.617.80.23
    fConstraints only in training46.884.020.90.18
    + +![](images/cb5866837bd91e1c068cb52b00d977f0571ea65be8444eb29600cd8f46473a43.jpg) +Figure 4. Qualitative visualization of grasping results in Table 2. + +![](images/8b88280a72b062a531f60522b51540f206a8a042824d9ac4c4351dfceb1ff654.jpg) +Figure 5. Visualization of the ablation study. Two rows show different views of each grasp. + +constraints introduced in both training and sampling stages. + +# 5.2. Ablation Study + +In this section, we conduct ablation studies to evaluate the contributions of the proposed physical constraint objectives as well as the LLM-enhanced representation in our Dex-Grasp Anything generator. These studies are performed on + +Table 4. Evaluating Dataset Quality and Cross-Dataset Generalization. Model performance is compared on DexGraspNet and RealDex, with training on either DexGraspNet or our dataset. The best result within each group is highlighted in **bold**. + +
    MethodTest TrainDexGraspNetRealDex
    Suc.6 ↑Suc.1 ↑Pen. ↓Div ↑Suc.6 ↑Suc.1 ↑Pen. ↓Div ↑
    SceneDiffuserDexGraspNet26.666.931.00.1516.152.129.20.13
    DGA dataset40.770.622.20.3624.557.131.00.27
    GraspTTADexGraspNet18.667.824.50.1325.564.831.60.11
    DGA dataset28.073.023.90.2132.976.232.10.20
    UGGDexGraspNet46.979.025.20.1433.674.533.00.13
    DGA dataset49.185.926.20.2242.977.334.40.22
    OursDexGraspNet53.690.421.50.2238.477.519.20.17
    DGA-curated55.987.320.90.2852.685.721.50.25
    DGA dataset58.688.517.80.3853.484.422.40.32
    + +the testing set of the DexGraspNet dataset. The quantitative results are presented in Table 3, where where we incrementally add the three physical constraints and the LLM enhancement (lines a-e) and compare with a model that uses only physical-aware training, excluding the physical-guided sampler (line f). Qualitative results are shown in Figure 5, with additional samples provided in the supplementary materials. These analyses emphasize the crucial role of each physical constraint, the LLM enhancement, as well as the physics-aware training paradigm and physics-guided sampler in enhancing the system's overall performance. + +# 5.3. Evaluation for DexGrasp Anything Dataset + +By gathering high-quality data from various existing sources and augmenting it with our physics-aware diffusion generator, we have constructed the largest and most diverse dexterous grasping dataset to date. This not only enhances the performance of our generator but also benefits other dexterous grasp generation methods. + +Setup. We train our DexGrasp Anything generator, SceneDiffuser, UGG, and GraspTTA on the training sets of both the DexGraspNet and DexGrasp Anything datasets. We evaluate the models on the testing sets of DexGraspNet and RealDex datasets. + +Results. As shown in Table 4, our findings indicate that training on the DexGrasp Anything dataset significantly improves the diversity of the sampling results for DexGrasp Anything generator, UGG, SceneDiffuser and GraspTTA. This is achieved without compromising, and in some cases improving, the grasping success rate and penetration metrics. To further validate our approach, we provide a more comprehensive evaluation in the supplementary materials. The qualitative comparison results are illustrated in Figure 6. For a variety of target objects, models trained on the DGA dataset generate significantly more diverse grasping poses, while maintaining high-quality results. + +![](images/4dc85c6ab98431866c9eea689ab9dce9eb6bd58590a4b720094886d353a91228.jpg) +Figure 6. Visualization of cross-dataset evaluation results shown in Table 4. The top row shows models trained on DexGraspNet, while the bottom row displays models trained on our dataset. + +![](images/67e2c4bba0cdf81afe0b171b791142bf78e1226409898006d122f3cfc7f78c13.jpg) +Figure 7. Real-world evaluation for our method. + +# 5.4. Real-world Application + +Harnessing physics and semantic priors, and trained on our diverse, high-quality dataset, DexGrasp Anything is highly capable of producing robust and practicable grasping poses in real-world environments. To validate its performance, we deploy the model on a real ShadowHand robot, as shown in Figure 7. The pre-grasping motion sequence is generated following the approach in [19]. The real-world experiments demonstrate that our grasping motions are reasonable and stable for unseen real objects, proving the universality and practicability of our method. More video demos are available in the supplementary materials. + +# 6. Conclusions + +We introduce DexGrasp Anything, a physics-aware diffusion generator designed for universal and robust dexterous grasp generation. It deeply incorporates three tailored physical constraints through a physics-aware training paradigm and a physics-guided sampler. Moreover, we present the largest and most diverse dataset for dexterous grasp generation to date. Extensive experiments demonstrate that our method and dataset significantly enhance the quality and diversity of dexterous grasp generation. We believe our contributions will pave the way for future advancements towards the universal robotic dexterous grasping. + +# References + +[1] Hyungjin Chung, Jeongsol Kim, Michael T. McCann, Marc Louis Klasky, and J. C. Ye. 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Geodiff: a geometric diffusion model for molecular conformation generation. *ArXiv*, abs/2203.02923, 2022. 2 +[47] Yinzhen Xu, Weikang Wan, Jialiang Zhang, Haoran Liu, Zikang Shan, Hao Shen, Ruicheng Wang, Haoran Geng, Yijia Weng, Jiayi Chen, et al. Unidexgrasp: Universal robotic dexterous grasping via learning diverse proposal generation and goal-conditioned policy. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4737-4746, 2023. 1, 2, 3, 4, 5, 6, 7 +[48] Lingxiao Yang, Shutong Ding, Yifan Cai, Jingyi Yu, Jingya Wang, and Ye Shi. Guidance with spherical gaussian constraint for conditional diffusion. ArXiv, abs/2402.03201, 2024.5 +[49] Hui Zhang, Sammy Christen, Zicong Fan, Otmar Hilliges, and Jie Song. GraspXL: Generating grasping motions for diverse objects at scale. In European Conference on Computer Vision (ECCV), 2024. 6 +[50] Longwen Zhang, Ziyu Wang, Qixuan Zhang, Qiwei Qiu, Anqi Pang, Haoran Jiang, Wei Yang, Lan Xu, and Jingyi Yu. Clay: A controllable large-scale generative model for creating high-quality 3d assets. ACM Transactions on Graphics (TOG), 43(4):1-20, 2024. 2 +[51] Zhengshen Zhang, Lei Zhou, Chenchen Liu, Zhiyang Liu, Chengran Yuan, Sheng Guo, Ruiteng Zhao, Marcelo H Ang Jr, and Francis EH Tay. Dexgrasp-diffusion: Diffusion-based unified functional grasp synthesis pipeline for multideterous robotic hands. arXiv preprint arXiv:2407.09899, 2024. 1, 2 +[52] Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip HS Torr, and Vladlen Koltun. Point transformer. In Proceedings of \ No newline at end of file diff --git a/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/images.zip b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..5a8b784e2530cadd0694bcde146c04466e5f6bb6 --- /dev/null +++ b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f7a1c1ff0a2fa985fbac147cbe2cab0b102e0fc32fcbd3f2cc05ba229f09da0b +size 767752 diff --git a/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/layout.json b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..db2deb087cf14ff3c1d414e62f20cd8e41300dc6 --- /dev/null +++ b/2025/DexGrasp Anything_ Towards Universal Robotic Dexterous Grasping with Physics Awareness/layout.json @@ -0,0 +1,8436 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 91, + 102, + 520, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 102, + 520, + 138 + ], + "spans": [ + { + "bbox": [ + 91, + 102, + 520, + 138 + ], + "type": "text", + "content": "DexGrasp Anything: Towards Universal Robotic Dexterous Grasping with Physics Awareness" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "spans": [ + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "text", + "content": "Yiming Zhong" + }, + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "inline_equation", + "content": "^{1,\\ast}" + }, + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "text", + "content": ", Qi Jiang" + }, + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "inline_equation", + "content": "^{1,\\ast}" + }, + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "text", + "content": ", Jingyi Yu" + }, + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "text", + "content": ", Yuexin Ma" + }, + { + "bbox": [ + 170, + 159, + 438, + 175 + ], + "type": "inline_equation", + "content": "^{1,\\dagger}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 241, + 175, + 371, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 241, + 175, + 371, + 190 + ], + "spans": [ + { + "bbox": [ + 241, + 175, + 371, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 241, + 175, + 371, + 190 + ], + "type": "text", + "content": " ShanghaiTech University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 128, + 190, + 480, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 190, + 480, + 204 + ], + "spans": [ + { + "bbox": [ + 128, + 190, + 480, + 204 + ], + "type": "text", + "content": "{zhongym2024,jiangqi2022,yujingyi,mayuexin} " + }, + { + "bbox": [ + 128, + 190, + 480, + 204 + ], + "type": "inline_equation", + "content": "@" + }, + { + "bbox": [ + 128, + 190, + 480, + 204 + ], + "type": "text", + "content": " shanghaiitech.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 59, + 212, + 334, + 390 + ], + "blocks": [ + { + "bbox": [ + 59, + 212, + 334, + 390 + ], + "lines": [ + { + "bbox": [ + 59, + 212, + 334, + 390 + ], + "spans": [ + { + "bbox": [ + 59, + 212, + 334, + 390 + ], + "type": "image", + "image_path": "8db0ec43ed0ff0d9a42fe0d2f94f3203c2c49a19add0ffb527937137c5956566.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 393, + 555, + 417 + ], + "lines": [ + { + "bbox": [ + 55, + 393, + 555, + 417 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 555, + 417 + ], + "type": "text", + "content": "Figure 1. We present DexGrasp Anything, consistently surpassing previous dexterous grasping generation methods across five benchmarks. Visualization of our method's results are shown on the left." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 337, + 213, + 555, + 389 + ], + "blocks": [ + { + "bbox": [ + 337, + 213, + 555, + 389 + ], + "lines": [ + { + "bbox": [ + 337, + 213, + 555, + 389 + ], + "spans": [ + { + "bbox": [ + 337, + 213, + 555, + 389 + ], + "type": "image", + "image_path": "d0952ab27855a19267a787a4cbe6e4b8b09561b6239b3b70c1f9e66726021657.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 152, + 426, + 200, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 426, + 200, + 438 + ], + "spans": [ + { + "bbox": [ + 152, + 426, + 200, + 438 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 54, + 455, + 297, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 455, + 297, + 648 + ], + "spans": [ + { + "bbox": [ + 54, + 455, + 297, + 648 + ], + "type": "text", + "content": "A dexterous hand capable of grasping any object is essential for the development of general-purpose embodied intelligent robots. However, due to the high degree of freedom in dexterous hands and the vast diversity of objects, generating high-quality, usable grasping poses in a robust manner is a significant challenge. In this paper, we introduce DexGrasp Anything, a method that effectively integrates physical constraints into both the training and sampling phases of a diffusion-based generative model, achieving state-of-the-art performance across nearly all open datasets. Additionally, we present a new dexterous grasping dataset containing over 3.4 million diverse grasping poses for more than 15k different objects, demonstrating its potential to advance universal dexterous grasping. Code and dataset are available at https://github.com/4DVLab/DexGrasp-Anything" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 426, + 394, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 426, + 394, + 438 + ], + "spans": [ + { + "bbox": [ + 315, + 426, + 394, + 438 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 449, + 555, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 592 + ], + "type": "text", + "content": "Dexterous grasping, serving as a foundational capability for robotic manipulation tasks, has attracted significant attention. Five-fingered dexterous hands, which closely resemble the structure of the human hand, offer significantly greater flexibility, manipulation precision, and versatility compared to simpler grippers (e.g. parallel jaw, vacuum gripper). As robots are being deployed in human environments, dexterous hands have become increasingly vital due to their ability to interact with a wide range of objects as humans and use tools designed for humans. Therefore, a precise, robust, and versatile dexterous grasping method lies at the heart of interactions in embodied intelligence." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "content": "Earlier approaches [5, 18, 25, 28, 29, 35] on dexterous grasping have primarily relied on analytical methods, where grasping poses were optimized to meet specific physical constraints. These methods, however, face significant challenges due to the large search space and the complexity of optimizing for high degrees of freedom in dexterous hands, leading to low success rates. In contrast, data-driven methods [10, 11, 17, 21, 43-45, 47, 51] leverage large-scale datasets to learn useful priors, narrowing the search space and providing strong guidance for search ini" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 664, + 141, + 674 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 664, + 141, + 674 + ], + "spans": [ + { + "bbox": [ + 66, + 664, + 141, + 674 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 664, + 141, + 674 + ], + "type": "text", + "content": " * Equal contribution." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 56, + 674, + 295, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 674, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 56, + 674, + 295, + 712 + ], + "type": "inline_equation", + "content": "^{2\\dagger}" + }, + { + "bbox": [ + 56, + 674, + 295, + 712 + ], + "type": "text", + "content": " Corresponding author. This work was supported by NSFC (No.62206173), Shanghai Frontiers Science Center of Human-centered Artificial Intelligence (ShangHAI), MoE Key Laboratory of Intelligent Perception and Human-Machine Collaboration (KLIP-HuMaCo)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 784, + 317, + 792 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 784, + 317, + 792 + ], + "spans": [ + { + "bbox": [ + 293, + 784, + 317, + 792 + ], + "type": "text", + "content": "22584" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "content": "tialization. Regression-based methods [17, 45] that directly predict grasp parameters from object inputs often suffer from mode collapse and averaging, resulting in a limited diversity of generated grasp poses. Recently, generative methods [11, 47] have gained significant attention for their ability to enhance the diversity of generated grasp poses. Among these, diffusion models [8, 12, 39] have demonstrated a strong capability to capture the complexities of dexterous grasping and generate diverse grasp poses by iteratively transforming a simple distribution (e.g., Gaussian) into a complex, high-dimensional one [10, 21, 44, 51]. However, despite these advantages, current diffusion-based approaches [43, 45] often generate suboptimal grasp poses, resulting in hand-object penetration or insufficient contact with unsatisfactory success rates. These issues arise from the lack of constraints that enforce physical rules." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 267, + 295, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 267, + 295, + 531 + ], + "spans": [ + { + "bbox": [ + 56, + 267, + 295, + 531 + ], + "type": "text", + "content": "In this work, we propose a novel dexterous grasping generation method, namely DexGrasp Anything, that integrates three carefully designed physical constraint objectives into the diffusion model during both training and sampling phases. DexGrasp Anything exhibits superior robustness and strong generalization capabilities. Specifically, we introduce the surface pulling force to ensure grasp feasibility by pulling the hand's inner surface toward the object's surface while avoiding interference with parts that are already sufficiently distant. We also introduce the externalpenetration repulsion force to maintain geometric accuracy of interaction by effectively preventing significant collisions between the object and the dexterous hand, and the selfpenetration repulsion force to preserve the hand's geometry by enforcing a minimum distance between finger joints and applying repulsion when they get too close. Through our physics-aware training scheme and physics-guided sampler, these physical constraints enable our diffusion-based generator to produce practical and robust dexterous grasping poses across a wide range of objects. Through extensive experiments, we show our method achieves state-of-the-art performance on almost all open datasets, as Figure 1 shows." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "content": "To further improve the universality of diffusion-based generative method, massive amounts of high-quality training data is necessary. While many efforts have been made to build grasping datasets, they suffer from narrow data distribution[6, 17, 22], limited object categories [17, 41], and scalability issues [19]. In light of this, we dedicate substantial efforts to further enhancing the scale, diversity, and quality of the dexterous grasping datasets. We start by gathering available dexterous grasping data from multiple sources [15, 19, 40, 41, 47], including simulated data, real-captured data, and human hand grasping data, ensuring a diverse and comprehensive data distribution. We further scale up the dataset with a 'model-in-the-loop' strategy by using our grasping method and filtering method to continue generating high-quality data, inspired by the approach used in" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "SAM [14]. These efforts culminate in a very large-scale dexterous grasping dataset, DexGrasp Anything (DGA) Dataset with over 3.4 million grasping poses on more than 15k objects. Experimental results demonstrate that this new dataset provides substantial benefits to grasping methods within the community." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 324, + 144, + 529, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 144, + 529, + 156 + ], + "spans": [ + { + "bbox": [ + 324, + 144, + 529, + 156 + ], + "type": "text", + "content": "The main contribution of this work are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 157, + 553, + 264 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 157, + 553, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 157, + 553, + 204 + ], + "spans": [ + { + "bbox": [ + 314, + 157, + 553, + 204 + ], + "type": "text", + "content": "- We propose a physics-aware diffusion generator for dexterous grasping pose generation, which effectively integrates three key physical constraints into both the training and sampling phases of the diffusion model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 205, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 205, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 205, + 553, + 228 + ], + "type": "text", + "content": "- Our method achieves state-of-the-art performance on five dexterous grasping datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 228, + 553, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 264 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 264 + ], + "type": "text", + "content": "- We present a new high-quality dexterous grasping dataset, the largest and most diverse to date, significantly improving the generalization capability of existing methods." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 276, + 400, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 276, + 400, + 288 + ], + "spans": [ + { + "bbox": [ + 314, + 276, + 400, + 288 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 297, + 471, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 297, + 471, + 308 + ], + "spans": [ + { + "bbox": [ + 314, + 297, + 471, + 308 + ], + "type": "text", + "content": "2.1. Dexterous Grasp Generation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 316, + 553, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 553, + 398 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 553, + 398 + ], + "type": "text", + "content": "Dexterous Grasping serves as a fundamental component for various complex, human-like manipulation tasks, making it a long-standing area of research in robotics. Early works mainly use manually derived analytical methods [5, 18, 25, 28, 29, 35] that based on certain physical constraints. These methods are hindered by extremely large search space and complex optimization process, leading to low success rate." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 399, + 553, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 553, + 650 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 553, + 650 + ], + "type": "text", + "content": "Recently, data-driven approaches have emerged as a promising direction for dexterous grasping. Regression-based methods, such as [17, 45], often generate grasping poses with limited diversity, as they rely on direct predictions from input data and may fail to explore the full range of possible grasping configurations. In contrast, generative methods [11, 47] explicitly model the conditional probability distribution of dexterous hand poses given the target object, theoretically generating diverse poses. Diffusion model-based methods [10, 21, 51], in particular, stand out as a promising direction for more universal and robust robotic dexterous grasping for its exceptional capabilities in modeling various complex data distribution [9, 16, 20, 32, 46, 50] and generating diverse and highly realistic samples [27, 31, 33, 36]. However, existing diffusion model-based approaches are observed [43, 45] to yield sub-optimal grasping poses due to the absence of physical constraints during the training and sampling process. In this work, we delve into incorporating physical constraints into diffusion models to generate robust dexterous grasping poses for dexterous hands." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 659, + 469, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 659, + 469, + 671 + ], + "spans": [ + { + "bbox": [ + 314, + 659, + 469, + 671 + ], + "type": "text", + "content": "2.2. Dexterous Grasping Dataset" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "Collecting 3D dexterous grasping poses is notoriously expensive due to the complexity of hand structures. Most existing datasets are collected in simulators like" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22585" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 550, + 378 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 550, + 378 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 550, + 378 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 550, + 378 + ], + "type": "image", + "image_path": "a52f39c6157450f7a04fef57b6139b05d69308be4d5f156766f374526fb8383e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "lines": [ + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "text", + "content": "Figure 2. Overview of DexGrasp Anything. During training, object information is processed to extract combined semantic and spatial representations as conditioning inputs. At each noise training step, a clean-estimation of the noisy hand pose " + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\hat{h}_0" + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "text", + "content": " is derived from the predicted noise " + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\hat{\\varepsilon}_t" + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "text", + "content": ", with physics constraints guiding the noise distribution toward a cleaner, grasp-suitable distribution. During sampling, the Physics-Guided Sampler obtains the current observation " + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\hat{h}_0" + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "text", + "content": " at each denoising step and performs posterior sampling based on this observation. Physical constraints gradually guide the distribution toward a physically feasible grasp configuration " + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "inline_equation", + "content": "\\hat{h}_0^*" + }, + { + "bbox": [ + 55, + 386, + 555, + 453 + ], + "type": "text", + "content": ", enabling effective grasping of diverse objects." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 464, + 297, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 464, + 297, + 704 + ], + "spans": [ + { + "bbox": [ + 54, + 464, + 297, + 704 + ], + "type": "text", + "content": "GraspIt! [24] and IssacGym [23] through searching in the eigengrasp space [6, 17, 22] or optimization-based methods [15, 17, 41, 47] in parameter space. However, the search-based data often follow a narrow distribution due to the low-dimensional eigengrasp space, while the recent optimization-based data still suffer from relatively success rate and contained limit number of object categories. Some real-world datasets have been collected using teleoperation systems controlled by human operators. While these datasets capture human-like grasping poses, the data collection process is prohibitively expensive and difficult to scale up. Recent advances [30, 37, 38] have explored retargeting human hand poses to dexterous robotic hands, presenting a promising avenue for leveraging human hand data in robot hand training. Despite these advancements, existing datasets still face limitations in diversity, scalability, and quality. To address these challenges, we introduce the largest and most diverse dexterous grasping dataset to date and demonstrate that our dataset significantly enhances both the quality and diversity of generated dexterous" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 465, + 555, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 465, + 555, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 465, + 555, + 489 + ], + "type": "text", + "content": "grasping poses, providing substantial value to existing data-driven grasping generators." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 511, + 370, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 370, + 523 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 370, + 523 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 532, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 532, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 532, + 555, + 640 + ], + "type": "text", + "content": "We present DexGrasp Anything, an effective approach that enhances diffusion-based generators for dexterous grasping by integrating meticulously designed physical constraints. Figure 2 demonstrates an overview of our method. The following sections detail our problem formulation (Sec. 3.1), physics-aware constraints (Sec. 3.2), and the way to integrate constraints to the diffusion model's training (Sec. 3.3) and sampling processes (Sec. 3.4), and the LLM-enhanced object representation extraction module (Sec. 3.5)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 647, + 425, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 425, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 425, + 658 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 666, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 555, + 715 + ], + "type": "text", + "content": "Our goal is to generate high-quality grasping poses capable of securely holding a given object. Specifically, given a 3D object observation " + }, + { + "bbox": [ + 313, + 666, + 555, + 715 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 313, + 666, + 555, + 715 + ], + "type": "text", + "content": ", we aim to sample a diverse set of dexterous grasping poses " + }, + { + "bbox": [ + 313, + 666, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{h} = \\{h_i\\}_{i=1}^n" + }, + { + "bbox": [ + 313, + 666, + 555, + 715 + ], + "type": "text", + "content": " from a condi-" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22586" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "content": "tional distribution " + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "inline_equation", + "content": "P(h|O)" + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "content": ", where the dexterous pose " + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "inline_equation", + "content": "h = (\\theta, \\mathrm{R}, \\mathrm{t}) \\in \\mathbb{R}^{33}" + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "content": " consists of the dexterous hand articulation " + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^{24}" + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "content": " (for ShadowHand), the global rotation " + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "inline_equation", + "content": "R \\in \\mathrm{SO}(3)" + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "content": " and the global translation vector " + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "inline_equation", + "content": "t \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "spans": [ + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "type": "text", + "content": "The conditional distribution " + }, + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "type": "inline_equation", + "content": "P(h|O)" + }, + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "type": "text", + "content": " is modeled using a diffusion model " + }, + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}(h_t,O,t)" + }, + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "type": "text", + "content": ", which iteratively transforms an isotropic Gaussian distribution " + }, + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,\\mathrm{I})" + }, + { + "bbox": [ + 55, + 120, + 295, + 167 + ], + "type": "text", + "content": " into the desired data distribution:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 86, + 176, + 247, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 176, + 247, + 209 + ], + "spans": [ + { + "bbox": [ + 86, + 176, + 247, + 209 + ], + "type": "interline_equation", + "content": "P (h _ {0} | O) = P (h _ {T}) \\prod_ {t = 1} ^ {T} P (h _ {t - 1} | h _ {t}, O),", + "image_path": "9b68d67c11694dd462fa8da34ae8e673770eb071ccffe8aa605fda81aa857cbf.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 65, + 210, + 295, + 237 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 210, + 295, + 237 + ], + "spans": [ + { + "bbox": [ + 65, + 210, + 295, + 237 + ], + "type": "interline_equation", + "content": "P \\left(h _ {t - 1} \\mid h _ {t}, O\\right) = \\mathcal {N} \\left(h _ {t - 1}; \\mu_ {\\phi} \\left(h _ {t}, O, t\\right), \\Sigma_ {\\phi} \\left(h _ {t}, O, t\\right)\\right). \\tag {1}", + "image_path": "a74b350d33ad2ce4e93a23a95d1af69b59a1c71d4553b5ca33068b4cd3107850.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 247, + 175, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 175, + 259 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 175, + 259 + ], + "type": "text", + "content": "3.2. Physical Constraints" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 266, + 296, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 266, + 296, + 338 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 296, + 338 + ], + "type": "text", + "content": "Diffusion model-based methods often fail to reach optimal performance in the absence of appropriate physical constraints. To address this, we present three tailored physical constraint objectives for our DexGrasp Anything generator, enabling the production of universal and robust dexterous grasping poses for a wide range of objects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 338, + 296, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 296, + 486 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 296, + 486 + ], + "type": "text", + "content": "Surface Pulling Force [47] is crucial for ensuring grasp feasibility. It enforces proximity between the inner surface of the robotic phalanges (represented by sampled point clouds) and the object's surface. This guidance signal applies a pulling force only to points that are closer than a specified threshold, ensuring that the points on the inner surface of the fingers are pulled towards the object's surface when they are near, but does not affect points that are already at a sufficient distance. Compute the squared Euclidean distance for each inner surface point " + }, + { + "bbox": [ + 55, + 338, + 296, + 486 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{dis}}^{(i)}" + }, + { + "bbox": [ + 55, + 338, + 296, + 486 + ], + "type": "text", + "content": " to its nearest neighbor on the object surface: " + }, + { + "bbox": [ + 55, + 338, + 296, + 486 + ], + "type": "inline_equation", + "content": "d_{i} = \\min_{j} \\| p_{\\mathrm{dis}}^{(i)} - p_{\\mathrm{obj}}^{(j)} \\|^2" + }, + { + "bbox": [ + 55, + 338, + 296, + 486 + ], + "type": "text", + "content": ". We compute the surface pulling force as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 133, + 495, + 295, + 523 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 495, + 295, + 523 + ], + "spans": [ + { + "bbox": [ + 133, + 495, + 295, + 523 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {S P F}} = \\frac {\\sum_ {i \\in S} \\sqrt {d _ {i}}}{| S | + \\eta}, \\tag {2}", + "image_path": "ac9ab648e0fa6f4e7c3df8efd03a95b2216e0d0e463079ac014aab7a7a29d6e1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "type": "inline_equation", + "content": "S = \\{i|d_i < d_{\\mathrm{Threshold}}\\}" + }, + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "type": "text", + "content": " represents the set of points within the threshold distance and " + }, + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 55, + 532, + 295, + 567 + ], + "type": "text", + "content": " is a numerical stability constant." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "text", + "content": "External-penetration Repulsion Force [10] retains the spatial accuracy of hand-object interactions. It minimizes the undesired intersection between the hand and object point clouds by leveraging the signed distances. Given an object point cloud " + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "inline_equation", + "content": "P_{obj}" + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "text", + "content": " with surface normals " + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "inline_equation", + "content": "N_{obj}" + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "text", + "content": ", and a hand point cloud " + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "inline_equation", + "content": "P_{hand}" + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "text", + "content": ", we first compute the nearest neighbor distance between each point in " + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "inline_equation", + "content": "P_{hand}" + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "inline_equation", + "content": "P_{obj}" + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "inline_equation", + "content": "d_i = \\min_j \\| P_{hand}^{(i)} - P_{obj}^{(j)} \\|" + }, + { + "bbox": [ + 55, + 568, + 296, + 689 + ], + "type": "text", + "content": ". We then calculate the signed distance between the hand and object points using the object normals:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 698, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 698, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 104, + 698, + 295, + 715 + ], + "type": "interline_equation", + "content": "s _ {i} = \\operatorname {s i g n} \\left(\\left(P _ {o b j} ^ {(j)} - P _ {\\text {h a n d}} ^ {(i)}\\right) \\cdot N _ {o b j} ^ {(j)}\\right). \\tag {3}", + "image_path": "3dd105e351d1d72bf2498467c6553dc0186b8d7f0ad8ceb52655bfbde542f4fb.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 554, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 107 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 107 + ], + "type": "text", + "content": "Finally, the external-penetration repulsion force is defined as the maximum signed distance across all points in the batch, averaged over the batch size " + }, + { + "bbox": [ + 313, + 72, + 554, + 107 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 72, + 554, + 107 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 375, + 118, + 554, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 118, + 554, + 150 + ], + "spans": [ + { + "bbox": [ + 375, + 118, + 554, + 150 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {E R F}} = \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\max _ {i} \\left(s _ {i}, d _ {i}\\right). \\tag {4}", + "image_path": "0f87b16ccb25f14c54aaa2d54b0f5ca4afe0c2b14b26216926f9f7b633b26bf7.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "spans": [ + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "text", + "content": "Self-Penetration Repulsion Force [47] upholds the hand structural geometry. It addresses the issue of hand points intersecting with each other by enforcing a minimum distance between them. This ensures that the hand maintains a realistic, physically plausible shape without finger collisions. Given a set of hand points " + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{hand}}" + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "text", + "content": ", we calculate the pairwise Euclidean distances between all points: " + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "inline_equation", + "content": "d_{ij} = \\| P_{\\mathrm{hand}}^{(i)} - P_{\\mathrm{hand}}^{(j)} \\|" + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "text", + "content": ", A repulsion force is applied when " + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "inline_equation", + "content": "d_{ij}" + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "text", + "content": " is smaller than a threshold " + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{Threshold}}" + }, + { + "bbox": [ + 313, + 158, + 555, + 278 + ], + "type": "text", + "content": ", and the self-penetration repulsion force is defined as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 353, + 288, + 554, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 288, + 554, + 317 + ], + "spans": [ + { + "bbox": [ + 353, + 288, + 554, + 317 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {S R F}} = \\frac {1}{B} \\sum_ {i, j} \\max \\left(0, d _ {\\text {T h r e s h o l d}} - d _ {i j}\\right). \\tag {5}", + "image_path": "2e40361d3307253ccc2df86e94b49a2ff81dc71ddf78d479a1ae19ef63ee9cd4.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 325, + 449, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 325, + 449, + 338 + ], + "spans": [ + { + "bbox": [ + 314, + 325, + 449, + 338 + ], + "type": "text", + "content": "3.3. Physics-Aware Training" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 343, + 554, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 343, + 554, + 368 + ], + "spans": [ + { + "bbox": [ + 313, + 343, + 554, + 368 + ], + "type": "text", + "content": "Diffusion Models are typically trained with a simple mean-squared error (MSE) objectives:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 361, + 376, + 553, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 376, + 553, + 392 + ], + "spans": [ + { + "bbox": [ + 361, + 376, + 553, + 392 + ], + "type": "interline_equation", + "content": "L _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, x _ {0}, \\epsilon} [ \\| \\epsilon - \\epsilon_ {\\phi} (h _ {t}, t) \\| ^ {2} ], \\tag {6}", + "image_path": "bc6dcb044c2d25ab91f0399fa321eaca36312f52ab64ae5e0284c2c5b559b6fc.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "type": "text", + "content": " is a corrupted version of the original data " + }, + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "type": "inline_equation", + "content": "h_0" + }, + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "type": "text", + "content": ". The data corruption follows a fixed noise schedule " + }, + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "type": "inline_equation", + "content": "\\beta_t" + }, + { + "bbox": [ + 313, + 399, + 554, + 423 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 349, + 433, + 553, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 433, + 553, + 454 + ], + "spans": [ + { + "bbox": [ + 349, + 433, + 553, + 454 + ], + "type": "interline_equation", + "content": "q \\left(h _ {t} \\mid h _ {t - 1}\\right) = \\mathcal {N} \\left(h _ {t}; \\sqrt {1 - \\beta_ {t}} h _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {7}", + "image_path": "35840491479f9952e1265f5f3a3be8aac420901d2662145145a19bb23611909c.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 386, + 451, + 507, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 451, + 507, + 464 + ], + "spans": [ + { + "bbox": [ + 386, + 451, + 507, + 464 + ], + "type": "interline_equation", + "content": "h _ {t} = \\sqrt {1 - \\beta_ {t}} h _ {t - 1} + \\sqrt {\\beta_ {t}} \\epsilon_ {t}.", + "image_path": "908413ba4ac501794b0be0d48f6b0d407af3828e15f68928488a140d5de8d658.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "type": "text", + "content": "With " + }, + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\Pi_{i = 1}^{t}\\alpha_{i}" + }, + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "type": "text", + "content": ", the corruption process can be directly conditioned on " + }, + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "type": "inline_equation", + "content": "h_0" + }, + { + "bbox": [ + 313, + 474, + 554, + 498 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 355, + 506, + 553, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 506, + 553, + 528 + ], + "spans": [ + { + "bbox": [ + 355, + 506, + 553, + 528 + ], + "type": "interline_equation", + "content": "q \\left(h _ {t} \\mid h _ {0}\\right) = \\mathcal {N} \\left(h _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} h _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {8}", + "image_path": "91baf9bf31e92f3e948d02b04afed26d078df3b0774cb2fcd11d7014018ec958.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 382, + 524, + 493, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 524, + 493, + 536 + ], + "spans": [ + { + "bbox": [ + 382, + 524, + 493, + 536 + ], + "type": "interline_equation", + "content": "h _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} h _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\bar {\\epsilon} _ {t}.", + "image_path": "bd00186721631b2bc5155afbbb0c147c6f979c7401b1bf8fdda9580da18130c9.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 545, + 554, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 664 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 664 + ], + "type": "text", + "content": "Since the training objective " + }, + { + "bbox": [ + 313, + 545, + 554, + 664 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{simple}}" + }, + { + "bbox": [ + 313, + 545, + 554, + 664 + ], + "type": "text", + "content": " is essentially a reweighted variational lower bound on negative log likelihood, it does not incorporate any explicit supervision regarding physical constraints. As a result, diffusion models often perform sub-optimally when directly generating dexterous grasping parameters, as observed in previous works [43, 45]. To facilitate our diffusion generator in capturing physics priors during training, we introduce the Physics-Aware Training paradigm, which incorporates the tailored physical constraints outlined in Sec. 3.2." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 665, + 555, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 716 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 716 + ], + "type": "text", + "content": "The training objective involving only corrupted data " + }, + { + "bbox": [ + 313, + 665, + 555, + 716 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 313, + 665, + 555, + 716 + ], + "type": "text", + "content": " is not well-suited for incorporating physical constraints. Using the diffusion process defined in Eq. 8, the estimated sample: " + }, + { + "bbox": [ + 313, + 665, + 555, + 716 + ], + "type": "inline_equation", + "content": "\\hat{h_0}(h_t) = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}} (h_t - \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon_\\phi(h_t, O, t))" + }, + { + "bbox": [ + 313, + 665, + 555, + 716 + ], + "type": "text", + "content": " could" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22587" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": "serve as a good proxy for introducing physical constraint into the training process of a diffusion model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 96, + 295, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 96, + 295, + 133 + ], + "spans": [ + { + "bbox": [ + 54, + 96, + 295, + 133 + ], + "type": "text", + "content": "We define the physically-aware training objective " + }, + { + "bbox": [ + 54, + 96, + 295, + 133 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{PADG}}" + }, + { + "bbox": [ + 54, + 96, + 295, + 133 + ], + "type": "text", + "content": " as a linear combination of the standard mean-squared objective and multiple physical-constraint objectives:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 73, + 137, + 295, + 169 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 137, + 295, + 169 + ], + "spans": [ + { + "bbox": [ + 73, + 137, + 295, + 169 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {P A D G}} = L _ {\\text {s i m p l e}} \\left(h _ {t}\\right) + \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h _ {0}} \\left(h _ {t}\\right), \\epsilon_ {\\phi}\\right), \\tag {9}", + "image_path": "6e9257a0937ac7c959ed163343b1c1debc05b45c19d0e8aba04d0fb390d78a95.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "spans": [ + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{PA}_i}(\\hat{h_0}(h_t), \\epsilon_\\phi)" + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "text", + "content": " physical constraint and " + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "inline_equation", + "content": "\\alpha_i" + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "text", + "content": " is the corresponding weighting coefficient. The gradient is propagated to " + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "text", + "content": " through the estimated clean sample " + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "inline_equation", + "content": "h_0" + }, + { + "bbox": [ + 55, + 175, + 295, + 223 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 79, + 228, + 295, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 228, + 295, + 258 + ], + "spans": [ + { + "bbox": [ + 79, + 228, + 295, + 258 + ], + "type": "interline_equation", + "content": "\\frac {\\partial L _ {\\mathrm {P A D G}}}{\\partial h _ {t}} = \\frac {\\partial L _ {\\text {s i m p l e}}}{\\partial h _ {t}} + \\sum_ {i = 1} ^ {m} \\alpha_ {i} \\frac {\\partial L _ {\\mathrm {P A} _ {i}}}{\\partial \\hat {h _ {0}}} \\cdot \\frac {\\partial \\hat {h _ {0}}}{\\partial h _ {t}}. \\tag {10}", + "image_path": "e59af668a388040425c35881a3e5e59f28efd530c02ac45d4015f23c592946be.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 263, + 200, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 263, + 200, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 263, + 200, + 277 + ], + "type": "text", + "content": "3.4. Physics-Guided Sampling" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 282, + 296, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 282, + 296, + 354 + ], + "spans": [ + { + "bbox": [ + 55, + 282, + 296, + 354 + ], + "type": "text", + "content": "Leveraging the learned physics priors, the well-trained diffusion generator is capable of producing physically plausible dexterous grasping poses for a given object. The physical constraints can be further enhanced during the sampling process by employing advanced sampling techniques [1, 4, 7, 48]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 354, + 296, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 296, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 296, + 401 + ], + "type": "text", + "content": "Classifier guidance [4] has explored the use of a time-dependent classifier " + }, + { + "bbox": [ + 55, + 354, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t" + }, + { + "bbox": [ + 55, + 354, + 296, + 401 + ], + "type": "text", + "content": " to steer the diffusion model towards specific conditional distributions. The guidance can be approximated as an offset in the posterior mean:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 65, + 407, + 294, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 407, + 294, + 421 + ], + "spans": [ + { + "bbox": [ + 65, + 407, + 294, + 421 + ], + "type": "interline_equation", + "content": "\\tilde {\\mu} _ {\\phi} \\left(x _ {t}, t\\right) \\leftarrow \\mu_ {\\phi} \\left(x _ {t}, t\\right) + s \\Sigma_ {\\theta , t} \\nabla_ {x _ {t}} \\log \\left(\\mathcal {F} _ {t} (y, x _ {t})\\right), \\tag {11}", + "image_path": "bb202b97f3d4bfa3ff44ac8fd62bff2f32faded164855902006a3109086030c5.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "text", + "content": " is the guidance strength. By estimating " + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "inline_equation", + "content": "\\hat{x_0}" + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "text", + "content": ", the guidance signal can be extended from a time-dependent classifier " + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t(y,x_t)" + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "text", + "content": " to arbitrary objective functions " + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "inline_equation", + "content": "L(x_0)" + }, + { + "bbox": [ + 55, + 427, + 296, + 487 + ], + "type": "text", + "content": " on clean samples. It can be achieved by mapping the objective to a density-like function:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 132, + 491, + 294, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 491, + 294, + 506 + ], + "spans": [ + { + "bbox": [ + 132, + 491, + 294, + 506 + ], + "type": "interline_equation", + "content": "\\mathcal {F} \\left(x _ {0}\\right) = \\mathcal {Z} e ^ {- L \\left(x _ {0}\\right)}, \\tag {12}", + "image_path": "5b0489e17cb797cc60ae95cc52f90c7f8b2c92bd2349c786ebf3d3806453f16e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 512, + 295, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 512, + 295, + 536 + ], + "spans": [ + { + "bbox": [ + 55, + 512, + 295, + 536 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 512, + 295, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 55, + 512, + 295, + 536 + ], + "type": "text", + "content": " is a normalizing constant. We define the Physics-Guided Sampler as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 64, + 542, + 294, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 542, + 294, + 588 + ], + "spans": [ + { + "bbox": [ + 64, + 542, + 294, + 588 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\widetilde {\\mu} _ {\\phi} (h _ {t}, O, t) \\leftarrow \\mu_ {\\phi} (h _ {t}, O, t) \\\\ + s \\Sigma_ {\\phi , t} \\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {P A _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right), \\epsilon_ {t}\\right). \\tag {13} \\\\ \\end{array}", + "image_path": "bed2e42d4cbbb6e93de569a4398dab5f45dac6d20ec5fc3a310de91c7fdd8696.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 595, + 295, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 595, + 295, + 632 + ], + "spans": [ + { + "bbox": [ + 55, + 595, + 295, + 632 + ], + "type": "text", + "content": "To alleviate the estimation bias on " + }, + { + "bbox": [ + 55, + 595, + 295, + 632 + ], + "type": "inline_equation", + "content": "\\hat{h_0}" + }, + { + "bbox": [ + 55, + 595, + 295, + 632 + ], + "type": "text", + "content": ", we apply the Spherical Gaussian Constraint [48] with a weighted gradient direction in practice. This is expressed as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 94, + 637, + 294, + 663 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 637, + 294, + 663 + ], + "spans": [ + { + "bbox": [ + 94, + 637, + 294, + 663 + ], + "type": "interline_equation", + "content": "\\tilde {\\mu} _ {\\phi} \\left(h _ {t}, O, t\\right) \\leftarrow \\mu_ {\\phi} \\left(h _ {t}, O, t\\right) + r \\frac {d _ {m}}{\\| d _ {m} \\|}, \\tag {14}", + "image_path": "3c3119d72bb5b59f6c088af61e4a6f53a515e58ca95f6880078619793ee1d5ee.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 668, + 295, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 668, + 295, + 681 + ], + "spans": [ + { + "bbox": [ + 55, + 668, + 295, + 681 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 668, + 295, + 681 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{m}} = d_{\\mathrm{sample}} + g_r(d^* - d_{\\mathrm{sample}})" + }, + { + "bbox": [ + 55, + 668, + 295, + 681 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 668, + 295, + 681 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{sample}} = \\Sigma_{\\phi, t} \\epsilon" + }, + { + "bbox": [ + 55, + 668, + 295, + 681 + ], + "type": "text", + "content": " and:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 66, + 686, + 295, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 686, + 295, + 717 + ], + "spans": [ + { + "bbox": [ + 66, + 686, + 295, + 717 + ], + "type": "interline_equation", + "content": "d ^ {*} = - \\sqrt {n} \\Sigma_ {\\phi , t} \\frac {\\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right) , \\epsilon_ {t}\\right)}{\\| \\nabla_ {h _ {t}} \\sum_ {i = 1} ^ {m} \\alpha_ {i} L _ {\\mathrm {P A} _ {i}} \\left(\\hat {h} _ {0} \\left(h _ {t}\\right) , \\epsilon_ {t}\\right) \\|}. \\tag {15}", + "image_path": "c1a74394e2a26de130ac233a4e02af46f173dac9b8c2b5c1cfd54417674714d8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "type": "text", + "content": "Incorporating physics constraints during training helps guide the noise distribution toward a cleaner, grasp-suitable form. However, due to sparse supervision in the training phase, we leverage the reverse process during sampling to obtain " + }, + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "type": "inline_equation", + "content": "\\hat{h}_0" + }, + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "type": "text", + "content": " at each step, applying posterior sampling to iteratively refine the grasp configuration. This iterative refinement allows the Physics-Guided Sampler to progressively adjust " + }, + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "type": "inline_equation", + "content": "\\hat{h}_0" + }, + { + "bbox": [ + 313, + 72, + 554, + 216 + ], + "type": "text", + "content": " under physics constraints, ultimately steering the distribution toward a physically feasible grasp configuration. Through this distributional framework, our model effectively generalizes to diverse objects, demonstrating robustness and adaptability in grasping tasks." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 222, + 537, + 235 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 222, + 537, + 235 + ], + "spans": [ + { + "bbox": [ + 313, + 222, + 537, + 235 + ], + "type": "text", + "content": "3.5. LLM-enhanced Representation Extraction" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "spans": [ + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "text", + "content": "To accomplish robust dexterous grasp generation for a targeted object, we boost the traditional object representation by complementing the geometry object feature with semantic prior from powerful LLMs. We employ a Point Transformer[52] to encode object point clouds, producing an " + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "inline_equation", + "content": "N \\times C" + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "text", + "content": " feature vector, where " + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{N}" + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "text", + "content": " represents the number of groups defined by the Point Transformer. To enrich these features with abundant semantic prior from LLM, we utilize the prompt: \"I want to grasp a [object label]. First, provide its object category, then give a detailed description of its shape before making a successful grip.\" We then parse the response and encode each sentence using a pre-trained BERT-large-uncased model. We extract the [CLS] token from each sentence and apply max-pooling on them. This results in an " + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "inline_equation", + "content": "1 \\times C" + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "text", + "content": " semantic feature vector that includes the rich prior knowledge from the LLM. The concatenated " + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "inline_equation", + "content": "(N + 1) \\times C" + }, + { + "bbox": [ + 313, + 240, + 555, + 480 + ], + "type": "text", + "content": " feature matrix is subsequently integrated into the diffusion backbone through a cross-attention mechanism, enhancing the model's capacity to generate precise and contextually relevant grasping poses." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 314, + 489, + 369, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 489, + 369, + 502 + ], + "spans": [ + { + "bbox": [ + 314, + 489, + 369, + 502 + ], + "type": "text", + "content": "4. Dataset" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 509, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 555, + 653 + ], + "type": "text", + "content": "The quality, diversity and scale of datasets are crucial for advancing dexterous grasping research, especially for diffusion-based generative methods. Training on a broader data distribution enables models to learn richer and more adaptable grasping strategies for arbitrary object. To inspire potential of methods towards universal dexterous grasping, we have developed a comprehensive dataset that significantly exceeds existing dexterous grasping datasets in both size and diversity. In the following sections, we provide a detailed overview of the data construction process, present key statistics, and highlight the characteristics of our DexGrasp Anything (DGA) dataset." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 659, + 424, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 424, + 671 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 424, + 671 + ], + "type": "text", + "content": "4.1. Data Construction" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Our data construction process begins with curating existing datasets from diverse sources. We gather three simulated datasets [15, 41, 47], a real-world dataset [19] col" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22588" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 86, + 553, + 194 + ], + "blocks": [ + { + "bbox": [ + 133, + 71, + 476, + 82 + ], + "lines": [ + { + "bbox": [ + 133, + 71, + 476, + 82 + ], + "spans": [ + { + "bbox": [ + 133, + 71, + 476, + 82 + ], + "type": "text", + "content": "Table 1. Comparison of dexterous grasp datasets. Our dataset achieves the largest scale to date." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 86, + 553, + 194 + ], + "lines": [ + { + "bbox": [ + 57, + 86, + 553, + 194 + ], + "spans": [ + { + "bbox": [ + 57, + 86, + 553, + 194 + ], + "type": "table", + "html": "
    DatasetPublication YearHand TypeSim./Real#Grasps#Objects#Grasps per objectConstruction method
    GRAB [40]ECCV 2020MANOReal1.64M51>10KCapture
    DDGdata [17]RSS 2020ShadowHandSim.6.9k565-GraspIt!
    MultiDex [15]ICRA 2023ShadowHandSim.16K58300Optimization
    DexGraspNet [41]ICRA 2023ShadowHandSim.1.32M5,355>200Optimization
    UniDexGrasp [47]CVPR 2023ShadowHandSim.1.12M5,519>150Optimization
    GraspXL [49]ECCV 2024Diverse HandSim-500K-GraspXL
    RealDex [19]IJCAI 2024ShadowHandReal59K52>200Human Annotation
    Our datasetCVPR 2025ShadowHandReal+Sim.3.40M15,698>200DexGrasp Anything + Filter
    ", + "image_path": "ee9c83225ac4e1e937ba549e998a7daec85a4b961df12d22e6b262e6e1d99eb8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "spans": [ + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "type": "text", + "content": "lected by human operator, alongside GRAB [40], a largescale human hand dataset, to maximize data diversity and richness. Leveraging advancements in robot teleoperation systems like AnyTeleop [30], we retarget the human hand dataset GRAB to dexterous hand parameters, creating DexGRAB, and filter it to retain only frames with hand-object contact. Next, we examine all collected data within IsaacGym [23], applying strict conditions to ensure stability and contact integrity. Specifically, we enforce that (1) objects do not shift more than " + }, + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "type": "inline_equation", + "content": "2\\mathrm{cm}" + }, + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "type": "text", + "content": " in any direction under force and that (2) hand-object penetration remains below " + }, + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "type": "inline_equation", + "content": "10\\mathrm{mm}" + }, + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "type": "text", + "content": " and object-hand penetration remains below " + }, + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "type": "inline_equation", + "content": "1\\mathrm{mm}" + }, + { + "bbox": [ + 54, + 204, + 294, + 395 + ], + "type": "text", + "content": " following [41]. The detailed process for computing the penetration is provided in the supplementary materials. This rigorous filtering process guarantees consistent high quality across all data sources." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 396, + 295, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 295, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 295, + 613 + ], + "type": "text", + "content": "Training our physics-aware diffusion generator on this dataset leads to higher success rates, greater diversity, and faster generation speeds for zero-shot dexterous grasping on unseen objects. Acting as a data engine, our model facilitates further dataset expansion in a \"model-in-the-loop\" manner. We meticulously selected object meshes from the Objaverse [2, 3] dataset, with the goal of ensuring broad category coverage and maintaining an even distribution across these categories. To achieve this, we examined all objects within 18 chosen categories and ultimately selected 10,034 distinct objects, covering 6,994 unique tags in the Objaverse data configuration. We apply approximate convex decomposition [42] to each mesh to reduce complexity and ensure water-tightness. Our trained generator then iteratively produces dexterous grasp poses, which are filtered under the same stringent standards. Finally, we combine the curated and generated data to form a large-scale and diverse dataset, crafted to advance research in dexterous grasping." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 622, + 120, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 622, + 120, + 634 + ], + "spans": [ + { + "bbox": [ + 55, + 622, + 120, + 634 + ], + "type": "text", + "content": "4.2. Statistics" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 641, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 295, + 713 + ], + "type": "text", + "content": "We present a comparative analysis of key metrics between our dataset and other existing datasets in Table 1. Our DGA dataset comprises two main components: The first component DGA-curated includes approximately 0.88 million grasping poses across 5,664 distinct objects, curated from various existing and diverse data sources. The second com" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 328, + 204, + 542, + 310 + ], + "blocks": [ + { + "bbox": [ + 328, + 204, + 542, + 310 + ], + "lines": [ + { + "bbox": [ + 328, + 204, + 542, + 310 + ], + "spans": [ + { + "bbox": [ + 328, + 204, + 542, + 310 + ], + "type": "image", + "image_path": "f80f3ea959868375a6dffa9afc585e7d92a516aff4e5a9e328e8345aee817e23.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 316, + 555, + 371 + ], + "lines": [ + { + "bbox": [ + 313, + 316, + 555, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 555, + 371 + ], + "type": "text", + "content": "Figure 3. t-SNE visualization of the object features in our dataset compared to existing datasets. Each point represents an object, and different markers and colors are used to distinguish between datasets. For clarity, we randomly sample " + }, + { + "bbox": [ + 313, + 316, + 555, + 371 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 313, + 316, + 555, + 371 + ], + "type": "text", + "content": " objects from each dataset for visualization." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 382, + 554, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 382, + 554, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 382, + 554, + 467 + ], + "type": "text", + "content": "ponent DGA-generated is generated with our DexGrasp Anything generator from the Objaverse [2, 3] dataset, containing approximately 2.52 million grasping poses spanning 10,034 different objects, covering 6,994 unique tags. In total, our dataset features over 3.4 million grasping poses across 15,698 objects from diverse data distribution, supporting in-depth research into dexterous grasping." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 477, + 408, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 477, + 408, + 488 + ], + "spans": [ + { + "bbox": [ + 314, + 477, + 408, + 488 + ], + "type": "text", + "content": "4.3. Characteristics" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 497, + 554, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 497, + 554, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 554, + 556 + ], + "type": "text", + "content": "Our dataset is characterized by a high degree of diversity and comprehensiveness, aimed at capturing a wide range of object and pose variations to advance the performance of dexterous hands in complex real-world environment. The key characteristics of our dataset can be presented as follow:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 558, + 555, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 314, + 558, + 553, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 558, + 553, + 593 + ], + "spans": [ + { + "bbox": [ + 314, + 558, + 553, + 593 + ], + "type": "text", + "content": "- Large data scale. Our dataset features over 3.4M strictly-tested grasping poses, which is significantly larger than all previous datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 594, + 555, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 594, + 555, + 701 + ], + "spans": [ + { + "bbox": [ + 314, + 594, + 555, + 701 + ], + "type": "text", + "content": "- Diverse objects. Our dataset encompasses 15,698 objects from a wide range of categories and sources, ensuring a high level of diversity. In Figure 3, we present a t-SNE visualization comparing object features from our dataset with those from existing datasets, using features extracted by a pre-trained Point Transformer. Object features from our dataset spread much wider across the feature space, suggesting that our dataset captures a broader variety or unique features that not be as present in existing datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 701, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 701, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 314, + 701, + 553, + 714 + ], + "type": "text", + "content": "- Diverse grasping poses. The wide variety of objects" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 784, + 317, + 792 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 784, + 317, + 792 + ], + "spans": [ + { + "bbox": [ + 293, + 784, + 317, + 792 + ], + "type": "text", + "content": "22589" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 101, + 555, + 189 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": "Table 2. Performance comparison across different methods and datasets. Bold numbers indicate the best scores, while underlined numbers indicate the second-best scores. DexGrasp Anything (w/ LLM) achieves the highest or near-highest performance across most metrics." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 101, + 555, + 189 + ], + "lines": [ + { + "bbox": [ + 57, + 101, + 555, + 189 + ], + "spans": [ + { + "bbox": [ + 57, + 101, + 555, + 189 + ], + "type": "table", + "html": "
    Dataset MethodDexGraspNetUniDexGraspMultiDexRealDexDexGRAB
    Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑Suc.6↑Suc.1↑Pen.↓Div↑
    UniDexGrasp [47]33.970.131.90.1423.765.524.50.1421.647.513.50.0827.159.439.00.1120.855.837.40.08
    GraspTTA [11]18.667.824.50.1321.065.321.20.1030.362.819.00.1113.346.440.10.0914.451.051.40.10
    SceneDiffuser [10]26.666.931.00.1528.374.825.10.1569.885.614.60.2721.756.142.00.0939.185.041.10.12
    UGG [21]46.979.025.20.1446.083.224.50.1455.393.410.30.1232.763.434.40.1042.790.633.20.12
    Ours53.690.421.50.2254.890.818.90.2572.296.39.60.2334.671.223.10.1456.591.828.60.12
    Ours(w/LLM)57.590.617.80.2353.191.218.80.2379.198.111.40.2244.873.727.70.1357.992.730.40.13
    ", + "image_path": "3b30be4a98a8911bb3ac04a1c739c7e7af07bfadfde464f5f79d4f774674a286.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 209, + 296, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 209, + 296, + 269 + ], + "spans": [ + { + "bbox": [ + 63, + 209, + 296, + 269 + ], + "type": "text", + "content": "contributes to a diverse range of grasping poses. Extensive experimental results in Sec. 5.3 demonstrate that our dataset significantly enhances the diversity of outcomes from existing methods, while maintaining or even improving the grasping success rate." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 280, + 137, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 280, + 137, + 294 + ], + "spans": [ + { + "bbox": [ + 55, + 280, + 137, + 294 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 300, + 137, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 137, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 137, + 312 + ], + "type": "text", + "content": "5.1. Comparison" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 318, + 296, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 296, + 461 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 296, + 461 + ], + "type": "text", + "content": "Metrics. Following previous works [10], we assess the grasping success rate (Suc. 6/Suc. 1) and maximum penetration (Pen.) in millimeters to gauge the quality of generated poses. A grasping pose is considered successful if the object's displacement, when an external force is applied, is less than " + }, + { + "bbox": [ + 55, + 318, + 296, + 461 + ], + "type": "inline_equation", + "content": "2\\mathrm{cm}" + }, + { + "bbox": [ + 55, + 318, + 296, + 461 + ], + "type": "text", + "content": " in at least one (Suc. 1) or all (Suc. 6) of the six axis-aligned directions in a 3D coordinate system. Additionally, we evaluate the diversity using the mean standard deviation of the pose parameters (Div.) across successful grasps in millimeters. All poses are evaluated in the IssacGym [23] simulator with the same configuration used in [10]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 462, + 296, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 296, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 296, + 617 + ], + "type": "text", + "content": "Implementation Details. Following [10], we employ a U-Net [34] structure for our diffusion backbone. An object-conditioned Point Transformer [52] encoder handles the point clouds, injected into the diffusion model using a cross-attention mechanism. All point clouds are downsampled to 2048 points before encoding. Our model is implemented using the PyTorch [26] platform, optimized with the Adam [13] algorithm at a learning rate of 0.0001. We follow the official train-test split of all datasets. All the compared methods are trained and inferred following their official code implementations. Training and evaluation are carried out on a Linux server equipped with four NVIDIA Tesla A40 GPUs until convergence." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "content": "Results. Table 2 presents the quantitative comparisons. Our method, leveraging a physics-aware training paradigm and a physics-guided sampler, demonstrates superior performance in both pose quality (Suc. 1, Suc. 6, and Pen.) and diversity (Div.) compared to previous methods across all five benchmarks. Qualitative results, shown in Figure 4, further illustrate that our approach produces more accurate grasping poses, benefiting from the effective physical" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 249, + 555, + 330 + ], + "blocks": [ + { + "bbox": [ + 313, + 207, + 555, + 240 + ], + "lines": [ + { + "bbox": [ + 313, + 207, + 555, + 240 + ], + "spans": [ + { + "bbox": [ + 313, + 207, + 555, + 240 + ], + "type": "text", + "content": "Table 3. Ablation study on incorporating physical constraints during both training and sampling stages and the LLM module. The evaluation is conducted on the DexGraspNet dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 249, + 555, + 330 + ], + "lines": [ + { + "bbox": [ + 317, + 249, + 555, + 330 + ], + "spans": [ + { + "bbox": [ + 317, + 249, + 555, + 330 + ], + "type": "table", + "html": "
    SRFERFSPFLLMSuc.6 ↑Suc.1 ↑Pen. ↓Div ↑
    a26.666.931.00.15
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    MethodTest TrainDexGraspNetRealDex
    Suc.6 ↑Suc.1 ↑Pen. ↓Div ↑Suc.6 ↑Suc.1 ↑Pen. ↓Div ↑
    SceneDiffuserDexGraspNet26.666.931.00.1516.152.129.20.13
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    GraspTTADexGraspNet18.667.824.50.1325.564.831.60.11
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    DGA dataset49.185.926.20.2242.977.334.40.22
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    DGA dataset58.688.517.80.3853.484.422.40.32
    ", + "image_path": "9a8f4ccbbb9e81a19f09f3f596874123388d65c8b204fd12d9b7c46507e7088b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 257, + 296, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 257, + 296, + 390 + ], + "spans": [ + { + "bbox": [ + 54, + 257, + 296, + 390 + ], + "type": "text", + "content": "the testing set of the DexGraspNet dataset. The quantitative results are presented in Table 3, where where we incrementally add the three physical constraints and the LLM enhancement (lines a-e) and compare with a model that uses only physical-aware training, excluding the physical-guided sampler (line f). Qualitative results are shown in Figure 5, with additional samples provided in the supplementary materials. These analyses emphasize the crucial role of each physical constraint, the LLM enhancement, as well as the physics-aware training paradigm and physics-guided sampler in enhancing the system's overall performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 408, + 282, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 408, + 282, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 408, + 282, + 422 + ], + "type": "text", + "content": "5.3. Evaluation for DexGrasp Anything Dataset" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 430, + 296, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 430, + 296, + 502 + ], + "spans": [ + { + "bbox": [ + 55, + 430, + 296, + 502 + ], + "type": "text", + "content": "By gathering high-quality data from various existing sources and augmenting it with our physics-aware diffusion generator, we have constructed the largest and most diverse dexterous grasping dataset to date. This not only enhances the performance of our generator but also benefits other dexterous grasp generation methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 506, + 296, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 296, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 296, + 567 + ], + "type": "text", + "content": "Setup. We train our DexGrasp Anything generator, SceneDiffuser, UGG, and GraspTTA on the training sets of both the DexGraspNet and DexGrasp Anything datasets. We evaluate the models on the testing sets of DexGraspNet and RealDex datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 570, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 715 + ], + "type": "text", + "content": "Results. As shown in Table 4, our findings indicate that training on the DexGrasp Anything dataset significantly improves the diversity of the sampling results for DexGrasp Anything generator, UGG, SceneDiffuser and GraspTTA. This is achieved without compromising, and in some cases improving, the grasping success rate and penetration metrics. To further validate our approach, we provide a more comprehensive evaluation in the supplementary materials. The qualitative comparison results are illustrated in Figure 6. For a variety of target objects, models trained on the DGA dataset generate significantly more diverse grasping poses, while maintaining high-quality results." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 70, + 556, + 198 + ], + "blocks": [ + { + "bbox": [ + 317, + 70, + 556, + 198 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 556, + 198 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 556, + 198 + ], + "type": "image", + "image_path": "4dc85c6ab98431866c9eea689ab9dce9eb6bd58590a4b720094886d353a91228.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 203, + 555, + 237 + ], + "lines": [ + { + "bbox": [ + 313, + 203, + 555, + 237 + ], + "spans": [ + { + "bbox": [ + 313, + 203, + 555, + 237 + ], + "type": "text", + "content": "Figure 6. Visualization of cross-dataset evaluation results shown in Table 4. The top row shows models trained on DexGraspNet, while the bottom row displays models trained on our dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 257, + 555, + 347 + ], + "blocks": [ + { + "bbox": [ + 316, + 257, + 555, + 347 + ], + "lines": [ + { + "bbox": [ + 316, + 257, + 555, + 347 + ], + "spans": [ + { + "bbox": [ + 316, + 257, + 555, + 347 + ], + "type": "image", + "image_path": "67e2c4bba0cdf81afe0b171b791142bf78e1226409898006d122f3cfc7f78c13.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 354, + 523, + 365 + ], + "lines": [ + { + "bbox": [ + 345, + 354, + 523, + 365 + ], + "spans": [ + { + "bbox": [ + 345, + 354, + 523, + 365 + ], + "type": "text", + "content": "Figure 7. Real-world evaluation for our method." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 378, + 447, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 447, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 447, + 392 + ], + "type": "text", + "content": "5.4. Real-world Application" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 402, + 556, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 402, + 556, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 402, + 556, + 534 + ], + "type": "text", + "content": "Harnessing physics and semantic priors, and trained on our diverse, high-quality dataset, DexGrasp Anything is highly capable of producing robust and practicable grasping poses in real-world environments. To validate its performance, we deploy the model on a real ShadowHand robot, as shown in Figure 7. The pre-grasping motion sequence is generated following the approach in [19]. The real-world experiments demonstrate that our grasping motions are reasonable and stable for unseen real objects, proving the universality and practicability of our method. More video demos are available in the supplementary materials." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 557, + 392, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 392, + 570 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 392, + 570 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "We introduce DexGrasp Anything, a physics-aware diffusion generator designed for universal and robust dexterous grasp generation. It deeply incorporates three tailored physical constraints through a physics-aware training paradigm and a physics-guided sampler. Moreover, we present the largest and most diverse dataset for dexterous grasp generation to date. Extensive experiments demonstrate that our method and dataset significantly enhance the quality and diversity of dexterous grasp generation. We believe our contributions will pave the way for future advancements towards the universal robotic dexterous grasping." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "22591" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "text", + "content": "[1] Hyungjin Chung, Jeongsol Kim, Michael T. 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In Proceedings of" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22593" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + }, + { + "para_blocks": [], + "discarded_blocks": [ + { + "bbox": [ + 75, + 72, + 296, + 96 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 72, + 296, + 96 + ], + "spans": [ + { + "bbox": [ + 75, + 72, + 296, + 96 + ], + "type": "text", + "content": "the IEEE/CVF international conference on computer vision, pages 16259-16268, 2021. 5, 7" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22594" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_content_list.json b/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9c0b5acba65117b1014a2c644854987875a9f75c --- /dev/null +++ b/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_content_list.json @@ -0,0 +1,2152 @@ +[ + { + "type": "text", + "text": "DexHandDiff: Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation", + "text_level": 1, + "bbox": [ + 217, + 128, + 782, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhixuan Liang $^{1,2\\dagger}$ Yao Mu $^{1}$ Yixiao Wang $^{2}$ Tianxing Chen $^{1}$ Wenqi Shao $^{1}$ Wei Zhan $^{2}$ Masayoshi Tomizuka $^{2‡}$ Ping Luo $^{1‡}$ Mingyu Ding $^{2}$", + "bbox": [ + 174, + 202, + 816, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ The University of Hong Kong $^{2}$ University of California, Berkeley", + "bbox": [ + 225, + 243, + 772, + 263 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zxliang, ymu, pluo}@cs.hku.hk {yixiao_wang, wzhan, tomizuka, myding}@berkeley.edu", + "bbox": [ + 132, + 263, + 864, + 279 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://dexdiffuser.github.io/", + "bbox": [ + 346, + 282, + 643, + 296 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 332, + 326, + 348 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dexterous manipulation with contact-rich interactions is crucial for advanced robotics. While recent diffusion-based planning approaches show promise for simple manipulation tasks, they often produce unrealistic ghost states (e.g., the object automatically moves without hand contact) or lack adaptability when handling complex sequential interactions. In this work, we introduce DexHandDiff, an interaction-aware diffusion planning framework for adaptive dexterous manipulation. DexHandDiff models joint state-action dynamics through a dual-phase diffusion process which consists of pre-interaction contact alignment and post-contact goal-directed control, enabling goal-adaptive generalizable dexterous manipulation. Additionally, we incorporate dynamics model-based dual guidance and leverage large language models for automated guidance function generation, enhancing generalizability for physical interactions and facilitating diverse goal adaptation through language cues. Experiments on physical interaction tasks such as door opening, pen and block reorientation, object relocation, and hammer striking demonstrate DexHandDiff's effectiveness on goals outside training distributions, achieving over twice the average success rate (59.2% vs. 29.5%) compared to existing methods. Our framework achieves an average of 70.7% success rate on goal adaptive dexterous tasks, highlighting its robustness and flexibility in contact-rich manipulation.", + "bbox": [ + 88, + 364, + 483, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 789, + 220, + 805 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dexterous manipulation, a cornerstone of advanced robotics with applications from service robotics to industrial automation, remains a challenging problem despite advances", + "bbox": [ + 89, + 815, + 483, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9ccf48ea0dbce3216c66d3427366175d916b5e3b62dd222d75c711ed874ea3d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 332, + 681, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f5f2ba62f6e5b3e645c279221d4d17e42545f4777b031753480dbcd4ce8343dd.jpg", + "image_caption": [], + "image_footnote": [ + "Dreamed $s^{door}$ changes, but $s^{hand}$ not, causing ghost states and wrong actions" + ], + "bbox": [ + 521, + 455, + 683, + 515 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2a32d7f2f87f788c1c6a76c645c888aecb42e5f54583a6d8340870b16bd72fb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 332, + 898, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0b75eddbc381ec0893846ea7b41a76bde1f95d79d4077f5b47809a16403fecf2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 455, + 890, + 536 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6d115e028e2f9e81ae2ac973eec4619bd7c5fc3e0a32fce29a1617a8a9df8bab.jpg", + "image_caption": [ + "Figure 1. (a) Previous diffusers directly apply goal guidance to object states, which causes ghost states, where objects appear to move independently without hand contact-a physically impossible scenario. (b) DexHandDiff introduces contact guidance that jointly influences both hand/object states and hand actions, while maintaining tight state-action coupling. It prevents ghost states, and enables precise goal adaptation. (c) Quantitative comparisons with previous methods on goal-shifted interaction tasks." + ], + "image_footnote": [], + "bbox": [ + 516, + 537, + 903, + 665 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in reinforcement learning (RL) [2, 4, 8, 47, 52] and imitation learning [23, 34]. Recently, diffusion-based planning [1, 14, 24, 28] has emerged as a promising new representative of imitation learning, capable of learning intricate motion trajectories from demonstration data for smoother and more adaptable control. However, current diffusion approaches are primarily designed for simpler gripper-based", + "bbox": [ + 511, + 794, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "This work was done during Zhixuan's visit to UC Berkeley.", + "bbox": [ + 107, + 875, + 429, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\ddagger$ Corresponding authors.", + "bbox": [ + 109, + 887, + 240, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1745", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(one Degree of Freedom) manipulation tasks, focusing on either trajectory completion or action replay by reaching target positions sequentially. They fall short in dexterous hand manipulation requiring part-aware precise interaction and exhibiting rich contact dynamics through multi-finger control and in-hand adjustment.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "More specifically, existing diffusion on action models [14, 56] (i.e. models generating actions) excel in well-defined tasks but often lack generalizability in adapting to complex or new tasks with flexible interaction requirements. They necessitate continual data collection for new goal configurations even within the same dynamics, limiting their effectiveness in contact-rich interactions. In contrast, diffusion on state methods [1, 24, 37], including those adapted from video diffusion models for imitation learning [6, 16], will produce unrealistic \"ghost states\" in interaction tasks. As shown in Fig. 1 and Fig. 2, the visualizations are rendered by setting states frame by frame with predicted output from state-based methods, and show objects react independently of physical contact (e.g. drawers opening on their own before the manipulator reaches them), which cannot actually happen and would result in failure. This issue arises because the object states can't be directly controlled. Actions must first influence dexterous hand's states before impacting the object, revealing the importance of modeling state transitions for physics-driven interactions.", + "bbox": [ + 91, + 185, + 482, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Thus, we propose DexHandDiff, an interaction-aware diffusion model tailored for adaptive dexterous manipulation that exhibits goal shifts or cost function variations while maintaining similar dynamics. DexHandDiff models joint state-action dynamics that takes the state output to guide and constrain the action output with realistic physical behavior. A dynamics model-based dual guide is incorporated to maintain coherence with dynamics observed in training data. It addresses the action-state consistency challenge first identified in Diffuser [24] which however prioritized generated state over action, as shown in Fig. 1.", + "bbox": [ + 89, + 489, + 482, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, DexHandDiff adopts a goal-adaptive diffusion mechanism with dual-phase process. 1) At first, precontact phase, it guides the manipulator to align with the object's key contact point, such as a handle or the center of object, ensuring stable alignment before initiating physical interaction. 2) In the subsequent post-contact phase, it introduces joint guidance over both the manipulator and the object states, enabling fine-grained control to achieve the target state for the object. This sequential approach integrates both action diffusion that prevents premature influence on the object's state before contact, and state diffusion that ensures effective goal alignment throughout. By generating states and actions in an interaction-aware manner, DexHandDiff produces more coherent and realistic trajectories suited to complex tasks like tool using. Furthermore, to automate guidance function design, DexHandDiff intro", + "bbox": [ + 89, + 657, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "duces an approach using large language models in the text-to-reward paradigm, that can generalize across diverse goals and cost functions via language cues.", + "bbox": [ + 511, + 90, + 903, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct experiments on multiple dexterous manipulation tasks to evaluate DexHandDiff's effectiveness, covering both in-domain and goal-adaptability challenges, e.g., adapting to new goal \"door closing\" from \"90-degree door opening\" training data. Results with up to $70.0\\%$ success rate on the 30-degree door task (vs. the next best $16.7\\%$ for Diffusion Policy) and $46.7\\%$ on the hammer nail half-drive task (vs. the next best $33.3\\%$ for Decision Diffuser), confirm DexHandDiff's robustness and adaptability in capturing complex hand-object-environment interactions.", + "bbox": [ + 511, + 137, + 903, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, DexHandDiff advances adaptive dexterous manipulation by: 1) We propose the first interaction-aware, goal-adaptive diffusion planner for dexterous manipulation, modeling manipulator-object-environment dependencies to handle sequential tasks with complex state transitions. 2) By jointly modeling state-action behaviors with dynamics-based dual guidance and LLM-based interaction guidance, DexHandDiff sets a new standard for adaptive planning in dexterous manipulation and for the first time extends text-to-reward concepts to diffusers. 3) Experimental validation on diverse dexterous manipulation tasks, demonstrating its robustness and adaptability. DexHandDiff achieves over twice the average success rate of the next best method (59.2% vs. 29.5%) across goal-directed tasks.", + "bbox": [ + 511, + 289, + 903, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 517, + 663, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dexterous Manipulation. Dexterous manipulation [12, 13, 19, 20, 32, 40, 42, 45, 48, 50] with multi-fingered hands enables complex tasks in unstructured environments by mimicking human hand flexibility. Initially, traditional methods using trajectory optimization and precise dynamics models [36, 41], struggled with high-dimensional action spaces and contact-rich dynamics. This led to the adoption of reinforcement learning (RL) [10, 41, 52, 58] for handling complex, high-DOF (degree of freedom) interactions. However, RL requires extensive online exploration and carefully designed reward functions [11, 36] where inadequate reward shaping can hardly learn and it limits adaptability [55, 57]. Demonstration-based methods [57] reduce sample complexity, but they struggle to generalize across sequential, contact-rich tasks. Our DexHandDiff addresses these challenges by explicitly modeling hand-object-environment interactions, enabling goal-adaptive planning without intricate reward shaping, thus allowing for more efficient learning in complex, sequential tasks.", + "bbox": [ + 511, + 547, + 903, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion-based Planning Methods. Planning with diffusion models has become prominent in imitation learning for robotic manipulation [1, 9, 14, 24, 28-30, 37]. Classifier-guided methods [24, 28] used task-specific classifiers to", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1746", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "condition policies, while classifier-free ones integrated task variations within diffusion model [1]. However, classifier-free methods lack flexibility for zero-shot explicit conditioning tasks due to reliance on training data configurations. DexHandDiff addresses this by performing classifier-guided diffusion over both state and action spaces, enabling precise interaction and rich-contact dynamics planning for more realistic, complex and adaptable manipulation.", + "bbox": [ + 89, + 90, + 483, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LLM-based Robot Policy Code Generation. Recent works [7, 27, 35, 51] have demonstrated the potential of LLMs in generating executable code for robotics tasks. Code as Policies [27] showed LLMs can effectively translate high-level task descriptions into functional robot control programs. Eureka [33] and Text2Reward [54] further advanced this direction by generating crucial parameters or complete reward functions from language descriptions, demonstrating well-structured prompts with comprehensive environment information can enable reliable reward shaping. Our work extends this text-to-code paradigm to imitation learning through diffusers. DexHandDiff provides a natural interface for LLM code generation through its guidance function formulation, bridging the gap between task specification and behavioral policies to learn.", + "bbox": [ + 89, + 215, + 483, + 443 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 89, + 454, + 217, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Diffusion Model as Policy", + "text_level": 1, + "bbox": [ + 89, + 479, + 323, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We formulate the dexterous manipulation planning problem within the Markov Decision Process (MDP) framework [39], defined as $\\mathcal{M} = (\\mathcal{S},\\mathcal{A},\\mathcal{T},\\mathcal{R},\\gamma)$ . The objective is to find an optimal action sequence $a_{0:T}^{*}$ that satisfies:", + "bbox": [ + 89, + 500, + 483, + 563 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {a} _ {0: T} ^ {*} = \\underset {\\boldsymbol {a} _ {0: T}} {\\arg \\max } \\mathcal {J} (\\boldsymbol {s} _ {0}, \\boldsymbol {a} _ {0: T}) = \\underset {\\boldsymbol {a} _ {0: T}} {\\arg \\max } \\sum_ {t = 0} ^ {T} \\gamma^ {t} R (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}), \\\\ \\text {w h e r e s t a t e t r a n s i t i o n s f o l l o w} \\boldsymbol {s} _ {t + 1} = \\mathcal {T} (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}). \\end{array} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 563, + 478, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following [1, 24], we leverage diffusion models to address this planning problem by treating state and action trajectories $\\pmb{\\tau}$ as sequential data. The reverse process of diffusion learns to denoise trajectories from a standard normal distribution through conditional probability $p_{\\theta}(\\pmb{\\tau}^{i-1} \\mid \\pmb{\\tau}^i)$ . The model is trained to maximize the likelihood:", + "bbox": [ + 89, + 614, + 483, + 703 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0}\\right) = \\int p \\left(\\boldsymbol {\\tau} ^ {N}\\right) \\prod_ {i = 1} ^ {N} p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i - 1} \\mid \\boldsymbol {\\tau} ^ {i}\\right) \\mathrm {d} \\boldsymbol {\\tau} ^ {1: N}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 703, + 482, + 737 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with the optimization objective inspired by ELBO,", + "bbox": [ + 89, + 736, + 426, + 750 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta^ {*} = \\arg \\min _ {\\theta} - \\mathbb {E} _ {\\boldsymbol {\\tau} ^ {0}} \\left[ \\log p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0}\\right) \\right]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 753, + 482, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For practical implementation, we adopt the simplified surrogate loss [22] that focuses on predicting the noise term:", + "bbox": [ + 89, + 775, + 482, + 805 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d e n o i s e}} (\\theta) = \\mathbb {E} _ {i, \\boldsymbol {\\tau} ^ {0} \\sim q, \\epsilon \\sim \\mathcal {N}} [ | | \\epsilon - \\epsilon_ {\\theta} (\\boldsymbol {\\tau} ^ {i}, i) | | ^ {2} ]. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 809, + 480, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Classifier-free Conditional Diffusion Policy", + "text_level": 1, + "bbox": [ + 89, + 833, + 455, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To generate high-reward trajectories, classifier-free guidance [15] has been transferred from image to trajectory generation [1]. This approach incorporates guidance signals", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\pmb{y}(\\tau)$ directly in the noise prediction model by:", + "bbox": [ + 513, + 90, + 825, + 107 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\epsilon} = \\epsilon_ {\\theta} (\\boldsymbol {\\tau} ^ {i}, \\varnothing , i) + \\omega \\left(\\epsilon_ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i}, \\boldsymbol {y}, i\\right) - \\epsilon_ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i}, \\varnothing , i\\right)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 109, + 903, + 126 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\omega$ controls the guidance strength, and $\\varnothing$ denotes the absence of conditioning. During sampling, trajectories are generated with the predicted modified noise $\\hat{\\epsilon}$ .", + "bbox": [ + 511, + 131, + 903, + 176 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Classifier-guided Diffusion Policy", + "text_level": 1, + "bbox": [ + 513, + 185, + 805, + 200 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from classifier-free diffusion models that condition relying solely on implicit representations within the training data, classifier-guided approach, enables direct reward or goal conditioning through gradient-based guidance.", + "bbox": [ + 511, + 207, + 903, + 267 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For reward maximization, it introduces trajectory optimality $\\mathcal{O}_t$ at timestep $t$ , following a Bernoulli distribution where $p(\\mathcal{O}_t = 1) = \\exp (\\gamma^t\\mathcal{R}(\\boldsymbol {s}_t,\\boldsymbol {a}_t))$ . The diffusion process can be naturally extended to incorporate conditioning by sampling from perturbed distributions:", + "bbox": [ + 511, + 267, + 903, + 342 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) = p (\\boldsymbol {\\tau} \\mid \\mathcal {O} _ {1: T} = 1) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) p \\left(\\mathcal {O} _ {1: T} = 1 \\mid \\boldsymbol {\\tau}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 344, + 903, + 361 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Under Lipschitz conditions on $p(\\mathcal{O}_{1:T} \\mid \\tau^i)$ [17], the reverse diffusion process follows:", + "bbox": [ + 511, + 363, + 903, + 393 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i - 1} \\mid \\boldsymbol {\\tau} ^ {i}, \\mathcal {O} _ {1: T}\\right) \\approx \\mathcal {N} \\left(\\boldsymbol {\\tau} ^ {i - 1}; \\mu_ {\\theta} + \\alpha \\Sigma g, \\Sigma\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 395, + 903, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the guidance gradient $g$ is:", + "bbox": [ + 513, + 416, + 735, + 431 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} g = \\nabla_ {\\tau} \\log p (\\mathcal {O} _ {1: T} | \\tau) | _ {\\tau = \\mu_ {\\theta}} \\\\ = \\sum_ {t = 0} ^ {T} \\gamma^ {t} \\nabla_ {\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}} \\mathcal {R} (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}) | _ {(\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}) = \\mu_ {t}} = \\nabla_ {\\boldsymbol {\\tau}} \\mathcal {I} (\\mu_ {\\theta}). \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 433, + 903, + 493 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For discrete goal conditioned tasks, the constraint can be simplified by directly substituting conditional values at each diffusion timestep $i \\in \\{0,1,\\dots,N\\}$ .", + "bbox": [ + 511, + 494, + 903, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Analysis of Diffusion-based Planning Methods for Interaction-intensive Tasks", + "text_level": 1, + "bbox": [ + 511, + 551, + 903, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Current diffusion-based methods are widely adopted for robotic manipulation but reveal significant limitations when applied to dexterous, sequential interaction tasks. Table 1 provides an overview of prominent diffusion-based methods (including Diffuser [24], Decision Diffuser [1], Diffusion Policy [14] and our DexHandDiff), categorizing each by their conditioning approach, action generation method, and goal adaptability. In this section, we analyze these challenges across three key dimensions.", + "bbox": [ + 511, + 594, + 906, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Action-only Diffusion is Limited in Explicit State Conditioning. Existing diffusion on action models like Diffusion Policy (DP) [14], excel in providing precise, consistent action control, benefiting from extensive training data and bypassing errors from inverse kinematics. They yield high performance when training data is sufficient and diverse. However, for tasks requiring variant multi-stage goals, action-only diffusion lacks the flexibility to perform explicit state guidance at intermediate stages, like aligning hand and object state at pre-grasp stage, hurting the adaptability of the whole planner. For example, DP trained on", + "bbox": [ + 511, + 734, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1747", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/e3df7ffbdfcd84cf482d833de34051f794da24b261e5fbd81249538bde2b20cf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodDiffusion on State or ActionDiffusion Condition TypeAction Gen MethodGoal AdaptabilityNo Ghost StatesInteraction Aware
    Diffuser [24]StateClassifier-GuidedInverse Dyn✓××
    Decision Diffuser [1]StateClassifier-FreeInverse Dyn× (if diverse data, then ✓)××
    Diffusion Policy [14]ActionClassifier-FreeDirect× (if diverse data, then ✓)✓×
    DexHandDiff (Ours)State & ActionClassifier-GuidedDirect✓✓✓
    ", + "bbox": [ + 125, + 88, + 870, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Comparison of diffusion-based approaches for robot manipulation. Quantitative results on door-opening are shown in Sec. 6.", + "bbox": [ + 89, + 179, + 903, + 194 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "data with opening the door to 90 degrees hardly adapt to open 30 or 60 degrees.", + "bbox": [ + 89, + 205, + 482, + 236 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ghost States in State-only Diffusion for Sequential Interaction. While state-based diffusion models offer the advantage of flexible goal specification, it is only effective in fully actuated tasks where all degrees of freedom (DoF) are directly controllable, such as MuJoCo [24, 46], and gripper pick-and-place (requiring only end-effector position control) [1, 14] tasks. In such scenarios, all states of the system can be manipulated directly. However, in contact-rich interaction task where indirect control exists, such as striking a nail with a hammer using a dexterous hand, additional uncontrollable DoFs, like the hammer head and nail positions, must be changed through transitions from the states of the hand. Applying generation across all states, including those of objects beyond the hand, will result in unrealistic \"ghost states\" where objects appear to move independently of contact but actually cannot, as illustrated in Fig. 1 and Fig. 2.", + "bbox": [ + 89, + 239, + 483, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Classifier-free vs. Classifier-guided Adaptability. Classifier free diffusion models, valued for not requiring external classifiers, encode task variations directly within the model. This structure is effective for tasks with constraints in observed configurations, but with limited goal adaptability in zero-shot or new-task scenarios. For instance, in the push-T task, DP cannot directly adapt to new target positions due to the fixed goal in training data. In contrast, classifier-guided methods, such as ours, mitigate this limitation by offering adaptable, gradient-based guidance, enabling direct conditioning on new goals or rewards, enhancing flexibility across a range of tasks.", + "bbox": [ + 89, + 486, + 483, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Method", + "text_level": 1, + "bbox": [ + 89, + 681, + 181, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Interaction-aware Diffusion-based Planning", + "text_level": 1, + "bbox": [ + 89, + 707, + 465, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address these limitations, we propose DexHandDiff, an interaction-aware diffusion planning framework (Fig. 3), maintaining physical consistency and enabling flexible goal adaptation for dexterous manipulation.", + "bbox": [ + 89, + 729, + 483, + 790 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Joint State-Action Diffusion Model. Our approach builds upon classifier-guided diffusion policies. But we jointly diffuse over the concatenated state-action space $\\pmb{\\tau} = [(\\pmb{a}_0, \\pmb{s}_0), (\\pmb{a}_1, \\pmb{s}_1), \\dots, (\\pmb{a}_T, \\pmb{s}_T)]$ , where state $\\pmb{s}$ includes both hand (24 joint angles and 3 position offsets) and task-specific object states (i.e. door hinge angle, pen pose etc.), and action $\\pmb{a}$ represents changes in controllable states (only", + "bbox": [ + 89, + 794, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3da810fba5018dc1e91f01a3ab7adf6f8ef1470731083885f672d6b1fd4e1982.jpg", + "image_caption": [ + "Figure 2. Demonstration of ghost states on the pen reorientation task. The visualizations are rendered by setting predicted states frame by frame, which cannot actually happen and will lead to failure. The pen appears to autonomously rotate to the desired pose without any hand manipulation, and the fingers look like moving to grasp the pen at the last frame." + ], + "image_footnote": [], + "bbox": [ + 516, + 203, + 638, + 295 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cd3157ebce89c2e6c7796c2ae61d80a6972677c6bde42e19bd402891f01b8fc0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 650, + 203, + 767, + 295 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f0f4c3cea822c0e2e50889113aa496646eec453802a4038cce1b36f024f991c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 781, + 203, + 900, + 295 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "hand joints and positions).", + "bbox": [ + 511, + 388, + 691, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This design choice directly addresses the above mentioned limitations: (1) By including states in the diffusion process, we enable explicit state conditioning and goal specification, overcoming the limitations of action-only approaches; (2) By classifier-guided diffusion, we allow flexible goal adaptation without exhaustive training data; (3) By jointly modeling states and actions, we maintain their physical coupling and prevent ghost states through carefully designed guidance. With denoised states guiding the generated actions, we effectively balance the state conditioning and action precision.", + "bbox": [ + 511, + 404, + 905, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Extended Behavior Model and Energy Function. According to Eq. 6, the standard conditional diffusion follows:", + "bbox": [ + 511, + 574, + 905, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) p \\left(\\mathcal {O} _ {1: T} = 1 \\mid \\boldsymbol {\\tau}\\right) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) h (\\boldsymbol {\\tau}), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 609, + 903, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we generalize $p(\\mathcal{O}_{1:T} = 1\\mid \\tau)$ as a behavior model $h(\\tau)$ . Then we further generalize this formulation through a product of experts framework [21], where each expert represents a specific behavior model:", + "bbox": [ + 511, + 631, + 905, + 686 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) \\prod_ {i = 1} ^ {n} h _ {i} (\\boldsymbol {\\tau}). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 688, + 903, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From the energy function perspective, each behavior model encoding task-specific objectives or constraints is:", + "bbox": [ + 511, + 723, + 905, + 752 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {i} (\\boldsymbol {\\tau}, c) = \\frac {1}{\\int e ^ {- \\varepsilon_ {i} (\\boldsymbol {\\tau} , c)} d \\boldsymbol {\\tau}} e ^ {- \\varepsilon_ {i} (\\boldsymbol {\\tau}, c)}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 752, + 903, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\varepsilon_{i}(\\pmb{\\tau}, c)$ represents the energy function for the $i$ -th guidance objective, with $c$ denoting task-specific conditions. This formulation allows combining multiple objectives (e.g., reaching the target state while maintaining physical consistency) via their respective guidance functions.", + "bbox": [ + 511, + 784, + 905, + 858 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Under appropriate smoothness conditions, the guidance gradient $g$ in the reverse diffusion process (Eq. 7) can be decomposed as the sum of individual guidance gradients:", + "bbox": [ + 511, + 858, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1748", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8658e549fb027002ab91b80536332c2b2d659c38e5f94dafe6ccb261302f21ea.jpg", + "image_caption": [ + "Figure 3. Framework of DexHandDiff. DexHandDiff employs joint state-action diffusion with interaction-aware guidance. Before interaction (top middle), guidance aligns the hand to the object contact point. Upon contact (bottom middle), additional guidance steers both hand and object states towards the goal (\"&\" means state concatenation at input level), enforcing physical constraints and avoiding ghost states. A learned dynamics model further ensures consistency between states and actions. Our DexHandDiff utilizes extended behavior model to aggregate multiple condition terms to guide the diffusion process." + ], + "image_footnote": [], + "bbox": [ + 112, + 92, + 880, + 319 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng = \\nabla_ {\\boldsymbol {\\tau}} \\log \\prod_ {i = 1} ^ {n} h _ {i} (\\boldsymbol {\\tau}) = \\sum_ {i = 1} ^ {n} \\nabla_ {\\boldsymbol {\\tau}} \\log h _ {i} (\\boldsymbol {\\tau}) = - \\sum_ {i = 1} ^ {n} \\nabla_ {\\boldsymbol {\\tau}} \\varepsilon_ {i} (\\boldsymbol {\\tau}, c).\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 395, + 483, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This enables integration of multiple guidance signals, each addressing different aspects of the interaction task, while maintaining a coherent optimization objective.", + "bbox": [ + 89, + 431, + 483, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dynamics-aware Generation. A key challenge in joint state-action diffusion is maintaining consistency between generated states and actions [24]. Our method addresses this through a learned dynamics model trained on demonstration data, constraining state-action generation via additional loss in diffusion training and serving as a guide in inference. By penalizing state-action pairs that violate observed dynamics, this guidance ensures our model maintains both state conditioning benefits and action feasibility.", + "bbox": [ + 89, + 479, + 483, + 604 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\varepsilon_ {\\mathrm {d y n}} (\\boldsymbol {\\tau}) = \\left| \\boldsymbol {s} _ {t + 1} - \\mathcal {T} \\left(\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}\\right) \\right| ^ {2}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 607, + 480, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{T}(s, a)$ is a separately trained dynamics model to ensure physically plausible motion patterns.", + "bbox": [ + 89, + 625, + 482, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Manipulation after Contact Task Guidance. For manipulation after contact tasks such as door opening and tool using, DexHandDiff employs a dual-phase interaction approach that acknowledges the fundamentally different nature of interaction before and after contact establishment. The framework automatically determines the phase transition based on the distance between the palm position and the designated contact point on the object, applying a smooth transition mask to blend between phases.", + "bbox": [ + 89, + 659, + 482, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the pre-grasp phase, our method focuses on guiding the manipulator to stably align with the contact point while preventing premature object movement. We engineer two primary guidance components: 1) Alignment guidance $\\epsilon_{\\mathrm{align}}$ that directs the end-effector towards precise contact point while maintaining natural approaching trajectory; 2) Dynamics consistency guidance $\\epsilon_{\\mathrm{dyn}}$ .", + "bbox": [ + 89, + 795, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Upon establishing contact (determined by palm-object proximity), the post-grasp phase activates additional guidance mechanisms: 1) Goal-directed guidance $\\epsilon_{\\mathrm{succ}}$ that steers the coupled hand-object system towards target configurations; 2) Physical constraint guidance $\\epsilon_{\\mathrm{penalty}}$ that prevents unrealistic state changes (e.g., limiting per-step changes in both door hinge and latch angles); 3) Continued dynamics guidance $\\epsilon_{\\mathrm{dyn}}$ to maintain motion feasibility.", + "bbox": [ + 511, + 397, + 906, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, the guidance energy function follows,", + "bbox": [ + 531, + 517, + 856, + 531 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon = \\left\\{ \\begin{array}{l l} \\epsilon_ {\\text {p r e}} = \\epsilon_ {\\text {a l i g n}} + \\epsilon_ {\\text {d y n}} & \\text {i f} | \\boldsymbol {s} _ {\\text {h a n d}} - \\boldsymbol {s} _ {\\text {c o n t a c t}} | > \\delta_ {1} \\\\ \\epsilon_ {\\text {p o s t}} = \\epsilon_ {\\text {s u c c}} + \\epsilon_ {\\text {d y n}} + \\epsilon_ {\\text {p e n a l t y}} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 534, + 903, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s_{\\text{hand}}$ and $s_{\\text{contact}}$ represents the states of dexterous hand and object contact point (e.g. door latch, hammer handle etc.) respectively, and $\\delta_1$ is a small threshold. The separated design of grasp proposal guidance $(\\epsilon_{\\text{align}})$ and task achieving guidance $(\\epsilon_{\\text{succ}})$ mirrors successful policies in prior work [47, 52], effective for dexterous manipulation. Besides, the $\\epsilon_{\\text{penalty}}$ ensures continuous object state transitions, corresponding to", + "bbox": [ + 511, + 566, + 906, + 686 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nh _ {p e n a l t y} \\triangleq 1 - H \\left(\\left| s _ {o b j} ^ {t + 1} - s _ {o b j} ^ {t} \\right| - \\delta_ {2}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 689, + 903, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\delta_{2}$ is another small threshold and $H(\\cdot)$ is the Heaviside step function [49]. Then $\\epsilon_{\\mathrm{penalty}}$ can be obtained by applying Eq. 11, becoming a Dirac delta function that directly sets value when satisfying the constraints.", + "bbox": [ + 511, + 710, + 905, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In-hand Manipulation Task Guidance. For tasks primarily involving in-hand manipulation (e.g., pen spinning, object reorientation), where objects are typically already in hand or quickly transition to in-hand states, we employ a simplified single-phase guidance structure: 1) Goal state guidance $\\epsilon_{\\mathrm{succ}}$ for achieving target object configurations; 2) Active finger motion guidance to ensure realistic object manipulation; 3) Dynamics consistency guidance $\\epsilon_{\\mathrm{dyn}}$ to maintain physical plausibility; 4) Physical constraint guidance", + "bbox": [ + 511, + 773, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1749", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\epsilon_{\\mathrm{penalty}}$ that prevents unrealistic state changes.", + "bbox": [ + 89, + 92, + 390, + 106 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon = \\epsilon_ {\\text {g o a l}} + \\epsilon_ {\\text {f i n g e r}} + \\epsilon_ {\\text {d y n}} + \\epsilon_ {\\text {p e n a l t y}}. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 108, + 480, + 122 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Specially, we define the behavior model that encourages active finger involvement as,", + "bbox": [ + 89, + 125, + 482, + 151 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nh _ {\\text {f i n g e r}} (\\tau , t) = H \\left(\\left| \\boldsymbol {s} _ {\\text {f i n g e r - j o i n t s}} ^ {t + 1} - \\boldsymbol {s} _ {\\text {f i n g e r - j o i n t s}} ^ {t}\\right| - \\delta_ {3}\\right), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 152, + 482, + 170 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $s_{\\text{finger-joints}}^t$ is the state vector of all finger joints at planning step $t$ . $\\delta_3$ is the third small threshold. $H(\\cdot)$ is also the Heaviside step function. This specialized handling prevents unrealistic \"ghost states\", as discussed in Sec. 4.", + "bbox": [ + 89, + 172, + 482, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. LLM-Based Guidance Generation", + "text_level": 1, + "bbox": [ + 89, + 239, + 390, + 255 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The design of task-specific guidance functions for diffusion policies traditionally requires significant manual effort, particularly for diverse dexterous manipulation tasks. To address this challenge, we leverage a two-stage Large Language Model (LLM) process for automated guidance generation, adopting text-to-reward paradigm [33, 54].", + "bbox": [ + 89, + 262, + 482, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall Pipeline. First, we feed the LLM with a 6-part template (including function purpose, guidance structure, environment description, function prototype, task instruction and few-shot hints) and public documents on simulation environments [38, 41] to generate task-specific prompts. Then, the generated task prompts are queried to another LLM to write guidance function code. Only few-shot hints require specific refinement, reducing human trial-and-error times from about 20 (for hand-craft energy function design) to around 5 while maintaining DexHandDiff performance.", + "bbox": [ + 89, + 357, + 482, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Environment Description. Our approach employs a comprehensive Pythonic environment abstraction that captures the complete interaction system. It encapsulates detailed robot joint configurations, and object-environment specifications from public documents, enabling LLM to generate precise guidance functions that account for the full complexity of dexterous manipulation tasks.", + "bbox": [ + 89, + 511, + 482, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Other Details. As previous works [54], once the guidance function code is generated, we execute the code in interpreter. This step may give us valuable feedback, e.g., syntax errors and runtime errors. We utilize the feedback from code execution as a tool for ongoing refinement within the LLM. Besides, our approach uses few-shot hints instead of examples to allow the model to access relevant functions and best practices without direct examples. Each guidance component is normalized over the trajectory horizon to ensure balanced contributions across objectives while preserving their temporal structure. Detailed examples of prompts and generated guidance functions are shown in Appx. E.", + "bbox": [ + 89, + 621, + 482, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 89, + 815, + 220, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our DexHandDiff on five challenging dexterous manipulation tasks with four from Adroit Hand [41] and one from Shadow Hand environment [38]. Both environments feature a 24-joint Shadow Hand simulator with up to", + "bbox": [ + 89, + 839, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "30 degrees of freedom, designed to closely match the hardware setting [44]. Detailed explanations of the five tasks are provided in Appendix B. We use the expert demonstrations collected by teleoperation from D4RL [18] for Adroit tasks (Door, Hammer, Pen and Relocate). However, Shadow Hand environment does not provide demonstration data, so we employ TQC+HER [3, 26] to collect 5000 expert trajectories for the Block Rotate-Z task.", + "bbox": [ + 511, + 90, + 903, + 210 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Performance Comparisons on Goal Adaptability in Interaction-Aware Tasks", + "text_level": 1, + "bbox": [ + 511, + 224, + 903, + 255 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate DexHandDiff in the Door environment to test its goal adaptability across various target angles. Specifically, we require the planners to open the door to 30, 50, 70, 90 and 110 degrees, as well as close the door (reversal task). Note that the training data only includes 90-degree door-opening demonstrations. For some of these tasks, we adjust the environment settings, such as expanding the door's range of motion, to satisfy the evaluation requirements.", + "bbox": [ + 511, + 262, + 903, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare DexHandDiff with five baselines: two classifier-guided methods (Diffuser [24] with Goal Inpainting that sets discrete goal states, and Diffuser with Guided Sampling that leverages continuous gradients for fine control), two classifier-free methods (Decision Diffuser [1] and Diffusion Policy [14] that apply diffusion on states and actions respectively), and a variant of DexHandDiff (denoted DexHandDiff-disc.) that uses goal inpainting. To enhance classifier-free methods' learning of goal condition, we use the difference between the current door angle and target angle as the condition, rather than a fixed $90^{\\circ}$ target.", + "bbox": [ + 511, + 383, + 905, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results are shown in Tab. 2. Classifier-free methods perform well on the $90^{\\circ}$ task, but their success declines sharply on new target angles, indicating limited adaptability to out-of-distribution targets. Classifier-guided methods demonstrate moderate but consistent performance across goal-adaptive tasks yet their overall success rates remain suboptimal due to imprecise state-action relation modeling in the policy. Our DexHandDiff achieves consistently high success rates across nearly all tasks. The slightly lower performance $(90.0\\%)$ on the training task $(90^{\\circ})$ compared to classifier-free methods stems from our additional guidance for adaptation. When ablating this, DexHandDiff achieves $96.7 \\pm 4.7\\%$ success rate on Open $90^{\\circ}$ , which is a reasonable trade-off for better generalization. Averaging a $59.2\\%$ success rate, over twice that of the next best method $(29.5\\%)$ , DexHandDiff demonstrates robust adaptability across both in-domain and goal-adaptive scenarios.", + "bbox": [ + 511, + 551, + 905, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Besides, we also observe a trend that goals closer to the original training data don't have higher success rates than others. We suppose it's because when target angle is close to training, learned dynamics often override guidance. We observed 8 out of 14 failures in 30 tries in $70^{\\circ}$ task opened to $90^{\\circ}$ instead, supporting our hypothesis. This learned bias", + "bbox": [ + 511, + 810, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1750", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/594c1346e3ba81147643ad300bfa46351d827bd7c8431bfad40b6adec37adc8f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodConditionOpen 30°Open 50°Open 70°Open 90°Open 110°Close DoorAverage
    Diffuser [24]Goal Inpainting16.7 ±4.716.7 ±12.56.7 ±4.756.7 ±9.410.0 ±8.2017.8
    Diffuser [24]Guided Sampling10.0 ±8.226.7 ±17.010.0 ±4.763.3 ±18.76.7 ±9.460.0 ±8.229.5
    Decision Diffuser [1]Embedding03.3 ±4.716.7 ±4.7100 ±030.0 ±8.2025.0
    Diffusion Policy [14]Embedding16.7 ±4.73.3 ±4.713.3 ±12.5100 ±03.3 ±4.7022.8
    DexHandDiff-disc.Goal Inpainting46.7 ±4.713.3 ±9.453.3 ±4.720.0 ±8.26.7 ±4.7023.3
    DexHandDiff (Ours)Guided Sampling70.0 ±8.256.7 ±4.753.3 ±8.290.0 ±8.226.7 ±14.158.3 ±13.459.2
    ", + "bbox": [ + 96, + 88, + 898, + 212 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1b9e88c9eb023f1fdb5bb3e6792dfc21b62417f962ea30a88b2607b9eec5573b.jpg", + "table_caption": [ + "Table 2. Success rates (in %) of different diffusion-based approaches in Adroit Hand [41] environment. All models were trained on the Open $90^{\\circ}$ task only, and we test their adaptability to other task goals in Adroit Door environment. All results and standard deviation are calculated over 3 tries for 10 random seeds. Best methods and those within $5\\%$ of the best are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
    EnvironmentTaskDiffuser [24] (Inpaint)Conditional DP [1, 14]DexHandDiff (Ours)
    DoorOpen 90°56.7 ±9.4100 ±090.0 ±8.2
    DoorOpen 30°16.7 ±4.716.7 ±4.770.0 ±8.2
    PenFull Re-orientation10.0 ±080.0 ±8.293.3 ±4.7
    PenHalf-side Re-orientation3.3 ±4.723.3 ±9.440.0 ±8.2
    HammerNail Full Drive53.3 ±9.476.7 ±9.490.0 ±8.2
    HammerNail Half Drive23.3 ±12.533.3 ±4.746.7 ±12.5
    RelocateFull Relocation56.7 ±4.796.7 ±4.796.7 ±4.7
    RelocateHalf-side Relocation53.3 ±4.786.7 ±12.593.3 ±4.7
    Manipulate BlockRotate-Z36.7 ±12.540.0 ±8.250.0 ±8.2
    Manipulate BlockHalf-side Rotate-Z30.0 ±026.7 ±4.736.7 ±4.7
    Average34.058.070.7
    ", + "bbox": [ + 135, + 266, + 864, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "is harder to correct than for more distant angles.", + "bbox": [ + 89, + 498, + 406, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2. Evaluation on Various Dexterous Tasks", + "text_level": 1, + "bbox": [ + 89, + 527, + 426, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate the cross-task adaptability and goal-oriented performance of DexHandDiff, we test it across multiple dexterous manipulation tasks in Door, Pen, Hammer, Relocate and Block environments, as summarized in Tab. 3. In addition to the Door task, the Pen task involves aligning a pen to the specified orientation, with a particularly challenging goal-adaptability variant, Half-side Re-orientation, where training data includes only right-hemisphere orientations while test goals require left-hemisphere rotations. Similarly, the Block Rotate-Z and Object Relocation tasks have block's half-side variant trained on positive goal yaw angles but tested on negative ones and object's target right-half table training but left-half testing. The Nail Half Drive requires the hand to drive a nail and stop halfway before retracting, testing control precision for partial goals.", + "bbox": [ + 88, + 551, + 482, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare DexHandDiff with two baselines: Diffuser [24] (Inpainting), using classifier-guided goal inpainting as in the previous section, and Conditional DP [1, 14], a classifier-free approach with state diffusion for Door, Hammer and Relocate tasks while action diffusion for Pen and Block tasks, as modeling dynamics for these tasks are particularly challenging, making direct action generation more effective than state-based diffusion. As shown in Tab. 3,", + "bbox": [ + 88, + 779, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2b6c434e4f3daef184002a8ee63ecab5df46a275706bc0ca90bbc98cce1c21ce.jpg", + "table_caption": [ + "Table 3. Overall performance of dexterous manipulation with goal adaptability on multiple environments and tasks. We compare our method with one classifier-guided baseline and one classifier-free baseline. The results are calculated over 3 tries for 10 random seeds." + ], + "table_footnote": [], + "table_body": "
    Adapt TasksDoor 30°Door 70°Pen HalfHammer HalfRelocate Half
    Diffuser [24]4.194.035.234.015.48
    DexHandDiff2.922.382.762.413.22
    ", + "bbox": [ + 516, + 496, + 905, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Quantitative results for preventing ghost states over 3 tries. (Conditional DP is not included due to its action-only.)", + "bbox": [ + 511, + 544, + 906, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DexHandDiff consistently achieves superior results across both in-domain and goal-adaptive tasks. Although conditional DP demonstrates $23.3\\%$ on the challenging pen half-side re-orientation, leveraging the inherent multi-modality and anisotropy of diffusion models, DexHandDiff still performs better $(40.0\\%)$ . These results underscore DexHand-Diff's robustness and adaptability across a range of tasks, demonstrating generalization on familiar goals and novel configuration challenges.", + "bbox": [ + 511, + 580, + 905, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3. Validation for Preventing Ghost States", + "text_level": 1, + "bbox": [ + 511, + 724, + 844, + 741 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We measured $L2$ distance between predicted and simulated hand-object states (normalized per dimension for fair comparison) in Tab. 4. DexHandDiff nearly halves baseline's gap across tasks, illustrating its ghost-state reduction effect.", + "bbox": [ + 511, + 747, + 906, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.4. Ablation on LLM-based Guidance Generation", + "text_level": 1, + "bbox": [ + 511, + 818, + 903, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5 presents results for different guidance methods on goal adaptability tasks. All three methods are based on the same joint state-action diffusion model. The Human Craft approach reflects our above results with manually de", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1751", + "bbox": [ + 483, + 945, + 511, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/85eb9938c943cee8041b3d45e9505d1b92c85d3d2e5220055aef3ecc30abdd3f.jpg", + "image_caption": [ + "Train Data (Open $90^{\\circ}$ )" + ], + "image_footnote": [], + "bbox": [ + 101, + 99, + 196, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0158ea85d9f5c42f662519057715d24be2eab043c77c97ba7acc3ebc0c18f3fd.jpg", + "image_caption": [ + "Inference (Open $30^{\\circ}$ ) Door Held in Position, Hand Released" + ], + "image_footnote": [], + "bbox": [ + 207, + 99, + 300, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5492a9c680fb635ab19e97456fe96c959d6b814e983472e853bd081d866bf209.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 99, + 398, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9606e97c9b3f083a30f108de36038d13c62a2a031ff4f5eba0d8439bf32350f3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 403, + 99, + 496, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bf3787fa6350e2b29beff894f61ba11683d87f192bb2a5f7e2a711c08596fafa.jpg", + "image_caption": [ + "Train Data (Full Drive)" + ], + "image_footnote": [], + "bbox": [ + 506, + 99, + 601, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a25922428512f171f217550500abf6ee52e363e992f6fd3e93a83d4d5fee6e50.jpg", + "image_caption": [ + "Inference (Half Drive) Nail Partially Driven, Hammer Retracts" + ], + "image_footnote": [], + "bbox": [ + 612, + 99, + 704, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/65e8f920315abdd9825731aeda4a304c16852e1af3f4476b2f32b6e0ee22c22b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 99, + 800, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a3fca96da4e8fa913c4750fdd0bc66bf0bfab19bc371c0240228ec3dd2782d11.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 99, + 898, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2a5053cf6a7e6e90500f5c84d0a2834db84faa9e6e4cd3d052279cac75e49064.jpg", + "image_caption": [ + "Train Data (Right Half)", + "Figure 4. Visualization results of goal-adaptive tasks by DexHandDiff. For each task, training data sample (with orange stroke) is followed by inference on novel goals beyond the training data. In the Door task, DexHandDiff guides the door to new target angle $(30^{\\circ})$ and holds the door in position when the hand releases, which cannot be attained by simply truncating actions from $90^{\\circ}$ training data. DexHandDiff avoids ghost states and achieves better goal adaptability." + ], + "image_footnote": [], + "bbox": [ + 101, + 189, + 196, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d7ecf3d91618a4c0ff64e5b890bd834e6b75338d7f326c3d4417daafda67ab10.jpg", + "image_caption": [ + "Inference (Left Half Re-orientation) Pen Aligned, Hand Stabilizes" + ], + "image_footnote": [], + "bbox": [ + 207, + 189, + 300, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/39d9e780cf8896bb00fe02b2e08e91976492d0ebfe9f6d10da22650d9a97f77a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 189, + 398, + 260 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c3d828791e65967a033c721eb6fe3432e668e9c1828c7278fbc16e84b4a92e3d.jpg", + "image_caption": [ + "Train Data (Goal Yaw Positive)" + ], + "image_footnote": [], + "bbox": [ + 403, + 189, + 496, + 260 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5d65f461468bce02c644cbf427b67f7048155392ef0b4f2308d697389dbee3bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 189, + 602, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/501f830adde4f3af7d0907b69ffe4c59a6cd39eaa18cc3ac5084f45a8e9d73ba.jpg", + "image_caption": [ + "tive) Inference (Goal Yaw Negative)" + ], + "image_footnote": [], + "bbox": [ + 611, + 189, + 704, + 260 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b12dbfbcde407649e1cc763b55737dc5051171811018b90427e820428b9069b6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 189, + 800, + 260 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b0933282bd38a4a9b1f31fa3793c2c3b02e78afacd69ecd6dc2ddf9344200700.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 189, + 898, + 260 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/52552eb741d7d1b4b236b5b0e2ea39b8037b59683e8b575bc42ee7484743fbc5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    TaskNaïve GuideHuman CraftLLM Gen
    Door Open 30°070.0 ±8.240.0 ±8.2
    Pen Half-side Re-orien20.0 ±8.240.0 ±8.226.7 ±4.7
    Hammer Half Nail20.0 ±8.246.7 ±12.543.3 ±9.4
    ", + "bbox": [ + 94, + 327, + 483, + 390 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "signed guidance. LLM Gen generate guidance functions with Claude Sonnet 3.5 [5]. And Naïve Guide directly guides the object to the goal, corresponding to ghost-state existing baseline. Results indicate that both Human Craft and LLM Gen significantly outperform Naïve Guide across tasks, with Human Craft achieving the highest success rates.", + "bbox": [ + 89, + 415, + 483, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.5. Ablation Study of DexHandDiff Framework", + "text_level": 1, + "bbox": [ + 89, + 515, + 465, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We analyze the contribution of each component in DexHandDiff through ablation studies (Tab. 6), across multiple door-opening tasks (open $30^{\\circ}$ , $50^{\\circ}$ , $70^{\\circ}$ , and $90^{\\circ}$ ), using the same training checkpoint for fair comparison. The baseline Diffuser[24] uses a basic goal-guidance strategy, while Dyn-guide enhances it with dynamics guidance for better state-action consistency. Joint S&A adopts joint state-action denoising like DexHandDiff but retains naive goal guidance. DexHandDiff incorporates all components and achieves the highest success rate of $67.5\\%$ , significantly outperforming the other configurations and demonstrating the effectiveness of our full design.", + "bbox": [ + 89, + 537, + 483, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.6. Visualizations", + "text_level": 1, + "bbox": [ + 89, + 727, + 235, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We visualize the behavior of DexHandDiff across various goal-adaptive dexterous tasks in Fig. 4. DexHandDiff ensures realistic contact by aligning hands with contact points first using joint dynamics modeling, eliminating ghost states. Notably, for example, DexHandDiff guides the door to new target angle and holds the door steady when the hand releases, which cannot be achieved by policies trained with slicing $90^{\\circ}$ data. These results underscore DexHandDiff's ability to maintain physically realistic interactions while adapting to novel goals.", + "bbox": [ + 89, + 750, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/365738ed86e7f34c15fb3cdbf3154afedc4154750da4811245fe138d4c0b2cf1.jpg", + "table_caption": [ + "Table 5. Ablation study on LLM-based guidance generation." + ], + "table_footnote": [], + "table_body": "
    MethodGoal GuidanceDynamics GuideJoint State ActionInteract MechanismOverall SR
    No-guide××××24.1
    Diffuser [24]✓×××27.5
    Dyn-guide✓✓××27.5
    Joint S&A✓×✓×30.8
    Dyn+Joint✓✓✓×31.7
    DexHandDiff✓✓✓✓67.5
    ", + "bbox": [ + 516, + 327, + 905, + 424 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.7. Efficiency", + "text_level": 1, + "bbox": [ + 513, + 477, + 625, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We test the control frequency of DexHandDiff on an RTX 3090 with receding horizon set as 8 for all tasks except Door (32 instead). The control frequency are reported below.", + "bbox": [ + 511, + 500, + 906, + 546 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/02fa21b2fca728ba5442ae859647a54e7976c18f5d2e71583e3b7f3b26ec9f62.jpg", + "table_caption": [ + "Table 6. Ablation study on DexHandDiff framework. We report the average success rates (overall SR) on Adroit Door environment over open $30^{\\circ}$ , $50^{\\circ}$ , $70^{\\circ}$ and $90^{\\circ}$ tasks." + ], + "table_footnote": [], + "table_body": "
    TaskDoorPenHammerRelocateBlock
    Freq.5.04 Hz5.88 Hz5.86 Hz5.78 Hz6.92 Hz
    ", + "bbox": [ + 565, + 550, + 856, + 584 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Control command frequency over 10 tries.", + "bbox": [ + 547, + 587, + 869, + 601 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Besides, our lightweight model (3.96M params, 3.27 GFLOPS) can be further accelerated via DPM Solver++ [31] (4x speedup) and command interpolation (reaching $36\\mathrm{Hz}$ ), sufficient for real robot control.", + "bbox": [ + 511, + 604, + 905, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 676, + 633, + 693 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work presents DexHandDiff, an interaction-aware diffusion planner for adaptive dexterous manipulation. By modeling joint state-action dynamics and incorporating a dual-phase diffusion mechanism, it addresses action-state consistency issues, including the \"ghost state\" and generalization problems observed in previous diffusion methods. DexHandDiff's design enables it to handle intricate multi-contact interactions through a pre-contact alignment and a post-contact control. We believe its potential to advance the field toward diverse dexterous tasks while remaining grounded in real physics and dynamics.", + "bbox": [ + 511, + 702, + 906, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Future Work can investigate deployment with hand states sensed and object poses estimated by vision models.", + "bbox": [ + 511, + 869, + 905, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1752", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 91, + 90, + 256, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This paper is partially supported by the General Research Fund of Hong Kong No.17200622 and 17209324.", + "bbox": [ + 91, + 114, + 480, + 146 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 162, + 187, + 176 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Ajay, Yilun Du, Abhi Gupta, Joshua B Tenenbaum, Tommi S Jaakkola, and Pulkit Agrawal. 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IEEE, 2019. 2" + ], + "bbox": [ + 91, + 90, + 480, + 571 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1755", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_model.json b/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_model.json new file mode 100644 index 0000000000000000000000000000000000000000..695f1ae7bd1f8ea5c1581c3f4d83525dbc97b2de --- /dev/null +++ b/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_model.json @@ -0,0 +1,2818 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.218, + 0.13, + 0.783, + 0.177 + ], + "angle": 0, + "content": "DexHandDiff: Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.203, + 0.818, + 0.24 + ], + "angle": 0, + "content": "Zhixuan Liang\\(^{1,2\\dagger}\\) Yao Mu\\(^{1}\\) Yixiao Wang\\(^{2}\\) Tianxing Chen\\(^{1}\\) Wenqi Shao\\(^{1}\\) Wei Zhan\\(^{2}\\) Masayoshi Tomizuka\\(^{2‡}\\) Ping Luo\\(^{1‡}\\) Mingyu Ding\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.226, + 0.244, + 0.773, + 0.264 + ], + "angle": 0, + "content": "\\(^{1}\\)The University of Hong Kong \\(^{2}\\)University of California, Berkeley" + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.265, + 0.865, + 0.28 + ], + "angle": 0, + "content": "{zxliang, ymu, pluo}@cs.hku.hk {yixiao_wang, wzhan, tomizuka, myding}@berkeley.edu" + }, + { + "type": "text", + "bbox": [ + 0.348, + 0.283, + 0.645, + 0.297 + ], + "angle": 0, + "content": "https://dexdiffuser.github.io/" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.333, + 0.327, + 0.349 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.366, + 0.485, + 0.76 + ], + "angle": 0, + "content": "Dexterous manipulation with contact-rich interactions is crucial for advanced robotics. While recent diffusion-based planning approaches show promise for simple manipulation tasks, they often produce unrealistic ghost states (e.g., the object automatically moves without hand contact) or lack adaptability when handling complex sequential interactions. In this work, we introduce DexHandDiff, an interaction-aware diffusion planning framework for adaptive dexterous manipulation. DexHandDiff models joint state-action dynamics through a dual-phase diffusion process which consists of pre-interaction contact alignment and post-contact goal-directed control, enabling goal-adaptive generalizable dexterous manipulation. Additionally, we incorporate dynamics model-based dual guidance and leverage large language models for automated guidance function generation, enhancing generalizability for physical interactions and facilitating diverse goal adaptation through language cues. Experiments on physical interaction tasks such as door opening, pen and block reorientation, object relocation, and hammer striking demonstrate DexHandDiff's effectiveness on goals outside training distributions, achieving over twice the average success rate (59.2% vs. 29.5%) compared to existing methods. Our framework achieves an average of 70.7% success rate on goal adaptive dexterous tasks, highlighting its robustness and flexibility in contact-rich manipulation." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.79, + 0.222, + 0.806 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.816, + 0.484, + 0.862 + ], + "angle": 0, + "content": "Dexterous manipulation, a cornerstone of advanced robotics with applications from service robotics to industrial automation, remains a challenging problem despite advances" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.333, + 0.683, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.457, + 0.684, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.522, + 0.517, + 0.684, + 0.537 + ], + "angle": 0, + "content": "Dreamed \\(s^{door}\\) changes, but \\(s^{hand}\\) not, causing ghost states and wrong actions" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.333, + 0.899, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.457, + 0.892, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.538, + 0.904, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.669, + 0.907, + 0.78 + ], + "angle": 0, + "content": "Figure 1. (a) Previous diffusers directly apply goal guidance to object states, which causes ghost states, where objects appear to move independently without hand contact-a physically impossible scenario. (b) DexHandDiff introduces contact guidance that jointly influences both hand/object states and hand actions, while maintaining tight state-action coupling. It prevents ghost states, and enables precise goal adaptation. (c) Quantitative comparisons with previous methods on goal-shifted interaction tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.903 + ], + "angle": 0, + "content": "in reinforcement learning (RL) [2, 4, 8, 47, 52] and imitation learning [23, 34]. Recently, diffusion-based planning [1, 14, 24, 28] has emerged as a promising new representative of imitation learning, capable of learning intricate motion trajectories from demonstration data for smoother and more adaptable control. However, current diffusion approaches are primarily designed for simpler gripper-based" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.43, + 0.888 + ], + "angle": 0, + "content": "This work was done during Zhixuan's visit to UC Berkeley." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.241, + 0.9 + ], + "angle": 0, + "content": "\\(\\ddagger\\) Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.43, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1745" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "(one Degree of Freedom) manipulation tasks, focusing on either trajectory completion or action replay by reaching target positions sequentially. They fall short in dexterous hand manipulation requiring part-aware precise interaction and exhibiting rich contact dynamics through multi-finger control and in-hand adjustment." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.186, + 0.483, + 0.488 + ], + "angle": 0, + "content": "More specifically, existing diffusion on action models [14, 56] (i.e. models generating actions) excel in well-defined tasks but often lack generalizability in adapting to complex or new tasks with flexible interaction requirements. They necessitate continual data collection for new goal configurations even within the same dynamics, limiting their effectiveness in contact-rich interactions. In contrast, diffusion on state methods [1, 24, 37], including those adapted from video diffusion models for imitation learning [6, 16], will produce unrealistic \"ghost states\" in interaction tasks. As shown in Fig. 1 and Fig. 2, the visualizations are rendered by setting states frame by frame with predicted output from state-based methods, and show objects react independently of physical contact (e.g. drawers opening on their own before the manipulator reaches them), which cannot actually happen and would result in failure. This issue arises because the object states can't be directly controlled. Actions must first influence dexterous hand's states before impacting the object, revealing the importance of modeling state transitions for physics-driven interactions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.491, + 0.483, + 0.656 + ], + "angle": 0, + "content": "Thus, we propose DexHandDiff, an interaction-aware diffusion model tailored for adaptive dexterous manipulation that exhibits goal shifts or cost function variations while maintaining similar dynamics. DexHandDiff models joint state-action dynamics that takes the state output to guide and constrain the action output with realistic physical behavior. A dynamics model-based dual guide is incorporated to maintain coherence with dynamics observed in training data. It addresses the action-state consistency challenge first identified in Diffuser [24] which however prioritized generated state over action, as shown in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Specifically, DexHandDiff adopts a goal-adaptive diffusion mechanism with dual-phase process. 1) At first, precontact phase, it guides the manipulator to align with the object's key contact point, such as a handle or the center of object, ensuring stable alignment before initiating physical interaction. 2) In the subsequent post-contact phase, it introduces joint guidance over both the manipulator and the object states, enabling fine-grained control to achieve the target state for the object. This sequential approach integrates both action diffusion that prevents premature influence on the object's state before contact, and state diffusion that ensures effective goal alignment throughout. By generating states and actions in an interaction-aware manner, DexHandDiff produces more coherent and realistic trajectories suited to complex tasks like tool using. Furthermore, to automate guidance function design, DexHandDiff intro" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "duces an approach using large language models in the text-to-reward paradigm, that can generalize across diverse goals and cost functions via language cues." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.138, + 0.905, + 0.289 + ], + "angle": 0, + "content": "We conduct experiments on multiple dexterous manipulation tasks to evaluate DexHandDiff's effectiveness, covering both in-domain and goal-adaptability challenges, e.g., adapting to new goal \"door closing\" from \"90-degree door opening\" training data. Results with up to \\(70.0\\%\\) success rate on the 30-degree door task (vs. the next best \\(16.7\\%\\) for Diffusion Policy) and \\(46.7\\%\\) on the hammer nail half-drive task (vs. the next best \\(33.3\\%\\) for Decision Diffuser), confirm DexHandDiff's robustness and adaptability in capturing complex hand-object-environment interactions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.29, + 0.905, + 0.501 + ], + "angle": 0, + "content": "In summary, DexHandDiff advances adaptive dexterous manipulation by: 1) We propose the first interaction-aware, goal-adaptive diffusion planner for dexterous manipulation, modeling manipulator-object-environment dependencies to handle sequential tasks with complex state transitions. 2) By jointly modeling state-action behaviors with dynamics-based dual guidance and LLM-based interaction guidance, DexHandDiff sets a new standard for adaptive planning in dexterous manipulation and for the first time extends text-to-reward concepts to diffusers. 3) Experimental validation on diverse dexterous manipulation tasks, demonstrating its robustness and adaptability. DexHandDiff achieves over twice the average success rate of the next best method (59.2% vs. 29.5%) across goal-directed tasks." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.518, + 0.664, + 0.535 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.549, + 0.905, + 0.836 + ], + "angle": 0, + "content": "Dexterous Manipulation. Dexterous manipulation [12, 13, 19, 20, 32, 40, 42, 45, 48, 50] with multi-fingered hands enables complex tasks in unstructured environments by mimicking human hand flexibility. Initially, traditional methods using trajectory optimization and precise dynamics models [36, 41], struggled with high-dimensional action spaces and contact-rich dynamics. This led to the adoption of reinforcement learning (RL) [10, 41, 52, 58] for handling complex, high-DOF (degree of freedom) interactions. However, RL requires extensive online exploration and carefully designed reward functions [11, 36] where inadequate reward shaping can hardly learn and it limits adaptability [55, 57]. Demonstration-based methods [57] reduce sample complexity, but they struggle to generalize across sequential, contact-rich tasks. Our DexHandDiff addresses these challenges by explicitly modeling hand-object-environment interactions, enabling goal-adaptive planning without intricate reward shaping, thus allowing for more efficient learning in complex, sequential tasks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Diffusion-based Planning Methods. Planning with diffusion models has become prominent in imitation learning for robotic manipulation [1, 9, 14, 24, 28-30, 37]. Classifier-guided methods [24, 28] used task-specific classifiers to" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1746" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.213 + ], + "angle": 0, + "content": "condition policies, while classifier-free ones integrated task variations within diffusion model [1]. However, classifier-free methods lack flexibility for zero-shot explicit conditioning tasks due to reliance on training data configurations. DexHandDiff addresses this by performing classifier-guided diffusion over both state and action spaces, enabling precise interaction and rich-contact dynamics planning for more realistic, complex and adaptable manipulation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.216, + 0.484, + 0.444 + ], + "angle": 0, + "content": "LLM-based Robot Policy Code Generation. Recent works [7, 27, 35, 51] have demonstrated the potential of LLMs in generating executable code for robotics tasks. Code as Policies [27] showed LLMs can effectively translate high-level task descriptions into functional robot control programs. Eureka [33] and Text2Reward [54] further advanced this direction by generating crucial parameters or complete reward functions from language descriptions, demonstrating well-structured prompts with comprehensive environment information can enable reliable reward shaping. Our work extends this text-to-code paradigm to imitation learning through diffusers. DexHandDiff provides a natural interface for LLM code generation through its guidance function formulation, bridging the gap between task specification and behavioral policies to learn." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.455, + 0.218, + 0.472 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.48, + 0.325, + 0.496 + ], + "angle": 0, + "content": "3.1. Diffusion Model as Policy" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.501, + 0.484, + 0.564 + ], + "angle": 0, + "content": "We formulate the dexterous manipulation planning problem within the Markov Decision Process (MDP) framework [39], defined as \\(\\mathcal{M} = (\\mathcal{S},\\mathcal{A},\\mathcal{T},\\mathcal{R},\\gamma)\\). The objective is to find an optimal action sequence \\(a_{0:T}^{*}\\) that satisfies:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.564, + 0.48, + 0.616 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {a} _ {0: T} ^ {*} = \\underset {\\boldsymbol {a} _ {0: T}} {\\arg \\max } \\mathcal {J} (\\boldsymbol {s} _ {0}, \\boldsymbol {a} _ {0: T}) = \\underset {\\boldsymbol {a} _ {0: T}} {\\arg \\max } \\sum_ {t = 0} ^ {T} \\gamma^ {t} R (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}), \\\\ \\text {w h e r e s t a t e t r a n s i t i o n s f o l l o w} \\boldsymbol {s} _ {t + 1} = \\mathcal {T} (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}). \\end{array} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.616, + 0.484, + 0.704 + ], + "angle": 0, + "content": "Following [1, 24], we leverage diffusion models to address this planning problem by treating state and action trajectories \\(\\pmb{\\tau}\\) as sequential data. The reverse process of diffusion learns to denoise trajectories from a standard normal distribution through conditional probability \\(p_{\\theta}(\\pmb{\\tau}^{i-1} \\mid \\pmb{\\tau}^i)\\). The model is trained to maximize the likelihood:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.704, + 0.483, + 0.738 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0}\\right) = \\int p \\left(\\boldsymbol {\\tau} ^ {N}\\right) \\prod_ {i = 1} ^ {N} p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i - 1} \\mid \\boldsymbol {\\tau} ^ {i}\\right) \\mathrm {d} \\boldsymbol {\\tau} ^ {1: N}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.737, + 0.428, + 0.751 + ], + "angle": 0, + "content": "with the optimization objective inspired by ELBO," + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.754, + 0.483, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\theta^ {*} = \\arg \\min _ {\\theta} - \\mathbb {E} _ {\\boldsymbol {\\tau} ^ {0}} \\left[ \\log p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0}\\right) \\right]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.776, + 0.483, + 0.806 + ], + "angle": 0, + "content": "For practical implementation, we adopt the simplified surrogate loss [22] that focuses on predicting the noise term:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.81, + 0.482, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d e n o i s e}} (\\theta) = \\mathbb {E} _ {i, \\boldsymbol {\\tau} ^ {0} \\sim q, \\epsilon \\sim \\mathcal {N}} [ | | \\epsilon - \\epsilon_ {\\theta} (\\boldsymbol {\\tau} ^ {i}, i) | | ^ {2} ]. \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.834, + 0.456, + 0.85 + ], + "angle": 0, + "content": "3.2. Classifier-free Conditional Diffusion Policy" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To generate high-reward trajectories, classifier-free guidance [15] has been transferred from image to trajectory generation [1]. This approach incorporates guidance signals" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.092, + 0.826, + 0.108 + ], + "angle": 0, + "content": "\\(\\pmb{y}(\\tau)\\) directly in the noise prediction model by:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.111, + 0.905, + 0.127 + ], + "angle": 0, + "content": "\\[\n\\hat {\\epsilon} = \\epsilon_ {\\theta} (\\boldsymbol {\\tau} ^ {i}, \\varnothing , i) + \\omega \\left(\\epsilon_ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i}, \\boldsymbol {y}, i\\right) - \\epsilon_ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i}, \\varnothing , i\\right)\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.132, + 0.905, + 0.178 + ], + "angle": 0, + "content": "where \\(\\omega\\) controls the guidance strength, and \\(\\varnothing\\) denotes the absence of conditioning. During sampling, trajectories are generated with the predicted modified noise \\(\\hat{\\epsilon}\\)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.186, + 0.806, + 0.202 + ], + "angle": 0, + "content": "3.3. Classifier-guided Diffusion Policy" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.208, + 0.905, + 0.268 + ], + "angle": 0, + "content": "Different from classifier-free diffusion models that condition relying solely on implicit representations within the training data, classifier-guided approach, enables direct reward or goal conditioning through gradient-based guidance." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.268, + 0.905, + 0.343 + ], + "angle": 0, + "content": "For reward maximization, it introduces trajectory optimality \\(\\mathcal{O}_t\\) at timestep \\(t\\), following a Bernoulli distribution where \\(p(\\mathcal{O}_t = 1) = \\exp (\\gamma^t\\mathcal{R}(\\boldsymbol {s}_t,\\boldsymbol {a}_t))\\). The diffusion process can be naturally extended to incorporate conditioning by sampling from perturbed distributions:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.345, + 0.905, + 0.362 + ], + "angle": 0, + "content": "\\[\n\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) = p (\\boldsymbol {\\tau} \\mid \\mathcal {O} _ {1: T} = 1) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) p \\left(\\mathcal {O} _ {1: T} = 1 \\mid \\boldsymbol {\\tau}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.364, + 0.904, + 0.394 + ], + "angle": 0, + "content": "Under Lipschitz conditions on \\(p(\\mathcal{O}_{1:T} \\mid \\tau^i)\\) [17], the reverse diffusion process follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.396, + 0.905, + 0.415 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i - 1} \\mid \\boldsymbol {\\tau} ^ {i}, \\mathcal {O} _ {1: T}\\right) \\approx \\mathcal {N} \\left(\\boldsymbol {\\tau} ^ {i - 1}; \\mu_ {\\theta} + \\alpha \\Sigma g, \\Sigma\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.417, + 0.736, + 0.432 + ], + "angle": 0, + "content": "where the guidance gradient \\(g\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.434, + 0.905, + 0.494 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} g = \\nabla_ {\\tau} \\log p (\\mathcal {O} _ {1: T} | \\tau) | _ {\\tau = \\mu_ {\\theta}} \\\\ = \\sum_ {t = 0} ^ {T} \\gamma^ {t} \\nabla_ {\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}} \\mathcal {R} (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}) | _ {(\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}) = \\mu_ {t}} = \\nabla_ {\\boldsymbol {\\tau}} \\mathcal {I} (\\mu_ {\\theta}). \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.495, + 0.905, + 0.54 + ], + "angle": 0, + "content": "For discrete goal conditioned tasks, the constraint can be simplified by directly substituting conditional values at each diffusion timestep \\( i \\in \\{0,1,\\dots,N\\} \\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.552, + 0.905, + 0.586 + ], + "angle": 0, + "content": "4. Analysis of Diffusion-based Planning Methods for Interaction-intensive Tasks" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.595, + 0.907, + 0.732 + ], + "angle": 0, + "content": "Current diffusion-based methods are widely adopted for robotic manipulation but reveal significant limitations when applied to dexterous, sequential interaction tasks. Table 1 provides an overview of prominent diffusion-based methods (including Diffuser [24], Decision Diffuser [1], Diffusion Policy [14] and our DexHandDiff), categorizing each by their conditioning approach, action generation method, and goal adaptability. In this section, we analyze these challenges across three key dimensions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Action-only Diffusion is Limited in Explicit State Conditioning. Existing diffusion on action models like Diffusion Policy (DP) [14], excel in providing precise, consistent action control, benefiting from extensive training data and bypassing errors from inverse kinematics. They yield high performance when training data is sufficient and diverse. However, for tasks requiring variant multi-stage goals, action-only diffusion lacks the flexibility to perform explicit state guidance at intermediate stages, like aligning hand and object state at pre-grasp stage, hurting the adaptability of the whole planner. For example, DP trained on" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1747" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.126, + 0.089, + 0.872, + 0.177 + ], + "angle": 0, + "content": "
    MethodDiffusion on State or ActionDiffusion Condition TypeAction Gen MethodGoal AdaptabilityNo Ghost StatesInteraction Aware
    Diffuser [24]StateClassifier-GuidedInverse Dyn✓××
    Decision Diffuser [1]StateClassifier-FreeInverse Dyn× (if diverse data, then ✓)××
    Diffusion Policy [14]ActionClassifier-FreeDirect× (if diverse data, then ✓)✓×
    DexHandDiff (Ours)State & ActionClassifier-GuidedDirect✓✓✓
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.18, + 0.905, + 0.195 + ], + "angle": 0, + "content": "Table 1. Comparison of diffusion-based approaches for robot manipulation. Quantitative results on door-opening are shown in Sec. 6." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.206, + 0.483, + 0.237 + ], + "angle": 0, + "content": "data with opening the door to 90 degrees hardly adapt to open 30 or 60 degrees." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.24, + 0.484, + 0.482 + ], + "angle": 0, + "content": "Ghost States in State-only Diffusion for Sequential Interaction. While state-based diffusion models offer the advantage of flexible goal specification, it is only effective in fully actuated tasks where all degrees of freedom (DoF) are directly controllable, such as MuJoCo [24, 46], and gripper pick-and-place (requiring only end-effector position control) [1, 14] tasks. In such scenarios, all states of the system can be manipulated directly. However, in contact-rich interaction task where indirect control exists, such as striking a nail with a hammer using a dexterous hand, additional uncontrollable DoFs, like the hammer head and nail positions, must be changed through transitions from the states of the hand. Applying generation across all states, including those of objects beyond the hand, will result in unrealistic \"ghost states\" where objects appear to move independently of contact but actually cannot, as illustrated in Fig. 1 and Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.487, + 0.484, + 0.668 + ], + "angle": 0, + "content": "Classifier-free vs. Classifier-guided Adaptability. Classifier free diffusion models, valued for not requiring external classifiers, encode task variations directly within the model. This structure is effective for tasks with constraints in observed configurations, but with limited goal adaptability in zero-shot or new-task scenarios. For instance, in the push-T task, DP cannot directly adapt to new target positions due to the fixed goal in training data. In contrast, classifier-guided methods, such as ours, mitigate this limitation by offering adaptable, gradient-based guidance, enabling direct conditioning on new goals or rewards, enhancing flexibility across a range of tasks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.682, + 0.182, + 0.699 + ], + "angle": 0, + "content": "5. Method" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.708, + 0.466, + 0.725 + ], + "angle": 0, + "content": "5.1. Interaction-aware Diffusion-based Planning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.73, + 0.484, + 0.791 + ], + "angle": 0, + "content": "To address these limitations, we propose DexHandDiff, an interaction-aware diffusion planning framework (Fig. 3), maintaining physical consistency and enabling flexible goal adaptation for dexterous manipulation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Joint State-Action Diffusion Model. Our approach builds upon classifier-guided diffusion policies. But we jointly diffuse over the concatenated state-action space \\(\\pmb{\\tau} = [(\\pmb{a}_0, \\pmb{s}_0), (\\pmb{a}_1, \\pmb{s}_1), \\dots, (\\pmb{a}_T, \\pmb{s}_T)]\\), where state \\(\\pmb{s}\\) includes both hand (24 joint angles and 3 position offsets) and task-specific object states (i.e. door hinge angle, pen pose etc.), and action \\(\\pmb{a}\\) represents changes in controllable states (only" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.204, + 0.639, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.204, + 0.769, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.782, + 0.204, + 0.901, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.299, + 0.906, + 0.382 + ], + "angle": 0, + "content": "Figure 2. Demonstration of ghost states on the pen reorientation task. The visualizations are rendered by setting predicted states frame by frame, which cannot actually happen and will lead to failure. The pen appears to autonomously rotate to the desired pose without any hand manipulation, and the fingers look like moving to grasp the pen at the last frame." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.39, + 0.692, + 0.404 + ], + "angle": 0, + "content": "hand joints and positions)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.405, + 0.906, + 0.571 + ], + "angle": 0, + "content": "This design choice directly addresses the above mentioned limitations: (1) By including states in the diffusion process, we enable explicit state conditioning and goal specification, overcoming the limitations of action-only approaches; (2) By classifier-guided diffusion, we allow flexible goal adaptation without exhaustive training data; (3) By jointly modeling states and actions, we maintain their physical coupling and prevent ghost states through carefully designed guidance. With denoised states guiding the generated actions, we effectively balance the state conditioning and action precision." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.575, + 0.906, + 0.606 + ], + "angle": 0, + "content": "Extended Behavior Model and Energy Function. According to Eq. 6, the standard conditional diffusion follows:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.61, + 0.905, + 0.627 + ], + "angle": 0, + "content": "\\[\n\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) p \\left(\\mathcal {O} _ {1: T} = 1 \\mid \\boldsymbol {\\tau}\\right) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) h (\\boldsymbol {\\tau}), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.632, + 0.906, + 0.688 + ], + "angle": 0, + "content": "where we generalize \\(p(\\mathcal{O}_{1:T} = 1\\mid \\tau)\\) as a behavior model \\(h(\\tau)\\). Then we further generalize this formulation through a product of experts framework [21], where each expert represents a specific behavior model:" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.689, + 0.905, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) \\prod_ {i = 1} ^ {n} h _ {i} (\\boldsymbol {\\tau}). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.724, + 0.906, + 0.753 + ], + "angle": 0, + "content": "From the energy function perspective, each behavior model encoding task-specific objectives or constraints is:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.753, + 0.905, + 0.782 + ], + "angle": 0, + "content": "\\[\nh _ {i} (\\boldsymbol {\\tau}, c) = \\frac {1}{\\int e ^ {- \\varepsilon_ {i} (\\boldsymbol {\\tau} , c)} d \\boldsymbol {\\tau}} e ^ {- \\varepsilon_ {i} (\\boldsymbol {\\tau}, c)}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.785, + 0.906, + 0.859 + ], + "angle": 0, + "content": "where \\(\\varepsilon_{i}(\\pmb{\\tau}, c)\\) represents the energy function for the \\(i\\)-th guidance objective, with \\(c\\) denoting task-specific conditions. This formulation allows combining multiple objectives (e.g., reaching the target state while maintaining physical consistency) via their respective guidance functions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.859, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Under appropriate smoothness conditions, the guidance gradient \\( g \\) in the reverse diffusion process (Eq. 7) can be decomposed as the sum of individual guidance gradients:" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1748" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.093, + 0.881, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.32, + 0.907, + 0.391 + ], + "angle": 0, + "content": "Figure 3. Framework of DexHandDiff. DexHandDiff employs joint state-action diffusion with interaction-aware guidance. Before interaction (top middle), guidance aligns the hand to the object contact point. Upon contact (bottom middle), additional guidance steers both hand and object states towards the goal (\"&\" means state concatenation at input level), enforcing physical constraints and avoiding ghost states. A learned dynamics model further ensures consistency between states and actions. Our DexHandDiff utilizes extended behavior model to aggregate multiple condition terms to guide the diffusion process." + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.396, + 0.484, + 0.431 + ], + "angle": 0, + "content": "\\[\ng = \\nabla_ {\\boldsymbol {\\tau}} \\log \\prod_ {i = 1} ^ {n} h _ {i} (\\boldsymbol {\\tau}) = \\sum_ {i = 1} ^ {n} \\nabla_ {\\boldsymbol {\\tau}} \\log h _ {i} (\\boldsymbol {\\tau}) = - \\sum_ {i = 1} ^ {n} \\nabla_ {\\boldsymbol {\\tau}} \\varepsilon_ {i} (\\boldsymbol {\\tau}, c).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.432, + 0.484, + 0.478 + ], + "angle": 0, + "content": "This enables integration of multiple guidance signals, each addressing different aspects of the interaction task, while maintaining a coherent optimization objective." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.48, + 0.484, + 0.606 + ], + "angle": 0, + "content": "Dynamics-aware Generation. A key challenge in joint state-action diffusion is maintaining consistency between generated states and actions [24]. Our method addresses this through a learned dynamics model trained on demonstration data, constraining state-action generation via additional loss in diffusion training and serving as a guide in inference. By penalizing state-action pairs that violate observed dynamics, this guidance ensures our model maintains both state conditioning benefits and action feasibility." + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.608, + 0.482, + 0.624 + ], + "angle": 0, + "content": "\\[\n\\varepsilon_ {\\mathrm {d y n}} (\\boldsymbol {\\tau}) = \\left| \\boldsymbol {s} _ {t + 1} - \\mathcal {T} \\left(\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}\\right) \\right| ^ {2}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.625, + 0.483, + 0.656 + ], + "angle": 0, + "content": "where \\(\\mathcal{T}(s, a)\\) is a separately trained dynamics model to ensure physically plausible motion patterns." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.483, + 0.795 + ], + "angle": 0, + "content": "Manipulation after Contact Task Guidance. For manipulation after contact tasks such as door opening and tool using, DexHandDiff employs a dual-phase interaction approach that acknowledges the fundamentally different nature of interaction before and after contact establishment. The framework automatically determines the phase transition based on the distance between the palm position and the designated contact point on the object, applying a smooth transition mask to blend between phases." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.903 + ], + "angle": 0, + "content": "In the pre-grasp phase, our method focuses on guiding the manipulator to stably align with the contact point while preventing premature object movement. We engineer two primary guidance components: 1) Alignment guidance \\(\\epsilon_{\\mathrm{align}}\\) that directs the end-effector towards precise contact point while maintaining natural approaching trajectory; 2) Dynamics consistency guidance \\(\\epsilon_{\\mathrm{dyn}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.907, + 0.518 + ], + "angle": 0, + "content": "Upon establishing contact (determined by palm-object proximity), the post-grasp phase activates additional guidance mechanisms: 1) Goal-directed guidance \\(\\epsilon_{\\mathrm{succ}}\\) that steers the coupled hand-object system towards target configurations; 2) Physical constraint guidance \\(\\epsilon_{\\mathrm{penalty}}\\) that prevents unrealistic state changes (e.g., limiting per-step changes in both door hinge and latch angles); 3) Continued dynamics guidance \\(\\epsilon_{\\mathrm{dyn}}\\) to maintain motion feasibility." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.518, + 0.857, + 0.532 + ], + "angle": 0, + "content": "Therefore, the guidance energy function follows," + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.535, + 0.905, + 0.568 + ], + "angle": 0, + "content": "\\[\n\\epsilon = \\left\\{ \\begin{array}{l l} \\epsilon_ {\\text {p r e}} = \\epsilon_ {\\text {a l i g n}} + \\epsilon_ {\\text {d y n}} & \\text {i f} | \\boldsymbol {s} _ {\\text {h a n d}} - \\boldsymbol {s} _ {\\text {c o n t a c t}} | > \\delta_ {1} \\\\ \\epsilon_ {\\text {p o s t}} = \\epsilon_ {\\text {s u c c}} + \\epsilon_ {\\text {d y n}} + \\epsilon_ {\\text {p e n a l t y}} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.907, + 0.687 + ], + "angle": 0, + "content": "where \\( s_{\\text{hand}} \\) and \\( s_{\\text{contact}} \\) represents the states of dexterous hand and object contact point (e.g. door latch, hammer handle etc.) respectively, and \\( \\delta_1 \\) is a small threshold. The separated design of grasp proposal guidance \\( (\\epsilon_{\\text{align}}) \\) and task achieving guidance \\( (\\epsilon_{\\text{succ}}) \\) mirrors successful policies in prior work [47, 52], effective for dexterous manipulation. Besides, the \\( \\epsilon_{\\text{penalty}} \\) ensures continuous object state transitions, corresponding to" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.69, + 0.905, + 0.709 + ], + "angle": 0, + "content": "\\[\nh _ {p e n a l t y} \\triangleq 1 - H \\left(\\left| s _ {o b j} ^ {t + 1} - s _ {o b j} ^ {t} \\right| - \\delta_ {2}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.712, + 0.906, + 0.773 + ], + "angle": 0, + "content": "where \\(\\delta_{2}\\) is another small threshold and \\(H(\\cdot)\\) is the Heaviside step function [49]. Then \\(\\epsilon_{\\mathrm{penalty}}\\) can be obtained by applying Eq. 11, becoming a Dirac delta function that directly sets value when satisfying the constraints." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.775, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In-hand Manipulation Task Guidance. For tasks primarily involving in-hand manipulation (e.g., pen spinning, object reorientation), where objects are typically already in hand or quickly transition to in-hand states, we employ a simplified single-phase guidance structure: 1) Goal state guidance \\(\\epsilon_{\\mathrm{succ}}\\) for achieving target object configurations; 2) Active finger motion guidance to ensure realistic object manipulation; 3) Dynamics consistency guidance \\(\\epsilon_{\\mathrm{dyn}}\\) to maintain physical plausibility; 4) Physical constraint guidance" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1749" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.093, + 0.391, + 0.107 + ], + "angle": 0, + "content": "\\(\\epsilon_{\\mathrm{penalty}}\\) that prevents unrealistic state changes." + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.109, + 0.482, + 0.123 + ], + "angle": 0, + "content": "\\[\n\\epsilon = \\epsilon_ {\\text {g o a l}} + \\epsilon_ {\\text {f i n g e r}} + \\epsilon_ {\\text {d y n}} + \\epsilon_ {\\text {p e n a l t y}}. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.125, + 0.483, + 0.152 + ], + "angle": 0, + "content": "Specially, we define the behavior model that encourages active finger involvement as," + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.154, + 0.483, + 0.171 + ], + "angle": 0, + "content": "\\[\nh _ {\\text {f i n g e r}} (\\tau , t) = H \\left(\\left| \\boldsymbol {s} _ {\\text {f i n g e r - j o i n t s}} ^ {t + 1} - \\boldsymbol {s} _ {\\text {f i n g e r - j o i n t s}} ^ {t}\\right| - \\delta_ {3}\\right), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.173, + 0.483, + 0.234 + ], + "angle": 0, + "content": "where \\( s_{\\text{finger-joints}}^t \\) is the state vector of all finger joints at planning step \\( t \\). \\( \\delta_3 \\) is the third small threshold. \\( H(\\cdot) \\) is also the Heaviside step function. This specialized handling prevents unrealistic \"ghost states\", as discussed in Sec. 4." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.241, + 0.391, + 0.256 + ], + "angle": 0, + "content": "5.2. LLM-Based Guidance Generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.263, + 0.483, + 0.354 + ], + "angle": 0, + "content": "The design of task-specific guidance functions for diffusion policies traditionally requires significant manual effort, particularly for diverse dexterous manipulation tasks. To address this challenge, we leverage a two-stage Large Language Model (LLM) process for automated guidance generation, adopting text-to-reward paradigm [33, 54]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.509 + ], + "angle": 0, + "content": "Overall Pipeline. First, we feed the LLM with a 6-part template (including function purpose, guidance structure, environment description, function prototype, task instruction and few-shot hints) and public documents on simulation environments [38, 41] to generate task-specific prompts. Then, the generated task prompts are queried to another LLM to write guidance function code. Only few-shot hints require specific refinement, reducing human trial-and-error times from about 20 (for hand-craft energy function design) to around 5 while maintaining DexHandDiff performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.512, + 0.483, + 0.619 + ], + "angle": 0, + "content": "Environment Description. Our approach employs a comprehensive Pythonic environment abstraction that captures the complete interaction system. It encapsulates detailed robot joint configurations, and object-environment specifications from public documents, enabling LLM to generate precise guidance functions that account for the full complexity of dexterous manipulation tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.622, + 0.483, + 0.803 + ], + "angle": 0, + "content": "Other Details. As previous works [54], once the guidance function code is generated, we execute the code in interpreter. This step may give us valuable feedback, e.g., syntax errors and runtime errors. We utilize the feedback from code execution as a tool for ongoing refinement within the LLM. Besides, our approach uses few-shot hints instead of examples to allow the model to access relevant functions and best practices without direct examples. Each guidance component is normalized over the trajectory horizon to ensure balanced contributions across objectives while preserving their temporal structure. Detailed examples of prompts and generated guidance functions are shown in Appx. E." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.816, + 0.222, + 0.833 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We evaluate our DexHandDiff on five challenging dexterous manipulation tasks with four from Adroit Hand [41] and one from Shadow Hand environment [38]. Both environments feature a 24-joint Shadow Hand simulator with up to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "30 degrees of freedom, designed to closely match the hardware setting [44]. Detailed explanations of the five tasks are provided in Appendix B. We use the expert demonstrations collected by teleoperation from D4RL [18] for Adroit tasks (Door, Hammer, Pen and Relocate). However, Shadow Hand environment does not provide demonstration data, so we employ TQC+HER [3, 26] to collect 5000 expert trajectories for the Block Rotate-Z task." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.225, + 0.905, + 0.256 + ], + "angle": 0, + "content": "6.1. Performance Comparisons on Goal Adaptability in Interaction-Aware Tasks" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.263, + 0.905, + 0.384 + ], + "angle": 0, + "content": "We evaluate DexHandDiff in the Door environment to test its goal adaptability across various target angles. Specifically, we require the planners to open the door to 30, 50, 70, 90 and 110 degrees, as well as close the door (reversal task). Note that the training data only includes 90-degree door-opening demonstrations. For some of these tasks, we adjust the environment settings, such as expanding the door's range of motion, to satisfy the evaluation requirements." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.385, + 0.906, + 0.552 + ], + "angle": 0, + "content": "We compare DexHandDiff with five baselines: two classifier-guided methods (Diffuser [24] with Goal Inpainting that sets discrete goal states, and Diffuser with Guided Sampling that leverages continuous gradients for fine control), two classifier-free methods (Decision Diffuser [1] and Diffusion Policy [14] that apply diffusion on states and actions respectively), and a variant of DexHandDiff (denoted DexHandDiff-disc.) that uses goal inpainting. To enhance classifier-free methods' learning of goal condition, we use the difference between the current door angle and target angle as the condition, rather than a fixed \\(90^{\\circ}\\) target." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.906, + 0.809 + ], + "angle": 0, + "content": "The results are shown in Tab. 2. Classifier-free methods perform well on the \\(90^{\\circ}\\) task, but their success declines sharply on new target angles, indicating limited adaptability to out-of-distribution targets. Classifier-guided methods demonstrate moderate but consistent performance across goal-adaptive tasks yet their overall success rates remain suboptimal due to imprecise state-action relation modeling in the policy. Our DexHandDiff achieves consistently high success rates across nearly all tasks. The slightly lower performance \\((90.0\\%)\\) on the training task \\((90^{\\circ})\\) compared to classifier-free methods stems from our additional guidance for adaptation. When ablating this, DexHandDiff achieves \\(96.7 \\pm 4.7\\%\\) success rate on Open \\(90^{\\circ}\\), which is a reasonable trade-off for better generalization. Averaging a \\(59.2\\%\\) success rate, over twice that of the next best method \\((29.5\\%)\\), DexHandDiff demonstrates robust adaptability across both in-domain and goal-adaptive scenarios." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Besides, we also observe a trend that goals closer to the original training data don't have higher success rates than others. We suppose it's because when target angle is close to training, learned dynamics often override guidance. We observed 8 out of 14 failures in 30 tries in \\(70^{\\circ}\\) task opened to \\(90^{\\circ}\\) instead, supporting our hypothesis. This learned bias" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1750" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.098, + 0.089, + 0.9, + 0.213 + ], + "angle": 0, + "content": "
    MethodConditionOpen 30°Open 50°Open 70°Open 90°Open 110°Close DoorAverage
    Diffuser [24]Goal Inpainting16.7 ±4.716.7 ±12.56.7 ±4.756.7 ±9.410.0 ±8.2017.8
    Diffuser [24]Guided Sampling10.0 ±8.226.7 ±17.010.0 ±4.763.3 ±18.76.7 ±9.460.0 ±8.229.5
    Decision Diffuser [1]Embedding03.3 ±4.716.7 ±4.7100 ±030.0 ±8.2025.0
    Diffusion Policy [14]Embedding16.7 ±4.73.3 ±4.713.3 ±12.5100 ±03.3 ±4.7022.8
    DexHandDiff-disc.Goal Inpainting46.7 ±4.713.3 ±9.453.3 ±4.720.0 ±8.26.7 ±4.7023.3
    DexHandDiff (Ours)Guided Sampling70.0 ±8.256.7 ±4.753.3 ±8.290.0 ±8.226.7 ±14.158.3 ±13.459.2
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.216, + 0.907, + 0.259 + ], + "angle": 0, + "content": "Table 2. Success rates (in %) of different diffusion-based approaches in Adroit Hand [41] environment. All models were trained on the Open \\(90^{\\circ}\\) task only, and we test their adaptability to other task goals in Adroit Door environment. All results and standard deviation are calculated over 3 tries for 10 random seeds. Best methods and those within \\(5\\%\\) of the best are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.137, + 0.267, + 0.865, + 0.457 + ], + "angle": 0, + "content": "
    EnvironmentTaskDiffuser [24] (Inpaint)Conditional DP [1, 14]DexHandDiff (Ours)
    DoorOpen 90°56.7 ±9.4100 ±090.0 ±8.2
    DoorOpen 30°16.7 ±4.716.7 ±4.770.0 ±8.2
    PenFull Re-orientation10.0 ±080.0 ±8.293.3 ±4.7
    PenHalf-side Re-orientation3.3 ±4.723.3 ±9.440.0 ±8.2
    HammerNail Full Drive53.3 ±9.476.7 ±9.490.0 ±8.2
    HammerNail Half Drive23.3 ±12.533.3 ±4.746.7 ±12.5
    RelocateFull Relocation56.7 ±4.796.7 ±4.796.7 ±4.7
    RelocateHalf-side Relocation53.3 ±4.786.7 ±12.593.3 ±4.7
    Manipulate BlockRotate-Z36.7 ±12.540.0 ±8.250.0 ±8.2
    Manipulate BlockHalf-side Rotate-Z30.0 ±026.7 ±4.736.7 ±4.7
    Average34.058.070.7
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.46, + 0.907, + 0.487 + ], + "angle": 0, + "content": "Table 3. Overall performance of dexterous manipulation with goal adaptability on multiple environments and tasks. We compare our method with one classifier-guided baseline and one classifier-free baseline. The results are calculated over 3 tries for 10 random seeds." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.499, + 0.408, + 0.515 + ], + "angle": 0, + "content": "is harder to correct than for more distant angles." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.529, + 0.428, + 0.543 + ], + "angle": 0, + "content": "6.2. Evaluation on Various Dexterous Tasks" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.552, + 0.483, + 0.779 + ], + "angle": 0, + "content": "To evaluate the cross-task adaptability and goal-oriented performance of DexHandDiff, we test it across multiple dexterous manipulation tasks in Door, Pen, Hammer, Relocate and Block environments, as summarized in Tab. 3. In addition to the Door task, the Pen task involves aligning a pen to the specified orientation, with a particularly challenging goal-adaptability variant, Half-side Re-orientation, where training data includes only right-hemisphere orientations while test goals require left-hemisphere rotations. Similarly, the Block Rotate-Z and Object Relocation tasks have block's half-side variant trained on positive goal yaw angles but tested on negative ones and object's target right-half table training but left-half testing. The Nail Half Drive requires the hand to drive a nail and stop halfway before retracting, testing control precision for partial goals." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.78, + 0.483, + 0.901 + ], + "angle": 0, + "content": "We compare DexHandDiff with two baselines: Diffuser [24] (Inpainting), using classifier-guided goal inpainting as in the previous section, and Conditional DP [1, 14], a classifier-free approach with state diffusion for Door, Hammer and Relocate tasks while action diffusion for Pen and Block tasks, as modeling dynamics for these tasks are particularly challenging, making direct action generation more effective than state-based diffusion. As shown in Tab. 3," + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.497, + 0.906, + 0.542 + ], + "angle": 0, + "content": "
    Adapt TasksDoor 30°Door 70°Pen HalfHammer HalfRelocate Half
    Diffuser [24]4.194.035.234.015.48
    DexHandDiff2.922.382.762.413.22
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.545, + 0.907, + 0.573 + ], + "angle": 0, + "content": "Table 4. Quantitative results for preventing ghost states over 3 tries. (Conditional DP is not included due to its action-only.)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.581, + 0.906, + 0.717 + ], + "angle": 0, + "content": "DexHandDiff consistently achieves superior results across both in-domain and goal-adaptive tasks. Although conditional DP demonstrates \\(23.3\\%\\) on the challenging pen half-side re-orientation, leveraging the inherent multi-modality and anisotropy of diffusion models, DexHandDiff still performs better \\((40.0\\%)\\). These results underscore DexHand-Diff's robustness and adaptability across a range of tasks, demonstrating generalization on familiar goals and novel configuration challenges." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.726, + 0.845, + 0.742 + ], + "angle": 0, + "content": "6.3. Validation for Preventing Ghost States" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.748, + 0.907, + 0.81 + ], + "angle": 0, + "content": "We measured \\( L2 \\) distance between predicted and simulated hand-object states (normalized per dimension for fair comparison) in Tab. 4. DexHandDiff nearly halves baseline's gap across tasks, illustrating its ghost-state reduction effect." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.905, + 0.833 + ], + "angle": 0, + "content": "6.4. Ablation on LLM-based Guidance Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Table 5 presents results for different guidance methods on goal adaptability tasks. All three methods are based on the same joint state-action diffusion model. The Human Craft approach reflects our above results with manually de" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.513, + 0.957 + ], + "angle": 0, + "content": "1751" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.103, + 0.091, + 0.203, + 0.1 + ], + "angle": 0, + "content": "Train Data (Open \\(90^{\\circ}\\))" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.101, + 0.197, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.091, + 0.479, + 0.1 + ], + "angle": 0, + "content": "Inference (Open \\(30^{\\circ}\\)) Door Held in Position, Hand Released" + }, + { + "type": "image", + "bbox": [ + 0.209, + 0.101, + 0.301, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.101, + 0.399, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.101, + 0.497, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.091, + 0.605, + 0.099 + ], + "angle": 0, + "content": "Train Data (Full Drive)" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.101, + 0.602, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.621, + 0.091, + 0.891, + 0.099 + ], + "angle": 0, + "content": "Inference (Half Drive) Nail Partially Driven, Hammer Retracts" + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.101, + 0.705, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.101, + 0.802, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.101, + 0.899, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.096, + 0.18, + 0.199, + 0.189 + ], + "angle": 0, + "content": "Train Data (Right Half)" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.19, + 0.197, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.18, + 0.492, + 0.189 + ], + "angle": 0, + "content": "Inference (Left Half Re-orientation) Pen Aligned, Hand Stabilizes" + }, + { + "type": "image", + "bbox": [ + 0.209, + 0.19, + 0.301, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.19, + 0.399, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.19, + 0.497, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.18, + 0.631, + 0.19 + ], + "angle": 0, + "content": "Train Data (Goal Yaw Positive)" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.19, + 0.603, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.612, + 0.181, + 0.77, + 0.19 + ], + "angle": 0, + "content": "tive) Inference (Goal Yaw Negative)" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.19, + 0.705, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.19, + 0.802, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.19, + 0.899, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.266, + 0.907, + 0.322 + ], + "angle": 0, + "content": "Figure 4. Visualization results of goal-adaptive tasks by DexHandDiff. For each task, training data sample (with orange stroke) is followed by inference on novel goals beyond the training data. In the Door task, DexHandDiff guides the door to new target angle \\((30^{\\circ})\\) and holds the door in position when the hand releases, which cannot be attained by simply truncating actions from \\(90^{\\circ}\\) training data. DexHandDiff avoids ghost states and achieves better goal adaptability." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.328, + 0.484, + 0.391 + ], + "angle": 0, + "content": "
    TaskNaïve GuideHuman CraftLLM Gen
    Door Open 30°070.0 ±8.240.0 ±8.2
    Pen Half-side Re-orien20.0 ±8.240.0 ±8.226.7 ±4.7
    Hammer Half Nail20.0 ±8.246.7 ±12.543.3 ±9.4
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.097, + 0.393, + 0.477, + 0.407 + ], + "angle": 0, + "content": "Table 5. Ablation study on LLM-based guidance generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.416, + 0.484, + 0.507 + ], + "angle": 0, + "content": "signed guidance. LLM Gen generate guidance functions with Claude Sonnet 3.5 [5]. And Naïve Guide directly guides the object to the goal, corresponding to ghost-state existing baseline. Results indicate that both Human Craft and LLM Gen significantly outperform Naïve Guide across tasks, with Human Craft achieving the highest success rates." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.516, + 0.466, + 0.531 + ], + "angle": 0, + "content": "6.5. Ablation Study of DexHandDiff Framework" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.538, + 0.484, + 0.719 + ], + "angle": 0, + "content": "We analyze the contribution of each component in DexHandDiff through ablation studies (Tab. 6), across multiple door-opening tasks (open \\(30^{\\circ}\\), \\(50^{\\circ}\\), \\(70^{\\circ}\\), and \\(90^{\\circ}\\)), using the same training checkpoint for fair comparison. The baseline Diffuser[24] uses a basic goal-guidance strategy, while Dyn-guide enhances it with dynamics guidance for better state-action consistency. Joint S&A adopts joint state-action denoising like DexHandDiff but retains naive goal guidance. DexHandDiff incorporates all components and achieves the highest success rate of \\(67.5\\%\\), significantly outperforming the other configurations and demonstrating the effectiveness of our full design." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.728, + 0.236, + 0.743 + ], + "angle": 0, + "content": "6.6. Visualizations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We visualize the behavior of DexHandDiff across various goal-adaptive dexterous tasks in Fig. 4. DexHandDiff ensures realistic contact by aligning hands with contact points first using joint dynamics modeling, eliminating ghost states. Notably, for example, DexHandDiff guides the door to new target angle and holds the door steady when the hand releases, which cannot be achieved by policies trained with slicing \\(90^{\\circ}\\) data. These results underscore DexHandDiff's ability to maintain physically realistic interactions while adapting to novel goals." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.328, + 0.906, + 0.425 + ], + "angle": 0, + "content": "
    MethodGoal GuidanceDynamics GuideJoint State ActionInteract MechanismOverall SR
    No-guide××××24.1
    Diffuser [24]✓×××27.5
    Dyn-guide✓✓××27.5
    Joint S&A✓×✓×30.8
    Dyn+Joint✓✓✓×31.7
    DexHandDiff✓✓✓✓67.5
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.426, + 0.907, + 0.468 + ], + "angle": 0, + "content": "Table 6. Ablation study on DexHandDiff framework. We report the average success rates (overall SR) on Adroit Door environment over open \\(30^{\\circ}\\), \\(50^{\\circ}\\), \\(70^{\\circ}\\) and \\(90^{\\circ}\\) tasks." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.478, + 0.627, + 0.495 + ], + "angle": 0, + "content": "6.7. Efficiency" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.501, + 0.907, + 0.547 + ], + "angle": 0, + "content": "We test the control frequency of DexHandDiff on an RTX 3090 with receding horizon set as 8 for all tasks except Door (32 instead). The control frequency are reported below." + }, + { + "type": "table", + "bbox": [ + 0.566, + 0.551, + 0.857, + 0.585 + ], + "angle": 0, + "content": "
    TaskDoorPenHammerRelocateBlock
    Freq.5.04 Hz5.88 Hz5.86 Hz5.78 Hz6.92 Hz
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.549, + 0.588, + 0.87, + 0.602 + ], + "angle": 0, + "content": "Table 7. Control command frequency over 10 tries." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.605, + 0.906, + 0.665 + ], + "angle": 0, + "content": "Besides, our lightweight model (3.96M params, 3.27 GFLOPS) can be further accelerated via DPM Solver++ [31] (4x speedup) and command interpolation (reaching \\(36\\mathrm{Hz}\\)), sufficient for real robot control." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.678, + 0.634, + 0.694 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.907, + 0.87 + ], + "angle": 0, + "content": "This work presents DexHandDiff, an interaction-aware diffusion planner for adaptive dexterous manipulation. By modeling joint state-action dynamics and incorporating a dual-phase diffusion mechanism, it addresses action-state consistency issues, including the \"ghost state\" and generalization problems observed in previous diffusion methods. DexHandDiff's design enables it to handle intricate multi-contact interactions through a pre-contact alignment and a post-contact control. We believe its potential to advance the field toward diverse dexterous tasks while remaining grounded in real physics and dynamics." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Future Work can investigate deployment with hand states sensed and object poses estimated by vision models." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1752" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.258, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.116, + 0.482, + 0.147 + ], + "angle": 0, + "content": "This paper is partially supported by the General Research Fund of Hong Kong No.17200622 and 17209324." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.163, + 0.188, + 0.178 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.188, + 0.484, + 0.256 + ], + "angle": 0, + "content": "[1] Anurag Ajay, Yilun Du, Abhi Gupta, Joshua B Tenenbaum, Tommi S Jaakkola, and Pulkit Agrawal. 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IEEE, 2019. 2" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.482, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1755" + } + ] +] \ No newline at end of file diff --git a/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_origin.pdf b/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1b27e7c6b55f38ecc1cbf1e7bc96b2023d8fc722 --- /dev/null +++ b/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/776fbd8b-c951-4932-8e6a-abc5a13d15dd_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8ea9f4d86310bcacf253d59935f69db89e2d8018e50c97fc5a09f32e22f5254f +size 1573127 diff --git a/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/full.md b/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4df1be9e6f303cf2113b28f4e3073970afb0e533 --- /dev/null +++ b/2025/DexHandDiff_ Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation/full.md @@ -0,0 +1,431 @@ +# DexHandDiff: Interaction-aware Diffusion Planning for Adaptive Dexterous Manipulation + +Zhixuan Liang $^{1,2\dagger}$ Yao Mu $^{1}$ Yixiao Wang $^{2}$ Tianxing Chen $^{1}$ Wenqi Shao $^{1}$ Wei Zhan $^{2}$ Masayoshi Tomizuka $^{2‡}$ Ping Luo $^{1‡}$ Mingyu Ding $^{2}$ + +$^{1}$ The University of Hong Kong $^{2}$ University of California, Berkeley + +{zxliang, ymu, pluo}@cs.hku.hk {yixiao_wang, wzhan, tomizuka, myding}@berkeley.edu + +https://dexdiffuser.github.io/ + +# Abstract + +Dexterous manipulation with contact-rich interactions is crucial for advanced robotics. While recent diffusion-based planning approaches show promise for simple manipulation tasks, they often produce unrealistic ghost states (e.g., the object automatically moves without hand contact) or lack adaptability when handling complex sequential interactions. In this work, we introduce DexHandDiff, an interaction-aware diffusion planning framework for adaptive dexterous manipulation. DexHandDiff models joint state-action dynamics through a dual-phase diffusion process which consists of pre-interaction contact alignment and post-contact goal-directed control, enabling goal-adaptive generalizable dexterous manipulation. Additionally, we incorporate dynamics model-based dual guidance and leverage large language models for automated guidance function generation, enhancing generalizability for physical interactions and facilitating diverse goal adaptation through language cues. Experiments on physical interaction tasks such as door opening, pen and block reorientation, object relocation, and hammer striking demonstrate DexHandDiff's effectiveness on goals outside training distributions, achieving over twice the average success rate (59.2% vs. 29.5%) compared to existing methods. Our framework achieves an average of 70.7% success rate on goal adaptive dexterous tasks, highlighting its robustness and flexibility in contact-rich manipulation. + +# 1. Introduction + +Dexterous manipulation, a cornerstone of advanced robotics with applications from service robotics to industrial automation, remains a challenging problem despite advances + +![](images/9ccf48ea0dbce3216c66d3427366175d916b5e3b62dd222d75c711ed874ea3d4.jpg) + +![](images/f5f2ba62f6e5b3e645c279221d4d17e42545f4777b031753480dbcd4ce8343dd.jpg) +Dreamed $s^{door}$ changes, but $s^{hand}$ not, causing ghost states and wrong actions + +![](images/2a32d7f2f87f788c1c6a76c645c888aecb42e5f54583a6d8340870b16bd72fb3.jpg) + +![](images/0b75eddbc381ec0893846ea7b41a76bde1f95d79d4077f5b47809a16403fecf2.jpg) + +![](images/6d115e028e2f9e81ae2ac973eec4619bd7c5fc3e0a32fce29a1617a8a9df8bab.jpg) +Figure 1. (a) Previous diffusers directly apply goal guidance to object states, which causes ghost states, where objects appear to move independently without hand contact-a physically impossible scenario. (b) DexHandDiff introduces contact guidance that jointly influences both hand/object states and hand actions, while maintaining tight state-action coupling. It prevents ghost states, and enables precise goal adaptation. (c) Quantitative comparisons with previous methods on goal-shifted interaction tasks. + +in reinforcement learning (RL) [2, 4, 8, 47, 52] and imitation learning [23, 34]. Recently, diffusion-based planning [1, 14, 24, 28] has emerged as a promising new representative of imitation learning, capable of learning intricate motion trajectories from demonstration data for smoother and more adaptable control. However, current diffusion approaches are primarily designed for simpler gripper-based + +(one Degree of Freedom) manipulation tasks, focusing on either trajectory completion or action replay by reaching target positions sequentially. They fall short in dexterous hand manipulation requiring part-aware precise interaction and exhibiting rich contact dynamics through multi-finger control and in-hand adjustment. + +More specifically, existing diffusion on action models [14, 56] (i.e. models generating actions) excel in well-defined tasks but often lack generalizability in adapting to complex or new tasks with flexible interaction requirements. They necessitate continual data collection for new goal configurations even within the same dynamics, limiting their effectiveness in contact-rich interactions. In contrast, diffusion on state methods [1, 24, 37], including those adapted from video diffusion models for imitation learning [6, 16], will produce unrealistic "ghost states" in interaction tasks. As shown in Fig. 1 and Fig. 2, the visualizations are rendered by setting states frame by frame with predicted output from state-based methods, and show objects react independently of physical contact (e.g. drawers opening on their own before the manipulator reaches them), which cannot actually happen and would result in failure. This issue arises because the object states can't be directly controlled. Actions must first influence dexterous hand's states before impacting the object, revealing the importance of modeling state transitions for physics-driven interactions. + +Thus, we propose DexHandDiff, an interaction-aware diffusion model tailored for adaptive dexterous manipulation that exhibits goal shifts or cost function variations while maintaining similar dynamics. DexHandDiff models joint state-action dynamics that takes the state output to guide and constrain the action output with realistic physical behavior. A dynamics model-based dual guide is incorporated to maintain coherence with dynamics observed in training data. It addresses the action-state consistency challenge first identified in Diffuser [24] which however prioritized generated state over action, as shown in Fig. 1. + +Specifically, DexHandDiff adopts a goal-adaptive diffusion mechanism with dual-phase process. 1) At first, precontact phase, it guides the manipulator to align with the object's key contact point, such as a handle or the center of object, ensuring stable alignment before initiating physical interaction. 2) In the subsequent post-contact phase, it introduces joint guidance over both the manipulator and the object states, enabling fine-grained control to achieve the target state for the object. This sequential approach integrates both action diffusion that prevents premature influence on the object's state before contact, and state diffusion that ensures effective goal alignment throughout. By generating states and actions in an interaction-aware manner, DexHandDiff produces more coherent and realistic trajectories suited to complex tasks like tool using. Furthermore, to automate guidance function design, DexHandDiff intro + +duces an approach using large language models in the text-to-reward paradigm, that can generalize across diverse goals and cost functions via language cues. + +We conduct experiments on multiple dexterous manipulation tasks to evaluate DexHandDiff's effectiveness, covering both in-domain and goal-adaptability challenges, e.g., adapting to new goal "door closing" from "90-degree door opening" training data. Results with up to $70.0\%$ success rate on the 30-degree door task (vs. the next best $16.7\%$ for Diffusion Policy) and $46.7\%$ on the hammer nail half-drive task (vs. the next best $33.3\%$ for Decision Diffuser), confirm DexHandDiff's robustness and adaptability in capturing complex hand-object-environment interactions. + +In summary, DexHandDiff advances adaptive dexterous manipulation by: 1) We propose the first interaction-aware, goal-adaptive diffusion planner for dexterous manipulation, modeling manipulator-object-environment dependencies to handle sequential tasks with complex state transitions. 2) By jointly modeling state-action behaviors with dynamics-based dual guidance and LLM-based interaction guidance, DexHandDiff sets a new standard for adaptive planning in dexterous manipulation and for the first time extends text-to-reward concepts to diffusers. 3) Experimental validation on diverse dexterous manipulation tasks, demonstrating its robustness and adaptability. DexHandDiff achieves over twice the average success rate of the next best method (59.2% vs. 29.5%) across goal-directed tasks. + +# 2. Related Works + +Dexterous Manipulation. Dexterous manipulation [12, 13, 19, 20, 32, 40, 42, 45, 48, 50] with multi-fingered hands enables complex tasks in unstructured environments by mimicking human hand flexibility. Initially, traditional methods using trajectory optimization and precise dynamics models [36, 41], struggled with high-dimensional action spaces and contact-rich dynamics. This led to the adoption of reinforcement learning (RL) [10, 41, 52, 58] for handling complex, high-DOF (degree of freedom) interactions. However, RL requires extensive online exploration and carefully designed reward functions [11, 36] where inadequate reward shaping can hardly learn and it limits adaptability [55, 57]. Demonstration-based methods [57] reduce sample complexity, but they struggle to generalize across sequential, contact-rich tasks. Our DexHandDiff addresses these challenges by explicitly modeling hand-object-environment interactions, enabling goal-adaptive planning without intricate reward shaping, thus allowing for more efficient learning in complex, sequential tasks. + +Diffusion-based Planning Methods. Planning with diffusion models has become prominent in imitation learning for robotic manipulation [1, 9, 14, 24, 28-30, 37]. Classifier-guided methods [24, 28] used task-specific classifiers to + +condition policies, while classifier-free ones integrated task variations within diffusion model [1]. However, classifier-free methods lack flexibility for zero-shot explicit conditioning tasks due to reliance on training data configurations. DexHandDiff addresses this by performing classifier-guided diffusion over both state and action spaces, enabling precise interaction and rich-contact dynamics planning for more realistic, complex and adaptable manipulation. + +LLM-based Robot Policy Code Generation. Recent works [7, 27, 35, 51] have demonstrated the potential of LLMs in generating executable code for robotics tasks. Code as Policies [27] showed LLMs can effectively translate high-level task descriptions into functional robot control programs. Eureka [33] and Text2Reward [54] further advanced this direction by generating crucial parameters or complete reward functions from language descriptions, demonstrating well-structured prompts with comprehensive environment information can enable reliable reward shaping. Our work extends this text-to-code paradigm to imitation learning through diffusers. DexHandDiff provides a natural interface for LLM code generation through its guidance function formulation, bridging the gap between task specification and behavioral policies to learn. + +# 3. Preliminary + +# 3.1. Diffusion Model as Policy + +We formulate the dexterous manipulation planning problem within the Markov Decision Process (MDP) framework [39], defined as $\mathcal{M} = (\mathcal{S},\mathcal{A},\mathcal{T},\mathcal{R},\gamma)$ . The objective is to find an optimal action sequence $a_{0:T}^{*}$ that satisfies: + +$$ +\begin{array}{l} \boldsymbol {a} _ {0: T} ^ {*} = \underset {\boldsymbol {a} _ {0: T}} {\arg \max } \mathcal {J} (\boldsymbol {s} _ {0}, \boldsymbol {a} _ {0: T}) = \underset {\boldsymbol {a} _ {0: T}} {\arg \max } \sum_ {t = 0} ^ {T} \gamma^ {t} R (\boldsymbol {s} _ {t}, \boldsymbol {a} _ {t}), \\ \text {w h e r e s t a t e t r a n s i t i o n s f o l l o w} \boldsymbol {s} _ {t + 1} = \mathcal {T} (\boldsymbol {s} _ {t}, \boldsymbol {a} _ {t}). \end{array} \tag {1} +$$ + +Following [1, 24], we leverage diffusion models to address this planning problem by treating state and action trajectories $\pmb{\tau}$ as sequential data. The reverse process of diffusion learns to denoise trajectories from a standard normal distribution through conditional probability $p_{\theta}(\pmb{\tau}^{i-1} \mid \pmb{\tau}^i)$ . The model is trained to maximize the likelihood: + +$$ +p _ {\theta} \left(\boldsymbol {\tau} ^ {0}\right) = \int p \left(\boldsymbol {\tau} ^ {N}\right) \prod_ {i = 1} ^ {N} p _ {\theta} \left(\boldsymbol {\tau} ^ {i - 1} \mid \boldsymbol {\tau} ^ {i}\right) \mathrm {d} \boldsymbol {\tau} ^ {1: N}, \tag {2} +$$ + +with the optimization objective inspired by ELBO, + +$$ +\theta^ {*} = \arg \min _ {\theta} - \mathbb {E} _ {\boldsymbol {\tau} ^ {0}} \left[ \log p _ {\theta} \left(\boldsymbol {\tau} ^ {0}\right) \right]. \tag {3} +$$ + +For practical implementation, we adopt the simplified surrogate loss [22] that focuses on predicting the noise term: + +$$ +\mathcal {L} _ {\text {d e n o i s e}} (\theta) = \mathbb {E} _ {i, \boldsymbol {\tau} ^ {0} \sim q, \epsilon \sim \mathcal {N}} [ | | \epsilon - \epsilon_ {\theta} (\boldsymbol {\tau} ^ {i}, i) | | ^ {2} ]. \tag {4} +$$ + +# 3.2. Classifier-free Conditional Diffusion Policy + +To generate high-reward trajectories, classifier-free guidance [15] has been transferred from image to trajectory generation [1]. This approach incorporates guidance signals + +$\pmb{y}(\tau)$ directly in the noise prediction model by: + +$$ +\hat {\epsilon} = \epsilon_ {\theta} (\boldsymbol {\tau} ^ {i}, \varnothing , i) + \omega \left(\epsilon_ {\theta} \left(\boldsymbol {\tau} ^ {i}, \boldsymbol {y}, i\right) - \epsilon_ {\theta} \left(\boldsymbol {\tau} ^ {i}, \varnothing , i\right)\right), \tag {5} +$$ + +where $\omega$ controls the guidance strength, and $\varnothing$ denotes the absence of conditioning. During sampling, trajectories are generated with the predicted modified noise $\hat{\epsilon}$ . + +# 3.3. Classifier-guided Diffusion Policy + +Different from classifier-free diffusion models that condition relying solely on implicit representations within the training data, classifier-guided approach, enables direct reward or goal conditioning through gradient-based guidance. + +For reward maximization, it introduces trajectory optimality $\mathcal{O}_t$ at timestep $t$ , following a Bernoulli distribution where $p(\mathcal{O}_t = 1) = \exp (\gamma^t\mathcal{R}(\boldsymbol {s}_t,\boldsymbol {a}_t))$ . The diffusion process can be naturally extended to incorporate conditioning by sampling from perturbed distributions: + +$$ +\tilde {p} _ {\theta} (\boldsymbol {\tau}) = p (\boldsymbol {\tau} \mid \mathcal {O} _ {1: T} = 1) \propto p _ {\theta} (\boldsymbol {\tau}) p \left(\mathcal {O} _ {1: T} = 1 \mid \boldsymbol {\tau}\right) \tag {6} +$$ + +Under Lipschitz conditions on $p(\mathcal{O}_{1:T} \mid \tau^i)$ [17], the reverse diffusion process follows: + +$$ +p _ {\theta} \left(\boldsymbol {\tau} ^ {i - 1} \mid \boldsymbol {\tau} ^ {i}, \mathcal {O} _ {1: T}\right) \approx \mathcal {N} \left(\boldsymbol {\tau} ^ {i - 1}; \mu_ {\theta} + \alpha \Sigma g, \Sigma\right), \tag {7} +$$ + +where the guidance gradient $g$ is: + +$$ +\begin{array}{l} g = \nabla_ {\tau} \log p (\mathcal {O} _ {1: T} | \tau) | _ {\tau = \mu_ {\theta}} \\ = \sum_ {t = 0} ^ {T} \gamma^ {t} \nabla_ {\boldsymbol {s} _ {t}, \boldsymbol {a} _ {t}} \mathcal {R} (\boldsymbol {s} _ {t}, \boldsymbol {a} _ {t}) | _ {(\boldsymbol {s} _ {t}, \boldsymbol {a} _ {t}) = \mu_ {t}} = \nabla_ {\boldsymbol {\tau}} \mathcal {I} (\mu_ {\theta}). \tag {8} \\ \end{array} +$$ + +For discrete goal conditioned tasks, the constraint can be simplified by directly substituting conditional values at each diffusion timestep $i \in \{0,1,\dots,N\}$ . + +# 4. Analysis of Diffusion-based Planning Methods for Interaction-intensive Tasks + +Current diffusion-based methods are widely adopted for robotic manipulation but reveal significant limitations when applied to dexterous, sequential interaction tasks. Table 1 provides an overview of prominent diffusion-based methods (including Diffuser [24], Decision Diffuser [1], Diffusion Policy [14] and our DexHandDiff), categorizing each by their conditioning approach, action generation method, and goal adaptability. In this section, we analyze these challenges across three key dimensions. + +Action-only Diffusion is Limited in Explicit State Conditioning. Existing diffusion on action models like Diffusion Policy (DP) [14], excel in providing precise, consistent action control, benefiting from extensive training data and bypassing errors from inverse kinematics. They yield high performance when training data is sufficient and diverse. However, for tasks requiring variant multi-stage goals, action-only diffusion lacks the flexibility to perform explicit state guidance at intermediate stages, like aligning hand and object state at pre-grasp stage, hurting the adaptability of the whole planner. For example, DP trained on + +
    MethodDiffusion on State or ActionDiffusion Condition TypeAction Gen MethodGoal AdaptabilityNo Ghost StatesInteraction Aware
    Diffuser [24]StateClassifier-GuidedInverse Dyn✓××
    Decision Diffuser [1]StateClassifier-FreeInverse Dyn× (if diverse data, then ✓)××
    Diffusion Policy [14]ActionClassifier-FreeDirect× (if diverse data, then ✓)✓×
    DexHandDiff (Ours)State & ActionClassifier-GuidedDirect✓✓✓
    + +Table 1. Comparison of diffusion-based approaches for robot manipulation. Quantitative results on door-opening are shown in Sec. 6. + +data with opening the door to 90 degrees hardly adapt to open 30 or 60 degrees. + +Ghost States in State-only Diffusion for Sequential Interaction. While state-based diffusion models offer the advantage of flexible goal specification, it is only effective in fully actuated tasks where all degrees of freedom (DoF) are directly controllable, such as MuJoCo [24, 46], and gripper pick-and-place (requiring only end-effector position control) [1, 14] tasks. In such scenarios, all states of the system can be manipulated directly. However, in contact-rich interaction task where indirect control exists, such as striking a nail with a hammer using a dexterous hand, additional uncontrollable DoFs, like the hammer head and nail positions, must be changed through transitions from the states of the hand. Applying generation across all states, including those of objects beyond the hand, will result in unrealistic "ghost states" where objects appear to move independently of contact but actually cannot, as illustrated in Fig. 1 and Fig. 2. + +Classifier-free vs. Classifier-guided Adaptability. Classifier free diffusion models, valued for not requiring external classifiers, encode task variations directly within the model. This structure is effective for tasks with constraints in observed configurations, but with limited goal adaptability in zero-shot or new-task scenarios. For instance, in the push-T task, DP cannot directly adapt to new target positions due to the fixed goal in training data. In contrast, classifier-guided methods, such as ours, mitigate this limitation by offering adaptable, gradient-based guidance, enabling direct conditioning on new goals or rewards, enhancing flexibility across a range of tasks. + +# 5. Method + +# 5.1. Interaction-aware Diffusion-based Planning + +To address these limitations, we propose DexHandDiff, an interaction-aware diffusion planning framework (Fig. 3), maintaining physical consistency and enabling flexible goal adaptation for dexterous manipulation. + +Joint State-Action Diffusion Model. Our approach builds upon classifier-guided diffusion policies. But we jointly diffuse over the concatenated state-action space $\pmb{\tau} = [(\pmb{a}_0, \pmb{s}_0), (\pmb{a}_1, \pmb{s}_1), \dots, (\pmb{a}_T, \pmb{s}_T)]$ , where state $\pmb{s}$ includes both hand (24 joint angles and 3 position offsets) and task-specific object states (i.e. door hinge angle, pen pose etc.), and action $\pmb{a}$ represents changes in controllable states (only + +![](images/3da810fba5018dc1e91f01a3ab7adf6f8ef1470731083885f672d6b1fd4e1982.jpg) +Figure 2. Demonstration of ghost states on the pen reorientation task. The visualizations are rendered by setting predicted states frame by frame, which cannot actually happen and will lead to failure. The pen appears to autonomously rotate to the desired pose without any hand manipulation, and the fingers look like moving to grasp the pen at the last frame. + +![](images/cd3157ebce89c2e6c7796c2ae61d80a6972677c6bde42e19bd402891f01b8fc0.jpg) + +![](images/f0f4c3cea822c0e2e50889113aa496646eec453802a4038cce1b36f024f991c8.jpg) + +hand joints and positions). + +This design choice directly addresses the above mentioned limitations: (1) By including states in the diffusion process, we enable explicit state conditioning and goal specification, overcoming the limitations of action-only approaches; (2) By classifier-guided diffusion, we allow flexible goal adaptation without exhaustive training data; (3) By jointly modeling states and actions, we maintain their physical coupling and prevent ghost states through carefully designed guidance. With denoised states guiding the generated actions, we effectively balance the state conditioning and action precision. + +Extended Behavior Model and Energy Function. According to Eq. 6, the standard conditional diffusion follows: + +$$ +\tilde {p} _ {\theta} (\boldsymbol {\tau}) \propto p _ {\theta} (\boldsymbol {\tau}) p \left(\mathcal {O} _ {1: T} = 1 \mid \boldsymbol {\tau}\right) \propto p _ {\theta} (\boldsymbol {\tau}) h (\boldsymbol {\tau}), \tag {9} +$$ + +where we generalize $p(\mathcal{O}_{1:T} = 1\mid \tau)$ as a behavior model $h(\tau)$ . Then we further generalize this formulation through a product of experts framework [21], where each expert represents a specific behavior model: + +$$ +\tilde {p} _ {\theta} (\boldsymbol {\tau}) \propto p _ {\theta} (\boldsymbol {\tau}) \prod_ {i = 1} ^ {n} h _ {i} (\boldsymbol {\tau}). \tag {10} +$$ + +From the energy function perspective, each behavior model encoding task-specific objectives or constraints is: + +$$ +h _ {i} (\boldsymbol {\tau}, c) = \frac {1}{\int e ^ {- \varepsilon_ {i} (\boldsymbol {\tau} , c)} d \boldsymbol {\tau}} e ^ {- \varepsilon_ {i} (\boldsymbol {\tau}, c)}, \tag {11} +$$ + +where $\varepsilon_{i}(\pmb{\tau}, c)$ represents the energy function for the $i$ -th guidance objective, with $c$ denoting task-specific conditions. This formulation allows combining multiple objectives (e.g., reaching the target state while maintaining physical consistency) via their respective guidance functions. + +Under appropriate smoothness conditions, the guidance gradient $g$ in the reverse diffusion process (Eq. 7) can be decomposed as the sum of individual guidance gradients: + +![](images/8658e549fb027002ab91b80536332c2b2d659c38e5f94dafe6ccb261302f21ea.jpg) +Figure 3. Framework of DexHandDiff. DexHandDiff employs joint state-action diffusion with interaction-aware guidance. Before interaction (top middle), guidance aligns the hand to the object contact point. Upon contact (bottom middle), additional guidance steers both hand and object states towards the goal ("&" means state concatenation at input level), enforcing physical constraints and avoiding ghost states. A learned dynamics model further ensures consistency between states and actions. Our DexHandDiff utilizes extended behavior model to aggregate multiple condition terms to guide the diffusion process. + +$$ +g = \nabla_ {\boldsymbol {\tau}} \log \prod_ {i = 1} ^ {n} h _ {i} (\boldsymbol {\tau}) = \sum_ {i = 1} ^ {n} \nabla_ {\boldsymbol {\tau}} \log h _ {i} (\boldsymbol {\tau}) = - \sum_ {i = 1} ^ {n} \nabla_ {\boldsymbol {\tau}} \varepsilon_ {i} (\boldsymbol {\tau}, c). +$$ + +This enables integration of multiple guidance signals, each addressing different aspects of the interaction task, while maintaining a coherent optimization objective. + +Dynamics-aware Generation. A key challenge in joint state-action diffusion is maintaining consistency between generated states and actions [24]. Our method addresses this through a learned dynamics model trained on demonstration data, constraining state-action generation via additional loss in diffusion training and serving as a guide in inference. By penalizing state-action pairs that violate observed dynamics, this guidance ensures our model maintains both state conditioning benefits and action feasibility. + +$$ +\varepsilon_ {\mathrm {d y n}} (\boldsymbol {\tau}) = \left| \boldsymbol {s} _ {t + 1} - \mathcal {T} \left(\boldsymbol {s} _ {t}, \boldsymbol {a} _ {t}\right) \right| ^ {2}, \tag {12} +$$ + +where $\mathcal{T}(s, a)$ is a separately trained dynamics model to ensure physically plausible motion patterns. + +Manipulation after Contact Task Guidance. For manipulation after contact tasks such as door opening and tool using, DexHandDiff employs a dual-phase interaction approach that acknowledges the fundamentally different nature of interaction before and after contact establishment. The framework automatically determines the phase transition based on the distance between the palm position and the designated contact point on the object, applying a smooth transition mask to blend between phases. + +In the pre-grasp phase, our method focuses on guiding the manipulator to stably align with the contact point while preventing premature object movement. We engineer two primary guidance components: 1) Alignment guidance $\epsilon_{\mathrm{align}}$ that directs the end-effector towards precise contact point while maintaining natural approaching trajectory; 2) Dynamics consistency guidance $\epsilon_{\mathrm{dyn}}$ . + +Upon establishing contact (determined by palm-object proximity), the post-grasp phase activates additional guidance mechanisms: 1) Goal-directed guidance $\epsilon_{\mathrm{succ}}$ that steers the coupled hand-object system towards target configurations; 2) Physical constraint guidance $\epsilon_{\mathrm{penalty}}$ that prevents unrealistic state changes (e.g., limiting per-step changes in both door hinge and latch angles); 3) Continued dynamics guidance $\epsilon_{\mathrm{dyn}}$ to maintain motion feasibility. + +Therefore, the guidance energy function follows, + +$$ +\epsilon = \left\{ \begin{array}{l l} \epsilon_ {\text {p r e}} = \epsilon_ {\text {a l i g n}} + \epsilon_ {\text {d y n}} & \text {i f} | \boldsymbol {s} _ {\text {h a n d}} - \boldsymbol {s} _ {\text {c o n t a c t}} | > \delta_ {1} \\ \epsilon_ {\text {p o s t}} = \epsilon_ {\text {s u c c}} + \epsilon_ {\text {d y n}} + \epsilon_ {\text {p e n a l t y}} & \text {o t h e r w i s e} \end{array} \right. \tag {13} +$$ + +where $s_{\text{hand}}$ and $s_{\text{contact}}$ represents the states of dexterous hand and object contact point (e.g. door latch, hammer handle etc.) respectively, and $\delta_1$ is a small threshold. The separated design of grasp proposal guidance $(\epsilon_{\text{align}})$ and task achieving guidance $(\epsilon_{\text{succ}})$ mirrors successful policies in prior work [47, 52], effective for dexterous manipulation. Besides, the $\epsilon_{\text{penalty}}$ ensures continuous object state transitions, corresponding to + +$$ +h _ {p e n a l t y} \triangleq 1 - H \left(\left| s _ {o b j} ^ {t + 1} - s _ {o b j} ^ {t} \right| - \delta_ {2}\right), \tag {14} +$$ + +where $\delta_{2}$ is another small threshold and $H(\cdot)$ is the Heaviside step function [49]. Then $\epsilon_{\mathrm{penalty}}$ can be obtained by applying Eq. 11, becoming a Dirac delta function that directly sets value when satisfying the constraints. + +In-hand Manipulation Task Guidance. For tasks primarily involving in-hand manipulation (e.g., pen spinning, object reorientation), where objects are typically already in hand or quickly transition to in-hand states, we employ a simplified single-phase guidance structure: 1) Goal state guidance $\epsilon_{\mathrm{succ}}$ for achieving target object configurations; 2) Active finger motion guidance to ensure realistic object manipulation; 3) Dynamics consistency guidance $\epsilon_{\mathrm{dyn}}$ to maintain physical plausibility; 4) Physical constraint guidance + +$\epsilon_{\mathrm{penalty}}$ that prevents unrealistic state changes. + +$$ +\epsilon = \epsilon_ {\text {g o a l}} + \epsilon_ {\text {f i n g e r}} + \epsilon_ {\text {d y n}} + \epsilon_ {\text {p e n a l t y}}. \tag {15} +$$ + +Specially, we define the behavior model that encourages active finger involvement as, + +$$ +h _ {\text {f i n g e r}} (\tau , t) = H \left(\left| \boldsymbol {s} _ {\text {f i n g e r - j o i n t s}} ^ {t + 1} - \boldsymbol {s} _ {\text {f i n g e r - j o i n t s}} ^ {t}\right| - \delta_ {3}\right), \tag {16} +$$ + +where $s_{\text{finger-joints}}^t$ is the state vector of all finger joints at planning step $t$ . $\delta_3$ is the third small threshold. $H(\cdot)$ is also the Heaviside step function. This specialized handling prevents unrealistic "ghost states", as discussed in Sec. 4. + +# 5.2. LLM-Based Guidance Generation + +The design of task-specific guidance functions for diffusion policies traditionally requires significant manual effort, particularly for diverse dexterous manipulation tasks. To address this challenge, we leverage a two-stage Large Language Model (LLM) process for automated guidance generation, adopting text-to-reward paradigm [33, 54]. + +Overall Pipeline. First, we feed the LLM with a 6-part template (including function purpose, guidance structure, environment description, function prototype, task instruction and few-shot hints) and public documents on simulation environments [38, 41] to generate task-specific prompts. Then, the generated task prompts are queried to another LLM to write guidance function code. Only few-shot hints require specific refinement, reducing human trial-and-error times from about 20 (for hand-craft energy function design) to around 5 while maintaining DexHandDiff performance. + +Environment Description. Our approach employs a comprehensive Pythonic environment abstraction that captures the complete interaction system. It encapsulates detailed robot joint configurations, and object-environment specifications from public documents, enabling LLM to generate precise guidance functions that account for the full complexity of dexterous manipulation tasks. + +Other Details. As previous works [54], once the guidance function code is generated, we execute the code in interpreter. This step may give us valuable feedback, e.g., syntax errors and runtime errors. We utilize the feedback from code execution as a tool for ongoing refinement within the LLM. Besides, our approach uses few-shot hints instead of examples to allow the model to access relevant functions and best practices without direct examples. Each guidance component is normalized over the trajectory horizon to ensure balanced contributions across objectives while preserving their temporal structure. Detailed examples of prompts and generated guidance functions are shown in Appx. E. + +# 6. Experiments + +We evaluate our DexHandDiff on five challenging dexterous manipulation tasks with four from Adroit Hand [41] and one from Shadow Hand environment [38]. Both environments feature a 24-joint Shadow Hand simulator with up to + +30 degrees of freedom, designed to closely match the hardware setting [44]. Detailed explanations of the five tasks are provided in Appendix B. We use the expert demonstrations collected by teleoperation from D4RL [18] for Adroit tasks (Door, Hammer, Pen and Relocate). However, Shadow Hand environment does not provide demonstration data, so we employ TQC+HER [3, 26] to collect 5000 expert trajectories for the Block Rotate-Z task. + +# 6.1. Performance Comparisons on Goal Adaptability in Interaction-Aware Tasks + +We evaluate DexHandDiff in the Door environment to test its goal adaptability across various target angles. Specifically, we require the planners to open the door to 30, 50, 70, 90 and 110 degrees, as well as close the door (reversal task). Note that the training data only includes 90-degree door-opening demonstrations. For some of these tasks, we adjust the environment settings, such as expanding the door's range of motion, to satisfy the evaluation requirements. + +We compare DexHandDiff with five baselines: two classifier-guided methods (Diffuser [24] with Goal Inpainting that sets discrete goal states, and Diffuser with Guided Sampling that leverages continuous gradients for fine control), two classifier-free methods (Decision Diffuser [1] and Diffusion Policy [14] that apply diffusion on states and actions respectively), and a variant of DexHandDiff (denoted DexHandDiff-disc.) that uses goal inpainting. To enhance classifier-free methods' learning of goal condition, we use the difference between the current door angle and target angle as the condition, rather than a fixed $90^{\circ}$ target. + +The results are shown in Tab. 2. Classifier-free methods perform well on the $90^{\circ}$ task, but their success declines sharply on new target angles, indicating limited adaptability to out-of-distribution targets. Classifier-guided methods demonstrate moderate but consistent performance across goal-adaptive tasks yet their overall success rates remain suboptimal due to imprecise state-action relation modeling in the policy. Our DexHandDiff achieves consistently high success rates across nearly all tasks. The slightly lower performance $(90.0\%)$ on the training task $(90^{\circ})$ compared to classifier-free methods stems from our additional guidance for adaptation. When ablating this, DexHandDiff achieves $96.7 \pm 4.7\%$ success rate on Open $90^{\circ}$ , which is a reasonable trade-off for better generalization. Averaging a $59.2\%$ success rate, over twice that of the next best method $(29.5\%)$ , DexHandDiff demonstrates robust adaptability across both in-domain and goal-adaptive scenarios. + +Besides, we also observe a trend that goals closer to the original training data don't have higher success rates than others. We suppose it's because when target angle is close to training, learned dynamics often override guidance. We observed 8 out of 14 failures in 30 tries in $70^{\circ}$ task opened to $90^{\circ}$ instead, supporting our hypothesis. This learned bias + +
    MethodConditionOpen 30°Open 50°Open 70°Open 90°Open 110°Close DoorAverage
    Diffuser [24]Goal Inpainting16.7 ±4.716.7 ±12.56.7 ±4.756.7 ±9.410.0 ±8.2017.8
    Diffuser [24]Guided Sampling10.0 ±8.226.7 ±17.010.0 ±4.763.3 ±18.76.7 ±9.460.0 ±8.229.5
    Decision Diffuser [1]Embedding03.3 ±4.716.7 ±4.7100 ±030.0 ±8.2025.0
    Diffusion Policy [14]Embedding16.7 ±4.73.3 ±4.713.3 ±12.5100 ±03.3 ±4.7022.8
    DexHandDiff-disc.Goal Inpainting46.7 ±4.713.3 ±9.453.3 ±4.720.0 ±8.26.7 ±4.7023.3
    DexHandDiff (Ours)Guided Sampling70.0 ±8.256.7 ±4.753.3 ±8.290.0 ±8.226.7 ±14.158.3 ±13.459.2
    + +Table 2. Success rates (in %) of different diffusion-based approaches in Adroit Hand [41] environment. All models were trained on the Open $90^{\circ}$ task only, and we test their adaptability to other task goals in Adroit Door environment. All results and standard deviation are calculated over 3 tries for 10 random seeds. Best methods and those within $5\%$ of the best are highlighted in bold. + +
    EnvironmentTaskDiffuser [24] (Inpaint)Conditional DP [1, 14]DexHandDiff (Ours)
    DoorOpen 90°56.7 ±9.4100 ±090.0 ±8.2
    DoorOpen 30°16.7 ±4.716.7 ±4.770.0 ±8.2
    PenFull Re-orientation10.0 ±080.0 ±8.293.3 ±4.7
    PenHalf-side Re-orientation3.3 ±4.723.3 ±9.440.0 ±8.2
    HammerNail Full Drive53.3 ±9.476.7 ±9.490.0 ±8.2
    HammerNail Half Drive23.3 ±12.533.3 ±4.746.7 ±12.5
    RelocateFull Relocation56.7 ±4.796.7 ±4.796.7 ±4.7
    RelocateHalf-side Relocation53.3 ±4.786.7 ±12.593.3 ±4.7
    Manipulate BlockRotate-Z36.7 ±12.540.0 ±8.250.0 ±8.2
    Manipulate BlockHalf-side Rotate-Z30.0 ±026.7 ±4.736.7 ±4.7
    Average34.058.070.7
    + +is harder to correct than for more distant angles. + +# 6.2. Evaluation on Various Dexterous Tasks + +To evaluate the cross-task adaptability and goal-oriented performance of DexHandDiff, we test it across multiple dexterous manipulation tasks in Door, Pen, Hammer, Relocate and Block environments, as summarized in Tab. 3. In addition to the Door task, the Pen task involves aligning a pen to the specified orientation, with a particularly challenging goal-adaptability variant, Half-side Re-orientation, where training data includes only right-hemisphere orientations while test goals require left-hemisphere rotations. Similarly, the Block Rotate-Z and Object Relocation tasks have block's half-side variant trained on positive goal yaw angles but tested on negative ones and object's target right-half table training but left-half testing. The Nail Half Drive requires the hand to drive a nail and stop halfway before retracting, testing control precision for partial goals. + +We compare DexHandDiff with two baselines: Diffuser [24] (Inpainting), using classifier-guided goal inpainting as in the previous section, and Conditional DP [1, 14], a classifier-free approach with state diffusion for Door, Hammer and Relocate tasks while action diffusion for Pen and Block tasks, as modeling dynamics for these tasks are particularly challenging, making direct action generation more effective than state-based diffusion. As shown in Tab. 3, + +Table 3. Overall performance of dexterous manipulation with goal adaptability on multiple environments and tasks. We compare our method with one classifier-guided baseline and one classifier-free baseline. The results are calculated over 3 tries for 10 random seeds. + +
    Adapt TasksDoor 30°Door 70°Pen HalfHammer HalfRelocate Half
    Diffuser [24]4.194.035.234.015.48
    DexHandDiff2.922.382.762.413.22
    + +Table 4. Quantitative results for preventing ghost states over 3 tries. (Conditional DP is not included due to its action-only.) + +DexHandDiff consistently achieves superior results across both in-domain and goal-adaptive tasks. Although conditional DP demonstrates $23.3\%$ on the challenging pen half-side re-orientation, leveraging the inherent multi-modality and anisotropy of diffusion models, DexHandDiff still performs better $(40.0\%)$ . These results underscore DexHand-Diff's robustness and adaptability across a range of tasks, demonstrating generalization on familiar goals and novel configuration challenges. + +# 6.3. Validation for Preventing Ghost States + +We measured $L2$ distance between predicted and simulated hand-object states (normalized per dimension for fair comparison) in Tab. 4. DexHandDiff nearly halves baseline's gap across tasks, illustrating its ghost-state reduction effect. + +# 6.4. Ablation on LLM-based Guidance Generation + +Table 5 presents results for different guidance methods on goal adaptability tasks. All three methods are based on the same joint state-action diffusion model. The Human Craft approach reflects our above results with manually de + +![](images/85eb9938c943cee8041b3d45e9505d1b92c85d3d2e5220055aef3ecc30abdd3f.jpg) +Train Data (Open $90^{\circ}$ ) + +![](images/0158ea85d9f5c42f662519057715d24be2eab043c77c97ba7acc3ebc0c18f3fd.jpg) +Inference (Open $30^{\circ}$ ) Door Held in Position, Hand Released + +![](images/5492a9c680fb635ab19e97456fe96c959d6b814e983472e853bd081d866bf209.jpg) + +![](images/9606e97c9b3f083a30f108de36038d13c62a2a031ff4f5eba0d8439bf32350f3.jpg) + +![](images/bf3787fa6350e2b29beff894f61ba11683d87f192bb2a5f7e2a711c08596fafa.jpg) +Train Data (Full Drive) + +![](images/a25922428512f171f217550500abf6ee52e363e992f6fd3e93a83d4d5fee6e50.jpg) +Inference (Half Drive) Nail Partially Driven, Hammer Retracts + +![](images/65e8f920315abdd9825731aeda4a304c16852e1af3f4476b2f32b6e0ee22c22b.jpg) + +![](images/a3fca96da4e8fa913c4750fdd0bc66bf0bfab19bc371c0240228ec3dd2782d11.jpg) + +![](images/2a5053cf6a7e6e90500f5c84d0a2834db84faa9e6e4cd3d052279cac75e49064.jpg) +Train Data (Right Half) +Figure 4. Visualization results of goal-adaptive tasks by DexHandDiff. For each task, training data sample (with orange stroke) is followed by inference on novel goals beyond the training data. In the Door task, DexHandDiff guides the door to new target angle $(30^{\circ})$ and holds the door in position when the hand releases, which cannot be attained by simply truncating actions from $90^{\circ}$ training data. DexHandDiff avoids ghost states and achieves better goal adaptability. + +![](images/d7ecf3d91618a4c0ff64e5b890bd834e6b75338d7f326c3d4417daafda67ab10.jpg) +Inference (Left Half Re-orientation) Pen Aligned, Hand Stabilizes + +![](images/39d9e780cf8896bb00fe02b2e08e91976492d0ebfe9f6d10da22650d9a97f77a.jpg) + +![](images/c3d828791e65967a033c721eb6fe3432e668e9c1828c7278fbc16e84b4a92e3d.jpg) +Train Data (Goal Yaw Positive) + +![](images/5d65f461468bce02c644cbf427b67f7048155392ef0b4f2308d697389dbee3bc.jpg) + +![](images/501f830adde4f3af7d0907b69ffe4c59a6cd39eaa18cc3ac5084f45a8e9d73ba.jpg) +tive) Inference (Goal Yaw Negative) + +![](images/b12dbfbcde407649e1cc763b55737dc5051171811018b90427e820428b9069b6.jpg) + +![](images/b0933282bd38a4a9b1f31fa3793c2c3b02e78afacd69ecd6dc2ddf9344200700.jpg) + +
    TaskNaïve GuideHuman CraftLLM Gen
    Door Open 30°070.0 ±8.240.0 ±8.2
    Pen Half-side Re-orien20.0 ±8.240.0 ±8.226.7 ±4.7
    Hammer Half Nail20.0 ±8.246.7 ±12.543.3 ±9.4
    + +signed guidance. LLM Gen generate guidance functions with Claude Sonnet 3.5 [5]. And Naïve Guide directly guides the object to the goal, corresponding to ghost-state existing baseline. Results indicate that both Human Craft and LLM Gen significantly outperform Naïve Guide across tasks, with Human Craft achieving the highest success rates. + +# 6.5. Ablation Study of DexHandDiff Framework + +We analyze the contribution of each component in DexHandDiff through ablation studies (Tab. 6), across multiple door-opening tasks (open $30^{\circ}$ , $50^{\circ}$ , $70^{\circ}$ , and $90^{\circ}$ ), using the same training checkpoint for fair comparison. The baseline Diffuser[24] uses a basic goal-guidance strategy, while Dyn-guide enhances it with dynamics guidance for better state-action consistency. Joint S&A adopts joint state-action denoising like DexHandDiff but retains naive goal guidance. DexHandDiff incorporates all components and achieves the highest success rate of $67.5\%$ , significantly outperforming the other configurations and demonstrating the effectiveness of our full design. + +# 6.6. Visualizations + +We visualize the behavior of DexHandDiff across various goal-adaptive dexterous tasks in Fig. 4. DexHandDiff ensures realistic contact by aligning hands with contact points first using joint dynamics modeling, eliminating ghost states. Notably, for example, DexHandDiff guides the door to new target angle and holds the door steady when the hand releases, which cannot be achieved by policies trained with slicing $90^{\circ}$ data. These results underscore DexHandDiff's ability to maintain physically realistic interactions while adapting to novel goals. + +Table 5. Ablation study on LLM-based guidance generation. + +
    MethodGoal GuidanceDynamics GuideJoint State ActionInteract MechanismOverall SR
    No-guide××××24.1
    Diffuser [24]✓×××27.5
    Dyn-guide✓✓××27.5
    Joint S&A✓×✓×30.8
    Dyn+Joint✓✓✓×31.7
    DexHandDiff✓✓✓✓67.5
    + +# 6.7. Efficiency + +We test the control frequency of DexHandDiff on an RTX 3090 with receding horizon set as 8 for all tasks except Door (32 instead). The control frequency are reported below. + +Table 6. Ablation study on DexHandDiff framework. We report the average success rates (overall SR) on Adroit Door environment over open $30^{\circ}$ , $50^{\circ}$ , $70^{\circ}$ and $90^{\circ}$ tasks. + +
    TaskDoorPenHammerRelocateBlock
    Freq.5.04 Hz5.88 Hz5.86 Hz5.78 Hz6.92 Hz
    + +Table 7. Control command frequency over 10 tries. + +Besides, our lightweight model (3.96M params, 3.27 GFLOPS) can be further accelerated via DPM Solver++ [31] (4x speedup) and command interpolation (reaching $36\mathrm{Hz}$ ), sufficient for real robot control. + +# 7. Conclusion + +This work presents DexHandDiff, an interaction-aware diffusion planner for adaptive dexterous manipulation. By modeling joint state-action dynamics and incorporating a dual-phase diffusion mechanism, it addresses action-state consistency issues, including the "ghost state" and generalization problems observed in previous diffusion methods. DexHandDiff's design enables it to handle intricate multi-contact interactions through a pre-contact alignment and a post-contact control. We believe its potential to advance the field toward diverse dexterous tasks while remaining grounded in real physics and dynamics. + +Future Work can investigate deployment with hand states sensed and object poses estimated by vision models. + +# Acknowledgements + +This paper is partially supported by the General Research Fund of Hong Kong No.17200622 and 17209324. + +# References + +[1] Anurag Ajay, Yilun Du, Abhi Gupta, Joshua B Tenenbaum, Tommi S Jaakkola, and Pulkit Agrawal. Is conditional generative modeling all you need for decision making? In The Eleventh International Conference on Learning Representations, 2023. 1, 2, 3, 4, 6, 7 +[2] Ilge Akkaya, Marcin Andrychowicz, Maciek Chociej, Mateusz Litwin, Bob McGrew, Arthur Petron, Alex Paino, Matthias Plappert, Glenn Powell, Raphael Ribas, et al. 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While recent diffusion-based planning approaches show promise for simple manipulation tasks, they often produce unrealistic ghost states (e.g., the object automatically moves without hand contact) or lack adaptability when handling complex sequential interactions. In this work, we introduce DexHandDiff, an interaction-aware diffusion planning framework for adaptive dexterous manipulation. DexHandDiff models joint state-action dynamics through a dual-phase diffusion process which consists of pre-interaction contact alignment and post-contact goal-directed control, enabling goal-adaptive generalizable dexterous manipulation. Additionally, we incorporate dynamics model-based dual guidance and leverage large language models for automated guidance function generation, enhancing generalizability for physical interactions and facilitating diverse goal adaptation through language cues. Experiments on physical interaction tasks such as door opening, pen and block reorientation, object relocation, and hammer striking demonstrate DexHandDiff's effectiveness on goals outside training distributions, achieving over twice the average success rate (59.2% vs. 29.5%) compared to existing methods. Our framework achieves an average of 70.7% success rate on goal adaptive dexterous tasks, highlighting its robustness and flexibility in contact-rich manipulation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 625, + 135, + 638 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 625, + 135, + 638 + ], + "spans": [ + { + "bbox": [ + 56, + 625, + 135, + 638 + ], + "type": "text", + "content": "1. 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(a) Previous diffusers directly apply goal guidance to object states, which causes ghost states, where objects appear to move independently without hand contact-a physically impossible scenario. (b) DexHandDiff introduces contact guidance that jointly influences both hand/object states and hand actions, while maintaining tight state-action coupling. It prevents ghost states, and enables precise goal adaptation. (c) Quantitative comparisons with previous methods on goal-shifted interaction tasks." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "content": "in reinforcement learning (RL) [2, 4, 8, 47, 52] and imitation learning [23, 34]. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 263, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 263, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 263, + 703 + ], + "type": "text", + "content": "This work was done during Zhixuan's visit to UC Berkeley." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 67, + 703, + 147, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 147, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 147, + 712 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 67, + 703, + 147, + 712 + ], + "type": "text", + "content": " Corresponding authors." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1745" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "(one Degree of Freedom) manipulation tasks, focusing on either trajectory completion or action replay by reaching target positions sequentially. They fall short in dexterous hand manipulation requiring part-aware precise interaction and exhibiting rich contact dynamics through multi-finger control and in-hand adjustment." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 147, + 295, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 147, + 295, + 386 + ], + "spans": [ + { + "bbox": [ + 56, + 147, + 295, + 386 + ], + "type": "text", + "content": "More specifically, existing diffusion on action models [14, 56] (i.e. models generating actions) excel in well-defined tasks but often lack generalizability in adapting to complex or new tasks with flexible interaction requirements. They necessitate continual data collection for new goal configurations even within the same dynamics, limiting their effectiveness in contact-rich interactions. In contrast, diffusion on state methods [1, 24, 37], including those adapted from video diffusion models for imitation learning [6, 16], will produce unrealistic \"ghost states\" in interaction tasks. As shown in Fig. 1 and Fig. 2, the visualizations are rendered by setting states frame by frame with predicted output from state-based methods, and show objects react independently of physical contact (e.g. drawers opening on their own before the manipulator reaches them), which cannot actually happen and would result in failure. This issue arises because the object states can't be directly controlled. Actions must first influence dexterous hand's states before impacting the object, revealing the importance of modeling state transitions for physics-driven interactions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 388, + 295, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 519 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 519 + ], + "type": "text", + "content": "Thus, we propose DexHandDiff, an interaction-aware diffusion model tailored for adaptive dexterous manipulation that exhibits goal shifts or cost function variations while maintaining similar dynamics. DexHandDiff models joint state-action dynamics that takes the state output to guide and constrain the action output with realistic physical behavior. A dynamics model-based dual guide is incorporated to maintain coherence with dynamics observed in training data. It addresses the action-state consistency challenge first identified in Diffuser [24] which however prioritized generated state over action, as shown in Fig. 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 713 + ], + "type": "text", + "content": "Specifically, DexHandDiff adopts a goal-adaptive diffusion mechanism with dual-phase process. 1) At first, precontact phase, it guides the manipulator to align with the object's key contact point, such as a handle or the center of object, ensuring stable alignment before initiating physical interaction. 2) In the subsequent post-contact phase, it introduces joint guidance over both the manipulator and the object states, enabling fine-grained control to achieve the target state for the object. This sequential approach integrates both action diffusion that prevents premature influence on the object's state before contact, and state diffusion that ensures effective goal alignment throughout. By generating states and actions in an interaction-aware manner, DexHandDiff produces more coherent and realistic trajectories suited to complex tasks like tool using. Furthermore, to automate guidance function design, DexHandDiff intro" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": "duces an approach using large language models in the text-to-reward paradigm, that can generalize across diverse goals and cost functions via language cues." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "text", + "content": "We conduct experiments on multiple dexterous manipulation tasks to evaluate DexHandDiff's effectiveness, covering both in-domain and goal-adaptability challenges, e.g., adapting to new goal \"door closing\" from \"90-degree door opening\" training data. Results with up to " + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "inline_equation", + "content": "70.0\\%" + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "text", + "content": " success rate on the 30-degree door task (vs. the next best " + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "inline_equation", + "content": "16.7\\%" + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "text", + "content": " for Diffusion Policy) and " + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "inline_equation", + "content": "46.7\\%" + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "text", + "content": " on the hammer nail half-drive task (vs. the next best " + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "inline_equation", + "content": "33.3\\%" + }, + { + "bbox": [ + 313, + 109, + 553, + 228 + ], + "type": "text", + "content": " for Decision Diffuser), confirm DexHandDiff's robustness and adaptability in capturing complex hand-object-environment interactions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 229, + 553, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 553, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 553, + 396 + ], + "type": "text", + "content": "In summary, DexHandDiff advances adaptive dexterous manipulation by: 1) We propose the first interaction-aware, goal-adaptive diffusion planner for dexterous manipulation, modeling manipulator-object-environment dependencies to handle sequential tasks with complex state transitions. 2) By jointly modeling state-action behaviors with dynamics-based dual guidance and LLM-based interaction guidance, DexHandDiff sets a new standard for adaptive planning in dexterous manipulation and for the first time extends text-to-reward concepts to diffusers. 3) Experimental validation on diverse dexterous manipulation tasks, demonstrating its robustness and adaptability. DexHandDiff achieves over twice the average success rate of the next best method (59.2% vs. 29.5%) across goal-directed tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 410, + 406, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 410, + 406, + 423 + ], + "spans": [ + { + "bbox": [ + 314, + 410, + 406, + 423 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 434, + 553, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 553, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 553, + 662 + ], + "type": "text", + "content": "Dexterous Manipulation. Dexterous manipulation [12, 13, 19, 20, 32, 40, 42, 45, 48, 50] with multi-fingered hands enables complex tasks in unstructured environments by mimicking human hand flexibility. Initially, traditional methods using trajectory optimization and precise dynamics models [36, 41], struggled with high-dimensional action spaces and contact-rich dynamics. This led to the adoption of reinforcement learning (RL) [10, 41, 52, 58] for handling complex, high-DOF (degree of freedom) interactions. However, RL requires extensive online exploration and carefully designed reward functions [11, 36] where inadequate reward shaping can hardly learn and it limits adaptability [55, 57]. Demonstration-based methods [57] reduce sample complexity, but they struggle to generalize across sequential, contact-rich tasks. Our DexHandDiff addresses these challenges by explicitly modeling hand-object-environment interactions, enabling goal-adaptive planning without intricate reward shaping, thus allowing for more efficient learning in complex, sequential tasks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "Diffusion-based Planning Methods. Planning with diffusion models has become prominent in imitation learning for robotic manipulation [1, 9, 14, 24, 28-30, 37]. Classifier-guided methods [24, 28] used task-specific classifiers to" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1746" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 168 + ], + "type": "text", + "content": "condition policies, while classifier-free ones integrated task variations within diffusion model [1]. However, classifier-free methods lack flexibility for zero-shot explicit conditioning tasks due to reliance on training data configurations. DexHandDiff addresses this by performing classifier-guided diffusion over both state and action spaces, enabling precise interaction and rich-contact dynamics planning for more realistic, complex and adaptable manipulation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 171, + 296, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 171, + 296, + 351 + ], + "spans": [ + { + "bbox": [ + 55, + 171, + 296, + 351 + ], + "type": "text", + "content": "LLM-based Robot Policy Code Generation. Recent works [7, 27, 35, 51] have demonstrated the potential of LLMs in generating executable code for robotics tasks. Code as Policies [27] showed LLMs can effectively translate high-level task descriptions into functional robot control programs. Eureka [33] and Text2Reward [54] further advanced this direction by generating crucial parameters or complete reward functions from language descriptions, demonstrating well-structured prompts with comprehensive environment information can enable reliable reward shaping. Our work extends this text-to-code paradigm to imitation learning through diffusers. DexHandDiff provides a natural interface for LLM code generation through its guidance function formulation, bridging the gap between task specification and behavioral policies to learn." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 360, + 133, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 360, + 133, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 360, + 133, + 373 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 380, + 198, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 380, + 198, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 198, + 392 + ], + "type": "text", + "content": "3.1. Diffusion Model as Policy" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 396, + 296, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 446 + ], + "type": "text", + "content": "We formulate the dexterous manipulation planning problem within the Markov Decision Process (MDP) framework [39], defined as " + }, + { + "bbox": [ + 55, + 396, + 296, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{M} = (\\mathcal{S},\\mathcal{A},\\mathcal{T},\\mathcal{R},\\gamma)" + }, + { + "bbox": [ + 55, + 396, + 296, + 446 + ], + "type": "text", + "content": ". The objective is to find an optimal action sequence " + }, + { + "bbox": [ + 55, + 396, + 296, + 446 + ], + "type": "inline_equation", + "content": "a_{0:T}^{*}" + }, + { + "bbox": [ + 55, + 396, + 296, + 446 + ], + "type": "text", + "content": " that satisfies:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 446, + 293, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 446, + 293, + 487 + ], + "spans": [ + { + "bbox": [ + 58, + 446, + 293, + 487 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {a} _ {0: T} ^ {*} = \\underset {\\boldsymbol {a} _ {0: T}} {\\arg \\max } \\mathcal {J} (\\boldsymbol {s} _ {0}, \\boldsymbol {a} _ {0: T}) = \\underset {\\boldsymbol {a} _ {0: T}} {\\arg \\max } \\sum_ {t = 0} ^ {T} \\gamma^ {t} R (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}), \\\\ \\text {w h e r e s t a t e t r a n s i t i o n s f o l l o w} \\boldsymbol {s} _ {t + 1} = \\mathcal {T} (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}). \\end{array} \\tag {1}", + "image_path": "6165bbf2c38619943d642fb8f07f99483055f4cf07d989932dc2c229d8347cfb.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 487, + 296, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 296, + 557 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 296, + 557 + ], + "type": "text", + "content": "Following [1, 24], we leverage diffusion models to address this planning problem by treating state and action trajectories " + }, + { + "bbox": [ + 55, + 487, + 296, + 557 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}" + }, + { + "bbox": [ + 55, + 487, + 296, + 557 + ], + "type": "text", + "content": " as sequential data. The reverse process of diffusion learns to denoise trajectories from a standard normal distribution through conditional probability " + }, + { + "bbox": [ + 55, + 487, + 296, + 557 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb{\\tau}^{i-1} \\mid \\pmb{\\tau}^i)" + }, + { + "bbox": [ + 55, + 487, + 296, + 557 + ], + "type": "text", + "content": ". The model is trained to maximize the likelihood:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 82, + 557, + 295, + 584 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 557, + 295, + 584 + ], + "spans": [ + { + "bbox": [ + 82, + 557, + 295, + 584 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0}\\right) = \\int p \\left(\\boldsymbol {\\tau} ^ {N}\\right) \\prod_ {i = 1} ^ {N} p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i - 1} \\mid \\boldsymbol {\\tau} ^ {i}\\right) \\mathrm {d} \\boldsymbol {\\tau} ^ {1: N}, \\tag {2}", + "image_path": "da3fc81020d3cc4e118073e31d28e515b5bcae50ac9303f09b2895592ded33d0.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 583, + 261, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 583, + 261, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 583, + 261, + 594 + ], + "type": "text", + "content": "with the optimization objective inspired by ELBO," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 103, + 597, + 295, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 597, + 295, + 613 + ], + "spans": [ + { + "bbox": [ + 103, + 597, + 295, + 613 + ], + "type": "interline_equation", + "content": "\\theta^ {*} = \\arg \\min _ {\\theta} - \\mathbb {E} _ {\\boldsymbol {\\tau} ^ {0}} \\left[ \\log p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0}\\right) \\right]. \\tag {3}", + "image_path": "0682378805fe44275f9c2ec923c0d83f7668d9d5d6dc98e7a1b6d1a3423b8015.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 614, + 295, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 614, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 55, + 614, + 295, + 638 + ], + "type": "text", + "content": "For practical implementation, we adopt the simplified surrogate loss [22] that focuses on predicting the noise term:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 84, + 641, + 294, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 641, + 294, + 654 + ], + "spans": [ + { + "bbox": [ + 84, + 641, + 294, + 654 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d e n o i s e}} (\\theta) = \\mathbb {E} _ {i, \\boldsymbol {\\tau} ^ {0} \\sim q, \\epsilon \\sim \\mathcal {N}} [ | | \\epsilon - \\epsilon_ {\\theta} (\\boldsymbol {\\tau} ^ {i}, i) | | ^ {2} ]. \\tag {4}", + "image_path": "a95ea685a2be2c0abcdd011d03b9a81a430443918455f43e3ce16b4fd401bc42.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 660, + 279, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 660, + 279, + 673 + ], + "spans": [ + { + "bbox": [ + 55, + 660, + 279, + 673 + ], + "type": "text", + "content": "3.2. Classifier-free Conditional Diffusion Policy" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "To generate high-reward trajectories, classifier-free guidance [15] has been transferred from image to trajectory generation [1]. This approach incorporates guidance signals" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 72, + 505, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 505, + 85 + ], + "type": "inline_equation", + "content": "\\pmb{y}(\\tau)" + }, + { + "bbox": [ + 314, + 72, + 505, + 85 + ], + "type": "text", + "content": " directly in the noise prediction model by:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 328, + 87, + 553, + 100 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 87, + 553, + 100 + ], + "spans": [ + { + "bbox": [ + 328, + 87, + 553, + 100 + ], + "type": "interline_equation", + "content": "\\hat {\\epsilon} = \\epsilon_ {\\theta} (\\boldsymbol {\\tau} ^ {i}, \\varnothing , i) + \\omega \\left(\\epsilon_ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i}, \\boldsymbol {y}, i\\right) - \\epsilon_ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i}, \\varnothing , i\\right)\\right), \\tag {5}", + "image_path": "166afcebb5e6f2fbb083f46151c492978ca311256ebc37c7cf337e87988621ad.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "spans": [ + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "type": "text", + "content": " controls the guidance strength, and " + }, + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "type": "inline_equation", + "content": "\\varnothing" + }, + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "type": "text", + "content": " denotes the absence of conditioning. During sampling, trajectories are generated with the predicted modified noise " + }, + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}" + }, + { + "bbox": [ + 313, + 104, + 553, + 140 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 147, + 493, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 147, + 493, + 159 + ], + "spans": [ + { + "bbox": [ + 314, + 147, + 493, + 159 + ], + "type": "text", + "content": "3.3. Classifier-guided Diffusion Policy" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 164, + 553, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 164, + 553, + 212 + ], + "spans": [ + { + "bbox": [ + 313, + 164, + 553, + 212 + ], + "type": "text", + "content": "Different from classifier-free diffusion models that condition relying solely on implicit representations within the training data, classifier-guided approach, enables direct reward or goal conditioning through gradient-based guidance." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "spans": [ + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "type": "text", + "content": "For reward maximization, it introduces trajectory optimality " + }, + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_t" + }, + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "type": "text", + "content": ", following a Bernoulli distribution where " + }, + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "type": "inline_equation", + "content": "p(\\mathcal{O}_t = 1) = \\exp (\\gamma^t\\mathcal{R}(\\boldsymbol {s}_t,\\boldsymbol {a}_t))" + }, + { + "bbox": [ + 313, + 212, + 553, + 271 + ], + "type": "text", + "content": ". The diffusion process can be naturally extended to incorporate conditioning by sampling from perturbed distributions:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 322, + 273, + 553, + 286 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 273, + 553, + 286 + ], + "spans": [ + { + "bbox": [ + 322, + 273, + 553, + 286 + ], + "type": "interline_equation", + "content": "\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) = p (\\boldsymbol {\\tau} \\mid \\mathcal {O} _ {1: T} = 1) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) p \\left(\\mathcal {O} _ {1: T} = 1 \\mid \\boldsymbol {\\tau}\\right) \\tag {6}", + "image_path": "6fe474c8859bf7220e7a36a2b1e2fe0b1a6850fd3aa5c6ee9d520900c13d110c.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 288, + 553, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 288, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 288, + 553, + 312 + ], + "type": "text", + "content": "Under Lipschitz conditions on " + }, + { + "bbox": [ + 313, + 288, + 553, + 312 + ], + "type": "inline_equation", + "content": "p(\\mathcal{O}_{1:T} \\mid \\tau^i)" + }, + { + "bbox": [ + 313, + 288, + 553, + 312 + ], + "type": "text", + "content": " [17], the reverse diffusion process follows:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 330, + 313, + 553, + 328 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 313, + 553, + 328 + ], + "spans": [ + { + "bbox": [ + 330, + 313, + 553, + 328 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i - 1} \\mid \\boldsymbol {\\tau} ^ {i}, \\mathcal {O} _ {1: T}\\right) \\approx \\mathcal {N} \\left(\\boldsymbol {\\tau} ^ {i - 1}; \\mu_ {\\theta} + \\alpha \\Sigma g, \\Sigma\\right), \\tag {7}", + "image_path": "592fb2fd82122298819ffbc4f7dab450bac3abe9257881a70f6758271939cfb6.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 314, + 330, + 450, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 330, + 450, + 342 + ], + "spans": [ + { + "bbox": [ + 314, + 330, + 450, + 342 + ], + "type": "text", + "content": "where the guidance gradient " + }, + { + "bbox": [ + 314, + 330, + 450, + 342 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 314, + 330, + 450, + 342 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 321, + 343, + 553, + 391 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 343, + 553, + 391 + ], + "spans": [ + { + "bbox": [ + 321, + 343, + 553, + 391 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} g = \\nabla_ {\\tau} \\log p (\\mathcal {O} _ {1: T} | \\tau) | _ {\\tau = \\mu_ {\\theta}} \\\\ = \\sum_ {t = 0} ^ {T} \\gamma^ {t} \\nabla_ {\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}} \\mathcal {R} (\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}) | _ {(\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}) = \\mu_ {t}} = \\nabla_ {\\boldsymbol {\\tau}} \\mathcal {I} (\\mu_ {\\theta}). \\tag {8} \\\\ \\end{array}", + "image_path": "b31705d1ce90b73a6d71b725dcf6cb700ad2a3020cfb395a0f1fab9cfb35ccff.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 392, + 553, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 553, + 427 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 553, + 427 + ], + "type": "text", + "content": "For discrete goal conditioned tasks, the constraint can be simplified by directly substituting conditional values at each diffusion timestep " + }, + { + "bbox": [ + 313, + 392, + 553, + 427 + ], + "type": "inline_equation", + "content": "i \\in \\{0,1,\\dots,N\\}" + }, + { + "bbox": [ + 313, + 392, + 553, + 427 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 437, + 553, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 553, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 553, + 464 + ], + "type": "text", + "content": "4. Analysis of Diffusion-based Planning Methods for Interaction-intensive Tasks" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 471, + 555, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 471, + 555, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 471, + 555, + 579 + ], + "type": "text", + "content": "Current diffusion-based methods are widely adopted for robotic manipulation but reveal significant limitations when applied to dexterous, sequential interaction tasks. Table 1 provides an overview of prominent diffusion-based methods (including Diffuser [24], Decision Diffuser [1], Diffusion Policy [14] and our DexHandDiff), categorizing each by their conditioning approach, action generation method, and goal adaptability. In this section, we analyze these challenges across three key dimensions." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 713 + ], + "type": "text", + "content": "Action-only Diffusion is Limited in Explicit State Conditioning. Existing diffusion on action models like Diffusion Policy (DP) [14], excel in providing precise, consistent action control, benefiting from extensive training data and bypassing errors from inverse kinematics. They yield high performance when training data is sufficient and diverse. However, for tasks requiring variant multi-stage goals, action-only diffusion lacks the flexibility to perform explicit state guidance at intermediate stages, like aligning hand and object state at pre-grasp stage, hurting the adaptability of the whole planner. For example, DP trained on" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1747" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 70, + 533, + 140 + ], + "blocks": [ + { + "bbox": [ + 77, + 70, + 533, + 140 + ], + "lines": [ + { + "bbox": [ + 77, + 70, + 533, + 140 + ], + "spans": [ + { + "bbox": [ + 77, + 70, + 533, + 140 + ], + "type": "table", + "html": "
    MethodDiffusion on State or ActionDiffusion Condition TypeAction Gen MethodGoal AdaptabilityNo Ghost StatesInteraction Aware
    Diffuser [24]StateClassifier-GuidedInverse Dyn✓××
    Decision Diffuser [1]StateClassifier-FreeInverse Dyn× (if diverse data, then ✓)××
    Diffusion Policy [14]ActionClassifier-FreeDirect× (if diverse data, then ✓)✓×
    DexHandDiff (Ours)State & ActionClassifier-GuidedDirect✓✓✓
    ", + "image_path": "e3df7ffbdfcd84cf482d833de34051f794da24b261e5fbd81249538bde2b20cf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 142, + 553, + 154 + ], + "lines": [ + { + "bbox": [ + 55, + 142, + 553, + 154 + ], + "spans": [ + { + "bbox": [ + 55, + 142, + 553, + 154 + ], + "type": "text", + "content": "Table 1. Comparison of diffusion-based approaches for robot manipulation. Quantitative results on door-opening are shown in Sec. 6." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 163, + 295, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 163, + 295, + 187 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 295, + 187 + ], + "type": "text", + "content": "data with opening the door to 90 degrees hardly adapt to open 30 or 60 degrees." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 190, + 296, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 190, + 296, + 381 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 296, + 381 + ], + "type": "text", + "content": "Ghost States in State-only Diffusion for Sequential Interaction. While state-based diffusion models offer the advantage of flexible goal specification, it is only effective in fully actuated tasks where all degrees of freedom (DoF) are directly controllable, such as MuJoCo [24, 46], and gripper pick-and-place (requiring only end-effector position control) [1, 14] tasks. In such scenarios, all states of the system can be manipulated directly. However, in contact-rich interaction task where indirect control exists, such as striking a nail with a hammer using a dexterous hand, additional uncontrollable DoFs, like the hammer head and nail positions, must be changed through transitions from the states of the hand. Applying generation across all states, including those of objects beyond the hand, will result in unrealistic \"ghost states\" where objects appear to move independently of contact but actually cannot, as illustrated in Fig. 1 and Fig. 2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 385, + 296, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 385, + 296, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 296, + 529 + ], + "type": "text", + "content": "Classifier-free vs. Classifier-guided Adaptability. Classifier free diffusion models, valued for not requiring external classifiers, encode task variations directly within the model. This structure is effective for tasks with constraints in observed configurations, but with limited goal adaptability in zero-shot or new-task scenarios. For instance, in the push-T task, DP cannot directly adapt to new target positions due to the fixed goal in training data. In contrast, classifier-guided methods, such as ours, mitigate this limitation by offering adaptable, gradient-based guidance, enabling direct conditioning on new goals or rewards, enhancing flexibility across a range of tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 540, + 111, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 111, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 111, + 553 + ], + "type": "text", + "content": "5. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 560, + 285, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 560, + 285, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 560, + 285, + 574 + ], + "type": "text", + "content": "5.1. Interaction-aware Diffusion-based Planning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 578, + 296, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 578, + 296, + 626 + ], + "spans": [ + { + "bbox": [ + 55, + 578, + 296, + 626 + ], + "type": "text", + "content": "To address these limitations, we propose DexHandDiff, an interaction-aware diffusion planning framework (Fig. 3), maintaining physical consistency and enabling flexible goal adaptation for dexterous manipulation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": "Joint State-Action Diffusion Model. Our approach builds upon classifier-guided diffusion policies. But we jointly diffuse over the concatenated state-action space " + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau} = [(\\pmb{a}_0, \\pmb{s}_0), (\\pmb{a}_1, \\pmb{s}_1), \\dots, (\\pmb{a}_T, \\pmb{s}_T)]" + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": ", where state " + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{s}" + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": " includes both hand (24 joint angles and 3 position offsets) and task-specific object states (i.e. door hinge angle, pen pose etc.), and action " + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{a}" + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": " represents changes in controllable states (only" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 161, + 391, + 234 + ], + "blocks": [ + { + "bbox": [ + 316, + 161, + 391, + 234 + ], + "lines": [ + { + "bbox": [ + 316, + 161, + 391, + 234 + ], + "spans": [ + { + "bbox": [ + 316, + 161, + 391, + 234 + ], + "type": "image", + "image_path": "3da810fba5018dc1e91f01a3ab7adf6f8ef1470731083885f672d6b1fd4e1982.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 236, + 554, + 302 + ], + "lines": [ + { + "bbox": [ + 313, + 236, + 554, + 302 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 554, + 302 + ], + "type": "text", + "content": "Figure 2. Demonstration of ghost states on the pen reorientation task. The visualizations are rendered by setting predicted states frame by frame, which cannot actually happen and will lead to failure. The pen appears to autonomously rotate to the desired pose without any hand manipulation, and the fingers look like moving to grasp the pen at the last frame." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 398, + 161, + 470, + 234 + ], + "blocks": [ + { + "bbox": [ + 398, + 161, + 470, + 234 + ], + "lines": [ + { + "bbox": [ + 398, + 161, + 470, + 234 + ], + "spans": [ + { + "bbox": [ + 398, + 161, + 470, + 234 + ], + "type": "image", + "image_path": "cd3157ebce89c2e6c7796c2ae61d80a6972677c6bde42e19bd402891f01b8fc0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 478, + 161, + 551, + 234 + ], + "blocks": [ + { + "bbox": [ + 478, + 161, + 551, + 234 + ], + "lines": [ + { + "bbox": [ + 478, + 161, + 551, + 234 + ], + "spans": [ + { + "bbox": [ + 478, + 161, + 551, + 234 + ], + "type": "image", + "image_path": "f0f4c3cea822c0e2e50889113aa496646eec453802a4038cce1b36f024f991c8.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 308, + 423, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 308, + 423, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 308, + 423, + 319 + ], + "type": "text", + "content": "hand joints and positions)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 320, + 554, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 320, + 554, + 452 + ], + "spans": [ + { + "bbox": [ + 313, + 320, + 554, + 452 + ], + "type": "text", + "content": "This design choice directly addresses the above mentioned limitations: (1) By including states in the diffusion process, we enable explicit state conditioning and goal specification, overcoming the limitations of action-only approaches; (2) By classifier-guided diffusion, we allow flexible goal adaptation without exhaustive training data; (3) By jointly modeling states and actions, we maintain their physical coupling and prevent ghost states through carefully designed guidance. With denoised states guiding the generated actions, we effectively balance the state conditioning and action precision." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 455, + 554, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 455, + 554, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 455, + 554, + 479 + ], + "type": "text", + "content": "Extended Behavior Model and Energy Function. According to Eq. 6, the standard conditional diffusion follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 338, + 483, + 553, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 483, + 553, + 496 + ], + "spans": [ + { + "bbox": [ + 338, + 483, + 553, + 496 + ], + "type": "interline_equation", + "content": "\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) p \\left(\\mathcal {O} _ {1: T} = 1 \\mid \\boldsymbol {\\tau}\\right) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) h (\\boldsymbol {\\tau}), \\tag {9}", + "image_path": "a2ebe35b7b236e65026355e2e783b5f389e5e45f77f1b674436533d06e5e66c4.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 500, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 500, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 500, + 554, + 544 + ], + "type": "text", + "content": "where we generalize " + }, + { + "bbox": [ + 313, + 500, + 554, + 544 + ], + "type": "inline_equation", + "content": "p(\\mathcal{O}_{1:T} = 1\\mid \\tau)" + }, + { + "bbox": [ + 313, + 500, + 554, + 544 + ], + "type": "text", + "content": " as a behavior model " + }, + { + "bbox": [ + 313, + 500, + 554, + 544 + ], + "type": "inline_equation", + "content": "h(\\tau)" + }, + { + "bbox": [ + 313, + 500, + 554, + 544 + ], + "type": "text", + "content": ". Then we further generalize this formulation through a product of experts framework [21], where each expert represents a specific behavior model:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 384, + 545, + 553, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 545, + 553, + 572 + ], + "spans": [ + { + "bbox": [ + 384, + 545, + 553, + 572 + ], + "type": "interline_equation", + "content": "\\tilde {p} _ {\\theta} (\\boldsymbol {\\tau}) \\propto p _ {\\theta} (\\boldsymbol {\\tau}) \\prod_ {i = 1} ^ {n} h _ {i} (\\boldsymbol {\\tau}). \\tag {10}", + "image_path": "53f9d2f405f0389a20b7d480b19e573dbdb1b56cd6a122259f983fdbe1e83519.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 573, + 554, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 573, + 554, + 596 + ], + "spans": [ + { + "bbox": [ + 313, + 573, + 554, + 596 + ], + "type": "text", + "content": "From the energy function perspective, each behavior model encoding task-specific objectives or constraints is:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 366, + 596, + 553, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 596, + 553, + 619 + ], + "spans": [ + { + "bbox": [ + 366, + 596, + 553, + 619 + ], + "type": "interline_equation", + "content": "h _ {i} (\\boldsymbol {\\tau}, c) = \\frac {1}{\\int e ^ {- \\varepsilon_ {i} (\\boldsymbol {\\tau} , c)} d \\boldsymbol {\\tau}} e ^ {- \\varepsilon_ {i} (\\boldsymbol {\\tau}, c)}, \\tag {11}", + "image_path": "558be4603c06feeaa1e036e206475c36547a9249f64bc90078a685ab4275c37b.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "spans": [ + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "type": "inline_equation", + "content": "\\varepsilon_{i}(\\pmb{\\tau}, c)" + }, + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "type": "text", + "content": " represents the energy function for the " + }, + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "type": "text", + "content": "-th guidance objective, with " + }, + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 621, + 554, + 680 + ], + "type": "text", + "content": " denoting task-specific conditions. This formulation allows combining multiple objectives (e.g., reaching the target state while maintaining physical consistency) via their respective guidance functions." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 680, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 680, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 680, + 554, + 713 + ], + "type": "text", + "content": "Under appropriate smoothness conditions, the guidance gradient " + }, + { + "bbox": [ + 313, + 680, + 554, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 680, + 554, + 713 + ], + "type": "text", + "content": " in the reverse diffusion process (Eq. 7) can be decomposed as the sum of individual guidance gradients:" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1748" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 73, + 539, + 253 + ], + "blocks": [ + { + "bbox": [ + 69, + 73, + 539, + 253 + ], + "lines": [ + { + "bbox": [ + 69, + 73, + 539, + 253 + ], + "spans": [ + { + "bbox": [ + 69, + 73, + 539, + 253 + ], + "type": "image", + "image_path": "8658e549fb027002ab91b80536332c2b2d659c38e5f94dafe6ccb261302f21ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 253, + 555, + 309 + ], + "lines": [ + { + "bbox": [ + 54, + 253, + 555, + 309 + ], + "spans": [ + { + "bbox": [ + 54, + 253, + 555, + 309 + ], + "type": "text", + "content": "Figure 3. Framework of DexHandDiff. DexHandDiff employs joint state-action diffusion with interaction-aware guidance. Before interaction (top middle), guidance aligns the hand to the object contact point. Upon contact (bottom middle), additional guidance steers both hand and object states towards the goal (\"&\" means state concatenation at input level), enforcing physical constraints and avoiding ghost states. A learned dynamics model further ensures consistency between states and actions. Our DexHandDiff utilizes extended behavior model to aggregate multiple condition terms to guide the diffusion process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 313, + 296, + 341 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 313, + 296, + 341 + ], + "spans": [ + { + "bbox": [ + 55, + 313, + 296, + 341 + ], + "type": "interline_equation", + "content": "g = \\nabla_ {\\boldsymbol {\\tau}} \\log \\prod_ {i = 1} ^ {n} h _ {i} (\\boldsymbol {\\tau}) = \\sum_ {i = 1} ^ {n} \\nabla_ {\\boldsymbol {\\tau}} \\log h _ {i} (\\boldsymbol {\\tau}) = - \\sum_ {i = 1} ^ {n} \\nabla_ {\\boldsymbol {\\tau}} \\varepsilon_ {i} (\\boldsymbol {\\tau}, c).", + "image_path": "5297b0f9e5a738aae44448d181b6be03d6d25a0f7acd45b32f1e1cd25d03c20b.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 342, + 296, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 296, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 296, + 378 + ], + "type": "text", + "content": "This enables integration of multiple guidance signals, each addressing different aspects of the interaction task, while maintaining a coherent optimization objective." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 380, + 296, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 380, + 296, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 296, + 479 + ], + "type": "text", + "content": "Dynamics-aware Generation. A key challenge in joint state-action diffusion is maintaining consistency between generated states and actions [24]. Our method addresses this through a learned dynamics model trained on demonstration data, constraining state-action generation via additional loss in diffusion training and serving as a guide in inference. By penalizing state-action pairs that violate observed dynamics, this guidance ensures our model maintains both state conditioning benefits and action feasibility." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 481, + 294, + 494 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 481, + 294, + 494 + ], + "spans": [ + { + "bbox": [ + 116, + 481, + 294, + 494 + ], + "type": "interline_equation", + "content": "\\varepsilon_ {\\mathrm {d y n}} (\\boldsymbol {\\tau}) = \\left| \\boldsymbol {s} _ {t + 1} - \\mathcal {T} \\left(\\boldsymbol {s} _ {t}, \\boldsymbol {a} _ {t}\\right) \\right| ^ {2}, \\tag {12}", + "image_path": "df79959720c06fd429d23b31064559b1e971c47a17b378c1f469ece3b61e6d08.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 495, + 295, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 295, + 519 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 295, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 495, + 295, + 519 + ], + "type": "inline_equation", + "content": "\\mathcal{T}(s, a)" + }, + { + "bbox": [ + 55, + 495, + 295, + 519 + ], + "type": "text", + "content": " is a separately trained dynamics model to ensure physically plausible motion patterns." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 522, + 295, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 295, + 629 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 295, + 629 + ], + "type": "text", + "content": "Manipulation after Contact Task Guidance. For manipulation after contact tasks such as door opening and tool using, DexHandDiff employs a dual-phase interaction approach that acknowledges the fundamentally different nature of interaction before and after contact establishment. The framework automatically determines the phase transition based on the distance between the palm position and the designated contact point on the object, applying a smooth transition mask to blend between phases." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": "In the pre-grasp phase, our method focuses on guiding the manipulator to stably align with the contact point while preventing premature object movement. We engineer two primary guidance components: 1) Alignment guidance " + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{align}}" + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": " that directs the end-effector towards precise contact point while maintaining natural approaching trajectory; 2) Dynamics consistency guidance " + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{dyn}}" + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "type": "text", + "content": "Upon establishing contact (determined by palm-object proximity), the post-grasp phase activates additional guidance mechanisms: 1) Goal-directed guidance " + }, + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{succ}}" + }, + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "type": "text", + "content": " that steers the coupled hand-object system towards target configurations; 2) Physical constraint guidance " + }, + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{penalty}}" + }, + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "type": "text", + "content": " that prevents unrealistic state changes (e.g., limiting per-step changes in both door hinge and latch angles); 3) Continued dynamics guidance " + }, + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{dyn}}" + }, + { + "bbox": [ + 313, + 315, + 555, + 410 + ], + "type": "text", + "content": " to maintain motion feasibility." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 325, + 410, + 524, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 410, + 524, + 421 + ], + "spans": [ + { + "bbox": [ + 325, + 410, + 524, + 421 + ], + "type": "text", + "content": "Therefore, the guidance energy function follows," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 324, + 423, + 553, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 423, + 553, + 449 + ], + "spans": [ + { + "bbox": [ + 324, + 423, + 553, + 449 + ], + "type": "interline_equation", + "content": "\\epsilon = \\left\\{ \\begin{array}{l l} \\epsilon_ {\\text {p r e}} = \\epsilon_ {\\text {a l i g n}} + \\epsilon_ {\\text {d y n}} & \\text {i f} | \\boldsymbol {s} _ {\\text {h a n d}} - \\boldsymbol {s} _ {\\text {c o n t a c t}} | > \\delta_ {1} \\\\ \\epsilon_ {\\text {p o s t}} = \\epsilon_ {\\text {s u c c}} + \\epsilon_ {\\text {d y n}} + \\epsilon_ {\\text {p e n a l t y}} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {13}", + "image_path": "bf34ac084707255918255f20ed6835564a5bc2b636289c5fd5f4e309545e79b0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "inline_equation", + "content": "s_{\\text{hand}}" + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "inline_equation", + "content": "s_{\\text{contact}}" + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "text", + "content": " represents the states of dexterous hand and object contact point (e.g. door latch, hammer handle etc.) respectively, and " + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "inline_equation", + "content": "\\delta_1" + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "text", + "content": " is a small threshold. The separated design of grasp proposal guidance " + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\text{align}})" + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "text", + "content": " and task achieving guidance " + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\text{succ}})" + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "text", + "content": " mirrors successful policies in prior work [47, 52], effective for dexterous manipulation. Besides, the " + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\text{penalty}}" + }, + { + "bbox": [ + 313, + 449, + 555, + 544 + ], + "type": "text", + "content": " ensures continuous object state transitions, corresponding to" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 353, + 546, + 553, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 546, + 553, + 561 + ], + "spans": [ + { + "bbox": [ + 353, + 546, + 553, + 561 + ], + "type": "interline_equation", + "content": "h _ {p e n a l t y} \\triangleq 1 - H \\left(\\left| s _ {o b j} ^ {t + 1} - s _ {o b j} ^ {t} \\right| - \\delta_ {2}\\right), \\tag {14}", + "image_path": "1e7a8d6215fff66f81b941143f51ba7dce7d79b3a80bd1dff1194c9c680b7f72.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "type": "inline_equation", + "content": "\\delta_{2}" + }, + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "type": "text", + "content": " is another small threshold and " + }, + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "type": "inline_equation", + "content": "H(\\cdot)" + }, + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "type": "text", + "content": " is the Heaviside step function [49]. Then " + }, + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{penalty}}" + }, + { + "bbox": [ + 313, + 563, + 554, + 612 + ], + "type": "text", + "content": " can be obtained by applying Eq. 11, becoming a Dirac delta function that directly sets value when satisfying the constraints." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 613, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 555, + 714 + ], + "type": "text", + "content": "In-hand Manipulation Task Guidance. For tasks primarily involving in-hand manipulation (e.g., pen spinning, object reorientation), where objects are typically already in hand or quickly transition to in-hand states, we employ a simplified single-phase guidance structure: 1) Goal state guidance " + }, + { + "bbox": [ + 313, + 613, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{succ}}" + }, + { + "bbox": [ + 313, + 613, + 555, + 714 + ], + "type": "text", + "content": " for achieving target object configurations; 2) Active finger motion guidance to ensure realistic object manipulation; 3) Dynamics consistency guidance " + }, + { + "bbox": [ + 313, + 613, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{dyn}}" + }, + { + "bbox": [ + 313, + 613, + 555, + 714 + ], + "type": "text", + "content": " to maintain physical plausibility; 4) Physical constraint guidance" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1749" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 73, + 239, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 73, + 239, + 84 + ], + "spans": [ + { + "bbox": [ + 55, + 73, + 239, + 84 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{penalty}}" + }, + { + "bbox": [ + 55, + 73, + 239, + 84 + ], + "type": "text", + "content": " that prevents unrealistic state changes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 113, + 86, + 294, + 97 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 86, + 294, + 97 + ], + "spans": [ + { + "bbox": [ + 113, + 86, + 294, + 97 + ], + "type": "interline_equation", + "content": "\\epsilon = \\epsilon_ {\\text {g o a l}} + \\epsilon_ {\\text {f i n g e r}} + \\epsilon_ {\\text {d y n}} + \\epsilon_ {\\text {p e n a l t y}}. \\tag {15}", + "image_path": "c6919642f94dfe9a8fee375a5bccfb38a1957a04c883085b14bf3cf62fd18cee.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 99, + 295, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 99, + 295, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 99, + 295, + 120 + ], + "type": "text", + "content": "Specially, we define the behavior model that encourages active finger involvement as," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 121, + 295, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 121, + 295, + 135 + ], + "spans": [ + { + "bbox": [ + 85, + 121, + 295, + 135 + ], + "type": "interline_equation", + "content": "h _ {\\text {f i n g e r}} (\\tau , t) = H \\left(\\left| \\boldsymbol {s} _ {\\text {f i n g e r - j o i n t s}} ^ {t + 1} - \\boldsymbol {s} _ {\\text {f i n g e r - j o i n t s}} ^ {t}\\right| - \\delta_ {3}\\right), \\tag {16}", + "image_path": "cf88eed47e7d6d44ca2a974da921b96cb648da90da914289886da68cf1ccd071.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "inline_equation", + "content": "s_{\\text{finger-joints}}^t" + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "text", + "content": " is the state vector of all finger joints at planning step " + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "inline_equation", + "content": "\\delta_3" + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "text", + "content": " is the third small threshold. " + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "inline_equation", + "content": "H(\\cdot)" + }, + { + "bbox": [ + 55, + 137, + 295, + 185 + ], + "type": "text", + "content": " is also the Heaviside step function. This specialized handling prevents unrealistic \"ghost states\", as discussed in Sec. 4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 190, + 239, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 190, + 239, + 202 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 239, + 202 + ], + "type": "text", + "content": "5.2. LLM-Based Guidance Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 208, + 295, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 208, + 295, + 280 + ], + "spans": [ + { + "bbox": [ + 55, + 208, + 295, + 280 + ], + "type": "text", + "content": "The design of task-specific guidance functions for diffusion policies traditionally requires significant manual effort, particularly for diverse dexterous manipulation tasks. To address this challenge, we leverage a two-stage Large Language Model (LLM) process for automated guidance generation, adopting text-to-reward paradigm [33, 54]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 283, + 295, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 403 + ], + "type": "text", + "content": "Overall Pipeline. First, we feed the LLM with a 6-part template (including function purpose, guidance structure, environment description, function prototype, task instruction and few-shot hints) and public documents on simulation environments [38, 41] to generate task-specific prompts. Then, the generated task prompts are queried to another LLM to write guidance function code. Only few-shot hints require specific refinement, reducing human trial-and-error times from about 20 (for hand-craft energy function design) to around 5 while maintaining DexHandDiff performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 405, + 295, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 405, + 295, + 490 + ], + "spans": [ + { + "bbox": [ + 55, + 405, + 295, + 490 + ], + "type": "text", + "content": "Environment Description. Our approach employs a comprehensive Pythonic environment abstraction that captures the complete interaction system. It encapsulates detailed robot joint configurations, and object-environment specifications from public documents, enabling LLM to generate precise guidance functions that account for the full complexity of dexterous manipulation tasks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 492, + 295, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 492, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 492, + 295, + 635 + ], + "type": "text", + "content": "Other Details. As previous works [54], once the guidance function code is generated, we execute the code in interpreter. This step may give us valuable feedback, e.g., syntax errors and runtime errors. We utilize the feedback from code execution as a tool for ongoing refinement within the LLM. Besides, our approach uses few-shot hints instead of examples to allow the model to access relevant functions and best practices without direct examples. Each guidance component is normalized over the trajectory horizon to ensure balanced contributions across objectives while preserving their temporal structure. Detailed examples of prompts and generated guidance functions are shown in Appx. E." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 646, + 135, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 646, + 135, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 646, + 135, + 659 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "We evaluate our DexHandDiff on five challenging dexterous manipulation tasks with four from Adroit Hand [41] and one from Shadow Hand environment [38]. Both environments feature a 24-joint Shadow Hand simulator with up to" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": "30 degrees of freedom, designed to closely match the hardware setting [44]. Detailed explanations of the five tasks are provided in Appendix B. We use the expert demonstrations collected by teleoperation from D4RL [18] for Adroit tasks (Door, Hammer, Pen and Relocate). However, Shadow Hand environment does not provide demonstration data, so we employ TQC+HER [3, 26] to collect 5000 expert trajectories for the Block Rotate-Z task." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 178, + 553, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 178, + 553, + 202 + ], + "spans": [ + { + "bbox": [ + 313, + 178, + 553, + 202 + ], + "type": "text", + "content": "6.1. Performance Comparisons on Goal Adaptability in Interaction-Aware Tasks" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 208, + 553, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 208, + 553, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 208, + 553, + 304 + ], + "type": "text", + "content": "We evaluate DexHandDiff in the Door environment to test its goal adaptability across various target angles. Specifically, we require the planners to open the door to 30, 50, 70, 90 and 110 degrees, as well as close the door (reversal task). Note that the training data only includes 90-degree door-opening demonstrations. For some of these tasks, we adjust the environment settings, such as expanding the door's range of motion, to satisfy the evaluation requirements." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 304, + 554, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 304, + 554, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 304, + 554, + 437 + ], + "type": "text", + "content": "We compare DexHandDiff with five baselines: two classifier-guided methods (Diffuser [24] with Goal Inpainting that sets discrete goal states, and Diffuser with Guided Sampling that leverages continuous gradients for fine control), two classifier-free methods (Decision Diffuser [1] and Diffusion Policy [14] that apply diffusion on states and actions respectively), and a variant of DexHandDiff (denoted DexHandDiff-disc.) that uses goal inpainting. To enhance classifier-free methods' learning of goal condition, we use the difference between the current door angle and target angle as the condition, rather than a fixed " + }, + { + "bbox": [ + 313, + 304, + 554, + 437 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 313, + 304, + 554, + 437 + ], + "type": "text", + "content": " target." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "content": "The results are shown in Tab. 2. Classifier-free methods perform well on the " + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "content": " task, but their success declines sharply on new target angles, indicating limited adaptability to out-of-distribution targets. Classifier-guided methods demonstrate moderate but consistent performance across goal-adaptive tasks yet their overall success rates remain suboptimal due to imprecise state-action relation modeling in the policy. Our DexHandDiff achieves consistently high success rates across nearly all tasks. The slightly lower performance " + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "inline_equation", + "content": "(90.0\\%)" + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "content": " on the training task " + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "inline_equation", + "content": "(90^{\\circ})" + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "content": " compared to classifier-free methods stems from our additional guidance for adaptation. When ablating this, DexHandDiff achieves " + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "inline_equation", + "content": "96.7 \\pm 4.7\\%" + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "content": " success rate on Open " + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "content": ", which is a reasonable trade-off for better generalization. Averaging a " + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "inline_equation", + "content": "59.2\\%" + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "content": " success rate, over twice that of the next best method " + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "inline_equation", + "content": "(29.5\\%)" + }, + { + "bbox": [ + 313, + 437, + 554, + 640 + ], + "type": "text", + "content": ", DexHandDiff demonstrates robust adaptability across both in-domain and goal-adaptive scenarios." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "content": "Besides, we also observe a trend that goals closer to the original training data don't have higher success rates than others. We suppose it's because when target angle is close to training, learned dynamics often override guidance. We observed 8 out of 14 failures in 30 tries in " + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "inline_equation", + "content": "70^{\\circ}" + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "content": " task opened to " + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "content": " instead, supporting our hypothesis. This learned bias" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1750" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 550, + 168 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 550, + 168 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 550, + 168 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 550, + 168 + ], + "type": "table", + "html": "
    MethodConditionOpen 30°Open 50°Open 70°Open 90°Open 110°Close DoorAverage
    Diffuser [24]Goal Inpainting16.7 ±4.716.7 ±12.56.7 ±4.756.7 ±9.410.0 ±8.2017.8
    Diffuser [24]Guided Sampling10.0 ±8.226.7 ±17.010.0 ±4.763.3 ±18.76.7 ±9.460.0 ±8.229.5
    Decision Diffuser [1]Embedding03.3 ±4.716.7 ±4.7100 ±030.0 ±8.2025.0
    Diffusion Policy [14]Embedding16.7 ±4.73.3 ±4.713.3 ±12.5100 ±03.3 ±4.7022.8
    DexHandDiff-disc.Goal Inpainting46.7 ±4.713.3 ±9.453.3 ±4.720.0 ±8.26.7 ±4.7023.3
    DexHandDiff (Ours)Guided Sampling70.0 ±8.256.7 ±4.753.3 ±8.290.0 ±8.226.7 ±14.158.3 ±13.459.2
    ", + "image_path": "594c1346e3ba81147643ad300bfa46351d827bd7c8431bfad40b6adec37adc8f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 83, + 211, + 529, + 361 + ], + "blocks": [ + { + "bbox": [ + 55, + 171, + 555, + 205 + ], + "lines": [ + { + "bbox": [ + 55, + 171, + 555, + 205 + ], + "spans": [ + { + "bbox": [ + 55, + 171, + 555, + 205 + ], + "type": "text", + "content": "Table 2. Success rates (in %) of different diffusion-based approaches in Adroit Hand [41] environment. All models were trained on the Open " + }, + { + "bbox": [ + 55, + 171, + 555, + 205 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 55, + 171, + 555, + 205 + ], + "type": "text", + "content": " task only, and we test their adaptability to other task goals in Adroit Door environment. All results and standard deviation are calculated over 3 tries for 10 random seeds. Best methods and those within " + }, + { + "bbox": [ + 55, + 171, + 555, + 205 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 55, + 171, + 555, + 205 + ], + "type": "text", + "content": " of the best are highlighted in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 211, + 529, + 361 + ], + "lines": [ + { + "bbox": [ + 83, + 211, + 529, + 361 + ], + "spans": [ + { + "bbox": [ + 83, + 211, + 529, + 361 + ], + "type": "table", + "html": "
    EnvironmentTaskDiffuser [24] (Inpaint)Conditional DP [1, 14]DexHandDiff (Ours)
    DoorOpen 90°56.7 ±9.4100 ±090.0 ±8.2
    DoorOpen 30°16.7 ±4.716.7 ±4.770.0 ±8.2
    PenFull Re-orientation10.0 ±080.0 ±8.293.3 ±4.7
    PenHalf-side Re-orientation3.3 ±4.723.3 ±9.440.0 ±8.2
    HammerNail Full Drive53.3 ±9.476.7 ±9.490.0 ±8.2
    HammerNail Half Drive23.3 ±12.533.3 ±4.746.7 ±12.5
    RelocateFull Relocation56.7 ±4.796.7 ±4.796.7 ±4.7
    RelocateHalf-side Relocation53.3 ±4.786.7 ±12.593.3 ±4.7
    Manipulate BlockRotate-Z36.7 ±12.540.0 ±8.250.0 ±8.2
    Manipulate BlockHalf-side Rotate-Z30.0 ±026.7 ±4.736.7 ±4.7
    Average34.058.070.7
    ", + "image_path": "1b9e88c9eb023f1fdb5bb3e6792dfc21b62417f962ea30a88b2607b9eec5573b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 395, + 249, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 395, + 249, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 395, + 249, + 407 + ], + "type": "text", + "content": "is harder to correct than for more distant angles." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 418, + 261, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 418, + 261, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 418, + 261, + 430 + ], + "type": "text", + "content": "6.2. Evaluation on Various Dexterous Tasks" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 437, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 437, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 54, + 437, + 295, + 616 + ], + "type": "text", + "content": "To evaluate the cross-task adaptability and goal-oriented performance of DexHandDiff, we test it across multiple dexterous manipulation tasks in Door, Pen, Hammer, Relocate and Block environments, as summarized in Tab. 3. In addition to the Door task, the Pen task involves aligning a pen to the specified orientation, with a particularly challenging goal-adaptability variant, Half-side Re-orientation, where training data includes only right-hemisphere orientations while test goals require left-hemisphere rotations. Similarly, the Block Rotate-Z and Object Relocation tasks have block's half-side variant trained on positive goal yaw angles but tested on negative ones and object's target right-half table training but left-half testing. The Nail Half Drive requires the hand to drive a nail and stop halfway before retracting, testing control precision for partial goals." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 617, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 617, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 617, + 295, + 713 + ], + "type": "text", + "content": "We compare DexHandDiff with two baselines: Diffuser [24] (Inpainting), using classifier-guided goal inpainting as in the previous section, and Conditional DP [1, 14], a classifier-free approach with state diffusion for Door, Hammer and Relocate tasks while action diffusion for Pen and Block tasks, as modeling dynamics for these tasks are particularly challenging, making direct action generation more effective than state-based diffusion. As shown in Tab. 3," + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 316, + 393, + 554, + 429 + ], + "blocks": [ + { + "bbox": [ + 55, + 364, + 555, + 385 + ], + "lines": [ + { + "bbox": [ + 55, + 364, + 555, + 385 + ], + "spans": [ + { + "bbox": [ + 55, + 364, + 555, + 385 + ], + "type": "text", + "content": "Table 3. Overall performance of dexterous manipulation with goal adaptability on multiple environments and tasks. We compare our method with one classifier-guided baseline and one classifier-free baseline. The results are calculated over 3 tries for 10 random seeds." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 393, + 554, + 429 + ], + "lines": [ + { + "bbox": [ + 316, + 393, + 554, + 429 + ], + "spans": [ + { + "bbox": [ + 316, + 393, + 554, + 429 + ], + "type": "table", + "html": "
    Adapt TasksDoor 30°Door 70°Pen HalfHammer HalfRelocate Half
    Diffuser [24]4.194.035.234.015.48
    DexHandDiff2.922.382.762.413.22
    ", + "image_path": "2b6c434e4f3daef184002a8ee63ecab5df46a275706bc0ca90bbc98cce1c21ce.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 431, + 555, + 453 + ], + "lines": [ + { + "bbox": [ + 313, + 431, + 555, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 555, + 453 + ], + "type": "text", + "content": "Table 4. Quantitative results for preventing ghost states over 3 tries. (Conditional DP is not included due to its action-only.)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 460, + 554, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 554, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 554, + 567 + ], + "type": "text", + "content": "DexHandDiff consistently achieves superior results across both in-domain and goal-adaptive tasks. Although conditional DP demonstrates " + }, + { + "bbox": [ + 313, + 460, + 554, + 567 + ], + "type": "inline_equation", + "content": "23.3\\%" + }, + { + "bbox": [ + 313, + 460, + 554, + 567 + ], + "type": "text", + "content": " on the challenging pen half-side re-orientation, leveraging the inherent multi-modality and anisotropy of diffusion models, DexHandDiff still performs better " + }, + { + "bbox": [ + 313, + 460, + 554, + 567 + ], + "type": "inline_equation", + "content": "(40.0\\%)" + }, + { + "bbox": [ + 313, + 460, + 554, + 567 + ], + "type": "text", + "content": ". These results underscore DexHand-Diff's robustness and adaptability across a range of tasks, demonstrating generalization on familiar goals and novel configuration challenges." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 574, + 517, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 517, + 587 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 517, + 587 + ], + "type": "text", + "content": "6.3. Validation for Preventing Ghost States" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 592, + 555, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 592, + 555, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 592, + 555, + 641 + ], + "type": "text", + "content": "We measured " + }, + { + "bbox": [ + 313, + 592, + 555, + 641 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 313, + 592, + 555, + 641 + ], + "type": "text", + "content": " distance between predicted and simulated hand-object states (normalized per dimension for fair comparison) in Tab. 4. DexHandDiff nearly halves baseline's gap across tasks, illustrating its ghost-state reduction effect." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 648, + 553, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 553, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 553, + 659 + ], + "type": "text", + "content": "6.4. Ablation on LLM-based Guidance Generation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "Table 5 presents results for different guidance methods on goal adaptability tasks. All three methods are based on the same joint state-action diffusion model. The Human Craft approach reflects our above results with manually de" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 313, + 757 + ], + "type": "text", + "content": "1751" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 79, + 120, + 137 + ], + "blocks": [ + { + "bbox": [ + 63, + 72, + 124, + 79 + ], + "lines": [ + { + "bbox": [ + 63, + 72, + 124, + 79 + ], + "spans": [ + { + "bbox": [ + 63, + 72, + 124, + 79 + ], + "type": "text", + "content": "Train Data (Open " + }, + { + "bbox": [ + 63, + 72, + 124, + 79 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 63, + 72, + 124, + 79 + ], + "type": "text", + "content": ")" + } + ] + } + ], + 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    TaskNaïve GuideHuman CraftLLM Gen
    Door Open 30°070.0 ±8.240.0 ±8.2
    Pen Half-side Re-orien20.0 ±8.240.0 ±8.226.7 ±4.7
    Hammer Half Nail20.0 ±8.246.7 ±12.543.3 ±9.4
    ", + "image_path": "52552eb741d7d1b4b236b5b0e2ea39b8037b59683e8b575bc42ee7484743fbc5.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "table_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 55, + 329, + 296, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 329, + 296, + 401 + ], + "spans": [ + { + "bbox": [ + 55, + 329, + 296, + 401 + ], + "type": "text", + "content": "signed guidance. LLM Gen generate guidance functions with Claude Sonnet 3.5 [5]. And Naïve Guide directly guides the object to the goal, corresponding to ghost-state existing baseline. Results indicate that both Human Craft and LLM Gen significantly outperform Naïve Guide across tasks, with Human Craft achieving the highest success rates." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 55, + 408, + 285, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 408, + 285, + 420 + ], + "spans": [ + { + "bbox": [ + 55, + 408, + 285, + 420 + ], + "type": "text", + "content": "6.5. Ablation Study of DexHandDiff Framework" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "text", + "content": "We analyze the contribution of each component in DexHandDiff through ablation studies (Tab. 6), across multiple door-opening tasks (open " + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "inline_equation", + "content": "30^{\\circ}" + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "inline_equation", + "content": "50^{\\circ}" + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "inline_equation", + "content": "70^{\\circ}" + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "text", + "content": "), using the same training checkpoint for fair comparison. The baseline Diffuser[24] uses a basic goal-guidance strategy, while Dyn-guide enhances it with dynamics guidance for better state-action consistency. Joint S&A adopts joint state-action denoising like DexHandDiff but retains naive goal guidance. DexHandDiff incorporates all components and achieves the highest success rate of " + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "inline_equation", + "content": "67.5\\%" + }, + { + "bbox": [ + 55, + 426, + 296, + 569 + ], + "type": "text", + "content": ", significantly outperforming the other configurations and demonstrating the effectiveness of our full design." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 55, + 576, + 144, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 576, + 144, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 576, + 144, + 588 + ], + "type": "text", + "content": "6.6. Visualizations" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": "We visualize the behavior of DexHandDiff across various goal-adaptive dexterous tasks in Fig. 4. DexHandDiff ensures realistic contact by aligning hands with contact points first using joint dynamics modeling, eliminating ghost states. Notably, for example, DexHandDiff guides the door to new target angle and holds the door steady when the hand releases, which cannot be achieved by policies trained with slicing " + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 55, + 594, + 296, + 714 + ], + "type": "text", + "content": " data. These results underscore DexHandDiff's ability to maintain physically realistic interactions while adapting to novel goals." + } + ] + } + ], + "index": 31 + }, + { + "type": "table", + "bbox": [ + 316, + 259, + 554, + 336 + ], + "blocks": [ + { + "bbox": [ + 59, + 311, + 291, + 322 + ], + "lines": [ + { + "bbox": [ + 59, + 311, + 291, + 322 + ], + "spans": [ + { + "bbox": [ + 59, + 311, + 291, + 322 + ], + "type": "text", + "content": "Table 5. Ablation study on LLM-based guidance generation." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 259, + 554, + 336 + ], + "lines": [ + { + "bbox": [ + 316, + 259, + 554, + 336 + ], + "spans": [ + { + "bbox": [ + 316, + 259, + 554, + 336 + ], + "type": "table", + "html": "
    MethodGoal GuidanceDynamics GuideJoint State ActionInteract MechanismOverall SR
    No-guide××××24.1
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    Joint S&A✓×✓×30.8
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    ", + "image_path": "365738ed86e7f34c15fb3cdbf3154afedc4154750da4811245fe138d4c0b2cf1.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "table_body" + } + ], + "index": 32 + }, + { + "bbox": [ + 314, + 378, + 383, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 378, + 383, + 392 + ], + "spans": [ + { + "bbox": [ + 314, + 378, + 383, + 392 + ], + "type": "text", + "content": "6.7. Efficiency" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 313, + 396, + 555, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 555, + 433 + ], + "type": "text", + "content": "We test the control frequency of DexHandDiff on an RTX 3090 with receding horizon set as 8 for all tasks except Door (32 instead). The control frequency are reported below." + } + ] + } + ], + "index": 35 + }, + { + "type": "table", + "bbox": [ + 346, + 436, + 524, + 463 + ], + "blocks": [ + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "lines": [ + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "spans": [ + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "text", + "content": "Table 6. Ablation study on DexHandDiff framework. We report the average success rates (overall SR) on Adroit Door environment over open " + }, + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "inline_equation", + "content": "30^{\\circ}" + }, + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "inline_equation", + "content": "50^{\\circ}" + }, + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "inline_equation", + "content": "70^{\\circ}" + }, + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 313, + 337, + 555, + 370 + ], + "type": "text", + "content": " tasks." + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 346, + 436, + 524, + 463 + ], + "lines": [ + { + "bbox": [ + 346, + 436, + 524, + 463 + ], + "spans": [ + { + "bbox": [ + 346, + 436, + 524, + 463 + ], + "type": "table", + "html": "
    TaskDoorPenHammerRelocateBlock
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    ", + "image_path": "02fa21b2fca728ba5442ae859647a54e7976c18f5d2e71583e3b7f3b26ec9f62.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "table_body" + } + ], + "index": 36 + }, + { + "bbox": [ + 335, + 465, + 532, + 476 + ], + "lines": [ + { + "bbox": [ + 335, + 465, + 532, + 476 + ], + "spans": [ + { + "bbox": [ + 335, + 465, + 532, + 476 + ], + "type": "text", + "content": "Table 7. Control command frequency over 10 tries." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 479, + 554, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 554, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 554, + 526 + ], + "type": "text", + "content": "Besides, our lightweight model (3.96M params, 3.27 GFLOPS) can be further accelerated via DPM Solver++ [31] (4x speedup) and command interpolation (reaching " + }, + { + "bbox": [ + 313, + 479, + 554, + 526 + ], + "type": "inline_equation", + "content": "36\\mathrm{Hz}" + }, + { + "bbox": [ + 313, + 479, + 554, + 526 + ], + "type": "text", + "content": "), sufficient for real robot control." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 314, + 536, + 388, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 536, + 388, + 549 + ], + "spans": [ + { + "bbox": [ + 314, + 536, + 388, + 549 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 313, + 556, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 555, + 689 + ], + "type": "text", + "content": "This work presents DexHandDiff, an interaction-aware diffusion planner for adaptive dexterous manipulation. By modeling joint state-action dynamics and incorporating a dual-phase diffusion mechanism, it addresses action-state consistency issues, including the \"ghost state\" and generalization problems observed in previous diffusion methods. DexHandDiff's design enables it to handle intricate multi-contact interactions through a pre-contact alignment and a post-contact control. We believe its potential to advance the field toward diverse dexterous tasks while remaining grounded in real physics and dynamics." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 713 + ], + "type": "text", + "content": "Future Work can investigate deployment with hand states sensed and object poses estimated by vision models." + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1752" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 157, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 91, + 294, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 91, + 294, + 116 + ], + "spans": [ + { + "bbox": [ + 56, + 91, + 294, + 116 + ], + "type": "text", + "content": "This paper is partially supported by the General Research Fund of Hong Kong No.17200622 and 17209324." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 129, + 115, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 129, + 115, + 140 + ], + "spans": [ + { + "bbox": [ + 56, + 129, + 115, + 140 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 148, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 62, + 148, + 296, + 202 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 148, + 296, + 202 + ], + "spans": [ + { + "bbox": [ + 62, + 148, + 296, + 202 + ], + "type": "text", + "content": "[1] Anurag Ajay, Yilun Du, Abhi Gupta, Joshua B Tenenbaum, Tommi S Jaakkola, and Pulkit Agrawal. 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IEEE, 2019. 2" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1755" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_content_list.json b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..070409db06bf0a4ae61886f07b358c315880325d --- /dev/null +++ b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_content_list.json @@ -0,0 +1,1560 @@ +[ + { + "type": "text", + "text": "DiC: Rethinking Conv3x3 Designs in Diffusion Models", + "text_level": 1, + "bbox": [ + 222, + 130, + 774, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yuchuan Tian $^{1*}$ , Jing Han $^{2*}$ , Chengcheng Wang $^{3}$ , Yuchen Liang $^{4}$ , Chao Xu $^{1}$ , Hanting Chen $^{3\\dagger}$", + "bbox": [ + 132, + 179, + 862, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ State Key Lab of General AI, School of Intelligence Science and Technology, Peking University.", + "bbox": [ + 205, + 200, + 787, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Artificial Intelligence, Beijing University of Posts and Telecommunications. $^{3}$ Huawei Noah's Ark Lab.", + "bbox": [ + 156, + 217, + 836, + 232 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ School of Mathematical Sciences, Peking University.", + "bbox": [ + 334, + 234, + 661, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tianyc@stu.pku.edu.cn, hj19910619@163.com, chenhanting@huawei.com", + "bbox": [ + 209, + 253, + 785, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 304, + 326, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models have shown exceptional performance in visual generation tasks. Recently, these models have shifted from traditional U-Shaped CNN-Attention hybrid structures to fully transformer-based isotropic architectures. While these transformers exhibit strong scalability and performance, their reliance on complicated self-tention operation results in slow inference speeds. Contrary to these works, we rethink one of the simplest yet fastest module in deep learning, 3x3 Convolution, to construct a scaled-up purely convolutional diffusion model. We first discover that an Encoder-Decoder Hourglass design outperforms scalable isotropic architectures for Conv3x3, but still underperforming our expectation. Further improving the architecture, we introduce sparse skip connections to reduce redundancy and improve scalability. Based on the architecture, we introduce conditioning improvements including stage-specific embeddings, mid-block condition injection, and conditional gating. These improvements lead to our proposed Diffusion CNN (DiC), which serves as a swift yet competitive diffusion architecture baseline. Experiments on various scales and settings show that DiC surpasses existing diffusion transformers by considering margins in terms of performance while keeping a good speed advantage. Project page: https://github.com/YuchuanTian/DiC", + "bbox": [ + 86, + 335, + 485, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 729, + 220, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion-based image generative models have recently gained significant attention, with notable works like Stable Diffusion [32] demonstrating impressive results. As these models continue to evolve, they are now capable of generating increasingly realistic images. Recent advancements, including Sora-related works, have extended this capability to video generation, producing high-quality, temporally consistent videos that rival real-world footage.", + "bbox": [ + 89, + 753, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ae6b7def6e1d260cf779795ea18621f2ef79849300af11dffb3e47ace91e01b6.jpg", + "image_caption": [ + "Figure 1. The Roadmap to a 3x3 Convolutional Diffusion Model. Performance is measured by FID $(\\downarrow)$ of the model trained at 200K iterations. A series of proposed model improvements gives DiC an advantage over Diffusion Transformers." + ], + "image_footnote": [], + "bbox": [ + 522, + 303, + 893, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The self-attention mechanism plays a pivotal role in many recent diffusion models. Early work [19, 36] fused convolutional U-Net structures with self-attention. More recently, architectures such as U-ViT [1] and DiT [30] have fully transitioned to attention-based designs, abandoning convolutional U-Nets entirely. These models demonstrate remarkable generative capabilities, particularly when scaled up. Newer text-to-image and text-to-video models, including Stable Diffusion 3 [14], FLUX [25], PixArt series [2-4], and OpenSora [24, 47], have also adopted fully transformer-based architectures, achieving impressive generation quality.", + "bbox": [ + 511, + 577, + 908, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unfortunately, diffusion models incorporating self-attention face significant computational overhead and latency when scaled up. Complex transformer architectures pose a considerable challenge for real-time, resource-constrained applications, where large-scale transformers are impractical due to their substantial time costs.", + "bbox": [ + 511, + 746, + 908, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Efforts have been made to accelerate self-attention in diffusion models. For instance, ToDo [35] and PixArt- $\\Sigma$ [3] implement more efficient self-attention mechanisms. However, these approaches remain confined to the self-attention", + "bbox": [ + 511, + 839, + 910, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal Contribution.", + "bbox": [ + 109, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2469", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "paradigm. Other works [37, 45] aim to replace self-attention with State-Space-Model-based architectures [16], attempting to bypass its inherent inefficiencies. Despite these innovations, the generation speed on typical latent-domain image resolutions remains suboptimal, failing to meet the demands of real-time or large-scale applications.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we rethink the simple yet efficient fully convolutional diffusion model architecture that offers significant speed advantages. As a counterpart to self-attention, convolution is widely regarded as hardware-friendly, with excellent support across various platforms. Among the many convolutional operations, the canonical 3x3 stride-1 convolution stands out for its exceptional speed, largely due to widespread hardware optimization techniques such as Winograd acceleration [26]. For instance, work like RepVGG [12] have demonstrated how simple convolutions can achieve both high efficiency and competitive performance.", + "bbox": [ + 89, + 184, + 482, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, 3x3 convolutions come with inherent limitations, particularly a constrained receptive field, which may hinder their scalability in complex generative tasks. We firstly perform initial trials to scale up purely 3x3-based CNNs within existing scalable frameworks, but these experiments yielded results that are still inferior to Diffusion Transformer counterparts.", + "bbox": [ + 89, + 352, + 482, + 458 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this, we propose a series of adaptations to conventional ConvNets, forming a roadmap (shown in Fig. 1) that tailors them specifically for a scaled-up diffusion model. Firstly, we focus on refining the model architecture to better leverage Conv3x3. Existing designs fall into three categories: isotropic architectures like DiT [30], isotropic architectures with skips like U-ViT [1], and encoder-decoder hourglass structures used in canonical CNN & self-attention hybrid models. Empirical observations reveal that the hourglass architecture is more effective for pure Conv3x3 models, because downsampling and upsampling in encoders expand the receptive field that makes up for the narrow scope of Conv3x3. Skip connections are also observed crucial, but traditional blockwise skips for cheap convolution block scale-ups are too dense to be efficient for large ConvNets. To address this, we introduce sparse skip connections that reduces the number of skips while ensuring essential information ows efficiently from encoder to decoder.", + "bbox": [ + 89, + 460, + 482, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Besides, we focus on improving conditioning to fit the hourglass ConvNet better. In existing models, a single set of condition embeddings is often mapped to different blocks across various stages. However, in encoder-decoder hourglass ConvNets, each stage operates in distinct feature spaces. Hence, we introduce stage-specific embeddings, ensuring each stage uses independent, non-overlapping condition embedding tables. We also carefully inspect the position for embedding injection, and we suggest inject conditions midblock for better performance. Additionally, we borrow conditional gating on feature-maps. In addition, we refined the", + "bbox": [ + 89, + 734, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "internal block structure, replacing all activation functions with GELU.", + "bbox": [ + 511, + 90, + 903, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With these enhancements, we propose DiC, a diffusion model made up of Conv3x3. The architectural and conditioning improvements collectively enable our model to achieve outstanding results while maintaining its speed advantage. Experiments on various scales and settings demonstrate DiC's performance advantage over Diffusion Transformers as well as its high-throughput characteristics.", + "bbox": [ + 511, + 121, + 906, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 239, + 653, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-Attention in Diffusion Architectures. Self-attention has become a cornerstone of modern diffusion architectures, thanks to its remarkable effectiveness in capturing long-range dependencies. Early UNet-based diffusion models [19, 36] incorporated Self-Attention layers in the higher stages of the network, where capturing global context is most critical. Dhariwal et al. took this further with ADM [11], extending self-attention across all stages, which significantly increased the model's generative capabilities.", + "bbox": [ + 511, + 266, + 906, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "More recent works [1, 21, 30] have fully embraced transformer-based architectures, replacing traditional U-Net backbones with full self-attention designs. These models not only achieve superior performance, but also exhibit excellent scalability, particularly at large model sizes and FLOPs. Most following work like PixArt- $\\alpha$ [2] and Stable Diffusion 3 adopt the full transformer backbone design that demonstrates outstanding Text-to-Image generation capabilities. Beyond these, some works continue to explore and refine the use of self-attention and transformer architectures in diffusion models, further pushing the boundaries of efficiency in transformer-based generative modeling. For instance, [3, 35, 38] looks at downsampled tokens for self-attention; [43] uses linear attention. Other works [37, 45] opt for State Space Models for diffusion, but SSMs suffer in terms of latency for ordinary-shaped images [37]. Some other work [6, 20, 22, 38] looks at a combination of U-Net and Self-Attention. In contrast to these works, we push architectural simplicity to the extreme by designing an entire diffusion model using $3 \\times 3$ convolutions. With carefully crafted structural optimizations, this streamlined network not only capitalizes on the speed advantages of $3 \\times 3$ convolutions but also achieves diffusion generation performance on par with transformer-based models.", + "bbox": [ + 511, + 402, + 908, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Efficient Convolution. Historically, architectures like AlexNet [23], VGG [34], and ResNet [18] have dominated computer vision tasks. While transformers [40] have later become the state-of-the-art for many vision applications, their high computational cost and latency make them less practical in resource-constrained environments, where CNNs still excel. Recent advancements have revisited and improved CNNs, enabling them to rival or even surpass transformers in both performance and efficiency.", + "bbox": [ + 511, + 763, + 908, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2470", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a9bdb0c45c276a477d04e20998bb7adea4726b5234dc668041a910f9bef7f8e3.jpg", + "image_caption": [ + "(a) Transformer Block" + ], + "image_footnote": [], + "bbox": [ + 130, + 90, + 500, + 233 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3750e0f96289aaae5cce311223414b963740f22204c4c4d08f679a3733b72b61.jpg", + "image_caption": [ + "(b) Conv 3x3 Basic Block (Ours)", + "Figure 2. Basic Blocks for scaled-up architectures. Compared to complicated Transformer blocks widely applied in [30], our Conv 3x3 Basic Block is much simpler and better supported by hardware, being the key to high throughput." + ], + "image_footnote": [], + "bbox": [ + 576, + 92, + 864, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For example, ConvNeXt [28] achieves transformer-level performance through macro and micro architectural changes, such as increasing kernel sizes and optimizing normalization. Deformable Convolutions (DCNs) [7, 41, 42] enhance the receptive field by learning spatially adaptive kernel shapes, while RepLKNet [13] utilizes massive $31 \\times 31$ kernels to capture long-range dependencies. Similarly, Wavelet Conv [15] operates in the frequency domain using wavelet transforms to extend CNN capabilities.", + "bbox": [ + 89, + 319, + 483, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "On the other hand, there is work that resort to improving the efficiency of simple convs. RepVGG [12] focuses on the potential of simple 3x3 convolutions, employing reparameterization tricks to enhance their effectiveness. Inspired by its speed potential, we explore the use of pure 3x3 convolutions in diffusion, combined with architectural and conditioning improvements, to achieve competitive results in diffusion-based generative models. However, we are not using tricks like re-parameterization [12]. Our approach demonstrates that even with a simple design, high-quality generation can be both efficient and effective.", + "bbox": [ + 89, + 455, + 483, + 622 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 638, + 181, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries: Conv3x3 as the Ingredient", + "text_level": 1, + "bbox": [ + 89, + 665, + 442, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We choose normal stride-1 full Conv3x3 as the major ingredient of model. Stride-1 3x3 convolutions are incredibly speedy, primarily due to extensive hardware and algorithmic optimizations in modern deep learning frameworks. The operation optimization benefits from the Winograd algorithm [26], which reduces the number of multiplications required for common convolution operations by $\\frac{5}{9}$ . For 3x3 kernels, this method significantly accelerates the computation by leveraging efficient matrix transformations.", + "bbox": [ + 89, + 686, + 483, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Additionally, unlike depth-wise convolution, 3x3 convolutions achieve a high degree of computational parallelism, allowing modern GPUs to fully utilize their processing power. This parallelism, combined with minimal memory access overhead, makes stride-1 3x3 convolutions particularly effi", + "bbox": [ + 89, + 825, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "cient. Compared to larger or more complex convolution operations, they offer an ideal trade-off between computational cost and representational power, making them a practical choice for real-time applications and large-scale models.", + "bbox": [ + 511, + 319, + 906, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Architectures for Scale-Up", + "text_level": 1, + "bbox": [ + 511, + 391, + 756, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our Basic Block. We revisit canonical diffusion models [11, 36] and figure out that $3 \\times 3$ convolutions are also widely applied. However, these models are not pure CNNs: the basic block unit within the model consists of two consecutive $3 \\times 3$ convolutional layers, followed by a self-attention module that attends within the entire image. Before each convolution, the input is normalized using GroupNorm, and then passed to the non-linear activation function of SiLU. Notably, the intermediate features within the block maintain the same number of channels, ensuring stable feature propagation. The overall block adopts a residual structure [18], where the input is directly added to the output via a shortcut connection.", + "bbox": [ + 511, + 414, + 906, + 608 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The roadmap to our proposed diffusion model DiC-a $3\\times 3$ convolutional denoiser starts from the revisited convolutional basic block mentioned above. In order to satisfy the ultimate goal of the roadmap, we remove the self-attention layers after the convolutions to form a minimal unit block (Basic Block) consisting of two $3\\times 3$ convolutions. Other block designs are temporarily left intact.", + "bbox": [ + 511, + 611, + 906, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mainstream Architectures. With this Conv 3x3 Basic Block as the foundation, we scale the model up by stacking multiple such blocks and increasing the network's depth and width, and we are faced up to numerous architectural choices (shown in Fig. 3):", + "bbox": [ + 511, + 717, + 905, + 792 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Isotropic Architecture. Inspired by DiT and subsequent works [2, 5, 17, 30], this design features a simple, vertically stacked structure. After patchification, the intermediate feature-map size is not changed throughout the entire model. It is widely adopted for its reputed scalability, particularly when scaled to large models.", + "2. Isotropic Architecture with Skip Connections. This ap-" + ], + "bbox": [ + 511, + 794, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2471", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ff010a3d9f2572f65049030f398c5a7ceb598fa97d2f04e0a71419b5b482daab.jpg", + "image_caption": [ + "(a) Isotropic" + ], + "image_footnote": [], + "bbox": [ + 107, + 98, + 176, + 199 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1afb77678da34059fa62b25216052f40fc302ea30c8b615763d247cf0256ade6.jpg", + "image_caption": [ + "(b) Isotropic + Skip" + ], + "image_footnote": [], + "bbox": [ + 187, + 99, + 276, + 199 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fd16a2e95a2ede1e3126f718b6a578328ef8e5dbc9eeb138052f9142693ec6f8.jpg", + "image_caption": [ + "(c) U-Net", + "Figure 3. Mainstream Diffusion Architectures. We try existing diffusion architectures (a,b,c) with Conv3x3 Basic Block. We further improve U-Net (d) with sparse-skips." + ], + "image_footnote": [], + "bbox": [ + 282, + 99, + 366, + 199 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a281c82ed30902596605cb1e7465167d3810eab89472c9cf74f7d011b6829729.jpg", + "image_caption": [ + "(d) U-Net + Sparse Skip" + ], + "image_footnote": [], + "bbox": [ + 377, + 99, + 464, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "proach extends the columnar isotropic architecture by introducing long skip connections between non-adjacent layers, similar to the design used in U-ViT [1]. Unlike traditional U-Net, despite the skip design, this architecture maintains a consistent spatial resolution throughout the network, avoiding any upsampling and downsampling operations.", + "bbox": [ + 89, + 273, + 483, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. U-Net Hourglass Architecture. This classical design [33] consists of an encoder and a decoder, forming a funnel-like shape. The encoder progressively downsamples the feature dimensions, while the decoder symmetrically upsamples the spatial dimensions. Apart from the hourglass backbone, each block in the encoder is connected to its corresponding decoder block via skip connections. This work is widely applied in earlier diffusion works [11, 19, 36].", + "bbox": [ + 89, + 364, + 483, + 484 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/61975b50ddc05a374a9f3dc92cc278e528bcdcfecbf045083d5c4d346b3f19d1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ImageNet 256×256, 200K,cfg=1.5
    ModelFLOPs (G)FID↓IS↑
    DiT-XL118.612.9694.26
    Isotropic115.629.3152.80
    Isotropic + Skip117.115.0785.51
    U-Net Hourglass115.214.6587.17
    U-Net + Sparse Skip116.111.49106.91
    ", + "bbox": [ + 93, + 496, + 475, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Comparing Architectures for Conv3x3 Scale-Up on ImageNet $256 \\times 256$ conditional generation. Conv3x3 taps its full potential with U-Net Hourglass architectures due to enlarged perception field; sparsifying skip connection further improves the model.", + "bbox": [ + 89, + 640, + 482, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Experimental Analysis. Using the foundational Conv 3x3 Basic Block, we conducted scaling experiments on the aforementioned architectural choices. The results, summarized in Tab. 1, indicate that the performance across all architectures was generally suboptimal. However, these experiments revealed several patterns that provide valuable insights for designing an effective 3x3 convolution-based diffusion model.", + "bbox": [ + 89, + 719, + 483, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Firstly, for diffusion models composed solely of $3 \\times 3$ convolutions, the encoder-decoder architecture hourglass is essential. This stems from a fundamental limitation of $3 \\times 3$ convolutions: their inherently restricted receptive field. In a purely isotropic, standard-transformer architecured setup,", + "bbox": [ + 89, + 825, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "each 3x3 convolution expands the receptive field by only one pixel in each direction. As a result, achieving a global receptive field would require a deep stack of convolutions, leading to inefficiencies in both computation and parameters. In contrast, an encoder-decoder architecture significantly mitigates this limitation. By progressively downsampling in the encoder and upsampling in the decoder, the 3x3 convolutions in higher stages can effectively perceive larger regions of the input. For instance, at deeper stages, a single 3x3 convolution can cover areas as large as 6x6 or 12x12 in the original image space, substantially increasing the model's receptive field. This hierarchical approach allows the model to efficiently capture both local and global context, making it far more effective for generative tasks.", + "bbox": [ + 511, + 90, + 903, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Secondly, skip connections are vital in Conv3x3-based architectures. On one hand, in encoder-decoder structures, they mitigate information loss during downsampling by passing feature maps directly to the decoder, enriching its representation. On the other hand, skips accelerate training and improve generation quality by providing additional gradient pathways and preserving important features, leading to more efficient and effective diffusion modeling.", + "bbox": [ + 511, + 303, + 905, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Above all, we adopt the U-Net as the general model architecture that we use.", + "bbox": [ + 511, + 425, + 905, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Improving U-Nets via Strided Skip. However, as scaling up our Conv3x3-based diffusion model requires stacking numerous convolutional layers, dense, block-wise skip connections become a bottleneck. Numerous blockwise skip features have to be concatenated to the features and get merged on the channel dimension within corresponding decoder blocks, consuming excessive computational costs. This inefficiency hampers the scalability of the model. To address this, we propose strided skip connections, where skips are applied only every few blocks instead of after each one. This approach improves the performance, and our experiments (in Tab. 1) show that it does yield better results compared with densely-connected skip designs.", + "bbox": [ + 511, + 455, + 905, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Conditioning Improvements", + "text_level": 1, + "bbox": [ + 511, + 665, + 766, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Apart from architectural improvements, we hold that conditioning could also be refined. After model scale-ups, previous conditioning designs need to be improved according to the architecture.", + "bbox": [ + 511, + 688, + 905, + 747 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stage-Specific Embeddings. In conventional diffusion models [11, 36], a unique embedding table is shared by previous models. However, in the scaled-up Conv3x3 model, we rely on an encoder-decoder structure to expand the receptive field. Each stage of the encoder-decoder operates with different channel dimensions, reflecting significant structural and functional differences between stages. Given that feature dimensions vary across stages, applying the same condition embedding uniformly on all blocks from different stages may not be ideal. The diverse roles and representations at", + "bbox": [ + 511, + 750, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2472", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "each stage suggest that a more stage-tailored approach to condition embedding could be more effective, as a single embedding set might not adequately capture the distinct characteristics of each stage.", + "bbox": [ + 89, + 90, + 485, + 154 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/24f7531be121a241503c645e85d6811afeaa38e6b3116f4162faa49d16551237.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ImageNet 256×256, 200K, CFG=1.5
    ModelFLOPs (G)FID↓IS↑
    Sparse-Skip U-Net116.111.49106.91
    + Stage-Spec. Emb.116.110.07121.30
    + Mid-Block Injection116.18.80134.25
    + DiT condition gating116.16.54162.34
    DiC (+ GELU)116.16.26170.04
    ", + "bbox": [ + 91, + 162, + 485, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Conditioning improvements on ImageNet $256 \\times 256$ conditional generation. The proposed conditioning improvements collectively bring considerable performance enhancement. Experiments are conducted using hyperparameters from [30] for 200K iterations.", + "bbox": [ + 89, + 300, + 483, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As an improvement, we propose using stage-specific condition embeddings for each stage of the encoder-decoder structure. Each stage will have its own independent embedding, with the embedding dimension aligned to that stage's feature dimension. This ensures that the condition embedding is tailored to the specific characteristics and scale of each stage.", + "bbox": [ + 89, + 372, + 483, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is worth mentioning that we analyzed the overhead introduced by the stage-specific embeddings. The results show that the added overhead is minimal. Specifically, adding the new stage-specific embeddings increased the model size by just 14.06M parameters, which accounts for only $2\\%$ of the total model size. The computational overhead introduced is even more negligible, with an increase of only 12M FLOPs, which has little impact on the overall computational efficiency. This demonstrates that the inclusion of stage-specific embeddings does not significantly affect the model's performance or computational cost.", + "bbox": [ + 88, + 478, + 483, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Beside, the label-drop operation on the embeddings across different stages should be synchronized during training. This prevents any leakage of label between stages and ensures that the model learns in a consistent and isolated manner, thereby improving the stability and performance of the diffusion model.", + "bbox": [ + 89, + 643, + 485, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Condition Injection Position. Another critical aspect of our design is determining the optimal position for injecting conditioning information. There are two prevalent strategies for condition injection in diffusion models. The first approach injects the condition at the very beginning of each block, typically through LayerNorm, as seen in models like [5, 30]. The second approach introduces the condition in the middle of the block, as utilized in [11, 36].", + "bbox": [ + 89, + 734, + 485, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through experimentation, we found that for our fully convolutional diffusion architecture, injecting the condition into the second convolutional layer within each block yields", + "bbox": [ + 89, + 854, + 485, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the best performance. This placement effectively modulates the feature representations, enhancing the model's generative quality without compromising its efficiency.", + "bbox": [ + 511, + 90, + 906, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Conditional Gating. In addition, we adopted the conditional gating mechanism from DiT's AdaLN [30]. On top of traditional affine conditioning that performs channel-wise affine mapping to the feature map, AdaLN introduces a gating vector that scales the features along the channel dimension, providing a more dynamic and fine-grained control over the conditioning process. This modification enhances the model's ability to adapt to different conditions and improves the overall generation quality. Our experiments show that this enhancement yields a notable performance boost, further demonstrating the effectiveness of this conditioning strategy in diffusion models.", + "bbox": [ + 511, + 136, + 908, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Minor Modification", + "text_level": 1, + "bbox": [ + 511, + 325, + 702, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We re-visit the activation function across the entire model. Inspired by ConvNeXt [28], we replaced the commonly used SiLU activation with GELU, which is a standard choice in transformer architectures. On top of other modifications, this change contributed to a modest but consistent improvement in performance. We are aware of potentially better activations [31, 44], but we stick to GeLU for simplicity.", + "bbox": [ + 511, + 348, + 908, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 467, + 648, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we provide experiments on various settings to demonstrate the outstanding performance of DiC model.", + "bbox": [ + 511, + 492, + 906, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment Setups", + "text_level": 1, + "bbox": [ + 511, + 531, + 697, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Model Configs. To benchmark against existing DiT [30] models, we designed our architectures at different scales: Small (S), Big (B), and Extra Large (XL), which align closely with DiT-S/2, DiT-B/2, and DiT-XL/2 in terms of both FLOPs and parameter count, as shown in Table 3. Additionally, we introduce a larger model, Huge (H), for further scalability testing. With 32.8M parameters and 5.9G FLOPs, DiC-S provides a lightweight solution, similar to DiT-S/2, with an efficient [6,6,5,6,6] encoder-decoder configuration. DiC-B scales up to 129.5M parameters and 23.5G FLOPs, which is comparable to DiT-B/2, leveraging a wider channel size of 192. DiC-XL has 702.3M parameters and 116.1G FLOPs, whose configuration rivals DiT-XL/2, with an enhanced encoder-decoder depth of [7,7,8,7,7]. DiC-H is further scaled up to [14,14,10,14,14] and is designed to evaluate the potentials of DiC models.", + "bbox": [ + 511, + 551, + 908, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Apart from normal FLOPs calculation, in Tab. 3 we also record actual FLOPs when taking Winograd acceleration [26] into account. As is introduced in Sec. 3.1, Winograd could reduce the computation of a stride-1 3x3 Convolution by $5/9$ . From statistics in Tab. 3, it could be observed that Winograd could reduce the amount of theoretical FLOPs of the proposed DiC by approximately a half.", + "bbox": [ + 511, + 795, + 910, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2473", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4e1b71657a574686184b7b0e4ee6d35b21c9bb05768004e9145e7b9096eab53d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelParams (M)FLOPs (G)Wino. FLOPs (G)Channel# GroupsEncoder-Decoder
    DiC-S32.85.92.99616[6,6,5,6,6]
    DiC-B129.523.511.819232[6,6,5,6,6]
    DiC-XL702.3116.157.238432[7,7,8,7,7]
    DiC-H1034.4204.497.238432[14,14,10,14,14]
    ", + "bbox": [ + 148, + 88, + 844, + 179 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiment Settings. We follow the standard training setup from previous research [5, 29, 30, 38], utilizing the same VAE (i.e., sd-vae-ft-ema) as in latent diffusion models [32] and the AdamW optimizer. All hyperparameters remain unchanged, including a global batch size of 256, a learning rate of $1e^{-4}$ , weight decay of 0, and a global seed of 0. Training is performed on the ImageNet 2012 dataset [10]. Our DiC-XL and DiC-H models are trained on 8 Ascend 910B NPUs.", + "bbox": [ + 88, + 234, + 480, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overhead Calculation. We calculate the FLOPs overhead of DiC models via torchprofile [27], an easy-to-use but comprehensive FLOPs calculator. The throughput is calculated on a single A100. Following the official sampling configurations of [30], we use batchsize 32 for throughput testing. We heat the GPU up via numerous warm-up runs before measuring the throughput. Flash attention [8, 9] is activated based on the original implementations of baselines.", + "bbox": [ + 88, + 369, + 482, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluating DiC on the Standard DiT Setting", + "text_level": 1, + "bbox": [ + 89, + 502, + 465, + 518 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9b7536aaacd7a1770860dde079091e8044b5b2c1058fffba28de9e6375c357a4.jpg", + "table_caption": [ + "Table 3. Configurations of DiC architecture with different model sizes. We align DiC architectures to DiTs in terms of both FLOPs and parameters. Wino. FLOPs takes the FLOPs saved by Winograd into consideration. # Groups stands for the number of groups in GroupNorm. Encoder-Decoder denotes the transformer block number of encoder and decoder module." + ], + "table_footnote": [], + "table_body": "
    ImageNet 256×256, 400K
    ModelFLOPs (G)FID↓IS↑
    DiT-S/26.167.4020.44
    DiC-S (Ours)5.958.6825.82
    DiT-B/223.042.8433.66
    DiC-B (Ours)23.532.3348.72
    DiT-XL/2118.620.0566.74
    DiC-XL (Ours)116.113.11100.15
    ", + "bbox": [ + 112, + 537, + 455, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with DiT Across Model Sizes. As shown in Table 4, our DiC models outperform the corresponding DiT models across all tested scales. Specifically, DiC-S achieves a significant reduction in FID, dropping from 67.40 to 58.68, while also surpassing DiT-S/2 in IS, increasing from 20.44 to 25.82. Similarly, DiC-B outperforms DiT-B/2 by a notable margin, reducing FID from 42.84 to 32.33 and increasing IS from 33.66 to 48.72.", + "bbox": [ + 89, + 763, + 482, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the large-scale model category, DiC-XL delivers a re", + "bbox": [ + 109, + 885, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "markable improvement over DiT-XL/2, with FID dropping from 20.05 to 13.11 and IS soaring from 66.74 to 100.15. These results highlight the effectiveness of our DiC models, which consistently achieve superior performance in both image quality and diversity, all while maintaining computational efficiency.", + "bbox": [ + 511, + 234, + 906, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with Diffusion Transformer Baselines. As different models use different settings, including training hyperparameters, the choice of samplers, training iterations et cetera, we adopt a universally-aligned setting (400K iterations on the DiT codebase) according to [38]. As shown in Table 6, our proposed DiC models consistently outperform baseline diffusion architectures on ImageNet $256 \\times 256$ , all under similar computational budgets. Despite having comparable FLOPs to models like DiT-XL/2 and PixArt- $\\alpha$ -XL/2, our DiC-XL achieves a significantly lower FID of 13.11 and an impressive IS of 100.15, showcasing its superior generative quality.", + "bbox": [ + 511, + 325, + 908, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Beyond performance, another standout is DiC's efficiency in speed. Despite the heavy computational demands of diffusion models, DiC-XL achieves a throughput of 313.7, which, while appearing lower, re-ects the use of Conv3x3's highly optimized operations. This architecture capitalizes on the inherent speed of simple convolutions, offering a practical balance between efficiency and quality.", + "bbox": [ + 511, + 506, + 908, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Even more impressively, DiC-H strikes a remarkable trade-off between model size and speed, delivering state-of-the-art FID of 11.36 and an IS of 106.52, with an improved throughput of 160.8. This demonstrates that our models can achieve unparalleled generation quality without the severe latency typically associated with transformer-based diffusion models. In real-world applications, these speed advantages make DiC a practical solution for high-quality image synthesis.", + "bbox": [ + 511, + 612, + 908, + 746 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fd7d98eed04fd4a6ae95bbddc4af5dbe1f0117f041aca051d4ad2a56866b7b7d.jpg", + "table_caption": [ + "Table 4. Comparing DiCs against DiTs across various model sizes. We compare models trained for 400K iterations with the standard setting of DiT. DiCs at all scales outperform DiTs at considerable margins." + ], + "table_footnote": [], + "table_body": "
    ImageNet 256×256, 400K
    ModelcfgFLOPsFID↓IS↑
    DiT-XL/21.5118.66.24150.10
    U-ViT-XL1.5113.05.66170.62
    DiC-XL1.5116.1 (57.2)3.89224.20
    ", + "bbox": [ + 531, + 757, + 883, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. Generation performance with classifier-free guidance. The proposed DiC is also performant on conditional generation.", + "bbox": [ + 511, + 857, + 906, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, we experiment the conditional generation", + "bbox": [ + 532, + 885, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2474", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5dc57917f55b41f516ad33c8189f84764b9eb4c73b3a7eef2f46df798eb6185d.jpg", + "image_caption": [ + "Figure 4. Comparing FID performance and FLOPs between DiTs and DiCs. Marker sizes represent relative model sizes." + ], + "image_footnote": [], + "bbox": [ + 114, + 90, + 460, + 280 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "capabilities of DiC model in Tab. 5. DiC-XL achieves an FID of 3.89 at merely 400K iterations, surpassing competitive Diffusion Transformer baselines by large margins. The results are yielded from conditional generation samples with $\\mathrm{cfg} = 1.5$ .", + "bbox": [ + 89, + 347, + 483, + 424 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. DiC on Larger Images", + "text_level": 1, + "bbox": [ + 89, + 434, + 302, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 7, we compare DiC models with DiT on ImageNet 512x512, after training for 400K iterations with standard DiT hyperparameters. The key takeaway from these results is the computational efficiency of DiC models. While DiT-XL/2 requires 524.7G FLOPs (with Winograd optimization), our DiC-XL model performs significantly better in terms of FID and IS, with only 464.3G FLOPs (228.7G after Winograd optimization). This improvement becomes even more evident in DiC-H, which offers a dramatic reduction in FID (12.89) and achieves a higher IS (101.78) with fewer FLOPs than DiT-XL/2.", + "bbox": [ + 89, + 457, + 483, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The key difference in computational complexity between DiC and DiT lies in their underlying architectures. DiC uses a pure convolutional approach, which scales linearly with the image size. In contrast, DiT employs self-attention, which incurs quadratic complexity with respect to the image size. Therefore, for larger images, such as $512 \\times 512$ , the computational gap between DiC and DiT becomes more pronounced. In spite of this, we are amazed that DiC models could still maintain an advantageous gap over DiTs. The advantage of DiC, on the other hand, is also outstanding in terms of throughput.", + "bbox": [ + 89, + 625, + 483, + 791 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Scaling to Excellence", + "text_level": 1, + "bbox": [ + 89, + 801, + 289, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we look at the scaled-up model (DiC-H) with increased training iterations, and the combination with diffusion techniques to discover the potential of DiC.", + "bbox": [ + 89, + 824, + 482, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Under DiT's plainest no-CFG setting. Table 8 presents the performance of DiC-H on ImageNet $256 \\times 256$ as training", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1aaeae87808f78bd4d8fb4fee6de332c429b8449287a06787c41a2f0911c9755.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ImageNet 256×256, 400K
    ModelFLOPs (G)TPFID↓IS↑
    U-ViT-XL [1]113.072.618.3576.59
    DiT-XL/2 [30]118.666.820.0566.74
    PixArt-α-XL/2 [2]118.464.124.7552.24
    DiffiT-XL/2 [17]118.564.136.8635.39
    DiT-LLaMA* [5]118.665.220.2270.10
    DiC-XL (Ours)116.1 (57.2)313.713.11100.15
    DiC-H (Ours)204.4 (97.2)160.811.36106.52
    ", + "bbox": [ + 519, + 94, + 903, + 241 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/32498af49b737f35d1388a9a62ad6fb92c5d20bc469f3abf6268544bccd1b691.jpg", + "table_caption": [ + "Table 6. The performance of DiCs and competitive diffusion architectures on ImageNet $256 \\times 256$ generation. The baselines are aligned under the official 400K-iteration setting of DiT-XL for a fair comparison. TP stands for throughput. FLOPs considering Winograd is reported for DiCs." + ], + "table_footnote": [], + "table_body": "
    ImageNet 512×512, 400K
    ModelG FLOPs (Wino.)TPFID↓IS↑
    DiT-XL/2524.716.220.9466.30
    DiC-XL464.3 (228.7)84.215.3293.55
    DiC-H817.2 (388.4)53.312.89101.78
    ", + "bbox": [ + 514, + 345, + 910, + 448 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9de57f05c504ca33beb6750ee741f4f17cb088450b82e0ca1c66fe04aee4dc0f.jpg", + "table_caption": [ + "Table 7. Comparing DiCs against DiTs on ImageNet $512 \\times 512$ generation. We compare models trained for 400K iterations with the standard setting of DiT. Please refer to the appendix for results from longer training iterations." + ], + "table_footnote": [], + "table_body": "
    ImageNet 256×256, Scale Up, w/ocfg
    ModelTraining StepsFID↓IS↑
    DiT-XL/22.4M10.67-
    DiT-XL/27M9.62-
    DiC-H400K11.36106.52
    DiC-H600K9.73118.57
    DiC-H800K8.96124.33
    ", + "bbox": [ + 545, + 518, + 870, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 8. Fast Convergence of DiC. The generation performance without classifier guidance of both models on ImageNet $256 \\times 256$ consistently improves as training progresses.", + "bbox": [ + 511, + 657, + 906, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "progresses. The performance of DiC-H improves steadily as the training progresses. At 600K steps, FID decreases to 9.73, matching the performance of DiT-XL/2 at 7M training steps; at 800K steps, DiC-H shows the best performance with an FID of 8.96. This table demonstrates the fast convergence of DiC-H, where both FID and IS consistently improve with training.", + "bbox": [ + 511, + 715, + 903, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Towards excellence with classifier-free guidance. Table 9 presents the comparison of various models' performance on ImageNet $256 \\times 256$ when training iteration is scaled up and classifier-free guidance is applied.", + "bbox": [ + 511, + 823, + 903, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The baseline model DiT-XL/2 achieves a throughput of", + "bbox": [ + 532, + 885, + 906, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2475", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5af93f4966b114a2fd8c665e66aadf8a88a8b3da715d118f011d4aa7becc4191.jpg", + "image_caption": [ + "Figure 5. Samples generated by DiC at 2M iterations. The samples are generated following the setting of DiT, at $cfg = 4$ ." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 903, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "66.8, processes a batch size of 256 for 7 million iterations, and yields an FID score of 2.27. The U-ViT-H model, while slightly lower in throughput at 63.9, uses a larger batch size of 1024, resulting in a slightly higher FID of 2.29. In comparison, our proposed DiC-H model shows a marked improvement when trained with a modest setting of batch size of 256 over 2 million iterations. DiC-H could achieve an FID of 2.25, with a throughput of 160.8. These results reveal that CNNs could reach performance that is no worse than Diffusion Transformers, and they have a great throughput advantage. Building upon this SiT-ow-based framework, we also combine DiC with the State-of-the-Art technique of Representation Alignment (REPA) [39, 46] to achieve much faster convergence. The details are in the appendix.", + "bbox": [ + 89, + 549, + 483, + 760 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/dfa28e4a08c0e6bd69b72c972fee509e91129f97c78fc243a4600f7562161d81.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ImageNet 256×256, Scale Up, w/cfg
    ModelTPBS×IterFID↓
    DiT-XL/266.8256×7M2.27
    U-ViT-H63.91024×500K2.29
    DiC-H (Ours)160.8256×2M2.25
    ", + "bbox": [ + 119, + 772, + 450, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 9. Generation performance of powerful baselines with classifier-free guidance. TP stands for throughput. The proposed DiC is also performant on conditional generation.", + "bbox": [ + 89, + 872, + 482, + 915 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 547, + 633, + 563 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we rethink the design of Conv3x3 in the context of diffusion models and introduced DiC, a purely 3x3-convolutional diffusion model. We initially explore various state-of-the-art diffusion architectures and find that the Encoder-Decoder U-Net structure performs the best. Building on this, we propose the sparse skip connection to reduce redundant block-wise connections and enhance efficiency of U-Net. In addition to architecture, we redesign the conditioning mechanism. We introduce stage-specific independent embeddings where each embedding is responsible for addressing conditioning within its assigned stage. We also propose mid-block condition injection and conditional gating, which are beneficial from empirical observations. Based on these improvements, our proposed Conv3x3 diffusion model not only achieves superior generative performance compared to Diffusion Transformers but also does so with significantly higher throughput.", + "bbox": [ + 509, + 573, + 906, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Above all, as an aspect that is always neglected in diffusion, we investigate the use of convolutions in diffusion models, and we hope this work could inspire further exploration into the use of convolutions in diffusion models.", + "bbox": [ + 511, + 830, + 908, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2476", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported by the National Key R&D Program of China under grant No. 2022ZD0160300 and the National Natural Science Foundation of China under grant No. 62276007. We gratefully acknowledge the support of MindSpore, CANN, and Ascend AI Processor used for this research.", + "bbox": [ + 89, + 90, + 485, + 181 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 196, + 187, + 210 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. All are worth words: A vit backbone for diffusion models. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023, pages 22669-22679. IEEE, 2023. 1, 2, 4, 7", + "[2] Junsong Chen, Jincheng Yu, Chongjian Ge, Lewei Yao, Enze Xie, Yue Wu, Zhongdao Wang, James Kwok, Ping Luo, Huchuan Lu, and Zhenguo Li. 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Open-sora: Democratizing efficient video production for all, 2024. 1" + ], + "bbox": [ + 516, + 92, + 906, + 486 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2478", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_model.json b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0a84638646b8237110ebeed62f73d0d90893bf0a --- /dev/null +++ b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_model.json @@ -0,0 +1,2156 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.223, + 0.131, + 0.776, + 0.154 + ], + "angle": 0, + "content": "DiC: Rethinking Conv3x3 Designs in Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.18, + 0.864, + 0.2 + ], + "angle": 0, + "content": "Yuchuan Tian\\(^{1*}\\), Jing Han\\(^{2*}\\), Chengcheng Wang\\(^{3}\\), Yuchen Liang\\(^{4}\\), Chao Xu\\(^{1}\\), Hanting Chen\\(^{3\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.201, + 0.789, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\) State Key Lab of General AI, School of Intelligence Science and Technology, Peking University." + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.218, + 0.838, + 0.233 + ], + "angle": 0, + "content": "\\(^{2}\\) School of Artificial Intelligence, Beijing University of Posts and Telecommunications. \\(^{3}\\) Huawei Noah's Ark Lab." + }, + { + "type": "text", + "bbox": [ + 0.336, + 0.236, + 0.662, + 0.251 + ], + "angle": 0, + "content": "\\(^{4}\\) School of Mathematical Sciences, Peking University." + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.255, + 0.787, + 0.269 + ], + "angle": 0, + "content": "tianyc@stu.pku.edu.cn, hj19910619@163.com, chenhanting@huawei.com" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.305, + 0.327, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.337, + 0.486, + 0.701 + ], + "angle": 0, + "content": "Diffusion models have shown exceptional performance in visual generation tasks. Recently, these models have shifted from traditional U-Shaped CNN-Attention hybrid structures to fully transformer-based isotropic architectures. While these transformers exhibit strong scalability and performance, their reliance on complicated self-tention operation results in slow inference speeds. Contrary to these works, we rethink one of the simplest yet fastest module in deep learning, 3x3 Convolution, to construct a scaled-up purely convolutional diffusion model. We first discover that an Encoder-Decoder Hourglass design outperforms scalable isotropic architectures for Conv3x3, but still underperforming our expectation. Further improving the architecture, we introduce sparse skip connections to reduce redundancy and improve scalability. Based on the architecture, we introduce conditioning improvements including stage-specific embeddings, mid-block condition injection, and conditional gating. These improvements lead to our proposed Diffusion CNN (DiC), which serves as a swift yet competitive diffusion architecture baseline. Experiments on various scales and settings show that DiC surpasses existing diffusion transformers by considering margins in terms of performance while keeping a good speed advantage. Project page: https://github.com/YuchuanTian/DiC" + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.73, + 0.222, + 0.745 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.755, + 0.485, + 0.876 + ], + "angle": 0, + "content": "Diffusion-based image generative models have recently gained significant attention, with notable works like Stable Diffusion [32] demonstrating impressive results. As these models continue to evolve, they are now capable of generating increasingly realistic images. Recent advancements, including Sora-related works, have extended this capability to video generation, producing high-quality, temporally consistent videos that rival real-world footage." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.304, + 0.895, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.501, + 0.908, + 0.558 + ], + "angle": 0, + "content": "Figure 1. The Roadmap to a 3x3 Convolutional Diffusion Model. Performance is measured by FID \\((\\downarrow)\\) of the model trained at 200K iterations. A series of proposed model improvements gives DiC an advantage over Diffusion Transformers." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.578, + 0.909, + 0.745 + ], + "angle": 0, + "content": "The self-attention mechanism plays a pivotal role in many recent diffusion models. Early work [19, 36] fused convolutional U-Net structures with self-attention. More recently, architectures such as U-ViT [1] and DiT [30] have fully transitioned to attention-based designs, abandoning convolutional U-Nets entirely. These models demonstrate remarkable generative capabilities, particularly when scaled up. Newer text-to-image and text-to-video models, including Stable Diffusion 3 [14], FLUX [25], PixArt series [2-4], and OpenSora [24, 47], have also adopted fully transformer-based architectures, achieving impressive generation quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.747, + 0.909, + 0.837 + ], + "angle": 0, + "content": "Unfortunately, diffusion models incorporating self-attention face significant computational overhead and latency when scaled up. Complex transformer architectures pose a considerable challenge for real-time, resource-constrained applications, where large-scale transformers are impractical due to their substantial time costs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.911, + 0.901 + ], + "angle": 0, + "content": "Efforts have been made to accelerate self-attention in diffusion models. For instance, ToDo [35] and PixArt-\\(\\Sigma\\) [3] implement more efficient self-attention mechanisms. However, these approaches remain confined to the self-attention" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Equal Contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2469" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "paradigm. Other works [37, 45] aim to replace self-attention with State-Space-Model-based architectures [16], attempting to bypass its inherent inefficiencies. Despite these innovations, the generation speed on typical latent-domain image resolutions remains suboptimal, failing to meet the demands of real-time or large-scale applications." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.185, + 0.483, + 0.35 + ], + "angle": 0, + "content": "In this work, we rethink the simple yet efficient fully convolutional diffusion model architecture that offers significant speed advantages. As a counterpart to self-attention, convolution is widely regarded as hardware-friendly, with excellent support across various platforms. Among the many convolutional operations, the canonical 3x3 stride-1 convolution stands out for its exceptional speed, largely due to widespread hardware optimization techniques such as Winograd acceleration [26]. For instance, work like RepVGG [12] have demonstrated how simple convolutions can achieve both high efficiency and competitive performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.353, + 0.483, + 0.459 + ], + "angle": 0, + "content": "However, 3x3 convolutions come with inherent limitations, particularly a constrained receptive field, which may hinder their scalability in complex generative tasks. We firstly perform initial trials to scale up purely 3x3-based CNNs within existing scalable frameworks, but these experiments yielded results that are still inferior to Diffusion Transformer counterparts." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.461, + 0.483, + 0.732 + ], + "angle": 0, + "content": "To address this, we propose a series of adaptations to conventional ConvNets, forming a roadmap (shown in Fig. 1) that tailors them specifically for a scaled-up diffusion model. Firstly, we focus on refining the model architecture to better leverage Conv3x3. Existing designs fall into three categories: isotropic architectures like DiT [30], isotropic architectures with skips like U-ViT [1], and encoder-decoder hourglass structures used in canonical CNN & self-attention hybrid models. Empirical observations reveal that the hourglass architecture is more effective for pure Conv3x3 models, because downsampling and upsampling in encoders expand the receptive field that makes up for the narrow scope of Conv3x3. Skip connections are also observed crucial, but traditional blockwise skips for cheap convolution block scale-ups are too dense to be efficient for large ConvNets. To address this, we introduce sparse skip connections that reduces the number of skips while ensuring essential information ows efficiently from encoder to decoder." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Besides, we focus on improving conditioning to fit the hourglass ConvNet better. In existing models, a single set of condition embeddings is often mapped to different blocks across various stages. However, in encoder-decoder hourglass ConvNets, each stage operates in distinct feature spaces. Hence, we introduce stage-specific embeddings, ensuring each stage uses independent, non-overlapping condition embedding tables. We also carefully inspect the position for embedding injection, and we suggest inject conditions midblock for better performance. Additionally, we borrow conditional gating on feature-maps. In addition, we refined the" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "internal block structure, replacing all activation functions with GELU." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.122, + 0.907, + 0.228 + ], + "angle": 0, + "content": "With these enhancements, we propose DiC, a diffusion model made up of Conv3x3. The architectural and conditioning improvements collectively enable our model to achieve outstanding results while maintaining its speed advantage. Experiments on various scales and settings demonstrate DiC's performance advantage over Diffusion Transformers as well as its high-throughput characteristics." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.241, + 0.655, + 0.258 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.267, + 0.907, + 0.403 + ], + "angle": 0, + "content": "Self-Attention in Diffusion Architectures. Self-attention has become a cornerstone of modern diffusion architectures, thanks to its remarkable effectiveness in capturing long-range dependencies. Early UNet-based diffusion models [19, 36] incorporated Self-Attention layers in the higher stages of the network, where capturing global context is most critical. Dhariwal et al. took this further with ADM [11], extending self-attention across all stages, which significantly increased the model's generative capabilities." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.403, + 0.909, + 0.763 + ], + "angle": 0, + "content": "More recent works [1, 21, 30] have fully embraced transformer-based architectures, replacing traditional U-Net backbones with full self-attention designs. These models not only achieve superior performance, but also exhibit excellent scalability, particularly at large model sizes and FLOPs. Most following work like PixArt-\\(\\alpha\\) [2] and Stable Diffusion 3 adopt the full transformer backbone design that demonstrates outstanding Text-to-Image generation capabilities. Beyond these, some works continue to explore and refine the use of self-attention and transformer architectures in diffusion models, further pushing the boundaries of efficiency in transformer-based generative modeling. For instance, [3, 35, 38] looks at downsampled tokens for self-attention; [43] uses linear attention. Other works [37, 45] opt for State Space Models for diffusion, but SSMs suffer in terms of latency for ordinary-shaped images [37]. Some other work [6, 20, 22, 38] looks at a combination of U-Net and Self-Attention. In contrast to these works, we push architectural simplicity to the extreme by designing an entire diffusion model using \\(3 \\times 3\\) convolutions. With carefully crafted structural optimizations, this streamlined network not only capitalizes on the speed advantages of \\(3 \\times 3\\) convolutions but also achieves diffusion generation performance on par with transformer-based models." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.765, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Efficient Convolution. Historically, architectures like AlexNet [23], VGG [34], and ResNet [18] have dominated computer vision tasks. While transformers [40] have later become the state-of-the-art for many vision applications, their high computational cost and latency make them less practical in resource-constrained environments, where CNNs still excel. Recent advancements have revisited and improved CNNs, enabling them to rival or even surpass transformers in both performance and efficiency." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2470" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.132, + 0.092, + 0.501, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.248, + 0.386, + 0.26 + ], + "angle": 0, + "content": "(a) Transformer Block" + }, + { + "type": "image", + "bbox": [ + 0.577, + 0.093, + 0.865, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.247, + 0.822, + 0.261 + ], + "angle": 0, + "content": "(b) Conv 3x3 Basic Block (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.265, + 0.908, + 0.294 + ], + "angle": 0, + "content": "Figure 2. Basic Blocks for scaled-up architectures. Compared to complicated Transformer blocks widely applied in [30], our Conv 3x3 Basic Block is much simpler and better supported by hardware, being the key to high throughput." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.32, + 0.484, + 0.456 + ], + "angle": 0, + "content": "For example, ConvNeXt [28] achieves transformer-level performance through macro and micro architectural changes, such as increasing kernel sizes and optimizing normalization. Deformable Convolutions (DCNs) [7, 41, 42] enhance the receptive field by learning spatially adaptive kernel shapes, while RepLKNet [13] utilizes massive \\(31 \\times 31\\) kernels to capture long-range dependencies. Similarly, Wavelet Conv [15] operates in the frequency domain using wavelet transforms to extend CNN capabilities." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.457, + 0.484, + 0.623 + ], + "angle": 0, + "content": "On the other hand, there is work that resort to improving the efficiency of simple convs. RepVGG [12] focuses on the potential of simple 3x3 convolutions, employing reparameterization tricks to enhance their effectiveness. Inspired by its speed potential, we explore the use of pure 3x3 convolutions in diffusion, combined with architectural and conditioning improvements, to achieve competitive results in diffusion-based generative models. However, we are not using tricks like re-parameterization [12]. Our approach demonstrates that even with a simple design, high-quality generation can be both efficient and effective." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.64, + 0.182, + 0.655 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.666, + 0.444, + 0.682 + ], + "angle": 0, + "content": "3.1. Preliminaries: Conv3x3 as the Ingredient" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.688, + 0.484, + 0.824 + ], + "angle": 0, + "content": "We choose normal stride-1 full Conv3x3 as the major ingredient of model. Stride-1 3x3 convolutions are incredibly speedy, primarily due to extensive hardware and algorithmic optimizations in modern deep learning frameworks. The operation optimization benefits from the Winograd algorithm [26], which reduces the number of multiplications required for common convolution operations by \\(\\frac{5}{9}\\). For 3x3 kernels, this method significantly accelerates the computation by leveraging efficient matrix transformations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.485, + 0.902 + ], + "angle": 0, + "content": "Additionally, unlike depth-wise convolution, 3x3 convolutions achieve a high degree of computational parallelism, allowing modern GPUs to fully utilize their processing power. This parallelism, combined with minimal memory access overhead, makes stride-1 3x3 convolutions particularly effi" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.32, + 0.907, + 0.381 + ], + "angle": 0, + "content": "cient. Compared to larger or more complex convolution operations, they offer an ideal trade-off between computational cost and representational power, making them a practical choice for real-time applications and large-scale models." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.392, + 0.757, + 0.409 + ], + "angle": 0, + "content": "3.2. Architectures for Scale-Up" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.415, + 0.908, + 0.609 + ], + "angle": 0, + "content": "Our Basic Block. We revisit canonical diffusion models [11, 36] and figure out that \\(3 \\times 3\\) convolutions are also widely applied. However, these models are not pure CNNs: the basic block unit within the model consists of two consecutive \\(3 \\times 3\\) convolutional layers, followed by a self-attention module that attends within the entire image. Before each convolution, the input is normalized using GroupNorm, and then passed to the non-linear activation function of SiLU. Notably, the intermediate features within the block maintain the same number of channels, ensuring stable feature propagation. The overall block adopts a residual structure [18], where the input is directly added to the output via a shortcut connection." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.612, + 0.907, + 0.718 + ], + "angle": 0, + "content": "The roadmap to our proposed diffusion model DiC-a \\(3\\times 3\\) convolutional denoiser starts from the revisited convolutional basic block mentioned above. In order to satisfy the ultimate goal of the roadmap, we remove the self-attention layers after the convolutions to form a minimal unit block (Basic Block) consisting of two \\(3\\times 3\\) convolutions. Other block designs are temporarily left intact." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.718, + 0.906, + 0.794 + ], + "angle": 0, + "content": "Mainstream Architectures. With this Conv 3x3 Basic Block as the foundation, we scale the model up by stacking multiple such blocks and increasing the network's depth and width, and we are faced up to numerous architectural choices (shown in Fig. 3):" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.884 + ], + "angle": 0, + "content": "1. Isotropic Architecture. Inspired by DiT and subsequent works [2, 5, 17, 30], this design features a simple, vertically stacked structure. After patchification, the intermediate feature-map size is not changed throughout the entire model. It is widely adopted for its reputed scalability, particularly when scaled to large models." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.886, + 0.907, + 0.902 + ], + "angle": 0, + "content": "2. Isotropic Architecture with Skip Connections. This ap-" + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2471" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.099, + 0.178, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.204, + 0.168, + 0.214 + ], + "angle": 0, + "content": "(a) Isotropic" + }, + { + "type": "image", + "bbox": [ + 0.188, + 0.1, + 0.277, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.182, + 0.204, + 0.266, + 0.214 + ], + "angle": 0, + "content": "(b) Isotropic + Skip" + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.1, + 0.367, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.204, + 0.341, + 0.214 + ], + "angle": 0, + "content": "(c) U-Net" + }, + { + "type": "image", + "bbox": [ + 0.379, + 0.1, + 0.465, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.369, + 0.204, + 0.471, + 0.214 + ], + "angle": 0, + "content": "(d) U-Net + Sparse Skip" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.221, + 0.483, + 0.263 + ], + "angle": 0, + "content": "Figure 3. Mainstream Diffusion Architectures. We try existing diffusion architectures (a,b,c) with Conv3x3 Basic Block. We further improve U-Net (d) with sparse-skips." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.275, + 0.484, + 0.365 + ], + "angle": 0, + "content": "proach extends the columnar isotropic architecture by introducing long skip connections between non-adjacent layers, similar to the design used in U-ViT [1]. Unlike traditional U-Net, despite the skip design, this architecture maintains a consistent spatial resolution throughout the network, avoiding any upsampling and downsampling operations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.365, + 0.484, + 0.486 + ], + "angle": 0, + "content": "3. U-Net Hourglass Architecture. This classical design [33] consists of an encoder and a decoder, forming a funnel-like shape. The encoder progressively downsamples the feature dimensions, while the decoder symmetrically upsamples the spatial dimensions. Apart from the hourglass backbone, each block in the encoder is connected to its corresponding decoder block via skip connections. This work is widely applied in earlier diffusion works [11, 19, 36]." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.497, + 0.477, + 0.637 + ], + "angle": 0, + "content": "
    ImageNet 256×256, 200K,cfg=1.5
    ModelFLOPs (G)FID↓IS↑
    DiT-XL118.612.9694.26
    Isotropic115.629.3152.80
    Isotropic + Skip117.115.0785.51
    U-Net Hourglass115.214.6587.17
    U-Net + Sparse Skip116.111.49106.91
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.641, + 0.483, + 0.71 + ], + "angle": 0, + "content": "Table 1. Comparing Architectures for Conv3x3 Scale-Up on ImageNet \\(256 \\times 256\\) conditional generation. Conv3x3 taps its full potential with U-Net Hourglass architectures due to enlarged perception field; sparsifying skip connection further improves the model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.825 + ], + "angle": 0, + "content": "Experimental Analysis. Using the foundational Conv 3x3 Basic Block, we conducted scaling experiments on the aforementioned architectural choices. The results, summarized in Tab. 1, indicate that the performance across all architectures was generally suboptimal. However, these experiments revealed several patterns that provide valuable insights for designing an effective 3x3 convolution-based diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Firstly, for diffusion models composed solely of \\(3 \\times 3\\) convolutions, the encoder-decoder architecture hourglass is essential. This stems from a fundamental limitation of \\(3 \\times 3\\) convolutions: their inherently restricted receptive field. In a purely isotropic, standard-transformer architecured setup," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.302 + ], + "angle": 0, + "content": "each 3x3 convolution expands the receptive field by only one pixel in each direction. As a result, achieving a global receptive field would require a deep stack of convolutions, leading to inefficiencies in both computation and parameters. In contrast, an encoder-decoder architecture significantly mitigates this limitation. By progressively downsampling in the encoder and upsampling in the decoder, the 3x3 convolutions in higher stages can effectively perceive larger regions of the input. For instance, at deeper stages, a single 3x3 convolution can cover areas as large as 6x6 or 12x12 in the original image space, substantially increasing the model's receptive field. This hierarchical approach allows the model to efficiently capture both local and global context, making it far more effective for generative tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.304, + 0.906, + 0.424 + ], + "angle": 0, + "content": "Secondly, skip connections are vital in Conv3x3-based architectures. On one hand, in encoder-decoder structures, they mitigate information loss during downsampling by passing feature maps directly to the decoder, enriching its representation. On the other hand, skips accelerate training and improve generation quality by providing additional gradient pathways and preserving important features, leading to more efficient and effective diffusion modeling." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.426, + 0.906, + 0.455 + ], + "angle": 0, + "content": "Above all, we adopt the U-Net as the general model architecture that we use." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.457, + 0.906, + 0.653 + ], + "angle": 0, + "content": "Improving U-Nets via Strided Skip. However, as scaling up our Conv3x3-based diffusion model requires stacking numerous convolutional layers, dense, block-wise skip connections become a bottleneck. Numerous blockwise skip features have to be concatenated to the features and get merged on the channel dimension within corresponding decoder blocks, consuming excessive computational costs. This inefficiency hampers the scalability of the model. To address this, we propose strided skip connections, where skips are applied only every few blocks instead of after each one. This approach improves the performance, and our experiments (in Tab. 1) show that it does yield better results compared with densely-connected skip designs." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.666, + 0.767, + 0.682 + ], + "angle": 0, + "content": "3.3. Conditioning Improvements" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.748 + ], + "angle": 0, + "content": "Apart from architectural improvements, we hold that conditioning could also be refined. After model scale-ups, previous conditioning designs need to be improved according to the architecture." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Stage-Specific Embeddings. In conventional diffusion models [11, 36], a unique embedding table is shared by previous models. However, in the scaled-up Conv3x3 model, we rely on an encoder-decoder structure to expand the receptive field. Each stage of the encoder-decoder operates with different channel dimensions, reflecting significant structural and functional differences between stages. Given that feature dimensions vary across stages, applying the same condition embedding uniformly on all blocks from different stages may not be ideal. The diverse roles and representations at" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2472" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.155 + ], + "angle": 0, + "content": "each stage suggest that a more stage-tailored approach to condition embedding could be more effective, as a single embedding set might not adequately capture the distinct characteristics of each stage." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.164, + 0.486, + 0.294 + ], + "angle": 0, + "content": "
    ImageNet 256×256, 200K, CFG=1.5
    ModelFLOPs (G)FID↓IS↑
    Sparse-Skip U-Net116.111.49106.91
    + Stage-Spec. Emb.116.110.07121.30
    + Mid-Block Injection116.18.80134.25
    + DiT condition gating116.16.54162.34
    DiC (+ GELU)116.16.26170.04
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.301, + 0.485, + 0.37 + ], + "angle": 0, + "content": "Table 2. Conditioning improvements on ImageNet \\(256 \\times 256\\) conditional generation. The proposed conditioning improvements collectively bring considerable performance enhancement. Experiments are conducted using hyperparameters from [30] for 200K iterations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.373, + 0.485, + 0.478 + ], + "angle": 0, + "content": "As an improvement, we propose using stage-specific condition embeddings for each stage of the encoder-decoder structure. Each stage will have its own independent embedding, with the embedding dimension aligned to that stage's feature dimension. This ensures that the condition embedding is tailored to the specific characteristics and scale of each stage." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.479, + 0.485, + 0.644 + ], + "angle": 0, + "content": "It is worth mentioning that we analyzed the overhead introduced by the stage-specific embeddings. The results show that the added overhead is minimal. Specifically, adding the new stage-specific embeddings increased the model size by just 14.06M parameters, which accounts for only \\(2\\%\\) of the total model size. The computational overhead introduced is even more negligible, with an increase of only 12M FLOPs, which has little impact on the overall computational efficiency. This demonstrates that the inclusion of stage-specific embeddings does not significantly affect the model's performance or computational cost." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.486, + 0.735 + ], + "angle": 0, + "content": "Beside, the label-drop operation on the embeddings across different stages should be synchronized during training. This prevents any leakage of label between stages and ensures that the model learns in a consistent and isolated manner, thereby improving the stability and performance of the diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.486, + 0.856 + ], + "angle": 0, + "content": "Condition Injection Position. Another critical aspect of our design is determining the optimal position for injecting conditioning information. There are two prevalent strategies for condition injection in diffusion models. The first approach injects the condition at the very beginning of each block, typically through LayerNorm, as seen in models like [5, 30]. The second approach introduces the condition in the middle of the block, as utilized in [11, 36]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Through experimentation, we found that for our fully convolutional diffusion architecture, injecting the condition into the second convolutional layer within each block yields" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.137 + ], + "angle": 0, + "content": "the best performance. This placement effectively modulates the feature representations, enhancing the model's generative quality without compromising its efficiency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.137, + 0.909, + 0.318 + ], + "angle": 0, + "content": "Conditional Gating. In addition, we adopted the conditional gating mechanism from DiT's AdaLN [30]. On top of traditional affine conditioning that performs channel-wise affine mapping to the feature map, AdaLN introduces a gating vector that scales the features along the channel dimension, providing a more dynamic and fine-grained control over the conditioning process. This modification enhances the model's ability to adapt to different conditions and improves the overall generation quality. Our experiments show that this enhancement yields a notable performance boost, further demonstrating the effectiveness of this conditioning strategy in diffusion models." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.327, + 0.704, + 0.342 + ], + "angle": 0, + "content": "3.4. Minor Modification" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.349, + 0.909, + 0.457 + ], + "angle": 0, + "content": "We re-visit the activation function across the entire model. Inspired by ConvNeXt [28], we replaced the commonly used SiLU activation with GELU, which is a standard choice in transformer architectures. On top of other modifications, this change contributed to a modest but consistent improvement in performance. We are aware of potentially better activations [31, 44], but we stick to GeLU for simplicity." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.468, + 0.649, + 0.485 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.493, + 0.907, + 0.525 + ], + "angle": 0, + "content": "In this section, we provide experiments on various settings to demonstrate the outstanding performance of DiC model." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.532, + 0.698, + 0.548 + ], + "angle": 0, + "content": "4.1. Experiment Setups" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.553, + 0.909, + 0.795 + ], + "angle": 0, + "content": "Model Configs. To benchmark against existing DiT [30] models, we designed our architectures at different scales: Small (S), Big (B), and Extra Large (XL), which align closely with DiT-S/2, DiT-B/2, and DiT-XL/2 in terms of both FLOPs and parameter count, as shown in Table 3. Additionally, we introduce a larger model, Huge (H), for further scalability testing. With 32.8M parameters and 5.9G FLOPs, DiC-S provides a lightweight solution, similar to DiT-S/2, with an efficient [6,6,5,6,6] encoder-decoder configuration. DiC-B scales up to 129.5M parameters and 23.5G FLOPs, which is comparable to DiT-B/2, leveraging a wider channel size of 192. DiC-XL has 702.3M parameters and 116.1G FLOPs, whose configuration rivals DiT-XL/2, with an enhanced encoder-decoder depth of [7,7,8,7,7]. DiC-H is further scaled up to [14,14,10,14,14] and is designed to evaluate the potentials of DiC models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.911, + 0.903 + ], + "angle": 0, + "content": "Apart from normal FLOPs calculation, in Tab. 3 we also record actual FLOPs when taking Winograd acceleration [26] into account. As is introduced in Sec. 3.1, Winograd could reduce the computation of a stride-1 3x3 Convolution by \\(5/9\\). From statistics in Tab. 3, it could be observed that Winograd could reduce the amount of theoretical FLOPs of the proposed DiC by approximately a half." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2473" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.15, + 0.089, + 0.845, + 0.18 + ], + "angle": 0, + "content": "
    ModelParams (M)FLOPs (G)Wino. FLOPs (G)Channel# GroupsEncoder-Decoder
    DiC-S32.85.92.99616[6,6,5,6,6]
    DiC-B129.523.511.819232[6,6,5,6,6]
    DiC-XL702.3116.157.238432[7,7,8,7,7]
    DiC-H1034.4204.497.238432[14,14,10,14,14]
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.185, + 0.908, + 0.227 + ], + "angle": 0, + "content": "Table 3. Configurations of DiC architecture with different model sizes. We align DiC architectures to DiTs in terms of both FLOPs and parameters. Wino. FLOPs takes the FLOPs saved by Winograd into consideration. # Groups stands for the number of groups in GroupNorm. Encoder-Decoder denotes the transformer block number of encoder and decoder module." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.235, + 0.482, + 0.369 + ], + "angle": 0, + "content": "Experiment Settings. We follow the standard training setup from previous research [5, 29, 30, 38], utilizing the same VAE (i.e., sd-vae-ft-ema) as in latent diffusion models [32] and the AdamW optimizer. All hyperparameters remain unchanged, including a global batch size of 256, a learning rate of \\(1e^{-4}\\), weight decay of 0, and a global seed of 0. Training is performed on the ImageNet 2012 dataset [10]. Our DiC-XL and DiC-H models are trained on 8 Ascend 910B NPUs." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.371, + 0.483, + 0.491 + ], + "angle": 0, + "content": "Overhead Calculation. We calculate the FLOPs overhead of DiC models via torchprofile [27], an easy-to-use but comprehensive FLOPs calculator. The throughput is calculated on a single A100. Following the official sampling configurations of [30], we use batchsize 32 for throughput testing. We heat the GPU up via numerous warm-up runs before measuring the throughput. Flash attention [8, 9] is activated based on the original implementations of baselines." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.503, + 0.467, + 0.52 + ], + "angle": 0, + "content": "4.2. Evaluating DiC on the Standard DiT Setting" + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.539, + 0.457, + 0.693 + ], + "angle": 0, + "content": "
    ImageNet 256×256, 400K
    ModelFLOPs (G)FID↓IS↑
    DiT-S/26.167.4020.44
    DiC-S (Ours)5.958.6825.82
    DiT-B/223.042.8433.66
    DiC-B (Ours)23.532.3348.72
    DiT-XL/2118.620.0566.74
    DiC-XL (Ours)116.113.11100.15
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.698, + 0.483, + 0.754 + ], + "angle": 0, + "content": "Table 4. Comparing DiCs against DiTs across various model sizes. We compare models trained for 400K iterations with the standard setting of DiT. DiCs at all scales outperform DiTs at considerable margins." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.764, + 0.483, + 0.884 + ], + "angle": 0, + "content": "Comparison with DiT Across Model Sizes. As shown in Table 4, our DiC models outperform the corresponding DiT models across all tested scales. Specifically, DiC-S achieves a significant reduction in FID, dropping from 67.40 to 58.68, while also surpassing DiT-S/2 in IS, increasing from 20.44 to 25.82. Similarly, DiC-B outperforms DiT-B/2 by a notable margin, reducing FID from 42.84 to 32.33 and increasing IS from 33.66 to 48.72." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.484, + 0.901 + ], + "angle": 0, + "content": "In the large-scale model category, DiC-XL delivers a re" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.235, + 0.907, + 0.326 + ], + "angle": 0, + "content": "markable improvement over DiT-XL/2, with FID dropping from 20.05 to 13.11 and IS soaring from 66.74 to 100.15. These results highlight the effectiveness of our DiC models, which consistently achieve superior performance in both image quality and diversity, all while maintaining computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.326, + 0.909, + 0.506 + ], + "angle": 0, + "content": "Comparison with Diffusion Transformer Baselines. As different models use different settings, including training hyperparameters, the choice of samplers, training iterations et cetera, we adopt a universally-aligned setting (400K iterations on the DiT codebase) according to [38]. As shown in Table 6, our proposed DiC models consistently outperform baseline diffusion architectures on ImageNet \\(256 \\times 256\\), all under similar computational budgets. Despite having comparable FLOPs to models like DiT-XL/2 and PixArt-\\(\\alpha\\)-XL/2, our DiC-XL achieves a significantly lower FID of 13.11 and an impressive IS of 100.15, showcasing its superior generative quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.507, + 0.909, + 0.612 + ], + "angle": 0, + "content": "Beyond performance, another standout is DiC's efficiency in speed. Despite the heavy computational demands of diffusion models, DiC-XL achieves a throughput of 313.7, which, while appearing lower, re-ects the use of Conv3x3's highly optimized operations. This architecture capitalizes on the inherent speed of simple convolutions, offering a practical balance between efficiency and quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.909, + 0.747 + ], + "angle": 0, + "content": "Even more impressively, DiC-H strikes a remarkable trade-off between model size and speed, delivering state-of-the-art FID of 11.36 and an IS of 106.52, with an improved throughput of 160.8. This demonstrates that our models can achieve unparalleled generation quality without the severe latency typically associated with transformer-based diffusion models. In real-world applications, these speed advantages make DiC a practical solution for high-quality image synthesis." + }, + { + "type": "table", + "bbox": [ + 0.532, + 0.758, + 0.885, + 0.853 + ], + "angle": 0, + "content": "
    ImageNet 256×256, 400K
    ModelcfgFLOPsFID↓IS↑
    DiT-XL/21.5118.66.24150.10
    U-ViT-XL1.5113.05.66170.62
    DiC-XL1.5116.1 (57.2)3.89224.20
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.858, + 0.908, + 0.885 + ], + "angle": 0, + "content": "Table 5. Generation performance with classifier-free guidance. The proposed DiC is also performant on conditional generation." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.886, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Furthermore, we experiment the conditional generation" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2474" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.092, + 0.462, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.293, + 0.486, + 0.324 + ], + "angle": 0, + "content": "Figure 4. Comparing FID performance and FLOPs between DiTs and DiCs. Marker sizes represent relative model sizes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.348, + 0.484, + 0.425 + ], + "angle": 0, + "content": "capabilities of DiC model in Tab. 5. DiC-XL achieves an FID of 3.89 at merely 400K iterations, surpassing competitive Diffusion Transformer baselines by large margins. The results are yielded from conditional generation samples with \\( \\mathrm{cfg} = 1.5 \\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.435, + 0.303, + 0.453 + ], + "angle": 0, + "content": "4.3. DiC on Larger Images" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.458, + 0.484, + 0.623 + ], + "angle": 0, + "content": "As shown in Table 7, we compare DiC models with DiT on ImageNet 512x512, after training for 400K iterations with standard DiT hyperparameters. The key takeaway from these results is the computational efficiency of DiC models. While DiT-XL/2 requires 524.7G FLOPs (with Winograd optimization), our DiC-XL model performs significantly better in terms of FID and IS, with only 464.3G FLOPs (228.7G after Winograd optimization). This improvement becomes even more evident in DiC-H, which offers a dramatic reduction in FID (12.89) and achieves a higher IS (101.78) with fewer FLOPs than DiT-XL/2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.625, + 0.484, + 0.792 + ], + "angle": 0, + "content": "The key difference in computational complexity between DiC and DiT lies in their underlying architectures. DiC uses a pure convolutional approach, which scales linearly with the image size. In contrast, DiT employs self-attention, which incurs quadratic complexity with respect to the image size. Therefore, for larger images, such as \\(512 \\times 512\\), the computational gap between DiC and DiT becomes more pronounced. In spite of this, we are amazed that DiC models could still maintain an advantageous gap over DiTs. The advantage of DiC, on the other hand, is also outstanding in terms of throughput." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.802, + 0.29, + 0.818 + ], + "angle": 0, + "content": "4.4. Scaling to Excellence" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.483, + 0.87 + ], + "angle": 0, + "content": "In this section, we look at the scaled-up model (DiC-H) with increased training iterations, and the combination with diffusion techniques to discover the potential of DiC." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Under DiT's plainest no-CFG setting. Table 8 presents the performance of DiC-H on ImageNet \\(256 \\times 256\\) as training" + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.095, + 0.905, + 0.242 + ], + "angle": 0, + "content": "
    ImageNet 256×256, 400K
    ModelFLOPs (G)TPFID↓IS↑
    U-ViT-XL [1]113.072.618.3576.59
    DiT-XL/2 [30]118.666.820.0566.74
    PixArt-α-XL/2 [2]118.464.124.7552.24
    DiffiT-XL/2 [17]118.564.136.8635.39
    DiT-LLaMA* [5]118.665.220.2270.10
    DiC-XL (Ours)116.1 (57.2)313.713.11100.15
    DiC-H (Ours)204.4 (97.2)160.811.36106.52
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.247, + 0.91, + 0.318 + ], + "angle": 0, + "content": "Table 6. The performance of DiCs and competitive diffusion architectures on ImageNet \\(256 \\times 256\\) generation. The baselines are aligned under the official 400K-iteration setting of DiT-XL for a fair comparison. TP stands for throughput. FLOPs considering Winograd is reported for DiCs." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.346, + 0.911, + 0.449 + ], + "angle": 0, + "content": "
    ImageNet 512×512, 400K
    ModelG FLOPs (Wino.)TPFID↓IS↑
    DiT-XL/2524.716.220.9466.30
    DiC-XL464.3 (228.7)84.215.3293.55
    DiC-H817.2 (388.4)53.312.89101.78
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.454, + 0.907, + 0.511 + ], + "angle": 0, + "content": "Table 7. Comparing DiCs against DiTs on ImageNet \\(512 \\times 512\\) generation. We compare models trained for 400K iterations with the standard setting of DiT. Please refer to the appendix for results from longer training iterations." + }, + { + "type": "table", + "bbox": [ + 0.546, + 0.52, + 0.872, + 0.654 + ], + "angle": 0, + "content": "
    ImageNet 256×256, Scale Up, w/ocfg
    ModelTraining StepsFID↓IS↑
    DiT-XL/22.4M10.67-
    DiT-XL/27M9.62-
    DiC-H400K11.36106.52
    DiC-H600K9.73118.57
    DiC-H800K8.96124.33
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.658, + 0.907, + 0.701 + ], + "angle": 0, + "content": "Table 8. Fast Convergence of DiC. The generation performance without classifier guidance of both models on ImageNet \\(256 \\times 256\\) consistently improves as training progresses." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.717, + 0.905, + 0.822 + ], + "angle": 0, + "content": "progresses. The performance of DiC-H improves steadily as the training progresses. At 600K steps, FID decreases to 9.73, matching the performance of DiT-XL/2 at 7M training steps; at 800K steps, DiC-H shows the best performance with an FID of 8.96. This table demonstrates the fast convergence of DiC-H, where both FID and IS consistently improve with training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.824, + 0.905, + 0.884 + ], + "angle": 0, + "content": "Towards excellence with classifier-free guidance. Table 9 presents the comparison of various models' performance on ImageNet \\(256 \\times 256\\) when training iteration is scaled up and classifier-free guidance is applied." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.886, + 0.907, + 0.902 + ], + "angle": 0, + "content": "The baseline model DiT-XL/2 achieves a throughput of" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2475" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.521, + 0.868, + 0.536 + ], + "angle": 0, + "content": "Figure 5. Samples generated by DiC at 2M iterations. The samples are generated following the setting of DiT, at \\(cfg = 4\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.55, + 0.484, + 0.761 + ], + "angle": 0, + "content": "66.8, processes a batch size of 256 for 7 million iterations, and yields an FID score of 2.27. The U-ViT-H model, while slightly lower in throughput at 63.9, uses a larger batch size of 1024, resulting in a slightly higher FID of 2.29. In comparison, our proposed DiC-H model shows a marked improvement when trained with a modest setting of batch size of 256 over 2 million iterations. DiC-H could achieve an FID of 2.25, with a throughput of 160.8. These results reveal that CNNs could reach performance that is no worse than Diffusion Transformers, and they have a great throughput advantage. Building upon this SiT-ow-based framework, we also combine DiC with the State-of-the-Art technique of Representation Alignment (REPA) [39, 46] to achieve much faster convergence. The details are in the appendix." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.773, + 0.452, + 0.868 + ], + "angle": 0, + "content": "
    ImageNet 256×256, Scale Up, w/cfg
    ModelTPBS×IterFID↓
    DiT-XL/266.8256×7M2.27
    U-ViT-H63.91024×500K2.29
    DiC-H (Ours)160.8256×2M2.25
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.873, + 0.483, + 0.916 + ], + "angle": 0, + "content": "Table 9. Generation performance of powerful baselines with classifier-free guidance. TP stands for throughput. The proposed DiC is also performant on conditional generation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.548, + 0.634, + 0.564 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.574, + 0.908, + 0.83 + ], + "angle": 0, + "content": "In this work, we rethink the design of Conv3x3 in the context of diffusion models and introduced DiC, a purely 3x3-convolutional diffusion model. We initially explore various state-of-the-art diffusion architectures and find that the Encoder-Decoder U-Net structure performs the best. Building on this, we propose the sparse skip connection to reduce redundant block-wise connections and enhance efficiency of U-Net. In addition to architecture, we redesign the conditioning mechanism. We introduce stage-specific independent embeddings where each embedding is responsible for addressing conditioning within its assigned stage. We also propose mid-block condition injection and conditional gating, which are beneficial from empirical observations. Based on these improvements, our proposed Conv3x3 diffusion model not only achieves superior generative performance compared to Diffusion Transformers but also does so with significantly higher throughput." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.831, + 0.909, + 0.89 + ], + "angle": 0, + "content": "Above all, as an aspect that is always neglected in diffusion, we investigate the use of convolutions in diffusion models, and we hope this work could inspire further exploration into the use of convolutions in diffusion models." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2476" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.182 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported by the National Key R&D Program of China under grant No. 2022ZD0160300 and the National Natural Science Foundation of China under grant No. 62276007. We gratefully acknowledge the support of MindSpore, CANN, and Ascend AI Processor used for this research." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.197, + 0.188, + 0.212 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.221, + 0.486, + 0.304 + ], + "angle": 0, + "content": "[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. All are worth words: A vit backbone for diffusion models. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023, pages 22669-22679. IEEE, 2023. 1, 2, 4, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.306, + 0.485, + 0.375 + ], + "angle": 0, + "content": "[2] Junsong Chen, Jincheng Yu, Chongjian Ge, Lewei Yao, Enze Xie, Yue Wu, Zhongdao Wang, James Kwok, Ping Luo, Huchuan Lu, and Zhenguo Li. 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Open-sora: Democratizing efficient video production for all, 2024. 1" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.907, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2478" + } + ] +] \ No newline at end of file diff --git a/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_origin.pdf b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..284654df445f94272dafdf5d7bfeccf0637f6117 --- /dev/null +++ b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/ec13b3df-7c93-4573-84f4-921e88721107_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9b79aca3219f896f431c0457d804e0a9cfc55a5cdb6b446710b5b777fba70c03 +size 659732 diff --git a/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/full.md b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..be77592a562a5d900b00be46727babce872844a8 --- /dev/null +++ b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/full.md @@ -0,0 +1,294 @@ +# DiC: Rethinking Conv3x3 Designs in Diffusion Models + +Yuchuan Tian $^{1*}$ , Jing Han $^{2*}$ , Chengcheng Wang $^{3}$ , Yuchen Liang $^{4}$ , Chao Xu $^{1}$ , Hanting Chen $^{3\dagger}$ + +$^{1}$ State Key Lab of General AI, School of Intelligence Science and Technology, Peking University. + +$^{2}$ School of Artificial Intelligence, Beijing University of Posts and Telecommunications. $^{3}$ Huawei Noah's Ark Lab. + +$^{4}$ School of Mathematical Sciences, Peking University. + +tianyc@stu.pku.edu.cn, hj19910619@163.com, chenhanting@huawei.com + +# Abstract + +Diffusion models have shown exceptional performance in visual generation tasks. Recently, these models have shifted from traditional U-Shaped CNN-Attention hybrid structures to fully transformer-based isotropic architectures. While these transformers exhibit strong scalability and performance, their reliance on complicated self-tention operation results in slow inference speeds. Contrary to these works, we rethink one of the simplest yet fastest module in deep learning, 3x3 Convolution, to construct a scaled-up purely convolutional diffusion model. We first discover that an Encoder-Decoder Hourglass design outperforms scalable isotropic architectures for Conv3x3, but still underperforming our expectation. Further improving the architecture, we introduce sparse skip connections to reduce redundancy and improve scalability. Based on the architecture, we introduce conditioning improvements including stage-specific embeddings, mid-block condition injection, and conditional gating. These improvements lead to our proposed Diffusion CNN (DiC), which serves as a swift yet competitive diffusion architecture baseline. Experiments on various scales and settings show that DiC surpasses existing diffusion transformers by considering margins in terms of performance while keeping a good speed advantage. Project page: https://github.com/YuchuanTian/DiC + +# 1. Introduction + +Diffusion-based image generative models have recently gained significant attention, with notable works like Stable Diffusion [32] demonstrating impressive results. As these models continue to evolve, they are now capable of generating increasingly realistic images. Recent advancements, including Sora-related works, have extended this capability to video generation, producing high-quality, temporally consistent videos that rival real-world footage. + +![](images/ae6b7def6e1d260cf779795ea18621f2ef79849300af11dffb3e47ace91e01b6.jpg) +Figure 1. The Roadmap to a 3x3 Convolutional Diffusion Model. Performance is measured by FID $(\downarrow)$ of the model trained at 200K iterations. A series of proposed model improvements gives DiC an advantage over Diffusion Transformers. + +The self-attention mechanism plays a pivotal role in many recent diffusion models. Early work [19, 36] fused convolutional U-Net structures with self-attention. More recently, architectures such as U-ViT [1] and DiT [30] have fully transitioned to attention-based designs, abandoning convolutional U-Nets entirely. These models demonstrate remarkable generative capabilities, particularly when scaled up. Newer text-to-image and text-to-video models, including Stable Diffusion 3 [14], FLUX [25], PixArt series [2-4], and OpenSora [24, 47], have also adopted fully transformer-based architectures, achieving impressive generation quality. + +Unfortunately, diffusion models incorporating self-attention face significant computational overhead and latency when scaled up. Complex transformer architectures pose a considerable challenge for real-time, resource-constrained applications, where large-scale transformers are impractical due to their substantial time costs. + +Efforts have been made to accelerate self-attention in diffusion models. For instance, ToDo [35] and PixArt- $\Sigma$ [3] implement more efficient self-attention mechanisms. However, these approaches remain confined to the self-attention + +paradigm. Other works [37, 45] aim to replace self-attention with State-Space-Model-based architectures [16], attempting to bypass its inherent inefficiencies. Despite these innovations, the generation speed on typical latent-domain image resolutions remains suboptimal, failing to meet the demands of real-time or large-scale applications. + +In this work, we rethink the simple yet efficient fully convolutional diffusion model architecture that offers significant speed advantages. As a counterpart to self-attention, convolution is widely regarded as hardware-friendly, with excellent support across various platforms. Among the many convolutional operations, the canonical 3x3 stride-1 convolution stands out for its exceptional speed, largely due to widespread hardware optimization techniques such as Winograd acceleration [26]. For instance, work like RepVGG [12] have demonstrated how simple convolutions can achieve both high efficiency and competitive performance. + +However, 3x3 convolutions come with inherent limitations, particularly a constrained receptive field, which may hinder their scalability in complex generative tasks. We firstly perform initial trials to scale up purely 3x3-based CNNs within existing scalable frameworks, but these experiments yielded results that are still inferior to Diffusion Transformer counterparts. + +To address this, we propose a series of adaptations to conventional ConvNets, forming a roadmap (shown in Fig. 1) that tailors them specifically for a scaled-up diffusion model. Firstly, we focus on refining the model architecture to better leverage Conv3x3. Existing designs fall into three categories: isotropic architectures like DiT [30], isotropic architectures with skips like U-ViT [1], and encoder-decoder hourglass structures used in canonical CNN & self-attention hybrid models. Empirical observations reveal that the hourglass architecture is more effective for pure Conv3x3 models, because downsampling and upsampling in encoders expand the receptive field that makes up for the narrow scope of Conv3x3. Skip connections are also observed crucial, but traditional blockwise skips for cheap convolution block scale-ups are too dense to be efficient for large ConvNets. To address this, we introduce sparse skip connections that reduces the number of skips while ensuring essential information ows efficiently from encoder to decoder. + +Besides, we focus on improving conditioning to fit the hourglass ConvNet better. In existing models, a single set of condition embeddings is often mapped to different blocks across various stages. However, in encoder-decoder hourglass ConvNets, each stage operates in distinct feature spaces. Hence, we introduce stage-specific embeddings, ensuring each stage uses independent, non-overlapping condition embedding tables. We also carefully inspect the position for embedding injection, and we suggest inject conditions midblock for better performance. Additionally, we borrow conditional gating on feature-maps. In addition, we refined the + +internal block structure, replacing all activation functions with GELU. + +With these enhancements, we propose DiC, a diffusion model made up of Conv3x3. The architectural and conditioning improvements collectively enable our model to achieve outstanding results while maintaining its speed advantage. Experiments on various scales and settings demonstrate DiC's performance advantage over Diffusion Transformers as well as its high-throughput characteristics. + +# 2. Related Work + +Self-Attention in Diffusion Architectures. Self-attention has become a cornerstone of modern diffusion architectures, thanks to its remarkable effectiveness in capturing long-range dependencies. Early UNet-based diffusion models [19, 36] incorporated Self-Attention layers in the higher stages of the network, where capturing global context is most critical. Dhariwal et al. took this further with ADM [11], extending self-attention across all stages, which significantly increased the model's generative capabilities. + +More recent works [1, 21, 30] have fully embraced transformer-based architectures, replacing traditional U-Net backbones with full self-attention designs. These models not only achieve superior performance, but also exhibit excellent scalability, particularly at large model sizes and FLOPs. Most following work like PixArt- $\alpha$ [2] and Stable Diffusion 3 adopt the full transformer backbone design that demonstrates outstanding Text-to-Image generation capabilities. Beyond these, some works continue to explore and refine the use of self-attention and transformer architectures in diffusion models, further pushing the boundaries of efficiency in transformer-based generative modeling. For instance, [3, 35, 38] looks at downsampled tokens for self-attention; [43] uses linear attention. Other works [37, 45] opt for State Space Models for diffusion, but SSMs suffer in terms of latency for ordinary-shaped images [37]. Some other work [6, 20, 22, 38] looks at a combination of U-Net and Self-Attention. In contrast to these works, we push architectural simplicity to the extreme by designing an entire diffusion model using $3 \times 3$ convolutions. With carefully crafted structural optimizations, this streamlined network not only capitalizes on the speed advantages of $3 \times 3$ convolutions but also achieves diffusion generation performance on par with transformer-based models. + +Efficient Convolution. Historically, architectures like AlexNet [23], VGG [34], and ResNet [18] have dominated computer vision tasks. While transformers [40] have later become the state-of-the-art for many vision applications, their high computational cost and latency make them less practical in resource-constrained environments, where CNNs still excel. Recent advancements have revisited and improved CNNs, enabling them to rival or even surpass transformers in both performance and efficiency. + +![](images/a9bdb0c45c276a477d04e20998bb7adea4726b5234dc668041a910f9bef7f8e3.jpg) +(a) Transformer Block + +![](images/3750e0f96289aaae5cce311223414b963740f22204c4c4d08f679a3733b72b61.jpg) +(b) Conv 3x3 Basic Block (Ours) +Figure 2. Basic Blocks for scaled-up architectures. Compared to complicated Transformer blocks widely applied in [30], our Conv 3x3 Basic Block is much simpler and better supported by hardware, being the key to high throughput. + +For example, ConvNeXt [28] achieves transformer-level performance through macro and micro architectural changes, such as increasing kernel sizes and optimizing normalization. Deformable Convolutions (DCNs) [7, 41, 42] enhance the receptive field by learning spatially adaptive kernel shapes, while RepLKNet [13] utilizes massive $31 \times 31$ kernels to capture long-range dependencies. Similarly, Wavelet Conv [15] operates in the frequency domain using wavelet transforms to extend CNN capabilities. + +On the other hand, there is work that resort to improving the efficiency of simple convs. RepVGG [12] focuses on the potential of simple 3x3 convolutions, employing reparameterization tricks to enhance their effectiveness. Inspired by its speed potential, we explore the use of pure 3x3 convolutions in diffusion, combined with architectural and conditioning improvements, to achieve competitive results in diffusion-based generative models. However, we are not using tricks like re-parameterization [12]. Our approach demonstrates that even with a simple design, high-quality generation can be both efficient and effective. + +# 3. Method + +# 3.1. Preliminaries: Conv3x3 as the Ingredient + +We choose normal stride-1 full Conv3x3 as the major ingredient of model. Stride-1 3x3 convolutions are incredibly speedy, primarily due to extensive hardware and algorithmic optimizations in modern deep learning frameworks. The operation optimization benefits from the Winograd algorithm [26], which reduces the number of multiplications required for common convolution operations by $\frac{5}{9}$ . For 3x3 kernels, this method significantly accelerates the computation by leveraging efficient matrix transformations. + +Additionally, unlike depth-wise convolution, 3x3 convolutions achieve a high degree of computational parallelism, allowing modern GPUs to fully utilize their processing power. This parallelism, combined with minimal memory access overhead, makes stride-1 3x3 convolutions particularly effi + +cient. Compared to larger or more complex convolution operations, they offer an ideal trade-off between computational cost and representational power, making them a practical choice for real-time applications and large-scale models. + +# 3.2. Architectures for Scale-Up + +Our Basic Block. We revisit canonical diffusion models [11, 36] and figure out that $3 \times 3$ convolutions are also widely applied. However, these models are not pure CNNs: the basic block unit within the model consists of two consecutive $3 \times 3$ convolutional layers, followed by a self-attention module that attends within the entire image. Before each convolution, the input is normalized using GroupNorm, and then passed to the non-linear activation function of SiLU. Notably, the intermediate features within the block maintain the same number of channels, ensuring stable feature propagation. The overall block adopts a residual structure [18], where the input is directly added to the output via a shortcut connection. + +The roadmap to our proposed diffusion model DiC-a $3\times 3$ convolutional denoiser starts from the revisited convolutional basic block mentioned above. In order to satisfy the ultimate goal of the roadmap, we remove the self-attention layers after the convolutions to form a minimal unit block (Basic Block) consisting of two $3\times 3$ convolutions. Other block designs are temporarily left intact. + +Mainstream Architectures. With this Conv 3x3 Basic Block as the foundation, we scale the model up by stacking multiple such blocks and increasing the network's depth and width, and we are faced up to numerous architectural choices (shown in Fig. 3): + +1. Isotropic Architecture. Inspired by DiT and subsequent works [2, 5, 17, 30], this design features a simple, vertically stacked structure. After patchification, the intermediate feature-map size is not changed throughout the entire model. It is widely adopted for its reputed scalability, particularly when scaled to large models. +2. Isotropic Architecture with Skip Connections. This ap- + +![](images/ff010a3d9f2572f65049030f398c5a7ceb598fa97d2f04e0a71419b5b482daab.jpg) +(a) Isotropic + +![](images/1afb77678da34059fa62b25216052f40fc302ea30c8b615763d247cf0256ade6.jpg) +(b) Isotropic + Skip + +![](images/fd16a2e95a2ede1e3126f718b6a578328ef8e5dbc9eeb138052f9142693ec6f8.jpg) +(c) U-Net +Figure 3. Mainstream Diffusion Architectures. We try existing diffusion architectures (a,b,c) with Conv3x3 Basic Block. We further improve U-Net (d) with sparse-skips. + +![](images/a281c82ed30902596605cb1e7465167d3810eab89472c9cf74f7d011b6829729.jpg) +(d) U-Net + Sparse Skip + +proach extends the columnar isotropic architecture by introducing long skip connections between non-adjacent layers, similar to the design used in U-ViT [1]. Unlike traditional U-Net, despite the skip design, this architecture maintains a consistent spatial resolution throughout the network, avoiding any upsampling and downsampling operations. + +3. U-Net Hourglass Architecture. This classical design [33] consists of an encoder and a decoder, forming a funnel-like shape. The encoder progressively downsamples the feature dimensions, while the decoder symmetrically upsamples the spatial dimensions. Apart from the hourglass backbone, each block in the encoder is connected to its corresponding decoder block via skip connections. This work is widely applied in earlier diffusion works [11, 19, 36]. + +
    ImageNet 256×256, 200K,cfg=1.5
    ModelFLOPs (G)FID↓IS↑
    DiT-XL118.612.9694.26
    Isotropic115.629.3152.80
    Isotropic + Skip117.115.0785.51
    U-Net Hourglass115.214.6587.17
    U-Net + Sparse Skip116.111.49106.91
    + +Table 1. Comparing Architectures for Conv3x3 Scale-Up on ImageNet $256 \times 256$ conditional generation. Conv3x3 taps its full potential with U-Net Hourglass architectures due to enlarged perception field; sparsifying skip connection further improves the model. + +Experimental Analysis. Using the foundational Conv 3x3 Basic Block, we conducted scaling experiments on the aforementioned architectural choices. The results, summarized in Tab. 1, indicate that the performance across all architectures was generally suboptimal. However, these experiments revealed several patterns that provide valuable insights for designing an effective 3x3 convolution-based diffusion model. + +Firstly, for diffusion models composed solely of $3 \times 3$ convolutions, the encoder-decoder architecture hourglass is essential. This stems from a fundamental limitation of $3 \times 3$ convolutions: their inherently restricted receptive field. In a purely isotropic, standard-transformer architecured setup, + +each 3x3 convolution expands the receptive field by only one pixel in each direction. As a result, achieving a global receptive field would require a deep stack of convolutions, leading to inefficiencies in both computation and parameters. In contrast, an encoder-decoder architecture significantly mitigates this limitation. By progressively downsampling in the encoder and upsampling in the decoder, the 3x3 convolutions in higher stages can effectively perceive larger regions of the input. For instance, at deeper stages, a single 3x3 convolution can cover areas as large as 6x6 or 12x12 in the original image space, substantially increasing the model's receptive field. This hierarchical approach allows the model to efficiently capture both local and global context, making it far more effective for generative tasks. + +Secondly, skip connections are vital in Conv3x3-based architectures. On one hand, in encoder-decoder structures, they mitigate information loss during downsampling by passing feature maps directly to the decoder, enriching its representation. On the other hand, skips accelerate training and improve generation quality by providing additional gradient pathways and preserving important features, leading to more efficient and effective diffusion modeling. + +Above all, we adopt the U-Net as the general model architecture that we use. + +Improving U-Nets via Strided Skip. However, as scaling up our Conv3x3-based diffusion model requires stacking numerous convolutional layers, dense, block-wise skip connections become a bottleneck. Numerous blockwise skip features have to be concatenated to the features and get merged on the channel dimension within corresponding decoder blocks, consuming excessive computational costs. This inefficiency hampers the scalability of the model. To address this, we propose strided skip connections, where skips are applied only every few blocks instead of after each one. This approach improves the performance, and our experiments (in Tab. 1) show that it does yield better results compared with densely-connected skip designs. + +# 3.3. Conditioning Improvements + +Apart from architectural improvements, we hold that conditioning could also be refined. After model scale-ups, previous conditioning designs need to be improved according to the architecture. + +Stage-Specific Embeddings. In conventional diffusion models [11, 36], a unique embedding table is shared by previous models. However, in the scaled-up Conv3x3 model, we rely on an encoder-decoder structure to expand the receptive field. Each stage of the encoder-decoder operates with different channel dimensions, reflecting significant structural and functional differences between stages. Given that feature dimensions vary across stages, applying the same condition embedding uniformly on all blocks from different stages may not be ideal. The diverse roles and representations at + +each stage suggest that a more stage-tailored approach to condition embedding could be more effective, as a single embedding set might not adequately capture the distinct characteristics of each stage. + +
    ImageNet 256×256, 200K, CFG=1.5
    ModelFLOPs (G)FID↓IS↑
    Sparse-Skip U-Net116.111.49106.91
    + Stage-Spec. Emb.116.110.07121.30
    + Mid-Block Injection116.18.80134.25
    + DiT condition gating116.16.54162.34
    DiC (+ GELU)116.16.26170.04
    + +Table 2. Conditioning improvements on ImageNet $256 \times 256$ conditional generation. The proposed conditioning improvements collectively bring considerable performance enhancement. Experiments are conducted using hyperparameters from [30] for 200K iterations. + +As an improvement, we propose using stage-specific condition embeddings for each stage of the encoder-decoder structure. Each stage will have its own independent embedding, with the embedding dimension aligned to that stage's feature dimension. This ensures that the condition embedding is tailored to the specific characteristics and scale of each stage. + +It is worth mentioning that we analyzed the overhead introduced by the stage-specific embeddings. The results show that the added overhead is minimal. Specifically, adding the new stage-specific embeddings increased the model size by just 14.06M parameters, which accounts for only $2\%$ of the total model size. The computational overhead introduced is even more negligible, with an increase of only 12M FLOPs, which has little impact on the overall computational efficiency. This demonstrates that the inclusion of stage-specific embeddings does not significantly affect the model's performance or computational cost. + +Beside, the label-drop operation on the embeddings across different stages should be synchronized during training. This prevents any leakage of label between stages and ensures that the model learns in a consistent and isolated manner, thereby improving the stability and performance of the diffusion model. + +Condition Injection Position. Another critical aspect of our design is determining the optimal position for injecting conditioning information. There are two prevalent strategies for condition injection in diffusion models. The first approach injects the condition at the very beginning of each block, typically through LayerNorm, as seen in models like [5, 30]. The second approach introduces the condition in the middle of the block, as utilized in [11, 36]. + +Through experimentation, we found that for our fully convolutional diffusion architecture, injecting the condition into the second convolutional layer within each block yields + +the best performance. This placement effectively modulates the feature representations, enhancing the model's generative quality without compromising its efficiency. + +Conditional Gating. In addition, we adopted the conditional gating mechanism from DiT's AdaLN [30]. On top of traditional affine conditioning that performs channel-wise affine mapping to the feature map, AdaLN introduces a gating vector that scales the features along the channel dimension, providing a more dynamic and fine-grained control over the conditioning process. This modification enhances the model's ability to adapt to different conditions and improves the overall generation quality. Our experiments show that this enhancement yields a notable performance boost, further demonstrating the effectiveness of this conditioning strategy in diffusion models. + +# 3.4. Minor Modification + +We re-visit the activation function across the entire model. Inspired by ConvNeXt [28], we replaced the commonly used SiLU activation with GELU, which is a standard choice in transformer architectures. On top of other modifications, this change contributed to a modest but consistent improvement in performance. We are aware of potentially better activations [31, 44], but we stick to GeLU for simplicity. + +# 4. Experiments + +In this section, we provide experiments on various settings to demonstrate the outstanding performance of DiC model. + +# 4.1. Experiment Setups + +Model Configs. To benchmark against existing DiT [30] models, we designed our architectures at different scales: Small (S), Big (B), and Extra Large (XL), which align closely with DiT-S/2, DiT-B/2, and DiT-XL/2 in terms of both FLOPs and parameter count, as shown in Table 3. Additionally, we introduce a larger model, Huge (H), for further scalability testing. With 32.8M parameters and 5.9G FLOPs, DiC-S provides a lightweight solution, similar to DiT-S/2, with an efficient [6,6,5,6,6] encoder-decoder configuration. DiC-B scales up to 129.5M parameters and 23.5G FLOPs, which is comparable to DiT-B/2, leveraging a wider channel size of 192. DiC-XL has 702.3M parameters and 116.1G FLOPs, whose configuration rivals DiT-XL/2, with an enhanced encoder-decoder depth of [7,7,8,7,7]. DiC-H is further scaled up to [14,14,10,14,14] and is designed to evaluate the potentials of DiC models. + +Apart from normal FLOPs calculation, in Tab. 3 we also record actual FLOPs when taking Winograd acceleration [26] into account. As is introduced in Sec. 3.1, Winograd could reduce the computation of a stride-1 3x3 Convolution by $5/9$ . From statistics in Tab. 3, it could be observed that Winograd could reduce the amount of theoretical FLOPs of the proposed DiC by approximately a half. + +
    ModelParams (M)FLOPs (G)Wino. FLOPs (G)Channel# GroupsEncoder-Decoder
    DiC-S32.85.92.99616[6,6,5,6,6]
    DiC-B129.523.511.819232[6,6,5,6,6]
    DiC-XL702.3116.157.238432[7,7,8,7,7]
    DiC-H1034.4204.497.238432[14,14,10,14,14]
    + +Experiment Settings. We follow the standard training setup from previous research [5, 29, 30, 38], utilizing the same VAE (i.e., sd-vae-ft-ema) as in latent diffusion models [32] and the AdamW optimizer. All hyperparameters remain unchanged, including a global batch size of 256, a learning rate of $1e^{-4}$ , weight decay of 0, and a global seed of 0. Training is performed on the ImageNet 2012 dataset [10]. Our DiC-XL and DiC-H models are trained on 8 Ascend 910B NPUs. + +Overhead Calculation. We calculate the FLOPs overhead of DiC models via torchprofile [27], an easy-to-use but comprehensive FLOPs calculator. The throughput is calculated on a single A100. Following the official sampling configurations of [30], we use batchsize 32 for throughput testing. We heat the GPU up via numerous warm-up runs before measuring the throughput. Flash attention [8, 9] is activated based on the original implementations of baselines. + +# 4.2. Evaluating DiC on the Standard DiT Setting + +Table 3. Configurations of DiC architecture with different model sizes. We align DiC architectures to DiTs in terms of both FLOPs and parameters. Wino. FLOPs takes the FLOPs saved by Winograd into consideration. # Groups stands for the number of groups in GroupNorm. Encoder-Decoder denotes the transformer block number of encoder and decoder module. + +
    ImageNet 256×256, 400K
    ModelFLOPs (G)FID↓IS↑
    DiT-S/26.167.4020.44
    DiC-S (Ours)5.958.6825.82
    DiT-B/223.042.8433.66
    DiC-B (Ours)23.532.3348.72
    DiT-XL/2118.620.0566.74
    DiC-XL (Ours)116.113.11100.15
    + +Comparison with DiT Across Model Sizes. As shown in Table 4, our DiC models outperform the corresponding DiT models across all tested scales. Specifically, DiC-S achieves a significant reduction in FID, dropping from 67.40 to 58.68, while also surpassing DiT-S/2 in IS, increasing from 20.44 to 25.82. Similarly, DiC-B outperforms DiT-B/2 by a notable margin, reducing FID from 42.84 to 32.33 and increasing IS from 33.66 to 48.72. + +In the large-scale model category, DiC-XL delivers a re + +markable improvement over DiT-XL/2, with FID dropping from 20.05 to 13.11 and IS soaring from 66.74 to 100.15. These results highlight the effectiveness of our DiC models, which consistently achieve superior performance in both image quality and diversity, all while maintaining computational efficiency. + +Comparison with Diffusion Transformer Baselines. As different models use different settings, including training hyperparameters, the choice of samplers, training iterations et cetera, we adopt a universally-aligned setting (400K iterations on the DiT codebase) according to [38]. As shown in Table 6, our proposed DiC models consistently outperform baseline diffusion architectures on ImageNet $256 \times 256$ , all under similar computational budgets. Despite having comparable FLOPs to models like DiT-XL/2 and PixArt- $\alpha$ -XL/2, our DiC-XL achieves a significantly lower FID of 13.11 and an impressive IS of 100.15, showcasing its superior generative quality. + +Beyond performance, another standout is DiC's efficiency in speed. Despite the heavy computational demands of diffusion models, DiC-XL achieves a throughput of 313.7, which, while appearing lower, re-ects the use of Conv3x3's highly optimized operations. This architecture capitalizes on the inherent speed of simple convolutions, offering a practical balance between efficiency and quality. + +Even more impressively, DiC-H strikes a remarkable trade-off between model size and speed, delivering state-of-the-art FID of 11.36 and an IS of 106.52, with an improved throughput of 160.8. This demonstrates that our models can achieve unparalleled generation quality without the severe latency typically associated with transformer-based diffusion models. In real-world applications, these speed advantages make DiC a practical solution for high-quality image synthesis. + +Table 4. Comparing DiCs against DiTs across various model sizes. We compare models trained for 400K iterations with the standard setting of DiT. DiCs at all scales outperform DiTs at considerable margins. + +
    ImageNet 256×256, 400K
    ModelcfgFLOPsFID↓IS↑
    DiT-XL/21.5118.66.24150.10
    U-ViT-XL1.5113.05.66170.62
    DiC-XL1.5116.1 (57.2)3.89224.20
    + +Table 5. Generation performance with classifier-free guidance. The proposed DiC is also performant on conditional generation. + +Furthermore, we experiment the conditional generation + +![](images/5dc57917f55b41f516ad33c8189f84764b9eb4c73b3a7eef2f46df798eb6185d.jpg) +Figure 4. Comparing FID performance and FLOPs between DiTs and DiCs. Marker sizes represent relative model sizes. + +capabilities of DiC model in Tab. 5. DiC-XL achieves an FID of 3.89 at merely 400K iterations, surpassing competitive Diffusion Transformer baselines by large margins. The results are yielded from conditional generation samples with $\mathrm{cfg} = 1.5$ . + +# 4.3. DiC on Larger Images + +As shown in Table 7, we compare DiC models with DiT on ImageNet 512x512, after training for 400K iterations with standard DiT hyperparameters. The key takeaway from these results is the computational efficiency of DiC models. While DiT-XL/2 requires 524.7G FLOPs (with Winograd optimization), our DiC-XL model performs significantly better in terms of FID and IS, with only 464.3G FLOPs (228.7G after Winograd optimization). This improvement becomes even more evident in DiC-H, which offers a dramatic reduction in FID (12.89) and achieves a higher IS (101.78) with fewer FLOPs than DiT-XL/2. + +The key difference in computational complexity between DiC and DiT lies in their underlying architectures. DiC uses a pure convolutional approach, which scales linearly with the image size. In contrast, DiT employs self-attention, which incurs quadratic complexity with respect to the image size. Therefore, for larger images, such as $512 \times 512$ , the computational gap between DiC and DiT becomes more pronounced. In spite of this, we are amazed that DiC models could still maintain an advantageous gap over DiTs. The advantage of DiC, on the other hand, is also outstanding in terms of throughput. + +# 4.4. Scaling to Excellence + +In this section, we look at the scaled-up model (DiC-H) with increased training iterations, and the combination with diffusion techniques to discover the potential of DiC. + +Under DiT's plainest no-CFG setting. Table 8 presents the performance of DiC-H on ImageNet $256 \times 256$ as training + +
    ImageNet 256×256, 400K
    ModelFLOPs (G)TPFID↓IS↑
    U-ViT-XL [1]113.072.618.3576.59
    DiT-XL/2 [30]118.666.820.0566.74
    PixArt-α-XL/2 [2]118.464.124.7552.24
    DiffiT-XL/2 [17]118.564.136.8635.39
    DiT-LLaMA* [5]118.665.220.2270.10
    DiC-XL (Ours)116.1 (57.2)313.713.11100.15
    DiC-H (Ours)204.4 (97.2)160.811.36106.52
    + +Table 6. The performance of DiCs and competitive diffusion architectures on ImageNet $256 \times 256$ generation. The baselines are aligned under the official 400K-iteration setting of DiT-XL for a fair comparison. TP stands for throughput. FLOPs considering Winograd is reported for DiCs. + +
    ImageNet 512×512, 400K
    ModelG FLOPs (Wino.)TPFID↓IS↑
    DiT-XL/2524.716.220.9466.30
    DiC-XL464.3 (228.7)84.215.3293.55
    DiC-H817.2 (388.4)53.312.89101.78
    + +Table 7. Comparing DiCs against DiTs on ImageNet $512 \times 512$ generation. We compare models trained for 400K iterations with the standard setting of DiT. Please refer to the appendix for results from longer training iterations. + +
    ImageNet 256×256, Scale Up, w/ocfg
    ModelTraining StepsFID↓IS↑
    DiT-XL/22.4M10.67-
    DiT-XL/27M9.62-
    DiC-H400K11.36106.52
    DiC-H600K9.73118.57
    DiC-H800K8.96124.33
    + +Table 8. Fast Convergence of DiC. The generation performance without classifier guidance of both models on ImageNet $256 \times 256$ consistently improves as training progresses. + +progresses. The performance of DiC-H improves steadily as the training progresses. At 600K steps, FID decreases to 9.73, matching the performance of DiT-XL/2 at 7M training steps; at 800K steps, DiC-H shows the best performance with an FID of 8.96. This table demonstrates the fast convergence of DiC-H, where both FID and IS consistently improve with training. + +Towards excellence with classifier-free guidance. Table 9 presents the comparison of various models' performance on ImageNet $256 \times 256$ when training iteration is scaled up and classifier-free guidance is applied. + +The baseline model DiT-XL/2 achieves a throughput of + +![](images/5af93f4966b114a2fd8c665e66aadf8a88a8b3da715d118f011d4aa7becc4191.jpg) +Figure 5. Samples generated by DiC at 2M iterations. The samples are generated following the setting of DiT, at $cfg = 4$ . + +66.8, processes a batch size of 256 for 7 million iterations, and yields an FID score of 2.27. The U-ViT-H model, while slightly lower in throughput at 63.9, uses a larger batch size of 1024, resulting in a slightly higher FID of 2.29. In comparison, our proposed DiC-H model shows a marked improvement when trained with a modest setting of batch size of 256 over 2 million iterations. DiC-H could achieve an FID of 2.25, with a throughput of 160.8. These results reveal that CNNs could reach performance that is no worse than Diffusion Transformers, and they have a great throughput advantage. Building upon this SiT-ow-based framework, we also combine DiC with the State-of-the-Art technique of Representation Alignment (REPA) [39, 46] to achieve much faster convergence. The details are in the appendix. + +
    ImageNet 256×256, Scale Up, w/cfg
    ModelTPBS×IterFID↓
    DiT-XL/266.8256×7M2.27
    U-ViT-H63.91024×500K2.29
    DiC-H (Ours)160.8256×2M2.25
    + +Table 9. Generation performance of powerful baselines with classifier-free guidance. TP stands for throughput. The proposed DiC is also performant on conditional generation. + +# 5. Conclusion + +In this work, we rethink the design of Conv3x3 in the context of diffusion models and introduced DiC, a purely 3x3-convolutional diffusion model. We initially explore various state-of-the-art diffusion architectures and find that the Encoder-Decoder U-Net structure performs the best. Building on this, we propose the sparse skip connection to reduce redundant block-wise connections and enhance efficiency of U-Net. In addition to architecture, we redesign the conditioning mechanism. We introduce stage-specific independent embeddings where each embedding is responsible for addressing conditioning within its assigned stage. We also propose mid-block condition injection and conditional gating, which are beneficial from empirical observations. Based on these improvements, our proposed Conv3x3 diffusion model not only achieves superior generative performance compared to Diffusion Transformers but also does so with significantly higher throughput. + +Above all, as an aspect that is always neglected in diffusion, we investigate the use of convolutions in diffusion models, and we hope this work could inspire further exploration into the use of convolutions in diffusion models. + +Acknowledgement. This work is supported by the National Key R&D Program of China under grant No. 2022ZD0160300 and the National Natural Science Foundation of China under grant No. 62276007. We gratefully acknowledge the support of MindSpore, CANN, and Ascend AI Processor used for this research. + +# References + +[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. All are worth words: A vit backbone for diffusion models. 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Open-sora: Democratizing efficient video production for all, 2024. 1 \ No newline at end of file diff --git a/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/images.zip b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7651b7e6b677ba46631c0c77f06626423fc5bf81 --- /dev/null +++ b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c7121fa7903739e4707f0657d717c036111998cde3b09b8e3d29c4d52ad4ab62 +size 593170 diff --git a/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/layout.json b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..036eda1828f50b7acaa1dad37fbbd60ab4646882 --- /dev/null +++ b/2025/DiC_ Rethinking Conv3x3 Designs in Diffusion Models/layout.json @@ -0,0 +1,7388 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 136, + 103, + 474, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 103, + 474, + 121 + ], + "spans": [ + { + "bbox": [ + 136, + 103, + 474, + 121 + ], + "type": "text", + "content": "DiC: Rethinking Conv3x3 Designs in Diffusion Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "spans": [ + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "text", + "content": "Yuchuan Tian" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "text", + "content": ", Jing Han" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "text", + "content": ", Chengcheng Wang" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "text", + "content": ", Yuchen Liang" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "text", + "content": ", Chao Xu" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "text", + "content": ", Hanting Chen" + }, + { + "bbox": [ + 81, + 142, + 528, + 158 + ], + "type": "inline_equation", + "content": "^{3\\dagger}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 126, + 159, + 482, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 159, + 482, + 171 + ], + "spans": [ + { + "bbox": [ + 126, + 159, + 482, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 126, + 159, + 482, + 171 + ], + "type": "text", + "content": " State Key Lab of General AI, School of Intelligence Science and Technology, Peking University." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 172, + 512, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 172, + 512, + 184 + ], + "spans": [ + { + "bbox": [ + 96, + 172, + 512, + 184 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 96, + 172, + 512, + 184 + ], + "type": "text", + "content": " School of Artificial Intelligence, Beijing University of Posts and Telecommunications. " + }, + { + "bbox": [ + 96, + 172, + 512, + 184 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 96, + 172, + 512, + 184 + ], + "type": "text", + "content": " Huawei Noah's Ark Lab." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 205, + 186, + 405, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 205, + 186, + 405, + 198 + ], + "spans": [ + { + "bbox": [ + 205, + 186, + 405, + 198 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 205, + 186, + 405, + 198 + ], + "type": "text", + "content": " School of Mathematical Sciences, Peking University." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 128, + 201, + 481, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 201, + 481, + 213 + ], + "spans": [ + { + "bbox": [ + 128, + 201, + 481, + 213 + ], + "type": "text", + "content": "tianyc@stu.pku.edu.cn, hj19910619@163.com, chenhanting@huawei.com" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 151, + 241, + 200, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 241, + 200, + 253 + ], + "spans": [ + { + "bbox": [ + 151, + 241, + 200, + 253 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 266, + 297, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 266, + 297, + 555 + ], + "spans": [ + { + "bbox": [ + 53, + 266, + 297, + 555 + ], + "type": "text", + "content": "Diffusion models have shown exceptional performance in visual generation tasks. Recently, these models have shifted from traditional U-Shaped CNN-Attention hybrid structures to fully transformer-based isotropic architectures. While these transformers exhibit strong scalability and performance, their reliance on complicated self-tention operation results in slow inference speeds. Contrary to these works, we rethink one of the simplest yet fastest module in deep learning, 3x3 Convolution, to construct a scaled-up purely convolutional diffusion model. We first discover that an Encoder-Decoder Hourglass design outperforms scalable isotropic architectures for Conv3x3, but still underperforming our expectation. Further improving the architecture, we introduce sparse skip connections to reduce redundancy and improve scalability. Based on the architecture, we introduce conditioning improvements including stage-specific embeddings, mid-block condition injection, and conditional gating. These improvements lead to our proposed Diffusion CNN (DiC), which serves as a swift yet competitive diffusion architecture baseline. Experiments on various scales and settings show that DiC surpasses existing diffusion transformers by considering margins in terms of performance while keeping a good speed advantage. Project page: https://github.com/YuchuanTian/DiC" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "spans": [ + { + "bbox": [ + 56, + 578, + 135, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 597, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 296, + 693 + ], + "type": "text", + "content": "Diffusion-based image generative models have recently gained significant attention, with notable works like Stable Diffusion [32] demonstrating impressive results. As these models continue to evolve, they are now capable of generating increasingly realistic images. Recent advancements, including Sora-related works, have extended this capability to video generation, producing high-quality, temporally consistent videos that rival real-world footage." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 320, + 240, + 547, + 392 + ], + "blocks": [ + { + "bbox": [ + 320, + 240, + 547, + 392 + ], + "lines": [ + { + "bbox": [ + 320, + 240, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 320, + 240, + 547, + 392 + ], + "type": "image", + "image_path": "ae6b7def6e1d260cf779795ea18621f2ef79849300af11dffb3e47ace91e01b6.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 396, + 555, + 441 + ], + "lines": [ + { + "bbox": [ + 313, + 396, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 555, + 441 + ], + "type": "text", + "content": "Figure 1. The Roadmap to a 3x3 Convolutional Diffusion Model. Performance is measured by FID " + }, + { + "bbox": [ + 313, + 396, + 555, + 441 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 313, + 396, + 555, + 441 + ], + "type": "text", + "content": " of the model trained at 200K iterations. A series of proposed model improvements gives DiC an advantage over Diffusion Transformers." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 457, + 556, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 457, + 556, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 457, + 556, + 590 + ], + "type": "text", + "content": "The self-attention mechanism plays a pivotal role in many recent diffusion models. Early work [19, 36] fused convolutional U-Net structures with self-attention. More recently, architectures such as U-ViT [1] and DiT [30] have fully transitioned to attention-based designs, abandoning convolutional U-Nets entirely. These models demonstrate remarkable generative capabilities, particularly when scaled up. Newer text-to-image and text-to-video models, including Stable Diffusion 3 [14], FLUX [25], PixArt series [2-4], and OpenSora [24, 47], have also adopted fully transformer-based architectures, achieving impressive generation quality." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 591, + 556, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 591, + 556, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 591, + 556, + 662 + ], + "type": "text", + "content": "Unfortunately, diffusion models incorporating self-attention face significant computational overhead and latency when scaled up. Complex transformer architectures pose a considerable challenge for real-time, resource-constrained applications, where large-scale transformers are impractical due to their substantial time costs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 665, + 557, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 557, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 557, + 713 + ], + "type": "text", + "content": "Efforts have been made to accelerate self-attention in diffusion models. For instance, ToDo [35] and PixArt-" + }, + { + "bbox": [ + 313, + 665, + 557, + 713 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 313, + 665, + 557, + 713 + ], + "type": "text", + "content": " [3] implement more efficient self-attention mechanisms. However, these approaches remain confined to the self-attention" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Equal Contribution." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2469" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "paradigm. Other works [37, 45] aim to replace self-attention with State-Space-Model-based architectures [16], attempting to bypass its inherent inefficiencies. Despite these innovations, the generation speed on typical latent-domain image resolutions remains suboptimal, failing to meet the demands of real-time or large-scale applications." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 146, + 295, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 146, + 295, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 295, + 277 + ], + "type": "text", + "content": "In this work, we rethink the simple yet efficient fully convolutional diffusion model architecture that offers significant speed advantages. As a counterpart to self-attention, convolution is widely regarded as hardware-friendly, with excellent support across various platforms. Among the many convolutional operations, the canonical 3x3 stride-1 convolution stands out for its exceptional speed, largely due to widespread hardware optimization techniques such as Winograd acceleration [26]. For instance, work like RepVGG [12] have demonstrated how simple convolutions can achieve both high efficiency and competitive performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 279, + 295, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 279, + 295, + 363 + ], + "spans": [ + { + "bbox": [ + 55, + 279, + 295, + 363 + ], + "type": "text", + "content": "However, 3x3 convolutions come with inherent limitations, particularly a constrained receptive field, which may hinder their scalability in complex generative tasks. We firstly perform initial trials to scale up purely 3x3-based CNNs within existing scalable frameworks, but these experiments yielded results that are still inferior to Diffusion Transformer counterparts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 365, + 295, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 295, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 295, + 579 + ], + "type": "text", + "content": "To address this, we propose a series of adaptations to conventional ConvNets, forming a roadmap (shown in Fig. 1) that tailors them specifically for a scaled-up diffusion model. Firstly, we focus on refining the model architecture to better leverage Conv3x3. Existing designs fall into three categories: isotropic architectures like DiT [30], isotropic architectures with skips like U-ViT [1], and encoder-decoder hourglass structures used in canonical CNN & self-attention hybrid models. Empirical observations reveal that the hourglass architecture is more effective for pure Conv3x3 models, because downsampling and upsampling in encoders expand the receptive field that makes up for the narrow scope of Conv3x3. Skip connections are also observed crucial, but traditional blockwise skips for cheap convolution block scale-ups are too dense to be efficient for large ConvNets. To address this, we introduce sparse skip connections that reduces the number of skips while ensuring essential information ows efficiently from encoder to decoder." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 713 + ], + "type": "text", + "content": "Besides, we focus on improving conditioning to fit the hourglass ConvNet better. In existing models, a single set of condition embeddings is often mapped to different blocks across various stages. However, in encoder-decoder hourglass ConvNets, each stage operates in distinct feature spaces. Hence, we introduce stage-specific embeddings, ensuring each stage uses independent, non-overlapping condition embedding tables. We also carefully inspect the position for embedding injection, and we suggest inject conditions midblock for better performance. Additionally, we borrow conditional gating on feature-maps. In addition, we refined the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": "internal block structure, replacing all activation functions with GELU." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 96, + 555, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 96, + 555, + 180 + ], + "spans": [ + { + "bbox": [ + 313, + 96, + 555, + 180 + ], + "type": "text", + "content": "With these enhancements, we propose DiC, a diffusion model made up of Conv3x3. The architectural and conditioning improvements collectively enable our model to achieve outstanding results while maintaining its speed advantage. Experiments on various scales and settings demonstrate DiC's performance advantage over Diffusion Transformers as well as its high-throughput characteristics." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 190, + 400, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 190, + 400, + 204 + ], + "spans": [ + { + "bbox": [ + 314, + 190, + 400, + 204 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 211, + 555, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 211, + 555, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 211, + 555, + 319 + ], + "type": "text", + "content": "Self-Attention in Diffusion Architectures. Self-attention has become a cornerstone of modern diffusion architectures, thanks to its remarkable effectiveness in capturing long-range dependencies. Early UNet-based diffusion models [19, 36] incorporated Self-Attention layers in the higher stages of the network, where capturing global context is most critical. Dhariwal et al. took this further with ADM [11], extending self-attention across all stages, which significantly increased the model's generative capabilities." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "type": "text", + "content": "More recent works [1, 21, 30] have fully embraced transformer-based architectures, replacing traditional U-Net backbones with full self-attention designs. These models not only achieve superior performance, but also exhibit excellent scalability, particularly at large model sizes and FLOPs. Most following work like PixArt-" + }, + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "type": "text", + "content": " [2] and Stable Diffusion 3 adopt the full transformer backbone design that demonstrates outstanding Text-to-Image generation capabilities. Beyond these, some works continue to explore and refine the use of self-attention and transformer architectures in diffusion models, further pushing the boundaries of efficiency in transformer-based generative modeling. For instance, [3, 35, 38] looks at downsampled tokens for self-attention; [43] uses linear attention. Other works [37, 45] opt for State Space Models for diffusion, but SSMs suffer in terms of latency for ordinary-shaped images [37]. Some other work [6, 20, 22, 38] looks at a combination of U-Net and Self-Attention. In contrast to these works, we push architectural simplicity to the extreme by designing an entire diffusion model using " + }, + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "type": "text", + "content": " convolutions. With carefully crafted structural optimizations, this streamlined network not only capitalizes on the speed advantages of " + }, + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 319, + 556, + 604 + ], + "type": "text", + "content": " convolutions but also achieves diffusion generation performance on par with transformer-based models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 713 + ], + "type": "text", + "content": "Efficient Convolution. Historically, architectures like AlexNet [23], VGG [34], and ResNet [18] have dominated computer vision tasks. While transformers [40] have later become the state-of-the-art for many vision applications, their high computational cost and latency make them less practical in resource-constrained environments, where CNNs still excel. Recent advancements have revisited and improved CNNs, enabling them to rival or even surpass transformers in both performance and efficiency." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2470" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 72, + 306, + 185 + ], + "blocks": [ + { + "bbox": [ + 80, + 72, + 306, + 185 + ], + "lines": [ + { + "bbox": [ + 80, + 72, + 306, + 185 + ], + "spans": [ + { + "bbox": [ + 80, + 72, + 306, + 185 + ], + "type": "image", + "image_path": "a9bdb0c45c276a477d04e20998bb7adea4726b5234dc668041a910f9bef7f8e3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 147, + 196, + 236, + 205 + ], + "lines": [ + { + "bbox": [ + 147, + 196, + 236, + 205 + ], + "spans": [ + { + "bbox": [ + 147, + 196, + 236, + 205 + ], + "type": "text", + "content": "(a) Transformer Block" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 353, + 73, + 529, + 186 + ], + "blocks": [ + { + "bbox": [ + 353, + 73, + 529, + 186 + ], + "lines": [ + { + "bbox": [ + 353, + 73, + 529, + 186 + ], + "spans": [ + { + "bbox": [ + 353, + 73, + 529, + 186 + ], + "type": "image", + "image_path": "3750e0f96289aaae5cce311223414b963740f22204c4c4d08f679a3733b72b61.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 377, + 195, + 503, + 206 + ], + "lines": [ + { + "bbox": [ + 377, + 195, + 503, + 206 + ], + "spans": [ + { + "bbox": [ + 377, + 195, + 503, + 206 + ], + "type": "text", + "content": "(b) Conv 3x3 Basic Block (Ours)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 209, + 555, + 232 + ], + "lines": [ + { + "bbox": [ + 55, + 209, + 555, + 232 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 555, + 232 + ], + "type": "text", + "content": "Figure 2. Basic Blocks for scaled-up architectures. Compared to complicated Transformer blocks widely applied in [30], our Conv 3x3 Basic Block is much simpler and better supported by hardware, being the key to high throughput." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 253, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 253, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 253, + 296, + 361 + ], + "type": "text", + "content": "For example, ConvNeXt [28] achieves transformer-level performance through macro and micro architectural changes, such as increasing kernel sizes and optimizing normalization. Deformable Convolutions (DCNs) [7, 41, 42] enhance the receptive field by learning spatially adaptive kernel shapes, while RepLKNet [13] utilizes massive " + }, + { + "bbox": [ + 55, + 253, + 296, + 361 + ], + "type": "inline_equation", + "content": "31 \\times 31" + }, + { + "bbox": [ + 55, + 253, + 296, + 361 + ], + "type": "text", + "content": " kernels to capture long-range dependencies. Similarly, Wavelet Conv [15] operates in the frequency domain using wavelet transforms to extend CNN capabilities." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 361, + 296, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 296, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 296, + 493 + ], + "type": "text", + "content": "On the other hand, there is work that resort to improving the efficiency of simple convs. RepVGG [12] focuses on the potential of simple 3x3 convolutions, employing reparameterization tricks to enhance their effectiveness. Inspired by its speed potential, we explore the use of pure 3x3 convolutions in diffusion, combined with architectural and conditioning improvements, to achieve competitive results in diffusion-based generative models. However, we are not using tricks like re-parameterization [12]. Our approach demonstrates that even with a simple design, high-quality generation can be both efficient and effective." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 506, + 111, + 518 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 111, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 111, + 518 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 527, + 271, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 527, + 271, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 527, + 271, + 540 + ], + "type": "text", + "content": "3.1. Preliminaries: Conv3x3 as the Ingredient" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 544, + 296, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 296, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 296, + 652 + ], + "type": "text", + "content": "We choose normal stride-1 full Conv3x3 as the major ingredient of model. Stride-1 3x3 convolutions are incredibly speedy, primarily due to extensive hardware and algorithmic optimizations in modern deep learning frameworks. The operation optimization benefits from the Winograd algorithm [26], which reduces the number of multiplications required for common convolution operations by " + }, + { + "bbox": [ + 55, + 544, + 296, + 652 + ], + "type": "inline_equation", + "content": "\\frac{5}{9}" + }, + { + "bbox": [ + 55, + 544, + 296, + 652 + ], + "type": "text", + "content": ". For 3x3 kernels, this method significantly accelerates the computation by leveraging efficient matrix transformations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": "Additionally, unlike depth-wise convolution, 3x3 convolutions achieve a high degree of computational parallelism, allowing modern GPUs to fully utilize their processing power. This parallelism, combined with minimal memory access overhead, makes stride-1 3x3 convolutions particularly effi" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 253, + 555, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 253, + 555, + 301 + ], + "spans": [ + { + "bbox": [ + 313, + 253, + 555, + 301 + ], + "type": "text", + "content": "cient. Compared to larger or more complex convolution operations, they offer an ideal trade-off between computational cost and representational power, making them a practical choice for real-time applications and large-scale models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 310, + 463, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 310, + 463, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 463, + 323 + ], + "type": "text", + "content": "3.2. Architectures for Scale-Up" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 328, + 555, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 328, + 555, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 328, + 555, + 482 + ], + "type": "text", + "content": "Our Basic Block. We revisit canonical diffusion models [11, 36] and figure out that " + }, + { + "bbox": [ + 313, + 328, + 555, + 482 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 328, + 555, + 482 + ], + "type": "text", + "content": " convolutions are also widely applied. However, these models are not pure CNNs: the basic block unit within the model consists of two consecutive " + }, + { + "bbox": [ + 313, + 328, + 555, + 482 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 313, + 328, + 555, + 482 + ], + "type": "text", + "content": " convolutional layers, followed by a self-attention module that attends within the entire image. Before each convolution, the input is normalized using GroupNorm, and then passed to the non-linear activation function of SiLU. Notably, the intermediate features within the block maintain the same number of channels, ensuring stable feature propagation. The overall block adopts a residual structure [18], where the input is directly added to the output via a shortcut connection." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "type": "text", + "content": "The roadmap to our proposed diffusion model DiC-a " + }, + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "type": "text", + "content": " convolutional denoiser starts from the revisited convolutional basic block mentioned above. In order to satisfy the ultimate goal of the roadmap, we remove the self-attention layers after the convolutions to form a minimal unit block (Basic Block) consisting of two " + }, + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 313, + 484, + 555, + 568 + ], + "type": "text", + "content": " convolutions. Other block designs are temporarily left intact." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 568, + 554, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 554, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 554, + 628 + ], + "type": "text", + "content": "Mainstream Architectures. With this Conv 3x3 Basic Block as the foundation, we scale the model up by stacking multiple such blocks and increasing the network's depth and width, and we are faced up to numerous architectural choices (shown in Fig. 3):" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 629, + 555, + 714 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 313, + 629, + 555, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 700 + ], + "type": "text", + "content": "1. Isotropic Architecture. Inspired by DiT and subsequent works [2, 5, 17, 30], this design features a simple, vertically stacked structure. After patchification, the intermediate feature-map size is not changed throughout the entire model. It is widely adopted for its reputed scalability, particularly when scaled to large models." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "content": "2. Isotropic Architecture with Skip Connections. This ap-" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2471" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 78, + 108, + 158 + ], + "blocks": [ + { + "bbox": [ + 66, + 78, + 108, + 158 + ], + "lines": [ + { + "bbox": [ + 66, + 78, + 108, + 158 + ], + "spans": [ + { + "bbox": [ + 66, + 78, + 108, + 158 + ], + "type": "image", + "image_path": "ff010a3d9f2572f65049030f398c5a7ceb598fa97d2f04e0a71419b5b482daab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 161, + 102, + 169 + ], + "lines": [ + { + "bbox": [ + 70, + 161, + 102, + 169 + ], + "spans": [ + { + "bbox": [ + 70, + 161, + 102, + 169 + ], + "type": "text", + "content": "(a) Isotropic" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 115, + 79, + 169, + 158 + ], + "blocks": [ + { + "bbox": [ + 115, + 79, + 169, + 158 + ], + "lines": [ + { + "bbox": [ + 115, + 79, + 169, + 158 + ], + "spans": [ + { + "bbox": [ + 115, + 79, + 169, + 158 + ], + "type": "image", + "image_path": "1afb77678da34059fa62b25216052f40fc302ea30c8b615763d247cf0256ade6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 111, + 161, + 162, + 169 + ], + "lines": [ + { + "bbox": [ + 111, + 161, + 162, + 169 + ], + "spans": [ + { + "bbox": [ + 111, + 161, + 162, + 169 + ], + "type": "text", + "content": "(b) Isotropic + Skip" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 173, + 79, + 224, + 158 + ], + "blocks": [ + { + "bbox": [ + 173, + 79, + 224, + 158 + ], + "lines": [ + { + "bbox": [ + 173, + 79, + 224, + 158 + ], + "spans": [ + { + "bbox": [ + 173, + 79, + 224, + 158 + ], + "type": "image", + "image_path": "fd16a2e95a2ede1e3126f718b6a578328ef8e5dbc9eeb138052f9142693ec6f8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 182, + 161, + 208, + 169 + ], + "lines": [ + { + "bbox": [ + 182, + 161, + 208, + 169 + ], + "spans": [ + { + "bbox": [ + 182, + 161, + 208, + 169 + ], + "type": "text", + "content": "(c) U-Net" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 175, + 295, + 208 + ], + "lines": [ + { + "bbox": [ + 55, + 175, + 295, + 208 + ], + "spans": [ + { + "bbox": [ + 55, + 175, + 295, + 208 + ], + "type": "text", + "content": "Figure 3. Mainstream Diffusion Architectures. We try existing diffusion architectures (a,b,c) with Conv3x3 Basic Block. We further improve U-Net (d) with sparse-skips." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 231, + 79, + 284, + 158 + ], + "blocks": [ + { + "bbox": [ + 231, + 79, + 284, + 158 + ], + "lines": [ + { + "bbox": [ + 231, + 79, + 284, + 158 + ], + "spans": [ + { + "bbox": [ + 231, + 79, + 284, + 158 + ], + "type": "image", + "image_path": "a281c82ed30902596605cb1e7465167d3810eab89472c9cf74f7d011b6829729.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 225, + 161, + 288, + 169 + ], + "lines": [ + { + "bbox": [ + 225, + 161, + 288, + 169 + ], + "spans": [ + { + "bbox": [ + 225, + 161, + 288, + 169 + ], + "type": "text", + "content": "(d) U-Net + Sparse Skip" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 217, + 296, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 296, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 296, + 289 + ], + "type": "text", + "content": "proach extends the columnar isotropic architecture by introducing long skip connections between non-adjacent layers, similar to the design used in U-ViT [1]. Unlike traditional U-Net, despite the skip design, this architecture maintains a consistent spatial resolution throughout the network, avoiding any upsampling and downsampling operations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 289, + 296, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 289, + 296, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 289, + 296, + 384 + ], + "type": "text", + "content": "3. U-Net Hourglass Architecture. This classical design [33] consists of an encoder and a decoder, forming a funnel-like shape. The encoder progressively downsamples the feature dimensions, while the decoder symmetrically upsamples the spatial dimensions. Apart from the hourglass backbone, each block in the encoder is connected to its corresponding decoder block via skip connections. This work is widely applied in earlier diffusion works [11, 19, 36]." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 57, + 393, + 291, + 504 + ], + "blocks": [ + { + "bbox": [ + 57, + 393, + 291, + 504 + ], + "lines": [ + { + "bbox": [ + 57, + 393, + 291, + 504 + ], + "spans": [ + { + "bbox": [ + 57, + 393, + 291, + 504 + ], + "type": "table", + "html": "
    ImageNet 256×256, 200K,cfg=1.5
    ModelFLOPs (G)FID↓IS↑
    DiT-XL118.612.9694.26
    Isotropic115.629.3152.80
    Isotropic + Skip117.115.0785.51
    U-Net Hourglass115.214.6587.17
    U-Net + Sparse Skip116.111.49106.91
    ", + "image_path": "61975b50ddc05a374a9f3dc92cc278e528bcdcfecbf045083d5c4d346b3f19d1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 507, + 295, + 562 + ], + "lines": [ + { + "bbox": [ + 55, + 507, + 295, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 507, + 295, + 562 + ], + "type": "text", + "content": "Table 1. Comparing Architectures for Conv3x3 Scale-Up on ImageNet " + }, + { + "bbox": [ + 55, + 507, + 295, + 562 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 507, + 295, + 562 + ], + "type": "text", + "content": " conditional generation. Conv3x3 taps its full potential with U-Net Hourglass architectures due to enlarged perception field; sparsifying skip connection further improves the model." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 570, + 296, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 653 + ], + "type": "text", + "content": "Experimental Analysis. Using the foundational Conv 3x3 Basic Block, we conducted scaling experiments on the aforementioned architectural choices. The results, summarized in Tab. 1, indicate that the performance across all architectures was generally suboptimal. However, these experiments revealed several patterns that provide valuable insights for designing an effective 3x3 convolution-based diffusion model." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": "Firstly, for diffusion models composed solely of " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": " convolutions, the encoder-decoder architecture hourglass is essential. This stems from a fundamental limitation of " + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": " convolutions: their inherently restricted receptive field. In a purely isotropic, standard-transformer architecured setup," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "type": "text", + "content": "each 3x3 convolution expands the receptive field by only one pixel in each direction. As a result, achieving a global receptive field would require a deep stack of convolutions, leading to inefficiencies in both computation and parameters. In contrast, an encoder-decoder architecture significantly mitigates this limitation. By progressively downsampling in the encoder and upsampling in the decoder, the 3x3 convolutions in higher stages can effectively perceive larger regions of the input. For instance, at deeper stages, a single 3x3 convolution can cover areas as large as 6x6 or 12x12 in the original image space, substantially increasing the model's receptive field. This hierarchical approach allows the model to efficiently capture both local and global context, making it far more effective for generative tasks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 240, + 554, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 240, + 554, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 240, + 554, + 335 + ], + "type": "text", + "content": "Secondly, skip connections are vital in Conv3x3-based architectures. On one hand, in encoder-decoder structures, they mitigate information loss during downsampling by passing feature maps directly to the decoder, enriching its representation. On the other hand, skips accelerate training and improve generation quality by providing additional gradient pathways and preserving important features, leading to more efficient and effective diffusion modeling." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 337, + 554, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 337, + 554, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 337, + 554, + 360 + ], + "type": "text", + "content": "Above all, we adopt the U-Net as the general model architecture that we use." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 361, + 554, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 554, + 517 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 554, + 517 + ], + "type": "text", + "content": "Improving U-Nets via Strided Skip. However, as scaling up our Conv3x3-based diffusion model requires stacking numerous convolutional layers, dense, block-wise skip connections become a bottleneck. Numerous blockwise skip features have to be concatenated to the features and get merged on the channel dimension within corresponding decoder blocks, consuming excessive computational costs. This inefficiency hampers the scalability of the model. To address this, we propose strided skip connections, where skips are applied only every few blocks instead of after each one. This approach improves the performance, and our experiments (in Tab. 1) show that it does yield better results compared with densely-connected skip designs." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 527, + 469, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 527, + 469, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 527, + 469, + 540 + ], + "type": "text", + "content": "3.3. Conditioning Improvements" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 545, + 554, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 592 + ], + "type": "text", + "content": "Apart from architectural improvements, we hold that conditioning could also be refined. After model scale-ups, previous conditioning designs need to be improved according to the architecture." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 594, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 713 + ], + "type": "text", + "content": "Stage-Specific Embeddings. In conventional diffusion models [11, 36], a unique embedding table is shared by previous models. However, in the scaled-up Conv3x3 model, we rely on an encoder-decoder structure to expand the receptive field. Each stage of the encoder-decoder operates with different channel dimensions, reflecting significant structural and functional differences between stages. Given that feature dimensions vary across stages, applying the same condition embedding uniformly on all blocks from different stages may not be ideal. The diverse roles and representations at" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2472" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 122 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 122 + ], + "type": "text", + "content": "each stage suggest that a more stage-tailored approach to condition embedding could be more effective, as a single embedding set might not adequately capture the distinct characteristics of each stage." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 129, + 297, + 232 + ], + "blocks": [ + { + "bbox": [ + 56, + 129, + 297, + 232 + ], + "lines": [ + { + "bbox": [ + 56, + 129, + 297, + 232 + ], + "spans": [ + { + "bbox": [ + 56, + 129, + 297, + 232 + ], + "type": "table", + "html": "
    ImageNet 256×256, 200K, CFG=1.5
    ModelFLOPs (G)FID↓IS↑
    Sparse-Skip U-Net116.111.49106.91
    + Stage-Spec. Emb.116.110.07121.30
    + Mid-Block Injection116.18.80134.25
    + DiT condition gating116.16.54162.34
    DiC (+ GELU)116.16.26170.04
    ", + "image_path": "24f7531be121a241503c645e85d6811afeaa38e6b3116f4162faa49d16551237.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 238, + 296, + 293 + ], + "lines": [ + { + "bbox": [ + 55, + 238, + 296, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 238, + 296, + 293 + ], + "type": "text", + "content": "Table 2. Conditioning improvements on ImageNet " + }, + { + "bbox": [ + 55, + 238, + 296, + 293 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 238, + 296, + 293 + ], + "type": "text", + "content": " conditional generation. The proposed conditioning improvements collectively bring considerable performance enhancement. Experiments are conducted using hyperparameters from [30] for 200K iterations." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 295, + 296, + 378 + ], + "type": "text", + "content": "As an improvement, we propose using stage-specific condition embeddings for each stage of the encoder-decoder structure. Each stage will have its own independent embedding, with the embedding dimension aligned to that stage's feature dimension. This ensures that the condition embedding is tailored to the specific characteristics and scale of each stage." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 379, + 296, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 379, + 296, + 510 + ], + "spans": [ + { + "bbox": [ + 54, + 379, + 296, + 510 + ], + "type": "text", + "content": "It is worth mentioning that we analyzed the overhead introduced by the stage-specific embeddings. The results show that the added overhead is minimal. Specifically, adding the new stage-specific embeddings increased the model size by just 14.06M parameters, which accounts for only " + }, + { + "bbox": [ + 54, + 379, + 296, + 510 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 54, + 379, + 296, + 510 + ], + "type": "text", + "content": " of the total model size. The computational overhead introduced is even more negligible, with an increase of only 12M FLOPs, which has little impact on the overall computational efficiency. This demonstrates that the inclusion of stage-specific embeddings does not significantly affect the model's performance or computational cost." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 510, + 297, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 297, + 582 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 297, + 582 + ], + "type": "text", + "content": "Beside, the label-drop operation on the embeddings across different stages should be synchronized during training. This prevents any leakage of label between stages and ensures that the model learns in a consistent and isolated manner, thereby improving the stability and performance of the diffusion model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 582, + 297, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 297, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 297, + 677 + ], + "type": "text", + "content": "Condition Injection Position. Another critical aspect of our design is determining the optimal position for injecting conditioning information. There are two prevalent strategies for condition injection in diffusion models. The first approach injects the condition at the very beginning of each block, typically through LayerNorm, as seen in models like [5, 30]. The second approach introduces the condition in the middle of the block, as utilized in [11, 36]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 677, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 297, + 715 + ], + "type": "text", + "content": "Through experimentation, we found that for our fully convolutional diffusion architecture, injecting the condition into the second convolutional layer within each block yields" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 108 + ], + "type": "text", + "content": "the best performance. This placement effectively modulates the feature representations, enhancing the model's generative quality without compromising its efficiency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 108, + 556, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 108, + 556, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 108, + 556, + 251 + ], + "type": "text", + "content": "Conditional Gating. In addition, we adopted the conditional gating mechanism from DiT's AdaLN [30]. On top of traditional affine conditioning that performs channel-wise affine mapping to the feature map, AdaLN introduces a gating vector that scales the features along the channel dimension, providing a more dynamic and fine-grained control over the conditioning process. This modification enhances the model's ability to adapt to different conditions and improves the overall generation quality. Our experiments show that this enhancement yields a notable performance boost, further demonstrating the effectiveness of this conditioning strategy in diffusion models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 258, + 430, + 270 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 258, + 430, + 270 + ], + "spans": [ + { + "bbox": [ + 313, + 258, + 430, + 270 + ], + "type": "text", + "content": "3.4. Minor Modification" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 276, + 556, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 556, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 556, + 361 + ], + "type": "text", + "content": "We re-visit the activation function across the entire model. Inspired by ConvNeXt [28], we replaced the commonly used SiLU activation with GELU, which is a standard choice in transformer architectures. On top of other modifications, this change contributed to a modest but consistent improvement in performance. We are aware of potentially better activations [31, 44], but we stick to GeLU for simplicity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 370, + 397, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 370, + 397, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 370, + 397, + 384 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 390, + 555, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 390, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 390, + 555, + 415 + ], + "type": "text", + "content": "In this section, we provide experiments on various settings to demonstrate the outstanding performance of DiC model." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 421, + 427, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 421, + 427, + 434 + ], + "spans": [ + { + "bbox": [ + 313, + 421, + 427, + 434 + ], + "type": "text", + "content": "4.1. Experiment Setups" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 437, + 556, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 556, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 556, + 629 + ], + "type": "text", + "content": "Model Configs. To benchmark against existing DiT [30] models, we designed our architectures at different scales: Small (S), Big (B), and Extra Large (XL), which align closely with DiT-S/2, DiT-B/2, and DiT-XL/2 in terms of both FLOPs and parameter count, as shown in Table 3. Additionally, we introduce a larger model, Huge (H), for further scalability testing. With 32.8M parameters and 5.9G FLOPs, DiC-S provides a lightweight solution, similar to DiT-S/2, with an efficient [6,6,5,6,6] encoder-decoder configuration. DiC-B scales up to 129.5M parameters and 23.5G FLOPs, which is comparable to DiT-B/2, leveraging a wider channel size of 192. DiC-XL has 702.3M parameters and 116.1G FLOPs, whose configuration rivals DiT-XL/2, with an enhanced encoder-decoder depth of [7,7,8,7,7]. DiC-H is further scaled up to [14,14,10,14,14] and is designed to evaluate the potentials of DiC models." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 630, + 557, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 557, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 557, + 715 + ], + "type": "text", + "content": "Apart from normal FLOPs calculation, in Tab. 3 we also record actual FLOPs when taking Winograd acceleration [26] into account. As is introduced in Sec. 3.1, Winograd could reduce the computation of a stride-1 3x3 Convolution by " + }, + { + "bbox": [ + 313, + 630, + 557, + 715 + ], + "type": "inline_equation", + "content": "5/9" + }, + { + "bbox": [ + 313, + 630, + 557, + 715 + ], + "type": "text", + "content": ". From statistics in Tab. 3, it could be observed that Winograd could reduce the amount of theoretical FLOPs of the proposed DiC by approximately a half." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2473" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 91, + 70, + 517, + 142 + ], + "blocks": [ + { + "bbox": [ + 91, + 70, + 517, + 142 + ], + "lines": [ + { + "bbox": [ + 91, + 70, + 517, + 142 + ], + "spans": [ + { + "bbox": [ + 91, + 70, + 517, + 142 + ], + "type": "table", + "html": "
    ModelParams (M)FLOPs (G)Wino. FLOPs (G)Channel# GroupsEncoder-Decoder
    DiC-S32.85.92.99616[6,6,5,6,6]
    DiC-B129.523.511.819232[6,6,5,6,6]
    DiC-XL702.3116.157.238432[7,7,8,7,7]
    DiC-H1034.4204.497.238432[14,14,10,14,14]
    ", + "image_path": "4e1b71657a574686184b7b0e4ee6d35b21c9bb05768004e9145e7b9096eab53d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 186, + 294, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 186, + 294, + 292 + ], + "spans": [ + { + "bbox": [ + 54, + 186, + 294, + 292 + ], + "type": "text", + "content": "Experiment Settings. We follow the standard training setup from previous research [5, 29, 30, 38], utilizing the same VAE (i.e., sd-vae-ft-ema) as in latent diffusion models [32] and the AdamW optimizer. All hyperparameters remain unchanged, including a global batch size of 256, a learning rate of " + }, + { + "bbox": [ + 54, + 186, + 294, + 292 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 54, + 186, + 294, + 292 + ], + "type": "text", + "content": ", weight decay of 0, and a global seed of 0. Training is performed on the ImageNet 2012 dataset [10]. Our DiC-XL and DiC-H models are trained on 8 Ascend 910B NPUs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 293, + 295, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 293, + 295, + 388 + ], + "spans": [ + { + "bbox": [ + 54, + 293, + 295, + 388 + ], + "type": "text", + "content": "Overhead Calculation. We calculate the FLOPs overhead of DiC models via torchprofile [27], an easy-to-use but comprehensive FLOPs calculator. The throughput is calculated on a single A100. Following the official sampling configurations of [30], we use batchsize 32 for throughput testing. We heat the GPU up via numerous warm-up runs before measuring the throughput. Flash attention [8, 9] is activated based on the original implementations of baselines." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 398, + 285, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 398, + 285, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 398, + 285, + 411 + ], + "type": "text", + "content": "4.2. Evaluating DiC on the Standard DiT Setting" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 69, + 426, + 279, + 548 + ], + "blocks": [ + { + "bbox": [ + 55, + 146, + 555, + 179 + ], + "lines": [ + { + "bbox": [ + 55, + 146, + 555, + 179 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 555, + 179 + ], + "type": "text", + "content": "Table 3. Configurations of DiC architecture with different model sizes. We align DiC architectures to DiTs in terms of both FLOPs and parameters. Wino. FLOPs takes the FLOPs saved by Winograd into consideration. # Groups stands for the number of groups in GroupNorm. Encoder-Decoder denotes the transformer block number of encoder and decoder module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 426, + 279, + 548 + ], + "lines": [ + { + "bbox": [ + 69, + 426, + 279, + 548 + ], + "spans": [ + { + "bbox": [ + 69, + 426, + 279, + 548 + ], + "type": "table", + "html": "
    ImageNet 256×256, 400K
    ModelFLOPs (G)FID↓IS↑
    DiT-S/26.167.4020.44
    DiC-S (Ours)5.958.6825.82
    DiT-B/223.042.8433.66
    DiC-B (Ours)23.532.3348.72
    DiT-XL/2118.620.0566.74
    DiC-XL (Ours)116.113.11100.15
    ", + "image_path": "9b7536aaacd7a1770860dde079091e8044b5b2c1058fffba28de9e6375c357a4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 605, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 700 + ], + "type": "text", + "content": "Comparison with DiT Across Model Sizes. As shown in Table 4, our DiC models outperform the corresponding DiT models across all tested scales. Specifically, DiC-S achieves a significant reduction in FID, dropping from 67.40 to 58.68, while also surpassing DiT-S/2 in IS, increasing from 20.44 to 25.82. Similarly, DiC-B outperforms DiT-B/2 by a notable margin, reducing FID from 42.84 to 32.33 and increasing IS from 33.66 to 48.72." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "type": "text", + "content": "In the large-scale model category, DiC-XL delivers a re" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 186, + 555, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 186, + 555, + 258 + ], + "spans": [ + { + "bbox": [ + 313, + 186, + 555, + 258 + ], + "type": "text", + "content": "markable improvement over DiT-XL/2, with FID dropping from 20.05 to 13.11 and IS soaring from 66.74 to 100.15. These results highlight the effectiveness of our DiC models, which consistently achieve superior performance in both image quality and diversity, all while maintaining computational efficiency." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 258, + 556, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 258, + 556, + 400 + ], + "spans": [ + { + "bbox": [ + 313, + 258, + 556, + 400 + ], + "type": "text", + "content": "Comparison with Diffusion Transformer Baselines. As different models use different settings, including training hyperparameters, the choice of samplers, training iterations et cetera, we adopt a universally-aligned setting (400K iterations on the DiT codebase) according to [38]. As shown in Table 6, our proposed DiC models consistently outperform baseline diffusion architectures on ImageNet " + }, + { + "bbox": [ + 313, + 258, + 556, + 400 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 258, + 556, + 400 + ], + "type": "text", + "content": ", all under similar computational budgets. Despite having comparable FLOPs to models like DiT-XL/2 and PixArt-" + }, + { + "bbox": [ + 313, + 258, + 556, + 400 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 258, + 556, + 400 + ], + "type": "text", + "content": "-XL/2, our DiC-XL achieves a significantly lower FID of 13.11 and an impressive IS of 100.15, showcasing its superior generative quality." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 401, + 556, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 401, + 556, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 401, + 556, + 484 + ], + "type": "text", + "content": "Beyond performance, another standout is DiC's efficiency in speed. Despite the heavy computational demands of diffusion models, DiC-XL achieves a throughput of 313.7, which, while appearing lower, re-ects the use of Conv3x3's highly optimized operations. This architecture capitalizes on the inherent speed of simple convolutions, offering a practical balance between efficiency and quality." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 485, + 556, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 556, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 556, + 591 + ], + "type": "text", + "content": "Even more impressively, DiC-H strikes a remarkable trade-off between model size and speed, delivering state-of-the-art FID of 11.36 and an IS of 106.52, with an improved throughput of 160.8. This demonstrates that our models can achieve unparalleled generation quality without the severe latency typically associated with transformer-based diffusion models. In real-world applications, these speed advantages make DiC a practical solution for high-quality image synthesis." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 325, + 600, + 541, + 675 + ], + "blocks": [ + { + "bbox": [ + 55, + 552, + 295, + 597 + ], + "lines": [ + { + "bbox": [ + 55, + 552, + 295, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 295, + 597 + ], + "type": "text", + "content": "Table 4. Comparing DiCs against DiTs across various model sizes. We compare models trained for 400K iterations with the standard setting of DiT. DiCs at all scales outperform DiTs at considerable margins." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 325, + 600, + 541, + 675 + ], + "lines": [ + { + "bbox": [ + 325, + 600, + 541, + 675 + ], + "spans": [ + { + "bbox": [ + 325, + 600, + 541, + 675 + ], + "type": "table", + "html": "
    ImageNet 256×256, 400K
    ModelcfgFLOPsFID↓IS↑
    DiT-XL/21.5118.66.24150.10
    U-ViT-XL1.5113.05.66170.62
    DiC-XL1.5116.1 (57.2)3.89224.20
    ", + "image_path": "fd7d98eed04fd4a6ae95bbddc4af5dbe1f0117f041aca051d4ad2a56866b7b7d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 679, + 555, + 700 + ], + "lines": [ + { + "bbox": [ + 313, + 679, + 555, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 679, + 555, + 700 + ], + "type": "text", + "content": "Table 5. Generation performance with classifier-free guidance. The proposed DiC is also performant on conditional generation." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 326, + 701, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 553, + 713 + ], + "type": "text", + "content": "Furthermore, we experiment the conditional generation" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2474" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 72, + 282, + 222 + ], + "blocks": [ + { + "bbox": [ + 70, + 72, + 282, + 222 + ], + "lines": [ + { + "bbox": [ + 70, + 72, + 282, + 222 + ], + "spans": [ + { + "bbox": [ + 70, + 72, + 282, + 222 + ], + "type": "image", + "image_path": "5dc57917f55b41f516ad33c8189f84764b9eb4c73b3a7eef2f46df798eb6185d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 232, + 297, + 256 + ], + "lines": [ + { + "bbox": [ + 55, + 232, + 297, + 256 + ], + "spans": [ + { + "bbox": [ + 55, + 232, + 297, + 256 + ], + "type": "text", + "content": "Figure 4. Comparing FID performance and FLOPs between DiTs and DiCs. Marker sizes represent relative model sizes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 275, + 296, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 275, + 296, + 336 + ], + "spans": [ + { + "bbox": [ + 55, + 275, + 296, + 336 + ], + "type": "text", + "content": "capabilities of DiC model in Tab. 5. DiC-XL achieves an FID of 3.89 at merely 400K iterations, surpassing competitive Diffusion Transformer baselines by large margins. The results are yielded from conditional generation samples with " + }, + { + "bbox": [ + 55, + 275, + 296, + 336 + ], + "type": "inline_equation", + "content": "\\mathrm{cfg} = 1.5" + }, + { + "bbox": [ + 55, + 275, + 296, + 336 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 344, + 185, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 344, + 185, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 185, + 358 + ], + "type": "text", + "content": "4.3. DiC on Larger Images" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 362, + 296, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 362, + 296, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 362, + 296, + 493 + ], + "type": "text", + "content": "As shown in Table 7, we compare DiC models with DiT on ImageNet 512x512, after training for 400K iterations with standard DiT hyperparameters. The key takeaway from these results is the computational efficiency of DiC models. While DiT-XL/2 requires 524.7G FLOPs (with Winograd optimization), our DiC-XL model performs significantly better in terms of FID and IS, with only 464.3G FLOPs (228.7G after Winograd optimization). This improvement becomes even more evident in DiC-H, which offers a dramatic reduction in FID (12.89) and achieves a higher IS (101.78) with fewer FLOPs than DiT-XL/2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 495, + 296, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 296, + 627 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 296, + 627 + ], + "type": "text", + "content": "The key difference in computational complexity between DiC and DiT lies in their underlying architectures. DiC uses a pure convolutional approach, which scales linearly with the image size. In contrast, DiT employs self-attention, which incurs quadratic complexity with respect to the image size. Therefore, for larger images, such as " + }, + { + "bbox": [ + 55, + 495, + 296, + 627 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 495, + 296, + 627 + ], + "type": "text", + "content": ", the computational gap between DiC and DiT becomes more pronounced. In spite of this, we are amazed that DiC models could still maintain an advantageous gap over DiTs. The advantage of DiC, on the other hand, is also outstanding in terms of throughput." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 635, + 177, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 177, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 177, + 647 + ], + "type": "text", + "content": "4.4. Scaling to Excellence" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": "In this section, we look at the scaled-up model (DiC-H) with increased training iterations, and the combination with diffusion techniques to discover the potential of DiC." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Under DiT's plainest no-CFG setting. Table 8 presents the performance of DiC-H on ImageNet " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " as training" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 318, + 75, + 553, + 191 + ], + "blocks": [ + { + "bbox": [ + 318, + 75, + 553, + 191 + ], + "lines": [ + { + "bbox": [ + 318, + 75, + 553, + 191 + ], + "spans": [ + { + "bbox": [ + 318, + 75, + 553, + 191 + ], + "type": "table", + "html": "
    ImageNet 256×256, 400K
    ModelFLOPs (G)TPFID↓IS↑
    U-ViT-XL [1]113.072.618.3576.59
    DiT-XL/2 [30]118.666.820.0566.74
    PixArt-α-XL/2 [2]118.464.124.7552.24
    DiffiT-XL/2 [17]118.564.136.8635.39
    DiT-LLaMA* [5]118.665.220.2270.10
    DiC-XL (Ours)116.1 (57.2)313.713.11100.15
    DiC-H (Ours)204.4 (97.2)160.811.36106.52
    ", + "image_path": "1aaeae87808f78bd4d8fb4fee6de332c429b8449287a06787c41a2f0911c9755.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 315, + 274, + 557, + 355 + ], + "blocks": [ + { + "bbox": [ + 313, + 195, + 556, + 251 + ], + "lines": [ + { + "bbox": [ + 313, + 195, + 556, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 195, + 556, + 251 + ], + "type": "text", + "content": "Table 6. The performance of DiCs and competitive diffusion architectures on ImageNet " + }, + { + "bbox": [ + 313, + 195, + 556, + 251 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 195, + 556, + 251 + ], + "type": "text", + "content": " generation. The baselines are aligned under the official 400K-iteration setting of DiT-XL for a fair comparison. TP stands for throughput. FLOPs considering Winograd is reported for DiCs." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 274, + 557, + 355 + ], + "lines": [ + { + "bbox": [ + 315, + 274, + 557, + 355 + ], + "spans": [ + { + "bbox": [ + 315, + 274, + 557, + 355 + ], + "type": "table", + "html": "
    ImageNet 512×512, 400K
    ModelG FLOPs (Wino.)TPFID↓IS↑
    DiT-XL/2524.716.220.9466.30
    DiC-XL464.3 (228.7)84.215.3293.55
    DiC-H817.2 (388.4)53.312.89101.78
    ", + "image_path": "32498af49b737f35d1388a9a62ad6fb92c5d20bc469f3abf6268544bccd1b691.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 334, + 411, + 533, + 517 + ], + "blocks": [ + { + "bbox": [ + 313, + 359, + 555, + 404 + ], + "lines": [ + { + "bbox": [ + 313, + 359, + 555, + 404 + ], + "spans": [ + { + "bbox": [ + 313, + 359, + 555, + 404 + ], + "type": "text", + "content": "Table 7. Comparing DiCs against DiTs on ImageNet " + }, + { + "bbox": [ + 313, + 359, + 555, + 404 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 313, + 359, + 555, + 404 + ], + "type": "text", + "content": " generation. We compare models trained for 400K iterations with the standard setting of DiT. Please refer to the appendix for results from longer training iterations." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 334, + 411, + 533, + 517 + ], + "lines": [ + { + "bbox": [ + 334, + 411, + 533, + 517 + ], + "spans": [ + { + "bbox": [ + 334, + 411, + 533, + 517 + ], + "type": "table", + "html": "
    ImageNet 256×256, Scale Up, w/ocfg
    ModelTraining StepsFID↓IS↑
    DiT-XL/22.4M10.67-
    DiT-XL/27M9.62-
    DiC-H400K11.36106.52
    DiC-H600K9.73118.57
    DiC-H800K8.96124.33
    ", + "image_path": "9de57f05c504ca33beb6750ee741f4f17cb088450b82e0ca1c66fe04aee4dc0f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 521, + 555, + 555 + ], + "lines": [ + { + "bbox": [ + 313, + 521, + 555, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 555, + 555 + ], + "type": "text", + "content": "Table 8. Fast Convergence of DiC. The generation performance without classifier guidance of both models on ImageNet " + }, + { + "bbox": [ + 313, + 521, + 555, + 555 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 521, + 555, + 555 + ], + "type": "text", + "content": " consistently improves as training progresses." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 567, + 553, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 567, + 553, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 567, + 553, + 651 + ], + "type": "text", + "content": "progresses. The performance of DiC-H improves steadily as the training progresses. At 600K steps, FID decreases to 9.73, matching the performance of DiT-XL/2 at 7M training steps; at 800K steps, DiC-H shows the best performance with an FID of 8.96. This table demonstrates the fast convergence of DiC-H, where both FID and IS consistently improve with training." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 652, + 553, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 652, + 553, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 652, + 553, + 700 + ], + "type": "text", + "content": "Towards excellence with classifier-free guidance. Table 9 presents the comparison of various models' performance on ImageNet " + }, + { + "bbox": [ + 313, + 652, + 553, + 700 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 652, + 553, + 700 + ], + "type": "text", + "content": " when training iteration is scaled up and classifier-free guidance is applied." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "content": "The baseline model DiT-XL/2 achieves a throughput of" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2475" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 553, + 401 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 401 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 401 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 401 + ], + "type": "image", + "image_path": "5af93f4966b114a2fd8c665e66aadf8a88a8b3da715d118f011d4aa7becc4191.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 78, + 412, + 531, + 424 + ], + "lines": [ + { + "bbox": [ + 78, + 412, + 531, + 424 + ], + "spans": [ + { + "bbox": [ + 78, + 412, + 531, + 424 + ], + "type": "text", + "content": "Figure 5. Samples generated by DiC at 2M iterations. The samples are generated following the setting of DiT, at " + }, + { + "bbox": [ + 78, + 412, + 531, + 424 + ], + "type": "inline_equation", + "content": "cfg = 4" + }, + { + "bbox": [ + 78, + 412, + 531, + 424 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 435, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 435, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 435, + 296, + 602 + ], + "type": "text", + "content": "66.8, processes a batch size of 256 for 7 million iterations, and yields an FID score of 2.27. The U-ViT-H model, while slightly lower in throughput at 63.9, uses a larger batch size of 1024, resulting in a slightly higher FID of 2.29. In comparison, our proposed DiC-H model shows a marked improvement when trained with a modest setting of batch size of 256 over 2 million iterations. DiC-H could achieve an FID of 2.25, with a throughput of 160.8. These results reveal that CNNs could reach performance that is no worse than Diffusion Transformers, and they have a great throughput advantage. Building upon this SiT-ow-based framework, we also combine DiC with the State-of-the-Art technique of Representation Alignment (REPA) [39, 46] to achieve much faster convergence. The details are in the appendix." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 73, + 612, + 276, + 687 + ], + "blocks": [ + { + "bbox": [ + 73, + 612, + 276, + 687 + ], + "lines": [ + { + "bbox": [ + 73, + 612, + 276, + 687 + ], + "spans": [ + { + "bbox": [ + 73, + 612, + 276, + 687 + ], + "type": "table", + "html": "
    ImageNet 256×256, Scale Up, w/cfg
    ModelTPBS×IterFID↓
    DiT-XL/266.8256×7M2.27
    U-ViT-H63.91024×500K2.29
    DiC-H (Ours)160.8256×2M2.25
    ", + "image_path": "dfa28e4a08c0e6bd69b72c972fee509e91129f97c78fc243a4600f7562161d81.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 691, + 295, + 725 + ], + "lines": [ + { + "bbox": [ + 55, + 691, + 295, + 725 + ], + "spans": [ + { + "bbox": [ + 55, + 691, + 295, + 725 + ], + "type": "text", + "content": "Table 9. Generation performance of powerful baselines with classifier-free guidance. TP stands for throughput. The proposed DiC is also performant on conditional generation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 434, + 388, + 446 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 388, + 446 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 388, + 446 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 312, + 454, + 555, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 454, + 555, + 657 + ], + "spans": [ + { + "bbox": [ + 312, + 454, + 555, + 657 + ], + "type": "text", + "content": "In this work, we rethink the design of Conv3x3 in the context of diffusion models and introduced DiC, a purely 3x3-convolutional diffusion model. We initially explore various state-of-the-art diffusion architectures and find that the Encoder-Decoder U-Net structure performs the best. Building on this, we propose the sparse skip connection to reduce redundant block-wise connections and enhance efficiency of U-Net. In addition to architecture, we redesign the conditioning mechanism. We introduce stage-specific independent embeddings where each embedding is responsible for addressing conditioning within its assigned stage. We also propose mid-block condition injection and conditional gating, which are beneficial from empirical observations. Based on these improvements, our proposed Conv3x3 diffusion model not only achieves superior generative performance compared to Diffusion Transformers but also does so with significantly higher throughput." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 658, + 556, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 658, + 556, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 658, + 556, + 704 + ], + "type": "text", + "content": "Above all, as an aspect that is always neglected in diffusion, we investigate the use of convolutions in diffusion models, and we hope this work could inspire further exploration into the use of convolutions in diffusion models." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2476" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 144 + ], + "type": "text", + "content": "Acknowledgement. This work is supported by the National Key R&D Program of China under grant No. 2022ZD0160300 and the National Natural Science Foundation of China under grant No. 62276007. We gratefully acknowledge the support of MindSpore, CANN, and Ascend AI Processor used for this research." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 156, + 115, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 156, + 115, + 167 + ], + "spans": [ + { + "bbox": [ + 56, + 156, + 115, + 167 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 175, + 297, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 175, + 297, + 240 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 175, + 297, + 240 + ], + "spans": [ + { + "bbox": [ + 61, + 175, + 297, + 240 + ], + "type": "text", + "content": "[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. All are worth words: A vit backbone for diffusion models. 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Open-sora: Democratizing efficient video production for all, 2024. 1" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2478" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_content_list.json b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ac3e5bc1fd9b23df11413213536981c8442cce --- /dev/null +++ b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_content_list.json @@ -0,0 +1,2049 @@ +[ + { + "type": "text", + "text": "DiET-GS: Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting", + "text_level": 1, + "bbox": [ + 114, + 128, + 883, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Seungjun Lee Gim Hee Lee", + "bbox": [ + 367, + 204, + 629, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Department of Computer Science, National University of Singapore", + "bbox": [ + 230, + 220, + 764, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "seungjun.lee@u.nus.edu, gimhee.lee@nus.edu.sg", + "bbox": [ + 299, + 242, + 697, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 272, + 326, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reconstructing sharp 3D representations from blurry multi-view images is a long-standing problem in computer vision. Recent works attempt to enhance high-quality novel view synthesis from the motion blur by leveraging event-based cameras, benefiting from high dynamic range and microsecond temporal resolution. However, they often reach sub-optimal visual quality in either restoring inaccurate color or losing fine-grained details. In this paper, we present DiET-GS, a diffusion prior and event stream-assisted motion deblurring 3DGS. Our framework effectively leverages blur-free event streams and diffusion prior in a two-stage training strategy. Specifically, we introduce the novel framework to constrain 3DGS with event double integral, achieving both accurate color and well-defined details. Additionally, we propose a simple technique to leverage diffusion prior to further enhance the edge details. Qualitative and quantitative results on both synthetic and real-world data demonstrate that our DiET-GS is capable of producing better quality of novel views compared to the existing baselines. Our project page is: DiET-GS.github.io.", + "bbox": [ + 89, + 305, + 483, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 614, + 220, + 630 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Novel view synthesis plays an important role in various vision applications such as scene understanding [17, 27, 58], virtual reality [18, 60], image processing [9, 29, 32], etc. To this end, Neural Radiance Fields (NeRF) [31] achieves notable success in generating high-quality novel views by reconstructing implicit 3D representations with a deep neural network. However, it falls short of real-time rendering and efficient training, limiting its application in real-world scenarios. Recently, 3D Gaussian Splatting (3DGS) [15] has emerged as an efficient alternative to NeRF by representing scenes with explicit 3D Gaussian primitives. The explicit representation of 3DGS serves as a lightweight replacement of the implicit neural representations used in NeRF, achieving better training and rendering efficiency as well as visual quality of novel views.", + "bbox": [ + 89, + 642, + 482, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To enable high-quality 3D reconstructions, both NeRF and 3DGS rely on multi-view images that are perfectly cap-", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/892bdddd09d60564a917d766a9f9f7023cebb13fc29051bde76a50e820f8dc82.jpg", + "image_caption": [ + "Figure 1. Given a set of blurry images and corresponding event streams, we propose a novel framework to construct deblurring 3DGS by jointly leveraging the EDI [33] formulation and a pretrained diffusion model as a prior. Our DiET-GS++ enables high-quality novel-view synthesis by recovering precise color and well-defined details from the blurry multi-view images." + ], + "image_footnote": [], + "bbox": [ + 516, + 273, + 903, + 459 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tured and free from any artifact. However, this preliminary condition is often unavailable in the real world. For example, a camera needs prolonged exposure time in a low light environment to allow enough light to reach the sensor for image formation. The camera has to remain absolutely still during this lengthy exposure time. Any camera motion during the capture leads to undesired motion blur. To circumvent this issue, a line of works [19, 29, 34, 54, 66] has attempted to recover sharp 3D representations from blurry multi-view images. Despite the promising potential, it is non-trivial to restore fine-grained details from blurry images alone and thus often leading to sub-optimal visual quality.", + "bbox": [ + 511, + 550, + 906, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several recent works have shown the efficacy of event-based cameras, significantly improving motion deblurring in images captured from standard frame-based cameras. Event sensors enable blur-free measurements of brightness changes, benefiting from higher dynamic range and temporal resolution compared to standard cameras. Motivated by this distinct competency, several recent works have explored the potential of recovering sharp 3D representations from event streams. Earlier works [1, 11, 42] focus on utilizing solely event-based data, lacking the capacity to preserve color information. E-NeRF [16] combines blurry", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21739", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "images into the framework as direct color supervision for 3D NeRF. Nonetheless, the estimated color exhibits blur around the edges since it does not account for the blur formation. $\\mathrm{E}^2\\mathrm{NeRF}$ and following works [3, 23, 37, 61] explicitly model the blur formation process to further enhance the color and edge details. However, most of these existing works still rely on blurry images alone to recover accurate color, often resulting in unwanted color artifacts. To supplement color guidance, Ev-DeblurNeRF [3] proposes to exploit the explicit relationship of Event Double Integral (EDI) between blurry images and event streams.", + "bbox": [ + 89, + 90, + 480, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose DiET-GS, a Diffusion prior and EvenT stream-assisted motion deblurring 3DGS. As illustrated in Fig. 1, our framework comprises two main stages: DiET-GS and DiET-GS++. Our Stage 1: DiET-GS first optimizes the deblurring 3DGS by jointly leveraging the real-captured event streams and the prior knowledge of a pretrained diffusion model. To restore both accurate color and well-defined details, we introduce a novel framework that uses the EDI prior to achieve 1) fine-grained details, 2) accurate color, and 3) regularization. Specifically, in addition to the EDI color guidance proposed by [3], we propose further constraints to recover fine-grained details by modeling EDI in the brightness domain through a learnable camera response function. This learnable approach naturally considers the potential variation between RGB values and pixel intensity, leading to better real-world adaptation and thus effectively recovering intricate details. The EDI constraints from both RGB space [3] and brightness domain enable mutual compensation between color fidelity and fine-grained details, resulting in optimal visual quality. Additionally, we derive a regularization term from the EDI prior to further facilitate the optimization by ensuring the cycle consistency among the objective terms.", + "bbox": [ + 91, + 260, + 483, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve more natural image refinement, we further incorporate diffusion prior in DiET-GS using the Renoised Score Distillation (RSD) proposed by [20]. Nonetheless, we empirically find that jointly leveraging both priors from real-captured data and a pretrained diffusion model often weakens the full effect of diffusion prior. Consequently, our Stage 2: DiET-GS++ is further introduced to maximize the effect of diffusion guidance by adding extra learnable parameters to each 3D Gaussian in the pretrained DiET-GS. Unlike [20], DiET-GS++ directly renders latent residual from the 3D Gaussians, resulting in a simpler framework to leverage RSD optimization. Finally, resulting images from DiET-GS are further refined by solely relying on diffusion prior while edge details are effectively enhanced.", + "bbox": [ + 89, + 609, + 482, + 820 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are summarized as follows:", + "bbox": [ + 109, + 823, + 450, + 837 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel framework to construct deblurring 3DGS by jointly leveraging event streams and the prior knowledge of a pretrained diffusion model.", + "- A two-stage train38ing strategy to effectively utilize real-" + ], + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "captured data and diffusion prior together. Once optimized, our method is capable of recovering well-defined details with accurate color from the input blurry images.", + "bbox": [ + 526, + 90, + 903, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Qualitative and quantitative results show that our framework significantly surpasses the existing baselines, achieving the best visual quality.", + "bbox": [ + 513, + 136, + 903, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 191, + 663, + 207 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event-based image deblurring. Recently, event-based cameras have gained significant popularity due to their high dynamic range and microseconds temporal resolution. Several methods have tried to leverage these distinct features to tackle image deblurring. Most notably, event-based double integral (EDI) [33] explicitly models the relationship between event streams and a blurry image jointly captured during the fixed exposure time. Subsequent works follow EDI by fusing the events and RGB frames [7, 48, 49, 59, 64] or using learning-based approaches [12, 50] to further improve visual quality. Another line of works exploits event cameras to recover sharp 3D representations such as NeRF and 3DGS from blurry multi-view images. Earlier works [11, 16, 28, 42] utilize an event generation model [6] to enable sharp novel view synthesis from a fast-moving camera while E-NeRF [16] combines RGB frames to further refine the color. Recent works [3, 23, 36, 37, 61] such as $\\mathrm{E}^2\\mathrm{NeRF}$ [36] and Ev-DeblurNeRF [3] combine blurry image formation [29] to model the camera motion during the exposure time while Ev-DeblurNeRF [3] further incorporates the EDI prior to provide additional color constraint to 3D NeRF. However, this color constraint often yields over-smoothed details by treating each RGB channel as brightness, which deviates from the real-world setting. In this work, we effectively restore intricate details by introducing a learnable brightness estimation function to the EDI formulation that better adapts to real-world settings.", + "bbox": [ + 511, + 217, + 906, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion-based image restoration. Diffusion models have been successfully repurposed for image restoration tasks such as super-resolution (SR) [8, 22, 44, 53, 57, 62], deblurring [5, 39, 56] and JPEG restoration [13, 43]. A comprehensive summary of diffusion-based restoration methods can be found in this recent survey [24]. Diffir [57] is a two-stage training approach that generates a prior representation from a diffusion model to restore an image. DvSR [56] surpasses regression-based methods by leveraging conditional diffusion models. More recently, diffusion prior has begun to be used for restoration of 3D representations such as NeRF. DiSR-NeRF [20] first attempts to leverage a pretrained diffusion model to construct superresolution (SR) NeRF by proposing a renoised variant of score distillation sampling [35], referred to as RSD optimization. In our approach, we propose a simpler framework to adopt RSD optimization compared to [20], further enhancing the edge details of the rendered image.", + "bbox": [ + 511, + 628, + 908, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21740", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/65033698090001786ccd679c2fd1cc8950192022e920be6f390dd7a0547547d5.jpg", + "image_caption": [ + "EDI Processing" + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 624, + 253 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d983686d4e3ace861cbc0513e660741b832734dfdf4b736a6daa4723bb2c20b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 88, + 905, + 255 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/64bfc19d431ff2b177e60b0d353fcef7514ad9014f1a2df87a3a00714ecda8e4.jpg", + "image_caption": [ + "Figure 2. Overall framework of our DiET-GS. Stage 1 (DiET-GS) optimizes the deblurring 3DGS with the event streams and diffusion prior. To preserve accurate color and clean details, we exploit the EDI prior in multiple ways, including color supervision $C$ , guidance for fine-grained details $I$ , and additional regularization $\\tilde{I}$ with EDI simulation. Stage 2 (DiET-GS++) is then employed to maximize the effect of diffusion prior by introducing extra learnable parameters $\\mathbf{f}_{\\mathbf{g}}$ . DiET-GS++ further refines the rendered images from DiET-GS, effectively enhancing rich edge features. More details are explained in Sec. 4.1 and Sec. 4.2." + ], + "image_footnote": [], + "bbox": [ + 96, + 256, + 116, + 272 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/34f5d840dc4d57e3c996b1693950927f200a644ef81872d3f34653ef24eaa773.jpg", + "image_caption": [ + "Bright Estimation" + ], + "image_footnote": [], + "bbox": [ + 192, + 257, + 210, + 272 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6cd02ff7a2a8eb11198d771f1a6a0074a7f79e892539924c563439ef3e231585.jpg", + "image_caption": [ + ": Pretrained VAE Encoder" + ], + "image_footnote": [], + "bbox": [ + 292, + 256, + 310, + 272 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/97b32b63acd91ac906180a8315ef49bdbbcd84990a4814f6256259471ea7c88d.jpg", + "image_caption": [ + ": Pretrained Diffusion UNet" + ], + "image_footnote": [], + "bbox": [ + 424, + 256, + 457, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 362, + 228, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Event Camera Model in Motion Deblurring. Event is triggered when the absolute difference of logarithmic brightness between time $t_j$ and $t_{j-1}$ exceeds $\\Theta_{p_j}$ at the same pixel location, where predefined threshold $\\Theta_{p_j} \\in \\mathbb{R}^+$ controls the sensitivity to brightness change. It follows that:", + "bbox": [ + 89, + 387, + 483, + 463 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\log (I (\\mathbf {u}, t _ {j})) - \\log (I (\\mathbf {u}, t _ {j - 1})) = p _ {j} \\cdot \\Theta_ {p _ {j}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 470, + 482, + 488 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $I(\\mathbf{u}, t)$ denotes instantaneous intensity at a pixel $\\mathbf{u}$ on a given time $t$ . Polarity $p_j \\in \\{-1, 1\\}$ specifies that either an increase or decrease in brightness. By denoting $\\log(I(\\mathbf{u}, t))$ as $L(t)$ , Eq. 1 can be generalized to any time interval $[t, t + \\Delta t]$ by accumulating event signals as follows:", + "bbox": [ + 89, + 496, + 483, + 571 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL (t + \\Delta t) - L (t) = \\Theta \\cdot \\mathbf {E} (t) = \\Theta \\int_ {t} ^ {t + \\Delta t} p \\delta (\\tau) \\mathrm {d} \\tau , \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 579, + 482, + 611 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\delta(\\tau)$ is impulse function with unit integral and polarity $p_j$ on threshold $\\Theta$ is omitted for brevity. By applying the $\\exp(\\cdot)$ function to both sides of Eq. 2, we can rewrite $I(t + \\Delta t) = I(t) \\cdot \\exp(\\Theta \\cdot \\mathbf{E}(t))$ to give the relationship between two instantaneous brightness observed at different time steps.", + "bbox": [ + 89, + 611, + 482, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We note that a blurry image taken from a conventional frame-based camera can be represented as averaging a sequence of sharp images $I$ acquired during the fixed exposure time $\\tau$ as follows:", + "bbox": [ + 89, + 700, + 483, + 761 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} ^ {\\mathbf {B}} (\\mathbf {u}, t) = \\frac {1}{\\tau} \\int_ {t - \\tau / 2} ^ {t + \\tau / 2} I (\\mathbf {u}, h) \\mathrm {d h}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 768, + 482, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{I}^{\\mathrm{B}}$ is the blurry image captured during the time interval $\\Delta T = [t - \\tau /2,t + \\tau /2]$ . By combining Eq. 2 and Eq. 3, the connection between the blurry image $\\mathbf{I}^{\\mathrm{B}}$ and the latent sharp image $I$ at the same timestep $t$ can be constructed as:", + "bbox": [ + 89, + 801, + 483, + 863 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} ^ {\\mathbf {B}} (\\mathbf {u}, t) = \\frac {I (\\mathbf {u} , t)}{\\tau} \\int_ {t - \\tau / 2} ^ {t + \\tau / 2} \\exp (\\Theta \\mathbf {E} (h)) \\mathrm {d h}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 871, + 482, + 904 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This relationship between the sharp image, blurry image, and event stream is known as Event-based Double Integral (EDI) [33]. Finally, we can remove motion blur from $\\mathbf{I}^{\\mathbf{B}}$ by solving for $I(\\mathbf{u},t)$ in Eq. 4 under the guidance of the event streams. We propose a novel framework to leverage the EDI prior to constrain 3D Gaussian Splatting in recovering sharp rendered images with better fine-grained details and colors.", + "bbox": [ + 511, + 364, + 906, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Prior in 3D. Score-based diffusion models [47, 51] are a popular type of generative model that learns a score function that represents the gradient of the log probability density with respect to the data. Several works on Text-to-3D generation [4, 10, 25, 26, 30, 35, 51, 55, 67] that leverage the score function of a pretrained diffusion model as a diffusion prior have shown remarkable results. Notably, Score Distillation Sampling (SDS) [35] uses a score function of a diffusion model as an optimization target, providing the gradient from the score function of a pretrained diffusion model to guide differentiable image parametrization $\\mathbf{z} = g(\\theta)$ without retraining the diffusion model from scratch. In 3D, $\\theta$ can be any learnable 3D representation [15, 31] with volume rendering function $g(\\cdot)$ . Recently, a variant of SDS has been introduced for image restoration task. Specifically, [20] proposes a renoised variant of SDS called Renoised Score Distillation (RSD) to use diffusion prior for super-resolution in 3D neural representation field.", + "bbox": [ + 511, + 474, + 906, + 746 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a data sample $\\mathbf{z}_0$ , the forward process obtains the noisy latent $\\mathbf{z}_t$ by adding Gaussian noise sample $\\epsilon \\in \\mathcal{N}(0,\\mathbf{I})$ at timestep $t$ : $\\mathbf{z}_t = \\sqrt{\\bar{\\alpha}_t}\\mathbf{z}_0 + \\sqrt{1 - \\bar{\\alpha}_t}\\epsilon$ , where $\\bar{\\alpha}_t$ is timestep-dependent noising coefficient. In the DDPM reverse process, a diffusion U-net is trained to predict the noise $\\epsilon (\\mathbf{z},y,t)$ to denoise $\\mathbf{z}_t$ into $\\mathbf{z}_{t-1}$ as follows: $\\mathbf{z}_{t-1} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{z}_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\bar{\\alpha}_t}}\\epsilon (\\mathbf{z}_t,y,t)) + \\sigma_t\\epsilon$ , where $y$ is the conditioning input and $\\sigma_t$ is the standard deviation of Gaussian noise samples. Given the predicted denoised latent $\\hat{\\mathbf{z}}_{t-1}$ from $\\mathbf{z}_t$ and the current noised latent $\\mathbf{z}_{t-1}$ at timestep $t-1$ , the ob", + "bbox": [ + 511, + 748, + 908, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21741", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "jective of RSD is formulated as $\\mathcal{L}_{rsd} = ||\\mathbf{z}_{t - 1} - \\hat{\\mathbf{z}}_{t - 1}||$ In this paper, we propose a simpler framework to leverage RSD optimization compared to [20].", + "bbox": [ + 88, + 90, + 480, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Our Method", + "text_level": 1, + "bbox": [ + 89, + 148, + 220, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 2 shows an illustration of our DiET-GS framework which consists of two stages. Stage 1 (cf. Sec. 4.1) constructs a deblurring 3DGS by leveraging an EDI constraint derived from real-captured data and the prior knowledge of a pretrained diffusion model. Stage 2 (cf. Sec. 4.2) further refines the resulting images from Stage 1 by solely relying on diffusion prior to further enhance the edge details.", + "bbox": [ + 89, + 174, + 482, + 282 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Stage 1: DiET-GS", + "text_level": 1, + "bbox": [ + 89, + 287, + 264, + 304 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The goal of Stage 1 is to construct a set of 3D Gaussians from 3D Gaussian Splatting (3DGS) [15] to render sharp images from blurry images and event streams. We name the 3D Gaussians trained in this stage as DiET-GS.", + "bbox": [ + 89, + 311, + 482, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Initialization. The construction of 3DGS requires point cloud initialization and camera calibrations with structure-from-motion (SfM) [45], which often fail with blurry images. We mitigate this issue by leveraging EDI from Eq. 4 to recover an initial set of sharp images suitable for SfM. Specifically, given an RGB blurry image $\\mathbf{C}^{\\mathrm{B}}$ and an event stream $\\mathbf{E}$ captured during an exposure time $\\tau$ , we reconstruct a sharp latent image $I$ from the grayscale of $\\mathbf{C}^{\\mathrm{B}}$ with EDI. This sharp image $I$ can then be warped to any timestep within the exposure period $[t - \\tau /2, t + \\tau /2]$ following $I(t + \\Delta t) = I(t)\\cdot \\exp (\\Theta \\cdot \\mathbf{E}(t))$ as shown in Eq. 2. We obtain a set of latent images for each training view by warping the recovered latent image $I$ to each of the $n$ timesteps uniformly sampled from the exposure time. The recovered sharp latent images are subsequently fed into SfM for the estimation of the camera poses and point cloud.", + "bbox": [ + 89, + 375, + 482, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Blur Reconstruction Loss. Let us denote the estimated camera poses along the approximated camera trajectory of a blurry image $\\mathbf{C}_i^{\\mathrm{B}}$ as $\\mathbf{P}_i = \\{p_{ij}\\}_{j=0}^{n-1}$ . Given the camera poses $\\mathbf{P}_i$ , we simulate the blurry image formation by discretizing Eq. 3 into:", + "bbox": [ + 89, + 619, + 483, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {C}} _ {i} ^ {\\mathbf {B}} = \\frac {1}{n} \\sum_ {j = 0} ^ {n - 1} g _ {\\theta} \\left(p _ {i j}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 704, + 482, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $g_{\\theta}(\\cdot)$ is the 3DGS with rendering function and $\\hat{\\mathbf{C}}^{\\mathbf{B}}$ is the estimated motion-blurred image. We can now use the real captured blurry images $\\{\\mathbf{C}^{\\mathbf{B}}\\}_{i = 0}^{k - 1}$ to supervise the simulated blurry images $\\{\\hat{\\mathbf{C}}^{\\mathbf{B}}\\}_{i = 0}^{k - 1}$ , where $k$ is the number of training views. Following the original 3DGS, we thus formulate a blur reconstruction loss to minimize the photometric error $\\mathcal{L}_{\\mathrm{P}}$ as $\\mathcal{L}_{\\mathrm{blur}} = \\mathcal{L}_{\\mathrm{p}}(\\mathbf{C}^{\\mathbf{B}},\\hat{\\mathbf{C}}^{\\mathbf{B}}) = (1 - \\lambda_1)\\mathcal{L}_1 + \\lambda_1\\mathcal{L}_{\\mathrm{D - SSIM}}$ .", + "bbox": [ + 89, + 743, + 482, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Event Reconstruction Loss. Since an event stream provides blur-free microsecond-level measurements, it can be", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "exploited to further aid fine-grained deblurring. To this end, we formulate an event reconstruction loss by leveraging the relation between brightness and generated events in Eq. 2. Specifically, we synthesize the left-hand side of Eq. 2 by defining the simulated log brightness $\\hat{L}(t_i)$ at time $t_i$ as:", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {L} \\left(t _ {i}\\right) = \\log \\left(h \\left(\\operatorname {C R F} \\left(\\hat {C} _ {i}\\right)\\right)\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 178, + 903, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{C}_i = g_\\theta(p_i)$ is the sharp image rendered from the 3DGS at camera pose $p_i$ corresponding to time $t_i$ , and $h(\\cdot)$ is a luma conversion function implemented by following the BT.601 [2] standard. Following [3], a learnable tone mapping function $\\mathrm{CRF}(\\cdot)$ is adopted to handle possible variations between the RGB and events response function.", + "bbox": [ + 511, + 205, + 903, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To simulate the brightness change in Eq. 2, we randomly sample two timesteps $t_\\alpha$ and $t_\\beta = t_\\alpha + \\Delta t$ along the camera trajectory and approximate the camera poses corresponding to the sampled timesteps via spherical linear interpolation [46] of the known camera poses $\\{\\mathbf{P}_i\\}_{i=0}^{k-1}$ . Given the approximated camera poses at $t_\\alpha$ and $t_\\beta$ , we can finally synthesize the brightness change $\\Delta \\hat{L}(t_\\alpha, t_\\beta) = \\hat{L}(t_\\beta) - \\hat{L}(t_\\alpha)$ between time $t_\\alpha$ and $t_\\beta$ by estimating the log brightness from Eq. 6. Considering that the right-hand side of Eq. 2 can serve as ground-truth supervision, we thus formulate the event construction loss $\\mathcal{L}_{\\mathrm{ev}}$ as follows: $\\mathcal{L}_{\\mathrm{ev}} = ||\\Delta \\hat{L}(t_\\alpha, t_\\beta) - \\Delta L(t_\\alpha, t_\\beta)||_2^2$ , where $L(t_\\alpha, t_\\beta)$ is the brightness difference observed from the event camera.", + "bbox": [ + 511, + 297, + 906, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Event Double Integration (EDI) Loss. Although $\\mathcal{L}_{\\mathrm{ev}}$ is capable of producing sharp details to a certain degree, it lacks supervision in areas where events are not triggered. Furthermore, it is not trivial to blindly recover color details from an event response since the only color supervision comes from $\\mathcal{L}_{\\mathrm{blur}}$ [3]. To this end, we propose a novel optimization problem that leverages EDI prior to further constrain the 3DGS in terms of 1) fine-grained details, 2) precise color and 3) regularizing the optimization.", + "bbox": [ + 511, + 505, + 905, + 641 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since EDI is defined in the monochrome brightness domain, we first model the EDI based on pixel intensity values. Specifically, we further exploit the composite function of the learnable camera response function $\\mathrm{CRF}(\\cdot)$ followed by $h(\\cdot)$ in Eq. 6 to estimate the brightness of given color images. Given the ground truth blurry image $\\mathbf{C^B}$ , the brightness of $\\mathbf{C^B}$ , denoted as $\\mathbf{I^B}$ , is obtained by $\\mathbf{I^B} = h(\\mathrm{CRF}(\\mathbf{C^B}))$ . We then recover the mid-exposure pose of image $I$ from $\\mathbf{I^B}$ using Eq. 4. Based on the latent image $I$ , a sharp latent image $I_{i}$ at a randomly sampled timestep $t_i$ can be recovered by warping $I$ to timestep $t_i$ as stated in the initialization step. Given $I_{i}$ as image-level supervision, we synthesize the brightness of color image $\\hat{C}_i$ rendered at the same timestep. Finally, the EDI loss in the monochrome pixel domain is formulated with the photometric error as follows: $\\mathcal{L}_{\\mathrm{edi\\_gray}} := \\mathcal{L}_{\\mathrm{p}}(I_i,\\hat{I}_i) = \\mathcal{L}_{\\mathrm{p}}(I_i,h(\\mathrm{CRF}(\\hat{C}_i))),$ where $\\hat{I}_i$ is the estimated brightness of rendered color", + "bbox": [ + 511, + 642, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21742", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2d41cd1ab4265721cc4f15ba2468aac1e08ad850b0604d4f14da63a87fe97e10.jpg", + "image_caption": [ + "Figure 3. Cycle consistency among the objective terms. $\\mathcal{L}_{\\mathrm{edi\\_simul}}$ follows the formulation of $\\mathcal{L}_{\\mathrm{edi\\_gray}}$ except for substituting $\\mathbf{C}^{\\mathbf{B}}$ to simulated blurry image $\\tilde{\\mathbf{C}}^{\\mathbf{B}}$ derived from $\\mathcal{L}_{\\mathrm{blur}}$ . It completes the cycle among the objective terms, further regularizing the fine-grained deblurring as shown in Fig. 6." + ], + "image_footnote": [], + "bbox": [ + 127, + 95, + 439, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\hat{C}_i$ . The learnable bright response function $\\mathrm{CRF}(\\cdot)$ allows $\\mathcal{L}_{\\mathrm{edi - gray}}$ to effectively restore fine-grained details for the overall image by naturally filling the gap between the rendered color space and the brightness change captured by the event sensor.", + "bbox": [ + 89, + 247, + 482, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although effective in restoring fine-grained details, we empirically find that $\\mathrm{CRF}(\\cdot)$ often distorts color due to the lack of sufficient color supervision as shown in Fig. 5. Inspired by [3], we produce sharp RGB color $C$ by treating each RGB channel of $\\mathbf{C^B}$ as blurry brightness $\\mathbf{I^B}$ in Eq. 4 and applying channel-wise deblurring with EDI. Finally, sharp color $C_i$ at a randomly sampled timestep $t_i$ is obtained by warping $C$ to the corresponding timestep. Given $C_i$ as color supervision, the EDI loss in the RGB space can be formulated as $\\mathcal{L}_{\\mathrm{edi\\_color}} = \\mathcal{L}_{\\mathrm{p}}(C_i,\\hat{C}_i)$ , where $\\hat{C}_i = g_\\theta (p_i)$ is the color image rendered at the same timestep as $C_i$ .", + "bbox": [ + 88, + 327, + 482, + 493 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition to the EDI loss described above for image-level supervision, we further leverage EDI for additional regularization. Specifically, we synthesize both sides of Eq. 4 by simply replacing $\\mathbf{I}^{\\mathbf{B}}$ with the simulated blurry brightness $\\hat{\\mathbf{I}}^{\\mathbf{B}} = h(\\mathrm{CRF}(\\hat{\\mathbf{C}}^{\\mathbf{B}}))$ , which is the estimated brightness of $\\hat{\\mathbf{C}}^{\\mathbf{B}}$ . The EDI simulation loss can then be formulated as $\\mathcal{L}_{\\mathrm{edi\\_simul}} = \\mathcal{L}_{\\mathrm{p}}(\\tilde{I}_i,\\hat{I}_i)$ , where $\\tilde{I}_i$ is the sharp supervision obtained from the simulated blurry brightness via EDI processing. As illustrated in Fig. 3, $\\mathcal{L}_{\\mathrm{edi\\_simul}}$ ensures cycle consistency among the objective terms, further facilitating the optimization as a regularization term.", + "bbox": [ + 88, + 496, + 482, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the EDI loss is given by combining all of the EDI-based objectives as: $\\mathcal{L}_{\\mathrm{edi}} = \\mathcal{L}_{\\mathrm{edi\\_gray}} + \\mathcal{L}_{\\mathrm{edi\\_color}} + \\mathcal{L}_{\\mathrm{edi\\_simul}}$ .", + "bbox": [ + 89, + 664, + 482, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Leveraging Diffusion Prior. Although event streams can provide blur-free details, they are susceptible to unnatural artifacts (Fig. 4b-4d) due to the unknown threshold $\\Theta$ in Eq. 2-4 and noise accumulated from the event [28]. Since pretrained diffusion model [40] has already learned the distribution of natural images from large amounts of diverse datasets, it is intuitive to leverage this \"data-driven\" prior in addition to our \"model-based\" losses such as $\\mathcal{L}_{\\mathrm{blur}}$ , $\\mathcal{L}_{\\mathrm{ev}}$ and $\\mathcal{L}_{\\mathrm{edi}}$ to further refine the output image more natural. Specifically, we adopt the RSD optimization strategy proposed in [20] to our framework. However, unlike [20], our setting lacks the clean images which are necessary to guide", + "bbox": [ + 89, + 719, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "noise prediction of diffusion model as conditional input. A straightforward solution is to utilize the sharp latent image $I$ from EDI processing as a surrogate for the clean image. Unfortunately, we empirically find that the EDI-processed images contain a lot of artifacts that are detrimental to the noise inference of the UNet in the diffusion model. We circumvent this issue by using the ground truth blurry images as an alternative.", + "bbox": [ + 511, + 90, + 903, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first render a blurry image $\\hat{\\mathbf{C}}^{\\mathbf{B}}$ from Eq. 3, and encode it to a latent $\\mathbf{z}_0 = \\mathcal{E}(\\hat{\\mathbf{C}}^{\\mathbf{B}})$ via a pretrained VAE encoder $\\mathcal{E}$ . Subsequently, we apply the forward process of the diffusion model by introducing noise at timesteps $t$ and $t - 1$ based on a predetermined noising schedule to get two noised latents $\\mathbf{z}_t$ and $\\mathbf{z}_{t - 1}$ . The UNet backbone [41] of the pretrained diffusion model takes $\\mathbf{z}_t$ as input and the ground truth blurry image $\\mathbf{C}^{\\mathbf{B}}$ as a condition to predict the noise residual $\\epsilon (\\mathbf{z}_t,y,t)$ . Given the predicted noise and $\\mathbf{z}_t$ , we then obtain the predicted denoised latent $\\hat{\\mathbf{z}}_{t - 1}$ via the DDPM reverse process. Finally, the RSD loss $\\mathcal{L}_{\\mathrm{rsd}}$ is formulated as an L1 error between $\\mathbf{z}_{t - 1}$ and $\\hat{\\mathbf{z}}_{t - 1}$ . Since the input of the diffusion model $\\hat{\\mathbf{C}}^{\\mathbf{B}}$ is obtained by averaging a set of rendered sharp images $\\{\\hat{C}\\}_{i = 0}^{n - 1}$ along the camera trajectory, the supervision from the RSD loss is transferred to each rendered image, making them more natural.", + "bbox": [ + 511, + 210, + 906, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training objective. The final objective $\\mathcal{L}_{s1}$ in Stage 1 is formulated as:", + "bbox": [ + 511, + 460, + 906, + 491 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s} 1} = \\lambda_ {\\text {b l u r}} \\mathcal {L} _ {\\text {b l u r}} + \\lambda_ {\\mathrm {e v}} \\mathcal {L} _ {\\mathrm {e v}} + \\lambda_ {\\text {e d i}} \\mathcal {L} _ {\\text {e d i}} + \\lambda_ {\\text {r s d}} \\mathcal {L} _ {\\text {r s d}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 503, + 906, + 520 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with the weight $\\lambda$ for each objective term.", + "bbox": [ + 511, + 531, + 792, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Stage 2: DiET-GS++", + "text_level": 1, + "bbox": [ + 511, + 558, + 709, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although the RSD optimization in Stage 1 allows DiET-GS to produce more natural and precise color as shown in the 2nd row of Fig. 6, we empirically find that the performance improvement gained falls short of our expectation (cf. Tab. 2). We postulate that this is due to the joint optimization of the event-based loss which are $\\mathcal{L}_{\\mathrm{ev}}$ and $\\mathcal{L}_{\\mathrm{edi}}$ and the RSD loss. Event-based supervision is derived from real-captured event streams, which tend to optimize 3DGS for a specific training scene. In contrast, the RSD loss regularizes rendered images according to the distribution of diverse natural images modeled by a pretrained diffusion model. Jointly optimizing these two constraints reaches an equilibrium between scene-specific details guided by the event-based loss and the prior knowledge of the pretrained diffusion model. Consequently, it is likely to weaken the full effectiveness of $\\mathcal{L}_{\\mathrm{rsd}}$ . To this end, we incorporate an additional training step to fully leverage the diffusion prior by introducing extra learnable parameters to DiET-GS. We name the final model trained on Stage 2 as DiET-GS++.", + "bbox": [ + 511, + 582, + 906, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we attach a zero-initialized Gaussian feature $\\mathbf{f}_{\\mathbf{g}} \\in \\mathbb{R}^{D}$ for each 3D Gaussian $\\mathbf{g}$ in the pretrained", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21743", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/88d094012b8496ea4a90e6d1ed707d0c03715cbe9e5a770b9307f59b1d3ab761.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    DatasetMetricMPRNet+GS [63]EDI+GS [33]EFNet+GS [48]BAD-NeRF [54]BAD-GS [66]E2NeRF [36]Ev-DeblurNeRF [3]DiET-GS (Ours)DiET-GS++ (Ours)
    EvDeblur -blenderPSNR↑18.7623.6921.0319.7822.2324.5424.7626.6926.23
    SSIM↑0.59120.76940.64130.63810.72130.79930.80380.86070.8478
    LPIPS↓0.35450.13750.32140.24900.20120.16240.17880.10640.1052
    MUSIQ↑24.1255.1335.1323.6332.4347.3142.3857.6759.91
    CLIP-IQA↑0.24130.27510.23140.18880.19930.21290.23000.27690.2960
    EvDeblur -CDAVISPSNR↑27.5132.9530.9728.4729.1231.5432.3034.2233.16
    SSIM↑0.75140.89220.85030.79810.81290.86870.88270.92230.9039
    LPIPS↓0.20130.07900.11420.25260.20120.10590.05710.04960.0502
    MUSIQ↑25.1240.0638.2319.9622.1238.8241.3245.8050.44
    CLIP-IQA↑0.21340.20080.19340.17910.18120.22350.22110.20720.2415
    ", + "bbox": [ + 94, + 89, + 906, + 231 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparisons on both synthetic and real-world dataset. The results are the average of every scenes within the dataset. The best results are in bold while the second best results are underscored.", + "bbox": [ + 89, + 233, + 906, + 262 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DiET-GS, where $D$ is the feature dimension. Given a camera pose $p$ , we use DiET-GS to render a deblurred image $\\hat{C}$ and a 2D feature map $\\mathbf{f}_{2\\mathrm{D}}$ by accumulating color and $\\mathbf{f_g}$ respectively. After encoding $\\hat{C}$ to the latent $\\mathbf{z}_0 = \\mathcal{E}(\\hat{C})$ , we subsequently obtain a refined latent $\\mathbf{z}'_0 = \\mathbf{z}_0 + \\mathbf{f}_{2\\mathrm{D}}$ by combining $\\mathbf{z}_0$ and $\\mathbf{f}_{2\\mathrm{D}}$ . Gaussian noise samples at timesteps $t$ and $t - 1$ are then introduced to $\\mathbf{z}'_0$ to get noised latents $\\mathbf{z}'_t$ and $\\mathbf{z}'_{t - 1}$ . Finally, given $\\hat{C}$ as conditional input, the UNet backbone of pretrained diffusion model predicts the noise residual of $\\mathbf{z}'_t$ to derive the denoised latent $\\hat{\\mathbf{z}}_{t - 1}^{\\prime}$ . The RSD loss between $\\mathbf{z}'_{t - 1}$ and $\\hat{\\mathbf{z}}_{t - 1}^{\\prime}$ is given as the optimization objective of Stage 2. We note that only the Gaussian features $\\mathbf{f_g}$ are trained during Stage 2, while the other parameters of DiET-GS remain fixed to preserve the prior of event streams derived in Stage 1. After optimization, our model can render latent residual $\\mathbf{f}_{2\\mathrm{D}}$ which contains rich edge details directly guided by the pretrained diffusion model. In the inference, the final sharp image $\\tilde{C}$ is obtained by decoding the refined latent $\\mathbf{z}_0'$ . Specifically, $\\tilde{C} = \\mathcal{D}(\\mathbf{z}_0') = \\mathcal{D}(\\mathbf{f}_{2\\mathrm{D}} + \\mathcal{E}(\\hat{C}))$ , where $\\mathcal{D}$ is pretrained VAE decoder (cf. Fig. 1).", + "bbox": [ + 88, + 268, + 485, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Discussion. Although Stage 2 of our framework uses RSD loss, we differ from [20] as follows: 1) We exploit the rendering capability of 3DGS to obtain the learnable latent residual $\\mathbf{f}_{\\mathrm{2D}}$ . In contrast, [20] manually creates $\\mathbf{f}_{\\mathrm{2D}}$ for all training poses and thus requires further synchronization of NeRF with the trained latent features after the RSD optimization. This synchronization stage is not necessary in our design since DiET-GS++ can directly render the learned latent residual from the Gaussian features $\\mathbf{f}_{\\mathrm{g}}$ , thus resulting in a simpler framework. Furthermore, our Stage 2 only takes $\\leq 20$ minutes of training time. 2) Our setting is more challenging than [20] due to the lack of ground truth clean images to condition the diffusion UNet. In this regard, we utilize the image rendered from DiET-GS as conditional input on the diffusion model to further enhance the edges.", + "bbox": [ + 89, + 580, + 485, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 821, + 223, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 845, + 308, + 862 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We build our framework based on the official code of 3DGS [15] and DiSR-NeRF [20]. Throughout Stage 1,", + "bbox": [ + 89, + 869, + 485, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we set the loss weights $\\lambda_{\\mathrm{blur}} = \\lambda_{\\mathrm{edi}} = \\lambda_{\\mathrm{rsd}} = 1.0$ and $\\lambda_{\\mathrm{ev}} = 0.1$ , and execute 100,000 iterations of training. During Stage 2, training spans 2,000 iterations with a linearly decreasing time schedule of ancestral sampling. The number of poses $n$ estimated for each blurry image in the initialization of 3DGS is set to 9. All experiments are conducted using a single NVIDIA RTX 6000 GPU.", + "bbox": [ + 511, + 268, + 908, + 377 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Datasets.", + "text_level": 1, + "bbox": [ + 511, + 387, + 620, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our DiET-GS and DiET-GS++ on both synthetic and real-world datasets proposed by [3]. EvDeblur-Blender Dataset is a synthetic dataset that consists of four synthetic scenes derived from DeblurNeRF [29]: factory, pool, tanabata and trolley. Blurry images are provided along with the corresponding synthetic event streams simulated by [38]. Motion blur is produced during a 40ms exposure time with a single fast continuous motion by averaging a set of images rendered at 1000 FPS in linear RGB space. We set $\\Theta = 0.2$ for the event threshold during training in synthetic scenes. The EvDeblur-CDAVIS Dataset contains five real-world scenes, each with 11 to 18 blurry training images paired with corresponding event streams. Color-DAVIS346 [21] is employed to capture both color events and standard frames at $346 \\times 260$ pixel resolution using an RGBG Bayer pattern. A 1000ms exposure time is given to produce motion blur. The event threshold is set to $\\Theta = 0.25$ for both negative and positive events during training in real-world scenes. Both synthetic and real-world datasets include five ground-truth (GT) sharp images captured from both seen and unseen viewpoints for each scene.", + "bbox": [ + 511, + 410, + 908, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Experiment Settings", + "text_level": 1, + "bbox": [ + 511, + 739, + 707, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline. Our baselines are divided into three categories. The first category is the naive combination of image deblurring methods and 3DGS, where images are initially deblurred and subsequently used as training views for 3DGS. Specifically, an image deblurring method MPR-Net [63], and event-based deblurring methods EDI [33] and EFNet [48] are adopted as baselines. The second category is the frame-only deblurring rendering methods, where only the RGB frames are utilized during training. We select", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21744", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/18db0bcf56394b45695e68112e9b2f02bf2b7a2b8f110cb956556ea4e6911036.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 88, + 207, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d75bba699426bf250492244e9e38c5a8601b32787d3065945fcdf8158cb743b8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 156, + 207, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/35c5df55eaf3674e61efebf839c93d09ff9507159068024d47ae5a4e7912309c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 222, + 207, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/00c993a9f60a7db29fb742029df1a33c7b7b7d5ec8a20a4ba326408ce33cda5c.jpg", + "image_caption": [ + "(a) Blur Image" + ], + "image_footnote": [], + "bbox": [ + 94, + 287, + 207, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b85bf3a6b2764149a297a54543bcb52903424bbe2a3e66d47eda6f306d23227d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 209, + 88, + 323, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/38f4161579d4e62c405c1e94e0d76c8acad37124cbfdd1f866b8db45a52f928e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 209, + 155, + 323, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3165f4747bc5c74d20ecc878b20943a2f510b1c695c4634e01db05b01b5610a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 209, + 222, + 323, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d977c564150d3d120c0b3970258798c1997ad5e9500d8dd88cf9e2599b992b6.jpg", + "image_caption": [ + "(b) EDI+GS [33]" + ], + "image_footnote": [], + "bbox": [ + 209, + 287, + 321, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4a7bd97688d3d372d30c561bfa9be0e398dc2a0607b8dbb23856d13b3f37dae9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 326, + 88, + 439, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a2fc8a6f06d0c7ae526629a0592daf11de08ae3505e864cd18aed38573a7a7ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 326, + 155, + 439, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/19c2909228b57ac44ee541a37060b0f943698010e142220e19969972f6158771.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 326, + 222, + 439, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3dbc9cb08e1b6703e05feebc0bdedf0bf4f7f2b9249f3c0c8de3b270ec8ffb54.jpg", + "image_caption": [ + "(c) E2NeRF [36]" + ], + "image_footnote": [], + "bbox": [ + 325, + 287, + 439, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0bbdd9d4b161b22da5f1ccf2ac2512ea6138869735363003a00fdf11d3d55966.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 441, + 88, + 555, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/379726381ce18b6cf28d1a1a6fc2dbfaf993eb1e8f842a8b2c30a6b79b444b36.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 441, + 155, + 553, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d60ab7a0dde9eccf5a0ee1864bac511275ef2c38459fc344f0988ff264557b24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 441, + 222, + 553, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aea6b1c2995d6583f0deebcb76486d8a9233a0c089af09ed12c1a014e024af1b.jpg", + "image_caption": [ + "(d) Ev-DeblurNeRF [3]" + ], + "image_footnote": [], + "bbox": [ + 441, + 287, + 553, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/31ac507a35be2b1a2010bd21e8d17b56a8bf0412d52c51f130fc34859446ee15.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 557, + 88, + 671, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1c01bfa4aa97c6f1a7b25cb2dcad3936a72ea30fe4caa8831f6f2ada9f4ccc86.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 557, + 155, + 671, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/046ab52cb79eb38976365c80164a6f5d6c40f3eac76e85c448ece5fb3e413771.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 557, + 222, + 671, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/496c655ebc6208c7e4dfd626ea17aaca1e692a9cc051a492956bc7e801e8045a.jpg", + "image_caption": [ + "(e) DiET-GS (Ours)" + ], + "image_footnote": [], + "bbox": [ + 557, + 287, + 669, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1f8335adda05b0a6e62aec3625ad585c25f4c9400e95307179a62fd20106de35.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 671, + 88, + 787, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/331ca518db6cc6f44f7bec99b766098f6ed97c43f3c2f7816bf15b68018db55b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 671, + 155, + 787, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ef1ca308be5bda4589226b9daae3c2712bc47b59276792d4a8bbc67ac72a6410.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 671, + 222, + 787, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f8b42523357b072eb3972c3c64bf441173ad84bf388e4deba4edcfa589072370.jpg", + "image_caption": [ + "(f) DiET-GS++ (Ours)" + ], + "image_footnote": [], + "bbox": [ + 671, + 287, + 785, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1d4958a3542074c8f445b7cdca285971590d41837988a33e9d17a0f09667c953.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 88, + 901, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/725694da54b91877b73a35d7d6a0d54b62e0f4faf724d9ba4bee8a64684221a9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 155, + 901, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/38890f81ebe533655dc1a592ae1f90464c5e11c71dcace2f4698755cd04edb44.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 222, + 901, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/413d5e601bb2076fb5bcc04886c0e6f58902a29782655301fb6385317657dc5a.jpg", + "image_caption": [ + "(g) GT" + ], + "image_footnote": [], + "bbox": [ + 787, + 287, + 901, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "BAD-NeRF [54] and BAD-GS [66] for this category. The third category is event-based deblurring rendering methods, where the RGB frames and event streams are jointly leveraged. We select E2NeRF [36] and Ev-DeblurNeRF [3] as the most recent works in this category with publicly available code. To fairly compare with our methods, we utilize camera poses estimated from COLMAP for all baselines instead of using GT poses provided by the dataset.", + "bbox": [ + 89, + 422, + 483, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation Metrics. We employ three standard metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and VGG-based Learned Perceptual Image Patch Similarity (LPIPS) [65] to evaluate the quality of the predicted views on the target views. Since our framework produces rich edge details under the guidance of generative model, different predicted views can be valid for the same blurry image. We thus follow [62] to additionally adopt MUSIQ [14] and CLIP-IQA [52] as No-Reference Image Quality Assessment (NR-IQA) metrics to further evaluate the effectiveness of our framework.", + "bbox": [ + 89, + 551, + 483, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Quantitative Comparisons", + "text_level": 1, + "bbox": [ + 89, + 726, + 331, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the quantitative results in Tab. 1. Our DiET-GS largely outperforms all baselines in PSNR, SSIM, and LPIPS on both synthetic and real-world datasets, showing the effectiveness of our framework to leverage EDI prior. Furthermore, our DiET-GS++ shows significant improvement in MUSIQ and CLIP-IQA metrics, achieving the best results but showing a slight drop in PSNR and SSIM metrics. As already discussed in [20, 62], since DiET-GS++ is solely guided by a pretrained generative model, the resulting images may contain more variation with respect to GT", + "bbox": [ + 89, + 750, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/540d35b5f48846028b87b3264178622240050ad16da3ed47c65589b6fc4bd71b.jpg", + "image_caption": [ + "Figure 4. Qualitative comparisons on both synthetic (1st-2nd rows) and real-world (3rd-4th rows) datasets. DiET-GS shows cleaner texture with more accurate details compared to the event-based baselines while DiET-GS++ further enhances these features with sharper definition, achieving the best visual quality." + ], + "image_footnote": [], + "bbox": [ + 517, + 420, + 612, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b9c56c413d40aa8476b9fb003959c6334aceea53b732aefb191d6d2f98a66a52.jpg", + "image_caption": [ + "(a) $\\mathcal{L}_{\\mathrm{edi.gray}}$" + ], + "image_footnote": [], + "bbox": [ + 517, + 494, + 612, + 566 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/119bfa17a1e8c84df2a8781df949d8456cabe8e8516807ef57f7aa2036a6199f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 420, + 709, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/31b6356b2ad17ceb3b757d96f2868cfbe86737a7d1045cb8a77788d1df808cc8.jpg", + "image_caption": [ + "(b) $\\mathcal{L}_{\\mathrm{edi\\_color}}$" + ], + "image_footnote": [], + "bbox": [ + 614, + 494, + 707, + 566 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1fa8ec8f906f962ea0618a6c2de45bbe355b76057d71b70c49105860127ad743.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 420, + 805, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3ac5dac25f7523cc4ee74a8379e246ea66ca21d99b8d3600001db2204fda774a.jpg", + "image_caption": [ + "(c) Both" + ], + "image_footnote": [], + "bbox": [ + 710, + 494, + 803, + 566 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67de5b9741b90e15d72083bcf471a7db7b4d0be41e5e5740536226d3c5537b85.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 807, + 420, + 901, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/49d20b6601bd515593bd614ad4f0df0ba931eeec7cbfe3e9ce6d5efc2b20e36b.jpg", + "image_caption": [ + "(d) GT", + "Figure 5. Ablation study on $\\mathcal{L}_{\\mathrm{edi\\_gray}}$ and $\\mathcal{L}_{\\mathrm{edi\\_color}}$" + ], + "image_footnote": [], + "bbox": [ + 807, + 494, + 901, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "samples compared to DiET-GS which is supervised by real-captured data. Nonetheless, DiET-GS++ still substantially improves the visual quality as shown in NR-IQA metrics. Qualitative comparisons in Sec. 5.5 further validate the effectiveness of our DiET-GS++. We also present the user study in the Supplementary material, thoroughly examining the efficacy of leveraging diffusion prior in Stage 2.", + "bbox": [ + 511, + 609, + 906, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Qualitative Comparisons", + "text_level": 1, + "bbox": [ + 511, + 726, + 741, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparisons on both Ev-DeblurBlender and Ev-DeblurCDAVIS datasets are shown in Fig. 4, making the following observations. 1) Relying solely on the EDIPreprocessed images to optimize the 3DGS yields unsatisfactory results, introducing numerous artifacts as shown in the 2nd column. While effective at recovering sharp edges, EDI often produces inaccurate details with relatively low visual quality, hindering effective optimization of the 3DGS. This highlights the need for additional objective terms proposed in our framework to further constrain the", + "bbox": [ + 511, + 750, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21745", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ef0a18bfebb35748597fd05535306fb2e3172547dfb998a02ba8f5ebafa987bc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    \\( \\mathcal{L}_{\\text{blur}} \\)\\( \\mathcal{L}_{\\text{ev}} \\)\\( \\mathcal{L}_{\\text{edi\\_gray}} \\)\\( \\mathcal{L}_{\\text{edi\\_color}} \\)\\( \\mathcal{L}_{\\text{edi\\_simul}} \\)\\( \\mathcal{L}_{\\text{rsd}} \\)(S1)\\( \\mathcal{L}_{\\text{rsd}} \\)(S2)PSNR↑SSIM↑LPIPS↓MUSIQ↑CLIP-IQA↑
    ✓29.730.77970.216024.770.2031
    ✓✓32.740.84600.117339.690.2776
    ✓✓✓33.910.87610.075244.250.2684
    ✓✓✓34.480.89150.082640.790.2450
    ✓✓✓✓34.920.90330.062443.790.2468
    ✓✓✓✓✓35.040.90680.058745.040.2490
    ✓✓✓✓✓✓34.890.90490.060045.370.2584
    ✓✓✓✓✓✓✓33.860.88460.063451.710.2955
    ", + "bbox": [ + 94, + 89, + 906, + 204 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. Ablation study on DiET-GS and DiET-GS++", + "bbox": [ + 328, + 209, + 666, + 223 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3DGS. 2) We find that our DiET-GS is capable of restoring cleaner textures and clearer edges compared to other baselines. For example, in the 3rd row, other baselines wrongly produce grid patterns on the wall stretched from the left object, while our DiET-GS restores more accurate texture on the same part. Similarly, in the 4th row, color jittering from E2NeRF and artifacts from EDI+GS and Ev-DeblurNeRF are observed, while DiET-GS exhibits cleaner details. The same observation is made for the text elements shown in the 1st and 2nd rows. 3) Our DiET-GS++ further refines the textures and edge details generated from DiET-GS, demonstrating the efficacy of fully leveraging diffusion prior in Stage 2. For instance, grid patterns on the wall in the 3rd row are further mitigated in DiET-GS++, while sharper edges are also observed in both text elements (1st-2nd rows) and non-text elements (4th row) compared to DiET-GS. Overall, our final model DiET-GS++ shows a marked improvement over the other baselines, consistently achieving more precise textures and well-defined details.", + "bbox": [ + 88, + 229, + 483, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Ablations", + "text_level": 1, + "bbox": [ + 89, + 534, + 202, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we present various ablation studies to validate the contributions of each component proposed in our DiET-GS++. All the quantitative evaluations are conducted on a real-world scene, namely, Figures sample.", + "bbox": [ + 89, + 559, + 483, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Event-based Supervision. As shown in the 1st-2nd rows of Tab. 2, simulating brightness change in $\\mathcal{L}_{\\mathrm{ev}}$ improves PSNR by $+3.01\\mathrm{dB}$ . Investigation of the EDI prior is conducted on the 3rd-6th rows of Tab. 2 along with qualitative results on Fig. 5 and the 1st row of Fig. 6. As shown in the 1st row of Fig. 5, using only $\\mathcal{L}_{\\mathrm{edi\\_gray}}$ yields sharper details, e.g. tiling on the background, and improves LPIPS scores compared to relying solely on $\\mathcal{L}_{\\mathrm{edi\\_color}}$ . However, color artifacts are also introduced due to the lack of sufficient color supervision. In contrast, $\\mathcal{L}_{\\mathrm{edi\\_color}}$ generates accurate color with higher PSNR and SSIM scores, though some details are over-smoothed. Leveraging both $\\mathcal{L}_{\\mathrm{edi\\_gray}}$ and $\\mathcal{L}_{\\mathrm{edi\\_color}}$ yields the best performance on all the PSNR, SSIM, and LPIPS metrics among the 3rd to 5th rows of Tab. 2, achieving both precise color and clear details. The 2nd row of Fig. 5 further shows the synergistic effect between the two constraints, where more well-defined details are produced when they are jointly utilized. Similarly,", + "bbox": [ + 89, + 628, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b8746770b0cfa4dae81a9e57cd75ecbef954bdb5141fa76115a4c5d0d45f3d95.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 228, + 645, + 301 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f09f4fcd182434cfab8f643d8e87fef59f33f0096788c6d4546691b2f61a8a9.jpg", + "image_caption": [ + "(a) wo $\\mathcal{L}_{\\mathrm{edi\\_simul}}$", + "(d) wo $\\mathcal{L}_{\\mathrm{rsd}}$ (S1)", + "Figure 6. Ablation on $\\mathcal{L}_{\\mathrm{edi\\_simul}}$ (1st row) and $\\mathcal{L}_{\\mathrm{rsd}}$ (S1) (2nd row)." + ], + "image_footnote": [], + "bbox": [ + 517, + 316, + 645, + 391 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/806fd112fc81929d71d268a46f6d44b6392c362f4eeb59c3fd49b1fb8e62e36e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 647, + 228, + 774, + 301 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0e2bda4e5e03e5211fc44370ff90fbb9edeed60f22042808f76d787d34f427a5.jpg", + "image_caption": [ + "(b) w $\\mathcal{L}_{\\mathrm{edi,simul}}$", + "(e) w $\\mathcal{L}_{\\mathrm{rsd}}$ (S1)" + ], + "image_footnote": [], + "bbox": [ + 647, + 316, + 772, + 391 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a5a4dd6dea09482e2a916e620329b265e176402b8bea7282fdd91a4babee976.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 228, + 901, + 301 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5a1e419e13e83eb31ab3c60f19f01da80814c726043fbe6ea92e5e0fbfb7dd2c.jpg", + "image_caption": [ + "(c) GT", + "(f) GT" + ], + "image_footnote": [], + "bbox": [ + 774, + 316, + 901, + 391 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "adding EDI simulation $\\mathcal{L}_{\\mathrm{edi\\_simul}}$ further aids fine-grained deblurring as shown in the red circles of Fig. 6, showing a $+0.12\\mathrm{dB}$ increase in PSNR.", + "bbox": [ + 511, + 434, + 906, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Diffusion prior. The following observations are made on the inclusion of diffusion prior. 1) The RSD optimization term in Stage 1 denoted as $\\mathcal{L}_{\\mathrm{rsd}}$ (S1) shows slight improvement in MUSIQ and CLIP-IQA by $+0.33$ and $+0.0094$ , respectively. 2) $\\mathcal{L}_{\\mathrm{rsd}}$ (S1) can also serve as additional color guidance since the real-captured blurry image with ground-truth color information is given to the diffusion model as conditional input during RSD optimization, further constraining the color of DiET-GS. As shown in the 2nd row of Fig. 6, our DiET-GS++ guided by $\\mathcal{L}_{\\mathrm{rsd}}$ (S1) (6e) generates better color compared to the version that omits RSD optimization in Stage 1 (6d). 4) $\\mathcal{L}_{\\mathrm{rsd}}$ (S1) yields marginal performance improvement in NR-IQA metrics compared to the $\\mathcal{L}_{\\mathrm{rsd}}$ (S2). As discussed in Sec. 4.2, joint optimization of event-based objectives and RSD loss tends to weaken the full effect of diffusion prior. However, considering the first and second findings, we still decide to exploit diffusion prior in Stage 1 and further adopt Stage 2 with additional parameters to fully leverage the guidance from the pretrained diffusion model.", + "bbox": [ + 511, + 487, + 908, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion.", + "text_level": 1, + "bbox": [ + 511, + 799, + 637, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DiET-GS is a novel framework that deblurs motion-blurred images using event streams and a pretrained score function. Our two-stage strategy leverages 3DGS with EDI constraints to recover sharp images with accurate color and fine details, while a diffusion prior enhances edge clarity.", + "bbox": [ + 511, + 824, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21746", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 162, + 187, + 179 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anish Bhattacharya, Ratnesh Madaan, Fernando Cladera, Sai Vemprala, Rogerio Bonatti, Kostas Daniilidis, Ashish Kapoor, Vijay Kumar, Nikolai Matni, and Jayesh K Gupta. Evdnerf: Reconstructing event data with dynamic neural radiance fields. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 5846-5855, 2024. 1", + "[2] RIR BT et al. 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Hifa: High-fidelity textto3d with advanced diffusion guidance. arXiv preprint arXiv:2305.18766, 3(5):7, 2023. 3" + ], + "bbox": [ + 516, + 92, + 903, + 402 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21749", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_model.json b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_model.json new file mode 100644 index 0000000000000000000000000000000000000000..42d46f4183b94a507f3a9c25b7bc612e3de50ac3 --- /dev/null +++ b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_model.json @@ -0,0 +1,2895 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.13, + 0.885, + 0.177 + ], + "angle": 0, + "content": "DiET-GS: Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting" + }, + { + "type": "text", + "bbox": [ + 0.368, + 0.205, + 0.63, + 0.221 + ], + "angle": 0, + "content": "Seungjun Lee Gim Hee Lee" + }, + { + "type": "text", + "bbox": [ + 0.232, + 0.222, + 0.766, + 0.24 + ], + "angle": 0, + "content": "Department of Computer Science, National University of Singapore" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.243, + 0.698, + 0.257 + ], + "angle": 0, + "content": "seungjun.lee@u.nus.edu, gimhee.lee@nus.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.273, + 0.327, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.306, + 0.485, + 0.609 + ], + "angle": 0, + "content": "Reconstructing sharp 3D representations from blurry multi-view images is a long-standing problem in computer vision. Recent works attempt to enhance high-quality novel view synthesis from the motion blur by leveraging event-based cameras, benefiting from high dynamic range and microsecond temporal resolution. However, they often reach sub-optimal visual quality in either restoring inaccurate color or losing fine-grained details. In this paper, we present DiET-GS, a diffusion prior and event stream-assisted motion deblurring 3DGS. Our framework effectively leverages blur-free event streams and diffusion prior in a two-stage training strategy. Specifically, we introduce the novel framework to constrain 3DGS with event double integral, achieving both accurate color and well-defined details. Additionally, we propose a simple technique to leverage diffusion prior to further enhance the edge details. Qualitative and quantitative results on both synthetic and real-world data demonstrate that our DiET-GS is capable of producing better quality of novel views compared to the existing baselines. Our project page is: DiET-GS.github.io." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.616, + 0.222, + 0.631 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.643, + 0.483, + 0.868 + ], + "angle": 0, + "content": "Novel view synthesis plays an important role in various vision applications such as scene understanding [17, 27, 58], virtual reality [18, 60], image processing [9, 29, 32], etc. To this end, Neural Radiance Fields (NeRF) [31] achieves notable success in generating high-quality novel views by reconstructing implicit 3D representations with a deep neural network. However, it falls short of real-time rendering and efficient training, limiting its application in real-world scenarios. Recently, 3D Gaussian Splatting (3DGS) [15] has emerged as an efficient alternative to NeRF by representing scenes with explicit 3D Gaussian primitives. The explicit representation of 3DGS serves as a lightweight replacement of the implicit neural representations used in NeRF, achieving better training and rendering efficiency as well as visual quality of novel views." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To enable high-quality 3D reconstructions, both NeRF and 3DGS rely on multi-view images that are perfectly cap-" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.274, + 0.905, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.462, + 0.907, + 0.546 + ], + "angle": 0, + "content": "Figure 1. Given a set of blurry images and corresponding event streams, we propose a novel framework to construct deblurring 3DGS by jointly leveraging the EDI [33] formulation and a pretrained diffusion model as a prior. Our DiET-GS++ enables high-quality novel-view synthesis by recovering precise color and well-defined details from the blurry multi-view images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.551, + 0.907, + 0.734 + ], + "angle": 0, + "content": "tured and free from any artifact. However, this preliminary condition is often unavailable in the real world. For example, a camera needs prolonged exposure time in a low light environment to allow enough light to reach the sensor for image formation. The camera has to remain absolutely still during this lengthy exposure time. Any camera motion during the capture leads to undesired motion blur. To circumvent this issue, a line of works [19, 29, 34, 54, 66] has attempted to recover sharp 3D representations from blurry multi-view images. Despite the promising potential, it is non-trivial to restore fine-grained details from blurry images alone and thus often leading to sub-optimal visual quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Several recent works have shown the efficacy of event-based cameras, significantly improving motion deblurring in images captured from standard frame-based cameras. Event sensors enable blur-free measurements of brightness changes, benefiting from higher dynamic range and temporal resolution compared to standard cameras. Motivated by this distinct competency, several recent works have explored the potential of recovering sharp 3D representations from event streams. Earlier works [1, 11, 42] focus on utilizing solely event-based data, lacking the capacity to preserve color information. E-NeRF [16] combines blurry" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21739" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.258 + ], + "angle": 0, + "content": "images into the framework as direct color supervision for 3D NeRF. Nonetheless, the estimated color exhibits blur around the edges since it does not account for the blur formation. \\(\\mathrm{E}^2\\mathrm{NeRF}\\) and following works [3, 23, 37, 61] explicitly model the blur formation process to further enhance the color and edge details. However, most of these existing works still rely on blurry images alone to recover accurate color, often resulting in unwanted color artifacts. To supplement color guidance, Ev-DeblurNeRF [3] proposes to exploit the explicit relationship of Event Double Integral (EDI) between blurry images and event streams." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.261, + 0.485, + 0.607 + ], + "angle": 0, + "content": "In this paper, we propose DiET-GS, a Diffusion prior and EvenT stream-assisted motion deblurring 3DGS. As illustrated in Fig. 1, our framework comprises two main stages: DiET-GS and DiET-GS++. Our Stage 1: DiET-GS first optimizes the deblurring 3DGS by jointly leveraging the real-captured event streams and the prior knowledge of a pretrained diffusion model. To restore both accurate color and well-defined details, we introduce a novel framework that uses the EDI prior to achieve 1) fine-grained details, 2) accurate color, and 3) regularization. Specifically, in addition to the EDI color guidance proposed by [3], we propose further constraints to recover fine-grained details by modeling EDI in the brightness domain through a learnable camera response function. This learnable approach naturally considers the potential variation between RGB values and pixel intensity, leading to better real-world adaptation and thus effectively recovering intricate details. The EDI constraints from both RGB space [3] and brightness domain enable mutual compensation between color fidelity and fine-grained details, resulting in optimal visual quality. Additionally, we derive a regularization term from the EDI prior to further facilitate the optimization by ensuring the cycle consistency among the objective terms." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.61, + 0.483, + 0.821 + ], + "angle": 0, + "content": "To achieve more natural image refinement, we further incorporate diffusion prior in DiET-GS using the Renoised Score Distillation (RSD) proposed by [20]. Nonetheless, we empirically find that jointly leveraging both priors from real-captured data and a pretrained diffusion model often weakens the full effect of diffusion prior. Consequently, our Stage 2: DiET-GS++ is further introduced to maximize the effect of diffusion guidance by adding extra learnable parameters to each 3D Gaussian in the pretrained DiET-GS. Unlike [20], DiET-GS++ directly renders latent residual from the 3D Gaussians, resulting in a simpler framework to leverage RSD optimization. Finally, resulting images from DiET-GS are further refined by solely relying on diffusion prior while edge details are effectively enhanced." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.824, + 0.451, + 0.838 + ], + "angle": 0, + "content": "Our main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.84, + 0.483, + 0.884 + ], + "angle": 0, + "content": "- A novel framework to construct deblurring 3DGS by jointly leveraging event streams and the prior knowledge of a pretrained diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "- A two-stage train38ing strategy to effectively utilize real-" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "captured data and diffusion prior together. Once optimized, our method is capable of recovering well-defined details with accurate color from the input blurry images." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.137, + 0.905, + 0.183 + ], + "angle": 0, + "content": "- Qualitative and quantitative results show that our framework significantly surpasses the existing baselines, achieving the best visual quality." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.192, + 0.664, + 0.208 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.218, + 0.907, + 0.626 + ], + "angle": 0, + "content": "Event-based image deblurring. Recently, event-based cameras have gained significant popularity due to their high dynamic range and microseconds temporal resolution. Several methods have tried to leverage these distinct features to tackle image deblurring. Most notably, event-based double integral (EDI) [33] explicitly models the relationship between event streams and a blurry image jointly captured during the fixed exposure time. Subsequent works follow EDI by fusing the events and RGB frames [7, 48, 49, 59, 64] or using learning-based approaches [12, 50] to further improve visual quality. Another line of works exploits event cameras to recover sharp 3D representations such as NeRF and 3DGS from blurry multi-view images. Earlier works [11, 16, 28, 42] utilize an event generation model [6] to enable sharp novel view synthesis from a fast-moving camera while E-NeRF [16] combines RGB frames to further refine the color. Recent works [3, 23, 36, 37, 61] such as \\(\\mathrm{E}^2\\mathrm{NeRF}\\) [36] and Ev-DeblurNeRF [3] combine blurry image formation [29] to model the camera motion during the exposure time while Ev-DeblurNeRF [3] further incorporates the EDI prior to provide additional color constraint to 3D NeRF. However, this color constraint often yields over-smoothed details by treating each RGB channel as brightness, which deviates from the real-world setting. In this work, we effectively restore intricate details by introducing a learnable brightness estimation function to the EDI formulation that better adapts to real-world settings." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.629, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Diffusion-based image restoration. Diffusion models have been successfully repurposed for image restoration tasks such as super-resolution (SR) [8, 22, 44, 53, 57, 62], deblurring [5, 39, 56] and JPEG restoration [13, 43]. A comprehensive summary of diffusion-based restoration methods can be found in this recent survey [24]. Diffir [57] is a two-stage training approach that generates a prior representation from a diffusion model to restore an image. DvSR [56] surpasses regression-based methods by leveraging conditional diffusion models. More recently, diffusion prior has begun to be used for restoration of 3D representations such as NeRF. DiSR-NeRF [20] first attempts to leverage a pretrained diffusion model to construct superresolution (SR) NeRF by proposing a renoised variant of score distillation sampling [35], referred to as RSD optimization. In our approach, we propose a simpler framework to adopt RSD optimization compared to [20], further enhancing the edge details of the rendered image." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21740" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.625, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.089, + 0.906, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.257, + 0.117, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.259, + 0.183, + 0.268 + ], + "angle": 0, + "content": "EDI Processing" + }, + { + "type": "image", + "bbox": [ + 0.194, + 0.258, + 0.212, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.217, + 0.26, + 0.284, + 0.269 + ], + "angle": 0, + "content": "Bright Estimation" + }, + { + "type": "image", + "bbox": [ + 0.294, + 0.257, + 0.312, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.318, + 0.26, + 0.414, + 0.268 + ], + "angle": 0, + "content": ": Pretrained VAE Encoder" + }, + { + "type": "image", + "bbox": [ + 0.425, + 0.257, + 0.458, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.462, + 0.26, + 0.567, + 0.27 + ], + "angle": 0, + "content": ": Pretrained Diffusion UNet" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.28, + 0.907, + 0.351 + ], + "angle": 0, + "content": "Figure 2. Overall framework of our DiET-GS. Stage 1 (DiET-GS) optimizes the deblurring 3DGS with the event streams and diffusion prior. To preserve accurate color and clean details, we exploit the EDI prior in multiple ways, including color supervision \\(C\\), guidance for fine-grained details \\(I\\), and additional regularization \\(\\tilde{I}\\) with EDI simulation. Stage 2 (DiET-GS++) is then employed to maximize the effect of diffusion prior by introducing extra learnable parameters \\(\\mathbf{f}_{\\mathbf{g}}\\). DiET-GS++ further refines the rendered images from DiET-GS, effectively enhancing rich edge features. More details are explained in Sec. 4.1 and Sec. 4.2." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.363, + 0.229, + 0.379 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.388, + 0.484, + 0.464 + ], + "angle": 0, + "content": "Event Camera Model in Motion Deblurring. Event is triggered when the absolute difference of logarithmic brightness between time \\( t_j \\) and \\( t_{j-1} \\) exceeds \\( \\Theta_{p_j} \\) at the same pixel location, where predefined threshold \\( \\Theta_{p_j} \\in \\mathbb{R}^+ \\) controls the sensitivity to brightness change. It follows that:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.472, + 0.483, + 0.489 + ], + "angle": 0, + "content": "\\[\n\\log (I (\\mathbf {u}, t _ {j})) - \\log (I (\\mathbf {u}, t _ {j - 1})) = p _ {j} \\cdot \\Theta_ {p _ {j}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.497, + 0.484, + 0.573 + ], + "angle": 0, + "content": "where \\( I(\\mathbf{u}, t) \\) denotes instantaneous intensity at a pixel \\( \\mathbf{u} \\) on a given time \\( t \\). Polarity \\( p_j \\in \\{-1, 1\\} \\) specifies that either an increase or decrease in brightness. By denoting \\( \\log(I(\\mathbf{u}, t)) \\) as \\( L(t) \\), Eq. 1 can be generalized to any time interval \\( [t, t + \\Delta t] \\) by accumulating event signals as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.58, + 0.483, + 0.612 + ], + "angle": 0, + "content": "\\[\nL (t + \\Delta t) - L (t) = \\Theta \\cdot \\mathbf {E} (t) = \\Theta \\int_ {t} ^ {t + \\Delta t} p \\delta (\\tau) \\mathrm {d} \\tau , \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.612, + 0.483, + 0.702 + ], + "angle": 0, + "content": "where \\(\\delta(\\tau)\\) is impulse function with unit integral and polarity \\(p_j\\) on threshold \\(\\Theta\\) is omitted for brevity. By applying the \\(\\exp(\\cdot)\\) function to both sides of Eq. 2, we can rewrite \\(I(t + \\Delta t) = I(t) \\cdot \\exp(\\Theta \\cdot \\mathbf{E}(t))\\) to give the relationship between two instantaneous brightness observed at different time steps." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.702, + 0.484, + 0.762 + ], + "angle": 0, + "content": "We note that a blurry image taken from a conventional frame-based camera can be represented as averaging a sequence of sharp images \\(I\\) acquired during the fixed exposure time \\(\\tau\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.769, + 0.483, + 0.801 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} ^ {\\mathbf {B}} (\\mathbf {u}, t) = \\frac {1}{\\tau} \\int_ {t - \\tau / 2} ^ {t + \\tau / 2} I (\\mathbf {u}, h) \\mathrm {d h}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.803, + 0.484, + 0.864 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}^{\\mathrm{B}}\\) is the blurry image captured during the time interval \\(\\Delta T = [t - \\tau /2,t + \\tau /2]\\). By combining Eq. 2 and Eq. 3, the connection between the blurry image \\(\\mathbf{I}^{\\mathrm{B}}\\) and the latent sharp image \\(I\\) at the same timestep \\(t\\) can be constructed as:" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.872, + 0.483, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} ^ {\\mathbf {B}} (\\mathbf {u}, t) = \\frac {I (\\mathbf {u} , t)}{\\tau} \\int_ {t - \\tau / 2} ^ {t + \\tau / 2} \\exp (\\Theta \\mathbf {E} (h)) \\mathrm {d h}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.365, + 0.907, + 0.47 + ], + "angle": 0, + "content": "This relationship between the sharp image, blurry image, and event stream is known as Event-based Double Integral (EDI) [33]. Finally, we can remove motion blur from \\(\\mathbf{I}^{\\mathbf{B}}\\) by solving for \\(I(\\mathbf{u},t)\\) in Eq. 4 under the guidance of the event streams. We propose a novel framework to leverage the EDI prior to constrain 3D Gaussian Splatting in recovering sharp rendered images with better fine-grained details and colors." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.475, + 0.908, + 0.747 + ], + "angle": 0, + "content": "Diffusion Prior in 3D. Score-based diffusion models [47, 51] are a popular type of generative model that learns a score function that represents the gradient of the log probability density with respect to the data. Several works on Text-to-3D generation [4, 10, 25, 26, 30, 35, 51, 55, 67] that leverage the score function of a pretrained diffusion model as a diffusion prior have shown remarkable results. Notably, Score Distillation Sampling (SDS) [35] uses a score function of a diffusion model as an optimization target, providing the gradient from the score function of a pretrained diffusion model to guide differentiable image parametrization \\(\\mathbf{z} = g(\\theta)\\) without retraining the diffusion model from scratch. In 3D, \\(\\theta\\) can be any learnable 3D representation [15, 31] with volume rendering function \\(g(\\cdot)\\). Recently, a variant of SDS has been introduced for image restoration task. Specifically, [20] proposes a renoised variant of SDS called Renoised Score Distillation (RSD) to use diffusion prior for super-resolution in 3D neural representation field." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Given a data sample \\(\\mathbf{z}_0\\), the forward process obtains the noisy latent \\(\\mathbf{z}_t\\) by adding Gaussian noise sample \\(\\epsilon \\in \\mathcal{N}(0,\\mathbf{I})\\) at timestep \\(t\\): \\(\\mathbf{z}_t = \\sqrt{\\bar{\\alpha}_t}\\mathbf{z}_0 + \\sqrt{1 - \\bar{\\alpha}_t}\\epsilon\\), where \\(\\bar{\\alpha}_t\\) is timestep-dependent noising coefficient. In the DDPM reverse process, a diffusion U-net is trained to predict the noise \\(\\epsilon (\\mathbf{z},y,t)\\) to denoise \\(\\mathbf{z}_t\\) into \\(\\mathbf{z}_{t-1}\\) as follows: \\(\\mathbf{z}_{t-1} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{z}_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\bar{\\alpha}_t}}\\epsilon (\\mathbf{z}_t,y,t)) + \\sigma_t\\epsilon\\), where \\(y\\) is the conditioning input and \\(\\sigma_t\\) is the standard deviation of Gaussian noise samples. Given the predicted denoised latent \\(\\hat{\\mathbf{z}}_{t-1}\\) from \\(\\mathbf{z}_t\\) and the current noised latent \\(\\mathbf{z}_{t-1}\\) at timestep \\(t-1\\), the ob" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21741" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.089, + 0.091, + 0.482, + 0.138 + ], + "angle": 0, + "content": "jective of RSD is formulated as \\(\\mathcal{L}_{rsd} = ||\\mathbf{z}_{t - 1} - \\hat{\\mathbf{z}}_{t - 1}||\\) In this paper, we propose a simpler framework to leverage RSD optimization compared to [20]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.149, + 0.221, + 0.166 + ], + "angle": 0, + "content": "4. Our Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.175, + 0.483, + 0.283 + ], + "angle": 0, + "content": "Fig. 2 shows an illustration of our DiET-GS framework which consists of two stages. Stage 1 (cf. Sec. 4.1) constructs a deblurring 3DGS by leveraging an EDI constraint derived from real-captured data and the prior knowledge of a pretrained diffusion model. Stage 2 (cf. Sec. 4.2) further refines the resulting images from Stage 1 by solely relying on diffusion prior to further enhance the edge details." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.289, + 0.266, + 0.305 + ], + "angle": 0, + "content": "4.1. Stage 1: DiET-GS" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.312, + 0.483, + 0.373 + ], + "angle": 0, + "content": "The goal of Stage 1 is to construct a set of 3D Gaussians from 3D Gaussian Splatting (3DGS) [15] to render sharp images from blurry images and event streams. We name the 3D Gaussians trained in this stage as DiET-GS." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.376, + 0.483, + 0.619 + ], + "angle": 0, + "content": "Initialization. The construction of 3DGS requires point cloud initialization and camera calibrations with structure-from-motion (SfM) [45], which often fail with blurry images. We mitigate this issue by leveraging EDI from Eq. 4 to recover an initial set of sharp images suitable for SfM. Specifically, given an RGB blurry image \\(\\mathbf{C}^{\\mathrm{B}}\\) and an event stream \\(\\mathbf{E}\\) captured during an exposure time \\(\\tau\\), we reconstruct a sharp latent image \\(I\\) from the grayscale of \\(\\mathbf{C}^{\\mathrm{B}}\\) with EDI. This sharp image \\(I\\) can then be warped to any timestep within the exposure period \\([t - \\tau /2, t + \\tau /2]\\) following \\(I(t + \\Delta t) = I(t)\\cdot \\exp (\\Theta \\cdot \\mathbf{E}(t))\\) as shown in Eq. 2. We obtain a set of latent images for each training view by warping the recovered latent image \\(I\\) to each of the \\(n\\) timesteps uniformly sampled from the exposure time. The recovered sharp latent images are subsequently fed into SfM for the estimation of the camera poses and point cloud." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.621, + 0.485, + 0.698 + ], + "angle": 0, + "content": "Blur Reconstruction Loss. Let us denote the estimated camera poses along the approximated camera trajectory of a blurry image \\(\\mathbf{C}_i^{\\mathrm{B}}\\) as \\(\\mathbf{P}_i = \\{p_{ij}\\}_{j=0}^{n-1}\\). Given the camera poses \\(\\mathbf{P}_i\\), we simulate the blurry image formation by discretizing Eq. 3 into:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.705, + 0.483, + 0.741 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {C}} _ {i} ^ {\\mathbf {B}} = \\frac {1}{n} \\sum_ {j = 0} ^ {n - 1} g _ {\\theta} \\left(p _ {i j}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.744, + 0.483, + 0.868 + ], + "angle": 0, + "content": "where \\(g_{\\theta}(\\cdot)\\) is the 3DGS with rendering function and \\(\\hat{\\mathbf{C}}^{\\mathbf{B}}\\) is the estimated motion-blurred image. We can now use the real captured blurry images \\(\\{\\mathbf{C}^{\\mathbf{B}}\\}_{i = 0}^{k - 1}\\) to supervise the simulated blurry images \\(\\{\\hat{\\mathbf{C}}^{\\mathbf{B}}\\}_{i = 0}^{k - 1}\\), where \\(k\\) is the number of training views. Following the original 3DGS, we thus formulate a blur reconstruction loss to minimize the photometric error \\(\\mathcal{L}_{\\mathrm{P}}\\) as \\(\\mathcal{L}_{\\mathrm{blur}} = \\mathcal{L}_{\\mathrm{p}}(\\mathbf{C}^{\\mathbf{B}},\\hat{\\mathbf{C}}^{\\mathbf{B}}) = (1 - \\lambda_1)\\mathcal{L}_1 + \\lambda_1\\mathcal{L}_{\\mathrm{D - SSIM}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Event Reconstruction Loss. Since an event stream provides blur-free microsecond-level measurements, it can be" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "exploited to further aid fine-grained deblurring. To this end, we formulate an event reconstruction loss by leveraging the relation between brightness and generated events in Eq. 2. Specifically, we synthesize the left-hand side of Eq. 2 by defining the simulated log brightness \\(\\hat{L}(t_i)\\) at time \\(t_i\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.179, + 0.905, + 0.197 + ], + "angle": 0, + "content": "\\[\n\\hat {L} \\left(t _ {i}\\right) = \\log \\left(h \\left(\\operatorname {C R F} \\left(\\hat {C} _ {i}\\right)\\right)\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.206, + 0.905, + 0.297 + ], + "angle": 0, + "content": "where \\(\\hat{C}_i = g_\\theta(p_i)\\) is the sharp image rendered from the 3DGS at camera pose \\(p_i\\) corresponding to time \\(t_i\\), and \\(h(\\cdot)\\) is a luma conversion function implemented by following the BT.601 [2] standard. Following [3], a learnable tone mapping function \\(\\mathrm{CRF}(\\cdot)\\) is adopted to handle possible variations between the RGB and events response function." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.298, + 0.907, + 0.499 + ], + "angle": 0, + "content": "To simulate the brightness change in Eq. 2, we randomly sample two timesteps \\(t_\\alpha\\) and \\(t_\\beta = t_\\alpha + \\Delta t\\) along the camera trajectory and approximate the camera poses corresponding to the sampled timesteps via spherical linear interpolation [46] of the known camera poses \\(\\{\\mathbf{P}_i\\}_{i=0}^{k-1}\\). Given the approximated camera poses at \\(t_\\alpha\\) and \\(t_\\beta\\), we can finally synthesize the brightness change \\(\\Delta \\hat{L}(t_\\alpha, t_\\beta) = \\hat{L}(t_\\beta) - \\hat{L}(t_\\alpha)\\) between time \\(t_\\alpha\\) and \\(t_\\beta\\) by estimating the log brightness from Eq. 6. Considering that the right-hand side of Eq. 2 can serve as ground-truth supervision, we thus formulate the event construction loss \\(\\mathcal{L}_{\\mathrm{ev}}\\) as follows: \\(\\mathcal{L}_{\\mathrm{ev}} = ||\\Delta \\hat{L}(t_\\alpha, t_\\beta) - \\Delta L(t_\\alpha, t_\\beta)||_2^2\\), where \\(L(t_\\alpha, t_\\beta)\\) is the brightness difference observed from the event camera." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.506, + 0.906, + 0.642 + ], + "angle": 0, + "content": "Event Double Integration (EDI) Loss. Although \\(\\mathcal{L}_{\\mathrm{ev}}\\) is capable of producing sharp details to a certain degree, it lacks supervision in areas where events are not triggered. Furthermore, it is not trivial to blindly recover color details from an event response since the only color supervision comes from \\(\\mathcal{L}_{\\mathrm{blur}}\\) [3]. To this end, we propose a novel optimization problem that leverages EDI prior to further constrain the 3DGS in terms of 1) fine-grained details, 2) precise color and 3) regularizing the optimization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Since EDI is defined in the monochrome brightness domain, we first model the EDI based on pixel intensity values. Specifically, we further exploit the composite function of the learnable camera response function \\(\\mathrm{CRF}(\\cdot)\\) followed by \\(h(\\cdot)\\) in Eq. 6 to estimate the brightness of given color images. Given the ground truth blurry image \\(\\mathbf{C^B}\\), the brightness of \\(\\mathbf{C^B}\\), denoted as \\(\\mathbf{I^B}\\), is obtained by \\(\\mathbf{I^B} = h(\\mathrm{CRF}(\\mathbf{C^B}))\\). We then recover the mid-exposure pose of image \\(I\\) from \\(\\mathbf{I^B}\\) using Eq. 4. Based on the latent image \\(I\\), a sharp latent image \\(I_{i}\\) at a randomly sampled timestep \\(t_i\\) can be recovered by warping \\(I\\) to timestep \\(t_i\\) as stated in the initialization step. Given \\(I_{i}\\) as image-level supervision, we synthesize the brightness of color image \\(\\hat{C}_i\\) rendered at the same timestep. Finally, the EDI loss in the monochrome pixel domain is formulated with the photometric error as follows: \\(\\mathcal{L}_{\\mathrm{edi\\_gray}} := \\mathcal{L}_{\\mathrm{p}}(I_i,\\hat{I}_i) = \\mathcal{L}_{\\mathrm{p}}(I_i,h(\\mathrm{CRF}(\\hat{C}_i))),\\) where \\(\\hat{I}_i\\) is the estimated brightness of rendered color" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21742" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.096, + 0.44, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.168, + 0.483, + 0.238 + ], + "angle": 0, + "content": "Figure 3. Cycle consistency among the objective terms. \\(\\mathcal{L}_{\\mathrm{edi\\_simul}}\\) follows the formulation of \\(\\mathcal{L}_{\\mathrm{edi\\_gray}}\\) except for substituting \\(\\mathbf{C}^{\\mathbf{B}}\\) to simulated blurry image \\(\\tilde{\\mathbf{C}}^{\\mathbf{B}}\\) derived from \\(\\mathcal{L}_{\\mathrm{blur}}\\). It completes the cycle among the objective terms, further regularizing the fine-grained deblurring as shown in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.248, + 0.483, + 0.325 + ], + "angle": 0, + "content": "\\(\\hat{C}_i\\). The learnable bright response function \\(\\mathrm{CRF}(\\cdot)\\) allows \\(\\mathcal{L}_{\\mathrm{edi - gray}}\\) to effectively restore fine-grained details for the overall image by naturally filling the gap between the rendered color space and the brightness change captured by the event sensor." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.328, + 0.483, + 0.494 + ], + "angle": 0, + "content": "Although effective in restoring fine-grained details, we empirically find that \\(\\mathrm{CRF}(\\cdot)\\) often distorts color due to the lack of sufficient color supervision as shown in Fig. 5. Inspired by [3], we produce sharp RGB color \\(C\\) by treating each RGB channel of \\(\\mathbf{C^B}\\) as blurry brightness \\(\\mathbf{I^B}\\) in Eq. 4 and applying channel-wise deblurring with EDI. Finally, sharp color \\(C_i\\) at a randomly sampled timestep \\(t_i\\) is obtained by warping \\(C\\) to the corresponding timestep. Given \\(C_i\\) as color supervision, the EDI loss in the RGB space can be formulated as \\(\\mathcal{L}_{\\mathrm{edi\\_color}} = \\mathcal{L}_{\\mathrm{p}}(C_i,\\hat{C}_i)\\), where \\(\\hat{C}_i = g_\\theta (p_i)\\) is the color image rendered at the same timestep as \\(C_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.497, + 0.483, + 0.663 + ], + "angle": 0, + "content": "In addition to the EDI loss described above for image-level supervision, we further leverage EDI for additional regularization. Specifically, we synthesize both sides of Eq. 4 by simply replacing \\(\\mathbf{I}^{\\mathbf{B}}\\) with the simulated blurry brightness \\(\\hat{\\mathbf{I}}^{\\mathbf{B}} = h(\\mathrm{CRF}(\\hat{\\mathbf{C}}^{\\mathbf{B}}))\\), which is the estimated brightness of \\(\\hat{\\mathbf{C}}^{\\mathbf{B}}\\). The EDI simulation loss can then be formulated as \\(\\mathcal{L}_{\\mathrm{edi\\_simul}} = \\mathcal{L}_{\\mathrm{p}}(\\tilde{I}_i,\\hat{I}_i)\\), where \\(\\tilde{I}_i\\) is the sharp supervision obtained from the simulated blurry brightness via EDI processing. As illustrated in Fig. 3, \\(\\mathcal{L}_{\\mathrm{edi\\_simul}}\\) ensures cycle consistency among the objective terms, further facilitating the optimization as a regularization term." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.665, + 0.483, + 0.711 + ], + "angle": 0, + "content": "Finally, the EDI loss is given by combining all of the EDI-based objectives as: \\(\\mathcal{L}_{\\mathrm{edi}} = \\mathcal{L}_{\\mathrm{edi\\_gray}} + \\mathcal{L}_{\\mathrm{edi\\_color}} + \\mathcal{L}_{\\mathrm{edi\\_simul}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Leveraging Diffusion Prior. Although event streams can provide blur-free details, they are susceptible to unnatural artifacts (Fig. 4b-4d) due to the unknown threshold \\(\\Theta\\) in Eq. 2-4 and noise accumulated from the event [28]. Since pretrained diffusion model [40] has already learned the distribution of natural images from large amounts of diverse datasets, it is intuitive to leverage this \"data-driven\" prior in addition to our \"model-based\" losses such as \\(\\mathcal{L}_{\\mathrm{blur}}\\), \\(\\mathcal{L}_{\\mathrm{ev}}\\) and \\(\\mathcal{L}_{\\mathrm{edi}}\\) to further refine the output image more natural. Specifically, we adopt the RSD optimization strategy proposed in [20] to our framework. However, unlike [20], our setting lacks the clean images which are necessary to guide" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "noise prediction of diffusion model as conditional input. A straightforward solution is to utilize the sharp latent image \\(I\\) from EDI processing as a surrogate for the clean image. Unfortunately, we empirically find that the EDI-processed images contain a lot of artifacts that are detrimental to the noise inference of the UNet in the diffusion model. We circumvent this issue by using the ground truth blurry images as an alternative." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.212, + 0.907, + 0.456 + ], + "angle": 0, + "content": "We first render a blurry image \\(\\hat{\\mathbf{C}}^{\\mathbf{B}}\\) from Eq. 3, and encode it to a latent \\(\\mathbf{z}_0 = \\mathcal{E}(\\hat{\\mathbf{C}}^{\\mathbf{B}})\\) via a pretrained VAE encoder \\(\\mathcal{E}\\). Subsequently, we apply the forward process of the diffusion model by introducing noise at timesteps \\(t\\) and \\(t - 1\\) based on a predetermined noising schedule to get two noised latents \\(\\mathbf{z}_t\\) and \\(\\mathbf{z}_{t - 1}\\). The UNet backbone [41] of the pretrained diffusion model takes \\(\\mathbf{z}_t\\) as input and the ground truth blurry image \\(\\mathbf{C}^{\\mathbf{B}}\\) as a condition to predict the noise residual \\(\\epsilon (\\mathbf{z}_t,y,t)\\). Given the predicted noise and \\(\\mathbf{z}_t\\), we then obtain the predicted denoised latent \\(\\hat{\\mathbf{z}}_{t - 1}\\) via the DDPM reverse process. Finally, the RSD loss \\(\\mathcal{L}_{\\mathrm{rsd}}\\) is formulated as an L1 error between \\(\\mathbf{z}_{t - 1}\\) and \\(\\hat{\\mathbf{z}}_{t - 1}\\). Since the input of the diffusion model \\(\\hat{\\mathbf{C}}^{\\mathbf{B}}\\) is obtained by averaging a set of rendered sharp images \\(\\{\\hat{C}\\}_{i = 0}^{n - 1}\\) along the camera trajectory, the supervision from the RSD loss is transferred to each rendered image, making them more natural." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.462, + 0.907, + 0.492 + ], + "angle": 0, + "content": "Training objective. The final objective \\(\\mathcal{L}_{s1}\\) in Stage 1 is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.505, + 0.907, + 0.521 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s} 1} = \\lambda_ {\\text {b l u r}} \\mathcal {L} _ {\\text {b l u r}} + \\lambda_ {\\mathrm {e v}} \\mathcal {L} _ {\\mathrm {e v}} + \\lambda_ {\\text {e d i}} \\mathcal {L} _ {\\text {e d i}} + \\lambda_ {\\text {r s d}} \\mathcal {L} _ {\\text {r s d}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.532, + 0.794, + 0.547 + ], + "angle": 0, + "content": "with the weight \\(\\lambda\\) for each objective term." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.559, + 0.71, + 0.575 + ], + "angle": 0, + "content": "4.2. Stage 2: DiET-GS++" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.907, + 0.87 + ], + "angle": 0, + "content": "Although the RSD optimization in Stage 1 allows DiET-GS to produce more natural and precise color as shown in the 2nd row of Fig. 6, we empirically find that the performance improvement gained falls short of our expectation (cf. Tab. 2). We postulate that this is due to the joint optimization of the event-based loss which are \\(\\mathcal{L}_{\\mathrm{ev}}\\) and \\(\\mathcal{L}_{\\mathrm{edi}}\\) and the RSD loss. Event-based supervision is derived from real-captured event streams, which tend to optimize 3DGS for a specific training scene. In contrast, the RSD loss regularizes rendered images according to the distribution of diverse natural images modeled by a pretrained diffusion model. Jointly optimizing these two constraints reaches an equilibrium between scene-specific details guided by the event-based loss and the prior knowledge of the pretrained diffusion model. Consequently, it is likely to weaken the full effectiveness of \\(\\mathcal{L}_{\\mathrm{rsd}}\\). To this end, we incorporate an additional training step to fully leverage the diffusion prior by introducing extra learnable parameters to DiET-GS. We name the final model trained on Stage 2 as DiET-GS++." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Specifically, we attach a zero-initialized Gaussian feature \\(\\mathbf{f}_{\\mathbf{g}} \\in \\mathbb{R}^{D}\\) for each 3D Gaussian \\(\\mathbf{g}\\) in the pretrained" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21743" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.09, + 0.907, + 0.232 + ], + "angle": 0, + "content": "
    DatasetMetricMPRNet+GS [63]EDI+GS [33]EFNet+GS [48]BAD-NeRF [54]BAD-GS [66]E2NeRF [36]Ev-DeblurNeRF [3]DiET-GS (Ours)DiET-GS++ (Ours)
    EvDeblur -blenderPSNR↑18.7623.6921.0319.7822.2324.5424.7626.6926.23
    SSIM↑0.59120.76940.64130.63810.72130.79930.80380.86070.8478
    LPIPS↓0.35450.13750.32140.24900.20120.16240.17880.10640.1052
    MUSIQ↑24.1255.1335.1323.6332.4347.3142.3857.6759.91
    CLIP-IQA↑0.24130.27510.23140.18880.19930.21290.23000.27690.2960
    EvDeblur -CDAVISPSNR↑27.5132.9530.9728.4729.1231.5432.3034.2233.16
    SSIM↑0.75140.89220.85030.79810.81290.86870.88270.92230.9039
    LPIPS↓0.20130.07900.11420.25260.20120.10590.05710.04960.0502
    MUSIQ↑25.1240.0638.2319.9622.1238.8241.3245.8050.44
    CLIP-IQA↑0.21340.20080.19340.17910.18120.22350.22110.20720.2415
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.234, + 0.907, + 0.263 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons on both synthetic and real-world dataset. The results are the average of every scenes within the dataset. The best results are in bold while the second best results are underscored." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.269, + 0.486, + 0.575 + ], + "angle": 0, + "content": "DiET-GS, where \\(D\\) is the feature dimension. Given a camera pose \\(p\\), we use DiET-GS to render a deblurred image \\(\\hat{C}\\) and a 2D feature map \\(\\mathbf{f}_{2\\mathrm{D}}\\) by accumulating color and \\(\\mathbf{f_g}\\) respectively. After encoding \\(\\hat{C}\\) to the latent \\(\\mathbf{z}_0 = \\mathcal{E}(\\hat{C})\\), we subsequently obtain a refined latent \\(\\mathbf{z}'_0 = \\mathbf{z}_0 + \\mathbf{f}_{2\\mathrm{D}}\\) by combining \\(\\mathbf{z}_0\\) and \\(\\mathbf{f}_{2\\mathrm{D}}\\). Gaussian noise samples at timesteps \\(t\\) and \\(t - 1\\) are then introduced to \\(\\mathbf{z}'_0\\) to get noised latents \\(\\mathbf{z}'_t\\) and \\(\\mathbf{z}'_{t - 1}\\). Finally, given \\(\\hat{C}\\) as conditional input, the UNet backbone of pretrained diffusion model predicts the noise residual of \\(\\mathbf{z}'_t\\) to derive the denoised latent \\(\\hat{\\mathbf{z}}_{t - 1}^{\\prime}\\). The RSD loss between \\(\\mathbf{z}'_{t - 1}\\) and \\(\\hat{\\mathbf{z}}_{t - 1}^{\\prime}\\) is given as the optimization objective of Stage 2. We note that only the Gaussian features \\(\\mathbf{f_g}\\) are trained during Stage 2, while the other parameters of DiET-GS remain fixed to preserve the prior of event streams derived in Stage 1. After optimization, our model can render latent residual \\(\\mathbf{f}_{2\\mathrm{D}}\\) which contains rich edge details directly guided by the pretrained diffusion model. In the inference, the final sharp image \\(\\tilde{C}\\) is obtained by decoding the refined latent \\(\\mathbf{z}_0'\\). Specifically, \\(\\tilde{C} = \\mathcal{D}(\\mathbf{z}_0') = \\mathcal{D}(\\mathbf{f}_{2\\mathrm{D}} + \\mathcal{E}(\\hat{C}))\\), where \\(\\mathcal{D}\\) is pretrained VAE decoder (cf. Fig. 1)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.581, + 0.486, + 0.81 + ], + "angle": 0, + "content": "Discussion. Although Stage 2 of our framework uses RSD loss, we differ from [20] as follows: 1) We exploit the rendering capability of 3DGS to obtain the learnable latent residual \\(\\mathbf{f}_{\\mathrm{2D}}\\). In contrast, [20] manually creates \\(\\mathbf{f}_{\\mathrm{2D}}\\) for all training poses and thus requires further synchronization of NeRF with the trained latent features after the RSD optimization. This synchronization stage is not necessary in our design since DiET-GS++ can directly render the learned latent residual from the Gaussian features \\(\\mathbf{f}_{\\mathrm{g}}\\), thus resulting in a simpler framework. Furthermore, our Stage 2 only takes \\(\\leq 20\\) minutes of training time. 2) Our setting is more challenging than [20] due to the lack of ground truth clean images to condition the diffusion UNet. In this regard, we utilize the image rendered from DiET-GS as conditional input on the diffusion model to further enhance the edges." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.822, + 0.225, + 0.839 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.847, + 0.31, + 0.863 + ], + "angle": 0, + "content": "5.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.87, + 0.486, + 0.903 + ], + "angle": 0, + "content": "We build our framework based on the official code of 3DGS [15] and DiSR-NeRF [20]. Throughout Stage 1," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.27, + 0.909, + 0.378 + ], + "angle": 0, + "content": "we set the loss weights \\(\\lambda_{\\mathrm{blur}} = \\lambda_{\\mathrm{edi}} = \\lambda_{\\mathrm{rsd}} = 1.0\\) and \\(\\lambda_{\\mathrm{ev}} = 0.1\\), and execute 100,000 iterations of training. During Stage 2, training spans 2,000 iterations with a linearly decreasing time schedule of ancestral sampling. The number of poses \\(n\\) estimated for each blurry image in the initialization of 3DGS is set to 9. All experiments are conducted using a single NVIDIA RTX 6000 GPU." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.388, + 0.622, + 0.403 + ], + "angle": 0, + "content": "5.2. Datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.411, + 0.909, + 0.73 + ], + "angle": 0, + "content": "We evaluate our DiET-GS and DiET-GS++ on both synthetic and real-world datasets proposed by [3]. EvDeblur-Blender Dataset is a synthetic dataset that consists of four synthetic scenes derived from DeblurNeRF [29]: factory, pool, tanabata and trolley. Blurry images are provided along with the corresponding synthetic event streams simulated by [38]. Motion blur is produced during a 40ms exposure time with a single fast continuous motion by averaging a set of images rendered at 1000 FPS in linear RGB space. We set \\(\\Theta = 0.2\\) for the event threshold during training in synthetic scenes. The EvDeblur-CDAVIS Dataset contains five real-world scenes, each with 11 to 18 blurry training images paired with corresponding event streams. Color-DAVIS346 [21] is employed to capture both color events and standard frames at \\(346 \\times 260\\) pixel resolution using an RGBG Bayer pattern. A 1000ms exposure time is given to produce motion blur. The event threshold is set to \\(\\Theta = 0.25\\) for both negative and positive events during training in real-world scenes. Both synthetic and real-world datasets include five ground-truth (GT) sharp images captured from both seen and unseen viewpoints for each scene." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.741, + 0.709, + 0.758 + ], + "angle": 0, + "content": "5.3. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Baseline. Our baselines are divided into three categories. The first category is the naive combination of image deblurring methods and 3DGS, where images are initially deblurred and subsequently used as training views for 3DGS. Specifically, an image deblurring method MPR-Net [63], and event-based deblurring methods EDI [33] and EFNet [48] are adopted as baselines. The second category is the frame-only deblurring rendering methods, where only the RGB frames are utilized during training. We select" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21744" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.209, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.157, + 0.208, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.223, + 0.208, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.288, + 0.208, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.357, + 0.186, + 0.368 + ], + "angle": 0, + "content": "(a) Blur Image" + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.089, + 0.324, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.156, + 0.324, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.223, + 0.324, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.288, + 0.323, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.357, + 0.307, + 0.368 + ], + "angle": 0, + "content": "(b) EDI+GS [33]" + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.089, + 0.441, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.156, + 0.441, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.223, + 0.441, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.326, + 0.288, + 0.44, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.341, + 0.357, + 0.423, + 0.368 + ], + "angle": 0, + "content": "(c) E2NeRF [36]" + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.089, + 0.556, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.156, + 0.555, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.223, + 0.555, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.288, + 0.555, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.442, + 0.357, + 0.554, + 0.368 + ], + "angle": 0, + "content": "(d) Ev-DeblurNeRF [3]" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.089, + 0.672, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.156, + 0.672, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.223, + 0.672, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.288, + 0.671, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.566, + 0.357, + 0.66, + 0.368 + ], + "angle": 0, + "content": "(e) DiET-GS (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.089, + 0.788, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.156, + 0.788, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.223, + 0.788, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.288, + 0.787, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.675, + 0.357, + 0.782, + 0.368 + ], + "angle": 0, + "content": "(f) DiET-GS++ (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.089, + 0.903, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.156, + 0.903, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.223, + 0.903, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.288, + 0.902, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.826, + 0.357, + 0.862, + 0.368 + ], + "angle": 0, + "content": "(g) GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.374, + 0.907, + 0.416 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparisons on both synthetic (1st-2nd rows) and real-world (3rd-4th rows) datasets. DiET-GS shows cleaner texture with more accurate details compared to the event-based baselines while DiET-GS++ further enhances these features with sharper definition, achieving the best visual quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.424, + 0.484, + 0.545 + ], + "angle": 0, + "content": "BAD-NeRF [54] and BAD-GS [66] for this category. The third category is event-based deblurring rendering methods, where the RGB frames and event streams are jointly leveraged. We select E2NeRF [36] and Ev-DeblurNeRF [3] as the most recent works in this category with publicly available code. To fairly compare with our methods, we utilize camera poses estimated from COLMAP for all baselines instead of using GT poses provided by the dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.552, + 0.484, + 0.718 + ], + "angle": 0, + "content": "Evaluation Metrics. We employ three standard metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and VGG-based Learned Perceptual Image Patch Similarity (LPIPS) [65] to evaluate the quality of the predicted views on the target views. Since our framework produces rich edge details under the guidance of generative model, different predicted views can be valid for the same blurry image. We thus follow [62] to additionally adopt MUSIQ [14] and CLIP-IQA [52] as No-Reference Image Quality Assessment (NR-IQA) metrics to further evaluate the effectiveness of our framework." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.727, + 0.332, + 0.743 + ], + "angle": 0, + "content": "5.4. Quantitative Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We show the quantitative results in Tab. 1. Our DiET-GS largely outperforms all baselines in PSNR, SSIM, and LPIPS on both synthetic and real-world datasets, showing the effectiveness of our framework to leverage EDI prior. Furthermore, our DiET-GS++ shows significant improvement in MUSIQ and CLIP-IQA metrics, achieving the best results but showing a slight drop in PSNR and SSIM metrics. As already discussed in [20, 62], since DiET-GS++ is solely guided by a pretrained generative model, the resulting images may contain more variation with respect to GT" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.421, + 0.613, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.495, + 0.613, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.57, + 0.599, + 0.583 + ], + "angle": 0, + "content": "(a) \\(\\mathcal{L}_{\\mathrm{edi.gray}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.421, + 0.71, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.495, + 0.708, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.622, + 0.57, + 0.698, + 0.583 + ], + "angle": 0, + "content": "(b) \\(\\mathcal{L}_{\\mathrm{edi\\_color}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.421, + 0.806, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.711, + 0.495, + 0.805, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.57, + 0.78, + 0.581 + ], + "angle": 0, + "content": "(c) Both" + }, + { + "type": "image", + "bbox": [ + 0.808, + 0.421, + 0.903, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.808, + 0.495, + 0.902, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.834, + 0.57, + 0.872, + 0.581 + ], + "angle": 0, + "content": "(d) GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.589, + 0.869, + 0.603 + ], + "angle": 0, + "content": "Figure 5. Ablation study on \\(\\mathcal{L}_{\\mathrm{edi\\_gray}}\\) and \\(\\mathcal{L}_{\\mathrm{edi\\_color}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.611, + 0.907, + 0.717 + ], + "angle": 0, + "content": "samples compared to DiET-GS which is supervised by real-captured data. Nonetheless, DiET-GS++ still substantially improves the visual quality as shown in NR-IQA metrics. Qualitative comparisons in Sec. 5.5 further validate the effectiveness of our DiET-GS++. We also present the user study in the Supplementary material, thoroughly examining the efficacy of leveraging diffusion prior in Stage 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.727, + 0.742, + 0.743 + ], + "angle": 0, + "content": "5.5. Qualitative Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Qualitative comparisons on both Ev-DeblurBlender and Ev-DeblurCDAVIS datasets are shown in Fig. 4, making the following observations. 1) Relying solely on the EDIPreprocessed images to optimize the 3DGS yields unsatisfactory results, introducing numerous artifacts as shown in the 2nd column. While effective at recovering sharp edges, EDI often produces inaccurate details with relatively low visual quality, hindering effective optimization of the 3DGS. This highlights the need for additional objective terms proposed in our framework to further constrain the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21745" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.09, + 0.907, + 0.205 + ], + "angle": 0, + "content": "
    \\( \\mathcal{L}_{\\text{blur}} \\)\\( \\mathcal{L}_{\\text{ev}} \\)\\( \\mathcal{L}_{\\text{edi\\_gray}} \\)\\( \\mathcal{L}_{\\text{edi\\_color}} \\)\\( \\mathcal{L}_{\\text{edi\\_simul}} \\)\\( \\mathcal{L}_{\\text{rsd}} \\)(S1)\\( \\mathcal{L}_{\\text{rsd}} \\)(S2)PSNR↑SSIM↑LPIPS↓MUSIQ↑CLIP-IQA↑
    ✓29.730.77970.216024.770.2031
    ✓✓32.740.84600.117339.690.2776
    ✓✓✓33.910.87610.075244.250.2684
    ✓✓✓34.480.89150.082640.790.2450
    ✓✓✓✓34.920.90330.062443.790.2468
    ✓✓✓✓✓35.040.90680.058745.040.2490
    ✓✓✓✓✓✓34.890.90490.060045.370.2584
    ✓✓✓✓✓✓✓33.860.88460.063451.710.2955
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.33, + 0.21, + 0.668, + 0.224 + ], + "angle": 0, + "content": "Table 2. Ablation study on DiET-GS and DiET-GS++" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.231, + 0.485, + 0.52 + ], + "angle": 0, + "content": "3DGS. 2) We find that our DiET-GS is capable of restoring cleaner textures and clearer edges compared to other baselines. For example, in the 3rd row, other baselines wrongly produce grid patterns on the wall stretched from the left object, while our DiET-GS restores more accurate texture on the same part. Similarly, in the 4th row, color jittering from E2NeRF and artifacts from EDI+GS and Ev-DeblurNeRF are observed, while DiET-GS exhibits cleaner details. The same observation is made for the text elements shown in the 1st and 2nd rows. 3) Our DiET-GS++ further refines the textures and edge details generated from DiET-GS, demonstrating the efficacy of fully leveraging diffusion prior in Stage 2. For instance, grid patterns on the wall in the 3rd row are further mitigated in DiET-GS++, while sharper edges are also observed in both text elements (1st-2nd rows) and non-text elements (4th row) compared to DiET-GS. Overall, our final model DiET-GS++ shows a marked improvement over the other baselines, consistently achieving more precise textures and well-defined details." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.535, + 0.204, + 0.549 + ], + "angle": 0, + "content": "5.6. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.56, + 0.484, + 0.621 + ], + "angle": 0, + "content": "In this section, we present various ablation studies to validate the contributions of each component proposed in our DiET-GS++. All the quantitative evaluations are conducted on a real-world scene, namely, Figures sample." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Event-based Supervision. As shown in the 1st-2nd rows of Tab. 2, simulating brightness change in \\(\\mathcal{L}_{\\mathrm{ev}}\\) improves PSNR by \\(+3.01\\mathrm{dB}\\). Investigation of the EDI prior is conducted on the 3rd-6th rows of Tab. 2 along with qualitative results on Fig. 5 and the 1st row of Fig. 6. As shown in the 1st row of Fig. 5, using only \\(\\mathcal{L}_{\\mathrm{edi\\_gray}}\\) yields sharper details, e.g. tiling on the background, and improves LPIPS scores compared to relying solely on \\(\\mathcal{L}_{\\mathrm{edi\\_color}}\\). However, color artifacts are also introduced due to the lack of sufficient color supervision. In contrast, \\(\\mathcal{L}_{\\mathrm{edi\\_color}}\\) generates accurate color with higher PSNR and SSIM scores, though some details are over-smoothed. Leveraging both \\(\\mathcal{L}_{\\mathrm{edi\\_gray}}\\) and \\(\\mathcal{L}_{\\mathrm{edi\\_color}}\\) yields the best performance on all the PSNR, SSIM, and LPIPS metrics among the 3rd to 5th rows of Tab. 2, achieving both precise color and clear details. The 2nd row of Fig. 5 further shows the synergistic effect between the two constraints, where more well-defined details are produced when they are jointly utilized. Similarly," + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.229, + 0.646, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.305, + 0.631, + 0.317 + ], + "angle": 0, + "content": "(a) wo \\(\\mathcal{L}_{\\mathrm{edi\\_simul}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.318, + 0.646, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.394, + 0.629, + 0.407 + ], + "angle": 0, + "content": "(d) wo \\(\\mathcal{L}_{\\mathrm{rsd}}\\) (S1)" + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.229, + 0.775, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.305, + 0.756, + 0.317 + ], + "angle": 0, + "content": "(b) w \\(\\mathcal{L}_{\\mathrm{edi,simul}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.318, + 0.774, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.668, + 0.394, + 0.753, + 0.406 + ], + "angle": 0, + "content": "(e) w \\(\\mathcal{L}_{\\mathrm{rsd}}\\) (S1)" + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.229, + 0.902, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.82, + 0.305, + 0.857, + 0.317 + ], + "angle": 0, + "content": "(c) GT" + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.318, + 0.902, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.82, + 0.394, + 0.856, + 0.405 + ], + "angle": 0, + "content": "(f) GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.413, + 0.902, + 0.427 + ], + "angle": 0, + "content": "Figure 6. Ablation on \\(\\mathcal{L}_{\\mathrm{edi\\_simul}}\\) (1st row) and \\(\\mathcal{L}_{\\mathrm{rsd}}\\) (S1) (2nd row)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.435, + 0.907, + 0.48 + ], + "angle": 0, + "content": "adding EDI simulation \\(\\mathcal{L}_{\\mathrm{edi\\_simul}}\\) further aids fine-grained deblurring as shown in the red circles of Fig. 6, showing a \\(+0.12\\mathrm{dB}\\) increase in PSNR." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.488, + 0.909, + 0.79 + ], + "angle": 0, + "content": "Diffusion prior. The following observations are made on the inclusion of diffusion prior. 1) The RSD optimization term in Stage 1 denoted as \\(\\mathcal{L}_{\\mathrm{rsd}}\\) (S1) shows slight improvement in MUSIQ and CLIP-IQA by \\(+0.33\\) and \\(+0.0094\\), respectively. 2) \\(\\mathcal{L}_{\\mathrm{rsd}}\\) (S1) can also serve as additional color guidance since the real-captured blurry image with ground-truth color information is given to the diffusion model as conditional input during RSD optimization, further constraining the color of DiET-GS. As shown in the 2nd row of Fig. 6, our DiET-GS++ guided by \\(\\mathcal{L}_{\\mathrm{rsd}}\\) (S1) (6e) generates better color compared to the version that omits RSD optimization in Stage 1 (6d). 4) \\(\\mathcal{L}_{\\mathrm{rsd}}\\) (S1) yields marginal performance improvement in NR-IQA metrics compared to the \\(\\mathcal{L}_{\\mathrm{rsd}}\\) (S2). As discussed in Sec. 4.2, joint optimization of event-based objectives and RSD loss tends to weaken the full effect of diffusion prior. However, considering the first and second findings, we still decide to exploit diffusion prior in Stage 1 and further adopt Stage 2 with additional parameters to fully leverage the guidance from the pretrained diffusion model." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.8, + 0.638, + 0.815 + ], + "angle": 0, + "content": "6. Conclusion." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.907, + 0.903 + ], + "angle": 0, + "content": "DiET-GS is a novel framework that deblurs motion-blurred images using event streams and a pretrained score function. Our two-stage strategy leverages 3DGS with EDI constraints to recover sharp images with accurate color and fine details, while a diffusion prior enhances edge clarity." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21746" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.152 + ], + "angle": 0, + "content": "Acknowledgement. This research / project is supported by the National Research Foundation (NRF) Singapore, under its NRF-Investigatorship Programme (Award ID. NRF-NRFI09-0008)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.164, + 0.188, + 0.18 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.189, + 0.482, + 0.285 + ], + "angle": 0, + "content": "[1] Anish Bhattacharya, Ratnesh Madaan, Fernando Cladera, Sai Vemprala, Rogerio Bonatti, Kostas Daniilidis, Ashish Kapoor, Vijay Kumar, Nikolai Matni, and Jayesh K Gupta. 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Hifa: High-fidelity textto3d with advanced diffusion guidance. arXiv preprint arXiv:2305.18766, 3(5):7, 2023. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21749" + } + ] +] \ No newline at end of file diff --git a/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_origin.pdf b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8e52a89f9e939326759b77d414b2a1df102e1d40 --- /dev/null +++ b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/78e0ff72-d618-47c9-b699-d7747a415149_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f893a72809ab5777ce4c78f7ad9936df9e1ec870d69483777668618f389cb415 +size 1149535 diff --git a/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/full.md b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/full.md new file mode 100644 index 0000000000000000000000000000000000000000..426dbb38cff75ea12a6d589ece8f8e659afef5b8 --- /dev/null +++ b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/full.md @@ -0,0 +1,403 @@ +# DiET-GS: Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting + +Seungjun Lee Gim Hee Lee + +Department of Computer Science, National University of Singapore + +seungjun.lee@u.nus.edu, gimhee.lee@nus.edu.sg + +# Abstract + +Reconstructing sharp 3D representations from blurry multi-view images is a long-standing problem in computer vision. Recent works attempt to enhance high-quality novel view synthesis from the motion blur by leveraging event-based cameras, benefiting from high dynamic range and microsecond temporal resolution. However, they often reach sub-optimal visual quality in either restoring inaccurate color or losing fine-grained details. In this paper, we present DiET-GS, a diffusion prior and event stream-assisted motion deblurring 3DGS. Our framework effectively leverages blur-free event streams and diffusion prior in a two-stage training strategy. Specifically, we introduce the novel framework to constrain 3DGS with event double integral, achieving both accurate color and well-defined details. Additionally, we propose a simple technique to leverage diffusion prior to further enhance the edge details. Qualitative and quantitative results on both synthetic and real-world data demonstrate that our DiET-GS is capable of producing better quality of novel views compared to the existing baselines. Our project page is: DiET-GS.github.io. + +# 1. Introduction + +Novel view synthesis plays an important role in various vision applications such as scene understanding [17, 27, 58], virtual reality [18, 60], image processing [9, 29, 32], etc. To this end, Neural Radiance Fields (NeRF) [31] achieves notable success in generating high-quality novel views by reconstructing implicit 3D representations with a deep neural network. However, it falls short of real-time rendering and efficient training, limiting its application in real-world scenarios. Recently, 3D Gaussian Splatting (3DGS) [15] has emerged as an efficient alternative to NeRF by representing scenes with explicit 3D Gaussian primitives. The explicit representation of 3DGS serves as a lightweight replacement of the implicit neural representations used in NeRF, achieving better training and rendering efficiency as well as visual quality of novel views. + +To enable high-quality 3D reconstructions, both NeRF and 3DGS rely on multi-view images that are perfectly cap- + +![](images/892bdddd09d60564a917d766a9f9f7023cebb13fc29051bde76a50e820f8dc82.jpg) +Figure 1. Given a set of blurry images and corresponding event streams, we propose a novel framework to construct deblurring 3DGS by jointly leveraging the EDI [33] formulation and a pretrained diffusion model as a prior. Our DiET-GS++ enables high-quality novel-view synthesis by recovering precise color and well-defined details from the blurry multi-view images. + +tured and free from any artifact. However, this preliminary condition is often unavailable in the real world. For example, a camera needs prolonged exposure time in a low light environment to allow enough light to reach the sensor for image formation. The camera has to remain absolutely still during this lengthy exposure time. Any camera motion during the capture leads to undesired motion blur. To circumvent this issue, a line of works [19, 29, 34, 54, 66] has attempted to recover sharp 3D representations from blurry multi-view images. Despite the promising potential, it is non-trivial to restore fine-grained details from blurry images alone and thus often leading to sub-optimal visual quality. + +Several recent works have shown the efficacy of event-based cameras, significantly improving motion deblurring in images captured from standard frame-based cameras. Event sensors enable blur-free measurements of brightness changes, benefiting from higher dynamic range and temporal resolution compared to standard cameras. Motivated by this distinct competency, several recent works have explored the potential of recovering sharp 3D representations from event streams. Earlier works [1, 11, 42] focus on utilizing solely event-based data, lacking the capacity to preserve color information. E-NeRF [16] combines blurry + +images into the framework as direct color supervision for 3D NeRF. Nonetheless, the estimated color exhibits blur around the edges since it does not account for the blur formation. $\mathrm{E}^2\mathrm{NeRF}$ and following works [3, 23, 37, 61] explicitly model the blur formation process to further enhance the color and edge details. However, most of these existing works still rely on blurry images alone to recover accurate color, often resulting in unwanted color artifacts. To supplement color guidance, Ev-DeblurNeRF [3] proposes to exploit the explicit relationship of Event Double Integral (EDI) between blurry images and event streams. + +In this paper, we propose DiET-GS, a Diffusion prior and EvenT stream-assisted motion deblurring 3DGS. As illustrated in Fig. 1, our framework comprises two main stages: DiET-GS and DiET-GS++. Our Stage 1: DiET-GS first optimizes the deblurring 3DGS by jointly leveraging the real-captured event streams and the prior knowledge of a pretrained diffusion model. To restore both accurate color and well-defined details, we introduce a novel framework that uses the EDI prior to achieve 1) fine-grained details, 2) accurate color, and 3) regularization. Specifically, in addition to the EDI color guidance proposed by [3], we propose further constraints to recover fine-grained details by modeling EDI in the brightness domain through a learnable camera response function. This learnable approach naturally considers the potential variation between RGB values and pixel intensity, leading to better real-world adaptation and thus effectively recovering intricate details. The EDI constraints from both RGB space [3] and brightness domain enable mutual compensation between color fidelity and fine-grained details, resulting in optimal visual quality. Additionally, we derive a regularization term from the EDI prior to further facilitate the optimization by ensuring the cycle consistency among the objective terms. + +To achieve more natural image refinement, we further incorporate diffusion prior in DiET-GS using the Renoised Score Distillation (RSD) proposed by [20]. Nonetheless, we empirically find that jointly leveraging both priors from real-captured data and a pretrained diffusion model often weakens the full effect of diffusion prior. Consequently, our Stage 2: DiET-GS++ is further introduced to maximize the effect of diffusion guidance by adding extra learnable parameters to each 3D Gaussian in the pretrained DiET-GS. Unlike [20], DiET-GS++ directly renders latent residual from the 3D Gaussians, resulting in a simpler framework to leverage RSD optimization. Finally, resulting images from DiET-GS are further refined by solely relying on diffusion prior while edge details are effectively enhanced. + +Our main contributions are summarized as follows: + +- A novel framework to construct deblurring 3DGS by jointly leveraging event streams and the prior knowledge of a pretrained diffusion model. +- A two-stage train38ing strategy to effectively utilize real- + +captured data and diffusion prior together. Once optimized, our method is capable of recovering well-defined details with accurate color from the input blurry images. + +- Qualitative and quantitative results show that our framework significantly surpasses the existing baselines, achieving the best visual quality. + +# 2. Related Works + +Event-based image deblurring. Recently, event-based cameras have gained significant popularity due to their high dynamic range and microseconds temporal resolution. Several methods have tried to leverage these distinct features to tackle image deblurring. Most notably, event-based double integral (EDI) [33] explicitly models the relationship between event streams and a blurry image jointly captured during the fixed exposure time. Subsequent works follow EDI by fusing the events and RGB frames [7, 48, 49, 59, 64] or using learning-based approaches [12, 50] to further improve visual quality. Another line of works exploits event cameras to recover sharp 3D representations such as NeRF and 3DGS from blurry multi-view images. Earlier works [11, 16, 28, 42] utilize an event generation model [6] to enable sharp novel view synthesis from a fast-moving camera while E-NeRF [16] combines RGB frames to further refine the color. Recent works [3, 23, 36, 37, 61] such as $\mathrm{E}^2\mathrm{NeRF}$ [36] and Ev-DeblurNeRF [3] combine blurry image formation [29] to model the camera motion during the exposure time while Ev-DeblurNeRF [3] further incorporates the EDI prior to provide additional color constraint to 3D NeRF. However, this color constraint often yields over-smoothed details by treating each RGB channel as brightness, which deviates from the real-world setting. In this work, we effectively restore intricate details by introducing a learnable brightness estimation function to the EDI formulation that better adapts to real-world settings. + +Diffusion-based image restoration. Diffusion models have been successfully repurposed for image restoration tasks such as super-resolution (SR) [8, 22, 44, 53, 57, 62], deblurring [5, 39, 56] and JPEG restoration [13, 43]. A comprehensive summary of diffusion-based restoration methods can be found in this recent survey [24]. Diffir [57] is a two-stage training approach that generates a prior representation from a diffusion model to restore an image. DvSR [56] surpasses regression-based methods by leveraging conditional diffusion models. More recently, diffusion prior has begun to be used for restoration of 3D representations such as NeRF. DiSR-NeRF [20] first attempts to leverage a pretrained diffusion model to construct superresolution (SR) NeRF by proposing a renoised variant of score distillation sampling [35], referred to as RSD optimization. In our approach, we propose a simpler framework to adopt RSD optimization compared to [20], further enhancing the edge details of the rendered image. + +![](images/65033698090001786ccd679c2fd1cc8950192022e920be6f390dd7a0547547d5.jpg) +EDI Processing + +![](images/d983686d4e3ace861cbc0513e660741b832734dfdf4b736a6daa4723bb2c20b7.jpg) + +![](images/64bfc19d431ff2b177e60b0d353fcef7514ad9014f1a2df87a3a00714ecda8e4.jpg) +Figure 2. Overall framework of our DiET-GS. Stage 1 (DiET-GS) optimizes the deblurring 3DGS with the event streams and diffusion prior. To preserve accurate color and clean details, we exploit the EDI prior in multiple ways, including color supervision $C$ , guidance for fine-grained details $I$ , and additional regularization $\tilde{I}$ with EDI simulation. Stage 2 (DiET-GS++) is then employed to maximize the effect of diffusion prior by introducing extra learnable parameters $\mathbf{f}_{\mathbf{g}}$ . DiET-GS++ further refines the rendered images from DiET-GS, effectively enhancing rich edge features. More details are explained in Sec. 4.1 and Sec. 4.2. + +![](images/34f5d840dc4d57e3c996b1693950927f200a644ef81872d3f34653ef24eaa773.jpg) +Bright Estimation + +![](images/6cd02ff7a2a8eb11198d771f1a6a0074a7f79e892539924c563439ef3e231585.jpg) +: Pretrained VAE Encoder + +![](images/97b32b63acd91ac906180a8315ef49bdbbcd84990a4814f6256259471ea7c88d.jpg) +: Pretrained Diffusion UNet + +# 3. Preliminaries + +Event Camera Model in Motion Deblurring. Event is triggered when the absolute difference of logarithmic brightness between time $t_j$ and $t_{j-1}$ exceeds $\Theta_{p_j}$ at the same pixel location, where predefined threshold $\Theta_{p_j} \in \mathbb{R}^+$ controls the sensitivity to brightness change. It follows that: + +$$ +\log (I (\mathbf {u}, t _ {j})) - \log (I (\mathbf {u}, t _ {j - 1})) = p _ {j} \cdot \Theta_ {p _ {j}}, \tag {1} +$$ + +where $I(\mathbf{u}, t)$ denotes instantaneous intensity at a pixel $\mathbf{u}$ on a given time $t$ . Polarity $p_j \in \{-1, 1\}$ specifies that either an increase or decrease in brightness. By denoting $\log(I(\mathbf{u}, t))$ as $L(t)$ , Eq. 1 can be generalized to any time interval $[t, t + \Delta t]$ by accumulating event signals as follows: + +$$ +L (t + \Delta t) - L (t) = \Theta \cdot \mathbf {E} (t) = \Theta \int_ {t} ^ {t + \Delta t} p \delta (\tau) \mathrm {d} \tau , \tag {2} +$$ + +where $\delta(\tau)$ is impulse function with unit integral and polarity $p_j$ on threshold $\Theta$ is omitted for brevity. By applying the $\exp(\cdot)$ function to both sides of Eq. 2, we can rewrite $I(t + \Delta t) = I(t) \cdot \exp(\Theta \cdot \mathbf{E}(t))$ to give the relationship between two instantaneous brightness observed at different time steps. + +We note that a blurry image taken from a conventional frame-based camera can be represented as averaging a sequence of sharp images $I$ acquired during the fixed exposure time $\tau$ as follows: + +$$ +\mathbf {I} ^ {\mathbf {B}} (\mathbf {u}, t) = \frac {1}{\tau} \int_ {t - \tau / 2} ^ {t + \tau / 2} I (\mathbf {u}, h) \mathrm {d h}, \tag {3} +$$ + +where $\mathbf{I}^{\mathrm{B}}$ is the blurry image captured during the time interval $\Delta T = [t - \tau /2,t + \tau /2]$ . By combining Eq. 2 and Eq. 3, the connection between the blurry image $\mathbf{I}^{\mathrm{B}}$ and the latent sharp image $I$ at the same timestep $t$ can be constructed as: + +$$ +\mathbf {I} ^ {\mathbf {B}} (\mathbf {u}, t) = \frac {I (\mathbf {u} , t)}{\tau} \int_ {t - \tau / 2} ^ {t + \tau / 2} \exp (\Theta \mathbf {E} (h)) \mathrm {d h}. \tag {4} +$$ + +This relationship between the sharp image, blurry image, and event stream is known as Event-based Double Integral (EDI) [33]. Finally, we can remove motion blur from $\mathbf{I}^{\mathbf{B}}$ by solving for $I(\mathbf{u},t)$ in Eq. 4 under the guidance of the event streams. We propose a novel framework to leverage the EDI prior to constrain 3D Gaussian Splatting in recovering sharp rendered images with better fine-grained details and colors. + +Diffusion Prior in 3D. Score-based diffusion models [47, 51] are a popular type of generative model that learns a score function that represents the gradient of the log probability density with respect to the data. Several works on Text-to-3D generation [4, 10, 25, 26, 30, 35, 51, 55, 67] that leverage the score function of a pretrained diffusion model as a diffusion prior have shown remarkable results. Notably, Score Distillation Sampling (SDS) [35] uses a score function of a diffusion model as an optimization target, providing the gradient from the score function of a pretrained diffusion model to guide differentiable image parametrization $\mathbf{z} = g(\theta)$ without retraining the diffusion model from scratch. In 3D, $\theta$ can be any learnable 3D representation [15, 31] with volume rendering function $g(\cdot)$ . Recently, a variant of SDS has been introduced for image restoration task. Specifically, [20] proposes a renoised variant of SDS called Renoised Score Distillation (RSD) to use diffusion prior for super-resolution in 3D neural representation field. + +Given a data sample $\mathbf{z}_0$ , the forward process obtains the noisy latent $\mathbf{z}_t$ by adding Gaussian noise sample $\epsilon \in \mathcal{N}(0,\mathbf{I})$ at timestep $t$ : $\mathbf{z}_t = \sqrt{\bar{\alpha}_t}\mathbf{z}_0 + \sqrt{1 - \bar{\alpha}_t}\epsilon$ , where $\bar{\alpha}_t$ is timestep-dependent noising coefficient. In the DDPM reverse process, a diffusion U-net is trained to predict the noise $\epsilon (\mathbf{z},y,t)$ to denoise $\mathbf{z}_t$ into $\mathbf{z}_{t-1}$ as follows: $\mathbf{z}_{t-1} = \frac{1}{\sqrt{\alpha_t}} (\mathbf{z}_t - \frac{1 - \alpha_t}{\sqrt{1 - \bar{\alpha}_t}}\epsilon (\mathbf{z}_t,y,t)) + \sigma_t\epsilon$ , where $y$ is the conditioning input and $\sigma_t$ is the standard deviation of Gaussian noise samples. Given the predicted denoised latent $\hat{\mathbf{z}}_{t-1}$ from $\mathbf{z}_t$ and the current noised latent $\mathbf{z}_{t-1}$ at timestep $t-1$ , the ob + +jective of RSD is formulated as $\mathcal{L}_{rsd} = ||\mathbf{z}_{t - 1} - \hat{\mathbf{z}}_{t - 1}||$ In this paper, we propose a simpler framework to leverage RSD optimization compared to [20]. + +# 4. Our Method + +Fig. 2 shows an illustration of our DiET-GS framework which consists of two stages. Stage 1 (cf. Sec. 4.1) constructs a deblurring 3DGS by leveraging an EDI constraint derived from real-captured data and the prior knowledge of a pretrained diffusion model. Stage 2 (cf. Sec. 4.2) further refines the resulting images from Stage 1 by solely relying on diffusion prior to further enhance the edge details. + +# 4.1. Stage 1: DiET-GS + +The goal of Stage 1 is to construct a set of 3D Gaussians from 3D Gaussian Splatting (3DGS) [15] to render sharp images from blurry images and event streams. We name the 3D Gaussians trained in this stage as DiET-GS. + +Initialization. The construction of 3DGS requires point cloud initialization and camera calibrations with structure-from-motion (SfM) [45], which often fail with blurry images. We mitigate this issue by leveraging EDI from Eq. 4 to recover an initial set of sharp images suitable for SfM. Specifically, given an RGB blurry image $\mathbf{C}^{\mathrm{B}}$ and an event stream $\mathbf{E}$ captured during an exposure time $\tau$ , we reconstruct a sharp latent image $I$ from the grayscale of $\mathbf{C}^{\mathrm{B}}$ with EDI. This sharp image $I$ can then be warped to any timestep within the exposure period $[t - \tau /2, t + \tau /2]$ following $I(t + \Delta t) = I(t)\cdot \exp (\Theta \cdot \mathbf{E}(t))$ as shown in Eq. 2. We obtain a set of latent images for each training view by warping the recovered latent image $I$ to each of the $n$ timesteps uniformly sampled from the exposure time. The recovered sharp latent images are subsequently fed into SfM for the estimation of the camera poses and point cloud. + +Blur Reconstruction Loss. Let us denote the estimated camera poses along the approximated camera trajectory of a blurry image $\mathbf{C}_i^{\mathrm{B}}$ as $\mathbf{P}_i = \{p_{ij}\}_{j=0}^{n-1}$ . Given the camera poses $\mathbf{P}_i$ , we simulate the blurry image formation by discretizing Eq. 3 into: + +$$ +\hat {\mathbf {C}} _ {i} ^ {\mathbf {B}} = \frac {1}{n} \sum_ {j = 0} ^ {n - 1} g _ {\theta} \left(p _ {i j}\right), \tag {5} +$$ + +where $g_{\theta}(\cdot)$ is the 3DGS with rendering function and $\hat{\mathbf{C}}^{\mathbf{B}}$ is the estimated motion-blurred image. We can now use the real captured blurry images $\{\mathbf{C}^{\mathbf{B}}\}_{i = 0}^{k - 1}$ to supervise the simulated blurry images $\{\hat{\mathbf{C}}^{\mathbf{B}}\}_{i = 0}^{k - 1}$ , where $k$ is the number of training views. Following the original 3DGS, we thus formulate a blur reconstruction loss to minimize the photometric error $\mathcal{L}_{\mathrm{P}}$ as $\mathcal{L}_{\mathrm{blur}} = \mathcal{L}_{\mathrm{p}}(\mathbf{C}^{\mathbf{B}},\hat{\mathbf{C}}^{\mathbf{B}}) = (1 - \lambda_1)\mathcal{L}_1 + \lambda_1\mathcal{L}_{\mathrm{D - SSIM}}$ . + +Event Reconstruction Loss. Since an event stream provides blur-free microsecond-level measurements, it can be + +exploited to further aid fine-grained deblurring. To this end, we formulate an event reconstruction loss by leveraging the relation between brightness and generated events in Eq. 2. Specifically, we synthesize the left-hand side of Eq. 2 by defining the simulated log brightness $\hat{L}(t_i)$ at time $t_i$ as: + +$$ +\hat {L} \left(t _ {i}\right) = \log \left(h \left(\operatorname {C R F} \left(\hat {C} _ {i}\right)\right)\right) \tag {6} +$$ + +where $\hat{C}_i = g_\theta(p_i)$ is the sharp image rendered from the 3DGS at camera pose $p_i$ corresponding to time $t_i$ , and $h(\cdot)$ is a luma conversion function implemented by following the BT.601 [2] standard. Following [3], a learnable tone mapping function $\mathrm{CRF}(\cdot)$ is adopted to handle possible variations between the RGB and events response function. + +To simulate the brightness change in Eq. 2, we randomly sample two timesteps $t_\alpha$ and $t_\beta = t_\alpha + \Delta t$ along the camera trajectory and approximate the camera poses corresponding to the sampled timesteps via spherical linear interpolation [46] of the known camera poses $\{\mathbf{P}_i\}_{i=0}^{k-1}$ . Given the approximated camera poses at $t_\alpha$ and $t_\beta$ , we can finally synthesize the brightness change $\Delta \hat{L}(t_\alpha, t_\beta) = \hat{L}(t_\beta) - \hat{L}(t_\alpha)$ between time $t_\alpha$ and $t_\beta$ by estimating the log brightness from Eq. 6. Considering that the right-hand side of Eq. 2 can serve as ground-truth supervision, we thus formulate the event construction loss $\mathcal{L}_{\mathrm{ev}}$ as follows: $\mathcal{L}_{\mathrm{ev}} = ||\Delta \hat{L}(t_\alpha, t_\beta) - \Delta L(t_\alpha, t_\beta)||_2^2$ , where $L(t_\alpha, t_\beta)$ is the brightness difference observed from the event camera. + +Event Double Integration (EDI) Loss. Although $\mathcal{L}_{\mathrm{ev}}$ is capable of producing sharp details to a certain degree, it lacks supervision in areas where events are not triggered. Furthermore, it is not trivial to blindly recover color details from an event response since the only color supervision comes from $\mathcal{L}_{\mathrm{blur}}$ [3]. To this end, we propose a novel optimization problem that leverages EDI prior to further constrain the 3DGS in terms of 1) fine-grained details, 2) precise color and 3) regularizing the optimization. + +Since EDI is defined in the monochrome brightness domain, we first model the EDI based on pixel intensity values. Specifically, we further exploit the composite function of the learnable camera response function $\mathrm{CRF}(\cdot)$ followed by $h(\cdot)$ in Eq. 6 to estimate the brightness of given color images. Given the ground truth blurry image $\mathbf{C^B}$ , the brightness of $\mathbf{C^B}$ , denoted as $\mathbf{I^B}$ , is obtained by $\mathbf{I^B} = h(\mathrm{CRF}(\mathbf{C^B}))$ . We then recover the mid-exposure pose of image $I$ from $\mathbf{I^B}$ using Eq. 4. Based on the latent image $I$ , a sharp latent image $I_{i}$ at a randomly sampled timestep $t_i$ can be recovered by warping $I$ to timestep $t_i$ as stated in the initialization step. Given $I_{i}$ as image-level supervision, we synthesize the brightness of color image $\hat{C}_i$ rendered at the same timestep. Finally, the EDI loss in the monochrome pixel domain is formulated with the photometric error as follows: $\mathcal{L}_{\mathrm{edi\_gray}} := \mathcal{L}_{\mathrm{p}}(I_i,\hat{I}_i) = \mathcal{L}_{\mathrm{p}}(I_i,h(\mathrm{CRF}(\hat{C}_i))),$ where $\hat{I}_i$ is the estimated brightness of rendered color + +![](images/2d41cd1ab4265721cc4f15ba2468aac1e08ad850b0604d4f14da63a87fe97e10.jpg) +Figure 3. Cycle consistency among the objective terms. $\mathcal{L}_{\mathrm{edi\_simul}}$ follows the formulation of $\mathcal{L}_{\mathrm{edi\_gray}}$ except for substituting $\mathbf{C}^{\mathbf{B}}$ to simulated blurry image $\tilde{\mathbf{C}}^{\mathbf{B}}$ derived from $\mathcal{L}_{\mathrm{blur}}$ . It completes the cycle among the objective terms, further regularizing the fine-grained deblurring as shown in Fig. 6. + +$\hat{C}_i$ . The learnable bright response function $\mathrm{CRF}(\cdot)$ allows $\mathcal{L}_{\mathrm{edi - gray}}$ to effectively restore fine-grained details for the overall image by naturally filling the gap between the rendered color space and the brightness change captured by the event sensor. + +Although effective in restoring fine-grained details, we empirically find that $\mathrm{CRF}(\cdot)$ often distorts color due to the lack of sufficient color supervision as shown in Fig. 5. Inspired by [3], we produce sharp RGB color $C$ by treating each RGB channel of $\mathbf{C^B}$ as blurry brightness $\mathbf{I^B}$ in Eq. 4 and applying channel-wise deblurring with EDI. Finally, sharp color $C_i$ at a randomly sampled timestep $t_i$ is obtained by warping $C$ to the corresponding timestep. Given $C_i$ as color supervision, the EDI loss in the RGB space can be formulated as $\mathcal{L}_{\mathrm{edi\_color}} = \mathcal{L}_{\mathrm{p}}(C_i,\hat{C}_i)$ , where $\hat{C}_i = g_\theta (p_i)$ is the color image rendered at the same timestep as $C_i$ . + +In addition to the EDI loss described above for image-level supervision, we further leverage EDI for additional regularization. Specifically, we synthesize both sides of Eq. 4 by simply replacing $\mathbf{I}^{\mathbf{B}}$ with the simulated blurry brightness $\hat{\mathbf{I}}^{\mathbf{B}} = h(\mathrm{CRF}(\hat{\mathbf{C}}^{\mathbf{B}}))$ , which is the estimated brightness of $\hat{\mathbf{C}}^{\mathbf{B}}$ . The EDI simulation loss can then be formulated as $\mathcal{L}_{\mathrm{edi\_simul}} = \mathcal{L}_{\mathrm{p}}(\tilde{I}_i,\hat{I}_i)$ , where $\tilde{I}_i$ is the sharp supervision obtained from the simulated blurry brightness via EDI processing. As illustrated in Fig. 3, $\mathcal{L}_{\mathrm{edi\_simul}}$ ensures cycle consistency among the objective terms, further facilitating the optimization as a regularization term. + +Finally, the EDI loss is given by combining all of the EDI-based objectives as: $\mathcal{L}_{\mathrm{edi}} = \mathcal{L}_{\mathrm{edi\_gray}} + \mathcal{L}_{\mathrm{edi\_color}} + \mathcal{L}_{\mathrm{edi\_simul}}$ . + +Leveraging Diffusion Prior. Although event streams can provide blur-free details, they are susceptible to unnatural artifacts (Fig. 4b-4d) due to the unknown threshold $\Theta$ in Eq. 2-4 and noise accumulated from the event [28]. Since pretrained diffusion model [40] has already learned the distribution of natural images from large amounts of diverse datasets, it is intuitive to leverage this "data-driven" prior in addition to our "model-based" losses such as $\mathcal{L}_{\mathrm{blur}}$ , $\mathcal{L}_{\mathrm{ev}}$ and $\mathcal{L}_{\mathrm{edi}}$ to further refine the output image more natural. Specifically, we adopt the RSD optimization strategy proposed in [20] to our framework. However, unlike [20], our setting lacks the clean images which are necessary to guide + +noise prediction of diffusion model as conditional input. A straightforward solution is to utilize the sharp latent image $I$ from EDI processing as a surrogate for the clean image. Unfortunately, we empirically find that the EDI-processed images contain a lot of artifacts that are detrimental to the noise inference of the UNet in the diffusion model. We circumvent this issue by using the ground truth blurry images as an alternative. + +We first render a blurry image $\hat{\mathbf{C}}^{\mathbf{B}}$ from Eq. 3, and encode it to a latent $\mathbf{z}_0 = \mathcal{E}(\hat{\mathbf{C}}^{\mathbf{B}})$ via a pretrained VAE encoder $\mathcal{E}$ . Subsequently, we apply the forward process of the diffusion model by introducing noise at timesteps $t$ and $t - 1$ based on a predetermined noising schedule to get two noised latents $\mathbf{z}_t$ and $\mathbf{z}_{t - 1}$ . The UNet backbone [41] of the pretrained diffusion model takes $\mathbf{z}_t$ as input and the ground truth blurry image $\mathbf{C}^{\mathbf{B}}$ as a condition to predict the noise residual $\epsilon (\mathbf{z}_t,y,t)$ . Given the predicted noise and $\mathbf{z}_t$ , we then obtain the predicted denoised latent $\hat{\mathbf{z}}_{t - 1}$ via the DDPM reverse process. Finally, the RSD loss $\mathcal{L}_{\mathrm{rsd}}$ is formulated as an L1 error between $\mathbf{z}_{t - 1}$ and $\hat{\mathbf{z}}_{t - 1}$ . Since the input of the diffusion model $\hat{\mathbf{C}}^{\mathbf{B}}$ is obtained by averaging a set of rendered sharp images $\{\hat{C}\}_{i = 0}^{n - 1}$ along the camera trajectory, the supervision from the RSD loss is transferred to each rendered image, making them more natural. + +Training objective. The final objective $\mathcal{L}_{s1}$ in Stage 1 is formulated as: + +$$ +\mathcal {L} _ {\mathrm {s} 1} = \lambda_ {\text {b l u r}} \mathcal {L} _ {\text {b l u r}} + \lambda_ {\mathrm {e v}} \mathcal {L} _ {\mathrm {e v}} + \lambda_ {\text {e d i}} \mathcal {L} _ {\text {e d i}} + \lambda_ {\text {r s d}} \mathcal {L} _ {\text {r s d}}, \tag {7} +$$ + +with the weight $\lambda$ for each objective term. + +# 4.2. Stage 2: DiET-GS++ + +Although the RSD optimization in Stage 1 allows DiET-GS to produce more natural and precise color as shown in the 2nd row of Fig. 6, we empirically find that the performance improvement gained falls short of our expectation (cf. Tab. 2). We postulate that this is due to the joint optimization of the event-based loss which are $\mathcal{L}_{\mathrm{ev}}$ and $\mathcal{L}_{\mathrm{edi}}$ and the RSD loss. Event-based supervision is derived from real-captured event streams, which tend to optimize 3DGS for a specific training scene. In contrast, the RSD loss regularizes rendered images according to the distribution of diverse natural images modeled by a pretrained diffusion model. Jointly optimizing these two constraints reaches an equilibrium between scene-specific details guided by the event-based loss and the prior knowledge of the pretrained diffusion model. Consequently, it is likely to weaken the full effectiveness of $\mathcal{L}_{\mathrm{rsd}}$ . To this end, we incorporate an additional training step to fully leverage the diffusion prior by introducing extra learnable parameters to DiET-GS. We name the final model trained on Stage 2 as DiET-GS++. + +Specifically, we attach a zero-initialized Gaussian feature $\mathbf{f}_{\mathbf{g}} \in \mathbb{R}^{D}$ for each 3D Gaussian $\mathbf{g}$ in the pretrained + +
    DatasetMetricMPRNet+GS [63]EDI+GS [33]EFNet+GS [48]BAD-NeRF [54]BAD-GS [66]E2NeRF [36]Ev-DeblurNeRF [3]DiET-GS (Ours)DiET-GS++ (Ours)
    EvDeblur -blenderPSNR↑18.7623.6921.0319.7822.2324.5424.7626.6926.23
    SSIM↑0.59120.76940.64130.63810.72130.79930.80380.86070.8478
    LPIPS↓0.35450.13750.32140.24900.20120.16240.17880.10640.1052
    MUSIQ↑24.1255.1335.1323.6332.4347.3142.3857.6759.91
    CLIP-IQA↑0.24130.27510.23140.18880.19930.21290.23000.27690.2960
    EvDeblur -CDAVISPSNR↑27.5132.9530.9728.4729.1231.5432.3034.2233.16
    SSIM↑0.75140.89220.85030.79810.81290.86870.88270.92230.9039
    LPIPS↓0.20130.07900.11420.25260.20120.10590.05710.04960.0502
    MUSIQ↑25.1240.0638.2319.9622.1238.8241.3245.8050.44
    CLIP-IQA↑0.21340.20080.19340.17910.18120.22350.22110.20720.2415
    + +Table 1. Quantitative comparisons on both synthetic and real-world dataset. The results are the average of every scenes within the dataset. The best results are in bold while the second best results are underscored. + +DiET-GS, where $D$ is the feature dimension. Given a camera pose $p$ , we use DiET-GS to render a deblurred image $\hat{C}$ and a 2D feature map $\mathbf{f}_{2\mathrm{D}}$ by accumulating color and $\mathbf{f_g}$ respectively. After encoding $\hat{C}$ to the latent $\mathbf{z}_0 = \mathcal{E}(\hat{C})$ , we subsequently obtain a refined latent $\mathbf{z}'_0 = \mathbf{z}_0 + \mathbf{f}_{2\mathrm{D}}$ by combining $\mathbf{z}_0$ and $\mathbf{f}_{2\mathrm{D}}$ . Gaussian noise samples at timesteps $t$ and $t - 1$ are then introduced to $\mathbf{z}'_0$ to get noised latents $\mathbf{z}'_t$ and $\mathbf{z}'_{t - 1}$ . Finally, given $\hat{C}$ as conditional input, the UNet backbone of pretrained diffusion model predicts the noise residual of $\mathbf{z}'_t$ to derive the denoised latent $\hat{\mathbf{z}}_{t - 1}^{\prime}$ . The RSD loss between $\mathbf{z}'_{t - 1}$ and $\hat{\mathbf{z}}_{t - 1}^{\prime}$ is given as the optimization objective of Stage 2. We note that only the Gaussian features $\mathbf{f_g}$ are trained during Stage 2, while the other parameters of DiET-GS remain fixed to preserve the prior of event streams derived in Stage 1. After optimization, our model can render latent residual $\mathbf{f}_{2\mathrm{D}}$ which contains rich edge details directly guided by the pretrained diffusion model. In the inference, the final sharp image $\tilde{C}$ is obtained by decoding the refined latent $\mathbf{z}_0'$ . Specifically, $\tilde{C} = \mathcal{D}(\mathbf{z}_0') = \mathcal{D}(\mathbf{f}_{2\mathrm{D}} + \mathcal{E}(\hat{C}))$ , where $\mathcal{D}$ is pretrained VAE decoder (cf. Fig. 1). + +Discussion. Although Stage 2 of our framework uses RSD loss, we differ from [20] as follows: 1) We exploit the rendering capability of 3DGS to obtain the learnable latent residual $\mathbf{f}_{\mathrm{2D}}$ . In contrast, [20] manually creates $\mathbf{f}_{\mathrm{2D}}$ for all training poses and thus requires further synchronization of NeRF with the trained latent features after the RSD optimization. This synchronization stage is not necessary in our design since DiET-GS++ can directly render the learned latent residual from the Gaussian features $\mathbf{f}_{\mathrm{g}}$ , thus resulting in a simpler framework. Furthermore, our Stage 2 only takes $\leq 20$ minutes of training time. 2) Our setting is more challenging than [20] due to the lack of ground truth clean images to condition the diffusion UNet. In this regard, we utilize the image rendered from DiET-GS as conditional input on the diffusion model to further enhance the edges. + +# 5. Experiments + +# 5.1. Implementation Details + +We build our framework based on the official code of 3DGS [15] and DiSR-NeRF [20]. Throughout Stage 1, + +we set the loss weights $\lambda_{\mathrm{blur}} = \lambda_{\mathrm{edi}} = \lambda_{\mathrm{rsd}} = 1.0$ and $\lambda_{\mathrm{ev}} = 0.1$ , and execute 100,000 iterations of training. During Stage 2, training spans 2,000 iterations with a linearly decreasing time schedule of ancestral sampling. The number of poses $n$ estimated for each blurry image in the initialization of 3DGS is set to 9. All experiments are conducted using a single NVIDIA RTX 6000 GPU. + +# 5.2. Datasets. + +We evaluate our DiET-GS and DiET-GS++ on both synthetic and real-world datasets proposed by [3]. EvDeblur-Blender Dataset is a synthetic dataset that consists of four synthetic scenes derived from DeblurNeRF [29]: factory, pool, tanabata and trolley. Blurry images are provided along with the corresponding synthetic event streams simulated by [38]. Motion blur is produced during a 40ms exposure time with a single fast continuous motion by averaging a set of images rendered at 1000 FPS in linear RGB space. We set $\Theta = 0.2$ for the event threshold during training in synthetic scenes. The EvDeblur-CDAVIS Dataset contains five real-world scenes, each with 11 to 18 blurry training images paired with corresponding event streams. Color-DAVIS346 [21] is employed to capture both color events and standard frames at $346 \times 260$ pixel resolution using an RGBG Bayer pattern. A 1000ms exposure time is given to produce motion blur. The event threshold is set to $\Theta = 0.25$ for both negative and positive events during training in real-world scenes. Both synthetic and real-world datasets include five ground-truth (GT) sharp images captured from both seen and unseen viewpoints for each scene. + +# 5.3. Experiment Settings + +Baseline. Our baselines are divided into three categories. The first category is the naive combination of image deblurring methods and 3DGS, where images are initially deblurred and subsequently used as training views for 3DGS. Specifically, an image deblurring method MPR-Net [63], and event-based deblurring methods EDI [33] and EFNet [48] are adopted as baselines. The second category is the frame-only deblurring rendering methods, where only the RGB frames are utilized during training. We select + +![](images/18db0bcf56394b45695e68112e9b2f02bf2b7a2b8f110cb956556ea4e6911036.jpg) + +![](images/d75bba699426bf250492244e9e38c5a8601b32787d3065945fcdf8158cb743b8.jpg) + +![](images/35c5df55eaf3674e61efebf839c93d09ff9507159068024d47ae5a4e7912309c.jpg) + +![](images/00c993a9f60a7db29fb742029df1a33c7b7b7d5ec8a20a4ba326408ce33cda5c.jpg) +(a) Blur Image + +![](images/b85bf3a6b2764149a297a54543bcb52903424bbe2a3e66d47eda6f306d23227d.jpg) + +![](images/38f4161579d4e62c405c1e94e0d76c8acad37124cbfdd1f866b8db45a52f928e.jpg) + +![](images/3165f4747bc5c74d20ecc878b20943a2f510b1c695c4634e01db05b01b5610a3.jpg) + +![](images/7d977c564150d3d120c0b3970258798c1997ad5e9500d8dd88cf9e2599b992b6.jpg) +(b) EDI+GS [33] + +![](images/4a7bd97688d3d372d30c561bfa9be0e398dc2a0607b8dbb23856d13b3f37dae9.jpg) + +![](images/a2fc8a6f06d0c7ae526629a0592daf11de08ae3505e864cd18aed38573a7a7ba.jpg) + +![](images/19c2909228b57ac44ee541a37060b0f943698010e142220e19969972f6158771.jpg) + +![](images/3dbc9cb08e1b6703e05feebc0bdedf0bf4f7f2b9249f3c0c8de3b270ec8ffb54.jpg) +(c) E2NeRF [36] + +![](images/0bbdd9d4b161b22da5f1ccf2ac2512ea6138869735363003a00fdf11d3d55966.jpg) + +![](images/379726381ce18b6cf28d1a1a6fc2dbfaf993eb1e8f842a8b2c30a6b79b444b36.jpg) + +![](images/d60ab7a0dde9eccf5a0ee1864bac511275ef2c38459fc344f0988ff264557b24.jpg) + +![](images/aea6b1c2995d6583f0deebcb76486d8a9233a0c089af09ed12c1a014e024af1b.jpg) +(d) Ev-DeblurNeRF [3] + +![](images/31ac507a35be2b1a2010bd21e8d17b56a8bf0412d52c51f130fc34859446ee15.jpg) + +![](images/1c01bfa4aa97c6f1a7b25cb2dcad3936a72ea30fe4caa8831f6f2ada9f4ccc86.jpg) + +![](images/046ab52cb79eb38976365c80164a6f5d6c40f3eac76e85c448ece5fb3e413771.jpg) + +![](images/496c655ebc6208c7e4dfd626ea17aaca1e692a9cc051a492956bc7e801e8045a.jpg) +(e) DiET-GS (Ours) + +![](images/1f8335adda05b0a6e62aec3625ad585c25f4c9400e95307179a62fd20106de35.jpg) + +![](images/331ca518db6cc6f44f7bec99b766098f6ed97c43f3c2f7816bf15b68018db55b.jpg) + +![](images/ef1ca308be5bda4589226b9daae3c2712bc47b59276792d4a8bbc67ac72a6410.jpg) + +![](images/f8b42523357b072eb3972c3c64bf441173ad84bf388e4deba4edcfa589072370.jpg) +(f) DiET-GS++ (Ours) + +![](images/1d4958a3542074c8f445b7cdca285971590d41837988a33e9d17a0f09667c953.jpg) + +![](images/725694da54b91877b73a35d7d6a0d54b62e0f4faf724d9ba4bee8a64684221a9.jpg) + +![](images/38890f81ebe533655dc1a592ae1f90464c5e11c71dcace2f4698755cd04edb44.jpg) + +![](images/413d5e601bb2076fb5bcc04886c0e6f58902a29782655301fb6385317657dc5a.jpg) +(g) GT + +BAD-NeRF [54] and BAD-GS [66] for this category. The third category is event-based deblurring rendering methods, where the RGB frames and event streams are jointly leveraged. We select E2NeRF [36] and Ev-DeblurNeRF [3] as the most recent works in this category with publicly available code. To fairly compare with our methods, we utilize camera poses estimated from COLMAP for all baselines instead of using GT poses provided by the dataset. + +Evaluation Metrics. We employ three standard metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and VGG-based Learned Perceptual Image Patch Similarity (LPIPS) [65] to evaluate the quality of the predicted views on the target views. Since our framework produces rich edge details under the guidance of generative model, different predicted views can be valid for the same blurry image. We thus follow [62] to additionally adopt MUSIQ [14] and CLIP-IQA [52] as No-Reference Image Quality Assessment (NR-IQA) metrics to further evaluate the effectiveness of our framework. + +# 5.4. Quantitative Comparisons + +We show the quantitative results in Tab. 1. Our DiET-GS largely outperforms all baselines in PSNR, SSIM, and LPIPS on both synthetic and real-world datasets, showing the effectiveness of our framework to leverage EDI prior. Furthermore, our DiET-GS++ shows significant improvement in MUSIQ and CLIP-IQA metrics, achieving the best results but showing a slight drop in PSNR and SSIM metrics. As already discussed in [20, 62], since DiET-GS++ is solely guided by a pretrained generative model, the resulting images may contain more variation with respect to GT + +![](images/540d35b5f48846028b87b3264178622240050ad16da3ed47c65589b6fc4bd71b.jpg) +Figure 4. Qualitative comparisons on both synthetic (1st-2nd rows) and real-world (3rd-4th rows) datasets. DiET-GS shows cleaner texture with more accurate details compared to the event-based baselines while DiET-GS++ further enhances these features with sharper definition, achieving the best visual quality. + +![](images/b9c56c413d40aa8476b9fb003959c6334aceea53b732aefb191d6d2f98a66a52.jpg) +(a) $\mathcal{L}_{\mathrm{edi.gray}}$ + +![](images/119bfa17a1e8c84df2a8781df949d8456cabe8e8516807ef57f7aa2036a6199f.jpg) + +![](images/31b6356b2ad17ceb3b757d96f2868cfbe86737a7d1045cb8a77788d1df808cc8.jpg) +(b) $\mathcal{L}_{\mathrm{edi\_color}}$ + +![](images/1fa8ec8f906f962ea0618a6c2de45bbe355b76057d71b70c49105860127ad743.jpg) + +![](images/3ac5dac25f7523cc4ee74a8379e246ea66ca21d99b8d3600001db2204fda774a.jpg) +(c) Both + +![](images/67de5b9741b90e15d72083bcf471a7db7b4d0be41e5e5740536226d3c5537b85.jpg) + +![](images/49d20b6601bd515593bd614ad4f0df0ba931eeec7cbfe3e9ce6d5efc2b20e36b.jpg) +(d) GT +Figure 5. Ablation study on $\mathcal{L}_{\mathrm{edi\_gray}}$ and $\mathcal{L}_{\mathrm{edi\_color}}$ + +samples compared to DiET-GS which is supervised by real-captured data. Nonetheless, DiET-GS++ still substantially improves the visual quality as shown in NR-IQA metrics. Qualitative comparisons in Sec. 5.5 further validate the effectiveness of our DiET-GS++. We also present the user study in the Supplementary material, thoroughly examining the efficacy of leveraging diffusion prior in Stage 2. + +# 5.5. Qualitative Comparisons + +Qualitative comparisons on both Ev-DeblurBlender and Ev-DeblurCDAVIS datasets are shown in Fig. 4, making the following observations. 1) Relying solely on the EDIPreprocessed images to optimize the 3DGS yields unsatisfactory results, introducing numerous artifacts as shown in the 2nd column. While effective at recovering sharp edges, EDI often produces inaccurate details with relatively low visual quality, hindering effective optimization of the 3DGS. This highlights the need for additional objective terms proposed in our framework to further constrain the + +
    \( \mathcal{L}_{\text{blur}} \)\( \mathcal{L}_{\text{ev}} \)\( \mathcal{L}_{\text{edi\_gray}} \)\( \mathcal{L}_{\text{edi\_color}} \)\( \mathcal{L}_{\text{edi\_simul}} \)\( \mathcal{L}_{\text{rsd}} \)(S1)\( \mathcal{L}_{\text{rsd}} \)(S2)PSNR↑SSIM↑LPIPS↓MUSIQ↑CLIP-IQA↑
    ✓29.730.77970.216024.770.2031
    ✓✓32.740.84600.117339.690.2776
    ✓✓✓33.910.87610.075244.250.2684
    ✓✓✓34.480.89150.082640.790.2450
    ✓✓✓✓34.920.90330.062443.790.2468
    ✓✓✓✓✓35.040.90680.058745.040.2490
    ✓✓✓✓✓✓34.890.90490.060045.370.2584
    ✓✓✓✓✓✓✓33.860.88460.063451.710.2955
    + +Table 2. Ablation study on DiET-GS and DiET-GS++ + +3DGS. 2) We find that our DiET-GS is capable of restoring cleaner textures and clearer edges compared to other baselines. For example, in the 3rd row, other baselines wrongly produce grid patterns on the wall stretched from the left object, while our DiET-GS restores more accurate texture on the same part. Similarly, in the 4th row, color jittering from E2NeRF and artifacts from EDI+GS and Ev-DeblurNeRF are observed, while DiET-GS exhibits cleaner details. The same observation is made for the text elements shown in the 1st and 2nd rows. 3) Our DiET-GS++ further refines the textures and edge details generated from DiET-GS, demonstrating the efficacy of fully leveraging diffusion prior in Stage 2. For instance, grid patterns on the wall in the 3rd row are further mitigated in DiET-GS++, while sharper edges are also observed in both text elements (1st-2nd rows) and non-text elements (4th row) compared to DiET-GS. Overall, our final model DiET-GS++ shows a marked improvement over the other baselines, consistently achieving more precise textures and well-defined details. + +# 5.6. Ablations + +In this section, we present various ablation studies to validate the contributions of each component proposed in our DiET-GS++. All the quantitative evaluations are conducted on a real-world scene, namely, Figures sample. + +Event-based Supervision. As shown in the 1st-2nd rows of Tab. 2, simulating brightness change in $\mathcal{L}_{\mathrm{ev}}$ improves PSNR by $+3.01\mathrm{dB}$ . Investigation of the EDI prior is conducted on the 3rd-6th rows of Tab. 2 along with qualitative results on Fig. 5 and the 1st row of Fig. 6. As shown in the 1st row of Fig. 5, using only $\mathcal{L}_{\mathrm{edi\_gray}}$ yields sharper details, e.g. tiling on the background, and improves LPIPS scores compared to relying solely on $\mathcal{L}_{\mathrm{edi\_color}}$ . However, color artifacts are also introduced due to the lack of sufficient color supervision. In contrast, $\mathcal{L}_{\mathrm{edi\_color}}$ generates accurate color with higher PSNR and SSIM scores, though some details are over-smoothed. Leveraging both $\mathcal{L}_{\mathrm{edi\_gray}}$ and $\mathcal{L}_{\mathrm{edi\_color}}$ yields the best performance on all the PSNR, SSIM, and LPIPS metrics among the 3rd to 5th rows of Tab. 2, achieving both precise color and clear details. The 2nd row of Fig. 5 further shows the synergistic effect between the two constraints, where more well-defined details are produced when they are jointly utilized. Similarly, + +![](images/b8746770b0cfa4dae81a9e57cd75ecbef954bdb5141fa76115a4c5d0d45f3d95.jpg) + +![](images/5f09f4fcd182434cfab8f643d8e87fef59f33f0096788c6d4546691b2f61a8a9.jpg) +(a) wo $\mathcal{L}_{\mathrm{edi\_simul}}$ +(d) wo $\mathcal{L}_{\mathrm{rsd}}$ (S1) +Figure 6. Ablation on $\mathcal{L}_{\mathrm{edi\_simul}}$ (1st row) and $\mathcal{L}_{\mathrm{rsd}}$ (S1) (2nd row). + +![](images/806fd112fc81929d71d268a46f6d44b6392c362f4eeb59c3fd49b1fb8e62e36e.jpg) + +![](images/0e2bda4e5e03e5211fc44370ff90fbb9edeed60f22042808f76d787d34f427a5.jpg) +(b) w $\mathcal{L}_{\mathrm{edi,simul}}$ +(e) w $\mathcal{L}_{\mathrm{rsd}}$ (S1) + +![](images/7a5a4dd6dea09482e2a916e620329b265e176402b8bea7282fdd91a4babee976.jpg) + +![](images/5a1e419e13e83eb31ab3c60f19f01da80814c726043fbe6ea92e5e0fbfb7dd2c.jpg) +(c) GT +(f) GT + +adding EDI simulation $\mathcal{L}_{\mathrm{edi\_simul}}$ further aids fine-grained deblurring as shown in the red circles of Fig. 6, showing a $+0.12\mathrm{dB}$ increase in PSNR. + +Diffusion prior. The following observations are made on the inclusion of diffusion prior. 1) The RSD optimization term in Stage 1 denoted as $\mathcal{L}_{\mathrm{rsd}}$ (S1) shows slight improvement in MUSIQ and CLIP-IQA by $+0.33$ and $+0.0094$ , respectively. 2) $\mathcal{L}_{\mathrm{rsd}}$ (S1) can also serve as additional color guidance since the real-captured blurry image with ground-truth color information is given to the diffusion model as conditional input during RSD optimization, further constraining the color of DiET-GS. As shown in the 2nd row of Fig. 6, our DiET-GS++ guided by $\mathcal{L}_{\mathrm{rsd}}$ (S1) (6e) generates better color compared to the version that omits RSD optimization in Stage 1 (6d). 4) $\mathcal{L}_{\mathrm{rsd}}$ (S1) yields marginal performance improvement in NR-IQA metrics compared to the $\mathcal{L}_{\mathrm{rsd}}$ (S2). As discussed in Sec. 4.2, joint optimization of event-based objectives and RSD loss tends to weaken the full effect of diffusion prior. However, considering the first and second findings, we still decide to exploit diffusion prior in Stage 1 and further adopt Stage 2 with additional parameters to fully leverage the guidance from the pretrained diffusion model. + +# 6. Conclusion. + +DiET-GS is a novel framework that deblurs motion-blurred images using event streams and a pretrained score function. Our two-stage strategy leverages 3DGS with EDI constraints to recover sharp images with accurate color and fine details, while a diffusion prior enhances edge clarity. + +# References + +[1] Anish Bhattacharya, Ratnesh Madaan, Fernando Cladera, Sai Vemprala, Rogerio Bonatti, Kostas Daniilidis, Ashish Kapoor, Vijay Kumar, Nikolai Matni, and Jayesh K Gupta. Evdnerf: Reconstructing event data with dynamic neural radiance fields. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 5846-5855, 2024. 1 +[2] RIR BT et al. 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Hifa: High-fidelity textto3d with advanced diffusion guidance. arXiv preprint arXiv:2305.18766, 3(5):7, 2023. 3 \ No newline at end of file diff --git a/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/images.zip b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8523bf8cad3ea54da99fab46056282f486f5cc72 --- /dev/null +++ b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8baf5ec66b726e2e2075bed6eeef3a97ec8722a3ace5a88ec802aad2c759d2fd +size 560237 diff --git a/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/layout.json b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..de0fd39f2d2f3190635c67c8b8a620b9f30d9bfb --- /dev/null +++ b/2025/DiET-GS_ Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting/layout.json @@ -0,0 +1,13680 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 70, + 102, + 541, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 102, + 541, + 140 + ], + "spans": [ + { + "bbox": [ + 70, + 102, + 541, + 140 + ], + "type": "text", + "content": "DiET-GS: Diffusion Prior and Event Stream-Assisted Motion Deblurring 3D Gaussian Splatting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 225, + 162, + 385, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 225, + 162, + 385, + 175 + ], + "spans": [ + { + "bbox": [ + 225, + 162, + 385, + 175 + ], + "type": "text", + "content": "Seungjun Lee Gim Hee Lee" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 141, + 175, + 468, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 175, + 468, + 190 + ], + "spans": [ + { + "bbox": [ + 141, + 175, + 468, + 190 + ], + "type": "text", + "content": "Department of Computer Science, National University of Singapore" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 183, + 192, + 427, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 183, + 192, + 427, + 203 + ], + "spans": [ + { + "bbox": [ + 183, + 192, + 427, + 203 + ], + "type": "text", + "content": "seungjun.lee@u.nus.edu, gimhee.lee@nus.edu.sg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 216, + 200, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 216, + 200, + 228 + ], + "spans": [ + { + "bbox": [ + 151, + 216, + 200, + 228 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 242, + 296, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 242, + 296, + 482 + ], + "spans": [ + { + "bbox": [ + 55, + 242, + 296, + 482 + ], + "type": "text", + "content": "Reconstructing sharp 3D representations from blurry multi-view images is a long-standing problem in computer vision. Recent works attempt to enhance high-quality novel view synthesis from the motion blur by leveraging event-based cameras, benefiting from high dynamic range and microsecond temporal resolution. However, they often reach sub-optimal visual quality in either restoring inaccurate color or losing fine-grained details. In this paper, we present DiET-GS, a diffusion prior and event stream-assisted motion deblurring 3DGS. Our framework effectively leverages blur-free event streams and diffusion prior in a two-stage training strategy. Specifically, we introduce the novel framework to constrain 3DGS with event double integral, achieving both accurate color and well-defined details. Additionally, we propose a simple technique to leverage diffusion prior to further enhance the edge details. Qualitative and quantitative results on both synthetic and real-world data demonstrate that our DiET-GS is capable of producing better quality of novel views compared to the existing baselines. Our project page is: DiET-GS.github.io." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 487, + 135, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 135, + 499 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 135, + 499 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 509, + 295, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 295, + 687 + ], + "type": "text", + "content": "Novel view synthesis plays an important role in various vision applications such as scene understanding [17, 27, 58], virtual reality [18, 60], image processing [9, 29, 32], etc. To this end, Neural Radiance Fields (NeRF) [31] achieves notable success in generating high-quality novel views by reconstructing implicit 3D representations with a deep neural network. However, it falls short of real-time rendering and efficient training, limiting its application in real-world scenarios. Recently, 3D Gaussian Splatting (3DGS) [15] has emerged as an efficient alternative to NeRF by representing scenes with explicit 3D Gaussian primitives. The explicit representation of 3DGS serves as a lightweight replacement of the implicit neural representations used in NeRF, achieving better training and rendering efficiency as well as visual quality of novel views." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "To enable high-quality 3D reconstructions, both NeRF and 3DGS rely on multi-view images that are perfectly cap-" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 316, + 217, + 553, + 364 + ], + "blocks": [ + { + "bbox": [ + 316, + 217, + 553, + 364 + ], + "lines": [ + { + "bbox": [ + 316, + 217, + 553, + 364 + ], + "spans": [ + { + "bbox": [ + 316, + 217, + 553, + 364 + ], + "type": "image", + "image_path": "892bdddd09d60564a917d766a9f9f7023cebb13fc29051bde76a50e820f8dc82.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 365, + 555, + 432 + ], + "lines": [ + { + "bbox": [ + 313, + 365, + 555, + 432 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 555, + 432 + ], + "type": "text", + "content": "Figure 1. Given a set of blurry images and corresponding event streams, we propose a novel framework to construct deblurring 3DGS by jointly leveraging the EDI [33] formulation and a pretrained diffusion model as a prior. Our DiET-GS++ enables high-quality novel-view synthesis by recovering precise color and well-defined details from the blurry multi-view images." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 436, + 555, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 436, + 555, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 436, + 555, + 581 + ], + "type": "text", + "content": "tured and free from any artifact. However, this preliminary condition is often unavailable in the real world. For example, a camera needs prolonged exposure time in a low light environment to allow enough light to reach the sensor for image formation. The camera has to remain absolutely still during this lengthy exposure time. Any camera motion during the capture leads to undesired motion blur. To circumvent this issue, a line of works [19, 29, 34, 54, 66] has attempted to recover sharp 3D representations from blurry multi-view images. Despite the promising potential, it is non-trivial to restore fine-grained details from blurry images alone and thus often leading to sub-optimal visual quality." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "Several recent works have shown the efficacy of event-based cameras, significantly improving motion deblurring in images captured from standard frame-based cameras. Event sensors enable blur-free measurements of brightness changes, benefiting from higher dynamic range and temporal resolution compared to standard cameras. Motivated by this distinct competency, several recent works have explored the potential of recovering sharp 3D representations from event streams. Earlier works [1, 11, 42] focus on utilizing solely event-based data, lacking the capacity to preserve color information. E-NeRF [16] combines blurry" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21739" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": "images into the framework as direct color supervision for 3D NeRF. Nonetheless, the estimated color exhibits blur around the edges since it does not account for the blur formation. " + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": " and following works [3, 23, 37, 61] explicitly model the blur formation process to further enhance the color and edge details. However, most of these existing works still rely on blurry images alone to recover accurate color, often resulting in unwanted color artifacts. To supplement color guidance, Ev-DeblurNeRF [3] proposes to exploit the explicit relationship of Event Double Integral (EDI) between blurry images and event streams." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 206, + 296, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 206, + 296, + 480 + ], + "spans": [ + { + "bbox": [ + 56, + 206, + 296, + 480 + ], + "type": "text", + "content": "In this paper, we propose DiET-GS, a Diffusion prior and EvenT stream-assisted motion deblurring 3DGS. As illustrated in Fig. 1, our framework comprises two main stages: DiET-GS and DiET-GS++. Our Stage 1: DiET-GS first optimizes the deblurring 3DGS by jointly leveraging the real-captured event streams and the prior knowledge of a pretrained diffusion model. To restore both accurate color and well-defined details, we introduce a novel framework that uses the EDI prior to achieve 1) fine-grained details, 2) accurate color, and 3) regularization. Specifically, in addition to the EDI color guidance proposed by [3], we propose further constraints to recover fine-grained details by modeling EDI in the brightness domain through a learnable camera response function. This learnable approach naturally considers the potential variation between RGB values and pixel intensity, leading to better real-world adaptation and thus effectively recovering intricate details. The EDI constraints from both RGB space [3] and brightness domain enable mutual compensation between color fidelity and fine-grained details, resulting in optimal visual quality. Additionally, we derive a regularization term from the EDI prior to further facilitate the optimization by ensuring the cycle consistency among the objective terms." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 483, + 295, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 295, + 650 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 295, + 650 + ], + "type": "text", + "content": "To achieve more natural image refinement, we further incorporate diffusion prior in DiET-GS using the Renoised Score Distillation (RSD) proposed by [20]. Nonetheless, we empirically find that jointly leveraging both priors from real-captured data and a pretrained diffusion model often weakens the full effect of diffusion prior. Consequently, our Stage 2: DiET-GS++ is further introduced to maximize the effect of diffusion guidance by adding extra learnable parameters to each 3D Gaussian in the pretrained DiET-GS. Unlike [20], DiET-GS++ directly renders latent residual from the 3D Gaussians, resulting in a simpler framework to leverage RSD optimization. Finally, resulting images from DiET-GS are further refined by solely relying on diffusion prior while edge details are effectively enhanced." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 652, + 276, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 652, + 276, + 663 + ], + "spans": [ + { + "bbox": [ + 67, + 652, + 276, + 663 + ], + "type": "text", + "content": "Our main contributions are summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 56, + 665, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 665, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 56, + 665, + 295, + 700 + ], + "type": "text", + "content": "- A novel framework to construct deblurring 3DGS by jointly leveraging event streams and the prior knowledge of a pretrained diffusion model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "content": "- A two-stage train38ing strategy to effectively utilize real-" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 322, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 322, + 72, + 553, + 108 + ], + "type": "text", + "content": "captured data and diffusion prior together. Once optimized, our method is capable of recovering well-defined details with accurate color from the input blurry images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 108, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 108, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 314, + 108, + 553, + 144 + ], + "type": "text", + "content": "- Qualitative and quantitative results show that our framework significantly surpasses the existing baselines, achieving the best visual quality." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 152, + 406, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 152, + 406, + 164 + ], + "spans": [ + { + "bbox": [ + 314, + 152, + 406, + 164 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 172, + 555, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 172, + 555, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 172, + 555, + 495 + ], + "type": "text", + "content": "Event-based image deblurring. Recently, event-based cameras have gained significant popularity due to their high dynamic range and microseconds temporal resolution. Several methods have tried to leverage these distinct features to tackle image deblurring. Most notably, event-based double integral (EDI) [33] explicitly models the relationship between event streams and a blurry image jointly captured during the fixed exposure time. Subsequent works follow EDI by fusing the events and RGB frames [7, 48, 49, 59, 64] or using learning-based approaches [12, 50] to further improve visual quality. Another line of works exploits event cameras to recover sharp 3D representations such as NeRF and 3DGS from blurry multi-view images. Earlier works [11, 16, 28, 42] utilize an event generation model [6] to enable sharp novel view synthesis from a fast-moving camera while E-NeRF [16] combines RGB frames to further refine the color. Recent works [3, 23, 36, 37, 61] such as " + }, + { + "bbox": [ + 313, + 172, + 555, + 495 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 313, + 172, + 555, + 495 + ], + "type": "text", + "content": " [36] and Ev-DeblurNeRF [3] combine blurry image formation [29] to model the camera motion during the exposure time while Ev-DeblurNeRF [3] further incorporates the EDI prior to provide additional color constraint to 3D NeRF. However, this color constraint often yields over-smoothed details by treating each RGB channel as brightness, which deviates from the real-world setting. In this work, we effectively restore intricate details by introducing a learnable brightness estimation function to the EDI formulation that better adapts to real-world settings." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 714 + ], + "type": "text", + "content": "Diffusion-based image restoration. Diffusion models have been successfully repurposed for image restoration tasks such as super-resolution (SR) [8, 22, 44, 53, 57, 62], deblurring [5, 39, 56] and JPEG restoration [13, 43]. A comprehensive summary of diffusion-based restoration methods can be found in this recent survey [24]. Diffir [57] is a two-stage training approach that generates a prior representation from a diffusion model to restore an image. DvSR [56] surpasses regression-based methods by leveraging conditional diffusion models. More recently, diffusion prior has begun to be used for restoration of 3D representations such as NeRF. DiSR-NeRF [20] first attempts to leverage a pretrained diffusion model to construct superresolution (SR) NeRF by proposing a renoised variant of score distillation sampling [35], referred to as RSD optimization. In our approach, we propose a simpler framework to adopt RSD optimization compared to [20], further enhancing the edge details of the rendered image." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21740" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 382, + 201 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 382, + 201 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 382, + 201 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 382, + 201 + ], + "type": "image", + "image_path": "65033698090001786ccd679c2fd1cc8950192022e920be6f390dd7a0547547d5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 74, + 205, + 111, + 212 + ], + "lines": [ + { + "bbox": [ + 74, + 205, + 111, + 212 + ], + "spans": [ + { + "bbox": [ + 74, + 205, + 111, + 212 + ], + "type": "text", + "content": "EDI Processing" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 385, + 70, + 554, + 202 + ], + "blocks": [ + { + "bbox": [ + 385, + 70, + 554, + 202 + ], + "lines": [ + { + "bbox": [ + 385, + 70, + 554, + 202 + ], + "spans": [ + { + "bbox": [ + 385, + 70, + 554, + 202 + ], + "type": "image", + "image_path": "d983686d4e3ace861cbc0513e660741b832734dfdf4b736a6daa4723bb2c20b7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 59, + 203, + 71, + 216 + ], + "blocks": [ + { + "bbox": [ + 59, + 203, + 71, + 216 + ], + "lines": [ + { + "bbox": [ + 59, + 203, + 71, + 216 + ], + "spans": [ + { + "bbox": [ + 59, + 203, + 71, + 216 + ], + "type": "image", + "image_path": "64bfc19d431ff2b177e60b0d353fcef7514ad9014f1a2df87a3a00714ecda8e4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "lines": [ + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "text", + "content": "Figure 2. Overall framework of our DiET-GS. Stage 1 (DiET-GS) optimizes the deblurring 3DGS with the event streams and diffusion prior. To preserve accurate color and clean details, we exploit the EDI prior in multiple ways, including color supervision " + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "text", + "content": ", guidance for fine-grained details " + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "text", + "content": ", and additional regularization " + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "inline_equation", + "content": "\\tilde{I}" + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "text", + "content": " with EDI simulation. Stage 2 (DiET-GS++) is then employed to maximize the effect of diffusion prior by introducing extra learnable parameters " + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathbf{g}}" + }, + { + "bbox": [ + 55, + 221, + 555, + 277 + ], + "type": "text", + "content": ". DiET-GS++ further refines the rendered images from DiET-GS, effectively enhancing rich edge features. More details are explained in Sec. 4.1 and Sec. 4.2." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 118, + 204, + 129, + 216 + ], + "blocks": [ + { + "bbox": [ + 118, + 204, + 129, + 216 + ], + "lines": [ + { + "bbox": [ + 118, + 204, + 129, + 216 + ], + "spans": [ + { + "bbox": [ + 118, + 204, + 129, + 216 + ], + "type": "image", + "image_path": "34f5d840dc4d57e3c996b1693950927f200a644ef81872d3f34653ef24eaa773.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 132, + 205, + 173, + 213 + ], + "lines": [ + { + "bbox": [ + 132, + 205, + 173, + 213 + ], + "spans": [ + { + "bbox": [ + 132, + 205, + 173, + 213 + ], + "type": "text", + "content": "Bright Estimation" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 179, + 203, + 190, + 216 + ], + "blocks": [ + { + "bbox": [ + 179, + 203, + 190, + 216 + ], + "lines": [ + { + "bbox": [ + 179, + 203, + 190, + 216 + ], + "spans": [ + { + "bbox": [ + 179, + 203, + 190, + 216 + ], + "type": "image", + "image_path": "6cd02ff7a2a8eb11198d771f1a6a0074a7f79e892539924c563439ef3e231585.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 194, + 205, + 253, + 212 + ], + "lines": [ + { + "bbox": [ + 194, + 205, + 253, + 212 + ], + "spans": [ + { + "bbox": [ + 194, + 205, + 253, + 212 + ], + "type": "text", + "content": ": Pretrained VAE Encoder" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 260, + 203, + 280, + 216 + ], + "blocks": [ + { + "bbox": [ + 260, + 203, + 280, + 216 + ], + "lines": [ + { + "bbox": [ + 260, + 203, + 280, + 216 + ], + "spans": [ + { + "bbox": [ + 260, + 203, + 280, + 216 + ], + "type": "image", + "image_path": "97b32b63acd91ac906180a8315ef49bdbbcd84990a4814f6256259471ea7c88d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 282, + 205, + 347, + 213 + ], + "lines": [ + { + "bbox": [ + 282, + 205, + 347, + 213 + ], + "spans": [ + { + "bbox": [ + 282, + 205, + 347, + 213 + ], + "type": "text", + "content": ": Pretrained Diffusion UNet" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 287, + 140, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 287, + 140, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 287, + 140, + 300 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "text", + "content": "Event Camera Model in Motion Deblurring. Event is triggered when the absolute difference of logarithmic brightness between time " + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "inline_equation", + "content": "t_j" + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "inline_equation", + "content": "t_{j-1}" + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "text", + "content": " exceeds " + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "inline_equation", + "content": "\\Theta_{p_j}" + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "text", + "content": " at the same pixel location, where predefined threshold " + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "inline_equation", + "content": "\\Theta_{p_j} \\in \\mathbb{R}^+" + }, + { + "bbox": [ + 55, + 307, + 296, + 367 + ], + "type": "text", + "content": " controls the sensitivity to brightness change. It follows that:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 92, + 373, + 295, + 387 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 373, + 295, + 387 + ], + "spans": [ + { + "bbox": [ + 92, + 373, + 295, + 387 + ], + "type": "interline_equation", + "content": "\\log (I (\\mathbf {u}, t _ {j})) - \\log (I (\\mathbf {u}, t _ {j - 1})) = p _ {j} \\cdot \\Theta_ {p _ {j}}, \\tag {1}", + "image_path": "6421fc4bb1207b1027670dea04ff5c14b95cb831c8712e231fee55b9c4e55fdb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "inline_equation", + "content": "I(\\mathbf{u}, t)" + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "content": " denotes instantaneous intensity at a pixel " + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "content": " on a given time " + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "content": ". Polarity " + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "inline_equation", + "content": "p_j \\in \\{-1, 1\\}" + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "content": " specifies that either an increase or decrease in brightness. By denoting " + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "inline_equation", + "content": "\\log(I(\\mathbf{u}, t))" + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "inline_equation", + "content": "L(t)" + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "content": ", Eq. 1 can be generalized to any time interval " + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "inline_equation", + "content": "[t, t + \\Delta t]" + }, + { + "bbox": [ + 55, + 393, + 296, + 453 + ], + "type": "text", + "content": " by accumulating event signals as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 70, + 459, + 295, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 459, + 295, + 484 + ], + "spans": [ + { + "bbox": [ + 70, + 459, + 295, + 484 + ], + "type": "interline_equation", + "content": "L (t + \\Delta t) - L (t) = \\Theta \\cdot \\mathbf {E} (t) = \\Theta \\int_ {t} ^ {t + \\Delta t} p \\delta (\\tau) \\mathrm {d} \\tau , \\tag {2}", + "image_path": "93459dfa8c99a5815b1953dcd915c936e1fb14c12e477ed09d44aa3484e66593.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\delta(\\tau)" + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "text", + "content": " is impulse function with unit integral and polarity " + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "inline_equation", + "content": "p_j" + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "text", + "content": " on threshold " + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "text", + "content": " is omitted for brevity. By applying the " + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "inline_equation", + "content": "\\exp(\\cdot)" + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "text", + "content": " function to both sides of Eq. 2, we can rewrite " + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "inline_equation", + "content": "I(t + \\Delta t) = I(t) \\cdot \\exp(\\Theta \\cdot \\mathbf{E}(t))" + }, + { + "bbox": [ + 55, + 484, + 295, + 555 + ], + "type": "text", + "content": " to give the relationship between two instantaneous brightness observed at different time steps." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 55, + 555, + 296, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 296, + 603 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 296, + 603 + ], + "type": "text", + "content": "We note that a blurry image taken from a conventional frame-based camera can be represented as averaging a sequence of sharp images " + }, + { + "bbox": [ + 55, + 555, + 296, + 603 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 555, + 296, + 603 + ], + "type": "text", + "content": " acquired during the fixed exposure time " + }, + { + "bbox": [ + 55, + 555, + 296, + 603 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 555, + 296, + 603 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 111, + 609, + 295, + 634 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 609, + 295, + 634 + ], + "spans": [ + { + "bbox": [ + 111, + 609, + 295, + 634 + ], + "type": "interline_equation", + "content": "\\mathbf {I} ^ {\\mathbf {B}} (\\mathbf {u}, t) = \\frac {1}{\\tau} \\int_ {t - \\tau / 2} ^ {t + \\tau / 2} I (\\mathbf {u}, h) \\mathrm {d h}, \\tag {3}", + "image_path": "ded065da71b9b02f9fbf8b5ff9e74d5b8a1a9f2df1674b47ddd49c7e5dc55f1a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{\\mathrm{B}}" + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "text", + "content": " is the blurry image captured during the time interval " + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "inline_equation", + "content": "\\Delta T = [t - \\tau /2,t + \\tau /2]" + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "text", + "content": ". By combining Eq. 2 and Eq. 3, the connection between the blurry image " + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{\\mathrm{B}}" + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "text", + "content": " and the latent sharp image " + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "text", + "content": " at the same timestep " + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 635, + 296, + 684 + ], + "type": "text", + "content": " can be constructed as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 90, + 690, + 295, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 690, + 295, + 716 + ], + "spans": [ + { + "bbox": [ + 90, + 690, + 295, + 716 + ], + "type": "interline_equation", + "content": "\\mathbf {I} ^ {\\mathbf {B}} (\\mathbf {u}, t) = \\frac {I (\\mathbf {u} , t)}{\\tau} \\int_ {t - \\tau / 2} ^ {t + \\tau / 2} \\exp (\\Theta \\mathbf {E} (h)) \\mathrm {d h}. \\tag {4}", + "image_path": "46d224b1a1b433f2ce2c01fd4cfaf28762cd62da102e850aedd61c57cc08f270.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 289, + 555, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 555, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 555, + 372 + ], + "type": "text", + "content": "This relationship between the sharp image, blurry image, and event stream is known as Event-based Double Integral (EDI) [33]. Finally, we can remove motion blur from " + }, + { + "bbox": [ + 313, + 289, + 555, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{\\mathbf{B}}" + }, + { + "bbox": [ + 313, + 289, + 555, + 372 + ], + "type": "text", + "content": " by solving for " + }, + { + "bbox": [ + 313, + 289, + 555, + 372 + ], + "type": "inline_equation", + "content": "I(\\mathbf{u},t)" + }, + { + "bbox": [ + 313, + 289, + 555, + 372 + ], + "type": "text", + "content": " in Eq. 4 under the guidance of the event streams. We propose a novel framework to leverage the EDI prior to constrain 3D Gaussian Splatting in recovering sharp rendered images with better fine-grained details and colors." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "type": "text", + "content": "Diffusion Prior in 3D. Score-based diffusion models [47, 51] are a popular type of generative model that learns a score function that represents the gradient of the log probability density with respect to the data. Several works on Text-to-3D generation [4, 10, 25, 26, 30, 35, 51, 55, 67] that leverage the score function of a pretrained diffusion model as a diffusion prior have shown remarkable results. Notably, Score Distillation Sampling (SDS) [35] uses a score function of a diffusion model as an optimization target, providing the gradient from the score function of a pretrained diffusion model to guide differentiable image parametrization " + }, + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = g(\\theta)" + }, + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "type": "text", + "content": " without retraining the diffusion model from scratch. In 3D, " + }, + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "type": "text", + "content": " can be any learnable 3D representation [15, 31] with volume rendering function " + }, + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 313, + 376, + 555, + 591 + ], + "type": "text", + "content": ". Recently, a variant of SDS has been introduced for image restoration task. Specifically, [20] proposes a renoised variant of SDS called Renoised Score Distillation (RSD) to use diffusion prior for super-resolution in 3D neural representation field." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": "Given a data sample " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": ", the forward process obtains the noisy latent " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " by adding Gaussian noise sample " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon \\in \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t = \\sqrt{\\bar{\\alpha}_t}\\mathbf{z}_0 + \\sqrt{1 - \\bar{\\alpha}_t}\\epsilon" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_t" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " is timestep-dependent noising coefficient. In the DDPM reverse process, a diffusion U-net is trained to predict the noise " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon (\\mathbf{z},y,t)" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " to denoise " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t-1}" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " as follows: " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t-1} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{z}_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\bar{\\alpha}_t}}\\epsilon (\\mathbf{z}_t,y,t)) + \\sigma_t\\epsilon" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " is the conditioning input and " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\sigma_t" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " is the standard deviation of Gaussian noise samples. Given the predicted denoised latent " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_{t-1}" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " and the current noised latent " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t-1}" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "inline_equation", + "content": "t-1" + }, + { + "bbox": [ + 313, + 593, + 556, + 713 + ], + "type": "text", + "content": ", the ob" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21741" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 72, + 294, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 72, + 294, + 109 + ], + "spans": [ + { + "bbox": [ + 54, + 72, + 294, + 109 + ], + "type": "text", + "content": "jective of RSD is formulated as " + }, + { + "bbox": [ + 54, + 72, + 294, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rsd} = ||\\mathbf{z}_{t - 1} - \\hat{\\mathbf{z}}_{t - 1}||" + }, + { + "bbox": [ + 54, + 72, + 294, + 109 + ], + "type": "text", + "content": " In this paper, we propose a simpler framework to leverage RSD optimization compared to [20]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 118, + 135, + 131 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 118, + 135, + 131 + ], + "spans": [ + { + "bbox": [ + 55, + 118, + 135, + 131 + ], + "type": "text", + "content": "4. Our Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 138, + 295, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 138, + 295, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 138, + 295, + 224 + ], + "type": "text", + "content": "Fig. 2 shows an illustration of our DiET-GS framework which consists of two stages. Stage 1 (cf. Sec. 4.1) constructs a deblurring 3DGS by leveraging an EDI constraint derived from real-captured data and the prior knowledge of a pretrained diffusion model. Stage 2 (cf. Sec. 4.2) further refines the resulting images from Stage 1 by solely relying on diffusion prior to further enhance the edge details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 228, + 162, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 228, + 162, + 241 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 162, + 241 + ], + "type": "text", + "content": "4.1. Stage 1: DiET-GS" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 247, + 295, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 295, + 295 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 295, + 295 + ], + "type": "text", + "content": "The goal of Stage 1 is to construct a set of 3D Gaussians from 3D Gaussian Splatting (3DGS) [15] to render sharp images from blurry images and event streams. We name the 3D Gaussians trained in this stage as DiET-GS." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": "Initialization. The construction of 3DGS requires point cloud initialization and camera calibrations with structure-from-motion (SfM) [45], which often fail with blurry images. We mitigate this issue by leveraging EDI from Eq. 4 to recover an initial set of sharp images suitable for SfM. Specifically, given an RGB blurry image " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^{\\mathrm{B}}" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " and an event stream " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " captured during an exposure time " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": ", we reconstruct a sharp latent image " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " from the grayscale of " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^{\\mathrm{B}}" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " with EDI. This sharp image " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " can then be warped to any timestep within the exposure period " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "[t - \\tau /2, t + \\tau /2]" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " following " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "I(t + \\Delta t) = I(t)\\cdot \\exp (\\Theta \\cdot \\mathbf{E}(t))" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " as shown in Eq. 2. We obtain a set of latent images for each training view by warping the recovered latent image " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " to each of the " + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 297, + 295, + 490 + ], + "type": "text", + "content": " timesteps uniformly sampled from the exposure time. The recovered sharp latent images are subsequently fed into SfM for the estimation of the camera poses and point cloud." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "text", + "content": "Blur Reconstruction Loss. Let us denote the estimated camera poses along the approximated camera trajectory of a blurry image " + }, + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i^{\\mathrm{B}}" + }, + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i = \\{p_{ij}\\}_{j=0}^{n-1}" + }, + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "text", + "content": ". Given the camera poses " + }, + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i" + }, + { + "bbox": [ + 55, + 491, + 296, + 552 + ], + "type": "text", + "content": ", we simulate the blurry image formation by discretizing Eq. 3 into:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 133, + 558, + 295, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 558, + 295, + 586 + ], + "spans": [ + { + "bbox": [ + 133, + 558, + 295, + 586 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {C}} _ {i} ^ {\\mathbf {B}} = \\frac {1}{n} \\sum_ {j = 0} ^ {n - 1} g _ {\\theta} \\left(p _ {i j}\\right), \\tag {5}", + "image_path": "3ba0f9441822774d93e406145a13a91a232d799a1aba04f6ac88c1a6c9368411.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "inline_equation", + "content": "g_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "content": " is the 3DGS with rendering function and " + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}^{\\mathbf{B}}" + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "content": " is the estimated motion-blurred image. We can now use the real captured blurry images " + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{C}^{\\mathbf{B}}\\}_{i = 0}^{k - 1}" + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "content": " to supervise the simulated blurry images " + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\mathbf{C}}^{\\mathbf{B}}\\}_{i = 0}^{k - 1}" + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "content": " is the number of training views. Following the original 3DGS, we thus formulate a blur reconstruction loss to minimize the photometric error " + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{P}}" + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{blur}} = \\mathcal{L}_{\\mathrm{p}}(\\mathbf{C}^{\\mathbf{B}},\\hat{\\mathbf{C}}^{\\mathbf{B}}) = (1 - \\lambda_1)\\mathcal{L}_1 + \\lambda_1\\mathcal{L}_{\\mathrm{D - SSIM}}" + }, + { + "bbox": [ + 55, + 589, + 295, + 687 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "Event Reconstruction Loss. Since an event stream provides blur-free microsecond-level measurements, it can be" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "exploited to further aid fine-grained deblurring. To this end, we formulate an event reconstruction loss by leveraging the relation between brightness and generated events in Eq. 2. Specifically, we synthesize the left-hand side of Eq. 2 by defining the simulated log brightness " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "\\hat{L}(t_i)" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 382, + 141, + 553, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 141, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 382, + 141, + 553, + 156 + ], + "type": "interline_equation", + "content": "\\hat {L} \\left(t _ {i}\\right) = \\log \\left(h \\left(\\operatorname {C R F} \\left(\\hat {C} _ {i}\\right)\\right)\\right) \\tag {6}", + "image_path": "2ab81aaebac0cc49e4e3af535544f0bad57b1210d8b01276c229a15dfef0ad9e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "inline_equation", + "content": "\\hat{C}_i = g_\\theta(p_i)" + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "text", + "content": " is the sharp image rendered from the 3DGS at camera pose " + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "text", + "content": " corresponding to time " + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "text", + "content": " is a luma conversion function implemented by following the BT.601 [2] standard. Following [3], a learnable tone mapping function " + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "inline_equation", + "content": "\\mathrm{CRF}(\\cdot)" + }, + { + "bbox": [ + 313, + 163, + 553, + 235 + ], + "type": "text", + "content": " is adopted to handle possible variations between the RGB and events response function." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": "To simulate the brightness change in Eq. 2, we randomly sample two timesteps " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "t_\\alpha" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "t_\\beta = t_\\alpha + \\Delta t" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": " along the camera trajectory and approximate the camera poses corresponding to the sampled timesteps via spherical linear interpolation [46] of the known camera poses " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{P}_i\\}_{i=0}^{k-1}" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": ". Given the approximated camera poses at " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "t_\\alpha" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "t_\\beta" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": ", we can finally synthesize the brightness change " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "\\Delta \\hat{L}(t_\\alpha, t_\\beta) = \\hat{L}(t_\\beta) - \\hat{L}(t_\\alpha)" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": " between time " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "t_\\alpha" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "t_\\beta" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": " by estimating the log brightness from Eq. 6. Considering that the right-hand side of Eq. 2 can serve as ground-truth supervision, we thus formulate the event construction loss " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ev}}" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": " as follows: " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ev}} = ||\\Delta \\hat{L}(t_\\alpha, t_\\beta) - \\Delta L(t_\\alpha, t_\\beta)||_2^2" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "inline_equation", + "content": "L(t_\\alpha, t_\\beta)" + }, + { + "bbox": [ + 313, + 236, + 555, + 395 + ], + "type": "text", + "content": " is the brightness difference observed from the event camera." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 400, + 554, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 400, + 554, + 508 + ], + "spans": [ + { + "bbox": [ + 313, + 400, + 554, + 508 + ], + "type": "text", + "content": "Event Double Integration (EDI) Loss. Although " + }, + { + "bbox": [ + 313, + 400, + 554, + 508 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ev}}" + }, + { + "bbox": [ + 313, + 400, + 554, + 508 + ], + "type": "text", + "content": " is capable of producing sharp details to a certain degree, it lacks supervision in areas where events are not triggered. Furthermore, it is not trivial to blindly recover color details from an event response since the only color supervision comes from " + }, + { + "bbox": [ + 313, + 400, + 554, + 508 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{blur}}" + }, + { + "bbox": [ + 313, + 400, + 554, + 508 + ], + "type": "text", + "content": " [3]. To this end, we propose a novel optimization problem that leverages EDI prior to further constrain the 3DGS in terms of 1) fine-grained details, 2) precise color and 3) regularizing the optimization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": "Since EDI is defined in the monochrome brightness domain, we first model the EDI based on pixel intensity values. Specifically, we further exploit the composite function of the learnable camera response function " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{CRF}(\\cdot)" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " followed by " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " in Eq. 6 to estimate the brightness of given color images. Given the ground truth blurry image " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C^B}" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": ", the brightness of " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C^B}" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{I^B}" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": ", is obtained by " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{I^B} = h(\\mathrm{CRF}(\\mathbf{C^B}))" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": ". We then recover the mid-exposure pose of image " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{I^B}" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " using Eq. 4. Based on the latent image " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": ", a sharp latent image " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " at a randomly sampled timestep " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " can be recovered by warping " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " to timestep " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " as stated in the initialization step. Given " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " as image-level supervision, we synthesize the brightness of color image " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\hat{C}_i" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " rendered at the same timestep. Finally, the EDI loss in the monochrome pixel domain is formulated with the photometric error as follows: " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_gray}} := \\mathcal{L}_{\\mathrm{p}}(I_i,\\hat{I}_i) = \\mathcal{L}_{\\mathrm{p}}(I_i,h(\\mathrm{CRF}(\\hat{C}_i)))," + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\hat{I}_i" + }, + { + "bbox": [ + 313, + 509, + 555, + 713 + ], + "type": "text", + "content": " is the estimated brightness of rendered color" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21742" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 76, + 269, + 131 + ], + "blocks": [ + { + "bbox": [ + 78, + 76, + 269, + 131 + ], + "lines": [ + { + "bbox": [ + 78, + 76, + 269, + 131 + ], + "spans": [ + { + "bbox": [ + 78, + 76, + 269, + 131 + ], + "type": "image", + "image_path": "2d41cd1ab4265721cc4f15ba2468aac1e08ad850b0604d4f14da63a87fe97e10.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "lines": [ + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "text", + "content": "Figure 3. Cycle consistency among the objective terms. " + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_simul}}" + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "text", + "content": " follows the formulation of " + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_gray}}" + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "text", + "content": " except for substituting " + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^{\\mathbf{B}}" + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "text", + "content": " to simulated blurry image " + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{C}}^{\\mathbf{B}}" + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "text", + "content": " derived from " + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{blur}}" + }, + { + "bbox": [ + 55, + 133, + 295, + 188 + ], + "type": "text", + "content": ". It completes the cycle among the objective terms, further regularizing the fine-grained deblurring as shown in Fig. 6." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 196, + 295, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 196, + 295, + 257 + ], + "spans": [ + { + "bbox": [ + 55, + 196, + 295, + 257 + ], + "type": "inline_equation", + "content": "\\hat{C}_i" + }, + { + "bbox": [ + 55, + 196, + 295, + 257 + ], + "type": "text", + "content": ". The learnable bright response function " + }, + { + "bbox": [ + 55, + 196, + 295, + 257 + ], + "type": "inline_equation", + "content": "\\mathrm{CRF}(\\cdot)" + }, + { + "bbox": [ + 55, + 196, + 295, + 257 + ], + "type": "text", + "content": " allows " + }, + { + "bbox": [ + 55, + 196, + 295, + 257 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi - gray}}" + }, + { + "bbox": [ + 55, + 196, + 295, + 257 + ], + "type": "text", + "content": " to effectively restore fine-grained details for the overall image by naturally filling the gap between the rendered color space and the brightness change captured by the event sensor." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "spans": [ + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": "Although effective in restoring fine-grained details, we empirically find that " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "\\mathrm{CRF}(\\cdot)" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " often distorts color due to the lack of sufficient color supervision as shown in Fig. 5. Inspired by [3], we produce sharp RGB color " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " by treating each RGB channel of " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "\\mathbf{C^B}" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " as blurry brightness " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "\\mathbf{I^B}" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " in Eq. 4 and applying channel-wise deblurring with EDI. Finally, sharp color " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " at a randomly sampled timestep " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " is obtained by warping " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " to the corresponding timestep. Given " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " as color supervision, the EDI loss in the RGB space can be formulated as " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_color}} = \\mathcal{L}_{\\mathrm{p}}(C_i,\\hat{C}_i)" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "\\hat{C}_i = g_\\theta (p_i)" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": " is the color image rendered at the same timestep as " + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 54, + 259, + 295, + 391 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "spans": [ + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "text", + "content": "In addition to the EDI loss described above for image-level supervision, we further leverage EDI for additional regularization. Specifically, we synthesize both sides of Eq. 4 by simply replacing " + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{\\mathbf{B}}" + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "text", + "content": " with the simulated blurry brightness " + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}^{\\mathbf{B}} = h(\\mathrm{CRF}(\\hat{\\mathbf{C}}^{\\mathbf{B}}))" + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "text", + "content": ", which is the estimated brightness of " + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}^{\\mathbf{B}}" + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "text", + "content": ". The EDI simulation loss can then be formulated as " + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_simul}} = \\mathcal{L}_{\\mathrm{p}}(\\tilde{I}_i,\\hat{I}_i)" + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "inline_equation", + "content": "\\tilde{I}_i" + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "text", + "content": " is the sharp supervision obtained from the simulated blurry brightness via EDI processing. As illustrated in Fig. 3, " + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_simul}}" + }, + { + "bbox": [ + 54, + 393, + 295, + 525 + ], + "type": "text", + "content": " ensures cycle consistency among the objective terms, further facilitating the optimization as a regularization term." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 526, + 295, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 526, + 295, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 526, + 295, + 563 + ], + "type": "text", + "content": "Finally, the EDI loss is given by combining all of the EDI-based objectives as: " + }, + { + "bbox": [ + 55, + 526, + 295, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi}} = \\mathcal{L}_{\\mathrm{edi\\_gray}} + \\mathcal{L}_{\\mathrm{edi\\_color}} + \\mathcal{L}_{\\mathrm{edi\\_simul}}" + }, + { + "bbox": [ + 55, + 526, + 295, + 563 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "text", + "content": "Leveraging Diffusion Prior. Although event streams can provide blur-free details, they are susceptible to unnatural artifacts (Fig. 4b-4d) due to the unknown threshold " + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "text", + "content": " in Eq. 2-4 and noise accumulated from the event [28]. Since pretrained diffusion model [40] has already learned the distribution of natural images from large amounts of diverse datasets, it is intuitive to leverage this \"data-driven\" prior in addition to our \"model-based\" losses such as " + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{blur}}" + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ev}}" + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi}}" + }, + { + "bbox": [ + 55, + 570, + 295, + 714 + ], + "type": "text", + "content": " to further refine the output image more natural. Specifically, we adopt the RSD optimization strategy proposed in [20] to our framework. However, unlike [20], our setting lacks the clean images which are necessary to guide" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": "noise prediction of diffusion model as conditional input. A straightforward solution is to utilize the sharp latent image " + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": " from EDI processing as a surrogate for the clean image. Unfortunately, we empirically find that the EDI-processed images contain a lot of artifacts that are detrimental to the noise inference of the UNet in the diffusion model. We circumvent this issue by using the ground truth blurry images as an alternative." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": "We first render a blurry image " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}^{\\mathbf{B}}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " from Eq. 3, and encode it to a latent " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0 = \\mathcal{E}(\\hat{\\mathbf{C}}^{\\mathbf{B}})" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " via a pretrained VAE encoder " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": ". Subsequently, we apply the forward process of the diffusion model by introducing noise at timesteps " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " based on a predetermined noising schedule to get two noised latents " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t - 1}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": ". The UNet backbone [41] of the pretrained diffusion model takes " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " as input and the ground truth blurry image " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^{\\mathbf{B}}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " as a condition to predict the noise residual " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\epsilon (\\mathbf{z}_t,y,t)" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": ". Given the predicted noise and " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": ", we then obtain the predicted denoised latent " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_{t - 1}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " via the DDPM reverse process. Finally, the RSD loss " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rsd}}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " is formulated as an L1 error between " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t - 1}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_{t - 1}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": ". Since the input of the diffusion model " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}^{\\mathbf{B}}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " is obtained by averaging a set of rendered sharp images " + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "inline_equation", + "content": "\\{\\hat{C}\\}_{i = 0}^{n - 1}" + }, + { + "bbox": [ + 313, + 167, + 555, + 361 + ], + "type": "text", + "content": " along the camera trajectory, the supervision from the RSD loss is transferred to each rendered image, making them more natural." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "type": "text", + "content": "Training objective. The final objective " + }, + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{s1}" + }, + { + "bbox": [ + 313, + 365, + 555, + 389 + ], + "type": "text", + "content": " in Stage 1 is formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 336, + 399, + 555, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 399, + 555, + 412 + ], + "spans": [ + { + "bbox": [ + 336, + 399, + 555, + 412 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s} 1} = \\lambda_ {\\text {b l u r}} \\mathcal {L} _ {\\text {b l u r}} + \\lambda_ {\\mathrm {e v}} \\mathcal {L} _ {\\mathrm {e v}} + \\lambda_ {\\text {e d i}} \\mathcal {L} _ {\\text {e d i}} + \\lambda_ {\\text {r s d}} \\mathcal {L} _ {\\text {r s d}}, \\tag {7}", + "image_path": "17609a5c326887080606ea958e7daae22f8592334bc7dcfbba2fbe35ffec6b13.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 421, + 485, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 421, + 485, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 421, + 485, + 433 + ], + "type": "text", + "content": "with the weight " + }, + { + "bbox": [ + 313, + 421, + 485, + 433 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 421, + 485, + 433 + ], + "type": "text", + "content": " for each objective term." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 442, + 434, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 442, + 434, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 442, + 434, + 455 + ], + "type": "text", + "content": "4.2. Stage 2: DiET-GS++" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": "Although the RSD optimization in Stage 1 allows DiET-GS to produce more natural and precise color as shown in the 2nd row of Fig. 6, we empirically find that the performance improvement gained falls short of our expectation (cf. Tab. 2). We postulate that this is due to the joint optimization of the event-based loss which are " + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ev}}" + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi}}" + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": " and the RSD loss. Event-based supervision is derived from real-captured event streams, which tend to optimize 3DGS for a specific training scene. In contrast, the RSD loss regularizes rendered images according to the distribution of diverse natural images modeled by a pretrained diffusion model. Jointly optimizing these two constraints reaches an equilibrium between scene-specific details guided by the event-based loss and the prior knowledge of the pretrained diffusion model. Consequently, it is likely to weaken the full effectiveness of " + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rsd}}" + }, + { + "bbox": [ + 313, + 461, + 555, + 689 + ], + "type": "text", + "content": ". To this end, we incorporate an additional training step to fully leverage the diffusion prior by introducing extra learnable parameters to DiET-GS. We name the final model trained on Stage 2 as DiET-GS++." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "Specifically, we attach a zero-initialized Gaussian feature " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathbf{g}} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " for each 3D Gaussian " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " in the pretrained" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21743" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 71, + 555, + 183 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 555, + 183 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 555, + 183 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 555, + 183 + ], + "type": "table", + "html": "
    DatasetMetricMPRNet+GS [63]EDI+GS [33]EFNet+GS [48]BAD-NeRF [54]BAD-GS [66]E2NeRF [36]Ev-DeblurNeRF [3]DiET-GS (Ours)DiET-GS++ (Ours)
    EvDeblur -blenderPSNR↑18.7623.6921.0319.7822.2324.5424.7626.6926.23
    SSIM↑0.59120.76940.64130.63810.72130.79930.80380.86070.8478
    LPIPS↓0.35450.13750.32140.24900.20120.16240.17880.10640.1052
    MUSIQ↑24.1255.1335.1323.6332.4347.3142.3857.6759.91
    CLIP-IQA↑0.24130.27510.23140.18880.19930.21290.23000.27690.2960
    EvDeblur -CDAVISPSNR↑27.5132.9530.9728.4729.1231.5432.3034.2233.16
    SSIM↑0.75140.89220.85030.79810.81290.86870.88270.92230.9039
    LPIPS↓0.20130.07900.11420.25260.20120.10590.05710.04960.0502
    MUSIQ↑25.1240.0638.2319.9622.1238.8241.3245.8050.44
    CLIP-IQA↑0.21340.20080.19340.17910.18120.22350.22110.20720.2415
    ", + "image_path": "88d094012b8496ea4a90e6d1ed707d0c03715cbe9e5a770b9307f59b1d3ab761.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 185, + 555, + 208 + ], + "lines": [ + { + "bbox": [ + 55, + 185, + 555, + 208 + ], + "spans": [ + { + "bbox": [ + 55, + 185, + 555, + 208 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons on both synthetic and real-world dataset. The results are the average of every scenes within the dataset. The best results are in bold while the second best results are underscored." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "spans": [ + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": "DiET-GS, where " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " is the feature dimension. Given a camera pose " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": ", we use DiET-GS to render a deblurred image " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " and a 2D feature map " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{2\\mathrm{D}}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " by accumulating color and " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{f_g}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " respectively. After encoding " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " to the latent " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0 = \\mathcal{E}(\\hat{C})" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": ", we subsequently obtain a refined latent " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}'_0 = \\mathbf{z}_0 + \\mathbf{f}_{2\\mathrm{D}}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " by combining " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{2\\mathrm{D}}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": ". Gaussian noise samples at timesteps " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " are then introduced to " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}'_0" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " to get noised latents " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}'_t" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}'_{t - 1}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": ". Finally, given " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " as conditional input, the UNet backbone of pretrained diffusion model predicts the noise residual of " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}'_t" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " to derive the denoised latent " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_{t - 1}^{\\prime}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": ". The RSD loss between " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}'_{t - 1}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_{t - 1}^{\\prime}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " is given as the optimization objective of Stage 2. We note that only the Gaussian features " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{f_g}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " are trained during Stage 2, while the other parameters of DiET-GS remain fixed to preserve the prior of event streams derived in Stage 1. After optimization, our model can render latent residual " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{2\\mathrm{D}}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " which contains rich edge details directly guided by the pretrained diffusion model. In the inference, the final sharp image " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\tilde{C}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " is obtained by decoding the refined latent " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0'" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\tilde{C} = \\mathcal{D}(\\mathbf{z}_0') = \\mathcal{D}(\\mathbf{f}_{2\\mathrm{D}} + \\mathcal{E}(\\hat{C}))" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 54, + 213, + 297, + 455 + ], + "type": "text", + "content": " is pretrained VAE decoder (cf. Fig. 1)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "text", + "content": "Discussion. Although Stage 2 of our framework uses RSD loss, we differ from [20] as follows: 1) We exploit the rendering capability of 3DGS to obtain the learnable latent residual " + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{2D}}" + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "text", + "content": ". In contrast, [20] manually creates " + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{2D}}" + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "text", + "content": " for all training poses and thus requires further synchronization of NeRF with the trained latent features after the RSD optimization. This synchronization stage is not necessary in our design since DiET-GS++ can directly render the learned latent residual from the Gaussian features " + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{g}}" + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "text", + "content": ", thus resulting in a simpler framework. Furthermore, our Stage 2 only takes " + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "inline_equation", + "content": "\\leq 20" + }, + { + "bbox": [ + 55, + 460, + 297, + 641 + ], + "type": "text", + "content": " minutes of training time. 2) Our setting is more challenging than [20] due to the lack of ground truth clean images to condition the diffusion UNet. In this regard, we utilize the image rendered from DiET-GS as conditional input on the diffusion model to further enhance the edges." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 651, + 137, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 651, + 137, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 651, + 137, + 664 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 670, + 189, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 670, + 189, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 670, + 189, + 683 + ], + "type": "text", + "content": "5.1. Implementation Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 297, + 715 + ], + "type": "text", + "content": "We build our framework based on the official code of 3DGS [15] and DiSR-NeRF [20]. Throughout Stage 1," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "type": "text", + "content": "we set the loss weights " + }, + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{blur}} = \\lambda_{\\mathrm{edi}} = \\lambda_{\\mathrm{rsd}} = 1.0" + }, + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{ev}} = 0.1" + }, + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "type": "text", + "content": ", and execute 100,000 iterations of training. During Stage 2, training spans 2,000 iterations with a linearly decreasing time schedule of ancestral sampling. The number of poses " + }, + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 213, + 556, + 299 + ], + "type": "text", + "content": " estimated for each blurry image in the initialization of 3DGS is set to 9. All experiments are conducted using a single NVIDIA RTX 6000 GPU." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 307, + 380, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 307, + 380, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 307, + 380, + 319 + ], + "type": "text", + "content": "5.2. Datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "type": "text", + "content": "We evaluate our DiET-GS and DiET-GS++ on both synthetic and real-world datasets proposed by [3]. EvDeblur-Blender Dataset is a synthetic dataset that consists of four synthetic scenes derived from DeblurNeRF [29]: factory, pool, tanabata and trolley. Blurry images are provided along with the corresponding synthetic event streams simulated by [38]. Motion blur is produced during a 40ms exposure time with a single fast continuous motion by averaging a set of images rendered at 1000 FPS in linear RGB space. We set " + }, + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "type": "inline_equation", + "content": "\\Theta = 0.2" + }, + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "type": "text", + "content": " for the event threshold during training in synthetic scenes. The EvDeblur-CDAVIS Dataset contains five real-world scenes, each with 11 to 18 blurry training images paired with corresponding event streams. Color-DAVIS346 [21] is employed to capture both color events and standard frames at " + }, + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "type": "inline_equation", + "content": "346 \\times 260" + }, + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "type": "text", + "content": " pixel resolution using an RGBG Bayer pattern. A 1000ms exposure time is given to produce motion blur. The event threshold is set to " + }, + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "type": "inline_equation", + "content": "\\Theta = 0.25" + }, + { + "bbox": [ + 313, + 325, + 556, + 578 + ], + "type": "text", + "content": " for both negative and positive events during training in real-world scenes. Both synthetic and real-world datasets include five ground-truth (GT) sharp images captured from both seen and unseen viewpoints for each scene." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 586, + 433, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 586, + 433, + 600 + ], + "spans": [ + { + "bbox": [ + 313, + 586, + 433, + 600 + ], + "type": "text", + "content": "5.3. Experiment Settings" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "Baseline. Our baselines are divided into three categories. The first category is the naive combination of image deblurring methods and 3DGS, where images are initially deblurred and subsequently used as training views for 3DGS. Specifically, an image deblurring method MPR-Net [63], and event-based deblurring methods EDI [33] and EFNet [48] are adopted as baselines. The second category is the frame-only deblurring rendering methods, where only the RGB frames are utilized during training. 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The third category is event-based deblurring rendering methods, where the RGB frames and event streams are jointly leveraged. We select E2NeRF [36] and Ev-DeblurNeRF [3] as the most recent works in this category with publicly available code. To fairly compare with our methods, we utilize camera poses estimated from COLMAP for all baselines instead of using GT poses provided by the dataset." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 55, + 437, + 296, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 296, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 296, + 568 + ], + "type": "text", + "content": "Evaluation Metrics. We employ three standard metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and VGG-based Learned Perceptual Image Patch Similarity (LPIPS) [65] to evaluate the quality of the predicted views on the target views. Since our framework produces rich edge details under the guidance of generative model, different predicted views can be valid for the same blurry image. We thus follow [62] to additionally adopt MUSIQ [14] and CLIP-IQA [52] as No-Reference Image Quality Assessment (NR-IQA) metrics to further evaluate the effectiveness of our framework." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 55, + 575, + 203, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 203, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 203, + 588 + ], + "type": "text", + "content": "5.4. Quantitative Comparisons" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "content": "We show the quantitative results in Tab. 1. Our DiET-GS largely outperforms all baselines in PSNR, SSIM, and LPIPS on both synthetic and real-world datasets, showing the effectiveness of our framework to leverage EDI prior. Furthermore, our DiET-GS++ shows significant improvement in MUSIQ and CLIP-IQA metrics, achieving the best results but showing a slight drop in PSNR and SSIM metrics. As already discussed in [20, 62], since DiET-GS++ is solely guided by a pretrained generative model, the resulting images may contain more variation with respect to GT" + } + ] + } + ], + "index": 39 + }, + { + "type": "image", + "bbox": [ + 317, + 333, + 375, + 392 + ], + "blocks": [ + { + "bbox": [ + 55, + 296, + 555, + 329 + ], + "lines": [ + { + "bbox": [ + 55, + 296, + 555, + 329 + ], + "spans": [ + { + "bbox": [ + 55, + 296, + 555, + 329 + ], + "type": "text", + "content": "Figure 4. Qualitative comparisons on both synthetic (1st-2nd rows) and real-world (3rd-4th rows) datasets. 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We also present the user study in the Supplementary material, thoroughly examining the efficacy of leveraging diffusion prior in Stage 2." + } + ] + } + ], + "index": 53 + }, + { + "bbox": [ + 313, + 575, + 454, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 575, + 454, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 575, + 454, + 588 + ], + "type": "text", + "content": "5.5. 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For example, in the 3rd row, other baselines wrongly produce grid patterns on the wall stretched from the left object, while our DiET-GS restores more accurate texture on the same part. Similarly, in the 4th row, color jittering from E2NeRF and artifacts from EDI+GS and Ev-DeblurNeRF are observed, while DiET-GS exhibits cleaner details. The same observation is made for the text elements shown in the 1st and 2nd rows. 3) Our DiET-GS++ further refines the textures and edge details generated from DiET-GS, demonstrating the efficacy of fully leveraging diffusion prior in Stage 2. For instance, grid patterns on the wall in the 3rd row are further mitigated in DiET-GS++, while sharper edges are also observed in both text elements (1st-2nd rows) and non-text elements (4th row) compared to DiET-GS. Overall, our final model DiET-GS++ shows a marked improvement over the other baselines, consistently achieving more precise textures and well-defined details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 423, + 124, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 423, + 124, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 423, + 124, + 434 + ], + "type": "text", + "content": "5.6. Ablations" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 443, + 296, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 443, + 296, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 296, + 491 + ], + "type": "text", + "content": "In this section, we present various ablation studies to validate the contributions of each component proposed in our DiET-GS++. All the quantitative evaluations are conducted on a real-world scene, namely, Figures sample." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "content": "Event-based Supervision. As shown in the 1st-2nd rows of Tab. 2, simulating brightness change in " + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ev}}" + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "content": " improves PSNR by " + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "inline_equation", + "content": "+3.01\\mathrm{dB}" + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "content": ". Investigation of the EDI prior is conducted on the 3rd-6th rows of Tab. 2 along with qualitative results on Fig. 5 and the 1st row of Fig. 6. As shown in the 1st row of Fig. 5, using only " + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_gray}}" + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "content": " yields sharper details, e.g. tiling on the background, and improves LPIPS scores compared to relying solely on " + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_color}}" + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "content": ". However, color artifacts are also introduced due to the lack of sufficient color supervision. In contrast, " + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_color}}" + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "content": " generates accurate color with higher PSNR and SSIM scores, though some details are over-smoothed. Leveraging both " + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_gray}}" + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{edi\\_color}}" + }, + { + "bbox": [ + 55, + 498, + 296, + 714 + ], + "type": "text", + "content": " yields the best performance on all the PSNR, SSIM, and LPIPS metrics among the 3rd to 5th rows of Tab. 2, achieving both precise color and clear details. The 2nd row of Fig. 5 further shows the synergistic effect between the two constraints, where more well-defined details are produced when they are jointly utilized. 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The following observations are made on the inclusion of diffusion prior. 1) The RSD optimization term in Stage 1 denoted as " + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rsd}}" + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "text", + "content": " (S1) shows slight improvement in MUSIQ and CLIP-IQA by " + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "inline_equation", + "content": "+0.33" + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "inline_equation", + "content": "+0.0094" + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "text", + "content": ", respectively. 2) " + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rsd}}" + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "text", + "content": " (S1) can also serve as additional color guidance since the real-captured blurry image with ground-truth color information is given to the diffusion model as conditional input during RSD optimization, further constraining the color of DiET-GS. As shown in the 2nd row of Fig. 6, our DiET-GS++ guided by " + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rsd}}" + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "text", + "content": " (S1) (6e) generates better color compared to the version that omits RSD optimization in Stage 1 (6d). 4) " + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rsd}}" + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "text", + "content": " (S1) yields marginal performance improvement in NR-IQA metrics compared to the " + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rsd}}" + }, + { + "bbox": [ + 313, + 386, + 556, + 625 + ], + "type": "text", + "content": " (S2). As discussed in Sec. 4.2, joint optimization of event-based objectives and RSD loss tends to weaken the full effect of diffusion prior. However, considering the first and second findings, we still decide to exploit diffusion prior in Stage 1 and further adopt Stage 2 with additional parameters to fully leverage the guidance from the pretrained diffusion model." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 633, + 390, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 633, + 390, + 645 + ], + "spans": [ + { + "bbox": [ + 313, + 633, + 390, + 645 + ], + "type": "text", + "content": "6. Conclusion." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 653, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 555, + 715 + ], + "type": "text", + "content": "DiET-GS is a novel framework that deblurs motion-blurred images using event streams and a pretrained score function. 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Hifa: High-fidelity textto3d with advanced diffusion guidance. arXiv preprint arXiv:2305.18766, 3(5):7, 2023. 3" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21749" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_content_list.json b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..aaff95e43c650e2627f618b8fc05fa23e3b23c5c --- /dev/null +++ b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_content_list.json @@ -0,0 +1,1638 @@ +[ + { + "type": "text", + "text": "DiGIT: Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer", + "text_level": 1, + "bbox": [ + 102, + 126, + 893, + 171 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ho-Joong Kim Yearang Lee Jung-Ho Hong Seong-Whan Lee\\*", + "bbox": [ + 194, + 194, + 794, + 213 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dept. of Artificial Intelligence, Korea University, Seoul, Korea", + "bbox": [ + 290, + 217, + 705, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{hojoong_kim, yr_lee, jungho-hong, sw.lee}@korea.ac.kr", + "bbox": [ + 261, + 234, + 730, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 276, + 326, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we examine a key limitation in query-based detectors for temporal action detection (TAD), which arises from their direct adaptation of originally designed architectures for object detection. Despite the effectiveness of the existing models, they struggle to fully address the unique challenges of TAD, such as the redundancy in multiscale features and the limited ability to capture sufficient temporal context. To address these issues, we propose a multi-dilated gated encoder and central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). Our approach replaces the existing encoder that consists of multi-scale deformable attention and feedforward network with our multi-dilated gated encoder. Our proposed encoder reduces the redundant information caused by multi-level features while maintaining the ability to capture fine-grained and long-range temporal information. Furthermore, we introduce a central-adjacent region integrated decoder that leverages a more comprehensive sampling strategy for deformable cross-attention to capture the essential information. Extensive experiments demonstrate that DiGIT achieves state-of-the-art performance on THUMOS14, ActivityNet v1.3, and HACS-Segment. Code is available at: https://github.com/Dotori-HJ/DGIT", + "bbox": [ + 86, + 308, + 485, + 656 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 671, + 220, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Temporal action detection (TAD) is crucial for video understanding and supports a wide range of real-world applications, including video surveillance, summarization, and retrieval. TAD aims to detect action instances within untrimmed videos by identifying action classes along with their start and end times. The most existing TAD methods [15, 27, 36, 47] are a snippet-based approach, which utilizes pre-extracted features to address long durations. This approach does not require the computational cost for the backbone network at the detection stage, enabling the detector to address a comprehensive length of features at once. The existing methods can be divided into three approaches:", + "bbox": [ + 89, + 696, + 483, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ae2df80e0561713561f32837f3635470b83e3e5403c32ffca110f5f352c3b18a.jpg", + "image_caption": [ + "Figure 1. Convergence curves with InternVideo2 [41] features on THUMOS14 [14]. Our method boosts the previous query-based detectors like TE-TAD [15] and TadTR [27]." + ], + "image_footnote": [], + "bbox": [ + 545, + 277, + 874, + 470 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "anchor-based [3, 21, 22, 29, 43, 49], anchor-free [6, 8, 20, 34, 36, 44, 47], and query-based [15, 27, 35, 37, 53].", + "bbox": [ + 511, + 522, + 903, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Query-based detectors, inspired by DETR [4], have attracted interest because of their potential to eliminate reliance on hand-crafted components, such as the sliding window and non-maximum suppression (NMS). This capability derives from their adoption of a set-prediction mechanism, which enables an end-to-end detection process through a one-to-one matching paradigm. Among them, TE-TAD [15] enables a full end-to-end detection process by reformulating the coordinate representation based on recent DETR-based network architectures, such as multiscale deformable attention [52]. However, despite these advancements, query-based detectors still rely on originally designed architectures for object detection, which is not fully suited to addressing the unique challenges of TAD. We identify two limitations within the encoder and decoder structures of existing query-based TAD models. (1) In the encoder, simply utilizing single-scale [27, 53] feature or multi-scale [15] features fails to extract the meaningful features needed to capture the diverse temporal scale information and distinct feature representations. (2) In the decoder, the deformable cross-attention mechanism focuses on the central regions of reference points, overlooking surrounding areas essential for accurately detecting the action instances.", + "bbox": [ + 511, + 553, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 114, + 887, + 240, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24286", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the encoder, existing query-based detectors employ either single-scale [27, 53] or multi-scale [15] features, but both approaches have inherent limitations. The single-scale approach [27, 53] processes feature at a single resolution throughout the encoder and decoder, intuitively restricting the model to capture varying durations. The multi-scale approach [15] combines features across multiple resolutions, enhancing the ability of the model to detect different lengths of actions by aggregating broader contextual information. However, despite the advantage of the multi-scale approach, it struggles to capture distinct feature representations at each level, resulting in highly correlated features across scales. Fig. 2 illustrates this issue by comparing layer-wise CKA [31] similarities on the pre-encoder and post-encoder features between an object detection model (DINO [48]) and a TAD model (TE-TAD [15]). As shown in Fig. 2 on the left, the pre-encoder features of TE-TAD show high similarity among high-level features (3-6) compared to DINO. This is due to the repeated use of single convolutional projections, where the final-layer feature is downsampled to produce multi-scale features. These highly similar pre-encoder features of TE-TAD cause the multiscale deformable attention to propagate redundant information across levels during encoding. Consequently, as shown in Fig. 2(b) on the right, the post-encoder features show high similarity across levels compared to DINO. This result suggests that utilizing multi-scale features from the initial stage leads to excessive redundancy.", + "bbox": [ + 89, + 90, + 483, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the decoder, deformable cross-attention relies on sampling points near the center of reference points, typically determined by multiplying the reference width by 0.5. However, this center-focused approach restricts the model from capturing the contextual information from the surrounding region, which is crucial for classifying action instances and determining their start and end boundaries. Fig. 3 shows the challenges of center-focused sampling through the example of actions like LongJump and HighJump, where both involve a similar running motion. When the model focuses only on the central motion (red box), identifying these two actions is challenging because the surrounding context (gray frames), such as the final landing motion, provides essential cues for identifying them. Furthermore, relying solely on the running motion makes it challenging to determine accurate start and end boundaries. These observations suggest that the center-focused sampling strategy is insufficient for capturing the full context of action instances.", + "bbox": [ + 89, + 518, + 483, + 790 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a multi-dilated gated encoder and a central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). First, we introduce a multi-dilated gated encoder (MDGE), which replaces the previous multi-scale deformable attention and feedforward network in the encoder. MDGE utilizes multidilated convolutions to capture diverse feature represen", + "bbox": [ + 89, + 795, + 483, + 902 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d3ad5ea598b3b953460938654b8437e1809e1b6a9680e392d9e9e1023fae8f50.jpg", + "image_caption": [ + "(a) DINO-5scale [48] with ResNet-50 [13] on COCO [23]" + ], + "image_footnote": [], + "bbox": [ + 552, + 90, + 689, + 195 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/abafb8f9c2111be27c57ecf5fd0df5c80bb61b630fa9a3678d57b034bd0a8015.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 725, + 90, + 864, + 195 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4f6becd25a51f63045452034b29c4791d76e20eab5083c2deb0f9562b3e9390b.jpg", + "image_caption": [ + "(b) TE-TAD [15] with InternVideo2 [41] on THUMOS14 [14]" + ], + "image_footnote": [], + "bbox": [ + 552, + 210, + 689, + 316 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b1847841f9b22e2b7327f09aeb6086a2cefb435a674001546860158a770465a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 725, + 210, + 862, + 316 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/46281f2e477ad915919dd7e7cafc57b39a8c4d234c2c97f28a3bbd7923789f06.jpg", + "image_caption": [ + "Figure 2. Layer-wise CKA similarity comparison between object detection and TAD. The left and right sides are extracted from pre-encoder and post-encoder features, respectively. The 1-5 or 1-6 labels on each axis correspond to the number of multi-scale feature levels used in the respective models." + ], + "image_footnote": [], + "bbox": [ + 514, + 404, + 905, + 448 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/167002ac5f2107ab328abedb4cf7ebe0efaba73694fdcbf0c56fc2da5eb30827.jpg", + "image_caption": [ + "(a) LongJump", + "(b) HighJump", + "Figure 3. Challenges of center-focused sampling in action distinction. Each sequence shows seven evenly sampled frames across the action duration, using examples from THUMOS14 [14]." + ], + "image_footnote": [], + "bbox": [ + 514, + 460, + 903, + 505 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tations across multiple receptive fields, reducing redundant information in multi-scale features while preserving the benefits of utilizing multi-scale information. Additionally, we present a central-adjacent region integrated decoder (CAID), which combines both central- and adjacent-region sampling based on the deformable cross-attention mechanism. By incorporating these two types of information, CAID enables the detector to capture a complete contextual view for each detection query. Extensive experiments demonstrate that DiGIT achieves state-of-the-art performance on popular benchmarks, and our method is adaptable to existing query-based detection frameworks.", + "bbox": [ + 511, + 565, + 905, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as three-fold:", + "bbox": [ + 511, + 747, + 831, + 760 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose DiGIT that combines multi-dilated gated encoder and central-adjacent region integrated decoder to address the unique challenges of TAD.", + "- As shown in Fig. 1, our method consistently achieves faster convergence and improves performance when applied to existing query-based detectors.", + "- Our experiments demonstrate that our DiGIT achieves state-of-the-art performance on THUMOS14, ActivityNet v1.3, and HACS-Segment." + ], + "bbox": [ + 511, + 762, + 903, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24287", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 91, + 89, + 232, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Action Recognition Action recognition is a fundamental task in video analysis. It involves classifying video sequences into specific action categories. I3D [5] extends the inception network by incorporating 3D convolutions, while R(2+1)D [38] improves efficiency by decomposing 3D convolutions into separate 2D spatial and 1D temporal operations. TSP [2] introduces temporal channel shifting to model temporal dynamics effectively without adding computational overhead. VideoMAEv2 [40] leverages masked reconstruction pretraining method based on transformer architecture for robust video representation learning. InternVideo2 [41] leverages both large-scale training data and a highly scalable model, further enhancing video representation learning. These models are utilized in various downstream tasks like TAD as a feature extraction method.", + "bbox": [ + 89, + 114, + 483, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Anchor-free Detector Anchor-free detectors [6, 8, 18, 20, 34, 36, 44, 47] provide flexibility in localizing action instances by utilizing an asymmetric modeling approach. ActionFormer [47] improves TAD performance by leveraging a transformer-based architecture to capture long-range dependencies in video data. TriDet [36] utilizes the trident prediction scheme and its proposed architecture. ActionMamba [6] improves the ActionFormer detector by utilizing Mamba [12] architecture at the temporal feature extraction. However, despite these advancements, anchor-free detectors still require hand-crafted components such as NMS to remove redundant proposals.", + "bbox": [ + 89, + 340, + 483, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Query-based Detector Query-based detectors, drawing inspiration from DETR [4], employ a set-prediction mechanism that minimizes dependence on hand-crafted components, eliminating the necessity for NMS. RTD-Net [37] and ReAct [35] utilize query-based detection approaches; however, they do not fully address one-to-one matching in their architectures. TadTR [27] introduces cross-window fusion, applying NMS only to overlapping areas in sliding windows, which partially reduces dependency on handcrafted components. DualDETR [53] divides the decoder into separate branches for instance-level and boundary-level decoding, whereas our CAID does not address split branch but unifies comprehensive range information within a single decoder. Both TadTR and DualDETR still rely on sliding windows, which require NMS to handle redundant areas, thereby limiting their applicability as a fully end-to-end detector. In contrast, TE-TAD [15] achieves a fully end-to-end approach for TAD by reformulating coordinate representation, removing the need for hand-crafted components like NMS and sliding windows. Building on TE-TAD, we propose DiGIT, which introduces MDGE, a multi-scale adapter, and CAID for the decoder. Although our DiGIT is primarily based on TE-TAD, our method is designed to be adaptable across various query-based detectors by replacing the encoder with MDGE and decoder with CAID.", + "bbox": [ + 89, + 523, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 89, + 604, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 511, + 114, + 643, + 130 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $X \\in \\mathbb{R}^{T_0 \\times C}$ represents the video feature sequence extracted by the backbone network, where $T_0$ denotes the temporal length of the sequence, and $C$ corresponds to the feature dimension. Each element of the sequence, denoted as $X = \\{x_t\\}_{t=1}^{T_0}$ , is associated with a snippet at timestep $t$ with each snippet covering a few consecutive frames. These snippets are processed using a pre-trained backbone network such as I3D [5] or InternVideo2 [41]. Each video contains multiple action instances, each defined by start and end timestamps $s$ and $e$ , as well as its action class $c$ . Formally, the set of action instances in a video is expressed as $\\mathcal{A} = \\{(s_n, e_n, c_n)\\}_{n=1}^N$ , where $N$ denotes the total number of action instances, and $s_n, e_n,$ and $c_n$ represent the start time, end time, and action class of the $n$ -th instance, respectively. The primary objective of TAD is to predict the set of action instances $\\mathcal{A}$ for a given video.", + "bbox": [ + 511, + 135, + 906, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The query-based detectors [15, 27, 53] employ $N_{q}$ queries to detect action instances. The set of queries is represented as $\\mathcal{Q}^{(0)} = \\{F_q^{(0)}, (c_q^{(0)}, d_q^{(0)})\\}_{q=1}^{N_q}$ , where $F_q^{(0)}$ is the initial embedding of the $q$ -th query, $c_q^{(0)}$ and $d_q^{(0)}$ denote the initial center and width reference point of the $q$ -th query, respectively. These queries interact with the encoded features through deformable cross-attention layers in the decoder, where they are iteratively refined across each layer $l$ :", + "bbox": [ + 511, + 377, + 908, + 506 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Q} ^ {(l)} = \\operatorname {D e c o d e r} ^ {(l)} \\left(\\mathcal {Q} ^ {(l - 1)}\\right) \\quad l = 1, \\dots , L _ {D}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 517, + 906, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $L_{D}$ denotes the number of decoder layer. The final refined queries $Q^{(L_D)}$ are then used for final predictions $\\hat{\\mathcal{A}}$ obtained through the classification and regression heads.", + "bbox": [ + 511, + 540, + 906, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. DiGIT", + "text_level": 1, + "bbox": [ + 511, + 592, + 601, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this part, we describe our method mainly based on TETAD, but our DiGIT can be applied to various query-based detectors by simply replacing the previous encoder and decoder architecture. The overall architecture of DiGIT is illustrated in Fig. 4. Our method mainly addresses three parts: (1) the multi-dilated gated encoder (MDGE), (2) the multi-scale adapter, which converts the single-scale feature into multi-scale features, providing diverse scale information for query selection and decoder, and (3) the central-adjacent region integrated decoder (CAID).", + "bbox": [ + 511, + 614, + 906, + 766 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "**Embedding** We project input features $X$ using a single convolutional neural network to align them with the dimension of the transformer architecture.", + "bbox": [ + 511, + 766, + 905, + 810 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nZ ^ {(0)} = \\operatorname {L a y e r N o r m} (\\operatorname {C o n v} (X)), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 816, + 906, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $Z^{(0)}\\in \\mathbb{R}^{D\\times T_0}$ represented the embedded features of the detector. Here, $D$ denotes the width of the encoder and decoder. In contrast to TE-TAD, we do not address the multi-scale features at the initial and encoding stages.", + "bbox": [ + 511, + 838, + 905, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24288", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b6aacd0e4406fdf6c12ad154bd1993858de8728bb4101a17ab8b4ed78380c882.jpg", + "image_caption": [ + "Figure 4. Overview of DiGIT. Our model processes video features through MDGE to capture distinct feature representations utilizing various receptive fields. Subsequently, CAID captures both central and adjacent region information, enhancing action boundary regression and classification. For simplicity, residual connection and layer normalization are omitted." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 880, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-Dilated Gated Encoder (MDGE) As discussed in Sec. 1, both single-scale and multi-scale approaches have inherent limitations. Single-scale methods struggle to capture long temporal dependencies. Conversely, multi-scale methods can capture a broader range of temporal scales but cause highly correlated features across each scale.", + "bbox": [ + 88, + 380, + 480, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address the limitations of both approaches, we introduce MDGE that replaces the previous multi-scale deformable encoder structure. Inspired by a previous work [7], MDGE applies multi-dilated convolutions to capture diverse receptive fields within a single encoder. This approach enables the model to extract short-term and long-term temporal features without relying on a multi-scale structure. Furthermore, inspired by gating mechanism [46], MDGE selectively filters out redundant information, retaining only the most relevant features across the different receptive fields. In the following, we describe the detailed structure of MDGE, which is composed of $L_{E}$ multi-dilated gated convolution layers.", + "bbox": [ + 88, + 470, + 482, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At each encoder layer $l$ , the input features $Z^{(l-1)}$ from the previous layer are first projected into two paths:", + "bbox": [ + 89, + 667, + 482, + 700 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nZ _ {\\text {c o n v}} ^ {(l)} = \\operatorname {L i n e a r} \\left(Z ^ {(l - 1)}\\right), \\quad Z _ {\\text {g a t e}} ^ {(l)} = \\operatorname {L i n e a r} \\left(Z ^ {(l - 1)}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 710, + 482, + 732 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Z_{\\mathrm{conv}}^{(l)} \\in \\mathbb{R}^{D_h \\times T_0}$ and $Z_{\\mathrm{gate}}^{(l)} \\in \\mathbb{R}^{D_h \\times T_0}$ . Here, $D_h$ represents the hidden dimension of the feedforward network within the transformer architecture. Instead of utilizing the feedforward network in the encoder, we expand the feature dimension before applying the dilated convolution. This approach retains a similar parameter to a single transformer layer that consists of an attention layer and a feedforward network. Each transformed features, $Z_{\\mathrm{conv}}^{(l)}$ and $Z_{\\mathrm{gate}}^{(l)}$ , are then processed in separate paths independently for multidilated convolution and gating mechanism, respectively.", + "bbox": [ + 89, + 743, + 482, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The transformed features for multi-dilated convolution $Z_{\\mathrm{conv}}^{(l)}$ are split along the channel dimension into $N_{d}$ equal subsets, denoted as $Z_{\\mathrm{conv}}^{(l,i)} \\in \\mathbb{R}^{(D_h / N_d) \\times T_0}$ , where $N_{d}$ is the number of parallel dilated convolutions. Each subset is processed by a dilated convolution with a different dilation rate, increasing from 1 up to $N_{d}$ . The output features for each subset are expressed as follows:", + "bbox": [ + 511, + 380, + 906, + 488 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nZ _ {\\text {d i l a t e d}} ^ {(l, i)} = \\operatorname {D i l a t e d C o n v} _ {(l, d _ {i})} \\left(Z _ {\\text {c o n v}} ^ {(l, i)}\\right) \\quad i = 1, \\dots , N _ {d}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 493, + 906, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d_{i}$ is the dilation rate for the $i$ -th convolution, set as $d_{i} = i$ . The increasing dilation rates provide varying receptive field sizes, allowing the model to capture both short- and long-term temporal features simultaneously. Our encoder has two main hyperparameters: the number of dilated convolutions $N_{d}$ and the kernel size.", + "bbox": [ + 511, + 518, + 905, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequently, the outputs of the dilated convolutions $Z_{\\mathrm{dilated}}^{(l,i)}$ are concatenated along the channel dimension:", + "bbox": [ + 513, + 609, + 905, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nZ _ {\\text {c o n c a t}} ^ {(l)} = \\operatorname {C o n c a t} \\left(Z _ {\\text {d i l a t e d}} ^ {(l, 1)}, \\dots , Z _ {\\text {d i l a t e d}} ^ {(l, N _ {d})}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 647, + 903, + 669 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following this concatenation, we apply a gating mechanism to selectively retain relevant features:", + "bbox": [ + 511, + 674, + 905, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nZ ^ {(l)} = Z _ {\\text {c o n c a t}} ^ {(l)} \\odot \\sigma \\left(Z _ {\\text {g a t e}} ^ {(l)}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 709, + 903, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma$ is an activation function and $\\odot$ denotes elementwise multiplication. Specifically, we use the SiLU activation function for the gate activation.", + "bbox": [ + 511, + 734, + 905, + 780 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Consequently, the encoding process across $L_{E}$ layers of MDGE can be summarized as follows:", + "bbox": [ + 511, + 781, + 906, + 810 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nZ ^ {(l)} = \\operatorname {M D G E} ^ {(l)} \\left(Z ^ {(l - 1)}\\right) \\quad l = 1, \\dots , L _ {E}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 815, + 903, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our MDGE design enables the encoder to capture diverse temporal relations by leveraging dilated convolutions and a gating mechanism without requiring explicit multiscale features at each layer.", + "bbox": [ + 511, + 839, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24289", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-Scale Adapter & Query Selection TE-TAD [15] employs a two-stage approach with multi-scale features for query selection. To take advantage of the two-stage approach and utilize multi-scale features for query selection, we introduce a multi-scale adapter that converts the single-scale feature to multi-scale features. Our multi-scale adapter utilizes the encoder output feature $Z^{(L_E)}$ to generate multi-scale representations. Specifically, $Z^{(L_E)}$ is progressively downsampled to produce a set of features at multiple levels, with each subsequent level reduced to half the temporal length of the previous one. We denote the $L$ levels of multi-scale features as follows:", + "bbox": [ + 89, + 90, + 483, + 271 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF ^ {(l)} = \\operatorname {D o w n S a m p l e} \\left(Z ^ {\\left(L _ {E}\\right)}\\right) + E ^ {(l)} \\quad l = 1, \\dots , L, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 279, + 482, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where each $F^{(l)} \\in \\mathbb{R}^{T_l \\times D}$ represents the resized feature at level $l$ , with $T_{l}$ being half the length of the previous level. To enable the decoder to distinguish between these multi-scale levels, we add a level-specific embedding $E^{(l)} \\in \\mathbb{R}^{1 \\times D}$ , applied consistently across all time steps. These multi-scale features are then utilized for the query selection process. Unlike the adaptive query selection (AQS) in TE-TAD [15] that enforces a strict uniform sampling of queries across the video, we apply a top- $k$ selection approach based on binary classification scores from the encoder.", + "bbox": [ + 89, + 304, + 483, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Subsequently, we utilize the top- $k$ indices to retrieve both the query embeddings and the corresponding reference points $(c_{q},d_{q})$ based on a time-aligned query generation method [15] that assigns temporal center points $c_{q}$ and widths $d_{q}$ , aligning them with their respective positions in the video. Additionally, the query embedding for each selected query is obtained by linearly projecting the corresponding top- $k$ multi-scale features. The input embedding of a decoder is denoted as follows:", + "bbox": [ + 89, + 457, + 483, + 592 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {q} ^ {(0)} = \\operatorname {L a y e r N o r m} \\left(\\operatorname {L i n e a r} \\left(F _ {\\mathrm {t o p k}}\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 599, + 482, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F_{\\mathrm{topk}}$ denotes the top- $k$ selected features.", + "bbox": [ + 89, + 626, + 403, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Central-Adjacent Region Integrated Decoder (CAID)", + "text_level": 1, + "bbox": [ + 89, + 641, + 482, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The previous query-based methods [15, 27] apply temporal deformable cross-attention that applies the center-focused sampling strategy. As discussed in Sec. 1, the center-focused sampling does not provide sufficient information for detecting the action instances. To address this issue, we introduce CAID, which combines central- and adjacent-region cross-attention. In standard deformable cross-attention, features are sampled around each reference point, defined by its center $c_{q}$ and duration $d_{q}$ . The sampling offset $\\Delta p_{mqk}$ for each head $m$ and sampling point $k$ is computed as:", + "bbox": [ + 89, + 656, + 483, + 821 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta p _ {m q k} = \\operatorname {L i n e a r} \\left(F _ {q}\\right) = W F _ {q} + b, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 830, + 482, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W$ and $b$ are learnable parameters for obtaining the sampling offset by linear projection. Generally, $W$ is initialized to zero and $b$ within the range $[-1, 1]$ . Using the", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "computed offset $\\Delta p_{mqk}$ , sampling points $p_{mqk}$ are determined based on the reference points as:", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {m q k} = c _ {q} + 0. 5 w _ {q} \\Delta p _ {m q k}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 130, + 903, + 147 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the factor $0.5w_{q}$ ensures the sampling points are initially positioned close to the center of each reference point. In our approach, we do not change how to obtain the sampling points when addressing central- and adjacent-region sampling. We change the initialization method for the bias value $b$ , which determines the initial sampling points.", + "bbox": [ + 511, + 152, + 903, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 4, our CAID contains two cross-attention layers sequentially: central-region cross-attention and adjacent-region cross-attention. For central-region cross-attention, the initial bias of sampling offsets $b$ are initialized uniformly within the range $[-1,1]$ , which is identical to the previous methods [15, 19, 25, 27, 48, 52]. As Eq. (11), this initialization constrains the initial bias for sampling points $b$ within $[-0.5,0.5]$ , focusing on the central region of the reference points. For adjacent-region cross-attention, the bias of sampling offsets $b$ are adjusted to capture surrounded points of central-region cross-attention. Specifically, half of the sampling offsets are initialized within the range $[-1.5,-0.5]$ to focus on the left, while the other half are initialized within the range $[0.5,1.5]$ to focus on the right. This adjustment, combined with Eq. (11), constraints in the initial sampling points $p_{mqk}$ within $[-0.75,-0.25]$ and $[0.25,0.75]$ . Overall, we sequentially apply self-attention, central-region cross-attention, adjacent-region cross-attention, and feedforward network across all $L_{D}$ layers, as shown in Fig. 4.", + "bbox": [ + 511, + 244, + 906, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Training and Inference", + "text_level": 1, + "bbox": [ + 513, + 553, + 725, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Following the previous works [15, 27], we use the bipartite matching loss [4]. The total loss $\\mathcal{L}_{total}$ is defined as follows:", + "bbox": [ + 511, + 575, + 905, + 619 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} (\\mathcal {A}, \\hat {\\mathcal {A}}) = \\sum_ {i = 1} ^ {N _ {q}} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\mathcal {A} _ {i}, \\hat {\\mathcal {A}} _ {\\pi (i)}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 625, + 903, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{match}$ denotes the bipartite matching loss, which considers both classification and regression loss between ground truth $\\mathcal{A}_i$ and predicted action instances $\\hat{\\mathcal{A}}_{\\pi(i)}$ from the last layer of the decoder. The permutation indices $\\pi(i)$ are obtained through bipartite matching [17]. This cost function $\\mathcal{L}_{match}$ is a composite of the classification, and regression loss. We use focal loss [24] for the classification loss to effectively manage class imbalance. For the regression loss, our method incorporates GIoU [33] and a log-ratio distance loss [15].", + "bbox": [ + 511, + 674, + 905, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference Following the previous work [15] that removes the need for post-processing steps, the predictions of DiGIT from the final layer of the decoder $\\hat{\\mathcal{A}}$ are directly used. For a fair comparison, we report both raw prediction results and NMS applied results.", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24290", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9f77dc9bf8ad8ad30e89091fe6f8de49aa36057baee16e393d12a340c74dd3b0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Training TypeHead TypeMethodFeatureTHUMOS14ActivityNet v1.3
    0.30.40.50.60.7Avg.0.50.750.95Avg.
    Full-AFSD [20]I3D [5]67.362.455.543.731.152.052.435.36.534.4
    TALLFormer [8]Swin-B [28]76.0-63.2-34.559.254.136.27.935.6
    ViT-TAD [45]ViT-B [9]85.180.974.261.845.469.555.838.58.837.4
    AdaTAD [26]VideoMAEv2-g [40]89.786.780.971.056.176.961.743.410.941.9
    Head onlyAnchor -freeTriDet [36]I3D [5] / R(2+1)D [38]83.680.172.962.447.469.354.738.08.436.8
    DyFADet [44]I3D [5] / R(2+1)D [38]84.080.172.761.147.969.258.139.68.438.5
    ActionFormer [47]I3D [5] / R(2+1)D [38]82.177.871.059.443.966.854.737.88.436.6
    ActionFormer [47]InternVideo2 [41]82.381.975.165.850.371.961.544.612.741.2
    ActionMamba [6]InternVideo2 [41]86.983.176.965.950.872.762.443.510.242.0
    Query -basedRTD-Net [37]I3D [5] / TSN [39]68.362.351.938.823.749.047.230.78.630.8
    ReAct [35]I3D [5] / TSN [39]69.265.057.147.835.655.049.633.08.632.6
    Self-DETR [16]I3D [5]74.669.560.047.631.856.752.333.78.433.8
    TadTR [27]I3D [5] / R(2+1)D [38]74.869.160.146.632.856.753.637.510.636.8
    DualDETR [53]I3D [5]82.978.070.458.544.466.852.635.07.834.3
    TE-TAD [15]I3D [5] / R(2+1)D [38]83.378.471.360.745.667.954.238.110.637.1
    DiGIT†I3D [5] / R(2+1)D [38]81.677.770.360.548.467.754.338.410.637.2
    DiGITI3D [5] / R(2+1)D [38]83.679.671.961.548.669.054.438.210.737.3
    TadTR [27]InternVideo2 [41]84.879.370.458.243.867.357.138.811.038.2
    TadTR [27] + OursInternVideo2 [41]86.181.873.761.746.369.960.241.011.240.5
    TE-TAD [15]InternVideo2 [41]84.381.173.762.649.570.361.341.810.941.1
    DiGIT†InternVideo2 [41]85.782.375.665.651.472.158.943.411.441.3
    DiGITInternVideo2 [41]87.684.277.667.352.573.862.043.111.342.0
    ", + "bbox": [ + 120, + 88, + 872, + 400 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Performance comparison with state-of-the-art methods on THUMOS14 and ActivityNet v1.3. In cases marked with $\\dagger$ , our method does not utilize NMS. For TadTR + Ours, we additionally apply our MDGE and CAID on TadTR.", + "bbox": [ + 89, + 402, + 906, + 433 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 443, + 223, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 89, + 468, + 171, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets We conduct experiments on three datasets: THUMOS14 [14], ActivityNet v1.3 [10], and HACS-Segment [50]. THUMOS14 consists of 20 action classes with 200 validation and 213 test videos, containing 3,007 and 3,358 action instances, respectively. ActivityNet v1.3 is a large-scale dataset with 200 action classes, including 10,024 videos for training and 4,926 videos for validation. HACS-Segment is another large-scale TAD dataset with extensive annotations, covering 200 activity classes similar to ActivityNet v1.3. It provides 37,613 videos for training and 5,981 videos for validation. These datasets provide a rigorous evaluation environment for our method, containing diverse actions and scenes.", + "bbox": [ + 89, + 489, + 482, + 685 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metric We follow the standard evaluation protocol for all datasets, utilizing mAP at different intersections over union (IoU) thresholds to evaluate TAD performance. The IoU thresholds for THUMOS14 are set at [0.3:0.7:0.1], while for ActivityNet v1.3 and HACS-Segment, the results are reported at IoU threshold [0.5, 0.75, 0.95] with the average mAP computed at [0.5:0.95:0.05].", + "bbox": [ + 89, + 686, + 482, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details We describe the implementation details for each dataset in the Supplementary Sec. A.", + "bbox": [ + 89, + 792, + 482, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 89, + 832, + 230, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "THUMOS14 Table 1 contains a comparison with the state-of-the-art methods on THUMOS14. Our DiGIT shows consistent improvements over TadTR [27] and TE-TAD [15] on", + "bbox": [ + 89, + 854, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "both I3D [5] and InternVideo2 [41] features. Even without applying NMS, our method outperforms the existing query-based detectors. Furthermore, our model outperforms the existing snippet-based head-only training methods, and our DiGIT shows a comparable performance even compared to the full training method.", + "bbox": [ + 511, + 444, + 906, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ActivityNet v1.3 Following the conventional approach [15, 27, 36, 47], the external classification score is used to evaluate ActivityNet v1.3. The pre-extracted classification scores are combined with class-agnostic predictions from a binary detector to obtain class labels. For $\\mathrm{R}(2 + 1)\\mathrm{D}$ [38] and InternVideo2 [41] features, classification results from CUHK [42] and InternVideo2 [41] are incorporated to obtain class scores, respectively. As demonstrated in Table 1, DiGIT achieves consistent improvements over TadTR and TE-TAD on ActivityNet v1.3. Furthermore, DiGIT demonstrates competitive performance compared to other types of state-of-the-art methods, demonstrating effectiveness across various datasets and feature extractors.", + "bbox": [ + 511, + 536, + 908, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "HACS-Segment Table 2 presents a comparison of our model with state-of-the-art methods on HACS-Segment. Our model achieves significant improvements over previous methods, establishing a new state-of-the-art performance, including mAP at higher IoU thresholds of 0.75 and 0.95. The stronger performance at the 0.95 IoU threshold indicates that DiGIT excels in precise action localization. Moreover, the superior performance of DiGIT on this larger dataset, compared to THUMOS14 and ActivityNet v1.3, demonstrates its scalability and robustness across varying data sizes and complexities.", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24291", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/68d7f8f7bad9768bfa448006268b6f950dda610d6e744dbba7b578647d7ad7ce.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Head TypeMethodFeaturemAP
    0.50.750.95Avg.
    Anchor -basedSSN [51]I3D [5]28.818.85.319.0
    G-TAD [43]I3D [5]41.127.68.327.5
    BMN [22]SlowFast [11]52.536.410.435.8
    TCANet [32]SlowFast [11]54.137.211.336.8
    Anchor -freeTALLFormer [8]Swin-B [28]55.036.111.836.5
    TriDet [36]I3D [5]54.536.811.536.8
    TriDet [36]SlowFast [11]56.739.311.738.6
    TriDet [36]VideoMAEv2-g [40]62.444.113.143.1
    DyFADet [44]SlowFast [11]57.839.811.839.2
    DyFADet [44]VideoMAEv2-g [40]64.044.814.144.3
    ActionFormer [47]InternVideo2 [41]62.644.612.743.3
    ActionMamba [6]InternVideo2 [41]64.045.713.344.6
    Query -basedTadTR [27]I3D [5]47.132.110.932.1
    TadTR [27]InternVideo2 [41]54.238.812.837.8
    TadTR [27] + OursInternVideo2 [41]55.040.013.839.0
    TE-TAD [15]InternVideo2 [41]60.445.616.544.1
    DiGIT†InternVideo2 [41]61.147.517.845.5
    DiGITInternVideo2 [41]62.447.917.645.9
    ", + "bbox": [ + 94, + 88, + 478, + 323 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5a8896336a5da505df404cc7e14a636797c23f3024161d6a641fa60a8827a93b.jpg", + "image_caption": [ + "Figure 5. Ablation study on MDGE with InternVideo2 features on THUMOS14. The heatmap shows mAP values for different combinations of kernel size and number of dilated convolutions." + ], + "image_footnote": [], + "bbox": [ + 169, + 392, + 403, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Further Analysis", + "text_level": 1, + "bbox": [ + 89, + 558, + 256, + 574 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study on MDGE Fig. 5 shows an ablation study on hyperparameters of MDGE, specifically the impact of kernel size and the number of dilated convolution layers $N_{d}$ on mAP performance. Excluding the configuration with a single dilated convolution that consistently yields lower mAP values, configurations with multiple dilated layers demonstrate improved performance. These results indicate that addressing diverse scale information is crucial for the encoder by utilizing our multi-dilated convolution that enables the model to capture diverse temporal relations. Furthermore, compared to the TE-TAD [15] baseline of 70.4 in Table 4, our MDGE consistently improves performance regardless of hyperparameter variations, demonstrating robustness across different configurations.", + "bbox": [ + 89, + 580, + 482, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study on CAID Table 3 demonstrates the effects of integrating the proposed adjacent-region cross-attention (ACA) into the decoder operation sequence. We evaluate several configurations, including variations of central-region cross-attention (CCA) with expanded initialization ranges $(1.5\\times$ and $2.0\\times)$ . CCA $(1.5\\times)$ and CCA $(2.0\\times)$ (Rows #2 and #3) show that simply increasing the initial", + "bbox": [ + 89, + 795, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e917d245ccb61616b38fad9270997c210740cf46cb5a49db7aefe13ba5405068.jpg", + "table_caption": [ + "Table 2. Performance comparison with state-of-the-art methods on HACS-Segment. In cases marked with $\\dagger$ , our method does not utilize NMS. For TadTR + Ours, we additionally apply our MDGE and CAID on TadTR." + ], + "table_footnote": [], + "table_body": "
    Decoder SequencemAP@AVG
    #1SA → CCA → FFN72.5
    #2SA → CCA (1.5×) → FFN72.6
    #3SA → CCA (2.0×) → FFN71.8
    #4SA → ACA → FFN69.2
    #5SA → CCA → CCA → FFN72.7
    #6SA → CCA → ACA → FFN73.8
    #7SA → ACA → CCA → FFN73.2
    ", + "bbox": [ + 573, + 88, + 841, + 207 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/50c77eb8bcfc1e0d8ddec4d6dde1a15794d27e22de124b3e4346dfb24c559ff4.jpg", + "table_caption": [ + "Table 3. Analysis of decoder operation sequences using InternVideo2 features on THUMOS14. SA refers to the self-attention layer. CCA denotes central-region cross-attention (as used in previous works such as [15, 27]). CCA $(1.5\\times$ and $2.0\\times)$ indicates an expansion of the initial sampling range of central-region cross-attention by 1.5 and 2.0 times, respectively, to cover a broader area around the reference points. ACA refers to adjacent-region cross-attention, and FFN represents the feedforward network." + ], + "table_footnote": [], + "table_body": "
    BaselineEnc.Dec.MDGECAIDmAP
    0.30.50.7Avg.
    TadTR [27]SS✓84.870.443.867.3
    ✓84.971.944.768.4
    ✓✓84.470.845.467.9
    ✓✓86.173.746.369.9
    TE-TAD [15]MM✓84.373.749.570.3
    85.274.649.970.8
    SM✓85.473.849.170.4
    87.075.851.972.5
    ✓✓85.574.651.071.4
    ✓✓87.677.652.573.8
    ", + "bbox": [ + 521, + 327, + 895, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation study on the contributions of each component using InternVideo2 features on THUMOS14. The first row for TadTR [27] and TE-TAD [15] represents the baseline performance. Enc. and Dec. refer to how scale information is handled in the encoder and decoder. S: single-scale. M: multi-scale.", + "bbox": [ + 511, + 484, + 903, + 555 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ization range of CCA to cover a broader area, similar range to CAID, does not show the improved performance compared to the original setting (Row #1). This indicates that simply expanding the initialization range does not benefit the detector. Moreover, when using ACA alone (Row #4), we observe a significant decrease in performance, underscoring the importance of balancing adjacent-region information with central-region information. Configurations that use two successive CCA layers (Row #5) show only marginal improvements, suggesting that additional central-region cross-attention alone does not significantly enhance performance. The highest mAP score is achieved by the sequence of SA $\\rightarrow$ CCA $\\rightarrow$ ACA $\\rightarrow$ FFN, which combines central-region cross-attention and adjacent-region cross-attention, which is our CAID (Row #6).", + "bbox": [ + 511, + 566, + 903, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Component Contribution Analysis Table 4 provides an analysis of the performance contributions from each proposed component, evaluated using InternVideo2 [41] features on THUMOS14 [14]. The first row for each method shows the baseline performance without our proposed enhancements, allowing for a direct comparison with subsequent configurations. Notably, converting multi-scale en", + "bbox": [ + 511, + 795, + 903, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24292", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/347bb2b36f97a6509fca9a41064eb0558b8a28d76e809c8fe51e94effbe56534.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    BaselineAQS [15]mAP
    0.30.50.7Avg.
    TE-TAD [15]✓85.673.747.670.3
    82.571.848.468.7
    DiGIT✓85.876.451.572.2
    87.677.652.573.8
    ", + "bbox": [ + 140, + 88, + 431, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation study on the query selection method using InternVideo2 features on THUMOS14.", + "bbox": [ + 89, + 184, + 483, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be6c3dbb41c7d17b3b9288b244a4e9c2752b49c0126f7e31c735d2738ce2e947.jpg", + "image_caption": [ + "Figure 6. Comparison of training and testing loss for the encoder classification matching loss using InternVideo2 features on THUMOS14. Our method significantly accelerates the convergence of the encoder." + ], + "image_footnote": [], + "bbox": [ + 125, + 217, + 433, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "coding to single-scale encoding alone in TE-TAD [15] results in minimal performance change $(70.3\\rightarrow 70.4)$ . This result aligns with our motivation, as shown in Fig. 2, which is that the previous multi-scale features contain redundant information. Furthermore, both MDGE and CAID show consistent improvements in both TadTR and TE-TAD, demonstrating the robustness and effectiveness of our approach across different baseline architectures.", + "bbox": [ + 89, + 411, + 483, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of MDGE In TE-TAD [15], adaptive query selection (AQS) is employed to sample initial queries across the entire video sequence uniformly. This process enforces a strict uniform selection of queries to prevent queries from being overly concentrated in certain areas, as might happen with a simple top-k selection. However, our observations suggest that this strict uniform condition is unnecessary when using a well-trained encoder, as provided by our MDGE. As shown in Table 5, removing AQS results in higher mAP scores for DiGIT, whereas the performance of TE-TAD declines without AQS. Furthermore, as illustrated in Fig. 6, DiGIT exhibits faster convergence and consistently lower loss values. These results indicate that our MDGE enhances the representational ability of the encoder and can reduce the heuristic part of the query selection, which positively impact overall detection performance.", + "bbox": [ + 89, + 532, + 483, + 775 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 89, + 787, + 272, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of Cosine Similarity on Encoder Output Features Fig. 7 presents a comparison of cosine similarity matrices for encoder output features between TE-TAD and DiGIT. Our DiGIT shows improved feature discriminability, indicating that MDGE captures distinct temporal patterns more effectively compared to TE-TAD [15].", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b4b907098c1eff613484ad33bc38f6b9037ddeeb094d349f0672c244e60ee36d.jpg", + "image_caption": [ + "(a) TE-TAD [15]" + ], + "image_footnote": [], + "bbox": [ + 522, + 89, + 707, + 222 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d5fdccaf7ddcbf6b978eeaed6d4d6b1533fe9097e46c254eda385152fcb4639.jpg", + "image_caption": [ + "(b) DiGIT" + ], + "image_footnote": [], + "bbox": [ + 712, + 90, + 898, + 222 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1f7fa3b7c35acea3d59f0e49efe20e9772232c7f99f14c0ae673dfa0efd1406f.jpg", + "image_caption": [ + "Figure 7. Comparison of cosine similarity on encoder output features between TE-TAD and DiGIT. Top: represents cosine similarity, with red boxes indicating regions of similarity among features within the ground truth. Bottom: displays the ground truth action timeline for reference. Sample taken from THUMOS14." + ], + "image_footnote": [], + "bbox": [ + 524, + 306, + 888, + 400 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f25b88c2f2a3f0389c02dbf73ae555c4d61eaa9fa2d1b3a7ada8f6498cd8345b.jpg", + "image_caption": [ + "Figure 8. Visualization of sampling offsets in cross-attention layers on THUMOS14. Each point denotes the mean value across the dataset, with error bars indicating the standard deviation." + ], + "image_footnote": [], + "bbox": [ + 524, + 401, + 887, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of Sampling Offsets Fig. 8 shows the distribution of sampling offsets relative to the center and width of each action query. The values 0, -1, and 1 correspond to the center $c_{q}$ , the start boundary $c_{q} - d_{q}$ , and the end boundary $c_{q} + d_{q}$ , respectively. This visualization shows that our method gathers information from diverse sampling points, covering both central and adjacent regions. Furthermore, while deformable attention allows learnable offsets, they remain close to their initial points, indicating the importance of the initial value of $b$ in Eq. (10).", + "bbox": [ + 511, + 544, + 906, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 709, + 633, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a multi-dilated gated encoder and central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). MDGE offers diverse receptive fields while maintaining a single-scale encoding structure by utilizing multi-dilated convolutions. CAID provides essential information to precisely detect action instances by focusing on both the central- and adjacent-regions of action instances. Extensive experiments demonstrate that DiGIT outperforms the previous query-based methods. Furthermore, our method consistently improves when integrated with the existing query-based detectors.", + "bbox": [ + 511, + 734, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24293", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant, funded by the Korea government (MSIT) (No. RS-2019-II190079, Artificial Intelligence Graduate School Program (Korea University), No. RS-2024-00457882, AI Research Hub Project, and No. RS-2022-II220984, Development of Artificial Intelligence Technology for Personalized Plug-and-Play Explanation and Verification of Explanation).", + "bbox": [ + 89, + 114, + 483, + 251 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 263, + 187, + 279 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18559-18569, 2024. 1, 2, 3, 6" + ], + "bbox": [ + 514, + 90, + 903, + 489 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "24296", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_model.json b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..505501bf3f631d2eb4453eb90954ae6052c23e27 --- /dev/null +++ b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_model.json @@ -0,0 +1,2290 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.103, + 0.127, + 0.895, + 0.172 + ], + "angle": 0, + "content": "DiGIT: Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer" + }, + { + "type": "text", + "bbox": [ + 0.196, + 0.195, + 0.795, + 0.214 + ], + "angle": 0, + "content": "Ho-Joong Kim Yearang Lee Jung-Ho Hong Seong-Whan Lee\\*" + }, + { + "type": "text", + "bbox": [ + 0.292, + 0.218, + 0.707, + 0.234 + ], + "angle": 0, + "content": "Dept. of Artificial Intelligence, Korea University, Seoul, Korea" + }, + { + "type": "text", + "bbox": [ + 0.262, + 0.235, + 0.732, + 0.25 + ], + "angle": 0, + "content": "{hojoong_kim, yr_lee, jungho-hong, sw.lee}@korea.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.277, + 0.327, + 0.293 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.309, + 0.486, + 0.657 + ], + "angle": 0, + "content": "In this paper, we examine a key limitation in query-based detectors for temporal action detection (TAD), which arises from their direct adaptation of originally designed architectures for object detection. Despite the effectiveness of the existing models, they struggle to fully address the unique challenges of TAD, such as the redundancy in multiscale features and the limited ability to capture sufficient temporal context. To address these issues, we propose a multi-dilated gated encoder and central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). Our approach replaces the existing encoder that consists of multi-scale deformable attention and feedforward network with our multi-dilated gated encoder. Our proposed encoder reduces the redundant information caused by multi-level features while maintaining the ability to capture fine-grained and long-range temporal information. Furthermore, we introduce a central-adjacent region integrated decoder that leverages a more comprehensive sampling strategy for deformable cross-attention to capture the essential information. Extensive experiments demonstrate that DiGIT achieves state-of-the-art performance on THUMOS14, ActivityNet v1.3, and HACS-Segment. Code is available at: https://github.com/Dotori-HJ/DGIT" + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.672, + 0.222, + 0.687 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.697, + 0.485, + 0.879 + ], + "angle": 0, + "content": "Temporal action detection (TAD) is crucial for video understanding and supports a wide range of real-world applications, including video surveillance, summarization, and retrieval. TAD aims to detect action instances within untrimmed videos by identifying action classes along with their start and end times. The most existing TAD methods [15, 27, 36, 47] are a snippet-based approach, which utilizes pre-extracted features to address long durations. This approach does not require the computational cost for the backbone network at the detection stage, enabling the detector to address a comprehensive length of features at once. The existing methods can be divided into three approaches:" + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.279, + 0.875, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.475, + 0.907, + 0.517 + ], + "angle": 0, + "content": "Figure 1. Convergence curves with InternVideo2 [41] features on THUMOS14 [14]. Our method boosts the previous query-based detectors like TE-TAD [15] and TadTR [27]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.523, + 0.905, + 0.553 + ], + "angle": 0, + "content": "anchor-based [3, 21, 22, 29, 43, 49], anchor-free [6, 8, 20, 34, 36, 44, 47], and query-based [15, 27, 35, 37, 53]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Query-based detectors, inspired by DETR [4], have attracted interest because of their potential to eliminate reliance on hand-crafted components, such as the sliding window and non-maximum suppression (NMS). This capability derives from their adoption of a set-prediction mechanism, which enables an end-to-end detection process through a one-to-one matching paradigm. Among them, TE-TAD [15] enables a full end-to-end detection process by reformulating the coordinate representation based on recent DETR-based network architectures, such as multiscale deformable attention [52]. However, despite these advancements, query-based detectors still rely on originally designed architectures for object detection, which is not fully suited to addressing the unique challenges of TAD. We identify two limitations within the encoder and decoder structures of existing query-based TAD models. (1) In the encoder, simply utilizing single-scale [27, 53] feature or multi-scale [15] features fails to extract the meaningful features needed to capture the diverse temporal scale information and distinct feature representations. (2) In the decoder, the deformable cross-attention mechanism focuses on the central regions of reference points, overlooking surrounding areas essential for accurately detecting the action instances." + }, + { + "type": "page_footnote", + "bbox": [ + 0.116, + 0.888, + 0.241, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24286" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.515 + ], + "angle": 0, + "content": "In the encoder, existing query-based detectors employ either single-scale [27, 53] or multi-scale [15] features, but both approaches have inherent limitations. The single-scale approach [27, 53] processes feature at a single resolution throughout the encoder and decoder, intuitively restricting the model to capture varying durations. The multi-scale approach [15] combines features across multiple resolutions, enhancing the ability of the model to detect different lengths of actions by aggregating broader contextual information. However, despite the advantage of the multi-scale approach, it struggles to capture distinct feature representations at each level, resulting in highly correlated features across scales. Fig. 2 illustrates this issue by comparing layer-wise CKA [31] similarities on the pre-encoder and post-encoder features between an object detection model (DINO [48]) and a TAD model (TE-TAD [15]). As shown in Fig. 2 on the left, the pre-encoder features of TE-TAD show high similarity among high-level features (3-6) compared to DINO. This is due to the repeated use of single convolutional projections, where the final-layer feature is downsampled to produce multi-scale features. These highly similar pre-encoder features of TE-TAD cause the multiscale deformable attention to propagate redundant information across levels during encoding. Consequently, as shown in Fig. 2(b) on the right, the post-encoder features show high similarity across levels compared to DINO. This result suggests that utilizing multi-scale features from the initial stage leads to excessive redundancy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.519, + 0.484, + 0.791 + ], + "angle": 0, + "content": "In the decoder, deformable cross-attention relies on sampling points near the center of reference points, typically determined by multiplying the reference width by 0.5. However, this center-focused approach restricts the model from capturing the contextual information from the surrounding region, which is crucial for classifying action instances and determining their start and end boundaries. Fig. 3 shows the challenges of center-focused sampling through the example of actions like LongJump and HighJump, where both involve a similar running motion. When the model focuses only on the central motion (red box), identifying these two actions is challenging because the surrounding context (gray frames), such as the final landing motion, provides essential cues for identifying them. Furthermore, relying solely on the running motion makes it challenging to determine accurate start and end boundaries. These observations suggest that the center-focused sampling strategy is insufficient for capturing the full context of action instances." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.484, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a multi-dilated gated encoder and a central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). First, we introduce a multi-dilated gated encoder (MDGE), which replaces the previous multi-scale deformable attention and feedforward network in the encoder. MDGE utilizes multidilated convolutions to capture diverse feature represen" + }, + { + "type": "image", + "bbox": [ + 0.553, + 0.092, + 0.691, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.092, + 0.865, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.558, + 0.197, + 0.863, + 0.21 + ], + "angle": 0, + "content": "(a) DINO-5scale [48] with ResNet-50 [13] on COCO [23]" + }, + { + "type": "image", + "bbox": [ + 0.553, + 0.212, + 0.69, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.726, + 0.212, + 0.864, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.318, + 0.874, + 0.33 + ], + "angle": 0, + "content": "(b) TE-TAD [15] with InternVideo2 [41] on THUMOS14 [14]" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.333, + 0.907, + 0.402 + ], + "angle": 0, + "content": "Figure 2. Layer-wise CKA similarity comparison between object detection and TAD. The left and right sides are extracted from pre-encoder and post-encoder features, respectively. The 1-5 or 1-6 labels on each axis correspond to the number of multi-scale feature levels used in the respective models." + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.405, + 0.906, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.45, + 0.748, + 0.462 + ], + "angle": 0, + "content": "(a) LongJump" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.462, + 0.905, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.507, + 0.748, + 0.519 + ], + "angle": 0, + "content": "(b) HighJump" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.52, + 0.907, + 0.561 + ], + "angle": 0, + "content": "Figure 3. Challenges of center-focused sampling in action distinction. Each sequence shows seven evenly sampled frames across the action duration, using examples from THUMOS14 [14]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.566, + 0.906, + 0.747 + ], + "angle": 0, + "content": "tations across multiple receptive fields, reducing redundant information in multi-scale features while preserving the benefits of utilizing multi-scale information. Additionally, we present a central-adjacent region integrated decoder (CAID), which combines both central- and adjacent-region sampling based on the deformable cross-attention mechanism. By incorporating these two types of information, CAID enables the detector to capture a complete contextual view for each detection query. Extensive experiments demonstrate that DiGIT achieves state-of-the-art performance on popular benchmarks, and our method is adaptable to existing query-based detection frameworks." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.748, + 0.833, + 0.761 + ], + "angle": 0, + "content": "Our contributions are summarized as three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.763, + 0.905, + 0.807 + ], + "angle": 0, + "content": "- We propose DiGIT that combines multi-dilated gated encoder and central-adjacent region integrated decoder to address the unique challenges of TAD." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.808, + 0.905, + 0.853 + ], + "angle": 0, + "content": "- As shown in Fig. 1, our method consistently achieves faster convergence and improves performance when applied to existing query-based detectors." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.853, + 0.905, + 0.899 + ], + "angle": 0, + "content": "- Our experiments demonstrate that our DiGIT achieves state-of-the-art performance on THUMOS14, ActivityNet v1.3, and HACS-Segment." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.763, + 0.905, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24287" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.09, + 0.233, + 0.105 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.341 + ], + "angle": 0, + "content": "Action Recognition Action recognition is a fundamental task in video analysis. It involves classifying video sequences into specific action categories. I3D [5] extends the inception network by incorporating 3D convolutions, while R(2+1)D [38] improves efficiency by decomposing 3D convolutions into separate 2D spatial and 1D temporal operations. TSP [2] introduces temporal channel shifting to model temporal dynamics effectively without adding computational overhead. VideoMAEv2 [40] leverages masked reconstruction pretraining method based on transformer architecture for robust video representation learning. InternVideo2 [41] leverages both large-scale training data and a highly scalable model, further enhancing video representation learning. These models are utilized in various downstream tasks like TAD as a feature extraction method." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.342, + 0.484, + 0.524 + ], + "angle": 0, + "content": "Anchor-free Detector Anchor-free detectors [6, 8, 18, 20, 34, 36, 44, 47] provide flexibility in localizing action instances by utilizing an asymmetric modeling approach. ActionFormer [47] improves TAD performance by leveraging a transformer-based architecture to capture long-range dependencies in video data. TriDet [36] utilizes the trident prediction scheme and its proposed architecture. ActionMamba [6] improves the ActionFormer detector by utilizing Mamba [12] architecture at the temporal feature extraction. However, despite these advancements, anchor-free detectors still require hand-crafted components such as NMS to remove redundant proposals." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.524, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Query-based Detector Query-based detectors, drawing inspiration from DETR [4], employ a set-prediction mechanism that minimizes dependence on hand-crafted components, eliminating the necessity for NMS. RTD-Net [37] and ReAct [35] utilize query-based detection approaches; however, they do not fully address one-to-one matching in their architectures. TadTR [27] introduces cross-window fusion, applying NMS only to overlapping areas in sliding windows, which partially reduces dependency on handcrafted components. DualDETR [53] divides the decoder into separate branches for instance-level and boundary-level decoding, whereas our CAID does not address split branch but unifies comprehensive range information within a single decoder. Both TadTR and DualDETR still rely on sliding windows, which require NMS to handle redundant areas, thereby limiting their applicability as a fully end-to-end detector. In contrast, TE-TAD [15] achieves a fully end-to-end approach for TAD by reformulating coordinate representation, removing the need for hand-crafted components like NMS and sliding windows. Building on TE-TAD, we propose DiGIT, which introduces MDGE, a multi-scale adapter, and CAID for the decoder. Although our DiGIT is primarily based on TE-TAD, our method is designed to be adaptable across various query-based detectors by replacing the encoder with MDGE and decoder with CAID." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.09, + 0.605, + 0.105 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.115, + 0.644, + 0.131 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.136, + 0.907, + 0.379 + ], + "angle": 0, + "content": "Let \\( X \\in \\mathbb{R}^{T_0 \\times C} \\) represents the video feature sequence extracted by the backbone network, where \\( T_0 \\) denotes the temporal length of the sequence, and \\( C \\) corresponds to the feature dimension. Each element of the sequence, denoted as \\( X = \\{x_t\\}_{t=1}^{T_0} \\), is associated with a snippet at timestep \\( t \\) with each snippet covering a few consecutive frames. These snippets are processed using a pre-trained backbone network such as I3D [5] or InternVideo2 [41]. Each video contains multiple action instances, each defined by start and end timestamps \\( s \\) and \\( e \\), as well as its action class \\( c \\). Formally, the set of action instances in a video is expressed as \\( \\mathcal{A} = \\{(s_n, e_n, c_n)\\}_{n=1}^N \\), where \\( N \\) denotes the total number of action instances, and \\( s_n, e_n, \\) and \\( c_n \\) represent the start time, end time, and action class of the \\( n \\)-th instance, respectively. The primary objective of TAD is to predict the set of action instances \\( \\mathcal{A} \\) for a given video." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.378, + 0.909, + 0.507 + ], + "angle": 0, + "content": "The query-based detectors [15, 27, 53] employ \\(N_{q}\\) queries to detect action instances. The set of queries is represented as \\(\\mathcal{Q}^{(0)} = \\{F_q^{(0)}, (c_q^{(0)}, d_q^{(0)})\\}_{q=1}^{N_q}\\), where \\(F_q^{(0)}\\) is the initial embedding of the \\(q\\)-th query, \\(c_q^{(0)}\\) and \\(d_q^{(0)}\\) denote the initial center and width reference point of the \\(q\\)-th query, respectively. These queries interact with the encoded features through deformable cross-attention layers in the decoder, where they are iteratively refined across each layer \\(l\\):" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.518, + 0.907, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Q} ^ {(l)} = \\operatorname {D e c o d e r} ^ {(l)} \\left(\\mathcal {Q} ^ {(l - 1)}\\right) \\quad l = 1, \\dots , L _ {D}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.541, + 0.908, + 0.587 + ], + "angle": 0, + "content": "where \\(L_{D}\\) denotes the number of decoder layer. The final refined queries \\(Q^{(L_D)}\\) are then used for final predictions \\(\\hat{\\mathcal{A}}\\) obtained through the classification and regression heads." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.593, + 0.602, + 0.608 + ], + "angle": 0, + "content": "3.2. DiGIT" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.616, + 0.907, + 0.767 + ], + "angle": 0, + "content": "In this part, we describe our method mainly based on TETAD, but our DiGIT can be applied to various query-based detectors by simply replacing the previous encoder and decoder architecture. The overall architecture of DiGIT is illustrated in Fig. 4. Our method mainly addresses three parts: (1) the multi-dilated gated encoder (MDGE), (2) the multi-scale adapter, which converts the single-scale feature into multi-scale features, providing diverse scale information for query selection and decoder, and (3) the central-adjacent region integrated decoder (CAID)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.767, + 0.906, + 0.811 + ], + "angle": 0, + "content": "**Embedding** We project input features \\( X \\) using a single convolutional neural network to align them with the dimension of the transformer architecture." + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.817, + 0.907, + 0.835 + ], + "angle": 0, + "content": "\\[\nZ ^ {(0)} = \\operatorname {L a y e r N o r m} (\\operatorname {C o n v} (X)), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.839, + 0.906, + 0.902 + ], + "angle": 0, + "content": "where \\(Z^{(0)}\\in \\mathbb{R}^{D\\times T_0}\\) represented the embedded features of the detector. Here, \\(D\\) denotes the width of the encoder and decoder. In contrast to TE-TAD, we do not address the multi-scale features at the initial and encoding stages." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24288" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.882, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.331, + 0.908, + 0.375 + ], + "angle": 0, + "content": "Figure 4. Overview of DiGIT. Our model processes video features through MDGE to capture distinct feature representations utilizing various receptive fields. Subsequently, CAID captures both central and adjacent region information, enhancing action boundary regression and classification. For simplicity, residual connection and layer normalization are omitted." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.381, + 0.482, + 0.472 + ], + "angle": 0, + "content": "Multi-Dilated Gated Encoder (MDGE) As discussed in Sec. 1, both single-scale and multi-scale approaches have inherent limitations. Single-scale methods struggle to capture long temporal dependencies. Conversely, multi-scale methods can capture a broader range of temporal scales but cause highly correlated features across each scale." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.472, + 0.483, + 0.669 + ], + "angle": 0, + "content": "To address the limitations of both approaches, we introduce MDGE that replaces the previous multi-scale deformable encoder structure. Inspired by a previous work [7], MDGE applies multi-dilated convolutions to capture diverse receptive fields within a single encoder. This approach enables the model to extract short-term and long-term temporal features without relying on a multi-scale structure. Furthermore, inspired by gating mechanism [46], MDGE selectively filters out redundant information, retaining only the most relevant features across the different receptive fields. In the following, we describe the detailed structure of MDGE, which is composed of \\( L_{E} \\) multi-dilated gated convolution layers." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.669, + 0.483, + 0.701 + ], + "angle": 0, + "content": "At each encoder layer \\(l\\), the input features \\(Z^{(l-1)}\\) from the previous layer are first projected into two paths:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.712, + 0.483, + 0.733 + ], + "angle": 0, + "content": "\\[\nZ _ {\\text {c o n v}} ^ {(l)} = \\operatorname {L i n e a r} \\left(Z ^ {(l - 1)}\\right), \\quad Z _ {\\text {g a t e}} ^ {(l)} = \\operatorname {L i n e a r} \\left(Z ^ {(l - 1)}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.744, + 0.483, + 0.902 + ], + "angle": 0, + "content": "where \\( Z_{\\mathrm{conv}}^{(l)} \\in \\mathbb{R}^{D_h \\times T_0} \\) and \\( Z_{\\mathrm{gate}}^{(l)} \\in \\mathbb{R}^{D_h \\times T_0} \\). Here, \\( D_h \\) represents the hidden dimension of the feedforward network within the transformer architecture. Instead of utilizing the feedforward network in the encoder, we expand the feature dimension before applying the dilated convolution. This approach retains a similar parameter to a single transformer layer that consists of an attention layer and a feedforward network. Each transformed features, \\( Z_{\\mathrm{conv}}^{(l)} \\) and \\( Z_{\\mathrm{gate}}^{(l)} \\), are then processed in separate paths independently for multidilated convolution and gating mechanism, respectively." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.381, + 0.907, + 0.489 + ], + "angle": 0, + "content": "The transformed features for multi-dilated convolution \\( Z_{\\mathrm{conv}}^{(l)} \\) are split along the channel dimension into \\( N_{d} \\) equal subsets, denoted as \\( Z_{\\mathrm{conv}}^{(l,i)} \\in \\mathbb{R}^{(D_h / N_d) \\times T_0} \\), where \\( N_{d} \\) is the number of parallel dilated convolutions. Each subset is processed by a dilated convolution with a different dilation rate, increasing from 1 up to \\( N_{d} \\). The output features for each subset are expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.494, + 0.907, + 0.515 + ], + "angle": 0, + "content": "\\[\nZ _ {\\text {d i l a t e d}} ^ {(l, i)} = \\operatorname {D i l a t e d C o n v} _ {(l, d _ {i})} \\left(Z _ {\\text {c o n v}} ^ {(l, i)}\\right) \\quad i = 1, \\dots , N _ {d}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.906, + 0.61 + ], + "angle": 0, + "content": "where \\(d_{i}\\) is the dilation rate for the \\(i\\)-th convolution, set as \\(d_{i} = i\\). The increasing dilation rates provide varying receptive field sizes, allowing the model to capture both short- and long-term temporal features simultaneously. Our encoder has two main hyperparameters: the number of dilated convolutions \\(N_{d}\\) and the kernel size." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.611, + 0.906, + 0.645 + ], + "angle": 0, + "content": "Subsequently, the outputs of the dilated convolutions \\( Z_{\\mathrm{dilated}}^{(l,i)} \\) are concatenated along the channel dimension:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.648, + 0.905, + 0.67 + ], + "angle": 0, + "content": "\\[\nZ _ {\\text {c o n c a t}} ^ {(l)} = \\operatorname {C o n c a t} \\left(Z _ {\\text {d i l a t e d}} ^ {(l, 1)}, \\dots , Z _ {\\text {d i l a t e d}} ^ {(l, N _ {d})}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.675, + 0.906, + 0.706 + ], + "angle": 0, + "content": "Following this concatenation, we apply a gating mechanism to selectively retain relevant features:" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.71, + 0.905, + 0.732 + ], + "angle": 0, + "content": "\\[\nZ ^ {(l)} = Z _ {\\text {c o n c a t}} ^ {(l)} \\odot \\sigma \\left(Z _ {\\text {g a t e}} ^ {(l)}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.736, + 0.906, + 0.781 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is an activation function and \\(\\odot\\) denotes elementwise multiplication. Specifically, we use the SiLU activation function for the gate activation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.782, + 0.907, + 0.811 + ], + "angle": 0, + "content": "Consequently, the encoding process across \\(L_{E}\\) layers of MDGE can be summarized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.816, + 0.905, + 0.836 + ], + "angle": 0, + "content": "\\[\nZ ^ {(l)} = \\operatorname {M D G E} ^ {(l)} \\left(Z ^ {(l - 1)}\\right) \\quad l = 1, \\dots , L _ {E}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Our MDGE design enables the encoder to capture diverse temporal relations by leveraging dilated convolutions and a gating mechanism without requiring explicit multiscale features at each layer." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24289" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.272 + ], + "angle": 0, + "content": "Multi-Scale Adapter & Query Selection TE-TAD [15] employs a two-stage approach with multi-scale features for query selection. To take advantage of the two-stage approach and utilize multi-scale features for query selection, we introduce a multi-scale adapter that converts the single-scale feature to multi-scale features. Our multi-scale adapter utilizes the encoder output feature \\( Z^{(L_E)} \\) to generate multi-scale representations. Specifically, \\( Z^{(L_E)} \\) is progressively downsampled to produce a set of features at multiple levels, with each subsequent level reduced to half the temporal length of the previous one. We denote the \\( L \\) levels of multi-scale features as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.28, + 0.483, + 0.298 + ], + "angle": 0, + "content": "\\[\nF ^ {(l)} = \\operatorname {D o w n S a m p l e} \\left(Z ^ {\\left(L _ {E}\\right)}\\right) + E ^ {(l)} \\quad l = 1, \\dots , L, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.305, + 0.484, + 0.456 + ], + "angle": 0, + "content": "where each \\( F^{(l)} \\in \\mathbb{R}^{T_l \\times D} \\) represents the resized feature at level \\( l \\), with \\( T_{l} \\) being half the length of the previous level. To enable the decoder to distinguish between these multi-scale levels, we add a level-specific embedding \\( E^{(l)} \\in \\mathbb{R}^{1 \\times D} \\), applied consistently across all time steps. These multi-scale features are then utilized for the query selection process. Unlike the adaptive query selection (AQS) in TE-TAD [15] that enforces a strict uniform sampling of queries across the video, we apply a top-\\( k \\) selection approach based on binary classification scores from the encoder." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.458, + 0.484, + 0.593 + ], + "angle": 0, + "content": "Subsequently, we utilize the top- \\(k\\) indices to retrieve both the query embeddings and the corresponding reference points \\((c_{q},d_{q})\\) based on a time-aligned query generation method [15] that assigns temporal center points \\(c_{q}\\) and widths \\(d_{q}\\), aligning them with their respective positions in the video. Additionally, the query embedding for each selected query is obtained by linearly projecting the corresponding top- \\(k\\) multi-scale features. The input embedding of a decoder is denoted as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.6, + 0.483, + 0.62 + ], + "angle": 0, + "content": "\\[\nF _ {q} ^ {(0)} = \\operatorname {L a y e r N o r m} \\left(\\operatorname {L i n e a r} \\left(F _ {\\mathrm {t o p k}}\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.627, + 0.404, + 0.641 + ], + "angle": 0, + "content": "where \\(F_{\\mathrm{topk}}\\) denotes the top- \\(k\\) selected features." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.642, + 0.483, + 0.656 + ], + "angle": 0, + "content": "Central-Adjacent Region Integrated Decoder (CAID)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.657, + 0.484, + 0.822 + ], + "angle": 0, + "content": "The previous query-based methods [15, 27] apply temporal deformable cross-attention that applies the center-focused sampling strategy. As discussed in Sec. 1, the center-focused sampling does not provide sufficient information for detecting the action instances. To address this issue, we introduce CAID, which combines central- and adjacent-region cross-attention. In standard deformable cross-attention, features are sampled around each reference point, defined by its center \\( c_{q} \\) and duration \\( d_{q} \\). The sampling offset \\( \\Delta p_{mqk} \\) for each head \\( m \\) and sampling point \\( k \\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.831, + 0.483, + 0.849 + ], + "angle": 0, + "content": "\\[\n\\Delta p _ {m q k} = \\operatorname {L i n e a r} \\left(F _ {q}\\right) = W F _ {q} + b, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\(W\\) and \\(b\\) are learnable parameters for obtaining the sampling offset by linear projection. Generally, \\(W\\) is initialized to zero and \\(b\\) within the range \\([-1, 1]\\). Using the" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "computed offset \\(\\Delta p_{mqk}\\), sampling points \\(p_{mqk}\\) are determined based on the reference points as:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.131, + 0.905, + 0.148 + ], + "angle": 0, + "content": "\\[\np _ {m q k} = c _ {q} + 0. 5 w _ {q} \\Delta p _ {m q k}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.154, + 0.905, + 0.244 + ], + "angle": 0, + "content": "where the factor \\(0.5w_{q}\\) ensures the sampling points are initially positioned close to the center of each reference point. In our approach, we do not change how to obtain the sampling points when addressing central- and adjacent-region sampling. We change the initialization method for the bias value \\(b\\), which determines the initial sampling points." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.245, + 0.907, + 0.547 + ], + "angle": 0, + "content": "As shown in Fig. 4, our CAID contains two cross-attention layers sequentially: central-region cross-attention and adjacent-region cross-attention. For central-region cross-attention, the initial bias of sampling offsets \\( b \\) are initialized uniformly within the range \\([-1,1]\\), which is identical to the previous methods [15, 19, 25, 27, 48, 52]. As Eq. (11), this initialization constrains the initial bias for sampling points \\( b \\) within \\([-0.5,0.5]\\), focusing on the central region of the reference points. For adjacent-region cross-attention, the bias of sampling offsets \\( b \\) are adjusted to capture surrounded points of central-region cross-attention. Specifically, half of the sampling offsets are initialized within the range \\([-1.5,-0.5]\\) to focus on the left, while the other half are initialized within the range \\([0.5,1.5]\\) to focus on the right. This adjustment, combined with Eq. (11), constraints in the initial sampling points \\( p_{mqk} \\) within \\([-0.75,-0.25]\\) and \\([0.25,0.75]\\). Overall, we sequentially apply self-attention, central-region cross-attention, adjacent-region cross-attention, and feedforward network across all \\( L_{D} \\) layers, as shown in Fig. 4." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.554, + 0.727, + 0.57 + ], + "angle": 0, + "content": "3.3. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.576, + 0.906, + 0.62 + ], + "angle": 0, + "content": "Training Following the previous works [15, 27], we use the bipartite matching loss [4]. The total loss \\(\\mathcal{L}_{total}\\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.626, + 0.905, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} (\\mathcal {A}, \\hat {\\mathcal {A}}) = \\sum_ {i = 1} ^ {N _ {q}} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\mathcal {A} _ {i}, \\hat {\\mathcal {A}} _ {\\pi (i)}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.906, + 0.825 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{match}\\) denotes the bipartite matching loss, which considers both classification and regression loss between ground truth \\(\\mathcal{A}_i\\) and predicted action instances \\(\\hat{\\mathcal{A}}_{\\pi(i)}\\) from the last layer of the decoder. The permutation indices \\(\\pi(i)\\) are obtained through bipartite matching [17]. This cost function \\(\\mathcal{L}_{match}\\) is a composite of the classification, and regression loss. We use focal loss [24] for the classification loss to effectively manage class imbalance. For the regression loss, our method incorporates GIoU [33] and a log-ratio distance loss [15]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Inference Following the previous work [15] that removes the need for post-processing steps, the predictions of DiGIT from the final layer of the decoder \\(\\hat{\\mathcal{A}}\\) are directly used. For a fair comparison, we report both raw prediction results and NMS applied results." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24290" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.122, + 0.089, + 0.874, + 0.401 + ], + "angle": 0, + "content": "
    Training TypeHead TypeMethodFeatureTHUMOS14ActivityNet v1.3
    0.30.40.50.60.7Avg.0.50.750.95Avg.
    Full-AFSD [20]I3D [5]67.362.455.543.731.152.052.435.36.534.4
    TALLFormer [8]Swin-B [28]76.0-63.2-34.559.254.136.27.935.6
    ViT-TAD [45]ViT-B [9]85.180.974.261.845.469.555.838.58.837.4
    AdaTAD [26]VideoMAEv2-g [40]89.786.780.971.056.176.961.743.410.941.9
    Head onlyAnchor -freeTriDet [36]I3D [5] / R(2+1)D [38]83.680.172.962.447.469.354.738.08.436.8
    DyFADet [44]I3D [5] / R(2+1)D [38]84.080.172.761.147.969.258.139.68.438.5
    ActionFormer [47]I3D [5] / R(2+1)D [38]82.177.871.059.443.966.854.737.88.436.6
    ActionFormer [47]InternVideo2 [41]82.381.975.165.850.371.961.544.612.741.2
    ActionMamba [6]InternVideo2 [41]86.983.176.965.950.872.762.443.510.242.0
    Query -basedRTD-Net [37]I3D [5] / TSN [39]68.362.351.938.823.749.047.230.78.630.8
    ReAct [35]I3D [5] / TSN [39]69.265.057.147.835.655.049.633.08.632.6
    Self-DETR [16]I3D [5]74.669.560.047.631.856.752.333.78.433.8
    TadTR [27]I3D [5] / R(2+1)D [38]74.869.160.146.632.856.753.637.510.636.8
    DualDETR [53]I3D [5]82.978.070.458.544.466.852.635.07.834.3
    TE-TAD [15]I3D [5] / R(2+1)D [38]83.378.471.360.745.667.954.238.110.637.1
    DiGIT†I3D [5] / R(2+1)D [38]81.677.770.360.548.467.754.338.410.637.2
    DiGITI3D [5] / R(2+1)D [38]83.679.671.961.548.669.054.438.210.737.3
    TadTR [27]InternVideo2 [41]84.879.370.458.243.867.357.138.811.038.2
    TadTR [27] + OursInternVideo2 [41]86.181.873.761.746.369.960.241.011.240.5
    TE-TAD [15]InternVideo2 [41]84.381.173.762.649.570.361.341.810.941.1
    DiGIT†InternVideo2 [41]85.782.375.665.651.472.158.943.411.441.3
    DiGITInternVideo2 [41]87.684.277.667.352.573.862.043.111.342.0
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.404, + 0.907, + 0.434 + ], + "angle": 0, + "content": "Table 1. Performance comparison with state-of-the-art methods on THUMOS14 and ActivityNet v1.3. In cases marked with \\(\\dagger\\), our method does not utilize NMS. For TadTR + Ours, we additionally apply our MDGE and CAID on TadTR." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.444, + 0.224, + 0.461 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.469, + 0.173, + 0.485 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.491, + 0.483, + 0.686 + ], + "angle": 0, + "content": "Datasets We conduct experiments on three datasets: THUMOS14 [14], ActivityNet v1.3 [10], and HACS-Segment [50]. THUMOS14 consists of 20 action classes with 200 validation and 213 test videos, containing 3,007 and 3,358 action instances, respectively. ActivityNet v1.3 is a large-scale dataset with 200 action classes, including 10,024 videos for training and 4,926 videos for validation. HACS-Segment is another large-scale TAD dataset with extensive annotations, covering 200 activity classes similar to ActivityNet v1.3. It provides 37,613 videos for training and 5,981 videos for validation. These datasets provide a rigorous evaluation environment for our method, containing diverse actions and scenes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.687, + 0.483, + 0.793 + ], + "angle": 0, + "content": "Evaluation Metric We follow the standard evaluation protocol for all datasets, utilizing mAP at different intersections over union (IoU) thresholds to evaluate TAD performance. The IoU thresholds for THUMOS14 are set at [0.3:0.7:0.1], while for ActivityNet v1.3 and HACS-Segment, the results are reported at IoU threshold [0.5, 0.75, 0.95] with the average mAP computed at [0.5:0.95:0.05]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.793, + 0.483, + 0.824 + ], + "angle": 0, + "content": "Implementation Details We describe the implementation details for each dataset in the Supplementary Sec. A." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.833, + 0.231, + 0.849 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.902 + ], + "angle": 0, + "content": "THUMOS14 Table 1 contains a comparison with the state-of-the-art methods on THUMOS14. Our DiGIT shows consistent improvements over TadTR [27] and TE-TAD [15] on" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.445, + 0.907, + 0.536 + ], + "angle": 0, + "content": "both I3D [5] and InternVideo2 [41] features. Even without applying NMS, our method outperforms the existing query-based detectors. Furthermore, our model outperforms the existing snippet-based head-only training methods, and our DiGIT shows a comparable performance even compared to the full training method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.537, + 0.909, + 0.734 + ], + "angle": 0, + "content": "ActivityNet v1.3 Following the conventional approach [15, 27, 36, 47], the external classification score is used to evaluate ActivityNet v1.3. The pre-extracted classification scores are combined with class-agnostic predictions from a binary detector to obtain class labels. For \\(\\mathrm{R}(2 + 1)\\mathrm{D}\\) [38] and InternVideo2 [41] features, classification results from CUHK [42] and InternVideo2 [41] are incorporated to obtain class scores, respectively. As demonstrated in Table 1, DiGIT achieves consistent improvements over TadTR and TE-TAD on ActivityNet v1.3. Furthermore, DiGIT demonstrates competitive performance compared to other types of state-of-the-art methods, demonstrating effectiveness across various datasets and feature extractors." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "HACS-Segment Table 2 presents a comparison of our model with state-of-the-art methods on HACS-Segment. Our model achieves significant improvements over previous methods, establishing a new state-of-the-art performance, including mAP at higher IoU thresholds of 0.75 and 0.95. The stronger performance at the 0.95 IoU threshold indicates that DiGIT excels in precise action localization. Moreover, the superior performance of DiGIT on this larger dataset, compared to THUMOS14 and ActivityNet v1.3, demonstrates its scalability and robustness across varying data sizes and complexities." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "24291" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.48, + 0.324 + ], + "angle": 0, + "content": "
    Head TypeMethodFeaturemAP
    0.50.750.95Avg.
    Anchor -basedSSN [51]I3D [5]28.818.85.319.0
    G-TAD [43]I3D [5]41.127.68.327.5
    BMN [22]SlowFast [11]52.536.410.435.8
    TCANet [32]SlowFast [11]54.137.211.336.8
    Anchor -freeTALLFormer [8]Swin-B [28]55.036.111.836.5
    TriDet [36]I3D [5]54.536.811.536.8
    TriDet [36]SlowFast [11]56.739.311.738.6
    TriDet [36]VideoMAEv2-g [40]62.444.113.143.1
    DyFADet [44]SlowFast [11]57.839.811.839.2
    DyFADet [44]VideoMAEv2-g [40]64.044.814.144.3
    ActionFormer [47]InternVideo2 [41]62.644.612.743.3
    ActionMamba [6]InternVideo2 [41]64.045.713.344.6
    Query -basedTadTR [27]I3D [5]47.132.110.932.1
    TadTR [27]InternVideo2 [41]54.238.812.837.8
    TadTR [27] + OursInternVideo2 [41]55.040.013.839.0
    TE-TAD [15]InternVideo2 [41]60.445.616.544.1
    DiGIT†InternVideo2 [41]61.147.517.845.5
    DiGITInternVideo2 [41]62.447.917.645.9
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.326, + 0.483, + 0.381 + ], + "angle": 0, + "content": "Table 2. Performance comparison with state-of-the-art methods on HACS-Segment. In cases marked with \\(\\dagger\\), our method does not utilize NMS. For TadTR + Ours, we additionally apply our MDGE and CAID on TadTR." + }, + { + "type": "image", + "bbox": [ + 0.171, + 0.393, + 0.404, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.506, + 0.483, + 0.548 + ], + "angle": 0, + "content": "Figure 5. Ablation study on MDGE with InternVideo2 features on THUMOS14. The heatmap shows mAP values for different combinations of kernel size and number of dilated convolutions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.559, + 0.258, + 0.575 + ], + "angle": 0, + "content": "4.3. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.582, + 0.483, + 0.793 + ], + "angle": 0, + "content": "Ablation Study on MDGE Fig. 5 shows an ablation study on hyperparameters of MDGE, specifically the impact of kernel size and the number of dilated convolution layers \\( N_{d} \\) on mAP performance. Excluding the configuration with a single dilated convolution that consistently yields lower mAP values, configurations with multiple dilated layers demonstrate improved performance. These results indicate that addressing diverse scale information is crucial for the encoder by utilizing our multi-dilated convolution that enables the model to capture diverse temporal relations. Furthermore, compared to the TE-TAD [15] baseline of 70.4 in Table 4, our MDGE consistently improves performance regardless of hyperparameter variations, demonstrating robustness across different configurations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Ablation Study on CAID Table 3 demonstrates the effects of integrating the proposed adjacent-region cross-attention (ACA) into the decoder operation sequence. We evaluate several configurations, including variations of central-region cross-attention (CCA) with expanded initialization ranges \\((1.5\\times\\) and \\(2.0\\times)\\). CCA \\((1.5\\times)\\) and CCA \\((2.0\\times)\\) (Rows #2 and #3) show that simply increasing the initial" + }, + { + "type": "table", + "bbox": [ + 0.575, + 0.089, + 0.843, + 0.208 + ], + "angle": 0, + "content": "
    Decoder SequencemAP@AVG
    #1SA → CCA → FFN72.5
    #2SA → CCA (1.5×) → FFN72.6
    #3SA → CCA (2.0×) → FFN71.8
    #4SA → ACA → FFN69.2
    #5SA → CCA → CCA → FFN72.7
    #6SA → CCA → ACA → FFN73.8
    #7SA → ACA → CCA → FFN73.2
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.211, + 0.905, + 0.321 + ], + "angle": 0, + "content": "Table 3. Analysis of decoder operation sequences using InternVideo2 features on THUMOS14. SA refers to the self-attention layer. CCA denotes central-region cross-attention (as used in previous works such as [15, 27]). CCA \\((1.5\\times\\) and \\(2.0\\times)\\) indicates an expansion of the initial sampling range of central-region cross-attention by 1.5 and 2.0 times, respectively, to cover a broader area around the reference points. ACA refers to adjacent-region cross-attention, and FFN represents the feedforward network." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.328, + 0.897, + 0.484 + ], + "angle": 0, + "content": "
    BaselineEnc.Dec.MDGECAIDmAP
    0.30.50.7Avg.
    TadTR [27]SS✓84.870.443.867.3
    ✓84.971.944.768.4
    ✓✓84.470.845.467.9
    ✓✓86.173.746.369.9
    TE-TAD [15]MM✓84.373.749.570.3
    85.274.649.970.8
    SM✓85.473.849.170.4
    87.075.851.972.5
    ✓✓85.574.651.071.4
    ✓✓87.677.652.573.8
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.486, + 0.905, + 0.556 + ], + "angle": 0, + "content": "Table 4. Ablation study on the contributions of each component using InternVideo2 features on THUMOS14. The first row for TadTR [27] and TE-TAD [15] represents the baseline performance. Enc. and Dec. refer to how scale information is handled in the encoder and decoder. S: single-scale. M: multi-scale." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.568, + 0.905, + 0.794 + ], + "angle": 0, + "content": "ization range of CCA to cover a broader area, similar range to CAID, does not show the improved performance compared to the original setting (Row #1). This indicates that simply expanding the initialization range does not benefit the detector. Moreover, when using ACA alone (Row #4), we observe a significant decrease in performance, underscoring the importance of balancing adjacent-region information with central-region information. Configurations that use two successive CCA layers (Row #5) show only marginal improvements, suggesting that additional central-region cross-attention alone does not significantly enhance performance. The highest mAP score is achieved by the sequence of SA \\(\\rightarrow\\) CCA \\(\\rightarrow\\) ACA \\(\\rightarrow\\) FFN, which combines central-region cross-attention and adjacent-region cross-attention, which is our CAID (Row #6)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Component Contribution Analysis Table 4 provides an analysis of the performance contributions from each proposed component, evaluated using InternVideo2 [41] features on THUMOS14 [14]. The first row for each method shows the baseline performance without our proposed enhancements, allowing for a direct comparison with subsequent configurations. Notably, converting multi-scale en" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24292" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.141, + 0.089, + 0.432, + 0.183 + ], + "angle": 0, + "content": "
    BaselineAQS [15]mAP
    0.30.50.7Avg.
    TE-TAD [15]✓85.673.747.670.3
    82.571.848.468.7
    DiGIT✓85.876.451.572.2
    87.677.652.573.8
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.185, + 0.484, + 0.213 + ], + "angle": 0, + "content": "Table 5. Ablation study on the query selection method using InternVideo2 features on THUMOS14." + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.218, + 0.434, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.346, + 0.484, + 0.401 + ], + "angle": 0, + "content": "Figure 6. Comparison of training and testing loss for the encoder classification matching loss using InternVideo2 features on THUMOS14. Our method significantly accelerates the convergence of the encoder." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.412, + 0.484, + 0.531 + ], + "angle": 0, + "content": "coding to single-scale encoding alone in TE-TAD [15] results in minimal performance change \\((70.3\\rightarrow 70.4)\\). This result aligns with our motivation, as shown in Fig. 2, which is that the previous multi-scale features contain redundant information. Furthermore, both MDGE and CAID show consistent improvements in both TadTR and TE-TAD, demonstrating the robustness and effectiveness of our approach across different baseline architectures." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.534, + 0.484, + 0.776 + ], + "angle": 0, + "content": "Effect of MDGE In TE-TAD [15], adaptive query selection (AQS) is employed to sample initial queries across the entire video sequence uniformly. This process enforces a strict uniform selection of queries to prevent queries from being overly concentrated in certain areas, as might happen with a simple top-k selection. However, our observations suggest that this strict uniform condition is unnecessary when using a well-trained encoder, as provided by our MDGE. As shown in Table 5, removing AQS results in higher mAP scores for DiGIT, whereas the performance of TE-TAD declines without AQS. Furthermore, as illustrated in Fig. 6, DiGIT exhibits faster convergence and consistently lower loss values. These results indicate that our MDGE enhances the representational ability of the encoder and can reduce the heuristic part of the query selection, which positively impact overall detection performance." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.788, + 0.274, + 0.803 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Visualization of Cosine Similarity on Encoder Output Features Fig. 7 presents a comparison of cosine similarity matrices for encoder output features between TE-TAD and DiGIT. Our DiGIT shows improved feature discriminability, indicating that MDGE captures distinct temporal patterns more effectively compared to TE-TAD [15]." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.09, + 0.709, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.569, + 0.224, + 0.662, + 0.236 + ], + "angle": 0, + "content": "(a) TE-TAD [15]" + }, + { + "type": "image", + "bbox": [ + 0.714, + 0.091, + 0.899, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.779, + 0.224, + 0.835, + 0.235 + ], + "angle": 0, + "content": "(b) DiGIT" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.238, + 0.907, + 0.306 + ], + "angle": 0, + "content": "Figure 7. Comparison of cosine similarity on encoder output features between TE-TAD and DiGIT. Top: represents cosine similarity, with red boxes indicating regions of similarity among features within the ground truth. Bottom: displays the ground truth action timeline for reference. Sample taken from THUMOS14." + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.307, + 0.889, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.402, + 0.888, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.498, + 0.906, + 0.541 + ], + "angle": 0, + "content": "Figure 8. Visualization of sampling offsets in cross-attention layers on THUMOS14. Each point denotes the mean value across the dataset, with error bars indicating the standard deviation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.545, + 0.907, + 0.697 + ], + "angle": 0, + "content": "Visualization of Sampling Offsets Fig. 8 shows the distribution of sampling offsets relative to the center and width of each action query. The values 0, -1, and 1 correspond to the center \\( c_{q} \\), the start boundary \\( c_{q} - d_{q} \\), and the end boundary \\( c_{q} + d_{q} \\), respectively. This visualization shows that our method gathers information from diverse sampling points, covering both central and adjacent regions. Furthermore, while deformable attention allows learnable offsets, they remain close to their initial points, indicating the importance of the initial value of \\( b \\) in Eq. (10)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.71, + 0.634, + 0.725 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.907, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a multi-dilated gated encoder and central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). MDGE offers diverse receptive fields while maintaining a single-scale encoding structure by utilizing multi-dilated convolutions. CAID provides essential information to precisely detect action instances by focusing on both the central- and adjacent-regions of action instances. Extensive experiments demonstrate that DiGIT outperforms the previous query-based methods. Furthermore, our method consistently improves when integrated with the existing query-based detectors." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24293" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.252 + ], + "angle": 0, + "content": "This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant, funded by the Korea government (MSIT) (No. RS-2019-II190079, Artificial Intelligence Graduate School Program (Korea University), No. RS-2024-00457882, AI Research Hub Project, and No. RS-2022-II220984, Development of Artificial Intelligence Technology for Personalized Plug-and-Play Explanation and Verification of Explanation)." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.264, + 0.188, + 0.28 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.29, + 0.484, + 0.365 + ], + "angle": 0, + "content": "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18559-18569, 2024. 1, 2, 3, 6" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.091, + 0.905, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24296" + } + ] +] \ No newline at end of file diff --git a/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_origin.pdf b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ddf329fa5d21d5294c8c134b327567b495d6ba7c --- /dev/null +++ b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/140a65e2-34a7-4d35-8450-c8ca2647aff6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:64474a6e29a09893ca524fb092cf71a0baa10b37f4e13c2da1200cdc1cfab8cd +size 4621682 diff --git a/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/full.md b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d5008af9c4b228ef8b11bc6e1df90f60589cab52 --- /dev/null +++ b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/full.md @@ -0,0 +1,329 @@ +# DiGIT: Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer + +Ho-Joong Kim Yearang Lee Jung-Ho Hong Seong-Whan Lee\* + +Dept. of Artificial Intelligence, Korea University, Seoul, Korea + +{hojoong_kim, yr_lee, jungho-hong, sw.lee}@korea.ac.kr + +# Abstract + +In this paper, we examine a key limitation in query-based detectors for temporal action detection (TAD), which arises from their direct adaptation of originally designed architectures for object detection. Despite the effectiveness of the existing models, they struggle to fully address the unique challenges of TAD, such as the redundancy in multiscale features and the limited ability to capture sufficient temporal context. To address these issues, we propose a multi-dilated gated encoder and central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). Our approach replaces the existing encoder that consists of multi-scale deformable attention and feedforward network with our multi-dilated gated encoder. Our proposed encoder reduces the redundant information caused by multi-level features while maintaining the ability to capture fine-grained and long-range temporal information. Furthermore, we introduce a central-adjacent region integrated decoder that leverages a more comprehensive sampling strategy for deformable cross-attention to capture the essential information. Extensive experiments demonstrate that DiGIT achieves state-of-the-art performance on THUMOS14, ActivityNet v1.3, and HACS-Segment. Code is available at: https://github.com/Dotori-HJ/DGIT + +# 1. Introduction + +Temporal action detection (TAD) is crucial for video understanding and supports a wide range of real-world applications, including video surveillance, summarization, and retrieval. TAD aims to detect action instances within untrimmed videos by identifying action classes along with their start and end times. The most existing TAD methods [15, 27, 36, 47] are a snippet-based approach, which utilizes pre-extracted features to address long durations. This approach does not require the computational cost for the backbone network at the detection stage, enabling the detector to address a comprehensive length of features at once. The existing methods can be divided into three approaches: + +![](images/ae2df80e0561713561f32837f3635470b83e3e5403c32ffca110f5f352c3b18a.jpg) +Figure 1. Convergence curves with InternVideo2 [41] features on THUMOS14 [14]. Our method boosts the previous query-based detectors like TE-TAD [15] and TadTR [27]. + +anchor-based [3, 21, 22, 29, 43, 49], anchor-free [6, 8, 20, 34, 36, 44, 47], and query-based [15, 27, 35, 37, 53]. + +Query-based detectors, inspired by DETR [4], have attracted interest because of their potential to eliminate reliance on hand-crafted components, such as the sliding window and non-maximum suppression (NMS). This capability derives from their adoption of a set-prediction mechanism, which enables an end-to-end detection process through a one-to-one matching paradigm. Among them, TE-TAD [15] enables a full end-to-end detection process by reformulating the coordinate representation based on recent DETR-based network architectures, such as multiscale deformable attention [52]. However, despite these advancements, query-based detectors still rely on originally designed architectures for object detection, which is not fully suited to addressing the unique challenges of TAD. We identify two limitations within the encoder and decoder structures of existing query-based TAD models. (1) In the encoder, simply utilizing single-scale [27, 53] feature or multi-scale [15] features fails to extract the meaningful features needed to capture the diverse temporal scale information and distinct feature representations. (2) In the decoder, the deformable cross-attention mechanism focuses on the central regions of reference points, overlooking surrounding areas essential for accurately detecting the action instances. + +In the encoder, existing query-based detectors employ either single-scale [27, 53] or multi-scale [15] features, but both approaches have inherent limitations. The single-scale approach [27, 53] processes feature at a single resolution throughout the encoder and decoder, intuitively restricting the model to capture varying durations. The multi-scale approach [15] combines features across multiple resolutions, enhancing the ability of the model to detect different lengths of actions by aggregating broader contextual information. However, despite the advantage of the multi-scale approach, it struggles to capture distinct feature representations at each level, resulting in highly correlated features across scales. Fig. 2 illustrates this issue by comparing layer-wise CKA [31] similarities on the pre-encoder and post-encoder features between an object detection model (DINO [48]) and a TAD model (TE-TAD [15]). As shown in Fig. 2 on the left, the pre-encoder features of TE-TAD show high similarity among high-level features (3-6) compared to DINO. This is due to the repeated use of single convolutional projections, where the final-layer feature is downsampled to produce multi-scale features. These highly similar pre-encoder features of TE-TAD cause the multiscale deformable attention to propagate redundant information across levels during encoding. Consequently, as shown in Fig. 2(b) on the right, the post-encoder features show high similarity across levels compared to DINO. This result suggests that utilizing multi-scale features from the initial stage leads to excessive redundancy. + +In the decoder, deformable cross-attention relies on sampling points near the center of reference points, typically determined by multiplying the reference width by 0.5. However, this center-focused approach restricts the model from capturing the contextual information from the surrounding region, which is crucial for classifying action instances and determining their start and end boundaries. Fig. 3 shows the challenges of center-focused sampling through the example of actions like LongJump and HighJump, where both involve a similar running motion. When the model focuses only on the central motion (red box), identifying these two actions is challenging because the surrounding context (gray frames), such as the final landing motion, provides essential cues for identifying them. Furthermore, relying solely on the running motion makes it challenging to determine accurate start and end boundaries. These observations suggest that the center-focused sampling strategy is insufficient for capturing the full context of action instances. + +In this paper, we propose a multi-dilated gated encoder and a central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). First, we introduce a multi-dilated gated encoder (MDGE), which replaces the previous multi-scale deformable attention and feedforward network in the encoder. MDGE utilizes multidilated convolutions to capture diverse feature represen + +![](images/d3ad5ea598b3b953460938654b8437e1809e1b6a9680e392d9e9e1023fae8f50.jpg) +(a) DINO-5scale [48] with ResNet-50 [13] on COCO [23] + +![](images/abafb8f9c2111be27c57ecf5fd0df5c80bb61b630fa9a3678d57b034bd0a8015.jpg) + +![](images/4f6becd25a51f63045452034b29c4791d76e20eab5083c2deb0f9562b3e9390b.jpg) +(b) TE-TAD [15] with InternVideo2 [41] on THUMOS14 [14] + +![](images/b1847841f9b22e2b7327f09aeb6086a2cefb435a674001546860158a770465a0.jpg) + +![](images/46281f2e477ad915919dd7e7cafc57b39a8c4d234c2c97f28a3bbd7923789f06.jpg) +Figure 2. Layer-wise CKA similarity comparison between object detection and TAD. The left and right sides are extracted from pre-encoder and post-encoder features, respectively. The 1-5 or 1-6 labels on each axis correspond to the number of multi-scale feature levels used in the respective models. + +![](images/167002ac5f2107ab328abedb4cf7ebe0efaba73694fdcbf0c56fc2da5eb30827.jpg) +(a) LongJump +(b) HighJump +Figure 3. Challenges of center-focused sampling in action distinction. Each sequence shows seven evenly sampled frames across the action duration, using examples from THUMOS14 [14]. + +tations across multiple receptive fields, reducing redundant information in multi-scale features while preserving the benefits of utilizing multi-scale information. Additionally, we present a central-adjacent region integrated decoder (CAID), which combines both central- and adjacent-region sampling based on the deformable cross-attention mechanism. By incorporating these two types of information, CAID enables the detector to capture a complete contextual view for each detection query. Extensive experiments demonstrate that DiGIT achieves state-of-the-art performance on popular benchmarks, and our method is adaptable to existing query-based detection frameworks. + +Our contributions are summarized as three-fold: + +- We propose DiGIT that combines multi-dilated gated encoder and central-adjacent region integrated decoder to address the unique challenges of TAD. +- As shown in Fig. 1, our method consistently achieves faster convergence and improves performance when applied to existing query-based detectors. +- Our experiments demonstrate that our DiGIT achieves state-of-the-art performance on THUMOS14, ActivityNet v1.3, and HACS-Segment. + +# 2. Related Work + +Action Recognition Action recognition is a fundamental task in video analysis. It involves classifying video sequences into specific action categories. I3D [5] extends the inception network by incorporating 3D convolutions, while R(2+1)D [38] improves efficiency by decomposing 3D convolutions into separate 2D spatial and 1D temporal operations. TSP [2] introduces temporal channel shifting to model temporal dynamics effectively without adding computational overhead. VideoMAEv2 [40] leverages masked reconstruction pretraining method based on transformer architecture for robust video representation learning. InternVideo2 [41] leverages both large-scale training data and a highly scalable model, further enhancing video representation learning. These models are utilized in various downstream tasks like TAD as a feature extraction method. + +Anchor-free Detector Anchor-free detectors [6, 8, 18, 20, 34, 36, 44, 47] provide flexibility in localizing action instances by utilizing an asymmetric modeling approach. ActionFormer [47] improves TAD performance by leveraging a transformer-based architecture to capture long-range dependencies in video data. TriDet [36] utilizes the trident prediction scheme and its proposed architecture. ActionMamba [6] improves the ActionFormer detector by utilizing Mamba [12] architecture at the temporal feature extraction. However, despite these advancements, anchor-free detectors still require hand-crafted components such as NMS to remove redundant proposals. + +Query-based Detector Query-based detectors, drawing inspiration from DETR [4], employ a set-prediction mechanism that minimizes dependence on hand-crafted components, eliminating the necessity for NMS. RTD-Net [37] and ReAct [35] utilize query-based detection approaches; however, they do not fully address one-to-one matching in their architectures. TadTR [27] introduces cross-window fusion, applying NMS only to overlapping areas in sliding windows, which partially reduces dependency on handcrafted components. DualDETR [53] divides the decoder into separate branches for instance-level and boundary-level decoding, whereas our CAID does not address split branch but unifies comprehensive range information within a single decoder. Both TadTR and DualDETR still rely on sliding windows, which require NMS to handle redundant areas, thereby limiting their applicability as a fully end-to-end detector. In contrast, TE-TAD [15] achieves a fully end-to-end approach for TAD by reformulating coordinate representation, removing the need for hand-crafted components like NMS and sliding windows. Building on TE-TAD, we propose DiGIT, which introduces MDGE, a multi-scale adapter, and CAID for the decoder. Although our DiGIT is primarily based on TE-TAD, our method is designed to be adaptable across various query-based detectors by replacing the encoder with MDGE and decoder with CAID. + +# 3. Method + +# 3.1. Preliminary + +Let $X \in \mathbb{R}^{T_0 \times C}$ represents the video feature sequence extracted by the backbone network, where $T_0$ denotes the temporal length of the sequence, and $C$ corresponds to the feature dimension. Each element of the sequence, denoted as $X = \{x_t\}_{t=1}^{T_0}$ , is associated with a snippet at timestep $t$ with each snippet covering a few consecutive frames. These snippets are processed using a pre-trained backbone network such as I3D [5] or InternVideo2 [41]. Each video contains multiple action instances, each defined by start and end timestamps $s$ and $e$ , as well as its action class $c$ . Formally, the set of action instances in a video is expressed as $\mathcal{A} = \{(s_n, e_n, c_n)\}_{n=1}^N$ , where $N$ denotes the total number of action instances, and $s_n, e_n,$ and $c_n$ represent the start time, end time, and action class of the $n$ -th instance, respectively. The primary objective of TAD is to predict the set of action instances $\mathcal{A}$ for a given video. + +The query-based detectors [15, 27, 53] employ $N_{q}$ queries to detect action instances. The set of queries is represented as $\mathcal{Q}^{(0)} = \{F_q^{(0)}, (c_q^{(0)}, d_q^{(0)})\}_{q=1}^{N_q}$ , where $F_q^{(0)}$ is the initial embedding of the $q$ -th query, $c_q^{(0)}$ and $d_q^{(0)}$ denote the initial center and width reference point of the $q$ -th query, respectively. These queries interact with the encoded features through deformable cross-attention layers in the decoder, where they are iteratively refined across each layer $l$ : + +$$ +\mathcal {Q} ^ {(l)} = \operatorname {D e c o d e r} ^ {(l)} \left(\mathcal {Q} ^ {(l - 1)}\right) \quad l = 1, \dots , L _ {D}, \tag {1} +$$ + +where $L_{D}$ denotes the number of decoder layer. The final refined queries $Q^{(L_D)}$ are then used for final predictions $\hat{\mathcal{A}}$ obtained through the classification and regression heads. + +# 3.2. DiGIT + +In this part, we describe our method mainly based on TETAD, but our DiGIT can be applied to various query-based detectors by simply replacing the previous encoder and decoder architecture. The overall architecture of DiGIT is illustrated in Fig. 4. Our method mainly addresses three parts: (1) the multi-dilated gated encoder (MDGE), (2) the multi-scale adapter, which converts the single-scale feature into multi-scale features, providing diverse scale information for query selection and decoder, and (3) the central-adjacent region integrated decoder (CAID). + +**Embedding** We project input features $X$ using a single convolutional neural network to align them with the dimension of the transformer architecture. + +$$ +Z ^ {(0)} = \operatorname {L a y e r N o r m} (\operatorname {C o n v} (X)), \tag {2} +$$ + +where $Z^{(0)}\in \mathbb{R}^{D\times T_0}$ represented the embedded features of the detector. Here, $D$ denotes the width of the encoder and decoder. In contrast to TE-TAD, we do not address the multi-scale features at the initial and encoding stages. + +![](images/b6aacd0e4406fdf6c12ad154bd1993858de8728bb4101a17ab8b4ed78380c882.jpg) +Figure 4. Overview of DiGIT. Our model processes video features through MDGE to capture distinct feature representations utilizing various receptive fields. Subsequently, CAID captures both central and adjacent region information, enhancing action boundary regression and classification. For simplicity, residual connection and layer normalization are omitted. + +Multi-Dilated Gated Encoder (MDGE) As discussed in Sec. 1, both single-scale and multi-scale approaches have inherent limitations. Single-scale methods struggle to capture long temporal dependencies. Conversely, multi-scale methods can capture a broader range of temporal scales but cause highly correlated features across each scale. + +To address the limitations of both approaches, we introduce MDGE that replaces the previous multi-scale deformable encoder structure. Inspired by a previous work [7], MDGE applies multi-dilated convolutions to capture diverse receptive fields within a single encoder. This approach enables the model to extract short-term and long-term temporal features without relying on a multi-scale structure. Furthermore, inspired by gating mechanism [46], MDGE selectively filters out redundant information, retaining only the most relevant features across the different receptive fields. In the following, we describe the detailed structure of MDGE, which is composed of $L_{E}$ multi-dilated gated convolution layers. + +At each encoder layer $l$ , the input features $Z^{(l-1)}$ from the previous layer are first projected into two paths: + +$$ +Z _ {\text {c o n v}} ^ {(l)} = \operatorname {L i n e a r} \left(Z ^ {(l - 1)}\right), \quad Z _ {\text {g a t e}} ^ {(l)} = \operatorname {L i n e a r} \left(Z ^ {(l - 1)}\right), \tag {3} +$$ + +where $Z_{\mathrm{conv}}^{(l)} \in \mathbb{R}^{D_h \times T_0}$ and $Z_{\mathrm{gate}}^{(l)} \in \mathbb{R}^{D_h \times T_0}$ . Here, $D_h$ represents the hidden dimension of the feedforward network within the transformer architecture. Instead of utilizing the feedforward network in the encoder, we expand the feature dimension before applying the dilated convolution. This approach retains a similar parameter to a single transformer layer that consists of an attention layer and a feedforward network. Each transformed features, $Z_{\mathrm{conv}}^{(l)}$ and $Z_{\mathrm{gate}}^{(l)}$ , are then processed in separate paths independently for multidilated convolution and gating mechanism, respectively. + +The transformed features for multi-dilated convolution $Z_{\mathrm{conv}}^{(l)}$ are split along the channel dimension into $N_{d}$ equal subsets, denoted as $Z_{\mathrm{conv}}^{(l,i)} \in \mathbb{R}^{(D_h / N_d) \times T_0}$ , where $N_{d}$ is the number of parallel dilated convolutions. Each subset is processed by a dilated convolution with a different dilation rate, increasing from 1 up to $N_{d}$ . The output features for each subset are expressed as follows: + +$$ +Z _ {\text {d i l a t e d}} ^ {(l, i)} = \operatorname {D i l a t e d C o n v} _ {(l, d _ {i})} \left(Z _ {\text {c o n v}} ^ {(l, i)}\right) \quad i = 1, \dots , N _ {d}, \tag {4} +$$ + +where $d_{i}$ is the dilation rate for the $i$ -th convolution, set as $d_{i} = i$ . The increasing dilation rates provide varying receptive field sizes, allowing the model to capture both short- and long-term temporal features simultaneously. Our encoder has two main hyperparameters: the number of dilated convolutions $N_{d}$ and the kernel size. + +Subsequently, the outputs of the dilated convolutions $Z_{\mathrm{dilated}}^{(l,i)}$ are concatenated along the channel dimension: + +$$ +Z _ {\text {c o n c a t}} ^ {(l)} = \operatorname {C o n c a t} \left(Z _ {\text {d i l a t e d}} ^ {(l, 1)}, \dots , Z _ {\text {d i l a t e d}} ^ {(l, N _ {d})}\right). \tag {5} +$$ + +Following this concatenation, we apply a gating mechanism to selectively retain relevant features: + +$$ +Z ^ {(l)} = Z _ {\text {c o n c a t}} ^ {(l)} \odot \sigma \left(Z _ {\text {g a t e}} ^ {(l)}\right), \tag {6} +$$ + +where $\sigma$ is an activation function and $\odot$ denotes elementwise multiplication. Specifically, we use the SiLU activation function for the gate activation. + +Consequently, the encoding process across $L_{E}$ layers of MDGE can be summarized as follows: + +$$ +Z ^ {(l)} = \operatorname {M D G E} ^ {(l)} \left(Z ^ {(l - 1)}\right) \quad l = 1, \dots , L _ {E}. \tag {7} +$$ + +Our MDGE design enables the encoder to capture diverse temporal relations by leveraging dilated convolutions and a gating mechanism without requiring explicit multiscale features at each layer. + +Multi-Scale Adapter & Query Selection TE-TAD [15] employs a two-stage approach with multi-scale features for query selection. To take advantage of the two-stage approach and utilize multi-scale features for query selection, we introduce a multi-scale adapter that converts the single-scale feature to multi-scale features. Our multi-scale adapter utilizes the encoder output feature $Z^{(L_E)}$ to generate multi-scale representations. Specifically, $Z^{(L_E)}$ is progressively downsampled to produce a set of features at multiple levels, with each subsequent level reduced to half the temporal length of the previous one. We denote the $L$ levels of multi-scale features as follows: + +$$ +F ^ {(l)} = \operatorname {D o w n S a m p l e} \left(Z ^ {\left(L _ {E}\right)}\right) + E ^ {(l)} \quad l = 1, \dots , L, \tag {8} +$$ + +where each $F^{(l)} \in \mathbb{R}^{T_l \times D}$ represents the resized feature at level $l$ , with $T_{l}$ being half the length of the previous level. To enable the decoder to distinguish between these multi-scale levels, we add a level-specific embedding $E^{(l)} \in \mathbb{R}^{1 \times D}$ , applied consistently across all time steps. These multi-scale features are then utilized for the query selection process. Unlike the adaptive query selection (AQS) in TE-TAD [15] that enforces a strict uniform sampling of queries across the video, we apply a top- $k$ selection approach based on binary classification scores from the encoder. + +Subsequently, we utilize the top- $k$ indices to retrieve both the query embeddings and the corresponding reference points $(c_{q},d_{q})$ based on a time-aligned query generation method [15] that assigns temporal center points $c_{q}$ and widths $d_{q}$ , aligning them with their respective positions in the video. Additionally, the query embedding for each selected query is obtained by linearly projecting the corresponding top- $k$ multi-scale features. The input embedding of a decoder is denoted as follows: + +$$ +F _ {q} ^ {(0)} = \operatorname {L a y e r N o r m} \left(\operatorname {L i n e a r} \left(F _ {\mathrm {t o p k}}\right)\right), \tag {9} +$$ + +where $F_{\mathrm{topk}}$ denotes the top- $k$ selected features. + +# Central-Adjacent Region Integrated Decoder (CAID) + +The previous query-based methods [15, 27] apply temporal deformable cross-attention that applies the center-focused sampling strategy. As discussed in Sec. 1, the center-focused sampling does not provide sufficient information for detecting the action instances. To address this issue, we introduce CAID, which combines central- and adjacent-region cross-attention. In standard deformable cross-attention, features are sampled around each reference point, defined by its center $c_{q}$ and duration $d_{q}$ . The sampling offset $\Delta p_{mqk}$ for each head $m$ and sampling point $k$ is computed as: + +$$ +\Delta p _ {m q k} = \operatorname {L i n e a r} \left(F _ {q}\right) = W F _ {q} + b, \tag {10} +$$ + +where $W$ and $b$ are learnable parameters for obtaining the sampling offset by linear projection. Generally, $W$ is initialized to zero and $b$ within the range $[-1, 1]$ . Using the + +computed offset $\Delta p_{mqk}$ , sampling points $p_{mqk}$ are determined based on the reference points as: + +$$ +p _ {m q k} = c _ {q} + 0. 5 w _ {q} \Delta p _ {m q k}, \tag {11} +$$ + +where the factor $0.5w_{q}$ ensures the sampling points are initially positioned close to the center of each reference point. In our approach, we do not change how to obtain the sampling points when addressing central- and adjacent-region sampling. We change the initialization method for the bias value $b$ , which determines the initial sampling points. + +As shown in Fig. 4, our CAID contains two cross-attention layers sequentially: central-region cross-attention and adjacent-region cross-attention. For central-region cross-attention, the initial bias of sampling offsets $b$ are initialized uniformly within the range $[-1,1]$ , which is identical to the previous methods [15, 19, 25, 27, 48, 52]. As Eq. (11), this initialization constrains the initial bias for sampling points $b$ within $[-0.5,0.5]$ , focusing on the central region of the reference points. For adjacent-region cross-attention, the bias of sampling offsets $b$ are adjusted to capture surrounded points of central-region cross-attention. Specifically, half of the sampling offsets are initialized within the range $[-1.5,-0.5]$ to focus on the left, while the other half are initialized within the range $[0.5,1.5]$ to focus on the right. This adjustment, combined with Eq. (11), constraints in the initial sampling points $p_{mqk}$ within $[-0.75,-0.25]$ and $[0.25,0.75]$ . Overall, we sequentially apply self-attention, central-region cross-attention, adjacent-region cross-attention, and feedforward network across all $L_{D}$ layers, as shown in Fig. 4. + +# 3.3. Training and Inference + +Training Following the previous works [15, 27], we use the bipartite matching loss [4]. The total loss $\mathcal{L}_{total}$ is defined as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} (\mathcal {A}, \hat {\mathcal {A}}) = \sum_ {i = 1} ^ {N _ {q}} \mathcal {L} _ {\text {m a t c h}} \left(\mathcal {A} _ {i}, \hat {\mathcal {A}} _ {\pi (i)}\right), \tag {12} +$$ + +where $\mathcal{L}_{match}$ denotes the bipartite matching loss, which considers both classification and regression loss between ground truth $\mathcal{A}_i$ and predicted action instances $\hat{\mathcal{A}}_{\pi(i)}$ from the last layer of the decoder. The permutation indices $\pi(i)$ are obtained through bipartite matching [17]. This cost function $\mathcal{L}_{match}$ is a composite of the classification, and regression loss. We use focal loss [24] for the classification loss to effectively manage class imbalance. For the regression loss, our method incorporates GIoU [33] and a log-ratio distance loss [15]. + +Inference Following the previous work [15] that removes the need for post-processing steps, the predictions of DiGIT from the final layer of the decoder $\hat{\mathcal{A}}$ are directly used. For a fair comparison, we report both raw prediction results and NMS applied results. + +
    Training TypeHead TypeMethodFeatureTHUMOS14ActivityNet v1.3
    0.30.40.50.60.7Avg.0.50.750.95Avg.
    Full-AFSD [20]I3D [5]67.362.455.543.731.152.052.435.36.534.4
    TALLFormer [8]Swin-B [28]76.0-63.2-34.559.254.136.27.935.6
    ViT-TAD [45]ViT-B [9]85.180.974.261.845.469.555.838.58.837.4
    AdaTAD [26]VideoMAEv2-g [40]89.786.780.971.056.176.961.743.410.941.9
    Head onlyAnchor -freeTriDet [36]I3D [5] / R(2+1)D [38]83.680.172.962.447.469.354.738.08.436.8
    DyFADet [44]I3D [5] / R(2+1)D [38]84.080.172.761.147.969.258.139.68.438.5
    ActionFormer [47]I3D [5] / R(2+1)D [38]82.177.871.059.443.966.854.737.88.436.6
    ActionFormer [47]InternVideo2 [41]82.381.975.165.850.371.961.544.612.741.2
    ActionMamba [6]InternVideo2 [41]86.983.176.965.950.872.762.443.510.242.0
    Query -basedRTD-Net [37]I3D [5] / TSN [39]68.362.351.938.823.749.047.230.78.630.8
    ReAct [35]I3D [5] / TSN [39]69.265.057.147.835.655.049.633.08.632.6
    Self-DETR [16]I3D [5]74.669.560.047.631.856.752.333.78.433.8
    TadTR [27]I3D [5] / R(2+1)D [38]74.869.160.146.632.856.753.637.510.636.8
    DualDETR [53]I3D [5]82.978.070.458.544.466.852.635.07.834.3
    TE-TAD [15]I3D [5] / R(2+1)D [38]83.378.471.360.745.667.954.238.110.637.1
    DiGIT†I3D [5] / R(2+1)D [38]81.677.770.360.548.467.754.338.410.637.2
    DiGITI3D [5] / R(2+1)D [38]83.679.671.961.548.669.054.438.210.737.3
    TadTR [27]InternVideo2 [41]84.879.370.458.243.867.357.138.811.038.2
    TadTR [27] + OursInternVideo2 [41]86.181.873.761.746.369.960.241.011.240.5
    TE-TAD [15]InternVideo2 [41]84.381.173.762.649.570.361.341.810.941.1
    DiGIT†InternVideo2 [41]85.782.375.665.651.472.158.943.411.441.3
    DiGITInternVideo2 [41]87.684.277.667.352.573.862.043.111.342.0
    + +Table 1. Performance comparison with state-of-the-art methods on THUMOS14 and ActivityNet v1.3. In cases marked with $\dagger$ , our method does not utilize NMS. For TadTR + Ours, we additionally apply our MDGE and CAID on TadTR. + +# 4. Experiments + +# 4.1. Setup + +Datasets We conduct experiments on three datasets: THUMOS14 [14], ActivityNet v1.3 [10], and HACS-Segment [50]. THUMOS14 consists of 20 action classes with 200 validation and 213 test videos, containing 3,007 and 3,358 action instances, respectively. ActivityNet v1.3 is a large-scale dataset with 200 action classes, including 10,024 videos for training and 4,926 videos for validation. HACS-Segment is another large-scale TAD dataset with extensive annotations, covering 200 activity classes similar to ActivityNet v1.3. It provides 37,613 videos for training and 5,981 videos for validation. These datasets provide a rigorous evaluation environment for our method, containing diverse actions and scenes. + +Evaluation Metric We follow the standard evaluation protocol for all datasets, utilizing mAP at different intersections over union (IoU) thresholds to evaluate TAD performance. The IoU thresholds for THUMOS14 are set at [0.3:0.7:0.1], while for ActivityNet v1.3 and HACS-Segment, the results are reported at IoU threshold [0.5, 0.75, 0.95] with the average mAP computed at [0.5:0.95:0.05]. + +Implementation Details We describe the implementation details for each dataset in the Supplementary Sec. A. + +# 4.2. Main Results + +THUMOS14 Table 1 contains a comparison with the state-of-the-art methods on THUMOS14. Our DiGIT shows consistent improvements over TadTR [27] and TE-TAD [15] on + +both I3D [5] and InternVideo2 [41] features. Even without applying NMS, our method outperforms the existing query-based detectors. Furthermore, our model outperforms the existing snippet-based head-only training methods, and our DiGIT shows a comparable performance even compared to the full training method. + +ActivityNet v1.3 Following the conventional approach [15, 27, 36, 47], the external classification score is used to evaluate ActivityNet v1.3. The pre-extracted classification scores are combined with class-agnostic predictions from a binary detector to obtain class labels. For $\mathrm{R}(2 + 1)\mathrm{D}$ [38] and InternVideo2 [41] features, classification results from CUHK [42] and InternVideo2 [41] are incorporated to obtain class scores, respectively. As demonstrated in Table 1, DiGIT achieves consistent improvements over TadTR and TE-TAD on ActivityNet v1.3. Furthermore, DiGIT demonstrates competitive performance compared to other types of state-of-the-art methods, demonstrating effectiveness across various datasets and feature extractors. + +HACS-Segment Table 2 presents a comparison of our model with state-of-the-art methods on HACS-Segment. Our model achieves significant improvements over previous methods, establishing a new state-of-the-art performance, including mAP at higher IoU thresholds of 0.75 and 0.95. The stronger performance at the 0.95 IoU threshold indicates that DiGIT excels in precise action localization. Moreover, the superior performance of DiGIT on this larger dataset, compared to THUMOS14 and ActivityNet v1.3, demonstrates its scalability and robustness across varying data sizes and complexities. + +
    Head TypeMethodFeaturemAP
    0.50.750.95Avg.
    Anchor -basedSSN [51]I3D [5]28.818.85.319.0
    G-TAD [43]I3D [5]41.127.68.327.5
    BMN [22]SlowFast [11]52.536.410.435.8
    TCANet [32]SlowFast [11]54.137.211.336.8
    Anchor -freeTALLFormer [8]Swin-B [28]55.036.111.836.5
    TriDet [36]I3D [5]54.536.811.536.8
    TriDet [36]SlowFast [11]56.739.311.738.6
    TriDet [36]VideoMAEv2-g [40]62.444.113.143.1
    DyFADet [44]SlowFast [11]57.839.811.839.2
    DyFADet [44]VideoMAEv2-g [40]64.044.814.144.3
    ActionFormer [47]InternVideo2 [41]62.644.612.743.3
    ActionMamba [6]InternVideo2 [41]64.045.713.344.6
    Query -basedTadTR [27]I3D [5]47.132.110.932.1
    TadTR [27]InternVideo2 [41]54.238.812.837.8
    TadTR [27] + OursInternVideo2 [41]55.040.013.839.0
    TE-TAD [15]InternVideo2 [41]60.445.616.544.1
    DiGIT†InternVideo2 [41]61.147.517.845.5
    DiGITInternVideo2 [41]62.447.917.645.9
    + +![](images/5a8896336a5da505df404cc7e14a636797c23f3024161d6a641fa60a8827a93b.jpg) +Figure 5. Ablation study on MDGE with InternVideo2 features on THUMOS14. The heatmap shows mAP values for different combinations of kernel size and number of dilated convolutions. + +# 4.3. Further Analysis + +Ablation Study on MDGE Fig. 5 shows an ablation study on hyperparameters of MDGE, specifically the impact of kernel size and the number of dilated convolution layers $N_{d}$ on mAP performance. Excluding the configuration with a single dilated convolution that consistently yields lower mAP values, configurations with multiple dilated layers demonstrate improved performance. These results indicate that addressing diverse scale information is crucial for the encoder by utilizing our multi-dilated convolution that enables the model to capture diverse temporal relations. Furthermore, compared to the TE-TAD [15] baseline of 70.4 in Table 4, our MDGE consistently improves performance regardless of hyperparameter variations, demonstrating robustness across different configurations. + +Ablation Study on CAID Table 3 demonstrates the effects of integrating the proposed adjacent-region cross-attention (ACA) into the decoder operation sequence. We evaluate several configurations, including variations of central-region cross-attention (CCA) with expanded initialization ranges $(1.5\times$ and $2.0\times)$ . CCA $(1.5\times)$ and CCA $(2.0\times)$ (Rows #2 and #3) show that simply increasing the initial + +Table 2. Performance comparison with state-of-the-art methods on HACS-Segment. In cases marked with $\dagger$ , our method does not utilize NMS. For TadTR + Ours, we additionally apply our MDGE and CAID on TadTR. + +
    Decoder SequencemAP@AVG
    #1SA → CCA → FFN72.5
    #2SA → CCA (1.5×) → FFN72.6
    #3SA → CCA (2.0×) → FFN71.8
    #4SA → ACA → FFN69.2
    #5SA → CCA → CCA → FFN72.7
    #6SA → CCA → ACA → FFN73.8
    #7SA → ACA → CCA → FFN73.2
    + +Table 3. Analysis of decoder operation sequences using InternVideo2 features on THUMOS14. SA refers to the self-attention layer. CCA denotes central-region cross-attention (as used in previous works such as [15, 27]). CCA $(1.5\times$ and $2.0\times)$ indicates an expansion of the initial sampling range of central-region cross-attention by 1.5 and 2.0 times, respectively, to cover a broader area around the reference points. ACA refers to adjacent-region cross-attention, and FFN represents the feedforward network. + +
    BaselineEnc.Dec.MDGECAIDmAP
    0.30.50.7Avg.
    TadTR [27]SS✓84.870.443.867.3
    ✓84.971.944.768.4
    ✓✓84.470.845.467.9
    ✓✓86.173.746.369.9
    TE-TAD [15]MM✓84.373.749.570.3
    85.274.649.970.8
    SM✓85.473.849.170.4
    87.075.851.972.5
    ✓✓85.574.651.071.4
    ✓✓87.677.652.573.8
    + +Table 4. Ablation study on the contributions of each component using InternVideo2 features on THUMOS14. The first row for TadTR [27] and TE-TAD [15] represents the baseline performance. Enc. and Dec. refer to how scale information is handled in the encoder and decoder. S: single-scale. M: multi-scale. + +ization range of CCA to cover a broader area, similar range to CAID, does not show the improved performance compared to the original setting (Row #1). This indicates that simply expanding the initialization range does not benefit the detector. Moreover, when using ACA alone (Row #4), we observe a significant decrease in performance, underscoring the importance of balancing adjacent-region information with central-region information. Configurations that use two successive CCA layers (Row #5) show only marginal improvements, suggesting that additional central-region cross-attention alone does not significantly enhance performance. The highest mAP score is achieved by the sequence of SA $\rightarrow$ CCA $\rightarrow$ ACA $\rightarrow$ FFN, which combines central-region cross-attention and adjacent-region cross-attention, which is our CAID (Row #6). + +Component Contribution Analysis Table 4 provides an analysis of the performance contributions from each proposed component, evaluated using InternVideo2 [41] features on THUMOS14 [14]. The first row for each method shows the baseline performance without our proposed enhancements, allowing for a direct comparison with subsequent configurations. Notably, converting multi-scale en + +
    BaselineAQS [15]mAP
    0.30.50.7Avg.
    TE-TAD [15]✓85.673.747.670.3
    82.571.848.468.7
    DiGIT✓85.876.451.572.2
    87.677.652.573.8
    + +Table 5. Ablation study on the query selection method using InternVideo2 features on THUMOS14. + +![](images/be6c3dbb41c7d17b3b9288b244a4e9c2752b49c0126f7e31c735d2738ce2e947.jpg) +Figure 6. Comparison of training and testing loss for the encoder classification matching loss using InternVideo2 features on THUMOS14. Our method significantly accelerates the convergence of the encoder. + +coding to single-scale encoding alone in TE-TAD [15] results in minimal performance change $(70.3\rightarrow 70.4)$ . This result aligns with our motivation, as shown in Fig. 2, which is that the previous multi-scale features contain redundant information. Furthermore, both MDGE and CAID show consistent improvements in both TadTR and TE-TAD, demonstrating the robustness and effectiveness of our approach across different baseline architectures. + +Effect of MDGE In TE-TAD [15], adaptive query selection (AQS) is employed to sample initial queries across the entire video sequence uniformly. This process enforces a strict uniform selection of queries to prevent queries from being overly concentrated in certain areas, as might happen with a simple top-k selection. However, our observations suggest that this strict uniform condition is unnecessary when using a well-trained encoder, as provided by our MDGE. As shown in Table 5, removing AQS results in higher mAP scores for DiGIT, whereas the performance of TE-TAD declines without AQS. Furthermore, as illustrated in Fig. 6, DiGIT exhibits faster convergence and consistently lower loss values. These results indicate that our MDGE enhances the representational ability of the encoder and can reduce the heuristic part of the query selection, which positively impact overall detection performance. + +# 4.4. Qualitative Results + +Visualization of Cosine Similarity on Encoder Output Features Fig. 7 presents a comparison of cosine similarity matrices for encoder output features between TE-TAD and DiGIT. Our DiGIT shows improved feature discriminability, indicating that MDGE captures distinct temporal patterns more effectively compared to TE-TAD [15]. + +![](images/b4b907098c1eff613484ad33bc38f6b9037ddeeb094d349f0672c244e60ee36d.jpg) +(a) TE-TAD [15] + +![](images/0d5fdccaf7ddcbf6b978eeaed6d4d6b1533fe9097e46c254eda385152fcb4639.jpg) +(b) DiGIT + +![](images/1f7fa3b7c35acea3d59f0e49efe20e9772232c7f99f14c0ae673dfa0efd1406f.jpg) +Figure 7. Comparison of cosine similarity on encoder output features between TE-TAD and DiGIT. Top: represents cosine similarity, with red boxes indicating regions of similarity among features within the ground truth. Bottom: displays the ground truth action timeline for reference. Sample taken from THUMOS14. + +![](images/f25b88c2f2a3f0389c02dbf73ae555c4d61eaa9fa2d1b3a7ada8f6498cd8345b.jpg) +Figure 8. Visualization of sampling offsets in cross-attention layers on THUMOS14. Each point denotes the mean value across the dataset, with error bars indicating the standard deviation. + +Visualization of Sampling Offsets Fig. 8 shows the distribution of sampling offsets relative to the center and width of each action query. The values 0, -1, and 1 correspond to the center $c_{q}$ , the start boundary $c_{q} - d_{q}$ , and the end boundary $c_{q} + d_{q}$ , respectively. This visualization shows that our method gathers information from diverse sampling points, covering both central and adjacent regions. Furthermore, while deformable attention allows learnable offsets, they remain close to their initial points, indicating the importance of the initial value of $b$ in Eq. (10). + +# 5. Conclusion + +In this paper, we propose a multi-dilated gated encoder and central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). MDGE offers diverse receptive fields while maintaining a single-scale encoding structure by utilizing multi-dilated convolutions. CAID provides essential information to precisely detect action instances by focusing on both the central- and adjacent-regions of action instances. Extensive experiments demonstrate that DiGIT outperforms the previous query-based methods. Furthermore, our method consistently improves when integrated with the existing query-based detectors. + +# Acknowledgement + +This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant, funded by the Korea government (MSIT) (No. RS-2019-II190079, Artificial Intelligence Graduate School Program (Korea University), No. RS-2024-00457882, AI Research Hub Project, and No. RS-2022-II220984, Development of Artificial Intelligence Technology for Personalized Plug-and-Play Explanation and Verification of Explanation). + +# References + +[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. Diagnosing error in temporal action detectors. In Proceedings of the European Conference on Computer Vision, pages 256-272, 2018. 12 +[2] Humam Alwassel, Silvio Giancola, and Bernard Ghanem. TSP: Temporally-sensitive pretraining of video encoders for localization tasks. 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DINO: DETR with improved denoising anchor boxes for end-to-end object detection. In Proceedings of the European Conference on Computer Vision, 2022. 2, 5 + +[49] Chen Zhao, Ali K Thabet, and Bernard Ghanem. Video self-stitching graph network for temporal action localization. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 13658-13667, 2021. 1 +[50] Hang Zhao, Antonio Torralba, Lorenzo Torresani, and Zhicheng Yan. HACS: Human action clips and segments dataset for recognition and temporal localization. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 8668-8678, 2019. 6, 12, 14 +[51] Yue Zhao, Yuanjun Xiong, Limin Wang, Zhirong Wu, Xiaou Tang, and Dahua Lin. Temporal action detection with structured segment networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 2914-2923, 2017. 7 +[52] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable DETR: Deformable transformers for end-to-end object detection. In International Conference on Learning Representations, 2020. 1, 5 +[53] Yuhan Zhu, Guozhen Zhang, Jing Tan, Gangshan Wu, and Limin Wang. Dual DETRs for multi-label temporal action detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18559-18569, 2024. 1, 2, 3, 6 \ No newline at end of file diff --git a/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/images.zip b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..63dfd5d9fcf268bbeff675a56574df33d63d0bc1 --- /dev/null +++ b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:420e6bd4b9269fb49e9d52069fe7325ea13f110b783437a3aa1146de8484fc2b +size 621337 diff --git a/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/layout.json b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..c3fbe5d1dcbed533ea10594d2efabde66c175fa2 --- /dev/null +++ b/2025/DiGIT_ Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer/layout.json @@ -0,0 +1,9317 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 63, + 100, + 547, + 136 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 100, + 547, + 136 + ], + "spans": [ + { + "bbox": [ + 63, + 100, + 547, + 136 + ], + "type": "text", + "content": "DiGIT: Multi-Dilated Gated Encoder and Central-Adjacent Region Integrated Decoder for Temporal Action Detection Transformer" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 119, + 154, + 486, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 154, + 486, + 169 + ], + "spans": [ + { + "bbox": [ + 119, + 154, + 486, + 169 + ], + "type": "text", + "content": "Ho-Joong Kim Yearang Lee Jung-Ho Hong Seong-Whan Lee\\*" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 178, + 172, + 432, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 178, + 172, + 432, + 185 + ], + "spans": [ + { + "bbox": [ + 178, + 172, + 432, + 185 + ], + "type": "text", + "content": "Dept. of Artificial Intelligence, Korea University, Seoul, Korea" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 160, + 186, + 447, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 160, + 186, + 447, + 198 + ], + "spans": [ + { + "bbox": [ + 160, + 186, + 447, + 198 + ], + "type": "text", + "content": "{hojoong_kim, yr_lee, jungho-hong, sw.lee}@korea.ac.kr" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 219, + 200, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 219, + 200, + 232 + ], + "spans": [ + { + "bbox": [ + 151, + 219, + 200, + 232 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 244, + 297, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 244, + 297, + 520 + ], + "spans": [ + { + "bbox": [ + 53, + 244, + 297, + 520 + ], + "type": "text", + "content": "In this paper, we examine a key limitation in query-based detectors for temporal action detection (TAD), which arises from their direct adaptation of originally designed architectures for object detection. Despite the effectiveness of the existing models, they struggle to fully address the unique challenges of TAD, such as the redundancy in multiscale features and the limited ability to capture sufficient temporal context. To address these issues, we propose a multi-dilated gated encoder and central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). Our approach replaces the existing encoder that consists of multi-scale deformable attention and feedforward network with our multi-dilated gated encoder. Our proposed encoder reduces the redundant information caused by multi-level features while maintaining the ability to capture fine-grained and long-range temporal information. Furthermore, we introduce a central-adjacent region integrated decoder that leverages a more comprehensive sampling strategy for deformable cross-attention to capture the essential information. Extensive experiments demonstrate that DiGIT achieves state-of-the-art performance on THUMOS14, ActivityNet v1.3, and HACS-Segment. Code is available at: https://github.com/Dotori-HJ/DGIT" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 532, + 135, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 532, + 135, + 544 + ], + "spans": [ + { + "bbox": [ + 56, + 532, + 135, + 544 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 552, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 296, + 696 + ], + "type": "text", + "content": "Temporal action detection (TAD) is crucial for video understanding and supports a wide range of real-world applications, including video surveillance, summarization, and retrieval. TAD aims to detect action instances within untrimmed videos by identifying action classes along with their start and end times. The most existing TAD methods [15, 27, 36, 47] are a snippet-based approach, which utilizes pre-extracted features to address long durations. This approach does not require the computational cost for the backbone network at the detection stage, enabling the detector to address a comprehensive length of features at once. The existing methods can be divided into three approaches:" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 334, + 220, + 535, + 373 + ], + "blocks": [ + { + "bbox": [ + 334, + 220, + 535, + 373 + ], + "lines": [ + { + "bbox": [ + 334, + 220, + 535, + 373 + ], + "spans": [ + { + "bbox": [ + 334, + 220, + 535, + 373 + ], + "type": "image", + "image_path": "ae2df80e0561713561f32837f3635470b83e3e5403c32ffca110f5f352c3b18a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 376, + 555, + 409 + ], + "lines": [ + { + "bbox": [ + 313, + 376, + 555, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 555, + 409 + ], + "type": "text", + "content": "Figure 1. Convergence curves with InternVideo2 [41] features on THUMOS14 [14]. Our method boosts the previous query-based detectors like TE-TAD [15] and TadTR [27]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 414, + 553, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 414, + 553, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 414, + 553, + 437 + ], + "type": "text", + "content": "anchor-based [3, 21, 22, 29, 43, 49], anchor-free [6, 8, 20, 34, 36, 44, 47], and query-based [15, 27, 35, 37, 53]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 555, + 715 + ], + "type": "text", + "content": "Query-based detectors, inspired by DETR [4], have attracted interest because of their potential to eliminate reliance on hand-crafted components, such as the sliding window and non-maximum suppression (NMS). This capability derives from their adoption of a set-prediction mechanism, which enables an end-to-end detection process through a one-to-one matching paradigm. Among them, TE-TAD [15] enables a full end-to-end detection process by reformulating the coordinate representation based on recent DETR-based network architectures, such as multiscale deformable attention [52]. However, despite these advancements, query-based detectors still rely on originally designed architectures for object detection, which is not fully suited to addressing the unique challenges of TAD. We identify two limitations within the encoder and decoder structures of existing query-based TAD models. (1) In the encoder, simply utilizing single-scale [27, 53] feature or multi-scale [15] features fails to extract the meaningful features needed to capture the diverse temporal scale information and distinct feature representations. (2) In the decoder, the deformable cross-attention mechanism focuses on the central regions of reference points, overlooking surrounding areas essential for accurately detecting the action instances." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 703, + 147, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 703, + 147, + 712 + ], + "spans": [ + { + "bbox": [ + 70, + 703, + 147, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "24286" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 407 + ], + "type": "text", + "content": "In the encoder, existing query-based detectors employ either single-scale [27, 53] or multi-scale [15] features, but both approaches have inherent limitations. The single-scale approach [27, 53] processes feature at a single resolution throughout the encoder and decoder, intuitively restricting the model to capture varying durations. The multi-scale approach [15] combines features across multiple resolutions, enhancing the ability of the model to detect different lengths of actions by aggregating broader contextual information. However, despite the advantage of the multi-scale approach, it struggles to capture distinct feature representations at each level, resulting in highly correlated features across scales. Fig. 2 illustrates this issue by comparing layer-wise CKA [31] similarities on the pre-encoder and post-encoder features between an object detection model (DINO [48]) and a TAD model (TE-TAD [15]). As shown in Fig. 2 on the left, the pre-encoder features of TE-TAD show high similarity among high-level features (3-6) compared to DINO. This is due to the repeated use of single convolutional projections, where the final-layer feature is downsampled to produce multi-scale features. These highly similar pre-encoder features of TE-TAD cause the multiscale deformable attention to propagate redundant information across levels during encoding. Consequently, as shown in Fig. 2(b) on the right, the post-encoder features show high similarity across levels compared to DINO. This result suggests that utilizing multi-scale features from the initial stage leads to excessive redundancy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 411, + 296, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 296, + 626 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 296, + 626 + ], + "type": "text", + "content": "In the decoder, deformable cross-attention relies on sampling points near the center of reference points, typically determined by multiplying the reference width by 0.5. However, this center-focused approach restricts the model from capturing the contextual information from the surrounding region, which is crucial for classifying action instances and determining their start and end boundaries. Fig. 3 shows the challenges of center-focused sampling through the example of actions like LongJump and HighJump, where both involve a similar running motion. When the model focuses only on the central motion (red box), identifying these two actions is challenging because the surrounding context (gray frames), such as the final landing motion, provides essential cues for identifying them. Furthermore, relying solely on the running motion makes it challenging to determine accurate start and end boundaries. These observations suggest that the center-focused sampling strategy is insufficient for capturing the full context of action instances." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 296, + 715 + ], + "type": "text", + "content": "In this paper, we propose a multi-dilated gated encoder and a central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). First, we introduce a multi-dilated gated encoder (MDGE), which replaces the previous multi-scale deformable attention and feedforward network in the encoder. MDGE utilizes multidilated convolutions to capture diverse feature represen" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 338, + 72, + 422, + 155 + ], + "blocks": [ + { + "bbox": [ + 338, + 72, + 422, + 155 + ], + "lines": [ + { + "bbox": [ + 338, + 72, + 422, + 155 + ], + "spans": [ + { + "bbox": [ + 338, + 72, + 422, + 155 + ], + "type": "image", + "image_path": "d3ad5ea598b3b953460938654b8437e1809e1b6a9680e392d9e9e1023fae8f50.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 341, + 156, + 528, + 166 + ], + "lines": [ + { + "bbox": [ + 341, + 156, + 528, + 166 + ], + "spans": [ + { + "bbox": [ + 341, + 156, + 528, + 166 + ], + "type": "text", + "content": "(a) DINO-5scale [48] with ResNet-50 [13] on COCO [23]" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 444, + 72, + 529, + 155 + ], + "blocks": [ + { + "bbox": [ + 444, + 72, + 529, + 155 + ], + "lines": [ + { + "bbox": [ + 444, + 72, + 529, + 155 + ], + "spans": [ + { + "bbox": [ + 444, + 72, + 529, + 155 + ], + "type": "image", + "image_path": "abafb8f9c2111be27c57ecf5fd0df5c80bb61b630fa9a3678d57b034bd0a8015.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 338, + 167, + 422, + 251 + ], + "blocks": [ + { + "bbox": [ + 338, + 167, + 422, + 251 + ], + "lines": [ + { + "bbox": [ + 338, + 167, + 422, + 251 + ], + "spans": [ + { + "bbox": [ + 338, + 167, + 422, + 251 + ], + "type": "image", + "image_path": "4f6becd25a51f63045452034b29c4791d76e20eab5083c2deb0f9562b3e9390b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 334, + 251, + 534, + 261 + ], + "lines": [ + { + "bbox": [ + 334, + 251, + 534, + 261 + ], + "spans": [ + { + "bbox": [ + 334, + 251, + 534, + 261 + ], + "type": "text", + "content": "(b) TE-TAD [15] with InternVideo2 [41] on THUMOS14 [14]" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 444, + 167, + 528, + 251 + ], + "blocks": [ + { + "bbox": [ + 444, + 167, + 528, + 251 + ], + "lines": [ + { + "bbox": [ + 444, + 167, + 528, + 251 + ], + "spans": [ + { + "bbox": [ + 444, + 167, + 528, + 251 + ], + "type": "image", + "image_path": "b1847841f9b22e2b7327f09aeb6086a2cefb435a674001546860158a770465a0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 320, + 554, + 355 + ], + "blocks": [ + { + "bbox": [ + 313, + 263, + 555, + 318 + ], + "lines": [ + { + "bbox": [ + 313, + 263, + 555, + 318 + ], + "spans": [ + { + "bbox": [ + 313, + 263, + 555, + 318 + ], + "type": "text", + "content": "Figure 2. Layer-wise CKA similarity comparison between object detection and TAD. The left and right sides are extracted from pre-encoder and post-encoder features, respectively. The 1-5 or 1-6 labels on each axis correspond to the number of multi-scale feature levels used in the respective models." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 315, + 320, + 554, + 355 + ], + "lines": [ + { + "bbox": [ + 315, + 320, + 554, + 355 + ], + "spans": [ + { + "bbox": [ + 315, + 320, + 554, + 355 + ], + "type": "image", + "image_path": "46281f2e477ad915919dd7e7cafc57b39a8c4d234c2c97f28a3bbd7923789f06.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 315, + 365, + 553, + 400 + ], + "blocks": [ + { + "bbox": [ + 411, + 356, + 457, + 365 + ], + "lines": [ + { + "bbox": [ + 411, + 356, + 457, + 365 + ], + "spans": [ + { + "bbox": [ + 411, + 356, + 457, + 365 + ], + "type": "text", + "content": "(a) LongJump" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 315, + 365, + 553, + 400 + ], + "lines": [ + { + "bbox": [ + 315, + 365, + 553, + 400 + ], + "spans": [ + { + "bbox": [ + 315, + 365, + 553, + 400 + ], + "type": "image", + "image_path": "167002ac5f2107ab328abedb4cf7ebe0efaba73694fdcbf0c56fc2da5eb30827.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 401, + 457, + 411 + ], + "lines": [ + { + "bbox": [ + 411, + 401, + 457, + 411 + ], + "spans": [ + { + "bbox": [ + 411, + 401, + 457, + 411 + ], + "type": "text", + "content": "(b) HighJump" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 411, + 555, + 444 + ], + "lines": [ + { + "bbox": [ + 313, + 411, + 555, + 444 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 555, + 444 + ], + "type": "text", + "content": "Figure 3. Challenges of center-focused sampling in action distinction. Each sequence shows seven evenly sampled frames across the action duration, using examples from THUMOS14 [14]." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 448, + 554, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 448, + 554, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 448, + 554, + 591 + ], + "type": "text", + "content": "tations across multiple receptive fields, reducing redundant information in multi-scale features while preserving the benefits of utilizing multi-scale information. Additionally, we present a central-adjacent region integrated decoder (CAID), which combines both central- and adjacent-region sampling based on the deformable cross-attention mechanism. By incorporating these two types of information, CAID enables the detector to capture a complete contextual view for each detection query. Extensive experiments demonstrate that DiGIT achieves state-of-the-art performance on popular benchmarks, and our method is adaptable to existing query-based detection frameworks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 592, + 509, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 592, + 509, + 602 + ], + "spans": [ + { + "bbox": [ + 313, + 592, + 509, + 602 + ], + "type": "text", + "content": "Our contributions are summarized as three-fold:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 604, + 553, + 712 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 314, + 604, + 553, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 604, + 553, + 639 + ], + "spans": [ + { + "bbox": [ + 314, + 604, + 553, + 639 + ], + "type": "text", + "content": "- We propose DiGIT that combines multi-dilated gated encoder and central-adjacent region integrated decoder to address the unique challenges of TAD." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 314, + 639, + 553, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 639, + 553, + 675 + ], + "spans": [ + { + "bbox": [ + 314, + 639, + 553, + 675 + ], + "type": "text", + "content": "- As shown in Fig. 1, our method consistently achieves faster convergence and improves performance when applied to existing query-based detectors." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 675, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 675, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 675, + 553, + 712 + ], + "type": "text", + "content": "- Our experiments demonstrate that our DiGIT achieves state-of-the-art performance on THUMOS14, ActivityNet v1.3, and HACS-Segment." + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24287" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 142, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 142, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 142, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 270 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 270 + ], + "type": "text", + "content": "Action Recognition Action recognition is a fundamental task in video analysis. It involves classifying video sequences into specific action categories. I3D [5] extends the inception network by incorporating 3D convolutions, while R(2+1)D [38] improves efficiency by decomposing 3D convolutions into separate 2D spatial and 1D temporal operations. TSP [2] introduces temporal channel shifting to model temporal dynamics effectively without adding computational overhead. VideoMAEv2 [40] leverages masked reconstruction pretraining method based on transformer architecture for robust video representation learning. InternVideo2 [41] leverages both large-scale training data and a highly scalable model, further enhancing video representation learning. These models are utilized in various downstream tasks like TAD as a feature extraction method." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 270, + 296, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 270, + 296, + 415 + ], + "spans": [ + { + "bbox": [ + 55, + 270, + 296, + 415 + ], + "type": "text", + "content": "Anchor-free Detector Anchor-free detectors [6, 8, 18, 20, 34, 36, 44, 47] provide flexibility in localizing action instances by utilizing an asymmetric modeling approach. ActionFormer [47] improves TAD performance by leveraging a transformer-based architecture to capture long-range dependencies in video data. TriDet [36] utilizes the trident prediction scheme and its proposed architecture. ActionMamba [6] improves the ActionFormer detector by utilizing Mamba [12] architecture at the temporal feature extraction. However, despite these advancements, anchor-free detectors still require hand-crafted components such as NMS to remove redundant proposals." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 415, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 415, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 415, + 296, + 714 + ], + "type": "text", + "content": "Query-based Detector Query-based detectors, drawing inspiration from DETR [4], employ a set-prediction mechanism that minimizes dependence on hand-crafted components, eliminating the necessity for NMS. RTD-Net [37] and ReAct [35] utilize query-based detection approaches; however, they do not fully address one-to-one matching in their architectures. TadTR [27] introduces cross-window fusion, applying NMS only to overlapping areas in sliding windows, which partially reduces dependency on handcrafted components. DualDETR [53] divides the decoder into separate branches for instance-level and boundary-level decoding, whereas our CAID does not address split branch but unifies comprehensive range information within a single decoder. Both TadTR and DualDETR still rely on sliding windows, which require NMS to handle redundant areas, thereby limiting their applicability as a fully end-to-end detector. In contrast, TE-TAD [15] achieves a fully end-to-end approach for TAD by reformulating coordinate representation, removing the need for hand-crafted components like NMS and sliding windows. Building on TE-TAD, we propose DiGIT, which introduces MDGE, a multi-scale adapter, and CAID for the decoder. Although our DiGIT is primarily based on TE-TAD, our method is designed to be adaptable across various query-based detectors by replacing the encoder with MDGE and decoder with CAID." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 314, + 71, + 370, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 71, + 370, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 370, + 83 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 91, + 394, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 394, + 103 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 394, + 103 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{T_0 \\times C}" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " represents the video feature sequence extracted by the backbone network, where " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "T_0" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " denotes the temporal length of the sequence, and " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " corresponds to the feature dimension. Each element of the sequence, denoted as " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "X = \\{x_t\\}_{t=1}^{T_0}" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": ", is associated with a snippet at timestep " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " with each snippet covering a few consecutive frames. These snippets are processed using a pre-trained backbone network such as I3D [5] or InternVideo2 [41]. Each video contains multiple action instances, each defined by start and end timestamps " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": ", as well as its action class " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": ". Formally, the set of action instances in a video is expressed as " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{A} = \\{(s_n, e_n, c_n)\\}_{n=1}^N" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " denotes the total number of action instances, and " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "s_n, e_n," + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "c_n" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " represent the start time, end time, and action class of the " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": "-th instance, respectively. The primary objective of TAD is to predict the set of action instances " + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 313, + 107, + 555, + 300 + ], + "type": "text", + "content": " for a given video." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "spans": [ + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": "The query-based detectors [15, 27, 53] employ " + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "inline_equation", + "content": "N_{q}" + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": " queries to detect action instances. The set of queries is represented as " + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}^{(0)} = \\{F_q^{(0)}, (c_q^{(0)}, d_q^{(0)})\\}_{q=1}^{N_q}" + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "inline_equation", + "content": "F_q^{(0)}" + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": " is the initial embedding of the " + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": "-th query, " + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "inline_equation", + "content": "c_q^{(0)}" + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "inline_equation", + "content": "d_q^{(0)}" + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": " denote the initial center and width reference point of the " + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": "-th query, respectively. These queries interact with the encoded features through deformable cross-attention layers in the decoder, where they are iteratively refined across each layer " + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 313, + 299, + 556, + 401 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 343, + 410, + 555, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 410, + 555, + 425 + ], + "spans": [ + { + "bbox": [ + 343, + 410, + 555, + 425 + ], + "type": "interline_equation", + "content": "\\mathcal {Q} ^ {(l)} = \\operatorname {D e c o d e r} ^ {(l)} \\left(\\mathcal {Q} ^ {(l - 1)}\\right) \\quad l = 1, \\dots , L _ {D}, \\tag {1}", + "image_path": "569e1f8daf5f3a903aebc57300555eb020b2f16bce088b961f868192825f01ff.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "type": "inline_equation", + "content": "L_{D}" + }, + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "type": "text", + "content": " denotes the number of decoder layer. The final refined queries " + }, + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "type": "inline_equation", + "content": "Q^{(L_D)}" + }, + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "type": "text", + "content": " are then used for final predictions " + }, + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{A}}" + }, + { + "bbox": [ + 313, + 428, + 555, + 464 + ], + "type": "text", + "content": " obtained through the classification and regression heads." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 469, + 368, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 469, + 368, + 481 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 368, + 481 + ], + "type": "text", + "content": "3.2. DiGIT" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 487, + 555, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 555, + 607 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 555, + 607 + ], + "type": "text", + "content": "In this part, we describe our method mainly based on TETAD, but our DiGIT can be applied to various query-based detectors by simply replacing the previous encoder and decoder architecture. The overall architecture of DiGIT is illustrated in Fig. 4. Our method mainly addresses three parts: (1) the multi-dilated gated encoder (MDGE), (2) the multi-scale adapter, which converts the single-scale feature into multi-scale features, providing diverse scale information for query selection and decoder, and (3) the central-adjacent region integrated decoder (CAID)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 607, + 554, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 607, + 554, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 607, + 554, + 642 + ], + "type": "text", + "content": "**Embedding** We project input features " + }, + { + "bbox": [ + 313, + 607, + 554, + 642 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 313, + 607, + 554, + 642 + ], + "type": "text", + "content": " using a single convolutional neural network to align them with the dimension of the transformer architecture." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 375, + 647, + 555, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 647, + 555, + 661 + ], + "spans": [ + { + "bbox": [ + 375, + 647, + 555, + 661 + ], + "type": "interline_equation", + "content": "Z ^ {(0)} = \\operatorname {L a y e r N o r m} (\\operatorname {C o n v} (X)), \\tag {2}", + "image_path": "e57e31697f8786e7815ed4b0b742200c7661717b7a404702c770dcc6b01f8c5d.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 664, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 664, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 664, + 554, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 664, + 554, + 714 + ], + "type": "inline_equation", + "content": "Z^{(0)}\\in \\mathbb{R}^{D\\times T_0}" + }, + { + "bbox": [ + 313, + 664, + 554, + 714 + ], + "type": "text", + "content": " represented the embedded features of the detector. Here, " + }, + { + "bbox": [ + 313, + 664, + 554, + 714 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 664, + 554, + 714 + ], + "type": "text", + "content": " denotes the width of the encoder and decoder. In contrast to TE-TAD, we do not address the multi-scale features at the initial and encoding stages." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24288" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 539, + 259 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 539, + 259 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 539, + 259 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 539, + 259 + ], + "type": "image", + "image_path": "b6aacd0e4406fdf6c12ad154bd1993858de8728bb4101a17ab8b4ed78380c882.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 262, + 555, + 297 + ], + "lines": [ + { + "bbox": [ + 54, + 262, + 555, + 297 + ], + "spans": [ + { + "bbox": [ + 54, + 262, + 555, + 297 + ], + "type": "text", + "content": "Figure 4. Overview of DiGIT. Our model processes video features through MDGE to capture distinct feature representations utilizing various receptive fields. Subsequently, CAID captures both central and adjacent region information, enhancing action boundary regression and classification. For simplicity, residual connection and layer normalization are omitted." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 301, + 294, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 301, + 294, + 373 + ], + "spans": [ + { + "bbox": [ + 54, + 301, + 294, + 373 + ], + "type": "text", + "content": "Multi-Dilated Gated Encoder (MDGE) As discussed in Sec. 1, both single-scale and multi-scale approaches have inherent limitations. Single-scale methods struggle to capture long temporal dependencies. Conversely, multi-scale methods can capture a broader range of temporal scales but cause highly correlated features across each scale." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 373, + 295, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 373, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 54, + 373, + 295, + 529 + ], + "type": "text", + "content": "To address the limitations of both approaches, we introduce MDGE that replaces the previous multi-scale deformable encoder structure. Inspired by a previous work [7], MDGE applies multi-dilated convolutions to capture diverse receptive fields within a single encoder. This approach enables the model to extract short-term and long-term temporal features without relying on a multi-scale structure. Furthermore, inspired by gating mechanism [46], MDGE selectively filters out redundant information, retaining only the most relevant features across the different receptive fields. In the following, we describe the detailed structure of MDGE, which is composed of " + }, + { + "bbox": [ + 54, + 373, + 295, + 529 + ], + "type": "inline_equation", + "content": "L_{E}" + }, + { + "bbox": [ + 54, + 373, + 295, + 529 + ], + "type": "text", + "content": " multi-dilated gated convolution layers." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 529, + 295, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 529, + 295, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 529, + 295, + 555 + ], + "type": "text", + "content": "At each encoder layer " + }, + { + "bbox": [ + 55, + 529, + 295, + 555 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 529, + 295, + 555 + ], + "type": "text", + "content": ", the input features " + }, + { + "bbox": [ + 55, + 529, + 295, + 555 + ], + "type": "inline_equation", + "content": "Z^{(l-1)}" + }, + { + "bbox": [ + 55, + 529, + 295, + 555 + ], + "type": "text", + "content": " from the previous layer are first projected into two paths:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 563, + 295, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 563, + 295, + 580 + ], + "spans": [ + { + "bbox": [ + 67, + 563, + 295, + 580 + ], + "type": "interline_equation", + "content": "Z _ {\\text {c o n v}} ^ {(l)} = \\operatorname {L i n e a r} \\left(Z ^ {(l - 1)}\\right), \\quad Z _ {\\text {g a t e}} ^ {(l)} = \\operatorname {L i n e a r} \\left(Z ^ {(l - 1)}\\right), \\tag {3}", + "image_path": "e47c48c895110084751ae3b150d2f693a8513adde072556df6a119c1548d7bc2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{conv}}^{(l)} \\in \\mathbb{R}^{D_h \\times T_0}" + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{gate}}^{(l)} \\in \\mathbb{R}^{D_h \\times T_0}" + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "inline_equation", + "content": "D_h" + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "text", + "content": " represents the hidden dimension of the feedforward network within the transformer architecture. Instead of utilizing the feedforward network in the encoder, we expand the feature dimension before applying the dilated convolution. This approach retains a similar parameter to a single transformer layer that consists of an attention layer and a feedforward network. Each transformed features, " + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{conv}}^{(l)}" + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{gate}}^{(l)}" + }, + { + "bbox": [ + 55, + 589, + 295, + 714 + ], + "type": "text", + "content": ", are then processed in separate paths independently for multidilated convolution and gating mechanism, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "text", + "content": "The transformed features for multi-dilated convolution " + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{conv}}^{(l)}" + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "text", + "content": " are split along the channel dimension into " + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "text", + "content": " equal subsets, denoted as " + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{conv}}^{(l,i)} \\in \\mathbb{R}^{(D_h / N_d) \\times T_0}" + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "text", + "content": " is the number of parallel dilated convolutions. Each subset is processed by a dilated convolution with a different dilation rate, increasing from 1 up to " + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 313, + 301, + 555, + 387 + ], + "type": "text", + "content": ". The output features for each subset are expressed as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 322, + 391, + 555, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 391, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 322, + 391, + 555, + 407 + ], + "type": "interline_equation", + "content": "Z _ {\\text {d i l a t e d}} ^ {(l, i)} = \\operatorname {D i l a t e d C o n v} _ {(l, d _ {i})} \\left(Z _ {\\text {c o n v}} ^ {(l, i)}\\right) \\quad i = 1, \\dots , N _ {d}, \\tag {4}", + "image_path": "02c56de521b5957b52e41d1514df6367f720452df8694d2c8f40cec35440f500.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "text", + "content": " is the dilation rate for the " + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "text", + "content": "-th convolution, set as " + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "inline_equation", + "content": "d_{i} = i" + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "text", + "content": ". The increasing dilation rates provide varying receptive field sizes, allowing the model to capture both short- and long-term temporal features simultaneously. Our encoder has two main hyperparameters: the number of dilated convolutions " + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 313, + 411, + 554, + 483 + ], + "type": "text", + "content": " and the kernel size." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 483, + 554, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 483, + 554, + 510 + ], + "spans": [ + { + "bbox": [ + 314, + 483, + 554, + 510 + ], + "type": "text", + "content": "Subsequently, the outputs of the dilated convolutions " + }, + { + "bbox": [ + 314, + 483, + 554, + 510 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{dilated}}^{(l,i)}" + }, + { + "bbox": [ + 314, + 483, + 554, + 510 + ], + "type": "text", + "content": " are concatenated along the channel dimension:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 354, + 513, + 553, + 530 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 513, + 553, + 530 + ], + "spans": [ + { + "bbox": [ + 354, + 513, + 553, + 530 + ], + "type": "interline_equation", + "content": "Z _ {\\text {c o n c a t}} ^ {(l)} = \\operatorname {C o n c a t} \\left(Z _ {\\text {d i l a t e d}} ^ {(l, 1)}, \\dots , Z _ {\\text {d i l a t e d}} ^ {(l, N _ {d})}\\right). \\tag {5}", + "image_path": "adc6d7e28949efc92946b7797cc1a537771b5f14c34f8de859a700d1f04177a1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 534, + 554, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 554, + 559 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 554, + 559 + ], + "type": "text", + "content": "Following this concatenation, we apply a gating mechanism to selectively retain relevant features:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 380, + 562, + 553, + 579 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 562, + 553, + 579 + ], + "spans": [ + { + "bbox": [ + 380, + 562, + 553, + 579 + ], + "type": "interline_equation", + "content": "Z ^ {(l)} = Z _ {\\text {c o n c a t}} ^ {(l)} \\odot \\sigma \\left(Z _ {\\text {g a t e}} ^ {(l)}\\right), \\tag {6}", + "image_path": "5830885a63c5f3d9b9d74de9aafc541891728af2a4827cacbe19ae31a40280c3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 582, + 554, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 554, + 618 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 554, + 618 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 582, + 554, + 618 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 582, + 554, + 618 + ], + "type": "text", + "content": " is an activation function and " + }, + { + "bbox": [ + 313, + 582, + 554, + 618 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 313, + 582, + 554, + 618 + ], + "type": "text", + "content": " denotes elementwise multiplication. Specifically, we use the SiLU activation function for the gate activation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 619, + 555, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 619, + 555, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 619, + 555, + 642 + ], + "type": "text", + "content": "Consequently, the encoding process across " + }, + { + "bbox": [ + 313, + 619, + 555, + 642 + ], + "type": "inline_equation", + "content": "L_{E}" + }, + { + "bbox": [ + 313, + 619, + 555, + 642 + ], + "type": "text", + "content": " layers of MDGE can be summarized as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 345, + 646, + 553, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 646, + 553, + 662 + ], + "spans": [ + { + "bbox": [ + 345, + 646, + 553, + 662 + ], + "type": "interline_equation", + "content": "Z ^ {(l)} = \\operatorname {M D G E} ^ {(l)} \\left(Z ^ {(l - 1)}\\right) \\quad l = 1, \\dots , L _ {E}. \\tag {7}", + "image_path": "c633f1c550b28db946d587af205a6ec64f293f24cd38c27d0c97a23c223791db.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": "Our MDGE design enables the encoder to capture diverse temporal relations by leveraging dilated convolutions and a gating mechanism without requiring explicit multiscale features at each layer." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24289" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "type": "text", + "content": "Multi-Scale Adapter & Query Selection TE-TAD [15] employs a two-stage approach with multi-scale features for query selection. To take advantage of the two-stage approach and utilize multi-scale features for query selection, we introduce a multi-scale adapter that converts the single-scale feature to multi-scale features. Our multi-scale adapter utilizes the encoder output feature " + }, + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "type": "inline_equation", + "content": "Z^{(L_E)}" + }, + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "type": "text", + "content": " to generate multi-scale representations. Specifically, " + }, + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "type": "inline_equation", + "content": "Z^{(L_E)}" + }, + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "type": "text", + "content": " is progressively downsampled to produce a set of features at multiple levels, with each subsequent level reduced to half the temporal length of the previous one. We denote the " + }, + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 72, + 296, + 215 + ], + "type": "text", + "content": " levels of multi-scale features as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 63, + 221, + 295, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 221, + 295, + 236 + ], + "spans": [ + { + "bbox": [ + 63, + 221, + 295, + 236 + ], + "type": "interline_equation", + "content": "F ^ {(l)} = \\operatorname {D o w n S a m p l e} \\left(Z ^ {\\left(L _ {E}\\right)}\\right) + E ^ {(l)} \\quad l = 1, \\dots , L, \\tag {8}", + "image_path": "f3359713c5f467a3e5f0d49897e7002bc0a0992f287371e00b66387abfa3a702.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "text", + "content": "where each " + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "inline_equation", + "content": "F^{(l)} \\in \\mathbb{R}^{T_l \\times D}" + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "text", + "content": " represents the resized feature at level " + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "inline_equation", + "content": "T_{l}" + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "text", + "content": " being half the length of the previous level. To enable the decoder to distinguish between these multi-scale levels, we add a level-specific embedding " + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "inline_equation", + "content": "E^{(l)} \\in \\mathbb{R}^{1 \\times D}" + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "text", + "content": ", applied consistently across all time steps. These multi-scale features are then utilized for the query selection process. Unlike the adaptive query selection (AQS) in TE-TAD [15] that enforces a strict uniform sampling of queries across the video, we apply a top-" + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 241, + 296, + 361 + ], + "type": "text", + "content": " selection approach based on binary classification scores from the encoder." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "text", + "content": "Subsequently, we utilize the top- " + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "text", + "content": " indices to retrieve both the query embeddings and the corresponding reference points " + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "inline_equation", + "content": "(c_{q},d_{q})" + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "text", + "content": " based on a time-aligned query generation method [15] that assigns temporal center points " + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "inline_equation", + "content": "c_{q}" + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "text", + "content": " and widths " + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "inline_equation", + "content": "d_{q}" + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "text", + "content": ", aligning them with their respective positions in the video. Additionally, the query embedding for each selected query is obtained by linearly projecting the corresponding top- " + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 362, + 296, + 469 + ], + "type": "text", + "content": " multi-scale features. The input embedding of a decoder is denoted as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 475, + 295, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 475, + 295, + 491 + ], + "spans": [ + { + "bbox": [ + 102, + 475, + 295, + 491 + ], + "type": "interline_equation", + "content": "F _ {q} ^ {(0)} = \\operatorname {L a y e r N o r m} \\left(\\operatorname {L i n e a r} \\left(F _ {\\mathrm {t o p k}}\\right)\\right), \\tag {9}", + "image_path": "191cb266898d914afcc9a5656824ac3ecf6f51bf8118f6e370823a86156e061d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 496, + 247, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 496, + 247, + 507 + ], + "spans": [ + { + "bbox": [ + 55, + 496, + 247, + 507 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 496, + 247, + 507 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{topk}}" + }, + { + "bbox": [ + 55, + 496, + 247, + 507 + ], + "type": "text", + "content": " denotes the top- " + }, + { + "bbox": [ + 55, + 496, + 247, + 507 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 496, + 247, + 507 + ], + "type": "text", + "content": " selected features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 508, + 295, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 508, + 295, + 519 + ], + "spans": [ + { + "bbox": [ + 55, + 508, + 295, + 519 + ], + "type": "text", + "content": "Central-Adjacent Region Integrated Decoder (CAID)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "text", + "content": "The previous query-based methods [15, 27] apply temporal deformable cross-attention that applies the center-focused sampling strategy. As discussed in Sec. 1, the center-focused sampling does not provide sufficient information for detecting the action instances. To address this issue, we introduce CAID, which combines central- and adjacent-region cross-attention. In standard deformable cross-attention, features are sampled around each reference point, defined by its center " + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "inline_equation", + "content": "c_{q}" + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "text", + "content": " and duration " + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "inline_equation", + "content": "d_{q}" + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "text", + "content": ". The sampling offset " + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\Delta p_{mqk}" + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "text", + "content": " for each head " + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "text", + "content": " and sampling point " + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 520, + 296, + 651 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 103, + 658, + 295, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 658, + 295, + 672 + ], + "spans": [ + { + "bbox": [ + 103, + 658, + 295, + 672 + ], + "type": "interline_equation", + "content": "\\Delta p _ {m q k} = \\operatorname {L i n e a r} \\left(F _ {q}\\right) = W F _ {q} + b, \\tag {10}", + "image_path": "b44edc21a1190e6220f691602af605b0cf901e2d93db1365050356ec977f15e9.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " are learnable parameters for obtaining the sampling offset by linear projection. Generally, " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " is initialized to zero and " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " within the range " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": ". Using the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "computed offset " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\Delta p_{mqk}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": ", sampling points " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "p_{mqk}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": " are determined based on the reference points as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 376, + 103, + 553, + 117 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 103, + 553, + 117 + ], + "spans": [ + { + "bbox": [ + 376, + 103, + 553, + 117 + ], + "type": "interline_equation", + "content": "p _ {m q k} = c _ {q} + 0. 5 w _ {q} \\Delta p _ {m q k}, \\tag {11}", + "image_path": "7998d859ced4d9de8e482be69237c13aa86ca3df2521bd8ed04129d4618a1486.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 121, + 553, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 121, + 553, + 193 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 553, + 193 + ], + "type": "text", + "content": "where the factor " + }, + { + "bbox": [ + 313, + 121, + 553, + 193 + ], + "type": "inline_equation", + "content": "0.5w_{q}" + }, + { + "bbox": [ + 313, + 121, + 553, + 193 + ], + "type": "text", + "content": " ensures the sampling points are initially positioned close to the center of each reference point. In our approach, we do not change how to obtain the sampling points when addressing central- and adjacent-region sampling. We change the initialization method for the bias value " + }, + { + "bbox": [ + 313, + 121, + 553, + 193 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 121, + 553, + 193 + ], + "type": "text", + "content": ", which determines the initial sampling points." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": "As shown in Fig. 4, our CAID contains two cross-attention layers sequentially: central-region cross-attention and adjacent-region cross-attention. For central-region cross-attention, the initial bias of sampling offsets " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": " are initialized uniformly within the range " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "[-1,1]" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": ", which is identical to the previous methods [15, 19, 25, 27, 48, 52]. As Eq. (11), this initialization constrains the initial bias for sampling points " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": " within " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "[-0.5,0.5]" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": ", focusing on the central region of the reference points. For adjacent-region cross-attention, the bias of sampling offsets " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": " are adjusted to capture surrounded points of central-region cross-attention. Specifically, half of the sampling offsets are initialized within the range " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "[-1.5,-0.5]" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": " to focus on the left, while the other half are initialized within the range " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "[0.5,1.5]" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": " to focus on the right. This adjustment, combined with Eq. (11), constraints in the initial sampling points " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "p_{mqk}" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": " within " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "[-0.75,-0.25]" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "[0.25,0.75]" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": ". Overall, we sequentially apply self-attention, central-region cross-attention, adjacent-region cross-attention, and feedforward network across all " + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "inline_equation", + "content": "L_{D}" + }, + { + "bbox": [ + 313, + 194, + 555, + 433 + ], + "type": "text", + "content": " layers, as shown in Fig. 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 438, + 444, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 438, + 444, + 451 + ], + "spans": [ + { + "bbox": [ + 314, + 438, + 444, + 451 + ], + "type": "text", + "content": "3.3. Training and Inference" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 456, + 554, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 554, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 554, + 491 + ], + "type": "text", + "content": "Training Following the previous works [15, 27], we use the bipartite matching loss [4]. The total loss " + }, + { + "bbox": [ + 313, + 456, + 554, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total}" + }, + { + "bbox": [ + 313, + 456, + 554, + 491 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 352, + 495, + 553, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 495, + 553, + 529 + ], + "spans": [ + { + "bbox": [ + 352, + 495, + 553, + 529 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} (\\mathcal {A}, \\hat {\\mathcal {A}}) = \\sum_ {i = 1} ^ {N _ {q}} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\mathcal {A} _ {i}, \\hat {\\mathcal {A}} _ {\\pi (i)}\\right), \\tag {12}", + "image_path": "c5b5b92781790597fce7fa8059d5ef83802ad721b9860527c9a7a9be0dd8bff8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{match}" + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "content": " denotes the bipartite matching loss, which considers both classification and regression loss between ground truth " + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_i" + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "content": " and predicted action instances " + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{A}}_{\\pi(i)}" + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "content": " from the last layer of the decoder. The permutation indices " + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\pi(i)" + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "content": " are obtained through bipartite matching [17]. This cost function " + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{match}" + }, + { + "bbox": [ + 313, + 534, + 554, + 653 + ], + "type": "text", + "content": " is a composite of the classification, and regression loss. We use focal loss [24] for the classification loss to effectively manage class imbalance. For the regression loss, our method incorporates GIoU [33] and a log-ratio distance loss [15]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "Inference Following the previous work [15] that removes the need for post-processing steps, the predictions of DiGIT from the final layer of the decoder " + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{A}}" + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": " are directly used. For a fair comparison, we report both raw prediction results and NMS applied results." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24290" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 70, + 534, + 317 + ], + "blocks": [ + { + "bbox": [ + 74, + 70, + 534, + 317 + ], + "lines": [ + { + "bbox": [ + 74, + 70, + 534, + 317 + ], + "spans": [ + { + "bbox": [ + 74, + 70, + 534, + 317 + ], + "type": "table", + "html": "
    Training TypeHead TypeMethodFeatureTHUMOS14ActivityNet v1.3
    0.30.40.50.60.7Avg.0.50.750.95Avg.
    Full-AFSD [20]I3D [5]67.362.455.543.731.152.052.435.36.534.4
    TALLFormer [8]Swin-B [28]76.0-63.2-34.559.254.136.27.935.6
    ViT-TAD [45]ViT-B [9]85.180.974.261.845.469.555.838.58.837.4
    AdaTAD [26]VideoMAEv2-g [40]89.786.780.971.056.176.961.743.410.941.9
    Head onlyAnchor -freeTriDet [36]I3D [5] / R(2+1)D [38]83.680.172.962.447.469.354.738.08.436.8
    DyFADet [44]I3D [5] / R(2+1)D [38]84.080.172.761.147.969.258.139.68.438.5
    ActionFormer [47]I3D [5] / R(2+1)D [38]82.177.871.059.443.966.854.737.88.436.6
    ActionFormer [47]InternVideo2 [41]82.381.975.165.850.371.961.544.612.741.2
    ActionMamba [6]InternVideo2 [41]86.983.176.965.950.872.762.443.510.242.0
    Query -basedRTD-Net [37]I3D [5] / TSN [39]68.362.351.938.823.749.047.230.78.630.8
    ReAct [35]I3D [5] / TSN [39]69.265.057.147.835.655.049.633.08.632.6
    Self-DETR [16]I3D [5]74.669.560.047.631.856.752.333.78.433.8
    TadTR [27]I3D [5] / R(2+1)D [38]74.869.160.146.632.856.753.637.510.636.8
    DualDETR [53]I3D [5]82.978.070.458.544.466.852.635.07.834.3
    TE-TAD [15]I3D [5] / R(2+1)D [38]83.378.471.360.745.667.954.238.110.637.1
    DiGIT†I3D [5] / R(2+1)D [38]81.677.770.360.548.467.754.338.410.637.2
    DiGITI3D [5] / R(2+1)D [38]83.679.671.961.548.669.054.438.210.737.3
    TadTR [27]InternVideo2 [41]84.879.370.458.243.867.357.138.811.038.2
    TadTR [27] + OursInternVideo2 [41]86.181.873.761.746.369.960.241.011.240.5
    TE-TAD [15]InternVideo2 [41]84.381.173.762.649.570.361.341.810.941.1
    DiGIT†InternVideo2 [41]85.782.375.665.651.472.158.943.411.441.3
    DiGITInternVideo2 [41]87.684.277.667.352.573.862.043.111.342.0
    ", + "image_path": "9f77dc9bf8ad8ad30e89091fe6f8de49aa36057baee16e393d12a340c74dd3b0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 319, + 555, + 343 + ], + "lines": [ + { + "bbox": [ + 55, + 319, + 555, + 343 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 555, + 343 + ], + "type": "text", + "content": "Table 1. Performance comparison with state-of-the-art methods on THUMOS14 and ActivityNet v1.3. In cases marked with " + }, + { + "bbox": [ + 55, + 319, + 555, + 343 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 55, + 319, + 555, + 343 + ], + "type": "text", + "content": ", our method does not utilize NMS. For TadTR + Ours, we additionally apply our MDGE and CAID on TadTR." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 351, + 137, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 351, + 137, + 365 + ], + "spans": [ + { + "bbox": [ + 55, + 351, + 137, + 365 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 371, + 105, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 371, + 105, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 371, + 105, + 384 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 388, + 295, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 388, + 295, + 543 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 295, + 543 + ], + "type": "text", + "content": "Datasets We conduct experiments on three datasets: THUMOS14 [14], ActivityNet v1.3 [10], and HACS-Segment [50]. THUMOS14 consists of 20 action classes with 200 validation and 213 test videos, containing 3,007 and 3,358 action instances, respectively. ActivityNet v1.3 is a large-scale dataset with 200 action classes, including 10,024 videos for training and 4,926 videos for validation. HACS-Segment is another large-scale TAD dataset with extensive annotations, covering 200 activity classes similar to ActivityNet v1.3. It provides 37,613 videos for training and 5,981 videos for validation. These datasets provide a rigorous evaluation environment for our method, containing diverse actions and scenes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 544, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 295, + 628 + ], + "type": "text", + "content": "Evaluation Metric We follow the standard evaluation protocol for all datasets, utilizing mAP at different intersections over union (IoU) thresholds to evaluate TAD performance. The IoU thresholds for THUMOS14 are set at [0.3:0.7:0.1], while for ActivityNet v1.3 and HACS-Segment, the results are reported at IoU threshold [0.5, 0.75, 0.95] with the average mAP computed at [0.5:0.95:0.05]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 628, + 295, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 295, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 295, + 652 + ], + "type": "text", + "content": "Implementation Details We describe the implementation details for each dataset in the Supplementary Sec. A." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 659, + 141, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 659, + 141, + 672 + ], + "spans": [ + { + "bbox": [ + 55, + 659, + 141, + 672 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "content": "THUMOS14 Table 1 contains a comparison with the state-of-the-art methods on THUMOS14. Our DiGIT shows consistent improvements over TadTR [27] and TE-TAD [15] on" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 352, + 555, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 352, + 555, + 424 + ], + "spans": [ + { + "bbox": [ + 313, + 352, + 555, + 424 + ], + "type": "text", + "content": "both I3D [5] and InternVideo2 [41] features. Even without applying NMS, our method outperforms the existing query-based detectors. Furthermore, our model outperforms the existing snippet-based head-only training methods, and our DiGIT shows a comparable performance even compared to the full training method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 425, + 556, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 425, + 556, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 425, + 556, + 581 + ], + "type": "text", + "content": "ActivityNet v1.3 Following the conventional approach [15, 27, 36, 47], the external classification score is used to evaluate ActivityNet v1.3. The pre-extracted classification scores are combined with class-agnostic predictions from a binary detector to obtain class labels. For " + }, + { + "bbox": [ + 313, + 425, + 556, + 581 + ], + "type": "inline_equation", + "content": "\\mathrm{R}(2 + 1)\\mathrm{D}" + }, + { + "bbox": [ + 313, + 425, + 556, + 581 + ], + "type": "text", + "content": " [38] and InternVideo2 [41] features, classification results from CUHK [42] and InternVideo2 [41] are incorporated to obtain class scores, respectively. As demonstrated in Table 1, DiGIT achieves consistent improvements over TadTR and TE-TAD on ActivityNet v1.3. Furthermore, DiGIT demonstrates competitive performance compared to other types of state-of-the-art methods, demonstrating effectiveness across various datasets and feature extractors." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "HACS-Segment Table 2 presents a comparison of our model with state-of-the-art methods on HACS-Segment. Our model achieves significant improvements over previous methods, establishing a new state-of-the-art performance, including mAP at higher IoU thresholds of 0.75 and 0.95. The stronger performance at the 0.95 IoU threshold indicates that DiGIT excels in precise action localization. Moreover, the superior performance of DiGIT on this larger dataset, compared to THUMOS14 and ActivityNet v1.3, demonstrates its scalability and robustness across varying data sizes and complexities." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "24291" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 293, + 256 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 293, + 256 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 293, + 256 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 293, + 256 + ], + "type": "table", + "html": "
    Head TypeMethodFeaturemAP
    0.50.750.95Avg.
    Anchor -basedSSN [51]I3D [5]28.818.85.319.0
    G-TAD [43]I3D [5]41.127.68.327.5
    BMN [22]SlowFast [11]52.536.410.435.8
    TCANet [32]SlowFast [11]54.137.211.336.8
    Anchor -freeTALLFormer [8]Swin-B [28]55.036.111.836.5
    TriDet [36]I3D [5]54.536.811.536.8
    TriDet [36]SlowFast [11]56.739.311.738.6
    TriDet [36]VideoMAEv2-g [40]62.444.113.143.1
    DyFADet [44]SlowFast [11]57.839.811.839.2
    DyFADet [44]VideoMAEv2-g [40]64.044.814.144.3
    ActionFormer [47]InternVideo2 [41]62.644.612.743.3
    ActionMamba [6]InternVideo2 [41]64.045.713.344.6
    Query -basedTadTR [27]I3D [5]47.132.110.932.1
    TadTR [27]InternVideo2 [41]54.238.812.837.8
    TadTR [27] + OursInternVideo2 [41]55.040.013.839.0
    TE-TAD [15]InternVideo2 [41]60.445.616.544.1
    DiGIT†InternVideo2 [41]61.147.517.845.5
    DiGITInternVideo2 [41]62.447.917.645.9
    ", + "image_path": "68d7f8f7bad9768bfa448006268b6f950dda610d6e744dbba7b578647d7ad7ce.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 104, + 311, + 247, + 399 + ], + "blocks": [ + { + "bbox": [ + 104, + 311, + 247, + 399 + ], + "lines": [ + { + "bbox": [ + 104, + 311, + 247, + 399 + ], + "spans": [ + { + "bbox": [ + 104, + 311, + 247, + 399 + ], + "type": "image", + "image_path": "5a8896336a5da505df404cc7e14a636797c23f3024161d6a641fa60a8827a93b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 400, + 295, + 434 + ], + "lines": [ + { + "bbox": [ + 55, + 400, + 295, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 400, + 295, + 434 + ], + "type": "text", + "content": "Figure 5. Ablation study on MDGE with InternVideo2 features on THUMOS14. The heatmap shows mAP values for different combinations of kernel size and number of dilated convolutions." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 442, + 157, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 442, + 157, + 455 + ], + "spans": [ + { + "bbox": [ + 55, + 442, + 157, + 455 + ], + "type": "text", + "content": "4.3. Further Analysis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 460, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 460, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 460, + 295, + 628 + ], + "type": "text", + "content": "Ablation Study on MDGE Fig. 5 shows an ablation study on hyperparameters of MDGE, specifically the impact of kernel size and the number of dilated convolution layers " + }, + { + "bbox": [ + 55, + 460, + 295, + 628 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 55, + 460, + 295, + 628 + ], + "type": "text", + "content": " on mAP performance. Excluding the configuration with a single dilated convolution that consistently yields lower mAP values, configurations with multiple dilated layers demonstrate improved performance. These results indicate that addressing diverse scale information is crucial for the encoder by utilizing our multi-dilated convolution that enables the model to capture diverse temporal relations. Furthermore, compared to the TE-TAD [15] baseline of 70.4 in Table 4, our MDGE consistently improves performance regardless of hyperparameter variations, demonstrating robustness across different configurations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": "Ablation Study on CAID Table 3 demonstrates the effects of integrating the proposed adjacent-region cross-attention (ACA) into the decoder operation sequence. We evaluate several configurations, including variations of central-region cross-attention (CCA) with expanded initialization ranges " + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "inline_equation", + "content": "(1.5\\times" + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "inline_equation", + "content": "2.0\\times)" + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": ". CCA " + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "inline_equation", + "content": "(1.5\\times)" + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": " and CCA " + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "inline_equation", + "content": "(2.0\\times)" + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": " (Rows #2 and #3) show that simply increasing the initial" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 351, + 70, + 515, + 164 + ], + "blocks": [ + { + "bbox": [ + 55, + 258, + 295, + 301 + ], + "lines": [ + { + "bbox": [ + 55, + 258, + 295, + 301 + ], + "spans": [ + { + "bbox": [ + 55, + 258, + 295, + 301 + ], + "type": "text", + "content": "Table 2. Performance comparison with state-of-the-art methods on HACS-Segment. In cases marked with " + }, + { + "bbox": [ + 55, + 258, + 295, + 301 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 55, + 258, + 295, + 301 + ], + "type": "text", + "content": ", our method does not utilize NMS. For TadTR + Ours, we additionally apply our MDGE and CAID on TadTR." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 351, + 70, + 515, + 164 + ], + "lines": [ + { + "bbox": [ + 351, + 70, + 515, + 164 + ], + "spans": [ + { + "bbox": [ + 351, + 70, + 515, + 164 + ], + "type": "table", + "html": "
    Decoder SequencemAP@AVG
    #1SA → CCA → FFN72.5
    #2SA → CCA (1.5×) → FFN72.6
    #3SA → CCA (2.0×) → FFN71.8
    #4SA → ACA → FFN69.2
    #5SA → CCA → CCA → FFN72.7
    #6SA → CCA → ACA → FFN73.8
    #7SA → ACA → CCA → FFN73.2
    ", + "image_path": "e917d245ccb61616b38fad9270997c210740cf46cb5a49db7aefe13ba5405068.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 319, + 259, + 548, + 383 + ], + "blocks": [ + { + "bbox": [ + 313, + 167, + 553, + 254 + ], + "lines": [ + { + "bbox": [ + 313, + 167, + 553, + 254 + ], + "spans": [ + { + "bbox": [ + 313, + 167, + 553, + 254 + ], + "type": "text", + "content": "Table 3. Analysis of decoder operation sequences using InternVideo2 features on THUMOS14. SA refers to the self-attention layer. CCA denotes central-region cross-attention (as used in previous works such as [15, 27]). CCA " + }, + { + "bbox": [ + 313, + 167, + 553, + 254 + ], + "type": "inline_equation", + "content": "(1.5\\times" + }, + { + "bbox": [ + 313, + 167, + 553, + 254 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 167, + 553, + 254 + ], + "type": "inline_equation", + "content": "2.0\\times)" + }, + { + "bbox": [ + 313, + 167, + 553, + 254 + ], + "type": "text", + "content": " indicates an expansion of the initial sampling range of central-region cross-attention by 1.5 and 2.0 times, respectively, to cover a broader area around the reference points. ACA refers to adjacent-region cross-attention, and FFN represents the feedforward network." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 259, + 548, + 383 + ], + "lines": [ + { + "bbox": [ + 319, + 259, + 548, + 383 + ], + "spans": [ + { + "bbox": [ + 319, + 259, + 548, + 383 + ], + "type": "table", + "html": "
    BaselineEnc.Dec.MDGECAIDmAP
    0.30.50.7Avg.
    TadTR [27]SS✓84.870.443.867.3
    ✓84.971.944.768.4
    ✓✓84.470.845.467.9
    ✓✓86.173.746.369.9
    TE-TAD [15]MM✓84.373.749.570.3
    85.274.649.970.8
    SM✓85.473.849.170.4
    87.075.851.972.5
    ✓✓85.574.651.071.4
    ✓✓87.677.652.573.8
    ", + "image_path": "50c77eb8bcfc1e0d8ddec4d6dde1a15794d27e22de124b3e4346dfb24c559ff4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 384, + 553, + 440 + ], + "lines": [ + { + "bbox": [ + 313, + 384, + 553, + 440 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 553, + 440 + ], + "type": "text", + "content": "Table 4. Ablation study on the contributions of each component using InternVideo2 features on THUMOS14. The first row for TadTR [27] and TE-TAD [15] represents the baseline performance. Enc. and Dec. refer to how scale information is handled in the encoder and decoder. S: single-scale. M: multi-scale." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "type": "text", + "content": "ization range of CCA to cover a broader area, similar range to CAID, does not show the improved performance compared to the original setting (Row #1). This indicates that simply expanding the initialization range does not benefit the detector. Moreover, when using ACA alone (Row #4), we observe a significant decrease in performance, underscoring the importance of balancing adjacent-region information with central-region information. Configurations that use two successive CCA layers (Row #5) show only marginal improvements, suggesting that additional central-region cross-attention alone does not significantly enhance performance. The highest mAP score is achieved by the sequence of SA " + }, + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "type": "text", + "content": " CCA " + }, + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "type": "text", + "content": " ACA " + }, + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 449, + 553, + 628 + ], + "type": "text", + "content": " FFN, which combines central-region cross-attention and adjacent-region cross-attention, which is our CAID (Row #6)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 553, + 713 + ], + "type": "text", + "content": "Component Contribution Analysis Table 4 provides an analysis of the performance contributions from each proposed component, evaluated using InternVideo2 [41] features on THUMOS14 [14]. The first row for each method shows the baseline performance without our proposed enhancements, allowing for a direct comparison with subsequent configurations. Notably, converting multi-scale en" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24292" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 70, + 264, + 144 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 264, + 144 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 264, + 144 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 264, + 144 + ], + "type": "table", + "html": "
    BaselineAQS [15]mAP
    0.30.50.7Avg.
    TE-TAD [15]✓85.673.747.670.3
    82.571.848.468.7
    DiGIT✓85.876.451.572.2
    87.677.652.573.8
    ", + "image_path": "347bb2b36f97a6509fca9a41064eb0558b8a28d76e809c8fe51e94effbe56534.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 146, + 296, + 168 + ], + "lines": [ + { + "bbox": [ + 55, + 146, + 296, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 296, + 168 + ], + "type": "text", + "content": "Table 5. Ablation study on the query selection method using InternVideo2 features on THUMOS14." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 77, + 172, + 265, + 274 + ], + "blocks": [ + { + "bbox": [ + 77, + 172, + 265, + 274 + ], + "lines": [ + { + "bbox": [ + 77, + 172, + 265, + 274 + ], + "spans": [ + { + "bbox": [ + 77, + 172, + 265, + 274 + ], + "type": "image", + "image_path": "be6c3dbb41c7d17b3b9288b244a4e9c2752b49c0126f7e31c735d2738ce2e947.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 274, + 296, + 317 + ], + "lines": [ + { + "bbox": [ + 55, + 274, + 296, + 317 + ], + "spans": [ + { + "bbox": [ + 55, + 274, + 296, + 317 + ], + "type": "text", + "content": "Figure 6. Comparison of training and testing loss for the encoder classification matching loss using InternVideo2 features on THUMOS14. Our method significantly accelerates the convergence of the encoder." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 326, + 296, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 326, + 296, + 420 + ], + "spans": [ + { + "bbox": [ + 55, + 326, + 296, + 420 + ], + "type": "text", + "content": "coding to single-scale encoding alone in TE-TAD [15] results in minimal performance change " + }, + { + "bbox": [ + 55, + 326, + 296, + 420 + ], + "type": "inline_equation", + "content": "(70.3\\rightarrow 70.4)" + }, + { + "bbox": [ + 55, + 326, + 296, + 420 + ], + "type": "text", + "content": ". This result aligns with our motivation, as shown in Fig. 2, which is that the previous multi-scale features contain redundant information. Furthermore, both MDGE and CAID show consistent improvements in both TadTR and TE-TAD, demonstrating the robustness and effectiveness of our approach across different baseline architectures." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 422, + 296, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 296, + 614 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 296, + 614 + ], + "type": "text", + "content": "Effect of MDGE In TE-TAD [15], adaptive query selection (AQS) is employed to sample initial queries across the entire video sequence uniformly. This process enforces a strict uniform selection of queries to prevent queries from being overly concentrated in certain areas, as might happen with a simple top-k selection. However, our observations suggest that this strict uniform condition is unnecessary when using a well-trained encoder, as provided by our MDGE. As shown in Table 5, removing AQS results in higher mAP scores for DiGIT, whereas the performance of TE-TAD declines without AQS. Furthermore, as illustrated in Fig. 6, DiGIT exhibits faster convergence and consistently lower loss values. These results indicate that our MDGE enhances the representational ability of the encoder and can reduce the heuristic part of the query selection, which positively impact overall detection performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 624, + 167, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 167, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 167, + 635 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "Visualization of Cosine Similarity on Encoder Output Features Fig. 7 presents a comparison of cosine similarity matrices for encoder output features between TE-TAD and DiGIT. Our DiGIT shows improved feature discriminability, indicating that MDGE captures distinct temporal patterns more effectively compared to TE-TAD [15]." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 320, + 71, + 433, + 176 + ], + "blocks": [ + { + "bbox": [ + 320, + 71, + 433, + 176 + ], + "lines": [ + { + "bbox": [ + 320, + 71, + 433, + 176 + ], + "spans": [ + { + "bbox": [ + 320, + 71, + 433, + 176 + ], + "type": "image", + "image_path": "b4b907098c1eff613484ad33bc38f6b9037ddeeb094d349f0672c244e60ee36d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 348, + 177, + 405, + 186 + ], + "lines": [ + { + "bbox": [ + 348, + 177, + 405, + 186 + ], + "spans": [ + { + "bbox": [ + 348, + 177, + 405, + 186 + ], + "type": "text", + "content": "(a) TE-TAD [15]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 436, + 72, + 550, + 176 + ], + "blocks": [ + { + "bbox": [ + 436, + 72, + 550, + 176 + ], + "lines": [ + { + "bbox": [ + 436, + 72, + 550, + 176 + ], + "spans": [ + { + "bbox": [ + 436, + 72, + 550, + 176 + ], + "type": "image", + "image_path": "0d5fdccaf7ddcbf6b978eeaed6d4d6b1533fe9097e46c254eda385152fcb4639.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 476, + 177, + 511, + 186 + ], + "lines": [ + { + "bbox": [ + 476, + 177, + 511, + 186 + ], + "spans": [ + { + "bbox": [ + 476, + 177, + 511, + 186 + ], + "type": "text", + "content": "(b) DiGIT" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 321, + 243, + 544, + 317 + ], + "blocks": [ + { + "bbox": [ + 313, + 188, + 555, + 242 + ], + "lines": [ + { + "bbox": [ + 313, + 188, + 555, + 242 + ], + "spans": [ + { + "bbox": [ + 313, + 188, + 555, + 242 + ], + "type": "text", + "content": "Figure 7. Comparison of cosine similarity on encoder output features between TE-TAD and DiGIT. Top: represents cosine similarity, with red boxes indicating regions of similarity among features within the ground truth. Bottom: displays the ground truth action timeline for reference. Sample taken from THUMOS14." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 321, + 243, + 544, + 317 + ], + "lines": [ + { + "bbox": [ + 321, + 243, + 544, + 317 + ], + "spans": [ + { + "bbox": [ + 321, + 243, + 544, + 317 + ], + "type": "image", + "image_path": "1f7fa3b7c35acea3d59f0e49efe20e9772232c7f99f14c0ae673dfa0efd1406f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 321, + 318, + 543, + 392 + ], + "blocks": [ + { + "bbox": [ + 321, + 318, + 543, + 392 + ], + "lines": [ + { + "bbox": [ + 321, + 318, + 543, + 392 + ], + "spans": [ + { + "bbox": [ + 321, + 318, + 543, + 392 + ], + "type": "image", + "image_path": "f25b88c2f2a3f0389c02dbf73ae555c4d61eaa9fa2d1b3a7ada8f6498cd8345b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 394, + 554, + 428 + ], + "lines": [ + { + "bbox": [ + 313, + 394, + 554, + 428 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 554, + 428 + ], + "type": "text", + "content": "Figure 8. Visualization of sampling offsets in cross-attention layers on THUMOS14. Each point denotes the mean value across the dataset, with error bars indicating the standard deviation." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "content": "Visualization of Sampling Offsets Fig. 8 shows the distribution of sampling offsets relative to the center and width of each action query. The values 0, -1, and 1 correspond to the center " + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "inline_equation", + "content": "c_{q}" + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "content": ", the start boundary " + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "inline_equation", + "content": "c_{q} - d_{q}" + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "content": ", and the end boundary " + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "inline_equation", + "content": "c_{q} + d_{q}" + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "content": ", respectively. This visualization shows that our method gathers information from diverse sampling points, covering both central and adjacent regions. Furthermore, while deformable attention allows learnable offsets, they remain close to their initial points, indicating the importance of the initial value of " + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 431, + 555, + 552 + ], + "type": "text", + "content": " in Eq. (10)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 562, + 388, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 562, + 388, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 562, + 388, + 574 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": "In this paper, we propose a multi-dilated gated encoder and central-adjacent region integrated decoder for temporal action detection transformer (DiGIT). MDGE offers diverse receptive fields while maintaining a single-scale encoding structure by utilizing multi-dilated convolutions. CAID provides essential information to precisely detect action instances by focusing on both the central- and adjacent-regions of action instances. Extensive experiments demonstrate that DiGIT outperforms the previous query-based methods. Furthermore, our method consistently improves when integrated with the existing query-based detectors." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24293" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 199 + ], + "type": "text", + "content": "This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant, funded by the Korea government (MSIT) (No. RS-2019-II190079, Artificial Intelligence Graduate School Program (Korea University), No. RS-2024-00457882, AI Research Hub Project, and No. RS-2022-II220984, Development of Artificial Intelligence Technology for Personalized Plug-and-Play Explanation and Verification of Explanation)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 209, + 115, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 209, + 115, + 221 + ], + "spans": [ + { + "bbox": [ + 56, + 209, + 115, + 221 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 229, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 62, + 229, + 296, + 289 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 229, + 296, + 289 + ], + "spans": [ + { + "bbox": [ + 62, + 229, + 296, + 289 + ], + "type": "text", + "content": "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18559-18569, 2024. 1, 2, 3, 6" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24296" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiG_ Scalable and Efficient Diffusion Models with Gated Linear Attention/283f0e42-855f-4918-822c-d5c1219d1790_content_list.json b/2025/DiG_ Scalable and Efficient Diffusion Models with Gated Linear Attention/283f0e42-855f-4918-822c-d5c1219d1790_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..90d96b5f8f317c97351cacc377344e8b9de92afc --- /dev/null +++ b/2025/DiG_ Scalable and Efficient Diffusion Models with Gated Linear Attention/283f0e42-855f-4918-822c-d5c1219d1790_content_list.json @@ -0,0 +1,1623 @@ +[ + { + "type": "text", + "text": "DiG: Scalable and Efficient Diffusion Models with Gated Linear Attention", + "text_level": 1, + "bbox": [ + 124, + 130, + 870, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lianghui Zhu $^{1,2,\\diamond}$ Zilong Huang $^{2\\boxtimes}$ Bencheng Liao $^{1}$ Jun Hao Liew $^{2}$ Hanshu Yan $^{2}$ Jiashi Feng $^{2}$ Xinggang Wang $^{1\\boxtimes}$", + "bbox": [ + 125, + 178, + 869, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of EIC, Huazhong University of Science & Technology $^{2}$ ByteDance Code & Models: hustvl/DiG", + "bbox": [ + 181, + 239, + 815, + 279 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/af605692327dbf1c561d3a45ad122762b91a2fcda97f565ad6d071c5600191e0.jpg", + "image_caption": [ + "Figure 1. Image generation with the proposed Diffusion Gated Linear Attention Transformers (DiG). We show selected samples from our class-conditional DiG-XL/2 models trained on ImageNet at $512 \\times 512$ and $256 \\times 256$ resolution, respectively." + ], + "image_footnote": [], + "bbox": [ + 94, + 297, + 903, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 762, + 326, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models with large-scale pre-training have achieved significant success in the field of visual content generation, particularly exemplified by Diffusion Trans", + "bbox": [ + 89, + 794, + 482, + 840 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "formers (DiT). However, DiT models have faced challenges with quadratic complexity efficiency, especially when handling long sequences. In this paper, we aim to incorporate the sub-quadratic modeling capability of Gated Linear Attention (GLA) into the 2D diffusion backbone. Specifically, we introduce Diffusion Gated Linear Attention Transformers (DiG), a simple, adoptable solution with minimal parameter overhead. We offer two variants, i,e, a plain and U-shape architecture, showing superior efficiency and", + "bbox": [ + 509, + 763, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "This work was done when Lianghui Zhu was interning at ByteDance. Corresponding authors: Xinggang Wang (xgwang@hust.edu.cn) and Zilong Huang (zilong.huang2020@gmail.com)", + "bbox": [ + 89, + 849, + 482, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7664", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "competitive effectiveness. In addition to superior performance to DiT and other sub-quadratic-time diffusion models at $256 \\times 256$ resolution, DiG demonstrates greater efficiency than these methods starting from a 512 resolution. Specifically, DiG-S/2 is $2.5 \\times$ faster and saves $75.7\\%$ GPU memory compared to DiT-S/2 at a 1792 resolution. Additionally, DiG-XL/2 is $4.2 \\times$ faster than the Mamba-based model at a 1024 resolution and $1.8 \\times$ faster than DiT with FlashAttention-2 at a 2048 resolution.", + "bbox": [ + 88, + 90, + 482, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 256, + 222, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, diffusion models [4, 20, 32, 53, 56, 61, 65, 66] have emerged as potent deep generative models [13, 49] renowned for their ability to generate high-quality images. Their rapid evolution has spurred extensive applications across various fields, including image-to-image generation [8, 67], text-to-image generation [19, 47, 51], speech synthesis [7, 29], video generation [21, 34, 36], and 3D generation [43, 68]. Concurrent with the rapid development of sampling algorithms [33, 38, 54], the principal techniques have evolved into two main categories based on their architectural backbones: U-Net-based methods [20, 55] and ViT-based methods [14]. U-Net-based approaches continue to leverage the convolutional neural network (CNN) architecture [31, 50], whose hierarchical feature modeling ability benefits visual generation tasks. On the other hand, ViT-based methods [1, 39, 64] innovate by incorporating self-attention mechanisms [59] instead of traditional sampling blocks, resulting in streamlined yet effective performance.", + "bbox": [ + 91, + 281, + 482, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to their excellent scalability in terms of performance, ViT-based methods [39] have been adopted as backbones in the most advanced diffusion works, including PixArt [5, 6], Sora [3], Stable Diffusion 3 [15], etc. However, the self-attention mechanism in ViT-based architectures scales quadratically with the input sequence length, making them resource-intensive when dealing with long sequence generation tasks, e.g., high-resolution image generation and video generation. Recent works such as Mamba [18, 69], RWKV [40] and Gated Linear Attention Transformer (GLA) [63], try to improve the long-sequence processing efficiency by integrating Recurrent Neural Network (RNN) like architecture and hardware-aware algorithms. Since a data-dependent gating mechanism is crucial for 1D modeling [45], GLA shows outstanding performance among the above methods.", + "bbox": [ + 91, + 554, + 482, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the success of GLA in the natural language processing domain, it is appealing that we can transfer this success from language generation to visual content generation by designing a scalable and efficient diffusion backbone with the advanced linear attention [10, 25, 26] method. However, visual generation with linear models, such as Mamba, RWKV, and GLA, often faces two challenges, i.e.,", + "bbox": [ + 89, + 795, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "unidirectional scanning modeling and lack of local awareness. Previous approaches [16, 23] have often addressed the first issue by performing bidirectional scanning within the same block. Nevertheless, such methods result in a significant increase in time consumption and numerical instability. To address these challenges, we propose Diffusion GLA (DiG), which incorporates a lightweight spatial reorient & enhancement module (SREM) for block-wise scanning direction controlling and local awareness. For the first issue, SREM changes the sequence direction with minimal number of matrix operations and assigns different scanning in a block-by-block manner. The scanning directions contain four basic patterns and enable each patch in sequences to be aware of other patches following 4 directions. For the second issue, we also incorporate a depth-wise convolution (DWConv) [9] in the SREM to provide local awareness with extremely small amounts of parameters. Inspired by U-Net [50], we further propose a U-shape variant of DiG and analyze the improvements. Crucially, this paper presents a systematic ablation study and a comprehensive evaluation of the proposed modules and architectures. It is important to highlight that DiG adheres to the first practices of linear attention transformers in diffusion generation, demonstrating superior efficiency in quadratic and sub-quadratic diffusion models.", + "bbox": [ + 511, + 90, + 903, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared with the ViT-based method, i.e., DiT [39], DiG presents competitive performance on ImageNet [12] $256 \\times 256$ generation when using the same hyperparameters. Furthermore, DiG is more efficient in terms of training speed and GPU memory starting from a 512 resolution. The efficiency in terms of memory and speed empowers DiG to alleviate the resource constraint problem of long- sequence visual generation tasks. Specifically, DiG demonstrates significant efficiency improvements over comparable models: DiG-S/2 achieves a $2.5 \\times$ faster training speed and saves $75.7\\%$ GPU memory compared to DiT-S/2 at a $1792 \\times 1792$ resolution as shown in Fig. 2. Furthermore, with the same model size, DiG-XL/2 is $4.2 \\times$ faster than the recent Mamba-based diffusion model at 1024 resolution and $1.8 \\times$ faster than DiT with well-designed CUDA-optimized FlashAttention-2 [11] at 2048 resolution as shown in Fig. 3.", + "bbox": [ + 511, + 469, + 903, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows:", + "bbox": [ + 532, + 710, + 893, + 724 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Diffusion GLA (DiG), which incorporates an efficient DiG block for both global visual context modeling through block-wise scanning, and local visual awareness. To the best of our knowledge, DiG is the first exploration for diffusion backbone with linear attention.", + "- Without the burden of quadratic attention, the proposed DiG exhibits higher efficiency in both training speed and GPU memory cost while maintaining a similar modeling ability as DiT. Notably, DiG is $4.2 \\times$ faster than" + ], + "bbox": [ + 513, + 727, + 903, + 862 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "Multi-path scanning and summation can easily lead to numerical NaN during training [16].", + "bbox": [ + 511, + 875, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7665", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/27cb37a8e1c4ec60a4565c134665beedc43a7aff0e94269ef6fd3b55c4e8507d.jpg", + "image_caption": [ + "(a) Speed Comparison", + "Figure 2. Efficiency comparison among DiT [39] with Attention [59], DiS [16] with Mamba [18], and our DiG model. DiG achieves higher training speed while costs lower GPU memory in dealing with high-resolution images. For example, DiG is $2.5 \\times$ faster than DiT and saves $75.7\\%$ GPU memory with a resolution of $1792 \\times 1792$ , i.e., 12544 tokens per image. Patch size for all models is 2." + ], + "image_footnote": [], + "bbox": [ + 98, + 111, + 480, + 305 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9b4a3954cb66d8aa29b4c6972d791d91dfed700afb52478d182968235cbb8489.jpg", + "image_caption": [ + "(b) GPU Memory Comparison" + ], + "image_footnote": [], + "bbox": [ + 511, + 104, + 893, + 305 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/05bfdd792b26f8ec68fe370e6e0af89ffc7d2e0cdba4225eccb40f9bc76e4614.jpg", + "image_caption": [ + "(a) FPS Comparison w/ img_size = 1024", + "Figure 3. FPS comparison among DiS [16] with Mamba [18], DiT [39] with Attention [59], DiT with Flash Attention-2 (Flash-DiT) [11] and our DiG model varying from different model sizes. We take DiG as a baseline. With a resolution of $1024 \\times 1024$ , DiG is $2.0 \\times$ faster than DiS at small size while $4.2 \\times$ faster at XL size. Furthermore, DiG-XL/2 is $1.8 \\times$ faster than the most well-designed high-optimized Flash-DiT-XL/2 with a resolution of $2048 \\times 2048$ ." + ], + "image_footnote": [], + "bbox": [ + 94, + 381, + 478, + 579 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f57999b0e76a8524aa97708646ea1bc5a4316db67c6a736aa0380cf94bdfdad0.jpg", + "image_caption": [ + "(b) FPS Comparison w/ img_size = 2048" + ], + "image_footnote": [], + "bbox": [ + 511, + 381, + 895, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the Mamba-based diffusion model at 1024 resolution and $1.8 \\times$ faster than DiT with well-designed CUDA-optimized FlashAttention-2 [11] at 2048 resolution.", + "bbox": [ + 102, + 652, + 482, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- We conduct extensive experiments on the ImageNet $256 \\times 256$ . The results demonstrate that DiG presents scalable ability and achieves comparable performance when compared with DiT. Besides, higher efficiency makes DiG promising to serve as the next-generation backbone for diffusion models in the context of large-scale long-sequence generation.", + "bbox": [ + 89, + 699, + 482, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 820, + 233, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Linear Attention Transformer", + "text_level": 1, + "bbox": [ + 89, + 847, + 357, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from standard autoregressive Transformer [60] which models the global attention matrix, the original lin", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ear attention [26] is essentially a linear RNN with matrix-valued-format hidden states. Linear attention introduces a similarity kernel $k(x,y)$ with an associated feature map $\\phi(\\cdot)$ , i.e., $k(x,y) = \\langle \\phi(x), \\phi(y) \\rangle$ . The calculation of output $\\mathbf{O} \\in \\mathbb{R}^{L \\times d}$ (here $L$ is the sequence length and $d$ is the dimension) can be represented as follows:", + "bbox": [ + 511, + 652, + 906, + 744 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {O} _ {t} = \\frac {\\sum_ {i = 1} ^ {t} k \\left(\\mathbf {Q} _ {t} , \\mathbf {K} _ {i}\\right) \\mathbf {V} _ {i}}{\\sum_ {i = 1} ^ {t} k \\left(\\mathbf {Q} _ {t} , \\mathbf {K} _ {i}\\right)} = \\frac {\\phi \\left(\\mathbf {Q} _ {t}\\right) \\sum_ {i = 1} ^ {t} \\phi \\left(\\mathbf {K} _ {i}\\right) ^ {\\top} \\mathbf {V} _ {i}}{\\phi \\left(\\mathbf {Q} _ {t}\\right) \\sum_ {i = 1} ^ {t} \\phi \\left(\\mathbf {K} _ {i}\\right) ^ {\\top}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 757, + 903, + 806 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} + \\phi (\\mathbf {K} _ {i}) \\mathbf {V} _ {i}, z _ {t} = z _ {t - 1} + \\phi (\\mathbf {K} _ {i}) ^ {\\top}, \\mathbf {O} _ {t} = \\frac {\\phi (\\mathbf {Q} _ {t}) \\mathbf {S} _ {t}}{\\phi (\\mathbf {Q} _ {t}) z _ {t}},\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 809, + 931, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where query $\\mathbf{Q}$ , key $\\mathbf{K}$ , value $\\mathbf{V}$ have shapes of $L\\times d$ and $t$ is the index of current token. By denoting hidden state $\\mathbf{S}_t = \\sum_{i = 1}^{t}\\phi (\\mathbf{K}_i)\\mathbf{V}_i$ and normalizer $z_{t} = \\sum_{i = 1}^{t}\\phi (\\mathbf{K}_{i})^{\\top}$ where", + "bbox": [ + 511, + 854, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7666", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbf{S}_t \\in \\mathbb{R}^{d \\times d}$ , $z_t \\in \\mathbb{R}^{d \\times 1}$ , the Eq. (1) can be rewritten as the Eq. 2. Recent works set $\\phi(\\cdot)$ to be the identity [35, 57] and remove $z_t$ [44], resulting linear attention Transformer with the following format:", + "bbox": [ + 89, + 89, + 483, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} + \\mathbf {K} _ {t} ^ {\\top} \\mathbf {V} _ {t}, \\quad \\mathbf {O} _ {t} = \\mathbf {Q} _ {t} \\mathbf {S} _ {t}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 157, + 482, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Directly using a linear attention Transformer for visual generation leads to poor performance due to the unidirectional modeling, so we propose a lightweight spatial reorient & enhancement module to take care of both modeling global context in four directions block by block and local information.", + "bbox": [ + 89, + 183, + 483, + 273 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2. Backbones in Diffusion Models", + "text_level": 1, + "bbox": [ + 89, + 281, + 366, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing diffusion models typically employ U-Net as backbones [17, 20, 48] for image generation. Recently, Vision Transformer (ViT)-based backbones [1, 3, 5, 6, 39] receive significant attention due to the scalability of transformer and its natural fit for multi-modal learning. However, ViT-based architectures suffer from quadratic complexity, limiting their practicability in long sequence generation tasks, such as high-resolution image synthesis, video generation etc. To mitigate this, recent works explore subquadratic-time approaches to efficiently handle long sequences. For example, DiS [16], DiffuSSM [62], and ZigMa [23] employ state-space models as diffusion backbones for better computation efficiency. Diffusion-RWKV [62] adopt an RWKV architecture in diffusion models for image generation.", + "bbox": [ + 89, + 303, + 483, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our DiG also follows this line of research, aiming at improving the efficiency of long sequence processing by adopting Gated Linear Attention Transformer (GLA) as diffusion backbones. Our proposed adaptation maintains the fundamental structure and benefits of GLA while introducing a few crucial modifications necessary for generating high-fidelity visual data.", + "bbox": [ + 89, + 515, + 483, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 632, + 181, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 657, + 230, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gated Linear Attention Transformer. The Gated Linear Attention Transformer (GLA) [63] combines a data-dependent gating mechanism and linear attention, achieving superior recurrent modeling performance. Given an input $\\mathrm{X} \\in \\mathbb{R}^{L \\times d}$ (here $L$ is the sequence length and $d$ is the dimension), GLA calculates the query, key, and value vectors as follows:", + "bbox": [ + 89, + 679, + 483, + 782 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} = \\mathbf {X} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} \\mathbf {W} _ {K}, \\mathbf {V} = \\mathbf {X} \\mathbf {W} _ {V}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 792, + 482, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{W}_Q$ , $\\mathbf{W}_K$ , and $\\mathbf{W}_V$ are linear projection weights. The dimension number of $\\mathbf{Q}$ , $\\mathbf{K}$ is $d_k$ , and $d_v$ is for $\\mathbf{V}$ . Next, GLA compute the gating matrix $\\mathbf{G}$ as follows:", + "bbox": [ + 89, + 816, + 482, + 862 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {G} _ {t} = \\alpha_ {t} ^ {\\top} \\beta_ {t} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\alpha = \\sigma \\left(\\mathbf {X} \\mathbf {W} _ {\\alpha} + b _ {\\alpha}\\right) ^ {\\frac {1}{\\tau}} \\in \\mathbb {R} ^ {L \\times d _ {k}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 867, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\beta = \\sigma \\left(\\mathbf {X} \\mathbf {W} _ {\\beta} + b _ {\\beta}\\right) ^ {\\frac {1}{\\tau}} \\in \\mathbb {R} ^ {L \\times d _ {v}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 89, + 903, + 109 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t$ is the index of token, $\\sigma$ is the sigmoid function, $b$ is the bias term, and $\\tau \\in \\mathbb{R}$ is a temperature term. As shown in Fig. 4, the final output $\\mathbf{Y}_t$ is obtained as follows:", + "bbox": [ + 511, + 114, + 906, + 160 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b220c2890808ebaf80222fec3f472dc1ff9ba8f2f058e2218f9aa05f647ca33c.jpg", + "image_caption": [ + "Figure 4. Pipeline of GLA." + ], + "image_footnote": [], + "bbox": [ + 519, + 174, + 864, + 263 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {t - 1} ^ {\\prime} = \\mathbf {G} _ {t} \\odot \\mathbf {S} _ {t - 1} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 294, + 906, + 313 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} ^ {\\prime} + \\mathbf {K} _ {t} ^ {\\top} V _ {t} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 315, + 903, + 333 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {O} _ {t} = \\mathbf {Q} _ {t} ^ {\\top} \\mathbf {S} _ {t} \\in \\mathbb {R} ^ {1 \\times d _ {v}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 335, + 903, + 354 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R} _ {t} = \\operatorname {S w i s h} \\left(\\mathbf {X} _ {t} \\mathbf {W} _ {r} + b _ {r}\\right) \\in \\mathbb {R} ^ {1 \\times d _ {v}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 357, + 903, + 375 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} _ {t} = \\left(\\mathbf {R} _ {t} \\odot \\operatorname {L N} \\left(\\mathbf {O} _ {t}\\right)\\right) \\mathbf {W} _ {O} \\in \\mathbb {R} ^ {1 \\times d}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 378, + 903, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where Swish is the Swish [46] activation function, and $\\odot$ is the element-wise multiplication operation. In subsequent sections, we use $\\mathbf{GLA}(\\cdot)$ to refer to the gated linear attention computation for the input sequence.", + "bbox": [ + 511, + 407, + 906, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion Models. Before introducing the proposed method, we provide a brief review of diffusion models (DDPM) [20]. The DDPM takes noise as an input and samples images by iterative denoising the input. The forward process of DDPM begins with a stochastic process where the initial image $x_0$ is gradually corrupted by noise and is finally transformed into a simpler, noise-dominated state. The forward noisng process can be represented as follows:", + "bbox": [ + 511, + 488, + 906, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {1: T} \\mid x _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(x _ {t} \\mid x _ {t - 1}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 619, + 903, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) I\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 664, + 903, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x_{1:T}$ is the sequence of noised images from time $t = 1$ to $t = T$ . Then, DDPM learns the reverse process that recovers the original image with learned $\\mu_{\\theta}$ and $\\Sigma_{\\theta}$ :", + "bbox": [ + 511, + 694, + 905, + 739 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}\\right), \\Sigma_ {\\theta} \\left(x _ {t}\\right)\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 751, + 903, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta$ are the parameters of the denoiser, and are trained with the variational lower bound [53] on the loglikelihood of the observed data $x_0$ .", + "bbox": [ + 511, + 780, + 906, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} (\\theta) = - p \\left(x _ {0} \\mid x _ {1}\\right) \\\\ + \\sum_ {t} D _ {K L} \\left(q ^ {*} \\left(x _ {t - 1} \\mid x _ {t}, x _ {0}\\right) \\| p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right)\\right), \\tag {15} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 835, + 903, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7667", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e2a3f82aaf26620ae71812bbe36d38a6ada73386ad306dcb48ecdfbb16f7d081.jpg", + "image_caption": [ + "(a) Plain DiG", + "(b) U-shape DiG", + "(d) Block-by-Block Scanning Directions of DiG Controlled by SREM" + ], + "image_footnote": [], + "bbox": [ + 98, + 104, + 676, + 537 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cedd6545b528765d4dd733c03091e2d40ddbd24b65ff381c84a6c486ca364295.jpg", + "image_caption": [ + "(c) DiG Block", + "Figure 5. The overview of the proposed DiG models. The figure presents the (a) plain DiG, denoted as DiG, (b) U-shape DiG, denoted as U-DiG, (c) DiG block, and (d) block-by-block scanning directions of DiG controlled by the SREM." + ], + "image_footnote": [], + "bbox": [ + 686, + 104, + 898, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}$ is the full loss. To further simplify the training process of DDPM, researchers reparameterize $\\mu_{\\theta}$ as a noise prediction network $\\epsilon_{\\theta}$ and minimize the mean squared error loss $\\mathcal{L}_{\\mathrm{simple}}$ between $\\epsilon_{\\theta}(x_t)$ and the true Gaussian noise $\\epsilon_{t}$ :", + "bbox": [ + 89, + 598, + 482, + 660 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s i m p l e}} (\\theta) = \\left\\| \\epsilon_ {\\theta} \\left(x _ {t}\\right) - \\epsilon_ {t} \\right\\| _ {2} ^ {2}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 665, + 482, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, to train a diffusion model that can learn a variable reverse process covariance $\\Sigma_{\\theta}$ , we need to optimize the full $D_{KL}$ term. In this paper, we follow DiT [39]'s training recipe where we use the simple loss $\\mathcal{L}_{\\mathrm{simple}}$ to train the noise prediction network $\\epsilon_{\\theta}$ and use the full loss $\\mathcal{L}$ to train the covariance prediction network $\\Sigma_{\\theta}$ . After the training process, we follow the stochastic sampling process to generate images from the learned $\\epsilon_{\\theta}$ and $\\Sigma_{\\theta}$ .", + "bbox": [ + 89, + 689, + 483, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Diffusion GLA", + "text_level": 1, + "bbox": [ + 89, + 816, + 241, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We present two variants of Diffusion GLA (DiG), as shown in Fig. 5. Our goal is to be as faithful to the standard GLA architecture as possible to retain its scaling ability and high-efficiency properties. We follow some of the best practices", + "bbox": [ + 89, + 839, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of previous vision transformer architectures [1, 14, 39] to propose plain DiG and U-shape DiG, which are denoted as DiG and U-DiG, respectively. DiG first takes a spatial representation $z$ output by the VAE encoder [28, 48] as input. For example, given a $256 \\times 256 \\times 3$ image, we obtain a spatial representation $z$ of shape $32 \\times 32 \\times 4$ after the VAE encoder. DiG subsequently converts this spatial input into a token sequence $\\mathbf{z}_p \\in \\mathbb{R}^{T \\times (P^2 \\cdot C)}$ through a patchify layer, where $T$ is length of token sequence, $C$ is the number of spatial representation channels, $P$ is the size of image patches, and halving $P$ will quadruple $T$ . Specifically, $p$ for DiG is 2, while for U-DiG, $p$ is 1. Next, we linearly project the $\\mathbf{z}_p$ to the vector with dimension $D$ and add frequency-based positional embeddings $\\mathbf{E}_{pos} \\in \\mathbb{R}^{T \\times D}$ to all projected tokens as follows:", + "bbox": [ + 511, + 598, + 906, + 825 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {0} = \\left[ \\mathbf {z} _ {p} ^ {1} \\mathbf {W}; \\mathbf {z} _ {p} ^ {2} \\mathbf {W}; \\dots ; \\mathbf {z} _ {p} ^ {T} \\mathbf {W} \\right] + \\mathbf {E} _ {p o s}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 837, + 906, + 858 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_p^t$ is the $t$ -th patch of $\\mathbf{z}_p$ , $\\mathbf{W} \\in \\mathbb{R}^{(P^2 \\cdot C) \\times D}$ is the learnable projection matrix. As for conditional information", + "bbox": [ + 511, + 867, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7668", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "such as noise timesteps $t \\in \\mathbb{R}$ , and class labels $y \\in \\mathbb{R}$ , we adopt multi-layer perception (MLP) and embedding layer as timestep embedder and label embedder, respectively.", + "bbox": [ + 89, + 90, + 485, + 137 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {t} = \\mathbf {M L P} (t), \\quad \\mathbf {y} = \\mathbf {E m b e d} (y), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 143, + 482, + 161 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{t} \\in \\mathbb{R}^{1 \\times D}$ is time embedding and $\\mathbf{y} \\in \\mathbb{R}^{1 \\times D}$ is label embedding. We then send the token sequence $(\\mathbf{z}_{l-1})$ to the $l$ -th block of the DiG encoder, and obtain the output $\\mathbf{z}_l$ . For the U-DiG variant, there are down-sampling and upsampling modules between different stages, and shortcuts in the same stage. Finally, we normalize the output token sequence $\\mathbf{z}_L$ , and feed it to the linear projection head to get the final predicted noise $\\hat{\\mathbf{p}}_{noise}$ and predicted covariance $\\hat{\\mathbf{p}}_{covariance}$ , as follows:", + "bbox": [ + 89, + 166, + 483, + 305 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {l} = \\operatorname {D i G} _ {l} (\\mathbf {z} _ {l - 1}, \\mathbf {t}, \\mathbf {y}), \\quad \\mathbf {z} _ {n} = \\operatorname {N o r m} (\\mathbf {z} _ {L}), \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 311, + 482, + 327 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {p}} _ {\\text {n o i s e}}, \\hat {\\mathbf {p}} _ {\\text {c o v a r i a n c e}} = \\operatorname {L i n e a r} (\\mathbf {z} _ {n}), \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 334, + 482, + 351 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{DiG}_l$ is the $l$ -th diffusion GLA block, $L$ is the number of blocks, and Norm is the normalization layer. The $\\hat{\\mathbf{p}}_{noise}$ and $\\hat{\\mathbf{p}}_{covariance}$ have the same shape as the input spatial representation, i.e., $32 \\times 32 \\times 4$ .", + "bbox": [ + 89, + 357, + 483, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. DiG Block", + "text_level": 1, + "bbox": [ + 89, + 425, + 209, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The original GLA block processes input sequence in a recurrent manner, which only enables causal modeling for 1-D sequence. Previous methods [16, 23] employ multi-path scanning within the same block to model global context, but this leads to a significant increase in time consumption and numerical instability [16], as shown in Table 1. To model the global context efficiently, we introduce the DiG block as shown in Fig. 5, which incorporates a spatial reorient & enhancement module (SREM) that enables lightweight spatial recognition and controls block-wise scanning directions.", + "bbox": [ + 89, + 446, + 482, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Specifically, we present the forward process of DiG block in Algo. 1. Following the widespread usage of adaptive normalization layers [41] in GANs [2, 24] and diffusion models [13, 39], we add and normalize the input timestep embedding $\\mathbf{t}$ and label embedding $\\mathbf{y}$ to regress the scale parameter $\\alpha$ , $\\gamma$ , and shift parameter $\\beta$ . Then, we launch gated linear attention (GLA) and feedforward network (FFN) with the adjustment of regressed adaptive layer norm (adaLN) parameters. Finally, we send the sequence to the SREM module as shown in Fig. 6. Specifically, we reshape the sequence to 2D and launch a lightweight $3\\times 3$ depth-wise convolution (DWConv2d) layer to perceive local spatial information. However, we notice that using traditional initialization for DWConv2d leads to slow convergence because convolutional weights are dispersed around. To address this problem, we use identity initialization that only sets the convolutional kernel center as 1, and the surroundings to 0. For the last step of SREM, we alternate transpose and flip operations block-by-block to efficiently control block-wise scanning directions using minimal number of matrix operations.", + "bbox": [ + 89, + 599, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/faaf2a99d96064949c6a9fdba6390238bdbd7befbbd09193c5916786ff0600de.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Extra OperationsIf Stable?Time (s)
    Matrix OPsScanning
    Bidirectional31×2.18
    4-directional133×4.02
    Block-by-Block20✓1.56
    ", + "bbox": [ + 514, + 89, + 939, + 174 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Experimental results of different scanning strategies. Given $I = {32},p = 2$ ,all experiments are conducted with XL size models. Extra operations include matrix operations and scanning operations, which both increase the time consumption.", + "bbox": [ + 511, + 176, + 906, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Architecture Details", + "text_level": 1, + "bbox": [ + 511, + 239, + 705, + 255 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use $N$ DiG blocks, each operating at the hidden dimension size $D$ . Following previous works [14, 39, 63], we follow standard transformer setting that scales $N$ , $D$ , and attention heads number. Particularly, we provide four configurations: S, B, L, and XL, for the two different variants, as shown in the Table 2. They cover a wide range of flop allocations, ranging from 4.10 Gflops to 89.40 Gflops, presenting a way to gauge the scaling performance and efficiency. Notably, DiG consumes $70.8\\%$ to $76.3\\%$ Gflops, and U-DiG only consumes $66.0\\%$ to $67.6\\%$ Gflops when compared with the same model size DiT baselines. Both the proposed two variants are computationally efficient.", + "bbox": [ + 511, + 263, + 906, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Efficiency Analysis", + "text_level": 1, + "bbox": [ + 511, + 454, + 694, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GPU contains two important components, i.e., high bandwidth memory (HBM) and SRAM. HBM has a bigger memory size but SRAM has a larger bandwidth. To make full use of SRAM and modeling sequences in a parallel form, we follow GLA to split a whole sequence into many chunks that can complete calculations on SRAM. We denote the chunk size as $M$ , the training complexity is thus $O\\left(\\frac{T}{M}(M^2D + MD^2)\\right) = O(TMD + TD^2)$ , which is less than the traditional attention's complexity $O(T^2D)$ when $T > D$ . Furthermore, the scaling analysis of speed and GPU memory are shown in Fig. 2 and Fig. 3, which demonstrate the high efficiency of the proposed DiG: DiG shows notable efficiency gains: DiG-S/2 is $2.5 \\times$ faster and saves $75.7\\%$ GPU memory compared to DiT-S/2 at $1792 \\times 1792$ . Additionally, DiG-XL/2 is $4.2 \\times$ faster than the Mamba-based model at 1024 resolution and $1.8 \\times$ faster than DiT with FlashAttention-2 at 2048.", + "bbox": [ + 511, + 476, + 908, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 511, + 747, + 638, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 511, + 772, + 720, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets and metrics. Following previous works [39], we use ImageNet [12] for class-conditional image generation learning at a resolution of $256 \\times 256$ . The ImageNet dataset contains 1,281,167 training images varying from 1,000 different classes. We use horizontal flipping for data augmentation. We measure the generation performance with Frechet Inception Distance (FID) [37], Incep", + "bbox": [ + 511, + 794, + 906, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7669", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2f16cf905580bc18114864fe07bdc9bb4944cb4974e83def9695a42b0408e798.jpg", + "image_caption": [ + "Figure 6. Details of the Spatial Reorient & Enhancement Module (SREM)." + ], + "image_footnote": [], + "bbox": [ + 122, + 95, + 300, + 324 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Algorithm 1: DiG Block Process.", + "text_level": 1, + "bbox": [ + 336, + 95, + 552, + 108 + ], + "page_idx": 6 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [], + "code_body": "Input: token sequence $\\mathbf{z}_{l-1}$ : (B, T, D), timestep embed $\\mathbf{t}$ : (B, 1, D), label embed $\\mathbf{y}$ : (B, 1, D) \nOutput: token sequence $\\mathbf{z}_l$ : (B, T, D) \n $\\alpha_1, \\beta_1, \\gamma_1, \\alpha_2, \\beta_2, \\gamma_2$ : (B, 1, D) $\\leftarrow$ MLP $(\\mathbf{t} + \\mathbf{y})$ // regress parameters of adaLN \n $\\mathbf{z}_{l-1}^{\\prime}$ : (B, T, D) $\\leftarrow$ $\\mathbf{z}_{l-1} + \\alpha_1 \\odot$ GLA(Norm( $\\mathbf{z}_{l-1}$ ) $\\odot$ $(1 + \\gamma_1) + \\beta_1)$ $\\mathbf{z}_{l-1}^{\\prime\\prime}$ : (B, T, D) $\\leftarrow$ $\\mathbf{z}_{l-1}^{\\prime} + \\alpha_2 \\odot$ FFN(Norm( $\\mathbf{z}_{l-1}^{\\prime}$ ) $\\odot$ $(1 + \\gamma_2) + \\beta_2)$ $\\mathbf{z}_{l-1}^{\\prime\\prime}$ : (B, $\\sqrt{T}, \\sqrt{T}, D$ ) $\\leftarrow$ DWConv2d(reshape2d( $\\mathbf{z}_{l-1}^{\\prime\\prime}$ ) // SREM module \nif $l \\% 2 == 0$ then \n $\\mathbf{z}_{l-1}^{\\prime\\prime}$ : (B, $\\sqrt{T}, \\sqrt{T}, D$ ) $\\leftarrow$ transpose( $\\mathbf{z}_{l-1}^{\\prime\\prime}$ ) // transpose the token matrix every two block \n $\\mathbf{z}_l$ : (B, T, D) $\\leftarrow$ flatten( $\\mathbf{z}_{l-1}^{\\prime\\prime}$ ) // flatten the token matrix into 1-D sequence \nend \nelse \n $\\mathbf{z}_{l-1}^{\\prime\\prime}$ : (B, T, D) $\\leftarrow$ flatten( $\\mathbf{z}_{l-1}^{\\prime\\prime}$ ) // flatten the token matrix into 1-D sequence \n $\\mathbf{z}_l$ : (B, T, D) $\\leftarrow$ flip( $\\mathbf{z}_{l-1}^{\\prime\\prime}$ ) // flip the token sequence every two block \nend \nReturn: $\\mathbf{z}_l$", + "bbox": [ + 334, + 112, + 861, + 357 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7b78433193dada11d859e78fc50fe89a208cc4a880db01b8041a1af0032fdd1e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelLayers NHidden Size DGflopsGflopsDiG/GflopsDiT
    DiG-S123844.3070.8%
    DiG-B1276817.0774.1%
    DiG-L24102461.6676.3%
    DiG-XL28115289.4075.3%
    U-DiG-S201284.1067.6%
    U-DiG-B2025615.2066.0%
    U-DiG-L4032053.5766.3%
    U-DiG-XL4041679.0966.6%
    ", + "bbox": [ + 91, + 385, + 488, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Details of DiG models. We follow DiT [39] model configurations for the Small (S), Base (B), Large (L), and XLarge (XL) variants. Given $I = {32},p = 2$ for DiG, $p = 1$ for U-DiG.", + "bbox": [ + 89, + 539, + 483, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion Score [52], sFID [37], and Precision/Recall [30].", + "bbox": [ + 89, + 588, + 442, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation details. We use AdamW optimizer with a constant learning rate of $1e - 4$ . Following the previous works [39], we utilize the exponential moving average (EMA) of DiG weights during training with a decay rate of 0.9999. We generate all images with the EMA model. For the training of ImageNet, we use an off-the-shelf pretrained variational autoencoder (VAE) [27, 49].", + "bbox": [ + 89, + 612, + 483, + 719 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Model Analysis", + "text_level": 1, + "bbox": [ + 89, + 727, + 245, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of spatial reorient & enhancement module. As shown in Table 3, we analyze the effectiveness of the proposed spatial reorient & enhancement module (SREM). We take the DiT-S/2 as our baseline method. The naive plain DiG with only causal modeling has significantly fewer flops and parameters, but also poor FID performance due to the lack of global context. We first add the bidirectional scanning to DiG and observe significant improvement, i.e., 69.28 FID, which demonstrates the importance of global context. Experiment without identity initialization", + "bbox": [ + 89, + 750, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/956d2ad69a13dcd84ea52ce4b803951b31b3a392a53e2365ecfd5536168c8436.jpg", + "image_caption": [ + "Figure 7. Scaling analysis with DiG model scales and patch sizes. for DWConv2d (the $\\times$ symbol), leads to worse FID, while the DWConv2d with identity initialization can improve performance a lot. The experiment with DWConv2d proves the importance of identity initialization and local awareness. The experiment with full SREM brings the best performance, taking care of both local information and global context. Experiments in the last three rows indicate that the more suitable position for SREM is after the FFN." + ], + "image_footnote": [], + "bbox": [ + 519, + 375, + 861, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Scaling model scales and patch sizes. We investigate the scaling ability of DiG among four different model scales and three patch sizes on the ImageNet dataset. As depicted in Fig. 7, the performance improves as the models scale from S/2 to XL/2 and the patch size from 2 to 8. The results demonstrate the scaling ability of DiG, indicating its potential as a large foundational diffusion model.", + "bbox": [ + 511, + 744, + 906, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Structural ablation from DiG to U-DiG. We evaluate the structural benefits from DiG to U-DiG. As shown in", + "bbox": [ + 511, + 869, + 906, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7670", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d25f562c4e5225d2e2e9eb06c4f9e9de3fb915753357d5c4a6fa329474f90dae.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelSpatial Reorient & Enhancement ModuleSREM PositionFlops (G)Params (M)FID-50K
    BidirectionalDWConv2d4-directional
    Baseline Method.
    DiT-S/26.0633.068.4
    Ours.
    DiG-S/24.2933.0175.84
    DiG-S/2✓After FFN4.2933.069.28
    DiG-S/2✓✓After FFN4.3033.196.83
    DiG-S/2✓✓After FFN4.3033.163.84
    DiG-S/2✓✓✓After FFN4.3033.162.06
    DiG-S/2✓✓✓Before Attn.4.3033.162.34
    DiG-S/2✓✓✓Between Attn. & FFN4.3033.162.93
    ", + "bbox": [ + 99, + 88, + 893, + 277 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7314e7dca9223d641de11df41568512a6d355458b66da3bccf9eff6074d37db0.jpg", + "table_caption": [ + "Table 3. Ablation of the proposed Spatial Reorient & Enhancement Module (SREM). We validate the effectiveness of each SREM component and use the same hyperparameters for all models. The \"half right and half wrong symbol\" $(\\star)$ means use DWConv2d without the identity initialization. We mark the best result in bold." + ], + "table_footnote": [ + "Table 4. Benchmarking class-conditional image generation on ImageNet $256 \\times 256$ . DiG models adopt the same hyperparameters as DiT [39] for fair comparison. G is the classifier-free guidance. We mark the best results in bold." + ], + "table_body": "
    ModelFID↓sFID↓IS↑P↑R↑
    ADM [13]10.946.02100.980.690.63
    ADM-U7.495.13127.490.720.63
    ADM-G4.595.25186.700.820.52
    ADM-G, ADM-U3.946.14215.840.830.53
    CDM [22]4.88-158.71--
    LDM-8 [49]15.51-79.030.650.63
    LDM-8-G7.76-209.520.840.35
    LDM-4-G3.95-178.220.810.55
    LDM-4-G3.60-247.670.870.48
    Other sub-quadratic-time diffusion methods.
    DiM-H/2 [58]2.40----
    DiS-H/2 [16]2.104.55271.320.820.58
    DiMSUM-L/2-G [42]2.110.59---
    Baselines and Ours.
    DiT-S/2 (400K) [39]68.40----
    DiG-S/2 (400K)62.0611.7722.810.390.56
    DiT-B/2 (400K)43.47----
    DiG-B/2 (400K)39.508.5037.210.510.63
    DiT-L/2 (400K)23.33----
    DiG-L/2 (400K)22.906.9159.870.600.64
    DiT-XL/2 (400K)19.47----
    DiG-XL/2 (400K)18.536.0668.530.630.64
    DiT-XL/2 (7M)9.626.85121.500.670.67
    DiG-XL/2 (1.2M)8.606.46130.030.680.68
    DiT-XL/2-G (7M)2.274.60278.240.830.57
    DiG-XL/2-G (1.2M)2.074.53278.950.820.60
    ", + "bbox": [ + 94, + 327, + 478, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5, both the shortcut and hierarchical structures contribute positively to the metrics. Notably, for the generation task at a 512 resolution, U-DiG-S/1 achieves a remarkable improvement over DiG-S/2, with an FID gain exceeding 16.2, which demonstrates the effectiveness of U-DiG in generating high-resolution images.", + "bbox": [ + 89, + 809, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ccc203e46ee2d686efbc5833b9b88007436181491c168a7162ba21c4e42623fb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    w/ short cutw/ hierarchyFID-50K
    IN-256IN-512
    DiT-S/268.40NaN
    DiG-S/262.0699.04
    DiG-S/2✓57.0191.42
    U-DiG-S/1✓✓52.2082.62
    ", + "bbox": [ + 514, + 327, + 910, + 433 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Structural ablation from DiG to U-DiG.", + "bbox": [ + 563, + 435, + 854, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 511, + 457, + 653, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We mainly compare the proposed plain DiG with DiT [39]. For class-conditional image generation on ImageNet $256 \\times 256$ , as shown in Table 4, the proposed DiG has fewer FLOPs but outperforms DiT among four model scales with 400K training iterations with the same hyperparameters. Furthermore, the DiG-XL/2 (1.2M) with classifier-free guidance also presents competitive results when compared with concurrent sub-quadratic-time diffusion methods.", + "bbox": [ + 511, + 479, + 906, + 601 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 614, + 633, + 630 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present DiG, a cost-effective alternative to the vanilla Transformer for diffusion models in image generation tasks. In particular, DiG explores Gated Linear Attention Transformers (GLA), attaining comparable effectiveness and superior efficiency in long-sequence image generation tasks. Experimentally, DiG shows comparable performance to prior diffusion models on class-conditional ImageNet $256 \\times 256$ benchmark while significantly reducing the computational burden starting from a 512 resolution. We hope this work can open up the possibility for other long-sequence generation tasks, such as video and audio modeling.", + "bbox": [ + 511, + 638, + 906, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Although DiG shows superior efficiency in diffusion image generation, building a large foundation model like Sora [3] upon DiG is still an area that needs to be explored further.", + "bbox": [ + 511, + 839, + 908, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7671", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments and Disclosure of Funding", + "text_level": 1, + "bbox": [ + 91, + 89, + 475, + 108 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was partially supported by the National Science and Technology Major Project under Grant No. 2023YFF0905400.", + "bbox": [ + 89, + 114, + 482, + 160 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 176, + 187, + 191 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. 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PMLR, 2024. 2" + ], + "bbox": [ + 91, + 92, + 480, + 900 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7674", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DiG_ Scalable and Efficient Diffusion Models with Gated Linear Attention/283f0e42-855f-4918-822c-d5c1219d1790_model.json b/2025/DiG_ Scalable and Efficient Diffusion Models with Gated Linear Attention/283f0e42-855f-4918-822c-d5c1219d1790_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b8657f3984498d8bae25af436d17d676f6c6f276 --- /dev/null +++ b/2025/DiG_ Scalable and Efficient Diffusion Models with Gated Linear Attention/283f0e42-855f-4918-822c-d5c1219d1790_model.json @@ -0,0 +1,2444 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.125, + 0.131, + 0.872, + 0.152 + ], + "angle": 0, + "content": "DiG: Scalable and Efficient Diffusion Models with Gated Linear Attention" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.179, + 0.87, + 0.224 + ], + "angle": 0, + "content": "Lianghui Zhu \\(^{1,2,\\diamond}\\) Zilong Huang \\(^{2\\boxtimes}\\) Bencheng Liao \\(^{1}\\) Jun Hao Liew \\(^{2}\\) Hanshu Yan \\(^{2}\\) Jiashi Feng \\(^{2}\\) Xinggang Wang \\(^{1\\boxtimes}\\)" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.24, + 0.816, + 0.28 + ], + "angle": 0, + "content": "\\(^{1}\\) School of EIC, Huazhong University of Science & Technology \\(^{2}\\) ByteDance Code & Models: hustvl/DiG" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.298, + 0.904, + 0.716 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.719, + 0.908, + 0.749 + ], + "angle": 0, + "content": "Figure 1. Image generation with the proposed Diffusion Gated Linear Attention Transformers (DiG). We show selected samples from our class-conditional DiG-XL/2 models trained on ImageNet at \\(512 \\times 512\\) and \\(256 \\times 256\\) resolution, respectively." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.763, + 0.327, + 0.779 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.483, + 0.841 + ], + "angle": 0, + "content": "Diffusion models with large-scale pre-training have achieved significant success in the field of visual content generation, particularly exemplified by Diffusion Trans" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.764, + 0.907, + 0.901 + ], + "angle": 0, + "content": "formers (DiT). However, DiT models have faced challenges with quadratic complexity efficiency, especially when handling long sequences. In this paper, we aim to incorporate the sub-quadratic modeling capability of Gated Linear Attention (GLA) into the 2D diffusion backbone. Specifically, we introduce Diffusion Gated Linear Attention Transformers (DiG), a simple, adoptable solution with minimal parameter overhead. We offer two variants, i,e, a plain and U-shape architecture, showing superior efficiency and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.851, + 0.483, + 0.901 + ], + "angle": 0, + "content": "This work was done when Lianghui Zhu was interning at ByteDance. Corresponding authors: Xinggang Wang (xgwang@hust.edu.cn) and Zilong Huang (zilong.huang2020@gmail.com)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7664" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.089, + 0.092, + 0.483, + 0.226 + ], + "angle": 0, + "content": "competitive effectiveness. In addition to superior performance to DiT and other sub-quadratic-time diffusion models at \\(256 \\times 256\\) resolution, DiG demonstrates greater efficiency than these methods starting from a 512 resolution. Specifically, DiG-S/2 is \\(2.5 \\times\\) faster and saves \\(75.7\\%\\) GPU memory compared to DiT-S/2 at a 1792 resolution. Additionally, DiG-XL/2 is \\(4.2 \\times\\) faster than the Mamba-based model at a 1024 resolution and \\(1.8 \\times\\) faster than DiT with FlashAttention-2 at a 2048 resolution." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.257, + 0.223, + 0.273 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.282, + 0.483, + 0.553 + ], + "angle": 0, + "content": "In recent years, diffusion models [4, 20, 32, 53, 56, 61, 65, 66] have emerged as potent deep generative models [13, 49] renowned for their ability to generate high-quality images. Their rapid evolution has spurred extensive applications across various fields, including image-to-image generation [8, 67], text-to-image generation [19, 47, 51], speech synthesis [7, 29], video generation [21, 34, 36], and 3D generation [43, 68]. Concurrent with the rapid development of sampling algorithms [33, 38, 54], the principal techniques have evolved into two main categories based on their architectural backbones: U-Net-based methods [20, 55] and ViT-based methods [14]. U-Net-based approaches continue to leverage the convolutional neural network (CNN) architecture [31, 50], whose hierarchical feature modeling ability benefits visual generation tasks. On the other hand, ViT-based methods [1, 39, 64] innovate by incorporating self-attention mechanisms [59] instead of traditional sampling blocks, resulting in streamlined yet effective performance." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.555, + 0.483, + 0.794 + ], + "angle": 0, + "content": "Due to their excellent scalability in terms of performance, ViT-based methods [39] have been adopted as backbones in the most advanced diffusion works, including PixArt [5, 6], Sora [3], Stable Diffusion 3 [15], etc. However, the self-attention mechanism in ViT-based architectures scales quadratically with the input sequence length, making them resource-intensive when dealing with long sequence generation tasks, e.g., high-resolution image generation and video generation. Recent works such as Mamba [18, 69], RWKV [40] and Gated Linear Attention Transformer (GLA) [63], try to improve the long-sequence processing efficiency by integrating Recurrent Neural Network (RNN) like architecture and hardware-aware algorithms. Since a data-dependent gating mechanism is crucial for 1D modeling [45], GLA shows outstanding performance among the above methods." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Motivated by the success of GLA in the natural language processing domain, it is appealing that we can transfer this success from language generation to visual content generation by designing a scalable and efficient diffusion backbone with the advanced linear attention [10, 25, 26] method. However, visual generation with linear models, such as Mamba, RWKV, and GLA, often faces two challenges, i.e.," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.468 + ], + "angle": 0, + "content": "unidirectional scanning modeling and lack of local awareness. Previous approaches [16, 23] have often addressed the first issue by performing bidirectional scanning within the same block. Nevertheless, such methods result in a significant increase in time consumption and numerical instability. To address these challenges, we propose Diffusion GLA (DiG), which incorporates a lightweight spatial reorient & enhancement module (SREM) for block-wise scanning direction controlling and local awareness. For the first issue, SREM changes the sequence direction with minimal number of matrix operations and assigns different scanning in a block-by-block manner. The scanning directions contain four basic patterns and enable each patch in sequences to be aware of other patches following 4 directions. For the second issue, we also incorporate a depth-wise convolution (DWConv) [9] in the SREM to provide local awareness with extremely small amounts of parameters. Inspired by U-Net [50], we further propose a U-shape variant of DiG and analyze the improvements. Crucially, this paper presents a systematic ablation study and a comprehensive evaluation of the proposed modules and architectures. It is important to highlight that DiG adheres to the first practices of linear attention transformers in diffusion generation, demonstrating superior efficiency in quadratic and sub-quadratic diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.47, + 0.905, + 0.711 + ], + "angle": 0, + "content": "Compared with the ViT-based method, i.e., DiT [39], DiG presents competitive performance on ImageNet [12] \\(256 \\times 256\\) generation when using the same hyperparameters. Furthermore, DiG is more efficient in terms of training speed and GPU memory starting from a 512 resolution. The efficiency in terms of memory and speed empowers DiG to alleviate the resource constraint problem of long- sequence visual generation tasks. Specifically, DiG demonstrates significant efficiency improvements over comparable models: DiG-S/2 achieves a \\(2.5 \\times\\) faster training speed and saves \\(75.7\\%\\) GPU memory compared to DiT-S/2 at a \\(1792 \\times 1792\\) resolution as shown in Fig. 2. Furthermore, with the same model size, DiG-XL/2 is \\(4.2 \\times\\) faster than the recent Mamba-based diffusion model at 1024 resolution and \\(1.8 \\times\\) faster than DiT with well-designed CUDA-optimized FlashAttention-2 [11] at 2048 resolution as shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.712, + 0.895, + 0.726 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.728, + 0.905, + 0.801 + ], + "angle": 0, + "content": "- We propose Diffusion GLA (DiG), which incorporates an efficient DiG block for both global visual context modeling through block-wise scanning, and local visual awareness. To the best of our knowledge, DiG is the first exploration for diffusion backbone with linear attention." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.804, + 0.905, + 0.863 + ], + "angle": 0, + "content": "- Without the burden of quadratic attention, the proposed DiG exhibits higher efficiency in both training speed and GPU memory cost while maintaining a similar modeling ability as DiT. Notably, DiG is \\(4.2 \\times\\) faster than" + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.728, + 0.905, + 0.863 + ], + "angle": 0, + "content": null + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Multi-path scanning and summation can easily lead to numerical NaN during training [16]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7665" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.093, + 0.377, + 0.109 + ], + "angle": 0, + "content": "(a) Speed Comparison" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.112, + 0.481, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.601, + 0.093, + 0.824, + 0.109 + ], + "angle": 0, + "content": "(b) GPU Memory Comparison" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.105, + 0.895, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.307, + 0.908, + 0.351 + ], + "angle": 0, + "content": "Figure 2. Efficiency comparison among DiT [39] with Attention [59], DiS [16] with Mamba [18], and our DiG model. DiG achieves higher training speed while costs lower GPU memory in dealing with high-resolution images. For example, DiG is \\(2.5 \\times\\) faster than DiT and saves \\(75.7\\%\\) GPU memory with a resolution of \\(1792 \\times 1792\\), i.e., 12544 tokens per image. Patch size for all models is 2." + }, + { + "type": "image_caption", + "bbox": [ + 0.16, + 0.365, + 0.451, + 0.381 + ], + "angle": 0, + "content": "(a) FPS Comparison w/ img_size = 1024" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.382, + 0.48, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.582, + 0.365, + 0.874, + 0.381 + ], + "angle": 0, + "content": "(b) FPS Comparison w/ img_size = 2048" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.382, + 0.896, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.581, + 0.908, + 0.637 + ], + "angle": 0, + "content": "Figure 3. FPS comparison among DiS [16] with Mamba [18], DiT [39] with Attention [59], DiT with Flash Attention-2 (Flash-DiT) [11] and our DiG model varying from different model sizes. We take DiG as a baseline. With a resolution of \\(1024 \\times 1024\\), DiG is \\(2.0 \\times\\) faster than DiS at small size while \\(4.2 \\times\\) faster at XL size. Furthermore, DiG-XL/2 is \\(1.8 \\times\\) faster than the most well-designed high-optimized Flash-DiT-XL/2 with a resolution of \\(2048 \\times 2048\\)." + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.654, + 0.483, + 0.699 + ], + "angle": 0, + "content": "the Mamba-based diffusion model at 1024 resolution and \\(1.8 \\times\\) faster than DiT with well-designed CUDA-optimized FlashAttention-2 [11] at 2048 resolution." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.7, + 0.483, + 0.806 + ], + "angle": 0, + "content": "- We conduct extensive experiments on the ImageNet \\(256 \\times 256\\). The results demonstrate that DiG presents scalable ability and achieves comparable performance when compared with DiT. Besides, higher efficiency makes DiG promising to serve as the next-generation backbone for diffusion models in the context of large-scale long-sequence generation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.821, + 0.234, + 0.837 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.848, + 0.359, + 0.862 + ], + "angle": 0, + "content": "2.1. Linear Attention Transformer" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Different from standard autoregressive Transformer [60] which models the global attention matrix, the original lin" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.654, + 0.907, + 0.745 + ], + "angle": 0, + "content": "ear attention [26] is essentially a linear RNN with matrix-valued-format hidden states. Linear attention introduces a similarity kernel \\( k(x,y) \\) with an associated feature map \\( \\phi(\\cdot) \\), i.e., \\( k(x,y) = \\langle \\phi(x), \\phi(y) \\rangle \\). The calculation of output \\( \\mathbf{O} \\in \\mathbb{R}^{L \\times d} \\) (here \\( L \\) is the sequence length and \\( d \\) is the dimension) can be represented as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.758, + 0.905, + 0.808 + ], + "angle": 0, + "content": "\\[\n\\mathbf {O} _ {t} = \\frac {\\sum_ {i = 1} ^ {t} k \\left(\\mathbf {Q} _ {t} , \\mathbf {K} _ {i}\\right) \\mathbf {V} _ {i}}{\\sum_ {i = 1} ^ {t} k \\left(\\mathbf {Q} _ {t} , \\mathbf {K} _ {i}\\right)} = \\frac {\\phi \\left(\\mathbf {Q} _ {t}\\right) \\sum_ {i = 1} ^ {t} \\phi \\left(\\mathbf {K} _ {i}\\right) ^ {\\top} \\mathbf {V} _ {i}}{\\phi \\left(\\mathbf {Q} _ {t}\\right) \\sum_ {i = 1} ^ {t} \\phi \\left(\\mathbf {K} _ {i}\\right) ^ {\\top}}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.81, + 0.932, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} + \\phi (\\mathbf {K} _ {i}) \\mathbf {V} _ {i}, z _ {t} = z _ {t - 1} + \\phi (\\mathbf {K} _ {i}) ^ {\\top}, \\mathbf {O} _ {t} = \\frac {\\phi (\\mathbf {Q} _ {t}) \\mathbf {S} _ {t}}{\\phi (\\mathbf {Q} _ {t}) z _ {t}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.903 + ], + "angle": 0, + "content": "where query \\(\\mathbf{Q}\\), key \\(\\mathbf{K}\\), value \\(\\mathbf{V}\\) have shapes of \\(L\\times d\\) and \\(t\\) is the index of current token. By denoting hidden state \\(\\mathbf{S}_t = \\sum_{i = 1}^{t}\\phi (\\mathbf{K}_i)\\mathbf{V}_i\\) and normalizer \\(z_{t} = \\sum_{i = 1}^{t}\\phi (\\mathbf{K}_{i})^{\\top}\\) where" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7666" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.09, + 0.485, + 0.152 + ], + "angle": 0, + "content": "\\(\\mathbf{S}_t \\in \\mathbb{R}^{d \\times d}\\), \\(z_t \\in \\mathbb{R}^{d \\times 1}\\), the Eq. (1) can be rewritten as the Eq. 2. Recent works set \\(\\phi(\\cdot)\\) to be the identity [35, 57] and remove \\(z_t\\) [44], resulting linear attention Transformer with the following format:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.159, + 0.483, + 0.177 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} + \\mathbf {K} _ {t} ^ {\\top} \\mathbf {V} _ {t}, \\quad \\mathbf {O} _ {t} = \\mathbf {Q} _ {t} \\mathbf {S} _ {t}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.184, + 0.484, + 0.274 + ], + "angle": 0, + "content": "Directly using a linear attention Transformer for visual generation leads to poor performance due to the unidirectional modeling, so we propose a lightweight spatial reorient & enhancement module to take care of both modeling global context in four directions block by block and local information." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.282, + 0.367, + 0.297 + ], + "angle": 0, + "content": "2.2. Backbones in Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.304, + 0.484, + 0.516 + ], + "angle": 0, + "content": "Existing diffusion models typically employ U-Net as backbones [17, 20, 48] for image generation. Recently, Vision Transformer (ViT)-based backbones [1, 3, 5, 6, 39] receive significant attention due to the scalability of transformer and its natural fit for multi-modal learning. However, ViT-based architectures suffer from quadratic complexity, limiting their practicability in long sequence generation tasks, such as high-resolution image synthesis, video generation etc. To mitigate this, recent works explore subquadratic-time approaches to efficiently handle long sequences. For example, DiS [16], DiffuSSM [62], and ZigMa [23] employ state-space models as diffusion backbones for better computation efficiency. Diffusion-RWKV [62] adopt an RWKV architecture in diffusion models for image generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.516, + 0.484, + 0.621 + ], + "angle": 0, + "content": "Our DiG also follows this line of research, aiming at improving the efficiency of long sequence processing by adopting Gated Linear Attention Transformer (GLA) as diffusion backbones. Our proposed adaptation maintains the fundamental structure and benefits of GLA while introducing a few crucial modifications necessary for generating high-fidelity visual data." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.633, + 0.183, + 0.648 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.658, + 0.232, + 0.672 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.68, + 0.484, + 0.784 + ], + "angle": 0, + "content": "Gated Linear Attention Transformer. The Gated Linear Attention Transformer (GLA) [63] combines a data-dependent gating mechanism and linear attention, achieving superior recurrent modeling performance. Given an input \\( \\mathrm{X} \\in \\mathbb{R}^{L \\times d} \\) (here \\( L \\) is the sequence length and \\( d \\) is the dimension), GLA calculates the query, key, and value vectors as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.793, + 0.483, + 0.81 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} = \\mathbf {X} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} \\mathbf {W} _ {K}, \\mathbf {V} = \\mathbf {X} \\mathbf {W} _ {V}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.817, + 0.483, + 0.863 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}_Q\\), \\(\\mathbf{W}_K\\), and \\(\\mathbf{W}_V\\) are linear projection weights. The dimension number of \\(\\mathbf{Q}\\), \\(\\mathbf{K}\\) is \\(d_k\\), and \\(d_v\\) is for \\(\\mathbf{V}\\). Next, GLA compute the gating matrix \\(\\mathbf{G}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.868, + 0.483, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathbf {G} _ {t} = \\alpha_ {t} ^ {\\top} \\beta_ {t} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\alpha = \\sigma \\left(\\mathbf {X} \\mathbf {W} _ {\\alpha} + b _ {\\alpha}\\right) ^ {\\frac {1}{\\tau}} \\in \\mathbb {R} ^ {L \\times d _ {k}}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.09, + 0.905, + 0.11 + ], + "angle": 0, + "content": "\\[\n\\beta = \\sigma \\left(\\mathbf {X} \\mathbf {W} _ {\\beta} + b _ {\\beta}\\right) ^ {\\frac {1}{\\tau}} \\in \\mathbb {R} ^ {L \\times d _ {v}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.907, + 0.161 + ], + "angle": 0, + "content": "where \\(t\\) is the index of token, \\(\\sigma\\) is the sigmoid function, \\(b\\) is the bias term, and \\(\\tau \\in \\mathbb{R}\\) is a temperature term. As shown in Fig. 4, the final output \\(\\mathbf{Y}_t\\) is obtained as follows:" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.175, + 0.866, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.627, + 0.271, + 0.793, + 0.285 + ], + "angle": 0, + "content": "Figure 4. Pipeline of GLA." + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.295, + 0.907, + 0.314 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {t - 1} ^ {\\prime} = \\mathbf {G} _ {t} \\odot \\mathbf {S} _ {t - 1} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.316, + 0.905, + 0.334 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} ^ {\\prime} + \\mathbf {K} _ {t} ^ {\\top} V _ {t} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.337, + 0.905, + 0.355 + ], + "angle": 0, + "content": "\\[\n\\mathbf {O} _ {t} = \\mathbf {Q} _ {t} ^ {\\top} \\mathbf {S} _ {t} \\in \\mathbb {R} ^ {1 \\times d _ {v}}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.358, + 0.905, + 0.376 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R} _ {t} = \\operatorname {S w i s h} \\left(\\mathbf {X} _ {t} \\mathbf {W} _ {r} + b _ {r}\\right) \\in \\mathbb {R} ^ {1 \\times d _ {v}}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.379, + 0.905, + 0.397 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} _ {t} = \\left(\\mathbf {R} _ {t} \\odot \\operatorname {L N} \\left(\\mathbf {O} _ {t}\\right)\\right) \\mathbf {W} _ {O} \\in \\mathbb {R} ^ {1 \\times d}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.409, + 0.907, + 0.47 + ], + "angle": 0, + "content": "where Swish is the Swish [46] activation function, and \\(\\odot\\) is the element-wise multiplication operation. In subsequent sections, we use \\(\\mathbf{GLA}(\\cdot)\\) to refer to the gated linear attention computation for the input sequence." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.489, + 0.907, + 0.61 + ], + "angle": 0, + "content": "Diffusion Models. Before introducing the proposed method, we provide a brief review of diffusion models (DDPM) [20]. The DDPM takes noise as an input and samples images by iterative denoising the input. The forward process of DDPM begins with a stochastic process where the initial image \\( x_0 \\) is gradually corrupted by noise and is finally transformed into a simpler, noise-dominated state. The forward noisng process can be represented as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.621, + 0.905, + 0.663 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {1: T} \\mid x _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(x _ {t} \\mid x _ {t - 1}\\right), \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.665, + 0.905, + 0.683 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) I\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.695, + 0.906, + 0.741 + ], + "angle": 0, + "content": "where \\( x_{1:T} \\) is the sequence of noised images from time \\( t = 1 \\) to \\( t = T \\). Then, DDPM learns the reverse process that recovers the original image with learned \\( \\mu_{\\theta} \\) and \\( \\Sigma_{\\theta} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.752, + 0.905, + 0.77 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}\\right), \\Sigma_ {\\theta} \\left(x _ {t}\\right)\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.907, + 0.826 + ], + "angle": 0, + "content": "where \\(\\theta\\) are the parameters of the denoiser, and are trained with the variational lower bound [53] on the loglikelihood of the observed data \\(x_0\\)." + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.837, + 0.905, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} (\\theta) = - p \\left(x _ {0} \\mid x _ {1}\\right) \\\\ + \\sum_ {t} D _ {K L} \\left(q ^ {*} \\left(x _ {t - 1} \\mid x _ {t}, x _ {0}\\right) \\| p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right)\\right), \\tag {15} \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7667" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.132, + 0.089, + 0.231, + 0.105 + ], + "angle": 0, + "content": "(a) Plain DiG" + }, + { + "type": "image_caption", + "bbox": [ + 0.406, + 0.089, + 0.528, + 0.105 + ], + "angle": 0, + "content": "(b) U-shape DiG" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.106, + 0.677, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.54, + 0.65, + 0.556 + ], + "angle": 0, + "content": "(d) Block-by-Block Scanning Directions of DiG Controlled by SREM" + }, + { + "type": "image_caption", + "bbox": [ + 0.728, + 0.089, + 0.83, + 0.105 + ], + "angle": 0, + "content": "(c) DiG Block" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.106, + 0.9, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.563, + 0.908, + 0.591 + ], + "angle": 0, + "content": "Figure 5. The overview of the proposed DiG models. The figure presents the (a) plain DiG, denoted as DiG, (b) U-shape DiG, denoted as U-DiG, (c) DiG block, and (d) block-by-block scanning directions of DiG controlled by the SREM." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.661 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}\\) is the full loss. To further simplify the training process of DDPM, researchers reparameterize \\(\\mu_{\\theta}\\) as a noise prediction network \\(\\epsilon_{\\theta}\\) and minimize the mean squared error loss \\(\\mathcal{L}_{\\mathrm{simple}}\\) between \\(\\epsilon_{\\theta}(x_t)\\) and the true Gaussian noise \\(\\epsilon_{t}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.666, + 0.483, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s i m p l e}} (\\theta) = \\left\\| \\epsilon_ {\\theta} \\left(x _ {t}\\right) - \\epsilon_ {t} \\right\\| _ {2} ^ {2}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.484, + 0.812 + ], + "angle": 0, + "content": "However, to train a diffusion model that can learn a variable reverse process covariance \\(\\Sigma_{\\theta}\\), we need to optimize the full \\(D_{KL}\\) term. In this paper, we follow DiT [39]'s training recipe where we use the simple loss \\(\\mathcal{L}_{\\mathrm{simple}}\\) to train the noise prediction network \\(\\epsilon_{\\theta}\\) and use the full loss \\(\\mathcal{L}\\) to train the covariance prediction network \\(\\Sigma_{\\theta}\\). After the training process, we follow the stochastic sampling process to generate images from the learned \\(\\epsilon_{\\theta}\\) and \\(\\Sigma_{\\theta}\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.242, + 0.833 + ], + "angle": 0, + "content": "3.2. Diffusion GLA" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We present two variants of Diffusion GLA (DiG), as shown in Fig. 5. Our goal is to be as faithful to the standard GLA architecture as possible to retain its scaling ability and high-efficiency properties. We follow some of the best practices" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.907, + 0.827 + ], + "angle": 0, + "content": "of previous vision transformer architectures [1, 14, 39] to propose plain DiG and U-shape DiG, which are denoted as DiG and U-DiG, respectively. DiG first takes a spatial representation \\(z\\) output by the VAE encoder [28, 48] as input. For example, given a \\(256 \\times 256 \\times 3\\) image, we obtain a spatial representation \\(z\\) of shape \\(32 \\times 32 \\times 4\\) after the VAE encoder. DiG subsequently converts this spatial input into a token sequence \\(\\mathbf{z}_p \\in \\mathbb{R}^{T \\times (P^2 \\cdot C)}\\) through a patchify layer, where \\(T\\) is length of token sequence, \\(C\\) is the number of spatial representation channels, \\(P\\) is the size of image patches, and halving \\(P\\) will quadruple \\(T\\). Specifically, \\(p\\) for DiG is 2, while for U-DiG, \\(p\\) is 1. Next, we linearly project the \\(\\mathbf{z}_p\\) to the vector with dimension \\(D\\) and add frequency-based positional embeddings \\(\\mathbf{E}_{pos} \\in \\mathbb{R}^{T \\times D}\\) to all projected tokens as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.838, + 0.907, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {0} = \\left[ \\mathbf {z} _ {p} ^ {1} \\mathbf {W}; \\mathbf {z} _ {p} ^ {2} \\mathbf {W}; \\dots ; \\mathbf {z} _ {p} ^ {T} \\mathbf {W} \\right] + \\mathbf {E} _ {p o s}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.868, + 0.907, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_p^t\\) is the \\(t\\)-th patch of \\(\\mathbf{z}_p\\), \\(\\mathbf{W} \\in \\mathbb{R}^{(P^2 \\cdot C) \\times D}\\) is the learnable projection matrix. As for conditional information" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7668" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.138 + ], + "angle": 0, + "content": "such as noise timesteps \\(t \\in \\mathbb{R}\\), and class labels \\(y \\in \\mathbb{R}\\), we adopt multi-layer perception (MLP) and embedding layer as timestep embedder and label embedder, respectively." + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.145, + 0.483, + 0.162 + ], + "angle": 0, + "content": "\\[\n\\mathbf {t} = \\mathbf {M L P} (t), \\quad \\mathbf {y} = \\mathbf {E m b e d} (y), \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.167, + 0.485, + 0.306 + ], + "angle": 0, + "content": "where \\(\\mathbf{t} \\in \\mathbb{R}^{1 \\times D}\\) is time embedding and \\(\\mathbf{y} \\in \\mathbb{R}^{1 \\times D}\\) is label embedding. We then send the token sequence \\((\\mathbf{z}_{l-1})\\) to the \\(l\\)-th block of the DiG encoder, and obtain the output \\(\\mathbf{z}_l\\). For the U-DiG variant, there are down-sampling and upsampling modules between different stages, and shortcuts in the same stage. Finally, we normalize the output token sequence \\(\\mathbf{z}_L\\), and feed it to the linear projection head to get the final predicted noise \\(\\hat{\\mathbf{p}}_{noise}\\) and predicted covariance \\(\\hat{\\mathbf{p}}_{covariance}\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.123, + 0.312, + 0.483, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {l} = \\operatorname {D i G} _ {l} (\\mathbf {z} _ {l - 1}, \\mathbf {t}, \\mathbf {y}), \\quad \\mathbf {z} _ {n} = \\operatorname {N o r m} (\\mathbf {z} _ {L}), \\tag {19}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.335, + 0.483, + 0.352 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {p}} _ {\\text {n o i s e}}, \\hat {\\mathbf {p}} _ {\\text {c o v a r i a n c e}} = \\operatorname {L i n e a r} (\\mathbf {z} _ {n}), \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.358, + 0.485, + 0.419 + ], + "angle": 0, + "content": "where \\(\\mathbf{DiG}_l\\) is the \\(l\\)-th diffusion GLA block, \\(L\\) is the number of blocks, and Norm is the normalization layer. The \\(\\hat{\\mathbf{p}}_{noise}\\) and \\(\\hat{\\mathbf{p}}_{covariance}\\) have the same shape as the input spatial representation, i.e., \\(32 \\times 32 \\times 4\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.426, + 0.21, + 0.44 + ], + "angle": 0, + "content": "3.3. DiG Block" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.483, + 0.599 + ], + "angle": 0, + "content": "The original GLA block processes input sequence in a recurrent manner, which only enables causal modeling for 1-D sequence. Previous methods [16, 23] employ multi-path scanning within the same block to model global context, but this leads to a significant increase in time consumption and numerical instability [16], as shown in Table 1. To model the global context efficiently, we introduce the DiG block as shown in Fig. 5, which incorporates a spatial reorient & enhancement module (SREM) that enables lightweight spatial recognition and controls block-wise scanning directions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.6, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Specifically, we present the forward process of DiG block in Algo. 1. Following the widespread usage of adaptive normalization layers [41] in GANs [2, 24] and diffusion models [13, 39], we add and normalize the input timestep embedding \\(\\mathbf{t}\\) and label embedding \\(\\mathbf{y}\\) to regress the scale parameter \\(\\alpha\\), \\(\\gamma\\), and shift parameter \\(\\beta\\). Then, we launch gated linear attention (GLA) and feedforward network (FFN) with the adjustment of regressed adaptive layer norm (adaLN) parameters. Finally, we send the sequence to the SREM module as shown in Fig. 6. Specifically, we reshape the sequence to 2D and launch a lightweight \\(3\\times 3\\) depth-wise convolution (DWConv2d) layer to perceive local spatial information. However, we notice that using traditional initialization for DWConv2d leads to slow convergence because convolutional weights are dispersed around. To address this problem, we use identity initialization that only sets the convolutional kernel center as 1, and the surroundings to 0. For the last step of SREM, we alternate transpose and flip operations block-by-block to efficiently control block-wise scanning directions using minimal number of matrix operations." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.09, + 0.94, + 0.175 + ], + "angle": 0, + "content": "
    Extra OperationsIf Stable?Time (s)
    Matrix OPsScanning
    Bidirectional31×2.18
    4-directional133×4.02
    Block-by-Block20✓1.56
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.178, + 0.907, + 0.234 + ], + "angle": 0, + "content": "Table 1. Experimental results of different scanning strategies. Given \\( I = {32},p = 2 \\) ,all experiments are conducted with XL size models. Extra operations include matrix operations and scanning operations, which both increase the time consumption." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.241, + 0.706, + 0.256 + ], + "angle": 0, + "content": "3.4. Architecture Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.264, + 0.907, + 0.446 + ], + "angle": 0, + "content": "We use \\(N\\) DiG blocks, each operating at the hidden dimension size \\(D\\). Following previous works [14, 39, 63], we follow standard transformer setting that scales \\(N\\), \\(D\\), and attention heads number. Particularly, we provide four configurations: S, B, L, and XL, for the two different variants, as shown in the Table 2. They cover a wide range of flop allocations, ranging from 4.10 Gflops to 89.40 Gflops, presenting a way to gauge the scaling performance and efficiency. Notably, DiG consumes \\(70.8\\%\\) to \\(76.3\\%\\) Gflops, and U-DiG only consumes \\(66.0\\%\\) to \\(67.6\\%\\) Gflops when compared with the same model size DiT baselines. Both the proposed two variants are computationally efficient." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.455, + 0.696, + 0.471 + ], + "angle": 0, + "content": "3.5. Efficiency Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.477, + 0.909, + 0.734 + ], + "angle": 0, + "content": "GPU contains two important components, i.e., high bandwidth memory (HBM) and SRAM. HBM has a bigger memory size but SRAM has a larger bandwidth. To make full use of SRAM and modeling sequences in a parallel form, we follow GLA to split a whole sequence into many chunks that can complete calculations on SRAM. We denote the chunk size as \\( M \\), the training complexity is thus \\( O\\left(\\frac{T}{M}(M^2D + MD^2)\\right) = O(TMD + TD^2) \\), which is less than the traditional attention's complexity \\( O(T^2D) \\) when \\( T > D \\). Furthermore, the scaling analysis of speed and GPU memory are shown in Fig. 2 and Fig. 3, which demonstrate the high efficiency of the proposed DiG: DiG shows notable efficiency gains: DiG-S/2 is \\( 2.5 \\times \\) faster and saves \\( 75.7\\% \\) GPU memory compared to DiT-S/2 at \\( 1792 \\times 1792 \\). Additionally, DiG-XL/2 is \\( 4.2 \\times \\) faster than the Mamba-based model at 1024 resolution and \\( 1.8 \\times \\) faster than DiT with FlashAttention-2 at 2048." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.748, + 0.64, + 0.765 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.773, + 0.722, + 0.789 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Datasets and metrics. Following previous works [39], we use ImageNet [12] for class-conditional image generation learning at a resolution of \\(256 \\times 256\\). The ImageNet dataset contains 1,281,167 training images varying from 1,000 different classes. We use horizontal flipping for data augmentation. We measure the generation performance with Frechet Inception Distance (FID) [37], Incep" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7669" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.096, + 0.302, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.331, + 0.327, + 0.358 + ], + "angle": 0, + "content": "Figure 6. Details of the Spatial Reorient & Enhancement Module (SREM)." + }, + { + "type": "title", + "bbox": [ + 0.338, + 0.096, + 0.553, + 0.109 + ], + "angle": 0, + "content": "Algorithm 1: DiG Block Process." + }, + { + "type": "algorithm", + "bbox": [ + 0.336, + 0.113, + 0.862, + 0.358 + ], + "angle": 0, + "content": "Input: token sequence \\(\\mathbf{z}_{l-1}\\) : (B, T, D), timestep embed \\(\\mathbf{t}\\) : (B, 1, D), label embed \\(\\mathbf{y}\\) : (B, 1, D) \nOutput: token sequence \\(\\mathbf{z}_l\\) : (B, T, D) \n\\(\\alpha_1, \\beta_1, \\gamma_1, \\alpha_2, \\beta_2, \\gamma_2\\) : (B, 1, D) \\(\\leftarrow\\) MLP \\((\\mathbf{t} + \\mathbf{y})\\) // regress parameters of adaLN \n\\(\\mathbf{z}_{l-1}^{\\prime}\\) : (B, T, D) \\(\\leftarrow\\) \\(\\mathbf{z}_{l-1} + \\alpha_1 \\odot\\) GLA(Norm(\\(\\mathbf{z}_{l-1}\\)) \\(\\odot\\) \\((1 + \\gamma_1) + \\beta_1)\\) \n\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\) : (B, T, D) \\(\\leftarrow\\) \\(\\mathbf{z}_{l-1}^{\\prime} + \\alpha_2 \\odot\\) FFN(Norm(\\(\\mathbf{z}_{l-1}^{\\prime}\\)) \\(\\odot\\) \\((1 + \\gamma_2) + \\beta_2)\\) \n\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\) : (B, \\(\\sqrt{T}, \\sqrt{T}, D\\)) \\(\\leftarrow\\) DWConv2d(reshape2d(\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\)) // SREM module \nif \\(l \\% 2 == 0\\) then \n\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\) : (B, \\(\\sqrt{T}, \\sqrt{T}, D\\)) \\(\\leftarrow\\) transpose(\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\)) // transpose the token matrix every two block \n\\(\\mathbf{z}_l\\) : (B, T, D) \\(\\leftarrow\\) flatten(\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\)) // flatten the token matrix into 1-D sequence \nend \nelse \n\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\) : (B, T, D) \\(\\leftarrow\\) flatten(\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\)) // flatten the token matrix into 1-D sequence \n\\(\\mathbf{z}_l\\) : (B, T, D) \\(\\leftarrow\\) flip(\\(\\mathbf{z}_{l-1}^{\\prime\\prime}\\)) // flip the token sequence every two block \nend \nReturn: \\(\\mathbf{z}_l\\)" + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.386, + 0.49, + 0.538 + ], + "angle": 0, + "content": "
    ModelLayers NHidden Size DGflopsGflopsDiG/GflopsDiT
    DiG-S123844.3070.8%
    DiG-B1276817.0774.1%
    DiG-L24102461.6676.3%
    DiG-XL28115289.4075.3%
    U-DiG-S201284.1067.6%
    U-DiG-B2025615.2066.0%
    U-DiG-L4032053.5766.3%
    U-DiG-XL4041679.0966.6%
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.54, + 0.484, + 0.582 + ], + "angle": 0, + "content": "Table 2. Details of DiG models. We follow DiT [39] model configurations for the Small (S), Base (B), Large (L), and XLarge (XL) variants. Given \\( I = {32},p = 2 \\) for DiG, \\( p = 1 \\) for U-DiG." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.589, + 0.444, + 0.605 + ], + "angle": 0, + "content": "tion Score [52], sFID [37], and Precision/Recall [30]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.613, + 0.484, + 0.72 + ], + "angle": 0, + "content": "Implementation details. We use AdamW optimizer with a constant learning rate of \\(1e - 4\\). Following the previous works [39], we utilize the exponential moving average (EMA) of DiG weights during training with a decay rate of 0.9999. We generate all images with the EMA model. For the training of ImageNet, we use an off-the-shelf pretrained variational autoencoder (VAE) [27, 49]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.728, + 0.246, + 0.744 + ], + "angle": 0, + "content": "4.2. Model Analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Effect of spatial reorient & enhancement module. As shown in Table 3, we analyze the effectiveness of the proposed spatial reorient & enhancement module (SREM). We take the DiT-S/2 as our baseline method. The naive plain DiG with only causal modeling has significantly fewer flops and parameters, but also poor FID performance due to the lack of global context. We first add the bidirectional scanning to DiG and observe significant improvement, i.e., 69.28 FID, which demonstrates the importance of global context. Experiment without identity initialization" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.375, + 0.862, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.587, + 0.907, + 0.727 + ], + "angle": 0, + "content": "Figure 7. Scaling analysis with DiG model scales and patch sizes. for DWConv2d (the \\(\\times\\) symbol), leads to worse FID, while the DWConv2d with identity initialization can improve performance a lot. The experiment with DWConv2d proves the importance of identity initialization and local awareness. The experiment with full SREM brings the best performance, taking care of both local information and global context. Experiments in the last three rows indicate that the more suitable position for SREM is after the FFN." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.746, + 0.907, + 0.852 + ], + "angle": 0, + "content": "Scaling model scales and patch sizes. We investigate the scaling ability of DiG among four different model scales and three patch sizes on the ImageNet dataset. As depicted in Fig. 7, the performance improves as the models scale from S/2 to XL/2 and the patch size from 2 to 8. The results demonstrate the scaling ability of DiG, indicating its potential as a large foundational diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.907, + 0.9 + ], + "angle": 0, + "content": "Structural ablation from DiG to U-DiG. We evaluate the structural benefits from DiG to U-DiG. As shown in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7670" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.895, + 0.278 + ], + "angle": 0, + "content": "
    ModelSpatial Reorient & Enhancement ModuleSREM PositionFlops (G)Params (M)FID-50K
    BidirectionalDWConv2d4-directional
    Baseline Method.
    DiT-S/26.0633.068.4
    Ours.
    DiG-S/24.2933.0175.84
    DiG-S/2✓After FFN4.2933.069.28
    DiG-S/2✓✓After FFN4.3033.196.83
    DiG-S/2✓✓After FFN4.3033.163.84
    DiG-S/2✓✓✓After FFN4.3033.162.06
    DiG-S/2✓✓✓Before Attn.4.3033.162.34
    DiG-S/2✓✓✓Between Attn. & FFN4.3033.162.93
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.28, + 0.905, + 0.322 + ], + "angle": 0, + "content": "Table 3. Ablation of the proposed Spatial Reorient & Enhancement Module (SREM). We validate the effectiveness of each SREM component and use the same hyperparameters for all models. The \"half right and half wrong symbol\" \\((\\star)\\) means use DWConv2d without the identity initialization. We mark the best result in bold." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.328, + 0.479, + 0.737 + ], + "angle": 0, + "content": "
    ModelFID↓sFID↓IS↑P↑R↑
    ADM [13]10.946.02100.980.690.63
    ADM-U7.495.13127.490.720.63
    ADM-G4.595.25186.700.820.52
    ADM-G, ADM-U3.946.14215.840.830.53
    CDM [22]4.88-158.71--
    LDM-8 [49]15.51-79.030.650.63
    LDM-8-G7.76-209.520.840.35
    LDM-4-G3.95-178.220.810.55
    LDM-4-G3.60-247.670.870.48
    Other sub-quadratic-time diffusion methods.
    DiM-H/2 [58]2.40----
    DiS-H/2 [16]2.104.55271.320.820.58
    DiMSUM-L/2-G [42]2.110.59---
    Baselines and Ours.
    DiT-S/2 (400K) [39]68.40----
    DiG-S/2 (400K)62.0611.7722.810.390.56
    DiT-B/2 (400K)43.47----
    DiG-B/2 (400K)39.508.5037.210.510.63
    DiT-L/2 (400K)23.33----
    DiG-L/2 (400K)22.906.9159.870.600.64
    DiT-XL/2 (400K)19.47----
    DiG-XL/2 (400K)18.536.0668.530.630.64
    DiT-XL/2 (7M)9.626.85121.500.670.67
    DiG-XL/2 (1.2M)8.606.46130.030.680.68
    DiT-XL/2-G (7M)2.274.60278.240.830.57
    DiG-XL/2-G (1.2M)2.074.53278.950.820.60
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.09, + 0.738, + 0.483, + 0.793 + ], + "angle": 0, + "content": "Table 4. Benchmarking class-conditional image generation on ImageNet \\(256 \\times 256\\). DiG models adopt the same hyperparameters as DiT [39] for fair comparison. G is the classifier-free guidance. We mark the best results in bold." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Table 5, both the shortcut and hierarchical structures contribute positively to the metrics. Notably, for the generation task at a 512 resolution, U-DiG-S/1 achieves a remarkable improvement over DiG-S/2, with an FID gain exceeding 16.2, which demonstrates the effectiveness of U-DiG in generating high-resolution images." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.328, + 0.911, + 0.434 + ], + "angle": 0, + "content": "
    w/ short cutw/ hierarchyFID-50K
    IN-256IN-512
    DiT-S/268.40NaN
    DiG-S/262.0699.04
    DiG-S/2✓57.0191.42
    U-DiG-S/1✓✓52.2082.62
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.565, + 0.436, + 0.855, + 0.449 + ], + "angle": 0, + "content": "Table 5. Structural ablation from DiG to U-DiG." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.458, + 0.654, + 0.473 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.907, + 0.602 + ], + "angle": 0, + "content": "We mainly compare the proposed plain DiG with DiT [39]. For class-conditional image generation on ImageNet \\(256 \\times 256\\), as shown in Table 4, the proposed DiG has fewer FLOPs but outperforms DiT among four model scales with 400K training iterations with the same hyperparameters. Furthermore, the DiG-XL/2 (1.2M) with classifier-free guidance also presents competitive results when compared with concurrent sub-quadratic-time diffusion methods." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.615, + 0.634, + 0.631 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.64, + 0.907, + 0.822 + ], + "angle": 0, + "content": "In this work, we present DiG, a cost-effective alternative to the vanilla Transformer for diffusion models in image generation tasks. In particular, DiG explores Gated Linear Attention Transformers (GLA), attaining comparable effectiveness and superior efficiency in long-sequence image generation tasks. Experimentally, DiG shows comparable performance to prior diffusion models on class-conditional ImageNet \\(256 \\times 256\\) benchmark while significantly reducing the computational burden starting from a 512 resolution. We hope this work can open up the possibility for other long-sequence generation tasks, such as video and audio modeling." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Limitations. Although DiG shows superior efficiency in diffusion image generation, building a large foundation model like Sora [3] upon DiG is still an area that needs to be explored further." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7671" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.09, + 0.476, + 0.109 + ], + "angle": 0, + "content": "Acknowledgments and Disclosure of Funding" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.116, + 0.483, + 0.161 + ], + "angle": 0, + "content": "This work was partially supported by the National Science and Technology Major Project under Grant No. 2023YFF0905400." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.177, + 0.188, + 0.193 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.202, + 0.483, + 0.271 + ], + "angle": 0, + "content": "[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. 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Image generation with the proposed Diffusion Gated Linear Attention Transformers (DiG). We show selected samples from our class-conditional DiG-XL/2 models trained on ImageNet at $512 \times 512$ and $256 \times 256$ resolution, respectively. + +# Abstract + +Diffusion models with large-scale pre-training have achieved significant success in the field of visual content generation, particularly exemplified by Diffusion Trans + +formers (DiT). However, DiT models have faced challenges with quadratic complexity efficiency, especially when handling long sequences. In this paper, we aim to incorporate the sub-quadratic modeling capability of Gated Linear Attention (GLA) into the 2D diffusion backbone. Specifically, we introduce Diffusion Gated Linear Attention Transformers (DiG), a simple, adoptable solution with minimal parameter overhead. We offer two variants, i,e, a plain and U-shape architecture, showing superior efficiency and + +competitive effectiveness. In addition to superior performance to DiT and other sub-quadratic-time diffusion models at $256 \times 256$ resolution, DiG demonstrates greater efficiency than these methods starting from a 512 resolution. Specifically, DiG-S/2 is $2.5 \times$ faster and saves $75.7\%$ GPU memory compared to DiT-S/2 at a 1792 resolution. Additionally, DiG-XL/2 is $4.2 \times$ faster than the Mamba-based model at a 1024 resolution and $1.8 \times$ faster than DiT with FlashAttention-2 at a 2048 resolution. + +# 1. Introduction + +In recent years, diffusion models [4, 20, 32, 53, 56, 61, 65, 66] have emerged as potent deep generative models [13, 49] renowned for their ability to generate high-quality images. Their rapid evolution has spurred extensive applications across various fields, including image-to-image generation [8, 67], text-to-image generation [19, 47, 51], speech synthesis [7, 29], video generation [21, 34, 36], and 3D generation [43, 68]. Concurrent with the rapid development of sampling algorithms [33, 38, 54], the principal techniques have evolved into two main categories based on their architectural backbones: U-Net-based methods [20, 55] and ViT-based methods [14]. U-Net-based approaches continue to leverage the convolutional neural network (CNN) architecture [31, 50], whose hierarchical feature modeling ability benefits visual generation tasks. On the other hand, ViT-based methods [1, 39, 64] innovate by incorporating self-attention mechanisms [59] instead of traditional sampling blocks, resulting in streamlined yet effective performance. + +Due to their excellent scalability in terms of performance, ViT-based methods [39] have been adopted as backbones in the most advanced diffusion works, including PixArt [5, 6], Sora [3], Stable Diffusion 3 [15], etc. However, the self-attention mechanism in ViT-based architectures scales quadratically with the input sequence length, making them resource-intensive when dealing with long sequence generation tasks, e.g., high-resolution image generation and video generation. Recent works such as Mamba [18, 69], RWKV [40] and Gated Linear Attention Transformer (GLA) [63], try to improve the long-sequence processing efficiency by integrating Recurrent Neural Network (RNN) like architecture and hardware-aware algorithms. Since a data-dependent gating mechanism is crucial for 1D modeling [45], GLA shows outstanding performance among the above methods. + +Motivated by the success of GLA in the natural language processing domain, it is appealing that we can transfer this success from language generation to visual content generation by designing a scalable and efficient diffusion backbone with the advanced linear attention [10, 25, 26] method. However, visual generation with linear models, such as Mamba, RWKV, and GLA, often faces two challenges, i.e., + +unidirectional scanning modeling and lack of local awareness. Previous approaches [16, 23] have often addressed the first issue by performing bidirectional scanning within the same block. Nevertheless, such methods result in a significant increase in time consumption and numerical instability. To address these challenges, we propose Diffusion GLA (DiG), which incorporates a lightweight spatial reorient & enhancement module (SREM) for block-wise scanning direction controlling and local awareness. For the first issue, SREM changes the sequence direction with minimal number of matrix operations and assigns different scanning in a block-by-block manner. The scanning directions contain four basic patterns and enable each patch in sequences to be aware of other patches following 4 directions. For the second issue, we also incorporate a depth-wise convolution (DWConv) [9] in the SREM to provide local awareness with extremely small amounts of parameters. Inspired by U-Net [50], we further propose a U-shape variant of DiG and analyze the improvements. Crucially, this paper presents a systematic ablation study and a comprehensive evaluation of the proposed modules and architectures. It is important to highlight that DiG adheres to the first practices of linear attention transformers in diffusion generation, demonstrating superior efficiency in quadratic and sub-quadratic diffusion models. + +Compared with the ViT-based method, i.e., DiT [39], DiG presents competitive performance on ImageNet [12] $256 \times 256$ generation when using the same hyperparameters. Furthermore, DiG is more efficient in terms of training speed and GPU memory starting from a 512 resolution. The efficiency in terms of memory and speed empowers DiG to alleviate the resource constraint problem of long- sequence visual generation tasks. Specifically, DiG demonstrates significant efficiency improvements over comparable models: DiG-S/2 achieves a $2.5 \times$ faster training speed and saves $75.7\%$ GPU memory compared to DiT-S/2 at a $1792 \times 1792$ resolution as shown in Fig. 2. Furthermore, with the same model size, DiG-XL/2 is $4.2 \times$ faster than the recent Mamba-based diffusion model at 1024 resolution and $1.8 \times$ faster than DiT with well-designed CUDA-optimized FlashAttention-2 [11] at 2048 resolution as shown in Fig. 3. + +Our main contributions can be summarized as follows: + +- We propose Diffusion GLA (DiG), which incorporates an efficient DiG block for both global visual context modeling through block-wise scanning, and local visual awareness. To the best of our knowledge, DiG is the first exploration for diffusion backbone with linear attention. +- Without the burden of quadratic attention, the proposed DiG exhibits higher efficiency in both training speed and GPU memory cost while maintaining a similar modeling ability as DiT. Notably, DiG is $4.2 \times$ faster than + +![](images/27cb37a8e1c4ec60a4565c134665beedc43a7aff0e94269ef6fd3b55c4e8507d.jpg) +(a) Speed Comparison +Figure 2. Efficiency comparison among DiT [39] with Attention [59], DiS [16] with Mamba [18], and our DiG model. DiG achieves higher training speed while costs lower GPU memory in dealing with high-resolution images. For example, DiG is $2.5 \times$ faster than DiT and saves $75.7\%$ GPU memory with a resolution of $1792 \times 1792$ , i.e., 12544 tokens per image. Patch size for all models is 2. + +![](images/9b4a3954cb66d8aa29b4c6972d791d91dfed700afb52478d182968235cbb8489.jpg) +(b) GPU Memory Comparison + +![](images/05bfdd792b26f8ec68fe370e6e0af89ffc7d2e0cdba4225eccb40f9bc76e4614.jpg) +(a) FPS Comparison w/ img_size = 1024 +Figure 3. FPS comparison among DiS [16] with Mamba [18], DiT [39] with Attention [59], DiT with Flash Attention-2 (Flash-DiT) [11] and our DiG model varying from different model sizes. We take DiG as a baseline. With a resolution of $1024 \times 1024$ , DiG is $2.0 \times$ faster than DiS at small size while $4.2 \times$ faster at XL size. Furthermore, DiG-XL/2 is $1.8 \times$ faster than the most well-designed high-optimized Flash-DiT-XL/2 with a resolution of $2048 \times 2048$ . + +![](images/f57999b0e76a8524aa97708646ea1bc5a4316db67c6a736aa0380cf94bdfdad0.jpg) +(b) FPS Comparison w/ img_size = 2048 + +the Mamba-based diffusion model at 1024 resolution and $1.8 \times$ faster than DiT with well-designed CUDA-optimized FlashAttention-2 [11] at 2048 resolution. + +- We conduct extensive experiments on the ImageNet $256 \times 256$ . The results demonstrate that DiG presents scalable ability and achieves comparable performance when compared with DiT. Besides, higher efficiency makes DiG promising to serve as the next-generation backbone for diffusion models in the context of large-scale long-sequence generation. + +# 2. Related Work + +# 2.1. Linear Attention Transformer + +Different from standard autoregressive Transformer [60] which models the global attention matrix, the original lin + +ear attention [26] is essentially a linear RNN with matrix-valued-format hidden states. Linear attention introduces a similarity kernel $k(x,y)$ with an associated feature map $\phi(\cdot)$ , i.e., $k(x,y) = \langle \phi(x), \phi(y) \rangle$ . The calculation of output $\mathbf{O} \in \mathbb{R}^{L \times d}$ (here $L$ is the sequence length and $d$ is the dimension) can be represented as follows: + +$$ +\mathbf {O} _ {t} = \frac {\sum_ {i = 1} ^ {t} k \left(\mathbf {Q} _ {t} , \mathbf {K} _ {i}\right) \mathbf {V} _ {i}}{\sum_ {i = 1} ^ {t} k \left(\mathbf {Q} _ {t} , \mathbf {K} _ {i}\right)} = \frac {\phi \left(\mathbf {Q} _ {t}\right) \sum_ {i = 1} ^ {t} \phi \left(\mathbf {K} _ {i}\right) ^ {\top} \mathbf {V} _ {i}}{\phi \left(\mathbf {Q} _ {t}\right) \sum_ {i = 1} ^ {t} \phi \left(\mathbf {K} _ {i}\right) ^ {\top}}, \tag {1} +$$ + +$$ +\mathbf {S} _ {t} = \mathbf {S} _ {t - 1} + \phi (\mathbf {K} _ {i}) \mathbf {V} _ {i}, z _ {t} = z _ {t - 1} + \phi (\mathbf {K} _ {i}) ^ {\top}, \mathbf {O} _ {t} = \frac {\phi (\mathbf {Q} _ {t}) \mathbf {S} _ {t}}{\phi (\mathbf {Q} _ {t}) z _ {t}}, +$$ + +where query $\mathbf{Q}$ , key $\mathbf{K}$ , value $\mathbf{V}$ have shapes of $L\times d$ and $t$ is the index of current token. By denoting hidden state $\mathbf{S}_t = \sum_{i = 1}^{t}\phi (\mathbf{K}_i)\mathbf{V}_i$ and normalizer $z_{t} = \sum_{i = 1}^{t}\phi (\mathbf{K}_{i})^{\top}$ where + +$\mathbf{S}_t \in \mathbb{R}^{d \times d}$ , $z_t \in \mathbb{R}^{d \times 1}$ , the Eq. (1) can be rewritten as the Eq. 2. Recent works set $\phi(\cdot)$ to be the identity [35, 57] and remove $z_t$ [44], resulting linear attention Transformer with the following format: + +$$ +\mathbf {S} _ {t} = \mathbf {S} _ {t - 1} + \mathbf {K} _ {t} ^ {\top} \mathbf {V} _ {t}, \quad \mathbf {O} _ {t} = \mathbf {Q} _ {t} \mathbf {S} _ {t}. \tag {3} +$$ + +Directly using a linear attention Transformer for visual generation leads to poor performance due to the unidirectional modeling, so we propose a lightweight spatial reorient & enhancement module to take care of both modeling global context in four directions block by block and local information. + +# 2.2. Backbones in Diffusion Models + +Existing diffusion models typically employ U-Net as backbones [17, 20, 48] for image generation. Recently, Vision Transformer (ViT)-based backbones [1, 3, 5, 6, 39] receive significant attention due to the scalability of transformer and its natural fit for multi-modal learning. However, ViT-based architectures suffer from quadratic complexity, limiting their practicability in long sequence generation tasks, such as high-resolution image synthesis, video generation etc. To mitigate this, recent works explore subquadratic-time approaches to efficiently handle long sequences. For example, DiS [16], DiffuSSM [62], and ZigMa [23] employ state-space models as diffusion backbones for better computation efficiency. Diffusion-RWKV [62] adopt an RWKV architecture in diffusion models for image generation. + +Our DiG also follows this line of research, aiming at improving the efficiency of long sequence processing by adopting Gated Linear Attention Transformer (GLA) as diffusion backbones. Our proposed adaptation maintains the fundamental structure and benefits of GLA while introducing a few crucial modifications necessary for generating high-fidelity visual data. + +# 3. Method + +# 3.1. Preliminaries + +Gated Linear Attention Transformer. The Gated Linear Attention Transformer (GLA) [63] combines a data-dependent gating mechanism and linear attention, achieving superior recurrent modeling performance. Given an input $\mathrm{X} \in \mathbb{R}^{L \times d}$ (here $L$ is the sequence length and $d$ is the dimension), GLA calculates the query, key, and value vectors as follows: + +$$ +\mathbf {Q} = \mathbf {X} \mathbf {W} _ {Q}, \mathbf {K} = \mathbf {X} \mathbf {W} _ {K}, \mathbf {V} = \mathbf {X} \mathbf {W} _ {V}, \tag {4} +$$ + +where $\mathbf{W}_Q$ , $\mathbf{W}_K$ , and $\mathbf{W}_V$ are linear projection weights. The dimension number of $\mathbf{Q}$ , $\mathbf{K}$ is $d_k$ , and $d_v$ is for $\mathbf{V}$ . Next, GLA compute the gating matrix $\mathbf{G}$ as follows: + +$$ +\mathbf {G} _ {t} = \alpha_ {t} ^ {\top} \beta_ {t} \in \mathbb {R} ^ {d _ {k} \times d _ {v}}, \alpha = \sigma \left(\mathbf {X} \mathbf {W} _ {\alpha} + b _ {\alpha}\right) ^ {\frac {1}{\tau}} \in \mathbb {R} ^ {L \times d _ {k}}, \tag {5} +$$ + +$$ +\beta = \sigma \left(\mathbf {X} \mathbf {W} _ {\beta} + b _ {\beta}\right) ^ {\frac {1}{\tau}} \in \mathbb {R} ^ {L \times d _ {v}}, \tag {6} +$$ + +where $t$ is the index of token, $\sigma$ is the sigmoid function, $b$ is the bias term, and $\tau \in \mathbb{R}$ is a temperature term. As shown in Fig. 4, the final output $\mathbf{Y}_t$ is obtained as follows: + +![](images/b220c2890808ebaf80222fec3f472dc1ff9ba8f2f058e2218f9aa05f647ca33c.jpg) +Figure 4. Pipeline of GLA. + +$$ +\mathbf {S} _ {t - 1} ^ {\prime} = \mathbf {G} _ {t} \odot \mathbf {S} _ {t - 1} \in \mathbb {R} ^ {d _ {k} \times d _ {v}}, \tag {7} +$$ + +$$ +\mathbf {S} _ {t} = \mathbf {S} _ {t - 1} ^ {\prime} + \mathbf {K} _ {t} ^ {\top} V _ {t} \in \mathbb {R} ^ {d _ {k} \times d _ {v}}, \tag {8} +$$ + +$$ +\mathbf {O} _ {t} = \mathbf {Q} _ {t} ^ {\top} \mathbf {S} _ {t} \in \mathbb {R} ^ {1 \times d _ {v}}, \tag {9} +$$ + +$$ +\mathbf {R} _ {t} = \operatorname {S w i s h} \left(\mathbf {X} _ {t} \mathbf {W} _ {r} + b _ {r}\right) \in \mathbb {R} ^ {1 \times d _ {v}}, \tag {10} +$$ + +$$ +\mathbf {Y} _ {t} = \left(\mathbf {R} _ {t} \odot \operatorname {L N} \left(\mathbf {O} _ {t}\right)\right) \mathbf {W} _ {O} \in \mathbb {R} ^ {1 \times d}, \tag {11} +$$ + +where Swish is the Swish [46] activation function, and $\odot$ is the element-wise multiplication operation. In subsequent sections, we use $\mathbf{GLA}(\cdot)$ to refer to the gated linear attention computation for the input sequence. + +Diffusion Models. Before introducing the proposed method, we provide a brief review of diffusion models (DDPM) [20]. The DDPM takes noise as an input and samples images by iterative denoising the input. The forward process of DDPM begins with a stochastic process where the initial image $x_0$ is gradually corrupted by noise and is finally transformed into a simpler, noise-dominated state. The forward noisng process can be represented as follows: + +$$ +q \left(x _ {1: T} \mid x _ {0}\right) = \prod_ {t = 1} ^ {T} q \left(x _ {t} \mid x _ {t - 1}\right), \tag {12} +$$ + +$$ +q \left(x _ {t} \mid x _ {0}\right) = \mathcal {N} \left(x _ {t}; \sqrt {\bar {\alpha} _ {t}} x _ {0}, (1 - \bar {\alpha} _ {t}) I\right), \tag {13} +$$ + +where $x_{1:T}$ is the sequence of noised images from time $t = 1$ to $t = T$ . Then, DDPM learns the reverse process that recovers the original image with learned $\mu_{\theta}$ and $\Sigma_{\theta}$ : + +$$ +p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right) = \mathcal {N} \left(x _ {t - 1}; \mu_ {\theta} \left(x _ {t}\right), \Sigma_ {\theta} \left(x _ {t}\right)\right), \tag {14} +$$ + +where $\theta$ are the parameters of the denoiser, and are trained with the variational lower bound [53] on the loglikelihood of the observed data $x_0$ . + +$$ +\begin{array}{l} \mathcal {L} (\theta) = - p \left(x _ {0} \mid x _ {1}\right) \\ + \sum_ {t} D _ {K L} \left(q ^ {*} \left(x _ {t - 1} \mid x _ {t}, x _ {0}\right) \| p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right)\right), \tag {15} \\ \end{array} +$$ + +![](images/e2a3f82aaf26620ae71812bbe36d38a6ada73386ad306dcb48ecdfbb16f7d081.jpg) +(a) Plain DiG +(b) U-shape DiG +(d) Block-by-Block Scanning Directions of DiG Controlled by SREM + +![](images/cedd6545b528765d4dd733c03091e2d40ddbd24b65ff381c84a6c486ca364295.jpg) +(c) DiG Block +Figure 5. The overview of the proposed DiG models. The figure presents the (a) plain DiG, denoted as DiG, (b) U-shape DiG, denoted as U-DiG, (c) DiG block, and (d) block-by-block scanning directions of DiG controlled by the SREM. + +where $\mathcal{L}$ is the full loss. To further simplify the training process of DDPM, researchers reparameterize $\mu_{\theta}$ as a noise prediction network $\epsilon_{\theta}$ and minimize the mean squared error loss $\mathcal{L}_{\mathrm{simple}}$ between $\epsilon_{\theta}(x_t)$ and the true Gaussian noise $\epsilon_{t}$ : + +$$ +\mathcal {L} _ {\text {s i m p l e}} (\theta) = \left\| \epsilon_ {\theta} \left(x _ {t}\right) - \epsilon_ {t} \right\| _ {2} ^ {2}. \tag {16} +$$ + +However, to train a diffusion model that can learn a variable reverse process covariance $\Sigma_{\theta}$ , we need to optimize the full $D_{KL}$ term. In this paper, we follow DiT [39]'s training recipe where we use the simple loss $\mathcal{L}_{\mathrm{simple}}$ to train the noise prediction network $\epsilon_{\theta}$ and use the full loss $\mathcal{L}$ to train the covariance prediction network $\Sigma_{\theta}$ . After the training process, we follow the stochastic sampling process to generate images from the learned $\epsilon_{\theta}$ and $\Sigma_{\theta}$ . + +# 3.2. Diffusion GLA + +We present two variants of Diffusion GLA (DiG), as shown in Fig. 5. Our goal is to be as faithful to the standard GLA architecture as possible to retain its scaling ability and high-efficiency properties. We follow some of the best practices + +of previous vision transformer architectures [1, 14, 39] to propose plain DiG and U-shape DiG, which are denoted as DiG and U-DiG, respectively. DiG first takes a spatial representation $z$ output by the VAE encoder [28, 48] as input. For example, given a $256 \times 256 \times 3$ image, we obtain a spatial representation $z$ of shape $32 \times 32 \times 4$ after the VAE encoder. DiG subsequently converts this spatial input into a token sequence $\mathbf{z}_p \in \mathbb{R}^{T \times (P^2 \cdot C)}$ through a patchify layer, where $T$ is length of token sequence, $C$ is the number of spatial representation channels, $P$ is the size of image patches, and halving $P$ will quadruple $T$ . Specifically, $p$ for DiG is 2, while for U-DiG, $p$ is 1. Next, we linearly project the $\mathbf{z}_p$ to the vector with dimension $D$ and add frequency-based positional embeddings $\mathbf{E}_{pos} \in \mathbb{R}^{T \times D}$ to all projected tokens as follows: + +$$ +\mathbf {z} _ {0} = \left[ \mathbf {z} _ {p} ^ {1} \mathbf {W}; \mathbf {z} _ {p} ^ {2} \mathbf {W}; \dots ; \mathbf {z} _ {p} ^ {T} \mathbf {W} \right] + \mathbf {E} _ {p o s}, \tag {17} +$$ + +where $\mathbf{z}_p^t$ is the $t$ -th patch of $\mathbf{z}_p$ , $\mathbf{W} \in \mathbb{R}^{(P^2 \cdot C) \times D}$ is the learnable projection matrix. As for conditional information + +such as noise timesteps $t \in \mathbb{R}$ , and class labels $y \in \mathbb{R}$ , we adopt multi-layer perception (MLP) and embedding layer as timestep embedder and label embedder, respectively. + +$$ +\mathbf {t} = \mathbf {M L P} (t), \quad \mathbf {y} = \mathbf {E m b e d} (y), \tag {18} +$$ + +where $\mathbf{t} \in \mathbb{R}^{1 \times D}$ is time embedding and $\mathbf{y} \in \mathbb{R}^{1 \times D}$ is label embedding. We then send the token sequence $(\mathbf{z}_{l-1})$ to the $l$ -th block of the DiG encoder, and obtain the output $\mathbf{z}_l$ . For the U-DiG variant, there are down-sampling and upsampling modules between different stages, and shortcuts in the same stage. Finally, we normalize the output token sequence $\mathbf{z}_L$ , and feed it to the linear projection head to get the final predicted noise $\hat{\mathbf{p}}_{noise}$ and predicted covariance $\hat{\mathbf{p}}_{covariance}$ , as follows: + +$$ +\mathbf {z} _ {l} = \operatorname {D i G} _ {l} (\mathbf {z} _ {l - 1}, \mathbf {t}, \mathbf {y}), \quad \mathbf {z} _ {n} = \operatorname {N o r m} (\mathbf {z} _ {L}), \tag {19} +$$ + +$$ +\hat {\mathbf {p}} _ {\text {n o i s e}}, \hat {\mathbf {p}} _ {\text {c o v a r i a n c e}} = \operatorname {L i n e a r} (\mathbf {z} _ {n}), \tag {20} +$$ + +where $\mathbf{DiG}_l$ is the $l$ -th diffusion GLA block, $L$ is the number of blocks, and Norm is the normalization layer. The $\hat{\mathbf{p}}_{noise}$ and $\hat{\mathbf{p}}_{covariance}$ have the same shape as the input spatial representation, i.e., $32 \times 32 \times 4$ . + +# 3.3. DiG Block + +The original GLA block processes input sequence in a recurrent manner, which only enables causal modeling for 1-D sequence. Previous methods [16, 23] employ multi-path scanning within the same block to model global context, but this leads to a significant increase in time consumption and numerical instability [16], as shown in Table 1. To model the global context efficiently, we introduce the DiG block as shown in Fig. 5, which incorporates a spatial reorient & enhancement module (SREM) that enables lightweight spatial recognition and controls block-wise scanning directions. + +Specifically, we present the forward process of DiG block in Algo. 1. Following the widespread usage of adaptive normalization layers [41] in GANs [2, 24] and diffusion models [13, 39], we add and normalize the input timestep embedding $\mathbf{t}$ and label embedding $\mathbf{y}$ to regress the scale parameter $\alpha$ , $\gamma$ , and shift parameter $\beta$ . Then, we launch gated linear attention (GLA) and feedforward network (FFN) with the adjustment of regressed adaptive layer norm (adaLN) parameters. Finally, we send the sequence to the SREM module as shown in Fig. 6. Specifically, we reshape the sequence to 2D and launch a lightweight $3\times 3$ depth-wise convolution (DWConv2d) layer to perceive local spatial information. However, we notice that using traditional initialization for DWConv2d leads to slow convergence because convolutional weights are dispersed around. To address this problem, we use identity initialization that only sets the convolutional kernel center as 1, and the surroundings to 0. For the last step of SREM, we alternate transpose and flip operations block-by-block to efficiently control block-wise scanning directions using minimal number of matrix operations. + +
    Extra OperationsIf Stable?Time (s)
    Matrix OPsScanning
    Bidirectional31×2.18
    4-directional133×4.02
    Block-by-Block20✓1.56
    + +Table 1. Experimental results of different scanning strategies. Given $I = {32},p = 2$ ,all experiments are conducted with XL size models. Extra operations include matrix operations and scanning operations, which both increase the time consumption. + +# 3.4. Architecture Details + +We use $N$ DiG blocks, each operating at the hidden dimension size $D$ . Following previous works [14, 39, 63], we follow standard transformer setting that scales $N$ , $D$ , and attention heads number. Particularly, we provide four configurations: S, B, L, and XL, for the two different variants, as shown in the Table 2. They cover a wide range of flop allocations, ranging from 4.10 Gflops to 89.40 Gflops, presenting a way to gauge the scaling performance and efficiency. Notably, DiG consumes $70.8\%$ to $76.3\%$ Gflops, and U-DiG only consumes $66.0\%$ to $67.6\%$ Gflops when compared with the same model size DiT baselines. Both the proposed two variants are computationally efficient. + +# 3.5. Efficiency Analysis + +GPU contains two important components, i.e., high bandwidth memory (HBM) and SRAM. HBM has a bigger memory size but SRAM has a larger bandwidth. To make full use of SRAM and modeling sequences in a parallel form, we follow GLA to split a whole sequence into many chunks that can complete calculations on SRAM. We denote the chunk size as $M$ , the training complexity is thus $O\left(\frac{T}{M}(M^2D + MD^2)\right) = O(TMD + TD^2)$ , which is less than the traditional attention's complexity $O(T^2D)$ when $T > D$ . Furthermore, the scaling analysis of speed and GPU memory are shown in Fig. 2 and Fig. 3, which demonstrate the high efficiency of the proposed DiG: DiG shows notable efficiency gains: DiG-S/2 is $2.5 \times$ faster and saves $75.7\%$ GPU memory compared to DiT-S/2 at $1792 \times 1792$ . Additionally, DiG-XL/2 is $4.2 \times$ faster than the Mamba-based model at 1024 resolution and $1.8 \times$ faster than DiT with FlashAttention-2 at 2048. + +# 4. Experiment + +# 4.1. Experimental Settings + +Datasets and metrics. Following previous works [39], we use ImageNet [12] for class-conditional image generation learning at a resolution of $256 \times 256$ . The ImageNet dataset contains 1,281,167 training images varying from 1,000 different classes. We use horizontal flipping for data augmentation. We measure the generation performance with Frechet Inception Distance (FID) [37], Incep + +![](images/2f16cf905580bc18114864fe07bdc9bb4944cb4974e83def9695a42b0408e798.jpg) +Figure 6. Details of the Spatial Reorient & Enhancement Module (SREM). + +# Algorithm 1: DiG Block Process. + +Input: token sequence $\mathbf{z}_{l-1}$ : (B, T, D), timestep embed $\mathbf{t}$ : (B, 1, D), label embed $\mathbf{y}$ : (B, 1, D) +Output: token sequence $\mathbf{z}_l$ : (B, T, D) + $\alpha_1, \beta_1, \gamma_1, \alpha_2, \beta_2, \gamma_2$ : (B, 1, D) $\leftarrow$ MLP $(\mathbf{t} + \mathbf{y})$ // regress parameters of adaLN + $\mathbf{z}_{l-1}^{\prime}$ : (B, T, D) $\leftarrow$ $\mathbf{z}_{l-1} + \alpha_1 \odot$ GLA(Norm( $\mathbf{z}_{l-1}$ ) $\odot$ $(1 + \gamma_1) + \beta_1)$ $\mathbf{z}_{l-1}^{\prime\prime}$ : (B, T, D) $\leftarrow$ $\mathbf{z}_{l-1}^{\prime} + \alpha_2 \odot$ FFN(Norm( $\mathbf{z}_{l-1}^{\prime}$ ) $\odot$ $(1 + \gamma_2) + \beta_2)$ $\mathbf{z}_{l-1}^{\prime\prime}$ : (B, $\sqrt{T}, \sqrt{T}, D$ ) $\leftarrow$ DWConv2d(reshape2d( $\mathbf{z}_{l-1}^{\prime\prime}$ ) // SREM module +if $l \% 2 == 0$ then + $\mathbf{z}_{l-1}^{\prime\prime}$ : (B, $\sqrt{T}, \sqrt{T}, D$ ) $\leftarrow$ transpose( $\mathbf{z}_{l-1}^{\prime\prime}$ ) // transpose the token matrix every two block + $\mathbf{z}_l$ : (B, T, D) $\leftarrow$ flatten( $\mathbf{z}_{l-1}^{\prime\prime}$ ) // flatten the token matrix into 1-D sequence +end +else + $\mathbf{z}_{l-1}^{\prime\prime}$ : (B, T, D) $\leftarrow$ flatten( $\mathbf{z}_{l-1}^{\prime\prime}$ ) // flatten the token matrix into 1-D sequence + $\mathbf{z}_l$ : (B, T, D) $\leftarrow$ flip( $\mathbf{z}_{l-1}^{\prime\prime}$ ) // flip the token sequence every two block +end +Return: $\mathbf{z}_l$ + +
    ModelLayers NHidden Size DGflopsGflopsDiG/GflopsDiT
    DiG-S123844.3070.8%
    DiG-B1276817.0774.1%
    DiG-L24102461.6676.3%
    DiG-XL28115289.4075.3%
    U-DiG-S201284.1067.6%
    U-DiG-B2025615.2066.0%
    U-DiG-L4032053.5766.3%
    U-DiG-XL4041679.0966.6%
    + +Table 2. Details of DiG models. We follow DiT [39] model configurations for the Small (S), Base (B), Large (L), and XLarge (XL) variants. Given $I = {32},p = 2$ for DiG, $p = 1$ for U-DiG. + +tion Score [52], sFID [37], and Precision/Recall [30]. + +Implementation details. We use AdamW optimizer with a constant learning rate of $1e - 4$ . Following the previous works [39], we utilize the exponential moving average (EMA) of DiG weights during training with a decay rate of 0.9999. We generate all images with the EMA model. For the training of ImageNet, we use an off-the-shelf pretrained variational autoencoder (VAE) [27, 49]. + +# 4.2. Model Analysis + +Effect of spatial reorient & enhancement module. As shown in Table 3, we analyze the effectiveness of the proposed spatial reorient & enhancement module (SREM). We take the DiT-S/2 as our baseline method. The naive plain DiG with only causal modeling has significantly fewer flops and parameters, but also poor FID performance due to the lack of global context. We first add the bidirectional scanning to DiG and observe significant improvement, i.e., 69.28 FID, which demonstrates the importance of global context. Experiment without identity initialization + +![](images/956d2ad69a13dcd84ea52ce4b803951b31b3a392a53e2365ecfd5536168c8436.jpg) +Figure 7. Scaling analysis with DiG model scales and patch sizes. for DWConv2d (the $\times$ symbol), leads to worse FID, while the DWConv2d with identity initialization can improve performance a lot. The experiment with DWConv2d proves the importance of identity initialization and local awareness. The experiment with full SREM brings the best performance, taking care of both local information and global context. Experiments in the last three rows indicate that the more suitable position for SREM is after the FFN. + +Scaling model scales and patch sizes. We investigate the scaling ability of DiG among four different model scales and three patch sizes on the ImageNet dataset. As depicted in Fig. 7, the performance improves as the models scale from S/2 to XL/2 and the patch size from 2 to 8. The results demonstrate the scaling ability of DiG, indicating its potential as a large foundational diffusion model. + +Structural ablation from DiG to U-DiG. We evaluate the structural benefits from DiG to U-DiG. As shown in + +
    ModelSpatial Reorient & Enhancement ModuleSREM PositionFlops (G)Params (M)FID-50K
    BidirectionalDWConv2d4-directional
    Baseline Method.
    DiT-S/26.0633.068.4
    Ours.
    DiG-S/24.2933.0175.84
    DiG-S/2✓After FFN4.2933.069.28
    DiG-S/2✓✓After FFN4.3033.196.83
    DiG-S/2✓✓After FFN4.3033.163.84
    DiG-S/2✓✓✓After FFN4.3033.162.06
    DiG-S/2✓✓✓Before Attn.4.3033.162.34
    DiG-S/2✓✓✓Between Attn. & FFN4.3033.162.93
    + +Table 3. Ablation of the proposed Spatial Reorient & Enhancement Module (SREM). We validate the effectiveness of each SREM component and use the same hyperparameters for all models. The "half right and half wrong symbol" $(\star)$ means use DWConv2d without the identity initialization. We mark the best result in bold. + +
    ModelFID↓sFID↓IS↑P↑R↑
    ADM [13]10.946.02100.980.690.63
    ADM-U7.495.13127.490.720.63
    ADM-G4.595.25186.700.820.52
    ADM-G, ADM-U3.946.14215.840.830.53
    CDM [22]4.88-158.71--
    LDM-8 [49]15.51-79.030.650.63
    LDM-8-G7.76-209.520.840.35
    LDM-4-G3.95-178.220.810.55
    LDM-4-G3.60-247.670.870.48
    Other sub-quadratic-time diffusion methods.
    DiM-H/2 [58]2.40----
    DiS-H/2 [16]2.104.55271.320.820.58
    DiMSUM-L/2-G [42]2.110.59---
    Baselines and Ours.
    DiT-S/2 (400K) [39]68.40----
    DiG-S/2 (400K)62.0611.7722.810.390.56
    DiT-B/2 (400K)43.47----
    DiG-B/2 (400K)39.508.5037.210.510.63
    DiT-L/2 (400K)23.33----
    DiG-L/2 (400K)22.906.9159.870.600.64
    DiT-XL/2 (400K)19.47----
    DiG-XL/2 (400K)18.536.0668.530.630.64
    DiT-XL/2 (7M)9.626.85121.500.670.67
    DiG-XL/2 (1.2M)8.606.46130.030.680.68
    DiT-XL/2-G (7M)2.274.60278.240.830.57
    DiG-XL/2-G (1.2M)2.074.53278.950.820.60
    + +Table 4. Benchmarking class-conditional image generation on ImageNet $256 \times 256$ . DiG models adopt the same hyperparameters as DiT [39] for fair comparison. G is the classifier-free guidance. We mark the best results in bold. + +Table 5, both the shortcut and hierarchical structures contribute positively to the metrics. Notably, for the generation task at a 512 resolution, U-DiG-S/1 achieves a remarkable improvement over DiG-S/2, with an FID gain exceeding 16.2, which demonstrates the effectiveness of U-DiG in generating high-resolution images. + +
    w/ short cutw/ hierarchyFID-50K
    IN-256IN-512
    DiT-S/268.40NaN
    DiG-S/262.0699.04
    DiG-S/2✓57.0191.42
    U-DiG-S/1✓✓52.2082.62
    + +Table 5. Structural ablation from DiG to U-DiG. + +# 4.3. Main Results + +We mainly compare the proposed plain DiG with DiT [39]. For class-conditional image generation on ImageNet $256 \times 256$ , as shown in Table 4, the proposed DiG has fewer FLOPs but outperforms DiT among four model scales with 400K training iterations with the same hyperparameters. Furthermore, the DiG-XL/2 (1.2M) with classifier-free guidance also presents competitive results when compared with concurrent sub-quadratic-time diffusion methods. + +# 5. Conclusion + +In this work, we present DiG, a cost-effective alternative to the vanilla Transformer for diffusion models in image generation tasks. In particular, DiG explores Gated Linear Attention Transformers (GLA), attaining comparable effectiveness and superior efficiency in long-sequence image generation tasks. Experimentally, DiG shows comparable performance to prior diffusion models on class-conditional ImageNet $256 \times 256$ benchmark while significantly reducing the computational burden starting from a 512 resolution. We hope this work can open up the possibility for other long-sequence generation tasks, such as video and audio modeling. + +Limitations. Although DiG shows superior efficiency in diffusion image generation, building a large foundation model like Sora [3] upon DiG is still an area that needs to be explored further. + +# Acknowledgments and Disclosure of Funding + +This work was partially supported by the National Science and Technology Major Project under Grant No. 2023YFF0905400. + +# References + +[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. All are worth words: A vit backbone for diffusion models. 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However, DiT models have faced challenges with quadratic complexity efficiency, especially when handling long sequences. In this paper, we aim to incorporate the sub-quadratic modeling capability of Gated Linear Attention (GLA) into the 2D diffusion backbone. Specifically, we introduce Diffusion Gated Linear Attention Transformers (DiG), a simple, adoptable solution with minimal parameter overhead. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 673, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 673, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 673, + 295, + 713 + ], + "type": "text", + "content": "This work was done when Lianghui Zhu was interning at ByteDance. Corresponding authors: Xinggang Wang (xgwang@hust.edu.cn) and Zilong Huang (zilong.huang2020@gmail.com)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7664" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "spans": [ + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "text", + "content": "competitive effectiveness. In addition to superior performance to DiT and other sub-quadratic-time diffusion models at " + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "text", + "content": " resolution, DiG demonstrates greater efficiency than these methods starting from a 512 resolution. Specifically, DiG-S/2 is " + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "inline_equation", + "content": "2.5 \\times" + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "text", + "content": " faster and saves " + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "inline_equation", + "content": "75.7\\%" + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "text", + "content": " GPU memory compared to DiT-S/2 at a 1792 resolution. Additionally, DiG-XL/2 is " + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "inline_equation", + "content": "4.2 \\times" + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "text", + "content": " faster than the Mamba-based model at a 1024 resolution and " + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "inline_equation", + "content": "1.8 \\times" + }, + { + "bbox": [ + 54, + 72, + 295, + 178 + ], + "type": "text", + "content": " faster than DiT with FlashAttention-2 at a 2048 resolution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 203, + 136, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 203, + 136, + 216 + ], + "spans": [ + { + "bbox": [ + 55, + 203, + 136, + 216 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 223, + 295, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 223, + 295, + 437 + ], + "spans": [ + { + "bbox": [ + 56, + 223, + 295, + 437 + ], + "type": "text", + "content": "In recent years, diffusion models [4, 20, 32, 53, 56, 61, 65, 66] have emerged as potent deep generative models [13, 49] renowned for their ability to generate high-quality images. Their rapid evolution has spurred extensive applications across various fields, including image-to-image generation [8, 67], text-to-image generation [19, 47, 51], speech synthesis [7, 29], video generation [21, 34, 36], and 3D generation [43, 68]. Concurrent with the rapid development of sampling algorithms [33, 38, 54], the principal techniques have evolved into two main categories based on their architectural backbones: U-Net-based methods [20, 55] and ViT-based methods [14]. U-Net-based approaches continue to leverage the convolutional neural network (CNN) architecture [31, 50], whose hierarchical feature modeling ability benefits visual generation tasks. On the other hand, ViT-based methods [1, 39, 64] innovate by incorporating self-attention mechanisms [59] instead of traditional sampling blocks, resulting in streamlined yet effective performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 439, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 439, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 56, + 439, + 295, + 628 + ], + "type": "text", + "content": "Due to their excellent scalability in terms of performance, ViT-based methods [39] have been adopted as backbones in the most advanced diffusion works, including PixArt [5, 6], Sora [3], Stable Diffusion 3 [15], etc. However, the self-attention mechanism in ViT-based architectures scales quadratically with the input sequence length, making them resource-intensive when dealing with long sequence generation tasks, e.g., high-resolution image generation and video generation. Recent works such as Mamba [18, 69], RWKV [40] and Gated Linear Attention Transformer (GLA) [63], try to improve the long-sequence processing efficiency by integrating Recurrent Neural Network (RNN) like architecture and hardware-aware algorithms. Since a data-dependent gating mechanism is crucial for 1D modeling [45], GLA shows outstanding performance among the above methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": "Motivated by the success of GLA in the natural language processing domain, it is appealing that we can transfer this success from language generation to visual content generation by designing a scalable and efficient diffusion backbone with the advanced linear attention [10, 25, 26] method. However, visual generation with linear models, such as Mamba, RWKV, and GLA, often faces two challenges, i.e.," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 370 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 370 + ], + "type": "text", + "content": "unidirectional scanning modeling and lack of local awareness. Previous approaches [16, 23] have often addressed the first issue by performing bidirectional scanning within the same block. Nevertheless, such methods result in a significant increase in time consumption and numerical instability. To address these challenges, we propose Diffusion GLA (DiG), which incorporates a lightweight spatial reorient & enhancement module (SREM) for block-wise scanning direction controlling and local awareness. For the first issue, SREM changes the sequence direction with minimal number of matrix operations and assigns different scanning in a block-by-block manner. The scanning directions contain four basic patterns and enable each patch in sequences to be aware of other patches following 4 directions. For the second issue, we also incorporate a depth-wise convolution (DWConv) [9] in the SREM to provide local awareness with extremely small amounts of parameters. Inspired by U-Net [50], we further propose a U-shape variant of DiG and analyze the improvements. Crucially, this paper presents a systematic ablation study and a comprehensive evaluation of the proposed modules and architectures. It is important to highlight that DiG adheres to the first practices of linear attention transformers in diffusion generation, demonstrating superior efficiency in quadratic and sub-quadratic diffusion models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "text", + "content": "Compared with the ViT-based method, i.e., DiT [39], DiG presents competitive performance on ImageNet [12] " + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "text", + "content": " generation when using the same hyperparameters. Furthermore, DiG is more efficient in terms of training speed and GPU memory starting from a 512 resolution. The efficiency in terms of memory and speed empowers DiG to alleviate the resource constraint problem of long- sequence visual generation tasks. Specifically, DiG demonstrates significant efficiency improvements over comparable models: DiG-S/2 achieves a " + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "inline_equation", + "content": "2.5 \\times" + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "text", + "content": " faster training speed and saves " + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "inline_equation", + "content": "75.7\\%" + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "text", + "content": " GPU memory compared to DiT-S/2 at a " + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "inline_equation", + "content": "1792 \\times 1792" + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "text", + "content": " resolution as shown in Fig. 2. Furthermore, with the same model size, DiG-XL/2 is " + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "inline_equation", + "content": "4.2 \\times" + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "text", + "content": " faster than the recent Mamba-based diffusion model at 1024 resolution and " + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "inline_equation", + "content": "1.8 \\times" + }, + { + "bbox": [ + 313, + 372, + 553, + 563 + ], + "type": "text", + "content": " faster than DiT with well-designed CUDA-optimized FlashAttention-2 [11] at 2048 resolution as shown in Fig. 3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 326, + 563, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 563, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 326, + 563, + 547, + 574 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 576, + 553, + 683 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 314, + 576, + 553, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 576, + 553, + 634 + ], + "spans": [ + { + "bbox": [ + 314, + 576, + 553, + 634 + ], + "type": "text", + "content": "- We propose Diffusion GLA (DiG), which incorporates an efficient DiG block for both global visual context modeling through block-wise scanning, and local visual awareness. To the best of our knowledge, DiG is the first exploration for diffusion backbone with linear attention." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 636, + 553, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 636, + 553, + 683 + ], + "spans": [ + { + "bbox": [ + 314, + 636, + 553, + 683 + ], + "type": "text", + "content": "- Without the burden of quadratic attention, the proposed DiG exhibits higher efficiency in both training speed and GPU memory cost while maintaining a similar modeling ability as DiT. Notably, DiG is " + }, + { + "bbox": [ + 314, + 636, + 553, + 683 + ], + "type": "inline_equation", + "content": "4.2 \\times" + }, + { + "bbox": [ + 314, + 636, + 553, + 683 + ], + "type": "text", + "content": " faster than" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 553, + 713 + ], + "type": "text", + "content": "Multi-path scanning and summation can easily lead to numerical NaN during training [16]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7665" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 88, + 294, + 242 + ], + "blocks": [ + { + "bbox": [ + 129, + 73, + 230, + 86 + ], + "lines": [ + { + "bbox": [ + 129, + 73, + 230, + 86 + ], + "spans": [ + { + "bbox": [ + 129, + 73, + 230, + 86 + ], + "type": "text", + "content": "(a) Speed Comparison" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 60, + 88, + 294, + 242 + ], + "lines": [ + { + "bbox": [ + 60, + 88, + 294, + 242 + ], + "spans": [ + { + "bbox": [ + 60, + 88, + 294, + 242 + ], + "type": "image", + "image_path": "27cb37a8e1c4ec60a4565c134665beedc43a7aff0e94269ef6fd3b55c4e8507d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "lines": [ + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "type": "text", + "content": "Figure 2. Efficiency comparison among DiT [39] with Attention [59], DiS [16] with Mamba [18], and our DiG model. DiG achieves higher training speed while costs lower GPU memory in dealing with high-resolution images. For example, DiG is " + }, + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "type": "inline_equation", + "content": "2.5 \\times" + }, + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "type": "text", + "content": " faster than DiT and saves " + }, + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "type": "inline_equation", + "content": "75.7\\%" + }, + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "type": "text", + "content": " GPU memory with a resolution of " + }, + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "type": "inline_equation", + "content": "1792 \\times 1792" + }, + { + "bbox": [ + 54, + 243, + 555, + 277 + ], + "type": "text", + "content": ", i.e., 12544 tokens per image. Patch size for all models is 2." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 313, + 83, + 547, + 242 + ], + "blocks": [ + { + "bbox": [ + 367, + 73, + 504, + 86 + ], + "lines": [ + { + "bbox": [ + 367, + 73, + 504, + 86 + ], + "spans": [ + { + "bbox": [ + 367, + 73, + 504, + 86 + ], + "type": "text", + "content": "(b) GPU Memory Comparison" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 83, + 547, + 242 + ], + "lines": [ + { + "bbox": [ + 313, + 83, + 547, + 242 + ], + "spans": [ + { + "bbox": [ + 313, + 83, + 547, + 242 + ], + "type": "image", + "image_path": "9b4a3954cb66d8aa29b4c6972d791d91dfed700afb52478d182968235cbb8489.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 58, + 302, + 293, + 459 + ], + "blocks": [ + { + "bbox": [ + 97, + 289, + 276, + 301 + ], + "lines": [ + { + "bbox": [ + 97, + 289, + 276, + 301 + ], + "spans": [ + { + "bbox": [ + 97, + 289, + 276, + 301 + ], + "type": "text", + "content": "(a) FPS Comparison w/ img_size = 1024" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 302, + 293, + 459 + ], + "lines": [ + { + "bbox": [ + 58, + 302, + 293, + 459 + ], + "spans": [ + { + "bbox": [ + 58, + 302, + 293, + 459 + ], + "type": "image", + "image_path": "05bfdd792b26f8ec68fe370e6e0af89ffc7d2e0cdba4225eccb40f9bc76e4614.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "lines": [ + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "spans": [ + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "text", + "content": "Figure 3. FPS comparison among DiS [16] with Mamba [18], DiT [39] with Attention [59], DiT with Flash Attention-2 (Flash-DiT) [11] and our DiG model varying from different model sizes. We take DiG as a baseline. With a resolution of " + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "text", + "content": ", DiG is " + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "inline_equation", + "content": "2.0 \\times" + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "text", + "content": " faster than DiS at small size while " + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "inline_equation", + "content": "4.2 \\times" + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "text", + "content": " faster at XL size. Furthermore, DiG-XL/2 is " + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "inline_equation", + "content": "1.8 \\times" + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "text", + "content": " faster than the most well-designed high-optimized Flash-DiT-XL/2 with a resolution of " + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "inline_equation", + "content": "2048 \\times 2048" + }, + { + "bbox": [ + 54, + 460, + 555, + 504 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 313, + 302, + 548, + 459 + ], + "blocks": [ + { + "bbox": [ + 356, + 289, + 534, + 301 + ], + "lines": [ + { + "bbox": [ + 356, + 289, + 534, + 301 + ], + "spans": [ + { + "bbox": [ + 356, + 289, + 534, + 301 + ], + "type": "text", + "content": "(b) FPS Comparison w/ img_size = 2048" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 302, + 548, + 459 + ], + "lines": [ + { + "bbox": [ + 313, + 302, + 548, + 459 + ], + "spans": [ + { + "bbox": [ + 313, + 302, + 548, + 459 + ], + "type": "image", + "image_path": "f57999b0e76a8524aa97708646ea1bc5a4316db67c6a736aa0380cf94bdfdad0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 63, + 517, + 295, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 517, + 295, + 553 + ], + "spans": [ + { + "bbox": [ + 63, + 517, + 295, + 553 + ], + "type": "text", + "content": "the Mamba-based diffusion model at 1024 resolution and " + }, + { + "bbox": [ + 63, + 517, + 295, + 553 + ], + "type": "inline_equation", + "content": "1.8 \\times" + }, + { + "bbox": [ + 63, + 517, + 295, + 553 + ], + "type": "text", + "content": " faster than DiT with well-designed CUDA-optimized FlashAttention-2 [11] at 2048 resolution." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 554, + 295, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 554, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 55, + 554, + 295, + 638 + ], + "type": "text", + "content": "- We conduct extensive experiments on the ImageNet " + }, + { + "bbox": [ + 55, + 554, + 295, + 638 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 554, + 295, + 638 + ], + "type": "text", + "content": ". The results demonstrate that DiG presents scalable ability and achieves comparable performance when compared with DiT. Besides, higher efficiency makes DiG promising to serve as the next-generation backbone for diffusion models in the context of large-scale long-sequence generation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 650, + 143, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 650, + 143, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 650, + 143, + 662 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 671, + 219, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 671, + 219, + 682 + ], + "spans": [ + { + "bbox": [ + 55, + 671, + 219, + 682 + ], + "type": "text", + "content": "2.1. Linear Attention Transformer" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "Different from standard autoregressive Transformer [60] which models the global attention matrix, the original lin" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "text", + "content": "ear attention [26] is essentially a linear RNN with matrix-valued-format hidden states. Linear attention introduces a similarity kernel " + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "inline_equation", + "content": "k(x,y)" + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "text", + "content": " with an associated feature map " + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "inline_equation", + "content": "k(x,y) = \\langle \\phi(x), \\phi(y) \\rangle" + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "text", + "content": ". The calculation of output " + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{O} \\in \\mathbb{R}^{L \\times d}" + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "text", + "content": " (here " + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "text", + "content": " is the sequence length and " + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 517, + 555, + 590 + ], + "type": "text", + "content": " is the dimension) can be represented as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 319, + 600, + 553, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 600, + 553, + 639 + ], + "spans": [ + { + "bbox": [ + 319, + 600, + 553, + 639 + ], + "type": "interline_equation", + "content": "\\mathbf {O} _ {t} = \\frac {\\sum_ {i = 1} ^ {t} k \\left(\\mathbf {Q} _ {t} , \\mathbf {K} _ {i}\\right) \\mathbf {V} _ {i}}{\\sum_ {i = 1} ^ {t} k \\left(\\mathbf {Q} _ {t} , \\mathbf {K} _ {i}\\right)} = \\frac {\\phi \\left(\\mathbf {Q} _ {t}\\right) \\sum_ {i = 1} ^ {t} \\phi \\left(\\mathbf {K} _ {i}\\right) ^ {\\top} \\mathbf {V} _ {i}}{\\phi \\left(\\mathbf {Q} _ {t}\\right) \\sum_ {i = 1} ^ {t} \\phi \\left(\\mathbf {K} _ {i}\\right) ^ {\\top}}, \\tag {1}", + "image_path": "34ad39a0a681de4f1636582ce088c8da6ec1a38dbe56fcbb21495729beebbe60.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 641, + 570, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 570, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 570, + 677 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} + \\phi (\\mathbf {K} _ {i}) \\mathbf {V} _ {i}, z _ {t} = z _ {t - 1} + \\phi (\\mathbf {K} _ {i}) ^ {\\top}, \\mathbf {O} _ {t} = \\frac {\\phi (\\mathbf {Q} _ {t}) \\mathbf {S} _ {t}}{\\phi (\\mathbf {Q} _ {t}) z _ {t}},", + "image_path": "beeed99ff0b60a864f556f8167ebc898c8200192bfe103837a98814e6d3879e1.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": "where query " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": ", value " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " have shapes of " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "L\\times d" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " is the index of current token. By denoting hidden state " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_t = \\sum_{i = 1}^{t}\\phi (\\mathbf{K}_i)\\mathbf{V}_i" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " and normalizer " + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "inline_equation", + "content": "z_{t} = \\sum_{i = 1}^{t}\\phi (\\mathbf{K}_{i})^{\\top}" + }, + { + "bbox": [ + 313, + 677, + 555, + 715 + ], + "type": "text", + "content": " where" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7666" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_t \\in \\mathbb{R}^{d \\times d}" + }, + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "inline_equation", + "content": "z_t \\in \\mathbb{R}^{d \\times 1}" + }, + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "text", + "content": ", the Eq. (1) can be rewritten as the Eq. 2. Recent works set " + }, + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "text", + "content": " to be the identity [35, 57] and remove " + }, + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "inline_equation", + "content": "z_t" + }, + { + "bbox": [ + 55, + 71, + 296, + 120 + ], + "type": "text", + "content": " [44], resulting linear attention Transformer with the following format:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 99, + 125, + 295, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 125, + 295, + 140 + ], + "spans": [ + { + "bbox": [ + 99, + 125, + 295, + 140 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} + \\mathbf {K} _ {t} ^ {\\top} \\mathbf {V} _ {t}, \\quad \\mathbf {O} _ {t} = \\mathbf {Q} _ {t} \\mathbf {S} _ {t}. \\tag {3}", + "image_path": "4510c347a93a43197ff7f61354c1403a6c73405579468f9929e996f16976b455.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 145, + 296, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 145, + 296, + 217 + ], + "spans": [ + { + "bbox": [ + 55, + 145, + 296, + 217 + ], + "type": "text", + "content": "Directly using a linear attention Transformer for visual generation leads to poor performance due to the unidirectional modeling, so we propose a lightweight spatial reorient & enhancement module to take care of both modeling global context in four directions block by block and local information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 223, + 224, + 235 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 223, + 224, + 235 + ], + "spans": [ + { + "bbox": [ + 55, + 223, + 224, + 235 + ], + "type": "text", + "content": "2.2. Backbones in Diffusion Models" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 240, + 296, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 240, + 296, + 408 + ], + "spans": [ + { + "bbox": [ + 55, + 240, + 296, + 408 + ], + "type": "text", + "content": "Existing diffusion models typically employ U-Net as backbones [17, 20, 48] for image generation. Recently, Vision Transformer (ViT)-based backbones [1, 3, 5, 6, 39] receive significant attention due to the scalability of transformer and its natural fit for multi-modal learning. However, ViT-based architectures suffer from quadratic complexity, limiting their practicability in long sequence generation tasks, such as high-resolution image synthesis, video generation etc. To mitigate this, recent works explore subquadratic-time approaches to efficiently handle long sequences. For example, DiS [16], DiffuSSM [62], and ZigMa [23] employ state-space models as diffusion backbones for better computation efficiency. Diffusion-RWKV [62] adopt an RWKV architecture in diffusion models for image generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 408, + 296, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 408, + 296, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 408, + 296, + 491 + ], + "type": "text", + "content": "Our DiG also follows this line of research, aiming at improving the efficiency of long sequence processing by adopting Gated Linear Attention Transformer (GLA) as diffusion backbones. Our proposed adaptation maintains the fundamental structure and benefits of GLA while introducing a few crucial modifications necessary for generating high-fidelity visual data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 501, + 111, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 501, + 111, + 513 + ], + "spans": [ + { + "bbox": [ + 55, + 501, + 111, + 513 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 521, + 141, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 141, + 532 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 141, + 532 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "spans": [ + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "type": "text", + "content": "Gated Linear Attention Transformer. The Gated Linear Attention Transformer (GLA) [63] combines a data-dependent gating mechanism and linear attention, achieving superior recurrent modeling performance. Given an input " + }, + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "type": "inline_equation", + "content": "\\mathrm{X} \\in \\mathbb{R}^{L \\times d}" + }, + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "type": "text", + "content": " (here " + }, + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "type": "text", + "content": " is the sequence length and " + }, + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 538, + 296, + 620 + ], + "type": "text", + "content": " is the dimension), GLA calculates the query, key, and value vectors as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 93, + 628, + 295, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 628, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 93, + 628, + 295, + 641 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} = \\mathbf {X} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} \\mathbf {W} _ {K}, \\mathbf {V} = \\mathbf {X} \\mathbf {W} _ {V}, \\tag {4}", + "image_path": "bbbe5515ce98a23de3ae2622c06a182aaae83fb41ee394f13a9f82577cf9feb8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_Q" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_K" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_V" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": " are linear projection weights. The dimension number of " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "d_k" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "d_v" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": " is for " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": ". Next, GLA compute the gating matrix " + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 55, + 647, + 295, + 683 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 687, + 295, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 687, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 687, + 295, + 713 + ], + "type": "interline_equation", + "content": "\\mathbf {G} _ {t} = \\alpha_ {t} ^ {\\top} \\beta_ {t} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\alpha = \\sigma \\left(\\mathbf {X} \\mathbf {W} _ {\\alpha} + b _ {\\alpha}\\right) ^ {\\frac {1}{\\tau}} \\in \\mathbb {R} ^ {L \\times d _ {k}}, \\tag {5}", + "image_path": "f52fdaade55e2aa31074efe131cbdb367df9bf60a14daf8d03ca73236ee88e24.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 366, + 71, + 553, + 87 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 71, + 553, + 87 + ], + "spans": [ + { + "bbox": [ + 366, + 71, + 553, + 87 + ], + "type": "interline_equation", + "content": "\\beta = \\sigma \\left(\\mathbf {X} \\mathbf {W} _ {\\beta} + b _ {\\beta}\\right) ^ {\\frac {1}{\\tau}} \\in \\mathbb {R} ^ {L \\times d _ {v}}, \\tag {6}", + "image_path": "57faa8a42e610f48d74ae3bde275dd5ff448956f352d92b3cf92a701c1382f40.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "text", + "content": " is the index of token, " + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "text", + "content": " is the sigmoid function, " + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "text", + "content": " is the bias term, and " + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "inline_equation", + "content": "\\tau \\in \\mathbb{R}" + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "text", + "content": " is a temperature term. As shown in Fig. 4, the final output " + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_t" + }, + { + "bbox": [ + 313, + 91, + 555, + 127 + ], + "type": "text", + "content": " is obtained as follows:" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 318, + 138, + 529, + 209 + ], + "blocks": [ + { + "bbox": [ + 318, + 138, + 529, + 209 + ], + "lines": [ + { + "bbox": [ + 318, + 138, + 529, + 209 + ], + "spans": [ + { + "bbox": [ + 318, + 138, + 529, + 209 + ], + "type": "image", + "image_path": "b220c2890808ebaf80222fec3f472dc1ff9ba8f2f058e2218f9aa05f647ca33c.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 383, + 214, + 485, + 225 + ], + "lines": [ + { + "bbox": [ + 383, + 214, + 485, + 225 + ], + "spans": [ + { + "bbox": [ + 383, + 214, + 485, + 225 + ], + "type": "text", + "content": "Figure 4. Pipeline of GLA." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 353, + 233, + 555, + 248 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 233, + 555, + 248 + ], + "spans": [ + { + "bbox": [ + 353, + 233, + 555, + 248 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {t - 1} ^ {\\prime} = \\mathbf {G} _ {t} \\odot \\mathbf {S} _ {t - 1} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\tag {7}", + "image_path": "7fc4905d4e84bd20d4299d4a4e4c9965cff68f72972e71e241549f4813958bfe.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 364, + 250, + 553, + 264 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 250, + 553, + 264 + ], + "spans": [ + { + "bbox": [ + 364, + 250, + 553, + 264 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {t} = \\mathbf {S} _ {t - 1} ^ {\\prime} + \\mathbf {K} _ {t} ^ {\\top} V _ {t} \\in \\mathbb {R} ^ {d _ {k} \\times d _ {v}}, \\tag {8}", + "image_path": "24575330d441799f4de21337c3c1291479ebca1a7d8c117b17322183f826803d.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 362, + 266, + 553, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 266, + 553, + 281 + ], + "spans": [ + { + "bbox": [ + 362, + 266, + 553, + 281 + ], + "type": "interline_equation", + "content": "\\mathbf {O} _ {t} = \\mathbf {Q} _ {t} ^ {\\top} \\mathbf {S} _ {t} \\in \\mathbb {R} ^ {1 \\times d _ {v}}, \\tag {9}", + "image_path": "9f61d4524b56e9a54d87c187895bdfe6dae389acceb3bbbef70f04b0550d1588.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 362, + 283, + 553, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 283, + 553, + 297 + ], + "spans": [ + { + "bbox": [ + 362, + 283, + 553, + 297 + ], + "type": "interline_equation", + "content": "\\mathbf {R} _ {t} = \\operatorname {S w i s h} \\left(\\mathbf {X} _ {t} \\mathbf {W} _ {r} + b _ {r}\\right) \\in \\mathbb {R} ^ {1 \\times d _ {v}}, \\tag {10}", + "image_path": "a36850ed0d8cee9415ff0e364e1fbc8f914f14017b228d687326be2248200b29.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 362, + 300, + 553, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 300, + 553, + 314 + ], + "spans": [ + { + "bbox": [ + 362, + 300, + 553, + 314 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} _ {t} = \\left(\\mathbf {R} _ {t} \\odot \\operatorname {L N} \\left(\\mathbf {O} _ {t}\\right)\\right) \\mathbf {W} _ {O} \\in \\mathbb {R} ^ {1 \\times d}, \\tag {11}", + "image_path": "17b913b99e92b3f37d1c93fd6e68fc97b73915259798931e3e6c9fa050fecfa3.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 323, + 555, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 555, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 555, + 372 + ], + "type": "text", + "content": "where Swish is the Swish [46] activation function, and " + }, + { + "bbox": [ + 313, + 323, + 555, + 372 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 313, + 323, + 555, + 372 + ], + "type": "text", + "content": " is the element-wise multiplication operation. In subsequent sections, we use " + }, + { + "bbox": [ + 313, + 323, + 555, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{GLA}(\\cdot)" + }, + { + "bbox": [ + 313, + 323, + 555, + 372 + ], + "type": "text", + "content": " to refer to the gated linear attention computation for the input sequence." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 387, + 555, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 387, + 555, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 555, + 483 + ], + "type": "text", + "content": "Diffusion Models. Before introducing the proposed method, we provide a brief review of diffusion models (DDPM) [20]. The DDPM takes noise as an input and samples images by iterative denoising the input. The forward process of DDPM begins with a stochastic process where the initial image " + }, + { + "bbox": [ + 313, + 387, + 555, + 483 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 313, + 387, + 555, + 483 + ], + "type": "text", + "content": " is gradually corrupted by noise and is finally transformed into a simpler, noise-dominated state. The forward noisng process can be represented as follows:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 347, + 491, + 553, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 491, + 553, + 525 + ], + "spans": [ + { + "bbox": [ + 347, + 491, + 553, + 525 + ], + "type": "interline_equation", + "content": "q \\left(x _ {1: T} \\mid x _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(x _ {t} \\mid x _ {t - 1}\\right), \\tag {12}", + "image_path": "f149646635c8de014d2670cf061dd21b0cec89c107a556d5d4db6fb8922897a3.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 357, + 526, + 553, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 526, + 553, + 540 + ], + "spans": [ + { + "bbox": [ + 357, + 526, + 553, + 540 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) I\\right), \\tag {13}", + "image_path": "4b0efb1c628b26d9e6c93f5f78813e8e481fa252925e2942a9c173d23bca5255.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "inline_equation", + "content": "x_{1:T}" + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "text", + "content": " is the sequence of noised images from time " + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "inline_equation", + "content": "t = T" + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "text", + "content": ". Then, DDPM learns the reverse process that recovers the original image with learned " + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}" + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\theta}" + }, + { + "bbox": [ + 313, + 550, + 554, + 586 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 332, + 595, + 553, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 595, + 553, + 609 + ], + "spans": [ + { + "bbox": [ + 332, + 595, + 553, + 609 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}\\right), \\Sigma_ {\\theta} \\left(x _ {t}\\right)\\right), \\tag {14}", + "image_path": "7eccdbcdc2fea954b5efe872f967cef19effe0cde80314c6d98c345a584f17ac.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 618, + 555, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 555, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 555, + 654 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 618, + 555, + 654 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 618, + 555, + 654 + ], + "type": "text", + "content": " are the parameters of the denoiser, and are trained with the variational lower bound [53] on the loglikelihood of the observed data " + }, + { + "bbox": [ + 313, + 618, + 555, + 654 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 313, + 618, + 555, + 654 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 320, + 662, + 553, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 662, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 320, + 662, + 553, + 713 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} (\\theta) = - p \\left(x _ {0} \\mid x _ {1}\\right) \\\\ + \\sum_ {t} D _ {K L} \\left(q ^ {*} \\left(x _ {t - 1} \\mid x _ {t}, x _ {0}\\right) \\| p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right)\\right), \\tag {15} \\\\ \\end{array}", + "image_path": "22d5d486e95269a6dbb1112a48cef6c906853bff7aa8db48b8e13e8bb2d59ba2.jpg" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7667" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 83, + 414, + 426 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 141, + 83 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 141, + 83 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 141, + 83 + ], + "type": "text", + "content": "(a) Plain DiG" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 248, + 70, + 323, + 83 + ], + "lines": [ + { + "bbox": [ + 248, + 70, + 323, + 83 + ], + "spans": [ + { + "bbox": [ + 248, + 70, + 323, + 83 + ], + "type": "text", + "content": "(b) U-shape DiG" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 60, + 83, + 414, + 426 + ], + "lines": [ + { + "bbox": [ + 60, + 83, + 414, + 426 + ], + "spans": [ + { + "bbox": [ + 60, + 83, + 414, + 426 + ], + "type": "image", + "image_path": "e2a3f82aaf26620ae71812bbe36d38a6ada73386ad306dcb48ecdfbb16f7d081.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 427, + 397, + 440 + ], + "lines": [ + { + "bbox": [ + 88, + 427, + 397, + 440 + ], + "spans": [ + { + "bbox": [ + 88, + 427, + 397, + 440 + ], + "type": "text", + "content": "(d) Block-by-Block Scanning Directions of DiG Controlled by SREM" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 420, + 83, + 550, + 437 + ], + "blocks": [ + { + "bbox": [ + 445, + 70, + 507, + 83 + ], + "lines": [ + { + "bbox": [ + 445, + 70, + 507, + 83 + ], + "spans": [ + { + "bbox": [ + 445, + 70, + 507, + 83 + ], + "type": "text", + "content": "(c) DiG Block" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 420, + 83, + 550, + 437 + ], + "lines": [ + { + "bbox": [ + 420, + 83, + 550, + 437 + ], + "spans": [ + { + "bbox": [ + 420, + 83, + 550, + 437 + ], + "type": "image", + "image_path": "cedd6545b528765d4dd733c03091e2d40ddbd24b65ff381c84a6c486ca364295.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 445, + 555, + 468 + ], + "lines": [ + { + "bbox": [ + 55, + 445, + 555, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 555, + 468 + ], + "type": "text", + "content": "Figure 5. The overview of the proposed DiG models. The figure presents the (a) plain DiG, denoted as DiG, (b) U-shape DiG, denoted as U-DiG, (c) DiG block, and (d) block-by-block scanning directions of DiG controlled by the SREM." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "text", + "content": " is the full loss. To further simplify the training process of DDPM, researchers reparameterize " + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}" + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "text", + "content": " as a noise prediction network " + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "text", + "content": " and minimize the mean squared error loss " + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{simple}}" + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t)" + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "text", + "content": " and the true Gaussian noise " + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 55, + 474, + 295, + 523 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 527, + 295, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 527, + 295, + 541 + ], + "spans": [ + { + "bbox": [ + 116, + 527, + 295, + 541 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s i m p l e}} (\\theta) = \\left\\| \\epsilon_ {\\theta} \\left(x _ {t}\\right) - \\epsilon_ {t} \\right\\| _ {2} ^ {2}. \\tag {16}", + "image_path": "0e0ef2d8ecb41fa62904cfc31bb4a5aab60adf358edcc9582618afa811d73a4d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": "However, to train a diffusion model that can learn a variable reverse process covariance " + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\theta}" + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": ", we need to optimize the full " + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "inline_equation", + "content": "D_{KL}" + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": " term. In this paper, we follow DiT [39]'s training recipe where we use the simple loss " + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{simple}}" + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": " to train the noise prediction network " + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": " and use the full loss " + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": " to train the covariance prediction network " + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\theta}" + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": ". After the training process, we follow the stochastic sampling process to generate images from the learned " + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\theta}" + }, + { + "bbox": [ + 55, + 546, + 296, + 643 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 647, + 148, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 148, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 148, + 659 + ], + "type": "text", + "content": "3.2. Diffusion GLA" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": "We present two variants of Diffusion GLA (DiG), as shown in Fig. 5. Our goal is to be as faithful to the standard GLA architecture as possible to retain its scaling ability and high-efficiency properties. We follow some of the best practices" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": "of previous vision transformer architectures [1, 14, 39] to propose plain DiG and U-shape DiG, which are denoted as DiG and U-DiG, respectively. DiG first takes a spatial representation " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " output by the VAE encoder [28, 48] as input. For example, given a " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "256 \\times 256 \\times 3" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " image, we obtain a spatial representation " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " of shape " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "32 \\times 32 \\times 4" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " after the VAE encoder. DiG subsequently converts this spatial input into a token sequence " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_p \\in \\mathbb{R}^{T \\times (P^2 \\cdot C)}" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " through a patchify layer, where " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " is length of token sequence, " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " is the number of spatial representation channels, " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " is the size of image patches, and halving " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " will quadruple " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " for DiG is 2, while for U-DiG, " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " is 1. Next, we linearly project the " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_p" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " to the vector with dimension " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " and add frequency-based positional embeddings " + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{pos} \\in \\mathbb{R}^{T \\times D}" + }, + { + "bbox": [ + 313, + 474, + 555, + 654 + ], + "type": "text", + "content": " to all projected tokens as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 353, + 663, + 555, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 663, + 555, + 680 + ], + "spans": [ + { + "bbox": [ + 353, + 663, + 555, + 680 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {0} = \\left[ \\mathbf {z} _ {p} ^ {1} \\mathbf {W}; \\mathbf {z} _ {p} ^ {2} \\mathbf {W}; \\dots ; \\mathbf {z} _ {p} ^ {T} \\mathbf {W} \\right] + \\mathbf {E} _ {p o s}, \\tag {17}", + "image_path": "137da0d13a00a6d08109c88a96f34dd0de9f1a07f13738508793121091036894.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_p^t" + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "text", + "content": "-th patch of " + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_p" + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{(P^2 \\cdot C) \\times D}" + }, + { + "bbox": [ + 313, + 687, + 555, + 714 + ], + "type": "text", + "content": " is the learnable projection matrix. As for conditional information" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7668" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "text", + "content": "such as noise timesteps " + }, + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "inline_equation", + "content": "t \\in \\mathbb{R}" + }, + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "text", + "content": ", and class labels " + }, + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}" + }, + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "text", + "content": ", we adopt multi-layer perception (MLP) and embedding layer as timestep embedder and label embedder, respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 114, + 295, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 114, + 295, + 128 + ], + "spans": [ + { + "bbox": [ + 104, + 114, + 295, + 128 + ], + "type": "interline_equation", + "content": "\\mathbf {t} = \\mathbf {M L P} (t), \\quad \\mathbf {y} = \\mathbf {E m b e d} (y), \\tag {18}", + "image_path": "1667169e4367ab481ab1318d87e037fb36e083d3edfd797af791f3610fc67ae7.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{t} \\in \\mathbb{R}^{1 \\times D}" + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": " is time embedding and " + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{y} \\in \\mathbb{R}^{1 \\times D}" + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": " is label embedding. We then send the token sequence " + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "inline_equation", + "content": "(\\mathbf{z}_{l-1})" + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": " to the " + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": "-th block of the DiG encoder, and obtain the output " + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_l" + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": ". For the U-DiG variant, there are down-sampling and upsampling modules between different stages, and shortcuts in the same stage. Finally, we normalize the output token sequence " + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_L" + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": ", and feed it to the linear projection head to get the final predicted noise " + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_{noise}" + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": " and predicted covariance " + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_{covariance}" + }, + { + "bbox": [ + 55, + 132, + 296, + 242 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 75, + 247, + 295, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 247, + 295, + 259 + ], + "spans": [ + { + "bbox": [ + 75, + 247, + 295, + 259 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {l} = \\operatorname {D i G} _ {l} (\\mathbf {z} _ {l - 1}, \\mathbf {t}, \\mathbf {y}), \\quad \\mathbf {z} _ {n} = \\operatorname {N o r m} (\\mathbf {z} _ {L}), \\tag {19}", + "image_path": "9ee9a65d7bbe0c4f6b835d4a08fb29ddc30cd07323d4997cb2abd4ce81aa373d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 265, + 295, + 278 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 265, + 295, + 278 + ], + "spans": [ + { + "bbox": [ + 102, + 265, + 295, + 278 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {p}} _ {\\text {n o i s e}}, \\hat {\\mathbf {p}} _ {\\text {c o v a r i a n c e}} = \\operatorname {L i n e a r} (\\mathbf {z} _ {n}), \\tag {20}", + "image_path": "2257cbee33102752bedb04ee37af12e02b9f75f8628f1c3316b6533217c833fd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{DiG}_l" + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "text", + "content": "-th diffusion GLA block, " + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "text", + "content": " is the number of blocks, and Norm is the normalization layer. The " + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_{noise}" + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_{covariance}" + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "text", + "content": " have the same shape as the input spatial representation, i.e., " + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "inline_equation", + "content": "32 \\times 32 \\times 4" + }, + { + "bbox": [ + 55, + 283, + 296, + 331 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 337, + 128, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 337, + 128, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 337, + 128, + 348 + ], + "type": "text", + "content": "3.3. DiG Block" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 354, + 295, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 295, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 295, + 474 + ], + "type": "text", + "content": "The original GLA block processes input sequence in a recurrent manner, which only enables causal modeling for 1-D sequence. Previous methods [16, 23] employ multi-path scanning within the same block to model global context, but this leads to a significant increase in time consumption and numerical instability [16], as shown in Table 1. To model the global context efficiently, we introduce the DiG block as shown in Fig. 5, which incorporates a spatial reorient & enhancement module (SREM) that enables lightweight spatial recognition and controls block-wise scanning directions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": "Specifically, we present the forward process of DiG block in Algo. 1. Following the widespread usage of adaptive normalization layers [41] in GANs [2, 24] and diffusion models [13, 39], we add and normalize the input timestep embedding " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": " and label embedding " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": " to regress the scale parameter " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": ", and shift parameter " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": ". Then, we launch gated linear attention (GLA) and feedforward network (FFN) with the adjustment of regressed adaptive layer norm (adaLN) parameters. Finally, we send the sequence to the SREM module as shown in Fig. 6. Specifically, we reshape the sequence to 2D and launch a lightweight " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": " depth-wise convolution (DWConv2d) layer to perceive local spatial information. However, we notice that using traditional initialization for DWConv2d leads to slow convergence because convolutional weights are dispersed around. To address this problem, we use identity initialization that only sets the convolutional kernel center as 1, and the surroundings to 0. For the last step of SREM, we alternate transpose and flip operations block-by-block to efficiently control block-wise scanning directions using minimal number of matrix operations." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 315, + 71, + 575, + 138 + ], + "blocks": [ + { + "bbox": [ + 315, + 71, + 575, + 138 + ], + "lines": [ + { + "bbox": [ + 315, + 71, + 575, + 138 + ], + "spans": [ + { + "bbox": [ + 315, + 71, + 575, + 138 + ], + "type": "table", + "html": "
    Extra OperationsIf Stable?Time (s)
    Matrix OPsScanning
    Bidirectional31×2.18
    4-directional133×4.02
    Block-by-Block20✓1.56
    ", + "image_path": "faaf2a99d96064949c6a9fdba6390238bdbd7befbbd09193c5916786ff0600de.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 140, + 555, + 185 + ], + "lines": [ + { + "bbox": [ + 313, + 140, + 555, + 185 + ], + "spans": [ + { + "bbox": [ + 313, + 140, + 555, + 185 + ], + "type": "text", + "content": "Table 1. Experimental results of different scanning strategies. Given " + }, + { + "bbox": [ + 313, + 140, + 555, + 185 + ], + "type": "inline_equation", + "content": "I = {32},p = 2" + }, + { + "bbox": [ + 313, + 140, + 555, + 185 + ], + "type": "text", + "content": " ,all experiments are conducted with XL size models. Extra operations include matrix operations and scanning operations, which both increase the time consumption." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 190, + 432, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 190, + 432, + 202 + ], + "spans": [ + { + "bbox": [ + 313, + 190, + 432, + 202 + ], + "type": "text", + "content": "3.4. Architecture Details" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": "We use " + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": " DiG blocks, each operating at the hidden dimension size " + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": ". Following previous works [14, 39, 63], we follow standard transformer setting that scales " + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": ", and attention heads number. Particularly, we provide four configurations: S, B, L, and XL, for the two different variants, as shown in the Table 2. They cover a wide range of flop allocations, ranging from 4.10 Gflops to 89.40 Gflops, presenting a way to gauge the scaling performance and efficiency. Notably, DiG consumes " + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "inline_equation", + "content": "70.8\\%" + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "inline_equation", + "content": "76.3\\%" + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": " Gflops, and U-DiG only consumes " + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "inline_equation", + "content": "66.0\\%" + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "inline_equation", + "content": "67.6\\%" + }, + { + "bbox": [ + 313, + 209, + 555, + 353 + ], + "type": "text", + "content": " Gflops when compared with the same model size DiT baselines. Both the proposed two variants are computationally efficient." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 360, + 425, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 360, + 425, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 360, + 425, + 373 + ], + "type": "text", + "content": "3.5. Efficiency Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": "GPU contains two important components, i.e., high bandwidth memory (HBM) and SRAM. HBM has a bigger memory size but SRAM has a larger bandwidth. To make full use of SRAM and modeling sequences in a parallel form, we follow GLA to split a whole sequence into many chunks that can complete calculations on SRAM. We denote the chunk size as " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": ", the training complexity is thus " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "O\\left(\\frac{T}{M}(M^2D + MD^2)\\right) = O(TMD + TD^2)" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": ", which is less than the traditional attention's complexity " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "O(T^2D)" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "T > D" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": ". Furthermore, the scaling analysis of speed and GPU memory are shown in Fig. 2 and Fig. 3, which demonstrate the high efficiency of the proposed DiG: DiG shows notable efficiency gains: DiG-S/2 is " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "2.5 \\times" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": " faster and saves " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "75.7\\%" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": " GPU memory compared to DiT-S/2 at " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "1792 \\times 1792" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": ". Additionally, DiG-XL/2 is " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "4.2 \\times" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": " faster than the Mamba-based model at 1024 resolution and " + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "inline_equation", + "content": "1.8 \\times" + }, + { + "bbox": [ + 313, + 377, + 556, + 581 + ], + "type": "text", + "content": " faster than DiT with FlashAttention-2 at 2048." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 592, + 391, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 592, + 391, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 592, + 391, + 605 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 612, + 441, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 612, + 441, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 612, + 441, + 624 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "content": "Datasets and metrics. Following previous works [39], we use ImageNet [12] for class-conditional image generation learning at a resolution of " + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 629, + 555, + 715 + ], + "type": "text", + "content": ". The ImageNet dataset contains 1,281,167 training images varying from 1,000 different classes. We use horizontal flipping for data augmentation. We measure the generation performance with Frechet Inception Distance (FID) [37], Incep" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7669" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 76, + 184, + 257 + ], + "blocks": [ + { + "bbox": [ + 75, + 76, + 184, + 257 + ], + "lines": [ + { + "bbox": [ + 75, + 76, + 184, + 257 + ], + "spans": [ + { + "bbox": [ + 75, + 76, + 184, + 257 + ], + "type": "image", + "image_path": "2f16cf905580bc18114864fe07bdc9bb4944cb4974e83def9695a42b0408e798.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 262, + 200, + 283 + ], + "lines": [ + { + "bbox": [ + 59, + 262, + 200, + 283 + ], + "spans": [ + { + "bbox": [ + 59, + 262, + 200, + 283 + ], + "type": "text", + "content": "Figure 6. Details of the Spatial Reorient & Enhancement Module (SREM)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 206, + 76, + 338, + 86 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 206, + 76, + 338, + 86 + ], + "spans": [ + { + "bbox": [ + 206, + 76, + 338, + 86 + ], + "type": "text", + "content": "Algorithm 1: DiG Block Process." + } + ] + } + ], + "index": 2 + }, + { + "type": "code", + "bbox": [ + 205, + 89, + 527, + 283 + ], + "blocks": [ + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "lines": [ + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "spans": [ + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": "Input: token sequence " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, T, D), timestep embed " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, 1, D), label embed " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, 1, D) \nOutput: token sequence " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_l" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, T, D) \n" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\alpha_1, \\beta_1, \\gamma_1, \\alpha_2, \\beta_2, \\gamma_2" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, 1, D) " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " MLP " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "(\\mathbf{t} + \\mathbf{y})" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " // regress parameters of adaLN \n" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, T, D) " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1} + \\alpha_1 \\odot" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " GLA(Norm(" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "(1 + \\gamma_1) + \\beta_1)" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, T, D) " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime} + \\alpha_2 \\odot" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " FFN(Norm(" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "(1 + \\gamma_2) + \\beta_2)" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\sqrt{T}, \\sqrt{T}, D" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " DWConv2d(reshape2d(" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") // SREM module \nif " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "l \\% 2 == 0" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " then \n" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\sqrt{T}, \\sqrt{T}, D" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " transpose(" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") // transpose the token matrix every two block \n" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_l" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, T, D) " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " flatten(" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") // flatten the token matrix into 1-D sequence \nend \nelse \n" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, T, D) " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " flatten(" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") // flatten the token matrix into 1-D sequence \n" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_l" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " : (B, T, D) " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": " flip(" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{l-1}^{\\prime\\prime}" + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "text", + "content": ") // flip the token sequence every two block \nend \nReturn: " + }, + { + "bbox": [ + 205, + 89, + 527, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_l" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "code_body" + } + ], + "index": 3, + "sub_type": "algorithm" + }, + { + "type": "table", + "bbox": [ + 56, + 305, + 299, + 426 + ], + "blocks": [ + { + "bbox": [ + 56, + 305, + 299, + 426 + ], + "lines": [ + { + "bbox": [ + 56, + 305, + 299, + 426 + ], + "spans": [ + { + "bbox": [ + 56, + 305, + 299, + 426 + ], + "type": "table", + "html": "
    ModelLayers NHidden Size DGflopsGflopsDiG/GflopsDiT
    DiG-S123844.3070.8%
    DiG-B1276817.0774.1%
    DiG-L24102461.6676.3%
    DiG-XL28115289.4075.3%
    U-DiG-S201284.1067.6%
    U-DiG-B2025615.2066.0%
    U-DiG-L4032053.5766.3%
    U-DiG-XL4041679.0966.6%
    ", + "image_path": "7b78433193dada11d859e78fc50fe89a208cc4a880db01b8041a1af0032fdd1e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 427, + 296, + 460 + ], + "lines": [ + { + "bbox": [ + 55, + 427, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 296, + 460 + ], + "type": "text", + "content": "Table 2. Details of DiG models. We follow DiT [39] model configurations for the Small (S), Base (B), Large (L), and XLarge (XL) variants. Given " + }, + { + "bbox": [ + 55, + 427, + 296, + 460 + ], + "type": "inline_equation", + "content": "I = {32},p = 2" + }, + { + "bbox": [ + 55, + 427, + 296, + 460 + ], + "type": "text", + "content": " for DiG, " + }, + { + "bbox": [ + 55, + 427, + 296, + 460 + ], + "type": "inline_equation", + "content": "p = 1" + }, + { + "bbox": [ + 55, + 427, + 296, + 460 + ], + "type": "text", + "content": " for U-DiG." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 466, + 271, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 466, + 271, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 466, + 271, + 479 + ], + "type": "text", + "content": "tion Score [52], sFID [37], and Precision/Recall [30]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": "Implementation details. We use AdamW optimizer with a constant learning rate of " + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 55, + 485, + 296, + 570 + ], + "type": "text", + "content": ". Following the previous works [39], we utilize the exponential moving average (EMA) of DiG weights during training with a decay rate of 0.9999. We generate all images with the EMA model. For the training of ImageNet, we use an off-the-shelf pretrained variational autoencoder (VAE) [27, 49]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 576, + 150, + 589 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 576, + 150, + 589 + ], + "spans": [ + { + "bbox": [ + 55, + 576, + 150, + 589 + ], + "type": "text", + "content": "4.2. Model Analysis" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 296, + 713 + ], + "type": "text", + "content": "Effect of spatial reorient & enhancement module. As shown in Table 3, we analyze the effectiveness of the proposed spatial reorient & enhancement module (SREM). We take the DiT-S/2 as our baseline method. The naive plain DiG with only causal modeling has significantly fewer flops and parameters, but also poor FID performance due to the lack of global context. We first add the bidirectional scanning to DiG and observe significant improvement, i.e., 69.28 FID, which demonstrates the importance of global context. Experiment without identity initialization" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 297, + 527, + 460 + ], + "blocks": [ + { + "bbox": [ + 318, + 297, + 527, + 460 + ], + "lines": [ + { + "bbox": [ + 318, + 297, + 527, + 460 + ], + "spans": [ + { + "bbox": [ + 318, + 297, + 527, + 460 + ], + "type": "image", + "image_path": "956d2ad69a13dcd84ea52ce4b803951b31b3a392a53e2365ecfd5536168c8436.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 464, + 555, + 575 + ], + "lines": [ + { + "bbox": [ + 313, + 464, + 555, + 575 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 555, + 575 + ], + "type": "text", + "content": "Figure 7. Scaling analysis with DiG model scales and patch sizes. for DWConv2d (the " + }, + { + "bbox": [ + 313, + 464, + 555, + 575 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 313, + 464, + 555, + 575 + ], + "type": "text", + "content": " symbol), leads to worse FID, while the DWConv2d with identity initialization can improve performance a lot. The experiment with DWConv2d proves the importance of identity initialization and local awareness. The experiment with full SREM brings the best performance, taking care of both local information and global context. Experiments in the last three rows indicate that the more suitable position for SREM is after the FFN." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 555, + 674 + ], + "type": "text", + "content": "Scaling model scales and patch sizes. We investigate the scaling ability of DiG among four different model scales and three patch sizes on the ImageNet dataset. As depicted in Fig. 7, the performance improves as the models scale from S/2 to XL/2 and the patch size from 2 to 8. The results demonstrate the scaling ability of DiG, indicating its potential as a large foundational diffusion model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 689, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 712 + ], + "type": "text", + "content": "Structural ablation from DiG to U-DiG. We evaluate the structural benefits from DiG to U-DiG. As shown in" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7670" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 547, + 220 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 547, + 220 + ], + "type": "table", + "html": "
    ModelSpatial Reorient & Enhancement ModuleSREM PositionFlops (G)Params (M)FID-50K
    BidirectionalDWConv2d4-directional
    Baseline Method.
    DiT-S/26.0633.068.4
    Ours.
    DiG-S/24.2933.0175.84
    DiG-S/2✓After FFN4.2933.069.28
    DiG-S/2✓✓After FFN4.3033.196.83
    DiG-S/2✓✓After FFN4.3033.163.84
    DiG-S/2✓✓✓After FFN4.3033.162.06
    DiG-S/2✓✓✓Before Attn.4.3033.162.34
    DiG-S/2✓✓✓Between Attn. & FFN4.3033.162.93
    ", + "image_path": "d25f562c4e5225d2e2e9eb06c4f9e9de3fb915753357d5c4a6fa329474f90dae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 259, + 293, + 583 + ], + "blocks": [ + { + "bbox": [ + 55, + 221, + 553, + 255 + ], + "lines": [ + { + "bbox": [ + 55, + 221, + 553, + 255 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 553, + 255 + ], + "type": "text", + "content": "Table 3. Ablation of the proposed Spatial Reorient & Enhancement Module (SREM). We validate the effectiveness of each SREM component and use the same hyperparameters for all models. The \"half right and half wrong symbol\" " + }, + { + "bbox": [ + 55, + 221, + 553, + 255 + ], + "type": "inline_equation", + "content": "(\\star)" + }, + { + "bbox": [ + 55, + 221, + 553, + 255 + ], + "type": "text", + "content": " means use DWConv2d without the identity initialization. We mark the best result in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 259, + 293, + 583 + ], + "lines": [ + { + "bbox": [ + 58, + 259, + 293, + 583 + ], + "spans": [ + { + "bbox": [ + 58, + 259, + 293, + 583 + ], + "type": "table", + "html": "
    ModelFID↓sFID↓IS↑P↑R↑
    ADM [13]10.946.02100.980.690.63
    ADM-U7.495.13127.490.720.63
    ADM-G4.595.25186.700.820.52
    ADM-G, ADM-U3.946.14215.840.830.53
    CDM [22]4.88-158.71--
    LDM-8 [49]15.51-79.030.650.63
    LDM-8-G7.76-209.520.840.35
    LDM-4-G3.95-178.220.810.55
    LDM-4-G3.60-247.670.870.48
    Other sub-quadratic-time diffusion methods.
    DiM-H/2 [58]2.40----
    DiS-H/2 [16]2.104.55271.320.820.58
    DiMSUM-L/2-G [42]2.110.59---
    Baselines and Ours.
    DiT-S/2 (400K) [39]68.40----
    DiG-S/2 (400K)62.0611.7722.810.390.56
    DiT-B/2 (400K)43.47----
    DiG-B/2 (400K)39.508.5037.210.510.63
    DiT-L/2 (400K)23.33----
    DiG-L/2 (400K)22.906.9159.870.600.64
    DiT-XL/2 (400K)19.47----
    DiG-XL/2 (400K)18.536.0668.530.630.64
    DiT-XL/2 (7M)9.626.85121.500.670.67
    DiG-XL/2 (1.2M)8.606.46130.030.680.68
    DiT-XL/2-G (7M)2.274.60278.240.830.57
    DiG-XL/2-G (1.2M)2.074.53278.950.820.60
    ", + "image_path": "7314e7dca9223d641de11df41568512a6d355458b66da3bccf9eff6074d37db0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 584, + 295, + 628 + ], + "lines": [ + { + "bbox": [ + 55, + 584, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 584, + 295, + 628 + ], + "type": "text", + "content": "Table 4. Benchmarking class-conditional image generation on ImageNet " + }, + { + "bbox": [ + 55, + 584, + 295, + 628 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 584, + 295, + 628 + ], + "type": "text", + "content": ". DiG models adopt the same hyperparameters as DiT [39] for fair comparison. G is the classifier-free guidance. We mark the best results in bold." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 715 + ], + "type": "text", + "content": "Table 5, both the shortcut and hierarchical structures contribute positively to the metrics. Notably, for the generation task at a 512 resolution, U-DiG-S/1 achieves a remarkable improvement over DiG-S/2, with an FID gain exceeding 16.2, which demonstrates the effectiveness of U-DiG in generating high-resolution images." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 315, + 259, + 557, + 343 + ], + "blocks": [ + { + "bbox": [ + 315, + 259, + 557, + 343 + ], + "lines": [ + { + "bbox": [ + 315, + 259, + 557, + 343 + ], + "spans": [ + { + "bbox": [ + 315, + 259, + 557, + 343 + ], + "type": "table", + "html": "
    w/ short cutw/ hierarchyFID-50K
    IN-256IN-512
    DiT-S/268.40NaN
    DiG-S/262.0699.04
    DiG-S/2✓57.0191.42
    U-DiG-S/1✓✓52.2082.62
    ", + "image_path": "ccc203e46ee2d686efbc5833b9b88007436181491c168a7162ba21c4e42623fb.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 345, + 345, + 523, + 355 + ], + "lines": [ + { + "bbox": [ + 345, + 345, + 523, + 355 + ], + "spans": [ + { + "bbox": [ + 345, + 345, + 523, + 355 + ], + "type": "text", + "content": "Table 5. Structural ablation from DiG to U-DiG." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 362, + 400, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 362, + 400, + 374 + ], + "spans": [ + { + "bbox": [ + 313, + 362, + 400, + 374 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 380, + 555, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 555, + 476 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 555, + 476 + ], + "type": "text", + "content": "We mainly compare the proposed plain DiG with DiT [39]. For class-conditional image generation on ImageNet " + }, + { + "bbox": [ + 313, + 380, + 555, + 476 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 380, + 555, + 476 + ], + "type": "text", + "content": ", as shown in Table 4, the proposed DiG has fewer FLOPs but outperforms DiT among four model scales with 400K training iterations with the same hyperparameters. Furthermore, the DiG-XL/2 (1.2M) with classifier-free guidance also presents competitive results when compared with concurrent sub-quadratic-time diffusion methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 487, + 388, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 388, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 388, + 499 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 506, + 555, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 555, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 555, + 651 + ], + "type": "text", + "content": "In this work, we present DiG, a cost-effective alternative to the vanilla Transformer for diffusion models in image generation tasks. In particular, DiG explores Gated Linear Attention Transformers (GLA), attaining comparable effectiveness and superior efficiency in long-sequence image generation tasks. Experimentally, DiG shows comparable performance to prior diffusion models on class-conditional ImageNet " + }, + { + "bbox": [ + 313, + 506, + 555, + 651 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 506, + 555, + 651 + ], + "type": "text", + "content": " benchmark while significantly reducing the computational burden starting from a 512 resolution. We hope this work can open up the possibility for other long-sequence generation tasks, such as video and audio modeling." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 556, + 715 + ], + "type": "text", + "content": "Limitations. Although DiG shows superior efficiency in diffusion image generation, building a large foundation model like Sora [3] upon DiG is still an area that needs to be explored further." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7671" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 291, + 86 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 291, + 86 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 291, + 86 + ], + "type": "text", + "content": "Acknowledgments and Disclosure of Funding" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 295, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 295, + 127 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 295, + 127 + ], + "type": "text", + "content": "This work was partially supported by the National Science and Technology Major Project under Grant No. 2023YFF0905400." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 140, + 115, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 140, + 115, + 152 + ], + "spans": [ + { + "bbox": [ + 56, + 140, + 115, + 152 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 159, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 159, + 295, + 214 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 159, + 295, + 214 + ], + "spans": [ + { + "bbox": [ + 61, + 159, + 295, + 214 + ], + "type": "text", + "content": "[1] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. 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PMLR, 2024. 2" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7674" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/3d88adc0-2039-46a2-83ba-83308b59f70d_content_list.json b/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/3d88adc0-2039-46a2-83ba-83308b59f70d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4f54b7dc60fc63a30197f47845140115c5ae46a3 --- /dev/null +++ b/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/3d88adc0-2039-46a2-83ba-83308b59f70d_content_list.json @@ -0,0 +1,1612 @@ +[ + { + "type": "text", + "text": "DiN: Diffusion Model for Robust Medical VQA with Semantic Noisy Labels", + "text_level": 1, + "bbox": [ + 117, + 130, + 879, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Erjian Guo1 Zhen Zhao2 Zicheng Wang1 Tong Chen1 Yunyi Liu1 Luping Zhou1* \n1University of Sydney Shanghai AI Laboratory", + "bbox": [ + 150, + 179, + 851, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 251, + 326, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Medical Visual Question Answering (Med-VQA) systems benefit the interpretation of medical images containing critical clinical information. However, the challenge of noisy labels and limited high-quality datasets remains underexplored. To address this, we establish the first benchmark for noisy labels in Med-VQA by simulating human mislabeling with semantically designed noise types. More importantly, we introduce the DiN framework, which leverages a diffusion model to handle noisy labels in Med-VQA. Unlike the dominant classification-based VQA approaches that directly predict answers, our Answer Diffuser (AD) module employs a coarse-to-fine process, refining answer candidates with a diffusion model for improved accuracy. The Answer Condition Generator (ACG) further enhances this process by generating task-specific conditional information via integrating answer embeddings with fused image-question features. To address label noise, our Noisy Label Refinement(NLR) module introduces a robust loss function and dynamic answer adjustment to further boost the performance of the AD module. Our DiN framework consistently outperforms existing methods across multiple benchmarks with varying noise levels1.", + "bbox": [ + 88, + 282, + 483, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 645, + 220, + 659 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Medical Visual Question Answering (Med-VQA) tasks focus on accurately responding to medical inquiries by integrating visual information from medical images [6, 26, 39]. It holds great potential in applications like assisting diagnosis, enhancing patient understanding, and supporting clinical education [3, 36]. Recently, VQA models have achieved impressive results in the natural VQA domain [13, 38, 46]. This success has largely been driven by the availability of large-scale natural VQA datasets with well-structured accurate annotations [25, 29]. However, for Med-VQA, the annotation process poses unique challenges. It requires specialized medical expertise and skills from annotators, lead", + "bbox": [ + 89, + 670, + 482, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0333255bbcd2958904f191cd821042e7c8e35989a5e50f6396aa3b80543b983f.jpg", + "image_caption": [ + "(a) Classification-based" + ], + "image_footnote": [], + "bbox": [ + 521, + 252, + 699, + 315 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/47e58569552ea3abe9c7d8509dd133934de7ccb3bcedc3a7872ad9b4615806ad.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 253, + 890, + 315 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fdc7156e577d74d106ed7b51edd7940973a748d654df64f26b92bc4f65ab92d3.jpg", + "image_caption": [ + "(b) Generation-based", + "Figure 1. Comparison between our diffusion-based method and previous Med-VQA approaches. Previous Med-VQA methods, designed for clean label datasets, include classification-based (a) and generation-based (b) approaches. In contrast, our diffusion-based method (c) classifies answers from a generative perspective and denoises answers by Answer Diffuser with the support of Answer Condition Generator and the Noisy Label Refinement module (employed only during the training process)." + ], + "image_footnote": [], + "bbox": [ + 522, + 330, + 898, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing to increased complexity and higher potential for label noise [34, 35, 51]. Additionally, inter-observer variability among medical professionals further complicates the annotation process, contributing to labeling inconsistencies [16, 31, 43]. While the issue of noisy labels is a well-known challenge in machine learning, it has not been thoroughly explored in Med-VQA, despite the need for highly accurate medical annotations.", + "bbox": [ + 511, + 609, + 906, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While existing label-denoising methods have shown promise, they are primarily designed for uni-modal tasks like image classification or segmentation [23, 42, 50]. Directly applying them for the multi-modal Med-VQA task is not suitable for two key reasons. First, conventional noise models, such as random label shuffling, fail to capture the semantic nuances essential in Med-VQA, where label noise often retains medically relevant information rather than arbitrary noise. We argue that noisy labels in VQA should retain semantic coherence aligned with human cognitive levels. As shown in Fig. 2, examples of noisy QA", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author, luping.zhou@sydney.edu.au. Zhou is supported by Australian Research Council (ARC DP200103223). \n1Code: https://github.com/Erjian96/DiN", + "bbox": [ + 89, + 862, + 482, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14337", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/34f5f03b75efbc476203ce40121b91cba3f71c8268c679a5e1d8a15774e2cdbf.jpg", + "image_caption": [ + "Figure 2. Visualization of the semantic answer pairs in t-SNE and examples of noisy answers. Similar colors represent the degree of feature similarity from a pretrained BERT model. We randomly display 8 semantic pairs in the t-SNE plots of VQA-RAD dataset. Ground-truth labels are replaced with their semantic pairs, which we refer to as semantically noisy answers [47]." + ], + "image_footnote": [], + "bbox": [ + 114, + 88, + 470, + 296 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/495e599bdf21ce37a4cfd859e151f21e799e3a9a5a50da8fa625a8f3422ccc01.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 473, + 90, + 609, + 189 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8a689d5ad00407c0aa6dd2fa58d32202f13720cdbd4c063d1ea0bb29ea21fb97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 473, + 190, + 609, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Question Type: Open", + "bbox": [ + 620, + 104, + 756, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Question: Why is free air present in image?", + "bbox": [ + 620, + 119, + 877, + 133 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Random Noisy: Ribs", + "bbox": [ + 620, + 133, + 753, + 146 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic Noisy: Hydropneumothorax", + "bbox": [ + 620, + 147, + 851, + 160 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Ground-truth: Pneumothorax", + "bbox": [ + 620, + 161, + 805, + 172 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Question Type: Closed", + "bbox": [ + 620, + 204, + 764, + 219 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Question: Is the heart enlarged?", + "bbox": [ + 620, + 219, + 813, + 233 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Random Noisy: Skin", + "bbox": [ + 620, + 233, + 751, + 246 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic Noisy: Yes", + "bbox": [ + 620, + 247, + 751, + 260 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Ground-truth: No", + "bbox": [ + 620, + 261, + 738, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pairs and their corresponding t-SNE representations illustrate this difference: unlike the arbitrary and meaningless answers generated by random noise, our constructed semantic noise resembles real-world scenarios, closer to human mislabeling. Second, these methods are not equipped to handle the complexity of Med-VQA, which integrates both image and text modalities. For example, co-teaching methods [44] add considerable model complexity by requiring two branch networks, while Noise Transition Matrix (NTM) methods [11] struggle with noisy label distribution estimation as the number of Med-VQA classes grows. While current leading methods like SNLC [47] in the natural VQA domain focus on improving representation through robust contrastive loss, these studies address noise in a relatively coarse way and fall short when dealing with the medically relevant label noise in Med-VQA. For instance, with a $20\\%$ noise ratio, SNLC [47] achieves $62\\%$ accuracy on MedVQA with random noise but drops to $58\\%$ when handling our semantic noise. In summary, our constructed semantic noise in Med-VQA is both practically relevant and presents a more challenging task to effectively handle.", + "bbox": [ + 88, + 377, + 483, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the literature, two main approaches have emerged for medical VQA: classification-based and generation-based methods, as shown in Figure 1. Classification-based methods are generally straightforward and efficient but often struggle with low-frequency answers, which becomes especially pronounced in complex domains like Med-VQA [1, 9]. In contrast, generation-based methods offer more flexibility by constructing answers instead of selecting from predefined categories; however, they inevitably generate unrealistic or non-existent answers, reducing overall accuracy and reliability [27, 30]. To this end, motivated by the success of diffusion models in label refinement [2, 33], we propose leveraging them to bridge the gap between classi", + "bbox": [ + 89, + 704, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "fication and generation approaches, enabling answer classification from a generative perspective. Diffusion models can offer a balance between classification and generative approaches for Med-VQA. Prior studies [4, 12] have also demonstrated that the probabilistic nature of diffusion models effectively handles data and label uncertainty, leading to more robust predictions. Conditioned on discriminative feature and label information, diffusion models offer a promising solution for the noisy labels in Med-VQA, using their stochastic nature to reconstruct class prototypes during reverse sampling and generate probability intervals across class labels.", + "bbox": [ + 511, + 378, + 906, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To improve Med-VQA performance in the presence of noisy labels and harness the benefits of diffusion models, we propose the conditional Diffusion model for Med-VQA with Noisy labels (DiN) framework to address challenging semantic noisy labels. To mimic human-like mislabeling, we construct the training set by replacing ground-truth answers with semantically related noisy pairs, selected using a pre-trained BERT model. To the best of our knowledge, this is the first study addressing Med-VQA with noisy labels and the first application of diffusion models to this task. Our framework comprises three key modules. The Answer Denoiser (AD) module leverages robust conditional diffusion models, utilizing their powerful gradual refinement capabilities for Med-VQA. As shown in Figure 1, the generative process begins with a noisy label estimation, which is progressively refined to recover a clean label, analogous to the reverse denoising process in diffusion models. This allows coarse-to-fine filtering of potential answers, significantly improving accuracy and robustness. However, the effectiveness of the AD module's refinement is highly dependent on the generation conditions, and the lack of accurate clean labels exacerbates this challenge. To this end, we further pro", + "bbox": [ + 511, + 568, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14338", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pose the Answer Condition Generator (ACG) and Noisy Label Refinement (NLR) module to provide more accurate and reliable conditions. The ACG adopts a transformer decoder to fuse multi-modal image and question features, as well as learnable candidate embedding for delivering more informative generation conditions. The NLR, utilized only during training, refines noisy ground-truth labels dynamically through pseudo-labels generated by an auxiliary classifier to supervise the AD module. This synergy across modules enhances precision and robustness in managing noisy labels for Med-VQA tasks.", + "bbox": [ + 89, + 90, + 480, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our main contributions are summarized as follows.", + "bbox": [ + 109, + 258, + 447, + 272 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the DiN framework, the first to address MedVQA tasks with noisy labels (NM-VQA) by integrating a diffusion model that classifies answers from a generative and coarse-to-fine perspective.", + "- We introduce semantic noise types tailored to Med-VQA tasks and construct challenging benchmark datasets that simulate human labeling errors based on an thorough analysis of existing datasets.", + "- We design the Answer Condition Generator (ACG) and Noisy Label Refinement (NLR) modules to support the diffusion-based Answer Diffuser (AD). ACG guides AD with conditions, while NLR refines noisy labels using pseudo-labels from an auxiliary classifier.", + "- Our method consistently outperforms existing approaches on two Med-VQA datasets with varying noise ratios, demonstrating its robustness and effectiveness." + ], + "bbox": [ + 91, + 273, + 482, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 531, + 232, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Medical Visual Question Answering", + "text_level": 1, + "bbox": [ + 89, + 556, + 401, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Med-VQA is still in its early stages, and its current performance remains unsatisfactory. Most methods, such as those in [7, 27, 30, 31], adopt a classification-based approach, where each answer is treated as a class, and a model predicts the answer by applying classification to the fused image-question features. This classification-based approach simplifies the task by reducing its complexity and narrowing the answer search space. Alternatively, some studies [8, 19] approach VQA as a generation problem, generating answers word by word. These generation-based methods face challenges due to the vast search space, often leading to inaccurate answers, which limits their effectiveness in medical VQA. However, existing Med-VQA methods assume that the entire training dataset consists of clean labels, overlooking the challenge of noisy labels (NM-VQA). To address this gap, we introduce Med-VQA datasets with noisy labels and propose a solution for the NM-VQA problem.", + "bbox": [ + 89, + 579, + 482, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Learning with Noise Labels and Noise Types", + "text_level": 1, + "bbox": [ + 89, + 847, + 467, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning with noise labels has been extensively studied in recent works. For example, some methods estimated", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "noise transition matrices to correct label noise in a class-wise manner [11, 22]. Other popular methods reduced the effects of noisy labels by using noise-tolerant loss functions [47]. However, these methods tend to perform poorly when confronted with high noise rates and a large number of classes in Med-VQA tasks. One typical alternative way is coteaching-based methods CoDis [44], which require two branch networks, and introduce a double number of additional parameters, thereby exacerbating the issue of model complexity in Med-VQA tasks that necessitate both image and text encoders within a single network. Given these challenges, it is valuable to explore methods for developing robust Med-VQA models under reasonable noisy data. Most methods to deal with artificially synthesized noisy labels were initially proposed for classification tasks [17]. In these studies, synthesized noisy labels typically focus on both symmetric and asymmetric label noise. Symmetric noise flips labels randomly with equal probability, while asymmetric noise flips labels based on fixed rules. However, when it comes to Med-VQA tasks, symmetric and asymmetric noise models appear unreasonable. Unlike the traditionally synthesized label noise for classification, we propose the semantic label noise for Med-VQA tasks.", + "bbox": [ + 511, + 90, + 903, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Diffusion Models", + "text_level": 1, + "bbox": [ + 513, + 449, + 681, + 464 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models [2, 18, 32, 33, 45] are a new class of generative model. During training, they initially add noise to labels through a forward process until they approximate a Gaussian distribution. Then, in the reverse process, they learn to denoise and recover the original labels [15, 37, 48]. In recent years, their remarkable success in the generative domain, particularly in visual generation [33], has been groundbreaking, completely surpassing previous generative models. Due to its progressive refinement of labels and continuous improvements in training and inference efficiency, the diffusion model has been applied in various fields, such as recommendation systems [40] and image detection [5]. For example, the CARD [12] model transforms deterministic classification into a conditional label generation process, enabling more flexible uncertainty modeling in the labeling process. However, to our knowledge, diffusion models have not yet been applied to tackle Med-VQA tasks. Therefore, to address this gap, we aim to fully leverage the unique characteristics of diffusion models for Med-VQA tasks.", + "bbox": [ + 511, + 472, + 906, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 513, + 775, + 611, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem setting", + "text_level": 1, + "bbox": [ + 513, + 800, + 669, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the context of Med-VQA tasks with noisy labels (NMVQA) problem, our task involves an input set of medical images $\\mathcal{V} = \\{v_{i}\\}_{i = 1}^{N}$ and a set of questions $\\mathcal{Q} = \\{q_j\\}_{j = 1}^M$ with the corresponding answers $\\mathcal{A} = \\{a_j\\}_{j = 1}^M$ . Each image $v_{i}$ is associated with $M_{i}$ questions and answers,", + "bbox": [ + 511, + 823, + 903, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14339", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/31fd7da671a952ebd0d89229b86a349d4a5c18645aad210c955259fe5254dae0.jpg", + "image_caption": [ + "Figure 3. The proposed DiN framework consists of three key modules: 1) Answer Condition Generator (ACG): This module interacts the image and question multi-modal features with features of the image-question pair knowledge from Answer Condition Embedding (ACE) to obtain Med-VQA condition information. 2) Noisy Label Refinement (NLR): This module contains a robust loss function, $\\mathcal{L}_{RFL}$ , which supervises the proto-answer, to mitigate the impact of noisy original answers on the two encoders' acquisition of medical domain knowledge. The Answer adjustment of NLR uses proto-answers and original noisy answers to generate pseudo-label to supervise the AD module. 3) Answer Diffuser (AD): This module refines the noisy answer distribution, simulating a generation process to select the correct answers. Notably, we use only the AD Module to predict answers without the NLR module during inference process." + ], + "image_footnote": [], + "bbox": [ + 138, + 90, + 864, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "while $\\sum_{i=1}^{N} M_i$ equals $M$ . For the convenience of description, we use the subscript $k$ to represent the index of each image-question-answer pair and there are $K$ image-question-answer pairs in total. Specifically, $v_k \\in \\mathbb{R}^{H \\times W \\times C}$ represents an input image with a size of $H \\times W$ and $C$ channels, while $a_k \\in \\{0,1\\}^L$ serves as the one-hot encoded ground truth answer label, where $L$ is the total number of answer classes. Note that only noisy labels are available during the training stage, while the clean labels are only available during the inference stage and are used solely for validating the model's performance.", + "bbox": [ + 88, + 503, + 486, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overview", + "text_level": 1, + "bbox": [ + 89, + 681, + 202, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The DiN framework, shown in Figure 3, comprises three main modules: Answer Condition Generator module (ACG) introduced in Sec. 3.3, Noisy Label Refinement module (NLR) described in Sec. 3.4, and Answer Diffuser module (AD) detailed in Sec. 3.5. The input image $v_{k}$ and question $q_{k}$ are processed by Vision Encoder and Text Encoder, respectively, to extract visual features $f_{k}^{v}$ and question features $f_{k}^{q}$ . The fused features produce key embeddings $K_{ey}$ and value embeddings $V_{value}$ , which are fed into the ACG module. There, they interact with learnable answer embeddings $Q_{uery}$ to generate an answer-aware condition $f_{k}^{c}$ . This condition is then used by the AD module to generate the predicted answer $y_{k}$ via a denoising pro", + "bbox": [ + 89, + 703, + 485, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "cess. Simultaneously, $f_{k}^{c}$ is fed into the NLR module to train an auxiliary classifier, which yields a proto-answer $\\hat{y}_k$ . The proto-answer is then refined to create a pseudo-label $\\bar{y}_n$ used to supervise the generation of the $y_{k}$ . Note that the NLR module will be discarded in the inference stage, and the AD module will generate the answer predictions.", + "bbox": [ + 511, + 505, + 908, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Answer Condition Generator Module", + "text_level": 1, + "bbox": [ + 511, + 604, + 839, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The newly proposed ACG module is designed to generate an answer-aware condition, $f_{k}^{c}$ , for Noisy Label Refinement module (NLR) and Answer Diffuser module (AD). As introduced in Sec. 3.2, we obtain visual features $f_{k}^{v}$ and question features $f_{k}^{q}$ from input images and questions by Vision Encoder and Text Encoder. These features are then fused to produce key embeddings $K_{ey}$ and value embeddings $V_{value}$ , which are fed into the ACG module. In the ACG module, we introduce learnable candidate answer embeddings to query the existence of each answer class to a given image-question pair. For the $L$ answer classes, we need $L$ candidate answer embeddings initialized randomly and updated during training. A self-attention mechanism is applied to compute relationships between the answer embeddings, yielding query embeddings $Q_{query}$ . Cross-attention is then used to combine $Q_{query}$ with $K_{ey}$ and $V_{value}$ , producing a fused feature $f_{k}^{f}$ that captures the interaction between answer embeddings and image-question features. Finally, the", + "bbox": [ + 511, + 626, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14340", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "feature $f_{k}^{c} = \\mathrm{Linear}(f_{k}^{f})$ is generated as conditions to guide the generative process in the AD module, while $f_{k}^{f}$ is simultaneously sent to the NLR module to train the auxiliary classifier.", + "bbox": [ + 89, + 89, + 480, + 154 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Noisy Label Refinement Module", + "text_level": 1, + "bbox": [ + 89, + 162, + 375, + 179 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering that the model learning will suffer severely from label noise, in this part, we tackle the problem by proposing a Noisy Label Refinement module (NLR), where we first propose a new noise robust loss function to improve the noise resilience of our method and we further come up with an answer adjustment strategy to generate accurate refined pseudo-label $\\bar{y}_k$ to supervise the generation of $y_{k}$ in the Answer Diffuser module.", + "bbox": [ + 89, + 184, + 483, + 304 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we first feed the condition $f_{k}^{c}$ into an auxiliary classifier, which is a one-layer linear MLP, to generate the proto-answer probability distribution $\\hat{p}_{k}$ . However, on one hand, the noisy supervision $a_{k}$ will greatly influence the accuracy of the proto-answer. On the other hand, the class imbalance problem in Med-VQA is much more severe than other tasks, such bias will severely influence the answer generation. Therefore, we introduce a new noise robust focal loss function (RFL) to tackle the issues, where we incorporate a symmetric cross entropy loss with a focal loss, aiming to improve noise resilience and balance the effects of class imbalance. The RFL is then formulated as follows:", + "bbox": [ + 89, + 306, + 483, + 487 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {R F L} = - \\sum_ {l = 1} ^ {L} a _ {k} (1 - \\hat {p} _ {k}) ^ {\\gamma} \\log \\hat {p} _ {k} - \\sum_ {l = 1} ^ {L} \\hat {p} _ {k} \\log a _ {k}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 496, + 483, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma$ is the hyper-parameter and we set $\\gamma = 1$ by default.", + "bbox": [ + 89, + 547, + 482, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Benefiting from our newly proposed RFL loss, the model is prone to generate correct answers during the training process. Therefore, we further propose an Answer Adjustment (AA) strategy to generate a set of accurate refined pseudolabels to supervise the generation of $y_{k}$ in the Answer Diffuser module. In particular, we assume the given answer is clean if the predicted proto-answer matches the original answer, otherwise, we generate a soft label using a weighted combination of the predicted proto-answer $\\hat{p}_k$ and the given noisy label distribution $a_{k}$ , which can be denoted as:", + "bbox": [ + 89, + 563, + 483, + 713 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {y} _ {k} = \\left\\{ \\begin{array}{l l} w _ {t} \\hat {p} _ {j} + (1 - w _ {t}) a _ {k}, & \\hat {p} _ {k} \\neq a _ {k} \\\\ a _ {k}, & \\hat {p} _ {k} = a _ {k} \\end{array} , \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 724, + 483, + 766 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{t}$ is the weighting parameter. Note that the learning status can be estimated by the confidence scores of the predictions [10], we thereby design $w_{t}$ based on the model's prediction reflecting the overall learning status. Given the current training iteration $t$ , we denote $w_{t}$ as:", + "bbox": [ + 89, + 775, + 483, + 851 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {t} = \\tau w _ {t - 1} + (1 - \\tau) \\frac {1}{B} \\sum_ {k = 1} ^ {B} \\hat {p} _ {k}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 862, + 483, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau \\in (0,1)$ is the momentum decay of EMA, set as 0.99. The $B$ indicates the number of samples within a minibatch. Through the newly proposed answer adjustment strategy, we can obtain a set of accurate refined pseudolabels $\\bar{y}$ to supervise the generation of the final prediction $y$ in the Answer Diffuser module, which will greatly improve the prediction performance of the model.", + "bbox": [ + 511, + 90, + 905, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Answer Diffuser Module", + "text_level": 1, + "bbox": [ + 511, + 205, + 741, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the ability of diffusion-based classifiers to manage data and label uncertainty effectively, we propose a diffusion-based classifier called the Answer Diffuser module. This module addresses the unique challenges of NM-VQA by classifying answers from a generative perspective, which helps mitigate issues like generating non-existent answers—a common problem in handling noisy labels [4, 12]. By using refined soft labels as supervision, the Answer Diffuser produces accurate, noise-resistant predictions that are particularly robust in noisy-label settings.", + "bbox": [ + 511, + 227, + 905, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the condition feature $f^c$ and the refined soft label $\\bar{y}$ , following the forward and reverse process of the diffusion models, we gradually introduce noise to the refined soft label $\\bar{y}$ to obtain the noisy label $\\bar{y}_T$ after $T$ steps, and progressively refine a random probability distribution $\\bar{y}_T$ to predict the answer distribution $y$ that is close to the pseudo-label distribution $\\bar{y}$ after $T$ steps. Notably, the forward can be represented as:", + "bbox": [ + 511, + 378, + 906, + 500 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\bar {y} _ {t} | \\bar {y} _ {t - 1}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t}; \\mu_ {t} \\left(\\bar {y} _ {t - 1}, f ^ {c}, t\\right), \\beta_ {t} \\mathbf {I}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 508, + 906, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {t} = \\sqrt {1 - \\beta_ {t}} \\bar {y} _ {t - 1} + (1 - \\sqrt {1 - \\beta_ {t}}) f ^ {c}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 535, + 905, + 554 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta_{t}$ is the variance schedule. Consequently, obtaining $\\bar{y}_t$ with an arbitrary timestep $t$ can be represented as:", + "bbox": [ + 511, + 559, + 905, + 590 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\bar {y} _ {t} | \\bar {y}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\bar {y} + \\left(1 - \\sqrt {\\bar {\\alpha} _ {t}}\\right) f ^ {c}, \\left(1 - \\bar {\\alpha} _ {t}\\right) \\mathbf {I}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 599, + 905, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where $\\alpha_{t} = 1 - \\beta_{t}$ and $\\bar{\\alpha}_{t} = \\prod_{t}\\alpha_{t}$ . It should be noted that $\\mu_{t}$ can be viewed as an interpolation between soft pseudo-label $\\bar{y}$ from NLR module and the predicted condition $f^{c}$ from ACG module, which gradually generates task-specific conditional information to suit the NM-VQA task.", + "bbox": [ + 511, + 626, + 905, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The reverse process continuously perform denoising process from $\\bar{y}_T$ to obtain $y$ , which we hope to be close to $\\bar{y}$ , where we learn a diffusion model $\\theta$ to predict the noise level at each timestep, which can be represented as:", + "bbox": [ + 511, + 702, + 905, + 762 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\bar {y} _ {t - 1} \\mid \\bar {y} _ {t}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t - 1}; \\mu_ {\\theta} \\left(\\bar {y} _ {t}, f ^ {c}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 771, + 903, + 790 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $\\mu_{\\theta}(\\bar{y}_t, f^c, t)$ is predicted mean value of the noise distribution at timestep $t$ , $\\sigma_t^2$ is $\\frac{1 - \\bar{\\alpha}_{t-1}}{1 - \\bar{\\alpha}_t} \\beta_t$ . Our target is to encourage the predicted answer distribution to be close to the refined pseudo-label distribution $\\bar{y}$ . Therefore, we adopt a MSE loss as a supervision, which can be denoted as:", + "bbox": [ + 511, + 799, + 905, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i f} = \\operatorname {M S E} (y; \\bar {y}). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 642, + 885, + 903, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14341", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Training and Inference", + "text_level": 1, + "bbox": [ + 89, + 90, + 303, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During the training process, we jointly optimize $\\mathcal{L}_{dif}$ and $\\mathcal{L}_{RFL}$ , which on one hand targets at generating refined correct pseudo-labels that are robust to label noise as the supervision for our Answer Diffuser, on the other hand, we encourage the Answer Diffuser to generate existent and accurate answer predictions, further reducing the impact of noisy labels. Therefore, the overall loss during training can be expressed as:", + "bbox": [ + 89, + 112, + 483, + 233 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d i f}} + \\alpha \\mathcal {L} _ {R F L}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 247, + 483, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha$ is hyperparameter to balance different losses.", + "bbox": [ + 89, + 276, + 449, + 290 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It should be noticed that during the inference stage, we only adopt the AD Module to predict answers while discarding the NLR module, as the NLR module targets at providing a precise supervision for the AD module learning. The corresponding noisy distribution $\\bar{y}_T$ is replaced with randomly generated Gaussian noise. The model gradually refines the random distribution through the reverse process and obtains the final predicted probability distribution $y$ . The ultimate prediction class label $\\hat{y} = \\arg \\max_l(y_l)$ , where $l$ indicates the index of the categories, is the answer with the highest probability score.", + "bbox": [ + 89, + 291, + 483, + 457 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 89, + 472, + 215, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 89, + 497, + 192, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "VQA-RAD [20] is the most widely used radiology dataset for Med-VQA, comprising 315 images and 3,515 question-answer pairs, with each image corresponding to at least one question-answer pair. $58\\%$ of the questions are close-end questions and the rest are openend questions. PathVQA [14] is constructed by extracting images along with corresponding captions from digital resources such as electronic textbooks and online libraries. It consists of 32,799 question-answer pairs, including 4,998 pathology images. Open-end questions account for $50.2\\%$ of all questions and the rest are closed questions. To ensure comparability, both of the datasets have been divided following the MMQ method [7].", + "bbox": [ + 89, + 518, + 483, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Noise Patterns and Analysis", + "text_level": 1, + "bbox": [ + 89, + 726, + 341, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Due to the lack of suitable Med-VQA datasets with noisy labels and the difficulty of creating new datasets, we adopt semantic noisy types from the natural VQA domain [47] to existing medical VQA datasets. [47] demonstrates controlled semantic label noise by simulating human mislabeling behavior, which is more realistic than conventional random noise. We also follow the conventional VQA methods to validate our model by random label shuffling.", + "bbox": [ + 89, + 750, + 482, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The questions in Med-VQA tasks include two categories: closed-end (e.g., Yes/No questions with one-word", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "answers) and open-end (e.g., wh-questions with longer responses). Following [47], for closed-ended answers, we use symmetric noise by randomly flipping the answer choices. Moreover, for open-ended answers, we create a semantic space of frequent answers using a pre-trained BERT model [21] to simulate human annotation errors. For each sample, the original answer is replaced by its closest noisy label within this semantic space. Our experiments highlight the sensitivity of prior Med-VQA methods to noisy labels, and we evaluate performance using $10\\%$ and $20\\%$ semantic noise ratios in the training datasets of VQA-RAD and PathVQA. Figure 2 visualizes our noisy pairs and the t-SNE representation of the semantic space, where ground-truth labels are replaced with semantically similar noisy labels. Moreover, we compare the performance of different methods by introducing random noise with a $20\\%$ noise ratio into the training datasets of VQA-RAD and PathVQA. As shown in Table 1 and Table 2, at the same noise ratio, semantic noise impacts model performance more significantly than random noise and more closely resembles the type of noise encountered in actual clinical scenarios.", + "bbox": [ + 511, + 90, + 906, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 511, + 420, + 732, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method is trained on a single Nvidia 3090Ti GPU. We employ the Swin Transformer [28] as the vision encoder and the BERT model [21] as the text encoder. Our baseline model contains the Swin Transformer and BERT as encoder with transformer decoder without any answer denoise methods. The Adam optimizer is used, with an initial learning rate set to 1e-5. We adopt a batch size of 16 and a maximum of 100 epochs. The loss weight $\\alpha$ is set to 0.5 for both datasets. For our model evaluation, we use only the AD Module to predict answers without the NLR module to ensure that the model parameters are at a similar level to those of other methods for comparison. The DiN framework is trained in an end-to-end fashion. The Med-VQA performance is assessed by accuracy scores.", + "bbox": [ + 511, + 441, + 908, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Performance Comparison", + "text_level": 1, + "bbox": [ + 511, + 666, + 750, + 683 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our proposed method with MMBERT [19] and Q2ATransformer [27], which are among the top performers in Med-VQA task. Notably, previous Med-VQA methods were not designed to address the issue of noisy labels. To fill this gap, we employ two mainstream uni-modal label denoising methods to compare. SimT [11] estimates noise transition matrices to correct label noise in a class-wise manner. CoDis [44], a co-teaching-based label denoising method, uses two sub-networks to select the clean label dataset based on the small-loss principle. We also compare our method with SNLC [47], the first method designed for natural VQA with noisy labels. As shown in Table 1 and Table 2, our DiN framework consistently outperforms the compared models on both datasets. The biggest drawback", + "bbox": [ + 511, + 688, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14342", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/269c9c2dc1151177cbdfd2bdf70af85706ca0f942112d219c6b8578112948241.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Performance comparison on the VQA-RAD dataset. 'Open' indicates the open-end question and 'close' indicates the close-end question. The overall performance is the average performance of both question types. The best results are bold. Notably, SimT [11] and CoDis [44] are up-to-date representatives of NTM-based and co-teaching-based approaches, respectively." + ], + "table_body": "
    Noise TypeMethodVQA-RAD
    OpenCloseOverall
    CleanUpper Bound78.1780.0879.13
    10%-Semantic NoiseBaseline67.8668.8568.25
    MMBERT [19]63.3668.2166.42
    Q2ATransformer [27]66.7970.1768.48
    SimT [11]66.9369.7368.04
    CoDis [44]68.0270.5469.53
    SNLC [47]67.8371.3569.65
    DiN (Ours)72.6875.8174.24
    20%-Semantic NoiseBaseline54.2357.1456.01
    MMBERT [19]52.6856.6455.25
    Q2ATransformer [27]55.4360.0358.25
    SimT [11]53.7657.0555.82
    CoDis [44]54.1957.2856.42
    SNLC [47]56.4561.3058.88
    DiN (Ours)58.0663.1762.28
    20%-Random NoiseBaseline56.7160.3058.88
    MMBERT [19]55.4359.5957.97
    Q2ATransformer [27]58.0462.3760.68
    SimT [11]57.8662.8560.90
    CoDis [44]59.9560.5660.32
    SNLC [47]59.2163.8462.03
    DiN (Ours)61.0465.7763.93
    ", + "bbox": [ + 109, + 88, + 467, + 347 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of these two Med-VQA methods is that neither is designed to address the issue of noisy labels, so they cannot prevent overfitting noisy patterns during the training process for NM-VQA tasks. SimT [11] did not bring significant performance improvements, primarily due to the limitations of the noise transition matrix (NTM), which only effectively captures noise patterns in simple noisy classification tasks. CoDis [44] performed better than NTM-based methods; but its two-branch co-teaching method doubles the parameters and uses a small-loss selection strategy better suited for simpler noise. SNLC [47], designed for noisy labels in natural VQA, relies on a basic robust loss function and fails to deliver competitive performance in the medical domain. In contrast, our DiN framework is specifically tailored for noisy labels in Med-VQA tasks. Figure 4 visualizes four examples of predicted answers from both the training and test sets across two datasets. In the training set, our method successfully corrects semantic noisy labels post-training, while in the test set, our model generates accurate predictions in multiple instances. This design allows DiN to consistently outperform other methods, demonstrating its effectiveness in addressing the unique challenges of NM-VQA tasks.", + "bbox": [ + 91, + 476, + 482, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 829, + 243, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To assess the contributions of our DiN framework, we conducted extensive ablation studies to demonstrate the efficiency of the different components of our model.", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a30b523cfe025dcf570c07583167a5c27b628e130f5f84338439404613e4b180.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Performance comparison on the PathVQA dataset. 'Open' indicates the open-end question and 'close' indicates the close-end question. The overall performance is the average performance of both question types. The best results are bold. Notably, SimT [11] and CoDis [44] are up-to-date representatives of NTM-based and co-teaching-based approaches, respectively." + ], + "table_body": "
    Noise TypeMethodPathVQA
    OpenCloseOverall
    CleanUpper Bound52.6486.4572.61
    10%-Semantic NoiseBaseline37.8375.8162.32
    MMBERT [19]34.1873.2158.73
    Q2ATransformer [27]38.4276.8562.61
    SimT [11]36.5475.3562.06
    CoDis [44]37.8676.2863.02
    SNLC [47]38.8578.3364.18
    DiN (Ours)40.5480.2866.67
    20%-Semantic NoiseBaseline29.0670.0155.28
    MMBERT [19]27.1368.3552.41
    Q2ATransformer [27]30.1671.1156.28
    SimT [11]29.3870.6955.93
    CoDis [44]30.3671.1856.55
    SNLC [47]30.8871.2356.72
    DiN (Ours)32.4772.5658.14
    20%-Random NoiseBaseline32.2973.5357.03
    MMBERT [19]30.4572.0655.41
    Q2ATransformer [27]34.5074.7458.64
    SimT [11]35.1774.9159.01
    CoDis [44]35.6674.5058.96
    SNLC [47]36.7475.0359.71
    DiN (Ours)37.8576.1660.84
    ", + "bbox": [ + 532, + 88, + 887, + 347 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/801c448f4c01459c27d945f6a79722c01aec3a975f1771e224f9d57d52aa2b65.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Ablation study of our method on the VQA-RAD dataset with $10\\%$ -Semantic Noise. ACG indicates our answer condition generator module, AD indicates our answer diffuser module. Note that our noisy label refinement module includes two parts, i.e., an answer adjust module (AA) and a noise robust focal loss function (RFL). Also note that the baseline method includes the vision encoder and the text encoder (Encoder), the auxiliary classifier (Classifier) and our ACG module." + ], + "table_body": "
    ChoiceEncodersClassifierACGADRFLAAOpenCloseOverallOpenCloseOverall
    0✓✓✓67.8668.8568.2554.2357.1456.01
    1✓✓✓✓68.4670.7169.5655.0859.2757.64
    2✓✓✓✓70.7171.9271.1555.8660.8659.13
    3✓✓✓✓✓70.7373.0872.2556.2161.5460.57
    4✓✓✓✓✓71.1574.2972.7556.9762.2061.24
    5✓✓✓✓✓✓72.6875.8174.2458.0663.1762.28
    ", + "bbox": [ + 516, + 458, + 911, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5.1. Impact of Answer Condition Generator", + "text_level": 1, + "bbox": [ + 511, + 667, + 834, + 683 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The ACG module provides conditional information to support the generative process in the AD module and features for training the auxiliary classifier in the NLR module. When only the encoders, ACG, and the auxiliary classifier are used for answer prediction (i.e., the fused image-question features are sent through ACG to interact with the candidate answer embeddings, and the output feature $f_{k}^{c}$ is used to train the auxiliary classifier), the accuracy is limited to $68.25\\%$ overall accuracy (Choice 0 in Table 3), primarily due to rapid overfitting and the inability to effectively handle noisy labels. Notably, incorporating the AD module with the conditional information from ACG significantly enhances the overall accuracy to $71.15\\%$ (Choice 2). The ACG module not only enhances the auxiliary classi", + "bbox": [ + 511, + 688, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14343", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b74ab40e8180e9815bfad6a792dd23dfc6851340cd590a3ad9433e082242ba15.jpg", + "image_caption": [ + "Train Set with Noisy Answers", + "Test Set without Answers", + "Figure 4. Visualization of example results from our DiN framework on the VQA-RAD and PathVQA datasets. The first row presents examples from the training set with $10\\%$ -Semantic Noise, where our method corrects the noisy incorrect answers during the training process. The second row shows two examples from the test sets of both datasets." + ], + "image_footnote": [], + "bbox": [ + 133, + 88, + 259, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cf25b1b2dcc3de79481d3492b703e91baefed1a499fa8568234770061b72c566.jpg", + "image_caption": [], + "image_footnote": [ + "Question: Where is/are the lesion located?", + "Noisy Answers : Left temporal lobe", + "Our Prediction: Right temporal lobe" + ], + "bbox": [ + 465, + 128, + 491, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4f7ddf81e80f6d5b49a5d88a8533e0437aab68204363ce9fde23dd49ad459fb6.jpg", + "image_caption": [ + "Train Set with Noisy Answers", + "Test Set without Answers" + ], + "image_footnote": [], + "bbox": [ + 495, + 90, + 630, + 164 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e8510b7b4a05bbf9202d52b29c8f1c0ff09af110b03e9053aa94eb3e5fd26096.jpg", + "image_caption": [], + "image_footnote": [ + "Question: What shows the bland cytology that typifies neuroendocrine tumors?", + "Noisy Answers : Low magnification", + "Our Prediction : High magnification" + ], + "bbox": [ + 834, + 138, + 862, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/031c34d8e5f701a714e01e1af22441675e71f5692d1fd759c0482de9b7768d57.jpg", + "image_caption": [], + "image_footnote": [ + "Question: What type of sequence is displayed in this image?", + "Our Prediction : T2 weighted MRI" + ], + "bbox": [ + 460, + 217, + 480, + 234 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7eb0f32f5575ee0c47c67c507ddbf567de2ea5976c87ad1ab3e01f43b94f4e26.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 514, + 166, + 607, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7932e2226505010c3b7696e84342c8b372f10bd146230ef65fe436b6d07deffd.jpg", + "image_caption": [], + "image_footnote": [ + "Question: What is the poorly cohesive tumor in the retina seen abutting?", + "Our Prediction : Optic nerve" + ], + "bbox": [ + 802, + 218, + 821, + 233 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/732664f98b27dc4d0ca279fef8c306114bf304fc784a32ef141a96a679c97b12.jpg", + "table_caption": [ + "VQA-RAD", + "PathVQA" + ], + "table_footnote": [], + "table_body": "
    NameChoiceVQA-RAD with 10% Noise
    OpenCloseOverall
    \\(L_r\\)CE [49]70.7373.0872.25
    Focal [24]71.4373.8573.10
    SCE [41]71.8673.8673.50
    RFL (ours)72.6875.8174.24
    \\(L_{dif}\\)KL72.8675.3874.00
    MSE72.6875.8174.24
    \\(\\alpha\\)0.171.7974.2373.75
    0.572.6875.8174.24
    172.1675.9274.18
    Step T1072.5175.7674.03
    5072.6875.8174.24
    10071.9374.6673.87
    ", + "bbox": [ + 158, + 339, + 416, + 493 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation studies on different hyperparameters, i.e., $\\alpha$ that balances different loss functions and the number of timesteps $T$ in our answer diffuser module, and ablation studies on different options of loss functions in our noisy label refinement module.", + "bbox": [ + 89, + 503, + 483, + 560 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "fier's ability to capture medical domain knowledge but also strengthens the diffusion-based AD module by providing reliable Med-VQA condition information.", + "bbox": [ + 89, + 585, + 483, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5.2. Impact of Noisy Label Refinement", + "text_level": 1, + "bbox": [ + 89, + 638, + 375, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Noisy Label Refinement (NLR) module comprises two sub-components: Robust Loss (RFL) and answer adjustment (AA). The RFL is designed to mitigate the impact of noise on the encoders' features. As shown in Table 3, incorporating the RFL leads to an increase in overall accuracy from $68.25\\%$ to $69.56\\%$ without using AD module and from $71.15\\%$ (Choice 2) to $72.75\\%$ (Choice 4) with AD module. We experimented with different combinations of robust loss functions and found that our proposed RFL is the most effective for NM-VQA tasks, as demonstrated in Table 4. The answer adjustment (AA) component is specifically designed to reduce noise impact on the Answer Diffuser (AD) module. The addition of the AA component enhances the overall accuracy from $71.15\\%$ (Choice 2) to $72.25\\%$ (Choice 3) and further from $72.75\\%$ (Choice 4) to $74.24\\%$ (Choice 5) with the assistance of RFL.", + "bbox": [ + 89, + 657, + 483, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5.3.Impact of Answer Diffuser", + "text_level": 1, + "bbox": [ + 511, + 343, + 746, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Table 3, incorporating the AD module for Med-VQA prediction enhances the overall performance from $68.25\\%$ (Choice 0) to $71.15\\%$ (Choice 2). When all our proposed modules are combined, the overall performance further improves to $74.24\\%$ (Choice 5). We also examined the hyperparameter $\\alpha$ , which balances the AD module and the auxiliary classifier, and the type of $L_{dif}$ as detailed in Table 4. Our framework demonstrates insensitivity to both choices. We selected $\\alpha = 0.5$ and MSE loss as $L_{dif}$ . Furthermore, we investigated the impact of varying $T$ on model performance, as presented in Table 4. While increasing $T$ results in higher computational costs, our model achieves optimal performance at $T = 50$ . This differs from the image generation, where 1000 steps are typically used. This distinction is likely due to the precise pixel-level generation required in image tasks, whereas our model focuses on deriving a class probability distribution.", + "bbox": [ + 511, + 364, + 906, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 648, + 633, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In conclusion, we have introduced DiN as the first approach to address the Med-VQA with noisy labels. Our method uses the inherent robustness of diffusion models as AD module to deal with noisy data. We designed the ACG module to fuse image, question features and candidate answering embeddings, generating condition information supporting both the AD and NLR modules. Additionally, the NLR module reduces the effect of noisy labels with robust loss functions and refines the original answers to produce pseudo-labels, further improving model performance. Extensive experiments validate the superiority of our DiN framework. While our method has some limitations, the diffusion model introduces Gaussian noise during training, which may slightly increase training time but does not affect inference time.", + "bbox": [ + 511, + 676, + 906, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14344", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahul Ambati and Chakravardhan Reddy Dudyala. A sequence-to-sequence model approach for imagecef 2018 medical domain visual question answering. In 2018 15th IEEE India Council International Conference (INDICON), pages 1-6. IEEE, 2018. 2", + "[2] James Betker, Gabriel Goh, Li Jing, Tim Brooks, Jianfeng Wang, Linjie Li, Long Ouyang, Juntang Zhuang, Joyce Lee, Yufei Guo, et al. Improving image generation with better captions. 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Springer, 2024. 1" + ], + "bbox": [ + 516, + 92, + 903, + 852 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14346", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/3d88adc0-2039-46a2-83ba-83308b59f70d_model.json b/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/3d88adc0-2039-46a2-83ba-83308b59f70d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e1a0055792a1d0533b04ad72dc3455ebe7004f7d --- /dev/null +++ b/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/3d88adc0-2039-46a2-83ba-83308b59f70d_model.json @@ -0,0 +1,2365 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.119, + 0.131, + 0.88, + 0.152 + ], + "angle": 0, + "content": "DiN: Diffusion Model for Robust Medical VQA with Semantic Noisy Labels" + }, + { + "type": "text", + "bbox": [ + 0.151, + 0.18, + 0.852, + 0.218 + ], + "angle": 0, + "content": "Erjian Guo1 Zhen Zhao2 Zicheng Wang1 Tong Chen1 Yunyi Liu1 Luping Zhou1* \n1University of Sydney Shanghai AI Laboratory" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.252, + 0.327, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.283, + 0.485, + 0.617 + ], + "angle": 0, + "content": "Medical Visual Question Answering (Med-VQA) systems benefit the interpretation of medical images containing critical clinical information. However, the challenge of noisy labels and limited high-quality datasets remains underexplored. To address this, we establish the first benchmark for noisy labels in Med-VQA by simulating human mislabeling with semantically designed noise types. More importantly, we introduce the DiN framework, which leverages a diffusion model to handle noisy labels in Med-VQA. Unlike the dominant classification-based VQA approaches that directly predict answers, our Answer Diffuser (AD) module employs a coarse-to-fine process, refining answer candidates with a diffusion model for improved accuracy. The Answer Condition Generator (ACG) further enhances this process by generating task-specific conditional information via integrating answer embeddings with fused image-question features. To address label noise, our Noisy Label Refinement(NLR) module introduces a robust loss function and dynamic answer adjustment to further boost the performance of the AD module. Our DiN framework consistently outperforms existing methods across multiple benchmarks with varying noise levels1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.646, + 0.222, + 0.66 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.671, + 0.483, + 0.854 + ], + "angle": 0, + "content": "Medical Visual Question Answering (Med-VQA) tasks focus on accurately responding to medical inquiries by integrating visual information from medical images [6, 26, 39]. It holds great potential in applications like assisting diagnosis, enhancing patient understanding, and supporting clinical education [3, 36]. Recently, VQA models have achieved impressive results in the natural VQA domain [13, 38, 46]. This success has largely been driven by the availability of large-scale natural VQA datasets with well-structured accurate annotations [25, 29]. However, for Med-VQA, the annotation process poses unique challenges. It requires specialized medical expertise and skills from annotators, lead" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.253, + 0.7, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.319, + 0.665, + 0.33 + ], + "angle": 0, + "content": "(a) Classification-based" + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.255, + 0.892, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.756, + 0.319, + 0.85, + 0.328 + ], + "angle": 0, + "content": "(b) Generation-based" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.332, + 0.899, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.466, + 0.907, + 0.579 + ], + "angle": 0, + "content": "Figure 1. Comparison between our diffusion-based method and previous Med-VQA approaches. Previous Med-VQA methods, designed for clean label datasets, include classification-based (a) and generation-based (b) approaches. In contrast, our diffusion-based method (c) classifies answers from a generative perspective and denoises answers by Answer Diffuser with the support of Answer Condition Generator and the Noisy Label Refinement module (employed only during the training process)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.611, + 0.907, + 0.732 + ], + "angle": 0, + "content": "ing to increased complexity and higher potential for label noise [34, 35, 51]. Additionally, inter-observer variability among medical professionals further complicates the annotation process, contributing to labeling inconsistencies [16, 31, 43]. While the issue of noisy labels is a well-known challenge in machine learning, it has not been thoroughly explored in Med-VQA, despite the need for highly accurate medical annotations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "While existing label-denoising methods have shown promise, they are primarily designed for uni-modal tasks like image classification or segmentation [23, 42, 50]. Directly applying them for the multi-modal Med-VQA task is not suitable for two key reasons. First, conventional noise models, such as random label shuffling, fail to capture the semantic nuances essential in Med-VQA, where label noise often retains medically relevant information rather than arbitrary noise. We argue that noisy labels in VQA should retain semantic coherence aligned with human cognitive levels. As shown in Fig. 2, examples of noisy QA" + }, + { + "type": "page_footnote", + "bbox": [ + 0.09, + 0.863, + 0.483, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author, luping.zhou@sydney.edu.au. Zhou is supported by Australian Research Council (ARC DP200103223). \n1Code: https://github.com/Erjian96/DiN" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14337" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.089, + 0.472, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.475, + 0.091, + 0.611, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.475, + 0.191, + 0.611, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.621, + 0.106, + 0.758, + 0.12 + ], + "angle": 0, + "content": "Question Type: Open" + }, + { + "type": "text", + "bbox": [ + 0.621, + 0.12, + 0.878, + 0.135 + ], + "angle": 0, + "content": "Question: Why is free air present in image?" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.135, + 0.754, + 0.147 + ], + "angle": 0, + "content": "Random Noisy: Ribs" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.148, + 0.852, + 0.161 + ], + "angle": 0, + "content": "Semantic Noisy: Hydropneumothorax" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.162, + 0.807, + 0.174 + ], + "angle": 0, + "content": "Ground-truth: Pneumothorax" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.205, + 0.766, + 0.22 + ], + "angle": 0, + "content": "Question Type: Closed" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.22, + 0.815, + 0.234 + ], + "angle": 0, + "content": "Question: Is the heart enlarged?" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.234, + 0.753, + 0.247 + ], + "angle": 0, + "content": "Random Noisy: Skin" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.248, + 0.753, + 0.261 + ], + "angle": 0, + "content": "Semantic Noisy: Yes" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.262, + 0.74, + 0.274 + ], + "angle": 0, + "content": "Ground-truth: No" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.31, + 0.907, + 0.354 + ], + "angle": 0, + "content": "Figure 2. Visualization of the semantic answer pairs in t-SNE and examples of noisy answers. Similar colors represent the degree of feature similarity from a pretrained BERT model. We randomly display 8 semantic pairs in the t-SNE plots of VQA-RAD dataset. Ground-truth labels are replaced with their semantic pairs, which we refer to as semantically noisy answers [47]." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.378, + 0.485, + 0.697 + ], + "angle": 0, + "content": "pairs and their corresponding t-SNE representations illustrate this difference: unlike the arbitrary and meaningless answers generated by random noise, our constructed semantic noise resembles real-world scenarios, closer to human mislabeling. Second, these methods are not equipped to handle the complexity of Med-VQA, which integrates both image and text modalities. For example, co-teaching methods [44] add considerable model complexity by requiring two branch networks, while Noise Transition Matrix (NTM) methods [11] struggle with noisy label distribution estimation as the number of Med-VQA classes grows. While current leading methods like SNLC [47] in the natural VQA domain focus on improving representation through robust contrastive loss, these studies address noise in a relatively coarse way and fall short when dealing with the medically relevant label noise in Med-VQA. For instance, with a \\(20\\%\\) noise ratio, SNLC [47] achieves \\(62\\%\\) accuracy on MedVQA with random noise but drops to \\(58\\%\\) when handling our semantic noise. In summary, our constructed semantic noise in Med-VQA is both practically relevant and presents a more challenging task to effectively handle." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In the literature, two main approaches have emerged for medical VQA: classification-based and generation-based methods, as shown in Figure 1. Classification-based methods are generally straightforward and efficient but often struggle with low-frequency answers, which becomes especially pronounced in complex domains like Med-VQA [1, 9]. In contrast, generation-based methods offer more flexibility by constructing answers instead of selecting from predefined categories; however, they inevitably generate unrealistic or non-existent answers, reducing overall accuracy and reliability [27, 30]. To this end, motivated by the success of diffusion models in label refinement [2, 33], we propose leveraging them to bridge the gap between classi" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.379, + 0.907, + 0.559 + ], + "angle": 0, + "content": "fication and generation approaches, enabling answer classification from a generative perspective. Diffusion models can offer a balance between classification and generative approaches for Med-VQA. Prior studies [4, 12] have also demonstrated that the probabilistic nature of diffusion models effectively handles data and label uncertainty, leading to more robust predictions. Conditioned on discriminative feature and label information, diffusion models offer a promising solution for the noisy labels in Med-VQA, using their stochastic nature to reconstruct class prototypes during reverse sampling and generate probability intervals across class labels." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.909, + 0.903 + ], + "angle": 0, + "content": "To improve Med-VQA performance in the presence of noisy labels and harness the benefits of diffusion models, we propose the conditional Diffusion model for Med-VQA with Noisy labels (DiN) framework to address challenging semantic noisy labels. To mimic human-like mislabeling, we construct the training set by replacing ground-truth answers with semantically related noisy pairs, selected using a pre-trained BERT model. To the best of our knowledge, this is the first study addressing Med-VQA with noisy labels and the first application of diffusion models to this task. Our framework comprises three key modules. The Answer Denoiser (AD) module leverages robust conditional diffusion models, utilizing their powerful gradual refinement capabilities for Med-VQA. As shown in Figure 1, the generative process begins with a noisy label estimation, which is progressively refined to recover a clean label, analogous to the reverse denoising process in diffusion models. This allows coarse-to-fine filtering of potential answers, significantly improving accuracy and robustness. However, the effectiveness of the AD module's refinement is highly dependent on the generation conditions, and the lack of accurate clean labels exacerbates this challenge. To this end, we further pro" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14338" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.257 + ], + "angle": 0, + "content": "pose the Answer Condition Generator (ACG) and Noisy Label Refinement (NLR) module to provide more accurate and reliable conditions. The ACG adopts a transformer decoder to fuse multi-modal image and question features, as well as learnable candidate embedding for delivering more informative generation conditions. The NLR, utilized only during training, refines noisy ground-truth labels dynamically through pseudo-labels generated by an auxiliary classifier to supervise the AD module. This synergy across modules enhances precision and robustness in managing noisy labels for Med-VQA tasks." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.259, + 0.449, + 0.273 + ], + "angle": 0, + "content": "Our main contributions are summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.274, + 0.483, + 0.334 + ], + "angle": 0, + "content": "- We propose the DiN framework, the first to address MedVQA tasks with noisy labels (NM-VQA) by integrating a diffusion model that classifies answers from a generative and coarse-to-fine perspective." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.335, + 0.483, + 0.395 + ], + "angle": 0, + "content": "- We introduce semantic noise types tailored to Med-VQA tasks and construct challenging benchmark datasets that simulate human labeling errors based on an thorough analysis of existing datasets." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.395, + 0.483, + 0.47 + ], + "angle": 0, + "content": "- We design the Answer Condition Generator (ACG) and Noisy Label Refinement (NLR) modules to support the diffusion-based Answer Diffuser (AD). ACG guides AD with conditions, while NLR refines noisy labels using pseudo-labels from an auxiliary classifier." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.471, + 0.483, + 0.515 + ], + "angle": 0, + "content": "- Our method consistently outperforms existing approaches on two Med-VQA datasets with varying noise ratios, demonstrating its robustness and effectiveness." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.274, + 0.483, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.532, + 0.233, + 0.547 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.557, + 0.403, + 0.573 + ], + "angle": 0, + "content": "2.1. Medical Visual Question Answering" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.58, + 0.483, + 0.837 + ], + "angle": 0, + "content": "Med-VQA is still in its early stages, and its current performance remains unsatisfactory. Most methods, such as those in [7, 27, 30, 31], adopt a classification-based approach, where each answer is treated as a class, and a model predicts the answer by applying classification to the fused image-question features. This classification-based approach simplifies the task by reducing its complexity and narrowing the answer search space. Alternatively, some studies [8, 19] approach VQA as a generation problem, generating answers word by word. These generation-based methods face challenges due to the vast search space, often leading to inaccurate answers, which limits their effectiveness in medical VQA. However, existing Med-VQA methods assume that the entire training dataset consists of clean labels, overlooking the challenge of noisy labels (NM-VQA). To address this gap, we introduce Med-VQA datasets with noisy labels and propose a solution for the NM-VQA problem." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.848, + 0.468, + 0.865 + ], + "angle": 0, + "content": "2.2. Learning with Noise Labels and Noise Types" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Learning with noise labels has been extensively studied in recent works. For example, some methods estimated" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.44 + ], + "angle": 0, + "content": "noise transition matrices to correct label noise in a class-wise manner [11, 22]. Other popular methods reduced the effects of noisy labels by using noise-tolerant loss functions [47]. However, these methods tend to perform poorly when confronted with high noise rates and a large number of classes in Med-VQA tasks. One typical alternative way is coteaching-based methods CoDis [44], which require two branch networks, and introduce a double number of additional parameters, thereby exacerbating the issue of model complexity in Med-VQA tasks that necessitate both image and text encoders within a single network. Given these challenges, it is valuable to explore methods for developing robust Med-VQA models under reasonable noisy data. Most methods to deal with artificially synthesized noisy labels were initially proposed for classification tasks [17]. In these studies, synthesized noisy labels typically focus on both symmetric and asymmetric label noise. Symmetric noise flips labels randomly with equal probability, while asymmetric noise flips labels based on fixed rules. However, when it comes to Med-VQA tasks, symmetric and asymmetric noise models appear unreasonable. Unlike the traditionally synthesized label noise for classification, we propose the semantic label noise for Med-VQA tasks." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.45, + 0.682, + 0.465 + ], + "angle": 0, + "content": "2.3. Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.473, + 0.907, + 0.76 + ], + "angle": 0, + "content": "Diffusion models [2, 18, 32, 33, 45] are a new class of generative model. During training, they initially add noise to labels through a forward process until they approximate a Gaussian distribution. Then, in the reverse process, they learn to denoise and recover the original labels [15, 37, 48]. In recent years, their remarkable success in the generative domain, particularly in visual generation [33], has been groundbreaking, completely surpassing previous generative models. Due to its progressive refinement of labels and continuous improvements in training and inference efficiency, the diffusion model has been applied in various fields, such as recommendation systems [40] and image detection [5]. For example, the CARD [12] model transforms deterministic classification into a conditional label generation process, enabling more flexible uncertainty modeling in the labeling process. However, to our knowledge, diffusion models have not yet been applied to tackle Med-VQA tasks. Therefore, to address this gap, we aim to fully leverage the unique characteristics of diffusion models for Med-VQA tasks." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.776, + 0.612, + 0.79 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.801, + 0.671, + 0.817 + ], + "angle": 0, + "content": "3.1. Problem setting" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.824, + 0.905, + 0.901 + ], + "angle": 0, + "content": "In the context of Med-VQA tasks with noisy labels (NMVQA) problem, our task involves an input set of medical images \\(\\mathcal{V} = \\{v_{i}\\}_{i = 1}^{N}\\) and a set of questions \\(\\mathcal{Q} = \\{q_j\\}_{j = 1}^M\\) with the corresponding answers \\(\\mathcal{A} = \\{a_j\\}_{j = 1}^M\\). Each image \\(v_{i}\\) is associated with \\(M_{i}\\) questions and answers," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14339" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.092, + 0.865, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.382, + 0.908, + 0.482 + ], + "angle": 0, + "content": "Figure 3. The proposed DiN framework consists of three key modules: 1) Answer Condition Generator (ACG): This module interacts the image and question multi-modal features with features of the image-question pair knowledge from Answer Condition Embedding (ACE) to obtain Med-VQA condition information. 2) Noisy Label Refinement (NLR): This module contains a robust loss function, \\(\\mathcal{L}_{RFL}\\), which supervises the proto-answer, to mitigate the impact of noisy original answers on the two encoders' acquisition of medical domain knowledge. The Answer adjustment of NLR uses proto-answers and original noisy answers to generate pseudo-label to supervise the AD module. 3) Answer Diffuser (AD): This module refines the noisy answer distribution, simulating a generation process to select the correct answers. Notably, we use only the AD Module to predict answers without the NLR module during inference process." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.505, + 0.487, + 0.675 + ], + "angle": 0, + "content": "while \\(\\sum_{i=1}^{N} M_i\\) equals \\(M\\). For the convenience of description, we use the subscript \\(k\\) to represent the index of each image-question-answer pair and there are \\(K\\) image-question-answer pairs in total. Specifically, \\(v_k \\in \\mathbb{R}^{H \\times W \\times C}\\) represents an input image with a size of \\(H \\times W\\) and \\(C\\) channels, while \\(a_k \\in \\{0,1\\}^L\\) serves as the one-hot encoded ground truth answer label, where \\(L\\) is the total number of answer classes. Note that only noisy labels are available during the training stage, while the clean labels are only available during the inference stage and are used solely for validating the model's performance." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.682, + 0.204, + 0.698 + ], + "angle": 0, + "content": "3.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.486, + 0.903 + ], + "angle": 0, + "content": "The DiN framework, shown in Figure 3, comprises three main modules: Answer Condition Generator module (ACG) introduced in Sec. 3.3, Noisy Label Refinement module (NLR) described in Sec. 3.4, and Answer Diffuser module (AD) detailed in Sec. 3.5. The input image \\( v_{k} \\) and question \\( q_{k} \\) are processed by Vision Encoder and Text Encoder, respectively, to extract visual features \\( f_{k}^{v} \\) and question features \\( f_{k}^{q} \\). The fused features produce key embeddings \\( K_{ey} \\) and value embeddings \\( V_{value} \\), which are fed into the ACG module. There, they interact with learnable answer embeddings \\( Q_{uery} \\) to generate an answer-aware condition \\( f_{k}^{c} \\). This condition is then used by the AD module to generate the predicted answer \\( y_{k} \\) via a denoising pro" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.506, + 0.909, + 0.6 + ], + "angle": 0, + "content": "cess. Simultaneously, \\( f_{k}^{c} \\) is fed into the NLR module to train an auxiliary classifier, which yields a proto-answer \\( \\hat{y}_k \\). The proto-answer is then refined to create a pseudo-label \\( \\bar{y}_n \\) used to supervise the generation of the \\( y_{k} \\). Note that the NLR module will be discarded in the inference stage, and the AD module will generate the answer predictions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.605, + 0.84, + 0.621 + ], + "angle": 0, + "content": "3.3. Answer Condition Generator Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.909, + 0.903 + ], + "angle": 0, + "content": "The newly proposed ACG module is designed to generate an answer-aware condition, \\( f_{k}^{c} \\), for Noisy Label Refinement module (NLR) and Answer Diffuser module (AD). As introduced in Sec. 3.2, we obtain visual features \\( f_{k}^{v} \\) and question features \\( f_{k}^{q} \\) from input images and questions by Vision Encoder and Text Encoder. These features are then fused to produce key embeddings \\( K_{ey} \\) and value embeddings \\( V_{value} \\), which are fed into the ACG module. In the ACG module, we introduce learnable candidate answer embeddings to query the existence of each answer class to a given image-question pair. For the \\( L \\) answer classes, we need \\( L \\) candidate answer embeddings initialized randomly and updated during training. A self-attention mechanism is applied to compute relationships between the answer embeddings, yielding query embeddings \\( Q_{query} \\). Cross-attention is then used to combine \\( Q_{query} \\) with \\( K_{ey} \\) and \\( V_{value} \\), producing a fused feature \\( f_{k}^{f} \\) that captures the interaction between answer embeddings and image-question features. Finally, the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14340" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.09, + 0.482, + 0.155 + ], + "angle": 0, + "content": "feature \\( f_{k}^{c} = \\mathrm{Linear}(f_{k}^{f}) \\) is generated as conditions to guide the generative process in the AD module, while \\( f_{k}^{f} \\) is simultaneously sent to the NLR module to train the auxiliary classifier." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.163, + 0.376, + 0.18 + ], + "angle": 0, + "content": "3.4. Noisy Label Refinement Module" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.185, + 0.484, + 0.305 + ], + "angle": 0, + "content": "Considering that the model learning will suffer severely from label noise, in this part, we tackle the problem by proposing a Noisy Label Refinement module (NLR), where we first propose a new noise robust loss function to improve the noise resilience of our method and we further come up with an answer adjustment strategy to generate accurate refined pseudo-label \\(\\bar{y}_k\\) to supervise the generation of \\(y_{k}\\) in the Answer Diffuser module." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.307, + 0.484, + 0.488 + ], + "angle": 0, + "content": "Specifically, we first feed the condition \\( f_{k}^{c} \\) into an auxiliary classifier, which is a one-layer linear MLP, to generate the proto-answer probability distribution \\( \\hat{p}_{k} \\). However, on one hand, the noisy supervision \\( a_{k} \\) will greatly influence the accuracy of the proto-answer. On the other hand, the class imbalance problem in Med-VQA is much more severe than other tasks, such bias will severely influence the answer generation. Therefore, we introduce a new noise robust focal loss function (RFL) to tackle the issues, where we incorporate a symmetric cross entropy loss with a focal loss, aiming to improve noise resilience and balance the effects of class imbalance. The RFL is then formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.497, + 0.484, + 0.539 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {R F L} = - \\sum_ {l = 1} ^ {L} a _ {k} (1 - \\hat {p} _ {k}) ^ {\\gamma} \\log \\hat {p} _ {k} - \\sum_ {l = 1} ^ {L} \\hat {p} _ {k} \\log a _ {k}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.548, + 0.483, + 0.563 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is the hyper-parameter and we set \\(\\gamma = 1\\) by default." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.564, + 0.484, + 0.714 + ], + "angle": 0, + "content": "Benefiting from our newly proposed RFL loss, the model is prone to generate correct answers during the training process. Therefore, we further propose an Answer Adjustment (AA) strategy to generate a set of accurate refined pseudolabels to supervise the generation of \\( y_{k} \\) in the Answer Diffuser module. In particular, we assume the given answer is clean if the predicted proto-answer matches the original answer, otherwise, we generate a soft label using a weighted combination of the predicted proto-answer \\( \\hat{p}_k \\) and the given noisy label distribution \\( a_{k} \\), which can be denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.725, + 0.484, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\bar {y} _ {k} = \\left\\{ \\begin{array}{l l} w _ {t} \\hat {p} _ {j} + (1 - w _ {t}) a _ {k}, & \\hat {p} _ {k} \\neq a _ {k} \\\\ a _ {k}, & \\hat {p} _ {k} = a _ {k} \\end{array} , \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.776, + 0.484, + 0.852 + ], + "angle": 0, + "content": "where \\( w_{t} \\) is the weighting parameter. Note that the learning status can be estimated by the confidence scores of the predictions [10], we thereby design \\( w_{t} \\) based on the model's prediction reflecting the overall learning status. Given the current training iteration \\( t \\), we denote \\( w_{t} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.863, + 0.484, + 0.905 + ], + "angle": 0, + "content": "\\[\nw _ {t} = \\tau w _ {t - 1} + (1 - \\tau) \\frac {1}{B} \\sum_ {k = 1} ^ {B} \\hat {p} _ {k}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.198 + ], + "angle": 0, + "content": "where \\(\\tau \\in (0,1)\\) is the momentum decay of EMA, set as 0.99. The \\(B\\) indicates the number of samples within a minibatch. Through the newly proposed answer adjustment strategy, we can obtain a set of accurate refined pseudolabels \\(\\bar{y}\\) to supervise the generation of the final prediction \\(y\\) in the Answer Diffuser module, which will greatly improve the prediction performance of the model." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.206, + 0.742, + 0.221 + ], + "angle": 0, + "content": "3.5. Answer Diffuser Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.228, + 0.906, + 0.379 + ], + "angle": 0, + "content": "Given the ability of diffusion-based classifiers to manage data and label uncertainty effectively, we propose a diffusion-based classifier called the Answer Diffuser module. This module addresses the unique challenges of NM-VQA by classifying answers from a generative perspective, which helps mitigate issues like generating non-existent answers—a common problem in handling noisy labels [4, 12]. By using refined soft labels as supervision, the Answer Diffuser produces accurate, noise-resistant predictions that are particularly robust in noisy-label settings." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.379, + 0.907, + 0.501 + ], + "angle": 0, + "content": "With the condition feature \\( f^c \\) and the refined soft label \\( \\bar{y} \\), following the forward and reverse process of the diffusion models, we gradually introduce noise to the refined soft label \\( \\bar{y} \\) to obtain the noisy label \\( \\bar{y}_T \\) after \\( T \\) steps, and progressively refine a random probability distribution \\( \\bar{y}_T \\) to predict the answer distribution \\( y \\) that is close to the pseudo-label distribution \\( \\bar{y} \\) after \\( T \\) steps. Notably, the forward can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.51, + 0.907, + 0.528 + ], + "angle": 0, + "content": "\\[\nq \\left(\\bar {y} _ {t} | \\bar {y} _ {t - 1}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t}; \\mu_ {t} \\left(\\bar {y} _ {t - 1}, f ^ {c}, t\\right), \\beta_ {t} \\mathbf {I}\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.536, + 0.906, + 0.555 + ], + "angle": 0, + "content": "\\[\n\\mu_ {t} = \\sqrt {1 - \\beta_ {t}} \\bar {y} _ {t - 1} + (1 - \\sqrt {1 - \\beta_ {t}}) f ^ {c}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.56, + 0.906, + 0.591 + ], + "angle": 0, + "content": "where \\(\\beta_{t}\\) is the variance schedule. Consequently, obtaining \\(\\bar{y}_t\\) with an arbitrary timestep \\(t\\) can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.6, + 0.906, + 0.618 + ], + "angle": 0, + "content": "\\[\nq \\left(\\bar {y} _ {t} | \\bar {y}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\bar {y} + \\left(1 - \\sqrt {\\bar {\\alpha} _ {t}}\\right) f ^ {c}, \\left(1 - \\bar {\\alpha} _ {t}\\right) \\mathbf {I}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.906, + 0.702 + ], + "angle": 0, + "content": "Where \\(\\alpha_{t} = 1 - \\beta_{t}\\) and \\(\\bar{\\alpha}_{t} = \\prod_{t}\\alpha_{t}\\). It should be noted that \\(\\mu_{t}\\) can be viewed as an interpolation between soft pseudo-label \\(\\bar{y}\\) from NLR module and the predicted condition \\(f^{c}\\) from ACG module, which gradually generates task-specific conditional information to suit the NM-VQA task." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.906, + 0.763 + ], + "angle": 0, + "content": "The reverse process continuously perform denoising process from \\(\\bar{y}_T\\) to obtain \\(y\\), which we hope to be close to \\(\\bar{y}\\), where we learn a diffusion model \\(\\theta\\) to predict the noise level at each timestep, which can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.772, + 0.905, + 0.791 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\bar {y} _ {t - 1} \\mid \\bar {y} _ {t}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t - 1}; \\mu_ {\\theta} \\left(\\bar {y} _ {t}, f ^ {c}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.8, + 0.906, + 0.875 + ], + "angle": 0, + "content": "where the \\(\\mu_{\\theta}(\\bar{y}_t, f^c, t)\\) is predicted mean value of the noise distribution at timestep \\(t\\), \\(\\sigma_t^2\\) is \\(\\frac{1 - \\bar{\\alpha}_{t-1}}{1 - \\bar{\\alpha}_t} \\beta_t\\). Our target is to encourage the predicted answer distribution to be close to the refined pseudo-label distribution \\(\\bar{y}\\). Therefore, we adopt a MSE loss as a supervision, which can be denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.643, + 0.886, + 0.905, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i f} = \\operatorname {M S E} (y; \\bar {y}). \\tag {8}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14341" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.305, + 0.108 + ], + "angle": 0, + "content": "3.6. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.484, + 0.234 + ], + "angle": 0, + "content": "During the training process, we jointly optimize \\(\\mathcal{L}_{dif}\\) and \\(\\mathcal{L}_{RFL}\\), which on one hand targets at generating refined correct pseudo-labels that are robust to label noise as the supervision for our Answer Diffuser, on the other hand, we encourage the Answer Diffuser to generate existent and accurate answer predictions, further reducing the impact of noisy labels. Therefore, the overall loss during training can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.248, + 0.484, + 0.265 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d i f}} + \\alpha \\mathcal {L} _ {R F L}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.277, + 0.45, + 0.291 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is hyperparameter to balance different losses." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.292, + 0.484, + 0.458 + ], + "angle": 0, + "content": "It should be noticed that during the inference stage, we only adopt the AD Module to predict answers while discarding the NLR module, as the NLR module targets at providing a precise supervision for the AD module learning. The corresponding noisy distribution \\(\\bar{y}_T\\) is replaced with randomly generated Gaussian noise. The model gradually refines the random distribution through the reverse process and obtains the final predicted probability distribution \\(y\\). The ultimate prediction class label \\(\\hat{y} = \\arg \\max_l(y_l)\\), where \\(l\\) indicates the index of the categories, is the answer with the highest probability score." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.473, + 0.216, + 0.489 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.498, + 0.194, + 0.512 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.52, + 0.484, + 0.718 + ], + "angle": 0, + "content": "VQA-RAD [20] is the most widely used radiology dataset for Med-VQA, comprising 315 images and 3,515 question-answer pairs, with each image corresponding to at least one question-answer pair. \\(58\\%\\) of the questions are close-end questions and the rest are openend questions. PathVQA [14] is constructed by extracting images along with corresponding captions from digital resources such as electronic textbooks and online libraries. It consists of 32,799 question-answer pairs, including 4,998 pathology images. Open-end questions account for \\(50.2\\%\\) of all questions and the rest are closed questions. To ensure comparability, both of the datasets have been divided following the MMQ method [7]." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.727, + 0.342, + 0.743 + ], + "angle": 0, + "content": "4.2. Noise Patterns and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.87 + ], + "angle": 0, + "content": "Due to the lack of suitable Med-VQA datasets with noisy labels and the difficulty of creating new datasets, we adopt semantic noisy types from the natural VQA domain [47] to existing medical VQA datasets. [47] demonstrates controlled semantic label noise by simulating human mislabeling behavior, which is more realistic than conventional random noise. We also follow the conventional VQA methods to validate our model by random label shuffling." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "The questions in Med-VQA tasks include two categories: closed-end (e.g., Yes/No questions with one-word" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.41 + ], + "angle": 0, + "content": "answers) and open-end (e.g., wh-questions with longer responses). Following [47], for closed-ended answers, we use symmetric noise by randomly flipping the answer choices. Moreover, for open-ended answers, we create a semantic space of frequent answers using a pre-trained BERT model [21] to simulate human annotation errors. For each sample, the original answer is replaced by its closest noisy label within this semantic space. Our experiments highlight the sensitivity of prior Med-VQA methods to noisy labels, and we evaluate performance using \\(10\\%\\) and \\(20\\%\\) semantic noise ratios in the training datasets of VQA-RAD and PathVQA. Figure 2 visualizes our noisy pairs and the t-SNE representation of the semantic space, where ground-truth labels are replaced with semantically similar noisy labels. Moreover, we compare the performance of different methods by introducing random noise with a \\(20\\%\\) noise ratio into the training datasets of VQA-RAD and PathVQA. As shown in Table 1 and Table 2, at the same noise ratio, semantic noise impacts model performance more significantly than random noise and more closely resembles the type of noise encountered in actual clinical scenarios." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.421, + 0.733, + 0.437 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.443, + 0.909, + 0.656 + ], + "angle": 0, + "content": "Our method is trained on a single Nvidia 3090Ti GPU. We employ the Swin Transformer [28] as the vision encoder and the BERT model [21] as the text encoder. Our baseline model contains the Swin Transformer and BERT as encoder with transformer decoder without any answer denoise methods. The Adam optimizer is used, with an initial learning rate set to 1e-5. We adopt a batch size of 16 and a maximum of 100 epochs. The loss weight \\(\\alpha\\) is set to 0.5 for both datasets. For our model evaluation, we use only the AD Module to predict answers without the NLR module to ensure that the model parameters are at a similar level to those of other methods for comparison. The DiN framework is trained in an end-to-end fashion. The Med-VQA performance is assessed by accuracy scores." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.667, + 0.75, + 0.684 + ], + "angle": 0, + "content": "4.4. Performance Comparison" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.909, + 0.903 + ], + "angle": 0, + "content": "We compare our proposed method with MMBERT [19] and Q2ATransformer [27], which are among the top performers in Med-VQA task. Notably, previous Med-VQA methods were not designed to address the issue of noisy labels. To fill this gap, we employ two mainstream uni-modal label denoising methods to compare. SimT [11] estimates noise transition matrices to correct label noise in a class-wise manner. CoDis [44], a co-teaching-based label denoising method, uses two sub-networks to select the clean label dataset based on the small-loss principle. We also compare our method with SNLC [47], the first method designed for natural VQA with noisy labels. As shown in Table 1 and Table 2, our DiN framework consistently outperforms the compared models on both datasets. The biggest drawback" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14342" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.111, + 0.089, + 0.468, + 0.348 + ], + "angle": 0, + "content": "
    Noise TypeMethodVQA-RAD
    OpenCloseOverall
    CleanUpper Bound78.1780.0879.13
    10%-Semantic NoiseBaseline67.8668.8568.25
    MMBERT [19]63.3668.2166.42
    Q2ATransformer [27]66.7970.1768.48
    SimT [11]66.9369.7368.04
    CoDis [44]68.0270.5469.53
    SNLC [47]67.8371.3569.65
    DiN (Ours)72.6875.8174.24
    20%-Semantic NoiseBaseline54.2357.1456.01
    MMBERT [19]52.6856.6455.25
    Q2ATransformer [27]55.4360.0358.25
    SimT [11]53.7657.0555.82
    CoDis [44]54.1957.2856.42
    SNLC [47]56.4561.3058.88
    DiN (Ours)58.0663.1762.28
    20%-Random NoiseBaseline56.7160.3058.88
    MMBERT [19]55.4359.5957.97
    Q2ATransformer [27]58.0462.3760.68
    SimT [11]57.8662.8560.90
    CoDis [44]59.9560.5660.32
    SNLC [47]59.2163.8462.03
    DiN (Ours)61.0465.7763.93
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.442 + ], + "angle": 0, + "content": "Table 1. Performance comparison on the VQA-RAD dataset. 'Open' indicates the open-end question and 'close' indicates the close-end question. The overall performance is the average performance of both question types. The best results are bold. Notably, SimT [11] and CoDis [44] are up-to-date representatives of NTM-based and co-teaching-based approaches, respectively." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.477, + 0.483, + 0.809 + ], + "angle": 0, + "content": "of these two Med-VQA methods is that neither is designed to address the issue of noisy labels, so they cannot prevent overfitting noisy patterns during the training process for NM-VQA tasks. SimT [11] did not bring significant performance improvements, primarily due to the limitations of the noise transition matrix (NTM), which only effectively captures noise patterns in simple noisy classification tasks. CoDis [44] performed better than NTM-based methods; but its two-branch co-teaching method doubles the parameters and uses a small-loss selection strategy better suited for simpler noise. SNLC [47], designed for noisy labels in natural VQA, relies on a basic robust loss function and fails to deliver competitive performance in the medical domain. In contrast, our DiN framework is specifically tailored for noisy labels in Med-VQA tasks. Figure 4 visualizes four examples of predicted answers from both the training and test sets across two datasets. In the training set, our method successfully corrects semantic noisy labels post-training, while in the test set, our model generates accurate predictions in multiple instances. This design allows DiN to consistently outperform other methods, demonstrating its effectiveness in addressing the unique challenges of NM-VQA tasks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.83, + 0.245, + 0.846 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To assess the contributions of our DiN framework, we conducted extensive ablation studies to demonstrate the efficiency of the different components of our model." + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.089, + 0.888, + 0.348 + ], + "angle": 0, + "content": "
    Noise TypeMethodPathVQA
    OpenCloseOverall
    CleanUpper Bound52.6486.4572.61
    10%-Semantic NoiseBaseline37.8375.8162.32
    MMBERT [19]34.1873.2158.73
    Q2ATransformer [27]38.4276.8562.61
    SimT [11]36.5475.3562.06
    CoDis [44]37.8676.2863.02
    SNLC [47]38.8578.3364.18
    DiN (Ours)40.5480.2866.67
    20%-Semantic NoiseBaseline29.0670.0155.28
    MMBERT [19]27.1368.3552.41
    Q2ATransformer [27]30.1671.1156.28
    SimT [11]29.3870.6955.93
    CoDis [44]30.3671.1856.55
    SNLC [47]30.8871.2356.72
    DiN (Ours)32.4772.5658.14
    20%-Random NoiseBaseline32.2973.5357.03
    MMBERT [19]30.4572.0655.41
    Q2ATransformer [27]34.5074.7458.64
    SimT [11]35.1774.9159.01
    CoDis [44]35.6674.5058.96
    SNLC [47]36.7475.0359.71
    DiN (Ours)37.8576.1660.84
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.513, + 0.358, + 0.907, + 0.442 + ], + "angle": 0, + "content": "Table 2. Performance comparison on the PathVQA dataset. 'Open' indicates the open-end question and 'close' indicates the close-end question. The overall performance is the average performance of both question types. The best results are bold. Notably, SimT [11] and CoDis [44] are up-to-date representatives of NTM-based and co-teaching-based approaches, respectively." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.459, + 0.912, + 0.516 + ], + "angle": 0, + "content": "
    ChoiceEncodersClassifierACGADRFLAAOpenCloseOverallOpenCloseOverall
    0✓✓✓67.8668.8568.2554.2357.1456.01
    1✓✓✓✓68.4670.7169.5655.0859.2757.64
    2✓✓✓✓70.7171.9271.1555.8660.8659.13
    3✓✓✓✓✓70.7373.0872.2556.2161.5460.57
    4✓✓✓✓✓71.1574.2972.7556.9762.2061.24
    5✓✓✓✓✓✓72.6875.8174.2458.0663.1762.28
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.513, + 0.526, + 0.907, + 0.637 + ], + "angle": 0, + "content": "Table 3. Ablation study of our method on the VQA-RAD dataset with \\(10\\%\\) -Semantic Noise. ACG indicates our answer condition generator module, AD indicates our answer diffuser module. Note that our noisy label refinement module includes two parts, i.e., an answer adjust module (AA) and a noise robust focal loss function (RFL). Also note that the baseline method includes the vision encoder and the text encoder (Encoder), the auxiliary classifier (Classifier) and our ACG module." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.669, + 0.836, + 0.684 + ], + "angle": 0, + "content": "4.5.1. Impact of Answer Condition Generator" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.901 + ], + "angle": 0, + "content": "The ACG module provides conditional information to support the generative process in the AD module and features for training the auxiliary classifier in the NLR module. When only the encoders, ACG, and the auxiliary classifier are used for answer prediction (i.e., the fused image-question features are sent through ACG to interact with the candidate answer embeddings, and the output feature \\( f_{k}^{c} \\) is used to train the auxiliary classifier), the accuracy is limited to \\( 68.25\\% \\) overall accuracy (Choice 0 in Table 3), primarily due to rapid overfitting and the inability to effectively handle noisy labels. Notably, incorporating the AD module with the conditional information from ACG significantly enhances the overall accuracy to \\( 71.15\\% \\) (Choice 2). The ACG module not only enhances the auxiliary classi" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14343" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.089, + 0.26, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.273, + 0.101, + 0.437, + 0.113 + ], + "angle": 0, + "content": "Train Set with Noisy Answers" + }, + { + "type": "image_footnote", + "bbox": [ + 0.276, + 0.114, + 0.488, + 0.125 + ], + "angle": 0, + "content": "Question: Where is/are the lesion located?" + }, + { + "type": "image_footnote", + "bbox": [ + 0.277, + 0.128, + 0.457, + 0.14 + ], + "angle": 0, + "content": "Noisy Answers : Left temporal lobe" + }, + { + "type": "image_footnote", + "bbox": [ + 0.277, + 0.142, + 0.466, + 0.156 + ], + "angle": 0, + "content": "Our Prediction: Right temporal lobe" + }, + { + "type": "image", + "bbox": [ + 0.467, + 0.129, + 0.492, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.091, + 0.631, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.101, + 0.806, + 0.113 + ], + "angle": 0, + "content": "Train Set with Noisy Answers" + }, + { + "type": "image_footnote", + "bbox": [ + 0.647, + 0.114, + 0.856, + 0.136 + ], + "angle": 0, + "content": "Question: What shows the bland cytology that typifies neuroendocrine tumors?" + }, + { + "type": "image_footnote", + "bbox": [ + 0.647, + 0.138, + 0.829, + 0.15 + ], + "angle": 0, + "content": "Noisy Answers : Low magnification" + }, + { + "type": "image_footnote", + "bbox": [ + 0.647, + 0.151, + 0.834, + 0.162 + ], + "angle": 0, + "content": "Our Prediction : High magnification" + }, + { + "type": "list", + "bbox": [ + 0.647, + 0.101, + 0.856, + 0.162 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.836, + 0.139, + 0.864, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.179, + 0.413, + 0.19 + ], + "angle": 0, + "content": "Test Set without Answers" + }, + { + "type": "image_footnote", + "bbox": [ + 0.276, + 0.194, + 0.456, + 0.218 + ], + "angle": 0, + "content": "Question: What type of sequence is displayed in this image?" + }, + { + "type": "image_footnote", + "bbox": [ + 0.277, + 0.219, + 0.456, + 0.23 + ], + "angle": 0, + "content": "Our Prediction : T2 weighted MRI" + }, + { + "type": "image", + "bbox": [ + 0.462, + 0.218, + 0.482, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.167, + 0.608, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.179, + 0.783, + 0.19 + ], + "angle": 0, + "content": "Test Set without Answers" + }, + { + "type": "image_footnote", + "bbox": [ + 0.647, + 0.194, + 0.84, + 0.216 + ], + "angle": 0, + "content": "Question: What is the poorly cohesive tumor in the retina seen abutting?" + }, + { + "type": "image_footnote", + "bbox": [ + 0.648, + 0.218, + 0.797, + 0.23 + ], + "angle": 0, + "content": "Our Prediction : Optic nerve" + }, + { + "type": "image", + "bbox": [ + 0.803, + 0.219, + 0.822, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.276, + 0.25, + 0.337, + 0.262 + ], + "angle": 0, + "content": "VQA-RAD" + }, + { + "type": "table_caption", + "bbox": [ + 0.638, + 0.25, + 0.693, + 0.262 + ], + "angle": 0, + "content": "PathVQA" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.275, + 0.908, + 0.318 + ], + "angle": 0, + "content": "Figure 4. Visualization of example results from our DiN framework on the VQA-RAD and PathVQA datasets. The first row presents examples from the training set with \\(10\\%\\) -Semantic Noise, where our method corrects the noisy incorrect answers during the training process. The second row shows two examples from the test sets of both datasets." + }, + { + "type": "table", + "bbox": [ + 0.159, + 0.34, + 0.418, + 0.494 + ], + "angle": 0, + "content": "
    NameChoiceVQA-RAD with 10% Noise
    OpenCloseOverall
    \\(L_r\\)CE [49]70.7373.0872.25
    Focal [24]71.4373.8573.10
    SCE [41]71.8673.8673.50
    RFL (ours)72.6875.8174.24
    \\(L_{dif}\\)KL72.8675.3874.00
    MSE72.6875.8174.24
    \\(\\alpha\\)0.171.7974.2373.75
    0.572.6875.8174.24
    172.1675.9274.18
    Step T1072.5175.7674.03
    5072.6875.8174.24
    10071.9374.6673.87
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.504, + 0.484, + 0.561 + ], + "angle": 0, + "content": "Table 4. Ablation studies on different hyperparameters, i.e., \\(\\alpha\\) that balances different loss functions and the number of timesteps \\(T\\) in our answer diffuser module, and ablation studies on different options of loss functions in our noisy label refinement module." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.587, + 0.484, + 0.632 + ], + "angle": 0, + "content": "fier's ability to capture medical domain knowledge but also strengthens the diffusion-based AD module by providing reliable Med-VQA condition information." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.64, + 0.376, + 0.656 + ], + "angle": 0, + "content": "4.5.2. Impact of Noisy Label Refinement" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.484, + 0.9 + ], + "angle": 0, + "content": "The Noisy Label Refinement (NLR) module comprises two sub-components: Robust Loss (RFL) and answer adjustment (AA). The RFL is designed to mitigate the impact of noise on the encoders' features. As shown in Table 3, incorporating the RFL leads to an increase in overall accuracy from \\(68.25\\%\\) to \\(69.56\\%\\) without using AD module and from \\(71.15\\%\\) (Choice 2) to \\(72.75\\%\\) (Choice 4) with AD module. We experimented with different combinations of robust loss functions and found that our proposed RFL is the most effective for NM-VQA tasks, as demonstrated in Table 4. The answer adjustment (AA) component is specifically designed to reduce noise impact on the Answer Diffuser (AD) module. The addition of the AA component enhances the overall accuracy from \\(71.15\\%\\) (Choice 2) to \\(72.25\\%\\) (Choice 3) and further from \\(72.75\\%\\) (Choice 4) to \\(74.24\\%\\) (Choice 5) with the assistance of RFL." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.344, + 0.747, + 0.359 + ], + "angle": 0, + "content": "4.5.3.Impact of Answer Diffuser" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.366, + 0.907, + 0.624 + ], + "angle": 0, + "content": "As shown in Table 3, incorporating the AD module for Med-VQA prediction enhances the overall performance from \\(68.25\\%\\) (Choice 0) to \\(71.15\\%\\) (Choice 2). When all our proposed modules are combined, the overall performance further improves to \\(74.24\\%\\) (Choice 5). We also examined the hyperparameter \\(\\alpha\\), which balances the AD module and the auxiliary classifier, and the type of \\(L_{dif}\\) as detailed in Table 4. Our framework demonstrates insensitivity to both choices. We selected \\(\\alpha = 0.5\\) and MSE loss as \\(L_{dif}\\). Furthermore, we investigated the impact of varying \\(T\\) on model performance, as presented in Table 4. While increasing \\(T\\) results in higher computational costs, our model achieves optimal performance at \\(T = 50\\). This differs from the image generation, where 1000 steps are typically used. This distinction is likely due to the precise pixel-level generation required in image tasks, whereas our model focuses on deriving a class probability distribution." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.65, + 0.634, + 0.667 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.678, + 0.907, + 0.889 + ], + "angle": 0, + "content": "In conclusion, we have introduced DiN as the first approach to address the Med-VQA with noisy labels. Our method uses the inherent robustness of diffusion models as AD module to deal with noisy data. We designed the ACG module to fuse image, question features and candidate answering embeddings, generating condition information supporting both the AD and NLR modules. Additionally, the NLR module reduces the effect of noisy labels with robust loss functions and refines the original answers to produce pseudo-labels, further improving model performance. Extensive experiments validate the superiority of our DiN framework. While our method has some limitations, the diffusion model introduces Gaussian noise during training, which may slightly increase training time but does not affect inference time." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14344" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.184 + ], + "angle": 0, + "content": "[1] Rahul Ambati and Chakravardhan Reddy Dudyala. A sequence-to-sequence model approach for imagecef 2018 medical domain visual question answering. In 2018 15th IEEE India Council International Conference (INDICON), pages 1-6. 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However, the challenge of noisy labels and limited high-quality datasets remains underexplored. To address this, we establish the first benchmark for noisy labels in Med-VQA by simulating human mislabeling with semantically designed noise types. More importantly, we introduce the DiN framework, which leverages a diffusion model to handle noisy labels in Med-VQA. Unlike the dominant classification-based VQA approaches that directly predict answers, our Answer Diffuser (AD) module employs a coarse-to-fine process, refining answer candidates with a diffusion model for improved accuracy. The Answer Condition Generator (ACG) further enhances this process by generating task-specific conditional information via integrating answer embeddings with fused image-question features. To address label noise, our Noisy Label Refinement(NLR) module introduces a robust loss function and dynamic answer adjustment to further boost the performance of the AD module. Our DiN framework consistently outperforms existing methods across multiple benchmarks with varying noise levels1. + +# 1. Introduction + +Medical Visual Question Answering (Med-VQA) tasks focus on accurately responding to medical inquiries by integrating visual information from medical images [6, 26, 39]. It holds great potential in applications like assisting diagnosis, enhancing patient understanding, and supporting clinical education [3, 36]. Recently, VQA models have achieved impressive results in the natural VQA domain [13, 38, 46]. This success has largely been driven by the availability of large-scale natural VQA datasets with well-structured accurate annotations [25, 29]. However, for Med-VQA, the annotation process poses unique challenges. It requires specialized medical expertise and skills from annotators, lead + +![](images/0333255bbcd2958904f191cd821042e7c8e35989a5e50f6396aa3b80543b983f.jpg) +(a) Classification-based + +![](images/47e58569552ea3abe9c7d8509dd133934de7ccb3bcedc3a7872ad9b4615806ad.jpg) + +![](images/fdc7156e577d74d106ed7b51edd7940973a748d654df64f26b92bc4f65ab92d3.jpg) +(b) Generation-based +Figure 1. Comparison between our diffusion-based method and previous Med-VQA approaches. Previous Med-VQA methods, designed for clean label datasets, include classification-based (a) and generation-based (b) approaches. In contrast, our diffusion-based method (c) classifies answers from a generative perspective and denoises answers by Answer Diffuser with the support of Answer Condition Generator and the Noisy Label Refinement module (employed only during the training process). + +ing to increased complexity and higher potential for label noise [34, 35, 51]. Additionally, inter-observer variability among medical professionals further complicates the annotation process, contributing to labeling inconsistencies [16, 31, 43]. While the issue of noisy labels is a well-known challenge in machine learning, it has not been thoroughly explored in Med-VQA, despite the need for highly accurate medical annotations. + +While existing label-denoising methods have shown promise, they are primarily designed for uni-modal tasks like image classification or segmentation [23, 42, 50]. Directly applying them for the multi-modal Med-VQA task is not suitable for two key reasons. First, conventional noise models, such as random label shuffling, fail to capture the semantic nuances essential in Med-VQA, where label noise often retains medically relevant information rather than arbitrary noise. We argue that noisy labels in VQA should retain semantic coherence aligned with human cognitive levels. As shown in Fig. 2, examples of noisy QA + +![](images/34f5f03b75efbc476203ce40121b91cba3f71c8268c679a5e1d8a15774e2cdbf.jpg) +Figure 2. Visualization of the semantic answer pairs in t-SNE and examples of noisy answers. Similar colors represent the degree of feature similarity from a pretrained BERT model. We randomly display 8 semantic pairs in the t-SNE plots of VQA-RAD dataset. Ground-truth labels are replaced with their semantic pairs, which we refer to as semantically noisy answers [47]. + +![](images/495e599bdf21ce37a4cfd859e151f21e799e3a9a5a50da8fa625a8f3422ccc01.jpg) + +![](images/8a689d5ad00407c0aa6dd2fa58d32202f13720cdbd4c063d1ea0bb29ea21fb97.jpg) + +Question Type: Open + +Question: Why is free air present in image? + +Random Noisy: Ribs + +Semantic Noisy: Hydropneumothorax + +Ground-truth: Pneumothorax + +Question Type: Closed + +Question: Is the heart enlarged? + +Random Noisy: Skin + +Semantic Noisy: Yes + +Ground-truth: No + +pairs and their corresponding t-SNE representations illustrate this difference: unlike the arbitrary and meaningless answers generated by random noise, our constructed semantic noise resembles real-world scenarios, closer to human mislabeling. Second, these methods are not equipped to handle the complexity of Med-VQA, which integrates both image and text modalities. For example, co-teaching methods [44] add considerable model complexity by requiring two branch networks, while Noise Transition Matrix (NTM) methods [11] struggle with noisy label distribution estimation as the number of Med-VQA classes grows. While current leading methods like SNLC [47] in the natural VQA domain focus on improving representation through robust contrastive loss, these studies address noise in a relatively coarse way and fall short when dealing with the medically relevant label noise in Med-VQA. For instance, with a $20\%$ noise ratio, SNLC [47] achieves $62\%$ accuracy on MedVQA with random noise but drops to $58\%$ when handling our semantic noise. In summary, our constructed semantic noise in Med-VQA is both practically relevant and presents a more challenging task to effectively handle. + +In the literature, two main approaches have emerged for medical VQA: classification-based and generation-based methods, as shown in Figure 1. Classification-based methods are generally straightforward and efficient but often struggle with low-frequency answers, which becomes especially pronounced in complex domains like Med-VQA [1, 9]. In contrast, generation-based methods offer more flexibility by constructing answers instead of selecting from predefined categories; however, they inevitably generate unrealistic or non-existent answers, reducing overall accuracy and reliability [27, 30]. To this end, motivated by the success of diffusion models in label refinement [2, 33], we propose leveraging them to bridge the gap between classi + +fication and generation approaches, enabling answer classification from a generative perspective. Diffusion models can offer a balance between classification and generative approaches for Med-VQA. Prior studies [4, 12] have also demonstrated that the probabilistic nature of diffusion models effectively handles data and label uncertainty, leading to more robust predictions. Conditioned on discriminative feature and label information, diffusion models offer a promising solution for the noisy labels in Med-VQA, using their stochastic nature to reconstruct class prototypes during reverse sampling and generate probability intervals across class labels. + +To improve Med-VQA performance in the presence of noisy labels and harness the benefits of diffusion models, we propose the conditional Diffusion model for Med-VQA with Noisy labels (DiN) framework to address challenging semantic noisy labels. To mimic human-like mislabeling, we construct the training set by replacing ground-truth answers with semantically related noisy pairs, selected using a pre-trained BERT model. To the best of our knowledge, this is the first study addressing Med-VQA with noisy labels and the first application of diffusion models to this task. Our framework comprises three key modules. The Answer Denoiser (AD) module leverages robust conditional diffusion models, utilizing their powerful gradual refinement capabilities for Med-VQA. As shown in Figure 1, the generative process begins with a noisy label estimation, which is progressively refined to recover a clean label, analogous to the reverse denoising process in diffusion models. This allows coarse-to-fine filtering of potential answers, significantly improving accuracy and robustness. However, the effectiveness of the AD module's refinement is highly dependent on the generation conditions, and the lack of accurate clean labels exacerbates this challenge. To this end, we further pro + +pose the Answer Condition Generator (ACG) and Noisy Label Refinement (NLR) module to provide more accurate and reliable conditions. The ACG adopts a transformer decoder to fuse multi-modal image and question features, as well as learnable candidate embedding for delivering more informative generation conditions. The NLR, utilized only during training, refines noisy ground-truth labels dynamically through pseudo-labels generated by an auxiliary classifier to supervise the AD module. This synergy across modules enhances precision and robustness in managing noisy labels for Med-VQA tasks. + +Our main contributions are summarized as follows. + +- We propose the DiN framework, the first to address MedVQA tasks with noisy labels (NM-VQA) by integrating a diffusion model that classifies answers from a generative and coarse-to-fine perspective. +- We introduce semantic noise types tailored to Med-VQA tasks and construct challenging benchmark datasets that simulate human labeling errors based on an thorough analysis of existing datasets. +- We design the Answer Condition Generator (ACG) and Noisy Label Refinement (NLR) modules to support the diffusion-based Answer Diffuser (AD). ACG guides AD with conditions, while NLR refines noisy labels using pseudo-labels from an auxiliary classifier. +- Our method consistently outperforms existing approaches on two Med-VQA datasets with varying noise ratios, demonstrating its robustness and effectiveness. + +# 2. Related Work + +# 2.1. Medical Visual Question Answering + +Med-VQA is still in its early stages, and its current performance remains unsatisfactory. Most methods, such as those in [7, 27, 30, 31], adopt a classification-based approach, where each answer is treated as a class, and a model predicts the answer by applying classification to the fused image-question features. This classification-based approach simplifies the task by reducing its complexity and narrowing the answer search space. Alternatively, some studies [8, 19] approach VQA as a generation problem, generating answers word by word. These generation-based methods face challenges due to the vast search space, often leading to inaccurate answers, which limits their effectiveness in medical VQA. However, existing Med-VQA methods assume that the entire training dataset consists of clean labels, overlooking the challenge of noisy labels (NM-VQA). To address this gap, we introduce Med-VQA datasets with noisy labels and propose a solution for the NM-VQA problem. + +# 2.2. Learning with Noise Labels and Noise Types + +Learning with noise labels has been extensively studied in recent works. For example, some methods estimated + +noise transition matrices to correct label noise in a class-wise manner [11, 22]. Other popular methods reduced the effects of noisy labels by using noise-tolerant loss functions [47]. However, these methods tend to perform poorly when confronted with high noise rates and a large number of classes in Med-VQA tasks. One typical alternative way is coteaching-based methods CoDis [44], which require two branch networks, and introduce a double number of additional parameters, thereby exacerbating the issue of model complexity in Med-VQA tasks that necessitate both image and text encoders within a single network. Given these challenges, it is valuable to explore methods for developing robust Med-VQA models under reasonable noisy data. Most methods to deal with artificially synthesized noisy labels were initially proposed for classification tasks [17]. In these studies, synthesized noisy labels typically focus on both symmetric and asymmetric label noise. Symmetric noise flips labels randomly with equal probability, while asymmetric noise flips labels based on fixed rules. However, when it comes to Med-VQA tasks, symmetric and asymmetric noise models appear unreasonable. Unlike the traditionally synthesized label noise for classification, we propose the semantic label noise for Med-VQA tasks. + +# 2.3. Diffusion Models + +Diffusion models [2, 18, 32, 33, 45] are a new class of generative model. During training, they initially add noise to labels through a forward process until they approximate a Gaussian distribution. Then, in the reverse process, they learn to denoise and recover the original labels [15, 37, 48]. In recent years, their remarkable success in the generative domain, particularly in visual generation [33], has been groundbreaking, completely surpassing previous generative models. Due to its progressive refinement of labels and continuous improvements in training and inference efficiency, the diffusion model has been applied in various fields, such as recommendation systems [40] and image detection [5]. For example, the CARD [12] model transforms deterministic classification into a conditional label generation process, enabling more flexible uncertainty modeling in the labeling process. However, to our knowledge, diffusion models have not yet been applied to tackle Med-VQA tasks. Therefore, to address this gap, we aim to fully leverage the unique characteristics of diffusion models for Med-VQA tasks. + +# 3. Methods + +# 3.1. Problem setting + +In the context of Med-VQA tasks with noisy labels (NMVQA) problem, our task involves an input set of medical images $\mathcal{V} = \{v_{i}\}_{i = 1}^{N}$ and a set of questions $\mathcal{Q} = \{q_j\}_{j = 1}^M$ with the corresponding answers $\mathcal{A} = \{a_j\}_{j = 1}^M$ . Each image $v_{i}$ is associated with $M_{i}$ questions and answers, + +![](images/31fd7da671a952ebd0d89229b86a349d4a5c18645aad210c955259fe5254dae0.jpg) +Figure 3. The proposed DiN framework consists of three key modules: 1) Answer Condition Generator (ACG): This module interacts the image and question multi-modal features with features of the image-question pair knowledge from Answer Condition Embedding (ACE) to obtain Med-VQA condition information. 2) Noisy Label Refinement (NLR): This module contains a robust loss function, $\mathcal{L}_{RFL}$ , which supervises the proto-answer, to mitigate the impact of noisy original answers on the two encoders' acquisition of medical domain knowledge. The Answer adjustment of NLR uses proto-answers and original noisy answers to generate pseudo-label to supervise the AD module. 3) Answer Diffuser (AD): This module refines the noisy answer distribution, simulating a generation process to select the correct answers. Notably, we use only the AD Module to predict answers without the NLR module during inference process. + +while $\sum_{i=1}^{N} M_i$ equals $M$ . For the convenience of description, we use the subscript $k$ to represent the index of each image-question-answer pair and there are $K$ image-question-answer pairs in total. Specifically, $v_k \in \mathbb{R}^{H \times W \times C}$ represents an input image with a size of $H \times W$ and $C$ channels, while $a_k \in \{0,1\}^L$ serves as the one-hot encoded ground truth answer label, where $L$ is the total number of answer classes. Note that only noisy labels are available during the training stage, while the clean labels are only available during the inference stage and are used solely for validating the model's performance. + +# 3.2. Overview + +The DiN framework, shown in Figure 3, comprises three main modules: Answer Condition Generator module (ACG) introduced in Sec. 3.3, Noisy Label Refinement module (NLR) described in Sec. 3.4, and Answer Diffuser module (AD) detailed in Sec. 3.5. The input image $v_{k}$ and question $q_{k}$ are processed by Vision Encoder and Text Encoder, respectively, to extract visual features $f_{k}^{v}$ and question features $f_{k}^{q}$ . The fused features produce key embeddings $K_{ey}$ and value embeddings $V_{value}$ , which are fed into the ACG module. There, they interact with learnable answer embeddings $Q_{uery}$ to generate an answer-aware condition $f_{k}^{c}$ . This condition is then used by the AD module to generate the predicted answer $y_{k}$ via a denoising pro + +cess. Simultaneously, $f_{k}^{c}$ is fed into the NLR module to train an auxiliary classifier, which yields a proto-answer $\hat{y}_k$ . The proto-answer is then refined to create a pseudo-label $\bar{y}_n$ used to supervise the generation of the $y_{k}$ . Note that the NLR module will be discarded in the inference stage, and the AD module will generate the answer predictions. + +# 3.3. Answer Condition Generator Module + +The newly proposed ACG module is designed to generate an answer-aware condition, $f_{k}^{c}$ , for Noisy Label Refinement module (NLR) and Answer Diffuser module (AD). As introduced in Sec. 3.2, we obtain visual features $f_{k}^{v}$ and question features $f_{k}^{q}$ from input images and questions by Vision Encoder and Text Encoder. These features are then fused to produce key embeddings $K_{ey}$ and value embeddings $V_{value}$ , which are fed into the ACG module. In the ACG module, we introduce learnable candidate answer embeddings to query the existence of each answer class to a given image-question pair. For the $L$ answer classes, we need $L$ candidate answer embeddings initialized randomly and updated during training. A self-attention mechanism is applied to compute relationships between the answer embeddings, yielding query embeddings $Q_{query}$ . Cross-attention is then used to combine $Q_{query}$ with $K_{ey}$ and $V_{value}$ , producing a fused feature $f_{k}^{f}$ that captures the interaction between answer embeddings and image-question features. Finally, the + +feature $f_{k}^{c} = \mathrm{Linear}(f_{k}^{f})$ is generated as conditions to guide the generative process in the AD module, while $f_{k}^{f}$ is simultaneously sent to the NLR module to train the auxiliary classifier. + +# 3.4. Noisy Label Refinement Module + +Considering that the model learning will suffer severely from label noise, in this part, we tackle the problem by proposing a Noisy Label Refinement module (NLR), where we first propose a new noise robust loss function to improve the noise resilience of our method and we further come up with an answer adjustment strategy to generate accurate refined pseudo-label $\bar{y}_k$ to supervise the generation of $y_{k}$ in the Answer Diffuser module. + +Specifically, we first feed the condition $f_{k}^{c}$ into an auxiliary classifier, which is a one-layer linear MLP, to generate the proto-answer probability distribution $\hat{p}_{k}$ . However, on one hand, the noisy supervision $a_{k}$ will greatly influence the accuracy of the proto-answer. On the other hand, the class imbalance problem in Med-VQA is much more severe than other tasks, such bias will severely influence the answer generation. Therefore, we introduce a new noise robust focal loss function (RFL) to tackle the issues, where we incorporate a symmetric cross entropy loss with a focal loss, aiming to improve noise resilience and balance the effects of class imbalance. The RFL is then formulated as follows: + +$$ +\mathcal {L} _ {R F L} = - \sum_ {l = 1} ^ {L} a _ {k} (1 - \hat {p} _ {k}) ^ {\gamma} \log \hat {p} _ {k} - \sum_ {l = 1} ^ {L} \hat {p} _ {k} \log a _ {k}, \tag {1} +$$ + +where $\gamma$ is the hyper-parameter and we set $\gamma = 1$ by default. + +Benefiting from our newly proposed RFL loss, the model is prone to generate correct answers during the training process. Therefore, we further propose an Answer Adjustment (AA) strategy to generate a set of accurate refined pseudolabels to supervise the generation of $y_{k}$ in the Answer Diffuser module. In particular, we assume the given answer is clean if the predicted proto-answer matches the original answer, otherwise, we generate a soft label using a weighted combination of the predicted proto-answer $\hat{p}_k$ and the given noisy label distribution $a_{k}$ , which can be denoted as: + +$$ +\bar {y} _ {k} = \left\{ \begin{array}{l l} w _ {t} \hat {p} _ {j} + (1 - w _ {t}) a _ {k}, & \hat {p} _ {k} \neq a _ {k} \\ a _ {k}, & \hat {p} _ {k} = a _ {k} \end{array} , \right. \tag {2} +$$ + +where $w_{t}$ is the weighting parameter. Note that the learning status can be estimated by the confidence scores of the predictions [10], we thereby design $w_{t}$ based on the model's prediction reflecting the overall learning status. Given the current training iteration $t$ , we denote $w_{t}$ as: + +$$ +w _ {t} = \tau w _ {t - 1} + (1 - \tau) \frac {1}{B} \sum_ {k = 1} ^ {B} \hat {p} _ {k}, \tag {3} +$$ + +where $\tau \in (0,1)$ is the momentum decay of EMA, set as 0.99. The $B$ indicates the number of samples within a minibatch. Through the newly proposed answer adjustment strategy, we can obtain a set of accurate refined pseudolabels $\bar{y}$ to supervise the generation of the final prediction $y$ in the Answer Diffuser module, which will greatly improve the prediction performance of the model. + +# 3.5. Answer Diffuser Module + +Given the ability of diffusion-based classifiers to manage data and label uncertainty effectively, we propose a diffusion-based classifier called the Answer Diffuser module. This module addresses the unique challenges of NM-VQA by classifying answers from a generative perspective, which helps mitigate issues like generating non-existent answers—a common problem in handling noisy labels [4, 12]. By using refined soft labels as supervision, the Answer Diffuser produces accurate, noise-resistant predictions that are particularly robust in noisy-label settings. + +With the condition feature $f^c$ and the refined soft label $\bar{y}$ , following the forward and reverse process of the diffusion models, we gradually introduce noise to the refined soft label $\bar{y}$ to obtain the noisy label $\bar{y}_T$ after $T$ steps, and progressively refine a random probability distribution $\bar{y}_T$ to predict the answer distribution $y$ that is close to the pseudo-label distribution $\bar{y}$ after $T$ steps. Notably, the forward can be represented as: + +$$ +q \left(\bar {y} _ {t} | \bar {y} _ {t - 1}, f ^ {c}\right) = \mathcal {N} \left(\bar {y} _ {t}; \mu_ {t} \left(\bar {y} _ {t - 1}, f ^ {c}, t\right), \beta_ {t} \mathbf {I}\right), \tag {4} +$$ + +$$ +\mu_ {t} = \sqrt {1 - \beta_ {t}} \bar {y} _ {t - 1} + (1 - \sqrt {1 - \beta_ {t}}) f ^ {c}, \tag {5} +$$ + +where $\beta_{t}$ is the variance schedule. Consequently, obtaining $\bar{y}_t$ with an arbitrary timestep $t$ can be represented as: + +$$ +q \left(\bar {y} _ {t} | \bar {y}, f ^ {c}\right) = \mathcal {N} \left(\bar {y} _ {t}; \sqrt {\bar {\alpha} _ {t}} \bar {y} + \left(1 - \sqrt {\bar {\alpha} _ {t}}\right) f ^ {c}, \left(1 - \bar {\alpha} _ {t}\right) \mathbf {I}\right), \tag {6} +$$ + +Where $\alpha_{t} = 1 - \beta_{t}$ and $\bar{\alpha}_{t} = \prod_{t}\alpha_{t}$ . It should be noted that $\mu_{t}$ can be viewed as an interpolation between soft pseudo-label $\bar{y}$ from NLR module and the predicted condition $f^{c}$ from ACG module, which gradually generates task-specific conditional information to suit the NM-VQA task. + +The reverse process continuously perform denoising process from $\bar{y}_T$ to obtain $y$ , which we hope to be close to $\bar{y}$ , where we learn a diffusion model $\theta$ to predict the noise level at each timestep, which can be represented as: + +$$ +p _ {\theta} \left(\bar {y} _ {t - 1} \mid \bar {y} _ {t}, f ^ {c}\right) = \mathcal {N} \left(\bar {y} _ {t - 1}; \mu_ {\theta} \left(\bar {y} _ {t}, f ^ {c}, t\right), \sigma_ {t} ^ {2} \mathbf {I}\right), \tag {7} +$$ + +where the $\mu_{\theta}(\bar{y}_t, f^c, t)$ is predicted mean value of the noise distribution at timestep $t$ , $\sigma_t^2$ is $\frac{1 - \bar{\alpha}_{t-1}}{1 - \bar{\alpha}_t} \beta_t$ . Our target is to encourage the predicted answer distribution to be close to the refined pseudo-label distribution $\bar{y}$ . Therefore, we adopt a MSE loss as a supervision, which can be denoted as: + +$$ +\mathcal {L} _ {d i f} = \operatorname {M S E} (y; \bar {y}). \tag {8} +$$ + +# 3.6. Training and Inference + +During the training process, we jointly optimize $\mathcal{L}_{dif}$ and $\mathcal{L}_{RFL}$ , which on one hand targets at generating refined correct pseudo-labels that are robust to label noise as the supervision for our Answer Diffuser, on the other hand, we encourage the Answer Diffuser to generate existent and accurate answer predictions, further reducing the impact of noisy labels. Therefore, the overall loss during training can be expressed as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {d i f}} + \alpha \mathcal {L} _ {R F L}, \tag {9} +$$ + +where $\alpha$ is hyperparameter to balance different losses. + +It should be noticed that during the inference stage, we only adopt the AD Module to predict answers while discarding the NLR module, as the NLR module targets at providing a precise supervision for the AD module learning. The corresponding noisy distribution $\bar{y}_T$ is replaced with randomly generated Gaussian noise. The model gradually refines the random distribution through the reverse process and obtains the final predicted probability distribution $y$ . The ultimate prediction class label $\hat{y} = \arg \max_l(y_l)$ , where $l$ indicates the index of the categories, is the answer with the highest probability score. + +# 4. Experiment + +# 4.1. Datasets + +VQA-RAD [20] is the most widely used radiology dataset for Med-VQA, comprising 315 images and 3,515 question-answer pairs, with each image corresponding to at least one question-answer pair. $58\%$ of the questions are close-end questions and the rest are openend questions. PathVQA [14] is constructed by extracting images along with corresponding captions from digital resources such as electronic textbooks and online libraries. It consists of 32,799 question-answer pairs, including 4,998 pathology images. Open-end questions account for $50.2\%$ of all questions and the rest are closed questions. To ensure comparability, both of the datasets have been divided following the MMQ method [7]. + +# 4.2. Noise Patterns and Analysis + +Due to the lack of suitable Med-VQA datasets with noisy labels and the difficulty of creating new datasets, we adopt semantic noisy types from the natural VQA domain [47] to existing medical VQA datasets. [47] demonstrates controlled semantic label noise by simulating human mislabeling behavior, which is more realistic than conventional random noise. We also follow the conventional VQA methods to validate our model by random label shuffling. + +The questions in Med-VQA tasks include two categories: closed-end (e.g., Yes/No questions with one-word + +answers) and open-end (e.g., wh-questions with longer responses). Following [47], for closed-ended answers, we use symmetric noise by randomly flipping the answer choices. Moreover, for open-ended answers, we create a semantic space of frequent answers using a pre-trained BERT model [21] to simulate human annotation errors. For each sample, the original answer is replaced by its closest noisy label within this semantic space. Our experiments highlight the sensitivity of prior Med-VQA methods to noisy labels, and we evaluate performance using $10\%$ and $20\%$ semantic noise ratios in the training datasets of VQA-RAD and PathVQA. Figure 2 visualizes our noisy pairs and the t-SNE representation of the semantic space, where ground-truth labels are replaced with semantically similar noisy labels. Moreover, we compare the performance of different methods by introducing random noise with a $20\%$ noise ratio into the training datasets of VQA-RAD and PathVQA. As shown in Table 1 and Table 2, at the same noise ratio, semantic noise impacts model performance more significantly than random noise and more closely resembles the type of noise encountered in actual clinical scenarios. + +# 4.3. Implementation Details + +Our method is trained on a single Nvidia 3090Ti GPU. We employ the Swin Transformer [28] as the vision encoder and the BERT model [21] as the text encoder. Our baseline model contains the Swin Transformer and BERT as encoder with transformer decoder without any answer denoise methods. The Adam optimizer is used, with an initial learning rate set to 1e-5. We adopt a batch size of 16 and a maximum of 100 epochs. The loss weight $\alpha$ is set to 0.5 for both datasets. For our model evaluation, we use only the AD Module to predict answers without the NLR module to ensure that the model parameters are at a similar level to those of other methods for comparison. The DiN framework is trained in an end-to-end fashion. The Med-VQA performance is assessed by accuracy scores. + +# 4.4. Performance Comparison + +We compare our proposed method with MMBERT [19] and Q2ATransformer [27], which are among the top performers in Med-VQA task. Notably, previous Med-VQA methods were not designed to address the issue of noisy labels. To fill this gap, we employ two mainstream uni-modal label denoising methods to compare. SimT [11] estimates noise transition matrices to correct label noise in a class-wise manner. CoDis [44], a co-teaching-based label denoising method, uses two sub-networks to select the clean label dataset based on the small-loss principle. We also compare our method with SNLC [47], the first method designed for natural VQA with noisy labels. As shown in Table 1 and Table 2, our DiN framework consistently outperforms the compared models on both datasets. The biggest drawback + +
    Noise TypeMethodVQA-RAD
    OpenCloseOverall
    CleanUpper Bound78.1780.0879.13
    10%-Semantic NoiseBaseline67.8668.8568.25
    MMBERT [19]63.3668.2166.42
    Q2ATransformer [27]66.7970.1768.48
    SimT [11]66.9369.7368.04
    CoDis [44]68.0270.5469.53
    SNLC [47]67.8371.3569.65
    DiN (Ours)72.6875.8174.24
    20%-Semantic NoiseBaseline54.2357.1456.01
    MMBERT [19]52.6856.6455.25
    Q2ATransformer [27]55.4360.0358.25
    SimT [11]53.7657.0555.82
    CoDis [44]54.1957.2856.42
    SNLC [47]56.4561.3058.88
    DiN (Ours)58.0663.1762.28
    20%-Random NoiseBaseline56.7160.3058.88
    MMBERT [19]55.4359.5957.97
    Q2ATransformer [27]58.0462.3760.68
    SimT [11]57.8662.8560.90
    CoDis [44]59.9560.5660.32
    SNLC [47]59.2163.8462.03
    DiN (Ours)61.0465.7763.93
    + +Table 1. Performance comparison on the VQA-RAD dataset. 'Open' indicates the open-end question and 'close' indicates the close-end question. The overall performance is the average performance of both question types. The best results are bold. Notably, SimT [11] and CoDis [44] are up-to-date representatives of NTM-based and co-teaching-based approaches, respectively. + +of these two Med-VQA methods is that neither is designed to address the issue of noisy labels, so they cannot prevent overfitting noisy patterns during the training process for NM-VQA tasks. SimT [11] did not bring significant performance improvements, primarily due to the limitations of the noise transition matrix (NTM), which only effectively captures noise patterns in simple noisy classification tasks. CoDis [44] performed better than NTM-based methods; but its two-branch co-teaching method doubles the parameters and uses a small-loss selection strategy better suited for simpler noise. SNLC [47], designed for noisy labels in natural VQA, relies on a basic robust loss function and fails to deliver competitive performance in the medical domain. In contrast, our DiN framework is specifically tailored for noisy labels in Med-VQA tasks. Figure 4 visualizes four examples of predicted answers from both the training and test sets across two datasets. In the training set, our method successfully corrects semantic noisy labels post-training, while in the test set, our model generates accurate predictions in multiple instances. This design allows DiN to consistently outperform other methods, demonstrating its effectiveness in addressing the unique challenges of NM-VQA tasks. + +# 4.5. Ablation Study + +To assess the contributions of our DiN framework, we conducted extensive ablation studies to demonstrate the efficiency of the different components of our model. + +
    Noise TypeMethodPathVQA
    OpenCloseOverall
    CleanUpper Bound52.6486.4572.61
    10%-Semantic NoiseBaseline37.8375.8162.32
    MMBERT [19]34.1873.2158.73
    Q2ATransformer [27]38.4276.8562.61
    SimT [11]36.5475.3562.06
    CoDis [44]37.8676.2863.02
    SNLC [47]38.8578.3364.18
    DiN (Ours)40.5480.2866.67
    20%-Semantic NoiseBaseline29.0670.0155.28
    MMBERT [19]27.1368.3552.41
    Q2ATransformer [27]30.1671.1156.28
    SimT [11]29.3870.6955.93
    CoDis [44]30.3671.1856.55
    SNLC [47]30.8871.2356.72
    DiN (Ours)32.4772.5658.14
    20%-Random NoiseBaseline32.2973.5357.03
    MMBERT [19]30.4572.0655.41
    Q2ATransformer [27]34.5074.7458.64
    SimT [11]35.1774.9159.01
    CoDis [44]35.6674.5058.96
    SNLC [47]36.7475.0359.71
    DiN (Ours)37.8576.1660.84
    + +Table 2. Performance comparison on the PathVQA dataset. 'Open' indicates the open-end question and 'close' indicates the close-end question. The overall performance is the average performance of both question types. The best results are bold. Notably, SimT [11] and CoDis [44] are up-to-date representatives of NTM-based and co-teaching-based approaches, respectively. + +
    ChoiceEncodersClassifierACGADRFLAAOpenCloseOverallOpenCloseOverall
    0✓✓✓67.8668.8568.2554.2357.1456.01
    1✓✓✓✓68.4670.7169.5655.0859.2757.64
    2✓✓✓✓70.7171.9271.1555.8660.8659.13
    3✓✓✓✓✓70.7373.0872.2556.2161.5460.57
    4✓✓✓✓✓71.1574.2972.7556.9762.2061.24
    5✓✓✓✓✓✓72.6875.8174.2458.0663.1762.28
    + +Table 3. Ablation study of our method on the VQA-RAD dataset with $10\%$ -Semantic Noise. ACG indicates our answer condition generator module, AD indicates our answer diffuser module. Note that our noisy label refinement module includes two parts, i.e., an answer adjust module (AA) and a noise robust focal loss function (RFL). Also note that the baseline method includes the vision encoder and the text encoder (Encoder), the auxiliary classifier (Classifier) and our ACG module. + +# 4.5.1. Impact of Answer Condition Generator + +The ACG module provides conditional information to support the generative process in the AD module and features for training the auxiliary classifier in the NLR module. When only the encoders, ACG, and the auxiliary classifier are used for answer prediction (i.e., the fused image-question features are sent through ACG to interact with the candidate answer embeddings, and the output feature $f_{k}^{c}$ is used to train the auxiliary classifier), the accuracy is limited to $68.25\%$ overall accuracy (Choice 0 in Table 3), primarily due to rapid overfitting and the inability to effectively handle noisy labels. Notably, incorporating the AD module with the conditional information from ACG significantly enhances the overall accuracy to $71.15\%$ (Choice 2). The ACG module not only enhances the auxiliary classi + +![](images/b74ab40e8180e9815bfad6a792dd23dfc6851340cd590a3ad9433e082242ba15.jpg) +Train Set with Noisy Answers +Test Set without Answers +Figure 4. Visualization of example results from our DiN framework on the VQA-RAD and PathVQA datasets. The first row presents examples from the training set with $10\%$ -Semantic Noise, where our method corrects the noisy incorrect answers during the training process. The second row shows two examples from the test sets of both datasets. + +![](images/cf25b1b2dcc3de79481d3492b703e91baefed1a499fa8568234770061b72c566.jpg) +Question: Where is/are the lesion located? +Noisy Answers : Left temporal lobe +Our Prediction: Right temporal lobe + +![](images/4f7ddf81e80f6d5b49a5d88a8533e0437aab68204363ce9fde23dd49ad459fb6.jpg) +Train Set with Noisy Answers +Test Set without Answers + +![](images/e8510b7b4a05bbf9202d52b29c8f1c0ff09af110b03e9053aa94eb3e5fd26096.jpg) +Question: What shows the bland cytology that typifies neuroendocrine tumors? +Noisy Answers : Low magnification +Our Prediction : High magnification + +![](images/031c34d8e5f701a714e01e1af22441675e71f5692d1fd759c0482de9b7768d57.jpg) +Question: What type of sequence is displayed in this image? +Our Prediction : T2 weighted MRI + +![](images/7eb0f32f5575ee0c47c67c507ddbf567de2ea5976c87ad1ab3e01f43b94f4e26.jpg) + +![](images/7932e2226505010c3b7696e84342c8b372f10bd146230ef65fe436b6d07deffd.jpg) +Question: What is the poorly cohesive tumor in the retina seen abutting? +Our Prediction : Optic nerve + +VQA-RAD +PathVQA + +
    NameChoiceVQA-RAD with 10% Noise
    OpenCloseOverall
    \(L_r\)CE [49]70.7373.0872.25
    Focal [24]71.4373.8573.10
    SCE [41]71.8673.8673.50
    RFL (ours)72.6875.8174.24
    \(L_{dif}\)KL72.8675.3874.00
    MSE72.6875.8174.24
    \(\alpha\)0.171.7974.2373.75
    0.572.6875.8174.24
    172.1675.9274.18
    Step T1072.5175.7674.03
    5072.6875.8174.24
    10071.9374.6673.87
    + +Table 4. Ablation studies on different hyperparameters, i.e., $\alpha$ that balances different loss functions and the number of timesteps $T$ in our answer diffuser module, and ablation studies on different options of loss functions in our noisy label refinement module. + +fier's ability to capture medical domain knowledge but also strengthens the diffusion-based AD module by providing reliable Med-VQA condition information. + +# 4.5.2. Impact of Noisy Label Refinement + +The Noisy Label Refinement (NLR) module comprises two sub-components: Robust Loss (RFL) and answer adjustment (AA). The RFL is designed to mitigate the impact of noise on the encoders' features. As shown in Table 3, incorporating the RFL leads to an increase in overall accuracy from $68.25\%$ to $69.56\%$ without using AD module and from $71.15\%$ (Choice 2) to $72.75\%$ (Choice 4) with AD module. We experimented with different combinations of robust loss functions and found that our proposed RFL is the most effective for NM-VQA tasks, as demonstrated in Table 4. The answer adjustment (AA) component is specifically designed to reduce noise impact on the Answer Diffuser (AD) module. The addition of the AA component enhances the overall accuracy from $71.15\%$ (Choice 2) to $72.25\%$ (Choice 3) and further from $72.75\%$ (Choice 4) to $74.24\%$ (Choice 5) with the assistance of RFL. + +# 4.5.3.Impact of Answer Diffuser + +As shown in Table 3, incorporating the AD module for Med-VQA prediction enhances the overall performance from $68.25\%$ (Choice 0) to $71.15\%$ (Choice 2). When all our proposed modules are combined, the overall performance further improves to $74.24\%$ (Choice 5). We also examined the hyperparameter $\alpha$ , which balances the AD module and the auxiliary classifier, and the type of $L_{dif}$ as detailed in Table 4. Our framework demonstrates insensitivity to both choices. We selected $\alpha = 0.5$ and MSE loss as $L_{dif}$ . Furthermore, we investigated the impact of varying $T$ on model performance, as presented in Table 4. While increasing $T$ results in higher computational costs, our model achieves optimal performance at $T = 50$ . This differs from the image generation, where 1000 steps are typically used. This distinction is likely due to the precise pixel-level generation required in image tasks, whereas our model focuses on deriving a class probability distribution. + +# 5. Conclusion + +In conclusion, we have introduced DiN as the first approach to address the Med-VQA with noisy labels. Our method uses the inherent robustness of diffusion models as AD module to deal with noisy data. We designed the ACG module to fuse image, question features and candidate answering embeddings, generating condition information supporting both the AD and NLR modules. 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Springer, 2024. 1 \ No newline at end of file diff --git a/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/images.zip b/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2cf810d38c437cbd67f1a27e3fe9b56c0594cc77 --- /dev/null +++ b/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1912dac0e6ff7772ac9fee8b97dc97a6373e158fa2535a4f713d41bf51a36d7d +size 450554 diff --git a/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/layout.json b/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..33d51eb79ac044b70fc0885af420fb92837da74c --- /dev/null +++ b/2025/DiN_ Diffusion Model for Robust Medical VQA with Semantic Noisy Labels/layout.json @@ -0,0 +1,9786 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 72, + 103, + 538, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 103, + 538, + 120 + ], + "spans": [ + { + "bbox": [ + 72, + 103, + 538, + 120 + ], + "type": "text", + "content": "DiN: Diffusion Model for Robust Medical VQA with Semantic Noisy Labels" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 92, + 142, + 521, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 142, + 521, + 172 + ], + "spans": [ + { + "bbox": [ + 92, + 142, + 521, + 172 + ], + "type": "text", + "content": "Erjian Guo1 Zhen Zhao2 Zicheng Wang1 Tong Chen1 Yunyi Liu1 Luping Zhou1* \n1University of Sydney Shanghai AI Laboratory" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 199, + 200, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 199, + 200, + 211 + ], + "spans": [ + { + "bbox": [ + 151, + 199, + 200, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 224, + 296, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 224, + 296, + 488 + ], + "spans": [ + { + "bbox": [ + 54, + 224, + 296, + 488 + ], + "type": "text", + "content": "Medical Visual Question Answering (Med-VQA) systems benefit the interpretation of medical images containing critical clinical information. However, the challenge of noisy labels and limited high-quality datasets remains underexplored. To address this, we establish the first benchmark for noisy labels in Med-VQA by simulating human mislabeling with semantically designed noise types. More importantly, we introduce the DiN framework, which leverages a diffusion model to handle noisy labels in Med-VQA. Unlike the dominant classification-based VQA approaches that directly predict answers, our Answer Diffuser (AD) module employs a coarse-to-fine process, refining answer candidates with a diffusion model for improved accuracy. The Answer Condition Generator (ACG) further enhances this process by generating task-specific conditional information via integrating answer embeddings with fused image-question features. To address label noise, our Noisy Label Refinement(NLR) module introduces a robust loss function and dynamic answer adjustment to further boost the performance of the AD module. Our DiN framework consistently outperforms existing methods across multiple benchmarks with varying noise levels1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 511, + 135, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 511, + 135, + 522 + ], + "spans": [ + { + "bbox": [ + 55, + 511, + 135, + 522 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 531, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 531, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 531, + 295, + 676 + ], + "type": "text", + "content": "Medical Visual Question Answering (Med-VQA) tasks focus on accurately responding to medical inquiries by integrating visual information from medical images [6, 26, 39]. It holds great potential in applications like assisting diagnosis, enhancing patient understanding, and supporting clinical education [3, 36]. Recently, VQA models have achieved impressive results in the natural VQA domain [13, 38, 46]. This success has largely been driven by the availability of large-scale natural VQA datasets with well-structured accurate annotations [25, 29]. However, for Med-VQA, the annotation process poses unique challenges. It requires specialized medical expertise and skills from annotators, lead" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 319, + 200, + 428, + 250 + ], + "blocks": [ + { + "bbox": [ + 319, + 200, + 428, + 250 + ], + "lines": [ + { + "bbox": [ + 319, + 200, + 428, + 250 + ], + "spans": [ + { + "bbox": [ + 319, + 200, + 428, + 250 + ], + "type": "image", + "image_path": "0333255bbcd2958904f191cd821042e7c8e35989a5e50f6396aa3b80543b983f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 252, + 406, + 261 + ], + "lines": [ + { + "bbox": [ + 343, + 252, + 406, + 261 + ], + "spans": [ + { + "bbox": [ + 343, + 252, + 406, + 261 + ], + "type": "text", + "content": "(a) Classification-based" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 441, + 201, + 545, + 250 + ], + "blocks": [ + { + "bbox": [ + 441, + 201, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 441, + 201, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 441, + 201, + 545, + 250 + ], + "type": "image", + "image_path": "47e58569552ea3abe9c7d8509dd133934de7ccb3bcedc3a7872ad9b4615806ad.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 320, + 262, + 550, + 355 + ], + "blocks": [ + { + "bbox": [ + 462, + 252, + 520, + 259 + ], + "lines": [ + { + "bbox": [ + 462, + 252, + 520, + 259 + ], + "spans": [ + { + "bbox": [ + 462, + 252, + 520, + 259 + ], + "type": "text", + "content": "(b) Generation-based" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 320, + 262, + 550, + 355 + ], + "lines": [ + { + "bbox": [ + 320, + 262, + 550, + 355 + ], + "spans": [ + { + "bbox": [ + 320, + 262, + 550, + 355 + ], + "type": "image", + "image_path": "fdc7156e577d74d106ed7b51edd7940973a748d654df64f26b92bc4f65ab92d3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 369, + 555, + 458 + ], + "lines": [ + { + "bbox": [ + 313, + 369, + 555, + 458 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 555, + 458 + ], + "type": "text", + "content": "Figure 1. Comparison between our diffusion-based method and previous Med-VQA approaches. Previous Med-VQA methods, designed for clean label datasets, include classification-based (a) and generation-based (b) approaches. In contrast, our diffusion-based method (c) classifies answers from a generative perspective and denoises answers by Answer Diffuser with the support of Answer Condition Generator and the Noisy Label Refinement module (employed only during the training process)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 483, + 555, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 555, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 555, + 579 + ], + "type": "text", + "content": "ing to increased complexity and higher potential for label noise [34, 35, 51]. Additionally, inter-observer variability among medical professionals further complicates the annotation process, contributing to labeling inconsistencies [16, 31, 43]. While the issue of noisy labels is a well-known challenge in machine learning, it has not been thoroughly explored in Med-VQA, despite the need for highly accurate medical annotations." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "While existing label-denoising methods have shown promise, they are primarily designed for uni-modal tasks like image classification or segmentation [23, 42, 50]. Directly applying them for the multi-modal Med-VQA task is not suitable for two key reasons. First, conventional noise models, such as random label shuffling, fail to capture the semantic nuances essential in Med-VQA, where label noise often retains medically relevant information rather than arbitrary noise. We argue that noisy labels in VQA should retain semantic coherence aligned with human cognitive levels. As shown in Fig. 2, examples of noisy QA" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 683, + 295, + 713 + ], + "type": "text", + "content": "*Corresponding author, luping.zhou@sydney.edu.au. Zhou is supported by Australian Research Council (ARC DP200103223). \n1Code: https://github.com/Erjian96/DiN" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14337" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 70, + 288, + 235 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 288, + 235 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 288, + 235 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 288, + 235 + ], + "type": "image", + "image_path": "34f5f03b75efbc476203ce40121b91cba3f71c8268c679a5e1d8a15774e2cdbf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 245, + 555, + 280 + ], + "lines": [ + { + "bbox": [ + 54, + 245, + 555, + 280 + ], + "spans": [ + { + "bbox": [ + 54, + 245, + 555, + 280 + ], + "type": "text", + "content": "Figure 2. Visualization of the semantic answer pairs in t-SNE and examples of noisy answers. Similar colors represent the degree of feature similarity from a pretrained BERT model. We randomly display 8 semantic pairs in the t-SNE plots of VQA-RAD dataset. Ground-truth labels are replaced with their semantic pairs, which we refer to as semantically noisy answers [47]." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 290, + 72, + 373, + 150 + ], + "blocks": [ + { + "bbox": [ + 290, + 72, + 373, + 150 + ], + "lines": [ + { + "bbox": [ + 290, + 72, + 373, + 150 + ], + "spans": [ + { + "bbox": [ + 290, + 72, + 373, + 150 + ], + "type": "image", + "image_path": "495e599bdf21ce37a4cfd859e151f21e799e3a9a5a50da8fa625a8f3422ccc01.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 290, + 151, + 373, + 228 + ], + "blocks": [ + { + "bbox": [ + 290, + 151, + 373, + 228 + ], + "lines": [ + { + "bbox": [ + 290, + 151, + 373, + 228 + ], + "spans": [ + { + "bbox": [ + 290, + 151, + 373, + 228 + ], + "type": "image", + "image_path": "8a689d5ad00407c0aa6dd2fa58d32202f13720cdbd4c063d1ea0bb29ea21fb97.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 380, + 83, + 463, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 83, + 463, + 95 + ], + "spans": [ + { + "bbox": [ + 380, + 83, + 463, + 95 + ], + "type": "text", + "content": "Question Type: Open" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 380, + 95, + 537, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 95, + 537, + 106 + ], + "spans": [ + { + "bbox": [ + 380, + 95, + 537, + 106 + ], + "type": "text", + "content": "Question: Why is free air present in image?" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 380, + 106, + 461, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 106, + 461, + 116 + ], + "spans": [ + { + "bbox": [ + 380, + 106, + 461, + 116 + ], + "type": "text", + "content": "Random Noisy: Ribs" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 380, + 117, + 521, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 117, + 521, + 127 + ], + "spans": [ + { + "bbox": [ + 380, + 117, + 521, + 127 + ], + "type": "text", + "content": "Semantic Noisy: Hydropneumothorax" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 380, + 128, + 493, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 128, + 493, + 137 + ], + "spans": [ + { + "bbox": [ + 380, + 128, + 493, + 137 + ], + "type": "text", + "content": "Ground-truth: Pneumothorax" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 380, + 162, + 468, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 162, + 468, + 174 + ], + "spans": [ + { + "bbox": [ + 380, + 162, + 468, + 174 + ], + "type": "text", + "content": "Question Type: Closed" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 380, + 174, + 498, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 174, + 498, + 185 + ], + "spans": [ + { + "bbox": [ + 380, + 174, + 498, + 185 + ], + "type": "text", + "content": "Question: Is the heart enlarged?" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 380, + 185, + 460, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 185, + 460, + 195 + ], + "spans": [ + { + "bbox": [ + 380, + 185, + 460, + 195 + ], + "type": "text", + "content": "Random Noisy: Skin" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 380, + 196, + 460, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 196, + 460, + 206 + ], + "spans": [ + { + "bbox": [ + 380, + 196, + 460, + 206 + ], + "type": "text", + "content": "Semantic Noisy: Yes" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 380, + 207, + 452, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 207, + 452, + 217 + ], + "spans": [ + { + "bbox": [ + 380, + 207, + 452, + 217 + ], + "type": "text", + "content": "Ground-truth: No" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "spans": [ + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "type": "text", + "content": "pairs and their corresponding t-SNE representations illustrate this difference: unlike the arbitrary and meaningless answers generated by random noise, our constructed semantic noise resembles real-world scenarios, closer to human mislabeling. Second, these methods are not equipped to handle the complexity of Med-VQA, which integrates both image and text modalities. For example, co-teaching methods [44] add considerable model complexity by requiring two branch networks, while Noise Transition Matrix (NTM) methods [11] struggle with noisy label distribution estimation as the number of Med-VQA classes grows. While current leading methods like SNLC [47] in the natural VQA domain focus on improving representation through robust contrastive loss, these studies address noise in a relatively coarse way and fall short when dealing with the medically relevant label noise in Med-VQA. For instance, with a " + }, + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "type": "text", + "content": " noise ratio, SNLC [47] achieves " + }, + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "type": "inline_equation", + "content": "62\\%" + }, + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "type": "text", + "content": " accuracy on MedVQA with random noise but drops to " + }, + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "type": "inline_equation", + "content": "58\\%" + }, + { + "bbox": [ + 54, + 299, + 296, + 552 + ], + "type": "text", + "content": " when handling our semantic noise. In summary, our constructed semantic noise in Med-VQA is both practically relevant and presents a more challenging task to effectively handle." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "type": "text", + "content": "In the literature, two main approaches have emerged for medical VQA: classification-based and generation-based methods, as shown in Figure 1. Classification-based methods are generally straightforward and efficient but often struggle with low-frequency answers, which becomes especially pronounced in complex domains like Med-VQA [1, 9]. In contrast, generation-based methods offer more flexibility by constructing answers instead of selecting from predefined categories; however, they inevitably generate unrealistic or non-existent answers, reducing overall accuracy and reliability [27, 30]. To this end, motivated by the success of diffusion models in label refinement [2, 33], we propose leveraging them to bridge the gap between classi" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 300, + 555, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 555, + 442 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 555, + 442 + ], + "type": "text", + "content": "fication and generation approaches, enabling answer classification from a generative perspective. Diffusion models can offer a balance between classification and generative approaches for Med-VQA. Prior studies [4, 12] have also demonstrated that the probabilistic nature of diffusion models effectively handles data and label uncertainty, leading to more robust predictions. Conditioned on discriminative feature and label information, diffusion models offer a promising solution for the noisy labels in Med-VQA, using their stochastic nature to reconstruct class prototypes during reverse sampling and generate probability intervals across class labels." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 556, + 715 + ], + "type": "text", + "content": "To improve Med-VQA performance in the presence of noisy labels and harness the benefits of diffusion models, we propose the conditional Diffusion model for Med-VQA with Noisy labels (DiN) framework to address challenging semantic noisy labels. To mimic human-like mislabeling, we construct the training set by replacing ground-truth answers with semantically related noisy pairs, selected using a pre-trained BERT model. To the best of our knowledge, this is the first study addressing Med-VQA with noisy labels and the first application of diffusion models to this task. Our framework comprises three key modules. The Answer Denoiser (AD) module leverages robust conditional diffusion models, utilizing their powerful gradual refinement capabilities for Med-VQA. As shown in Figure 1, the generative process begins with a noisy label estimation, which is progressively refined to recover a clean label, analogous to the reverse denoising process in diffusion models. This allows coarse-to-fine filtering of potential answers, significantly improving accuracy and robustness. However, the effectiveness of the AD module's refinement is highly dependent on the generation conditions, and the lack of accurate clean labels exacerbates this challenge. To this end, we further pro" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14338" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "content": "pose the Answer Condition Generator (ACG) and Noisy Label Refinement (NLR) module to provide more accurate and reliable conditions. The ACG adopts a transformer decoder to fuse multi-modal image and question features, as well as learnable candidate embedding for delivering more informative generation conditions. The NLR, utilized only during training, refines noisy ground-truth labels dynamically through pseudo-labels generated by an auxiliary classifier to supervise the AD module. This synergy across modules enhances precision and robustness in managing noisy labels for Med-VQA tasks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 205, + 274, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 205, + 274, + 216 + ], + "spans": [ + { + "bbox": [ + 67, + 205, + 274, + 216 + ], + "type": "text", + "content": "Our main contributions are summarized as follows." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 217, + 295, + 407 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 56, + 217, + 295, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 217, + 295, + 264 + ], + "spans": [ + { + "bbox": [ + 56, + 217, + 295, + 264 + ], + "type": "text", + "content": "- We propose the DiN framework, the first to address MedVQA tasks with noisy labels (NM-VQA) by integrating a diffusion model that classifies answers from a generative and coarse-to-fine perspective." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 265, + 295, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 265, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 56, + 265, + 295, + 312 + ], + "type": "text", + "content": "- We introduce semantic noise types tailored to Med-VQA tasks and construct challenging benchmark datasets that simulate human labeling errors based on an thorough analysis of existing datasets." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 312, + 295, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 312, + 295, + 372 + ], + "spans": [ + { + "bbox": [ + 56, + 312, + 295, + 372 + ], + "type": "text", + "content": "- We design the Answer Condition Generator (ACG) and Noisy Label Refinement (NLR) modules to support the diffusion-based Answer Diffuser (AD). ACG guides AD with conditions, while NLR refines noisy labels using pseudo-labels from an auxiliary classifier." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 373, + 295, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 373, + 295, + 407 + ], + "spans": [ + { + "bbox": [ + 56, + 373, + 295, + 407 + ], + "type": "text", + "content": "- Our method consistently outperforms existing approaches on two Med-VQA datasets with varying noise ratios, demonstrating its robustness and effectiveness." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 421, + 142, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 421, + 142, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 421, + 142, + 433 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 441, + 246, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 441, + 246, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 441, + 246, + 453 + ], + "type": "text", + "content": "2.1. Medical Visual Question Answering" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 459, + 295, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 295, + 662 + ], + "type": "text", + "content": "Med-VQA is still in its early stages, and its current performance remains unsatisfactory. Most methods, such as those in [7, 27, 30, 31], adopt a classification-based approach, where each answer is treated as a class, and a model predicts the answer by applying classification to the fused image-question features. This classification-based approach simplifies the task by reducing its complexity and narrowing the answer search space. Alternatively, some studies [8, 19] approach VQA as a generation problem, generating answers word by word. These generation-based methods face challenges due to the vast search space, often leading to inaccurate answers, which limits their effectiveness in medical VQA. However, existing Med-VQA methods assume that the entire training dataset consists of clean labels, overlooking the challenge of noisy labels (NM-VQA). To address this gap, we introduce Med-VQA datasets with noisy labels and propose a solution for the NM-VQA problem." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 671, + 286, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 671, + 286, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 671, + 286, + 685 + ], + "type": "text", + "content": "2.2. Learning with Noise Labels and Noise Types" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "Learning with noise labels has been extensively studied in recent works. For example, some methods estimated" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 553, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 348 + ], + "type": "text", + "content": "noise transition matrices to correct label noise in a class-wise manner [11, 22]. Other popular methods reduced the effects of noisy labels by using noise-tolerant loss functions [47]. However, these methods tend to perform poorly when confronted with high noise rates and a large number of classes in Med-VQA tasks. One typical alternative way is coteaching-based methods CoDis [44], which require two branch networks, and introduce a double number of additional parameters, thereby exacerbating the issue of model complexity in Med-VQA tasks that necessitate both image and text encoders within a single network. Given these challenges, it is valuable to explore methods for developing robust Med-VQA models under reasonable noisy data. Most methods to deal with artificially synthesized noisy labels were initially proposed for classification tasks [17]. In these studies, synthesized noisy labels typically focus on both symmetric and asymmetric label noise. Symmetric noise flips labels randomly with equal probability, while asymmetric noise flips labels based on fixed rules. However, when it comes to Med-VQA tasks, symmetric and asymmetric noise models appear unreasonable. Unlike the traditionally synthesized label noise for classification, we propose the semantic label noise for Med-VQA tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 356, + 417, + 368 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 356, + 417, + 368 + ], + "spans": [ + { + "bbox": [ + 314, + 356, + 417, + 368 + ], + "type": "text", + "content": "2.3. Diffusion Models" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 374, + 555, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 374, + 555, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 374, + 555, + 601 + ], + "type": "text", + "content": "Diffusion models [2, 18, 32, 33, 45] are a new class of generative model. During training, they initially add noise to labels through a forward process until they approximate a Gaussian distribution. Then, in the reverse process, they learn to denoise and recover the original labels [15, 37, 48]. In recent years, their remarkable success in the generative domain, particularly in visual generation [33], has been groundbreaking, completely surpassing previous generative models. Due to its progressive refinement of labels and continuous improvements in training and inference efficiency, the diffusion model has been applied in various fields, such as recommendation systems [40] and image detection [5]. For example, the CARD [12] model transforms deterministic classification into a conditional label generation process, enabling more flexible uncertainty modeling in the labeling process. However, to our knowledge, diffusion models have not yet been applied to tackle Med-VQA tasks. Therefore, to address this gap, we aim to fully leverage the unique characteristics of diffusion models for Med-VQA tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 614, + 374, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 614, + 374, + 625 + ], + "spans": [ + { + "bbox": [ + 314, + 614, + 374, + 625 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 314, + 634, + 410, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 634, + 410, + 647 + ], + "spans": [ + { + "bbox": [ + 314, + 634, + 410, + 647 + ], + "type": "text", + "content": "3.1. Problem setting" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "text", + "content": "In the context of Med-VQA tasks with noisy labels (NMVQA) problem, our task involves an input set of medical images " + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{v_{i}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "text", + "content": " and a set of questions " + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Q} = \\{q_j\\}_{j = 1}^M" + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "text", + "content": " with the corresponding answers " + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{A} = \\{a_j\\}_{j = 1}^M" + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "text", + "content": ". Each image " + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "text", + "content": " is associated with " + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 313, + 652, + 553, + 713 + ], + "type": "text", + "content": " questions and answers," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14339" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 72, + 529, + 293 + ], + "blocks": [ + { + "bbox": [ + 85, + 72, + 529, + 293 + ], + "lines": [ + { + "bbox": [ + 85, + 72, + 529, + 293 + ], + "spans": [ + { + "bbox": [ + 85, + 72, + 529, + 293 + ], + "type": "image", + "image_path": "31fd7da671a952ebd0d89229b86a349d4a5c18645aad210c955259fe5254dae0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 302, + 555, + 381 + ], + "lines": [ + { + "bbox": [ + 54, + 302, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 54, + 302, + 555, + 381 + ], + "type": "text", + "content": "Figure 3. The proposed DiN framework consists of three key modules: 1) Answer Condition Generator (ACG): This module interacts the image and question multi-modal features with features of the image-question pair knowledge from Answer Condition Embedding (ACE) to obtain Med-VQA condition information. 2) Noisy Label Refinement (NLR): This module contains a robust loss function, " + }, + { + "bbox": [ + 54, + 302, + 555, + 381 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{RFL}" + }, + { + "bbox": [ + 54, + 302, + 555, + 381 + ], + "type": "text", + "content": ", which supervises the proto-answer, to mitigate the impact of noisy original answers on the two encoders' acquisition of medical domain knowledge. The Answer adjustment of NLR uses proto-answers and original noisy answers to generate pseudo-label to supervise the AD module. 3) Answer Diffuser (AD): This module refines the noisy answer distribution, simulating a generation process to select the correct answers. Notably, we use only the AD Module to predict answers without the NLR module during inference process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "spans": [ + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": "while " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{N} M_i" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": " equals " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": ". For the convenience of description, we use the subscript " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": " to represent the index of each image-question-answer pair and there are " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": " image-question-answer pairs in total. Specifically, " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "v_k \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": " represents an input image with a size of " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": " channels, while " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "a_k \\in \\{0,1\\}^L" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": " serves as the one-hot encoded ground truth answer label, where " + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 54, + 399, + 298, + 534 + ], + "type": "text", + "content": " is the total number of answer classes. Note that only noisy labels are available during the training stage, while the clean labels are only available during the inference stage and are used solely for validating the model's performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 540, + 124, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 124, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 124, + 552 + ], + "type": "text", + "content": "3.2. Overview" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": "The DiN framework, shown in Figure 3, comprises three main modules: Answer Condition Generator module (ACG) introduced in Sec. 3.3, Noisy Label Refinement module (NLR) described in Sec. 3.4, and Answer Diffuser module (AD) detailed in Sec. 3.5. The input image " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "v_{k}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": " and question " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "q_{k}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": " are processed by Vision Encoder and Text Encoder, respectively, to extract visual features " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "f_{k}^{v}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": " and question features " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "f_{k}^{q}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": ". The fused features produce key embeddings " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "K_{ey}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": " and value embeddings " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "V_{value}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": ", which are fed into the ACG module. There, they interact with learnable answer embeddings " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "Q_{uery}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": " to generate an answer-aware condition " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "f_{k}^{c}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": ". This condition is then used by the AD module to generate the predicted answer " + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "inline_equation", + "content": "y_{k}" + }, + { + "bbox": [ + 55, + 557, + 297, + 715 + ], + "type": "text", + "content": " via a denoising pro" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "text", + "content": "cess. Simultaneously, " + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "inline_equation", + "content": "f_{k}^{c}" + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "text", + "content": " is fed into the NLR module to train an auxiliary classifier, which yields a proto-answer " + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "inline_equation", + "content": "\\hat{y}_k" + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "text", + "content": ". The proto-answer is then refined to create a pseudo-label " + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "inline_equation", + "content": "\\bar{y}_n" + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "text", + "content": " used to supervise the generation of the " + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "inline_equation", + "content": "y_{k}" + }, + { + "bbox": [ + 313, + 400, + 556, + 475 + ], + "type": "text", + "content": ". Note that the NLR module will be discarded in the inference stage, and the AD module will generate the answer predictions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 479, + 514, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 514, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 514, + 491 + ], + "type": "text", + "content": "3.3. Answer Condition Generator Module" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": "The newly proposed ACG module is designed to generate an answer-aware condition, " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "f_{k}^{c}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": ", for Noisy Label Refinement module (NLR) and Answer Diffuser module (AD). As introduced in Sec. 3.2, we obtain visual features " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "f_{k}^{v}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": " and question features " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "f_{k}^{q}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": " from input images and questions by Vision Encoder and Text Encoder. These features are then fused to produce key embeddings " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "K_{ey}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": " and value embeddings " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "V_{value}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": ", which are fed into the ACG module. In the ACG module, we introduce learnable candidate answer embeddings to query the existence of each answer class to a given image-question pair. For the " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": " answer classes, we need " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": " candidate answer embeddings initialized randomly and updated during training. A self-attention mechanism is applied to compute relationships between the answer embeddings, yielding query embeddings " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "Q_{query}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": ". Cross-attention is then used to combine " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "Q_{query}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "K_{ey}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "V_{value}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": ", producing a fused feature " + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "inline_equation", + "content": "f_{k}^{f}" + }, + { + "bbox": [ + 313, + 496, + 556, + 715 + ], + "type": "text", + "content": " that captures the interaction between answer embeddings and image-question features. Finally, the" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14340" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 71, + 294, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 71, + 294, + 122 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 294, + 122 + ], + "type": "text", + "content": "feature " + }, + { + "bbox": [ + 55, + 71, + 294, + 122 + ], + "type": "inline_equation", + "content": "f_{k}^{c} = \\mathrm{Linear}(f_{k}^{f})" + }, + { + "bbox": [ + 55, + 71, + 294, + 122 + ], + "type": "text", + "content": " is generated as conditions to guide the generative process in the AD module, while " + }, + { + "bbox": [ + 55, + 71, + 294, + 122 + ], + "type": "inline_equation", + "content": "f_{k}^{f}" + }, + { + "bbox": [ + 55, + 71, + 294, + 122 + ], + "type": "text", + "content": " is simultaneously sent to the NLR module to train the auxiliary classifier." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 129, + 230, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 129, + 230, + 142 + ], + "spans": [ + { + "bbox": [ + 55, + 129, + 230, + 142 + ], + "type": "text", + "content": "3.4. Noisy Label Refinement Module" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 146, + 296, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 146, + 296, + 241 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 296, + 241 + ], + "type": "text", + "content": "Considering that the model learning will suffer severely from label noise, in this part, we tackle the problem by proposing a Noisy Label Refinement module (NLR), where we first propose a new noise robust loss function to improve the noise resilience of our method and we further come up with an answer adjustment strategy to generate accurate refined pseudo-label " + }, + { + "bbox": [ + 55, + 146, + 296, + 241 + ], + "type": "inline_equation", + "content": "\\bar{y}_k" + }, + { + "bbox": [ + 55, + 146, + 296, + 241 + ], + "type": "text", + "content": " to supervise the generation of " + }, + { + "bbox": [ + 55, + 146, + 296, + 241 + ], + "type": "inline_equation", + "content": "y_{k}" + }, + { + "bbox": [ + 55, + 146, + 296, + 241 + ], + "type": "text", + "content": " in the Answer Diffuser module." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "spans": [ + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "type": "text", + "content": "Specifically, we first feed the condition " + }, + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "type": "inline_equation", + "content": "f_{k}^{c}" + }, + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "type": "text", + "content": " into an auxiliary classifier, which is a one-layer linear MLP, to generate the proto-answer probability distribution " + }, + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\hat{p}_{k}" + }, + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "type": "text", + "content": ". However, on one hand, the noisy supervision " + }, + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "type": "inline_equation", + "content": "a_{k}" + }, + { + "bbox": [ + 55, + 243, + 296, + 386 + ], + "type": "text", + "content": " will greatly influence the accuracy of the proto-answer. On the other hand, the class imbalance problem in Med-VQA is much more severe than other tasks, such bias will severely influence the answer generation. Therefore, we introduce a new noise robust focal loss function (RFL) to tackle the issues, where we incorporate a symmetric cross entropy loss with a focal loss, aiming to improve noise resilience and balance the effects of class imbalance. The RFL is then formulated as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 393, + 296, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 393, + 296, + 426 + ], + "spans": [ + { + "bbox": [ + 62, + 393, + 296, + 426 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {R F L} = - \\sum_ {l = 1} ^ {L} a _ {k} (1 - \\hat {p} _ {k}) ^ {\\gamma} \\log \\hat {p} _ {k} - \\sum_ {l = 1} ^ {L} \\hat {p} _ {k} \\log a _ {k}, \\tag {1}", + "image_path": "2f9d2dae34b735b379719695dbb476ec2908f4a9a7fb7f992c8e11b0ed17f0c7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 434, + 295, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 295, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 295, + 445 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 434, + 295, + 445 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 434, + 295, + 445 + ], + "type": "text", + "content": " is the hyper-parameter and we set " + }, + { + "bbox": [ + 55, + 434, + 295, + 445 + ], + "type": "inline_equation", + "content": "\\gamma = 1" + }, + { + "bbox": [ + 55, + 434, + 295, + 445 + ], + "type": "text", + "content": " by default." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "spans": [ + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "type": "text", + "content": "Benefiting from our newly proposed RFL loss, the model is prone to generate correct answers during the training process. Therefore, we further propose an Answer Adjustment (AA) strategy to generate a set of accurate refined pseudolabels to supervise the generation of " + }, + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "type": "inline_equation", + "content": "y_{k}" + }, + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "type": "text", + "content": " in the Answer Diffuser module. In particular, we assume the given answer is clean if the predicted proto-answer matches the original answer, otherwise, we generate a soft label using a weighted combination of the predicted proto-answer " + }, + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "type": "inline_equation", + "content": "\\hat{p}_k" + }, + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "type": "text", + "content": " and the given noisy label distribution " + }, + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "type": "inline_equation", + "content": "a_{k}" + }, + { + "bbox": [ + 55, + 446, + 296, + 565 + ], + "type": "text", + "content": ", which can be denoted as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 93, + 574, + 296, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 574, + 296, + 607 + ], + "spans": [ + { + "bbox": [ + 93, + 574, + 296, + 607 + ], + "type": "interline_equation", + "content": "\\bar {y} _ {k} = \\left\\{ \\begin{array}{l l} w _ {t} \\hat {p} _ {j} + (1 - w _ {t}) a _ {k}, & \\hat {p} _ {k} \\neq a _ {k} \\\\ a _ {k}, & \\hat {p} _ {k} = a _ {k} \\end{array} , \\right. \\tag {2}", + "image_path": "2d46eaa7c73b51dce37546ee9543b2997e5d16df25eca58950832d855092bd26.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "spans": [ + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "text", + "content": " is the weighting parameter. Note that the learning status can be estimated by the confidence scores of the predictions [10], we thereby design " + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "text", + "content": " based on the model's prediction reflecting the overall learning status. Given the current training iteration " + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "text", + "content": ", we denote " + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 55, + 614, + 296, + 674 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 107, + 683, + 296, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 683, + 296, + 716 + ], + "spans": [ + { + "bbox": [ + 107, + 683, + 296, + 716 + ], + "type": "interline_equation", + "content": "w _ {t} = \\tau w _ {t - 1} + (1 - \\tau) \\frac {1}{B} \\sum_ {k = 1} ^ {B} \\hat {p} _ {k}, \\tag {3}", + "image_path": "e740fbffad7d39e041001b185eb98f742e98a6a96f78ad54f70dd9975028848d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "\\tau \\in (0,1)" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " is the momentum decay of EMA, set as 0.99. The " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " indicates the number of samples within a minibatch. Through the newly proposed answer adjustment strategy, we can obtain a set of accurate refined pseudolabels " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " to supervise the generation of the final prediction " + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 72, + 554, + 156 + ], + "type": "text", + "content": " in the Answer Diffuser module, which will greatly improve the prediction performance of the model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 163, + 454, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 163, + 454, + 175 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 454, + 175 + ], + "type": "text", + "content": "3.5. Answer Diffuser Module" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 180, + 554, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 554, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 554, + 300 + ], + "type": "text", + "content": "Given the ability of diffusion-based classifiers to manage data and label uncertainty effectively, we propose a diffusion-based classifier called the Answer Diffuser module. This module addresses the unique challenges of NM-VQA by classifying answers from a generative perspective, which helps mitigate issues like generating non-existent answers—a common problem in handling noisy labels [4, 12]. By using refined soft labels as supervision, the Answer Diffuser produces accurate, noise-resistant predictions that are particularly robust in noisy-label settings." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": "With the condition feature " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "f^c" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": " and the refined soft label " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": ", following the forward and reverse process of the diffusion models, we gradually introduce noise to the refined soft label " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": " to obtain the noisy label " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\bar{y}_T" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": " after " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": " steps, and progressively refine a random probability distribution " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\bar{y}_T" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": " to predict the answer distribution " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": " that is close to the pseudo-label distribution " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": " after " + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 300, + 555, + 396 + ], + "type": "text", + "content": " steps. Notably, the forward can be represented as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 342, + 403, + 555, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 403, + 555, + 418 + ], + "spans": [ + { + "bbox": [ + 342, + 403, + 555, + 418 + ], + "type": "interline_equation", + "content": "q \\left(\\bar {y} _ {t} | \\bar {y} _ {t - 1}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t}; \\mu_ {t} \\left(\\bar {y} _ {t - 1}, f ^ {c}, t\\right), \\beta_ {t} \\mathbf {I}\\right), \\tag {4}", + "image_path": "9248274b27fcd23bac82cea5c69045697e49fbc4d9c01285d8f67c0239971236.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 424, + 554, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 424, + 554, + 439 + ], + "spans": [ + { + "bbox": [ + 350, + 424, + 554, + 439 + ], + "type": "interline_equation", + "content": "\\mu_ {t} = \\sqrt {1 - \\beta_ {t}} \\bar {y} _ {t - 1} + (1 - \\sqrt {1 - \\beta_ {t}}) f ^ {c}, \\tag {5}", + "image_path": "3271a4a46c1af8430d704617e69c431e0953b02e7382c9bbdfee57ad7ceccb1e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "spans": [ + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "type": "text", + "content": " is the variance schedule. Consequently, obtaining " + }, + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "type": "inline_equation", + "content": "\\bar{y}_t" + }, + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "type": "text", + "content": " with an arbitrary timestep " + }, + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 443, + 554, + 468 + ], + "type": "text", + "content": " can be represented as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 475, + 554, + 489 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 475, + 554, + 489 + ], + "spans": [ + { + "bbox": [ + 318, + 475, + 554, + 489 + ], + "type": "interline_equation", + "content": "q \\left(\\bar {y} _ {t} | \\bar {y}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\bar {y} + \\left(1 - \\sqrt {\\bar {\\alpha} _ {t}}\\right) f ^ {c}, \\left(1 - \\bar {\\alpha} _ {t}\\right) \\mathbf {I}\\right), \\tag {6}", + "image_path": "aa4912ac1e854383372b277c7272f9bba4c03483dd6f2a111e04c0d2e2a4bf28.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\prod_{t}\\alpha_{t}" + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "text", + "content": ". It should be noted that " + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "inline_equation", + "content": "\\mu_{t}" + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "text", + "content": " can be viewed as an interpolation between soft pseudo-label " + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "text", + "content": " from NLR module and the predicted condition " + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "inline_equation", + "content": "f^{c}" + }, + { + "bbox": [ + 313, + 496, + 554, + 555 + ], + "type": "text", + "content": " from ACG module, which gradually generates task-specific conditional information to suit the NM-VQA task." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "text", + "content": "The reverse process continuously perform denoising process from " + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "inline_equation", + "content": "\\bar{y}_T" + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "text", + "content": ", which we hope to be close to " + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "text", + "content": ", where we learn a diffusion model " + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 556, + 554, + 604 + ], + "type": "text", + "content": " to predict the noise level at each timestep, which can be represented as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 339, + 611, + 553, + 626 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 611, + 553, + 626 + ], + "spans": [ + { + "bbox": [ + 339, + 611, + 553, + 626 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\bar {y} _ {t - 1} \\mid \\bar {y} _ {t}, f ^ {c}\\right) = \\mathcal {N} \\left(\\bar {y} _ {t - 1}; \\mu_ {\\theta} \\left(\\bar {y} _ {t}, f ^ {c}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {7}", + "image_path": "504cbd98ea020be694e04ec791841ced049ce1edef1820539c3e963939b97702.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "spans": [ + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}(\\bar{y}_t, f^c, t)" + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "text", + "content": " is predicted mean value of the noise distribution at timestep " + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "inline_equation", + "content": "\\sigma_t^2" + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "inline_equation", + "content": "\\frac{1 - \\bar{\\alpha}_{t-1}}{1 - \\bar{\\alpha}_t} \\beta_t" + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "text", + "content": ". Our target is to encourage the predicted answer distribution to be close to the refined pseudo-label distribution " + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "inline_equation", + "content": "\\bar{y}" + }, + { + "bbox": [ + 313, + 633, + 554, + 693 + ], + "type": "text", + "content": ". Therefore, we adopt a MSE loss as a supervision, which can be denoted as:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 393, + 701, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 393, + 701, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 393, + 701, + 553, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i f} = \\operatorname {M S E} (y; \\bar {y}). \\tag {8}", + "image_path": "5fc8eee083250c02740da0cb483ef55c5c56994373bbe56981f1a9c79214ac14.jpg" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14341" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 186, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 186, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 186, + 85 + ], + "type": "text", + "content": "3.6. Training and Inference" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "text", + "content": "During the training process, we jointly optimize " + }, + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dif}" + }, + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{RFL}" + }, + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "text", + "content": ", which on one hand targets at generating refined correct pseudo-labels that are robust to label noise as the supervision for our Answer Diffuser, on the other hand, we encourage the Answer Diffuser to generate existent and accurate answer predictions, further reducing the impact of noisy labels. Therefore, the overall loss during training can be expressed as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 122, + 196, + 296, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 196, + 296, + 209 + ], + "spans": [ + { + "bbox": [ + 122, + 196, + 296, + 209 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d i f}} + \\alpha \\mathcal {L} _ {R F L}, \\tag {9}", + "image_path": "11ca82b28aa3302a5f5451336fadb48a55732a29c1ab27c348aa1d5889ff4ff0.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 219, + 275, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 219, + 275, + 230 + ], + "spans": [ + { + "bbox": [ + 55, + 219, + 275, + 230 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 219, + 275, + 230 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 219, + 275, + 230 + ], + "type": "text", + "content": " is hyperparameter to balance different losses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "spans": [ + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "text", + "content": "It should be noticed that during the inference stage, we only adopt the AD Module to predict answers while discarding the NLR module, as the NLR module targets at providing a precise supervision for the AD module learning. The corresponding noisy distribution " + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "inline_equation", + "content": "\\bar{y}_T" + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "text", + "content": " is replaced with randomly generated Gaussian noise. The model gradually refines the random distribution through the reverse process and obtains the final predicted probability distribution " + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "text", + "content": ". The ultimate prediction class label " + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "inline_equation", + "content": "\\hat{y} = \\arg \\max_l(y_l)" + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 231, + 296, + 362 + ], + "type": "text", + "content": " indicates the index of the categories, is the answer with the highest probability score." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 374, + 132, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 374, + 132, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 374, + 132, + 387 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 394, + 118, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 394, + 118, + 405 + ], + "spans": [ + { + "bbox": [ + 55, + 394, + 118, + 405 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 411, + 296, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 296, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 296, + 568 + ], + "type": "text", + "content": "VQA-RAD [20] is the most widely used radiology dataset for Med-VQA, comprising 315 images and 3,515 question-answer pairs, with each image corresponding to at least one question-answer pair. " + }, + { + "bbox": [ + 55, + 411, + 296, + 568 + ], + "type": "inline_equation", + "content": "58\\%" + }, + { + "bbox": [ + 55, + 411, + 296, + 568 + ], + "type": "text", + "content": " of the questions are close-end questions and the rest are openend questions. PathVQA [14] is constructed by extracting images along with corresponding captions from digital resources such as electronic textbooks and online libraries. It consists of 32,799 question-answer pairs, including 4,998 pathology images. Open-end questions account for " + }, + { + "bbox": [ + 55, + 411, + 296, + 568 + ], + "type": "inline_equation", + "content": "50.2\\%" + }, + { + "bbox": [ + 55, + 411, + 296, + 568 + ], + "type": "text", + "content": " of all questions and the rest are closed questions. To ensure comparability, both of the datasets have been divided following the MMQ method [7]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 575, + 209, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 575, + 209, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 575, + 209, + 588 + ], + "type": "text", + "content": "4.2. Noise Patterns and Analysis" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 594, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 689 + ], + "type": "text", + "content": "Due to the lack of suitable Med-VQA datasets with noisy labels and the difficulty of creating new datasets, we adopt semantic noisy types from the natural VQA domain [47] to existing medical VQA datasets. [47] demonstrates controlled semantic label noise by simulating human mislabeling behavior, which is more realistic than conventional random noise. We also follow the conventional VQA methods to validate our model by random label shuffling." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "The questions in Med-VQA tasks include two categories: closed-end (e.g., Yes/No questions with one-word" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "type": "text", + "content": "answers) and open-end (e.g., wh-questions with longer responses). Following [47], for closed-ended answers, we use symmetric noise by randomly flipping the answer choices. Moreover, for open-ended answers, we create a semantic space of frequent answers using a pre-trained BERT model [21] to simulate human annotation errors. For each sample, the original answer is replaced by its closest noisy label within this semantic space. Our experiments highlight the sensitivity of prior Med-VQA methods to noisy labels, and we evaluate performance using " + }, + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "type": "text", + "content": " semantic noise ratios in the training datasets of VQA-RAD and PathVQA. Figure 2 visualizes our noisy pairs and the t-SNE representation of the semantic space, where ground-truth labels are replaced with semantically similar noisy labels. Moreover, we compare the performance of different methods by introducing random noise with a " + }, + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 313, + 72, + 555, + 324 + ], + "type": "text", + "content": " noise ratio into the training datasets of VQA-RAD and PathVQA. As shown in Table 1 and Table 2, at the same noise ratio, semantic noise impacts model performance more significantly than random noise and more closely resembles the type of noise encountered in actual clinical scenarios." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 333, + 448, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 333, + 448, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 333, + 448, + 346 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 350, + 556, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 556, + 519 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 556, + 519 + ], + "type": "text", + "content": "Our method is trained on a single Nvidia 3090Ti GPU. We employ the Swin Transformer [28] as the vision encoder and the BERT model [21] as the text encoder. Our baseline model contains the Swin Transformer and BERT as encoder with transformer decoder without any answer denoise methods. The Adam optimizer is used, with an initial learning rate set to 1e-5. We adopt a batch size of 16 and a maximum of 100 epochs. The loss weight " + }, + { + "bbox": [ + 313, + 350, + 556, + 519 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 350, + 556, + 519 + ], + "type": "text", + "content": " is set to 0.5 for both datasets. For our model evaluation, we use only the AD Module to predict answers without the NLR module to ensure that the model parameters are at a similar level to those of other methods for comparison. The DiN framework is trained in an end-to-end fashion. The Med-VQA performance is assessed by accuracy scores." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 528, + 459, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 528, + 459, + 541 + ], + "spans": [ + { + "bbox": [ + 313, + 528, + 459, + 541 + ], + "type": "text", + "content": "4.4. Performance Comparison" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 545, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 556, + 715 + ], + "type": "text", + "content": "We compare our proposed method with MMBERT [19] and Q2ATransformer [27], which are among the top performers in Med-VQA task. Notably, previous Med-VQA methods were not designed to address the issue of noisy labels. To fill this gap, we employ two mainstream uni-modal label denoising methods to compare. SimT [11] estimates noise transition matrices to correct label noise in a class-wise manner. CoDis [44], a co-teaching-based label denoising method, uses two sub-networks to select the clean label dataset based on the small-loss principle. We also compare our method with SNLC [47], the first method designed for natural VQA with noisy labels. As shown in Table 1 and Table 2, our DiN framework consistently outperforms the compared models on both datasets. The biggest drawback" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14342" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 286, + 275 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 286, + 275 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 286, + 275 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 286, + 275 + ], + "type": "table", + "html": "
    Noise TypeMethodVQA-RAD
    OpenCloseOverall
    CleanUpper Bound78.1780.0879.13
    10%-Semantic NoiseBaseline67.8668.8568.25
    MMBERT [19]63.3668.2166.42
    Q2ATransformer [27]66.7970.1768.48
    SimT [11]66.9369.7368.04
    CoDis [44]68.0270.5469.53
    SNLC [47]67.8371.3569.65
    DiN (Ours)72.6875.8174.24
    20%-Semantic NoiseBaseline54.2357.1456.01
    MMBERT [19]52.6856.6455.25
    Q2ATransformer [27]55.4360.0358.25
    SimT [11]53.7657.0555.82
    CoDis [44]54.1957.2856.42
    SNLC [47]56.4561.3058.88
    DiN (Ours)58.0663.1762.28
    20%-Random NoiseBaseline56.7160.3058.88
    MMBERT [19]55.4359.5957.97
    Q2ATransformer [27]58.0462.3760.68
    SimT [11]57.8662.8560.90
    CoDis [44]59.9560.5660.32
    SNLC [47]59.2163.8462.03
    DiN (Ours)61.0465.7763.93
    ", + "image_path": "269c9c2dc1151177cbdfd2bdf70af85706ca0f942112d219c6b8578112948241.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 283, + 295, + 350 + ], + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 350 + ], + "type": "text", + "content": "Table 1. Performance comparison on the VQA-RAD dataset. 'Open' indicates the open-end question and 'close' indicates the close-end question. The overall performance is the average performance of both question types. The best results are bold. Notably, SimT [11] and CoDis [44] are up-to-date representatives of NTM-based and co-teaching-based approaches, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 377, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 377, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 56, + 377, + 295, + 640 + ], + "type": "text", + "content": "of these two Med-VQA methods is that neither is designed to address the issue of noisy labels, so they cannot prevent overfitting noisy patterns during the training process for NM-VQA tasks. SimT [11] did not bring significant performance improvements, primarily due to the limitations of the noise transition matrix (NTM), which only effectively captures noise patterns in simple noisy classification tasks. CoDis [44] performed better than NTM-based methods; but its two-branch co-teaching method doubles the parameters and uses a small-loss selection strategy better suited for simpler noise. SNLC [47], designed for noisy labels in natural VQA, relies on a basic robust loss function and fails to deliver competitive performance in the medical domain. In contrast, our DiN framework is specifically tailored for noisy labels in Med-VQA tasks. Figure 4 visualizes four examples of predicted answers from both the training and test sets across two datasets. In the training set, our method successfully corrects semantic noisy labels post-training, while in the test set, our model generates accurate predictions in multiple instances. This design allows DiN to consistently outperform other methods, demonstrating its effectiveness in addressing the unique challenges of NM-VQA tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 657, + 149, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 657, + 149, + 670 + ], + "spans": [ + { + "bbox": [ + 55, + 657, + 149, + 670 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "To assess the contributions of our DiN framework, we conducted extensive ablation studies to demonstrate the efficiency of the different components of our model." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 326, + 70, + 543, + 275 + ], + "blocks": [ + { + "bbox": [ + 326, + 70, + 543, + 275 + ], + "lines": [ + { + "bbox": [ + 326, + 70, + 543, + 275 + ], + "spans": [ + { + "bbox": [ + 326, + 70, + 543, + 275 + ], + "type": "table", + "html": "
    Noise TypeMethodPathVQA
    OpenCloseOverall
    CleanUpper Bound52.6486.4572.61
    10%-Semantic NoiseBaseline37.8375.8162.32
    MMBERT [19]34.1873.2158.73
    Q2ATransformer [27]38.4276.8562.61
    SimT [11]36.5475.3562.06
    CoDis [44]37.8676.2863.02
    SNLC [47]38.8578.3364.18
    DiN (Ours)40.5480.2866.67
    20%-Semantic NoiseBaseline29.0670.0155.28
    MMBERT [19]27.1368.3552.41
    Q2ATransformer [27]30.1671.1156.28
    SimT [11]29.3870.6955.93
    CoDis [44]30.3671.1856.55
    SNLC [47]30.8871.2356.72
    DiN (Ours)32.4772.5658.14
    20%-Random NoiseBaseline32.2973.5357.03
    MMBERT [19]30.4572.0655.41
    Q2ATransformer [27]34.5074.7458.64
    SimT [11]35.1774.9159.01
    CoDis [44]35.6674.5058.96
    SNLC [47]36.7475.0359.71
    DiN (Ours)37.8576.1660.84
    ", + "image_path": "a30b523cfe025dcf570c07583167a5c27b628e130f5f84338439404613e4b180.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 313, + 283, + 555, + 350 + ], + "lines": [ + { + "bbox": [ + 313, + 283, + 555, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 283, + 555, + 350 + ], + "type": "text", + "content": "Table 2. Performance comparison on the PathVQA dataset. 'Open' indicates the open-end question and 'close' indicates the close-end question. The overall performance is the average performance of both question types. The best results are bold. Notably, SimT [11] and CoDis [44] are up-to-date representatives of NTM-based and co-teaching-based approaches, respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 316, + 363, + 558, + 408 + ], + "blocks": [ + { + "bbox": [ + 316, + 363, + 558, + 408 + ], + "lines": [ + { + "bbox": [ + 316, + 363, + 558, + 408 + ], + "spans": [ + { + "bbox": [ + 316, + 363, + 558, + 408 + ], + "type": "table", + "html": "
    ChoiceEncodersClassifierACGADRFLAAOpenCloseOverallOpenCloseOverall
    0✓✓✓67.8668.8568.2554.2357.1456.01
    1✓✓✓✓68.4670.7169.5655.0859.2757.64
    2✓✓✓✓70.7171.9271.1555.8660.8659.13
    3✓✓✓✓✓70.7373.0872.2556.2161.5460.57
    4✓✓✓✓✓71.1574.2972.7556.9762.2061.24
    5✓✓✓✓✓✓72.6875.8174.2458.0663.1762.28
    ", + "image_path": "801c448f4c01459c27d945f6a79722c01aec3a975f1771e224f9d57d52aa2b65.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 313, + 416, + 555, + 504 + ], + "lines": [ + { + "bbox": [ + 313, + 416, + 555, + 504 + ], + "spans": [ + { + "bbox": [ + 313, + 416, + 555, + 504 + ], + "type": "text", + "content": "Table 3. Ablation study of our method on the VQA-RAD dataset with " + }, + { + "bbox": [ + 313, + 416, + 555, + 504 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 313, + 416, + 555, + 504 + ], + "type": "text", + "content": " -Semantic Noise. ACG indicates our answer condition generator module, AD indicates our answer diffuser module. Note that our noisy label refinement module includes two parts, i.e., an answer adjust module (AA) and a noise robust focal loss function (RFL). Also note that the baseline method includes the vision encoder and the text encoder (Encoder), the auxiliary classifier (Classifier) and our ACG module." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 529, + 511, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 511, + 541 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 511, + 541 + ], + "type": "text", + "content": "4.5.1. Impact of Answer Condition Generator" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": "The ACG module provides conditional information to support the generative process in the AD module and features for training the auxiliary classifier in the NLR module. When only the encoders, ACG, and the auxiliary classifier are used for answer prediction (i.e., the fused image-question features are sent through ACG to interact with the candidate answer embeddings, and the output feature " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "f_{k}^{c}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " is used to train the auxiliary classifier), the accuracy is limited to " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "68.25\\%" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " overall accuracy (Choice 0 in Table 3), primarily due to rapid overfitting and the inability to effectively handle noisy labels. Notably, incorporating the AD module with the conditional information from ACG significantly enhances the overall accuracy to " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "71.15\\%" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " (Choice 2). The ACG module not only enhances the auxiliary classi" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14343" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 70, + 159, + 196 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 159, + 196 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 159, + 196 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 159, + 196 + ], + "type": "image", + "image_path": "b74ab40e8180e9815bfad6a792dd23dfc6851340cd590a3ad9433e082242ba15.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 167, + 79, + 267, + 89 + ], + "lines": [ + { + "bbox": [ + 167, + 79, + 267, + 89 + ], + "spans": [ + { + "bbox": [ + 167, + 79, + 267, + 89 + ], + "type": "text", + "content": "Train Set with Noisy Answers" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 169, + 141, + 252, + 150 + ], + "lines": [ + { + "bbox": [ + 169, + 141, + 252, + 150 + ], + "spans": [ + { + "bbox": [ + 169, + 141, + 252, + 150 + ], + "type": "text", + "content": "Test Set without Answers" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 217, + 555, + 251 + ], + "lines": [ + { + "bbox": [ + 54, + 217, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 54, + 217, + 555, + 251 + ], + "type": "text", + "content": "Figure 4. Visualization of example results from our DiN framework on the VQA-RAD and PathVQA datasets. The first row presents examples from the training set with " + }, + { + "bbox": [ + 54, + 217, + 555, + 251 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 54, + 217, + 555, + 251 + ], + "type": "text", + "content": " -Semantic Noise, where our method corrects the noisy incorrect answers during the training process. The second row shows two examples from the test sets of both datasets." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 285, + 102, + 301, + 125 + ], + "blocks": [ + { + "bbox": [ + 168, + 90, + 298, + 99 + ], + "lines": [ + { + "bbox": [ + 168, + 90, + 298, + 99 + ], + "spans": [ + { + "bbox": [ + 168, + 90, + 298, + 99 + ], + "type": "text", + "content": "Question: Where is/are the lesion located?" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 169, + 101, + 279, + 110 + ], + "lines": [ + { + "bbox": [ + 169, + 101, + 279, + 110 + ], + "spans": [ + { + "bbox": [ + 169, + 101, + 279, + 110 + ], + "type": "text", + "content": "Noisy Answers : Left temporal lobe" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 169, + 112, + 285, + 123 + ], + "lines": [ + { + "bbox": [ + 169, + 112, + 285, + 123 + ], + 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    NameChoiceVQA-RAD with 10% Noise
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    Focal [24]71.4373.8573.10
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    ", + "image_path": "732664f98b27dc4d0ca279fef8c306114bf304fc784a32ef141a96a679c97b12.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "table_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 55, + 399, + 296, + 444 + ], + "lines": [ + { + "bbox": [ + 55, + 399, + 296, + 444 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 296, + 444 + ], + "type": "text", + "content": "Table 4. Ablation studies on different hyperparameters, i.e., " + }, + { + "bbox": [ + 55, + 399, + 296, + 444 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 399, + 296, + 444 + ], + "type": "text", + "content": " that balances different loss functions and the number of timesteps " + }, + { + "bbox": [ + 55, + 399, + 296, + 444 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 399, + 296, + 444 + ], + "type": "text", + "content": " in our answer diffuser module, and ablation studies on different options of loss functions in our noisy label refinement module." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 464, + 296, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 464, + 296, + 500 + ], + "spans": [ + { + "bbox": [ + 55, + 464, + 296, + 500 + ], + "type": "text", + "content": "fier's ability to capture medical domain knowledge but also strengthens the diffusion-based AD module by providing reliable Med-VQA condition information." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 55, + 506, + 230, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 230, + 519 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 230, + 519 + ], + "type": "text", + "content": "4.5.2. Impact of Noisy Label Refinement" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": "The Noisy Label Refinement (NLR) module comprises two sub-components: Robust Loss (RFL) and answer adjustment (AA). The RFL is designed to mitigate the impact of noise on the encoders' features. As shown in Table 3, incorporating the RFL leads to an increase in overall accuracy from " + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "inline_equation", + "content": "68.25\\%" + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "inline_equation", + "content": "69.56\\%" + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": " without using AD module and from " + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "inline_equation", + "content": "71.15\\%" + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": " (Choice 2) to " + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "inline_equation", + "content": "72.75\\%" + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": " (Choice 4) with AD module. We experimented with different combinations of robust loss functions and found that our proposed RFL is the most effective for NM-VQA tasks, as demonstrated in Table 4. The answer adjustment (AA) component is specifically designed to reduce noise impact on the Answer Diffuser (AD) module. The addition of the AA component enhances the overall accuracy from " + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "inline_equation", + "content": "71.15\\%" + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": " (Choice 2) to " + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "inline_equation", + "content": "72.25\\%" + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": " (Choice 3) and further from " + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "inline_equation", + "content": "72.75\\%" + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": " (Choice 4) to " + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "inline_equation", + "content": "74.24\\%" + }, + { + "bbox": [ + 55, + 521, + 296, + 712 + ], + "type": "text", + "content": " (Choice 5) with the assistance of RFL." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 272, + 457, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 272, + 457, + 284 + ], + "spans": [ + { + "bbox": [ + 313, + 272, + 457, + 284 + ], + "type": "text", + "content": "4.5.3.Impact of Answer Diffuser" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": "As shown in Table 3, incorporating the AD module for Med-VQA prediction enhances the overall performance from " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "68.25\\%" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": " (Choice 0) to " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "71.15\\%" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": " (Choice 2). When all our proposed modules are combined, the overall performance further improves to " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "74.24\\%" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": " (Choice 5). We also examined the hyperparameter " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": ", which balances the AD module and the auxiliary classifier, and the type of " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "L_{dif}" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": " as detailed in Table 4. Our framework demonstrates insensitivity to both choices. We selected " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": " and MSE loss as " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "L_{dif}" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": ". Furthermore, we investigated the impact of varying " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": " on model performance, as presented in Table 4. While increasing " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": " results in higher computational costs, our model achieves optimal performance at " + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "inline_equation", + "content": "T = 50" + }, + { + "bbox": [ + 313, + 289, + 555, + 494 + ], + "type": "text", + "content": ". This differs from the image generation, where 1000 steps are typically used. This distinction is likely due to the precise pixel-level generation required in image tasks, whereas our model focuses on deriving a class probability distribution." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 514, + 388, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 514, + 388, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 514, + 388, + 528 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 536, + 555, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 555, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 555, + 704 + ], + "type": "text", + "content": "In conclusion, we have introduced DiN as the first approach to address the Med-VQA with noisy labels. Our method uses the inherent robustness of diffusion models as AD module to deal with noisy data. We designed the ACG module to fuse image, question features and candidate answering embeddings, generating condition information supporting both the AD and NLR modules. Additionally, the NLR module reduces the effect of noisy labels with robust loss functions and refines the original answers to produce pseudo-labels, further improving model performance. Extensive experiments validate the superiority of our DiN framework. 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Springer, 2024. 1" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14346" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/e57c9036-ad52-4521-ad16-43207f593def_content_list.json b/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/e57c9036-ad52-4521-ad16-43207f593def_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..058431ca6c8f45745e269e2bf4fb450ca7912301 --- /dev/null +++ b/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/e57c9036-ad52-4521-ad16-43207f593def_content_list.json @@ -0,0 +1,1613 @@ +[ + { + "type": "text", + "text": "DiSRT-In-Bed: Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery", + "text_level": 1, + "bbox": [ + 111, + 128, + 885, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jing Gao Ce Zheng Laszlo A. Jeni Zackory Erickson Carnegie Mellon University", + "bbox": [ + 220, + 203, + 776, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{jinggao2, cezheng, laszlojeni, zerickso}@andrew.cmu.edu", + "bbox": [ + 248, + 241, + 743, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 291, + 326, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In-bed human mesh recovery can be crucial and enabling for several healthcare applications, including sleep pattern monitoring, rehabilitation support, and pressure ulcer prevention. However, it is difficult to collect large real-world visual datasets in this domain, in part due to privacy and expense constraints, which in turn presents significant challenges for training and deploying deep learning models. Existing in-bed human mesh estimation methods often rely heavily on real-world data, limiting their ability to generalize across different in-bed scenarios, such as varying coverings and environmental settings. To address this, we propose a Sim-to-Real Transfer Framework for in-bed human mesh recovery from overhead depth images, which leverages large-scale synthetic data alongside limited or no real-world samples. We introduce a diffusion model that bridges the gap between synthetic data and real data to support generalization in real-world in-bed pose and body inference scenarios. Extensive experiments and ablation studies validate the effectiveness of our framework, demonstrating significant improvements in robustness and adaptability across diverse healthcare scenarios. Project page can be found at https://jing-g2.github.io/DiSRT-In-Bed/.", + "bbox": [ + 89, + 324, + 483, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 690, + 220, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human mesh recovery, the process of estimating 3D human body shapes and poses from camera or sensor data, is a challenging problem with significant applications in healthcare. In-bed human mesh recovery, in particular, plays a vital role in assessing patient well-being, monitoring mobility, and detecting health risks, such as pressure ulcers.", + "bbox": [ + 89, + 717, + 482, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, collecting labeled real-world data in healthcare settings is costly, time-consuming, and often constrained by privacy concerns. Alternative sensing technologies, like pressure sensing mats, are expensive, require direct patient contact, and can lose calibration over time, limiting their reliability. Thermal sensors, while contact-free, are highly", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cd673b44470249cbf7ad127f9d630a5900bd75cfce3a7d83ed48d45f134ce8bc.jpg", + "image_caption": [ + "Figure 1. Impact of real-world data scarcity on in-bed human mesh recovery. BodyMAP shows significant performance degradation when trained with limited real-world data, while our method maintains robust accuracy. 'Sim' indicates training with all synthetic data and $n\\%$ Real' indicates training with $n\\%$ of the real data from the training dataset." + ], + "image_footnote": [], + "bbox": [ + 517, + 290, + 903, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sensitive to environmental factors. In addition, both RGB cameras and thermal sensors often struggle with occlusions in bed, such as blankets. Given these limitations, depth cameras emerge as a practical solution, offering a balance of accuracy, affordability, and privacy protection, while avoiding the drawbacks of other sensor types.", + "bbox": [ + 511, + 520, + 906, + 611 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Furthermore, general human mesh recovery tasks benefit from abundant real-world data featuring individuals in standing or active poses [7, 37]. Such dependence on large-scale real-world data limits the adaptability and performance of deep learning models for human mesh prediction in clinical settings, where data collection is challenging and often privacy-constrained.", + "bbox": [ + 511, + 612, + 905, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the challenge of limited training data, utilizing synthetic data presents a promising solution. Large-scale simulated depth datasets can be efficiently generated without preserving any personally identifiable information, eliminating the need for sensitive real-world data. Building on this strategy, prior work [3, 4, 36] has demonstrated good performance in the in-bed human mesh recovery task. However, they struggle to effectively bridge the domain gap between synthetic and real-world data, leading to significant performance degradation when the proportion of real-world data in the training set is low, as shown in Fig. 1. Thus, to further enhance generalization, we propose a novel", + "bbox": [ + 511, + 719, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1829", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "diffusion-based pipeline for in-bed human mesh recovery. Diffusion models are particularly well-suited for this scenario due to their strong ability to handle uncertainties, such as noise and variations in depth images. By leveraging the diffusion framework, our method mitigates the domain gap between real and synthetic data while enhancing generalization across diverse real-world environments (e.g., different hospitals or room setups). This ensures smooth and coherent predictions across varied settings for real-world applications. We conduct extensive experiments, comparing with baselines and performing ablations, to demonstrate the method's effectiveness in real-world scenarios with occlusions and varying conditions.", + "bbox": [ + 89, + 90, + 480, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 109, + 289, + 413, + 301 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a Sim-to-Real Transfer Framework for in-bed human mesh recovery that effectively leverages synthetic data to improve performance in real-world healthcare settings with limited labeled real data.", + "- We introduce a diffusion-based architecture, enabling the diffusion process to bridge the domain gap between synthetic and real-world data and achieve strong generalization across different environment settings.", + "- We conduct extensive experiments, including comparisons with state-of-the-art methods, ablation studies, and generalization tests across different real-world settings, to assess the performance of our approach." + ], + "bbox": [ + 89, + 304, + 483, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 500, + 232, + 516 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. 3D Human Pose and Mesh Estimation", + "text_level": 1, + "bbox": [ + 89, + 526, + 418, + 541 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With significant progress in 3D human pose estimation [25, 27, 43, 46], researchers are seeking to go beyond just pose prediction. Human mesh recovery, which provides a more detailed 3D representation of the human body, has gained increasing interest. As a foundational human parametric model, SMPL [22] has been widely adopted in numerous works [11, 12, 14, 18-20, 38, 40, 44] to recover human mesh by predicting SMPL parameters. HybrIK [13] and its extension, HybrIK-X [15], introduce hybrid inverse kinematics techniques that convert 3D joints into body-part rotations through twist-and-swing decomposition. HMR2.0 [7] employs a straightforward yet effective transformer-based network, setting a foundation for subsequent work. TokenHMR [5] introduces a tokenized approach to representing human pose and shape, effectively handling occlusions by reframing the problem as token prediction.", + "bbox": [ + 89, + 547, + 482, + 790 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Diffusion Models for Human Pose and Mesh Estimation", + "text_level": 1, + "bbox": [ + 89, + 801, + 482, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion generative models [10, 32] have shown remarkable success across diverse computer vision tasks, including image inpainting [33, 42], text-to-image generation [17, 28-30, 41], and image-to-image translation [2]. Leveraging", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "their powerful capability to manage uncertainty and refine distributions, these models have been effectively applied to 3D human pose estimation and human mesh recovery tasks [1, 8, 16, 24, 31, 34, 35, 45]. DiffPose [8] pioneers diffusion-based 3D pose prediction from 2D sequences. Extending to human mesh recovery, HMDiff [6] applies a distribution alignment technique to provide input-specific information within the diffusion process, simplifying mesh estimation. Similarly, ScoreHMR [34] uses a diffusion model as a prior for SMPL body model parameters, guiding the denoising process with observed 2D keypoints.", + "bbox": [ + 511, + 90, + 903, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. In-Bed Human Pose and mesh Estimation", + "text_level": 1, + "bbox": [ + 511, + 265, + 870, + 279 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast to general human pose estimation and mesh recovery tasks, where numerous large-scale datasets are available for training, in-bed human pose estimation and mesh recovery present unique challenges. These challenges stem from the limited availability of suitable datasets, the reliance on depth images as input, and the nature of in-bed poses. Individuals are often lying in various orientations on the bed and are partially covered by blankets, leading to heavy occlusions and constrained body positions. As one of the prior works, Pyramid Fusion [39] introduces a pyramid scheme to effectively fuse four input modalities—RGB, pressure, depth, and infrared images—for human mesh estimation. However, subsequent approaches removed RGB images from the input due to privacy concerns in clinical deployments. PressureNet [3] employs pressure images as input, using a multi-stage CNN-based framework to produce human mesh outputs, while BodyPressure [4] focuses on depth images to infer both human mesh and pressure maps. The recent BodyMAP [36] simplifies the processes used in PressureNet [3] and BPBnet [4], predicting human mesh using depth and pressure images. In contrast, we focus on improving the generalization of the in-bed human mesh recovery from depth images by leveraging synthetic data and introducing a novel diffusion-based pipeline.", + "bbox": [ + 511, + 286, + 906, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries on Diffusion Models", + "text_level": 1, + "bbox": [ + 511, + 675, + 823, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models [10, 32] are probabilistic generative models that learn to transform random noise into the target data distribution via a forward and reverse process.", + "bbox": [ + 511, + 700, + 903, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the forward diffusion process, a data sample $\\mathbf{x}_0$ is progressively noised by adding Gaussian noise according to a fixed variance schedule $\\sigma_t$ over a sequence of $T$ timesteps. This process forms a Markov chain with the transitions:", + "bbox": [ + 511, + 746, + 903, + 806 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\alpha_ {t}} \\mathbf {x} _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 808, + 903, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_t$ represents the noisy sample at step $t$ , constant $\\alpha_t = 1 - \\sigma_t^2$ , and $\\mathcal{N}(\\cdot)$ denotes the Gaussian distribution. The final sample $\\mathbf{x}_t$ is approximately Gaussian noise.", + "bbox": [ + 511, + 825, + 903, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The forward diffusion process defined in [10] allows us to directly sample an arbitrary step of the noised latent $\\mathbf{x}_t$", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1830", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ea7fe9bcb5aa91300b54bdded3acd9bfbed957b8826210110487de3d2c66aa1e.jpg", + "image_caption": [ + "Figure 2. Overview of the Proposed Sim-to-Real Transfer Framework. The framework comprises three stages: In the Synthetic Data Generation stage (left), a large, diverse set of synthetic depth images is generated within a simulated environment. In the training stage, the diffusion model $\\mathcal{D}$ conditions on the synthetic depth image $\\mathbf{c}_{\\mathrm{syn}}$ to denoise SMPL parameters $\\mathbf{x}_t$ in the reverse process, which begins at timestep $T$ and progresses toward timestep 0, yielding the estimated human mesh $\\hat{\\mathcal{M}}_{\\mathrm{syn}}$ . In the fine-tuning stage, the model conditions on real depth images $\\mathbf{c}_{\\mathrm{real}}$ to estimate the human mesh $\\hat{\\mathcal{M}}_{\\mathrm{real}}$ . The symbol $g'$ in the diffusion model indicates the gender flag associated with the input. The 'Ref.' in the figure denotes the corresponding synthetic depth image during training and the corresponding RGB image for visualization purposes only." + ], + "image_footnote": [], + "bbox": [ + 114, + 88, + 883, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "conditioned on the input $\\mathbf{x}_0$ as follows:", + "bbox": [ + 89, + 479, + 352, + 494 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 500, + 482, + 516 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\quad \\epsilon \\sim \\mathcal {N} (0, \\mathbf {I}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 535, + 480, + 550 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = 1 - \\sigma_{t}^{2}$ and $\\bar{\\alpha}_{t} = \\prod_{i=0}^{t} \\alpha_{i}$ are fixed hyperparameters.", + "bbox": [ + 89, + 551, + 482, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the reverse diffusion process, the model aims to recover the original data sample $\\mathbf{x}_0$ from $\\mathbf{x}_t$ . A diffusion model parameterized as $\\omega$ (often a neural network) is trained to approximate this reverse process defined as:", + "bbox": [ + 89, + 582, + 483, + 642 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\omega} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\omega} \\left(\\mathbf {x} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 647, + 480, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although specific formulations for the estimated mean $\\mu_{\\omega}(\\mathbf{x}_t,t)$ vary [10, 26, 32], each reverse denoising step can be expressed as a function $f$ of $\\mathbf{x}_t$ and the diffusion model $\\omega$ to yield $\\mathbf{x}_{t - 1}$ as follows:", + "bbox": [ + 89, + 669, + 483, + 729 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = f \\left(\\mathbf {x} _ {t}, \\omega\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 734, + 480, + 751 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "During inference, Gaussian noise $\\mathbf{x}_t$ is sampled, and the model iteratively denoises it to generate the target sample $\\mathbf{x}_0$ using the trained diffusion model $\\omega$ .", + "bbox": [ + 89, + 755, + 483, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 89, + 814, + 225, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our proposed framework addresses the challenge of developing reliable and generalizable in-bed human mesh recovery models in scenarios with limited or no real-world data. By leveraging a large volume of synthetic data generated", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "through simulation, combined with a small amount of real-world data, our framework effectively reduces the reliance on costly and privacy-sensitive real-world data collection. The framework comprises three key stages: synthetic data generation (Sec. 4.1), model design (Sec. 4.2), and pipeline training and fine-tuning (Sec. 4.3). The overview pipeline is shown in Fig. 2.", + "bbox": [ + 511, + 479, + 905, + 584 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Throughout our approach, we utilize the SMPL [22] model to represent 3D human bodies. The SMPL model is a parametric human body model that represents a human figure as a mesh of vertices, controlled by a set of pose and shape parameters. Specifically, given the joint angles $\\pmb{\\theta} \\in \\mathbb{R}^{23 \\times 3}$ and shape parameters $\\beta \\in \\mathbb{R}^{10}$ , the SMPL model can output a 3D human mesh $\\mathbf{V} \\in \\mathbb{R}^{6890 \\times 3}$ consisting of 6,890 vertices. The SMPL parameters can be defined as $\\mathbf{x} = \\left[ \\begin{array}{cccc} \\beta & \\theta & \\mathbf{s} & \\mathbf{u} & \\mathbf{v} \\end{array} \\right]^{\\top} \\in \\mathbb{R}^{88}$ , where $\\mathbf{s} \\in \\mathbb{R}^3$ is the global translation, and $\\mathbf{u} \\in \\mathbb{R}^3$ with $\\mathbf{v} \\in \\mathbb{R}^3$ are used to represent the global rotation.", + "bbox": [ + 511, + 585, + 906, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Synthetic Data Generation", + "text_level": 1, + "bbox": [ + 511, + 770, + 756, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Obtaining labeled data for in-bed scenarios across diverse healthcare environments presents a significant challenge, limiting the deployment of deep learning models in this domain. In contrast, simulation offers a low-cost and efficient solution for generating abundant, high-quality depth data along with ground truth annotation for human mesh in resting positions. By incorporating prior information such as", + "bbox": [ + 511, + 794, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1831", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "bed dimensions and camera-to-bed distance, we can construct simulated environments that closely replicate the real-world settings.", + "bbox": [ + 89, + 90, + 482, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following BodyPressure [4], which introduces a physics-based simulation pipeline to generate synthetic in-bed human depth and pressure images, we adopt this approach to create a diverse and realistic dataset. The pipeline simulates human bodies at rest on a soft mattress, producing depth data from a fixed camera position relative to SMPL-based body configurations on a bed. By sampling human shape $\\beta$ , joint angles $\\theta$ , and global translation $(s_x, s_y)$ from uniform distributions, we generate a variety of data. Additionally, simulated depth images with blankets are created by draping various types of blankets over parts of the body. This dataset further includes diverse human shapes, poses, and bed scene complexities.", + "bbox": [ + 89, + 136, + 483, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While synthetic data generation can enhance dataset diversity and increase the number of training samples, it also introduces an inherent domain gap between synthetic and real-world data. As a result, models may perform well in synthetic settings but struggle in real-world applications, which undermines their practical utility. Therefore, in the following sections, we focus on bridging this simulation-to-reality gap within the framework for in-bed scenes.", + "bbox": [ + 89, + 333, + 483, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Diffusion-Based In-Bed Mesh Recovery", + "text_level": 1, + "bbox": [ + 89, + 460, + 429, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Recovering in-bed human mesh from depth images is not a straightforward one-to-one mapping problem, as prior works [3, 4, 36] state. Depth images of in-bed scenarios can vary significantly based on external conditions, such as the presence or absence of a blanket, while the underlying body pose and shape remain the same. This variability introduces ambiguity in the mapping from depth images to human mesh. Additionally, multiple plausible human mesh configurations can correspond to the same depth image due to inherent ambiguities. To address this, we reformulate the in-bed human mesh recovery task as a conditional generative problem. Inspired by recent advancements in diffusion models for image generation [10, 32], we design a diffusion model to learn the distribution of plausible SMPL body configurations, denoted as $p_{\\mathrm{SMPL}}$ , conditioned on depth images during training and fine-tuning.", + "bbox": [ + 89, + 483, + 483, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2.1. Diffusion Process", + "text_level": 1, + "bbox": [ + 89, + 731, + 256, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In contrast to the diffusion process used in image generation, which operates directly on images, we conduct forward noise-adding and reverse denoising processes on the SMPL body parameters $\\mathbf{x}$ for in-bed human mesh recovery.", + "bbox": [ + 89, + 750, + 482, + 810 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the forward process, we follow the Eq. 3 to obtain noisy versions $\\mathbf{x}_t$ of the initial SMPL body parameters $\\mathbf{x}_0$ over $t$ timesteps.", + "bbox": [ + 89, + 810, + 482, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the reverse process, we incorporate depth images $\\mathbf{c}$ as a conditional input to the diffusion model, modifying Eq. 4 as follows:", + "bbox": [ + 89, + 854, + 483, + 898 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\mathcal {D}} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}, \\mathbf {c}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\mathcal {D}} \\left(\\mathbf {x} _ {t}, t, \\mathbf {c}\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 90, + 905, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{D}$ represents our diffusion model designed for the in-bed human mesh recovery task.", + "bbox": [ + 511, + 113, + 903, + 142 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a training sample $\\mathbf{x}_0$ , we train the diffusion model $\\mathcal{D}$ to learn the denoising transition $p_{\\mathcal{D}}(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t, \\mathbf{c})$ , ensuring it closely approximates the corresponding forward process $q(\\mathbf{x}_t \\mid \\mathbf{x}_{t - 1}, \\mathbf{x}_0)$ . In image generation tasks, this process typically involves having the diffusion model approximate the noise term $\\epsilon$ that produces $\\mathbf{x}_t$ from $\\mathbf{x}_0$ in the forward process.", + "bbox": [ + 511, + 143, + 905, + 247 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, in our case, if we assume SMPL body parameters $\\mathbf{x}_t$ follow a standard Gaussian distribution, the diffusion model struggles to produce reasonable SMPL parameters, as early denoising iterations may yield unfeasible human meshes. To address this, we diffuse toward the initial sample $\\mathbf{x}_0$ to ensure consistency throughout the denoising process. For any timestep $t$ , the estimated initial SMPL parameters $\\mathbf{z}_t$ can be represented as:", + "bbox": [ + 511, + 250, + 905, + 369 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {t} = \\mathcal {D} \\left(\\mathbf {x} _ {t}, t, \\mathbf {c}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 651, + 376, + 903, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The objective of training and fine-tuning the diffusion model $\\mathcal{D}$ for in-bed human mesh recovery is to minimize", + "bbox": [ + 511, + 398, + 905, + 428 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\mathbf {x} _ {0} \\sim p _ {\\mathrm {S M P L}}} \\mathbb {E} _ {t \\sim \\mathcal {U} \\{0, T \\}, \\mathbf {x} _ {t} \\sim q (\\cdot | \\mathbf {x} _ {0})} \\| \\mathbf {z} _ {t} - \\mathbf {x} _ {0} \\|, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 436, + 903, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{U}(\\cdot)$ denotes sample from a uniform distribution.", + "bbox": [ + 511, + 459, + 880, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the inference, the learned mean $\\mu_{\\mathcal{D}}$ in the Eq. 6 can be formulated as:", + "bbox": [ + 511, + 474, + 903, + 502 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {\\mathcal {D}} = \\frac {\\sqrt {\\bar {\\alpha} _ {t - 1}} (1 - \\alpha_ {t})}{1 - \\bar {\\alpha} _ {t}} \\mathbf {z} _ {t} + \\frac {\\sqrt {\\alpha_ {t}} (1 - \\bar {\\alpha} _ {t - 1})}{1 - \\bar {\\alpha} _ {t}} \\mathbf {x} _ {t}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 506, + 903, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t}$ and $\\bar{\\alpha}_{t - 1}$ are derived from hyper-parameters. Then, we sample from the transition distribution in each denoising step to compute $\\mathbf{x}_{t - 1}$ as follows:", + "bbox": [ + 511, + 542, + 903, + 587 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\mu_ {\\mathcal {D}} (\\mathbf {x} _ {t}, t, \\mathbf {c}) + \\sigma^ {2} \\epsilon \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 593, + 903, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following this reverse process, we iteratively denoise the SMPL latent from noise $\\mathbf{x}_T$ at timestep $T$ down to the target SMPL latent $\\mathbf{x}_0$ at timestep 0.", + "bbox": [ + 511, + 616, + 905, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2.2. Model Architecture", + "text_level": 1, + "bbox": [ + 511, + 670, + 694, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We introduce a network that takes noised SMPL parameters $\\mathbf{x}_t$ , depth images $\\mathbf{c}$ , and the timestep $t$ as inputs and outputs the denoised SMPL parameters $\\mathbf{z}_t$ as illustrated in Fig. 3. The reverse diffusion process leverages the depth feature latent to infer denoised SMPL parameters. The noisy SMPL parameters $\\mathbf{x}_t$ are processed through an MLP encoder to obtain the SMPL parameter latent, and a uniform sampler generates the time embedding for the timestep $t$ . These inputs—SMPL parameter latent, depth images, and time embedding—are then processed through residual and attention blocks.", + "bbox": [ + 511, + 688, + 905, + 852 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following the design of the diffusion U-Net model [29], we incorporate residual and attention blocks to process image inputs and replace batch and layer normalization with", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1832", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/acf44a0107ca596b4cba690274666b1f598cf688e295d8f3202bf1455bc3975f.jpg", + "image_caption": [ + "Figure 3. Diffusion Model Architecture. Dashed lines around specific layers indicate optional layers that may be omitted in certain blocks of the model implementation." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 480, + 327 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "adaptive normalization layers initialized to zero [28] across the network. Specifically, the SMPL latent is aligned to have the same dimension as the time embedding, allowing them to be combined and fed into each adaptive normalization layer to produce scale and shift parameters, $\\gamma$ and $\\beta$ , through a linear MLP. This approach enables dynamic adjustments of normalization parameters, enhancing the network's ability to handle conditional information effectively in diffusion models.", + "bbox": [ + 88, + 387, + 482, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Within the network, multiple down-sampling residual blocks follow the initial convolutional layer, succeeded by two additional residual blocks. Attention blocks are attached separately before the last few residual blocks. In the final block, current noised SMPL latent and embedded $t$ are omitted in subsequent layers, allowing the regressor to map the single output latents from all intermediate blocks to the target SMPL parameters.", + "bbox": [ + 88, + 523, + 482, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following the SMPL parameter predictor module, the SMPL model [22] returns the human mesh $\\hat{\\mathcal{M}}$ given the estimated SMPL parameters $\\mathbf{z}_t$ . Additionally, a set of gender flags $\\mathbf{g} \\in \\mathbb{R}^2$ controls the gender of the generated human mesh. In this work, we only have two gender flags, where $[0,1]$ represents the female SMPL model and $[1,0]$ the male model. The 3D Cartesian joint positions $\\hat{\\mathbf{J}} \\in \\mathbb{R}^{24 \\times 3}$ can be extracted from the human mesh vertices $\\hat{\\mathbf{V}} \\in \\mathbb{R}^{6890 \\times 3}$ of each human mesh $\\hat{\\mathcal{M}}$ .", + "bbox": [ + 89, + 643, + 482, + 780 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Training Strategy", + "text_level": 1, + "bbox": [ + 89, + 790, + 264, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As described above, the output of our diffusion model $\\mathcal{D}$ consists of the estimated in-bed SMPL body parameters $\\mathbf{z}_t = \\left[\\hat{\\beta} \\hat{\\theta} \\hat{\\mathbf{s}} \\hat{\\mathbf{u}} \\hat{\\mathbf{v}}\\right]^\\top$ , which includes the predicted body shape parameters $\\hat{\\beta}$ , joint angles $\\hat{\\theta}$ , global translation $\\hat{\\mathbf{s}}$ , and global rotation parameters $\\hat{\\mathbf{u}} = \\{u_x, u_y, u_z\\}$", + "bbox": [ + 89, + 811, + 482, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and $\\hat{\\mathbf{v}} = \\{v_x,v_y,v_z\\}$ . Each rotation component $\\phi_{i}$ for $i\\in \\{x,y,z\\}$ can be calculated as $\\phi_{i} = \\mathrm{atan2}(u_{i},v_{i})$", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Synthetic training stage: Previous works [4, 36] rely on joint training with both synthetic and real-world data, assuming ample real-world data is available and overlooking the effects of the large synthetic-to-real data imbalance. In contrast, our framework decouples training on synthetic and real-world data to address the limited availability of real-world data and the high ratio of synthetic to real samples. During the synthetic data training phase, our goal is to establish a strong prior based on the diverse range of human resting postures available in the synthetic dataset, enabling the model to produce a reasonable coarse in-bed human pose without requiring real-world data. Our proposed diffusion-based network is trained for a reasonable number of steps on synthetic depth data alone, using a fixed learning rate to prevent convergence to local optima.", + "bbox": [ + 511, + 122, + 903, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fine-tuning stage: Given the variable quantity of real-world data, we employ a linearly adjusted learning rate scheduler that automatically adapts based on the amount of available depth data. This adaptive learning rate strategy facilitates rapid convergence and enhances generalization to real-world scenarios during fine-tuning, as demonstrated by our ablation study in Sec 5.5.", + "bbox": [ + 511, + 348, + 903, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss: The total loss used to train and fine-tune the diffusion model contains two components: SMPL parameter loss and vertex position loss. An expansion of each term in the loss function can be found in the supplementary material.", + "bbox": [ + 511, + 453, + 903, + 513 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\mathrm {S M P L}} + \\lambda_ {\\mathrm {v 2 v}} \\mathcal {L} _ {\\mathrm {v 2 v}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 529, + 903, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{\\mathrm{v2v}}$ is a tunable hyper-parameter.", + "bbox": [ + 511, + 551, + 782, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 511, + 580, + 645, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 511, + 606, + 712, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "[21] provides a comprehensive collection of in-bed resting poses across two settings. In the home setting, data were collected from 102 human participants, with each pose captured under three occlusion conditions: thin sheet, thicker blanket, and no covering. Clever et al. [4] provide SMPL ground truth labels for the real-world SLP home setting data. For training, data from the first 80 participants (1-80, excluding participant 7 due to calibration errors, totaling 10,665 real samples) in the SLP are used either partially or fully during fine-tuning to represent different synthetic-to-real data ratios. For evaluation, data from the remaining 22 participants (81-102, with 2,970 real samples) are used to assess all methods. Additionally, the SLP dataset includes data from a hospital setting, comprising 7 participants without SMPL ground truth labels. Thus, we evaluate our method on the hospital setting data through qualitative visualizations.", + "bbox": [ + 511, + 628, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1833", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8705590f47010287cc821d2bf6906af2fc042fb03684323b074747f4c2aef80d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Data Split\nReal-Sim RatioSim\n0:97495Sim+11%Real\n1:80Sim+24%Real\n1:38Sim+37%Real\n1:25Sim+49%Real\n1:18Sim+100%Real\n1:9
    MethodMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVE
    HMR2.0 [7]157.23182.2787.09104.6582.8596.54145.35140.2790.90108.9076.9490.39
    BodyPressure [4]103.47115.3189.87104.6790.46105.9781.2999.0578.2594.6572.9386.78
    BodyMAP [36]330.52365.4385.7990.1476.0789.8069.5183.0161.7774.9657.0669.95
    DiSRT-In-Bed(Ours)109.73121.5974.3778.0367.1473.1858.0466.6655.9464.1450.8161.18
    ", + "bbox": [ + 94, + 80, + 903, + 189 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cbb867203f871291e2574cde06f7512983f45ad8eded4db96b1443bfb4b35e9d.jpg", + "table_caption": [ + "Table 1. Comparison to Baselines across Different Data Splits. In the 'Data Split' row, 'Sim' indicates training with all synthetic data, while 'n%Real' indicates training with $n\\%$ of the real data from the SLP training dataset. In the 'Real-Sim Ratio' row, the number represents the approximate ratio of depth images between synthetic and real datasets. All values in the table are in millimeters (mm)." + ], + "table_footnote": [], + "table_body": "
    MethodUncoverCover 1Cover 23D Shape Error(cm)↓
    MPJPEPVEMPJPEPVEMPJPEPVEheightChestWaistHips
    HMR2.0 [7]69.6781.6679.8693.7481.2995.765.418.3011.247.66
    BodyPressure [4]67.0679.9276.3990.7875.3689.653.963.894.843.37
    BodyMAP [36]51.2662.3460.3573.9759.5573.543.433.174.243.53
    DiSRT-In-Bed(Ours)46.0155.0753.7864.8052.6563.683.255.177.165.20
    ", + "bbox": [ + 142, + 247, + 854, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison to Baselines across Different Covering Situations. 'Uncover' refers to testing depth images without coverings, 'Cover 1' denotes images with a thin blanket, and 'Cover 2' denotes images with a thick blanket. All MPJPE and PVE values are in millimeters (mm), while 3D Shape Errors are in centimeters (cm).", + "bbox": [ + 89, + 356, + 906, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "BodyPressureSD [4] is generated using the physical simulation mentioned in Sec. 4.1 and serves as a benchmark for sim-to-real tasks. The dataset consists of 97,495 samples, corresponding to the three covering conditions in the SLP dataset, and significantly increases the diversity of human resting poses and body shapes. All synthetic data from BodyPressureSD are used during the training stage of the sim-to-real framework to establish a strong prior on human pose and shape before fine-tuning.", + "bbox": [ + 88, + 412, + 480, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. For pose and shape accuracy evaluation, we report the 3D mean-per-joint position error (MPJPE) and 3D per-vertex error (PVE). For each sample, MPJPE is calculated as the Mean Euclidean Distance between the inferred and ground truth positions of 24 3D joints, while PVE measures the mean Euclidean distance across the 6,890 3D vertex positions of the SMPL model.", + "bbox": [ + 88, + 549, + 482, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Implementation Details", + "text_level": 1, + "bbox": [ + 89, + 666, + 307, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The diffusion model architecture consists of 6 downsampling layers within residual blocks, matching the downsampling depth of ResNet18 [9], and includes three attention blocks positioned before the final three residual blocks. The number of diffusion timesteps is set to 100 during training. For data augmentation, we shuffle the input depth images with random rotations, random erasures, and random noise additions during both training and fine-tuning, using a batch size of 32. All models are optimized with the AdamW [23] optimizer, using an initial learning rate of $1 \\times 10^{-4}$ and a weight decay of $5 \\times 10^{-4}$ , trained on a single NVIDIA GeForce RTX 4090 GPU. We set $\\lambda_{\\mathrm{v2v}} = 1$ in the diffusion loss. For testing, we employ a DDIM sampling strategy with 5 timesteps to accelerate inference.", + "bbox": [ + 88, + 688, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparison to State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 511, + 411, + 862, + 428 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct several experiments to demonstrate the effectiveness of our method for in-bed human mesh recovery. We choose the current SOTA model HMR2.0 [7], which is designed for single-person mesh recovery from general RGB images, as a baseline. Since our task involves single-channel depth images as input, we modify HMR2.0 by repeating the depth image across channels to match the RGB input format, making it compatible with our scenario. We also compare our method with BodyMAP [36] and BodyPressure [4], designed specifically for the in-bed scenario. Tab. 1 presents quantitative comparisons between our method and baselines across different data splits.", + "bbox": [ + 509, + 438, + 906, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\triangle$ Generalization with limited real data: With high real-to-simulation ratios, our method consistently outperforms previous methods in MPJPE and PVE metrics. Notably, our approach reduces these errors by over $10\\%$ under extreme real-simulation data ratios, such as 1:80 and 1:38. When trained solely on simulation data, our model slightly underperforms BodyPressure, as BodyPressure uses a separate network for human shape parameter prediction. However, BodyPressure's approach introduces a strong bias, leading to degraded performance when limited real-world data is available. Our method demonstrates strong generalization when limited real-world data is available.", + "bbox": [ + 511, + 623, + 908, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\triangle$ Robustness across occlusion: As shown in Tab. 2, we compare models trained on all simulation and real training data across various covering conditions. Our method achieves improved mesh recovery accuracy in all cases compared to prior literature and baselines. Moreover, the stability of our results (less performance drop) across vary-", + "bbox": [ + 511, + 809, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1834", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1555a55c24b271582270eaaa859e9b8b91e13c844bd2368de90e98d82fe2eccf.jpg", + "image_caption": [ + "Figure 4. Visualization of Human Mesh Estimated from limited Real-World Data in Home Settings. The left three columns show the input depth images, RGB reference images, and ground truth mesh respectively. 'Sim' denotes using all simulation data in the training stage, 'n%Real' denotes the 'n' ratio of real data used in the fine-tuning in our method and jointly training in the baseline. 'Uncover' refers to no blanket in the bed, 'Cover 1' indicates the participant is covered with a thin blanket, and 'Cover 2' means the participant is covered with a thick blanket. The red arrows in the figures point out the mismatch between mesh prediction and the reference images." + ], + "image_footnote": [], + "bbox": [ + 138, + 77, + 864, + 481 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing degrees of occlusion underscores the robustness of our method, making it more reliable in real-world healthcare settings where patients are often partially covered.", + "bbox": [ + 88, + 569, + 482, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\triangle$ Visualization: Fig. 4 presents the visual comparisons between our method and the SOTA in-bed mesh recovery method BodyMAP [36] under different covering conditions and real-data availability. BodyMAP struggles to estimate accurate human meshes when trained on simulation data alone, highlighting its limitations in addressing simulation-to-real domain gaps. In contrast, our method can capture meaningful pose information. Further, as shown in cases with $11\\%$ and $24\\%$ real data, our method's predictions align more closely with input images across all covering scenarios. With $24\\%$ real data, our model remains largely unaffected by coverings, consistently aligning well with the reference image and ground truth.", + "bbox": [ + 88, + 614, + 482, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Generalization to Different Real-World Settings", + "text_level": 1, + "bbox": [ + 89, + 816, + 482, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate our method's generalization ability across different environment settings, we compare our 'Sim+100%Real' model with BodyMAP[36] on unla", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "beled hospital-setting depth images5.1. Since ground truth meshes are not available for this setting, we only provide qualitative comparisons. As shown in Fig. 6, our method recovers more accurate human meshes compared to BodyMAP [36]. Notably, for the challenging self-hugging pose, our method accurately captures the crossed arms, whereas BodyMAP [36] fails to replicate this detail. Additional generalization experimental results are available in the supplementary material.", + "bbox": [ + 511, + 569, + 906, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 719, + 666, + 736 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5.1. Effectiveness of Sim-to-Real Transfer Framework", + "text_level": 1, + "bbox": [ + 511, + 743, + 903, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To highlight the benefits of synthetic data, we plot MPJPE and PVE for our method and baselines [4, 36] trained with and without synthetic data, under various real-data availability settings, in Fig. 5a. Row-wise comparisons reveal that adding synthetic data significantly enhances performance across all real-world data utilization percentages, especially for the baselines. Our diffusion-based framework further enhances predictions by $10 - 35\\%$ in MPJPE, even when only trained on a small portion of real data.", + "bbox": [ + 511, + 763, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1835", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e409f5cba7e4e928a4edd3559cc1aaac55a1b90050832ef28f9d0d781e6b676.jpg", + "image_caption": [ + "(a) Ablation on Synthetic Data" + ], + "image_footnote": [], + "bbox": [ + 102, + 84, + 361, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6910f8f500e10b2c0ba7378ea078fc066b3c187856aae4d8fad4533f99af1b0a.jpg", + "image_caption": [ + "(b) Ablation on Training Strategies" + ], + "image_footnote": [], + "bbox": [ + 370, + 84, + 625, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4a884d669488dd385f1fb3640e265590c23630821795145e7ee81146ea9b379d.jpg", + "image_caption": [ + "(c) Ablation on Different Architectures", + "Figure 5. Ablation Study on Diffusion-Based Sim-to-Real Transfer Framework." + ], + "image_footnote": [], + "bbox": [ + 638, + 85, + 893, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b2c169e9ba2b91c48ac33e58eee25af9cd28cb99be8e12b67b86404c26548f40.jpg", + "image_caption": [ + "Figure 6. Visualization of Human Mesh estimated from the Real-World Data in Hospital Settings. Ground truth mesh is not available for this scenario. The red arrows in the figures point out the mismatch between mesh prediction and the reference images." + ], + "image_footnote": [], + "bbox": [ + 124, + 276, + 455, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Additionally, Fig. 5b illustrates the impact of applying our Sim-to-Real (S2R) training strategy as detailed in 4.3. Once BodyMAP incorporates our S2R training strategy, it achieves a substantial improvement over its original training scheme. Moreover, our method further outperforms BodyMAP+S2R, underscoring the combined benefit of the proposed framework and model architecture in handling generalization challenges for the in-bed scenario.", + "bbox": [ + 89, + 723, + 482, + 844 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5.2. Effectiveness of Diffusion Model Architecture", + "text_level": 1, + "bbox": [ + 89, + 851, + 452, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare our diffusion model architecture (DiSRT-In-Bed) with three design choices as illustrated in Fig. 5c.", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Design Choice 1 — Number of Downsampling Blocks — 6 v.s. 4: Our final model configuration includes 6 convolutional downsampling layers, similar to the ResNet-18 architecture [9] used in BodyMAP [36]. We observe a decrease in MPJPE when using 6 downsampling blocks rather than only 4.", + "bbox": [ + 511, + 280, + 903, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Design Choice 2 — Conditioning Technique — Conditioning with adaptive normalization v.s. in-context conditioning: We evaluate our conditioning approach (Section 4.2.2) against the commonly used in-context conditioning techniques [17, 41], which concatenates depth features and SMPL latent representations of equal size along the channel dimension. While retaining adaptive layer normalization, this approach uses only the timestep embedding to predict the scale and shift within blocks. However, we see that in-context conditioning is less effective for depth image conditioning, as it requires expanding the lower-dimensional SMPL parameters to match the higher dimensionality of the depth images before concatenation, which reduces the efficiency of feature integration.", + "bbox": [ + 511, + 371, + 905, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Design Choice 3 - With Attention Block vs. Without Attention Block — We assess the impact of incorporating attention blocks in the final layers of the diffusion model. The results indicate that adding attention blocks noticeably improves in-bed pose prediction performance.", + "bbox": [ + 511, + 582, + 903, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 671, + 633, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present a diffusion-based framework for in-bed human mesh recovery, designed to enhance generalization and accuracy in healthcare environments with limited real-world data. By leveraging synthetic data and a Sim-to-Real Transfer Framework, our approach effectively addresses challenges posed by privacy concerns, occlusions, and data scarcity. Extensive experiments demonstrated the robustness of our method across varying covering conditions and high real-to-simulation ratios, consistently outperforming existing methods in MPJPE and PVE metrics. Additionally, our model's adaptability across different environments and reduced reliance on real-world data offer an efficient and scalable solution for clinical deployment.", + "bbox": [ + 511, + 696, + 906, + 893 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1836", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Qingyuan Cai, Xuecai Hu, Saihui Hou, Li Yao, and Yongzhen Huang. Disentangled diffusion-based 3d human pose estimation with hierarchical spatial and temporal denoiser. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 882-890, 2024. 2", + "[2] Jooyoung Choi, Sungwon Kim, Yonghyun Jeong, Youngjune Gwon, and Sungroh Yoon. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15085-15099, 2023. 2" + ], + "bbox": [ + 516, + 90, + 905, + 626 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1838", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/e57c9036-ad52-4521-ad16-43207f593def_model.json b/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/e57c9036-ad52-4521-ad16-43207f593def_model.json new file mode 100644 index 0000000000000000000000000000000000000000..168ae7b10b1e8410f77148f7d27873e54fdc7e26 --- /dev/null +++ b/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/e57c9036-ad52-4521-ad16-43207f593def_model.json @@ -0,0 +1,2167 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.112, + 0.13, + 0.887, + 0.177 + ], + "angle": 0, + "content": "DiSRT-In-Bed: Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.204, + 0.777, + 0.24 + ], + "angle": 0, + "content": "Jing Gao Ce Zheng Laszlo A. Jeni Zackory Erickson Carnegie Mellon University" + }, + { + "type": "text", + "bbox": [ + 0.249, + 0.242, + 0.744, + 0.258 + ], + "angle": 0, + "content": "{jinggao2, cezheng, laszlojeni, zerickso}@andrew.cmu.edu" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.325, + 0.485, + 0.658 + ], + "angle": 0, + "content": "In-bed human mesh recovery can be crucial and enabling for several healthcare applications, including sleep pattern monitoring, rehabilitation support, and pressure ulcer prevention. However, it is difficult to collect large real-world visual datasets in this domain, in part due to privacy and expense constraints, which in turn presents significant challenges for training and deploying deep learning models. Existing in-bed human mesh estimation methods often rely heavily on real-world data, limiting their ability to generalize across different in-bed scenarios, such as varying coverings and environmental settings. To address this, we propose a Sim-to-Real Transfer Framework for in-bed human mesh recovery from overhead depth images, which leverages large-scale synthetic data alongside limited or no real-world samples. We introduce a diffusion model that bridges the gap between synthetic data and real data to support generalization in real-world in-bed pose and body inference scenarios. Extensive experiments and ablation studies validate the effectiveness of our framework, demonstrating significant improvements in robustness and adaptability across diverse healthcare scenarios. Project page can be found at https://jing-g2.github.io/DiSRT-In-Bed/." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.691, + 0.222, + 0.707 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.718, + 0.483, + 0.809 + ], + "angle": 0, + "content": "Human mesh recovery, the process of estimating 3D human body shapes and poses from camera or sensor data, is a challenging problem with significant applications in healthcare. In-bed human mesh recovery, in particular, plays a vital role in assessing patient well-being, monitoring mobility, and detecting health risks, such as pressure ulcers." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "However, collecting labeled real-world data in healthcare settings is costly, time-consuming, and often constrained by privacy concerns. Alternative sensing technologies, like pressure sensing mats, are expensive, require direct patient contact, and can lose calibration over time, limiting their reliability. Thermal sensors, while contact-free, are highly" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.291, + 0.905, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.427, + 0.907, + 0.51 + ], + "angle": 0, + "content": "Figure 1. Impact of real-world data scarcity on in-bed human mesh recovery. BodyMAP shows significant performance degradation when trained with limited real-world data, while our method maintains robust accuracy. 'Sim' indicates training with all synthetic data and \\(n\\%\\) Real' indicates training with \\(n\\%\\) of the real data from the training dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.521, + 0.907, + 0.612 + ], + "angle": 0, + "content": "sensitive to environmental factors. In addition, both RGB cameras and thermal sensors often struggle with occlusions in bed, such as blankets. Given these limitations, depth cameras emerge as a practical solution, offering a balance of accuracy, affordability, and privacy protection, while avoiding the drawbacks of other sensor types." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.906, + 0.718 + ], + "angle": 0, + "content": "Furthermore, general human mesh recovery tasks benefit from abundant real-world data featuring individuals in standing or active poses [7, 37]. Such dependence on large-scale real-world data limits the adaptability and performance of deep learning models for human mesh prediction in clinical settings, where data collection is challenging and often privacy-constrained." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.901 + ], + "angle": 0, + "content": "To address the challenge of limited training data, utilizing synthetic data presents a promising solution. Large-scale simulated depth datasets can be efficiently generated without preserving any personally identifiable information, eliminating the need for sensitive real-world data. Building on this strategy, prior work [3, 4, 36] has demonstrated good performance in the in-bed human mesh recovery task. However, they struggle to effectively bridge the domain gap between synthetic and real-world data, leading to significant performance degradation when the proportion of real-world data in the training set is low, as shown in Fig. 1. Thus, to further enhance generalization, we propose a novel" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1829" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.288 + ], + "angle": 0, + "content": "diffusion-based pipeline for in-bed human mesh recovery. Diffusion models are particularly well-suited for this scenario due to their strong ability to handle uncertainties, such as noise and variations in depth images. By leveraging the diffusion framework, our method mitigates the domain gap between real and synthetic data while enhancing generalization across diverse real-world environments (e.g., different hospitals or room setups). This ensures smooth and coherent predictions across varied settings for real-world applications. We conduct extensive experiments, comparing with baselines and performing ablations, to demonstrate the method's effectiveness in real-world scenarios with occlusions and varying conditions." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.29, + 0.414, + 0.303 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.305, + 0.483, + 0.365 + ], + "angle": 0, + "content": "- We propose a Sim-to-Real Transfer Framework for in-bed human mesh recovery that effectively leverages synthetic data to improve performance in real-world healthcare settings with limited labeled real data." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.365, + 0.483, + 0.425 + ], + "angle": 0, + "content": "- We introduce a diffusion-based architecture, enabling the diffusion process to bridge the domain gap between synthetic and real-world data and achieve strong generalization across different environment settings." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.426, + 0.484, + 0.486 + ], + "angle": 0, + "content": "- We conduct extensive experiments, including comparisons with state-of-the-art methods, ablation studies, and generalization tests across different real-world settings, to assess the performance of our approach." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.305, + 0.484, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.501, + 0.233, + 0.517 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.527, + 0.419, + 0.542 + ], + "angle": 0, + "content": "2.1. 3D Human Pose and Mesh Estimation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.549, + 0.483, + 0.791 + ], + "angle": 0, + "content": "With significant progress in 3D human pose estimation [25, 27, 43, 46], researchers are seeking to go beyond just pose prediction. Human mesh recovery, which provides a more detailed 3D representation of the human body, has gained increasing interest. As a foundational human parametric model, SMPL [22] has been widely adopted in numerous works [11, 12, 14, 18-20, 38, 40, 44] to recover human mesh by predicting SMPL parameters. HybrIK [13] and its extension, HybrIK-X [15], introduce hybrid inverse kinematics techniques that convert 3D joints into body-part rotations through twist-and-swing decomposition. HMR2.0 [7] employs a straightforward yet effective transformer-based network, setting a foundation for subsequent work. TokenHMR [5] introduces a tokenized approach to representing human pose and shape, effectively handling occlusions by reframing the problem as token prediction." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.803, + 0.483, + 0.833 + ], + "angle": 0, + "content": "2.2. Diffusion Models for Human Pose and Mesh Estimation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Diffusion generative models [10, 32] have shown remarkable success across diverse computer vision tasks, including image inpainting [33, 42], text-to-image generation [17, 28-30, 41], and image-to-image translation [2]. Leveraging" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.259 + ], + "angle": 0, + "content": "their powerful capability to manage uncertainty and refine distributions, these models have been effectively applied to 3D human pose estimation and human mesh recovery tasks [1, 8, 16, 24, 31, 34, 35, 45]. DiffPose [8] pioneers diffusion-based 3D pose prediction from 2D sequences. Extending to human mesh recovery, HMDiff [6] applies a distribution alignment technique to provide input-specific information within the diffusion process, simplifying mesh estimation. Similarly, ScoreHMR [34] uses a diffusion model as a prior for SMPL body model parameters, guiding the denoising process with observed 2D keypoints." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.266, + 0.871, + 0.28 + ], + "angle": 0, + "content": "2.3. In-Bed Human Pose and mesh Estimation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.287, + 0.907, + 0.651 + ], + "angle": 0, + "content": "In contrast to general human pose estimation and mesh recovery tasks, where numerous large-scale datasets are available for training, in-bed human pose estimation and mesh recovery present unique challenges. These challenges stem from the limited availability of suitable datasets, the reliance on depth images as input, and the nature of in-bed poses. Individuals are often lying in various orientations on the bed and are partially covered by blankets, leading to heavy occlusions and constrained body positions. As one of the prior works, Pyramid Fusion [39] introduces a pyramid scheme to effectively fuse four input modalities—RGB, pressure, depth, and infrared images—for human mesh estimation. However, subsequent approaches removed RGB images from the input due to privacy concerns in clinical deployments. PressureNet [3] employs pressure images as input, using a multi-stage CNN-based framework to produce human mesh outputs, while BodyPressure [4] focuses on depth images to infer both human mesh and pressure maps. The recent BodyMAP [36] simplifies the processes used in PressureNet [3] and BPBnet [4], predicting human mesh using depth and pressure images. In contrast, we focus on improving the generalization of the in-bed human mesh recovery from depth images by leveraging synthetic data and introducing a novel diffusion-based pipeline." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.676, + 0.825, + 0.692 + ], + "angle": 0, + "content": "3. Preliminaries on Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.702, + 0.905, + 0.746 + ], + "angle": 0, + "content": "Diffusion models [10, 32] are probabilistic generative models that learn to transform random noise into the target data distribution via a forward and reverse process." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.747, + 0.905, + 0.807 + ], + "angle": 0, + "content": "In the forward diffusion process, a data sample \\(\\mathbf{x}_0\\) is progressively noised by adding Gaussian noise according to a fixed variance schedule \\(\\sigma_t\\) over a sequence of \\(T\\) timesteps. This process forms a Markov chain with the transitions:" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.809, + 0.905, + 0.825 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\alpha_ {t}} \\mathbf {x} _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.826, + 0.905, + 0.871 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_t\\) represents the noisy sample at step \\(t\\), constant \\(\\alpha_t = 1 - \\sigma_t^2\\), and \\(\\mathcal{N}(\\cdot)\\) denotes the Gaussian distribution. The final sample \\(\\mathbf{x}_t\\) is approximately Gaussian noise." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "The forward diffusion process defined in [10] allows us to directly sample an arbitrary step of the noised latent \\(\\mathbf{x}_t\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1830" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.089, + 0.885, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.368, + 0.908, + 0.466 + ], + "angle": 0, + "content": "Figure 2. Overview of the Proposed Sim-to-Real Transfer Framework. The framework comprises three stages: In the Synthetic Data Generation stage (left), a large, diverse set of synthetic depth images is generated within a simulated environment. In the training stage, the diffusion model \\(\\mathcal{D}\\) conditions on the synthetic depth image \\(\\mathbf{c}_{\\mathrm{syn}}\\) to denoise SMPL parameters \\(\\mathbf{x}_t\\) in the reverse process, which begins at timestep \\(T\\) and progresses toward timestep 0, yielding the estimated human mesh \\(\\hat{\\mathcal{M}}_{\\mathrm{syn}}\\). In the fine-tuning stage, the model conditions on real depth images \\(\\mathbf{c}_{\\mathrm{real}}\\) to estimate the human mesh \\(\\hat{\\mathcal{M}}_{\\mathrm{real}}\\). The symbol \\(g'\\) in the diffusion model indicates the gender flag associated with the input. The 'Ref.' in the figure denotes the corresponding synthetic depth image during training and the corresponding RGB image for visualization purposes only." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.48, + 0.353, + 0.495 + ], + "angle": 0, + "content": "conditioned on the input \\(\\mathbf{x}_0\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.5, + 0.483, + 0.517 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.536, + 0.482, + 0.551 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\quad \\epsilon \\sim \\mathcal {N} (0, \\mathbf {I}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.552, + 0.483, + 0.582 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = 1 - \\sigma_{t}^{2}\\) and \\(\\bar{\\alpha}_{t} = \\prod_{i=0}^{t} \\alpha_{i}\\) are fixed hyperparameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.583, + 0.484, + 0.643 + ], + "angle": 0, + "content": "In the reverse diffusion process, the model aims to recover the original data sample \\(\\mathbf{x}_0\\) from \\(\\mathbf{x}_t\\). A diffusion model parameterized as \\(\\omega\\) (often a neural network) is trained to approximate this reverse process defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.648, + 0.482, + 0.665 + ], + "angle": 0, + "content": "\\[\np _ {\\omega} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\omega} \\left(\\mathbf {x} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.484, + 0.73 + ], + "angle": 0, + "content": "Although specific formulations for the estimated mean \\(\\mu_{\\omega}(\\mathbf{x}_t,t)\\) vary [10, 26, 32], each reverse denoising step can be expressed as a function \\(f\\) of \\(\\mathbf{x}_t\\) and the diffusion model \\(\\omega\\) to yield \\(\\mathbf{x}_{t - 1}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.226, + 0.736, + 0.482, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = f \\left(\\mathbf {x} _ {t}, \\omega\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.756, + 0.484, + 0.802 + ], + "angle": 0, + "content": "During inference, Gaussian noise \\(\\mathbf{x}_t\\) is sampled, and the model iteratively denoises it to generate the target sample \\(\\mathbf{x}_0\\) using the trained diffusion model \\(\\omega\\)." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.815, + 0.226, + 0.833 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Our proposed framework addresses the challenge of developing reliable and generalizable in-bed human mesh recovery models in scenarios with limited or no real-world data. By leveraging a large volume of synthetic data generated" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.906, + 0.585 + ], + "angle": 0, + "content": "through simulation, combined with a small amount of real-world data, our framework effectively reduces the reliance on costly and privacy-sensitive real-world data collection. The framework comprises three key stages: synthetic data generation (Sec. 4.1), model design (Sec. 4.2), and pipeline training and fine-tuning (Sec. 4.3). The overview pipeline is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.587, + 0.907, + 0.756 + ], + "angle": 0, + "content": "Throughout our approach, we utilize the SMPL [22] model to represent 3D human bodies. The SMPL model is a parametric human body model that represents a human figure as a mesh of vertices, controlled by a set of pose and shape parameters. Specifically, given the joint angles \\(\\pmb{\\theta} \\in \\mathbb{R}^{23 \\times 3}\\) and shape parameters \\(\\beta \\in \\mathbb{R}^{10}\\), the SMPL model can output a 3D human mesh \\(\\mathbf{V} \\in \\mathbb{R}^{6890 \\times 3}\\) consisting of 6,890 vertices. The SMPL parameters can be defined as \\(\\mathbf{x} = \\left[ \\begin{array}{cccc} \\beta & \\theta & \\mathbf{s} & \\mathbf{u} & \\mathbf{v} \\end{array} \\right]^{\\top} \\in \\mathbb{R}^{88}\\), where \\(\\mathbf{s} \\in \\mathbb{R}^3\\) is the global translation, and \\(\\mathbf{u} \\in \\mathbb{R}^3\\) with \\(\\mathbf{v} \\in \\mathbb{R}^3\\) are used to represent the global rotation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.771, + 0.757, + 0.788 + ], + "angle": 0, + "content": "4.1. Synthetic Data Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Obtaining labeled data for in-bed scenarios across diverse healthcare environments presents a significant challenge, limiting the deployment of deep learning models in this domain. In contrast, simulation offers a low-cost and efficient solution for generating abundant, high-quality depth data along with ground truth annotation for human mesh in resting positions. By incorporating prior information such as" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1831" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.136 + ], + "angle": 0, + "content": "bed dimensions and camera-to-bed distance, we can construct simulated environments that closely replicate the real-world settings." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.137, + 0.484, + 0.333 + ], + "angle": 0, + "content": "Following BodyPressure [4], which introduces a physics-based simulation pipeline to generate synthetic in-bed human depth and pressure images, we adopt this approach to create a diverse and realistic dataset. The pipeline simulates human bodies at rest on a soft mattress, producing depth data from a fixed camera position relative to SMPL-based body configurations on a bed. By sampling human shape \\(\\beta\\), joint angles \\(\\theta\\), and global translation \\((s_x, s_y)\\) from uniform distributions, we generate a variety of data. Additionally, simulated depth images with blankets are created by draping various types of blankets over parts of the body. This dataset further includes diverse human shapes, poses, and bed scene complexities." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.334, + 0.484, + 0.455 + ], + "angle": 0, + "content": "While synthetic data generation can enhance dataset diversity and increase the number of training samples, it also introduces an inherent domain gap between synthetic and real-world data. As a result, models may perform well in synthetic settings but struggle in real-world applications, which undermines their practical utility. Therefore, in the following sections, we focus on bridging this simulation-to-reality gap within the framework for in-bed scenes." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.462, + 0.43, + 0.478 + ], + "angle": 0, + "content": "4.2. Diffusion-Based In-Bed Mesh Recovery" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.484, + 0.484, + 0.726 + ], + "angle": 0, + "content": "Recovering in-bed human mesh from depth images is not a straightforward one-to-one mapping problem, as prior works [3, 4, 36] state. Depth images of in-bed scenarios can vary significantly based on external conditions, such as the presence or absence of a blanket, while the underlying body pose and shape remain the same. This variability introduces ambiguity in the mapping from depth images to human mesh. Additionally, multiple plausible human mesh configurations can correspond to the same depth image due to inherent ambiguities. To address this, we reformulate the in-bed human mesh recovery task as a conditional generative problem. Inspired by recent advancements in diffusion models for image generation [10, 32], we design a diffusion model to learn the distribution of plausible SMPL body configurations, denoted as \\( p_{\\mathrm{SMPL}} \\), conditioned on depth images during training and fine-tuning." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.732, + 0.258, + 0.745 + ], + "angle": 0, + "content": "4.2.1. Diffusion Process" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.811 + ], + "angle": 0, + "content": "In contrast to the diffusion process used in image generation, which operates directly on images, we conduct forward noise-adding and reverse denoising processes on the SMPL body parameters \\(\\mathbf{x}\\) for in-bed human mesh recovery." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.856 + ], + "angle": 0, + "content": "In the forward process, we follow the Eq. 3 to obtain noisy versions \\(\\mathbf{x}_t\\) of the initial SMPL body parameters \\(\\mathbf{x}_0\\) over \\(t\\) timesteps." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.9 + ], + "angle": 0, + "content": "In the reverse process, we incorporate depth images \\(\\mathbf{c}\\) as a conditional input to the diffusion model, modifying Eq. 4 as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.091, + 0.906, + 0.108 + ], + "angle": 0, + "content": "\\[\np _ {\\mathcal {D}} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}, \\mathbf {c}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\mathcal {D}} \\left(\\mathbf {x} _ {t}, t, \\mathbf {c}\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.114, + 0.905, + 0.143 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}\\) represents our diffusion model designed for the in-bed human mesh recovery task." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.144, + 0.906, + 0.248 + ], + "angle": 0, + "content": "Given a training sample \\(\\mathbf{x}_0\\), we train the diffusion model \\(\\mathcal{D}\\) to learn the denoising transition \\(p_{\\mathcal{D}}(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t, \\mathbf{c})\\), ensuring it closely approximates the corresponding forward process \\(q(\\mathbf{x}_t \\mid \\mathbf{x}_{t - 1}, \\mathbf{x}_0)\\). In image generation tasks, this process typically involves having the diffusion model approximate the noise term \\(\\epsilon\\) that produces \\(\\mathbf{x}_t\\) from \\(\\mathbf{x}_0\\) in the forward process." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.25, + 0.906, + 0.37 + ], + "angle": 0, + "content": "However, in our case, if we assume SMPL body parameters \\(\\mathbf{x}_t\\) follow a standard Gaussian distribution, the diffusion model struggles to produce reasonable SMPL parameters, as early denoising iterations may yield unfeasible human meshes. To address this, we diffuse toward the initial sample \\(\\mathbf{x}_0\\) to ensure consistency throughout the denoising process. For any timestep \\(t\\), the estimated initial SMPL parameters \\(\\mathbf{z}_t\\) can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.653, + 0.377, + 0.905, + 0.394 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {t} = \\mathcal {D} \\left(\\mathbf {x} _ {t}, t, \\mathbf {c}\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.399, + 0.906, + 0.429 + ], + "angle": 0, + "content": "The objective of training and fine-tuning the diffusion model \\(\\mathcal{D}\\) for in-bed human mesh recovery is to minimize" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.438, + 0.905, + 0.456 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\mathbf {x} _ {0} \\sim p _ {\\mathrm {S M P L}}} \\mathbb {E} _ {t \\sim \\mathcal {U} \\{0, T \\}, \\mathbf {x} _ {t} \\sim q (\\cdot | \\mathbf {x} _ {0})} \\| \\mathbf {z} _ {t} - \\mathbf {x} _ {0} \\|, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.46, + 0.882, + 0.474 + ], + "angle": 0, + "content": "where \\(\\mathcal{U}(\\cdot)\\) denotes sample from a uniform distribution." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.475, + 0.905, + 0.503 + ], + "angle": 0, + "content": "In the inference, the learned mean \\(\\mu_{\\mathcal{D}}\\) in the Eq. 6 can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.507, + 0.905, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mu_ {\\mathcal {D}} = \\frac {\\sqrt {\\bar {\\alpha} _ {t - 1}} (1 - \\alpha_ {t})}{1 - \\bar {\\alpha} _ {t}} \\mathbf {z} _ {t} + \\frac {\\sqrt {\\alpha_ {t}} (1 - \\bar {\\alpha} _ {t - 1})}{1 - \\bar {\\alpha} _ {t}} \\mathbf {x} _ {t}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.544, + 0.905, + 0.588 + ], + "angle": 0, + "content": "where \\(\\alpha_{t}\\) and \\(\\bar{\\alpha}_{t - 1}\\) are derived from hyper-parameters. Then, we sample from the transition distribution in each denoising step to compute \\(\\mathbf{x}_{t - 1}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.594, + 0.905, + 0.611 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\mu_ {\\mathcal {D}} (\\mathbf {x} _ {t}, t, \\mathbf {c}) + \\sigma^ {2} \\epsilon \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.617, + 0.906, + 0.663 + ], + "angle": 0, + "content": "Following this reverse process, we iteratively denoise the SMPL latent from noise \\(\\mathbf{x}_T\\) at timestep \\(T\\) down to the target SMPL latent \\(\\mathbf{x}_0\\) at timestep 0." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.671, + 0.696, + 0.684 + ], + "angle": 0, + "content": "4.2.2. Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.853 + ], + "angle": 0, + "content": "We introduce a network that takes noised SMPL parameters \\(\\mathbf{x}_t\\), depth images \\(\\mathbf{c}\\), and the timestep \\(t\\) as inputs and outputs the denoised SMPL parameters \\(\\mathbf{z}_t\\) as illustrated in Fig. 3. The reverse diffusion process leverages the depth feature latent to infer denoised SMPL parameters. The noisy SMPL parameters \\(\\mathbf{x}_t\\) are processed through an MLP encoder to obtain the SMPL parameter latent, and a uniform sampler generates the time embedding for the timestep \\(t\\). These inputs—SMPL parameter latent, depth images, and time embedding—are then processed through residual and attention blocks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Following the design of the diffusion U-Net model [29], we incorporate residual and attention blocks to process image inputs and replace batch and layer normalization with" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1832" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.482, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.332, + 0.483, + 0.375 + ], + "angle": 0, + "content": "Figure 3. Diffusion Model Architecture. Dashed lines around specific layers indicate optional layers that may be omitted in certain blocks of the model implementation." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.388, + 0.483, + 0.522 + ], + "angle": 0, + "content": "adaptive normalization layers initialized to zero [28] across the network. Specifically, the SMPL latent is aligned to have the same dimension as the time embedding, allowing them to be combined and fed into each adaptive normalization layer to produce scale and shift parameters, \\(\\gamma\\) and \\(\\beta\\), through a linear MLP. This approach enables dynamic adjustments of normalization parameters, enhancing the network's ability to handle conditional information effectively in diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.524, + 0.483, + 0.644 + ], + "angle": 0, + "content": "Within the network, multiple down-sampling residual blocks follow the initial convolutional layer, succeeded by two additional residual blocks. Attention blocks are attached separately before the last few residual blocks. In the final block, current noised SMPL latent and embedded \\( t \\) are omitted in subsequent layers, allowing the regressor to map the single output latents from all intermediate blocks to the target SMPL parameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.483, + 0.781 + ], + "angle": 0, + "content": "Following the SMPL parameter predictor module, the SMPL model [22] returns the human mesh \\(\\hat{\\mathcal{M}}\\) given the estimated SMPL parameters \\(\\mathbf{z}_t\\). Additionally, a set of gender flags \\(\\mathbf{g} \\in \\mathbb{R}^2\\) controls the gender of the generated human mesh. In this work, we only have two gender flags, where \\([0,1]\\) represents the female SMPL model and \\([1,0]\\) the male model. The 3D Cartesian joint positions \\(\\hat{\\mathbf{J}} \\in \\mathbb{R}^{24 \\times 3}\\) can be extracted from the human mesh vertices \\(\\hat{\\mathbf{V}} \\in \\mathbb{R}^{6890 \\times 3}\\) of each human mesh \\(\\hat{\\mathcal{M}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.791, + 0.265, + 0.807 + ], + "angle": 0, + "content": "4.3. Training Strategy" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.813, + 0.483, + 0.903 + ], + "angle": 0, + "content": "As described above, the output of our diffusion model \\(\\mathcal{D}\\) consists of the estimated in-bed SMPL body parameters \\(\\mathbf{z}_t = \\left[\\hat{\\beta} \\hat{\\theta} \\hat{\\mathbf{s}} \\hat{\\mathbf{u}} \\hat{\\mathbf{v}}\\right]^\\top\\), which includes the predicted body shape parameters \\(\\hat{\\beta}\\), joint angles \\(\\hat{\\theta}\\), global translation \\(\\hat{\\mathbf{s}}\\), and global rotation parameters \\(\\hat{\\mathbf{u}} = \\{u_x, u_y, u_z\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "and \\(\\hat{\\mathbf{v}} = \\{v_x,v_y,v_z\\}\\). Each rotation component \\(\\phi_{i}\\) for \\(i\\in \\{x,y,z\\}\\) can be calculated as \\(\\phi_{i} = \\mathrm{atan2}(u_{i},v_{i})\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.123, + 0.905, + 0.348 + ], + "angle": 0, + "content": "Synthetic training stage: Previous works [4, 36] rely on joint training with both synthetic and real-world data, assuming ample real-world data is available and overlooking the effects of the large synthetic-to-real data imbalance. In contrast, our framework decouples training on synthetic and real-world data to address the limited availability of real-world data and the high ratio of synthetic to real samples. During the synthetic data training phase, our goal is to establish a strong prior based on the diverse range of human resting postures available in the synthetic dataset, enabling the model to produce a reasonable coarse in-bed human pose without requiring real-world data. Our proposed diffusion-based network is trained for a reasonable number of steps on synthetic depth data alone, using a fixed learning rate to prevent convergence to local optima." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.349, + 0.905, + 0.453 + ], + "angle": 0, + "content": "Fine-tuning stage: Given the variable quantity of real-world data, we employ a linearly adjusted learning rate scheduler that automatically adapts based on the amount of available depth data. This adaptive learning rate strategy facilitates rapid convergence and enhances generalization to real-world scenarios during fine-tuning, as demonstrated by our ablation study in Sec 5.5." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.454, + 0.905, + 0.515 + ], + "angle": 0, + "content": "Loss: The total loss used to train and fine-tune the diffusion model contains two components: SMPL parameter loss and vertex position loss. An expansion of each term in the loss function can be found in the supplementary material." + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.53, + 0.905, + 0.547 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\mathrm {S M P L}} + \\lambda_ {\\mathrm {v 2 v}} \\mathcal {L} _ {\\mathrm {v 2 v}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.553, + 0.783, + 0.569 + ], + "angle": 0, + "content": "where \\(\\lambda_{\\mathrm{v2v}}\\) is a tunable hyper-parameter." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.582, + 0.646, + 0.599 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.607, + 0.713, + 0.622 + ], + "angle": 0, + "content": "5.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.905, + 0.901 + ], + "angle": 0, + "content": "[21] provides a comprehensive collection of in-bed resting poses across two settings. In the home setting, data were collected from 102 human participants, with each pose captured under three occlusion conditions: thin sheet, thicker blanket, and no covering. Clever et al. [4] provide SMPL ground truth labels for the real-world SLP home setting data. For training, data from the first 80 participants (1-80, excluding participant 7 due to calibration errors, totaling 10,665 real samples) in the SLP are used either partially or fully during fine-tuning to represent different synthetic-to-real data ratios. For evaluation, data from the remaining 22 participants (81-102, with 2,970 real samples) are used to assess all methods. Additionally, the SLP dataset includes data from a hospital setting, comprising 7 participants without SMPL ground truth labels. Thus, we evaluate our method on the hospital setting data through qualitative visualizations." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1833" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.082, + 0.905, + 0.19 + ], + "angle": 0, + "content": "
    Data Split\nReal-Sim RatioSim\n0:97495Sim+11%Real\n1:80Sim+24%Real\n1:38Sim+37%Real\n1:25Sim+49%Real\n1:18Sim+100%Real\n1:9
    MethodMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVE
    HMR2.0 [7]157.23182.2787.09104.6582.8596.54145.35140.2790.90108.9076.9490.39
    BodyPressure [4]103.47115.3189.87104.6790.46105.9781.2999.0578.2594.6572.9386.78
    BodyMAP [36]330.52365.4385.7990.1476.0789.8069.5183.0161.7774.9657.0669.95
    DiSRT-In-Bed(Ours)109.73121.5974.3778.0367.1473.1858.0466.6655.9464.1450.8161.18
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.193, + 0.907, + 0.237 + ], + "angle": 0, + "content": "Table 1. Comparison to Baselines across Different Data Splits. In the 'Data Split' row, 'Sim' indicates training with all synthetic data, while 'n%Real' indicates training with \\( n\\% \\) of the real data from the SLP training dataset. In the 'Real-Sim Ratio' row, the number represents the approximate ratio of depth images between synthetic and real datasets. All values in the table are in millimeters (mm)." + }, + { + "type": "table", + "bbox": [ + 0.143, + 0.248, + 0.856, + 0.354 + ], + "angle": 0, + "content": "
    MethodUncoverCover 1Cover 23D Shape Error(cm)↓
    MPJPEPVEMPJPEPVEMPJPEPVEheightChestWaistHips
    HMR2.0 [7]69.6781.6679.8693.7481.2995.765.418.3011.247.66
    BodyPressure [4]67.0679.9276.3990.7875.3689.653.963.894.843.37
    BodyMAP [36]51.2662.3460.3573.9759.5573.543.433.174.243.53
    DiSRT-In-Bed(Ours)46.0155.0753.7864.8052.6563.683.255.177.165.20
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.357, + 0.907, + 0.4 + ], + "angle": 0, + "content": "Table 2. Comparison to Baselines across Different Covering Situations. 'Uncover' refers to testing depth images without coverings, 'Cover 1' denotes images with a thin blanket, and 'Cover 2' denotes images with a thick blanket. All MPJPE and PVE values are in millimeters (mm), while 3D Shape Errors are in centimeters (cm)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.413, + 0.482, + 0.548 + ], + "angle": 0, + "content": "BodyPressureSD [4] is generated using the physical simulation mentioned in Sec. 4.1 and serves as a benchmark for sim-to-real tasks. The dataset consists of 97,495 samples, corresponding to the three covering conditions in the SLP dataset, and significantly increases the diversity of human resting poses and body shapes. All synthetic data from BodyPressureSD are used during the training stage of the sim-to-real framework to establish a strong prior on human pose and shape before fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.55, + 0.483, + 0.655 + ], + "angle": 0, + "content": "Metrics. For pose and shape accuracy evaluation, we report the 3D mean-per-joint position error (MPJPE) and 3D per-vertex error (PVE). For each sample, MPJPE is calculated as the Mean Euclidean Distance between the inferred and ground truth positions of 24 3D joints, while PVE measures the mean Euclidean distance across the 6,890 3D vertex positions of the SMPL model." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.667, + 0.308, + 0.683 + ], + "angle": 0, + "content": "5.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.689, + 0.483, + 0.901 + ], + "angle": 0, + "content": "The diffusion model architecture consists of 6 downsampling layers within residual blocks, matching the downsampling depth of ResNet18 [9], and includes three attention blocks positioned before the final three residual blocks. The number of diffusion timesteps is set to 100 during training. For data augmentation, we shuffle the input depth images with random rotations, random erasures, and random noise additions during both training and fine-tuning, using a batch size of 32. All models are optimized with the AdamW [23] optimizer, using an initial learning rate of \\(1 \\times 10^{-4}\\) and a weight decay of \\(5 \\times 10^{-4}\\), trained on a single NVIDIA GeForce RTX 4090 GPU. We set \\(\\lambda_{\\mathrm{v2v}} = 1\\) in the diffusion loss. For testing, we employ a DDIM sampling strategy with 5 timesteps to accelerate inference." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.412, + 0.863, + 0.429 + ], + "angle": 0, + "content": "5.3. Comparison to State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.439, + 0.907, + 0.621 + ], + "angle": 0, + "content": "We conduct several experiments to demonstrate the effectiveness of our method for in-bed human mesh recovery. We choose the current SOTA model HMR2.0 [7], which is designed for single-person mesh recovery from general RGB images, as a baseline. Since our task involves single-channel depth images as input, we modify HMR2.0 by repeating the depth image across channels to match the RGB input format, making it compatible with our scenario. We also compare our method with BodyMAP [36] and BodyPressure [4], designed specifically for the in-bed scenario. Tab. 1 presents quantitative comparisons between our method and baselines across different data splits." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.624, + 0.909, + 0.806 + ], + "angle": 0, + "content": "\\(\\triangle\\) Generalization with limited real data: With high real-to-simulation ratios, our method consistently outperforms previous methods in MPJPE and PVE metrics. Notably, our approach reduces these errors by over \\(10\\%\\) under extreme real-simulation data ratios, such as 1:80 and 1:38. When trained solely on simulation data, our model slightly underperforms BodyPressure, as BodyPressure uses a separate network for human shape parameter prediction. However, BodyPressure's approach introduces a strong bias, leading to degraded performance when limited real-world data is available. Our method demonstrates strong generalization when limited real-world data is available." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.903 + ], + "angle": 0, + "content": "\\(\\triangle\\) Robustness across occlusion: As shown in Tab. 2, we compare models trained on all simulation and real training data across various covering conditions. Our method achieves improved mesh recovery accuracy in all cases compared to prior literature and baselines. Moreover, the stability of our results (less performance drop) across vary-" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1834" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.078, + 0.866, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.486, + 0.908, + 0.557 + ], + "angle": 0, + "content": "Figure 4. Visualization of Human Mesh Estimated from limited Real-World Data in Home Settings. The left three columns show the input depth images, RGB reference images, and ground truth mesh respectively. 'Sim' denotes using all simulation data in the training stage, 'n%Real' denotes the 'n' ratio of real data used in the fine-tuning in our method and jointly training in the baseline. 'Uncover' refers to no blanket in the bed, 'Cover 1' indicates the participant is covered with a thin blanket, and 'Cover 2' means the participant is covered with a thick blanket. The red arrows in the figures point out the mismatch between mesh prediction and the reference images." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.57, + 0.483, + 0.616 + ], + "angle": 0, + "content": "ing degrees of occlusion underscores the robustness of our method, making it more reliable in real-world healthcare settings where patients are often partially covered." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.615, + 0.483, + 0.812 + ], + "angle": 0, + "content": "\\(\\triangle\\) Visualization: Fig. 4 presents the visual comparisons between our method and the SOTA in-bed mesh recovery method BodyMAP [36] under different covering conditions and real-data availability. BodyMAP struggles to estimate accurate human meshes when trained on simulation data alone, highlighting its limitations in addressing simulation-to-real domain gaps. In contrast, our method can capture meaningful pose information. Further, as shown in cases with \\(11\\%\\) and \\(24\\%\\) real data, our method's predictions align more closely with input images across all covering scenarios. With \\(24\\%\\) real data, our model remains largely unaffected by coverings, consistently aligning well with the reference image and ground truth." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.818, + 0.483, + 0.851 + ], + "angle": 0, + "content": "5.4. Generalization to Different Real-World Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To evaluate our method's generalization ability across different environment settings, we compare our 'Sim+100%Real' model with BodyMAP[36] on unla" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.57, + 0.907, + 0.707 + ], + "angle": 0, + "content": "beled hospital-setting depth images5.1. Since ground truth meshes are not available for this setting, we only provide qualitative comparisons. As shown in Fig. 6, our method recovers more accurate human meshes compared to BodyMAP [36]. Notably, for the challenging self-hugging pose, our method accurately captures the crossed arms, whereas BodyMAP [36] fails to replicate this detail. Additional generalization experimental results are available in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.72, + 0.667, + 0.737 + ], + "angle": 0, + "content": "5.5. Ablation Study" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.744, + 0.905, + 0.759 + ], + "angle": 0, + "content": "5.5.1. Effectiveness of Sim-to-Real Transfer Framework" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.901 + ], + "angle": 0, + "content": "To highlight the benefits of synthetic data, we plot MPJPE and PVE for our method and baselines [4, 36] trained with and without synthetic data, under various real-data availability settings, in Fig. 5a. Row-wise comparisons reveal that adding synthetic data significantly enhances performance across all real-world data utilization percentages, especially for the baselines. Our diffusion-based framework further enhances predictions by \\(10 - 35\\%\\) in MPJPE, even when only trained on a small portion of real data." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1835" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.085, + 0.362, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.151, + 0.237, + 0.314, + 0.249 + ], + "angle": 0, + "content": "(a) Ablation on Synthetic Data" + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.085, + 0.627, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.406, + 0.237, + 0.592, + 0.25 + ], + "angle": 0, + "content": "(b) Ablation on Training Strategies" + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.086, + 0.895, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.663, + 0.237, + 0.869, + 0.249 + ], + "angle": 0, + "content": "(c) Ablation on Different Architectures" + }, + { + "type": "image_caption", + "bbox": [ + 0.248, + 0.253, + 0.747, + 0.267 + ], + "angle": 0, + "content": "Figure 5. Ablation Study on Diffusion-Based Sim-to-Real Transfer Framework." + }, + { + "type": "image", + "bbox": [ + 0.125, + 0.277, + 0.457, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.655, + 0.483, + 0.711 + ], + "angle": 0, + "content": "Figure 6. Visualization of Human Mesh estimated from the Real-World Data in Hospital Settings. Ground truth mesh is not available for this scenario. The red arrows in the figures point out the mismatch between mesh prediction and the reference images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.724, + 0.483, + 0.845 + ], + "angle": 0, + "content": "Additionally, Fig. 5b illustrates the impact of applying our Sim-to-Real (S2R) training strategy as detailed in 4.3. Once BodyMAP incorporates our S2R training strategy, it achieves a substantial improvement over its original training scheme. Moreover, our method further outperforms BodyMAP+S2R, underscoring the combined benefit of the proposed framework and model architecture in handling generalization challenges for the in-bed scenario." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.852, + 0.454, + 0.866 + ], + "angle": 0, + "content": "5.5.2. Effectiveness of Diffusion Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We compare our diffusion model architecture (DiSRT-In-Bed) with three design choices as illustrated in Fig. 5c." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.281, + 0.905, + 0.37 + ], + "angle": 0, + "content": "Design Choice 1 — Number of Downsampling Blocks — 6 v.s. 4: Our final model configuration includes 6 convolutional downsampling layers, similar to the ResNet-18 architecture [9] used in BodyMAP [36]. We observe a decrease in MPJPE when using 6 downsampling blocks rather than only 4." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.372, + 0.906, + 0.583 + ], + "angle": 0, + "content": "Design Choice 2 — Conditioning Technique — Conditioning with adaptive normalization v.s. in-context conditioning: We evaluate our conditioning approach (Section 4.2.2) against the commonly used in-context conditioning techniques [17, 41], which concatenates depth features and SMPL latent representations of equal size along the channel dimension. While retaining adaptive layer normalization, this approach uses only the timestep embedding to predict the scale and shift within blocks. However, we see that in-context conditioning is less effective for depth image conditioning, as it requires expanding the lower-dimensional SMPL parameters to match the higher dimensionality of the depth images before concatenation, which reduces the efficiency of feature integration." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.905, + 0.659 + ], + "angle": 0, + "content": "Design Choice 3 - With Attention Block vs. Without Attention Block — We assess the impact of incorporating attention blocks in the final layers of the diffusion model. The results indicate that adding attention blocks noticeably improves in-bed pose prediction performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.672, + 0.634, + 0.687 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.698, + 0.907, + 0.895 + ], + "angle": 0, + "content": "In this work, we present a diffusion-based framework for in-bed human mesh recovery, designed to enhance generalization and accuracy in healthcare environments with limited real-world data. By leveraging synthetic data and a Sim-to-Real Transfer Framework, our approach effectively addresses challenges posed by privacy concerns, occlusions, and data scarcity. Extensive experiments demonstrated the robustness of our method across varying covering conditions and high real-to-simulation ratios, consistently outperforming existing methods in MPJPE and PVE metrics. Additionally, our model's adaptability across different environments and reduced reliance on real-world data offer an efficient and scalable solution for clinical deployment." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1836" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.184 + ], + "angle": 0, + "content": "[1] Qingyuan Cai, Xuecai Hu, Saihui Hou, Li Yao, and Yongzhen Huang. Disentangled diffusion-based 3d human pose estimation with hierarchical spatial and temporal denoiser. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 882-890, 2024. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.186, + 0.484, + 0.24 + ], + "angle": 0, + "content": "[2] Jooyoung Choi, Sungwon Kim, Yonghyun Jeong, Youngjune Gwon, and Sungroh Yoon. 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Jeni Zackory Erickson Carnegie Mellon University + +{jinggao2, cezheng, laszlojeni, zerickso}@andrew.cmu.edu + +# Abstract + +In-bed human mesh recovery can be crucial and enabling for several healthcare applications, including sleep pattern monitoring, rehabilitation support, and pressure ulcer prevention. However, it is difficult to collect large real-world visual datasets in this domain, in part due to privacy and expense constraints, which in turn presents significant challenges for training and deploying deep learning models. Existing in-bed human mesh estimation methods often rely heavily on real-world data, limiting their ability to generalize across different in-bed scenarios, such as varying coverings and environmental settings. To address this, we propose a Sim-to-Real Transfer Framework for in-bed human mesh recovery from overhead depth images, which leverages large-scale synthetic data alongside limited or no real-world samples. We introduce a diffusion model that bridges the gap between synthetic data and real data to support generalization in real-world in-bed pose and body inference scenarios. Extensive experiments and ablation studies validate the effectiveness of our framework, demonstrating significant improvements in robustness and adaptability across diverse healthcare scenarios. Project page can be found at https://jing-g2.github.io/DiSRT-In-Bed/. + +# 1. Introduction + +Human mesh recovery, the process of estimating 3D human body shapes and poses from camera or sensor data, is a challenging problem with significant applications in healthcare. In-bed human mesh recovery, in particular, plays a vital role in assessing patient well-being, monitoring mobility, and detecting health risks, such as pressure ulcers. + +However, collecting labeled real-world data in healthcare settings is costly, time-consuming, and often constrained by privacy concerns. Alternative sensing technologies, like pressure sensing mats, are expensive, require direct patient contact, and can lose calibration over time, limiting their reliability. Thermal sensors, while contact-free, are highly + +![](images/cd673b44470249cbf7ad127f9d630a5900bd75cfce3a7d83ed48d45f134ce8bc.jpg) +Figure 1. Impact of real-world data scarcity on in-bed human mesh recovery. BodyMAP shows significant performance degradation when trained with limited real-world data, while our method maintains robust accuracy. 'Sim' indicates training with all synthetic data and $n\%$ Real' indicates training with $n\%$ of the real data from the training dataset. + +sensitive to environmental factors. In addition, both RGB cameras and thermal sensors often struggle with occlusions in bed, such as blankets. Given these limitations, depth cameras emerge as a practical solution, offering a balance of accuracy, affordability, and privacy protection, while avoiding the drawbacks of other sensor types. + +Furthermore, general human mesh recovery tasks benefit from abundant real-world data featuring individuals in standing or active poses [7, 37]. Such dependence on large-scale real-world data limits the adaptability and performance of deep learning models for human mesh prediction in clinical settings, where data collection is challenging and often privacy-constrained. + +To address the challenge of limited training data, utilizing synthetic data presents a promising solution. Large-scale simulated depth datasets can be efficiently generated without preserving any personally identifiable information, eliminating the need for sensitive real-world data. Building on this strategy, prior work [3, 4, 36] has demonstrated good performance in the in-bed human mesh recovery task. However, they struggle to effectively bridge the domain gap between synthetic and real-world data, leading to significant performance degradation when the proportion of real-world data in the training set is low, as shown in Fig. 1. Thus, to further enhance generalization, we propose a novel + +diffusion-based pipeline for in-bed human mesh recovery. Diffusion models are particularly well-suited for this scenario due to their strong ability to handle uncertainties, such as noise and variations in depth images. By leveraging the diffusion framework, our method mitigates the domain gap between real and synthetic data while enhancing generalization across diverse real-world environments (e.g., different hospitals or room setups). This ensures smooth and coherent predictions across varied settings for real-world applications. We conduct extensive experiments, comparing with baselines and performing ablations, to demonstrate the method's effectiveness in real-world scenarios with occlusions and varying conditions. + +Our contributions are summarized as follows: + +- We propose a Sim-to-Real Transfer Framework for in-bed human mesh recovery that effectively leverages synthetic data to improve performance in real-world healthcare settings with limited labeled real data. +- We introduce a diffusion-based architecture, enabling the diffusion process to bridge the domain gap between synthetic and real-world data and achieve strong generalization across different environment settings. +- We conduct extensive experiments, including comparisons with state-of-the-art methods, ablation studies, and generalization tests across different real-world settings, to assess the performance of our approach. + +# 2. Related Work + +# 2.1. 3D Human Pose and Mesh Estimation + +With significant progress in 3D human pose estimation [25, 27, 43, 46], researchers are seeking to go beyond just pose prediction. Human mesh recovery, which provides a more detailed 3D representation of the human body, has gained increasing interest. As a foundational human parametric model, SMPL [22] has been widely adopted in numerous works [11, 12, 14, 18-20, 38, 40, 44] to recover human mesh by predicting SMPL parameters. HybrIK [13] and its extension, HybrIK-X [15], introduce hybrid inverse kinematics techniques that convert 3D joints into body-part rotations through twist-and-swing decomposition. HMR2.0 [7] employs a straightforward yet effective transformer-based network, setting a foundation for subsequent work. TokenHMR [5] introduces a tokenized approach to representing human pose and shape, effectively handling occlusions by reframing the problem as token prediction. + +# 2.2. Diffusion Models for Human Pose and Mesh Estimation + +Diffusion generative models [10, 32] have shown remarkable success across diverse computer vision tasks, including image inpainting [33, 42], text-to-image generation [17, 28-30, 41], and image-to-image translation [2]. Leveraging + +their powerful capability to manage uncertainty and refine distributions, these models have been effectively applied to 3D human pose estimation and human mesh recovery tasks [1, 8, 16, 24, 31, 34, 35, 45]. DiffPose [8] pioneers diffusion-based 3D pose prediction from 2D sequences. Extending to human mesh recovery, HMDiff [6] applies a distribution alignment technique to provide input-specific information within the diffusion process, simplifying mesh estimation. Similarly, ScoreHMR [34] uses a diffusion model as a prior for SMPL body model parameters, guiding the denoising process with observed 2D keypoints. + +# 2.3. In-Bed Human Pose and mesh Estimation + +In contrast to general human pose estimation and mesh recovery tasks, where numerous large-scale datasets are available for training, in-bed human pose estimation and mesh recovery present unique challenges. These challenges stem from the limited availability of suitable datasets, the reliance on depth images as input, and the nature of in-bed poses. Individuals are often lying in various orientations on the bed and are partially covered by blankets, leading to heavy occlusions and constrained body positions. As one of the prior works, Pyramid Fusion [39] introduces a pyramid scheme to effectively fuse four input modalities—RGB, pressure, depth, and infrared images—for human mesh estimation. However, subsequent approaches removed RGB images from the input due to privacy concerns in clinical deployments. PressureNet [3] employs pressure images as input, using a multi-stage CNN-based framework to produce human mesh outputs, while BodyPressure [4] focuses on depth images to infer both human mesh and pressure maps. The recent BodyMAP [36] simplifies the processes used in PressureNet [3] and BPBnet [4], predicting human mesh using depth and pressure images. In contrast, we focus on improving the generalization of the in-bed human mesh recovery from depth images by leveraging synthetic data and introducing a novel diffusion-based pipeline. + +# 3. Preliminaries on Diffusion Models + +Diffusion models [10, 32] are probabilistic generative models that learn to transform random noise into the target data distribution via a forward and reverse process. + +In the forward diffusion process, a data sample $\mathbf{x}_0$ is progressively noised by adding Gaussian noise according to a fixed variance schedule $\sigma_t$ over a sequence of $T$ timesteps. This process forms a Markov chain with the transitions: + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {\alpha_ {t}} \mathbf {x} _ {t - 1}, (1 - \alpha_ {t}) \mathbf {I}\right), \tag {1} +$$ + +where $\mathbf{x}_t$ represents the noisy sample at step $t$ , constant $\alpha_t = 1 - \sigma_t^2$ , and $\mathcal{N}(\cdot)$ denotes the Gaussian distribution. The final sample $\mathbf{x}_t$ is approximately Gaussian noise. + +The forward diffusion process defined in [10] allows us to directly sample an arbitrary step of the noised latent $\mathbf{x}_t$ + +![](images/ea7fe9bcb5aa91300b54bdded3acd9bfbed957b8826210110487de3d2c66aa1e.jpg) +Figure 2. Overview of the Proposed Sim-to-Real Transfer Framework. The framework comprises three stages: In the Synthetic Data Generation stage (left), a large, diverse set of synthetic depth images is generated within a simulated environment. In the training stage, the diffusion model $\mathcal{D}$ conditions on the synthetic depth image $\mathbf{c}_{\mathrm{syn}}$ to denoise SMPL parameters $\mathbf{x}_t$ in the reverse process, which begins at timestep $T$ and progresses toward timestep 0, yielding the estimated human mesh $\hat{\mathcal{M}}_{\mathrm{syn}}$ . In the fine-tuning stage, the model conditions on real depth images $\mathbf{c}_{\mathrm{real}}$ to estimate the human mesh $\hat{\mathcal{M}}_{\mathrm{real}}$ . The symbol $g'$ in the diffusion model indicates the gender flag associated with the input. The 'Ref.' in the figure denotes the corresponding synthetic depth image during training and the corresponding RGB image for visualization purposes only. + +conditioned on the input $\mathbf{x}_0$ as follows: + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {0}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right) \tag {2} +$$ + +$$ +\mathbf {x} _ {t} = \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \quad \epsilon \sim \mathcal {N} (0, \mathbf {I}), \tag {3} +$$ + +where $\alpha_{t} = 1 - \sigma_{t}^{2}$ and $\bar{\alpha}_{t} = \prod_{i=0}^{t} \alpha_{i}$ are fixed hyperparameters. + +In the reverse diffusion process, the model aims to recover the original data sample $\mathbf{x}_0$ from $\mathbf{x}_t$ . A diffusion model parameterized as $\omega$ (often a neural network) is trained to approximate this reverse process defined as: + +$$ +p _ {\omega} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) = \mathcal {N} \left(\mathbf {x} _ {t - 1}; \mu_ {\omega} \left(\mathbf {x} _ {t}, t\right), \sigma_ {t} ^ {2} \mathbf {I}\right), \tag {4} +$$ + +Although specific formulations for the estimated mean $\mu_{\omega}(\mathbf{x}_t,t)$ vary [10, 26, 32], each reverse denoising step can be expressed as a function $f$ of $\mathbf{x}_t$ and the diffusion model $\omega$ to yield $\mathbf{x}_{t - 1}$ as follows: + +$$ +\mathbf {x} _ {t - 1} = f \left(\mathbf {x} _ {t}, \omega\right). \tag {5} +$$ + +During inference, Gaussian noise $\mathbf{x}_t$ is sampled, and the model iteratively denoises it to generate the target sample $\mathbf{x}_0$ using the trained diffusion model $\omega$ . + +# 4. Methodology + +Our proposed framework addresses the challenge of developing reliable and generalizable in-bed human mesh recovery models in scenarios with limited or no real-world data. By leveraging a large volume of synthetic data generated + +through simulation, combined with a small amount of real-world data, our framework effectively reduces the reliance on costly and privacy-sensitive real-world data collection. The framework comprises three key stages: synthetic data generation (Sec. 4.1), model design (Sec. 4.2), and pipeline training and fine-tuning (Sec. 4.3). The overview pipeline is shown in Fig. 2. + +Throughout our approach, we utilize the SMPL [22] model to represent 3D human bodies. The SMPL model is a parametric human body model that represents a human figure as a mesh of vertices, controlled by a set of pose and shape parameters. Specifically, given the joint angles $\pmb{\theta} \in \mathbb{R}^{23 \times 3}$ and shape parameters $\beta \in \mathbb{R}^{10}$ , the SMPL model can output a 3D human mesh $\mathbf{V} \in \mathbb{R}^{6890 \times 3}$ consisting of 6,890 vertices. The SMPL parameters can be defined as $\mathbf{x} = \left[ \begin{array}{cccc} \beta & \theta & \mathbf{s} & \mathbf{u} & \mathbf{v} \end{array} \right]^{\top} \in \mathbb{R}^{88}$ , where $\mathbf{s} \in \mathbb{R}^3$ is the global translation, and $\mathbf{u} \in \mathbb{R}^3$ with $\mathbf{v} \in \mathbb{R}^3$ are used to represent the global rotation. + +# 4.1. Synthetic Data Generation + +Obtaining labeled data for in-bed scenarios across diverse healthcare environments presents a significant challenge, limiting the deployment of deep learning models in this domain. In contrast, simulation offers a low-cost and efficient solution for generating abundant, high-quality depth data along with ground truth annotation for human mesh in resting positions. By incorporating prior information such as + +bed dimensions and camera-to-bed distance, we can construct simulated environments that closely replicate the real-world settings. + +Following BodyPressure [4], which introduces a physics-based simulation pipeline to generate synthetic in-bed human depth and pressure images, we adopt this approach to create a diverse and realistic dataset. The pipeline simulates human bodies at rest on a soft mattress, producing depth data from a fixed camera position relative to SMPL-based body configurations on a bed. By sampling human shape $\beta$ , joint angles $\theta$ , and global translation $(s_x, s_y)$ from uniform distributions, we generate a variety of data. Additionally, simulated depth images with blankets are created by draping various types of blankets over parts of the body. This dataset further includes diverse human shapes, poses, and bed scene complexities. + +While synthetic data generation can enhance dataset diversity and increase the number of training samples, it also introduces an inherent domain gap between synthetic and real-world data. As a result, models may perform well in synthetic settings but struggle in real-world applications, which undermines their practical utility. Therefore, in the following sections, we focus on bridging this simulation-to-reality gap within the framework for in-bed scenes. + +# 4.2. Diffusion-Based In-Bed Mesh Recovery + +Recovering in-bed human mesh from depth images is not a straightforward one-to-one mapping problem, as prior works [3, 4, 36] state. Depth images of in-bed scenarios can vary significantly based on external conditions, such as the presence or absence of a blanket, while the underlying body pose and shape remain the same. This variability introduces ambiguity in the mapping from depth images to human mesh. Additionally, multiple plausible human mesh configurations can correspond to the same depth image due to inherent ambiguities. To address this, we reformulate the in-bed human mesh recovery task as a conditional generative problem. Inspired by recent advancements in diffusion models for image generation [10, 32], we design a diffusion model to learn the distribution of plausible SMPL body configurations, denoted as $p_{\mathrm{SMPL}}$ , conditioned on depth images during training and fine-tuning. + +# 4.2.1. Diffusion Process + +In contrast to the diffusion process used in image generation, which operates directly on images, we conduct forward noise-adding and reverse denoising processes on the SMPL body parameters $\mathbf{x}$ for in-bed human mesh recovery. + +In the forward process, we follow the Eq. 3 to obtain noisy versions $\mathbf{x}_t$ of the initial SMPL body parameters $\mathbf{x}_0$ over $t$ timesteps. + +In the reverse process, we incorporate depth images $\mathbf{c}$ as a conditional input to the diffusion model, modifying Eq. 4 as follows: + +$$ +p _ {\mathcal {D}} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}, \mathbf {c}\right) = \mathcal {N} \left(\mathbf {x} _ {t - 1}; \mu_ {\mathcal {D}} \left(\mathbf {x} _ {t}, t, \mathbf {c}\right), \sigma_ {t} ^ {2} \mathbf {I}\right), \tag {6} +$$ + +where $\mathcal{D}$ represents our diffusion model designed for the in-bed human mesh recovery task. + +Given a training sample $\mathbf{x}_0$ , we train the diffusion model $\mathcal{D}$ to learn the denoising transition $p_{\mathcal{D}}(\mathbf{x}_{t - 1} \mid \mathbf{x}_t, \mathbf{c})$ , ensuring it closely approximates the corresponding forward process $q(\mathbf{x}_t \mid \mathbf{x}_{t - 1}, \mathbf{x}_0)$ . In image generation tasks, this process typically involves having the diffusion model approximate the noise term $\epsilon$ that produces $\mathbf{x}_t$ from $\mathbf{x}_0$ in the forward process. + +However, in our case, if we assume SMPL body parameters $\mathbf{x}_t$ follow a standard Gaussian distribution, the diffusion model struggles to produce reasonable SMPL parameters, as early denoising iterations may yield unfeasible human meshes. To address this, we diffuse toward the initial sample $\mathbf{x}_0$ to ensure consistency throughout the denoising process. For any timestep $t$ , the estimated initial SMPL parameters $\mathbf{z}_t$ can be represented as: + +$$ +\mathbf {z} _ {t} = \mathcal {D} \left(\mathbf {x} _ {t}, t, \mathbf {c}\right) \tag {7} +$$ + +The objective of training and fine-tuning the diffusion model $\mathcal{D}$ for in-bed human mesh recovery is to minimize + +$$ +\mathbb {E} _ {\mathbf {x} _ {0} \sim p _ {\mathrm {S M P L}}} \mathbb {E} _ {t \sim \mathcal {U} \{0, T \}, \mathbf {x} _ {t} \sim q (\cdot | \mathbf {x} _ {0})} \| \mathbf {z} _ {t} - \mathbf {x} _ {0} \|, \tag {8} +$$ + +where $\mathcal{U}(\cdot)$ denotes sample from a uniform distribution. + +In the inference, the learned mean $\mu_{\mathcal{D}}$ in the Eq. 6 can be formulated as: + +$$ +\mu_ {\mathcal {D}} = \frac {\sqrt {\bar {\alpha} _ {t - 1}} (1 - \alpha_ {t})}{1 - \bar {\alpha} _ {t}} \mathbf {z} _ {t} + \frac {\sqrt {\alpha_ {t}} (1 - \bar {\alpha} _ {t - 1})}{1 - \bar {\alpha} _ {t}} \mathbf {x} _ {t}, \tag {9} +$$ + +where $\alpha_{t}$ and $\bar{\alpha}_{t - 1}$ are derived from hyper-parameters. Then, we sample from the transition distribution in each denoising step to compute $\mathbf{x}_{t - 1}$ as follows: + +$$ +\mathbf {x} _ {t - 1} = \mu_ {\mathcal {D}} (\mathbf {x} _ {t}, t, \mathbf {c}) + \sigma^ {2} \epsilon \tag {10} +$$ + +Following this reverse process, we iteratively denoise the SMPL latent from noise $\mathbf{x}_T$ at timestep $T$ down to the target SMPL latent $\mathbf{x}_0$ at timestep 0. + +# 4.2.2. Model Architecture + +We introduce a network that takes noised SMPL parameters $\mathbf{x}_t$ , depth images $\mathbf{c}$ , and the timestep $t$ as inputs and outputs the denoised SMPL parameters $\mathbf{z}_t$ as illustrated in Fig. 3. The reverse diffusion process leverages the depth feature latent to infer denoised SMPL parameters. The noisy SMPL parameters $\mathbf{x}_t$ are processed through an MLP encoder to obtain the SMPL parameter latent, and a uniform sampler generates the time embedding for the timestep $t$ . These inputs—SMPL parameter latent, depth images, and time embedding—are then processed through residual and attention blocks. + +Following the design of the diffusion U-Net model [29], we incorporate residual and attention blocks to process image inputs and replace batch and layer normalization with + +![](images/acf44a0107ca596b4cba690274666b1f598cf688e295d8f3202bf1455bc3975f.jpg) +Figure 3. Diffusion Model Architecture. Dashed lines around specific layers indicate optional layers that may be omitted in certain blocks of the model implementation. + +adaptive normalization layers initialized to zero [28] across the network. Specifically, the SMPL latent is aligned to have the same dimension as the time embedding, allowing them to be combined and fed into each adaptive normalization layer to produce scale and shift parameters, $\gamma$ and $\beta$ , through a linear MLP. This approach enables dynamic adjustments of normalization parameters, enhancing the network's ability to handle conditional information effectively in diffusion models. + +Within the network, multiple down-sampling residual blocks follow the initial convolutional layer, succeeded by two additional residual blocks. Attention blocks are attached separately before the last few residual blocks. In the final block, current noised SMPL latent and embedded $t$ are omitted in subsequent layers, allowing the regressor to map the single output latents from all intermediate blocks to the target SMPL parameters. + +Following the SMPL parameter predictor module, the SMPL model [22] returns the human mesh $\hat{\mathcal{M}}$ given the estimated SMPL parameters $\mathbf{z}_t$ . Additionally, a set of gender flags $\mathbf{g} \in \mathbb{R}^2$ controls the gender of the generated human mesh. In this work, we only have two gender flags, where $[0,1]$ represents the female SMPL model and $[1,0]$ the male model. The 3D Cartesian joint positions $\hat{\mathbf{J}} \in \mathbb{R}^{24 \times 3}$ can be extracted from the human mesh vertices $\hat{\mathbf{V}} \in \mathbb{R}^{6890 \times 3}$ of each human mesh $\hat{\mathcal{M}}$ . + +# 4.3. Training Strategy + +As described above, the output of our diffusion model $\mathcal{D}$ consists of the estimated in-bed SMPL body parameters $\mathbf{z}_t = \left[\hat{\beta} \hat{\theta} \hat{\mathbf{s}} \hat{\mathbf{u}} \hat{\mathbf{v}}\right]^\top$ , which includes the predicted body shape parameters $\hat{\beta}$ , joint angles $\hat{\theta}$ , global translation $\hat{\mathbf{s}}$ , and global rotation parameters $\hat{\mathbf{u}} = \{u_x, u_y, u_z\}$ + +and $\hat{\mathbf{v}} = \{v_x,v_y,v_z\}$ . Each rotation component $\phi_{i}$ for $i\in \{x,y,z\}$ can be calculated as $\phi_{i} = \mathrm{atan2}(u_{i},v_{i})$ + +Synthetic training stage: Previous works [4, 36] rely on joint training with both synthetic and real-world data, assuming ample real-world data is available and overlooking the effects of the large synthetic-to-real data imbalance. In contrast, our framework decouples training on synthetic and real-world data to address the limited availability of real-world data and the high ratio of synthetic to real samples. During the synthetic data training phase, our goal is to establish a strong prior based on the diverse range of human resting postures available in the synthetic dataset, enabling the model to produce a reasonable coarse in-bed human pose without requiring real-world data. Our proposed diffusion-based network is trained for a reasonable number of steps on synthetic depth data alone, using a fixed learning rate to prevent convergence to local optima. + +Fine-tuning stage: Given the variable quantity of real-world data, we employ a linearly adjusted learning rate scheduler that automatically adapts based on the amount of available depth data. This adaptive learning rate strategy facilitates rapid convergence and enhances generalization to real-world scenarios during fine-tuning, as demonstrated by our ablation study in Sec 5.5. + +Loss: The total loss used to train and fine-tune the diffusion model contains two components: SMPL parameter loss and vertex position loss. An expansion of each term in the loss function can be found in the supplementary material. + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\mathrm {S M P L}} + \lambda_ {\mathrm {v 2 v}} \mathcal {L} _ {\mathrm {v 2 v}}, \tag {11} +$$ + +where $\lambda_{\mathrm{v2v}}$ is a tunable hyper-parameter. + +# 5. Experiments + +# 5.1. Datasets and Metrics + +[21] provides a comprehensive collection of in-bed resting poses across two settings. In the home setting, data were collected from 102 human participants, with each pose captured under three occlusion conditions: thin sheet, thicker blanket, and no covering. Clever et al. [4] provide SMPL ground truth labels for the real-world SLP home setting data. For training, data from the first 80 participants (1-80, excluding participant 7 due to calibration errors, totaling 10,665 real samples) in the SLP are used either partially or fully during fine-tuning to represent different synthetic-to-real data ratios. For evaluation, data from the remaining 22 participants (81-102, with 2,970 real samples) are used to assess all methods. Additionally, the SLP dataset includes data from a hospital setting, comprising 7 participants without SMPL ground truth labels. Thus, we evaluate our method on the hospital setting data through qualitative visualizations. + +
    Data Split +Real-Sim RatioSim +0:97495Sim+11%Real +1:80Sim+24%Real +1:38Sim+37%Real +1:25Sim+49%Real +1:18Sim+100%Real +1:9
    MethodMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVE
    HMR2.0 [7]157.23182.2787.09104.6582.8596.54145.35140.2790.90108.9076.9490.39
    BodyPressure [4]103.47115.3189.87104.6790.46105.9781.2999.0578.2594.6572.9386.78
    BodyMAP [36]330.52365.4385.7990.1476.0789.8069.5183.0161.7774.9657.0669.95
    DiSRT-In-Bed(Ours)109.73121.5974.3778.0367.1473.1858.0466.6655.9464.1450.8161.18
    + +Table 1. Comparison to Baselines across Different Data Splits. In the 'Data Split' row, 'Sim' indicates training with all synthetic data, while 'n%Real' indicates training with $n\%$ of the real data from the SLP training dataset. In the 'Real-Sim Ratio' row, the number represents the approximate ratio of depth images between synthetic and real datasets. All values in the table are in millimeters (mm). + +
    MethodUncoverCover 1Cover 23D Shape Error(cm)↓
    MPJPEPVEMPJPEPVEMPJPEPVEheightChestWaistHips
    HMR2.0 [7]69.6781.6679.8693.7481.2995.765.418.3011.247.66
    BodyPressure [4]67.0679.9276.3990.7875.3689.653.963.894.843.37
    BodyMAP [36]51.2662.3460.3573.9759.5573.543.433.174.243.53
    DiSRT-In-Bed(Ours)46.0155.0753.7864.8052.6563.683.255.177.165.20
    + +Table 2. Comparison to Baselines across Different Covering Situations. 'Uncover' refers to testing depth images without coverings, 'Cover 1' denotes images with a thin blanket, and 'Cover 2' denotes images with a thick blanket. All MPJPE and PVE values are in millimeters (mm), while 3D Shape Errors are in centimeters (cm). + +BodyPressureSD [4] is generated using the physical simulation mentioned in Sec. 4.1 and serves as a benchmark for sim-to-real tasks. The dataset consists of 97,495 samples, corresponding to the three covering conditions in the SLP dataset, and significantly increases the diversity of human resting poses and body shapes. All synthetic data from BodyPressureSD are used during the training stage of the sim-to-real framework to establish a strong prior on human pose and shape before fine-tuning. + +Metrics. For pose and shape accuracy evaluation, we report the 3D mean-per-joint position error (MPJPE) and 3D per-vertex error (PVE). For each sample, MPJPE is calculated as the Mean Euclidean Distance between the inferred and ground truth positions of 24 3D joints, while PVE measures the mean Euclidean distance across the 6,890 3D vertex positions of the SMPL model. + +# 5.2. Implementation Details + +The diffusion model architecture consists of 6 downsampling layers within residual blocks, matching the downsampling depth of ResNet18 [9], and includes three attention blocks positioned before the final three residual blocks. The number of diffusion timesteps is set to 100 during training. For data augmentation, we shuffle the input depth images with random rotations, random erasures, and random noise additions during both training and fine-tuning, using a batch size of 32. All models are optimized with the AdamW [23] optimizer, using an initial learning rate of $1 \times 10^{-4}$ and a weight decay of $5 \times 10^{-4}$ , trained on a single NVIDIA GeForce RTX 4090 GPU. We set $\lambda_{\mathrm{v2v}} = 1$ in the diffusion loss. For testing, we employ a DDIM sampling strategy with 5 timesteps to accelerate inference. + +# 5.3. Comparison to State-of-the-Art Methods + +We conduct several experiments to demonstrate the effectiveness of our method for in-bed human mesh recovery. We choose the current SOTA model HMR2.0 [7], which is designed for single-person mesh recovery from general RGB images, as a baseline. Since our task involves single-channel depth images as input, we modify HMR2.0 by repeating the depth image across channels to match the RGB input format, making it compatible with our scenario. We also compare our method with BodyMAP [36] and BodyPressure [4], designed specifically for the in-bed scenario. Tab. 1 presents quantitative comparisons between our method and baselines across different data splits. + +$\triangle$ Generalization with limited real data: With high real-to-simulation ratios, our method consistently outperforms previous methods in MPJPE and PVE metrics. Notably, our approach reduces these errors by over $10\%$ under extreme real-simulation data ratios, such as 1:80 and 1:38. When trained solely on simulation data, our model slightly underperforms BodyPressure, as BodyPressure uses a separate network for human shape parameter prediction. However, BodyPressure's approach introduces a strong bias, leading to degraded performance when limited real-world data is available. Our method demonstrates strong generalization when limited real-world data is available. + +$\triangle$ Robustness across occlusion: As shown in Tab. 2, we compare models trained on all simulation and real training data across various covering conditions. Our method achieves improved mesh recovery accuracy in all cases compared to prior literature and baselines. Moreover, the stability of our results (less performance drop) across vary- + +![](images/1555a55c24b271582270eaaa859e9b8b91e13c844bd2368de90e98d82fe2eccf.jpg) +Figure 4. Visualization of Human Mesh Estimated from limited Real-World Data in Home Settings. The left three columns show the input depth images, RGB reference images, and ground truth mesh respectively. 'Sim' denotes using all simulation data in the training stage, 'n%Real' denotes the 'n' ratio of real data used in the fine-tuning in our method and jointly training in the baseline. 'Uncover' refers to no blanket in the bed, 'Cover 1' indicates the participant is covered with a thin blanket, and 'Cover 2' means the participant is covered with a thick blanket. The red arrows in the figures point out the mismatch between mesh prediction and the reference images. + +ing degrees of occlusion underscores the robustness of our method, making it more reliable in real-world healthcare settings where patients are often partially covered. + +$\triangle$ Visualization: Fig. 4 presents the visual comparisons between our method and the SOTA in-bed mesh recovery method BodyMAP [36] under different covering conditions and real-data availability. BodyMAP struggles to estimate accurate human meshes when trained on simulation data alone, highlighting its limitations in addressing simulation-to-real domain gaps. In contrast, our method can capture meaningful pose information. Further, as shown in cases with $11\%$ and $24\%$ real data, our method's predictions align more closely with input images across all covering scenarios. With $24\%$ real data, our model remains largely unaffected by coverings, consistently aligning well with the reference image and ground truth. + +# 5.4. Generalization to Different Real-World Settings + +To evaluate our method's generalization ability across different environment settings, we compare our 'Sim+100%Real' model with BodyMAP[36] on unla + +beled hospital-setting depth images5.1. Since ground truth meshes are not available for this setting, we only provide qualitative comparisons. As shown in Fig. 6, our method recovers more accurate human meshes compared to BodyMAP [36]. Notably, for the challenging self-hugging pose, our method accurately captures the crossed arms, whereas BodyMAP [36] fails to replicate this detail. Additional generalization experimental results are available in the supplementary material. + +# 5.5. Ablation Study + +# 5.5.1. Effectiveness of Sim-to-Real Transfer Framework + +To highlight the benefits of synthetic data, we plot MPJPE and PVE for our method and baselines [4, 36] trained with and without synthetic data, under various real-data availability settings, in Fig. 5a. Row-wise comparisons reveal that adding synthetic data significantly enhances performance across all real-world data utilization percentages, especially for the baselines. Our diffusion-based framework further enhances predictions by $10 - 35\%$ in MPJPE, even when only trained on a small portion of real data. + +![](images/8e409f5cba7e4e928a4edd3559cc1aaac55a1b90050832ef28f9d0d781e6b676.jpg) +(a) Ablation on Synthetic Data + +![](images/6910f8f500e10b2c0ba7378ea078fc066b3c187856aae4d8fad4533f99af1b0a.jpg) +(b) Ablation on Training Strategies + +![](images/4a884d669488dd385f1fb3640e265590c23630821795145e7ee81146ea9b379d.jpg) +(c) Ablation on Different Architectures +Figure 5. Ablation Study on Diffusion-Based Sim-to-Real Transfer Framework. + +![](images/b2c169e9ba2b91c48ac33e58eee25af9cd28cb99be8e12b67b86404c26548f40.jpg) +Figure 6. Visualization of Human Mesh estimated from the Real-World Data in Hospital Settings. Ground truth mesh is not available for this scenario. The red arrows in the figures point out the mismatch between mesh prediction and the reference images. + +Additionally, Fig. 5b illustrates the impact of applying our Sim-to-Real (S2R) training strategy as detailed in 4.3. Once BodyMAP incorporates our S2R training strategy, it achieves a substantial improvement over its original training scheme. Moreover, our method further outperforms BodyMAP+S2R, underscoring the combined benefit of the proposed framework and model architecture in handling generalization challenges for the in-bed scenario. + +# 5.5.2. Effectiveness of Diffusion Model Architecture + +We compare our diffusion model architecture (DiSRT-In-Bed) with three design choices as illustrated in Fig. 5c. + +Design Choice 1 — Number of Downsampling Blocks — 6 v.s. 4: Our final model configuration includes 6 convolutional downsampling layers, similar to the ResNet-18 architecture [9] used in BodyMAP [36]. We observe a decrease in MPJPE when using 6 downsampling blocks rather than only 4. + +Design Choice 2 — Conditioning Technique — Conditioning with adaptive normalization v.s. in-context conditioning: We evaluate our conditioning approach (Section 4.2.2) against the commonly used in-context conditioning techniques [17, 41], which concatenates depth features and SMPL latent representations of equal size along the channel dimension. While retaining adaptive layer normalization, this approach uses only the timestep embedding to predict the scale and shift within blocks. However, we see that in-context conditioning is less effective for depth image conditioning, as it requires expanding the lower-dimensional SMPL parameters to match the higher dimensionality of the depth images before concatenation, which reduces the efficiency of feature integration. + +Design Choice 3 - With Attention Block vs. Without Attention Block — We assess the impact of incorporating attention blocks in the final layers of the diffusion model. The results indicate that adding attention blocks noticeably improves in-bed pose prediction performance. + +# 6. Conclusion + +In this work, we present a diffusion-based framework for in-bed human mesh recovery, designed to enhance generalization and accuracy in healthcare environments with limited real-world data. By leveraging synthetic data and a Sim-to-Real Transfer Framework, our approach effectively addresses challenges posed by privacy concerns, occlusions, and data scarcity. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14644-14654, 2023. 2 + +[39] Yu Yin, Joseph P Robinson, and Yun Fu. Multimodal in-bed pose and shape estimation under the blankets. In Proceedings of the 30th ACM International Conference on Multimedia, pages 2411-2419, 2022. 2 +[40] Hongwen Zhang, Yating Tian, Xinchi Zhou, Wanli Ouyang, Yebin Liu, Limin Wang, and Zhenan Sun. Pymaf: 3d human pose and shape regression with pyramidal mesh alignment feedback loop. In Proceedings of the IEEE International Conference on Computer Vision, 2021. 2 +[41] Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3836-3847, 2023. 2, 8 +[42] Zhixing Zhang, Bichen Wu, Xiaoyan Wang, Yaqiao Luo, Luxin Zhang, Yinan Zhao, Peter Vajda, Dimitris Metaxas, and Licheng Yu. Avid: Any-length video inpainting with diffusion model. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15085-15099, 2023. 2 \ No newline at end of file diff --git a/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/images.zip b/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2b4be3290cb208aa380740d43990c05bdb67d131 --- /dev/null +++ b/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:25186e5f2a33fba05c8e2ea6df1cf34b84447bf1693c855ba35932643030f012 +size 601965 diff --git a/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/layout.json b/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f3cb9a732123758ac7afde5450bbbb273e7ba6ad --- /dev/null +++ b/2025/DiSRT-In-Bed_ Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery/layout.json @@ -0,0 +1,8729 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 68, + 102, + 542, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 102, + 542, + 140 + ], + "spans": [ + { + "bbox": [ + 68, + 102, + 542, + 140 + ], + "type": "text", + "content": "DiSRT-In-Bed: Diffusion-Based Sim-to-Real Transfer Framework for In-Bed Human Mesh Recovery" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 135, + 161, + 475, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 161, + 475, + 190 + ], + "spans": [ + { + "bbox": [ + 135, + 161, + 475, + 190 + ], + "type": "text", + "content": "Jing Gao Ce Zheng Laszlo A. Jeni Zackory Erickson Carnegie Mellon University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 152, + 191, + 455, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 191, + 455, + 204 + ], + "spans": [ + { + "bbox": [ + 152, + 191, + 455, + 204 + ], + "type": "text", + "content": "{jinggao2, cezheng, laszlojeni, zerickso}@andrew.cmu.edu" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 152, + 231, + 200, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 231, + 200, + 243 + ], + "spans": [ + { + "bbox": [ + 152, + 231, + 200, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 257, + 296, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 257, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 257, + 296, + 521 + ], + "type": "text", + "content": "In-bed human mesh recovery can be crucial and enabling for several healthcare applications, including sleep pattern monitoring, rehabilitation support, and pressure ulcer prevention. However, it is difficult to collect large real-world visual datasets in this domain, in part due to privacy and expense constraints, which in turn presents significant challenges for training and deploying deep learning models. Existing in-bed human mesh estimation methods often rely heavily on real-world data, limiting their ability to generalize across different in-bed scenarios, such as varying coverings and environmental settings. To address this, we propose a Sim-to-Real Transfer Framework for in-bed human mesh recovery from overhead depth images, which leverages large-scale synthetic data alongside limited or no real-world samples. We introduce a diffusion model that bridges the gap between synthetic data and real data to support generalization in real-world in-bed pose and body inference scenarios. 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In-bed human mesh recovery, in particular, plays a vital role in assessing patient well-being, monitoring mobility, and detecting health risks, such as pressure ulcers." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "However, collecting labeled real-world data in healthcare settings is costly, time-consuming, and often constrained by privacy concerns. Alternative sensing technologies, like pressure sensing mats, are expensive, require direct patient contact, and can lose calibration over time, limiting their reliability. 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'Sim' indicates training with all synthetic data and " + }, + { + "bbox": [ + 313, + 338, + 555, + 403 + ], + "type": "inline_equation", + "content": "n\\%" + }, + { + "bbox": [ + 313, + 338, + 555, + 403 + ], + "type": "text", + "content": " Real' indicates training with " + }, + { + "bbox": [ + 313, + 338, + 555, + 403 + ], + "type": "inline_equation", + "content": "n\\%" + }, + { + "bbox": [ + 313, + 338, + 555, + 403 + ], + "type": "text", + "content": " of the real data from the training dataset." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 412, + 555, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 412, + 555, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 412, + 555, + 484 + ], + "type": "text", + "content": "sensitive to environmental factors. In addition, both RGB cameras and thermal sensors often struggle with occlusions in bed, such as blankets. Given these limitations, depth cameras emerge as a practical solution, offering a balance of accuracy, affordability, and privacy protection, while avoiding the drawbacks of other sensor types." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 485, + 554, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 554, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 554, + 568 + ], + "type": "text", + "content": "Furthermore, general human mesh recovery tasks benefit from abundant real-world data featuring individuals in standing or active poses [7, 37]. Such dependence on large-scale real-world data limits the adaptability and performance of deep learning models for human mesh prediction in clinical settings, where data collection is challenging and often privacy-constrained." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 713 + ], + "type": "text", + "content": "To address the challenge of limited training data, utilizing synthetic data presents a promising solution. Large-scale simulated depth datasets can be efficiently generated without preserving any personally identifiable information, eliminating the need for sensitive real-world data. Building on this strategy, prior work [3, 4, 36] has demonstrated good performance in the in-bed human mesh recovery task. However, they struggle to effectively bridge the domain gap between synthetic and real-world data, leading to significant performance degradation when the proportion of real-world data in the training set is low, as shown in Fig. 1. Thus, to further enhance generalization, we propose a novel" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1829" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": "diffusion-based pipeline for in-bed human mesh recovery. Diffusion models are particularly well-suited for this scenario due to their strong ability to handle uncertainties, such as noise and variations in depth images. By leveraging the diffusion framework, our method mitigates the domain gap between real and synthetic data while enhancing generalization across diverse real-world environments (e.g., different hospitals or room setups). This ensures smooth and coherent predictions across varied settings for real-world applications. We conduct extensive experiments, comparing with baselines and performing ablations, to demonstrate the method's effectiveness in real-world scenarios with occlusions and varying conditions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 229, + 253, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 229, + 253, + 239 + ], + "spans": [ + { + "bbox": [ + 67, + 229, + 253, + 239 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 241, + 296, + 384 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 241, + 295, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 241, + 295, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 241, + 295, + 289 + ], + "type": "text", + "content": "- We propose a Sim-to-Real Transfer Framework for in-bed human mesh recovery that effectively leverages synthetic data to improve performance in real-world healthcare settings with limited labeled real data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 289, + 295, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 289, + 295, + 336 + ], + "spans": [ + { + "bbox": [ + 56, + 289, + 295, + 336 + ], + "type": "text", + "content": "- We introduce a diffusion-based architecture, enabling the diffusion process to bridge the domain gap between synthetic and real-world data and achieve strong generalization across different environment settings." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 337, + 296, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 337, + 296, + 384 + ], + "spans": [ + { + "bbox": [ + 56, + 337, + 296, + 384 + ], + "type": "text", + "content": "- We conduct extensive experiments, including comparisons with state-of-the-art methods, ablation studies, and generalization tests across different real-world settings, to assess the performance of our approach." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 396, + 142, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 142, + 409 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 142, + 409 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 417, + 256, + 429 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 417, + 256, + 429 + ], + "spans": [ + { + "bbox": [ + 55, + 417, + 256, + 429 + ], + "type": "text", + "content": "2.1. 3D Human Pose and Mesh Estimation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 434, + 295, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 295, + 626 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 295, + 626 + ], + "type": "text", + "content": "With significant progress in 3D human pose estimation [25, 27, 43, 46], researchers are seeking to go beyond just pose prediction. Human mesh recovery, which provides a more detailed 3D representation of the human body, has gained increasing interest. As a foundational human parametric model, SMPL [22] has been widely adopted in numerous works [11, 12, 14, 18-20, 38, 40, 44] to recover human mesh by predicting SMPL parameters. HybrIK [13] and its extension, HybrIK-X [15], introduce hybrid inverse kinematics techniques that convert 3D joints into body-part rotations through twist-and-swing decomposition. HMR2.0 [7] employs a straightforward yet effective transformer-based network, setting a foundation for subsequent work. TokenHMR [5] introduces a tokenized approach to representing human pose and shape, effectively handling occlusions by reframing the problem as token prediction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 635, + 295, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 635, + 295, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 635, + 295, + 659 + ], + "type": "text", + "content": "2.2. Diffusion Models for Human Pose and Mesh Estimation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Diffusion generative models [10, 32] have shown remarkable success across diverse computer vision tasks, including image inpainting [33, 42], text-to-image generation [17, 28-30, 41], and image-to-image translation [2]. Leveraging" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 205 + ], + "type": "text", + "content": "their powerful capability to manage uncertainty and refine distributions, these models have been effectively applied to 3D human pose estimation and human mesh recovery tasks [1, 8, 16, 24, 31, 34, 35, 45]. DiffPose [8] pioneers diffusion-based 3D pose prediction from 2D sequences. Extending to human mesh recovery, HMDiff [6] applies a distribution alignment technique to provide input-specific information within the diffusion process, simplifying mesh estimation. Similarly, ScoreHMR [34] uses a diffusion model as a prior for SMPL body model parameters, guiding the denoising process with observed 2D keypoints." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 210, + 533, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 210, + 533, + 221 + ], + "spans": [ + { + "bbox": [ + 313, + 210, + 533, + 221 + ], + "type": "text", + "content": "2.3. In-Bed Human Pose and mesh Estimation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 227, + 555, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 227, + 555, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 227, + 555, + 515 + ], + "type": "text", + "content": "In contrast to general human pose estimation and mesh recovery tasks, where numerous large-scale datasets are available for training, in-bed human pose estimation and mesh recovery present unique challenges. These challenges stem from the limited availability of suitable datasets, the reliance on depth images as input, and the nature of in-bed poses. Individuals are often lying in various orientations on the bed and are partially covered by blankets, leading to heavy occlusions and constrained body positions. As one of the prior works, Pyramid Fusion [39] introduces a pyramid scheme to effectively fuse four input modalities—RGB, pressure, depth, and infrared images—for human mesh estimation. However, subsequent approaches removed RGB images from the input due to privacy concerns in clinical deployments. PressureNet [3] employs pressure images as input, using a multi-stage CNN-based framework to produce human mesh outputs, while BodyPressure [4] focuses on depth images to infer both human mesh and pressure maps. The recent BodyMAP [36] simplifies the processes used in PressureNet [3] and BPBnet [4], predicting human mesh using depth and pressure images. In contrast, we focus on improving the generalization of the in-bed human mesh recovery from depth images by leveraging synthetic data and introducing a novel diffusion-based pipeline." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 535, + 504, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 535, + 504, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 535, + 504, + 548 + ], + "type": "text", + "content": "3. Preliminaries on Diffusion Models" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 555, + 553, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 553, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 553, + 590 + ], + "type": "text", + "content": "Diffusion models [10, 32] are probabilistic generative models that learn to transform random noise into the target data distribution via a forward and reverse process." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "type": "text", + "content": "In the forward diffusion process, a data sample " + }, + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "type": "text", + "content": " is progressively noised by adding Gaussian noise according to a fixed variance schedule " + }, + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "type": "inline_equation", + "content": "\\sigma_t" + }, + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "type": "text", + "content": " over a sequence of " + }, + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 591, + 553, + 639 + ], + "type": "text", + "content": " timesteps. This process forms a Markov chain with the transitions:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 342, + 640, + 553, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 640, + 553, + 653 + ], + "spans": [ + { + "bbox": [ + 342, + 640, + 553, + 653 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\alpha_ {t}} \\mathbf {x} _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}", + "image_path": "07022340530fecd38864a841960cef095b8e518a3f319cfbbb815defb0eef9f4.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "content": " represents the noisy sample at step " + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "content": ", constant " + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "inline_equation", + "content": "\\alpha_t = 1 - \\sigma_t^2" + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\cdot)" + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "content": " denotes the Gaussian distribution. The final sample " + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 313, + 654, + 553, + 689 + ], + "type": "text", + "content": " is approximately Gaussian noise." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "The forward diffusion process defined in [10] allows us to directly sample an arbitrary step of the noised latent " + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1830" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 70, + 541, + 289 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 541, + 289 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 541, + 289 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 541, + 289 + ], + "type": "image", + "image_path": "ea7fe9bcb5aa91300b54bdded3acd9bfbed957b8826210110487de3d2c66aa1e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "lines": [ + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "spans": [ + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "text", + "content": "Figure 2. Overview of the Proposed Sim-to-Real Transfer Framework. The framework comprises three stages: In the Synthetic Data Generation stage (left), a large, diverse set of synthetic depth images is generated within a simulated environment. In the training stage, the diffusion model " + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "text", + "content": " conditions on the synthetic depth image " + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "text", + "content": " to denoise SMPL parameters " + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "text", + "content": " in the reverse process, which begins at timestep " + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "text", + "content": " and progresses toward timestep 0, yielding the estimated human mesh " + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{M}}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 54, + 291, + 555, + 369 + ], + "type": "text", + "content": ". 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The 'Ref.' in the figure denotes the corresponding synthetic depth image during training and the corresponding RGB image for visualization purposes only." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 380, + 216, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 380, + 216, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 216, + 392 + ], + "type": "text", + "content": "conditioned on the input " + }, + { + "bbox": [ + 55, + 380, + 216, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 55, + 380, + 216, + 392 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 93, + 396, + 295, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 396, + 295, + 409 + ], + "spans": [ + { + "bbox": [ + 93, + 396, + 295, + 409 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right) \\tag {2}", + "image_path": "58691dbfd0db1ae2cb79694582cd13f979f3241e06ddcabbfa92c29830e0bb90.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 424, + 294, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 424, + 294, + 436 + ], + "spans": [ + { + "bbox": [ + 88, + 424, + 294, + 436 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\quad \\epsilon \\sim \\mathcal {N} (0, \\mathbf {I}), \\tag {3}", + "image_path": "9417455f5dcd95b3f3de9db34cdeb4895899e45a059540b977b5349597a3ebc2.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 437, + 295, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 295, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 295, + 460 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 437, + 295, + 460 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\sigma_{t}^{2}" + }, + { + "bbox": [ + 55, + 437, + 295, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 437, + 295, + 460 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\prod_{i=0}^{t} \\alpha_{i}" + }, + { + "bbox": [ + 55, + 437, + 295, + 460 + ], + "type": "text", + "content": " are fixed hyperparameters." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "type": "text", + "content": "In the reverse diffusion process, the model aims to recover the original data sample " + }, + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "type": "text", + "content": ". A diffusion model parameterized as " + }, + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 55, + 461, + 296, + 509 + ], + "type": "text", + "content": " (often a neural network) is trained to approximate this reverse process defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 513, + 294, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 513, + 294, + 526 + ], + "spans": [ + { + "bbox": [ + 88, + 513, + 294, + 526 + ], + "type": "interline_equation", + "content": "p _ {\\omega} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\omega} \\left(\\mathbf {x} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {4}", + "image_path": "ca97909ae94ad29ebfc947a805c55f717368915bc6b110cbfe8e8ed5bd120de1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "text", + "content": "Although specific formulations for the estimated mean " + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\mu_{\\omega}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "text", + "content": " vary [10, 26, 32], each reverse denoising step can be expressed as a function " + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "text", + "content": " and the diffusion model " + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "text", + "content": " to yield " + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t - 1}" + }, + { + "bbox": [ + 55, + 530, + 296, + 578 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 138, + 582, + 294, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 582, + 294, + 595 + ], + "spans": [ + { + "bbox": [ + 138, + 582, + 294, + 595 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = f \\left(\\mathbf {x} _ {t}, \\omega\\right). \\tag {5}", + "image_path": "1c9ebf52b06bc904c094615244aa2931e6df750d77b321bb215493770eaf747b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "type": "text", + "content": "During inference, Gaussian noise " + }, + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "type": "text", + "content": " is sampled, and the model iteratively denoises it to generate the target sample " + }, + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "type": "text", + "content": " using the trained diffusion model " + }, + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 55, + 598, + 296, + 635 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 645, + 138, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 645, + 138, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 645, + 138, + 659 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Our proposed framework addresses the challenge of developing reliable and generalizable in-bed human mesh recovery models in scenarios with limited or no real-world data. By leveraging a large volume of synthetic data generated" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 380, + 554, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 554, + 463 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 554, + 463 + ], + "type": "text", + "content": "through simulation, combined with a small amount of real-world data, our framework effectively reduces the reliance on costly and privacy-sensitive real-world data collection. The framework comprises three key stages: synthetic data generation (Sec. 4.1), model design (Sec. 4.2), and pipeline training and fine-tuning (Sec. 4.3). The overview pipeline is shown in Fig. 2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "content": "Throughout our approach, we utilize the SMPL [22] model to represent 3D human bodies. The SMPL model is a parametric human body model that represents a human figure as a mesh of vertices, controlled by a set of pose and shape parameters. Specifically, given the joint angles " + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta} \\in \\mathbb{R}^{23 \\times 3}" + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "content": " and shape parameters " + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "inline_equation", + "content": "\\beta \\in \\mathbb{R}^{10}" + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "content": ", the SMPL model can output a 3D human mesh " + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{6890 \\times 3}" + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "content": " consisting of 6,890 vertices. The SMPL parameters can be defined as " + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = \\left[ \\begin{array}{cccc} \\beta & \\theta & \\mathbf{s} & \\mathbf{u} & \\mathbf{v} \\end{array} \\right]^{\\top} \\in \\mathbb{R}^{88}" + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{s} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "content": " is the global translation, and " + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{u} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{v} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 313, + 464, + 555, + 598 + ], + "type": "text", + "content": " are used to represent the global rotation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 610, + 463, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 610, + 463, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 610, + 463, + 624 + ], + "type": "text", + "content": "4.1. Synthetic Data Generation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 713 + ], + "type": "text", + "content": "Obtaining labeled data for in-bed scenarios across diverse healthcare environments presents a significant challenge, limiting the deployment of deep learning models in this domain. In contrast, simulation offers a low-cost and efficient solution for generating abundant, high-quality depth data along with ground truth annotation for human mesh in resting positions. By incorporating prior information such as" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1831" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 107 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 107 + ], + "type": "text", + "content": "bed dimensions and camera-to-bed distance, we can construct simulated environments that closely replicate the real-world settings." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "spans": [ + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "type": "text", + "content": "Following BodyPressure [4], which introduces a physics-based simulation pipeline to generate synthetic in-bed human depth and pressure images, we adopt this approach to create a diverse and realistic dataset. The pipeline simulates human bodies at rest on a soft mattress, producing depth data from a fixed camera position relative to SMPL-based body configurations on a bed. By sampling human shape " + }, + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "type": "text", + "content": ", joint angles " + }, + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "type": "text", + "content": ", and global translation " + }, + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "type": "inline_equation", + "content": "(s_x, s_y)" + }, + { + "bbox": [ + 55, + 108, + 296, + 263 + ], + "type": "text", + "content": " from uniform distributions, we generate a variety of data. Additionally, simulated depth images with blankets are created by draping various types of blankets over parts of the body. This dataset further includes diverse human shapes, poses, and bed scene complexities." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 264, + 296, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 264, + 296, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 264, + 296, + 360 + ], + "type": "text", + "content": "While synthetic data generation can enhance dataset diversity and increase the number of training samples, it also introduces an inherent domain gap between synthetic and real-world data. As a result, models may perform well in synthetic settings but struggle in real-world applications, which undermines their practical utility. Therefore, in the following sections, we focus on bridging this simulation-to-reality gap within the framework for in-bed scenes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 365, + 263, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 263, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 263, + 378 + ], + "type": "text", + "content": "4.2. Diffusion-Based In-Bed Mesh Recovery" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 383, + 296, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 383, + 296, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 383, + 296, + 574 + ], + "type": "text", + "content": "Recovering in-bed human mesh from depth images is not a straightforward one-to-one mapping problem, as prior works [3, 4, 36] state. Depth images of in-bed scenarios can vary significantly based on external conditions, such as the presence or absence of a blanket, while the underlying body pose and shape remain the same. This variability introduces ambiguity in the mapping from depth images to human mesh. Additionally, multiple plausible human mesh configurations can correspond to the same depth image due to inherent ambiguities. To address this, we reformulate the in-bed human mesh recovery task as a conditional generative problem. Inspired by recent advancements in diffusion models for image generation [10, 32], we design a diffusion model to learn the distribution of plausible SMPL body configurations, denoted as " + }, + { + "bbox": [ + 55, + 383, + 296, + 574 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{SMPL}}" + }, + { + "bbox": [ + 55, + 383, + 296, + 574 + ], + "type": "text", + "content": ", conditioned on depth images during training and fine-tuning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 579, + 157, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 579, + 157, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 579, + 157, + 590 + ], + "type": "text", + "content": "4.2.1. Diffusion Process" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 594, + 295, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 642 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 642 + ], + "type": "text", + "content": "In contrast to the diffusion process used in image generation, which operates directly on images, we conduct forward noise-adding and reverse denoising processes on the SMPL body parameters " + }, + { + "bbox": [ + 55, + 594, + 295, + 642 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 594, + 295, + 642 + ], + "type": "text", + "content": " for in-bed human mesh recovery." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "type": "text", + "content": "In the forward process, we follow the Eq. 3 to obtain noisy versions " + }, + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "type": "text", + "content": " of the initial SMPL body parameters " + }, + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 642, + 295, + 677 + ], + "type": "text", + "content": " timesteps." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 296, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 712 + ], + "type": "text", + "content": "In the reverse process, we incorporate depth images " + }, + { + "bbox": [ + 55, + 677, + 296, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 55, + 677, + 296, + 712 + ], + "type": "text", + "content": " as a conditional input to the diffusion model, modifying Eq. 4 as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 330, + 72, + 554, + 85 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 72, + 554, + 85 + ], + "spans": [ + { + "bbox": [ + 330, + 72, + 554, + 85 + ], + "type": "interline_equation", + "content": "p _ {\\mathcal {D}} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}, \\mathbf {c}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\mathcal {D}} \\left(\\mathbf {x} _ {t}, t, \\mathbf {c}\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {6}", + "image_path": "86b78ece788dbc6e26b3c74e88979e13dc705d84154004fd542f1f6bf9dca4ee.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 90, + 553, + 113 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 90, + 553, + 113 + ], + "spans": [ + { + "bbox": [ + 313, + 90, + 553, + 113 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 90, + 553, + 113 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 90, + 553, + 113 + ], + "type": "text", + "content": " represents our diffusion model designed for the in-bed human mesh recovery task." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "spans": [ + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "content": "Given a training sample " + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "content": ", we train the diffusion model " + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "content": " to learn the denoising transition " + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "inline_equation", + "content": "p_{\\mathcal{D}}(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t, \\mathbf{c})" + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "content": ", ensuring it closely approximates the corresponding forward process " + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_t \\mid \\mathbf{x}_{t - 1}, \\mathbf{x}_0)" + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "content": ". In image generation tasks, this process typically involves having the diffusion model approximate the noise term " + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "content": " that produces " + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 313, + 114, + 554, + 196 + ], + "type": "text", + "content": " in the forward process." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "text", + "content": "However, in our case, if we assume SMPL body parameters " + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "text", + "content": " follow a standard Gaussian distribution, the diffusion model struggles to produce reasonable SMPL parameters, as early denoising iterations may yield unfeasible human meshes. To address this, we diffuse toward the initial sample " + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "text", + "content": " to ensure consistency throughout the denoising process. For any timestep " + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "text", + "content": ", the estimated initial SMPL parameters " + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 198, + 554, + 293 + ], + "type": "text", + "content": " can be represented as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 399, + 298, + 553, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 399, + 298, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 399, + 298, + 553, + 312 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {t} = \\mathcal {D} \\left(\\mathbf {x} _ {t}, t, \\mathbf {c}\\right) \\tag {7}", + "image_path": "115266d093b04b6ca9baa9703121538de24a4ae63c96d275f154e569fa1e9abb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 316, + 554, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 316, + 554, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 316, + 554, + 339 + ], + "type": "text", + "content": "The objective of training and fine-tuning the diffusion model " + }, + { + "bbox": [ + 313, + 316, + 554, + 339 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 316, + 554, + 339 + ], + "type": "text", + "content": " for in-bed human mesh recovery is to minimize" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 349, + 346, + 553, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 346, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 349, + 346, + 553, + 361 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\mathbf {x} _ {0} \\sim p _ {\\mathrm {S M P L}}} \\mathbb {E} _ {t \\sim \\mathcal {U} \\{0, T \\}, \\mathbf {x} _ {t} \\sim q (\\cdot | \\mathbf {x} _ {0})} \\| \\mathbf {z} _ {t} - \\mathbf {x} _ {0} \\|, \\tag {8}", + "image_path": "d283425f2aca14ce165b2a4f5aa383de02580de906a5a06e53296801e44daf91.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 364, + 539, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 539, + 375 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 539, + 375 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 364, + 539, + 375 + ], + "type": "inline_equation", + "content": "\\mathcal{U}(\\cdot)" + }, + { + "bbox": [ + 313, + 364, + 539, + 375 + ], + "type": "text", + "content": " denotes sample from a uniform distribution." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 376, + 553, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 553, + 398 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 553, + 398 + ], + "type": "text", + "content": "In the inference, the learned mean " + }, + { + "bbox": [ + 313, + 376, + 553, + 398 + ], + "type": "inline_equation", + "content": "\\mu_{\\mathcal{D}}" + }, + { + "bbox": [ + 313, + 376, + 553, + 398 + ], + "type": "text", + "content": " in the Eq. 6 can be formulated as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 331, + 401, + 553, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 401, + 553, + 427 + ], + "spans": [ + { + "bbox": [ + 331, + 401, + 553, + 427 + ], + "type": "interline_equation", + "content": "\\mu_ {\\mathcal {D}} = \\frac {\\sqrt {\\bar {\\alpha} _ {t - 1}} (1 - \\alpha_ {t})}{1 - \\bar {\\alpha} _ {t}} \\mathbf {z} _ {t} + \\frac {\\sqrt {\\alpha_ {t}} (1 - \\bar {\\alpha} _ {t - 1})}{1 - \\bar {\\alpha} _ {t}} \\mathbf {x} _ {t}, \\tag {9}", + "image_path": "187075a214da355f2e219b27e30a4539c7ff84419798f021fbb461e59e1caf05.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t - 1}" + }, + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "type": "text", + "content": " are derived from hyper-parameters. Then, we sample from the transition distribution in each denoising step to compute " + }, + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t - 1}" + }, + { + "bbox": [ + 313, + 430, + 553, + 465 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 378, + 470, + 553, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 470, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 378, + 470, + 553, + 483 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\mu_ {\\mathcal {D}} (\\mathbf {x} _ {t}, t, \\mathbf {c}) + \\sigma^ {2} \\epsilon \\tag {10}", + "image_path": "4ae6a92eb3fd42214c0c365e9540b1a6b80d2a55910a47f9376cd512c781913b.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "spans": [ + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "type": "text", + "content": "Following this reverse process, we iteratively denoise the SMPL latent from noise " + }, + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "type": "text", + "content": " down to the target SMPL latent " + }, + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 313, + 488, + 554, + 525 + ], + "type": "text", + "content": " at timestep 0." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 531, + 425, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 425, + 541 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 425, + 541 + ], + "type": "text", + "content": "4.2.2. Model Architecture" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "text", + "content": "We introduce a network that takes noised SMPL parameters " + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "text", + "content": ", depth images " + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "text", + "content": ", and the timestep " + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "text", + "content": " as inputs and outputs the denoised SMPL parameters " + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "text", + "content": " as illustrated in Fig. 3. The reverse diffusion process leverages the depth feature latent to infer denoised SMPL parameters. The noisy SMPL parameters " + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "text", + "content": " are processed through an MLP encoder to obtain the SMPL parameter latent, and a uniform sampler generates the time embedding for the timestep " + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 545, + 554, + 675 + ], + "type": "text", + "content": ". These inputs—SMPL parameter latent, depth images, and time embedding—are then processed through residual and attention blocks." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Following the design of the diffusion U-Net model [29], we incorporate residual and attention blocks to process image inputs and replace batch and layer normalization with" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1832" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 294, + 259 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 294, + 259 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 294, + 259 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 294, + 259 + ], + "type": "image", + "image_path": "acf44a0107ca596b4cba690274666b1f598cf688e295d8f3202bf1455bc3975f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 262, + 295, + 297 + ], + "lines": [ + { + "bbox": [ + 55, + 262, + 295, + 297 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 295, + 297 + ], + "type": "text", + "content": "Figure 3. Diffusion Model Architecture. Dashed lines around specific layers indicate optional layers that may be omitted in certain blocks of the model implementation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 307, + 295, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 307, + 295, + 413 + ], + "spans": [ + { + "bbox": [ + 54, + 307, + 295, + 413 + ], + "type": "text", + "content": "adaptive normalization layers initialized to zero [28] across the network. Specifically, the SMPL latent is aligned to have the same dimension as the time embedding, allowing them to be combined and fed into each adaptive normalization layer to produce scale and shift parameters, " + }, + { + "bbox": [ + 54, + 307, + 295, + 413 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 54, + 307, + 295, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 307, + 295, + 413 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 54, + 307, + 295, + 413 + ], + "type": "text", + "content": ", through a linear MLP. This approach enables dynamic adjustments of normalization parameters, enhancing the network's ability to handle conditional information effectively in diffusion models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 415, + 295, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 415, + 295, + 510 + ], + "spans": [ + { + "bbox": [ + 54, + 415, + 295, + 510 + ], + "type": "text", + "content": "Within the network, multiple down-sampling residual blocks follow the initial convolutional layer, succeeded by two additional residual blocks. Attention blocks are attached separately before the last few residual blocks. In the final block, current noised SMPL latent and embedded " + }, + { + "bbox": [ + 54, + 415, + 295, + 510 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 54, + 415, + 295, + 510 + ], + "type": "text", + "content": " are omitted in subsequent layers, allowing the regressor to map the single output latents from all intermediate blocks to the target SMPL parameters." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": "Following the SMPL parameter predictor module, the SMPL model [22] returns the human mesh " + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{M}}" + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": " given the estimated SMPL parameters " + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": ". Additionally, a set of gender flags " + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "inline_equation", + "content": "\\mathbf{g} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": " controls the gender of the generated human mesh. In this work, we only have two gender flags, where " + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": " represents the female SMPL model and " + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "inline_equation", + "content": "[1,0]" + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": " the male model. The 3D Cartesian joint positions " + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{J}} \\in \\mathbb{R}^{24 \\times 3}" + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": " can be extracted from the human mesh vertices " + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{V}} \\in \\mathbb{R}^{6890 \\times 3}" + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": " of each human mesh " + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{M}}" + }, + { + "bbox": [ + 55, + 510, + 295, + 618 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 626, + 162, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 626, + 162, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 626, + 162, + 639 + ], + "type": "text", + "content": "4.3. Training Strategy" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "text", + "content": "As described above, the output of our diffusion model " + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "text", + "content": " consists of the estimated in-bed SMPL body parameters " + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t = \\left[\\hat{\\beta} \\hat{\\theta} \\hat{\\mathbf{s}} \\hat{\\mathbf{u}} \\hat{\\mathbf{v}}\\right]^\\top" + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "text", + "content": ", which includes the predicted body shape parameters " + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\beta}" + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "text", + "content": ", joint angles " + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "text", + "content": ", global translation " + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "text", + "content": ", and global rotation parameters " + }, + { + "bbox": [ + 55, + 643, + 295, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{u}} = \\{u_x, u_y, u_z\\}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{v}} = \\{v_x,v_y,v_z\\}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": ". Each rotation component " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\phi_{i}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "i\\in \\{x,y,z\\}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": " can be calculated as " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\phi_{i} = \\mathrm{atan2}(u_{i},v_{i})" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 97, + 553, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 97, + 553, + 275 + ], + "spans": [ + { + "bbox": [ + 313, + 97, + 553, + 275 + ], + "type": "text", + "content": "Synthetic training stage: Previous works [4, 36] rely on joint training with both synthetic and real-world data, assuming ample real-world data is available and overlooking the effects of the large synthetic-to-real data imbalance. In contrast, our framework decouples training on synthetic and real-world data to address the limited availability of real-world data and the high ratio of synthetic to real samples. During the synthetic data training phase, our goal is to establish a strong prior based on the diverse range of human resting postures available in the synthetic dataset, enabling the model to produce a reasonable coarse in-bed human pose without requiring real-world data. Our proposed diffusion-based network is trained for a reasonable number of steps on synthetic depth data alone, using a fixed learning rate to prevent convergence to local optima." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 276, + 553, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 553, + 358 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 553, + 358 + ], + "type": "text", + "content": "Fine-tuning stage: Given the variable quantity of real-world data, we employ a linearly adjusted learning rate scheduler that automatically adapts based on the amount of available depth data. This adaptive learning rate strategy facilitates rapid convergence and enhances generalization to real-world scenarios during fine-tuning, as demonstrated by our ablation study in Sec 5.5." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 359, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 359, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 359, + 553, + 407 + ], + "type": "text", + "content": "Loss: The total loss used to train and fine-tune the diffusion model contains two components: SMPL parameter loss and vertex position loss. An expansion of each term in the loss function can be found in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 378, + 419, + 553, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 419, + 553, + 433 + ], + "spans": [ + { + "bbox": [ + 378, + 419, + 553, + 433 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\mathrm {S M P L}} + \\lambda_ {\\mathrm {v 2 v}} \\mathcal {L} _ {\\mathrm {v 2 v}}, \\tag {11}", + "image_path": "a7b40bbf6f31ca74142aef8b4fe54d13eb6e9eb06f5d0bf59f873e7d06498c13.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 437, + 479, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 479, + 450 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 479, + 450 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 437, + 479, + 450 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{v2v}}" + }, + { + "bbox": [ + 313, + 437, + 479, + 450 + ], + "type": "text", + "content": " is a tunable hyper-parameter." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 460, + 395, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 395, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 395, + 474 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 480, + 436, + 492 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 480, + 436, + 492 + ], + "spans": [ + { + "bbox": [ + 313, + 480, + 436, + 492 + ], + "type": "text", + "content": "5.1. Datasets and Metrics" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 498, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 553, + 713 + ], + "type": "text", + "content": "[21] provides a comprehensive collection of in-bed resting poses across two settings. In the home setting, data were collected from 102 human participants, with each pose captured under three occlusion conditions: thin sheet, thicker blanket, and no covering. Clever et al. [4] provide SMPL ground truth labels for the real-world SLP home setting data. For training, data from the first 80 participants (1-80, excluding participant 7 due to calibration errors, totaling 10,665 real samples) in the SLP are used either partially or fully during fine-tuning to represent different synthetic-to-real data ratios. For evaluation, data from the remaining 22 participants (81-102, with 2,970 real samples) are used to assess all methods. Additionally, the SLP dataset includes data from a hospital setting, comprising 7 participants without SMPL ground truth labels. Thus, we evaluate our method on the hospital setting data through qualitative visualizations." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1833" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 64, + 553, + 150 + ], + "blocks": [ + { + "bbox": [ + 58, + 64, + 553, + 150 + ], + "lines": [ + { + "bbox": [ + 58, + 64, + 553, + 150 + ], + "spans": [ + { + "bbox": [ + 58, + 64, + 553, + 150 + ], + "type": "table", + "html": "
    Data Split\nReal-Sim RatioSim\n0:97495Sim+11%Real\n1:80Sim+24%Real\n1:38Sim+37%Real\n1:25Sim+49%Real\n1:18Sim+100%Real\n1:9
    MethodMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVEMPJPEPVE
    HMR2.0 [7]157.23182.2787.09104.6582.8596.54145.35140.2790.90108.9076.9490.39
    BodyPressure [4]103.47115.3189.87104.6790.46105.9781.2999.0578.2594.6572.9386.78
    BodyMAP [36]330.52365.4385.7990.1476.0789.8069.5183.0161.7774.9657.0669.95
    DiSRT-In-Bed(Ours)109.73121.5974.3778.0367.1473.1858.0466.6655.9464.1450.8161.18
    ", + "image_path": "8705590f47010287cc821d2bf6906af2fc042fb03684323b074747f4c2aef80d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 87, + 196, + 523, + 280 + ], + "blocks": [ + { + "bbox": [ + 55, + 152, + 555, + 187 + ], + "lines": [ + { + "bbox": [ + 55, + 152, + 555, + 187 + ], + "spans": [ + { + "bbox": [ + 55, + 152, + 555, + 187 + ], + "type": "text", + "content": "Table 1. Comparison to Baselines across Different Data Splits. In the 'Data Split' row, 'Sim' indicates training with all synthetic data, while 'n%Real' indicates training with " + }, + { + "bbox": [ + 55, + 152, + 555, + 187 + ], + "type": "inline_equation", + "content": "n\\%" + }, + { + "bbox": [ + 55, + 152, + 555, + 187 + ], + "type": "text", + "content": " of the real data from the SLP training dataset. In the 'Real-Sim Ratio' row, the number represents the approximate ratio of depth images between synthetic and real datasets. All values in the table are in millimeters (mm)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 87, + 196, + 523, + 280 + ], + "lines": [ + { + "bbox": [ + 87, + 196, + 523, + 280 + ], + "spans": [ + { + "bbox": [ + 87, + 196, + 523, + 280 + ], + "type": "table", + "html": "
    MethodUncoverCover 1Cover 23D Shape Error(cm)↓
    MPJPEPVEMPJPEPVEMPJPEPVEheightChestWaistHips
    HMR2.0 [7]69.6781.6679.8693.7481.2995.765.418.3011.247.66
    BodyPressure [4]67.0679.9276.3990.7875.3689.653.963.894.843.37
    BodyMAP [36]51.2662.3460.3573.9759.5573.543.433.174.243.53
    DiSRT-In-Bed(Ours)46.0155.0753.7864.8052.6563.683.255.177.165.20
    ", + "image_path": "cbb867203f871291e2574cde06f7512983f45ad8eded4db96b1443bfb4b35e9d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 282, + 555, + 316 + ], + "lines": [ + { + "bbox": [ + 55, + 282, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 282, + 555, + 316 + ], + "type": "text", + "content": "Table 2. Comparison to Baselines across Different Covering Situations. 'Uncover' refers to testing depth images without coverings, 'Cover 1' denotes images with a thin blanket, and 'Cover 2' denotes images with a thick blanket. All MPJPE and PVE values are in millimeters (mm), while 3D Shape Errors are in centimeters (cm)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 327, + 294, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 327, + 294, + 434 + ], + "spans": [ + { + "bbox": [ + 54, + 327, + 294, + 434 + ], + "type": "text", + "content": "BodyPressureSD [4] is generated using the physical simulation mentioned in Sec. 4.1 and serves as a benchmark for sim-to-real tasks. The dataset consists of 97,495 samples, corresponding to the three covering conditions in the SLP dataset, and significantly increases the diversity of human resting poses and body shapes. All synthetic data from BodyPressureSD are used during the training stage of the sim-to-real framework to establish a strong prior on human pose and shape before fine-tuning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 435, + 295, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 435, + 295, + 518 + ], + "spans": [ + { + "bbox": [ + 54, + 435, + 295, + 518 + ], + "type": "text", + "content": "Metrics. For pose and shape accuracy evaluation, we report the 3D mean-per-joint position error (MPJPE) and 3D per-vertex error (PVE). For each sample, MPJPE is calculated as the Mean Euclidean Distance between the inferred and ground truth positions of 24 3D joints, while PVE measures the mean Euclidean distance across the 6,890 3D vertex positions of the SMPL model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 528, + 188, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 528, + 188, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 528, + 188, + 540 + ], + "type": "text", + "content": "5.2. Implementation Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "type": "text", + "content": "The diffusion model architecture consists of 6 downsampling layers within residual blocks, matching the downsampling depth of ResNet18 [9], and includes three attention blocks positioned before the final three residual blocks. The number of diffusion timesteps is set to 100 during training. For data augmentation, we shuffle the input depth images with random rotations, random erasures, and random noise additions during both training and fine-tuning, using a batch size of 32. All models are optimized with the AdamW [23] optimizer, using an initial learning rate of " + }, + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "type": "text", + "content": " and a weight decay of " + }, + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "type": "text", + "content": ", trained on a single NVIDIA GeForce RTX 4090 GPU. We set " + }, + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{v2v}} = 1" + }, + { + "bbox": [ + 54, + 545, + 295, + 713 + ], + "type": "text", + "content": " in the diffusion loss. For testing, we employ a DDIM sampling strategy with 5 timesteps to accelerate inference." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 326, + 528, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 326, + 528, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 326, + 528, + 339 + ], + "type": "text", + "content": "5.3. Comparison to State-of-the-Art Methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 347, + 555, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 347, + 555, + 491 + ], + "spans": [ + { + "bbox": [ + 312, + 347, + 555, + 491 + ], + "type": "text", + "content": "We conduct several experiments to demonstrate the effectiveness of our method for in-bed human mesh recovery. We choose the current SOTA model HMR2.0 [7], which is designed for single-person mesh recovery from general RGB images, as a baseline. Since our task involves single-channel depth images as input, we modify HMR2.0 by repeating the depth image across channels to match the RGB input format, making it compatible with our scenario. We also compare our method with BodyMAP [36] and BodyPressure [4], designed specifically for the in-bed scenario. Tab. 1 presents quantitative comparisons between our method and baselines across different data splits." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 494, + 556, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 494, + 556, + 638 + ], + "spans": [ + { + "bbox": [ + 313, + 494, + 556, + 638 + ], + "type": "inline_equation", + "content": "\\triangle" + }, + { + "bbox": [ + 313, + 494, + 556, + 638 + ], + "type": "text", + "content": " Generalization with limited real data: With high real-to-simulation ratios, our method consistently outperforms previous methods in MPJPE and PVE metrics. Notably, our approach reduces these errors by over " + }, + { + "bbox": [ + 313, + 494, + 556, + 638 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 313, + 494, + 556, + 638 + ], + "type": "text", + "content": " under extreme real-simulation data ratios, such as 1:80 and 1:38. When trained solely on simulation data, our model slightly underperforms BodyPressure, as BodyPressure uses a separate network for human shape parameter prediction. However, BodyPressure's approach introduces a strong bias, leading to degraded performance when limited real-world data is available. Our method demonstrates strong generalization when limited real-world data is available." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\triangle" + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": " Robustness across occlusion: As shown in Tab. 2, we compare models trained on all simulation and real training data across various covering conditions. Our method achieves improved mesh recovery accuracy in all cases compared to prior literature and baselines. Moreover, the stability of our results (less performance drop) across vary-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1834" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 61, + 529, + 381 + ], + "blocks": [ + { + "bbox": [ + 85, + 61, + 529, + 381 + ], + "lines": [ + { + "bbox": [ + 85, + 61, + 529, + 381 + ], + "spans": [ + { + "bbox": [ + 85, + 61, + 529, + 381 + ], + "type": "image", + "image_path": "1555a55c24b271582270eaaa859e9b8b91e13c844bd2368de90e98d82fe2eccf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 384, + 555, + 441 + ], + "lines": [ + { + "bbox": [ + 54, + 384, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 54, + 384, + 555, + 441 + ], + "type": "text", + "content": "Figure 4. Visualization of Human Mesh Estimated from limited Real-World Data in Home Settings. The left three columns show the input depth images, RGB reference images, and ground truth mesh respectively. 'Sim' denotes using all simulation data in the training stage, 'n%Real' denotes the 'n' ratio of real data used in the fine-tuning in our method and jointly training in the baseline. 'Uncover' refers to no blanket in the bed, 'Cover 1' indicates the participant is covered with a thin blanket, and 'Cover 2' means the participant is covered with a thick blanket. The red arrows in the figures point out the mismatch between mesh prediction and the reference images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 451, + 295, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 451, + 295, + 487 + ], + "spans": [ + { + "bbox": [ + 54, + 451, + 295, + 487 + ], + "type": "text", + "content": "ing degrees of occlusion underscores the robustness of our method, making it more reliable in real-world healthcare settings where patients are often partially covered." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "spans": [ + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "inline_equation", + "content": "\\triangle" + }, + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "text", + "content": " Visualization: Fig. 4 presents the visual comparisons between our method and the SOTA in-bed mesh recovery method BodyMAP [36] under different covering conditions and real-data availability. BodyMAP struggles to estimate accurate human meshes when trained on simulation data alone, highlighting its limitations in addressing simulation-to-real domain gaps. In contrast, our method can capture meaningful pose information. Further, as shown in cases with " + }, + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "inline_equation", + "content": "11\\%" + }, + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "inline_equation", + "content": "24\\%" + }, + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "text", + "content": " real data, our method's predictions align more closely with input images across all covering scenarios. With " + }, + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "inline_equation", + "content": "24\\%" + }, + { + "bbox": [ + 54, + 487, + 295, + 643 + ], + "type": "text", + "content": " real data, our model remains largely unaffected by coverings, consistently aligning well with the reference image and ground truth." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 647, + 295, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 295, + 673 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 295, + 673 + ], + "type": "text", + "content": "5.4. Generalization to Different Real-World Settings" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "To evaluate our method's generalization ability across different environment settings, we compare our 'Sim+100%Real' model with BodyMAP[36] on unla" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 451, + 555, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 451, + 555, + 559 + ], + "spans": [ + { + "bbox": [ + 313, + 451, + 555, + 559 + ], + "type": "text", + "content": "beled hospital-setting depth images5.1. Since ground truth meshes are not available for this setting, we only provide qualitative comparisons. As shown in Fig. 6, our method recovers more accurate human meshes compared to BodyMAP [36]. Notably, for the challenging self-hugging pose, our method accurately captures the crossed arms, whereas BodyMAP [36] fails to replicate this detail. Additional generalization experimental results are available in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 570, + 408, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 408, + 583 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 408, + 583 + ], + "type": "text", + "content": "5.5. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 589, + 553, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 589, + 553, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 589, + 553, + 601 + ], + "type": "text", + "content": "5.5.1. Effectiveness of Sim-to-Real Transfer Framework" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": "To highlight the benefits of synthetic data, we plot MPJPE and PVE for our method and baselines [4, 36] trained with and without synthetic data, under various real-data availability settings, in Fig. 5a. Row-wise comparisons reveal that adding synthetic data significantly enhances performance across all real-world data utilization percentages, especially for the baselines. Our diffusion-based framework further enhances predictions by " + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "inline_equation", + "content": "10 - 35\\%" + }, + { + "bbox": [ + 313, + 605, + 555, + 713 + ], + "type": "text", + "content": " in MPJPE, even when only trained on a small portion of real data." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1835" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 67, + 221, + 183 + ], + "blocks": [ + { + "bbox": [ + 63, + 67, + 221, + 183 + ], + "lines": [ + { + "bbox": [ + 63, + 67, + 221, + 183 + ], + "spans": [ + { + "bbox": [ + 63, + 67, + 221, + 183 + ], + "type": "image", + "image_path": "8e409f5cba7e4e928a4edd3559cc1aaac55a1b90050832ef28f9d0d781e6b676.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 92, + 187, + 192, + 197 + ], + "lines": [ + { + "bbox": [ + 92, + 187, + 192, + 197 + ], + "spans": [ + { + "bbox": [ + 92, + 187, + 192, + 197 + ], + "type": "text", + "content": "(a) Ablation on Synthetic Data" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 227, + 67, + 383, + 183 + ], + "blocks": [ + { + "bbox": [ + 227, + 67, + 383, + 183 + ], + "lines": [ + { + "bbox": [ + 227, + 67, + 383, + 183 + ], + "spans": [ + { + "bbox": [ + 227, + 67, + 383, + 183 + ], + "type": "image", + "image_path": "6910f8f500e10b2c0ba7378ea078fc066b3c187856aae4d8fad4533f99af1b0a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 248, + 187, + 362, + 198 + ], + "lines": [ + { + "bbox": [ + 248, + 187, + 362, + 198 + ], + "spans": [ + { + "bbox": [ + 248, + 187, + 362, + 198 + ], + "type": "text", + "content": "(b) Ablation on Training Strategies" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 391, + 68, + 547, + 184 + ], + "blocks": [ + { + "bbox": [ + 391, + 68, + 547, + 184 + ], + "lines": [ + { + "bbox": [ + 391, + 68, + 547, + 184 + ], + "spans": [ + { + "bbox": [ + 391, + 68, + 547, + 184 + ], + "type": "image", + "image_path": "4a884d669488dd385f1fb3640e265590c23630821795145e7ee81146ea9b379d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 405, + 187, + 531, + 197 + ], + "lines": [ + { + "bbox": [ + 405, + 187, + 531, + 197 + ], + "spans": [ + { + "bbox": [ + 405, + 187, + 531, + 197 + ], + "type": "text", + "content": "(c) Ablation on Different Architectures" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 151, + 200, + 457, + 211 + ], + "lines": [ + { + "bbox": [ + 151, + 200, + 457, + 211 + ], + "spans": [ + { + "bbox": [ + 151, + 200, + 457, + 211 + ], + "type": "text", + "content": "Figure 5. Ablation Study on Diffusion-Based Sim-to-Real Transfer Framework." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 76, + 219, + 279, + 517 + ], + "blocks": [ + { + "bbox": [ + 76, + 219, + 279, + 517 + ], + "lines": [ + { + "bbox": [ + 76, + 219, + 279, + 517 + ], + "spans": [ + { + "bbox": [ + 76, + 219, + 279, + 517 + ], + "type": "image", + "image_path": "b2c169e9ba2b91c48ac33e58eee25af9cd28cb99be8e12b67b86404c26548f40.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 518, + 295, + 563 + ], + "lines": [ + { + "bbox": [ + 55, + 518, + 295, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 518, + 295, + 563 + ], + "type": "text", + "content": "Figure 6. Visualization of Human Mesh estimated from the Real-World Data in Hospital Settings. Ground truth mesh is not available for this scenario. The red arrows in the figures point out the mismatch between mesh prediction and the reference images." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 573, + 295, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 573, + 295, + 669 + ], + "spans": [ + { + "bbox": [ + 55, + 573, + 295, + 669 + ], + "type": "text", + "content": "Additionally, Fig. 5b illustrates the impact of applying our Sim-to-Real (S2R) training strategy as detailed in 4.3. Once BodyMAP incorporates our S2R training strategy, it achieves a substantial improvement over its original training scheme. Moreover, our method further outperforms BodyMAP+S2R, underscoring the combined benefit of the proposed framework and model architecture in handling generalization challenges for the in-bed scenario." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 674, + 277, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 674, + 277, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 674, + 277, + 685 + ], + "type": "text", + "content": "5.5.2. Effectiveness of Diffusion Model Architecture" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "We compare our diffusion model architecture (DiSRT-In-Bed) with three design choices as illustrated in Fig. 5c." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 222, + 553, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 222, + 553, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 222, + 553, + 293 + ], + "type": "text", + "content": "Design Choice 1 — Number of Downsampling Blocks — 6 v.s. 4: Our final model configuration includes 6 convolutional downsampling layers, similar to the ResNet-18 architecture [9] used in BodyMAP [36]. We observe a decrease in MPJPE when using 6 downsampling blocks rather than only 4." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 294, + 554, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 294, + 554, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 294, + 554, + 461 + ], + "type": "text", + "content": "Design Choice 2 — Conditioning Technique — Conditioning with adaptive normalization v.s. in-context conditioning: We evaluate our conditioning approach (Section 4.2.2) against the commonly used in-context conditioning techniques [17, 41], which concatenates depth features and SMPL latent representations of equal size along the channel dimension. While retaining adaptive layer normalization, this approach uses only the timestep embedding to predict the scale and shift within blocks. However, we see that in-context conditioning is less effective for depth image conditioning, as it requires expanding the lower-dimensional SMPL parameters to match the higher dimensionality of the depth images before concatenation, which reduces the efficiency of feature integration." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 461, + 553, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 553, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 553, + 521 + ], + "type": "text", + "content": "Design Choice 3 - With Attention Block vs. Without Attention Block — We assess the impact of incorporating attention blocks in the final layers of the diffusion model. The results indicate that adding attention blocks noticeably improves in-bed pose prediction performance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 532, + 388, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 532, + 388, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 532, + 388, + 544 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 552, + 555, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 555, + 708 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 555, + 708 + ], + "type": "text", + "content": "In this work, we present a diffusion-based framework for in-bed human mesh recovery, designed to enhance generalization and accuracy in healthcare environments with limited real-world data. By leveraging synthetic data and a Sim-to-Real Transfer Framework, our approach effectively addresses challenges posed by privacy concerns, occlusions, and data scarcity. Extensive experiments demonstrated the robustness of our method across varying covering conditions and high real-to-simulation ratios, consistently outperforming existing methods in MPJPE and PVE metrics. Additionally, our model's adaptability across different environments and reduced reliance on real-world data offer an efficient and scalable solution for clinical deployment." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1836" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "type": "text", + "content": "[1] Qingyuan Cai, Xuecai Hu, Saihui Hou, Li Yao, and Yongzhen Huang. 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As the amount of observation data increases, the challenge is not just to make accurate predictions but also to understand the underlying mechanisms for those predictions. Good interpretation is important in scientific workflows, as it allows for better decision-making by providing insights into the data. This paper introduces an automatic way of obtaining such interpretable-by-design models, by learning programs that interleave neural networks. We propose DiSciPLE (Discovering Scientific Programs using LLMs and Evolution) an evolutionary algorithm that leverages common sense and prior knowledge of large language models (LLMs) to create Python programs explaining visual data. Additionally, we propose two improvements: a program critic and a program simplifier to improve our method further to synthesize good programs. On three different real-world problems, DiSciPLE learns state-of-the-art programs on novel tasks with no prior literature. For example, we can learn programs with $35\\%$ lower error than the closest non-interpretable baseline for population density estimation.", + "bbox": [ + 86, + 316, + 483, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 662, + 220, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Many modern scientific workflows are built on top of visual data. Researchers in remote sensing, climate science, ecology, and other sciences use images as a window into our world to estimate population density, the amount of biomass, poverty indicators, and so on. There is a massively increasing volume of visual data, be it from an ever-expanding set of satellites, widespread camera traps, or images uploaded on the web, that is available to domain experts, and computer vision has the potential to meaningfully assist scientists in using it for scientific insight.", + "bbox": [ + 89, + 688, + 482, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scientific applications of computer vision, however, are demanding tasks because we want models that not only predict outcomes but also reveal underlying mechanisms. For example, a researcher who studies demography may be able", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/239a1fa224d2d23ab06b1aed856559ef2c458a9436535081349933e953fb0928.jpg", + "image_caption": [ + "Figure 1. We introduce a framework to discover interpretable, predictive programs for scientific computer vision tasks." + ], + "image_footnote": [], + "bbox": [ + 514, + 282, + 905, + 398 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to train excellent predictive models that learn the relationships between a satellite image and the population. However, understanding why certain regions are densely populated is crucial for urban planning and policy decisions — black-box predictions offer no interpretation of what makes a region have a high population. Scientists themselves want to derive insight from the models, not just predict.", + "bbox": [ + 511, + 444, + 906, + 550 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While there have been many works that train interpretable vision models (for example concept-bottlenecks [20, 27]), these models are often limited to simple functions of primitive concepts, such as bag of words. These simple functions do not scale to the realistic complexity of our visual world and the complex relationships between its many rich scientific indicators, resulting in poor accuracy. A promising direction to model rich relationships without foregoing interpretability is to learn programs on top of conceptual primitives. Recently, code generation methods such as ViperGPT and VisProg [14, 36] have demonstrated that large language models are able to synthesize programs with competitive performance on many vision tasks, and the representations are interpretable by construction because programs are human-readable. However, while these methods work well for established vision tasks, they often fail to generalize to scientific applications of computer vision because the tasks are new and outside the scope of the training data on the internet. LLMs lack the requisite knowledge to answer novel or domain-specific questions, and as we will show, directly applying such zero-shot code generation methods on scientific domains is not effective.", + "bbox": [ + 511, + 553, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "29258", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "How can we automatically discover accurate and interpretable programs from the volumes of visual data in scientific applications? This paper introduces DiSciPLE, a framework for Discovering Scientific Programs using LLMs and Evolution. Given a large dataset of images, our approach synthesizes a program to solve the task. As the name suggests, DiSciPLE introduces an evolutionary search algorithm that starts with zero-shot programs from LLMs and iteratively improves them over the dataset. The discovered programs are able to interleave neural networks, in particular open-world foundation models, for segmentation with logical and mathematical operations, enabling powerful predictions while also being interpretable. Our framework makes several improvements to integrate evolutionary search with LLMs, using program simplification and critics to provide fine-grained guidance that accelerates search.", + "bbox": [ + 89, + 90, + 480, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In three different scientific applications of computer vision, DiSciPLE is able to learn state-of-the-art programs for novel tasks that have no prior documented solutions in existing literature. Our approach significantly outperforms neural networks at estimating population density from satellite imagery. Our method also obtains strong out-of-distribution performance at estimating a region's biomass, generalizing to geographical regions outside of the training set significantly better than all other baselines. Our contributions are:", + "bbox": [ + 89, + 333, + 480, + 467 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a novel framework DiSciPLE, that can produce interpretable, reliable, and sample-efficient programs for scientific discovery.", + "- We present two key components: a critic and a program simplification method to DiSciPLE that can further improve the search resulting in better programs.", + "- We propose benchmarks for the task of scientific visual discovery containing real-world high-dimensional visual data for three problems in two domains. Using these benchmarks, we show that programs from DiSciPLE are more interpretable, reliable, and data-efficient." + ], + "bbox": [ + 89, + 468, + 480, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 89, + 648, + 238, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Concept bottlenecks. Concept bottleneck [20, 32, 41] is an approach used to create interpretable-yet-powerful classifiers. The key idea is to train a deep model to predict a set of low-level concepts and then learn a linear classifier. Such concept bottlenecks are the basis in several areas such as fine-grained recognition [11, 17, 37, 44] and zero-shot learning [1, 19, 21]. However in order to train these models, expensive data is needed for the bottleneck concepts themselves. One way to reduce this annotation cost is to ask questions in an information-theoretically optimal way [2, 3]. Researchers have also automated the pipeline by using LLMs as a knowledge base to propose bottlenecks [15, 27, 33]. [4] proposed an evolutionary algorithm to discover interpretable concept bottlenecks without prior information. While these models are interpretable, they are", + "bbox": [ + 89, + 674, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "very simple in terms of expressive power. In this work, we instead evolve interpretable programs, that are more expressive than a bag of words.", + "bbox": [ + 511, + 90, + 903, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Symbolic regression. Symbolic regression (SR) [5] is a technique for learning equations through evolutionary search. Several methods have been proposed to improve the search efficiency [24], however, most SR techniques cannot solve problems beyond simple mathematical formulas, with simple mathematical primitives. This is partly because the solution search space becomes combinatorial larger. As a result, SR methods fail to work for images, which are high-dimensional. Our method instead focuses on problems with high-dimensional visual data, by leveraging vision foundation models as primitives. Like DiSciPLE, recent work on SR [12, 22, 28, 34] has also looked at using LLMs to better guide the search. However, these methods are only tested on lower-dimensional problems for formula discovery. We instead propose an approach that is complementary to SR. Methods for SR cannot be applied directly in higher-dimensional open-world visual problems, on the other hand on low-dimensional problems existing tools for SR [12] would perform better. The focus of this work is on such real-world problems, where the primitive functions are more complex than mathematical operations and can even be open-world, such as text-to-image segmentation.", + "bbox": [ + 511, + 154, + 903, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neuro-Symbolic Program Learning [6, 26] is another avenue for learning programs for observation datasets or question answering. These methods typically try to learn both discrete program structures together with neural networks. However, since this optimization is nondifferentiable these methods require reinforcement learning [18] or complex non-differentiable optimization techniques [10]. The hard optimization issue makes the problem of learning programs sample inefficient in real-world settings. We alternatively use LLMs ability to program to better guide the search for such programs.", + "bbox": [ + 511, + 503, + 903, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Program synthesis with LLMs. Several works have utilized LLM coding ability in different applications such as VQA [13, 36] and robot manipulation [23]. While the zero-shot inferred code work very well on domains well-known to the internet, they tend to perform poorly on problems in scientific domains, as shown by our results.", + "bbox": [ + 511, + 686, + 903, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scientific applications. Researchers in numerous scientific domains have used machine learning tools to build predictive models for their quantities of interest. In this work, we focus on two such scientific domain: demography and climate science. For both these domains, we use remote sensing vision-language foundation models as primitives, along with mathematical and image operators. In", + "bbox": [ + 511, + 794, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "29259", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "demography, we focus on the problems of socioeconomic indicator prediction [43], namely population density and poverty [30, 40]. In climate science we focus on the problem of aboveground biomass prediction (AGB) [31].", + "bbox": [ + 89, + 90, + 483, + 154 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 89, + 164, + 225, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our key contribution is a program search framework that leverages LLMs to perform evolutionary search. In Sec. 3.1 we formalize the problem of program search. In Sec. 3.2, we present our method of incorporating LLMs in this framework. Finally, in Sec. 3.3, 3.4 and 3.5, we discuss the improvements to this framework to speed-up the search.", + "bbox": [ + 89, + 190, + 483, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 89, + 290, + 294, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our system receives as input a dataset $\\mathcal{D} = \\{(x_1, y_1), (x_2, y_2), \\ldots, (x_n, y_n)\\}$ consisting of inputs $x_i \\in X$ and quantities of interest $y_i \\in Y$ . For example, when estimating geospatial indicators like poverty, $x_i$ may be a latitude and longitude, along with other metadata about that location. The system must produce an interpretable program $P: X \\to Y$ that maps inputs to corresponding outputs. As is typical with standard supervised learning, we also assume a loss function or metric $\\mathcal{M}$ that measures how good a particular prediction is, and seek a program that yields the best evaluation score:", + "bbox": [ + 89, + 311, + 483, + 479 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns (P; \\mathcal {D}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathcal {M} \\left(P \\left(x _ {i}\\right), y _ {i}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 489, + 483, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For example, in the case of population density a good metric used by domain experts is L2 error over log i.e. $\\mathcal{M}(y', y) = ||\\log(y') - \\log(y)||_2$ [29, 30].", + "bbox": [ + 89, + 537, + 482, + 584 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For our programs to be interpretable, they must put together modules or primitives in an interpretable way. We conceptualize these primitives as a library of functions $\\mathcal{F} = \\{f_1, f_2 \\ldots f_k\\}$ , that can be used to construct a program $P$ . Given that we are analyzing visual data, a key primitive will be an open-vocabulary recognition model that is applied to images associated with a data point. For example, when estimating poverty for a location, we can define a primitive that queries the satellite images available at that location and uses an open-vocabulary recognition engine [25] to detect various concepts. Recent advances in recognition have produced such foundation models for a range of modalities [25, 35]. In addition, we will assume basic mathematical, logical and image operators such as logarithms, elementwise maximum, or a distance transform. We note that the set of primitives is often not specific to the task and can be shared across a range of problems in a domain. That said, the set of primitives can be expanded upon if needed by domain experts for particular problems; for example, a climate scientist may want to include a function that can look up the average temperature at a particular place and time.", + "bbox": [ + 89, + 584, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: DiSciPLE's learning loop" + ], + "code_body": "Input: Observation set $\\mathcal{D} = \\{(x_1,y_1),(x_2,y_2),\\ldots ,(x_n,y_n)\\}$ , metric $\\mathcal{M}$ , an objective prompt $p_o$ , a set of primitive function $\\mathcal{F} = \\{f_1,f_2\\dots f_k\\}$ Hyperparams : Mutation probability $\\rho_{m}$ total generations $T$ population size $M$ crossover $p_c$ and mutation $p_m$ prompts. Output: A program $P^{*}$ in the form of a program that explains the observations best. \n1 $B^0\\gets \\{\\}$ // Initialize a programs bank \n2 for $i = 1,\\dots ,M$ do \n3 $\\begin{array}{r}P_i^0\\leftarrow \\mathcal{L}\\mathcal{L}\\mathcal{M}(p_o)\\\\ B^0\\leftarrow B^0\\cup \\{P_i^0\\} \\end{array}$ \n4 \n5 $P^{*}\\gets P_{i}^{0}$ // Evolution loop \n6 for $t = 0,\\dots ,T$ do \n7 $B^{t + 1}\\gets \\{\\}$ \n8 for $i = 1,\\dots ,M$ do \n9 $P_{k_1}^t,P_{k_2}^t\\gets$ sample_parents $(B_{t}) / /$ Sample parents for crossover $P_{i}^{t + 1}\\gets$ $\\mathcal{L}\\mathcal{L}\\mathcal{M}(P_{k_1}^t,P_{k_2}^t,s(P_{k_1}^t;\\mathcal{D}),s(P_{k_2}^t;\\mathcal{D}),p_o,p_c)$ // crossover operation \n11 if $u\\sim \\mathcal{U}(0,1) < \\rho_m$ then \n12 $\\begin{array}{r}\\Bigl {\\backslash}P_i^{t + 1}\\gets \\mathcal{L}\\mathcal{L}\\mathcal{M}(P_k^{t + 1},s(P_k^{t + 1};\\mathcal{D}),p_o,p_m)\\\\ //\\text{mutation operation}\\\\ //\\text{critique and simplification}\\\\ P_i^{t + 1}\\gets \\text{critic}(P_i^{t + 1})P_i^{t + 1}\\gets \\text{simplifier}(P_i^{t + 1})\\\\ P^*\\gets P_i^{t + 1}\\\\ B^{t + 1}\\gets B^{t + 1}\\cup \\{P_i^{t + 1}\\} \\end{array}$ \n13 \n14 if $s(P_i^{t + 1};\\mathcal{D}) > s(P^*;\\mathcal{D})$ then \n15 \n16", + "bbox": [ + 516, + 111, + 903, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finally, to enable us to effectively search the programs space and leverage the conceptual understanding of LLMs, we assume that we have a natural language description desc of the quantity of interest $Y$ . For example, this may be the phrase \"population density\". As we will see, this information is useful in guiding the LLM to search the space.", + "bbox": [ + 511, + 612, + 906, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Putting everything together, our proposed system, DiS-ciPLE (Discovering Scientific Programs using LLMs and Evolution), takes as input the dataset $\\mathcal{D}$ , the metric $\\mathcal{M}$ , the set of primitives $\\mathcal{F}$ and the textual description desc. It produces an interpretable and accurate program $P$ that maps inputs $X$ to the output quantity of interest $Y$ .", + "bbox": [ + 511, + 703, + 906, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Evolutionary Search for Programs", + "text_level": 1, + "bbox": [ + 511, + 801, + 815, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To search through the vast, discrete space of programs, DiS-ciPLE adapts evolutionary search. Evolutionary program search typically starts with a large population of random programs. These programs are then sampled based on their fitness as parents. The parent programs create a new popu", + "bbox": [ + 511, + 824, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "29260", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b59e300c314a83c954cdb2539ea698a67ed082c08e2520d712aa28d66a6c6097.jpg", + "image_caption": [ + "Figure 2. Overview of our evolutionary algorithm with critic and simplification. We start with a population of programs to solve a task. We sample pairs of programs based on their fitness score and perform crossover/mutations over them to produce new programs. The generated program is further improved by passing it through a critic and then an analytical simplification step. This program is then evaluated and put in the next generation of programs. The evaluation score of the program is used to determine the fitness for the next generation." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 903, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "lation of programs through crossover and mutation. Newer generations improve over the previous as the population is getting optimized for the fitness function. We use the metric $\\mathcal{M}$ as the fitness function in our work.", + "bbox": [ + 88, + 458, + 482, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We keep the overall evolutionary algorithm the same and replace key steps with an LLM. First, we provide the LLM with a prompt for the objective to generate initial programs. To leverage the prior knowledge of LLMs, we use a prompt $p_o$ that mentions the specified description of the quantity of interest: \"Given a satellite image, write a function to estimate $\\langle desc \\rangle$ \". We do not expect the LLM to answer such a difficult scientific question without leveraging the observations $\\mathcal{D}$ ; however, the prompt prevents the evolutionary algorithm from searching in completely random directions. As a result, our initial population is not entirely random.", + "bbox": [ + 88, + 518, + 482, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Second, instead of using symbolic methods for crossover/mutation, we use an LLM to perform these operations. LLMs have common sense about programming, resulting in better modifications when performing these operations. More specifically, let $P_{k_1}^t$ and $P_{k_2}^t$ be two programs sampled from the $t^{th}$ generation selected as parents based on the fitness function. To perform a crossover operation we pass, the objective prompt $p_o$ , the two programs $P_{k_1}^t$ and $P_{k_2}^t$ , their corresponding scores (using Eq. (1)), along with a crossover prompt $p_c$ to obtain a new program:", + "bbox": [ + 89, + 686, + 482, + 840 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {k} ^ {t + 1} = \\mathcal {L L M} \\left(P _ {k _ {1}} ^ {t}, P _ {k _ {2}} ^ {t}, s \\left(P _ {k _ {1}} ^ {t}; \\mathcal {D}\\right), s \\left(P _ {k _ {2}} ^ {t}; \\mathcal {D}\\right), p _ {o}, p _ {c}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 852, + 482, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The crossover prompt instructs the LLM to make use of", + "bbox": [ + 109, + 885, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the two-parent programs to come up with a new program. The LLM is able to combine elements from the parents to produce something new (see Fig. 2). Plase refer to the supplementary for more examples. We also mutate a program with some probability using a mutation prompt $p_m$ .", + "bbox": [ + 511, + 459, + 906, + 535 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n{ } ^ { m } P _ { k } ^ { t + 1 } = \\mathcal { L L M } ( P _ { k } ^ { t + 1 } , s ( P _ { k } ^ { t + 1 } ; \\mathcal { D } ) , p _ { o } , p _ { m } ) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 556, + 903, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We present the exact prompts for crossover and mutation in the supplementary. Note that both operations also include the objective prompt preventing the LLM from generating programs far away from the objective.", + "bbox": [ + 511, + 584, + 906, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Feature Set Prediction", + "text_level": 1, + "bbox": [ + 511, + 652, + 720, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Solutions for many problems require a combination of multiple features. Optimizing for the correct combination of features is challenging for an LLM, as we are not doing gradient-based optimization. Therefore instead of prompting the LLM to directly generate a predictor for $y$ , we prompt it to create a list of predictive features. We then learn a regressor on top of this list and use both of them as the final program. Since both the program and regressor are interpretable, our final program is also interpretable.", + "bbox": [ + 511, + 674, + 906, + 811 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Program Critic", + "text_level": 1, + "bbox": [ + 511, + 818, + 668, + 833 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The only form of supervision our method gets is the score $s(P; \\mathcal{D})$ by evaluating the program $P$ on observations. However, since we perform crossover and mutation through an LLM, we can provide finer information to aid the search.", + "bbox": [ + 511, + 839, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "29261", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More specifically, we propose a critic that performs a finer-grained evaluation of the program that we get after crossover/mutation. In most visual domains, the data can categorically distributed by using the same set of foundational primitives. Our critic performs a stratified evaluation by partitioning the observation data into multiple categories and evaluating the program on individual strata.", + "bbox": [ + 89, + 90, + 483, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} = d _ {1} \\cup d _ {2} \\cup \\dots \\cup d _ {c}, \\quad \\text {w h e r e} d _ {i} \\cap d _ {j} = \\emptyset \\text {f o r} i \\neq j \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 210, + 482, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since all the problems in our benchmark are geospatial, we use a critic that takes the satellite image corresponding to each input and uses a segmentation model to partition the observation dataset into land-use categories. The critic obtains per-partition score $s(P; d_i)$ and prompts the LLM to improve the program on categories the model is bad. The addition of a critic improves the programs on data overlooked by existing programs, resulting in reliable programs.", + "bbox": [ + 89, + 241, + 483, + 363 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Program Simplification", + "text_level": 1, + "bbox": [ + 89, + 375, + 307, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Successive steps of crossovers and mutations of programs result in large programs with many redundancies, hurting interpretability. We propose an analytical approach to simplify the programs and remove the redundant parts of it. Our generated programs can be represented as a directed acyclic graphs (DAG) (we use the abstract syntax tree (AST); see supplementary). In these DAGs, all the constants and the arguments of the function are root nodes. Only the return statement and the unused variables are the leaf nodes. Any leaf node that is not a return statement, is a piece of code that is not needed and can be removed. We then recursively remove all the leaf nodes that are not return statements.", + "bbox": [ + 89, + 397, + 483, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While removing such nodes (unreachable by the return statement) is useful, there could still be features that do not contribute but are returned by the program. Recall that we use linear regression on the list of features. The weights assigned to individual features by the regression model are useful indicators of which features are redundant. We remove the features that have a significantly smaller weight compared to the largest weight (a threshold of $5\\%$ works well). Removing these features from the return statement results in several newly created leaf nodes. We therefore, redo the recursive leaf node removal to simplify the program further. Each generated program is first improved through the critic and then simplified before adding back to the population. Algorithm 1 shows the complete process.", + "bbox": [ + 89, + 579, + 483, + 790 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Results", + "text_level": 1, + "bbox": [ + 89, + 806, + 176, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation details", + "text_level": 1, + "bbox": [ + 89, + 832, + 303, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For all our main experiments we used an open-source LLM llama-3-8b-instruct [9]. However, in the supplementary, we also explore other open-source language models. All", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/98a33248b20d2a617b5ffccfbcf8e22c8822cb6653aed7046cefc9e927382cf7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 87, + 903, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/00a718972c6f377c0e6cead23e5da70fe1794e0d7f4442bd9439c858b86290fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 213, + 903, + 334 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2731187ffb8201584adaaf3f92982b6c9ea921218c62d81b121c6ea63f997448.jpg", + "image_caption": [ + "Figure 3. The best-performing programs the 3 benchmark problems as Python programs (left) and the corresponding DAG representation (right). The DAG representation allows better visualization of the importance of different components. The thickness of the red edges shows the importance of a component. Black edges represent cases when measuring influences is unnecessary. This occurs when removing the connection results in bugs or for a single input/output node. For finer details, refer to the digital version." + ], + "image_footnote": [], + "bbox": [ + 517, + 338, + 903, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the visual data in our benchmarks comes from satellite images, so to allow inferring semantic information from it, we use a black-box open-world foundational model for satellite images, GRAFT [25]. Some experiments use ground-truth annotations from OpenStreetMaps [39] as an alternative to disentangle the effect of segmentation from discovery.", + "bbox": [ + 511, + 609, + 905, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We run our evolutionary method for $T = 15$ generations with a population size of $M = 100$ . For all the problems, the input observation is from different locations around the world. We split this data into three parts. Two-thirds of the easternmost observations are used to create a training-testing split. The remaining one-third of the data is used to evaluate reliability (out-of-distribution generalization). We also release this benchmark for future research in this area.", + "bbox": [ + 511, + 700, + 905, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Benchmark for Visual Program Discovery for Scientific Applications", + "text_level": 1, + "bbox": [ + 511, + 832, + 903, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the novelty of the visual program discovery task, there exists no pre-existing benchmark. We define a new", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "29262", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "benchmark for this task, drawing on scientifically relevant geospatial problems. Concretely, we choose two different problems in Demography: population density and poverty indicators, and in Climate Science: AGB estimation.", + "bbox": [ + 89, + 90, + 480, + 150 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is important to note that for these problems, true relationships between variables of interest are unknown. As such, an LLM cannot be expected to produce a good program in a zero-shot manner, as it has never seen these relationships before. This is in contrast to problems like VQA [36] where the reasoning required to answer a question is well-known and we can simply rely on the LLM's world knowledge. For scientific discovery, actual data is needed to discover the right reasoning. We next present the observation datasets, metrics, and overview of primitives.", + "bbox": [ + 89, + 152, + 480, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1. Population Density", + "text_level": 1, + "bbox": [ + 89, + 311, + 269, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Observation Dataset: The problem seeks to predict the population density by observing the satellite images of a region [29, 30]. We obtain the population density values $(y_{i})$ for various locations in the USA by using ACS Community Surveys 5-year estimates [38]. Input observations $(x_{i})$ are sentinel-2 images at a resolution of $10\\mathrm{m}$ [7]. For this experiment, we also use OpenStreetMap masks [39] for 42 land-use concepts (see supplementary) as part of the input.", + "bbox": [ + 89, + 330, + 480, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metric and Primitives: Population density values are aggregated at the county block group level. The predicted population densities are thus also aggregated at this level. The metric is the per-block group averaged L2 error after applying a log transformation. Along with the arithmetic, and logical primitives (see supplementary), we use open-vocabulary segmentation as a primitive. The segmentation function returns a binary mask for an input concept.", + "bbox": [ + 89, + 452, + 480, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2. Poverty Indicator", + "text_level": 1, + "bbox": [ + 89, + 580, + 261, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Observation Dataset: For poverty estimation, we use data from SustainBench [42]. The dataset contains coordinate location as input and wealth asset index as output.", + "bbox": [ + 89, + 599, + 480, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metric and Primitives: We use L2 error for each location as the evaluation metric. To obtain semantic land use information about a location, we first define a get_satellite_image function, that returns a satellite image for any location. This can be used in conjunction with the open-world satellite image recognition model to obtain semantic information. Moreover, we also include primitives that return average annual temperature, precipitation, nightlight intensity, and elevation at the input location.", + "bbox": [ + 89, + 646, + 480, + 781 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.3. Aboveground Biomass", + "text_level": 1, + "bbox": [ + 89, + 791, + 294, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Observation Dataset: Similar to poverty estimation, the observation variables are an input location and the output AGB estimate. We use NASA's GEDI [8] to obtain the observation value for three US states. We use data from Massachusetts and Maine (North-East) as the train/test set and Washington (NorthWest) as the out-of-distribution set.", + "bbox": [ + 89, + 810, + 480, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metric and Primitives: We use L2 error as the metric and the same primitives as poverty estimation.", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Experimental Setup", + "text_level": 1, + "bbox": [ + 513, + 131, + 702, + 148 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the same set of training data we compare our best generated program with a set of baselines.", + "bbox": [ + 511, + 152, + 903, + 183 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Mean: A naive baseline that use the mean of the training observation as the prediction.", + "2. Concept Bottleneck (CB): Similar to [20, 32, 41], we first extract a list of relevant features and train classifiers on them. CB is interpretable due to the bottleneck, however, it is not very expressive (see supplementary).", + "3. Deep models: We use deep models such as ResNets [16] as baseline. We use a small and large variant for each. Please refer to the supplementary for more details and comparisons to other deep models such as transformers.", + "4. Zero-shot: This baseline tests how good would LLMs be on their own in generating programs solely relying on prior knowledge without any observation. Since the generated programs can vary drastically, we report an average of 5 different zero-shot programs.", + "5. Random Search: Instead of evolutionary search, this baseline relies on the stochasticity of LLMs to perform a random search. If DiSciPLE is better at searching, it should do better than random searching for the same number of calls to an LLM." + ], + "bbox": [ + 514, + 184, + 903, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Results and Discussion", + "text_level": 1, + "bbox": [ + 513, + 496, + 723, + 510 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first test our programs on unseen in-domain observations close to the regions used for training (Tab. 1 (left)). We observe that DiSciPLE outperforms all interpretable baselines. It can even outperform a deep model in many cases, specifically on population density estimation, while being more interpretable. DiSciPLE also outperforms zero-shot program inference from LLMs. As discussed before, this is in line with the fact that DiSciPLEis uncovering new relationships that may not be known to us, and by extension, to the LLM. The performance of random search while better than zero-shot is significantly worse than DiSciPLE. This shows that DiSciPLE is able to perform a faster search, by only searching in a meaningful space. DiSciPLE effectively leverages data to perform this novel discovery.", + "bbox": [ + 511, + 518, + 906, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Are our programs reliable? If a program is reliable, it should be able to generalize to other regions. Tab. 1 (right) shows DiSciPLE's performance on such an out-of-distribution set. Here DiSciPLE outperforms all baselines including deep networks. This suggests that we can learn a model that generalizes better to the in-distribution training data, due to its interpretable-by-design representation.", + "bbox": [ + 511, + 750, + 903, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also show these results qualitatively in Fig. 4, by comparing population density predictions of DiSciPLE and the baselines to the true population density. DiS", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "29263", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ad9454e87aaf4ce8985c931a4c3b4f40c6a234b0ec8137fb8732805b5dc97924.jpg", + "table_caption": [ + "Table 1. Performance of our programs on in-distribution (left) and out-of-distribution (right) observations across various problems in the proposed benchmark. This shows the reliability of programs produced by DiSciPLE (red is best and blue is second best)." + ], + "table_footnote": [], + "table_body": "
    Population DensityIn distributionOOD
    PovertyAGBPopulation DensityPovertyAGB
    L2-LogL1-LogL1RMSEL1RMSEL2-LogL1-LogL1RMSEL1RMSE
    Mean0.66960.65401.6131.83642.1550.650.67340.65611.5911.84474.1583.02
    CB0.82980.72791.2291.47626.3333.490.79510.71121.2571.50444.1963.52
    Deep - Small0.44310.50061.2381.63730.7237.030.66230.59671.2841.65435.2753.06
    Deep - Large0.39740.48431.1701.47821.1527.860.44600.51151.3441.74135.4170.30
    Zero-shot0.47020.53711.5251.75438.8046.410.70200.64121.5101.77355.1164.32
    Random Search0.43530.51181.2771.67929.4036.700.67630.62981.4181.84042.3252.53
    Ours0.26070.37781.0771.31424.7932.990.38070.44261.1341.42031.1042.93
    ", + "bbox": [ + 91, + 128, + 923, + 280 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bbf362d544a495c5e8d99219c2278803d904b668133d9ace316e7a010063648b.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of DiSciPLE with other baselines on the tasks of population density. DiSciPLE Can map to the true population density maps much more accurately than the baselines (Refer to the supplementary for more comparisons). The maps display population density as the base-10 log of people/mi²." + ], + "image_footnote": [], + "bbox": [ + 96, + 305, + 478, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ciPLE can model the fine-grained changes in population in unseen regions significantly better than the baselines (refer to supplementary for comparison to other baselines).", + "bbox": [ + 89, + 599, + 483, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Are our programs data-efficient? Our methods are only trained on a maximum of 4000 observations. Fig. 5 further shows that even with a smaller amount of training data, our approach shows minimal degradation compared to deep networks. This suggests that while deep models can generalize with a lot more data, our model does not need as much data to begin with, making it data-efficient.", + "bbox": [ + 89, + 666, + 482, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Are our programs interpretable? Our programs are interpretable-by-design as we can visualize the contributing factors. Fig. 3 shows such programs (left) for the problems in our benchmark. An expert working with DiSciPLE to figure out such programs can edit parts of the program and figure out how much do the components matters.", + "bbox": [ + 89, + 794, + 482, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform this step of understanding the influence of", + "bbox": [ + 109, + 885, + 483, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7252e5736f37d64ebcd118e4a5491da14aa2177ea357a696603c4ab8eb32a51c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 516, + 309, + 906, + 419 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b4f798ad7b7be7f2af08a9e8d89abf1e16b56cbfc81b15fdd3603e0ca5edf839.jpg", + "image_caption": [ + "Figure 5. Performance of DiSciPLE compared to deep model as we reduce the amount of training observation (L2 error). The Oracle (blue) uses a program learned from all observations but uses only partial observation for parameter training. While the errors get worse as we reduce the observation data, the drop is significantly less severe for DiSciPLE compared to deep models." + ], + "image_footnote": [], + "bbox": [ + 517, + 421, + 903, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "individual operations by removing each operation in our program and measuring its effects on the final score. The DAGs on the right of each program show the program structure and the red edges show the influence of each component proportional to the width. This visualization can allow experts to understand which operations are important for the model. For example, in the program for population density Fig. 3, we can see that semantic concepts such as \"highway\" and \"residential building\" are very important.", + "bbox": [ + 511, + 652, + 908, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Can our method perform better than expert humans? Our method would only be useful in real-world scenarios if it could come up with stronger or comparable programs to human experts. We test this on the task of AGB, by providing 2 experts (PhD students actively working on AGB) with a user interface with the same information as our method.", + "bbox": [ + 511, + 810, + 908, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "29264", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/991eec9dbf77669d0b68f5c77028a80bb41d628abfc7db38f40314f2633e0ec7.jpg", + "table_caption": [ + "Table 2. Performance of our method as we successively remove the components. Both critic and simplification lead to performance improvement for our method." + ], + "table_footnote": [], + "table_body": "
    SetCriticSimpli.TestOOD
    L2 logL1 logL2 logL1 log
    XXX0.31590.42960.48350.5178
    ✓XX0.29060.40490.42580.4826
    ✓✓X0.28730.39840.41840.4684
    ✓✓✓0.26070.37780.38070.4426
    ", + "bbox": [ + 89, + 141, + 488, + 234 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Note that finding experts actively working on difficult scientific problems is challenging. Given this constraint, experiments with 2 experts provide a feasible and insightful evaluation. The experts took about 1.5 hours to use their domain knowledge and iterate over programs for AGB. However, the best program they could come up with had an L1 error of 34.48 on the in-distribution set and 52.85 on the OOD set (compared to 24.79 and 31.10 for DiSciPLE). We figure this is primarily because experts need to spend more time on the problem. In general, experts would spend numerous days to come up with a good program, while our method can come up with a better program faster.", + "bbox": [ + 88, + 260, + 485, + 443 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablations", + "text_level": 1, + "bbox": [ + 89, + 450, + 202, + 467 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "How important is the role of feature-set prediction, critic, and simplification? Table 2 measures the performance of our model on the task of population density as we successively add these components to the evolutionary algorithm. The addition of feature set prediction instead of a single feature helps, as it allows our method to learn expressive linear regression parameters instead of letting the LLM come up with them. Further adding the critic results in further improvement as programs start covering richer concepts resulting in better generalization. Finally adding simplification also improves the program. We posit that simplification removes irrelevant features preventing the LLM from focusing on them when performing crossovers.", + "bbox": [ + 88, + 473, + 483, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "How important are common sense and prior knowledge of LLMs? The two major advantages an LLM provides over traditional tree-search are: 1) better crossover and mutation as LLMs can understand the meaning of the primitives. 2) use of prior knowledge for better-guided search. Therefore we remove these two sources of information and test how well can our method perform. To remove the understanding of functions we rename them with meaningless terms and remove the descriptions. To remove the context of the problem we remove the objective prompt. Tab. 3, show the performance of our method on density estimation after removing each of these prompts. Without common sense, the search cannot even progress away from the initial random programs, resulting in worse-than-mean results", + "bbox": [ + 88, + 688, + 485, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/82d94e5fa086891816c681eb1d2cdc86f6f449ffe04404a02b295c9365e11f6b.jpg", + "table_caption": [ + "Table 3. Performance of our method when removing the context of the problem (objective prompt from the evolution, and when renaming and not describing the primitive functions). We see significant drops in performance, suggesting that both common sense and prior knowledge are important to perform an efficient search." + ], + "table_footnote": [], + "table_body": "
    MethodL1 logL2 log
    No common-sense0.84010.7186
    No problem context0.44980.5140
    DiSciPLE full0.26070.3778
    ", + "bbox": [ + 578, + 170, + 841, + 234 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(L1 error of 0.84 vs 0.26 for DiSciPLE). This suggests that symbolic regression models, that have no understanding of open-world primitives, would struggle to search. If we just remove the context of the problem, the model does slightly better and can obtain results better than the mean and zero-shot programs (L1 error of 0.45). This suggests that while the search is moving in the objective's direction, it is slow.", + "bbox": [ + 511, + 260, + 908, + 367 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 511, + 378, + 764, + 396 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations: One of our limitation is that we can only differentiably optimize learnable parameters in the last computational layer. This could miss out on programs with useful parameters in some intermediate computation layers. We attempted to make the whole pipeline differentiable, however the model performance did not improve much. Many of the operations in our pipeline even though differentiable have zero-gradient in large part of input space, making gradient optimization challenging. In future work, we plan to use initialization tricks for non-linear optimization and second-order optimization to obtain even more expressive models.", + "bbox": [ + 511, + 405, + 908, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion: We present DiSciPLE - an evolutionary algorithm that leverages the prior-knowledge and common sense abilities of LLMs to create interpretable, reliable and data-efficient programs for real-world scientific visual data. This allows us to create programs that are more powerful than existing interpretable counterparts and more insightful than deeper uninterpretable models. We show its prowess on 3 scientific applications by proposing a benchmark for visual program discovery. We believe that using DiSciPLE in tandem with a human expert can rapidly speed up the scientific process and result in numerous novel discoveries.", + "bbox": [ + 511, + 589, + 908, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This research is based upon work supported in part by the ODNI-IARPA via 2021-20111000006, the NSF STC-LEAP, the U.S. DARPA ECOLE Program No. #HR00112390060 and NSF grants 2403015 and 2403016. This work would not have been possible without the help from domain experts. 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PhD thesis, STANFORD UNIVERSITY, 2017. 3", + "[41] Yue Yang, Artemis Panagopoulou, Shenghao Zhou, Daniel Jin, Chris Callison-Burch, and Mark Yatskar. Language in a bottle: Language model guided concept bottlenecks for interpretable image classification. In CVPR, 2023. 2, 6", + "[42] Christopher Yeh, Chenlin Meng, Sherrie Wang, Anne Driscoll, Erik Rozi, Patrick Liu, Jihyeon Lee, Marshall" + ], + "bbox": [ + 91, + 90, + 480, + 900 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "Burke, David B Lobell, and Stefano Ermon. Sustain-bench: Benchmarks for monitoring the sustainable development goals with machine learning. arXiv preprint arXiv:2111.04724, 2021. 6", + "[43] Xixian Yong and Xiao Zhou. MuseCL: Predicting urban socioeconomic indicators via multi-semantic contrastive learning. CoRR, 2024. 3", + "[44] Bolei Zhou, Yiyou Sun, David Bau, and Antonio Torralba. Interpretable basis decomposition for visual explanation. In ECCV, 2018. 2" + ], + "bbox": [ + 516, + 92, + 903, + 231 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "29267", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DiSciPLE_ Learning Interpretable Programs for Scientific Visual Discovery/01086b46-2a5a-4e5d-8038-ecfacbe0a732_model.json b/2025/DiSciPLE_ Learning Interpretable Programs for Scientific Visual Discovery/01086b46-2a5a-4e5d-8038-ecfacbe0a732_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e547787b0802673ce8a4b36cf22ea3963c1d1420 --- /dev/null +++ b/2025/DiSciPLE_ Learning Interpretable Programs for Scientific Visual Discovery/01086b46-2a5a-4e5d-8038-ecfacbe0a732_model.json @@ -0,0 +1,2035 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.112, + 0.131, + 0.885, + 0.154 + ], + "angle": 0, + "content": "DiSciPLE: Learning Interpretable Programs for Scientific Visual Discovery" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.18, + 0.916, + 0.218 + ], + "angle": 0, + "content": "Utkarsh Mall1 Cheng Perng Phoo2 Mia Chiquier1 Bharath Hariharan2 Kavita Bala2 Carl Vondrick1 \n1Columbia University Cornell University" + }, + { + "type": "text", + "bbox": [ + 0.374, + 0.22, + 0.651, + 0.233 + ], + "angle": 0, + "content": "Correspondence: um2171@columbia.edu" + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.235, + 0.605, + 0.252 + ], + "angle": 0, + "content": "disciple.cs.columbia.edu" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.318, + 0.485, + 0.637 + ], + "angle": 0, + "content": "Visual data is used in numerous different scientific workflows ranging from remote sensing to ecology. As the amount of observation data increases, the challenge is not just to make accurate predictions but also to understand the underlying mechanisms for those predictions. Good interpretation is important in scientific workflows, as it allows for better decision-making by providing insights into the data. This paper introduces an automatic way of obtaining such interpretable-by-design models, by learning programs that interleave neural networks. We propose DiSciPLE (Discovering Scientific Programs using LLMs and Evolution) an evolutionary algorithm that leverages common sense and prior knowledge of large language models (LLMs) to create Python programs explaining visual data. Additionally, we propose two improvements: a program critic and a program simplifier to improve our method further to synthesize good programs. On three different real-world problems, DiSciPLE learns state-of-the-art programs on novel tasks with no prior literature. For example, we can learn programs with \\(35\\%\\) lower error than the closest non-interpretable baseline for population density estimation." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.664, + 0.222, + 0.68 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.483, + 0.84 + ], + "angle": 0, + "content": "Many modern scientific workflows are built on top of visual data. Researchers in remote sensing, climate science, ecology, and other sciences use images as a window into our world to estimate population density, the amount of biomass, poverty indicators, and so on. There is a massively increasing volume of visual data, be it from an ever-expanding set of satellites, widespread camera traps, or images uploaded on the web, that is available to domain experts, and computer vision has the potential to meaningfully assist scientists in using it for scientific insight." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Scientific applications of computer vision, however, are demanding tasks because we want models that not only predict outcomes but also reveal underlying mechanisms. For example, a researcher who studies demography may be able" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.284, + 0.906, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.41, + 0.907, + 0.438 + ], + "angle": 0, + "content": "Figure 1. We introduce a framework to discover interpretable, predictive programs for scientific computer vision tasks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.445, + 0.907, + 0.551 + ], + "angle": 0, + "content": "to train excellent predictive models that learn the relationships between a satellite image and the population. However, understanding why certain regions are densely populated is crucial for urban planning and policy decisions — black-box predictions offer no interpretation of what makes a region have a high population. Scientists themselves want to derive insight from the models, not just predict." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.909, + 0.901 + ], + "angle": 0, + "content": "While there have been many works that train interpretable vision models (for example concept-bottlenecks [20, 27]), these models are often limited to simple functions of primitive concepts, such as bag of words. These simple functions do not scale to the realistic complexity of our visual world and the complex relationships between its many rich scientific indicators, resulting in poor accuracy. A promising direction to model rich relationships without foregoing interpretability is to learn programs on top of conceptual primitives. Recently, code generation methods such as ViperGPT and VisProg [14, 36] have demonstrated that large language models are able to synthesize programs with competitive performance on many vision tasks, and the representations are interpretable by construction because programs are human-readable. However, while these methods work well for established vision tasks, they often fail to generalize to scientific applications of computer vision because the tasks are new and outside the scope of the training data on the internet. LLMs lack the requisite knowledge to answer novel or domain-specific questions, and as we will show, directly applying such zero-shot code generation methods on scientific domains is not effective." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29258" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.333 + ], + "angle": 0, + "content": "How can we automatically discover accurate and interpretable programs from the volumes of visual data in scientific applications? This paper introduces DiSciPLE, a framework for Discovering Scientific Programs using LLMs and Evolution. Given a large dataset of images, our approach synthesizes a program to solve the task. As the name suggests, DiSciPLE introduces an evolutionary search algorithm that starts with zero-shot programs from LLMs and iteratively improves them over the dataset. The discovered programs are able to interleave neural networks, in particular open-world foundation models, for segmentation with logical and mathematical operations, enabling powerful predictions while also being interpretable. Our framework makes several improvements to integrate evolutionary search with LLMs, using program simplification and critics to provide fine-grained guidance that accelerates search." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.334, + 0.482, + 0.468 + ], + "angle": 0, + "content": "In three different scientific applications of computer vision, DiSciPLE is able to learn state-of-the-art programs for novel tasks that have no prior documented solutions in existing literature. Our approach significantly outperforms neural networks at estimating population density from satellite imagery. Our method also obtains strong out-of-distribution performance at estimating a region's biomass, generalizing to geographical regions outside of the training set significantly better than all other baselines. Our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.469, + 0.481, + 0.514 + ], + "angle": 0, + "content": "- We introduce a novel framework DiSciPLE, that can produce interpretable, reliable, and sample-efficient programs for scientific discovery." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.515, + 0.481, + 0.559 + ], + "angle": 0, + "content": "- We present two key components: a critic and a program simplification method to DiSciPLE that can further improve the search resulting in better programs." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.56, + 0.481, + 0.635 + ], + "angle": 0, + "content": "- We propose benchmarks for the task of scientific visual discovery containing real-world high-dimensional visual data for three problems in two domains. Using these benchmarks, we show that programs from DiSciPLE are more interpretable, reliable, and data-efficient." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.469, + 0.481, + 0.635 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.649, + 0.24, + 0.665 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Concept bottlenecks. Concept bottleneck [20, 32, 41] is an approach used to create interpretable-yet-powerful classifiers. The key idea is to train a deep model to predict a set of low-level concepts and then learn a linear classifier. Such concept bottlenecks are the basis in several areas such as fine-grained recognition [11, 17, 37, 44] and zero-shot learning [1, 19, 21]. However in order to train these models, expensive data is needed for the bottleneck concepts themselves. One way to reduce this annotation cost is to ask questions in an information-theoretically optimal way [2, 3]. Researchers have also automated the pipeline by using LLMs as a knowledge base to propose bottlenecks [15, 27, 33]. [4] proposed an evolutionary algorithm to discover interpretable concept bottlenecks without prior information. While these models are interpretable, they are" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.138 + ], + "angle": 0, + "content": "very simple in terms of expressive power. In this work, we instead evolve interpretable programs, that are more expressive than a bag of words." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.155, + 0.905, + 0.486 + ], + "angle": 0, + "content": "Symbolic regression. Symbolic regression (SR) [5] is a technique for learning equations through evolutionary search. Several methods have been proposed to improve the search efficiency [24], however, most SR techniques cannot solve problems beyond simple mathematical formulas, with simple mathematical primitives. This is partly because the solution search space becomes combinatorial larger. As a result, SR methods fail to work for images, which are high-dimensional. Our method instead focuses on problems with high-dimensional visual data, by leveraging vision foundation models as primitives. Like DiSciPLE, recent work on SR [12, 22, 28, 34] has also looked at using LLMs to better guide the search. However, these methods are only tested on lower-dimensional problems for formula discovery. We instead propose an approach that is complementary to SR. Methods for SR cannot be applied directly in higher-dimensional open-world visual problems, on the other hand on low-dimensional problems existing tools for SR [12] would perform better. The focus of this work is on such real-world problems, where the primitive functions are more complex than mathematical operations and can even be open-world, such as text-to-image segmentation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.504, + 0.905, + 0.671 + ], + "angle": 0, + "content": "Neuro-Symbolic Program Learning [6, 26] is another avenue for learning programs for observation datasets or question answering. These methods typically try to learn both discrete program structures together with neural networks. However, since this optimization is nondifferentiable these methods require reinforcement learning [18] or complex non-differentiable optimization techniques [10]. The hard optimization issue makes the problem of learning programs sample inefficient in real-world settings. We alternatively use LLMs ability to program to better guide the search for such programs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.687, + 0.905, + 0.779 + ], + "angle": 0, + "content": "Program synthesis with LLMs. Several works have utilized LLM coding ability in different applications such as VQA [13, 36] and robot manipulation [23]. While the zero-shot inferred code work very well on domains well-known to the internet, they tend to perform poorly on problems in scientific domains, as shown by our results." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Scientific applications. Researchers in numerous scientific domains have used machine learning tools to build predictive models for their quantities of interest. In this work, we focus on two such scientific domain: demography and climate science. For both these domains, we use remote sensing vision-language foundation models as primitives, along with mathematical and image operators. In" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29259" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.155 + ], + "angle": 0, + "content": "demography, we focus on the problems of socioeconomic indicator prediction [43], namely population density and poverty [30, 40]. In climate science we focus on the problem of aboveground biomass prediction (AGB) [31]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.165, + 0.226, + 0.183 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.191, + 0.485, + 0.283 + ], + "angle": 0, + "content": "Our key contribution is a program search framework that leverages LLMs to perform evolutionary search. In Sec. 3.1 we formalize the problem of program search. In Sec. 3.2, we present our method of incorporating LLMs in this framework. Finally, in Sec. 3.3, 3.4 and 3.5, we discuss the improvements to this framework to speed-up the search." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.291, + 0.295, + 0.307 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.313, + 0.485, + 0.48 + ], + "angle": 0, + "content": "Our system receives as input a dataset \\(\\mathcal{D} = \\{(x_1, y_1), (x_2, y_2), \\ldots, (x_n, y_n)\\}\\) consisting of inputs \\(x_i \\in X\\) and quantities of interest \\(y_i \\in Y\\). For example, when estimating geospatial indicators like poverty, \\(x_i\\) may be a latitude and longitude, along with other metadata about that location. The system must produce an interpretable program \\(P: X \\to Y\\) that maps inputs to corresponding outputs. As is typical with standard supervised learning, we also assume a loss function or metric \\(\\mathcal{M}\\) that measures how good a particular prediction is, and seek a program that yields the best evaluation score:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.49, + 0.484, + 0.53 + ], + "angle": 0, + "content": "\\[\ns (P; \\mathcal {D}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathcal {M} \\left(P \\left(x _ {i}\\right), y _ {i}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.539, + 0.483, + 0.585 + ], + "angle": 0, + "content": "For example, in the case of population density a good metric used by domain experts is L2 error over log i.e. \\(\\mathcal{M}(y', y) = ||\\log(y') - \\log(y)||_2\\) [29, 30]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.484, + 0.902 + ], + "angle": 0, + "content": "For our programs to be interpretable, they must put together modules or primitives in an interpretable way. We conceptualize these primitives as a library of functions \\(\\mathcal{F} = \\{f_1, f_2 \\ldots f_k\\}\\), that can be used to construct a program \\(P\\). Given that we are analyzing visual data, a key primitive will be an open-vocabulary recognition model that is applied to images associated with a data point. For example, when estimating poverty for a location, we can define a primitive that queries the satellite images available at that location and uses an open-vocabulary recognition engine [25] to detect various concepts. Recent advances in recognition have produced such foundation models for a range of modalities [25, 35]. In addition, we will assume basic mathematical, logical and image operators such as logarithms, elementwise maximum, or a distance transform. We note that the set of primitives is often not specific to the task and can be shared across a range of problems in a domain. That said, the set of primitives can be expanded upon if needed by domain experts for particular problems; for example, a climate scientist may want to include a function that can look up the average temperature at a particular place and time." + }, + { + "type": "code_caption", + "bbox": [ + 0.526, + 0.095, + 0.792, + 0.111 + ], + "angle": 0, + "content": "Algorithm 1: DiSciPLE's learning loop" + }, + { + "type": "algorithm", + "bbox": [ + 0.517, + 0.112, + 0.905, + 0.584 + ], + "angle": 0, + "content": "Input: Observation set \\(\\mathcal{D} = \\{(x_1,y_1),(x_2,y_2),\\ldots ,(x_n,y_n)\\}\\) , metric \\(\\mathcal{M}\\) , an objective prompt \\(p_o\\) , a set of primitive function \\(\\mathcal{F} = \\{f_1,f_2\\dots f_k\\}\\) Hyperparams : Mutation probability \\(\\rho_{m}\\) total generations \\(T\\) population size \\(M\\) crossover \\(p_c\\) and mutation \\(p_m\\) prompts. Output: A program \\(P^{*}\\) in the form of a program that explains the observations best. \n1 \\(B^0\\gets \\{\\}\\) // Initialize a programs bank \n2 for \\(i = 1,\\dots ,M\\) do \n3 \\(\\begin{array}{r}P_i^0\\leftarrow \\mathcal{L}\\mathcal{L}\\mathcal{M}(p_o)\\\\ B^0\\leftarrow B^0\\cup \\{P_i^0\\} \\end{array}\\) \n4 \n5 \\(P^{*}\\gets P_{i}^{0}\\) // Evolution loop \n6 for \\(t = 0,\\dots ,T\\) do \n7 \\(B^{t + 1}\\gets \\{\\}\\) \n8 for \\(i = 1,\\dots ,M\\) do \n9 \\(P_{k_1}^t,P_{k_2}^t\\gets\\) sample_parents \\((B_{t}) / /\\) Sample parents for crossover \\(P_{i}^{t + 1}\\gets\\) \\(\\mathcal{L}\\mathcal{L}\\mathcal{M}(P_{k_1}^t,P_{k_2}^t,s(P_{k_1}^t;\\mathcal{D}),s(P_{k_2}^t;\\mathcal{D}),p_o,p_c)\\) // crossover operation \n11 if \\(u\\sim \\mathcal{U}(0,1) < \\rho_m\\) then \n12 \\(\\begin{array}{r}\\Bigl {\\backslash}P_i^{t + 1}\\gets \\mathcal{L}\\mathcal{L}\\mathcal{M}(P_k^{t + 1},s(P_k^{t + 1};\\mathcal{D}),p_o,p_m)\\\\ //\\text{mutation operation}\\\\ //\\text{critique and simplification}\\\\ P_i^{t + 1}\\gets \\text{critic}(P_i^{t + 1})P_i^{t + 1}\\gets \\text{simplifier}(P_i^{t + 1})\\\\ P^*\\gets P_i^{t + 1}\\\\ B^{t + 1}\\gets B^{t + 1}\\cup \\{P_i^{t + 1}\\} \\end{array}\\) \n13 \n14 if \\(s(P_i^{t + 1};\\mathcal{D}) > s(P^*;\\mathcal{D})\\) then \n15 \n16" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.907, + 0.704 + ], + "angle": 0, + "content": "Finally, to enable us to effectively search the programs space and leverage the conceptual understanding of LLMs, we assume that we have a natural language description desc of the quantity of interest \\( Y \\). For example, this may be the phrase \"population density\". As we will see, this information is useful in guiding the LLM to search the space." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.795 + ], + "angle": 0, + "content": "Putting everything together, our proposed system, DiS-ciPLE (Discovering Scientific Programs using LLMs and Evolution), takes as input the dataset \\(\\mathcal{D}\\), the metric \\(\\mathcal{M}\\), the set of primitives \\(\\mathcal{F}\\) and the textual description desc. It produces an interpretable and accurate program \\(P\\) that maps inputs \\(X\\) to the output quantity of interest \\(Y\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.816, + 0.82 + ], + "angle": 0, + "content": "3.2. Evolutionary Search for Programs" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.907, + 0.903 + ], + "angle": 0, + "content": "To search through the vast, discrete space of programs, DiS-ciPLE adapts evolutionary search. Evolutionary program search typically starts with a large population of random programs. These programs are then sampled based on their fitness as parents. The parent programs create a new popu" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "29260" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.905, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.376, + 0.908, + 0.435 + ], + "angle": 0, + "content": "Figure 2. Overview of our evolutionary algorithm with critic and simplification. We start with a population of programs to solve a task. We sample pairs of programs based on their fitness score and perform crossover/mutations over them to produce new programs. The generated program is further improved by passing it through a critic and then an analytical simplification step. This program is then evaluated and put in the next generation of programs. The evaluation score of the program is used to determine the fitness for the next generation." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.459, + 0.483, + 0.518 + ], + "angle": 0, + "content": "lation of programs through crossover and mutation. Newer generations improve over the previous as the population is getting optimized for the fitness function. We use the metric \\(\\mathcal{M}\\) as the fitness function in our work." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.52, + 0.483, + 0.687 + ], + "angle": 0, + "content": "We keep the overall evolutionary algorithm the same and replace key steps with an LLM. First, we provide the LLM with a prompt for the objective to generate initial programs. To leverage the prior knowledge of LLMs, we use a prompt \\( p_o \\) that mentions the specified description of the quantity of interest: \"Given a satellite image, write a function to estimate \\( \\langle desc \\rangle \\)\". We do not expect the LLM to answer such a difficult scientific question without leveraging the observations \\( \\mathcal{D} \\); however, the prompt prevents the evolutionary algorithm from searching in completely random directions. As a result, our initial population is not entirely random." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.687, + 0.483, + 0.841 + ], + "angle": 0, + "content": "Second, instead of using symbolic methods for crossover/mutation, we use an LLM to perform these operations. LLMs have common sense about programming, resulting in better modifications when performing these operations. More specifically, let \\( P_{k_1}^t \\) and \\( P_{k_2}^t \\) be two programs sampled from the \\( t^{th} \\) generation selected as parents based on the fitness function. To perform a crossover operation we pass, the objective prompt \\( p_o \\), the two programs \\( P_{k_1}^t \\) and \\( P_{k_2}^t \\), their corresponding scores (using Eq. (1)), along with a crossover prompt \\( p_c \\) to obtain a new program:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.853, + 0.483, + 0.884 + ], + "angle": 0, + "content": "\\[\nP _ {k} ^ {t + 1} = \\mathcal {L L M} \\left(P _ {k _ {1}} ^ {t}, P _ {k _ {2}} ^ {t}, s \\left(P _ {k _ {1}} ^ {t}; \\mathcal {D}\\right), s \\left(P _ {k _ {2}} ^ {t}; \\mathcal {D}\\right), p _ {o}, p _ {c}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.484, + 0.901 + ], + "angle": 0, + "content": "The crossover prompt instructs the LLM to make use of" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.46, + 0.907, + 0.536 + ], + "angle": 0, + "content": "the two-parent programs to come up with a new program. The LLM is able to combine elements from the parents to produce something new (see Fig. 2). Plase refer to the supplementary for more examples. We also mutate a program with some probability using a mutation prompt \\( p_m \\)." + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.557, + 0.905, + 0.577 + ], + "angle": 0, + "content": "\\[\n{ } ^ { m } P _ { k } ^ { t + 1 } = \\mathcal { L L M } ( P _ { k } ^ { t + 1 } , s ( P _ { k } ^ { t + 1 } ; \\mathcal { D } ) , p _ { o } , p _ { m } ) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.585, + 0.907, + 0.645 + ], + "angle": 0, + "content": "We present the exact prompts for crossover and mutation in the supplementary. Note that both operations also include the objective prompt preventing the LLM from generating programs far away from the objective." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.653, + 0.722, + 0.667 + ], + "angle": 0, + "content": "3.3. Feature Set Prediction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.812 + ], + "angle": 0, + "content": "Solutions for many problems require a combination of multiple features. Optimizing for the correct combination of features is challenging for an LLM, as we are not doing gradient-based optimization. Therefore instead of prompting the LLM to directly generate a predictor for \\( y \\), we prompt it to create a list of predictive features. We then learn a regressor on top of this list and use both of them as the final program. Since both the program and regressor are interpretable, our final program is also interpretable." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.669, + 0.834 + ], + "angle": 0, + "content": "3.4. Program Critic" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.901 + ], + "angle": 0, + "content": "The only form of supervision our method gets is the score \\( s(P; \\mathcal{D}) \\) by evaluating the program \\( P \\) on observations. However, since we perform crossover and mutation through an LLM, we can provide finer information to aid the search." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "29261" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.198 + ], + "angle": 0, + "content": "More specifically, we propose a critic that performs a finer-grained evaluation of the program that we get after crossover/mutation. In most visual domains, the data can categorically distributed by using the same set of foundational primitives. Our critic performs a stratified evaluation by partitioning the observation data into multiple categories and evaluating the program on individual strata." + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.212, + 0.483, + 0.228 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} = d _ {1} \\cup d _ {2} \\cup \\dots \\cup d _ {c}, \\quad \\text {w h e r e} d _ {i} \\cap d _ {j} = \\emptyset \\text {f o r} i \\neq j \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.242, + 0.484, + 0.364 + ], + "angle": 0, + "content": "Since all the problems in our benchmark are geospatial, we use a critic that takes the satellite image corresponding to each input and uses a segmentation model to partition the observation dataset into land-use categories. The critic obtains per-partition score \\( s(P; d_i) \\) and prompts the LLM to improve the program on categories the model is bad. The addition of a critic improves the programs on data overlooked by existing programs, resulting in reliable programs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.375, + 0.308, + 0.391 + ], + "angle": 0, + "content": "3.5. Program Simplification" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.398, + 0.484, + 0.578 + ], + "angle": 0, + "content": "Successive steps of crossovers and mutations of programs result in large programs with many redundancies, hurting interpretability. We propose an analytical approach to simplify the programs and remove the redundant parts of it. Our generated programs can be represented as a directed acyclic graphs (DAG) (we use the abstract syntax tree (AST); see supplementary). In these DAGs, all the constants and the arguments of the function are root nodes. Only the return statement and the unused variables are the leaf nodes. Any leaf node that is not a return statement, is a piece of code that is not needed and can be removed. We then recursively remove all the leaf nodes that are not return statements." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.58, + 0.484, + 0.791 + ], + "angle": 0, + "content": "While removing such nodes (unreachable by the return statement) is useful, there could still be features that do not contribute but are returned by the program. Recall that we use linear regression on the list of features. The weights assigned to individual features by the regression model are useful indicators of which features are redundant. We remove the features that have a significantly smaller weight compared to the largest weight (a threshold of \\(5\\%\\) works well). Removing these features from the return statement results in several newly created leaf nodes. We therefore, redo the recursive leaf node removal to simplify the program further. Each generated program is first improved through the critic and then simplified before adding back to the population. Algorithm 1 shows the complete process." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.807, + 0.178, + 0.822 + ], + "angle": 0, + "content": "4. Results" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.833, + 0.305, + 0.849 + ], + "angle": 0, + "content": "4.1. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "For all our main experiments we used an open-source LLM llama-3-8b-instruct [9]. However, in the supplementary, we also explore other open-source language models. All" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.088, + 0.905, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.214, + 0.905, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.339, + 0.904, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.472, + 0.907, + 0.583 + ], + "angle": 0, + "content": "Figure 3. The best-performing programs the 3 benchmark problems as Python programs (left) and the corresponding DAG representation (right). The DAG representation allows better visualization of the importance of different components. The thickness of the red edges shows the importance of a component. Black edges represent cases when measuring influences is unnecessary. This occurs when removing the connection results in bugs or for a single input/output node. For finer details, refer to the digital version." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.611, + 0.906, + 0.701 + ], + "angle": 0, + "content": "the visual data in our benchmarks comes from satellite images, so to allow inferring semantic information from it, we use a black-box open-world foundational model for satellite images, GRAFT [25]. Some experiments use ground-truth annotations from OpenStreetMaps [39] as an alternative to disentangle the effect of segmentation from discovery." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.702, + 0.906, + 0.822 + ], + "angle": 0, + "content": "We run our evolutionary method for \\( T = 15 \\) generations with a population size of \\( M = 100 \\). For all the problems, the input observation is from different locations around the world. We split this data into three parts. Two-thirds of the easternmost observations are used to create a training-testing split. The remaining one-third of the data is used to evaluate reliability (out-of-distribution generalization). We also release this benchmark for future research in this area." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.833, + 0.905, + 0.865 + ], + "angle": 0, + "content": "4.2. Benchmark for Visual Program Discovery for Scientific Applications" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Given the novelty of the visual program discovery task, there exists no pre-existing benchmark. We define a new" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29262" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.151 + ], + "angle": 0, + "content": "benchmark for this task, drawing on scientifically relevant geospatial problems. Concretely, we choose two different problems in Demography: population density and poverty indicators, and in Climate Science: AGB estimation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.482, + 0.304 + ], + "angle": 0, + "content": "It is important to note that for these problems, true relationships between variables of interest are unknown. As such, an LLM cannot be expected to produce a good program in a zero-shot manner, as it has never seen these relationships before. This is in contrast to problems like VQA [36] where the reasoning required to answer a question is well-known and we can simply rely on the LLM's world knowledge. For scientific discovery, actual data is needed to discover the right reasoning. We next present the observation datasets, metrics, and overview of primitives." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.312, + 0.27, + 0.327 + ], + "angle": 0, + "content": "4.2.1. Population Density" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.332, + 0.482, + 0.451 + ], + "angle": 0, + "content": "Observation Dataset: The problem seeks to predict the population density by observing the satellite images of a region [29, 30]. We obtain the population density values \\((y_{i})\\) for various locations in the USA by using ACS Community Surveys 5-year estimates [38]. Input observations \\((x_{i})\\) are sentinel-2 images at a resolution of \\(10\\mathrm{m}\\) [7]. For this experiment, we also use OpenStreetMap masks [39] for 42 land-use concepts (see supplementary) as part of the input." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.453, + 0.482, + 0.573 + ], + "angle": 0, + "content": "Metric and Primitives: Population density values are aggregated at the county block group level. The predicted population densities are thus also aggregated at this level. The metric is the per-block group averaged L2 error after applying a log transformation. Along with the arithmetic, and logical primitives (see supplementary), we use open-vocabulary segmentation as a primitive. The segmentation function returns a binary mask for an input concept." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.582, + 0.262, + 0.597 + ], + "angle": 0, + "content": "4.2.2. Poverty Indicator" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.601, + 0.482, + 0.646 + ], + "angle": 0, + "content": "Observation Dataset: For poverty estimation, we use data from SustainBench [42]. The dataset contains coordinate location as input and wealth asset index as output." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.647, + 0.482, + 0.782 + ], + "angle": 0, + "content": "Metric and Primitives: We use L2 error for each location as the evaluation metric. To obtain semantic land use information about a location, we first define a get_satellite_image function, that returns a satellite image for any location. This can be used in conjunction with the open-world satellite image recognition model to obtain semantic information. Moreover, we also include primitives that return average annual temperature, precipitation, nightlight intensity, and elevation at the input location." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.792, + 0.295, + 0.806 + ], + "angle": 0, + "content": "4.2.3. Aboveground Biomass" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.482, + 0.9 + ], + "angle": 0, + "content": "Observation Dataset: Similar to poverty estimation, the observation variables are an input location and the output AGB estimate. We use NASA's GEDI [8] to obtain the observation value for three US states. We use data from Massachusetts and Maine (North-East) as the train/test set and Washington (NorthWest) as the out-of-distribution set." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.122 + ], + "angle": 0, + "content": "Metric and Primitives: We use L2 error as the metric and the same primitives as poverty estimation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.132, + 0.704, + 0.149 + ], + "angle": 0, + "content": "4.3. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.154, + 0.905, + 0.184 + ], + "angle": 0, + "content": "For the same set of training data we compare our best generated program with a set of baselines." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.185, + 0.905, + 0.214 + ], + "angle": 0, + "content": "1. Mean: A naive baseline that use the mean of the training observation as the prediction." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.215, + 0.905, + 0.275 + ], + "angle": 0, + "content": "2. Concept Bottleneck (CB): Similar to [20, 32, 41], we first extract a list of relevant features and train classifiers on them. CB is interpretable due to the bottleneck, however, it is not very expressive (see supplementary)." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.276, + 0.905, + 0.335 + ], + "angle": 0, + "content": "3. Deep models: We use deep models such as ResNets [16] as baseline. We use a small and large variant for each. Please refer to the supplementary for more details and comparisons to other deep models such as transformers." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.336, + 0.905, + 0.411 + ], + "angle": 0, + "content": "4. Zero-shot: This baseline tests how good would LLMs be on their own in generating programs solely relying on prior knowledge without any observation. Since the generated programs can vary drastically, we report an average of 5 different zero-shot programs." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.411, + 0.905, + 0.485 + ], + "angle": 0, + "content": "5. Random Search: Instead of evolutionary search, this baseline relies on the stochasticity of LLMs to perform a random search. If DiSciPLE is better at searching, it should do better than random searching for the same number of calls to an LLM." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.185, + 0.905, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.497, + 0.725, + 0.511 + ], + "angle": 0, + "content": "4.4. Results and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.907, + 0.73 + ], + "angle": 0, + "content": "We first test our programs on unseen in-domain observations close to the regions used for training (Tab. 1 (left)). We observe that DiSciPLE outperforms all interpretable baselines. It can even outperform a deep model in many cases, specifically on population density estimation, while being more interpretable. DiSciPLE also outperforms zero-shot program inference from LLMs. As discussed before, this is in line with the fact that DiSciPLEis uncovering new relationships that may not be known to us, and by extension, to the LLM. The performance of random search while better than zero-shot is significantly worse than DiSciPLE. This shows that DiSciPLE is able to perform a faster search, by only searching in a meaningful space. DiSciPLE effectively leverages data to perform this novel discovery." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.905, + 0.856 + ], + "angle": 0, + "content": "Are our programs reliable? If a program is reliable, it should be able to generalize to other regions. Tab. 1 (right) shows DiSciPLE's performance on such an out-of-distribution set. Here DiSciPLE outperforms all baselines including deep networks. This suggests that we can learn a model that generalizes better to the in-distribution training data, due to its interpretable-by-design representation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "We also show these results qualitatively in Fig. 4, by comparing population density predictions of DiSciPLE and the baselines to the true population density. DiS" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "29263" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.908, + 0.119 + ], + "angle": 0, + "content": "Table 1. Performance of our programs on in-distribution (left) and out-of-distribution (right) observations across various problems in the proposed benchmark. This shows the reliability of programs produced by DiSciPLE (red is best and blue is second best)." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.13, + 0.924, + 0.281 + ], + "angle": 0, + "content": "
    Population DensityIn distributionOOD
    PovertyAGBPopulation DensityPovertyAGB
    L2-LogL1-LogL1RMSEL1RMSEL2-LogL1-LogL1RMSEL1RMSE
    Mean0.66960.65401.6131.83642.1550.650.67340.65611.5911.84474.1583.02
    CB0.82980.72791.2291.47626.3333.490.79510.71121.2571.50444.1963.52
    Deep - Small0.44310.50061.2381.63730.7237.030.66230.59671.2841.65435.2753.06
    Deep - Large0.39740.48431.1701.47821.1527.860.44600.51151.3441.74135.4170.30
    Zero-shot0.47020.53711.5251.75438.8046.410.70200.64121.5101.77355.1164.32
    Random Search0.43530.51181.2771.67929.4036.700.67630.62981.4181.84042.3252.53
    Ours0.26070.37781.0771.31424.7932.990.38070.44261.1341.42031.1042.93
    " + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.306, + 0.479, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.503, + 0.484, + 0.573 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of DiSciPLE with other baselines on the tasks of population density. DiSciPLE Can map to the true population density maps much more accurately than the baselines (Refer to the supplementary for more comparisons). The maps display population density as the base-10 log of people/mi²." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.6, + 0.484, + 0.648 + ], + "angle": 0, + "content": "ciPLE can model the fine-grained changes in population in unseen regions significantly better than the baselines (refer to supplementary for comparison to other baselines)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.667, + 0.483, + 0.775 + ], + "angle": 0, + "content": "Are our programs data-efficient? Our methods are only trained on a maximum of 4000 observations. Fig. 5 further shows that even with a smaller amount of training data, our approach shows minimal degradation compared to deep networks. This suggests that while deep models can generalize with a lot more data, our model does not need as much data to begin with, making it data-efficient." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.483, + 0.884 + ], + "angle": 0, + "content": "Are our programs interpretable? Our programs are interpretable-by-design as we can visualize the contributing factors. Fig. 3 shows such programs (left) for the problems in our benchmark. An expert working with DiSciPLE to figure out such programs can edit parts of the program and figure out how much do the components matters." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We perform this step of understanding the influence of" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.31, + 0.907, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.422, + 0.905, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.542, + 0.907, + 0.626 + ], + "angle": 0, + "content": "Figure 5. Performance of DiSciPLE compared to deep model as we reduce the amount of training observation (L2 error). The Oracle (blue) uses a program learned from all observations but uses only partial observation for parameter training. While the errors get worse as we reduce the observation data, the drop is significantly less severe for DiSciPLE compared to deep models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.654, + 0.909, + 0.79 + ], + "angle": 0, + "content": "individual operations by removing each operation in our program and measuring its effects on the final score. The DAGs on the right of each program show the program structure and the red edges show the influence of each component proportional to the width. This visualization can allow experts to understand which operations are important for the model. For example, in the program for population density Fig. 3, we can see that semantic concepts such as \"highway\" and \"residential building\" are very important." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Can our method perform better than expert humans? Our method would only be useful in real-world scenarios if it could come up with stronger or comparable programs to human experts. We test this on the task of AGB, by providing 2 experts (PhD students actively working on AGB) with a user interface with the same information as our method." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "29264" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.486, + 0.132 + ], + "angle": 0, + "content": "Table 2. Performance of our method as we successively remove the components. Both critic and simplification lead to performance improvement for our method." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.142, + 0.49, + 0.236 + ], + "angle": 0, + "content": "
    SetCriticSimpli.TestOOD
    L2 logL1 logL2 logL1 log
    XXX0.31590.42960.48350.5178
    ✓XX0.29060.40490.42580.4826
    ✓✓X0.28730.39840.41840.4684
    ✓✓✓0.26070.37780.38070.4426
    " + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.261, + 0.486, + 0.444 + ], + "angle": 0, + "content": "Note that finding experts actively working on difficult scientific problems is challenging. Given this constraint, experiments with 2 experts provide a feasible and insightful evaluation. The experts took about 1.5 hours to use their domain knowledge and iterate over programs for AGB. However, the best program they could come up with had an L1 error of 34.48 on the in-distribution set and 52.85 on the OOD set (compared to 24.79 and 31.10 for DiSciPLE). We figure this is primarily because experts need to spend more time on the problem. In general, experts would spend numerous days to come up with a good program, while our method can come up with a better program faster." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.452, + 0.204, + 0.468 + ], + "angle": 0, + "content": "4.5. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.474, + 0.485, + 0.673 + ], + "angle": 0, + "content": "How important is the role of feature-set prediction, critic, and simplification? Table 2 measures the performance of our model on the task of population density as we successively add these components to the evolutionary algorithm. The addition of feature set prediction instead of a single feature helps, as it allows our method to learn expressive linear regression parameters instead of letting the LLM come up with them. Further adding the critic results in further improvement as programs start covering richer concepts resulting in better generalization. Finally adding simplification also improves the program. We posit that simplification removes irrelevant features preventing the LLM from focusing on them when performing crossovers." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.689, + 0.486, + 0.903 + ], + "angle": 0, + "content": "How important are common sense and prior knowledge of LLMs? The two major advantages an LLM provides over traditional tree-search are: 1) better crossover and mutation as LLMs can understand the meaning of the primitives. 2) use of prior knowledge for better-guided search. Therefore we remove these two sources of information and test how well can our method perform. To remove the understanding of functions we rename them with meaningless terms and remove the descriptions. To remove the context of the problem we remove the objective prompt. Tab. 3, show the performance of our method on density estimation after removing each of these prompts. Without common sense, the search cannot even progress away from the initial random programs, resulting in worse-than-mean results" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.089, + 0.908, + 0.161 + ], + "angle": 0, + "content": "Table 3. Performance of our method when removing the context of the problem (objective prompt from the evolution, and when renaming and not describing the primitive functions). We see significant drops in performance, suggesting that both common sense and prior knowledge are important to perform an efficient search." + }, + { + "type": "table", + "bbox": [ + 0.58, + 0.171, + 0.843, + 0.236 + ], + "angle": 0, + "content": "
    MethodL1 logL2 log
    No common-sense0.84010.7186
    No problem context0.44980.5140
    DiSciPLE full0.26070.3778
    " + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.261, + 0.909, + 0.368 + ], + "angle": 0, + "content": "(L1 error of 0.84 vs 0.26 for DiSciPLE). This suggests that symbolic regression models, that have no understanding of open-world primitives, would struggle to search. If we just remove the context of the problem, the model does slightly better and can obtain results better than the mean and zero-shot programs (L1 error of 0.45). This suggests that while the search is moving in the objective's direction, it is slow." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.38, + 0.766, + 0.397 + ], + "angle": 0, + "content": "5. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.406, + 0.909, + 0.573 + ], + "angle": 0, + "content": "Limitations: One of our limitation is that we can only differentiably optimize learnable parameters in the last computational layer. This could miss out on programs with useful parameters in some intermediate computation layers. We attempted to make the whole pipeline differentiable, however the model performance did not improve much. Many of the operations in our pipeline even though differentiable have zero-gradient in large part of input space, making gradient optimization challenging. In future work, we plan to use initialization tricks for non-linear optimization and second-order optimization to obtain even more expressive models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.59, + 0.909, + 0.758 + ], + "angle": 0, + "content": "Conclusion: We present DiSciPLE - an evolutionary algorithm that leverages the prior-knowledge and common sense abilities of LLMs to create interpretable, reliable and data-efficient programs for real-world scientific visual data. This allows us to create programs that are more powerful than existing interpretable counterparts and more insightful than deeper uninterpretable models. We show its prowess on 3 scientific applications by proposing a benchmark for visual program discovery. We believe that using DiSciPLE in tandem with a human expert can rapidly speed up the scientific process and result in numerous novel discoveries." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.775, + 0.909, + 0.898 + ], + "angle": 0, + "content": "Acknowledgements This research is based upon work supported in part by the ODNI-IARPA via 2021-20111000006, the NSF STC-LEAP, the U.S. DARPA ECOLE Program No. #HR00112390060 and NSF grants 2403015 and 2403016. This work would not have been possible without the help from domain experts. 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As the amount of observation data increases, the challenge is not just to make accurate predictions but also to understand the underlying mechanisms for those predictions. Good interpretation is important in scientific workflows, as it allows for better decision-making by providing insights into the data. This paper introduces an automatic way of obtaining such interpretable-by-design models, by learning programs that interleave neural networks. We propose DiSciPLE (Discovering Scientific Programs using LLMs and Evolution) an evolutionary algorithm that leverages common sense and prior knowledge of large language models (LLMs) to create Python programs explaining visual data. Additionally, we propose two improvements: a program critic and a program simplifier to improve our method further to synthesize good programs. On three different real-world problems, DiSciPLE learns state-of-the-art programs on novel tasks with no prior literature. For example, we can learn programs with $35\%$ lower error than the closest non-interpretable baseline for population density estimation. + +# 1. Introduction + +Many modern scientific workflows are built on top of visual data. Researchers in remote sensing, climate science, ecology, and other sciences use images as a window into our world to estimate population density, the amount of biomass, poverty indicators, and so on. There is a massively increasing volume of visual data, be it from an ever-expanding set of satellites, widespread camera traps, or images uploaded on the web, that is available to domain experts, and computer vision has the potential to meaningfully assist scientists in using it for scientific insight. + +Scientific applications of computer vision, however, are demanding tasks because we want models that not only predict outcomes but also reveal underlying mechanisms. For example, a researcher who studies demography may be able + +![](images/239a1fa224d2d23ab06b1aed856559ef2c458a9436535081349933e953fb0928.jpg) +Figure 1. We introduce a framework to discover interpretable, predictive programs for scientific computer vision tasks. + +to train excellent predictive models that learn the relationships between a satellite image and the population. However, understanding why certain regions are densely populated is crucial for urban planning and policy decisions — black-box predictions offer no interpretation of what makes a region have a high population. Scientists themselves want to derive insight from the models, not just predict. + +While there have been many works that train interpretable vision models (for example concept-bottlenecks [20, 27]), these models are often limited to simple functions of primitive concepts, such as bag of words. These simple functions do not scale to the realistic complexity of our visual world and the complex relationships between its many rich scientific indicators, resulting in poor accuracy. A promising direction to model rich relationships without foregoing interpretability is to learn programs on top of conceptual primitives. Recently, code generation methods such as ViperGPT and VisProg [14, 36] have demonstrated that large language models are able to synthesize programs with competitive performance on many vision tasks, and the representations are interpretable by construction because programs are human-readable. However, while these methods work well for established vision tasks, they often fail to generalize to scientific applications of computer vision because the tasks are new and outside the scope of the training data on the internet. LLMs lack the requisite knowledge to answer novel or domain-specific questions, and as we will show, directly applying such zero-shot code generation methods on scientific domains is not effective. + +How can we automatically discover accurate and interpretable programs from the volumes of visual data in scientific applications? This paper introduces DiSciPLE, a framework for Discovering Scientific Programs using LLMs and Evolution. Given a large dataset of images, our approach synthesizes a program to solve the task. As the name suggests, DiSciPLE introduces an evolutionary search algorithm that starts with zero-shot programs from LLMs and iteratively improves them over the dataset. The discovered programs are able to interleave neural networks, in particular open-world foundation models, for segmentation with logical and mathematical operations, enabling powerful predictions while also being interpretable. Our framework makes several improvements to integrate evolutionary search with LLMs, using program simplification and critics to provide fine-grained guidance that accelerates search. + +In three different scientific applications of computer vision, DiSciPLE is able to learn state-of-the-art programs for novel tasks that have no prior documented solutions in existing literature. Our approach significantly outperforms neural networks at estimating population density from satellite imagery. Our method also obtains strong out-of-distribution performance at estimating a region's biomass, generalizing to geographical regions outside of the training set significantly better than all other baselines. Our contributions are: + +- We introduce a novel framework DiSciPLE, that can produce interpretable, reliable, and sample-efficient programs for scientific discovery. +- We present two key components: a critic and a program simplification method to DiSciPLE that can further improve the search resulting in better programs. +- We propose benchmarks for the task of scientific visual discovery containing real-world high-dimensional visual data for three problems in two domains. Using these benchmarks, we show that programs from DiSciPLE are more interpretable, reliable, and data-efficient. + +# 2. Related Works + +Concept bottlenecks. Concept bottleneck [20, 32, 41] is an approach used to create interpretable-yet-powerful classifiers. The key idea is to train a deep model to predict a set of low-level concepts and then learn a linear classifier. Such concept bottlenecks are the basis in several areas such as fine-grained recognition [11, 17, 37, 44] and zero-shot learning [1, 19, 21]. However in order to train these models, expensive data is needed for the bottleneck concepts themselves. One way to reduce this annotation cost is to ask questions in an information-theoretically optimal way [2, 3]. Researchers have also automated the pipeline by using LLMs as a knowledge base to propose bottlenecks [15, 27, 33]. [4] proposed an evolutionary algorithm to discover interpretable concept bottlenecks without prior information. While these models are interpretable, they are + +very simple in terms of expressive power. In this work, we instead evolve interpretable programs, that are more expressive than a bag of words. + +Symbolic regression. Symbolic regression (SR) [5] is a technique for learning equations through evolutionary search. Several methods have been proposed to improve the search efficiency [24], however, most SR techniques cannot solve problems beyond simple mathematical formulas, with simple mathematical primitives. This is partly because the solution search space becomes combinatorial larger. As a result, SR methods fail to work for images, which are high-dimensional. Our method instead focuses on problems with high-dimensional visual data, by leveraging vision foundation models as primitives. Like DiSciPLE, recent work on SR [12, 22, 28, 34] has also looked at using LLMs to better guide the search. However, these methods are only tested on lower-dimensional problems for formula discovery. We instead propose an approach that is complementary to SR. Methods for SR cannot be applied directly in higher-dimensional open-world visual problems, on the other hand on low-dimensional problems existing tools for SR [12] would perform better. The focus of this work is on such real-world problems, where the primitive functions are more complex than mathematical operations and can even be open-world, such as text-to-image segmentation. + +Neuro-Symbolic Program Learning [6, 26] is another avenue for learning programs for observation datasets or question answering. These methods typically try to learn both discrete program structures together with neural networks. However, since this optimization is nondifferentiable these methods require reinforcement learning [18] or complex non-differentiable optimization techniques [10]. The hard optimization issue makes the problem of learning programs sample inefficient in real-world settings. We alternatively use LLMs ability to program to better guide the search for such programs. + +Program synthesis with LLMs. Several works have utilized LLM coding ability in different applications such as VQA [13, 36] and robot manipulation [23]. While the zero-shot inferred code work very well on domains well-known to the internet, they tend to perform poorly on problems in scientific domains, as shown by our results. + +Scientific applications. Researchers in numerous scientific domains have used machine learning tools to build predictive models for their quantities of interest. In this work, we focus on two such scientific domain: demography and climate science. For both these domains, we use remote sensing vision-language foundation models as primitives, along with mathematical and image operators. In + +demography, we focus on the problems of socioeconomic indicator prediction [43], namely population density and poverty [30, 40]. In climate science we focus on the problem of aboveground biomass prediction (AGB) [31]. + +# 3. Methodology + +Our key contribution is a program search framework that leverages LLMs to perform evolutionary search. In Sec. 3.1 we formalize the problem of program search. In Sec. 3.2, we present our method of incorporating LLMs in this framework. Finally, in Sec. 3.3, 3.4 and 3.5, we discuss the improvements to this framework to speed-up the search. + +# 3.1. Problem Formulation + +Our system receives as input a dataset $\mathcal{D} = \{(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)\}$ consisting of inputs $x_i \in X$ and quantities of interest $y_i \in Y$ . For example, when estimating geospatial indicators like poverty, $x_i$ may be a latitude and longitude, along with other metadata about that location. The system must produce an interpretable program $P: X \to Y$ that maps inputs to corresponding outputs. As is typical with standard supervised learning, we also assume a loss function or metric $\mathcal{M}$ that measures how good a particular prediction is, and seek a program that yields the best evaluation score: + +$$ +s (P; \mathcal {D}) = \frac {1}{n} \sum_ {i = 1} ^ {n} \mathcal {M} \left(P \left(x _ {i}\right), y _ {i}\right) \tag {1} +$$ + +For example, in the case of population density a good metric used by domain experts is L2 error over log i.e. $\mathcal{M}(y', y) = ||\log(y') - \log(y)||_2$ [29, 30]. + +For our programs to be interpretable, they must put together modules or primitives in an interpretable way. We conceptualize these primitives as a library of functions $\mathcal{F} = \{f_1, f_2 \ldots f_k\}$ , that can be used to construct a program $P$ . Given that we are analyzing visual data, a key primitive will be an open-vocabulary recognition model that is applied to images associated with a data point. For example, when estimating poverty for a location, we can define a primitive that queries the satellite images available at that location and uses an open-vocabulary recognition engine [25] to detect various concepts. Recent advances in recognition have produced such foundation models for a range of modalities [25, 35]. In addition, we will assume basic mathematical, logical and image operators such as logarithms, elementwise maximum, or a distance transform. We note that the set of primitives is often not specific to the task and can be shared across a range of problems in a domain. That said, the set of primitives can be expanded upon if needed by domain experts for particular problems; for example, a climate scientist may want to include a function that can look up the average temperature at a particular place and time. + +Algorithm 1: DiSciPLE's learning loop +Input: Observation set $\mathcal{D} = \{(x_1,y_1),(x_2,y_2),\ldots ,(x_n,y_n)\}$ , metric $\mathcal{M}$ , an objective prompt $p_o$ , a set of primitive function $\mathcal{F} = \{f_1,f_2\dots f_k\}$ Hyperparams : Mutation probability $\rho_{m}$ total generations $T$ population size $M$ crossover $p_c$ and mutation $p_m$ prompts. Output: A program $P^{*}$ in the form of a program that explains the observations best. +1 $B^0\gets \{\}$ // Initialize a programs bank +2 for $i = 1,\dots ,M$ do +3 $\begin{array}{r}P_i^0\leftarrow \mathcal{L}\mathcal{L}\mathcal{M}(p_o)\\ B^0\leftarrow B^0\cup \{P_i^0\} \end{array}$ +4 +5 $P^{*}\gets P_{i}^{0}$ // Evolution loop +6 for $t = 0,\dots ,T$ do +7 $B^{t + 1}\gets \{\}$ +8 for $i = 1,\dots ,M$ do +9 $P_{k_1}^t,P_{k_2}^t\gets$ sample_parents $(B_{t}) / /$ Sample parents for crossover $P_{i}^{t + 1}\gets$ $\mathcal{L}\mathcal{L}\mathcal{M}(P_{k_1}^t,P_{k_2}^t,s(P_{k_1}^t;\mathcal{D}),s(P_{k_2}^t;\mathcal{D}),p_o,p_c)$ // crossover operation +11 if $u\sim \mathcal{U}(0,1) < \rho_m$ then +12 $\begin{array}{r}\Bigl {\backslash}P_i^{t + 1}\gets \mathcal{L}\mathcal{L}\mathcal{M}(P_k^{t + 1},s(P_k^{t + 1};\mathcal{D}),p_o,p_m)\\ //\text{mutation operation}\\ //\text{critique and simplification}\\ P_i^{t + 1}\gets \text{critic}(P_i^{t + 1})P_i^{t + 1}\gets \text{simplifier}(P_i^{t + 1})\\ P^*\gets P_i^{t + 1}\\ B^{t + 1}\gets B^{t + 1}\cup \{P_i^{t + 1}\} \end{array}$ +13 +14 if $s(P_i^{t + 1};\mathcal{D}) > s(P^*;\mathcal{D})$ then +15 +16 + +Finally, to enable us to effectively search the programs space and leverage the conceptual understanding of LLMs, we assume that we have a natural language description desc of the quantity of interest $Y$ . For example, this may be the phrase "population density". As we will see, this information is useful in guiding the LLM to search the space. + +Putting everything together, our proposed system, DiS-ciPLE (Discovering Scientific Programs using LLMs and Evolution), takes as input the dataset $\mathcal{D}$ , the metric $\mathcal{M}$ , the set of primitives $\mathcal{F}$ and the textual description desc. It produces an interpretable and accurate program $P$ that maps inputs $X$ to the output quantity of interest $Y$ . + +# 3.2. Evolutionary Search for Programs + +To search through the vast, discrete space of programs, DiS-ciPLE adapts evolutionary search. Evolutionary program search typically starts with a large population of random programs. These programs are then sampled based on their fitness as parents. The parent programs create a new popu + +![](images/b59e300c314a83c954cdb2539ea698a67ed082c08e2520d712aa28d66a6c6097.jpg) +Figure 2. Overview of our evolutionary algorithm with critic and simplification. We start with a population of programs to solve a task. We sample pairs of programs based on their fitness score and perform crossover/mutations over them to produce new programs. The generated program is further improved by passing it through a critic and then an analytical simplification step. This program is then evaluated and put in the next generation of programs. The evaluation score of the program is used to determine the fitness for the next generation. + +lation of programs through crossover and mutation. Newer generations improve over the previous as the population is getting optimized for the fitness function. We use the metric $\mathcal{M}$ as the fitness function in our work. + +We keep the overall evolutionary algorithm the same and replace key steps with an LLM. First, we provide the LLM with a prompt for the objective to generate initial programs. To leverage the prior knowledge of LLMs, we use a prompt $p_o$ that mentions the specified description of the quantity of interest: "Given a satellite image, write a function to estimate $\langle desc \rangle$ ". We do not expect the LLM to answer such a difficult scientific question without leveraging the observations $\mathcal{D}$ ; however, the prompt prevents the evolutionary algorithm from searching in completely random directions. As a result, our initial population is not entirely random. + +Second, instead of using symbolic methods for crossover/mutation, we use an LLM to perform these operations. LLMs have common sense about programming, resulting in better modifications when performing these operations. More specifically, let $P_{k_1}^t$ and $P_{k_2}^t$ be two programs sampled from the $t^{th}$ generation selected as parents based on the fitness function. To perform a crossover operation we pass, the objective prompt $p_o$ , the two programs $P_{k_1}^t$ and $P_{k_2}^t$ , their corresponding scores (using Eq. (1)), along with a crossover prompt $p_c$ to obtain a new program: + +$$ +P _ {k} ^ {t + 1} = \mathcal {L L M} \left(P _ {k _ {1}} ^ {t}, P _ {k _ {2}} ^ {t}, s \left(P _ {k _ {1}} ^ {t}; \mathcal {D}\right), s \left(P _ {k _ {2}} ^ {t}; \mathcal {D}\right), p _ {o}, p _ {c}\right) \tag {2} +$$ + +The crossover prompt instructs the LLM to make use of + +the two-parent programs to come up with a new program. The LLM is able to combine elements from the parents to produce something new (see Fig. 2). Plase refer to the supplementary for more examples. We also mutate a program with some probability using a mutation prompt $p_m$ . + +$$ +{ } ^ { m } P _ { k } ^ { t + 1 } = \mathcal { L L M } ( P _ { k } ^ { t + 1 } , s ( P _ { k } ^ { t + 1 } ; \mathcal { D } ) , p _ { o } , p _ { m } ) \tag {3} +$$ + +We present the exact prompts for crossover and mutation in the supplementary. Note that both operations also include the objective prompt preventing the LLM from generating programs far away from the objective. + +# 3.3. Feature Set Prediction + +Solutions for many problems require a combination of multiple features. Optimizing for the correct combination of features is challenging for an LLM, as we are not doing gradient-based optimization. Therefore instead of prompting the LLM to directly generate a predictor for $y$ , we prompt it to create a list of predictive features. We then learn a regressor on top of this list and use both of them as the final program. Since both the program and regressor are interpretable, our final program is also interpretable. + +# 3.4. Program Critic + +The only form of supervision our method gets is the score $s(P; \mathcal{D})$ by evaluating the program $P$ on observations. However, since we perform crossover and mutation through an LLM, we can provide finer information to aid the search. + +More specifically, we propose a critic that performs a finer-grained evaluation of the program that we get after crossover/mutation. In most visual domains, the data can categorically distributed by using the same set of foundational primitives. Our critic performs a stratified evaluation by partitioning the observation data into multiple categories and evaluating the program on individual strata. + +$$ +\mathcal {D} = d _ {1} \cup d _ {2} \cup \dots \cup d _ {c}, \quad \text {w h e r e} d _ {i} \cap d _ {j} = \emptyset \text {f o r} i \neq j \tag {4} +$$ + +Since all the problems in our benchmark are geospatial, we use a critic that takes the satellite image corresponding to each input and uses a segmentation model to partition the observation dataset into land-use categories. The critic obtains per-partition score $s(P; d_i)$ and prompts the LLM to improve the program on categories the model is bad. The addition of a critic improves the programs on data overlooked by existing programs, resulting in reliable programs. + +# 3.5. Program Simplification + +Successive steps of crossovers and mutations of programs result in large programs with many redundancies, hurting interpretability. We propose an analytical approach to simplify the programs and remove the redundant parts of it. Our generated programs can be represented as a directed acyclic graphs (DAG) (we use the abstract syntax tree (AST); see supplementary). In these DAGs, all the constants and the arguments of the function are root nodes. Only the return statement and the unused variables are the leaf nodes. Any leaf node that is not a return statement, is a piece of code that is not needed and can be removed. We then recursively remove all the leaf nodes that are not return statements. + +While removing such nodes (unreachable by the return statement) is useful, there could still be features that do not contribute but are returned by the program. Recall that we use linear regression on the list of features. The weights assigned to individual features by the regression model are useful indicators of which features are redundant. We remove the features that have a significantly smaller weight compared to the largest weight (a threshold of $5\%$ works well). Removing these features from the return statement results in several newly created leaf nodes. We therefore, redo the recursive leaf node removal to simplify the program further. Each generated program is first improved through the critic and then simplified before adding back to the population. Algorithm 1 shows the complete process. + +# 4. Results + +# 4.1. Implementation details + +For all our main experiments we used an open-source LLM llama-3-8b-instruct [9]. However, in the supplementary, we also explore other open-source language models. All + +![](images/98a33248b20d2a617b5ffccfbcf8e22c8822cb6653aed7046cefc9e927382cf7.jpg) + +![](images/00a718972c6f377c0e6cead23e5da70fe1794e0d7f4442bd9439c858b86290fd.jpg) + +![](images/2731187ffb8201584adaaf3f92982b6c9ea921218c62d81b121c6ea63f997448.jpg) +Figure 3. The best-performing programs the 3 benchmark problems as Python programs (left) and the corresponding DAG representation (right). The DAG representation allows better visualization of the importance of different components. The thickness of the red edges shows the importance of a component. Black edges represent cases when measuring influences is unnecessary. This occurs when removing the connection results in bugs or for a single input/output node. For finer details, refer to the digital version. + +the visual data in our benchmarks comes from satellite images, so to allow inferring semantic information from it, we use a black-box open-world foundational model for satellite images, GRAFT [25]. Some experiments use ground-truth annotations from OpenStreetMaps [39] as an alternative to disentangle the effect of segmentation from discovery. + +We run our evolutionary method for $T = 15$ generations with a population size of $M = 100$ . For all the problems, the input observation is from different locations around the world. We split this data into three parts. Two-thirds of the easternmost observations are used to create a training-testing split. The remaining one-third of the data is used to evaluate reliability (out-of-distribution generalization). We also release this benchmark for future research in this area. + +# 4.2. Benchmark for Visual Program Discovery for Scientific Applications + +Given the novelty of the visual program discovery task, there exists no pre-existing benchmark. We define a new + +benchmark for this task, drawing on scientifically relevant geospatial problems. Concretely, we choose two different problems in Demography: population density and poverty indicators, and in Climate Science: AGB estimation. + +It is important to note that for these problems, true relationships between variables of interest are unknown. As such, an LLM cannot be expected to produce a good program in a zero-shot manner, as it has never seen these relationships before. This is in contrast to problems like VQA [36] where the reasoning required to answer a question is well-known and we can simply rely on the LLM's world knowledge. For scientific discovery, actual data is needed to discover the right reasoning. We next present the observation datasets, metrics, and overview of primitives. + +# 4.2.1. Population Density + +Observation Dataset: The problem seeks to predict the population density by observing the satellite images of a region [29, 30]. We obtain the population density values $(y_{i})$ for various locations in the USA by using ACS Community Surveys 5-year estimates [38]. Input observations $(x_{i})$ are sentinel-2 images at a resolution of $10\mathrm{m}$ [7]. For this experiment, we also use OpenStreetMap masks [39] for 42 land-use concepts (see supplementary) as part of the input. + +Metric and Primitives: Population density values are aggregated at the county block group level. The predicted population densities are thus also aggregated at this level. The metric is the per-block group averaged L2 error after applying a log transformation. Along with the arithmetic, and logical primitives (see supplementary), we use open-vocabulary segmentation as a primitive. The segmentation function returns a binary mask for an input concept. + +# 4.2.2. Poverty Indicator + +Observation Dataset: For poverty estimation, we use data from SustainBench [42]. The dataset contains coordinate location as input and wealth asset index as output. + +Metric and Primitives: We use L2 error for each location as the evaluation metric. To obtain semantic land use information about a location, we first define a get_satellite_image function, that returns a satellite image for any location. This can be used in conjunction with the open-world satellite image recognition model to obtain semantic information. Moreover, we also include primitives that return average annual temperature, precipitation, nightlight intensity, and elevation at the input location. + +# 4.2.3. Aboveground Biomass + +Observation Dataset: Similar to poverty estimation, the observation variables are an input location and the output AGB estimate. We use NASA's GEDI [8] to obtain the observation value for three US states. We use data from Massachusetts and Maine (North-East) as the train/test set and Washington (NorthWest) as the out-of-distribution set. + +Metric and Primitives: We use L2 error as the metric and the same primitives as poverty estimation. + +# 4.3. Experimental Setup + +For the same set of training data we compare our best generated program with a set of baselines. + +1. Mean: A naive baseline that use the mean of the training observation as the prediction. +2. Concept Bottleneck (CB): Similar to [20, 32, 41], we first extract a list of relevant features and train classifiers on them. CB is interpretable due to the bottleneck, however, it is not very expressive (see supplementary). +3. Deep models: We use deep models such as ResNets [16] as baseline. We use a small and large variant for each. Please refer to the supplementary for more details and comparisons to other deep models such as transformers. +4. Zero-shot: This baseline tests how good would LLMs be on their own in generating programs solely relying on prior knowledge without any observation. Since the generated programs can vary drastically, we report an average of 5 different zero-shot programs. +5. Random Search: Instead of evolutionary search, this baseline relies on the stochasticity of LLMs to perform a random search. If DiSciPLE is better at searching, it should do better than random searching for the same number of calls to an LLM. + +# 4.4. Results and Discussion + +We first test our programs on unseen in-domain observations close to the regions used for training (Tab. 1 (left)). We observe that DiSciPLE outperforms all interpretable baselines. It can even outperform a deep model in many cases, specifically on population density estimation, while being more interpretable. DiSciPLE also outperforms zero-shot program inference from LLMs. As discussed before, this is in line with the fact that DiSciPLEis uncovering new relationships that may not be known to us, and by extension, to the LLM. The performance of random search while better than zero-shot is significantly worse than DiSciPLE. This shows that DiSciPLE is able to perform a faster search, by only searching in a meaningful space. DiSciPLE effectively leverages data to perform this novel discovery. + +Are our programs reliable? If a program is reliable, it should be able to generalize to other regions. Tab. 1 (right) shows DiSciPLE's performance on such an out-of-distribution set. Here DiSciPLE outperforms all baselines including deep networks. This suggests that we can learn a model that generalizes better to the in-distribution training data, due to its interpretable-by-design representation. + +We also show these results qualitatively in Fig. 4, by comparing population density predictions of DiSciPLE and the baselines to the true population density. DiS + +Table 1. Performance of our programs on in-distribution (left) and out-of-distribution (right) observations across various problems in the proposed benchmark. This shows the reliability of programs produced by DiSciPLE (red is best and blue is second best). + +
    Population DensityIn distributionOOD
    PovertyAGBPopulation DensityPovertyAGB
    L2-LogL1-LogL1RMSEL1RMSEL2-LogL1-LogL1RMSEL1RMSE
    Mean0.66960.65401.6131.83642.1550.650.67340.65611.5911.84474.1583.02
    CB0.82980.72791.2291.47626.3333.490.79510.71121.2571.50444.1963.52
    Deep - Small0.44310.50061.2381.63730.7237.030.66230.59671.2841.65435.2753.06
    Deep - Large0.39740.48431.1701.47821.1527.860.44600.51151.3441.74135.4170.30
    Zero-shot0.47020.53711.5251.75438.8046.410.70200.64121.5101.77355.1164.32
    Random Search0.43530.51181.2771.67929.4036.700.67630.62981.4181.84042.3252.53
    Ours0.26070.37781.0771.31424.7932.990.38070.44261.1341.42031.1042.93
    + +![](images/bbf362d544a495c5e8d99219c2278803d904b668133d9ace316e7a010063648b.jpg) +Figure 4. Qualitative comparison of DiSciPLE with other baselines on the tasks of population density. DiSciPLE Can map to the true population density maps much more accurately than the baselines (Refer to the supplementary for more comparisons). The maps display population density as the base-10 log of people/mi². + +ciPLE can model the fine-grained changes in population in unseen regions significantly better than the baselines (refer to supplementary for comparison to other baselines). + +Are our programs data-efficient? Our methods are only trained on a maximum of 4000 observations. Fig. 5 further shows that even with a smaller amount of training data, our approach shows minimal degradation compared to deep networks. This suggests that while deep models can generalize with a lot more data, our model does not need as much data to begin with, making it data-efficient. + +Are our programs interpretable? Our programs are interpretable-by-design as we can visualize the contributing factors. Fig. 3 shows such programs (left) for the problems in our benchmark. An expert working with DiSciPLE to figure out such programs can edit parts of the program and figure out how much do the components matters. + +We perform this step of understanding the influence of + +![](images/7252e5736f37d64ebcd118e4a5491da14aa2177ea357a696603c4ab8eb32a51c.jpg) + +![](images/b4f798ad7b7be7f2af08a9e8d89abf1e16b56cbfc81b15fdd3603e0ca5edf839.jpg) +Figure 5. Performance of DiSciPLE compared to deep model as we reduce the amount of training observation (L2 error). The Oracle (blue) uses a program learned from all observations but uses only partial observation for parameter training. While the errors get worse as we reduce the observation data, the drop is significantly less severe for DiSciPLE compared to deep models. + +individual operations by removing each operation in our program and measuring its effects on the final score. The DAGs on the right of each program show the program structure and the red edges show the influence of each component proportional to the width. This visualization can allow experts to understand which operations are important for the model. For example, in the program for population density Fig. 3, we can see that semantic concepts such as "highway" and "residential building" are very important. + +Can our method perform better than expert humans? Our method would only be useful in real-world scenarios if it could come up with stronger or comparable programs to human experts. We test this on the task of AGB, by providing 2 experts (PhD students actively working on AGB) with a user interface with the same information as our method. + +Table 2. Performance of our method as we successively remove the components. Both critic and simplification lead to performance improvement for our method. + +
    SetCriticSimpli.TestOOD
    L2 logL1 logL2 logL1 log
    XXX0.31590.42960.48350.5178
    ✓XX0.29060.40490.42580.4826
    ✓✓X0.28730.39840.41840.4684
    ✓✓✓0.26070.37780.38070.4426
    + +Note that finding experts actively working on difficult scientific problems is challenging. Given this constraint, experiments with 2 experts provide a feasible and insightful evaluation. The experts took about 1.5 hours to use their domain knowledge and iterate over programs for AGB. However, the best program they could come up with had an L1 error of 34.48 on the in-distribution set and 52.85 on the OOD set (compared to 24.79 and 31.10 for DiSciPLE). We figure this is primarily because experts need to spend more time on the problem. In general, experts would spend numerous days to come up with a good program, while our method can come up with a better program faster. + +# 4.5. Ablations + +How important is the role of feature-set prediction, critic, and simplification? Table 2 measures the performance of our model on the task of population density as we successively add these components to the evolutionary algorithm. The addition of feature set prediction instead of a single feature helps, as it allows our method to learn expressive linear regression parameters instead of letting the LLM come up with them. Further adding the critic results in further improvement as programs start covering richer concepts resulting in better generalization. Finally adding simplification also improves the program. We posit that simplification removes irrelevant features preventing the LLM from focusing on them when performing crossovers. + +How important are common sense and prior knowledge of LLMs? The two major advantages an LLM provides over traditional tree-search are: 1) better crossover and mutation as LLMs can understand the meaning of the primitives. 2) use of prior knowledge for better-guided search. Therefore we remove these two sources of information and test how well can our method perform. To remove the understanding of functions we rename them with meaningless terms and remove the descriptions. To remove the context of the problem we remove the objective prompt. Tab. 3, show the performance of our method on density estimation after removing each of these prompts. Without common sense, the search cannot even progress away from the initial random programs, resulting in worse-than-mean results + +Table 3. Performance of our method when removing the context of the problem (objective prompt from the evolution, and when renaming and not describing the primitive functions). We see significant drops in performance, suggesting that both common sense and prior knowledge are important to perform an efficient search. + +
    MethodL1 logL2 log
    No common-sense0.84010.7186
    No problem context0.44980.5140
    DiSciPLE full0.26070.3778
    + +(L1 error of 0.84 vs 0.26 for DiSciPLE). This suggests that symbolic regression models, that have no understanding of open-world primitives, would struggle to search. If we just remove the context of the problem, the model does slightly better and can obtain results better than the mean and zero-shot programs (L1 error of 0.45). This suggests that while the search is moving in the objective's direction, it is slow. + +# 5. Discussion and Conclusion + +Limitations: One of our limitation is that we can only differentiably optimize learnable parameters in the last computational layer. This could miss out on programs with useful parameters in some intermediate computation layers. We attempted to make the whole pipeline differentiable, however the model performance did not improve much. Many of the operations in our pipeline even though differentiable have zero-gradient in large part of input space, making gradient optimization challenging. In future work, we plan to use initialization tricks for non-linear optimization and second-order optimization to obtain even more expressive models. + +Conclusion: We present DiSciPLE - an evolutionary algorithm that leverages the prior-knowledge and common sense abilities of LLMs to create interpretable, reliable and data-efficient programs for real-world scientific visual data. This allows us to create programs that are more powerful than existing interpretable counterparts and more insightful than deeper uninterpretable models. We show its prowess on 3 scientific applications by proposing a benchmark for visual program discovery. We believe that using DiSciPLE in tandem with a human expert can rapidly speed up the scientific process and result in numerous novel discoveries. + +Acknowledgements This research is based upon work supported in part by the ODNI-IARPA via 2021-20111000006, the NSF STC-LEAP, the U.S. DARPA ECOLE Program No. #HR00112390060 and NSF grants 2403015 and 2403016. This work would not have been possible without the help from domain experts. We thank Pierre Gentine, Juan Nathaniel, Rong-Yu Gu, and Aya Lahlou for their valuable assistance with experiments and data. + +# References + +[1] Zeynep Akata, Scott Reed, Daniel Walter, Honglak Lee, and Bernt Schiele. Evaluation of output embeddings for fine-grained image classification. In CVPR, 2015. 2 +[2] Aditya Chattopadhyay, Kwan Ho Ryan Chan, and Rene Vidal. Bootstrapping variational information pursuit with large language and vision models for interpretable image classification. 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As the amount of observation data increases, the challenge is not just to make accurate predictions but also to understand the underlying mechanisms for those predictions. Good interpretation is important in scientific workflows, as it allows for better decision-making by providing insights into the data. This paper introduces an automatic way of obtaining such interpretable-by-design models, by learning programs that interleave neural networks. We propose DiSciPLE (Discovering Scientific Programs using LLMs and Evolution) an evolutionary algorithm that leverages common sense and prior knowledge of large language models (LLMs) to create Python programs explaining visual data. Additionally, we propose two improvements: a program critic and a program simplifier to improve our method further to synthesize good programs. On three different real-world problems, DiSciPLE learns state-of-the-art programs on novel tasks with no prior literature. For example, we can learn programs with " + }, + { + "bbox": [ + 53, + 251, + 296, + 504 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 53, + 251, + 296, + 504 + ], + "type": "text", + "content": " lower error than the closest non-interpretable baseline for population density estimation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 525, + 135, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 525, + 135, + 538 + ], + "spans": [ + { + "bbox": [ + 56, + 525, + 135, + 538 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 545, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 295, + 665 + ], + "type": "text", + "content": "Many modern scientific workflows are built on top of visual data. Researchers in remote sensing, climate science, ecology, and other sciences use images as a window into our world to estimate population density, the amount of biomass, poverty indicators, and so on. There is a massively increasing volume of visual data, be it from an ever-expanding set of satellites, widespread camera traps, or images uploaded on the web, that is available to domain experts, and computer vision has the potential to meaningfully assist scientists in using it for scientific insight." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Scientific applications of computer vision, however, are demanding tasks because we want models that not only predict outcomes but also reveal underlying mechanisms. 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We introduce a framework to discover interpretable, predictive programs for scientific computer vision tasks." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 352, + 555, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 352, + 555, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 352, + 555, + 436 + ], + "type": "text", + "content": "to train excellent predictive models that learn the relationships between a satellite image and the population. However, understanding why certain regions are densely populated is crucial for urban planning and policy decisions — black-box predictions offer no interpretation of what makes a region have a high population. Scientists themselves want to derive insight from the models, not just predict." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 438, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 556, + 713 + ], + "type": "text", + "content": "While there have been many works that train interpretable vision models (for example concept-bottlenecks [20, 27]), these models are often limited to simple functions of primitive concepts, such as bag of words. These simple functions do not scale to the realistic complexity of our visual world and the complex relationships between its many rich scientific indicators, resulting in poor accuracy. A promising direction to model rich relationships without foregoing interpretability is to learn programs on top of conceptual primitives. Recently, code generation methods such as ViperGPT and VisProg [14, 36] have demonstrated that large language models are able to synthesize programs with competitive performance on many vision tasks, and the representations are interpretable by construction because programs are human-readable. However, while these methods work well for established vision tasks, they often fail to generalize to scientific applications of computer vision because the tasks are new and outside the scope of the training data on the internet. LLMs lack the requisite knowledge to answer novel or domain-specific questions, and as we will show, directly applying such zero-shot code generation methods on scientific domains is not effective." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29258" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 263 + ], + "type": "text", + "content": "How can we automatically discover accurate and interpretable programs from the volumes of visual data in scientific applications? This paper introduces DiSciPLE, a framework for Discovering Scientific Programs using LLMs and Evolution. Given a large dataset of images, our approach synthesizes a program to solve the task. As the name suggests, DiSciPLE introduces an evolutionary search algorithm that starts with zero-shot programs from LLMs and iteratively improves them over the dataset. The discovered programs are able to interleave neural networks, in particular open-world foundation models, for segmentation with logical and mathematical operations, enabling powerful predictions while also being interpretable. Our framework makes several improvements to integrate evolutionary search with LLMs, using program simplification and critics to provide fine-grained guidance that accelerates search." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 264, + 294, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 264, + 294, + 370 + ], + "spans": [ + { + "bbox": [ + 55, + 264, + 294, + 370 + ], + "type": "text", + "content": "In three different scientific applications of computer vision, DiSciPLE is able to learn state-of-the-art programs for novel tasks that have no prior documented solutions in existing literature. Our approach significantly outperforms neural networks at estimating population density from satellite imagery. Our method also obtains strong out-of-distribution performance at estimating a region's biomass, generalizing to geographical regions outside of the training set significantly better than all other baselines. Our contributions are:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 371, + 294, + 502 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 371, + 294, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 371, + 294, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 371, + 294, + 407 + ], + "type": "text", + "content": "- We introduce a novel framework DiSciPLE, that can produce interpretable, reliable, and sample-efficient programs for scientific discovery." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 407, + 294, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 407, + 294, + 442 + ], + "spans": [ + { + "bbox": [ + 56, + 407, + 294, + 442 + ], + "type": "text", + "content": "- We present two key components: a critic and a program simplification method to DiSciPLE that can further improve the search resulting in better programs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 443, + 294, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 443, + 294, + 502 + ], + "spans": [ + { + "bbox": [ + 56, + 443, + 294, + 502 + ], + "type": "text", + "content": "- We propose benchmarks for the task of scientific visual discovery containing real-world high-dimensional visual data for three problems in two domains. Using these benchmarks, we show that programs from DiSciPLE are more interpretable, reliable, and data-efficient." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 514, + 146, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 146, + 526 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 146, + 526 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "content": "Concept bottlenecks. Concept bottleneck [20, 32, 41] is an approach used to create interpretable-yet-powerful classifiers. The key idea is to train a deep model to predict a set of low-level concepts and then learn a linear classifier. Such concept bottlenecks are the basis in several areas such as fine-grained recognition [11, 17, 37, 44] and zero-shot learning [1, 19, 21]. However in order to train these models, expensive data is needed for the bottleneck concepts themselves. One way to reduce this annotation cost is to ask questions in an information-theoretically optimal way [2, 3]. Researchers have also automated the pipeline by using LLMs as a knowledge base to propose bottlenecks [15, 27, 33]. [4] proposed an evolutionary algorithm to discover interpretable concept bottlenecks without prior information. While these models are interpretable, they are" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 109 + ], + "type": "text", + "content": "very simple in terms of expressive power. In this work, we instead evolve interpretable programs, that are more expressive than a bag of words." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 122, + 553, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 122, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 122, + 553, + 384 + ], + "type": "text", + "content": "Symbolic regression. Symbolic regression (SR) [5] is a technique for learning equations through evolutionary search. Several methods have been proposed to improve the search efficiency [24], however, most SR techniques cannot solve problems beyond simple mathematical formulas, with simple mathematical primitives. This is partly because the solution search space becomes combinatorial larger. As a result, SR methods fail to work for images, which are high-dimensional. Our method instead focuses on problems with high-dimensional visual data, by leveraging vision foundation models as primitives. Like DiSciPLE, recent work on SR [12, 22, 28, 34] has also looked at using LLMs to better guide the search. However, these methods are only tested on lower-dimensional problems for formula discovery. We instead propose an approach that is complementary to SR. Methods for SR cannot be applied directly in higher-dimensional open-world visual problems, on the other hand on low-dimensional problems existing tools for SR [12] would perform better. The focus of this work is on such real-world problems, where the primitive functions are more complex than mathematical operations and can even be open-world, such as text-to-image segmentation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 399, + 553, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 553, + 531 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 553, + 531 + ], + "type": "text", + "content": "Neuro-Symbolic Program Learning [6, 26] is another avenue for learning programs for observation datasets or question answering. These methods typically try to learn both discrete program structures together with neural networks. However, since this optimization is nondifferentiable these methods require reinforcement learning [18] or complex non-differentiable optimization techniques [10]. The hard optimization issue makes the problem of learning programs sample inefficient in real-world settings. We alternatively use LLMs ability to program to better guide the search for such programs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 544, + 553, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 553, + 616 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 553, + 616 + ], + "type": "text", + "content": "Program synthesis with LLMs. Several works have utilized LLM coding ability in different applications such as VQA [13, 36] and robot manipulation [23]. While the zero-shot inferred code work very well on domains well-known to the internet, they tend to perform poorly on problems in scientific domains, as shown by our results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 629, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 553, + 713 + ], + "type": "text", + "content": "Scientific applications. Researchers in numerous scientific domains have used machine learning tools to build predictive models for their quantities of interest. In this work, we focus on two such scientific domain: demography and climate science. For both these domains, we use remote sensing vision-language foundation models as primitives, along with mathematical and image operators. In" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29259" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 122 + ], + "type": "text", + "content": "demography, we focus on the problems of socioeconomic indicator prediction [43], namely population density and poverty [30, 40]. In climate science we focus on the problem of aboveground biomass prediction (AGB) [31]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 130, + 138, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 130, + 138, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 130, + 138, + 144 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 151, + 296, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 151, + 296, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 151, + 296, + 224 + ], + "type": "text", + "content": "Our key contribution is a program search framework that leverages LLMs to perform evolutionary search. In Sec. 3.1 we formalize the problem of program search. In Sec. 3.2, we present our method of incorporating LLMs in this framework. Finally, in Sec. 3.3, 3.4 and 3.5, we discuss the improvements to this framework to speed-up the search." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 230, + 180, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 230, + 180, + 243 + ], + "spans": [ + { + "bbox": [ + 55, + 230, + 180, + 243 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "text", + "content": "Our system receives as input a dataset " + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x_1, y_1), (x_2, y_2), \\ldots, (x_n, y_n)\\}" + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "text", + "content": " consisting of inputs " + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "inline_equation", + "content": "x_i \\in X" + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "text", + "content": " and quantities of interest " + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "inline_equation", + "content": "y_i \\in Y" + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "text", + "content": ". For example, when estimating geospatial indicators like poverty, " + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "text", + "content": " may be a latitude and longitude, along with other metadata about that location. The system must produce an interpretable program " + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "inline_equation", + "content": "P: X \\to Y" + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "text", + "content": " that maps inputs to corresponding outputs. As is typical with standard supervised learning, we also assume a loss function or metric " + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 247, + 296, + 380 + ], + "type": "text", + "content": " that measures how good a particular prediction is, and seek a program that yields the best evaluation score:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 110, + 388, + 296, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 388, + 296, + 419 + ], + "spans": [ + { + "bbox": [ + 110, + 388, + 296, + 419 + ], + "type": "interline_equation", + "content": "s (P; \\mathcal {D}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathcal {M} \\left(P \\left(x _ {i}\\right), y _ {i}\\right) \\tag {1}", + "image_path": "7bada709242349a18db2f902c8198ffb00dab741f65040564342397c4302a10f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 426, + 295, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 426, + 295, + 463 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 295, + 463 + ], + "type": "text", + "content": "For example, in the case of population density a good metric used by domain experts is L2 error over log i.e. " + }, + { + "bbox": [ + 55, + 426, + 295, + 463 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(y', y) = ||\\log(y') - \\log(y)||_2" + }, + { + "bbox": [ + 55, + 426, + 295, + 463 + ], + "type": "text", + "content": " [29, 30]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": "For our programs to be interpretable, they must put together modules or primitives in an interpretable way. We conceptualize these primitives as a library of functions " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F} = \\{f_1, f_2 \\ldots f_k\\}" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ", that can be used to construct a program " + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 463, + 296, + 714 + ], + "type": "text", + "content": ". Given that we are analyzing visual data, a key primitive will be an open-vocabulary recognition model that is applied to images associated with a data point. For example, when estimating poverty for a location, we can define a primitive that queries the satellite images available at that location and uses an open-vocabulary recognition engine [25] to detect various concepts. Recent advances in recognition have produced such foundation models for a range of modalities [25, 35]. In addition, we will assume basic mathematical, logical and image operators such as logarithms, elementwise maximum, or a distance transform. We note that the set of primitives is often not specific to the task and can be shared across a range of problems in a domain. That said, the set of primitives can be expanded upon if needed by domain experts for particular problems; for example, a climate scientist may want to include a function that can look up the average temperature at a particular place and time." + } + ] + } + ], + "index": 7 + }, + { + "type": "code", + "bbox": [ + 316, + 88, + 553, + 462 + ], + "blocks": [ + { + "bbox": [ + 321, + 75, + 484, + 87 + ], + "lines": [ + { + "bbox": [ + 321, + 75, + 484, + 87 + ], + "spans": [ + { + "bbox": [ + 321, + 75, + 484, + 87 + ], + "type": "text", + "content": "Algorithm 1: DiSciPLE's learning loop" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "lines": [ + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "spans": [ + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": "Input: Observation set " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x_1,y_1),(x_2,y_2),\\ldots ,(x_n,y_n)\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " , metric " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " , an objective prompt " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " , a set of primitive function " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{F} = \\{f_1,f_2\\dots f_k\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " Hyperparams : Mutation probability " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "\\rho_{m}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " total generations " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " population size " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " crossover " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "p_c" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " and mutation " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " prompts. Output: A program " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "P^{*}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " in the form of a program that explains the observations best. \n1 " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "B^0\\gets \\{\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " // Initialize a programs bank \n2 for " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "i = 1,\\dots ,M" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " do \n3 " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "\\begin{array}{r}P_i^0\\leftarrow \\mathcal{L}\\mathcal{L}\\mathcal{M}(p_o)\\\\ B^0\\leftarrow B^0\\cup \\{P_i^0\\} \\end{array}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " \n4 \n5 " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "P^{*}\\gets P_{i}^{0}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " // Evolution loop \n6 for " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "t = 0,\\dots ,T" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " do \n7 " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "B^{t + 1}\\gets \\{\\}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " \n8 for " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "i = 1,\\dots ,M" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " do \n9 " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "P_{k_1}^t,P_{k_2}^t\\gets" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " sample_parents " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "(B_{t}) / /" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " Sample parents for crossover " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "P_{i}^{t + 1}\\gets" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}\\mathcal{L}\\mathcal{M}(P_{k_1}^t,P_{k_2}^t,s(P_{k_1}^t;\\mathcal{D}),s(P_{k_2}^t;\\mathcal{D}),p_o,p_c)" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " // crossover operation \n11 if " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "u\\sim \\mathcal{U}(0,1) < \\rho_m" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " then \n12 " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "\\begin{array}{r}\\Bigl {\\backslash}P_i^{t + 1}\\gets \\mathcal{L}\\mathcal{L}\\mathcal{M}(P_k^{t + 1},s(P_k^{t + 1};\\mathcal{D}),p_o,p_m)\\\\ //\\text{mutation operation}\\\\ //\\text{critique and simplification}\\\\ P_i^{t + 1}\\gets \\text{critic}(P_i^{t + 1})P_i^{t + 1}\\gets \\text{simplifier}(P_i^{t + 1})\\\\ P^*\\gets P_i^{t + 1}\\\\ B^{t + 1}\\gets B^{t + 1}\\cup \\{P_i^{t + 1}\\} \\end{array}" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " \n13 \n14 if " + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "inline_equation", + "content": "s(P_i^{t + 1};\\mathcal{D}) > s(P^*;\\mathcal{D})" + }, + { + "bbox": [ + 316, + 88, + 553, + 462 + ], + "type": "text", + "content": " then \n15 \n16" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_body" + } + ], + "index": 9, + "sub_type": "algorithm" + }, + { + "bbox": [ + 313, + 485, + 555, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 555, + 557 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 555, + 557 + ], + "type": "text", + "content": "Finally, to enable us to effectively search the programs space and leverage the conceptual understanding of LLMs, we assume that we have a natural language description desc of the quantity of interest " + }, + { + "bbox": [ + 313, + 485, + 555, + 557 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 313, + 485, + 555, + 557 + ], + "type": "text", + "content": ". For example, this may be the phrase \"population density\". As we will see, this information is useful in guiding the LLM to search the space." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "text", + "content": "Putting everything together, our proposed system, DiS-ciPLE (Discovering Scientific Programs using LLMs and Evolution), takes as input the dataset " + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "text", + "content": ", the metric " + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "text", + "content": ", the set of primitives " + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "text", + "content": " and the textual description desc. It produces an interpretable and accurate program " + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "text", + "content": " that maps inputs " + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "text", + "content": " to the output quantity of interest " + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 313, + 557, + 555, + 629 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 635, + 499, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 499, + 649 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 499, + 649 + ], + "type": "text", + "content": "3.2. Evolutionary Search for Programs" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 653, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 555, + 715 + ], + "type": "text", + "content": "To search through the vast, discrete space of programs, DiS-ciPLE adapts evolutionary search. Evolutionary program search typically starts with a large population of random programs. These programs are then sampled based on their fitness as parents. The parent programs create a new popu" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "29260" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 553, + 289 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 553, + 289 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 553, + 289 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 553, + 289 + ], + "type": "image", + "image_path": "b59e300c314a83c954cdb2539ea698a67ed082c08e2520d712aa28d66a6c6097.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 297, + 555, + 344 + ], + "lines": [ + { + "bbox": [ + 54, + 297, + 555, + 344 + ], + "spans": [ + { + "bbox": [ + 54, + 297, + 555, + 344 + ], + "type": "text", + "content": "Figure 2. Overview of our evolutionary algorithm with critic and simplification. We start with a population of programs to solve a task. We sample pairs of programs based on their fitness score and perform crossover/mutations over them to produce new programs. The generated program is further improved by passing it through a critic and then an analytical simplification step. This program is then evaluated and put in the next generation of programs. The evaluation score of the program is used to determine the fitness for the next generation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 363, + 295, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 363, + 295, + 410 + ], + "spans": [ + { + "bbox": [ + 54, + 363, + 295, + 410 + ], + "type": "text", + "content": "lation of programs through crossover and mutation. Newer generations improve over the previous as the population is getting optimized for the fitness function. We use the metric " + }, + { + "bbox": [ + 54, + 363, + 295, + 410 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 54, + 363, + 295, + 410 + ], + "type": "text", + "content": " as the fitness function in our work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "type": "text", + "content": "We keep the overall evolutionary algorithm the same and replace key steps with an LLM. First, we provide the LLM with a prompt for the objective to generate initial programs. To leverage the prior knowledge of LLMs, we use a prompt " + }, + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "type": "text", + "content": " that mentions the specified description of the quantity of interest: \"Given a satellite image, write a function to estimate " + }, + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "type": "inline_equation", + "content": "\\langle desc \\rangle" + }, + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "type": "text", + "content": "\". We do not expect the LLM to answer such a difficult scientific question without leveraging the observations " + }, + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 54, + 411, + 295, + 544 + ], + "type": "text", + "content": "; however, the prompt prevents the evolutionary algorithm from searching in completely random directions. As a result, our initial population is not entirely random." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "content": "Second, instead of using symbolic methods for crossover/mutation, we use an LLM to perform these operations. LLMs have common sense about programming, resulting in better modifications when performing these operations. More specifically, let " + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "inline_equation", + "content": "P_{k_1}^t" + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "inline_equation", + "content": "P_{k_2}^t" + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "content": " be two programs sampled from the " + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "inline_equation", + "content": "t^{th}" + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "content": " generation selected as parents based on the fitness function. To perform a crossover operation we pass, the objective prompt " + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "content": ", the two programs " + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "inline_equation", + "content": "P_{k_1}^t" + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "inline_equation", + "content": "P_{k_2}^t" + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "content": ", their corresponding scores (using Eq. (1)), along with a crossover prompt " + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "inline_equation", + "content": "p_c" + }, + { + "bbox": [ + 55, + 544, + 295, + 666 + ], + "type": "text", + "content": " to obtain a new program:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 64, + 675, + 295, + 700 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 675, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 64, + 675, + 295, + 700 + ], + "type": "interline_equation", + "content": "P _ {k} ^ {t + 1} = \\mathcal {L L M} \\left(P _ {k _ {1}} ^ {t}, P _ {k _ {2}} ^ {t}, s \\left(P _ {k _ {1}} ^ {t}; \\mathcal {D}\\right), s \\left(P _ {k _ {2}} ^ {t}; \\mathcal {D}\\right), p _ {o}, p _ {c}\\right) \\tag {2}", + "image_path": "8a1339d4b61d8442ccf7e3780662c111f9be0187c3a64d315a56a3c730dea86d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "type": "text", + "content": "The crossover prompt instructs the LLM to make use of" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 364, + 555, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 555, + 424 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 555, + 424 + ], + "type": "text", + "content": "the two-parent programs to come up with a new program. The LLM is able to combine elements from the parents to produce something new (see Fig. 2). Plase refer to the supplementary for more examples. We also mutate a program with some probability using a mutation prompt " + }, + { + "bbox": [ + 313, + 364, + 555, + 424 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 313, + 364, + 555, + 424 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 343, + 441, + 553, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 441, + 553, + 456 + ], + "spans": [ + { + "bbox": [ + 343, + 441, + 553, + 456 + ], + "type": "interline_equation", + "content": "{ } ^ { m } P _ { k } ^ { t + 1 } = \\mathcal { L L M } ( P _ { k } ^ { t + 1 } , s ( P _ { k } ^ { t + 1 } ; \\mathcal { D } ) , p _ { o } , p _ { m } ) \\tag {3}", + "image_path": "99bd9b9248ebd7012683601576d50b5ed221f1339bf43e58d7d673b9400092ed.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 463, + 555, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 463, + 555, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 463, + 555, + 510 + ], + "type": "text", + "content": "We present the exact prompts for crossover and mutation in the supplementary. Note that both operations also include the objective prompt preventing the LLM from generating programs far away from the objective." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 517, + 441, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 441, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 441, + 528 + ], + "type": "text", + "content": "3.3. Feature Set Prediction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 534, + 555, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 643 + ], + "type": "text", + "content": "Solutions for many problems require a combination of multiple features. Optimizing for the correct combination of features is challenging for an LLM, as we are not doing gradient-based optimization. Therefore instead of prompting the LLM to directly generate a predictor for " + }, + { + "bbox": [ + 313, + 534, + 555, + 643 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 534, + 555, + 643 + ], + "type": "text", + "content": ", we prompt it to create a list of predictive features. We then learn a regressor on top of this list and use both of them as the final program. Since both the program and regressor are interpretable, our final program is also interpretable." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 648, + 409, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 409, + 660 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 409, + 660 + ], + "type": "text", + "content": "3.4. Program Critic" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": "The only form of supervision our method gets is the score " + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "inline_equation", + "content": "s(P; \\mathcal{D})" + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": " by evaluating the program " + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": " on observations. However, since we perform crossover and mutation through an LLM, we can provide finer information to aid the search." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29261" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 156 + ], + "type": "text", + "content": "More specifically, we propose a critic that performs a finer-grained evaluation of the program that we get after crossover/mutation. In most visual domains, the data can categorically distributed by using the same set of foundational primitives. Our critic performs a stratified evaluation by partitioning the observation data into multiple categories and evaluating the program on individual strata." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 167, + 295, + 180 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 167, + 295, + 180 + ], + "spans": [ + { + "bbox": [ + 61, + 167, + 295, + 180 + ], + "type": "interline_equation", + "content": "\\mathcal {D} = d _ {1} \\cup d _ {2} \\cup \\dots \\cup d _ {c}, \\quad \\text {w h e r e} d _ {i} \\cap d _ {j} = \\emptyset \\text {f o r} i \\neq j \\tag {4}", + "image_path": "901331ba75d18c94f62bb3fe830fdda2681cce5a7f3430d4f3d96f0d94586635.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 191, + 296, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 191, + 296, + 288 + ], + "spans": [ + { + "bbox": [ + 55, + 191, + 296, + 288 + ], + "type": "text", + "content": "Since all the problems in our benchmark are geospatial, we use a critic that takes the satellite image corresponding to each input and uses a segmentation model to partition the observation dataset into land-use categories. The critic obtains per-partition score " + }, + { + "bbox": [ + 55, + 191, + 296, + 288 + ], + "type": "inline_equation", + "content": "s(P; d_i)" + }, + { + "bbox": [ + 55, + 191, + 296, + 288 + ], + "type": "text", + "content": " and prompts the LLM to improve the program on categories the model is bad. The addition of a critic improves the programs on data overlooked by existing programs, resulting in reliable programs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 297, + 188, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 297, + 188, + 309 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 188, + 309 + ], + "type": "text", + "content": "3.5. Program Simplification" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 315, + 296, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 315, + 296, + 457 + ], + "spans": [ + { + "bbox": [ + 55, + 315, + 296, + 457 + ], + "type": "text", + "content": "Successive steps of crossovers and mutations of programs result in large programs with many redundancies, hurting interpretability. We propose an analytical approach to simplify the programs and remove the redundant parts of it. Our generated programs can be represented as a directed acyclic graphs (DAG) (we use the abstract syntax tree (AST); see supplementary). In these DAGs, all the constants and the arguments of the function are root nodes. Only the return statement and the unused variables are the leaf nodes. Any leaf node that is not a return statement, is a piece of code that is not needed and can be removed. We then recursively remove all the leaf nodes that are not return statements." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 459, + 296, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 296, + 626 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 296, + 626 + ], + "type": "text", + "content": "While removing such nodes (unreachable by the return statement) is useful, there could still be features that do not contribute but are returned by the program. Recall that we use linear regression on the list of features. The weights assigned to individual features by the regression model are useful indicators of which features are redundant. We remove the features that have a significantly smaller weight compared to the largest weight (a threshold of " + }, + { + "bbox": [ + 55, + 459, + 296, + 626 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 55, + 459, + 296, + 626 + ], + "type": "text", + "content": " works well). Removing these features from the return statement results in several newly created leaf nodes. We therefore, redo the recursive leaf node removal to simplify the program further. Each generated program is first improved through the critic and then simplified before adding back to the population. Algorithm 1 shows the complete process." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 639, + 108, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 639, + 108, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 639, + 108, + 651 + ], + "type": "text", + "content": "4. Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 659, + 186, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 659, + 186, + 672 + ], + "spans": [ + { + "bbox": [ + 55, + 659, + 186, + 672 + ], + "type": "text", + "content": "4.1. Implementation details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "For all our main experiments we used an open-source LLM llama-3-8b-instruct [9]. However, in the supplementary, we also explore other open-source language models. All" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 69, + 553, + 167 + ], + "blocks": [ + { + "bbox": [ + 317, + 69, + 553, + 167 + ], + "lines": [ + { + "bbox": [ + 317, + 69, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 317, + 69, + 553, + 167 + ], + "type": "image", + "image_path": "98a33248b20d2a617b5ffccfbcf8e22c8822cb6653aed7046cefc9e927382cf7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 316, + 169, + 553, + 265 + ], + "blocks": [ + { + "bbox": [ + 316, + 169, + 553, + 265 + ], + "lines": [ + { + "bbox": [ + 316, + 169, + 553, + 265 + ], + "spans": [ + { + "bbox": [ + 316, + 169, + 553, + 265 + ], + "type": "image", + "image_path": "00a718972c6f377c0e6cead23e5da70fe1794e0d7f4442bd9439c858b86290fd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 317, + 268, + 553, + 365 + ], + "blocks": [ + { + "bbox": [ + 317, + 268, + 553, + 365 + ], + "lines": [ + { + "bbox": [ + 317, + 268, + 553, + 365 + ], + "spans": [ + { + "bbox": [ + 317, + 268, + 553, + 365 + ], + "type": "image", + "image_path": "2731187ffb8201584adaaf3f92982b6c9ea921218c62d81b121c6ea63f997448.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 373, + 555, + 461 + ], + "lines": [ + { + "bbox": [ + 313, + 373, + 555, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 555, + 461 + ], + "type": "text", + "content": "Figure 3. The best-performing programs the 3 benchmark problems as Python programs (left) and the corresponding DAG representation (right). The DAG representation allows better visualization of the importance of different components. The thickness of the red edges shows the importance of a component. Black edges represent cases when measuring influences is unnecessary. This occurs when removing the connection results in bugs or for a single input/output node. For finer details, refer to the digital version." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 483, + 554, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 554, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 554, + 555 + ], + "type": "text", + "content": "the visual data in our benchmarks comes from satellite images, so to allow inferring semantic information from it, we use a black-box open-world foundational model for satellite images, GRAFT [25]. Some experiments use ground-truth annotations from OpenStreetMaps [39] as an alternative to disentangle the effect of segmentation from discovery." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 555, + 554, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 554, + 651 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 554, + 651 + ], + "type": "text", + "content": "We run our evolutionary method for " + }, + { + "bbox": [ + 313, + 555, + 554, + 651 + ], + "type": "inline_equation", + "content": "T = 15" + }, + { + "bbox": [ + 313, + 555, + 554, + 651 + ], + "type": "text", + "content": " generations with a population size of " + }, + { + "bbox": [ + 313, + 555, + 554, + 651 + ], + "type": "inline_equation", + "content": "M = 100" + }, + { + "bbox": [ + 313, + 555, + 554, + 651 + ], + "type": "text", + "content": ". For all the problems, the input observation is from different locations around the world. We split this data into three parts. Two-thirds of the easternmost observations are used to create a training-testing split. The remaining one-third of the data is used to evaluate reliability (out-of-distribution generalization). We also release this benchmark for future research in this area." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 659, + 553, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 553, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 553, + 685 + ], + "type": "text", + "content": "4.2. Benchmark for Visual Program Discovery for Scientific Applications" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "Given the novelty of the visual program discovery task, there exists no pre-existing benchmark. We define a new" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29262" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 119 + ], + "type": "text", + "content": "benchmark for this task, drawing on scientifically relevant geospatial problems. Concretely, we choose two different problems in Demography: population density and poverty indicators, and in Climate Science: AGB estimation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 294, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 294, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 294, + 240 + ], + "type": "text", + "content": "It is important to note that for these problems, true relationships between variables of interest are unknown. As such, an LLM cannot be expected to produce a good program in a zero-shot manner, as it has never seen these relationships before. This is in contrast to problems like VQA [36] where the reasoning required to answer a question is well-known and we can simply rely on the LLM's world knowledge. For scientific discovery, actual data is needed to discover the right reasoning. We next present the observation datasets, metrics, and overview of primitives." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 247, + 165, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 165, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 165, + 258 + ], + "type": "text", + "content": "4.2.1. Population Density" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "type": "text", + "content": "Observation Dataset: The problem seeks to predict the population density by observing the satellite images of a region [29, 30]. We obtain the population density values " + }, + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "type": "inline_equation", + "content": "(y_{i})" + }, + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "type": "text", + "content": " for various locations in the USA by using ACS Community Surveys 5-year estimates [38]. Input observations " + }, + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "type": "inline_equation", + "content": "(x_{i})" + }, + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "type": "text", + "content": " are sentinel-2 images at a resolution of " + }, + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "type": "inline_equation", + "content": "10\\mathrm{m}" + }, + { + "bbox": [ + 55, + 262, + 294, + 357 + ], + "type": "text", + "content": " [7]. For this experiment, we also use OpenStreetMap masks [39] for 42 land-use concepts (see supplementary) as part of the input." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 358, + 294, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 358, + 294, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 358, + 294, + 453 + ], + "type": "text", + "content": "Metric and Primitives: Population density values are aggregated at the county block group level. The predicted population densities are thus also aggregated at this level. The metric is the per-block group averaged L2 error after applying a log transformation. Along with the arithmetic, and logical primitives (see supplementary), we use open-vocabulary segmentation as a primitive. The segmentation function returns a binary mask for an input concept." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 460, + 160, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 460, + 160, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 460, + 160, + 472 + ], + "type": "text", + "content": "4.2.2. Poverty Indicator" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 475, + 294, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 294, + 511 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 294, + 511 + ], + "type": "text", + "content": "Observation Dataset: For poverty estimation, we use data from SustainBench [42]. The dataset contains coordinate location as input and wealth asset index as output." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 512, + 294, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 512, + 294, + 619 + ], + "spans": [ + { + "bbox": [ + 55, + 512, + 294, + 619 + ], + "type": "text", + "content": "Metric and Primitives: We use L2 error for each location as the evaluation metric. To obtain semantic land use information about a location, we first define a get_satellite_image function, that returns a satellite image for any location. This can be used in conjunction with the open-world satellite image recognition model to obtain semantic information. Moreover, we also include primitives that return average annual temperature, precipitation, nightlight intensity, and elevation at the input location." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 627, + 180, + 638 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 627, + 180, + 638 + ], + "spans": [ + { + "bbox": [ + 55, + 627, + 180, + 638 + ], + "type": "text", + "content": "4.2.3. Aboveground Biomass" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 642, + 294, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 294, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 294, + 712 + ], + "type": "text", + "content": "Observation Dataset: Similar to poverty estimation, the observation variables are an input location and the output AGB estimate. We use NASA's GEDI [8] to obtain the observation value for three US states. We use data from Massachusetts and Maine (North-East) as the train/test set and Washington (NorthWest) as the out-of-distribution set." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "Metric and Primitives: We use L2 error as the metric and the same primitives as poverty estimation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 104, + 430, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 104, + 430, + 118 + ], + "spans": [ + { + "bbox": [ + 314, + 104, + 430, + 118 + ], + "type": "text", + "content": "4.3. Experimental Setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 121, + 553, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 121, + 553, + 145 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 553, + 145 + ], + "type": "text", + "content": "For the same set of training data we compare our best generated program with a set of baselines." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 146, + 553, + 384 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 315, + 146, + 553, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 146, + 553, + 169 + ], + "spans": [ + { + "bbox": [ + 315, + 146, + 553, + 169 + ], + "type": "text", + "content": "1. Mean: A naive baseline that use the mean of the training observation as the prediction." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 170, + 553, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 170, + 553, + 217 + ], + "spans": [ + { + "bbox": [ + 315, + 170, + 553, + 217 + ], + "type": "text", + "content": "2. Concept Bottleneck (CB): Similar to [20, 32, 41], we first extract a list of relevant features and train classifiers on them. CB is interpretable due to the bottleneck, however, it is not very expressive (see supplementary)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 218, + 553, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 218, + 553, + 265 + ], + "spans": [ + { + "bbox": [ + 315, + 218, + 553, + 265 + ], + "type": "text", + "content": "3. Deep models: We use deep models such as ResNets [16] as baseline. We use a small and large variant for each. Please refer to the supplementary for more details and comparisons to other deep models such as transformers." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 266, + 553, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 266, + 553, + 325 + ], + "spans": [ + { + "bbox": [ + 315, + 266, + 553, + 325 + ], + "type": "text", + "content": "4. Zero-shot: This baseline tests how good would LLMs be on their own in generating programs solely relying on prior knowledge without any observation. Since the generated programs can vary drastically, we report an average of 5 different zero-shot programs." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 325, + 553, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 325, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 315, + 325, + 553, + 384 + ], + "type": "text", + "content": "5. Random Search: Instead of evolutionary search, this baseline relies on the stochasticity of LLMs to perform a random search. If DiSciPLE is better at searching, it should do better than random searching for the same number of calls to an LLM." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 393, + 443, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 393, + 443, + 404 + ], + "spans": [ + { + "bbox": [ + 314, + 393, + 443, + 404 + ], + "type": "text", + "content": "4.4. Results and Discussion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 411, + 555, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 555, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 555, + 578 + ], + "type": "text", + "content": "We first test our programs on unseen in-domain observations close to the regions used for training (Tab. 1 (left)). We observe that DiSciPLE outperforms all interpretable baselines. It can even outperform a deep model in many cases, specifically on population density estimation, while being more interpretable. DiSciPLE also outperforms zero-shot program inference from LLMs. As discussed before, this is in line with the fact that DiSciPLEis uncovering new relationships that may not be known to us, and by extension, to the LLM. The performance of random search while better than zero-shot is significantly worse than DiSciPLE. This shows that DiSciPLE is able to perform a faster search, by only searching in a meaningful space. DiSciPLE effectively leverages data to perform this novel discovery." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 594, + 553, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 553, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 553, + 677 + ], + "type": "text", + "content": "Are our programs reliable? If a program is reliable, it should be able to generalize to other regions. Tab. 1 (right) shows DiSciPLE's performance on such an out-of-distribution set. Here DiSciPLE outperforms all baselines including deep networks. This suggests that we can learn a model that generalizes better to the in-distribution training data, due to its interpretable-by-design representation." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "We also show these results qualitatively in Fig. 4, by comparing population density predictions of DiSciPLE and the baselines to the true population density. DiS" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29263" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 102, + 565, + 222 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 94 + ], + "type": "text", + "content": "Table 1. Performance of our programs on in-distribution (left) and out-of-distribution (right) observations across various problems in the proposed benchmark. This shows the reliability of programs produced by DiSciPLE (red is best and blue is second best)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 102, + 565, + 222 + ], + "lines": [ + { + "bbox": [ + 56, + 102, + 565, + 222 + ], + "spans": [ + { + "bbox": [ + 56, + 102, + 565, + 222 + ], + "type": "table", + "html": "
    Population DensityIn distributionOOD
    PovertyAGBPopulation DensityPovertyAGB
    L2-LogL1-LogL1RMSEL1RMSEL2-LogL1-LogL1RMSEL1RMSE
    Mean0.66960.65401.6131.83642.1550.650.67340.65611.5911.84474.1583.02
    CB0.82980.72791.2291.47626.3333.490.79510.71121.2571.50444.1963.52
    Deep - Small0.44310.50061.2381.63730.7237.030.66230.59671.2841.65435.2753.06
    Deep - Large0.39740.48431.1701.47821.1527.860.44600.51151.3441.74135.4170.30
    Zero-shot0.47020.53711.5251.75438.8046.410.70200.64121.5101.77355.1164.32
    Random Search0.43530.51181.2771.67929.4036.700.67630.62981.4181.84042.3252.53
    Ours0.26070.37781.0771.31424.7932.990.38070.44261.1341.42031.1042.93
    ", + "image_path": "ad9454e87aaf4ce8985c931a4c3b4f40c6a234b0ec8137fb8732805b5dc97924.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 59, + 242, + 293, + 389 + ], + "blocks": [ + { + "bbox": [ + 59, + 242, + 293, + 389 + ], + "lines": [ + { + "bbox": [ + 59, + 242, + 293, + 389 + ], + "spans": [ + { + "bbox": [ + 59, + 242, + 293, + 389 + ], + "type": "image", + "image_path": "bbf362d544a495c5e8d99219c2278803d904b668133d9ace316e7a010063648b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 398, + 296, + 453 + ], + "lines": [ + { + "bbox": [ + 55, + 398, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 398, + 296, + 453 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of DiSciPLE with other baselines on the tasks of population density. DiSciPLE Can map to the true population density maps much more accurately than the baselines (Refer to the supplementary for more comparisons). The maps display population density as the base-10 log of people/mi²." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 296, + 513 + ], + "type": "text", + "content": "ciPLE can model the fine-grained changes in population in unseen regions significantly better than the baselines (refer to supplementary for comparison to other baselines)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 528, + 295, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 528, + 295, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 528, + 295, + 613 + ], + "type": "text", + "content": "Are our programs data-efficient? Our methods are only trained on a maximum of 4000 observations. Fig. 5 further shows that even with a smaller amount of training data, our approach shows minimal degradation compared to deep networks. This suggests that while deep models can generalize with a lot more data, our model does not need as much data to begin with, making it data-efficient." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 629, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 295, + 700 + ], + "type": "text", + "content": "Are our programs interpretable? Our programs are interpretable-by-design as we can visualize the contributing factors. Fig. 3 shows such programs (left) for the problems in our benchmark. An expert working with DiSciPLE to figure out such programs can edit parts of the program and figure out how much do the components matters." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 296, + 713 + ], + "type": "text", + "content": "We perform this step of understanding the influence of" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 245, + 555, + 332 + ], + "blocks": [ + { + "bbox": [ + 316, + 245, + 555, + 332 + ], + "lines": [ + { + "bbox": [ + 316, + 245, + 555, + 332 + ], + "spans": [ + { + "bbox": [ + 316, + 245, + 555, + 332 + ], + "type": "image", + "image_path": "7252e5736f37d64ebcd118e4a5491da14aa2177ea357a696603c4ab8eb32a51c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 334, + 553, + 422 + ], + "blocks": [ + { + "bbox": [ + 317, + 334, + 553, + 422 + ], + "lines": [ + { + "bbox": [ + 317, + 334, + 553, + 422 + ], + "spans": [ + { + "bbox": [ + 317, + 334, + 553, + 422 + ], + "type": "image", + "image_path": "b4f798ad7b7be7f2af08a9e8d89abf1e16b56cbfc81b15fdd3603e0ca5edf839.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 429, + 555, + 495 + ], + "lines": [ + { + "bbox": [ + 313, + 429, + 555, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 429, + 555, + 495 + ], + "type": "text", + "content": "Figure 5. Performance of DiSciPLE compared to deep model as we reduce the amount of training observation (L2 error). The Oracle (blue) uses a program learned from all observations but uses only partial observation for parameter training. While the errors get worse as we reduce the observation data, the drop is significantly less severe for DiSciPLE compared to deep models." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "content": "individual operations by removing each operation in our program and measuring its effects on the final score. The DAGs on the right of each program show the program structure and the red edges show the influence of each component proportional to the width. This visualization can allow experts to understand which operations are important for the model. For example, in the program for population density Fig. 3, we can see that semantic concepts such as \"highway\" and \"residential building\" are very important." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 556, + 713 + ], + "type": "text", + "content": "Can our method perform better than expert humans? Our method would only be useful in real-world scenarios if it could come up with stronger or comparable programs to human experts. We test this on the task of AGB, by providing 2 experts (PhD students actively working on AGB) with a user interface with the same information as our method." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "29264" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 112, + 299, + 186 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 297, + 104 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 297, + 104 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 297, + 104 + ], + "type": "text", + "content": "Table 2. Performance of our method as we successively remove the components. Both critic and simplification lead to performance improvement for our method." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 112, + 299, + 186 + ], + "lines": [ + { + "bbox": [ + 55, + 112, + 299, + 186 + ], + "spans": [ + { + "bbox": [ + 55, + 112, + 299, + 186 + ], + "type": "table", + "html": "
    SetCriticSimpli.TestOOD
    L2 logL1 logL2 logL1 log
    XXX0.31590.42960.48350.5178
    ✓XX0.29060.40490.42580.4826
    ✓✓X0.28730.39840.41840.4684
    ✓✓✓0.26070.37780.38070.4426
    ", + "image_path": "991eec9dbf77669d0b68f5c77028a80bb41d628abfc7db38f40314f2633e0ec7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 206, + 297, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 206, + 297, + 351 + ], + "spans": [ + { + "bbox": [ + 54, + 206, + 297, + 351 + ], + "type": "text", + "content": "Note that finding experts actively working on difficult scientific problems is challenging. Given this constraint, experiments with 2 experts provide a feasible and insightful evaluation. The experts took about 1.5 hours to use their domain knowledge and iterate over programs for AGB. However, the best program they could come up with had an L1 error of 34.48 on the in-distribution set and 52.85 on the OOD set (compared to 24.79 and 31.10 for DiSciPLE). We figure this is primarily because experts need to spend more time on the problem. In general, experts would spend numerous days to come up with a good program, while our method can come up with a better program faster." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 357, + 124, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 124, + 370 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 124, + 370 + ], + "type": "text", + "content": "4.5. Ablations" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 375, + 296, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 375, + 296, + 533 + ], + "spans": [ + { + "bbox": [ + 54, + 375, + 296, + 533 + ], + "type": "text", + "content": "How important is the role of feature-set prediction, critic, and simplification? Table 2 measures the performance of our model on the task of population density as we successively add these components to the evolutionary algorithm. The addition of feature set prediction instead of a single feature helps, as it allows our method to learn expressive linear regression parameters instead of letting the LLM come up with them. Further adding the critic results in further improvement as programs start covering richer concepts resulting in better generalization. Finally adding simplification also improves the program. We posit that simplification removes irrelevant features preventing the LLM from focusing on them when performing crossovers." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 545, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 545, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 545, + 297, + 715 + ], + "type": "text", + "content": "How important are common sense and prior knowledge of LLMs? The two major advantages an LLM provides over traditional tree-search are: 1) better crossover and mutation as LLMs can understand the meaning of the primitives. 2) use of prior knowledge for better-guided search. Therefore we remove these two sources of information and test how well can our method perform. To remove the understanding of functions we rename them with meaningless terms and remove the descriptions. To remove the context of the problem we remove the objective prompt. Tab. 3, show the performance of our method on density estimation after removing each of these prompts. Without common sense, the search cannot even progress away from the initial random programs, resulting in worse-than-mean results" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 354, + 135, + 515, + 186 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 555, + 127 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 555, + 127 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 555, + 127 + ], + "type": "text", + "content": "Table 3. Performance of our method when removing the context of the problem (objective prompt from the evolution, and when renaming and not describing the primitive functions). We see significant drops in performance, suggesting that both common sense and prior knowledge are important to perform an efficient search." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 354, + 135, + 515, + 186 + ], + "lines": [ + { + "bbox": [ + 354, + 135, + 515, + 186 + ], + "spans": [ + { + "bbox": [ + 354, + 135, + 515, + 186 + ], + "type": "table", + "html": "
    MethodL1 logL2 log
    No common-sense0.84010.7186
    No problem context0.44980.5140
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    ", + "image_path": "82d94e5fa086891816c681eb1d2cdc86f6f449ffe04404a02b295c9365e11f6b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 206, + 556, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 206, + 556, + 291 + ], + "spans": [ + { + "bbox": [ + 313, + 206, + 556, + 291 + ], + "type": "text", + "content": "(L1 error of 0.84 vs 0.26 for DiSciPLE). This suggests that symbolic regression models, that have no understanding of open-world primitives, would struggle to search. If we just remove the context of the problem, the model does slightly better and can obtain results better than the mean and zero-shot programs (L1 error of 0.45). This suggests that while the search is moving in the objective's direction, it is slow." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 300, + 468, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 468, + 314 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 468, + 314 + ], + "type": "text", + "content": "5. Discussion and Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 321, + 556, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 321, + 556, + 453 + ], + "spans": [ + { + "bbox": [ + 313, + 321, + 556, + 453 + ], + "type": "text", + "content": "Limitations: One of our limitation is that we can only differentiably optimize learnable parameters in the last computational layer. This could miss out on programs with useful parameters in some intermediate computation layers. We attempted to make the whole pipeline differentiable, however the model performance did not improve much. Many of the operations in our pipeline even though differentiable have zero-gradient in large part of input space, making gradient optimization challenging. In future work, we plan to use initialization tricks for non-linear optimization and second-order optimization to obtain even more expressive models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 467, + 556, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 556, + 600 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 556, + 600 + ], + "type": "text", + "content": "Conclusion: We present DiSciPLE - an evolutionary algorithm that leverages the prior-knowledge and common sense abilities of LLMs to create interpretable, reliable and data-efficient programs for real-world scientific visual data. This allows us to create programs that are more powerful than existing interpretable counterparts and more insightful than deeper uninterpretable models. We show its prowess on 3 scientific applications by proposing a benchmark for visual program discovery. We believe that using DiSciPLE in tandem with a human expert can rapidly speed up the scientific process and result in numerous novel discoveries." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 613, + 556, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 556, + 711 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 556, + 711 + ], + "type": "text", + "content": "Acknowledgements This research is based upon work supported in part by the ODNI-IARPA via 2021-20111000006, the NSF STC-LEAP, the U.S. DARPA ECOLE Program No. #HR00112390060 and NSF grants 2403015 and 2403016. This work would not have been possible without the help from domain experts. 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In ECCV, 2018. 2" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "29267" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/3a6773a0-380b-4fb7-a04b-955503269a41_content_list.json b/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/3a6773a0-380b-4fb7-a04b-955503269a41_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ebf178648823ba1100683088560871b108cd28fc --- /dev/null +++ b/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/3a6773a0-380b-4fb7-a04b-955503269a41_content_list.json @@ -0,0 +1,1619 @@ +[ + { + "type": "text", + "text": "DITASK: Multi-Task Fine-Tuning with Diffeomorphic Transformations", + "text_level": 1, + "bbox": [ + 135, + 130, + 861, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Krishna Sri Ipsit Mantri Purdue University West Lafayette, USA mantrik@purdue.edu", + "bbox": [ + 169, + 180, + 362, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Carola-Bibiane Schonlieb \nUniversity of Cambridge \nCambridge, UK \ncbs31@cam.ac.uk", + "bbox": [ + 405, + 180, + 609, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bruno Ribeiro Purdue University West Lafayette, USA ribeirob@purdue.edu", + "bbox": [ + 655, + 181, + 825, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chaim Baskin \nBen-Gurion University of the Negev \nBeer Sheva, Israel \nchaimbaskin@bgu.ac.il", + "bbox": [ + 228, + 258, + 517, + 329 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Moshe Eliasof \nUniversity of Cambridge \nCambridge, UK \nme532@cam.ac.uk", + "bbox": [ + 570, + 258, + 769, + 328 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 259, + 364, + 336, + 380 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pre-trained Vision Transformers now serve as powerful tools for computer vision. Yet, efficiently adapting them for multiple tasks remains a challenge that arises from the need to modify the rich hidden representations encoded by the learned weight matrices, without inducing interference between tasks. Current parameter-efficient methods like LoRA, which apply low-rank updates, force tasks to compete within constrained subspaces, ultimately degrading performance. We introduce DITASK a novel Diffeomorphic Multi-Task Fine-Tuning approach that maintains pre-trained representations by preserving weight matrix singular vectors, while enabling task-specific adaptations through neural diffeomorphic transformations of the singular values. By following this approach, DITASK enables both shared and task-specific feature modulations with minimal added parameters. Our theoretical analysis shows that DITASK achieves full-rank updates during optimization, preserving the geometric structure of pretrained features, and establishing a new paradigm for efficient multi-task learning (MTL). Our experiments on PASCAL MTL and NYUD show that DITASK achieves state-of-the-art performance across four dense prediction tasks, using $75\\%$ fewer parameters than existing methods. Our code is available here.", + "bbox": [ + 109, + 397, + 485, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 112, + 809, + 243, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision Transformers (ViTs) have emerged as compelling models for computer vision, achieving remarkable performance across various tasks by leveraging self-attention mechanisms [12, 48] and large-scale pretraining [39, 42] on extensive datasets like ImageNet", + "bbox": [ + 109, + 835, + 485, + 912 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "21k [10]. These models encode essential visual knowledge in their weight matrices through singular vectors that characterize the principal directions in the input space and output spaces [36, 40]. However, existing fine", + "bbox": [ + 511, + 364, + 885, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c14483aae385f4519c9a56be63c5e97bf8d961cc247baabcb557441834c6a862.jpg", + "image_caption": [ + "Figure 1. Performanceefficiency trade-off in multi-task learning (MTL) on PASCAL MTL tasks. DITASK outperforms single-task fine-tuning with fewer parameters than fixed-rank methods (LoRA [19]) and other PEFT approaches (Adapter [18]). The gray region shows negative relative improvement over single-task tuning, highlighting the challenge of achieving gains under tight parameter budgets." + ], + "image_footnote": [], + "bbox": [ + 519, + 445, + 875, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tuning methods based on low-rank adaptation (LoRA) [1, 19] may not preserve these learned singular vectors. In Figure 2, we illustrate the importance of preserving the singular vectors; recovering a noisy image by ad", + "bbox": [ + 511, + 851, + 885, + 912 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25218", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/76a775a55846fbc7c0b5f273c843bcff559535cfc274cbc13b3aac42e033e69a.jpg", + "image_caption": [ + "Original Image", + "LoRA - PSNR: 22.97 dB" + ], + "image_footnote": [], + "bbox": [ + 135, + 99, + 292, + 220 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f475352239a431517e72f3e7122e59d8ef7d6abff5139a924c600e84ba68e531.jpg", + "image_caption": [ + "Noisy Image", + "DTASK-PSNR:25.10 dB" + ], + "image_footnote": [], + "bbox": [ + 305, + 99, + 460, + 220 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/820bca12110f903e1527a53fdecaa048f14bea49d32ea4fdc699efef72bcc8e0.jpg", + "image_caption": [ + "Figure 2. Image recovery comparison of LoRA and DiTASK. Preserving singular vectors enables DiTASK to achieve a higher peak signal-to-noise ratio (PSNR)." + ], + "image_footnote": [], + "bbox": [ + 135, + 229, + 292, + 351 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9231f22a4d59c606a9cb522094f6781e7de147952cd5d88c544c361b0f93cf56.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 231, + 460, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "justing only its singular values while keeping singular vectors yields superior performance than using LoRA, which may not preserve the singular vectors of the image. Singular vectors encode crucial image details, and low-rank denoising methods can lose these details, resulting in poor denoising quality. Preserving singular vectors serves as an implicit regularizer. This motivating example suggests that useful adaptations can be achieved through singular value modulation and inspires us to design a mathematically-ground method to achieve this goal.", + "bbox": [ + 109, + 438, + 483, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fine-tuning of pre-trained ViTs for downstream tasks, such as few-shot learning [20, 37], typically involves adapting the learned representations to the target application. However, the substantial size of these models calls for a resource-efficient fine-tuning technique. Parameter-efficient and low-rank optimization approaches, such as LoRA [19], offer promising solutions by reducing the number of trainable parameters. This strategy not only enhances resource efficiency (e.g., lower VRAM and FLOPS requirements), but also helps keep valuable pretrained filters that capture essential visual knowledge [6] by preventing catastrophic forgetting [16, 30].", + "bbox": [ + 111, + 607, + 483, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the context of single-task fine-tuning, parameter-efficient and low-rank methods have proven highly successful [18, 19, 23, 31]. However, in Multi-Task Learning (MTL) settings, these methods were shown to struggle [1]. Particularly, MTL typically requires isolating task gradients to prevent task interference (e.g., enforcing gradient orthogonality [45, 56]), a requirement that becomes increasingly challenging as the dimension or", + "bbox": [ + 111, + 791, + 483, + 912 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "rank of the gradients decreases. Thus, we face a tradeoff between lowering the number of trainable parameters and maintaining task performance. Evidently, as shown in Figure 1, existing methods can offer performance enhancement in MTL settings only when significantly increasing the number of trainable, effectively undermining their purpose of lightweight adaptation.", + "bbox": [ + 511, + 90, + 883, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conjecture, inspired by recent studies [5] that identified an incremental learning phenomenon in transformers, that the underperformance of LoRA methods in MTL settings happens because of the direct and nonprincipled modification of weight matrices' singular vectors. These updates force distinct tasks to compete within the same constrained subspace. The key insight of our approach is realizing that while low-rank representations offer sufficient dimensionality for individual tasks, constraining multiple tasks to share the same low-rank subspace creates interference. An optimal subspace for one task may be suboptimal for others. Yet, existing methods force this competition by maintaining a single shared low-rank space, while a unique subspace for each task, like in MTLoRA [1], may not take advantage of task synergies.", + "bbox": [ + 511, + 198, + 883, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach. To address the limitations of existing low-rank fine-tuning methods, we introduce Diffeomorphic Multi-Task Adaptation (DiTASK), a novel approach leveraging neural diffeomorphisms parameterized by Continuous Piecewise Affine-Based (CPAB) transformations [14, 15]. Specifically, DiTASK preserves pre-trained feature patterns by retaining the singular vectors of learned weight matrices while dynamically adjusting singular values through neural diffeomorphic transformations at each optimization step. Our diffeomorphic transformations are parameterized by Continuous Piecewise Affine (CPA) [14, 15] velocity fields over the weight matrix domain, ensuring continuous, invertible deformations. This design enables adaptation across multiple tasks while preserving the knowledge embedded during pre-training. We validate DiTASK on the PASCAL MTL dataset [13], a widely used benchmark for dense prediction tasks such as semantic segmentation, edge detection, and human body part segmentation. Our method achieves a $26.27\\%$ improvement in average task performance while reducing parameter usage by $4\\times$ compared to state-of-the-art methods like MTLoRA [1], demonstrating the effectiveness of preserving pre-trained feature directions for efficient multi-task fine-tuning.", + "bbox": [ + 511, + 441, + 883, + 818 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are as follows:", + "text_level": 1, + "bbox": [ + 513, + 820, + 743, + 833 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel approach to MTL fine-tuning that leverages neural diffeomorphisms for singular value adaptation, enabling fine-tuning weight updates while preserving pre-trained representation structure.", + "- We develop an efficient parametrization using learn" + ], + "bbox": [ + 514, + 835, + 883, + 911 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25219", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9cb3befc335fdf19c210421c47ab880d8f7825259e5b7657a57ff04ae94c2240.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 117, + 102, + 568, + 233 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0891b82b79f754e2fa86d6eb253c646377a6046191087731dbb79e90b09df15d.jpg", + "image_caption": [ + "Figure 3. Overview of our DiTASK within Multi-Task Learning (MTL). (Left) Input features $\\mathbf{x}$ are transformed via a modulated weight matrix $\\mathbf{W}_A$ , constructed by applying a neural diffeomorphism $f^\\theta$ to the singular values of a pre-trained weight matrix $\\mathbf{W}$ , resulting in updated features $\\mathbf{W}_A\\mathbf{x}$ . (Right) We use two sets of DiTASK modules: a joint transformation module for learning task synergies, and task-specific modules for individual adaptations. The transformed outputs serve as inputs to a shared decoder. This setup enables flexible, parameter-efficient fine-tuning while preserving the singular vectors of pre-trained weights." + ], + "image_footnote": [], + "bbox": [ + 666, + 78, + 864, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "able CPA velocity fields that require only 32 additional trainable parameters per layer.", + "bbox": [ + 125, + 369, + 483, + 400 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We theoretically analyze the properties of DiTASK, showing that it requires less memory than other low-rank Transformer adaptation methods.", + "- DITASK demonstrates state-of-the-art performance on PASCAL MTL tasks, achieving $26.27\\%$ improvement over existing methods like MTLoRA." + ], + "bbox": [ + 112, + 401, + 483, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The rest of the paper is organized as follows: In Section 2, we discuss the related work on parameter-efficient fine-tuning and MTL. In Section 3, we provide the mathematical background to understand DiTASK. Section 4 details DiTASK for learning diffeomorphic singular value adjustment, and Section 5 presents experimental results and analyses.", + "bbox": [ + 111, + 492, + 483, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 112, + 613, + 254, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work lies at the intersection of four research areas: multi-task vision learning, parameter-efficient fine-tuning, neural network adaptation, and diffeomorphisms. We discuss each area with a focus on how they relate to weight matrix transformations and singular value adaptation.", + "bbox": [ + 111, + 640, + 483, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-Task Learning in Vision. Multi-task learning models in vision typically adopt an encoder-decoder structure, where a shared encoder captures common features, and task-specific decoders handle individual objectives [35]. This approach has proven particularly effective for dense prediction tasks, with different decoders handling semantic segmentation, depth estimation, and surface normal prediction while sharing a common feature backbone [24]. While recent work has extended this framework to Vision Transformers (ViTs) [12], these adaptations face unique challenges due to their large parameter count and the complex in", + "bbox": [ + 111, + 729, + 483, + 911 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "teractions between task-specific updates. To address these issues, DiTASK introduces an encoder adaptation strategy that modulates singular values while retaining pre-trained singular vectors, rather than modifying full weight matrices or adding task-specific layers. This leverages the encoder-decoder framework for efficient adaptation of the shared encoder.", + "bbox": [ + 511, + 369, + 883, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Parameter-Efficient Fine-tuning Methods. These methods reduce computational overhead for model adaptation using various strategies. Adapter-based approaches [18] insert small trainable modules between transformer layers. Visual Prompt Tuning (VPT) [22] introduces trainable parameters in ViT input tokens, distinguishing it from standard adaptation approaches. Compactor [31] and BitFit [58] add minimal trainable parameters, enabling lightweight gradients via Kronecker products of rank-one and low-rank matrices and fine-tuning only biases, respectively. Hyperformers [31] use hypernetworks to generate adapter layers for multi-task language learning, while Polyhistor [27] adapts this for dense vision tasks. VL-Adapter [44] introduces adapters for joint Vision-Language (VL) multi-task fine-tuning.", + "bbox": [ + 511, + 477, + 883, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With the introduction of GPT-2 [38] and the rise in parameter sizes and task variety, methods like Low-Rank Adaptation (LoRA)[19] have gained traction in both language and vision. These methods restrict weight updates to fixed low-dimensional subspaces, enhancing resource efficiency. Other approaches, such as SVFT[25], enforce sparse singular values, while DoRA [26] decouples the magnitude and direction of weight update columns. In contrast, ReFT [53] uses low-rank approximation to adapt representations rather than weights.", + "bbox": [ + 511, + 709, + 883, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although most of these methods are not specifically designed for multi-task learning (MTL), MTLoRA [1] has applied LoRA within an MTL framework. By en", + "bbox": [ + 511, + 866, + 883, + 912 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25220", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "abling both task-agnostic and task-specific adaptations along with joint inference, MTLoRA has achieved state-of-the-art results on dense vision tasks. However, these methods, while effective in preserving pre-trained knowledge, still impose subspace constraints that can degrade performance relative to single-task baselines.", + "bbox": [ + 111, + 90, + 480, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "DiTASK takes a fundamentally different approach: instead of adding modules or modifying weights directly, we preserve the pre-trained singular vectors while enabling flexible adaptation via diffeomorphisms of singular values. This allows us to maintain both architectural efficiency and rich feature adaptability, without altering the input-output mapping learned during pre-training.", + "bbox": [ + 111, + 198, + 483, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-Task Learning Dynamics and Challenges. A recent study of Transformer training dynamics reveals an incremental learning phenomenon where weight update ranks gradually increase during training [5]. This finding challenges the effectiveness of fixed-rank adaptation methods in MTL settings. While MTLoRA [1] attempts to address this through task-agnostic and task-specific modules, it still operates within fixed low-rank constraints. Similarly, gradient interference mitigation techniques like PCGrad address conflicts between task updates but do not provide the flexibility needed for diverse task adaptations. In contrast, DITASK aligns with natural learning dynamics by preserving the full-rank structure through singular vector retention while enabling task-specific adaptations via neural diffeomorphisms [14, 15], uniquely combining parameter efficiency with the adaptability needed for effective multi-task learning.", + "bbox": [ + 111, + 335, + 483, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffeomorphisms in Neural Networks. A bijective mapping $f: \\mathcal{M} \\to \\mathcal{N}$ between two differentiable manifolds $\\mathcal{M}$ and $\\mathcal{N}$ is a diffeomorphism if both $f$ and its inverse $f^{-1}: \\mathcal{N} \\to \\mathcal{M}$ are differentiable. Learning diffeomorphisms poses computational challenges, as early methods were constrained by complex, infinite-dimensional spaces [43], and later Markov Chain Monte Carlo methods remained demanding [2, 3, 60]. Freifeld et al. [14, 15] addressed these issues with Continuous Piecewise-Affine Based (CPAB) transformations, a finite-dimensional approach suited for precise 1D diffeomorphisms, ideal for neural activation functions. CPAB offers linear complexity, supports parallelization, and achieves sub-linear performance in practice [15]. Initially developed for alignment and regression, CPAB is now widely applied in neural networks. For instance, in spatial transformer layers with CPAB [11], temporal alignment [34], novel loss function for time-series analysis [52], image animation [49], geometry-guided fine", + "bbox": [ + 111, + 625, + 483, + 912 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/24066c73dd4518010926f62f585287380b8b807a83e867ddddde5e9ba9709dbd.jpg", + "image_caption": [ + "Figure 4. DiTASK in the $i$ -th Swin Transformer stage for multi-task learning. Task-agnostic modules are applied in all blocks except the last, which uses task-specific modules to capture task-dependent features." + ], + "image_footnote": [], + "bbox": [ + 519, + 88, + 883, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tuning [32] and trainable CPAB-based activation function [8, 33].", + "bbox": [ + 511, + 549, + 883, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Preliminaries and Background", + "text_level": 1, + "bbox": [ + 511, + 595, + 795, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We combine two key components: the weights in ViTs, and the mathematical framework of CPAB diffeomorphisms. We now provide the background for understanding the coupling of these concepts in DiTASK.", + "bbox": [ + 511, + 621, + 883, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Learned Weights in ViTs", + "text_level": 1, + "bbox": [ + 511, + 693, + 740, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ViTs encode visual knowledge in their weight matrices, which can be analyzed through Singular Value Decomposition (SVD). Assume we have a weight matrix that transforms inputs from $c_{1}$ to $c_{2}$ channels, denoted by $\\mathbf{W} \\in \\mathbb{R}^{c_2 \\times c_1}$ , then its SVD reads:", + "bbox": [ + 511, + 717, + 883, + 792 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} = \\mathbf {U} \\boldsymbol {\\Sigma} \\mathbf {V} ^ {\\top}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 805, + 883, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{U} \\in \\mathbb{R}^{c_2 \\times c_2}$ , $\\pmb{\\Sigma} \\in \\mathbb{R}^{c_2 \\times c_1}$ , $\\mathbf{V} \\in \\mathbb{R}^{c_1 \\times c_1}$ . We refer to $\\mathbf{U}$ as the left singular vectors, $\\pmb{\\Sigma}$ as the singular values, and $\\mathbf{V}$ as the right singular vectors. Notably, $\\mathbf{U}$ and $\\mathbf{V}$ form orthonormal bases for the output and input spaces of the linear map represented by $\\mathbf{W}$ , respectively.", + "bbox": [ + 511, + 835, + 883, + 912 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25221", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These bases characterize how the network transforms visual features across layers and hidden dimensions.", + "bbox": [ + 109, + 90, + 485, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Problem Setup. Throughout this paper, we assume $K$ tasks $\\mathcal{T} = \\{T_1,\\dots ,T_K\\}$ . Each task $T_{k}$ has an associated dataset $\\mathcal{D}_k = \\{(x_i^k,y_i^k)\\}_{i = 1}^{N_k}$ where $x_{i}^{k}\\in \\mathcal{X}$ and $y_{i}^{k}\\in \\mathcal{Y}_{k}$ represent the input-output pairs. The goal is to train a neural network to minimize a supervised loss between the prediction and ground-truth output. Following [1], we use a Swin Transformer [28], which processes input images by dividing them into nonoverlapping patches and progressively merging patches to reduce spatial resolution while increasing feature dimension across stages. Formally, the Swin Transformer processes images through $L$ stages, with the $l$ -th stage operating on feature maps of resolution $\\frac{H}{2^l}\\times \\frac{W}{2^l}$ with $C_l$ channels. The key operation in each stage is a Window-based Multi-head Self-Attention (W-MSA):", + "bbox": [ + 109, + 121, + 485, + 347 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {W} - \\mathrm {M S A} (Q, K, V) = \\operatorname {S o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d}}\\right) V, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 354, + 483, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Q, K, V \\in \\mathbb{R}^{M \\times d}$ are query, key, and value matrices for windows of size $M$ . The corresponding weight matrices $\\mathbf{W}_l^{(q)}, \\mathbf{W}_l^{(k)}, \\mathbf{W}_l^{(v)} \\in \\mathbb{R}^{d \\times d}$ for these projections in layer $l$ are central to our DiTASK, because in Section 4 we dynamically adjust their singular values for multi-task adaptations. The MTL objective minimizes a weighted combination of $K$ task losses:", + "bbox": [ + 109, + 397, + 483, + 506 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Theta} \\sum_ {k = 1} ^ {K} \\lambda_ {k} \\mathcal {L} _ {k} (\\Theta ; \\mathcal {D} _ {k}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 513, + 483, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_k$ and $\\lambda_{k}$ represent the loss function and weight for the $k$ -th task, respectively. In Figure 4, we illustrate the overall architecture used in this paper.", + "bbox": [ + 109, + 563, + 483, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. CPAB Diffeomorphisms for Weight Transformation", + "text_level": 1, + "bbox": [ + 112, + 616, + 483, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As we show later in Section 4, our DiTASK modifies singular values $\\Sigma$ while preserving the structure of weight matrices. To achieve that, transformations that are smooth, invertible, and monotone, are required. Continuous Piecewise Affine-Based (CPAB) [14, 15] diffeomorphisms satisfy these conditions while being efficient in terms of parameters and computing diffeomorphisms. We now turn to define CPAB formally.", + "bbox": [ + 109, + 654, + 485, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Definition 3.1 (CPAB Transformation). Given a closed interval $\\Omega = [a,b]$ partitioned into $\\mathcal{N}_{\\mathcal{P}}$ intervals, a CPAB transformation is defined through a velocity field $v^{\\theta}:\\Omega \\to \\mathbb{R}$ that is continuous and piecewise-affine within each interval. This velocity field, parameterized by $\\pmb {\\theta}\\in \\mathbb{R}^{\\mathcal{N}_{\\mathcal{P}} - 1}$ , yields a diffeomorphism $f^{\\theta}$ of the form:", + "bbox": [ + 109, + 782, + 485, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {\\boldsymbol {\\theta}} (x) = x + \\int_ {0} ^ {1} v ^ {\\boldsymbol {\\theta}} \\left(f ^ {\\boldsymbol {\\theta}} (x, \\tau)\\right) d \\tau . \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 881, + 483, + 916 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For practical implementation, we use the Python package from Martinez et al. [34], and provide additional details in the supplementary material. CPAB transformations are ideal for our settings, shown in Section 4, because they provide: (i) Low parameter overhead. Only $\\mathcal{O}(\\mathcal{N}_{\\mathcal{P}})$ parameters, where typically $\\mathcal{N}_{\\mathcal{P}} \\leq 128$ ; (ii) Differentiability. Enables gradient-based optimization; (iii) Computational efficiency. Computing Equation (4) is of linear complexity; (iv) Stability. CPAB transformations are Lipschitz continuous [15].", + "bbox": [ + 511, + 90, + 883, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. DiTASK: Diffeomorphic Multi-Task Adaptation", + "text_level": 1, + "bbox": [ + 511, + 253, + 883, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We introduce DITASK (Diffeomorphic Multi-Task Adaptation), a novel approach for efficient multi-task fine-tuning. Our method is grounded in a fundamental analysis of how neural networks process information through their weight matrices. We draw insights from linear algebra to the workings of a linear layer of neural network in Section 4.1 relating it to SVD. In Section 4.2, we formally introduce DITASK and elaborate on its properties that motivate our design choices in Section 4.3.", + "bbox": [ + 511, + 296, + 883, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Understanding Weight Matrices", + "text_level": 1, + "bbox": [ + 511, + 455, + 795, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now show that by considering the SVD of weight matrices, we can gain insights on the course of action of linear layers, that later, in Section 4.2, serves as a mathematically grounded motivation for the design of our DiTASK. Specifically, we note that a linear layer with weight matrix $\\mathbf{W} \\in \\mathbb{R}^{c_2 \\times c_1}$ , and its SVD decomposition $\\mathbf{W} = \\mathbf{U} \\boldsymbol{\\Sigma} \\mathbf{V}^{\\top}$ , can be viewed as a linear map $g: \\mathbb{R}^{c_1} \\to \\mathbb{R}^{c_2}$ , such that the following equality holds:", + "bbox": [ + 511, + 479, + 883, + 601 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng (\\mathbf {x}) = \\mathbf {W} \\mathbf {x} = \\sum_ {i = 1} ^ {p} \\sigma_ {i} \\langle \\mathbf {x}, \\mathbf {v} _ {i} \\rangle \\mathbf {u} _ {i}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 607, + 883, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{U} = [\\mathbf{u}_1, \\dots, \\mathbf{u}_{c_2}]$ , $\\mathbf{V} = [\\mathbf{v}_1, \\dots, \\mathbf{v}_{c_1}]$ , and $\\boldsymbol{\\Sigma} = \\text{diag}([\\sigma_1, \\sigma_2, \\dots, \\sigma_p])$ , $p = \\min(c_1, c_2)$ . The basis vectors in $\\mathbf{U}$ are the left singular vectors, $\\mathbf{V}$ are right singular vectors, and $\\boldsymbol{\\Sigma}$ are the singular values of $\\mathbf{W}$ .", + "bbox": [ + 511, + 654, + 883, + 714 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, the orientations encoded by the left and right singular vectors represent features present in the output and input spaces of the linear transformation $g$ , respectively. Multi-task learning requires adapting these orientations jointly for all tasks, while minimizing task interference to prevent performance degradation. Below, we describe how to achieve effective multi-task adaptation using diffeomorphisms, by preserving the singular vectors $\\mathbf{U}$ , $\\mathbf{V}$ and modifying $\\mathbf{W}$ in a principled manner.", + "bbox": [ + 511, + 714, + 883, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Adaptation with DITASK", + "text_level": 1, + "bbox": [ + 511, + 858, + 741, + 875 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a learned weight matrix $\\mathbf{W} = \\mathbf{U}\\pmb{\\Sigma}\\mathbf{V}^{\\top} \\in \\mathbb{R}^{c_2 \\times c_1}$ from a ViT, we transform the singular values $\\pmb{\\Sigma}$ by a", + "bbox": [ + 511, + 880, + 883, + 912 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25222", + "bbox": [ + 478, + 950, + 517, + 963 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "learned neural diffeomorphism $f^{\\theta}$ described in Equation (4), to get the adapted weight matrix $\\mathbf{W}_A$ as follows:", + "bbox": [ + 111, + 90, + 485, + 135 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} _ {A} = \\mathbf {U} \\left[ \\begin{array}{c c c c} f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {1}\\right) & 0 & \\dots & 0 \\\\ 0 & f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {2}\\right) & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {p}\\right) \\end{array} \\right] \\mathbf {V} ^ {\\top}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 143, + 483, + 228 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During fine-tuning, we freeze $\\mathbf{W}$ and learn only the parameters $\\theta$ of the CPA velocity field. This allows DiTASK to adapt to multiple tasks using $\\mathcal{O}(\\mathcal{N}_{\\mathcal{P}})$ additional parameters (where typically $\\mathcal{N}_{\\mathcal{P}} \\leq 128$ ), which is significantly smaller than methods with low-rank $r$ using $\\mathcal{O}(r(c_1 + c_2))$ . We describe this process in the Section 1, and compare the computational cost of DiTASK with other fine-tuning methods in the supplementary material.", + "bbox": [ + 111, + 229, + 483, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Multi-Task Adaptation with DiTASK. To enable both multi and task-specific adaptation, we learn two sets of neural diffeomorphic transformations in every pretrained weight matrix $\\mathbf{W}$ , shown in Section 1, that include: (i) Joint Adaptation parameters, denoted by $\\theta_{j}$ , to allow task synergies which are crucial for MTL [21, 47]; and (ii) Task-wise Adaptation parameters, denoted by $\\{\\theta_k\\}_{k=1}^K$ to enable learning nuances for each task.", + "bbox": [ + 111, + 364, + 483, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Properties of DITASK", + "text_level": 1, + "bbox": [ + 112, + 496, + 313, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we motivate our design choices and discuss the properties that make DiTASK an effective and parameter-efficient fine-tuning method for MTL.", + "bbox": [ + 111, + 518, + 483, + 564 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Feature Space Preservation. As discussed in Section 4.1, pre-trained weight matrices encode feature transformations through their singular vectors, where $\\mathbf{U}$ and $\\mathbf{V}$ form orthonormal bases for output and input spaces, respectively. These bases capture the orientation of patterns learned during pre-training, each weighted by its corresponding singular value. In contrast to traditional low-rank methods like LoRA, which constrain adaptations to fixed low-dimensional subspaces, potentially losing important features, our DiTASK preserves these learned bases entirely. This preservation allows us to achieve superior multi-task performance with fewer parameters, as shown in Figure 1. Specifically, while low-rank methods require increasing their rank (and thus parameters and departure from being low-rank) to match single-task performance, our DiTASK maintains the learned feature space of pre-trained ViTs through a targeted and mathematically-ground singular value modulation.", + "bbox": [ + 111, + 565, + 483, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Feature Relativity Preservation. The order of singular values $\\sigma_{1} \\geq \\sigma_{2} \\geq \\ldots \\geq \\sigma_{p}$ in weight matrices of ViTs encode the relative importance of features learned during pre-training on large-scale datasets like", + "bbox": [ + 111, + 851, + 483, + 912 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ImageNet-21k. By utilizing diffeomorphisms, which are smooth, invertible, and monotone, by definition, we preserve this ordering. That is, if $f^{\\theta}$ is a diffeomorphism, then $f^{\\theta}(\\sigma_1) \\geq f^{\\theta}(\\sigma_2) \\geq \\ldots \\geq f^{\\theta}(\\sigma_p)$ in Equation (6). Our choice of CPAB transformations implements this with only $\\mathcal{N}_{\\mathcal{P}} \\leq 128$ parameters per weight matrix, compared to the $\\mathcal{O}(r(c_1 + c_2))$ parameters required by low-rank adaptation methods. Our experiments in Section 5 demonstrate that preserving feature hierarchy through diffeomorphic transformations enables effective multi-task generalization while maintaining parameter efficiency.", + "bbox": [ + 511, + 90, + 883, + 272 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 287, + 645, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate DiTASK on multiple MTL benchmarks and compare it with other adaptation methods. Section 5.1 details the experimental setup and baselines, Section 5.2 discusses our main findings, and Section 5.3 presents few ablation studies of DiTASK. We seek to address three key research questions:", + "bbox": [ + 511, + 314, + 883, + 405 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(RQ1) Can a selective modification of singular values while preserving singular vectors bridge the performance gap between decoder-only and full fine-tuning?", + "(RQ2) Does full-rank preservation by singular value modulation outperform low-rank adaptation methods?", + "(RQ3) How does DiTASK compare to other parameter-efficient adaptation methods?" + ], + "bbox": [ + 511, + 406, + 883, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 513, + 523, + 702, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets and Tasks. We evaluate DiTASK on the PASCAL-MTL dataset [13] (PASCAL-Context split) following the literature on multi-task dense prediction [46, 54, 55]. This dataset includes 4,998 training and 5,105 validation images with annotations for semantic segmentation (21 classes), human part segmentation (7 classes), surface normal estimation, and saliency detection. Additional experiments on the NYUD dataset [41] are provided in Table 4.", + "bbox": [ + 511, + 547, + 883, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We use the Swin-Tiny [28] architecture, pre-trained on ImageNet-21k [39] as the backbone encoder, similar to [1]. To ensure a fair comparison, we incorporate the HRNet [50] decoder, which accounts for $6\\%$ of the total parameters, as in previous works [1, 46]. Following MTINet [46], we apply cross-entropy loss for segmentation tasks, $\\ell_1$ loss for surface normals, and balanced cross-entropy [9] for saliency detection, with same task weights $\\{\\lambda_k\\}_{k=1}^K$ used in MTINet. In all experiments, we follow the evaluation protocol from Agiza et al. [1].", + "bbox": [ + 511, + 683, + 883, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We benchmark our DiTASK with three categories of methods:", + "bbox": [ + 511, + 849, + 883, + 878 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "- Full Fine-Tuning: Methods that modify all weight matrices (single-task, MTL decoder, full MTL)", + "bbox": [ + 511, + 881, + 883, + 912 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25223", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/093e1790cbb85a981c5a605109ef1d69d111dc9257c167a4eb25583b3024eb96.jpg", + "table_caption": [ + "Table 1. Performance on PASCAL Context for Multi-Task Learning. Comparison of DITASK with full fine-tuning, adapter-based, and fixed-rank methods across four dense prediction tasks: semantic segmentation, human part segmentation, saliency detection, and surface normal estimation. Metrics are MIOU (↑) and RMSE (↓), with $\\Delta m$ denoting relative improvement over single-task tuning. DITASK achieves strong performance with minimal trainable parameters and supports joint inference across tasks." + ], + "table_footnote": [], + "table_body": "
    MethodSEMSEG (MIOU ↑)HUMAN PARTS (MIOU ↑)SALIENCY (MIOU ↑)NORMALS (RMSE ↓)Δm(%)Trainable Swin Parameters (M)Single Inference For All Tasks
    FULL FINE-TUNING
    Single Task67.2161.9362.3517.970.00112.62×
    MTL - Dec. Only65.0953.4857.4620.69- 9.950✓
    MTL - Full67.5660.2465.2116.64+ 2.2328.12✓
    ADAPTER-BASED
    VPT-shallow [22]62.9652.2758.3120.90-11.180.63×
    VPT-deep [22]64.3552.5458.1521.07-10.851.49×
    Compactor++ [23]67.2655.6959.4719.54- 5.840.72×
    Bitfit [58]68.5755.9960.6419.42- 4.600.91×
    Compactor [23]68.0856.4160.0819.22- 4.550.84×
    Adapter [17]69.2157.3861.2818.83- 2.719.26×
    VL-Adapter [44]70.2159.1562.2919.26- 1.832.80×
    Polyhistor [27]70.8759.1565.5417.77+ 2.347.02×
    HyperFormer [31]71.4360.7365.5417.77+ 2.6470.83×
    FIXED-RANK
    MTL - DoRA [26]52.3650.8263.5318.32-10.026.40✓
    MTL - ReFT [53]68.7556.4958.7620.54- 6.6316.16✓
    MTL - SVFT [25]64.4455.9463.0317.86- 3.023.83✓
    LoRA [19]70.1257.7361.9018.96- 2.170.93×
    MTLoRA [1] (r = 16)68.1958.9964.4817.03+ 1.353.01✓
    MTLoRA [1] (r = 32)67.7459.4664.9016.59+ 2.164.14✓
    MTLoRA [1] (r = 64)67.9059.8465.4016.60+ 2.556.40✓
    Single Task - DITASK72.2062.3365.7016.55+ 5.331.60 (×4)×
    MTL - DITASK (Ours)69.6662.0265.0017.10+ 3.221.61✓
    ", + "bbox": [ + 120, + 162, + 874, + 483 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b69559b76bbfcbe8acbe553c19e1e52deee856f0e24a1a130badc4353c9ab945.jpg", + "table_caption": [ + "Table 2. Effect of Backbone Size - Relative improvement increases with increasing capacity of the backbone" + ], + "table_footnote": [], + "table_body": "
    MethodSEMSEG (MIOU ↑)HUMAN PARTS (MIOU ↑)SALIENCY (MIOU ↑)NORMALS (RMSE ↓)Δm(%)Trainable Swin Parameters (M)
    DITASK + Swin-Tiny69.6662.0265.0017.10+3.221.61
    DITASK + Swin-Small74.4963.2064.5817.58+4.681.66
    DITASK + Swin-Base75.8665.9764.1817.29+6.523.14
    DITASK + Swin-Large76.2367.5364.0716.90+7.797.13
    ", + "bbox": [ + 119, + 513, + 874, + 614 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Adapter-based: Methods that add task-specific layers while preserving main weights (Adapter [18], BitFit [58], VPT [22], Compactor [23], VL-Adapter [44], HyperFormer [31], Polyhistor [27])", + "- Fixed-Rank: Methods that constrain updates to low-rank subspaces (LoRA [19], DoRA [26], SVFT [25], ReFT [53], MTLoRA [1])" + ], + "bbox": [ + 112, + 638, + 482, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Results and Discussion", + "text_level": 1, + "bbox": [ + 112, + 752, + 323, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 presents our main results, addressing (RQ1)-(RQ3) on the effectiveness of DiTASK for multi-task learning (MTL).", + "bbox": [ + 109, + 775, + 482, + 820 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Bridging the Efficiency Performance Gap. DiTASK achieves a $+3.22\\%$ relative improvement over single-task baselines using only 1.61M trainable encoder parameters. This outperforms both decoder-only tuning $(-9.95\\%)$ and full fine-tuning $(+2.23\\%)$ , demonstrating that modulating singular values while preserving pre", + "bbox": [ + 109, + 821, + 482, + 911 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "trained feature directions enables an effective balance between parameter efficiency and performance.", + "bbox": [ + 511, + 638, + 880, + 669 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with Fixed Low-Rank Methods. DTASK outperforms the state-of-the-art MTLoRA by $26.27\\%$ in $\\Delta m$ , using $4\\times$ fewer parameters (Figure 5). Most fixed-rank methods yield negative $\\Delta m$ due to task interference from shared low-rank subspaces. By modulating singular values independently per task while preserving full-rank structure, DTASK mitigates this interference. Similar trends are observed on NYUD (Table 4).", + "bbox": [ + 511, + 670, + 883, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Parameter Efficiency and Task Performance. DITASK is the only parameter-efficient method to consistently improve over single-task baselines, showing that modulating singular values while preserving pretrained directions effectively balances efficiency and performance.", + "bbox": [ + 511, + 806, + 883, + 893 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25224", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eccec0d3520f16116ec3e609739488da7c1e5f8b7bf5b6485f521e01ee574bd7.jpg", + "image_caption": [ + "Figure 5. Comparison of adaptation parameter budget of the shared encoder, excluding LayerNorm parameters." + ], + "image_footnote": [], + "bbox": [ + 119, + 93, + 473, + 253 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1fd63e0067350b2a74e44a2e9be5574b7a90133cd6dc3a510b23b6f7724f4cbb.jpg", + "table_caption": [ + "Table 3. Comparison of computational efficiency between DiTASK and MTLoRA. DiTASK reduces batch runtime by $\\approx 22\\%$ , lowers memory usage, and uses $500\\times$ fewer adaptation parameters." + ], + "table_footnote": [], + "table_body": "
    MethodBatch Runtime (seconds)Max GPU Mem (Megabytes)# Adaptation Params
    MTLoRA35.20±1.05235094.86M
    DiTASK27.31±5.29229068.5K
    ", + "bbox": [ + 114, + 383, + 483, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 112, + 477, + 264, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We analyze key components of DiTASK to understand their contributions to multi-task performance.", + "bbox": [ + 111, + 503, + 482, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Computational Efficiency. DITASK uses only 8.5K adaptation parameters, compared to MTLoRA's 4.86M, while achieving $22\\%$ faster batch processing (27.31s vs 35.20s) and reduced memory usage (see Table 3). The efficiency gains stem from our compact CPAB parameterization of singular value transformations.", + "bbox": [ + 111, + 534, + 483, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Joint vs Task-Wise Singular Value Modulation. We evaluate three configurations of singular value modulation, shown in Figure 7. Joint Adaptation alone, with shared modulation across tasks, achieves an improvement of $2.77\\%$ . Task-Wise Adaptation alone, which modulates singular values independently for each task, yields $2.85\\%$ . The Combined approach, DiTASK, incorporates both strategies and reaches the highest improvement at $3.22\\%$ , supporting the use of both shared and task-specific transformations.", + "bbox": [ + 111, + 625, + 483, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model Scaling Analysis. The effectiveness of DiTASK scales with model capacity (Table 2). This scaling effect indicates that larger models provide richer singular value spaces, enabling more effective task-specific adaptation.", + "bbox": [ + 111, + 776, + 483, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Comparison. In Figure 6, we present a visual comparison between MTLoRA and our DiTASK on the semantic segmentation task from PASCAL MTL. DiTASK demonstrates tighter and clearer boundaries, more consistent segmentation, and improved class sep", + "bbox": [ + 111, + 837, + 483, + 912 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a974d43fd63cbef66e9c1dd943f54ad9c0310f8cd975a972d5ebd605f9d64b19.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodSEMSEG(MIOU↑)DEPTH(RMSE↓)Δm(%)Trainable Params(in M)
    Single Task33.180.6670112.62
    MTL - Dec. Only28.370.832-19.611.00
    MTL - Full35.290.734-1.8428.5
    MTLoRA37.180.635+8.426.26
    Single Task - DITASK44.010.644+18.041.61
    DITASK43.850.606+20.651.61
    ", + "bbox": [ + 514, + 88, + 883, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Comparison of DiTASK and MTLoRA on the NYUD [41] multi-task dataset for semantic segmentation (MIOU) and depth estimation (RMSE).", + "bbox": [ + 511, + 196, + 883, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ec6f7c48c2de61254869e5ad473a3f87f6a12d7f67603f51d031c67fdb0ec1b4.jpg", + "image_caption": [ + "Figure 6. Semantic segmentation predictions on PASCAL MTL using MTLoRA and D1TASK." + ], + "image_footnote": [], + "bbox": [ + 517, + 260, + 885, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "aration. For example, in the dimly lit sofa scene in the second column, MTLoRA struggles to correctly predict the sofa boundary, while DITASK offers a better prediction.", + "bbox": [ + 511, + 501, + 883, + 560 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 582, + 633, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce DiTASK, a novel MTL fine-tuning approach that leverages neural diffeomorphisms for singular value adaptation while preserving the structure of pre-trained representations. We observe that existing methods, which restrict weight updates to fixed low-rank subspaces for resource efficiency, often suffer from multi-task performance degradation relative to single-task baselines. We conjecture that the singular vectors of pre-trained weight matrices capture rich features, and preserving them during MTL adaptation enhances performance. By using neural diffeomorphisms, DiTASK maintains feature space and relational structure while requiring less memory than other low-rank adaptation methods. We evaluate DiTASK on the PASCAL MTL and NYUD MTL datasets, with extensive ablation studies demonstrating its effectiveness. Our results show that DiTASK achieves state-of-the-art MTL performance with $75\\%$ fewer trainable parameters, underscoring the importance of preserving singular vectors in pre-trained weights.", + "bbox": [ + 509, + 609, + 885, + 912 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25225", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 114, + 89, + 209, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ahmed Agiza, Marina Neseem, and Sherief Reda. Mtlora: Low-rank adaptation approach for efficient multi-task learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16196-16205, 2024. 1, 2, 3, 4, 5, 6, 7", + "[2] Stéphanie Allissonnière, Estelle Kuhn, and Alain Trouve. Construction of bayesian deformable models via a stochastic approximation algorithm: a convergence study. 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URL https://arxiv.org/abs/1910.04867.", + "[60] Miaomiao Zhang and P Thomas Fletcher. Bayesian statistical shape analysis on the manifold of diffeomorphisms. Algorithmic Advances in Riemannian Geometry and Applications: For Machine Learning, Computer Vision, Statistics, and Optimization, pages 1-23, 2016. 4" + ], + "bbox": [ + 116, + 90, + 485, + 625 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "25229", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/3a6773a0-380b-4fb7-a04b-955503269a41_model.json b/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/3a6773a0-380b-4fb7-a04b-955503269a41_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ff1453cdd26b5c1aa5102aa9f7bed7296bd68482 --- /dev/null +++ b/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/3a6773a0-380b-4fb7-a04b-955503269a41_model.json @@ -0,0 +1,2424 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.137, + 0.131, + 0.862, + 0.153 + ], + "angle": 0, + "content": "DITASK: Multi-Task Fine-Tuning with Diffeomorphic Transformations" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.181, + 0.364, + 0.252 + ], + "angle": 0, + "content": "Krishna Sri Ipsit Mantri Purdue University West Lafayette, USA mantrik@purdue.edu" + }, + { + "type": "text", + "bbox": [ + 0.406, + 0.181, + 0.611, + 0.251 + ], + "angle": 0, + "content": "Carola-Bibiane Schonlieb \nUniversity of Cambridge \nCambridge, UK \ncbs31@cam.ac.uk" + }, + { + "type": "text", + "bbox": [ + 0.656, + 0.182, + 0.826, + 0.251 + ], + "angle": 0, + "content": "Bruno Ribeiro Purdue University West Lafayette, USA ribeirob@purdue.edu" + }, + { + "type": "text", + "bbox": [ + 0.229, + 0.26, + 0.518, + 0.33 + ], + "angle": 0, + "content": "Chaim Baskin \nBen-Gurion University of the Negev \nBeer Sheva, Israel \nchaimbaskin@bgu.ac.il" + }, + { + "type": "text", + "bbox": [ + 0.571, + 0.26, + 0.77, + 0.329 + ], + "angle": 0, + "content": "Moshe Eliasof \nUniversity of Cambridge \nCambridge, UK \nme532@cam.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.26, + 0.365, + 0.338, + 0.381 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.398, + 0.486, + 0.775 + ], + "angle": 0, + "content": "Pre-trained Vision Transformers now serve as powerful tools for computer vision. Yet, efficiently adapting them for multiple tasks remains a challenge that arises from the need to modify the rich hidden representations encoded by the learned weight matrices, without inducing interference between tasks. Current parameter-efficient methods like LoRA, which apply low-rank updates, force tasks to compete within constrained subspaces, ultimately degrading performance. We introduce DITASK a novel Diffeomorphic Multi-Task Fine-Tuning approach that maintains pre-trained representations by preserving weight matrix singular vectors, while enabling task-specific adaptations through neural diffeomorphic transformations of the singular values. By following this approach, DITASK enables both shared and task-specific feature modulations with minimal added parameters. Our theoretical analysis shows that DITASK achieves full-rank updates during optimization, preserving the geometric structure of pretrained features, and establishing a new paradigm for efficient multi-task learning (MTL). Our experiments on PASCAL MTL and NYUD show that DITASK achieves state-of-the-art performance across four dense prediction tasks, using \\(75\\%\\) fewer parameters than existing methods. Our code is available here." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.81, + 0.245, + 0.825 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.837, + 0.486, + 0.913 + ], + "angle": 0, + "content": "Vision Transformers (ViTs) have emerged as compelling models for computer vision, achieving remarkable performance across various tasks by leveraging self-attention mechanisms [12, 48] and large-scale pretraining [39, 42] on extensive datasets like ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.366, + 0.887, + 0.428 + ], + "angle": 0, + "content": "21k [10]. These models encode essential visual knowledge in their weight matrices through singular vectors that characterize the principal directions in the input space and output spaces [36, 40]. However, existing fine" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.446, + 0.877, + 0.721 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.736, + 0.885, + 0.834 + ], + "angle": 0, + "content": "Figure 1. Performanceefficiency trade-off in multi-task learning (MTL) on PASCAL MTL tasks. DITASK outperforms single-task fine-tuning with fewer parameters than fixed-rank methods (LoRA [19]) and other PEFT approaches (Adapter [18]). The gray region shows negative relative improvement over single-task tuning, highlighting the challenge of achieving gains under tight parameter budgets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.852, + 0.887, + 0.913 + ], + "angle": 0, + "content": "tuning methods based on low-rank adaptation (LoRA) [1, 19] may not preserve these learned singular vectors. In Figure 2, we illustrate the importance of preserving the singular vectors; recovering a noisy image by ad" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.951, + 0.519, + 0.963 + ], + "angle": 0, + "content": "25218" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.175, + 0.09, + 0.255, + 0.101 + ], + "angle": 0, + "content": "Original Image" + }, + { + "type": "image", + "bbox": [ + 0.137, + 0.101, + 0.293, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.221, + 0.279, + 0.231 + ], + "angle": 0, + "content": "LoRA - PSNR: 22.97 dB" + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.091, + 0.418, + 0.1 + ], + "angle": 0, + "content": "Noisy Image" + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.101, + 0.461, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.221, + 0.459, + 0.231 + ], + "angle": 0, + "content": "DTASK-PSNR:25.10 dB" + }, + { + "type": "image", + "bbox": [ + 0.137, + 0.231, + 0.293, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.232, + 0.461, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.364, + 0.484, + 0.406 + ], + "angle": 0, + "content": "Figure 2. Image recovery comparison of LoRA and DiTASK. Preserving singular vectors enables DiTASK to achieve a higher peak signal-to-noise ratio (PSNR)." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.439, + 0.484, + 0.605 + ], + "angle": 0, + "content": "justing only its singular values while keeping singular vectors yields superior performance than using LoRA, which may not preserve the singular vectors of the image. Singular vectors encode crucial image details, and low-rank denoising methods can lose these details, resulting in poor denoising quality. Preserving singular vectors serves as an implicit regularizer. This motivating example suggests that useful adaptations can be achieved through singular value modulation and inspires us to design a mathematically-ground method to achieve this goal." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.608, + 0.484, + 0.789 + ], + "angle": 0, + "content": "Fine-tuning of pre-trained ViTs for downstream tasks, such as few-shot learning [20, 37], typically involves adapting the learned representations to the target application. However, the substantial size of these models calls for a resource-efficient fine-tuning technique. Parameter-efficient and low-rank optimization approaches, such as LoRA [19], offer promising solutions by reducing the number of trainable parameters. This strategy not only enhances resource efficiency (e.g., lower VRAM and FLOPS requirements), but also helps keep valuable pretrained filters that capture essential visual knowledge [6] by preventing catastrophic forgetting [16, 30]." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.792, + 0.484, + 0.913 + ], + "angle": 0, + "content": "In the context of single-task fine-tuning, parameter-efficient and low-rank methods have proven highly successful [18, 19, 23, 31]. However, in Multi-Task Learning (MTL) settings, these methods were shown to struggle [1]. Particularly, MTL typically requires isolating task gradients to prevent task interference (e.g., enforcing gradient orthogonality [45, 56]), a requirement that becomes increasingly challenging as the dimension or" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.885, + 0.198 + ], + "angle": 0, + "content": "rank of the gradients decreases. Thus, we face a tradeoff between lowering the number of trainable parameters and maintaining task performance. Evidently, as shown in Figure 1, existing methods can offer performance enhancement in MTL settings only when significantly increasing the number of trainable, effectively undermining their purpose of lightweight adaptation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.199, + 0.885, + 0.44 + ], + "angle": 0, + "content": "We conjecture, inspired by recent studies [5] that identified an incremental learning phenomenon in transformers, that the underperformance of LoRA methods in MTL settings happens because of the direct and nonprincipled modification of weight matrices' singular vectors. These updates force distinct tasks to compete within the same constrained subspace. The key insight of our approach is realizing that while low-rank representations offer sufficient dimensionality for individual tasks, constraining multiple tasks to share the same low-rank subspace creates interference. An optimal subspace for one task may be suboptimal for others. Yet, existing methods force this competition by maintaining a single shared low-rank space, while a unique subspace for each task, like in MTLoRA [1], may not take advantage of task synergies." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.442, + 0.885, + 0.819 + ], + "angle": 0, + "content": "Our approach. To address the limitations of existing low-rank fine-tuning methods, we introduce Diffeomorphic Multi-Task Adaptation (DiTASK), a novel approach leveraging neural diffeomorphisms parameterized by Continuous Piecewise Affine-Based (CPAB) transformations [14, 15]. Specifically, DiTASK preserves pre-trained feature patterns by retaining the singular vectors of learned weight matrices while dynamically adjusting singular values through neural diffeomorphic transformations at each optimization step. Our diffeomorphic transformations are parameterized by Continuous Piecewise Affine (CPA) [14, 15] velocity fields over the weight matrix domain, ensuring continuous, invertible deformations. This design enables adaptation across multiple tasks while preserving the knowledge embedded during pre-training. We validate DiTASK on the PASCAL MTL dataset [13], a widely used benchmark for dense prediction tasks such as semantic segmentation, edge detection, and human body part segmentation. Our method achieves a \\(26.27\\%\\) improvement in average task performance while reducing parameter usage by \\(4\\times\\) compared to state-of-the-art methods like MTLoRA [1], demonstrating the effectiveness of preserving pre-trained feature directions for efficient multi-task fine-tuning." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.821, + 0.744, + 0.834 + ], + "angle": 0, + "content": "Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.837, + 0.883, + 0.896 + ], + "angle": 0, + "content": "- We propose a novel approach to MTL fine-tuning that leverages neural diffeomorphisms for singular value adaptation, enabling fine-tuning weight updates while preserving pre-trained representation structure." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.898, + 0.884, + 0.912 + ], + "angle": 0, + "content": "- We develop an efficient parametrization using learn" + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.837, + 0.884, + 0.912 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.519, + 0.963 + ], + "angle": 0, + "content": "25219" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.103, + 0.57, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.079, + 0.865, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.275, + 0.885, + 0.348 + ], + "angle": 0, + "content": "Figure 3. Overview of our DiTASK within Multi-Task Learning (MTL). (Left) Input features \\(\\mathbf{x}\\) are transformed via a modulated weight matrix \\(\\mathbf{W}_A\\), constructed by applying a neural diffeomorphism \\(f^\\theta\\) to the singular values of a pre-trained weight matrix \\(\\mathbf{W}\\), resulting in updated features \\(\\mathbf{W}_A\\mathbf{x}\\). (Right) We use two sets of DiTASK modules: a joint transformation module for learning task synergies, and task-specific modules for individual adaptations. The transformed outputs serve as inputs to a shared decoder. This setup enables flexible, parameter-efficient fine-tuning while preserving the singular vectors of pre-trained weights." + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.371, + 0.484, + 0.401 + ], + "angle": 0, + "content": "able CPA velocity fields that require only 32 additional trainable parameters per layer." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.402, + 0.484, + 0.446 + ], + "angle": 0, + "content": "- We theoretically analyze the properties of DiTASK, showing that it requires less memory than other low-rank Transformer adaptation methods." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.447, + 0.484, + 0.492 + ], + "angle": 0, + "content": "- DITASK demonstrates state-of-the-art performance on PASCAL MTL tasks, achieving \\(26.27\\%\\) improvement over existing methods like MTLoRA." + }, + { + "type": "list", + "bbox": [ + 0.114, + 0.402, + 0.484, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.493, + 0.484, + 0.599 + ], + "angle": 0, + "content": "The rest of the paper is organized as follows: In Section 2, we discuss the related work on parameter-efficient fine-tuning and MTL. In Section 3, we provide the mathematical background to understand DiTASK. Section 4 details DiTASK for learning diffeomorphic singular value adjustment, and Section 5 presents experimental results and analyses." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.614, + 0.255, + 0.63 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.641, + 0.484, + 0.729 + ], + "angle": 0, + "content": "Our work lies at the intersection of four research areas: multi-task vision learning, parameter-efficient fine-tuning, neural network adaptation, and diffeomorphisms. We discuss each area with a focus on how they relate to weight matrix transformations and singular value adaptation." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.731, + 0.484, + 0.912 + ], + "angle": 0, + "content": "Multi-Task Learning in Vision. Multi-task learning models in vision typically adopt an encoder-decoder structure, where a shared encoder captures common features, and task-specific decoders handle individual objectives [35]. This approach has proven particularly effective for dense prediction tasks, with different decoders handling semantic segmentation, depth estimation, and surface normal prediction while sharing a common feature backbone [24]. While recent work has extended this framework to Vision Transformers (ViTs) [12], these adaptations face unique challenges due to their large parameter count and the complex in" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.371, + 0.885, + 0.476 + ], + "angle": 0, + "content": "teractions between task-specific updates. To address these issues, DiTASK introduces an encoder adaptation strategy that modulates singular values while retaining pre-trained singular vectors, rather than modifying full weight matrices or adding task-specific layers. This leverages the encoder-decoder framework for efficient adaptation of the shared encoder." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.478, + 0.885, + 0.704 + ], + "angle": 0, + "content": "Parameter-Efficient Fine-tuning Methods. These methods reduce computational overhead for model adaptation using various strategies. Adapter-based approaches [18] insert small trainable modules between transformer layers. Visual Prompt Tuning (VPT) [22] introduces trainable parameters in ViT input tokens, distinguishing it from standard adaptation approaches. Compactor [31] and BitFit [58] add minimal trainable parameters, enabling lightweight gradients via Kronecker products of rank-one and low-rank matrices and fine-tuning only biases, respectively. Hyperformers [31] use hypernetworks to generate adapter layers for multi-task language learning, while Polyhistor [27] adapts this for dense vision tasks. VL-Adapter [44] introduces adapters for joint Vision-Language (VL) multi-task fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.71, + 0.885, + 0.862 + ], + "angle": 0, + "content": "With the introduction of GPT-2 [38] and the rise in parameter sizes and task variety, methods like Low-Rank Adaptation (LoRA)[19] have gained traction in both language and vision. These methods restrict weight updates to fixed low-dimensional subspaces, enhancing resource efficiency. Other approaches, such as SVFT[25], enforce sparse singular values, while DoRA [26] decouples the magnitude and direction of weight update columns. In contrast, ReFT [53] uses low-rank approximation to adapt representations rather than weights." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.867, + 0.885, + 0.913 + ], + "angle": 0, + "content": "Although most of these methods are not specifically designed for multi-task learning (MTL), MTLoRA [1] has applied LoRA within an MTL framework. By en" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.519, + 0.963 + ], + "angle": 0, + "content": "25220" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.112, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "abling both task-agnostic and task-specific adaptations along with joint inference, MTLoRA has achieved state-of-the-art results on dense vision tasks. However, these methods, while effective in preserving pre-trained knowledge, still impose subspace constraints that can degrade performance relative to single-task baselines." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.199, + 0.484, + 0.32 + ], + "angle": 0, + "content": "DiTASK takes a fundamentally different approach: instead of adding modules or modifying weights directly, we preserve the pre-trained singular vectors while enabling flexible adaptation via diffeomorphisms of singular values. This allows us to maintain both architectural efficiency and rich feature adaptability, without altering the input-output mapping learned during pre-training." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.337, + 0.485, + 0.609 + ], + "angle": 0, + "content": "Multi-Task Learning Dynamics and Challenges. A recent study of Transformer training dynamics reveals an incremental learning phenomenon where weight update ranks gradually increase during training [5]. This finding challenges the effectiveness of fixed-rank adaptation methods in MTL settings. While MTLoRA [1] attempts to address this through task-agnostic and task-specific modules, it still operates within fixed low-rank constraints. Similarly, gradient interference mitigation techniques like PCGrad address conflicts between task updates but do not provide the flexibility needed for diverse task adaptations. In contrast, DITASK aligns with natural learning dynamics by preserving the full-rank structure through singular vector retention while enabling task-specific adaptations via neural diffeomorphisms [14, 15], uniquely combining parameter efficiency with the adaptability needed for effective multi-task learning." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.625, + 0.484, + 0.913 + ], + "angle": 0, + "content": "Diffeomorphisms in Neural Networks. A bijective mapping \\( f: \\mathcal{M} \\to \\mathcal{N} \\) between two differentiable manifolds \\( \\mathcal{M} \\) and \\( \\mathcal{N} \\) is a diffeomorphism if both \\( f \\) and its inverse \\( f^{-1}: \\mathcal{N} \\to \\mathcal{M} \\) are differentiable. Learning diffeomorphisms poses computational challenges, as early methods were constrained by complex, infinite-dimensional spaces [43], and later Markov Chain Monte Carlo methods remained demanding [2, 3, 60]. Freifeld et al. [14, 15] addressed these issues with Continuous Piecewise-Affine Based (CPAB) transformations, a finite-dimensional approach suited for precise 1D diffeomorphisms, ideal for neural activation functions. CPAB offers linear complexity, supports parallelization, and achieves sub-linear performance in practice [15]. Initially developed for alignment and regression, CPAB is now widely applied in neural networks. For instance, in spatial transformer layers with CPAB [11], temporal alignment [34], novel loss function for time-series analysis [52], image animation [49], geometry-guided fine" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.089, + 0.885, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.467, + 0.884, + 0.522 + ], + "angle": 0, + "content": "Figure 4. DiTASK in the \\(i\\)-th Swin Transformer stage for multi-task learning. Task-agnostic modules are applied in all blocks except the last, which uses task-specific modules to capture task-dependent features." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.55, + 0.884, + 0.581 + ], + "angle": 0, + "content": "tuning [32] and trainable CPAB-based activation function [8, 33]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.596, + 0.796, + 0.614 + ], + "angle": 0, + "content": "3. Preliminaries and Background" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.622, + 0.884, + 0.683 + ], + "angle": 0, + "content": "We combine two key components: the weights in ViTs, and the mathematical framework of CPAB diffeomorphisms. We now provide the background for understanding the coupling of these concepts in DiTASK." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.694, + 0.741, + 0.71 + ], + "angle": 0, + "content": "3.1. Learned Weights in ViTs" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.884, + 0.793 + ], + "angle": 0, + "content": "ViTs encode visual knowledge in their weight matrices, which can be analyzed through Singular Value Decomposition (SVD). Assume we have a weight matrix that transforms inputs from \\( c_{1} \\) to \\( c_{2} \\) channels, denoted by \\( \\mathbf{W} \\in \\mathbb{R}^{c_2 \\times c_1} \\), then its SVD reads:" + }, + { + "type": "equation", + "bbox": [ + 0.647, + 0.806, + 0.884, + 0.823 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} = \\mathbf {U} \\boldsymbol {\\Sigma} \\mathbf {V} ^ {\\top}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.836, + 0.885, + 0.913 + ], + "angle": 0, + "content": "where \\(\\mathbf{U} \\in \\mathbb{R}^{c_2 \\times c_2}\\), \\(\\pmb{\\Sigma} \\in \\mathbb{R}^{c_2 \\times c_1}\\), \\(\\mathbf{V} \\in \\mathbb{R}^{c_1 \\times c_1}\\). We refer to \\(\\mathbf{U}\\) as the left singular vectors, \\(\\pmb{\\Sigma}\\) as the singular values, and \\(\\mathbf{V}\\) as the right singular vectors. Notably, \\(\\mathbf{U}\\) and \\(\\mathbf{V}\\) form orthonormal bases for the output and input spaces of the linear map represented by \\(\\mathbf{W}\\), respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.518, + 0.963 + ], + "angle": 0, + "content": "25221" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.111, + 0.092, + 0.486, + 0.121 + ], + "angle": 0, + "content": "These bases characterize how the network transforms visual features across layers and hidden dimensions." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.122, + 0.486, + 0.348 + ], + "angle": 0, + "content": "Problem Setup. Throughout this paper, we assume \\(K\\) tasks \\(\\mathcal{T} = \\{T_1,\\dots ,T_K\\}\\). Each task \\(T_{k}\\) has an associated dataset \\(\\mathcal{D}_k = \\{(x_i^k,y_i^k)\\}_{i = 1}^{N_k}\\) where \\(x_{i}^{k}\\in \\mathcal{X}\\) and \\(y_{i}^{k}\\in \\mathcal{Y}_{k}\\) represent the input-output pairs. The goal is to train a neural network to minimize a supervised loss between the prediction and ground-truth output. Following [1], we use a Swin Transformer [28], which processes input images by dividing them into nonoverlapping patches and progressively merging patches to reduce spatial resolution while increasing feature dimension across stages. Formally, the Swin Transformer processes images through \\(L\\) stages, with the \\(l\\)-th stage operating on feature maps of resolution \\(\\frac{H}{2^l}\\times \\frac{W}{2^l}\\) with \\(C_l\\) channels. The key operation in each stage is a Window-based Multi-head Self-Attention (W-MSA):" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.355, + 0.484, + 0.391 + ], + "angle": 0, + "content": "\\[\n\\mathrm {W} - \\mathrm {M S A} (Q, K, V) = \\operatorname {S o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d}}\\right) V, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.398, + 0.484, + 0.507 + ], + "angle": 0, + "content": "where \\(Q, K, V \\in \\mathbb{R}^{M \\times d}\\) are query, key, and value matrices for windows of size \\(M\\). The corresponding weight matrices \\(\\mathbf{W}_l^{(q)}, \\mathbf{W}_l^{(k)}, \\mathbf{W}_l^{(v)} \\in \\mathbb{R}^{d \\times d}\\) for these projections in layer \\(l\\) are central to our DiTASK, because in Section 4 we dynamically adjust their singular values for multi-task adaptations. The MTL objective minimizes a weighted combination of \\(K\\) task losses:" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.515, + 0.484, + 0.556 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Theta} \\sum_ {k = 1} ^ {K} \\lambda_ {k} \\mathcal {L} _ {k} (\\Theta ; \\mathcal {D} _ {k}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.564, + 0.484, + 0.61 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_k\\) and \\(\\lambda_{k}\\) represent the loss function and weight for the \\(k\\)-th task, respectively. In Figure 4, we illustrate the overall architecture used in this paper." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.617, + 0.484, + 0.648 + ], + "angle": 0, + "content": "3.2. CPAB Diffeomorphisms for Weight Transformation" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.655, + 0.486, + 0.777 + ], + "angle": 0, + "content": "As we show later in Section 4, our DiTASK modifies singular values \\(\\Sigma\\) while preserving the structure of weight matrices. To achieve that, transformations that are smooth, invertible, and monotone, are required. Continuous Piecewise Affine-Based (CPAB) [14, 15] diffeomorphisms satisfy these conditions while being efficient in terms of parameters and computing diffeomorphisms. We now turn to define CPAB formally." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.784, + 0.486, + 0.875 + ], + "angle": 0, + "content": "Definition 3.1 (CPAB Transformation). Given a closed interval \\(\\Omega = [a,b]\\) partitioned into \\(\\mathcal{N}_{\\mathcal{P}}\\) intervals, a CPAB transformation is defined through a velocity field \\(v^{\\theta}:\\Omega \\to \\mathbb{R}\\) that is continuous and piecewise-affine within each interval. This velocity field, parameterized by \\(\\pmb {\\theta}\\in \\mathbb{R}^{\\mathcal{N}_{\\mathcal{P}} - 1}\\), yields a diffeomorphism \\(f^{\\theta}\\) of the form:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.882, + 0.484, + 0.917 + ], + "angle": 0, + "content": "\\[\nf ^ {\\boldsymbol {\\theta}} (x) = x + \\int_ {0} ^ {1} v ^ {\\boldsymbol {\\theta}} \\left(f ^ {\\boldsymbol {\\theta}} (x, \\tau)\\right) d \\tau . \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.885, + 0.244 + ], + "angle": 0, + "content": "For practical implementation, we use the Python package from Martinez et al. [34], and provide additional details in the supplementary material. CPAB transformations are ideal for our settings, shown in Section 4, because they provide: (i) Low parameter overhead. Only \\(\\mathcal{O}(\\mathcal{N}_{\\mathcal{P}})\\) parameters, where typically \\(\\mathcal{N}_{\\mathcal{P}} \\leq 128\\); (ii) Differentiability. Enables gradient-based optimization; (iii) Computational efficiency. Computing Equation (4) is of linear complexity; (iv) Stability. CPAB transformations are Lipschitz continuous [15]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.255, + 0.884, + 0.29 + ], + "angle": 0, + "content": "4. DiTASK: Diffeomorphic Multi-Task Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.297, + 0.885, + 0.448 + ], + "angle": 0, + "content": "We introduce DITASK (Diffeomorphic Multi-Task Adaptation), a novel approach for efficient multi-task fine-tuning. Our method is grounded in a fundamental analysis of how neural networks process information through their weight matrices. We draw insights from linear algebra to the workings of a linear layer of neural network in Section 4.1 relating it to SVD. In Section 4.2, we formally introduce DITASK and elaborate on its properties that motivate our design choices in Section 4.3." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.457, + 0.797, + 0.473 + ], + "angle": 0, + "content": "4.1. Understanding Weight Matrices" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.884, + 0.602 + ], + "angle": 0, + "content": "We now show that by considering the SVD of weight matrices, we can gain insights on the course of action of linear layers, that later, in Section 4.2, serves as a mathematically grounded motivation for the design of our DiTASK. Specifically, we note that a linear layer with weight matrix \\(\\mathbf{W} \\in \\mathbb{R}^{c_2 \\times c_1}\\), and its SVD decomposition \\(\\mathbf{W} = \\mathbf{U} \\boldsymbol{\\Sigma} \\mathbf{V}^{\\top}\\), can be viewed as a linear map \\(g: \\mathbb{R}^{c_1} \\to \\mathbb{R}^{c_2}\\), such that the following equality holds:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.608, + 0.884, + 0.647 + ], + "angle": 0, + "content": "\\[\ng (\\mathbf {x}) = \\mathbf {W} \\mathbf {x} = \\sum_ {i = 1} ^ {p} \\sigma_ {i} \\langle \\mathbf {x}, \\mathbf {v} _ {i} \\rangle \\mathbf {u} _ {i}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.655, + 0.885, + 0.715 + ], + "angle": 0, + "content": "where \\(\\mathbf{U} = [\\mathbf{u}_1, \\dots, \\mathbf{u}_{c_2}]\\), \\(\\mathbf{V} = [\\mathbf{v}_1, \\dots, \\mathbf{v}_{c_1}]\\), and \\(\\boldsymbol{\\Sigma} = \\text{diag}([\\sigma_1, \\sigma_2, \\dots, \\sigma_p])\\), \\(p = \\min(c_1, c_2)\\). The basis vectors in \\(\\mathbf{U}\\) are the left singular vectors, \\(\\mathbf{V}\\) are right singular vectors, and \\(\\boldsymbol{\\Sigma}\\) are the singular values of \\(\\mathbf{W}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.715, + 0.885, + 0.852 + ], + "angle": 0, + "content": "Specifically, the orientations encoded by the left and right singular vectors represent features present in the output and input spaces of the linear transformation \\( g \\), respectively. Multi-task learning requires adapting these orientations jointly for all tasks, while minimizing task interference to prevent performance degradation. Below, we describe how to achieve effective multi-task adaptation using diffeomorphisms, by preserving the singular vectors \\( \\mathbf{U} \\), \\( \\mathbf{V} \\) and modifying \\( \\mathbf{W} \\) in a principled manner." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.859, + 0.743, + 0.875 + ], + "angle": 0, + "content": "4.2. Adaptation with DITASK" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.881, + 0.884, + 0.914 + ], + "angle": 0, + "content": "Given a learned weight matrix \\(\\mathbf{W} = \\mathbf{U}\\pmb{\\Sigma}\\mathbf{V}^{\\top} \\in \\mathbb{R}^{c_2 \\times c_1}\\) from a ViT, we transform the singular values \\(\\pmb{\\Sigma}\\) by a" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.519, + 0.964 + ], + "angle": 0, + "content": "25222" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.112, + 0.091, + 0.486, + 0.136 + ], + "angle": 0, + "content": "learned neural diffeomorphism \\(f^{\\theta}\\) described in Equation (4), to get the adapted weight matrix \\(\\mathbf{W}_A\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.145, + 0.484, + 0.229 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} _ {A} = \\mathbf {U} \\left[ \\begin{array}{c c c c} f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {1}\\right) & 0 & \\dots & 0 \\\\ 0 & f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {2}\\right) & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {p}\\right) \\end{array} \\right] \\mathbf {V} ^ {\\top}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.23, + 0.484, + 0.365 + ], + "angle": 0, + "content": "During fine-tuning, we freeze \\(\\mathbf{W}\\) and learn only the parameters \\(\\theta\\) of the CPA velocity field. This allows DiTASK to adapt to multiple tasks using \\(\\mathcal{O}(\\mathcal{N}_{\\mathcal{P}})\\) additional parameters (where typically \\(\\mathcal{N}_{\\mathcal{P}} \\leq 128\\)), which is significantly smaller than methods with low-rank \\(r\\) using \\(\\mathcal{O}(r(c_1 + c_2))\\). We describe this process in the Section 1, and compare the computational cost of DiTASK with other fine-tuning methods in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.366, + 0.484, + 0.489 + ], + "angle": 0, + "content": "Multi-Task Adaptation with DiTASK. To enable both multi and task-specific adaptation, we learn two sets of neural diffeomorphic transformations in every pretrained weight matrix \\(\\mathbf{W}\\), shown in Section 1, that include: (i) Joint Adaptation parameters, denoted by \\(\\theta_{j}\\), to allow task synergies which are crucial for MTL [21, 47]; and (ii) Task-wise Adaptation parameters, denoted by \\(\\{\\theta_k\\}_{k=1}^K\\) to enable learning nuances for each task." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.497, + 0.315, + 0.512 + ], + "angle": 0, + "content": "4.3. Properties of DITASK" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.52, + 0.484, + 0.565 + ], + "angle": 0, + "content": "In this section, we motivate our design choices and discuss the properties that make DiTASK an effective and parameter-efficient fine-tuning method for MTL." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.566, + 0.484, + 0.851 + ], + "angle": 0, + "content": "Feature Space Preservation. As discussed in Section 4.1, pre-trained weight matrices encode feature transformations through their singular vectors, where \\(\\mathbf{U}\\) and \\(\\mathbf{V}\\) form orthonormal bases for output and input spaces, respectively. These bases capture the orientation of patterns learned during pre-training, each weighted by its corresponding singular value. In contrast to traditional low-rank methods like LoRA, which constrain adaptations to fixed low-dimensional subspaces, potentially losing important features, our DiTASK preserves these learned bases entirely. This preservation allows us to achieve superior multi-task performance with fewer parameters, as shown in Figure 1. Specifically, while low-rank methods require increasing their rank (and thus parameters and departure from being low-rank) to match single-task performance, our DiTASK maintains the learned feature space of pre-trained ViTs through a targeted and mathematically-ground singular value modulation." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.852, + 0.484, + 0.913 + ], + "angle": 0, + "content": "Feature Relativity Preservation. The order of singular values \\(\\sigma_{1} \\geq \\sigma_{2} \\geq \\ldots \\geq \\sigma_{p}\\) in weight matrices of ViTs encode the relative importance of features learned during pre-training on large-scale datasets like" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.885, + 0.273 + ], + "angle": 0, + "content": "ImageNet-21k. By utilizing diffeomorphisms, which are smooth, invertible, and monotone, by definition, we preserve this ordering. That is, if \\( f^{\\theta} \\) is a diffeomorphism, then \\( f^{\\theta}(\\sigma_1) \\geq f^{\\theta}(\\sigma_2) \\geq \\ldots \\geq f^{\\theta}(\\sigma_p) \\) in Equation (6). Our choice of CPAB transformations implements this with only \\( \\mathcal{N}_{\\mathcal{P}} \\leq 128 \\) parameters per weight matrix, compared to the \\( \\mathcal{O}(r(c_1 + c_2)) \\) parameters required by low-rank adaptation methods. Our experiments in Section 5 demonstrate that preserving feature hierarchy through diffeomorphic transformations enables effective multi-task generalization while maintaining parameter efficiency." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.289, + 0.646, + 0.307 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.315, + 0.884, + 0.406 + ], + "angle": 0, + "content": "We evaluate DiTASK on multiple MTL benchmarks and compare it with other adaptation methods. Section 5.1 details the experimental setup and baselines, Section 5.2 discusses our main findings, and Section 5.3 presents few ablation studies of DiTASK. We seek to address three key research questions:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.407, + 0.884, + 0.451 + ], + "angle": 0, + "content": "(RQ1) Can a selective modification of singular values while preserving singular vectors bridge the performance gap between decoder-only and full fine-tuning?" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.452, + 0.883, + 0.481 + ], + "angle": 0, + "content": "(RQ2) Does full-rank preservation by singular value modulation outperform low-rank adaptation methods?" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.482, + 0.883, + 0.512 + ], + "angle": 0, + "content": "(RQ3) How does DiTASK compare to other parameter-efficient adaptation methods?" + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.407, + 0.884, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.524, + 0.704, + 0.541 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.548, + 0.884, + 0.683 + ], + "angle": 0, + "content": "Datasets and Tasks. We evaluate DiTASK on the PASCAL-MTL dataset [13] (PASCAL-Context split) following the literature on multi-task dense prediction [46, 54, 55]. This dataset includes 4,998 training and 5,105 validation images with annotations for semantic segmentation (21 classes), human part segmentation (7 classes), surface normal estimation, and saliency detection. Additional experiments on the NYUD dataset [41] are provided in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.684, + 0.884, + 0.85 + ], + "angle": 0, + "content": "Implementation Details. We use the Swin-Tiny [28] architecture, pre-trained on ImageNet-21k [39] as the backbone encoder, similar to [1]. To ensure a fair comparison, we incorporate the HRNet [50] decoder, which accounts for \\(6\\%\\) of the total parameters, as in previous works [1, 46]. Following MTINet [46], we apply cross-entropy loss for segmentation tasks, \\(\\ell_1\\) loss for surface normals, and balanced cross-entropy [9] for saliency detection, with same task weights \\(\\{\\lambda_k\\}_{k=1}^K\\) used in MTINet. In all experiments, we follow the evaluation protocol from Agiza et al. [1]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.851, + 0.884, + 0.88 + ], + "angle": 0, + "content": "Baselines. We benchmark our DiTASK with three categories of methods:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.882, + 0.884, + 0.913 + ], + "angle": 0, + "content": "- Full Fine-Tuning: Methods that modify all weight matrices (single-task, MTL decoder, full MTL)" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.518, + 0.963 + ], + "angle": 0, + "content": "25223" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.111, + 0.089, + 0.888, + 0.158 + ], + "angle": 0, + "content": "Table 1. Performance on PASCAL Context for Multi-Task Learning. Comparison of DITASK with full fine-tuning, adapter-based, and fixed-rank methods across four dense prediction tasks: semantic segmentation, human part segmentation, saliency detection, and surface normal estimation. Metrics are MIOU (↑) and RMSE (↓), with \\(\\Delta m\\) denoting relative improvement over single-task tuning. DITASK achieves strong performance with minimal trainable parameters and supports joint inference across tasks." + }, + { + "type": "table", + "bbox": [ + 0.121, + 0.164, + 0.875, + 0.484 + ], + "angle": 0, + "content": "
    MethodSEMSEG (MIOU ↑)HUMAN PARTS (MIOU ↑)SALIENCY (MIOU ↑)NORMALS (RMSE ↓)Δm(%)Trainable Swin Parameters (M)Single Inference For All Tasks
    FULL FINE-TUNING
    Single Task67.2161.9362.3517.970.00112.62×
    MTL - Dec. Only65.0953.4857.4620.69- 9.950✓
    MTL - Full67.5660.2465.2116.64+ 2.2328.12✓
    ADAPTER-BASED
    VPT-shallow [22]62.9652.2758.3120.90-11.180.63×
    VPT-deep [22]64.3552.5458.1521.07-10.851.49×
    Compactor++ [23]67.2655.6959.4719.54- 5.840.72×
    Bitfit [58]68.5755.9960.6419.42- 4.600.91×
    Compactor [23]68.0856.4160.0819.22- 4.550.84×
    Adapter [17]69.2157.3861.2818.83- 2.719.26×
    VL-Adapter [44]70.2159.1562.2919.26- 1.832.80×
    Polyhistor [27]70.8759.1565.5417.77+ 2.347.02×
    HyperFormer [31]71.4360.7365.5417.77+ 2.6470.83×
    FIXED-RANK
    MTL - DoRA [26]52.3650.8263.5318.32-10.026.40✓
    MTL - ReFT [53]68.7556.4958.7620.54- 6.6316.16✓
    MTL - SVFT [25]64.4455.9463.0317.86- 3.023.83✓
    LoRA [19]70.1257.7361.9018.96- 2.170.93×
    MTLoRA [1] (r = 16)68.1958.9964.4817.03+ 1.353.01✓
    MTLoRA [1] (r = 32)67.7459.4664.9016.59+ 2.164.14✓
    MTLoRA [1] (r = 64)67.9059.8465.4016.60+ 2.556.40✓
    Single Task - DITASK72.2062.3365.7016.55+ 5.331.60 (×4)×
    MTL - DITASK (Ours)69.6662.0265.0017.10+ 3.221.61✓
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.176, + 0.496, + 0.82, + 0.51 + ], + "angle": 0, + "content": "Table 2. Effect of Backbone Size - Relative improvement increases with increasing capacity of the backbone" + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.515, + 0.875, + 0.616 + ], + "angle": 0, + "content": "
    MethodSEMSEG (MIOU ↑)HUMAN PARTS (MIOU ↑)SALIENCY (MIOU ↑)NORMALS (RMSE ↓)Δm(%)Trainable Swin Parameters (M)
    DITASK + Swin-Tiny69.6662.0265.0017.10+3.221.61
    DITASK + Swin-Small74.4963.2064.5817.58+4.681.66
    DITASK + Swin-Base75.8665.9764.1817.29+6.523.14
    DITASK + Swin-Large76.2367.5364.0716.90+7.797.13
    " + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.64, + 0.483, + 0.7 + ], + "angle": 0, + "content": "- Adapter-based: Methods that add task-specific layers while preserving main weights (Adapter [18], BitFit [58], VPT [22], Compactor [23], VL-Adapter [44], HyperFormer [31], Polyhistor [27])" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.701, + 0.483, + 0.745 + ], + "angle": 0, + "content": "- Fixed-Rank: Methods that constrain updates to low-rank subspaces (LoRA [19], DoRA [26], SVFT [25], ReFT [53], MTLoRA [1])" + }, + { + "type": "list", + "bbox": [ + 0.114, + 0.64, + 0.483, + 0.745 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.753, + 0.325, + 0.768 + ], + "angle": 0, + "content": "5.2. Results and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.776, + 0.483, + 0.821 + ], + "angle": 0, + "content": "Table 1 presents our main results, addressing (RQ1)-(RQ3) on the effectiveness of DiTASK for multi-task learning (MTL)." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.822, + 0.483, + 0.912 + ], + "angle": 0, + "content": "Bridging the Efficiency Performance Gap. DiTASK achieves a \\(+3.22\\%\\) relative improvement over single-task baselines using only 1.61M trainable encoder parameters. This outperforms both decoder-only tuning \\((-9.95\\%)\\) and full fine-tuning \\((+2.23\\%)\\), demonstrating that modulating singular values while preserving pre" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.64, + 0.882, + 0.67 + ], + "angle": 0, + "content": "trained feature directions enables an effective balance between parameter efficiency and performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.671, + 0.885, + 0.805 + ], + "angle": 0, + "content": "Comparison with Fixed Low-Rank Methods. DTASK outperforms the state-of-the-art MTLoRA by \\(26.27\\%\\) in \\(\\Delta m\\), using \\(4\\times\\) fewer parameters (Figure 5). Most fixed-rank methods yield negative \\(\\Delta m\\) due to task interference from shared low-rank subspaces. By modulating singular values independently per task while preserving full-rank structure, DTASK mitigates this interference. Similar trends are observed on NYUD (Table 4)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.807, + 0.885, + 0.895 + ], + "angle": 0, + "content": "Parameter Efficiency and Task Performance. DITASK is the only parameter-efficient method to consistently improve over single-task baselines, showing that modulating singular values while preserving pretrained directions effectively balances efficiency and performance." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.518, + 0.963 + ], + "angle": 0, + "content": "25224" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.094, + 0.475, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.268, + 0.483, + 0.297 + ], + "angle": 0, + "content": "Figure 5. Comparison of adaptation parameter budget of the shared encoder, excluding LayerNorm parameters." + }, + { + "type": "table_caption", + "bbox": [ + 0.112, + 0.317, + 0.485, + 0.373 + ], + "angle": 0, + "content": "Table 3. Comparison of computational efficiency between DiTASK and MTLoRA. DiTASK reduces batch runtime by \\(\\approx 22\\%\\), lowers memory usage, and uses \\(500\\times\\) fewer adaptation parameters." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.384, + 0.484, + 0.449 + ], + "angle": 0, + "content": "
    MethodBatch Runtime (seconds)Max GPU Mem (Megabytes)# Adaptation Params
    MTLoRA35.20±1.05235094.86M
    DiTASK27.31±5.29229068.5K
    " + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.478, + 0.266, + 0.495 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.505, + 0.483, + 0.534 + ], + "angle": 0, + "content": "We analyze key components of DiTASK to understand their contributions to multi-task performance." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.535, + 0.484, + 0.625 + ], + "angle": 0, + "content": "Computational Efficiency. DITASK uses only 8.5K adaptation parameters, compared to MTLoRA's 4.86M, while achieving \\(22\\%\\) faster batch processing (27.31s vs 35.20s) and reduced memory usage (see Table 3). The efficiency gains stem from our compact CPAB parameterization of singular value transformations." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.626, + 0.484, + 0.775 + ], + "angle": 0, + "content": "Joint vs Task-Wise Singular Value Modulation. We evaluate three configurations of singular value modulation, shown in Figure 7. Joint Adaptation alone, with shared modulation across tasks, achieves an improvement of \\(2.77\\%\\). Task-Wise Adaptation alone, which modulates singular values independently for each task, yields \\(2.85\\%\\). The Combined approach, DiTASK, incorporates both strategies and reaches the highest improvement at \\(3.22\\%\\), supporting the use of both shared and task-specific transformations." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.777, + 0.484, + 0.837 + ], + "angle": 0, + "content": "Model Scaling Analysis. The effectiveness of DiTASK scales with model capacity (Table 2). This scaling effect indicates that larger models provide richer singular value spaces, enabling more effective task-specific adaptation." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.838, + 0.484, + 0.913 + ], + "angle": 0, + "content": "Qualitative Comparison. In Figure 6, we present a visual comparison between MTLoRA and our DiTASK on the semantic segmentation task from PASCAL MTL. DiTASK demonstrates tighter and clearer boundaries, more consistent segmentation, and improved class sep" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.089, + 0.885, + 0.188 + ], + "angle": 0, + "content": "
    MethodSEMSEG(MIOU↑)DEPTH(RMSE↓)Δm(%)Trainable Params(in M)
    Single Task33.180.6670112.62
    MTL - Dec. Only28.370.832-19.611.00
    MTL - Full35.290.734-1.8428.5
    MTLoRA37.180.635+8.426.26
    Single Task - DITASK44.010.644+18.041.61
    DITASK43.850.606+20.651.61
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.198, + 0.884, + 0.24 + ], + "angle": 0, + "content": "Table 4. Comparison of DiTASK and MTLoRA on the NYUD [41] multi-task dataset for semantic segmentation (MIOU) and depth estimation (RMSE)." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.261, + 0.887, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.442, + 0.884, + 0.47 + ], + "angle": 0, + "content": "Figure 6. Semantic segmentation predictions on PASCAL MTL using MTLoRA and D1TASK." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.502, + 0.884, + 0.561 + ], + "angle": 0, + "content": "aration. For example, in the dimly lit sofa scene in the second column, MTLoRA struggles to correctly predict the sofa boundary, while DITASK offers a better prediction." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.583, + 0.634, + 0.599 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.61, + 0.886, + 0.913 + ], + "angle": 0, + "content": "In this paper, we introduce DiTASK, a novel MTL fine-tuning approach that leverages neural diffeomorphisms for singular value adaptation while preserving the structure of pre-trained representations. We observe that existing methods, which restrict weight updates to fixed low-rank subspaces for resource efficiency, often suffer from multi-task performance degradation relative to single-task baselines. We conjecture that the singular vectors of pre-trained weight matrices capture rich features, and preserving them during MTL adaptation enhances performance. By using neural diffeomorphisms, DiTASK maintains feature space and relational structure while requiring less memory than other low-rank adaptation methods. We evaluate DiTASK on the PASCAL MTL and NYUD MTL datasets, with extensive ablation studies demonstrating its effectiveness. Our results show that DiTASK achieves state-of-the-art MTL performance with \\(75\\%\\) fewer trainable parameters, underscoring the importance of preserving singular vectors in pre-trained weights." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.518, + 0.963 + ], + "angle": 0, + "content": "25225" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.115, + 0.09, + 0.21, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.123, + 0.116, + 0.486, + 0.206 + ], + "angle": 0, + "content": "[1] Ahmed Agiza, Marina Neseem, and Sherief Reda. Mtlora: Low-rank adaptation approach for efficient multi-task learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16196-16205, 2024. 1, 2, 3, 4, 5, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.123, + 0.208, + 0.485, + 0.268 + ], + "angle": 0, + "content": "[2] Stéphanie Allissonnière, Estelle Kuhn, and Alain Trouve. 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Yet, efficiently adapting them for multiple tasks remains a challenge that arises from the need to modify the rich hidden representations encoded by the learned weight matrices, without inducing interference between tasks. Current parameter-efficient methods like LoRA, which apply low-rank updates, force tasks to compete within constrained subspaces, ultimately degrading performance. We introduce DITASK a novel Diffeomorphic Multi-Task Fine-Tuning approach that maintains pre-trained representations by preserving weight matrix singular vectors, while enabling task-specific adaptations through neural diffeomorphic transformations of the singular values. By following this approach, DITASK enables both shared and task-specific feature modulations with minimal added parameters. Our theoretical analysis shows that DITASK achieves full-rank updates during optimization, preserving the geometric structure of pretrained features, and establishing a new paradigm for efficient multi-task learning (MTL). Our experiments on PASCAL MTL and NYUD show that DITASK achieves state-of-the-art performance across four dense prediction tasks, using $75\%$ fewer parameters than existing methods. Our code is available here. + +# 1. Introduction + +Vision Transformers (ViTs) have emerged as compelling models for computer vision, achieving remarkable performance across various tasks by leveraging self-attention mechanisms [12, 48] and large-scale pretraining [39, 42] on extensive datasets like ImageNet + +21k [10]. These models encode essential visual knowledge in their weight matrices through singular vectors that characterize the principal directions in the input space and output spaces [36, 40]. However, existing fine + +![](images/c14483aae385f4519c9a56be63c5e97bf8d961cc247baabcb557441834c6a862.jpg) +Figure 1. Performanceefficiency trade-off in multi-task learning (MTL) on PASCAL MTL tasks. DITASK outperforms single-task fine-tuning with fewer parameters than fixed-rank methods (LoRA [19]) and other PEFT approaches (Adapter [18]). The gray region shows negative relative improvement over single-task tuning, highlighting the challenge of achieving gains under tight parameter budgets. + +tuning methods based on low-rank adaptation (LoRA) [1, 19] may not preserve these learned singular vectors. In Figure 2, we illustrate the importance of preserving the singular vectors; recovering a noisy image by ad + +![](images/76a775a55846fbc7c0b5f273c843bcff559535cfc274cbc13b3aac42e033e69a.jpg) +Original Image +LoRA - PSNR: 22.97 dB + +![](images/f475352239a431517e72f3e7122e59d8ef7d6abff5139a924c600e84ba68e531.jpg) +Noisy Image +DTASK-PSNR:25.10 dB + +![](images/820bca12110f903e1527a53fdecaa048f14bea49d32ea4fdc699efef72bcc8e0.jpg) +Figure 2. Image recovery comparison of LoRA and DiTASK. Preserving singular vectors enables DiTASK to achieve a higher peak signal-to-noise ratio (PSNR). + +![](images/9231f22a4d59c606a9cb522094f6781e7de147952cd5d88c544c361b0f93cf56.jpg) + +justing only its singular values while keeping singular vectors yields superior performance than using LoRA, which may not preserve the singular vectors of the image. Singular vectors encode crucial image details, and low-rank denoising methods can lose these details, resulting in poor denoising quality. Preserving singular vectors serves as an implicit regularizer. This motivating example suggests that useful adaptations can be achieved through singular value modulation and inspires us to design a mathematically-ground method to achieve this goal. + +Fine-tuning of pre-trained ViTs for downstream tasks, such as few-shot learning [20, 37], typically involves adapting the learned representations to the target application. However, the substantial size of these models calls for a resource-efficient fine-tuning technique. Parameter-efficient and low-rank optimization approaches, such as LoRA [19], offer promising solutions by reducing the number of trainable parameters. This strategy not only enhances resource efficiency (e.g., lower VRAM and FLOPS requirements), but also helps keep valuable pretrained filters that capture essential visual knowledge [6] by preventing catastrophic forgetting [16, 30]. + +In the context of single-task fine-tuning, parameter-efficient and low-rank methods have proven highly successful [18, 19, 23, 31]. However, in Multi-Task Learning (MTL) settings, these methods were shown to struggle [1]. Particularly, MTL typically requires isolating task gradients to prevent task interference (e.g., enforcing gradient orthogonality [45, 56]), a requirement that becomes increasingly challenging as the dimension or + +rank of the gradients decreases. Thus, we face a tradeoff between lowering the number of trainable parameters and maintaining task performance. Evidently, as shown in Figure 1, existing methods can offer performance enhancement in MTL settings only when significantly increasing the number of trainable, effectively undermining their purpose of lightweight adaptation. + +We conjecture, inspired by recent studies [5] that identified an incremental learning phenomenon in transformers, that the underperformance of LoRA methods in MTL settings happens because of the direct and nonprincipled modification of weight matrices' singular vectors. These updates force distinct tasks to compete within the same constrained subspace. The key insight of our approach is realizing that while low-rank representations offer sufficient dimensionality for individual tasks, constraining multiple tasks to share the same low-rank subspace creates interference. An optimal subspace for one task may be suboptimal for others. Yet, existing methods force this competition by maintaining a single shared low-rank space, while a unique subspace for each task, like in MTLoRA [1], may not take advantage of task synergies. + +Our approach. To address the limitations of existing low-rank fine-tuning methods, we introduce Diffeomorphic Multi-Task Adaptation (DiTASK), a novel approach leveraging neural diffeomorphisms parameterized by Continuous Piecewise Affine-Based (CPAB) transformations [14, 15]. Specifically, DiTASK preserves pre-trained feature patterns by retaining the singular vectors of learned weight matrices while dynamically adjusting singular values through neural diffeomorphic transformations at each optimization step. Our diffeomorphic transformations are parameterized by Continuous Piecewise Affine (CPA) [14, 15] velocity fields over the weight matrix domain, ensuring continuous, invertible deformations. This design enables adaptation across multiple tasks while preserving the knowledge embedded during pre-training. We validate DiTASK on the PASCAL MTL dataset [13], a widely used benchmark for dense prediction tasks such as semantic segmentation, edge detection, and human body part segmentation. Our method achieves a $26.27\%$ improvement in average task performance while reducing parameter usage by $4\times$ compared to state-of-the-art methods like MTLoRA [1], demonstrating the effectiveness of preserving pre-trained feature directions for efficient multi-task fine-tuning. + +# Our contributions are as follows: + +- We propose a novel approach to MTL fine-tuning that leverages neural diffeomorphisms for singular value adaptation, enabling fine-tuning weight updates while preserving pre-trained representation structure. +- We develop an efficient parametrization using learn + +![](images/9cb3befc335fdf19c210421c47ab880d8f7825259e5b7657a57ff04ae94c2240.jpg) + +![](images/0891b82b79f754e2fa86d6eb253c646377a6046191087731dbb79e90b09df15d.jpg) +Figure 3. Overview of our DiTASK within Multi-Task Learning (MTL). (Left) Input features $\mathbf{x}$ are transformed via a modulated weight matrix $\mathbf{W}_A$ , constructed by applying a neural diffeomorphism $f^\theta$ to the singular values of a pre-trained weight matrix $\mathbf{W}$ , resulting in updated features $\mathbf{W}_A\mathbf{x}$ . (Right) We use two sets of DiTASK modules: a joint transformation module for learning task synergies, and task-specific modules for individual adaptations. The transformed outputs serve as inputs to a shared decoder. This setup enables flexible, parameter-efficient fine-tuning while preserving the singular vectors of pre-trained weights. + +able CPA velocity fields that require only 32 additional trainable parameters per layer. + +- We theoretically analyze the properties of DiTASK, showing that it requires less memory than other low-rank Transformer adaptation methods. +- DITASK demonstrates state-of-the-art performance on PASCAL MTL tasks, achieving $26.27\%$ improvement over existing methods like MTLoRA. + +The rest of the paper is organized as follows: In Section 2, we discuss the related work on parameter-efficient fine-tuning and MTL. In Section 3, we provide the mathematical background to understand DiTASK. Section 4 details DiTASK for learning diffeomorphic singular value adjustment, and Section 5 presents experimental results and analyses. + +# 2. Related Work + +Our work lies at the intersection of four research areas: multi-task vision learning, parameter-efficient fine-tuning, neural network adaptation, and diffeomorphisms. We discuss each area with a focus on how they relate to weight matrix transformations and singular value adaptation. + +Multi-Task Learning in Vision. Multi-task learning models in vision typically adopt an encoder-decoder structure, where a shared encoder captures common features, and task-specific decoders handle individual objectives [35]. This approach has proven particularly effective for dense prediction tasks, with different decoders handling semantic segmentation, depth estimation, and surface normal prediction while sharing a common feature backbone [24]. While recent work has extended this framework to Vision Transformers (ViTs) [12], these adaptations face unique challenges due to their large parameter count and the complex in + +teractions between task-specific updates. To address these issues, DiTASK introduces an encoder adaptation strategy that modulates singular values while retaining pre-trained singular vectors, rather than modifying full weight matrices or adding task-specific layers. This leverages the encoder-decoder framework for efficient adaptation of the shared encoder. + +Parameter-Efficient Fine-tuning Methods. These methods reduce computational overhead for model adaptation using various strategies. Adapter-based approaches [18] insert small trainable modules between transformer layers. Visual Prompt Tuning (VPT) [22] introduces trainable parameters in ViT input tokens, distinguishing it from standard adaptation approaches. Compactor [31] and BitFit [58] add minimal trainable parameters, enabling lightweight gradients via Kronecker products of rank-one and low-rank matrices and fine-tuning only biases, respectively. Hyperformers [31] use hypernetworks to generate adapter layers for multi-task language learning, while Polyhistor [27] adapts this for dense vision tasks. VL-Adapter [44] introduces adapters for joint Vision-Language (VL) multi-task fine-tuning. + +With the introduction of GPT-2 [38] and the rise in parameter sizes and task variety, methods like Low-Rank Adaptation (LoRA)[19] have gained traction in both language and vision. These methods restrict weight updates to fixed low-dimensional subspaces, enhancing resource efficiency. Other approaches, such as SVFT[25], enforce sparse singular values, while DoRA [26] decouples the magnitude and direction of weight update columns. In contrast, ReFT [53] uses low-rank approximation to adapt representations rather than weights. + +Although most of these methods are not specifically designed for multi-task learning (MTL), MTLoRA [1] has applied LoRA within an MTL framework. By en + +abling both task-agnostic and task-specific adaptations along with joint inference, MTLoRA has achieved state-of-the-art results on dense vision tasks. However, these methods, while effective in preserving pre-trained knowledge, still impose subspace constraints that can degrade performance relative to single-task baselines. + +DiTASK takes a fundamentally different approach: instead of adding modules or modifying weights directly, we preserve the pre-trained singular vectors while enabling flexible adaptation via diffeomorphisms of singular values. This allows us to maintain both architectural efficiency and rich feature adaptability, without altering the input-output mapping learned during pre-training. + +Multi-Task Learning Dynamics and Challenges. A recent study of Transformer training dynamics reveals an incremental learning phenomenon where weight update ranks gradually increase during training [5]. This finding challenges the effectiveness of fixed-rank adaptation methods in MTL settings. While MTLoRA [1] attempts to address this through task-agnostic and task-specific modules, it still operates within fixed low-rank constraints. Similarly, gradient interference mitigation techniques like PCGrad address conflicts between task updates but do not provide the flexibility needed for diverse task adaptations. In contrast, DITASK aligns with natural learning dynamics by preserving the full-rank structure through singular vector retention while enabling task-specific adaptations via neural diffeomorphisms [14, 15], uniquely combining parameter efficiency with the adaptability needed for effective multi-task learning. + +Diffeomorphisms in Neural Networks. A bijective mapping $f: \mathcal{M} \to \mathcal{N}$ between two differentiable manifolds $\mathcal{M}$ and $\mathcal{N}$ is a diffeomorphism if both $f$ and its inverse $f^{-1}: \mathcal{N} \to \mathcal{M}$ are differentiable. Learning diffeomorphisms poses computational challenges, as early methods were constrained by complex, infinite-dimensional spaces [43], and later Markov Chain Monte Carlo methods remained demanding [2, 3, 60]. Freifeld et al. [14, 15] addressed these issues with Continuous Piecewise-Affine Based (CPAB) transformations, a finite-dimensional approach suited for precise 1D diffeomorphisms, ideal for neural activation functions. CPAB offers linear complexity, supports parallelization, and achieves sub-linear performance in practice [15]. Initially developed for alignment and regression, CPAB is now widely applied in neural networks. For instance, in spatial transformer layers with CPAB [11], temporal alignment [34], novel loss function for time-series analysis [52], image animation [49], geometry-guided fine + +![](images/24066c73dd4518010926f62f585287380b8b807a83e867ddddde5e9ba9709dbd.jpg) +Figure 4. DiTASK in the $i$ -th Swin Transformer stage for multi-task learning. Task-agnostic modules are applied in all blocks except the last, which uses task-specific modules to capture task-dependent features. + +tuning [32] and trainable CPAB-based activation function [8, 33]. + +# 3. Preliminaries and Background + +We combine two key components: the weights in ViTs, and the mathematical framework of CPAB diffeomorphisms. We now provide the background for understanding the coupling of these concepts in DiTASK. + +# 3.1. Learned Weights in ViTs + +ViTs encode visual knowledge in their weight matrices, which can be analyzed through Singular Value Decomposition (SVD). Assume we have a weight matrix that transforms inputs from $c_{1}$ to $c_{2}$ channels, denoted by $\mathbf{W} \in \mathbb{R}^{c_2 \times c_1}$ , then its SVD reads: + +$$ +\mathbf {W} = \mathbf {U} \boldsymbol {\Sigma} \mathbf {V} ^ {\top}, \tag {1} +$$ + +where $\mathbf{U} \in \mathbb{R}^{c_2 \times c_2}$ , $\pmb{\Sigma} \in \mathbb{R}^{c_2 \times c_1}$ , $\mathbf{V} \in \mathbb{R}^{c_1 \times c_1}$ . We refer to $\mathbf{U}$ as the left singular vectors, $\pmb{\Sigma}$ as the singular values, and $\mathbf{V}$ as the right singular vectors. Notably, $\mathbf{U}$ and $\mathbf{V}$ form orthonormal bases for the output and input spaces of the linear map represented by $\mathbf{W}$ , respectively. + +These bases characterize how the network transforms visual features across layers and hidden dimensions. + +Problem Setup. Throughout this paper, we assume $K$ tasks $\mathcal{T} = \{T_1,\dots ,T_K\}$ . Each task $T_{k}$ has an associated dataset $\mathcal{D}_k = \{(x_i^k,y_i^k)\}_{i = 1}^{N_k}$ where $x_{i}^{k}\in \mathcal{X}$ and $y_{i}^{k}\in \mathcal{Y}_{k}$ represent the input-output pairs. The goal is to train a neural network to minimize a supervised loss between the prediction and ground-truth output. Following [1], we use a Swin Transformer [28], which processes input images by dividing them into nonoverlapping patches and progressively merging patches to reduce spatial resolution while increasing feature dimension across stages. Formally, the Swin Transformer processes images through $L$ stages, with the $l$ -th stage operating on feature maps of resolution $\frac{H}{2^l}\times \frac{W}{2^l}$ with $C_l$ channels. The key operation in each stage is a Window-based Multi-head Self-Attention (W-MSA): + +$$ +\mathrm {W} - \mathrm {M S A} (Q, K, V) = \operatorname {S o f t m a x} \left(\frac {Q K ^ {\top}}{\sqrt {d}}\right) V, \tag {2} +$$ + +where $Q, K, V \in \mathbb{R}^{M \times d}$ are query, key, and value matrices for windows of size $M$ . The corresponding weight matrices $\mathbf{W}_l^{(q)}, \mathbf{W}_l^{(k)}, \mathbf{W}_l^{(v)} \in \mathbb{R}^{d \times d}$ for these projections in layer $l$ are central to our DiTASK, because in Section 4 we dynamically adjust their singular values for multi-task adaptations. The MTL objective minimizes a weighted combination of $K$ task losses: + +$$ +\min _ {\Theta} \sum_ {k = 1} ^ {K} \lambda_ {k} \mathcal {L} _ {k} (\Theta ; \mathcal {D} _ {k}), \tag {3} +$$ + +where $\mathcal{L}_k$ and $\lambda_{k}$ represent the loss function and weight for the $k$ -th task, respectively. In Figure 4, we illustrate the overall architecture used in this paper. + +# 3.2. CPAB Diffeomorphisms for Weight Transformation + +As we show later in Section 4, our DiTASK modifies singular values $\Sigma$ while preserving the structure of weight matrices. To achieve that, transformations that are smooth, invertible, and monotone, are required. Continuous Piecewise Affine-Based (CPAB) [14, 15] diffeomorphisms satisfy these conditions while being efficient in terms of parameters and computing diffeomorphisms. We now turn to define CPAB formally. + +Definition 3.1 (CPAB Transformation). Given a closed interval $\Omega = [a,b]$ partitioned into $\mathcal{N}_{\mathcal{P}}$ intervals, a CPAB transformation is defined through a velocity field $v^{\theta}:\Omega \to \mathbb{R}$ that is continuous and piecewise-affine within each interval. This velocity field, parameterized by $\pmb {\theta}\in \mathbb{R}^{\mathcal{N}_{\mathcal{P}} - 1}$ , yields a diffeomorphism $f^{\theta}$ of the form: + +$$ +f ^ {\boldsymbol {\theta}} (x) = x + \int_ {0} ^ {1} v ^ {\boldsymbol {\theta}} \left(f ^ {\boldsymbol {\theta}} (x, \tau)\right) d \tau . \tag {4} +$$ + +For practical implementation, we use the Python package from Martinez et al. [34], and provide additional details in the supplementary material. CPAB transformations are ideal for our settings, shown in Section 4, because they provide: (i) Low parameter overhead. Only $\mathcal{O}(\mathcal{N}_{\mathcal{P}})$ parameters, where typically $\mathcal{N}_{\mathcal{P}} \leq 128$ ; (ii) Differentiability. Enables gradient-based optimization; (iii) Computational efficiency. Computing Equation (4) is of linear complexity; (iv) Stability. CPAB transformations are Lipschitz continuous [15]. + +# 4. DiTASK: Diffeomorphic Multi-Task Adaptation + +We introduce DITASK (Diffeomorphic Multi-Task Adaptation), a novel approach for efficient multi-task fine-tuning. Our method is grounded in a fundamental analysis of how neural networks process information through their weight matrices. We draw insights from linear algebra to the workings of a linear layer of neural network in Section 4.1 relating it to SVD. In Section 4.2, we formally introduce DITASK and elaborate on its properties that motivate our design choices in Section 4.3. + +# 4.1. Understanding Weight Matrices + +We now show that by considering the SVD of weight matrices, we can gain insights on the course of action of linear layers, that later, in Section 4.2, serves as a mathematically grounded motivation for the design of our DiTASK. Specifically, we note that a linear layer with weight matrix $\mathbf{W} \in \mathbb{R}^{c_2 \times c_1}$ , and its SVD decomposition $\mathbf{W} = \mathbf{U} \boldsymbol{\Sigma} \mathbf{V}^{\top}$ , can be viewed as a linear map $g: \mathbb{R}^{c_1} \to \mathbb{R}^{c_2}$ , such that the following equality holds: + +$$ +g (\mathbf {x}) = \mathbf {W} \mathbf {x} = \sum_ {i = 1} ^ {p} \sigma_ {i} \langle \mathbf {x}, \mathbf {v} _ {i} \rangle \mathbf {u} _ {i}, \tag {5} +$$ + +where $\mathbf{U} = [\mathbf{u}_1, \dots, \mathbf{u}_{c_2}]$ , $\mathbf{V} = [\mathbf{v}_1, \dots, \mathbf{v}_{c_1}]$ , and $\boldsymbol{\Sigma} = \text{diag}([\sigma_1, \sigma_2, \dots, \sigma_p])$ , $p = \min(c_1, c_2)$ . The basis vectors in $\mathbf{U}$ are the left singular vectors, $\mathbf{V}$ are right singular vectors, and $\boldsymbol{\Sigma}$ are the singular values of $\mathbf{W}$ . + +Specifically, the orientations encoded by the left and right singular vectors represent features present in the output and input spaces of the linear transformation $g$ , respectively. Multi-task learning requires adapting these orientations jointly for all tasks, while minimizing task interference to prevent performance degradation. Below, we describe how to achieve effective multi-task adaptation using diffeomorphisms, by preserving the singular vectors $\mathbf{U}$ , $\mathbf{V}$ and modifying $\mathbf{W}$ in a principled manner. + +# 4.2. Adaptation with DITASK + +Given a learned weight matrix $\mathbf{W} = \mathbf{U}\pmb{\Sigma}\mathbf{V}^{\top} \in \mathbb{R}^{c_2 \times c_1}$ from a ViT, we transform the singular values $\pmb{\Sigma}$ by a + +learned neural diffeomorphism $f^{\theta}$ described in Equation (4), to get the adapted weight matrix $\mathbf{W}_A$ as follows: + +$$ +\mathbf {W} _ {A} = \mathbf {U} \left[ \begin{array}{c c c c} f ^ {\boldsymbol {\theta}} \left(\sigma_ {1}\right) & 0 & \dots & 0 \\ 0 & f ^ {\boldsymbol {\theta}} \left(\sigma_ {2}\right) & \dots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \dots & f ^ {\boldsymbol {\theta}} \left(\sigma_ {p}\right) \end{array} \right] \mathbf {V} ^ {\top}. \tag {6} +$$ + +During fine-tuning, we freeze $\mathbf{W}$ and learn only the parameters $\theta$ of the CPA velocity field. This allows DiTASK to adapt to multiple tasks using $\mathcal{O}(\mathcal{N}_{\mathcal{P}})$ additional parameters (where typically $\mathcal{N}_{\mathcal{P}} \leq 128$ ), which is significantly smaller than methods with low-rank $r$ using $\mathcal{O}(r(c_1 + c_2))$ . We describe this process in the Section 1, and compare the computational cost of DiTASK with other fine-tuning methods in the supplementary material. + +Multi-Task Adaptation with DiTASK. To enable both multi and task-specific adaptation, we learn two sets of neural diffeomorphic transformations in every pretrained weight matrix $\mathbf{W}$ , shown in Section 1, that include: (i) Joint Adaptation parameters, denoted by $\theta_{j}$ , to allow task synergies which are crucial for MTL [21, 47]; and (ii) Task-wise Adaptation parameters, denoted by $\{\theta_k\}_{k=1}^K$ to enable learning nuances for each task. + +# 4.3. Properties of DITASK + +In this section, we motivate our design choices and discuss the properties that make DiTASK an effective and parameter-efficient fine-tuning method for MTL. + +Feature Space Preservation. As discussed in Section 4.1, pre-trained weight matrices encode feature transformations through their singular vectors, where $\mathbf{U}$ and $\mathbf{V}$ form orthonormal bases for output and input spaces, respectively. These bases capture the orientation of patterns learned during pre-training, each weighted by its corresponding singular value. In contrast to traditional low-rank methods like LoRA, which constrain adaptations to fixed low-dimensional subspaces, potentially losing important features, our DiTASK preserves these learned bases entirely. This preservation allows us to achieve superior multi-task performance with fewer parameters, as shown in Figure 1. Specifically, while low-rank methods require increasing their rank (and thus parameters and departure from being low-rank) to match single-task performance, our DiTASK maintains the learned feature space of pre-trained ViTs through a targeted and mathematically-ground singular value modulation. + +Feature Relativity Preservation. The order of singular values $\sigma_{1} \geq \sigma_{2} \geq \ldots \geq \sigma_{p}$ in weight matrices of ViTs encode the relative importance of features learned during pre-training on large-scale datasets like + +ImageNet-21k. By utilizing diffeomorphisms, which are smooth, invertible, and monotone, by definition, we preserve this ordering. That is, if $f^{\theta}$ is a diffeomorphism, then $f^{\theta}(\sigma_1) \geq f^{\theta}(\sigma_2) \geq \ldots \geq f^{\theta}(\sigma_p)$ in Equation (6). Our choice of CPAB transformations implements this with only $\mathcal{N}_{\mathcal{P}} \leq 128$ parameters per weight matrix, compared to the $\mathcal{O}(r(c_1 + c_2))$ parameters required by low-rank adaptation methods. Our experiments in Section 5 demonstrate that preserving feature hierarchy through diffeomorphic transformations enables effective multi-task generalization while maintaining parameter efficiency. + +# 5. Experiments + +We evaluate DiTASK on multiple MTL benchmarks and compare it with other adaptation methods. Section 5.1 details the experimental setup and baselines, Section 5.2 discusses our main findings, and Section 5.3 presents few ablation studies of DiTASK. We seek to address three key research questions: + +(RQ1) Can a selective modification of singular values while preserving singular vectors bridge the performance gap between decoder-only and full fine-tuning? +(RQ2) Does full-rank preservation by singular value modulation outperform low-rank adaptation methods? +(RQ3) How does DiTASK compare to other parameter-efficient adaptation methods? + +# 5.1. Experimental Setup + +Datasets and Tasks. We evaluate DiTASK on the PASCAL-MTL dataset [13] (PASCAL-Context split) following the literature on multi-task dense prediction [46, 54, 55]. This dataset includes 4,998 training and 5,105 validation images with annotations for semantic segmentation (21 classes), human part segmentation (7 classes), surface normal estimation, and saliency detection. Additional experiments on the NYUD dataset [41] are provided in Table 4. + +Implementation Details. We use the Swin-Tiny [28] architecture, pre-trained on ImageNet-21k [39] as the backbone encoder, similar to [1]. To ensure a fair comparison, we incorporate the HRNet [50] decoder, which accounts for $6\%$ of the total parameters, as in previous works [1, 46]. Following MTINet [46], we apply cross-entropy loss for segmentation tasks, $\ell_1$ loss for surface normals, and balanced cross-entropy [9] for saliency detection, with same task weights $\{\lambda_k\}_{k=1}^K$ used in MTINet. In all experiments, we follow the evaluation protocol from Agiza et al. [1]. + +Baselines. We benchmark our DiTASK with three categories of methods: + +- Full Fine-Tuning: Methods that modify all weight matrices (single-task, MTL decoder, full MTL) + +Table 1. Performance on PASCAL Context for Multi-Task Learning. Comparison of DITASK with full fine-tuning, adapter-based, and fixed-rank methods across four dense prediction tasks: semantic segmentation, human part segmentation, saliency detection, and surface normal estimation. Metrics are MIOU (↑) and RMSE (↓), with $\Delta m$ denoting relative improvement over single-task tuning. DITASK achieves strong performance with minimal trainable parameters and supports joint inference across tasks. + +
    MethodSEMSEG (MIOU ↑)HUMAN PARTS (MIOU ↑)SALIENCY (MIOU ↑)NORMALS (RMSE ↓)Δm(%)Trainable Swin Parameters (M)Single Inference For All Tasks
    FULL FINE-TUNING
    Single Task67.2161.9362.3517.970.00112.62×
    MTL - Dec. Only65.0953.4857.4620.69- 9.950✓
    MTL - Full67.5660.2465.2116.64+ 2.2328.12✓
    ADAPTER-BASED
    VPT-shallow [22]62.9652.2758.3120.90-11.180.63×
    VPT-deep [22]64.3552.5458.1521.07-10.851.49×
    Compactor++ [23]67.2655.6959.4719.54- 5.840.72×
    Bitfit [58]68.5755.9960.6419.42- 4.600.91×
    Compactor [23]68.0856.4160.0819.22- 4.550.84×
    Adapter [17]69.2157.3861.2818.83- 2.719.26×
    VL-Adapter [44]70.2159.1562.2919.26- 1.832.80×
    Polyhistor [27]70.8759.1565.5417.77+ 2.347.02×
    HyperFormer [31]71.4360.7365.5417.77+ 2.6470.83×
    FIXED-RANK
    MTL - DoRA [26]52.3650.8263.5318.32-10.026.40✓
    MTL - ReFT [53]68.7556.4958.7620.54- 6.6316.16✓
    MTL - SVFT [25]64.4455.9463.0317.86- 3.023.83✓
    LoRA [19]70.1257.7361.9018.96- 2.170.93×
    MTLoRA [1] (r = 16)68.1958.9964.4817.03+ 1.353.01✓
    MTLoRA [1] (r = 32)67.7459.4664.9016.59+ 2.164.14✓
    MTLoRA [1] (r = 64)67.9059.8465.4016.60+ 2.556.40✓
    Single Task - DITASK72.2062.3365.7016.55+ 5.331.60 (×4)×
    MTL - DITASK (Ours)69.6662.0265.0017.10+ 3.221.61✓
    + +Table 2. Effect of Backbone Size - Relative improvement increases with increasing capacity of the backbone + +
    MethodSEMSEG (MIOU ↑)HUMAN PARTS (MIOU ↑)SALIENCY (MIOU ↑)NORMALS (RMSE ↓)Δm(%)Trainable Swin Parameters (M)
    DITASK + Swin-Tiny69.6662.0265.0017.10+3.221.61
    DITASK + Swin-Small74.4963.2064.5817.58+4.681.66
    DITASK + Swin-Base75.8665.9764.1817.29+6.523.14
    DITASK + Swin-Large76.2367.5364.0716.90+7.797.13
    + +- Adapter-based: Methods that add task-specific layers while preserving main weights (Adapter [18], BitFit [58], VPT [22], Compactor [23], VL-Adapter [44], HyperFormer [31], Polyhistor [27]) +- Fixed-Rank: Methods that constrain updates to low-rank subspaces (LoRA [19], DoRA [26], SVFT [25], ReFT [53], MTLoRA [1]) + +# 5.2. Results and Discussion + +Table 1 presents our main results, addressing (RQ1)-(RQ3) on the effectiveness of DiTASK for multi-task learning (MTL). + +Bridging the Efficiency Performance Gap. DiTASK achieves a $+3.22\%$ relative improvement over single-task baselines using only 1.61M trainable encoder parameters. This outperforms both decoder-only tuning $(-9.95\%)$ and full fine-tuning $(+2.23\%)$ , demonstrating that modulating singular values while preserving pre + +trained feature directions enables an effective balance between parameter efficiency and performance. + +Comparison with Fixed Low-Rank Methods. DTASK outperforms the state-of-the-art MTLoRA by $26.27\%$ in $\Delta m$ , using $4\times$ fewer parameters (Figure 5). Most fixed-rank methods yield negative $\Delta m$ due to task interference from shared low-rank subspaces. By modulating singular values independently per task while preserving full-rank structure, DTASK mitigates this interference. Similar trends are observed on NYUD (Table 4). + +Parameter Efficiency and Task Performance. DITASK is the only parameter-efficient method to consistently improve over single-task baselines, showing that modulating singular values while preserving pretrained directions effectively balances efficiency and performance. + +![](images/eccec0d3520f16116ec3e609739488da7c1e5f8b7bf5b6485f521e01ee574bd7.jpg) +Figure 5. Comparison of adaptation parameter budget of the shared encoder, excluding LayerNorm parameters. + +Table 3. Comparison of computational efficiency between DiTASK and MTLoRA. DiTASK reduces batch runtime by $\approx 22\%$ , lowers memory usage, and uses $500\times$ fewer adaptation parameters. + +
    MethodBatch Runtime (seconds)Max GPU Mem (Megabytes)# Adaptation Params
    MTLoRA35.20±1.05235094.86M
    DiTASK27.31±5.29229068.5K
    + +# 5.3. Ablation Study + +We analyze key components of DiTASK to understand their contributions to multi-task performance. + +Computational Efficiency. DITASK uses only 8.5K adaptation parameters, compared to MTLoRA's 4.86M, while achieving $22\%$ faster batch processing (27.31s vs 35.20s) and reduced memory usage (see Table 3). The efficiency gains stem from our compact CPAB parameterization of singular value transformations. + +Joint vs Task-Wise Singular Value Modulation. We evaluate three configurations of singular value modulation, shown in Figure 7. Joint Adaptation alone, with shared modulation across tasks, achieves an improvement of $2.77\%$ . Task-Wise Adaptation alone, which modulates singular values independently for each task, yields $2.85\%$ . The Combined approach, DiTASK, incorporates both strategies and reaches the highest improvement at $3.22\%$ , supporting the use of both shared and task-specific transformations. + +Model Scaling Analysis. The effectiveness of DiTASK scales with model capacity (Table 2). This scaling effect indicates that larger models provide richer singular value spaces, enabling more effective task-specific adaptation. + +Qualitative Comparison. In Figure 6, we present a visual comparison between MTLoRA and our DiTASK on the semantic segmentation task from PASCAL MTL. DiTASK demonstrates tighter and clearer boundaries, more consistent segmentation, and improved class sep + +
    MethodSEMSEG(MIOU↑)DEPTH(RMSE↓)Δm(%)Trainable Params(in M)
    Single Task33.180.6670112.62
    MTL - Dec. Only28.370.832-19.611.00
    MTL - Full35.290.734-1.8428.5
    MTLoRA37.180.635+8.426.26
    Single Task - DITASK44.010.644+18.041.61
    DITASK43.850.606+20.651.61
    + +Table 4. Comparison of DiTASK and MTLoRA on the NYUD [41] multi-task dataset for semantic segmentation (MIOU) and depth estimation (RMSE). + +![](images/ec6f7c48c2de61254869e5ad473a3f87f6a12d7f67603f51d031c67fdb0ec1b4.jpg) +Figure 6. Semantic segmentation predictions on PASCAL MTL using MTLoRA and D1TASK. + +aration. For example, in the dimly lit sofa scene in the second column, MTLoRA struggles to correctly predict the sofa boundary, while DITASK offers a better prediction. + +# 6. Conclusion + +In this paper, we introduce DiTASK, a novel MTL fine-tuning approach that leverages neural diffeomorphisms for singular value adaptation while preserving the structure of pre-trained representations. We observe that existing methods, which restrict weight updates to fixed low-rank subspaces for resource efficiency, often suffer from multi-task performance degradation relative to single-task baselines. 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Algorithmic Advances in Riemannian Geometry and Applications: For Machine Learning, Computer Vision, Statistics, and Optimization, pages 1-23, 2016. 4 \ No newline at end of file diff --git a/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/images.zip b/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7a045b10c0aaf384c19ee9684fabc386e29ac59f --- /dev/null +++ b/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e2cc30acf1eb2f7f2827f95f81744f263dc3cde38c360fe056219707d8c47945 +size 483600 diff --git a/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/layout.json b/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..5fd998cebdd82ac7c4b3600a212b0ed801784157 --- /dev/null +++ b/2025/DiTASK_ Multi-Task Fine-Tuning with Diffeomorphic Transformations/layout.json @@ -0,0 +1,9421 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 83, + 103, + 527, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 103, + 527, + 121 + ], + "spans": [ + { + "bbox": [ + 83, + 103, + 527, + 121 + ], + "type": "text", + "content": "DITASK: Multi-Task Fine-Tuning with Diffeomorphic Transformations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 143, + 222, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 143, + 222, + 199 + ], + "spans": [ + { + "bbox": [ + 104, + 143, + 222, + 199 + ], + "type": "text", + "content": "Krishna Sri Ipsit Mantri Purdue University West Lafayette, USA mantrik@purdue.edu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 248, + 143, + 373, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 248, + 143, + 373, + 198 + ], + "spans": [ + { + "bbox": [ + 248, + 143, + 373, + 198 + ], + "type": "text", + "content": "Carola-Bibiane Schonlieb \nUniversity of Cambridge \nCambridge, UK \ncbs31@cam.ac.uk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 401, + 144, + 505, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 401, + 144, + 505, + 198 + ], + "spans": [ + { + "bbox": [ + 401, + 144, + 505, + 198 + ], + "type": "text", + "content": "Bruno Ribeiro Purdue University West Lafayette, USA ribeirob@purdue.edu" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 140, + 205, + 317, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 205, + 317, + 261 + ], + "spans": [ + { + "bbox": [ + 140, + 205, + 317, + 261 + ], + "type": "text", + "content": "Chaim Baskin \nBen-Gurion University of the Negev \nBeer Sheva, Israel \nchaimbaskin@bgu.ac.il" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 349, + 205, + 471, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 205, + 471, + 260 + ], + "spans": [ + { + "bbox": [ + 349, + 205, + 471, + 260 + ], + "type": "text", + "content": "Moshe Eliasof \nUniversity of Cambridge \nCambridge, UK \nme532@cam.ac.uk" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 159, + 289, + 206, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 289, + 206, + 301 + ], + "spans": [ + { + "bbox": [ + 159, + 289, + 206, + 301 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 315, + 297, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 315, + 297, + 613 + ], + "spans": [ + { + "bbox": [ + 67, + 315, + 297, + 613 + ], + "type": "text", + "content": "Pre-trained Vision Transformers now serve as powerful tools for computer vision. Yet, efficiently adapting them for multiple tasks remains a challenge that arises from the need to modify the rich hidden representations encoded by the learned weight matrices, without inducing interference between tasks. Current parameter-efficient methods like LoRA, which apply low-rank updates, force tasks to compete within constrained subspaces, ultimately degrading performance. We introduce DITASK a novel Diffeomorphic Multi-Task Fine-Tuning approach that maintains pre-trained representations by preserving weight matrix singular vectors, while enabling task-specific adaptations through neural diffeomorphic transformations of the singular values. By following this approach, DITASK enables both shared and task-specific feature modulations with minimal added parameters. Our theoretical analysis shows that DITASK achieves full-rank updates during optimization, preserving the geometric structure of pretrained features, and establishing a new paradigm for efficient multi-task learning (MTL). Our experiments on PASCAL MTL and NYUD show that DITASK achieves state-of-the-art performance across four dense prediction tasks, using " + }, + { + "bbox": [ + 67, + 315, + 297, + 613 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 67, + 315, + 297, + 613 + ], + "type": "text", + "content": " fewer parameters than existing methods. Our code is available here." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 641, + 149, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 641, + 149, + 653 + ], + "spans": [ + { + "bbox": [ + 69, + 641, + 149, + 653 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 67, + 662, + 297, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 662, + 297, + 723 + ], + "spans": [ + { + "bbox": [ + 67, + 662, + 297, + 723 + ], + "type": "text", + "content": "Vision Transformers (ViTs) have emerged as compelling models for computer vision, achieving remarkable performance across various tasks by leveraging self-attention mechanisms [12, 48] and large-scale pretraining [39, 42] on extensive datasets like ImageNet" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 289, + 542, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 542, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 542, + 338 + ], + "type": "text", + "content": "21k [10]. These models encode essential visual knowledge in their weight matrices through singular vectors that characterize the principal directions in the input space and output spaces [36, 40]. However, existing fine" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 318, + 353, + 536, + 571 + ], + "blocks": [ + { + "bbox": [ + 318, + 353, + 536, + 571 + ], + "lines": [ + { + "bbox": [ + 318, + 353, + 536, + 571 + ], + "spans": [ + { + "bbox": [ + 318, + 353, + 536, + 571 + ], + "type": "image", + "image_path": "c14483aae385f4519c9a56be63c5e97bf8d961cc247baabcb557441834c6a862.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 582, + 541, + 660 + ], + "lines": [ + { + "bbox": [ + 313, + 582, + 541, + 660 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 541, + 660 + ], + "type": "text", + "content": "Figure 1. Performanceefficiency trade-off in multi-task learning (MTL) on PASCAL MTL tasks. DITASK outperforms single-task fine-tuning with fewer parameters than fixed-rank methods (LoRA [19]) and other PEFT approaches (Adapter [18]). The gray region shows negative relative improvement over single-task tuning, highlighting the challenge of achieving gains under tight parameter budgets." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 674, + 542, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 674, + 542, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 674, + 542, + 723 + ], + "type": "text", + "content": "tuning methods based on low-rank adaptation (LoRA) [1, 19] may not preserve these learned singular vectors. In Figure 2, we illustrate the importance of preserving the singular vectors; recovering a noisy image by ad" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. 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Image recovery comparison of LoRA and DiTASK. Preserving singular vectors enables DiTASK to achieve a higher peak signal-to-noise ratio (PSNR)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 187, + 183, + 282, + 278 + ], + "blocks": [ + { + "bbox": [ + 187, + 183, + 282, + 278 + ], + "lines": [ + { + "bbox": [ + 187, + 183, + 282, + 278 + ], + "spans": [ + { + "bbox": [ + 187, + 183, + 282, + 278 + ], + "type": "image", + "image_path": "9231f22a4d59c606a9cb522094f6781e7de147952cd5d88c544c361b0f93cf56.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 347, + 296, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 347, + 296, + 479 + ], + "spans": [ + { + "bbox": [ + 67, + 347, + 296, + 479 + ], + "type": "text", + "content": "justing only its singular values while keeping singular vectors yields superior performance than using LoRA, which may not preserve the singular vectors of the image. Singular vectors encode crucial image details, and low-rank denoising methods can lose these details, resulting in poor denoising quality. Preserving singular vectors serves as an implicit regularizer. This motivating example suggests that useful adaptations can be achieved through singular value modulation and inspires us to design a mathematically-ground method to achieve this goal." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 68, + 481, + 296, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 481, + 296, + 624 + ], + "spans": [ + { + "bbox": [ + 68, + 481, + 296, + 624 + ], + "type": "text", + "content": "Fine-tuning of pre-trained ViTs for downstream tasks, such as few-shot learning [20, 37], typically involves adapting the learned representations to the target application. However, the substantial size of these models calls for a resource-efficient fine-tuning technique. Parameter-efficient and low-rank optimization approaches, such as LoRA [19], offer promising solutions by reducing the number of trainable parameters. This strategy not only enhances resource efficiency (e.g., lower VRAM and FLOPS requirements), but also helps keep valuable pretrained filters that capture essential visual knowledge [6] by preventing catastrophic forgetting [16, 30]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 68, + 627, + 296, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 627, + 296, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 627, + 296, + 723 + ], + "type": "text", + "content": "In the context of single-task fine-tuning, parameter-efficient and low-rank methods have proven highly successful [18, 19, 23, 31]. However, in Multi-Task Learning (MTL) settings, these methods were shown to struggle [1]. Particularly, MTL typically requires isolating task gradients to prevent task interference (e.g., enforcing gradient orthogonality [45, 56]), a requirement that becomes increasingly challenging as the dimension or" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 541, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 541, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 541, + 156 + ], + "type": "text", + "content": "rank of the gradients decreases. Thus, we face a tradeoff between lowering the number of trainable parameters and maintaining task performance. Evidently, as shown in Figure 1, existing methods can offer performance enhancement in MTL settings only when significantly increasing the number of trainable, effectively undermining their purpose of lightweight adaptation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 157, + 541, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 157, + 541, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 157, + 541, + 348 + ], + "type": "text", + "content": "We conjecture, inspired by recent studies [5] that identified an incremental learning phenomenon in transformers, that the underperformance of LoRA methods in MTL settings happens because of the direct and nonprincipled modification of weight matrices' singular vectors. These updates force distinct tasks to compete within the same constrained subspace. The key insight of our approach is realizing that while low-rank representations offer sufficient dimensionality for individual tasks, constraining multiple tasks to share the same low-rank subspace creates interference. An optimal subspace for one task may be suboptimal for others. Yet, existing methods force this competition by maintaining a single shared low-rank space, while a unique subspace for each task, like in MTLoRA [1], may not take advantage of task synergies." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 350, + 541, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 541, + 648 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 541, + 648 + ], + "type": "text", + "content": "Our approach. To address the limitations of existing low-rank fine-tuning methods, we introduce Diffeomorphic Multi-Task Adaptation (DiTASK), a novel approach leveraging neural diffeomorphisms parameterized by Continuous Piecewise Affine-Based (CPAB) transformations [14, 15]. Specifically, DiTASK preserves pre-trained feature patterns by retaining the singular vectors of learned weight matrices while dynamically adjusting singular values through neural diffeomorphic transformations at each optimization step. Our diffeomorphic transformations are parameterized by Continuous Piecewise Affine (CPA) [14, 15] velocity fields over the weight matrix domain, ensuring continuous, invertible deformations. This design enables adaptation across multiple tasks while preserving the knowledge embedded during pre-training. We validate DiTASK on the PASCAL MTL dataset [13], a widely used benchmark for dense prediction tasks such as semantic segmentation, edge detection, and human body part segmentation. Our method achieves a " + }, + { + "bbox": [ + 313, + 350, + 541, + 648 + ], + "type": "inline_equation", + "content": "26.27\\%" + }, + { + "bbox": [ + 313, + 350, + 541, + 648 + ], + "type": "text", + "content": " improvement in average task performance while reducing parameter usage by " + }, + { + "bbox": [ + 313, + 350, + 541, + 648 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 313, + 350, + 541, + 648 + ], + "type": "text", + "content": " compared to state-of-the-art methods like MTLoRA [1], demonstrating the effectiveness of preserving pre-trained feature directions for efficient multi-task fine-tuning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 650, + 455, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 650, + 455, + 660 + ], + "spans": [ + { + "bbox": [ + 314, + 650, + 455, + 660 + ], + "type": "text", + "content": "Our contributions are as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 662, + 541, + 722 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 315, + 662, + 540, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 662, + 540, + 709 + ], + "spans": [ + { + "bbox": [ + 315, + 662, + 540, + 709 + ], + "type": "text", + "content": "- We propose a novel approach to MTL fine-tuning that leverages neural diffeomorphisms for singular value adaptation, enabling fine-tuning weight updates while preserving pre-trained representation structure." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 711, + 541, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 711, + 541, + 722 + ], + "spans": [ + { + "bbox": [ + 315, + 711, + 541, + 722 + ], + "type": "text", + "content": "- We develop an efficient parametrization using learn" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "25219" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 81, + 348, + 185 + ], + "blocks": [ + { + "bbox": [ + 72, + 81, + 348, + 185 + ], + "lines": [ + { + "bbox": [ + 72, + 81, + 348, + 185 + ], + "spans": [ + { + "bbox": [ + 72, + 81, + 348, + 185 + ], + "type": "image", + "image_path": "9cb3befc335fdf19c210421c47ab880d8f7825259e5b7657a57ff04ae94c2240.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 408, + 62, + 529, + 209 + ], + "blocks": [ + { + "bbox": [ + 408, + 62, + 529, + 209 + ], + "lines": [ + { + "bbox": [ + 408, + 62, + 529, + 209 + ], + "spans": [ + { + "bbox": [ + 408, + 62, + 529, + 209 + ], + "type": "image", + "image_path": "0891b82b79f754e2fa86d6eb253c646377a6046191087731dbb79e90b09df15d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "lines": [ + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "spans": [ + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "text", + "content": "Figure 3. Overview of our DiTASK within Multi-Task Learning (MTL). (Left) Input features " + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "text", + "content": " are transformed via a modulated weight matrix " + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_A" + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "text", + "content": ", constructed by applying a neural diffeomorphism " + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "inline_equation", + "content": "f^\\theta" + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "text", + "content": " to the singular values of a pre-trained weight matrix " + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "text", + "content": ", resulting in updated features " + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_A\\mathbf{x}" + }, + { + "bbox": [ + 67, + 217, + 541, + 275 + ], + "type": "text", + "content": ". (Right) We use two sets of DiTASK modules: a joint transformation module for learning task synergies, and task-specific modules for individual adaptations. The transformed outputs serve as inputs to a shared decoder. This setup enables flexible, parameter-efficient fine-tuning while preserving the singular vectors of pre-trained weights." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 77, + 293, + 296, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 293, + 296, + 317 + ], + "spans": [ + { + "bbox": [ + 77, + 293, + 296, + 317 + ], + "type": "text", + "content": "able CPA velocity fields that require only 32 additional trainable parameters per layer." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 318, + 296, + 389 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 69, + 318, + 296, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 318, + 296, + 353 + ], + "spans": [ + { + "bbox": [ + 69, + 318, + 296, + 353 + ], + "type": "text", + "content": "- We theoretically analyze the properties of DiTASK, showing that it requires less memory than other low-rank Transformer adaptation methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 354, + 296, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 354, + 296, + 389 + ], + "spans": [ + { + "bbox": [ + 69, + 354, + 296, + 389 + ], + "type": "text", + "content": "- DITASK demonstrates state-of-the-art performance on PASCAL MTL tasks, achieving " + }, + { + "bbox": [ + 69, + 354, + 296, + 389 + ], + "type": "inline_equation", + "content": "26.27\\%" + }, + { + "bbox": [ + 69, + 354, + 296, + 389 + ], + "type": "text", + "content": " improvement over existing methods like MTLoRA." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 68, + 390, + 296, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 390, + 296, + 474 + ], + "spans": [ + { + "bbox": [ + 68, + 390, + 296, + 474 + ], + "type": "text", + "content": "The rest of the paper is organized as follows: In Section 2, we discuss the related work on parameter-efficient fine-tuning and MTL. In Section 3, we provide the mathematical background to understand DiTASK. Section 4 details DiTASK for learning diffeomorphic singular value adjustment, and Section 5 presents experimental results and analyses." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 486, + 156, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 486, + 156, + 498 + ], + "spans": [ + { + "bbox": [ + 69, + 486, + 156, + 498 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 68, + 507, + 296, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 507, + 296, + 577 + ], + "spans": [ + { + "bbox": [ + 68, + 507, + 296, + 577 + ], + "type": "text", + "content": "Our work lies at the intersection of four research areas: multi-task vision learning, parameter-efficient fine-tuning, neural network adaptation, and diffeomorphisms. We discuss each area with a focus on how they relate to weight matrix transformations and singular value adaptation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 68, + 578, + 296, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 578, + 296, + 722 + ], + "spans": [ + { + "bbox": [ + 68, + 578, + 296, + 722 + ], + "type": "text", + "content": "Multi-Task Learning in Vision. Multi-task learning models in vision typically adopt an encoder-decoder structure, where a shared encoder captures common features, and task-specific decoders handle individual objectives [35]. This approach has proven particularly effective for dense prediction tasks, with different decoders handling semantic segmentation, depth estimation, and surface normal prediction while sharing a common feature backbone [24]. While recent work has extended this framework to Vision Transformers (ViTs) [12], these adaptations face unique challenges due to their large parameter count and the complex in" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 293, + 541, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 541, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 541, + 376 + ], + "type": "text", + "content": "teractions between task-specific updates. To address these issues, DiTASK introduces an encoder adaptation strategy that modulates singular values while retaining pre-trained singular vectors, rather than modifying full weight matrices or adding task-specific layers. This leverages the encoder-decoder framework for efficient adaptation of the shared encoder." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 378, + 541, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 541, + 557 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 541, + 557 + ], + "type": "text", + "content": "Parameter-Efficient Fine-tuning Methods. These methods reduce computational overhead for model adaptation using various strategies. Adapter-based approaches [18] insert small trainable modules between transformer layers. Visual Prompt Tuning (VPT) [22] introduces trainable parameters in ViT input tokens, distinguishing it from standard adaptation approaches. Compactor [31] and BitFit [58] add minimal trainable parameters, enabling lightweight gradients via Kronecker products of rank-one and low-rank matrices and fine-tuning only biases, respectively. Hyperformers [31] use hypernetworks to generate adapter layers for multi-task language learning, while Polyhistor [27] adapts this for dense vision tasks. VL-Adapter [44] introduces adapters for joint Vision-Language (VL) multi-task fine-tuning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 562, + 541, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 562, + 541, + 682 + ], + "spans": [ + { + "bbox": [ + 313, + 562, + 541, + 682 + ], + "type": "text", + "content": "With the introduction of GPT-2 [38] and the rise in parameter sizes and task variety, methods like Low-Rank Adaptation (LoRA)[19] have gained traction in both language and vision. These methods restrict weight updates to fixed low-dimensional subspaces, enhancing resource efficiency. Other approaches, such as SVFT[25], enforce sparse singular values, while DoRA [26] decouples the magnitude and direction of weight update columns. In contrast, ReFT [53] uses low-rank approximation to adapt representations rather than weights." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 686, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 686, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 686, + 541, + 723 + ], + "type": "text", + "content": "Although most of these methods are not specifically designed for multi-task learning (MTL), MTLoRA [1] has applied LoRA within an MTL framework. By en" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "25220" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 68, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 68, + 72, + 294, + 144 + ], + "type": "text", + "content": "abling both task-agnostic and task-specific adaptations along with joint inference, MTLoRA has achieved state-of-the-art results on dense vision tasks. However, these methods, while effective in preserving pre-trained knowledge, still impose subspace constraints that can degrade performance relative to single-task baselines." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 68, + 157, + 296, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 157, + 296, + 253 + ], + "spans": [ + { + "bbox": [ + 68, + 157, + 296, + 253 + ], + "type": "text", + "content": "DiTASK takes a fundamentally different approach: instead of adding modules or modifying weights directly, we preserve the pre-trained singular vectors while enabling flexible adaptation via diffeomorphisms of singular values. This allows us to maintain both architectural efficiency and rich feature adaptability, without altering the input-output mapping learned during pre-training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 266, + 296, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 266, + 296, + 482 + ], + "spans": [ + { + "bbox": [ + 68, + 266, + 296, + 482 + ], + "type": "text", + "content": "Multi-Task Learning Dynamics and Challenges. A recent study of Transformer training dynamics reveals an incremental learning phenomenon where weight update ranks gradually increase during training [5]. This finding challenges the effectiveness of fixed-rank adaptation methods in MTL settings. While MTLoRA [1] attempts to address this through task-agnostic and task-specific modules, it still operates within fixed low-rank constraints. Similarly, gradient interference mitigation techniques like PCGrad address conflicts between task updates but do not provide the flexibility needed for diverse task adaptations. In contrast, DITASK aligns with natural learning dynamics by preserving the full-rank structure through singular vector retention while enabling task-specific adaptations via neural diffeomorphisms [14, 15], uniquely combining parameter efficiency with the adaptability needed for effective multi-task learning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "text", + "content": "Diffeomorphisms in Neural Networks. A bijective mapping " + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "inline_equation", + "content": "f: \\mathcal{M} \\to \\mathcal{N}" + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "text", + "content": " between two differentiable manifolds " + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "text", + "content": " is a diffeomorphism if both " + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "text", + "content": " and its inverse " + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "inline_equation", + "content": "f^{-1}: \\mathcal{N} \\to \\mathcal{M}" + }, + { + "bbox": [ + 68, + 495, + 296, + 723 + ], + "type": "text", + "content": " are differentiable. Learning diffeomorphisms poses computational challenges, as early methods were constrained by complex, infinite-dimensional spaces [43], and later Markov Chain Monte Carlo methods remained demanding [2, 3, 60]. Freifeld et al. [14, 15] addressed these issues with Continuous Piecewise-Affine Based (CPAB) transformations, a finite-dimensional approach suited for precise 1D diffeomorphisms, ideal for neural activation functions. CPAB offers linear complexity, supports parallelization, and achieves sub-linear performance in practice [15]. Initially developed for alignment and regression, CPAB is now widely applied in neural networks. For instance, in spatial transformer layers with CPAB [11], temporal alignment [34], novel loss function for time-series analysis [52], image animation [49], geometry-guided fine" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 318, + 70, + 541, + 363 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 541, + 363 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 541, + 363 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 541, + 363 + ], + "type": "image", + "image_path": "24066c73dd4518010926f62f585287380b8b807a83e867ddddde5e9ba9709dbd.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 369, + 541, + 413 + ], + "lines": [ + { + "bbox": [ + 313, + 369, + 541, + 413 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 541, + 413 + ], + "type": "text", + "content": "Figure 4. DiTASK in the " + }, + { + "bbox": [ + 313, + 369, + 541, + 413 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 369, + 541, + 413 + ], + "type": "text", + "content": "-th Swin Transformer stage for multi-task learning. Task-agnostic modules are applied in all blocks except the last, which uses task-specific modules to capture task-dependent features." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 435, + 541, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 435, + 541, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 435, + 541, + 460 + ], + "type": "text", + "content": "tuning [32] and trainable CPAB-based activation function [8, 33]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 472, + 487, + 486 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 487, + 486 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 487, + 486 + ], + "type": "text", + "content": "3. Preliminaries and Background" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 492, + 541, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 541, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 541, + 540 + ], + "type": "text", + "content": "We combine two key components: the weights in ViTs, and the mathematical framework of CPAB diffeomorphisms. We now provide the background for understanding the coupling of these concepts in DiTASK." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 549, + 453, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 549, + 453, + 562 + ], + "spans": [ + { + "bbox": [ + 313, + 549, + 453, + 562 + ], + "type": "text", + "content": "3.1. Learned Weights in ViTs" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "type": "text", + "content": "ViTs encode visual knowledge in their weight matrices, which can be analyzed through Singular Value Decomposition (SVD). Assume we have a weight matrix that transforms inputs from " + }, + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "type": "inline_equation", + "content": "c_{1}" + }, + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "type": "inline_equation", + "content": "c_{2}" + }, + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "type": "text", + "content": " channels, denoted by " + }, + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{c_2 \\times c_1}" + }, + { + "bbox": [ + 313, + 568, + 541, + 628 + ], + "type": "text", + "content": ", then its SVD reads:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 395, + 638, + 541, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 638, + 541, + 651 + ], + "spans": [ + { + "bbox": [ + 395, + 638, + 541, + 651 + ], + "type": "interline_equation", + "content": "\\mathbf {W} = \\mathbf {U} \\boldsymbol {\\Sigma} \\mathbf {V} ^ {\\top}, \\tag {1}", + "image_path": "1d74fd4b7d12aef4fdd3be3d4e6ea5bb8594803af113208cfd3d0636541e0d79.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathbf{U} \\in \\mathbb{R}^{c_2 \\times c_2}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma} \\in \\mathbb{R}^{c_2 \\times c_1}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{c_1 \\times c_1}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": ". We refer to " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": " as the left singular vectors, " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": " as the singular values, and " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": " as the right singular vectors. Notably, " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": " form orthonormal bases for the output and input spaces of the linear map represented by " + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 313, + 662, + 541, + 723 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "25221" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 72, + 297, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 72, + 297, + 95 + ], + "spans": [ + { + "bbox": [ + 67, + 72, + 297, + 95 + ], + "type": "text", + "content": "These bases characterize how the network transforms visual features across layers and hidden dimensions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "spans": [ + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": "Problem Setup. Throughout this paper, we assume " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": " tasks " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{T_1,\\dots ,T_K\\}" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": ". Each task " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": " has an associated dataset " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k = \\{(x_i^k,y_i^k)\\}_{i = 1}^{N_k}" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "x_{i}^{k}\\in \\mathcal{X}" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "y_{i}^{k}\\in \\mathcal{Y}_{k}" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": " represent the input-output pairs. The goal is to train a neural network to minimize a supervised loss between the prediction and ground-truth output. Following [1], we use a Swin Transformer [28], which processes input images by dividing them into nonoverlapping patches and progressively merging patches to reduce spatial resolution while increasing feature dimension across stages. Formally, the Swin Transformer processes images through " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": " stages, with the " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": "-th stage operating on feature maps of resolution " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "\\frac{H}{2^l}\\times \\frac{W}{2^l}" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "inline_equation", + "content": "C_l" + }, + { + "bbox": [ + 67, + 96, + 297, + 275 + ], + "type": "text", + "content": " channels. The key operation in each stage is a Window-based Multi-head Self-Attention (W-MSA):" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 91, + 281, + 296, + 309 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 281, + 296, + 309 + ], + "spans": [ + { + "bbox": [ + 91, + 281, + 296, + 309 + ], + "type": "interline_equation", + "content": "\\mathrm {W} - \\mathrm {M S A} (Q, K, V) = \\operatorname {S o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d}}\\right) V, \\tag {2}", + "image_path": "685abee6cbd8c589689467724baeb1136b5a2ccc08ea2cf4b07566330d16ee7d.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "spans": [ + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "inline_equation", + "content": "Q, K, V \\in \\mathbb{R}^{M \\times d}" + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "text", + "content": " are query, key, and value matrices for windows of size " + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "text", + "content": ". The corresponding weight matrices " + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_l^{(q)}, \\mathbf{W}_l^{(k)}, \\mathbf{W}_l^{(v)} \\in \\mathbb{R}^{d \\times d}" + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "text", + "content": " for these projections in layer " + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "text", + "content": " are central to our DiTASK, because in Section 4 we dynamically adjust their singular values for multi-task adaptations. The MTL objective minimizes a weighted combination of " + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 67, + 315, + 296, + 401 + ], + "type": "text", + "content": " task losses:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 134, + 407, + 296, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 407, + 296, + 440 + ], + "spans": [ + { + "bbox": [ + 134, + 407, + 296, + 440 + ], + "type": "interline_equation", + "content": "\\min _ {\\Theta} \\sum_ {k = 1} ^ {K} \\lambda_ {k} \\mathcal {L} _ {k} (\\Theta ; \\mathcal {D} _ {k}), \\tag {3}", + "image_path": "d587d79891203c49e8ee80204100adde38801988b662dd460c5d3c392b4b90c1.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_k" + }, + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\lambda_{k}" + }, + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "type": "text", + "content": " represent the loss function and weight for the " + }, + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 67, + 446, + 296, + 483 + ], + "type": "text", + "content": "-th task, respectively. In Figure 4, we illustrate the overall architecture used in this paper." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 488, + 296, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 488, + 296, + 513 + ], + "spans": [ + { + "bbox": [ + 69, + 488, + 296, + 513 + ], + "type": "text", + "content": "3.2. CPAB Diffeomorphisms for Weight Transformation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 518, + 297, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 518, + 297, + 615 + ], + "spans": [ + { + "bbox": [ + 67, + 518, + 297, + 615 + ], + "type": "text", + "content": "As we show later in Section 4, our DiTASK modifies singular values " + }, + { + "bbox": [ + 67, + 518, + 297, + 615 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 67, + 518, + 297, + 615 + ], + "type": "text", + "content": " while preserving the structure of weight matrices. To achieve that, transformations that are smooth, invertible, and monotone, are required. Continuous Piecewise Affine-Based (CPAB) [14, 15] diffeomorphisms satisfy these conditions while being efficient in terms of parameters and computing diffeomorphisms. We now turn to define CPAB formally." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "spans": [ + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "text", + "content": "Definition 3.1 (CPAB Transformation). Given a closed interval " + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "inline_equation", + "content": "\\Omega = [a,b]" + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "text", + "content": " partitioned into " + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathcal{P}}" + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "text", + "content": " intervals, a CPAB transformation is defined through a velocity field " + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "inline_equation", + "content": "v^{\\theta}:\\Omega \\to \\mathbb{R}" + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "text", + "content": " that is continuous and piecewise-affine within each interval. This velocity field, parameterized by " + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "inline_equation", + "content": "\\pmb {\\theta}\\in \\mathbb{R}^{\\mathcal{N}_{\\mathcal{P}} - 1}" + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "text", + "content": ", yields a diffeomorphism " + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "inline_equation", + "content": "f^{\\theta}" + }, + { + "bbox": [ + 67, + 620, + 297, + 693 + ], + "type": "text", + "content": " of the form:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 111, + 698, + 296, + 726 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 698, + 296, + 726 + ], + "spans": [ + { + "bbox": [ + 111, + 698, + 296, + 726 + ], + "type": "interline_equation", + "content": "f ^ {\\boldsymbol {\\theta}} (x) = x + \\int_ {0} ^ {1} v ^ {\\boldsymbol {\\theta}} \\left(f ^ {\\boldsymbol {\\theta}} (x, \\tau)\\right) d \\tau . \\tag {4}", + "image_path": "54f2d4f1e192173afdb2f18684efc84ff416914d0df3ebfea9b0f637c6f37fe8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 541, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 541, + 193 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 541, + 193 + ], + "type": "text", + "content": "For practical implementation, we use the Python package from Martinez et al. [34], and provide additional details in the supplementary material. CPAB transformations are ideal for our settings, shown in Section 4, because they provide: (i) Low parameter overhead. Only " + }, + { + "bbox": [ + 313, + 72, + 541, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\mathcal{N}_{\\mathcal{P}})" + }, + { + "bbox": [ + 313, + 72, + 541, + 193 + ], + "type": "text", + "content": " parameters, where typically " + }, + { + "bbox": [ + 313, + 72, + 541, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathcal{P}} \\leq 128" + }, + { + "bbox": [ + 313, + 72, + 541, + 193 + ], + "type": "text", + "content": "; (ii) Differentiability. Enables gradient-based optimization; (iii) Computational efficiency. Computing Equation (4) is of linear complexity; (iv) Stability. CPAB transformations are Lipschitz continuous [15]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 201, + 541, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 201, + 541, + 229 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 541, + 229 + ], + "type": "text", + "content": "4. DiTASK: Diffeomorphic Multi-Task Adaptation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 235, + 541, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 235, + 541, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 235, + 541, + 354 + ], + "type": "text", + "content": "We introduce DITASK (Diffeomorphic Multi-Task Adaptation), a novel approach for efficient multi-task fine-tuning. Our method is grounded in a fundamental analysis of how neural networks process information through their weight matrices. We draw insights from linear algebra to the workings of a linear layer of neural network in Section 4.1 relating it to SVD. In Section 4.2, we formally introduce DITASK and elaborate on its properties that motivate our design choices in Section 4.3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 361, + 487, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 487, + 374 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 487, + 374 + ], + "type": "text", + "content": "4.1. Understanding Weight Matrices" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "type": "text", + "content": "We now show that by considering the SVD of weight matrices, we can gain insights on the course of action of linear layers, that later, in Section 4.2, serves as a mathematically grounded motivation for the design of our DiTASK. Specifically, we note that a linear layer with weight matrix " + }, + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{c_2 \\times c_1}" + }, + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "type": "text", + "content": ", and its SVD decomposition " + }, + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = \\mathbf{U} \\boldsymbol{\\Sigma} \\mathbf{V}^{\\top}" + }, + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "type": "text", + "content": ", can be viewed as a linear map " + }, + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "type": "inline_equation", + "content": "g: \\mathbb{R}^{c_1} \\to \\mathbb{R}^{c_2}" + }, + { + "bbox": [ + 313, + 380, + 541, + 476 + ], + "type": "text", + "content": ", such that the following equality holds:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 359, + 481, + 541, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 481, + 541, + 512 + ], + "spans": [ + { + "bbox": [ + 359, + 481, + 541, + 512 + ], + "type": "interline_equation", + "content": "g (\\mathbf {x}) = \\mathbf {W} \\mathbf {x} = \\sum_ {i = 1} ^ {p} \\sigma_ {i} \\langle \\mathbf {x}, \\mathbf {v} _ {i} \\rangle \\mathbf {u} _ {i}, \\tag {5}", + "image_path": "b2326bf79c77326993cb240eecb39ae634553d281745e5f6c32a90cf79d921c4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "spans": [ + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "inline_equation", + "content": "\\mathbf{U} = [\\mathbf{u}_1, \\dots, \\mathbf{u}_{c_2}]" + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "inline_equation", + "content": "\\mathbf{V} = [\\mathbf{v}_1, \\dots, \\mathbf{v}_{c_1}]" + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Sigma} = \\text{diag}([\\sigma_1, \\sigma_2, \\dots, \\sigma_p])" + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "inline_equation", + "content": "p = \\min(c_1, c_2)" + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": ". The basis vectors in " + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": " are the left singular vectors, " + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": " are right singular vectors, and " + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Sigma}" + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": " are the singular values of " + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 313, + 518, + 541, + 566 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "text", + "content": "Specifically, the orientations encoded by the left and right singular vectors represent features present in the output and input spaces of the linear transformation " + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "text", + "content": ", respectively. Multi-task learning requires adapting these orientations jointly for all tasks, while minimizing task interference to prevent performance degradation. Below, we describe how to achieve effective multi-task adaptation using diffeomorphisms, by preserving the singular vectors " + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "text", + "content": " and modifying " + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 313, + 566, + 541, + 674 + ], + "type": "text", + "content": " in a principled manner." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 680, + 454, + 693 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 680, + 454, + 693 + ], + "spans": [ + { + "bbox": [ + 313, + 680, + 454, + 693 + ], + "type": "text", + "content": "4.2. Adaptation with DITASK" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 697, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 697, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 697, + 541, + 723 + ], + "type": "text", + "content": "Given a learned weight matrix " + }, + { + "bbox": [ + 313, + 697, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = \\mathbf{U}\\pmb{\\Sigma}\\mathbf{V}^{\\top} \\in \\mathbb{R}^{c_2 \\times c_1}" + }, + { + "bbox": [ + 313, + 697, + 541, + 723 + ], + "type": "text", + "content": " from a ViT, we transform the singular values " + }, + { + "bbox": [ + 313, + 697, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}" + }, + { + "bbox": [ + 313, + 697, + 541, + 723 + ], + "type": "text", + "content": " by a" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "text", + "content": "25222" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 68, + 72, + 297, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 72, + 297, + 107 + ], + "spans": [ + { + "bbox": [ + 68, + 72, + 297, + 107 + ], + "type": "text", + "content": "learned neural diffeomorphism " + }, + { + "bbox": [ + 68, + 72, + 297, + 107 + ], + "type": "inline_equation", + "content": "f^{\\theta}" + }, + { + "bbox": [ + 68, + 72, + 297, + 107 + ], + "type": "text", + "content": " described in Equation (4), to get the adapted weight matrix " + }, + { + "bbox": [ + 68, + 72, + 297, + 107 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_A" + }, + { + "bbox": [ + 68, + 72, + 297, + 107 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 77, + 114, + 296, + 181 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 114, + 296, + 181 + ], + "spans": [ + { + "bbox": [ + 77, + 114, + 296, + 181 + ], + "type": "interline_equation", + "content": "\\mathbf {W} _ {A} = \\mathbf {U} \\left[ \\begin{array}{c c c c} f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {1}\\right) & 0 & \\dots & 0 \\\\ 0 & f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {2}\\right) & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & f ^ {\\boldsymbol {\\theta}} \\left(\\sigma_ {p}\\right) \\end{array} \\right] \\mathbf {V} ^ {\\top}. \\tag {6}", + "image_path": "9ebeb72d63f404881f1f7b2219dbb2f8a5bdaa919669fd9965635b9a2d5477ce.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "spans": [ + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "text", + "content": "During fine-tuning, we freeze " + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "text", + "content": " and learn only the parameters " + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "text", + "content": " of the CPA velocity field. This allows DiTASK to adapt to multiple tasks using " + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\mathcal{N}_{\\mathcal{P}})" + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "text", + "content": " additional parameters (where typically " + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathcal{P}} \\leq 128" + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "text", + "content": "), which is significantly smaller than methods with low-rank " + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(r(c_1 + c_2))" + }, + { + "bbox": [ + 68, + 182, + 296, + 289 + ], + "type": "text", + "content": ". We describe this process in the Section 1, and compare the computational cost of DiTASK with other fine-tuning methods in the supplementary material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "spans": [ + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "type": "text", + "content": "Multi-Task Adaptation with DiTASK. To enable both multi and task-specific adaptation, we learn two sets of neural diffeomorphic transformations in every pretrained weight matrix " + }, + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "type": "text", + "content": ", shown in Section 1, that include: (i) Joint Adaptation parameters, denoted by " + }, + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\theta_{j}" + }, + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "type": "text", + "content": ", to allow task synergies which are crucial for MTL [21, 47]; and (ii) Task-wise Adaptation parameters, denoted by " + }, + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "type": "inline_equation", + "content": "\\{\\theta_k\\}_{k=1}^K" + }, + { + "bbox": [ + 68, + 289, + 296, + 387 + ], + "type": "text", + "content": " to enable learning nuances for each task." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 393, + 192, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 393, + 192, + 405 + ], + "spans": [ + { + "bbox": [ + 69, + 393, + 192, + 405 + ], + "type": "text", + "content": "4.3. Properties of DITASK" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 411, + 296, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 411, + 296, + 447 + ], + "spans": [ + { + "bbox": [ + 68, + 411, + 296, + 447 + ], + "type": "text", + "content": "In this section, we motivate our design choices and discuss the properties that make DiTASK an effective and parameter-efficient fine-tuning method for MTL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 448, + 296, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 448, + 296, + 673 + ], + "spans": [ + { + "bbox": [ + 68, + 448, + 296, + 673 + ], + "type": "text", + "content": "Feature Space Preservation. As discussed in Section 4.1, pre-trained weight matrices encode feature transformations through their singular vectors, where " + }, + { + "bbox": [ + 68, + 448, + 296, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 68, + 448, + 296, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 68, + 448, + 296, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 68, + 448, + 296, + 673 + ], + "type": "text", + "content": " form orthonormal bases for output and input spaces, respectively. These bases capture the orientation of patterns learned during pre-training, each weighted by its corresponding singular value. In contrast to traditional low-rank methods like LoRA, which constrain adaptations to fixed low-dimensional subspaces, potentially losing important features, our DiTASK preserves these learned bases entirely. This preservation allows us to achieve superior multi-task performance with fewer parameters, as shown in Figure 1. Specifically, while low-rank methods require increasing their rank (and thus parameters and departure from being low-rank) to match single-task performance, our DiTASK maintains the learned feature space of pre-trained ViTs through a targeted and mathematically-ground singular value modulation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 674, + 296, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 674, + 296, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 674, + 296, + 723 + ], + "type": "text", + "content": "Feature Relativity Preservation. The order of singular values " + }, + { + "bbox": [ + 68, + 674, + 296, + 723 + ], + "type": "inline_equation", + "content": "\\sigma_{1} \\geq \\sigma_{2} \\geq \\ldots \\geq \\sigma_{p}" + }, + { + "bbox": [ + 68, + 674, + 296, + 723 + ], + "type": "text", + "content": " in weight matrices of ViTs encode the relative importance of features learned during pre-training on large-scale datasets like" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "text", + "content": "ImageNet-21k. By utilizing diffeomorphisms, which are smooth, invertible, and monotone, by definition, we preserve this ordering. That is, if " + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "inline_equation", + "content": "f^{\\theta}" + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "text", + "content": " is a diffeomorphism, then " + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "inline_equation", + "content": "f^{\\theta}(\\sigma_1) \\geq f^{\\theta}(\\sigma_2) \\geq \\ldots \\geq f^{\\theta}(\\sigma_p)" + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "text", + "content": " in Equation (6). Our choice of CPAB transformations implements this with only " + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathcal{P}} \\leq 128" + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "text", + "content": " parameters per weight matrix, compared to the " + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(r(c_1 + c_2))" + }, + { + "bbox": [ + 313, + 72, + 541, + 216 + ], + "type": "text", + "content": " parameters required by low-rank adaptation methods. Our experiments in Section 5 demonstrate that preserving feature hierarchy through diffeomorphic transformations enables effective multi-task generalization while maintaining parameter efficiency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 228, + 395, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 228, + 395, + 243 + ], + "spans": [ + { + "bbox": [ + 314, + 228, + 395, + 243 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 249, + 541, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 249, + 541, + 321 + ], + "spans": [ + { + "bbox": [ + 313, + 249, + 541, + 321 + ], + "type": "text", + "content": "We evaluate DiTASK on multiple MTL benchmarks and compare it with other adaptation methods. Section 5.1 details the experimental setup and baselines, Section 5.2 discusses our main findings, and Section 5.3 presents few ablation studies of DiTASK. We seek to address three key research questions:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 322, + 541, + 405 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 313, + 322, + 541, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 322, + 541, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 322, + 541, + 357 + ], + "type": "text", + "content": "(RQ1) Can a selective modification of singular values while preserving singular vectors bridge the performance gap between decoder-only and full fine-tuning?" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 357, + 540, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 540, + 380 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 540, + 380 + ], + "type": "text", + "content": "(RQ2) Does full-rank preservation by singular value modulation outperform low-rank adaptation methods?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 381, + 540, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 381, + 540, + 405 + ], + "spans": [ + { + "bbox": [ + 313, + 381, + 540, + 405 + ], + "type": "text", + "content": "(RQ3) How does DiTASK compare to other parameter-efficient adaptation methods?" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 415, + 430, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 415, + 430, + 428 + ], + "spans": [ + { + "bbox": [ + 314, + 415, + 430, + 428 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 434, + 541, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 541, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 541, + 540 + ], + "type": "text", + "content": "Datasets and Tasks. We evaluate DiTASK on the PASCAL-MTL dataset [13] (PASCAL-Context split) following the literature on multi-task dense prediction [46, 54, 55]. This dataset includes 4,998 training and 5,105 validation images with annotations for semantic segmentation (21 classes), human part segmentation (7 classes), surface normal estimation, and saliency detection. Additional experiments on the NYUD dataset [41] are provided in Table 4." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "spans": [ + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "type": "text", + "content": "Implementation Details. We use the Swin-Tiny [28] architecture, pre-trained on ImageNet-21k [39] as the backbone encoder, similar to [1]. To ensure a fair comparison, we incorporate the HRNet [50] decoder, which accounts for " + }, + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "type": "text", + "content": " of the total parameters, as in previous works [1, 46]. Following MTINet [46], we apply cross-entropy loss for segmentation tasks, " + }, + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "type": "text", + "content": " loss for surface normals, and balanced cross-entropy [9] for saliency detection, with same task weights " + }, + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "type": "inline_equation", + "content": "\\{\\lambda_k\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 541, + 541, + 673 + ], + "type": "text", + "content": " used in MTINet. In all experiments, we follow the evaluation protocol from Agiza et al. [1]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 673, + 541, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 673, + 541, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 673, + 541, + 696 + ], + "type": "text", + "content": "Baselines. We benchmark our DiTASK with three categories of methods:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "type": "text", + "content": "- Full Fine-Tuning: Methods that modify all weight matrices (single-task, MTL decoder, full MTL)" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "25223" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 129, + 535, + 383 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 543, + 125 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 543, + 125 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 543, + 125 + ], + "type": "text", + "content": "Table 1. Performance on PASCAL Context for Multi-Task Learning. Comparison of DITASK with full fine-tuning, adapter-based, and fixed-rank methods across four dense prediction tasks: semantic segmentation, human part segmentation, saliency detection, and surface normal estimation. Metrics are MIOU (↑) and RMSE (↓), with " + }, + { + "bbox": [ + 67, + 70, + 543, + 125 + ], + "type": "inline_equation", + "content": "\\Delta m" + }, + { + "bbox": [ + 67, + 70, + 543, + 125 + ], + "type": "text", + "content": " denoting relative improvement over single-task tuning. DITASK achieves strong performance with minimal trainable parameters and supports joint inference across tasks." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 129, + 535, + 383 + ], + "lines": [ + { + "bbox": [ + 74, + 129, + 535, + 383 + ], + "spans": [ + { + "bbox": [ + 74, + 129, + 535, + 383 + ], + "type": "table", + "html": "
    MethodSEMSEG (MIOU ↑)HUMAN PARTS (MIOU ↑)SALIENCY (MIOU ↑)NORMALS (RMSE ↓)Δm(%)Trainable Swin Parameters (M)Single Inference For All Tasks
    FULL FINE-TUNING
    Single Task67.2161.9362.3517.970.00112.62×
    MTL - Dec. Only65.0953.4857.4620.69- 9.950✓
    MTL - Full67.5660.2465.2116.64+ 2.2328.12✓
    ADAPTER-BASED
    VPT-shallow [22]62.9652.2758.3120.90-11.180.63×
    VPT-deep [22]64.3552.5458.1521.07-10.851.49×
    Compactor++ [23]67.2655.6959.4719.54- 5.840.72×
    Bitfit [58]68.5755.9960.6419.42- 4.600.91×
    Compactor [23]68.0856.4160.0819.22- 4.550.84×
    Adapter [17]69.2157.3861.2818.83- 2.719.26×
    VL-Adapter [44]70.2159.1562.2919.26- 1.832.80×
    Polyhistor [27]70.8759.1565.5417.77+ 2.347.02×
    HyperFormer [31]71.4360.7365.5417.77+ 2.6470.83×
    FIXED-RANK
    MTL - DoRA [26]52.3650.8263.5318.32-10.026.40✓
    MTL - ReFT [53]68.7556.4958.7620.54- 6.6316.16✓
    MTL - SVFT [25]64.4455.9463.0317.86- 3.023.83✓
    LoRA [19]70.1257.7361.9018.96- 2.170.93×
    MTLoRA [1] (r = 16)68.1958.9964.4817.03+ 1.353.01✓
    MTLoRA [1] (r = 32)67.7459.4664.9016.59+ 2.164.14✓
    MTLoRA [1] (r = 64)67.9059.8465.4016.60+ 2.556.40✓
    Single Task - DITASK72.2062.3365.7016.55+ 5.331.60 (×4)×
    MTL - DITASK (Ours)69.6662.0265.0017.10+ 3.221.61✓
    ", + "image_path": "093e1790cbb85a981c5a605109ef1d69d111dc9257c167a4eb25583b3024eb96.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 73, + 407, + 535, + 487 + ], + "blocks": [ + { + "bbox": [ + 107, + 392, + 501, + 403 + ], + "lines": [ + { + "bbox": [ + 107, + 392, + 501, + 403 + ], + "spans": [ + { + "bbox": [ + 107, + 392, + 501, + 403 + ], + "type": "text", + "content": "Table 2. Effect of Backbone Size - Relative improvement increases with increasing capacity of the backbone" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 407, + 535, + 487 + ], + "lines": [ + { + "bbox": [ + 73, + 407, + 535, + 487 + ], + "spans": [ + { + "bbox": [ + 73, + 407, + 535, + 487 + ], + "type": "table", + "html": "
    MethodSEMSEG (MIOU ↑)HUMAN PARTS (MIOU ↑)SALIENCY (MIOU ↑)NORMALS (RMSE ↓)Δm(%)Trainable Swin Parameters (M)
    DITASK + Swin-Tiny69.6662.0265.0017.10+3.221.61
    DITASK + Swin-Small74.4963.2064.5817.58+4.681.66
    DITASK + Swin-Base75.8665.9764.1817.29+6.523.14
    DITASK + Swin-Large76.2367.5364.0716.90+7.797.13
    ", + "image_path": "b69559b76bbfcbe8acbe553c19e1e52deee856f0e24a1a130badc4353c9ab945.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 506, + 295, + 590 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 69, + 506, + 295, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 506, + 295, + 554 + ], + "spans": [ + { + "bbox": [ + 69, + 506, + 295, + 554 + ], + "type": "text", + "content": "- Adapter-based: Methods that add task-specific layers while preserving main weights (Adapter [18], BitFit [58], VPT [22], Compactor [23], VL-Adapter [44], HyperFormer [31], Polyhistor [27])" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 555, + 295, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 555, + 295, + 590 + ], + "spans": [ + { + "bbox": [ + 69, + 555, + 295, + 590 + ], + "type": "text", + "content": "- Fixed-Rank: Methods that constrain updates to low-rank subspaces (LoRA [19], DoRA [26], SVFT [25], ReFT [53], MTLoRA [1])" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 69, + 596, + 198, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 596, + 198, + 608 + ], + "spans": [ + { + "bbox": [ + 69, + 596, + 198, + 608 + ], + "type": "text", + "content": "5.2. Results and Discussion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 614, + 295, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 614, + 295, + 650 + ], + "spans": [ + { + "bbox": [ + 67, + 614, + 295, + 650 + ], + "type": "text", + "content": "Table 1 presents our main results, addressing (RQ1)-(RQ3) on the effectiveness of DiTASK for multi-task learning (MTL)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "spans": [ + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "type": "text", + "content": "Bridging the Efficiency Performance Gap. DiTASK achieves a " + }, + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "type": "inline_equation", + "content": "+3.22\\%" + }, + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "type": "text", + "content": " relative improvement over single-task baselines using only 1.61M trainable encoder parameters. This outperforms both decoder-only tuning " + }, + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "type": "inline_equation", + "content": "(-9.95\\%)" + }, + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "type": "text", + "content": " and full fine-tuning " + }, + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "type": "inline_equation", + "content": "(+2.23\\%)" + }, + { + "bbox": [ + 67, + 651, + 295, + 722 + ], + "type": "text", + "content": ", demonstrating that modulating singular values while preserving pre" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 506, + 539, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 539, + 530 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 539, + 530 + ], + "type": "text", + "content": "trained feature directions enables an effective balance between parameter efficiency and performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "text", + "content": "Comparison with Fixed Low-Rank Methods. DTASK outperforms the state-of-the-art MTLoRA by " + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "inline_equation", + "content": "26.27\\%" + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "inline_equation", + "content": "\\Delta m" + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "text", + "content": ", using " + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "text", + "content": " fewer parameters (Figure 5). Most fixed-rank methods yield negative " + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "inline_equation", + "content": "\\Delta m" + }, + { + "bbox": [ + 313, + 531, + 541, + 637 + ], + "type": "text", + "content": " due to task interference from shared low-rank subspaces. By modulating singular values independently per task while preserving full-rank structure, DTASK mitigates this interference. Similar trends are observed on NYUD (Table 4)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 639, + 541, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 639, + 541, + 708 + ], + "spans": [ + { + "bbox": [ + 313, + 639, + 541, + 708 + ], + "type": "text", + "content": "Parameter Efficiency and Task Performance. DITASK is the only parameter-efficient method to consistently improve over single-task baselines, showing that modulating singular values while preserving pretrained directions effectively balances efficiency and performance." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "25224" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 74, + 290, + 201 + ], + "blocks": [ + { + "bbox": [ + 73, + 74, + 290, + 201 + ], + "lines": [ + { + "bbox": [ + 73, + 74, + 290, + 201 + ], + "spans": [ + { + "bbox": [ + 73, + 74, + 290, + 201 + ], + "type": "image", + "image_path": "eccec0d3520f16116ec3e609739488da7c1e5f8b7bf5b6485f521e01ee574bd7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 212, + 295, + 235 + ], + "lines": [ + { + "bbox": [ + 69, + 212, + 295, + 235 + ], + "spans": [ + { + "bbox": [ + 69, + 212, + 295, + 235 + ], + "type": "text", + "content": "Figure 5. Comparison of adaptation parameter budget of the shared encoder, excluding LayerNorm parameters." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 70, + 304, + 296, + 355 + ], + "blocks": [ + { + "bbox": [ + 68, + 251, + 296, + 295 + ], + "lines": [ + { + "bbox": [ + 68, + 251, + 296, + 295 + ], + "spans": [ + { + "bbox": [ + 68, + 251, + 296, + 295 + ], + "type": "text", + "content": "Table 3. Comparison of computational efficiency between DiTASK and MTLoRA. DiTASK reduces batch runtime by " + }, + { + "bbox": [ + 68, + 251, + 296, + 295 + ], + "type": "inline_equation", + "content": "\\approx 22\\%" + }, + { + "bbox": [ + 68, + 251, + 296, + 295 + ], + "type": "text", + "content": ", lowers memory usage, and uses " + }, + { + "bbox": [ + 68, + 251, + 296, + 295 + ], + "type": "inline_equation", + "content": "500\\times" + }, + { + "bbox": [ + 68, + 251, + 296, + 295 + ], + "type": "text", + "content": " fewer adaptation parameters." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 304, + 296, + 355 + ], + "lines": [ + { + "bbox": [ + 70, + 304, + 296, + 355 + ], + "spans": [ + { + "bbox": [ + 70, + 304, + 296, + 355 + ], + "type": "table", + "html": "
    MethodBatch Runtime (seconds)Max GPU Mem (Megabytes)# Adaptation Params
    MTLoRA35.20±1.05235094.86M
    DiTASK27.31±5.29229068.5K
    ", + "image_path": "1fd63e0067350b2a74e44a2e9be5574b7a90133cd6dc3a510b23b6f7724f4cbb.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 378, + 162, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 378, + 162, + 392 + ], + "spans": [ + { + "bbox": [ + 69, + 378, + 162, + 392 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 399, + 295, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 399, + 295, + 422 + ], + "spans": [ + { + "bbox": [ + 68, + 399, + 295, + 422 + ], + "type": "text", + "content": "We analyze key components of DiTASK to understand their contributions to multi-task performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 423, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 423, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 68, + 423, + 296, + 495 + ], + "type": "text", + "content": "Computational Efficiency. DITASK uses only 8.5K adaptation parameters, compared to MTLoRA's 4.86M, while achieving " + }, + { + "bbox": [ + 68, + 423, + 296, + 495 + ], + "type": "inline_equation", + "content": "22\\%" + }, + { + "bbox": [ + 68, + 423, + 296, + 495 + ], + "type": "text", + "content": " faster batch processing (27.31s vs 35.20s) and reduced memory usage (see Table 3). The efficiency gains stem from our compact CPAB parameterization of singular value transformations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "spans": [ + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "type": "text", + "content": "Joint vs Task-Wise Singular Value Modulation. We evaluate three configurations of singular value modulation, shown in Figure 7. Joint Adaptation alone, with shared modulation across tasks, achieves an improvement of " + }, + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "type": "inline_equation", + "content": "2.77\\%" + }, + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "type": "text", + "content": ". Task-Wise Adaptation alone, which modulates singular values independently for each task, yields " + }, + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "type": "inline_equation", + "content": "2.85\\%" + }, + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "type": "text", + "content": ". The Combined approach, DiTASK, incorporates both strategies and reaches the highest improvement at " + }, + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "type": "inline_equation", + "content": "3.22\\%" + }, + { + "bbox": [ + 68, + 495, + 296, + 613 + ], + "type": "text", + "content": ", supporting the use of both shared and task-specific transformations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 68, + 615, + 296, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 615, + 296, + 662 + ], + "spans": [ + { + "bbox": [ + 68, + 615, + 296, + 662 + ], + "type": "text", + "content": "Model Scaling Analysis. The effectiveness of DiTASK scales with model capacity (Table 2). This scaling effect indicates that larger models provide richer singular value spaces, enabling more effective task-specific adaptation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 68, + 663, + 296, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 663, + 296, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 663, + 296, + 723 + ], + "type": "text", + "content": "Qualitative Comparison. In Figure 6, we present a visual comparison between MTLoRA and our DiTASK on the semantic segmentation task from PASCAL MTL. DiTASK demonstrates tighter and clearer boundaries, more consistent segmentation, and improved class sep" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 315, + 70, + 541, + 148 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 541, + 148 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 541, + 148 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 541, + 148 + ], + "type": "table", + "html": "
    MethodSEMSEG(MIOU↑)DEPTH(RMSE↓)Δm(%)Trainable Params(in M)
    Single Task33.180.6670112.62
    MTL - Dec. Only28.370.832-19.611.00
    MTL - Full35.290.734-1.8428.5
    MTLoRA37.180.635+8.426.26
    Single Task - DITASK44.010.644+18.041.61
    DITASK43.850.606+20.651.61
    ", + "image_path": "a974d43fd63cbef66e9c1dd943f54ad9c0310f8cd975a972d5ebd605f9d64b19.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 156, + 541, + 190 + ], + "lines": [ + { + "bbox": [ + 313, + 156, + 541, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 156, + 541, + 190 + ], + "type": "text", + "content": "Table 4. Comparison of DiTASK and MTLoRA on the NYUD [41] multi-task dataset for semantic segmentation (MIOU) and depth estimation (RMSE)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 317, + 206, + 542, + 342 + ], + "blocks": [ + { + "bbox": [ + 317, + 206, + 542, + 342 + ], + "lines": [ + { + "bbox": [ + 317, + 206, + 542, + 342 + ], + "spans": [ + { + "bbox": [ + 317, + 206, + 542, + 342 + ], + "type": "image", + "image_path": "ec6f7c48c2de61254869e5ad473a3f87f6a12d7f67603f51d031c67fdb0ec1b4.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 350, + 541, + 372 + ], + "lines": [ + { + "bbox": [ + 313, + 350, + 541, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 541, + 372 + ], + "type": "text", + "content": "Figure 6. Semantic segmentation predictions on PASCAL MTL using MTLoRA and D1TASK." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 397, + 541, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 397, + 541, + 444 + ], + "spans": [ + { + "bbox": [ + 313, + 397, + 541, + 444 + ], + "type": "text", + "content": "aration. For example, in the dimly lit sofa scene in the second column, MTLoRA struggles to correctly predict the sofa boundary, while DITASK offers a better prediction." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 461, + 388, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 388, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 388, + 474 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 312, + 483, + 542, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 483, + 542, + 723 + ], + "spans": [ + { + "bbox": [ + 312, + 483, + 542, + 723 + ], + "type": "text", + "content": "In this paper, we introduce DiTASK, a novel MTL fine-tuning approach that leverages neural diffeomorphisms for singular value adaptation while preserving the structure of pre-trained representations. We observe that existing methods, which restrict weight updates to fixed low-rank subspaces for resource efficiency, often suffer from multi-task performance degradation relative to single-task baselines. We conjecture that the singular vectors of pre-trained weight matrices capture rich features, and preserving them during MTL adaptation enhances performance. By using neural diffeomorphisms, DiTASK maintains feature space and relational structure while requiring less memory than other low-rank adaptation methods. We evaluate DiTASK on the PASCAL MTL and NYUD MTL datasets, with extensive ablation studies demonstrating its effectiveness. Our results show that DiTASK achieves state-of-the-art MTL performance with " + }, + { + "bbox": [ + 312, + 483, + 542, + 723 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 312, + 483, + 542, + 723 + ], + "type": "text", + "content": " fewer trainable parameters, underscoring the importance of preserving singular vectors in pre-trained weights." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "25225" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 70, + 71, + 128, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 71, + 128, + 83 + ], + "spans": [ + { + "bbox": [ + 70, + 71, + 128, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 91, + 297, + 723 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 75, + 91, + 297, + 163 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 91, + 297, + 163 + ], + "spans": [ + { + "bbox": [ + 75, + 91, + 297, + 163 + ], + "type": "text", + "content": "[1] Ahmed Agiza, Marina Neseem, and Sherief Reda. 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Algorithmic Advances in Riemannian Geometry and Applications: For Machine Learning, Computer Vision, Statistics, and Optimization, pages 1-23, 2016. 4" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "25229" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_content_list.json b/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8dec7fec4e6c74afe09233ae689e9f5f84ae94e1 --- /dev/null +++ b/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_content_list.json @@ -0,0 +1,1714 @@ +[ + { + "type": "text", + "text": "DiTCtrl: Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation", + "text_level": 1, + "bbox": [ + 109, + 128, + 887, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Minghong Cai $^{1\\dagger}$", + "bbox": [ + 117, + 210, + 250, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiaodong Cun", + "bbox": [ + 289, + 210, + 416, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yong Zhang", + "bbox": [ + 290, + 232, + 397, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiaoyu Li $^{3}$", + "bbox": [ + 455, + 210, + 563, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ying Shan3", + "bbox": [ + 437, + 232, + 531, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wenze Liu", + "bbox": [ + 596, + 210, + 692, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiangyu Yue $^{1,5}$", + "bbox": [ + 571, + 232, + 712, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhaoyang Zhang3", + "bbox": [ + 733, + 210, + 877, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 MMLab, CUHK", + "bbox": [ + 267, + 256, + 415, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ ARC Lab, Tencent PCG", + "bbox": [ + 214, + 277, + 419, + 294 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ GVC Lab, Great Bay University", + "bbox": [ + 454, + 256, + 723, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "4 Tencent AI Lab", + "bbox": [ + 460, + 277, + 599, + 294 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "5 SHIAE, CUHK", + "bbox": [ + 638, + 277, + 777, + 294 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/58678c5263655cb2fa1fa5b176d9a2563fa17b7964f3957c7d2bf67bfbf2436e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 93, + 315, + 248, + 396 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fb5a8100d4883f4a1c194f89a2f5ff285c0c70bf8de02533bcf5a3136305f08c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 254, + 315, + 410, + 396 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2a3349ce53efda2227ff7a5bd97154aca84e2be0bde5e56bd0b7a52ca3bd34aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 315, + 571, + 396 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d9924f5d3388e8ff26127ca2d1fa3469dd2b8ad9aa1eec1c70eb3b5bc16dde17.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 315, + 736, + 396 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9f5ac1bd7c2133423bdd6a5eb88cb05193b7d1fec52cb24c2e1ff71bb7ee8b01.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 743, + 315, + 901, + 396 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(a) \"Athlete glides across ocean waters $\\rightarrow$ snow mountain $\\rightarrow$ sand dunes\"", + "bbox": [ + 223, + 397, + 767, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2367f95cacedec59e0a11f7091dfa624508618b09043af9520f128b800b9e9f5.jpg", + "image_caption": [ + "Figure 1. Our method DiTCtrl takes multiple text prompts as input and demonstrates superior capability in generating longer videos with multiple events, long-range coherence and smooth transitions as output." + ], + "image_footnote": [], + "bbox": [ + 93, + 417, + 248, + 498 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ae654abacba3f0c532773db7bdd1fa9022f33099ad2feb338750395215331e49.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 254, + 417, + 410, + 498 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/04218186e0de6a64535885b085f65661805f1d3885a7a90f7c9d2d42a2825049.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 417, + 571, + 498 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4a780560bbb1057dfeea584da6709aca6c3e058bd793ad2d5509289509abf526.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 417, + 736, + 498 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/17bb71710c0f95cb3afc2d4202f603a86af44a391dc85dbeb78112c9decf63d8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 743, + 417, + 901, + 498 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(b) \"Frosty pine: close-up shot $\\rightarrow$ medium shot $\\rightarrow$ forest vista, cinematic\"", + "bbox": [ + 220, + 498, + 772, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 556, + 326, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sora-like video generation models have achieved remarkable progress with a Multi-Modal Diffusion Transformer (MM-DiT) architecture. However, the current video generation models predominantly focus on single-prompt, struggling to generate coherent scenes with multiple sequential prompts that better reflect real-world dynamic scenarios. While some pioneering works have explored multi-prompt video generation, they face significant challenges including strict training data requirements, weak prompt following, and unnatural transitions. To address these problems, we propose DiTCtrl, a training-free multi-prompt video generation method under MM-DiT architectures for the first time. Our key idea is to take the multi-prompt video generation task as temporal video editing with smooth transitions. To achieve this goal, we first analyze MM-DiT's attention mechanism, finding that the 3D full attention behaves similarly to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic", + "bbox": [ + 88, + 589, + 485, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "control across different prompts with attention sharing for multi-prompt video generation. Based on our careful design, the video generated by DiTCtrl achieves smooth transitions and consistent object motion given multiple sequential prompts without additional training. Besides, we also present MPVBench, a new benchmark specially designed for multi-prompt video generation to evaluate the performance of multi-prompt generation. Extensive experiments demonstrate that our method achieves state-of-the-art performance without additional training. Code is available at https://github.com/TencentARC/DiTCtrl.", + "bbox": [ + 511, + 558, + 908, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 753, + 643, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-video (T2V) generation has made remarkable progress in the AIGC era [10, 44, 50], and breakthroughs such as Sora [30] have demonstrated impressive capabilities in generating longer videos through DiT [32] architecture and large-scale pertaining. However, feeding sequential prompts into current state-of-the-art text-to-video generation models (e.g., Kling [2], Gen3 [1], CogVideoX [48]) directly will produce isolated video sequences without natu", + "bbox": [ + 511, + 779, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Work done during an internship at Tencent ARC Lab.", + "bbox": [ + 89, + 873, + 383, + 886 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Corresponding Author", + "bbox": [ + 91, + 887, + 227, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7763", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ral transitions, as shown in Fig. 6 (First row). On the other hand, when multiple prompts are consolidated into a single-prompt describing long-term temporal changes, the generated results fail to capture semantic transitions effectively, as demonstrated in Fig. 6 (Second row). This limitation stems from their fundamental design and single-prompt training paradigm, making them inadequate for depicting real-world scenarios' dynamic, multi-event nature.", + "bbox": [ + 89, + 90, + 480, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although pioneering works [4, 29, 42] have begun exploring multi-prompt video generation, they face significant challenges. e.g., training such extended video generation models [29, 42] from scratch would require unprecedented computational resources and datasets that are practically unfeasible when the model size increases. Current zero-shot longer video generation methods [23, 36, 43] still mainly focus on the single prompt situation with longer length. Moreover, all previous works [4, 23, 29, 36, 42] are specifically designed under UNet architecture which restricts the abilities of more complex motions and increase the difficulties in multi-prompt generation. However, since Sora's [30] groundbreaking demonstration of two-minute video generation, highlighting the scalability potential of DiT architectures [32]. Subsequent explorations have led to influential developments, notably in image generation models (Stable Diffusion 3 [13], FLUX.1 [6]) and video generations (CogVideoX [48], Mochi1 [14]). They [6, 13, 14, 48] all adopt a specific kind of DiT architecture, i.e., MultiModal Diffusion Transformer (MM-DiT [13]) as the basic unit. This architecture effectively maps text and images (or video) into a unified sequence for attention computation, enabling deeper model scale abilities and achieving superior performances.", + "bbox": [ + 91, + 217, + 486, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Thus, to keep the abilities of the pre-trained single prompt T2V model and take advantage of the performance of the diffusion transformer, we propose DiTCtrl, a training-free multi-prompt video generation method under the pre-trained MM-DiT video generation model. Our key observation is that the multi-prompt video generation can be considered a two-step problem: 1) Video editing over time: The new video is generated through the previous video with a new prompt. 2) Video transition over time: Two generated videos need to keep a smooth transition between clips. Thus, to perform consistent video editing, inspired by the UNet-based image editing techniques [9, 19], we explore the characteristic of the attention modules in the MM-DiT block for the first time, finding that the 3D full attention has similar behaviors to that of the cross-/self-attention blocks in the UNet-like diffusion models [10, 44]. We thus apply a KV-sharing method between the video clips of different prompts to maintain the semantic consistency of the key objects [9] with the 3D attention control. Besides, we utilize a latent blending strategy for transitions between clips to connect the video clip seamlessly. Finally, to systematically evaluate our method and facilitate", + "bbox": [ + 89, + 583, + 486, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "future research in multi-prompt video generation, we also introduce MPVBench, a new benchmark with diverse transition types and specialized metrics for assessing multi-prompt transitions. Extensive experiments on this benchmark demonstrate that our method achieves state-of-the-art performance while maintaining computational efficiency.", + "bbox": [ + 511, + 90, + 908, + 183 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper can be summarized as:", + "bbox": [ + 532, + 188, + 890, + 204 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose DiTCtrl, the first tuning-free approach based on MM-DiT architecture for coherent multi-prompt video generation. Our method incorporates a novel KV-sharing mechanism and latent blending strategy, enabling seamless transitions between different prompts without additional training.", + "- We pioneer the analysis of MM-DiT's attention mechanism, finding that 3D full attention has similar behaviors to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic control across different prompts for enhanced generation consistency.", + "- We introduce MPVBench, a new benchmark specially designed for multi-prompt video generation, featuring diverse transition types and specialized metrics for multi-prompt video evaluation.", + "- Extensive experiments demonstrate that our method achieves state-of-the-art performance on multi-prompt video generation while maintaining computational efficiency." + ], + "bbox": [ + 513, + 217, + 905, + 518 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 551, + 656, + 568 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video Diffusion Model. Diffusion models have achieved significant success in the field of text-to-image generation [28, 37-39], and these advancements have also propelled progress in video generation from text or images [3, 7, 8, 10, 11, 15, 16, 21, 40]. Among these methods, animateDiff [16] attempts to turn existing text-to-image diffusion models with a motion module. Other models such as Imagen Video [21] and Make-a-Video [40] train a cascade model of spatial and temporal layers directly in pixel space. To improve efficiency, many other works [3, 7, 8, 10, 11, 15] generate the videos in latent space, leveraging an auto-encoder to compress the video into a compact latent. Notably, most of these text-to-video models utilize a U-Net architecture. Subsequently, the introduction of Sora [30] demonstrates the scalability and advantages of diffusion transformer architecture [32]. Recent works such as CogVideoX [48], Mochi1 [14], and Movie Gen [33] have adopted the DiT architecture and achieved impressive results. In this work, we build upon the open-source model CogVideoX [48], a DiT-based architecture, to explore attention control mechanisms for multi-prompt long video generation.", + "bbox": [ + 511, + 583, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7764", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Long Video Generation. Training diffusion models on long videos often requires significant computational resources. Consequently, current video diffusion models are typically trained on videos with a limited number of frames. As a result, the quality of generated videos often degrades significantly during inference when generating longer videos. To address this problem, some works [17, 18, 42, 46] employ an autoregressive mechanism for long video generation. However, due to error accumulation, these methods often suffer from quality degradation after a few iterations. Alternatively, tuning-free methods [4, 23, 36, 41, 43] have been developed to extend off-the-shelf short-video diffusion models for generating long videos without additional training. For instance, Gen-L-Video [43] processes long videos as short video clips with temporal overlapping during the denoising process. FreeNoise [36] explores the influence of initial noises and conducts temporal attention fusion based on the sliding window for temporal consistency. MultiDiffusion [5] and Mimicmotion [49] introduces the latents blending strategy to achieve smooth transitions. Inspired by these works, we propose a novel KV-sharing mechanism and latent blending strategy for seamless transitions between different segments without additional training.", + "bbox": [ + 89, + 90, + 483, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image/Video Editing with Attention Control. Attention control is gaining popularity due to its ability to perform zero-shot image or video editing without the need for additional data. In the realm of image editing, MasaCtrl [9] enhances the existing self-attention mechanism in diffusion models by introducing mutual self-attention. This allows for querying correlated content and textures from source images, ensuring consistent and coherent edits. Prompt-to-Prompt [19] utilizes cross-attention layers to control the relation between text prompts and images, which has also been adopted in many image editing works [12, 31, 47]. When it comes to video editing [24, 25, 35], temporal consistency needs to be considered during attention control. Video-P2P [25] extend the cross-attention control from Prompt-to-Prompt to video editing. FateZero [35] fuses self-attention with a blending mask obtained by cross-attention features from the source prompt. However, all these works are designed for video-to-video translation editing with structure preservation. Differently, we aim for appearance-consistent video editing over time. Besides, none of these works explore attention control in diffusion transformers. In this paper, we are the first to analyze how the full attention in diffusion transformers could be utilized for video editing over time in multi-prompt video generation.", + "bbox": [ + 89, + 455, + 483, + 818 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 829, + 181, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We tackle the challenge of zero-shot, multi-prompt longer video generation without the need for model training or optimization. This allows us to generate high-quality videos with", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/54b0bfbd0dc4a67cf8c77184f4712b43d52a532396a7d36afb59b50e6de95a40.jpg", + "image_caption": [ + "Figure 2. MM-DiT Attention Analysis. We find the attention matrix in MM-DiT attention can be divided into four different regions. As for the prompt of \"a cat watch a black mouse\", each text token shows a high-light response using the average of the text-to-video and video-to-text attention." + ], + "image_footnote": [], + "bbox": [ + 516, + 89, + 903, + 328 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "smooth and precise inter-prompt transitions, covering various transition types (e.g., style, camera movement, and location changes). Formally, given a pre-trained single prompt text-to-video diffusion model $\\mathcal{F}$ and a sequence of $n$ prompts $\\{P_1,P_2,\\dots,P_n\\}$ , the proposed DiTCtrl can generate a coherent longer video $\\nu_{\\{1,\\dots,n\\}}$ that faithfully follows these prompts over time, which can be formulated as:", + "bbox": [ + 511, + 428, + 908, + 532 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {\\{1, \\dots , n \\}} = \\operatorname {D i T C h r l} \\left\\{\\mathcal {F} \\left(P _ {1}\\right), \\dots , \\mathcal {F} \\left(P _ {n}\\right) \\right\\}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 547, + 906, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Below, we first give a careful analysis of MM-DiT's attention mechanisms (Sec. 3.1). This analysis enables us to design a mask-guided full-attention KV-sharing mechanism for video editing over time (Sec. 3.2) in multi-prompt video generation. Finally, to ensure temporal coherence across different semantic segments, we further incorporate a latent blending strategy that enables smooth transitions in longer videos with multiple prompts (Sec. 3.3).", + "bbox": [ + 511, + 578, + 908, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. MM-DiT Attention Mechanism Analysis", + "text_level": 1, + "bbox": [ + 511, + 710, + 859, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The MM-DiT is the fundamental architecture of the current SOTA method of Text-to-image/Video models [6, 13, 14, 48], which is fundamentally distinct from prior UNet architectures since it maps text and videos into a unified sequence for attention computation. Although it has been widely utilized, the properties of its inner attention mechanism remain insufficiently explored, which restricts its applications in our multi-prompt longer video generation task. Therefore, for the first time, we conducted a comprehensive analysis of the regional attention patterns in the 3D full attention map based on the open-source video model, i.e. CogVideoX [48].", + "bbox": [ + 511, + 734, + 908, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7765", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, due to the concatenation of the vision and text prompt, each attention matrix can be decomposed into four distinct regions, corresponding to different attention operations: video-to-video attention, text-to-text attention, text-to-video attention, and video-to-text attention. Below, we give the details of each region-inspired previous UNet-like structure with individual attentions [19].", + "bbox": [ + 89, + 90, + 485, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Text-to-Video and Video-to-Text Attention. Previous UNet-like architectures incorporate cross-attention for video-text alignment. In MM-DiT, the text-to-video and video-to-text attention play a similar role. To validate its efficiency, we conduct a detailed analysis of the attention patterns, as illustrated in Fig. 2. Specifically, we compute the averaged attention values across all layers and attention heads, then extract attention values by selecting specific columns or rows corresponding to token indices in both text-to-video and video-to-text regions. These attention values are subsequently reshaped into an $F \\times H \\times W$ format, allowing us to visualize the semantic activation maps for individual frames. As demonstrated in Fig. 2, these visualizations show remarkable precision in token-level semantic localization, effectively capturing fine-grained relationships between textual descriptions and visual elements. This discovered capability for precise semantic control and localization provides a strong foundation for adapting established image/video editing techniques to enhance the consistency and quality of multi-prompt video generation.", + "bbox": [ + 91, + 220, + 485, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Text-to-Text and Video-to-Video Attention. Text-to-text and video-to-video regional attention are somehow new from the respective UNet structure. As illustrated in Fig. 3, our analysis reveals similar patterns in both components. In the text-to-text attention component (Fig. 3(a)(b), where (a) represents the attention pattern for shorter prompts and (b) illustrates the pattern for longer prompts), we observe a prominent diagonal pattern, indicating that each text token primarily attends to its neighboring tokens. Notably, there are distinct vertical lines that shift backward as the text sequence length increases, suggesting that all tokens maintain significant attention to the special tokens at the end of the text sequence. For the video-to-video attention component, since MMDiT flat the spatial and temporal token for 3D attention calculation, our analysis at the single-frame level reveals a distinctive diagonal pattern in spatial attention (Fig. 3(c)). More significantly, when examining attention maps constructed from tokens at identical spatial positions across different frames, we also observe a pronounced diagonal pattern (Fig. 3(d)). This characteristic mirrors those found in recent UNet-based video models of the spatial-attention and temporal attention, such as VideoCrafter [26] and Lavie [45], aligning with the findings reported in [27]. Since previous works only train the specific part of the diffusion model for more advanced control and generation, our", + "bbox": [ + 91, + 523, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3c91eef475f2f256590d336575d85a1a731d7d3d09a6f935da8844902677907f.jpg", + "image_caption": [ + "(a) Text-text attn (short)" + ], + "image_footnote": [], + "bbox": [ + 517, + 87, + 689, + 218 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6123dcb80cb2c8ad31a152ce6832e7e7140b64ceb1890bb365d9b8d81e5640aa.jpg", + "image_caption": [ + "(b) Text-text attn (long)" + ], + "image_footnote": [], + "bbox": [ + 696, + 88, + 901, + 217 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9031609d1eb9a26a492629d326d68d1b42c96801be0d4aa66a34ddc33d7a3772.jpg", + "image_caption": [ + "(c) Video-video spatial atm", + "Figure 3. MM-DiT Text-to-Text and Video-to-Video Attention Visualization. We find that the current MM-DiT has a stronger potential to construct the individual attention in the previous UNet-like structure [10, 11, 44]." + ], + "image_footnote": [], + "bbox": [ + 516, + 238, + 689, + 367 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5cfa187cfbe8e3dcf5b461d2a593273cb83e6aefa671983292f4efc82c6de775.jpg", + "image_caption": [ + "(d) Video-video temporal attn" + ], + "image_footnote": [], + "bbox": [ + 699, + 238, + 901, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "finding provides strong evidence for these methods from MM-DiT perspectives.", + "bbox": [ + 511, + 479, + 903, + 510 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall, the presence of these consistent diagonal patterns in the MM-DiT architecture demonstrates robust frame-to-frame correlations, which proves essential for maintaining spatial-temporal coherence and preserving motion fidelity throughout the video sequence.", + "bbox": [ + 511, + 513, + 906, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Consistent Video Generation Over Time", + "text_level": 1, + "bbox": [ + 511, + 603, + 857, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the previous analysis, we propose the masked-guided KV-sharing strategy for consistent video generation over time for our multi-prompt video generation task. As shown in Fig. 4, to generate the consistent video between prompt $P_{i-1}$ and prompt $P_i$ , we utilize the intermediate attentions from the $i-1$ -th and $i$ -th prompt in MM-DiT to generate the attention masks of the specified foreground object (\"knight\" in Fig. 4). This is achieved by averaging the Text-Video/Video-Text parts of the 3D full attention across all heads and layers with the given object tokens, then thresholded to obtain binary masks $M$ . Inspired by MasaCtrl [9], we leverage the masks to conduct mask-guided attention fusion based on the key and values from the prompt $P_{i-1}$ to generate the new attention features of the prompt $P_i$ .", + "bbox": [ + 511, + 627, + 908, + 851 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We denote $M_{i-1}$ and $M_i$ as masks extracted for the foreground objects in videos $\\mathcal{V}_{i-1}$ and $\\mathcal{V}_i$ , respectively. With these masks, we can restrict the object in $\\mathcal{V}_i$ to query con", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7766", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/796902e7231a12f01d3557494a96f641431b0f6660b865cb7d65b15a1d61483b.jpg", + "image_caption": [ + "Figure 4. Pipeline of the proposed DiTCtrl. Note that initial latents are assumed to be 5 frames here. The first three frames are used to generate the contents of $P_{i-1}$ , and the last three frames are used to generate contents of $P_i$ . The pink latent represents the overlapping frame, while the blue and green latents are used to distinguish different prompt segments. Our method tries to synthesize content-consistent videos based on multi-prompts. The first video is synthesized with source text prompt $P_{i-1}$ . During the denoising process for video synthesis, we convert the full-attention into masked-guided KV-sharing strategy to query video contents from source video $\\mathcal{V}_{i-1}$ , so that we can synthesize content-consistent video under the modified target prompt $P_i$ ." + ], + "image_footnote": [], + "bbox": [ + 133, + 88, + 867, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tents information only from the object region in $\\mathcal{V}_{i - 1}$", + "bbox": [ + 89, + 434, + 447, + 450 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {o} ^ {l} = \\text {A t t e n t i o n} \\left(Q _ {i} ^ {l}, K _ {i - 1} ^ {l}, V _ {i - 1} ^ {l}; M _ {i - 1}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 460, + 483, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {b} ^ {l} = \\text {A t t e n t i o n} \\left(Q _ {i} ^ {l}, K _ {i - 1} ^ {l}, V _ {i - 1} ^ {l}; 1 - M _ {i - 1}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 483, + 483, + 501 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {f} ^ {l} = f _ {o} ^ {l} * M _ {i} + f _ {b} ^ {l} * (1 - M _ {i}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 503, + 483, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{f}^l$ is the final attention output. The object regions and the background regions in the current video query the content information from corresponding restricted areas rather than all the last video features.", + "bbox": [ + 89, + 535, + 483, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Latent Blending Strategy for Transition", + "text_level": 1, + "bbox": [ + 89, + 607, + 431, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While our previous methods enable semantic consistency between adjacent video segments, achieving smooth transitions between different semantic segments still needs to be carefully designed. Thus, we propose a latent blending strategy to ensure temporal coherence across different semantic segments, inspired by recent works [5, 36, 49].", + "bbox": [ + 89, + 630, + 483, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated in Fig. 5, our approach introduces overlapped regions between adjacent semantic video segments. For each frame position in the overlapped region, we apply a position-dependent weight function that follows a symmetric distribution, in which frames closer to their respective segments receive higher weights while those at the boundaries receive lower weights. This weighting scheme ensures smooth transitions between different semantic contexts.", + "bbox": [ + 89, + 720, + 483, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The blended latent feature $\\mathbf{z}_t$ for frame $t$ is calculated as:", + "bbox": [ + 109, + 843, + 478, + 857 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {t} = \\frac {\\sum_ {i = 1} ^ {n} w \\left(t _ {i}\\right) \\cdot \\mathbf {z} _ {t _ {i}}}{\\sum_ {i = 1} ^ {n} w \\left(t _ {i}\\right)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 869, + 483, + 905 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c194410755933bea6aeff1591361f0de70d065b07164e912dbc75430f0043e6e.jpg", + "image_caption": [ + "Figure 5. Latent blending strategy for video transition between video clips." + ], + "image_footnote": [], + "bbox": [ + 517, + 431, + 901, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw \\left(t _ {i}\\right) = \\min \\left(\\frac {2 \\left(t _ {i} + 0 . 5\\right)}{T}, 2 - \\frac {2 \\left(t _ {i} + 0 . 5\\right)}{T}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 580, + 906, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_{t_i}$ is latent feature corresponding to $t$ -th frame in $i$ -th latent segment, $n$ is number of overlapped segments, $T$ denotes the frames number of one latent segment and $w(t_{i})$ is a position-dependent weight function.", + "bbox": [ + 511, + 619, + 906, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To conclude, our approach employs the latent blending strategy and kv-sharing mechanism simultaneously during each denoising step. We process segment pairs sequentially, feeding them as one batch into the MM-DiT block for mask-guided kv-sharing (Fig. 4), then blend their denoised latents progressively (Fig. 5).", + "bbox": [ + 511, + 680, + 908, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 784, + 645, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Setup. We implement DiTCtrl based on CogVideoX-2B [48], which is an open-source text-to-video diffusion model based on MM-DiT. In our experimental setup, we generate multiprompt conditioned videos, where each video clip is composed of 49 frames with a resolution of $480 \\times 720$ . The sample step is configured to 50. The kv-sharing steps are set", + "bbox": [ + 511, + 809, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7767", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f92efa0a08f0c2c9f543c0857fb455bf123b6ece8235e438f1d9c79e2118d6ad.jpg", + "image_caption": [ + "Figure 6. Comparison of generation results across methods. Freenoise+DiT is our implementation of Freenoise on CogVideoX." + ], + "image_footnote": [], + "bbox": [ + 130, + 88, + 859, + 400 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "as [2,25], and the kv-sharing layers are specified as [25,30]. For latent sampling, the number of frames is set to 13, and the overlap size is set to 6 in our experiments. All these experiments are conducted on a single NVIDIA A100 GPU. Baselines. We mainly compare the proposed tuning-free method to current state-of-the-art multi-prompt video generation methods [36, 41, 43] and leading commercial solutions Kling [2]. Gen-L-Video, FreeNoise, and VideoInfinity are built upon the VideoCrafter2 [11] framework. To ensure a fair comparison of base models, we implement FreeNoise [36] as an enhanced baseline by directly incorporating their noise rescheduling strategy into the CogVideoX framework.", + "bbox": [ + 89, + 431, + 485, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. MPVBench", + "text_level": 1, + "bbox": [ + 89, + 637, + 217, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MPVBench contains a diverse prompt dataset and a new metric customized for multi-prompt generation. Specifically, leveraging GPT-4, we produce 130 long-form prompts of 10 different transition modes. Then, for multi-prompt video generation, we observe that the distribution of the CLIP features differs between single-prompt and multi-prompt scenarios. As shown in Fig. 7, the feature points of real video (from DAVIS [34]) follow a continuous curve, while those of two concatenated isolated videos follow two continuous curves with a breakpoint in the middle. Since the common CLIP similarity calculates the average of neighborhood similarities, the difference between real video and isolated video only occurs at the breakpoint, which becomes very small when divided by the number of frames. To address this limitation, we propose CSCV (Clip Similarity Coefficient of Variation), a metric specifically designed to evaluate the", + "bbox": [ + 89, + 659, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/89d31997b80dbd44171f783ccc097540532c484391077051188dc8bd7ac4e8a9.jpg", + "image_caption": [ + "Figure 7. t-SNE visualization of CLIP embeddings. Each point represents the CLIP embedding of a single video frame after dimensionality reduction. The visualization demonstrates that conventional multi-prompt videos form distinct clusters, while our method produces a more continuous distribution, indicating smoother semantic transitions. More details and discussions will be given in the supplementary." + ], + "image_footnote": [], + "bbox": [ + 516, + 431, + 905, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "transition smoothness of multi-prompt videos, defined as:", + "bbox": [ + 511, + 715, + 893, + 729 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} = \\mathbf {x} _ {i} ^ {\\top} \\mathbf {x} _ {i + 1}, \\quad i = 1, \\dots , n - 1 \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 743, + 906, + 762 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {s c o r e} = \\frac {1}{1 + \\lambda \\cdot \\frac {\\sigma (s)}{\\mu (s)}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 779, + 906, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_i$ denotes frame features, $\\sigma$ and $\\mu$ are standard deviation and average respectively. The Coefficient of Variation $CV = \\sigma(s) / \\mu(s)$ describes the degree of uniformity, which can largely punish the isolated situation. The function $\\frac{1}{1 + \\lambda(\\cdot)}$ projects the score to $[0, 1]$ , the larger the better. We also re", + "bbox": [ + 511, + 821, + 908, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7768", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9bef15b71ff223a9b93f8252c8d8bc69238964a102f6df39f1daf1256a134ae9.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Evaluation metrics. Comparison of performance metrics for various video generation methods as benchmarked by MPVBench. Bold values represent the best performance within each group." + ], + "table_body": "
    MethodCSCVMotion smoothnessText-Image similarity
    Gen-L-Video67.28%97.66%30.60%
    FreeNoise84.37%97.22%32.69%
    FreeNoise+DiT78.74%97.76%30.90%
    Video-Infinity74.97%97.31%32.35%
    DiTCtrl(w/o kv-sharing)81.79%97.35%31.37%
    DiTCtrl(Ours)84.90%97.80%30.68%
    ", + "bbox": [ + 91, + 88, + 483, + 209 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "port the Text-Image similarity by using CLIP Similarity [20] to assess the alignment between given prompts and output video clips, and Motion smoothness from VBench [22] to evaluate whether the motion in the generated video is smooth, and follows the physical law of the real world.", + "bbox": [ + 88, + 292, + 482, + 369 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Qualitative Results", + "text_level": 1, + "bbox": [ + 89, + 378, + 272, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The qualitative comparison with previous multi-prompt video generation methods is shown in Fig. 6. Notably, when multiple prompts are consolidated into a single-prompt describing long-term temporal changes, the generated result by Kling [2] fails to capture semantic transitions effectively, where the sun remains present while no clouds appear, which does not align with the text. Gen-L-Video [43] suffers from severe temporal jittering, compromising overall video quality. Video-Infinity [41] and FreeNoise [36] both demonstrate successful scene-level semantic changes but lack physically plausible motion. For instance, in Fig. 6, vehicles appear to be in motion while remaining spatially fixed, which is a limitation inherent to their UNet base-model abilities. In contrast, FreeNoise+DiT leverages the DiT architecture's abilities to achieve more realistic object motion but struggles with semantic transitions, resulting in noticeable discontinuities between segments. Our DiTCtrl preserves the inherent capabilities of the pre-trained DiT model while addressing these limitations, enabling smooth semantic transitions and maintaining motion coherence throughout the video sequence. For a more comprehensive evaluation, we provide additional comparisons with extensive qualitative examples in the supplementary.", + "bbox": [ + 91, + 400, + 483, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.Quantitative Results", + "text_level": 1, + "bbox": [ + 89, + 757, + 284, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct the automatic evaluation with our MPVBench. From Table 1 one can see that our method achieves the highest CSCV score, demonstrating superior transition handling and overall stability in generation patterns. While FreeNoise ranks second with relatively strong stability, other methods significantly lag behind in this aspect, which is consistent with the t-SNE visualization of CLIP embedding as shown in Fig. 7. In terms of motion smoothness, our approach", + "bbox": [ + 88, + 779, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f300ae9b33e298464df08c497df1305fe394b64e7c6a817648b3a30c776a1115.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. User study. Human evaluation of different video generation methods across multiple aspects. Scores range from 1 to 5, with higher scores indicating better performance. Bold values represent the best performance within each metric." + ], + "table_body": "
    MethodOverall preferenceMotion PatternTemporal ConsistencyText Alignment
    Gen-L-Video1.151.141.081.25
    FreeNoise3.022.902.993.08
    FreeNoise+DiT3.813.933.753.78
    Video-Infinity2.902.852.912.98
    DiTCtrl(Ours)4.114.174.263.91
    ", + "bbox": [ + 514, + 89, + 901, + 195 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "exhibits superior performance in motion quality and consistency. Regarding Text-Image Similarity metrics, although FreeNoise and Video-Infinity achieve higher scores, this can be attributed to our method's kv-sharing mechanism, where subsequent video segments inherently learn from preceding semantic content.", + "bbox": [ + 511, + 277, + 906, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Fig. 6, our design choice allows the road surface to gradually transition to snowy conditions while retaining features from the previous scene. Despite potentially lower text-image alignment scores, it ensures superior semantic continuity in the sequences. In practice, this trade-off doesn't negatively impact the visual quality in multi-prompt scenarios, as demonstrated by our user study in Table 2.", + "bbox": [ + 511, + 369, + 908, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Human Evaluation", + "text_level": 1, + "bbox": [ + 511, + 484, + 694, + 498 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We invited 28 users to evaluate five models: GenL-Video [43], Video-Infinity [41], FreeNoise [36], FreeNoise+DiT and our method. We employ a Forced Ranking Scale, where items are ranked from 1 to 5, with the highest rank receiving a score of 5 and the lowest rank receiving a score of 1. Participants score each method considering overall preference, motion pattern, temporal consistency and text alignment over 16 videos generated by different scenarios. As clearly indicated in Table 2, generated videos from our method significantly outperform other state-of-the-art approaches in all four criteria, demonstrating superior capability in producing videos with natural semantic transitions that better align with human preferences for visual coherence and continuity.", + "bbox": [ + 511, + 506, + 908, + 719 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. More Applications", + "text_level": 1, + "bbox": [ + 511, + 727, + 692, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Single-prompt Longer Video Generation. Our method can naturally work on single-prompt longer video generation. As illustrated in Fig. 8, using the prompt \"A white SUV drives on a steep dirt road\", our approach successfully generates videos that are more than 12 times longer than the original length, while maintaining consistent motion patterns and environmental coherence.", + "bbox": [ + 511, + 750, + 906, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Video Editing. We show how we use our methods to achieve video editing performance (\"word swap\" and \"reweight\") in Fig. 9.", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7769", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/81a3fe89a97e2cdbe66f920f0bff4c0ca52b3c53a799846742bbc7efe7b3353a.jpg", + "image_caption": [ + "Figure 8. Single prompt longer video generation example." + ], + "image_footnote": [], + "bbox": [ + 93, + 87, + 169, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/42cfac057008656e04fea8b395256eef5c6efc0ddfb346b041b4752e1145cb5f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 171, + 88, + 246, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/915b897244663dba44f6057c6408138a2158877002fe703cbb2537b53d58d8ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 250, + 88, + 325, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bec49ae1beaf3e7e3cc1f5af51813f1eab7d514119ae7c92157720769fa5cfa7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 326, + 88, + 401, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4a166e35c420a552eb08113a20c12749d4d543b1b6d46106e428a0ce317d6d23.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 403, + 88, + 480, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/62af6fbb09bb241195a8a708eeede4b3c54516d00c58e19f3a9b1b32030cb5cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 189, + 480, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2d79ea0c30453d279e940732894611efa0bb4ff2a34f584c40c60ea5c577f78a.jpg", + "image_caption": [ + "(a) Word swap" + ], + "image_footnote": [], + "bbox": [ + 94, + 239, + 480, + 289 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/65dc7528e00907a8cfc0d16e43cff28d5589d421c4070487757030dc2c4a2b38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 297, + 480, + 348 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a522caf5224a56e5ce8afa0764dfe69d83dc5f43d7c4c2a4eb4d226e48b4f32.jpg", + "image_caption": [ + "(b) Video reweight", + "Figure 9. Video editing example." + ], + "image_footnote": [], + "bbox": [ + 94, + 348, + 480, + 398 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Word Swap: removing our latent blending strategy of our approach DiTCtrl, we can achieve the video editing performance of Word Swap. Specifically, we just use masked-guided KV-sharing strategy to share keys and values from source prompt $P_{source}$ branch, so that we can synthesize a new video to preserve the original composition while also addressing the content of the new prompt $P_{target}$ .", + "- Reweight: Similar to prompt-to-prompt [19], through reweighting the specific columns and rows corresponding to specified token (e.g. \"pink\") in the MM-DiT's Text-Video attention and Video-Text attention, we can also achieve the video editing performance of reweight." + ], + "bbox": [ + 89, + 441, + 482, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 635, + 243, + 651 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conducted ablation studies to validate the effectiveness of DiTCtrl's key components: latent blending strategy, KV-sharing mechanism, and mask-guided generation as shown in Fig. 10. The first row shows results that directly using text-to-video models results in abrupt scene changes and disconnected motion patterns, failing to maintain continuity in the athlete's movements from surfing to skiing. The second row demonstrates that DiTCtrl without the latent blending strategy achieves basic video editing capabilities but lacks smooth transitions between scenes. Without KV-sharing (third row), DiTCtrl exhibits unstable environmental transitions and significant motion artifacts, with inconsistent character scaling and deformed movements. Moreover, DiTCtrl without mask guidance (fourth row) improves motion coherence and transitions but struggles with object attribute confusion across different prompts and environments.", + "bbox": [ + 88, + 657, + 485, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/597c2d48425f4096644bc7849d3f9b79ef7631bdd4ec7fcf7a8538a8e8022268.jpg", + "image_caption": [ + "Figure 10. Visualization of ablation component in DiTCtrl." + ], + "image_footnote": [], + "bbox": [ + 516, + 88, + 903, + 295 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On the other hand, The full DiTCtrl implementation provides the most precise control over generated content, demonstrating superior object consistency and smoother transitions between prompts while maintaining desired motion patterns. These results validate our analysis of MM-DiT's attention mechanism and its role in enabling accurate semantic control.", + "bbox": [ + 511, + 337, + 906, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 455, + 633, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce DiTCtrl, a novel, tuning-free method for multi-prompt video generation using the MM-DiT architecture. Our pioneering analysis of MM-DiT's attention mechanism reveals similarities with the cross/self-attention blocks in UNet-like diffusion models, enabling mask-guided semantic control across prompts. With mask-guided kv-sharing mechanism and latent blending strategy, DiTCtrl ensures smooth transitions and consistent object motion between semantic segments, without extra training. We also present MPVBench, a new benchmark with diverse transition types and specialized metrics for assessing multi-prompt transitions.", + "bbox": [ + 511, + 482, + 908, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation & Future Work. While our method demonstrates state-of-the-art performance, there remain two primary limitations. First, compared to image generation models, current open-source video generation models exhibit relatively weaker conceptual composition capabilities, occasionally resulting in attribute binding errors across different semantic segments. Second, the computational overhead of DiT-based architectures presents challenges for inference speed. These limitations suggest promising directions for future research in enhancing semantic understanding and architectural efficiency.", + "bbox": [ + 511, + 662, + 908, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (Grant No. 62306261), and The Shun Hing Institute of Advanced Engineering (SHIAE) Grant (No. 8115074).", + "bbox": [ + 511, + 829, + 906, + 890 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7770", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Gen-3. https://runwayml.com/research/introducing-gen-3-alpha,,2024.1", + "[2] Kling. https://kling.kuaishou.com/en, 2024.1, 6.7", + "[3] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Magicvideo: Efficient video generation with latent diffusion models. arXiv preprint arXiv:2211.11018, 2022. 1" + ], + "bbox": [ + 516, + 92, + 906, + 729 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7772", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_model.json b/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c0e718fbb38b7cd8c7a25dccb4b914acee78d8fc --- /dev/null +++ b/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_model.json @@ -0,0 +1,2398 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.111, + 0.13, + 0.888, + 0.177 + ], + "angle": 0, + "content": "DiTCtrl: Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.211, + 0.251, + 0.231 + ], + "angle": 0, + "content": "Minghong Cai\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.29, + 0.212, + 0.417, + 0.231 + ], + "angle": 0, + "content": "Xiaodong Cun" + }, + { + "type": "text", + "bbox": [ + 0.292, + 0.233, + 0.398, + 0.251 + ], + "angle": 0, + "content": "Yong Zhang" + }, + { + "type": "text", + "bbox": [ + 0.456, + 0.212, + 0.565, + 0.23 + ], + "angle": 0, + "content": "Xiaoyu Li\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.439, + 0.233, + 0.532, + 0.251 + ], + "angle": 0, + "content": "Ying Shan3" + }, + { + "type": "text", + "bbox": [ + 0.598, + 0.212, + 0.693, + 0.23 + ], + "angle": 0, + "content": "Wenze Liu" + }, + { + "type": "text", + "bbox": [ + 0.573, + 0.233, + 0.713, + 0.251 + ], + "angle": 0, + "content": "Xiangyu Yue\\(^{1,5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.734, + 0.212, + 0.879, + 0.231 + ], + "angle": 0, + "content": "Zhaoyang Zhang3" + }, + { + "type": "text", + "bbox": [ + 0.269, + 0.257, + 0.416, + 0.274 + ], + "angle": 0, + "content": "1 MMLab, CUHK" + }, + { + "type": "text", + "bbox": [ + 0.215, + 0.278, + 0.42, + 0.295 + ], + "angle": 0, + "content": "\\(^{3}\\)ARC Lab, Tencent PCG" + }, + { + "type": "text", + "bbox": [ + 0.455, + 0.257, + 0.724, + 0.276 + ], + "angle": 0, + "content": "\\(^{2}\\) GVC Lab, Great Bay University" + }, + { + "type": "text", + "bbox": [ + 0.461, + 0.279, + 0.6, + 0.295 + ], + "angle": 0, + "content": "4 Tencent AI Lab" + }, + { + "type": "text", + "bbox": [ + 0.64, + 0.279, + 0.778, + 0.295 + ], + "angle": 0, + "content": "5 SHIAE, CUHK" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.316, + 0.249, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.255, + 0.316, + 0.411, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.316, + 0.573, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.316, + 0.737, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.745, + 0.316, + 0.902, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.225, + 0.398, + 0.769, + 0.414 + ], + "angle": 0, + "content": "(a) \"Athlete glides across ocean waters \\(\\rightarrow\\) snow mountain \\(\\rightarrow\\) sand dunes\"" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.418, + 0.249, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.255, + 0.418, + 0.411, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.418, + 0.573, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.418, + 0.737, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.745, + 0.418, + 0.902, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.499, + 0.773, + 0.515 + ], + "angle": 0, + "content": "(b) \"Frosty pine: close-up shot \\(\\rightarrow\\) medium shot \\(\\rightarrow\\) forest vista, cinematic\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.517, + 0.907, + 0.545 + ], + "angle": 0, + "content": "Figure 1. Our method DiTCtrl takes multiple text prompts as input and demonstrates superior capability in generating longer videos with multiple events, long-range coherence and smooth transitions as output." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.558, + 0.327, + 0.573 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.59, + 0.486, + 0.864 + ], + "angle": 0, + "content": "Sora-like video generation models have achieved remarkable progress with a Multi-Modal Diffusion Transformer (MM-DiT) architecture. However, the current video generation models predominantly focus on single-prompt, struggling to generate coherent scenes with multiple sequential prompts that better reflect real-world dynamic scenarios. While some pioneering works have explored multi-prompt video generation, they face significant challenges including strict training data requirements, weak prompt following, and unnatural transitions. To address these problems, we propose DiTCtrl, a training-free multi-prompt video generation method under MM-DiT architectures for the first time. Our key idea is to take the multi-prompt video generation task as temporal video editing with smooth transitions. To achieve this goal, we first analyze MM-DiT's attention mechanism, finding that the 3D full attention behaves similarly to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.559, + 0.909, + 0.726 + ], + "angle": 0, + "content": "control across different prompts with attention sharing for multi-prompt video generation. Based on our careful design, the video generated by DiTCtrl achieves smooth transitions and consistent object motion given multiple sequential prompts without additional training. Besides, we also present MPVBench, a new benchmark specially designed for multi-prompt video generation to evaluate the performance of multi-prompt generation. Extensive experiments demonstrate that our method achieves state-of-the-art performance without additional training. Code is available at https://github.com/TencentARC/DiTCtrl." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.754, + 0.645, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Text-to-video (T2V) generation has made remarkable progress in the AIGC era [10, 44, 50], and breakthroughs such as Sora [30] have demonstrated impressive capabilities in generating longer videos through DiT [32] architecture and large-scale pertaining. However, feeding sequential prompts into current state-of-the-art text-to-video generation models (e.g., Kling [2], Gen3 [1], CogVideoX [48]) directly will produce isolated video sequences without natu" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.874, + 0.385, + 0.887 + ], + "angle": 0, + "content": "† Work done during an internship at Tencent ARC Lab." + }, + { + "type": "page_footnote", + "bbox": [ + 0.093, + 0.888, + 0.228, + 0.9 + ], + "angle": 0, + "content": "Corresponding Author" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.874, + 0.385, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7763" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.212 + ], + "angle": 0, + "content": "ral transitions, as shown in Fig. 6 (First row). On the other hand, when multiple prompts are consolidated into a single-prompt describing long-term temporal changes, the generated results fail to capture semantic transitions effectively, as demonstrated in Fig. 6 (Second row). This limitation stems from their fundamental design and single-prompt training paradigm, making them inadequate for depicting real-world scenarios' dynamic, multi-event nature." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.218, + 0.487, + 0.581 + ], + "angle": 0, + "content": "Although pioneering works [4, 29, 42] have begun exploring multi-prompt video generation, they face significant challenges. e.g., training such extended video generation models [29, 42] from scratch would require unprecedented computational resources and datasets that are practically unfeasible when the model size increases. Current zero-shot longer video generation methods [23, 36, 43] still mainly focus on the single prompt situation with longer length. Moreover, all previous works [4, 23, 29, 36, 42] are specifically designed under UNet architecture which restricts the abilities of more complex motions and increase the difficulties in multi-prompt generation. However, since Sora's [30] groundbreaking demonstration of two-minute video generation, highlighting the scalability potential of DiT architectures [32]. Subsequent explorations have led to influential developments, notably in image generation models (Stable Diffusion 3 [13], FLUX.1 [6]) and video generations (CogVideoX [48], Mochi1 [14]). They [6, 13, 14, 48] all adopt a specific kind of DiT architecture, i.e., MultiModal Diffusion Transformer (MM-DiT [13]) as the basic unit. This architecture effectively maps text and images (or video) into a unified sequence for attention computation, enabling deeper model scale abilities and achieving superior performances." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.487, + 0.902 + ], + "angle": 0, + "content": "Thus, to keep the abilities of the pre-trained single prompt T2V model and take advantage of the performance of the diffusion transformer, we propose DiTCtrl, a training-free multi-prompt video generation method under the pre-trained MM-DiT video generation model. Our key observation is that the multi-prompt video generation can be considered a two-step problem: 1) Video editing over time: The new video is generated through the previous video with a new prompt. 2) Video transition over time: Two generated videos need to keep a smooth transition between clips. Thus, to perform consistent video editing, inspired by the UNet-based image editing techniques [9, 19], we explore the characteristic of the attention modules in the MM-DiT block for the first time, finding that the 3D full attention has similar behaviors to that of the cross-/self-attention blocks in the UNet-like diffusion models [10, 44]. We thus apply a KV-sharing method between the video clips of different prompts to maintain the semantic consistency of the key objects [9] with the 3D attention control. Besides, we utilize a latent blending strategy for transitions between clips to connect the video clip seamlessly. Finally, to systematically evaluate our method and facilitate" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.909, + 0.184 + ], + "angle": 0, + "content": "future research in multi-prompt video generation, we also introduce MPVBench, a new benchmark with diverse transition types and specialized metrics for assessing multi-prompt transitions. Extensive experiments on this benchmark demonstrate that our method achieves state-of-the-art performance while maintaining computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.189, + 0.892, + 0.205 + ], + "angle": 0, + "content": "The contributions of this paper can be summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.218, + 0.905, + 0.308 + ], + "angle": 0, + "content": "- We propose DiTCtrl, the first tuning-free approach based on MM-DiT architecture for coherent multi-prompt video generation. Our method incorporates a novel KV-sharing mechanism and latent blending strategy, enabling seamless transitions between different prompts without additional training." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.31, + 0.906, + 0.399 + ], + "angle": 0, + "content": "- We pioneer the analysis of MM-DiT's attention mechanism, finding that 3D full attention has similar behaviors to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic control across different prompts for enhanced generation consistency." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.4, + 0.906, + 0.459 + ], + "angle": 0, + "content": "- We introduce MPVBench, a new benchmark specially designed for multi-prompt video generation, featuring diverse transition types and specialized metrics for multi-prompt video evaluation." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.46, + 0.905, + 0.519 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that our method achieves state-of-the-art performance on multi-prompt video generation while maintaining computational efficiency." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.218, + 0.906, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.553, + 0.657, + 0.569 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.584, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Video Diffusion Model. Diffusion models have achieved significant success in the field of text-to-image generation [28, 37-39], and these advancements have also propelled progress in video generation from text or images [3, 7, 8, 10, 11, 15, 16, 21, 40]. Among these methods, animateDiff [16] attempts to turn existing text-to-image diffusion models with a motion module. Other models such as Imagen Video [21] and Make-a-Video [40] train a cascade model of spatial and temporal layers directly in pixel space. To improve efficiency, many other works [3, 7, 8, 10, 11, 15] generate the videos in latent space, leveraging an auto-encoder to compress the video into a compact latent. Notably, most of these text-to-video models utilize a U-Net architecture. Subsequently, the introduction of Sora [30] demonstrates the scalability and advantages of diffusion transformer architecture [32]. Recent works such as CogVideoX [48], Mochi1 [14], and Movie Gen [33] have adopted the DiT architecture and achieved impressive results. In this work, we build upon the open-source model CogVideoX [48], a DiT-based architecture, to explore attention control mechanisms for multi-prompt long video generation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7764" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.44 + ], + "angle": 0, + "content": "Long Video Generation. Training diffusion models on long videos often requires significant computational resources. Consequently, current video diffusion models are typically trained on videos with a limited number of frames. As a result, the quality of generated videos often degrades significantly during inference when generating longer videos. To address this problem, some works [17, 18, 42, 46] employ an autoregressive mechanism for long video generation. However, due to error accumulation, these methods often suffer from quality degradation after a few iterations. Alternatively, tuning-free methods [4, 23, 36, 41, 43] have been developed to extend off-the-shelf short-video diffusion models for generating long videos without additional training. For instance, Gen-L-Video [43] processes long videos as short video clips with temporal overlapping during the denoising process. FreeNoise [36] explores the influence of initial noises and conducts temporal attention fusion based on the sliding window for temporal consistency. MultiDiffusion [5] and Mimicmotion [49] introduces the latents blending strategy to achieve smooth transitions. Inspired by these works, we propose a novel KV-sharing mechanism and latent blending strategy for seamless transitions between different segments without additional training." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.457, + 0.484, + 0.819 + ], + "angle": 0, + "content": "Image/Video Editing with Attention Control. Attention control is gaining popularity due to its ability to perform zero-shot image or video editing without the need for additional data. In the realm of image editing, MasaCtrl [9] enhances the existing self-attention mechanism in diffusion models by introducing mutual self-attention. This allows for querying correlated content and textures from source images, ensuring consistent and coherent edits. Prompt-to-Prompt [19] utilizes cross-attention layers to control the relation between text prompts and images, which has also been adopted in many image editing works [12, 31, 47]. When it comes to video editing [24, 25, 35], temporal consistency needs to be considered during attention control. Video-P2P [25] extend the cross-attention control from Prompt-to-Prompt to video editing. FateZero [35] fuses self-attention with a blending mask obtained by cross-attention features from the source prompt. However, all these works are designed for video-to-video translation editing with structure preservation. Differently, we aim for appearance-consistent video editing over time. Besides, none of these works explore attention control in diffusion transformers. In this paper, we are the first to analyze how the full attention in diffusion transformers could be utilized for video editing over time in multi-prompt video generation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.83, + 0.182, + 0.845 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We tackle the challenge of zero-shot, multi-prompt longer video generation without the need for model training or optimization. This allows us to generate high-quality videos with" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.09, + 0.905, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.33, + 0.907, + 0.4 + ], + "angle": 0, + "content": "Figure 2. MM-DiT Attention Analysis. We find the attention matrix in MM-DiT attention can be divided into four different regions. As for the prompt of \"a cat watch a black mouse\", each text token shows a high-light response using the average of the text-to-video and video-to-text attention." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.429, + 0.909, + 0.534 + ], + "angle": 0, + "content": "smooth and precise inter-prompt transitions, covering various transition types (e.g., style, camera movement, and location changes). Formally, given a pre-trained single prompt text-to-video diffusion model \\(\\mathcal{F}\\) and a sequence of \\(n\\) prompts \\(\\{P_1,P_2,\\dots,P_n\\}\\), the proposed DiTCtrl can generate a coherent longer video \\(\\nu_{\\{1,\\dots,n\\}}\\) that faithfully follows these prompts over time, which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.548, + 0.907, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {\\{1, \\dots , n \\}} = \\operatorname {D i T C h r l} \\left\\{\\mathcal {F} \\left(P _ {1}\\right), \\dots , \\mathcal {F} \\left(P _ {n}\\right) \\right\\}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.579, + 0.909, + 0.701 + ], + "angle": 0, + "content": "Below, we first give a careful analysis of MM-DiT's attention mechanisms (Sec. 3.1). This analysis enables us to design a mask-guided full-attention KV-sharing mechanism for video editing over time (Sec. 3.2) in multi-prompt video generation. Finally, to ensure temporal coherence across different semantic segments, we further incorporate a latent blending strategy that enables smooth transitions in longer videos with multiple prompts (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.712, + 0.861, + 0.729 + ], + "angle": 0, + "content": "3.1. MM-DiT Attention Mechanism Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.901 + ], + "angle": 0, + "content": "The MM-DiT is the fundamental architecture of the current SOTA method of Text-to-image/Video models [6, 13, 14, 48], which is fundamentally distinct from prior UNet architectures since it maps text and videos into a unified sequence for attention computation. Although it has been widely utilized, the properties of its inner attention mechanism remain insufficiently explored, which restricts its applications in our multi-prompt longer video generation task. Therefore, for the first time, we conducted a comprehensive analysis of the regional attention patterns in the 3D full attention map based on the open-source video model, i.e. CogVideoX [48]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7765" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.198 + ], + "angle": 0, + "content": "As shown in Fig. 2, due to the concatenation of the vision and text prompt, each attention matrix can be decomposed into four distinct regions, corresponding to different attention operations: video-to-video attention, text-to-text attention, text-to-video attention, and video-to-text attention. Below, we give the details of each region-inspired previous UNet-like structure with individual attentions [19]." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.221, + 0.486, + 0.522 + ], + "angle": 0, + "content": "Text-to-Video and Video-to-Text Attention. Previous UNet-like architectures incorporate cross-attention for video-text alignment. In MM-DiT, the text-to-video and video-to-text attention play a similar role. To validate its efficiency, we conduct a detailed analysis of the attention patterns, as illustrated in Fig. 2. Specifically, we compute the averaged attention values across all layers and attention heads, then extract attention values by selecting specific columns or rows corresponding to token indices in both text-to-video and video-to-text regions. These attention values are subsequently reshaped into an \\( F \\times H \\times W \\) format, allowing us to visualize the semantic activation maps for individual frames. As demonstrated in Fig. 2, these visualizations show remarkable precision in token-level semantic localization, effectively capturing fine-grained relationships between textual descriptions and visual elements. This discovered capability for precise semantic control and localization provides a strong foundation for adapting established image/video editing techniques to enhance the consistency and quality of multi-prompt video generation." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.524, + 0.485, + 0.902 + ], + "angle": 0, + "content": "Text-to-Text and Video-to-Video Attention. Text-to-text and video-to-video regional attention are somehow new from the respective UNet structure. As illustrated in Fig. 3, our analysis reveals similar patterns in both components. In the text-to-text attention component (Fig. 3(a)(b), where (a) represents the attention pattern for shorter prompts and (b) illustrates the pattern for longer prompts), we observe a prominent diagonal pattern, indicating that each text token primarily attends to its neighboring tokens. Notably, there are distinct vertical lines that shift backward as the text sequence length increases, suggesting that all tokens maintain significant attention to the special tokens at the end of the text sequence. For the video-to-video attention component, since MMDiT flat the spatial and temporal token for 3D attention calculation, our analysis at the single-frame level reveals a distinctive diagonal pattern in spatial attention (Fig. 3(c)). More significantly, when examining attention maps constructed from tokens at identical spatial positions across different frames, we also observe a pronounced diagonal pattern (Fig. 3(d)). This characteristic mirrors those found in recent UNet-based video models of the spatial-attention and temporal attention, such as VideoCrafter [26] and Lavie [45], aligning with the findings reported in [27]. Since previous works only train the specific part of the diffusion model for more advanced control and generation, our" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.088, + 0.691, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.221, + 0.682, + 0.234 + ], + "angle": 0, + "content": "(a) Text-text attn (short)" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.089, + 0.902, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.719, + 0.221, + 0.863, + 0.234 + ], + "angle": 0, + "content": "(b) Text-text attn (long)" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.239, + 0.691, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.369, + 0.697, + 0.383 + ], + "angle": 0, + "content": "(c) Video-video spatial atm" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.239, + 0.902, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.369, + 0.896, + 0.383 + ], + "angle": 0, + "content": "(d) Video-video temporal attn" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.395, + 0.908, + 0.452 + ], + "angle": 0, + "content": "Figure 3. MM-DiT Text-to-Text and Video-to-Video Attention Visualization. We find that the current MM-DiT has a stronger potential to construct the individual attention in the previous UNet-like structure [10, 11, 44]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.481, + 0.905, + 0.511 + ], + "angle": 0, + "content": "finding provides strong evidence for these methods from MM-DiT perspectives." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.514, + 0.908, + 0.59 + ], + "angle": 0, + "content": "Overall, the presence of these consistent diagonal patterns in the MM-DiT architecture demonstrates robust frame-to-frame correlations, which proves essential for maintaining spatial-temporal coherence and preserving motion fidelity throughout the video sequence." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.604, + 0.859, + 0.619 + ], + "angle": 0, + "content": "3.2. Consistent Video Generation Over Time" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.628, + 0.909, + 0.852 + ], + "angle": 0, + "content": "Based on the previous analysis, we propose the masked-guided KV-sharing strategy for consistent video generation over time for our multi-prompt video generation task. As shown in Fig. 4, to generate the consistent video between prompt \\( P_{i-1} \\) and prompt \\( P_i \\), we utilize the intermediate attentions from the \\( i-1 \\)-th and \\( i \\)-th prompt in MM-DiT to generate the attention masks of the specified foreground object (\"knight\" in Fig. 4). This is achieved by averaging the Text-Video/Video-Text parts of the 3D full attention across all heads and layers with the given object tokens, then thresholded to obtain binary masks \\( M \\). Inspired by MasaCtrl [9], we leverage the masks to conduct mask-guided attention fusion based on the key and values from the prompt \\( P_{i-1} \\) to generate the new attention features of the prompt \\( P_i \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.91, + 0.903 + ], + "angle": 0, + "content": "We denote \\( M_{i-1} \\) and \\( M_i \\) as masks extracted for the foreground objects in videos \\( \\mathcal{V}_{i-1} \\) and \\( \\mathcal{V}_i \\), respectively. With these masks, we can restrict the object in \\( \\mathcal{V}_i \\) to query con" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7766" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.089, + 0.868, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.331, + 0.908, + 0.415 + ], + "angle": 0, + "content": "Figure 4. Pipeline of the proposed DiTCtrl. Note that initial latents are assumed to be 5 frames here. The first three frames are used to generate the contents of \\( P_{i-1} \\), and the last three frames are used to generate contents of \\( P_i \\). The pink latent represents the overlapping frame, while the blue and green latents are used to distinguish different prompt segments. Our method tries to synthesize content-consistent videos based on multi-prompts. The first video is synthesized with source text prompt \\( P_{i-1} \\). During the denoising process for video synthesis, we convert the full-attention into masked-guided KV-sharing strategy to query video contents from source video \\( \\mathcal{V}_{i-1} \\), so that we can synthesize content-consistent video under the modified target prompt \\( P_i \\)." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.435, + 0.449, + 0.451 + ], + "angle": 0, + "content": "tents information only from the object region in \\(\\mathcal{V}_{i - 1}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.462, + 0.484, + 0.481 + ], + "angle": 0, + "content": "\\[\nf _ {o} ^ {l} = \\text {A t t e n t i o n} \\left(Q _ {i} ^ {l}, K _ {i - 1} ^ {l}, V _ {i - 1} ^ {l}; M _ {i - 1}\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.484, + 0.484, + 0.502 + ], + "angle": 0, + "content": "\\[\nf _ {b} ^ {l} = \\text {A t t e n t i o n} \\left(Q _ {i} ^ {l}, K _ {i - 1} ^ {l}, V _ {i - 1} ^ {l}; 1 - M _ {i - 1}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.504, + 0.484, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\bar {f} ^ {l} = f _ {o} ^ {l} * M _ {i} + f _ {b} ^ {l} * (1 - M _ {i}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.536, + 0.484, + 0.596 + ], + "angle": 0, + "content": "where \\(\\bar{f}^l\\) is the final attention output. The object regions and the background regions in the current video query the content information from corresponding restricted areas rather than all the last video features." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.608, + 0.433, + 0.625 + ], + "angle": 0, + "content": "3.3. Latent Blending Strategy for Transition" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.631, + 0.484, + 0.72 + ], + "angle": 0, + "content": "While our previous methods enable semantic consistency between adjacent video segments, achieving smooth transitions between different semantic segments still needs to be carefully designed. Thus, we propose a latent blending strategy to ensure temporal coherence across different semantic segments, inspired by recent works [5, 36, 49]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.722, + 0.484, + 0.842 + ], + "angle": 0, + "content": "As illustrated in Fig. 5, our approach introduces overlapped regions between adjacent semantic video segments. For each frame position in the overlapped region, we apply a position-dependent weight function that follows a symmetric distribution, in which frames closer to their respective segments receive higher weights while those at the boundaries receive lower weights. This weighting scheme ensures smooth transitions between different semantic contexts." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.844, + 0.479, + 0.858 + ], + "angle": 0, + "content": "The blended latent feature \\(\\mathbf{z}_t\\) for frame \\(t\\) is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.87, + 0.484, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {t} = \\frac {\\sum_ {i = 1} ^ {n} w \\left(t _ {i}\\right) \\cdot \\mathbf {z} _ {t _ {i}}}{\\sum_ {i = 1} ^ {n} w \\left(t _ {i}\\right)}, \\tag {5}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.433, + 0.903, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.53, + 0.906, + 0.558 + ], + "angle": 0, + "content": "Figure 5. Latent blending strategy for video transition between video clips." + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.582, + 0.907, + 0.617 + ], + "angle": 0, + "content": "\\[\nw \\left(t _ {i}\\right) = \\min \\left(\\frac {2 \\left(t _ {i} + 0 . 5\\right)}{T}, 2 - \\frac {2 \\left(t _ {i} + 0 . 5\\right)}{T}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.621, + 0.907, + 0.681 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_{t_i}\\) is latent feature corresponding to \\(t\\)-th frame in \\(i\\)-th latent segment, \\(n\\) is number of overlapped segments, \\(T\\) denotes the frames number of one latent segment and \\(w(t_{i})\\) is a position-dependent weight function." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.681, + 0.909, + 0.773 + ], + "angle": 0, + "content": "To conclude, our approach employs the latent blending strategy and kv-sharing mechanism simultaneously during each denoising step. We process segment pairs sequentially, feeding them as one batch into the MM-DiT block for mask-guided kv-sharing (Fig. 4), then blend their denoised latents progressively (Fig. 5)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.785, + 0.646, + 0.802 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Setup. We implement DiTCtrl based on CogVideoX-2B [48], which is an open-source text-to-video diffusion model based on MM-DiT. In our experimental setup, we generate multiprompt conditioned videos, where each video clip is composed of 49 frames with a resolution of \\(480 \\times 720\\). The sample step is configured to 50. The kv-sharing steps are set" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7767" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.131, + 0.089, + 0.861, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.405, + 0.873, + 0.42 + ], + "angle": 0, + "content": "Figure 6. Comparison of generation results across methods. Freenoise+DiT is our implementation of Freenoise on CogVideoX." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.433, + 0.486, + 0.629 + ], + "angle": 0, + "content": "as [2,25], and the kv-sharing layers are specified as [25,30]. For latent sampling, the number of frames is set to 13, and the overlap size is set to 6 in our experiments. All these experiments are conducted on a single NVIDIA A100 GPU. Baselines. We mainly compare the proposed tuning-free method to current state-of-the-art multi-prompt video generation methods [36, 41, 43] and leading commercial solutions Kling [2]. Gen-L-Video, FreeNoise, and VideoInfinity are built upon the VideoCrafter2 [11] framework. To ensure a fair comparison of base models, we implement FreeNoise [36] as an enhanced baseline by directly incorporating their noise rescheduling strategy into the CogVideoX framework." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.638, + 0.218, + 0.652 + ], + "angle": 0, + "content": "4.1. MPVBench" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.901 + ], + "angle": 0, + "content": "MPVBench contains a diverse prompt dataset and a new metric customized for multi-prompt generation. Specifically, leveraging GPT-4, we produce 130 long-form prompts of 10 different transition modes. Then, for multi-prompt video generation, we observe that the distribution of the CLIP features differs between single-prompt and multi-prompt scenarios. As shown in Fig. 7, the feature points of real video (from DAVIS [34]) follow a continuous curve, while those of two concatenated isolated videos follow two continuous curves with a breakpoint in the middle. Since the common CLIP similarity calculates the average of neighborhood similarities, the difference between real video and isolated video only occurs at the breakpoint, which becomes very small when divided by the number of frames. To address this limitation, we propose CSCV (Clip Similarity Coefficient of Variation), a metric specifically designed to evaluate the" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.432, + 0.906, + 0.577 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.591, + 0.909, + 0.689 + ], + "angle": 0, + "content": "Figure 7. t-SNE visualization of CLIP embeddings. Each point represents the CLIP embedding of a single video frame after dimensionality reduction. The visualization demonstrates that conventional multi-prompt videos form distinct clusters, while our method produces a more continuous distribution, indicating smoother semantic transitions. More details and discussions will be given in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.716, + 0.894, + 0.731 + ], + "angle": 0, + "content": "transition smoothness of multi-prompt videos, defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.744, + 0.907, + 0.763 + ], + "angle": 0, + "content": "\\[\ns _ {i} = \\mathbf {x} _ {i} ^ {\\top} \\mathbf {x} _ {i + 1}, \\quad i = 1, \\dots , n - 1 \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.78, + 0.907, + 0.818 + ], + "angle": 0, + "content": "\\[\n\\operatorname {s c o r e} = \\frac {1}{1 + \\lambda \\cdot \\frac {\\sigma (s)}{\\mu (s)}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.823, + 0.909, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_i\\) denotes frame features, \\(\\sigma\\) and \\(\\mu\\) are standard deviation and average respectively. The Coefficient of Variation \\(CV = \\sigma(s) / \\mu(s)\\) describes the degree of uniformity, which can largely punish the isolated situation. The function \\(\\frac{1}{1 + \\lambda(\\cdot)}\\) projects the score to \\([0, 1]\\), the larger the better. We also re" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7768" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.089, + 0.485, + 0.21 + ], + "angle": 0, + "content": "
    MethodCSCVMotion smoothnessText-Image similarity
    Gen-L-Video67.28%97.66%30.60%
    FreeNoise84.37%97.22%32.69%
    FreeNoise+DiT78.74%97.76%30.90%
    Video-Infinity74.97%97.31%32.35%
    DiTCtrl(w/o kv-sharing)81.79%97.35%31.37%
    DiTCtrl(Ours)84.90%97.80%30.68%
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.09, + 0.211, + 0.485, + 0.268 + ], + "angle": 0, + "content": "Table 1. Evaluation metrics. Comparison of performance metrics for various video generation methods as benchmarked by MPVBench. Bold values represent the best performance within each group." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.293, + 0.483, + 0.37 + ], + "angle": 0, + "content": "port the Text-Image similarity by using CLIP Similarity [20] to assess the alignment between given prompts and output video clips, and Motion smoothness from VBench [22] to evaluate whether the motion in the generated video is smooth, and follows the physical law of the real world." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.379, + 0.274, + 0.394 + ], + "angle": 0, + "content": "4.2. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.401, + 0.485, + 0.749 + ], + "angle": 0, + "content": "The qualitative comparison with previous multi-prompt video generation methods is shown in Fig. 6. Notably, when multiple prompts are consolidated into a single-prompt describing long-term temporal changes, the generated result by Kling [2] fails to capture semantic transitions effectively, where the sun remains present while no clouds appear, which does not align with the text. Gen-L-Video [43] suffers from severe temporal jittering, compromising overall video quality. Video-Infinity [41] and FreeNoise [36] both demonstrate successful scene-level semantic changes but lack physically plausible motion. For instance, in Fig. 6, vehicles appear to be in motion while remaining spatially fixed, which is a limitation inherent to their UNet base-model abilities. In contrast, FreeNoise+DiT leverages the DiT architecture's abilities to achieve more realistic object motion but struggles with semantic transitions, resulting in noticeable discontinuities between segments. Our DiTCtrl preserves the inherent capabilities of the pre-trained DiT model while addressing these limitations, enabling smooth semantic transitions and maintaining motion coherence throughout the video sequence. For a more comprehensive evaluation, we provide additional comparisons with extensive qualitative examples in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.758, + 0.285, + 0.773 + ], + "angle": 0, + "content": "4.3.Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.78, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We conduct the automatic evaluation with our MPVBench. From Table 1 one can see that our method achieves the highest CSCV score, demonstrating superior transition handling and overall stability in generation patterns. While FreeNoise ranks second with relatively strong stability, other methods significantly lag behind in this aspect, which is consistent with the t-SNE visualization of CLIP embedding as shown in Fig. 7. In terms of motion smoothness, our approach" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.09, + 0.903, + 0.196 + ], + "angle": 0, + "content": "
    MethodOverall preferenceMotion PatternTemporal ConsistencyText Alignment
    Gen-L-Video1.151.141.081.25
    FreeNoise3.022.902.993.08
    FreeNoise+DiT3.813.933.753.78
    Video-Infinity2.902.852.912.98
    DiTCtrl(Ours)4.114.174.263.91
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.513, + 0.197, + 0.907, + 0.252 + ], + "angle": 0, + "content": "Table 2. User study. Human evaluation of different video generation methods across multiple aspects. Scores range from 1 to 5, with higher scores indicating better performance. Bold values represent the best performance within each metric." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.279, + 0.907, + 0.368 + ], + "angle": 0, + "content": "exhibits superior performance in motion quality and consistency. Regarding Text-Image Similarity metrics, although FreeNoise and Video-Infinity achieve higher scores, this can be attributed to our method's kv-sharing mechanism, where subsequent video segments inherently learn from preceding semantic content." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.37, + 0.909, + 0.476 + ], + "angle": 0, + "content": "As shown in Fig. 6, our design choice allows the road surface to gradually transition to snowy conditions while retaining features from the previous scene. Despite potentially lower text-image alignment scores, it ensures superior semantic continuity in the sequences. In practice, this trade-off doesn't negatively impact the visual quality in multi-prompt scenarios, as demonstrated by our user study in Table 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.485, + 0.696, + 0.499 + ], + "angle": 0, + "content": "4.4. Human Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.507, + 0.909, + 0.72 + ], + "angle": 0, + "content": "We invited 28 users to evaluate five models: GenL-Video [43], Video-Infinity [41], FreeNoise [36], FreeNoise+DiT and our method. We employ a Forced Ranking Scale, where items are ranked from 1 to 5, with the highest rank receiving a score of 5 and the lowest rank receiving a score of 1. Participants score each method considering overall preference, motion pattern, temporal consistency and text alignment over 16 videos generated by different scenarios. As clearly indicated in Table 2, generated videos from our method significantly outperform other state-of-the-art approaches in all four criteria, demonstrating superior capability in producing videos with natural semantic transitions that better align with human preferences for visual coherence and continuity." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.728, + 0.694, + 0.744 + ], + "angle": 0, + "content": "4.5. More Applications" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.854 + ], + "angle": 0, + "content": "Single-prompt Longer Video Generation. Our method can naturally work on single-prompt longer video generation. As illustrated in Fig. 8, using the prompt \"A white SUV drives on a steep dirt road\", our approach successfully generates videos that are more than 12 times longer than the original length, while maintaining consistent motion patterns and environmental coherence." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Video Editing. We show how we use our methods to achieve video editing performance (\"word swap\" and \"reweight\") in Fig. 9." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7769" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.088, + 0.171, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.172, + 0.089, + 0.248, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.25, + 0.089, + 0.326, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.089, + 0.403, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.404, + 0.089, + 0.482, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.172, + 0.468, + 0.186 + ], + "angle": 0, + "content": "Figure 8. Single prompt longer video generation example." + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.19, + 0.482, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.241, + 0.482, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.29, + 0.307, + 0.299 + ], + "angle": 0, + "content": "(a) Word swap" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.299, + 0.482, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.349, + 0.482, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.399, + 0.315, + 0.409 + ], + "angle": 0, + "content": "(b) Video reweight" + }, + { + "type": "image_caption", + "bbox": [ + 0.185, + 0.411, + 0.388, + 0.425 + ], + "angle": 0, + "content": "Figure 9. Video editing example." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.442, + 0.483, + 0.547 + ], + "angle": 0, + "content": "- Word Swap: removing our latent blending strategy of our approach DiTCtrl, we can achieve the video editing performance of Word Swap. Specifically, we just use masked-guided KV-sharing strategy to share keys and values from source prompt \\( P_{source} \\) branch, so that we can synthesize a new video to preserve the original composition while also addressing the content of the new prompt \\( P_{target} \\)." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.548, + 0.483, + 0.623 + ], + "angle": 0, + "content": "- Reweight: Similar to prompt-to-prompt [19], through reweighting the specific columns and rows corresponding to specified token (e.g. \"pink\") in the MM-DiT's Text-Video attention and Video-Text attention, we can also achieve the video editing performance of reweight." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.442, + 0.483, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.636, + 0.244, + 0.652 + ], + "angle": 0, + "content": "4.6. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.659, + 0.486, + 0.901 + ], + "angle": 0, + "content": "We conducted ablation studies to validate the effectiveness of DiTCtrl's key components: latent blending strategy, KV-sharing mechanism, and mask-guided generation as shown in Fig. 10. The first row shows results that directly using text-to-video models results in abrupt scene changes and disconnected motion patterns, failing to maintain continuity in the athlete's movements from surfing to skiing. The second row demonstrates that DiTCtrl without the latent blending strategy achieves basic video editing capabilities but lacks smooth transitions between scenes. Without KV-sharing (third row), DiTCtrl exhibits unstable environmental transitions and significant motion artifacts, with inconsistent character scaling and deformed movements. Moreover, DiTCtrl without mask guidance (fourth row) improves motion coherence and transitions but struggles with object attribute confusion across different prompts and environments." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.089, + 0.905, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.303, + 0.893, + 0.318 + ], + "angle": 0, + "content": "Figure 10. Visualization of ablation component in DiTCtrl." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.338, + 0.908, + 0.443 + ], + "angle": 0, + "content": "On the other hand, The full DiTCtrl implementation provides the most precise control over generated content, demonstrating superior object consistency and smoother transitions between prompts while maintaining desired motion patterns. These results validate our analysis of MM-DiT's attention mechanism and its role in enabling accurate semantic control." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.457, + 0.634, + 0.473 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.483, + 0.909, + 0.663 + ], + "angle": 0, + "content": "In this paper, we introduce DiTCtrl, a novel, tuning-free method for multi-prompt video generation using the MM-DiT architecture. Our pioneering analysis of MM-DiT's attention mechanism reveals similarities with the cross/self-attention blocks in UNet-like diffusion models, enabling mask-guided semantic control across prompts. With mask-guided kv-sharing mechanism and latent blending strategy, DiTCtrl ensures smooth transitions and consistent object motion between semantic segments, without extra training. We also present MPVBench, a new benchmark with diverse transition types and specialized metrics for assessing multi-prompt transitions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.664, + 0.909, + 0.83 + ], + "angle": 0, + "content": "Limitation & Future Work. While our method demonstrates state-of-the-art performance, there remain two primary limitations. First, compared to image generation models, current open-source video generation models exhibit relatively weaker conceptual composition capabilities, occasionally resulting in attribute binding errors across different semantic segments. Second, the computational overhead of DiT-based architectures presents challenges for inference speed. These limitations suggest promising directions for future research in enhancing semantic understanding and architectural efficiency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.83, + 0.908, + 0.891 + ], + "angle": 0, + "content": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (Grant No. 62306261), and The Shun Hing Institute of Advanced Engineering (SHIAE) Grant (No. 8115074)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7770" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.484, + 0.142 + ], + "angle": 0, + "content": "[1] Gen-3. https://runwayml.com/research/introducing-gen-3-alpha,,2024.1" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.143, + 0.484, + 0.167 + ], + "angle": 0, + "content": "[2] Kling. https://kling.kuaishou.com/en, 2024.1, 6.7" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.169, + 0.484, + 0.223 + ], + "angle": 0, + "content": "[3] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Magicvideo: Efficient video generation with latent diffusion models. arXiv preprint arXiv:2211.11018, 2022. 1" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.907, + 0.73 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7772" + } + ] +] \ No newline at end of file diff --git a/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_origin.pdf b/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0d34b6dfea0686d6446cc836c702c6f3af5ccbe2 --- /dev/null +++ b/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/b01bdc90-e200-44b3-add7-aa954711fd9c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1083aa0ed56222e7d557b1e70ddd8694563692cad213d451fb4f64a19acd529c +size 2565322 diff --git a/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/full.md b/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fbde31330fa5c455f4a59ed9cc781a6729602a46 --- /dev/null +++ b/2025/DiTCtrl_ Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation/full.md @@ -0,0 +1,336 @@ +# DiTCtrl: Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation + +Minghong Cai $^{1\dagger}$ + +Xiaodong Cun + +Yong Zhang + +Xiaoyu Li $^{3}$ + +Ying Shan3 + +Wenze Liu + +Xiangyu Yue $^{1,5}$ + +Zhaoyang Zhang3 + +1 MMLab, CUHK + +$^{3}$ ARC Lab, Tencent PCG + +$^{2}$ GVC Lab, Great Bay University + +4 Tencent AI Lab + +5 SHIAE, CUHK + +![](images/58678c5263655cb2fa1fa5b176d9a2563fa17b7964f3957c7d2bf67bfbf2436e.jpg) + +![](images/fb5a8100d4883f4a1c194f89a2f5ff285c0c70bf8de02533bcf5a3136305f08c.jpg) + +![](images/2a3349ce53efda2227ff7a5bd97154aca84e2be0bde5e56bd0b7a52ca3bd34aa.jpg) + +![](images/d9924f5d3388e8ff26127ca2d1fa3469dd2b8ad9aa1eec1c70eb3b5bc16dde17.jpg) + +![](images/9f5ac1bd7c2133423bdd6a5eb88cb05193b7d1fec52cb24c2e1ff71bb7ee8b01.jpg) + +(a) "Athlete glides across ocean waters $\rightarrow$ snow mountain $\rightarrow$ sand dunes" + +![](images/2367f95cacedec59e0a11f7091dfa624508618b09043af9520f128b800b9e9f5.jpg) +Figure 1. Our method DiTCtrl takes multiple text prompts as input and demonstrates superior capability in generating longer videos with multiple events, long-range coherence and smooth transitions as output. + +![](images/ae654abacba3f0c532773db7bdd1fa9022f33099ad2feb338750395215331e49.jpg) + +![](images/04218186e0de6a64535885b085f65661805f1d3885a7a90f7c9d2d42a2825049.jpg) + +![](images/4a780560bbb1057dfeea584da6709aca6c3e058bd793ad2d5509289509abf526.jpg) + +![](images/17bb71710c0f95cb3afc2d4202f603a86af44a391dc85dbeb78112c9decf63d8.jpg) + +(b) "Frosty pine: close-up shot $\rightarrow$ medium shot $\rightarrow$ forest vista, cinematic" + +# Abstract + +Sora-like video generation models have achieved remarkable progress with a Multi-Modal Diffusion Transformer (MM-DiT) architecture. However, the current video generation models predominantly focus on single-prompt, struggling to generate coherent scenes with multiple sequential prompts that better reflect real-world dynamic scenarios. While some pioneering works have explored multi-prompt video generation, they face significant challenges including strict training data requirements, weak prompt following, and unnatural transitions. To address these problems, we propose DiTCtrl, a training-free multi-prompt video generation method under MM-DiT architectures for the first time. Our key idea is to take the multi-prompt video generation task as temporal video editing with smooth transitions. To achieve this goal, we first analyze MM-DiT's attention mechanism, finding that the 3D full attention behaves similarly to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic + +control across different prompts with attention sharing for multi-prompt video generation. Based on our careful design, the video generated by DiTCtrl achieves smooth transitions and consistent object motion given multiple sequential prompts without additional training. Besides, we also present MPVBench, a new benchmark specially designed for multi-prompt video generation to evaluate the performance of multi-prompt generation. Extensive experiments demonstrate that our method achieves state-of-the-art performance without additional training. Code is available at https://github.com/TencentARC/DiTCtrl. + +# 1. Introduction + +Text-to-video (T2V) generation has made remarkable progress in the AIGC era [10, 44, 50], and breakthroughs such as Sora [30] have demonstrated impressive capabilities in generating longer videos through DiT [32] architecture and large-scale pertaining. However, feeding sequential prompts into current state-of-the-art text-to-video generation models (e.g., Kling [2], Gen3 [1], CogVideoX [48]) directly will produce isolated video sequences without natu + +ral transitions, as shown in Fig. 6 (First row). On the other hand, when multiple prompts are consolidated into a single-prompt describing long-term temporal changes, the generated results fail to capture semantic transitions effectively, as demonstrated in Fig. 6 (Second row). This limitation stems from their fundamental design and single-prompt training paradigm, making them inadequate for depicting real-world scenarios' dynamic, multi-event nature. + +Although pioneering works [4, 29, 42] have begun exploring multi-prompt video generation, they face significant challenges. e.g., training such extended video generation models [29, 42] from scratch would require unprecedented computational resources and datasets that are practically unfeasible when the model size increases. Current zero-shot longer video generation methods [23, 36, 43] still mainly focus on the single prompt situation with longer length. Moreover, all previous works [4, 23, 29, 36, 42] are specifically designed under UNet architecture which restricts the abilities of more complex motions and increase the difficulties in multi-prompt generation. However, since Sora's [30] groundbreaking demonstration of two-minute video generation, highlighting the scalability potential of DiT architectures [32]. Subsequent explorations have led to influential developments, notably in image generation models (Stable Diffusion 3 [13], FLUX.1 [6]) and video generations (CogVideoX [48], Mochi1 [14]). They [6, 13, 14, 48] all adopt a specific kind of DiT architecture, i.e., MultiModal Diffusion Transformer (MM-DiT [13]) as the basic unit. This architecture effectively maps text and images (or video) into a unified sequence for attention computation, enabling deeper model scale abilities and achieving superior performances. + +Thus, to keep the abilities of the pre-trained single prompt T2V model and take advantage of the performance of the diffusion transformer, we propose DiTCtrl, a training-free multi-prompt video generation method under the pre-trained MM-DiT video generation model. Our key observation is that the multi-prompt video generation can be considered a two-step problem: 1) Video editing over time: The new video is generated through the previous video with a new prompt. 2) Video transition over time: Two generated videos need to keep a smooth transition between clips. Thus, to perform consistent video editing, inspired by the UNet-based image editing techniques [9, 19], we explore the characteristic of the attention modules in the MM-DiT block for the first time, finding that the 3D full attention has similar behaviors to that of the cross-/self-attention blocks in the UNet-like diffusion models [10, 44]. We thus apply a KV-sharing method between the video clips of different prompts to maintain the semantic consistency of the key objects [9] with the 3D attention control. Besides, we utilize a latent blending strategy for transitions between clips to connect the video clip seamlessly. Finally, to systematically evaluate our method and facilitate + +future research in multi-prompt video generation, we also introduce MPVBench, a new benchmark with diverse transition types and specialized metrics for assessing multi-prompt transitions. Extensive experiments on this benchmark demonstrate that our method achieves state-of-the-art performance while maintaining computational efficiency. + +The contributions of this paper can be summarized as: + +- We propose DiTCtrl, the first tuning-free approach based on MM-DiT architecture for coherent multi-prompt video generation. Our method incorporates a novel KV-sharing mechanism and latent blending strategy, enabling seamless transitions between different prompts without additional training. +- We pioneer the analysis of MM-DiT's attention mechanism, finding that 3D full attention has similar behaviors to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic control across different prompts for enhanced generation consistency. +- We introduce MPVBench, a new benchmark specially designed for multi-prompt video generation, featuring diverse transition types and specialized metrics for multi-prompt video evaluation. +- Extensive experiments demonstrate that our method achieves state-of-the-art performance on multi-prompt video generation while maintaining computational efficiency. + +# 2. Related Work + +Video Diffusion Model. Diffusion models have achieved significant success in the field of text-to-image generation [28, 37-39], and these advancements have also propelled progress in video generation from text or images [3, 7, 8, 10, 11, 15, 16, 21, 40]. Among these methods, animateDiff [16] attempts to turn existing text-to-image diffusion models with a motion module. Other models such as Imagen Video [21] and Make-a-Video [40] train a cascade model of spatial and temporal layers directly in pixel space. To improve efficiency, many other works [3, 7, 8, 10, 11, 15] generate the videos in latent space, leveraging an auto-encoder to compress the video into a compact latent. Notably, most of these text-to-video models utilize a U-Net architecture. Subsequently, the introduction of Sora [30] demonstrates the scalability and advantages of diffusion transformer architecture [32]. Recent works such as CogVideoX [48], Mochi1 [14], and Movie Gen [33] have adopted the DiT architecture and achieved impressive results. In this work, we build upon the open-source model CogVideoX [48], a DiT-based architecture, to explore attention control mechanisms for multi-prompt long video generation. + +Long Video Generation. Training diffusion models on long videos often requires significant computational resources. Consequently, current video diffusion models are typically trained on videos with a limited number of frames. As a result, the quality of generated videos often degrades significantly during inference when generating longer videos. To address this problem, some works [17, 18, 42, 46] employ an autoregressive mechanism for long video generation. However, due to error accumulation, these methods often suffer from quality degradation after a few iterations. Alternatively, tuning-free methods [4, 23, 36, 41, 43] have been developed to extend off-the-shelf short-video diffusion models for generating long videos without additional training. For instance, Gen-L-Video [43] processes long videos as short video clips with temporal overlapping during the denoising process. FreeNoise [36] explores the influence of initial noises and conducts temporal attention fusion based on the sliding window for temporal consistency. MultiDiffusion [5] and Mimicmotion [49] introduces the latents blending strategy to achieve smooth transitions. Inspired by these works, we propose a novel KV-sharing mechanism and latent blending strategy for seamless transitions between different segments without additional training. + +Image/Video Editing with Attention Control. Attention control is gaining popularity due to its ability to perform zero-shot image or video editing without the need for additional data. In the realm of image editing, MasaCtrl [9] enhances the existing self-attention mechanism in diffusion models by introducing mutual self-attention. This allows for querying correlated content and textures from source images, ensuring consistent and coherent edits. Prompt-to-Prompt [19] utilizes cross-attention layers to control the relation between text prompts and images, which has also been adopted in many image editing works [12, 31, 47]. When it comes to video editing [24, 25, 35], temporal consistency needs to be considered during attention control. Video-P2P [25] extend the cross-attention control from Prompt-to-Prompt to video editing. FateZero [35] fuses self-attention with a blending mask obtained by cross-attention features from the source prompt. However, all these works are designed for video-to-video translation editing with structure preservation. Differently, we aim for appearance-consistent video editing over time. Besides, none of these works explore attention control in diffusion transformers. In this paper, we are the first to analyze how the full attention in diffusion transformers could be utilized for video editing over time in multi-prompt video generation. + +# 3. Method + +We tackle the challenge of zero-shot, multi-prompt longer video generation without the need for model training or optimization. This allows us to generate high-quality videos with + +![](images/54b0bfbd0dc4a67cf8c77184f4712b43d52a532396a7d36afb59b50e6de95a40.jpg) +Figure 2. MM-DiT Attention Analysis. We find the attention matrix in MM-DiT attention can be divided into four different regions. As for the prompt of "a cat watch a black mouse", each text token shows a high-light response using the average of the text-to-video and video-to-text attention. + +smooth and precise inter-prompt transitions, covering various transition types (e.g., style, camera movement, and location changes). Formally, given a pre-trained single prompt text-to-video diffusion model $\mathcal{F}$ and a sequence of $n$ prompts $\{P_1,P_2,\dots,P_n\}$ , the proposed DiTCtrl can generate a coherent longer video $\nu_{\{1,\dots,n\}}$ that faithfully follows these prompts over time, which can be formulated as: + +$$ +\mathcal {V} _ {\{1, \dots , n \}} = \operatorname {D i T C h r l} \left\{\mathcal {F} \left(P _ {1}\right), \dots , \mathcal {F} \left(P _ {n}\right) \right\}. \tag {1} +$$ + +Below, we first give a careful analysis of MM-DiT's attention mechanisms (Sec. 3.1). This analysis enables us to design a mask-guided full-attention KV-sharing mechanism for video editing over time (Sec. 3.2) in multi-prompt video generation. Finally, to ensure temporal coherence across different semantic segments, we further incorporate a latent blending strategy that enables smooth transitions in longer videos with multiple prompts (Sec. 3.3). + +# 3.1. MM-DiT Attention Mechanism Analysis + +The MM-DiT is the fundamental architecture of the current SOTA method of Text-to-image/Video models [6, 13, 14, 48], which is fundamentally distinct from prior UNet architectures since it maps text and videos into a unified sequence for attention computation. Although it has been widely utilized, the properties of its inner attention mechanism remain insufficiently explored, which restricts its applications in our multi-prompt longer video generation task. Therefore, for the first time, we conducted a comprehensive analysis of the regional attention patterns in the 3D full attention map based on the open-source video model, i.e. CogVideoX [48]. + +As shown in Fig. 2, due to the concatenation of the vision and text prompt, each attention matrix can be decomposed into four distinct regions, corresponding to different attention operations: video-to-video attention, text-to-text attention, text-to-video attention, and video-to-text attention. Below, we give the details of each region-inspired previous UNet-like structure with individual attentions [19]. + +Text-to-Video and Video-to-Text Attention. Previous UNet-like architectures incorporate cross-attention for video-text alignment. In MM-DiT, the text-to-video and video-to-text attention play a similar role. To validate its efficiency, we conduct a detailed analysis of the attention patterns, as illustrated in Fig. 2. Specifically, we compute the averaged attention values across all layers and attention heads, then extract attention values by selecting specific columns or rows corresponding to token indices in both text-to-video and video-to-text regions. These attention values are subsequently reshaped into an $F \times H \times W$ format, allowing us to visualize the semantic activation maps for individual frames. As demonstrated in Fig. 2, these visualizations show remarkable precision in token-level semantic localization, effectively capturing fine-grained relationships between textual descriptions and visual elements. This discovered capability for precise semantic control and localization provides a strong foundation for adapting established image/video editing techniques to enhance the consistency and quality of multi-prompt video generation. + +Text-to-Text and Video-to-Video Attention. Text-to-text and video-to-video regional attention are somehow new from the respective UNet structure. As illustrated in Fig. 3, our analysis reveals similar patterns in both components. In the text-to-text attention component (Fig. 3(a)(b), where (a) represents the attention pattern for shorter prompts and (b) illustrates the pattern for longer prompts), we observe a prominent diagonal pattern, indicating that each text token primarily attends to its neighboring tokens. Notably, there are distinct vertical lines that shift backward as the text sequence length increases, suggesting that all tokens maintain significant attention to the special tokens at the end of the text sequence. For the video-to-video attention component, since MMDiT flat the spatial and temporal token for 3D attention calculation, our analysis at the single-frame level reveals a distinctive diagonal pattern in spatial attention (Fig. 3(c)). More significantly, when examining attention maps constructed from tokens at identical spatial positions across different frames, we also observe a pronounced diagonal pattern (Fig. 3(d)). This characteristic mirrors those found in recent UNet-based video models of the spatial-attention and temporal attention, such as VideoCrafter [26] and Lavie [45], aligning with the findings reported in [27]. Since previous works only train the specific part of the diffusion model for more advanced control and generation, our + +![](images/3c91eef475f2f256590d336575d85a1a731d7d3d09a6f935da8844902677907f.jpg) +(a) Text-text attn (short) + +![](images/6123dcb80cb2c8ad31a152ce6832e7e7140b64ceb1890bb365d9b8d81e5640aa.jpg) +(b) Text-text attn (long) + +![](images/9031609d1eb9a26a492629d326d68d1b42c96801be0d4aa66a34ddc33d7a3772.jpg) +(c) Video-video spatial atm +Figure 3. MM-DiT Text-to-Text and Video-to-Video Attention Visualization. We find that the current MM-DiT has a stronger potential to construct the individual attention in the previous UNet-like structure [10, 11, 44]. + +![](images/5cfa187cfbe8e3dcf5b461d2a593273cb83e6aefa671983292f4efc82c6de775.jpg) +(d) Video-video temporal attn + +finding provides strong evidence for these methods from MM-DiT perspectives. + +Overall, the presence of these consistent diagonal patterns in the MM-DiT architecture demonstrates robust frame-to-frame correlations, which proves essential for maintaining spatial-temporal coherence and preserving motion fidelity throughout the video sequence. + +# 3.2. Consistent Video Generation Over Time + +Based on the previous analysis, we propose the masked-guided KV-sharing strategy for consistent video generation over time for our multi-prompt video generation task. As shown in Fig. 4, to generate the consistent video between prompt $P_{i-1}$ and prompt $P_i$ , we utilize the intermediate attentions from the $i-1$ -th and $i$ -th prompt in MM-DiT to generate the attention masks of the specified foreground object ("knight" in Fig. 4). This is achieved by averaging the Text-Video/Video-Text parts of the 3D full attention across all heads and layers with the given object tokens, then thresholded to obtain binary masks $M$ . Inspired by MasaCtrl [9], we leverage the masks to conduct mask-guided attention fusion based on the key and values from the prompt $P_{i-1}$ to generate the new attention features of the prompt $P_i$ . + +We denote $M_{i-1}$ and $M_i$ as masks extracted for the foreground objects in videos $\mathcal{V}_{i-1}$ and $\mathcal{V}_i$ , respectively. With these masks, we can restrict the object in $\mathcal{V}_i$ to query con + +![](images/796902e7231a12f01d3557494a96f641431b0f6660b865cb7d65b15a1d61483b.jpg) +Figure 4. Pipeline of the proposed DiTCtrl. Note that initial latents are assumed to be 5 frames here. The first three frames are used to generate the contents of $P_{i-1}$ , and the last three frames are used to generate contents of $P_i$ . The pink latent represents the overlapping frame, while the blue and green latents are used to distinguish different prompt segments. Our method tries to synthesize content-consistent videos based on multi-prompts. The first video is synthesized with source text prompt $P_{i-1}$ . During the denoising process for video synthesis, we convert the full-attention into masked-guided KV-sharing strategy to query video contents from source video $\mathcal{V}_{i-1}$ , so that we can synthesize content-consistent video under the modified target prompt $P_i$ . + +tents information only from the object region in $\mathcal{V}_{i - 1}$ + +$$ +f _ {o} ^ {l} = \text {A t t e n t i o n} \left(Q _ {i} ^ {l}, K _ {i - 1} ^ {l}, V _ {i - 1} ^ {l}; M _ {i - 1}\right), \tag {2} +$$ + +$$ +f _ {b} ^ {l} = \text {A t t e n t i o n} \left(Q _ {i} ^ {l}, K _ {i - 1} ^ {l}, V _ {i - 1} ^ {l}; 1 - M _ {i - 1}\right), \tag {3} +$$ + +$$ +\bar {f} ^ {l} = f _ {o} ^ {l} * M _ {i} + f _ {b} ^ {l} * (1 - M _ {i}), \tag {4} +$$ + +where $\bar{f}^l$ is the final attention output. The object regions and the background regions in the current video query the content information from corresponding restricted areas rather than all the last video features. + +# 3.3. Latent Blending Strategy for Transition + +While our previous methods enable semantic consistency between adjacent video segments, achieving smooth transitions between different semantic segments still needs to be carefully designed. Thus, we propose a latent blending strategy to ensure temporal coherence across different semantic segments, inspired by recent works [5, 36, 49]. + +As illustrated in Fig. 5, our approach introduces overlapped regions between adjacent semantic video segments. For each frame position in the overlapped region, we apply a position-dependent weight function that follows a symmetric distribution, in which frames closer to their respective segments receive higher weights while those at the boundaries receive lower weights. This weighting scheme ensures smooth transitions between different semantic contexts. + +The blended latent feature $\mathbf{z}_t$ for frame $t$ is calculated as: + +$$ +\mathbf {z} _ {t} = \frac {\sum_ {i = 1} ^ {n} w \left(t _ {i}\right) \cdot \mathbf {z} _ {t _ {i}}}{\sum_ {i = 1} ^ {n} w \left(t _ {i}\right)}, \tag {5} +$$ + +![](images/c194410755933bea6aeff1591361f0de70d065b07164e912dbc75430f0043e6e.jpg) +Figure 5. Latent blending strategy for video transition between video clips. + +$$ +w \left(t _ {i}\right) = \min \left(\frac {2 \left(t _ {i} + 0 . 5\right)}{T}, 2 - \frac {2 \left(t _ {i} + 0 . 5\right)}{T}\right), \tag {6} +$$ + +where $\mathbf{z}_{t_i}$ is latent feature corresponding to $t$ -th frame in $i$ -th latent segment, $n$ is number of overlapped segments, $T$ denotes the frames number of one latent segment and $w(t_{i})$ is a position-dependent weight function. + +To conclude, our approach employs the latent blending strategy and kv-sharing mechanism simultaneously during each denoising step. We process segment pairs sequentially, feeding them as one batch into the MM-DiT block for mask-guided kv-sharing (Fig. 4), then blend their denoised latents progressively (Fig. 5). + +# 4. Experiments + +Setup. We implement DiTCtrl based on CogVideoX-2B [48], which is an open-source text-to-video diffusion model based on MM-DiT. In our experimental setup, we generate multiprompt conditioned videos, where each video clip is composed of 49 frames with a resolution of $480 \times 720$ . The sample step is configured to 50. The kv-sharing steps are set + +![](images/f92efa0a08f0c2c9f543c0857fb455bf123b6ece8235e438f1d9c79e2118d6ad.jpg) +Figure 6. Comparison of generation results across methods. Freenoise+DiT is our implementation of Freenoise on CogVideoX. + +as [2,25], and the kv-sharing layers are specified as [25,30]. For latent sampling, the number of frames is set to 13, and the overlap size is set to 6 in our experiments. All these experiments are conducted on a single NVIDIA A100 GPU. Baselines. We mainly compare the proposed tuning-free method to current state-of-the-art multi-prompt video generation methods [36, 41, 43] and leading commercial solutions Kling [2]. Gen-L-Video, FreeNoise, and VideoInfinity are built upon the VideoCrafter2 [11] framework. To ensure a fair comparison of base models, we implement FreeNoise [36] as an enhanced baseline by directly incorporating their noise rescheduling strategy into the CogVideoX framework. + +# 4.1. MPVBench + +MPVBench contains a diverse prompt dataset and a new metric customized for multi-prompt generation. Specifically, leveraging GPT-4, we produce 130 long-form prompts of 10 different transition modes. Then, for multi-prompt video generation, we observe that the distribution of the CLIP features differs between single-prompt and multi-prompt scenarios. As shown in Fig. 7, the feature points of real video (from DAVIS [34]) follow a continuous curve, while those of two concatenated isolated videos follow two continuous curves with a breakpoint in the middle. Since the common CLIP similarity calculates the average of neighborhood similarities, the difference between real video and isolated video only occurs at the breakpoint, which becomes very small when divided by the number of frames. To address this limitation, we propose CSCV (Clip Similarity Coefficient of Variation), a metric specifically designed to evaluate the + +![](images/89d31997b80dbd44171f783ccc097540532c484391077051188dc8bd7ac4e8a9.jpg) +Figure 7. t-SNE visualization of CLIP embeddings. Each point represents the CLIP embedding of a single video frame after dimensionality reduction. The visualization demonstrates that conventional multi-prompt videos form distinct clusters, while our method produces a more continuous distribution, indicating smoother semantic transitions. More details and discussions will be given in the supplementary. + +transition smoothness of multi-prompt videos, defined as: + +$$ +s _ {i} = \mathbf {x} _ {i} ^ {\top} \mathbf {x} _ {i + 1}, \quad i = 1, \dots , n - 1 \tag {7} +$$ + +$$ +\operatorname {s c o r e} = \frac {1}{1 + \lambda \cdot \frac {\sigma (s)}{\mu (s)}}, \tag {8} +$$ + +where $\mathbf{x}_i$ denotes frame features, $\sigma$ and $\mu$ are standard deviation and average respectively. The Coefficient of Variation $CV = \sigma(s) / \mu(s)$ describes the degree of uniformity, which can largely punish the isolated situation. The function $\frac{1}{1 + \lambda(\cdot)}$ projects the score to $[0, 1]$ , the larger the better. We also re + +
    MethodCSCVMotion smoothnessText-Image similarity
    Gen-L-Video67.28%97.66%30.60%
    FreeNoise84.37%97.22%32.69%
    FreeNoise+DiT78.74%97.76%30.90%
    Video-Infinity74.97%97.31%32.35%
    DiTCtrl(w/o kv-sharing)81.79%97.35%31.37%
    DiTCtrl(Ours)84.90%97.80%30.68%
    + +Table 1. Evaluation metrics. Comparison of performance metrics for various video generation methods as benchmarked by MPVBench. Bold values represent the best performance within each group. + +port the Text-Image similarity by using CLIP Similarity [20] to assess the alignment between given prompts and output video clips, and Motion smoothness from VBench [22] to evaluate whether the motion in the generated video is smooth, and follows the physical law of the real world. + +# 4.2. Qualitative Results + +The qualitative comparison with previous multi-prompt video generation methods is shown in Fig. 6. Notably, when multiple prompts are consolidated into a single-prompt describing long-term temporal changes, the generated result by Kling [2] fails to capture semantic transitions effectively, where the sun remains present while no clouds appear, which does not align with the text. Gen-L-Video [43] suffers from severe temporal jittering, compromising overall video quality. Video-Infinity [41] and FreeNoise [36] both demonstrate successful scene-level semantic changes but lack physically plausible motion. For instance, in Fig. 6, vehicles appear to be in motion while remaining spatially fixed, which is a limitation inherent to their UNet base-model abilities. In contrast, FreeNoise+DiT leverages the DiT architecture's abilities to achieve more realistic object motion but struggles with semantic transitions, resulting in noticeable discontinuities between segments. Our DiTCtrl preserves the inherent capabilities of the pre-trained DiT model while addressing these limitations, enabling smooth semantic transitions and maintaining motion coherence throughout the video sequence. For a more comprehensive evaluation, we provide additional comparisons with extensive qualitative examples in the supplementary. + +# 4.3.Quantitative Results + +We conduct the automatic evaluation with our MPVBench. From Table 1 one can see that our method achieves the highest CSCV score, demonstrating superior transition handling and overall stability in generation patterns. While FreeNoise ranks second with relatively strong stability, other methods significantly lag behind in this aspect, which is consistent with the t-SNE visualization of CLIP embedding as shown in Fig. 7. In terms of motion smoothness, our approach + +
    MethodOverall preferenceMotion PatternTemporal ConsistencyText Alignment
    Gen-L-Video1.151.141.081.25
    FreeNoise3.022.902.993.08
    FreeNoise+DiT3.813.933.753.78
    Video-Infinity2.902.852.912.98
    DiTCtrl(Ours)4.114.174.263.91
    + +Table 2. User study. Human evaluation of different video generation methods across multiple aspects. Scores range from 1 to 5, with higher scores indicating better performance. Bold values represent the best performance within each metric. + +exhibits superior performance in motion quality and consistency. Regarding Text-Image Similarity metrics, although FreeNoise and Video-Infinity achieve higher scores, this can be attributed to our method's kv-sharing mechanism, where subsequent video segments inherently learn from preceding semantic content. + +As shown in Fig. 6, our design choice allows the road surface to gradually transition to snowy conditions while retaining features from the previous scene. Despite potentially lower text-image alignment scores, it ensures superior semantic continuity in the sequences. In practice, this trade-off doesn't negatively impact the visual quality in multi-prompt scenarios, as demonstrated by our user study in Table 2. + +# 4.4. Human Evaluation + +We invited 28 users to evaluate five models: GenL-Video [43], Video-Infinity [41], FreeNoise [36], FreeNoise+DiT and our method. We employ a Forced Ranking Scale, where items are ranked from 1 to 5, with the highest rank receiving a score of 5 and the lowest rank receiving a score of 1. Participants score each method considering overall preference, motion pattern, temporal consistency and text alignment over 16 videos generated by different scenarios. As clearly indicated in Table 2, generated videos from our method significantly outperform other state-of-the-art approaches in all four criteria, demonstrating superior capability in producing videos with natural semantic transitions that better align with human preferences for visual coherence and continuity. + +# 4.5. More Applications + +Single-prompt Longer Video Generation. Our method can naturally work on single-prompt longer video generation. As illustrated in Fig. 8, using the prompt "A white SUV drives on a steep dirt road", our approach successfully generates videos that are more than 12 times longer than the original length, while maintaining consistent motion patterns and environmental coherence. + +Video Editing. We show how we use our methods to achieve video editing performance ("word swap" and "reweight") in Fig. 9. + +![](images/81a3fe89a97e2cdbe66f920f0bff4c0ca52b3c53a799846742bbc7efe7b3353a.jpg) +Figure 8. Single prompt longer video generation example. + +![](images/42cfac057008656e04fea8b395256eef5c6efc0ddfb346b041b4752e1145cb5f.jpg) + +![](images/915b897244663dba44f6057c6408138a2158877002fe703cbb2537b53d58d8ce.jpg) + +![](images/bec49ae1beaf3e7e3cc1f5af51813f1eab7d514119ae7c92157720769fa5cfa7.jpg) + +![](images/4a166e35c420a552eb08113a20c12749d4d543b1b6d46106e428a0ce317d6d23.jpg) + +![](images/62af6fbb09bb241195a8a708eeede4b3c54516d00c58e19f3a9b1b32030cb5cc.jpg) + +![](images/2d79ea0c30453d279e940732894611efa0bb4ff2a34f584c40c60ea5c577f78a.jpg) +(a) Word swap + +![](images/65dc7528e00907a8cfc0d16e43cff28d5589d421c4070487757030dc2c4a2b38.jpg) + +![](images/7a522caf5224a56e5ce8afa0764dfe69d83dc5f43d7c4c2a4eb4d226e48b4f32.jpg) +(b) Video reweight +Figure 9. Video editing example. + +- Word Swap: removing our latent blending strategy of our approach DiTCtrl, we can achieve the video editing performance of Word Swap. Specifically, we just use masked-guided KV-sharing strategy to share keys and values from source prompt $P_{source}$ branch, so that we can synthesize a new video to preserve the original composition while also addressing the content of the new prompt $P_{target}$ . +- Reweight: Similar to prompt-to-prompt [19], through reweighting the specific columns and rows corresponding to specified token (e.g. "pink") in the MM-DiT's Text-Video attention and Video-Text attention, we can also achieve the video editing performance of reweight. + +# 4.6. Ablation Study + +We conducted ablation studies to validate the effectiveness of DiTCtrl's key components: latent blending strategy, KV-sharing mechanism, and mask-guided generation as shown in Fig. 10. The first row shows results that directly using text-to-video models results in abrupt scene changes and disconnected motion patterns, failing to maintain continuity in the athlete's movements from surfing to skiing. The second row demonstrates that DiTCtrl without the latent blending strategy achieves basic video editing capabilities but lacks smooth transitions between scenes. Without KV-sharing (third row), DiTCtrl exhibits unstable environmental transitions and significant motion artifacts, with inconsistent character scaling and deformed movements. Moreover, DiTCtrl without mask guidance (fourth row) improves motion coherence and transitions but struggles with object attribute confusion across different prompts and environments. + +![](images/597c2d48425f4096644bc7849d3f9b79ef7631bdd4ec7fcf7a8538a8e8022268.jpg) +Figure 10. Visualization of ablation component in DiTCtrl. + +On the other hand, The full DiTCtrl implementation provides the most precise control over generated content, demonstrating superior object consistency and smoother transitions between prompts while maintaining desired motion patterns. These results validate our analysis of MM-DiT's attention mechanism and its role in enabling accurate semantic control. + +# 5. Conclusion + +In this paper, we introduce DiTCtrl, a novel, tuning-free method for multi-prompt video generation using the MM-DiT architecture. Our pioneering analysis of MM-DiT's attention mechanism reveals similarities with the cross/self-attention blocks in UNet-like diffusion models, enabling mask-guided semantic control across prompts. With mask-guided kv-sharing mechanism and latent blending strategy, DiTCtrl ensures smooth transitions and consistent object motion between semantic segments, without extra training. We also present MPVBench, a new benchmark with diverse transition types and specialized metrics for assessing multi-prompt transitions. + +Limitation & Future Work. While our method demonstrates state-of-the-art performance, there remain two primary limitations. First, compared to image generation models, current open-source video generation models exhibit relatively weaker conceptual composition capabilities, occasionally resulting in attribute binding errors across different semantic segments. Second, the computational overhead of DiT-based architectures presents challenges for inference speed. These limitations suggest promising directions for future research in enhancing semantic understanding and architectural efficiency. + +Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (Grant No. 62306261), and The Shun Hing Institute of Advanced Engineering (SHIAE) Grant (No. 8115074). + +# References + +[1] Gen-3. https://runwayml.com/research/introducing-gen-3-alpha,,2024.1 +[2] Kling. https://kling.kuaishou.com/en, 2024.1, 6.7 +[3] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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"\\rightarrow" + }, + { + "bbox": [ + 137, + 315, + 470, + 327 + ], + "type": "text", + "content": " sand dunes\"" + } + ] + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 57, + 331, + 152, + 395 + ], + "blocks": [ + { + "bbox": [ + 57, + 331, + 152, + 395 + ], + "lines": [ + { + "bbox": [ + 57, + 331, + 152, + 395 + ], + "spans": [ + { + "bbox": [ + 57, + 331, + 152, + 395 + ], + "type": "image", + "image_path": "2367f95cacedec59e0a11f7091dfa624508618b09043af9520f128b800b9e9f5.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 409, + 555, + 431 + ], + "lines": [ + { + "bbox": [ + 55, + 409, + 555, + 431 + ], + "spans": [ + { + "bbox": [ + 55, + 409, + 555, + 431 + ], + "type": "text", + "content": "Figure 1. Our method DiTCtrl takes multiple text prompts as input and demonstrates superior capability in generating longer videos with multiple events, long-range coherence and smooth transitions as output." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 156, + 331, + 251, + 395 + ], + "blocks": [ + { + "bbox": [ + 156, + 331, + 251, + 395 + ], + "lines": [ + { + "bbox": [ + 156, + 331, + 251, + 395 + ], + "spans": [ + { + "bbox": [ + 156, + 331, + 251, + 395 + ], + "type": "image", + "image_path": "ae654abacba3f0c532773db7bdd1fa9022f33099ad2feb338750395215331e49.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 255, + 331, + 350, + 395 + ], + "blocks": [ + { + "bbox": [ + 255, + 331, + 350, + 395 + ], + "lines": [ + { + "bbox": [ + 255, + 331, + 350, + 395 + ], + "spans": [ + { + "bbox": [ + 255, + 331, + 350, + 395 + ], + "type": "image", + "image_path": "04218186e0de6a64535885b085f65661805f1d3885a7a90f7c9d2d42a2825049.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 356, + 331, + 451, + 395 + ], + "blocks": [ + { + "bbox": [ + 356, + 331, + 451, + 395 + ], + "lines": [ + { + "bbox": [ + 356, + 331, + 451, + 395 + ], + "spans": [ + { + "bbox": [ + 356, + 331, + 451, + 395 + ], + "type": "image", + "image_path": "4a780560bbb1057dfeea584da6709aca6c3e058bd793ad2d5509289509abf526.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 455, + 331, + 552, + 395 + ], + "blocks": [ + { + "bbox": [ + 455, + 331, + 552, + 395 + ], + "lines": [ + { + "bbox": [ + 455, + 331, + 552, + 395 + ], + "spans": [ + { + "bbox": [ + 455, + 331, + 552, + 395 + ], + "type": "image", + "image_path": "17bb71710c0f95cb3afc2d4202f603a86af44a391dc85dbeb78112c9decf63d8.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "bbox": [ + 135, + 395, + 473, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 395, + 473, + 407 + ], + "spans": [ + { + "bbox": [ + 135, + 395, + 473, + 407 + ], + "type": "text", + "content": "(b) \"Frosty pine: close-up shot " + }, + { + "bbox": [ + 135, + 395, + 473, + 407 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 135, + 395, + 473, + 407 + ], + "type": "text", + "content": " medium shot " + }, + { + "bbox": [ + 135, + 395, + 473, + 407 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 135, + 395, + 473, + 407 + ], + "type": "text", + "content": " forest vista, cinematic\"" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 152, + 441, + 200, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 441, + 200, + 453 + ], + "spans": [ + { + "bbox": [ + 152, + 441, + 200, + 453 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 54, + 467, + 297, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 467, + 297, + 684 + ], + "spans": [ + { + "bbox": [ + 54, + 467, + 297, + 684 + ], + "type": "text", + "content": "Sora-like video generation models have achieved remarkable progress with a Multi-Modal Diffusion Transformer (MM-DiT) architecture. However, the current video generation models predominantly focus on single-prompt, struggling to generate coherent scenes with multiple sequential prompts that better reflect real-world dynamic scenarios. While some pioneering works have explored multi-prompt video generation, they face significant challenges including strict training data requirements, weak prompt following, and unnatural transitions. To address these problems, we propose DiTCtrl, a training-free multi-prompt video generation method under MM-DiT architectures for the first time. Our key idea is to take the multi-prompt video generation task as temporal video editing with smooth transitions. To achieve this goal, we first analyze MM-DiT's attention mechanism, finding that the 3D full attention behaves similarly to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 442, + 556, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 442, + 556, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 442, + 556, + 574 + ], + "type": "text", + "content": "control across different prompts with attention sharing for multi-prompt video generation. Based on our careful design, the video generated by DiTCtrl achieves smooth transitions and consistent object motion given multiple sequential prompts without additional training. Besides, we also present MPVBench, a new benchmark specially designed for multi-prompt video generation to evaluate the performance of multi-prompt generation. Extensive experiments demonstrate that our method achieves state-of-the-art performance without additional training. Code is available at https://github.com/TencentARC/DiTCtrl." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 314, + 597, + 394, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 597, + 394, + 609 + ], + "spans": [ + { + "bbox": [ + 314, + 597, + 394, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": "Text-to-video (T2V) generation has made remarkable progress in the AIGC era [10, 44, 50], and breakthroughs such as Sora [30] have demonstrated impressive capabilities in generating longer videos through DiT [32] architecture and large-scale pertaining. However, feeding sequential prompts into current state-of-the-art text-to-video generation models (e.g., Kling [2], Gen3 [1], CogVideoX [48]) directly will produce isolated video sequences without natu" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 692, + 235, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 692, + 235, + 702 + ], + "spans": [ + { + "bbox": [ + 55, + 692, + 235, + 702 + ], + "type": "text", + "content": "† Work done during an internship at Tencent ARC Lab." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 56, + 703, + 139, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 703, + 139, + 712 + ], + "spans": [ + { + "bbox": [ + 56, + 703, + 139, + 712 + ], + "type": "text", + "content": "Corresponding Author" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7763" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 167 + ], + "type": "text", + "content": "ral transitions, as shown in Fig. 6 (First row). On the other hand, when multiple prompts are consolidated into a single-prompt describing long-term temporal changes, the generated results fail to capture semantic transitions effectively, as demonstrated in Fig. 6 (Second row). This limitation stems from their fundamental design and single-prompt training paradigm, making them inadequate for depicting real-world scenarios' dynamic, multi-event nature." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 172, + 298, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 172, + 298, + 460 + ], + "spans": [ + { + "bbox": [ + 56, + 172, + 298, + 460 + ], + "type": "text", + "content": "Although pioneering works [4, 29, 42] have begun exploring multi-prompt video generation, they face significant challenges. e.g., training such extended video generation models [29, 42] from scratch would require unprecedented computational resources and datasets that are practically unfeasible when the model size increases. Current zero-shot longer video generation methods [23, 36, 43] still mainly focus on the single prompt situation with longer length. Moreover, all previous works [4, 23, 29, 36, 42] are specifically designed under UNet architecture which restricts the abilities of more complex motions and increase the difficulties in multi-prompt generation. However, since Sora's [30] groundbreaking demonstration of two-minute video generation, highlighting the scalability potential of DiT architectures [32]. Subsequent explorations have led to influential developments, notably in image generation models (Stable Diffusion 3 [13], FLUX.1 [6]) and video generations (CogVideoX [48], Mochi1 [14]). They [6, 13, 14, 48] all adopt a specific kind of DiT architecture, i.e., MultiModal Diffusion Transformer (MM-DiT [13]) as the basic unit. This architecture effectively maps text and images (or video) into a unified sequence for attention computation, enabling deeper model scale abilities and achieving superior performances." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 462, + 298, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 298, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 298, + 714 + ], + "type": "text", + "content": "Thus, to keep the abilities of the pre-trained single prompt T2V model and take advantage of the performance of the diffusion transformer, we propose DiTCtrl, a training-free multi-prompt video generation method under the pre-trained MM-DiT video generation model. Our key observation is that the multi-prompt video generation can be considered a two-step problem: 1) Video editing over time: The new video is generated through the previous video with a new prompt. 2) Video transition over time: Two generated videos need to keep a smooth transition between clips. Thus, to perform consistent video editing, inspired by the UNet-based image editing techniques [9, 19], we explore the characteristic of the attention modules in the MM-DiT block for the first time, finding that the 3D full attention has similar behaviors to that of the cross-/self-attention blocks in the UNet-like diffusion models [10, 44]. We thus apply a KV-sharing method between the video clips of different prompts to maintain the semantic consistency of the key objects [9] with the 3D attention control. Besides, we utilize a latent blending strategy for transitions between clips to connect the video clip seamlessly. Finally, to systematically evaluate our method and facilitate" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 72, + 556, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 556, + 145 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 556, + 145 + ], + "type": "text", + "content": "future research in multi-prompt video generation, we also introduce MPVBench, a new benchmark with diverse transition types and specialized metrics for assessing multi-prompt transitions. Extensive experiments on this benchmark demonstrate that our method achieves state-of-the-art performance while maintaining computational efficiency." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 326, + 149, + 545, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 149, + 545, + 162 + ], + "spans": [ + { + "bbox": [ + 326, + 149, + 545, + 162 + ], + "type": "text", + "content": "The contributions of this paper can be summarized as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 172, + 554, + 411 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 314, + 172, + 553, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 172, + 553, + 243 + ], + "spans": [ + { + "bbox": [ + 314, + 172, + 553, + 243 + ], + "type": "text", + "content": "- We propose DiTCtrl, the first tuning-free approach based on MM-DiT architecture for coherent multi-prompt video generation. Our method incorporates a novel KV-sharing mechanism and latent blending strategy, enabling seamless transitions between different prompts without additional training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 245, + 554, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 245, + 554, + 316 + ], + "spans": [ + { + "bbox": [ + 314, + 245, + 554, + 316 + ], + "type": "text", + "content": "- We pioneer the analysis of MM-DiT's attention mechanism, finding that 3D full attention has similar behaviors to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic control across different prompts for enhanced generation consistency." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 316, + 554, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 316, + 554, + 363 + ], + "spans": [ + { + "bbox": [ + 314, + 316, + 554, + 363 + ], + "type": "text", + "content": "- We introduce MPVBench, a new benchmark specially designed for multi-prompt video generation, featuring diverse transition types and specialized metrics for multi-prompt video evaluation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 364, + 553, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 364, + 553, + 411 + ], + "spans": [ + { + "bbox": [ + 314, + 364, + 553, + 411 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that our method achieves state-of-the-art performance on multi-prompt video generation while maintaining computational efficiency." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 437, + 402, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 437, + 402, + 450 + ], + "spans": [ + { + "bbox": [ + 314, + 437, + 402, + 450 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 462, + 556, + 715 + ], + "type": "text", + "content": "Video Diffusion Model. Diffusion models have achieved significant success in the field of text-to-image generation [28, 37-39], and these advancements have also propelled progress in video generation from text or images [3, 7, 8, 10, 11, 15, 16, 21, 40]. Among these methods, animateDiff [16] attempts to turn existing text-to-image diffusion models with a motion module. Other models such as Imagen Video [21] and Make-a-Video [40] train a cascade model of spatial and temporal layers directly in pixel space. To improve efficiency, many other works [3, 7, 8, 10, 11, 15] generate the videos in latent space, leveraging an auto-encoder to compress the video into a compact latent. Notably, most of these text-to-video models utilize a U-Net architecture. Subsequently, the introduction of Sora [30] demonstrates the scalability and advantages of diffusion transformer architecture [32]. Recent works such as CogVideoX [48], Mochi1 [14], and Movie Gen [33] have adopted the DiT architecture and achieved impressive results. In this work, we build upon the open-source model CogVideoX [48], a DiT-based architecture, to explore attention control mechanisms for multi-prompt long video generation." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7764" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 348 + ], + "type": "text", + "content": "Long Video Generation. Training diffusion models on long videos often requires significant computational resources. Consequently, current video diffusion models are typically trained on videos with a limited number of frames. As a result, the quality of generated videos often degrades significantly during inference when generating longer videos. To address this problem, some works [17, 18, 42, 46] employ an autoregressive mechanism for long video generation. However, due to error accumulation, these methods often suffer from quality degradation after a few iterations. Alternatively, tuning-free methods [4, 23, 36, 41, 43] have been developed to extend off-the-shelf short-video diffusion models for generating long videos without additional training. For instance, Gen-L-Video [43] processes long videos as short video clips with temporal overlapping during the denoising process. FreeNoise [36] explores the influence of initial noises and conducts temporal attention fusion based on the sliding window for temporal consistency. MultiDiffusion [5] and Mimicmotion [49] introduces the latents blending strategy to achieve smooth transitions. Inspired by these works, we propose a novel KV-sharing mechanism and latent blending strategy for seamless transitions between different segments without additional training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 361, + 296, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 296, + 648 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 296, + 648 + ], + "type": "text", + "content": "Image/Video Editing with Attention Control. Attention control is gaining popularity due to its ability to perform zero-shot image or video editing without the need for additional data. In the realm of image editing, MasaCtrl [9] enhances the existing self-attention mechanism in diffusion models by introducing mutual self-attention. This allows for querying correlated content and textures from source images, ensuring consistent and coherent edits. Prompt-to-Prompt [19] utilizes cross-attention layers to control the relation between text prompts and images, which has also been adopted in many image editing works [12, 31, 47]. When it comes to video editing [24, 25, 35], temporal consistency needs to be considered during attention control. Video-P2P [25] extend the cross-attention control from Prompt-to-Prompt to video editing. FateZero [35] fuses self-attention with a blending mask obtained by cross-attention features from the source prompt. However, all these works are designed for video-to-video translation editing with structure preservation. Differently, we aim for appearance-consistent video editing over time. Besides, none of these works explore attention control in diffusion transformers. In this paper, we are the first to analyze how the full attention in diffusion transformers could be utilized for video editing over time in multi-prompt video generation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 657, + 111, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 657, + 111, + 669 + ], + "spans": [ + { + "bbox": [ + 55, + 657, + 111, + 669 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "We tackle the challenge of zero-shot, multi-prompt longer video generation without the need for model training or optimization. This allows us to generate high-quality videos with" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 316, + 71, + 553, + 260 + ], + "blocks": [ + { + "bbox": [ + 316, + 71, + 553, + 260 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 553, + 260 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 553, + 260 + ], + "type": "image", + "image_path": "54b0bfbd0dc4a67cf8c77184f4712b43d52a532396a7d36afb59b50e6de95a40.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 261, + 555, + 316 + ], + "lines": [ + { + "bbox": [ + 313, + 261, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 261, + 555, + 316 + ], + "type": "text", + "content": "Figure 2. MM-DiT Attention Analysis. We find the attention matrix in MM-DiT attention can be divided into four different regions. As for the prompt of \"a cat watch a black mouse\", each text token shows a high-light response using the average of the text-to-video and video-to-text attention." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "text", + "content": "smooth and precise inter-prompt transitions, covering various transition types (e.g., style, camera movement, and location changes). Formally, given a pre-trained single prompt text-to-video diffusion model " + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "text", + "content": " and a sequence of " + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "text", + "content": " prompts " + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "inline_equation", + "content": "\\{P_1,P_2,\\dots,P_n\\}" + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "text", + "content": ", the proposed DiTCtrl can generate a coherent longer video " + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "inline_equation", + "content": "\\nu_{\\{1,\\dots,n\\}}" + }, + { + "bbox": [ + 313, + 339, + 556, + 422 + ], + "type": "text", + "content": " that faithfully follows these prompts over time, which can be formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 348, + 434, + 555, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 434, + 555, + 447 + ], + "spans": [ + { + "bbox": [ + 348, + 434, + 555, + 447 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {\\{1, \\dots , n \\}} = \\operatorname {D i T C h r l} \\left\\{\\mathcal {F} \\left(P _ {1}\\right), \\dots , \\mathcal {F} \\left(P _ {n}\\right) \\right\\}. \\tag {1}", + "image_path": "be35933e337d52734b8a4bafd0aa03ce8a9433aa31a5f5cc4cfa8623b1ef28af.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 458, + 556, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 458, + 556, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 458, + 556, + 555 + ], + "type": "text", + "content": "Below, we first give a careful analysis of MM-DiT's attention mechanisms (Sec. 3.1). This analysis enables us to design a mask-guided full-attention KV-sharing mechanism for video editing over time (Sec. 3.2) in multi-prompt video generation. Finally, to ensure temporal coherence across different semantic segments, we further incorporate a latent blending strategy that enables smooth transitions in longer videos with multiple prompts (Sec. 3.3)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 563, + 526, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 563, + 526, + 577 + ], + "spans": [ + { + "bbox": [ + 313, + 563, + 526, + 577 + ], + "type": "text", + "content": "3.1. MM-DiT Attention Mechanism Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 713 + ], + "type": "text", + "content": "The MM-DiT is the fundamental architecture of the current SOTA method of Text-to-image/Video models [6, 13, 14, 48], which is fundamentally distinct from prior UNet architectures since it maps text and videos into a unified sequence for attention computation. Although it has been widely utilized, the properties of its inner attention mechanism remain insufficiently explored, which restricts its applications in our multi-prompt longer video generation task. Therefore, for the first time, we conducted a comprehensive analysis of the regional attention patterns in the 3D full attention map based on the open-source video model, i.e. CogVideoX [48]." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7765" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 156 + ], + "type": "text", + "content": "As shown in Fig. 2, due to the concatenation of the vision and text prompt, each attention matrix can be decomposed into four distinct regions, corresponding to different attention operations: video-to-video attention, text-to-text attention, text-to-video attention, and video-to-text attention. Below, we give the details of each region-inspired previous UNet-like structure with individual attentions [19]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 175, + 297, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 175, + 297, + 413 + ], + "spans": [ + { + "bbox": [ + 56, + 175, + 297, + 413 + ], + "type": "text", + "content": "Text-to-Video and Video-to-Text Attention. Previous UNet-like architectures incorporate cross-attention for video-text alignment. In MM-DiT, the text-to-video and video-to-text attention play a similar role. To validate its efficiency, we conduct a detailed analysis of the attention patterns, as illustrated in Fig. 2. Specifically, we compute the averaged attention values across all layers and attention heads, then extract attention values by selecting specific columns or rows corresponding to token indices in both text-to-video and video-to-text regions. These attention values are subsequently reshaped into an " + }, + { + "bbox": [ + 56, + 175, + 297, + 413 + ], + "type": "inline_equation", + "content": "F \\times H \\times W" + }, + { + "bbox": [ + 56, + 175, + 297, + 413 + ], + "type": "text", + "content": " format, allowing us to visualize the semantic activation maps for individual frames. As demonstrated in Fig. 2, these visualizations show remarkable precision in token-level semantic localization, effectively capturing fine-grained relationships between textual descriptions and visual elements. This discovered capability for precise semantic control and localization provides a strong foundation for adapting established image/video editing techniques to enhance the consistency and quality of multi-prompt video generation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 415, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 415, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 415, + 296, + 714 + ], + "type": "text", + "content": "Text-to-Text and Video-to-Video Attention. Text-to-text and video-to-video regional attention are somehow new from the respective UNet structure. As illustrated in Fig. 3, our analysis reveals similar patterns in both components. In the text-to-text attention component (Fig. 3(a)(b), where (a) represents the attention pattern for shorter prompts and (b) illustrates the pattern for longer prompts), we observe a prominent diagonal pattern, indicating that each text token primarily attends to its neighboring tokens. Notably, there are distinct vertical lines that shift backward as the text sequence length increases, suggesting that all tokens maintain significant attention to the special tokens at the end of the text sequence. For the video-to-video attention component, since MMDiT flat the spatial and temporal token for 3D attention calculation, our analysis at the single-frame level reveals a distinctive diagonal pattern in spatial attention (Fig. 3(c)). More significantly, when examining attention maps constructed from tokens at identical spatial positions across different frames, we also observe a pronounced diagonal pattern (Fig. 3(d)). This characteristic mirrors those found in recent UNet-based video models of the spatial-attention and temporal attention, such as VideoCrafter [26] and Lavie [45], aligning with the findings reported in [27]. Since previous works only train the specific part of the diffusion model for more advanced control and generation, our" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 317, + 69, + 422, + 173 + ], + "blocks": [ + { + "bbox": [ + 317, + 69, + 422, + 173 + ], + "lines": [ + { + "bbox": [ + 317, + 69, + 422, + 173 + ], + "spans": [ + { + "bbox": [ + 317, + 69, + 422, + 173 + ], + "type": "image", + "image_path": "3c91eef475f2f256590d336575d85a1a731d7d3d09a6f935da8844902677907f.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 175, + 417, + 185 + ], + "lines": [ + { + "bbox": [ + 326, + 175, + 417, + 185 + ], + "spans": [ + { + "bbox": [ + 326, + 175, + 417, + 185 + ], + "type": "text", + "content": "(a) Text-text attn (short)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 426, + 70, + 552, + 172 + ], + "blocks": [ + { + "bbox": [ + 426, + 70, + 552, + 172 + ], + "lines": [ + { + "bbox": [ + 426, + 70, + 552, + 172 + ], + "spans": [ + { + "bbox": [ + 426, + 70, + 552, + 172 + ], + "type": "image", + "image_path": "6123dcb80cb2c8ad31a152ce6832e7e7140b64ceb1890bb365d9b8d81e5640aa.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 175, + 528, + 185 + ], + "lines": [ + { + "bbox": [ + 440, + 175, + 528, + 185 + ], + "spans": [ + { + "bbox": [ + 440, + 175, + 528, + 185 + ], + "type": "text", + "content": "(b) Text-text attn (long)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 316, + 189, + 422, + 291 + ], + "blocks": [ + { + "bbox": [ + 316, + 189, + 422, + 291 + ], + "lines": [ + { + "bbox": [ + 316, + 189, + 422, + 291 + ], + "spans": [ + { + "bbox": [ + 316, + 189, + 422, + 291 + ], + "type": "image", + "image_path": "9031609d1eb9a26a492629d326d68d1b42c96801be0d4aa66a34ddc33d7a3772.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 292, + 426, + 303 + ], + "lines": [ + { + "bbox": [ + 324, + 292, + 426, + 303 + ], + "spans": [ + { + "bbox": [ + 324, + 292, + 426, + 303 + ], + "type": "text", + "content": "(c) Video-video spatial atm" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 312, + 555, + 357 + ], + "lines": [ + { + "bbox": [ + 313, + 312, + 555, + 357 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 555, + 357 + ], + "type": "text", + "content": "Figure 3. MM-DiT Text-to-Text and Video-to-Video Attention Visualization. We find that the current MM-DiT has a stronger potential to construct the individual attention in the previous UNet-like structure [10, 11, 44]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 428, + 189, + 552, + 291 + ], + "blocks": [ + { + "bbox": [ + 428, + 189, + 552, + 291 + ], + "lines": [ + { + "bbox": [ + 428, + 189, + 552, + 291 + ], + "spans": [ + { + "bbox": [ + 428, + 189, + 552, + 291 + ], + "type": "image", + "image_path": "5cfa187cfbe8e3dcf5b461d2a593273cb83e6aefa671983292f4efc82c6de775.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 436, + 292, + 548, + 303 + ], + "lines": [ + { + "bbox": [ + 436, + 292, + 548, + 303 + ], + "spans": [ + { + "bbox": [ + 436, + 292, + 548, + 303 + ], + "type": "text", + "content": "(d) Video-video temporal attn" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 380, + 553, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 553, + 404 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 553, + 404 + ], + "type": "text", + "content": "finding provides strong evidence for these methods from MM-DiT perspectives." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 467 + ], + "type": "text", + "content": "Overall, the presence of these consistent diagonal patterns in the MM-DiT architecture demonstrates robust frame-to-frame correlations, which proves essential for maintaining spatial-temporal coherence and preserving motion fidelity throughout the video sequence." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 478, + 525, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 478, + 525, + 490 + ], + "spans": [ + { + "bbox": [ + 313, + 478, + 525, + 490 + ], + "type": "text", + "content": "3.2. Consistent Video Generation Over Time" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "content": "Based on the previous analysis, we propose the masked-guided KV-sharing strategy for consistent video generation over time for our multi-prompt video generation task. As shown in Fig. 4, to generate the consistent video between prompt " + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "inline_equation", + "content": "P_{i-1}" + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "content": " and prompt " + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "content": ", we utilize the intermediate attentions from the " + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "inline_equation", + "content": "i-1" + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "content": "-th and " + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "content": "-th prompt in MM-DiT to generate the attention masks of the specified foreground object (\"knight\" in Fig. 4). This is achieved by averaging the Text-Video/Video-Text parts of the 3D full attention across all heads and layers with the given object tokens, then thresholded to obtain binary masks " + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "content": ". Inspired by MasaCtrl [9], we leverage the masks to conduct mask-guided attention fusion based on the key and values from the prompt " + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "inline_equation", + "content": "P_{i-1}" + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "content": " to generate the new attention features of the prompt " + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 313, + 497, + 556, + 674 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "We denote " + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "inline_equation", + "content": "M_{i-1}" + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "inline_equation", + "content": "M_i" + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": " as masks extracted for the foreground objects in videos " + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_{i-1}" + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_i" + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": ", respectively. With these masks, we can restrict the object in " + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_i" + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": " to query con" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7766" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 70, + 531, + 255 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 531, + 255 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 531, + 255 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 531, + 255 + ], + "type": "image", + "image_path": "796902e7231a12f01d3557494a96f641431b0f6660b865cb7d65b15a1d61483b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "lines": [ + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "spans": [ + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "text", + "content": "Figure 4. Pipeline of the proposed DiTCtrl. Note that initial latents are assumed to be 5 frames here. The first three frames are used to generate the contents of " + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "inline_equation", + "content": "P_{i-1}" + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "text", + "content": ", and the last three frames are used to generate contents of " + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "text", + "content": ". The pink latent represents the overlapping frame, while the blue and green latents are used to distinguish different prompt segments. Our method tries to synthesize content-consistent videos based on multi-prompts. The first video is synthesized with source text prompt " + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "inline_equation", + "content": "P_{i-1}" + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "text", + "content": ". During the denoising process for video synthesis, we convert the full-attention into masked-guided KV-sharing strategy to query video contents from source video " + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_{i-1}" + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "text", + "content": ", so that we can synthesize content-consistent video under the modified target prompt " + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 54, + 262, + 555, + 328 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 344, + 274, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 344, + 274, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 274, + 357 + ], + "type": "text", + "content": "tents information only from the object region in " + }, + { + "bbox": [ + 55, + 344, + 274, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_{i - 1}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 365, + 296, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 365, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 85, + 365, + 296, + 380 + ], + "type": "interline_equation", + "content": "f _ {o} ^ {l} = \\text {A t t e n t i o n} \\left(Q _ {i} ^ {l}, K _ {i - 1} ^ {l}, V _ {i - 1} ^ {l}; M _ {i - 1}\\right), \\tag {2}", + "image_path": "b543711ef01adb852b0956fc39b4de9daf7c8b603d61d235cb6edcdf792f3fd2.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 383, + 296, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 383, + 296, + 397 + ], + "spans": [ + { + "bbox": [ + 86, + 383, + 296, + 397 + ], + "type": "interline_equation", + "content": "f _ {b} ^ {l} = \\text {A t t e n t i o n} \\left(Q _ {i} ^ {l}, K _ {i - 1} ^ {l}, V _ {i - 1} ^ {l}; 1 - M _ {i - 1}\\right), \\tag {3}", + "image_path": "5c8bd591a324379d9a05f72233d0e55cb6665efa374c15d79190ddf686df4809.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 399, + 296, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 399, + 296, + 413 + ], + "spans": [ + { + "bbox": [ + 86, + 399, + 296, + 413 + ], + "type": "interline_equation", + "content": "\\bar {f} ^ {l} = f _ {o} ^ {l} * M _ {i} + f _ {b} ^ {l} * (1 - M _ {i}), \\tag {4}", + "image_path": "cbb973bae67b69d725dba735987a468765bf33df5488587d0b06e22413575f41.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 424, + 296, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 424, + 296, + 472 + ], + "spans": [ + { + "bbox": [ + 55, + 424, + 296, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 424, + 296, + 472 + ], + "type": "inline_equation", + "content": "\\bar{f}^l" + }, + { + "bbox": [ + 55, + 424, + 296, + 472 + ], + "type": "text", + "content": " is the final attention output. The object regions and the background regions in the current video query the content information from corresponding restricted areas rather than all the last video features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 481, + 264, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 481, + 264, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 481, + 264, + 495 + ], + "type": "text", + "content": "3.3. Latent Blending Strategy for Transition" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 499, + 296, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 499, + 296, + 570 + ], + "spans": [ + { + "bbox": [ + 55, + 499, + 296, + 570 + ], + "type": "text", + "content": "While our previous methods enable semantic consistency between adjacent video segments, achieving smooth transitions between different semantic segments still needs to be carefully designed. Thus, we propose a latent blending strategy to ensure temporal coherence across different semantic segments, inspired by recent works [5, 36, 49]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 571, + 296, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 571, + 296, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 571, + 296, + 666 + ], + "type": "text", + "content": "As illustrated in Fig. 5, our approach introduces overlapped regions between adjacent semantic video segments. For each frame position in the overlapped region, we apply a position-dependent weight function that follows a symmetric distribution, in which frames closer to their respective segments receive higher weights while those at the boundaries receive lower weights. This weighting scheme ensures smooth transitions between different semantic contexts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 67, + 668, + 293, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 668, + 293, + 679 + ], + "spans": [ + { + "bbox": [ + 67, + 668, + 293, + 679 + ], + "type": "text", + "content": "The blended latent feature " + }, + { + "bbox": [ + 67, + 668, + 293, + 679 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 67, + 668, + 293, + 679 + ], + "type": "text", + "content": " for frame " + }, + { + "bbox": [ + 67, + 668, + 293, + 679 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 67, + 668, + 293, + 679 + ], + "type": "text", + "content": " is calculated as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 126, + 689, + 296, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 689, + 296, + 717 + ], + "spans": [ + { + "bbox": [ + 126, + 689, + 296, + 717 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {t} = \\frac {\\sum_ {i = 1} ^ {n} w \\left(t _ {i}\\right) \\cdot \\mathbf {z} _ {t _ {i}}}{\\sum_ {i = 1} ^ {n} w \\left(t _ {i}\\right)}, \\tag {5}", + "image_path": "0028f2689e103a8ab7c172fb70c962b1ab9c4b1cbf03333a174f7a849e153178.jpg" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 317, + 342, + 552, + 411 + ], + "blocks": [ + { + "bbox": [ + 317, + 342, + 552, + 411 + ], + "lines": [ + { + "bbox": [ + 317, + 342, + 552, + 411 + ], + "spans": [ + { + "bbox": [ + 317, + 342, + 552, + 411 + ], + "type": "image", + "image_path": "c194410755933bea6aeff1591361f0de70d065b07164e912dbc75430f0043e6e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 419, + 554, + 441 + ], + "lines": [ + { + "bbox": [ + 313, + 419, + 554, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 554, + 441 + ], + "type": "text", + "content": "Figure 5. Latent blending strategy for video transition between video clips." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 338, + 460, + 555, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 460, + 555, + 488 + ], + "spans": [ + { + "bbox": [ + 338, + 460, + 555, + 488 + ], + "type": "interline_equation", + "content": "w \\left(t _ {i}\\right) = \\min \\left(\\frac {2 \\left(t _ {i} + 0 . 5\\right)}{T}, 2 - \\frac {2 \\left(t _ {i} + 0 . 5\\right)}{T}\\right), \\tag {6}", + "image_path": "6cb7af59b017b49e491287404dc5889cf29b19756f876734fd6ed5ad0c3de835.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t_i}" + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "text", + "content": " is latent feature corresponding to " + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "text", + "content": "-th frame in " + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "text", + "content": "-th latent segment, " + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "text", + "content": " is number of overlapped segments, " + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "text", + "content": " denotes the frames number of one latent segment and " + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "inline_equation", + "content": "w(t_{i})" + }, + { + "bbox": [ + 313, + 491, + 555, + 539 + ], + "type": "text", + "content": " is a position-dependent weight function." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 539, + 556, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 539, + 556, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 539, + 556, + 612 + ], + "type": "text", + "content": "To conclude, our approach employs the latent blending strategy and kv-sharing mechanism simultaneously during each denoising step. We process segment pairs sequentially, feeding them as one batch into the MM-DiT block for mask-guided kv-sharing (Fig. 4), then blend their denoised latents progressively (Fig. 5)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 621, + 395, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 621, + 395, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 621, + 395, + 635 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": "Setup. We implement DiTCtrl based on CogVideoX-2B [48], which is an open-source text-to-video diffusion model based on MM-DiT. In our experimental setup, we generate multiprompt conditioned videos, where each video clip is composed of 49 frames with a resolution of " + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "inline_equation", + "content": "480 \\times 720" + }, + { + "bbox": [ + 313, + 641, + 556, + 715 + ], + "type": "text", + "content": ". The sample step is configured to 50. The kv-sharing steps are set" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7767" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 70, + 526, + 317 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 526, + 317 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 526, + 317 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 526, + 317 + ], + "type": "image", + "image_path": "f92efa0a08f0c2c9f543c0857fb455bf123b6ece8235e438f1d9c79e2118d6ad.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 74, + 320, + 534, + 332 + ], + "lines": [ + { + "bbox": [ + 74, + 320, + 534, + 332 + ], + "spans": [ + { + "bbox": [ + 74, + 320, + 534, + 332 + ], + "type": "text", + "content": "Figure 6. Comparison of generation results across methods. Freenoise+DiT is our implementation of Freenoise on CogVideoX." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 342, + 297, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 342, + 297, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 297, + 498 + ], + "type": "text", + "content": "as [2,25], and the kv-sharing layers are specified as [25,30]. For latent sampling, the number of frames is set to 13, and the overlap size is set to 6 in our experiments. All these experiments are conducted on a single NVIDIA A100 GPU. Baselines. We mainly compare the proposed tuning-free method to current state-of-the-art multi-prompt video generation methods [36, 41, 43] and leading commercial solutions Kling [2]. Gen-L-Video, FreeNoise, and VideoInfinity are built upon the VideoCrafter2 [11] framework. To ensure a fair comparison of base models, we implement FreeNoise [36] as an enhanced baseline by directly incorporating their noise rescheduling strategy into the CogVideoX framework." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 505, + 133, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 133, + 516 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 133, + 516 + ], + "type": "text", + "content": "4.1. MPVBench" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "content": "MPVBench contains a diverse prompt dataset and a new metric customized for multi-prompt generation. Specifically, leveraging GPT-4, we produce 130 long-form prompts of 10 different transition modes. Then, for multi-prompt video generation, we observe that the distribution of the CLIP features differs between single-prompt and multi-prompt scenarios. As shown in Fig. 7, the feature points of real video (from DAVIS [34]) follow a continuous curve, while those of two concatenated isolated videos follow two continuous curves with a breakpoint in the middle. Since the common CLIP similarity calculates the average of neighborhood similarities, the difference between real video and isolated video only occurs at the breakpoint, which becomes very small when divided by the number of frames. To address this limitation, we propose CSCV (Clip Similarity Coefficient of Variation), a metric specifically designed to evaluate the" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 316, + 342, + 554, + 456 + ], + "blocks": [ + { + "bbox": [ + 316, + 342, + 554, + 456 + ], + "lines": [ + { + "bbox": [ + 316, + 342, + 554, + 456 + ], + "spans": [ + { + "bbox": [ + 316, + 342, + 554, + 456 + ], + "type": "image", + "image_path": "89d31997b80dbd44171f783ccc097540532c484391077051188dc8bd7ac4e8a9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 468, + 556, + 545 + ], + "lines": [ + { + "bbox": [ + 313, + 468, + 556, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 556, + 545 + ], + "type": "text", + "content": "Figure 7. t-SNE visualization of CLIP embeddings. Each point represents the CLIP embedding of a single video frame after dimensionality reduction. The visualization demonstrates that conventional multi-prompt videos form distinct clusters, while our method produces a more continuous distribution, indicating smoother semantic transitions. More details and discussions will be given in the supplementary." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 567, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 567, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 567, + 547, + 578 + ], + "type": "text", + "content": "transition smoothness of multi-prompt videos, defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 365, + 589, + 555, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 589, + 555, + 604 + ], + "spans": [ + { + "bbox": [ + 365, + 589, + 555, + 604 + ], + "type": "interline_equation", + "content": "s _ {i} = \\mathbf {x} _ {i} ^ {\\top} \\mathbf {x} _ {i + 1}, \\quad i = 1, \\dots , n - 1 \\tag {7}", + "image_path": "51e1cacef21f92574655384f81e8f0e8c4c911fec219982648ea53af5ebd6154.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 388, + 617, + 555, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 617, + 555, + 647 + ], + "spans": [ + { + "bbox": [ + 388, + 617, + 555, + 647 + ], + "type": "interline_equation", + "content": "\\operatorname {s c o r e} = \\frac {1}{1 + \\lambda \\cdot \\frac {\\sigma (s)}{\\mu (s)}}, \\tag {8}", + "image_path": "a00a45649d2861b8ad6a89247a3d2aca275ee756565b6bf9b9960c3f026825f9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "text", + "content": " denotes frame features, " + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "text", + "content": " are standard deviation and average respectively. The Coefficient of Variation " + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "inline_equation", + "content": "CV = \\sigma(s) / \\mu(s)" + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "text", + "content": " describes the degree of uniformity, which can largely punish the isolated situation. The function " + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\frac{1}{1 + \\lambda(\\cdot)}" + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "text", + "content": " projects the score to " + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "inline_equation", + "content": "[0, 1]" + }, + { + "bbox": [ + 313, + 651, + 556, + 714 + ], + "type": "text", + "content": ", the larger the better. We also re" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7768" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 296, + 166 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 296, + 166 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 296, + 166 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 296, + 166 + ], + "type": "table", + "html": "
    MethodCSCVMotion smoothnessText-Image similarity
    Gen-L-Video67.28%97.66%30.60%
    FreeNoise84.37%97.22%32.69%
    FreeNoise+DiT78.74%97.76%30.90%
    Video-Infinity74.97%97.31%32.35%
    DiTCtrl(w/o kv-sharing)81.79%97.35%31.37%
    DiTCtrl(Ours)84.90%97.80%30.68%
    ", + "image_path": "9bef15b71ff223a9b93f8252c8d8bc69238964a102f6df39f1daf1256a134ae9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 167, + 296, + 212 + ], + "lines": [ + { + "bbox": [ + 55, + 167, + 296, + 212 + ], + "spans": [ + { + "bbox": [ + 55, + 167, + 296, + 212 + ], + "type": "text", + "content": "Table 1. Evaluation metrics. Comparison of performance metrics for various video generation methods as benchmarked by MPVBench. Bold values represent the best performance within each group." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 232, + 295, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 232, + 295, + 293 + ], + "spans": [ + { + "bbox": [ + 54, + 232, + 295, + 293 + ], + "type": "text", + "content": "port the Text-Image similarity by using CLIP Similarity [20] to assess the alignment between given prompts and output video clips, and Motion smoothness from VBench [22] to evaluate whether the motion in the generated video is smooth, and follows the physical law of the real world." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 300, + 167, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 300, + 167, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 300, + 167, + 312 + ], + "type": "text", + "content": "4.2. Qualitative Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 317, + 296, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 317, + 296, + 593 + ], + "spans": [ + { + "bbox": [ + 56, + 317, + 296, + 593 + ], + "type": "text", + "content": "The qualitative comparison with previous multi-prompt video generation methods is shown in Fig. 6. Notably, when multiple prompts are consolidated into a single-prompt describing long-term temporal changes, the generated result by Kling [2] fails to capture semantic transitions effectively, where the sun remains present while no clouds appear, which does not align with the text. Gen-L-Video [43] suffers from severe temporal jittering, compromising overall video quality. Video-Infinity [41] and FreeNoise [36] both demonstrate successful scene-level semantic changes but lack physically plausible motion. For instance, in Fig. 6, vehicles appear to be in motion while remaining spatially fixed, which is a limitation inherent to their UNet base-model abilities. In contrast, FreeNoise+DiT leverages the DiT architecture's abilities to achieve more realistic object motion but struggles with semantic transitions, resulting in noticeable discontinuities between segments. Our DiTCtrl preserves the inherent capabilities of the pre-trained DiT model while addressing these limitations, enabling smooth semantic transitions and maintaining motion coherence throughout the video sequence. For a more comprehensive evaluation, we provide additional comparisons with extensive qualitative examples in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 600, + 174, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 600, + 174, + 612 + ], + "spans": [ + { + "bbox": [ + 55, + 600, + 174, + 612 + ], + "type": "text", + "content": "4.3.Quantitative Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 617, + 295, + 714 + ], + "type": "text", + "content": "We conduct the automatic evaluation with our MPVBench. From Table 1 one can see that our method achieves the highest CSCV score, demonstrating superior transition handling and overall stability in generation patterns. While FreeNoise ranks second with relatively strong stability, other methods significantly lag behind in this aspect, which is consistent with the t-SNE visualization of CLIP embedding as shown in Fig. 7. In terms of motion smoothness, our approach" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 315, + 71, + 552, + 155 + ], + "blocks": [ + { + "bbox": [ + 315, + 71, + 552, + 155 + ], + "lines": [ + { + "bbox": [ + 315, + 71, + 552, + 155 + ], + "spans": [ + { + "bbox": [ + 315, + 71, + 552, + 155 + ], + "type": "table", + "html": "
    MethodOverall preferenceMotion PatternTemporal ConsistencyText Alignment
    Gen-L-Video1.151.141.081.25
    FreeNoise3.022.902.993.08
    FreeNoise+DiT3.813.933.753.78
    Video-Infinity2.902.852.912.98
    DiTCtrl(Ours)4.114.174.263.91
    ", + "image_path": "f300ae9b33e298464df08c497df1305fe394b64e7c6a817648b3a30c776a1115.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 313, + 156, + 555, + 199 + ], + "lines": [ + { + "bbox": [ + 313, + 156, + 555, + 199 + ], + "spans": [ + { + "bbox": [ + 313, + 156, + 555, + 199 + ], + "type": "text", + "content": "Table 2. User study. Human evaluation of different video generation methods across multiple aspects. Scores range from 1 to 5, with higher scores indicating better performance. Bold values represent the best performance within each metric." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 220, + 555, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 220, + 555, + 291 + ], + "spans": [ + { + "bbox": [ + 313, + 220, + 555, + 291 + ], + "type": "text", + "content": "exhibits superior performance in motion quality and consistency. Regarding Text-Image Similarity metrics, although FreeNoise and Video-Infinity achieve higher scores, this can be attributed to our method's kv-sharing mechanism, where subsequent video segments inherently learn from preceding semantic content." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 293, + 556, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 556, + 376 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 556, + 376 + ], + "type": "text", + "content": "As shown in Fig. 6, our design choice allows the road surface to gradually transition to snowy conditions while retaining features from the previous scene. Despite potentially lower text-image alignment scores, it ensures superior semantic continuity in the sequences. In practice, this trade-off doesn't negatively impact the visual quality in multi-prompt scenarios, as demonstrated by our user study in Table 2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 384, + 425, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 425, + 395 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 425, + 395 + ], + "type": "text", + "content": "4.4. Human Evaluation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 401, + 556, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 401, + 556, + 570 + ], + "spans": [ + { + "bbox": [ + 313, + 401, + 556, + 570 + ], + "type": "text", + "content": "We invited 28 users to evaluate five models: GenL-Video [43], Video-Infinity [41], FreeNoise [36], FreeNoise+DiT and our method. We employ a Forced Ranking Scale, where items are ranked from 1 to 5, with the highest rank receiving a score of 5 and the lowest rank receiving a score of 1. Participants score each method considering overall preference, motion pattern, temporal consistency and text alignment over 16 videos generated by different scenarios. As clearly indicated in Table 2, generated videos from our method significantly outperform other state-of-the-art approaches in all four criteria, demonstrating superior capability in producing videos with natural semantic transitions that better align with human preferences for visual coherence and continuity." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 576, + 424, + 589 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 576, + 424, + 589 + ], + "spans": [ + { + "bbox": [ + 313, + 576, + 424, + 589 + ], + "type": "text", + "content": "4.5. More Applications" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 594, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 676 + ], + "type": "text", + "content": "Single-prompt Longer Video Generation. Our method can naturally work on single-prompt longer video generation. As illustrated in Fig. 8, using the prompt \"A white SUV drives on a steep dirt road\", our approach successfully generates videos that are more than 12 times longer than the original length, while maintaining consistent motion patterns and environmental coherence." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "Video Editing. We show how we use our methods to achieve video editing performance (\"word swap\" and \"reweight\") in Fig. 9." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7769" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 69, + 104, + 134 + ], + "blocks": [ + { + "bbox": [ + 57, + 69, + 104, + 134 + ], + "lines": [ + { + "bbox": [ + 57, + 69, + 104, + 134 + ], + "spans": [ + { + "bbox": [ + 57, + 69, + 104, + 134 + ], + "type": "image", + "image_path": "81a3fe89a97e2cdbe66f920f0bff4c0ca52b3c53a799846742bbc7efe7b3353a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 136, + 286, + 147 + ], + "lines": [ + { + "bbox": [ + 65, + 136, + 286, + 147 + ], + "spans": [ + { + "bbox": [ + 65, + 136, + 286, + 147 + ], + "type": "text", + "content": "Figure 8. 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Video editing example." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 350, + 295, + 493 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 55, + 350, + 295, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 350, + 295, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 295, + 433 + ], + "type": "text", + "content": "- Word Swap: removing our latent blending strategy of our approach DiTCtrl, we can achieve the video editing performance of Word Swap. Specifically, we just use masked-guided KV-sharing strategy to share keys and values from source prompt " + }, + { + "bbox": [ + 55, + 350, + 295, + 433 + ], + "type": "inline_equation", + "content": "P_{source}" + }, + { + "bbox": [ + 55, + 350, + 295, + 433 + ], + "type": "text", + "content": " branch, so that we can synthesize a new video to preserve the original composition while also addressing the content of the new prompt " + }, + { + "bbox": [ + 55, + 350, + 295, + 433 + ], + "type": "inline_equation", + "content": "P_{target}" + }, + { + "bbox": [ + 55, + 350, + 295, + 433 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 434, + 295, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 295, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 295, + 493 + ], + "type": "text", + "content": "- Reweight: Similar to prompt-to-prompt [19], through reweighting the specific columns and rows corresponding to specified token (e.g. \"pink\") in the MM-DiT's Text-Video attention and Video-Text attention, we can also achieve the video editing performance of reweight." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 503, + 149, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 503, + 149, + 516 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 149, + 516 + ], + "type": "text", + "content": "4.6. Ablation Study" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 54, + 521, + 297, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 521, + 297, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 521, + 297, + 713 + ], + "type": "text", + "content": "We conducted ablation studies to validate the effectiveness of DiTCtrl's key components: latent blending strategy, KV-sharing mechanism, and mask-guided generation as shown in Fig. 10. The first row shows results that directly using text-to-video models results in abrupt scene changes and disconnected motion patterns, failing to maintain continuity in the athlete's movements from surfing to skiing. The second row demonstrates that DiTCtrl without the latent blending strategy achieves basic video editing capabilities but lacks smooth transitions between scenes. Without KV-sharing (third row), DiTCtrl exhibits unstable environmental transitions and significant motion artifacts, with inconsistent character scaling and deformed movements. Moreover, DiTCtrl without mask guidance (fourth row) improves motion coherence and transitions but struggles with object attribute confusion across different prompts and environments." + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 316, + 70, + 553, + 234 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 553, + 234 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 553, + 234 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 553, + 234 + ], + "type": "image", + "image_path": "597c2d48425f4096644bc7849d3f9b79ef7631bdd4ec7fcf7a8538a8e8022268.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 239, + 546, + 251 + ], + "lines": [ + { + "bbox": [ + 321, + 239, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 321, + 239, + 546, + 251 + ], + "type": "text", + "content": "Figure 10. Visualization of ablation component in DiTCtrl." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 267, + 555, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 267, + 555, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 267, + 555, + 350 + ], + "type": "text", + "content": "On the other hand, The full DiTCtrl implementation provides the most precise control over generated content, demonstrating superior object consistency and smoother transitions between prompts while maintaining desired motion patterns. These results validate our analysis of MM-DiT's attention mechanism and its role in enabling accurate semantic control." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 314, + 361, + 388, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 361, + 388, + 374 + ], + "spans": [ + { + "bbox": [ + 314, + 361, + 388, + 374 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 382, + 556, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 382, + 556, + 525 + ], + "spans": [ + { + "bbox": [ + 313, + 382, + 556, + 525 + ], + "type": "text", + "content": "In this paper, we introduce DiTCtrl, a novel, tuning-free method for multi-prompt video generation using the MM-DiT architecture. Our pioneering analysis of MM-DiT's attention mechanism reveals similarities with the cross/self-attention blocks in UNet-like diffusion models, enabling mask-guided semantic control across prompts. With mask-guided kv-sharing mechanism and latent blending strategy, DiTCtrl ensures smooth transitions and consistent object motion between semantic segments, without extra training. We also present MPVBench, a new benchmark with diverse transition types and specialized metrics for assessing multi-prompt transitions." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 525, + 556, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 525, + 556, + 657 + ], + "spans": [ + { + "bbox": [ + 313, + 525, + 556, + 657 + ], + "type": "text", + "content": "Limitation & Future Work. While our method demonstrates state-of-the-art performance, there remain two primary limitations. First, compared to image generation models, current open-source video generation models exhibit relatively weaker conceptual composition capabilities, occasionally resulting in attribute binding errors across different semantic segments. Second, the computational overhead of DiT-based architectures presents challenges for inference speed. These limitations suggest promising directions for future research in enhancing semantic understanding and architectural efficiency." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 657, + 555, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 657, + 555, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 657, + 555, + 705 + ], + "type": "text", + "content": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (Grant No. 62306261), and The Shun Hing Institute of Advanced Engineering (SHIAE) Grant (No. 8115074)." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7770" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 704 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 112 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 112 + ], + "type": "text", + "content": "[1] Gen-3. https://runwayml.com/research/introducing-gen-3-alpha,,2024.1" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 113, + 296, + 132 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 113, + 296, + 132 + ], + "spans": [ + { + "bbox": [ + 62, + 113, + 296, + 132 + ], + "type": "text", + "content": "[2] Kling. https://kling.kuaishou.com/en, 2024.1, 6.7" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 133, + 296, + 176 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 133, + 296, + 176 + ], + "spans": [ + { + "bbox": [ + 62, + 133, + 296, + 176 + ], + "type": "text", + "content": "[3] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Magicvideo: Efficient video generation with latent diffusion models. arXiv preprint arXiv:2211.11018, 2022. 1" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7772" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_content_list.json b/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..141f60e846a92fcd5dee070e8a1d0f4254277a83 --- /dev/null +++ b/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_content_list.json @@ -0,0 +1,1812 @@ +[ + { + "type": "text", + "text": "Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution", + "text_level": 1, + "bbox": [ + 215, + 130, + 782, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xingyuan Li $^{1\\dagger}$ , Zirui Wang $^{1\\dagger}$ , Yang Zou $^{2}$ , Zhixin Chen $^{3}$ , Jun Ma $^{1}$ , Zhiying Jiang $^{4}$ , Long Ma $^{1}$ , Jinyuan Liu $^{1*}$", + "bbox": [ + 243, + 200, + 750, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Software Technology & DUT-RU International School of ISE, Dalian University of Technology", + "bbox": [ + 181, + 241, + 815, + 256 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "$^{2}$ School of Computer Science, Northwestern Polytechnical University", + "3Graduate School of Information, Production, and Systems, Waseda University", + "4 College of Information Science and Technology, Dalian Maritime University xingyuan_lxy@163.com atlantis918@hotmail.com" + ], + "bbox": [ + 264, + 257, + 730, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/22532a8bf8e4e5ba7b73d8e9c93f6c3aa6f7bdfc4abdf73373234aec849328cf.jpg", + "image_caption": [ + "Figure 1. The left side shows a comparison between existing super-resolution methods and our proposed DiffISR. Our method introduces additional visual guidance based on the Fourier Transform, as well as foundational model-based perception guidance. The right side demonstrates that our method outperforms other methods in both detection and segmentation tasks." + ], + "image_footnote": [], + "bbox": [ + 93, + 349, + 906, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 589, + 326, + 606 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Infrared imaging is essential for autonomous driving and robotic operations as a supportive modality due to its reliable performance in challenging environments. Despite its popularity, the limitations of infrared cameras, such as low spatial resolution and complex degradations, consistently challenge imaging quality and subsequent visual tasks. Hence, infrared image super-resolution (IISR) has been developed to address this challenge. While recent developments in diffusion models have greatly advanced this field, current methods to solve it either ignore the unique modal characteristics of infrared imaging or overlook the machine perception requirements. To bridge these gaps, we propose DifIISR, an infrared image super-resolution diffusion model optimized for visual quality and perceptual performance. Our approach achieves task-based guidance for diffusion by injecting gradients derived from visual and", + "bbox": [ + 86, + 636, + 485, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "perceptual priors into the noise during the reverse process. Specifically, we introduce an infrared thermal spectrum distribution regulation to preserve visual fidelity, ensuring that the reconstructed infrared images closely align with high-resolution images by matching their frequency components. Subsequently, we incorporate various visual foundational models as the perceptual guidance for downstream visual tasks, infusing generalizable perceptual features beneficial for detection and segmentation. As a result, our approach gains superior visual results while attaining State-Of-The-Art downstream task performance. Code is available at https://github.com/zirui0625/DifIISR", + "bbox": [ + 511, + 592, + 908, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 799, + 645, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The objective of infrared image super-resolution (IISR) is to reconstruct a high-resolution (HR) infrared image from its low-resolution (LR) counterpart [51]. The consistent performance of infrared imaging under challenging conditions allows its application to span various fields [31, 44, 45],", + "bbox": [ + 511, + 824, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Equal contribution. *Corresponding author.", + "bbox": [ + 114, + 886, + 357, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7534", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "such as object detection [28, 40, 41], semantic segmentation [24, 30], and autonomous driving [2, 42]. Despite its great potential, the inherent limitations of infrared cameras — such as high noise levels, reduced spatial resolution, and limited dynamic range — continually affect the quality of infrared images.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conventionally, CNN-based methods [18, 33, 61-63] address this challenge by mapping interpolated LR images to HR images and then enhancing the details (e.g., SR-CNN [35]). Although CNN-based super-resolution methods have significantly advanced this field, they are limited by the perceptual field of local convolution operations. To overcome this, Transformer-based methods [3, 4, 56, 60] model long-range dependencies to capture global context. Liang et al. [26] proposed SwinIR significantly improving super-resolution performance by integrating CNNs with the Swin Transformer. Lately, Li et al. [25] proposed CoRPLE, which leverages a Contourlet residual framework to restore infrared-specific high-frequency features.", + "bbox": [ + 89, + 184, + 482, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, the diffusion model has introduced a novel paradigm for image super-resolution tasks, offering a fresh approach that goes beyond the CNN- and Transformer-based methods [11], leveraging its capacity to learn implicit priors of the underlying data distribution [39]. Yue et al. proposed ResShift [55], which applies an iterative sampling procedure to shift the residual between the LR and the desired HR image during inference. Unlike other diffusion models, Wang et al. [49] accelerate the diffusion-based SR model to a single inference step while maintaining satisfactory performance. These methods generally achieve visually pleasing results when applied to visible images.", + "bbox": [ + 89, + 383, + 482, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, existing methods often fail to extend effectively to infrared imaging, particularly in downstream tasks such as infrared image object detection and semantic segmentation. A common approach for task-oriented infrared image super-resolution is to adapt an RGB super-resolution model to infrared data, and then connect it to a downstream detection or segmentation module. Unfortunately, this approach faces two significant challenges: 1) Ignoring the unique modal characteristics of infrared imaging, which include distinct thermal spectrum distributions. Infrared image reconstruction quality is particularly sensitive to high-frequency components due to longer wavelengths and reduced atmospheric scattering effects. 2) Overlooking the machine perception requirements. While the model may reconstruct visually appealing images, these results are often sub-optimal for specific perceptual tasks. The objectives of visual domain optimization and perceptual domain optimization can differ significantly [28]. For instance, diffusion-based super-resolution models typically focus on \"seeking visually appealing\" results, often at the expense of structural information of targets and textural details critical for machine vision. Given these limitations, we ask, \"Why", + "bbox": [ + 89, + 569, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "not develop a super-resolution model that reconstructs infrared images to be both visually appealing and perceptually salient?\"", + "bbox": [ + 511, + 90, + 903, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, as shown in figure 1, we propose a task-oriented infrared image super-resolution method that optimizes the diffusion process through gradient-based guidance. Specifically, we inject the gradient of a designed prior loss into the noise estimation at each training step, refining the model's performance across iterations. Our guidance consists of two components. First, to ensure visual consistency, we introduce visual guidance via infrared thermal spectral distribution modulation, which ensures the reconstructed images align with high-resolution counterparts by preserving their spectral characteristics. Second, we integrate perceptual guidance by leveraging powerful pretrained vision models, such as VGG [37] and SAM [22], to infuse the diffusion process with generalized perceptual features. Extensive experiments demonstrate that our proposed method excels in both visual quality and downstream task performance. Our contributions can be summarized as follows:", + "bbox": [ + 511, + 137, + 906, + 407 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a solution for infrared image super-resolution by integrating gradient-based priors into the noise during diffusion, enabling task-based guidance in sampling, and achieving simultaneous optimization in both visual and perceptual-specific domains.", + "- We introduce a thermal spectrum distribution regulation to preserve the visual fidelity of infrared images, guiding the diffusion process to learn the unique infrared image frequency distribution.", + "- We propose perceptual guidance for the diffusion process, incorporating generalizable perceptual features from foundational models for visual tasks. This notably enhances performance in detection and segmentation." + ], + "bbox": [ + 513, + 412, + 903, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 513, + 625, + 651, + 640 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image Super-Resolution", + "text_level": 1, + "bbox": [ + 513, + 650, + 736, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since the pioneering work of SRCNN [13] was proposed, deep learning has gradually become the mainstream approach for image super-resolution (SR). The initial works [13, 21, 23, 63] mainly focused on utilizing convolutional neural networks (CNNs) [12] for image super-resolution tasks and optimizing the network by minimizing the mean square error (MSE) between the super-resolved image (SR) and their corresponding high-resolution (HR) counterparts. Subsequently, GAN-based super-resolution methods were proposed, drawing significant attention. For example, both BSRGAN [57] and Real-ESRGAN [48] employ GANs for super-resolution tasks and introduce training samples with more realistic types of degradations to achieve better results. While these methods improve the quality of the low-resolution images, they often fail to produce stable", + "bbox": [ + 511, + 674, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7535", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "outcomes, resulting in artifacts in the images. LDL [27] and DeSRA [53] attempt to address this issue, but they still struggle to generate images with natural details. Recently, diffusion models have been widely applied to image super-resolution tasks, such as ResShift [55] and SinSR [49]. However, these methods are not designed specifically for the characteristics of infrared images and overlook the requirements of machine perception [64], so they do not perform well in infrared image super-resolution (IISR).", + "bbox": [ + 89, + 90, + 483, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Diffusion Methods", + "text_level": 1, + "bbox": [ + 89, + 234, + 269, + 250 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Diffusion Denoising Probabilistic Model (DDPM) [16] is a generative model with stability and controllability. Since it was proposed, it has attracted widespread attention. The main focus of the diffusion model is to train a denoising autoencoder, which estimates the reverse process of the Markov diffusion process by predicting the noise. Diffusion models were initially applied to image generation tasks and have been continuously improved in recent years [1, 32, 34, 38, 39]. ControlNet [58] introduces control conditions into pre-trained diffusion models, expanding the application scope of diffusion models in image generation. DDIM [38] proposes a non-Markovian generation method, significantly enhancing the inference speed of diffusion models. Diffusion models have demonstrated exceptional capabilities not only in image generation tasks but also in various other tasks, showing great potential. With the introduction of several related methods [8, 9, 19, 36, 49, 55], diffusion models have also been validated to achieve remarkable results in the field of image super-resolution.", + "bbox": [ + 89, + 258, + 483, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 559, + 228, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first introduce the background of Denoising Diffusion Probabilistic Models [16]. DDPM obtains samples $x_0 \\sim p_{\\mathrm{data}}(x)$ from the data distribution. In a diffusion model, noise is gradually added to the sampled $x_0$ over time steps up to $T$ , eventually resulting in $x_T \\sim \\mathcal{N}(0, \\mathbf{I})$ , which can be approximated as a standard Gaussian distribution. This process is also referred to as the forward process of the diffusion model, and it can be represented as:", + "bbox": [ + 89, + 584, + 483, + 705 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {0}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 715, + 482, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = \\prod_{s = 1}^{t}(1 - \\beta_{s})$ , and $\\beta_{s}$ are fixed or learned variance schedule. After obtaining $x_{T}$ , the denoising model $\\epsilon_{\\phi}$ learns to predict the noise $\\epsilon$ added during the forward process, thereby removing the noise from $x_{T}$ . Specifically, the denoising model $\\epsilon_{\\phi}$ predicts the noise by optimizing the re-weighted evidence lower bound, which can be written as:", + "bbox": [ + 89, + 741, + 483, + 833 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s i m p l e}} (\\phi) = \\mathbb {E} _ {x _ {0}, t, \\epsilon} \\left[ \\| \\epsilon_ {\\phi} (x _ {t}, t) - \\epsilon \\| ^ {2} \\right]. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 842, + 482, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this formula, $\\epsilon_{\\phi}(x_t,t)$ represents the noise predicted by the model, and $t$ is randomly sampled from a predefined", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "range of time steps. During the training process, the denoising model $\\epsilon_{\\phi}$ is optimized by minimizing $\\mathcal{L}_{\\mathrm{simple}}(\\phi)$ , ultimately resulting in a model capable of accurately predicting the noise.", + "bbox": [ + 511, + 90, + 905, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After training the denoising model $\\epsilon_{\\phi}$ , we sample $x_{T} \\sim \\mathcal{N}(0, \\mathbf{I})$ and iteratively refine it using the denoising model. This process is also known as the reverse process, and the specific formula can be represented as:", + "bbox": [ + 511, + 152, + 906, + 212 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, t\\right), \\Sigma_ {\\theta} \\left(x _ {t}, t\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 224, + 906, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mu_{\\theta}(x_t,t)$ is the mean function from step $t$ to $t - 1$ and $\\Sigma_{\\theta}(x_t,t)$ is the covariance. Due to the slow sampling process of DDPM, DDIM proposes using a non-Markovian diffusion process, which significantly improves the model's sampling speed. The improved sampling formula can be expressed as:", + "bbox": [ + 511, + 253, + 905, + 344 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\hat {x} _ {0} \\left(x _ {t}\\right) + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\phi} \\left(x _ {t}, t\\right) + \\sigma_ {t} z, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 357, + 903, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sigma_{t}$ is the variance of the noise and $z$ follows a standard normal distribution. $\\hat{x}_0(x_t)$ is the predicted $x_0$ from $x_{t}$ , and the prediction formula is:", + "bbox": [ + 511, + 395, + 905, + 439 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} _ {0} (x _ {t}) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\phi} (x _ {t}, t)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 450, + 905, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When $\\sigma_{t}$ equals 0, it is evident that the DDIM sampling process can be regarded as a deterministic process, which allows for quick sampling results from the noise.", + "bbox": [ + 511, + 494, + 905, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 513, + 553, + 604, + 569 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. Our main objective is to address the problem of infrared image super-resolution using a diffusion model enhanced by gradient-based guidance, as shown in figure 2. Specifically, inspired by [10], we propose a method that fine-tunes the diffusion model by introducing an additional guidance mechanism. In addition, we incorporate a dual optimization approach combining visual and perceptual aspects to better adapt the diffusion model to the task of infrared image super-resolution.", + "bbox": [ + 511, + 579, + 906, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Loss-gradient Guidance", + "text_level": 1, + "bbox": [ + 511, + 726, + 735, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The reverse process of diffusion models often requires multiple constraints to generate stable, high-quality images. Most methods tend to guide the reverse process by adding weighted constraints to the final loss function. In contrast, our approach addresses this issue from the perspective of posterior sampling. Inspired by [10], we introduce additional priors and compute the gradient of the resulting loss function, injecting the gradient into the noise estimated at each step to better handle the problem of adding constraints during the reverse process of diffusion models.", + "bbox": [ + 511, + 750, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7536", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/379c92573d6032ebc81cd95d1d50b9894f923708399b96abac0e47c30f807258.jpg", + "image_caption": [ + "Figure 2. Overall architecture of our proposed method: the vanilla super-resolution diffusion process is marked in black, whereas our proposed additional visual and perceptual priors are marked in red." + ], + "image_footnote": [], + "bbox": [ + 91, + 85, + 903, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generally, the noise predicted by the denoising model at timestep $t$ is often correlated with the score of the denoising model at the current timestep [39]. Specifically, it can be represented as:", + "bbox": [ + 89, + 402, + 483, + 463 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {\\phi} \\left(x _ {t}, t\\right) = - \\sqrt {1 - \\alpha_ {t}} \\nabla_ {x _ {t}} \\log p \\left(x _ {t}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 478, + 482, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\nabla_{x_t}\\log p(x_t)$ is the gradient of $x_{t}$ with respect to the probability density function $\\log p(x_{t})$ , but now we need to consider not only $\\nabla_{x_t}\\log p(x_t)$ , we also need to incorporate optimization of $g$ during the diffusion model sampling. In our work, $g$ represents the guidance obtained by feeding $x_0$ into $\\mathcal{M}$ , and $\\mathcal{M}$ is a forward operator. The relationship between $g$ and $x_0$ can be expressed as $g = \\mathcal{M}(x_0)$ . Therefore, the score of the denoising model at timestep $t$ becomes $\\nabla_{x_t}\\log p(x_t\\mid g)$ .", + "bbox": [ + 89, + 510, + 483, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\nabla_{x_t}\\log p(x_t\\mid g)$ is unknown, and we need to use the known $\\nabla_{x_t}\\log p(x_t)$ to derive $\\nabla_{x_t}\\log p(x_t\\mid g)$ . According to Bayes' theorem, we can write:", + "bbox": [ + 89, + 648, + 483, + 694 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {x _ {t}} \\log p (x _ {t} \\mid g) = \\nabla_ {x _ {t}} \\log p (x _ {t}) + \\nabla_ {x _ {t}} \\log p (g \\mid x _ {t}). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 709, + 482, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From this, it can be seen that $\\nabla_{x_t}\\log p(x_t)$ is known, and the problem changes from calculating $\\nabla_{x_t}\\log p(x_t\\mid g)$ to calculating $\\nabla_{x_t}\\log p(g\\mid x_t)$ . Inspired by [10], we can derive the formula:", + "bbox": [ + 89, + 739, + 483, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {x _ {t}} \\log p (g \\mid x _ {t}) \\simeq \\nabla_ {x _ {t}} \\log p (g \\mid \\hat {x} _ {0} (x _ {t})) \\tag {8} \\\\ \\simeq - \\rho \\nabla_ {x _ {t}} \\| g - \\mathcal {M} (\\hat {x} _ {0} (x _ {t})) \\| _ {2} ^ {2}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 813, + 482, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\nabla_{x_t}\\| g - \\mathcal{M}(\\hat{x}_0(x_t))\\| _2^2$ also can be represented as $\\nabla \\mathcal{L}_g$ . Therefore, we can express the noise prediction ad", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "justed according to condition $g$ as:", + "bbox": [ + 511, + 402, + 743, + 417 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\epsilon_ {\\phi} ^ {\\prime} = \\epsilon_ {\\phi} \\left(x _ {t}, t\\right) + \\rho \\sqrt {1 - \\alpha_ {t}} \\nabla_ {x _ {t}} \\| g - \\mathcal {M} \\left(\\hat {x} _ {0} \\left(x _ {t}\\right)\\right) \\| _ {2} ^ {2} \\tag {9} \\\\ = \\epsilon_ {\\phi} (x _ {t}, t) + \\rho \\sqrt {1 - \\alpha_ {t}} \\nabla \\mathcal {L} _ {g}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 428, + 903, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\phi}^{\\prime}$ represents the adjusted noise, obtained by adding the gradient of the guidance loss $\\nabla \\mathcal{L}_g$ to the noise predicted by the original denoising model.", + "bbox": [ + 511, + 479, + 903, + 525 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, by applying gradient guidance to the noise predicted by the diffusion model, we impose constraints on the reverse process of the diffusion model. More detailed derivations and pseudocode of our method can be found in the supplementary materials.", + "bbox": [ + 511, + 526, + 905, + 601 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Visual-perceptual Dual Optimization", + "text_level": 1, + "bbox": [ + 511, + 609, + 833, + 627 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now, let's explain the composition of our guidance $\\mathcal{L}_g$ in detail. Specifically, $\\mathcal{L}_g$ can be divided into two parts: visual loss $\\mathcal{L}_{\\mathrm{visual}}$ and perceptual loss $\\mathcal{L}_{\\mathrm{perceptual}}$ .", + "bbox": [ + 511, + 633, + 905, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\nu$ - visual guidance. To guide the diffusion process in reconstructing infrared images towards infrared-specific visual characteristics, we propose $\\mathcal{L}_{\\mathrm{visual}}$ to regularize the distribution of high- and low-frequency information as visual guidance $\\nu$ . Here, $\\nu$ replaces the forward operator $\\mathcal{M}$ in equation 8. Given the HR image $\\mathbf{I}_{HR}$ and the super-resolved image $\\mathbf{I}_{SR}$ , we first use Fast Fourier Transforms (FFT) to transform their spatial domain representation into the frequency domain, formally:", + "bbox": [ + 511, + 680, + 905, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\mathbf {I}} _ {H R} = \\mathcal {F} (\\mathbf {I} _ {H R}), \\hat {\\mathbf {I}} _ {S R} = \\mathcal {F} (\\mathbf {I} _ {S R}), \\\\ \\mathcal {F} (u, v) = \\sum_ {x = 0} ^ {H - 1} \\sum_ {y = 0} ^ {W - 1} I (x, y) \\cdot e ^ {- i \\frac {2 \\pi}{H} u x} \\cdot e ^ {- i \\frac {2 \\pi}{W} v y}. \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 839, + 903, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7537", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{F}(u,v)$ denotes the FFT of the image at frequency coordinates $(u,v)$ , and $\\hat{\\mathbf{I}}_{HR}$ is the transformed HR images. In the frequency domain, we first shift the zero-frequency component, which represents the mean intensity of the image, to the center of the spectrum for both HR and SR images, yielding $\\hat{\\mathbf{I}}_{HR}^{\\mathrm{shift}}$ and $\\hat{\\mathbf{I}}_{SR}^{\\mathrm{shift}}$ . Following this, we compute the magnitude spectra $\\mathbf{M}_{HR}$ and $\\mathbf{M}_{SR}$ by applying logarithmic compression to the Fourier-transformed images. This step ensures a balanced consideration of both high-frequency and low-frequency components during comparison. To focus the loss on matching the frequency distribution patterns rather than absolute intensity differences, we normalize the magnitude spectra to have zero mean and unit variance, resulting in the normalized spectra $\\mathbf{M}_{HR}^{\\mathrm{norm}}$ and $\\mathbf{M}_{SR}^{\\mathrm{norm}}$ . Finally, the Visual Loss $\\mathcal{L}_{\\mathrm{visual}}$ is computed as the mean squared error between the normalized magnitude spectra of the HR and SR images:", + "bbox": [ + 89, + 90, + 483, + 349 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {v i s u a l}} = \\left(\\overbrace {N \\left(\\log \\left(1 + | \\hat {\\mathbf {I}} _ {H R} ^ {\\text {n o r m}} |\\right)\\right)} ^ {\\mathrm {M} _ {H R} ^ {\\text {n o r m}}} - \\overbrace {N \\left(\\log \\left(1 + | \\hat {\\mathbf {I}} _ {S R} ^ {\\text {n o r m}} |\\right)\\right)} ^ {\\mathrm {M} _ {S R} ^ {\\text {n o r m}}}\\right) ^ {2}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 349, + 483, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N(\\cdot)$ represents the normalization operation. Visual Loss plays a critical role in preserving the frequency distribution of the infrared image.", + "bbox": [ + 89, + 409, + 483, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal{P}$ - perceptual guidance. Large models provide many priors for current methods [14, 15], to regularize the diffusion process to better align with machine perception, we adopt $\\mathcal{L}_{\\mathrm{perceptual}}$ that consists of the VGG Loss $\\mathcal{L}_{\\mathrm{VGG}}$ and the Segmentation Loss $\\mathcal{L}_{\\mathrm{seg}}$ as perceptual guidance $\\mathcal{P}$ . Here, $\\mathcal{P}$ replaces the forward operator $\\mathcal{M}$ in equation 8. Given the HR image $\\mathbf{I}_{HR}$ and the super-resolved image $\\mathbf{I}_{SR}$ , the VGG Loss is computed by mean squared error between the extracted features of the HR and SR images from a pretrained deep neural network. This guides the model to capture nuanced aspects of images, including textures, edges, and shapes, which are crucial for preserving visual fidelity. To enhance the semantic fidelity of the reconstructed images, we regulate the diffusion process using the Segment Anything Model (SAM) [22] and propose the Segmentation Loss $\\mathcal{L}_{\\mathrm{seg}}$ . Given the HR image $\\mathbf{I}_{HR}$ and the super-resolved image $\\mathbf{I}_{SR}$ , we use a locked SAM to segment the masks $\\mathbf{S}_{HR}$ and $\\mathbf{S}_{SR}$ for $\\mathbf{I}_{HR}$ and $\\mathbf{I}_{SR}$ , respectively. The Segmentation Loss $\\mathcal{L}_{\\mathrm{seg}}$ is then computed by mean squared error between $\\mathbf{S}_{HR}$ and $\\mathbf{S}_{SR}$ , providing effective high-level supervision for the reconstructed images.", + "bbox": [ + 89, + 455, + 483, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Perceptual Loss $\\mathcal{L}_{\\mathrm{perceptual}}$ is computed by integrating the VGG-based and segmentation-based losses, as:", + "bbox": [ + 89, + 772, + 482, + 801 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p e r c e p t u a l}} = \\overbrace {\\left\\| \\phi_ {l} \\left(\\mathbf {I} _ {H R}\\right) - \\phi_ {l} \\left(\\mathbf {I} _ {S R}\\right) \\right\\| _ {2} ^ {2}} ^ {\\mathcal {L} _ {\\mathrm {V G G}}} + \\overbrace {\\left\\| \\mathbf {S} _ {H R} - \\mathbf {S} _ {S R} \\right\\| _ {2} ^ {2}} ^ {\\mathcal {L} _ {\\mathrm {s e g}}}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 803, + 480, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi_l(\\cdot)$ represents the feature map extracted from the $l$ -th layer of a pre-trained deep neural network (in our experiment, VGG-16).", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The incorporation of visual and perceptual guidance refines each iteration of the diffusion, facilitating a more optimized denoising procedure. This not only improves visual fidelity but also enhances perceptual performance.", + "bbox": [ + 511, + 90, + 906, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 166, + 645, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 513, + 191, + 720, + 208 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset and evaluation metrics. To ensure the fairness of the experiment, we used the same training [28] and test sets [28, 43, 54], as CoRPLE [25]. We use the infrared image dataset $\\mathrm{M}^3\\mathrm{FD}$ [28] to train the model and evaluate its performance using three datasets: $\\mathrm{M}^3\\mathrm{FD}$ [28], RoadScene [54], and TNO [43]. We adopt five metrics to evaluate the performance of our model quantitatively: CLIP-IQA [46], MUSIQ [20], PSNR, LPIPS [59], and SSIM [50]. Among them, CLIPIQA and MUSIQ are no-reference metrics. CLIPIQA leverages the CLIP model [35] to assess image quality, while MUSIQ uses a multi-scale feature extraction approach for quality evaluation. We mainly rely on CLIPIQA and MUSIQ as evaluation metrics to compare the performance of different methods.", + "bbox": [ + 511, + 215, + 906, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Our network was trained on a GeForce RTX 4090 GPU. Our backbone model and specific experimental parameter settings largely follow ResShift [55]. Notably, ResShift uses the residual between high-resolution (HR) and low-resolution images (LR) as the noise for the diffusion model, meaning that we can effectively apply gradient guidance on the residual between HR and LR images. During training, our approach differs from ResShift in that we initially perform 200K iterations on a new training set to enable the model to develop basic infrared image super-resolution capabilities. Subsequently, we incorporate conditional (visual and perceptual) guidance into the model and conduct an additional 50K training iterations to achieve improved results.", + "bbox": [ + 511, + 428, + 908, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Experiments on Infrared SR", + "text_level": 1, + "bbox": [ + 513, + 648, + 769, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform a comprehensive comparison of our approach with eleven SOTA methods, including ESRGAN [47], RealSR-JPEG [17], BSRGAN [57], SwinIR [26], RealESRGAN [48], HAT [5], DAT [6], ResShift [55], CoPRLE [25], Bi-DiffSR [7] and SinSR [49]. Table 1, 2 presents our quantitative comparison results compared with the above methods and Figure 3 presents our qualitative results.", + "bbox": [ + 511, + 672, + 906, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative Comparison. Table 1 presents a quantitative comparison of CLIPIQA and MUSIQ on the $\\mathbf{M}^3\\mathrm{FD}$ dataset against various methods. CLIPIQA inherits the powerful representation capabilities of CLIP, demonstrating stable and robust performance in evaluating the perceptual quality of natural images. Our method outperforms other methods on both metrics across all three test sets, indicating that our approach better aligns with the human perceptual system.", + "bbox": [ + 511, + 780, + 908, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7538", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/30bc001061367158c7f21dc0f88c2f1f78452ef6535728462530b1cd15dfc510.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    DatasetsSet5Set15Set20
    MethodsCLIP-IQA↑MUSIQ↑CLIP-IQA↑MUSIQ↑CLIP-IQA↑MUSIQ↑
    Low Resolution1-0.216724.6090.204923.0630.223022.446
    ESRGAN [47]ECCV'180.213040.8190.203840.7450.180436.654
    RealSR-JPEG [17]CVPR'200.361548.4190.357349.2250.327747.213
    BSRGAN [57]CVPR'210.329053.1190.319452.6440.330151.917
    SwinIR [26]CVPR'210.216037.1560.223037.9700.225834.919
    RealESRGAN [48]ICCV'210.278054.3060.242453.1630.252351.647
    HAT [5]CVPR'230.229838.0500.237739.7430.246635.633
    DAT [6]ICCV'230.229737.5380.241039.4190.251835.750
    ResShift [55]NeurIPS'230.470150.7690.442852.8710.408251.244
    CoRPLE [25]ECCV'240.233936.2810.228136.4580.228134.270
    SinSR [49]CVPR'240.587754.3550.576254.1060.535753.187
    Bi-DiffSR [7]NeurIPS'240.315135.3560.275836.1020.267436.537
    DifiISROurs0.614455.1940.590654.5040.548453.636
    High Resolution-0.220034.0660.216134.4100.213932.024
    ", + "bbox": [ + 94, + 88, + 903, + 345 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e0cf26c12dd9e82cc35d59a19d6026e18f4a75cc81cc733dc48f6e2182c46cae.jpg", + "table_caption": [ + "Table 1. No-reference Metrics Comparison of infrared image super-resolution with SOTA methods on ${\\mathrm{M}}^{3}\\mathrm{{FD}}$ datasets." + ], + "table_footnote": [], + "table_body": "
    MetricsDatasets
    Set5Set15Set20
    ResShiftSinSRBi-DiffSRDifIISRResShiftSinSRBi-DiffSRDifIISRResShiftSinSRBi-DiffSRDifIISR
    PSNR↑30.10131.64532.02232.27930.28331.98832.14532.35130.97633.43833.44733.451
    SSIM↑0.83290.84810.85790.86370.82280.84260.84710.85780.84460.88530.88740.8941
    LPIPS↓0.31790.27370.28160.27040.35370.28170.29240.28450.35070.25490.28200.2735
    ", + "bbox": [ + 96, + 382, + 901, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Reference-based Metrics Comparison with diffusion-based methods on ${\\mathrm{M}}^{3}\\mathrm{{FD}}$ datasets.", + "bbox": [ + 210, + 491, + 781, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, our method achieves superior performance on MUSIQ compared to all other methods, demonstrating that it can also achieve excellent results in multi-scale image quality assessment.", + "bbox": [ + 88, + 532, + 482, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is worth noting that we also compared our method against HR images on no-reference metrics. Our method significantly outperforms HR images in no-reference visual quality metrics, demonstrating an enhancement over the HR images. However, this improvement introduces a challenge: in comparison to traditional methods on reference-based metrics such as PSNR, LPIPS, and SSIM, our approach shows less advantage, as our results differ significantly from the HR images. Nevertheless, our method still leads diffusion-based methods on reference-based metrics, as shown in Table 2. This demonstrates that our approach leverages the powerful generative capabilities of diffusion to produce high-quality images while also preserving essential detail features from the HR images under both visual and perceptual guidance.", + "bbox": [ + 88, + 593, + 482, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Results. The qualitative results shown in Figure 3 emphasize the superiority of our method in visual performance compared to other approaches. Additional ex", + "bbox": [ + 88, + 819, + 482, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "amples can be found in the supplementary materials. We selected one image from each of the three datasets, Set5, Set15, and Set20, for qualitative analysis to ensure comprehensive evaluation. Our method achieves more natural details in portraits, avoiding color discrepancies and better matching the contours of the true image. For vehicle details, our method accurately reproduces the grille at the front of the vehicle in the true image, whereas other methods tend to blur these details. This demonstrates that our method also has distinct advantages in qualitative results.", + "bbox": [ + 511, + 532, + 906, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 694, + 666, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiments on the effectiveness of guidance. We conducted ablation experiments to evaluate the effectiveness of visual and perceptual guidance on the infrared super-resolution task, as shown in Table 3. We assessed the super-resolution results under four conditions: without guidance, with only visual guidance, with only perceptual guidance, and with both visual and perceptual guidance. The results show that the infrared image super-resolution performance is best when both guidances are applied.", + "bbox": [ + 511, + 718, + 903, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiments on the guidance combinations. We conducted ablation experiments on different guidance combinations of various methods, as shown in Table 4. In the", + "bbox": [ + 511, + 854, + 903, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "Evaluate the low-resolution image after enlarging it to match the resolution of the high-resolution image through interpolation.", + "bbox": [ + 89, + 875, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7539", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d90b6ce804fc1a0e05b2e9df4b82dca4dd2c8cfc8c8c31dffd421f780fe5693d.jpg", + "image_caption": [ + "Set5 (x4)" + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 263, + 186 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67699fe7d4b7b00e41bb277acb732f1a2f9c86765fb0f4a474d67eb152ffbbf0.jpg", + "image_caption": [ + "HR" + ], + "image_footnote": [], + "bbox": [ + 267, + 89, + 377, + 130 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f7c72990d34a2b92120c2ae98ffe32509c3be4de389570d2ffe4777957c2fd3d.jpg", + "image_caption": [ + "BSRGAN" + ], + "image_footnote": [], + "bbox": [ + 385, + 89, + 495, + 130 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d38f56050f511afa69977724ef6ff1e7c1891f2853244fa182d483bb63b55e18.jpg", + "image_caption": [ + "ESRGAN" + ], + "image_footnote": [], + "bbox": [ + 503, + 89, + 611, + 130 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e7e3742df12fe89166b5577ec4e83c73f189304dca8dcca0f293f8ac60c20a74.jpg", + "image_caption": [ + "RealESRGAN" + ], + "image_footnote": [], + "bbox": [ + 620, + 90, + 727, + 130 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4a920fdf9f2ce32ec2980f0e15e5d2f36bdc9f2c215f9cbc1460ee101bd430fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 90, + 903, + 186 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d0632e727ae2d78e3aaafe025def38d351542b30415f7deebcd708b2d3c09ce8.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 620, + 146, + 727, + 186 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/556119d78f8ca955873cbd1b8897312ea7fe09e6afde675c002c47c9a9add68f.jpg", + "image_caption": [ + "Set15 (x4)" + ], + "image_footnote": [], + "bbox": [ + 94, + 204, + 263, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e3b00f1f23bdc0dcfbb5710ffb78ed78533e7fa4ecc2a3c1f5f1c0c5c9fd92c6.jpg", + "image_caption": [ + "HR" + ], + "image_footnote": [], + "bbox": [ + 267, + 204, + 377, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d68eb34e38ea2478a751ee9d5321dae93bc8aafed7ed024005e03cf4b08786c3.jpg", + "image_caption": [ + "BSRGAN" + ], + "image_footnote": [], + "bbox": [ + 385, + 204, + 495, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4c43ddf6f2a0d8fa00aac5931cdc1bbd9dab92e35c3811f35abc911a072fc5f7.jpg", + "image_caption": [ + "ESRGAN" + ], + "image_footnote": [], + "bbox": [ + 503, + 204, + 611, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d57f7186f7b8504d60f31fe6dc6cc03fbd9bd8221ea28d60c9676af253fa5c3.jpg", + "image_caption": [ + "RealESRGAN" + ], + "image_footnote": [], + "bbox": [ + 620, + 204, + 727, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2879c678ebb94bcf57fd3d49e187d4a4596d7b12ed414d0d358e94fee75d2b46.jpg", + "image_caption": [ + "Ours (full size)", + "Ours (full size)" + ], + "image_footnote": [], + "bbox": [ + 736, + 204, + 903, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a1cc24243c3c6d7b502b53530928f79f7905def74fb3bd946ff6d24c34ed7ad6.jpg", + "image_caption": [ + "Set20 (x4)" + ], + "image_footnote": [], + "bbox": [ + 94, + 318, + 263, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0509c151f56c315b59e892c618883097341e2fea1167e8afada3db2979e3a505.jpg", + "image_caption": [ + "HR" + ], + "image_footnote": [], + "bbox": [ + 267, + 318, + 377, + 359 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/97b87fd7ff49ce4575d8b322f1efe99fd4801affc70995ded494d5c4be6dbccb.jpg", + "image_caption": [ + "BSRGAN" + ], + "image_footnote": [], + "bbox": [ + 385, + 318, + 495, + 359 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e093eabeeb6df8daa0e976fe9bca88251cdd57ad4ff1531ba4c81a8c7e47ee5.jpg", + "image_caption": [ + "ESRGAN" + ], + "image_footnote": [], + "bbox": [ + 503, + 318, + 611, + 359 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05a8acbfab36fa8248d7bc2f30d44ced2969ebfc1610f802b5e1f6af90326c6d.jpg", + "image_caption": [ + "Ours", + "RealESRGAN" + ], + "image_footnote": [], + "bbox": [ + 620, + 318, + 728, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "perceptual-based setup, which involves using a perceptual loss gradient for guidance, we performed three sets of experiments: (1) without the visual loss, (2) directly adding the visual loss $\\sum \\mathcal{L}$ , and (3) incorporating the gradient of the loss $\\nabla \\mathcal{L}$ into the noise. The experimental results demonstrate that incorporating the gradient of the loss into the noise yields the best performance. We also conducted experiments in a visual-based setup, the results under the visual-based setup also follow this trend.", + "bbox": [ + 89, + 484, + 483, + 621 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Experiments on Infrared Object Detection", + "text_level": 1, + "bbox": [ + 89, + 633, + 452, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setup. We employ YOLOv5-s for infrared image object detection, fine-tuning it specifically on the $\\mathbf{M}^3\\mathrm{FD}$ dataset. The model is fine-tuned with a batch size of 16, using the SGD optimizer with learning rate of 0.01.", + "bbox": [ + 89, + 657, + 482, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Comparison. The left section of Figure 6 presents a quantitative comparison of detection results across SOTA methods. In the top-right quadrant of the plot, the overall mAP of each model is displayed, while the other three quadrants represent the performance across individual categories. Our model consistently outperforms all other models in each detection category, demonstrating its superior ability in object detection tasks. Notably, in the truck detection category, our model achieves a $5.6\\%$ improvement over the best-competing method, underscoring its robustness in identifying challenging classes.", + "bbox": [ + 89, + 718, + 482, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Comparison. The qualitative results in Figure", + "bbox": [ + 89, + 885, + 482, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/10e06865cd7d705f997a73657299e619311b72acbd914d52aa495f6c956d0e96.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    VisualPerceptualPSNRCLIP-IQAmAPmIoU
    --33.4660.510231.240.9
    ✓-34.5280.536531.741.3
    -✓33.9230.523032.842.2
    ✓✓34.5750.537933.142.4
    ", + "bbox": [ + 503, + 479, + 901, + 565 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a683b3b71a2d492e19d9ff9eb0c880c6e5be1a4d14d7f17235b8786a51a18873.jpg", + "table_caption": [ + "Table 3. Ablation study on the effectiveness of multiple guidance." + ], + "table_footnote": [], + "table_body": "
    GuidePSNRCLIP-IQAmAPmIoU
    Perceptual Base-33.9230.523032.842.2
    + Visual∑L34.0610.534232.542.0
    + Visual∇L34.5750.537933.142.4
    Visual Base-34.5280.536531.741.3
    + Task∑L34.5610.537132.841.9
    + Task∇L34.5750.537933.142.4
    ", + "bbox": [ + 519, + 616, + 898, + 729 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation study for different guidance combinations.", + "bbox": [ + 527, + 739, + 888, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4 demonstrate the superiority of our method in object detection. Other methods frequently miss at least one label or make errors. For example, in the first row, some methods fail to detect the person on the right side of the image, with none capable of detecting both signs above simultaneously. Only our method consistently achieves the best detection prediction results.", + "bbox": [ + 511, + 794, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7540", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bfaaf9d948e358f425f2697b393c2252596c6cba541b1968149d0a7d6b8b7521.jpg", + "image_caption": [ + "Figure 4. Detection performance comparison of infrared image super-resolution with SOTA methods on $\\mathbf{M}^3\\mathrm{FD}$ datasets." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 903, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ee50d64148aea64a89ef72ef45fe989480e7eff66f36cf4c982fde5d2ba46e3.jpg", + "image_caption": [ + "Figure 5. Segmentation performance comparison of infrared image super-resolution with SOTA methods on FMB datasets." + ], + "image_footnote": [], + "bbox": [ + 96, + 281, + 898, + 409 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d959f3aeab8d4aab6ce8ed09c951182ca22a2ab2b4600a869a53d1f0200b951c.jpg", + "image_caption": [ + "Figure 6. Quantitative comparison of detection and segmentation results with SOTA methods." + ], + "image_footnote": [], + "bbox": [ + 96, + 462, + 478, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Experiments on Infrared Image Segmentation", + "text_level": 1, + "bbox": [ + 89, + 691, + 478, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Setup. We perform semantic segmentation on the FMB dataset [29], the SegFormer-b1 model [52] is used as the backbone. The model is trained using the AdamW optimizer, with a learning rate of 6e-05.", + "bbox": [ + 89, + 717, + 482, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quantitative Comparison. The right section of Figure 6 presents a quantitative comparison of semantic segmentation results. The top-right quadrant of the circle represents the comparison of mIoU, while the remaining three quadrants depict the performance of other models across the three primary segmentation classes. Overall, our model achieves the best results in each category. Notably, it achieves the highest improvement in truck, with an im", + "bbox": [ + 89, + 779, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "provement of $7.4\\%$ . It also improves by $5.4\\%$ and $3.0\\%$ in car and human, respectively.", + "bbox": [ + 511, + 465, + 903, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Comparison. The figure 5 presents a qualitative comparison of segmentation results from various SOTA methods. These results reveal that other methods often fail to segment complete objects, or they struggle with segmenting all relevant elements. For example, in other models, only part of the sign occurs, leaving parts of it undetected. While RealESRGAN shows some improvement, it still falls short of our method. Similarly, in the right image, other models fail to recognize the farthest poles and cannot fully capture the shapes of the people.", + "bbox": [ + 511, + 497, + 906, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 666, + 633, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a task-oriented infrared image super-resolution diffusion model, namely DiffIISR. Specifically, we introduce infrared thermal spectral distribution modulation as visual guidance to ensure consistency with high-resolution images by matching frequency components. In addition, we incorporate foundational vision models to provide perception guidance, which enhances detection and segmentation performance. With the above guidance, our method further optimizes each iteration of the diffusion process, refining the model at each denoising step and achieving superior visual and perceptual performance.", + "bbox": [ + 511, + 691, + 906, + 844 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments: This work was partially supported by the National Natural Science Foundation of China (No.62302078 and No.62372080), and China Postdoctoral Science Foundation (2023M730741).", + "bbox": [ + 511, + 845, + 903, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7541", + "bbox": [ + 482, + 944, + 513, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 118, + 187, + 133 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne Van Den Berg. 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Residual dense network for image super-resolution." + ], + "bbox": [ + 91, + 90, + 480, + 900 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2472-2481, 2018. 2", + "[64] Yang Zou, Zhixin Chen, Zhipeng Zhang, Xingyuan Li, Long Ma, Jinyuan Liu, Peng Wang, and Yanning Zhang. Contourlet refinement gate framework for thermal spectrum distribution regularized infrared image super-resolution. arXiv preprint arXiv:2411.12530, 2024. 3" + ], + "bbox": [ + 516, + 92, + 903, + 190 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7544", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_model.json b/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8e3e20bd2116878d5cec5a6a5a0c03d3ca80ccdd --- /dev/null +++ b/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_model.json @@ -0,0 +1,2686 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.216, + 0.131, + 0.784, + 0.177 + ], + "angle": 0, + "content": "Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.202, + 0.751, + 0.24 + ], + "angle": 0, + "content": "Xingyuan Li\\(^{1\\dagger}\\), Zirui Wang\\(^{1\\dagger}\\), Yang Zou\\(^{2}\\), Zhixin Chen\\(^{3}\\), Jun Ma\\(^{1}\\), Zhiying Jiang\\(^{4}\\), Long Ma\\(^{1}\\), Jinyuan Liu\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.242, + 0.816, + 0.257 + ], + "angle": 0, + "content": "\\(^{1}\\) School of Software Technology & DUT-RU International School of ISE, Dalian University of Technology" + }, + { + "type": "text", + "bbox": [ + 0.288, + 0.258, + 0.708, + 0.275 + ], + "angle": 0, + "content": "\\(^{2}\\) School of Computer Science, Northwestern Polytechnical University" + }, + { + "type": "text", + "bbox": [ + 0.265, + 0.277, + 0.732, + 0.292 + ], + "angle": 0, + "content": "3Graduate School of Information, Production, and Systems, Waseda University" + }, + { + "type": "text", + "bbox": [ + 0.266, + 0.294, + 0.731, + 0.327 + ], + "angle": 0, + "content": "4 College of Information Science and Technology, Dalian Maritime University xingyuan_lxy@163.com atlantis918@hotmail.com" + }, + { + "type": "list", + "bbox": [ + 0.265, + 0.258, + 0.732, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.351, + 0.907, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.536, + 0.908, + 0.579 + ], + "angle": 0, + "content": "Figure 1. The left side shows a comparison between existing super-resolution methods and our proposed DiffISR. Our method introduces additional visual guidance based on the Fourier Transform, as well as foundational model-based perception guidance. The right side demonstrates that our method outperforms other methods in both detection and segmentation tasks." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.59, + 0.327, + 0.607 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.637, + 0.486, + 0.879 + ], + "angle": 0, + "content": "Infrared imaging is essential for autonomous driving and robotic operations as a supportive modality due to its reliable performance in challenging environments. Despite its popularity, the limitations of infrared cameras, such as low spatial resolution and complex degradations, consistently challenge imaging quality and subsequent visual tasks. Hence, infrared image super-resolution (IISR) has been developed to address this challenge. While recent developments in diffusion models have greatly advanced this field, current methods to solve it either ignore the unique modal characteristics of infrared imaging or overlook the machine perception requirements. To bridge these gaps, we propose DifIISR, an infrared image super-resolution diffusion model optimized for visual quality and perceptual performance. Our approach achieves task-based guidance for diffusion by injecting gradients derived from visual and" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.593, + 0.909, + 0.775 + ], + "angle": 0, + "content": "perceptual priors into the noise during the reverse process. Specifically, we introduce an infrared thermal spectrum distribution regulation to preserve visual fidelity, ensuring that the reconstructed infrared images closely align with high-resolution images by matching their frequency components. Subsequently, we incorporate various visual foundational models as the perceptual guidance for downstream visual tasks, infusing generalizable perceptual features beneficial for detection and segmentation. As a result, our approach gains superior visual results while attaining State-Of-The-Art downstream task performance. Code is available at https://github.com/zirui0625/DifIISR" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.8, + 0.646, + 0.815 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.909, + 0.903 + ], + "angle": 0, + "content": "The objective of infrared image super-resolution (IISR) is to reconstruct a high-resolution (HR) infrared image from its low-resolution (LR) counterpart [51]. The consistent performance of infrared imaging under challenging conditions allows its application to span various fields [31, 44, 45]," + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.887, + 0.359, + 0.901 + ], + "angle": 0, + "content": "† Equal contribution. *Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7534" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "such as object detection [28, 40, 41], semantic segmentation [24, 30], and autonomous driving [2, 42]. Despite its great potential, the inherent limitations of infrared cameras — such as high noise levels, reduced spatial resolution, and limited dynamic range — continually affect the quality of infrared images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.185, + 0.483, + 0.382 + ], + "angle": 0, + "content": "Conventionally, CNN-based methods [18, 33, 61-63] address this challenge by mapping interpolated LR images to HR images and then enhancing the details (e.g., SR-CNN [35]). Although CNN-based super-resolution methods have significantly advanced this field, they are limited by the perceptual field of local convolution operations. To overcome this, Transformer-based methods [3, 4, 56, 60] model long-range dependencies to capture global context. Liang et al. [26] proposed SwinIR significantly improving super-resolution performance by integrating CNNs with the Swin Transformer. Lately, Li et al. [25] proposed CoRPLE, which leverages a Contourlet residual framework to restore infrared-specific high-frequency features." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.385, + 0.483, + 0.567 + ], + "angle": 0, + "content": "Recently, the diffusion model has introduced a novel paradigm for image super-resolution tasks, offering a fresh approach that goes beyond the CNN- and Transformer-based methods [11], leveraging its capacity to learn implicit priors of the underlying data distribution [39]. Yue et al. proposed ResShift [55], which applies an iterative sampling procedure to shift the residual between the LR and the desired HR image during inference. Unlike other diffusion models, Wang et al. [49] accelerate the diffusion-based SR model to a single inference step while maintaining satisfactory performance. These methods generally achieve visually pleasing results when applied to visible images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.57, + 0.483, + 0.901 + ], + "angle": 0, + "content": "However, existing methods often fail to extend effectively to infrared imaging, particularly in downstream tasks such as infrared image object detection and semantic segmentation. A common approach for task-oriented infrared image super-resolution is to adapt an RGB super-resolution model to infrared data, and then connect it to a downstream detection or segmentation module. Unfortunately, this approach faces two significant challenges: 1) Ignoring the unique modal characteristics of infrared imaging, which include distinct thermal spectrum distributions. Infrared image reconstruction quality is particularly sensitive to high-frequency components due to longer wavelengths and reduced atmospheric scattering effects. 2) Overlooking the machine perception requirements. While the model may reconstruct visually appealing images, these results are often sub-optimal for specific perceptual tasks. The objectives of visual domain optimization and perceptual domain optimization can differ significantly [28]. For instance, diffusion-based super-resolution models typically focus on \"seeking visually appealing\" results, often at the expense of structural information of targets and textural details critical for machine vision. Given these limitations, we ask, \"Why" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "not develop a super-resolution model that reconstructs infrared images to be both visually appealing and perceptually salient?\"" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.138, + 0.907, + 0.408 + ], + "angle": 0, + "content": "To this end, as shown in figure 1, we propose a task-oriented infrared image super-resolution method that optimizes the diffusion process through gradient-based guidance. Specifically, we inject the gradient of a designed prior loss into the noise estimation at each training step, refining the model's performance across iterations. Our guidance consists of two components. First, to ensure visual consistency, we introduce visual guidance via infrared thermal spectral distribution modulation, which ensures the reconstructed images align with high-resolution counterparts by preserving their spectral characteristics. Second, we integrate perceptual guidance by leveraging powerful pretrained vision models, such as VGG [37] and SAM [22], to infuse the diffusion process with generalized perceptual features. Extensive experiments demonstrate that our proposed method excels in both visual quality and downstream task performance. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.413, + 0.905, + 0.488 + ], + "angle": 0, + "content": "- We propose a solution for infrared image super-resolution by integrating gradient-based priors into the noise during diffusion, enabling task-based guidance in sampling, and achieving simultaneous optimization in both visual and perceptual-specific domains." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.489, + 0.905, + 0.548 + ], + "angle": 0, + "content": "- We introduce a thermal spectrum distribution regulation to preserve the visual fidelity of infrared images, guiding the diffusion process to learn the unique infrared image frequency distribution." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.549, + 0.905, + 0.61 + ], + "angle": 0, + "content": "- We propose perceptual guidance for the diffusion process, incorporating generalizable perceptual features from foundational models for visual tasks. This notably enhances performance in detection and segmentation." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.413, + 0.905, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.625, + 0.652, + 0.641 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.651, + 0.738, + 0.667 + ], + "angle": 0, + "content": "2.1. Image Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Since the pioneering work of SRCNN [13] was proposed, deep learning has gradually become the mainstream approach for image super-resolution (SR). The initial works [13, 21, 23, 63] mainly focused on utilizing convolutional neural networks (CNNs) [12] for image super-resolution tasks and optimizing the network by minimizing the mean square error (MSE) between the super-resolved image (SR) and their corresponding high-resolution (HR) counterparts. Subsequently, GAN-based super-resolution methods were proposed, drawing significant attention. For example, both BSRGAN [57] and Real-ESRGAN [48] employ GANs for super-resolution tasks and introduce training samples with more realistic types of degradations to achieve better results. While these methods improve the quality of the low-resolution images, they often fail to produce stable" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7535" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.228 + ], + "angle": 0, + "content": "outcomes, resulting in artifacts in the images. LDL [27] and DeSRA [53] attempt to address this issue, but they still struggle to generate images with natural details. Recently, diffusion models have been widely applied to image super-resolution tasks, such as ResShift [55] and SinSR [49]. However, these methods are not designed specifically for the characteristics of infrared images and overlook the requirements of machine perception [64], so they do not perform well in infrared image super-resolution (IISR)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.236, + 0.27, + 0.251 + ], + "angle": 0, + "content": "2.2. Diffusion Methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.259, + 0.485, + 0.548 + ], + "angle": 0, + "content": "The Diffusion Denoising Probabilistic Model (DDPM) [16] is a generative model with stability and controllability. Since it was proposed, it has attracted widespread attention. The main focus of the diffusion model is to train a denoising autoencoder, which estimates the reverse process of the Markov diffusion process by predicting the noise. Diffusion models were initially applied to image generation tasks and have been continuously improved in recent years [1, 32, 34, 38, 39]. ControlNet [58] introduces control conditions into pre-trained diffusion models, expanding the application scope of diffusion models in image generation. DDIM [38] proposes a non-Markovian generation method, significantly enhancing the inference speed of diffusion models. Diffusion models have demonstrated exceptional capabilities not only in image generation tasks but also in various other tasks, showing great potential. With the introduction of several related methods [8, 9, 19, 36, 49, 55], diffusion models have also been validated to achieve remarkable results in the field of image super-resolution." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.56, + 0.229, + 0.575 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.484, + 0.706 + ], + "angle": 0, + "content": "We first introduce the background of Denoising Diffusion Probabilistic Models [16]. DDPM obtains samples \\( x_0 \\sim p_{\\mathrm{data}}(x) \\) from the data distribution. In a diffusion model, noise is gradually added to the sampled \\( x_0 \\) over time steps up to \\( T \\), eventually resulting in \\( x_T \\sim \\mathcal{N}(0, \\mathbf{I}) \\), which can be approximated as a standard Gaussian distribution. This process is also referred to as the forward process of the diffusion model, and it can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.716, + 0.483, + 0.734 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {0}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.742, + 0.484, + 0.834 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = \\prod_{s = 1}^{t}(1 - \\beta_{s})\\), and \\(\\beta_{s}\\) are fixed or learned variance schedule. After obtaining \\(x_{T}\\), the denoising model \\(\\epsilon_{\\phi}\\) learns to predict the noise \\(\\epsilon\\) added during the forward process, thereby removing the noise from \\(x_{T}\\). Specifically, the denoising model \\(\\epsilon_{\\phi}\\) predicts the noise by optimizing the re-weighted evidence lower bound, which can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.843, + 0.483, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s i m p l e}} (\\phi) = \\mathbb {E} _ {x _ {0}, t, \\epsilon} \\left[ \\| \\epsilon_ {\\phi} (x _ {t}, t) - \\epsilon \\| ^ {2} \\right]. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In this formula, \\(\\epsilon_{\\phi}(x_t,t)\\) represents the noise predicted by the model, and \\(t\\) is randomly sampled from a predefined" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.152 + ], + "angle": 0, + "content": "range of time steps. During the training process, the denoising model \\(\\epsilon_{\\phi}\\) is optimized by minimizing \\(\\mathcal{L}_{\\mathrm{simple}}(\\phi)\\), ultimately resulting in a model capable of accurately predicting the noise." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.153, + 0.907, + 0.213 + ], + "angle": 0, + "content": "After training the denoising model \\(\\epsilon_{\\phi}\\), we sample \\(x_{T} \\sim \\mathcal{N}(0, \\mathbf{I})\\) and iteratively refine it using the denoising model. This process is also known as the reverse process, and the specific formula can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.225, + 0.907, + 0.243 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, t\\right), \\Sigma_ {\\theta} \\left(x _ {t}, t\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.254, + 0.906, + 0.345 + ], + "angle": 0, + "content": "where \\(\\mu_{\\theta}(x_t,t)\\) is the mean function from step \\(t\\) to \\(t - 1\\) and \\(\\Sigma_{\\theta}(x_t,t)\\) is the covariance. Due to the slow sampling process of DDPM, DDIM proposes using a non-Markovian diffusion process, which significantly improves the model's sampling speed. The improved sampling formula can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.358, + 0.905, + 0.395 + ], + "angle": 0, + "content": "\\[\nx _ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\hat {x} _ {0} \\left(x _ {t}\\right) + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\phi} \\left(x _ {t}, t\\right) + \\sigma_ {t} z, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.396, + 0.906, + 0.44 + ], + "angle": 0, + "content": "where \\(\\sigma_{t}\\) is the variance of the noise and \\(z\\) follows a standard normal distribution. \\(\\hat{x}_0(x_t)\\) is the predicted \\(x_0\\) from \\(x_{t}\\), and the prediction formula is:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.451, + 0.906, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\hat {x} _ {0} (x _ {t}) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\phi} (x _ {t}, t)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.495, + 0.906, + 0.541 + ], + "angle": 0, + "content": "When \\(\\sigma_{t}\\) equals 0, it is evident that the DDIM sampling process can be regarded as a deterministic process, which allows for quick sampling results from the noise." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.554, + 0.605, + 0.57 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.907, + 0.716 + ], + "angle": 0, + "content": "Overview. Our main objective is to address the problem of infrared image super-resolution using a diffusion model enhanced by gradient-based guidance, as shown in figure 2. Specifically, inspired by [10], we propose a method that fine-tunes the diffusion model by introducing an additional guidance mechanism. In addition, we incorporate a dual optimization approach combining visual and perceptual aspects to better adapt the diffusion model to the task of infrared image super-resolution." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.727, + 0.736, + 0.743 + ], + "angle": 0, + "content": "4.1. Loss-gradient Guidance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.902 + ], + "angle": 0, + "content": "The reverse process of diffusion models often requires multiple constraints to generate stable, high-quality images. Most methods tend to guide the reverse process by adding weighted constraints to the final loss function. In contrast, our approach addresses this issue from the perspective of posterior sampling. Inspired by [10], we introduce additional priors and compute the gradient of the resulting loss function, injecting the gradient into the noise estimated at each step to better handle the problem of adding constraints during the reverse process of diffusion models." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7536" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.087, + 0.905, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.348, + 0.908, + 0.378 + ], + "angle": 0, + "content": "Figure 2. Overall architecture of our proposed method: the vanilla super-resolution diffusion process is marked in black, whereas our proposed additional visual and perceptual priors are marked in red." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.403, + 0.484, + 0.464 + ], + "angle": 0, + "content": "Generally, the noise predicted by the denoising model at timestep \\( t \\) is often correlated with the score of the denoising model at the current timestep [39]. Specifically, it can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.479, + 0.483, + 0.497 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {\\phi} \\left(x _ {t}, t\\right) = - \\sqrt {1 - \\alpha_ {t}} \\nabla_ {x _ {t}} \\log p \\left(x _ {t}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.511, + 0.484, + 0.649 + ], + "angle": 0, + "content": "where \\(\\nabla_{x_t}\\log p(x_t)\\) is the gradient of \\(x_{t}\\) with respect to the probability density function \\(\\log p(x_{t})\\), but now we need to consider not only \\(\\nabla_{x_t}\\log p(x_t)\\), we also need to incorporate optimization of \\(g\\) during the diffusion model sampling. In our work, \\(g\\) represents the guidance obtained by feeding \\(x_0\\) into \\(\\mathcal{M}\\), and \\(\\mathcal{M}\\) is a forward operator. The relationship between \\(g\\) and \\(x_0\\) can be expressed as \\(g = \\mathcal{M}(x_0)\\). Therefore, the score of the denoising model at timestep \\(t\\) becomes \\(\\nabla_{x_t}\\log p(x_t\\mid g)\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.65, + 0.484, + 0.695 + ], + "angle": 0, + "content": "\\(\\nabla_{x_t}\\log p(x_t\\mid g)\\) is unknown, and we need to use the known \\(\\nabla_{x_t}\\log p(x_t)\\) to derive \\(\\nabla_{x_t}\\log p(x_t\\mid g)\\). According to Bayes' theorem, we can write:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.71, + 0.483, + 0.741 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {x _ {t}} \\log p (x _ {t} \\mid g) = \\nabla_ {x _ {t}} \\log p (x _ {t}) + \\nabla_ {x _ {t}} \\log p (g \\mid x _ {t}). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.741, + 0.484, + 0.802 + ], + "angle": 0, + "content": "From this, it can be seen that \\(\\nabla_{x_t}\\log p(x_t)\\) is known, and the problem changes from calculating \\(\\nabla_{x_t}\\log p(x_t\\mid g)\\) to calculating \\(\\nabla_{x_t}\\log p(g\\mid x_t)\\). Inspired by [10], we can derive the formula:" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.814, + 0.483, + 0.854 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {x _ {t}} \\log p (g \\mid x _ {t}) \\simeq \\nabla_ {x _ {t}} \\log p (g \\mid \\hat {x} _ {0} (x _ {t})) \\tag {8} \\\\ \\simeq - \\rho \\nabla_ {x _ {t}} \\| g - \\mathcal {M} (\\hat {x} _ {0} (x _ {t})) \\| _ {2} ^ {2}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.87, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\(\\nabla_{x_t}\\| g - \\mathcal{M}(\\hat{x}_0(x_t))\\| _2^2\\) also can be represented as \\(\\nabla \\mathcal{L}_g\\). Therefore, we can express the noise prediction ad" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.403, + 0.744, + 0.419 + ], + "angle": 0, + "content": "justed according to condition \\(g\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.429, + 0.905, + 0.47 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\epsilon_ {\\phi} ^ {\\prime} = \\epsilon_ {\\phi} \\left(x _ {t}, t\\right) + \\rho \\sqrt {1 - \\alpha_ {t}} \\nabla_ {x _ {t}} \\| g - \\mathcal {M} \\left(\\hat {x} _ {0} \\left(x _ {t}\\right)\\right) \\| _ {2} ^ {2} \\tag {9} \\\\ = \\epsilon_ {\\phi} (x _ {t}, t) + \\rho \\sqrt {1 - \\alpha_ {t}} \\nabla \\mathcal {L} _ {g}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.905, + 0.526 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\phi}^{\\prime}\\) represents the adjusted noise, obtained by adding the gradient of the guidance loss \\(\\nabla \\mathcal{L}_g\\) to the noise predicted by the original denoising model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.527, + 0.906, + 0.602 + ], + "angle": 0, + "content": "Thus, by applying gradient guidance to the noise predicted by the diffusion model, we impose constraints on the reverse process of the diffusion model. More detailed derivations and pseudocode of our method can be found in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.611, + 0.834, + 0.628 + ], + "angle": 0, + "content": "4.2. Visual-perceptual Dual Optimization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.635, + 0.906, + 0.681 + ], + "angle": 0, + "content": "Now, let's explain the composition of our guidance \\(\\mathcal{L}_g\\) in detail. Specifically, \\(\\mathcal{L}_g\\) can be divided into two parts: visual loss \\(\\mathcal{L}_{\\mathrm{visual}}\\) and perceptual loss \\(\\mathcal{L}_{\\mathrm{perceptual}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.681, + 0.906, + 0.817 + ], + "angle": 0, + "content": "\\(\\nu\\) - visual guidance. To guide the diffusion process in reconstructing infrared images towards infrared-specific visual characteristics, we propose \\(\\mathcal{L}_{\\mathrm{visual}}\\) to regularize the distribution of high- and low-frequency information as visual guidance \\(\\nu\\). Here, \\(\\nu\\) replaces the forward operator \\(\\mathcal{M}\\) in equation 8. Given the HR image \\(\\mathbf{I}_{HR}\\) and the super-resolved image \\(\\mathbf{I}_{SR}\\), we first use Fast Fourier Transforms (FFT) to transform their spatial domain representation into the frequency domain, formally:" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.84, + 0.905, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\mathbf {I}} _ {H R} = \\mathcal {F} (\\mathbf {I} _ {H R}), \\hat {\\mathbf {I}} _ {S R} = \\mathcal {F} (\\mathbf {I} _ {S R}), \\\\ \\mathcal {F} (u, v) = \\sum_ {x = 0} ^ {H - 1} \\sum_ {y = 0} ^ {W - 1} I (x, y) \\cdot e ^ {- i \\frac {2 \\pi}{H} u x} \\cdot e ^ {- i \\frac {2 \\pi}{W} v y}. \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7537" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.485, + 0.35 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}(u,v)\\) denotes the FFT of the image at frequency coordinates \\((u,v)\\), and \\(\\hat{\\mathbf{I}}_{HR}\\) is the transformed HR images. In the frequency domain, we first shift the zero-frequency component, which represents the mean intensity of the image, to the center of the spectrum for both HR and SR images, yielding \\(\\hat{\\mathbf{I}}_{HR}^{\\mathrm{shift}}\\) and \\(\\hat{\\mathbf{I}}_{SR}^{\\mathrm{shift}}\\). Following this, we compute the magnitude spectra \\(\\mathbf{M}_{HR}\\) and \\(\\mathbf{M}_{SR}\\) by applying logarithmic compression to the Fourier-transformed images. This step ensures a balanced consideration of both high-frequency and low-frequency components during comparison. To focus the loss on matching the frequency distribution patterns rather than absolute intensity differences, we normalize the magnitude spectra to have zero mean and unit variance, resulting in the normalized spectra \\(\\mathbf{M}_{HR}^{\\mathrm{norm}}\\) and \\(\\mathbf{M}_{SR}^{\\mathrm{norm}}\\). Finally, the Visual Loss \\(\\mathcal{L}_{\\mathrm{visual}}\\) is computed as the mean squared error between the normalized magnitude spectra of the HR and SR images:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.351, + 0.484, + 0.409 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {v i s u a l}} = \\left(\\overbrace {N \\left(\\log \\left(1 + | \\hat {\\mathbf {I}} _ {H R} ^ {\\text {n o r m}} |\\right)\\right)} ^ {\\mathrm {M} _ {H R} ^ {\\text {n o r m}}} - \\overbrace {N \\left(\\log \\left(1 + | \\hat {\\mathbf {I}} _ {S R} ^ {\\text {n o r m}} |\\right)\\right)} ^ {\\mathrm {M} _ {S R} ^ {\\text {n o r m}}}\\right) ^ {2}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.41, + 0.484, + 0.455 + ], + "angle": 0, + "content": "where \\(N(\\cdot)\\) represents the normalization operation. Visual Loss plays a critical role in preserving the frequency distribution of the infrared image." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.456, + 0.484, + 0.773 + ], + "angle": 0, + "content": "\\(\\mathcal{P}\\) - perceptual guidance. Large models provide many priors for current methods [14, 15], to regularize the diffusion process to better align with machine perception, we adopt \\(\\mathcal{L}_{\\mathrm{perceptual}}\\) that consists of the VGG Loss \\(\\mathcal{L}_{\\mathrm{VGG}}\\) and the Segmentation Loss \\(\\mathcal{L}_{\\mathrm{seg}}\\) as perceptual guidance \\(\\mathcal{P}\\). Here, \\(\\mathcal{P}\\) replaces the forward operator \\(\\mathcal{M}\\) in equation 8. Given the HR image \\(\\mathbf{I}_{HR}\\) and the super-resolved image \\(\\mathbf{I}_{SR}\\), the VGG Loss is computed by mean squared error between the extracted features of the HR and SR images from a pretrained deep neural network. This guides the model to capture nuanced aspects of images, including textures, edges, and shapes, which are crucial for preserving visual fidelity. To enhance the semantic fidelity of the reconstructed images, we regulate the diffusion process using the Segment Anything Model (SAM) [22] and propose the Segmentation Loss \\(\\mathcal{L}_{\\mathrm{seg}}\\). Given the HR image \\(\\mathbf{I}_{HR}\\) and the super-resolved image \\(\\mathbf{I}_{SR}\\), we use a locked SAM to segment the masks \\(\\mathbf{S}_{HR}\\) and \\(\\mathbf{S}_{SR}\\) for \\(\\mathbf{I}_{HR}\\) and \\(\\mathbf{I}_{SR}\\), respectively. The Segmentation Loss \\(\\mathcal{L}_{\\mathrm{seg}}\\) is then computed by mean squared error between \\(\\mathbf{S}_{HR}\\) and \\(\\mathbf{S}_{SR}\\), providing effective high-level supervision for the reconstructed images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.773, + 0.483, + 0.802 + ], + "angle": 0, + "content": "The Perceptual Loss \\(\\mathcal{L}_{\\mathrm{perceptual}}\\) is computed by integrating the VGG-based and segmentation-based losses, as:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.804, + 0.482, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p e r c e p t u a l}} = \\overbrace {\\left\\| \\phi_ {l} \\left(\\mathbf {I} _ {H R}\\right) - \\phi_ {l} \\left(\\mathbf {I} _ {S R}\\right) \\right\\| _ {2} ^ {2}} ^ {\\mathcal {L} _ {\\mathrm {V G G}}} + \\overbrace {\\left\\| \\mathbf {S} _ {H R} - \\mathbf {S} _ {S R} \\right\\| _ {2} ^ {2}} ^ {\\mathcal {L} _ {\\mathrm {s e g}}}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "where \\(\\phi_l(\\cdot)\\) represents the feature map extracted from the \\(l\\)-th layer of a pre-trained deep neural network (in our experiment, VGG-16)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.152 + ], + "angle": 0, + "content": "The incorporation of visual and perceptual guidance refines each iteration of the diffusion, facilitating a more optimized denoising procedure. This not only improves visual fidelity but also enhances perceptual performance." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.167, + 0.646, + 0.184 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.193, + 0.722, + 0.209 + ], + "angle": 0, + "content": "5.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.216, + 0.907, + 0.427 + ], + "angle": 0, + "content": "Dataset and evaluation metrics. To ensure the fairness of the experiment, we used the same training [28] and test sets [28, 43, 54], as CoRPLE [25]. We use the infrared image dataset \\(\\mathrm{M}^3\\mathrm{FD}\\) [28] to train the model and evaluate its performance using three datasets: \\(\\mathrm{M}^3\\mathrm{FD}\\) [28], RoadScene [54], and TNO [43]. We adopt five metrics to evaluate the performance of our model quantitatively: CLIP-IQA [46], MUSIQ [20], PSNR, LPIPS [59], and SSIM [50]. Among them, CLIPIQA and MUSIQ are no-reference metrics. CLIPIQA leverages the CLIP model [35] to assess image quality, while MUSIQ uses a multi-scale feature extraction approach for quality evaluation. We mainly rely on CLIPIQA and MUSIQ as evaluation metrics to compare the performance of different methods." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.429, + 0.909, + 0.64 + ], + "angle": 0, + "content": "Implementation Details. Our network was trained on a GeForce RTX 4090 GPU. Our backbone model and specific experimental parameter settings largely follow ResShift [55]. Notably, ResShift uses the residual between high-resolution (HR) and low-resolution images (LR) as the noise for the diffusion model, meaning that we can effectively apply gradient guidance on the residual between HR and LR images. During training, our approach differs from ResShift in that we initially perform 200K iterations on a new training set to enable the model to develop basic infrared image super-resolution capabilities. Subsequently, we incorporate conditional (visual and perceptual) guidance into the model and conduct an additional 50K training iterations to achieve improved results." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.65, + 0.771, + 0.667 + ], + "angle": 0, + "content": "5.2. Experiments on Infrared SR" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.674, + 0.907, + 0.78 + ], + "angle": 0, + "content": "We perform a comprehensive comparison of our approach with eleven SOTA methods, including ESRGAN [47], RealSR-JPEG [17], BSRGAN [57], SwinIR [26], RealESRGAN [48], HAT [5], DAT [6], ResShift [55], CoPRLE [25], Bi-DiffSR [7] and SinSR [49]. Table 1, 2 presents our quantitative comparison results compared with the above methods and Figure 3 presents our qualitative results." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.781, + 0.909, + 0.902 + ], + "angle": 0, + "content": "Quantitative Comparison. Table 1 presents a quantitative comparison of CLIPIQA and MUSIQ on the \\(\\mathbf{M}^3\\mathrm{FD}\\) dataset against various methods. CLIPIQA inherits the powerful representation capabilities of CLIP, demonstrating stable and robust performance in evaluating the perceptual quality of natural images. Our method outperforms other methods on both metrics across all three test sets, indicating that our approach better aligns with the human perceptual system." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7538" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.904, + 0.346 + ], + "angle": 0, + "content": "
    DatasetsSet5Set15Set20
    MethodsCLIP-IQA↑MUSIQ↑CLIP-IQA↑MUSIQ↑CLIP-IQA↑MUSIQ↑
    Low Resolution1-0.216724.6090.204923.0630.223022.446
    ESRGAN [47]ECCV'180.213040.8190.203840.7450.180436.654
    RealSR-JPEG [17]CVPR'200.361548.4190.357349.2250.327747.213
    BSRGAN [57]CVPR'210.329053.1190.319452.6440.330151.917
    SwinIR [26]CVPR'210.216037.1560.223037.9700.225834.919
    RealESRGAN [48]ICCV'210.278054.3060.242453.1630.252351.647
    HAT [5]CVPR'230.229838.0500.237739.7430.246635.633
    DAT [6]ICCV'230.229737.5380.241039.4190.251835.750
    ResShift [55]NeurIPS'230.470150.7690.442852.8710.408251.244
    CoRPLE [25]ECCV'240.233936.2810.228136.4580.228134.270
    SinSR [49]CVPR'240.587754.3550.576254.1060.535753.187
    Bi-DiffSR [7]NeurIPS'240.315135.3560.275836.1020.267436.537
    DifiISROurs0.614455.1940.590654.5040.548453.636
    High Resolution-0.220034.0660.216134.4100.213932.024
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.148, + 0.356, + 0.848, + 0.371 + ], + "angle": 0, + "content": "Table 1. No-reference Metrics Comparison of infrared image super-resolution with SOTA methods on \\( {\\mathrm{M}}^{3}\\mathrm{{FD}} \\) datasets." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.383, + 0.902, + 0.481 + ], + "angle": 0, + "content": "
    MetricsDatasets
    Set5Set15Set20
    ResShiftSinSRBi-DiffSRDifIISRResShiftSinSRBi-DiffSRDifIISRResShiftSinSRBi-DiffSRDifIISR
    PSNR↑30.10131.64532.02232.27930.28331.98832.14532.35130.97633.43833.44733.451
    SSIM↑0.83290.84810.85790.86370.82280.84260.84710.85780.84460.88530.88740.8941
    LPIPS↓0.31790.27370.28160.27040.35370.28170.29240.28450.35070.25490.28200.2735
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.212, + 0.492, + 0.782, + 0.506 + ], + "angle": 0, + "content": "Table 2. Reference-based Metrics Comparison with diffusion-based methods on \\( {\\mathrm{M}}^{3}\\mathrm{{FD}} \\) datasets." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.533, + 0.483, + 0.594 + ], + "angle": 0, + "content": "Additionally, our method achieves superior performance on MUSIQ compared to all other methods, demonstrating that it can also achieve excellent results in multi-scale image quality assessment." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.594, + 0.483, + 0.82 + ], + "angle": 0, + "content": "It is worth noting that we also compared our method against HR images on no-reference metrics. Our method significantly outperforms HR images in no-reference visual quality metrics, demonstrating an enhancement over the HR images. However, this improvement introduces a challenge: in comparison to traditional methods on reference-based metrics such as PSNR, LPIPS, and SSIM, our approach shows less advantage, as our results differ significantly from the HR images. Nevertheless, our method still leads diffusion-based methods on reference-based metrics, as shown in Table 2. This demonstrates that our approach leverages the powerful generative capabilities of diffusion to produce high-quality images while also preserving essential detail features from the HR images under both visual and perceptual guidance." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.82, + 0.483, + 0.866 + ], + "angle": 0, + "content": "Qualitative Results. The qualitative results shown in Figure 3 emphasize the superiority of our method in visual performance compared to other approaches. Additional ex" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.533, + 0.907, + 0.685 + ], + "angle": 0, + "content": "amples can be found in the supplementary materials. We selected one image from each of the three datasets, Set5, Set15, and Set20, for qualitative analysis to ensure comprehensive evaluation. Our method achieves more natural details in portraits, avoiding color discrepancies and better matching the contours of the true image. For vehicle details, our method accurately reproduces the grille at the front of the vehicle in the true image, whereas other methods tend to blur these details. This demonstrates that our method also has distinct advantages in qualitative results." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.695, + 0.667, + 0.712 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.719, + 0.905, + 0.854 + ], + "angle": 0, + "content": "Experiments on the effectiveness of guidance. We conducted ablation experiments to evaluate the effectiveness of visual and perceptual guidance on the infrared super-resolution task, as shown in Table 3. We assessed the super-resolution results under four conditions: without guidance, with only visual guidance, with only perceptual guidance, and with both visual and perceptual guidance. The results show that the infrared image super-resolution performance is best when both guidances are applied." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.9 + ], + "angle": 0, + "content": "Experiments on the guidance combinations. We conducted ablation experiments on different guidance combinations of various methods, as shown in Table 4. In the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.875, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Evaluate the low-resolution image after enlarging it to match the resolution of the high-resolution image through interpolation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7539" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.264, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.19, + 0.209, + 0.203 + ], + "angle": 0, + "content": "Set5 (x4)" + }, + { + "type": "image", + "bbox": [ + 0.269, + 0.09, + 0.379, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.134, + 0.335, + 0.145 + ], + "angle": 0, + "content": "HR" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.09, + 0.496, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.409, + 0.134, + 0.472, + 0.145 + ], + "angle": 0, + "content": "BSRGAN" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.09, + 0.612, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.134, + 0.589, + 0.145 + ], + "angle": 0, + "content": "ESRGAN" + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.091, + 0.728, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.134, + 0.72, + 0.145 + ], + "angle": 0, + "content": "RealESRGAN" + }, + { + "type": "image", + "bbox": [ + 0.737, + 0.091, + 0.904, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.147, + 0.728, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.658, + 0.19, + 0.691, + 0.202 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.191, + 0.868, + 0.204 + ], + "angle": 0, + "content": "Ours (full size)" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.205, + 0.264, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.146, + 0.305, + 0.213, + 0.318 + ], + "angle": 0, + "content": "Set15 (x4)" + }, + { + "type": "image", + "bbox": [ + 0.269, + 0.205, + 0.378, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.248, + 0.335, + 0.259 + ], + "angle": 0, + "content": "HR" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.205, + 0.496, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.409, + 0.248, + 0.472, + 0.259 + ], + "angle": 0, + "content": "BSRGAN" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.205, + 0.612, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.248, + 0.589, + 0.259 + ], + "angle": 0, + "content": "ESRGAN" + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.205, + 0.728, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.247, + 0.72, + 0.259 + ], + "angle": 0, + "content": "RealESRGAN" + }, + { + "type": "image", + "bbox": [ + 0.737, + 0.205, + 0.904, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.305, + 0.691, + 0.317 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.319, + 0.264, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.146, + 0.419, + 0.213, + 0.432 + ], + "angle": 0, + "content": "Set20 (x4)" + }, + { + "type": "image", + "bbox": [ + 0.269, + 0.319, + 0.378, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.363, + 0.335, + 0.374 + ], + "angle": 0, + "content": "HR" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.319, + 0.496, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.409, + 0.363, + 0.472, + 0.374 + ], + "angle": 0, + "content": "BSRGAN" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.319, + 0.612, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.363, + 0.589, + 0.374 + ], + "angle": 0, + "content": "ESRGAN" + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.319, + 0.729, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.363, + 0.719, + 0.374 + ], + "angle": 0, + "content": "RealESRGAN" + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.305, + 0.868, + 0.318 + ], + "angle": 0, + "content": "Ours (full size)" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.486, + 0.484, + 0.622 + ], + "angle": 0, + "content": "perceptual-based setup, which involves using a perceptual loss gradient for guidance, we performed three sets of experiments: (1) without the visual loss, (2) directly adding the visual loss \\(\\sum \\mathcal{L}\\), and (3) incorporating the gradient of the loss \\(\\nabla \\mathcal{L}\\) into the noise. The experimental results demonstrate that incorporating the gradient of the loss into the noise yields the best performance. We also conducted experiments in a visual-based setup, the results under the visual-based setup also follow this trend." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.634, + 0.453, + 0.65 + ], + "angle": 0, + "content": "5.4. Experiments on Infrared Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.658, + 0.483, + 0.718 + ], + "angle": 0, + "content": "Setup. We employ YOLOv5-s for infrared image object detection, fine-tuning it specifically on the \\(\\mathbf{M}^3\\mathrm{FD}\\) dataset. The model is fine-tuned with a batch size of 16, using the SGD optimizer with learning rate of 0.01." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.719, + 0.483, + 0.885 + ], + "angle": 0, + "content": "Quantitative Comparison. The left section of Figure 6 presents a quantitative comparison of detection results across SOTA methods. In the top-right quadrant of the plot, the overall mAP of each model is displayed, while the other three quadrants represent the performance across individual categories. Our model consistently outperforms all other models in each detection category, demonstrating its superior ability in object detection tasks. Notably, in the truck detection category, our model achieves a \\(5.6\\%\\) improvement over the best-competing method, underscoring its robustness in identifying challenging classes." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Qualitative Comparison. The qualitative results in Figure" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.48, + 0.902, + 0.566 + ], + "angle": 0, + "content": "
    VisualPerceptualPSNRCLIP-IQAmAPmIoU
    --33.4660.510231.240.9
    ✓-34.5280.536531.741.3
    -✓33.9230.523032.842.2
    ✓✓34.5750.537933.142.4
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.576, + 0.904, + 0.59 + ], + "angle": 0, + "content": "Table 3. Ablation study on the effectiveness of multiple guidance." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.617, + 0.9, + 0.731 + ], + "angle": 0, + "content": "
    GuidePSNRCLIP-IQAmAPmIoU
    Perceptual Base-33.9230.523032.842.2
    + Visual∑L34.0610.534232.542.0
    + Visual∇L34.5750.537933.142.4
    Visual Base-34.5280.536531.741.3
    + Task∑L34.5610.537132.841.9
    + Task∇L34.5750.537933.142.4
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.529, + 0.741, + 0.889, + 0.755 + ], + "angle": 0, + "content": "Table 4. Ablation study for different guidance combinations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.901 + ], + "angle": 0, + "content": "4 demonstrate the superiority of our method in object detection. Other methods frequently miss at least one label or make errors. For example, in the first row, some methods fail to detect the person on the right side of the image, with none capable of detecting both signs above simultaneously. Only our method consistently achieves the best detection prediction results." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7540" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.142, + 0.251, + 0.855, + 0.266 + ], + "angle": 0, + "content": "Figure 4. Detection performance comparison of infrared image super-resolution with SOTA methods on \\(\\mathbf{M}^3\\mathrm{FD}\\) datasets." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.282, + 0.9, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.425, + 0.861, + 0.44 + ], + "angle": 0, + "content": "Figure 5. Segmentation performance comparison of infrared image super-resolution with SOTA methods on FMB datasets." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.463, + 0.48, + 0.622 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.633, + 0.483, + 0.661 + ], + "angle": 0, + "content": "Figure 6. Quantitative comparison of detection and segmentation results with SOTA methods." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.692, + 0.48, + 0.709 + ], + "angle": 0, + "content": "5.5. Experiments on Infrared Image Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.718, + 0.483, + 0.778 + ], + "angle": 0, + "content": "Setup. We perform semantic segmentation on the FMB dataset [29], the SegFormer-b1 model [52] is used as the backbone. The model is trained using the AdamW optimizer, with a learning rate of 6e-05." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Quantitative Comparison. The right section of Figure 6 presents a quantitative comparison of semantic segmentation results. The top-right quadrant of the circle represents the comparison of mIoU, while the remaining three quadrants depict the performance of other models across the three primary segmentation classes. Overall, our model achieves the best results in each category. Notably, it achieves the highest improvement in truck, with an im" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.466, + 0.905, + 0.496 + ], + "angle": 0, + "content": "provement of \\(7.4\\%\\). It also improves by \\(5.4\\%\\) and \\(3.0\\%\\) in car and human, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.498, + 0.907, + 0.651 + ], + "angle": 0, + "content": "Qualitative Comparison. The figure 5 presents a qualitative comparison of segmentation results from various SOTA methods. These results reveal that other methods often fail to segment complete objects, or they struggle with segmenting all relevant elements. For example, in other models, only part of the sign occurs, leaving parts of it undetected. While RealESRGAN shows some improvement, it still falls short of our method. Similarly, in the right image, other models fail to recognize the farthest poles and cannot fully capture the shapes of the people." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.667, + 0.634, + 0.683 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.692, + 0.907, + 0.845 + ], + "angle": 0, + "content": "In this paper, we propose a task-oriented infrared image super-resolution diffusion model, namely DiffIISR. Specifically, we introduce infrared thermal spectral distribution modulation as visual guidance to ensure consistency with high-resolution images by matching frequency components. In addition, we incorporate foundational vision models to provide perception guidance, which enhances detection and segmentation performance. With the above guidance, our method further optimizes each iteration of the diffusion process, refining the model at each denoising step and achieving superior visual and perceptual performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.846, + 0.905, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments: This work was partially supported by the National Natural Science Foundation of China (No.62302078 and No.62372080), and China Postdoctoral Science Foundation (2023M730741)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.958 + ], + "angle": 0, + "content": "7541" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.119, + 0.188, + 0.135 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.145, + 0.483, + 0.213 + ], + "angle": 0, + "content": "[1] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne Van Den Berg. 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Contourlet refinement gate framework for thermal spectrum distribution regularized infrared image super-resolution. arXiv preprint arXiv:2411.12530, 2024. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7544" + } + ] +] \ No newline at end of file diff --git a/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_origin.pdf b/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2ee0ad60ac950521d2494f4efc6b9afba630299e --- /dev/null +++ b/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/7a53821b-b747-463f-8310-ef76d61abca9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c9672267d3523fdad69ef751a0c54a9c08a0214d4363bacd71dedf665d8a3387 +size 3795728 diff --git a/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/full.md b/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c0dc69ef18382adda63fcbf95acb54f0f140c9da --- /dev/null +++ b/2025/DifIISR_ A Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution/full.md @@ -0,0 +1,373 @@ +# Diffusion Model with Gradient Guidance for Infrared Image Super-Resolution + +Xingyuan Li $^{1\dagger}$ , Zirui Wang $^{1\dagger}$ , Yang Zou $^{2}$ , Zhixin Chen $^{3}$ , Jun Ma $^{1}$ , Zhiying Jiang $^{4}$ , Long Ma $^{1}$ , Jinyuan Liu $^{1*}$ + +$^{1}$ School of Software Technology & DUT-RU International School of ISE, Dalian University of Technology + +$^{2}$ School of Computer Science, Northwestern Polytechnical University +3Graduate School of Information, Production, and Systems, Waseda University +4 College of Information Science and Technology, Dalian Maritime University xingyuan_lxy@163.com atlantis918@hotmail.com + +![](images/22532a8bf8e4e5ba7b73d8e9c93f6c3aa6f7bdfc4abdf73373234aec849328cf.jpg) +Figure 1. The left side shows a comparison between existing super-resolution methods and our proposed DiffISR. Our method introduces additional visual guidance based on the Fourier Transform, as well as foundational model-based perception guidance. The right side demonstrates that our method outperforms other methods in both detection and segmentation tasks. + +# Abstract + +Infrared imaging is essential for autonomous driving and robotic operations as a supportive modality due to its reliable performance in challenging environments. Despite its popularity, the limitations of infrared cameras, such as low spatial resolution and complex degradations, consistently challenge imaging quality and subsequent visual tasks. Hence, infrared image super-resolution (IISR) has been developed to address this challenge. While recent developments in diffusion models have greatly advanced this field, current methods to solve it either ignore the unique modal characteristics of infrared imaging or overlook the machine perception requirements. To bridge these gaps, we propose DifIISR, an infrared image super-resolution diffusion model optimized for visual quality and perceptual performance. Our approach achieves task-based guidance for diffusion by injecting gradients derived from visual and + +perceptual priors into the noise during the reverse process. Specifically, we introduce an infrared thermal spectrum distribution regulation to preserve visual fidelity, ensuring that the reconstructed infrared images closely align with high-resolution images by matching their frequency components. Subsequently, we incorporate various visual foundational models as the perceptual guidance for downstream visual tasks, infusing generalizable perceptual features beneficial for detection and segmentation. As a result, our approach gains superior visual results while attaining State-Of-The-Art downstream task performance. Code is available at https://github.com/zirui0625/DifIISR + +# 1. Introduction + +The objective of infrared image super-resolution (IISR) is to reconstruct a high-resolution (HR) infrared image from its low-resolution (LR) counterpart [51]. The consistent performance of infrared imaging under challenging conditions allows its application to span various fields [31, 44, 45], + +such as object detection [28, 40, 41], semantic segmentation [24, 30], and autonomous driving [2, 42]. Despite its great potential, the inherent limitations of infrared cameras — such as high noise levels, reduced spatial resolution, and limited dynamic range — continually affect the quality of infrared images. + +Conventionally, CNN-based methods [18, 33, 61-63] address this challenge by mapping interpolated LR images to HR images and then enhancing the details (e.g., SR-CNN [35]). Although CNN-based super-resolution methods have significantly advanced this field, they are limited by the perceptual field of local convolution operations. To overcome this, Transformer-based methods [3, 4, 56, 60] model long-range dependencies to capture global context. Liang et al. [26] proposed SwinIR significantly improving super-resolution performance by integrating CNNs with the Swin Transformer. Lately, Li et al. [25] proposed CoRPLE, which leverages a Contourlet residual framework to restore infrared-specific high-frequency features. + +Recently, the diffusion model has introduced a novel paradigm for image super-resolution tasks, offering a fresh approach that goes beyond the CNN- and Transformer-based methods [11], leveraging its capacity to learn implicit priors of the underlying data distribution [39]. Yue et al. proposed ResShift [55], which applies an iterative sampling procedure to shift the residual between the LR and the desired HR image during inference. Unlike other diffusion models, Wang et al. [49] accelerate the diffusion-based SR model to a single inference step while maintaining satisfactory performance. These methods generally achieve visually pleasing results when applied to visible images. + +However, existing methods often fail to extend effectively to infrared imaging, particularly in downstream tasks such as infrared image object detection and semantic segmentation. A common approach for task-oriented infrared image super-resolution is to adapt an RGB super-resolution model to infrared data, and then connect it to a downstream detection or segmentation module. Unfortunately, this approach faces two significant challenges: 1) Ignoring the unique modal characteristics of infrared imaging, which include distinct thermal spectrum distributions. Infrared image reconstruction quality is particularly sensitive to high-frequency components due to longer wavelengths and reduced atmospheric scattering effects. 2) Overlooking the machine perception requirements. While the model may reconstruct visually appealing images, these results are often sub-optimal for specific perceptual tasks. The objectives of visual domain optimization and perceptual domain optimization can differ significantly [28]. For instance, diffusion-based super-resolution models typically focus on "seeking visually appealing" results, often at the expense of structural information of targets and textural details critical for machine vision. Given these limitations, we ask, "Why + +not develop a super-resolution model that reconstructs infrared images to be both visually appealing and perceptually salient?" + +To this end, as shown in figure 1, we propose a task-oriented infrared image super-resolution method that optimizes the diffusion process through gradient-based guidance. Specifically, we inject the gradient of a designed prior loss into the noise estimation at each training step, refining the model's performance across iterations. Our guidance consists of two components. First, to ensure visual consistency, we introduce visual guidance via infrared thermal spectral distribution modulation, which ensures the reconstructed images align with high-resolution counterparts by preserving their spectral characteristics. Second, we integrate perceptual guidance by leveraging powerful pretrained vision models, such as VGG [37] and SAM [22], to infuse the diffusion process with generalized perceptual features. Extensive experiments demonstrate that our proposed method excels in both visual quality and downstream task performance. Our contributions can be summarized as follows: + +- We propose a solution for infrared image super-resolution by integrating gradient-based priors into the noise during diffusion, enabling task-based guidance in sampling, and achieving simultaneous optimization in both visual and perceptual-specific domains. +- We introduce a thermal spectrum distribution regulation to preserve the visual fidelity of infrared images, guiding the diffusion process to learn the unique infrared image frequency distribution. +- We propose perceptual guidance for the diffusion process, incorporating generalizable perceptual features from foundational models for visual tasks. This notably enhances performance in detection and segmentation. + +# 2. Related work + +# 2.1. Image Super-Resolution + +Since the pioneering work of SRCNN [13] was proposed, deep learning has gradually become the mainstream approach for image super-resolution (SR). The initial works [13, 21, 23, 63] mainly focused on utilizing convolutional neural networks (CNNs) [12] for image super-resolution tasks and optimizing the network by minimizing the mean square error (MSE) between the super-resolved image (SR) and their corresponding high-resolution (HR) counterparts. Subsequently, GAN-based super-resolution methods were proposed, drawing significant attention. For example, both BSRGAN [57] and Real-ESRGAN [48] employ GANs for super-resolution tasks and introduce training samples with more realistic types of degradations to achieve better results. While these methods improve the quality of the low-resolution images, they often fail to produce stable + +outcomes, resulting in artifacts in the images. LDL [27] and DeSRA [53] attempt to address this issue, but they still struggle to generate images with natural details. Recently, diffusion models have been widely applied to image super-resolution tasks, such as ResShift [55] and SinSR [49]. However, these methods are not designed specifically for the characteristics of infrared images and overlook the requirements of machine perception [64], so they do not perform well in infrared image super-resolution (IISR). + +# 2.2. Diffusion Methods + +The Diffusion Denoising Probabilistic Model (DDPM) [16] is a generative model with stability and controllability. Since it was proposed, it has attracted widespread attention. The main focus of the diffusion model is to train a denoising autoencoder, which estimates the reverse process of the Markov diffusion process by predicting the noise. Diffusion models were initially applied to image generation tasks and have been continuously improved in recent years [1, 32, 34, 38, 39]. ControlNet [58] introduces control conditions into pre-trained diffusion models, expanding the application scope of diffusion models in image generation. DDIM [38] proposes a non-Markovian generation method, significantly enhancing the inference speed of diffusion models. Diffusion models have demonstrated exceptional capabilities not only in image generation tasks but also in various other tasks, showing great potential. With the introduction of several related methods [8, 9, 19, 36, 49, 55], diffusion models have also been validated to achieve remarkable results in the field of image super-resolution. + +# 3. Preliminaries + +We first introduce the background of Denoising Diffusion Probabilistic Models [16]. DDPM obtains samples $x_0 \sim p_{\mathrm{data}}(x)$ from the data distribution. In a diffusion model, noise is gradually added to the sampled $x_0$ over time steps up to $T$ , eventually resulting in $x_T \sim \mathcal{N}(0, \mathbf{I})$ , which can be approximated as a standard Gaussian distribution. This process is also referred to as the forward process of the diffusion model, and it can be represented as: + +$$ +q \left(x _ {t} \mid x _ {0}\right) = \mathcal {N} \left(x _ {t}; \sqrt {\alpha_ {t}} x _ {0}, (1 - \alpha_ {t}) \mathbf {I}\right), \tag {1} +$$ + +where $\alpha_{t} = \prod_{s = 1}^{t}(1 - \beta_{s})$ , and $\beta_{s}$ are fixed or learned variance schedule. After obtaining $x_{T}$ , the denoising model $\epsilon_{\phi}$ learns to predict the noise $\epsilon$ added during the forward process, thereby removing the noise from $x_{T}$ . Specifically, the denoising model $\epsilon_{\phi}$ predicts the noise by optimizing the re-weighted evidence lower bound, which can be written as: + +$$ +\mathcal {L} _ {\text {s i m p l e}} (\phi) = \mathbb {E} _ {x _ {0}, t, \epsilon} \left[ \| \epsilon_ {\phi} (x _ {t}, t) - \epsilon \| ^ {2} \right]. \tag {2} +$$ + +In this formula, $\epsilon_{\phi}(x_t,t)$ represents the noise predicted by the model, and $t$ is randomly sampled from a predefined + +range of time steps. During the training process, the denoising model $\epsilon_{\phi}$ is optimized by minimizing $\mathcal{L}_{\mathrm{simple}}(\phi)$ , ultimately resulting in a model capable of accurately predicting the noise. + +After training the denoising model $\epsilon_{\phi}$ , we sample $x_{T} \sim \mathcal{N}(0, \mathbf{I})$ and iteratively refine it using the denoising model. This process is also known as the reverse process, and the specific formula can be represented as: + +$$ +p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right) = \mathcal {N} \left(x _ {t - 1}; \mu_ {\theta} \left(x _ {t}, t\right), \Sigma_ {\theta} \left(x _ {t}, t\right)\right), \tag {3} +$$ + +where $\mu_{\theta}(x_t,t)$ is the mean function from step $t$ to $t - 1$ and $\Sigma_{\theta}(x_t,t)$ is the covariance. Due to the slow sampling process of DDPM, DDIM proposes using a non-Markovian diffusion process, which significantly improves the model's sampling speed. The improved sampling formula can be expressed as: + +$$ +x _ {t - 1} = \sqrt {\alpha_ {t - 1}} \hat {x} _ {0} \left(x _ {t}\right) + \sqrt {1 - \alpha_ {t - 1} - \sigma_ {t} ^ {2}} \epsilon_ {\phi} \left(x _ {t}, t\right) + \sigma_ {t} z, \tag {4} +$$ + +where $\sigma_{t}$ is the variance of the noise and $z$ follows a standard normal distribution. $\hat{x}_0(x_t)$ is the predicted $x_0$ from $x_{t}$ , and the prediction formula is: + +$$ +\hat {x} _ {0} (x _ {t}) = \frac {1}{\sqrt {\alpha_ {t}}} \left(x _ {t} - \sqrt {1 - \alpha_ {t}} \epsilon_ {\phi} (x _ {t}, t)\right). \tag {5} +$$ + +When $\sigma_{t}$ equals 0, it is evident that the DDIM sampling process can be regarded as a deterministic process, which allows for quick sampling results from the noise. + +# 4. Method + +Overview. Our main objective is to address the problem of infrared image super-resolution using a diffusion model enhanced by gradient-based guidance, as shown in figure 2. Specifically, inspired by [10], we propose a method that fine-tunes the diffusion model by introducing an additional guidance mechanism. In addition, we incorporate a dual optimization approach combining visual and perceptual aspects to better adapt the diffusion model to the task of infrared image super-resolution. + +# 4.1. Loss-gradient Guidance + +The reverse process of diffusion models often requires multiple constraints to generate stable, high-quality images. Most methods tend to guide the reverse process by adding weighted constraints to the final loss function. In contrast, our approach addresses this issue from the perspective of posterior sampling. Inspired by [10], we introduce additional priors and compute the gradient of the resulting loss function, injecting the gradient into the noise estimated at each step to better handle the problem of adding constraints during the reverse process of diffusion models. + +![](images/379c92573d6032ebc81cd95d1d50b9894f923708399b96abac0e47c30f807258.jpg) +Figure 2. Overall architecture of our proposed method: the vanilla super-resolution diffusion process is marked in black, whereas our proposed additional visual and perceptual priors are marked in red. + +Generally, the noise predicted by the denoising model at timestep $t$ is often correlated with the score of the denoising model at the current timestep [39]. Specifically, it can be represented as: + +$$ +\epsilon_ {\phi} \left(x _ {t}, t\right) = - \sqrt {1 - \alpha_ {t}} \nabla_ {x _ {t}} \log p \left(x _ {t}\right), \tag {6} +$$ + +where $\nabla_{x_t}\log p(x_t)$ is the gradient of $x_{t}$ with respect to the probability density function $\log p(x_{t})$ , but now we need to consider not only $\nabla_{x_t}\log p(x_t)$ , we also need to incorporate optimization of $g$ during the diffusion model sampling. In our work, $g$ represents the guidance obtained by feeding $x_0$ into $\mathcal{M}$ , and $\mathcal{M}$ is a forward operator. The relationship between $g$ and $x_0$ can be expressed as $g = \mathcal{M}(x_0)$ . Therefore, the score of the denoising model at timestep $t$ becomes $\nabla_{x_t}\log p(x_t\mid g)$ . + +$\nabla_{x_t}\log p(x_t\mid g)$ is unknown, and we need to use the known $\nabla_{x_t}\log p(x_t)$ to derive $\nabla_{x_t}\log p(x_t\mid g)$ . According to Bayes' theorem, we can write: + +$$ +\nabla_ {x _ {t}} \log p (x _ {t} \mid g) = \nabla_ {x _ {t}} \log p (x _ {t}) + \nabla_ {x _ {t}} \log p (g \mid x _ {t}). \tag {7} +$$ + +From this, it can be seen that $\nabla_{x_t}\log p(x_t)$ is known, and the problem changes from calculating $\nabla_{x_t}\log p(x_t\mid g)$ to calculating $\nabla_{x_t}\log p(g\mid x_t)$ . Inspired by [10], we can derive the formula: + +$$ +\begin{array}{l} \nabla_ {x _ {t}} \log p (g \mid x _ {t}) \simeq \nabla_ {x _ {t}} \log p (g \mid \hat {x} _ {0} (x _ {t})) \tag {8} \\ \simeq - \rho \nabla_ {x _ {t}} \| g - \mathcal {M} (\hat {x} _ {0} (x _ {t})) \| _ {2} ^ {2}, \\ \end{array} +$$ + +where $\nabla_{x_t}\| g - \mathcal{M}(\hat{x}_0(x_t))\| _2^2$ also can be represented as $\nabla \mathcal{L}_g$ . Therefore, we can express the noise prediction ad + +justed according to condition $g$ as: + +$$ +\begin{array}{l} \epsilon_ {\phi} ^ {\prime} = \epsilon_ {\phi} \left(x _ {t}, t\right) + \rho \sqrt {1 - \alpha_ {t}} \nabla_ {x _ {t}} \| g - \mathcal {M} \left(\hat {x} _ {0} \left(x _ {t}\right)\right) \| _ {2} ^ {2} \tag {9} \\ = \epsilon_ {\phi} (x _ {t}, t) + \rho \sqrt {1 - \alpha_ {t}} \nabla \mathcal {L} _ {g}, \\ \end{array} +$$ + +where $\epsilon_{\phi}^{\prime}$ represents the adjusted noise, obtained by adding the gradient of the guidance loss $\nabla \mathcal{L}_g$ to the noise predicted by the original denoising model. + +Thus, by applying gradient guidance to the noise predicted by the diffusion model, we impose constraints on the reverse process of the diffusion model. More detailed derivations and pseudocode of our method can be found in the supplementary materials. + +# 4.2. Visual-perceptual Dual Optimization + +Now, let's explain the composition of our guidance $\mathcal{L}_g$ in detail. Specifically, $\mathcal{L}_g$ can be divided into two parts: visual loss $\mathcal{L}_{\mathrm{visual}}$ and perceptual loss $\mathcal{L}_{\mathrm{perceptual}}$ . + +$\nu$ - visual guidance. To guide the diffusion process in reconstructing infrared images towards infrared-specific visual characteristics, we propose $\mathcal{L}_{\mathrm{visual}}$ to regularize the distribution of high- and low-frequency information as visual guidance $\nu$ . Here, $\nu$ replaces the forward operator $\mathcal{M}$ in equation 8. Given the HR image $\mathbf{I}_{HR}$ and the super-resolved image $\mathbf{I}_{SR}$ , we first use Fast Fourier Transforms (FFT) to transform their spatial domain representation into the frequency domain, formally: + +$$ +\begin{array}{l} \hat {\mathbf {I}} _ {H R} = \mathcal {F} (\mathbf {I} _ {H R}), \hat {\mathbf {I}} _ {S R} = \mathcal {F} (\mathbf {I} _ {S R}), \\ \mathcal {F} (u, v) = \sum_ {x = 0} ^ {H - 1} \sum_ {y = 0} ^ {W - 1} I (x, y) \cdot e ^ {- i \frac {2 \pi}{H} u x} \cdot e ^ {- i \frac {2 \pi}{W} v y}. \tag {10} \\ \end{array} +$$ + +where $\mathcal{F}(u,v)$ denotes the FFT of the image at frequency coordinates $(u,v)$ , and $\hat{\mathbf{I}}_{HR}$ is the transformed HR images. In the frequency domain, we first shift the zero-frequency component, which represents the mean intensity of the image, to the center of the spectrum for both HR and SR images, yielding $\hat{\mathbf{I}}_{HR}^{\mathrm{shift}}$ and $\hat{\mathbf{I}}_{SR}^{\mathrm{shift}}$ . Following this, we compute the magnitude spectra $\mathbf{M}_{HR}$ and $\mathbf{M}_{SR}$ by applying logarithmic compression to the Fourier-transformed images. This step ensures a balanced consideration of both high-frequency and low-frequency components during comparison. To focus the loss on matching the frequency distribution patterns rather than absolute intensity differences, we normalize the magnitude spectra to have zero mean and unit variance, resulting in the normalized spectra $\mathbf{M}_{HR}^{\mathrm{norm}}$ and $\mathbf{M}_{SR}^{\mathrm{norm}}$ . Finally, the Visual Loss $\mathcal{L}_{\mathrm{visual}}$ is computed as the mean squared error between the normalized magnitude spectra of the HR and SR images: + +$$ +\mathcal {L} _ {\text {v i s u a l}} = \left(\overbrace {N \left(\log \left(1 + | \hat {\mathbf {I}} _ {H R} ^ {\text {n o r m}} |\right)\right)} ^ {\mathrm {M} _ {H R} ^ {\text {n o r m}}} - \overbrace {N \left(\log \left(1 + | \hat {\mathbf {I}} _ {S R} ^ {\text {n o r m}} |\right)\right)} ^ {\mathrm {M} _ {S R} ^ {\text {n o r m}}}\right) ^ {2}, \tag {11} +$$ + +where $N(\cdot)$ represents the normalization operation. Visual Loss plays a critical role in preserving the frequency distribution of the infrared image. + +$\mathcal{P}$ - perceptual guidance. Large models provide many priors for current methods [14, 15], to regularize the diffusion process to better align with machine perception, we adopt $\mathcal{L}_{\mathrm{perceptual}}$ that consists of the VGG Loss $\mathcal{L}_{\mathrm{VGG}}$ and the Segmentation Loss $\mathcal{L}_{\mathrm{seg}}$ as perceptual guidance $\mathcal{P}$ . Here, $\mathcal{P}$ replaces the forward operator $\mathcal{M}$ in equation 8. Given the HR image $\mathbf{I}_{HR}$ and the super-resolved image $\mathbf{I}_{SR}$ , the VGG Loss is computed by mean squared error between the extracted features of the HR and SR images from a pretrained deep neural network. This guides the model to capture nuanced aspects of images, including textures, edges, and shapes, which are crucial for preserving visual fidelity. To enhance the semantic fidelity of the reconstructed images, we regulate the diffusion process using the Segment Anything Model (SAM) [22] and propose the Segmentation Loss $\mathcal{L}_{\mathrm{seg}}$ . Given the HR image $\mathbf{I}_{HR}$ and the super-resolved image $\mathbf{I}_{SR}$ , we use a locked SAM to segment the masks $\mathbf{S}_{HR}$ and $\mathbf{S}_{SR}$ for $\mathbf{I}_{HR}$ and $\mathbf{I}_{SR}$ , respectively. The Segmentation Loss $\mathcal{L}_{\mathrm{seg}}$ is then computed by mean squared error between $\mathbf{S}_{HR}$ and $\mathbf{S}_{SR}$ , providing effective high-level supervision for the reconstructed images. + +The Perceptual Loss $\mathcal{L}_{\mathrm{perceptual}}$ is computed by integrating the VGG-based and segmentation-based losses, as: + +$$ +\mathcal {L} _ {\text {p e r c e p t u a l}} = \overbrace {\left\| \phi_ {l} \left(\mathbf {I} _ {H R}\right) - \phi_ {l} \left(\mathbf {I} _ {S R}\right) \right\| _ {2} ^ {2}} ^ {\mathcal {L} _ {\mathrm {V G G}}} + \overbrace {\left\| \mathbf {S} _ {H R} - \mathbf {S} _ {S R} \right\| _ {2} ^ {2}} ^ {\mathcal {L} _ {\mathrm {s e g}}}, \tag {12} +$$ + +where $\phi_l(\cdot)$ represents the feature map extracted from the $l$ -th layer of a pre-trained deep neural network (in our experiment, VGG-16). + +The incorporation of visual and perceptual guidance refines each iteration of the diffusion, facilitating a more optimized denoising procedure. This not only improves visual fidelity but also enhances perceptual performance. + +# 5. Experiments + +# 5.1. Experimental Settings + +Dataset and evaluation metrics. To ensure the fairness of the experiment, we used the same training [28] and test sets [28, 43, 54], as CoRPLE [25]. We use the infrared image dataset $\mathrm{M}^3\mathrm{FD}$ [28] to train the model and evaluate its performance using three datasets: $\mathrm{M}^3\mathrm{FD}$ [28], RoadScene [54], and TNO [43]. We adopt five metrics to evaluate the performance of our model quantitatively: CLIP-IQA [46], MUSIQ [20], PSNR, LPIPS [59], and SSIM [50]. Among them, CLIPIQA and MUSIQ are no-reference metrics. CLIPIQA leverages the CLIP model [35] to assess image quality, while MUSIQ uses a multi-scale feature extraction approach for quality evaluation. We mainly rely on CLIPIQA and MUSIQ as evaluation metrics to compare the performance of different methods. + +Implementation Details. Our network was trained on a GeForce RTX 4090 GPU. Our backbone model and specific experimental parameter settings largely follow ResShift [55]. Notably, ResShift uses the residual between high-resolution (HR) and low-resolution images (LR) as the noise for the diffusion model, meaning that we can effectively apply gradient guidance on the residual between HR and LR images. During training, our approach differs from ResShift in that we initially perform 200K iterations on a new training set to enable the model to develop basic infrared image super-resolution capabilities. Subsequently, we incorporate conditional (visual and perceptual) guidance into the model and conduct an additional 50K training iterations to achieve improved results. + +# 5.2. Experiments on Infrared SR + +We perform a comprehensive comparison of our approach with eleven SOTA methods, including ESRGAN [47], RealSR-JPEG [17], BSRGAN [57], SwinIR [26], RealESRGAN [48], HAT [5], DAT [6], ResShift [55], CoPRLE [25], Bi-DiffSR [7] and SinSR [49]. Table 1, 2 presents our quantitative comparison results compared with the above methods and Figure 3 presents our qualitative results. + +Quantitative Comparison. Table 1 presents a quantitative comparison of CLIPIQA and MUSIQ on the $\mathbf{M}^3\mathrm{FD}$ dataset against various methods. CLIPIQA inherits the powerful representation capabilities of CLIP, demonstrating stable and robust performance in evaluating the perceptual quality of natural images. Our method outperforms other methods on both metrics across all three test sets, indicating that our approach better aligns with the human perceptual system. + +
    DatasetsSet5Set15Set20
    MethodsCLIP-IQA↑MUSIQ↑CLIP-IQA↑MUSIQ↑CLIP-IQA↑MUSIQ↑
    Low Resolution1-0.216724.6090.204923.0630.223022.446
    ESRGAN [47]ECCV'180.213040.8190.203840.7450.180436.654
    RealSR-JPEG [17]CVPR'200.361548.4190.357349.2250.327747.213
    BSRGAN [57]CVPR'210.329053.1190.319452.6440.330151.917
    SwinIR [26]CVPR'210.216037.1560.223037.9700.225834.919
    RealESRGAN [48]ICCV'210.278054.3060.242453.1630.252351.647
    HAT [5]CVPR'230.229838.0500.237739.7430.246635.633
    DAT [6]ICCV'230.229737.5380.241039.4190.251835.750
    ResShift [55]NeurIPS'230.470150.7690.442852.8710.408251.244
    CoRPLE [25]ECCV'240.233936.2810.228136.4580.228134.270
    SinSR [49]CVPR'240.587754.3550.576254.1060.535753.187
    Bi-DiffSR [7]NeurIPS'240.315135.3560.275836.1020.267436.537
    DifiISROurs0.614455.1940.590654.5040.548453.636
    High Resolution-0.220034.0660.216134.4100.213932.024
    + +Table 1. No-reference Metrics Comparison of infrared image super-resolution with SOTA methods on ${\mathrm{M}}^{3}\mathrm{{FD}}$ datasets. + +
    MetricsDatasets
    Set5Set15Set20
    ResShiftSinSRBi-DiffSRDifIISRResShiftSinSRBi-DiffSRDifIISRResShiftSinSRBi-DiffSRDifIISR
    PSNR↑30.10131.64532.02232.27930.28331.98832.14532.35130.97633.43833.44733.451
    SSIM↑0.83290.84810.85790.86370.82280.84260.84710.85780.84460.88530.88740.8941
    LPIPS↓0.31790.27370.28160.27040.35370.28170.29240.28450.35070.25490.28200.2735
    + +Table 2. Reference-based Metrics Comparison with diffusion-based methods on ${\mathrm{M}}^{3}\mathrm{{FD}}$ datasets. + +Additionally, our method achieves superior performance on MUSIQ compared to all other methods, demonstrating that it can also achieve excellent results in multi-scale image quality assessment. + +It is worth noting that we also compared our method against HR images on no-reference metrics. Our method significantly outperforms HR images in no-reference visual quality metrics, demonstrating an enhancement over the HR images. However, this improvement introduces a challenge: in comparison to traditional methods on reference-based metrics such as PSNR, LPIPS, and SSIM, our approach shows less advantage, as our results differ significantly from the HR images. Nevertheless, our method still leads diffusion-based methods on reference-based metrics, as shown in Table 2. This demonstrates that our approach leverages the powerful generative capabilities of diffusion to produce high-quality images while also preserving essential detail features from the HR images under both visual and perceptual guidance. + +Qualitative Results. The qualitative results shown in Figure 3 emphasize the superiority of our method in visual performance compared to other approaches. Additional ex + +amples can be found in the supplementary materials. We selected one image from each of the three datasets, Set5, Set15, and Set20, for qualitative analysis to ensure comprehensive evaluation. Our method achieves more natural details in portraits, avoiding color discrepancies and better matching the contours of the true image. For vehicle details, our method accurately reproduces the grille at the front of the vehicle in the true image, whereas other methods tend to blur these details. This demonstrates that our method also has distinct advantages in qualitative results. + +# 5.3. Ablation Study + +Experiments on the effectiveness of guidance. We conducted ablation experiments to evaluate the effectiveness of visual and perceptual guidance on the infrared super-resolution task, as shown in Table 3. We assessed the super-resolution results under four conditions: without guidance, with only visual guidance, with only perceptual guidance, and with both visual and perceptual guidance. The results show that the infrared image super-resolution performance is best when both guidances are applied. + +Experiments on the guidance combinations. We conducted ablation experiments on different guidance combinations of various methods, as shown in Table 4. In the + +![](images/d90b6ce804fc1a0e05b2e9df4b82dca4dd2c8cfc8c8c31dffd421f780fe5693d.jpg) +Set5 (x4) + +![](images/67699fe7d4b7b00e41bb277acb732f1a2f9c86765fb0f4a474d67eb152ffbbf0.jpg) +HR + +![](images/f7c72990d34a2b92120c2ae98ffe32509c3be4de389570d2ffe4777957c2fd3d.jpg) +BSRGAN + +![](images/d38f56050f511afa69977724ef6ff1e7c1891f2853244fa182d483bb63b55e18.jpg) +ESRGAN + +![](images/e7e3742df12fe89166b5577ec4e83c73f189304dca8dcca0f293f8ac60c20a74.jpg) +RealESRGAN + +![](images/4a920fdf9f2ce32ec2980f0e15e5d2f36bdc9f2c215f9cbc1460ee101bd430fe.jpg) + +![](images/d0632e727ae2d78e3aaafe025def38d351542b30415f7deebcd708b2d3c09ce8.jpg) +Ours + +![](images/556119d78f8ca955873cbd1b8897312ea7fe09e6afde675c002c47c9a9add68f.jpg) +Set15 (x4) + +![](images/e3b00f1f23bdc0dcfbb5710ffb78ed78533e7fa4ecc2a3c1f5f1c0c5c9fd92c6.jpg) +HR + +![](images/d68eb34e38ea2478a751ee9d5321dae93bc8aafed7ed024005e03cf4b08786c3.jpg) +BSRGAN + +![](images/4c43ddf6f2a0d8fa00aac5931cdc1bbd9dab92e35c3811f35abc911a072fc5f7.jpg) +ESRGAN + +![](images/6d57f7186f7b8504d60f31fe6dc6cc03fbd9bd8221ea28d60c9676af253fa5c3.jpg) +RealESRGAN + +![](images/2879c678ebb94bcf57fd3d49e187d4a4596d7b12ed414d0d358e94fee75d2b46.jpg) +Ours (full size) +Ours (full size) + +![](images/a1cc24243c3c6d7b502b53530928f79f7905def74fb3bd946ff6d24c34ed7ad6.jpg) +Set20 (x4) + +![](images/0509c151f56c315b59e892c618883097341e2fea1167e8afada3db2979e3a505.jpg) +HR + +![](images/97b87fd7ff49ce4575d8b322f1efe99fd4801affc70995ded494d5c4be6dbccb.jpg) +BSRGAN + +![](images/6e093eabeeb6df8daa0e976fe9bca88251cdd57ad4ff1531ba4c81a8c7e47ee5.jpg) +ESRGAN + +![](images/05a8acbfab36fa8248d7bc2f30d44ced2969ebfc1610f802b5e1f6af90326c6d.jpg) +Ours +RealESRGAN + +perceptual-based setup, which involves using a perceptual loss gradient for guidance, we performed three sets of experiments: (1) without the visual loss, (2) directly adding the visual loss $\sum \mathcal{L}$ , and (3) incorporating the gradient of the loss $\nabla \mathcal{L}$ into the noise. The experimental results demonstrate that incorporating the gradient of the loss into the noise yields the best performance. We also conducted experiments in a visual-based setup, the results under the visual-based setup also follow this trend. + +# 5.4. Experiments on Infrared Object Detection + +Setup. We employ YOLOv5-s for infrared image object detection, fine-tuning it specifically on the $\mathbf{M}^3\mathrm{FD}$ dataset. The model is fine-tuned with a batch size of 16, using the SGD optimizer with learning rate of 0.01. + +Quantitative Comparison. The left section of Figure 6 presents a quantitative comparison of detection results across SOTA methods. In the top-right quadrant of the plot, the overall mAP of each model is displayed, while the other three quadrants represent the performance across individual categories. Our model consistently outperforms all other models in each detection category, demonstrating its superior ability in object detection tasks. Notably, in the truck detection category, our model achieves a $5.6\%$ improvement over the best-competing method, underscoring its robustness in identifying challenging classes. + +Qualitative Comparison. The qualitative results in Figure + +
    VisualPerceptualPSNRCLIP-IQAmAPmIoU
    --33.4660.510231.240.9
    ✓-34.5280.536531.741.3
    -✓33.9230.523032.842.2
    ✓✓34.5750.537933.142.4
    + +Table 3. Ablation study on the effectiveness of multiple guidance. + +
    GuidePSNRCLIP-IQAmAPmIoU
    Perceptual Base-33.9230.523032.842.2
    + Visual∑L34.0610.534232.542.0
    + Visual∇L34.5750.537933.142.4
    Visual Base-34.5280.536531.741.3
    + Task∑L34.5610.537132.841.9
    + Task∇L34.5750.537933.142.4
    + +Table 4. Ablation study for different guidance combinations. + +4 demonstrate the superiority of our method in object detection. Other methods frequently miss at least one label or make errors. For example, in the first row, some methods fail to detect the person on the right side of the image, with none capable of detecting both signs above simultaneously. Only our method consistently achieves the best detection prediction results. + +![](images/bfaaf9d948e358f425f2697b393c2252596c6cba541b1968149d0a7d6b8b7521.jpg) +Figure 4. Detection performance comparison of infrared image super-resolution with SOTA methods on $\mathbf{M}^3\mathrm{FD}$ datasets. + +![](images/8ee50d64148aea64a89ef72ef45fe989480e7eff66f36cf4c982fde5d2ba46e3.jpg) +Figure 5. Segmentation performance comparison of infrared image super-resolution with SOTA methods on FMB datasets. + +![](images/d959f3aeab8d4aab6ce8ed09c951182ca22a2ab2b4600a869a53d1f0200b951c.jpg) +Figure 6. Quantitative comparison of detection and segmentation results with SOTA methods. + +# 5.5. Experiments on Infrared Image Segmentation + +Setup. We perform semantic segmentation on the FMB dataset [29], the SegFormer-b1 model [52] is used as the backbone. The model is trained using the AdamW optimizer, with a learning rate of 6e-05. + +Quantitative Comparison. The right section of Figure 6 presents a quantitative comparison of semantic segmentation results. The top-right quadrant of the circle represents the comparison of mIoU, while the remaining three quadrants depict the performance of other models across the three primary segmentation classes. Overall, our model achieves the best results in each category. Notably, it achieves the highest improvement in truck, with an im + +provement of $7.4\%$ . It also improves by $5.4\%$ and $3.0\%$ in car and human, respectively. + +Qualitative Comparison. The figure 5 presents a qualitative comparison of segmentation results from various SOTA methods. These results reveal that other methods often fail to segment complete objects, or they struggle with segmenting all relevant elements. For example, in other models, only part of the sign occurs, leaving parts of it undetected. While RealESRGAN shows some improvement, it still falls short of our method. Similarly, in the right image, other models fail to recognize the farthest poles and cannot fully capture the shapes of the people. + +# 6. Conclusion + +In this paper, we propose a task-oriented infrared image super-resolution diffusion model, namely DiffIISR. Specifically, we introduce infrared thermal spectral distribution modulation as visual guidance to ensure consistency with high-resolution images by matching frequency components. In addition, we incorporate foundational vision models to provide perception guidance, which enhances detection and segmentation performance. With the above guidance, our method further optimizes each iteration of the diffusion process, refining the model at each denoising step and achieving superior visual and perceptual performance. + +Acknowledgments: This work was partially supported by the National Natural Science Foundation of China (No.62302078 and No.62372080), and China Postdoctoral Science Foundation (2023M730741). + +# References + +[1] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne Van Den Berg. Structured denoising diffusion models in discrete state-spaces. In Proceedings of the Advances in Neural Information Processing Systems, pages 17981-17993, 2021. 3 +[2] Bing Cao, Yiming Sun, Pengfei Zhu, and Qinghua Hu. Multi-modal gated mixture of local-to-global experts for dynamic image fusion. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 23555-23564, 2023. 2 +[3] Jiezhang Cao, Yawei Li, Kai Zhang, and Luc Van Gool. 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Residual dense network for image super-resolution. + +In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2472-2481, 2018. 2 +[64] Yang Zou, Zhixin Chen, Zhipeng Zhang, Xingyuan Li, Long Ma, Jinyuan Liu, Peng Wang, and Yanning Zhang. 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The left side shows a comparison between existing super-resolution methods and our proposed DiffISR. Our method introduces additional visual guidance based on the Fourier Transform, as well as foundational model-based perception guidance. The right side demonstrates that our method outperforms other methods in both detection and segmentation tasks." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 151, + 467, + 200, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 467, + 200, + 480 + ], + "spans": [ + { + "bbox": [ + 151, + 467, + 200, + 480 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 53, + 504, + 297, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 504, + 297, + 696 + ], + "spans": [ + { + "bbox": [ + 53, + 504, + 297, + 696 + ], + "type": "text", + "content": "Infrared imaging is essential for autonomous driving and robotic operations as a supportive modality due to its reliable performance in challenging environments. Despite its popularity, the limitations of infrared cameras, such as low spatial resolution and complex degradations, consistently challenge imaging quality and subsequent visual tasks. Hence, infrared image super-resolution (IISR) has been developed to address this challenge. While recent developments in diffusion models have greatly advanced this field, current methods to solve it either ignore the unique modal characteristics of infrared imaging or overlook the machine perception requirements. To bridge these gaps, we propose DifIISR, an infrared image super-resolution diffusion model optimized for visual quality and perceptual performance. Our approach achieves task-based guidance for diffusion by injecting gradients derived from visual and" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 469, + 556, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 469, + 556, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 556, + 613 + ], + "type": "text", + "content": "perceptual priors into the noise during the reverse process. Specifically, we introduce an infrared thermal spectrum distribution regulation to preserve visual fidelity, ensuring that the reconstructed infrared images closely align with high-resolution images by matching their frequency components. Subsequently, we incorporate various visual foundational models as the perceptual guidance for downstream visual tasks, infusing generalizable perceptual features beneficial for detection and segmentation. As a result, our approach gains superior visual results while attaining State-Of-The-Art downstream task performance. Code is available at https://github.com/zirui0625/DifIISR" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 633, + 395, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 633, + 395, + 645 + ], + "spans": [ + { + "bbox": [ + 314, + 633, + 395, + 645 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "content": "The objective of infrared image super-resolution (IISR) is to reconstruct a high-resolution (HR) infrared image from its low-resolution (LR) counterpart [51]. The consistent performance of infrared imaging under challenging conditions allows its application to span various fields [31, 44, 45]," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 702, + 219, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 702, + 219, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 702, + 219, + 713 + ], + "type": "text", + "content": "† Equal contribution. *Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7534" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "such as object detection [28, 40, 41], semantic segmentation [24, 30], and autonomous driving [2, 42]. Despite its great potential, the inherent limitations of infrared cameras — such as high noise levels, reduced spatial resolution, and limited dynamic range — continually affect the quality of infrared images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 146, + 295, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 146, + 295, + 302 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 295, + 302 + ], + "type": "text", + "content": "Conventionally, CNN-based methods [18, 33, 61-63] address this challenge by mapping interpolated LR images to HR images and then enhancing the details (e.g., SR-CNN [35]). Although CNN-based super-resolution methods have significantly advanced this field, they are limited by the perceptual field of local convolution operations. To overcome this, Transformer-based methods [3, 4, 56, 60] model long-range dependencies to capture global context. Liang et al. [26] proposed SwinIR significantly improving super-resolution performance by integrating CNNs with the Swin Transformer. Lately, Li et al. [25] proposed CoRPLE, which leverages a Contourlet residual framework to restore infrared-specific high-frequency features." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 304, + 295, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 304, + 295, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 304, + 295, + 449 + ], + "type": "text", + "content": "Recently, the diffusion model has introduced a novel paradigm for image super-resolution tasks, offering a fresh approach that goes beyond the CNN- and Transformer-based methods [11], leveraging its capacity to learn implicit priors of the underlying data distribution [39]. Yue et al. proposed ResShift [55], which applies an iterative sampling procedure to shift the residual between the LR and the desired HR image during inference. Unlike other diffusion models, Wang et al. [49] accelerate the diffusion-based SR model to a single inference step while maintaining satisfactory performance. These methods generally achieve visually pleasing results when applied to visible images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 451, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 451, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 451, + 295, + 713 + ], + "type": "text", + "content": "However, existing methods often fail to extend effectively to infrared imaging, particularly in downstream tasks such as infrared image object detection and semantic segmentation. A common approach for task-oriented infrared image super-resolution is to adapt an RGB super-resolution model to infrared data, and then connect it to a downstream detection or segmentation module. Unfortunately, this approach faces two significant challenges: 1) Ignoring the unique modal characteristics of infrared imaging, which include distinct thermal spectrum distributions. Infrared image reconstruction quality is particularly sensitive to high-frequency components due to longer wavelengths and reduced atmospheric scattering effects. 2) Overlooking the machine perception requirements. While the model may reconstruct visually appealing images, these results are often sub-optimal for specific perceptual tasks. The objectives of visual domain optimization and perceptual domain optimization can differ significantly [28]. For instance, diffusion-based super-resolution models typically focus on \"seeking visually appealing\" results, often at the expense of structural information of targets and textural details critical for machine vision. Given these limitations, we ask, \"Why" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": "not develop a super-resolution model that reconstructs infrared images to be both visually appealing and perceptually salient?\"" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 109, + 555, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 109, + 555, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 109, + 555, + 323 + ], + "type": "text", + "content": "To this end, as shown in figure 1, we propose a task-oriented infrared image super-resolution method that optimizes the diffusion process through gradient-based guidance. Specifically, we inject the gradient of a designed prior loss into the noise estimation at each training step, refining the model's performance across iterations. Our guidance consists of two components. First, to ensure visual consistency, we introduce visual guidance via infrared thermal spectral distribution modulation, which ensures the reconstructed images align with high-resolution counterparts by preserving their spectral characteristics. Second, we integrate perceptual guidance by leveraging powerful pretrained vision models, such as VGG [37] and SAM [22], to infuse the diffusion process with generalized perceptual features. Extensive experiments demonstrate that our proposed method excels in both visual quality and downstream task performance. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 327, + 553, + 483 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 314, + 327, + 553, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 327, + 553, + 386 + ], + "spans": [ + { + "bbox": [ + 314, + 327, + 553, + 386 + ], + "type": "text", + "content": "- We propose a solution for infrared image super-resolution by integrating gradient-based priors into the noise during diffusion, enabling task-based guidance in sampling, and achieving simultaneous optimization in both visual and perceptual-specific domains." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 387, + 553, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 387, + 553, + 434 + ], + "spans": [ + { + "bbox": [ + 314, + 387, + 553, + 434 + ], + "type": "text", + "content": "- We introduce a thermal spectrum distribution regulation to preserve the visual fidelity of infrared images, guiding the diffusion process to learn the unique infrared image frequency distribution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 434, + 553, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 434, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 314, + 434, + 553, + 483 + ], + "type": "text", + "content": "- We propose perceptual guidance for the diffusion process, incorporating generalizable perceptual features from foundational models for visual tasks. This notably enhances performance in detection and segmentation." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 495, + 399, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 495, + 399, + 507 + ], + "spans": [ + { + "bbox": [ + 314, + 495, + 399, + 507 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 515, + 451, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 515, + 451, + 528 + ], + "spans": [ + { + "bbox": [ + 314, + 515, + 451, + 528 + ], + "type": "text", + "content": "2.1. Image Super-Resolution" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 713 + ], + "type": "text", + "content": "Since the pioneering work of SRCNN [13] was proposed, deep learning has gradually become the mainstream approach for image super-resolution (SR). The initial works [13, 21, 23, 63] mainly focused on utilizing convolutional neural networks (CNNs) [12] for image super-resolution tasks and optimizing the network by minimizing the mean square error (MSE) between the super-resolved image (SR) and their corresponding high-resolution (HR) counterparts. Subsequently, GAN-based super-resolution methods were proposed, drawing significant attention. For example, both BSRGAN [57] and Real-ESRGAN [48] employ GANs for super-resolution tasks and introduce training samples with more realistic types of degradations to achieve better results. While these methods improve the quality of the low-resolution images, they often fail to produce stable" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7535" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 180 + ], + "type": "text", + "content": "outcomes, resulting in artifacts in the images. LDL [27] and DeSRA [53] attempt to address this issue, but they still struggle to generate images with natural details. Recently, diffusion models have been widely applied to image super-resolution tasks, such as ResShift [55] and SinSR [49]. However, these methods are not designed specifically for the characteristics of infrared images and overlook the requirements of machine perception [64], so they do not perform well in infrared image super-resolution (IISR)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 186, + 165, + 198 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 186, + 165, + 198 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 165, + 198 + ], + "type": "text", + "content": "2.2. Diffusion Methods" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 205, + 296, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 205, + 296, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 205, + 296, + 434 + ], + "type": "text", + "content": "The Diffusion Denoising Probabilistic Model (DDPM) [16] is a generative model with stability and controllability. Since it was proposed, it has attracted widespread attention. The main focus of the diffusion model is to train a denoising autoencoder, which estimates the reverse process of the Markov diffusion process by predicting the noise. Diffusion models were initially applied to image generation tasks and have been continuously improved in recent years [1, 32, 34, 38, 39]. ControlNet [58] introduces control conditions into pre-trained diffusion models, expanding the application scope of diffusion models in image generation. DDIM [38] proposes a non-Markovian generation method, significantly enhancing the inference speed of diffusion models. Diffusion models have demonstrated exceptional capabilities not only in image generation tasks but also in various other tasks, showing great potential. With the introduction of several related methods [8, 9, 19, 36, 49, 55], diffusion models have also been validated to achieve remarkable results in the field of image super-resolution." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 443, + 140, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 443, + 140, + 455 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 140, + 455 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "text", + "content": "We first introduce the background of Denoising Diffusion Probabilistic Models [16]. DDPM obtains samples " + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_0 \\sim p_{\\mathrm{data}}(x)" + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "text", + "content": " from the data distribution. In a diffusion model, noise is gradually added to the sampled " + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "text", + "content": " over time steps up to " + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "text", + "content": ", eventually resulting in " + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_T \\sim \\mathcal{N}(0, \\mathbf{I})" + }, + { + "bbox": [ + 55, + 463, + 296, + 559 + ], + "type": "text", + "content": ", which can be approximated as a standard Gaussian distribution. This process is also referred to as the forward process of the diffusion model, and it can be represented as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 94, + 567, + 295, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 567, + 295, + 581 + ], + "spans": [ + { + "bbox": [ + 94, + 567, + 295, + 581 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {0}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}", + "image_path": "bbc24b284fb9c75894240f0b6eebcc9b03d37124fd58dcf81cfff308c33151e3.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = \\prod_{s = 1}^{t}(1 - \\beta_{s})" + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "inline_equation", + "content": "\\beta_{s}" + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "content": " are fixed or learned variance schedule. After obtaining " + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "content": ", the denoising model " + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}" + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "content": " learns to predict the noise " + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "content": " added during the forward process, thereby removing the noise from " + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "content": ". Specifically, the denoising model " + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}" + }, + { + "bbox": [ + 55, + 587, + 296, + 660 + ], + "type": "text", + "content": " predicts the noise by optimizing the re-weighted evidence lower bound, which can be written as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 94, + 667, + 295, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 667, + 295, + 682 + ], + "spans": [ + { + "bbox": [ + 94, + 667, + 295, + 682 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s i m p l e}} (\\phi) = \\mathbb {E} _ {x _ {0}, t, \\epsilon} \\left[ \\| \\epsilon_ {\\phi} (x _ {t}, t) - \\epsilon \\| ^ {2} \\right]. \\tag {2}", + "image_path": "596a0eee72c322596cbe2102798dd3ae411fd5e744ae431386fc63b1f8c64987.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "In this formula, " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}(x_t,t)" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " represents the noise predicted by the model, and " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " is randomly sampled from a predefined" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": "range of time steps. During the training process, the denoising model " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": " is optimized by minimizing " + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{simple}}(\\phi)" + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": ", ultimately resulting in a model capable of accurately predicting the noise." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 121, + 555, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 121, + 555, + 168 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 555, + 168 + ], + "type": "text", + "content": "After training the denoising model " + }, + { + "bbox": [ + 313, + 121, + 555, + 168 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}" + }, + { + "bbox": [ + 313, + 121, + 555, + 168 + ], + "type": "text", + "content": ", we sample " + }, + { + "bbox": [ + 313, + 121, + 555, + 168 + ], + "type": "inline_equation", + "content": "x_{T} \\sim \\mathcal{N}(0, \\mathbf{I})" + }, + { + "bbox": [ + 313, + 121, + 555, + 168 + ], + "type": "text", + "content": " and iteratively refine it using the denoising model. This process is also known as the reverse process, and the specific formula can be represented as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 337, + 178, + 555, + 192 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 178, + 555, + 192 + ], + "spans": [ + { + "bbox": [ + 337, + 178, + 555, + 192 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, t\\right), \\Sigma_ {\\theta} \\left(x _ {t}, t\\right)\\right), \\tag {3}", + "image_path": "3bf513d749933c9fab96b5c16c62f117a8e7cdc838215f6c0a65ab6d14c492cb.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "text", + "content": " is the mean function from step " + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 313, + 201, + 554, + 273 + ], + "type": "text", + "content": " is the covariance. Due to the slow sampling process of DDPM, DDIM proposes using a non-Markovian diffusion process, which significantly improves the model's sampling speed. The improved sampling formula can be expressed as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 283, + 553, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 283, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 315, + 283, + 553, + 312 + ], + "type": "interline_equation", + "content": "x _ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\hat {x} _ {0} \\left(x _ {t}\\right) + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\phi} \\left(x _ {t}, t\\right) + \\sigma_ {t} z, \\tag {4}", + "image_path": "bc12c1bbd585e74b17395d61983224a76ae4d0ce27634eb83be71d92df6b1283.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "text", + "content": " is the variance of the noise and " + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "text", + "content": " follows a standard normal distribution. " + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "inline_equation", + "content": "\\hat{x}_0(x_t)" + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "text", + "content": " is the predicted " + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 313, + 554, + 348 + ], + "type": "text", + "content": ", and the prediction formula is:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 347, + 357, + 554, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 357, + 554, + 384 + ], + "spans": [ + { + "bbox": [ + 347, + 357, + 554, + 384 + ], + "type": "interline_equation", + "content": "\\hat {x} _ {0} (x _ {t}) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\phi} (x _ {t}, t)\\right). \\tag {5}", + "image_path": "90ee8fff8062ead162b9dab21045dcb5441be5a5c8611493e20b57b59848efa2.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 392, + 554, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 554, + 428 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 554, + 428 + ], + "type": "text", + "content": "When " + }, + { + "bbox": [ + 313, + 392, + 554, + 428 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 313, + 392, + 554, + 428 + ], + "type": "text", + "content": " equals 0, it is evident that the DDIM sampling process can be regarded as a deterministic process, which allows for quick sampling results from the noise." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 438, + 370, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 438, + 370, + 451 + ], + "spans": [ + { + "bbox": [ + 314, + 438, + 370, + 451 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 459, + 555, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 555, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 555, + 567 + ], + "type": "text", + "content": "Overview. Our main objective is to address the problem of infrared image super-resolution using a diffusion model enhanced by gradient-based guidance, as shown in figure 2. Specifically, inspired by [10], we propose a method that fine-tunes the diffusion model by introducing an additional guidance mechanism. In addition, we incorporate a dual optimization approach combining visual and perceptual aspects to better adapt the diffusion model to the task of infrared image super-resolution." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 575, + 450, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 575, + 450, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 575, + 450, + 588 + ], + "type": "text", + "content": "4.1. Loss-gradient Guidance" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": "The reverse process of diffusion models often requires multiple constraints to generate stable, high-quality images. Most methods tend to guide the reverse process by adding weighted constraints to the final loss function. In contrast, our approach addresses this issue from the perspective of posterior sampling. Inspired by [10], we introduce additional priors and compute the gradient of the resulting loss function, injecting the gradient into the noise estimated at each step to better handle the problem of adding constraints during the reverse process of diffusion models." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "7536" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 68, + 553, + 270 + ], + "blocks": [ + { + "bbox": [ + 56, + 68, + 553, + 270 + ], + "lines": [ + { + "bbox": [ + 56, + 68, + 553, + 270 + ], + "spans": [ + { + "bbox": [ + 56, + 68, + 553, + 270 + ], + "type": "image", + "image_path": "379c92573d6032ebc81cd95d1d50b9894f923708399b96abac0e47c30f807258.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 275, + 555, + 299 + ], + "lines": [ + { + "bbox": [ + 55, + 275, + 555, + 299 + ], + "spans": [ + { + "bbox": [ + 55, + 275, + 555, + 299 + ], + "type": "text", + "content": "Figure 2. Overall architecture of our proposed method: the vanilla super-resolution diffusion process is marked in black, whereas our proposed additional visual and perceptual priors are marked in red." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 319, + 296, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 319, + 296, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 296, + 367 + ], + "type": "text", + "content": "Generally, the noise predicted by the denoising model at timestep " + }, + { + "bbox": [ + 55, + 319, + 296, + 367 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 319, + 296, + 367 + ], + "type": "text", + "content": " is often correlated with the score of the denoising model at the current timestep [39]. Specifically, it can be represented as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 99, + 379, + 295, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 379, + 295, + 393 + ], + "spans": [ + { + "bbox": [ + 99, + 379, + 295, + 393 + ], + "type": "interline_equation", + "content": "\\epsilon_ {\\phi} \\left(x _ {t}, t\\right) = - \\sqrt {1 - \\alpha_ {t}} \\nabla_ {x _ {t}} \\log p \\left(x _ {t}\\right), \\tag {6}", + "image_path": "31e5b7cbe4cdd6f174cea6c89cfd8087229136dad9cdee4fa0b7db7a1ca796cc.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(x_t)" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " is the gradient of " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " with respect to the probability density function " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "\\log p(x_{t})" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": ", but now we need to consider not only " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(x_t)" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": ", we also need to incorporate optimization of " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " during the diffusion model sampling. In our work, " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " represents the guidance obtained by feeding " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " is a forward operator. The relationship between " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " can be expressed as " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "g = \\mathcal{M}(x_0)" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": ". Therefore, the score of the denoising model at timestep " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": " becomes " + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(x_t\\mid g)" + }, + { + "bbox": [ + 55, + 404, + 296, + 514 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 514, + 296, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 296, + 550 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 296, + 550 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(x_t\\mid g)" + }, + { + "bbox": [ + 55, + 514, + 296, + 550 + ], + "type": "text", + "content": " is unknown, and we need to use the known " + }, + { + "bbox": [ + 55, + 514, + 296, + 550 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(x_t)" + }, + { + "bbox": [ + 55, + 514, + 296, + 550 + ], + "type": "text", + "content": " to derive " + }, + { + "bbox": [ + 55, + 514, + 296, + 550 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(x_t\\mid g)" + }, + { + "bbox": [ + 55, + 514, + 296, + 550 + ], + "type": "text", + "content": ". According to Bayes' theorem, we can write:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 64, + 562, + 295, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 562, + 295, + 586 + ], + "spans": [ + { + "bbox": [ + 64, + 562, + 295, + 586 + ], + "type": "interline_equation", + "content": "\\nabla_ {x _ {t}} \\log p (x _ {t} \\mid g) = \\nabla_ {x _ {t}} \\log p (x _ {t}) + \\nabla_ {x _ {t}} \\log p (g \\mid x _ {t}). \\tag {7}", + "image_path": "2ad5a855719d00203b5f2c89e66ebcd9db64d66261ea427ae5b63d588d1fc91e.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "type": "text", + "content": "From this, it can be seen that " + }, + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(x_t)" + }, + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "type": "text", + "content": " is known, and the problem changes from calculating " + }, + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(x_t\\mid g)" + }, + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "type": "text", + "content": " to calculating " + }, + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\log p(g\\mid x_t)" + }, + { + "bbox": [ + 55, + 586, + 296, + 635 + ], + "type": "text", + "content": ". Inspired by [10], we can derive the formula:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 644, + 295, + 676 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 644, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 69, + 644, + 295, + 676 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {x _ {t}} \\log p (g \\mid x _ {t}) \\simeq \\nabla_ {x _ {t}} \\log p (g \\mid \\hat {x} _ {0} (x _ {t})) \\tag {8} \\\\ \\simeq - \\rho \\nabla_ {x _ {t}} \\| g - \\mathcal {M} (\\hat {x} _ {0} (x _ {t})) \\| _ {2} ^ {2}, \\\\ \\end{array}", + "image_path": "25a57217676e62b384791f064054179557268c4c3ecef567575ac87207b81ee2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\nabla_{x_t}\\| g - \\mathcal{M}(\\hat{x}_0(x_t))\\| _2^2" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " also can be represented as " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{L}_g" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": ". Therefore, we can express the noise prediction ad" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 319, + 455, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 455, + 331 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 455, + 331 + ], + "type": "text", + "content": "justed according to condition " + }, + { + "bbox": [ + 313, + 319, + 455, + 331 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 319, + 455, + 331 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 323, + 339, + 553, + 372 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 339, + 553, + 372 + ], + "spans": [ + { + "bbox": [ + 323, + 339, + 553, + 372 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\epsilon_ {\\phi} ^ {\\prime} = \\epsilon_ {\\phi} \\left(x _ {t}, t\\right) + \\rho \\sqrt {1 - \\alpha_ {t}} \\nabla_ {x _ {t}} \\| g - \\mathcal {M} \\left(\\hat {x} _ {0} \\left(x _ {t}\\right)\\right) \\| _ {2} ^ {2} \\tag {9} \\\\ = \\epsilon_ {\\phi} (x _ {t}, t) + \\rho \\sqrt {1 - \\alpha_ {t}} \\nabla \\mathcal {L} _ {g}, \\\\ \\end{array}", + "image_path": "0b68644e695d7c3a2d8b6ba6d2c85583d6670d1ac76f08e8d6fe6dd95e6942f5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 380, + 553, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 553, + 416 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 553, + 416 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 380, + 553, + 416 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}^{\\prime}" + }, + { + "bbox": [ + 313, + 380, + 553, + 416 + ], + "type": "text", + "content": " represents the adjusted noise, obtained by adding the gradient of the guidance loss " + }, + { + "bbox": [ + 313, + 380, + 553, + 416 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{L}_g" + }, + { + "bbox": [ + 313, + 380, + 553, + 416 + ], + "type": "text", + "content": " to the noise predicted by the original denoising model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 417, + 554, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 417, + 554, + 476 + ], + "spans": [ + { + "bbox": [ + 313, + 417, + 554, + 476 + ], + "type": "text", + "content": "Thus, by applying gradient guidance to the noise predicted by the diffusion model, we impose constraints on the reverse process of the diffusion model. More detailed derivations and pseudocode of our method can be found in the supplementary materials." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 483, + 510, + 497 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 510, + 497 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 510, + 497 + ], + "type": "text", + "content": "4.2. Visual-perceptual Dual Optimization" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "text", + "content": "Now, let's explain the composition of our guidance " + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_g" + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "text", + "content": " in detail. Specifically, " + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_g" + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "text", + "content": " can be divided into two parts: visual loss " + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{visual}}" + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "text", + "content": " and perceptual loss " + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{perceptual}}" + }, + { + "bbox": [ + 313, + 502, + 554, + 539 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "text", + "content": " - visual guidance. To guide the diffusion process in reconstructing infrared images towards infrared-specific visual characteristics, we propose " + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{visual}}" + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "text", + "content": " to regularize the distribution of high- and low-frequency information as visual guidance " + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "text", + "content": " replaces the forward operator " + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "text", + "content": " in equation 8. Given the HR image " + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{HR}" + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "text", + "content": " and the super-resolved image " + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{SR}" + }, + { + "bbox": [ + 313, + 539, + 554, + 647 + ], + "type": "text", + "content": ", we first use Fast Fourier Transforms (FFT) to transform their spatial domain representation into the frequency domain, formally:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 328, + 665, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 665, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 328, + 665, + 553, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\mathbf {I}} _ {H R} = \\mathcal {F} (\\mathbf {I} _ {H R}), \\hat {\\mathbf {I}} _ {S R} = \\mathcal {F} (\\mathbf {I} _ {S R}), \\\\ \\mathcal {F} (u, v) = \\sum_ {x = 0} ^ {H - 1} \\sum_ {y = 0} ^ {W - 1} I (x, y) \\cdot e ^ {- i \\frac {2 \\pi}{H} u x} \\cdot e ^ {- i \\frac {2 \\pi}{W} v y}. \\tag {10} \\\\ \\end{array}", + "image_path": "3ad32a298a902798b30e15eb37f74be0fc22f5c47ef480b78ee94356daecde21.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7537" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(u,v)" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": " denotes the FFT of the image at frequency coordinates " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}_{HR}" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": " is the transformed HR images. In the frequency domain, we first shift the zero-frequency component, which represents the mean intensity of the image, to the center of the spectrum for both HR and SR images, yielding " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}_{HR}^{\\mathrm{shift}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}_{SR}^{\\mathrm{shift}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": ". Following this, we compute the magnitude spectra " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{HR}" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{SR}" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": " by applying logarithmic compression to the Fourier-transformed images. This step ensures a balanced consideration of both high-frequency and low-frequency components during comparison. To focus the loss on matching the frequency distribution patterns rather than absolute intensity differences, we normalize the magnitude spectra to have zero mean and unit variance, resulting in the normalized spectra " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{HR}^{\\mathrm{norm}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{SR}^{\\mathrm{norm}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": ". Finally, the Visual Loss " + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{visual}}" + }, + { + "bbox": [ + 55, + 72, + 296, + 277 + ], + "type": "text", + "content": " is computed as the mean squared error between the normalized magnitude spectra of the HR and SR images:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 277, + 296, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 277, + 296, + 323 + ], + "spans": [ + { + "bbox": [ + 59, + 277, + 296, + 323 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {v i s u a l}} = \\left(\\overbrace {N \\left(\\log \\left(1 + | \\hat {\\mathbf {I}} _ {H R} ^ {\\text {n o r m}} |\\right)\\right)} ^ {\\mathrm {M} _ {H R} ^ {\\text {n o r m}}} - \\overbrace {N \\left(\\log \\left(1 + | \\hat {\\mathbf {I}} _ {S R} ^ {\\text {n o r m}} |\\right)\\right)} ^ {\\mathrm {M} _ {S R} ^ {\\text {n o r m}}}\\right) ^ {2}, \\tag {11}", + "image_path": "8ea789dceca12c49fd69f82b45969e62e8fed25d6385e405641af7d4586bb920.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 324, + 296, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 296, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 296, + 360 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 324, + 296, + 360 + ], + "type": "inline_equation", + "content": "N(\\cdot)" + }, + { + "bbox": [ + 55, + 324, + 296, + 360 + ], + "type": "text", + "content": " represents the normalization operation. Visual Loss plays a critical role in preserving the frequency distribution of the infrared image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "spans": [ + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " - perceptual guidance. Large models provide many priors for current methods [14, 15], to regularize the diffusion process to better align with machine perception, we adopt " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{perceptual}}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " that consists of the VGG Loss " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{VGG}}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " and the Segmentation Loss " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " as perceptual guidance " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " replaces the forward operator " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " in equation 8. Given the HR image " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{HR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " and the super-resolved image " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{SR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": ", the VGG Loss is computed by mean squared error between the extracted features of the HR and SR images from a pretrained deep neural network. This guides the model to capture nuanced aspects of images, including textures, edges, and shapes, which are crucial for preserving visual fidelity. To enhance the semantic fidelity of the reconstructed images, we regulate the diffusion process using the Segment Anything Model (SAM) [22] and propose the Segmentation Loss " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": ". Given the HR image " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{HR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " and the super-resolved image " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{SR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": ", we use a locked SAM to segment the masks " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{HR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{SR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{HR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{SR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": ", respectively. The Segmentation Loss " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " is then computed by mean squared error between " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{HR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{SR}" + }, + { + "bbox": [ + 55, + 361, + 296, + 612 + ], + "type": "text", + "content": ", providing effective high-level supervision for the reconstructed images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 612, + 295, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 612, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 612, + 295, + 635 + ], + "type": "text", + "content": "The Perceptual Loss " + }, + { + "bbox": [ + 55, + 612, + 295, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{perceptual}}" + }, + { + "bbox": [ + 55, + 612, + 295, + 635 + ], + "type": "text", + "content": " is computed by integrating the VGG-based and segmentation-based losses, as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 636, + 294, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 636, + 294, + 677 + ], + "spans": [ + { + "bbox": [ + 62, + 636, + 294, + 677 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p e r c e p t u a l}} = \\overbrace {\\left\\| \\phi_ {l} \\left(\\mathbf {I} _ {H R}\\right) - \\phi_ {l} \\left(\\mathbf {I} _ {S R}\\right) \\right\\| _ {2} ^ {2}} ^ {\\mathcal {L} _ {\\mathrm {V G G}}} + \\overbrace {\\left\\| \\mathbf {S} _ {H R} - \\mathbf {S} _ {S R} \\right\\| _ {2} ^ {2}} ^ {\\mathcal {L} _ {\\mathrm {s e g}}}, \\tag {12}", + "image_path": "399e0a24786e812151276b687cef02d5f233b3011c6ebcb822a47120b60223f4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\phi_l(\\cdot)" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": " represents the feature map extracted from the " + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "-th layer of a pre-trained deep neural network (in our experiment, VGG-16)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "type": "text", + "content": "The incorporation of visual and perceptual guidance refines each iteration of the diffusion, facilitating a more optimized denoising procedure. This not only improves visual fidelity but also enhances perceptual performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 132, + 395, + 145 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 132, + 395, + 145 + ], + "spans": [ + { + "bbox": [ + 314, + 132, + 395, + 145 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 152, + 441, + 165 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 152, + 441, + 165 + ], + "spans": [ + { + "bbox": [ + 314, + 152, + 441, + 165 + ], + "type": "text", + "content": "5.1. Experimental Settings" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 171, + 555, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 171, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 171, + 555, + 338 + ], + "type": "text", + "content": "Dataset and evaluation metrics. To ensure the fairness of the experiment, we used the same training [28] and test sets [28, 43, 54], as CoRPLE [25]. We use the infrared image dataset " + }, + { + "bbox": [ + 313, + 171, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathrm{M}^3\\mathrm{FD}" + }, + { + "bbox": [ + 313, + 171, + 555, + 338 + ], + "type": "text", + "content": " [28] to train the model and evaluate its performance using three datasets: " + }, + { + "bbox": [ + 313, + 171, + 555, + 338 + ], + "type": "inline_equation", + "content": "\\mathrm{M}^3\\mathrm{FD}" + }, + { + "bbox": [ + 313, + 171, + 555, + 338 + ], + "type": "text", + "content": " [28], RoadScene [54], and TNO [43]. We adopt five metrics to evaluate the performance of our model quantitatively: CLIP-IQA [46], MUSIQ [20], PSNR, LPIPS [59], and SSIM [50]. Among them, CLIPIQA and MUSIQ are no-reference metrics. CLIPIQA leverages the CLIP model [35] to assess image quality, while MUSIQ uses a multi-scale feature extraction approach for quality evaluation. We mainly rely on CLIPIQA and MUSIQ as evaluation metrics to compare the performance of different methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 339, + 556, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 556, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 556, + 506 + ], + "type": "text", + "content": "Implementation Details. Our network was trained on a GeForce RTX 4090 GPU. Our backbone model and specific experimental parameter settings largely follow ResShift [55]. Notably, ResShift uses the residual between high-resolution (HR) and low-resolution images (LR) as the noise for the diffusion model, meaning that we can effectively apply gradient guidance on the residual between HR and LR images. During training, our approach differs from ResShift in that we initially perform 200K iterations on a new training set to enable the model to develop basic infrared image super-resolution capabilities. Subsequently, we incorporate conditional (visual and perceptual) guidance into the model and conduct an additional 50K training iterations to achieve improved results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 514, + 471, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 514, + 471, + 528 + ], + "spans": [ + { + "bbox": [ + 314, + 514, + 471, + 528 + ], + "type": "text", + "content": "5.2. Experiments on Infrared SR" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 533, + 555, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 617 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 617 + ], + "type": "text", + "content": "We perform a comprehensive comparison of our approach with eleven SOTA methods, including ESRGAN [47], RealSR-JPEG [17], BSRGAN [57], SwinIR [26], RealESRGAN [48], HAT [5], DAT [6], ResShift [55], CoPRLE [25], Bi-DiffSR [7] and SinSR [49]. Table 1, 2 presents our quantitative comparison results compared with the above methods and Figure 3 presents our qualitative results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "content": "Quantitative Comparison. Table 1 presents a quantitative comparison of CLIPIQA and MUSIQ on the " + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^3\\mathrm{FD}" + }, + { + "bbox": [ + 313, + 618, + 556, + 714 + ], + "type": "text", + "content": " dataset against various methods. CLIPIQA inherits the powerful representation capabilities of CLIP, demonstrating stable and robust performance in evaluating the perceptual quality of natural images. Our method outperforms other methods on both metrics across all three test sets, indicating that our approach better aligns with the human perceptual system." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7538" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 553, + 274 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 553, + 274 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 553, + 274 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 553, + 274 + ], + "type": "table", + "html": "
    DatasetsSet5Set15Set20
    MethodsCLIP-IQA↑MUSIQ↑CLIP-IQA↑MUSIQ↑CLIP-IQA↑MUSIQ↑
    Low Resolution1-0.216724.6090.204923.0630.223022.446
    ESRGAN [47]ECCV'180.213040.8190.203840.7450.180436.654
    RealSR-JPEG [17]CVPR'200.361548.4190.357349.2250.327747.213
    BSRGAN [57]CVPR'210.329053.1190.319452.6440.330151.917
    SwinIR [26]CVPR'210.216037.1560.223037.9700.225834.919
    RealESRGAN [48]ICCV'210.278054.3060.242453.1630.252351.647
    HAT [5]CVPR'230.229838.0500.237739.7430.246635.633
    DAT [6]ICCV'230.229737.5380.241039.4190.251835.750
    ResShift [55]NeurIPS'230.470150.7690.442852.8710.408251.244
    CoRPLE [25]ECCV'240.233936.2810.228136.4580.228134.270
    SinSR [49]CVPR'240.587754.3550.576254.1060.535753.187
    Bi-DiffSR [7]NeurIPS'240.315135.3560.275836.1020.267436.537
    DifiISROurs0.614455.1940.590654.5040.548453.636
    High Resolution-0.220034.0660.216134.4100.213932.024
    ", + "image_path": "30bc001061367158c7f21dc0f88c2f1f78452ef6535728462530b1cd15dfc510.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 303, + 552, + 380 + ], + "blocks": [ + { + "bbox": [ + 90, + 281, + 518, + 293 + ], + "lines": [ + { + "bbox": [ + 90, + 281, + 518, + 293 + ], + "spans": [ + { + "bbox": [ + 90, + 281, + 518, + 293 + ], + "type": "text", + "content": "Table 1. No-reference Metrics Comparison of infrared image super-resolution with SOTA methods on " + }, + { + "bbox": [ + 90, + 281, + 518, + 293 + ], + "type": "inline_equation", + "content": "{\\mathrm{M}}^{3}\\mathrm{{FD}}" + }, + { + "bbox": [ + 90, + 281, + 518, + 293 + ], + "type": "text", + "content": " datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 303, + 552, + 380 + ], + "lines": [ + { + "bbox": [ + 59, + 303, + 552, + 380 + ], + "spans": [ + { + "bbox": [ + 59, + 303, + 552, + 380 + ], + "type": "table", + "html": "
    MetricsDatasets
    Set5Set15Set20
    ResShiftSinSRBi-DiffSRDifIISRResShiftSinSRBi-DiffSRDifIISRResShiftSinSRBi-DiffSRDifIISR
    PSNR↑30.10131.64532.02232.27930.28331.98832.14532.35130.97633.43833.44733.451
    SSIM↑0.83290.84810.85790.86370.82280.84260.84710.85780.84460.88530.88740.8941
    LPIPS↓0.31790.27370.28160.27040.35370.28170.29240.28450.35070.25490.28200.2735
    ", + "image_path": "e0cf26c12dd9e82cc35d59a19d6026e18f4a75cc81cc733dc48f6e2182c46cae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 129, + 389, + 478, + 400 + ], + "lines": [ + { + "bbox": [ + 129, + 389, + 478, + 400 + ], + "spans": [ + { + "bbox": [ + 129, + 389, + 478, + 400 + ], + "type": "text", + "content": "Table 2. Reference-based Metrics Comparison with diffusion-based methods on " + }, + { + "bbox": [ + 129, + 389, + 478, + 400 + ], + "type": "inline_equation", + "content": "{\\mathrm{M}}^{3}\\mathrm{{FD}}" + }, + { + "bbox": [ + 129, + 389, + 478, + 400 + ], + "type": "text", + "content": " datasets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 422, + 295, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 422, + 295, + 470 + ], + "spans": [ + { + "bbox": [ + 54, + 422, + 295, + 470 + ], + "type": "text", + "content": "Additionally, our method achieves superior performance on MUSIQ compared to all other methods, demonstrating that it can also achieve excellent results in multi-scale image quality assessment." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 470, + 295, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 470, + 295, + 649 + ], + "spans": [ + { + "bbox": [ + 54, + 470, + 295, + 649 + ], + "type": "text", + "content": "It is worth noting that we also compared our method against HR images on no-reference metrics. Our method significantly outperforms HR images in no-reference visual quality metrics, demonstrating an enhancement over the HR images. However, this improvement introduces a challenge: in comparison to traditional methods on reference-based metrics such as PSNR, LPIPS, and SSIM, our approach shows less advantage, as our results differ significantly from the HR images. Nevertheless, our method still leads diffusion-based methods on reference-based metrics, as shown in Table 2. This demonstrates that our approach leverages the powerful generative capabilities of diffusion to produce high-quality images while also preserving essential detail features from the HR images under both visual and perceptual guidance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 649, + 295, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 649, + 295, + 685 + ], + "spans": [ + { + "bbox": [ + 54, + 649, + 295, + 685 + ], + "type": "text", + "content": "Qualitative Results. The qualitative results shown in Figure 3 emphasize the superiority of our method in visual performance compared to other approaches. Additional ex" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 422, + 555, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 422, + 555, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 422, + 555, + 542 + ], + "type": "text", + "content": "amples can be found in the supplementary materials. We selected one image from each of the three datasets, Set5, Set15, and Set20, for qualitative analysis to ensure comprehensive evaluation. Our method achieves more natural details in portraits, avoiding color discrepancies and better matching the contours of the true image. For vehicle details, our method accurately reproduces the grille at the front of the vehicle in the true image, whereas other methods tend to blur these details. This demonstrates that our method also has distinct advantages in qualitative results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 550, + 408, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 550, + 408, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 550, + 408, + 563 + ], + "type": "text", + "content": "5.3. 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The experimental results demonstrate that incorporating the gradient of the loss into the noise yields the best performance. We also conducted experiments in a visual-based setup, the results under the visual-based setup also follow this trend." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 55, + 502, + 277, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 277, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 277, + 514 + ], + "type": "text", + "content": "5.4. Experiments on Infrared Object Detection" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 55, + 521, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 568 + ], + "type": "text", + "content": "Setup. We employ YOLOv5-s for infrared image object detection, fine-tuning it specifically on the " + }, + { + "bbox": [ + 55, + 521, + 295, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^3\\mathrm{FD}" + }, + { + "bbox": [ + 55, + 521, + 295, + 568 + ], + "type": "text", + "content": " dataset. The model is fine-tuned with a batch size of 16, using the SGD optimizer with learning rate of 0.01." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 55, + 569, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 569, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 569, + 295, + 700 + ], + "type": "text", + "content": "Quantitative Comparison. The left section of Figure 6 presents a quantitative comparison of detection results across SOTA methods. In the top-right quadrant of the plot, the overall mAP of each model is displayed, while the other three quadrants represent the performance across individual categories. Our model consistently outperforms all other models in each detection category, demonstrating its superior ability in object detection tasks. Notably, in the truck detection category, our model achieves a " + }, + { + "bbox": [ + 55, + 569, + 295, + 700 + ], + "type": "inline_equation", + "content": "5.6\\%" + }, + { + "bbox": [ + 55, + 569, + 295, + 700 + ], + "type": "text", + "content": " improvement over the best-competing method, underscoring its robustness in identifying challenging classes." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "content": "Qualitative Comparison. The qualitative results in Figure" + } + ] + } + ], + "index": 41 + }, + { + "type": "table", + "bbox": [ + 308, + 380, + 552, + 448 + ], + "blocks": [ + { + "bbox": [ + 308, + 380, + 552, + 448 + ], + "lines": [ + { + "bbox": [ + 308, + 380, + 552, + 448 + ], + "spans": [ + { + "bbox": [ + 308, + 380, + 552, + 448 + ], + "type": "table", + "html": "
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For example, in the first row, some methods fail to detect the person on the right side of the image, with none capable of detecting both signs above simultaneously. Only our method consistently achieves the best detection prediction results." + } + ] + } + ], + "index": 46 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7540" + } + ] + } + ], + "index": 47 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 553, + 190 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 190 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 190 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 190 + ], + "type": "image", + "image_path": "bfaaf9d948e358f425f2697b393c2252596c6cba541b1968149d0a7d6b8b7521.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 86, + 198, + 523, + 210 + ], + "lines": [ + { + "bbox": [ + 86, + 198, + 523, + 210 + ], + "spans": [ + { + "bbox": [ + 86, + 198, + 523, + 210 + ], + "type": "text", + "content": "Figure 4. 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Segmentation performance comparison of infrared image super-resolution with SOTA methods on FMB datasets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 59, + 366, + 293, + 492 + ], + "blocks": [ + { + "bbox": [ + 59, + 366, + 293, + 492 + ], + "lines": [ + { + "bbox": [ + 59, + 366, + 293, + 492 + ], + "spans": [ + { + "bbox": [ + 59, + 366, + 293, + 492 + ], + "type": "image", + "image_path": "d959f3aeab8d4aab6ce8ed09c951182ca22a2ab2b4600a869a53d1f0200b951c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 501, + 295, + 523 + ], + "lines": [ + { + "bbox": [ + 55, + 501, + 295, + 523 + ], + "spans": [ + { + "bbox": [ + 55, + 501, + 295, + 523 + ], + "type": "text", + "content": "Figure 6. Quantitative comparison of detection and segmentation results with SOTA methods." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 548, + 293, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 293, + 561 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 293, + 561 + ], + "type": "text", + "content": "5.5. Experiments on Infrared Image Segmentation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 568, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 568, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 295, + 616 + ], + "type": "text", + "content": "Setup. We perform semantic segmentation on the FMB dataset [29], the SegFormer-b1 model [52] is used as the backbone. The model is trained using the AdamW optimizer, with a learning rate of 6e-05." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 296, + 713 + ], + "type": "text", + "content": "Quantitative Comparison. The right section of Figure 6 presents a quantitative comparison of semantic segmentation results. The top-right quadrant of the circle represents the comparison of mIoU, while the remaining three quadrants depict the performance of other models across the three primary segmentation classes. Overall, our model achieves the best results in each category. Notably, it achieves the highest improvement in truck, with an im" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "type": "text", + "content": "provement of " + }, + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "type": "inline_equation", + "content": "7.4\\%" + }, + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "type": "text", + "content": ". It also improves by " + }, + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "type": "inline_equation", + "content": "3.0\\%" + }, + { + "bbox": [ + 313, + 369, + 553, + 392 + ], + "type": "text", + "content": " in car and human, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 394, + 555, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 555, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 555, + 515 + ], + "type": "text", + "content": "Qualitative Comparison. The figure 5 presents a qualitative comparison of segmentation results from various SOTA methods. These results reveal that other methods often fail to segment complete objects, or they struggle with segmenting all relevant elements. For example, in other models, only part of the sign occurs, leaving parts of it undetected. While RealESRGAN shows some improvement, it still falls short of our method. Similarly, in the right image, other models fail to recognize the farthest poles and cannot fully capture the shapes of the people." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 528, + 388, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 528, + 388, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 528, + 388, + 540 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 548, + 555, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 548, + 555, + 669 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 555, + 669 + ], + "type": "text", + "content": "In this paper, we propose a task-oriented infrared image super-resolution diffusion model, namely DiffIISR. Specifically, we introduce infrared thermal spectral distribution modulation as visual guidance to ensure consistency with high-resolution images by matching frequency components. In addition, we incorporate foundational vision models to provide perception guidance, which enhances detection and segmentation performance. With the above guidance, our method further optimizes each iteration of the diffusion process, refining the model at each denoising step and achieving superior visual and perceptual performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 670, + 553, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 670, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 670, + 553, + 712 + ], + "type": "text", + "content": "Acknowledgments: This work was partially supported by the National Natural Science Foundation of China (No.62302078 and No.62372080), and China Postdoctoral Science Foundation (2023M730741)." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "text", + "content": "7541" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 94, + 115, + 106 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 94, + 115, + 106 + ], + "spans": [ + { + "bbox": [ + 56, + 94, + 115, + 106 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 114, + 295, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 114, + 295, + 168 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 114, + 295, + 168 + ], + "spans": [ + { + "bbox": [ + 61, + 114, + 295, + 168 + ], + "type": "text", + "content": "[1] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne Van Den Berg. 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Comparison between PCE-Palm [20] and the proposed Diff-Palm. (a) PCE-Palm adopts conditional GAN with Bézier creases [44] as input to generate palmprint datasets. Diff-Palm introduces a polynomial crease and a novel diffusion model for synthesizing datasets with adjustable intra-class variations. (b) The average performance of recognition models, trained on three types of datasets (real data, PCE-Palm generated, and Diff-Palm generated) and evaluated on five public datasets. (FT: Fine-tune) Code: https://github.com/Ukuer/Diff-Palm" + ], + "image_footnote": [], + "bbox": [ + 116, + 300, + 571, + 476 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7f86fd6c7f83b79e6ad53d028f70dac47169c45083093b9b89f60eb8d4a45c63.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 311, + 879, + 474 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 547, + 326, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Palmprint recognition is significantly limited by the lack of large-scale publicly available datasets. Previous methods have adopted Bezier curves to simulate the palm creases, which then serve as input for conditional GANs to generate realistic palmprints. However, without employing real data fine-tuning, the performance of the recognition model trained on these synthetic datasets would drastically decline, indicating a large gap between generated and real palmprints. This is primarily due to the utilization of an inaccurate palm crease representation and challenges in balancing intra-class variation with identity consistency. To address this, we introduce a polynomial-based palm crease representation that provides a new palm crease generation mechanism more closely aligned with the real distribution. We also propose the palm creases conditioned diffusion model with a novel intra-class variation control method. By applying our proposed $K$ -step noise-sharing sampling, we are able to synthesize palmprint datasets with large intraclass variation and high identity consistency. Experimen", + "bbox": [ + 88, + 580, + 485, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tal results show that, for the first time, recognition models trained solely on our synthetic datasets, without any fine-tuning, outperform those trained on real datasets. Furthermore, our approach achieves superior recognition performance as the number of generated identities increases.", + "bbox": [ + 511, + 549, + 906, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 659, + 643, + 674 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Palmprint recognition has gained widespread interest for its highly discriminative, user-friendly, and privacy-friendly nature [11]. However, its further development is severely limited by the lack of large-scale public datasets. With the remarkable results achieved by deep generative models, such as Generative Adversarial Networks (GANs) [15] and Diffusion models [18], generating datasets for recognition tasks is a promising and valuable approach to replace the collection of large-scale real datasets [21].", + "bbox": [ + 509, + 686, + 906, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although existing palmprint generation methods, including RPG-Palm [33] and PCE-Palm [20] have obtained impressive results, they still rely on fine-tuning with real data to obtain good recognition performance. Specifically, they generate large-scale data to pre-train the recognition mod", + "bbox": [ + 511, + 824, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. † Corresponding authors.", + "bbox": [ + 107, + 886, + 354, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26367", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "els and then fine-tune them with real data. However, without fine-tuning, the recognition model's performance suffers from significant degradation, indicating a large gap between the generated data and real data.", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We have identified two principal factors contributing to the observed issue. The first factor is the inaccurate representation of palm creases. Existing methods [20, 33] employ manually designed Bézier curves [44] to simulate palm creases. However, these curves significantly differ from the actual patterns found in genuine palmprints, resulting in a substantial divergence between synthetic and real palmprint data. Furthermore, the use of merely three control points per Bézier curve restricts its expressiveness. The second factor is the challenges in balancing intra-class variation with identity consistency. In the context of palmprint image generation, these methods [20, 33] employ conditional GANs and simulate intra-class variations of palmprints by adding a simple random noise. This strategy, however, yields datasets with large intra-class variation and low identity consistency compared to real datasets, thereby leading to diminished performance.", + "bbox": [ + 89, + 154, + 482, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the aforementioned issues, we propose a novel framework to generate realistic palmprint datasets with large intra-class variation and high identity consistency, which achieves superior performance compared to the existing SOTA method, i.e., PCE-Palm [20], as shown in Fig.1. Specifically, we utilize polynomial curves to describe palm creases, termed polynomial creases. To achieve a more accurate and expressive representation, we employ fourth-order polynomial curves parameterized by five coefficients, which substantially expands the sampling space. Based on the statistical analysis of real palm creases, we estimate a multivariate Gaussian distribution for the coefficients of polynomial curves. Subsequently, we develop a new sampling mechanism that obtains coefficients from the estimated Gaussian distribution to synthesize polynomial palm creases. This approach effectively reduces the discrepancy between synthetic and real palm creases.", + "bbox": [ + 89, + 414, + 482, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, we introduce a novel intra-class variation controllable diffusion model, designed to generate palmprints datasets that exhibit substantial variation while preserving high identity consistency. Diffusion models [18] synthesize images via a denoising sampling process. However, the inherent randomness of this process typically results in uncontrollable variation within the same identity class, potentially compromising identity consistency. This issue can lead to generated datasets with excessive intraclass variation and diminished identity consistency. To tackle this problem, we propose a simple yet effective sampling method, termed $K$ -step noise-sharing sampling. This method enhances the diffusion model by employing shared noise across samples within the same identity during the sampling process, instead of distinct noise sequences. By", + "bbox": [ + 89, + 674, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "adjusting the parameter $K$ , we are able to generate datasets with a spectrum of intra-class variations. Notably, the proposed $K$ -step noise-sharing sampling can be used as a plug-and-play module applied in other diffusion models.", + "bbox": [ + 511, + 90, + 903, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our experimental setup, we train recognition models with synthetic datasets, and evaluate them directly on publicly available datasets without employing any real data fine-tuning. Our contributions are as follows:", + "bbox": [ + 511, + 152, + 903, + 212 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a more realistic palm crease representation based on polynomial curves, which not only exhibits high expressive capability but also ensures that generated palm creases align with the distribution of real ones.", + "- We propose a novel intra-class variation controllable diffusion model with a $K$ -step noise-sharing sampling. It utilizes palm creases as identity conditions, enabling the synthesis of palmprint datasets that exhibit large intra-class variation while preserving high identity consistency.", + "- Through extensive open-set experiments, we demonstrate for the first time that recognition models trained solely on synthetic datasets generated by our method outperform those trained on real datasets, without the benefit of real data fine-tuning. Moreover, our approach shows a significant improvement in performance as the number of generated identities increases." + ], + "bbox": [ + 511, + 215, + 903, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 511, + 472, + 653, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Data Generation for Biometric Recognition", + "text_level": 1, + "bbox": [ + 511, + 497, + 880, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With advancements in generation methods [3], various models have been employed to create synthetic samples in the field of biometrics, such as face generation [7, 12, 13, 22, 28, 29, 38], and fingerprint synthesis [1, 9, 34]. For palmprint generation, Bézierpalm [44] firstly utilizes Bézier curves to represent palm creases and generates new identities by sampling random curves. Subsequently, both RPG-Palm [33] and PCE-Palm [20] employ Bézier curves as an identity condition and GAN-based generative models for palmprint generation. Although these methods can produce visually realistic palmprint images, they still need to be finetuned with real data to achieve satisfactory results.", + "bbox": [ + 511, + 520, + 903, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Conditional Diffusion Models", + "text_level": 1, + "bbox": [ + 511, + 712, + 774, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models have achieved remarkable performance in numerous visual tasks [4, 45]. To enable controllable generation, two main conditional control mechanisms are employed. The first is the embedding-based conditional approach [23, 30], where the embedding is typically derived from the output of a pre-trained model. This extracted embedding is then incorporated into the UNet network architecture through a cross-attention mechanism. The second is the channel-based conditional approach [27, 31], where conditional images are concatenated with the diffused image through channels. For our research, we utilize", + "bbox": [ + 511, + 734, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26368", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9dd6175ec47ba75ea9f2bdb771e3f7a0aec1d666037b3f91ef5f59ae2ba99c64.jpg", + "image_caption": [ + "Figure 2. Comparison of (a) Bézier creases [44] and (b) proposed polynomial creases." + ], + "image_footnote": [], + "bbox": [ + 99, + 85, + 473, + 344 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the channel-based conditional diffusion model as our baseline, as it ensures a strong correspondence between conditional images and generated images. Furthermore, we draw comparisons with the embedding-based conditional model, IDiff-Face [2], an identity-conditioned face generation method with impressive recognition performance.", + "bbox": [ + 89, + 401, + 483, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Recognition Methods", + "text_level": 1, + "bbox": [ + 89, + 503, + 292, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Deep learning has significantly advanced biometric recognition, especially in facial recognition, where margin-based methods like CosFace [36] and ArcFace [6] have shown exceptional performance. Similarly, in palmprint recognition, several deep learning methods have been proposed [10, 14, 19, 39, 40, 46], many of which introduce refined networks accompanied by margin-based loss. Thus, this paper adopts ArcFace as the palmprint recognition baseline to compare different generation methods, as in PCE-Palm [20].", + "bbox": [ + 89, + 525, + 483, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 89, + 676, + 191, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first introduce a polynomial representation for palm creases, which synthesize pseudo palm creases as identity conditions for generating realistic palmprints. We then propose an intra-class variation controllable diffusion model, which includes palm creases conditioned diffusion and a $K$ -step noise-sharing sampling mechanism. Utilizing these components, we are able to generate palmprint datasets with adjustable levels of intra-class variations.", + "bbox": [ + 89, + 702, + 483, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Polynomial Representation for Palm Creases", + "text_level": 1, + "bbox": [ + 89, + 833, + 470, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Current palmprint generation models [20, 33] rely on palm creases as identity control conditions, making palm crease representation a crucial task for palmprint genera", + "bbox": [ + 89, + 854, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion. These models all employ second-order Bézier curves to represent palm creases [44], as follows,", + "bbox": [ + 511, + 90, + 906, + 122 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {B} (t) = (1 - t) ^ {2} \\mathbf {P} _ {s} + 2 t (1 - t) \\mathbf {P} _ {c} + t ^ {2} \\mathbf {P} _ {e}, \\qquad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 130, + 906, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{P}_s, \\mathbf{P}_c, \\mathbf{P}_e$ represent starting point, control point, and ending point respectively, which are randomly sampled within a predefined artificial area range, and $t$ is the parameter ranging from 0 to 1, determining the position along the curve, as shown in Fig.2 (a). However, although existing generation-based methods [20, 33] can produce visually realistic palmprint images, the distribution of simulated creases is quite different from that of real palm creases, leading to the requirement of fine-tuning on real data.", + "bbox": [ + 511, + 157, + 906, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To overcome this limitation, this paper focuses on enhancing palm crease representation to align more closely with the distribution of real palm creases. Consequently, we propose a polynomial representation for palm creases, and derive the estimated distribution of the representation parameters through statistical analysis. The proposed polynomial representation is defined as follows,", + "bbox": [ + 511, + 294, + 905, + 398 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ny ^ {i} = a _ {4} ^ {i} x ^ {4} + a _ {3} ^ {i} x ^ {3} + a _ {2} ^ {i} x ^ {2} + a _ {1} ^ {i} x + a _ {0}, \\qquad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 407, + 906, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $[a_4^i, a_3^i, a_2^i, a_1^i, a_0^i]$ denote polynomial coefficients, and $i(i = 1, 2, 3)$ represents three principal lines of the palmprint. Compared to the second-order Bézier curves, a fourth-order polynomial representation provides sufficient expressiveness to capture the smoothness of palm creases. Additionally, considering the physiological basis and distinct distribution of palm creases, it is essential to sample curve parameters that reflect the actual distribution.", + "bbox": [ + 511, + 435, + 905, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig.2 (b), we manually label the points on the three principal lines of 1000 palmprint ROI images selected from publicly available datasets. For each line, the polynomial coefficients are calculated using the least squares method, based on $n$ labeled points $((x_0,y_0),(x_1,y_1),\\ldots ,(x_{n - 1},y_{n - 1}))$ , as follows,", + "bbox": [ + 511, + 556, + 905, + 648 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} ^ {\\mathrm {T}} = \\left(\\mathbf {X} ^ {\\mathrm {T}} \\mathbf {X}\\right) ^ {- 1} \\mathbf {X} ^ {\\mathrm {T}} \\mathbf {y}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 655, + 903, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{a}^{\\mathrm{T}}$ represents coefficient vector $[a_0, a_1, \\ldots, a_4]^{\\mathrm{T}}$ , $\\mathbf{y}$ represents vector $[y_0, y_1, \\ldots, y_{n-1}]^{\\mathrm{T}}$ , and $\\mathbf{X} \\in \\mathbb{R}^{n \\times 5}$ is a Vandermonde matrix. We apply this formula to get coefficient vectors $(\\mathbf{a}^1, \\mathbf{a}^2, \\mathbf{a}^3)$ of three principal lines.", + "bbox": [ + 511, + 681, + 905, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this way, polynomial coefficients of three principal lines $(\\mathbf{a}^1,\\mathbf{a}^2,\\mathbf{a}^3)$ are calculated for each palmprint sample. Then, we conduct a statistical analysis of the polynomial coefficients. Partial visualization results are shown in Fig.3, from which we observe that the coefficient approximately follows a Gaussian distribution. More statistical results are provided in the supplementary materials. Consequently, we represent the distribution of $a_j^i$ as $p(a_j^i)\\sim N(\\mu_j^i,(\\sigma^2)_j^i)$ , where $\\mu_j^i$ and $(\\sigma^2)_j^i$ denote mean and variance of $a_j^i$ . Therefore, the coefficient vector $\\mathbf{a}^i$ follows the joint distribution", + "bbox": [ + 511, + 744, + 906, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26369", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/800a0f0dc5d12a8a2dfac9317efeb3b93de58d4ac7e784401de5a741c7d999ec.jpg", + "image_caption": [ + "Figure 3. Statistical analysis of polynomial coefficients: (a) Quantile-Quantile Plot of coefficients $a_4^1$ . (b) Histogram and Kernel Density Estimate (KDE) Plot of coefficients $a_4^1$ . (c) Contour Plot of coefficients $a_4^1$ and $a_3^1$ ." + ], + "image_footnote": [], + "bbox": [ + 106, + 89, + 472, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$p(a_0^i,a_1^i,\\ldots ,a_4^i)$ , which is a multivariate Gaussian distribution expressed as follows,", + "bbox": [ + 89, + 316, + 483, + 347 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\mathbf {a} ^ {i}\\right) \\sim \\mathcal {N} \\left(\\mu^ {i}, \\Sigma^ {i}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 359, + 482, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu^i, \\Sigma^i$ are the mean vector and covariance matrix of $\\mathbf{a}^i$ . By employing the proposed representation and estimated distribution, the complex palm creases located on a plane are mapped into a parameter space that conforms to a multivariate Gaussian distribution. This allows us to effortlessly sample the polynomial coefficients from the statistical distribution and then produce three principal lines using polynomial representation.", + "bbox": [ + 89, + 393, + 483, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Additionally, we also record the coordinates of two endpoints of each line, i.e., the starting point $x_{s}^{i}$ and the ending point $x_{e}^{i}$ , and calculate their statistical distribution. By following the same approach, we determine the range for synthesizing polynomial creases by sampling from the estimated distribution. With the addition of minor random straight lines to simulate wrinkles, a pseudo palm crease image is generated, as shown in Fig.2.", + "bbox": [ + 89, + 515, + 483, + 637 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A palm creases similarity control mechanism is proposed by scaling the variance of the estimated Gaussian distribution by a factor of $\\gamma^2$ . Specifically, as $\\mathbf{a}^i$ is sampled from $\\mathcal{N}(\\mu^i,\\gamma^2\\Sigma^i)$ , a smaller $\\gamma$ (less than 1) results in a higher degree of similarity in the generated palm creases, while a larger $\\gamma$ (greater than 1) leads to lower similarity.", + "bbox": [ + 89, + 638, + 483, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Palm Creases conditioned Diffusion Model", + "text_level": 1, + "bbox": [ + 89, + 741, + 454, + 757 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion models [4] are trained to recover an image from random noise. In contrast to GANs, which consist of two networks and utilize an adversarial loss, diffusion models adopt two processes: the diffusion process and the denoising process. The diffusion process is typically defined as a Markov chain composed of several diffusion steps. At each step, the model introduces a small amount of Gaussian noise with varying variances into the data. After a total of $T$ steps, the data is degraded to pure Gaussian noise. The", + "bbox": [ + 89, + 763, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "diffusion process [4] is expressed as,", + "bbox": [ + 511, + 90, + 759, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(x _ {t} \\mid x _ {t - 1}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {1 - \\beta_ {t}} x _ {t - 1}, \\beta_ {t} I\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 118, + 906, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x_{t}$ and $x_{t-1}$ represent the data at diffusion step $t$ and $t-1$ respectively, and $\\beta_{t}$ is the variance schedule determined in advance that controls the amount of noise added.", + "bbox": [ + 511, + 148, + 903, + 193 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The denoising process aims to learn the reverse of the diffusion process, and recover data $x_0$ from Gaussian noise $x_{T}$ step by step. An UNet network is trained to predict the noise at the $t$ step and thereby restore $x_{t - 1}$ from $x_{t}$ . Since we aim to use the diffusion model to generate palmprint datasets, unconditional diffusion is insufficient to meet our requirements. To control the identity of generated palmprint images, we use the palm crease image as a condition. The consistent palm crease image is extracted from the real palmprint image using a palm creases extraction module (PCEM) [20]. Then, the palm creases are adopted to govern the identity of the generated palmprints. Therefore, we choose to integrate the condition image into the UNet through channel concatenation. Specifically, paired palm crease images and corrupted palmprint images are concatenated and sent to the network, as shown in Fig.4(a). We use the following training objective [4],", + "bbox": [ + 511, + 195, + 906, + 452 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = E _ {t, x _ {t}, \\epsilon} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t, y) \\| _ {2} ^ {2} \\right], \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 463, + 906, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}$ represents the parameterized network, and $y$ stands for palm crease image.", + "bbox": [ + 511, + 493, + 905, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. The $K$ -step Noise-sharing Sampling", + "text_level": 1, + "bbox": [ + 511, + 534, + 821, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To generate new samples, the diffusion model follows the reverse diffusion process. Starting from random Gaussian noise, the model iteratively applies the learned denoiser to remove noise and generate final outputs. The iterative sampling process [4] is expressed as follows,", + "bbox": [ + 511, + 556, + 905, + 632 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (x _ {t}, t, y)\\right) + \\sigma_ {t} z _ {t}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 643, + 906, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t}$ is defined as $1 - \\beta_{t}$ , and $\\bar{\\alpha}_{t} \\coloneqq \\Pi_{i=0}^{t} \\alpha_{i}$ . The $\\sigma_{t}$ is step-dependent constants, and $z_{t}$ is a random noise sampled from $\\mathcal{N}(\\mathbf{0}, \\mathbf{I})$ . After the iterative process concludes, the estimate of $x_{0}$ , derived from the final iteration, is the synthesized palmprint. To control the diversity of generated results, many diffusion-based methods adopt text prompts [4, 16]. However, palmprint images are relatively simple, comprising primarily of crease and skin components, which complicates the use of text descriptions to govern diversity. We have observed that the random noise added at each step provides the randomness of the sampling process. Therefore, by controlling the random noise added to samples within the same identity, we manipulate the intra-class variation of the generated datasets effectively.", + "bbox": [ + 511, + 688, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26370", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/92236f242aebf703ad424bf51a0531de5c581d8ecf63a838c08f3da0b7e2f053.jpg", + "image_caption": [ + "Figure 4. The proposed intra-class variation controllable diffusion model. (a) Training process: palm crease images, extracted from palmprints using PCEM [20], are employed as conditions and concatenated with diffused palmprint images, serving as input for the UNet. (b) Sampling process: polynomial creases, as synthetic identity, are first generated and adopted to create consistent samples. The $K$ -step noise-sharing sampling is applied to obtain palmprint datasets with varying degrees of intra-class variations." + ], + "image_footnote": [], + "bbox": [ + 107, + 93, + 428, + 215 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/df9f8e5f7618bdf5ebedccd82ce52cac2708c76e741fa03e9f8bd0dc8596399b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 436, + 93, + 883, + 215 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b49c051b7aaf053bc3a90222f77370b9b16dd9136e89dfeef9bc90e595928ab3.jpg", + "image_caption": [ + "Figure 5. Generated palmprint results under different noise-sharing strategies. The figure illustrates the outcomes of applying noise-sharing in the last $K = 500$ steps (top) versus the first $K = 500$ steps (bottom) of a total $T = 1000$ steps during the sampling process for the same identity." + ], + "image_footnote": [], + "bbox": [ + 91, + 287, + 482, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The $K$ -step noise-sharing sampling is proposed to generate palmprint datasets with varying degrees of intra-class variations. Specifically, suppose generating the $j$ -th sample of the $i$ -th identity with the palm crease image $y^i$ , we rewrite sampling process Eq.7 as follows:", + "bbox": [ + 89, + 625, + 482, + 700 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ x _ {t - 1} \\right] _ {j} ^ {i} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\left[ x _ {t} \\right] _ {j} ^ {i} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(\\left[ x _ {t} \\right] _ {j} ^ {i}, t, y ^ {i}\\right)\\right) + \\sigma_ {t} \\left[ z _ {t} \\right] _ {j} ^ {i}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 710, + 482, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $[z_{t}]_{j}^{i}$ is the random noise sampled from a standard Gaussian distribution, influencing the diversity of samples. We aim to utilize the same shared noise $[z_{t}]^{i}$ , instead of a series of different $[z_{t}]_{j}^{i}$ to samples under the same identity condition. We select a continuous $K$ -step sequence within the total $T$ steps and apply this, as shown in Fig.4(b).", + "bbox": [ + 89, + 750, + 482, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Additionally, we have found that the application of noise-sharing in the first $K$ steps and the last $K$ steps during the sampling process exhibits distinct behaviors. With $K = 500$ and a total of $T = 1000$ steps, the sampling", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "process under the same identity yields the results shown in Fig.5. When noise-sharing is applied in the first $K$ steps, the generated results maintain a consistent style, while the details of the palm creases exhibit minor variations, leading to a generated dataset with low identity consistency. Conversely, when noise-sharing is applied in the last $K$ steps, the generated results present diverse styles, but the consistency of the palm crease details improves. This suggests that during the sampling process, the style information of the palmprint is generated first, followed by the restoration of texture details.", + "bbox": [ + 511, + 291, + 906, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, we apply noise-sharing in the last $K$ steps. As $K$ increases, the crease consistency in the sampled results under the same identity tends to improve. However, when $K$ continues to increase, the stylistic diversity of the sampled results becomes restricted. We conduct experiments on datasets generated using different values of $K$ .", + "bbox": [ + 511, + 457, + 906, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 564, + 645, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setups", + "text_level": 1, + "bbox": [ + 511, + 589, + 710, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments under an open-set protocol, splitting each public dataset into training and test sets with a 1:1 ratio with no overlapping identities (IDs). We utilize the TAR (True Accept Rate) @FAR (False Accept Rate) metric to evaluate the performance of recognition models.", + "bbox": [ + 511, + 612, + 905, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets We do not use public datasets to train our generative models to ensure a fair comparison, which also places our method in a more challenging cross-dataset setting. Instead, we adopt an anonymous dataset collected from the Internet, which has been processed to include 48,000 palmprint images. We utilize publicly available datasets for evaluation and to train recognition models as baselines. Experiments are conducted on following public datasets: CASIA [35], PolyU [41], Tongji [42], MPD [43], XJTU-UP [32], IITD [24], and NTU-CP-v1 [26].", + "bbox": [ + 511, + 688, + 905, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generation Model Training Setups Our conditional diffusion models utilize a UNet backbone [8] that takes a four-channel input and 64 base channels with five resolution levels. The multipliers for the number of channels used", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "26371", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e52f4b3d506f3dc0c047999d2fdbc52b25635fc22b5ffaa01af4aebb85c3944d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 112, + 88, + 305, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/50c4c9e4537e061af4593df7201bcf0816b245128b8124857f589af115934e8b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 308, + 88, + 496, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8e4e17ecff8455568029ed2451f06c57bfda269935c5a146fa44e5464f5ff863.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 88, + 691, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5cb2df37ed5165089ba84cdaad5e7aea87fe25be464d071568e849481adb3326.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 89, + 883, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cfefa960045e69b67daf960c9a53653d4b3b2c9493234130440f0c25626c05be.jpg", + "image_caption": [ + "Figure 6. Comparison score plots for synthetic datasets generated by different methods and real datasets. The genuine and imposter comparison scores are calculated with features, which are extracted by a pre-trained ArcFace model from datasets." + ], + "image_footnote": [], + "bbox": [ + 112, + 186, + 305, + 279 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c2842aca655fcd6b214e2fd6bca35c33526965221e7af3dcf16c34942f23a527.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 308, + 186, + 496, + 279 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/760fa31a3cf3e7f60d30c40932b8bad72e85bdb6e8763e950ef52081d3eac498.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 186, + 691, + 279 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1adea6eeee046bdf2a855528e12ff0dec8c22f7f2e60a435a3d568cb6716c2fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 188, + 883, + 279 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fbdb9dc4bf428d9da193d7f123bab1675b395606054abde9990043718f6d8dd4.jpg", + "image_caption": [ + "Figure 7. Example images of datasets generated by Diff-Palm with $K$ -step sharing-noise sampling for $K = 0, 200, 500$ , and 800." + ], + "image_footnote": [], + "bbox": [ + 107, + 330, + 475, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "on those levels are 1, 1, 2, 3, and 4, respectively. Attention blocks are applied in residual blocks of the last resolution level. During the training process, we adopt the AdamW optimizer [25], set the learning rate $1e - 4$ , and train the network for a total of $30k$ steps. We apply an EMA to the weights of the model with an exponential factor of 0.9999. The batch size is 64 and is equally split across 4 GPUs. For the diffusion process, we set $T = 1000$ steps and adopt a linear diffusion variance schedule. In subsequent experiments, we default to generating datasets with $2k$ IDs and 20 samples per ID.", + "bbox": [ + 88, + 595, + 482, + 761 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Recognition Model Training Setups We train ArcFace models [6] with a modified Resnet-18 [17] backbone for palmprint recognition. Palmprint images are resized to $112 \\times 112$ and trained with ArcFace loss ( $m = 0.5$ , $s = 64$ ) over 20 epochs using a stochastic gradient descent (SGD) optimizer. We use an initial learning rate of $1e - 1$ , momentum of 0.9, weight decay of $5e - 4$ , and a step learning rate schedule, which divides the learning rate by 10 at 7-th and 15-th epoch. RandAugment [5] is adopted for data augmen", + "bbox": [ + 89, + 763, + 482, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/932da4aee1958b0f2d35fa59cfb27e44ce70e04a20ad491a4c1325927b357457.jpg", + "image_caption": [ + "Figure 8. The t-SNE polt of features extracted from real, PCE-Palm generated, and Diff-Palm generated datasets. Colors denote different datasets, while shapes within the same color correspond to different identities." + ], + "image_footnote": [], + "bbox": [ + 532, + 342, + 877, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tation with parameters (4, 4). We double the number of IDs in the training set by horizontally flipping the palmprint images. Training is implemented on 4 NVIDIA V100 GPUs with a batch size of 256. Consistent hyperparameters are used for all recognition models across various datasets.", + "bbox": [ + 511, + 622, + 906, + 699 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 511, + 710, + 718, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluating Intra-Class Variation We generate datasets by Diff-Palm with $K$ -step sharing-noise sampling for $K = 0, 200, 500$ and 800. Then, we use the ArcFace model pretrained on real datasets to extract features from synthesized datasets and calculate genuine and imposter score distributions. Comparison score plots and example images are shown in Fig.6 and Fig.7 respectively. As $K$ increases, intraclass variation decreases, and the genuine distribution shifts right. The verification performance in Tab.1 reveals that the recognition model trained on the synthesized dataset with $K = 500$ achieves higher recognition performance.", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "26372", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a414025c76301923713f50956081b4d177d54a3bccbc299978f6b53e8e86d597.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodsConfigsScore DistributionsPerformance (TAR@FAR=1e-6) ↑
    Kγgenuine meanstdimposter meanstdCASIAPolyUTongJiMPDXJTU-UPAvg.
    Diff-Palm01.00.3500.1240.0690.1120.72780.73920.51510.34060.15270.4951
    Diff-Palm2001.00.5490.1180.0690.1110.84200.91110.81130.42370.60180.7180
    Diff-Palm5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm8001.00.9220.0720.0690.1120.83540.90140.85920.33690.50350.6873
    PCE-Palm(Bézier)--0.4020.1710.0990.1160.67960.77400.61490.29720.41500.5561
    PCE-Palm(poly)-1.00.3510.1860.0410.1100.82200.86870.76740.43730.59740.6986
    Diff-Palm(Bézier)500-0.6290.1980.1710.1140.67220.82360.72460.27320.36580.5719
    Diff-Palm(poly)5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm5000.250.7480.1210.1070.1130.84400.91340.84100.41620.57940.7188
    Diff-Palm5000.50.7640.1180.0880.1170.86130.92300.87000.42680.58230.7327
    Diff-Palm5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm5002.00.7840.1020.0700.1090.80530.93080.91620.36970.48900.7022
    Diff-Palm5004.00.7800.1030.0950.1080.77930.88040.86620.30410.43410.6528
    Diff-Palm(first K)5001.00.4750.0430.1170.110.76490.75710.51360.25020.03070.4633
    Diff-Palm(last K)5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    ", + "bbox": [ + 91, + 88, + 906, + 380 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7aab10ed9eb34bd03e0143f909803f5804a1d15245fbe75673653a2fb95dc26b.jpg", + "table_caption": [ + "Table 1. Verification performance of recognition models(ArcFace [6]) with the same hyperparameters used for various generated datasets, and without any fine-tuning on real data. Synthetic datasets default to be generated with ${2k}$ IDs and 20 samples per ID." + ], + "table_footnote": [], + "table_body": "
    MethodsKIdentityDintraUclassPerf.
    Diff-Palm00.59231.0000.8970.4951
    Diff-Palm2000.96670.96150.9800.7189
    Diff-Palm5000.99810.93720.9960.7729
    Diff-Palm8000.99960.66590.9990.6873
    PCE-Palm(Bézier)-0.60461.18940.6530.5561
    PCE-Palm(poly)-0.68501.18160.9580.6986
    Diff-Palm(Bézier)5000.99520.96910.6940.5719
    Diff-Palm(poly)5000.99810.93720.9960.7729
    ", + "bbox": [ + 94, + 431, + 483, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Evaluation of synthetic datasets. $C_{\\text{identity}}$ , $D_{\\text{intra}}$ , and $U_{\\text{class}}$ represent identity consistency, intra-class diversity, and class uniqueness, respectively.", + "bbox": [ + 89, + 582, + 482, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparing Palm Crease Representations We compare the performance of PCE-Palm [20] and our diffusion model by training them on different types of palm crease representations: Bézier creases [44] and polynomial creases, respectively. Each model is trained using consistent hyperparameters, with the only difference being the type of crease images used. As evidenced in Tab.1, the polynomial creases method significantly outperforms the Bézier creases. This result indicates that our polynomial crease representation more accurately bridges the gap between synthetic and real palmprints.", + "bbox": [ + 88, + 642, + 482, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluating Identity and Diversity Metrics We adopt identity consistency, intra-class diversity, and class uniqueness metrics from [22] to evaluate the respective properties of synthetic datasets. As shown in Tab.2, for our Diff-Palm, there exists a trade-off between identity consistency and intra-class diversity as parameter $K$ is adjusted. For", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$K = 500$ , the generated dataset strikes a balance between them, leading to optimal recognition performance. When comparing generative methods with different palm crease representations, it is evident that the use of Bezier creases leads to a noticeable decline in class uniqueness, as opposed to polynomial creases. Our analyses indicate that the superior performance of our method is due to the effective balance between identity consistency and intra-class diversity achieved by the intra-class variation controllable method, as well as the enhanced class uniqueness resulting from the use of polynomial creases. In contrast, PCE-Palm suffers from low identity consistency and reduced class uniqueness, leading the poor performance. These analysis results are also validated by the t-SNE visualization, as shown in Fig.8. Further Details about these metrics are provided in the supplementary materials.", + "bbox": [ + 511, + 434, + 906, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Palm Crease Similarity on Recognition We synthesize polynomial crease datasets with varying $\\gamma$ values to generate palmprint datasets through diffusion models. As shown in Tab.1, results indicate that recognition performance declines when $\\gamma$ is either greater than 1 or less than 1, corresponding to the expansion or contraction of the estimated distribution's variance. We believe that when $\\gamma > 1$ , the generated data disrupts original distribution patterns, while when $\\gamma < 1$ , training recognition models becomes increasingly difficult. These results confirm the reasonableness and validity of our estimated distributions.", + "bbox": [ + 511, + 681, + 908, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparing with Real Datasets and Other Methods We utilize seven public datasets to create a mixed dataset containing 2.2k IDs. The current SOTA palmprint gen", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "26373", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8717aa188a9007854cd2b088ca3cb4d32ca94b02e72556c921598a737388ef33.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodsConfigsPerformance (TAR@FAR=1e-6) ↑
    #IDs# per ID#ImagesFT w/ RealCASIAPolyUTongJiMPDXJTU-UPAvg.
    Real data2.2k-29.3k✘0.92000.91960.92090.38770.62470.7546
    IDiff-Face [2]2k2040k✘0.79770.77200.61150.18470.26670.5265
    Vec2Face [37]2k2040k✘0.82010.81050.81990.25750.25780.5932
    PCE-Palm [20]2k2040k✘0.67960.77400.61490.29720.41500.5561
    Diff-Palm2k2040k✘0.87820.96010.94600.46430.61610.7729
    PCE-Palm [20]2k2040k✓0.94150.97920.93930.66620.79480.8642
    Diff-Palm2k2040k✓0.97870.98590.97440.59790.84330.8760
    Diff-Palm5k20100k✘0.89720.97570.95900.50480.75340.8180
    Diff-Palm10k20200k✘0.90720.98180.96320.56870.81430.8470
    Diff-Palm20k20400k✘0.93830.97950.97830.63040.86550.8784
    Diff-Palm30k20600k✘0.94720.97720.97720.66510.90150.8937
    Diff-Palm40k20800k✘0.94500.97990.98020.66410.90430.8947
    Diff-Palm50k201M✘0.95420.98220.98480.68140.90320.9011
    Diff-Palm60k201.2M✘0.95570.98650.98250.68560.90290.9026
    Diff-Palm2k50100k✘0.88100.93350.91850.47790.72140.7865
    Diff-Palm2k100200k✘0.90060.94360.94430.55220.74820.8178
    Diff-Palm2k150300k✘0.88170.96690.94820.55590.80430.8314
    Diff-Palm2k200400k✘0.91430.97100.94550.57750.84940.8515
    ", + "bbox": [ + 112, + 88, + 883, + 435 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Verification performance of the recognition models across five public datasets, with the same hyperparameters used for both real and synthesized datasets. Diff-Palm is trained with $K = 500$ and $\\gamma = 1.0$ by default.", + "bbox": [ + 89, + 439, + 906, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "eration method, PCE-Palm [20], and the face generation method [2, 37], are trained for comparison. By default, we train the recognition models on synthetic datasets without employing real data fine-tuning. As shown in Tab.3, the recognition model trained on the dataset generated by our method outperforms the models trained on real data across three public datasets, and achieves an average improvement. Furthermore, our approach significantly surpasses both PCE-Palm and facial models. We also conduct fine-tuning experiments using real data for a comprehensive comparison with PCE-Palm. More results are provided in the supplementary materials.", + "bbox": [ + 88, + 483, + 482, + 665 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of Synthesized Identity and Sample Quantity We generate datasets with varying numbers of identities, maintaining 20 samples per identity, to train recognition models. As evidenced in Tab.3, the performance of the recognition model steadily improves as the number of identities increases. The highest performance is observed when the number of identities reaches $60k$ . We also explore the impact of varying the number of samples per identity while keeping the number of identities constant. As shown in Tab.3, increasing the number of samples per identity from 20 to 200 results in continuous performance improvement. These findings demonstrate the scalability of our approach.", + "bbox": [ + 89, + 669, + 482, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation and Discussion of $K$ -Step Noise-Sharing Sampling We generate palmprint datasets using two different noise-sharing strategies (i.e., applied during the first $K$", + "bbox": [ + 89, + 854, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "steps or the last $K$ steps) and evaluate their performance. As shown in Tab.1, applying noise-sharing during the first $K$ steps results in lower intra-class diversity in the generated datasets, leading to poorer recognition performance. Additionally, the $K$ step noise-sharing sampling can serve as a plug-and-play method applicable to other diffusion-based generative models. We provide results applying this method to IDiff-Face [2] in the supplementary materials.", + "bbox": [ + 511, + 483, + 906, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 618, + 633, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes a polynomial-based palm crease representation, capable of generating a large-scale dataset with a distribution closely resembling that of real palm crease. Subsequently, an intra-class variation controllable diffusion model is introduced, with a simple yet effective $K$ -step noise-sharing sampling, which enables the generation of palmprint datasets with adjustable intra-class variations. Experimental results indicate that our proposed method significantly reduces the gap between generated and real datasets. It is also the first time that the palmprint recognition model trained solely on our generated data, yet outperforms the model trained on real data.", + "bbox": [ + 511, + 643, + 906, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments We would like to acknowledge Zhiyuan Wang and Yang Wu for their assistance in polynomial creases. This work is partly supported by the grants of the National Natural Science Foundation of China under Nos.62476077, 62076086, and 62272142.", + "bbox": [ + 511, + 825, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "26374", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Keivan Bahmani, Richard Plesh, Peter Johnson, Stephanie Schuckers, and Timothy Swyka. 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IEEE TCSVT, 2019. 3" + ], + "bbox": [ + 514, + 90, + 903, + 372 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "26376", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Diff-Palm_ Realistic Palmprint Generation with Polynomial Creases and Intra-Class Variation Controllable Diffusion Models/c6971867-defc-4d26-9a52-6e7c2c442721_model.json b/2025/Diff-Palm_ Realistic Palmprint Generation with Polynomial Creases and Intra-Class Variation Controllable Diffusion Models/c6971867-defc-4d26-9a52-6e7c2c442721_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3ffc731f5ab8bd4dbc093c8542697765f52d3e93 --- /dev/null +++ b/2025/Diff-Palm_ Realistic Palmprint Generation with Polynomial Creases and Intra-Class Variation Controllable Diffusion Models/c6971867-defc-4d26-9a52-6e7c2c442721_model.json @@ -0,0 +1,2035 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.157, + 0.13, + 0.842, + 0.175 + ], + "angle": 0, + "content": "Diff-Palm: Realistic Palmprint Generation with Polynomial Creases and Intra-Class Variation Controllable Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.203, + 0.874, + 0.24 + ], + "angle": 0, + "content": "Jianlong Jin\\(^{1*}\\), Chenglong Zhao\\(^{2*}\\), Ruixin Zhang\\(^{2}\\), Sheng Shang\\(^{1}\\), Jianqing Xu\\(^{2}\\), Jingyun Zhang\\(^{3}\\), ShaoMing Wang\\(^{3}\\), Yang Zhao\\(^{1}\\), Shouhong Ding\\(^{2\\dagger}\\), Wei Jia\\(^{1\\dagger}\\), Yunsheng Wu\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.24, + 0.753, + 0.257 + ], + "angle": 0, + "content": "1 Hefei University of Technology, 2 Tencent Youtu Lab, 3 Tencent WeChat Pay Lab33" + }, + { + "type": "text", + "bbox": [ + 0.284, + 0.26, + 0.71, + 0.275 + ], + "angle": 0, + "content": "jianlong@mail.hfut.edu.cn, lornezhao@tencent.com" + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.301, + 0.573, + 0.477 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.312, + 0.88, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.479, + 0.908, + 0.537 + ], + "angle": 0, + "content": "Figure 1. Comparison between PCE-Palm [20] and the proposed Diff-Palm. (a) PCE-Palm adopts conditional GAN with Bézier creases [44] as input to generate palmprint datasets. Diff-Palm introduces a polynomial crease and a novel diffusion model for synthesizing datasets with adjustable intra-class variations. (b) The average performance of recognition models, trained on three types of datasets (real data, PCE-Palm generated, and Diff-Palm generated) and evaluated on five public datasets. (FT: Fine-tune) Code: https://github.com/Ukuer/Diff-Palm" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.548, + 0.327, + 0.563 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.582, + 0.486, + 0.87 + ], + "angle": 0, + "content": "Palmprint recognition is significantly limited by the lack of large-scale publicly available datasets. Previous methods have adopted Bezier curves to simulate the palm creases, which then serve as input for conditional GANs to generate realistic palmprints. However, without employing real data fine-tuning, the performance of the recognition model trained on these synthetic datasets would drastically decline, indicating a large gap between generated and real palmprints. This is primarily due to the utilization of an inaccurate palm crease representation and challenges in balancing intra-class variation with identity consistency. To address this, we introduce a polynomial-based palm crease representation that provides a new palm crease generation mechanism more closely aligned with the real distribution. We also propose the palm creases conditioned diffusion model with a novel intra-class variation control method. By applying our proposed \\(K\\)-step noise-sharing sampling, we are able to synthesize palmprint datasets with large intraclass variation and high identity consistency. Experimen" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.55, + 0.907, + 0.626 + ], + "angle": 0, + "content": "tal results show that, for the first time, recognition models trained solely on our synthetic datasets, without any fine-tuning, outperform those trained on real datasets. Furthermore, our approach achieves superior recognition performance as the number of generated identities increases." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.66, + 0.645, + 0.675 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.688, + 0.907, + 0.824 + ], + "angle": 0, + "content": "Palmprint recognition has gained widespread interest for its highly discriminative, user-friendly, and privacy-friendly nature [11]. However, its further development is severely limited by the lack of large-scale public datasets. With the remarkable results achieved by deep generative models, such as Generative Adversarial Networks (GANs) [15] and Diffusion models [18], generating datasets for recognition tasks is a promising and valuable approach to replace the collection of large-scale real datasets [21]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Although existing palmprint generation methods, including RPG-Palm [33] and PCE-Palm [20] have obtained impressive results, they still rely on fine-tuning with real data to obtain good recognition performance. Specifically, they generate large-scale data to pre-train the recognition mod" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.887, + 0.356, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution. † Corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26367" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "els and then fine-tune them with real data. However, without fine-tuning, the recognition model's performance suffers from significant degradation, indicating a large gap between the generated data and real data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.155, + 0.483, + 0.412 + ], + "angle": 0, + "content": "We have identified two principal factors contributing to the observed issue. The first factor is the inaccurate representation of palm creases. Existing methods [20, 33] employ manually designed Bézier curves [44] to simulate palm creases. However, these curves significantly differ from the actual patterns found in genuine palmprints, resulting in a substantial divergence between synthetic and real palmprint data. Furthermore, the use of merely three control points per Bézier curve restricts its expressiveness. The second factor is the challenges in balancing intra-class variation with identity consistency. In the context of palmprint image generation, these methods [20, 33] employ conditional GANs and simulate intra-class variations of palmprints by adding a simple random noise. This strategy, however, yields datasets with large intra-class variation and low identity consistency compared to real datasets, thereby leading to diminished performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.415, + 0.483, + 0.672 + ], + "angle": 0, + "content": "To address the aforementioned issues, we propose a novel framework to generate realistic palmprint datasets with large intra-class variation and high identity consistency, which achieves superior performance compared to the existing SOTA method, i.e., PCE-Palm [20], as shown in Fig.1. Specifically, we utilize polynomial curves to describe palm creases, termed polynomial creases. To achieve a more accurate and expressive representation, we employ fourth-order polynomial curves parameterized by five coefficients, which substantially expands the sampling space. Based on the statistical analysis of real palm creases, we estimate a multivariate Gaussian distribution for the coefficients of polynomial curves. Subsequently, we develop a new sampling mechanism that obtains coefficients from the estimated Gaussian distribution to synthesize polynomial palm creases. This approach effectively reduces the discrepancy between synthetic and real palm creases." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Furthermore, we introduce a novel intra-class variation controllable diffusion model, designed to generate palmprints datasets that exhibit substantial variation while preserving high identity consistency. Diffusion models [18] synthesize images via a denoising sampling process. However, the inherent randomness of this process typically results in uncontrollable variation within the same identity class, potentially compromising identity consistency. This issue can lead to generated datasets with excessive intraclass variation and diminished identity consistency. To tackle this problem, we propose a simple yet effective sampling method, termed \\(K\\)-step noise-sharing sampling. This method enhances the diffusion model by employing shared noise across samples within the same identity during the sampling process, instead of distinct noise sequences. By" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.152 + ], + "angle": 0, + "content": "adjusting the parameter \\(K\\), we are able to generate datasets with a spectrum of intra-class variations. Notably, the proposed \\(K\\)-step noise-sharing sampling can be used as a plug-and-play module applied in other diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.153, + 0.905, + 0.213 + ], + "angle": 0, + "content": "In our experimental setup, we train recognition models with synthetic datasets, and evaluate them directly on publicly available datasets without employing any real data fine-tuning. Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.217, + 0.904, + 0.275 + ], + "angle": 0, + "content": "- We introduce a more realistic palm crease representation based on polynomial curves, which not only exhibits high expressive capability but also ensures that generated palm creases align with the distribution of real ones." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.277, + 0.904, + 0.351 + ], + "angle": 0, + "content": "- We propose a novel intra-class variation controllable diffusion model with a \\(K\\)-step noise-sharing sampling. It utilizes palm creases as identity conditions, enabling the synthesis of palmprint datasets that exhibit large intra-class variation while preserving high identity consistency." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.353, + 0.904, + 0.456 + ], + "angle": 0, + "content": "- Through extensive open-set experiments, we demonstrate for the first time that recognition models trained solely on synthetic datasets generated by our method outperform those trained on real datasets, without the benefit of real data fine-tuning. Moreover, our approach shows a significant improvement in performance as the number of generated identities increases." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.217, + 0.904, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.473, + 0.655, + 0.488 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.498, + 0.881, + 0.514 + ], + "angle": 0, + "content": "2.1. Data Generation for Biometric Recognition" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.521, + 0.905, + 0.701 + ], + "angle": 0, + "content": "With advancements in generation methods [3], various models have been employed to create synthetic samples in the field of biometrics, such as face generation [7, 12, 13, 22, 28, 29, 38], and fingerprint synthesis [1, 9, 34]. For palmprint generation, Bézierpalm [44] firstly utilizes Bézier curves to represent palm creases and generates new identities by sampling random curves. Subsequently, both RPG-Palm [33] and PCE-Palm [20] employ Bézier curves as an identity condition and GAN-based generative models for palmprint generation. Although these methods can produce visually realistic palmprint images, they still need to be finetuned with real data to achieve satisfactory results." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.713, + 0.776, + 0.727 + ], + "angle": 0, + "content": "2.2. Conditional Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Diffusion models have achieved remarkable performance in numerous visual tasks [4, 45]. To enable controllable generation, two main conditional control mechanisms are employed. The first is the embedding-based conditional approach [23, 30], where the embedding is typically derived from the output of a pre-trained model. This extracted embedding is then incorporated into the UNet network architecture through a cross-attention mechanism. The second is the channel-based conditional approach [27, 31], where conditional images are concatenated with the diffused image through channels. For our research, we utilize" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "26368" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.087, + 0.475, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.389 + ], + "angle": 0, + "content": "Figure 2. Comparison of (a) Bézier creases [44] and (b) proposed polynomial creases." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.402, + 0.484, + 0.496 + ], + "angle": 0, + "content": "the channel-based conditional diffusion model as our baseline, as it ensures a strong correspondence between conditional images and generated images. Furthermore, we draw comparisons with the embedding-based conditional model, IDiff-Face [2], an identity-conditioned face generation method with impressive recognition performance." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.504, + 0.294, + 0.52 + ], + "angle": 0, + "content": "2.3. Recognition Methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.526, + 0.484, + 0.664 + ], + "angle": 0, + "content": "Deep learning has significantly advanced biometric recognition, especially in facial recognition, where margin-based methods like CosFace [36] and ArcFace [6] have shown exceptional performance. Similarly, in palmprint recognition, several deep learning methods have been proposed [10, 14, 19, 39, 40, 46], many of which introduce refined networks accompanied by margin-based loss. Thus, this paper adopts ArcFace as the palmprint recognition baseline to compare different generation methods, as in PCE-Palm [20]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.677, + 0.192, + 0.693 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.703, + 0.484, + 0.825 + ], + "angle": 0, + "content": "In this section, we first introduce a polynomial representation for palm creases, which synthesize pseudo palm creases as identity conditions for generating realistic palmprints. We then propose an intra-class variation controllable diffusion model, which includes palm creases conditioned diffusion and a \\(K\\)-step noise-sharing sampling mechanism. Utilizing these components, we are able to generate palmprint datasets with adjustable levels of intra-class variations." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.834, + 0.472, + 0.85 + ], + "angle": 0, + "content": "3.1. Polynomial Representation for Palm Creases" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Current palmprint generation models [20, 33] rely on palm creases as identity control conditions, making palm crease representation a crucial task for palmprint genera" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.123 + ], + "angle": 0, + "content": "tion. These models all employ second-order Bézier curves to represent palm creases [44], as follows," + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.131, + 0.907, + 0.15 + ], + "angle": 0, + "content": "\\[\n\\mathbf {B} (t) = (1 - t) ^ {2} \\mathbf {P} _ {s} + 2 t (1 - t) \\mathbf {P} _ {c} + t ^ {2} \\mathbf {P} _ {e}, \\qquad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.158, + 0.907, + 0.295 + ], + "angle": 0, + "content": "where \\(\\mathbf{P}_s, \\mathbf{P}_c, \\mathbf{P}_e\\) represent starting point, control point, and ending point respectively, which are randomly sampled within a predefined artificial area range, and \\(t\\) is the parameter ranging from 0 to 1, determining the position along the curve, as shown in Fig.2 (a). However, although existing generation-based methods [20, 33] can produce visually realistic palmprint images, the distribution of simulated creases is quite different from that of real palm creases, leading to the requirement of fine-tuning on real data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.295, + 0.906, + 0.4 + ], + "angle": 0, + "content": "To overcome this limitation, this paper focuses on enhancing palm crease representation to align more closely with the distribution of real palm creases. Consequently, we propose a polynomial representation for palm creases, and derive the estimated distribution of the representation parameters through statistical analysis. The proposed polynomial representation is defined as follows," + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.408, + 0.907, + 0.428 + ], + "angle": 0, + "content": "\\[\ny ^ {i} = a _ {4} ^ {i} x ^ {4} + a _ {3} ^ {i} x ^ {3} + a _ {2} ^ {i} x ^ {2} + a _ {1} ^ {i} x + a _ {0}, \\qquad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.436, + 0.906, + 0.557 + ], + "angle": 0, + "content": "where \\([a_4^i, a_3^i, a_2^i, a_1^i, a_0^i]\\) denote polynomial coefficients, and \\(i(i = 1, 2, 3)\\) represents three principal lines of the palmprint. Compared to the second-order Bézier curves, a fourth-order polynomial representation provides sufficient expressiveness to capture the smoothness of palm creases. Additionally, considering the physiological basis and distinct distribution of palm creases, it is essential to sample curve parameters that reflect the actual distribution." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.557, + 0.906, + 0.649 + ], + "angle": 0, + "content": "As shown in Fig.2 (b), we manually label the points on the three principal lines of 1000 palmprint ROI images selected from publicly available datasets. For each line, the polynomial coefficients are calculated using the least squares method, based on \\( n \\) labeled points \\( ((x_0,y_0),(x_1,y_1),\\ldots ,(x_{n - 1},y_{n - 1})) \\), as follows," + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.656, + 0.905, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} ^ {\\mathrm {T}} = \\left(\\mathbf {X} ^ {\\mathrm {T}} \\mathbf {X}\\right) ^ {- 1} \\mathbf {X} ^ {\\mathrm {T}} \\mathbf {y}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.683, + 0.906, + 0.745 + ], + "angle": 0, + "content": "where \\(\\mathbf{a}^{\\mathrm{T}}\\) represents coefficient vector \\([a_0, a_1, \\ldots, a_4]^{\\mathrm{T}}\\), \\(\\mathbf{y}\\) represents vector \\([y_0, y_1, \\ldots, y_{n-1}]^{\\mathrm{T}}\\), and \\(\\mathbf{X} \\in \\mathbb{R}^{n \\times 5}\\) is a Vandermonde matrix. We apply this formula to get coefficient vectors \\((\\mathbf{a}^1, \\mathbf{a}^2, \\mathbf{a}^3)\\) of three principal lines." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.745, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In this way, polynomial coefficients of three principal lines \\((\\mathbf{a}^1,\\mathbf{a}^2,\\mathbf{a}^3)\\) are calculated for each palmprint sample. Then, we conduct a statistical analysis of the polynomial coefficients. Partial visualization results are shown in Fig.3, from which we observe that the coefficient approximately follows a Gaussian distribution. More statistical results are provided in the supplementary materials. Consequently, we represent the distribution of \\(a_j^i\\) as \\(p(a_j^i)\\sim N(\\mu_j^i,(\\sigma^2)_j^i)\\), where \\(\\mu_j^i\\) and \\((\\sigma^2)_j^i\\) denote mean and variance of \\(a_j^i\\). Therefore, the coefficient vector \\(\\mathbf{a}^i\\) follows the joint distribution" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26369" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.09, + 0.473, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.244, + 0.485, + 0.3 + ], + "angle": 0, + "content": "Figure 3. Statistical analysis of polynomial coefficients: (a) Quantile-Quantile Plot of coefficients \\( a_4^1 \\). (b) Histogram and Kernel Density Estimate (KDE) Plot of coefficients \\( a_4^1 \\). (c) Contour Plot of coefficients \\( a_4^1 \\) and \\( a_3^1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.318, + 0.484, + 0.348 + ], + "angle": 0, + "content": "\\(p(a_0^i,a_1^i,\\ldots ,a_4^i)\\) , which is a multivariate Gaussian distribution expressed as follows," + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.361, + 0.483, + 0.38 + ], + "angle": 0, + "content": "\\[\np \\left(\\mathbf {a} ^ {i}\\right) \\sim \\mathcal {N} \\left(\\mu^ {i}, \\Sigma^ {i}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.394, + 0.484, + 0.516 + ], + "angle": 0, + "content": "where \\(\\mu^i, \\Sigma^i\\) are the mean vector and covariance matrix of \\(\\mathbf{a}^i\\). By employing the proposed representation and estimated distribution, the complex palm creases located on a plane are mapped into a parameter space that conforms to a multivariate Gaussian distribution. This allows us to effortlessly sample the polynomial coefficients from the statistical distribution and then produce three principal lines using polynomial representation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.516, + 0.484, + 0.638 + ], + "angle": 0, + "content": "Additionally, we also record the coordinates of two endpoints of each line, i.e., the starting point \\( x_{s}^{i} \\) and the ending point \\( x_{e}^{i} \\), and calculate their statistical distribution. By following the same approach, we determine the range for synthesizing polynomial creases by sampling from the estimated distribution. With the addition of minor random straight lines to simulate wrinkles, a pseudo palm crease image is generated, as shown in Fig.2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.639, + 0.484, + 0.73 + ], + "angle": 0, + "content": "A palm creases similarity control mechanism is proposed by scaling the variance of the estimated Gaussian distribution by a factor of \\(\\gamma^2\\). Specifically, as \\(\\mathbf{a}^i\\) is sampled from \\(\\mathcal{N}(\\mu^i,\\gamma^2\\Sigma^i)\\), a smaller \\(\\gamma\\) (less than 1) results in a higher degree of similarity in the generated palm creases, while a larger \\(\\gamma\\) (greater than 1) leads to lower similarity." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.742, + 0.455, + 0.758 + ], + "angle": 0, + "content": "3.2. Palm Creases conditioned Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Diffusion models [4] are trained to recover an image from random noise. In contrast to GANs, which consist of two networks and utilize an adversarial loss, diffusion models adopt two processes: the diffusion process and the denoising process. The diffusion process is typically defined as a Markov chain composed of several diffusion steps. At each step, the model introduces a small amount of Gaussian noise with varying variances into the data. After a total of \\( T \\) steps, the data is degraded to pure Gaussian noise. The" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.76, + 0.107 + ], + "angle": 0, + "content": "diffusion process [4] is expressed as," + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.119, + 0.907, + 0.138 + ], + "angle": 0, + "content": "\\[\np \\left(x _ {t} \\mid x _ {t - 1}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {1 - \\beta_ {t}} x _ {t - 1}, \\beta_ {t} I\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.15, + 0.905, + 0.194 + ], + "angle": 0, + "content": "where \\( x_{t} \\) and \\( x_{t-1} \\) represent the data at diffusion step \\( t \\) and \\( t-1 \\) respectively, and \\( \\beta_{t} \\) is the variance schedule determined in advance that controls the amount of noise added." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.196, + 0.907, + 0.453 + ], + "angle": 0, + "content": "The denoising process aims to learn the reverse of the diffusion process, and recover data \\( x_0 \\) from Gaussian noise \\( x_{T} \\) step by step. An UNet network is trained to predict the noise at the \\( t \\) step and thereby restore \\( x_{t - 1} \\) from \\( x_{t} \\). Since we aim to use the diffusion model to generate palmprint datasets, unconditional diffusion is insufficient to meet our requirements. To control the identity of generated palmprint images, we use the palm crease image as a condition. The consistent palm crease image is extracted from the real palmprint image using a palm creases extraction module (PCEM) [20]. Then, the palm creases are adopted to govern the identity of the generated palmprints. Therefore, we choose to integrate the condition image into the UNet through channel concatenation. Specifically, paired palm crease images and corrupted palmprint images are concatenated and sent to the network, as shown in Fig.4(a). We use the following training objective [4]," + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.464, + 0.907, + 0.483 + ], + "angle": 0, + "content": "\\[\nL = E _ {t, x _ {t}, \\epsilon} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t, y) \\| _ {2} ^ {2} \\right], \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.494, + 0.906, + 0.525 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}\\) represents the parameterized network, and \\(y\\) stands for palm crease image." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.535, + 0.822, + 0.551 + ], + "angle": 0, + "content": "3.3. The \\(K\\)-step Noise-sharing Sampling" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.557, + 0.906, + 0.633 + ], + "angle": 0, + "content": "To generate new samples, the diffusion model follows the reverse diffusion process. Starting from random Gaussian noise, the model iteratively applies the learned denoiser to remove noise and generate final outputs. The iterative sampling process [4] is expressed as follows," + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.644, + 0.907, + 0.68 + ], + "angle": 0, + "content": "\\[\nx _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (x _ {t}, t, y)\\right) + \\sigma_ {t} z _ {t}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.901 + ], + "angle": 0, + "content": "where \\(\\alpha_{t}\\) is defined as \\(1 - \\beta_{t}\\), and \\(\\bar{\\alpha}_{t} \\coloneqq \\Pi_{i=0}^{t} \\alpha_{i}\\). The \\(\\sigma_{t}\\) is step-dependent constants, and \\(z_{t}\\) is a random noise sampled from \\(\\mathcal{N}(\\mathbf{0}, \\mathbf{I})\\). After the iterative process concludes, the estimate of \\(x_{0}\\), derived from the final iteration, is the synthesized palmprint. To control the diversity of generated results, many diffusion-based methods adopt text prompts [4, 16]. However, palmprint images are relatively simple, comprising primarily of crease and skin components, which complicates the use of text descriptions to govern diversity. We have observed that the random noise added at each step provides the randomness of the sampling process. Therefore, by controlling the random noise added to samples within the same identity, we manipulate the intra-class variation of the generated datasets effectively." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26370" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.094, + 0.429, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.094, + 0.885, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.22, + 0.907, + 0.276 + ], + "angle": 0, + "content": "Figure 4. The proposed intra-class variation controllable diffusion model. (a) Training process: palm crease images, extracted from palmprints using PCEM [20], are employed as conditions and concatenated with diffused palmprint images, serving as input for the UNet. (b) Sampling process: polynomial creases, as synthetic identity, are first generated and adopted to create consistent samples. The \\(K\\)-step noise-sharing sampling is applied to obtain palmprint datasets with varying degrees of intra-class variations." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.288, + 0.483, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.538, + 0.483, + 0.608 + ], + "angle": 0, + "content": "Figure 5. Generated palmprint results under different noise-sharing strategies. The figure illustrates the outcomes of applying noise-sharing in the last \\( K = 500 \\) steps (top) versus the first \\( K = 500 \\) steps (bottom) of a total \\( T = 1000 \\) steps during the sampling process for the same identity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.625, + 0.483, + 0.701 + ], + "angle": 0, + "content": "The \\(K\\)-step noise-sharing sampling is proposed to generate palmprint datasets with varying degrees of intra-class variations. Specifically, suppose generating the \\(j\\)-th sample of the \\(i\\)-th identity with the palm crease image \\(y^i\\), we rewrite sampling process Eq.7 as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.712, + 0.483, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\left[ x _ {t - 1} \\right] _ {j} ^ {i} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\left[ x _ {t} \\right] _ {j} ^ {i} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(\\left[ x _ {t} \\right] _ {j} ^ {i}, t, y ^ {i}\\right)\\right) + \\sigma_ {t} \\left[ z _ {t} \\right] _ {j} ^ {i}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.84 + ], + "angle": 0, + "content": "where \\([z_{t}]_{j}^{i}\\) is the random noise sampled from a standard Gaussian distribution, influencing the diversity of samples. We aim to utilize the same shared noise \\([z_{t}]^{i}\\), instead of a series of different \\([z_{t}]_{j}^{i}\\) to samples under the same identity condition. We select a continuous \\(K\\)-step sequence within the total \\(T\\) steps and apply this, as shown in Fig.4(b)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Additionally, we have found that the application of noise-sharing in the first \\( K \\) steps and the last \\( K \\) steps during the sampling process exhibits distinct behaviors. With \\( K = 500 \\) and a total of \\( T = 1000 \\) steps, the sampling" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.292, + 0.907, + 0.456 + ], + "angle": 0, + "content": "process under the same identity yields the results shown in Fig.5. When noise-sharing is applied in the first \\(K\\) steps, the generated results maintain a consistent style, while the details of the palm creases exhibit minor variations, leading to a generated dataset with low identity consistency. Conversely, when noise-sharing is applied in the last \\(K\\) steps, the generated results present diverse styles, but the consistency of the palm crease details improves. This suggests that during the sampling process, the style information of the palmprint is generated first, followed by the restoration of texture details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.458, + 0.907, + 0.549 + ], + "angle": 0, + "content": "Therefore, we apply noise-sharing in the last \\(K\\) steps. As \\(K\\) increases, the crease consistency in the sampled results under the same identity tends to improve. However, when \\(K\\) continues to increase, the stylistic diversity of the sampled results becomes restricted. We conduct experiments on datasets generated using different values of \\(K\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.565, + 0.646, + 0.581 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.59, + 0.711, + 0.607 + ], + "angle": 0, + "content": "4.1. Experimental Setups" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.613, + 0.906, + 0.688 + ], + "angle": 0, + "content": "We conduct experiments under an open-set protocol, splitting each public dataset into training and test sets with a 1:1 ratio with no overlapping identities (IDs). We utilize the TAR (True Accept Rate) @FAR (False Accept Rate) metric to evaluate the performance of recognition models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.84 + ], + "angle": 0, + "content": "Datasets We do not use public datasets to train our generative models to ensure a fair comparison, which also places our method in a more challenging cross-dataset setting. Instead, we adopt an anonymous dataset collected from the Internet, which has been processed to include 48,000 palmprint images. We utilize publicly available datasets for evaluation and to train recognition models as baselines. Experiments are conducted on following public datasets: CASIA [35], PolyU [41], Tongji [42], MPD [43], XJTU-UP [32], IITD [24], and NTU-CP-v1 [26]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Generation Model Training Setups Our conditional diffusion models utilize a UNet backbone [8] that takes a four-channel input and 64 base channels with five resolution levels. The multipliers for the number of channels used" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26371" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.089, + 0.307, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.309, + 0.089, + 0.498, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.692, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.09, + 0.885, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.187, + 0.307, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.309, + 0.187, + 0.498, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.187, + 0.692, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.189, + 0.885, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.292, + 0.908, + 0.321 + ], + "angle": 0, + "content": "Figure 6. Comparison score plots for synthetic datasets generated by different methods and real datasets. The genuine and imposter comparison scores are calculated with features, which are extracted by a pre-trained ArcFace model from datasets." + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.332, + 0.476, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.545, + 0.483, + 0.574 + ], + "angle": 0, + "content": "Figure 7. Example images of datasets generated by Diff-Palm with \\( K \\)-step sharing-noise sampling for \\( K = 0, 200, 500 \\), and 800." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.596, + 0.483, + 0.762 + ], + "angle": 0, + "content": "on those levels are 1, 1, 2, 3, and 4, respectively. Attention blocks are applied in residual blocks of the last resolution level. During the training process, we adopt the AdamW optimizer [25], set the learning rate \\( 1e - 4 \\), and train the network for a total of \\( 30k \\) steps. We apply an EMA to the weights of the model with an exponential factor of 0.9999. The batch size is 64 and is equally split across 4 GPUs. For the diffusion process, we set \\( T = 1000 \\) steps and adopt a linear diffusion variance schedule. In subsequent experiments, we default to generating datasets with \\( 2k \\) IDs and 20 samples per ID." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Recognition Model Training Setups We train ArcFace models [6] with a modified Resnet-18 [17] backbone for palmprint recognition. Palmprint images are resized to \\( 112 \\times 112 \\) and trained with ArcFace loss (\\( m = 0.5 \\), \\( s = 64 \\)) over 20 epochs using a stochastic gradient descent (SGD) optimizer. We use an initial learning rate of \\( 1e - 1 \\), momentum of 0.9, weight decay of \\( 5e - 4 \\), and a step learning rate schedule, which divides the learning rate by 10 at 7-th and 15-th epoch. RandAugment [5] is adopted for data augmen" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.343, + 0.878, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.548, + 0.908, + 0.604 + ], + "angle": 0, + "content": "Figure 8. The t-SNE polt of features extracted from real, PCE-Palm generated, and Diff-Palm generated datasets. Colors denote different datasets, while shapes within the same color correspond to different identities." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.623, + 0.907, + 0.7 + ], + "angle": 0, + "content": "tation with parameters (4, 4). We double the number of IDs in the training set by horizontally flipping the palmprint images. Training is implemented on 4 NVIDIA V100 GPUs with a batch size of 256. Consistent hyperparameters are used for all recognition models across various datasets." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.711, + 0.719, + 0.728 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Evaluating Intra-Class Variation We generate datasets by Diff-Palm with \\( K \\)-step sharing-noise sampling for \\( K = 0, 200, 500 \\) and 800. Then, we use the ArcFace model pretrained on real datasets to extract features from synthesized datasets and calculate genuine and imposter score distributions. Comparison score plots and example images are shown in Fig.6 and Fig.7 respectively. As \\( K \\) increases, intraclass variation decreases, and the genuine distribution shifts right. The verification performance in Tab.1 reveals that the recognition model trained on the synthesized dataset with \\( K = 500 \\) achieves higher recognition performance." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26372" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.907, + 0.381 + ], + "angle": 0, + "content": "
    MethodsConfigsScore DistributionsPerformance (TAR@FAR=1e-6) ↑
    Kγgenuine meanstdimposter meanstdCASIAPolyUTongJiMPDXJTU-UPAvg.
    Diff-Palm01.00.3500.1240.0690.1120.72780.73920.51510.34060.15270.4951
    Diff-Palm2001.00.5490.1180.0690.1110.84200.91110.81130.42370.60180.7180
    Diff-Palm5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm8001.00.9220.0720.0690.1120.83540.90140.85920.33690.50350.6873
    PCE-Palm(Bézier)--0.4020.1710.0990.1160.67960.77400.61490.29720.41500.5561
    PCE-Palm(poly)-1.00.3510.1860.0410.1100.82200.86870.76740.43730.59740.6986
    Diff-Palm(Bézier)500-0.6290.1980.1710.1140.67220.82360.72460.27320.36580.5719
    Diff-Palm(poly)5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm5000.250.7480.1210.1070.1130.84400.91340.84100.41620.57940.7188
    Diff-Palm5000.50.7640.1180.0880.1170.86130.92300.87000.42680.58230.7327
    Diff-Palm5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm5002.00.7840.1020.0700.1090.80530.93080.91620.36970.48900.7022
    Diff-Palm5004.00.7800.1030.0950.1080.77930.88040.86620.30410.43410.6528
    Diff-Palm(first K)5001.00.4750.0430.1170.110.76490.75710.51360.25020.03070.4633
    Diff-Palm(last K)5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.39, + 0.907, + 0.419 + ], + "angle": 0, + "content": "Table 1. Verification performance of recognition models(ArcFace [6]) with the same hyperparameters used for various generated datasets, and without any fine-tuning on real data. Synthetic datasets default to be generated with \\( {2k} \\) IDs and 20 samples per ID." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.432, + 0.485, + 0.572 + ], + "angle": 0, + "content": "
    MethodsKIdentityDintraUclassPerf.
    Diff-Palm00.59231.0000.8970.4951
    Diff-Palm2000.96670.96150.9800.7189
    Diff-Palm5000.99810.93720.9960.7729
    Diff-Palm8000.99960.66590.9990.6873
    PCE-Palm(Bézier)-0.60461.18940.6530.5561
    PCE-Palm(poly)-0.68501.18160.9580.6986
    Diff-Palm(Bézier)5000.99520.96910.6940.5719
    Diff-Palm(poly)5000.99810.93720.9960.7729
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.583, + 0.483, + 0.626 + ], + "angle": 0, + "content": "Table 2. Evaluation of synthetic datasets. \\( C_{\\text{identity}} \\), \\( D_{\\text{intra}} \\), and \\( U_{\\text{class}} \\) represent identity consistency, intra-class diversity, and class uniqueness, respectively." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.643, + 0.483, + 0.809 + ], + "angle": 0, + "content": "Comparing Palm Crease Representations We compare the performance of PCE-Palm [20] and our diffusion model by training them on different types of palm crease representations: Bézier creases [44] and polynomial creases, respectively. Each model is trained using consistent hyperparameters, with the only difference being the type of crease images used. As evidenced in Tab.1, the polynomial creases method significantly outperforms the Bézier creases. This result indicates that our polynomial crease representation more accurately bridges the gap between synthetic and real palmprints." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Evaluating Identity and Diversity Metrics We adopt identity consistency, intra-class diversity, and class uniqueness metrics from [22] to evaluate the respective properties of synthetic datasets. As shown in Tab.2, for our Diff-Palm, there exists a trade-off between identity consistency and intra-class diversity as parameter \\( K \\) is adjusted. For" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.435, + 0.908, + 0.678 + ], + "angle": 0, + "content": "\\(K = 500\\), the generated dataset strikes a balance between them, leading to optimal recognition performance. When comparing generative methods with different palm crease representations, it is evident that the use of Bezier creases leads to a noticeable decline in class uniqueness, as opposed to polynomial creases. Our analyses indicate that the superior performance of our method is due to the effective balance between identity consistency and intra-class diversity achieved by the intra-class variation controllable method, as well as the enhanced class uniqueness resulting from the use of polynomial creases. In contrast, PCE-Palm suffers from low identity consistency and reduced class uniqueness, leading the poor performance. These analysis results are also validated by the t-SNE visualization, as shown in Fig.8. Further Details about these metrics are provided in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.682, + 0.909, + 0.851 + ], + "angle": 0, + "content": "Effect of Palm Crease Similarity on Recognition We synthesize polynomial crease datasets with varying \\(\\gamma\\) values to generate palmprint datasets through diffusion models. As shown in Tab.1, results indicate that recognition performance declines when \\(\\gamma\\) is either greater than 1 or less than 1, corresponding to the expansion or contraction of the estimated distribution's variance. We believe that when \\(\\gamma > 1\\), the generated data disrupts original distribution patterns, while when \\(\\gamma < 1\\), training recognition models becomes increasingly difficult. These results confirm the reasonableness and validity of our estimated distributions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Comparing with Real Datasets and Other Methods We utilize seven public datasets to create a mixed dataset containing 2.2k IDs. The current SOTA palmprint gen" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26373" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.113, + 0.089, + 0.885, + 0.436 + ], + "angle": 0, + "content": "
    MethodsConfigsPerformance (TAR@FAR=1e-6) ↑
    #IDs# per ID#ImagesFT w/ RealCASIAPolyUTongJiMPDXJTU-UPAvg.
    Real data2.2k-29.3k✘0.92000.91960.92090.38770.62470.7546
    IDiff-Face [2]2k2040k✘0.79770.77200.61150.18470.26670.5265
    Vec2Face [37]2k2040k✘0.82010.81050.81990.25750.25780.5932
    PCE-Palm [20]2k2040k✘0.67960.77400.61490.29720.41500.5561
    Diff-Palm2k2040k✘0.87820.96010.94600.46430.61610.7729
    PCE-Palm [20]2k2040k✓0.94150.97920.93930.66620.79480.8642
    Diff-Palm2k2040k✓0.97870.98590.97440.59790.84330.8760
    Diff-Palm5k20100k✘0.89720.97570.95900.50480.75340.8180
    Diff-Palm10k20200k✘0.90720.98180.96320.56870.81430.8470
    Diff-Palm20k20400k✘0.93830.97950.97830.63040.86550.8784
    Diff-Palm30k20600k✘0.94720.97720.97720.66510.90150.8937
    Diff-Palm40k20800k✘0.94500.97990.98020.66410.90430.8947
    Diff-Palm50k201M✘0.95420.98220.98480.68140.90320.9011
    Diff-Palm60k201.2M✘0.95570.98650.98250.68560.90290.9026
    Diff-Palm2k50100k✘0.88100.93350.91850.47790.72140.7865
    Diff-Palm2k100200k✘0.90060.94360.94430.55220.74820.8178
    Diff-Palm2k150300k✘0.88170.96690.94820.55590.80430.8314
    Diff-Palm2k200400k✘0.91430.97100.94550.57750.84940.8515
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.44, + 0.907, + 0.469 + ], + "angle": 0, + "content": "Table 3. Verification performance of the recognition models across five public datasets, with the same hyperparameters used for both real and synthesized datasets. Diff-Palm is trained with \\( K = 500 \\) and \\( \\gamma = 1.0 \\) by default." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.484, + 0.483, + 0.666 + ], + "angle": 0, + "content": "eration method, PCE-Palm [20], and the face generation method [2, 37], are trained for comparison. By default, we train the recognition models on synthetic datasets without employing real data fine-tuning. As shown in Tab.3, the recognition model trained on the dataset generated by our method outperforms the models trained on real data across three public datasets, and achieves an average improvement. Furthermore, our approach significantly surpasses both PCE-Palm and facial models. We also conduct fine-tuning experiments using real data for a comprehensive comparison with PCE-Palm. More results are provided in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.483, + 0.852 + ], + "angle": 0, + "content": "Impact of Synthesized Identity and Sample Quantity We generate datasets with varying numbers of identities, maintaining 20 samples per identity, to train recognition models. As evidenced in Tab.3, the performance of the recognition model steadily improves as the number of identities increases. The highest performance is observed when the number of identities reaches \\(60k\\). We also explore the impact of varying the number of samples per identity while keeping the number of identities constant. As shown in Tab.3, increasing the number of samples per identity from 20 to 200 results in continuous performance improvement. These findings demonstrate the scalability of our approach." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Ablation and Discussion of \\( K \\)-Step Noise-Sharing Sampling We generate palmprint datasets using two different noise-sharing strategies (i.e., applied during the first \\( K \\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.484, + 0.907, + 0.606 + ], + "angle": 0, + "content": "steps or the last \\( K \\) steps) and evaluate their performance. As shown in Tab.1, applying noise-sharing during the first \\( K \\) steps results in lower intra-class diversity in the generated datasets, leading to poorer recognition performance. Additionally, the \\( K \\) step noise-sharing sampling can serve as a plug-and-play method applicable to other diffusion-based generative models. We provide results applying this method to IDiff-Face [2] in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.619, + 0.634, + 0.635 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.645, + 0.907, + 0.825 + ], + "angle": 0, + "content": "This paper proposes a polynomial-based palm crease representation, capable of generating a large-scale dataset with a distribution closely resembling that of real palm crease. Subsequently, an intra-class variation controllable diffusion model is introduced, with a simple yet effective \\( K \\)-step noise-sharing sampling, which enables the generation of palmprint datasets with adjustable intra-class variations. Experimental results indicate that our proposed method significantly reduces the gap between generated and real datasets. It is also the first time that the palmprint recognition model trained solely on our generated data, yet outperforms the model trained on real data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments We would like to acknowledge Zhiyuan Wang and Yang Wu for their assistance in polynomial creases. This work is partly supported by the grants of the National Natural Science Foundation of China under Nos.62476077, 62076086, and 62272142." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26374" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.184 + ], + "angle": 0, + "content": "[1] Keivan Bahmani, Richard Plesh, Peter Johnson, Stephanie Schuckers, and Timothy Swyka. 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Comparison between PCE-Palm [20] and the proposed Diff-Palm. (a) PCE-Palm adopts conditional GAN with Bézier creases [44] as input to generate palmprint datasets. Diff-Palm introduces a polynomial crease and a novel diffusion model for synthesizing datasets with adjustable intra-class variations. (b) The average performance of recognition models, trained on three types of datasets (real data, PCE-Palm generated, and Diff-Palm generated) and evaluated on five public datasets. (FT: Fine-tune) Code: https://github.com/Ukuer/Diff-Palm + +![](images/7f86fd6c7f83b79e6ad53d028f70dac47169c45083093b9b89f60eb8d4a45c63.jpg) + +# Abstract + +Palmprint recognition is significantly limited by the lack of large-scale publicly available datasets. Previous methods have adopted Bezier curves to simulate the palm creases, which then serve as input for conditional GANs to generate realistic palmprints. However, without employing real data fine-tuning, the performance of the recognition model trained on these synthetic datasets would drastically decline, indicating a large gap between generated and real palmprints. This is primarily due to the utilization of an inaccurate palm crease representation and challenges in balancing intra-class variation with identity consistency. To address this, we introduce a polynomial-based palm crease representation that provides a new palm crease generation mechanism more closely aligned with the real distribution. We also propose the palm creases conditioned diffusion model with a novel intra-class variation control method. By applying our proposed $K$ -step noise-sharing sampling, we are able to synthesize palmprint datasets with large intraclass variation and high identity consistency. Experimen + +tal results show that, for the first time, recognition models trained solely on our synthetic datasets, without any fine-tuning, outperform those trained on real datasets. Furthermore, our approach achieves superior recognition performance as the number of generated identities increases. + +# 1. Introduction + +Palmprint recognition has gained widespread interest for its highly discriminative, user-friendly, and privacy-friendly nature [11]. However, its further development is severely limited by the lack of large-scale public datasets. With the remarkable results achieved by deep generative models, such as Generative Adversarial Networks (GANs) [15] and Diffusion models [18], generating datasets for recognition tasks is a promising and valuable approach to replace the collection of large-scale real datasets [21]. + +Although existing palmprint generation methods, including RPG-Palm [33] and PCE-Palm [20] have obtained impressive results, they still rely on fine-tuning with real data to obtain good recognition performance. Specifically, they generate large-scale data to pre-train the recognition mod + +els and then fine-tune them with real data. However, without fine-tuning, the recognition model's performance suffers from significant degradation, indicating a large gap between the generated data and real data. + +We have identified two principal factors contributing to the observed issue. The first factor is the inaccurate representation of palm creases. Existing methods [20, 33] employ manually designed Bézier curves [44] to simulate palm creases. However, these curves significantly differ from the actual patterns found in genuine palmprints, resulting in a substantial divergence between synthetic and real palmprint data. Furthermore, the use of merely three control points per Bézier curve restricts its expressiveness. The second factor is the challenges in balancing intra-class variation with identity consistency. In the context of palmprint image generation, these methods [20, 33] employ conditional GANs and simulate intra-class variations of palmprints by adding a simple random noise. This strategy, however, yields datasets with large intra-class variation and low identity consistency compared to real datasets, thereby leading to diminished performance. + +To address the aforementioned issues, we propose a novel framework to generate realistic palmprint datasets with large intra-class variation and high identity consistency, which achieves superior performance compared to the existing SOTA method, i.e., PCE-Palm [20], as shown in Fig.1. Specifically, we utilize polynomial curves to describe palm creases, termed polynomial creases. To achieve a more accurate and expressive representation, we employ fourth-order polynomial curves parameterized by five coefficients, which substantially expands the sampling space. Based on the statistical analysis of real palm creases, we estimate a multivariate Gaussian distribution for the coefficients of polynomial curves. Subsequently, we develop a new sampling mechanism that obtains coefficients from the estimated Gaussian distribution to synthesize polynomial palm creases. This approach effectively reduces the discrepancy between synthetic and real palm creases. + +Furthermore, we introduce a novel intra-class variation controllable diffusion model, designed to generate palmprints datasets that exhibit substantial variation while preserving high identity consistency. Diffusion models [18] synthesize images via a denoising sampling process. However, the inherent randomness of this process typically results in uncontrollable variation within the same identity class, potentially compromising identity consistency. This issue can lead to generated datasets with excessive intraclass variation and diminished identity consistency. To tackle this problem, we propose a simple yet effective sampling method, termed $K$ -step noise-sharing sampling. This method enhances the diffusion model by employing shared noise across samples within the same identity during the sampling process, instead of distinct noise sequences. By + +adjusting the parameter $K$ , we are able to generate datasets with a spectrum of intra-class variations. Notably, the proposed $K$ -step noise-sharing sampling can be used as a plug-and-play module applied in other diffusion models. + +In our experimental setup, we train recognition models with synthetic datasets, and evaluate them directly on publicly available datasets without employing any real data fine-tuning. Our contributions are as follows: + +- We introduce a more realistic palm crease representation based on polynomial curves, which not only exhibits high expressive capability but also ensures that generated palm creases align with the distribution of real ones. +- We propose a novel intra-class variation controllable diffusion model with a $K$ -step noise-sharing sampling. It utilizes palm creases as identity conditions, enabling the synthesis of palmprint datasets that exhibit large intra-class variation while preserving high identity consistency. +- Through extensive open-set experiments, we demonstrate for the first time that recognition models trained solely on synthetic datasets generated by our method outperform those trained on real datasets, without the benefit of real data fine-tuning. Moreover, our approach shows a significant improvement in performance as the number of generated identities increases. + +# 2. Related Work + +# 2.1. Data Generation for Biometric Recognition + +With advancements in generation methods [3], various models have been employed to create synthetic samples in the field of biometrics, such as face generation [7, 12, 13, 22, 28, 29, 38], and fingerprint synthesis [1, 9, 34]. For palmprint generation, Bézierpalm [44] firstly utilizes Bézier curves to represent palm creases and generates new identities by sampling random curves. Subsequently, both RPG-Palm [33] and PCE-Palm [20] employ Bézier curves as an identity condition and GAN-based generative models for palmprint generation. Although these methods can produce visually realistic palmprint images, they still need to be finetuned with real data to achieve satisfactory results. + +# 2.2. Conditional Diffusion Models + +Diffusion models have achieved remarkable performance in numerous visual tasks [4, 45]. To enable controllable generation, two main conditional control mechanisms are employed. The first is the embedding-based conditional approach [23, 30], where the embedding is typically derived from the output of a pre-trained model. This extracted embedding is then incorporated into the UNet network architecture through a cross-attention mechanism. The second is the channel-based conditional approach [27, 31], where conditional images are concatenated with the diffused image through channels. For our research, we utilize + +![](images/9dd6175ec47ba75ea9f2bdb771e3f7a0aec1d666037b3f91ef5f59ae2ba99c64.jpg) +Figure 2. Comparison of (a) Bézier creases [44] and (b) proposed polynomial creases. + +the channel-based conditional diffusion model as our baseline, as it ensures a strong correspondence between conditional images and generated images. Furthermore, we draw comparisons with the embedding-based conditional model, IDiff-Face [2], an identity-conditioned face generation method with impressive recognition performance. + +# 2.3. Recognition Methods + +Deep learning has significantly advanced biometric recognition, especially in facial recognition, where margin-based methods like CosFace [36] and ArcFace [6] have shown exceptional performance. Similarly, in palmprint recognition, several deep learning methods have been proposed [10, 14, 19, 39, 40, 46], many of which introduce refined networks accompanied by margin-based loss. Thus, this paper adopts ArcFace as the palmprint recognition baseline to compare different generation methods, as in PCE-Palm [20]. + +# 3. Methods + +In this section, we first introduce a polynomial representation for palm creases, which synthesize pseudo palm creases as identity conditions for generating realistic palmprints. We then propose an intra-class variation controllable diffusion model, which includes palm creases conditioned diffusion and a $K$ -step noise-sharing sampling mechanism. Utilizing these components, we are able to generate palmprint datasets with adjustable levels of intra-class variations. + +# 3.1. Polynomial Representation for Palm Creases + +Current palmprint generation models [20, 33] rely on palm creases as identity control conditions, making palm crease representation a crucial task for palmprint genera + +tion. These models all employ second-order Bézier curves to represent palm creases [44], as follows, + +$$ +\mathbf {B} (t) = (1 - t) ^ {2} \mathbf {P} _ {s} + 2 t (1 - t) \mathbf {P} _ {c} + t ^ {2} \mathbf {P} _ {e}, \qquad (1) +$$ + +where $\mathbf{P}_s, \mathbf{P}_c, \mathbf{P}_e$ represent starting point, control point, and ending point respectively, which are randomly sampled within a predefined artificial area range, and $t$ is the parameter ranging from 0 to 1, determining the position along the curve, as shown in Fig.2 (a). However, although existing generation-based methods [20, 33] can produce visually realistic palmprint images, the distribution of simulated creases is quite different from that of real palm creases, leading to the requirement of fine-tuning on real data. + +To overcome this limitation, this paper focuses on enhancing palm crease representation to align more closely with the distribution of real palm creases. Consequently, we propose a polynomial representation for palm creases, and derive the estimated distribution of the representation parameters through statistical analysis. The proposed polynomial representation is defined as follows, + +$$ +y ^ {i} = a _ {4} ^ {i} x ^ {4} + a _ {3} ^ {i} x ^ {3} + a _ {2} ^ {i} x ^ {2} + a _ {1} ^ {i} x + a _ {0}, \qquad (2) +$$ + +where $[a_4^i, a_3^i, a_2^i, a_1^i, a_0^i]$ denote polynomial coefficients, and $i(i = 1, 2, 3)$ represents three principal lines of the palmprint. Compared to the second-order Bézier curves, a fourth-order polynomial representation provides sufficient expressiveness to capture the smoothness of palm creases. Additionally, considering the physiological basis and distinct distribution of palm creases, it is essential to sample curve parameters that reflect the actual distribution. + +As shown in Fig.2 (b), we manually label the points on the three principal lines of 1000 palmprint ROI images selected from publicly available datasets. For each line, the polynomial coefficients are calculated using the least squares method, based on $n$ labeled points $((x_0,y_0),(x_1,y_1),\ldots ,(x_{n - 1},y_{n - 1}))$ , as follows, + +$$ +\mathbf {a} ^ {\mathrm {T}} = \left(\mathbf {X} ^ {\mathrm {T}} \mathbf {X}\right) ^ {- 1} \mathbf {X} ^ {\mathrm {T}} \mathbf {y}, \tag {3} +$$ + +where $\mathbf{a}^{\mathrm{T}}$ represents coefficient vector $[a_0, a_1, \ldots, a_4]^{\mathrm{T}}$ , $\mathbf{y}$ represents vector $[y_0, y_1, \ldots, y_{n-1}]^{\mathrm{T}}$ , and $\mathbf{X} \in \mathbb{R}^{n \times 5}$ is a Vandermonde matrix. We apply this formula to get coefficient vectors $(\mathbf{a}^1, \mathbf{a}^2, \mathbf{a}^3)$ of three principal lines. + +In this way, polynomial coefficients of three principal lines $(\mathbf{a}^1,\mathbf{a}^2,\mathbf{a}^3)$ are calculated for each palmprint sample. Then, we conduct a statistical analysis of the polynomial coefficients. Partial visualization results are shown in Fig.3, from which we observe that the coefficient approximately follows a Gaussian distribution. More statistical results are provided in the supplementary materials. Consequently, we represent the distribution of $a_j^i$ as $p(a_j^i)\sim N(\mu_j^i,(\sigma^2)_j^i)$ , where $\mu_j^i$ and $(\sigma^2)_j^i$ denote mean and variance of $a_j^i$ . Therefore, the coefficient vector $\mathbf{a}^i$ follows the joint distribution + +![](images/800a0f0dc5d12a8a2dfac9317efeb3b93de58d4ac7e784401de5a741c7d999ec.jpg) +Figure 3. Statistical analysis of polynomial coefficients: (a) Quantile-Quantile Plot of coefficients $a_4^1$ . (b) Histogram and Kernel Density Estimate (KDE) Plot of coefficients $a_4^1$ . (c) Contour Plot of coefficients $a_4^1$ and $a_3^1$ . + +$p(a_0^i,a_1^i,\ldots ,a_4^i)$ , which is a multivariate Gaussian distribution expressed as follows, + +$$ +p \left(\mathbf {a} ^ {i}\right) \sim \mathcal {N} \left(\mu^ {i}, \Sigma^ {i}\right), \tag {4} +$$ + +where $\mu^i, \Sigma^i$ are the mean vector and covariance matrix of $\mathbf{a}^i$ . By employing the proposed representation and estimated distribution, the complex palm creases located on a plane are mapped into a parameter space that conforms to a multivariate Gaussian distribution. This allows us to effortlessly sample the polynomial coefficients from the statistical distribution and then produce three principal lines using polynomial representation. + +Additionally, we also record the coordinates of two endpoints of each line, i.e., the starting point $x_{s}^{i}$ and the ending point $x_{e}^{i}$ , and calculate their statistical distribution. By following the same approach, we determine the range for synthesizing polynomial creases by sampling from the estimated distribution. With the addition of minor random straight lines to simulate wrinkles, a pseudo palm crease image is generated, as shown in Fig.2. + +A palm creases similarity control mechanism is proposed by scaling the variance of the estimated Gaussian distribution by a factor of $\gamma^2$ . Specifically, as $\mathbf{a}^i$ is sampled from $\mathcal{N}(\mu^i,\gamma^2\Sigma^i)$ , a smaller $\gamma$ (less than 1) results in a higher degree of similarity in the generated palm creases, while a larger $\gamma$ (greater than 1) leads to lower similarity. + +# 3.2. Palm Creases conditioned Diffusion Model + +Diffusion models [4] are trained to recover an image from random noise. In contrast to GANs, which consist of two networks and utilize an adversarial loss, diffusion models adopt two processes: the diffusion process and the denoising process. The diffusion process is typically defined as a Markov chain composed of several diffusion steps. At each step, the model introduces a small amount of Gaussian noise with varying variances into the data. After a total of $T$ steps, the data is degraded to pure Gaussian noise. The + +diffusion process [4] is expressed as, + +$$ +p \left(x _ {t} \mid x _ {t - 1}\right) = \mathcal {N} \left(x _ {t}; \sqrt {1 - \beta_ {t}} x _ {t - 1}, \beta_ {t} I\right), \tag {5} +$$ + +where $x_{t}$ and $x_{t-1}$ represent the data at diffusion step $t$ and $t-1$ respectively, and $\beta_{t}$ is the variance schedule determined in advance that controls the amount of noise added. + +The denoising process aims to learn the reverse of the diffusion process, and recover data $x_0$ from Gaussian noise $x_{T}$ step by step. An UNet network is trained to predict the noise at the $t$ step and thereby restore $x_{t - 1}$ from $x_{t}$ . Since we aim to use the diffusion model to generate palmprint datasets, unconditional diffusion is insufficient to meet our requirements. To control the identity of generated palmprint images, we use the palm crease image as a condition. The consistent palm crease image is extracted from the real palmprint image using a palm creases extraction module (PCEM) [20]. Then, the palm creases are adopted to govern the identity of the generated palmprints. Therefore, we choose to integrate the condition image into the UNet through channel concatenation. Specifically, paired palm crease images and corrupted palmprint images are concatenated and sent to the network, as shown in Fig.4(a). We use the following training objective [4], + +$$ +L = E _ {t, x _ {t}, \epsilon} \left[ \| \epsilon - \epsilon_ {\theta} (x _ {t}, t, y) \| _ {2} ^ {2} \right], \tag {6} +$$ + +where $\epsilon_{\theta}$ represents the parameterized network, and $y$ stands for palm crease image. + +# 3.3. The $K$ -step Noise-sharing Sampling + +To generate new samples, the diffusion model follows the reverse diffusion process. Starting from random Gaussian noise, the model iteratively applies the learned denoiser to remove noise and generate final outputs. The iterative sampling process [4] is expressed as follows, + +$$ +x _ {t - 1} = \frac {1}{\sqrt {\alpha_ {t}}} \left(x _ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} (x _ {t}, t, y)\right) + \sigma_ {t} z _ {t}, \tag {7} +$$ + +where $\alpha_{t}$ is defined as $1 - \beta_{t}$ , and $\bar{\alpha}_{t} \coloneqq \Pi_{i=0}^{t} \alpha_{i}$ . The $\sigma_{t}$ is step-dependent constants, and $z_{t}$ is a random noise sampled from $\mathcal{N}(\mathbf{0}, \mathbf{I})$ . After the iterative process concludes, the estimate of $x_{0}$ , derived from the final iteration, is the synthesized palmprint. To control the diversity of generated results, many diffusion-based methods adopt text prompts [4, 16]. However, palmprint images are relatively simple, comprising primarily of crease and skin components, which complicates the use of text descriptions to govern diversity. We have observed that the random noise added at each step provides the randomness of the sampling process. Therefore, by controlling the random noise added to samples within the same identity, we manipulate the intra-class variation of the generated datasets effectively. + +![](images/92236f242aebf703ad424bf51a0531de5c581d8ecf63a838c08f3da0b7e2f053.jpg) +Figure 4. The proposed intra-class variation controllable diffusion model. (a) Training process: palm crease images, extracted from palmprints using PCEM [20], are employed as conditions and concatenated with diffused palmprint images, serving as input for the UNet. (b) Sampling process: polynomial creases, as synthetic identity, are first generated and adopted to create consistent samples. The $K$ -step noise-sharing sampling is applied to obtain palmprint datasets with varying degrees of intra-class variations. + +![](images/df9f8e5f7618bdf5ebedccd82ce52cac2708c76e741fa03e9f8bd0dc8596399b.jpg) + +![](images/b49c051b7aaf053bc3a90222f77370b9b16dd9136e89dfeef9bc90e595928ab3.jpg) +Figure 5. Generated palmprint results under different noise-sharing strategies. The figure illustrates the outcomes of applying noise-sharing in the last $K = 500$ steps (top) versus the first $K = 500$ steps (bottom) of a total $T = 1000$ steps during the sampling process for the same identity. + +The $K$ -step noise-sharing sampling is proposed to generate palmprint datasets with varying degrees of intra-class variations. Specifically, suppose generating the $j$ -th sample of the $i$ -th identity with the palm crease image $y^i$ , we rewrite sampling process Eq.7 as follows: + +$$ +\left[ x _ {t - 1} \right] _ {j} ^ {i} = \frac {1}{\sqrt {\alpha_ {t}}} \left(\left[ x _ {t} \right] _ {j} ^ {i} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} \left(\left[ x _ {t} \right] _ {j} ^ {i}, t, y ^ {i}\right)\right) + \sigma_ {t} \left[ z _ {t} \right] _ {j} ^ {i}, \tag {8} +$$ + +where $[z_{t}]_{j}^{i}$ is the random noise sampled from a standard Gaussian distribution, influencing the diversity of samples. We aim to utilize the same shared noise $[z_{t}]^{i}$ , instead of a series of different $[z_{t}]_{j}^{i}$ to samples under the same identity condition. We select a continuous $K$ -step sequence within the total $T$ steps and apply this, as shown in Fig.4(b). + +Additionally, we have found that the application of noise-sharing in the first $K$ steps and the last $K$ steps during the sampling process exhibits distinct behaviors. With $K = 500$ and a total of $T = 1000$ steps, the sampling + +process under the same identity yields the results shown in Fig.5. When noise-sharing is applied in the first $K$ steps, the generated results maintain a consistent style, while the details of the palm creases exhibit minor variations, leading to a generated dataset with low identity consistency. Conversely, when noise-sharing is applied in the last $K$ steps, the generated results present diverse styles, but the consistency of the palm crease details improves. This suggests that during the sampling process, the style information of the palmprint is generated first, followed by the restoration of texture details. + +Therefore, we apply noise-sharing in the last $K$ steps. As $K$ increases, the crease consistency in the sampled results under the same identity tends to improve. However, when $K$ continues to increase, the stylistic diversity of the sampled results becomes restricted. We conduct experiments on datasets generated using different values of $K$ . + +# 4. Experiments + +# 4.1. Experimental Setups + +We conduct experiments under an open-set protocol, splitting each public dataset into training and test sets with a 1:1 ratio with no overlapping identities (IDs). We utilize the TAR (True Accept Rate) @FAR (False Accept Rate) metric to evaluate the performance of recognition models. + +Datasets We do not use public datasets to train our generative models to ensure a fair comparison, which also places our method in a more challenging cross-dataset setting. Instead, we adopt an anonymous dataset collected from the Internet, which has been processed to include 48,000 palmprint images. We utilize publicly available datasets for evaluation and to train recognition models as baselines. Experiments are conducted on following public datasets: CASIA [35], PolyU [41], Tongji [42], MPD [43], XJTU-UP [32], IITD [24], and NTU-CP-v1 [26]. + +Generation Model Training Setups Our conditional diffusion models utilize a UNet backbone [8] that takes a four-channel input and 64 base channels with five resolution levels. The multipliers for the number of channels used + +![](images/e52f4b3d506f3dc0c047999d2fdbc52b25635fc22b5ffaa01af4aebb85c3944d.jpg) + +![](images/50c4c9e4537e061af4593df7201bcf0816b245128b8124857f589af115934e8b.jpg) + +![](images/8e4e17ecff8455568029ed2451f06c57bfda269935c5a146fa44e5464f5ff863.jpg) + +![](images/5cb2df37ed5165089ba84cdaad5e7aea87fe25be464d071568e849481adb3326.jpg) + +![](images/cfefa960045e69b67daf960c9a53653d4b3b2c9493234130440f0c25626c05be.jpg) +Figure 6. Comparison score plots for synthetic datasets generated by different methods and real datasets. The genuine and imposter comparison scores are calculated with features, which are extracted by a pre-trained ArcFace model from datasets. + +![](images/c2842aca655fcd6b214e2fd6bca35c33526965221e7af3dcf16c34942f23a527.jpg) + +![](images/760fa31a3cf3e7f60d30c40932b8bad72e85bdb6e8763e950ef52081d3eac498.jpg) + +![](images/1adea6eeee046bdf2a855528e12ff0dec8c22f7f2e60a435a3d568cb6716c2fe.jpg) + +![](images/fbdb9dc4bf428d9da193d7f123bab1675b395606054abde9990043718f6d8dd4.jpg) +Figure 7. Example images of datasets generated by Diff-Palm with $K$ -step sharing-noise sampling for $K = 0, 200, 500$ , and 800. + +on those levels are 1, 1, 2, 3, and 4, respectively. Attention blocks are applied in residual blocks of the last resolution level. During the training process, we adopt the AdamW optimizer [25], set the learning rate $1e - 4$ , and train the network for a total of $30k$ steps. We apply an EMA to the weights of the model with an exponential factor of 0.9999. The batch size is 64 and is equally split across 4 GPUs. For the diffusion process, we set $T = 1000$ steps and adopt a linear diffusion variance schedule. In subsequent experiments, we default to generating datasets with $2k$ IDs and 20 samples per ID. + +Recognition Model Training Setups We train ArcFace models [6] with a modified Resnet-18 [17] backbone for palmprint recognition. Palmprint images are resized to $112 \times 112$ and trained with ArcFace loss ( $m = 0.5$ , $s = 64$ ) over 20 epochs using a stochastic gradient descent (SGD) optimizer. We use an initial learning rate of $1e - 1$ , momentum of 0.9, weight decay of $5e - 4$ , and a step learning rate schedule, which divides the learning rate by 10 at 7-th and 15-th epoch. RandAugment [5] is adopted for data augmen + +![](images/932da4aee1958b0f2d35fa59cfb27e44ce70e04a20ad491a4c1325927b357457.jpg) +Figure 8. The t-SNE polt of features extracted from real, PCE-Palm generated, and Diff-Palm generated datasets. Colors denote different datasets, while shapes within the same color correspond to different identities. + +tation with parameters (4, 4). We double the number of IDs in the training set by horizontally flipping the palmprint images. Training is implemented on 4 NVIDIA V100 GPUs with a batch size of 256. Consistent hyperparameters are used for all recognition models across various datasets. + +# 4.2. Experimental Results + +Evaluating Intra-Class Variation We generate datasets by Diff-Palm with $K$ -step sharing-noise sampling for $K = 0, 200, 500$ and 800. Then, we use the ArcFace model pretrained on real datasets to extract features from synthesized datasets and calculate genuine and imposter score distributions. Comparison score plots and example images are shown in Fig.6 and Fig.7 respectively. As $K$ increases, intraclass variation decreases, and the genuine distribution shifts right. The verification performance in Tab.1 reveals that the recognition model trained on the synthesized dataset with $K = 500$ achieves higher recognition performance. + +
    MethodsConfigsScore DistributionsPerformance (TAR@FAR=1e-6) ↑
    Kγgenuine meanstdimposter meanstdCASIAPolyUTongJiMPDXJTU-UPAvg.
    Diff-Palm01.00.3500.1240.0690.1120.72780.73920.51510.34060.15270.4951
    Diff-Palm2001.00.5490.1180.0690.1110.84200.91110.81130.42370.60180.7180
    Diff-Palm5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm8001.00.9220.0720.0690.1120.83540.90140.85920.33690.50350.6873
    PCE-Palm(Bézier)--0.4020.1710.0990.1160.67960.77400.61490.29720.41500.5561
    PCE-Palm(poly)-1.00.3510.1860.0410.1100.82200.86870.76740.43730.59740.6986
    Diff-Palm(Bézier)500-0.6290.1980.1710.1140.67220.82360.72460.27320.36580.5719
    Diff-Palm(poly)5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm5000.250.7480.1210.1070.1130.84400.91340.84100.41620.57940.7188
    Diff-Palm5000.50.7640.1180.0880.1170.86130.92300.87000.42680.58230.7327
    Diff-Palm5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm5002.00.7840.1020.0700.1090.80530.93080.91620.36970.48900.7022
    Diff-Palm5004.00.7800.1030.0950.1080.77930.88040.86620.30410.43410.6528
    Diff-Palm(first K)5001.00.4750.0430.1170.110.76490.75710.51360.25020.03070.4633
    Diff-Palm(last K)5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    + +Table 1. Verification performance of recognition models(ArcFace [6]) with the same hyperparameters used for various generated datasets, and without any fine-tuning on real data. Synthetic datasets default to be generated with ${2k}$ IDs and 20 samples per ID. + +
    MethodsKIdentityDintraUclassPerf.
    Diff-Palm00.59231.0000.8970.4951
    Diff-Palm2000.96670.96150.9800.7189
    Diff-Palm5000.99810.93720.9960.7729
    Diff-Palm8000.99960.66590.9990.6873
    PCE-Palm(Bézier)-0.60461.18940.6530.5561
    PCE-Palm(poly)-0.68501.18160.9580.6986
    Diff-Palm(Bézier)5000.99520.96910.6940.5719
    Diff-Palm(poly)5000.99810.93720.9960.7729
    + +Table 2. Evaluation of synthetic datasets. $C_{\text{identity}}$ , $D_{\text{intra}}$ , and $U_{\text{class}}$ represent identity consistency, intra-class diversity, and class uniqueness, respectively. + +Comparing Palm Crease Representations We compare the performance of PCE-Palm [20] and our diffusion model by training them on different types of palm crease representations: Bézier creases [44] and polynomial creases, respectively. Each model is trained using consistent hyperparameters, with the only difference being the type of crease images used. As evidenced in Tab.1, the polynomial creases method significantly outperforms the Bézier creases. This result indicates that our polynomial crease representation more accurately bridges the gap between synthetic and real palmprints. + +Evaluating Identity and Diversity Metrics We adopt identity consistency, intra-class diversity, and class uniqueness metrics from [22] to evaluate the respective properties of synthetic datasets. As shown in Tab.2, for our Diff-Palm, there exists a trade-off between identity consistency and intra-class diversity as parameter $K$ is adjusted. For + +$K = 500$ , the generated dataset strikes a balance between them, leading to optimal recognition performance. When comparing generative methods with different palm crease representations, it is evident that the use of Bezier creases leads to a noticeable decline in class uniqueness, as opposed to polynomial creases. Our analyses indicate that the superior performance of our method is due to the effective balance between identity consistency and intra-class diversity achieved by the intra-class variation controllable method, as well as the enhanced class uniqueness resulting from the use of polynomial creases. In contrast, PCE-Palm suffers from low identity consistency and reduced class uniqueness, leading the poor performance. These analysis results are also validated by the t-SNE visualization, as shown in Fig.8. Further Details about these metrics are provided in the supplementary materials. + +Effect of Palm Crease Similarity on Recognition We synthesize polynomial crease datasets with varying $\gamma$ values to generate palmprint datasets through diffusion models. As shown in Tab.1, results indicate that recognition performance declines when $\gamma$ is either greater than 1 or less than 1, corresponding to the expansion or contraction of the estimated distribution's variance. We believe that when $\gamma > 1$ , the generated data disrupts original distribution patterns, while when $\gamma < 1$ , training recognition models becomes increasingly difficult. These results confirm the reasonableness and validity of our estimated distributions. + +Comparing with Real Datasets and Other Methods We utilize seven public datasets to create a mixed dataset containing 2.2k IDs. The current SOTA palmprint gen + +
    MethodsConfigsPerformance (TAR@FAR=1e-6) ↑
    #IDs# per ID#ImagesFT w/ RealCASIAPolyUTongJiMPDXJTU-UPAvg.
    Real data2.2k-29.3k✘0.92000.91960.92090.38770.62470.7546
    IDiff-Face [2]2k2040k✘0.79770.77200.61150.18470.26670.5265
    Vec2Face [37]2k2040k✘0.82010.81050.81990.25750.25780.5932
    PCE-Palm [20]2k2040k✘0.67960.77400.61490.29720.41500.5561
    Diff-Palm2k2040k✘0.87820.96010.94600.46430.61610.7729
    PCE-Palm [20]2k2040k✓0.94150.97920.93930.66620.79480.8642
    Diff-Palm2k2040k✓0.97870.98590.97440.59790.84330.8760
    Diff-Palm5k20100k✘0.89720.97570.95900.50480.75340.8180
    Diff-Palm10k20200k✘0.90720.98180.96320.56870.81430.8470
    Diff-Palm20k20400k✘0.93830.97950.97830.63040.86550.8784
    Diff-Palm30k20600k✘0.94720.97720.97720.66510.90150.8937
    Diff-Palm40k20800k✘0.94500.97990.98020.66410.90430.8947
    Diff-Palm50k201M✘0.95420.98220.98480.68140.90320.9011
    Diff-Palm60k201.2M✘0.95570.98650.98250.68560.90290.9026
    Diff-Palm2k50100k✘0.88100.93350.91850.47790.72140.7865
    Diff-Palm2k100200k✘0.90060.94360.94430.55220.74820.8178
    Diff-Palm2k150300k✘0.88170.96690.94820.55590.80430.8314
    Diff-Palm2k200400k✘0.91430.97100.94550.57750.84940.8515
    + +Table 3. Verification performance of the recognition models across five public datasets, with the same hyperparameters used for both real and synthesized datasets. Diff-Palm is trained with $K = 500$ and $\gamma = 1.0$ by default. + +eration method, PCE-Palm [20], and the face generation method [2, 37], are trained for comparison. By default, we train the recognition models on synthetic datasets without employing real data fine-tuning. As shown in Tab.3, the recognition model trained on the dataset generated by our method outperforms the models trained on real data across three public datasets, and achieves an average improvement. Furthermore, our approach significantly surpasses both PCE-Palm and facial models. We also conduct fine-tuning experiments using real data for a comprehensive comparison with PCE-Palm. More results are provided in the supplementary materials. + +Impact of Synthesized Identity and Sample Quantity We generate datasets with varying numbers of identities, maintaining 20 samples per identity, to train recognition models. As evidenced in Tab.3, the performance of the recognition model steadily improves as the number of identities increases. The highest performance is observed when the number of identities reaches $60k$ . We also explore the impact of varying the number of samples per identity while keeping the number of identities constant. As shown in Tab.3, increasing the number of samples per identity from 20 to 200 results in continuous performance improvement. These findings demonstrate the scalability of our approach. + +Ablation and Discussion of $K$ -Step Noise-Sharing Sampling We generate palmprint datasets using two different noise-sharing strategies (i.e., applied during the first $K$ + +steps or the last $K$ steps) and evaluate their performance. As shown in Tab.1, applying noise-sharing during the first $K$ steps results in lower intra-class diversity in the generated datasets, leading to poorer recognition performance. Additionally, the $K$ step noise-sharing sampling can serve as a plug-and-play method applicable to other diffusion-based generative models. We provide results applying this method to IDiff-Face [2] in the supplementary materials. + +# 5. Conclusion + +This paper proposes a polynomial-based palm crease representation, capable of generating a large-scale dataset with a distribution closely resembling that of real palm crease. Subsequently, an intra-class variation controllable diffusion model is introduced, with a simple yet effective $K$ -step noise-sharing sampling, which enables the generation of palmprint datasets with adjustable intra-class variations. Experimental results indicate that our proposed method significantly reduces the gap between generated and real datasets. It is also the first time that the palmprint recognition model trained solely on our generated data, yet outperforms the model trained on real data. + +Acknowledgments We would like to acknowledge Zhiyuan Wang and Yang Wu for their assistance in polynomial creases. This work is partly supported by the grants of the National Natural Science Foundation of China under Nos.62476077, 62076086, and 62272142. + +# References + +[1] Keivan Bahmani, Richard Plesh, Peter Johnson, Stephanie Schuckers, and Timothy Swyka. High fidelity fingerprint generation: Quality, uniqueness, and privacy. In 2021 IEEE International Conference on Image Processing (ICIP), pages 3018-3022. IEEE, 2021. 2 +[2] Fadi Boutros, Jonas Henry Grebe, Arjan Kuijper, and Naser Damer. Idiff-face: Synthetic-based face recognition through fizzy identity-conditioned diffusion model. 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Comparison between PCE-Palm [20] and the proposed Diff-Palm. (a) PCE-Palm adopts conditional GAN with Bézier creases [44] as input to generate palmprint datasets. Diff-Palm introduces a polynomial crease and a novel diffusion model for synthesizing datasets with adjustable intra-class variations. (b) The average performance of recognition models, trained on three types of datasets (real data, PCE-Palm generated, and Diff-Palm generated) and evaluated on five public datasets. (FT: Fine-tune) Code: https://github.com/Ukuer/Diff-Palm" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 377, + 247, + 538, + 376 + ], + "blocks": [ + { + "bbox": [ + 377, + 247, + 538, + 376 + ], + "lines": [ + { + "bbox": [ + 377, + 247, + 538, + 376 + ], + "spans": [ + { + "bbox": [ + 377, + 247, + 538, + 376 + ], + "type": "image", + "image_path": "7f86fd6c7f83b79e6ad53d028f70dac47169c45083093b9b89f60eb8d4a45c63.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 151, + 434, + 200, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 434, + 200, + 445 + ], + "spans": [ + { + "bbox": [ + 151, + 434, + 200, + 445 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 54, + 460, + 297, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 460, + 297, + 689 + ], + "spans": [ + { + "bbox": [ + 54, + 460, + 297, + 689 + ], + "type": "text", + "content": "Palmprint recognition is significantly limited by the lack of large-scale publicly available datasets. Previous methods have adopted Bezier curves to simulate the palm creases, which then serve as input for conditional GANs to generate realistic palmprints. However, without employing real data fine-tuning, the performance of the recognition model trained on these synthetic datasets would drastically decline, indicating a large gap between generated and real palmprints. This is primarily due to the utilization of an inaccurate palm crease representation and challenges in balancing intra-class variation with identity consistency. To address this, we introduce a polynomial-based palm crease representation that provides a new palm crease generation mechanism more closely aligned with the real distribution. We also propose the palm creases conditioned diffusion model with a novel intra-class variation control method. By applying our proposed " + }, + { + "bbox": [ + 54, + 460, + 297, + 689 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 54, + 460, + 297, + 689 + ], + "type": "text", + "content": "-step noise-sharing sampling, we are able to synthesize palmprint datasets with large intraclass variation and high identity consistency. Experimen" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 435, + 555, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 435, + 555, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 435, + 555, + 495 + ], + "type": "text", + "content": "tal results show that, for the first time, recognition models trained solely on our synthetic datasets, without any fine-tuning, outperform those trained on real datasets. Furthermore, our approach achieves superior recognition performance as the number of generated identities increases." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 522, + 394, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 522, + 394, + 534 + ], + "spans": [ + { + "bbox": [ + 314, + 522, + 394, + 534 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 544, + 555, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 544, + 555, + 652 + ], + "spans": [ + { + "bbox": [ + 312, + 544, + 555, + 652 + ], + "type": "text", + "content": "Palmprint recognition has gained widespread interest for its highly discriminative, user-friendly, and privacy-friendly nature [11]. However, its further development is severely limited by the lack of large-scale public datasets. With the remarkable results achieved by deep generative models, such as Generative Adversarial Networks (GANs) [15] and Diffusion models [18], generating datasets for recognition tasks is a promising and valuable approach to replace the collection of large-scale real datasets [21]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 556, + 715 + ], + "type": "text", + "content": "Although existing palmprint generation methods, including RPG-Palm [33] and PCE-Palm [20] have obtained impressive results, they still rely on fine-tuning with real data to obtain good recognition performance. Specifically, they generate large-scale data to pre-train the recognition mod" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 702, + 217, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 702, + 217, + 713 + ], + "spans": [ + { + "bbox": [ + 66, + 702, + 217, + 713 + ], + "type": "text", + "content": "*Equal contribution. † Corresponding authors." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26367" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "els and then fine-tune them with real data. However, without fine-tuning, the recognition model's performance suffers from significant degradation, indicating a large gap between the generated data and real data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 122, + 295, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 122, + 295, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 122, + 295, + 326 + ], + "type": "text", + "content": "We have identified two principal factors contributing to the observed issue. The first factor is the inaccurate representation of palm creases. Existing methods [20, 33] employ manually designed Bézier curves [44] to simulate palm creases. However, these curves significantly differ from the actual patterns found in genuine palmprints, resulting in a substantial divergence between synthetic and real palmprint data. Furthermore, the use of merely three control points per Bézier curve restricts its expressiveness. The second factor is the challenges in balancing intra-class variation with identity consistency. In the context of palmprint image generation, these methods [20, 33] employ conditional GANs and simulate intra-class variations of palmprints by adding a simple random noise. This strategy, however, yields datasets with large intra-class variation and low identity consistency compared to real datasets, thereby leading to diminished performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 328, + 295, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 328, + 295, + 532 + ], + "spans": [ + { + "bbox": [ + 55, + 328, + 295, + 532 + ], + "type": "text", + "content": "To address the aforementioned issues, we propose a novel framework to generate realistic palmprint datasets with large intra-class variation and high identity consistency, which achieves superior performance compared to the existing SOTA method, i.e., PCE-Palm [20], as shown in Fig.1. Specifically, we utilize polynomial curves to describe palm creases, termed polynomial creases. To achieve a more accurate and expressive representation, we employ fourth-order polynomial curves parameterized by five coefficients, which substantially expands the sampling space. Based on the statistical analysis of real palm creases, we estimate a multivariate Gaussian distribution for the coefficients of polynomial curves. Subsequently, we develop a new sampling mechanism that obtains coefficients from the estimated Gaussian distribution to synthesize polynomial palm creases. This approach effectively reduces the discrepancy between synthetic and real palm creases." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "type": "text", + "content": "Furthermore, we introduce a novel intra-class variation controllable diffusion model, designed to generate palmprints datasets that exhibit substantial variation while preserving high identity consistency. Diffusion models [18] synthesize images via a denoising sampling process. However, the inherent randomness of this process typically results in uncontrollable variation within the same identity class, potentially compromising identity consistency. This issue can lead to generated datasets with excessive intraclass variation and diminished identity consistency. To tackle this problem, we propose a simple yet effective sampling method, termed " + }, + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 534, + 295, + 714 + ], + "type": "text", + "content": "-step noise-sharing sampling. This method enhances the diffusion model by employing shared noise across samples within the same identity during the sampling process, instead of distinct noise sequences. By" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "adjusting the parameter " + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": ", we are able to generate datasets with a spectrum of intra-class variations. Notably, the proposed " + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 72, + 553, + 120 + ], + "type": "text", + "content": "-step noise-sharing sampling can be used as a plug-and-play module applied in other diffusion models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 121, + 553, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 121, + 553, + 168 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 553, + 168 + ], + "type": "text", + "content": "In our experimental setup, we train recognition models with synthetic datasets, and evaluate them directly on publicly available datasets without employing any real data fine-tuning. Our contributions are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 171, + 553, + 361 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 313, + 171, + 553, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 171, + 553, + 217 + ], + "spans": [ + { + "bbox": [ + 313, + 171, + 553, + 217 + ], + "type": "text", + "content": "- We introduce a more realistic palm crease representation based on polynomial curves, which not only exhibits high expressive capability but also ensures that generated palm creases align with the distribution of real ones." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 219, + 553, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 219, + 553, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 553, + 277 + ], + "type": "text", + "content": "- We propose a novel intra-class variation controllable diffusion model with a " + }, + { + "bbox": [ + 313, + 219, + 553, + 277 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 219, + 553, + 277 + ], + "type": "text", + "content": "-step noise-sharing sampling. It utilizes palm creases as identity conditions, enabling the synthesis of palmprint datasets that exhibit large intra-class variation while preserving high identity consistency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 279, + 553, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 279, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 279, + 553, + 361 + ], + "type": "text", + "content": "- Through extensive open-set experiments, we demonstrate for the first time that recognition models trained solely on synthetic datasets generated by our method outperform those trained on real datasets, without the benefit of real data fine-tuning. Moreover, our approach shows a significant improvement in performance as the number of generated identities increases." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 374, + 400, + 386 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 374, + 400, + 386 + ], + "spans": [ + { + "bbox": [ + 313, + 374, + 400, + 386 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 394, + 539, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 539, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 539, + 407 + ], + "type": "text", + "content": "2.1. Data Generation for Biometric Recognition" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 412, + 553, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 412, + 553, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 412, + 553, + 555 + ], + "type": "text", + "content": "With advancements in generation methods [3], various models have been employed to create synthetic samples in the field of biometrics, such as face generation [7, 12, 13, 22, 28, 29, 38], and fingerprint synthesis [1, 9, 34]. For palmprint generation, Bézierpalm [44] firstly utilizes Bézier curves to represent palm creases and generates new identities by sampling random curves. Subsequently, both RPG-Palm [33] and PCE-Palm [20] employ Bézier curves as an identity condition and GAN-based generative models for palmprint generation. Although these methods can produce visually realistic palmprint images, they still need to be finetuned with real data to achieve satisfactory results." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 564, + 474, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 474, + 575 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 474, + 575 + ], + "type": "text", + "content": "2.2. Conditional Diffusion Models" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 582, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 553, + 713 + ], + "type": "text", + "content": "Diffusion models have achieved remarkable performance in numerous visual tasks [4, 45]. To enable controllable generation, two main conditional control mechanisms are employed. The first is the embedding-based conditional approach [23, 30], where the embedding is typically derived from the output of a pre-trained model. This extracted embedding is then incorporated into the UNet network architecture through a cross-attention mechanism. The second is the channel-based conditional approach [27, 31], where conditional images are concatenated with the diffused image through channels. For our research, we utilize" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26368" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 68, + 290, + 273 + ], + "blocks": [ + { + "bbox": [ + 61, + 68, + 290, + 273 + ], + "lines": [ + { + "bbox": [ + 61, + 68, + 290, + 273 + ], + "spans": [ + { + "bbox": [ + 61, + 68, + 290, + 273 + ], + "type": "image", + "image_path": "9dd6175ec47ba75ea9f2bdb771e3f7a0aec1d666037b3f91ef5f59ae2ba99c64.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 283, + 295, + 308 + ], + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 308 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 308 + ], + "type": "text", + "content": "Figure 2. Comparison of (a) Bézier creases [44] and (b) proposed polynomial creases." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 296, + 392 + ], + "type": "text", + "content": "the channel-based conditional diffusion model as our baseline, as it ensures a strong correspondence between conditional images and generated images. Furthermore, we draw comparisons with the embedding-based conditional model, IDiff-Face [2], an identity-conditioned face generation method with impressive recognition performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 399, + 179, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 179, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 179, + 411 + ], + "type": "text", + "content": "2.3. Recognition Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 416, + 296, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 416, + 296, + 525 + ], + "spans": [ + { + "bbox": [ + 55, + 416, + 296, + 525 + ], + "type": "text", + "content": "Deep learning has significantly advanced biometric recognition, especially in facial recognition, where margin-based methods like CosFace [36] and ArcFace [6] have shown exceptional performance. Similarly, in palmprint recognition, several deep learning methods have been proposed [10, 14, 19, 39, 40, 46], many of which introduce refined networks accompanied by margin-based loss. Thus, this paper adopts ArcFace as the palmprint recognition baseline to compare different generation methods, as in PCE-Palm [20]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 536, + 117, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 117, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 117, + 548 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 556, + 296, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 556, + 296, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 556, + 296, + 653 + ], + "type": "text", + "content": "In this section, we first introduce a polynomial representation for palm creases, which synthesize pseudo palm creases as identity conditions for generating realistic palmprints. We then propose an intra-class variation controllable diffusion model, which includes palm creases conditioned diffusion and a " + }, + { + "bbox": [ + 55, + 556, + 296, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 556, + 296, + 653 + ], + "type": "text", + "content": "-step noise-sharing sampling mechanism. Utilizing these components, we are able to generate palmprint datasets with adjustable levels of intra-class variations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 660, + 288, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 660, + 288, + 673 + ], + "spans": [ + { + "bbox": [ + 55, + 660, + 288, + 673 + ], + "type": "text", + "content": "3.1. Polynomial Representation for Palm Creases" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "Current palmprint generation models [20, 33] rely on palm creases as identity control conditions, making palm crease representation a crucial task for palmprint genera" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "content": "tion. These models all employ second-order Bézier curves to represent palm creases [44], as follows," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 351, + 103, + 555, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 103, + 555, + 118 + ], + "spans": [ + { + "bbox": [ + 351, + 103, + 555, + 118 + ], + "type": "interline_equation", + "content": "\\mathbf {B} (t) = (1 - t) ^ {2} \\mathbf {P} _ {s} + 2 t (1 - t) \\mathbf {P} _ {c} + t ^ {2} \\mathbf {P} _ {e}, \\qquad (1)", + "image_path": "3cd6974e766470765943cd5ff8cc6b5dacb33b519a36a53de1971cb30e96c82a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 125, + 555, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 125, + 555, + 233 + ], + "spans": [ + { + "bbox": [ + 313, + 125, + 555, + 233 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 125, + 555, + 233 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_s, \\mathbf{P}_c, \\mathbf{P}_e" + }, + { + "bbox": [ + 313, + 125, + 555, + 233 + ], + "type": "text", + "content": " represent starting point, control point, and ending point respectively, which are randomly sampled within a predefined artificial area range, and " + }, + { + "bbox": [ + 313, + 125, + 555, + 233 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 125, + 555, + 233 + ], + "type": "text", + "content": " is the parameter ranging from 0 to 1, determining the position along the curve, as shown in Fig.2 (a). However, although existing generation-based methods [20, 33] can produce visually realistic palmprint images, the distribution of simulated creases is quite different from that of real palm creases, leading to the requirement of fine-tuning on real data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 233, + 554, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 233, + 554, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 233, + 554, + 316 + ], + "type": "text", + "content": "To overcome this limitation, this paper focuses on enhancing palm crease representation to align more closely with the distribution of real palm creases. Consequently, we propose a polynomial representation for palm creases, and derive the estimated distribution of the representation parameters through statistical analysis. The proposed polynomial representation is defined as follows," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 356, + 323, + 555, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 323, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 356, + 323, + 555, + 338 + ], + "type": "interline_equation", + "content": "y ^ {i} = a _ {4} ^ {i} x ^ {4} + a _ {3} ^ {i} x ^ {3} + a _ {2} ^ {i} x ^ {2} + a _ {1} ^ {i} x + a _ {0}, \\qquad (2)", + "image_path": "eb8b0055a09092519f6a2198d59312a9cecfdad2dd82a9a03b5c1da165fca56b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 345, + 554, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 345, + 554, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 345, + 554, + 441 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 345, + 554, + 441 + ], + "type": "inline_equation", + "content": "[a_4^i, a_3^i, a_2^i, a_1^i, a_0^i]" + }, + { + "bbox": [ + 313, + 345, + 554, + 441 + ], + "type": "text", + "content": " denote polynomial coefficients, and " + }, + { + "bbox": [ + 313, + 345, + 554, + 441 + ], + "type": "inline_equation", + "content": "i(i = 1, 2, 3)" + }, + { + "bbox": [ + 313, + 345, + 554, + 441 + ], + "type": "text", + "content": " represents three principal lines of the palmprint. Compared to the second-order Bézier curves, a fourth-order polynomial representation provides sufficient expressiveness to capture the smoothness of palm creases. Additionally, considering the physiological basis and distinct distribution of palm creases, it is essential to sample curve parameters that reflect the actual distribution." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 441, + 554, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 441, + 554, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 441, + 554, + 514 + ], + "type": "text", + "content": "As shown in Fig.2 (b), we manually label the points on the three principal lines of 1000 palmprint ROI images selected from publicly available datasets. For each line, the polynomial coefficients are calculated using the least squares method, based on " + }, + { + "bbox": [ + 313, + 441, + 554, + 514 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 313, + 441, + 554, + 514 + ], + "type": "text", + "content": " labeled points " + }, + { + "bbox": [ + 313, + 441, + 554, + 514 + ], + "type": "inline_equation", + "content": "((x_0,y_0),(x_1,y_1),\\ldots ,(x_{n - 1},y_{n - 1}))" + }, + { + "bbox": [ + 313, + 441, + 554, + 514 + ], + "type": "text", + "content": ", as follows," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 389, + 519, + 553, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 519, + 553, + 534 + ], + "spans": [ + { + "bbox": [ + 389, + 519, + 553, + 534 + ], + "type": "interline_equation", + "content": "\\mathbf {a} ^ {\\mathrm {T}} = \\left(\\mathbf {X} ^ {\\mathrm {T}} \\mathbf {X}\\right) ^ {- 1} \\mathbf {X} ^ {\\mathrm {T}} \\mathbf {y}, \\tag {3}", + "image_path": "3fbd72831b0d9f70acf4371e2c6de391abd8a3f77dbfdbb7ec1720648453ec64.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{a}^{\\mathrm{T}}" + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "text", + "content": " represents coefficient vector " + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "inline_equation", + "content": "[a_0, a_1, \\ldots, a_4]^{\\mathrm{T}}" + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "text", + "content": " represents vector " + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "inline_equation", + "content": "[y_0, y_1, \\ldots, y_{n-1}]^{\\mathrm{T}}" + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{n \\times 5}" + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "text", + "content": " is a Vandermonde matrix. We apply this formula to get coefficient vectors " + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "inline_equation", + "content": "(\\mathbf{a}^1, \\mathbf{a}^2, \\mathbf{a}^3)" + }, + { + "bbox": [ + 313, + 540, + 554, + 590 + ], + "type": "text", + "content": " of three principal lines." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "content": "In this way, polynomial coefficients of three principal lines " + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{a}^1,\\mathbf{a}^2,\\mathbf{a}^3)" + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "content": " are calculated for each palmprint sample. Then, we conduct a statistical analysis of the polynomial coefficients. Partial visualization results are shown in Fig.3, from which we observe that the coefficient approximately follows a Gaussian distribution. More statistical results are provided in the supplementary materials. Consequently, we represent the distribution of " + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "inline_equation", + "content": "a_j^i" + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "inline_equation", + "content": "p(a_j^i)\\sim N(\\mu_j^i,(\\sigma^2)_j^i)" + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mu_j^i" + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "inline_equation", + "content": "(\\sigma^2)_j^i" + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "content": " denote mean and variance of " + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "inline_equation", + "content": "a_j^i" + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "content": ". Therefore, the coefficient vector " + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{a}^i" + }, + { + "bbox": [ + 313, + 590, + 555, + 714 + ], + "type": "text", + "content": " follows the joint distribution" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26369" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 71, + 289, + 182 + ], + "blocks": [ + { + "bbox": [ + 65, + 71, + 289, + 182 + ], + "lines": [ + { + "bbox": [ + 65, + 71, + 289, + 182 + ], + "spans": [ + { + "bbox": [ + 65, + 71, + 289, + 182 + ], + "type": "image", + "image_path": "800a0f0dc5d12a8a2dfac9317efeb3b93de58d4ac7e784401de5a741c7d999ec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "lines": [ + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "spans": [ + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "text", + "content": "Figure 3. Statistical analysis of polynomial coefficients: (a) Quantile-Quantile Plot of coefficients " + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "inline_equation", + "content": "a_4^1" + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "text", + "content": ". (b) Histogram and Kernel Density Estimate (KDE) Plot of coefficients " + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "inline_equation", + "content": "a_4^1" + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "text", + "content": ". (c) Contour Plot of coefficients " + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "inline_equation", + "content": "a_4^1" + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "inline_equation", + "content": "a_3^1" + }, + { + "bbox": [ + 55, + 193, + 296, + 237 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "type": "inline_equation", + "content": "p(a_0^i,a_1^i,\\ldots ,a_4^i)" + }, + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "type": "text", + "content": " , which is a multivariate Gaussian distribution expressed as follows," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 134, + 285, + 295, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 285, + 295, + 300 + ], + "spans": [ + { + "bbox": [ + 134, + 285, + 295, + 300 + ], + "type": "interline_equation", + "content": "p \\left(\\mathbf {a} ^ {i}\\right) \\sim \\mathcal {N} \\left(\\mu^ {i}, \\Sigma^ {i}\\right), \\tag {4}", + "image_path": "f13f2c3010955a9df881cabaf972a9cd9f487cdb9d75ec4e788b20f30f45f5e7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 312, + 296, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 312, + 296, + 408 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 296, + 408 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 312, + 296, + 408 + ], + "type": "inline_equation", + "content": "\\mu^i, \\Sigma^i" + }, + { + "bbox": [ + 55, + 312, + 296, + 408 + ], + "type": "text", + "content": " are the mean vector and covariance matrix of " + }, + { + "bbox": [ + 55, + 312, + 296, + 408 + ], + "type": "inline_equation", + "content": "\\mathbf{a}^i" + }, + { + "bbox": [ + 55, + 312, + 296, + 408 + ], + "type": "text", + "content": ". By employing the proposed representation and estimated distribution, the complex palm creases located on a plane are mapped into a parameter space that conforms to a multivariate Gaussian distribution. This allows us to effortlessly sample the polynomial coefficients from the statistical distribution and then produce three principal lines using polynomial representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 408, + 296, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 408, + 296, + 505 + ], + "spans": [ + { + "bbox": [ + 55, + 408, + 296, + 505 + ], + "type": "text", + "content": "Additionally, we also record the coordinates of two endpoints of each line, i.e., the starting point " + }, + { + "bbox": [ + 55, + 408, + 296, + 505 + ], + "type": "inline_equation", + "content": "x_{s}^{i}" + }, + { + "bbox": [ + 55, + 408, + 296, + 505 + ], + "type": "text", + "content": " and the ending point " + }, + { + "bbox": [ + 55, + 408, + 296, + 505 + ], + "type": "inline_equation", + "content": "x_{e}^{i}" + }, + { + "bbox": [ + 55, + 408, + 296, + 505 + ], + "type": "text", + "content": ", and calculate their statistical distribution. By following the same approach, we determine the range for synthesizing polynomial creases by sampling from the estimated distribution. With the addition of minor random straight lines to simulate wrinkles, a pseudo palm crease image is generated, as shown in Fig.2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "text", + "content": "A palm creases similarity control mechanism is proposed by scaling the variance of the estimated Gaussian distribution by a factor of " + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\gamma^2" + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "text", + "content": ". Specifically, as " + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\mathbf{a}^i" + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "text", + "content": " is sampled from " + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mu^i,\\gamma^2\\Sigma^i)" + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "text", + "content": ", a smaller " + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "text", + "content": " (less than 1) results in a higher degree of similarity in the generated palm creases, while a larger " + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 55, + 506, + 296, + 578 + ], + "type": "text", + "content": " (greater than 1) leads to lower similarity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 587, + 278, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 278, + 600 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 278, + 600 + ], + "type": "text", + "content": "3.2. Palm Creases conditioned Diffusion Model" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "Diffusion models [4] are trained to recover an image from random noise. In contrast to GANs, which consist of two networks and utilize an adversarial loss, diffusion models adopt two processes: the diffusion process and the denoising process. The diffusion process is typically defined as a Markov chain composed of several diffusion steps. At each step, the model introduces a small amount of Gaussian noise with varying variances into the data. After a total of " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " steps, the data is degraded to pure Gaussian noise. The" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 465, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 465, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 465, + 84 + ], + "type": "text", + "content": "diffusion process [4] is expressed as," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 350, + 94, + 555, + 109 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 94, + 555, + 109 + ], + "spans": [ + { + "bbox": [ + 350, + 94, + 555, + 109 + ], + "type": "interline_equation", + "content": "p \\left(x _ {t} \\mid x _ {t - 1}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {1 - \\beta_ {t}} x _ {t - 1}, \\beta_ {t} I\\right), \\tag {5}", + "image_path": "e2977c6991efb40c4c9919b9f087e81cb08413e1efa12e8271b34353114b72a7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "spans": [ + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "inline_equation", + "content": "x_{t-1}" + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "text", + "content": " represent the data at diffusion step " + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "inline_equation", + "content": "t-1" + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "text", + "content": " respectively, and " + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 313, + 118, + 553, + 153 + ], + "type": "text", + "content": " is the variance schedule determined in advance that controls the amount of noise added." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "spans": [ + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "text", + "content": "The denoising process aims to learn the reverse of the diffusion process, and recover data " + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "text", + "content": " from Gaussian noise " + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "text", + "content": " step by step. An UNet network is trained to predict the noise at the " + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "text", + "content": " step and thereby restore " + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "inline_equation", + "content": "x_{t - 1}" + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 155, + 555, + 358 + ], + "type": "text", + "content": ". Since we aim to use the diffusion model to generate palmprint datasets, unconditional diffusion is insufficient to meet our requirements. To control the identity of generated palmprint images, we use the palm crease image as a condition. The consistent palm crease image is extracted from the real palmprint image using a palm creases extraction module (PCEM) [20]. Then, the palm creases are adopted to govern the identity of the generated palmprints. Therefore, we choose to integrate the condition image into the UNet through channel concatenation. Specifically, paired palm crease images and corrupted palmprint images are concatenated and sent to the network, as shown in Fig.4(a). We use the following training objective [4]," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 367, + 367, + 555, + 382 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 367, + 555, + 382 + ], + "spans": [ + { + "bbox": [ + 367, + 367, + 555, + 382 + ], + "type": "interline_equation", + "content": "L = E _ {t, x _ {t}, \\epsilon} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t, y) \\| _ {2} ^ {2} \\right], \\tag {6}", + "image_path": "2c6c4835385f7ef33a9f88077f68874b6cbfedb244e848ba3e6e68b1c62a6c4e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 391, + 554, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 554, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 554, + 415 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 391, + 554, + 415 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 391, + 554, + 415 + ], + "type": "text", + "content": " represents the parameterized network, and " + }, + { + "bbox": [ + 313, + 391, + 554, + 415 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 391, + 554, + 415 + ], + "type": "text", + "content": " stands for palm crease image." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 423, + 503, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 423, + 503, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 423, + 503, + 436 + ], + "type": "text", + "content": "3.3. The " + }, + { + "bbox": [ + 313, + 423, + 503, + 436 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 423, + 503, + 436 + ], + "type": "text", + "content": "-step Noise-sharing Sampling" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 441, + 554, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 441, + 554, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 441, + 554, + 501 + ], + "type": "text", + "content": "To generate new samples, the diffusion model follows the reverse diffusion process. Starting from random Gaussian noise, the model iteratively applies the learned denoiser to remove noise and generate final outputs. The iterative sampling process [4] is expressed as follows," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 329, + 510, + 555, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 510, + 555, + 538 + ], + "spans": [ + { + "bbox": [ + 329, + 510, + 555, + 538 + ], + "type": "interline_equation", + "content": "x _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (x _ {t}, t, y)\\right) + \\sigma_ {t} z _ {t}, \\tag {7}", + "image_path": "e13de65816ecefc833577370f177f4f5cb6ee0095c9b9f72f496d8a36a8401df.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " is defined as " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "1 - \\beta_{t}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} \\coloneqq \\Pi_{i=0}^{t} \\alpha_{i}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " is step-dependent constants, and " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": " is a random noise sampled from " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{0}, \\mathbf{I})" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ". After the iterative process concludes, the estimate of " + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "inline_equation", + "content": "x_{0}" + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": ", derived from the final iteration, is the synthesized palmprint. To control the diversity of generated results, many diffusion-based methods adopt text prompts [4, 16]. However, palmprint images are relatively simple, comprising primarily of crease and skin components, which complicates the use of text descriptions to govern diversity. We have observed that the random noise added at each step provides the randomness of the sampling process. Therefore, by controlling the random noise added to samples within the same identity, we manipulate the intra-class variation of the generated datasets effectively." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "26370" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 74, + 262, + 171 + ], + "blocks": [ + { + "bbox": [ + 66, + 74, + 262, + 171 + ], + "lines": [ + { + "bbox": [ + 66, + 74, + 262, + 171 + ], + "spans": [ + { + "bbox": [ + 66, + 74, + 262, + 171 + ], + "type": "image", + "image_path": "92236f242aebf703ad424bf51a0531de5c581d8ecf63a838c08f3da0b7e2f053.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 174, + 555, + 218 + ], + "lines": [ + { + "bbox": [ + 55, + 174, + 555, + 218 + ], + "spans": [ + { + "bbox": [ + 55, + 174, + 555, + 218 + ], + "type": "text", + "content": "Figure 4. The proposed intra-class variation controllable diffusion model. (a) Training process: palm crease images, extracted from palmprints using PCEM [20], are employed as conditions and concatenated with diffused palmprint images, serving as input for the UNet. (b) Sampling process: polynomial creases, as synthetic identity, are first generated and adopted to create consistent samples. The " + }, + { + "bbox": [ + 55, + 174, + 555, + 218 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 174, + 555, + 218 + ], + "type": "text", + "content": "-step noise-sharing sampling is applied to obtain palmprint datasets with varying degrees of intra-class variations." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 267, + 74, + 541, + 171 + ], + "blocks": [ + { + "bbox": [ + 267, + 74, + 541, + 171 + ], + "lines": [ + { + "bbox": [ + 267, + 74, + 541, + 171 + ], + "spans": [ + { + "bbox": [ + 267, + 74, + 541, + 171 + ], + "type": "image", + "image_path": "df9f8e5f7618bdf5ebedccd82ce52cac2708c76e741fa03e9f8bd0dc8596399b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 56, + 228, + 295, + 418 + ], + "blocks": [ + { + "bbox": [ + 56, + 228, + 295, + 418 + ], + "lines": [ + { + "bbox": [ + 56, + 228, + 295, + 418 + ], + "spans": [ + { + "bbox": [ + 56, + 228, + 295, + 418 + ], + "type": "image", + "image_path": "b49c051b7aaf053bc3a90222f77370b9b16dd9136e89dfeef9bc90e595928ab3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "lines": [ + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "spans": [ + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "type": "text", + "content": "Figure 5. Generated palmprint results under different noise-sharing strategies. The figure illustrates the outcomes of applying noise-sharing in the last " + }, + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "type": "inline_equation", + "content": "K = 500" + }, + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "type": "text", + "content": " steps (top) versus the first " + }, + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "type": "inline_equation", + "content": "K = 500" + }, + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "type": "text", + "content": " steps (bottom) of a total " + }, + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "type": "inline_equation", + "content": "T = 1000" + }, + { + "bbox": [ + 55, + 426, + 295, + 481 + ], + "type": "text", + "content": " steps during the sampling process for the same identity." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "text", + "content": "-step noise-sharing sampling is proposed to generate palmprint datasets with varying degrees of intra-class variations. Specifically, suppose generating the " + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "text", + "content": "-th sample of the " + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "text", + "content": "-th identity with the palm crease image " + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "inline_equation", + "content": "y^i" + }, + { + "bbox": [ + 55, + 495, + 295, + 555 + ], + "type": "text", + "content": ", we rewrite sampling process Eq.7 as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 563, + 295, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 563, + 295, + 583 + ], + "spans": [ + { + "bbox": [ + 63, + 563, + 295, + 583 + ], + "type": "interline_equation", + "content": "\\left[ x _ {t - 1} \\right] _ {j} ^ {i} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\left[ x _ {t} \\right] _ {j} ^ {i} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(\\left[ x _ {t} \\right] _ {j} ^ {i}, t, y ^ {i}\\right)\\right) + \\sigma_ {t} \\left[ z _ {t} \\right] _ {j} ^ {i}, \\tag {8}", + "image_path": "d99a7d8ff834f2c5f468be9fc74a63020dcc50529621f09e15a20900757cf7d4.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "inline_equation", + "content": "[z_{t}]_{j}^{i}" + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "text", + "content": " is the random noise sampled from a standard Gaussian distribution, influencing the diversity of samples. We aim to utilize the same shared noise " + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "inline_equation", + "content": "[z_{t}]^{i}" + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "text", + "content": ", instead of a series of different " + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "inline_equation", + "content": "[z_{t}]_{j}^{i}" + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "text", + "content": " to samples under the same identity condition. We select a continuous " + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "text", + "content": "-step sequence within the total " + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 594, + 295, + 665 + ], + "type": "text", + "content": " steps and apply this, as shown in Fig.4(b)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Additionally, we have found that the application of noise-sharing in the first " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " steps and the last " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " steps during the sampling process exhibits distinct behaviors. With " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "K = 500" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " and a total of " + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "inline_equation", + "content": "T = 1000" + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": " steps, the sampling" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 231, + 555, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 231, + 555, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 231, + 555, + 361 + ], + "type": "text", + "content": "process under the same identity yields the results shown in Fig.5. When noise-sharing is applied in the first " + }, + { + "bbox": [ + 313, + 231, + 555, + 361 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 231, + 555, + 361 + ], + "type": "text", + "content": " steps, the generated results maintain a consistent style, while the details of the palm creases exhibit minor variations, leading to a generated dataset with low identity consistency. Conversely, when noise-sharing is applied in the last " + }, + { + "bbox": [ + 313, + 231, + 555, + 361 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 231, + 555, + 361 + ], + "type": "text", + "content": " steps, the generated results present diverse styles, but the consistency of the palm crease details improves. This suggests that during the sampling process, the style information of the palmprint is generated first, followed by the restoration of texture details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "spans": [ + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "text", + "content": "Therefore, we apply noise-sharing in the last " + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "text", + "content": " steps. As " + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "text", + "content": " increases, the crease consistency in the sampled results under the same identity tends to improve. However, when " + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "text", + "content": " continues to increase, the stylistic diversity of the sampled results becomes restricted. We conduct experiments on datasets generated using different values of " + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 362, + 555, + 434 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 447, + 395, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 447, + 395, + 460 + ], + "spans": [ + { + "bbox": [ + 313, + 447, + 395, + 460 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 467, + 435, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 435, + 480 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 435, + 480 + ], + "type": "text", + "content": "4.1. Experimental Setups" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 485, + 554, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 485, + 554, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 485, + 554, + 544 + ], + "type": "text", + "content": "We conduct experiments under an open-set protocol, splitting each public dataset into training and test sets with a 1:1 ratio with no overlapping identities (IDs). We utilize the TAR (True Accept Rate) @FAR (False Accept Rate) metric to evaluate the performance of recognition models." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 665 + ], + "type": "text", + "content": "Datasets We do not use public datasets to train our generative models to ensure a fair comparison, which also places our method in a more challenging cross-dataset setting. Instead, we adopt an anonymous dataset collected from the Internet, which has been processed to include 48,000 palmprint images. We utilize publicly available datasets for evaluation and to train recognition models as baselines. Experiments are conducted on following public datasets: CASIA [35], PolyU [41], Tongji [42], MPD [43], XJTU-UP [32], IITD [24], and NTU-CP-v1 [26]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "Generation Model Training Setups Our conditional diffusion models utilize a UNet backbone [8] that takes a four-channel input and 64 base channels with five resolution levels. The multipliers for the number of channels used" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26371" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 187, + 144 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 187, + 144 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 187, + 144 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 187, + 144 + ], + "type": "image", + "image_path": "e52f4b3d506f3dc0c047999d2fdbc52b25635fc22b5ffaa01af4aebb85c3944d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 189, + 70, + 304, + 144 + ], + "blocks": [ + { + "bbox": [ + 189, + 70, + 304, + 144 + ], + "lines": [ + { + "bbox": [ + 189, + 70, + 304, + 144 + ], + "spans": [ + { + "bbox": [ + 189, + 70, + 304, + 144 + ], + "type": "image", + "image_path": "50c4c9e4537e061af4593df7201bcf0816b245128b8124857f589af115934e8b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 423, + 144 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 423, + 144 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 423, + 144 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 423, + 144 + ], + "type": "image", + "image_path": "8e4e17ecff8455568029ed2451f06c57bfda269935c5a146fa44e5464f5ff863.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 425, + 71, + 541, + 144 + ], + "blocks": [ + { + "bbox": [ + 425, + 71, + 541, + 144 + ], + "lines": [ + { + "bbox": [ + 425, + 71, + 541, + 144 + ], + "spans": [ + { + "bbox": [ + 425, + 71, + 541, + 144 + ], + "type": "image", + "image_path": "5cb2df37ed5165089ba84cdaad5e7aea87fe25be464d071568e849481adb3326.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 69, + 148, + 187, + 221 + ], + "blocks": [ + { + "bbox": [ + 69, + 148, + 187, + 221 + ], + "lines": [ + { + "bbox": [ + 69, + 148, + 187, + 221 + ], + "spans": [ + { + "bbox": [ + 69, + 148, + 187, + 221 + ], + "type": "image", + "image_path": "cfefa960045e69b67daf960c9a53653d4b3b2c9493234130440f0c25626c05be.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 231, + 555, + 254 + ], + "lines": [ + { + "bbox": [ + 55, + 231, + 555, + 254 + ], + "spans": [ + { + "bbox": [ + 55, + 231, + 555, + 254 + ], + "type": "text", + "content": "Figure 6. Comparison score plots for synthetic datasets generated by different methods and real datasets. The genuine and imposter comparison scores are calculated with features, which are extracted by a pre-trained ArcFace model from datasets." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 189, + 148, + 304, + 221 + ], + "blocks": [ + { + "bbox": [ + 189, + 148, + 304, + 221 + ], + "lines": [ + { + "bbox": [ + 189, + 148, + 304, + 221 + ], + "spans": [ + { + "bbox": [ + 189, + 148, + 304, + 221 + ], + "type": "image", + "image_path": "c2842aca655fcd6b214e2fd6bca35c33526965221e7af3dcf16c34942f23a527.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 306, + 148, + 423, + 221 + ], + "blocks": [ + { + "bbox": [ + 306, + 148, + 423, + 221 + ], + "lines": [ + { + "bbox": [ + 306, + 148, + 423, + 221 + ], + "spans": [ + { + "bbox": [ + 306, + 148, + 423, + 221 + ], + "type": "image", + "image_path": "760fa31a3cf3e7f60d30c40932b8bad72e85bdb6e8763e950ef52081d3eac498.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 425, + 149, + 541, + 221 + ], + "blocks": [ + { + "bbox": [ + 425, + 149, + 541, + 221 + ], + "lines": [ + { + "bbox": [ + 425, + 149, + 541, + 221 + ], + "spans": [ + { + "bbox": [ + 425, + 149, + 541, + 221 + ], + "type": "image", + "image_path": "1adea6eeee046bdf2a855528e12ff0dec8c22f7f2e60a435a3d568cb6716c2fe.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 66, + 262, + 291, + 425 + ], + "blocks": [ + { + "bbox": [ + 66, + 262, + 291, + 425 + ], + "lines": [ + { + "bbox": [ + 66, + 262, + 291, + 425 + ], + "spans": [ + { + "bbox": [ + 66, + 262, + 291, + 425 + ], + "type": "image", + "image_path": "fbdb9dc4bf428d9da193d7f123bab1675b395606054abde9990043718f6d8dd4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 431, + 295, + 454 + ], + "lines": [ + { + "bbox": [ + 55, + 431, + 295, + 454 + ], + "spans": [ + { + "bbox": [ + 55, + 431, + 295, + 454 + ], + "type": "text", + "content": "Figure 7. Example images of datasets generated by Diff-Palm with " + }, + { + "bbox": [ + 55, + 431, + 295, + 454 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 431, + 295, + 454 + ], + "type": "text", + "content": "-step sharing-noise sampling for " + }, + { + "bbox": [ + 55, + 431, + 295, + 454 + ], + "type": "inline_equation", + "content": "K = 0, 200, 500" + }, + { + "bbox": [ + 55, + 431, + 295, + 454 + ], + "type": "text", + "content": ", and 800." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "spans": [ + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "text", + "content": "on those levels are 1, 1, 2, 3, and 4, respectively. Attention blocks are applied in residual blocks of the last resolution level. During the training process, we adopt the AdamW optimizer [25], set the learning rate " + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "text", + "content": ", and train the network for a total of " + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "inline_equation", + "content": "30k" + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "text", + "content": " steps. We apply an EMA to the weights of the model with an exponential factor of 0.9999. The batch size is 64 and is equally split across 4 GPUs. For the diffusion process, we set " + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "inline_equation", + "content": "T = 1000" + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "text", + "content": " steps and adopt a linear diffusion variance schedule. In subsequent experiments, we default to generating datasets with " + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "inline_equation", + "content": "2k" + }, + { + "bbox": [ + 54, + 472, + 295, + 603 + ], + "type": "text", + "content": " IDs and 20 samples per ID." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "content": "Recognition Model Training Setups We train ArcFace models [6] with a modified Resnet-18 [17] backbone for palmprint recognition. Palmprint images are resized to " + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "inline_equation", + "content": "112 \\times 112" + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "content": " and trained with ArcFace loss (" + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "inline_equation", + "content": "m = 0.5" + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "inline_equation", + "content": "s = 64" + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "content": ") over 20 epochs using a stochastic gradient descent (SGD) optimizer. We use an initial learning rate of " + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "inline_equation", + "content": "1e - 1" + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "content": ", momentum of 0.9, weight decay of " + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "inline_equation", + "content": "5e - 4" + }, + { + "bbox": [ + 55, + 605, + 295, + 715 + ], + "type": "text", + "content": ", and a step learning rate schedule, which divides the learning rate by 10 at 7-th and 15-th epoch. RandAugment [5] is adopted for data augmen" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 326, + 271, + 537, + 427 + ], + "blocks": [ + { + "bbox": [ + 326, + 271, + 537, + 427 + ], + "lines": [ + { + "bbox": [ + 326, + 271, + 537, + 427 + ], + "spans": [ + { + "bbox": [ + 326, + 271, + 537, + 427 + ], + "type": "image", + "image_path": "932da4aee1958b0f2d35fa59cfb27e44ce70e04a20ad491a4c1325927b357457.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 434, + 555, + 478 + ], + "lines": [ + { + "bbox": [ + 313, + 434, + 555, + 478 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 555, + 478 + ], + "type": "text", + "content": "Figure 8. The t-SNE polt of features extracted from real, PCE-Palm generated, and Diff-Palm generated datasets. Colors denote different datasets, while shapes within the same color correspond to different identities." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 493, + 555, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 493, + 555, + 554 + ], + "spans": [ + { + "bbox": [ + 313, + 493, + 555, + 554 + ], + "type": "text", + "content": "tation with parameters (4, 4). We double the number of IDs in the training set by horizontally flipping the palmprint images. Training is implemented on 4 NVIDIA V100 GPUs with a batch size of 256. Consistent hyperparameters are used for all recognition models across various datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 563, + 440, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 563, + 440, + 576 + ], + "spans": [ + { + "bbox": [ + 313, + 563, + 440, + 576 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "Evaluating Intra-Class Variation We generate datasets by Diff-Palm with " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "-step sharing-noise sampling for " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "K = 0, 200, 500" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " and 800. Then, we use the ArcFace model pretrained on real datasets to extract features from synthesized datasets and calculate genuine and imposter score distributions. Comparison score plots and example images are shown in Fig.6 and Fig.7 respectively. As " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " increases, intraclass variation decreases, and the genuine distribution shifts right. The verification performance in Tab.1 reveals that the recognition model trained on the synthesized dataset with " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "K = 500" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " achieves higher recognition performance." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26372" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 555, + 301 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 555, + 301 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 555, + 301 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 555, + 301 + ], + "type": "table", + "html": "
    MethodsConfigsScore DistributionsPerformance (TAR@FAR=1e-6) ↑
    Kγgenuine meanstdimposter meanstdCASIAPolyUTongJiMPDXJTU-UPAvg.
    Diff-Palm01.00.3500.1240.0690.1120.72780.73920.51510.34060.15270.4951
    Diff-Palm2001.00.5490.1180.0690.1110.84200.91110.81130.42370.60180.7180
    Diff-Palm5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm8001.00.9220.0720.0690.1120.83540.90140.85920.33690.50350.6873
    PCE-Palm(Bézier)--0.4020.1710.0990.1160.67960.77400.61490.29720.41500.5561
    PCE-Palm(poly)-1.00.3510.1860.0410.1100.82200.86870.76740.43730.59740.6986
    Diff-Palm(Bézier)500-0.6290.1980.1710.1140.67220.82360.72460.27320.36580.5719
    Diff-Palm(poly)5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm5000.250.7480.1210.1070.1130.84400.91340.84100.41620.57940.7188
    Diff-Palm5000.50.7640.1180.0880.1170.86130.92300.87000.42680.58230.7327
    Diff-Palm5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    Diff-Palm5002.00.7840.1020.0700.1090.80530.93080.91620.36970.48900.7022
    Diff-Palm5004.00.7800.1030.0950.1080.77930.88040.86620.30410.43410.6528
    Diff-Palm(first K)5001.00.4750.0430.1170.110.76490.75710.51360.25020.03070.4633
    Diff-Palm(last K)5001.00.7660.1080.0680.1120.87820.96010.94600.46430.61610.7729
    ", + "image_path": "a414025c76301923713f50956081b4d177d54a3bccbc299978f6b53e8e86d597.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 342, + 296, + 453 + ], + "blocks": [ + { + "bbox": [ + 55, + 308, + 555, + 331 + ], + "lines": [ + { + "bbox": [ + 55, + 308, + 555, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 308, + 555, + 331 + ], + "type": "text", + "content": "Table 1. Verification performance of recognition models(ArcFace [6]) with the same hyperparameters used for various generated datasets, and without any fine-tuning on real data. Synthetic datasets default to be generated with " + }, + { + "bbox": [ + 55, + 308, + 555, + 331 + ], + "type": "inline_equation", + "content": "{2k}" + }, + { + "bbox": [ + 55, + 308, + 555, + 331 + ], + "type": "text", + "content": " IDs and 20 samples per ID." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 342, + 296, + 453 + ], + "lines": [ + { + "bbox": [ + 58, + 342, + 296, + 453 + ], + "spans": [ + { + "bbox": [ + 58, + 342, + 296, + 453 + ], + "type": "table", + "html": "
    MethodsKIdentityDintraUclassPerf.
    Diff-Palm00.59231.0000.8970.4951
    Diff-Palm2000.96670.96150.9800.7189
    Diff-Palm5000.99810.93720.9960.7729
    Diff-Palm8000.99960.66590.9990.6873
    PCE-Palm(Bézier)-0.60461.18940.6530.5561
    PCE-Palm(poly)-0.68501.18160.9580.6986
    Diff-Palm(Bézier)5000.99520.96910.6940.5719
    Diff-Palm(poly)5000.99810.93720.9960.7729
    ", + "image_path": "7aab10ed9eb34bd03e0143f909803f5804a1d15245fbe75673653a2fb95dc26b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "lines": [ + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "type": "text", + "content": "Table 2. Evaluation of synthetic datasets. " + }, + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "type": "inline_equation", + "content": "C_{\\text{identity}}" + }, + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "type": "inline_equation", + "content": "D_{\\text{intra}}" + }, + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "type": "inline_equation", + "content": "U_{\\text{class}}" + }, + { + "bbox": [ + 55, + 461, + 295, + 495 + ], + "type": "text", + "content": " represent identity consistency, intra-class diversity, and class uniqueness, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 509, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 509, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 54, + 509, + 295, + 640 + ], + "type": "text", + "content": "Comparing Palm Crease Representations We compare the performance of PCE-Palm [20] and our diffusion model by training them on different types of palm crease representations: Bézier creases [44] and polynomial creases, respectively. Each model is trained using consistent hyperparameters, with the only difference being the type of crease images used. As evidenced in Tab.1, the polynomial creases method significantly outperforms the Bézier creases. This result indicates that our polynomial crease representation more accurately bridges the gap between synthetic and real palmprints." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "Evaluating Identity and Diversity Metrics We adopt identity consistency, intra-class diversity, and class uniqueness metrics from [22] to evaluate the respective properties of synthetic datasets. As shown in Tab.2, for our Diff-Palm, there exists a trade-off between identity consistency and intra-class diversity as parameter " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": " is adjusted. For" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 344, + 555, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 344, + 555, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 344, + 555, + 536 + ], + "type": "inline_equation", + "content": "K = 500" + }, + { + "bbox": [ + 313, + 344, + 555, + 536 + ], + "type": "text", + "content": ", the generated dataset strikes a balance between them, leading to optimal recognition performance. When comparing generative methods with different palm crease representations, it is evident that the use of Bezier creases leads to a noticeable decline in class uniqueness, as opposed to polynomial creases. Our analyses indicate that the superior performance of our method is due to the effective balance between identity consistency and intra-class diversity achieved by the intra-class variation controllable method, as well as the enhanced class uniqueness resulting from the use of polynomial creases. In contrast, PCE-Palm suffers from low identity consistency and reduced class uniqueness, leading the poor performance. These analysis results are also validated by the t-SNE visualization, as shown in Fig.8. Further Details about these metrics are provided in the supplementary materials." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "text", + "content": "Effect of Palm Crease Similarity on Recognition We synthesize polynomial crease datasets with varying " + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "text", + "content": " values to generate palmprint datasets through diffusion models. As shown in Tab.1, results indicate that recognition performance declines when " + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "text", + "content": " is either greater than 1 or less than 1, corresponding to the expansion or contraction of the estimated distribution's variance. We believe that when " + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "inline_equation", + "content": "\\gamma > 1" + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "text", + "content": ", the generated data disrupts original distribution patterns, while when " + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "inline_equation", + "content": "\\gamma < 1" + }, + { + "bbox": [ + 313, + 540, + 556, + 673 + ], + "type": "text", + "content": ", training recognition models becomes increasingly difficult. These results confirm the reasonableness and validity of our estimated distributions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "Comparing with Real Datasets and Other Methods We utilize seven public datasets to create a mixed dataset containing 2.2k IDs. The current SOTA palmprint gen" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26373" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 70, + 541, + 345 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 541, + 345 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 541, + 345 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 541, + 345 + ], + "type": "table", + "html": "
    MethodsConfigsPerformance (TAR@FAR=1e-6) ↑
    #IDs# per ID#ImagesFT w/ RealCASIAPolyUTongJiMPDXJTU-UPAvg.
    Real data2.2k-29.3k✘0.92000.91960.92090.38770.62470.7546
    IDiff-Face [2]2k2040k✘0.79770.77200.61150.18470.26670.5265
    Vec2Face [37]2k2040k✘0.82010.81050.81990.25750.25780.5932
    PCE-Palm [20]2k2040k✘0.67960.77400.61490.29720.41500.5561
    Diff-Palm2k2040k✘0.87820.96010.94600.46430.61610.7729
    PCE-Palm [20]2k2040k✓0.94150.97920.93930.66620.79480.8642
    Diff-Palm2k2040k✓0.97870.98590.97440.59790.84330.8760
    Diff-Palm5k20100k✘0.89720.97570.95900.50480.75340.8180
    Diff-Palm10k20200k✘0.90720.98180.96320.56870.81430.8470
    Diff-Palm20k20400k✘0.93830.97950.97830.63040.86550.8784
    Diff-Palm30k20600k✘0.94720.97720.97720.66510.90150.8937
    Diff-Palm40k20800k✘0.94500.97990.98020.66410.90430.8947
    Diff-Palm50k201M✘0.95420.98220.98480.68140.90320.9011
    Diff-Palm60k201.2M✘0.95570.98650.98250.68560.90290.9026
    Diff-Palm2k50100k✘0.88100.93350.91850.47790.72140.7865
    Diff-Palm2k100200k✘0.90060.94360.94430.55220.74820.8178
    Diff-Palm2k150300k✘0.88170.96690.94820.55590.80430.8314
    Diff-Palm2k200400k✘0.91430.97100.94550.57750.84940.8515
    ", + "image_path": "8717aa188a9007854cd2b088ca3cb4d32ca94b02e72556c921598a737388ef33.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 348, + 555, + 371 + ], + "lines": [ + { + "bbox": [ + 55, + 348, + 555, + 371 + ], + "spans": [ + { + "bbox": [ + 55, + 348, + 555, + 371 + ], + "type": "text", + "content": "Table 3. Verification performance of the recognition models across five public datasets, with the same hyperparameters used for both real and synthesized datasets. Diff-Palm is trained with " + }, + { + "bbox": [ + 55, + 348, + 555, + 371 + ], + "type": "inline_equation", + "content": "K = 500" + }, + { + "bbox": [ + 55, + 348, + 555, + 371 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 348, + 555, + 371 + ], + "type": "inline_equation", + "content": "\\gamma = 1.0" + }, + { + "bbox": [ + 55, + 348, + 555, + 371 + ], + "type": "text", + "content": " by default." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 383, + 295, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 383, + 295, + 527 + ], + "spans": [ + { + "bbox": [ + 54, + 383, + 295, + 527 + ], + "type": "text", + "content": "eration method, PCE-Palm [20], and the face generation method [2, 37], are trained for comparison. By default, we train the recognition models on synthetic datasets without employing real data fine-tuning. As shown in Tab.3, the recognition model trained on the dataset generated by our method outperforms the models trained on real data across three public datasets, and achieves an average improvement. Furthermore, our approach significantly surpasses both PCE-Palm and facial models. We also conduct fine-tuning experiments using real data for a comprehensive comparison with PCE-Palm. More results are provided in the supplementary materials." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 530, + 295, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 295, + 674 + ], + "spans": [ + { + "bbox": [ + 55, + 530, + 295, + 674 + ], + "type": "text", + "content": "Impact of Synthesized Identity and Sample Quantity We generate datasets with varying numbers of identities, maintaining 20 samples per identity, to train recognition models. As evidenced in Tab.3, the performance of the recognition model steadily improves as the number of identities increases. The highest performance is observed when the number of identities reaches " + }, + { + "bbox": [ + 55, + 530, + 295, + 674 + ], + "type": "inline_equation", + "content": "60k" + }, + { + "bbox": [ + 55, + 530, + 295, + 674 + ], + "type": "text", + "content": ". We also explore the impact of varying the number of samples per identity while keeping the number of identities constant. As shown in Tab.3, increasing the number of samples per identity from 20 to 200 results in continuous performance improvement. These findings demonstrate the scalability of our approach." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "Ablation and Discussion of " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "-Step Noise-Sharing Sampling We generate palmprint datasets using two different noise-sharing strategies (i.e., applied during the first " + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "inline_equation", + "content": "K" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "type": "text", + "content": "steps or the last " + }, + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "type": "text", + "content": " steps) and evaluate their performance. As shown in Tab.1, applying noise-sharing during the first " + }, + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "type": "text", + "content": " steps results in lower intra-class diversity in the generated datasets, leading to poorer recognition performance. Additionally, the " + }, + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 383, + 555, + 479 + ], + "type": "text", + "content": " step noise-sharing sampling can serve as a plug-and-play method applicable to other diffusion-based generative models. We provide results applying this method to IDiff-Face [2] in the supplementary materials." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 490, + 388, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 490, + 388, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 490, + 388, + 502 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 510, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 555, + 653 + ], + "type": "text", + "content": "This paper proposes a polynomial-based palm crease representation, capable of generating a large-scale dataset with a distribution closely resembling that of real palm crease. Subsequently, an intra-class variation controllable diffusion model is introduced, with a simple yet effective " + }, + { + "bbox": [ + 313, + 510, + 555, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 510, + 555, + 653 + ], + "type": "text", + "content": "-step noise-sharing sampling, which enables the generation of palmprint datasets with adjustable intra-class variations. Experimental results indicate that our proposed method significantly reduces the gap between generated and real datasets. It is also the first time that the palmprint recognition model trained solely on our generated data, yet outperforms the model trained on real data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 654, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 713 + ], + "type": "text", + "content": "Acknowledgments We would like to acknowledge Zhiyuan Wang and Yang Wu for their assistance in polynomial creases. This work is partly supported by the grants of the National Natural Science Foundation of China under Nos.62476077, 62076086, and 62272142." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26374" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 145 + ], + "type": "text", + "content": "[1] Keivan Bahmani, Richard Plesh, Peter Johnson, Stephanie Schuckers, and Timothy Swyka. 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IEEE TCSVT, 2019. 3" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "26376" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Diff2Flow_ Training Flow Matching Models via Diffusion Model Alignment/fbb4858e-0a86-4812-87cf-57f08dfebd6c_content_list.json b/2025/Diff2Flow_ Training Flow Matching Models via Diffusion Model Alignment/fbb4858e-0a86-4812-87cf-57f08dfebd6c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dae1d48d14a4bd1fbd736c641b565c7d1bfa88b0 --- /dev/null +++ b/2025/Diff2Flow_ Training Flow Matching Models via Diffusion Model Alignment/fbb4858e-0a86-4812-87cf-57f08dfebd6c_content_list.json @@ -0,0 +1,1787 @@ +[ + { + "type": "text", + "text": "Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment", + "text_level": 1, + "bbox": [ + 138, + 150, + 856, + 171 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Johannes Schusterbauer*", + "bbox": [ + 197, + 198, + 390, + 214 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ming Gui*", + "bbox": [ + 426, + 198, + 513, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Frank Fundel", + "bbox": [ + 550, + 198, + 653, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Björn Ommer", + "bbox": [ + 689, + 198, + 797, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "CompVis @ LMU Munich, MCML", + "bbox": [ + 361, + 215, + 630, + 232 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 261, + 263, + 336, + 279 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for finetuning, while diffusion models like Stable Diffusion benefit from efficient architectures and ecosystem support. This work addresses the critical challenge of efficiently transferring knowledge from pre-trained diffusion models to flow matching. We propose Diff2Flow, a novel framework that systematically bridges diffusion and FM paradigms by rescaling timesteps, aligning interpolants, and deriving FM-compatible velocity fields from diffusion predictions. This alignment enables direct and efficient FM finetuning of diffusion priors with no extra computation overhead. Our experiments demonstrate that Diff2Flow outperforms naive FM and diffusion finetuning particularly under parameter-efficient constraints, while achieving superior or competitive performance across diverse downstream tasks compared to state-of-the-art methods. We will release our code at https://github.com/CompVis/diff2flow.", + "bbox": [ + 109, + 294, + 485, + 594 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 112, + 619, + 236, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, diffusion models [19, 57] have gained substantial popularity due to their exceptional generative capabilities, which have redefined the boundaries of image generation [42, 43, 46, 48]. Among these, foundation models such as Stable Diffusion [46] stand out, not only for their high-fidelity outputs but also for their useful representations and adaptability to downstream tasks, including depth estimation [14, 24], surface normal prediction [7], segmentation [63], and semantic correspondences [11, 60].", + "bbox": [ + 109, + 643, + 482, + 772 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Meanwhile, Flow Matching (FM) [1, 30, 32] has emerged as a promising alternative, empirically offering faster inference and improved performance [8, 37]. While state-of-the-art foundational models based on flow matching, such as Flux [26] or SDv3 [8], show remarkable generative capabilities, their large size ( $>8\\mathrm{B}$ parameters) requires", + "bbox": [ + 109, + 772, + 482, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "high-end hardware for both training and inference, making them particularly computationally expensive. This makes fine-tuning impractical, especially in resource-constrained environments and significantly limits their practical adoption. In contrast, Stable Diffusion's [46] efficient architecture and widespread ecosystem make it a pragmatic choice. This raises an important question: Can the knowledge captured by existing foundational diffusion models be efficiently transferred to a flow matching model? How can we bridge the gap between diffusion and flow matching with minimal additional training, leveraging both the pre-trained prior and the advantageous properties of flow matching?", + "bbox": [ + 509, + 265, + 883, + 438 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This work explores the relationship between the diffusion and flow matching paradigms. Although both methods can be generalized under a common framework [1, 25, 37], the actual implementations differ in several key aspects, including the definition of interpolants between the Gaussian noise prior and data samples, timestep scaling, and training objectives. These differences make it difficult to directly use a pre-trained diffusion model as a starting prior for flow matching training, as the two paradigms are not inherently well aligned.", + "bbox": [ + 509, + 441, + 883, + 584 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address this challenge, we propose a novel framework that effectively \"warps\" diffusion into flow matching, enabling seamless knowledge transfer between the two paradigms. This requires re-scaling their respective timesteps, aligning their differing interpolant formulations, and deriving the velocity field required for flow matching from the diffusion model's predictions, based on its parameterization. By systematically establishing these correspondences, we enable a smooth transition between diffusion and flow matching. To this end, we introduce a training methodology termed Diff2Flow, which initializes the flow matching model with a pretrained diffusion prior and directly finetunes it using the flow matching objective. Our analysis reveals that directly applying the FM loss to a diffusion model without incorporating our proposed adjustments significantly slows convergence and degrades overall model performance, whereas Diff2Flow provides a flexible and efficient approach with minimal finetuning overhead.", + "bbox": [ + 509, + 588, + 883, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The benefits of this alignment become particularly evident when finetuning only a small subset of parameters.", + "bbox": [ + 511, + 849, + 883, + 878 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 116, + 16, + 189, + 54 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 243, + 13, + 799, + 56 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal Contribution", + "bbox": [ + 130, + 864, + 235, + 878 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28347", + "bbox": [ + 478, + 921, + 517, + 931 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Under such constrained computational budgets, the performance gap between naïve FM finetuning and our alignment-aware approach becomes more pronounced. Specifically, we show that directly applying the FM objective with parameter efficient finetuning (PEFT) leads to very suboptimal performance. Leveraging Diff2Flow with its alignment-informed training strategy, PEFT enhances training efficiency and minimizes memory consumption while maintaining high performance.", + "bbox": [ + 111, + 113, + 483, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We show the efficiency of our method on a diverse set of downstream tasks. ① We show that when finetuning on a high-aesthetics dataset [6] on the text-to-image task, we outperform diffusion-based finetuning while converging significantly faster than naively training with the flow matching objective. This empirically demonstrates that smartly aligning timestep scaling and objective significantly facilitate learning, and additionally mitigate the zero-terminal SNR issue [28] common in diffusion models, where full black or white images can't be generated. ② When repurposing the model to generate images at resolutions different from the pre-trained sweet-spot resolution (similar to [17]), our method achieves superior results compared to standard diffusion and flow matching fine-tuning. ③ We show that we can apply Reflow [32] using Diff2Flow on a base diffusion model, a method that straightens sampling trajectories, resulting in faster inference speed. By rectifying the sampling trajectories of Stable Diffusion v1.5 we can generate images with as few as 2 sampling steps without consistency distillation [58]. ④ Finally, we demonstrate the effectiveness of our method on domain adaptation, leveraging the Stable Diffusion prior to predicting affine-invariant depth maps similar to Marigold [24] and DepthFM [14], achieving state-of-the-art results with reduced training time.", + "bbox": [ + 114, + 242, + 485, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 112, + 597, + 246, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion and Flow Matching Models Diffusion models [19, 57] have demonstrated wide-ranging capabilities in data synthesis, extending from image [10, 44, 46, 48] and video [3, 15, 20] to audio generation [31] and beyond. While these models excel at producing high-fidelity outputs, they often require extensive sampling time, necessitating techniques like distillation [39, 49, 50, 58], noise schedule optimization [23], or training-free sampling [34, 56] to achieve faster generation. Following diffusion models, flow matching models [1, 30, 32] have gained attention due to their benefit of straighter probability paths. These models have been shown to perform competitively or surpass diffusion models in terms of both speed and quality [8, 37, 54].", + "bbox": [ + 111, + 621, + 483, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The relationship between diffusion and flow matching models has been explored in Lee et al. [27], demonstrating that finetuning a flow matching model based on a pretrained diffusion model is feasible. Our work extends this by explicitly formulating a method to map discrete diffu", + "bbox": [ + 111, + 806, + 483, + 878 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ed31aa870acccdc5eac51072d97d3fcd34088abf7708123b196ffa196d32b9b7.jpg", + "image_caption": [ + "Figure 1. We introduce a novel finetuning technique to traverse between flow matching and diffusion, which enables effectively aligning the two processes with minimal additional training. The interpolant on the flow matching trajectory is computed as a function $f$ of the diffusion timestep $t$ , the sample $x$ , and the associated diffusion coefficients. Our approach further enables a velocity prediction $\\hat{\\mathbf{v}}$ regardless of the diffusion model's parameterization." + ], + "image_footnote": [], + "bbox": [ + 581, + 113, + 810, + 218 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sion trajectory to a continuous flow matching trajectory. Furthermore, we empirically demonstrate that our strategy works for various diffusion parameterization objectives and present results that go beyond reflow [32], achieving competitive performance on several benchmarks.", + "bbox": [ + 511, + 354, + 883, + 428 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Parameter-efficient Finetuning As foundational models expand in size and complexity, parameter-efficient finetuning (PEFT) techniques such as Low-Rank Adaptation (LoRA) [21] offer viable alternatives to full model finetuning. Originally developed for large language models, LoRA and other PEFT techniques have since been applied effectively to diffusion models [47], proving valuable across a broad range of tasks. These include domain-specific finetuning [67], additional image conditioning [59], image editing [12], distillation [36] and among others. By updating only a low-rank decomposition of the weight matrix, LoRA reduces memory requirements and alleviate catastrophic forgetting [2], making it highly adaptable for targeted adjustments in large foundational models.", + "bbox": [ + 511, + 467, + 883, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Knowledge in Generative Models Following the rise of text-to-image diffusion models [41, 43, 44, 46, 48], numerous studies have explored methods to extract information from diffusion priors. Many works have effectively utilized the diffusion prior for tasks such as monocular depth estimation [9, 14, 16, 24, 38, 51], surface normal prediction [7], and semantic correspondences [11, 35, 60]. While these approaches predominantly focus on distilling information into another diffusion model, our work explores the transfer of this knowledge to flow matching models and hereby leverages the inherent advantages of flow matching, including more efficient inference and enhanced task performance.", + "bbox": [ + 511, + 707, + 883, + 878 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28348", + "bbox": [ + 478, + 921, + 517, + 933 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 112, + 112, + 199, + 126 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we explain our algorithm and the process of aligning the trajectories. We begin by discussing the definition of diffusion and flow matching models. Following this, we describe how we traverse between the two trajectories as depicted in Fig. 1 and use the diffusion model to generate a reasonable estimate of the flow velocity.", + "bbox": [ + 112, + 135, + 483, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Diffusion and Flow Matching", + "text_level": 1, + "bbox": [ + 112, + 229, + 362, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models (DM) [19, 56, 57] gradually diffuse data by typically adding noise to real data samples $x_0 \\sim p_0(x_0)$ in a predefined discrete forward process, which can be characterized by", + "bbox": [ + 112, + 252, + 483, + 309 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\alpha_ {t} x _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 318, + 483, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t}$ and $\\sigma_{t}$ are the predefined noise schedules, $t$ is the discrete timestep, and $x_{t}$ is the resulting noisy sample, often referred to as the interpolant. In the setting of variance preserving schedules $\\sigma_{t} = \\sqrt{1 - \\alpha_{t}^{2}}$ , and the interpolant $x_{t}$ is then $x_{t} = \\alpha_{t}x_{0} + \\sqrt{1 - \\alpha_{t}^{2}}\\epsilon$ with $\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})$ . A neural network, parameterized by $\\theta$ , is learned to reverse the forward process by gradually removing noise from $x_{t}$ . Ho et al. [19] propose the simplified loss term", + "bbox": [ + 112, + 345, + 483, + 460 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, \\epsilon , x _ {0} \\sim p (x _ {0})} | | \\epsilon_ {t} - \\epsilon_ {\\theta} (x _ {t}, t) | | ^ {2}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 470, + 483, + 488 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where predicting $\\epsilon$ instead of $x_0$ is observed to yield better results and enhance convergence. There also exists the $v$ -parameterization [49], defined as", + "bbox": [ + 112, + 496, + 483, + 540 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv _ {t} = \\alpha_ {t} \\epsilon - \\sigma_ {t} x _ {0}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 241, + 551, + 482, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Flow matching (FM) models [1, 30, 32], another flexible class of generative models, utilizes the same idea of gradually deteriorating data samples and then synthesizing new data by reversing the process. We adopt the setting from Lipman et al. [30] where $x_0$ represents noise, and $x_{1}$ corresponds to data. The interpolant on the continuous timesteps $t\\in [0,1]$ is defined as", + "bbox": [ + 112, + 580, + 483, + 681 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} = t x _ {1} + (1 - t) x _ {0}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 693, + 483, + 707 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $x_0$ is typically a Gaussian noise sample. The model $\\mathbf{v}_{\\theta}$ is trained to regress a vector field along the trajectory, following the linear path that points from $x_0$ to $x_1$ using the following objective:", + "bbox": [ + 112, + 717, + 483, + 773 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {F M}} = \\mathbb {E} _ {t, x _ {0} \\sim \\mathcal {N} (0, \\mathbf {I}), x _ {1} \\sim p (x _ {1})} | | (x _ {1} - x _ {0}) - \\mathbf {v} _ {\\theta} (x _ {t}, t) | | ^ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 784, + 483, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sampling from a flow matching model is accomplished by integrating over the trajectory of the learned ODE, e.g. using the forward Euler method with the update rule", + "bbox": [ + 112, + 810, + 483, + 854 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t + t _ {\\Delta}} = x _ {t} + t _ {\\Delta} \\mathbf {v} _ {\\theta} \\left(x _ {t}, t\\right) \\quad \\forall t \\in [ 0, 1), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 864, + 483, + 880 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9081a7732ea58e32104025b51711d3579b5b8bbe42aed62f2b565d12db2c9460.jpg", + "image_caption": [ + "Normal timesteps $t_{\\mathrm{DM}}$", + "Figure 2. Although non-integer-shifted DDIM timesteps are neither defined nor trained, generated images remain of high quality." + ], + "image_footnote": [], + "bbox": [ + 555, + 125, + 689, + 178 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9699245a95cfa8af7539d90e69a4b91e20895de3da817142b443be717c983fd7.jpg", + "image_caption": [ + "Shifted timesteps $t_{\\mathrm{DM}}$" + ], + "image_footnote": [], + "bbox": [ + 707, + 125, + 841, + 178 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $t_{\\delta} = 1 / N$ and $N$ being the number of function evaluations (NFE). We generate a discrete sequence that approximates the path by advancing in small increments along the ODE. The trajectory's smoothness, or \"straightness,\" is critical, as it determines the number of steps required to achieve accurate results, trading off computational cost and fidelity. Straighter paths allow smaller $N$ , whereas paths with higher curvature require more steps for simulating the ODE.", + "bbox": [ + 511, + 244, + 880, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reflow In FM training, we randomly sample from a Gaussian distribution and form pairs with the data points to create the interpolant $x_{t}$ . This random pairing leads to curved sampling trajectories, increasing the curvature of the ODE trajectories during inference [61]. To straighten these trajectories, Liu et al. [32] propose Reflow, which iteratively trains on samples obtained from a pre-trained flow matching model. Given an already trained ODE model $\\mathbf{v}_{\\Phi}$ , Reflow first samples $x_0 \\sim \\mathcal{N}(0,\\mathbf{I})$ and integrates along the ODE trajectory using Eq. (6) to obtain a corresponding data sample $x_{1}$ . This process generates image-noise pairings. Training on this paired data has been found to reduce inference cost by straightening the sampling trajectories [32, 33, 64].", + "bbox": [ + 511, + 376, + 883, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Diffusion Prior for Flow Matching Model", + "text_level": 1, + "bbox": [ + 511, + 570, + 846, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Flow matching methods are known for straighter trajectories and more efficient inference [14, 61]. Hence, transforming the diffusion prior into a flow matching equivalent offers the potential for improvements in inference speed and performance [8, 37]. While previous research has successfully adapted diffusion priors for other downstream diffusion tasks, our approach combines these advantages with those of flow matching models.", + "bbox": [ + 511, + 592, + 880, + 707 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Importantly, recent works on utilizing flow matching models to inherit a diffusion prior for downstream applications, such as DepthFM [14], have shown significant promise in accelerating inference compared to diffusion models. While this approach provides faster sampling than its diffusion model's counterpart, this inheritance method has limitations: DepthFM finetunes from a $v$ -parameterized text-to-image diffusion model [46] directly. This approach requires the flow matching model to \"warp\" the $v$ -parameterization to predict velocity, a different parameterization scheme. This introduces misalignments in the training objective, the interpolant, and the timesteps.", + "bbox": [ + 511, + 707, + 880, + 878 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28349", + "bbox": [ + 478, + 921, + 517, + 931 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address these limitations, we propose a novel strategy that enables a seamless transition between diffusion and flow matching trajectories. Our method minimizes misalignments and yields more accurate velocity predictions. In addition to monocular depth estimation, we demonstrate that our approach generalizes to other downstream tasks and offers a versatile and efficient solution for leveraging prior information from diffusion model.", + "bbox": [ + 111, + 113, + 483, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Traversing Between Trajectories", + "text_level": 1, + "bbox": [ + 112, + 251, + 379, + 266 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let us transform a foundation diffusion model's trajectory $x_{t}$ by applying two invertible operations, one $f_{t}$ that reparameterizes $t \\in [0,T]$ and one $f_{x}$ that transforms $x$ to an alternate trajectory, defined by the following equation:", + "bbox": [ + 112, + 276, + 483, + 334 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {x} \\left(f _ {t}\\right) = f _ {x} \\left(x _ {f _ {t}}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 241, + 347, + 483, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The boundary conditions need to satisfy $\\bar{x}(f_0) = x_0$ and $\\bar{x}(f_T) = x_T$ to ensure that the starting and target samples are the same. This is different to Shaul et al. [55] since our approach rectifies the trajectories, which requires the exact alignment of the starting and the target distribution.", + "bbox": [ + 112, + 376, + 483, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to construct $f_{t}$ and $f_{x}$ reasonably, we need to probe into the diffusion and flow matching model and investigate how the interpolants are related. Let $x^{\\mathrm{DM}}$ represent a data sample on the diffusion trajectory and $x^{\\mathrm{FM}}$ a data sample on the flow matching trajectory. Similarly, $t_{\\mathrm{DM}}$ is the diffusion timestep and $t_{\\mathrm{FM}}$ is the flow matching timestep. Following the convention of diffusion and flow matching literature [1, 19, 30, 32, 57], diffusion operates on discrete timesteps $t_{\\mathrm{DM}} \\in \\mathbb{Z}_{\\geq 0} \\cap [0,T]$ , where $x_{t_{\\mathrm{DM}} = 0}^{\\mathrm{DM}}$ represents the data samples and $x_{t_{\\mathrm{DM}} = T}^{\\mathrm{DM}}$ corresponds to the Gaussian noise. In contrast, flow matching uses continuous timesteps $t_{\\mathrm{FM}} \\in [0,1]$ with $x_{t_{\\mathrm{FM}} = 1}^{\\mathrm{FM}}$ representing the data samples and $x_{t_{\\mathrm{FM}} = 0}^{\\mathrm{FM}}$ representing the Gaussian noise. To summarize, the boundary condition enforces $x_{t_{\\mathrm{DM}} = 0}^{\\mathrm{DM}} = x_{t_{\\mathrm{FM}} = 1}^{\\mathrm{FM}}$ and $x_{t_{\\mathrm{DM}} = T}^{\\mathrm{DM}} = x_{t_{\\mathrm{FM}} = 0}^{\\mathrm{FM}}$ , while we seek two invertible mappings $f_{t}: [0,T] \\to [0,1]$ which maps $t_{\\mathrm{DM}}$ to $t_{\\mathrm{FM}}$ , and $f_{x}: [0,1] \\times \\mathbb{R}^{d} \\to \\mathbb{R}^{d}$ which maps $x^{\\mathrm{DM}}$ to $x^{\\mathrm{FM}}$ . The diffusion interpolant is", + "bbox": [ + 112, + 449, + 483, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} = \\alpha_ {t _ {\\mathrm {D M}}} x _ {0} ^ {\\mathrm {D M}} + \\sigma_ {t _ {\\mathrm {D M}}} x _ {T} ^ {\\mathrm {D M}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 717, + 483, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t_{\\mathrm{DM}}}^2 +\\sigma_{t_{\\mathrm{DM}}}^2 = 1$ for the variance-preserving schedule and $\\alpha_{t_{\\mathrm{DM}}} = 1$ $\\forall t_{\\mathrm{DM}}$ with $\\sigma_{t_{\\mathrm{DM}}}$ monotonically increasing over time for the variance-exploding schedule [19, 57].", + "bbox": [ + 112, + 747, + 483, + 791 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The flow matching interpolant is defined as", + "bbox": [ + 112, + 792, + 385, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}} = t _ {\\mathrm {F M}} x _ {1} ^ {\\mathrm {F M}} + \\left(1 - t _ {\\mathrm {F M}}\\right) x _ {0} ^ {\\mathrm {F M}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 819, + 482, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are multiple ways to define $f_{x}$ so that the diffusion trajectory can be transformed and warped into a linear equa", + "bbox": [ + 112, + 849, + 483, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion, one being", + "bbox": [ + 511, + 114, + 609, + 127 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} f _ {x} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}\\right) = \\frac {\\alpha_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {0} ^ {\\mathrm {D M}} + \\frac {\\sigma_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {T} ^ {\\mathrm {D M}} \\tag {10} \\\\ = \\frac {1}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 133, + 883, + 195 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "yielding a scaled version of $x_{t_{\\mathrm{DM}}}^{\\mathrm{DM}}$", + "bbox": [ + 511, + 203, + 720, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To design $f_{t}$ as an invertible mapping between the discrete space $t_{\\mathrm{DM}}$ and the continuous space $t_{\\mathrm{FM}}$ , we start by establishing an invertible transformation function that enables continuous interpolation between discrete points in $t_{\\mathrm{DM}}$ while aligning with $f_{x}$ . To ensure continuity and invertibility, we define $f_{t}$ as a piecewise linear function and interpolate between these discrete points. Let $t_{\\overline{\\mathrm{DM}}} \\in [0,T]$ be a continuous interpolated time space of the discrete $t_{\\mathrm{DM}}$ . The correlation between Eq. (9) and Eq. (10) allows to calculate $t_{\\mathrm{FM}}$ via the diffusion coefficients:", + "bbox": [ + 511, + 218, + 880, + 359 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {t} \\left(t _ {\\mathrm {D M}}\\right) = \\frac {\\alpha_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 367, + 880, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where in both variance-preserving and variance-exploding diffusion schedules $f_{t}(t_{\\mathrm{DM}})$ is monotonic. While the diffusion coefficients $\\alpha_{t}$ and $\\sigma_{t}$ are not defined for all $t_{\\overline{\\mathrm{DM}}}$ , we interpolate between the corresponding nearest neighbors. Let $t_{\\mathrm{DM}_1}$ and $t_{\\mathrm{DM}_2}$ be the nearest neighbors of $t_{\\overline{\\mathrm{DM}}}$ and we design $f_{t}$ to be just as a linear interpolation in between. Interestingly, we find that although the continuous values of $t_{\\overline{\\mathrm{DM}}}$ were not trained during the foundation model's training, direct inference with these values still produces reasonable results, as shown in Fig. 2. Specifically, instead of performing DDIM inference at discrete timesteps $t_{\\mathrm{DDIM}} \\in \\mathbb{Z}_{\\geq 0} \\cap [0,1000]$ , we do inference at $t_{\\mathrm{DDIM}} + 0.5$ with linearly interpolated $\\alpha_{t}$ and $\\sigma_{t}$ . We hypothesize that timesteps represented as sinusoidal embeddings create a well-defined continuous time space. This observation lays the foundation for interpolating timestep embeddings and traversing trajectories.", + "bbox": [ + 511, + 402, + 883, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With $t_{\\overline{\\mathrm{DM}}}$ defined on the continuous domain, the inverse $f_{t}^{-1}(t_{\\mathrm{FM}})$ can be defined as follows. First, we find $t_{\\mathrm{DM}_1}$ and $t_{\\mathrm{DM}_2}$ in the discrete timesteps such that $f_{t}(t_{\\mathrm{DM}_{1}})$ and $f_{t}(t_{\\mathrm{DM}_{2}})$ are the two nearest neighbors of $t_{\\mathrm{FM}}$ with $f_{t}(t_{\\mathrm{DM}_{1}})\\leqslant t_{\\mathrm{FM}}\\leqslant f_{t}(t_{\\mathrm{DM}_{2}})$ . Next, we perform a linear interpolation between the two neighbors to reverse the mapping from $t_\\mathrm{FM}$ to $t_{\\overline{\\mathrm{DM}}}$ :", + "bbox": [ + 511, + 645, + 880, + 746 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right) = t _ {\\mathrm {D M} _ {1}} + \\frac {t _ {\\mathrm {F M}} - f _ {t} \\left(t _ {\\mathrm {D M} _ {1}}\\right)}{f _ {t} \\left(t _ {\\mathrm {D M} _ {2}}\\right) - f _ {t} \\left(t _ {\\mathrm {D M} _ {1}}\\right)} \\left(t _ {\\mathrm {D M} _ {2}} - t _ {\\mathrm {D M} _ {1}}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 753, + 880, + 796 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With $f_{t}(\\cdot)$ bidirectionally defined as in Eq. (11) and Eq. (12), we deduce the bidirectional mapping from the FM trajectory $x^{\\mathrm{FM}}$ back to the DM trajectory $x^{\\mathrm{DM}}$ :", + "bbox": [ + 511, + 796, + 880, + 839 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {x} ^ {- 1} \\left(x _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}}\\right) = \\left(\\alpha_ {f _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right)} + \\sigma_ {f _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right)}\\right) x _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 845, + 880, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28350", + "bbox": [ + 478, + 921, + 517, + 931 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Unifying the Objectives", + "text_level": 1, + "bbox": [ + 112, + 113, + 318, + 128 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While traversing between the diffusion and flow matching trajectories is explained in the previous chapter, it is still essential to unify the training and inference objectives. Prior works [14, 64] fine-tuned the model to adapt the diffusion prior, originally predicting $\\epsilon$ or $v$ , to directly predict velocity. However, these approaches force the model to transition between different parameterizations, therefore requiring longer convergence times and also ultimately impacting model performance. In contrast, our method unites the objectives by leveraging the diffusion prior and utilizing the relationships between the parameterizations. We term this technique Objective change as we incorporate both trajectory traversal and a principled objective realignment to facilitate velocity prediction based on the diffusion prior. This approach is broadly applicable across different parameterizations; here, we demonstrate its effectiveness using $v$ -parameterization.", + "bbox": [ + 111, + 136, + 483, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $v_{\\theta}(x^{\\mathrm{DM}}, t_{\\mathrm{DM}})$ be the $v$ -prediction (Eq. (3)) from a pre-trained diffusion model. Using the notation of Eq. (8)", + "bbox": [ + 112, + 378, + 483, + 409 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv _ {\\theta} \\left(x ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) = \\alpha_ {t _ {\\mathrm {D M}}} x _ {T} ^ {\\mathrm {D M}} - \\sigma_ {t _ {\\mathrm {D M}}} x _ {0} ^ {\\mathrm {D M}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 417, + 482, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x_0$ and the corresponding $x_{T}$ can be estimated as", + "bbox": [ + 112, + 448, + 460, + 462 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {x _ {0} ^ {\\mathrm {D M}}} = \\alpha_ {t _ {\\mathrm {D M}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} - \\sigma_ {t _ {\\mathrm {D M}}} v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 473, + 483, + 501 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {x _ {T} ^ {\\mathrm {D M}}} = \\alpha_ {t _ {\\mathrm {D M}}} v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) - \\sigma_ {t _ {\\mathrm {D M}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}},\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 497, + 419, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with the wide hat symbol indicating an estimate predicted by the model. An approximation for the velocity $\\mathbf{v}$ at the corresponding FM data point $x^{\\mathrm{FM}}$ is then formulated with", + "bbox": [ + 112, + 526, + 483, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Diff2Flow Training", + "text_level": 1, + "bbox": [ + 114, + 594, + 323, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: Data Sample $x_{1}^{\\mathrm{FM}}$ , Noise sample $x_{0}^{\\mathrm{FM}}$ , Timestep $t_{\\mathrm{FM}} \\in [0,1]$", + "bbox": [ + 114, + 612, + 483, + 642 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Compute the interpolant $x_{t_{\\mathrm{FM}}}^{\\mathrm{FM}}$ $\\triangleright$ Eq. (9)", + "2: Reparameterize $t_{\\mathrm{FM}}$ to $t_{\\overline{\\mathrm{DM}}}$ using $f_{t}^{-1}$ $\\triangleright$ Eq. (12)", + "3: Reparameterize $x_{t_{\\mathrm{FM}}}^{\\mathrm{FM}}$ to $x_{t_{\\mathrm{DM}}}^{\\mathrm{DM}}$ using $f_{x}^{-1}$ $\\triangleright$ Eq. (13)", + "4: Approximate velocity prediction $\\mathbf{v}_{\\theta}$ $\\triangleright$ Eq. (16)", + "5: Take gradient descent step on $\\mathcal{L}_{\\mathrm{FM}}$ $\\triangleright$ Eq. (5)" + ], + "bbox": [ + 122, + 642, + 483, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 2 Diff2Flow Sampling", + "text_level": 1, + "bbox": [ + 114, + 734, + 328, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: Noise sample $x_0^{\\mathrm{FM}}$ , Number of sampling steps $N$", + "bbox": [ + 114, + 753, + 482, + 768 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: for $t = 0, \\frac{1}{N}, \\dots, \\frac{N - 1}{N}$ do", + "2: Reparameterize $t_{\\mathrm{FM}}$ to $t_{\\overline{\\mathrm{DM}}}$ using $f_{t}^{-1}$ $\\triangleright$ Eq. (12)", + "3: Reparameterize $x_{t_{\\mathrm{FM}}}^{\\mathrm{FM}}$ to $x_{t_{\\mathrm{DM}}}^{\\mathrm{DM}}$ using $f_{x}^{-1}$ $\\triangleright$ Eq. (13)", + "4: Approximate velocity prediction $\\mathbf{v}_{\\theta}$ $\\triangleright$ Eq. (16)", + "5: $x_{t + 1 / N}\\gets x_t + \\frac{1}{N}\\mathbf{v}_\\theta$ $\\triangleright$ Eq. (6)", + "6: end for", + "7: return $x_{1}$" + ], + "bbox": [ + 122, + 768, + 482, + 871 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "respect to the boundary conditions defined in Eq. (7):", + "bbox": [ + 511, + 114, + 844, + 128 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {v} _ {\\theta} \\left(x ^ {\\mathrm {F M}}, t _ {\\mathrm {F M}}\\right) = \\widehat {x _ {1} ^ {\\mathrm {F M}}} - \\widehat {x _ {0} ^ {\\mathrm {F M}}} \\\\ = \\widehat {x _ {0} ^ {\\mathrm {D M}}} - \\widehat {x _ {T} ^ {\\mathrm {D M}}} \\\\ = \\left(\\alpha_ {t _ {\\mathrm {D M}}} - \\sigma t _ {\\mathrm {D M}}\\right) \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} - v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right)\\right). \\tag {16} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 138, + 880, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While we demonstrate the transition specifically from $v$ -parameterization to velocity, this approach is versatile and can be readily applied to other parameterizations, such as $\\epsilon$ -parameterization, by following the same method outlined above. Algorithm 1 and Algorithm 2 summarize this approach in more detail. In summary, our main objective is to estimate the velocity using the prediction on the diffusion trajectory. We use standard Euler steps for inference.", + "bbox": [ + 511, + 214, + 880, + 327 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Parameter-efficient Finetuning", + "text_level": 1, + "bbox": [ + 511, + 338, + 769, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prior works [36, 47] have demonstrated that parameter-efficient finetuning (PEFT) can be advantageous in tasks like domain adaptation and model distillation for generative models. PEFT reduces the number of parameters requiring updates, lowers memory demands during training, and theoretically mitigates catastrophic forgetting [2, 21]. In our approach, we utilize Low-Rank Adaptation (LoRA) [21], which achieves parameter efficiency by freezing the main model weights and updating only a low-rank decomposition of the weight matrices. Given a weight matrix $W_0 \\in \\mathbb{R}^{d \\times k}$ , we freeze $W$ and constrain the matrix's update with a low-rank decomposition $W_0 + \\Delta W = W_0 + BA$ , where $B \\in \\mathbb{R}^{d \\times r}$ and $A \\in \\mathbb{R}^{r \\times k}$ with the rank $r \\leq \\min(d, k)$ . The modified forward pass for an input $x$ is then $h = W_0x + \\Delta Wx = W_0x + BAx$ . We observe that LoRA does not work out of the box when training a diffusion model with a flow matching objective, likely due to the shift required to adapt to a new parameterization scheme. In other words, LoRA struggles with the significant adjustment required when reconfiguring the model from a diffusion-based parameterization to a velocity prediction paradigm. This observation also underscores why naive application of a flow matching objective to a pretrained diffusion model is not effective; it forces the model to unlearn the old parameterization and switch to an entirely new one. In contrast, LoRA performs well when incorporating our proposed objective change that aligns the trajectories. Here, LoRA provides an efficient balance, achieving strong results with minimal parameter updates and showing further improvements as more parameters are fine-tuned.", + "bbox": [ + 511, + 361, + 883, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 803, + 635, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Text-to-Image Synthesis", + "text_level": 1, + "bbox": [ + 511, + 827, + 720, + 842 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We start with the text-to-image task, the original task on which the diffusion prior model was trained. Specifically,", + "bbox": [ + 511, + 849, + 880, + 878 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28351", + "bbox": [ + 478, + 921, + 516, + 931 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ffaed77126368d386aa79621bf5d4fb29c263ee39e2dcaf4c73ca2e18f0d3209.jpg", + "image_caption": [ + "Figure 3. Qualitative results for our finetuned Text-to-Image models using different objectives. DM, FM and Diff2Flow stand for diffusion finetuning, flow matching finetuning, and our method. Images are generated with the same seed, NFEs, and CFG = 4.0." + ], + "image_footnote": [], + "bbox": [ + 169, + 112, + 442, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b622d6684982948d4a6fea8c1c52849c4bd72cbb7174fd63bdf140398e5fce78.jpg", + "image_caption": [ + "Figure 4. Our finetuning objective, both with and without PEFT effectively addresses the issue of non-zero-terminal SNR of DMs. The generations align faithfully to the input prompts." + ], + "image_footnote": [], + "bbox": [ + 165, + 352, + 431, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we use Stable Diffusion 2.1 [46] as our diffusion prior, pretrained at a resolution of $768 \\times 768$ , and fine-tune it to generate images at a lower resolution of $512 \\times 512$ . This resolution shift allows us to investigate the effectiveness of different fine-tuning techniques in bridging resolution gaps.", + "bbox": [ + 111, + 590, + 483, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Starting from the SD2.1 prior, we continue training with different objectives on the LAION-Aesthetics dataset [53] and evaluate model performance on COCO 2017 [29]. Fig. 5 shows that simply continuing diffusion training with an FM objective yields weak performance, especially when constraining model capacity with LoRA. In contrast, our method consistently surpasses continued diffusion training, both with and without classifier-free guidance, converging in as few as $2.5\\mathrm{k}$ iterations. Note that all models show poor FID results without training due to the resolution mismatch.", + "bbox": [ + 111, + 662, + 483, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We present qualitative results in Fig. 3 and Fig. 4, where we use the same sampling hyperparameters and fix the initial Gaussian noise. A key issue that we also address in the transition from the diffusion model to flow matching is the", + "bbox": [ + 111, + 821, + 483, + 878 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1de8f67edeee919bef1e21302f6eb4b503328928b0e3b89df1ae1a03b7be0f3c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodFID ↓CLIP ↑Aesthetics Score ↑
    SD1.556.7726.345.32
    SD1.5 (cont. training)56.3626.335.90
    Diff2Flow52.8026.545.99
    ", + "bbox": [ + 532, + 111, + 864, + 171 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Eval on COCO-2017 5k with 25 Euler/DDIM steps.", + "bbox": [ + 526, + 181, + 867, + 195 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "problem of non-zero terminal SNR [28], which typically results in images generated by stable diffusion models having, on average, gray tones instead of true black or white. Our training paradigm solves this problem, illustrated in Fig. 4.", + "bbox": [ + 509, + 219, + 880, + 276 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, we investigate the scenario where diffusion training is resumed with our method without any changes in resolution or task objectives. Specifically, we initialize from an SD1.5 checkpoint and continue training on the LAION-Aesthetics dataset at a resolution of $512 \\times 512$ . The corresponding evaluation metrics are reported in Tab. 1. Consistent with observations in SD3 [8], the rectified trajectories of Diff2Flow yield superior performance compared to the baseline SD model. We show that converting a diffusion model to its flow-matching counterpart also leads to performance improvements within the same generative task.", + "bbox": [ + 509, + 276, + 880, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Rectifying the Trajectories", + "text_level": 1, + "bbox": [ + 511, + 441, + 741, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition to fine-tuning diffusion models for resolution changes, we can also optimize them for straighter sampling trajectories to enable faster generation speeds. A popular approach to this is Reflow [32], which modifies the flow-matching training objective by replacing the random Gaussian noise terms in Eq. (5) with calculated noise derived from a pre-trained prior ODE to ensure that each noise-image pair is aligned according to the ODE. Quantitative results are presented in Tab. 3, where our method demonstrates competitive performance over various number of function evaluations (NFEs), including low NFEs such as 2 and 4, while only fine-tuning less than $7\\%$ of the parameters. Qualitative results using reflow with 4 inference steps are shown in Fig. 6 and in the Appendix.", + "bbox": [ + 509, + 463, + 883, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Monocular Depth Estimation", + "text_level": 1, + "bbox": [ + 511, + 670, + 759, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition to common tasks, we also show the versatility of our approach for domain adaptation finetuning. Previous methods have shown strong performance in using largescale image generative models for affine-invariant monocular depth estimation [9, 14, 24]. Marigold [24] directly finetune Stable Diffusion on synthetic image-depth data using the standard $v$ -parameterized Diffusion loss (Equation (3)). Following a similar setup, DepthFM [14] propose to convert Stable Diffusion into a flow matching model by training with the flow matching (see Equation (5)) loss. This approach requires aligning the model's outputs to a different objective, interpolant, and timestep scaling (with $t_{\\mathrm{DM}} \\in [0,1000]$ in diffusion versus $t_{\\mathrm{FM}} \\in [0,1]$ in flow matching).", + "bbox": [ + 509, + 691, + 883, + 878 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28352", + "bbox": [ + 478, + 921, + 517, + 931 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ed958eb0c1765c2c8f3487292fae5d8377b92978a6795ea2cd9f758112611900.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 192, + 109, + 467, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c7492738fcf9907c4740f74d2301875dbb8bcfacbd5ef6e2654f450fcff0f63.jpg", + "image_caption": [ + "(b)", + "Figure 5. Text-to-Image FID on the COCO 2017 [29] validation dataset. Light curves indicate results without Classifier-free Guidance [18]. a) We show that both FM and Diff2Flow converge to the same performance, given sufficient training and model capacity (full fine-tuning). However, our method removes the computational overhead from learning how to adjust the network output, resulting in faster convergence. b) Given limited modeling capacity (LoRA) the difference is more pronounced, where the FM model fails to close the gap to Diff2Flow, indicating that finetuning a portion of the parameters is enough to transfer a diffusion model to a flow matching model." + ], + "image_footnote": [], + "bbox": [ + 540, + 109, + 805, + 204 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/32a8f1f6aa16848ba86dda9aa6645cdbdca846bc8dcb3983ef530f6faa1f84a6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodTraining samplesNYUv2 [40]KITTI [13]ETH3D [52]ScanNet [5]DIODE [62]
    AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑
    Depth Anything [65] (CVPR '24)62M4.398.17.694.712.788.2——6.695.2
    Depth Anything v2 [66] (arXiv '24)62M4.497.97.594.813.286.2——6.595.4
    Metric3D [68] (ICCV '23)8M5.096.65.897.06.496.57.494.122.480.5
    Metric3D v2 [22] (TPAMI '24)16M4.398.14.498.24.298.3—†—†13.689.5
    Marigold [24] (CVPR '24)74K5.596.49.991.66.596.06.495.130.877.3
    GeoWizard [9] (ECCV '24)278K5.296.69.792.16.496.16.195.329.779.2
    reproduced by [38]278K5.796.214.482.07.594.36.195.831.477.1
    DepthFM [14] (AAAI '25)74K6.095.59.190.26.595.46.694.922.478.5
    E2E FT [38] (WACV '25)74K5.296.69.691.96.295.95.896.230.277.9
    Lotus-G [16] (arXiv '24)59K5.496.611.387.76.296.16.096.0——
    Diff2Flow74K5.796.78.792.05.597.46.295.721.679.5
    Diff2Flow (LoRA)74K5.996.49.590.86.096.86.495.522.678.5
    ", + "bbox": [ + 112, + 308, + 883, + 500 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3652c1ed82e2806af85c53fa2bd9b2c106aa25de67d686ed8463df0a48af35da.jpg", + "table_caption": [ + "Table 2. Comparison to state-of-the-art depth estimation methods. We compare discriminative (top) and generative models (bottom). Numbers obtained from [38]. ${}^{ \\dagger }$ Metric3D v2 [22] was trained on ScanNet,so zero-shot evaluation is not possible. We also show the results reproduced by [38] for GeoWizard. All of our results are generated with NFE= 10 and an ensemble size of 4 ." + ], + "table_footnote": [], + "table_body": "
    Method#Params ↓StepsFID ↓CLIP ↑
    SDv1.5+DPM Solver [34] (NeurIPS '22)0.9B2520.100.318
    Rectified Flow [32] (ICLR '23)0.9B2521.650.315
    Diff2Flow (LoRA)62M2521.450.314
    PeRFlow [64] (arXiv '24)0.9B422.970.294
    Diff2Flow (LoRA)62M425.290.313
    Rectified Flow [32] (ICLR '23)0.9B231.350.296
    Diff2Flow (LoRA)62M232.310.305
    ", + "bbox": [ + 114, + 573, + 486, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. We fine-tune all our models with LoRA, and apply only 1-rectified flow according to Liu et al. [32]. We get competitive results with state-of-the-art reflow models.", + "bbox": [ + 112, + 709, + 483, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This process incurs significant computational cost, limiting the training efficiency and final performance. However, the flow matching nature of DepthFM allows for faster inference, at slightly reduced performance when given enough training. Our method mitigates this problem, accelerating training, and improving performance. The training and evaluation metrics are provided in the Appendix.", + "bbox": [ + 111, + 777, + 483, + 878 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9970ebf7ad1728f06d921f5ac6c3e90bc367172da9b080bc7ad0bd4f7fd3374b.jpg", + "image_caption": [ + "Figure 6. SD1.5 [46] + Diff2Flow-Reflow, 4-step inference results." + ], + "image_footnote": [], + "bbox": [ + 550, + 573, + 647, + 648 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ff86adc39d021c2268fc6f72b9632e19491265e5b7880b4074779f1ddbe9fdaf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 647, + 573, + 741, + 648 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e2cd60cb02465f6f3322b5745f15f89420a0c1ab46ff544f0f8a1512b23e62cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 741, + 573, + 838, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results Table 2 compares our method with both discriminative and generative depth predictors. Trained exclusively on synthetic data, our method matches or outperforms the prior state-of-the-art in monocular depth estimation, as shown in Figure 8. The diffusion-based Marigold model [24] struggles to achieve high accuracy with a limited number of sampling steps. In contrast to both DepthFM and Marigold, our method achieves competitive performance after very few training iterations and with only two sampling steps. The performance difference becomes even more pronounced when training with LoRA, where model capacity is limited. Figure 8b shows that this limitation prevents a", + "bbox": [ + 509, + 707, + 883, + 878 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28353", + "bbox": [ + 478, + 921, + 517, + 933 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f62519c233e7ab65e3612da256dabdf55d7819a95250902520839fa6814b7cc8.jpg", + "image_caption": [ + "Figure 7. Zero-shot qualitative results on real-world imagery. Our methods produce depth predictions with perceptually higher fidelity and finer detail. All predictions are made using the optimal settings of the models. Best viewed when zoomed in." + ], + "image_footnote": [], + "bbox": [ + 127, + 111, + 859, + 277 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/50613c8e738a25a5c0475ebd9d1ae306ed702d078f35a453a1c4ad0aa60914a4.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 148, + 330, + 465, + 424 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d2817253b6f26e24931d528490a9372138c02b22aab64a98f9bd2a300a40034.jpg", + "image_caption": [ + "(b)", + "Figure 8. Results on NYUv2 depth benchmark [40] with 4 ensemble members. a) With full fine-tuning we find that FM adapts to the I2D task very quickly, but adding the objective change leads to even quicker convergence and better results. In contrast, the diffusion-based counterpart [24] suffers from slower convergence and requires more inference steps. b) The difference between FM and Diff2Flow is even more pronounced if we limit the capacity of the model by using Low-Rank adaptations. With Diff2Flow, the model does not need to learn to change the objective and can focus only on the task itself." + ], + "image_footnote": [], + "bbox": [ + 526, + 330, + 843, + 424 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "straightforward application of the FM loss to the diffusion model. DepthFM struggles here as the model has to learn the adaptation from the $v$ -parameterization to the FM objective. The successful adaptation of the diffusion-based image prior to flow matching supports our initial hypothesis that the integration of our objective change facilitates this transformation. In Table 4, we present an ablation study on performance with different numbers of trainable parameters. Fine-tuning just $1/4$ of the original parameters is sufficient to achieve competitive performance with previous methods, particularly with the fully finetuned DepthFM model. Figure 7 qualitatively compares our method with state-of-the-art depth estimators on in-the-wild images. While discriminative methods often lack detail and fidelity, generative models capture fine details and avoid the averaging effect common to discriminative approaches.", + "bbox": [ + 111, + 540, + 483, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 112, + 782, + 223, + 797 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce a novel framework, Diff2Flow, that effectively converts pre-trained diffusion into flow matching models, providing a twofold optimization. First, this approach allows us to efficiently use the diffusion model's prior by exploiting its powerful generative capabilities with", + "bbox": [ + 111, + 806, + 483, + 878 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/638c0acc1ec7952a342bb011839bedcb18c5d54ac24b06fac72c73a3ae845323.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Method#Params ↓AbsRel ↓δ1 ↑
    Marigold + E2E FT [38]866M5.296.6
    Diff2Flow866M5.796.7
    Diff2Flow (LoRA base)222M5.996.4
    Diff2Flow (LoRA small)62M6.995.0
    ", + "bbox": [ + 535, + 537, + 857, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Zero-shot evaluation on NYUv2 [40] for different number of trainable parameters. We can achieve competitive performance with only a fraction of previous SOTA methods.", + "bbox": [ + 511, + 626, + 883, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "out retraining from scratch. Second, by adapting it to the flow matching paradigm, we gain key benefits unique to flow matching: fast inference suitable for downstream tasks, and the ability to straighten sampling trajectories through techniques such as reflow, which further improves efficiency and performance. As a result, Diff2Flow not only improves training and inference efficiency but also delivers competitive performance in diverse tasks, including text-to-image synthesis and monocular depth estimation. By using parameter-efficient fine-tuning methods such as LoRA, our framework further minimizes computational requirements and demonstrates a practical, scalable way to merge diffusion and flow matching paradigms in generative modeling.", + "bbox": [ + 509, + 691, + 883, + 878 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28354", + "bbox": [ + 478, + 921, + 517, + 931 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 112, + 112, + 264, + 128 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This project has been supported by the bidders project KLIMA-MEMES, the German Federal Ministry for Economic Affairs and Climate Action within the project \"NXT GEN AI METHODS - Generative Methoden für Percep tion, Prädiktion und Planung\", the project \"GeniusRobot\" (01IS24083), funded by the Federal Ministry of Education and Research (BMBF), and the German Research Foundation (DFG) project 421703927. The authors acknowledge the Gauss Center for Supercomputing for providing compute through the NIC on JUWELS at JSC and the HPC resources supplied by the Erlangen National High Performance Computing Center (NHR@FAU funded by DFG project 440719683) under the NHR project JA-22883.", + "bbox": [ + 111, + 135, + 485, + 308 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 114, + 330, + 205, + 344 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Michael S Albergo, Nicholas M Boffi, and Eric Vanden-Eijnden. Stochastic interpolants: A unifying framework for flows and diffusions. arXiv preprint arXiv:2303.08797, 2023. 1, 2, 3, 4", + "[2] Dan Biderman, Jacob Portes, Jose Javier Gonzalez Ortiz, Mansheej Paul, Philip Greengard, Connor Jennings, Daniel King, Sam Havens, Vitaliy Chiley, Jonathan Frankle, et al. Lora learns less and forgets less. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9043-9053, 2023. 7" + ], + "bbox": [ + 514, + 114, + 880, + 527 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "28357", + "bbox": [ + 478, + 921, + 517, + 931 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Diff2Flow_ Training Flow Matching Models via Diffusion Model Alignment/fbb4858e-0a86-4812-87cf-57f08dfebd6c_model.json b/2025/Diff2Flow_ Training Flow Matching Models via Diffusion Model Alignment/fbb4858e-0a86-4812-87cf-57f08dfebd6c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d81f9fbcbd1c8c0b564171d9f03807cb213c1344 --- /dev/null +++ b/2025/Diff2Flow_ Training Flow Matching Models via Diffusion Model Alignment/fbb4858e-0a86-4812-87cf-57f08dfebd6c_model.json @@ -0,0 +1,2697 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.117, + 0.017, + 0.191, + 0.055 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.244, + 0.015, + 0.8, + 0.058 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.14, + 0.151, + 0.857, + 0.172 + ], + "angle": 0, + "content": "Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment" + }, + { + "type": "text", + "bbox": [ + 0.198, + 0.199, + 0.391, + 0.215 + ], + "angle": 0, + "content": "Johannes Schusterbauer*" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.199, + 0.514, + 0.216 + ], + "angle": 0, + "content": "Ming Gui*" + }, + { + "type": "text", + "bbox": [ + 0.551, + 0.199, + 0.654, + 0.216 + ], + "angle": 0, + "content": "Frank Fundel" + }, + { + "type": "text", + "bbox": [ + 0.691, + 0.199, + 0.798, + 0.216 + ], + "angle": 0, + "content": "Björn Ommer" + }, + { + "type": "text", + "bbox": [ + 0.362, + 0.217, + 0.632, + 0.233 + ], + "angle": 0, + "content": "CompVis @ LMU Munich, MCML" + }, + { + "type": "title", + "bbox": [ + 0.262, + 0.265, + 0.337, + 0.28 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.295, + 0.486, + 0.595 + ], + "angle": 0, + "content": "Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for finetuning, while diffusion models like Stable Diffusion benefit from efficient architectures and ecosystem support. This work addresses the critical challenge of efficiently transferring knowledge from pre-trained diffusion models to flow matching. We propose Diff2Flow, a novel framework that systematically bridges diffusion and FM paradigms by rescaling timesteps, aligning interpolants, and deriving FM-compatible velocity fields from diffusion predictions. This alignment enables direct and efficient FM finetuning of diffusion priors with no extra computation overhead. Our experiments demonstrate that Diff2Flow outperforms naive FM and diffusion finetuning particularly under parameter-efficient constraints, while achieving superior or competitive performance across diverse downstream tasks compared to state-of-the-art methods. We will release our code at https://github.com/CompVis/diff2flow." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.621, + 0.238, + 0.635 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.644, + 0.483, + 0.773 + ], + "angle": 0, + "content": "Recently, diffusion models [19, 57] have gained substantial popularity due to their exceptional generative capabilities, which have redefined the boundaries of image generation [42, 43, 46, 48]. Among these, foundation models such as Stable Diffusion [46] stand out, not only for their high-fidelity outputs but also for their useful representations and adaptability to downstream tasks, including depth estimation [14, 24], surface normal prediction [7], segmentation [63], and semantic correspondences [11, 60]." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.773, + 0.483, + 0.859 + ], + "angle": 0, + "content": "Meanwhile, Flow Matching (FM) [1, 30, 32] has emerged as a promising alternative, empirically offering faster inference and improved performance [8, 37]. While state-of-the-art foundational models based on flow matching, such as Flux [26] or SDv3 [8], show remarkable generative capabilities, their large size (\\(>8\\mathrm{B}\\) parameters) requires" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.266, + 0.885, + 0.439 + ], + "angle": 0, + "content": "high-end hardware for both training and inference, making them particularly computationally expensive. This makes fine-tuning impractical, especially in resource-constrained environments and significantly limits their practical adoption. In contrast, Stable Diffusion's [46] efficient architecture and widespread ecosystem make it a pragmatic choice. This raises an important question: Can the knowledge captured by existing foundational diffusion models be efficiently transferred to a flow matching model? How can we bridge the gap between diffusion and flow matching with minimal additional training, leveraging both the pre-trained prior and the advantageous properties of flow matching?" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.442, + 0.884, + 0.585 + ], + "angle": 0, + "content": "This work explores the relationship between the diffusion and flow matching paradigms. Although both methods can be generalized under a common framework [1, 25, 37], the actual implementations differ in several key aspects, including the definition of interpolants between the Gaussian noise prior and data samples, timestep scaling, and training objectives. These differences make it difficult to directly use a pre-trained diffusion model as a starting prior for flow matching training, as the two paradigms are not inherently well aligned." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.589, + 0.884, + 0.846 + ], + "angle": 0, + "content": "To address this challenge, we propose a novel framework that effectively \"warps\" diffusion into flow matching, enabling seamless knowledge transfer between the two paradigms. This requires re-scaling their respective timesteps, aligning their differing interpolant formulations, and deriving the velocity field required for flow matching from the diffusion model's predictions, based on its parameterization. By systematically establishing these correspondences, we enable a smooth transition between diffusion and flow matching. To this end, we introduce a training methodology termed Diff2Flow, which initializes the flow matching model with a pretrained diffusion prior and directly finetunes it using the flow matching objective. Our analysis reveals that directly applying the FM loss to a diffusion model without incorporating our proposed adjustments significantly slows convergence and degrades overall model performance, whereas Diff2Flow provides a flexible and efficient approach with minimal finetuning overhead." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.85, + 0.884, + 0.88 + ], + "angle": 0, + "content": "The benefits of this alignment become particularly evident when finetuning only a small subset of parameters." + }, + { + "type": "page_footnote", + "bbox": [ + 0.131, + 0.866, + 0.236, + 0.879 + ], + "angle": 0, + "content": "* Equal Contribution" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.922, + 0.518, + 0.933 + ], + "angle": 0, + "content": "28347" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.112, + 0.114, + 0.484, + 0.242 + ], + "angle": 0, + "content": "Under such constrained computational budgets, the performance gap between naïve FM finetuning and our alignment-aware approach becomes more pronounced. Specifically, we show that directly applying the FM objective with parameter efficient finetuning (PEFT) leads to very suboptimal performance. Leveraging Diff2Flow with its alignment-informed training strategy, PEFT enhances training efficiency and minimizes memory consumption while maintaining high performance." + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.243, + 0.486, + 0.586 + ], + "angle": 0, + "content": "We show the efficiency of our method on a diverse set of downstream tasks. ① We show that when finetuning on a high-aesthetics dataset [6] on the text-to-image task, we outperform diffusion-based finetuning while converging significantly faster than naively training with the flow matching objective. This empirically demonstrates that smartly aligning timestep scaling and objective significantly facilitate learning, and additionally mitigate the zero-terminal SNR issue [28] common in diffusion models, where full black or white images can't be generated. ② When repurposing the model to generate images at resolutions different from the pre-trained sweet-spot resolution (similar to [17]), our method achieves superior results compared to standard diffusion and flow matching fine-tuning. ③ We show that we can apply Reflow [32] using Diff2Flow on a base diffusion model, a method that straightens sampling trajectories, resulting in faster inference speed. By rectifying the sampling trajectories of Stable Diffusion v1.5 we can generate images with as few as 2 sampling steps without consistency distillation [58]. ④ Finally, we demonstrate the effectiveness of our method on domain adaptation, leveraging the Stable Diffusion prior to predicting affine-invariant depth maps similar to Marigold [24] and DepthFM [14], achieving state-of-the-art results with reduced training time." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.598, + 0.248, + 0.613 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.622, + 0.484, + 0.807 + ], + "angle": 0, + "content": "Diffusion and Flow Matching Models Diffusion models [19, 57] have demonstrated wide-ranging capabilities in data synthesis, extending from image [10, 44, 46, 48] and video [3, 15, 20] to audio generation [31] and beyond. While these models excel at producing high-fidelity outputs, they often require extensive sampling time, necessitating techniques like distillation [39, 49, 50, 58], noise schedule optimization [23], or training-free sampling [34, 56] to achieve faster generation. Following diffusion models, flow matching models [1, 30, 32] have gained attention due to their benefit of straighter probability paths. These models have been shown to perform competitively or surpass diffusion models in terms of both speed and quality [8, 37, 54]." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.808, + 0.484, + 0.88 + ], + "angle": 0, + "content": "The relationship between diffusion and flow matching models has been explored in Lee et al. [27], demonstrating that finetuning a flow matching model based on a pretrained diffusion model is feasible. Our work extends this by explicitly formulating a method to map discrete diffu" + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.114, + 0.812, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.23, + 0.885, + 0.324 + ], + "angle": 0, + "content": "Figure 1. We introduce a novel finetuning technique to traverse between flow matching and diffusion, which enables effectively aligning the two processes with minimal additional training. The interpolant on the flow matching trajectory is computed as a function \\( f \\) of the diffusion timestep \\( t \\), the sample \\( x \\), and the associated diffusion coefficients. Our approach further enables a velocity prediction \\( \\hat{\\mathbf{v}} \\) regardless of the diffusion model's parameterization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.356, + 0.884, + 0.429 + ], + "angle": 0, + "content": "sion trajectory to a continuous flow matching trajectory. Furthermore, we empirically demonstrate that our strategy works for various diffusion parameterization objectives and present results that go beyond reflow [32], achieving competitive performance on several benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.468, + 0.884, + 0.669 + ], + "angle": 0, + "content": "Parameter-efficient Finetuning As foundational models expand in size and complexity, parameter-efficient finetuning (PEFT) techniques such as Low-Rank Adaptation (LoRA) [21] offer viable alternatives to full model finetuning. Originally developed for large language models, LoRA and other PEFT techniques have since been applied effectively to diffusion models [47], proving valuable across a broad range of tasks. These include domain-specific finetuning [67], additional image conditioning [59], image editing [12], distillation [36] and among others. By updating only a low-rank decomposition of the weight matrix, LoRA reduces memory requirements and alleviate catastrophic forgetting [2], making it highly adaptable for targeted adjustments in large foundational models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.708, + 0.885, + 0.88 + ], + "angle": 0, + "content": "Knowledge in Generative Models Following the rise of text-to-image diffusion models [41, 43, 44, 46, 48], numerous studies have explored methods to extract information from diffusion priors. Many works have effectively utilized the diffusion prior for tasks such as monocular depth estimation [9, 14, 16, 24, 38, 51], surface normal prediction [7], and semantic correspondences [11, 35, 60]. While these approaches predominantly focus on distilling information into another diffusion model, our work explores the transfer of this knowledge to flow matching models and hereby leverages the inherent advantages of flow matching, including more efficient inference and enhanced task performance." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.922, + 0.518, + 0.934 + ], + "angle": 0, + "content": "28348" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.114, + 0.113, + 0.2, + 0.127 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.136, + 0.484, + 0.222 + ], + "angle": 0, + "content": "In this section, we explain our algorithm and the process of aligning the trajectories. We begin by discussing the definition of diffusion and flow matching models. Following this, we describe how we traverse between the two trajectories as depicted in Fig. 1 and use the diffusion model to generate a reasonable estimate of the flow velocity." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.231, + 0.363, + 0.246 + ], + "angle": 0, + "content": "3.1. Diffusion and Flow Matching" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.253, + 0.484, + 0.31 + ], + "angle": 0, + "content": "Diffusion models (DM) [19, 56, 57] gradually diffuse data by typically adding noise to real data samples \\( x_0 \\sim p_0(x_0) \\) in a predefined discrete forward process, which can be characterized by" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.319, + 0.484, + 0.337 + ], + "angle": 0, + "content": "\\[\np \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\alpha_ {t} x _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.346, + 0.484, + 0.462 + ], + "angle": 0, + "content": "where \\(\\alpha_{t}\\) and \\(\\sigma_{t}\\) are the predefined noise schedules, \\(t\\) is the discrete timestep, and \\(x_{t}\\) is the resulting noisy sample, often referred to as the interpolant. In the setting of variance preserving schedules \\(\\sigma_{t} = \\sqrt{1 - \\alpha_{t}^{2}}\\), and the interpolant \\(x_{t}\\) is then \\(x_{t} = \\alpha_{t}x_{0} + \\sqrt{1 - \\alpha_{t}^{2}}\\epsilon\\) with \\(\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})\\). A neural network, parameterized by \\(\\theta\\), is learned to reverse the forward process by gradually removing noise from \\(x_{t}\\). Ho et al. [19] propose the simplified loss term" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.471, + 0.484, + 0.489 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, \\epsilon , x _ {0} \\sim p (x _ {0})} | | \\epsilon_ {t} - \\epsilon_ {\\theta} (x _ {t}, t) | | ^ {2}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.497, + 0.484, + 0.541 + ], + "angle": 0, + "content": "where predicting \\(\\epsilon\\) instead of \\(x_0\\) is observed to yield better results and enhance convergence. There also exists the \\(v\\)-parameterization [49], defined as" + }, + { + "type": "equation", + "bbox": [ + 0.243, + 0.552, + 0.483, + 0.567 + ], + "angle": 0, + "content": "\\[\nv _ {t} = \\alpha_ {t} \\epsilon - \\sigma_ {t} x _ {0}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.582, + 0.484, + 0.682 + ], + "angle": 0, + "content": "Flow matching (FM) models [1, 30, 32], another flexible class of generative models, utilizes the same idea of gradually deteriorating data samples and then synthesizing new data by reversing the process. We adopt the setting from Lipman et al. [30] where \\( x_0 \\) represents noise, and \\( x_{1} \\) corresponds to data. The interpolant on the continuous timesteps \\( t\\in [0,1] \\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.227, + 0.694, + 0.484, + 0.708 + ], + "angle": 0, + "content": "\\[\nx _ {t} = t x _ {1} + (1 - t) x _ {0}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.718, + 0.484, + 0.775 + ], + "angle": 0, + "content": "where \\( x_0 \\) is typically a Gaussian noise sample. The model \\( \\mathbf{v}_{\\theta} \\) is trained to regress a vector field along the trajectory, following the linear path that points from \\( x_0 \\) to \\( x_1 \\) using the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.785, + 0.484, + 0.803 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {F M}} = \\mathbb {E} _ {t, x _ {0} \\sim \\mathcal {N} (0, \\mathbf {I}), x _ {1} \\sim p (x _ {1})} | | (x _ {1} - x _ {0}) - \\mathbf {v} _ {\\theta} (x _ {t}, t) | | ^ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.811, + 0.484, + 0.855 + ], + "angle": 0, + "content": "Sampling from a flow matching model is accomplished by integrating over the trajectory of the learned ODE, e.g. using the forward Euler method with the update rule" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.865, + 0.484, + 0.881 + ], + "angle": 0, + "content": "\\[\nx _ {t + t _ {\\Delta}} = x _ {t} + t _ {\\Delta} \\mathbf {v} _ {\\theta} \\left(x _ {t}, t\\right) \\quad \\forall t \\in [ 0, 1), \\tag {6}\n\\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.553, + 0.113, + 0.692, + 0.125 + ], + "angle": 0, + "content": "Normal timesteps \\(t_{\\mathrm{DM}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.556, + 0.125, + 0.69, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.708, + 0.113, + 0.845, + 0.126 + ], + "angle": 0, + "content": "Shifted timesteps \\(t_{\\mathrm{DM}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.126, + 0.843, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.193, + 0.882, + 0.22 + ], + "angle": 0, + "content": "Figure 2. Although non-integer-shifted DDIM timesteps are neither defined nor trained, generated images remain of high quality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.245, + 0.882, + 0.36 + ], + "angle": 0, + "content": "with \\( t_{\\delta} = 1 / N \\) and \\( N \\) being the number of function evaluations (NFE). We generate a discrete sequence that approximates the path by advancing in small increments along the ODE. The trajectory's smoothness, or \"straightness,\" is critical, as it determines the number of steps required to achieve accurate results, trading off computational cost and fidelity. Straighter paths allow smaller \\( N \\), whereas paths with higher curvature require more steps for simulating the ODE." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.377, + 0.884, + 0.563 + ], + "angle": 0, + "content": "Reflow In FM training, we randomly sample from a Gaussian distribution and form pairs with the data points to create the interpolant \\( x_{t} \\). This random pairing leads to curved sampling trajectories, increasing the curvature of the ODE trajectories during inference [61]. To straighten these trajectories, Liu et al. [32] propose Reflow, which iteratively trains on samples obtained from a pre-trained flow matching model. Given an already trained ODE model \\( \\mathbf{v}_{\\Phi} \\), Reflow first samples \\( x_0 \\sim \\mathcal{N}(0,\\mathbf{I}) \\) and integrates along the ODE trajectory using Eq. (6) to obtain a corresponding data sample \\( x_{1} \\). This process generates image-noise pairings. Training on this paired data has been found to reduce inference cost by straightening the sampling trajectories [32, 33, 64]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.571, + 0.847, + 0.587 + ], + "angle": 0, + "content": "3.2. Diffusion Prior for Flow Matching Model" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.593, + 0.882, + 0.708 + ], + "angle": 0, + "content": "Flow matching methods are known for straighter trajectories and more efficient inference [14, 61]. Hence, transforming the diffusion prior into a flow matching equivalent offers the potential for improvements in inference speed and performance [8, 37]. While previous research has successfully adapted diffusion priors for other downstream diffusion tasks, our approach combines these advantages with those of flow matching models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.708, + 0.882, + 0.879 + ], + "angle": 0, + "content": "Importantly, recent works on utilizing flow matching models to inherit a diffusion prior for downstream applications, such as DepthFM [14], have shown significant promise in accelerating inference compared to diffusion models. While this approach provides faster sampling than its diffusion model's counterpart, this inheritance method has limitations: DepthFM finetunes from a \\( v \\)-parameterized text-to-image diffusion model [46] directly. This approach requires the flow matching model to \"warp\" the \\( v \\)-parameterization to predict velocity, a different parameterization scheme. This introduces misalignments in the training objective, the interpolant, and the timesteps." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.922, + 0.518, + 0.933 + ], + "angle": 0, + "content": "28349" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.112, + 0.114, + 0.484, + 0.228 + ], + "angle": 0, + "content": "To address these limitations, we propose a novel strategy that enables a seamless transition between diffusion and flow matching trajectories. Our method minimizes misalignments and yields more accurate velocity predictions. In addition to monocular depth estimation, we demonstrate that our approach generalizes to other downstream tasks and offers a versatile and efficient solution for leveraging prior information from diffusion model." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.252, + 0.38, + 0.267 + ], + "angle": 0, + "content": "3.2.1 Traversing Between Trajectories" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.277, + 0.485, + 0.335 + ], + "angle": 0, + "content": "Let us transform a foundation diffusion model's trajectory \\( x_{t} \\) by applying two invertible operations, one \\( f_{t} \\) that reparameterizes \\( t \\in [0,T] \\) and one \\( f_{x} \\) that transforms \\( x \\) to an alternate trajectory, defined by the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.243, + 0.348, + 0.484, + 0.365 + ], + "angle": 0, + "content": "\\[\n\\bar {x} \\left(f _ {t}\\right) = f _ {x} \\left(x _ {f _ {t}}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.377, + 0.484, + 0.448 + ], + "angle": 0, + "content": "The boundary conditions need to satisfy \\( \\bar{x}(f_0) = x_0 \\) and \\( \\bar{x}(f_T) = x_T \\) to ensure that the starting and target samples are the same. This is different to Shaul et al. [55] since our approach rectifies the trajectories, which requires the exact alignment of the starting and the target distribution." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.45, + 0.484, + 0.707 + ], + "angle": 0, + "content": "In order to construct \\( f_{t} \\) and \\( f_{x} \\) reasonably, we need to probe into the diffusion and flow matching model and investigate how the interpolants are related. Let \\( x^{\\mathrm{DM}} \\) represent a data sample on the diffusion trajectory and \\( x^{\\mathrm{FM}} \\) a data sample on the flow matching trajectory. Similarly, \\( t_{\\mathrm{DM}} \\) is the diffusion timestep and \\( t_{\\mathrm{FM}} \\) is the flow matching timestep. Following the convention of diffusion and flow matching literature [1, 19, 30, 32, 57], diffusion operates on discrete timesteps \\( t_{\\mathrm{DM}} \\in \\mathbb{Z}_{\\geq 0} \\cap [0,T] \\), where \\( x_{t_{\\mathrm{DM}} = 0}^{\\mathrm{DM}} \\) represents the data samples and \\( x_{t_{\\mathrm{DM}} = T}^{\\mathrm{DM}} \\) corresponds to the Gaussian noise. In contrast, flow matching uses continuous timesteps \\( t_{\\mathrm{FM}} \\in [0,1] \\) with \\( x_{t_{\\mathrm{FM}} = 1}^{\\mathrm{FM}} \\) representing the data samples and \\( x_{t_{\\mathrm{FM}} = 0}^{\\mathrm{FM}} \\) representing the Gaussian noise. To summarize, the boundary condition enforces \\( x_{t_{\\mathrm{DM}} = 0}^{\\mathrm{DM}} = x_{t_{\\mathrm{FM}} = 1}^{\\mathrm{FM}} \\) and \\( x_{t_{\\mathrm{DM}} = T}^{\\mathrm{DM}} = x_{t_{\\mathrm{FM}} = 0}^{\\mathrm{FM}} \\), while we seek two invertible mappings \\( f_{t}: [0,T] \\to [0,1] \\) which maps \\( t_{\\mathrm{DM}} \\) to \\( t_{\\mathrm{FM}} \\), and \\( f_{x}: [0,1] \\times \\mathbb{R}^{d} \\to \\mathbb{R}^{d} \\) which maps \\( x^{\\mathrm{DM}} \\) to \\( x^{\\mathrm{FM}} \\). The diffusion interpolant is" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.718, + 0.484, + 0.737 + ], + "angle": 0, + "content": "\\[\nx _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} = \\alpha_ {t _ {\\mathrm {D M}}} x _ {0} ^ {\\mathrm {D M}} + \\sigma_ {t _ {\\mathrm {D M}}} x _ {T} ^ {\\mathrm {D M}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.748, + 0.484, + 0.792 + ], + "angle": 0, + "content": "where \\(\\alpha_{t_{\\mathrm{DM}}}^2 +\\sigma_{t_{\\mathrm{DM}}}^2 = 1\\) for the variance-preserving schedule and \\(\\alpha_{t_{\\mathrm{DM}}} = 1\\) \\(\\forall t_{\\mathrm{DM}}\\) with \\(\\sigma_{t_{\\mathrm{DM}}}\\) monotonically increasing over time for the variance-exploding schedule [19, 57]." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.794, + 0.386, + 0.807 + ], + "angle": 0, + "content": "The flow matching interpolant is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.82, + 0.483, + 0.838 + ], + "angle": 0, + "content": "\\[\nx _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}} = t _ {\\mathrm {F M}} x _ {1} ^ {\\mathrm {F M}} + \\left(1 - t _ {\\mathrm {F M}}\\right) x _ {0} ^ {\\mathrm {F M}}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.85, + 0.484, + 0.88 + ], + "angle": 0, + "content": "There are multiple ways to define \\( f_{x} \\) so that the diffusion trajectory can be transformed and warped into a linear equa" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.61, + 0.128 + ], + "angle": 0, + "content": "tion, one being" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.135, + 0.884, + 0.196 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} f _ {x} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}\\right) = \\frac {\\alpha_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {0} ^ {\\mathrm {D M}} + \\frac {\\sigma_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {T} ^ {\\mathrm {D M}} \\tag {10} \\\\ = \\frac {1}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.204, + 0.722, + 0.219 + ], + "angle": 0, + "content": "yielding a scaled version of \\(x_{t_{\\mathrm{DM}}}^{\\mathrm{DM}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.219, + 0.882, + 0.361 + ], + "angle": 0, + "content": "To design \\( f_{t} \\) as an invertible mapping between the discrete space \\( t_{\\mathrm{DM}} \\) and the continuous space \\( t_{\\mathrm{FM}} \\), we start by establishing an invertible transformation function that enables continuous interpolation between discrete points in \\( t_{\\mathrm{DM}} \\) while aligning with \\( f_{x} \\). To ensure continuity and invertibility, we define \\( f_{t} \\) as a piecewise linear function and interpolate between these discrete points. Let \\( t_{\\overline{\\mathrm{DM}}} \\in [0,T] \\) be a continuous interpolated time space of the discrete \\( t_{\\mathrm{DM}} \\). The correlation between Eq. (9) and Eq. (10) allows to calculate \\( t_{\\mathrm{FM}} \\) via the diffusion coefficients:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.368, + 0.882, + 0.397 + ], + "angle": 0, + "content": "\\[\nf _ {t} \\left(t _ {\\mathrm {D M}}\\right) = \\frac {\\alpha_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.403, + 0.884, + 0.645 + ], + "angle": 0, + "content": "where in both variance-preserving and variance-exploding diffusion schedules \\( f_{t}(t_{\\mathrm{DM}}) \\) is monotonic. While the diffusion coefficients \\( \\alpha_{t} \\) and \\( \\sigma_{t} \\) are not defined for all \\( t_{\\overline{\\mathrm{DM}}} \\), we interpolate between the corresponding nearest neighbors. Let \\( t_{\\mathrm{DM}_1} \\) and \\( t_{\\mathrm{DM}_2} \\) be the nearest neighbors of \\( t_{\\overline{\\mathrm{DM}}} \\) and we design \\( f_{t} \\) to be just as a linear interpolation in between. Interestingly, we find that although the continuous values of \\( t_{\\overline{\\mathrm{DM}}} \\) were not trained during the foundation model's training, direct inference with these values still produces reasonable results, as shown in Fig. 2. Specifically, instead of performing DDIM inference at discrete timesteps \\( t_{\\mathrm{DDIM}} \\in \\mathbb{Z}_{\\geq 0} \\cap [0,1000] \\), we do inference at \\( t_{\\mathrm{DDIM}} + 0.5 \\) with linearly interpolated \\( \\alpha_{t} \\) and \\( \\sigma_{t} \\). We hypothesize that timesteps represented as sinusoidal embeddings create a well-defined continuous time space. This observation lays the foundation for interpolating timestep embeddings and traversing trajectories." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.646, + 0.882, + 0.747 + ], + "angle": 0, + "content": "With \\( t_{\\overline{\\mathrm{DM}}} \\) defined on the continuous domain, the inverse \\( f_{t}^{-1}(t_{\\mathrm{FM}}) \\) can be defined as follows. First, we find \\( t_{\\mathrm{DM}_1} \\) and \\( t_{\\mathrm{DM}_2} \\) in the discrete timesteps such that \\( f_{t}(t_{\\mathrm{DM}_{1}}) \\) and \\( f_{t}(t_{\\mathrm{DM}_{2}}) \\) are the two nearest neighbors of \\( t_{\\mathrm{FM}} \\) with \\( f_{t}(t_{\\mathrm{DM}_{1}})\\leqslant t_{\\mathrm{FM}}\\leqslant f_{t}(t_{\\mathrm{DM}_{2}}) \\). Next, we perform a linear interpolation between the two neighbors to reverse the mapping from \\( t_\\mathrm{FM} \\) to \\( t_{\\overline{\\mathrm{DM}}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.754, + 0.882, + 0.797 + ], + "angle": 0, + "content": "\\[\nf _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right) = t _ {\\mathrm {D M} _ {1}} + \\frac {t _ {\\mathrm {F M}} - f _ {t} \\left(t _ {\\mathrm {D M} _ {1}}\\right)}{f _ {t} \\left(t _ {\\mathrm {D M} _ {2}}\\right) - f _ {t} \\left(t _ {\\mathrm {D M} _ {1}}\\right)} \\left(t _ {\\mathrm {D M} _ {2}} - t _ {\\mathrm {D M} _ {1}}\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.797, + 0.882, + 0.84 + ], + "angle": 0, + "content": "With \\( f_{t}(\\cdot) \\) bidirectionally defined as in Eq. (11) and Eq. (12), we deduce the bidirectional mapping from the FM trajectory \\( x^{\\mathrm{FM}} \\) back to the DM trajectory \\( x^{\\mathrm{DM}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.846, + 0.882, + 0.867 + ], + "angle": 0, + "content": "\\[\nf _ {x} ^ {- 1} \\left(x _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}}\\right) = \\left(\\alpha_ {f _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right)} + \\sigma_ {f _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right)}\\right) x _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}}. \\tag {13}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.922, + 0.518, + 0.933 + ], + "angle": 0, + "content": "28350" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.114, + 0.114, + 0.32, + 0.129 + ], + "angle": 0, + "content": "3.2.2 Unifying the Objectives" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.137, + 0.484, + 0.379 + ], + "angle": 0, + "content": "While traversing between the diffusion and flow matching trajectories is explained in the previous chapter, it is still essential to unify the training and inference objectives. Prior works [14, 64] fine-tuned the model to adapt the diffusion prior, originally predicting \\(\\epsilon\\) or \\(v\\), to directly predict velocity. However, these approaches force the model to transition between different parameterizations, therefore requiring longer convergence times and also ultimately impacting model performance. In contrast, our method unites the objectives by leveraging the diffusion prior and utilizing the relationships between the parameterizations. We term this technique Objective change as we incorporate both trajectory traversal and a principled objective realignment to facilitate velocity prediction based on the diffusion prior. This approach is broadly applicable across different parameterizations; here, we demonstrate its effectiveness using \\(v\\)-parameterization." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.38, + 0.484, + 0.41 + ], + "angle": 0, + "content": "Let \\( v_{\\theta}(x^{\\mathrm{DM}}, t_{\\mathrm{DM}}) \\) be the \\( v \\)-prediction (Eq. (3)) from a pre-trained diffusion model. Using the notation of Eq. (8)" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.419, + 0.483, + 0.437 + ], + "angle": 0, + "content": "\\[\nv _ {\\theta} \\left(x ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) = \\alpha_ {t _ {\\mathrm {D M}}} x _ {T} ^ {\\mathrm {D M}} - \\sigma_ {t _ {\\mathrm {D M}}} x _ {0} ^ {\\mathrm {D M}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.449, + 0.462, + 0.463 + ], + "angle": 0, + "content": "where \\( x_0 \\) and the corresponding \\( x_{T} \\) can be estimated as" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.474, + 0.484, + 0.502 + ], + "angle": 0, + "content": "\\[\n\\widehat {x _ {0} ^ {\\mathrm {D M}}} = \\alpha_ {t _ {\\mathrm {D M}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} - \\sigma_ {t _ {\\mathrm {D M}}} v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.498, + 0.42, + 0.518 + ], + "angle": 0, + "content": "\\[\n\\widehat {x _ {T} ^ {\\mathrm {D M}}} = \\alpha_ {t _ {\\mathrm {D M}}} v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) - \\sigma_ {t _ {\\mathrm {D M}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.527, + 0.484, + 0.571 + ], + "angle": 0, + "content": "with the wide hat symbol indicating an estimate predicted by the model. An approximation for the velocity \\(\\mathbf{v}\\) at the corresponding FM data point \\(x^{\\mathrm{FM}}\\) is then formulated with" + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.595, + 0.324, + 0.61 + ], + "angle": 0, + "content": "Algorithm 1 Diff2Flow Training" + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.613, + 0.484, + 0.643 + ], + "angle": 0, + "content": "Require: Data Sample \\(x_{1}^{\\mathrm{FM}}\\), Noise sample \\(x_{0}^{\\mathrm{FM}}\\), Timestep \\(t_{\\mathrm{FM}} \\in [0,1]\\)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.643, + 0.484, + 0.658 + ], + "angle": 0, + "content": "1: Compute the interpolant \\(x_{t_{\\mathrm{FM}}}^{\\mathrm{FM}}\\) \\(\\triangleright\\) Eq. (9)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.659, + 0.484, + 0.674 + ], + "angle": 0, + "content": "2: Reparameterize \\(t_{\\mathrm{FM}}\\) to \\(t_{\\overline{\\mathrm{DM}}}\\) using \\(f_{t}^{-1}\\) \\(\\triangleright\\) Eq. (12)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.674, + 0.484, + 0.689 + ], + "angle": 0, + "content": "3: Reparameterize \\(x_{t_{\\mathrm{FM}}}^{\\mathrm{FM}}\\) to \\(x_{t_{\\mathrm{DM}}}^{\\mathrm{DM}}\\) using \\(f_{x}^{-1}\\) \\(\\triangleright\\) Eq. (13)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.689, + 0.484, + 0.702 + ], + "angle": 0, + "content": "4: Approximate velocity prediction \\(\\mathbf{v}_{\\theta}\\) \\(\\triangleright\\) Eq. (16)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.703, + 0.484, + 0.717 + ], + "angle": 0, + "content": "5: Take gradient descent step on \\(\\mathcal{L}_{\\mathrm{FM}}\\) \\(\\triangleright\\) Eq. (5)" + }, + { + "type": "list", + "bbox": [ + 0.124, + 0.643, + 0.484, + 0.717 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.736, + 0.33, + 0.751 + ], + "angle": 0, + "content": "Algorithm 2 Diff2Flow Sampling" + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.755, + 0.483, + 0.77 + ], + "angle": 0, + "content": "Require: Noise sample \\(x_0^{\\mathrm{FM}}\\), Number of sampling steps \\(N\\)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.77, + 0.305, + 0.786 + ], + "angle": 0, + "content": "1: for \\( t = 0, \\frac{1}{N}, \\dots, \\frac{N - 1}{N} \\) do" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.786, + 0.483, + 0.801 + ], + "angle": 0, + "content": "2: Reparameterize \\(t_{\\mathrm{FM}}\\) to \\(t_{\\overline{\\mathrm{DM}}}\\) using \\(f_{t}^{-1}\\) \\(\\triangleright\\) Eq. (12)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.801, + 0.483, + 0.816 + ], + "angle": 0, + "content": "3: Reparameterize \\(x_{t_{\\mathrm{FM}}}^{\\mathrm{FM}}\\) to \\(x_{t_{\\mathrm{DM}}}^{\\mathrm{DM}}\\) using \\(f_{x}^{-1}\\) \\(\\triangleright\\) Eq. (13)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.816, + 0.483, + 0.829 + ], + "angle": 0, + "content": "4: Approximate velocity prediction \\(\\mathbf{v}_{\\theta}\\) \\(\\triangleright\\) Eq. (16)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.829, + 0.483, + 0.844 + ], + "angle": 0, + "content": "5: \\(x_{t + 1 / N}\\gets x_t + \\frac{1}{N}\\mathbf{v}_\\theta\\) \\(\\triangleright\\) Eq. (6)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.845, + 0.192, + 0.857 + ], + "angle": 0, + "content": "6: end for" + }, + { + "type": "text", + "bbox": [ + 0.125, + 0.858, + 0.205, + 0.872 + ], + "angle": 0, + "content": "7: return \\( x_{1} \\)" + }, + { + "type": "list", + "bbox": [ + 0.124, + 0.77, + 0.483, + 0.872 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.115, + 0.845, + 0.129 + ], + "angle": 0, + "content": "respect to the boundary conditions defined in Eq. (7):" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.14, + 0.882, + 0.213 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {v} _ {\\theta} \\left(x ^ {\\mathrm {F M}}, t _ {\\mathrm {F M}}\\right) = \\widehat {x _ {1} ^ {\\mathrm {F M}}} - \\widehat {x _ {0} ^ {\\mathrm {F M}}} \\\\ = \\widehat {x _ {0} ^ {\\mathrm {D M}}} - \\widehat {x _ {T} ^ {\\mathrm {D M}}} \\\\ = \\left(\\alpha_ {t _ {\\mathrm {D M}}} - \\sigma t _ {\\mathrm {D M}}\\right) \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} - v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right)\\right). \\tag {16} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.215, + 0.882, + 0.328 + ], + "angle": 0, + "content": "While we demonstrate the transition specifically from \\( v \\)-parameterization to velocity, this approach is versatile and can be readily applied to other parameterizations, such as \\( \\epsilon \\)-parameterization, by following the same method outlined above. Algorithm 1 and Algorithm 2 summarize this approach in more detail. In summary, our main objective is to estimate the velocity using the prediction on the diffusion trajectory. We use standard Euler steps for inference." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.339, + 0.771, + 0.354 + ], + "angle": 0, + "content": "3.3. Parameter-efficient Finetuning" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.362, + 0.884, + 0.79 + ], + "angle": 0, + "content": "Prior works [36, 47] have demonstrated that parameter-efficient finetuning (PEFT) can be advantageous in tasks like domain adaptation and model distillation for generative models. PEFT reduces the number of parameters requiring updates, lowers memory demands during training, and theoretically mitigates catastrophic forgetting [2, 21]. In our approach, we utilize Low-Rank Adaptation (LoRA) [21], which achieves parameter efficiency by freezing the main model weights and updating only a low-rank decomposition of the weight matrices. Given a weight matrix \\( W_0 \\in \\mathbb{R}^{d \\times k} \\), we freeze \\( W \\) and constrain the matrix's update with a low-rank decomposition \\( W_0 + \\Delta W = W_0 + BA \\), where \\( B \\in \\mathbb{R}^{d \\times r} \\) and \\( A \\in \\mathbb{R}^{r \\times k} \\) with the rank \\( r \\leq \\min(d, k) \\). The modified forward pass for an input \\( x \\) is then \\( h = W_0x + \\Delta Wx = W_0x + BAx \\). We observe that LoRA does not work out of the box when training a diffusion model with a flow matching objective, likely due to the shift required to adapt to a new parameterization scheme. In other words, LoRA struggles with the significant adjustment required when reconfiguring the model from a diffusion-based parameterization to a velocity prediction paradigm. This observation also underscores why naive application of a flow matching objective to a pretrained diffusion model is not effective; it forces the model to unlearn the old parameterization and switch to an entirely new one. In contrast, LoRA performs well when incorporating our proposed objective change that aligns the trajectories. Here, LoRA provides an efficient balance, achieving strong results with minimal parameter updates and showing further improvements as more parameters are fine-tuned." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.804, + 0.637, + 0.82 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.828, + 0.722, + 0.843 + ], + "angle": 0, + "content": "4.1. Text-to-Image Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.85, + 0.882, + 0.879 + ], + "angle": 0, + "content": "We start with the text-to-image task, the original task on which the diffusion prior model was trained. Specifically," + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.922, + 0.517, + 0.933 + ], + "angle": 0, + "content": "28351" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.171, + 0.113, + 0.444, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.284, + 0.484, + 0.337 + ], + "angle": 0, + "content": "Figure 3. Qualitative results for our finetuned Text-to-Image models using different objectives. DM, FM and Diff2Flow stand for diffusion finetuning, flow matching finetuning, and our method. Images are generated with the same seed, NFEs, and CFG = 4.0." + }, + { + "type": "image", + "bbox": [ + 0.166, + 0.353, + 0.432, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.524, + 0.484, + 0.566 + ], + "angle": 0, + "content": "Figure 4. Our finetuning objective, both with and without PEFT effectively addresses the issue of non-zero-terminal SNR of DMs. The generations align faithfully to the input prompts." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.592, + 0.484, + 0.663 + ], + "angle": 0, + "content": "we use Stable Diffusion 2.1 [46] as our diffusion prior, pretrained at a resolution of \\(768 \\times 768\\), and fine-tune it to generate images at a lower resolution of \\(512 \\times 512\\). This resolution shift allows us to investigate the effectiveness of different fine-tuning techniques in bridging resolution gaps." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.664, + 0.484, + 0.807 + ], + "angle": 0, + "content": "Starting from the SD2.1 prior, we continue training with different objectives on the LAION-Aesthetics dataset [53] and evaluate model performance on COCO 2017 [29]. Fig. 5 shows that simply continuing diffusion training with an FM objective yields weak performance, especially when constraining model capacity with LoRA. In contrast, our method consistently surpasses continued diffusion training, both with and without classifier-free guidance, converging in as few as \\(2.5\\mathrm{k}\\) iterations. Note that all models show poor FID results without training due to the resolution mismatch." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.822, + 0.484, + 0.879 + ], + "angle": 0, + "content": "We present qualitative results in Fig. 3 and Fig. 4, where we use the same sampling hyperparameters and fix the initial Gaussian noise. A key issue that we also address in the transition from the diffusion model to flow matching is the" + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.112, + 0.865, + 0.172 + ], + "angle": 0, + "content": "
    MethodFID ↓CLIP ↑Aesthetics Score ↑
    SD1.556.7726.345.32
    SD1.5 (cont. training)56.3626.335.90
    Diff2Flow52.8026.545.99
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.527, + 0.182, + 0.868, + 0.196 + ], + "angle": 0, + "content": "Table 1. Eval on COCO-2017 5k with 25 Euler/DDIM steps." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.22, + 0.882, + 0.277 + ], + "angle": 0, + "content": "problem of non-zero terminal SNR [28], which typically results in images generated by stable diffusion models having, on average, gray tones instead of true black or white. Our training paradigm solves this problem, illustrated in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.277, + 0.882, + 0.435 + ], + "angle": 0, + "content": "Furthermore, we investigate the scenario where diffusion training is resumed with our method without any changes in resolution or task objectives. Specifically, we initialize from an SD1.5 checkpoint and continue training on the LAION-Aesthetics dataset at a resolution of \\(512 \\times 512\\). The corresponding evaluation metrics are reported in Tab. 1. Consistent with observations in SD3 [8], the rectified trajectories of Diff2Flow yield superior performance compared to the baseline SD model. We show that converting a diffusion model to its flow-matching counterpart also leads to performance improvements within the same generative task." + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.442, + 0.742, + 0.457 + ], + "angle": 0, + "content": "4.2. Rectifying the Trajectories" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.464, + 0.884, + 0.664 + ], + "angle": 0, + "content": "In addition to fine-tuning diffusion models for resolution changes, we can also optimize them for straighter sampling trajectories to enable faster generation speeds. A popular approach to this is Reflow [32], which modifies the flow-matching training objective by replacing the random Gaussian noise terms in Eq. (5) with calculated noise derived from a pre-trained prior ODE to ensure that each noise-image pair is aligned according to the ODE. Quantitative results are presented in Tab. 3, where our method demonstrates competitive performance over various number of function evaluations (NFEs), including low NFEs such as 2 and 4, while only fine-tuning less than \\(7\\%\\) of the parameters. Qualitative results using reflow with 4 inference steps are shown in Fig. 6 and in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.671, + 0.761, + 0.687 + ], + "angle": 0, + "content": "4.3. Monocular Depth Estimation" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.693, + 0.884, + 0.88 + ], + "angle": 0, + "content": "In addition to common tasks, we also show the versatility of our approach for domain adaptation finetuning. Previous methods have shown strong performance in using largescale image generative models for affine-invariant monocular depth estimation [9, 14, 24]. Marigold [24] directly finetune Stable Diffusion on synthetic image-depth data using the standard \\(v\\)-parameterized Diffusion loss (Equation (3)). Following a similar setup, DepthFM [14] propose to convert Stable Diffusion into a flow matching model by training with the flow matching (see Equation (5)) loss. This approach requires aligning the model's outputs to a different objective, interpolant, and timestep scaling (with \\(t_{\\mathrm{DM}} \\in [0,1000]\\) in diffusion versus \\(t_{\\mathrm{FM}} \\in [0,1]\\) in flow matching)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.922, + 0.518, + 0.933 + ], + "angle": 0, + "content": "28352" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.193, + 0.111, + 0.468, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.317, + 0.208, + 0.334, + 0.219 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.111, + 0.807, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.664, + 0.208, + 0.682, + 0.219 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.23, + 0.885, + 0.298 + ], + "angle": 0, + "content": "Figure 5. Text-to-Image FID on the COCO 2017 [29] validation dataset. Light curves indicate results without Classifier-free Guidance [18]. a) We show that both FM and Diff2Flow converge to the same performance, given sufficient training and model capacity (full fine-tuning). However, our method removes the computational overhead from learning how to adjust the network output, resulting in faster convergence. b) Given limited modeling capacity (LoRA) the difference is more pronounced, where the FM model fails to close the gap to Diff2Flow, indicating that finetuning a portion of the parameters is enough to transfer a diffusion model to a flow matching model." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.309, + 0.885, + 0.501 + ], + "angle": 0, + "content": "
    MethodTraining samplesNYUv2 [40]KITTI [13]ETH3D [52]ScanNet [5]DIODE [62]
    AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑
    Depth Anything [65] (CVPR '24)62M4.398.17.694.712.788.2——6.695.2
    Depth Anything v2 [66] (arXiv '24)62M4.497.97.594.813.286.2——6.595.4
    Metric3D [68] (ICCV '23)8M5.096.65.897.06.496.57.494.122.480.5
    Metric3D v2 [22] (TPAMI '24)16M4.398.14.498.24.298.3—†—†13.689.5
    Marigold [24] (CVPR '24)74K5.596.49.991.66.596.06.495.130.877.3
    GeoWizard [9] (ECCV '24)278K5.296.69.792.16.496.16.195.329.779.2
    reproduced by [38]278K5.796.214.482.07.594.36.195.831.477.1
    DepthFM [14] (AAAI '25)74K6.095.59.190.26.595.46.694.922.478.5
    E2E FT [38] (WACV '25)74K5.296.69.691.96.295.95.896.230.277.9
    Lotus-G [16] (arXiv '24)59K5.496.611.387.76.296.16.096.0——
    Diff2Flow74K5.796.78.792.05.597.46.295.721.679.5
    Diff2Flow (LoRA)74K5.996.49.590.86.096.86.495.522.678.5
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.112, + 0.512, + 0.884, + 0.553 + ], + "angle": 0, + "content": "Table 2. Comparison to state-of-the-art depth estimation methods. We compare discriminative (top) and generative models (bottom). Numbers obtained from [38]. \\( {}^{ \\dagger } \\) Metric3D v2 [22] was trained on ScanNet,so zero-shot evaluation is not possible. We also show the results reproduced by [38] for GeoWizard. All of our results are generated with NFE= 10 and an ensemble size of 4 ." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.574, + 0.487, + 0.699 + ], + "angle": 0, + "content": "
    Method#Params ↓StepsFID ↓CLIP ↑
    SDv1.5+DPM Solver [34] (NeurIPS '22)0.9B2520.100.318
    Rectified Flow [32] (ICLR '23)0.9B2521.650.315
    Diff2Flow (LoRA)62M2521.450.314
    PeRFlow [64] (arXiv '24)0.9B422.970.294
    Diff2Flow (LoRA)62M425.290.313
    Rectified Flow [32] (ICLR '23)0.9B231.350.296
    Diff2Flow (LoRA)62M232.310.305
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.71, + 0.484, + 0.749 + ], + "angle": 0, + "content": "Table 3. We fine-tune all our models with LoRA, and apply only 1-rectified flow according to Liu et al. [32]. We get competitive results with state-of-the-art reflow models." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.779, + 0.484, + 0.88 + ], + "angle": 0, + "content": "This process incurs significant computational cost, limiting the training efficiency and final performance. However, the flow matching nature of DepthFM allows for faster inference, at slightly reduced performance when given enough training. Our method mitigates this problem, accelerating training, and improving performance. The training and evaluation metrics are provided in the Appendix." + }, + { + "type": "image", + "bbox": [ + 0.552, + 0.574, + 0.648, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.574, + 0.743, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.743, + 0.574, + 0.839, + 0.648 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.662, + 0.882, + 0.675 + ], + "angle": 0, + "content": "Figure 6. SD1.5 [46] + Diff2Flow-Reflow, 4-step inference results." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.708, + 0.884, + 0.879 + ], + "angle": 0, + "content": "Results Table 2 compares our method with both discriminative and generative depth predictors. Trained exclusively on synthetic data, our method matches or outperforms the prior state-of-the-art in monocular depth estimation, as shown in Figure 8. The diffusion-based Marigold model [24] struggles to achieve high accuracy with a limited number of sampling steps. In contrast to both DepthFM and Marigold, our method achieves competitive performance after very few training iterations and with only two sampling steps. The performance difference becomes even more pronounced when training with LoRA, where model capacity is limited. Figure 8b shows that this limitation prevents a" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.922, + 0.518, + 0.934 + ], + "angle": 0, + "content": "28353" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.128, + 0.112, + 0.861, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.291, + 0.884, + 0.319 + ], + "angle": 0, + "content": "Figure 7. Zero-shot qualitative results on real-world imagery. Our methods produce depth predictions with perceptually higher fidelity and finer detail. All predictions are made using the optimal settings of the models. Best viewed when zoomed in." + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.331, + 0.466, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.276, + 0.427, + 0.292, + 0.438 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.331, + 0.844, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.655, + 0.427, + 0.671, + 0.438 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.45, + 0.884, + 0.515 + ], + "angle": 0, + "content": "Figure 8. Results on NYUv2 depth benchmark [40] with 4 ensemble members. a) With full fine-tuning we find that FM adapts to the I2D task very quickly, but adding the objective change leads to even quicker convergence and better results. In contrast, the diffusion-based counterpart [24] suffers from slower convergence and requires more inference steps. b) The difference between FM and Diff2Flow is even more pronounced if we limit the capacity of the model by using Low-Rank adaptations. With Diff2Flow, the model does not need to learn to change the objective and can focus only on the task itself." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.541, + 0.484, + 0.77 + ], + "angle": 0, + "content": "straightforward application of the FM loss to the diffusion model. DepthFM struggles here as the model has to learn the adaptation from the \\( v \\)-parameterization to the FM objective. The successful adaptation of the diffusion-based image prior to flow matching supports our initial hypothesis that the integration of our objective change facilitates this transformation. In Table 4, we present an ablation study on performance with different numbers of trainable parameters. Fine-tuning just \\( 1/4 \\) of the original parameters is sufficient to achieve competitive performance with previous methods, particularly with the fully finetuned DepthFM model. Figure 7 qualitatively compares our method with state-of-the-art depth estimators on in-the-wild images. While discriminative methods often lack detail and fidelity, generative models capture fine details and avoid the averaging effect common to discriminative approaches." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.783, + 0.225, + 0.798 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.807, + 0.484, + 0.88 + ], + "angle": 0, + "content": "We introduce a novel framework, Diff2Flow, that effectively converts pre-trained diffusion into flow matching models, providing a twofold optimization. First, this approach allows us to efficiently use the diffusion model's prior by exploiting its powerful generative capabilities with" + }, + { + "type": "table", + "bbox": [ + 0.537, + 0.538, + 0.858, + 0.617 + ], + "angle": 0, + "content": "
    Method#Params ↓AbsRel ↓δ1 ↑
    Marigold + E2E FT [38]866M5.296.6
    Diff2Flow866M5.796.7
    Diff2Flow (LoRA base)222M5.996.4
    Diff2Flow (LoRA small)62M6.995.0
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.627, + 0.884, + 0.667 + ], + "angle": 0, + "content": "Table 4. Zero-shot evaluation on NYUv2 [40] for different number of trainable parameters. We can achieve competitive performance with only a fraction of previous SOTA methods." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.693, + 0.884, + 0.879 + ], + "angle": 0, + "content": "out retraining from scratch. Second, by adapting it to the flow matching paradigm, we gain key benefits unique to flow matching: fast inference suitable for downstream tasks, and the ability to straighten sampling trajectories through techniques such as reflow, which further improves efficiency and performance. As a result, Diff2Flow not only improves training and inference efficiency but also delivers competitive performance in diverse tasks, including text-to-image synthesis and monocular depth estimation. By using parameter-efficient fine-tuning methods such as LoRA, our framework further minimizes computational requirements and demonstrates a practical, scalable way to merge diffusion and flow matching paradigms in generative modeling." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.922, + 0.518, + 0.933 + ], + "angle": 0, + "content": "28354" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.114, + 0.113, + 0.266, + 0.129 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.136, + 0.486, + 0.309 + ], + "angle": 0, + "content": "This project has been supported by the bidders project KLIMA-MEMES, the German Federal Ministry for Economic Affairs and Climate Action within the project \"NXT GEN AI METHODS - Generative Methoden für Percep tion, Prädiktion und Planung\", the project \"GeniusRobot\" (01IS24083), funded by the Federal Ministry of Education and Research (BMBF), and the German Research Foundation (DFG) project 421703927. The authors acknowledge the Gauss Center for Supercomputing for providing compute through the NIC on JUWELS at JSC and the HPC resources supplied by the Erlangen National High Performance Computing Center (NHR@FAU funded by DFG project 440719683) under the NHR project JA-22883." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.331, + 0.206, + 0.345 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.122, + 0.354, + 0.484, + 0.406 + ], + "angle": 0, + "content": "[1] Michael S Albergo, Nicholas M Boffi, and Eric Vanden-Eijnden. Stochastic interpolants: A unifying framework for flows and diffusions. arXiv preprint arXiv:2303.08797, 2023. 1, 2, 3, 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.122, + 0.407, + 0.484, + 0.473 + ], + "angle": 0, + "content": "[2] Dan Biderman, Jacob Portes, Jose Javier Gonzalez Ortiz, Mansheej Paul, Philip Greengard, Connor Jennings, Daniel King, Sam Havens, Vitaliy Chiley, Jonathan Frankle, et al. 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However, current foundation FM models are computationally prohibitive for finetuning, while diffusion models like Stable Diffusion benefit from efficient architectures and ecosystem support. This work addresses the critical challenge of efficiently transferring knowledge from pre-trained diffusion models to flow matching. We propose Diff2Flow, a novel framework that systematically bridges diffusion and FM paradigms by rescaling timesteps, aligning interpolants, and deriving FM-compatible velocity fields from diffusion predictions. This alignment enables direct and efficient FM finetuning of diffusion priors with no extra computation overhead. Our experiments demonstrate that Diff2Flow outperforms naive FM and diffusion finetuning particularly under parameter-efficient constraints, while achieving superior or competitive performance across diverse downstream tasks compared to state-of-the-art methods. We will release our code at https://github.com/CompVis/diff2flow. + +# 1. Introduction + +Recently, diffusion models [19, 57] have gained substantial popularity due to their exceptional generative capabilities, which have redefined the boundaries of image generation [42, 43, 46, 48]. Among these, foundation models such as Stable Diffusion [46] stand out, not only for their high-fidelity outputs but also for their useful representations and adaptability to downstream tasks, including depth estimation [14, 24], surface normal prediction [7], segmentation [63], and semantic correspondences [11, 60]. + +Meanwhile, Flow Matching (FM) [1, 30, 32] has emerged as a promising alternative, empirically offering faster inference and improved performance [8, 37]. While state-of-the-art foundational models based on flow matching, such as Flux [26] or SDv3 [8], show remarkable generative capabilities, their large size ( $>8\mathrm{B}$ parameters) requires + +high-end hardware for both training and inference, making them particularly computationally expensive. This makes fine-tuning impractical, especially in resource-constrained environments and significantly limits their practical adoption. In contrast, Stable Diffusion's [46] efficient architecture and widespread ecosystem make it a pragmatic choice. This raises an important question: Can the knowledge captured by existing foundational diffusion models be efficiently transferred to a flow matching model? How can we bridge the gap between diffusion and flow matching with minimal additional training, leveraging both the pre-trained prior and the advantageous properties of flow matching? + +This work explores the relationship between the diffusion and flow matching paradigms. Although both methods can be generalized under a common framework [1, 25, 37], the actual implementations differ in several key aspects, including the definition of interpolants between the Gaussian noise prior and data samples, timestep scaling, and training objectives. These differences make it difficult to directly use a pre-trained diffusion model as a starting prior for flow matching training, as the two paradigms are not inherently well aligned. + +To address this challenge, we propose a novel framework that effectively "warps" diffusion into flow matching, enabling seamless knowledge transfer between the two paradigms. This requires re-scaling their respective timesteps, aligning their differing interpolant formulations, and deriving the velocity field required for flow matching from the diffusion model's predictions, based on its parameterization. By systematically establishing these correspondences, we enable a smooth transition between diffusion and flow matching. To this end, we introduce a training methodology termed Diff2Flow, which initializes the flow matching model with a pretrained diffusion prior and directly finetunes it using the flow matching objective. Our analysis reveals that directly applying the FM loss to a diffusion model without incorporating our proposed adjustments significantly slows convergence and degrades overall model performance, whereas Diff2Flow provides a flexible and efficient approach with minimal finetuning overhead. + +The benefits of this alignment become particularly evident when finetuning only a small subset of parameters. + +Under such constrained computational budgets, the performance gap between naïve FM finetuning and our alignment-aware approach becomes more pronounced. Specifically, we show that directly applying the FM objective with parameter efficient finetuning (PEFT) leads to very suboptimal performance. Leveraging Diff2Flow with its alignment-informed training strategy, PEFT enhances training efficiency and minimizes memory consumption while maintaining high performance. + +We show the efficiency of our method on a diverse set of downstream tasks. ① We show that when finetuning on a high-aesthetics dataset [6] on the text-to-image task, we outperform diffusion-based finetuning while converging significantly faster than naively training with the flow matching objective. This empirically demonstrates that smartly aligning timestep scaling and objective significantly facilitate learning, and additionally mitigate the zero-terminal SNR issue [28] common in diffusion models, where full black or white images can't be generated. ② When repurposing the model to generate images at resolutions different from the pre-trained sweet-spot resolution (similar to [17]), our method achieves superior results compared to standard diffusion and flow matching fine-tuning. ③ We show that we can apply Reflow [32] using Diff2Flow on a base diffusion model, a method that straightens sampling trajectories, resulting in faster inference speed. By rectifying the sampling trajectories of Stable Diffusion v1.5 we can generate images with as few as 2 sampling steps without consistency distillation [58]. ④ Finally, we demonstrate the effectiveness of our method on domain adaptation, leveraging the Stable Diffusion prior to predicting affine-invariant depth maps similar to Marigold [24] and DepthFM [14], achieving state-of-the-art results with reduced training time. + +# 2. Related Work + +Diffusion and Flow Matching Models Diffusion models [19, 57] have demonstrated wide-ranging capabilities in data synthesis, extending from image [10, 44, 46, 48] and video [3, 15, 20] to audio generation [31] and beyond. While these models excel at producing high-fidelity outputs, they often require extensive sampling time, necessitating techniques like distillation [39, 49, 50, 58], noise schedule optimization [23], or training-free sampling [34, 56] to achieve faster generation. Following diffusion models, flow matching models [1, 30, 32] have gained attention due to their benefit of straighter probability paths. These models have been shown to perform competitively or surpass diffusion models in terms of both speed and quality [8, 37, 54]. + +The relationship between diffusion and flow matching models has been explored in Lee et al. [27], demonstrating that finetuning a flow matching model based on a pretrained diffusion model is feasible. Our work extends this by explicitly formulating a method to map discrete diffu + +![](images/ed31aa870acccdc5eac51072d97d3fcd34088abf7708123b196ffa196d32b9b7.jpg) +Figure 1. We introduce a novel finetuning technique to traverse between flow matching and diffusion, which enables effectively aligning the two processes with minimal additional training. The interpolant on the flow matching trajectory is computed as a function $f$ of the diffusion timestep $t$ , the sample $x$ , and the associated diffusion coefficients. Our approach further enables a velocity prediction $\hat{\mathbf{v}}$ regardless of the diffusion model's parameterization. + +sion trajectory to a continuous flow matching trajectory. Furthermore, we empirically demonstrate that our strategy works for various diffusion parameterization objectives and present results that go beyond reflow [32], achieving competitive performance on several benchmarks. + +Parameter-efficient Finetuning As foundational models expand in size and complexity, parameter-efficient finetuning (PEFT) techniques such as Low-Rank Adaptation (LoRA) [21] offer viable alternatives to full model finetuning. Originally developed for large language models, LoRA and other PEFT techniques have since been applied effectively to diffusion models [47], proving valuable across a broad range of tasks. These include domain-specific finetuning [67], additional image conditioning [59], image editing [12], distillation [36] and among others. By updating only a low-rank decomposition of the weight matrix, LoRA reduces memory requirements and alleviate catastrophic forgetting [2], making it highly adaptable for targeted adjustments in large foundational models. + +Knowledge in Generative Models Following the rise of text-to-image diffusion models [41, 43, 44, 46, 48], numerous studies have explored methods to extract information from diffusion priors. Many works have effectively utilized the diffusion prior for tasks such as monocular depth estimation [9, 14, 16, 24, 38, 51], surface normal prediction [7], and semantic correspondences [11, 35, 60]. While these approaches predominantly focus on distilling information into another diffusion model, our work explores the transfer of this knowledge to flow matching models and hereby leverages the inherent advantages of flow matching, including more efficient inference and enhanced task performance. + +# 3. Method + +In this section, we explain our algorithm and the process of aligning the trajectories. We begin by discussing the definition of diffusion and flow matching models. Following this, we describe how we traverse between the two trajectories as depicted in Fig. 1 and use the diffusion model to generate a reasonable estimate of the flow velocity. + +# 3.1. Diffusion and Flow Matching + +Diffusion models (DM) [19, 56, 57] gradually diffuse data by typically adding noise to real data samples $x_0 \sim p_0(x_0)$ in a predefined discrete forward process, which can be characterized by + +$$ +p \left(x _ {t} \mid x _ {0}\right) = \mathcal {N} \left(x _ {t}; \alpha_ {t} x _ {0}, \sigma_ {t} ^ {2} \mathbf {I}\right), \tag {1} +$$ + +where $\alpha_{t}$ and $\sigma_{t}$ are the predefined noise schedules, $t$ is the discrete timestep, and $x_{t}$ is the resulting noisy sample, often referred to as the interpolant. In the setting of variance preserving schedules $\sigma_{t} = \sqrt{1 - \alpha_{t}^{2}}$ , and the interpolant $x_{t}$ is then $x_{t} = \alpha_{t}x_{0} + \sqrt{1 - \alpha_{t}^{2}}\epsilon$ with $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ . A neural network, parameterized by $\theta$ , is learned to reverse the forward process by gradually removing noise from $x_{t}$ . Ho et al. [19] propose the simplified loss term + +$$ +\mathcal {L} _ {\text {s i m p l e}} = \mathbb {E} _ {t, \epsilon , x _ {0} \sim p (x _ {0})} | | \epsilon_ {t} - \epsilon_ {\theta} (x _ {t}, t) | | ^ {2}, \tag {2} +$$ + +where predicting $\epsilon$ instead of $x_0$ is observed to yield better results and enhance convergence. There also exists the $v$ -parameterization [49], defined as + +$$ +v _ {t} = \alpha_ {t} \epsilon - \sigma_ {t} x _ {0}. \tag {3} +$$ + +Flow matching (FM) models [1, 30, 32], another flexible class of generative models, utilizes the same idea of gradually deteriorating data samples and then synthesizing new data by reversing the process. We adopt the setting from Lipman et al. [30] where $x_0$ represents noise, and $x_{1}$ corresponds to data. The interpolant on the continuous timesteps $t\in [0,1]$ is defined as + +$$ +x _ {t} = t x _ {1} + (1 - t) x _ {0}, \tag {4} +$$ + +where $x_0$ is typically a Gaussian noise sample. The model $\mathbf{v}_{\theta}$ is trained to regress a vector field along the trajectory, following the linear path that points from $x_0$ to $x_1$ using the following objective: + +$$ +\mathcal {L} _ {\mathrm {F M}} = \mathbb {E} _ {t, x _ {0} \sim \mathcal {N} (0, \mathbf {I}), x _ {1} \sim p (x _ {1})} | | (x _ {1} - x _ {0}) - \mathbf {v} _ {\theta} (x _ {t}, t) | | ^ {2}. \tag {5} +$$ + +Sampling from a flow matching model is accomplished by integrating over the trajectory of the learned ODE, e.g. using the forward Euler method with the update rule + +$$ +x _ {t + t _ {\Delta}} = x _ {t} + t _ {\Delta} \mathbf {v} _ {\theta} \left(x _ {t}, t\right) \quad \forall t \in [ 0, 1), \tag {6} +$$ + +![](images/9081a7732ea58e32104025b51711d3579b5b8bbe42aed62f2b565d12db2c9460.jpg) +Normal timesteps $t_{\mathrm{DM}}$ +Figure 2. Although non-integer-shifted DDIM timesteps are neither defined nor trained, generated images remain of high quality. + +![](images/9699245a95cfa8af7539d90e69a4b91e20895de3da817142b443be717c983fd7.jpg) +Shifted timesteps $t_{\mathrm{DM}}$ + +with $t_{\delta} = 1 / N$ and $N$ being the number of function evaluations (NFE). We generate a discrete sequence that approximates the path by advancing in small increments along the ODE. The trajectory's smoothness, or "straightness," is critical, as it determines the number of steps required to achieve accurate results, trading off computational cost and fidelity. Straighter paths allow smaller $N$ , whereas paths with higher curvature require more steps for simulating the ODE. + +Reflow In FM training, we randomly sample from a Gaussian distribution and form pairs with the data points to create the interpolant $x_{t}$ . This random pairing leads to curved sampling trajectories, increasing the curvature of the ODE trajectories during inference [61]. To straighten these trajectories, Liu et al. [32] propose Reflow, which iteratively trains on samples obtained from a pre-trained flow matching model. Given an already trained ODE model $\mathbf{v}_{\Phi}$ , Reflow first samples $x_0 \sim \mathcal{N}(0,\mathbf{I})$ and integrates along the ODE trajectory using Eq. (6) to obtain a corresponding data sample $x_{1}$ . This process generates image-noise pairings. Training on this paired data has been found to reduce inference cost by straightening the sampling trajectories [32, 33, 64]. + +# 3.2. Diffusion Prior for Flow Matching Model + +Flow matching methods are known for straighter trajectories and more efficient inference [14, 61]. Hence, transforming the diffusion prior into a flow matching equivalent offers the potential for improvements in inference speed and performance [8, 37]. While previous research has successfully adapted diffusion priors for other downstream diffusion tasks, our approach combines these advantages with those of flow matching models. + +Importantly, recent works on utilizing flow matching models to inherit a diffusion prior for downstream applications, such as DepthFM [14], have shown significant promise in accelerating inference compared to diffusion models. While this approach provides faster sampling than its diffusion model's counterpart, this inheritance method has limitations: DepthFM finetunes from a $v$ -parameterized text-to-image diffusion model [46] directly. This approach requires the flow matching model to "warp" the $v$ -parameterization to predict velocity, a different parameterization scheme. This introduces misalignments in the training objective, the interpolant, and the timesteps. + +To address these limitations, we propose a novel strategy that enables a seamless transition between diffusion and flow matching trajectories. Our method minimizes misalignments and yields more accurate velocity predictions. In addition to monocular depth estimation, we demonstrate that our approach generalizes to other downstream tasks and offers a versatile and efficient solution for leveraging prior information from diffusion model. + +# 3.2.1 Traversing Between Trajectories + +Let us transform a foundation diffusion model's trajectory $x_{t}$ by applying two invertible operations, one $f_{t}$ that reparameterizes $t \in [0,T]$ and one $f_{x}$ that transforms $x$ to an alternate trajectory, defined by the following equation: + +$$ +\bar {x} \left(f _ {t}\right) = f _ {x} \left(x _ {f _ {t}}\right). \tag {7} +$$ + +The boundary conditions need to satisfy $\bar{x}(f_0) = x_0$ and $\bar{x}(f_T) = x_T$ to ensure that the starting and target samples are the same. This is different to Shaul et al. [55] since our approach rectifies the trajectories, which requires the exact alignment of the starting and the target distribution. + +In order to construct $f_{t}$ and $f_{x}$ reasonably, we need to probe into the diffusion and flow matching model and investigate how the interpolants are related. Let $x^{\mathrm{DM}}$ represent a data sample on the diffusion trajectory and $x^{\mathrm{FM}}$ a data sample on the flow matching trajectory. Similarly, $t_{\mathrm{DM}}$ is the diffusion timestep and $t_{\mathrm{FM}}$ is the flow matching timestep. Following the convention of diffusion and flow matching literature [1, 19, 30, 32, 57], diffusion operates on discrete timesteps $t_{\mathrm{DM}} \in \mathbb{Z}_{\geq 0} \cap [0,T]$ , where $x_{t_{\mathrm{DM}} = 0}^{\mathrm{DM}}$ represents the data samples and $x_{t_{\mathrm{DM}} = T}^{\mathrm{DM}}$ corresponds to the Gaussian noise. In contrast, flow matching uses continuous timesteps $t_{\mathrm{FM}} \in [0,1]$ with $x_{t_{\mathrm{FM}} = 1}^{\mathrm{FM}}$ representing the data samples and $x_{t_{\mathrm{FM}} = 0}^{\mathrm{FM}}$ representing the Gaussian noise. To summarize, the boundary condition enforces $x_{t_{\mathrm{DM}} = 0}^{\mathrm{DM}} = x_{t_{\mathrm{FM}} = 1}^{\mathrm{FM}}$ and $x_{t_{\mathrm{DM}} = T}^{\mathrm{DM}} = x_{t_{\mathrm{FM}} = 0}^{\mathrm{FM}}$ , while we seek two invertible mappings $f_{t}: [0,T] \to [0,1]$ which maps $t_{\mathrm{DM}}$ to $t_{\mathrm{FM}}$ , and $f_{x}: [0,1] \times \mathbb{R}^{d} \to \mathbb{R}^{d}$ which maps $x^{\mathrm{DM}}$ to $x^{\mathrm{FM}}$ . The diffusion interpolant is + +$$ +x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}} = \alpha_ {t _ {\mathrm {D M}}} x _ {0} ^ {\mathrm {D M}} + \sigma_ {t _ {\mathrm {D M}}} x _ {T} ^ {\mathrm {D M}}, \tag {8} +$$ + +where $\alpha_{t_{\mathrm{DM}}}^2 +\sigma_{t_{\mathrm{DM}}}^2 = 1$ for the variance-preserving schedule and $\alpha_{t_{\mathrm{DM}}} = 1$ $\forall t_{\mathrm{DM}}$ with $\sigma_{t_{\mathrm{DM}}}$ monotonically increasing over time for the variance-exploding schedule [19, 57]. + +The flow matching interpolant is defined as + +$$ +x _ {t _ {\mathrm {F M}}} ^ {\mathrm {F M}} = t _ {\mathrm {F M}} x _ {1} ^ {\mathrm {F M}} + \left(1 - t _ {\mathrm {F M}}\right) x _ {0} ^ {\mathrm {F M}}. \tag {9} +$$ + +There are multiple ways to define $f_{x}$ so that the diffusion trajectory can be transformed and warped into a linear equa + +tion, one being + +$$ +\begin{array}{l} f _ {x} \left(x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}}\right) = \frac {\alpha_ {t _ {\mathrm {D M}}}}{\alpha_ {t _ {\mathrm {D M}}} + \sigma_ {t _ {\mathrm {D M}}}} x _ {0} ^ {\mathrm {D M}} + \frac {\sigma_ {t _ {\mathrm {D M}}}}{\alpha_ {t _ {\mathrm {D M}}} + \sigma_ {t _ {\mathrm {D M}}}} x _ {T} ^ {\mathrm {D M}} \tag {10} \\ = \frac {1}{\alpha_ {t _ {\mathrm {D M}}} + \sigma_ {t _ {\mathrm {D M}}}} x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}}, \\ \end{array} +$$ + +yielding a scaled version of $x_{t_{\mathrm{DM}}}^{\mathrm{DM}}$ + +To design $f_{t}$ as an invertible mapping between the discrete space $t_{\mathrm{DM}}$ and the continuous space $t_{\mathrm{FM}}$ , we start by establishing an invertible transformation function that enables continuous interpolation between discrete points in $t_{\mathrm{DM}}$ while aligning with $f_{x}$ . To ensure continuity and invertibility, we define $f_{t}$ as a piecewise linear function and interpolate between these discrete points. Let $t_{\overline{\mathrm{DM}}} \in [0,T]$ be a continuous interpolated time space of the discrete $t_{\mathrm{DM}}$ . The correlation between Eq. (9) and Eq. (10) allows to calculate $t_{\mathrm{FM}}$ via the diffusion coefficients: + +$$ +f _ {t} \left(t _ {\mathrm {D M}}\right) = \frac {\alpha_ {t _ {\mathrm {D M}}}}{\alpha_ {t _ {\mathrm {D M}}} + \sigma_ {t _ {\mathrm {D M}}}}, \tag {11} +$$ + +where in both variance-preserving and variance-exploding diffusion schedules $f_{t}(t_{\mathrm{DM}})$ is monotonic. While the diffusion coefficients $\alpha_{t}$ and $\sigma_{t}$ are not defined for all $t_{\overline{\mathrm{DM}}}$ , we interpolate between the corresponding nearest neighbors. Let $t_{\mathrm{DM}_1}$ and $t_{\mathrm{DM}_2}$ be the nearest neighbors of $t_{\overline{\mathrm{DM}}}$ and we design $f_{t}$ to be just as a linear interpolation in between. Interestingly, we find that although the continuous values of $t_{\overline{\mathrm{DM}}}$ were not trained during the foundation model's training, direct inference with these values still produces reasonable results, as shown in Fig. 2. Specifically, instead of performing DDIM inference at discrete timesteps $t_{\mathrm{DDIM}} \in \mathbb{Z}_{\geq 0} \cap [0,1000]$ , we do inference at $t_{\mathrm{DDIM}} + 0.5$ with linearly interpolated $\alpha_{t}$ and $\sigma_{t}$ . We hypothesize that timesteps represented as sinusoidal embeddings create a well-defined continuous time space. This observation lays the foundation for interpolating timestep embeddings and traversing trajectories. + +With $t_{\overline{\mathrm{DM}}}$ defined on the continuous domain, the inverse $f_{t}^{-1}(t_{\mathrm{FM}})$ can be defined as follows. First, we find $t_{\mathrm{DM}_1}$ and $t_{\mathrm{DM}_2}$ in the discrete timesteps such that $f_{t}(t_{\mathrm{DM}_{1}})$ and $f_{t}(t_{\mathrm{DM}_{2}})$ are the two nearest neighbors of $t_{\mathrm{FM}}$ with $f_{t}(t_{\mathrm{DM}_{1}})\leqslant t_{\mathrm{FM}}\leqslant f_{t}(t_{\mathrm{DM}_{2}})$ . Next, we perform a linear interpolation between the two neighbors to reverse the mapping from $t_\mathrm{FM}$ to $t_{\overline{\mathrm{DM}}}$ : + +$$ +f _ {t} ^ {- 1} \left(t _ {\mathrm {F M}}\right) = t _ {\mathrm {D M} _ {1}} + \frac {t _ {\mathrm {F M}} - f _ {t} \left(t _ {\mathrm {D M} _ {1}}\right)}{f _ {t} \left(t _ {\mathrm {D M} _ {2}}\right) - f _ {t} \left(t _ {\mathrm {D M} _ {1}}\right)} \left(t _ {\mathrm {D M} _ {2}} - t _ {\mathrm {D M} _ {1}}\right). \tag {12} +$$ + +With $f_{t}(\cdot)$ bidirectionally defined as in Eq. (11) and Eq. (12), we deduce the bidirectional mapping from the FM trajectory $x^{\mathrm{FM}}$ back to the DM trajectory $x^{\mathrm{DM}}$ : + +$$ +f _ {x} ^ {- 1} \left(x _ {t _ {\mathrm {F M}}} ^ {\mathrm {F M}}\right) = \left(\alpha_ {f _ {t} ^ {- 1} \left(t _ {\mathrm {F M}}\right)} + \sigma_ {f _ {t} ^ {- 1} \left(t _ {\mathrm {F M}}\right)}\right) x _ {t _ {\mathrm {F M}}} ^ {\mathrm {F M}}. \tag {13} +$$ + +# 3.2.2 Unifying the Objectives + +While traversing between the diffusion and flow matching trajectories is explained in the previous chapter, it is still essential to unify the training and inference objectives. Prior works [14, 64] fine-tuned the model to adapt the diffusion prior, originally predicting $\epsilon$ or $v$ , to directly predict velocity. However, these approaches force the model to transition between different parameterizations, therefore requiring longer convergence times and also ultimately impacting model performance. In contrast, our method unites the objectives by leveraging the diffusion prior and utilizing the relationships between the parameterizations. We term this technique Objective change as we incorporate both trajectory traversal and a principled objective realignment to facilitate velocity prediction based on the diffusion prior. This approach is broadly applicable across different parameterizations; here, we demonstrate its effectiveness using $v$ -parameterization. + +Let $v_{\theta}(x^{\mathrm{DM}}, t_{\mathrm{DM}})$ be the $v$ -prediction (Eq. (3)) from a pre-trained diffusion model. Using the notation of Eq. (8) + +$$ +v _ {\theta} \left(x ^ {\mathrm {D M}}, t _ {\mathrm {D M}}\right) = \alpha_ {t _ {\mathrm {D M}}} x _ {T} ^ {\mathrm {D M}} - \sigma_ {t _ {\mathrm {D M}}} x _ {0} ^ {\mathrm {D M}} \tag {14} +$$ + +where $x_0$ and the corresponding $x_{T}$ can be estimated as + +$$ +\widehat {x _ {0} ^ {\mathrm {D M}}} = \alpha_ {t _ {\mathrm {D M}}} x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}} - \sigma_ {t _ {\mathrm {D M}}} v _ {\theta} \left(x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}}, t _ {\mathrm {D M}}\right) \tag {15} +$$ + +$$ +\widehat {x _ {T} ^ {\mathrm {D M}}} = \alpha_ {t _ {\mathrm {D M}}} v _ {\theta} \left(x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}}, t _ {\mathrm {D M}}\right) - \sigma_ {t _ {\mathrm {D M}}} x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}}, +$$ + +with the wide hat symbol indicating an estimate predicted by the model. An approximation for the velocity $\mathbf{v}$ at the corresponding FM data point $x^{\mathrm{FM}}$ is then formulated with + +# Algorithm 1 Diff2Flow Training + +Require: Data Sample $x_{1}^{\mathrm{FM}}$ , Noise sample $x_{0}^{\mathrm{FM}}$ , Timestep $t_{\mathrm{FM}} \in [0,1]$ + +1: Compute the interpolant $x_{t_{\mathrm{FM}}}^{\mathrm{FM}}$ $\triangleright$ Eq. (9) +2: Reparameterize $t_{\mathrm{FM}}$ to $t_{\overline{\mathrm{DM}}}$ using $f_{t}^{-1}$ $\triangleright$ Eq. (12) +3: Reparameterize $x_{t_{\mathrm{FM}}}^{\mathrm{FM}}$ to $x_{t_{\mathrm{DM}}}^{\mathrm{DM}}$ using $f_{x}^{-1}$ $\triangleright$ Eq. (13) +4: Approximate velocity prediction $\mathbf{v}_{\theta}$ $\triangleright$ Eq. (16) +5: Take gradient descent step on $\mathcal{L}_{\mathrm{FM}}$ $\triangleright$ Eq. (5) + +# Algorithm 2 Diff2Flow Sampling + +Require: Noise sample $x_0^{\mathrm{FM}}$ , Number of sampling steps $N$ + +1: for $t = 0, \frac{1}{N}, \dots, \frac{N - 1}{N}$ do +2: Reparameterize $t_{\mathrm{FM}}$ to $t_{\overline{\mathrm{DM}}}$ using $f_{t}^{-1}$ $\triangleright$ Eq. (12) +3: Reparameterize $x_{t_{\mathrm{FM}}}^{\mathrm{FM}}$ to $x_{t_{\mathrm{DM}}}^{\mathrm{DM}}$ using $f_{x}^{-1}$ $\triangleright$ Eq. (13) +4: Approximate velocity prediction $\mathbf{v}_{\theta}$ $\triangleright$ Eq. (16) +5: $x_{t + 1 / N}\gets x_t + \frac{1}{N}\mathbf{v}_\theta$ $\triangleright$ Eq. (6) +6: end for +7: return $x_{1}$ + +respect to the boundary conditions defined in Eq. (7): + +$$ +\begin{array}{l} \mathbf {v} _ {\theta} \left(x ^ {\mathrm {F M}}, t _ {\mathrm {F M}}\right) = \widehat {x _ {1} ^ {\mathrm {F M}}} - \widehat {x _ {0} ^ {\mathrm {F M}}} \\ = \widehat {x _ {0} ^ {\mathrm {D M}}} - \widehat {x _ {T} ^ {\mathrm {D M}}} \\ = \left(\alpha_ {t _ {\mathrm {D M}}} - \sigma t _ {\mathrm {D M}}\right) \left(x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}} - v _ {\theta} \left(x _ {t _ {\mathrm {D M}}} ^ {\mathrm {D M}}, t _ {\mathrm {D M}}\right)\right). \tag {16} \\ \end{array} +$$ + +While we demonstrate the transition specifically from $v$ -parameterization to velocity, this approach is versatile and can be readily applied to other parameterizations, such as $\epsilon$ -parameterization, by following the same method outlined above. Algorithm 1 and Algorithm 2 summarize this approach in more detail. In summary, our main objective is to estimate the velocity using the prediction on the diffusion trajectory. We use standard Euler steps for inference. + +# 3.3. Parameter-efficient Finetuning + +Prior works [36, 47] have demonstrated that parameter-efficient finetuning (PEFT) can be advantageous in tasks like domain adaptation and model distillation for generative models. PEFT reduces the number of parameters requiring updates, lowers memory demands during training, and theoretically mitigates catastrophic forgetting [2, 21]. In our approach, we utilize Low-Rank Adaptation (LoRA) [21], which achieves parameter efficiency by freezing the main model weights and updating only a low-rank decomposition of the weight matrices. Given a weight matrix $W_0 \in \mathbb{R}^{d \times k}$ , we freeze $W$ and constrain the matrix's update with a low-rank decomposition $W_0 + \Delta W = W_0 + BA$ , where $B \in \mathbb{R}^{d \times r}$ and $A \in \mathbb{R}^{r \times k}$ with the rank $r \leq \min(d, k)$ . The modified forward pass for an input $x$ is then $h = W_0x + \Delta Wx = W_0x + BAx$ . We observe that LoRA does not work out of the box when training a diffusion model with a flow matching objective, likely due to the shift required to adapt to a new parameterization scheme. In other words, LoRA struggles with the significant adjustment required when reconfiguring the model from a diffusion-based parameterization to a velocity prediction paradigm. This observation also underscores why naive application of a flow matching objective to a pretrained diffusion model is not effective; it forces the model to unlearn the old parameterization and switch to an entirely new one. In contrast, LoRA performs well when incorporating our proposed objective change that aligns the trajectories. Here, LoRA provides an efficient balance, achieving strong results with minimal parameter updates and showing further improvements as more parameters are fine-tuned. + +# 4. Experiments + +# 4.1. Text-to-Image Synthesis + +We start with the text-to-image task, the original task on which the diffusion prior model was trained. Specifically, + +![](images/ffaed77126368d386aa79621bf5d4fb29c263ee39e2dcaf4c73ca2e18f0d3209.jpg) +Figure 3. Qualitative results for our finetuned Text-to-Image models using different objectives. DM, FM and Diff2Flow stand for diffusion finetuning, flow matching finetuning, and our method. Images are generated with the same seed, NFEs, and CFG = 4.0. + +![](images/b622d6684982948d4a6fea8c1c52849c4bd72cbb7174fd63bdf140398e5fce78.jpg) +Figure 4. Our finetuning objective, both with and without PEFT effectively addresses the issue of non-zero-terminal SNR of DMs. The generations align faithfully to the input prompts. + +we use Stable Diffusion 2.1 [46] as our diffusion prior, pretrained at a resolution of $768 \times 768$ , and fine-tune it to generate images at a lower resolution of $512 \times 512$ . This resolution shift allows us to investigate the effectiveness of different fine-tuning techniques in bridging resolution gaps. + +Starting from the SD2.1 prior, we continue training with different objectives on the LAION-Aesthetics dataset [53] and evaluate model performance on COCO 2017 [29]. Fig. 5 shows that simply continuing diffusion training with an FM objective yields weak performance, especially when constraining model capacity with LoRA. In contrast, our method consistently surpasses continued diffusion training, both with and without classifier-free guidance, converging in as few as $2.5\mathrm{k}$ iterations. Note that all models show poor FID results without training due to the resolution mismatch. + +We present qualitative results in Fig. 3 and Fig. 4, where we use the same sampling hyperparameters and fix the initial Gaussian noise. A key issue that we also address in the transition from the diffusion model to flow matching is the + +
    MethodFID ↓CLIP ↑Aesthetics Score ↑
    SD1.556.7726.345.32
    SD1.5 (cont. training)56.3626.335.90
    Diff2Flow52.8026.545.99
    + +Table 1. Eval on COCO-2017 5k with 25 Euler/DDIM steps. + +problem of non-zero terminal SNR [28], which typically results in images generated by stable diffusion models having, on average, gray tones instead of true black or white. Our training paradigm solves this problem, illustrated in Fig. 4. + +Furthermore, we investigate the scenario where diffusion training is resumed with our method without any changes in resolution or task objectives. Specifically, we initialize from an SD1.5 checkpoint and continue training on the LAION-Aesthetics dataset at a resolution of $512 \times 512$ . The corresponding evaluation metrics are reported in Tab. 1. Consistent with observations in SD3 [8], the rectified trajectories of Diff2Flow yield superior performance compared to the baseline SD model. We show that converting a diffusion model to its flow-matching counterpart also leads to performance improvements within the same generative task. + +# 4.2. Rectifying the Trajectories + +In addition to fine-tuning diffusion models for resolution changes, we can also optimize them for straighter sampling trajectories to enable faster generation speeds. A popular approach to this is Reflow [32], which modifies the flow-matching training objective by replacing the random Gaussian noise terms in Eq. (5) with calculated noise derived from a pre-trained prior ODE to ensure that each noise-image pair is aligned according to the ODE. Quantitative results are presented in Tab. 3, where our method demonstrates competitive performance over various number of function evaluations (NFEs), including low NFEs such as 2 and 4, while only fine-tuning less than $7\%$ of the parameters. Qualitative results using reflow with 4 inference steps are shown in Fig. 6 and in the Appendix. + +# 4.3. Monocular Depth Estimation + +In addition to common tasks, we also show the versatility of our approach for domain adaptation finetuning. Previous methods have shown strong performance in using largescale image generative models for affine-invariant monocular depth estimation [9, 14, 24]. Marigold [24] directly finetune Stable Diffusion on synthetic image-depth data using the standard $v$ -parameterized Diffusion loss (Equation (3)). Following a similar setup, DepthFM [14] propose to convert Stable Diffusion into a flow matching model by training with the flow matching (see Equation (5)) loss. This approach requires aligning the model's outputs to a different objective, interpolant, and timestep scaling (with $t_{\mathrm{DM}} \in [0,1000]$ in diffusion versus $t_{\mathrm{FM}} \in [0,1]$ in flow matching). + +![](images/ed958eb0c1765c2c8f3487292fae5d8377b92978a6795ea2cd9f758112611900.jpg) +(a) + +![](images/2c7492738fcf9907c4740f74d2301875dbb8bcfacbd5ef6e2654f450fcff0f63.jpg) +(b) +Figure 5. Text-to-Image FID on the COCO 2017 [29] validation dataset. Light curves indicate results without Classifier-free Guidance [18]. a) We show that both FM and Diff2Flow converge to the same performance, given sufficient training and model capacity (full fine-tuning). However, our method removes the computational overhead from learning how to adjust the network output, resulting in faster convergence. b) Given limited modeling capacity (LoRA) the difference is more pronounced, where the FM model fails to close the gap to Diff2Flow, indicating that finetuning a portion of the parameters is enough to transfer a diffusion model to a flow matching model. + +
    MethodTraining samplesNYUv2 [40]KITTI [13]ETH3D [52]ScanNet [5]DIODE [62]
    AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑
    Depth Anything [65] (CVPR '24)62M4.398.17.694.712.788.2——6.695.2
    Depth Anything v2 [66] (arXiv '24)62M4.497.97.594.813.286.2——6.595.4
    Metric3D [68] (ICCV '23)8M5.096.65.897.06.496.57.494.122.480.5
    Metric3D v2 [22] (TPAMI '24)16M4.398.14.498.24.298.3—†—†13.689.5
    Marigold [24] (CVPR '24)74K5.596.49.991.66.596.06.495.130.877.3
    GeoWizard [9] (ECCV '24)278K5.296.69.792.16.496.16.195.329.779.2
    reproduced by [38]278K5.796.214.482.07.594.36.195.831.477.1
    DepthFM [14] (AAAI '25)74K6.095.59.190.26.595.46.694.922.478.5
    E2E FT [38] (WACV '25)74K5.296.69.691.96.295.95.896.230.277.9
    Lotus-G [16] (arXiv '24)59K5.496.611.387.76.296.16.096.0——
    Diff2Flow74K5.796.78.792.05.597.46.295.721.679.5
    Diff2Flow (LoRA)74K5.996.49.590.86.096.86.495.522.678.5
    + +Table 2. Comparison to state-of-the-art depth estimation methods. We compare discriminative (top) and generative models (bottom). Numbers obtained from [38]. ${}^{ \dagger }$ Metric3D v2 [22] was trained on ScanNet,so zero-shot evaluation is not possible. We also show the results reproduced by [38] for GeoWizard. All of our results are generated with NFE= 10 and an ensemble size of 4 . + +
    Method#Params ↓StepsFID ↓CLIP ↑
    SDv1.5+DPM Solver [34] (NeurIPS '22)0.9B2520.100.318
    Rectified Flow [32] (ICLR '23)0.9B2521.650.315
    Diff2Flow (LoRA)62M2521.450.314
    PeRFlow [64] (arXiv '24)0.9B422.970.294
    Diff2Flow (LoRA)62M425.290.313
    Rectified Flow [32] (ICLR '23)0.9B231.350.296
    Diff2Flow (LoRA)62M232.310.305
    + +Table 3. We fine-tune all our models with LoRA, and apply only 1-rectified flow according to Liu et al. [32]. We get competitive results with state-of-the-art reflow models. + +This process incurs significant computational cost, limiting the training efficiency and final performance. However, the flow matching nature of DepthFM allows for faster inference, at slightly reduced performance when given enough training. Our method mitigates this problem, accelerating training, and improving performance. The training and evaluation metrics are provided in the Appendix. + +![](images/9970ebf7ad1728f06d921f5ac6c3e90bc367172da9b080bc7ad0bd4f7fd3374b.jpg) +Figure 6. SD1.5 [46] + Diff2Flow-Reflow, 4-step inference results. + +![](images/ff86adc39d021c2268fc6f72b9632e19491265e5b7880b4074779f1ddbe9fdaf.jpg) + +![](images/e2cd60cb02465f6f3322b5745f15f89420a0c1ab46ff544f0f8a1512b23e62cb.jpg) + +Results Table 2 compares our method with both discriminative and generative depth predictors. Trained exclusively on synthetic data, our method matches or outperforms the prior state-of-the-art in monocular depth estimation, as shown in Figure 8. The diffusion-based Marigold model [24] struggles to achieve high accuracy with a limited number of sampling steps. In contrast to both DepthFM and Marigold, our method achieves competitive performance after very few training iterations and with only two sampling steps. The performance difference becomes even more pronounced when training with LoRA, where model capacity is limited. Figure 8b shows that this limitation prevents a + +![](images/f62519c233e7ab65e3612da256dabdf55d7819a95250902520839fa6814b7cc8.jpg) +Figure 7. Zero-shot qualitative results on real-world imagery. Our methods produce depth predictions with perceptually higher fidelity and finer detail. All predictions are made using the optimal settings of the models. Best viewed when zoomed in. + +![](images/50613c8e738a25a5c0475ebd9d1ae306ed702d078f35a453a1c4ad0aa60914a4.jpg) +(a) + +![](images/3d2817253b6f26e24931d528490a9372138c02b22aab64a98f9bd2a300a40034.jpg) +(b) +Figure 8. Results on NYUv2 depth benchmark [40] with 4 ensemble members. a) With full fine-tuning we find that FM adapts to the I2D task very quickly, but adding the objective change leads to even quicker convergence and better results. In contrast, the diffusion-based counterpart [24] suffers from slower convergence and requires more inference steps. b) The difference between FM and Diff2Flow is even more pronounced if we limit the capacity of the model by using Low-Rank adaptations. With Diff2Flow, the model does not need to learn to change the objective and can focus only on the task itself. + +straightforward application of the FM loss to the diffusion model. DepthFM struggles here as the model has to learn the adaptation from the $v$ -parameterization to the FM objective. The successful adaptation of the diffusion-based image prior to flow matching supports our initial hypothesis that the integration of our objective change facilitates this transformation. In Table 4, we present an ablation study on performance with different numbers of trainable parameters. Fine-tuning just $1/4$ of the original parameters is sufficient to achieve competitive performance with previous methods, particularly with the fully finetuned DepthFM model. Figure 7 qualitatively compares our method with state-of-the-art depth estimators on in-the-wild images. While discriminative methods often lack detail and fidelity, generative models capture fine details and avoid the averaging effect common to discriminative approaches. + +# 5. Conclusion + +We introduce a novel framework, Diff2Flow, that effectively converts pre-trained diffusion into flow matching models, providing a twofold optimization. First, this approach allows us to efficiently use the diffusion model's prior by exploiting its powerful generative capabilities with + +
    Method#Params ↓AbsRel ↓δ1 ↑
    Marigold + E2E FT [38]866M5.296.6
    Diff2Flow866M5.796.7
    Diff2Flow (LoRA base)222M5.996.4
    Diff2Flow (LoRA small)62M6.995.0
    + +Table 4. Zero-shot evaluation on NYUv2 [40] for different number of trainable parameters. We can achieve competitive performance with only a fraction of previous SOTA methods. + +out retraining from scratch. Second, by adapting it to the flow matching paradigm, we gain key benefits unique to flow matching: fast inference suitable for downstream tasks, and the ability to straighten sampling trajectories through techniques such as reflow, which further improves efficiency and performance. As a result, Diff2Flow not only improves training and inference efficiency but also delivers competitive performance in diverse tasks, including text-to-image synthesis and monocular depth estimation. By using parameter-efficient fine-tuning methods such as LoRA, our framework further minimizes computational requirements and demonstrates a practical, scalable way to merge diffusion and flow matching paradigms in generative modeling. + +# Acknowledgement + +This project has been supported by the bidders project KLIMA-MEMES, the German Federal Ministry for Economic Affairs and Climate Action within the project "NXT GEN AI METHODS - Generative Methoden für Percep tion, Prädiktion und Planung", the project "GeniusRobot" (01IS24083), funded by the Federal Ministry of Education and Research (BMBF), and the German Research Foundation (DFG) project 421703927. The authors acknowledge the Gauss Center for Supercomputing for providing compute through the NIC on JUWELS at JSC and the HPC resources supplied by the Erlangen National High Performance Computing Center (NHR@FAU funded by DFG project 440719683) under the NHR project JA-22883. + +# References + +[1] Michael S Albergo, Nicholas M Boffi, and Eric Vanden-Eijnden. Stochastic interpolants: A unifying framework for flows and diffusions. arXiv preprint arXiv:2303.08797, 2023. 1, 2, 3, 4 +[2] Dan Biderman, Jacob Portes, Jose Javier Gonzalez Ortiz, Mansheej Paul, Philip Greengard, Connor Jennings, Daniel King, Sam Havens, Vitaliy Chiley, Jonathan Frankle, et al. Lora learns less and forgets less. Transactions on Machine Learning Research, 2024. 2, 5 +[3] Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. Align your latents: High-resolution video synthesis with latent diffusion models. 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However, current foundation FM models are computationally prohibitive for finetuning, while diffusion models like Stable Diffusion benefit from efficient architectures and ecosystem support. This work addresses the critical challenge of efficiently transferring knowledge from pre-trained diffusion models to flow matching. We propose Diff2Flow, a novel framework that systematically bridges diffusion and FM paradigms by rescaling timesteps, aligning interpolants, and deriving FM-compatible velocity fields from diffusion predictions. This alignment enables direct and efficient FM finetuning of diffusion priors with no extra computation overhead. Our experiments demonstrate that Diff2Flow outperforms naive FM and diffusion finetuning particularly under parameter-efficient constraints, while achieving superior or competitive performance across diverse downstream tasks compared to state-of-the-art methods. 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Among these, foundation models such as Stable Diffusion [46] stand out, not only for their high-fidelity outputs but also for their useful representations and adaptability to downstream tasks, including depth estimation [14, 24], surface normal prediction [7], segmentation [63], and semantic correspondences [11, 60]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 67, + 612, + 295, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 612, + 295, + 680 + ], + "spans": [ + { + "bbox": [ + 67, + 612, + 295, + 680 + ], + "type": "text", + "content": "Meanwhile, Flow Matching (FM) [1, 30, 32] has emerged as a promising alternative, empirically offering faster inference and improved performance [8, 37]. While state-of-the-art foundational models based on flow matching, such as Flux [26] or SDv3 [8], show remarkable generative capabilities, their large size (" + }, + { + "bbox": [ + 67, + 612, + 295, + 680 + ], + "type": "inline_equation", + "content": ">8\\mathrm{B}" + }, + { + "bbox": [ + 67, + 612, + 295, + 680 + ], + "type": "text", + "content": " parameters) requires" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 210, + 541, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 210, + 541, + 347 + ], + "spans": [ + { + "bbox": [ + 312, + 210, + 541, + 347 + ], + "type": "text", + "content": "high-end hardware for both training and inference, making them particularly computationally expensive. This makes fine-tuning impractical, especially in resource-constrained environments and significantly limits their practical adoption. In contrast, Stable Diffusion's [46] efficient architecture and widespread ecosystem make it a pragmatic choice. This raises an important question: Can the knowledge captured by existing foundational diffusion models be efficiently transferred to a flow matching model? How can we bridge the gap between diffusion and flow matching with minimal additional training, leveraging both the pre-trained prior and the advantageous properties of flow matching?" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 350, + 541, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 350, + 541, + 463 + ], + "spans": [ + { + "bbox": [ + 312, + 350, + 541, + 463 + ], + "type": "text", + "content": "This work explores the relationship between the diffusion and flow matching paradigms. Although both methods can be generalized under a common framework [1, 25, 37], the actual implementations differ in several key aspects, including the definition of interpolants between the Gaussian noise prior and data samples, timestep scaling, and training objectives. These differences make it difficult to directly use a pre-trained diffusion model as a starting prior for flow matching training, as the two paradigms are not inherently well aligned." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 466, + 541, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 466, + 541, + 670 + ], + "spans": [ + { + "bbox": [ + 312, + 466, + 541, + 670 + ], + "type": "text", + "content": "To address this challenge, we propose a novel framework that effectively \"warps\" diffusion into flow matching, enabling seamless knowledge transfer between the two paradigms. This requires re-scaling their respective timesteps, aligning their differing interpolant formulations, and deriving the velocity field required for flow matching from the diffusion model's predictions, based on its parameterization. By systematically establishing these correspondences, we enable a smooth transition between diffusion and flow matching. To this end, we introduce a training methodology termed Diff2Flow, which initializes the flow matching model with a pretrained diffusion prior and directly finetunes it using the flow matching objective. Our analysis reveals that directly applying the FM loss to a diffusion model without incorporating our proposed adjustments significantly slows convergence and degrades overall model performance, whereas Diff2Flow provides a flexible and efficient approach with minimal finetuning overhead." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 673, + 541, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 673, + 541, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 673, + 541, + 696 + ], + "type": "text", + "content": "The benefits of this alignment become particularly evident when finetuning only a small subset of parameters." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 71, + 13, + 116, + 43 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 13, + 116, + 43 + ], + "spans": [ + { + "bbox": [ + 71, + 13, + 116, + 43 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 149, + 11, + 489, + 45 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 11, + 489, + 45 + ], + "spans": [ + { + "bbox": [ + 149, + 11, + 489, + 45 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 80, + 685, + 144, + 696 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 685, + 144, + 696 + ], + "spans": [ + { + "bbox": [ + 80, + 685, + 144, + 696 + ], + "type": "text", + "content": "* Equal Contribution" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "text", + "content": "28347" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 68, + 90, + 296, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 90, + 296, + 191 + ], + "spans": [ + { + "bbox": [ + 68, + 90, + 296, + 191 + ], + "type": "text", + "content": "Under such constrained computational budgets, the performance gap between naïve FM finetuning and our alignment-aware approach becomes more pronounced. Specifically, we show that directly applying the FM objective with parameter efficient finetuning (PEFT) leads to very suboptimal performance. Leveraging Diff2Flow with its alignment-informed training strategy, PEFT enhances training efficiency and minimizes memory consumption while maintaining high performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 192, + 297, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 192, + 297, + 464 + ], + "spans": [ + { + "bbox": [ + 70, + 192, + 297, + 464 + ], + "type": "text", + "content": "We show the efficiency of our method on a diverse set of downstream tasks. ① We show that when finetuning on a high-aesthetics dataset [6] on the text-to-image task, we outperform diffusion-based finetuning while converging significantly faster than naively training with the flow matching objective. This empirically demonstrates that smartly aligning timestep scaling and objective significantly facilitate learning, and additionally mitigate the zero-terminal SNR issue [28] common in diffusion models, where full black or white images can't be generated. ② When repurposing the model to generate images at resolutions different from the pre-trained sweet-spot resolution (similar to [17]), our method achieves superior results compared to standard diffusion and flow matching fine-tuning. ③ We show that we can apply Reflow [32] using Diff2Flow on a base diffusion model, a method that straightens sampling trajectories, resulting in faster inference speed. By rectifying the sampling trajectories of Stable Diffusion v1.5 we can generate images with as few as 2 sampling steps without consistency distillation [58]. ④ Finally, we demonstrate the effectiveness of our method on domain adaptation, leveraging the Stable Diffusion prior to predicting affine-invariant depth maps similar to Marigold [24] and DepthFM [14], achieving state-of-the-art results with reduced training time." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 473, + 151, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 473, + 151, + 485 + ], + "spans": [ + { + "bbox": [ + 69, + 473, + 151, + 485 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 492, + 296, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 492, + 296, + 639 + ], + "spans": [ + { + "bbox": [ + 68, + 492, + 296, + 639 + ], + "type": "text", + "content": "Diffusion and Flow Matching Models Diffusion models [19, 57] have demonstrated wide-ranging capabilities in data synthesis, extending from image [10, 44, 46, 48] and video [3, 15, 20] to audio generation [31] and beyond. While these models excel at producing high-fidelity outputs, they often require extensive sampling time, necessitating techniques like distillation [39, 49, 50, 58], noise schedule optimization [23], or training-free sampling [34, 56] to achieve faster generation. Following diffusion models, flow matching models [1, 30, 32] have gained attention due to their benefit of straighter probability paths. These models have been shown to perform competitively or surpass diffusion models in terms of both speed and quality [8, 37, 54]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 639, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 639, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 68, + 639, + 296, + 696 + ], + "type": "text", + "content": "The relationship between diffusion and flow matching models has been explored in Lee et al. [27], demonstrating that finetuning a flow matching model based on a pretrained diffusion model is feasible. Our work extends this by explicitly formulating a method to map discrete diffu" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 356, + 90, + 496, + 173 + ], + "blocks": [ + { + "bbox": [ + 356, + 90, + 496, + 173 + ], + "lines": [ + { + "bbox": [ + 356, + 90, + 496, + 173 + ], + "spans": [ + { + "bbox": [ + 356, + 90, + 496, + 173 + ], + "type": "image", + "image_path": "ed31aa870acccdc5eac51072d97d3fcd34088abf7708123b196ffa196d32b9b7.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "lines": [ + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "spans": [ + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "text", + "content": "Figure 1. We introduce a novel finetuning technique to traverse between flow matching and diffusion, which enables effectively aligning the two processes with minimal additional training. The interpolant on the flow matching trajectory is computed as a function " + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "text", + "content": " of the diffusion timestep " + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "text", + "content": ", the sample " + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "text", + "content": ", and the associated diffusion coefficients. Our approach further enables a velocity prediction " + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{v}}" + }, + { + "bbox": [ + 313, + 182, + 541, + 256 + ], + "type": "text", + "content": " regardless of the diffusion model's parameterization." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 281, + 541, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 541, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 541, + 339 + ], + "type": "text", + "content": "sion trajectory to a continuous flow matching trajectory. Furthermore, we empirically demonstrate that our strategy works for various diffusion parameterization objectives and present results that go beyond reflow [32], achieving competitive performance on several benchmarks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 370, + 541, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 370, + 541, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 370, + 541, + 529 + ], + "type": "text", + "content": "Parameter-efficient Finetuning As foundational models expand in size and complexity, parameter-efficient finetuning (PEFT) techniques such as Low-Rank Adaptation (LoRA) [21] offer viable alternatives to full model finetuning. Originally developed for large language models, LoRA and other PEFT techniques have since been applied effectively to diffusion models [47], proving valuable across a broad range of tasks. These include domain-specific finetuning [67], additional image conditioning [59], image editing [12], distillation [36] and among others. By updating only a low-rank decomposition of the weight matrix, LoRA reduces memory requirements and alleviate catastrophic forgetting [2], making it highly adaptable for targeted adjustments in large foundational models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 560, + 541, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 560, + 541, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 560, + 541, + 696 + ], + "type": "text", + "content": "Knowledge in Generative Models Following the rise of text-to-image diffusion models [41, 43, 44, 46, 48], numerous studies have explored methods to extract information from diffusion priors. Many works have effectively utilized the diffusion prior for tasks such as monocular depth estimation [9, 14, 16, 24, 38, 51], surface normal prediction [7], and semantic correspondences [11, 35, 60]. While these approaches predominantly focus on distilling information into another diffusion model, our work explores the transfer of this knowledge to flow matching models and hereby leverages the inherent advantages of flow matching, including more efficient inference and enhanced task performance." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 730, + 317, + 739 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 317, + 739 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 317, + 739 + ], + "type": "text", + "content": "28348" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 89, + 122, + 100 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 89, + 122, + 100 + ], + "spans": [ + { + "bbox": [ + 69, + 89, + 122, + 100 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 107, + 296, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 107, + 296, + 175 + ], + "spans": [ + { + "bbox": [ + 69, + 107, + 296, + 175 + ], + "type": "text", + "content": "In this section, we explain our algorithm and the process of aligning the trajectories. We begin by discussing the definition of diffusion and flow matching models. Following this, we describe how we traverse between the two trajectories as depicted in Fig. 1 and use the diffusion model to generate a reasonable estimate of the flow velocity." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 182, + 222, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 182, + 222, + 194 + ], + "spans": [ + { + "bbox": [ + 69, + 182, + 222, + 194 + ], + "type": "text", + "content": "3.1. Diffusion and Flow Matching" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 200, + 296, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 200, + 296, + 245 + ], + "spans": [ + { + "bbox": [ + 69, + 200, + 296, + 245 + ], + "type": "text", + "content": "Diffusion models (DM) [19, 56, 57] gradually diffuse data by typically adding noise to real data samples " + }, + { + "bbox": [ + 69, + 200, + 296, + 245 + ], + "type": "inline_equation", + "content": "x_0 \\sim p_0(x_0)" + }, + { + "bbox": [ + 69, + 200, + 296, + 245 + ], + "type": "text", + "content": " in a predefined discrete forward process, which can be characterized by" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 123, + 252, + 296, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 252, + 296, + 266 + ], + "spans": [ + { + "bbox": [ + 123, + 252, + 296, + 266 + ], + "type": "interline_equation", + "content": "p \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\alpha_ {t} x _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {1}", + "image_path": "60726530f012187f98e250f83bb14ad29d085a9db43e8e4db6a19517f6e39d97.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "spans": [ + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": " are the predefined noise schedules, " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": " is the discrete timestep, and " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": " is the resulting noisy sample, often referred to as the interpolant. In the setting of variance preserving schedules " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "\\sigma_{t} = \\sqrt{1 - \\alpha_{t}^{2}}" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": ", and the interpolant " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": " is then " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "x_{t} = \\alpha_{t}x_{0} + \\sqrt{1 - \\alpha_{t}^{2}}\\epsilon" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": ". A neural network, parameterized by " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": ", is learned to reverse the forward process by gradually removing noise from " + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 69, + 274, + 296, + 365 + ], + "type": "text", + "content": ". Ho et al. [19] propose the simplified loss term" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 373, + 296, + 387 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 373, + 296, + 387 + ], + "spans": [ + { + "bbox": [ + 104, + 373, + 296, + 387 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, \\epsilon , x _ {0} \\sim p (x _ {0})} | | \\epsilon_ {t} - \\epsilon_ {\\theta} (x _ {t}, t) | | ^ {2}, \\tag {2}", + "image_path": "5bc18d73f8dc601fb3127c95cbd3125fc1eb5592fdabe2ba920614df4809cbc3.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "spans": [ + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "type": "text", + "content": "where predicting " + }, + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "type": "text", + "content": " is observed to yield better results and enhance convergence. There also exists the " + }, + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 69, + 393, + 296, + 428 + ], + "type": "text", + "content": "-parameterization [49], defined as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 148, + 437, + 295, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 437, + 295, + 449 + ], + "spans": [ + { + "bbox": [ + 148, + 437, + 295, + 449 + ], + "type": "interline_equation", + "content": "v _ {t} = \\alpha_ {t} \\epsilon - \\sigma_ {t} x _ {0}. \\tag {3}", + "image_path": "43c3d52571b8143c19a8ee41f4e548b06e8e2e581ce8d2240d36d95ef7101aaf.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "spans": [ + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "type": "text", + "content": "Flow matching (FM) models [1, 30, 32], another flexible class of generative models, utilizes the same idea of gradually deteriorating data samples and then synthesizing new data by reversing the process. We adopt the setting from Lipman et al. [30] where " + }, + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "type": "text", + "content": " represents noise, and " + }, + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "type": "inline_equation", + "content": "x_{1}" + }, + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "type": "text", + "content": " corresponds to data. The interpolant on the continuous timesteps " + }, + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "type": "inline_equation", + "content": "t\\in [0,1]" + }, + { + "bbox": [ + 69, + 460, + 296, + 540 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 138, + 549, + 296, + 560 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 549, + 296, + 560 + ], + "spans": [ + { + "bbox": [ + 138, + 549, + 296, + 560 + ], + "type": "interline_equation", + "content": "x _ {t} = t x _ {1} + (1 - t) x _ {0}, \\tag {4}", + "image_path": "60dc2a73c8fb0105cac422b5a66c50cc18c52c17674f62ae7070138aea73e25e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "spans": [ + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "text", + "content": " is typically a Gaussian noise sample. The model " + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\theta}" + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "text", + "content": " is trained to regress a vector field along the trajectory, following the linear path that points from " + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "inline_equation", + "content": "x_1" + }, + { + "bbox": [ + 69, + 568, + 296, + 613 + ], + "type": "text", + "content": " using the following objective:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 74, + 621, + 296, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 621, + 296, + 635 + ], + "spans": [ + { + "bbox": [ + 74, + 621, + 296, + 635 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {F M}} = \\mathbb {E} _ {t, x _ {0} \\sim \\mathcal {N} (0, \\mathbf {I}), x _ {1} \\sim p (x _ {1})} | | (x _ {1} - x _ {0}) - \\mathbf {v} _ {\\theta} (x _ {t}, t) | | ^ {2}. \\tag {5}", + "image_path": "0a47ba499ebd38105f292350ec11c9c6ba6a893f819630d7927a806ab22c88c2.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 69, + 642, + 296, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 642, + 296, + 677 + ], + "spans": [ + { + "bbox": [ + 69, + 642, + 296, + 677 + ], + "type": "text", + "content": "Sampling from a flow matching model is accomplished by integrating over the trajectory of the learned ODE, e.g. using the forward Euler method with the update rule" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 100, + 685, + 296, + 697 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 685, + 296, + 697 + ], + "spans": [ + { + "bbox": [ + 100, + 685, + 296, + 697 + ], + "type": "interline_equation", + "content": "x _ {t + t _ {\\Delta}} = x _ {t} + t _ {\\Delta} \\mathbf {v} _ {\\theta} \\left(x _ {t}, t\\right) \\quad \\forall t \\in [ 0, 1), \\tag {6}", + "image_path": "2780d18419179b3b7a785040fc6f1bd4d6dc5fe11473408438645c68f1262736.jpg" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 340, + 99, + 422, + 141 + ], + "blocks": [ + { + "bbox": [ + 338, + 89, + 423, + 99 + ], + "lines": [ + { + "bbox": [ + 338, + 89, + 423, + 99 + ], + "spans": [ + { + "bbox": [ + 338, + 89, + 423, + 99 + ], + "type": "text", + "content": "Normal timesteps " + }, + { + "bbox": [ + 338, + 89, + 423, + 99 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}}" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 340, + 99, + 422, + 141 + ], + "lines": [ + { + "bbox": [ + 340, + 99, + 422, + 141 + ], + "spans": [ + { + "bbox": [ + 340, + 99, + 422, + 141 + ], + "type": "image", + "image_path": "9081a7732ea58e32104025b51711d3579b5b8bbe42aed62f2b565d12db2c9460.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 152, + 539, + 174 + ], + "lines": [ + { + "bbox": [ + 313, + 152, + 539, + 174 + ], + "spans": [ + { + "bbox": [ + 313, + 152, + 539, + 174 + ], + "type": "text", + "content": "Figure 2. Although non-integer-shifted DDIM timesteps are neither defined nor trained, generated images remain of high quality." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 433, + 99, + 515, + 141 + ], + "blocks": [ + { + "bbox": [ + 433, + 89, + 517, + 99 + ], + "lines": [ + { + "bbox": [ + 433, + 89, + 517, + 99 + ], + "spans": [ + { + "bbox": [ + 433, + 89, + 517, + 99 + ], + "type": "text", + "content": "Shifted timesteps " + }, + { + "bbox": [ + 433, + 89, + 517, + 99 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}}" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 433, + 99, + 515, + 141 + ], + "lines": [ + { + "bbox": [ + 433, + 99, + 515, + 141 + ], + "spans": [ + { + "bbox": [ + 433, + 99, + 515, + 141 + ], + "type": "image", + "image_path": "9699245a95cfa8af7539d90e69a4b91e20895de3da817142b443be717c983fd7.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "spans": [ + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "type": "inline_equation", + "content": "t_{\\delta} = 1 / N" + }, + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "type": "text", + "content": " being the number of function evaluations (NFE). We generate a discrete sequence that approximates the path by advancing in small increments along the ODE. The trajectory's smoothness, or \"straightness,\" is critical, as it determines the number of steps required to achieve accurate results, trading off computational cost and fidelity. Straighter paths allow smaller " + }, + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 194, + 539, + 285 + ], + "type": "text", + "content": ", whereas paths with higher curvature require more steps for simulating the ODE." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "text", + "content": "Reflow In FM training, we randomly sample from a Gaussian distribution and form pairs with the data points to create the interpolant " + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "text", + "content": ". This random pairing leads to curved sampling trajectories, increasing the curvature of the ODE trajectories during inference [61]. To straighten these trajectories, Liu et al. [32] propose Reflow, which iteratively trains on samples obtained from a pre-trained flow matching model. Given an already trained ODE model " + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\Phi}" + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "text", + "content": ", Reflow first samples " + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "inline_equation", + "content": "x_0 \\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "text", + "content": " and integrates along the ODE trajectory using Eq. (6) to obtain a corresponding data sample " + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "inline_equation", + "content": "x_{1}" + }, + { + "bbox": [ + 313, + 298, + 541, + 445 + ], + "type": "text", + "content": ". This process generates image-noise pairings. Training on this paired data has been found to reduce inference cost by straightening the sampling trajectories [32, 33, 64]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 452, + 518, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 452, + 518, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 452, + 518, + 464 + ], + "type": "text", + "content": "3.2. Diffusion Prior for Flow Matching Model" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 469, + 539, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 469, + 539, + 560 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 539, + 560 + ], + "type": "text", + "content": "Flow matching methods are known for straighter trajectories and more efficient inference [14, 61]. Hence, transforming the diffusion prior into a flow matching equivalent offers the potential for improvements in inference speed and performance [8, 37]. While previous research has successfully adapted diffusion priors for other downstream diffusion tasks, our approach combines these advantages with those of flow matching models." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 560, + 539, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 560, + 539, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 560, + 539, + 696 + ], + "type": "text", + "content": "Importantly, recent works on utilizing flow matching models to inherit a diffusion prior for downstream applications, such as DepthFM [14], have shown significant promise in accelerating inference compared to diffusion models. While this approach provides faster sampling than its diffusion model's counterpart, this inheritance method has limitations: DepthFM finetunes from a " + }, + { + "bbox": [ + 313, + 560, + 539, + 696 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 313, + 560, + 539, + 696 + ], + "type": "text", + "content": "-parameterized text-to-image diffusion model [46] directly. This approach requires the flow matching model to \"warp\" the " + }, + { + "bbox": [ + 313, + 560, + 539, + 696 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 313, + 560, + 539, + 696 + ], + "type": "text", + "content": "-parameterization to predict velocity, a different parameterization scheme. This introduces misalignments in the training objective, the interpolant, and the timesteps." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "text", + "content": "28349" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 68, + 90, + 296, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 90, + 296, + 180 + ], + "spans": [ + { + "bbox": [ + 68, + 90, + 296, + 180 + ], + "type": "text", + "content": "To address these limitations, we propose a novel strategy that enables a seamless transition between diffusion and flow matching trajectories. Our method minimizes misalignments and yields more accurate velocity predictions. In addition to monocular depth estimation, we demonstrate that our approach generalizes to other downstream tasks and offers a versatile and efficient solution for leveraging prior information from diffusion model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 199, + 232, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 199, + 232, + 211 + ], + "spans": [ + { + "bbox": [ + 69, + 199, + 232, + 211 + ], + "type": "text", + "content": "3.2.1 Traversing Between Trajectories" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "spans": [ + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "text", + "content": "Let us transform a foundation diffusion model's trajectory " + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "text", + "content": " by applying two invertible operations, one " + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "text", + "content": " that reparameterizes " + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "inline_equation", + "content": "t \\in [0,T]" + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "text", + "content": " and one " + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "inline_equation", + "content": "f_{x}" + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "text", + "content": " that transforms " + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 69, + 219, + 296, + 265 + ], + "type": "text", + "content": " to an alternate trajectory, defined by the following equation:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 148, + 275, + 296, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 275, + 296, + 289 + ], + "spans": [ + { + "bbox": [ + 148, + 275, + 296, + 289 + ], + "type": "interline_equation", + "content": "\\bar {x} \\left(f _ {t}\\right) = f _ {x} \\left(x _ {f _ {t}}\\right). \\tag {7}", + "image_path": "5fa1b9e3d30c19af4a40cbec5995194f23edaab538d45729be0caf0dbee44ea7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 298, + 296, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 298, + 296, + 354 + ], + "spans": [ + { + "bbox": [ + 69, + 298, + 296, + 354 + ], + "type": "text", + "content": "The boundary conditions need to satisfy " + }, + { + "bbox": [ + 69, + 298, + 296, + 354 + ], + "type": "inline_equation", + "content": "\\bar{x}(f_0) = x_0" + }, + { + "bbox": [ + 69, + 298, + 296, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 69, + 298, + 296, + 354 + ], + "type": "inline_equation", + "content": "\\bar{x}(f_T) = x_T" + }, + { + "bbox": [ + 69, + 298, + 296, + 354 + ], + "type": "text", + "content": " to ensure that the starting and target samples are the same. This is different to Shaul et al. [55] since our approach rectifies the trajectories, which requires the exact alignment of the starting and the target distribution." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "spans": [ + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": "In order to construct " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "f_{x}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " reasonably, we need to probe into the diffusion and flow matching model and investigate how the interpolants are related. Let " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{DM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " represent a data sample on the diffusion trajectory and " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " a data sample on the flow matching trajectory. Similarly, " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " is the diffusion timestep and " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " is the flow matching timestep. Following the convention of diffusion and flow matching literature [1, 19, 30, 32, 57], diffusion operates on discrete timesteps " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}} \\in \\mathbb{Z}_{\\geq 0} \\cap [0,T]" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_{t_{\\mathrm{DM}} = 0}^{\\mathrm{DM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " represents the data samples and " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_{t_{\\mathrm{DM}} = T}^{\\mathrm{DM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " corresponds to the Gaussian noise. In contrast, flow matching uses continuous timesteps " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{FM}} \\in [0,1]" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_{t_{\\mathrm{FM}} = 1}^{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " representing the data samples and " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_{t_{\\mathrm{FM}} = 0}^{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " representing the Gaussian noise. To summarize, the boundary condition enforces " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_{t_{\\mathrm{DM}} = 0}^{\\mathrm{DM}} = x_{t_{\\mathrm{FM}} = 1}^{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x_{t_{\\mathrm{DM}} = T}^{\\mathrm{DM}} = x_{t_{\\mathrm{FM}} = 0}^{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": ", while we seek two invertible mappings " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "f_{t}: [0,T] \\to [0,1]" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " which maps " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "f_{x}: [0,1] \\times \\mathbb{R}^{d} \\to \\mathbb{R}^{d}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " which maps " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{DM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 356, + 296, + 559 + ], + "type": "text", + "content": ". The diffusion interpolant is" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 125, + 568, + 296, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 568, + 296, + 583 + ], + "spans": [ + { + "bbox": [ + 125, + 568, + 296, + 583 + ], + "type": "interline_equation", + "content": "x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} = \\alpha_ {t _ {\\mathrm {D M}}} x _ {0} ^ {\\mathrm {D M}} + \\sigma_ {t _ {\\mathrm {D M}}} x _ {T} ^ {\\mathrm {D M}}, \\tag {8}", + "image_path": "7ac0b83e89e2bba4139ac03e62857000dd2012b8a1498571fe7c102ed5772522.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "spans": [ + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "inline_equation", + "content": "\\alpha_{t_{\\mathrm{DM}}}^2 +\\sigma_{t_{\\mathrm{DM}}}^2 = 1" + }, + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "text", + "content": " for the variance-preserving schedule and " + }, + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "inline_equation", + "content": "\\alpha_{t_{\\mathrm{DM}}} = 1" + }, + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "inline_equation", + "content": "\\forall t_{\\mathrm{DM}}" + }, + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "inline_equation", + "content": "\\sigma_{t_{\\mathrm{DM}}}" + }, + { + "bbox": [ + 69, + 592, + 296, + 627 + ], + "type": "text", + "content": " monotonically increasing over time for the variance-exploding schedule [19, 57]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 628, + 236, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 628, + 236, + 639 + ], + "spans": [ + { + "bbox": [ + 69, + 628, + 236, + 639 + ], + "type": "text", + "content": "The flow matching interpolant is defined as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 119, + 649, + 295, + 663 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 649, + 295, + 663 + ], + "spans": [ + { + "bbox": [ + 119, + 649, + 295, + 663 + ], + "type": "interline_equation", + "content": "x _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}} = t _ {\\mathrm {F M}} x _ {1} ^ {\\mathrm {F M}} + \\left(1 - t _ {\\mathrm {F M}}\\right) x _ {0} ^ {\\mathrm {F M}}. \\tag {9}", + "image_path": "f88119dd62d9c1836563eeea9a9ab75430866ac2419e99acf6460b595dd82501.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 673, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 673, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 69, + 673, + 296, + 696 + ], + "type": "text", + "content": "There are multiple ways to define " + }, + { + "bbox": [ + 69, + 673, + 296, + 696 + ], + "type": "inline_equation", + "content": "f_{x}" + }, + { + "bbox": [ + 69, + 673, + 296, + 696 + ], + "type": "text", + "content": " so that the diffusion trajectory can be transformed and warped into a linear equa" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 91, + 373, + 101 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 373, + 101 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 373, + 101 + ], + "type": "text", + "content": "tion, one being" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 324, + 106, + 541, + 155 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 106, + 541, + 155 + ], + "spans": [ + { + "bbox": [ + 324, + 106, + 541, + 155 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} f _ {x} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}\\right) = \\frac {\\alpha_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {0} ^ {\\mathrm {D M}} + \\frac {\\sigma_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {T} ^ {\\mathrm {D M}} \\tag {10} \\\\ = \\frac {1}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, \\\\ \\end{array}", + "image_path": "966406d3530d3ef216db12b955f10c56b7215efa96512ccf6008d85fbb0cbc1d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 161, + 441, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 161, + 441, + 173 + ], + "spans": [ + { + "bbox": [ + 313, + 161, + 441, + 173 + ], + "type": "text", + "content": "yielding a scaled version of " + }, + { + "bbox": [ + 313, + 161, + 441, + 173 + ], + "type": "inline_equation", + "content": "x_{t_{\\mathrm{DM}}}^{\\mathrm{DM}}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "spans": [ + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": "To design " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": " as an invertible mapping between the discrete space " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}}" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": " and the continuous space " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{FM}}" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": ", we start by establishing an invertible transformation function that enables continuous interpolation between discrete points in " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}}" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": " while aligning with " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "f_{x}" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": ". To ensure continuity and invertibility, we define " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": " as a piecewise linear function and interpolate between these discrete points. Let " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "t_{\\overline{\\mathrm{DM}}} \\in [0,T]" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": " be a continuous interpolated time space of the discrete " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}}" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": ". The correlation between Eq. (9) and Eq. (10) allows to calculate " + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{FM}}" + }, + { + "bbox": [ + 313, + 173, + 539, + 285 + ], + "type": "text", + "content": " via the diffusion coefficients:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 378, + 291, + 539, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 291, + 539, + 314 + ], + "spans": [ + { + "bbox": [ + 378, + 291, + 539, + 314 + ], + "type": "interline_equation", + "content": "f _ {t} \\left(t _ {\\mathrm {D M}}\\right) = \\frac {\\alpha_ {t _ {\\mathrm {D M}}}}{\\alpha_ {t _ {\\mathrm {D M}}} + \\sigma_ {t _ {\\mathrm {D M}}}}, \\tag {11}", + "image_path": "a72c15c6fd74b720062f67ee958f36f07d17135651b5e4233f2052779b5c3f96.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": "where in both variance-preserving and variance-exploding diffusion schedules " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "f_{t}(t_{\\mathrm{DM}})" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " is monotonic. While the diffusion coefficients " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " are not defined for all " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "t_{\\overline{\\mathrm{DM}}}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": ", we interpolate between the corresponding nearest neighbors. Let " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}_1}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}_2}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " be the nearest neighbors of " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "t_{\\overline{\\mathrm{DM}}}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " and we design " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " to be just as a linear interpolation in between. Interestingly, we find that although the continuous values of " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "t_{\\overline{\\mathrm{DM}}}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " were not trained during the foundation model's training, direct inference with these values still produces reasonable results, as shown in Fig. 2. Specifically, instead of performing DDIM inference at discrete timesteps " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DDIM}} \\in \\mathbb{Z}_{\\geq 0} \\cap [0,1000]" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": ", we do inference at " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DDIM}} + 0.5" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " with linearly interpolated " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 313, + 319, + 541, + 510 + ], + "type": "text", + "content": ". We hypothesize that timesteps represented as sinusoidal embeddings create a well-defined continuous time space. This observation lays the foundation for interpolating timestep embeddings and traversing trajectories." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": "With " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "t_{\\overline{\\mathrm{DM}}}" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": " defined on the continuous domain, the inverse " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "f_{t}^{-1}(t_{\\mathrm{FM}})" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": " can be defined as follows. First, we find " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}_1}" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}_2}" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": " in the discrete timesteps such that " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "f_{t}(t_{\\mathrm{DM}_{1}})" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "f_{t}(t_{\\mathrm{DM}_{2}})" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": " are the two nearest neighbors of " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{FM}}" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "f_{t}(t_{\\mathrm{DM}_{1}})\\leqslant t_{\\mathrm{FM}}\\leqslant f_{t}(t_{\\mathrm{DM}_{2}})" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": ". Next, we perform a linear interpolation between the two neighbors to reverse the mapping from " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "t_\\mathrm{FM}" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "inline_equation", + "content": "t_{\\overline{\\mathrm{DM}}}" + }, + { + "bbox": [ + 313, + 511, + 539, + 591 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 597, + 539, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 597, + 539, + 631 + ], + "spans": [ + { + "bbox": [ + 317, + 597, + 539, + 631 + ], + "type": "interline_equation", + "content": "f _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right) = t _ {\\mathrm {D M} _ {1}} + \\frac {t _ {\\mathrm {F M}} - f _ {t} \\left(t _ {\\mathrm {D M} _ {1}}\\right)}{f _ {t} \\left(t _ {\\mathrm {D M} _ {2}}\\right) - f _ {t} \\left(t _ {\\mathrm {D M} _ {1}}\\right)} \\left(t _ {\\mathrm {D M} _ {2}} - t _ {\\mathrm {D M} _ {1}}\\right). \\tag {12}", + "image_path": "34ffecd0e9285e55f00d2252dcc7a356c5fa7dc621bf2de13821198bd71f9bf4.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "type": "text", + "content": "With " + }, + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "type": "inline_equation", + "content": "f_{t}(\\cdot)" + }, + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "type": "text", + "content": " bidirectionally defined as in Eq. (11) and Eq. (12), we deduce the bidirectional mapping from the FM trajectory " + }, + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{FM}}" + }, + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "type": "text", + "content": " back to the DM trajectory " + }, + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{DM}}" + }, + { + "bbox": [ + 313, + 631, + 539, + 665 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 345, + 670, + 539, + 686 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 670, + 539, + 686 + ], + "spans": [ + { + "bbox": [ + 345, + 670, + 539, + 686 + ], + "type": "interline_equation", + "content": "f _ {x} ^ {- 1} \\left(x _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}}\\right) = \\left(\\alpha_ {f _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right)} + \\sigma_ {f _ {t} ^ {- 1} \\left(t _ {\\mathrm {F M}}\\right)}\\right) x _ {t _ {\\mathrm {F M}}} ^ {\\mathrm {F M}}. \\tag {13}", + "image_path": "f375061799140f9bc57d305ed5e858c1cad8bb800a4fe9546aa8141d1c3e996d.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "text", + "content": "28350" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 90, + 195, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 90, + 195, + 102 + ], + "spans": [ + { + "bbox": [ + 69, + 90, + 195, + 102 + ], + "type": "text", + "content": "3.2.2 Unifying the Objectives" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "spans": [ + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "type": "text", + "content": "While traversing between the diffusion and flow matching trajectories is explained in the previous chapter, it is still essential to unify the training and inference objectives. Prior works [14, 64] fine-tuned the model to adapt the diffusion prior, originally predicting " + }, + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "type": "text", + "content": ", to directly predict velocity. However, these approaches force the model to transition between different parameterizations, therefore requiring longer convergence times and also ultimately impacting model performance. In contrast, our method unites the objectives by leveraging the diffusion prior and utilizing the relationships between the parameterizations. We term this technique Objective change as we incorporate both trajectory traversal and a principled objective realignment to facilitate velocity prediction based on the diffusion prior. This approach is broadly applicable across different parameterizations; here, we demonstrate its effectiveness using " + }, + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 68, + 108, + 296, + 300 + ], + "type": "text", + "content": "-parameterization." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 300, + 296, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 300, + 296, + 324 + ], + "spans": [ + { + "bbox": [ + 69, + 300, + 296, + 324 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 69, + 300, + 296, + 324 + ], + "type": "inline_equation", + "content": "v_{\\theta}(x^{\\mathrm{DM}}, t_{\\mathrm{DM}})" + }, + { + "bbox": [ + 69, + 300, + 296, + 324 + ], + "type": "text", + "content": " be the " + }, + { + "bbox": [ + 69, + 300, + 296, + 324 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 69, + 300, + 296, + 324 + ], + "type": "text", + "content": "-prediction (Eq. (3)) from a pre-trained diffusion model. Using the notation of Eq. (8)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 110, + 331, + 295, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 331, + 295, + 346 + ], + "spans": [ + { + "bbox": [ + 110, + 331, + 295, + 346 + ], + "type": "interline_equation", + "content": "v _ {\\theta} \\left(x ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) = \\alpha_ {t _ {\\mathrm {D M}}} x _ {T} ^ {\\mathrm {D M}} - \\sigma_ {t _ {\\mathrm {D M}}} x _ {0} ^ {\\mathrm {D M}} \\tag {14}", + "image_path": "363de692d8d9cfee590a3cb492a2fb0f2a23bd4aa5ae56e32f9fef571d4b8f33.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 355, + 282, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 355, + 282, + 366 + ], + "spans": [ + { + "bbox": [ + 69, + 355, + 282, + 366 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 355, + 282, + 366 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 69, + 355, + 282, + 366 + ], + "type": "text", + "content": " and the corresponding " + }, + { + "bbox": [ + 69, + 355, + 282, + 366 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 69, + 355, + 282, + 366 + ], + "type": "text", + "content": " can be estimated as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 375, + 296, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 375, + 296, + 397 + ], + "spans": [ + { + "bbox": [ + 107, + 375, + 296, + 397 + ], + "type": "interline_equation", + "content": "\\widehat {x _ {0} ^ {\\mathrm {D M}}} = \\alpha_ {t _ {\\mathrm {D M}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} - \\sigma_ {t _ {\\mathrm {D M}}} v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) \\tag {15}", + "image_path": "c55045f3763c00e401ea635788861d2965074eb90932d68b6f6315d20fc00865.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 108, + 394, + 257, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 394, + 257, + 410 + ], + "spans": [ + { + "bbox": [ + 108, + 394, + 257, + 410 + ], + "type": "interline_equation", + "content": "\\widehat {x _ {T} ^ {\\mathrm {D M}}} = \\alpha_ {t _ {\\mathrm {D M}}} v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right) - \\sigma_ {t _ {\\mathrm {D M}}} x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}},", + "image_path": "2c6b0e4c0494c1fab6925069365feaa92eb4dab0501fa8731eef8fd2ed355d79.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 417, + 296, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 417, + 296, + 452 + ], + "spans": [ + { + "bbox": [ + 69, + 417, + 296, + 452 + ], + "type": "text", + "content": "with the wide hat symbol indicating an estimate predicted by the model. An approximation for the velocity " + }, + { + "bbox": [ + 69, + 417, + 296, + 452 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 69, + 417, + 296, + 452 + ], + "type": "text", + "content": " at the corresponding FM data point " + }, + { + "bbox": [ + 69, + 417, + 296, + 452 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{FM}}" + }, + { + "bbox": [ + 69, + 417, + 296, + 452 + ], + "type": "text", + "content": " is then formulated with" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 70, + 471, + 198, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 471, + 198, + 483 + ], + "spans": [ + { + "bbox": [ + 70, + 471, + 198, + 483 + ], + "type": "text", + "content": "Algorithm 1 Diff2Flow Training" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 70, + 485, + 296, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 485, + 296, + 509 + ], + "spans": [ + { + "bbox": [ + 70, + 485, + 296, + 509 + ], + "type": "text", + "content": "Require: Data Sample " + }, + { + "bbox": [ + 70, + 485, + 296, + 509 + ], + "type": "inline_equation", + "content": "x_{1}^{\\mathrm{FM}}" + }, + { + "bbox": [ + 70, + 485, + 296, + 509 + ], + "type": "text", + "content": ", Noise sample " + }, + { + "bbox": [ + 70, + 485, + 296, + 509 + ], + "type": "inline_equation", + "content": "x_{0}^{\\mathrm{FM}}" + }, + { + "bbox": [ + 70, + 485, + 296, + 509 + ], + "type": "text", + "content": ", Timestep " + }, + { + "bbox": [ + 70, + 485, + 296, + 509 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{FM}} \\in [0,1]" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 75, + 509, + 296, + 567 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 75, + 509, + 296, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 509, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 75, + 509, + 296, + 521 + ], + "type": "text", + "content": "1: Compute the interpolant " + }, + { + "bbox": [ + 75, + 509, + 296, + 521 + ], + "type": "inline_equation", + "content": "x_{t_{\\mathrm{FM}}}^{\\mathrm{FM}}" + }, + { + "bbox": [ + 75, + 509, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 75, + 509, + 296, + 521 + ], + "type": "text", + "content": " Eq. 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(16)" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 75, + 656, + 295, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 656, + 295, + 668 + ], + "spans": [ + { + "bbox": [ + 75, + 656, + 295, + 668 + ], + "type": "text", + "content": "5: " + }, + { + "bbox": [ + 75, + 656, + 295, + 668 + ], + "type": "inline_equation", + "content": "x_{t + 1 / N}\\gets x_t + \\frac{1}{N}\\mathbf{v}_\\theta" + }, + { + "bbox": [ + 75, + 656, + 295, + 668 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 75, + 656, + 295, + 668 + ], + "type": "text", + "content": " Eq. (6)" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 75, + 669, + 117, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 669, + 117, + 678 + ], + "spans": [ + { + "bbox": [ + 75, + 669, + 117, + 678 + ], + "type": "text", + "content": "6: end for" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 76, + 679, + 125, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 679, + 125, + 690 + ], + "spans": [ + { + "bbox": [ + 76, + 679, + 125, + 690 + ], + "type": "text", + "content": "7: return " + }, + { + "bbox": [ + 76, + 679, + 125, + 690 + ], + "type": "inline_equation", + "content": "x_{1}" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 91, + 517, + 102 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 91, + 517, + 102 + ], + "spans": [ + { + "bbox": [ + 313, + 91, + 517, + 102 + ], + "type": "text", + "content": "respect to the boundary conditions defined in Eq. (7):" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 321, + 110, + 539, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 110, + 539, + 168 + ], + "spans": [ + { + "bbox": [ + 321, + 110, + 539, + 168 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {v} _ {\\theta} \\left(x ^ {\\mathrm {F M}}, t _ {\\mathrm {F M}}\\right) = \\widehat {x _ {1} ^ {\\mathrm {F M}}} - \\widehat {x _ {0} ^ {\\mathrm {F M}}} \\\\ = \\widehat {x _ {0} ^ {\\mathrm {D M}}} - \\widehat {x _ {T} ^ {\\mathrm {D M}}} \\\\ = \\left(\\alpha_ {t _ {\\mathrm {D M}}} - \\sigma t _ {\\mathrm {D M}}\\right) \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}} - v _ {\\theta} \\left(x _ {t _ {\\mathrm {D M}}} ^ {\\mathrm {D M}}, t _ {\\mathrm {D M}}\\right)\\right). \\tag {16} \\\\ \\end{array}", + "image_path": "e9a1a8118a85d405b09c751843e2f9800845bdcad1280b97a8c4674be761c287.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 170, + 539, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 170, + 539, + 259 + ], + "spans": [ + { + "bbox": [ + 313, + 170, + 539, + 259 + ], + "type": "text", + "content": "While we demonstrate the transition specifically from " + }, + { + "bbox": [ + 313, + 170, + 539, + 259 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 313, + 170, + 539, + 259 + ], + "type": "text", + "content": "-parameterization to velocity, this approach is versatile and can be readily applied to other parameterizations, such as " + }, + { + "bbox": [ + 313, + 170, + 539, + 259 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 170, + 539, + 259 + ], + "type": "text", + "content": "-parameterization, by following the same method outlined above. Algorithm 1 and Algorithm 2 summarize this approach in more detail. In summary, our main objective is to estimate the velocity using the prediction on the diffusion trajectory. We use standard Euler steps for inference." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 268, + 471, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 268, + 471, + 280 + ], + "spans": [ + { + "bbox": [ + 313, + 268, + 471, + 280 + ], + "type": "text", + "content": "3.3. Parameter-efficient Finetuning" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "spans": [ + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": "Prior works [36, 47] have demonstrated that parameter-efficient finetuning (PEFT) can be advantageous in tasks like domain adaptation and model distillation for generative models. PEFT reduces the number of parameters requiring updates, lowers memory demands during training, and theoretically mitigates catastrophic forgetting [2, 21]. In our approach, we utilize Low-Rank Adaptation (LoRA) [21], which achieves parameter efficiency by freezing the main model weights and updating only a low-rank decomposition of the weight matrices. Given a weight matrix " + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "inline_equation", + "content": "W_0 \\in \\mathbb{R}^{d \\times k}" + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": ", we freeze " + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": " and constrain the matrix's update with a low-rank decomposition " + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "inline_equation", + "content": "W_0 + \\Delta W = W_0 + BA" + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "inline_equation", + "content": "B \\in \\mathbb{R}^{d \\times r}" + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "inline_equation", + "content": "A \\in \\mathbb{R}^{r \\times k}" + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": " with the rank " + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "inline_equation", + "content": "r \\leq \\min(d, k)" + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": ". The modified forward pass for an input " + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": " is then " + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "inline_equation", + "content": "h = W_0x + \\Delta Wx = W_0x + BAx" + }, + { + "bbox": [ + 313, + 286, + 541, + 625 + ], + "type": "text", + "content": ". We observe that LoRA does not work out of the box when training a diffusion model with a flow matching objective, likely due to the shift required to adapt to a new parameterization scheme. In other words, LoRA struggles with the significant adjustment required when reconfiguring the model from a diffusion-based parameterization to a velocity prediction paradigm. This observation also underscores why naive application of a flow matching objective to a pretrained diffusion model is not effective; it forces the model to unlearn the old parameterization and switch to an entirely new one. In contrast, LoRA performs well when incorporating our proposed objective change that aligns the trajectories. Here, LoRA provides an efficient balance, achieving strong results with minimal parameter updates and showing further improvements as more parameters are fine-tuned." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 636, + 389, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 636, + 389, + 649 + ], + "spans": [ + { + "bbox": [ + 313, + 636, + 389, + 649 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 655, + 441, + 667 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 655, + 441, + 667 + ], + "spans": [ + { + "bbox": [ + 313, + 655, + 441, + 667 + ], + "type": "text", + "content": "4.1. Text-to-Image Synthesis" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 673, + 539, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 673, + 539, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 673, + 539, + 696 + ], + "type": "text", + "content": "We start with the text-to-image task, the original task on which the diffusion prior model was trained. Specifically," + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 730, + 316, + 738 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 316, + 738 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 316, + 738 + ], + "type": "text", + "content": "28351" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 104, + 89, + 271, + 210 + ], + "blocks": [ + { + "bbox": [ + 104, + 89, + 271, + 210 + ], + "lines": [ + { + "bbox": [ + 104, + 89, + 271, + 210 + ], + "spans": [ + { + "bbox": [ + 104, + 89, + 271, + 210 + ], + "type": "image", + "image_path": "ffaed77126368d386aa79621bf5d4fb29c263ee39e2dcaf4c73ca2e18f0d3209.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 224, + 296, + 266 + ], + "lines": [ + { + "bbox": [ + 68, + 224, + 296, + 266 + ], + "spans": [ + { + "bbox": [ + 68, + 224, + 296, + 266 + ], + "type": "text", + "content": "Figure 3. Qualitative results for our finetuned Text-to-Image models using different objectives. DM, FM and Diff2Flow stand for diffusion finetuning, flow matching finetuning, and our method. Images are generated with the same seed, NFEs, and CFG = 4.0." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 101, + 279, + 264, + 406 + ], + "blocks": [ + { + "bbox": [ + 101, + 279, + 264, + 406 + ], + "lines": [ + { + "bbox": [ + 101, + 279, + 264, + 406 + ], + "spans": [ + { + "bbox": [ + 101, + 279, + 264, + 406 + ], + "type": "image", + "image_path": "b622d6684982948d4a6fea8c1c52849c4bd72cbb7174fd63bdf140398e5fce78.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 415, + 296, + 448 + ], + "lines": [ + { + "bbox": [ + 68, + 415, + 296, + 448 + ], + "spans": [ + { + "bbox": [ + 68, + 415, + 296, + 448 + ], + "type": "text", + "content": "Figure 4. Our finetuning objective, both with and without PEFT effectively addresses the issue of non-zero-terminal SNR of DMs. The generations align faithfully to the input prompts." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 468, + 296, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 468, + 296, + 525 + ], + "spans": [ + { + "bbox": [ + 68, + 468, + 296, + 525 + ], + "type": "text", + "content": "we use Stable Diffusion 2.1 [46] as our diffusion prior, pretrained at a resolution of " + }, + { + "bbox": [ + 68, + 468, + 296, + 525 + ], + "type": "inline_equation", + "content": "768 \\times 768" + }, + { + "bbox": [ + 68, + 468, + 296, + 525 + ], + "type": "text", + "content": ", and fine-tune it to generate images at a lower resolution of " + }, + { + "bbox": [ + 68, + 468, + 296, + 525 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 68, + 468, + 296, + 525 + ], + "type": "text", + "content": ". This resolution shift allows us to investigate the effectiveness of different fine-tuning techniques in bridging resolution gaps." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 525, + 296, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 525, + 296, + 639 + ], + "spans": [ + { + "bbox": [ + 68, + 525, + 296, + 639 + ], + "type": "text", + "content": "Starting from the SD2.1 prior, we continue training with different objectives on the LAION-Aesthetics dataset [53] and evaluate model performance on COCO 2017 [29]. Fig. 5 shows that simply continuing diffusion training with an FM objective yields weak performance, especially when constraining model capacity with LoRA. In contrast, our method consistently surpasses continued diffusion training, both with and without classifier-free guidance, converging in as few as " + }, + { + "bbox": [ + 68, + 525, + 296, + 639 + ], + "type": "inline_equation", + "content": "2.5\\mathrm{k}" + }, + { + "bbox": [ + 68, + 525, + 296, + 639 + ], + "type": "text", + "content": " iterations. Note that all models show poor FID results without training due to the resolution mismatch." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 651, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 651, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 68, + 651, + 296, + 696 + ], + "type": "text", + "content": "We present qualitative results in Fig. 3 and Fig. 4, where we use the same sampling hyperparameters and fix the initial Gaussian noise. A key issue that we also address in the transition from the diffusion model to flow matching is the" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 326, + 88, + 529, + 136 + ], + "blocks": [ + { + "bbox": [ + 326, + 88, + 529, + 136 + ], + "lines": [ + { + "bbox": [ + 326, + 88, + 529, + 136 + ], + "spans": [ + { + "bbox": [ + 326, + 88, + 529, + 136 + ], + "type": "table", + "html": "
    MethodFID ↓CLIP ↑Aesthetics Score ↑
    SD1.556.7726.345.32
    SD1.5 (cont. training)56.3626.335.90
    Diff2Flow52.8026.545.99
    ", + "image_path": "1de8f67edeee919bef1e21302f6eb4b503328928b0e3b89df1ae1a03b7be0f3c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 322, + 144, + 531, + 155 + ], + "lines": [ + { + "bbox": [ + 322, + 144, + 531, + 155 + ], + "spans": [ + { + "bbox": [ + 322, + 144, + 531, + 155 + ], + "type": "text", + "content": "Table 1. Eval on COCO-2017 5k with 25 Euler/DDIM steps." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 312, + 174, + 539, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 174, + 539, + 219 + ], + "spans": [ + { + "bbox": [ + 312, + 174, + 539, + 219 + ], + "type": "text", + "content": "problem of non-zero terminal SNR [28], which typically results in images generated by stable diffusion models having, on average, gray tones instead of true black or white. Our training paradigm solves this problem, illustrated in Fig. 4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 219, + 539, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 219, + 539, + 344 + ], + "spans": [ + { + "bbox": [ + 312, + 219, + 539, + 344 + ], + "type": "text", + "content": "Furthermore, we investigate the scenario where diffusion training is resumed with our method without any changes in resolution or task objectives. Specifically, we initialize from an SD1.5 checkpoint and continue training on the LAION-Aesthetics dataset at a resolution of " + }, + { + "bbox": [ + 312, + 219, + 539, + 344 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 312, + 219, + 539, + 344 + ], + "type": "text", + "content": ". The corresponding evaluation metrics are reported in Tab. 1. Consistent with observations in SD3 [8], the rectified trajectories of Diff2Flow yield superior performance compared to the baseline SD model. We show that converting a diffusion model to its flow-matching counterpart also leads to performance improvements within the same generative task." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 350, + 454, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 454, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 454, + 361 + ], + "type": "text", + "content": "4.2. Rectifying the Trajectories" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 367, + 541, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 367, + 541, + 525 + ], + "spans": [ + { + "bbox": [ + 312, + 367, + 541, + 525 + ], + "type": "text", + "content": "In addition to fine-tuning diffusion models for resolution changes, we can also optimize them for straighter sampling trajectories to enable faster generation speeds. A popular approach to this is Reflow [32], which modifies the flow-matching training objective by replacing the random Gaussian noise terms in Eq. (5) with calculated noise derived from a pre-trained prior ODE to ensure that each noise-image pair is aligned according to the ODE. Quantitative results are presented in Tab. 3, where our method demonstrates competitive performance over various number of function evaluations (NFEs), including low NFEs such as 2 and 4, while only fine-tuning less than " + }, + { + "bbox": [ + 312, + 367, + 541, + 525 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 312, + 367, + 541, + 525 + ], + "type": "text", + "content": " of the parameters. Qualitative results using reflow with 4 inference steps are shown in Fig. 6 and in the Appendix." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 531, + 465, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 531, + 465, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 531, + 465, + 544 + ], + "type": "text", + "content": "4.3. Monocular Depth Estimation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "spans": [ + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "text", + "content": "In addition to common tasks, we also show the versatility of our approach for domain adaptation finetuning. Previous methods have shown strong performance in using largescale image generative models for affine-invariant monocular depth estimation [9, 14, 24]. Marigold [24] directly finetune Stable Diffusion on synthetic image-depth data using the standard " + }, + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "text", + "content": "-parameterized Diffusion loss (Equation (3)). Following a similar setup, DepthFM [14] propose to convert Stable Diffusion into a flow matching model by training with the flow matching (see Equation (5)) loss. This approach requires aligning the model's outputs to a different objective, interpolant, and timestep scaling (with " + }, + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{DM}} \\in [0,1000]" + }, + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "text", + "content": " in diffusion versus " + }, + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{FM}} \\in [0,1]" + }, + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "text", + "content": " in flow matching)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "text", + "content": "28352" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 118, + 87, + 286, + 162 + ], + "blocks": [ + { + "bbox": [ + 118, + 87, + 286, + 162 + ], + "lines": [ + { + "bbox": [ + 118, + 87, + 286, + 162 + ], + "spans": [ + { + "bbox": [ + 118, + 87, + 286, + 162 + ], + "type": "image", + "image_path": "ed958eb0c1765c2c8f3487292fae5d8377b92978a6795ea2cd9f758112611900.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 194, + 164, + 204, + 173 + ], + "lines": [ + { + "bbox": [ + 194, + 164, + 204, + 173 + ], + "spans": [ + { + "bbox": [ + 194, + 164, + 204, + 173 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 331, + 87, + 493, + 162 + ], + "blocks": [ + { + "bbox": [ + 331, + 87, + 493, + 162 + ], + "lines": [ + { + "bbox": [ + 331, + 87, + 493, + 162 + ], + "spans": [ + { + "bbox": [ + 331, + 87, + 493, + 162 + ], + "type": "image", + "image_path": "2c7492738fcf9907c4740f74d2301875dbb8bcfacbd5ef6e2654f450fcff0f63.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 406, + 164, + 417, + 173 + ], + "lines": [ + { + "bbox": [ + 406, + 164, + 417, + 173 + ], + "spans": [ + { + "bbox": [ + 406, + 164, + 417, + 173 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 68, + 182, + 541, + 236 + ], + "lines": [ + { + "bbox": [ + 68, + 182, + 541, + 236 + ], + "spans": [ + { + "bbox": [ + 68, + 182, + 541, + 236 + ], + "type": "text", + "content": "Figure 5. Text-to-Image FID on the COCO 2017 [29] validation dataset. Light curves indicate results without Classifier-free Guidance [18]. a) We show that both FM and Diff2Flow converge to the same performance, given sufficient training and model capacity (full fine-tuning). However, our method removes the computational overhead from learning how to adjust the network output, resulting in faster convergence. b) Given limited modeling capacity (LoRA) the difference is more pronounced, where the FM model fails to close the gap to Diff2Flow, indicating that finetuning a portion of the parameters is enough to transfer a diffusion model to a flow matching model." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 69, + 244, + 541, + 396 + ], + "blocks": [ + { + "bbox": [ + 69, + 244, + 541, + 396 + ], + "lines": [ + { + "bbox": [ + 69, + 244, + 541, + 396 + ], + "spans": [ + { + "bbox": [ + 69, + 244, + 541, + 396 + ], + "type": "table", + "html": "
    MethodTraining samplesNYUv2 [40]KITTI [13]ETH3D [52]ScanNet [5]DIODE [62]
    AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑AbsRel↓δ1↑
    Depth Anything [65] (CVPR '24)62M4.398.17.694.712.788.2——6.695.2
    Depth Anything v2 [66] (arXiv '24)62M4.497.97.594.813.286.2——6.595.4
    Metric3D [68] (ICCV '23)8M5.096.65.897.06.496.57.494.122.480.5
    Metric3D v2 [22] (TPAMI '24)16M4.398.14.498.24.298.3—†—†13.689.5
    Marigold [24] (CVPR '24)74K5.596.49.991.66.596.06.495.130.877.3
    GeoWizard [9] (ECCV '24)278K5.296.69.792.16.496.16.195.329.779.2
    reproduced by [38]278K5.796.214.482.07.594.36.195.831.477.1
    DepthFM [14] (AAAI '25)74K6.095.59.190.26.595.46.694.922.478.5
    E2E FT [38] (WACV '25)74K5.296.69.691.96.295.95.896.230.277.9
    Lotus-G [16] (arXiv '24)59K5.496.611.387.76.296.16.096.0——
    Diff2Flow74K5.796.78.792.05.597.46.295.721.679.5
    Diff2Flow (LoRA)74K5.996.49.590.86.096.86.495.522.678.5
    ", + "image_path": "32a8f1f6aa16848ba86dda9aa6645cdbdca846bc8dcb3983ef530f6faa1f84a6.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 70, + 454, + 298, + 553 + ], + "blocks": [ + { + "bbox": [ + 68, + 405, + 541, + 437 + ], + "lines": [ + { + "bbox": [ + 68, + 405, + 541, + 437 + ], + "spans": [ + { + "bbox": [ + 68, + 405, + 541, + 437 + ], + "type": "text", + "content": "Table 2. Comparison to state-of-the-art depth estimation methods. We compare discriminative (top) and generative models (bottom). Numbers obtained from [38]. " + }, + { + "bbox": [ + 68, + 405, + 541, + 437 + ], + "type": "inline_equation", + "content": "{}^{ \\dagger }" + }, + { + "bbox": [ + 68, + 405, + 541, + 437 + ], + "type": "text", + "content": " Metric3D v2 [22] was trained on ScanNet,so zero-shot evaluation is not possible. We also show the results reproduced by [38] for GeoWizard. All of our results are generated with NFE= 10 and an ensemble size of 4 ." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 454, + 298, + 553 + ], + "lines": [ + { + "bbox": [ + 70, + 454, + 298, + 553 + ], + "spans": [ + { + "bbox": [ + 70, + 454, + 298, + 553 + ], + "type": "table", + "html": "
    Method#Params ↓StepsFID ↓CLIP ↑
    SDv1.5+DPM Solver [34] (NeurIPS '22)0.9B2520.100.318
    Rectified Flow [32] (ICLR '23)0.9B2521.650.315
    Diff2Flow (LoRA)62M2521.450.314
    PeRFlow [64] (arXiv '24)0.9B422.970.294
    Diff2Flow (LoRA)62M425.290.313
    Rectified Flow [32] (ICLR '23)0.9B231.350.296
    Diff2Flow (LoRA)62M232.310.305
    ", + "image_path": "3652c1ed82e2806af85c53fa2bd9b2c106aa25de67d686ed8463df0a48af35da.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 562, + 296, + 593 + ], + "lines": [ + { + "bbox": [ + 69, + 562, + 296, + 593 + ], + "spans": [ + { + "bbox": [ + 69, + 562, + 296, + 593 + ], + "type": "text", + "content": "Table 3. We fine-tune all our models with LoRA, and apply only 1-rectified flow according to Liu et al. [32]. We get competitive results with state-of-the-art reflow models." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 68, + 616, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 616, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 68, + 616, + 296, + 696 + ], + "type": "text", + "content": "This process incurs significant computational cost, limiting the training efficiency and final performance. However, the flow matching nature of DepthFM allows for faster inference, at slightly reduced performance when given enough training. Our method mitigates this problem, accelerating training, and improving performance. The training and evaluation metrics are provided in the Appendix." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 337, + 454, + 396, + 514 + ], + "blocks": [ + { + "bbox": [ + 337, + 454, + 396, + 514 + ], + "lines": [ + { + "bbox": [ + 337, + 454, + 396, + 514 + ], + "spans": [ + { + "bbox": [ + 337, + 454, + 396, + 514 + ], + "type": "image", + "image_path": "9970ebf7ad1728f06d921f5ac6c3e90bc367172da9b080bc7ad0bd4f7fd3374b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 524, + 539, + 534 + ], + "lines": [ + { + "bbox": [ + 313, + 524, + 539, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 524, + 539, + 534 + ], + "type": "text", + "content": "Figure 6. SD1.5 [46] + Diff2Flow-Reflow, 4-step inference results." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 396, + 454, + 454, + 514 + ], + "blocks": [ + { + "bbox": [ + 396, + 454, + 454, + 514 + ], + "lines": [ + { + "bbox": [ + 396, + 454, + 454, + 514 + ], + "spans": [ + { + "bbox": [ + 396, + 454, + 454, + 514 + ], + "type": "image", + "image_path": "ff86adc39d021c2268fc6f72b9632e19491265e5b7880b4074779f1ddbe9fdaf.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 454, + 454, + 513, + 513 + ], + "blocks": [ + { + "bbox": [ + 454, + 454, + 513, + 513 + ], + "lines": [ + { + "bbox": [ + 454, + 454, + 513, + 513 + ], + "spans": [ + { + "bbox": [ + 454, + 454, + 513, + 513 + ], + "type": "image", + "image_path": "e2cd60cb02465f6f3322b5745f15f89420a0c1ab46ff544f0f8a1512b23e62cb.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 560, + 541, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 560, + 541, + 696 + ], + "spans": [ + { + "bbox": [ + 312, + 560, + 541, + 696 + ], + "type": "text", + "content": "Results Table 2 compares our method with both discriminative and generative depth predictors. Trained exclusively on synthetic data, our method matches or outperforms the prior state-of-the-art in monocular depth estimation, as shown in Figure 8. The diffusion-based Marigold model [24] struggles to achieve high accuracy with a limited number of sampling steps. In contrast to both DepthFM and Marigold, our method achieves competitive performance after very few training iterations and with only two sampling steps. The performance difference becomes even more pronounced when training with LoRA, where model capacity is limited. Figure 8b shows that this limitation prevents a" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 730, + 317, + 739 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 317, + 739 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 317, + 739 + ], + "type": "text", + "content": "28353" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 88, + 526, + 220 + ], + "blocks": [ + { + "bbox": [ + 78, + 88, + 526, + 220 + ], + "lines": [ + { + "bbox": [ + 78, + 88, + 526, + 220 + ], + "spans": [ + { + "bbox": [ + 78, + 88, + 526, + 220 + ], + "type": "image", + "image_path": "f62519c233e7ab65e3612da256dabdf55d7819a95250902520839fa6814b7cc8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 230, + 541, + 252 + ], + "lines": [ + { + "bbox": [ + 68, + 230, + 541, + 252 + ], + "spans": [ + { + "bbox": [ + 68, + 230, + 541, + 252 + ], + "type": "text", + "content": "Figure 7. Zero-shot qualitative results on real-world imagery. Our methods produce depth predictions with perceptually higher fidelity and finer detail. All predictions are made using the optimal settings of the models. Best viewed when zoomed in." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 91, + 262, + 285, + 336 + ], + "blocks": [ + { + "bbox": [ + 91, + 262, + 285, + 336 + ], + "lines": [ + { + "bbox": [ + 91, + 262, + 285, + 336 + ], + "spans": [ + { + "bbox": [ + 91, + 262, + 285, + 336 + ], + "type": "image", + "image_path": "50613c8e738a25a5c0475ebd9d1ae306ed702d078f35a453a1c4ad0aa60914a4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 168, + 338, + 178, + 346 + ], + "lines": [ + { + "bbox": [ + 168, + 338, + 178, + 346 + ], + "spans": [ + { + "bbox": [ + 168, + 338, + 178, + 346 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 322, + 262, + 516, + 336 + ], + "blocks": [ + { + "bbox": [ + 322, + 262, + 516, + 336 + ], + "lines": [ + { + "bbox": [ + 322, + 262, + 516, + 336 + ], + "spans": [ + { + "bbox": [ + 322, + 262, + 516, + 336 + ], + "type": "image", + "image_path": "3d2817253b6f26e24931d528490a9372138c02b22aab64a98f9bd2a300a40034.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 400, + 338, + 410, + 346 + ], + "lines": [ + { + "bbox": [ + 400, + 338, + 410, + 346 + ], + "spans": [ + { + "bbox": [ + 400, + 338, + 410, + 346 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 68, + 356, + 541, + 407 + ], + "lines": [ + { + "bbox": [ + 68, + 356, + 541, + 407 + ], + "spans": [ + { + "bbox": [ + 68, + 356, + 541, + 407 + ], + "type": "text", + "content": "Figure 8. Results on NYUv2 depth benchmark [40] with 4 ensemble members. a) With full fine-tuning we find that FM adapts to the I2D task very quickly, but adding the objective change leads to even quicker convergence and better results. In contrast, the diffusion-based counterpart [24] suffers from slower convergence and requires more inference steps. b) The difference between FM and Diff2Flow is even more pronounced if we limit the capacity of the model by using Low-Rank adaptations. With Diff2Flow, the model does not need to learn to change the objective and can focus only on the task itself." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 428, + 296, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 428, + 296, + 609 + ], + "spans": [ + { + "bbox": [ + 68, + 428, + 296, + 609 + ], + "type": "text", + "content": "straightforward application of the FM loss to the diffusion model. DepthFM struggles here as the model has to learn the adaptation from the " + }, + { + "bbox": [ + 68, + 428, + 296, + 609 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 68, + 428, + 296, + 609 + ], + "type": "text", + "content": "-parameterization to the FM objective. The successful adaptation of the diffusion-based image prior to flow matching supports our initial hypothesis that the integration of our objective change facilitates this transformation. In Table 4, we present an ablation study on performance with different numbers of trainable parameters. Fine-tuning just " + }, + { + "bbox": [ + 68, + 428, + 296, + 609 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 68, + 428, + 296, + 609 + ], + "type": "text", + "content": " of the original parameters is sufficient to achieve competitive performance with previous methods, particularly with the fully finetuned DepthFM model. Figure 7 qualitatively compares our method with state-of-the-art depth estimators on in-the-wild images. While discriminative methods often lack detail and fidelity, generative models capture fine details and avoid the averaging effect common to discriminative approaches." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 620, + 137, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 620, + 137, + 632 + ], + "spans": [ + { + "bbox": [ + 69, + 620, + 137, + 632 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 68, + 639, + 296, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 639, + 296, + 696 + ], + "spans": [ + { + "bbox": [ + 68, + 639, + 296, + 696 + ], + "type": "text", + "content": "We introduce a novel framework, Diff2Flow, that effectively converts pre-trained diffusion into flow matching models, providing a twofold optimization. First, this approach allows us to efficiently use the diffusion model's prior by exploiting its powerful generative capabilities with" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 328, + 426, + 525, + 488 + ], + "blocks": [ + { + "bbox": [ + 328, + 426, + 525, + 488 + ], + "lines": [ + { + "bbox": [ + 328, + 426, + 525, + 488 + ], + "spans": [ + { + "bbox": [ + 328, + 426, + 525, + 488 + ], + "type": "table", + "html": "
    Method#Params ↓AbsRel ↓δ1 ↑
    Marigold + E2E FT [38]866M5.296.6
    Diff2Flow866M5.796.7
    Diff2Flow (LoRA base)222M5.996.4
    Diff2Flow (LoRA small)62M6.995.0
    ", + "image_path": "638c0acc1ec7952a342bb011839bedcb18c5d54ac24b06fac72c73a3ae845323.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 496, + 541, + 528 + ], + "lines": [ + { + "bbox": [ + 313, + 496, + 541, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 541, + 528 + ], + "type": "text", + "content": "Table 4. Zero-shot evaluation on NYUv2 [40] for different number of trainable parameters. We can achieve competitive performance with only a fraction of previous SOTA methods." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "spans": [ + { + "bbox": [ + 312, + 548, + 541, + 696 + ], + "type": "text", + "content": "out retraining from scratch. Second, by adapting it to the flow matching paradigm, we gain key benefits unique to flow matching: fast inference suitable for downstream tasks, and the ability to straighten sampling trajectories through techniques such as reflow, which further improves efficiency and performance. As a result, Diff2Flow not only improves training and inference efficiency but also delivers competitive performance in diverse tasks, including text-to-image synthesis and monocular depth estimation. By using parameter-efficient fine-tuning methods such as LoRA, our framework further minimizes computational requirements and demonstrates a practical, scalable way to merge diffusion and flow matching paradigms in generative modeling." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "text", + "content": "28354" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 89, + 162, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 89, + 162, + 102 + ], + "spans": [ + { + "bbox": [ + 69, + 89, + 162, + 102 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 68, + 107, + 297, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 107, + 297, + 244 + ], + "spans": [ + { + "bbox": [ + 68, + 107, + 297, + 244 + ], + "type": "text", + "content": "This project has been supported by the bidders project KLIMA-MEMES, the German Federal Ministry for Economic Affairs and Climate Action within the project \"NXT GEN AI METHODS - Generative Methoden für Percep tion, Prädiktion und Planung\", the project \"GeniusRobot\" (01IS24083), funded by the Federal Ministry of Education and Research (BMBF), and the German Research Foundation (DFG) project 421703927. The authors acknowledge the Gauss Center for Supercomputing for providing compute through the NIC on JUWELS at JSC and the HPC resources supplied by the Erlangen National High Performance Computing Center (NHR@FAU funded by DFG project 440719683) under the NHR project JA-22883." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 262, + 126, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 262, + 126, + 273 + ], + "spans": [ + { + "bbox": [ + 70, + 262, + 126, + 273 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 74, + 280, + 296, + 696 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 74, + 280, + 296, + 321 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 280, + 296, + 321 + ], + "spans": [ + { + "bbox": [ + 74, + 280, + 296, + 321 + ], + "type": "text", + "content": "[1] Michael S Albergo, Nicholas M Boffi, and Eric Vanden-Eijnden. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9043-9053, 2023. 7" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "spans": [ + { + "bbox": [ + 293, + 730, + 317, + 738 + ], + "type": "text", + "content": "28357" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_content_list.json b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f1d49b984d520e3017807fcff9bcc66e37192802 --- /dev/null +++ b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_content_list.json @@ -0,0 +1,2187 @@ +[ + { + "type": "text", + "text": "DiffCAM: Data-Driven Saliency Maps by Capturing Feature Differences", + "text_level": 1, + "bbox": [ + 133, + 130, + 867, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xingjian Li, Qiming Zhao, Peelesh Bisht, Mostofa Rafid Uddin, Jin Yu Kim, Bryan Zhang, Min Xu* Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213, United States", + "bbox": [ + 104, + 180, + 898, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 268, + 328, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, the interpretability of Deep Neural Networks (DNNs) has garnered significant attention, particularly due to their widespread deployment in critical domains like healthcare, finance, and autonomous systems. To address the challenge of understanding how DNNs make decisions, Explainable AI (XAI) methods, such as saliency maps, have been developed to provide insights into the inner workings of these models. This paper introduces DiffCAM, a novel XAI method designed to overcome limitations in existing Class Activation Map (CAM)-based techniques, which often rely on decision boundary gradients to estimate feature importance. DiffCAM differentiates itself by considering the actual data distribution of the reference class, identifying feature importance based on how a target example differs from reference examples. This approach captures the most discriminative features without relying on decision boundaries or prediction results, making DiffCAM applicable to a broader range of models, including foundation models. Through extensive experiments, we demonstrate the superior performance and flexibility of DiffCAM in providing meaningful explanations across diverse datasets and scenarios.", + "bbox": [ + 91, + 301, + 483, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 665, + 223, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep Neural Networks (DNNs) [20, 43, 52] are often referred to as black-box models due to the difficulty in understanding how they extract features and make decisions. This lack of interpretability raises significant concerns in critical areas such as healthcare, finance, and autonomous systems. To address this challenge, Explainable AI (XAI) methods are designed to make the decision-making processes of AI systems more transparent and understandable to humans [2, 27]. It allows users and stakeholders to gain insight into how AI models arrive at specific outcomes [48].", + "bbox": [ + 89, + 691, + 482, + 843 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among the XAI approaches, saliency map is a common technique used to explain deep vision models. A saliency", + "bbox": [ + 89, + 843, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "map is a visualization that highlights the critical parts of an image that significantly influence a model's prediction.", + "bbox": [ + 511, + 268, + 903, + 300 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In deep convolutional neural networks (CNNs), the activation map of each convolutional channel in deep layers naturally provides such information of spatial attention. This nature motivates popular solutions, such as Class Activation Map (CAM) [60], GradCAM [41] and ScoreCAM [55], which calculate a saliency map by a weighted aggregation of those feature channels. To estimate the feature importance, GradCAM calculates the gradient of the prediction (typically the probability of a target class) with respect to the input features. This gradient essentially measures the sensitivity of the prediction to variances in the input image or deep features, revealing the fastest direction in the feature space to change the model's decision. CAM and ScoreCAM adopt the similar idea to estimate the feature importance while avoiding gradient calculation.", + "bbox": [ + 511, + 303, + 906, + 531 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the widely application of those CAM-based approaches, there still exists an essential limitation of them in estimating the feature importance. Here we illustrate our core idea by a simplified binary classification model predicting their language test result (Pass or Fail) according to their historical reading and writing scores. Intuitively, writing is learned as a more dominant feature for the prediction as it is usually harder than reading. This results in a decision boundary which lean to separate low and high write scores. When explaining a specific prediction, existing CAM-based approaches consider the direction orthogonal to the decision boundary as the feature importance vector, i.e., indicating the writing score is a more important feature for the prediction. However, this is counter-intuitive in case that the explained data point is not a representative one among its class. For example, when explaining why the student $x_{t}$ is predicted as Fail, CAM-based approaches assign a higher importance on writing to which the final prediction is more sensitive. However, the writing score of $x_{t}$ is as high as the average of the Pass group and higher than most of the Fail students. Therefore, reading is a better feature to explain the failure of $x_{t}$ , i.e., if $x_{t}$ 's reading is as good as the Pass group, $x_{t}$ will be predicted as Pass.", + "bbox": [ + 511, + 534, + 908, + 882 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Another relevant technique, counterfactual explanation", + "bbox": [ + 532, + 885, + 906, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 109, + 886, + 238, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10327", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a7bb57364ac63296e4d91ff20f2f709acdced3631ec57d658aee2d97b85976b6.jpg", + "image_caption": [ + "Figure 1. Motivation of DiffCAM. Existing CAM-based approaches resort to reach the decision boundary (e.g., GradCAM and ScoreCAM) or the nearest virtual example (e.g., counterfactual explanations) in the fastest direction, ignoring the actual data distribution for most representative examples. DiffCAM instead looks for the optimal direction that best represents the difference from a specified reference group. From this perspective, DiffCAM attributes Fail of $x_{t}$ mainly to its low Reading score, while traditional CAM-based approaches prefer Writing as the main reason." + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 478, + 311 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[16, 45], aims to find the closest virtual example on the data manifold that requires minimal changes to the input example to reach this virtual example. While it focuses more on the most discriminative feature from a data perspective, it still fails in capturing the difference between the target example and the majority of a reference class (the Pass class). As illustrated in Figure 1, the considered counterpart example is usually a virtual point near the decision boundary instead of a representative point among the real population of the reference class.", + "bbox": [ + 89, + 476, + 482, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The above analyses motivate us to design a novel CAM-based XAI approach by considering the actual data distribution of the reference class rather than the decision boundary. More specifically, given a group of reference examples, we aim to find the optimal direction (representing the feature importance vector) that optimally distinguish the target example from the reference group. This direction is the one on which the projections of reference examples are most distant to the target point, while maximally preserve their inherent common features. By this way, the feature importance vector represents only the most discriminative ingredients in the feature space. The exact solution is introduced in the Method section. We name our method DiffCAM as it explains model outputs by capturing essential feature differences. DiffCAM maintains the explanation format of saliency map and can be applied to more scenarios. The main difference between DiffCAM and existing CAM-based explanations can be summarized as follows.", + "bbox": [ + 89, + 628, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Given a trained model to be explained, DiffCAM captures information about how is the target example different from the actual data points from the reference group, instead of considering how to quickly pass the decision boundary.", + "- DiffCAM is a more flexible and general framework. By using all the different classes as the reference group, DiffCAM functions similar to existing CAM-based approaches. By using one whole class as the reference group, DiffCAM provides counterfactual explanations. Beyond those, DiffCAM can also explain how a target example differs from a specific set of other examples, which may even belong to the same class with the target one.", + "- DiffCAM generates saliency maps without relying on the prediction results. This makes DiffCAM applicable to general feature extractors such as foundation models from self-supervised pre-training." + ], + "bbox": [ + 511, + 90, + 903, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the experiment section, we demonstrate the effects of DiffCAM with several datasets covering general computer vision and medical imaging datasets.", + "bbox": [ + 511, + 349, + 906, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 410, + 653, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Explainable AI", + "text_level": 1, + "bbox": [ + 513, + 434, + 666, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Explainable Artificial Intelligence (XAI) focuses on making complex machine learning models more interpretable, addressing the \"black-box\" nature of many advanced AI systems [26, 30]. The primary goal is to provide human-understandable explanations of a model's decisions, which is critical for improving trust, accountability, and ethical AI usage [21], especially in high-stakes fields like healthcare [24, 49, 50].", + "bbox": [ + 511, + 458, + 906, + 579 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "XAI techniques are broadly categorized into intrinsic methods, which involve building models that are inherently interpretable [37], and post-hoc methods, which generate explanations for pre-existing models without great changes to their structures [44, 59]. Post-hoc techniques are widely used for deep learning models, which are often too complex for intrinsic interpretability [4].", + "bbox": [ + 511, + 580, + 905, + 685 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key challenge in XAI is balancing the trade-off between a model's accuracy and its interpretability. In deep learning, where models are often highly effective but opaque, post-hoc methods, such as feature attribution and counterfactual reasoning, have become powerful tools for making predictions understandable [28].", + "bbox": [ + 511, + 686, + 905, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Attribution Explanations", + "text_level": 1, + "bbox": [ + 511, + 786, + 743, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attribution-based methods play a crucial role in explaining behaviors by neural networks in tasks such as image classification [5, 22]. These methods identify which parts of an input image are most influential in a model's decision-making process [1, 33]. In the context of visual explanations, saliency mapping is often used in image classification", + "bbox": [ + 511, + 809, + 905, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10328", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tasks to illustrate influential regions without modifying the underlying model [10, 19]. However, these methods may struggle with fine-grained tasks where subtle distinctions require more detailed and nuanced explanations [4].", + "bbox": [ + 89, + 90, + 480, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GradCAM [41] is widely used for generating visual explanations in neural networks by highlighting important regions contributing to a model's decision. Methods like GradCAM++ [9], ScoreCAM [55], Ablation-CAM [12], XGrad-CAM [14], EigenCAM [29], LayerCAM [17], and SmoothGradCAM++ [32] further refine this approach, offering more discriminative or interpretable saliency maps. Additionally, some saliency mapping techniques that differ from CAM-based methods such as Gradient*Input [42] and Integrated Gradient [46], are designed to highlight critical regions contributing to the model's decision by calculation on input images rather than using deep features.", + "bbox": [ + 89, + 152, + 482, + 333 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We also note different attribution methods such as LIME and SHAP, and Layer-wise Relevance Propagation (LRP) which are popular for enhancing AI explainability. LIME [35] provides locally faithful explanations by perturbing inputs, SHAP [39] is motivated by the game theory, and LRP [8] calculates relevance scores via attribution propagation. These methods are also important but not the main focus of our paper.", + "bbox": [ + 89, + 334, + 483, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Counterfactual Explanation", + "text_level": 1, + "bbox": [ + 89, + 465, + 341, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "One limitation of Attribution Explanation lies in its inability to identify attributes that distinguish a specific class from other classes, i.e. failing to address \"Why not a class\". Counterfactual Explanation introduced in [47, 53], was designed to provide insights into machine learning models, aiding decision-making in domains such as law and policy through counterfactual reasoning. In visual tasks, CE can be operationalized as \"for class A to be correct, class B would require modifications to these specific parts.\" These modifications can be achieved through adversarial attacks [13, 51] or GAN-based methods [15, 25, 31, 38, 40].", + "bbox": [ + 89, + 491, + 482, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work is more relevant to the saliency map based counterfactual explanation work. GALORE [56] introduced a \"generative explanation framework\" that unifies attribution-based, deliberative, and counterfactual explanations into a combined attribution map aligned with classifier predictions and confidence scores. Similarly, [34] measured the changes required to traverse from the learned manifold to the contrastive manifold and integrated this approach into Grad-CAM to generate heatmaps. Content-Aware Counterfactual Explanation (CCE) [57] proposed a content-aware counterfactual perturbation algorithm that generates positive-negative saliency-based explanations.", + "bbox": [ + 89, + 657, + 482, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach differs from GALORE and CEE by not performing counterfactual comparisons at the saliency map level. Instead, we distinguish attributes of similar classes at the feature level, localizing a distinction heatmap that high-", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "lights the unique features of the target class compared to other classes. The counterfactual explanation consists of the distinction heatmap for the target class A and another distinction heatmap for the counterfactual class B, which shares common features with A.", + "bbox": [ + 511, + 90, + 905, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 179, + 604, + 195 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. General Framework", + "text_level": 1, + "bbox": [ + 513, + 204, + 705, + 219 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed DiffCAM approach follows the general framework of Class Activation Map (CAM) [60]. We consider deep convolutional neural networks. For simplification, we assume the deep model to be explained is composed of a deep feature extractor and a fully connected layer, which is a common architecture for modern DNNs. Let's define $\\mathbf{x}$ as a target example to be explained, and $d$ as the number of feature channels of the last convolutional layer. By passing forward $\\mathbf{x}$ , we get $\\mathbf{A}_k(\\mathbf{x})(k\\in [1,2,\\dots,d])$ as the $k$ -th activation map. The goal of CAM-based approaches is to generate a saliency map $M_{c}(\\mathbf{x})$ explaining the prediction towards class $c$ with $\\mathbf{x}$ as input. Specifically, a feature importance vector $\\mathbf{w}^c\\in \\mathbb{R}^d$ is used to aggregate all the activation maps as", + "bbox": [ + 511, + 227, + 906, + 440 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {c} (\\mathbf {x}) = \\sum_ {k = 1} ^ {d} \\mathbf {w} _ {k} ^ {c} \\mathbf {A} _ {k} (\\mathbf {x}). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 450, + 905, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the original CAM method [60], $\\mathbf{w}_k^c$ are directly taken from the weights of the fully connected layer. Specifically, for class $c$ , the weight $\\mathbf{w}_k^c$ is the $k$ -th component of the fully connected layer's weights $\\mathbf{W}_c$ for that class. Many following work [9, 12, 14, 17, 29, 41, 55] adopt this general framework and differ in their ways of calculating $\\mathbf{w}_k^c$ . Here we summarize two main categories from existing approaches, which focus on the gradient and individual contribution of each feature channel respectively.", + "bbox": [ + 511, + 497, + 905, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GradCAM: $\\mathbf{w}_k^c$ are computed based on the gradients of the class score $y^{c}(\\mathbf{x})$ with respect to the activation map $\\mathbf{A}_k(\\mathbf{x})$ . Specifically, $\\mathbf{w}_k^c$ is the global average of the gradients across all spatial locations in the feature map as", + "bbox": [ + 511, + 633, + 905, + 694 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} _ {k} ^ {c} = \\frac {1}{Z} \\sum_ {i, j} \\frac {\\partial y ^ {c}}{\\partial \\mathbf {A} _ {k} ^ {i , j} (\\mathbf {x})} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 703, + 906, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{A}_k^{i,j}(\\mathbf{x})$ is the activation at spatial location $(i,j)$ of the feature map and $Z$ is a normalization term.", + "bbox": [ + 511, + 753, + 906, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ScoreCAM: $\\mathbf{w}_k^c$ are measured by the increase in the $c$ -th class score when the feature map $\\mathbf{A}_k(\\mathbf{x})$ is activated. For the $k$ -th feature channel, it first creates the corresponding masked input $\\tilde{\\mathbf{x}}_k = \\mathbf{A}_k(\\mathbf{x}) \\odot \\mathbf{x}$ , and then calculate the feature importance vector as", + "bbox": [ + 511, + 785, + 905, + 859 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} _ {k} ^ {c} = \\frac {y ^ {c} \\left(\\tilde {\\mathbf {x}} _ {k}\\right)}{\\sum_ {k} y ^ {c} \\left(\\tilde {\\mathbf {x}} _ {k}\\right)}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 869, + 905, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10329", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8474e6930d814b64156745ac11bac91754282d858d943a5a16de9a29aac3f1cd.jpg", + "image_caption": [ + "Figure 2. Overview of the DiffCAM framework and applications. Given a target image and a set of reference examples, DiffCAM computes deep feature embeddings, identifies the direction that captures differences between the target and references, and generates a saliency map highlighting key distinguishing features. DiffCAM can provide flexible explanations according to the selection of reference examples." + ], + "image_footnote": [], + "bbox": [ + 122, + 84, + 880, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. DiffCAM Implementation", + "text_level": 1, + "bbox": [ + 89, + 420, + 328, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, DiffCAM regards the explanation problem as looking for the feature components that best distinguish the target example (to be explained) and a group of reference examples. Suppose the example we aim to explain is $\\mathbf{x}$ . According to the explanation type we are interested in, a set of $n$ examples $\\{\\hat{\\mathbf{x}}^{(i)}\\}_{i=1}^{n}$ is determined as the reference group. Note that the class labels of $\\{\\hat{\\mathbf{x}}^{(i)}\\}_{i=1}^{n}$ can be flexible, i.e., they may have the same, different or no labels. We generate the deep embedding $\\mathbf{z} \\in \\mathbb{R}^d$ by performing average pooling along the spatial dimension on the whole feature map $\\mathbf{A}(\\mathbf{x})$ , and get $\\{\\hat{\\mathbf{z}}^{(i)}\\}_{i=1}^{n}$ for the reference examples.", + "bbox": [ + 89, + 443, + 483, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The feature importance vector $\\mathbf{w}$ is defined as the optimal direction in the feature space that represents the most discriminative features relative to the reference data. Specifically, the projections of $\\{\\hat{\\mathbf{z}}^{(i)}\\}_{i = 1}^{n}$ on $\\mathbf{w}$ are expected to have the largest distance with $\\mathbf{z}$ while maintain as much commonality as possible.", + "bbox": [ + 89, + 609, + 483, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To solve the optimal $\\mathbf{w}$ , we apply fundamental mathematical tools in linear algebra and convex optimization. Formally, denoting the mean reference position by $\\hat{\\mu} = \\frac{1}{n}\\sum_{i=1}^{n}\\hat{\\mathbf{z}}^{(i)}$ , the distance between the target example and the reference group along $\\mathbf{w}$ can be defined as $\\|\\mathbf{w}^T z - \\mathbf{w}^T\\hat{\\mu}\\|^2$ . The variance among the reference examples projected on $\\mathbf{w}$ is $\\frac{1}{n}\\sum_{i=1}^{n}\\|\\mathbf{w}^T\\hat{\\mathbf{z}}^{(i)} - \\mathbf{w}^T\\hat{\\mu}\\|^2$ . The measure can be written as", + "bbox": [ + 89, + 700, + 483, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} J (\\mathbf {w}) = \\frac {\\left\\| \\mathbf {w} ^ {T} z - \\mathbf {w} ^ {T} \\hat {\\mu} \\right\\| ^ {2}}{\\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {w} ^ {T} \\hat {\\mathbf {z}} ^ {(i)} - \\mathbf {w} ^ {T} \\hat {\\mu} \\right\\| ^ {2}} (4) \\\\ = \\frac {\\mathbf {w} ^ {T} \\mathbf {S} _ {\\mu} \\mathbf {w}}{\\mathbf {w} ^ {T} \\mathbf {S} _ {\\mathbf {v}} \\mathbf {w}}, (5) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 827, + 482, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{S}_{\\mu} = (\\mathbf{z} - \\hat{\\mu})(\\mathbf{z} - \\hat{\\mu})^T$ represents discrimination between the target example and the reference group, and $\\mathbf{S}_{\\mathbf{v}} = \\sum_{i=1}^{n} (\\hat{\\mathbf{z}}^{(i)} - \\hat{\\mu})(\\hat{\\mathbf{z}}^{(i)} - \\hat{\\mu})^T$ represents internal variation among the reference examples. By differentiating and setting to zero, we find the optimal $\\mathbf{w}$ that maximizes $J(\\mathbf{w})$ as", + "bbox": [ + 511, + 420, + 906, + 511 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} ^ {*} = \\underset {\\mathbf {w}} {\\operatorname {a r g m a x}} J (w) = \\mathbf {S _ {v}} ^ {- 1} (\\mathbf {z} - \\hat {\\mu}). \\qquad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 513, + 906, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Detailed derivation is put in Section A in Appendix. For supervised trained models, the inverse matrix $\\mathbf{S}_{\\mathbf{v}}^{-1}$ can be pre-calculated over training examples to avoid high inference complexity. We further adopt the Tikhonov regularization to ensure stability in calculating the inverse matrix. A small regularization term $\\lambda \\mathbf{I}$ is added onto $\\mathbf{S}_{\\mathbf{v}}$ when calculating the inverse. The solved $\\mathbf{w}^*$ is finally used to generate the saliency map by calculating the weighted aggregation of the feature channels as", + "bbox": [ + 511, + 547, + 908, + 681 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} ^ {\\text {D i f f C A M}} (\\mathbf {x}) = \\sum_ {k = 1} ^ {d} \\mathbf {w} _ {k} ^ {*} \\mathbf {A} _ {k} (\\mathbf {x}). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 694, + 906, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A flexibility of DiffCAM lies in the selection of the reference group. In most cases, we use all the remaining classes as reference when answering the \"Why is\" question. For large-scale datasets with diverse classes (e.g., ImageNet), we empirically recommend to select a subset of similar classes (with k-Nearest-Neighbor search) as the reference group to obtain more discriminative features. To answer the \"Why not\" question or analyze internal variations, the corresponding target class will be specified as the reference group. An illustrative overview is presented in Figure 2.", + "bbox": [ + 511, + 750, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10330", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7c10b0da4c79ec90cc1f0bf90a7d7507a7cf400560201b1806e51f2eeea63e16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 133, + 80, + 212, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4314fabba3db1756bc361f0e616f453d1eac9e51ad7fb5a6febf722bc902c3b6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 80, + 305, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0a1ae22eece566148dec42d94a9ed8fc5d79fd02f6dd172a04ccfdf7ea6759bf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 312, + 80, + 403, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4f2b0dcbcb90cff3457207e84f3ae86869ef352bd197ba2365ef04143e764bff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 80, + 491, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/739522f9a1e0507e42e9a6f5cfe72c80cbf557078f675dd128fdb8c7c7be5f35.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 80, + 586, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c908354be5a8ab8f1a01cfc2495cb0539cf0bfa1b0bfde4eda1bfff28c52f6f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 596, + 80, + 676, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/92cc9cde518738b4606771727ef43404efe7df54635199bd7113335bb4125ed1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 80, + 769, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/424b333fb05c40ef55e5fa309254a7dfd7dfd0ed1640cdd3e1a5daff5108a478.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 781, + 80, + 862, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9a42477457be27549f5aa994f6a3835593abbe86d8ab70b51798d75684f37e81.jpg", + "image_caption": [ + "Original Image" + ], + "image_footnote": [], + "bbox": [ + 133, + 161, + 212, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/183a2fba3c39974566d0290ce755aa5bcb784bcf9bdf34f1209b9103d6495a42.jpg", + "image_caption": [ + "GradCAM for 7" + ], + "image_footnote": [], + "bbox": [ + 225, + 161, + 305, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c096343f9cd4aeb32ed4e5dc11cace02cb087c2c7365fc46dafcb3fd7967270f.jpg", + "image_caption": [ + "SmoothGradCAM++ for 7" + ], + "image_footnote": [], + "bbox": [ + 316, + 161, + 398, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fa1bd860c354fa306b72db92c3a80fbc41e89d0a6e32cfc5153799dba53a853d.jpg", + "image_caption": [ + "ScoreCAM for 7" + ], + "image_footnote": [], + "bbox": [ + 413, + 161, + 491, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/784c4879e6b85a8c89620f0e6fb320af4f4982e79b758b2b96a965c5d8f0b35c.jpg", + "image_caption": [ + "DiffCAM for 7" + ], + "image_footnote": [], + "bbox": [ + 504, + 161, + 584, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c4b4aa9cdc687abea425e3bbf56789c42dd8a66d3217b21e697ab77b7b976293.jpg", + "image_caption": [ + "DiffCAM (7 against 1)" + ], + "image_footnote": [], + "bbox": [ + 596, + 161, + 676, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b6e2765a76465a18a8899dddc60e80028288cfc90c23b19193a344cb5ea1e774.jpg", + "image_caption": [ + "DiffCAM (7 against 2)" + ], + "image_footnote": [], + "bbox": [ + 691, + 161, + 769, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7fb071201f8dc32e63da19aedf649e60b1c799a2d0d6fda0b61bc18ea04d598c.jpg", + "image_caption": [ + "DiffCAM (7 against 9)" + ], + "image_footnote": [], + "bbox": [ + 782, + 161, + 862, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0c66abb70c3f47e8d454bf687e85195af733ebcc680aae9931381014ebdc7325.jpg", + "image_caption": [ + "Original Image", + "Figure 3. Given MNIST images 3, 7, 9 as input, the 2nd-5th columns show saliency maps generated by XAI methods. The last three columns present counterfactual saliency maps which highlight differences between the target digit and selected counterfactual classes." + ], + "image_footnote": [], + "bbox": [ + 133, + 234, + 212, + 295 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d5e89567a4ebb3664408d36314c4793e622083820a6e5d1f27db960732790d8a.jpg", + "image_caption": [ + "GradCAM for 9" + ], + "image_footnote": [], + "bbox": [ + 225, + 234, + 305, + 295 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f74c1941f9e2b3e443d68d38c023ca552951dfce537fc31fdde11594170e41b1.jpg", + "image_caption": [ + "SmoothGradCAM++ for 9" + ], + "image_footnote": [], + "bbox": [ + 316, + 234, + 398, + 295 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/09db1cfd13f52dc1e4905d0df3c117c08edee76f57eb4dd82495cc8010718166.jpg", + "image_caption": [ + "ScoreCAM for 9" + ], + "image_footnote": [], + "bbox": [ + 413, + 234, + 491, + 295 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e9ffb108c0fef355ad74ad346e252e816c6b31d7d0bc5782b677f182bd887a70.jpg", + "image_caption": [ + "DiffCAM for 9" + ], + "image_footnote": [], + "bbox": [ + 504, + 234, + 584, + 295 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4fa7fca8d3faa7fc4f73d99aa1beec7e106061992d7724a9b1d80009f2909094.jpg", + "image_caption": [ + "DiffCAM (9 against 0)" + ], + "image_footnote": [], + "bbox": [ + 596, + 234, + 676, + 295 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a10d969f8b1a9486ad5ef007ff8d51ae488eefa3cb776ae1c679b6b00d2d1aaa.jpg", + "image_caption": [ + "DiffCAM (9 against 7)" + ], + "image_footnote": [], + "bbox": [ + 689, + 234, + 769, + 295 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bd0ba1b9633920cc44d051a7ee91a3ac21265667936ed6a2155b200a914318b9.jpg", + "image_caption": [ + "DiffCAM (9 against 8)" + ], + "image_footnote": [], + "bbox": [ + 782, + 234, + 862, + 295 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 351, + 223, + 368 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate DiffCAM through extensive qualitative and quantitative experiments in Section 4.1 and 4.2, respectively. Then we present results with SSL models in Section 4.3 and sanity check in Section 4.4. Finally, Section 4.5 presents a case study on abnormality localization in medical imaging to highlight DiffCAM's practical applications.", + "bbox": [ + 89, + 377, + 483, + 468 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Qualitative Evaluation", + "text_level": 1, + "bbox": [ + 89, + 479, + 302, + 496 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section provides qualitative evaluation results for the three task types introduced in the Method part. We examine DiffCAM's ability to highlight discriminative features for both the \"Why is\" and \"Why not\" questions, and its potential in revealing internal pattern variance as well. We use the MNIST [23] dataset due to its simplicity and clear patterns, which make it a good fit for the demonstration purpose.", + "bbox": [ + 89, + 503, + 483, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Discriminant Visual Attention", + "text_level": 1, + "bbox": [ + 89, + 633, + 354, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The second to fifth columns in Figure 3 demonstrate the effects of general explanation results which answers the \"Why is\" question. For DiffCAM, we use all examples from other classes as the reference group. Compared against the baseline methods, DiffCAM tends to highlight more comprehensive object patterns instead of only a small region of the most discriminative patterns. This observation backups our motivation that DiffCAM aims to capture the features which truly reflect the feature difference for real data distribution although some the direction may not be the fastest to reach decision boundaries. The results also align better with human perception of distinctive digit features. By assigning another similar digit as the reference group, DiffCAM is able to obtain discriminative features similar to counterfactual explanations. As shown in the last three columns of Figure 3, the highlighted regions accurately represent the", + "bbox": [ + 89, + 659, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "key differences, e.g., the bottom part makes the image of 9 not a digit 0. More qualitative results for discriminant visual attention are put in Section B in Appendix.", + "bbox": [ + 511, + 352, + 906, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.2 Intra-class Variance", + "text_level": 1, + "bbox": [ + 511, + 417, + 707, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While intra-class variance has rarely been discussed in existing XAI research, it is valuable in practice for model debugging and data engineering. Our work fills this gap and offers potential in this important task.", + "bbox": [ + 511, + 440, + 905, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Figure 4, the top row shows difficult examples of the digit 0 along with their incorrect predicted labels (mostly classified as 6), illustrating how subtle variations in shape and structure within the same class can lead to misclassification. The bottom row presents the corresponding saliency maps generated by DiffCAM, using the training set of digit 0 as the reference group, and highlights the patterns in each image that deviated the most from the majority. The results demonstrate that features like abnormal breaks in the loops and additional curves or dots were identified as influential differences that distinguish these hard cases from typical instances of digit 0. We can reasonably suspect these anomalies as the main factors contributing to incorrect predictions. In practice, such analyses can guide further data processing efforts to deploy a more robust model.", + "bbox": [ + 511, + 501, + 906, + 728 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/31565cb70882b8cca2564a43f2bd1f178928a71a707f543e7c08f92d1b71621c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 524, + 744, + 589, + 801 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0b088d3309dfc7997b6c05174c125364f145ec0c8df81889b8df7a840419ebfd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 746, + 663, + 801 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c5af04ea14d628374d4c174063626c2bbac698efad51309ee45424c4efb8e5f3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 676, + 746, + 740, + 801 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/235c045f6c7e3cec32b060012a8604e04a0cbaa246fe1303e91e40b23062eccd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 753, + 744, + 818, + 801 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/77567290b5edbbe8e5df4419cb93d2fefb988fdd6439dda3a7bff60135328de0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 830, + 744, + 893, + 801 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f0c5016da750fbbf1965ca46ee213236a5a7111ee6d57d21993e24c5d7e805ee.jpg", + "image_caption": [ + "Figure 4. Visualization of intra-Class Variance with DiffCAM on MNIST digits." + ], + "image_footnote": [], + "bbox": [ + 524, + 806, + 589, + 862 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/eecd0683ddeb1363737916e83d632b44d72ff87d8447551d81a1fe9837ebb5c9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 601, + 806, + 666, + 862 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/34d6dcc5cb95dace69fec6ff147ec22151b83ff29c73d40fd1f64fe16fe39a4a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 676, + 806, + 740, + 862 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f12642126eb06cfdba868e47446e6844ee2fd46ba439b770691eaac85ae8a34f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 753, + 806, + 818, + 862 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a6e514365845cc5c43a07572681b63009c5c9adf56c66448da1241b72eebf8d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 828, + 806, + 893, + 862 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10331", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b2d8fe7343f645c0289e0fadd1f29b51d5eb9092caac6879c3cfdda1dffa43d6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Arch.MetricExplanation Methods
    GradCAMScoreCAMLayerCAMXGradCAMDiffCAM
    ResNet-50IoU0.5280.5110.5350.4470.534
    AUPRC0.7270.7090.7380.6340.741
    Inception-v3IoU0.5240.5640.5830.5240.583
    AUPRC0.7260.7710.7920.7260.794
    ", + "bbox": [ + 178, + 88, + 821, + 183 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Evaluation of object localization on ImageNet.", + "bbox": [ + 331, + 193, + 663, + 207 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fe7a537a661408c3c9e5347f03482b1dae3240dd9903beed992f4cb249ec9782.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 220, + 163, + 282 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2082072b5df5a2f7abb6896021313a598602db7df2ecab46f6bb0b40843e9ca5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 174, + 220, + 243, + 281 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c2dbf3e7913c39f031511c8189f5f269b9289ec776b65f8016c038e078da028d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 253, + 220, + 320, + 280 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d11233a949c2fa225f7262580460b8040d05fccab411195591cbb8534f664776.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 330, + 220, + 398, + 280 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/32beef8c6d12eab7f37c0f89e68529d8c2af234ff80935c744bc5ccbf2115159.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 410, + 220, + 477, + 280 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4d3311a93729c1a818db85ee101adbc706b4b64863267829c4431e7c82da2111.jpg", + "image_caption": [ + "Figure 5. Illustration of the faithfulness and object localization test on ImageNet validation images. The left most column are original images with red rectangles as the object locations. The right most are masked images by ROAD according to the DiffCAM results." + ], + "image_footnote": [], + "bbox": [ + 96, + 287, + 163, + 345 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/644316dc5d23b9a0767e80a32aa099b71646dffe54b2cc0236187d52e89257d6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 174, + 287, + 241, + 345 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8a80a85e6c755ed435c16658e9a87b7ae686117a68ee323a9b730791438232c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 253, + 287, + 320, + 345 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4f399bb65418f3353c8c66b574cef0c09bfa78fd69aa1288060c6a0022d4f9ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 331, + 287, + 398, + 345 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e2f3ba3d761a9bfba9f739f06ad7f1ff6f12e82c1b27dc386c14dcb0df0029a6.jpg", + "image_caption": [ + "Figure 6. ROAD evaluation on the ImageNet dataset." + ], + "image_footnote": [], + "bbox": [ + 410, + 287, + 477, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Quantitative Evaluation", + "text_level": 1, + "bbox": [ + 89, + 440, + 312, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we report our quantitative experimental results. Following common practice, we measure faithfulness and localization performance on ImageNet to assess the quality of saliency maps. To improve computational efficiency, we pre-calculate the mean feature for each class and build a search index with Faiss-gpu [18]. During inference, we retrieve the top 100 most similar mean features as the reference group for each target image. Figure 5 presents showcases for the two experiments. We also quantitatively evaluate DiffCAM on counterfactual explanation tasks using the ResNet-50 model pre-trained on the fine-grained dataset CUB-200-2011 [54].", + "bbox": [ + 89, + 463, + 483, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Faithfulness", + "text_level": 1, + "bbox": [ + 89, + 664, + 230, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In XAI research, faithfulness refers to the extent to which an explanation method accurately reflects the true reasoning process of a machine learning model. Specifically, denoting I as the input image, we assess the faithfulness of a saliency map M by masking a set of pixels S $\\subseteq$ I to the input and observing the change in the model's prediction as $\\Delta f(S) = f(I) - f(I\\backslash S)$ , where S is determined by selecting the positions with top values in M. Based on this principal, we adopt Remove and Debias (ROAD) [36], which replaces the removed pixels with the mean pixel values from their neighbors. Considering the settings with $[25\\%, 50\\%, 75\\%]$ top important pixels replaced, we plot ROAD curves to show the average prediction probability decrease for each case. Experiments are conducted on 1000 random examples", + "bbox": [ + 89, + 688, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/204fab0f23763a11ca322e3b29cde28512b59c0850185e45ba612de6fc522c8f.jpg", + "image_caption": [ + "(a) ResNet-50" + ], + "image_footnote": [], + "bbox": [ + 517, + 226, + 694, + 334 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/06e83773c8c291a051135a612c9cd836d976344fe655684d3d185aeb94fa4cee.jpg", + "image_caption": [ + "(b) Inception-v3" + ], + "image_footnote": [], + "bbox": [ + 709, + 227, + 885, + 334 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "from the validation set of ImageNet. As shown in Figure 6, DiffCAM shows competitive level of faithfulness among various state-of-the-art baseline methods.", + "bbox": [ + 511, + 393, + 906, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2 Object Localization", + "text_level": 1, + "bbox": [ + 511, + 462, + 705, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Besides faithfulness, we are also interested in whether an XAI method provides interpretable information for humans. This is usually assessed through the task of object localization. Following the ScoreCAM paper, we consider images with a single bounding box for the target class and restrict the object to occupy less than half of the entire image. We randomly select 500 images from the ImageNet validation set that satisfy these conditions.", + "bbox": [ + 511, + 487, + 906, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Regarding the evaluation metric, we do not adopt the previous energy-based pointing method [55], as it tends to favor explanation results that overly concentrate pixel scores onto a small number of pixels. This approach is susceptible to artificial manipulation of sharpening the score distribution. Therefore, we employ conventional metrics Intersection over Union (IoU) and Area Under the Precision-Recall Curve (AUPRC) to assess the accuracy with which the generated saliency maps align with the object bounding boxes. Results in Table 1 show that DiffCAM achieves the best overall localization accuracy along with LayerCAM. More visualization results for localization evaluation are put in Section C in Appendix.", + "bbox": [ + 511, + 609, + 908, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.3 Counterfactual Explanation", + "text_level": 1, + "bbox": [ + 511, + 829, + 763, + 844 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Most Existing methods of counterfactual explanation resort to create an artificial example that yields a different prediction regarding the counterfactual class. These modifications", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10332", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/17199b221d679ce957ffd2e27521eb962c1fe57fcd5e8c4367c7b03cbea1dc4a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MetricRandom CounterfactualSimilar Counterfactual
    GoyalCounteRGANGALOREDiffCAMGoyalCounteRGANGALOREDiffCAM
    R0.030.060.090.150.120.170.160.17
    P0.770.740.810.830.570.560.600.61
    PIoU0.180.200.160.180.150.140.150.20
    ", + "bbox": [ + 124, + 88, + 874, + 167 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison of counterfactual explanation methods for Beginner and Advanced Users.", + "bbox": [ + 215, + 178, + 779, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1c99bf3a09e92a8d19ca22450cb08b5a92c9a00b0dba65c0abe0dbac84f24e94.jpg", + "image_caption": [ + "Figure 7. DiffCAM results answering \"why is\" and \"why not\" with SSL models Moco-v3 (column 2,3) and DINO (column 4,5)." + ], + "image_footnote": [], + "bbox": [ + 140, + 205, + 859, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "can be achieved through adversarial attacks and image synthesis. However, the perturbed or synthesized features often do not reside within the natural image space, limiting their applicability in expert domains. DiffCAM belongs to the direction of saliency map based counterfactual explanation that highlights which areas of the input would need modification to change the prediction.", + "bbox": [ + 88, + 474, + 482, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For performance evaluation, we mostly adopt the state-of-the-art saliency map based counterfactual method GALORE [56], using CUB-200-2011 with part annotations as the benchmark. Then the counterfactual ground truth is represented by $\\mathcal{G}^c = \\{(p_i,a_i,b_i)\\}_{i = 1}^N$ , where parts are denoted as $p$ , and $a$ and $b$ refer to the target and counterfactual classes, respectively. GALORE [56] uses Precision (P), Recall (R) and Part Intersection over Union (PIoU) as evaluation metrics. We additionally employ F1-Score to provide a more representative measure of model performance across different thresholds. We also follow GALORE [56] to consider both a random class and similar class as the counterfactual reference. More details for the evaluation metrics are introduced in Section D.1 in Appendix.", + "bbox": [ + 88, + 582, + 482, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in the Table 2, DiffCAM outperforms other state-of-the-art counterfactual explanation methods across nearly all metrics. While CounteRGAN achieves a slightly higher average P IoU on randomly selected counterfactual classes, DiffCAM excels overall. The F1 results in Figure 9a and 9b (see Appendix) show that DiffCAM demonstrates better robustness than GALORE in the selection of different", + "bbox": [ + 88, + 795, + 482, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "counterfactual classes. Figure 9c and 9d show that for similar counterfactual classes, DiffCAM achieves a significantly higher F1 score compared to GALORE. For randomly selected counterfactual classes, DiffCAM reaches a slightly higher F1 score at a faster rate and sustains this advantage across the range of thresholds shown. We provide additional experimental results in Section D.2 in Appendix.", + "bbox": [ + 511, + 474, + 906, + 582 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Applicability on SSL and ViT Models", + "text_level": 1, + "bbox": [ + 511, + 594, + 836, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DiffCAM can be directly applied to SSL models as it doesn't rely on class-specific predictions. By reshaping patch tokens and incorporating the class token, DiffCAM can also be adapted to ViT models. To verify the results, we apply DiffCAM on MoCo-v3 with the ResNet-50 backbone and DINO with the ViT backbone. Results in Fig. 7 show SSL models can extract reasonable features, while DINO offers richer and more fine-grained semantics. DiffCAM faithfully reflects these capacity differences.", + "bbox": [ + 511, + 619, + 906, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Sanity Check", + "text_level": 1, + "bbox": [ + 511, + 768, + 653, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sanity check is another method to examine whether an explanation method is really tied to the model [3] to further confirm its faithfulness. Specifically, we check whether the explanation results change when randomizing weights from a trained model. DiffCAM passes sanity check with common experimental settings. Detailed results are demonstrated in Section E in Appendix.", + "bbox": [ + 511, + 794, + 905, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10333", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/974c31c9cbe817367f59aa7eb458498e70dc084bd0ffd93fba984f1c9d23ec46.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelDatasetSaliency Methods (AUPRC)
    DiffCAMGradCAMScoreCAMLayerCAMXGradCAMIGGBP
    InceptionV3RSNA0.4920.4670.3280.3660.4660.3170.174
    SIIM0.0930.0760.0720.0710.0760.0630.072
    ", + "bbox": [ + 125, + 80, + 872, + 147 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Evaluation of Saliency Methods on InceptionNetV3 using AUPRC Metric", + "bbox": [ + 251, + 156, + 743, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8d2cb26d7c3bfac33f72ade55a384629ea2ac3e158523336d74a07c6dbdb83c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 195, + 181, + 267 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f1551dca88697ab4036b963c72b0cad7a01a8d42b94b9557ca9195a55a192f90.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 196, + 196, + 279, + 267 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c171f335861b2a1fb462b3a918d4c6d2941fd7762f192897718460d4f1f5bdcd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 294, + 196, + 377, + 267 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/272c12c77f3de0192f4e59d8241e01495f1f49d04229f73f9c437380a4c95fee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 393, + 196, + 478, + 267 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d365084ffc195e4448e142cfe11fad3e6698e892e591ff514dacc21e70bd211c.jpg", + "image_caption": [ + "Figure 8. Abnormality localization evaluation on the RSNA Pneumonia Detection Challenge dataset [6]. From left to right: original images, DiffCAM, GradCAM, and ScoreCAM results." + ], + "image_footnote": [], + "bbox": [ + 94, + 270, + 181, + 340 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d995729c9d99523f979e10d50ad06bc75ac6b75113f0f7765b35d69d786b2d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 194, + 270, + 279, + 340 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fc42efc58ff91ed67ffab6c8c4b9fbcf311ea3e955cebb9949fdd8bae6762374.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 294, + 270, + 377, + 340 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e31a4567fb7b1232bebd17a85e269781133cbe6c575daa500a0da7bfa4a32858.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 393, + 271, + 478, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Case Study: Abnormality Localization for Medical Imaging", + "text_level": 1, + "bbox": [ + 89, + 421, + 482, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this case study, we demonstrate the potential of DiffCAM in medical imaging applications. Specifically, we consider abnormality localization in chest X-ray images [7], using the RSNA Pneumonia Detection Challenge dataset [6] and SIIM-ACR Pneumothorax Segmentation dataset [58] as benchmarks. The former contains bounding boxes indicating potential areas of pneumonia for positive cases, and the latter provides associated masks for pneumothorax images. For each dataset, we train an Inception-v3 model [11, 47] for image-level binary classification and evaluate XAI methods regarding abnormality localization. More details of the task background, dataset information and model training strategies are put in Section F.1 in Appendix.", + "bbox": [ + 89, + 460, + 482, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We qualitatively compare the saliency maps produced by seven state-of-the-art methods, covering both gradient-based and activation-based baselines including GradCAM, ScoreCAM, LayerCAM), Axiom-based GradCAM (XGradCAM), Integrated Gradients (IG) [46], and Guided Backpropagation (GBP). For localization performance, we adopt the area under the precision-recall curve (AUPRC) as it better handles imbalanced data, common in medical images with small ground truth masks. Unlike ROC-AUC, AUPRC emphasizes the accuracy of positive pixels, making it especially suitable for identifying subtle abnormalities in medical imaging.", + "bbox": [ + 89, + 657, + 482, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results are presented in Table 3. On the RSNA dataset with bounding boxes as ground truth, DiffCAM achieves the highest AUPRC (0.492). GradCAM is shown very robust on medical applications, outperforming most ad", + "bbox": [ + 89, + 839, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "vanced methods which work well on general computer vision, whereas DiffCAM improves it with a remarkable margin. The SIIM task is more challenging and all methods deliver relatively low AUPRC scores. DiffCAM is still significantly superior to all the baseline methods.", + "bbox": [ + 511, + 198, + 903, + 272 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Two typical showcases from the RSNA datasets are presented in Figure 8, where the ground truth pneumonia areas are annotated as yellow boxes. The results demonstrate that DiffCAM captures more complete abnormality regions than baseline methods. This observation again coincides with our motivation that gradient-based approaches can't accurately capture the real feature difference between example groups (here we are interested in differences between healthy people and patients). We provide more random visualization examples in Section F.2 in Appendix.", + "bbox": [ + 511, + 273, + 906, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 511, + 441, + 635, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DiffCAM assumes that a linear classifier is attached to the final deep feature layer, from which the optimal feature importance vector is derived. While many modern DNN architectures (e.g., ResNet, Inception, MobileNet, Vision Transformer) adhere to this design, extending DiffCAM to handle more general scenarios remains a topic for future work.", + "bbox": [ + 511, + 467, + 905, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 574, + 633, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents DiffCAM, a novel approach for generating saliency maps by emphasizing the differences between target examples and reference data distributions. It addresses the limitations of traditional CAM-based approaches by providing more comprehensive and intuitive explanations that better align with human understanding. Extensive experiments across various datasets demonstrate DiffCAM's robustness and superior performance. As interpretability becomes increasingly critical in deep learning applications, especially high-stake tasks such as medical imaging, our work offers both an effective XAI tool and a valuable new perspective for further research.", + "bbox": [ + 511, + 599, + 906, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 511, + 797, + 692, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank Shun Jin, Damian Chng and Gunika Goyal for their contributions to our initial idea exploration. This work was supported in part by US NSF grant DBI-2238093. M.R.U. was supported in part by a fellowship from CMU CMLH.", + "bbox": [ + 511, + 824, + 905, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10334", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kumar Abhishek and Deeksha Kamath. Attribution-based xai methods in computer vision: A review, 2022. 2", + "[2] Amina Adadi and Mohammed Barrada. Peeking inside the black-box: a survey on explainable artificial intelligence (xai). 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2921-2929, 2016. 1, 3" + ], + "bbox": [ + 91, + 92, + 480, + 526 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10337", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_model.json b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..88531478cebaad00e1db6ddd00ada522c0c7ffae --- /dev/null +++ b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_model.json @@ -0,0 +1,2928 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.134, + 0.131, + 0.868, + 0.153 + ], + "angle": 0, + "content": "DiffCAM: Data-Driven Saliency Maps by Capturing Feature Differences" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.181, + 0.899, + 0.234 + ], + "angle": 0, + "content": "Xingjian Li, Qiming Zhao, Peelesh Bisht, Mostofa Rafid Uddin, Jin Yu Kim, Bryan Zhang, Min Xu* Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213, United States" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.269, + 0.329, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.302, + 0.485, + 0.633 + ], + "angle": 0, + "content": "In recent years, the interpretability of Deep Neural Networks (DNNs) has garnered significant attention, particularly due to their widespread deployment in critical domains like healthcare, finance, and autonomous systems. To address the challenge of understanding how DNNs make decisions, Explainable AI (XAI) methods, such as saliency maps, have been developed to provide insights into the inner workings of these models. This paper introduces DiffCAM, a novel XAI method designed to overcome limitations in existing Class Activation Map (CAM)-based techniques, which often rely on decision boundary gradients to estimate feature importance. DiffCAM differentiates itself by considering the actual data distribution of the reference class, identifying feature importance based on how a target example differs from reference examples. This approach captures the most discriminative features without relying on decision boundaries or prediction results, making DiffCAM applicable to a broader range of models, including foundation models. Through extensive experiments, we demonstrate the superior performance and flexibility of DiffCAM in providing meaningful explanations across diverse datasets and scenarios." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.666, + 0.224, + 0.682 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.692, + 0.483, + 0.844 + ], + "angle": 0, + "content": "Deep Neural Networks (DNNs) [20, 43, 52] are often referred to as black-box models due to the difficulty in understanding how they extract features and make decisions. This lack of interpretability raises significant concerns in critical areas such as healthcare, finance, and autonomous systems. To address this challenge, Explainable AI (XAI) methods are designed to make the decision-making processes of AI systems more transparent and understandable to humans [2, 27]. It allows users and stakeholders to gain insight into how AI models arrive at specific outcomes [48]." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.844, + 0.484, + 0.875 + ], + "angle": 0, + "content": "Among the XAI approaches, saliency map is a common technique used to explain deep vision models. A saliency" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.27, + 0.905, + 0.301 + ], + "angle": 0, + "content": "map is a visualization that highlights the critical parts of an image that significantly influence a model's prediction." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.304, + 0.907, + 0.532 + ], + "angle": 0, + "content": "In deep convolutional neural networks (CNNs), the activation map of each convolutional channel in deep layers naturally provides such information of spatial attention. This nature motivates popular solutions, such as Class Activation Map (CAM) [60], GradCAM [41] and ScoreCAM [55], which calculate a saliency map by a weighted aggregation of those feature channels. To estimate the feature importance, GradCAM calculates the gradient of the prediction (typically the probability of a target class) with respect to the input features. This gradient essentially measures the sensitivity of the prediction to variances in the input image or deep features, revealing the fastest direction in the feature space to change the model's decision. CAM and ScoreCAM adopt the similar idea to estimate the feature importance while avoiding gradient calculation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.535, + 0.909, + 0.883 + ], + "angle": 0, + "content": "Despite the widely application of those CAM-based approaches, there still exists an essential limitation of them in estimating the feature importance. Here we illustrate our core idea by a simplified binary classification model predicting their language test result (Pass or Fail) according to their historical reading and writing scores. Intuitively, writing is learned as a more dominant feature for the prediction as it is usually harder than reading. This results in a decision boundary which lean to separate low and high write scores. When explaining a specific prediction, existing CAM-based approaches consider the direction orthogonal to the decision boundary as the feature importance vector, i.e., indicating the writing score is a more important feature for the prediction. However, this is counter-intuitive in case that the explained data point is not a representative one among its class. For example, when explaining why the student \\( x_{t} \\) is predicted as Fail, CAM-based approaches assign a higher importance on writing to which the final prediction is more sensitive. However, the writing score of \\( x_{t} \\) is as high as the average of the Pass group and higher than most of the Fail students. Therefore, reading is a better feature to explain the failure of \\( x_{t} \\), i.e., if \\( x_{t} \\)'s reading is as good as the Pass group, \\( x_{t} \\) will be predicted as Pass." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.886, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Another relevant technique, counterfactual explanation" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.239, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10327" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.09, + 0.48, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.324, + 0.485, + 0.451 + ], + "angle": 0, + "content": "Figure 1. Motivation of DiffCAM. Existing CAM-based approaches resort to reach the decision boundary (e.g., GradCAM and ScoreCAM) or the nearest virtual example (e.g., counterfactual explanations) in the fastest direction, ignoring the actual data distribution for most representative examples. DiffCAM instead looks for the optimal direction that best represents the difference from a specified reference group. From this perspective, DiffCAM attributes Fail of \\( x_{t} \\) mainly to its low Reading score, while traditional CAM-based approaches prefer Writing as the main reason." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.477, + 0.483, + 0.628 + ], + "angle": 0, + "content": "[16, 45], aims to find the closest virtual example on the data manifold that requires minimal changes to the input example to reach this virtual example. While it focuses more on the most discriminative feature from a data perspective, it still fails in capturing the difference between the target example and the majority of a reference class (the Pass class). As illustrated in Figure 1, the considered counterpart example is usually a virtual point near the decision boundary instead of a representative point among the real population of the reference class." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.63, + 0.483, + 0.901 + ], + "angle": 0, + "content": "The above analyses motivate us to design a novel CAM-based XAI approach by considering the actual data distribution of the reference class rather than the decision boundary. More specifically, given a group of reference examples, we aim to find the optimal direction (representing the feature importance vector) that optimally distinguish the target example from the reference group. This direction is the one on which the projections of reference examples are most distant to the target point, while maximally preserve their inherent common features. By this way, the feature importance vector represents only the most discriminative ingredients in the feature space. The exact solution is introduced in the Method section. We name our method DiffCAM as it explains model outputs by capturing essential feature differences. DiffCAM maintains the explanation format of saliency map and can be applied to more scenarios. The main difference between DiffCAM and existing CAM-based explanations can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.092, + 0.905, + 0.167 + ], + "angle": 0, + "content": "- Given a trained model to be explained, DiffCAM captures information about how is the target example different from the actual data points from the reference group, instead of considering how to quickly pass the decision boundary." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.167, + 0.905, + 0.288 + ], + "angle": 0, + "content": "- DiffCAM is a more flexible and general framework. By using all the different classes as the reference group, DiffCAM functions similar to existing CAM-based approaches. By using one whole class as the reference group, DiffCAM provides counterfactual explanations. Beyond those, DiffCAM can also explain how a target example differs from a specific set of other examples, which may even belong to the same class with the target one." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.288, + 0.905, + 0.349 + ], + "angle": 0, + "content": "- DiffCAM generates saliency maps without relying on the prediction results. This makes DiffCAM applicable to general feature extractors such as foundation models from self-supervised pre-training." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.092, + 0.905, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.351, + 0.907, + 0.397 + ], + "angle": 0, + "content": "In the experiment section, we demonstrate the effects of DiffCAM with several datasets covering general computer vision and medical imaging datasets." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.411, + 0.655, + 0.426 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.435, + 0.667, + 0.452 + ], + "angle": 0, + "content": "2.1. Explainable AI" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.459, + 0.907, + 0.58 + ], + "angle": 0, + "content": "Explainable Artificial Intelligence (XAI) focuses on making complex machine learning models more interpretable, addressing the \"black-box\" nature of many advanced AI systems [26, 30]. The primary goal is to provide human-understandable explanations of a model's decisions, which is critical for improving trust, accountability, and ethical AI usage [21], especially in high-stakes fields like healthcare [24, 49, 50]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.581, + 0.906, + 0.686 + ], + "angle": 0, + "content": "XAI techniques are broadly categorized into intrinsic methods, which involve building models that are inherently interpretable [37], and post-hoc methods, which generate explanations for pre-existing models without great changes to their structures [44, 59]. Post-hoc techniques are widely used for deep learning models, which are often too complex for intrinsic interpretability [4]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.687, + 0.906, + 0.777 + ], + "angle": 0, + "content": "A key challenge in XAI is balancing the trade-off between a model's accuracy and its interpretability. In deep learning, where models are often highly effective but opaque, post-hoc methods, such as feature attribution and counterfactual reasoning, have become powerful tools for making predictions understandable [28]." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.787, + 0.744, + 0.803 + ], + "angle": 0, + "content": "2.2. Attribution Explanations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Attribution-based methods play a crucial role in explaining behaviors by neural networks in tasks such as image classification [5, 22]. These methods identify which parts of an input image are most influential in a model's decision-making process [1, 33]. In the context of visual explanations, saliency mapping is often used in image classification" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10328" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "tasks to illustrate influential regions without modifying the underlying model [10, 19]. However, these methods may struggle with fine-grained tasks where subtle distinctions require more detailed and nuanced explanations [4]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.153, + 0.483, + 0.334 + ], + "angle": 0, + "content": "GradCAM [41] is widely used for generating visual explanations in neural networks by highlighting important regions contributing to a model's decision. Methods like GradCAM++ [9], ScoreCAM [55], Ablation-CAM [12], XGrad-CAM [14], EigenCAM [29], LayerCAM [17], and SmoothGradCAM++ [32] further refine this approach, offering more discriminative or interpretable saliency maps. Additionally, some saliency mapping techniques that differ from CAM-based methods such as Gradient*Input [42] and Integrated Gradient [46], are designed to highlight critical regions contributing to the model's decision by calculation on input images rather than using deep features." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.335, + 0.484, + 0.456 + ], + "angle": 0, + "content": "We also note different attribution methods such as LIME and SHAP, and Layer-wise Relevance Propagation (LRP) which are popular for enhancing AI explainability. LIME [35] provides locally faithful explanations by perturbing inputs, SHAP [39] is motivated by the game theory, and LRP [8] calculates relevance scores via attribution propagation. These methods are also important but not the main focus of our paper." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.467, + 0.342, + 0.484 + ], + "angle": 0, + "content": "2.3. Counterfactual Explanation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.492, + 0.483, + 0.657 + ], + "angle": 0, + "content": "One limitation of Attribution Explanation lies in its inability to identify attributes that distinguish a specific class from other classes, i.e. failing to address \"Why not a class\". Counterfactual Explanation introduced in [47, 53], was designed to provide insights into machine learning models, aiding decision-making in domains such as law and policy through counterfactual reasoning. In visual tasks, CE can be operationalized as \"for class A to be correct, class B would require modifications to these specific parts.\" These modifications can be achieved through adversarial attacks [13, 51] or GAN-based methods [15, 25, 31, 38, 40]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.84 + ], + "angle": 0, + "content": "Our work is more relevant to the saliency map based counterfactual explanation work. GALORE [56] introduced a \"generative explanation framework\" that unifies attribution-based, deliberative, and counterfactual explanations into a combined attribution map aligned with classifier predictions and confidence scores. Similarly, [34] measured the changes required to traverse from the learned manifold to the contrastive manifold and integrated this approach into Grad-CAM to generate heatmaps. Content-Aware Counterfactual Explanation (CCE) [57] proposed a content-aware counterfactual perturbation algorithm that generates positive-negative saliency-based explanations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Our approach differs from GALORE and CEE by not performing counterfactual comparisons at the saliency map level. Instead, we distinguish attributes of similar classes at the feature level, localizing a distinction heatmap that high-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.168 + ], + "angle": 0, + "content": "lights the unique features of the target class compared to other classes. The counterfactual explanation consists of the distinction heatmap for the target class A and another distinction heatmap for the counterfactual class B, which shares common features with A." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.18, + 0.605, + 0.196 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.205, + 0.707, + 0.22 + ], + "angle": 0, + "content": "3.1. General Framework" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.228, + 0.907, + 0.441 + ], + "angle": 0, + "content": "The proposed DiffCAM approach follows the general framework of Class Activation Map (CAM) [60]. We consider deep convolutional neural networks. For simplification, we assume the deep model to be explained is composed of a deep feature extractor and a fully connected layer, which is a common architecture for modern DNNs. Let's define \\(\\mathbf{x}\\) as a target example to be explained, and \\(d\\) as the number of feature channels of the last convolutional layer. By passing forward \\(\\mathbf{x}\\), we get \\(\\mathbf{A}_k(\\mathbf{x})(k\\in [1,2,\\dots,d])\\) as the \\(k\\)-th activation map. The goal of CAM-based approaches is to generate a saliency map \\(M_{c}(\\mathbf{x})\\) explaining the prediction towards class \\(c\\) with \\(\\mathbf{x}\\) as input. Specifically, a feature importance vector \\(\\mathbf{w}^c\\in \\mathbb{R}^d\\) is used to aggregate all the activation maps as" + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.451, + 0.906, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {c} (\\mathbf {x}) = \\sum_ {k = 1} ^ {d} \\mathbf {w} _ {k} ^ {c} \\mathbf {A} _ {k} (\\mathbf {x}). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.498, + 0.906, + 0.634 + ], + "angle": 0, + "content": "In the original CAM method [60], \\(\\mathbf{w}_k^c\\) are directly taken from the weights of the fully connected layer. Specifically, for class \\(c\\), the weight \\(\\mathbf{w}_k^c\\) is the \\(k\\)-th component of the fully connected layer's weights \\(\\mathbf{W}_c\\) for that class. Many following work [9, 12, 14, 17, 29, 41, 55] adopt this general framework and differ in their ways of calculating \\(\\mathbf{w}_k^c\\). Here we summarize two main categories from existing approaches, which focus on the gradient and individual contribution of each feature channel respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.634, + 0.906, + 0.695 + ], + "angle": 0, + "content": "GradCAM: \\(\\mathbf{w}_k^c\\) are computed based on the gradients of the class score \\(y^{c}(\\mathbf{x})\\) with respect to the activation map \\(\\mathbf{A}_k(\\mathbf{x})\\). Specifically, \\(\\mathbf{w}_k^c\\) is the global average of the gradients across all spatial locations in the feature map as" + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.704, + 0.907, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} _ {k} ^ {c} = \\frac {1}{Z} \\sum_ {i, j} \\frac {\\partial y ^ {c}}{\\partial \\mathbf {A} _ {k} ^ {i , j} (\\mathbf {x})} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.754, + 0.907, + 0.785 + ], + "angle": 0, + "content": "where \\(\\mathbf{A}_k^{i,j}(\\mathbf{x})\\) is the activation at spatial location \\((i,j)\\) of the feature map and \\(Z\\) is a normalization term." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.786, + 0.906, + 0.861 + ], + "angle": 0, + "content": "ScoreCAM: \\(\\mathbf{w}_k^c\\) are measured by the increase in the \\(c\\)-th class score when the feature map \\(\\mathbf{A}_k(\\mathbf{x})\\) is activated. For the \\(k\\)-th feature channel, it first creates the corresponding masked input \\(\\tilde{\\mathbf{x}}_k = \\mathbf{A}_k(\\mathbf{x}) \\odot \\mathbf{x}\\), and then calculate the feature importance vector as" + }, + { + "type": "equation", + "bbox": [ + 0.644, + 0.871, + 0.906, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} _ {k} ^ {c} = \\frac {y ^ {c} \\left(\\tilde {\\mathbf {x}} _ {k}\\right)}{\\sum_ {k} y ^ {c} \\left(\\tilde {\\mathbf {x}} _ {k}\\right)}. \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10329" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.085, + 0.881, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.36, + 0.908, + 0.406 + ], + "angle": 0, + "content": "Figure 2. Overview of the DiffCAM framework and applications. Given a target image and a set of reference examples, DiffCAM computes deep feature embeddings, identifies the direction that captures differences between the target and references, and generates a saliency map highlighting key distinguishing features. DiffCAM can provide flexible explanations according to the selection of reference examples." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.421, + 0.33, + 0.437 + ], + "angle": 0, + "content": "3.2. DiffCAM Implementation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.444, + 0.484, + 0.611 + ], + "angle": 0, + "content": "Intuitively, DiffCAM regards the explanation problem as looking for the feature components that best distinguish the target example (to be explained) and a group of reference examples. Suppose the example we aim to explain is \\(\\mathbf{x}\\). According to the explanation type we are interested in, a set of \\(n\\) examples \\(\\{\\hat{\\mathbf{x}}^{(i)}\\}_{i=1}^{n}\\) is determined as the reference group. Note that the class labels of \\(\\{\\hat{\\mathbf{x}}^{(i)}\\}_{i=1}^{n}\\) can be flexible, i.e., they may have the same, different or no labels. We generate the deep embedding \\(\\mathbf{z} \\in \\mathbb{R}^d\\) by performing average pooling along the spatial dimension on the whole feature map \\(\\mathbf{A}(\\mathbf{x})\\), and get \\(\\{\\hat{\\mathbf{z}}^{(i)}\\}_{i=1}^{n}\\) for the reference examples." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.611, + 0.484, + 0.701 + ], + "angle": 0, + "content": "The feature importance vector \\(\\mathbf{w}\\) is defined as the optimal direction in the feature space that represents the most discriminative features relative to the reference data. Specifically, the projections of \\(\\{\\hat{\\mathbf{z}}^{(i)}\\}_{i = 1}^{n}\\) on \\(\\mathbf{w}\\) are expected to have the largest distance with \\(\\mathbf{z}\\) while maintain as much commonality as possible." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.701, + 0.484, + 0.822 + ], + "angle": 0, + "content": "To solve the optimal \\(\\mathbf{w}\\), we apply fundamental mathematical tools in linear algebra and convex optimization. Formally, denoting the mean reference position by \\(\\hat{\\mu} = \\frac{1}{n}\\sum_{i=1}^{n}\\hat{\\mathbf{z}}^{(i)}\\), the distance between the target example and the reference group along \\(\\mathbf{w}\\) can be defined as \\(\\|\\mathbf{w}^T z - \\mathbf{w}^T\\hat{\\mu}\\|^2\\). The variance among the reference examples projected on \\(\\mathbf{w}\\) is \\(\\frac{1}{n}\\sum_{i=1}^{n}\\|\\mathbf{w}^T\\hat{\\mathbf{z}}^{(i)} - \\mathbf{w}^T\\hat{\\mu}\\|^2\\). The measure can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.828, + 0.483, + 0.9 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} J (\\mathbf {w}) = \\frac {\\left\\| \\mathbf {w} ^ {T} z - \\mathbf {w} ^ {T} \\hat {\\mu} \\right\\| ^ {2}}{\\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {w} ^ {T} \\hat {\\mathbf {z}} ^ {(i)} - \\mathbf {w} ^ {T} \\hat {\\mu} \\right\\| ^ {2}} (4) \\\\ = \\frac {\\mathbf {w} ^ {T} \\mathbf {S} _ {\\mu} \\mathbf {w}}{\\mathbf {w} ^ {T} \\mathbf {S} _ {\\mathbf {v}} \\mathbf {w}}, (5) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.421, + 0.907, + 0.512 + ], + "angle": 0, + "content": "where \\(\\mathbf{S}_{\\mu} = (\\mathbf{z} - \\hat{\\mu})(\\mathbf{z} - \\hat{\\mu})^T\\) represents discrimination between the target example and the reference group, and \\(\\mathbf{S}_{\\mathbf{v}} = \\sum_{i=1}^{n} (\\hat{\\mathbf{z}}^{(i)} - \\hat{\\mu})(\\hat{\\mathbf{z}}^{(i)} - \\hat{\\mu})^T\\) represents internal variation among the reference examples. By differentiating and setting to zero, we find the optimal \\(\\mathbf{w}\\) that maximizes \\(J(\\mathbf{w})\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.514, + 0.907, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} ^ {*} = \\underset {\\mathbf {w}} {\\operatorname {a r g m a x}} J (w) = \\mathbf {S _ {v}} ^ {- 1} (\\mathbf {z} - \\hat {\\mu}). \\qquad (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.548, + 0.909, + 0.683 + ], + "angle": 0, + "content": "Detailed derivation is put in Section A in Appendix. For supervised trained models, the inverse matrix \\(\\mathbf{S}_{\\mathbf{v}}^{-1}\\) can be pre-calculated over training examples to avoid high inference complexity. We further adopt the Tikhonov regularization to ensure stability in calculating the inverse matrix. A small regularization term \\(\\lambda \\mathbf{I}\\) is added onto \\(\\mathbf{S}_{\\mathbf{v}}\\) when calculating the inverse. The solved \\(\\mathbf{w}^*\\) is finally used to generate the saliency map by calculating the weighted aggregation of the feature channels as" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.695, + 0.907, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} ^ {\\text {D i f f C A M}} (\\mathbf {x}) = \\sum_ {k = 1} ^ {d} \\mathbf {w} _ {k} ^ {*} \\mathbf {A} _ {k} (\\mathbf {x}). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.903 + ], + "angle": 0, + "content": "A flexibility of DiffCAM lies in the selection of the reference group. In most cases, we use all the remaining classes as reference when answering the \"Why is\" question. For large-scale datasets with diverse classes (e.g., ImageNet), we empirically recommend to select a subset of similar classes (with k-Nearest-Neighbor search) as the reference group to obtain more discriminative features. To answer the \"Why not\" question or analyze internal variations, the corresponding target class will be specified as the reference group. An illustrative overview is presented in Figure 2." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10330" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.082, + 0.214, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.154, + 0.203, + 0.163 + ], + "angle": 0, + "content": "Original Image" + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.082, + 0.307, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.154, + 0.295, + 0.162 + ], + "angle": 0, + "content": "GradCAM for 7" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.082, + 0.404, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.154, + 0.407, + 0.162 + ], + "angle": 0, + "content": "SmoothGradCAM++ for 7" + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.082, + 0.493, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.421, + 0.154, + 0.482, + 0.162 + ], + "angle": 0, + "content": "ScoreCAM for 7" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.082, + 0.588, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.52, + 0.154, + 0.57, + 0.162 + ], + "angle": 0, + "content": "DiffCAM for 7" + }, + { + "type": "image", + "bbox": [ + 0.598, + 0.082, + 0.678, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.154, + 0.678, + 0.162 + ], + "angle": 0, + "content": "DiffCAM (7 against 1)" + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.082, + 0.771, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.154, + 0.77, + 0.162 + ], + "angle": 0, + "content": "DiffCAM (7 against 2)" + }, + { + "type": "image", + "bbox": [ + 0.782, + 0.082, + 0.863, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.154, + 0.862, + 0.162 + ], + "angle": 0, + "content": "DiffCAM (7 against 9)" + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.162, + 0.214, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.146, + 0.228, + 0.202, + 0.235 + ], + "angle": 0, + "content": "Original Image" + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.162, + 0.307, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.24, + 0.228, + 0.294, + 0.235 + ], + "angle": 0, + "content": "GradCAM for 9" + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.162, + 0.4, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.314, + 0.228, + 0.405, + 0.235 + ], + "angle": 0, + "content": "SmoothGradCAM++ for 9" + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.162, + 0.493, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.425, + 0.228, + 0.48, + 0.235 + ], + "angle": 0, + "content": "ScoreCAM for 9" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.162, + 0.585, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.228, + 0.57, + 0.235 + ], + "angle": 0, + "content": "DiffCAM for 9" + }, + { + "type": "image", + "bbox": [ + 0.598, + 0.162, + 0.678, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.598, + 0.228, + 0.676, + 0.236 + ], + "angle": 0, + "content": "DiffCAM (9 against 0)" + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.162, + 0.771, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.228, + 0.77, + 0.236 + ], + "angle": 0, + "content": "DiffCAM (9 against 7)" + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.162, + 0.863, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.228, + 0.862, + 0.236 + ], + "angle": 0, + "content": "DiffCAM (9 against 8)" + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.235, + 0.214, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.235, + 0.307, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.235, + 0.4, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.235, + 0.493, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.235, + 0.585, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.598, + 0.235, + 0.678, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.235, + 0.771, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.235, + 0.863, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.309, + 0.908, + 0.339 + ], + "angle": 0, + "content": "Figure 3. Given MNIST images 3, 7, 9 as input, the 2nd-5th columns show saliency maps generated by XAI methods. The last three columns present counterfactual saliency maps which highlight differences between the target digit and selected counterfactual classes." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.352, + 0.224, + 0.369 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.378, + 0.484, + 0.469 + ], + "angle": 0, + "content": "We evaluate DiffCAM through extensive qualitative and quantitative experiments in Section 4.1 and 4.2, respectively. Then we present results with SSL models in Section 4.3 and sanity check in Section 4.4. Finally, Section 4.5 presents a case study on abnormality localization in medical imaging to highlight DiffCAM's practical applications." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.481, + 0.303, + 0.497 + ], + "angle": 0, + "content": "4.1. Qualitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.505, + 0.484, + 0.611 + ], + "angle": 0, + "content": "This section provides qualitative evaluation results for the three task types introduced in the Method part. We examine DiffCAM's ability to highlight discriminative features for both the \"Why is\" and \"Why not\" questions, and its potential in revealing internal pattern variance as well. We use the MNIST [23] dataset due to its simplicity and clear patterns, which make it a good fit for the demonstration purpose." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.634, + 0.356, + 0.648 + ], + "angle": 0, + "content": "4.1.1 Discriminant Visual Attention" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.484, + 0.901 + ], + "angle": 0, + "content": "The second to fifth columns in Figure 3 demonstrate the effects of general explanation results which answers the \"Why is\" question. For DiffCAM, we use all examples from other classes as the reference group. Compared against the baseline methods, DiffCAM tends to highlight more comprehensive object patterns instead of only a small region of the most discriminative patterns. This observation backups our motivation that DiffCAM aims to capture the features which truly reflect the feature difference for real data distribution although some the direction may not be the fastest to reach decision boundaries. The results also align better with human perception of distinctive digit features. By assigning another similar digit as the reference group, DiffCAM is able to obtain discriminative features similar to counterfactual explanations. As shown in the last three columns of Figure 3, the highlighted regions accurately represent the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.353, + 0.907, + 0.4 + ], + "angle": 0, + "content": "key differences, e.g., the bottom part makes the image of 9 not a digit 0. More qualitative results for discriminant visual attention are put in Section B in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.418, + 0.708, + 0.431 + ], + "angle": 0, + "content": "4.1.2 Intra-class Variance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.441, + 0.906, + 0.501 + ], + "angle": 0, + "content": "While intra-class variance has rarely been discussed in existing XAI research, it is valuable in practice for model debugging and data engineering. Our work fills this gap and offers potential in this important task." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.502, + 0.907, + 0.729 + ], + "angle": 0, + "content": "In Figure 4, the top row shows difficult examples of the digit 0 along with their incorrect predicted labels (mostly classified as 6), illustrating how subtle variations in shape and structure within the same class can lead to misclassification. The bottom row presents the corresponding saliency maps generated by DiffCAM, using the training set of digit 0 as the reference group, and highlights the patterns in each image that deviated the most from the majority. The results demonstrate that features like abnormal breaks in the loops and additional curves or dots were identified as influential differences that distinguish these hard cases from typical instances of digit 0. We can reasonably suspect these anomalies as the main factors contributing to incorrect predictions. In practice, such analyses can guide further data processing efforts to deploy a more robust model." + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.746, + 0.59, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.747, + 0.665, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.747, + 0.741, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.746, + 0.819, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.831, + 0.746, + 0.894, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.808, + 0.591, + 0.863 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.808, + 0.667, + 0.863 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.807, + 0.741, + 0.863 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.807, + 0.819, + 0.863 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.83, + 0.808, + 0.894, + 0.863 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.876, + 0.907, + 0.904 + ], + "angle": 0, + "content": "Figure 4. Visualization of intra-Class Variance with DiffCAM on MNIST digits." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10331" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.179, + 0.089, + 0.822, + 0.184 + ], + "angle": 0, + "content": "
    Arch.MetricExplanation Methods
    GradCAMScoreCAMLayerCAMXGradCAMDiffCAM
    ResNet-50IoU0.5280.5110.5350.4470.534
    AUPRC0.7270.7090.7380.6340.741
    Inception-v3IoU0.5240.5640.5830.5240.583
    AUPRC0.7260.7710.7920.7260.794
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.333, + 0.194, + 0.664, + 0.208 + ], + "angle": 0, + "content": "Table 1. Evaluation of object localization on ImageNet." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.221, + 0.165, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.176, + 0.222, + 0.244, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.222, + 0.321, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.331, + 0.222, + 0.4, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.222, + 0.478, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.288, + 0.165, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.176, + 0.289, + 0.243, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.289, + 0.321, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.332, + 0.289, + 0.4, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.289, + 0.478, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.414 + ], + "angle": 0, + "content": "Figure 5. Illustration of the faithfulness and object localization test on ImageNet validation images. The left most column are original images with red rectangles as the object locations. The right most are masked images by ROAD according to the DiffCAM results." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.441, + 0.313, + 0.456 + ], + "angle": 0, + "content": "4.2. Quantitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.464, + 0.484, + 0.645 + ], + "angle": 0, + "content": "In this section, we report our quantitative experimental results. Following common practice, we measure faithfulness and localization performance on ImageNet to assess the quality of saliency maps. To improve computational efficiency, we pre-calculate the mean feature for each class and build a search index with Faiss-gpu [18]. During inference, we retrieve the top 100 most similar mean features as the reference group for each target image. Figure 5 presents showcases for the two experiments. We also quantitatively evaluate DiffCAM on counterfactual explanation tasks using the ResNet-50 model pre-trained on the fine-grained dataset CUB-200-2011 [54]." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.665, + 0.231, + 0.68 + ], + "angle": 0, + "content": "4.2.1 Faithfulness" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.689, + 0.484, + 0.901 + ], + "angle": 0, + "content": "In XAI research, faithfulness refers to the extent to which an explanation method accurately reflects the true reasoning process of a machine learning model. Specifically, denoting I as the input image, we assess the faithfulness of a saliency map M by masking a set of pixels S \\(\\subseteq\\) I to the input and observing the change in the model's prediction as \\(\\Delta f(S) = f(I) - f(I\\backslash S)\\), where S is determined by selecting the positions with top values in M. Based on this principal, we adopt Remove and Debias (ROAD) [36], which replaces the removed pixels with the mean pixel values from their neighbors. Considering the settings with \\([25\\%, 50\\%, 75\\%]\\) top important pixels replaced, we plot ROAD curves to show the average prediction probability decrease for each case. Experiments are conducted on 1000 random examples" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.227, + 0.695, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.337, + 0.652, + 0.349 + ], + "angle": 0, + "content": "(a) ResNet-50" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.228, + 0.887, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.763, + 0.337, + 0.851, + 0.349 + ], + "angle": 0, + "content": "(b) Inception-v3" + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.361, + 0.867, + 0.376 + ], + "angle": 0, + "content": "Figure 6. ROAD evaluation on the ImageNet dataset." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.394, + 0.907, + 0.438 + ], + "angle": 0, + "content": "from the validation set of ImageNet. As shown in Figure 6, DiffCAM shows competitive level of faithfulness among various state-of-the-art baseline methods." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.463, + 0.706, + 0.478 + ], + "angle": 0, + "content": "4.2.2 Object Localization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.488, + 0.907, + 0.609 + ], + "angle": 0, + "content": "Besides faithfulness, we are also interested in whether an XAI method provides interpretable information for humans. This is usually assessed through the task of object localization. Following the ScoreCAM paper, we consider images with a single bounding box for the target class and restrict the object to occupy less than half of the entire image. We randomly select 500 images from the ImageNet validation set that satisfy these conditions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.61, + 0.909, + 0.807 + ], + "angle": 0, + "content": "Regarding the evaluation metric, we do not adopt the previous energy-based pointing method [55], as it tends to favor explanation results that overly concentrate pixel scores onto a small number of pixels. This approach is susceptible to artificial manipulation of sharpening the score distribution. Therefore, we employ conventional metrics Intersection over Union (IoU) and Area Under the Precision-Recall Curve (AUPRC) to assess the accuracy with which the generated saliency maps align with the object bounding boxes. Results in Table 1 show that DiffCAM achieves the best overall localization accuracy along with LayerCAM. More visualization results for localization evaluation are put in Section C in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.83, + 0.764, + 0.845 + ], + "angle": 0, + "content": "4.2.3 Counterfactual Explanation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.901 + ], + "angle": 0, + "content": "Most Existing methods of counterfactual explanation resort to create an artificial example that yields a different prediction regarding the counterfactual class. These modifications" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10332" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.125, + 0.089, + 0.875, + 0.169 + ], + "angle": 0, + "content": "
    MetricRandom CounterfactualSimilar Counterfactual
    GoyalCounteRGANGALOREDiffCAMGoyalCounteRGANGALOREDiffCAM
    R0.030.060.090.150.120.170.160.17
    P0.770.740.810.830.570.560.600.61
    PIoU0.180.200.160.180.150.140.150.20
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.217, + 0.179, + 0.781, + 0.194 + ], + "angle": 0, + "content": "Table 2. Comparison of counterfactual explanation methods for Beginner and Advanced Users." + }, + { + "type": "image", + "bbox": [ + 0.141, + 0.206, + 0.861, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.434, + 0.879, + 0.449 + ], + "angle": 0, + "content": "Figure 7. DiffCAM results answering \"why is\" and \"why not\" with SSL models Moco-v3 (column 2,3) and DINO (column 4,5)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.475, + 0.483, + 0.581 + ], + "angle": 0, + "content": "can be achieved through adversarial attacks and image synthesis. However, the perturbed or synthesized features often do not reside within the natural image space, limiting their applicability in expert domains. DiffCAM belongs to the direction of saliency map based counterfactual explanation that highlights which areas of the input would need modification to change the prediction." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.583, + 0.483, + 0.794 + ], + "angle": 0, + "content": "For performance evaluation, we mostly adopt the state-of-the-art saliency map based counterfactual method GALORE [56], using CUB-200-2011 with part annotations as the benchmark. Then the counterfactual ground truth is represented by \\(\\mathcal{G}^c = \\{(p_i,a_i,b_i)\\}_{i = 1}^N\\), where parts are denoted as \\(p\\), and \\(a\\) and \\(b\\) refer to the target and counterfactual classes, respectively. GALORE [56] uses Precision (P), Recall (R) and Part Intersection over Union (PIoU) as evaluation metrics. We additionally employ F1-Score to provide a more representative measure of model performance across different thresholds. We also follow GALORE [56] to consider both a random class and similar class as the counterfactual reference. More details for the evaluation metrics are introduced in Section D.1 in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.796, + 0.483, + 0.9 + ], + "angle": 0, + "content": "As shown in the Table 2, DiffCAM outperforms other state-of-the-art counterfactual explanation methods across nearly all metrics. While CounteRGAN achieves a slightly higher average P IoU on randomly selected counterfactual classes, DiffCAM excels overall. The F1 results in Figure 9a and 9b (see Appendix) show that DiffCAM demonstrates better robustness than GALORE in the selection of different" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.475, + 0.907, + 0.583 + ], + "angle": 0, + "content": "counterfactual classes. Figure 9c and 9d show that for similar counterfactual classes, DiffCAM achieves a significantly higher F1 score compared to GALORE. For randomly selected counterfactual classes, DiffCAM reaches a slightly higher F1 score at a faster rate and sustains this advantage across the range of thresholds shown. We provide additional experimental results in Section D.2 in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.595, + 0.838, + 0.612 + ], + "angle": 0, + "content": "4.3. Applicability on SSL and ViT Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.62, + 0.907, + 0.756 + ], + "angle": 0, + "content": "DiffCAM can be directly applied to SSL models as it doesn't rely on class-specific predictions. By reshaping patch tokens and incorporating the class token, DiffCAM can also be adapted to ViT models. To verify the results, we apply DiffCAM on MoCo-v3 with the ResNet-50 backbone and DINO with the ViT backbone. Results in Fig. 7 show SSL models can extract reasonable features, while DINO offers richer and more fine-grained semantics. DiffCAM faithfully reflects these capacity differences." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.77, + 0.655, + 0.787 + ], + "angle": 0, + "content": "4.4. Sanity Check" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.903 + ], + "angle": 0, + "content": "Sanity check is another method to examine whether an explanation method is really tied to the model [3] to further confirm its faithfulness. Specifically, we check whether the explanation results change when randomizing weights from a trained model. DiffCAM passes sanity check with common experimental settings. Detailed results are demonstrated in Section E in Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10333" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.126, + 0.082, + 0.874, + 0.148 + ], + "angle": 0, + "content": "
    ModelDatasetSaliency Methods (AUPRC)
    DiffCAMGradCAMScoreCAMLayerCAMXGradCAMIGGBP
    InceptionV3RSNA0.4920.4670.3280.3660.4660.3170.174
    SIIM0.0930.0760.0720.0710.0760.0630.072
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.252, + 0.157, + 0.744, + 0.171 + ], + "angle": 0, + "content": "Table 3. Evaluation of Saliency Methods on InceptionNetV3 using AUPRC Metric" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.196, + 0.182, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.197, + 0.197, + 0.281, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.295, + 0.197, + 0.379, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.395, + 0.197, + 0.479, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.271, + 0.182, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.196, + 0.271, + 0.281, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.295, + 0.271, + 0.379, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.395, + 0.272, + 0.479, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.353, + 0.483, + 0.395 + ], + "angle": 0, + "content": "Figure 8. Abnormality localization evaluation on the RSNA Pneumonia Detection Challenge dataset [6]. From left to right: original images, DiffCAM, GradCAM, and ScoreCAM results." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.422, + 0.483, + 0.455 + ], + "angle": 0, + "content": "4.5. Case Study: Abnormality Localization for Medical Imaging" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.462, + 0.483, + 0.657 + ], + "angle": 0, + "content": "In this case study, we demonstrate the potential of DiffCAM in medical imaging applications. Specifically, we consider abnormality localization in chest X-ray images [7], using the RSNA Pneumonia Detection Challenge dataset [6] and SIIM-ACR Pneumothorax Segmentation dataset [58] as benchmarks. The former contains bounding boxes indicating potential areas of pneumonia for positive cases, and the latter provides associated masks for pneumothorax images. For each dataset, we train an Inception-v3 model [11, 47] for image-level binary classification and evaluate XAI methods regarding abnormality localization. More details of the task background, dataset information and model training strategies are put in Section F.1 in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.659, + 0.483, + 0.839 + ], + "angle": 0, + "content": "We qualitatively compare the saliency maps produced by seven state-of-the-art methods, covering both gradient-based and activation-based baselines including GradCAM, ScoreCAM, LayerCAM), Axiom-based GradCAM (XGradCAM), Integrated Gradients (IG) [46], and Guided Backpropagation (GBP). For localization performance, we adopt the area under the precision-recall curve (AUPRC) as it better handles imbalanced data, common in medical images with small ground truth masks. Unlike ROC-AUC, AUPRC emphasizes the accuracy of positive pixels, making it especially suitable for identifying subtle abnormalities in medical imaging." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Results are presented in Table 3. On the RSNA dataset with bounding boxes as ground truth, DiffCAM achieves the highest AUPRC (0.492). GradCAM is shown very robust on medical applications, outperforming most ad" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.199, + 0.905, + 0.273 + ], + "angle": 0, + "content": "vanced methods which work well on general computer vision, whereas DiffCAM improves it with a remarkable margin. The SIIM task is more challenging and all methods deliver relatively low AUPRC scores. DiffCAM is still significantly superior to all the baseline methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.275, + 0.907, + 0.427 + ], + "angle": 0, + "content": "Two typical showcases from the RSNA datasets are presented in Figure 8, where the ground truth pneumonia areas are annotated as yellow boxes. The results demonstrate that DiffCAM captures more complete abnormality regions than baseline methods. This observation again coincides with our motivation that gradient-based approaches can't accurately capture the real feature difference between example groups (here we are interested in differences between healthy people and patients). We provide more random visualization examples in Section F.2 in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.442, + 0.637, + 0.457 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.468, + 0.906, + 0.558 + ], + "angle": 0, + "content": "DiffCAM assumes that a linear classifier is attached to the final deep feature layer, from which the optimal feature importance vector is derived. While many modern DNN architectures (e.g., ResNet, Inception, MobileNet, Vision Transformer) adhere to this design, extending DiffCAM to handle more general scenarios remains a topic for future work." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.575, + 0.634, + 0.591 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.601, + 0.907, + 0.783 + ], + "angle": 0, + "content": "This paper presents DiffCAM, a novel approach for generating saliency maps by emphasizing the differences between target examples and reference data distributions. It addresses the limitations of traditional CAM-based approaches by providing more comprehensive and intuitive explanations that better align with human understanding. Extensive experiments across various datasets demonstrate DiffCAM's robustness and superior performance. As interpretability becomes increasingly critical in deep learning applications, especially high-stake tasks such as medical imaging, our work offers both an effective XAI tool and a valuable new perspective for further research." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.799, + 0.694, + 0.816 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.906, + 0.9 + ], + "angle": 0, + "content": "We thank Shun Jin, Damian Chng and Gunika Goyal for their contributions to our initial idea exploration. This work was supported in part by US NSF grant DBI-2238093. M.R.U. was supported in part by a fellowship from CMU CMLH." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10334" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.143 + ], + "angle": 0, + "content": "[1] Kumar Abhishek and Deeksha Kamath. Attribution-based xai methods in computer vision: A review, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.146, + 0.483, + 0.186 + ], + "angle": 0, + "content": "[2] Amina Adadi and Mohammed Barrada. Peeking inside the black-box: a survey on explainable artificial intelligence (xai). 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2921-2929, 2016. 1, 3" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.482, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "10337" + } + ] +] \ No newline at end of file diff --git a/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_origin.pdf b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f8ddc6b0e8ffe3cc4a20adc94a289c07d1d59b4e --- /dev/null +++ b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/bf2fdff3-427c-4aae-800f-e13a073ec24c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2df86cc1cbdf317c0191e54b5861169bca973dd64202944b057533e114f6b1cb +size 6685410 diff --git a/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/full.md b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a0050c75a726f2fecd4f4a1dbc5fa703392fd8fd --- /dev/null +++ b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/full.md @@ -0,0 +1,414 @@ +# DiffCAM: Data-Driven Saliency Maps by Capturing Feature Differences + +Xingjian Li, Qiming Zhao, Peelesh Bisht, Mostofa Rafid Uddin, Jin Yu Kim, Bryan Zhang, Min Xu* Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213, United States + +# Abstract + +In recent years, the interpretability of Deep Neural Networks (DNNs) has garnered significant attention, particularly due to their widespread deployment in critical domains like healthcare, finance, and autonomous systems. To address the challenge of understanding how DNNs make decisions, Explainable AI (XAI) methods, such as saliency maps, have been developed to provide insights into the inner workings of these models. This paper introduces DiffCAM, a novel XAI method designed to overcome limitations in existing Class Activation Map (CAM)-based techniques, which often rely on decision boundary gradients to estimate feature importance. DiffCAM differentiates itself by considering the actual data distribution of the reference class, identifying feature importance based on how a target example differs from reference examples. This approach captures the most discriminative features without relying on decision boundaries or prediction results, making DiffCAM applicable to a broader range of models, including foundation models. Through extensive experiments, we demonstrate the superior performance and flexibility of DiffCAM in providing meaningful explanations across diverse datasets and scenarios. + +# 1. Introduction + +Deep Neural Networks (DNNs) [20, 43, 52] are often referred to as black-box models due to the difficulty in understanding how they extract features and make decisions. This lack of interpretability raises significant concerns in critical areas such as healthcare, finance, and autonomous systems. To address this challenge, Explainable AI (XAI) methods are designed to make the decision-making processes of AI systems more transparent and understandable to humans [2, 27]. It allows users and stakeholders to gain insight into how AI models arrive at specific outcomes [48]. + +Among the XAI approaches, saliency map is a common technique used to explain deep vision models. A saliency + +map is a visualization that highlights the critical parts of an image that significantly influence a model's prediction. + +In deep convolutional neural networks (CNNs), the activation map of each convolutional channel in deep layers naturally provides such information of spatial attention. This nature motivates popular solutions, such as Class Activation Map (CAM) [60], GradCAM [41] and ScoreCAM [55], which calculate a saliency map by a weighted aggregation of those feature channels. To estimate the feature importance, GradCAM calculates the gradient of the prediction (typically the probability of a target class) with respect to the input features. This gradient essentially measures the sensitivity of the prediction to variances in the input image or deep features, revealing the fastest direction in the feature space to change the model's decision. CAM and ScoreCAM adopt the similar idea to estimate the feature importance while avoiding gradient calculation. + +Despite the widely application of those CAM-based approaches, there still exists an essential limitation of them in estimating the feature importance. Here we illustrate our core idea by a simplified binary classification model predicting their language test result (Pass or Fail) according to their historical reading and writing scores. Intuitively, writing is learned as a more dominant feature for the prediction as it is usually harder than reading. This results in a decision boundary which lean to separate low and high write scores. When explaining a specific prediction, existing CAM-based approaches consider the direction orthogonal to the decision boundary as the feature importance vector, i.e., indicating the writing score is a more important feature for the prediction. However, this is counter-intuitive in case that the explained data point is not a representative one among its class. For example, when explaining why the student $x_{t}$ is predicted as Fail, CAM-based approaches assign a higher importance on writing to which the final prediction is more sensitive. However, the writing score of $x_{t}$ is as high as the average of the Pass group and higher than most of the Fail students. Therefore, reading is a better feature to explain the failure of $x_{t}$ , i.e., if $x_{t}$ 's reading is as good as the Pass group, $x_{t}$ will be predicted as Pass. + +Another relevant technique, counterfactual explanation + +![](images/a7bb57364ac63296e4d91ff20f2f709acdced3631ec57d658aee2d97b85976b6.jpg) +Figure 1. Motivation of DiffCAM. Existing CAM-based approaches resort to reach the decision boundary (e.g., GradCAM and ScoreCAM) or the nearest virtual example (e.g., counterfactual explanations) in the fastest direction, ignoring the actual data distribution for most representative examples. DiffCAM instead looks for the optimal direction that best represents the difference from a specified reference group. From this perspective, DiffCAM attributes Fail of $x_{t}$ mainly to its low Reading score, while traditional CAM-based approaches prefer Writing as the main reason. + +[16, 45], aims to find the closest virtual example on the data manifold that requires minimal changes to the input example to reach this virtual example. While it focuses more on the most discriminative feature from a data perspective, it still fails in capturing the difference between the target example and the majority of a reference class (the Pass class). As illustrated in Figure 1, the considered counterpart example is usually a virtual point near the decision boundary instead of a representative point among the real population of the reference class. + +The above analyses motivate us to design a novel CAM-based XAI approach by considering the actual data distribution of the reference class rather than the decision boundary. More specifically, given a group of reference examples, we aim to find the optimal direction (representing the feature importance vector) that optimally distinguish the target example from the reference group. This direction is the one on which the projections of reference examples are most distant to the target point, while maximally preserve their inherent common features. By this way, the feature importance vector represents only the most discriminative ingredients in the feature space. The exact solution is introduced in the Method section. We name our method DiffCAM as it explains model outputs by capturing essential feature differences. DiffCAM maintains the explanation format of saliency map and can be applied to more scenarios. The main difference between DiffCAM and existing CAM-based explanations can be summarized as follows. + +- Given a trained model to be explained, DiffCAM captures information about how is the target example different from the actual data points from the reference group, instead of considering how to quickly pass the decision boundary. +- DiffCAM is a more flexible and general framework. By using all the different classes as the reference group, DiffCAM functions similar to existing CAM-based approaches. By using one whole class as the reference group, DiffCAM provides counterfactual explanations. Beyond those, DiffCAM can also explain how a target example differs from a specific set of other examples, which may even belong to the same class with the target one. +- DiffCAM generates saliency maps without relying on the prediction results. This makes DiffCAM applicable to general feature extractors such as foundation models from self-supervised pre-training. + +In the experiment section, we demonstrate the effects of DiffCAM with several datasets covering general computer vision and medical imaging datasets. + +# 2. Related Work + +# 2.1. Explainable AI + +Explainable Artificial Intelligence (XAI) focuses on making complex machine learning models more interpretable, addressing the "black-box" nature of many advanced AI systems [26, 30]. The primary goal is to provide human-understandable explanations of a model's decisions, which is critical for improving trust, accountability, and ethical AI usage [21], especially in high-stakes fields like healthcare [24, 49, 50]. + +XAI techniques are broadly categorized into intrinsic methods, which involve building models that are inherently interpretable [37], and post-hoc methods, which generate explanations for pre-existing models without great changes to their structures [44, 59]. Post-hoc techniques are widely used for deep learning models, which are often too complex for intrinsic interpretability [4]. + +A key challenge in XAI is balancing the trade-off between a model's accuracy and its interpretability. In deep learning, where models are often highly effective but opaque, post-hoc methods, such as feature attribution and counterfactual reasoning, have become powerful tools for making predictions understandable [28]. + +# 2.2. Attribution Explanations + +Attribution-based methods play a crucial role in explaining behaviors by neural networks in tasks such as image classification [5, 22]. These methods identify which parts of an input image are most influential in a model's decision-making process [1, 33]. In the context of visual explanations, saliency mapping is often used in image classification + +tasks to illustrate influential regions without modifying the underlying model [10, 19]. However, these methods may struggle with fine-grained tasks where subtle distinctions require more detailed and nuanced explanations [4]. + +GradCAM [41] is widely used for generating visual explanations in neural networks by highlighting important regions contributing to a model's decision. Methods like GradCAM++ [9], ScoreCAM [55], Ablation-CAM [12], XGrad-CAM [14], EigenCAM [29], LayerCAM [17], and SmoothGradCAM++ [32] further refine this approach, offering more discriminative or interpretable saliency maps. Additionally, some saliency mapping techniques that differ from CAM-based methods such as Gradient*Input [42] and Integrated Gradient [46], are designed to highlight critical regions contributing to the model's decision by calculation on input images rather than using deep features. + +We also note different attribution methods such as LIME and SHAP, and Layer-wise Relevance Propagation (LRP) which are popular for enhancing AI explainability. LIME [35] provides locally faithful explanations by perturbing inputs, SHAP [39] is motivated by the game theory, and LRP [8] calculates relevance scores via attribution propagation. These methods are also important but not the main focus of our paper. + +# 2.3. Counterfactual Explanation + +One limitation of Attribution Explanation lies in its inability to identify attributes that distinguish a specific class from other classes, i.e. failing to address "Why not a class". Counterfactual Explanation introduced in [47, 53], was designed to provide insights into machine learning models, aiding decision-making in domains such as law and policy through counterfactual reasoning. In visual tasks, CE can be operationalized as "for class A to be correct, class B would require modifications to these specific parts." These modifications can be achieved through adversarial attacks [13, 51] or GAN-based methods [15, 25, 31, 38, 40]. + +Our work is more relevant to the saliency map based counterfactual explanation work. GALORE [56] introduced a "generative explanation framework" that unifies attribution-based, deliberative, and counterfactual explanations into a combined attribution map aligned with classifier predictions and confidence scores. Similarly, [34] measured the changes required to traverse from the learned manifold to the contrastive manifold and integrated this approach into Grad-CAM to generate heatmaps. Content-Aware Counterfactual Explanation (CCE) [57] proposed a content-aware counterfactual perturbation algorithm that generates positive-negative saliency-based explanations. + +Our approach differs from GALORE and CEE by not performing counterfactual comparisons at the saliency map level. Instead, we distinguish attributes of similar classes at the feature level, localizing a distinction heatmap that high- + +lights the unique features of the target class compared to other classes. The counterfactual explanation consists of the distinction heatmap for the target class A and another distinction heatmap for the counterfactual class B, which shares common features with A. + +# 3. Method + +# 3.1. General Framework + +The proposed DiffCAM approach follows the general framework of Class Activation Map (CAM) [60]. We consider deep convolutional neural networks. For simplification, we assume the deep model to be explained is composed of a deep feature extractor and a fully connected layer, which is a common architecture for modern DNNs. Let's define $\mathbf{x}$ as a target example to be explained, and $d$ as the number of feature channels of the last convolutional layer. By passing forward $\mathbf{x}$ , we get $\mathbf{A}_k(\mathbf{x})(k\in [1,2,\dots,d])$ as the $k$ -th activation map. The goal of CAM-based approaches is to generate a saliency map $M_{c}(\mathbf{x})$ explaining the prediction towards class $c$ with $\mathbf{x}$ as input. Specifically, a feature importance vector $\mathbf{w}^c\in \mathbb{R}^d$ is used to aggregate all the activation maps as + +$$ +\mathbf {M} _ {c} (\mathbf {x}) = \sum_ {k = 1} ^ {d} \mathbf {w} _ {k} ^ {c} \mathbf {A} _ {k} (\mathbf {x}). \tag {1} +$$ + +In the original CAM method [60], $\mathbf{w}_k^c$ are directly taken from the weights of the fully connected layer. Specifically, for class $c$ , the weight $\mathbf{w}_k^c$ is the $k$ -th component of the fully connected layer's weights $\mathbf{W}_c$ for that class. Many following work [9, 12, 14, 17, 29, 41, 55] adopt this general framework and differ in their ways of calculating $\mathbf{w}_k^c$ . Here we summarize two main categories from existing approaches, which focus on the gradient and individual contribution of each feature channel respectively. + +GradCAM: $\mathbf{w}_k^c$ are computed based on the gradients of the class score $y^{c}(\mathbf{x})$ with respect to the activation map $\mathbf{A}_k(\mathbf{x})$ . Specifically, $\mathbf{w}_k^c$ is the global average of the gradients across all spatial locations in the feature map as + +$$ +\mathbf {w} _ {k} ^ {c} = \frac {1}{Z} \sum_ {i, j} \frac {\partial y ^ {c}}{\partial \mathbf {A} _ {k} ^ {i , j} (\mathbf {x})} \tag {2} +$$ + +where $\mathbf{A}_k^{i,j}(\mathbf{x})$ is the activation at spatial location $(i,j)$ of the feature map and $Z$ is a normalization term. + +ScoreCAM: $\mathbf{w}_k^c$ are measured by the increase in the $c$ -th class score when the feature map $\mathbf{A}_k(\mathbf{x})$ is activated. For the $k$ -th feature channel, it first creates the corresponding masked input $\tilde{\mathbf{x}}_k = \mathbf{A}_k(\mathbf{x}) \odot \mathbf{x}$ , and then calculate the feature importance vector as + +$$ +\mathbf {w} _ {k} ^ {c} = \frac {y ^ {c} \left(\tilde {\mathbf {x}} _ {k}\right)}{\sum_ {k} y ^ {c} \left(\tilde {\mathbf {x}} _ {k}\right)}. \tag {3} +$$ + +![](images/8474e6930d814b64156745ac11bac91754282d858d943a5a16de9a29aac3f1cd.jpg) +Figure 2. Overview of the DiffCAM framework and applications. Given a target image and a set of reference examples, DiffCAM computes deep feature embeddings, identifies the direction that captures differences between the target and references, and generates a saliency map highlighting key distinguishing features. DiffCAM can provide flexible explanations according to the selection of reference examples. + +# 3.2. DiffCAM Implementation + +Intuitively, DiffCAM regards the explanation problem as looking for the feature components that best distinguish the target example (to be explained) and a group of reference examples. Suppose the example we aim to explain is $\mathbf{x}$ . According to the explanation type we are interested in, a set of $n$ examples $\{\hat{\mathbf{x}}^{(i)}\}_{i=1}^{n}$ is determined as the reference group. Note that the class labels of $\{\hat{\mathbf{x}}^{(i)}\}_{i=1}^{n}$ can be flexible, i.e., they may have the same, different or no labels. We generate the deep embedding $\mathbf{z} \in \mathbb{R}^d$ by performing average pooling along the spatial dimension on the whole feature map $\mathbf{A}(\mathbf{x})$ , and get $\{\hat{\mathbf{z}}^{(i)}\}_{i=1}^{n}$ for the reference examples. + +The feature importance vector $\mathbf{w}$ is defined as the optimal direction in the feature space that represents the most discriminative features relative to the reference data. Specifically, the projections of $\{\hat{\mathbf{z}}^{(i)}\}_{i = 1}^{n}$ on $\mathbf{w}$ are expected to have the largest distance with $\mathbf{z}$ while maintain as much commonality as possible. + +To solve the optimal $\mathbf{w}$ , we apply fundamental mathematical tools in linear algebra and convex optimization. Formally, denoting the mean reference position by $\hat{\mu} = \frac{1}{n}\sum_{i=1}^{n}\hat{\mathbf{z}}^{(i)}$ , the distance between the target example and the reference group along $\mathbf{w}$ can be defined as $\|\mathbf{w}^T z - \mathbf{w}^T\hat{\mu}\|^2$ . The variance among the reference examples projected on $\mathbf{w}$ is $\frac{1}{n}\sum_{i=1}^{n}\|\mathbf{w}^T\hat{\mathbf{z}}^{(i)} - \mathbf{w}^T\hat{\mu}\|^2$ . The measure can be written as + +$$ +\begin{array}{l} J (\mathbf {w}) = \frac {\left\| \mathbf {w} ^ {T} z - \mathbf {w} ^ {T} \hat {\mu} \right\| ^ {2}}{\sum_ {i = 1} ^ {n} \left\| \mathbf {w} ^ {T} \hat {\mathbf {z}} ^ {(i)} - \mathbf {w} ^ {T} \hat {\mu} \right\| ^ {2}} (4) \\ = \frac {\mathbf {w} ^ {T} \mathbf {S} _ {\mu} \mathbf {w}}{\mathbf {w} ^ {T} \mathbf {S} _ {\mathbf {v}} \mathbf {w}}, (5) \\ \end{array} +$$ + +where $\mathbf{S}_{\mu} = (\mathbf{z} - \hat{\mu})(\mathbf{z} - \hat{\mu})^T$ represents discrimination between the target example and the reference group, and $\mathbf{S}_{\mathbf{v}} = \sum_{i=1}^{n} (\hat{\mathbf{z}}^{(i)} - \hat{\mu})(\hat{\mathbf{z}}^{(i)} - \hat{\mu})^T$ represents internal variation among the reference examples. By differentiating and setting to zero, we find the optimal $\mathbf{w}$ that maximizes $J(\mathbf{w})$ as + +$$ +\mathbf {w} ^ {*} = \underset {\mathbf {w}} {\operatorname {a r g m a x}} J (w) = \mathbf {S _ {v}} ^ {- 1} (\mathbf {z} - \hat {\mu}). \qquad (6) +$$ + +Detailed derivation is put in Section A in Appendix. For supervised trained models, the inverse matrix $\mathbf{S}_{\mathbf{v}}^{-1}$ can be pre-calculated over training examples to avoid high inference complexity. We further adopt the Tikhonov regularization to ensure stability in calculating the inverse matrix. A small regularization term $\lambda \mathbf{I}$ is added onto $\mathbf{S}_{\mathbf{v}}$ when calculating the inverse. The solved $\mathbf{w}^*$ is finally used to generate the saliency map by calculating the weighted aggregation of the feature channels as + +$$ +\mathbf {M} ^ {\text {D i f f C A M}} (\mathbf {x}) = \sum_ {k = 1} ^ {d} \mathbf {w} _ {k} ^ {*} \mathbf {A} _ {k} (\mathbf {x}). \tag {7} +$$ + +A flexibility of DiffCAM lies in the selection of the reference group. In most cases, we use all the remaining classes as reference when answering the "Why is" question. For large-scale datasets with diverse classes (e.g., ImageNet), we empirically recommend to select a subset of similar classes (with k-Nearest-Neighbor search) as the reference group to obtain more discriminative features. To answer the "Why not" question or analyze internal variations, the corresponding target class will be specified as the reference group. An illustrative overview is presented in Figure 2. + +![](images/7c10b0da4c79ec90cc1f0bf90a7d7507a7cf400560201b1806e51f2eeea63e16.jpg) + +![](images/4314fabba3db1756bc361f0e616f453d1eac9e51ad7fb5a6febf722bc902c3b6.jpg) + +![](images/0a1ae22eece566148dec42d94a9ed8fc5d79fd02f6dd172a04ccfdf7ea6759bf.jpg) + +![](images/4f2b0dcbcb90cff3457207e84f3ae86869ef352bd197ba2365ef04143e764bff.jpg) + +![](images/739522f9a1e0507e42e9a6f5cfe72c80cbf557078f675dd128fdb8c7c7be5f35.jpg) + +![](images/c908354be5a8ab8f1a01cfc2495cb0539cf0bfa1b0bfde4eda1bfff28c52f6f1.jpg) + +![](images/92cc9cde518738b4606771727ef43404efe7df54635199bd7113335bb4125ed1.jpg) + +![](images/424b333fb05c40ef55e5fa309254a7dfd7dfd0ed1640cdd3e1a5daff5108a478.jpg) + +![](images/9a42477457be27549f5aa994f6a3835593abbe86d8ab70b51798d75684f37e81.jpg) +Original Image + +![](images/183a2fba3c39974566d0290ce755aa5bcb784bcf9bdf34f1209b9103d6495a42.jpg) +GradCAM for 7 + +![](images/c096343f9cd4aeb32ed4e5dc11cace02cb087c2c7365fc46dafcb3fd7967270f.jpg) +SmoothGradCAM++ for 7 + +![](images/fa1bd860c354fa306b72db92c3a80fbc41e89d0a6e32cfc5153799dba53a853d.jpg) +ScoreCAM for 7 + +![](images/784c4879e6b85a8c89620f0e6fb320af4f4982e79b758b2b96a965c5d8f0b35c.jpg) +DiffCAM for 7 + +![](images/c4b4aa9cdc687abea425e3bbf56789c42dd8a66d3217b21e697ab77b7b976293.jpg) +DiffCAM (7 against 1) + +![](images/b6e2765a76465a18a8899dddc60e80028288cfc90c23b19193a344cb5ea1e774.jpg) +DiffCAM (7 against 2) + +![](images/7fb071201f8dc32e63da19aedf649e60b1c799a2d0d6fda0b61bc18ea04d598c.jpg) +DiffCAM (7 against 9) + +![](images/0c66abb70c3f47e8d454bf687e85195af733ebcc680aae9931381014ebdc7325.jpg) +Original Image +Figure 3. Given MNIST images 3, 7, 9 as input, the 2nd-5th columns show saliency maps generated by XAI methods. The last three columns present counterfactual saliency maps which highlight differences between the target digit and selected counterfactual classes. + +![](images/d5e89567a4ebb3664408d36314c4793e622083820a6e5d1f27db960732790d8a.jpg) +GradCAM for 9 + +![](images/f74c1941f9e2b3e443d68d38c023ca552951dfce537fc31fdde11594170e41b1.jpg) +SmoothGradCAM++ for 9 + +![](images/09db1cfd13f52dc1e4905d0df3c117c08edee76f57eb4dd82495cc8010718166.jpg) +ScoreCAM for 9 + +![](images/e9ffb108c0fef355ad74ad346e252e816c6b31d7d0bc5782b677f182bd887a70.jpg) +DiffCAM for 9 + +![](images/4fa7fca8d3faa7fc4f73d99aa1beec7e106061992d7724a9b1d80009f2909094.jpg) +DiffCAM (9 against 0) + +![](images/a10d969f8b1a9486ad5ef007ff8d51ae488eefa3cb776ae1c679b6b00d2d1aaa.jpg) +DiffCAM (9 against 7) + +![](images/bd0ba1b9633920cc44d051a7ee91a3ac21265667936ed6a2155b200a914318b9.jpg) +DiffCAM (9 against 8) + +# 4. Experiments + +We evaluate DiffCAM through extensive qualitative and quantitative experiments in Section 4.1 and 4.2, respectively. Then we present results with SSL models in Section 4.3 and sanity check in Section 4.4. Finally, Section 4.5 presents a case study on abnormality localization in medical imaging to highlight DiffCAM's practical applications. + +# 4.1. Qualitative Evaluation + +This section provides qualitative evaluation results for the three task types introduced in the Method part. We examine DiffCAM's ability to highlight discriminative features for both the "Why is" and "Why not" questions, and its potential in revealing internal pattern variance as well. We use the MNIST [23] dataset due to its simplicity and clear patterns, which make it a good fit for the demonstration purpose. + +# 4.1.1 Discriminant Visual Attention + +The second to fifth columns in Figure 3 demonstrate the effects of general explanation results which answers the "Why is" question. For DiffCAM, we use all examples from other classes as the reference group. Compared against the baseline methods, DiffCAM tends to highlight more comprehensive object patterns instead of only a small region of the most discriminative patterns. This observation backups our motivation that DiffCAM aims to capture the features which truly reflect the feature difference for real data distribution although some the direction may not be the fastest to reach decision boundaries. The results also align better with human perception of distinctive digit features. By assigning another similar digit as the reference group, DiffCAM is able to obtain discriminative features similar to counterfactual explanations. As shown in the last three columns of Figure 3, the highlighted regions accurately represent the + +key differences, e.g., the bottom part makes the image of 9 not a digit 0. More qualitative results for discriminant visual attention are put in Section B in Appendix. + +# 4.1.2 Intra-class Variance + +While intra-class variance has rarely been discussed in existing XAI research, it is valuable in practice for model debugging and data engineering. Our work fills this gap and offers potential in this important task. + +In Figure 4, the top row shows difficult examples of the digit 0 along with their incorrect predicted labels (mostly classified as 6), illustrating how subtle variations in shape and structure within the same class can lead to misclassification. The bottom row presents the corresponding saliency maps generated by DiffCAM, using the training set of digit 0 as the reference group, and highlights the patterns in each image that deviated the most from the majority. The results demonstrate that features like abnormal breaks in the loops and additional curves or dots were identified as influential differences that distinguish these hard cases from typical instances of digit 0. We can reasonably suspect these anomalies as the main factors contributing to incorrect predictions. In practice, such analyses can guide further data processing efforts to deploy a more robust model. + +![](images/31565cb70882b8cca2564a43f2bd1f178928a71a707f543e7c08f92d1b71621c.jpg) + +![](images/0b088d3309dfc7997b6c05174c125364f145ec0c8df81889b8df7a840419ebfd.jpg) + +![](images/c5af04ea14d628374d4c174063626c2bbac698efad51309ee45424c4efb8e5f3.jpg) + +![](images/235c045f6c7e3cec32b060012a8604e04a0cbaa246fe1303e91e40b23062eccd.jpg) + +![](images/77567290b5edbbe8e5df4419cb93d2fefb988fdd6439dda3a7bff60135328de0.jpg) + +![](images/f0c5016da750fbbf1965ca46ee213236a5a7111ee6d57d21993e24c5d7e805ee.jpg) +Figure 4. Visualization of intra-Class Variance with DiffCAM on MNIST digits. + +![](images/eecd0683ddeb1363737916e83d632b44d72ff87d8447551d81a1fe9837ebb5c9.jpg) + +![](images/34d6dcc5cb95dace69fec6ff147ec22151b83ff29c73d40fd1f64fe16fe39a4a.jpg) + +![](images/f12642126eb06cfdba868e47446e6844ee2fd46ba439b770691eaac85ae8a34f.jpg) + +![](images/a6e514365845cc5c43a07572681b63009c5c9adf56c66448da1241b72eebf8d4.jpg) + +
    Arch.MetricExplanation Methods
    GradCAMScoreCAMLayerCAMXGradCAMDiffCAM
    ResNet-50IoU0.5280.5110.5350.4470.534
    AUPRC0.7270.7090.7380.6340.741
    Inception-v3IoU0.5240.5640.5830.5240.583
    AUPRC0.7260.7710.7920.7260.794
    + +Table 1. Evaluation of object localization on ImageNet. + +![](images/fe7a537a661408c3c9e5347f03482b1dae3240dd9903beed992f4cb249ec9782.jpg) + +![](images/2082072b5df5a2f7abb6896021313a598602db7df2ecab46f6bb0b40843e9ca5.jpg) + +![](images/c2dbf3e7913c39f031511c8189f5f269b9289ec776b65f8016c038e078da028d.jpg) + +![](images/d11233a949c2fa225f7262580460b8040d05fccab411195591cbb8534f664776.jpg) + +![](images/32beef8c6d12eab7f37c0f89e68529d8c2af234ff80935c744bc5ccbf2115159.jpg) + +![](images/4d3311a93729c1a818db85ee101adbc706b4b64863267829c4431e7c82da2111.jpg) +Figure 5. Illustration of the faithfulness and object localization test on ImageNet validation images. The left most column are original images with red rectangles as the object locations. The right most are masked images by ROAD according to the DiffCAM results. + +![](images/644316dc5d23b9a0767e80a32aa099b71646dffe54b2cc0236187d52e89257d6.jpg) + +![](images/8a80a85e6c755ed435c16658e9a87b7ae686117a68ee323a9b730791438232c8.jpg) + +![](images/4f399bb65418f3353c8c66b574cef0c09bfa78fd69aa1288060c6a0022d4f9ed.jpg) + +![](images/e2f3ba3d761a9bfba9f739f06ad7f1ff6f12e82c1b27dc386c14dcb0df0029a6.jpg) +Figure 6. ROAD evaluation on the ImageNet dataset. + +# 4.2. Quantitative Evaluation + +In this section, we report our quantitative experimental results. Following common practice, we measure faithfulness and localization performance on ImageNet to assess the quality of saliency maps. To improve computational efficiency, we pre-calculate the mean feature for each class and build a search index with Faiss-gpu [18]. During inference, we retrieve the top 100 most similar mean features as the reference group for each target image. Figure 5 presents showcases for the two experiments. We also quantitatively evaluate DiffCAM on counterfactual explanation tasks using the ResNet-50 model pre-trained on the fine-grained dataset CUB-200-2011 [54]. + +# 4.2.1 Faithfulness + +In XAI research, faithfulness refers to the extent to which an explanation method accurately reflects the true reasoning process of a machine learning model. Specifically, denoting I as the input image, we assess the faithfulness of a saliency map M by masking a set of pixels S $\subseteq$ I to the input and observing the change in the model's prediction as $\Delta f(S) = f(I) - f(I\backslash S)$ , where S is determined by selecting the positions with top values in M. Based on this principal, we adopt Remove and Debias (ROAD) [36], which replaces the removed pixels with the mean pixel values from their neighbors. Considering the settings with $[25\%, 50\%, 75\%]$ top important pixels replaced, we plot ROAD curves to show the average prediction probability decrease for each case. Experiments are conducted on 1000 random examples + +![](images/204fab0f23763a11ca322e3b29cde28512b59c0850185e45ba612de6fc522c8f.jpg) +(a) ResNet-50 + +![](images/06e83773c8c291a051135a612c9cd836d976344fe655684d3d185aeb94fa4cee.jpg) +(b) Inception-v3 + +from the validation set of ImageNet. As shown in Figure 6, DiffCAM shows competitive level of faithfulness among various state-of-the-art baseline methods. + +# 4.2.2 Object Localization + +Besides faithfulness, we are also interested in whether an XAI method provides interpretable information for humans. This is usually assessed through the task of object localization. Following the ScoreCAM paper, we consider images with a single bounding box for the target class and restrict the object to occupy less than half of the entire image. We randomly select 500 images from the ImageNet validation set that satisfy these conditions. + +Regarding the evaluation metric, we do not adopt the previous energy-based pointing method [55], as it tends to favor explanation results that overly concentrate pixel scores onto a small number of pixels. This approach is susceptible to artificial manipulation of sharpening the score distribution. Therefore, we employ conventional metrics Intersection over Union (IoU) and Area Under the Precision-Recall Curve (AUPRC) to assess the accuracy with which the generated saliency maps align with the object bounding boxes. Results in Table 1 show that DiffCAM achieves the best overall localization accuracy along with LayerCAM. More visualization results for localization evaluation are put in Section C in Appendix. + +# 4.2.3 Counterfactual Explanation + +Most Existing methods of counterfactual explanation resort to create an artificial example that yields a different prediction regarding the counterfactual class. These modifications + +
    MetricRandom CounterfactualSimilar Counterfactual
    GoyalCounteRGANGALOREDiffCAMGoyalCounteRGANGALOREDiffCAM
    R0.030.060.090.150.120.170.160.17
    P0.770.740.810.830.570.560.600.61
    PIoU0.180.200.160.180.150.140.150.20
    + +Table 2. Comparison of counterfactual explanation methods for Beginner and Advanced Users. + +![](images/1c99bf3a09e92a8d19ca22450cb08b5a92c9a00b0dba65c0abe0dbac84f24e94.jpg) +Figure 7. DiffCAM results answering "why is" and "why not" with SSL models Moco-v3 (column 2,3) and DINO (column 4,5). + +can be achieved through adversarial attacks and image synthesis. However, the perturbed or synthesized features often do not reside within the natural image space, limiting their applicability in expert domains. DiffCAM belongs to the direction of saliency map based counterfactual explanation that highlights which areas of the input would need modification to change the prediction. + +For performance evaluation, we mostly adopt the state-of-the-art saliency map based counterfactual method GALORE [56], using CUB-200-2011 with part annotations as the benchmark. Then the counterfactual ground truth is represented by $\mathcal{G}^c = \{(p_i,a_i,b_i)\}_{i = 1}^N$ , where parts are denoted as $p$ , and $a$ and $b$ refer to the target and counterfactual classes, respectively. GALORE [56] uses Precision (P), Recall (R) and Part Intersection over Union (PIoU) as evaluation metrics. We additionally employ F1-Score to provide a more representative measure of model performance across different thresholds. We also follow GALORE [56] to consider both a random class and similar class as the counterfactual reference. More details for the evaluation metrics are introduced in Section D.1 in Appendix. + +As shown in the Table 2, DiffCAM outperforms other state-of-the-art counterfactual explanation methods across nearly all metrics. While CounteRGAN achieves a slightly higher average P IoU on randomly selected counterfactual classes, DiffCAM excels overall. The F1 results in Figure 9a and 9b (see Appendix) show that DiffCAM demonstrates better robustness than GALORE in the selection of different + +counterfactual classes. Figure 9c and 9d show that for similar counterfactual classes, DiffCAM achieves a significantly higher F1 score compared to GALORE. For randomly selected counterfactual classes, DiffCAM reaches a slightly higher F1 score at a faster rate and sustains this advantage across the range of thresholds shown. We provide additional experimental results in Section D.2 in Appendix. + +# 4.3. Applicability on SSL and ViT Models + +DiffCAM can be directly applied to SSL models as it doesn't rely on class-specific predictions. By reshaping patch tokens and incorporating the class token, DiffCAM can also be adapted to ViT models. To verify the results, we apply DiffCAM on MoCo-v3 with the ResNet-50 backbone and DINO with the ViT backbone. Results in Fig. 7 show SSL models can extract reasonable features, while DINO offers richer and more fine-grained semantics. DiffCAM faithfully reflects these capacity differences. + +# 4.4. Sanity Check + +Sanity check is another method to examine whether an explanation method is really tied to the model [3] to further confirm its faithfulness. Specifically, we check whether the explanation results change when randomizing weights from a trained model. DiffCAM passes sanity check with common experimental settings. Detailed results are demonstrated in Section E in Appendix. + +
    ModelDatasetSaliency Methods (AUPRC)
    DiffCAMGradCAMScoreCAMLayerCAMXGradCAMIGGBP
    InceptionV3RSNA0.4920.4670.3280.3660.4660.3170.174
    SIIM0.0930.0760.0720.0710.0760.0630.072
    + +Table 3. Evaluation of Saliency Methods on InceptionNetV3 using AUPRC Metric + +![](images/8d2cb26d7c3bfac33f72ade55a384629ea2ac3e158523336d74a07c6dbdb83c6.jpg) + +![](images/f1551dca88697ab4036b963c72b0cad7a01a8d42b94b9557ca9195a55a192f90.jpg) + +![](images/c171f335861b2a1fb462b3a918d4c6d2941fd7762f192897718460d4f1f5bdcd.jpg) + +![](images/272c12c77f3de0192f4e59d8241e01495f1f49d04229f73f9c437380a4c95fee.jpg) + +![](images/d365084ffc195e4448e142cfe11fad3e6698e892e591ff514dacc21e70bd211c.jpg) +Figure 8. Abnormality localization evaluation on the RSNA Pneumonia Detection Challenge dataset [6]. From left to right: original images, DiffCAM, GradCAM, and ScoreCAM results. + +![](images/0d995729c9d99523f979e10d50ad06bc75ac6b75113f0f7765b35d69d786b2d3.jpg) + +![](images/fc42efc58ff91ed67ffab6c8c4b9fbcf311ea3e955cebb9949fdd8bae6762374.jpg) + +![](images/e31a4567fb7b1232bebd17a85e269781133cbe6c575daa500a0da7bfa4a32858.jpg) + +# 4.5. Case Study: Abnormality Localization for Medical Imaging + +In this case study, we demonstrate the potential of DiffCAM in medical imaging applications. Specifically, we consider abnormality localization in chest X-ray images [7], using the RSNA Pneumonia Detection Challenge dataset [6] and SIIM-ACR Pneumothorax Segmentation dataset [58] as benchmarks. The former contains bounding boxes indicating potential areas of pneumonia for positive cases, and the latter provides associated masks for pneumothorax images. For each dataset, we train an Inception-v3 model [11, 47] for image-level binary classification and evaluate XAI methods regarding abnormality localization. More details of the task background, dataset information and model training strategies are put in Section F.1 in Appendix. + +We qualitatively compare the saliency maps produced by seven state-of-the-art methods, covering both gradient-based and activation-based baselines including GradCAM, ScoreCAM, LayerCAM), Axiom-based GradCAM (XGradCAM), Integrated Gradients (IG) [46], and Guided Backpropagation (GBP). For localization performance, we adopt the area under the precision-recall curve (AUPRC) as it better handles imbalanced data, common in medical images with small ground truth masks. Unlike ROC-AUC, AUPRC emphasizes the accuracy of positive pixels, making it especially suitable for identifying subtle abnormalities in medical imaging. + +Results are presented in Table 3. On the RSNA dataset with bounding boxes as ground truth, DiffCAM achieves the highest AUPRC (0.492). GradCAM is shown very robust on medical applications, outperforming most ad + +vanced methods which work well on general computer vision, whereas DiffCAM improves it with a remarkable margin. The SIIM task is more challenging and all methods deliver relatively low AUPRC scores. DiffCAM is still significantly superior to all the baseline methods. + +Two typical showcases from the RSNA datasets are presented in Figure 8, where the ground truth pneumonia areas are annotated as yellow boxes. The results demonstrate that DiffCAM captures more complete abnormality regions than baseline methods. This observation again coincides with our motivation that gradient-based approaches can't accurately capture the real feature difference between example groups (here we are interested in differences between healthy people and patients). We provide more random visualization examples in Section F.2 in Appendix. + +# 5. Limitations + +DiffCAM assumes that a linear classifier is attached to the final deep feature layer, from which the optimal feature importance vector is derived. While many modern DNN architectures (e.g., ResNet, Inception, MobileNet, Vision Transformer) adhere to this design, extending DiffCAM to handle more general scenarios remains a topic for future work. + +# 6. Conclusion + +This paper presents DiffCAM, a novel approach for generating saliency maps by emphasizing the differences between target examples and reference data distributions. It addresses the limitations of traditional CAM-based approaches by providing more comprehensive and intuitive explanations that better align with human understanding. Extensive experiments across various datasets demonstrate DiffCAM's robustness and superior performance. As interpretability becomes increasingly critical in deep learning applications, especially high-stake tasks such as medical imaging, our work offers both an effective XAI tool and a valuable new perspective for further research. + +# 7. Acknowledgement + +We thank Shun Jin, Damian Chng and Gunika Goyal for their contributions to our initial idea exploration. This work was supported in part by US NSF grant DBI-2238093. M.R.U. was supported in part by a fellowship from CMU CMLH. + +# References + +[1] Kumar Abhishek and Deeksha Kamath. Attribution-based xai methods in computer vision: A review, 2022. 2 +[2] Amina Adadi and Mohammed Barrada. Peeking inside the black-box: a survey on explainable artificial intelligence (xai). IEEE access, 6:52138-52160, 2018. 1 +[3] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. Sanity checks for saliency maps. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2921-2929, 2016. 1, 3 \ No newline at end of file diff --git a/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/images.zip b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..bce16fe1c6bec768bec6f87944b134a4674e1b06 --- /dev/null +++ b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:01e423b1092905541c6d0333479fe33b0043b657868905cde5e30ba2febf929a +size 515555 diff --git a/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/layout.json b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4f761565220cdaedd89900b292e082d15c521e2c --- /dev/null +++ b/2025/DiffCAM_ Data-Driven Saliency Maps by Capturing Feature Differences/layout.json @@ -0,0 +1,10754 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 82, + 103, + 531, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 103, + 531, + 121 + ], + "spans": [ + { + "bbox": [ + 82, + 103, + 531, + 121 + ], + "type": "text", + "content": "DiffCAM: Data-Driven Saliency Maps by Capturing Feature Differences" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 143, + 550, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 143, + 550, + 185 + ], + "spans": [ + { + "bbox": [ + 64, + 143, + 550, + 185 + ], + "type": "text", + "content": "Xingjian Li, Qiming Zhao, Peelesh Bisht, Mostofa Rafid Uddin, Jin Yu Kim, Bryan Zhang, Min Xu* Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213, United States" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 213, + 201, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 213, + 201, + 225 + ], + "spans": [ + { + "bbox": [ + 151, + 213, + 201, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 239, + 296, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 239, + 296, + 501 + ], + "spans": [ + { + "bbox": [ + 56, + 239, + 296, + 501 + ], + "type": "text", + "content": "In recent years, the interpretability of Deep Neural Networks (DNNs) has garnered significant attention, particularly due to their widespread deployment in critical domains like healthcare, finance, and autonomous systems. To address the challenge of understanding how DNNs make decisions, Explainable AI (XAI) methods, such as saliency maps, have been developed to provide insights into the inner workings of these models. This paper introduces DiffCAM, a novel XAI method designed to overcome limitations in existing Class Activation Map (CAM)-based techniques, which often rely on decision boundary gradients to estimate feature importance. DiffCAM differentiates itself by considering the actual data distribution of the reference class, identifying feature importance based on how a target example differs from reference examples. This approach captures the most discriminative features without relying on decision boundaries or prediction results, making DiffCAM applicable to a broader range of models, including foundation models. Through extensive experiments, we demonstrate the superior performance and flexibility of DiffCAM in providing meaningful explanations across diverse datasets and scenarios." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 527, + 137, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 527, + 137, + 540 + ], + "spans": [ + { + "bbox": [ + 56, + 527, + 137, + 540 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 548, + 295, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 295, + 668 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 295, + 668 + ], + "type": "text", + "content": "Deep Neural Networks (DNNs) [20, 43, 52] are often referred to as black-box models due to the difficulty in understanding how they extract features and make decisions. This lack of interpretability raises significant concerns in critical areas such as healthcare, finance, and autonomous systems. To address this challenge, Explainable AI (XAI) methods are designed to make the decision-making processes of AI systems more transparent and understandable to humans [2, 27]. It allows users and stakeholders to gain insight into how AI models arrive at specific outcomes [48]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 668, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 668, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 668, + 296, + 693 + ], + "type": "text", + "content": "Among the XAI approaches, saliency map is a common technique used to explain deep vision models. A saliency" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 213, + 553, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 553, + 238 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 553, + 238 + ], + "type": "text", + "content": "map is a visualization that highlights the critical parts of an image that significantly influence a model's prediction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 240, + 555, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 240, + 555, + 421 + ], + "spans": [ + { + "bbox": [ + 313, + 240, + 555, + 421 + ], + "type": "text", + "content": "In deep convolutional neural networks (CNNs), the activation map of each convolutional channel in deep layers naturally provides such information of spatial attention. This nature motivates popular solutions, such as Class Activation Map (CAM) [60], GradCAM [41] and ScoreCAM [55], which calculate a saliency map by a weighted aggregation of those feature channels. To estimate the feature importance, GradCAM calculates the gradient of the prediction (typically the probability of a target class) with respect to the input features. This gradient essentially measures the sensitivity of the prediction to variances in the input image or deep features, revealing the fastest direction in the feature space to change the model's decision. CAM and ScoreCAM adopt the similar idea to estimate the feature importance while avoiding gradient calculation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "spans": [ + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "text", + "content": "Despite the widely application of those CAM-based approaches, there still exists an essential limitation of them in estimating the feature importance. Here we illustrate our core idea by a simplified binary classification model predicting their language test result (Pass or Fail) according to their historical reading and writing scores. Intuitively, writing is learned as a more dominant feature for the prediction as it is usually harder than reading. This results in a decision boundary which lean to separate low and high write scores. When explaining a specific prediction, existing CAM-based approaches consider the direction orthogonal to the decision boundary as the feature importance vector, i.e., indicating the writing score is a more important feature for the prediction. However, this is counter-intuitive in case that the explained data point is not a representative one among its class. For example, when explaining why the student " + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "text", + "content": " is predicted as Fail, CAM-based approaches assign a higher importance on writing to which the final prediction is more sensitive. However, the writing score of " + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "text", + "content": " is as high as the average of the Pass group and higher than most of the Fail students. Therefore, reading is a better feature to explain the failure of " + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "text", + "content": ", i.e., if " + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "text", + "content": "'s reading is as good as the Pass group, " + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 423, + 556, + 699 + ], + "type": "text", + "content": " will be predicted as Pass." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 326, + 701, + 555, + 714 + ], + "type": "text", + "content": "Another relevant technique, counterfactual explanation" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 702, + 146, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 146, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 146, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10327" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 293, + 247 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 293, + 247 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 293, + 247 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 293, + 247 + ], + "type": "image", + "image_path": "a7bb57364ac63296e4d91ff20f2f709acdced3631ec57d658aee2d97b85976b6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 256, + 296, + 357 + ], + "lines": [ + { + "bbox": [ + 55, + 256, + 296, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 256, + 296, + 357 + ], + "type": "text", + "content": "Figure 1. Motivation of DiffCAM. Existing CAM-based approaches resort to reach the decision boundary (e.g., GradCAM and ScoreCAM) or the nearest virtual example (e.g., counterfactual explanations) in the fastest direction, ignoring the actual data distribution for most representative examples. DiffCAM instead looks for the optimal direction that best represents the difference from a specified reference group. From this perspective, DiffCAM attributes Fail of " + }, + { + "bbox": [ + 55, + 256, + 296, + 357 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 55, + 256, + 296, + 357 + ], + "type": "text", + "content": " mainly to its low Reading score, while traditional CAM-based approaches prefer Writing as the main reason." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 377, + 295, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 377, + 295, + 497 + ], + "spans": [ + { + "bbox": [ + 55, + 377, + 295, + 497 + ], + "type": "text", + "content": "[16, 45], aims to find the closest virtual example on the data manifold that requires minimal changes to the input example to reach this virtual example. While it focuses more on the most discriminative feature from a data perspective, it still fails in capturing the difference between the target example and the majority of a reference class (the Pass class). As illustrated in Figure 1, the considered counterpart example is usually a virtual point near the decision boundary instead of a representative point among the real population of the reference class." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 713 + ], + "type": "text", + "content": "The above analyses motivate us to design a novel CAM-based XAI approach by considering the actual data distribution of the reference class rather than the decision boundary. More specifically, given a group of reference examples, we aim to find the optimal direction (representing the feature importance vector) that optimally distinguish the target example from the reference group. This direction is the one on which the projections of reference examples are most distant to the target point, while maximally preserve their inherent common features. By this way, the feature importance vector represents only the most discriminative ingredients in the feature space. The exact solution is introduced in the Method section. We name our method DiffCAM as it explains model outputs by capturing essential feature differences. DiffCAM maintains the explanation format of saliency map and can be applied to more scenarios. The main difference between DiffCAM and existing CAM-based explanations can be summarized as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 276 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 314, + 72, + 553, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 553, + 132 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 553, + 132 + ], + "type": "text", + "content": "- Given a trained model to be explained, DiffCAM captures information about how is the target example different from the actual data points from the reference group, instead of considering how to quickly pass the decision boundary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 132, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 132, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 314, + 132, + 553, + 228 + ], + "type": "text", + "content": "- DiffCAM is a more flexible and general framework. By using all the different classes as the reference group, DiffCAM functions similar to existing CAM-based approaches. By using one whole class as the reference group, DiffCAM provides counterfactual explanations. Beyond those, DiffCAM can also explain how a target example differs from a specific set of other examples, which may even belong to the same class with the target one." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 228, + 553, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 276 + ], + "type": "text", + "content": "- DiffCAM generates saliency maps without relying on the prediction results. This makes DiffCAM applicable to general feature extractors such as foundation models from self-supervised pre-training." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 277, + 555, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 314 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 314 + ], + "type": "text", + "content": "In the experiment section, we demonstrate the effects of DiffCAM with several datasets covering general computer vision and medical imaging datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 325, + 400, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 325, + 400, + 337 + ], + "spans": [ + { + "bbox": [ + 314, + 325, + 400, + 337 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 344, + 408, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 344, + 408, + 357 + ], + "spans": [ + { + "bbox": [ + 314, + 344, + 408, + 357 + ], + "type": "text", + "content": "2.1. Explainable AI" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 363, + 555, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 363, + 555, + 459 + ], + "spans": [ + { + "bbox": [ + 313, + 363, + 555, + 459 + ], + "type": "text", + "content": "Explainable Artificial Intelligence (XAI) focuses on making complex machine learning models more interpretable, addressing the \"black-box\" nature of many advanced AI systems [26, 30]. The primary goal is to provide human-understandable explanations of a model's decisions, which is critical for improving trust, accountability, and ethical AI usage [21], especially in high-stakes fields like healthcare [24, 49, 50]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 460, + 554, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 554, + 543 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 554, + 543 + ], + "type": "text", + "content": "XAI techniques are broadly categorized into intrinsic methods, which involve building models that are inherently interpretable [37], and post-hoc methods, which generate explanations for pre-existing models without great changes to their structures [44, 59]. Post-hoc techniques are widely used for deep learning models, which are often too complex for intrinsic interpretability [4]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 544, + 554, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 554, + 615 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 554, + 615 + ], + "type": "text", + "content": "A key challenge in XAI is balancing the trade-off between a model's accuracy and its interpretability. In deep learning, where models are often highly effective but opaque, post-hoc methods, such as feature attribution and counterfactual reasoning, have become powerful tools for making predictions understandable [28]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 623, + 455, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 623, + 455, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 623, + 455, + 635 + ], + "type": "text", + "content": "2.2. Attribution Explanations" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 641, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 554, + 713 + ], + "type": "text", + "content": "Attribution-based methods play a crucial role in explaining behaviors by neural networks in tasks such as image classification [5, 22]. These methods identify which parts of an input image are most influential in a model's decision-making process [1, 33]. In the context of visual explanations, saliency mapping is often used in image classification" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10328" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 120 + ], + "type": "text", + "content": "tasks to illustrate influential regions without modifying the underlying model [10, 19]. However, these methods may struggle with fine-grained tasks where subtle distinctions require more detailed and nuanced explanations [4]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 121, + 295, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 121, + 295, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 121, + 295, + 264 + ], + "type": "text", + "content": "GradCAM [41] is widely used for generating visual explanations in neural networks by highlighting important regions contributing to a model's decision. Methods like GradCAM++ [9], ScoreCAM [55], Ablation-CAM [12], XGrad-CAM [14], EigenCAM [29], LayerCAM [17], and SmoothGradCAM++ [32] further refine this approach, offering more discriminative or interpretable saliency maps. Additionally, some saliency mapping techniques that differ from CAM-based methods such as Gradient*Input [42] and Integrated Gradient [46], are designed to highlight critical regions contributing to the model's decision by calculation on input images rather than using deep features." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 265, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 265, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 265, + 296, + 361 + ], + "type": "text", + "content": "We also note different attribution methods such as LIME and SHAP, and Layer-wise Relevance Propagation (LRP) which are popular for enhancing AI explainability. LIME [35] provides locally faithful explanations by perturbing inputs, SHAP [39] is motivated by the game theory, and LRP [8] calculates relevance scores via attribution propagation. These methods are also important but not the main focus of our paper." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 369, + 209, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 369, + 209, + 383 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 209, + 383 + ], + "type": "text", + "content": "2.3. Counterfactual Explanation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 389, + 295, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 389, + 295, + 520 + ], + "spans": [ + { + "bbox": [ + 55, + 389, + 295, + 520 + ], + "type": "text", + "content": "One limitation of Attribution Explanation lies in its inability to identify attributes that distinguish a specific class from other classes, i.e. failing to address \"Why not a class\". Counterfactual Explanation introduced in [47, 53], was designed to provide insights into machine learning models, aiding decision-making in domains such as law and policy through counterfactual reasoning. In visual tasks, CE can be operationalized as \"for class A to be correct, class B would require modifications to these specific parts.\" These modifications can be achieved through adversarial attacks [13, 51] or GAN-based methods [15, 25, 31, 38, 40]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 521, + 295, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 665 + ], + "type": "text", + "content": "Our work is more relevant to the saliency map based counterfactual explanation work. GALORE [56] introduced a \"generative explanation framework\" that unifies attribution-based, deliberative, and counterfactual explanations into a combined attribution map aligned with classifier predictions and confidence scores. Similarly, [34] measured the changes required to traverse from the learned manifold to the contrastive manifold and integrated this approach into Grad-CAM to generate heatmaps. Content-Aware Counterfactual Explanation (CCE) [57] proposed a content-aware counterfactual perturbation algorithm that generates positive-negative saliency-based explanations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "Our approach differs from GALORE and CEE by not performing counterfactual comparisons at the saliency map level. Instead, we distinguish attributes of similar classes at the feature level, localizing a distinction heatmap that high-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": "lights the unique features of the target class compared to other classes. The counterfactual explanation consists of the distinction heatmap for the target class A and another distinction heatmap for the counterfactual class B, which shares common features with A." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 142, + 370, + 155 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 142, + 370, + 155 + ], + "spans": [ + { + "bbox": [ + 314, + 142, + 370, + 155 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 162, + 432, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 162, + 432, + 174 + ], + "spans": [ + { + "bbox": [ + 314, + 162, + 432, + 174 + ], + "type": "text", + "content": "3.1. General Framework" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": "The proposed DiffCAM approach follows the general framework of Class Activation Map (CAM) [60]. We consider deep convolutional neural networks. For simplification, we assume the deep model to be explained is composed of a deep feature extractor and a fully connected layer, which is a common architecture for modern DNNs. Let's define " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": " as a target example to be explained, and " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": " as the number of feature channels of the last convolutional layer. By passing forward " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": ", we get " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_k(\\mathbf{x})(k\\in [1,2,\\dots,d])" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": " as the " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": "-th activation map. The goal of CAM-based approaches is to generate a saliency map " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "M_{c}(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": " explaining the prediction towards class " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": " as input. Specifically, a feature importance vector " + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^c\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 180, + 555, + 349 + ], + "type": "text", + "content": " is used to aggregate all the activation maps as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 381, + 357, + 554, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 357, + 554, + 389 + ], + "spans": [ + { + "bbox": [ + 381, + 357, + 554, + 389 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {c} (\\mathbf {x}) = \\sum_ {k = 1} ^ {d} \\mathbf {w} _ {k} ^ {c} \\mathbf {A} _ {k} (\\mathbf {x}). \\tag {1}", + "image_path": "4cb6f1ce3bff81914be261aec31b9bd76e9e7c873ccfa083c91dfc07fc9cbffa.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "content": "In the original CAM method [60], " + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k^c" + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "content": " are directly taken from the weights of the fully connected layer. Specifically, for class " + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "content": ", the weight " + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k^c" + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "content": "-th component of the fully connected layer's weights " + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_c" + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "content": " for that class. Many following work [9, 12, 14, 17, 29, 41, 55] adopt this general framework and differ in their ways of calculating " + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k^c" + }, + { + "bbox": [ + 313, + 394, + 554, + 502 + ], + "type": "text", + "content": ". Here we summarize two main categories from existing approaches, which focus on the gradient and individual contribution of each feature channel respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "text", + "content": "GradCAM: " + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k^c" + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "text", + "content": " are computed based on the gradients of the class score " + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "inline_equation", + "content": "y^{c}(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "text", + "content": " with respect to the activation map " + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_k(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k^c" + }, + { + "bbox": [ + 313, + 502, + 554, + 550 + ], + "type": "text", + "content": " is the global average of the gradients across all spatial locations in the feature map as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 385, + 557, + 555, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 557, + 555, + 587 + ], + "spans": [ + { + "bbox": [ + 385, + 557, + 555, + 587 + ], + "type": "interline_equation", + "content": "\\mathbf {w} _ {k} ^ {c} = \\frac {1}{Z} \\sum_ {i, j} \\frac {\\partial y ^ {c}}{\\partial \\mathbf {A} _ {k} ^ {i , j} (\\mathbf {x})} \\tag {2}", + "image_path": "3a9c1ba8ab08964b9ecf90dfffc216576422c00aa187ab18f8db4e96606ca441.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "spans": [ + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_k^{i,j}(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "type": "text", + "content": " is the activation at spatial location " + }, + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "type": "text", + "content": " of the feature map and " + }, + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 313, + 597, + 555, + 621 + ], + "type": "text", + "content": " is a normalization term." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "spans": [ + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "text", + "content": "ScoreCAM: " + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k^c" + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "text", + "content": " are measured by the increase in the " + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "text", + "content": "-th class score when the feature map " + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_k(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "text", + "content": " is activated. For the " + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "text", + "content": "-th feature channel, it first creates the corresponding masked input " + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}_k = \\mathbf{A}_k(\\mathbf{x}) \\odot \\mathbf{x}" + }, + { + "bbox": [ + 313, + 622, + 554, + 681 + ], + "type": "text", + "content": ", and then calculate the feature importance vector as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 394, + 689, + 554, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 689, + 554, + 717 + ], + "spans": [ + { + "bbox": [ + 394, + 689, + 554, + 717 + ], + "type": "interline_equation", + "content": "\\mathbf {w} _ {k} ^ {c} = \\frac {y ^ {c} \\left(\\tilde {\\mathbf {x}} _ {k}\\right)}{\\sum_ {k} y ^ {c} \\left(\\tilde {\\mathbf {x}} _ {k}\\right)}. \\tag {3}", + "image_path": "b11feabcba1ebc801c89b19864c448331e4aad824cfc8014c18cc0bc17188bbd.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10329" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 67, + 539, + 274 + ], + "blocks": [ + { + "bbox": [ + 75, + 67, + 539, + 274 + ], + "lines": [ + { + "bbox": [ + 75, + 67, + 539, + 274 + ], + "spans": [ + { + "bbox": [ + 75, + 67, + 539, + 274 + ], + "type": "image", + "image_path": "8474e6930d814b64156745ac11bac91754282d858d943a5a16de9a29aac3f1cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 285, + 555, + 321 + ], + "lines": [ + { + "bbox": [ + 54, + 285, + 555, + 321 + ], + "spans": [ + { + "bbox": [ + 54, + 285, + 555, + 321 + ], + "type": "text", + "content": "Figure 2. Overview of the DiffCAM framework and applications. Given a target image and a set of reference examples, DiffCAM computes deep feature embeddings, identifies the direction that captures differences between the target and references, and generates a saliency map highlighting key distinguishing features. DiffCAM can provide flexible explanations according to the selection of reference examples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 333, + 201, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 333, + 201, + 346 + ], + "spans": [ + { + "bbox": [ + 55, + 333, + 201, + 346 + ], + "type": "text", + "content": "3.2. DiffCAM Implementation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": "Intuitively, DiffCAM regards the explanation problem as looking for the feature components that best distinguish the target example (to be explained) and a group of reference examples. Suppose the example we aim to explain is " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": ". According to the explanation type we are interested in, a set of " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " examples " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\mathbf{x}}^{(i)}\\}_{i=1}^{n}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " is determined as the reference group. Note that the class labels of " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\mathbf{x}}^{(i)}\\}_{i=1}^{n}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " can be flexible, i.e., they may have the same, different or no labels. We generate the deep embedding " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " by performing average pooling along the spatial dimension on the whole feature map " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\mathbf{A}(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": ", and get " + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\mathbf{z}}^{(i)}\\}_{i=1}^{n}" + }, + { + "bbox": [ + 55, + 351, + 296, + 483 + ], + "type": "text", + "content": " for the reference examples." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "text", + "content": "The feature importance vector " + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "text", + "content": " is defined as the optimal direction in the feature space that represents the most discriminative features relative to the reference data. Specifically, the projections of " + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\mathbf{z}}^{(i)}\\}_{i = 1}^{n}" + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "text", + "content": " are expected to have the largest distance with " + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 55, + 483, + 296, + 555 + ], + "type": "text", + "content": " while maintain as much commonality as possible." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "text", + "content": "To solve the optimal " + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "text", + "content": ", we apply fundamental mathematical tools in linear algebra and convex optimization. Formally, denoting the mean reference position by " + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\hat{\\mu} = \\frac{1}{n}\\sum_{i=1}^{n}\\hat{\\mathbf{z}}^{(i)}" + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "text", + "content": ", the distance between the target example and the reference group along " + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "text", + "content": " can be defined as " + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\|\\mathbf{w}^T z - \\mathbf{w}^T\\hat{\\mu}\\|^2" + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "text", + "content": ". The variance among the reference examples projected on " + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "inline_equation", + "content": "\\frac{1}{n}\\sum_{i=1}^{n}\\|\\mathbf{w}^T\\hat{\\mathbf{z}}^{(i)} - \\mathbf{w}^T\\hat{\\mu}\\|^2" + }, + { + "bbox": [ + 55, + 555, + 296, + 651 + ], + "type": "text", + "content": ". The measure can be written as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 655, + 295, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 655, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 104, + 655, + 295, + 712 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} J (\\mathbf {w}) = \\frac {\\left\\| \\mathbf {w} ^ {T} z - \\mathbf {w} ^ {T} \\hat {\\mu} \\right\\| ^ {2}}{\\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {w} ^ {T} \\hat {\\mathbf {z}} ^ {(i)} - \\mathbf {w} ^ {T} \\hat {\\mu} \\right\\| ^ {2}} (4) \\\\ = \\frac {\\mathbf {w} ^ {T} \\mathbf {S} _ {\\mu} \\mathbf {w}}{\\mathbf {w} ^ {T} \\mathbf {S} _ {\\mathbf {v}} \\mathbf {w}}, (5) \\\\ \\end{array}", + "image_path": "86dd73e8b96e90fd8793e2fdfb5587b666df44512c6afa70667b1ffc7204c559.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "spans": [ + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{\\mu} = (\\mathbf{z} - \\hat{\\mu})(\\mathbf{z} - \\hat{\\mu})^T" + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "text", + "content": " represents discrimination between the target example and the reference group, and " + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{\\mathbf{v}} = \\sum_{i=1}^{n} (\\hat{\\mathbf{z}}^{(i)} - \\hat{\\mu})(\\hat{\\mathbf{z}}^{(i)} - \\hat{\\mu})^T" + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "text", + "content": " represents internal variation among the reference examples. By differentiating and setting to zero, we find the optimal " + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "text", + "content": " that maximizes " + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "inline_equation", + "content": "J(\\mathbf{w})" + }, + { + "bbox": [ + 313, + 333, + 555, + 405 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 357, + 407, + 555, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 407, + 555, + 427 + ], + "spans": [ + { + "bbox": [ + 357, + 407, + 555, + 427 + ], + "type": "interline_equation", + "content": "\\mathbf {w} ^ {*} = \\underset {\\mathbf {w}} {\\operatorname {a r g m a x}} J (w) = \\mathbf {S _ {v}} ^ {- 1} (\\mathbf {z} - \\hat {\\mu}). \\qquad (6)", + "image_path": "e20d9cbc52d09898527dc3ab17d864c1fbc53d90bb4589543bf6173579d3c58e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "text", + "content": "Detailed derivation is put in Section A in Appendix. For supervised trained models, the inverse matrix " + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{\\mathbf{v}}^{-1}" + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "text", + "content": " can be pre-calculated over training examples to avoid high inference complexity. We further adopt the Tikhonov regularization to ensure stability in calculating the inverse matrix. A small regularization term " + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\lambda \\mathbf{I}" + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "text", + "content": " is added onto " + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{\\mathbf{v}}" + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "text", + "content": " when calculating the inverse. The solved " + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^*" + }, + { + "bbox": [ + 313, + 434, + 556, + 540 + ], + "type": "text", + "content": " is finally used to generate the saliency map by calculating the weighted aggregation of the feature channels as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 367, + 550, + 555, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 550, + 555, + 583 + ], + "spans": [ + { + "bbox": [ + 367, + 550, + 555, + 583 + ], + "type": "interline_equation", + "content": "\\mathbf {M} ^ {\\text {D i f f C A M}} (\\mathbf {x}) = \\sum_ {k = 1} ^ {d} \\mathbf {w} _ {k} ^ {*} \\mathbf {A} _ {k} (\\mathbf {x}). \\tag {7}", + "image_path": "988727a2c94d16a51a88075a3c244a7cd1547ec98c85944f59d80647469ba277.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "content": "A flexibility of DiffCAM lies in the selection of the reference group. In most cases, we use all the remaining classes as reference when answering the \"Why is\" question. For large-scale datasets with diverse classes (e.g., ImageNet), we empirically recommend to select a subset of similar classes (with k-Nearest-Neighbor search) as the reference group to obtain more discriminative features. To answer the \"Why not\" question or analyze internal variations, the corresponding target class will be specified as the reference group. An illustrative overview is presented in Figure 2." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10330" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 64, + 130, + 119 + ], + "blocks": [ + { + "bbox": [ + 82, + 64, + 130, + 119 + ], + "lines": [ + { + "bbox": [ + 82, + 64, + 130, + 119 + ], + "spans": [ + { + "bbox": [ + 82, + 64, + 130, + 119 + ], + "type": "image", + "image_path": "7c10b0da4c79ec90cc1f0bf90a7d7507a7cf400560201b1806e51f2eeea63e16.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 138, + 64, + 187, + 119 + ], + 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Experiments" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 55, + 299, + 296, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 299, + 296, + 371 + ], + "spans": [ + { + "bbox": [ + 55, + 299, + 296, + 371 + ], + "type": "text", + "content": "We evaluate DiffCAM through extensive qualitative and quantitative experiments in Section 4.1 and 4.2, respectively. Then we present results with SSL models in Section 4.3 and sanity check in Section 4.4. Finally, Section 4.5 presents a case study on abnormality localization in medical imaging to highlight DiffCAM's practical applications." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 55, + 380, + 185, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 380, + 185, + 393 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 185, + 393 + ], + "type": "text", + "content": "4.1. 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We use the MNIST [23] dataset due to its simplicity and clear patterns, which make it a good fit for the demonstration purpose." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 55, + 502, + 217, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 217, + 513 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 217, + 513 + ], + "type": "text", + "content": "4.1.1 Discriminant Visual Attention" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 296, + 713 + ], + "type": "text", + "content": "The second to fifth columns in Figure 3 demonstrate the effects of general explanation results which answers the \"Why is\" question. For DiffCAM, we use all examples from other classes as the reference group. Compared against the baseline methods, DiffCAM tends to highlight more comprehensive object patterns instead of only a small region of the most discriminative patterns. This observation backups our motivation that DiffCAM aims to capture the features which truly reflect the feature difference for real data distribution although some the direction may not be the fastest to reach decision boundaries. The results also align better with human perception of distinctive digit features. By assigning another similar digit as the reference group, DiffCAM is able to obtain discriminative features similar to counterfactual explanations. As shown in the last three columns of Figure 3, the highlighted regions accurately represent the" + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 313, + 279, + 555, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 279, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 279, + 555, + 316 + ], + "type": "text", + "content": "key differences, e.g., the bottom part makes the image of 9 not a digit 0. More qualitative results for discriminant visual attention are put in Section B in Appendix." + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 313, + 331, + 433, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 433, + 341 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 433, + 341 + ], + "type": "text", + "content": "4.1.2 Intra-class Variance" + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 313, + 349, + 554, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 349, + 554, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 349, + 554, + 396 + ], + "type": "text", + "content": "While intra-class variance has rarely been discussed in existing XAI research, it is valuable in practice for model debugging and data engineering. Our work fills this gap and offers potential in this important task." + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 313, + 397, + 555, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 397, + 555, + 577 + ], + "spans": [ + { + "bbox": [ + 313, + 397, + 555, + 577 + ], + "type": "text", + "content": "In Figure 4, the top row shows difficult examples of the digit 0 along with their incorrect predicted labels (mostly classified as 6), illustrating how subtle variations in shape and structure within the same class can lead to misclassification. The bottom row presents the corresponding saliency maps generated by DiffCAM, using the training set of digit 0 as the reference group, and highlights the patterns in each image that deviated the most from the majority. The results demonstrate that features like abnormal breaks in the loops and additional curves or dots were identified as influential differences that distinguish these hard cases from typical instances of digit 0. We can reasonably suspect these anomalies as the main factors contributing to incorrect predictions. 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    Arch.MetricExplanation Methods
    GradCAMScoreCAMLayerCAMXGradCAMDiffCAM
    ResNet-50IoU0.5280.5110.5350.4470.534
    AUPRC0.7270.7090.7380.6340.741
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    ", + "image_path": "b2d8fe7343f645c0289e0fadd1f29b51d5eb9092caac6879c3cfdda1dffa43d6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 203, + 153, + 406, + 164 + ], + "lines": [ + { + "bbox": [ + 203, + 153, + 406, + 164 + ], + "spans": [ + { + "bbox": [ + 203, + 153, + 406, + 164 + ], + "type": "text", + "content": "Table 1. Evaluation of object localization on ImageNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 59, + 175, + 100, + 224 + ], + "blocks": [ + { + "bbox": [ + 59, + 175, + 100, + 224 + ], + "lines": [ + { + "bbox": [ + 59, + 175, + 100, + 224 + ], + "spans": [ + { + "bbox": [ + 59, + 175, + 100, + 224 + ], + "type": "image", + "image_path": "fe7a537a661408c3c9e5347f03482b1dae3240dd9903beed992f4cb249ec9782.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 107, + 175, + 149, + 223 + ], + "blocks": [ + { + "bbox": [ + 107, + 175, + 149, + 223 + ], + "lines": [ + { + "bbox": [ + 107, + 175, + 149, + 223 + ], + "spans": [ + { + "bbox": [ + 107, + 175, + 149, + 223 + ], + "type": "image", + "image_path": "2082072b5df5a2f7abb6896021313a598602db7df2ecab46f6bb0b40843e9ca5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 155, + 175, + 196, + 222 + ], + "blocks": [ + { + "bbox": [ + 155, + 175, + 196, + 222 + ], + "lines": [ + { + "bbox": [ + 155, + 175, + 196, + 222 + ], + "spans": [ + { + "bbox": [ + 155, + 175, + 196, + 222 + ], + "type": "image", + "image_path": "c2dbf3e7913c39f031511c8189f5f269b9289ec776b65f8016c038e078da028d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 202, + 175, + 244, + 222 + ], + "blocks": [ + { + "bbox": [ + 202, + 175, + 244, + 222 + ], + "lines": [ + { + "bbox": [ + 202, + 175, + 244, + 222 + ], + "spans": [ + { + "bbox": [ + 202, + 175, + 244, + 222 + ], + "type": "image", + "image_path": "d11233a949c2fa225f7262580460b8040d05fccab411195591cbb8534f664776.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 251, + 175, + 292, + 222 + ], + "blocks": [ + { + "bbox": [ + 251, + 175, + 292, + 222 + ], + "lines": [ + { + "bbox": [ + 251, + 175, + 292, + 222 + ], + "spans": [ + { + "bbox": [ + 251, + 175, + 292, + 222 + ], + "type": "image", + "image_path": "32beef8c6d12eab7f37c0f89e68529d8c2af234ff80935c744bc5ccbf2115159.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 59, + 228, + 100, + 274 + ], + "blocks": [ + { + "bbox": [ + 59, + 228, + 100, + 274 + ], + "lines": [ + { + "bbox": [ + 59, + 228, + 100, + 274 + ], + "spans": [ + { + "bbox": [ + 59, + 228, + 100, + 274 + ], + "type": "image", + "image_path": "4d3311a93729c1a818db85ee101adbc706b4b64863267829c4431e7c82da2111.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 283, + 295, + 327 + ], + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 327 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 327 + ], + "type": "text", + "content": "Figure 5. Illustration of the faithfulness and object localization test on ImageNet validation images. The left most column are original images with red rectangles as the object locations. The right most are masked images by ROAD according to the DiffCAM results." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 107, + 228, + 148, + 274 + ], + "blocks": [ + { + "bbox": [ + 107, + 228, + 148, + 274 + ], + "lines": [ + { + "bbox": [ + 107, + 228, + 148, + 274 + ], + "spans": [ + { + "bbox": [ + 107, + 228, + 148, + 274 + ], + "type": "image", + "image_path": "644316dc5d23b9a0767e80a32aa099b71646dffe54b2cc0236187d52e89257d6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 155, + 228, + 196, + 274 + ], + "blocks": [ + { + "bbox": [ + 155, + 228, + 196, + 274 + ], + "lines": [ + { + "bbox": [ + 155, + 228, + 196, + 274 + ], + "spans": [ + { + "bbox": [ + 155, + 228, + 196, + 274 + ], + "type": "image", + "image_path": "8a80a85e6c755ed435c16658e9a87b7ae686117a68ee323a9b730791438232c8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 203, + 228, + 244, + 274 + ], + "blocks": [ + { + "bbox": [ + 203, + 228, + 244, + 274 + ], + "lines": [ + { + "bbox": [ + 203, + 228, + 244, + 274 + ], + "spans": [ + { + "bbox": [ + 203, + 228, + 244, + 274 + ], + "type": "image", + "image_path": "4f399bb65418f3353c8c66b574cef0c09bfa78fd69aa1288060c6a0022d4f9ed.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 251, + 228, + 292, + 274 + ], + "blocks": [ + { + "bbox": [ + 251, + 228, + 292, + 274 + ], + "lines": [ + { + "bbox": [ + 251, + 228, + 292, + 274 + ], + "spans": [ + { + "bbox": [ + 251, + 228, + 292, + 274 + ], + "type": "image", + "image_path": "e2f3ba3d761a9bfba9f739f06ad7f1ff6f12e82c1b27dc386c14dcb0df0029a6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 285, + 530, + 297 + ], + "lines": [ + { + "bbox": [ + 337, + 285, + 530, + 297 + ], + "spans": [ + { + "bbox": [ + 337, + 285, + 530, + 297 + ], + "type": "text", + "content": "Figure 6. ROAD evaluation on the ImageNet dataset." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 349, + 191, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 349, + 191, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 191, + 361 + ], + "type": "text", + "content": "4.2. Quantitative Evaluation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 367, + 296, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 367, + 296, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 367, + 296, + 510 + ], + "type": "text", + "content": "In this section, we report our quantitative experimental results. Following common practice, we measure faithfulness and localization performance on ImageNet to assess the quality of saliency maps. To improve computational efficiency, we pre-calculate the mean feature for each class and build a search index with Faiss-gpu [18]. During inference, we retrieve the top 100 most similar mean features as the reference group for each target image. Figure 5 presents showcases for the two experiments. We also quantitatively evaluate DiffCAM on counterfactual explanation tasks using the ResNet-50 model pre-trained on the fine-grained dataset CUB-200-2011 [54]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 526, + 141, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 526, + 141, + 538 + ], + "spans": [ + { + "bbox": [ + 55, + 526, + 141, + 538 + ], + "type": "text", + "content": "4.2.1 Faithfulness" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "content": "In XAI research, faithfulness refers to the extent to which an explanation method accurately reflects the true reasoning process of a machine learning model. Specifically, denoting I as the input image, we assess the faithfulness of a saliency map M by masking a set of pixels S " + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\subseteq" + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "content": " I to the input and observing the change in the model's prediction as " + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\Delta f(S) = f(I) - f(I\\backslash S)" + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "content": ", where S is determined by selecting the positions with top values in M. Based on this principal, we adopt Remove and Debias (ROAD) [36], which replaces the removed pixels with the mean pixel values from their neighbors. Considering the settings with " + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "inline_equation", + "content": "[25\\%, 50\\%, 75\\%]" + }, + { + "bbox": [ + 55, + 545, + 296, + 713 + ], + "type": "text", + "content": " top important pixels replaced, we plot ROAD curves to show the average prediction probability decrease for each case. Experiments are conducted on 1000 random examples" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 317, + 179, + 425, + 265 + ], + "blocks": [ + { + "bbox": [ + 317, + 179, + 425, + 265 + ], + "lines": [ + { + "bbox": [ + 317, + 179, + 425, + 265 + ], + "spans": [ + { + "bbox": [ + 317, + 179, + 425, + 265 + ], + "type": "image", + "image_path": "204fab0f23763a11ca322e3b29cde28512b59c0850185e45ba612de6fc522c8f.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 352, + 266, + 399, + 276 + ], + "lines": [ + { + "bbox": [ + 352, + 266, + 399, + 276 + ], + "spans": [ + { + "bbox": [ + 352, + 266, + 399, + 276 + ], + "type": "text", + "content": "(a) ResNet-50" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 434, + 180, + 542, + 265 + ], + "blocks": [ + { + "bbox": [ + 434, + 180, + 542, + 265 + ], + "lines": [ + { + "bbox": [ + 434, + 180, + 542, + 265 + ], + "spans": [ + { + "bbox": [ + 434, + 180, + 542, + 265 + ], + "type": "image", + "image_path": "06e83773c8c291a051135a612c9cd836d976344fe655684d3d185aeb94fa4cee.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 466, + 266, + 520, + 276 + ], + "lines": [ + { + "bbox": [ + 466, + 266, + 520, + 276 + ], + "spans": [ + { + "bbox": [ + 466, + 266, + 520, + 276 + ], + "type": "text", + "content": "(b) Inception-v3" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 312, + 555, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 555, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 555, + 346 + ], + "type": "text", + "content": "from the validation set of ImageNet. As shown in Figure 6, DiffCAM shows competitive level of faithfulness among various state-of-the-art baseline methods." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 366, + 432, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 366, + 432, + 378 + ], + "spans": [ + { + "bbox": [ + 313, + 366, + 432, + 378 + ], + "type": "text", + "content": "4.2.2 Object Localization" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 386, + 555, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 386, + 555, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 386, + 555, + 482 + ], + "type": "text", + "content": "Besides faithfulness, we are also interested in whether an XAI method provides interpretable information for humans. This is usually assessed through the task of object localization. Following the ScoreCAM paper, we consider images with a single bounding box for the target class and restrict the object to occupy less than half of the entire image. We randomly select 500 images from the ImageNet validation set that satisfy these conditions." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 483, + 556, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 556, + 639 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 556, + 639 + ], + "type": "text", + "content": "Regarding the evaluation metric, we do not adopt the previous energy-based pointing method [55], as it tends to favor explanation results that overly concentrate pixel scores onto a small number of pixels. This approach is susceptible to artificial manipulation of sharpening the score distribution. Therefore, we employ conventional metrics Intersection over Union (IoU) and Area Under the Precision-Recall Curve (AUPRC) to assess the accuracy with which the generated saliency maps align with the object bounding boxes. Results in Table 1 show that DiffCAM achieves the best overall localization accuracy along with LayerCAM. More visualization results for localization evaluation are put in Section C in Appendix." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 657, + 467, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 657, + 467, + 669 + ], + "spans": [ + { + "bbox": [ + 313, + 657, + 467, + 669 + ], + "type": "text", + "content": "4.2.3 Counterfactual Explanation" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "Most Existing methods of counterfactual explanation resort to create an artificial example that yields a different prediction regarding the counterfactual class. These modifications" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10332" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 76, + 70, + 535, + 133 + ], + "blocks": [ + { + "bbox": [ + 76, + 70, + 535, + 133 + ], + "lines": [ + { + "bbox": [ + 76, + 70, + 535, + 133 + ], + "spans": [ + { + "bbox": [ + 76, + 70, + 535, + 133 + ], + "type": "table", + "html": "
    MetricRandom CounterfactualSimilar Counterfactual
    GoyalCounteRGANGALOREDiffCAMGoyalCounteRGANGALOREDiffCAM
    R0.030.060.090.150.120.170.160.17
    P0.770.740.810.830.570.560.600.61
    PIoU0.180.200.160.180.150.140.150.20
    ", + "image_path": "17199b221d679ce957ffd2e27521eb962c1fe57fcd5e8c4367c7b03cbea1dc4a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 132, + 141, + 477, + 153 + ], + "lines": [ + { + "bbox": [ + 132, + 141, + 477, + 153 + ], + "spans": [ + { + "bbox": [ + 132, + 141, + 477, + 153 + ], + "type": "text", + "content": "Table 2. Comparison of counterfactual explanation methods for Beginner and Advanced Users." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 86, + 163, + 526, + 338 + ], + "blocks": [ + { + "bbox": [ + 86, + 163, + 526, + 338 + ], + "lines": [ + { + "bbox": [ + 86, + 163, + 526, + 338 + ], + "spans": [ + { + "bbox": [ + 86, + 163, + 526, + 338 + ], + "type": "image", + "image_path": "1c99bf3a09e92a8d19ca22450cb08b5a92c9a00b0dba65c0abe0dbac84f24e94.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 71, + 343, + 537, + 355 + ], + "lines": [ + { + "bbox": [ + 71, + 343, + 537, + 355 + ], + "spans": [ + { + "bbox": [ + 71, + 343, + 537, + 355 + ], + "type": "text", + "content": "Figure 7. DiffCAM results answering \"why is\" and \"why not\" with SSL models Moco-v3 (column 2,3) and DINO (column 4,5)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 376, + 295, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 376, + 295, + 460 + ], + "spans": [ + { + "bbox": [ + 54, + 376, + 295, + 460 + ], + "type": "text", + "content": "can be achieved through adversarial attacks and image synthesis. However, the perturbed or synthesized features often do not reside within the natural image space, limiting their applicability in expert domains. DiffCAM belongs to the direction of saliency map based counterfactual explanation that highlights which areas of the input would need modification to change the prediction." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "text", + "content": "For performance evaluation, we mostly adopt the state-of-the-art saliency map based counterfactual method GALORE [56], using CUB-200-2011 with part annotations as the benchmark. Then the counterfactual ground truth is represented by " + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^c = \\{(p_i,a_i,b_i)\\}_{i = 1}^N" + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "text", + "content": ", where parts are denoted as " + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 54, + 461, + 295, + 628 + ], + "type": "text", + "content": " refer to the target and counterfactual classes, respectively. GALORE [56] uses Precision (P), Recall (R) and Part Intersection over Union (PIoU) as evaluation metrics. We additionally employ F1-Score to provide a more representative measure of model performance across different thresholds. We also follow GALORE [56] to consider both a random class and similar class as the counterfactual reference. More details for the evaluation metrics are introduced in Section D.1 in Appendix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 630, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 630, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 54, + 630, + 295, + 712 + ], + "type": "text", + "content": "As shown in the Table 2, DiffCAM outperforms other state-of-the-art counterfactual explanation methods across nearly all metrics. While CounteRGAN achieves a slightly higher average P IoU on randomly selected counterfactual classes, DiffCAM excels overall. The F1 results in Figure 9a and 9b (see Appendix) show that DiffCAM demonstrates better robustness than GALORE in the selection of different" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 376, + 555, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 376, + 555, + 461 + ], + "spans": [ + { + "bbox": [ + 313, + 376, + 555, + 461 + ], + "type": "text", + "content": "counterfactual classes. Figure 9c and 9d show that for similar counterfactual classes, DiffCAM achieves a significantly higher F1 score compared to GALORE. For randomly selected counterfactual classes, DiffCAM reaches a slightly higher F1 score at a faster rate and sustains this advantage across the range of thresholds shown. We provide additional experimental results in Section D.2 in Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 471, + 512, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 471, + 512, + 484 + ], + "spans": [ + { + "bbox": [ + 313, + 471, + 512, + 484 + ], + "type": "text", + "content": "4.3. Applicability on SSL and ViT Models" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 491, + 555, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 491, + 555, + 598 + ], + "spans": [ + { + "bbox": [ + 313, + 491, + 555, + 598 + ], + "type": "text", + "content": "DiffCAM can be directly applied to SSL models as it doesn't rely on class-specific predictions. By reshaping patch tokens and incorporating the class token, DiffCAM can also be adapted to ViT models. To verify the results, we apply DiffCAM on MoCo-v3 with the ResNet-50 backbone and DINO with the ViT backbone. Results in Fig. 7 show SSL models can extract reasonable features, while DINO offers richer and more fine-grained semantics. DiffCAM faithfully reflects these capacity differences." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 609, + 400, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 609, + 400, + 623 + ], + "spans": [ + { + "bbox": [ + 313, + 609, + 400, + 623 + ], + "type": "text", + "content": "4.4. Sanity Check" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": "Sanity check is another method to examine whether an explanation method is really tied to the model [3] to further confirm its faithfulness. Specifically, we check whether the explanation results change when randomizing weights from a trained model. DiffCAM passes sanity check with common experimental settings. Detailed results are demonstrated in Section E in Appendix." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10333" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 64, + 534, + 117 + ], + "blocks": [ + { + "bbox": [ + 77, + 64, + 534, + 117 + ], + "lines": [ + { + "bbox": [ + 77, + 64, + 534, + 117 + ], + "spans": [ + { + "bbox": [ + 77, + 64, + 534, + 117 + ], + "type": "table", + "html": "
    ModelDatasetSaliency Methods (AUPRC)
    DiffCAMGradCAMScoreCAMLayerCAMXGradCAMIGGBP
    InceptionV3RSNA0.4920.4670.3280.3660.4660.3170.174
    SIIM0.0930.0760.0720.0710.0760.0630.072
    ", + "image_path": "974c31c9cbe817367f59aa7eb458498e70dc084bd0ffd93fba984f1c9d23ec46.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 154, + 124, + 455, + 135 + ], + "lines": [ + { + "bbox": [ + 154, + 124, + 455, + 135 + ], + "spans": [ + { + "bbox": [ + 154, + 124, + 455, + 135 + ], + "type": "text", + "content": "Table 3. Evaluation of Saliency Methods on InceptionNetV3 using AUPRC Metric" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 59, + 155, + 111, + 212 + ], + "blocks": [ + { + "bbox": [ + 59, + 155, + 111, + 212 + ], + "lines": [ + { + "bbox": [ + 59, + 155, + 111, + 212 + ], + "spans": [ + { + "bbox": [ + 59, + 155, + 111, + 212 + ], + "type": "image", + "image_path": "8d2cb26d7c3bfac33f72ade55a384629ea2ac3e158523336d74a07c6dbdb83c6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 120, + 156, + 171, + 212 + ], + "blocks": [ + { + "bbox": [ + 120, + 156, + 171, + 212 + ], + "lines": [ + { + "bbox": [ + 120, + 156, + 171, + 212 + ], + "spans": [ + { + "bbox": [ + 120, + 156, + 171, + 212 + ], + "type": "image", + "image_path": "f1551dca88697ab4036b963c72b0cad7a01a8d42b94b9557ca9195a55a192f90.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 180, + 156, + 231, + 212 + ], + "blocks": [ + { + "bbox": [ + 180, + 156, + 231, + 212 + ], + "lines": [ + { + "bbox": [ + 180, + 156, + 231, + 212 + ], + "spans": [ + { + "bbox": [ + 180, + 156, + 231, + 212 + ], + "type": "image", + "image_path": "c171f335861b2a1fb462b3a918d4c6d2941fd7762f192897718460d4f1f5bdcd.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 241, + 156, + 293, + 212 + ], + "blocks": [ + { + "bbox": [ + 241, + 156, + 293, + 212 + ], + "lines": [ + { + "bbox": [ + 241, + 156, + 293, + 212 + ], + "spans": [ + { + "bbox": [ + 241, + 156, + 293, + 212 + ], + "type": "image", + "image_path": "272c12c77f3de0192f4e59d8241e01495f1f49d04229f73f9c437380a4c95fee.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 58, + 214, + 111, + 270 + ], + "blocks": [ + { + "bbox": [ + 58, + 214, + 111, + 270 + ], + "lines": [ + { + "bbox": [ + 58, + 214, + 111, + 270 + ], + "spans": [ + { + "bbox": [ + 58, + 214, + 111, + 270 + ], + "type": "image", + "image_path": "d365084ffc195e4448e142cfe11fad3e6698e892e591ff514dacc21e70bd211c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 279, + 295, + 312 + ], + "lines": [ + { + "bbox": [ + 55, + 279, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 279, + 295, + 312 + ], + "type": "text", + "content": "Figure 8. Abnormality localization evaluation on the RSNA Pneumonia Detection Challenge dataset [6]. From left to right: original images, DiffCAM, GradCAM, and ScoreCAM results." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 119, + 214, + 171, + 270 + ], + "blocks": [ + { + "bbox": [ + 119, + 214, + 171, + 270 + ], + "lines": [ + { + "bbox": [ + 119, + 214, + 171, + 270 + ], + "spans": [ + { + "bbox": [ + 119, + 214, + 171, + 270 + ], + "type": "image", + "image_path": "0d995729c9d99523f979e10d50ad06bc75ac6b75113f0f7765b35d69d786b2d3.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 180, + 214, + 231, + 270 + ], + "blocks": [ + { + "bbox": [ + 180, + 214, + 231, + 270 + ], + "lines": [ + { + "bbox": [ + 180, + 214, + 231, + 270 + ], + "spans": [ + { + "bbox": [ + 180, + 214, + 231, + 270 + ], + "type": "image", + "image_path": "fc42efc58ff91ed67ffab6c8c4b9fbcf311ea3e955cebb9949fdd8bae6762374.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 241, + 215, + 293, + 270 + ], + "blocks": [ + { + "bbox": [ + 241, + 215, + 293, + 270 + ], + "lines": [ + { + "bbox": [ + 241, + 215, + 293, + 270 + ], + "spans": [ + { + "bbox": [ + 241, + 215, + 293, + 270 + ], + "type": "image", + "image_path": "e31a4567fb7b1232bebd17a85e269781133cbe6c575daa500a0da7bfa4a32858.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 334, + 295, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 334, + 295, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 334, + 295, + 360 + ], + "type": "text", + "content": "4.5. Case Study: Abnormality Localization for Medical Imaging" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 365, + 295, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 295, + 520 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 295, + 520 + ], + "type": "text", + "content": "In this case study, we demonstrate the potential of DiffCAM in medical imaging applications. Specifically, we consider abnormality localization in chest X-ray images [7], using the RSNA Pneumonia Detection Challenge dataset [6] and SIIM-ACR Pneumothorax Segmentation dataset [58] as benchmarks. The former contains bounding boxes indicating potential areas of pneumonia for positive cases, and the latter provides associated masks for pneumothorax images. For each dataset, we train an Inception-v3 model [11, 47] for image-level binary classification and evaluate XAI methods regarding abnormality localization. More details of the task background, dataset information and model training strategies are put in Section F.1 in Appendix." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 295, + 664 + ], + "type": "text", + "content": "We qualitatively compare the saliency maps produced by seven state-of-the-art methods, covering both gradient-based and activation-based baselines including GradCAM, ScoreCAM, LayerCAM), Axiom-based GradCAM (XGradCAM), Integrated Gradients (IG) [46], and Guided Backpropagation (GBP). For localization performance, we adopt the area under the precision-recall curve (AUPRC) as it better handles imbalanced data, common in medical images with small ground truth masks. Unlike ROC-AUC, AUPRC emphasizes the accuracy of positive pixels, making it especially suitable for identifying subtle abnormalities in medical imaging." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "Results are presented in Table 3. On the RSNA dataset with bounding boxes as ground truth, DiffCAM achieves the highest AUPRC (0.492). GradCAM is shown very robust on medical applications, outperforming most ad" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 157, + 553, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 157, + 553, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 157, + 553, + 216 + ], + "type": "text", + "content": "vanced methods which work well on general computer vision, whereas DiffCAM improves it with a remarkable margin. The SIIM task is more challenging and all methods deliver relatively low AUPRC scores. DiffCAM is still significantly superior to all the baseline methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 217, + 555, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 555, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 555, + 338 + ], + "type": "text", + "content": "Two typical showcases from the RSNA datasets are presented in Figure 8, where the ground truth pneumonia areas are annotated as yellow boxes. The results demonstrate that DiffCAM captures more complete abnormality regions than baseline methods. This observation again coincides with our motivation that gradient-based approaches can't accurately capture the real feature difference between example groups (here we are interested in differences between healthy people and patients). We provide more random visualization examples in Section F.2 in Appendix." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 350, + 389, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 389, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 389, + 361 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 370, + 554, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 370, + 554, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 370, + 554, + 441 + ], + "type": "text", + "content": "DiffCAM assumes that a linear classifier is attached to the final deep feature layer, from which the optimal feature importance vector is derived. While many modern DNN architectures (e.g., ResNet, Inception, MobileNet, Vision Transformer) adhere to this design, extending DiffCAM to handle more general scenarios remains a topic for future work." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 455, + 388, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 455, + 388, + 468 + ], + "spans": [ + { + "bbox": [ + 313, + 455, + 388, + 468 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 475, + 555, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 555, + 620 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 555, + 620 + ], + "type": "text", + "content": "This paper presents DiffCAM, a novel approach for generating saliency maps by emphasizing the differences between target examples and reference data distributions. It addresses the limitations of traditional CAM-based approaches by providing more comprehensive and intuitive explanations that better align with human understanding. Extensive experiments across various datasets demonstrate DiffCAM's robustness and superior performance. As interpretability becomes increasingly critical in deep learning applications, especially high-stake tasks such as medical imaging, our work offers both an effective XAI tool and a valuable new perspective for further research." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 632, + 424, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 632, + 424, + 646 + ], + "spans": [ + { + "bbox": [ + 313, + 632, + 424, + 646 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 554, + 712 + ], + "type": "text", + "content": "We thank Shun Jin, Damian Chng and Gunika Goyal for their contributions to our initial idea exploration. This work was supported in part by US NSF grant DBI-2238093. 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(a) All models use the EDSR-baseline [31] encoder, except HiNOTE [35] which has its own. (b) Compared to SRNO [54], DiffFNO is strengthened by the fusion of spectral and spatial features and efficient refinement by a diffusion process." + ], + "image_footnote": [], + "bbox": [ + 517, + 380, + 859, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 566, + 326, + 583 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly improving the reconstruction of high-frequency image details that are crucial for superresolution tasks. Gated Fusion Mechanism (GFM) adaptively complements WFNO's spectral features with spatial features from an Attention-based Neural Operator (AttnNO). This enhances the network's capability to capture both global structures and local details. Adaptive Time-Step (ATS) ODE solver, a deterministic sampling strategy, accelerates inference without sacrificing output quality by dynamically adjusting integration step sizes ATS. Extensive experiments demonstrate that DiffFNO achieves state-of-the-art (SOTA) results, outperforming existing methods across various scaling factors by a margin of 2-4 dB in", + "bbox": [ + 88, + 601, + 485, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "PSNR, including those beyond the training distribution. It also achieves this at lower inference time (Fig. 1 (a)). Our approach sets a new standard in super-resolution, delivering both superior accuracy and computational efficiency.", + "bbox": [ + 511, + 569, + 908, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 661, + 645, + 678 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image super-resolution (SR) reconstructs high-resolution (HR) images from low-resolution (LR) inputs, recovering lost fine details to enhance visual quality. SR is crucial for applications like medical imaging [12], satellite imagery [23, 52], and video games [38]. However, multiple HR images can correspond to the same LR input due to information loss during downsampling. This ambiguity requires algorithms capable of inferring plausible and perceptually accurate high-frequency content from limited data.", + "bbox": [ + 509, + 686, + 906, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning, particularly Convolutional Neural Networks (CNNs) [58], has significantly advanced SR. Dong et al. introduced SRCNN [9], demonstrating the effectiveness of end-to-end learning for SR. Subsequent models achieved remarkable performance using deeper architectures and at", + "bbox": [ + 511, + 825, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 114, + 875, + 243, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work Done during the visit at Peking University.", + "bbox": [ + 114, + 887, + 382, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "150", + "bbox": [ + 486, + 944, + 511, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tention mechanisms [6, 30, 31, 34, 57].", + "bbox": [ + 89, + 90, + 351, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models have emerged as powerful generative frameworks modeling complex data distributions via iterative denoising processes [11, 14, 45]. Their ability to generate high-fidelity images is well-suited for inferring missing fine details. In SR, diffusion models progressively refine an LR image by modeling the conditional distribution of HR images given the LR input [15, 25, 41, 51]. This iterative process reconstructs intricate textures and high-frequency components, producing realistic outputs.", + "bbox": [ + 89, + 108, + 483, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, diffusion models are computationally intensive due to the iterative reverse diffusion process [46]. To address this, recent research explores efficient sampling strategies to accelerate reverse diffusion. One approach is approximating the diffusion process through deterministic Ordinary Differential Equation (ODE), which can be solved in fewer steps [33]. This accelerates inference and provides consistent, reproducible results.", + "bbox": [ + 89, + 244, + 483, + 366 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Arbitrary-scale SR models [7, 17, 24], which can upsample images at user-defined scales beyond those seen in training, have gained attention in recent years. Methods involving attention mechanisms [5] and representing images as continuous functions [10] have been explored. Operator-learning methods such as Super-Resolution Neural Operators (SRNO) [54] and HiNOTE [35] have further advanced this field. However, the inherent differences between physics simulations and real-world images introduce challenges from computational demands to the difficulty in restoring high-frequency details.", + "bbox": [ + 89, + 368, + 483, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these limitations, our contributions are:", + "text_level": 1, + "bbox": [ + 89, + 536, + 447, + 550 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(1) We propose Weighted Fourier Neural Operator (WFNO) strengthened by iterative refinement from a diffusion framework for high-frequency reconstruction, detailed in Fig. 2. Through Mode Rebalancing (MR), WFNO learns to emphasize the most critical frequency components. This greatly enhances high-frequency image detail reconstruction, overcoming the limitations of standard FNOs and MLPs, which underrepresent such details due to mode truncation and spectral bias, respectively. (2) We develop Gated Fusion Mechanism (GFM) to dynamically adjust the influence of Fourier space features from WFNO and complementary spatial domain features from an Attention-based Neural Operator (AttnNO). AttnNO is lightweight, sharing an encoder with and running in parallel to WFNO. (3) Additionally, we present Adaptive Time-Step (ATS) ODE solver, which flexibly adjusts integration step sizes based on data characteristics by assessing the complexity of image regions, thereby reducing computational overhead without compromising quality. (4) DiffFNO achieves state-of-the-art results on multiple SR benchmarks, outperforming existing methods by 2-4 dB in PSNR in reconstruction quality. It also offers competitive inference time as Fig. 1 (a) shows. DiffFNO remains robust across various upscaling factors—even those", + "bbox": [ + 89, + 551, + 483, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "unseen during training.", + "bbox": [ + 513, + 90, + 666, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 119, + 653, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Operators and Fourier Methods. Neural Operators (NO) [22] have emerged as a powerful framework for learning mappings between infinite-dimensional function spaces, providing resolution-invariant models that generalize across different input resolutions. Unlike traditional neural networks that map finite-dimensional vectors to other vectors, neural operators learn mappings from functions to functions [27], making them well-suited for tasks involving continuous data or data at varying resolutions.", + "bbox": [ + 511, + 143, + 903, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-Layer Perceptrons (MLPs) often exhibit a spectral bias, favoring low-frequency functions [39]. This limits their ability to capture fine textures and sharp edges. To overcome these limitations, techniques like positional encodings and Fourier feature mappings capture high-frequency details by embedding input coordinates into a higher-dimensional sinusoidal space, allowing the network to represent complex patterns [44, 47].", + "bbox": [ + 511, + 281, + 903, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fourier Neural Operator (FNO) [26] is a variant of NO that uses spectral convolution to efficiently capture global data patterns, modeling long-range dependencies with lower computational complexity than traditional CNNs. In physics and climate settings [19, 29, 55], FNOs can handle arbitrary input resolutions without retraining. Although successful, FNOs may still lose high-frequency information due to mode truncation (discarding higher-frequency Fourier modes). This loss impairs tasks such as SR that rely on detailed reconstruction [13, 48, 49].", + "bbox": [ + 511, + 402, + 905, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The Mode Rebalancing mechanism in WFNO overcomes these limitations. Instead of being truncated, all Fourier modes are preserved, with additional learnable weights to modulate their impact on reconstruction. Fine-grained feature representation is further enhanced by AttnNO, which captures local details by processing data directly in the spatial domain", + "bbox": [ + 511, + 553, + 905, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion-Based SR and Efficient Sampling. Diffusion models have gained prominence as powerful generative models capable of producing high-quality images through iterative denoising techniques [14, 42]. In the context of SR, diffusion models have been employed to model the conditional distribution of HR images given LR inputs, achieving higher resolutions after progressive enhancement [40, 41].", + "bbox": [ + 511, + 659, + 905, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite their effectiveness, diffusion models are computationally intensive due to the large number of time steps required in the reverse diffusion process. Such computational demands pose significant challenges for practical applications [20], especially in real-time or resource-constrained settings. Current solutions include: (i) Deterministic Sampling via ODE Solvers: By reformulating the stochastic reverse diffusion as a deterministic ODE, advanced ODE solvers can be employed to reduce the number of sam", + "bbox": [ + 511, + 765, + 905, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "151", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b686c698376773941977f8fe89298fcea1a039a8a18df6cd817336dfacdcdf59.jpg", + "image_caption": [ + "Figure 2. The proposed Diffusion Fourier Neural Opeartor (DiffFNO) architecture for arbitrary-scale super-resolution begins by lifting a low-resolution input image $\\mathbf{x}_{\\mathrm{LR}}(\\mathbf{r})$ into a feature space using a convolutional encoder. Features extracted by the Weighted Fourier Neural Operator (WFNO) and an Attention-based Neural Operator (AttnNO) are combined using a Gated Fusion Mechanism (GFM). The fused features are then projected into RGB space, where Adaptive Time-Step (ATS) ODE solver efficiently completes the reverse diffusion process with both accuracy and speed. This pipeline generates $\\mathbf{x}_{\\mathrm{HR}}(\\mathbf{r})$ , a high-resolution version of the input image." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 897, + 385 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "pling steps [21]. Methods like Denoising Diffusion Implicit Models (DDIM) [45] and DPM-Solver [2, 33] have demonstrated the ability to generate high-quality images with significantly fewer steps. (ii) Operator Learning for Fast Sampling: Neural operators accelerates sampling by learning the solution operator of the reverse diffusion process [8, 59]. (iii) Progressive Distillation: Training a distilled model to approximate the behavior of the full diffusion model allows faster sampling with fewer steps [37, 43]. Although effective, this method may require extensive retraining and potentially compromise image quality for increased speed.", + "bbox": [ + 88, + 479, + 482, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Applying these acceleration methods to diffusion-based SR enables faster inference while maintaining high image quality. With efficient sampling methods, diffusion models become more practical for SR tasks, balancing performance and computational efficiency [32].", + "bbox": [ + 88, + 647, + 482, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DiffFNO adopts (i) for its simplicity and the robustness of established numerical methods. We also strength it with the ATS strategy, which adjusts integration step sizes adaptively to balance speed and quality.", + "bbox": [ + 88, + 724, + 482, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Proposed DiffFNO", + "text_level": 1, + "bbox": [ + 89, + 803, + 310, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Network Architecture and Novel Components", + "text_level": 1, + "bbox": [ + 89, + 830, + 478, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of the proposed DiffFNO is shown in Fig. 1 (b). It has three parts: (i) A CNN encoder extracts features from LR images. Unlike the simple linear transfor", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mations in standard FNO setups for physics simulations, our encoder is tailored for SR, extracting complex patterns and textures needed for high-quality reconstructions. We use the EDSR-baseline [31] and RDN models [58] in our experiments. (ii) WFNO and GFM: WFNO captures both global and local details alongside the AttnNO. GFM combines these into a unified HR feature map, which is then projected into RGB. (iii) ATS ODE solver accelerates inference speed by taking fewer, larger, and dynamically adjusted steps toward the reconstructed HR image. Fig. 2 illustrates these components in detail.", + "bbox": [ + 511, + 479, + 906, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The network minimizes the difference between the predicted image and the true image. The loss function is:", + "bbox": [ + 511, + 646, + 906, + 676 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\theta) = \\mathbb {E} _ {t, \\mathbf {x} _ {0}} \\left[ \\| s _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\nabla_ {\\mathbf {x} _ {t}} \\log p _ {t} \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) \\| _ {2} ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 684, + 906, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_t$ (i.e. $\\mathbf{x}_{\\mathrm{LR}}$ ) is obtained by adding noise to $\\mathbf{x}_0$ (i.e. $\\mathbf{x}_{\\mathrm{HR}}$ ). $s_{\\theta}(\\mathbf{x}_t, t)$ is the neural network approximating the true score function. $\\nabla \\mathbf{x}_t \\log p_t(\\mathbf{x}_t | \\mathbf{x}_0)$ is the true score function.", + "bbox": [ + 511, + 717, + 905, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Weighted Fourier Neural Operator", + "text_level": 1, + "bbox": [ + 511, + 771, + 820, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Fourier Neural Operator (FNO) [26] is an efficient NO variant designed to learn mappings between function spaces. It operates directly on inputs of arbitrary resolutions, performing upscaling by mapping low-resolution inputs to high-resolution outputs. It first transforms the input data into the frequency domain, applies the learned filters, and then transforms the data back to the spatial domain.", + "bbox": [ + 511, + 794, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "152", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spectral convolution and mode truncation greatly enhance computational efficiency.", + "bbox": [ + 89, + 90, + 482, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathbf{x}_{\\mathrm{LR}}(\\mathbf{r})$ denote the low-resolution input function (e.g., an image), where $\\mathbf{r} \\in \\mathbb{R}^2$ represents spatial coordinates. The goal is to learn an operator $\\mathcal{G}$ such that:", + "bbox": [ + 89, + 121, + 482, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {\\mathrm {H R}} (\\mathbf {r}) = \\mathcal {G} \\left[ \\mathbf {x} _ {\\mathrm {L R}} (\\mathbf {r}) \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 180, + 482, + 198 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_{\\mathrm{HR}}(\\mathbf{r})$ is the output function (e.g., the super-resolved image). The FNO models $\\mathcal{G}$ by stacking:", + "bbox": [ + 89, + 209, + 482, + 239 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} _ {l + 1} (\\mathbf {r}) = \\sigma \\left(\\mathcal {W} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) + \\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r})\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 252, + 482, + 270 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{v}_l(\\mathbf{r})$ is the feature representation at layer $l$ evaluated at spatial location $\\mathbf{r}$ , and $\\mathbf{v}_{l + 1}(\\mathbf{r})$ is its updated representation in the following layer; $\\sigma$ is a nonlinear activation function; $\\mathcal{W}_l$ is a linear transformation. $\\kappa_{l}$ , the integral operator at layer $l$ , transforms the features into the Fourier domain. Fourier modes are then truncated for computational efficiency. Global convolution is performed with a pointwise multiplication between the transformed features and the learned Fourier coefficients.", + "bbox": [ + 89, + 281, + 483, + 417 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) = \\mathcal {F} ^ {- 1} \\left(\\mathbf {P} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathcal {F} [ \\mathbf {v} _ {l} ] (\\boldsymbol {\\xi})\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 429, + 482, + 449 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{F}$ and $\\mathcal{F}^{-1}$ denote the Fourier and inverse Fourier transforms, respectively. $\\xi$ is the frequency domain variables. $\\mathcal{F}[\\mathbf{v}_l](\\pmb {\\xi})$ is the Fourier transform of $\\mathbf{v}_l$ , evaluated at frequency $\\pmb{\\xi}$ . $\\mathbf{P}_l(\\pmb {\\xi})$ is a complex-valued tensor of learnable parameters representing the Fourier domain filters.", + "bbox": [ + 89, + 459, + 483, + 535 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, mode truncation underrepresents high-frequency components that are critical to SR of real-world images. To address this limitation, we introduce Mode Rebalancing. A learned weighting function $\\mathbf{w}_l(\\boldsymbol {\\xi})$ is applied to the Fourier modes to amplify or attenuate specific frequency components. It is defined at layer $l$ as:", + "bbox": [ + 89, + 536, + 483, + 626 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} _ {l} (\\boldsymbol {\\xi}) = 1 + \\gamma_ {l} \\cdot \\| \\boldsymbol {\\xi} \\| ^ {\\alpha}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 638, + 482, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{l}$ is a learnable scalar parameter at layer $l$ that controls the strength of the weighting; $\\alpha$ is a hyperparameter (0.7 in our experiments or optionally a learnable parameter) that determines how the weight scales with the frequency magnitude $\\|\\pmb{\\xi}\\|$ . $\\mathbf{w}(\\pmb{\\xi})$ assigns higher weights to higher frequencies when $\\alpha > 0$ , thus emphasizing high-frequency components. This yields an updated $\\mathcal{K}_{l}$ :", + "bbox": [ + 89, + 667, + 483, + 773 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) = \\mathcal {F} ^ {- 1} \\left(\\mathbf {w} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathbf {P} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathcal {F} [ \\mathbf {v} _ {l} ] (\\boldsymbol {\\xi})\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 786, + 482, + 804 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Gated Fusion Mechanism", + "text_level": 1, + "bbox": [ + 89, + 816, + 323, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While WFNO excels at capturing global dependencies through spectral convolutions, it may not fully exploit local interactions critical for detailed image reconstruction. We incorporate AttnNO to complement WFNO by capturing", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "local dependencies. Working in tandem, they learn mappings from the low-resolution input function to the high-resolution output function. Gated Fusion Mechanism optimally combines the complementary features from both operators, adaptively balancing the contributions of each to a fused feature map, which is then fed to a projection layer.", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Efficient implementation of the kernel integral using the Galerkin-type attention mechanism [4] has been explored in the neural operator applied to SR tasks [35, 54]. Our AttnNO is composed of bicubic interpolation, Galerkin attention, and nonlinearity, sharing an encoder with WFNO. AttnNO models local interactions in the spatial domain, focusing on the most relevant spatial regions during the convolution process. Given the complementary role of AttnNO to WFNO, we simplify its structure to improve runtime.", + "bbox": [ + 511, + 181, + 905, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While previous works have applied gating mechanisms in different contexts, our approach differs significantly. Zheng et al. [60] use gating within recurrent CRF networks primarily for semantic segmentation, controlling the information flow for boundary refinement rather than fusing feature maps with distinct representations. Hu et al. [16] introduced channel-wise gating in Squeeze-and-Excitation (SE) blocks, focusing on adaptively recalibrating feature channels within a single network stream. In contrast, our Gated Fusion Mechanism applies spatial gating to integrate global dependencies captured by WFNO and local information from AttnNO. This mechanism adaptively combines both operators' feature maps, enhancing high-resolution image reconstruction by balancing global and local contributions at each spatial location.", + "bbox": [ + 511, + 318, + 905, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathbf{v}_{\\mathrm{WFNO}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}$ and $\\mathbf{v}_{\\mathrm{AttnNO}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}$ denote the feature maps obtained from WFNO and AttnNO, respectively, where $B$ is the batch size, $H$ and $W$ are the height and width of the feature maps, and $C$ is the number of channels. We first concatenate the feature maps along the channel dimension and pass them through a convolutional layer followed by a sigmoid activation to produce a gating map $\\mathbf{G} \\in \\mathbb{R}^{B \\times H \\times W \\times 1}$ :", + "bbox": [ + 511, + 542, + 905, + 666 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {G} = \\sigma \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(\\left[ \\mathbf {v} _ {\\mathrm {W F N O}}, \\mathbf {v} _ {\\mathrm {A t t n N O}} \\right]\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 678, + 903, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $[\\cdot ,\\cdot ]$ denotes concatenation along the channel dimension; $\\mathrm{Conv}_{1\\times 1}$ is a $1\\times 1$ convolutional layer that reduces the concatenated features to a single-channel gating map; $\\sigma (\\cdot)$ is the sigmoid activation function applied element-wise.", + "bbox": [ + 511, + 707, + 903, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The fused feature map $\\mathbf{v}_{\\mathrm{fused}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}$ is the element-wise weighted sum of the two feature maps:", + "bbox": [ + 511, + 767, + 903, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} _ {\\text {f u s e d}} = \\mathbf {G} \\odot \\mathbf {v} _ {\\mathrm {W F N O}} + (1 - \\mathbf {G}) \\odot \\mathbf {v} _ {\\mathrm {A t t n N O}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 811, + 903, + 828 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\odot$ denotes element-wise multiplication, and subtraction is performed element-wise. The gating map $\\mathbf{G}$ is broadcast across the channel dimension to match the dimensions of the feature maps.", + "bbox": [ + 511, + 839, + 905, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "153", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gated Fusion Mechanism brings two advantages compared to a naive concatenation strategy: (i) Captures complementary Information: WFNO models global dependencies through spectral convolutions, effectively modeling long-range interactions and overall structure. In contrast, AttnNO excels at capturing local dependencies and fine-grained details via attention mechanisms. (ii) Balances contributions dynamically: Gated Fusion Mechanism elicits the importance of each feature map at each spatial location, dynamically balancing global and local information.", + "bbox": [ + 89, + 90, + 483, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Forward Diffusion Process and Noise Schedule", + "text_level": 1, + "bbox": [ + 89, + 251, + 482, + 266 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motivation. NOs are well-suited for SR tasks due to their inherent resolution invariance and their ability to model global dependencies efficiently. Diffusion models can iteratively refine a low-resolution image to a high-resolution one, capturing the complex conditional distribution of high-resolution images given low-resolution inputs.", + "bbox": [ + 89, + 273, + 483, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DiffFNO leverages the strengths of both frameworks. WFNO is a powerful mechanism for handling arbitrary resolutions and capturing high-frequency details, while the diffusion process iteratively improves reconstruction output.", + "bbox": [ + 89, + 364, + 482, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our framework, the forward diffusion process models the degradation of HR images to LR images, which in our case is primarily due to downscaling. To incorporate this degradation into the diffusion model framework, we define a forward process that simulates the downscaling effect over continuous time $t \\in [0,T]$ . At, the image $\\mathbf{x}_T$ closely resemble the observed LR image $\\mathbf{x}_{\\mathrm{LR}}$ after significant degradation. We adopt a modified variance-preserving (VP) stochastic differential equation (SDE):", + "bbox": [ + 89, + 425, + 483, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd \\mathbf {x} _ {t} = - \\frac {1}{2} \\beta (t) (\\mathbf {x} _ {t} - \\mathbf {D x} _ {t}) d t + \\sqrt {\\beta (t)} d \\mathbf {w}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 571, + 482, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta (t)$ is the noise schedule; $\\mathbf{D}$ is the downsampling operator that reduces the resolution of the image; $d\\mathbf{w}$ is the standard Wiener process.", + "bbox": [ + 89, + 609, + 482, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this formulation, the term $\\mathbf{x} - \\mathbf{D}\\mathbf{x}$ quantifies the high-frequency details lost during downscaling. The drift term $-\\frac{1}{2}\\beta(t)(\\mathbf{x} - \\mathbf{D}\\mathbf{x})dt$ models the gradual removal of these details, while the diffusion term $\\sqrt{\\beta(t)}d\\mathbf{w}$ adds Gaussian noise to simulate further degradation.", + "bbox": [ + 89, + 654, + 482, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Noise Schedule $\\beta (t)$ . We define the noise schedule $\\beta (t)$ as a simple and effective linear function increasing over the time interval $[0,T]$ :", + "bbox": [ + 89, + 732, + 482, + 777 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\beta (t) = \\beta_ {\\min } + \\left(\\beta_ {\\max } - \\beta_ {\\min }\\right) \\cdot \\frac {t}{T}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 787, + 482, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta_{\\mathrm{min}} = 0.1$ and $\\beta_{\\mathrm{max}} = 20$ . This linear schedule ensures a gradual increase in the degradation strength from minimal degradation at $t = 0$ to maximum degradation at $t = T$ .", + "bbox": [ + 89, + 824, + 482, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Relation to Image Degradation. At each time $t$ , the image $\\mathbf{x}_t$ progressively loses high-frequency details due to the", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "drift toward $\\mathbf{D}\\mathbf{x}_t$ , the downscaled version of the image. The added Gaussian noise further simulates the information loss inherent in downscaling. At $t = T$ , the image $\\mathbf{x}_T$ approximates the observed low-resolution image $\\mathbf{x}_{\\mathrm{LR}}$ . The reverse diffusion process then aims to recover the high-resolution image $\\mathbf{x}_0$ (i.e. $\\mathbf{x}_{\\mathrm{HR}}$ ) from $\\mathbf{x}_T$ by reversing the degradation.", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Choice of $\\beta(t)$ . The linear noise schedule is chosen for its simplicity and effectiveness. It provides a straightforward way to control the rate of degradation over time. Parameters $\\beta_{\\mathrm{min}}$ and $\\beta_{\\mathrm{max}}$ are selected to balance the trade-off between sufficient degradation (to simulate downscaling) and numerical stability of the diffusion process.", + "bbox": [ + 511, + 181, + 903, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Downsampling Operator D. The operator D is defined to reduce the spatial dimensions of the image by the desired scaling factor. We use bicubic downsampling.", + "bbox": [ + 511, + 273, + 903, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Adaptive Time-Step", + "text_level": 1, + "bbox": [ + 511, + 330, + 702, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The standard reverse diffusion process is stochastic and requires a large number of sampling steps, making it computationally expensive. To accelerate inference, we reformulate the reverse diffusion as a deterministic Ordinary Differential Equation (ODE), allowing us to use advanced ODE solvers for faster sampling. The ODE solver integrates the reverse diffusion process, and its output is the super-resolved image. The reverse diffusion process can be described by a Stochastic Differential Equation (SDE) [46]:", + "bbox": [ + 511, + 354, + 905, + 491 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd \\mathbf {x} = [ f (\\mathbf {x}, t) - g (t) ^ {2} \\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}) ] d t + g (t) d \\bar {\\mathbf {w}} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 517, + 903, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{x}$ is the data; $t$ is the time variable; $f(\\mathbf{x}, t)$ and $g(t)$ are drift and diffusion coefficients; $\\nabla_{\\mathbf{x}} \\log p_t(\\mathbf{x})$ is the score function; $\\bar{\\mathbf{w}}$ is the reverse-time Wiener process. By removing the stochastic term, we obtain the probability flow ODE, which deterministically transports the data from the noise distribution to the data distribution.", + "bbox": [ + 511, + 547, + 905, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our ATS ODE solver comprises three key components: 1. Adaptive Time Step Selection Using a Learned Function. Optimizing the allocation of time steps based on data characteristics has been explored in previous works [28, 53]. We discretize the time interval $[0,T]$ into $N$ non-uniform time steps $\\{t_i\\}_{i = 0}^N$ , where $t_0 = 0$ and $t_N = T$ . We introduce a learned function $\\phi_{\\psi}(t)$ as a weighted sum of polynomial basis functions, where the weight is parameterized by a set of learnable coefficients $\\psi = \\{\\psi_{1},\\psi_{2},\\dots ,\\psi_{K}\\}$ , which adaptively determines the distribution of time steps based on the data characteristics.", + "bbox": [ + 511, + 638, + 903, + 805 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Parameterization of $\\phi_{\\psi}(t)$ . We define $\\phi_{\\psi}(t)$ as a normalized weighted sum of $K$ predefined monotonically increasing basis functions $\\{\\phi_k(t)\\}_{k=1}^K$ :", + "bbox": [ + 511, + 806, + 903, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {\\psi} (t) = \\frac {\\sum_ {k = 1} ^ {K} \\psi_ {k} \\phi_ {k} (t)}{\\sum_ {k = 1} ^ {K} \\psi_ {k} \\phi_ {k} (T)}, \\quad \\psi_ {k} = \\exp (\\omega_ {k}), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 864, + 903, + 905 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "154", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where each basis function $\\phi_k(t) = t^k$ for $k = 1,2,\\ldots ,K$ is polynomial. $\\omega_{k}$ are unconstrained learnable parameters that ensure $\\psi_{k}\\geq 0$ through the exponential mapping. We set $K = 3$ to balance model flexibility with computational efficiency. This setup allows $\\phi_{\\psi}(t)$ to capture nonlinear timestep distributions without excessive complexity.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Selection of Time Steps. Using the learned function $\\phi_{\\psi}(t)$ , we map uniformly spaced normalized values $s_i = \\frac{i}{N}$ to non-uniform time steps $t_i$ :", + "bbox": [ + 89, + 181, + 480, + 227 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nt _ {i} = \\phi_ {\\psi} ^ {- 1} \\left(s _ {i}\\right) = \\phi_ {\\psi} ^ {- 1} \\left(\\frac {i}{N}\\right), \\quad i = 0, 1, \\dots , N \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 237, + 480, + 270 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since $\\phi_{\\psi}(t)$ is monotonically increasing, its inverse function $\\phi_{\\psi}^{-1}(s)$ exists and can be efficiently computed.", + "bbox": [ + 89, + 279, + 480, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2. Neural Operator Score Network. The score function, representing the gradient of the log probability density $\\log p_t(\\mathbf{x})$ , is approximated using a neural network $s_\\theta(\\mathbf{x}, t)$ parameterized by $\\theta$ :", + "bbox": [ + 89, + 311, + 480, + 371 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}) \\approx s _ {\\theta} (\\mathbf {x}, t). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 381, + 480, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In our architecture, $s_{\\theta}$ consists of: (i) An encoder that extracts features from $\\mathbf{x}_{\\mathrm{LR}}$ ; (ii) WFNO for capturing global dependencies and high-frequency details; (iii) AttnNO for modeling local dependencies and fine-grained structures; (iv) Gated Fusion Mechanism to dynamically combine features; (v) Time embedding $\\mathbf{e}(t)$ incorporating the time variable $t$ into our neural network $s_{\\theta}(\\mathbf{x},t)$ using sinusoidal positional embeddings [14, 50], concatenating it and encoded features along the channel dimension.", + "bbox": [ + 89, + 409, + 480, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3. Efficient Solver. We solve the reverse-time stochastic differential equation (SDE) of the diffusion process, transformed into an ODE:", + "bbox": [ + 89, + 545, + 480, + 589 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {d \\mathbf {x}}{d t} = f (\\mathbf {x}, t) - \\frac {1}{2} g (t) ^ {2} \\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 597, + 480, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{x} \\in \\mathbb{R}^d$ is the image estimate at time $t$ in the reverse diffusion process; $f(\\mathbf{x}, t)$ and $g(t)$ are coefficients derived from the forward diffusion process.", + "bbox": [ + 89, + 637, + 480, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the Variance Preserving (VP) SDE commonly used in diffusion models, the coefficients are defined as:", + "bbox": [ + 89, + 683, + 480, + 712 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nf (\\mathbf {x}, t) = - \\frac {1}{2} \\beta (t) \\mathbf {x}, \\quad g (t) = \\sqrt {\\beta (t)}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 720, + 480, + 751 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\beta (t)$ is a predefined noise schedule specific to the diffusion process and is consistent with our DiffFNO. By substituting the score function approximation from Eq. (14), we define the approximate drift function:", + "bbox": [ + 89, + 760, + 480, + 821 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta} (\\mathbf {x}, t) = f (\\mathbf {x}, t) - \\frac {1}{2} g (t) ^ {2} s _ {\\theta} (\\mathbf {x}, t). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 830, + 480, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The adaptive time steps $\\{t_i\\}_{i = 0}^N$ discretize the ODE. We apply the Runge-Kutta 4th-order (RK4) method, as it", + "bbox": [ + 89, + 869, + 480, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "balances computational cost and accuracy, requiring fewer steps than lower-order methods while retaining precision.", + "bbox": [ + 511, + 90, + 903, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The benefits of ATS are threefold: (i) Deterministic Sampling: It consistently produces the same results for identical inputs, improving reproducibility. (ii) Reduced Computation: Fewer sampling steps significantly decrease inference time. (iii) High-Quality Reconstruction: It maintains high-quality reconstruction by efficiently allocating computational resources.", + "bbox": [ + 511, + 121, + 903, + 226 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 239, + 643, + 257 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets and Evaluation Metrics. We use the DIV2K [1] dataset for training. For evaluation, we use the DIV2K validation set and four standard datasets: Set5 [3], Set14 [56], BSD100 [36], and Urban100 [18].", + "bbox": [ + 511, + 266, + 903, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our model on upscaling factors of $\\times 2$ , $\\times 3$ , $\\times 4$ , $\\times 6$ , $\\times 8$ , and $\\times 12$ . Notably, scales $\\times 6$ , $\\times 8$ , and $\\times 12$ are outside the training distribution, as the training scales are uniformly sampled from $\\times 1$ to $\\times 4$ . This setup assesses our model's ability to generalize to arbitrary scales. We use Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) as our evaluation metrics.", + "bbox": [ + 511, + 327, + 903, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Results. Building on the quantitative gains of our model, we also present qualitative results to illustrate the visual improvements achieved. We compare our proposed DiffFNO model with several SOTA arbitrary-scale SR methods, including Meta-SR [17], LIIF [7], LTE [24], SRNO [54], LIT [5], LMI [10], and HiNOTE [35]. All models are trained on the DIV2K dataset with identical settings to ensure a fair comparison in Tables 1 and 2.", + "bbox": [ + 511, + 431, + 905, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Among the compared methods, Meta-SR performs adequately at lower scales but struggles at higher scaling factors due to its generalized approach that lacks specialized mechanisms for fine detail capture. LIIF and LTE improve upon Meta-SR by using local implicit functions and frequency-based estimations, respectively, which enhance high-frequency texture representation. However, they still face limitations in capturing non-periodic textures and high-frequency details, resulting in blurred textures at larger scales. LIT and LMI further advance performance by integrating attention mechanisms and MLP-mixer architectures, effectively preserving high-frequency textures and handling diverse scales, but they may not generalize well across datasets with varying distributions. SRNO and HiNOTE employ neural operator frameworks with attention mechanisms and frequency-aware loss priors to better capture global spatial properties and enhance high-frequency detail reconstruction. We observed mixed results between SRNO and HiNOTE: at certain scaling factors, one outperforms the other, indicating their varying strengths at different resolutions. Overall, their neural operator foundation improves the handling of arbitrary scaling but may increase computational demands.", + "bbox": [ + 511, + 553, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "155", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f6a78486668d9bf1f32f6db7d34b794c8ba18e722f78231a0137e299bd6a5f00.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 106, + 88, + 401, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c2c07897b3a6fe1deab6db301463391d4551525a54a87e3557d35c93f40dc176.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 426, + 90, + 513, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/61e7b5bf4bce650d66c649155dc9a3ee0c223ec01567ab8e455c2e3812c1ff18.jpg", + "image_caption": [ + "Bicubic" + ], + "image_footnote": [], + "bbox": [ + 426, + 172, + 513, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0ca9eb3285676b46290af8641ce7429bcc762867ea9903e3c85184a756c2720e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 519, + 90, + 604, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/318696a0a14cf43053d81eb9c170bfa72a731d90134e1569b927f358942a1ce6.jpg", + "image_caption": [ + "Meta-SR [17]" + ], + "image_footnote": [], + "bbox": [ + 517, + 172, + 604, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d6d4738fb7833d1b05bab97c7d7bda416c3e21785f519c9717e7d386c9930b7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 611, + 90, + 697, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9c32e506bbabadbcf51e6b590e684cb86ca756b995ad267a760cdd82ea15b5ce.jpg", + "image_caption": [ + "LTE [24]" + ], + "image_footnote": [], + "bbox": [ + 611, + 172, + 697, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7dd738fcc61237869b36c50835f2944a5e9c85ecaacbd5ad4fea50b698ca853e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 90, + 794, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1bc2b5d8820a803f889bc993e96765b6a90ba793b3dfb1a3ebed36bd2d404d6d.jpg", + "image_caption": [ + "LIIF [7]" + ], + "image_footnote": [], + "bbox": [ + 707, + 172, + 794, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7057b283ab21024e6267a1e34845344d4c5ddef5613a25127b977c329bff8118.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 90, + 892, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1581a15597084136634bb164a4611fc86f43dcf7ff70424383d464587ba166a1.jpg", + "image_caption": [ + "LIT [5]", + "GT" + ], + "image_footnote": [], + "bbox": [ + 805, + 172, + 892, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b0653be3f8ab9d447ae236ac78205347330b834d136b85ce55a7fc7c711ff53f.jpg", + "image_caption": [ + "BSD100 [36], $\\times 12$", + "Urban100 [18], $\\times 7.6$" + ], + "image_footnote": [], + "bbox": [ + 102, + 258, + 401, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d3cc2b0715b22e77eca562cd05178a24687f4bb4eb8c6f8158d88f294e7e85cc.jpg", + "image_caption": [ + "LMI [10]" + ], + "image_footnote": [], + "bbox": [ + 426, + 261, + 514, + 327 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/39c2c61f700511c146b9fd63dc96bf3b1b5fc2079a3025cbac7fd1df1dd7212e.jpg", + "image_caption": [ + "Bicubic", + "LMI [10]" + ], + "image_footnote": [], + "bbox": [ + 426, + 345, + 514, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3859aaa3b29436756c41fa92e6bb8b68a9082217a1973ddc06b8c3e33b4562e0.jpg", + "image_caption": [ + "SRNO [54]" + ], + "image_footnote": [], + "bbox": [ + 519, + 261, + 606, + 327 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4c9801f8a51d438e49a1d0aa13222f70dcdffa419d8fd846fa89fba88aedac20.jpg", + "image_caption": [ + "Meta-SR [17]", + "SRNO [54]" + ], + "image_footnote": [], + "bbox": [ + 519, + 345, + 606, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e72bfa7309a3d85f1c5946da061fa54101576c1807d15add558c01d3b2b062a6.jpg", + "image_caption": [ + "HiNOTE [35]" + ], + "image_footnote": [], + "bbox": [ + 612, + 261, + 699, + 327 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d628f1a9639b1aaedc5c2d3190b00c39cb02242855fea84eb6523114cb1067e3.jpg", + "image_caption": [ + "LTE [24]", + "HiNOTE [35]" + ], + "image_footnote": [], + "bbox": [ + 612, + 345, + 699, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/160fc1212b6d92d9039404df323a64b6502cef8b78b0c8b79057ea718f725cb1.jpg", + "image_caption": [ + "DiffFNO (ours)" + ], + "image_footnote": [], + "bbox": [ + 709, + 261, + 795, + 327 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f64f62505d5b61d1c9eb247ae05dbebd5d14c5ade24b04069b703adecbd48084.jpg", + "image_caption": [ + "LIIF [7]", + "DiffFNO (ours)" + ], + "image_footnote": [], + "bbox": [ + 709, + 345, + 795, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e286017c55c082415c6495ca85889ecf4a2d7b9a8914f556dc4a20e3402a2739.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 807, + 261, + 893, + 327 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5bbb72a13b191f8ee358abb061013f5dec45d94ca8b124880459ab4531baba23.jpg", + "image_caption": [ + "LIT [5]", + "GT" + ], + "image_footnote": [], + "bbox": [ + 807, + 345, + 893, + 412 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/81c643cd70177fd17f4cb5964f690104239eadadffd6d5b40375b71d2840fc51.jpg", + "table_caption": [ + "Figure 3. Qualitative comparison on integer and continuous super-resolution scales. The models use RDN [58] as their encoder (except HiNOTE [35], has its own). In the HR image, the cropped patch is outlined in green." + ], + "table_footnote": [], + "table_body": "
    Modelx2x3x4x6x8x12
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    EDSR-MetaSR [17]33.320.91330.100.80028.230.83026.100.79224.770.74223.950.720
    EDSR-LTE [24]33.830.92130.500.88028.790.85226.550.80025.050.76024.200.736
    EDSR-LIIF [7]34.360.92530.940.88529.310.85527.020.81425.440.77124.320.743
    EDSR-LIT [5]34.810.92831.390.89029.700.86027.440.81525.780.77524.690.745
    EDSR-LMI [10]35.400.93031.880.89530.400.86527.950.82026.160.78025.560.750
    EDSR-SRNO [54]34.850.92831.450.89030.050.86327.360.81026.000.77225.910.760
    EDSR-DiffFNO (Ours)35.720.93232.500.90530.880.87028.290.83026.780.79026.480.775
    HiNOTE†[35]35.290.93131.900.89530.460.84227.830.79926.410.77226.230.732
    RDN-MetaSR [17]33.500.92030.320.89328.410.86126.290.81024.900.78024.010.790
    RDN-LTE [24]33.980.92230.650.88228.940.85226.700.80225.200.76224.350.732
    RDN-LIIF [7]34.510.92731.090.88729.460.85727.170.81225.590.77224.470.742
    RDN-LIT [5]34.960.93031.540.89229.850.86227.590.81725.930.77724.840.747
    RDN-LMI [10]35.550.93232.030.89730.550.86728.100.82226.310.78225.710.752
    RDN-SRNO [54]35.000.93031.600.89230.200.86227.510.81226.150.77226.060.762
    RDN-DiffFNO (Ours)35.870.93432.650.90231.030.87228.440.83226.930.79226.630.777
    ", + "bbox": [ + 94, + 472, + 901, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. PSNR/SSIM comparison on the DIV2K [1] validation set using EDSR [31] and RDN [58] encoders. HiNOTE [35] uses its own.", + "bbox": [ + 91, + 739, + 901, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our DiffFNO model consistently achieves the highest PSNR and SSIM scores across all scaling factors and datasets. The performance gap widens at larger scaling factors $(\\times 8$ and $\\times 12$ ), demonstrating a superior generalization to the out-of-distribution scales. The improvements are more pronounced on complex datasets like Urban100, which contain intricate textures and structures. By combining WFNO and AttnNO features through the Gated Fusion", + "bbox": [ + 89, + 766, + 482, + 886 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Mechanism, which adaptively balances global and local features, DiffFNO synthesizes global and local dependencies. The ATS ODE solver efficiently refines high-resolution images, further enhancing quality. This combination addresses the limitations of prior models, such as spectral bias and insufficient high-frequency detail capture.", + "bbox": [ + 511, + 766, + 903, + 857 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results. Fig. 3 compares arbitrary-scale SR methods on a BSD100 image (scaling factor of $\\times 12$ ) with", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "156", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c3936d04a4a58ca2a03b241afd694bff8e5a12bdce72c6c8ed26166708405e41.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelSet5Set14BSD100Urban100
    ×2×3×4×6×8×2×3×4×6×8×2×3×4×6×8×2×3×4×6×8
    MetaSR [17]37.5034.0531.5228.2326.0233.5130.0328.0225.5324.0231.0228.0526.5224.8223.5232.0228.0325.8223.5222.03
    LIIF [7]38.0234.4232.0428.5726.2534.0330.4328.4325.8424.3331.5228.5527.0325.0323.8332.5228.5326.0323.8322.33
    LTE [24]38.2134.6332.2528.7626.4434.2230.6528.6426.0524.5231.7128.7327.2325.2324.0332.7228.7526.2324.0322.53
    SRNO [54]38.3234.8432.6929.3827.2834.2730.7128.9726.7625.2632.4329.3727.8326.0424.9933.3329.1426.9824.4323.02
    LIT [5]38.5335.0232.8229.5127.4234.4430.8329.0326.8225.3332.5229.5127.9226.1225.0133.4229.2227.0224.5223.12
    LMI [10]38.7235.1432.9529.6327.5534.6331.0229.2427.0525.5532.7229.7428.0426.2525.1433.6229.4427.2424.6323.23
    HNOTE [35]39.0135.2233.0829.8527.7435.0231.2529.5527.3525.8533.0230.0528.1526.3525.2534.0329.8327.5524.7323.34
    DiffFNO (Ours)39.7235.3033.1630.2327.9336.0131.5430.2227.5826.0233.5630.2428.2126.4525.3034.1929.9927.7424.8023.35
    ", + "bbox": [ + 94, + 88, + 903, + 229 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a2c75a672ad8598bc3a60b2864a54aa1d6b99f0c4137cb6e124705f157481268.jpg", + "table_caption": [ + "Table 2. PSNR comparison on four benchmark datasets: Set5 [3], Set14 [56], BSD100 [36], and Urban100 [18]. All models use RDN [58] as their encoder, besides HiNOTE [35] which has its own." + ], + "table_footnote": [], + "table_body": "
    Model×2×3×4×6×8×12InferenceSteps
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    SRNO [54]33.810.92030.530.88028.740.85026.590.80025.100.76024.180.730147-
    FNO [26]34.360.92530.940.88529.310.85527.020.81025.440.77024.320.74085-
    WFNO34.810.92831.390.88829.700.85827.440.81525.780.77524.690.74597-
    WFNO-AttnNO35.400.93031.880.89230.400.86227.950.82026.160.78025.560.7501391000
    DiffFNO(-w, -a, -s)34.850.92831.450.89030.050.86027.360.81526.000.77525.910.7602041000
    DiffFNO(-a, -s)35.290.93031.900.89330.460.86327.830.82026.410.78026.230.7652311000
    DiffFNO(-s)35.700.93232.480.89630.850.86628.260.82526.750.78526.450.7702661000
    DiffFNO35.720.93232.500.90030.880.87028.290.83026.780.79026.480.77514130
    ", + "bbox": [ + 91, + 270, + 903, + 416 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation study of variants of DiffFNO on the DIV2K [1] validation set. All use EDSR-baseline [31] backbone as their encoder. Inference times are measured in milliseconds (ms). WFNO-AttnNO has Gated Fusion Mechanism.", + "bbox": [ + 89, + 426, + 903, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "fine-grained details like animal fur and rock textures and an Urban100 (continuous scaling factor of $\\times 7.6$ ) image featuring large structures and fine local details such as reflections on the grass. SRNO and HiNOTE capture multiscale details effectively, from the animal's body to tiny gaps between glass panels. However, DiffFNO reconstructs crisper edges with fewer artifacts, enhancing texture in animal fur pattern and reflections. WFNO captures large-scale patterns, while AttnNO and Gated Fusion Mechanism preserve intricate textures. This multiscale approach followed by a diffusion process enhanced by the ATS's ODE solver further reduces visual artifacts.", + "bbox": [ + 88, + 468, + 482, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation Studies. Extensive ablation studies validate the effectiveness and complementary nature of new components in DiffFNO. Table 3 reports the PSNR results on the DIV2K validation set for different model variants with scaling factors from $\\times 2$ to $\\times 12$ . -w denotes leaving out the Mode Rebalancing (yielding the default FNO [26]). -a denotes omitting AttnNO. -s denotes the removal of ATS ODE solver. We also measure inference time by averaging over 100 runs, and report inference steps. We establish a baseline with SRNO, whose architecture is the most similar to our DiffFNO aamong the methods covered in our study. Overall, we observe notable improvements with the addition of model components. The complete DiffFNO achieves the highest PSNR and SSIM values across all upscaling factors.", + "bbox": [ + 89, + 654, + 482, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Mode Rebalancing. Incorporating Mode Rebalancing into WFNO boosted performance compared to the", + "bbox": [ + 89, + 869, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "default FNO [26], at the cost of a slightly increased number of parameters and inference time.", + "bbox": [ + 511, + 468, + 903, + 497 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Gated Fusion Mechanism and AttnNO. The Gated Fusion Mechanism introduces minimal computational overhead. In addition, extra computational cost incurred by Attention-based Neural Operator is effectively mitigated by running it in parallel with WFNO while employing a shared encoder.", + "bbox": [ + 511, + 500, + 903, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of ATS ODE Solver: ATS dramatically reduces the number of inference steps from 1,000 to just 30, which substantially improves the inference time while delivering competitive performance (Tab. 3). DiffFNO outperforms the SOTA in both PSNR and inference time (Fig. 1 (a)).", + "bbox": [ + 511, + 589, + 903, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 680, + 633, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose Diffusion Fourier Neural Opeartor (DiffFNO) for arbitrary-scale image super-resolution. DiffFNO is made of Weighted Fourier Neural Operator with a Mode Rebalancing mechanism to emphasize high-frequency details. It is complemented by a Attention-based Neural Operator through a Gated Fusion Mechanism that effectively adjusts the influence of global and local features. Image reconstruction is further refined by a diffusion process augmented with an Adaptive Time-Step ODE solver that dynamically allocates time steps, drastically cutting down inference time without compromising output quality. Experiments demonstrate DiffFNO's competitiveness in both reconstruction quality and inference time across various benchmarks, establishing a new state-of-the-art.", + "bbox": [ + 509, + 705, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "157", + "bbox": [ + 486, + 944, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 118, + 187, + 133 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2017. 6, 7, 8", + "[2] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. Analytic-DPM: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. 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In Proceedings of the IEEE international conference on computer vision, pages 1529-1537, 2015. 4" + ], + "bbox": [ + 91, + 92, + 480, + 642 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "160", + "bbox": [ + 488, + 945, + 509, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DiffFNO_ Diffusion Fourier Neural Operator/3a04b4ef-d06b-4b04-9301-be75af2eacee_model.json b/2025/DiffFNO_ Diffusion Fourier Neural Operator/3a04b4ef-d06b-4b04-9301-be75af2eacee_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9fd2cd7d4c2e47e954c3640dc0fbd64b090909d5 --- /dev/null +++ b/2025/DiffFNO_ Diffusion Fourier Neural Operator/3a04b4ef-d06b-4b04-9301-be75af2eacee_model.json @@ -0,0 +1,2840 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.271, + 0.131, + 0.73, + 0.154 + ], + "angle": 0, + "content": "DiffFNO: Diffusion Fourier Neural Operator" + }, + { + "type": "text", + "bbox": [ + 0.384, + 0.193, + 0.612, + 0.213 + ], + "angle": 0, + "content": "Xiaoyi Liu\\(^{1,*}\\) Hao Tang\\(^{2,\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.268, + 0.223, + 0.73, + 0.243 + ], + "angle": 0, + "content": "\\(^{1}\\)Washington University in St. Louis \\(^{2}\\)Peking University" + }, + { + "type": "text", + "bbox": [ + 0.335, + 0.245, + 0.663, + 0.26 + ], + "angle": 0, + "content": "jasonl@wustl.edu haotang@pku.edu.cn" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.303, + 0.45, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.503, + 0.418, + 0.516 + ], + "angle": 0, + "content": "(a) PSNR and inference time for \\(\\times 4\\) super-resolution" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.308, + 0.861, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.381, + 0.861, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.615, + 0.501, + 0.766, + 0.515 + ], + "angle": 0, + "content": "(b) DiffFNO vs SRNO [54]" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.527, + 0.908, + 0.557 + ], + "angle": 0, + "content": "Figure 1. (a) All models use the EDSR-baseline [31] encoder, except HiNOTE [35] which has its own. (b) Compared to SRNO [54], DiffFNO is strengthened by the fusion of spectral and spatial features and efficient refinement by a diffusion process." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.568, + 0.327, + 0.584 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.602, + 0.486, + 0.86 + ], + "angle": 0, + "content": "We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly improving the reconstruction of high-frequency image details that are crucial for superresolution tasks. Gated Fusion Mechanism (GFM) adaptively complements WFNO's spectral features with spatial features from an Attention-based Neural Operator (AttnNO). This enhances the network's capability to capture both global structures and local details. Adaptive Time-Step (ATS) ODE solver, a deterministic sampling strategy, accelerates inference without sacrificing output quality by dynamically adjusting integration step sizes ATS. Extensive experiments demonstrate that DiffFNO achieves state-of-the-art (SOTA) results, outperforming existing methods across various scaling factors by a margin of 2-4 dB in" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.57, + 0.909, + 0.633 + ], + "angle": 0, + "content": "PSNR, including those beyond the training distribution. It also achieves this at lower inference time (Fig. 1 (a)). Our approach sets a new standard in super-resolution, delivering both superior accuracy and computational efficiency." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.662, + 0.646, + 0.679 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.688, + 0.907, + 0.825 + ], + "angle": 0, + "content": "Image super-resolution (SR) reconstructs high-resolution (HR) images from low-resolution (LR) inputs, recovering lost fine details to enhance visual quality. SR is crucial for applications like medical imaging [12], satellite imagery [23, 52], and video games [38]. However, multiple HR images can correspond to the same LR input due to information loss during downsampling. This ambiguity requires algorithms capable of inferring plausible and perceptually accurate high-frequency content from limited data." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Deep learning, particularly Convolutional Neural Networks (CNNs) [58], has significantly advanced SR. Dong et al. introduced SRCNN [9], demonstrating the effectiveness of end-to-end learning for SR. Subsequent models achieved remarkable performance using deeper architectures and at" + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.875, + 0.244, + 0.888 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.888, + 0.383, + 0.901 + ], + "angle": 0, + "content": "*Work Done during the visit at Peking University." + }, + { + "type": "list", + "bbox": [ + 0.115, + 0.875, + 0.383, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.945, + 0.512, + 0.957 + ], + "angle": 0, + "content": "150" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.352, + 0.106 + ], + "angle": 0, + "content": "tention mechanisms [6, 30, 31, 34, 57]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.109, + 0.484, + 0.244 + ], + "angle": 0, + "content": "Diffusion models have emerged as powerful generative frameworks modeling complex data distributions via iterative denoising processes [11, 14, 45]. Their ability to generate high-fidelity images is well-suited for inferring missing fine details. In SR, diffusion models progressively refine an LR image by modeling the conditional distribution of HR images given the LR input [15, 25, 41, 51]. This iterative process reconstructs intricate textures and high-frequency components, producing realistic outputs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.246, + 0.484, + 0.367 + ], + "angle": 0, + "content": "However, diffusion models are computationally intensive due to the iterative reverse diffusion process [46]. To address this, recent research explores efficient sampling strategies to accelerate reverse diffusion. One approach is approximating the diffusion process through deterministic Ordinary Differential Equation (ODE), which can be solved in fewer steps [33]. This accelerates inference and provides consistent, reproducible results." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.369, + 0.484, + 0.535 + ], + "angle": 0, + "content": "Arbitrary-scale SR models [7, 17, 24], which can upsample images at user-defined scales beyond those seen in training, have gained attention in recent years. Methods involving attention mechanisms [5] and representing images as continuous functions [10] have been explored. Operator-learning methods such as Super-Resolution Neural Operators (SRNO) [54] and HiNOTE [35] have further advanced this field. However, the inherent differences between physics simulations and real-world images introduce challenges from computational demands to the difficulty in restoring high-frequency details." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.537, + 0.449, + 0.551 + ], + "angle": 0, + "content": "To address these limitations, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.484, + 0.902 + ], + "angle": 0, + "content": "(1) We propose Weighted Fourier Neural Operator (WFNO) strengthened by iterative refinement from a diffusion framework for high-frequency reconstruction, detailed in Fig. 2. Through Mode Rebalancing (MR), WFNO learns to emphasize the most critical frequency components. This greatly enhances high-frequency image detail reconstruction, overcoming the limitations of standard FNOs and MLPs, which underrepresent such details due to mode truncation and spectral bias, respectively. (2) We develop Gated Fusion Mechanism (GFM) to dynamically adjust the influence of Fourier space features from WFNO and complementary spatial domain features from an Attention-based Neural Operator (AttnNO). AttnNO is lightweight, sharing an encoder with and running in parallel to WFNO. (3) Additionally, we present Adaptive Time-Step (ATS) ODE solver, which flexibly adjusts integration step sizes based on data characteristics by assessing the complexity of image regions, thereby reducing computational overhead without compromising quality. (4) DiffFNO achieves state-of-the-art results on multiple SR benchmarks, outperforming existing methods by 2-4 dB in PSNR in reconstruction quality. It also offers competitive inference time as Fig. 1 (a) shows. DiffFNO remains robust across various upscaling factors—even those" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.092, + 0.668, + 0.107 + ], + "angle": 0, + "content": "unseen during training." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.12, + 0.655, + 0.136 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.145, + 0.905, + 0.281 + ], + "angle": 0, + "content": "Neural Operators and Fourier Methods. Neural Operators (NO) [22] have emerged as a powerful framework for learning mappings between infinite-dimensional function spaces, providing resolution-invariant models that generalize across different input resolutions. Unlike traditional neural networks that map finite-dimensional vectors to other vectors, neural operators learn mappings from functions to functions [27], making them well-suited for tasks involving continuous data or data at varying resolutions." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.282, + 0.905, + 0.403 + ], + "angle": 0, + "content": "Multi-Layer Perceptrons (MLPs) often exhibit a spectral bias, favoring low-frequency functions [39]. This limits their ability to capture fine textures and sharp edges. To overcome these limitations, techniques like positional encodings and Fourier feature mappings capture high-frequency details by embedding input coordinates into a higher-dimensional sinusoidal space, allowing the network to represent complex patterns [44, 47]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.403, + 0.906, + 0.553 + ], + "angle": 0, + "content": "Fourier Neural Operator (FNO) [26] is a variant of NO that uses spectral convolution to efficiently capture global data patterns, modeling long-range dependencies with lower computational complexity than traditional CNNs. In physics and climate settings [19, 29, 55], FNOs can handle arbitrary input resolutions without retraining. Although successful, FNOs may still lose high-frequency information due to mode truncation (discarding higher-frequency Fourier modes). This loss impairs tasks such as SR that rely on detailed reconstruction [13, 48, 49]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.554, + 0.906, + 0.659 + ], + "angle": 0, + "content": "The Mode Rebalancing mechanism in WFNO overcomes these limitations. Instead of being truncated, all Fourier modes are preserved, with additional learnable weights to modulate their impact on reconstruction. Fine-grained feature representation is further enhanced by AttnNO, which captures local details by processing data directly in the spatial domain" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.66, + 0.906, + 0.765 + ], + "angle": 0, + "content": "Diffusion-Based SR and Efficient Sampling. Diffusion models have gained prominence as powerful generative models capable of producing high-quality images through iterative denoising techniques [14, 42]. In the context of SR, diffusion models have been employed to model the conditional distribution of HR images given LR inputs, achieving higher resolutions after progressive enhancement [40, 41]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.766, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Despite their effectiveness, diffusion models are computationally intensive due to the large number of time steps required in the reverse diffusion process. Such computational demands pose significant challenges for practical applications [20], especially in real-time or resource-constrained settings. Current solutions include: (i) Deterministic Sampling via ODE Solvers: By reformulating the stochastic reverse diffusion as a deterministic ODE, advanced ODE solvers can be employed to reduce the number of sam" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "151" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.898, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.398, + 0.908, + 0.471 + ], + "angle": 0, + "content": "Figure 2. The proposed Diffusion Fourier Neural Opeartor (DiffFNO) architecture for arbitrary-scale super-resolution begins by lifting a low-resolution input image \\(\\mathbf{x}_{\\mathrm{LR}}(\\mathbf{r})\\) into a feature space using a convolutional encoder. Features extracted by the Weighted Fourier Neural Operator (WFNO) and an Attention-based Neural Operator (AttnNO) are combined using a Gated Fusion Mechanism (GFM). The fused features are then projected into RGB space, where Adaptive Time-Step (ATS) ODE solver efficiently completes the reverse diffusion process with both accuracy and speed. This pipeline generates \\(\\mathbf{x}_{\\mathrm{HR}}(\\mathbf{r})\\), a high-resolution version of the input image." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.48, + 0.483, + 0.648 + ], + "angle": 0, + "content": "pling steps [21]. Methods like Denoising Diffusion Implicit Models (DDIM) [45] and DPM-Solver [2, 33] have demonstrated the ability to generate high-quality images with significantly fewer steps. (ii) Operator Learning for Fast Sampling: Neural operators accelerates sampling by learning the solution operator of the reverse diffusion process [8, 59]. (iii) Progressive Distillation: Training a distilled model to approximate the behavior of the full diffusion model allows faster sampling with fewer steps [37, 43]. Although effective, this method may require extensive retraining and potentially compromise image quality for increased speed." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.648, + 0.483, + 0.724 + ], + "angle": 0, + "content": "Applying these acceleration methods to diffusion-based SR enables faster inference while maintaining high image quality. With efficient sampling methods, diffusion models become more practical for SR tasks, balancing performance and computational efficiency [32]." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.725, + 0.483, + 0.787 + ], + "angle": 0, + "content": "DiffFNO adopts (i) for its simplicity and the robustness of established numerical methods. We also strength it with the ATS strategy, which adjusts integration step sizes adaptively to balance speed and quality." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.804, + 0.312, + 0.822 + ], + "angle": 0, + "content": "3. The Proposed DiffFNO" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.831, + 0.479, + 0.848 + ], + "angle": 0, + "content": "3.1. Network Architecture and Novel Components" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "An overview of the proposed DiffFNO is shown in Fig. 1 (b). It has three parts: (i) A CNN encoder extracts features from LR images. Unlike the simple linear transfor" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.907, + 0.646 + ], + "angle": 0, + "content": "mations in standard FNO setups for physics simulations, our encoder is tailored for SR, extracting complex patterns and textures needed for high-quality reconstructions. We use the EDSR-baseline [31] and RDN models [58] in our experiments. (ii) WFNO and GFM: WFNO captures both global and local details alongside the AttnNO. GFM combines these into a unified HR feature map, which is then projected into RGB. (iii) ATS ODE solver accelerates inference speed by taking fewer, larger, and dynamically adjusted steps toward the reconstructed HR image. Fig. 2 illustrates these components in detail." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.647, + 0.907, + 0.678 + ], + "angle": 0, + "content": "The network minimizes the difference between the predicted image and the true image. The loss function is:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.685, + 0.907, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\theta) = \\mathbb {E} _ {t, \\mathbf {x} _ {0}} \\left[ \\| s _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\nabla_ {\\mathbf {x} _ {t}} \\log p _ {t} \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) \\| _ {2} ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.906, + 0.765 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_t\\) (i.e. \\(\\mathbf{x}_{\\mathrm{LR}}\\)) is obtained by adding noise to \\(\\mathbf{x}_0\\) (i.e. \\(\\mathbf{x}_{\\mathrm{HR}}\\)). \\(s_{\\theta}(\\mathbf{x}_t, t)\\) is the neural network approximating the true score function. \\(\\nabla \\mathbf{x}_t \\log p_t(\\mathbf{x}_t | \\mathbf{x}_0)\\) is the true score function." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.772, + 0.821, + 0.789 + ], + "angle": 0, + "content": "3.2. Weighted Fourier Neural Operator" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.907, + 0.901 + ], + "angle": 0, + "content": "The Fourier Neural Operator (FNO) [26] is an efficient NO variant designed to learn mappings between function spaces. It operates directly on inputs of arbitrary resolutions, performing upscaling by mapping low-resolution inputs to high-resolution outputs. It first transforms the input data into the frequency domain, applies the learned filters, and then transforms the data back to the spatial domain." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "152" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.121 + ], + "angle": 0, + "content": "Spectral convolution and mode truncation greatly enhance computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.122, + 0.483, + 0.168 + ], + "angle": 0, + "content": "Let \\(\\mathbf{x}_{\\mathrm{LR}}(\\mathbf{r})\\) denote the low-resolution input function (e.g., an image), where \\(\\mathbf{r} \\in \\mathbb{R}^2\\) represents spatial coordinates. The goal is to learn an operator \\(\\mathcal{G}\\) such that:" + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.181, + 0.483, + 0.199 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {\\mathrm {H R}} (\\mathbf {r}) = \\mathcal {G} \\left[ \\mathbf {x} _ {\\mathrm {L R}} (\\mathbf {r}) \\right], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.21, + 0.483, + 0.24 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_{\\mathrm{HR}}(\\mathbf{r})\\) is the output function (e.g., the super-resolved image). The FNO models \\(\\mathcal{G}\\) by stacking:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.253, + 0.483, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} _ {l + 1} (\\mathbf {r}) = \\sigma \\left(\\mathcal {W} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) + \\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r})\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.282, + 0.484, + 0.418 + ], + "angle": 0, + "content": "where \\(\\mathbf{v}_l(\\mathbf{r})\\) is the feature representation at layer \\(l\\) evaluated at spatial location \\(\\mathbf{r}\\), and \\(\\mathbf{v}_{l + 1}(\\mathbf{r})\\) is its updated representation in the following layer; \\(\\sigma\\) is a nonlinear activation function; \\(\\mathcal{W}_l\\) is a linear transformation. \\(\\kappa_{l}\\), the integral operator at layer \\(l\\), transforms the features into the Fourier domain. Fourier modes are then truncated for computational efficiency. Global convolution is performed with a pointwise multiplication between the transformed features and the learned Fourier coefficients." + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.43, + 0.483, + 0.45 + ], + "angle": 0, + "content": "\\[\n\\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) = \\mathcal {F} ^ {- 1} \\left(\\mathbf {P} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathcal {F} [ \\mathbf {v} _ {l} ] (\\boldsymbol {\\xi})\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.46, + 0.484, + 0.536 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}\\) and \\(\\mathcal{F}^{-1}\\) denote the Fourier and inverse Fourier transforms, respectively. \\(\\xi\\) is the frequency domain variables. \\(\\mathcal{F}[\\mathbf{v}_l](\\pmb {\\xi})\\) is the Fourier transform of \\(\\mathbf{v}_l\\), evaluated at frequency \\(\\pmb{\\xi}\\). \\(\\mathbf{P}_l(\\pmb {\\xi})\\) is a complex-valued tensor of learnable parameters representing the Fourier domain filters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.537, + 0.484, + 0.627 + ], + "angle": 0, + "content": "However, mode truncation underrepresents high-frequency components that are critical to SR of real-world images. To address this limitation, we introduce Mode Rebalancing. A learned weighting function \\(\\mathbf{w}_l(\\boldsymbol {\\xi})\\) is applied to the Fourier modes to amplify or attenuate specific frequency components. It is defined at layer \\(l\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.64, + 0.483, + 0.657 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} _ {l} (\\boldsymbol {\\xi}) = 1 + \\gamma_ {l} \\cdot \\| \\boldsymbol {\\xi} \\| ^ {\\alpha}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.669, + 0.484, + 0.775 + ], + "angle": 0, + "content": "where \\(\\gamma_{l}\\) is a learnable scalar parameter at layer \\(l\\) that controls the strength of the weighting; \\(\\alpha\\) is a hyperparameter (0.7 in our experiments or optionally a learnable parameter) that determines how the weight scales with the frequency magnitude \\(\\|\\pmb{\\xi}\\|\\). \\(\\mathbf{w}(\\pmb{\\xi})\\) assigns higher weights to higher frequencies when \\(\\alpha > 0\\), thus emphasizing high-frequency components. This yields an updated \\(\\mathcal{K}_{l}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.787, + 0.483, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) = \\mathcal {F} ^ {- 1} \\left(\\mathbf {w} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathbf {P} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathcal {F} [ \\mathbf {v} _ {l} ] (\\boldsymbol {\\xi})\\right). \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.817, + 0.325, + 0.832 + ], + "angle": 0, + "content": "3.3. Gated Fusion Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.902 + ], + "angle": 0, + "content": "While WFNO excels at capturing global dependencies through spectral convolutions, it may not fully exploit local interactions critical for detailed image reconstruction. We incorporate AttnNO to complement WFNO by capturing" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.182 + ], + "angle": 0, + "content": "local dependencies. Working in tandem, they learn mappings from the low-resolution input function to the high-resolution output function. Gated Fusion Mechanism optimally combines the complementary features from both operators, adaptively balancing the contributions of each to a fused feature map, which is then fed to a projection layer." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.183, + 0.906, + 0.318 + ], + "angle": 0, + "content": "Efficient implementation of the kernel integral using the Galerkin-type attention mechanism [4] has been explored in the neural operator applied to SR tasks [35, 54]. Our AttnNO is composed of bicubic interpolation, Galerkin attention, and nonlinearity, sharing an encoder with WFNO. AttnNO models local interactions in the spatial domain, focusing on the most relevant spatial regions during the convolution process. Given the complementary role of AttnNO to WFNO, we simplify its structure to improve runtime." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.319, + 0.906, + 0.544 + ], + "angle": 0, + "content": "While previous works have applied gating mechanisms in different contexts, our approach differs significantly. Zheng et al. [60] use gating within recurrent CRF networks primarily for semantic segmentation, controlling the information flow for boundary refinement rather than fusing feature maps with distinct representations. Hu et al. [16] introduced channel-wise gating in Squeeze-and-Excitation (SE) blocks, focusing on adaptively recalibrating feature channels within a single network stream. In contrast, our Gated Fusion Mechanism applies spatial gating to integrate global dependencies captured by WFNO and local information from AttnNO. This mechanism adaptively combines both operators' feature maps, enhancing high-resolution image reconstruction by balancing global and local contributions at each spatial location." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.544, + 0.906, + 0.667 + ], + "angle": 0, + "content": "Let \\(\\mathbf{v}_{\\mathrm{WFNO}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}\\) and \\(\\mathbf{v}_{\\mathrm{AttnNO}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}\\) denote the feature maps obtained from WFNO and AttnNO, respectively, where \\(B\\) is the batch size, \\(H\\) and \\(W\\) are the height and width of the feature maps, and \\(C\\) is the number of channels. We first concatenate the feature maps along the channel dimension and pass them through a convolutional layer followed by a sigmoid activation to produce a gating map \\(\\mathbf{G} \\in \\mathbb{R}^{B \\times H \\times W \\times 1}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.679, + 0.905, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\mathbf {G} = \\sigma \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(\\left[ \\mathbf {v} _ {\\mathrm {W F N O}}, \\mathbf {v} _ {\\mathrm {A t t n N O}} \\right]\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.708, + 0.905, + 0.768 + ], + "angle": 0, + "content": "where \\([\\cdot ,\\cdot ]\\) denotes concatenation along the channel dimension; \\(\\mathrm{Conv}_{1\\times 1}\\) is a \\(1\\times 1\\) convolutional layer that reduces the concatenated features to a single-channel gating map; \\(\\sigma (\\cdot)\\) is the sigmoid activation function applied element-wise." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.768, + 0.905, + 0.799 + ], + "angle": 0, + "content": "The fused feature map \\(\\mathbf{v}_{\\mathrm{fused}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}\\) is the element-wise weighted sum of the two feature maps:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.812, + 0.905, + 0.829 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} _ {\\text {f u s e d}} = \\mathbf {G} \\odot \\mathbf {v} _ {\\mathrm {W F N O}} + (1 - \\mathbf {G}) \\odot \\mathbf {v} _ {\\mathrm {A t t n N O}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.901 + ], + "angle": 0, + "content": "where \\(\\odot\\) denotes element-wise multiplication, and subtraction is performed element-wise. The gating map \\(\\mathbf{G}\\) is broadcast across the channel dimension to match the dimensions of the feature maps." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "153" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.243 + ], + "angle": 0, + "content": "Gated Fusion Mechanism brings two advantages compared to a naive concatenation strategy: (i) Captures complementary Information: WFNO models global dependencies through spectral convolutions, effectively modeling long-range interactions and overall structure. In contrast, AttnNO excels at capturing local dependencies and fine-grained details via attention mechanisms. (ii) Balances contributions dynamically: Gated Fusion Mechanism elicits the importance of each feature map at each spatial location, dynamically balancing global and local information." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.252, + 0.483, + 0.267 + ], + "angle": 0, + "content": "3.4. Forward Diffusion Process and Noise Schedule" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.275, + 0.484, + 0.365 + ], + "angle": 0, + "content": "Motivation. NOs are well-suited for SR tasks due to their inherent resolution invariance and their ability to model global dependencies efficiently. Diffusion models can iteratively refine a low-resolution image to a high-resolution one, capturing the complex conditional distribution of high-resolution images given low-resolution inputs." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.365, + 0.483, + 0.426 + ], + "angle": 0, + "content": "DiffFNO leverages the strengths of both frameworks. WFNO is a powerful mechanism for handling arbitrary resolutions and capturing high-frequency details, while the diffusion process iteratively improves reconstruction output." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.426, + 0.484, + 0.562 + ], + "angle": 0, + "content": "In our framework, the forward diffusion process models the degradation of HR images to LR images, which in our case is primarily due to downscaling. To incorporate this degradation into the diffusion model framework, we define a forward process that simulates the downscaling effect over continuous time \\( t \\in [0,T] \\). At, the image \\( \\mathbf{x}_T \\) closely resemble the observed LR image \\( \\mathbf{x}_{\\mathrm{LR}} \\) after significant degradation. We adopt a modified variance-preserving (VP) stochastic differential equation (SDE):" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.572, + 0.483, + 0.6 + ], + "angle": 0, + "content": "\\[\nd \\mathbf {x} _ {t} = - \\frac {1}{2} \\beta (t) (\\mathbf {x} _ {t} - \\mathbf {D x} _ {t}) d t + \\sqrt {\\beta (t)} d \\mathbf {w}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.61, + 0.483, + 0.655 + ], + "angle": 0, + "content": "where \\(\\beta (t)\\) is the noise schedule; \\(\\mathbf{D}\\) is the downsampling operator that reduces the resolution of the image; \\(d\\mathbf{w}\\) is the standard Wiener process." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.655, + 0.483, + 0.732 + ], + "angle": 0, + "content": "In this formulation, the term \\(\\mathbf{x} - \\mathbf{D}\\mathbf{x}\\) quantifies the high-frequency details lost during downscaling. The drift term \\(-\\frac{1}{2}\\beta(t)(\\mathbf{x} - \\mathbf{D}\\mathbf{x})dt\\) models the gradual removal of these details, while the diffusion term \\(\\sqrt{\\beta(t)}d\\mathbf{w}\\) adds Gaussian noise to simulate further degradation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.733, + 0.483, + 0.779 + ], + "angle": 0, + "content": "Noise Schedule \\(\\beta (t)\\). We define the noise schedule \\(\\beta (t)\\) as a simple and effective linear function increasing over the time interval \\([0,T]\\):" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.788, + 0.483, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\beta (t) = \\beta_ {\\min } + \\left(\\beta_ {\\max } - \\beta_ {\\min }\\right) \\cdot \\frac {t}{T}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.483, + 0.871 + ], + "angle": 0, + "content": "where \\(\\beta_{\\mathrm{min}} = 0.1\\) and \\(\\beta_{\\mathrm{max}} = 20\\). This linear schedule ensures a gradual increase in the degradation strength from minimal degradation at \\(t = 0\\) to maximum degradation at \\(t = T\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Relation to Image Degradation. At each time \\( t \\), the image \\( \\mathbf{x}_t \\) progressively loses high-frequency details due to the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.182 + ], + "angle": 0, + "content": "drift toward \\(\\mathbf{D}\\mathbf{x}_t\\), the downscaled version of the image. The added Gaussian noise further simulates the information loss inherent in downscaling. At \\(t = T\\), the image \\(\\mathbf{x}_T\\) approximates the observed low-resolution image \\(\\mathbf{x}_{\\mathrm{LR}}\\). The reverse diffusion process then aims to recover the high-resolution image \\(\\mathbf{x}_0\\) (i.e. \\(\\mathbf{x}_{\\mathrm{HR}}\\)) from \\(\\mathbf{x}_T\\) by reversing the degradation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.183, + 0.905, + 0.273 + ], + "angle": 0, + "content": "Choice of \\(\\beta(t)\\). The linear noise schedule is chosen for its simplicity and effectiveness. It provides a straightforward way to control the rate of degradation over time. Parameters \\(\\beta_{\\mathrm{min}}\\) and \\(\\beta_{\\mathrm{max}}\\) are selected to balance the trade-off between sufficient degradation (to simulate downscaling) and numerical stability of the diffusion process." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.274, + 0.905, + 0.32 + ], + "angle": 0, + "content": "Downsampling Operator D. The operator D is defined to reduce the spatial dimensions of the image by the desired scaling factor. We use bicubic downsampling." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.331, + 0.704, + 0.347 + ], + "angle": 0, + "content": "3.5. Adaptive Time-Step" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.355, + 0.906, + 0.492 + ], + "angle": 0, + "content": "The standard reverse diffusion process is stochastic and requires a large number of sampling steps, making it computationally expensive. To accelerate inference, we reformulate the reverse diffusion as a deterministic Ordinary Differential Equation (ODE), allowing us to use advanced ODE solvers for faster sampling. The ODE solver integrates the reverse diffusion process, and its output is the super-resolved image. The reverse diffusion process can be described by a Stochastic Differential Equation (SDE) [46]:" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.518, + 0.905, + 0.537 + ], + "angle": 0, + "content": "\\[\nd \\mathbf {x} = [ f (\\mathbf {x}, t) - g (t) ^ {2} \\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}) ] d t + g (t) d \\bar {\\mathbf {w}} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.548, + 0.906, + 0.638 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}\\) is the data; \\(t\\) is the time variable; \\(f(\\mathbf{x}, t)\\) and \\(g(t)\\) are drift and diffusion coefficients; \\(\\nabla_{\\mathbf{x}} \\log p_t(\\mathbf{x})\\) is the score function; \\(\\bar{\\mathbf{w}}\\) is the reverse-time Wiener process. By removing the stochastic term, we obtain the probability flow ODE, which deterministically transports the data from the noise distribution to the data distribution." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.64, + 0.905, + 0.806 + ], + "angle": 0, + "content": "Our ATS ODE solver comprises three key components: 1. Adaptive Time Step Selection Using a Learned Function. Optimizing the allocation of time steps based on data characteristics has been explored in previous works [28, 53]. We discretize the time interval \\([0,T]\\) into \\(N\\) non-uniform time steps \\(\\{t_i\\}_{i = 0}^N\\), where \\(t_0 = 0\\) and \\(t_N = T\\). We introduce a learned function \\(\\phi_{\\psi}(t)\\) as a weighted sum of polynomial basis functions, where the weight is parameterized by a set of learnable coefficients \\(\\psi = \\{\\psi_{1},\\psi_{2},\\dots ,\\psi_{K}\\}\\), which adaptively determines the distribution of time steps based on the data characteristics." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.807, + 0.905, + 0.855 + ], + "angle": 0, + "content": "Parameterization of \\(\\phi_{\\psi}(t)\\). We define \\(\\phi_{\\psi}(t)\\) as a normalized weighted sum of \\(K\\) predefined monotonically increasing basis functions \\(\\{\\phi_k(t)\\}_{k=1}^K\\):" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.865, + 0.905, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\phi_ {\\psi} (t) = \\frac {\\sum_ {k = 1} ^ {K} \\psi_ {k} \\phi_ {k} (t)}{\\sum_ {k = 1} ^ {K} \\psi_ {k} \\phi_ {k} (T)}, \\quad \\psi_ {k} = \\exp (\\omega_ {k}), \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "154" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.091, + 0.482, + 0.182 + ], + "angle": 0, + "content": "where each basis function \\(\\phi_k(t) = t^k\\) for \\(k = 1,2,\\ldots ,K\\) is polynomial. \\(\\omega_{k}\\) are unconstrained learnable parameters that ensure \\(\\psi_{k}\\geq 0\\) through the exponential mapping. We set \\(K = 3\\) to balance model flexibility with computational efficiency. This setup allows \\(\\phi_{\\psi}(t)\\) to capture nonlinear timestep distributions without excessive complexity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.182, + 0.482, + 0.228 + ], + "angle": 0, + "content": "Selection of Time Steps. Using the learned function \\(\\phi_{\\psi}(t)\\), we map uniformly spaced normalized values \\(s_i = \\frac{i}{N}\\) to non-uniform time steps \\(t_i\\):" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.238, + 0.482, + 0.271 + ], + "angle": 0, + "content": "\\[\nt _ {i} = \\phi_ {\\psi} ^ {- 1} \\left(s _ {i}\\right) = \\phi_ {\\psi} ^ {- 1} \\left(\\frac {i}{N}\\right), \\quad i = 0, 1, \\dots , N \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.28, + 0.482, + 0.311 + ], + "angle": 0, + "content": "Since \\(\\phi_{\\psi}(t)\\) is monotonically increasing, its inverse function \\(\\phi_{\\psi}^{-1}(s)\\) exists and can be efficiently computed." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.312, + 0.482, + 0.372 + ], + "angle": 0, + "content": "2. Neural Operator Score Network. The score function, representing the gradient of the log probability density \\(\\log p_t(\\mathbf{x})\\), is approximated using a neural network \\(s_\\theta(\\mathbf{x}, t)\\) parameterized by \\(\\theta\\):" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.382, + 0.482, + 0.4 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}) \\approx s _ {\\theta} (\\mathbf {x}, t). \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.41, + 0.482, + 0.544 + ], + "angle": 0, + "content": "In our architecture, \\( s_{\\theta} \\) consists of: (i) An encoder that extracts features from \\( \\mathbf{x}_{\\mathrm{LR}} \\); (ii) WFNO for capturing global dependencies and high-frequency details; (iii) AttnNO for modeling local dependencies and fine-grained structures; (iv) Gated Fusion Mechanism to dynamically combine features; (v) Time embedding \\( \\mathbf{e}(t) \\) incorporating the time variable \\( t \\) into our neural network \\( s_{\\theta}(\\mathbf{x},t) \\) using sinusoidal positional embeddings [14, 50], concatenating it and encoded features along the channel dimension." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.546, + 0.482, + 0.59 + ], + "angle": 0, + "content": "3. Efficient Solver. We solve the reverse-time stochastic differential equation (SDE) of the diffusion process, transformed into an ODE:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.598, + 0.482, + 0.628 + ], + "angle": 0, + "content": "\\[\n\\frac {d \\mathbf {x}}{d t} = f (\\mathbf {x}, t) - \\frac {1}{2} g (t) ^ {2} \\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.638, + 0.482, + 0.683 + ], + "angle": 0, + "content": "where \\(\\mathbf{x} \\in \\mathbb{R}^d\\) is the image estimate at time \\(t\\) in the reverse diffusion process; \\(f(\\mathbf{x}, t)\\) and \\(g(t)\\) are coefficients derived from the forward diffusion process." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.684, + 0.482, + 0.713 + ], + "angle": 0, + "content": "For the Variance Preserving (VP) SDE commonly used in diffusion models, the coefficients are defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.722, + 0.482, + 0.752 + ], + "angle": 0, + "content": "\\[\nf (\\mathbf {x}, t) = - \\frac {1}{2} \\beta (t) \\mathbf {x}, \\quad g (t) = \\sqrt {\\beta (t)}, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.761, + 0.482, + 0.822 + ], + "angle": 0, + "content": "where \\(\\beta (t)\\) is a predefined noise schedule specific to the diffusion process and is consistent with our DiffFNO. By substituting the score function approximation from Eq. (14), we define the approximate drift function:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.831, + 0.482, + 0.861 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta} (\\mathbf {x}, t) = f (\\mathbf {x}, t) - \\frac {1}{2} g (t) ^ {2} s _ {\\theta} (\\mathbf {x}, t). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.87, + 0.482, + 0.901 + ], + "angle": 0, + "content": "The adaptive time steps \\(\\{t_i\\}_{i = 0}^N\\) discretize the ODE. We apply the Runge-Kutta 4th-order (RK4) method, as it" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.121 + ], + "angle": 0, + "content": "balances computational cost and accuracy, requiring fewer steps than lower-order methods while retaining precision." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.122, + 0.905, + 0.227 + ], + "angle": 0, + "content": "The benefits of ATS are threefold: (i) Deterministic Sampling: It consistently produces the same results for identical inputs, improving reproducibility. (ii) Reduced Computation: Fewer sampling steps significantly decrease inference time. (iii) High-Quality Reconstruction: It maintains high-quality reconstruction by efficiently allocating computational resources." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.241, + 0.644, + 0.258 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.267, + 0.905, + 0.327 + ], + "angle": 0, + "content": "Datasets and Evaluation Metrics. We use the DIV2K [1] dataset for training. For evaluation, we use the DIV2K validation set and four standard datasets: Set5 [3], Set14 [56], BSD100 [36], and Urban100 [18]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.328, + 0.905, + 0.432 + ], + "angle": 0, + "content": "We evaluate our model on upscaling factors of \\(\\times 2\\), \\(\\times 3\\), \\(\\times 4\\), \\(\\times 6\\), \\(\\times 8\\), and \\(\\times 12\\). Notably, scales \\(\\times 6\\), \\(\\times 8\\), and \\(\\times 12\\) are outside the training distribution, as the training scales are uniformly sampled from \\(\\times 1\\) to \\(\\times 4\\). This setup assesses our model's ability to generalize to arbitrary scales. We use Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) as our evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.433, + 0.906, + 0.553 + ], + "angle": 0, + "content": "Quantitative Results. Building on the quantitative gains of our model, we also present qualitative results to illustrate the visual improvements achieved. We compare our proposed DiffFNO model with several SOTA arbitrary-scale SR methods, including Meta-SR [17], LIIF [7], LTE [24], SRNO [54], LIT [5], LMI [10], and HiNOTE [35]. All models are trained on the DIV2K dataset with identical settings to ensure a fair comparison in Tables 1 and 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Among the compared methods, Meta-SR performs adequately at lower scales but struggles at higher scaling factors due to its generalized approach that lacks specialized mechanisms for fine detail capture. LIIF and LTE improve upon Meta-SR by using local implicit functions and frequency-based estimations, respectively, which enhance high-frequency texture representation. However, they still face limitations in capturing non-periodic textures and high-frequency details, resulting in blurred textures at larger scales. LIT and LMI further advance performance by integrating attention mechanisms and MLP-mixer architectures, effectively preserving high-frequency textures and handling diverse scales, but they may not generalize well across datasets with varying distributions. SRNO and HiNOTE employ neural operator frameworks with attention mechanisms and frequency-aware loss priors to better capture global spatial properties and enhance high-frequency detail reconstruction. We observed mixed results between SRNO and HiNOTE: at certain scaling factors, one outperforms the other, indicating their varying strengths at different resolutions. Overall, their neural operator foundation improves the handling of arbitrary scaling but may increase computational demands." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "155" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.402, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.195, + 0.246, + 0.312, + 0.259 + ], + "angle": 0, + "content": "BSD100 [36], \\(\\times 12\\)" + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.091, + 0.514, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.446, + 0.161, + 0.493, + 0.172 + ], + "angle": 0, + "content": "Bicubic" + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.174, + 0.514, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.441, + 0.245, + 0.498, + 0.258 + ], + "angle": 0, + "content": "LMI [10]" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.091, + 0.605, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.16, + 0.603, + 0.173 + ], + "angle": 0, + "content": "Meta-SR [17]" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.174, + 0.606, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.245, + 0.597, + 0.258 + ], + "angle": 0, + "content": "SRNO [54]" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.091, + 0.698, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.628, + 0.16, + 0.682, + 0.173 + ], + "angle": 0, + "content": "LTE [24]" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.174, + 0.698, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.614, + 0.245, + 0.696, + 0.258 + ], + "angle": 0, + "content": "HiNOTE [35]" + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.091, + 0.795, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.727, + 0.161, + 0.776, + 0.173 + ], + "angle": 0, + "content": "LIIF [7]" + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.174, + 0.795, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.245, + 0.799, + 0.258 + ], + "angle": 0, + "content": "DiffFNO (ours)" + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.091, + 0.893, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.826, + 0.161, + 0.871, + 0.173 + ], + "angle": 0, + "content": "LIT [5]" + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.174, + 0.893, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.839, + 0.246, + 0.86, + 0.257 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.26, + 0.402, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.418, + 0.318, + 0.43 + ], + "angle": 0, + "content": "Urban100 [18], \\(\\times 7.6\\)" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.262, + 0.515, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.448, + 0.333, + 0.495, + 0.344 + ], + "angle": 0, + "content": "Bicubic" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.346, + 0.515, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.442, + 0.416, + 0.5, + 0.43 + ], + "angle": 0, + "content": "LMI [10]" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.262, + 0.607, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.333, + 0.606, + 0.345 + ], + "angle": 0, + "content": "Meta-SR [17]" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.346, + 0.607, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.528, + 0.416, + 0.598, + 0.43 + ], + "angle": 0, + "content": "SRNO [54]" + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.262, + 0.7, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.333, + 0.683, + 0.345 + ], + "angle": 0, + "content": "LTE [24]" + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.346, + 0.7, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.616, + 0.416, + 0.698, + 0.429 + ], + "angle": 0, + "content": "HiNOTE [35]" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.262, + 0.797, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.333, + 0.777, + 0.345 + ], + "angle": 0, + "content": "LIIF [7]" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.346, + 0.797, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.416, + 0.801, + 0.429 + ], + "angle": 0, + "content": "DiffFNO (ours)" + }, + { + "type": "image", + "bbox": [ + 0.808, + 0.262, + 0.895, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.333, + 0.872, + 0.345 + ], + "angle": 0, + "content": "LIT [5]" + }, + { + "type": "image", + "bbox": [ + 0.808, + 0.346, + 0.895, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.84, + 0.416, + 0.86, + 0.428 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.444, + 0.907, + 0.471 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison on integer and continuous super-resolution scales. The models use RDN [58] as their encoder (except HiNOTE [35], has its own). In the HR image, the cropped patch is outlined in green." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.473, + 0.903, + 0.729 + ], + "angle": 0, + "content": "
    Modelx2x3x4x6x8x12
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    EDSR-MetaSR [17]33.320.91330.100.80028.230.83026.100.79224.770.74223.950.720
    EDSR-LTE [24]33.830.92130.500.88028.790.85226.550.80025.050.76024.200.736
    EDSR-LIIF [7]34.360.92530.940.88529.310.85527.020.81425.440.77124.320.743
    EDSR-LIT [5]34.810.92831.390.89029.700.86027.440.81525.780.77524.690.745
    EDSR-LMI [10]35.400.93031.880.89530.400.86527.950.82026.160.78025.560.750
    EDSR-SRNO [54]34.850.92831.450.89030.050.86327.360.81026.000.77225.910.760
    EDSR-DiffFNO (Ours)35.720.93232.500.90530.880.87028.290.83026.780.79026.480.775
    HiNOTE†[35]35.290.93131.900.89530.460.84227.830.79926.410.77226.230.732
    RDN-MetaSR [17]33.500.92030.320.89328.410.86126.290.81024.900.78024.010.790
    RDN-LTE [24]33.980.92230.650.88228.940.85226.700.80225.200.76224.350.732
    RDN-LIIF [7]34.510.92731.090.88729.460.85727.170.81225.590.77224.470.742
    RDN-LIT [5]34.960.93031.540.89229.850.86227.590.81725.930.77724.840.747
    RDN-LMI [10]35.550.93232.030.89730.550.86728.100.82226.310.78225.710.752
    RDN-SRNO [54]35.000.93031.600.89230.200.86227.510.81226.150.77226.060.762
    RDN-DiffFNO (Ours)35.870.93432.650.90231.030.87228.440.83226.930.79226.630.777
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.74, + 0.903, + 0.754 + ], + "angle": 0, + "content": "Table 1. PSNR/SSIM comparison on the DIV2K [1] validation set using EDSR [31] and RDN [58] encoders. HiNOTE [35] uses its own." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.767, + 0.483, + 0.887 + ], + "angle": 0, + "content": "Our DiffFNO model consistently achieves the highest PSNR and SSIM scores across all scaling factors and datasets. The performance gap widens at larger scaling factors \\((\\times 8\\) and \\(\\times 12\\)), demonstrating a superior generalization to the out-of-distribution scales. The improvements are more pronounced on complex datasets like Urban100, which contain intricate textures and structures. By combining WFNO and AttnNO features through the Gated Fusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.767, + 0.905, + 0.858 + ], + "angle": 0, + "content": "Mechanism, which adaptively balances global and local features, DiffFNO synthesizes global and local dependencies. The ATS ODE solver efficiently refines high-resolution images, further enhancing quality. This combination addresses the limitations of prior models, such as spectral bias and insufficient high-frequency detail capture." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Qualitative Results. Fig. 3 compares arbitrary-scale SR methods on a BSD100 image (scaling factor of \\(\\times 12\\)) with" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "156" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.904, + 0.231 + ], + "angle": 0, + "content": "
    ModelSet5Set14BSD100Urban100
    ×2×3×4×6×8×2×3×4×6×8×2×3×4×6×8×2×3×4×6×8
    MetaSR [17]37.5034.0531.5228.2326.0233.5130.0328.0225.5324.0231.0228.0526.5224.8223.5232.0228.0325.8223.5222.03
    LIIF [7]38.0234.4232.0428.5726.2534.0330.4328.4325.8424.3331.5228.5527.0325.0323.8332.5228.5326.0323.8322.33
    LTE [24]38.2134.6332.2528.7626.4434.2230.6528.6426.0524.5231.7128.7327.2325.2324.0332.7228.7526.2324.0322.53
    SRNO [54]38.3234.8432.6929.3827.2834.2730.7128.9726.7625.2632.4329.3727.8326.0424.9933.3329.1426.9824.4323.02
    LIT [5]38.5335.0232.8229.5127.4234.4430.8329.0326.8225.3332.5229.5127.9226.1225.0133.4229.2227.0224.5223.12
    LMI [10]38.7235.1432.9529.6327.5534.6331.0229.2427.0525.5532.7229.7428.0426.2525.1433.6229.4427.2424.6323.23
    HNOTE [35]39.0135.2233.0829.8527.7435.0231.2529.5527.3525.8533.0230.0528.1526.3525.2534.0329.8327.5524.7323.34
    DiffFNO (Ours)39.7235.3033.1630.2327.9336.0131.5430.2227.5826.0233.5630.2428.2126.4525.3034.1929.9927.7424.8023.35
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.242, + 0.905, + 0.269 + ], + "angle": 0, + "content": "Table 2. PSNR comparison on four benchmark datasets: Set5 [3], Set14 [56], BSD100 [36], and Urban100 [18]. All models use RDN [58] as their encoder, besides HiNOTE [35] which has its own." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.271, + 0.905, + 0.417 + ], + "angle": 0, + "content": "
    Model×2×3×4×6×8×12InferenceSteps
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    SRNO [54]33.810.92030.530.88028.740.85026.590.80025.100.76024.180.730147-
    FNO [26]34.360.92530.940.88529.310.85527.020.81025.440.77024.320.74085-
    WFNO34.810.92831.390.88829.700.85827.440.81525.780.77524.690.74597-
    WFNO-AttnNO35.400.93031.880.89230.400.86227.950.82026.160.78025.560.7501391000
    DiffFNO(-w, -a, -s)34.850.92831.450.89030.050.86027.360.81526.000.77525.910.7602041000
    DiffFNO(-a, -s)35.290.93031.900.89330.460.86327.830.82026.410.78026.230.7652311000
    DiffFNO(-s)35.700.93232.480.89630.850.86628.260.82526.750.78526.450.7702661000
    DiffFNO35.720.93232.500.90030.880.87028.290.83026.780.79026.480.77514130
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.428, + 0.905, + 0.456 + ], + "angle": 0, + "content": "Table 3. Ablation study of variants of DiffFNO on the DIV2K [1] validation set. All use EDSR-baseline [31] backbone as their encoder. Inference times are measured in milliseconds (ms). WFNO-AttnNO has Gated Fusion Mechanism." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.469, + 0.483, + 0.65 + ], + "angle": 0, + "content": "fine-grained details like animal fur and rock textures and an Urban100 (continuous scaling factor of \\(\\times 7.6\\)) image featuring large structures and fine local details such as reflections on the grass. SRNO and HiNOTE capture multiscale details effectively, from the animal's body to tiny gaps between glass panels. However, DiffFNO reconstructs crisper edges with fewer artifacts, enhancing texture in animal fur pattern and reflections. WFNO captures large-scale patterns, while AttnNO and Gated Fusion Mechanism preserve intricate textures. This multiscale approach followed by a diffusion process enhanced by the ATS's ODE solver further reduces visual artifacts." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.655, + 0.483, + 0.867 + ], + "angle": 0, + "content": "Ablation Studies. Extensive ablation studies validate the effectiveness and complementary nature of new components in DiffFNO. Table 3 reports the PSNR results on the DIV2K validation set for different model variants with scaling factors from \\(\\times 2\\) to \\(\\times 12\\). -w denotes leaving out the Mode Rebalancing (yielding the default FNO [26]). -a denotes omitting AttnNO. -s denotes the removal of ATS ODE solver. We also measure inference time by averaging over 100 runs, and report inference steps. We establish a baseline with SRNO, whose architecture is the most similar to our DiffFNO aamong the methods covered in our study. Overall, we observe notable improvements with the addition of model components. The complete DiffFNO achieves the highest PSNR and SSIM values across all upscaling factors." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Effect of Mode Rebalancing. Incorporating Mode Rebalancing into WFNO boosted performance compared to the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.469, + 0.905, + 0.498 + ], + "angle": 0, + "content": "default FNO [26], at the cost of a slightly increased number of parameters and inference time." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.5, + 0.905, + 0.59 + ], + "angle": 0, + "content": "Effect of Gated Fusion Mechanism and AttnNO. The Gated Fusion Mechanism introduces minimal computational overhead. In addition, extra computational cost incurred by Attention-based Neural Operator is effectively mitigated by running it in parallel with WFNO while employing a shared encoder." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.59, + 0.905, + 0.667 + ], + "angle": 0, + "content": "Effect of ATS ODE Solver: ATS dramatically reduces the number of inference steps from 1,000 to just 30, which substantially improves the inference time while delivering competitive performance (Tab. 3). DiffFNO outperforms the SOTA in both PSNR and inference time (Fig. 1 (a))." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.681, + 0.634, + 0.697 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.706, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We propose Diffusion Fourier Neural Opeartor (DiffFNO) for arbitrary-scale image super-resolution. DiffFNO is made of Weighted Fourier Neural Operator with a Mode Rebalancing mechanism to emphasize high-frequency details. It is complemented by a Attention-based Neural Operator through a Gated Fusion Mechanism that effectively adjusts the influence of global and local features. Image reconstruction is further refined by a diffusion process augmented with an Adaptive Time-Step ODE solver that dynamically allocates time steps, drastically cutting down inference time without compromising output quality. Experiments demonstrate DiffFNO's competitiveness in both reconstruction quality and inference time across various benchmarks, establishing a new state-of-the-art." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.945, + 0.511, + 0.956 + ], + "angle": 0, + "content": "157" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.119, + 0.188, + 0.135 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.145, + 0.483, + 0.2 + ], + "angle": 0, + "content": "[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2017. 6, 7, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.201, + 0.483, + 0.257 + ], + "angle": 0, + "content": "[2] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. Analytic-DPM: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. 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In Proceedings of the IEEE international conference on computer vision, pages 1529-1537, 2015. 4" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.482, + 0.643 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.489, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "160" + } + ] +] \ No newline at end of file diff --git a/2025/DiffFNO_ Diffusion Fourier Neural Operator/3a04b4ef-d06b-4b04-9301-be75af2eacee_origin.pdf b/2025/DiffFNO_ Diffusion Fourier Neural Operator/3a04b4ef-d06b-4b04-9301-be75af2eacee_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1ee5a681a78e7b780d45bfadc5aa5d1194844f46 --- /dev/null +++ b/2025/DiffFNO_ Diffusion Fourier Neural Operator/3a04b4ef-d06b-4b04-9301-be75af2eacee_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b3fb1837dfe91d8979e7589f216806b75386f250b0751c16dbf08d40d2b40cf6 +size 898830 diff --git a/2025/DiffFNO_ Diffusion Fourier Neural Operator/full.md b/2025/DiffFNO_ Diffusion Fourier Neural Operator/full.md new file mode 100644 index 0000000000000000000000000000000000000000..03b4a51ec1713de77aec3c1c581423e88cfa06d8 --- /dev/null +++ b/2025/DiffFNO_ Diffusion Fourier Neural Operator/full.md @@ -0,0 +1,421 @@ +# DiffFNO: Diffusion Fourier Neural Operator + +Xiaoyi Liu $^{1,*}$ Hao Tang $^{2,\dagger}$ + +$^{1}$ Washington University in St. Louis $^{2}$ Peking University + +jasonl@wustl.edu haotang@pku.edu.cn + +![](images/609f2bd51bcd6389a20a70162b9f687cf29fbaf897c28a2012f59775830eb1ed.jpg) +(a) PSNR and inference time for $\times 4$ super-resolution + +![](images/c79e23bf2ba96c66c53019cdc9a42e5649c151d673c5d66f6e8604d703b655bd.jpg) + +![](images/28e1056c8210af192a322365ae464e43a733e1c0c1c803565cd264651a66608d.jpg) +(b) DiffFNO vs SRNO [54] +Figure 1. (a) All models use the EDSR-baseline [31] encoder, except HiNOTE [35] which has its own. (b) Compared to SRNO [54], DiffFNO is strengthened by the fusion of spectral and spatial features and efficient refinement by a diffusion process. + +# Abstract + +We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly improving the reconstruction of high-frequency image details that are crucial for superresolution tasks. Gated Fusion Mechanism (GFM) adaptively complements WFNO's spectral features with spatial features from an Attention-based Neural Operator (AttnNO). This enhances the network's capability to capture both global structures and local details. Adaptive Time-Step (ATS) ODE solver, a deterministic sampling strategy, accelerates inference without sacrificing output quality by dynamically adjusting integration step sizes ATS. Extensive experiments demonstrate that DiffFNO achieves state-of-the-art (SOTA) results, outperforming existing methods across various scaling factors by a margin of 2-4 dB in + +PSNR, including those beyond the training distribution. It also achieves this at lower inference time (Fig. 1 (a)). Our approach sets a new standard in super-resolution, delivering both superior accuracy and computational efficiency. + +# 1. Introduction + +Image super-resolution (SR) reconstructs high-resolution (HR) images from low-resolution (LR) inputs, recovering lost fine details to enhance visual quality. SR is crucial for applications like medical imaging [12], satellite imagery [23, 52], and video games [38]. However, multiple HR images can correspond to the same LR input due to information loss during downsampling. This ambiguity requires algorithms capable of inferring plausible and perceptually accurate high-frequency content from limited data. + +Deep learning, particularly Convolutional Neural Networks (CNNs) [58], has significantly advanced SR. Dong et al. introduced SRCNN [9], demonstrating the effectiveness of end-to-end learning for SR. Subsequent models achieved remarkable performance using deeper architectures and at + +tention mechanisms [6, 30, 31, 34, 57]. + +Diffusion models have emerged as powerful generative frameworks modeling complex data distributions via iterative denoising processes [11, 14, 45]. Their ability to generate high-fidelity images is well-suited for inferring missing fine details. In SR, diffusion models progressively refine an LR image by modeling the conditional distribution of HR images given the LR input [15, 25, 41, 51]. This iterative process reconstructs intricate textures and high-frequency components, producing realistic outputs. + +However, diffusion models are computationally intensive due to the iterative reverse diffusion process [46]. To address this, recent research explores efficient sampling strategies to accelerate reverse diffusion. One approach is approximating the diffusion process through deterministic Ordinary Differential Equation (ODE), which can be solved in fewer steps [33]. This accelerates inference and provides consistent, reproducible results. + +Arbitrary-scale SR models [7, 17, 24], which can upsample images at user-defined scales beyond those seen in training, have gained attention in recent years. Methods involving attention mechanisms [5] and representing images as continuous functions [10] have been explored. Operator-learning methods such as Super-Resolution Neural Operators (SRNO) [54] and HiNOTE [35] have further advanced this field. However, the inherent differences between physics simulations and real-world images introduce challenges from computational demands to the difficulty in restoring high-frequency details. + +# To address these limitations, our contributions are: + +(1) We propose Weighted Fourier Neural Operator (WFNO) strengthened by iterative refinement from a diffusion framework for high-frequency reconstruction, detailed in Fig. 2. Through Mode Rebalancing (MR), WFNO learns to emphasize the most critical frequency components. This greatly enhances high-frequency image detail reconstruction, overcoming the limitations of standard FNOs and MLPs, which underrepresent such details due to mode truncation and spectral bias, respectively. (2) We develop Gated Fusion Mechanism (GFM) to dynamically adjust the influence of Fourier space features from WFNO and complementary spatial domain features from an Attention-based Neural Operator (AttnNO). AttnNO is lightweight, sharing an encoder with and running in parallel to WFNO. (3) Additionally, we present Adaptive Time-Step (ATS) ODE solver, which flexibly adjusts integration step sizes based on data characteristics by assessing the complexity of image regions, thereby reducing computational overhead without compromising quality. (4) DiffFNO achieves state-of-the-art results on multiple SR benchmarks, outperforming existing methods by 2-4 dB in PSNR in reconstruction quality. It also offers competitive inference time as Fig. 1 (a) shows. DiffFNO remains robust across various upscaling factors—even those + +unseen during training. + +# 2. Related Work + +Neural Operators and Fourier Methods. Neural Operators (NO) [22] have emerged as a powerful framework for learning mappings between infinite-dimensional function spaces, providing resolution-invariant models that generalize across different input resolutions. Unlike traditional neural networks that map finite-dimensional vectors to other vectors, neural operators learn mappings from functions to functions [27], making them well-suited for tasks involving continuous data or data at varying resolutions. + +Multi-Layer Perceptrons (MLPs) often exhibit a spectral bias, favoring low-frequency functions [39]. This limits their ability to capture fine textures and sharp edges. To overcome these limitations, techniques like positional encodings and Fourier feature mappings capture high-frequency details by embedding input coordinates into a higher-dimensional sinusoidal space, allowing the network to represent complex patterns [44, 47]. + +Fourier Neural Operator (FNO) [26] is a variant of NO that uses spectral convolution to efficiently capture global data patterns, modeling long-range dependencies with lower computational complexity than traditional CNNs. In physics and climate settings [19, 29, 55], FNOs can handle arbitrary input resolutions without retraining. Although successful, FNOs may still lose high-frequency information due to mode truncation (discarding higher-frequency Fourier modes). This loss impairs tasks such as SR that rely on detailed reconstruction [13, 48, 49]. + +The Mode Rebalancing mechanism in WFNO overcomes these limitations. Instead of being truncated, all Fourier modes are preserved, with additional learnable weights to modulate their impact on reconstruction. Fine-grained feature representation is further enhanced by AttnNO, which captures local details by processing data directly in the spatial domain + +Diffusion-Based SR and Efficient Sampling. Diffusion models have gained prominence as powerful generative models capable of producing high-quality images through iterative denoising techniques [14, 42]. In the context of SR, diffusion models have been employed to model the conditional distribution of HR images given LR inputs, achieving higher resolutions after progressive enhancement [40, 41]. + +Despite their effectiveness, diffusion models are computationally intensive due to the large number of time steps required in the reverse diffusion process. Such computational demands pose significant challenges for practical applications [20], especially in real-time or resource-constrained settings. Current solutions include: (i) Deterministic Sampling via ODE Solvers: By reformulating the stochastic reverse diffusion as a deterministic ODE, advanced ODE solvers can be employed to reduce the number of sam + +![](images/b686c698376773941977f8fe89298fcea1a039a8a18df6cd817336dfacdcdf59.jpg) +Figure 2. The proposed Diffusion Fourier Neural Opeartor (DiffFNO) architecture for arbitrary-scale super-resolution begins by lifting a low-resolution input image $\mathbf{x}_{\mathrm{LR}}(\mathbf{r})$ into a feature space using a convolutional encoder. Features extracted by the Weighted Fourier Neural Operator (WFNO) and an Attention-based Neural Operator (AttnNO) are combined using a Gated Fusion Mechanism (GFM). The fused features are then projected into RGB space, where Adaptive Time-Step (ATS) ODE solver efficiently completes the reverse diffusion process with both accuracy and speed. This pipeline generates $\mathbf{x}_{\mathrm{HR}}(\mathbf{r})$ , a high-resolution version of the input image. + +pling steps [21]. Methods like Denoising Diffusion Implicit Models (DDIM) [45] and DPM-Solver [2, 33] have demonstrated the ability to generate high-quality images with significantly fewer steps. (ii) Operator Learning for Fast Sampling: Neural operators accelerates sampling by learning the solution operator of the reverse diffusion process [8, 59]. (iii) Progressive Distillation: Training a distilled model to approximate the behavior of the full diffusion model allows faster sampling with fewer steps [37, 43]. Although effective, this method may require extensive retraining and potentially compromise image quality for increased speed. + +Applying these acceleration methods to diffusion-based SR enables faster inference while maintaining high image quality. With efficient sampling methods, diffusion models become more practical for SR tasks, balancing performance and computational efficiency [32]. + +DiffFNO adopts (i) for its simplicity and the robustness of established numerical methods. We also strength it with the ATS strategy, which adjusts integration step sizes adaptively to balance speed and quality. + +# 3. The Proposed DiffFNO + +# 3.1. Network Architecture and Novel Components + +An overview of the proposed DiffFNO is shown in Fig. 1 (b). It has three parts: (i) A CNN encoder extracts features from LR images. Unlike the simple linear transfor + +mations in standard FNO setups for physics simulations, our encoder is tailored for SR, extracting complex patterns and textures needed for high-quality reconstructions. We use the EDSR-baseline [31] and RDN models [58] in our experiments. (ii) WFNO and GFM: WFNO captures both global and local details alongside the AttnNO. GFM combines these into a unified HR feature map, which is then projected into RGB. (iii) ATS ODE solver accelerates inference speed by taking fewer, larger, and dynamically adjusted steps toward the reconstructed HR image. Fig. 2 illustrates these components in detail. + +The network minimizes the difference between the predicted image and the true image. The loss function is: + +$$ +\mathcal {L} (\theta) = \mathbb {E} _ {t, \mathbf {x} _ {0}} \left[ \| s _ {\theta} \left(\mathbf {x} _ {t}, t\right) - \nabla_ {\mathbf {x} _ {t}} \log p _ {t} \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {0}\right) \| _ {2} ^ {2} \right], \tag {1} +$$ + +where $\mathbf{x}_t$ (i.e. $\mathbf{x}_{\mathrm{LR}}$ ) is obtained by adding noise to $\mathbf{x}_0$ (i.e. $\mathbf{x}_{\mathrm{HR}}$ ). $s_{\theta}(\mathbf{x}_t, t)$ is the neural network approximating the true score function. $\nabla \mathbf{x}_t \log p_t(\mathbf{x}_t | \mathbf{x}_0)$ is the true score function. + +# 3.2. Weighted Fourier Neural Operator + +The Fourier Neural Operator (FNO) [26] is an efficient NO variant designed to learn mappings between function spaces. It operates directly on inputs of arbitrary resolutions, performing upscaling by mapping low-resolution inputs to high-resolution outputs. It first transforms the input data into the frequency domain, applies the learned filters, and then transforms the data back to the spatial domain. + +Spectral convolution and mode truncation greatly enhance computational efficiency. + +Let $\mathbf{x}_{\mathrm{LR}}(\mathbf{r})$ denote the low-resolution input function (e.g., an image), where $\mathbf{r} \in \mathbb{R}^2$ represents spatial coordinates. The goal is to learn an operator $\mathcal{G}$ such that: + +$$ +\mathbf {x} _ {\mathrm {H R}} (\mathbf {r}) = \mathcal {G} \left[ \mathbf {x} _ {\mathrm {L R}} (\mathbf {r}) \right], \tag {2} +$$ + +where $\mathbf{x}_{\mathrm{HR}}(\mathbf{r})$ is the output function (e.g., the super-resolved image). The FNO models $\mathcal{G}$ by stacking: + +$$ +\mathbf {v} _ {l + 1} (\mathbf {r}) = \sigma \left(\mathcal {W} _ {l} \mathbf {v} _ {l} (\mathbf {r}) + \mathcal {K} _ {l} \mathbf {v} _ {l} (\mathbf {r})\right), \tag {3} +$$ + +where $\mathbf{v}_l(\mathbf{r})$ is the feature representation at layer $l$ evaluated at spatial location $\mathbf{r}$ , and $\mathbf{v}_{l + 1}(\mathbf{r})$ is its updated representation in the following layer; $\sigma$ is a nonlinear activation function; $\mathcal{W}_l$ is a linear transformation. $\kappa_{l}$ , the integral operator at layer $l$ , transforms the features into the Fourier domain. Fourier modes are then truncated for computational efficiency. Global convolution is performed with a pointwise multiplication between the transformed features and the learned Fourier coefficients. + +$$ +\mathcal {K} _ {l} \mathbf {v} _ {l} (\mathbf {r}) = \mathcal {F} ^ {- 1} \left(\mathbf {P} _ {l} (\boldsymbol {\xi}) \cdot \mathcal {F} [ \mathbf {v} _ {l} ] (\boldsymbol {\xi})\right), \tag {4} +$$ + +where $\mathcal{F}$ and $\mathcal{F}^{-1}$ denote the Fourier and inverse Fourier transforms, respectively. $\xi$ is the frequency domain variables. $\mathcal{F}[\mathbf{v}_l](\pmb {\xi})$ is the Fourier transform of $\mathbf{v}_l$ , evaluated at frequency $\pmb{\xi}$ . $\mathbf{P}_l(\pmb {\xi})$ is a complex-valued tensor of learnable parameters representing the Fourier domain filters. + +However, mode truncation underrepresents high-frequency components that are critical to SR of real-world images. To address this limitation, we introduce Mode Rebalancing. A learned weighting function $\mathbf{w}_l(\boldsymbol {\xi})$ is applied to the Fourier modes to amplify or attenuate specific frequency components. It is defined at layer $l$ as: + +$$ +\mathbf {w} _ {l} (\boldsymbol {\xi}) = 1 + \gamma_ {l} \cdot \| \boldsymbol {\xi} \| ^ {\alpha}, \tag {5} +$$ + +where $\gamma_{l}$ is a learnable scalar parameter at layer $l$ that controls the strength of the weighting; $\alpha$ is a hyperparameter (0.7 in our experiments or optionally a learnable parameter) that determines how the weight scales with the frequency magnitude $\|\pmb{\xi}\|$ . $\mathbf{w}(\pmb{\xi})$ assigns higher weights to higher frequencies when $\alpha > 0$ , thus emphasizing high-frequency components. This yields an updated $\mathcal{K}_{l}$ : + +$$ +\mathcal {K} _ {l} \mathbf {v} _ {l} (\mathbf {r}) = \mathcal {F} ^ {- 1} \left(\mathbf {w} _ {l} (\boldsymbol {\xi}) \cdot \mathbf {P} _ {l} (\boldsymbol {\xi}) \cdot \mathcal {F} [ \mathbf {v} _ {l} ] (\boldsymbol {\xi})\right). \tag {6} +$$ + +# 3.3. Gated Fusion Mechanism + +While WFNO excels at capturing global dependencies through spectral convolutions, it may not fully exploit local interactions critical for detailed image reconstruction. We incorporate AttnNO to complement WFNO by capturing + +local dependencies. Working in tandem, they learn mappings from the low-resolution input function to the high-resolution output function. Gated Fusion Mechanism optimally combines the complementary features from both operators, adaptively balancing the contributions of each to a fused feature map, which is then fed to a projection layer. + +Efficient implementation of the kernel integral using the Galerkin-type attention mechanism [4] has been explored in the neural operator applied to SR tasks [35, 54]. Our AttnNO is composed of bicubic interpolation, Galerkin attention, and nonlinearity, sharing an encoder with WFNO. AttnNO models local interactions in the spatial domain, focusing on the most relevant spatial regions during the convolution process. Given the complementary role of AttnNO to WFNO, we simplify its structure to improve runtime. + +While previous works have applied gating mechanisms in different contexts, our approach differs significantly. Zheng et al. [60] use gating within recurrent CRF networks primarily for semantic segmentation, controlling the information flow for boundary refinement rather than fusing feature maps with distinct representations. Hu et al. [16] introduced channel-wise gating in Squeeze-and-Excitation (SE) blocks, focusing on adaptively recalibrating feature channels within a single network stream. In contrast, our Gated Fusion Mechanism applies spatial gating to integrate global dependencies captured by WFNO and local information from AttnNO. This mechanism adaptively combines both operators' feature maps, enhancing high-resolution image reconstruction by balancing global and local contributions at each spatial location. + +Let $\mathbf{v}_{\mathrm{WFNO}} \in \mathbb{R}^{B \times H \times W \times C}$ and $\mathbf{v}_{\mathrm{AttnNO}} \in \mathbb{R}^{B \times H \times W \times C}$ denote the feature maps obtained from WFNO and AttnNO, respectively, where $B$ is the batch size, $H$ and $W$ are the height and width of the feature maps, and $C$ is the number of channels. We first concatenate the feature maps along the channel dimension and pass them through a convolutional layer followed by a sigmoid activation to produce a gating map $\mathbf{G} \in \mathbb{R}^{B \times H \times W \times 1}$ : + +$$ +\mathbf {G} = \sigma \left(\operatorname {C o n v} _ {1 \times 1} \left(\left[ \mathbf {v} _ {\mathrm {W F N O}}, \mathbf {v} _ {\mathrm {A t t n N O}} \right]\right)\right), \tag {7} +$$ + +where $[\cdot ,\cdot ]$ denotes concatenation along the channel dimension; $\mathrm{Conv}_{1\times 1}$ is a $1\times 1$ convolutional layer that reduces the concatenated features to a single-channel gating map; $\sigma (\cdot)$ is the sigmoid activation function applied element-wise. + +The fused feature map $\mathbf{v}_{\mathrm{fused}} \in \mathbb{R}^{B \times H \times W \times C}$ is the element-wise weighted sum of the two feature maps: + +$$ +\mathbf {v} _ {\text {f u s e d}} = \mathbf {G} \odot \mathbf {v} _ {\mathrm {W F N O}} + (1 - \mathbf {G}) \odot \mathbf {v} _ {\mathrm {A t t n N O}}, \tag {8} +$$ + +where $\odot$ denotes element-wise multiplication, and subtraction is performed element-wise. The gating map $\mathbf{G}$ is broadcast across the channel dimension to match the dimensions of the feature maps. + +Gated Fusion Mechanism brings two advantages compared to a naive concatenation strategy: (i) Captures complementary Information: WFNO models global dependencies through spectral convolutions, effectively modeling long-range interactions and overall structure. In contrast, AttnNO excels at capturing local dependencies and fine-grained details via attention mechanisms. (ii) Balances contributions dynamically: Gated Fusion Mechanism elicits the importance of each feature map at each spatial location, dynamically balancing global and local information. + +# 3.4. Forward Diffusion Process and Noise Schedule + +Motivation. NOs are well-suited for SR tasks due to their inherent resolution invariance and their ability to model global dependencies efficiently. Diffusion models can iteratively refine a low-resolution image to a high-resolution one, capturing the complex conditional distribution of high-resolution images given low-resolution inputs. + +DiffFNO leverages the strengths of both frameworks. WFNO is a powerful mechanism for handling arbitrary resolutions and capturing high-frequency details, while the diffusion process iteratively improves reconstruction output. + +In our framework, the forward diffusion process models the degradation of HR images to LR images, which in our case is primarily due to downscaling. To incorporate this degradation into the diffusion model framework, we define a forward process that simulates the downscaling effect over continuous time $t \in [0,T]$ . At, the image $\mathbf{x}_T$ closely resemble the observed LR image $\mathbf{x}_{\mathrm{LR}}$ after significant degradation. We adopt a modified variance-preserving (VP) stochastic differential equation (SDE): + +$$ +d \mathbf {x} _ {t} = - \frac {1}{2} \beta (t) (\mathbf {x} _ {t} - \mathbf {D x} _ {t}) d t + \sqrt {\beta (t)} d \mathbf {w}, \tag {9} +$$ + +where $\beta (t)$ is the noise schedule; $\mathbf{D}$ is the downsampling operator that reduces the resolution of the image; $d\mathbf{w}$ is the standard Wiener process. + +In this formulation, the term $\mathbf{x} - \mathbf{D}\mathbf{x}$ quantifies the high-frequency details lost during downscaling. The drift term $-\frac{1}{2}\beta(t)(\mathbf{x} - \mathbf{D}\mathbf{x})dt$ models the gradual removal of these details, while the diffusion term $\sqrt{\beta(t)}d\mathbf{w}$ adds Gaussian noise to simulate further degradation. + +Noise Schedule $\beta (t)$ . We define the noise schedule $\beta (t)$ as a simple and effective linear function increasing over the time interval $[0,T]$ : + +$$ +\beta (t) = \beta_ {\min } + \left(\beta_ {\max } - \beta_ {\min }\right) \cdot \frac {t}{T}, \tag {10} +$$ + +where $\beta_{\mathrm{min}} = 0.1$ and $\beta_{\mathrm{max}} = 20$ . This linear schedule ensures a gradual increase in the degradation strength from minimal degradation at $t = 0$ to maximum degradation at $t = T$ . + +Relation to Image Degradation. At each time $t$ , the image $\mathbf{x}_t$ progressively loses high-frequency details due to the + +drift toward $\mathbf{D}\mathbf{x}_t$ , the downscaled version of the image. The added Gaussian noise further simulates the information loss inherent in downscaling. At $t = T$ , the image $\mathbf{x}_T$ approximates the observed low-resolution image $\mathbf{x}_{\mathrm{LR}}$ . The reverse diffusion process then aims to recover the high-resolution image $\mathbf{x}_0$ (i.e. $\mathbf{x}_{\mathrm{HR}}$ ) from $\mathbf{x}_T$ by reversing the degradation. + +Choice of $\beta(t)$ . The linear noise schedule is chosen for its simplicity and effectiveness. It provides a straightforward way to control the rate of degradation over time. Parameters $\beta_{\mathrm{min}}$ and $\beta_{\mathrm{max}}$ are selected to balance the trade-off between sufficient degradation (to simulate downscaling) and numerical stability of the diffusion process. + +Downsampling Operator D. The operator D is defined to reduce the spatial dimensions of the image by the desired scaling factor. We use bicubic downsampling. + +# 3.5. Adaptive Time-Step + +The standard reverse diffusion process is stochastic and requires a large number of sampling steps, making it computationally expensive. To accelerate inference, we reformulate the reverse diffusion as a deterministic Ordinary Differential Equation (ODE), allowing us to use advanced ODE solvers for faster sampling. The ODE solver integrates the reverse diffusion process, and its output is the super-resolved image. The reverse diffusion process can be described by a Stochastic Differential Equation (SDE) [46]: + +$$ +d \mathbf {x} = [ f (\mathbf {x}, t) - g (t) ^ {2} \nabla_ {\mathbf {x}} \log p _ {t} (\mathbf {x}) ] d t + g (t) d \bar {\mathbf {w}} \tag {11} +$$ + +where $\mathbf{x}$ is the data; $t$ is the time variable; $f(\mathbf{x}, t)$ and $g(t)$ are drift and diffusion coefficients; $\nabla_{\mathbf{x}} \log p_t(\mathbf{x})$ is the score function; $\bar{\mathbf{w}}$ is the reverse-time Wiener process. By removing the stochastic term, we obtain the probability flow ODE, which deterministically transports the data from the noise distribution to the data distribution. + +Our ATS ODE solver comprises three key components: 1. Adaptive Time Step Selection Using a Learned Function. Optimizing the allocation of time steps based on data characteristics has been explored in previous works [28, 53]. We discretize the time interval $[0,T]$ into $N$ non-uniform time steps $\{t_i\}_{i = 0}^N$ , where $t_0 = 0$ and $t_N = T$ . We introduce a learned function $\phi_{\psi}(t)$ as a weighted sum of polynomial basis functions, where the weight is parameterized by a set of learnable coefficients $\psi = \{\psi_{1},\psi_{2},\dots ,\psi_{K}\}$ , which adaptively determines the distribution of time steps based on the data characteristics. + +Parameterization of $\phi_{\psi}(t)$ . We define $\phi_{\psi}(t)$ as a normalized weighted sum of $K$ predefined monotonically increasing basis functions $\{\phi_k(t)\}_{k=1}^K$ : + +$$ +\phi_ {\psi} (t) = \frac {\sum_ {k = 1} ^ {K} \psi_ {k} \phi_ {k} (t)}{\sum_ {k = 1} ^ {K} \psi_ {k} \phi_ {k} (T)}, \quad \psi_ {k} = \exp (\omega_ {k}), \tag {12} +$$ + +where each basis function $\phi_k(t) = t^k$ for $k = 1,2,\ldots ,K$ is polynomial. $\omega_{k}$ are unconstrained learnable parameters that ensure $\psi_{k}\geq 0$ through the exponential mapping. We set $K = 3$ to balance model flexibility with computational efficiency. This setup allows $\phi_{\psi}(t)$ to capture nonlinear timestep distributions without excessive complexity. + +Selection of Time Steps. Using the learned function $\phi_{\psi}(t)$ , we map uniformly spaced normalized values $s_i = \frac{i}{N}$ to non-uniform time steps $t_i$ : + +$$ +t _ {i} = \phi_ {\psi} ^ {- 1} \left(s _ {i}\right) = \phi_ {\psi} ^ {- 1} \left(\frac {i}{N}\right), \quad i = 0, 1, \dots , N \tag {13} +$$ + +Since $\phi_{\psi}(t)$ is monotonically increasing, its inverse function $\phi_{\psi}^{-1}(s)$ exists and can be efficiently computed. + +2. Neural Operator Score Network. The score function, representing the gradient of the log probability density $\log p_t(\mathbf{x})$ , is approximated using a neural network $s_\theta(\mathbf{x}, t)$ parameterized by $\theta$ : + +$$ +\nabla_ {\mathbf {x}} \log p _ {t} (\mathbf {x}) \approx s _ {\theta} (\mathbf {x}, t). \tag {14} +$$ + +In our architecture, $s_{\theta}$ consists of: (i) An encoder that extracts features from $\mathbf{x}_{\mathrm{LR}}$ ; (ii) WFNO for capturing global dependencies and high-frequency details; (iii) AttnNO for modeling local dependencies and fine-grained structures; (iv) Gated Fusion Mechanism to dynamically combine features; (v) Time embedding $\mathbf{e}(t)$ incorporating the time variable $t$ into our neural network $s_{\theta}(\mathbf{x},t)$ using sinusoidal positional embeddings [14, 50], concatenating it and encoded features along the channel dimension. + +3. Efficient Solver. We solve the reverse-time stochastic differential equation (SDE) of the diffusion process, transformed into an ODE: + +$$ +\frac {d \mathbf {x}}{d t} = f (\mathbf {x}, t) - \frac {1}{2} g (t) ^ {2} \nabla_ {\mathbf {x}} \log p _ {t} (\mathbf {x}), \tag {15} +$$ + +where $\mathbf{x} \in \mathbb{R}^d$ is the image estimate at time $t$ in the reverse diffusion process; $f(\mathbf{x}, t)$ and $g(t)$ are coefficients derived from the forward diffusion process. + +For the Variance Preserving (VP) SDE commonly used in diffusion models, the coefficients are defined as: + +$$ +f (\mathbf {x}, t) = - \frac {1}{2} \beta (t) \mathbf {x}, \quad g (t) = \sqrt {\beta (t)}, \tag {16} +$$ + +where $\beta (t)$ is a predefined noise schedule specific to the diffusion process and is consistent with our DiffFNO. By substituting the score function approximation from Eq. (14), we define the approximate drift function: + +$$ +f _ {\theta} (\mathbf {x}, t) = f (\mathbf {x}, t) - \frac {1}{2} g (t) ^ {2} s _ {\theta} (\mathbf {x}, t). \tag {17} +$$ + +The adaptive time steps $\{t_i\}_{i = 0}^N$ discretize the ODE. We apply the Runge-Kutta 4th-order (RK4) method, as it + +balances computational cost and accuracy, requiring fewer steps than lower-order methods while retaining precision. + +The benefits of ATS are threefold: (i) Deterministic Sampling: It consistently produces the same results for identical inputs, improving reproducibility. (ii) Reduced Computation: Fewer sampling steps significantly decrease inference time. (iii) High-Quality Reconstruction: It maintains high-quality reconstruction by efficiently allocating computational resources. + +# 4. Experiments + +Datasets and Evaluation Metrics. We use the DIV2K [1] dataset for training. For evaluation, we use the DIV2K validation set and four standard datasets: Set5 [3], Set14 [56], BSD100 [36], and Urban100 [18]. + +We evaluate our model on upscaling factors of $\times 2$ , $\times 3$ , $\times 4$ , $\times 6$ , $\times 8$ , and $\times 12$ . Notably, scales $\times 6$ , $\times 8$ , and $\times 12$ are outside the training distribution, as the training scales are uniformly sampled from $\times 1$ to $\times 4$ . This setup assesses our model's ability to generalize to arbitrary scales. We use Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) as our evaluation metrics. + +Quantitative Results. Building on the quantitative gains of our model, we also present qualitative results to illustrate the visual improvements achieved. We compare our proposed DiffFNO model with several SOTA arbitrary-scale SR methods, including Meta-SR [17], LIIF [7], LTE [24], SRNO [54], LIT [5], LMI [10], and HiNOTE [35]. All models are trained on the DIV2K dataset with identical settings to ensure a fair comparison in Tables 1 and 2. + +Among the compared methods, Meta-SR performs adequately at lower scales but struggles at higher scaling factors due to its generalized approach that lacks specialized mechanisms for fine detail capture. LIIF and LTE improve upon Meta-SR by using local implicit functions and frequency-based estimations, respectively, which enhance high-frequency texture representation. However, they still face limitations in capturing non-periodic textures and high-frequency details, resulting in blurred textures at larger scales. LIT and LMI further advance performance by integrating attention mechanisms and MLP-mixer architectures, effectively preserving high-frequency textures and handling diverse scales, but they may not generalize well across datasets with varying distributions. SRNO and HiNOTE employ neural operator frameworks with attention mechanisms and frequency-aware loss priors to better capture global spatial properties and enhance high-frequency detail reconstruction. We observed mixed results between SRNO and HiNOTE: at certain scaling factors, one outperforms the other, indicating their varying strengths at different resolutions. Overall, their neural operator foundation improves the handling of arbitrary scaling but may increase computational demands. + +![](images/f6a78486668d9bf1f32f6db7d34b794c8ba18e722f78231a0137e299bd6a5f00.jpg) + +![](images/c2c07897b3a6fe1deab6db301463391d4551525a54a87e3557d35c93f40dc176.jpg) + +![](images/61e7b5bf4bce650d66c649155dc9a3ee0c223ec01567ab8e455c2e3812c1ff18.jpg) +Bicubic + +![](images/0ca9eb3285676b46290af8641ce7429bcc762867ea9903e3c85184a756c2720e.jpg) + +![](images/318696a0a14cf43053d81eb9c170bfa72a731d90134e1569b927f358942a1ce6.jpg) +Meta-SR [17] + +![](images/d6d4738fb7833d1b05bab97c7d7bda416c3e21785f519c9717e7d386c9930b7d.jpg) + +![](images/9c32e506bbabadbcf51e6b590e684cb86ca756b995ad267a760cdd82ea15b5ce.jpg) +LTE [24] + +![](images/7dd738fcc61237869b36c50835f2944a5e9c85ecaacbd5ad4fea50b698ca853e.jpg) + +![](images/1bc2b5d8820a803f889bc993e96765b6a90ba793b3dfb1a3ebed36bd2d404d6d.jpg) +LIIF [7] + +![](images/7057b283ab21024e6267a1e34845344d4c5ddef5613a25127b977c329bff8118.jpg) + +![](images/1581a15597084136634bb164a4611fc86f43dcf7ff70424383d464587ba166a1.jpg) +LIT [5] +GT + +![](images/b0653be3f8ab9d447ae236ac78205347330b834d136b85ce55a7fc7c711ff53f.jpg) +BSD100 [36], $\times 12$ +Urban100 [18], $\times 7.6$ + +![](images/d3cc2b0715b22e77eca562cd05178a24687f4bb4eb8c6f8158d88f294e7e85cc.jpg) +LMI [10] + +![](images/39c2c61f700511c146b9fd63dc96bf3b1b5fc2079a3025cbac7fd1df1dd7212e.jpg) +Bicubic +LMI [10] + +![](images/3859aaa3b29436756c41fa92e6bb8b68a9082217a1973ddc06b8c3e33b4562e0.jpg) +SRNO [54] + +![](images/4c9801f8a51d438e49a1d0aa13222f70dcdffa419d8fd846fa89fba88aedac20.jpg) +Meta-SR [17] +SRNO [54] + +![](images/e72bfa7309a3d85f1c5946da061fa54101576c1807d15add558c01d3b2b062a6.jpg) +HiNOTE [35] + +![](images/d628f1a9639b1aaedc5c2d3190b00c39cb02242855fea84eb6523114cb1067e3.jpg) +LTE [24] +HiNOTE [35] + +![](images/160fc1212b6d92d9039404df323a64b6502cef8b78b0c8b79057ea718f725cb1.jpg) +DiffFNO (ours) + +![](images/f64f62505d5b61d1c9eb247ae05dbebd5d14c5ade24b04069b703adecbd48084.jpg) +LIIF [7] +DiffFNO (ours) + +![](images/e286017c55c082415c6495ca85889ecf4a2d7b9a8914f556dc4a20e3402a2739.jpg) + +![](images/5bbb72a13b191f8ee358abb061013f5dec45d94ca8b124880459ab4531baba23.jpg) +LIT [5] +GT + +Figure 3. Qualitative comparison on integer and continuous super-resolution scales. The models use RDN [58] as their encoder (except HiNOTE [35], has its own). In the HR image, the cropped patch is outlined in green. + +
    Modelx2x3x4x6x8x12
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    EDSR-MetaSR [17]33.320.91330.100.80028.230.83026.100.79224.770.74223.950.720
    EDSR-LTE [24]33.830.92130.500.88028.790.85226.550.80025.050.76024.200.736
    EDSR-LIIF [7]34.360.92530.940.88529.310.85527.020.81425.440.77124.320.743
    EDSR-LIT [5]34.810.92831.390.89029.700.86027.440.81525.780.77524.690.745
    EDSR-LMI [10]35.400.93031.880.89530.400.86527.950.82026.160.78025.560.750
    EDSR-SRNO [54]34.850.92831.450.89030.050.86327.360.81026.000.77225.910.760
    EDSR-DiffFNO (Ours)35.720.93232.500.90530.880.87028.290.83026.780.79026.480.775
    HiNOTE†[35]35.290.93131.900.89530.460.84227.830.79926.410.77226.230.732
    RDN-MetaSR [17]33.500.92030.320.89328.410.86126.290.81024.900.78024.010.790
    RDN-LTE [24]33.980.92230.650.88228.940.85226.700.80225.200.76224.350.732
    RDN-LIIF [7]34.510.92731.090.88729.460.85727.170.81225.590.77224.470.742
    RDN-LIT [5]34.960.93031.540.89229.850.86227.590.81725.930.77724.840.747
    RDN-LMI [10]35.550.93232.030.89730.550.86728.100.82226.310.78225.710.752
    RDN-SRNO [54]35.000.93031.600.89230.200.86227.510.81226.150.77226.060.762
    RDN-DiffFNO (Ours)35.870.93432.650.90231.030.87228.440.83226.930.79226.630.777
    + +Table 1. PSNR/SSIM comparison on the DIV2K [1] validation set using EDSR [31] and RDN [58] encoders. HiNOTE [35] uses its own. + +Our DiffFNO model consistently achieves the highest PSNR and SSIM scores across all scaling factors and datasets. The performance gap widens at larger scaling factors $(\times 8$ and $\times 12$ ), demonstrating a superior generalization to the out-of-distribution scales. The improvements are more pronounced on complex datasets like Urban100, which contain intricate textures and structures. By combining WFNO and AttnNO features through the Gated Fusion + +Mechanism, which adaptively balances global and local features, DiffFNO synthesizes global and local dependencies. The ATS ODE solver efficiently refines high-resolution images, further enhancing quality. This combination addresses the limitations of prior models, such as spectral bias and insufficient high-frequency detail capture. + +Qualitative Results. Fig. 3 compares arbitrary-scale SR methods on a BSD100 image (scaling factor of $\times 12$ ) with + +
    ModelSet5Set14BSD100Urban100
    ×2×3×4×6×8×2×3×4×6×8×2×3×4×6×8×2×3×4×6×8
    MetaSR [17]37.5034.0531.5228.2326.0233.5130.0328.0225.5324.0231.0228.0526.5224.8223.5232.0228.0325.8223.5222.03
    LIIF [7]38.0234.4232.0428.5726.2534.0330.4328.4325.8424.3331.5228.5527.0325.0323.8332.5228.5326.0323.8322.33
    LTE [24]38.2134.6332.2528.7626.4434.2230.6528.6426.0524.5231.7128.7327.2325.2324.0332.7228.7526.2324.0322.53
    SRNO [54]38.3234.8432.6929.3827.2834.2730.7128.9726.7625.2632.4329.3727.8326.0424.9933.3329.1426.9824.4323.02
    LIT [5]38.5335.0232.8229.5127.4234.4430.8329.0326.8225.3332.5229.5127.9226.1225.0133.4229.2227.0224.5223.12
    LMI [10]38.7235.1432.9529.6327.5534.6331.0229.2427.0525.5532.7229.7428.0426.2525.1433.6229.4427.2424.6323.23
    HNOTE [35]39.0135.2233.0829.8527.7435.0231.2529.5527.3525.8533.0230.0528.1526.3525.2534.0329.8327.5524.7323.34
    DiffFNO (Ours)39.7235.3033.1630.2327.9336.0131.5430.2227.5826.0233.5630.2428.2126.4525.3034.1929.9927.7424.8023.35
    + +Table 2. PSNR comparison on four benchmark datasets: Set5 [3], Set14 [56], BSD100 [36], and Urban100 [18]. All models use RDN [58] as their encoder, besides HiNOTE [35] which has its own. + +
    Model×2×3×4×6×8×12InferenceSteps
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    SRNO [54]33.810.92030.530.88028.740.85026.590.80025.100.76024.180.730147-
    FNO [26]34.360.92530.940.88529.310.85527.020.81025.440.77024.320.74085-
    WFNO34.810.92831.390.88829.700.85827.440.81525.780.77524.690.74597-
    WFNO-AttnNO35.400.93031.880.89230.400.86227.950.82026.160.78025.560.7501391000
    DiffFNO(-w, -a, -s)34.850.92831.450.89030.050.86027.360.81526.000.77525.910.7602041000
    DiffFNO(-a, -s)35.290.93031.900.89330.460.86327.830.82026.410.78026.230.7652311000
    DiffFNO(-s)35.700.93232.480.89630.850.86628.260.82526.750.78526.450.7702661000
    DiffFNO35.720.93232.500.90030.880.87028.290.83026.780.79026.480.77514130
    + +Table 3. Ablation study of variants of DiffFNO on the DIV2K [1] validation set. All use EDSR-baseline [31] backbone as their encoder. Inference times are measured in milliseconds (ms). WFNO-AttnNO has Gated Fusion Mechanism. + +fine-grained details like animal fur and rock textures and an Urban100 (continuous scaling factor of $\times 7.6$ ) image featuring large structures and fine local details such as reflections on the grass. SRNO and HiNOTE capture multiscale details effectively, from the animal's body to tiny gaps between glass panels. However, DiffFNO reconstructs crisper edges with fewer artifacts, enhancing texture in animal fur pattern and reflections. WFNO captures large-scale patterns, while AttnNO and Gated Fusion Mechanism preserve intricate textures. This multiscale approach followed by a diffusion process enhanced by the ATS's ODE solver further reduces visual artifacts. + +Ablation Studies. Extensive ablation studies validate the effectiveness and complementary nature of new components in DiffFNO. Table 3 reports the PSNR results on the DIV2K validation set for different model variants with scaling factors from $\times 2$ to $\times 12$ . -w denotes leaving out the Mode Rebalancing (yielding the default FNO [26]). -a denotes omitting AttnNO. -s denotes the removal of ATS ODE solver. We also measure inference time by averaging over 100 runs, and report inference steps. We establish a baseline with SRNO, whose architecture is the most similar to our DiffFNO aamong the methods covered in our study. Overall, we observe notable improvements with the addition of model components. The complete DiffFNO achieves the highest PSNR and SSIM values across all upscaling factors. + +Effect of Mode Rebalancing. Incorporating Mode Rebalancing into WFNO boosted performance compared to the + +default FNO [26], at the cost of a slightly increased number of parameters and inference time. + +Effect of Gated Fusion Mechanism and AttnNO. The Gated Fusion Mechanism introduces minimal computational overhead. In addition, extra computational cost incurred by Attention-based Neural Operator is effectively mitigated by running it in parallel with WFNO while employing a shared encoder. + +Effect of ATS ODE Solver: ATS dramatically reduces the number of inference steps from 1,000 to just 30, which substantially improves the inference time while delivering competitive performance (Tab. 3). DiffFNO outperforms the SOTA in both PSNR and inference time (Fig. 1 (a)). + +# 5. Conclusion + +We propose Diffusion Fourier Neural Opeartor (DiffFNO) for arbitrary-scale image super-resolution. DiffFNO is made of Weighted Fourier Neural Operator with a Mode Rebalancing mechanism to emphasize high-frequency details. 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(a) All models use the EDSR-baseline [31] encoder, except HiNOTE [35] which has its own. (b) Compared to SRNO [54], DiffFNO is strengthened by the fusion of spectral and spatial features and efficient refinement by a diffusion process." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 152, + 449, + 200, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 449, + 200, + 462 + ], + "spans": [ + { + "bbox": [ + 152, + 449, + 200, + 462 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 54, + 476, + 297, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 476, + 297, + 681 + ], + "spans": [ + { + "bbox": [ + 54, + 476, + 297, + 681 + ], + "type": "text", + "content": "We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly improving the reconstruction of high-frequency image details that are crucial for superresolution tasks. Gated Fusion Mechanism (GFM) adaptively complements WFNO's spectral features with spatial features from an Attention-based Neural Operator (AttnNO). This enhances the network's capability to capture both global structures and local details. Adaptive Time-Step (ATS) ODE solver, a deterministic sampling strategy, accelerates inference without sacrificing output quality by dynamically adjusting integration step sizes ATS. Extensive experiments demonstrate that DiffFNO achieves state-of-the-art (SOTA) results, outperforming existing methods across various scaling factors by a margin of 2-4 dB in" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 451, + 556, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 451, + 556, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 451, + 556, + 501 + ], + "type": "text", + "content": "PSNR, including those beyond the training distribution. It also achieves this at lower inference time (Fig. 1 (a)). Our approach sets a new standard in super-resolution, delivering both superior accuracy and computational efficiency." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 524, + 395, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 524, + 395, + 537 + ], + "spans": [ + { + "bbox": [ + 314, + 524, + 395, + 537 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 312, + 544, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 544, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 312, + 544, + 555, + 653 + ], + "type": "text", + "content": "Image super-resolution (SR) reconstructs high-resolution (HR) images from low-resolution (LR) inputs, recovering lost fine details to enhance visual quality. SR is crucial for applications like medical imaging [12], satellite imagery [23, 52], and video games [38]. However, multiple HR images can correspond to the same LR input due to information loss during downsampling. This ambiguity requires algorithms capable of inferring plausible and perceptually accurate high-frequency content from limited data." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 556, + 715 + ], + "type": "text", + "content": "Deep learning, particularly Convolutional Neural Networks (CNNs) [58], has significantly advanced SR. Dong et al. introduced SRCNN [9], demonstrating the effectiveness of end-to-end learning for SR. Subsequent models achieved remarkable performance using deeper architectures and at" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 693, + 149, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 693, + 149, + 703 + ], + "spans": [ + { + "bbox": [ + 70, + 693, + 149, + 703 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 70, + 703, + 234, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 703, + 234, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 703, + 234, + 713 + ], + "type": "text", + "content": "*Work Done during the visit at Peking University." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 298, + 748, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 748, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 748, + 313, + 757 + ], + "type": "text", + "content": "150" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 215, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 215, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 215, + 83 + ], + "type": "text", + "content": "tention mechanisms [6, 30, 31, 34, 57]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 86, + 296, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 86, + 296, + 193 + ], + "spans": [ + { + "bbox": [ + 55, + 86, + 296, + 193 + ], + "type": "text", + "content": "Diffusion models have emerged as powerful generative frameworks modeling complex data distributions via iterative denoising processes [11, 14, 45]. Their ability to generate high-fidelity images is well-suited for inferring missing fine details. In SR, diffusion models progressively refine an LR image by modeling the conditional distribution of HR images given the LR input [15, 25, 41, 51]. This iterative process reconstructs intricate textures and high-frequency components, producing realistic outputs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 194, + 296, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 194, + 296, + 290 + ], + "spans": [ + { + "bbox": [ + 55, + 194, + 296, + 290 + ], + "type": "text", + "content": "However, diffusion models are computationally intensive due to the iterative reverse diffusion process [46]. To address this, recent research explores efficient sampling strategies to accelerate reverse diffusion. One approach is approximating the diffusion process through deterministic Ordinary Differential Equation (ODE), which can be solved in fewer steps [33]. This accelerates inference and provides consistent, reproducible results." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 292, + 296, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 292, + 296, + 423 + ], + "spans": [ + { + "bbox": [ + 55, + 292, + 296, + 423 + ], + "type": "text", + "content": "Arbitrary-scale SR models [7, 17, 24], which can upsample images at user-defined scales beyond those seen in training, have gained attention in recent years. Methods involving attention mechanisms [5] and representing images as continuous functions [10] have been explored. Operator-learning methods such as Super-Resolution Neural Operators (SRNO) [54] and HiNOTE [35] have further advanced this field. However, the inherent differences between physics simulations and real-world images introduce challenges from computational demands to the difficulty in restoring high-frequency details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 425, + 274, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 425, + 274, + 436 + ], + "spans": [ + { + "bbox": [ + 55, + 425, + 274, + 436 + ], + "type": "text", + "content": "To address these limitations, our contributions are:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 437, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 296, + 714 + ], + "type": "text", + "content": "(1) We propose Weighted Fourier Neural Operator (WFNO) strengthened by iterative refinement from a diffusion framework for high-frequency reconstruction, detailed in Fig. 2. Through Mode Rebalancing (MR), WFNO learns to emphasize the most critical frequency components. This greatly enhances high-frequency image detail reconstruction, overcoming the limitations of standard FNOs and MLPs, which underrepresent such details due to mode truncation and spectral bias, respectively. (2) We develop Gated Fusion Mechanism (GFM) to dynamically adjust the influence of Fourier space features from WFNO and complementary spatial domain features from an Attention-based Neural Operator (AttnNO). AttnNO is lightweight, sharing an encoder with and running in parallel to WFNO. (3) Additionally, we present Adaptive Time-Step (ATS) ODE solver, which flexibly adjusts integration step sizes based on data characteristics by assessing the complexity of image regions, thereby reducing computational overhead without compromising quality. (4) DiffFNO achieves state-of-the-art results on multiple SR benchmarks, outperforming existing methods by 2-4 dB in PSNR in reconstruction quality. It also offers competitive inference time as Fig. 1 (a) shows. DiffFNO remains robust across various upscaling factors—even those" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 72, + 408, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 408, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 408, + 84 + ], + "type": "text", + "content": "unseen during training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 95, + 400, + 107 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 95, + 400, + 107 + ], + "spans": [ + { + "bbox": [ + 314, + 95, + 400, + 107 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 114, + 553, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 114, + 553, + 222 + ], + "spans": [ + { + "bbox": [ + 313, + 114, + 553, + 222 + ], + "type": "text", + "content": "Neural Operators and Fourier Methods. Neural Operators (NO) [22] have emerged as a powerful framework for learning mappings between infinite-dimensional function spaces, providing resolution-invariant models that generalize across different input resolutions. Unlike traditional neural networks that map finite-dimensional vectors to other vectors, neural operators learn mappings from functions to functions [27], making them well-suited for tasks involving continuous data or data at varying resolutions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 223, + 553, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 223, + 553, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 223, + 553, + 319 + ], + "type": "text", + "content": "Multi-Layer Perceptrons (MLPs) often exhibit a spectral bias, favoring low-frequency functions [39]. This limits their ability to capture fine textures and sharp edges. To overcome these limitations, techniques like positional encodings and Fourier feature mappings capture high-frequency details by embedding input coordinates into a higher-dimensional sinusoidal space, allowing the network to represent complex patterns [44, 47]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 319, + 554, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 554, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 554, + 437 + ], + "type": "text", + "content": "Fourier Neural Operator (FNO) [26] is a variant of NO that uses spectral convolution to efficiently capture global data patterns, modeling long-range dependencies with lower computational complexity than traditional CNNs. In physics and climate settings [19, 29, 55], FNOs can handle arbitrary input resolutions without retraining. Although successful, FNOs may still lose high-frequency information due to mode truncation (discarding higher-frequency Fourier modes). This loss impairs tasks such as SR that rely on detailed reconstruction [13, 48, 49]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 438, + 554, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 554, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 554, + 521 + ], + "type": "text", + "content": "The Mode Rebalancing mechanism in WFNO overcomes these limitations. Instead of being truncated, all Fourier modes are preserved, with additional learnable weights to modulate their impact on reconstruction. Fine-grained feature representation is further enhanced by AttnNO, which captures local details by processing data directly in the spatial domain" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 522, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 554, + 605 + ], + "type": "text", + "content": "Diffusion-Based SR and Efficient Sampling. Diffusion models have gained prominence as powerful generative models capable of producing high-quality images through iterative denoising techniques [14, 42]. In the context of SR, diffusion models have been employed to model the conditional distribution of HR images given LR inputs, achieving higher resolutions after progressive enhancement [40, 41]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 606, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 606, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 606, + 554, + 713 + ], + "type": "text", + "content": "Despite their effectiveness, diffusion models are computationally intensive due to the large number of time steps required in the reverse diffusion process. Such computational demands pose significant challenges for practical applications [20], especially in real-time or resource-constrained settings. Current solutions include: (i) Deterministic Sampling via ODE Solvers: By reformulating the stochastic reverse diffusion as a deterministic ODE, advanced ODE solvers can be employed to reduce the number of sam" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "151" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 549, + 305 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 549, + 305 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 549, + 305 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 549, + 305 + ], + "type": "image", + "image_path": "b686c698376773941977f8fe89298fcea1a039a8a18df6cd817336dfacdcdf59.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 315, + 555, + 373 + ], + "lines": [ + { + "bbox": [ + 54, + 315, + 555, + 373 + ], + "spans": [ + { + "bbox": [ + 54, + 315, + 555, + 373 + ], + "type": "text", + "content": "Figure 2. The proposed Diffusion Fourier Neural Opeartor (DiffFNO) architecture for arbitrary-scale super-resolution begins by lifting a low-resolution input image " + }, + { + "bbox": [ + 54, + 315, + 555, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{LR}}(\\mathbf{r})" + }, + { + "bbox": [ + 54, + 315, + 555, + 373 + ], + "type": "text", + "content": " into a feature space using a convolutional encoder. Features extracted by the Weighted Fourier Neural Operator (WFNO) and an Attention-based Neural Operator (AttnNO) are combined using a Gated Fusion Mechanism (GFM). The fused features are then projected into RGB space, where Adaptive Time-Step (ATS) ODE solver efficiently completes the reverse diffusion process with both accuracy and speed. This pipeline generates " + }, + { + "bbox": [ + 54, + 315, + 555, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{HR}}(\\mathbf{r})" + }, + { + "bbox": [ + 54, + 315, + 555, + 373 + ], + "type": "text", + "content": ", a high-resolution version of the input image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 380, + 295, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 380, + 295, + 513 + ], + "spans": [ + { + "bbox": [ + 54, + 380, + 295, + 513 + ], + "type": "text", + "content": "pling steps [21]. Methods like Denoising Diffusion Implicit Models (DDIM) [45] and DPM-Solver [2, 33] have demonstrated the ability to generate high-quality images with significantly fewer steps. (ii) Operator Learning for Fast Sampling: Neural operators accelerates sampling by learning the solution operator of the reverse diffusion process [8, 59]. (iii) Progressive Distillation: Training a distilled model to approximate the behavior of the full diffusion model allows faster sampling with fewer steps [37, 43]. Although effective, this method may require extensive retraining and potentially compromise image quality for increased speed." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 513, + 295, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 513, + 295, + 573 + ], + "spans": [ + { + "bbox": [ + 54, + 513, + 295, + 573 + ], + "type": "text", + "content": "Applying these acceleration methods to diffusion-based SR enables faster inference while maintaining high image quality. With efficient sampling methods, diffusion models become more practical for SR tasks, balancing performance and computational efficiency [32]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 574, + 295, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 574, + 295, + 623 + ], + "spans": [ + { + "bbox": [ + 54, + 574, + 295, + 623 + ], + "type": "text", + "content": "DiffFNO adopts (i) for its simplicity and the robustness of established numerical methods. We also strength it with the ATS strategy, which adjusts integration step sizes adaptively to balance speed and quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 636, + 190, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 636, + 190, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 636, + 190, + 651 + ], + "type": "text", + "content": "3. The Proposed DiffFNO" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 658, + 293, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 658, + 293, + 671 + ], + "spans": [ + { + "bbox": [ + 55, + 658, + 293, + 671 + ], + "type": "text", + "content": "3.1. Network Architecture and Novel Components" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "An overview of the proposed DiffFNO is shown in Fig. 1 (b). It has three parts: (i) A CNN encoder extracts features from LR images. Unlike the simple linear transfor" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 555, + 511 + ], + "type": "text", + "content": "mations in standard FNO setups for physics simulations, our encoder is tailored for SR, extracting complex patterns and textures needed for high-quality reconstructions. We use the EDSR-baseline [31] and RDN models [58] in our experiments. (ii) WFNO and GFM: WFNO captures both global and local details alongside the AttnNO. GFM combines these into a unified HR feature map, which is then projected into RGB. (iii) ATS ODE solver accelerates inference speed by taking fewer, larger, and dynamically adjusted steps toward the reconstructed HR image. Fig. 2 illustrates these components in detail." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 512, + 555, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 512, + 555, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 512, + 555, + 536 + ], + "type": "text", + "content": "The network minimizes the difference between the predicted image and the true image. The loss function is:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 325, + 542, + 555, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 542, + 555, + 563 + ], + "spans": [ + { + "bbox": [ + 325, + 542, + 555, + 563 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\theta) = \\mathbb {E} _ {t, \\mathbf {x} _ {0}} \\left[ \\| s _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\nabla_ {\\mathbf {x} _ {t}} \\log p _ {t} \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) \\| _ {2} ^ {2} \\right], \\tag {1}", + "image_path": "c5af848d2e30eeff779d49daca91c64553cdf68f46803e80cb540cae320821c4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "text", + "content": " (i.e. " + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{LR}}" + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "text", + "content": ") is obtained by adding noise to " + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "text", + "content": " (i.e. " + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{HR}}" + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "text", + "content": "). " + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "inline_equation", + "content": "s_{\\theta}(\\mathbf{x}_t, t)" + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "text", + "content": " is the neural network approximating the true score function. " + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "inline_equation", + "content": "\\nabla \\mathbf{x}_t \\log p_t(\\mathbf{x}_t | \\mathbf{x}_0)" + }, + { + "bbox": [ + 313, + 568, + 554, + 605 + ], + "type": "text", + "content": " is the true score function." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 611, + 502, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 611, + 502, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 611, + 502, + 624 + ], + "type": "text", + "content": "3.2. Weighted Fourier Neural Operator" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 629, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 555, + 713 + ], + "type": "text", + "content": "The Fourier Neural Operator (FNO) [26] is an efficient NO variant designed to learn mappings between function spaces. It operates directly on inputs of arbitrary resolutions, performing upscaling by mapping low-resolution inputs to high-resolution outputs. It first transforms the input data into the frequency domain, applies the learned filters, and then transforms the data back to the spatial domain." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "152" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": "Spectral convolution and mode truncation greatly enhance computational efficiency." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{LR}}(\\mathbf{r})" + }, + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "type": "text", + "content": " denote the low-resolution input function (e.g., an image), where " + }, + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{r} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "type": "text", + "content": " represents spatial coordinates. The goal is to learn an operator " + }, + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 55, + 96, + 295, + 133 + ], + "type": "text", + "content": " such that:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 130, + 143, + 295, + 157 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 143, + 295, + 157 + ], + "spans": [ + { + "bbox": [ + 130, + 143, + 295, + 157 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {\\mathrm {H R}} (\\mathbf {r}) = \\mathcal {G} \\left[ \\mathbf {x} _ {\\mathrm {L R}} (\\mathbf {r}) \\right], \\tag {2}", + "image_path": "1c62e4f46d7b147385fb0f2112b917e53335da47216297f3aa5bb58ab0bd7178.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 166, + 295, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 166, + 295, + 190 + ], + "spans": [ + { + "bbox": [ + 55, + 166, + 295, + 190 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 166, + 295, + 190 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{HR}}(\\mathbf{r})" + }, + { + "bbox": [ + 55, + 166, + 295, + 190 + ], + "type": "text", + "content": " is the output function (e.g., the super-resolved image). The FNO models " + }, + { + "bbox": [ + 55, + 166, + 295, + 190 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 55, + 166, + 295, + 190 + ], + "type": "text", + "content": " by stacking:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 101, + 200, + 295, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 200, + 295, + 214 + ], + "spans": [ + { + "bbox": [ + 101, + 200, + 295, + 214 + ], + "type": "interline_equation", + "content": "\\mathbf {v} _ {l + 1} (\\mathbf {r}) = \\sigma \\left(\\mathcal {W} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) + \\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r})\\right), \\tag {3}", + "image_path": "1e0de6dd4f653dd7c9ac0971bfffc8ca24b129151279204e311c3f4df0199aa0.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_l(\\mathbf{r})" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": " is the feature representation at layer " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": " evaluated at spatial location " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{l + 1}(\\mathbf{r})" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": " is its updated representation in the following layer; " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": " is a nonlinear activation function; " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_l" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": " is a linear transformation. " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "\\kappa_{l}" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": ", the integral operator at layer " + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 223, + 296, + 331 + ], + "type": "text", + "content": ", transforms the features into the Fourier domain. Fourier modes are then truncated for computational efficiency. Global convolution is performed with a pointwise multiplication between the transformed features and the learned Fourier coefficients." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 100, + 340, + 295, + 356 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 340, + 295, + 356 + ], + "spans": [ + { + "bbox": [ + 100, + 340, + 295, + 356 + ], + "type": "interline_equation", + "content": "\\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) = \\mathcal {F} ^ {- 1} \\left(\\mathbf {P} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathcal {F} [ \\mathbf {v} _ {l} ] (\\boldsymbol {\\xi})\\right), \\tag {4}", + "image_path": "4d04682f67ae97192255ebf7a4395f4ebd5341ba3a72efdf6516da7ba72e87ec.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "spans": [ + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{-1}" + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "content": " denote the Fourier and inverse Fourier transforms, respectively. " + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "content": " is the frequency domain variables. " + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{F}[\\mathbf{v}_l](\\pmb {\\xi})" + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "content": " is the Fourier transform of " + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_l" + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "content": ", evaluated at frequency " + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "inline_equation", + "content": "\\pmb{\\xi}" + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_l(\\pmb {\\xi})" + }, + { + "bbox": [ + 55, + 364, + 296, + 424 + ], + "type": "text", + "content": " is a complex-valued tensor of learnable parameters representing the Fourier domain filters." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 425, + 296, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 425, + 296, + 496 + ], + "spans": [ + { + "bbox": [ + 55, + 425, + 296, + 496 + ], + "type": "text", + "content": "However, mode truncation underrepresents high-frequency components that are critical to SR of real-world images. To address this limitation, we introduce Mode Rebalancing. A learned weighting function " + }, + { + "bbox": [ + 55, + 425, + 296, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_l(\\boldsymbol {\\xi})" + }, + { + "bbox": [ + 55, + 425, + 296, + 496 + ], + "type": "text", + "content": " is applied to the Fourier modes to amplify or attenuate specific frequency components. It is defined at layer " + }, + { + "bbox": [ + 55, + 425, + 296, + 496 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 425, + 296, + 496 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 126, + 506, + 295, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 506, + 295, + 520 + ], + "spans": [ + { + "bbox": [ + 126, + 506, + 295, + 520 + ], + "type": "interline_equation", + "content": "\\mathbf {w} _ {l} (\\boldsymbol {\\xi}) = 1 + \\gamma_ {l} \\cdot \\| \\boldsymbol {\\xi} \\| ^ {\\alpha}, \\tag {5}", + "image_path": "0b051d6e55cb4b31b5a817b3bec9502426428e297338febc2b90e336cfef1723.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\gamma_{l}" + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "content": " is a learnable scalar parameter at layer " + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "content": " that controls the strength of the weighting; " + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "content": " is a hyperparameter (0.7 in our experiments or optionally a learnable parameter) that determines how the weight scales with the frequency magnitude " + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\|\\pmb{\\xi}\\|" + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{w}(\\pmb{\\xi})" + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "content": " assigns higher weights to higher frequencies when " + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\alpha > 0" + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "content": ", thus emphasizing high-frequency components. This yields an updated " + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_{l}" + }, + { + "bbox": [ + 55, + 529, + 296, + 613 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 85, + 623, + 295, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 623, + 295, + 637 + ], + "spans": [ + { + "bbox": [ + 85, + 623, + 295, + 637 + ], + "type": "interline_equation", + "content": "\\mathcal {K} _ {l} \\mathbf {v} _ {l} (\\mathbf {r}) = \\mathcal {F} ^ {- 1} \\left(\\mathbf {w} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathbf {P} _ {l} (\\boldsymbol {\\xi}) \\cdot \\mathcal {F} [ \\mathbf {v} _ {l} ] (\\boldsymbol {\\xi})\\right). \\tag {6}", + "image_path": "4d1bfc6123b5216efcbaada84308160fb74dda2b008f1caf184878ae96d7fad5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 647, + 198, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 198, + 658 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 198, + 658 + ], + "type": "text", + "content": "3.3. Gated Fusion Mechanism" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "While WFNO excels at capturing global dependencies through spectral convolutions, it may not fully exploit local interactions critical for detailed image reconstruction. We incorporate AttnNO to complement WFNO by capturing" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "local dependencies. Working in tandem, they learn mappings from the low-resolution input function to the high-resolution output function. Gated Fusion Mechanism optimally combines the complementary features from both operators, adaptively balancing the contributions of each to a fused feature map, which is then fed to a projection layer." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 144, + 554, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 554, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 554, + 251 + ], + "type": "text", + "content": "Efficient implementation of the kernel integral using the Galerkin-type attention mechanism [4] has been explored in the neural operator applied to SR tasks [35, 54]. Our AttnNO is composed of bicubic interpolation, Galerkin attention, and nonlinearity, sharing an encoder with WFNO. AttnNO models local interactions in the spatial domain, focusing on the most relevant spatial regions during the convolution process. Given the complementary role of AttnNO to WFNO, we simplify its structure to improve runtime." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 252, + 554, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 252, + 554, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 252, + 554, + 430 + ], + "type": "text", + "content": "While previous works have applied gating mechanisms in different contexts, our approach differs significantly. Zheng et al. [60] use gating within recurrent CRF networks primarily for semantic segmentation, controlling the information flow for boundary refinement rather than fusing feature maps with distinct representations. Hu et al. [16] introduced channel-wise gating in Squeeze-and-Excitation (SE) blocks, focusing on adaptively recalibrating feature channels within a single network stream. In contrast, our Gated Fusion Mechanism applies spatial gating to integrate global dependencies captured by WFNO and local information from AttnNO. This mechanism adaptively combines both operators' feature maps, enhancing high-resolution image reconstruction by balancing global and local contributions at each spatial location." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{WFNO}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}" + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{AttnNO}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}" + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "content": " denote the feature maps obtained from WFNO and AttnNO, respectively, where " + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "content": " is the batch size, " + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "content": " are the height and width of the feature maps, and " + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "content": " is the number of channels. We first concatenate the feature maps along the channel dimension and pass them through a convolutional layer followed by a sigmoid activation to produce a gating map " + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "inline_equation", + "content": "\\mathbf{G} \\in \\mathbb{R}^{B \\times H \\times W \\times 1}" + }, + { + "bbox": [ + 313, + 430, + 554, + 528 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 355, + 537, + 553, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 537, + 553, + 552 + ], + "spans": [ + { + "bbox": [ + 355, + 537, + 553, + 552 + ], + "type": "interline_equation", + "content": "\\mathbf {G} = \\sigma \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(\\left[ \\mathbf {v} _ {\\mathrm {W F N O}}, \\mathbf {v} _ {\\mathrm {A t t n N O}} \\right]\\right)\\right), \\tag {7}", + "image_path": "0c9aa0280007855f01c1ce9c481b898b1721a1724e7f3b9ae0111df58fdec6e9.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "spans": [ + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "inline_equation", + "content": "[\\cdot ,\\cdot ]" + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "text", + "content": " denotes concatenation along the channel dimension; " + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_{1\\times 1}" + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "text", + "content": " convolutional layer that reduces the concatenated features to a single-channel gating map; " + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 313, + 560, + 553, + 608 + ], + "type": "text", + "content": " is the sigmoid activation function applied element-wise." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 608, + 553, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 608, + 553, + 632 + ], + "spans": [ + { + "bbox": [ + 313, + 608, + 553, + 632 + ], + "type": "text", + "content": "The fused feature map " + }, + { + "bbox": [ + 313, + 608, + 553, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{fused}} \\in \\mathbb{R}^{B \\times H \\times W \\times C}" + }, + { + "bbox": [ + 313, + 608, + 553, + 632 + ], + "type": "text", + "content": " is the element-wise weighted sum of the two feature maps:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 345, + 643, + 553, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 643, + 553, + 656 + ], + "spans": [ + { + "bbox": [ + 345, + 643, + 553, + 656 + ], + "type": "interline_equation", + "content": "\\mathbf {v} _ {\\text {f u s e d}} = \\mathbf {G} \\odot \\mathbf {v} _ {\\mathrm {W F N O}} + (1 - \\mathbf {G}) \\odot \\mathbf {v} _ {\\mathrm {A t t n N O}}, \\tag {8}", + "image_path": "8e2ac6c5d23944c2bd70c85788151263820d7f36724869f4f4c33a5ef07cdd2a.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": " denotes element-wise multiplication, and subtraction is performed element-wise. The gating map " + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 313, + 665, + 554, + 713 + ], + "type": "text", + "content": " is broadcast across the channel dimension to match the dimensions of the feature maps." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "153" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 192 + ], + "type": "text", + "content": "Gated Fusion Mechanism brings two advantages compared to a naive concatenation strategy: (i) Captures complementary Information: WFNO models global dependencies through spectral convolutions, effectively modeling long-range interactions and overall structure. In contrast, AttnNO excels at capturing local dependencies and fine-grained details via attention mechanisms. (ii) Balances contributions dynamically: Gated Fusion Mechanism elicits the importance of each feature map at each spatial location, dynamically balancing global and local information." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 199, + 295, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 199, + 295, + 211 + ], + "spans": [ + { + "bbox": [ + 55, + 199, + 295, + 211 + ], + "type": "text", + "content": "3.4. Forward Diffusion Process and Noise Schedule" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 217, + 296, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 217, + 296, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 296, + 289 + ], + "type": "text", + "content": "Motivation. NOs are well-suited for SR tasks due to their inherent resolution invariance and their ability to model global dependencies efficiently. Diffusion models can iteratively refine a low-resolution image to a high-resolution one, capturing the complex conditional distribution of high-resolution images given low-resolution inputs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 289, + 295, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 289, + 295, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 289, + 295, + 337 + ], + "type": "text", + "content": "DiffFNO leverages the strengths of both frameworks. WFNO is a powerful mechanism for handling arbitrary resolutions and capturing high-frequency details, while the diffusion process iteratively improves reconstruction output." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "type": "text", + "content": "In our framework, the forward diffusion process models the degradation of HR images to LR images, which in our case is primarily due to downscaling. To incorporate this degradation into the diffusion model framework, we define a forward process that simulates the downscaling effect over continuous time " + }, + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "type": "inline_equation", + "content": "t \\in [0,T]" + }, + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "type": "text", + "content": ". At, the image " + }, + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "type": "text", + "content": " closely resemble the observed LR image " + }, + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{LR}}" + }, + { + "bbox": [ + 55, + 337, + 296, + 445 + ], + "type": "text", + "content": " after significant degradation. We adopt a modified variance-preserving (VP) stochastic differential equation (SDE):" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 85, + 453, + 295, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 453, + 295, + 475 + ], + "spans": [ + { + "bbox": [ + 85, + 453, + 295, + 475 + ], + "type": "interline_equation", + "content": "d \\mathbf {x} _ {t} = - \\frac {1}{2} \\beta (t) (\\mathbf {x} _ {t} - \\mathbf {D x} _ {t}) d t + \\sqrt {\\beta (t)} d \\mathbf {w}, \\tag {9}", + "image_path": "665a6fce7c7b7fc92f56ad77fcacedb70a9be86781a5694d84faf99994e52e6c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "type": "inline_equation", + "content": "\\beta (t)" + }, + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "type": "text", + "content": " is the noise schedule; " + }, + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "type": "text", + "content": " is the downsampling operator that reduces the resolution of the image; " + }, + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "type": "inline_equation", + "content": "d\\mathbf{w}" + }, + { + "bbox": [ + 55, + 483, + 295, + 518 + ], + "type": "text", + "content": " is the standard Wiener process." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "type": "text", + "content": "In this formulation, the term " + }, + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{x} - \\mathbf{D}\\mathbf{x}" + }, + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "type": "text", + "content": " quantifies the high-frequency details lost during downscaling. The drift term " + }, + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "type": "inline_equation", + "content": "-\\frac{1}{2}\\beta(t)(\\mathbf{x} - \\mathbf{D}\\mathbf{x})dt" + }, + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "type": "text", + "content": " models the gradual removal of these details, while the diffusion term " + }, + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "type": "inline_equation", + "content": "\\sqrt{\\beta(t)}d\\mathbf{w}" + }, + { + "bbox": [ + 55, + 518, + 295, + 579 + ], + "type": "text", + "content": " adds Gaussian noise to simulate further degradation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "type": "text", + "content": "Noise Schedule " + }, + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "type": "inline_equation", + "content": "\\beta (t)" + }, + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "type": "text", + "content": ". We define the noise schedule " + }, + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "type": "inline_equation", + "content": "\\beta (t)" + }, + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "type": "text", + "content": " as a simple and effective linear function increasing over the time interval " + }, + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "type": "inline_equation", + "content": "[0,T]" + }, + { + "bbox": [ + 55, + 580, + 295, + 616 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 624, + 295, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 624, + 295, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 295, + 647 + ], + "type": "interline_equation", + "content": "\\beta (t) = \\beta_ {\\min } + \\left(\\beta_ {\\max } - \\beta_ {\\min }\\right) \\cdot \\frac {t}{T}, \\tag {10}", + "image_path": "317d06160f66282c82884de2fa78157dbdc5ac51a66eac08b2f26b6e0ac86ab5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{min}} = 0.1" + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{max}} = 20" + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": ". This linear schedule ensures a gradual increase in the degradation strength from minimal degradation at " + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": " to maximum degradation at " + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "inline_equation", + "content": "t = T" + }, + { + "bbox": [ + 55, + 653, + 295, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Relation to Image Degradation. At each time " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": ", the image " + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": " progressively loses high-frequency details due to the" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "drift toward " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{D}\\mathbf{x}_t" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": ", the downscaled version of the image. The added Gaussian noise further simulates the information loss inherent in downscaling. At " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "t = T" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": ", the image " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": " approximates the observed low-resolution image " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{LR}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": ". The reverse diffusion process then aims to recover the high-resolution image " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": " (i.e. " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{HR}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": ") from " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": " by reversing the degradation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "type": "text", + "content": "Choice of " + }, + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "type": "inline_equation", + "content": "\\beta(t)" + }, + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "type": "text", + "content": ". The linear noise schedule is chosen for its simplicity and effectiveness. It provides a straightforward way to control the rate of degradation over time. Parameters " + }, + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{min}}" + }, + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{max}}" + }, + { + "bbox": [ + 313, + 144, + 553, + 216 + ], + "type": "text", + "content": " are selected to balance the trade-off between sufficient degradation (to simulate downscaling) and numerical stability of the diffusion process." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 217, + 553, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 217, + 553, + 253 + ], + "spans": [ + { + "bbox": [ + 313, + 217, + 553, + 253 + ], + "type": "text", + "content": "Downsampling Operator D. The operator D is defined to reduce the spatial dimensions of the image by the desired scaling factor. We use bicubic downsampling." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 262, + 430, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 262, + 430, + 274 + ], + "spans": [ + { + "bbox": [ + 313, + 262, + 430, + 274 + ], + "type": "text", + "content": "3.5. Adaptive Time-Step" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 281, + 554, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 554, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 554, + 389 + ], + "type": "text", + "content": "The standard reverse diffusion process is stochastic and requires a large number of sampling steps, making it computationally expensive. To accelerate inference, we reformulate the reverse diffusion as a deterministic Ordinary Differential Equation (ODE), allowing us to use advanced ODE solvers for faster sampling. The ODE solver integrates the reverse diffusion process, and its output is the super-resolved image. The reverse diffusion process can be described by a Stochastic Differential Equation (SDE) [46]:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 324, + 410, + 553, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 410, + 553, + 425 + ], + "spans": [ + { + "bbox": [ + 324, + 410, + 553, + 425 + ], + "type": "interline_equation", + "content": "d \\mathbf {x} = [ f (\\mathbf {x}, t) - g (t) ^ {2} \\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}) ] d t + g (t) d \\bar {\\mathbf {w}} \\tag {11}", + "image_path": "38d2ae998aa9afb67e8b7eea4513bcae99d4d872643b5721f5fd9df9957e1f38.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "text", + "content": " is the data; " + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "text", + "content": " is the time variable; " + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x}, t)" + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "inline_equation", + "content": "g(t)" + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "text", + "content": " are drift and diffusion coefficients; " + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{x}} \\log p_t(\\mathbf{x})" + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "text", + "content": " is the score function; " + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{w}}" + }, + { + "bbox": [ + 313, + 434, + 554, + 505 + ], + "type": "text", + "content": " is the reverse-time Wiener process. By removing the stochastic term, we obtain the probability flow ODE, which deterministically transports the data from the noise distribution to the data distribution." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "content": "Our ATS ODE solver comprises three key components: 1. Adaptive Time Step Selection Using a Learned Function. Optimizing the allocation of time steps based on data characteristics has been explored in previous works [28, 53]. We discretize the time interval " + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "inline_equation", + "content": "[0,T]" + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "content": " non-uniform time steps " + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "inline_equation", + "content": "\\{t_i\\}_{i = 0}^N" + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "inline_equation", + "content": "t_0 = 0" + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "inline_equation", + "content": "t_N = T" + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "content": ". We introduce a learned function " + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "inline_equation", + "content": "\\phi_{\\psi}(t)" + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "content": " as a weighted sum of polynomial basis functions, where the weight is parameterized by a set of learnable coefficients " + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "inline_equation", + "content": "\\psi = \\{\\psi_{1},\\psi_{2},\\dots ,\\psi_{K}\\}" + }, + { + "bbox": [ + 313, + 506, + 553, + 638 + ], + "type": "text", + "content": ", which adaptively determines the distribution of time steps based on the data characteristics." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "text", + "content": "Parameterization of " + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "inline_equation", + "content": "\\phi_{\\psi}(t)" + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "text", + "content": ". We define " + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "inline_equation", + "content": "\\phi_{\\psi}(t)" + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "text", + "content": " as a normalized weighted sum of " + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "text", + "content": " predefined monotonically increasing basis functions " + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "inline_equation", + "content": "\\{\\phi_k(t)\\}_{k=1}^K" + }, + { + "bbox": [ + 313, + 639, + 553, + 677 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 334, + 685, + 553, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 685, + 553, + 717 + ], + "spans": [ + { + "bbox": [ + 334, + 685, + 553, + 717 + ], + "type": "interline_equation", + "content": "\\phi_ {\\psi} (t) = \\frac {\\sum_ {k = 1} ^ {K} \\psi_ {k} \\phi_ {k} (t)}{\\sum_ {k = 1} ^ {K} \\psi_ {k} \\phi_ {k} (T)}, \\quad \\psi_ {k} = \\exp (\\omega_ {k}), \\tag {12}", + "image_path": "51f898402bd3dbffcd2760eecf950bb04d1e18f857e5c94e0920ddd2c676c0be.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "154" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "where each basis function " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\phi_k(t) = t^k" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "k = 1,2,\\ldots ,K" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " is polynomial. " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\omega_{k}" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " are unconstrained learnable parameters that ensure " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\psi_{k}\\geq 0" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " through the exponential mapping. We set " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "K = 3" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " to balance model flexibility with computational efficiency. This setup allows " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\phi_{\\psi}(t)" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " to capture nonlinear timestep distributions without excessive complexity." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "type": "text", + "content": "Selection of Time Steps. Using the learned function " + }, + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "type": "inline_equation", + "content": "\\phi_{\\psi}(t)" + }, + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "type": "text", + "content": ", we map uniformly spaced normalized values " + }, + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "type": "inline_equation", + "content": "s_i = \\frac{i}{N}" + }, + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "type": "text", + "content": " to non-uniform time steps " + }, + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 55, + 144, + 294, + 180 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 188, + 294, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 188, + 294, + 214 + ], + "spans": [ + { + "bbox": [ + 69, + 188, + 294, + 214 + ], + "type": "interline_equation", + "content": "t _ {i} = \\phi_ {\\psi} ^ {- 1} \\left(s _ {i}\\right) = \\phi_ {\\psi} ^ {- 1} \\left(\\frac {i}{N}\\right), \\quad i = 0, 1, \\dots , N \\tag {13}", + "image_path": "d9b6eef6ca78ef700f4f3bc3ed498444be362f70fe46a8905c6651054f4af120.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 221, + 294, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 221, + 294, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 294, + 246 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 55, + 221, + 294, + 246 + ], + "type": "inline_equation", + "content": "\\phi_{\\psi}(t)" + }, + { + "bbox": [ + 55, + 221, + 294, + 246 + ], + "type": "text", + "content": " is monotonically increasing, its inverse function " + }, + { + "bbox": [ + 55, + 221, + 294, + 246 + ], + "type": "inline_equation", + "content": "\\phi_{\\psi}^{-1}(s)" + }, + { + "bbox": [ + 55, + 221, + 294, + 246 + ], + "type": "text", + "content": " exists and can be efficiently computed." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "spans": [ + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "type": "text", + "content": "2. Neural Operator Score Network. The score function, representing the gradient of the log probability density " + }, + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "type": "inline_equation", + "content": "\\log p_t(\\mathbf{x})" + }, + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "type": "text", + "content": ", is approximated using a neural network " + }, + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "type": "inline_equation", + "content": "s_\\theta(\\mathbf{x}, t)" + }, + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 247, + 294, + 294 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 124, + 302, + 294, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 302, + 294, + 316 + ], + "spans": [ + { + "bbox": [ + 124, + 302, + 294, + 316 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}) \\approx s _ {\\theta} (\\mathbf {x}, t). \\tag {14}", + "image_path": "951817b6bb45e4c5225245a4f2f9fa5a7e73f7adef4f98a50ccb1ce20963ec7e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "text", + "content": "In our architecture, " + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "inline_equation", + "content": "s_{\\theta}" + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "text", + "content": " consists of: (i) An encoder that extracts features from " + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{LR}}" + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "text", + "content": "; (ii) WFNO for capturing global dependencies and high-frequency details; (iii) AttnNO for modeling local dependencies and fine-grained structures; (iv) Gated Fusion Mechanism to dynamically combine features; (v) Time embedding " + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{e}(t)" + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "text", + "content": " incorporating the time variable " + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "text", + "content": " into our neural network " + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "inline_equation", + "content": "s_{\\theta}(\\mathbf{x},t)" + }, + { + "bbox": [ + 55, + 324, + 294, + 430 + ], + "type": "text", + "content": " using sinusoidal positional embeddings [14, 50], concatenating it and encoded features along the channel dimension." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 432, + 294, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 432, + 294, + 467 + ], + "spans": [ + { + "bbox": [ + 55, + 432, + 294, + 467 + ], + "type": "text", + "content": "3. Efficient Solver. We solve the reverse-time stochastic differential equation (SDE) of the diffusion process, transformed into an ODE:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 99, + 473, + 294, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 473, + 294, + 497 + ], + "spans": [ + { + "bbox": [ + 99, + 473, + 294, + 497 + ], + "type": "interline_equation", + "content": "\\frac {d \\mathbf {x}}{d t} = f (\\mathbf {x}, t) - \\frac {1}{2} g (t) ^ {2} \\nabla_ {\\mathbf {x}} \\log p _ {t} (\\mathbf {x}), \\tag {15}", + "image_path": "1668c2ae68ef4211f1bfae25e4f0d753c096c0aefd0922482726e67eb574262c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "text", + "content": " is the image estimate at time " + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "text", + "content": " in the reverse diffusion process; " + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x}, t)" + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "inline_equation", + "content": "g(t)" + }, + { + "bbox": [ + 55, + 505, + 294, + 540 + ], + "type": "text", + "content": " are coefficients derived from the forward diffusion process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 541, + 294, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 541, + 294, + 564 + ], + "spans": [ + { + "bbox": [ + 55, + 541, + 294, + 564 + ], + "type": "text", + "content": "For the Variance Preserving (VP) SDE commonly used in diffusion models, the coefficients are defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 96, + 571, + 294, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 571, + 294, + 595 + ], + "spans": [ + { + "bbox": [ + 96, + 571, + 294, + 595 + ], + "type": "interline_equation", + "content": "f (\\mathbf {x}, t) = - \\frac {1}{2} \\beta (t) \\mathbf {x}, \\quad g (t) = \\sqrt {\\beta (t)}, \\tag {16}", + "image_path": "bef0969717c1f369abf8927f2457c753c5152c29b1e9cf8642d756b9a8ffef32.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 602, + 294, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 602, + 294, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 602, + 294, + 651 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 602, + 294, + 651 + ], + "type": "inline_equation", + "content": "\\beta (t)" + }, + { + "bbox": [ + 55, + 602, + 294, + 651 + ], + "type": "text", + "content": " is a predefined noise schedule specific to the diffusion process and is consistent with our DiffFNO. By substituting the score function approximation from Eq. (14), we define the approximate drift function:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 100, + 658, + 294, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 658, + 294, + 681 + ], + "spans": [ + { + "bbox": [ + 100, + 658, + 294, + 681 + ], + "type": "interline_equation", + "content": "f _ {\\theta} (\\mathbf {x}, t) = f (\\mathbf {x}, t) - \\frac {1}{2} g (t) ^ {2} s _ {\\theta} (\\mathbf {x}, t). \\tag {17}", + "image_path": "db6b5623d8d2752c91c53d9f60e31f77179ff561fa5ca366b6e5cf1b50b3e38a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "type": "text", + "content": "The adaptive time steps " + }, + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "type": "inline_equation", + "content": "\\{t_i\\}_{i = 0}^N" + }, + { + "bbox": [ + 55, + 689, + 294, + 713 + ], + "type": "text", + "content": " discretize the ODE. We apply the Runge-Kutta 4th-order (RK4) method, as it" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 95 + ], + "type": "text", + "content": "balances computational cost and accuracy, requiring fewer steps than lower-order methods while retaining precision." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 96, + 553, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 96, + 553, + 179 + ], + "spans": [ + { + "bbox": [ + 313, + 96, + 553, + 179 + ], + "type": "text", + "content": "The benefits of ATS are threefold: (i) Deterministic Sampling: It consistently produces the same results for identical inputs, improving reproducibility. (ii) Reduced Computation: Fewer sampling steps significantly decrease inference time. (iii) High-Quality Reconstruction: It maintains high-quality reconstruction by efficiently allocating computational resources." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 190, + 394, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 190, + 394, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 190, + 394, + 204 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 211, + 553, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 211, + 553, + 258 + ], + "spans": [ + { + "bbox": [ + 313, + 211, + 553, + 258 + ], + "type": "text", + "content": "Datasets and Evaluation Metrics. We use the DIV2K [1] dataset for training. For evaluation, we use the DIV2K validation set and four standard datasets: Set5 [3], Set14 [56], BSD100 [36], and Urban100 [18]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": "We evaluate our model on upscaling factors of " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 3" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 6" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 8" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 12" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ". Notably, scales " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 6" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 8" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 12" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": " are outside the training distribution, as the training scales are uniformly sampled from " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 1" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 313, + 259, + 553, + 342 + ], + "type": "text", + "content": ". This setup assesses our model's ability to generalize to arbitrary scales. We use Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) as our evaluation metrics." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 342, + 554, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 554, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 554, + 437 + ], + "type": "text", + "content": "Quantitative Results. Building on the quantitative gains of our model, we also present qualitative results to illustrate the visual improvements achieved. We compare our proposed DiffFNO model with several SOTA arbitrary-scale SR methods, including Meta-SR [17], LIIF [7], LTE [24], SRNO [54], LIT [5], LMI [10], and HiNOTE [35]. All models are trained on the DIV2K dataset with identical settings to ensure a fair comparison in Tables 1 and 2." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 438, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 554, + 713 + ], + "type": "text", + "content": "Among the compared methods, Meta-SR performs adequately at lower scales but struggles at higher scaling factors due to its generalized approach that lacks specialized mechanisms for fine detail capture. LIIF and LTE improve upon Meta-SR by using local implicit functions and frequency-based estimations, respectively, which enhance high-frequency texture representation. However, they still face limitations in capturing non-periodic textures and high-frequency details, resulting in blurred textures at larger scales. LIT and LMI further advance performance by integrating attention mechanisms and MLP-mixer architectures, effectively preserving high-frequency textures and handling diverse scales, but they may not generalize well across datasets with varying distributions. SRNO and HiNOTE employ neural operator frameworks with attention mechanisms and frequency-aware loss priors to better capture global spatial properties and enhance high-frequency detail reconstruction. We observed mixed results between SRNO and HiNOTE: at certain scaling factors, one outperforms the other, indicating their varying strengths at different resolutions. Overall, their neural operator foundation improves the handling of arbitrary scaling but may increase computational demands." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "155" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 246, + 192 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 246, + 192 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 246, + 192 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 246, + 192 + ], + "type": "image", + "image_path": "f6a78486668d9bf1f32f6db7d34b794c8ba18e722f78231a0137e299bd6a5f00.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + 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Qualitative comparison on integer and continuous super-resolution scales. The models use RDN [58] as their encoder (except HiNOTE [35], has its own). In the HR image, the cropped patch is outlined in green." + } + ] + } + ], + "index": 44, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 374, + 552, + 577 + ], + "lines": [ + { + "bbox": [ + 58, + 374, + 552, + 577 + ], + "spans": [ + { + "bbox": [ + 58, + 374, + 552, + 577 + ], + "type": "table", + "html": "
    Modelx2x3x4x6x8x12
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    EDSR-MetaSR [17]33.320.91330.100.80028.230.83026.100.79224.770.74223.950.720
    EDSR-LTE [24]33.830.92130.500.88028.790.85226.550.80025.050.76024.200.736
    EDSR-LIIF [7]34.360.92530.940.88529.310.85527.020.81425.440.77124.320.743
    EDSR-LIT [5]34.810.92831.390.89029.700.86027.440.81525.780.77524.690.745
    EDSR-LMI [10]35.400.93031.880.89530.400.86527.950.82026.160.78025.560.750
    EDSR-SRNO [54]34.850.92831.450.89030.050.86327.360.81026.000.77225.910.760
    EDSR-DiffFNO (Ours)35.720.93232.500.90530.880.87028.290.83026.780.79026.480.775
    HiNOTE†[35]35.290.93131.900.89530.460.84227.830.79926.410.77226.230.732
    RDN-MetaSR [17]33.500.92030.320.89328.410.86126.290.81024.900.78024.010.790
    RDN-LTE [24]33.980.92230.650.88228.940.85226.700.80225.200.76224.350.732
    RDN-LIIF [7]34.510.92731.090.88729.460.85727.170.81225.590.77224.470.742
    RDN-LIT [5]34.960.93031.540.89229.850.86227.590.81725.930.77724.840.747
    RDN-LMI [10]35.550.93232.030.89730.550.86728.100.82226.310.78225.710.752
    RDN-SRNO [54]35.000.93031.600.89230.200.86227.510.81226.150.77226.060.762
    RDN-DiffFNO (Ours)35.870.93432.650.90231.030.87228.440.83226.930.79226.630.777
    ", + "image_path": "81c643cd70177fd17f4cb5964f690104239eadadffd6d5b40375b71d2840fc51.jpg" + } + ] + } + ], + "index": 45, + "angle": 0, + "type": "table_body" + } + ], + "index": 45 + }, + { + "bbox": [ + 56, + 586, + 552, + 597 + ], + "lines": [ + { + "bbox": [ + 56, + 586, + 552, + 597 + ], + "spans": [ + { + "bbox": [ + 56, + 586, + 552, + 597 + ], + "type": "text", + "content": "Table 1. PSNR/SSIM comparison on the DIV2K [1] validation set using EDSR [31] and RDN [58] encoders. HiNOTE [35] uses its own." + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 607, + 295, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 607, + 295, + 702 + ], + "spans": [ + { + "bbox": [ + 55, + 607, + 295, + 702 + ], + "type": "text", + "content": "Our DiffFNO model consistently achieves the highest PSNR and SSIM scores across all scaling factors and datasets. The performance gap widens at larger scaling factors " + }, + { + "bbox": [ + 55, + 607, + 295, + 702 + ], + "type": "inline_equation", + "content": "(\\times 8" + }, + { + "bbox": [ + 55, + 607, + 295, + 702 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 607, + 295, + 702 + ], + "type": "inline_equation", + "content": "\\times 12" + }, + { + "bbox": [ + 55, + 607, + 295, + 702 + ], + "type": "text", + "content": "), demonstrating a superior generalization to the out-of-distribution scales. The improvements are more pronounced on complex datasets like Urban100, which contain intricate textures and structures. By combining WFNO and AttnNO features through the Gated Fusion" + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 313, + 607, + 553, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 607, + 553, + 679 + ], + "spans": [ + { + "bbox": [ + 313, + 607, + 553, + 679 + ], + "type": "text", + "content": "Mechanism, which adaptively balances global and local features, DiffFNO synthesizes global and local dependencies. The ATS ODE solver efficiently refines high-resolution images, further enhancing quality. This combination addresses the limitations of prior models, such as spectral bias and insufficient high-frequency detail capture." + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "Qualitative Results. Fig. 3 compares arbitrary-scale SR methods on a BSD100 image (scaling factor of " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\times 12" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": ") with" + } + ] + } + ], + "index": 49 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "156" + } + ] + } + ], + "index": 50 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 553, + 182 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 553, + 182 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 553, + 182 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 553, + 182 + ], + "type": "table", + "html": "
    ModelSet5Set14BSD100Urban100
    ×2×3×4×6×8×2×3×4×6×8×2×3×4×6×8×2×3×4×6×8
    MetaSR [17]37.5034.0531.5228.2326.0233.5130.0328.0225.5324.0231.0228.0526.5224.8223.5232.0228.0325.8223.5222.03
    LIIF [7]38.0234.4232.0428.5726.2534.0330.4328.4325.8424.3331.5228.5527.0325.0323.8332.5228.5326.0323.8322.33
    LTE [24]38.2134.6332.2528.7626.4434.2230.6528.6426.0524.5231.7128.7327.2325.2324.0332.7228.7526.2324.0322.53
    SRNO [54]38.3234.8432.6929.3827.2834.2730.7128.9726.7625.2632.4329.3727.8326.0424.9933.3329.1426.9824.4323.02
    LIT [5]38.5335.0232.8229.5127.4234.4430.8329.0326.8225.3332.5229.5127.9226.1225.0133.4229.2227.0224.5223.12
    LMI [10]38.7235.1432.9529.6327.5534.6331.0229.2427.0525.5532.7229.7428.0426.2525.1433.6229.4427.2424.6323.23
    HNOTE [35]39.0135.2233.0829.8527.7435.0231.2529.5527.3525.8533.0230.0528.1526.3525.2534.0329.8327.5524.7323.34
    DiffFNO (Ours)39.7235.3033.1630.2327.9336.0131.5430.2227.5826.0233.5630.2428.2126.4525.3034.1929.9927.7424.8023.35
    ", + "image_path": "c3936d04a4a58ca2a03b241afd694bff8e5a12bdce72c6c8ed26166708405e41.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 214, + 553, + 330 + ], + "blocks": [ + { + "bbox": [ + 56, + 191, + 553, + 213 + ], + "lines": [ + { + "bbox": [ + 56, + 191, + 553, + 213 + ], + "spans": [ + { + "bbox": [ + 56, + 191, + 553, + 213 + ], + "type": "text", + "content": "Table 2. PSNR comparison on four benchmark datasets: Set5 [3], Set14 [56], BSD100 [36], and Urban100 [18]. All models use RDN [58] as their encoder, besides HiNOTE [35] which has its own." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 214, + 553, + 330 + ], + "lines": [ + { + "bbox": [ + 56, + 214, + 553, + 330 + ], + "spans": [ + { + "bbox": [ + 56, + 214, + 553, + 330 + ], + "type": "table", + "html": "
    Model×2×3×4×6×8×12InferenceSteps
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    SRNO [54]33.810.92030.530.88028.740.85026.590.80025.100.76024.180.730147-
    FNO [26]34.360.92530.940.88529.310.85527.020.81025.440.77024.320.74085-
    WFNO34.810.92831.390.88829.700.85827.440.81525.780.77524.690.74597-
    WFNO-AttnNO35.400.93031.880.89230.400.86227.950.82026.160.78025.560.7501391000
    DiffFNO(-w, -a, -s)34.850.92831.450.89030.050.86027.360.81526.000.77525.910.7602041000
    DiffFNO(-a, -s)35.290.93031.900.89330.460.86327.830.82026.410.78026.230.7652311000
    DiffFNO(-s)35.700.93232.480.89630.850.86628.260.82526.750.78526.450.7702661000
    DiffFNO35.720.93232.500.90030.880.87028.290.83026.780.79026.480.77514130
    ", + "image_path": "a2c75a672ad8598bc3a60b2864a54aa1d6b99f0c4137cb6e124705f157481268.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 338, + 553, + 361 + ], + "lines": [ + { + "bbox": [ + 55, + 338, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 553, + 361 + ], + "type": "text", + "content": "Table 3. Ablation study of variants of DiffFNO on the DIV2K [1] validation set. All use EDSR-baseline [31] backbone as their encoder. Inference times are measured in milliseconds (ms). WFNO-AttnNO has Gated Fusion Mechanism." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 371, + 295, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 371, + 295, + 514 + ], + "spans": [ + { + "bbox": [ + 54, + 371, + 295, + 514 + ], + "type": "text", + "content": "fine-grained details like animal fur and rock textures and an Urban100 (continuous scaling factor of " + }, + { + "bbox": [ + 54, + 371, + 295, + 514 + ], + "type": "inline_equation", + "content": "\\times 7.6" + }, + { + "bbox": [ + 54, + 371, + 295, + 514 + ], + "type": "text", + "content": ") image featuring large structures and fine local details such as reflections on the grass. SRNO and HiNOTE capture multiscale details effectively, from the animal's body to tiny gaps between glass panels. However, DiffFNO reconstructs crisper edges with fewer artifacts, enhancing texture in animal fur pattern and reflections. WFNO captures large-scale patterns, while AttnNO and Gated Fusion Mechanism preserve intricate textures. This multiscale approach followed by a diffusion process enhanced by the ATS's ODE solver further reduces visual artifacts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 518, + 295, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 518, + 295, + 686 + ], + "spans": [ + { + "bbox": [ + 55, + 518, + 295, + 686 + ], + "type": "text", + "content": "Ablation Studies. Extensive ablation studies validate the effectiveness and complementary nature of new components in DiffFNO. Table 3 reports the PSNR results on the DIV2K validation set for different model variants with scaling factors from " + }, + { + "bbox": [ + 55, + 518, + 295, + 686 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 55, + 518, + 295, + 686 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 518, + 295, + 686 + ], + "type": "inline_equation", + "content": "\\times 12" + }, + { + "bbox": [ + 55, + 518, + 295, + 686 + ], + "type": "text", + "content": ". -w denotes leaving out the Mode Rebalancing (yielding the default FNO [26]). -a denotes omitting AttnNO. -s denotes the removal of ATS ODE solver. We also measure inference time by averaging over 100 runs, and report inference steps. We establish a baseline with SRNO, whose architecture is the most similar to our DiffFNO aamong the methods covered in our study. Overall, we observe notable improvements with the addition of model components. The complete DiffFNO achieves the highest PSNR and SSIM values across all upscaling factors." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 713 + ], + "type": "text", + "content": "Effect of Mode Rebalancing. Incorporating Mode Rebalancing into WFNO boosted performance compared to the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 371, + 553, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 371, + 553, + 394 + ], + "spans": [ + { + "bbox": [ + 313, + 371, + 553, + 394 + ], + "type": "text", + "content": "default FNO [26], at the cost of a slightly increased number of parameters and inference time." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 396, + 553, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 553, + 467 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 553, + 467 + ], + "type": "text", + "content": "Effect of Gated Fusion Mechanism and AttnNO. The Gated Fusion Mechanism introduces minimal computational overhead. In addition, extra computational cost incurred by Attention-based Neural Operator is effectively mitigated by running it in parallel with WFNO while employing a shared encoder." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 467, + 553, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 553, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 553, + 528 + ], + "type": "text", + "content": "Effect of ATS ODE Solver: ATS dramatically reduces the number of inference steps from 1,000 to just 30, which substantially improves the inference time while delivering competitive performance (Tab. 3). DiffFNO outperforms the SOTA in both PSNR and inference time (Fig. 1 (a))." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 539, + 388, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 539, + 388, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 539, + 388, + 552 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 559, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 559, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 312, + 559, + 555, + 713 + ], + "type": "text", + "content": "We propose Diffusion Fourier Neural Opeartor (DiffFNO) for arbitrary-scale image super-resolution. DiffFNO is made of Weighted Fourier Neural Operator with a Mode Rebalancing mechanism to emphasize high-frequency details. It is complemented by a Attention-based Neural Operator through a Gated Fusion Mechanism that effectively adjusts the influence of global and local features. Image reconstruction is further refined by a diffusion process augmented with an Adaptive Time-Step ODE solver that dynamically allocates time steps, drastically cutting down inference time without compromising output quality. Experiments demonstrate DiffFNO's competitiveness in both reconstruction quality and inference time across various benchmarks, establishing a new state-of-the-art." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 748, + 312, + 757 + ], + "type": "text", + "content": "157" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 94, + 115, + 106 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 94, + 115, + 106 + ], + "spans": [ + { + "bbox": [ + 56, + 94, + 115, + 106 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 114, + 295, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 114, + 295, + 158 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 114, + 295, + 158 + ], + "spans": [ + { + "bbox": [ + 61, + 114, + 295, + 158 + ], + "type": "text", + "content": "[1] Eirikur Agustsson and Radu Timofte. 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In Proceedings of the IEEE international conference on computer vision, pages 1529-1537, 2015. 4" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 299, + 749, + 312, + 757 + ], + "type": "text", + "content": "160" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_content_list.json b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dd33427c15834d23e046b00fdc90f3b740cbe5cd --- /dev/null +++ b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_content_list.json @@ -0,0 +1,1761 @@ +[ + { + "type": "text", + "text": "DiffLO: Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement", + "text_level": 1, + "bbox": [ + 107, + 130, + 888, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yongshu Huang $^{1,2*}$ Chen Liu $^{1,2*}$ Minghang Zhu $^{1,2}$ Sheng Ao $^{1,2\\dagger}$ Chenglu Wen $^{1,2}$ Cheng Wang $^{1,2\\dagger}$ $^{1}$ Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University, China. \n $^{2}$ Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University, China.", + "bbox": [ + 101, + 179, + 931, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 286, + 326, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "LiDAR odometry is a critical module in autonomous driving systems, responsible for accurate localization by estimating the relative pose transformation between consecutive point cloud frames. However, existing studies frequently encounter challenges with unreliable pose estimation, due to the lack of in-depth understanding of scenario and the presence of noise interference. To address this challenge, we propose DiffLO, a semantic-aware LiDAR odometry network with diffusion-based refinement. To mitigate the impact of challenging cases such as dynamic, repetitive patterns, and low textures, we introduce a semantic distillation method that integrates semantic information into the odometry task. This allows the network to gain a semantic understanding of the scene, enabling it to focus more on the objects that are beneficial for pose estimation. Additionally, to enhance the robustness, we propose a diffusion-based refinement method. This method uses pose-related features as conditional constraints for generative diversity, iteratively refining the pose estimation to achieve greater accuracy. Comparative experiments on the KITTI odometry dataset demonstrate that the proposed method achieves state-of-the-art performance among existing learning-based approaches. Furthermore, the proposed DiffLO method outperforms the classic A-LOAM on most evaluation sequences. The code will be released at https://github.com/HyTree7/DiffLO.", + "bbox": [ + 89, + 319, + 483, + 713 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 744, + 220, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "LiDAR odometry (LO) is a well-studied problem in computer vision with numerous applications in Simultaneous Localization and Mapping (SLAM) [58], autonomous driving [54], and robotics [45]. The primary objective is to estimate the relative transformation between two frames based on the source and target point clouds.", + "bbox": [ + 89, + 770, + 482, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b42ddfbecd180b16ae9886bd3dc11dc223108334a0e043043b4005bf5c18c5b6.jpg", + "image_caption": [ + "Figure 1. (a) Predicts a coarse initial pose and applies iterative MLP-based refinement to refine the initial estimate. (b) Predicts a coarse initial pose and applies iterative Diffusion-based refinement, incorporating knowledge distillation to enable semantic understanding. Here, $\\hat{T}_k$ represents the noisy pose of the $k^{th}$ denoising step." + ], + "image_footnote": [], + "bbox": [ + 517, + 286, + 687, + 506 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0caa6faa8b4c9520049822435d36a373de813a2409a982cf249276c0de7621b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 286, + 903, + 507 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most classic geometry-based methods, such as Iterative Closest Point (ICP) [4], its variants [31] and others [35], work by iteratively minimizing the distance between corresponding points in two point clouds to achieve accurate alignment. However, they often struggle in sparse point cloud environments, complex dynamic scenes, or when the quality of the point cloud degrades [13, 27, 42]. This limitation arises due to their reliance on precise geometric correspondences.", + "bbox": [ + 509, + 613, + 906, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning-based methods have garnered significant attention in recent years. These methods learn feature representations from large-scale data to infer relative transformation between frames in an end-to-end manner, providing better scalability and the potential for multi-task learning. However, the accuracy of deep learning methods still lags behind traditional odometry techniques.", + "bbox": [ + 509, + 750, + 908, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We identify the following challenges faced by Deep Learning-based odometry methods: (1) To mitigate the effects of challenging cases such as dynamic objects and oc", + "bbox": [ + 511, + 854, + 906, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors contributed equally.", + "bbox": [ + 107, + 875, + 297, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding Author.", + "bbox": [ + 109, + 887, + 238, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17050", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "clusions, LO-Net [21] introduces a mask prediction network learning the compensation for dynamic objects to remove dynamic objects. Methods such as PWCLO-Net [42], TransLO [23], and EfficientLO [44] introduce a hierarchical embedding mask and apply pose feature weighting to filter dynamic object. However, these approach lacks a comprehensive understanding of object structures, leading to inaccuracies and resulting in cumulative errors; (2) Furthermore, these methods [18, 23, 24, 26, 42, 44] are deterministic prediction tasks, which limits their ability to adapt to newly emerging changes or complexities in the environment. Additionally, they can not provide information about prediction uncertainties.", + "bbox": [ + 89, + 90, + 480, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic segmentation network contains rich geometric information and intricate details about the scene. This insight motivates us to integrate semantic information into the odometry network, thereby enhancing its ability to filter out dynamic objects and manage occlusions effectively. To achieve this, as shown in Fig. 1, we propose a knowledge distillation approach that transfers semantic knowledge from a segmentation model to the odometry network. After training, the knowledge distillation component and segmentation model are dropped to avoid extra computation or network parameter. By leveraging the contextual knowledge provided by semantic segmentation, our approach aims to improve the overall accuracy and robustness of odometry in complex environments.", + "bbox": [ + 89, + 289, + 480, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models [11] are characterized by their robustness, and have achieved significant success across various tasks [8, 15, 22, 25]. These strengths have inspired us to explore their potential application to the LiDAR odometry task. In this paper, we propose reformulating the odometry task as a diffusion process. As shown in Fig. 1, we transition from a traditional MLP-based refinement approach to a diffusion-based refinement, shifting the task from a deterministic prediction framework to a probabilistic generative model. Specifically, Our approach consists of a forward process that progressively adds noise to the residual pose of the ground truth, followed by a reverse denoising process to refine the noisy pose estimate. We utilize coarse pose embedding, cost volume, semantic feature and geometry embedding as conditions to restrict generation diversity.", + "bbox": [ + 89, + 503, + 482, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 109, + 732, + 410, + 746 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To enhance the network's ability to focus on objects critical for pose estimation in the scene, we incorporate semantic awareness into odometry by distilling knowledge from a semantic segmentation model.", + "- We propose a novel diffusion-based refinement pipeline and design strong conditional guidance by combining semantic embedding, coarse pose embeddings, geometry embedding and cross-frame cost volume to control generation diversity. To the best of our knowledge, this is the first work to leverage diffusion probabilistic model in the" + ], + "bbox": [ + 89, + 750, + 478, + 896 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LiDAR odometry task.", + "bbox": [ + 527, + 90, + 679, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments on the KITTI odometry dataset [7] demonstrate that our method outperforms all existing learning-based odometry methods. On most sequences, our performance even surpasses A-LOAM with mapping.", + "bbox": [ + 513, + 106, + 903, + 166 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Relate Work", + "text_level": 1, + "bbox": [ + 513, + 195, + 643, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deep LiDAR Odometry", + "text_level": 1, + "bbox": [ + 513, + 224, + 730, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The field of visual depth odometry has advanced rapidly. However, research on LiDAR-based depth odometry remains challenging due to the inherent irregularity and complexity of point clouds. LO-Net [21] proposed an end-to-end deep odometry network that enhances robustness by learning the compensation for dynamic objects through a mask prediction network. PWCLO [42] first introduces a coarse-to-fine structure to LiDAR odometry, implementing a hierarchical refinement approach for estimated poses. LodoNet [52] projects 3D point clouds onto 2D spherical depth images to extract and match keypoints for odometry localization. EfficientLO [44] introduces a projection-aware representation of 3D point clouds, facilitating efficient learning for large-scale datasets. TransLO [23] develops a cross-frame transformer module that associates consecutive frames, thereby regressing relative pose estimations. DELO [1] innovatively employs partial optimal transportation of LiDAR feature descriptors to achieve robust localization estimation.", + "bbox": [ + 511, + 253, + 903, + 539 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. LiDAR-based semantic segmentation", + "text_level": 1, + "bbox": [ + 513, + 565, + 831, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LiDAR-based semantic segmentation aims to assign a semantic label to each point in the input LiDAR scan. These methods can generally be categorized into several approaches: point-based [14, 32, 33, 39], voxel-based [9, 57], projection-based [17, 29, 46], and hybrid methods that combine these techniques [37, 49]. These approaches consistently expand the receptive field by integrating fine-grained point features with coarse-grained contextual information, which enhances the network's ability to understand the scene structure and the unique characteristics of each point. Semantic information has also proven to be highly valuable in traditional non-deep learning methods, such as [3, 5, 19, 20, 56]. By leveraging semantic labels, these systems can enhance feature matching and improve robustness against challenging conditions like dynamic objects and occlusions.", + "bbox": [ + 511, + 593, + 903, + 834 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by these traditional methods, we explore integrating semantics into learning-based LiDAR odometry to address the challenges posed by dynamic objects, repetitive patterns, and low-texture environments.", + "bbox": [ + 511, + 840, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17051", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. 3D Diffusion Model", + "text_level": 1, + "bbox": [ + 89, + 90, + 277, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models have garnered significant attention and research in a variety of 3D point cloud processing tasks. For instance, Luo et al. [28] introduced a probabilistic model for point cloud generation, transforming the point cloud noise distribution into the desired point cloud shape distribution. Zhou et al. [55] combined a denoising diffusion model with a mixed point-voxel representation of 3D shapes for unconditional shape generation and conditional multimodal shape completion. Jiang et al. [15] proposed a point cloud registration framework based on an SE(3) diffusion model, framing the 3D registration task as a denoising diffusion process that iteratively refines the pose of the source point cloud to achieve precise alignment with the target point cloud. Difflow3D [25] presented an uncertainty-aware scene flow estimation network leveraging a diffusion probabilistic model, where iterative diffusion modules refine initial estimates to enhance the robustness of scene flow estimation. DiffLoc [22] formulates LiDAR localization as a conditional generation of poses, employing a diffusion model conditioned on geometric robust features and incorporating an iterative denoising process into APR to achieve accurate LiDAR localization.", + "bbox": [ + 89, + 113, + 483, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by the successful applications of diffusion models in tasks such as registration, scene flow estimation, and localization, we investigate the integration of diffusion models to improve the accuracy of LiDAR odometry.", + "bbox": [ + 89, + 446, + 483, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 522, + 181, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given two consecutive point cloud frames $PC_1 \\in \\mathbb{R}^{N \\times 3}$ and $PC_2 \\in \\mathbb{R}^{M \\times 3}$ , the goal of the LiDAR odometry task is to estimate the relative transformation between the two consecutive frames of point clouds. To solve this task, we propose DiffLO, a semantic-aware odometry network with diffusion-based refinement. DiffLO first hierarchically extracts point features (Sec. 3.1). Subsequently, we introduce a Semantic Perception Module (Sec. 3.2), which enables the odometry network to gain semantic understanding. Then, the initial pose is generated (Sec. 3.3) in the coarsest layer. We then utilize diffusion model with condition signals to refine the initial pose by predicting pose residuals from coarse to fine (Sec. 3.4). Lastly, the loss function will be presented in (Sec. 3.5).", + "bbox": [ + 89, + 547, + 483, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Multi-scale Feature Extraction", + "text_level": 1, + "bbox": [ + 89, + 770, + 362, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We utilize PointConv [47] for hierarchical feature extraction. At each level $l$ , dense input points and their features are first subsampled using furthest point sampling to create a sparse point set. Then, for each subsampled sparse point, k-nearest neighbor groups local dense points to form a local region for feature extraction. Next, a PointConv [47] layer aggregates features from the grouped local points, produc", + "bbox": [ + 89, + 794, + 483, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing a local feature for each sparse point. This process results in an L-level pyramid of point features.", + "bbox": [ + 511, + 90, + 906, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Semantic Perception Module", + "text_level": 1, + "bbox": [ + 511, + 128, + 769, + 145 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To guide the network's attention towards objects in the scene that are beneficial for pose estimation, such as buildings and pole-like structures. We introduce Semantic Perception Module (SPM). SPM consists of three components: Semantic Module, Semantic Segmentation Modle and Knowledge Distillation. We introduce a semantic segmentation model as the teacher network. A sub-network (the Semantic Module) within the odometry model is designated as the student model.", + "bbox": [ + 511, + 152, + 905, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "During the training stage, three modules collaborate to transfer semantic knowledge into the odometry model. Firstly, the Semantic Module takes the point cloud features $F$ in coarse layer as its input, the output can be expressed as follows:", + "bbox": [ + 511, + 289, + 905, + 363 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF _ {s t u} = M L P (F) + M L P (F) \\otimes \\sigma (M L P (F)), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 372, + 906, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\otimes$ indicates element-wise multiplication. $\\sigma (\\cdot)$ denotes the softmax operation along the feature dimension.", + "bbox": [ + 511, + 397, + 905, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Secondly, a pretrained 3D semantic segmentation model [16], with its network parameters frozen, is utilized here. We extract the per-point features from the final layer, denoted as $F_{seg} \\in \\mathbb{R}^{N \\times d}$ . These features are subsequently downsampled to $F_{tea} \\in \\mathbb{R}^{N' \\times d}$ to ensure compatibility in dimension with $F_{stu}$ . And we adjust the output dimension of the semantic regressor branch, ensuring that $F_{tea}$ and $F_{stu}$ share the same feature dimension $d$ for each point.", + "bbox": [ + 511, + 428, + 905, + 550 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, we utilize knowledge distillation [10] to transfer semantic knowledge from the segmentation module to the odometry model. This is achieved by optimizing the following distillation loss:", + "bbox": [ + 511, + 550, + 905, + 609 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {k d} = \\delta \\left(F _ {s t u}, F _ {t e a}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 618, + 903, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\delta (\\cdot ,\\cdot)$ measures the difference between the feature representations from the teacher network $F_{tea}$ and the student network $F_{stu}$ .", + "bbox": [ + 511, + 643, + 905, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finally, the semantic feature $F_{stu}$ is propagated to the following level for a denser optimization and simultaneously serves as a condition signal for diffusion-based refinement in Sec. 3.4, via an upsampling layer [6, 48].", + "bbox": [ + 511, + 689, + 905, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "During the inference stage, only the Semantic Module is retained to avoid additional computational overhead. The output $F_{stu}$ from the Semantic Module is still propagated to subsequent layers, serving as a conditional signal.", + "bbox": [ + 511, + 750, + 905, + 810 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By embedding semantic understanding into the odometry process, the model is better able to focus on objects in the scene that are beneficial for pose estimation. Meanwhile, the close integration of knowledge distillation improves both the efficiency and effectiveness of the overall system.", + "bbox": [ + 511, + 810, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17052", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/60b3ff2613959917e5c5a681698c1d935bdb88a4f5e6a3839e41463c512359a5.jpg", + "image_caption": [ + "Figure 2. The overall structure of DiffLO. The proposed pipeline comprises three core components: Pose Initialization, Semantic Perception Module, and Diffusion-based Pose Refinement. First, hierarchical point features are extracted from the input point cloud. Then, we enable the network to acquire semantic understanding through a knowledge distillation approach. Following this, an initial coarse pose estimate is generated. Finally, the Diffusion-based Pose Refinement module applies iterative refinement layers, conditioned on various signals, to improve the initial pose estimate, ultimately producing a more accurate and robust final pose. To optimize inference efficiency, the semantic segmentation component is discarded after the training phase." + ], + "image_footnote": [], + "bbox": [ + 98, + 90, + 898, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Semantic-Aware Pose Estimator", + "text_level": 1, + "bbox": [ + 89, + 539, + 374, + 554 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We enhance the pose estimation method from the PWCLO-Net [42] by incorporating semantic features into the pose estimation process. Taking the $l^{th}$ layer as example.", + "bbox": [ + 89, + 561, + 482, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE ^ {l} = M L P \\left(F ^ {l} \\oplus F _ {s t u} ^ {l} \\oplus U E ^ {l} \\oplus C E ^ {l}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 618, + 482, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM ^ {l} = \\sigma (M L P (F ^ {l} \\oplus F _ {s t u} ^ {l} \\oplus U M ^ {l} \\oplus E ^ {l})), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 660, + 482, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\oplus$ is the concatenation and $\\sigma (\\cdot)$ denotes the softmax operation. $F^l$ is the point cloud feature from $l$ layer, $CE^l$ is generated by cross-frame correlation [6, 43]. $F_{stu}^{l}$ , $UE^{l}$ and $UM^{l}$ are the results of upsampling the semantic feature $F_{stu}^{l + 1}$ , the embedding feature $E^{l + 1}$ and the embedding mask $M^{l + 1}$ respectively. The embedding features $E = \\{e_i|e_i\\in \\mathbb{R}^C\\}_{i = 1}^n$ , the embedding mask $M = \\{m_i|m_i\\in \\mathbb{R}^C\\}_{i = 1}^n$ . The pose is then generated by:", + "bbox": [ + 89, + 684, + 482, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq = \\frac {F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right)}{\\left| F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right) \\right|} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 815, + 482, + 852 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt = F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 864, + 482, + 904 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $FC(\\cdot)$ denotes the fully connected layer and $\\odot$ represents dot product. Following [42], the embedding features $E$ , embedding mask $M$ and semantic features are also propagated to denser layers for optimization.", + "bbox": [ + 511, + 539, + 906, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The coarse-level point cloud is sparse and has low resolution, which can lead to incorrect matches and inaccurate initial pose estimates. Inspired by recent success and denoising properties of the diffusion model [11], we design a novel diffusion-based pose refinement module to refine the coarse pose progressively.", + "bbox": [ + 511, + 599, + 906, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Diffusion-based Pose Refinement", + "text_level": 1, + "bbox": [ + 511, + 700, + 802, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we formulate the coarse pose residual as the diffusion latent variable, and residual pose are generated from the reverse process of diffusion model iteratively.", + "bbox": [ + 511, + 724, + 905, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the training stage, the diffusion model is trained to learn the underlying distribution of residual poses by recovering the ground truth residual pose from its corrupted version. The ground truth residual pose is calculated as follow:", + "bbox": [ + 511, + 771, + 905, + 844 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {0} = T _ {g t} \\cdot T _ {p r e d} ^ {- 1}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 845, + 903, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T_{0}$ is the ground truth residual pose, $T_{gt}$ is the ground truth pose and $T_{pred}$ is the coarse pose generated by the", + "bbox": [ + 511, + 869, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17053", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "previous layer or the initial pose.", + "bbox": [ + 89, + 90, + 308, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, in each training iteration, a random diffusion step, denoted as $k \\in \\{1, 2, \\dots, K\\}$ , is chosen. With a predefined variance schedule $\\beta_1, \\ldots, \\beta_k$ , we introduce noises to $T_0$ , resulting in the noisy residual pose $T_k$ .", + "bbox": [ + 89, + 106, + 483, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(T _ {k} \\mid T _ {0}\\right) = \\mathcal {N} \\left(T _ {k}; \\sqrt {\\bar {\\alpha} _ {k}} T _ {0}, (1 - \\bar {\\alpha} _ {k}) \\mathrm {I}\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 171, + 480, + 189 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT _ {k} = \\sqrt {\\bar {\\alpha} _ {k}} T _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {k}} \\epsilon , \\epsilon \\sim \\mathcal {N} (0, I) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 191, + 480, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "denoting $\\alpha_{k} = 1 - \\beta_{k}$ and $\\overline{\\alpha}_k = \\Pi_{i = 1}^k\\alpha_i$ . Eventually, the ground truth residual pose $T_{0}$ is turned into Gaussian noise when $k$ is large enough.", + "bbox": [ + 89, + 215, + 482, + 261 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the inference stage, the denoise model approximates the distribution $p(T_0|C)$ as the reversed diffusion process of gradually cleaning $T_{k}$ . Instead of predicting $\\epsilon$ as formulated by [12], we follow [34, 38] and predict the signal itself. Also, we constrain the generation diversity and control the reversed diffusion process by the condition information $C$ . In this way, we utilize a denoising network to predict the residual pose $\\hat{T_0}$ from noisy input $T_{k}$ , time step $t = k$ , and condition $C$ .", + "bbox": [ + 89, + 263, + 483, + 397 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {T} _ {0} = \\mathcal {M} _ {\\theta} \\left(T _ {k}, t, C\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 404, + 480, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{M}_{\\theta}(\\cdot ,\\cdot ,\\cdot)$ is the denoising network. The training objective is to minimize the following loss:", + "bbox": [ + 89, + 426, + 483, + 458 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e s} = \\mathbb {E} _ {T _ {0}, t}, \\left[ \\| t _ {g t} - t _ {p r e d} \\| _ {2} + \\| q _ {g t} - q _ {p r e d} \\| _ {2} \\right], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 463, + 480, + 481 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $t_{gt}$ and $q_{gt}$ are the translation vector and quaternion from $T_0$ , and $t_{pred}$ and $q_{pred}$ are their corresponding predicted values from $\\hat{T}_0$ .", + "bbox": [ + 89, + 486, + 482, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Design of Condition Signal. Inspired by [42, 43], we introduce the geometric feature $GE$ extracted from $PC_{1}$ along with a cost volume embedding $CE$ constructed using cross-frame correlation [6], with the corresponding hierarchical point cloud features as input, and residual pose embeddings $PE = T_{k} \\cdot PC_{1} - PC_{1}$ and the semantic feature $F_{stu}$ as conditional signals to constrain generation diversity. The condition signal is as follow:", + "bbox": [ + 89, + 532, + 483, + 654 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC = G E \\oplus C E \\oplus P E, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 660, + 480, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\oplus$ is the concatenation operation.", + "bbox": [ + 89, + 681, + 354, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We employ the augmented version [6] with Gate Recurrent Unit (GRU) to process the condition signal $C$ . This approach allows for the extraction of essential features from $C$ to generate the augmented condition signal $C'$ . Subsequently, the semantic-aware pose estimator in Sec. 3.3 is introduced to generate the residual pose $\\hat{T}_0$ . Here, $C'$ are treated as the cost volume embedding $CE$ in Eq. (3). Taking the $l^{th}$ refinement layer as example, the refined pose $T_{pred}^l$ is calculated as follow:", + "bbox": [ + 89, + 696, + 483, + 835 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT _ {p r e d} ^ {l} = \\hat {T} _ {0} ^ {l} \\cdot T _ {p r e d} ^ {l + 1}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 840, + 480, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the refined pose $T_{pred}^{l}$ will be the input to $l - 1^{th}$ refinement layer.", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training Loss", + "text_level": 1, + "bbox": [ + 513, + 90, + 656, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The network supervises the pose outputs from each level, along with the residual poses predicted by the diffusion model and the semantic features derived from the Semantic Module. Drawing from previous deep odometry research [21, 42], the training loss function for the odometry at the l-th level is as follows:", + "bbox": [ + 511, + 113, + 905, + 203 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} ^ {l} = \\left\\| t _ {g t} - t ^ {l} \\right\\| \\exp (- w _ {t}) + w _ {t} \\\\ + \\left\\| q _ {g t} - \\frac {q ^ {l}}{\\| q ^ {l} \\|} \\right\\| _ {2} \\exp (- w _ {q}) + w _ {q}, \\tag {14} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 213, + 903, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\| \\cdot \\|$ and $\\| \\cdot \\| _2$ denotes the $\\ell 1$ -norm and the $\\ell 2$ -norm respectively. $t_{gt}$ and $q_{gt}$ are the ground-truth translation vector and quaternion respectively. $t^l$ and $q^{l}$ are predicted pose from each level. $w_{t}$ and $w_{q}$ are two learnable parameters, which are introduced to eliminate the differences in scale and units between the translation vector and the quaternion. Then, a multi-scale supervised approach is adopted. The total training loss function $\\mathcal{L}$ is:", + "bbox": [ + 511, + 277, + 905, + 398 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {k d} + \\sum_ {l = 0} ^ {K} \\lambda^ {l} \\times \\left(\\mathcal {L} ^ {l} + \\mathcal {L} _ {r e s} ^ {l}\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 409, + 903, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $K$ is the total number of warp-refinement levels and $\\lambda^l$ denotes the weight of the l-th level.", + "bbox": [ + 511, + 459, + 905, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 511, + 503, + 637, + 520 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. KITTI Odometry Dataset", + "text_level": 1, + "bbox": [ + 511, + 527, + 748, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The KITTI odometry dataset [7] is a widely used standard dataset for evaluating visual odometry and SLAM algorithms. It includes multiple driving scenarios, encompassing urban, rural, and highway environments, with variations in weather and lighting conditions. The dataset consists of 22 sequences of LiDAR point clouds and their corresponding stereo images. In our experiments, we utilize the Velodyne LiDAR point clouds provided in the dataset. Since the ground truth poses (trajectories) are only available for sequences 00 to 10, we use these sequences for both training and testing.", + "bbox": [ + 511, + 551, + 906, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implement details", + "text_level": 1, + "bbox": [ + 511, + 726, + 687, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the training and evaluation process, N points are randomly sampled from the point clouds of two frames separately. It is not necessary for the original input point clouds to have the same number of points. In the proposed network, N is set to 8192. All training and evaluation experiments are conducted on a single NVIDIA RTX 3090 GPU. The Adam optimizer is employed with parameters $\\beta 1 = 0.9$ and $\\beta 2 = 0.999$ . The initial learning rate is set to 0.001 and is reduced by a factor of 0.8 every 8 epochs until it reaches 0.000001. The initial values of the trainable parameters $w_{t}$", + "bbox": [ + 511, + 750, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17054", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d9b5d4299f998573b595511d5da8975510d1235efdad75db255b826e35def077.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Method00010203040506\\( 07^{\\dagger} \\)\\( 08^{\\dagger} \\)\\( 09^{\\dagger} \\)\\( 10^{\\dagger} \\)Mean on 07-10
    \\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t _{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)
    ICP-po2po6.882.9911.212.588.213.3911.075.056.644.023.971.931.951.595.173.3510.044.936.932.898.914.747.7633.978
    ICP-po2pl3.801.7313.532.589.002.742.721.632.962.582.291.081.771.001.551.424.422.143.951.716.132.604.0131.968
    GICP [36]1.290.644.390.912.530.771.681.083.761.071.020.540.920.460.640.451.580.751.970.771.310.621.3750.648
    CLS [41]2.110.954.221.052.290.861.631.091.590.711.980.920.920.461.040.732.141.051.950.923.461.282.1480.995
    Full LOAM [50]0.780.531.430.550.920.550.860.650.710.500.570.380.650.390.630.501.120.440.770.480.790.570.8280.498
    Full A-LOAM0.760.311.970.504.531.450.930.490.620.390.480.250.610.280.430.261.060.320.730.311.020.400.8100.323
    LO-Net [21]1.470.721.360.471.520.711.030.660.510.651.040.690.710.501.700.892.120.771.370.581.800.931.7480.793
    PWCLO-Net [42]0.780.420.670.230.860.410.760.440.370.400.450.270.270.220.600.441.260.550.790.351.690.621.0850.490
    DELO [1]1.430.812.190.571.480.521.381.102.451.701.270.640.830.350.580.411.360.641.230.571.530.901.1750.630
    TransLO [23]0.850.381.160.450.880.341.000.710.340.180.630.410.730.310.550.431.290.500.950.461.180.610.9930.500
    EfficientLO [44]0.830.330.550.210.710.250.490.380.220.110.340.210.360.240.460.381.140.410.780.330.800.460.7950.395
    Ours0.600.270.360.150.710.260.570.400.300.170.330.220.280.170.370.271.120.440.680.280.660.320.7080.328
    ", + "bbox": [ + 93, + 88, + 903, + 229 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/673778385a6667a182e3863b53232dabc0da33324b64d4c01eb4fb7599240748.jpg", + "table_caption": [ + "Table 1. The LiDAR odometry experiment results on KITTI odometry dataset [7]. $t_{rel}, r_{rel}$ indicate the average translational RMSE (\\%) and rotational RMSE ( $^\\circ /100\\mathrm{m}$ ) respectively on all possible subsequences in the length of 100, 200, ..., 800m. $^\\dagger$ means the testing sequences. LOAM and A-LOAM is complete SLAM system, including back-end optimization. The best result for each sequence is bold, and the second best is underlined." + ], + "table_footnote": [], + "table_body": "
    Method07†08†Mean
    trelrreltrelrreltrelrrel
    LodoNet [53]1.861.642.040.971.9501.305
    Ours0.370.271.120.440.7450.355
    ", + "bbox": [ + 106, + 309, + 468, + 377 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fbbcab177cddbab7b593a537abc6c9f1d8398350159212e0a407d0e7324c280e.jpg", + "table_caption": [ + "Table 2. Comparison with learning-based odometry LodoNet on KITTI 07-08 sequences." + ], + "table_footnote": [], + "table_body": "
    Method09†10†Mean
    trelrreltrelrreltrelrrel
    Nubert et al. [30]1.540.681.780.691.660.685
    H-VLO [2]1.890.341.390.521.640.430
    Ours0.680.280.660.320.670.300
    ", + "bbox": [ + 106, + 431, + 468, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Comparison with learning-based odometry on KITTI 09-10 sequences.", + "bbox": [ + 89, + 518, + 482, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and $w_{q}$ are set to 0.0 and -2.5, respectively, as indicated in formula Eq. (14). For formula Eq. (15), the parameters are set as follows: $\\lambda_{3} = 1.6$ , $\\lambda_{2} = 0.8$ , $\\lambda_{1} = 0.4$ , $\\lambda_{0} = 0.2$ , and $L = 4$ . The batch size is 12.", + "bbox": [ + 89, + 575, + 482, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with The State-of-the-Art", + "text_level": 1, + "bbox": [ + 89, + 648, + 421, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our network with the state-of-the-art on KITTI dataset, including both classic methods and learning-based ones. Since existing training and testing sequence settings are inconsistent in different methods, we test and evaluate our framework accordingly for a fair comparison.", + "bbox": [ + 89, + 672, + 482, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "00-06 as training sequences and 07-10 as testing sequences. Quantitative results are listed in Tab. 1. The traditional methods we compare include ICP-point2point (ICP-po2po), ICP-point2plane (ICP-po2pl), GICP [36], CLS [41], which rely on iterative point cloud alignment. LOAM [50], its enhanced version A-LOAM is also included. While LOAM and A-LOAM have been widely recognized for their robust performance on the KITTI odometry benchmark, our method achieves superior accuracy on most sequences. As shown in Tab. 1, our approach outperforms Full A-LOAM,", + "bbox": [ + 89, + 750, + 482, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8a4c89b35dbf0b4fdc0c52f7037e2458ee6a359123689b9a43aa13bc44f2459e.jpg", + "image_caption": [ + "Figure 3. 2D trajectories of A-LOAM, EfficientLO, and our proposed method on KITTI sequences 02 and 10 with ground truth. It can be observed that our method performs the best." + ], + "image_footnote": [], + "bbox": [ + 524, + 313, + 890, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which has the mapping optimization. Additionally, the learning-based LiDAR odometry methods we compare include LO-Net [21], DELO [1], PWCLO-Net [42], TransLO [23], EfficientLO [44]. Compared to the current state-of-the-art method EfficientLO, our method DiffLO achieves an average improvement of $10.9\\%$ in transition accuracy and $16.9\\%$ in rotation accuracy.", + "bbox": [ + 511, + 536, + 906, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "00-06 and 09-10 as training sequences and 07-08 as testing sequences. We compare with a recent method LodoNet [52] in Tab. 2. Our method is trained on 00-06 sequences while LodoNet are trained on 00-06 and 09-10 sequences, even so, our method performs better than LodoNet on the test sequences.", + "bbox": [ + 511, + 642, + 906, + 732 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "00-08 as training sequences and 09-10 as testing sequences. We compare with recent method [2, 30]. Our method is trained on 00-06 sequences while others are trained on 00-08 sequences. As illustrated in Tab. 3, both our translation and rotation errors are smaller than theirs. Although our approach utilizes only LiDAR data, we achieve better results than the multi-modal method H-VLO.", + "bbox": [ + 511, + 732, + 908, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 847, + 666, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to analyze the effectiveness of each module, we remove or change components of our model to do the abla", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17055", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4a90371f9695606143bdcd27711989c149485571f5821fcb50193cf6719d5885.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Method07†08†09†10†Mean on 07-10
    trelrreltrelrreltrelrreltrelrreltrelrrel
    (a)Semanticw/o SPM0.520.461.190.530.530.180.930.420.7930.398
    Ours (full, with SPM)0.370.271.120.440.680.280.660.320.7080.328
    (b)Diffusionw/o diffusion4.833.826.773.055.292.227.093.975.9953.265
    with trans-based Mθ [40]0.390.341.360.550.730.291.070.480.8880.415
    with ptrans-based Mθ [51]0.450.281.190.450.540.220.720.410.7250.340
    Ours (GRU-based Mθ [6])0.370.271.120.440.680.280.660.320.7080.328
    (c)Conditionw/o cost volume0.450.351.200.490.700.281.090.950.8600.518
    w/o geometry feature0.400.271.180.470.610.240.960.460.7870.357
    w/o semantic feature0.470.311.330.560.750.230.640.480.7980.395
    w/o coarse pose embedding0.450.341.280.560.640.250.630.330.7500.370
    Ours (full, with all conditions)0.370.271.120.440.680.280.660.320.7080.328
    ", + "bbox": [ + 135, + 88, + 864, + 286 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. The ablation study results of LiDAR odometry on KITTI odometry dataset[7]. The best performance of each sequence is bold.", + "bbox": [ + 98, + 295, + 897, + 311 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ee2fccead9c463552b7cce4ce32bef4309ee49771ea81805a948d3ab298c2b31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 107, + 325, + 290, + 465 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce23967ba037522fbf48a3ba11417d023fc62dda5cc3567eb32c6552a8d23437.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 327, + 475, + 465 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/61b180e0795b45c3f9d5126785a646978c53ecd33c675e473c57649325642827.jpg", + "image_caption": [ + "(a) Sequence 01", + "(c) Sequence 06", + "Figure 4. 3D trajectories of A-LOAM, EfficientLO and our proposed method on KITTI sequences 01, 05, 06 and 09 with ground truth. Ours trajectory is more accurate than EfficientLO and the Full A-LOAM, which has the mapping optimization." + ], + "image_footnote": [], + "bbox": [ + 109, + 474, + 287, + 609 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/66179fc5f680d76638ffe38a2a8f58bd415cb06e8f7516f153bcd7b9419fa9a0.jpg", + "image_caption": [ + "(b) Sequence 05", + "(d) Sequence 09" + ], + "image_footnote": [], + "bbox": [ + 299, + 473, + 475, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion studies on KITTI odometry dataset (00-06 as training sequences and 07-10 as testing sequences).", + "bbox": [ + 89, + 700, + 482, + 732 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Study on Semantic Perception Module. We conducted ablation experiments to demonstrate the significance of the Semantic Perception Module (SPM) mentioned in Sec. 3.2. As shown in Tab. 4, SPM achieves an average improvement of $10.7\\%$ in transition accuracy and $17.6\\%$ in rotation accuracy. This indicates that SPM enhances accuracy by embedding semantic understand to the network, which helps the network to focus more on the objects in the scene that play a key role in pose estimation.", + "bbox": [ + 89, + 733, + 482, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Study on Diffusion Refinement. We conducted an ablation study by comparing results with and without the", + "bbox": [ + 89, + 869, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "diffusion-based refinement process (w/o diffusion). As shown in Tab. 4, the diffusion-based pose refinement significantly improved performance, reducing the average translation error by $88.2\\%$ (from $5.995\\%$ to $0.708\\%$ ) and the average rotation error by $90.0\\%$ (from $3.265^{\\circ} / 100\\mathrm{m}$ to $0.328^{\\circ} / 100\\mathrm{m}$ ). Additionally, we explored the performance of different denoising networks, including a transformer-based [40] network (trans-based), a point transformer-based [51] network (ptrans-based), and GRU-based [6] network. The results demonstrate the advantages of our denoising network over alternative approaches.", + "bbox": [ + 511, + 325, + 903, + 492 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Study on Condition signals. To evaluate the effectiveness of the diffusion condition signals, we conducted an ablation study by individually removing each designed condition signal, as shown in Tab. 4. Removing the cost volume led to a performance degradation (with translation error increasing by $21.5\\%$ and rotation error by $57.9\\%$ ), since cost volume captures the precise per-point correlation between two frames. The semantic feature also plays a crucial role in guiding diffusion generation, as it provides scene understanding. Consequently, its removal resulted in a significant drop in performance (led to a $12.7\\%$ increase in translation error and a $20.4\\%$ increase in rotation error). Additionally, removing the coarse pose embedding led to a decline in performance, as coarse pose embedding provides essential state information, which is closely related to the residual pose generated by the model. Finally, the absence of geometry features as guidance also resulted in a noticeable performance drop.", + "bbox": [ + 511, + 492, + 906, + 765 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Visualization", + "text_level": 1, + "bbox": [ + 511, + 771, + 651, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We visualize the trajectory of our network and analyze the benefits of Semantic Perception Module in this section.", + "bbox": [ + 511, + 794, + 903, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of Trajectory. The qualitative results are shown in Fig.3, 4 and 5. We compared our method with full A-LOAM, which includes mapping optimization, and EfficientLO [44]. Notably, in Seq.02 of Fig. 3, A-LOAM exhibits significant drift due to the presence of repetitive", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17056", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ab0593e8dacb7dd12fa283918fc579e412b13b7d94059b9502c9fc09bc0dfb5e.jpg", + "image_caption": [ + "Figure 5. Average translational and rotational error on KITTI sequences 00-10 on all possible subsequences in the length of 100, 200, ..., 800m. Our method has the best performance." + ], + "image_footnote": [], + "bbox": [ + 96, + 90, + 478, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0371a01e13e5f9b4686b76056b758a7ab3d60fd96d76e75ef1ea55f63982499a.jpg", + "image_caption": [ + "Figure 6. The visualization of semantic features is derived from the complete LiDAR point cloud of the initial frame. Additionally, the grayscale image captured from the camera view corresponds to the semantic segmentation image displayed below. Bounding boxes are utilized to delineate specific object categories." + ], + "image_footnote": [], + "bbox": [ + 94, + 275, + 478, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "structures and patterns in the scene, which impedes the algorithm's ability to accurately estimate pose. These figures show that our odometry can track the trajectory of the ground truth fairly well. At the same time, our method demonstrates the best average evaluation performance compared to A-LOAM and EfficientLO.", + "bbox": [ + 89, + 549, + 482, + 640 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of Semantic feature. The proposed network employs an embedding feature of 8,192 points to compute the pose transformation in the final pose output layer. Consequently, we visualize the semantic features of these 8,192 points. As illustrated in Fig. 6, vehicles, street lamps, fences, billboards, and other objects in the scene are segmented. This demonstrates that the Semantic Perception Module empowers the network with the capability of semantic understanding.", + "bbox": [ + 89, + 642, + 482, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of embedding mask. We visualize the embedding mask of the 8,192 points in the final pose output layer. As shown in Fig. 7, the mask of DiffLO integrated with the Semantic Perception Module (SPM) allocates weights more accurately compared to the mask of DiffLO without SPM. Points sampled from static and structured rigid objects, such as buildings, fences, and pole-like object, exhibit higher weights, while points from dynamic", + "bbox": [ + 89, + 779, + 482, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b5f7e4a433487d4c1024de72c7ea0a75175851b989799899aeac0936a06d614c.jpg", + "image_caption": [ + "Figure 7. The visualization of the embedding mask is based on the complete LiDAR point cloud of the initial frame. In the lower-left corner, the heatmap represents the mask of DiffLO integrated with the SPM. Conversely, the lower-right corner displays the heatmap for the mask of DiffLO without SPM. Above these visualizations, the corresponding grayscale image of the point cloud is presented." + ], + "image_footnote": [], + "bbox": [ + 519, + 90, + 901, + 253 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and low-texture objects, including cars, shrubs, and trees, receive lower weights. This demonstrates that the Semantic Perception Module (SPM) effectively helps the network focus on objects in the scene that are crucial for accurate pose estimation.", + "bbox": [ + 511, + 364, + 906, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Runtime Analysis", + "text_level": 1, + "bbox": [ + 513, + 459, + 687, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Efficiency is another extremely significant factor in real-time SLAM systems. The LiDAR points in the KITTI dataset are captured at a $10\\mathrm{Hz}$ frequency. Our method has only $76.9\\mathrm{ms}$ inference time, which satisfy the real-time application requirements (under $100\\mathrm{ms}$ ).", + "bbox": [ + 511, + 484, + 906, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 584, + 633, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce a diffusion model-based odometry network augmented with semantic awareness, targeting large-scale LiDAR odometry. Our approach innovatively applies knowledge distillation to transfer semantic information into the odometry network, thereby enhancing the network's semantic understanding. This allows the network to effectively mitigate the challenges posed by dynamic objects, repetitive patterns, and low-texture environments. Additionally, we incorporate a diffusion model conditioned on pose-related features to refine pose estimation. To the best of our knowledge, this is the first instance of utilizing diffusion models in odometry tasks. We evaluated our framework on the KITTI odometry dataset, and our method achieved state-of-the-art performance while ensuring the real-time requirement of pose prediction.", + "bbox": [ + 511, + 613, + 906, + 840 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This work was supported in part by Natural Science Foundation of China (No.62171393), and the Fundamental Research Funds for the Central Universities (No.20720220064).", + "bbox": [ + 511, + 840, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17057", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sk Aziz Ali, Djamila Aouada, Gerd Reis, and Didier Stricker. Delo: Deep evidential lidar odometry using partial optimal transport. 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In CVPR, pages 12786-12796, 2022. 1" + ], + "bbox": [ + 514, + 92, + 903, + 630 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17059", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_model.json b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c544105856ff3bdc3b62bd62614814c0b15edfb1 --- /dev/null +++ b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_model.json @@ -0,0 +1,2431 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.109, + 0.131, + 0.89, + 0.152 + ], + "angle": 0, + "content": "DiffLO: Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.18, + 0.933, + 0.253 + ], + "angle": 0, + "content": "Yongshu Huang\\(^{1,2*}\\) Chen Liu\\(^{1,2*}\\) Minghang Zhu\\(^{1,2}\\) Sheng Ao\\(^{1,2\\dagger}\\) Chenglu Wen\\(^{1,2}\\) Cheng Wang\\(^{1,2\\dagger}\\) \n\\(^{1}\\) Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University, China. \n\\(^{2}\\) Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University, China." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.32, + 0.485, + 0.714 + ], + "angle": 0, + "content": "LiDAR odometry is a critical module in autonomous driving systems, responsible for accurate localization by estimating the relative pose transformation between consecutive point cloud frames. However, existing studies frequently encounter challenges with unreliable pose estimation, due to the lack of in-depth understanding of scenario and the presence of noise interference. To address this challenge, we propose DiffLO, a semantic-aware LiDAR odometry network with diffusion-based refinement. To mitigate the impact of challenging cases such as dynamic, repetitive patterns, and low textures, we introduce a semantic distillation method that integrates semantic information into the odometry task. This allows the network to gain a semantic understanding of the scene, enabling it to focus more on the objects that are beneficial for pose estimation. Additionally, to enhance the robustness, we propose a diffusion-based refinement method. This method uses pose-related features as conditional constraints for generative diversity, iteratively refining the pose estimation to achieve greater accuracy. Comparative experiments on the KITTI odometry dataset demonstrate that the proposed method achieves state-of-the-art performance among existing learning-based approaches. Furthermore, the proposed DiffLO method outperforms the classic A-LOAM on most evaluation sequences. The code will be released at https://github.com/HyTree7/DiffLO." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.745, + 0.222, + 0.76 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.771, + 0.483, + 0.862 + ], + "angle": 0, + "content": "LiDAR odometry (LO) is a well-studied problem in computer vision with numerous applications in Simultaneous Localization and Mapping (SLAM) [58], autonomous driving [54], and robotics [45]. The primary objective is to estimate the relative transformation between two frames based on the source and target point clouds." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.287, + 0.689, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.287, + 0.904, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.514, + 0.907, + 0.598 + ], + "angle": 0, + "content": "Figure 1. (a) Predicts a coarse initial pose and applies iterative MLP-based refinement to refine the initial estimate. (b) Predicts a coarse initial pose and applies iterative Diffusion-based refinement, incorporating knowledge distillation to enable semantic understanding. Here, \\(\\hat{T}_k\\) represents the noisy pose of the \\(k^{th}\\) denoising step." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.614, + 0.907, + 0.749 + ], + "angle": 0, + "content": "Most classic geometry-based methods, such as Iterative Closest Point (ICP) [4], its variants [31] and others [35], work by iteratively minimizing the distance between corresponding points in two point clouds to achieve accurate alignment. However, they often struggle in sparse point cloud environments, complex dynamic scenes, or when the quality of the point cloud degrades [13, 27, 42]. This limitation arises due to their reliance on precise geometric correspondences." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.75, + 0.909, + 0.856 + ], + "angle": 0, + "content": "Deep learning-based methods have garnered significant attention in recent years. These methods learn feature representations from large-scale data to infer relative transformation between frames in an end-to-end manner, providing better scalability and the potential for multi-task learning. However, the accuracy of deep learning methods still lags behind traditional odometry techniques." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.908, + 0.902 + ], + "angle": 0, + "content": "We identify the following challenges faced by Deep Learning-based odometry methods: (1) To mitigate the effects of challenging cases such as dynamic objects and oc" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.875, + 0.298, + 0.888 + ], + "angle": 0, + "content": "*These authors contributed equally." + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.24, + 0.9 + ], + "angle": 0, + "content": "† Corresponding Author." + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.875, + 0.298, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17050" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.288 + ], + "angle": 0, + "content": "clusions, LO-Net [21] introduces a mask prediction network learning the compensation for dynamic objects to remove dynamic objects. Methods such as PWCLO-Net [42], TransLO [23], and EfficientLO [44] introduce a hierarchical embedding mask and apply pose feature weighting to filter dynamic object. However, these approach lacks a comprehensive understanding of object structures, leading to inaccuracies and resulting in cumulative errors; (2) Furthermore, these methods [18, 23, 24, 26, 42, 44] are deterministic prediction tasks, which limits their ability to adapt to newly emerging changes or complexities in the environment. Additionally, they can not provide information about prediction uncertainties." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.29, + 0.482, + 0.501 + ], + "angle": 0, + "content": "Semantic segmentation network contains rich geometric information and intricate details about the scene. This insight motivates us to integrate semantic information into the odometry network, thereby enhancing its ability to filter out dynamic objects and manage occlusions effectively. To achieve this, as shown in Fig. 1, we propose a knowledge distillation approach that transfers semantic knowledge from a segmentation model to the odometry network. After training, the knowledge distillation component and segmentation model are dropped to avoid extra computation or network parameter. By leveraging the contextual knowledge provided by semantic segmentation, our approach aims to improve the overall accuracy and robustness of odometry in complex environments." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.504, + 0.483, + 0.731 + ], + "angle": 0, + "content": "Diffusion models [11] are characterized by their robustness, and have achieved significant success across various tasks [8, 15, 22, 25]. These strengths have inspired us to explore their potential application to the LiDAR odometry task. In this paper, we propose reformulating the odometry task as a diffusion process. As shown in Fig. 1, we transition from a traditional MLP-based refinement approach to a diffusion-based refinement, shifting the task from a deterministic prediction framework to a probabilistic generative model. Specifically, Our approach consists of a forward process that progressively adds noise to the residual pose of the ground truth, followed by a reverse denoising process to refine the noisy pose estimate. We utilize coarse pose embedding, cost volume, semantic feature and geometry embedding as conditions to restrict generation diversity." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.733, + 0.411, + 0.747 + ], + "angle": 0, + "content": "In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.75, + 0.48, + 0.808 + ], + "angle": 0, + "content": "- To enhance the network's ability to focus on objects critical for pose estimation in the scene, we incorporate semantic awareness into odometry by distilling knowledge from a semantic segmentation model." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.811, + 0.48, + 0.897 + ], + "angle": 0, + "content": "- We propose a novel diffusion-based refinement pipeline and design strong conditional guidance by combining semantic embedding, coarse pose embeddings, geometry embedding and cross-frame cost volume to control generation diversity. To the best of our knowledge, this is the first work to leverage diffusion probabilistic model in the" + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.75, + 0.48, + 0.897 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.092, + 0.681, + 0.106 + ], + "angle": 0, + "content": "LiDAR odometry task." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.107, + 0.905, + 0.167 + ], + "angle": 0, + "content": "- Extensive experiments on the KITTI odometry dataset [7] demonstrate that our method outperforms all existing learning-based odometry methods. On most sequences, our performance even surpasses A-LOAM with mapping." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.196, + 0.644, + 0.211 + ], + "angle": 0, + "content": "2. Relate Work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.226, + 0.731, + 0.241 + ], + "angle": 0, + "content": "2.1. Deep LiDAR Odometry" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.254, + 0.905, + 0.54 + ], + "angle": 0, + "content": "The field of visual depth odometry has advanced rapidly. However, research on LiDAR-based depth odometry remains challenging due to the inherent irregularity and complexity of point clouds. LO-Net [21] proposed an end-to-end deep odometry network that enhances robustness by learning the compensation for dynamic objects through a mask prediction network. PWCLO [42] first introduces a coarse-to-fine structure to LiDAR odometry, implementing a hierarchical refinement approach for estimated poses. LodoNet [52] projects 3D point clouds onto 2D spherical depth images to extract and match keypoints for odometry localization. EfficientLO [44] introduces a projection-aware representation of 3D point clouds, facilitating efficient learning for large-scale datasets. TransLO [23] develops a cross-frame transformer module that associates consecutive frames, thereby regressing relative pose estimations. DELO [1] innovatively employs partial optimal transportation of LiDAR feature descriptors to achieve robust localization estimation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.566, + 0.833, + 0.581 + ], + "angle": 0, + "content": "2.2. LiDAR-based semantic segmentation" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.594, + 0.905, + 0.835 + ], + "angle": 0, + "content": "LiDAR-based semantic segmentation aims to assign a semantic label to each point in the input LiDAR scan. These methods can generally be categorized into several approaches: point-based [14, 32, 33, 39], voxel-based [9, 57], projection-based [17, 29, 46], and hybrid methods that combine these techniques [37, 49]. These approaches consistently expand the receptive field by integrating fine-grained point features with coarse-grained contextual information, which enhances the network's ability to understand the scene structure and the unique characteristics of each point. Semantic information has also proven to be highly valuable in traditional non-deep learning methods, such as [3, 5, 19, 20, 56]. By leveraging semantic labels, these systems can enhance feature matching and improve robustness against challenging conditions like dynamic objects and occlusions." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.841, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Inspired by these traditional methods, we explore integrating semantics into learning-based LiDAR odometry to address the challenges posed by dynamic objects, repetitive patterns, and low-texture environments." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17051" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.279, + 0.105 + ], + "angle": 0, + "content": "2.3. 3D Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.114, + 0.484, + 0.446 + ], + "angle": 0, + "content": "Diffusion models have garnered significant attention and research in a variety of 3D point cloud processing tasks. For instance, Luo et al. [28] introduced a probabilistic model for point cloud generation, transforming the point cloud noise distribution into the desired point cloud shape distribution. Zhou et al. [55] combined a denoising diffusion model with a mixed point-voxel representation of 3D shapes for unconditional shape generation and conditional multimodal shape completion. Jiang et al. [15] proposed a point cloud registration framework based on an SE(3) diffusion model, framing the 3D registration task as a denoising diffusion process that iteratively refines the pose of the source point cloud to achieve precise alignment with the target point cloud. Difflow3D [25] presented an uncertainty-aware scene flow estimation network leveraging a diffusion probabilistic model, where iterative diffusion modules refine initial estimates to enhance the robustness of scene flow estimation. DiffLoc [22] formulates LiDAR localization as a conditional generation of poses, employing a diffusion model conditioned on geometric robust features and incorporating an iterative denoising process into APR to achieve accurate LiDAR localization." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.484, + 0.509 + ], + "angle": 0, + "content": "Inspired by the successful applications of diffusion models in tasks such as registration, scene flow estimation, and localization, we investigate the integration of diffusion models to improve the accuracy of LiDAR odometry." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.523, + 0.182, + 0.538 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.548, + 0.484, + 0.761 + ], + "angle": 0, + "content": "Given two consecutive point cloud frames \\(PC_1 \\in \\mathbb{R}^{N \\times 3}\\) and \\(PC_2 \\in \\mathbb{R}^{M \\times 3}\\), the goal of the LiDAR odometry task is to estimate the relative transformation between the two consecutive frames of point clouds. To solve this task, we propose DiffLO, a semantic-aware odometry network with diffusion-based refinement. DiffLO first hierarchically extracts point features (Sec. 3.1). Subsequently, we introduce a Semantic Perception Module (Sec. 3.2), which enables the odometry network to gain semantic understanding. Then, the initial pose is generated (Sec. 3.3) in the coarsest layer. We then utilize diffusion model with condition signals to refine the initial pose by predicting pose residuals from coarse to fine (Sec. 3.4). Lastly, the loss function will be presented in (Sec. 3.5)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.771, + 0.364, + 0.787 + ], + "angle": 0, + "content": "3.1. Multi-scale Feature Extraction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We utilize PointConv [47] for hierarchical feature extraction. At each level \\( l \\), dense input points and their features are first subsampled using furthest point sampling to create a sparse point set. Then, for each subsampled sparse point, k-nearest neighbor groups local dense points to form a local region for feature extraction. Next, a PointConv [47] layer aggregates features from the grouped local points, produc" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.122 + ], + "angle": 0, + "content": "ing a local feature for each sparse point. This process results in an L-level pyramid of point features." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.13, + 0.771, + 0.146 + ], + "angle": 0, + "content": "3.2. Semantic Perception Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.153, + 0.906, + 0.289 + ], + "angle": 0, + "content": "To guide the network's attention towards objects in the scene that are beneficial for pose estimation, such as buildings and pole-like structures. We introduce Semantic Perception Module (SPM). SPM consists of three components: Semantic Module, Semantic Segmentation Modle and Knowledge Distillation. We introduce a semantic segmentation model as the teacher network. A sub-network (the Semantic Module) within the odometry model is designated as the student model." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.29, + 0.906, + 0.364 + ], + "angle": 0, + "content": "During the training stage, three modules collaborate to transfer semantic knowledge into the odometry model. Firstly, the Semantic Module takes the point cloud features \\( F \\) in coarse layer as its input, the output can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.373, + 0.907, + 0.39 + ], + "angle": 0, + "content": "\\[\nF _ {s t u} = M L P (F) + M L P (F) \\otimes \\sigma (M L P (F)), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.906, + 0.429 + ], + "angle": 0, + "content": "where \\(\\otimes\\) indicates element-wise multiplication. \\(\\sigma (\\cdot)\\) denotes the softmax operation along the feature dimension." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.429, + 0.906, + 0.551 + ], + "angle": 0, + "content": "Secondly, a pretrained 3D semantic segmentation model [16], with its network parameters frozen, is utilized here. We extract the per-point features from the final layer, denoted as \\( F_{seg} \\in \\mathbb{R}^{N \\times d} \\). These features are subsequently downsampled to \\( F_{tea} \\in \\mathbb{R}^{N' \\times d} \\) to ensure compatibility in dimension with \\( F_{stu} \\). And we adjust the output dimension of the semantic regressor branch, ensuring that \\( F_{tea} \\) and \\( F_{stu} \\) share the same feature dimension \\( d \\) for each point." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.551, + 0.906, + 0.611 + ], + "angle": 0, + "content": "Then, we utilize knowledge distillation [10] to transfer semantic knowledge from the segmentation module to the odometry model. This is achieved by optimizing the following distillation loss:" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.619, + 0.905, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {k d} = \\delta \\left(F _ {s t u}, F _ {t e a}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.906, + 0.689 + ], + "angle": 0, + "content": "where \\(\\delta (\\cdot ,\\cdot)\\) measures the difference between the feature representations from the teacher network \\(F_{tea}\\) and the student network \\(F_{stu}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.906, + 0.75 + ], + "angle": 0, + "content": "Finally, the semantic feature \\( F_{stu} \\) is propagated to the following level for a denser optimization and simultaneously serves as a condition signal for diffusion-based refinement in Sec. 3.4, via an upsampling layer [6, 48]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.906, + 0.811 + ], + "angle": 0, + "content": "During the inference stage, only the Semantic Module is retained to avoid additional computational overhead. The output \\( F_{stu} \\) from the Semantic Module is still propagated to subsequent layers, serving as a conditional signal." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.811, + 0.906, + 0.901 + ], + "angle": 0, + "content": "By embedding semantic understanding into the odometry process, the model is better able to focus on objects in the scene that are beneficial for pose estimation. Meanwhile, the close integration of knowledge distillation improves both the efficiency and effectiveness of the overall system." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17052" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.092, + 0.9, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.441, + 0.907, + 0.526 + ], + "angle": 0, + "content": "Figure 2. The overall structure of DiffLO. The proposed pipeline comprises three core components: Pose Initialization, Semantic Perception Module, and Diffusion-based Pose Refinement. First, hierarchical point features are extracted from the input point cloud. Then, we enable the network to acquire semantic understanding through a knowledge distillation approach. Following this, an initial coarse pose estimate is generated. Finally, the Diffusion-based Pose Refinement module applies iterative refinement layers, conditioned on various signals, to improve the initial pose estimate, ultimately producing a more accurate and robust final pose. To optimize inference efficiency, the semantic segmentation component is discarded after the training phase." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.54, + 0.375, + 0.555 + ], + "angle": 0, + "content": "3.3. Semantic-Aware Pose Estimator" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.563, + 0.483, + 0.61 + ], + "angle": 0, + "content": "We enhance the pose estimation method from the PWCLO-Net [42] by incorporating semantic features into the pose estimation process. Taking the \\( l^{th} \\) layer as example." + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.619, + 0.483, + 0.639 + ], + "angle": 0, + "content": "\\[\nE ^ {l} = M L P \\left(F ^ {l} \\oplus F _ {s t u} ^ {l} \\oplus U E ^ {l} \\oplus C E ^ {l}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.661, + 0.483, + 0.681 + ], + "angle": 0, + "content": "\\[\nM ^ {l} = \\sigma (M L P (F ^ {l} \\oplus F _ {s t u} ^ {l} \\oplus U M ^ {l} \\oplus E ^ {l})), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.685, + 0.483, + 0.807 + ], + "angle": 0, + "content": "where \\(\\oplus\\) is the concatenation and \\(\\sigma (\\cdot)\\) denotes the softmax operation. \\(F^l\\) is the point cloud feature from \\(l\\) layer, \\(CE^l\\) is generated by cross-frame correlation [6, 43]. \\(F_{stu}^{l}\\), \\(UE^{l}\\) and \\(UM^{l}\\) are the results of upsampling the semantic feature \\(F_{stu}^{l + 1}\\), the embedding feature \\(E^{l + 1}\\) and the embedding mask \\(M^{l + 1}\\) respectively. The embedding features \\(E = \\{e_i|e_i\\in \\mathbb{R}^C\\}_{i = 1}^n\\), the embedding mask \\(M = \\{m_i|m_i\\in \\mathbb{R}^C\\}_{i = 1}^n\\). The pose is then generated by:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.816, + 0.483, + 0.853 + ], + "angle": 0, + "content": "\\[\nq = \\frac {F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right)}{\\left| F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right) \\right|} \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.865, + 0.483, + 0.905 + ], + "angle": 0, + "content": "\\[\nt = F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.54, + 0.907, + 0.601 + ], + "angle": 0, + "content": "where \\(FC(\\cdot)\\) denotes the fully connected layer and \\(\\odot\\) represents dot product. Following [42], the embedding features \\(E\\), embedding mask \\(M\\) and semantic features are also propagated to denser layers for optimization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.601, + 0.907, + 0.692 + ], + "angle": 0, + "content": "The coarse-level point cloud is sparse and has low resolution, which can lead to incorrect matches and inaccurate initial pose estimates. Inspired by recent success and denoising properties of the diffusion model [11], we design a novel diffusion-based pose refinement module to refine the coarse pose progressively." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.702, + 0.803, + 0.717 + ], + "angle": 0, + "content": "3.4. Diffusion-based Pose Refinement" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.726, + 0.906, + 0.771 + ], + "angle": 0, + "content": "In this section, we formulate the coarse pose residual as the diffusion latent variable, and residual pose are generated from the reverse process of diffusion model iteratively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.772, + 0.906, + 0.845 + ], + "angle": 0, + "content": "During the training stage, the diffusion model is trained to learn the underlying distribution of residual poses by recovering the ground truth residual pose from its corrupted version. The ground truth residual pose is calculated as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.65, + 0.846, + 0.905, + 0.865 + ], + "angle": 0, + "content": "\\[\nT _ {0} = T _ {g t} \\cdot T _ {p r e d} ^ {- 1}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.903 + ], + "angle": 0, + "content": "where \\(T_{0}\\) is the ground truth residual pose, \\(T_{gt}\\) is the ground truth pose and \\(T_{pred}\\) is the coarse pose generated by the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17053" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.31, + 0.106 + ], + "angle": 0, + "content": "previous layer or the initial pose." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.107, + 0.484, + 0.168 + ], + "angle": 0, + "content": "Specifically, in each training iteration, a random diffusion step, denoted as \\( k \\in \\{1, 2, \\dots, K\\} \\), is chosen. With a predefined variance schedule \\( \\beta_1, \\ldots, \\beta_k \\), we introduce noises to \\( T_0 \\), resulting in the noisy residual pose \\( T_k \\)." + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.172, + 0.482, + 0.19 + ], + "angle": 0, + "content": "\\[\nq \\left(T _ {k} \\mid T _ {0}\\right) = \\mathcal {N} \\left(T _ {k}; \\sqrt {\\bar {\\alpha} _ {k}} T _ {0}, (1 - \\bar {\\alpha} _ {k}) \\mathrm {I}\\right) \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.193, + 0.482, + 0.211 + ], + "angle": 0, + "content": "\\[\nT _ {k} = \\sqrt {\\bar {\\alpha} _ {k}} T _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {k}} \\epsilon , \\epsilon \\sim \\mathcal {N} (0, I) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.217, + 0.483, + 0.262 + ], + "angle": 0, + "content": "denoting \\(\\alpha_{k} = 1 - \\beta_{k}\\) and \\(\\overline{\\alpha}_k = \\Pi_{i = 1}^k\\alpha_i\\) . Eventually, the ground truth residual pose \\(T_{0}\\) is turned into Gaussian noise when \\(k\\) is large enough." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.264, + 0.484, + 0.398 + ], + "angle": 0, + "content": "During the inference stage, the denoise model approximates the distribution \\( p(T_0|C) \\) as the reversed diffusion process of gradually cleaning \\( T_{k} \\). Instead of predicting \\( \\epsilon \\) as formulated by [12], we follow [34, 38] and predict the signal itself. Also, we constrain the generation diversity and control the reversed diffusion process by the condition information \\( C \\). In this way, we utilize a denoising network to predict the residual pose \\( \\hat{T_0} \\) from noisy input \\( T_{k} \\), time step \\( t = k \\), and condition \\( C \\)." + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.405, + 0.482, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\hat {T} _ {0} = \\mathcal {M} _ {\\theta} \\left(T _ {k}, t, C\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.427, + 0.484, + 0.459 + ], + "angle": 0, + "content": "where \\(\\mathcal{M}_{\\theta}(\\cdot ,\\cdot ,\\cdot)\\) is the denoising network. The training objective is to minimize the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.464, + 0.482, + 0.482 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e s} = \\mathbb {E} _ {T _ {0}, t}, \\left[ \\| t _ {g t} - t _ {p r e d} \\| _ {2} + \\| q _ {g t} - q _ {p r e d} \\| _ {2} \\right], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.487, + 0.483, + 0.532 + ], + "angle": 0, + "content": "where \\( t_{gt} \\) and \\( q_{gt} \\) are the translation vector and quaternion from \\( T_0 \\), and \\( t_{pred} \\) and \\( q_{pred} \\) are their corresponding predicted values from \\( \\hat{T}_0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.534, + 0.484, + 0.655 + ], + "angle": 0, + "content": "Design of Condition Signal. Inspired by [42, 43], we introduce the geometric feature \\(GE\\) extracted from \\(PC_{1}\\) along with a cost volume embedding \\(CE\\) constructed using cross-frame correlation [6], with the corresponding hierarchical point cloud features as input, and residual pose embeddings \\(PE = T_{k} \\cdot PC_{1} - PC_{1}\\) and the semantic feature \\(F_{stu}\\) as conditional signals to constrain generation diversity. The condition signal is as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.661, + 0.482, + 0.677 + ], + "angle": 0, + "content": "\\[\nC = G E \\oplus C E \\oplus P E, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.683, + 0.356, + 0.697 + ], + "angle": 0, + "content": "where \\(\\oplus\\) is the concatenation operation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.698, + 0.484, + 0.836 + ], + "angle": 0, + "content": "We employ the augmented version [6] with Gate Recurrent Unit (GRU) to process the condition signal \\( C \\). This approach allows for the extraction of essential features from \\( C \\) to generate the augmented condition signal \\( C' \\). Subsequently, the semantic-aware pose estimator in Sec. 3.3 is introduced to generate the residual pose \\( \\hat{T}_0 \\). Here, \\( C' \\) are treated as the cost volume embedding \\( CE \\) in Eq. (3). Taking the \\( l^{th} \\) refinement layer as example, the refined pose \\( T_{pred}^l \\) is calculated as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.841, + 0.482, + 0.866 + ], + "angle": 0, + "content": "\\[\nT _ {p r e d} ^ {l} = \\hat {T} _ {0} ^ {l} \\cdot T _ {p r e d} ^ {l + 1}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.87, + 0.483, + 0.902 + ], + "angle": 0, + "content": "the refined pose \\( T_{pred}^{l} \\) will be the input to \\( l - 1^{th} \\) refinement layer." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.091, + 0.657, + 0.107 + ], + "angle": 0, + "content": "3.5. Training Loss" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.114, + 0.906, + 0.204 + ], + "angle": 0, + "content": "The network supervises the pose outputs from each level, along with the residual poses predicted by the diffusion model and the semantic features derived from the Semantic Module. Drawing from previous deep odometry research [21, 42], the training loss function for the odometry at the l-th level is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.214, + 0.905, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} ^ {l} = \\left\\| t _ {g t} - t ^ {l} \\right\\| \\exp (- w _ {t}) + w _ {t} \\\\ + \\left\\| q _ {g t} - \\frac {q ^ {l}}{\\| q ^ {l} \\|} \\right\\| _ {2} \\exp (- w _ {q}) + w _ {q}, \\tag {14} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.279, + 0.906, + 0.4 + ], + "angle": 0, + "content": "where \\(\\| \\cdot \\|\\) and \\(\\| \\cdot \\| _2\\) denotes the \\(\\ell 1\\)-norm and the \\(\\ell 2\\)-norm respectively. \\(t_{gt}\\) and \\(q_{gt}\\) are the ground-truth translation vector and quaternion respectively. \\(t^l\\) and \\(q^{l}\\) are predicted pose from each level. \\(w_{t}\\) and \\(w_{q}\\) are two learnable parameters, which are introduced to eliminate the differences in scale and units between the translation vector and the quaternion. Then, a multi-scale supervised approach is adopted. The total training loss function \\(\\mathcal{L}\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.41, + 0.905, + 0.452 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {k d} + \\sum_ {l = 0} ^ {K} \\lambda^ {l} \\times \\left(\\mathcal {L} ^ {l} + \\mathcal {L} _ {r e s} ^ {l}\\right), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.46, + 0.906, + 0.491 + ], + "angle": 0, + "content": "where \\(K\\) is the total number of warp-refinement levels and \\(\\lambda^l\\) denotes the weight of the l-th level." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.504, + 0.638, + 0.521 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.528, + 0.749, + 0.544 + ], + "angle": 0, + "content": "4.1. KITTI Odometry Dataset" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.552, + 0.907, + 0.718 + ], + "angle": 0, + "content": "The KITTI odometry dataset [7] is a widely used standard dataset for evaluating visual odometry and SLAM algorithms. It includes multiple driving scenarios, encompassing urban, rural, and highway environments, with variations in weather and lighting conditions. The dataset consists of 22 sequences of LiDAR point clouds and their corresponding stereo images. In our experiments, we utilize the Velodyne LiDAR point clouds provided in the dataset. Since the ground truth poses (trajectories) are only available for sequences 00 to 10, we use these sequences for both training and testing." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.727, + 0.689, + 0.743 + ], + "angle": 0, + "content": "4.2. Implement details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In the training and evaluation process, N points are randomly sampled from the point clouds of two frames separately. It is not necessary for the original input point clouds to have the same number of points. In the proposed network, N is set to 8192. All training and evaluation experiments are conducted on a single NVIDIA RTX 3090 GPU. The Adam optimizer is employed with parameters \\(\\beta 1 = 0.9\\) and \\(\\beta 2 = 0.999\\). The initial learning rate is set to 0.001 and is reduced by a factor of 0.8 every 8 epochs until it reaches 0.000001. The initial values of the trainable parameters \\(w_{t}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17054" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.231 + ], + "angle": 0, + "content": "
    Method00010203040506\\( 07^{\\dagger} \\)\\( 08^{\\dagger} \\)\\( 09^{\\dagger} \\)\\( 10^{\\dagger} \\)Mean on 07-10
    \\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t _{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)
    ICP-po2po6.882.9911.212.588.213.3911.075.056.644.023.971.931.951.595.173.3510.044.936.932.898.914.747.7633.978
    ICP-po2pl3.801.7313.532.589.002.742.721.632.962.582.291.081.771.001.551.424.422.143.951.716.132.604.0131.968
    GICP [36]1.290.644.390.912.530.771.681.083.761.071.020.540.920.460.640.451.580.751.970.771.310.621.3750.648
    CLS [41]2.110.954.221.052.290.861.631.091.590.711.980.920.920.461.040.732.141.051.950.923.461.282.1480.995
    Full LOAM [50]0.780.531.430.550.920.550.860.650.710.500.570.380.650.390.630.501.120.440.770.480.790.570.8280.498
    Full A-LOAM0.760.311.970.504.531.450.930.490.620.390.480.250.610.280.430.261.060.320.730.311.020.400.8100.323
    LO-Net [21]1.470.721.360.471.520.711.030.660.510.651.040.690.710.501.700.892.120.771.370.581.800.931.7480.793
    PWCLO-Net [42]0.780.420.670.230.860.410.760.440.370.400.450.270.270.220.600.441.260.550.790.351.690.621.0850.490
    DELO [1]1.430.812.190.571.480.521.381.102.451.701.270.640.830.350.580.411.360.641.230.571.530.901.1750.630
    TransLO [23]0.850.381.160.450.880.341.000.710.340.180.630.410.730.310.550.431.290.500.950.461.180.610.9930.500
    EfficientLO [44]0.830.330.550.210.710.250.490.380.220.110.340.210.360.240.460.381.140.410.780.330.800.460.7950.395
    Ours0.600.270.360.150.710.260.570.400.300.170.330.220.280.170.370.271.120.440.680.280.660.320.7080.328
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.241, + 0.907, + 0.298 + ], + "angle": 0, + "content": "Table 1. The LiDAR odometry experiment results on KITTI odometry dataset [7]. \\( t_{rel}, r_{rel} \\) indicate the average translational RMSE (\\%) and rotational RMSE (\\( ^\\circ /100\\mathrm{m} \\)) respectively on all possible subsequences in the length of 100, 200, ..., 800m. \\( ^\\dagger \\) means the testing sequences. LOAM and A-LOAM is complete SLAM system, including back-end optimization. The best result for each sequence is bold, and the second best is underlined." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.31, + 0.47, + 0.378 + ], + "angle": 0, + "content": "
    Method07†08†Mean
    trelrreltrelrreltrelrrel
    LodoNet [53]1.861.642.040.971.9501.305
    Ours0.370.271.120.440.7450.355
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.387, + 0.483, + 0.418 + ], + "angle": 0, + "content": "Table 2. Comparison with learning-based odometry LodoNet on KITTI 07-08 sequences." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.432, + 0.47, + 0.508 + ], + "angle": 0, + "content": "
    Method09†10†Mean
    trelrreltrelrreltrelrrel
    Nubert et al. [30]1.540.681.780.691.660.685
    H-VLO [2]1.890.341.390.521.640.430
    Ours0.680.280.660.320.670.300
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.519, + 0.483, + 0.549 + ], + "angle": 0, + "content": "Table 3. Comparison with learning-based odometry on KITTI 09-10 sequences." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.576, + 0.483, + 0.637 + ], + "angle": 0, + "content": "and \\( w_{q} \\) are set to 0.0 and -2.5, respectively, as indicated in formula Eq. (14). For formula Eq. (15), the parameters are set as follows: \\( \\lambda_{3} = 1.6 \\), \\( \\lambda_{2} = 0.8 \\), \\( \\lambda_{1} = 0.4 \\), \\( \\lambda_{0} = 0.2 \\), and \\( L = 4 \\). The batch size is 12." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.649, + 0.423, + 0.667 + ], + "angle": 0, + "content": "4.3. Comparison with The State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.673, + 0.483, + 0.749 + ], + "angle": 0, + "content": "We compare our network with the state-of-the-art on KITTI dataset, including both classic methods and learning-based ones. Since existing training and testing sequence settings are inconsistent in different methods, we test and evaluate our framework accordingly for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.902 + ], + "angle": 0, + "content": "00-06 as training sequences and 07-10 as testing sequences. Quantitative results are listed in Tab. 1. The traditional methods we compare include ICP-point2point (ICP-po2po), ICP-point2plane (ICP-po2pl), GICP [36], CLS [41], which rely on iterative point cloud alignment. LOAM [50], its enhanced version A-LOAM is also included. While LOAM and A-LOAM have been widely recognized for their robust performance on the KITTI odometry benchmark, our method achieves superior accuracy on most sequences. As shown in Tab. 1, our approach outperforms Full A-LOAM," + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.314, + 0.891, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.482, + 0.907, + 0.525 + ], + "angle": 0, + "content": "Figure 3. 2D trajectories of A-LOAM, EfficientLO, and our proposed method on KITTI sequences 02 and 10 with ground truth. It can be observed that our method performs the best." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.537, + 0.907, + 0.642 + ], + "angle": 0, + "content": "which has the mapping optimization. Additionally, the learning-based LiDAR odometry methods we compare include LO-Net [21], DELO [1], PWCLO-Net [42], TransLO [23], EfficientLO [44]. Compared to the current state-of-the-art method EfficientLO, our method DiffLO achieves an average improvement of \\(10.9\\%\\) in transition accuracy and \\(16.9\\%\\) in rotation accuracy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.643, + 0.907, + 0.733 + ], + "angle": 0, + "content": "00-06 and 09-10 as training sequences and 07-08 as testing sequences. We compare with a recent method LodoNet [52] in Tab. 2. Our method is trained on 00-06 sequences while LodoNet are trained on 00-06 and 09-10 sequences, even so, our method performs better than LodoNet on the test sequences." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.733, + 0.909, + 0.84 + ], + "angle": 0, + "content": "00-08 as training sequences and 09-10 as testing sequences. We compare with recent method [2, 30]. Our method is trained on 00-06 sequences while others are trained on 00-08 sequences. As illustrated in Tab. 3, both our translation and rotation errors are smaller than theirs. Although our approach utilizes only LiDAR data, we achieve better results than the multi-modal method H-VLO." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.848, + 0.667, + 0.865 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In order to analyze the effectiveness of each module, we remove or change components of our model to do the abla" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17055" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.137, + 0.089, + 0.865, + 0.287 + ], + "angle": 0, + "content": "
    Method07†08†09†10†Mean on 07-10
    trelrreltrelrreltrelrreltrelrreltrelrrel
    (a)Semanticw/o SPM0.520.461.190.530.530.180.930.420.7930.398
    Ours (full, with SPM)0.370.271.120.440.680.280.660.320.7080.328
    (b)Diffusionw/o diffusion4.833.826.773.055.292.227.093.975.9953.265
    with trans-based Mθ [40]0.390.341.360.550.730.291.070.480.8880.415
    with ptrans-based Mθ [51]0.450.281.190.450.540.220.720.410.7250.340
    Ours (GRU-based Mθ [6])0.370.271.120.440.680.280.660.320.7080.328
    (c)Conditionw/o cost volume0.450.351.200.490.700.281.090.950.8600.518
    w/o geometry feature0.400.271.180.470.610.240.960.460.7870.357
    w/o semantic feature0.470.311.330.560.750.230.640.480.7980.395
    w/o coarse pose embedding0.450.341.280.560.640.250.630.330.7500.370
    Ours (full, with all conditions)0.370.271.120.440.680.280.660.320.7080.328
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.099, + 0.296, + 0.898, + 0.312 + ], + "angle": 0, + "content": "Table 4. The ablation study results of LiDAR odometry on KITTI odometry dataset[7]. The best performance of each sequence is bold." + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.327, + 0.291, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.47, + 0.227, + 0.479 + ], + "angle": 0, + "content": "(a) Sequence 01" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.328, + 0.476, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.47, + 0.417, + 0.479 + ], + "angle": 0, + "content": "(b) Sequence 05" + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.475, + 0.288, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.158, + 0.611, + 0.228, + 0.621 + ], + "angle": 0, + "content": "(c) Sequence 06" + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.474, + 0.477, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.346, + 0.611, + 0.417, + 0.621 + ], + "angle": 0, + "content": "(d) Sequence 09" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.629, + 0.483, + 0.686 + ], + "angle": 0, + "content": "Figure 4. 3D trajectories of A-LOAM, EfficientLO and our proposed method on KITTI sequences 01, 05, 06 and 09 with ground truth. Ours trajectory is more accurate than EfficientLO and the Full A-LOAM, which has the mapping optimization." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.702, + 0.483, + 0.733 + ], + "angle": 0, + "content": "tion studies on KITTI odometry dataset (00-06 as training sequences and 07-10 as testing sequences)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.483, + 0.869 + ], + "angle": 0, + "content": "Study on Semantic Perception Module. We conducted ablation experiments to demonstrate the significance of the Semantic Perception Module (SPM) mentioned in Sec. 3.2. As shown in Tab. 4, SPM achieves an average improvement of \\(10.7\\%\\) in transition accuracy and \\(17.6\\%\\) in rotation accuracy. This indicates that SPM enhances accuracy by embedding semantic understand to the network, which helps the network to focus more on the objects in the scene that play a key role in pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.871, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Study on Diffusion Refinement. We conducted an ablation study by comparing results with and without the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.326, + 0.905, + 0.493 + ], + "angle": 0, + "content": "diffusion-based refinement process (w/o diffusion). As shown in Tab. 4, the diffusion-based pose refinement significantly improved performance, reducing the average translation error by \\(88.2\\%\\) (from \\(5.995\\%\\) to \\(0.708\\%\\)) and the average rotation error by \\(90.0\\%\\) (from \\(3.265^{\\circ} / 100\\mathrm{m}\\) to \\(0.328^{\\circ} / 100\\mathrm{m}\\)). Additionally, we explored the performance of different denoising networks, including a transformer-based [40] network (trans-based), a point transformer-based [51] network (ptrans-based), and GRU-based [6] network. The results demonstrate the advantages of our denoising network over alternative approaches." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.493, + 0.907, + 0.766 + ], + "angle": 0, + "content": "Study on Condition signals. To evaluate the effectiveness of the diffusion condition signals, we conducted an ablation study by individually removing each designed condition signal, as shown in Tab. 4. Removing the cost volume led to a performance degradation (with translation error increasing by \\(21.5\\%\\) and rotation error by \\(57.9\\%\\)), since cost volume captures the precise per-point correlation between two frames. The semantic feature also plays a crucial role in guiding diffusion generation, as it provides scene understanding. Consequently, its removal resulted in a significant drop in performance (led to a \\(12.7\\%\\) increase in translation error and a \\(20.4\\%\\) increase in rotation error). Additionally, removing the coarse pose embedding led to a decline in performance, as coarse pose embedding provides essential state information, which is closely related to the residual pose generated by the model. Finally, the absence of geometry features as guidance also resulted in a noticeable performance drop." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.772, + 0.652, + 0.787 + ], + "angle": 0, + "content": "4.5. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.905, + 0.825 + ], + "angle": 0, + "content": "We visualize the trajectory of our network and analyze the benefits of Semantic Perception Module in this section." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Visualization of Trajectory. The qualitative results are shown in Fig.3, 4 and 5. We compared our method with full A-LOAM, which includes mapping optimization, and EfficientLO [44]. Notably, in Seq.02 of Fig. 3, A-LOAM exhibits significant drift due to the presence of repetitive" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17056" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.092, + 0.48, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.225, + 0.483, + 0.268 + ], + "angle": 0, + "content": "Figure 5. Average translational and rotational error on KITTI sequences 00-10 on all possible subsequences in the length of 100, 200, ..., 800m. Our method has the best performance." + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.276, + 0.48, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.462, + 0.483, + 0.534 + ], + "angle": 0, + "content": "Figure 6. The visualization of semantic features is derived from the complete LiDAR point cloud of the initial frame. Additionally, the grayscale image captured from the camera view corresponds to the semantic segmentation image displayed below. Bounding boxes are utilized to delineate specific object categories." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.55, + 0.483, + 0.641 + ], + "angle": 0, + "content": "structures and patterns in the scene, which impedes the algorithm's ability to accurately estimate pose. These figures show that our odometry can track the trajectory of the ground truth fairly well. At the same time, our method demonstrates the best average evaluation performance compared to A-LOAM and EfficientLO." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.643, + 0.483, + 0.779 + ], + "angle": 0, + "content": "Visualization of Semantic feature. The proposed network employs an embedding feature of 8,192 points to compute the pose transformation in the final pose output layer. Consequently, we visualize the semantic features of these 8,192 points. As illustrated in Fig. 6, vehicles, street lamps, fences, billboards, and other objects in the scene are segmented. This demonstrates that the Semantic Perception Module empowers the network with the capability of semantic understanding." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.903 + ], + "angle": 0, + "content": "Visualization of embedding mask. We visualize the embedding mask of the 8,192 points in the final pose output layer. As shown in Fig. 7, the mask of DiffLO integrated with the Semantic Perception Module (SPM) allocates weights more accurately compared to the mask of DiffLO without SPM. Points sampled from static and structured rigid objects, such as buildings, fences, and pole-like object, exhibit higher weights, while points from dynamic" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.091, + 0.902, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.26, + 0.907, + 0.345 + ], + "angle": 0, + "content": "Figure 7. The visualization of the embedding mask is based on the complete LiDAR point cloud of the initial frame. In the lower-left corner, the heatmap represents the mask of DiffLO integrated with the SPM. Conversely, the lower-right corner displays the heatmap for the mask of DiffLO without SPM. Above these visualizations, the corresponding grayscale image of the point cloud is presented." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.365, + 0.907, + 0.44 + ], + "angle": 0, + "content": "and low-texture objects, including cars, shrubs, and trees, receive lower weights. This demonstrates that the Semantic Perception Module (SPM) effectively helps the network focus on objects in the scene that are crucial for accurate pose estimation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.46, + 0.688, + 0.476 + ], + "angle": 0, + "content": "4.6. Runtime Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.486, + 0.907, + 0.563 + ], + "angle": 0, + "content": "Efficiency is another extremely significant factor in real-time SLAM systems. The LiDAR points in the KITTI dataset are captured at a \\(10\\mathrm{Hz}\\) frequency. Our method has only \\(76.9\\mathrm{ms}\\) inference time, which satisfy the real-time application requirements (under \\(100\\mathrm{ms}\\))." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.585, + 0.634, + 0.601 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.907, + 0.841 + ], + "angle": 0, + "content": "In this paper, we introduce a diffusion model-based odometry network augmented with semantic awareness, targeting large-scale LiDAR odometry. Our approach innovatively applies knowledge distillation to transfer semantic information into the odometry network, thereby enhancing the network's semantic understanding. This allows the network to effectively mitigate the challenges posed by dynamic objects, repetitive patterns, and low-texture environments. Additionally, we incorporate a diffusion model conditioned on pose-related features to refine pose estimation. To the best of our knowledge, this is the first instance of utilizing diffusion models in odometry tasks. We evaluated our framework on the KITTI odometry dataset, and our method achieved state-of-the-art performance while ensuring the real-time requirement of pose prediction." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.841, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements This work was supported in part by Natural Science Foundation of China (No.62171393), and the Fundamental Research Funds for the Central Universities (No.20720220064)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17057" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.169 + ], + "angle": 0, + "content": "[1] Sk Aziz Ali, Djamila Aouada, Gerd Reis, and Didier Stricker. 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In CVPR, pages 12786-12796, 2022. 1" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.093, + 0.905, + 0.631 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17059" + } + ] +] \ No newline at end of file diff --git a/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_origin.pdf b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a3bf4f890ef7c57183f79624d5bcc6a7ba860484 --- /dev/null +++ b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/0ca80052-baf1-4186-ab94-c84b3011f6df_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:99aa337511f28b81b3a7fa0e2b180b23838344e62b72c847e3c27b2790d8f634 +size 3762733 diff --git a/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/full.md b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5c928c729fbb9d864bd73dd749df5d19955325d4 --- /dev/null +++ b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/full.md @@ -0,0 +1,362 @@ +# DiffLO: Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement + +Yongshu Huang $^{1,2*}$ Chen Liu $^{1,2*}$ Minghang Zhu $^{1,2}$ Sheng Ao $^{1,2\dagger}$ Chenglu Wen $^{1,2}$ Cheng Wang $^{1,2\dagger}$ $^{1}$ Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University, China. + $^{2}$ Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University, China. + +# Abstract + +LiDAR odometry is a critical module in autonomous driving systems, responsible for accurate localization by estimating the relative pose transformation between consecutive point cloud frames. However, existing studies frequently encounter challenges with unreliable pose estimation, due to the lack of in-depth understanding of scenario and the presence of noise interference. To address this challenge, we propose DiffLO, a semantic-aware LiDAR odometry network with diffusion-based refinement. To mitigate the impact of challenging cases such as dynamic, repetitive patterns, and low textures, we introduce a semantic distillation method that integrates semantic information into the odometry task. This allows the network to gain a semantic understanding of the scene, enabling it to focus more on the objects that are beneficial for pose estimation. Additionally, to enhance the robustness, we propose a diffusion-based refinement method. This method uses pose-related features as conditional constraints for generative diversity, iteratively refining the pose estimation to achieve greater accuracy. Comparative experiments on the KITTI odometry dataset demonstrate that the proposed method achieves state-of-the-art performance among existing learning-based approaches. Furthermore, the proposed DiffLO method outperforms the classic A-LOAM on most evaluation sequences. The code will be released at https://github.com/HyTree7/DiffLO. + +# 1. Introduction + +LiDAR odometry (LO) is a well-studied problem in computer vision with numerous applications in Simultaneous Localization and Mapping (SLAM) [58], autonomous driving [54], and robotics [45]. The primary objective is to estimate the relative transformation between two frames based on the source and target point clouds. + +![](images/b42ddfbecd180b16ae9886bd3dc11dc223108334a0e043043b4005bf5c18c5b6.jpg) +Figure 1. (a) Predicts a coarse initial pose and applies iterative MLP-based refinement to refine the initial estimate. (b) Predicts a coarse initial pose and applies iterative Diffusion-based refinement, incorporating knowledge distillation to enable semantic understanding. Here, $\hat{T}_k$ represents the noisy pose of the $k^{th}$ denoising step. + +![](images/0caa6faa8b4c9520049822435d36a373de813a2409a982cf249276c0de7621b1.jpg) + +Most classic geometry-based methods, such as Iterative Closest Point (ICP) [4], its variants [31] and others [35], work by iteratively minimizing the distance between corresponding points in two point clouds to achieve accurate alignment. However, they often struggle in sparse point cloud environments, complex dynamic scenes, or when the quality of the point cloud degrades [13, 27, 42]. This limitation arises due to their reliance on precise geometric correspondences. + +Deep learning-based methods have garnered significant attention in recent years. These methods learn feature representations from large-scale data to infer relative transformation between frames in an end-to-end manner, providing better scalability and the potential for multi-task learning. However, the accuracy of deep learning methods still lags behind traditional odometry techniques. + +We identify the following challenges faced by Deep Learning-based odometry methods: (1) To mitigate the effects of challenging cases such as dynamic objects and oc + +clusions, LO-Net [21] introduces a mask prediction network learning the compensation for dynamic objects to remove dynamic objects. Methods such as PWCLO-Net [42], TransLO [23], and EfficientLO [44] introduce a hierarchical embedding mask and apply pose feature weighting to filter dynamic object. However, these approach lacks a comprehensive understanding of object structures, leading to inaccuracies and resulting in cumulative errors; (2) Furthermore, these methods [18, 23, 24, 26, 42, 44] are deterministic prediction tasks, which limits their ability to adapt to newly emerging changes or complexities in the environment. Additionally, they can not provide information about prediction uncertainties. + +Semantic segmentation network contains rich geometric information and intricate details about the scene. This insight motivates us to integrate semantic information into the odometry network, thereby enhancing its ability to filter out dynamic objects and manage occlusions effectively. To achieve this, as shown in Fig. 1, we propose a knowledge distillation approach that transfers semantic knowledge from a segmentation model to the odometry network. After training, the knowledge distillation component and segmentation model are dropped to avoid extra computation or network parameter. By leveraging the contextual knowledge provided by semantic segmentation, our approach aims to improve the overall accuracy and robustness of odometry in complex environments. + +Diffusion models [11] are characterized by their robustness, and have achieved significant success across various tasks [8, 15, 22, 25]. These strengths have inspired us to explore their potential application to the LiDAR odometry task. In this paper, we propose reformulating the odometry task as a diffusion process. As shown in Fig. 1, we transition from a traditional MLP-based refinement approach to a diffusion-based refinement, shifting the task from a deterministic prediction framework to a probabilistic generative model. Specifically, Our approach consists of a forward process that progressively adds noise to the residual pose of the ground truth, followed by a reverse denoising process to refine the noisy pose estimate. We utilize coarse pose embedding, cost volume, semantic feature and geometry embedding as conditions to restrict generation diversity. + +In summary, our contributions are as follows: + +- To enhance the network's ability to focus on objects critical for pose estimation in the scene, we incorporate semantic awareness into odometry by distilling knowledge from a semantic segmentation model. +- We propose a novel diffusion-based refinement pipeline and design strong conditional guidance by combining semantic embedding, coarse pose embeddings, geometry embedding and cross-frame cost volume to control generation diversity. To the best of our knowledge, this is the first work to leverage diffusion probabilistic model in the + +LiDAR odometry task. + +- Extensive experiments on the KITTI odometry dataset [7] demonstrate that our method outperforms all existing learning-based odometry methods. On most sequences, our performance even surpasses A-LOAM with mapping. + +# 2. Relate Work + +# 2.1. Deep LiDAR Odometry + +The field of visual depth odometry has advanced rapidly. However, research on LiDAR-based depth odometry remains challenging due to the inherent irregularity and complexity of point clouds. LO-Net [21] proposed an end-to-end deep odometry network that enhances robustness by learning the compensation for dynamic objects through a mask prediction network. PWCLO [42] first introduces a coarse-to-fine structure to LiDAR odometry, implementing a hierarchical refinement approach for estimated poses. LodoNet [52] projects 3D point clouds onto 2D spherical depth images to extract and match keypoints for odometry localization. EfficientLO [44] introduces a projection-aware representation of 3D point clouds, facilitating efficient learning for large-scale datasets. TransLO [23] develops a cross-frame transformer module that associates consecutive frames, thereby regressing relative pose estimations. DELO [1] innovatively employs partial optimal transportation of LiDAR feature descriptors to achieve robust localization estimation. + +# 2.2. LiDAR-based semantic segmentation + +LiDAR-based semantic segmentation aims to assign a semantic label to each point in the input LiDAR scan. These methods can generally be categorized into several approaches: point-based [14, 32, 33, 39], voxel-based [9, 57], projection-based [17, 29, 46], and hybrid methods that combine these techniques [37, 49]. These approaches consistently expand the receptive field by integrating fine-grained point features with coarse-grained contextual information, which enhances the network's ability to understand the scene structure and the unique characteristics of each point. Semantic information has also proven to be highly valuable in traditional non-deep learning methods, such as [3, 5, 19, 20, 56]. By leveraging semantic labels, these systems can enhance feature matching and improve robustness against challenging conditions like dynamic objects and occlusions. + +Inspired by these traditional methods, we explore integrating semantics into learning-based LiDAR odometry to address the challenges posed by dynamic objects, repetitive patterns, and low-texture environments. + +# 2.3. 3D Diffusion Model + +Diffusion models have garnered significant attention and research in a variety of 3D point cloud processing tasks. For instance, Luo et al. [28] introduced a probabilistic model for point cloud generation, transforming the point cloud noise distribution into the desired point cloud shape distribution. Zhou et al. [55] combined a denoising diffusion model with a mixed point-voxel representation of 3D shapes for unconditional shape generation and conditional multimodal shape completion. Jiang et al. [15] proposed a point cloud registration framework based on an SE(3) diffusion model, framing the 3D registration task as a denoising diffusion process that iteratively refines the pose of the source point cloud to achieve precise alignment with the target point cloud. Difflow3D [25] presented an uncertainty-aware scene flow estimation network leveraging a diffusion probabilistic model, where iterative diffusion modules refine initial estimates to enhance the robustness of scene flow estimation. DiffLoc [22] formulates LiDAR localization as a conditional generation of poses, employing a diffusion model conditioned on geometric robust features and incorporating an iterative denoising process into APR to achieve accurate LiDAR localization. + +Inspired by the successful applications of diffusion models in tasks such as registration, scene flow estimation, and localization, we investigate the integration of diffusion models to improve the accuracy of LiDAR odometry. + +# 3. Method + +Given two consecutive point cloud frames $PC_1 \in \mathbb{R}^{N \times 3}$ and $PC_2 \in \mathbb{R}^{M \times 3}$ , the goal of the LiDAR odometry task is to estimate the relative transformation between the two consecutive frames of point clouds. To solve this task, we propose DiffLO, a semantic-aware odometry network with diffusion-based refinement. DiffLO first hierarchically extracts point features (Sec. 3.1). Subsequently, we introduce a Semantic Perception Module (Sec. 3.2), which enables the odometry network to gain semantic understanding. Then, the initial pose is generated (Sec. 3.3) in the coarsest layer. We then utilize diffusion model with condition signals to refine the initial pose by predicting pose residuals from coarse to fine (Sec. 3.4). Lastly, the loss function will be presented in (Sec. 3.5). + +# 3.1. Multi-scale Feature Extraction + +We utilize PointConv [47] for hierarchical feature extraction. At each level $l$ , dense input points and their features are first subsampled using furthest point sampling to create a sparse point set. Then, for each subsampled sparse point, k-nearest neighbor groups local dense points to form a local region for feature extraction. Next, a PointConv [47] layer aggregates features from the grouped local points, produc + +ing a local feature for each sparse point. This process results in an L-level pyramid of point features. + +# 3.2. Semantic Perception Module + +To guide the network's attention towards objects in the scene that are beneficial for pose estimation, such as buildings and pole-like structures. We introduce Semantic Perception Module (SPM). SPM consists of three components: Semantic Module, Semantic Segmentation Modle and Knowledge Distillation. We introduce a semantic segmentation model as the teacher network. A sub-network (the Semantic Module) within the odometry model is designated as the student model. + +During the training stage, three modules collaborate to transfer semantic knowledge into the odometry model. Firstly, the Semantic Module takes the point cloud features $F$ in coarse layer as its input, the output can be expressed as follows: + +$$ +F _ {s t u} = M L P (F) + M L P (F) \otimes \sigma (M L P (F)), \tag {1} +$$ + +where $\otimes$ indicates element-wise multiplication. $\sigma (\cdot)$ denotes the softmax operation along the feature dimension. + +Secondly, a pretrained 3D semantic segmentation model [16], with its network parameters frozen, is utilized here. We extract the per-point features from the final layer, denoted as $F_{seg} \in \mathbb{R}^{N \times d}$ . These features are subsequently downsampled to $F_{tea} \in \mathbb{R}^{N' \times d}$ to ensure compatibility in dimension with $F_{stu}$ . And we adjust the output dimension of the semantic regressor branch, ensuring that $F_{tea}$ and $F_{stu}$ share the same feature dimension $d$ for each point. + +Then, we utilize knowledge distillation [10] to transfer semantic knowledge from the segmentation module to the odometry model. This is achieved by optimizing the following distillation loss: + +$$ +\mathcal {L} _ {k d} = \delta \left(F _ {s t u}, F _ {t e a}\right), \tag {2} +$$ + +where $\delta (\cdot ,\cdot)$ measures the difference between the feature representations from the teacher network $F_{tea}$ and the student network $F_{stu}$ . + +Finally, the semantic feature $F_{stu}$ is propagated to the following level for a denser optimization and simultaneously serves as a condition signal for diffusion-based refinement in Sec. 3.4, via an upsampling layer [6, 48]. + +During the inference stage, only the Semantic Module is retained to avoid additional computational overhead. The output $F_{stu}$ from the Semantic Module is still propagated to subsequent layers, serving as a conditional signal. + +By embedding semantic understanding into the odometry process, the model is better able to focus on objects in the scene that are beneficial for pose estimation. Meanwhile, the close integration of knowledge distillation improves both the efficiency and effectiveness of the overall system. + +![](images/60b3ff2613959917e5c5a681698c1d935bdb88a4f5e6a3839e41463c512359a5.jpg) +Figure 2. The overall structure of DiffLO. The proposed pipeline comprises three core components: Pose Initialization, Semantic Perception Module, and Diffusion-based Pose Refinement. First, hierarchical point features are extracted from the input point cloud. Then, we enable the network to acquire semantic understanding through a knowledge distillation approach. Following this, an initial coarse pose estimate is generated. Finally, the Diffusion-based Pose Refinement module applies iterative refinement layers, conditioned on various signals, to improve the initial pose estimate, ultimately producing a more accurate and robust final pose. To optimize inference efficiency, the semantic segmentation component is discarded after the training phase. + +# 3.3. Semantic-Aware Pose Estimator + +We enhance the pose estimation method from the PWCLO-Net [42] by incorporating semantic features into the pose estimation process. Taking the $l^{th}$ layer as example. + +$$ +E ^ {l} = M L P \left(F ^ {l} \oplus F _ {s t u} ^ {l} \oplus U E ^ {l} \oplus C E ^ {l}\right), \tag {3} +$$ + +$$ +M ^ {l} = \sigma (M L P (F ^ {l} \oplus F _ {s t u} ^ {l} \oplus U M ^ {l} \oplus E ^ {l})), \tag {4} +$$ + +where $\oplus$ is the concatenation and $\sigma (\cdot)$ denotes the softmax operation. $F^l$ is the point cloud feature from $l$ layer, $CE^l$ is generated by cross-frame correlation [6, 43]. $F_{stu}^{l}$ , $UE^{l}$ and $UM^{l}$ are the results of upsampling the semantic feature $F_{stu}^{l + 1}$ , the embedding feature $E^{l + 1}$ and the embedding mask $M^{l + 1}$ respectively. The embedding features $E = \{e_i|e_i\in \mathbb{R}^C\}_{i = 1}^n$ , the embedding mask $M = \{m_i|m_i\in \mathbb{R}^C\}_{i = 1}^n$ . The pose is then generated by: + +$$ +q = \frac {F C \left(\sum_ {i = 1} ^ {n} e _ {i} \odot m _ {i}\right)}{\left| F C \left(\sum_ {i = 1} ^ {n} e _ {i} \odot m _ {i}\right) \right|} \tag {5} +$$ + +$$ +t = F C \left(\sum_ {i = 1} ^ {n} e _ {i} \odot m _ {i}\right) \tag {6} +$$ + +where $FC(\cdot)$ denotes the fully connected layer and $\odot$ represents dot product. Following [42], the embedding features $E$ , embedding mask $M$ and semantic features are also propagated to denser layers for optimization. + +The coarse-level point cloud is sparse and has low resolution, which can lead to incorrect matches and inaccurate initial pose estimates. Inspired by recent success and denoising properties of the diffusion model [11], we design a novel diffusion-based pose refinement module to refine the coarse pose progressively. + +# 3.4. Diffusion-based Pose Refinement + +In this section, we formulate the coarse pose residual as the diffusion latent variable, and residual pose are generated from the reverse process of diffusion model iteratively. + +During the training stage, the diffusion model is trained to learn the underlying distribution of residual poses by recovering the ground truth residual pose from its corrupted version. The ground truth residual pose is calculated as follow: + +$$ +T _ {0} = T _ {g t} \cdot T _ {p r e d} ^ {- 1}, \tag {7} +$$ + +where $T_{0}$ is the ground truth residual pose, $T_{gt}$ is the ground truth pose and $T_{pred}$ is the coarse pose generated by the + +previous layer or the initial pose. + +Specifically, in each training iteration, a random diffusion step, denoted as $k \in \{1, 2, \dots, K\}$ , is chosen. With a predefined variance schedule $\beta_1, \ldots, \beta_k$ , we introduce noises to $T_0$ , resulting in the noisy residual pose $T_k$ . + +$$ +q \left(T _ {k} \mid T _ {0}\right) = \mathcal {N} \left(T _ {k}; \sqrt {\bar {\alpha} _ {k}} T _ {0}, (1 - \bar {\alpha} _ {k}) \mathrm {I}\right) \tag {8} +$$ + +$$ +T _ {k} = \sqrt {\bar {\alpha} _ {k}} T _ {0} + \sqrt {1 - \bar {\alpha} _ {k}} \epsilon , \epsilon \sim \mathcal {N} (0, I) \tag {9} +$$ + +denoting $\alpha_{k} = 1 - \beta_{k}$ and $\overline{\alpha}_k = \Pi_{i = 1}^k\alpha_i$ . Eventually, the ground truth residual pose $T_{0}$ is turned into Gaussian noise when $k$ is large enough. + +During the inference stage, the denoise model approximates the distribution $p(T_0|C)$ as the reversed diffusion process of gradually cleaning $T_{k}$ . Instead of predicting $\epsilon$ as formulated by [12], we follow [34, 38] and predict the signal itself. Also, we constrain the generation diversity and control the reversed diffusion process by the condition information $C$ . In this way, we utilize a denoising network to predict the residual pose $\hat{T_0}$ from noisy input $T_{k}$ , time step $t = k$ , and condition $C$ . + +$$ +\hat {T} _ {0} = \mathcal {M} _ {\theta} \left(T _ {k}, t, C\right), \tag {10} +$$ + +where $\mathcal{M}_{\theta}(\cdot ,\cdot ,\cdot)$ is the denoising network. The training objective is to minimize the following loss: + +$$ +\mathcal {L} _ {r e s} = \mathbb {E} _ {T _ {0}, t}, \left[ \| t _ {g t} - t _ {p r e d} \| _ {2} + \| q _ {g t} - q _ {p r e d} \| _ {2} \right], \tag {11} +$$ + +where $t_{gt}$ and $q_{gt}$ are the translation vector and quaternion from $T_0$ , and $t_{pred}$ and $q_{pred}$ are their corresponding predicted values from $\hat{T}_0$ . + +Design of Condition Signal. Inspired by [42, 43], we introduce the geometric feature $GE$ extracted from $PC_{1}$ along with a cost volume embedding $CE$ constructed using cross-frame correlation [6], with the corresponding hierarchical point cloud features as input, and residual pose embeddings $PE = T_{k} \cdot PC_{1} - PC_{1}$ and the semantic feature $F_{stu}$ as conditional signals to constrain generation diversity. The condition signal is as follow: + +$$ +C = G E \oplus C E \oplus P E, \tag {12} +$$ + +where $\oplus$ is the concatenation operation. + +We employ the augmented version [6] with Gate Recurrent Unit (GRU) to process the condition signal $C$ . This approach allows for the extraction of essential features from $C$ to generate the augmented condition signal $C'$ . Subsequently, the semantic-aware pose estimator in Sec. 3.3 is introduced to generate the residual pose $\hat{T}_0$ . Here, $C'$ are treated as the cost volume embedding $CE$ in Eq. (3). Taking the $l^{th}$ refinement layer as example, the refined pose $T_{pred}^l$ is calculated as follow: + +$$ +T _ {p r e d} ^ {l} = \hat {T} _ {0} ^ {l} \cdot T _ {p r e d} ^ {l + 1}, \tag {13} +$$ + +the refined pose $T_{pred}^{l}$ will be the input to $l - 1^{th}$ refinement layer. + +# 3.5. Training Loss + +The network supervises the pose outputs from each level, along with the residual poses predicted by the diffusion model and the semantic features derived from the Semantic Module. Drawing from previous deep odometry research [21, 42], the training loss function for the odometry at the l-th level is as follows: + +$$ +\begin{array}{l} \mathcal {L} ^ {l} = \left\| t _ {g t} - t ^ {l} \right\| \exp (- w _ {t}) + w _ {t} \\ + \left\| q _ {g t} - \frac {q ^ {l}}{\| q ^ {l} \|} \right\| _ {2} \exp (- w _ {q}) + w _ {q}, \tag {14} \\ \end{array} +$$ + +where $\| \cdot \|$ and $\| \cdot \| _2$ denotes the $\ell 1$ -norm and the $\ell 2$ -norm respectively. $t_{gt}$ and $q_{gt}$ are the ground-truth translation vector and quaternion respectively. $t^l$ and $q^{l}$ are predicted pose from each level. $w_{t}$ and $w_{q}$ are two learnable parameters, which are introduced to eliminate the differences in scale and units between the translation vector and the quaternion. Then, a multi-scale supervised approach is adopted. The total training loss function $\mathcal{L}$ is: + +$$ +\mathcal {L} = \mathcal {L} _ {k d} + \sum_ {l = 0} ^ {K} \lambda^ {l} \times \left(\mathcal {L} ^ {l} + \mathcal {L} _ {r e s} ^ {l}\right), \tag {15} +$$ + +where $K$ is the total number of warp-refinement levels and $\lambda^l$ denotes the weight of the l-th level. + +# 4. Experiment + +# 4.1. KITTI Odometry Dataset + +The KITTI odometry dataset [7] is a widely used standard dataset for evaluating visual odometry and SLAM algorithms. It includes multiple driving scenarios, encompassing urban, rural, and highway environments, with variations in weather and lighting conditions. The dataset consists of 22 sequences of LiDAR point clouds and their corresponding stereo images. In our experiments, we utilize the Velodyne LiDAR point clouds provided in the dataset. Since the ground truth poses (trajectories) are only available for sequences 00 to 10, we use these sequences for both training and testing. + +# 4.2. Implement details + +In the training and evaluation process, N points are randomly sampled from the point clouds of two frames separately. It is not necessary for the original input point clouds to have the same number of points. In the proposed network, N is set to 8192. All training and evaluation experiments are conducted on a single NVIDIA RTX 3090 GPU. The Adam optimizer is employed with parameters $\beta 1 = 0.9$ and $\beta 2 = 0.999$ . The initial learning rate is set to 0.001 and is reduced by a factor of 0.8 every 8 epochs until it reaches 0.000001. The initial values of the trainable parameters $w_{t}$ + +
    Method00010203040506\( 07^{\dagger} \)\( 08^{\dagger} \)\( 09^{\dagger} \)\( 10^{\dagger} \)Mean on 07-10
    \( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t _{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)\( t_{rel} \)\( r_{rel} \)
    ICP-po2po6.882.9911.212.588.213.3911.075.056.644.023.971.931.951.595.173.3510.044.936.932.898.914.747.7633.978
    ICP-po2pl3.801.7313.532.589.002.742.721.632.962.582.291.081.771.001.551.424.422.143.951.716.132.604.0131.968
    GICP [36]1.290.644.390.912.530.771.681.083.761.071.020.540.920.460.640.451.580.751.970.771.310.621.3750.648
    CLS [41]2.110.954.221.052.290.861.631.091.590.711.980.920.920.461.040.732.141.051.950.923.461.282.1480.995
    Full LOAM [50]0.780.531.430.550.920.550.860.650.710.500.570.380.650.390.630.501.120.440.770.480.790.570.8280.498
    Full A-LOAM0.760.311.970.504.531.450.930.490.620.390.480.250.610.280.430.261.060.320.730.311.020.400.8100.323
    LO-Net [21]1.470.721.360.471.520.711.030.660.510.651.040.690.710.501.700.892.120.771.370.581.800.931.7480.793
    PWCLO-Net [42]0.780.420.670.230.860.410.760.440.370.400.450.270.270.220.600.441.260.550.790.351.690.621.0850.490
    DELO [1]1.430.812.190.571.480.521.381.102.451.701.270.640.830.350.580.411.360.641.230.571.530.901.1750.630
    TransLO [23]0.850.381.160.450.880.341.000.710.340.180.630.410.730.310.550.431.290.500.950.461.180.610.9930.500
    EfficientLO [44]0.830.330.550.210.710.250.490.380.220.110.340.210.360.240.460.381.140.410.780.330.800.460.7950.395
    Ours0.600.270.360.150.710.260.570.400.300.170.330.220.280.170.370.271.120.440.680.280.660.320.7080.328
    + +Table 1. The LiDAR odometry experiment results on KITTI odometry dataset [7]. $t_{rel}, r_{rel}$ indicate the average translational RMSE (\%) and rotational RMSE ( $^\circ /100\mathrm{m}$ ) respectively on all possible subsequences in the length of 100, 200, ..., 800m. $^\dagger$ means the testing sequences. LOAM and A-LOAM is complete SLAM system, including back-end optimization. The best result for each sequence is bold, and the second best is underlined. + +
    Method07†08†Mean
    trelrreltrelrreltrelrrel
    LodoNet [53]1.861.642.040.971.9501.305
    Ours0.370.271.120.440.7450.355
    + +Table 2. Comparison with learning-based odometry LodoNet on KITTI 07-08 sequences. + +
    Method09†10†Mean
    trelrreltrelrreltrelrrel
    Nubert et al. [30]1.540.681.780.691.660.685
    H-VLO [2]1.890.341.390.521.640.430
    Ours0.680.280.660.320.670.300
    + +Table 3. Comparison with learning-based odometry on KITTI 09-10 sequences. + +and $w_{q}$ are set to 0.0 and -2.5, respectively, as indicated in formula Eq. (14). For formula Eq. (15), the parameters are set as follows: $\lambda_{3} = 1.6$ , $\lambda_{2} = 0.8$ , $\lambda_{1} = 0.4$ , $\lambda_{0} = 0.2$ , and $L = 4$ . The batch size is 12. + +# 4.3. Comparison with The State-of-the-Art + +We compare our network with the state-of-the-art on KITTI dataset, including both classic methods and learning-based ones. Since existing training and testing sequence settings are inconsistent in different methods, we test and evaluate our framework accordingly for a fair comparison. + +00-06 as training sequences and 07-10 as testing sequences. Quantitative results are listed in Tab. 1. The traditional methods we compare include ICP-point2point (ICP-po2po), ICP-point2plane (ICP-po2pl), GICP [36], CLS [41], which rely on iterative point cloud alignment. LOAM [50], its enhanced version A-LOAM is also included. While LOAM and A-LOAM have been widely recognized for their robust performance on the KITTI odometry benchmark, our method achieves superior accuracy on most sequences. As shown in Tab. 1, our approach outperforms Full A-LOAM, + +![](images/8a4c89b35dbf0b4fdc0c52f7037e2458ee6a359123689b9a43aa13bc44f2459e.jpg) +Figure 3. 2D trajectories of A-LOAM, EfficientLO, and our proposed method on KITTI sequences 02 and 10 with ground truth. It can be observed that our method performs the best. + +which has the mapping optimization. Additionally, the learning-based LiDAR odometry methods we compare include LO-Net [21], DELO [1], PWCLO-Net [42], TransLO [23], EfficientLO [44]. Compared to the current state-of-the-art method EfficientLO, our method DiffLO achieves an average improvement of $10.9\%$ in transition accuracy and $16.9\%$ in rotation accuracy. + +00-06 and 09-10 as training sequences and 07-08 as testing sequences. We compare with a recent method LodoNet [52] in Tab. 2. Our method is trained on 00-06 sequences while LodoNet are trained on 00-06 and 09-10 sequences, even so, our method performs better than LodoNet on the test sequences. + +00-08 as training sequences and 09-10 as testing sequences. We compare with recent method [2, 30]. Our method is trained on 00-06 sequences while others are trained on 00-08 sequences. As illustrated in Tab. 3, both our translation and rotation errors are smaller than theirs. Although our approach utilizes only LiDAR data, we achieve better results than the multi-modal method H-VLO. + +# 4.4. Ablation Study + +In order to analyze the effectiveness of each module, we remove or change components of our model to do the abla + +
    Method07†08†09†10†Mean on 07-10
    trelrreltrelrreltrelrreltrelrreltrelrrel
    (a)Semanticw/o SPM0.520.461.190.530.530.180.930.420.7930.398
    Ours (full, with SPM)0.370.271.120.440.680.280.660.320.7080.328
    (b)Diffusionw/o diffusion4.833.826.773.055.292.227.093.975.9953.265
    with trans-based Mθ [40]0.390.341.360.550.730.291.070.480.8880.415
    with ptrans-based Mθ [51]0.450.281.190.450.540.220.720.410.7250.340
    Ours (GRU-based Mθ [6])0.370.271.120.440.680.280.660.320.7080.328
    (c)Conditionw/o cost volume0.450.351.200.490.700.281.090.950.8600.518
    w/o geometry feature0.400.271.180.470.610.240.960.460.7870.357
    w/o semantic feature0.470.311.330.560.750.230.640.480.7980.395
    w/o coarse pose embedding0.450.341.280.560.640.250.630.330.7500.370
    Ours (full, with all conditions)0.370.271.120.440.680.280.660.320.7080.328
    + +Table 4. The ablation study results of LiDAR odometry on KITTI odometry dataset[7]. The best performance of each sequence is bold. + +![](images/ee2fccead9c463552b7cce4ce32bef4309ee49771ea81805a948d3ab298c2b31.jpg) + +![](images/ce23967ba037522fbf48a3ba11417d023fc62dda5cc3567eb32c6552a8d23437.jpg) + +![](images/61b180e0795b45c3f9d5126785a646978c53ecd33c675e473c57649325642827.jpg) +(a) Sequence 01 +(c) Sequence 06 +Figure 4. 3D trajectories of A-LOAM, EfficientLO and our proposed method on KITTI sequences 01, 05, 06 and 09 with ground truth. Ours trajectory is more accurate than EfficientLO and the Full A-LOAM, which has the mapping optimization. + +![](images/66179fc5f680d76638ffe38a2a8f58bd415cb06e8f7516f153bcd7b9419fa9a0.jpg) +(b) Sequence 05 +(d) Sequence 09 + +tion studies on KITTI odometry dataset (00-06 as training sequences and 07-10 as testing sequences). + +Study on Semantic Perception Module. We conducted ablation experiments to demonstrate the significance of the Semantic Perception Module (SPM) mentioned in Sec. 3.2. As shown in Tab. 4, SPM achieves an average improvement of $10.7\%$ in transition accuracy and $17.6\%$ in rotation accuracy. This indicates that SPM enhances accuracy by embedding semantic understand to the network, which helps the network to focus more on the objects in the scene that play a key role in pose estimation. + +Study on Diffusion Refinement. We conducted an ablation study by comparing results with and without the + +diffusion-based refinement process (w/o diffusion). As shown in Tab. 4, the diffusion-based pose refinement significantly improved performance, reducing the average translation error by $88.2\%$ (from $5.995\%$ to $0.708\%$ ) and the average rotation error by $90.0\%$ (from $3.265^{\circ} / 100\mathrm{m}$ to $0.328^{\circ} / 100\mathrm{m}$ ). Additionally, we explored the performance of different denoising networks, including a transformer-based [40] network (trans-based), a point transformer-based [51] network (ptrans-based), and GRU-based [6] network. The results demonstrate the advantages of our denoising network over alternative approaches. + +Study on Condition signals. To evaluate the effectiveness of the diffusion condition signals, we conducted an ablation study by individually removing each designed condition signal, as shown in Tab. 4. Removing the cost volume led to a performance degradation (with translation error increasing by $21.5\%$ and rotation error by $57.9\%$ ), since cost volume captures the precise per-point correlation between two frames. The semantic feature also plays a crucial role in guiding diffusion generation, as it provides scene understanding. Consequently, its removal resulted in a significant drop in performance (led to a $12.7\%$ increase in translation error and a $20.4\%$ increase in rotation error). Additionally, removing the coarse pose embedding led to a decline in performance, as coarse pose embedding provides essential state information, which is closely related to the residual pose generated by the model. Finally, the absence of geometry features as guidance also resulted in a noticeable performance drop. + +# 4.5. Visualization + +We visualize the trajectory of our network and analyze the benefits of Semantic Perception Module in this section. + +Visualization of Trajectory. The qualitative results are shown in Fig.3, 4 and 5. We compared our method with full A-LOAM, which includes mapping optimization, and EfficientLO [44]. Notably, in Seq.02 of Fig. 3, A-LOAM exhibits significant drift due to the presence of repetitive + +![](images/ab0593e8dacb7dd12fa283918fc579e412b13b7d94059b9502c9fc09bc0dfb5e.jpg) +Figure 5. Average translational and rotational error on KITTI sequences 00-10 on all possible subsequences in the length of 100, 200, ..., 800m. Our method has the best performance. + +![](images/0371a01e13e5f9b4686b76056b758a7ab3d60fd96d76e75ef1ea55f63982499a.jpg) +Figure 6. The visualization of semantic features is derived from the complete LiDAR point cloud of the initial frame. Additionally, the grayscale image captured from the camera view corresponds to the semantic segmentation image displayed below. Bounding boxes are utilized to delineate specific object categories. + +structures and patterns in the scene, which impedes the algorithm's ability to accurately estimate pose. These figures show that our odometry can track the trajectory of the ground truth fairly well. At the same time, our method demonstrates the best average evaluation performance compared to A-LOAM and EfficientLO. + +Visualization of Semantic feature. The proposed network employs an embedding feature of 8,192 points to compute the pose transformation in the final pose output layer. Consequently, we visualize the semantic features of these 8,192 points. As illustrated in Fig. 6, vehicles, street lamps, fences, billboards, and other objects in the scene are segmented. This demonstrates that the Semantic Perception Module empowers the network with the capability of semantic understanding. + +Visualization of embedding mask. We visualize the embedding mask of the 8,192 points in the final pose output layer. As shown in Fig. 7, the mask of DiffLO integrated with the Semantic Perception Module (SPM) allocates weights more accurately compared to the mask of DiffLO without SPM. Points sampled from static and structured rigid objects, such as buildings, fences, and pole-like object, exhibit higher weights, while points from dynamic + +![](images/b5f7e4a433487d4c1024de72c7ea0a75175851b989799899aeac0936a06d614c.jpg) +Figure 7. The visualization of the embedding mask is based on the complete LiDAR point cloud of the initial frame. In the lower-left corner, the heatmap represents the mask of DiffLO integrated with the SPM. Conversely, the lower-right corner displays the heatmap for the mask of DiffLO without SPM. Above these visualizations, the corresponding grayscale image of the point cloud is presented. + +and low-texture objects, including cars, shrubs, and trees, receive lower weights. This demonstrates that the Semantic Perception Module (SPM) effectively helps the network focus on objects in the scene that are crucial for accurate pose estimation. + +# 4.6. Runtime Analysis + +Efficiency is another extremely significant factor in real-time SLAM systems. The LiDAR points in the KITTI dataset are captured at a $10\mathrm{Hz}$ frequency. Our method has only $76.9\mathrm{ms}$ inference time, which satisfy the real-time application requirements (under $100\mathrm{ms}$ ). + +# 5. Conclusion + +In this paper, we introduce a diffusion model-based odometry network augmented with semantic awareness, targeting large-scale LiDAR odometry. Our approach innovatively applies knowledge distillation to transfer semantic information into the odometry network, thereby enhancing the network's semantic understanding. This allows the network to effectively mitigate the challenges posed by dynamic objects, repetitive patterns, and low-texture environments. Additionally, we incorporate a diffusion model conditioned on pose-related features to refine pose estimation. To the best of our knowledge, this is the first instance of utilizing diffusion models in odometry tasks. 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In CVPR, pages 12786-12796, 2022. 1 \ No newline at end of file diff --git a/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/images.zip b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..b5ecb34510c0c12f8c30b81e00475d9f606a2233 --- /dev/null +++ b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7b0de05b4a6c9d4cf4e26d9a6c062561ff3997f05115cfce628dd23475dc9b96 +size 670223 diff --git a/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/layout.json b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..09a014b3d0eb26f9eb3cc081e73fc2bb0e0df10f --- /dev/null +++ b/2025/DiffLO_ Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement/layout.json @@ -0,0 +1,9974 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 66, + 103, + 544, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 103, + 544, + 120 + ], + "spans": [ + { + "bbox": [ + 66, + 103, + 544, + 120 + ], + "type": "text", + "content": "DiffLO: Semantic-Aware LiDAR Odometry with Diffusion-Based Refinement" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "spans": [ + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "content": "Yongshu Huang" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "content": " Chen Liu" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "content": " Minghang Zhu" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "content": " Sheng Ao" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "inline_equation", + "content": "^{1,2\\dagger}" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "content": " Chenglu Wen" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "content": " Cheng Wang" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "inline_equation", + "content": "^{1,2\\dagger}" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "content": " Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University, China. \n" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 62, + 142, + 570, + 200 + ], + "type": "text", + "content": " Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University, China." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "spans": [ + { + "bbox": [ + 151, + 227, + 200, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 253, + 296, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 253, + 296, + 565 + ], + "spans": [ + { + "bbox": [ + 55, + 253, + 296, + 565 + ], + "type": "text", + "content": "LiDAR odometry is a critical module in autonomous driving systems, responsible for accurate localization by estimating the relative pose transformation between consecutive point cloud frames. However, existing studies frequently encounter challenges with unreliable pose estimation, due to the lack of in-depth understanding of scenario and the presence of noise interference. To address this challenge, we propose DiffLO, a semantic-aware LiDAR odometry network with diffusion-based refinement. To mitigate the impact of challenging cases such as dynamic, repetitive patterns, and low textures, we introduce a semantic distillation method that integrates semantic information into the odometry task. This allows the network to gain a semantic understanding of the scene, enabling it to focus more on the objects that are beneficial for pose estimation. Additionally, to enhance the robustness, we propose a diffusion-based refinement method. This method uses pose-related features as conditional constraints for generative diversity, iteratively refining the pose estimation to achieve greater accuracy. 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Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 610, + 295, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 610, + 295, + 682 + ], + "spans": [ + { + "bbox": [ + 55, + 610, + 295, + 682 + ], + "type": "text", + "content": "LiDAR odometry (LO) is a well-studied problem in computer vision with numerous applications in Simultaneous Localization and Mapping (SLAM) [58], autonomous driving [54], and robotics [45]. The primary objective is to estimate the relative transformation between two frames based on the source and target point clouds." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 317, + 227, + 421, + 401 + ], + "blocks": [ + { + "bbox": [ + 317, + 227, + 421, + 401 + ], + "lines": [ + { + "bbox": [ + 317, + 227, + 421, + 401 + ], + "spans": [ + { + "bbox": [ + 317, + 227, + 421, + 401 + ], + "type": "image", + "image_path": "b42ddfbecd180b16ae9886bd3dc11dc223108334a0e043043b4005bf5c18c5b6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 407, + 555, + 473 + ], + "lines": [ + { + "bbox": [ + 313, + 407, + 555, + 473 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 555, + 473 + ], + "type": "text", + "content": "Figure 1. (a) Predicts a coarse initial pose and applies iterative MLP-based refinement to refine the initial estimate. (b) Predicts a coarse initial pose and applies iterative Diffusion-based refinement, incorporating knowledge distillation to enable semantic understanding. Here, " + }, + { + "bbox": [ + 313, + 407, + 555, + 473 + ], + "type": "inline_equation", + "content": "\\hat{T}_k" + }, + { + "bbox": [ + 313, + 407, + 555, + 473 + ], + "type": "text", + "content": " represents the noisy pose of the " + }, + { + "bbox": [ + 313, + 407, + 555, + 473 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 313, + 407, + 555, + 473 + ], + "type": "text", + "content": " denoising step." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 422, + 227, + 553, + 402 + ], + "blocks": [ + { + "bbox": [ + 422, + 227, + 553, + 402 + ], + "lines": [ + { + "bbox": [ + 422, + 227, + 553, + 402 + ], + "spans": [ + { + "bbox": [ + 422, + 227, + 553, + 402 + ], + "type": "image", + "image_path": "0caa6faa8b4c9520049822435d36a373de813a2409a982cf249276c0de7621b1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 486, + 555, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 486, + 555, + 593 + ], + "spans": [ + { + "bbox": [ + 312, + 486, + 555, + 593 + ], + "type": "text", + "content": "Most classic geometry-based methods, such as Iterative Closest Point (ICP) [4], its variants [31] and others [35], work by iteratively minimizing the distance between corresponding points in two point clouds to achieve accurate alignment. However, they often struggle in sparse point cloud environments, complex dynamic scenes, or when the quality of the point cloud degrades [13, 27, 42]. This limitation arises due to their reliance on precise geometric correspondences." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 594, + 556, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 594, + 556, + 677 + ], + "spans": [ + { + "bbox": [ + 312, + 594, + 556, + 677 + ], + "type": "text", + "content": "Deep learning-based methods have garnered significant attention in recent years. These methods learn feature representations from large-scale data to infer relative transformation between frames in an end-to-end manner, providing better scalability and the potential for multi-task learning. However, the accuracy of deep learning methods still lags behind traditional odometry techniques." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 714 + ], + "type": "text", + "content": "We identify the following challenges faced by Deep Learning-based odometry methods: (1) To mitigate the effects of challenging cases such as dynamic objects and oc" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 182, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 182, + 703 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 182, + 703 + ], + "type": "text", + "content": "*These authors contributed equally." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 146, + 712 + ], + "type": "text", + "content": "† Corresponding Author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17050" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 228 + ], + "type": "text", + "content": "clusions, LO-Net [21] introduces a mask prediction network learning the compensation for dynamic objects to remove dynamic objects. Methods such as PWCLO-Net [42], TransLO [23], and EfficientLO [44] introduce a hierarchical embedding mask and apply pose feature weighting to filter dynamic object. However, these approach lacks a comprehensive understanding of object structures, leading to inaccuracies and resulting in cumulative errors; (2) Furthermore, these methods [18, 23, 24, 26, 42, 44] are deterministic prediction tasks, which limits their ability to adapt to newly emerging changes or complexities in the environment. Additionally, they can not provide information about prediction uncertainties." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 229, + 294, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 229, + 294, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 229, + 294, + 396 + ], + "type": "text", + "content": "Semantic segmentation network contains rich geometric information and intricate details about the scene. This insight motivates us to integrate semantic information into the odometry network, thereby enhancing its ability to filter out dynamic objects and manage occlusions effectively. To achieve this, as shown in Fig. 1, we propose a knowledge distillation approach that transfers semantic knowledge from a segmentation model to the odometry network. After training, the knowledge distillation component and segmentation model are dropped to avoid extra computation or network parameter. By leveraging the contextual knowledge provided by semantic segmentation, our approach aims to improve the overall accuracy and robustness of odometry in complex environments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 399, + 295, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 399, + 295, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 399, + 295, + 578 + ], + "type": "text", + "content": "Diffusion models [11] are characterized by their robustness, and have achieved significant success across various tasks [8, 15, 22, 25]. These strengths have inspired us to explore their potential application to the LiDAR odometry task. In this paper, we propose reformulating the odometry task as a diffusion process. As shown in Fig. 1, we transition from a traditional MLP-based refinement approach to a diffusion-based refinement, shifting the task from a deterministic prediction framework to a probabilistic generative model. Specifically, Our approach consists of a forward process that progressively adds noise to the residual pose of the ground truth, followed by a reverse denoising process to refine the noisy pose estimate. We utilize coarse pose embedding, cost volume, semantic feature and geometry embedding as conditions to restrict generation diversity." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 580, + 251, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 580, + 251, + 591 + ], + "spans": [ + { + "bbox": [ + 67, + 580, + 251, + 591 + ], + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 594, + 293, + 710 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 594, + 293, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 293, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 293, + 639 + ], + "type": "text", + "content": "- To enhance the network's ability to focus on objects critical for pose estimation in the scene, we incorporate semantic awareness into odometry by distilling knowledge from a semantic segmentation model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 642, + 293, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 293, + 710 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 293, + 710 + ], + "type": "text", + "content": "- We propose a novel diffusion-based refinement pipeline and design strong conditional guidance by combining semantic embedding, coarse pose embeddings, geometry embedding and cross-frame cost volume to control generation diversity. To the best of our knowledge, this is the first work to leverage diffusion probabilistic model in the" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 323, + 72, + 416, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 72, + 416, + 83 + ], + "spans": [ + { + "bbox": [ + 323, + 72, + 416, + 83 + ], + "type": "text", + "content": "LiDAR odometry task." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 84, + 553, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 84, + 553, + 132 + ], + "spans": [ + { + "bbox": [ + 314, + 84, + 553, + 132 + ], + "type": "text", + "content": "- Extensive experiments on the KITTI odometry dataset [7] demonstrate that our method outperforms all existing learning-based odometry methods. On most sequences, our performance even surpasses A-LOAM with mapping." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 155, + 394, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 155, + 394, + 167 + ], + "spans": [ + { + "bbox": [ + 314, + 155, + 394, + 167 + ], + "type": "text", + "content": "2. Relate Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 178, + 447, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 178, + 447, + 190 + ], + "spans": [ + { + "bbox": [ + 314, + 178, + 447, + 190 + ], + "type": "text", + "content": "2.1. Deep LiDAR Odometry" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 201, + 553, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 201, + 553, + 427 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 553, + 427 + ], + "type": "text", + "content": "The field of visual depth odometry has advanced rapidly. However, research on LiDAR-based depth odometry remains challenging due to the inherent irregularity and complexity of point clouds. LO-Net [21] proposed an end-to-end deep odometry network that enhances robustness by learning the compensation for dynamic objects through a mask prediction network. PWCLO [42] first introduces a coarse-to-fine structure to LiDAR odometry, implementing a hierarchical refinement approach for estimated poses. LodoNet [52] projects 3D point clouds onto 2D spherical depth images to extract and match keypoints for odometry localization. EfficientLO [44] introduces a projection-aware representation of 3D point clouds, facilitating efficient learning for large-scale datasets. TransLO [23] develops a cross-frame transformer module that associates consecutive frames, thereby regressing relative pose estimations. DELO [1] innovatively employs partial optimal transportation of LiDAR feature descriptors to achieve robust localization estimation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 448, + 509, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 448, + 509, + 460 + ], + "spans": [ + { + "bbox": [ + 314, + 448, + 509, + 460 + ], + "type": "text", + "content": "2.2. LiDAR-based semantic segmentation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 470, + 553, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 470, + 553, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 470, + 553, + 661 + ], + "type": "text", + "content": "LiDAR-based semantic segmentation aims to assign a semantic label to each point in the input LiDAR scan. These methods can generally be categorized into several approaches: point-based [14, 32, 33, 39], voxel-based [9, 57], projection-based [17, 29, 46], and hybrid methods that combine these techniques [37, 49]. These approaches consistently expand the receptive field by integrating fine-grained point features with coarse-grained contextual information, which enhances the network's ability to understand the scene structure and the unique characteristics of each point. Semantic information has also proven to be highly valuable in traditional non-deep learning methods, such as [3, 5, 19, 20, 56]. By leveraging semantic labels, these systems can enhance feature matching and improve robustness against challenging conditions like dynamic objects and occlusions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 666, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 553, + 713 + ], + "type": "text", + "content": "Inspired by these traditional methods, we explore integrating semantics into learning-based LiDAR odometry to address the challenges posed by dynamic objects, repetitive patterns, and low-texture environments." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "17051" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 170, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 170, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 170, + 83 + ], + "type": "text", + "content": "2.3. 3D Diffusion Model" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 90, + 296, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 90, + 296, + 353 + ], + "spans": [ + { + "bbox": [ + 55, + 90, + 296, + 353 + ], + "type": "text", + "content": "Diffusion models have garnered significant attention and research in a variety of 3D point cloud processing tasks. For instance, Luo et al. [28] introduced a probabilistic model for point cloud generation, transforming the point cloud noise distribution into the desired point cloud shape distribution. Zhou et al. [55] combined a denoising diffusion model with a mixed point-voxel representation of 3D shapes for unconditional shape generation and conditional multimodal shape completion. Jiang et al. [15] proposed a point cloud registration framework based on an SE(3) diffusion model, framing the 3D registration task as a denoising diffusion process that iteratively refines the pose of the source point cloud to achieve precise alignment with the target point cloud. Difflow3D [25] presented an uncertainty-aware scene flow estimation network leveraging a diffusion probabilistic model, where iterative diffusion modules refine initial estimates to enhance the robustness of scene flow estimation. DiffLoc [22] formulates LiDAR localization as a conditional generation of poses, employing a diffusion model conditioned on geometric robust features and incorporating an iterative denoising process into APR to achieve accurate LiDAR localization." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 354, + 296, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 296, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 296, + 403 + ], + "type": "text", + "content": "Inspired by the successful applications of diffusion models in tasks such as registration, scene flow estimation, and localization, we investigate the integration of diffusion models to improve the accuracy of LiDAR odometry." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 414, + 111, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 414, + 111, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 414, + 111, + 426 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 434, + 296, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 296, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 296, + 602 + ], + "type": "text", + "content": "Given two consecutive point cloud frames " + }, + { + "bbox": [ + 55, + 434, + 296, + 602 + ], + "type": "inline_equation", + "content": "PC_1 \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 55, + 434, + 296, + 602 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 434, + 296, + 602 + ], + "type": "inline_equation", + "content": "PC_2 \\in \\mathbb{R}^{M \\times 3}" + }, + { + "bbox": [ + 55, + 434, + 296, + 602 + ], + "type": "text", + "content": ", the goal of the LiDAR odometry task is to estimate the relative transformation between the two consecutive frames of point clouds. To solve this task, we propose DiffLO, a semantic-aware odometry network with diffusion-based refinement. DiffLO first hierarchically extracts point features (Sec. 3.1). Subsequently, we introduce a Semantic Perception Module (Sec. 3.2), which enables the odometry network to gain semantic understanding. Then, the initial pose is generated (Sec. 3.3) in the coarsest layer. We then utilize diffusion model with condition signals to refine the initial pose by predicting pose residuals from coarse to fine (Sec. 3.4). Lastly, the loss function will be presented in (Sec. 3.5)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 610, + 222, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 610, + 222, + 623 + ], + "spans": [ + { + "bbox": [ + 55, + 610, + 222, + 623 + ], + "type": "text", + "content": "3.1. Multi-scale Feature Extraction" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": "We utilize PointConv [47] for hierarchical feature extraction. At each level " + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 629, + 296, + 715 + ], + "type": "text", + "content": ", dense input points and their features are first subsampled using furthest point sampling to create a sparse point set. Then, for each subsampled sparse point, k-nearest neighbor groups local dense points to form a local region for feature extraction. Next, a PointConv [47] layer aggregates features from the grouped local points, produc" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 96 + ], + "type": "text", + "content": "ing a local feature for each sparse point. This process results in an L-level pyramid of point features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 102, + 471, + 115 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 102, + 471, + 115 + ], + "spans": [ + { + "bbox": [ + 313, + 102, + 471, + 115 + ], + "type": "text", + "content": "3.2. Semantic Perception Module" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 121, + 554, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 121, + 554, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 554, + 228 + ], + "type": "text", + "content": "To guide the network's attention towards objects in the scene that are beneficial for pose estimation, such as buildings and pole-like structures. We introduce Semantic Perception Module (SPM). SPM consists of three components: Semantic Module, Semantic Segmentation Modle and Knowledge Distillation. We introduce a semantic segmentation model as the teacher network. A sub-network (the Semantic Module) within the odometry model is designated as the student model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 229, + 554, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 554, + 288 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 554, + 288 + ], + "type": "text", + "content": "During the training stage, three modules collaborate to transfer semantic knowledge into the odometry model. Firstly, the Semantic Module takes the point cloud features " + }, + { + "bbox": [ + 313, + 229, + 554, + 288 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 313, + 229, + 554, + 288 + ], + "type": "text", + "content": " in coarse layer as its input, the output can be expressed as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 295, + 555, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 295, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 329, + 295, + 555, + 308 + ], + "type": "interline_equation", + "content": "F _ {s t u} = M L P (F) + M L P (F) \\otimes \\sigma (M L P (F)), \\tag {1}", + "image_path": "311cca8b338bd634dc26ae8f497367fa918e6431f1e8ca189bb7a6a7632d80eb.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 315, + 554, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 554, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 554, + 339 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 315, + 554, + 339 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 313, + 315, + 554, + 339 + ], + "type": "text", + "content": " indicates element-wise multiplication. " + }, + { + "bbox": [ + 313, + 315, + 554, + 339 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 313, + 315, + 554, + 339 + ], + "type": "text", + "content": " denotes the softmax operation along the feature dimension." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "text", + "content": "Secondly, a pretrained 3D semantic segmentation model [16], with its network parameters frozen, is utilized here. We extract the per-point features from the final layer, denoted as " + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "inline_equation", + "content": "F_{seg} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "text", + "content": ". These features are subsequently downsampled to " + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "inline_equation", + "content": "F_{tea} \\in \\mathbb{R}^{N' \\times d}" + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "text", + "content": " to ensure compatibility in dimension with " + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "inline_equation", + "content": "F_{stu}" + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "text", + "content": ". And we adjust the output dimension of the semantic regressor branch, ensuring that " + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "inline_equation", + "content": "F_{tea}" + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "inline_equation", + "content": "F_{stu}" + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "text", + "content": " share the same feature dimension " + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 339, + 554, + 436 + ], + "type": "text", + "content": " for each point." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 436, + 554, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 436, + 554, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 436, + 554, + 483 + ], + "type": "text", + "content": "Then, we utilize knowledge distillation [10] to transfer semantic knowledge from the segmentation module to the odometry model. This is achieved by optimizing the following distillation loss:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 389, + 490, + 553, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 490, + 553, + 504 + ], + "spans": [ + { + "bbox": [ + 389, + 490, + 553, + 504 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {k d} = \\delta \\left(F _ {s t u}, F _ {t e a}\\right), \\tag {2}", + "image_path": "535381301820dcbdf9f4748d0570c532d2f332f20dd030ef830271f0b07c3f2b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "type": "inline_equation", + "content": "\\delta (\\cdot ,\\cdot)" + }, + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "type": "text", + "content": " measures the difference between the feature representations from the teacher network " + }, + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "type": "inline_equation", + "content": "F_{tea}" + }, + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "type": "text", + "content": " and the student network " + }, + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "type": "inline_equation", + "content": "F_{stu}" + }, + { + "bbox": [ + 313, + 510, + 554, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 546, + 554, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 554, + 594 + ], + "type": "text", + "content": "Finally, the semantic feature " + }, + { + "bbox": [ + 313, + 546, + 554, + 594 + ], + "type": "inline_equation", + "content": "F_{stu}" + }, + { + "bbox": [ + 313, + 546, + 554, + 594 + ], + "type": "text", + "content": " is propagated to the following level for a denser optimization and simultaneously serves as a condition signal for diffusion-based refinement in Sec. 3.4, via an upsampling layer [6, 48]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": "During the inference stage, only the Semantic Module is retained to avoid additional computational overhead. The output " + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "inline_equation", + "content": "F_{stu}" + }, + { + "bbox": [ + 313, + 594, + 554, + 642 + ], + "type": "text", + "content": " from the Semantic Module is still propagated to subsequent layers, serving as a conditional signal." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 554, + 713 + ], + "type": "text", + "content": "By embedding semantic understanding into the odometry process, the model is better able to focus on objects in the scene that are beneficial for pose estimation. Meanwhile, the close integration of knowledge distillation improves both the efficiency and effectiveness of the overall system." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17052" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 72, + 550, + 345 + ], + "blocks": [ + { + "bbox": [ + 60, + 72, + 550, + 345 + ], + "lines": [ + { + "bbox": [ + 60, + 72, + 550, + 345 + ], + "spans": [ + { + "bbox": [ + 60, + 72, + 550, + 345 + ], + "type": "image", + "image_path": "60b3ff2613959917e5c5a681698c1d935bdb88a4f5e6a3839e41463c512359a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 349, + 555, + 416 + ], + "lines": [ + { + "bbox": [ + 55, + 349, + 555, + 416 + ], + "spans": [ + { + "bbox": [ + 55, + 349, + 555, + 416 + ], + "type": "text", + "content": "Figure 2. The overall structure of DiffLO. The proposed pipeline comprises three core components: Pose Initialization, Semantic Perception Module, and Diffusion-based Pose Refinement. First, hierarchical point features are extracted from the input point cloud. Then, we enable the network to acquire semantic understanding through a knowledge distillation approach. Following this, an initial coarse pose estimate is generated. Finally, the Diffusion-based Pose Refinement module applies iterative refinement layers, conditioned on various signals, to improve the initial pose estimate, ultimately producing a more accurate and robust final pose. To optimize inference efficiency, the semantic segmentation component is discarded after the training phase." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 427, + 229, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 427, + 229, + 439 + ], + "spans": [ + { + "bbox": [ + 55, + 427, + 229, + 439 + ], + "type": "text", + "content": "3.3. Semantic-Aware Pose Estimator" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 445, + 295, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 445, + 295, + 483 + ], + "spans": [ + { + "bbox": [ + 55, + 445, + 295, + 483 + ], + "type": "text", + "content": "We enhance the pose estimation method from the PWCLO-Net [42] by incorporating semantic features into the pose estimation process. Taking the " + }, + { + "bbox": [ + 55, + 445, + 295, + 483 + ], + "type": "inline_equation", + "content": "l^{th}" + }, + { + "bbox": [ + 55, + 445, + 295, + 483 + ], + "type": "text", + "content": " layer as example." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 92, + 490, + 295, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 490, + 295, + 506 + ], + "spans": [ + { + "bbox": [ + 92, + 490, + 295, + 506 + ], + "type": "interline_equation", + "content": "E ^ {l} = M L P \\left(F ^ {l} \\oplus F _ {s t u} ^ {l} \\oplus U E ^ {l} \\oplus C E ^ {l}\\right), \\tag {3}", + "image_path": "c0789d8e03bf12f6dc8b2151936bb1c506032e475ca8687add677822e3f6c05c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 523, + 295, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 523, + 295, + 539 + ], + "spans": [ + { + "bbox": [ + 86, + 523, + 295, + 539 + ], + "type": "interline_equation", + "content": "M ^ {l} = \\sigma (M L P (F ^ {l} \\oplus F _ {s t u} ^ {l} \\oplus U M ^ {l} \\oplus E ^ {l})), \\tag {4}", + "image_path": "64985babec23370b8705c61fa66486251820b3c06c0df5f2a6c0ddae2170b36f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " is the concatenation and " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " denotes the softmax operation. " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "F^l" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " is the point cloud feature from " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " layer, " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "CE^l" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " is generated by cross-frame correlation [6, 43]. " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "F_{stu}^{l}" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "UE^{l}" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "UM^{l}" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " are the results of upsampling the semantic feature " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "F_{stu}^{l + 1}" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": ", the embedding feature " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "E^{l + 1}" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " and the embedding mask " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "M^{l + 1}" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": " respectively. The embedding features " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "E = \\{e_i|e_i\\in \\mathbb{R}^C\\}_{i = 1}^n" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": ", the embedding mask " + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "inline_equation", + "content": "M = \\{m_i|m_i\\in \\mathbb{R}^C\\}_{i = 1}^n" + }, + { + "bbox": [ + 55, + 542, + 295, + 639 + ], + "type": "text", + "content": ". The pose is then generated by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 119, + 646, + 295, + 675 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 646, + 295, + 675 + ], + "spans": [ + { + "bbox": [ + 119, + 646, + 295, + 675 + ], + "type": "interline_equation", + "content": "q = \\frac {F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right)}{\\left| F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right) \\right|} \\tag {5}", + "image_path": "36c51a29235a282596b4e0d6ecd31a1508bd59a3d1d31cc2e17ae9a5f5ba466d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 129, + 685, + 295, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 685, + 295, + 716 + ], + "spans": [ + { + "bbox": [ + 129, + 685, + 295, + 716 + ], + "type": "interline_equation", + "content": "t = F C \\left(\\sum_ {i = 1} ^ {n} e _ {i} \\odot m _ {i}\\right) \\tag {6}", + "image_path": "a383ced2c8cbe40e21490d1b4e209e509734d727243072ba61129c0e30765485.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "inline_equation", + "content": "FC(\\cdot)" + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "text", + "content": " denotes the fully connected layer and " + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "text", + "content": " represents dot product. Following [42], the embedding features " + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "text", + "content": ", embedding mask " + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 427, + 555, + 475 + ], + "type": "text", + "content": " and semantic features are also propagated to denser layers for optimization." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 475, + 555, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 555, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 555, + 548 + ], + "type": "text", + "content": "The coarse-level point cloud is sparse and has low resolution, which can lead to incorrect matches and inaccurate initial pose estimates. Inspired by recent success and denoising properties of the diffusion model [11], we design a novel diffusion-based pose refinement module to refine the coarse pose progressively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 555, + 491, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 491, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 491, + 567 + ], + "type": "text", + "content": "3.4. Diffusion-based Pose Refinement" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 574, + 554, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 554, + 610 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 554, + 610 + ], + "type": "text", + "content": "In this section, we formulate the coarse pose residual as the diffusion latent variable, and residual pose are generated from the reverse process of diffusion model iteratively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 611, + 554, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 611, + 554, + 669 + ], + "spans": [ + { + "bbox": [ + 313, + 611, + 554, + 669 + ], + "type": "text", + "content": "During the training stage, the diffusion model is trained to learn the underlying distribution of residual poses by recovering the ground truth residual pose from its corrupted version. The ground truth residual pose is calculated as follow:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 397, + 670, + 553, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 670, + 553, + 685 + ], + "spans": [ + { + "bbox": [ + 397, + 670, + 553, + 685 + ], + "type": "interline_equation", + "content": "T _ {0} = T _ {g t} \\cdot T _ {p r e d} ^ {- 1}, \\tag {7}", + "image_path": "6003ee42e2b72470db964a28c8984271b1d938252e2b1fca8ec3ee90d11ce57f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "inline_equation", + "content": "T_{0}" + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": " is the ground truth residual pose, " + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "inline_equation", + "content": "T_{gt}" + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": " is the ground truth pose and " + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "inline_equation", + "content": "T_{pred}" + }, + { + "bbox": [ + 313, + 689, + 555, + 715 + ], + "type": "text", + "content": " is the coarse pose generated by the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17053" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 189, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 189, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 189, + 83 + ], + "type": "text", + "content": "previous layer or the initial pose." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "text", + "content": "Specifically, in each training iteration, a random diffusion step, denoted as " + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "inline_equation", + "content": "k \\in \\{1, 2, \\dots, K\\}" + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "text", + "content": ", is chosen. With a predefined variance schedule " + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "inline_equation", + "content": "\\beta_1, \\ldots, \\beta_k" + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "text", + "content": ", we introduce noises to " + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "inline_equation", + "content": "T_0" + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "text", + "content": ", resulting in the noisy residual pose " + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "inline_equation", + "content": "T_k" + }, + { + "bbox": [ + 55, + 84, + 296, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 96, + 136, + 294, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 136, + 294, + 150 + ], + "spans": [ + { + "bbox": [ + 96, + 136, + 294, + 150 + ], + "type": "interline_equation", + "content": "q \\left(T _ {k} \\mid T _ {0}\\right) = \\mathcal {N} \\left(T _ {k}; \\sqrt {\\bar {\\alpha} _ {k}} T _ {0}, (1 - \\bar {\\alpha} _ {k}) \\mathrm {I}\\right) \\tag {8}", + "image_path": "6528e66c9385290140d5a2073d9ca4bfb3d5a6535dbd9d5012f14d94eddd1350.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 152, + 294, + 167 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 152, + 294, + 167 + ], + "spans": [ + { + "bbox": [ + 94, + 152, + 294, + 167 + ], + "type": "interline_equation", + "content": "T _ {k} = \\sqrt {\\bar {\\alpha} _ {k}} T _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {k}} \\epsilon , \\epsilon \\sim \\mathcal {N} (0, I) \\tag {9}", + "image_path": "17ee66e89cde1f3e469dddb76f5b25d7291dc3583fb7368d1bf1f8001d65d78c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "spans": [ + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "text", + "content": "denoting " + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "inline_equation", + "content": "\\alpha_{k} = 1 - \\beta_{k}" + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}_k = \\Pi_{i = 1}^k\\alpha_i" + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "text", + "content": " . Eventually, the ground truth residual pose " + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "inline_equation", + "content": "T_{0}" + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "text", + "content": " is turned into Gaussian noise when " + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 55, + 171, + 295, + 207 + ], + "type": "text", + "content": " is large enough." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": "During the inference stage, the denoise model approximates the distribution " + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "inline_equation", + "content": "p(T_0|C)" + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": " as the reversed diffusion process of gradually cleaning " + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": ". Instead of predicting " + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": " as formulated by [12], we follow [34, 38] and predict the signal itself. Also, we constrain the generation diversity and control the reversed diffusion process by the condition information " + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": ". In this way, we utilize a denoising network to predict the residual pose " + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "inline_equation", + "content": "\\hat{T_0}" + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": " from noisy input " + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": ", time step " + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "inline_equation", + "content": "t = k" + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": ", and condition " + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 209, + 296, + 315 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 132, + 320, + 294, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 320, + 294, + 334 + ], + "spans": [ + { + "bbox": [ + 132, + 320, + 294, + 334 + ], + "type": "interline_equation", + "content": "\\hat {T} _ {0} = \\mathcal {M} _ {\\theta} \\left(T _ {k}, t, C\\right), \\tag {10}", + "image_path": "f713f262d50b646e850c13d96bbc6b350ce47539654d30e146a437a1de0d9b95.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 338, + 296, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 338, + 296, + 363 + ], + "spans": [ + { + "bbox": [ + 55, + 338, + 296, + 363 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 338, + 296, + 363 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\theta}(\\cdot ,\\cdot ,\\cdot)" + }, + { + "bbox": [ + 55, + 338, + 296, + 363 + ], + "type": "text", + "content": " is the denoising network. The training objective is to minimize the following loss:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 367, + 294, + 381 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 367, + 294, + 381 + ], + "spans": [ + { + "bbox": [ + 67, + 367, + 294, + 381 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e s} = \\mathbb {E} _ {T _ {0}, t}, \\left[ \\| t _ {g t} - t _ {p r e d} \\| _ {2} + \\| q _ {g t} - q _ {p r e d} \\| _ {2} \\right], \\tag {11}", + "image_path": "ad5e6973b4366407177005645e4521634fcb56f35bc6cded9dd5d27a2b866187.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "inline_equation", + "content": "t_{gt}" + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "inline_equation", + "content": "q_{gt}" + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "content": " are the translation vector and quaternion from " + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "inline_equation", + "content": "T_0" + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "inline_equation", + "content": "t_{pred}" + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "inline_equation", + "content": "q_{pred}" + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "content": " are their corresponding predicted values from " + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "inline_equation", + "content": "\\hat{T}_0" + }, + { + "bbox": [ + 55, + 385, + 295, + 421 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "text", + "content": "Design of Condition Signal. Inspired by [42, 43], we introduce the geometric feature " + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "inline_equation", + "content": "GE" + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "text", + "content": " extracted from " + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "inline_equation", + "content": "PC_{1}" + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "text", + "content": " along with a cost volume embedding " + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "text", + "content": " constructed using cross-frame correlation [6], with the corresponding hierarchical point cloud features as input, and residual pose embeddings " + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "inline_equation", + "content": "PE = T_{k} \\cdot PC_{1} - PC_{1}" + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "text", + "content": " and the semantic feature " + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "inline_equation", + "content": "F_{stu}" + }, + { + "bbox": [ + 55, + 422, + 296, + 518 + ], + "type": "text", + "content": " as conditional signals to constrain generation diversity. The condition signal is as follow:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 126, + 523, + 294, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 523, + 294, + 536 + ], + "spans": [ + { + "bbox": [ + 126, + 523, + 294, + 536 + ], + "type": "interline_equation", + "content": "C = G E \\oplus C E \\oplus P E, \\tag {12}", + "image_path": "fb802d7593a6d5a7d0e736269158c43bee2b1379375ac6afc59705fa1728e5a6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 540, + 217, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 540, + 217, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 540, + 217, + 552 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 540, + 217, + 552 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 55, + 540, + 217, + 552 + ], + "type": "text", + "content": " is the concatenation operation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "spans": [ + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": "We employ the augmented version [6] with Gate Recurrent Unit (GRU) to process the condition signal " + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": ". This approach allows for the extraction of essential features from " + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": " to generate the augmented condition signal " + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "inline_equation", + "content": "C'" + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": ". Subsequently, the semantic-aware pose estimator in Sec. 3.3 is introduced to generate the residual pose " + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "inline_equation", + "content": "\\hat{T}_0" + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "inline_equation", + "content": "C'" + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": " are treated as the cost volume embedding " + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": " in Eq. (3). Taking the " + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "inline_equation", + "content": "l^{th}" + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": " refinement layer as example, the refined pose " + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "inline_equation", + "content": "T_{pred}^l" + }, + { + "bbox": [ + 55, + 552, + 296, + 662 + ], + "type": "text", + "content": " is calculated as follow:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 132, + 666, + 294, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 666, + 294, + 685 + ], + "spans": [ + { + "bbox": [ + 132, + 666, + 294, + 685 + ], + "type": "interline_equation", + "content": "T _ {p r e d} ^ {l} = \\hat {T} _ {0} ^ {l} \\cdot T _ {p r e d} ^ {l + 1}, \\tag {13}", + "image_path": "930c60f5be33aa2cd80ebf36bf9b690141b5b32c23121aa127a315ba75d18a12.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "the refined pose " + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "inline_equation", + "content": "T_{pred}^{l}" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": " will be the input to " + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "inline_equation", + "content": "l - 1^{th}" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": " refinement layer." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 314, + 72, + 402, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 72, + 402, + 84 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 402, + 84 + ], + "type": "text", + "content": "3.5. Training Loss" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 90, + 554, + 161 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 90, + 554, + 161 + ], + "spans": [ + { + "bbox": [ + 313, + 90, + 554, + 161 + ], + "type": "text", + "content": "The network supervises the pose outputs from each level, along with the residual poses predicted by the diffusion model and the semantic features derived from the Semantic Module. Drawing from previous deep odometry research [21, 42], the training loss function for the odometry at the l-th level is as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 364, + 169, + 553, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 169, + 553, + 214 + ], + "spans": [ + { + "bbox": [ + 364, + 169, + 553, + 214 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} ^ {l} = \\left\\| t _ {g t} - t ^ {l} \\right\\| \\exp (- w _ {t}) + w _ {t} \\\\ + \\left\\| q _ {g t} - \\frac {q ^ {l}}{\\| q ^ {l} \\|} \\right\\| _ {2} \\exp (- w _ {q}) + w _ {q}, \\tag {14} \\\\ \\end{array}", + "image_path": "55b9572ff58b1b7ca0738a80be85eae7e5971d9962a0e9f02d1dd06d34ef63e0.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\| _2" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "\\ell 1" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": "-norm and the " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "\\ell 2" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": "-norm respectively. " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "t_{gt}" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "q_{gt}" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " are the ground-truth translation vector and quaternion respectively. " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "t^l" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "q^{l}" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " are predicted pose from each level. " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "w_{q}" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " are two learnable parameters, which are introduced to eliminate the differences in scale and units between the translation vector and the quaternion. Then, a multi-scale supervised approach is adopted. The total training loss function " + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 313, + 220, + 554, + 316 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 364, + 324, + 553, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 324, + 553, + 357 + ], + "spans": [ + { + "bbox": [ + 364, + 324, + 553, + 357 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {k d} + \\sum_ {l = 0} ^ {K} \\lambda^ {l} \\times \\left(\\mathcal {L} ^ {l} + \\mathcal {L} _ {r e s} ^ {l}\\right), \\tag {15}", + "image_path": "0c6d680a93ab69ff0fde2625ab0201f3dbe0c20e86790f7c7385f47aea34a7fd.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 364, + 554, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 364, + 554, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 364, + 554, + 388 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 364, + 554, + 388 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 364, + 554, + 388 + ], + "type": "text", + "content": " is the total number of warp-refinement levels and " + }, + { + "bbox": [ + 313, + 364, + 554, + 388 + ], + "type": "inline_equation", + "content": "\\lambda^l" + }, + { + "bbox": [ + 313, + 364, + 554, + 388 + ], + "type": "text", + "content": " denotes the weight of the l-th level." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 399, + 390, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 390, + 412 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 390, + 412 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 418, + 458, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 418, + 458, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 418, + 458, + 430 + ], + "type": "text", + "content": "4.1. KITTI Odometry Dataset" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 437, + 555, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 555, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 555, + 568 + ], + "type": "text", + "content": "The KITTI odometry dataset [7] is a widely used standard dataset for evaluating visual odometry and SLAM algorithms. It includes multiple driving scenarios, encompassing urban, rural, and highway environments, with variations in weather and lighting conditions. The dataset consists of 22 sequences of LiDAR point clouds and their corresponding stereo images. In our experiments, we utilize the Velodyne LiDAR point clouds provided in the dataset. Since the ground truth poses (trajectories) are only available for sequences 00 to 10, we use these sequences for both training and testing." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 575, + 421, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 575, + 421, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 575, + 421, + 588 + ], + "type": "text", + "content": "4.2. Implement details" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": "In the training and evaluation process, N points are randomly sampled from the point clouds of two frames separately. It is not necessary for the original input point clouds to have the same number of points. In the proposed network, N is set to 8192. All training and evaluation experiments are conducted on a single NVIDIA RTX 3090 GPU. The Adam optimizer is employed with parameters " + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\beta 1 = 0.9" + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\beta 2 = 0.999" + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "text", + "content": ". The initial learning rate is set to 0.001 and is reduced by a factor of 0.8 every 8 epochs until it reaches 0.000001. The initial values of the trainable parameters " + }, + { + "bbox": [ + 313, + 594, + 555, + 714 + ], + "type": "inline_equation", + "content": "w_{t}" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17054" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 553, + 182 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 182 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 182 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 182 + ], + "type": "table", + "html": "
    Method00010203040506\\( 07^{\\dagger} \\)\\( 08^{\\dagger} \\)\\( 09^{\\dagger} \\)\\( 10^{\\dagger} \\)Mean on 07-10
    \\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t _{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)\\( t_{rel} \\)\\( r_{rel} \\)
    ICP-po2po6.882.9911.212.588.213.3911.075.056.644.023.971.931.951.595.173.3510.044.936.932.898.914.747.7633.978
    ICP-po2pl3.801.7313.532.589.002.742.721.632.962.582.291.081.771.001.551.424.422.143.951.716.132.604.0131.968
    GICP [36]1.290.644.390.912.530.771.681.083.761.071.020.540.920.460.640.451.580.751.970.771.310.621.3750.648
    CLS [41]2.110.954.221.052.290.861.631.091.590.711.980.920.920.461.040.732.141.051.950.923.461.282.1480.995
    Full LOAM [50]0.780.531.430.550.920.550.860.650.710.500.570.380.650.390.630.501.120.440.770.480.790.570.8280.498
    Full A-LOAM0.760.311.970.504.531.450.930.490.620.390.480.250.610.280.430.261.060.320.730.311.020.400.8100.323
    LO-Net [21]1.470.721.360.471.520.711.030.660.510.651.040.690.710.501.700.892.120.771.370.581.800.931.7480.793
    PWCLO-Net [42]0.780.420.670.230.860.410.760.440.370.400.450.270.270.220.600.441.260.550.790.351.690.621.0850.490
    DELO [1]1.430.812.190.571.480.521.381.102.451.701.270.640.830.350.580.411.360.641.230.571.530.901.1750.630
    TransLO [23]0.850.381.160.450.880.341.000.710.340.180.630.410.730.310.550.431.290.500.950.461.180.610.9930.500
    EfficientLO [44]0.830.330.550.210.710.250.490.380.220.110.340.210.360.240.460.381.140.410.780.330.800.460.7950.395
    Ours0.600.270.360.150.710.260.570.400.300.170.330.220.280.170.370.271.120.440.680.280.660.320.7080.328
    ", + "image_path": "d9b5d4299f998573b595511d5da8975510d1235efdad75db255b826e35def077.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 65, + 245, + 287, + 299 + ], + "blocks": [ + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "lines": [ + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "text", + "content": "Table 1. The LiDAR odometry experiment results on KITTI odometry dataset [7]. " + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "inline_equation", + "content": "t_{rel}, r_{rel}" + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "text", + "content": " indicate the average translational RMSE (\\%) and rotational RMSE (" + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "inline_equation", + "content": "^\\circ /100\\mathrm{m}" + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "text", + "content": ") respectively on all possible subsequences in the length of 100, 200, ..., 800m. " + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "inline_equation", + "content": "^\\dagger" + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "text", + "content": " means the testing sequences. LOAM and A-LOAM is complete SLAM system, including back-end optimization. The best result for each sequence is bold, and the second best is underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 245, + 287, + 299 + ], + "lines": [ + { + "bbox": [ + 65, + 245, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 65, + 245, + 287, + 299 + ], + "type": "table", + "html": "
    Method07†08†Mean
    trelrreltrelrreltrelrrel
    LodoNet [53]1.861.642.040.971.9501.305
    Ours0.370.271.120.440.7450.355
    ", + "image_path": "673778385a6667a182e3863b53232dabc0da33324b64d4c01eb4fb7599240748.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 65, + 342, + 287, + 402 + ], + "blocks": [ + { + "bbox": [ + 55, + 306, + 295, + 331 + ], + "lines": [ + { + "bbox": [ + 55, + 306, + 295, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 306, + 295, + 331 + ], + "type": "text", + "content": "Table 2. Comparison with learning-based odometry LodoNet on KITTI 07-08 sequences." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 342, + 287, + 402 + ], + "lines": [ + { + "bbox": [ + 65, + 342, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 65, + 342, + 287, + 402 + ], + "type": "table", + "html": "
    Method09†10†Mean
    trelrreltrelrreltrelrrel
    Nubert et al. [30]1.540.681.780.691.660.685
    H-VLO [2]1.890.341.390.521.640.430
    Ours0.680.280.660.320.670.300
    ", + "image_path": "fbbcab177cddbab7b593a537abc6c9f1d8398350159212e0a407d0e7324c280e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 411, + 295, + 434 + ], + "lines": [ + { + "bbox": [ + 55, + 411, + 295, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 295, + 434 + ], + "type": "text", + "content": "Table 3. Comparison with learning-based odometry on KITTI 09-10 sequences." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "inline_equation", + "content": "w_{q}" + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "text", + "content": " are set to 0.0 and -2.5, respectively, as indicated in formula Eq. (14). For formula Eq. (15), the parameters are set as follows: " + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "inline_equation", + "content": "\\lambda_{3} = 1.6" + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 0.8" + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "inline_equation", + "content": "\\lambda_{1} = 0.4" + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "inline_equation", + "content": "\\lambda_{0} = 0.2" + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "inline_equation", + "content": "L = 4" + }, + { + "bbox": [ + 55, + 456, + 295, + 504 + ], + "type": "text", + "content": ". The batch size is 12." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 514, + 258, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 258, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 258, + 528 + ], + "type": "text", + "content": "4.3. Comparison with The State-of-the-Art" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 533, + 295, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 295, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 295, + 593 + ], + "type": "text", + "content": "We compare our network with the state-of-the-art on KITTI dataset, including both classic methods and learning-based ones. Since existing training and testing sequence settings are inconsistent in different methods, we test and evaluate our framework accordingly for a fair comparison." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 714 + ], + "type": "text", + "content": "00-06 as training sequences and 07-10 as testing sequences. Quantitative results are listed in Tab. 1. The traditional methods we compare include ICP-point2point (ICP-po2po), ICP-point2plane (ICP-po2pl), GICP [36], CLS [41], which rely on iterative point cloud alignment. LOAM [50], its enhanced version A-LOAM is also included. While LOAM and A-LOAM have been widely recognized for their robust performance on the KITTI odometry benchmark, our method achieves superior accuracy on most sequences. As shown in Tab. 1, our approach outperforms Full A-LOAM," + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 321, + 248, + 545, + 373 + ], + "blocks": [ + { + "bbox": [ + 321, + 248, + 545, + 373 + ], + "lines": [ + { + "bbox": [ + 321, + 248, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 321, + 248, + 545, + 373 + ], + "type": "image", + "image_path": "8a4c89b35dbf0b4fdc0c52f7037e2458ee6a359123689b9a43aa13bc44f2459e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 381, + 555, + 415 + ], + "lines": [ + { + "bbox": [ + 313, + 381, + 555, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 381, + 555, + 415 + ], + "type": "text", + "content": "Figure 3. 2D trajectories of A-LOAM, EfficientLO, and our proposed method on KITTI sequences 02 and 10 with ground truth. It can be observed that our method performs the best." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 425, + 555, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 425, + 555, + 508 + ], + "spans": [ + { + "bbox": [ + 313, + 425, + 555, + 508 + ], + "type": "text", + "content": "which has the mapping optimization. Additionally, the learning-based LiDAR odometry methods we compare include LO-Net [21], DELO [1], PWCLO-Net [42], TransLO [23], EfficientLO [44]. Compared to the current state-of-the-art method EfficientLO, our method DiffLO achieves an average improvement of " + }, + { + "bbox": [ + 313, + 425, + 555, + 508 + ], + "type": "inline_equation", + "content": "10.9\\%" + }, + { + "bbox": [ + 313, + 425, + 555, + 508 + ], + "type": "text", + "content": " in transition accuracy and " + }, + { + "bbox": [ + 313, + 425, + 555, + 508 + ], + "type": "inline_equation", + "content": "16.9\\%" + }, + { + "bbox": [ + 313, + 425, + 555, + 508 + ], + "type": "text", + "content": " in rotation accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 509, + 555, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 509, + 555, + 580 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 555, + 580 + ], + "type": "text", + "content": "00-06 and 09-10 as training sequences and 07-08 as testing sequences. We compare with a recent method LodoNet [52] in Tab. 2. Our method is trained on 00-06 sequences while LodoNet are trained on 00-06 and 09-10 sequences, even so, our method performs better than LodoNet on the test sequences." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 580, + 556, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 580, + 556, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 580, + 556, + 665 + ], + "type": "text", + "content": "00-08 as training sequences and 09-10 as testing sequences. We compare with recent method [2, 30]. Our method is trained on 00-06 sequences while others are trained on 00-08 sequences. As illustrated in Tab. 3, both our translation and rotation errors are smaller than theirs. Although our approach utilizes only LiDAR data, we achieve better results than the multi-modal method H-VLO." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 671, + 408, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 671, + 408, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 671, + 408, + 685 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "In order to analyze the effectiveness of each module, we remove or change components of our model to do the abla" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17055" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 70, + 529, + 227 + ], + "blocks": [ + { + "bbox": [ + 83, + 70, + 529, + 227 + ], + "lines": [ + { + "bbox": [ + 83, + 70, + 529, + 227 + ], + "spans": [ + { + "bbox": [ + 83, + 70, + 529, + 227 + ], + "type": "table", + "html": "
    Method07†08†09†10†Mean on 07-10
    trelrreltrelrreltrelrreltrelrreltrelrrel
    (a)Semanticw/o SPM0.520.461.190.530.530.180.930.420.7930.398
    Ours (full, with SPM)0.370.271.120.440.680.280.660.320.7080.328
    (b)Diffusionw/o diffusion4.833.826.773.055.292.227.093.975.9953.265
    with trans-based Mθ [40]0.390.341.360.550.730.291.070.480.8880.415
    with ptrans-based Mθ [51]0.450.281.190.450.540.220.720.410.7250.340
    Ours (GRU-based Mθ [6])0.370.271.120.440.680.280.660.320.7080.328
    (c)Conditionw/o cost volume0.450.351.200.490.700.281.090.950.8600.518
    w/o geometry feature0.400.271.180.470.610.240.960.460.7870.357
    w/o semantic feature0.470.311.330.560.750.230.640.480.7980.395
    w/o coarse pose embedding0.450.341.280.560.640.250.630.330.7500.370
    Ours (full, with all conditions)0.370.271.120.440.680.280.660.320.7080.328
    ", + "image_path": "4a90371f9695606143bdcd27711989c149485571f5821fcb50193cf6719d5885.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 60, + 234, + 549, + 247 + ], + "lines": [ + { + "bbox": [ + 60, + 234, + 549, + 247 + ], + "spans": [ + { + "bbox": [ + 60, + 234, + 549, + 247 + ], + "type": "text", + "content": "Table 4. The ablation study results of LiDAR odometry on KITTI odometry dataset[7]. The best performance of each sequence is bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 66, + 258, + 178, + 369 + ], + "blocks": [ + { + "bbox": [ + 66, + 258, + 178, + 369 + ], + "lines": [ + { + "bbox": [ + 66, + 258, + 178, + 369 + ], + "spans": [ + { + "bbox": [ + 66, + 258, + 178, + 369 + ], + "type": "image", + "image_path": "ee2fccead9c463552b7cce4ce32bef4309ee49771ea81805a948d3ab298c2b31.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 181, + 259, + 291, + 369 + ], + "blocks": [ + { + "bbox": [ + 181, + 259, + 291, + 369 + ], + "lines": [ + { + "bbox": [ + 181, + 259, + 291, + 369 + ], + "spans": [ + { + "bbox": [ + 181, + 259, + 291, + 369 + ], + "type": "image", + "image_path": "ce23967ba037522fbf48a3ba11417d023fc62dda5cc3567eb32c6552a8d23437.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 67, + 376, + 176, + 483 + ], + "blocks": [ + { + "bbox": [ + 95, + 372, + 138, + 379 + ], + "lines": [ + { + "bbox": [ + 95, + 372, + 138, + 379 + ], + "spans": [ + { + "bbox": [ + 95, + 372, + 138, + 379 + ], + "type": "text", + "content": "(a) Sequence 01" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 67, + 376, + 176, + 483 + ], + "lines": [ + { + "bbox": [ + 67, + 376, + 176, + 483 + ], + "spans": [ + { + "bbox": [ + 67, + 376, + 176, + 483 + ], + "type": "image", + "image_path": "61b180e0795b45c3f9d5126785a646978c53ecd33c675e473c57649325642827.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 96, + 483, + 139, + 491 + ], + "lines": [ + { + "bbox": [ + 96, + 483, + 139, + 491 + ], + "spans": [ + { + "bbox": [ + 96, + 483, + 139, + 491 + ], + "type": "text", + "content": "(c) Sequence 06" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 498, + 295, + 543 + ], + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 543 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 543 + ], + "type": "text", + "content": "Figure 4. 3D trajectories of A-LOAM, EfficientLO and our proposed method on KITTI sequences 01, 05, 06 and 09 with ground truth. Ours trajectory is more accurate than EfficientLO and the Full A-LOAM, which has the mapping optimization." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 183, + 375, + 291, + 483 + ], + "blocks": [ + { + "bbox": [ + 211, + 372, + 255, + 379 + ], + "lines": [ + { + "bbox": [ + 211, + 372, + 255, + 379 + ], + "spans": [ + { + "bbox": [ + 211, + 372, + 255, + 379 + ], + "type": "text", + "content": "(b) Sequence 05" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 183, + 375, + 291, + 483 + ], + "lines": [ + { + "bbox": [ + 183, + 375, + 291, + 483 + ], + "spans": [ + { + "bbox": [ + 183, + 375, + 291, + 483 + ], + "type": "image", + "image_path": "66179fc5f680d76638ffe38a2a8f58bd415cb06e8f7516f153bcd7b9419fa9a0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 211, + 483, + 255, + 491 + ], + "lines": [ + { + "bbox": [ + 211, + 483, + 255, + 491 + ], + "spans": [ + { + "bbox": [ + 211, + 483, + 255, + 491 + ], + "type": "text", + "content": "(d) Sequence 09" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 555, + 295, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 295, + 580 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 295, + 580 + ], + "type": "text", + "content": "tion studies on KITTI odometry dataset (00-06 as training sequences and 07-10 as testing sequences)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 581, + 295, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 295, + 688 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 295, + 688 + ], + "type": "text", + "content": "Study on Semantic Perception Module. We conducted ablation experiments to demonstrate the significance of the Semantic Perception Module (SPM) mentioned in Sec. 3.2. As shown in Tab. 4, SPM achieves an average improvement of " + }, + { + "bbox": [ + 55, + 581, + 295, + 688 + ], + "type": "inline_equation", + "content": "10.7\\%" + }, + { + "bbox": [ + 55, + 581, + 295, + 688 + ], + "type": "text", + "content": " in transition accuracy and " + }, + { + "bbox": [ + 55, + 581, + 295, + 688 + ], + "type": "inline_equation", + "content": "17.6\\%" + }, + { + "bbox": [ + 55, + 581, + 295, + 688 + ], + "type": "text", + "content": " in rotation accuracy. This indicates that SPM enhances accuracy by embedding semantic understand to the network, which helps the network to focus more on the objects in the scene that play a key role in pose estimation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 714 + ], + "type": "text", + "content": "Study on Diffusion Refinement. We conducted an ablation study by comparing results with and without the" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "text", + "content": "diffusion-based refinement process (w/o diffusion). As shown in Tab. 4, the diffusion-based pose refinement significantly improved performance, reducing the average translation error by " + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "inline_equation", + "content": "88.2\\%" + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "text", + "content": " (from " + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "inline_equation", + "content": "5.995\\%" + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "inline_equation", + "content": "0.708\\%" + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "text", + "content": ") and the average rotation error by " + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "inline_equation", + "content": "90.0\\%" + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "text", + "content": " (from " + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "inline_equation", + "content": "3.265^{\\circ} / 100\\mathrm{m}" + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "inline_equation", + "content": "0.328^{\\circ} / 100\\mathrm{m}" + }, + { + "bbox": [ + 313, + 258, + 553, + 390 + ], + "type": "text", + "content": "). Additionally, we explored the performance of different denoising networks, including a transformer-based [40] network (trans-based), a point transformer-based [51] network (ptrans-based), and GRU-based [6] network. The results demonstrate the advantages of our denoising network over alternative approaches." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "spans": [ + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "text", + "content": "Study on Condition signals. To evaluate the effectiveness of the diffusion condition signals, we conducted an ablation study by individually removing each designed condition signal, as shown in Tab. 4. Removing the cost volume led to a performance degradation (with translation error increasing by " + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "inline_equation", + "content": "21.5\\%" + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "text", + "content": " and rotation error by " + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "inline_equation", + "content": "57.9\\%" + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "text", + "content": "), since cost volume captures the precise per-point correlation between two frames. The semantic feature also plays a crucial role in guiding diffusion generation, as it provides scene understanding. Consequently, its removal resulted in a significant drop in performance (led to a " + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "inline_equation", + "content": "12.7\\%" + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "text", + "content": " increase in translation error and a " + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "inline_equation", + "content": "20.4\\%" + }, + { + "bbox": [ + 313, + 390, + 555, + 606 + ], + "type": "text", + "content": " increase in rotation error). Additionally, removing the coarse pose embedding led to a decline in performance, as coarse pose embedding provides essential state information, which is closely related to the residual pose generated by the model. Finally, the absence of geometry features as guidance also resulted in a noticeable performance drop." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 611, + 399, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 611, + 399, + 623 + ], + "spans": [ + { + "bbox": [ + 313, + 611, + 399, + 623 + ], + "type": "text", + "content": "4.5. Visualization" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 629, + 553, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 553, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 553, + 653 + ], + "type": "text", + "content": "We visualize the trajectory of our network and analyze the benefits of Semantic Perception Module in this section." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "Visualization of Trajectory. The qualitative results are shown in Fig.3, 4 and 5. We compared our method with full A-LOAM, which includes mapping optimization, and EfficientLO [44]. Notably, in Seq.02 of Fig. 3, A-LOAM exhibits significant drift due to the presence of repetitive" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17056" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 72, + 293, + 171 + ], + "blocks": [ + { + "bbox": [ + 59, + 72, + 293, + 171 + ], + "lines": [ + { + "bbox": [ + 59, + 72, + 293, + 171 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 293, + 171 + ], + "type": "image", + "image_path": "ab0593e8dacb7dd12fa283918fc579e412b13b7d94059b9502c9fc09bc0dfb5e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 178, + 295, + 212 + ], + "lines": [ + { + "bbox": [ + 55, + 178, + 295, + 212 + ], + "spans": [ + { + "bbox": [ + 55, + 178, + 295, + 212 + ], + "type": "text", + "content": "Figure 5. Average translational and rotational error on KITTI sequences 00-10 on all possible subsequences in the length of 100, 200, ..., 800m. Our method has the best performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 218, + 293, + 360 + ], + "blocks": [ + { + "bbox": [ + 58, + 218, + 293, + 360 + ], + "lines": [ + { + "bbox": [ + 58, + 218, + 293, + 360 + ], + "spans": [ + { + "bbox": [ + 58, + 218, + 293, + 360 + ], + "type": "image", + "image_path": "0371a01e13e5f9b4686b76056b758a7ab3d60fd96d76e75ef1ea55f63982499a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 365, + 295, + 422 + ], + "lines": [ + { + "bbox": [ + 55, + 365, + 295, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 295, + 422 + ], + "type": "text", + "content": "Figure 6. The visualization of semantic features is derived from the complete LiDAR point cloud of the initial frame. Additionally, the grayscale image captured from the camera view corresponds to the semantic segmentation image displayed below. Bounding boxes are utilized to delineate specific object categories." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 435, + 295, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 435, + 295, + 507 + ], + "spans": [ + { + "bbox": [ + 55, + 435, + 295, + 507 + ], + "type": "text", + "content": "structures and patterns in the scene, which impedes the algorithm's ability to accurately estimate pose. These figures show that our odometry can track the trajectory of the ground truth fairly well. At the same time, our method demonstrates the best average evaluation performance compared to A-LOAM and EfficientLO." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 509, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 295, + 616 + ], + "type": "text", + "content": "Visualization of Semantic feature. The proposed network employs an embedding feature of 8,192 points to compute the pose transformation in the final pose output layer. Consequently, we visualize the semantic features of these 8,192 points. As illustrated in Fig. 6, vehicles, street lamps, fences, billboards, and other objects in the scene are segmented. This demonstrates that the Semantic Perception Module empowers the network with the capability of semantic understanding." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 715 + ], + "type": "text", + "content": "Visualization of embedding mask. We visualize the embedding mask of the 8,192 points in the final pose output layer. As shown in Fig. 7, the mask of DiffLO integrated with the Semantic Perception Module (SPM) allocates weights more accurately compared to the mask of DiffLO without SPM. Points sampled from static and structured rigid objects, such as buildings, fences, and pole-like object, exhibit higher weights, while points from dynamic" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 318, + 72, + 552, + 201 + ], + "blocks": [ + { + "bbox": [ + 318, + 72, + 552, + 201 + ], + "lines": [ + { + "bbox": [ + 318, + 72, + 552, + 201 + ], + "spans": [ + { + "bbox": [ + 318, + 72, + 552, + 201 + ], + "type": "image", + "image_path": "b5f7e4a433487d4c1024de72c7ea0a75175851b989799899aeac0936a06d614c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 205, + 555, + 273 + ], + "lines": [ + { + "bbox": [ + 313, + 205, + 555, + 273 + ], + "spans": [ + { + "bbox": [ + 313, + 205, + 555, + 273 + ], + "type": "text", + "content": "Figure 7. The visualization of the embedding mask is based on the complete LiDAR point cloud of the initial frame. In the lower-left corner, the heatmap represents the mask of DiffLO integrated with the SPM. Conversely, the lower-right corner displays the heatmap for the mask of DiffLO without SPM. Above these visualizations, the corresponding grayscale image of the point cloud is presented." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 289, + 555, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 555, + 348 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 555, + 348 + ], + "type": "text", + "content": "and low-texture objects, including cars, shrubs, and trees, receive lower weights. This demonstrates that the Semantic Perception Module (SPM) effectively helps the network focus on objects in the scene that are crucial for accurate pose estimation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 364, + 421, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 364, + 421, + 376 + ], + "spans": [ + { + "bbox": [ + 314, + 364, + 421, + 376 + ], + "type": "text", + "content": "4.6. Runtime Analysis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "type": "text", + "content": "Efficiency is another extremely significant factor in real-time SLAM systems. The LiDAR points in the KITTI dataset are captured at a " + }, + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "type": "text", + "content": " frequency. Our method has only " + }, + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "type": "inline_equation", + "content": "76.9\\mathrm{ms}" + }, + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "type": "text", + "content": " inference time, which satisfy the real-time application requirements (under " + }, + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "type": "inline_equation", + "content": "100\\mathrm{ms}" + }, + { + "bbox": [ + 313, + 384, + 555, + 445 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 463, + 388, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 463, + 388, + 475 + ], + "spans": [ + { + "bbox": [ + 314, + 463, + 388, + 475 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 486, + 555, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 555, + 666 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 555, + 666 + ], + "type": "text", + "content": "In this paper, we introduce a diffusion model-based odometry network augmented with semantic awareness, targeting large-scale LiDAR odometry. Our approach innovatively applies knowledge distillation to transfer semantic information into the odometry network, thereby enhancing the network's semantic understanding. This allows the network to effectively mitigate the challenges posed by dynamic objects, repetitive patterns, and low-texture environments. Additionally, we incorporate a diffusion model conditioned on pose-related features to refine pose estimation. To the best of our knowledge, this is the first instance of utilizing diffusion models in odometry tasks. We evaluated our framework on the KITTI odometry dataset, and our method achieved state-of-the-art performance while ensuring the real-time requirement of pose prediction." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 555, + 713 + ], + "type": "text", + "content": "Acknowledgements This work was supported in part by Natural Science Foundation of China (No.62171393), and the Fundamental Research Funds for the Central Universities (No.20720220064)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17057" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 133 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 133 + ], + "type": "text", + "content": "[1] Sk Aziz Ali, Djamila Aouada, Gerd Reis, and Didier Stricker. 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In CVPR, pages 12786-12796, 2022. 1" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17059" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_content_list.json b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..315fe7ffe17ac69cbe1157e20552b19184ae235c --- /dev/null +++ b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_content_list.json @@ -0,0 +1,1730 @@ +[ + { + "type": "text", + "text": "DiffLocks: Generating 3D Hair from a Single Image using Diffusion Models", + "text_level": 1, + "bbox": [ + 276, + 130, + 722, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Radu Alexandru Rosu $^{1,\\ast}$ Keyu Wu $^{2,\\ast,\\dagger}$ Yao Feng $^{1,3}$ Youyi Zheng $^{2}$ Michael J. Black $^{4}$", + "bbox": [ + 129, + 202, + 859, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Meshcapade $^{2}$ Zhejiang University $^{3}$ Stanford University $^{4}$ Max Planck Institute for Intelligent Systems", + "bbox": [ + 133, + 222, + 857, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 273, + 326, + 289 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We address the task of generating 3D hair geometry from a single image, which is challenging due to the diversity of hairstyles and the lack of paired image-to-3D hair data. Previous methods are primarily trained on synthetic data and cope with the limited amount of such data by using low-dimensional intermediate representations, such as guide strands and scalp-level embeddings, that require post-processing to decode, upsample, and add realism. These approaches fail to reconstruct detailed hair, struggle with curly hair, or are limited to handling only a few hairstyles. To overcome these limitations, we propose DiffLocks, a novel framework that enables detailed reconstruction of a wide variety of hairstyles directly from a single image. First, we address the lack of 3D hair data by automating the creation of the largest synthetic hair dataset to date, containing 40K hairstyles. Second, we leverage the synthetic hair dataset to learn an image-conditioned diffusion-transformer model that generates accurate 3D strands from a single frontal image. By using a pretrained image backbone, our method generalizes to in-the-wild images despite being trained only on synthetic data. Our diffusion model predicts a scalp texture map in which any point in the map contains the latent code for an individual hair strand. These codes are directly decoded to 3D strands without post-processing techniques. Representing individual strands, instead of guide strands, enables the transformer to model the detailed spatial structure of complex hairstyles. With this, DiffLocks can recover highly curled hair, like afro hairstyles, from a single image for the first time. Data and code is available at https://radualexandru.github.io/difflocks/.", + "bbox": [ + 88, + 305, + 485, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 805, + 220, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Realistic 3D hair is a crucial component of digital humans [1, 2, 8, 12, 18, 38, 45], which have wide applications in", + "bbox": [ + 89, + 830, + 483, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/db46e02f03fa79dd37b82519b2e3ca7decd2033033d6e32ad605dd9619d50055.jpg", + "image_caption": [ + "Synthetic hair dataset" + ], + "image_footnote": [], + "bbox": [ + 513, + 273, + 642, + 387 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/48e98739e76eb057826c69742a7c3dbf7cf97b1ff733380d2bad5116eb3a28bd.jpg", + "image_caption": [ + "Real image" + ], + "image_footnote": [], + "bbox": [ + 653, + 271, + 756, + 386 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e2a01c26dff39a0937ad3d2695048e49ab11a189de18bc059b93609f174a9683.jpg", + "image_caption": [ + "3D hair", + "Figure 1. Given a single RGB image DiffLocks generates accurate 3D strands using a diffusion model. The model is trained on a novel synthetic hair dataset containing RGB images and corresponding 3D strands." + ], + "image_footnote": [], + "bbox": [ + 771, + 271, + 895, + 386 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "games, media and entertainment. Accurate hair representation greatly enhances the character's realism and overall visual quality. Unfortunately, both generating realistic hair and reconstructing it from an image are challenging due to the complex 3D geometry and the wide variety of hairstyles.", + "bbox": [ + 511, + 500, + 906, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Since the release of the first 3D synthetic hair dataset [11], numerous methods for hair reconstruction have been proposed. Multi-view capture methods [17, 29, 31, 54, 57] and video-based approaches [24, 41, 49] are able to reconstruct high-fidelity 3D hair but are time-intensive and challenging to deploy due to their reliance on expensive capture equipment or strict capture conditions.", + "bbox": [ + 511, + 579, + 908, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In contrast, single-view methods [3, 37, 48, 51, 55], which reconstruct 3D hair from a single image, are faster, more accessible, and user-friendly. These methods, however, often produce low-detail hair and handle only a restricted range of hairstyles. Furthermore, these methods struggle to handle male-pattern baldness and very curly hair such as afro-like hairstyles, which have a complex geometric structure (see [47]). Previous methods suffer from a lack of diverse and comprehensive hairstyle training datasets. To increase training set diversity, GroomGen [56], HAAR [42] and Fake It Till You Make It [46] use artist-created hairstyles together with data augmentation techniques to train their methods. However, their datasets are not released, do not have paired RGB images, or the creation pro", + "bbox": [ + 511, + 688, + 910, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Joint first author", + "bbox": [ + 107, + 875, + 205, + 886 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Work done during an internship at Meshcapade", + "bbox": [ + 107, + 887, + 364, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10847", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cess requires significant manual effort.", + "bbox": [ + 89, + 90, + 346, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To cope with limited training data, previous approaches rely on several intermediate representations to simplify the problem. Most prior methods rely on oriented filters to capture the structure of hair in images. They also do not model hair strands directly but, instead, use a smaller number of guide strands and then upsample these to generate a hairstyle. Additionally, several methods use variational autoencoding to compress the guide strands across the scalp into a low-dimensional representation. All of these approaches are designed to cope with limtied training data but have two effects: (1) they limit the ability to model the complex spatial relationships between individual strands, and (2) they limit realism by working with low-dimensional representations. Effectively, they work in a compressed low-dimensional space and then need to upsample the results and post-process them to increase realism.", + "bbox": [ + 89, + 109, + 483, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We take a different approach and focus on creating a sufficient amount of training data that we can remove the simplifying assumptions of previous methods. To that end, we present a novel 3D synthetic hair dataset consisting of 40K samples covering a wide variety of hairstyles; see Fig. 3. Each sample consists of 3D hair strands and a realistic RGB image rendered in Blender through path-tracing. We achieve this by automating the creation of the data using a variety of artist-inspired techniques. Traditional approaches are designed to create a single hairstyle using a small geometry node network tailored-made for that hairstyle. In contrast, we design a large and very general geometry node network in Blender that allows us to automatically create a large number of realistic hairstyles by changing the different parameters.", + "bbox": [ + 89, + 354, + 483, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We then leverage our dataset to train a novel hair diffusion framework, called DiffLocks, that is optionally conditioned on single RGB image in order to create highly detailed 3D strands; see Fig. 1. Specifically, we use Hourglass Diffusion Transformers (HDiT) [6] as a diffusion architecture and exploit features from a pretrained DINOv2 [30] model as a conditioning input to guide and control the generated results; see Fig. 2. The DINOv2 features are richer than the oriented filters used in many previous methods. Note that we directly regress the latent code for individual hair strands (instead of guide strands) enabling the transformer to learn detailed spatial relationships between strands across the scalp. With sufficient training data, there is no longer a need to first embed the hairstyle in a low-D scalp representation. We also model a density map that defines the probability of a strand being generated at each location on the scalp. All of these changes lead to increased realism, particularly for curly and balding hairstyles. Finally, our strand-based hair can be directly used in real-time game engines like Unreal Engine (Fig. 6) without additional heuristics to densify the hair or add fine-grained detail.", + "bbox": [ + 89, + 583, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key takeaway from our work is that, with sufficient training data, many of the key components of previous methods are no longer needed. For example, in contrast to the $32 \\times 32$ scalp map used by HAAR, our diffusion model predicts a scalp texture of size $256 \\times 256$ (each pixel containing a latent code for a single strand) from which DiffLocks directly decodes 3D strands. No post-processing is needed, such as hair upsampling or the addition of random noise (cf. [56]). The dataset already contains realistic hairstyles with flyaway strands, so the diffusion model learns to create them.", + "bbox": [ + 511, + 90, + 903, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are:", + "bbox": [ + 532, + 258, + 799, + 272 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- a novel 3D hair dataset containing 40K diverse and realistic 3D hairstyles with corresponding RGB images. We make the dataset public in order to support future research in hair modeling and synthesis,", + "- an improved scalp representation that facilitates the reconstruction of hair styles with different hair density (bald spots, male pattern baldness, etc.),", + "- a novel conditional scalp diffusion framework for robustly generating 3D hair directly from a single RGB image, bypassing a 2D orientation map. This framework can effectively create a variety of challenging hairstyles, while achieving the state-of-the-art performance and enable, for the first time, reconstruction of Afro-like and bald hairstyles. The model will be available for research." + ], + "bbox": [ + 511, + 275, + 903, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 511, + 503, + 661, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Hair Reconstruction. The pioneering hair reconstruction work of Paris et al. [31] set the stage for numerous multi-view-based hair reconstruction methods. Since then, various methods [17, 25, 26, 29, 57] reconstruct the 3D geometric features of hair constrained by a 2D orientation map. In many cases this requires specialized hardware or multicamera rigs. In contrast, monocular video based methods [24, 41, 44, 49] sacrifice some accuracy to avoid expensive and specialized equipment. While achieving impressive results, such methods still require carefully captured data. To relax the capture conditions, single-view-based methods [3, 37, 48, 51, 53, 53] employ deep neural networks to infer volumetric fields by exploiting data priors learned from 3D synthetic datasets. Such methods enable rapid 3D hair reconstruction but typically generate low fidelity hair and can handle only a limited range of hairstyles due to the significant lack of diversity in existing 3D hair datasets. Similar to these methods, our approach also reconstructs hair from a single image. However, our work focuses on fast and robust reconstruction of diverse hairstyles, including challenging types such as balding and tightly curled (afro-like) styles; such hairstyles have received relatively little attention.", + "bbox": [ + 511, + 531, + 906, + 864 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Hair Generation. In addition to hair reconstruction, hair generation is another challenge, which, if solved, could", + "bbox": [ + 511, + 869, + 908, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10848", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/11b00eeec5a8d13730cab3f5fda39811fc2edccd56d75fb8d9a08cace937f089.jpg", + "image_caption": [ + "Figure 2. Method. Given a single RGB image, we use a pretrained DINOv2 model to extract local and global features, which are used to guide a scalp diffusion model. The scalp diffusion model denoises a density map and a scalp texture containing latent codes for strand geometry. Finally, we probabilistically sample texels from the scalp texture and decode the latent code $\\mathbf{z}$ into strands of 256 points. Decoding in parallel 100K strands yields the final hairstyle." + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 890, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "provide synthetic data for learning high-quality hair reconstruction. Ren et al. [34] propose a heuristic example-based hair generation method that is significantly limited by the reference hair models. Saito et al. [37] encode a 3D hair dataset with a Variational autoencoder (VAE), enabling them to generate plausible yet overly smooth hairstyles. To achieve high-quality and diverse hairstyles, Perm [9] leverages existing public 3D datasets, disentangling the global shape and local details of hair strands. Despite progress, the scale and diversity of synthetic 3D hair datasets is still far from what is needed. GroomGen [56] and HAAR [42] incorporate parametrized variations based on high-quality hairstyles crafted by artists, further enhancing the diversity of 3D hair datasets. They also train generative models to produce 3D hairstyles from noisy inputs or text prompts. Recently, Curly-Cue [47] focuses on the principles behind curly, afro-style, hair and provides tools for animators to create realistic hairstyles. In our work, we propose a low-cost synthetic 3D hair generation pipeline and use it to construct a new dataset that is more diverse than previous ones, containing 40K 3D synthetic hairstyles. Additionally, we use this dataset to train a generative hair model that is conditioned on a single input image.", + "bbox": [ + 88, + 316, + 485, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image-To-3D via Diffusion Models. Early work on neural reconstruction of 3D objects from images [7, 28, 50] distills information from pretrained 2D diffusion models, such as Stable Diffusion [35], using techniques like Score Distillation Sampling (SDS) [33]. However, these pretrained models lack the multi-view information essential for accurate 3D reconstruction. To address this, later approaches [20, 21, 40] train custom 2D diffusion models to generate multi-view images from a given input, enabling more accurate 3D object reconstruction by integrating this multi-view data [13, 23]. While effective, this approach can be time-intensive due to the sampling and reconstruction processes, which has led to an alternative line of research focused on training diffusion models to generate 3D representations directly, such as meshes [22] or triplane repre", + "bbox": [ + 89, + 674, + 486, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sentations [4]. However, these methods often demand significant computational resources for 3D processing. In contrast, our method produces a 2D representation that contains 3D hair information, enabling direct decoding into 3D hair without the need for extensive multi-view generation or resource-intensive training of 3D diffusion models.", + "bbox": [ + 511, + 316, + 908, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 511, + 420, + 604, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present our pipeline for 3D hair reconstruction from a single image, consisting of three key stages: 1) A data generation pipeline using Blender's geometry nodes to create a large, diverse, image-3D paired synthetic hair dataset (Sec. 3.1); 2) Parameterization of hair strands and hairstyles into a canonical scalp space to obtain scalp textures (Sec. 3.2); And 3) training a conditional diffusion model, DiffLocks, using the generated synthetic images and the scalp textures as shown in Fig. 2.", + "bbox": [ + 511, + 445, + 908, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Data Generation", + "text_level": 1, + "bbox": [ + 511, + 589, + 679, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A key bottleneck in the field of 3D hair reconstruction is the limited availability of public datasets, with only 343 hairstyles for USC-HairSalon [11] and 10 for CT2Hair [39]. Additionally, these datasets lack corresponding 2D images, which limits their usability. Thus, here we propose a novel data generation pipeline, which uses Blender geometry nodes to add variation to a small set of manually defined guide strands as shown in Fig. 4. Next, we will describe the main steps of the pipeline.", + "bbox": [ + 511, + 609, + 908, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scalp creation. The first step in creating the new dataset is defining a scalp mesh onto which to build the hairstyles. Due to its wide applicability in the human-reconstruction field, we use the SMPL-X model [32] to define our scalp. We create a SMPL-X neutral body with mean body shape from which we manually select the vertices corresponding to the scalp and extract a mesh of 513 vertices as seen in Fig. 2. The scalp mesh is then UV-unwrapped into a single chart using an As-Rigid-As-Possible (ARAP) parametrization [43] in order to minimize distortions. This", + "bbox": [ + 511, + 750, + 910, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10849", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bf09dc3d1d7dc770e866fdca3b9cf68fa4dcba423c63eebe63b9a80c7200fe08.jpg", + "image_caption": [ + "Figure 3. Synthetic data. Sample RGB images from our synthetic hair dataset. Each sample from the dataset contains an image at $768 \\times 768$ resolution together with the corresponding 3D strand geometry of $\\approx 100\\mathrm{K}$ strands." + ], + "image_footnote": [], + "bbox": [ + 93, + 87, + 225, + 191 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/86f18bcb6d6fb40e8be568ab4b605b7b5b4a14a3a5d3cbf1b6400f4107944404.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 227, + 88, + 359, + 191 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/46556d4d30d62af92354bf4e34454212b7efb36d0a0177db0ec06a76ba2d862f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 88, + 495, + 191 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/be984e13daaa5becb3b5d841e5be95cc70632b5579896500c66d6bc4eb5f21a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 88, + 630, + 191 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5e9ef72ab27a9ea82de13d34626aca378d67ec8f8a813d6d0fa3279c92dda0ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 88, + 764, + 191 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9c6256f2749fded413ca15c16b15dcb513be9fe6510081a2557d19dc086b3ee8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 766, + 88, + 900, + 191 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6d188e4c76e1d5a0ee2d640fcb1f050618e3e7db1a85f5d0a57c33c8725a3658.jpg", + "image_caption": [ + "Figure 4. Base hairstyles. Starting from a coarse set of guide strands, our Blender pipeline is able to generate a wide variety of hairstyles, covering different lengths, curliness and density patterns. Best viewed zoomed in." + ], + "image_footnote": [], + "bbox": [ + 106, + 250, + 472, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "operation is done only once and need not be repeated for each subject since they all share the same SMPL-X body topology.", + "bbox": [ + 89, + 479, + 482, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Base hairstyle creation. The scalp mesh is imported into Blender and a series of hairstyles is manually created in the form of coarsely defined guide strands (Fig. 4). The base hairstyles define a starting point for the randomization process and therefore do not need to contain fine details, rather defining just the overall shape and direction of the hair. We manually create 75 base hairstyles, each represented by $\\approx 50$ strands. We note that this is not a labour intensive process, as each base hairstyle takes only a few minutes to create.", + "bbox": [ + 89, + 532, + 482, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Randomization pipeline. The guide strands are passed through a series of transformations defined as geometry nodes in Blender that gradually add more detail to the hair. The guide strands are first interpolated to 100K strands, after which clumping, curling and noise are applied. These operations are repeated multiple times with various intensities. Special attention must be given to prevent the hair from penetrating the scalp or intersecting with the body for which we apply shrinkwrap modifiers at various stages in the pipeline. In total the pipeline consists of 58 geometry nodes that transform the hair together with 349 auxiliary nodes that help feed parameters into the main nodes. We also define a hair BSDF using the Chiang model [5] for the strands material. Lastly we apply physics simulation to", + "bbox": [ + 89, + 689, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the strands using Blender's cloth simulation and randomize wind direction and gravity strength. A total of 110 parameters govern the whole Blender generation pipeline (geometry+material) and we select them at random with minimum and maximum ranges chosen empirically.", + "bbox": [ + 511, + 250, + 905, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Scene setup. In order to render realistic images, it is crucial to match the lighting of real scenes. For this, we use 255 HDRIs from Poly Haven1 and randomize their exposure and azimuthal angle. Additionally, we randomly select albedo, normal and roughness textures for the bodies from a library of artist-created SMPL-X textures. Furthermore, we also randomly change the face expression coefficients within the range $[-1, 1]$ . We keep the jaw closed since we observed it can cause issues with strands physics. To train our network for robustness to different camera parameters, we also randomize camera position (maintaining the look-at direction towards the head) and focal length in the range $40\\mathrm{mm}$ to $150\\mathrm{mm}$ . For a study on network robustness to camera parameters please refer to the SupMat.", + "bbox": [ + 511, + 330, + 905, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Full dataset. The full dataset contains 40K samples each containing 3D strands with $\\approx 100\\mathrm{K}$ strands and a corresponding RGB image rendered through path tracing at $768 \\times 768$ resolution. We additionally save a density map that defines the probability of a strand being generated at each texel of the scalp as shown in Fig. 5. The density map is especially useful for modelling hairstyles with balding patterns.", + "bbox": [ + 511, + 544, + 905, + 665 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Hairstyle Parameterization", + "text_level": 1, + "bbox": [ + 511, + 674, + 758, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Strand Parameterization. Formally, we represent a 3D strand as a set of $L$ 3D points $\\mathbf{S} = \\{\\mathbf{p}_1,\\mathbf{p}_2,\\dots ,\\mathbf{p}_L\\}$ , where $L = 256$ . A full hairstyle consists of a set of $\\approx 100\\mathrm{K}$ strands $\\mathbf{H} = \\{\\mathbf{S}_j\\}_{0}^{100\\mathrm{K}}$ . Similar to Neural Strands [36], we train a strand VAE to compress individual strands into a compact latent code $\\mathbf{z}\\in \\mathbb{R}^{64}$ . The encoder of the VAE denoted by $\\mathcal{E}()$ is modeled as a series of 1D convolutions and the decoder denoted by $\\mathcal{G}()$ is a modulated SIREN [27] that maps the latent code $\\mathbf{z}$ back to a series of 3D points $\\mathbf{S}$ .", + "bbox": [ + 511, + 696, + 905, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition to the position and direction loss proposed by Neural Strands [36], we incorporate a curvature loss $\\mathcal{L}_{\\mathrm{cur}}$ . This is motivated by the observation that, for highly coiled", + "bbox": [ + 511, + 832, + 905, + 878 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "$^{1}$ https://polyhaven.com/hdris", + "bbox": [ + 531, + 886, + 687, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10850", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "hair, it is more perceptually impactful to match the curvature of the strand rather than matching the position of every point along the strand (i.e., as long as the strand looks curvy, it is acceptable to commit errors in per-point position). For an evaluation of this observation please refer to the SupMat. We define the local curvature as the instantaneous change in direction: $\\kappa_{i} = \\mathbf{d}_{i + 1} - \\mathbf{d}_{i}$ where the direction is defined as the change in position: $\\mathbf{d}_i = \\mathbf{p}_{i + 1} - \\mathbf{p}_i$ . Therefore, the new curvature loss is defined as the L1 distance between the ground-truth and the prediction: $\\mathcal{L}_{\\mathrm{cur}} = \\sum_{0}^{L}|\\kappa_{i} - \\tilde{\\kappa}_{i}|$ , where $\\hat{\\kappa}_i$ is the curvature of the predicted strand.", + "bbox": [ + 89, + 90, + 483, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final training loss of our strands VAE is a weighted combination of a data term consisting of positional, directional and curvature losses together with a KL regularization term:", + "bbox": [ + 89, + 272, + 483, + 333 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {d a t a}} = \\sum_ {0} ^ {L} | \\mathbf {p} _ {i} - \\tilde {\\mathbf {p}} _ {i} | + \\lambda_ {1} | \\mathbf {d} _ {i} - \\tilde {\\mathbf {d}} _ {i} | + \\lambda_ {2} | \\boldsymbol {\\kappa} _ {i} - \\tilde {\\boldsymbol {\\kappa}} _ {i} | \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 338, + 482, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {V A E}} = \\mathcal {L} _ {\\mathrm {d a t a}} + \\lambda_ {\\mathrm {K L}} \\mathcal {L} _ {\\mathrm {K L}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 382, + 482, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For more details on the hyperparameters please refer to the SupMat.", + "bbox": [ + 89, + 406, + 483, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Neural Scalp Texture. Each 3D hairstyle generated from the Blender pipeline is parametrized onto the scalp surface using a regular 2D texture. Specifically, each strand $\\mathbf{S}$ is encoded to a latent code $\\mathbf{z}$ by the strand encoder $\\mathbf{z} = \\mathcal{E}(\\mathbf{S})$ and directly assigned to the texel corresponding to the root of the strand. If two strands are so close together that they are assigned the same texel on the scalp, one of them is chosen at random. This produces a raw scalp texture $\\mathbf{T}_{\\text{raw}} \\in \\mathbb{R}^{256 \\times 256 \\times 64}$ , as shown in Fig. 5c where each texel contains a latent strand code. Since not all regions of the scalp have an equal hair density, we introduce a density map $\\mathbf{D} \\in \\mathbb{R}^{256 \\times 256 \\times 1}$ with values in the range [0, 1] that defines the probability of a strand being present at each texel. For more discussion on the properties of the density map please refer to the SupMat.", + "bbox": [ + 89, + 454, + 483, + 679 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The aforementioned creation of the scalp texture can create sparse regions with no latent codes since not every texel will correspond to a strand. This sparsity is particularly evident for hairstyles with balding patterns and can cause issues when decoding the texture back to 3D since sampling a texel with no assigned latent code would yield undefined strand geometry. To avoid this issue, we interpolate the sparsely assigned latent codes by using a push-pull algorithm [16] that ensures that every texel on the scalp has a valid strand latent code as shown in Fig. 5d.", + "bbox": [ + 89, + 680, + 482, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the interpolated scalp texture $\\mathbf{T}$ , we can sample at UV-positions according to the density $\\mathbf{D}$ , and produce a full hairstyle $\\mathbf{H}$ by decoding each latent code:", + "bbox": [ + 89, + 830, + 483, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} = \\mathcal {G} (\\text {S a m p l e} (\\mathbf {T}, \\mathbf {D})) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 883, + 482, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\text{Sample}(\\cdot)$ performs probabilistic sampling in UV space such that regions with high density are sampled more often, allowing us to represent hairstyles with varying density of hair. To create a full hairstyle we sample 100K positions on the scalp and extract strand latent codes $\\mathbf{z}$ using bilinear interpolation.", + "bbox": [ + 511, + 90, + 903, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Conditional Scalp Diffusion", + "text_level": 1, + "bbox": [ + 511, + 189, + 763, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Diffusion framework. Similar to previous methods [42, 56] we train a generative model of scalp textures $\\mathbf{T}$ to learn the prior distribution over hairstyles. Furthermore, we condition the model on image data, enabling high-quality 3D hair generation from a single image. Specifically, we train a denoiser model $\\mathcal{D}_{\\theta}$ using a Hourglass Diffusion Transformer [6] architecture, which is particularly efficient for pixel-space diffusion tasks. We denote the clean training sample for the diffusion as the concatenation of scalp texture and density map: $\\mathbf{y} = [\\mathbf{T},\\mathbf{D}]$ and the noised input $\\mathbf{x} = \\mathbf{y} + \\mathbf{n}$ as a combination of the clean data $\\mathbf{y}$ and noise $\\mathbf{n} \\sim \\mathcal{N}(0,\\sigma^2\\mathbf{I})$ with noise level $\\sigma$ . Following EDM [14], we parametrize the denoiser to allow it to predict $\\mathbf{y}$ or $\\mathbf{n}$ , or something in between:", + "bbox": [ + 511, + 210, + 906, + 422 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {\\theta} (\\mathbf {x}; \\sigma) = c _ {\\text {s k i p}} (\\sigma) \\mathbf {x} + c _ {\\text {o u t}} (\\sigma) \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\sigma) \\mathbf {x}; c _ {\\text {n o i s e}} (\\sigma)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 431, + 906, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_{\\theta}$ is the network to train, $c_{\\mathrm{skip}}$ is as a skip connection modulator, $c_{\\mathrm{in}}$ and $c_{\\mathrm{out}}$ scale the input and output magnitude, and $c_{\\mathrm{noise}}$ is the time condition of the network. Please refer to the EDM paper [14] for more details.", + "bbox": [ + 511, + 455, + 905, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training loss for each spatial element and each noise level is defined as:", + "bbox": [ + 511, + 517, + 905, + 546 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, \\mathbf {y}, \\mathbf {n}, \\sigma\\right) = \\left\\| \\mathcal {D} _ {\\theta} (\\mathbf {y} + \\mathbf {n}; \\sigma) - \\mathbf {y} \\right\\| _ {2} ^ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 555, + 903, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss scaling. The denoising network outputs a clean scalp texture $\\mathbf{T}$ and a density map $\\mathbf{D}$ . However, we observe that not all channels of the scalp texture are equally significant, some encode relevant information such as length or curliness, while others are noisy and have little impact on the decoded strand. We propose to down-weight the loss of the channels of the scalp textures based on their perceptual change to the strand shape. Since we have no direct metric to evaluate perceptual change, we reuse the data term from the loss $\\mathcal{L}_{\\mathrm{data}}$ used to train the StrandVAE. More specifically, we first define the mean strand predicted by the VAE as $\\mathbf{S}_0 = \\mathcal{G}(\\mathbf{z}_0)$ by decoding from a zero latent vector $\\mathbf{z}_0 = [0]^{64}$ . Following that, we individually perturb each dimension of the latent code, decode a strand, and calculate the distance to the mean strand as measured by the loss. This can be seen as a metric that quantifies perceptual changes as a result of individual changes to the latent code dimensions. Therefore, the weight associated with each dimension of the latent code is:", + "bbox": [ + 511, + 589, + 906, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} = \\mathcal {L} _ {\\text {s t r a n d}} \\left(S _ {0}, \\mathcal {G} \\left(\\mathbf {z} _ {0} + \\epsilon \\cdot \\mathbf {j} _ {i}\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 885, + 903, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10851", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{j}_i$ is vector of zeros with a 1 at the i-th position and $\\epsilon$ is the perturbation strength which we empirically set to 0.8. We obtain a final weight vector by normalizing:", + "bbox": [ + 89, + 90, + 482, + 137 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} = \\frac {w _ {i}}{\\sum_ {0} ^ {6 4} w _ {i}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 236, + 146, + 482, + 180 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For an evaluation and discussion of the proposed weighting scheme, please see SupMat.", + "bbox": [ + 89, + 188, + 482, + 218 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition, we also incorporate a weighting term in order to equalize the error contribution across noise levels by taking the approach of EDM2 [15], which treats denoising as a form of multi-task learning and lets the network predict a log-variance of the uncertainty $u(\\sigma)$ for a certain noise level. Combining the per-channel weighting with the per-noise level weighting we obtain our final formulation for the diffusion loss as an expectation over noise levels and spatial dimensions:", + "bbox": [ + 89, + 219, + 483, + 354 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, u\\right) = \\mathbb {E} _ {\\mathbf {y}, \\mathbf {n}, \\sigma} \\left[ \\frac {\\mathbf {w}}{e ^ {u (\\sigma)}} \\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, \\mathbf {y}, \\mathbf {n}, \\sigma\\right) + u (\\sigma) \\right]. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 364, + 482, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RGB conditioning. Previous approaches have primarily relied on 2D orientation maps [31, 55] extracted using Gabor filters in order to align the generated strands with the image. However, orientation maps cannot infer the hair growth direction and tend to be noisy for heavily occluded hairstyles. In our work, we forego the need to compute orientation maps and instead condition our diffusion network using robust DINOv2 [30] features extracted from the image. Specifically, we use the pre-trained DINOv2-large model to encode the RGB image into a feature map $\\mathcal{F}_{map} \\in \\mathbb{R}^{55 \\times 55 \\times 1024}$ and a global CLS token $\\mathcal{F}_{cls} \\in \\mathbb{R}^{1024}$ . Additionally, our rendered images are sufficiently realistic such that the network trained only on synthetic data, can generalize to in-the-wild images.", + "bbox": [ + 89, + 407, + 482, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since the scalp texture and the RGB image are not spatially aligned, we add cross-attention layers before each downsampling layer of the denoiser and let the network learn which regions of the feature map $\\mathcal{F}_{map}$ it should attend to. The CLS token $\\mathcal{F}_{cls}$ is used to globally condition the network similar to the time condition $\\sigma$ as described in HDiT [6].", + "bbox": [ + 89, + 619, + 482, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, in order to use the same network both conditionally and unconditionally, we train the denoiser using Classifier-Free Guidance [10] by randomly dropping the conditioning signal with $10\\%$ probability (Fig. 8).", + "bbox": [ + 89, + 724, + 482, + 786 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For experiments on conditioning using DINOv2 features vs orientation maps, please refer to SupMat.", + "bbox": [ + 89, + 786, + 482, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 829, + 222, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate DiffLocks using both synthetic data and in-the-wild images. We also perform ablation studies to assess the importance of the different components of our method", + "bbox": [ + 89, + 854, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dd0e895f013d52904ef1681656a41255e8646fa764a8102ca0b7718a45f4e257.jpg", + "image_caption": [ + "(a) Synthetic Image" + ], + "image_footnote": [], + "bbox": [ + 526, + 89, + 614, + 157 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/64e3f621fa06331ec53edb1ac3461d19abc0072a32e3f182e29112dd5c79065b.jpg", + "image_caption": [ + "(b) Scalp density" + ], + "image_footnote": [], + "bbox": [ + 616, + 89, + 707, + 157 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/02d8c2cd6ac17284d3fcb7dcd1f579e71dc8df34866411f968e5b8f06012677e.jpg", + "image_caption": [ + "(c) Raw scalp texture" + ], + "image_footnote": [], + "bbox": [ + 709, + 89, + 800, + 157 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8fc377919fb412952e6cf3cb37189fe35f84b60da667958e87a1226f083f42bf.jpg", + "image_caption": [ + "(d) Interpolated texture" + ], + "image_footnote": [], + "bbox": [ + 800, + 89, + 890, + 157 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3664be4a609d78747f38714d5e88fa0f19d6e743f468cdfc4db6cce08f81b2b7.jpg", + "image_caption": [ + "Figure 5. Scalp interpolation. Embedding each strand onto a the scalp texture can leave gaps where no strand is present. In order to enable probabilistic sampling of strands, we interpolate the sparse strand embeddings to achieve a smooth scalp texture that can be sampled at any position according to the density.", + "RGB Input", + "Figure 6. Rendering/Simulation. Our generated hair can be directly imported into Blender or Unreal Engine as an Alembic file. In Unreal Engine, the hair can be rendered in real-time with high-quality physics simulation (see Supplemental Video)." + ], + "image_footnote": [], + "bbox": [ + 514, + 273, + 591, + 344 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b7dcbe045408ecd716fca43d09329ac96c5fa75c7925186d88e2a5f5368eafd7.jpg", + "image_caption": [ + "Blender offline(40 s)" + ], + "image_footnote": [], + "bbox": [ + 599, + 280, + 678, + 344 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fc2b9c8e9139e9e36c9dc6b36281fbafd0bac781693a6a2ee6bc72f1ca280f23.jpg", + "image_caption": [ + "Unreal Engine real-time(16 ms)" + ], + "image_footnote": [], + "bbox": [ + 681, + 279, + 831, + 344 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d5d8eef7de70f5e02ce1b6b75651b29ca3f1ee2155c27bf897dc86346a424681.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 831, + 279, + 892, + 344 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(Sec. 4.4). For implementation details and additional experiments, please refer to SupMat.", + "bbox": [ + 511, + 460, + 903, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method with Hairstep [55] and NeuralHDHair [48] as they are both state-of-the-art methods for reconstructing 3D hair from a single image. We also compare with the conditional 3D hair generation method of HAAR [42] although it is mainly designed for text-to-hair.", + "bbox": [ + 511, + 489, + 905, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Qualitative", + "text_level": 1, + "bbox": [ + 511, + 575, + 635, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The qualitative comparison with Hairstep, NeuralHDHair and HAAR is shown in Fig. 7. NeuralHDHair and HairStep tend to create hair that matches the overall shape from the image but that lacks fine-grained detail and curls, reconstructing strands that run parallel to each other. Furthermore, they cannot correctly reconstruct balding and afrolike hairstyles. In contrast, our method produces high-quality and realistic hair strands for a wide variety of images. Despite being a method designed for text-to-hair, we also compare with HAAR since they have released a pipeline for image-to-hairstyle by leveraging LLaVA to obtain text descriptions. We observe that their method often cannot match the hairstyle in the image.", + "bbox": [ + 511, + 597, + 906, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.Quantitative", + "text_level": 1, + "bbox": [ + 511, + 801, + 645, + 818 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative evaluation is performed using the synthetic dataset of Yuksel et al. [52] from which we use two medium-length hairstyles: straight and curly. To render RGB images of the dataset we use Unreal Engine instead of Blender in order to remove possible bias our method might", + "bbox": [ + 511, + 825, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10852", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b16c3056d429e98e19eb69f5c70e040e7cd99c4e1f1639f6b96e2b0a087d5ced.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison. We compare our method with HairStep [55], NeuralHDHair [48] and HAAR [42] on real images. Our method can robustly reconstruct a large variety of hairstyles with significantly more detail than previous approaches. We note that HAAR was designed to reconstruct hair given text captions, so we use LLaVA [19] to obtain text description of hair, followed by applying their text-to-3D method." + ], + "image_footnote": [], + "bbox": [ + 171, + 88, + 823, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "have towards the path-traced images. The accuracy and precision results are reported in Tab. 1.", + "bbox": [ + 89, + 731, + 482, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Additionally, we note that current synthetic datasets do not contain enough variety of hairstyles and propose a new synthetic dataset containing 10 representative hairstyles created by our Blender pipeline. We also evaluate our method and the baselines on this dataset and report the results in Tab. 2 although we recognize that our method has an advantage because it is trained on data created by the same Blender pipeline.", + "bbox": [ + 89, + 762, + 482, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Across the two datasets we observe that our method can", + "bbox": [ + 109, + 885, + 482, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "reconstruct the backside of the hair more faithfully, reinforcing the importance of varied data from which to learn a powerful prior. For the backside reconstruction, robustness to viewpoint, and more visualizations see SupMat.", + "bbox": [ + 511, + 731, + 906, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Runtime Performance", + "text_level": 1, + "bbox": [ + 511, + 801, + 720, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate the runtime performance in Tab. 3 by first dividing the hair reconstruction pipeline into three parts, 1) extraction of RGB features (DINOv2 features or in the case of the baseline methods: orientation maps, hair segmentation, etc.), 2) generation of the hair model, which in our", + "bbox": [ + 511, + 824, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10853", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4c3afe6db211e070478ec85f792ab024b144c3494b7b51d10e82d1f45c570045.jpg", + "image_caption": [ + "Figure 8. Unconditional generation. We train our diffusion model with Classifier-free Guidance [10] so that the same model can be evaluated both conditionally and unconditionally. Here we show unconditionally generated results where we observe a range of high-quality and diverse hairstyles." + ], + "image_footnote": [], + "bbox": [ + 101, + 90, + 477, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e66f72d74bc1b1fe65edbd64de74d4cb375b0ecec0b2b753accbc4d991c5c775.jpg", + "image_caption": [ + "RGB Input", + "Model:", + "Condition:", + "Figure 9. Ablation of conditioning signal and model architecture. Removing the local conditioning in the form of feature map $\\mathcal{F}_{map}$ and relying only on the global CLS token severely affects the ability to reconstruct hair. Also generating scalp textures using a VAE yields overly smooth reconstructions. The combination of diffusion and local+global conditioning captures the most detail." + ], + "image_footnote": [], + "bbox": [ + 96, + 367, + 171, + 431 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/44b79440f0ea3544fce4b83f503eaf3d011f31c18b67be64c13e69fd33f18572.jpg", + "image_caption": [ + "VAE", + "Global+Local" + ], + "image_footnote": [], + "bbox": [ + 240, + 364, + 312, + 431 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d6fa5e34fcdb03a427c5ec0e40e2ce310b699bc0c324abf554c4ca5384eb1d6b.jpg", + "image_caption": [ + "Diffusion", + "Global" + ], + "image_footnote": [], + "bbox": [ + 320, + 369, + 387, + 431 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0f371eac801f9e385cc859fc44d24e5758ca52956503211f7445db9ded8afd5c.jpg", + "image_caption": [ + "Diffusion", + "Global+Local" + ], + "image_footnote": [], + "bbox": [ + 398, + 361, + 470, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "case is the scalp texture while baseline methods create a 3D orientation field, 3) strand generation, which is the final step to either decode or grow the strands. All results are obtained on an NVIDIA H100 GPU. We observe that our method is overall the fastest as we do not need pre- or post-processing steps like head fitting, hair segmentation or hair growth and refinement. Note that our generated hair can be directly imported into Unreal Engine and rendered in real-time (60FPS) as shown in Fig. 6; see Supplemental Video.", + "bbox": [ + 89, + 578, + 483, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 741, + 243, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We perform an ablation study on the architecture and the importance of the conditioning signal in Fig. 9. Changing the scalp generation model to a VAE model similar to GroomGen [56] causes the hair to be overly smooth and lack local detail. Our proposed diffusion model conditioned with global and local features in the form of $\\mathcal{F}_{map}$ and $\\mathcal{F}_{cls}$ manages to capture the most detail. However, the local feature map is crucial and removing it causes the generated hair to deviate significantly from the input image.", + "bbox": [ + 89, + 763, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/178a60dc34851ac8cd5f8c595748d7bede468727b73b65a1ecd62e03e99b44db.jpg", + "table_caption": [ + "Thresholds: mm / degrees" + ], + "table_footnote": [], + "table_body": "
    Method2/203/304/402/203/304/402/203/304/40
    Precision(↑)Recall(↑)F-score(↑)
    NeuralHDHair [48]47.9165.0773.7631.5951.1064.6338.0057.1268.73
    HairStep[55]40.8855.9964.0732.1644.9653.1535.5049.0657.20
    Ours43.6068.3081.7934.9758.2771.7938.3562.4176.20
    ", + "bbox": [ + 517, + 97, + 903, + 143 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1d2dd0e876e5704971af68c0ed019a3f277770c12ac7843f41fab5dcd0dd93a3.jpg", + "table_caption": [ + "Table 1. Quantitative comparison with [48, 55] on [52]. It includes straight and curly hairstyles, please refer to the SupMat for more visualizations." + ], + "table_footnote": [], + "table_body": "
    MethodThresholds: mm / degrees
    2/203/304/402/203/304/402/203/304/40
    Precision(↑)Recall(↑)F-score(↑)
    NeuralHDHair [48]18.6536.2149.4619.2637.3351.6018.5535.7649.30
    HairStep[55]20.2235.5445.7320.8038.5352.8219.4234.3845.48
    Ours63.0684.1692.7857.9179.7189.8160.1381.6891.17
    ", + "bbox": [ + 517, + 191, + 903, + 247 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/500b4ae1ff73edf37dd2871fef74fdec193142117bfb8f33a6b4531f6ffa484d.jpg", + "table_caption": [ + "Table 2. Quantitative comparison with [48, 55] on the DiffLocks evaluation set. Our results show substantial improvement over the baseline, particularly when reconstructing the backside of the hair due to our model's ability to learn a powerful prior over hairstyles." + ], + "table_footnote": [], + "table_body": "
    HairStepNeuralHDHairOurs
    RGB features (↓)3.174.860.10
    hair model (↓)0.454.991.83
    strand creation (↓)49.788.470.40
    total (s) (↓)53.4018.322.33
    ", + "bbox": [ + 558, + 316, + 857, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Timing. Comparison of the time in seconds needed for each part of the hair creation pipeline.", + "bbox": [ + 511, + 372, + 906, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations and future work", + "text_level": 1, + "bbox": [ + 513, + 431, + 777, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Despite the large amount of data, there are still gaps in the synthetic dataset; e.g. it lacks hairstyles with braids, accessories, ponytails, and buns. However, we believe that further improvements to the pipeline will allow such details to be created. Furthermore, the generation pipeline can also be easily extended to beards and eyebrows.", + "bbox": [ + 511, + 460, + 905, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also note that DiffLocks prioritizes local hair details over perfect image alignment. However, for many tasks, generation or reconstruction is just the first step. When hair is animated with physics, the precise initial strand alignment is not critical, as the dynamic nature of hair makes the initial configuration transient.", + "bbox": [ + 511, + 553, + 905, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 666, + 633, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed a novel approach for generating 3D hair strands from a single image by first creating the largest dataset to date of synthetic hair paired with RGB images, and then by proposing an image-conditioned diffusion model based on scalp textures. Our method can create highly intricate 3D strands, surpassing previous methods and without requiring heuristic-based methods to increase the realism.", + "bbox": [ + 511, + 694, + 905, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments and Disclosures. We give thanks to Nathan Bajandas for all the Unreal images and videos. While MJB is a co-founder and Chief Scientist at Meshcapade, his research in this project was performed solely at, and funded solely by, the Max Planck Society.", + "bbox": [ + 511, + 816, + 905, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10854", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mengei Chai, Changxi Zheng, and Kun Zhou. A reduced model for interactive hairs. 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ACM Transactions on Graphics (TOG), 37(6):1-10, 2018. 1", + "[55] Yujian Zheng, Zirong Jin, Moran Li, Haibin Huang, Chongyang Ma, Shuguang Cui, and Xiaoguang Han. Hirstep: Transfer synthetic to real using strand and depth maps for single-view 3d hair modeling. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12726-12735, 2023. 1, 6, 7, 8", + "[56] Yuxiao Zhou, Menglei Chai, Alessandro Pepe, Markus Gross, and Thabo Beeler. Groomen: A high-quality generative hair model using hierarchical latent representations. ACM Transactions on Graphics (TOG), 42(6):1-16, 2023. 1, 2, 3, 5, 8", + "[57] Yuxiao Zhou, Menglei Chai, Daoye Wang, Sebastian Winberg, Erroll Wood, Kripasindhu Sarkar, Markus Gross, and Thabo Beeler. Groomcap: High-fidelity prior-free hair capture. arXiv preprint arXiv:2409.00831, 2024. 1, 2" + ], + "bbox": [ + 91, + 92, + 480, + 486 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10857", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_model.json b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0cad54d6104386f49d5a87befdafb23e494f0d49 --- /dev/null +++ b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_model.json @@ -0,0 +1,2576 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.277, + 0.131, + 0.723, + 0.177 + ], + "angle": 0, + "content": "DiffLocks: Generating 3D Hair from a Single Image using Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.203, + 0.861, + 0.222 + ], + "angle": 0, + "content": "Radu Alexandru Rosu\\(^{1,\\ast}\\) Keyu Wu\\(^{2,\\ast,\\dagger}\\) Yao Feng\\(^{1,3}\\) Youyi Zheng\\(^{2}\\) Michael J. Black\\(^{4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.223, + 0.858, + 0.24 + ], + "angle": 0, + "content": "\\(^{1}\\)Meshcapade \\(^{2}\\)Zhejiang University \\(^{3}\\)Stanford University \\(^{4}\\)Max Planck Institute for Intelligent Systems" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.274, + 0.327, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.306, + 0.486, + 0.775 + ], + "angle": 0, + "content": "We address the task of generating 3D hair geometry from a single image, which is challenging due to the diversity of hairstyles and the lack of paired image-to-3D hair data. Previous methods are primarily trained on synthetic data and cope with the limited amount of such data by using low-dimensional intermediate representations, such as guide strands and scalp-level embeddings, that require post-processing to decode, upsample, and add realism. These approaches fail to reconstruct detailed hair, struggle with curly hair, or are limited to handling only a few hairstyles. To overcome these limitations, we propose DiffLocks, a novel framework that enables detailed reconstruction of a wide variety of hairstyles directly from a single image. First, we address the lack of 3D hair data by automating the creation of the largest synthetic hair dataset to date, containing 40K hairstyles. Second, we leverage the synthetic hair dataset to learn an image-conditioned diffusion-transformer model that generates accurate 3D strands from a single frontal image. By using a pretrained image backbone, our method generalizes to in-the-wild images despite being trained only on synthetic data. Our diffusion model predicts a scalp texture map in which any point in the map contains the latent code for an individual hair strand. These codes are directly decoded to 3D strands without post-processing techniques. Representing individual strands, instead of guide strands, enables the transformer to model the detailed spatial structure of complex hairstyles. With this, DiffLocks can recover highly curled hair, like afro hairstyles, from a single image for the first time. Data and code is available at https://radualexandru.github.io/difflocks/." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.806, + 0.222, + 0.822 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.832, + 0.484, + 0.864 + ], + "angle": 0, + "content": "Realistic 3D hair is a crucial component of digital humans [1, 2, 8, 12, 18, 38, 45], which have wide applications in" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.274, + 0.643, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.389, + 0.646, + 0.401 + ], + "angle": 0, + "content": "Synthetic hair dataset" + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.272, + 0.758, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.389, + 0.741, + 0.401 + ], + "angle": 0, + "content": "Real image" + }, + { + "type": "image", + "bbox": [ + 0.772, + 0.272, + 0.897, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.807, + 0.389, + 0.855, + 0.4 + ], + "angle": 0, + "content": "3D hair" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.412, + 0.907, + 0.468 + ], + "angle": 0, + "content": "Figure 1. Given a single RGB image DiffLocks generates accurate 3D strands using a diffusion model. The model is trained on a novel synthetic hair dataset containing RGB images and corresponding 3D strands." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.501, + 0.907, + 0.577 + ], + "angle": 0, + "content": "games, media and entertainment. Accurate hair representation greatly enhances the character's realism and overall visual quality. Unfortunately, both generating realistic hair and reconstructing it from an image are challenging due to the complex 3D geometry and the wide variety of hairstyles." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.909, + 0.687 + ], + "angle": 0, + "content": "Since the release of the first 3D synthetic hair dataset [11], numerous methods for hair reconstruction have been proposed. Multi-view capture methods [17, 29, 31, 54, 57] and video-based approaches [24, 41, 49] are able to reconstruct high-fidelity 3D hair but are time-intensive and challenging to deploy due to their reliance on expensive capture equipment or strict capture conditions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.911, + 0.903 + ], + "angle": 0, + "content": "In contrast, single-view methods [3, 37, 48, 51, 55], which reconstruct 3D hair from a single image, are faster, more accessible, and user-friendly. These methods, however, often produce low-detail hair and handle only a restricted range of hairstyles. Furthermore, these methods struggle to handle male-pattern baldness and very curly hair such as afro-like hairstyles, which have a complex geometric structure (see [47]). Previous methods suffer from a lack of diverse and comprehensive hairstyle training datasets. To increase training set diversity, GroomGen [56], HAAR [42] and Fake It Till You Make It [46] use artist-created hairstyles together with data augmentation techniques to train their methods. However, their datasets are not released, do not have paired RGB images, or the creation pro" + }, + { + "type": "page_footnote", + "bbox": [ + 0.108, + 0.876, + 0.207, + 0.887 + ], + "angle": 0, + "content": "*Joint first author" + }, + { + "type": "page_footnote", + "bbox": [ + 0.108, + 0.888, + 0.366, + 0.9 + ], + "angle": 0, + "content": "†Work done during an internship at Meshcapade" + }, + { + "type": "list", + "bbox": [ + 0.108, + 0.876, + 0.366, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10847" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.348, + 0.106 + ], + "angle": 0, + "content": "cess requires significant manual effort." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.11, + 0.484, + 0.351 + ], + "angle": 0, + "content": "To cope with limited training data, previous approaches rely on several intermediate representations to simplify the problem. Most prior methods rely on oriented filters to capture the structure of hair in images. They also do not model hair strands directly but, instead, use a smaller number of guide strands and then upsample these to generate a hairstyle. Additionally, several methods use variational autoencoding to compress the guide strands across the scalp into a low-dimensional representation. All of these approaches are designed to cope with limtied training data but have two effects: (1) they limit the ability to model the complex spatial relationships between individual strands, and (2) they limit realism by working with low-dimensional representations. Effectively, they work in a compressed low-dimensional space and then need to upsample the results and post-process them to increase realism." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.355, + 0.484, + 0.581 + ], + "angle": 0, + "content": "We take a different approach and focus on creating a sufficient amount of training data that we can remove the simplifying assumptions of previous methods. To that end, we present a novel 3D synthetic hair dataset consisting of 40K samples covering a wide variety of hairstyles; see Fig. 3. Each sample consists of 3D hair strands and a realistic RGB image rendered in Blender through path-tracing. We achieve this by automating the creation of the data using a variety of artist-inspired techniques. Traditional approaches are designed to create a single hairstyle using a small geometry node network tailored-made for that hairstyle. In contrast, we design a large and very general geometry node network in Blender that allows us to automatically create a large number of realistic hairstyles by changing the different parameters." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We then leverage our dataset to train a novel hair diffusion framework, called DiffLocks, that is optionally conditioned on single RGB image in order to create highly detailed 3D strands; see Fig. 1. Specifically, we use Hourglass Diffusion Transformers (HDiT) [6] as a diffusion architecture and exploit features from a pretrained DINOv2 [30] model as a conditioning input to guide and control the generated results; see Fig. 2. The DINOv2 features are richer than the oriented filters used in many previous methods. Note that we directly regress the latent code for individual hair strands (instead of guide strands) enabling the transformer to learn detailed spatial relationships between strands across the scalp. With sufficient training data, there is no longer a need to first embed the hairstyle in a low-D scalp representation. We also model a density map that defines the probability of a strand being generated at each location on the scalp. All of these changes lead to increased realism, particularly for curly and balding hairstyles. Finally, our strand-based hair can be directly used in real-time game engines like Unreal Engine (Fig. 6) without additional heuristics to densify the hair or add fine-grained detail." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.257 + ], + "angle": 0, + "content": "A key takeaway from our work is that, with sufficient training data, many of the key components of previous methods are no longer needed. For example, in contrast to the \\(32 \\times 32\\) scalp map used by HAAR, our diffusion model predicts a scalp texture of size \\(256 \\times 256\\) (each pixel containing a latent code for a single strand) from which DiffLocks directly decodes 3D strands. No post-processing is needed, such as hair upsampling or the addition of random noise (cf. [56]). The dataset already contains realistic hairstyles with flyaway strands, so the diffusion model learns to create them." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.26, + 0.8, + 0.273 + ], + "angle": 0, + "content": "In summary, our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.276, + 0.905, + 0.336 + ], + "angle": 0, + "content": "- a novel 3D hair dataset containing 40K diverse and realistic 3D hairstyles with corresponding RGB images. We make the dataset public in order to support future research in hair modeling and synthesis," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.337, + 0.905, + 0.381 + ], + "angle": 0, + "content": "- an improved scalp representation that facilitates the reconstruction of hair styles with different hair density (bald spots, male pattern baldness, etc.)," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.381, + 0.905, + 0.486 + ], + "angle": 0, + "content": "- a novel conditional scalp diffusion framework for robustly generating 3D hair directly from a single RGB image, bypassing a 2D orientation map. This framework can effectively create a variety of challenging hairstyles, while achieving the state-of-the-art performance and enable, for the first time, reconstruction of Afro-like and bald hairstyles. The model will be available for research." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.276, + 0.905, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.505, + 0.663, + 0.521 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.532, + 0.907, + 0.865 + ], + "angle": 0, + "content": "3D Hair Reconstruction. The pioneering hair reconstruction work of Paris et al. [31] set the stage for numerous multi-view-based hair reconstruction methods. Since then, various methods [17, 25, 26, 29, 57] reconstruct the 3D geometric features of hair constrained by a 2D orientation map. In many cases this requires specialized hardware or multicamera rigs. In contrast, monocular video based methods [24, 41, 44, 49] sacrifice some accuracy to avoid expensive and specialized equipment. While achieving impressive results, such methods still require carefully captured data. To relax the capture conditions, single-view-based methods [3, 37, 48, 51, 53, 53] employ deep neural networks to infer volumetric fields by exploiting data priors learned from 3D synthetic datasets. Such methods enable rapid 3D hair reconstruction but typically generate low fidelity hair and can handle only a limited range of hairstyles due to the significant lack of diversity in existing 3D hair datasets. Similar to these methods, our approach also reconstructs hair from a single image. However, our work focuses on fast and robust reconstruction of diverse hairstyles, including challenging types such as balding and tightly curled (afro-like) styles; such hairstyles have received relatively little attention." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.909, + 0.903 + ], + "angle": 0, + "content": "3D Hair Generation. In addition to hair reconstruction, hair generation is another challenge, which, if solved, could" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "10848" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.09, + 0.892, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.24, + 0.908, + 0.298 + ], + "angle": 0, + "content": "Figure 2. Method. Given a single RGB image, we use a pretrained DINOv2 model to extract local and global features, which are used to guide a scalp diffusion model. The scalp diffusion model denoises a density map and a scalp texture containing latent codes for strand geometry. Finally, we probabilistically sample texels from the scalp texture and decode the latent code \\(\\mathbf{z}\\) into strands of 256 points. Decoding in parallel 100K strands yields the final hairstyle." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.318, + 0.486, + 0.668 + ], + "angle": 0, + "content": "provide synthetic data for learning high-quality hair reconstruction. Ren et al. [34] propose a heuristic example-based hair generation method that is significantly limited by the reference hair models. Saito et al. [37] encode a 3D hair dataset with a Variational autoencoder (VAE), enabling them to generate plausible yet overly smooth hairstyles. To achieve high-quality and diverse hairstyles, Perm [9] leverages existing public 3D datasets, disentangling the global shape and local details of hair strands. Despite progress, the scale and diversity of synthetic 3D hair datasets is still far from what is needed. GroomGen [56] and HAAR [42] incorporate parametrized variations based on high-quality hairstyles crafted by artists, further enhancing the diversity of 3D hair datasets. They also train generative models to produce 3D hairstyles from noisy inputs or text prompts. Recently, Curly-Cue [47] focuses on the principles behind curly, afro-style, hair and provides tools for animators to create realistic hairstyles. In our work, we propose a low-cost synthetic 3D hair generation pipeline and use it to construct a new dataset that is more diverse than previous ones, containing 40K 3D synthetic hairstyles. Additionally, we use this dataset to train a generative hair model that is conditioned on a single input image." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.487, + 0.902 + ], + "angle": 0, + "content": "Image-To-3D via Diffusion Models. Early work on neural reconstruction of 3D objects from images [7, 28, 50] distills information from pretrained 2D diffusion models, such as Stable Diffusion [35], using techniques like Score Distillation Sampling (SDS) [33]. However, these pretrained models lack the multi-view information essential for accurate 3D reconstruction. To address this, later approaches [20, 21, 40] train custom 2D diffusion models to generate multi-view images from a given input, enabling more accurate 3D object reconstruction by integrating this multi-view data [13, 23]. While effective, this approach can be time-intensive due to the sampling and reconstruction processes, which has led to an alternative line of research focused on training diffusion models to generate 3D representations directly, such as meshes [22] or triplane repre" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.318, + 0.909, + 0.41 + ], + "angle": 0, + "content": "sentations [4]. However, these methods often demand significant computational resources for 3D processing. In contrast, our method produces a 2D representation that contains 3D hair information, enabling direct decoding into 3D hair without the need for extensive multi-view generation or resource-intensive training of 3D diffusion models." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.421, + 0.606, + 0.436 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.446, + 0.909, + 0.584 + ], + "angle": 0, + "content": "In this section, we present our pipeline for 3D hair reconstruction from a single image, consisting of three key stages: 1) A data generation pipeline using Blender's geometry nodes to create a large, diverse, image-3D paired synthetic hair dataset (Sec. 3.1); 2) Parameterization of hair strands and hairstyles into a canonical scalp space to obtain scalp textures (Sec. 3.2); And 3) training a conditional diffusion model, DiffLocks, using the generated synthetic images and the scalp textures as shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.59, + 0.681, + 0.604 + ], + "angle": 0, + "content": "3.1. Data Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.611, + 0.909, + 0.748 + ], + "angle": 0, + "content": "A key bottleneck in the field of 3D hair reconstruction is the limited availability of public datasets, with only 343 hairstyles for USC-HairSalon [11] and 10 for CT2Hair [39]. Additionally, these datasets lack corresponding 2D images, which limits their usability. Thus, here we propose a novel data generation pipeline, which uses Blender geometry nodes to add variation to a small set of manually defined guide strands as shown in Fig. 4. Next, we will describe the main steps of the pipeline." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.911, + 0.903 + ], + "angle": 0, + "content": "Scalp creation. The first step in creating the new dataset is defining a scalp mesh onto which to build the hairstyles. Due to its wide applicability in the human-reconstruction field, we use the SMPL-X model [32] to define our scalp. We create a SMPL-X neutral body with mean body shape from which we manually select the vertices corresponding to the scalp and extract a mesh of 513 vertices as seen in Fig. 2. The scalp mesh is then UV-unwrapped into a single chart using an As-Rigid-As-Possible (ARAP) parametrization [43] in order to minimize distortions. This" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10849" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.088, + 0.226, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.089, + 0.36, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.089, + 0.496, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.089, + 0.631, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.089, + 0.765, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.089, + 0.901, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.196, + 0.908, + 0.224 + ], + "angle": 0, + "content": "Figure 3. Synthetic data. Sample RGB images from our synthetic hair dataset. Each sample from the dataset contains an image at \\(768 \\times 768\\) resolution together with the corresponding 3D strand geometry of \\(\\approx 100\\mathrm{K}\\) strands." + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.251, + 0.473, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.397, + 0.483, + 0.452 + ], + "angle": 0, + "content": "Figure 4. Base hairstyles. Starting from a coarse set of guide strands, our Blender pipeline is able to generate a wide variety of hairstyles, covering different lengths, curliness and density patterns. Best viewed zoomed in." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.481, + 0.483, + 0.527 + ], + "angle": 0, + "content": "operation is done only once and need not be repeated for each subject since they all share the same SMPL-X body topology." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.533, + 0.483, + 0.683 + ], + "angle": 0, + "content": "Base hairstyle creation. The scalp mesh is imported into Blender and a series of hairstyles is manually created in the form of coarsely defined guide strands (Fig. 4). The base hairstyles define a starting point for the randomization process and therefore do not need to contain fine details, rather defining just the overall shape and direction of the hair. We manually create 75 base hairstyles, each represented by \\(\\approx 50\\) strands. We note that this is not a labour intensive process, as each base hairstyle takes only a few minutes to create." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.69, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Randomization pipeline. The guide strands are passed through a series of transformations defined as geometry nodes in Blender that gradually add more detail to the hair. The guide strands are first interpolated to 100K strands, after which clumping, curling and noise are applied. These operations are repeated multiple times with various intensities. Special attention must be given to prevent the hair from penetrating the scalp or intersecting with the body for which we apply shrinkwrap modifiers at various stages in the pipeline. In total the pipeline consists of 58 geometry nodes that transform the hair together with 349 auxiliary nodes that help feed parameters into the main nodes. We also define a hair BSDF using the Chiang model [5] for the strands material. Lastly we apply physics simulation to" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.251, + 0.906, + 0.327 + ], + "angle": 0, + "content": "the strands using Blender's cloth simulation and randomize wind direction and gravity strength. A total of 110 parameters govern the whole Blender generation pipeline (geometry+material) and we select them at random with minimum and maximum ranges chosen empirically." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.331, + 0.906, + 0.542 + ], + "angle": 0, + "content": "Scene setup. In order to render realistic images, it is crucial to match the lighting of real scenes. For this, we use 255 HDRIs from Poly Haven1 and randomize their exposure and azimuthal angle. Additionally, we randomly select albedo, normal and roughness textures for the bodies from a library of artist-created SMPL-X textures. Furthermore, we also randomly change the face expression coefficients within the range \\([-1, 1]\\). We keep the jaw closed since we observed it can cause issues with strands physics. To train our network for robustness to different camera parameters, we also randomize camera position (maintaining the look-at direction towards the head) and focal length in the range \\(40\\mathrm{mm}\\) to \\(150\\mathrm{mm}\\). For a study on network robustness to camera parameters please refer to the SupMat." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.545, + 0.906, + 0.666 + ], + "angle": 0, + "content": "Full dataset. The full dataset contains 40K samples each containing 3D strands with \\(\\approx 100\\mathrm{K}\\) strands and a corresponding RGB image rendered through path tracing at \\(768 \\times 768\\) resolution. We additionally save a density map that defines the probability of a strand being generated at each texel of the scalp as shown in Fig. 5. The density map is especially useful for modelling hairstyles with balding patterns." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.675, + 0.759, + 0.691 + ], + "angle": 0, + "content": "3.2. Hairstyle Parameterization" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.697, + 0.906, + 0.833 + ], + "angle": 0, + "content": "Strand Parameterization. Formally, we represent a 3D strand as a set of \\(L\\) 3D points \\(\\mathbf{S} = \\{\\mathbf{p}_1,\\mathbf{p}_2,\\dots ,\\mathbf{p}_L\\}\\), where \\(L = 256\\). A full hairstyle consists of a set of \\(\\approx 100\\mathrm{K}\\) strands \\(\\mathbf{H} = \\{\\mathbf{S}_j\\}_{0}^{100\\mathrm{K}}\\). Similar to Neural Strands [36], we train a strand VAE to compress individual strands into a compact latent code \\(\\mathbf{z}\\in \\mathbb{R}^{64}\\). The encoder of the VAE denoted by \\(\\mathcal{E}()\\) is modeled as a series of 1D convolutions and the decoder denoted by \\(\\mathcal{G}()\\) is a modulated SIREN [27] that maps the latent code \\(\\mathbf{z}\\) back to a series of 3D points \\(\\mathbf{S}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.833, + 0.906, + 0.879 + ], + "angle": 0, + "content": "In addition to the position and direction loss proposed by Neural Strands [36], we incorporate a curvature loss \\(\\mathcal{L}_{\\mathrm{cur}}\\). This is motivated by the observation that, for highly coiled" + }, + { + "type": "page_footnote", + "bbox": [ + 0.532, + 0.887, + 0.688, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)https://polyhaven.com/hdris" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10850" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.484, + 0.271 + ], + "angle": 0, + "content": "hair, it is more perceptually impactful to match the curvature of the strand rather than matching the position of every point along the strand (i.e., as long as the strand looks curvy, it is acceptable to commit errors in per-point position). For an evaluation of this observation please refer to the SupMat. We define the local curvature as the instantaneous change in direction: \\(\\kappa_{i} = \\mathbf{d}_{i + 1} - \\mathbf{d}_{i}\\) where the direction is defined as the change in position: \\(\\mathbf{d}_i = \\mathbf{p}_{i + 1} - \\mathbf{p}_i\\). Therefore, the new curvature loss is defined as the L1 distance between the ground-truth and the prediction: \\(\\mathcal{L}_{\\mathrm{cur}} = \\sum_{0}^{L}|\\kappa_{i} - \\tilde{\\kappa}_{i}|\\), where \\(\\hat{\\kappa}_i\\) is the curvature of the predicted strand." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.273, + 0.484, + 0.334 + ], + "angle": 0, + "content": "The final training loss of our strands VAE is a weighted combination of a data term consisting of positional, directional and curvature losses together with a KL regularization term:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.339, + 0.483, + 0.379 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {d a t a}} = \\sum_ {0} ^ {L} | \\mathbf {p} _ {i} - \\tilde {\\mathbf {p}} _ {i} | + \\lambda_ {1} | \\mathbf {d} _ {i} - \\tilde {\\mathbf {d}} _ {i} | + \\lambda_ {2} | \\boldsymbol {\\kappa} _ {i} - \\tilde {\\boldsymbol {\\kappa}} _ {i} | \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.109, + 0.383, + 0.483, + 0.4 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {V A E}} = \\mathcal {L} _ {\\mathrm {d a t a}} + \\lambda_ {\\mathrm {K L}} \\mathcal {L} _ {\\mathrm {K L}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.407, + 0.484, + 0.438 + ], + "angle": 0, + "content": "For more details on the hyperparameters please refer to the SupMat." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.455, + 0.484, + 0.68 + ], + "angle": 0, + "content": "Neural Scalp Texture. Each 3D hairstyle generated from the Blender pipeline is parametrized onto the scalp surface using a regular 2D texture. Specifically, each strand \\(\\mathbf{S}\\) is encoded to a latent code \\(\\mathbf{z}\\) by the strand encoder \\(\\mathbf{z} = \\mathcal{E}(\\mathbf{S})\\) and directly assigned to the texel corresponding to the root of the strand. If two strands are so close together that they are assigned the same texel on the scalp, one of them is chosen at random. This produces a raw scalp texture \\(\\mathbf{T}_{\\text{raw}} \\in \\mathbb{R}^{256 \\times 256 \\times 64}\\), as shown in Fig. 5c where each texel contains a latent strand code. Since not all regions of the scalp have an equal hair density, we introduce a density map \\(\\mathbf{D} \\in \\mathbb{R}^{256 \\times 256 \\times 1}\\) with values in the range [0, 1] that defines the probability of a strand being present at each texel. For more discussion on the properties of the density map please refer to the SupMat." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.681, + 0.483, + 0.831 + ], + "angle": 0, + "content": "The aforementioned creation of the scalp texture can create sparse regions with no latent codes since not every texel will correspond to a strand. This sparsity is particularly evident for hairstyles with balding patterns and can cause issues when decoding the texture back to 3D since sampling a texel with no assigned latent code would yield undefined strand geometry. To avoid this issue, we interpolate the sparsely assigned latent codes by using a push-pull algorithm [16] that ensures that every texel on the scalp has a valid strand latent code as shown in Fig. 5d." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.832, + 0.484, + 0.877 + ], + "angle": 0, + "content": "With the interpolated scalp texture \\(\\mathbf{T}\\), we can sample at UV-positions according to the density \\(\\mathbf{D}\\), and produce a full hairstyle \\(\\mathbf{H}\\) by decoding each latent code:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.885, + 0.483, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} = \\mathcal {G} (\\text {S a m p l e} (\\mathbf {T}, \\mathbf {D})) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.183 + ], + "angle": 0, + "content": "where \\( \\text{Sample}(\\cdot) \\) performs probabilistic sampling in UV space such that regions with high density are sampled more often, allowing us to represent hairstyles with varying density of hair. To create a full hairstyle we sample 100K positions on the scalp and extract strand latent codes \\( \\mathbf{z} \\) using bilinear interpolation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.19, + 0.764, + 0.207 + ], + "angle": 0, + "content": "3.3. Conditional Scalp Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.212, + 0.907, + 0.424 + ], + "angle": 0, + "content": "Diffusion framework. Similar to previous methods [42, 56] we train a generative model of scalp textures \\(\\mathbf{T}\\) to learn the prior distribution over hairstyles. Furthermore, we condition the model on image data, enabling high-quality 3D hair generation from a single image. Specifically, we train a denoiser model \\(\\mathcal{D}_{\\theta}\\) using a Hourglass Diffusion Transformer [6] architecture, which is particularly efficient for pixel-space diffusion tasks. We denote the clean training sample for the diffusion as the concatenation of scalp texture and density map: \\(\\mathbf{y} = [\\mathbf{T},\\mathbf{D}]\\) and the noised input \\(\\mathbf{x} = \\mathbf{y} + \\mathbf{n}\\) as a combination of the clean data \\(\\mathbf{y}\\) and noise \\(\\mathbf{n} \\sim \\mathcal{N}(0,\\sigma^2\\mathbf{I})\\) with noise level \\(\\sigma\\). Following EDM [14], we parametrize the denoiser to allow it to predict \\(\\mathbf{y}\\) or \\(\\mathbf{n}\\), or something in between:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.432, + 0.907, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {\\theta} (\\mathbf {x}; \\sigma) = c _ {\\text {s k i p}} (\\sigma) \\mathbf {x} + c _ {\\text {o u t}} (\\sigma) \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\sigma) \\mathbf {x}; c _ {\\text {n o i s e}} (\\sigma)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.457, + 0.906, + 0.517 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_{\\theta}\\) is the network to train, \\(c_{\\mathrm{skip}}\\) is as a skip connection modulator, \\(c_{\\mathrm{in}}\\) and \\(c_{\\mathrm{out}}\\) scale the input and output magnitude, and \\(c_{\\mathrm{noise}}\\) is the time condition of the network. Please refer to the EDM paper [14] for more details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.518, + 0.906, + 0.547 + ], + "angle": 0, + "content": "The training loss for each spatial element and each noise level is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.556, + 0.905, + 0.573 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, \\mathbf {y}, \\mathbf {n}, \\sigma\\right) = \\left\\| \\mathcal {D} _ {\\theta} (\\mathbf {y} + \\mathbf {n}; \\sigma) - \\mathbf {y} \\right\\| _ {2} ^ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.59, + 0.907, + 0.876 + ], + "angle": 0, + "content": "Loss scaling. The denoising network outputs a clean scalp texture \\(\\mathbf{T}\\) and a density map \\(\\mathbf{D}\\). However, we observe that not all channels of the scalp texture are equally significant, some encode relevant information such as length or curliness, while others are noisy and have little impact on the decoded strand. We propose to down-weight the loss of the channels of the scalp textures based on their perceptual change to the strand shape. Since we have no direct metric to evaluate perceptual change, we reuse the data term from the loss \\(\\mathcal{L}_{\\mathrm{data}}\\) used to train the StrandVAE. More specifically, we first define the mean strand predicted by the VAE as \\(\\mathbf{S}_0 = \\mathcal{G}(\\mathbf{z}_0)\\) by decoding from a zero latent vector \\(\\mathbf{z}_0 = [0]^{64}\\). Following that, we individually perturb each dimension of the latent code, decode a strand, and calculate the distance to the mean strand as measured by the loss. This can be seen as a metric that quantifies perceptual changes as a result of individual changes to the latent code dimensions. Therefore, the weight associated with each dimension of the latent code is:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.886, + 0.905, + 0.902 + ], + "angle": 0, + "content": "\\[\nw _ {i} = \\mathcal {L} _ {\\text {s t r a n d}} \\left(S _ {0}, \\mathcal {G} \\left(\\mathbf {z} _ {0} + \\epsilon \\cdot \\mathbf {j} _ {i}\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10851" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.138 + ], + "angle": 0, + "content": "where \\(\\mathbf{j}_i\\) is vector of zeros with a 1 at the i-th position and \\(\\epsilon\\) is the perturbation strength which we empirically set to 0.8. We obtain a final weight vector by normalizing:" + }, + { + "type": "equation", + "bbox": [ + 0.237, + 0.147, + 0.483, + 0.181 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} = \\frac {w _ {i}}{\\sum_ {0} ^ {6 4} w _ {i}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.189, + 0.483, + 0.219 + ], + "angle": 0, + "content": "For an evaluation and discussion of the proposed weighting scheme, please see SupMat." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.22, + 0.484, + 0.356 + ], + "angle": 0, + "content": "In addition, we also incorporate a weighting term in order to equalize the error contribution across noise levels by taking the approach of EDM2 [15], which treats denoising as a form of multi-task learning and lets the network predict a log-variance of the uncertainty \\( u(\\sigma) \\) for a certain noise level. Combining the per-channel weighting with the per-noise level weighting we obtain our final formulation for the diffusion loss as an expectation over noise levels and spatial dimensions:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.365, + 0.483, + 0.394 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, u\\right) = \\mathbb {E} _ {\\mathbf {y}, \\mathbf {n}, \\sigma} \\left[ \\frac {\\mathbf {w}}{e ^ {u (\\sigma)}} \\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, \\mathbf {y}, \\mathbf {n}, \\sigma\\right) + u (\\sigma) \\right]. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.408, + 0.483, + 0.62 + ], + "angle": 0, + "content": "RGB conditioning. Previous approaches have primarily relied on 2D orientation maps [31, 55] extracted using Gabor filters in order to align the generated strands with the image. However, orientation maps cannot infer the hair growth direction and tend to be noisy for heavily occluded hairstyles. In our work, we forego the need to compute orientation maps and instead condition our diffusion network using robust DINOv2 [30] features extracted from the image. Specifically, we use the pre-trained DINOv2-large model to encode the RGB image into a feature map \\(\\mathcal{F}_{map} \\in \\mathbb{R}^{55 \\times 55 \\times 1024}\\) and a global CLS token \\(\\mathcal{F}_{cls} \\in \\mathbb{R}^{1024}\\). Additionally, our rendered images are sufficiently realistic such that the network trained only on synthetic data, can generalize to in-the-wild images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.62, + 0.483, + 0.726 + ], + "angle": 0, + "content": "Since the scalp texture and the RGB image are not spatially aligned, we add cross-attention layers before each downsampling layer of the denoiser and let the network learn which regions of the feature map \\(\\mathcal{F}_{map}\\) it should attend to. The CLS token \\(\\mathcal{F}_{cls}\\) is used to globally condition the network similar to the time condition \\(\\sigma\\) as described in HDiT [6]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.726, + 0.483, + 0.787 + ], + "angle": 0, + "content": "Furthermore, in order to use the same network both conditionally and unconditionally, we train the denoiser using Classifier-Free Guidance [10] by randomly dropping the conditioning signal with \\(10\\%\\) probability (Fig. 8)." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.787, + 0.483, + 0.817 + ], + "angle": 0, + "content": "For experiments on conditioning using DINOv2 features vs orientation maps, please refer to SupMat." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.83, + 0.223, + 0.848 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We evaluate DiffLocks using both synthetic data and in-the-wild images. We also perform ablation studies to assess the importance of the different components of our method" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.09, + 0.616, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.162, + 0.607, + 0.186 + ], + "angle": 0, + "content": "(a) Synthetic Image" + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.09, + 0.709, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.618, + 0.162, + 0.709, + 0.175 + ], + "angle": 0, + "content": "(b) Scalp density" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.09, + 0.801, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.717, + 0.162, + 0.8, + 0.185 + ], + "angle": 0, + "content": "(c) Raw scalp texture" + }, + { + "type": "image", + "bbox": [ + 0.802, + 0.09, + 0.892, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.803, + 0.162, + 0.888, + 0.185 + ], + "angle": 0, + "content": "(d) Interpolated texture" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.191, + 0.907, + 0.262 + ], + "angle": 0, + "content": "Figure 5. Scalp interpolation. Embedding each strand onto a the scalp texture can leave gaps where no strand is present. In order to enable probabilistic sampling of strands, we interpolate the sparse strand embeddings to achieve a smooth scalp texture that can be sampled at any position according to the density." + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.275, + 0.593, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.347, + 0.585, + 0.359 + ], + "angle": 0, + "content": "RGB Input" + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.281, + 0.679, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.347, + 0.674, + 0.37 + ], + "angle": 0, + "content": "Blender offline(40 s)" + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.28, + 0.832, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.685, + 0.347, + 0.894, + 0.371 + ], + "angle": 0, + "content": "Unreal Engine real-time(16 ms)" + }, + { + "type": "image", + "bbox": [ + 0.832, + 0.28, + 0.893, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.378, + 0.906, + 0.435 + ], + "angle": 0, + "content": "Figure 6. Rendering/Simulation. Our generated hair can be directly imported into Blender or Unreal Engine as an Alembic file. In Unreal Engine, the hair can be rendered in real-time with high-quality physics simulation (see Supplemental Video)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.461, + 0.904, + 0.491 + ], + "angle": 0, + "content": "(Sec. 4.4). For implementation details and additional experiments, please refer to SupMat." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.491, + 0.906, + 0.567 + ], + "angle": 0, + "content": "We compare our method with Hairstep [55] and NeuralHDHair [48] as they are both state-of-the-art methods for reconstructing 3D hair from a single image. We also compare with the conditional 3D hair generation method of HAAR [42] although it is mainly designed for text-to-hair." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.576, + 0.637, + 0.592 + ], + "angle": 0, + "content": "4.1. Qualitative" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.598, + 0.907, + 0.795 + ], + "angle": 0, + "content": "The qualitative comparison with Hairstep, NeuralHDHair and HAAR is shown in Fig. 7. NeuralHDHair and HairStep tend to create hair that matches the overall shape from the image but that lacks fine-grained detail and curls, reconstructing strands that run parallel to each other. Furthermore, they cannot correctly reconstruct balding and afrolike hairstyles. In contrast, our method produces high-quality and realistic hair strands for a wide variety of images. Despite being a method designed for text-to-hair, we also compare with HAAR since they have released a pipeline for image-to-hairstyle by leveraging LLaVA to obtain text descriptions. We observe that their method often cannot match the hairstyle in the image." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.647, + 0.819 + ], + "angle": 0, + "content": "4.2.Quantitative" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Quantitative evaluation is performed using the synthetic dataset of Yuksel et al. [52] from which we use two medium-length hairstyles: straight and curly. To render RGB images of the dataset we use Unreal Engine instead of Blender in order to remove possible bias our method might" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10852" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.172, + 0.089, + 0.825, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.654, + 0.908, + 0.71 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison. We compare our method with HairStep [55], NeuralHDHair [48] and HAAR [42] on real images. Our method can robustly reconstruct a large variety of hairstyles with significantly more detail than previous approaches. We note that HAAR was designed to reconstruct hair given text captions, so we use LLaVA [19] to obtain text description of hair, followed by applying their text-to-3D method." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.732, + 0.483, + 0.763 + ], + "angle": 0, + "content": "have towards the path-traced images. The accuracy and precision results are reported in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.763, + 0.483, + 0.884 + ], + "angle": 0, + "content": "Additionally, we note that current synthetic datasets do not contain enough variety of hairstyles and propose a new synthetic dataset containing 10 representative hairstyles created by our Blender pipeline. We also evaluate our method and the baselines on this dataset and report the results in Tab. 2 although we recognize that our method has an advantage because it is trained on data created by the same Blender pipeline." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.483, + 0.9 + ], + "angle": 0, + "content": "Across the two datasets we observe that our method can" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.732, + 0.907, + 0.793 + ], + "angle": 0, + "content": "reconstruct the backside of the hair more faithfully, reinforcing the importance of varied data from which to learn a powerful prior. For the backside reconstruction, robustness to viewpoint, and more visualizations see SupMat." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.722, + 0.818 + ], + "angle": 0, + "content": "4.3. Runtime Performance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We evaluate the runtime performance in Tab. 3 by first dividing the hair reconstruction pipeline into three parts, 1) extraction of RGB features (DINOv2 features or in the case of the baseline methods: orientation maps, hair segmentation, etc.), 2) generation of the hair model, which in our" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10853" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.092, + 0.478, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.276, + 0.484, + 0.348 + ], + "angle": 0, + "content": "Figure 8. Unconditional generation. We train our diffusion model with Classifier-free Guidance [10] so that the same model can be evaluated both conditionally and unconditionally. Here we show unconditionally generated results where we observe a range of high-quality and diverse hairstyles." + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.368, + 0.173, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.434, + 0.165, + 0.445 + ], + "angle": 0, + "content": "RGB Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.173, + 0.434, + 0.214, + 0.444 + ], + "angle": 0, + "content": "Model:" + }, + { + "type": "image_caption", + "bbox": [ + 0.172, + 0.447, + 0.232, + 0.458 + ], + "angle": 0, + "content": "Condition:" + }, + { + "type": "image", + "bbox": [ + 0.241, + 0.365, + 0.313, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.263, + 0.434, + 0.29, + 0.443 + ], + "angle": 0, + "content": "VAE" + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.447, + 0.313, + 0.458 + ], + "angle": 0, + "content": "Global+Local" + }, + { + "type": "image", + "bbox": [ + 0.321, + 0.371, + 0.388, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.329, + 0.434, + 0.377, + 0.444 + ], + "angle": 0, + "content": "Diffusion" + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.447, + 0.374, + 0.457 + ], + "angle": 0, + "content": "Global" + }, + { + "type": "image", + "bbox": [ + 0.399, + 0.362, + 0.471, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.407, + 0.434, + 0.46, + 0.444 + ], + "angle": 0, + "content": "Diffusion" + }, + { + "type": "image_caption", + "bbox": [ + 0.396, + 0.447, + 0.471, + 0.458 + ], + "angle": 0, + "content": "Global+Local" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.467, + 0.485, + 0.552 + ], + "angle": 0, + "content": "Figure 9. Ablation of conditioning signal and model architecture. Removing the local conditioning in the form of feature map \\(\\mathcal{F}_{map}\\) and relying only on the global CLS token severely affects the ability to reconstruct hair. Also generating scalp textures using a VAE yields overly smooth reconstructions. The combination of diffusion and local+global conditioning captures the most detail." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.579, + 0.484, + 0.73 + ], + "angle": 0, + "content": "case is the scalp texture while baseline methods create a 3D orientation field, 3) strand generation, which is the final step to either decode or grow the strands. All results are obtained on an NVIDIA H100 GPU. We observe that our method is overall the fastest as we do not need pre- or post-processing steps like head fitting, hair segmentation or hair growth and refinement. Note that our generated hair can be directly imported into Unreal Engine and rendered in real-time (60FPS) as shown in Fig. 6; see Supplemental Video." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.742, + 0.245, + 0.759 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.903 + ], + "angle": 0, + "content": "We perform an ablation study on the architecture and the importance of the conditioning signal in Fig. 9. Changing the scalp generation model to a VAE model similar to GroomGen [56] causes the hair to be overly smooth and lack local detail. Our proposed diffusion model conditioned with global and local features in the form of \\(\\mathcal{F}_{map}\\) and \\(\\mathcal{F}_{cls}\\) manages to capture the most detail. However, the local feature map is crucial and removing it causes the generated hair to deviate significantly from the input image." + }, + { + "type": "table_caption", + "bbox": [ + 0.698, + 0.089, + 0.81, + 0.098 + ], + "angle": 0, + "content": "Thresholds: mm / degrees" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.098, + 0.905, + 0.145 + ], + "angle": 0, + "content": "
    Method2/203/304/402/203/304/402/203/304/40
    Precision(↑)Recall(↑)F-score(↑)
    NeuralHDHair [48]47.9165.0773.7631.5951.1064.6338.0057.1268.73
    HairStep[55]40.8855.9964.0732.1644.9653.1535.5049.0657.20
    Ours43.6068.3081.7934.9758.2771.7938.3562.4176.20
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.147, + 0.905, + 0.187 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with [48, 55] on [52]. It includes straight and curly hairstyles, please refer to the SupMat for more visualizations." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.193, + 0.905, + 0.248 + ], + "angle": 0, + "content": "
    MethodThresholds: mm / degrees
    2/203/304/402/203/304/402/203/304/40
    Precision(↑)Recall(↑)F-score(↑)
    NeuralHDHair [48]18.6536.2149.4619.2637.3351.6018.5535.7649.30
    HairStep[55]20.2235.5445.7320.8038.5352.8219.4234.3845.48
    Ours63.0684.1692.7857.9179.7189.8160.1381.6891.17
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.25, + 0.907, + 0.307 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison with [48, 55] on the DiffLocks evaluation set. Our results show substantial improvement over the baseline, particularly when reconstructing the backside of the hair due to our model's ability to learn a powerful prior over hairstyles." + }, + { + "type": "table", + "bbox": [ + 0.56, + 0.318, + 0.859, + 0.372 + ], + "angle": 0, + "content": "
    HairStepNeuralHDHairOurs
    RGB features (↓)3.174.860.10
    hair model (↓)0.454.991.83
    strand creation (↓)49.788.470.40
    total (s) (↓)53.4018.322.33
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.373, + 0.907, + 0.403 + ], + "angle": 0, + "content": "Table 3. Timing. Comparison of the time in seconds needed for each part of the hair creation pipeline." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.432, + 0.779, + 0.449 + ], + "angle": 0, + "content": "5. Limitations and future work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.461, + 0.906, + 0.552 + ], + "angle": 0, + "content": "Despite the large amount of data, there are still gaps in the synthetic dataset; e.g. it lacks hairstyles with braids, accessories, ponytails, and buns. However, we believe that further improvements to the pipeline will allow such details to be created. Furthermore, the generation pipeline can also be easily extended to beards and eyebrows." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.554, + 0.906, + 0.645 + ], + "angle": 0, + "content": "We also note that DiffLocks prioritizes local hair details over perfect image alignment. However, for many tasks, generation or reconstruction is just the first step. When hair is animated with physics, the precise initial strand alignment is not critical, as the dynamic nature of hair makes the initial configuration transient." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.667, + 0.634, + 0.683 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.695, + 0.906, + 0.814 + ], + "angle": 0, + "content": "We proposed a novel approach for generating 3D hair strands from a single image by first creating the largest dataset to date of synthetic hair paired with RGB images, and then by proposing an image-conditioned diffusion model based on scalp textures. Our method can create highly intricate 3D strands, surpassing previous methods and without requiring heuristic-based methods to increase the realism." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.817, + 0.906, + 0.889 + ], + "angle": 0, + "content": "Acknowledgments and Disclosures. We give thanks to Nathan Bajandas for all the Unreal images and videos. 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Groomcap: High-fidelity prior-free hair capture. arXiv preprint arXiv:2409.00831, 2024. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.482, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "10857" + } + ] +] \ No newline at end of file diff --git a/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_origin.pdf b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..67a575345a2a9e496322cde8e1449dab76e34643 --- /dev/null +++ b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/8616985f-9ce1-4bd9-83a9-440f3fb3d484_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:404e78307d73e0334613654e280a2363f7a1fe7522d26be4223a9b879ac4e0ca +size 5113736 diff --git a/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/full.md b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..462bc23223ff3a3d6388c457b80d7364e90c50f6 --- /dev/null +++ b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/full.md @@ -0,0 +1,349 @@ +# DiffLocks: Generating 3D Hair from a Single Image using Diffusion Models + +Radu Alexandru Rosu $^{1,\ast}$ Keyu Wu $^{2,\ast,\dagger}$ Yao Feng $^{1,3}$ Youyi Zheng $^{2}$ Michael J. Black $^{4}$ + +$^{1}$ Meshcapade $^{2}$ Zhejiang University $^{3}$ Stanford University $^{4}$ Max Planck Institute for Intelligent Systems + +# Abstract + +We address the task of generating 3D hair geometry from a single image, which is challenging due to the diversity of hairstyles and the lack of paired image-to-3D hair data. Previous methods are primarily trained on synthetic data and cope with the limited amount of such data by using low-dimensional intermediate representations, such as guide strands and scalp-level embeddings, that require post-processing to decode, upsample, and add realism. These approaches fail to reconstruct detailed hair, struggle with curly hair, or are limited to handling only a few hairstyles. To overcome these limitations, we propose DiffLocks, a novel framework that enables detailed reconstruction of a wide variety of hairstyles directly from a single image. First, we address the lack of 3D hair data by automating the creation of the largest synthetic hair dataset to date, containing 40K hairstyles. Second, we leverage the synthetic hair dataset to learn an image-conditioned diffusion-transformer model that generates accurate 3D strands from a single frontal image. By using a pretrained image backbone, our method generalizes to in-the-wild images despite being trained only on synthetic data. Our diffusion model predicts a scalp texture map in which any point in the map contains the latent code for an individual hair strand. These codes are directly decoded to 3D strands without post-processing techniques. Representing individual strands, instead of guide strands, enables the transformer to model the detailed spatial structure of complex hairstyles. With this, DiffLocks can recover highly curled hair, like afro hairstyles, from a single image for the first time. Data and code is available at https://radualexandru.github.io/difflocks/. + +# 1. Introduction + +Realistic 3D hair is a crucial component of digital humans [1, 2, 8, 12, 18, 38, 45], which have wide applications in + +![](images/db46e02f03fa79dd37b82519b2e3ca7decd2033033d6e32ad605dd9619d50055.jpg) +Synthetic hair dataset + +![](images/48e98739e76eb057826c69742a7c3dbf7cf97b1ff733380d2bad5116eb3a28bd.jpg) +Real image + +![](images/e2a01c26dff39a0937ad3d2695048e49ab11a189de18bc059b93609f174a9683.jpg) +3D hair +Figure 1. Given a single RGB image DiffLocks generates accurate 3D strands using a diffusion model. The model is trained on a novel synthetic hair dataset containing RGB images and corresponding 3D strands. + +games, media and entertainment. Accurate hair representation greatly enhances the character's realism and overall visual quality. Unfortunately, both generating realistic hair and reconstructing it from an image are challenging due to the complex 3D geometry and the wide variety of hairstyles. + +Since the release of the first 3D synthetic hair dataset [11], numerous methods for hair reconstruction have been proposed. Multi-view capture methods [17, 29, 31, 54, 57] and video-based approaches [24, 41, 49] are able to reconstruct high-fidelity 3D hair but are time-intensive and challenging to deploy due to their reliance on expensive capture equipment or strict capture conditions. + +In contrast, single-view methods [3, 37, 48, 51, 55], which reconstruct 3D hair from a single image, are faster, more accessible, and user-friendly. These methods, however, often produce low-detail hair and handle only a restricted range of hairstyles. Furthermore, these methods struggle to handle male-pattern baldness and very curly hair such as afro-like hairstyles, which have a complex geometric structure (see [47]). Previous methods suffer from a lack of diverse and comprehensive hairstyle training datasets. To increase training set diversity, GroomGen [56], HAAR [42] and Fake It Till You Make It [46] use artist-created hairstyles together with data augmentation techniques to train their methods. However, their datasets are not released, do not have paired RGB images, or the creation pro + +cess requires significant manual effort. + +To cope with limited training data, previous approaches rely on several intermediate representations to simplify the problem. Most prior methods rely on oriented filters to capture the structure of hair in images. They also do not model hair strands directly but, instead, use a smaller number of guide strands and then upsample these to generate a hairstyle. Additionally, several methods use variational autoencoding to compress the guide strands across the scalp into a low-dimensional representation. All of these approaches are designed to cope with limtied training data but have two effects: (1) they limit the ability to model the complex spatial relationships between individual strands, and (2) they limit realism by working with low-dimensional representations. Effectively, they work in a compressed low-dimensional space and then need to upsample the results and post-process them to increase realism. + +We take a different approach and focus on creating a sufficient amount of training data that we can remove the simplifying assumptions of previous methods. To that end, we present a novel 3D synthetic hair dataset consisting of 40K samples covering a wide variety of hairstyles; see Fig. 3. Each sample consists of 3D hair strands and a realistic RGB image rendered in Blender through path-tracing. We achieve this by automating the creation of the data using a variety of artist-inspired techniques. Traditional approaches are designed to create a single hairstyle using a small geometry node network tailored-made for that hairstyle. In contrast, we design a large and very general geometry node network in Blender that allows us to automatically create a large number of realistic hairstyles by changing the different parameters. + +We then leverage our dataset to train a novel hair diffusion framework, called DiffLocks, that is optionally conditioned on single RGB image in order to create highly detailed 3D strands; see Fig. 1. Specifically, we use Hourglass Diffusion Transformers (HDiT) [6] as a diffusion architecture and exploit features from a pretrained DINOv2 [30] model as a conditioning input to guide and control the generated results; see Fig. 2. The DINOv2 features are richer than the oriented filters used in many previous methods. Note that we directly regress the latent code for individual hair strands (instead of guide strands) enabling the transformer to learn detailed spatial relationships between strands across the scalp. With sufficient training data, there is no longer a need to first embed the hairstyle in a low-D scalp representation. We also model a density map that defines the probability of a strand being generated at each location on the scalp. All of these changes lead to increased realism, particularly for curly and balding hairstyles. Finally, our strand-based hair can be directly used in real-time game engines like Unreal Engine (Fig. 6) without additional heuristics to densify the hair or add fine-grained detail. + +A key takeaway from our work is that, with sufficient training data, many of the key components of previous methods are no longer needed. For example, in contrast to the $32 \times 32$ scalp map used by HAAR, our diffusion model predicts a scalp texture of size $256 \times 256$ (each pixel containing a latent code for a single strand) from which DiffLocks directly decodes 3D strands. No post-processing is needed, such as hair upsampling or the addition of random noise (cf. [56]). The dataset already contains realistic hairstyles with flyaway strands, so the diffusion model learns to create them. + +In summary, our main contributions are: + +- a novel 3D hair dataset containing 40K diverse and realistic 3D hairstyles with corresponding RGB images. We make the dataset public in order to support future research in hair modeling and synthesis, +- an improved scalp representation that facilitates the reconstruction of hair styles with different hair density (bald spots, male pattern baldness, etc.), +- a novel conditional scalp diffusion framework for robustly generating 3D hair directly from a single RGB image, bypassing a 2D orientation map. This framework can effectively create a variety of challenging hairstyles, while achieving the state-of-the-art performance and enable, for the first time, reconstruction of Afro-like and bald hairstyles. The model will be available for research. + +# 2. Related Works + +3D Hair Reconstruction. The pioneering hair reconstruction work of Paris et al. [31] set the stage for numerous multi-view-based hair reconstruction methods. Since then, various methods [17, 25, 26, 29, 57] reconstruct the 3D geometric features of hair constrained by a 2D orientation map. In many cases this requires specialized hardware or multicamera rigs. In contrast, monocular video based methods [24, 41, 44, 49] sacrifice some accuracy to avoid expensive and specialized equipment. While achieving impressive results, such methods still require carefully captured data. To relax the capture conditions, single-view-based methods [3, 37, 48, 51, 53, 53] employ deep neural networks to infer volumetric fields by exploiting data priors learned from 3D synthetic datasets. Such methods enable rapid 3D hair reconstruction but typically generate low fidelity hair and can handle only a limited range of hairstyles due to the significant lack of diversity in existing 3D hair datasets. Similar to these methods, our approach also reconstructs hair from a single image. However, our work focuses on fast and robust reconstruction of diverse hairstyles, including challenging types such as balding and tightly curled (afro-like) styles; such hairstyles have received relatively little attention. + +3D Hair Generation. In addition to hair reconstruction, hair generation is another challenge, which, if solved, could + +![](images/11b00eeec5a8d13730cab3f5fda39811fc2edccd56d75fb8d9a08cace937f089.jpg) +Figure 2. Method. Given a single RGB image, we use a pretrained DINOv2 model to extract local and global features, which are used to guide a scalp diffusion model. The scalp diffusion model denoises a density map and a scalp texture containing latent codes for strand geometry. Finally, we probabilistically sample texels from the scalp texture and decode the latent code $\mathbf{z}$ into strands of 256 points. Decoding in parallel 100K strands yields the final hairstyle. + +provide synthetic data for learning high-quality hair reconstruction. Ren et al. [34] propose a heuristic example-based hair generation method that is significantly limited by the reference hair models. Saito et al. [37] encode a 3D hair dataset with a Variational autoencoder (VAE), enabling them to generate plausible yet overly smooth hairstyles. To achieve high-quality and diverse hairstyles, Perm [9] leverages existing public 3D datasets, disentangling the global shape and local details of hair strands. Despite progress, the scale and diversity of synthetic 3D hair datasets is still far from what is needed. GroomGen [56] and HAAR [42] incorporate parametrized variations based on high-quality hairstyles crafted by artists, further enhancing the diversity of 3D hair datasets. They also train generative models to produce 3D hairstyles from noisy inputs or text prompts. Recently, Curly-Cue [47] focuses on the principles behind curly, afro-style, hair and provides tools for animators to create realistic hairstyles. In our work, we propose a low-cost synthetic 3D hair generation pipeline and use it to construct a new dataset that is more diverse than previous ones, containing 40K 3D synthetic hairstyles. Additionally, we use this dataset to train a generative hair model that is conditioned on a single input image. + +Image-To-3D via Diffusion Models. Early work on neural reconstruction of 3D objects from images [7, 28, 50] distills information from pretrained 2D diffusion models, such as Stable Diffusion [35], using techniques like Score Distillation Sampling (SDS) [33]. However, these pretrained models lack the multi-view information essential for accurate 3D reconstruction. To address this, later approaches [20, 21, 40] train custom 2D diffusion models to generate multi-view images from a given input, enabling more accurate 3D object reconstruction by integrating this multi-view data [13, 23]. While effective, this approach can be time-intensive due to the sampling and reconstruction processes, which has led to an alternative line of research focused on training diffusion models to generate 3D representations directly, such as meshes [22] or triplane repre + +sentations [4]. However, these methods often demand significant computational resources for 3D processing. In contrast, our method produces a 2D representation that contains 3D hair information, enabling direct decoding into 3D hair without the need for extensive multi-view generation or resource-intensive training of 3D diffusion models. + +# 3. Method + +In this section, we present our pipeline for 3D hair reconstruction from a single image, consisting of three key stages: 1) A data generation pipeline using Blender's geometry nodes to create a large, diverse, image-3D paired synthetic hair dataset (Sec. 3.1); 2) Parameterization of hair strands and hairstyles into a canonical scalp space to obtain scalp textures (Sec. 3.2); And 3) training a conditional diffusion model, DiffLocks, using the generated synthetic images and the scalp textures as shown in Fig. 2. + +# 3.1. Data Generation + +A key bottleneck in the field of 3D hair reconstruction is the limited availability of public datasets, with only 343 hairstyles for USC-HairSalon [11] and 10 for CT2Hair [39]. Additionally, these datasets lack corresponding 2D images, which limits their usability. Thus, here we propose a novel data generation pipeline, which uses Blender geometry nodes to add variation to a small set of manually defined guide strands as shown in Fig. 4. Next, we will describe the main steps of the pipeline. + +Scalp creation. The first step in creating the new dataset is defining a scalp mesh onto which to build the hairstyles. Due to its wide applicability in the human-reconstruction field, we use the SMPL-X model [32] to define our scalp. We create a SMPL-X neutral body with mean body shape from which we manually select the vertices corresponding to the scalp and extract a mesh of 513 vertices as seen in Fig. 2. The scalp mesh is then UV-unwrapped into a single chart using an As-Rigid-As-Possible (ARAP) parametrization [43] in order to minimize distortions. This + +![](images/bf09dc3d1d7dc770e866fdca3b9cf68fa4dcba423c63eebe63b9a80c7200fe08.jpg) +Figure 3. Synthetic data. Sample RGB images from our synthetic hair dataset. Each sample from the dataset contains an image at $768 \times 768$ resolution together with the corresponding 3D strand geometry of $\approx 100\mathrm{K}$ strands. + +![](images/86f18bcb6d6fb40e8be568ab4b605b7b5b4a14a3a5d3cbf1b6400f4107944404.jpg) + +![](images/46556d4d30d62af92354bf4e34454212b7efb36d0a0177db0ec06a76ba2d862f.jpg) + +![](images/be984e13daaa5becb3b5d841e5be95cc70632b5579896500c66d6bc4eb5f21a2.jpg) + +![](images/5e9ef72ab27a9ea82de13d34626aca378d67ec8f8a813d6d0fa3279c92dda0ab.jpg) + +![](images/9c6256f2749fded413ca15c16b15dcb513be9fe6510081a2557d19dc086b3ee8.jpg) + +![](images/6d188e4c76e1d5a0ee2d640fcb1f050618e3e7db1a85f5d0a57c33c8725a3658.jpg) +Figure 4. Base hairstyles. Starting from a coarse set of guide strands, our Blender pipeline is able to generate a wide variety of hairstyles, covering different lengths, curliness and density patterns. Best viewed zoomed in. + +operation is done only once and need not be repeated for each subject since they all share the same SMPL-X body topology. + +Base hairstyle creation. The scalp mesh is imported into Blender and a series of hairstyles is manually created in the form of coarsely defined guide strands (Fig. 4). The base hairstyles define a starting point for the randomization process and therefore do not need to contain fine details, rather defining just the overall shape and direction of the hair. We manually create 75 base hairstyles, each represented by $\approx 50$ strands. We note that this is not a labour intensive process, as each base hairstyle takes only a few minutes to create. + +Randomization pipeline. The guide strands are passed through a series of transformations defined as geometry nodes in Blender that gradually add more detail to the hair. The guide strands are first interpolated to 100K strands, after which clumping, curling and noise are applied. These operations are repeated multiple times with various intensities. Special attention must be given to prevent the hair from penetrating the scalp or intersecting with the body for which we apply shrinkwrap modifiers at various stages in the pipeline. In total the pipeline consists of 58 geometry nodes that transform the hair together with 349 auxiliary nodes that help feed parameters into the main nodes. We also define a hair BSDF using the Chiang model [5] for the strands material. Lastly we apply physics simulation to + +the strands using Blender's cloth simulation and randomize wind direction and gravity strength. A total of 110 parameters govern the whole Blender generation pipeline (geometry+material) and we select them at random with minimum and maximum ranges chosen empirically. + +Scene setup. In order to render realistic images, it is crucial to match the lighting of real scenes. For this, we use 255 HDRIs from Poly Haven1 and randomize their exposure and azimuthal angle. Additionally, we randomly select albedo, normal and roughness textures for the bodies from a library of artist-created SMPL-X textures. Furthermore, we also randomly change the face expression coefficients within the range $[-1, 1]$ . We keep the jaw closed since we observed it can cause issues with strands physics. To train our network for robustness to different camera parameters, we also randomize camera position (maintaining the look-at direction towards the head) and focal length in the range $40\mathrm{mm}$ to $150\mathrm{mm}$ . For a study on network robustness to camera parameters please refer to the SupMat. + +Full dataset. The full dataset contains 40K samples each containing 3D strands with $\approx 100\mathrm{K}$ strands and a corresponding RGB image rendered through path tracing at $768 \times 768$ resolution. We additionally save a density map that defines the probability of a strand being generated at each texel of the scalp as shown in Fig. 5. The density map is especially useful for modelling hairstyles with balding patterns. + +# 3.2. Hairstyle Parameterization + +Strand Parameterization. Formally, we represent a 3D strand as a set of $L$ 3D points $\mathbf{S} = \{\mathbf{p}_1,\mathbf{p}_2,\dots ,\mathbf{p}_L\}$ , where $L = 256$ . A full hairstyle consists of a set of $\approx 100\mathrm{K}$ strands $\mathbf{H} = \{\mathbf{S}_j\}_{0}^{100\mathrm{K}}$ . Similar to Neural Strands [36], we train a strand VAE to compress individual strands into a compact latent code $\mathbf{z}\in \mathbb{R}^{64}$ . The encoder of the VAE denoted by $\mathcal{E}()$ is modeled as a series of 1D convolutions and the decoder denoted by $\mathcal{G}()$ is a modulated SIREN [27] that maps the latent code $\mathbf{z}$ back to a series of 3D points $\mathbf{S}$ . + +In addition to the position and direction loss proposed by Neural Strands [36], we incorporate a curvature loss $\mathcal{L}_{\mathrm{cur}}$ . This is motivated by the observation that, for highly coiled + +hair, it is more perceptually impactful to match the curvature of the strand rather than matching the position of every point along the strand (i.e., as long as the strand looks curvy, it is acceptable to commit errors in per-point position). For an evaluation of this observation please refer to the SupMat. We define the local curvature as the instantaneous change in direction: $\kappa_{i} = \mathbf{d}_{i + 1} - \mathbf{d}_{i}$ where the direction is defined as the change in position: $\mathbf{d}_i = \mathbf{p}_{i + 1} - \mathbf{p}_i$ . Therefore, the new curvature loss is defined as the L1 distance between the ground-truth and the prediction: $\mathcal{L}_{\mathrm{cur}} = \sum_{0}^{L}|\kappa_{i} - \tilde{\kappa}_{i}|$ , where $\hat{\kappa}_i$ is the curvature of the predicted strand. + +The final training loss of our strands VAE is a weighted combination of a data term consisting of positional, directional and curvature losses together with a KL regularization term: + +$$ +\mathcal {L} _ {\mathrm {d a t a}} = \sum_ {0} ^ {L} | \mathbf {p} _ {i} - \tilde {\mathbf {p}} _ {i} | + \lambda_ {1} | \mathbf {d} _ {i} - \tilde {\mathbf {d}} _ {i} | + \lambda_ {2} | \boldsymbol {\kappa} _ {i} - \tilde {\boldsymbol {\kappa}} _ {i} | \tag {1} +$$ + +$$ +\mathcal {L} _ {\mathrm {V A E}} = \mathcal {L} _ {\mathrm {d a t a}} + \lambda_ {\mathrm {K L}} \mathcal {L} _ {\mathrm {K L}}. \tag {2} +$$ + +For more details on the hyperparameters please refer to the SupMat. + +Neural Scalp Texture. Each 3D hairstyle generated from the Blender pipeline is parametrized onto the scalp surface using a regular 2D texture. Specifically, each strand $\mathbf{S}$ is encoded to a latent code $\mathbf{z}$ by the strand encoder $\mathbf{z} = \mathcal{E}(\mathbf{S})$ and directly assigned to the texel corresponding to the root of the strand. If two strands are so close together that they are assigned the same texel on the scalp, one of them is chosen at random. This produces a raw scalp texture $\mathbf{T}_{\text{raw}} \in \mathbb{R}^{256 \times 256 \times 64}$ , as shown in Fig. 5c where each texel contains a latent strand code. Since not all regions of the scalp have an equal hair density, we introduce a density map $\mathbf{D} \in \mathbb{R}^{256 \times 256 \times 1}$ with values in the range [0, 1] that defines the probability of a strand being present at each texel. For more discussion on the properties of the density map please refer to the SupMat. + +The aforementioned creation of the scalp texture can create sparse regions with no latent codes since not every texel will correspond to a strand. This sparsity is particularly evident for hairstyles with balding patterns and can cause issues when decoding the texture back to 3D since sampling a texel with no assigned latent code would yield undefined strand geometry. To avoid this issue, we interpolate the sparsely assigned latent codes by using a push-pull algorithm [16] that ensures that every texel on the scalp has a valid strand latent code as shown in Fig. 5d. + +With the interpolated scalp texture $\mathbf{T}$ , we can sample at UV-positions according to the density $\mathbf{D}$ , and produce a full hairstyle $\mathbf{H}$ by decoding each latent code: + +$$ +\mathbf {H} = \mathcal {G} (\text {S a m p l e} (\mathbf {T}, \mathbf {D})) \tag {3} +$$ + +where $\text{Sample}(\cdot)$ performs probabilistic sampling in UV space such that regions with high density are sampled more often, allowing us to represent hairstyles with varying density of hair. To create a full hairstyle we sample 100K positions on the scalp and extract strand latent codes $\mathbf{z}$ using bilinear interpolation. + +# 3.3. Conditional Scalp Diffusion + +Diffusion framework. Similar to previous methods [42, 56] we train a generative model of scalp textures $\mathbf{T}$ to learn the prior distribution over hairstyles. Furthermore, we condition the model on image data, enabling high-quality 3D hair generation from a single image. Specifically, we train a denoiser model $\mathcal{D}_{\theta}$ using a Hourglass Diffusion Transformer [6] architecture, which is particularly efficient for pixel-space diffusion tasks. We denote the clean training sample for the diffusion as the concatenation of scalp texture and density map: $\mathbf{y} = [\mathbf{T},\mathbf{D}]$ and the noised input $\mathbf{x} = \mathbf{y} + \mathbf{n}$ as a combination of the clean data $\mathbf{y}$ and noise $\mathbf{n} \sim \mathcal{N}(0,\sigma^2\mathbf{I})$ with noise level $\sigma$ . Following EDM [14], we parametrize the denoiser to allow it to predict $\mathbf{y}$ or $\mathbf{n}$ , or something in between: + +$$ +\mathcal {D} _ {\theta} (\mathbf {x}; \sigma) = c _ {\text {s k i p}} (\sigma) \mathbf {x} + c _ {\text {o u t}} (\sigma) \mathcal {F} _ {\theta} \left(c _ {\text {i n}} (\sigma) \mathbf {x}; c _ {\text {n o i s e}} (\sigma)\right) \tag {4} +$$ + +where $\mathcal{F}_{\theta}$ is the network to train, $c_{\mathrm{skip}}$ is as a skip connection modulator, $c_{\mathrm{in}}$ and $c_{\mathrm{out}}$ scale the input and output magnitude, and $c_{\mathrm{noise}}$ is the time condition of the network. Please refer to the EDM paper [14] for more details. + +The training loss for each spatial element and each noise level is defined as: + +$$ +\mathcal {L} \left(\mathcal {D} _ {\theta}, \mathbf {y}, \mathbf {n}, \sigma\right) = \left\| \mathcal {D} _ {\theta} (\mathbf {y} + \mathbf {n}; \sigma) - \mathbf {y} \right\| _ {2} ^ {2}. \tag {5} +$$ + +Loss scaling. The denoising network outputs a clean scalp texture $\mathbf{T}$ and a density map $\mathbf{D}$ . However, we observe that not all channels of the scalp texture are equally significant, some encode relevant information such as length or curliness, while others are noisy and have little impact on the decoded strand. We propose to down-weight the loss of the channels of the scalp textures based on their perceptual change to the strand shape. Since we have no direct metric to evaluate perceptual change, we reuse the data term from the loss $\mathcal{L}_{\mathrm{data}}$ used to train the StrandVAE. More specifically, we first define the mean strand predicted by the VAE as $\mathbf{S}_0 = \mathcal{G}(\mathbf{z}_0)$ by decoding from a zero latent vector $\mathbf{z}_0 = [0]^{64}$ . Following that, we individually perturb each dimension of the latent code, decode a strand, and calculate the distance to the mean strand as measured by the loss. This can be seen as a metric that quantifies perceptual changes as a result of individual changes to the latent code dimensions. Therefore, the weight associated with each dimension of the latent code is: + +$$ +w _ {i} = \mathcal {L} _ {\text {s t r a n d}} \left(S _ {0}, \mathcal {G} \left(\mathbf {z} _ {0} + \epsilon \cdot \mathbf {j} _ {i}\right)\right), \tag {6} +$$ + +where $\mathbf{j}_i$ is vector of zeros with a 1 at the i-th position and $\epsilon$ is the perturbation strength which we empirically set to 0.8. We obtain a final weight vector by normalizing: + +$$ +\mathbf {w} = \frac {w _ {i}}{\sum_ {0} ^ {6 4} w _ {i}}. \tag {7} +$$ + +For an evaluation and discussion of the proposed weighting scheme, please see SupMat. + +In addition, we also incorporate a weighting term in order to equalize the error contribution across noise levels by taking the approach of EDM2 [15], which treats denoising as a form of multi-task learning and lets the network predict a log-variance of the uncertainty $u(\sigma)$ for a certain noise level. Combining the per-channel weighting with the per-noise level weighting we obtain our final formulation for the diffusion loss as an expectation over noise levels and spatial dimensions: + +$$ +\mathcal {L} \left(\mathcal {D} _ {\theta}, u\right) = \mathbb {E} _ {\mathbf {y}, \mathbf {n}, \sigma} \left[ \frac {\mathbf {w}}{e ^ {u (\sigma)}} \mathcal {L} \left(\mathcal {D} _ {\theta}, \mathbf {y}, \mathbf {n}, \sigma\right) + u (\sigma) \right]. \tag {8} +$$ + +RGB conditioning. Previous approaches have primarily relied on 2D orientation maps [31, 55] extracted using Gabor filters in order to align the generated strands with the image. However, orientation maps cannot infer the hair growth direction and tend to be noisy for heavily occluded hairstyles. In our work, we forego the need to compute orientation maps and instead condition our diffusion network using robust DINOv2 [30] features extracted from the image. Specifically, we use the pre-trained DINOv2-large model to encode the RGB image into a feature map $\mathcal{F}_{map} \in \mathbb{R}^{55 \times 55 \times 1024}$ and a global CLS token $\mathcal{F}_{cls} \in \mathbb{R}^{1024}$ . Additionally, our rendered images are sufficiently realistic such that the network trained only on synthetic data, can generalize to in-the-wild images. + +Since the scalp texture and the RGB image are not spatially aligned, we add cross-attention layers before each downsampling layer of the denoiser and let the network learn which regions of the feature map $\mathcal{F}_{map}$ it should attend to. The CLS token $\mathcal{F}_{cls}$ is used to globally condition the network similar to the time condition $\sigma$ as described in HDiT [6]. + +Furthermore, in order to use the same network both conditionally and unconditionally, we train the denoiser using Classifier-Free Guidance [10] by randomly dropping the conditioning signal with $10\%$ probability (Fig. 8). + +For experiments on conditioning using DINOv2 features vs orientation maps, please refer to SupMat. + +# 4. Experiments + +We evaluate DiffLocks using both synthetic data and in-the-wild images. We also perform ablation studies to assess the importance of the different components of our method + +![](images/dd0e895f013d52904ef1681656a41255e8646fa764a8102ca0b7718a45f4e257.jpg) +(a) Synthetic Image + +![](images/64e3f621fa06331ec53edb1ac3461d19abc0072a32e3f182e29112dd5c79065b.jpg) +(b) Scalp density + +![](images/02d8c2cd6ac17284d3fcb7dcd1f579e71dc8df34866411f968e5b8f06012677e.jpg) +(c) Raw scalp texture + +![](images/8fc377919fb412952e6cf3cb37189fe35f84b60da667958e87a1226f083f42bf.jpg) +(d) Interpolated texture + +![](images/3664be4a609d78747f38714d5e88fa0f19d6e743f468cdfc4db6cce08f81b2b7.jpg) +Figure 5. Scalp interpolation. Embedding each strand onto a the scalp texture can leave gaps where no strand is present. In order to enable probabilistic sampling of strands, we interpolate the sparse strand embeddings to achieve a smooth scalp texture that can be sampled at any position according to the density. +RGB Input +Figure 6. Rendering/Simulation. Our generated hair can be directly imported into Blender or Unreal Engine as an Alembic file. In Unreal Engine, the hair can be rendered in real-time with high-quality physics simulation (see Supplemental Video). + +![](images/b7dcbe045408ecd716fca43d09329ac96c5fa75c7925186d88e2a5f5368eafd7.jpg) +Blender offline(40 s) + +![](images/fc2b9c8e9139e9e36c9dc6b36281fbafd0bac781693a6a2ee6bc72f1ca280f23.jpg) +Unreal Engine real-time(16 ms) + +![](images/d5d8eef7de70f5e02ce1b6b75651b29ca3f1ee2155c27bf897dc86346a424681.jpg) + +(Sec. 4.4). For implementation details and additional experiments, please refer to SupMat. + +We compare our method with Hairstep [55] and NeuralHDHair [48] as they are both state-of-the-art methods for reconstructing 3D hair from a single image. We also compare with the conditional 3D hair generation method of HAAR [42] although it is mainly designed for text-to-hair. + +# 4.1. Qualitative + +The qualitative comparison with Hairstep, NeuralHDHair and HAAR is shown in Fig. 7. NeuralHDHair and HairStep tend to create hair that matches the overall shape from the image but that lacks fine-grained detail and curls, reconstructing strands that run parallel to each other. Furthermore, they cannot correctly reconstruct balding and afrolike hairstyles. In contrast, our method produces high-quality and realistic hair strands for a wide variety of images. Despite being a method designed for text-to-hair, we also compare with HAAR since they have released a pipeline for image-to-hairstyle by leveraging LLaVA to obtain text descriptions. We observe that their method often cannot match the hairstyle in the image. + +# 4.2.Quantitative + +Quantitative evaluation is performed using the synthetic dataset of Yuksel et al. [52] from which we use two medium-length hairstyles: straight and curly. To render RGB images of the dataset we use Unreal Engine instead of Blender in order to remove possible bias our method might + +![](images/b16c3056d429e98e19eb69f5c70e040e7cd99c4e1f1639f6b96e2b0a087d5ced.jpg) +Figure 7. Qualitative comparison. We compare our method with HairStep [55], NeuralHDHair [48] and HAAR [42] on real images. Our method can robustly reconstruct a large variety of hairstyles with significantly more detail than previous approaches. We note that HAAR was designed to reconstruct hair given text captions, so we use LLaVA [19] to obtain text description of hair, followed by applying their text-to-3D method. + +have towards the path-traced images. The accuracy and precision results are reported in Tab. 1. + +Additionally, we note that current synthetic datasets do not contain enough variety of hairstyles and propose a new synthetic dataset containing 10 representative hairstyles created by our Blender pipeline. We also evaluate our method and the baselines on this dataset and report the results in Tab. 2 although we recognize that our method has an advantage because it is trained on data created by the same Blender pipeline. + +Across the two datasets we observe that our method can + +reconstruct the backside of the hair more faithfully, reinforcing the importance of varied data from which to learn a powerful prior. For the backside reconstruction, robustness to viewpoint, and more visualizations see SupMat. + +# 4.3. Runtime Performance + +We evaluate the runtime performance in Tab. 3 by first dividing the hair reconstruction pipeline into three parts, 1) extraction of RGB features (DINOv2 features or in the case of the baseline methods: orientation maps, hair segmentation, etc.), 2) generation of the hair model, which in our + +![](images/4c3afe6db211e070478ec85f792ab024b144c3494b7b51d10e82d1f45c570045.jpg) +Figure 8. Unconditional generation. We train our diffusion model with Classifier-free Guidance [10] so that the same model can be evaluated both conditionally and unconditionally. Here we show unconditionally generated results where we observe a range of high-quality and diverse hairstyles. + +![](images/e66f72d74bc1b1fe65edbd64de74d4cb375b0ecec0b2b753accbc4d991c5c775.jpg) +RGB Input +Model: +Condition: +Figure 9. Ablation of conditioning signal and model architecture. Removing the local conditioning in the form of feature map $\mathcal{F}_{map}$ and relying only on the global CLS token severely affects the ability to reconstruct hair. Also generating scalp textures using a VAE yields overly smooth reconstructions. The combination of diffusion and local+global conditioning captures the most detail. + +![](images/44b79440f0ea3544fce4b83f503eaf3d011f31c18b67be64c13e69fd33f18572.jpg) +VAE +Global+Local + +![](images/d6fa5e34fcdb03a427c5ec0e40e2ce310b699bc0c324abf554c4ca5384eb1d6b.jpg) +Diffusion +Global + +![](images/0f371eac801f9e385cc859fc44d24e5758ca52956503211f7445db9ded8afd5c.jpg) +Diffusion +Global+Local + +case is the scalp texture while baseline methods create a 3D orientation field, 3) strand generation, which is the final step to either decode or grow the strands. All results are obtained on an NVIDIA H100 GPU. We observe that our method is overall the fastest as we do not need pre- or post-processing steps like head fitting, hair segmentation or hair growth and refinement. Note that our generated hair can be directly imported into Unreal Engine and rendered in real-time (60FPS) as shown in Fig. 6; see Supplemental Video. + +# 4.4. Ablation Study + +We perform an ablation study on the architecture and the importance of the conditioning signal in Fig. 9. Changing the scalp generation model to a VAE model similar to GroomGen [56] causes the hair to be overly smooth and lack local detail. Our proposed diffusion model conditioned with global and local features in the form of $\mathcal{F}_{map}$ and $\mathcal{F}_{cls}$ manages to capture the most detail. However, the local feature map is crucial and removing it causes the generated hair to deviate significantly from the input image. + +Thresholds: mm / degrees + +
    Method2/203/304/402/203/304/402/203/304/40
    Precision(↑)Recall(↑)F-score(↑)
    NeuralHDHair [48]47.9165.0773.7631.5951.1064.6338.0057.1268.73
    HairStep[55]40.8855.9964.0732.1644.9653.1535.5049.0657.20
    Ours43.6068.3081.7934.9758.2771.7938.3562.4176.20
    + +Table 1. Quantitative comparison with [48, 55] on [52]. It includes straight and curly hairstyles, please refer to the SupMat for more visualizations. + +
    MethodThresholds: mm / degrees
    2/203/304/402/203/304/402/203/304/40
    Precision(↑)Recall(↑)F-score(↑)
    NeuralHDHair [48]18.6536.2149.4619.2637.3351.6018.5535.7649.30
    HairStep[55]20.2235.5445.7320.8038.5352.8219.4234.3845.48
    Ours63.0684.1692.7857.9179.7189.8160.1381.6891.17
    + +Table 2. Quantitative comparison with [48, 55] on the DiffLocks evaluation set. Our results show substantial improvement over the baseline, particularly when reconstructing the backside of the hair due to our model's ability to learn a powerful prior over hairstyles. + +
    HairStepNeuralHDHairOurs
    RGB features (↓)3.174.860.10
    hair model (↓)0.454.991.83
    strand creation (↓)49.788.470.40
    total (s) (↓)53.4018.322.33
    + +Table 3. Timing. Comparison of the time in seconds needed for each part of the hair creation pipeline. + +# 5. Limitations and future work + +Despite the large amount of data, there are still gaps in the synthetic dataset; e.g. it lacks hairstyles with braids, accessories, ponytails, and buns. However, we believe that further improvements to the pipeline will allow such details to be created. Furthermore, the generation pipeline can also be easily extended to beards and eyebrows. + +We also note that DiffLocks prioritizes local hair details over perfect image alignment. However, for many tasks, generation or reconstruction is just the first step. When hair is animated with physics, the precise initial strand alignment is not critical, as the dynamic nature of hair makes the initial configuration transient. + +# 6. Conclusion + +We proposed a novel approach for generating 3D hair strands from a single image by first creating the largest dataset to date of synthetic hair paired with RGB images, and then by proposing an image-conditioned diffusion model based on scalp textures. Our method can create highly intricate 3D strands, surpassing previous methods and without requiring heuristic-based methods to increase the realism. + +Acknowledgments and Disclosures. We give thanks to Nathan Bajandas for all the Unreal images and videos. While MJB is a co-founder and Chief Scientist at Meshcapade, his research in this project was performed solely at, and funded solely by, the Max Planck Society. + +# References + +[1] Mengei Chai, Changxi Zheng, and Kun Zhou. A reduced model for interactive hairs. ACM Transactions on Graphics (TOG), 33(4):1-11, 2014. 1 +[2] Menglei Chai, Linjie Luo, Kalyan Sunkavalli, Nathan Carr, Sunil Hadap, and Kun Zhou. High-quality hair modeling from a single portrait photo. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12726-12735, 2023. 1, 6, 7, 8 +[56] Yuxiao Zhou, Menglei Chai, Alessandro Pepe, Markus Gross, and Thabo Beeler. Groomen: A high-quality generative hair model using hierarchical latent representations. ACM Transactions on Graphics (TOG), 42(6):1-16, 2023. 1, 2, 3, 5, 8 +[57] Yuxiao Zhou, Menglei Chai, Daoye Wang, Sebastian Winberg, Erroll Wood, Kripasindhu Sarkar, Markus Gross, and Thabo Beeler. Groomcap: High-fidelity prior-free hair capture. arXiv preprint arXiv:2409.00831, 2024. 1, 2 \ No newline at end of file diff --git a/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/images.zip b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ff206dc7960e0dde8a93f4c2479450fa68d97cf0 --- /dev/null +++ b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a34af31561ef910b089302d0aee99c0397636979a1cab0092750f8d59d099472 +size 470788 diff --git a/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/layout.json b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..10e5ae22191d4bd4e62d396020cb4b8bf159dd6f --- /dev/null +++ b/2025/DiffLocks_ Generating 3D Hair from a Single Image using Diffusion Models/layout.json @@ -0,0 +1,9493 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 169, + 103, + 442, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 169, + 103, + 442, + 140 + ], + "spans": [ + { + "bbox": [ + 169, + 103, + 442, + 140 + ], + "type": "text", + "content": "DiffLocks: Generating 3D Hair from a Single Image using Diffusion Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "spans": [ + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "text", + "content": "Radu Alexandru Rosu" + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "inline_equation", + "content": "^{1,\\ast}" + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "text", + "content": " Keyu Wu" + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "inline_equation", + "content": "^{2,\\ast,\\dagger}" + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "text", + "content": " Yao Feng" + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "inline_equation", + "content": "^{1,3}" + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "text", + "content": " Youyi Zheng" + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 79, + 160, + 526, + 175 + ], + "type": "text", + "content": " Michael J. 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Previous methods are primarily trained on synthetic data and cope with the limited amount of such data by using low-dimensional intermediate representations, such as guide strands and scalp-level embeddings, that require post-processing to decode, upsample, and add realism. These approaches fail to reconstruct detailed hair, struggle with curly hair, or are limited to handling only a few hairstyles. To overcome these limitations, we propose DiffLocks, a novel framework that enables detailed reconstruction of a wide variety of hairstyles directly from a single image. First, we address the lack of 3D hair data by automating the creation of the largest synthetic hair dataset to date, containing 40K hairstyles. Second, we leverage the synthetic hair dataset to learn an image-conditioned diffusion-transformer model that generates accurate 3D strands from a single frontal image. 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Given a single RGB image DiffLocks generates accurate 3D strands using a diffusion model. The model is trained on a novel synthetic hair dataset containing RGB images and corresponding 3D strands." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 396, + 555, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 396, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 396, + 555, + 456 + ], + "type": "text", + "content": "games, media and entertainment. Accurate hair representation greatly enhances the character's realism and overall visual quality. Unfortunately, both generating realistic hair and reconstructing it from an image are challenging due to the complex 3D geometry and the wide variety of hairstyles." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 459, + 556, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 556, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 556, + 544 + ], + "type": "text", + "content": "Since the release of the first 3D synthetic hair dataset [11], numerous methods for hair reconstruction have been proposed. Multi-view capture methods [17, 29, 31, 54, 57] and video-based approaches [24, 41, 49] are able to reconstruct high-fidelity 3D hair but are time-intensive and challenging to deploy due to their reliance on expensive capture equipment or strict capture conditions." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 545, + 557, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 557, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 557, + 715 + ], + "type": "text", + "content": "In contrast, single-view methods [3, 37, 48, 51, 55], which reconstruct 3D hair from a single image, are faster, more accessible, and user-friendly. These methods, however, often produce low-detail hair and handle only a restricted range of hairstyles. Furthermore, these methods struggle to handle male-pattern baldness and very curly hair such as afro-like hairstyles, which have a complex geometric structure (see [47]). Previous methods suffer from a lack of diverse and comprehensive hairstyle training datasets. To increase training set diversity, GroomGen [56], HAAR [42] and Fake It Till You Make It [46] use artist-created hairstyles together with data augmentation techniques to train their methods. However, their datasets are not released, do not have paired RGB images, or the creation pro" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 693, + 126, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 693, + 126, + 702 + ], + "spans": [ + { + "bbox": [ + 66, + 693, + 126, + 702 + ], + "type": "text", + "content": "*Joint first author" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 66, + 703, + 223, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 703, + 223, + 712 + ], + "spans": [ + { + "bbox": [ + 66, + 703, + 223, + 712 + ], + "type": "text", + "content": "†Work done during an internship at Meshcapade" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10847" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 212, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 212, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 212, + 83 + ], + "type": "text", + "content": "cess requires significant manual effort." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 87, + 296, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 87, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 87, + 296, + 277 + ], + "type": "text", + "content": "To cope with limited training data, previous approaches rely on several intermediate representations to simplify the problem. Most prior methods rely on oriented filters to capture the structure of hair in images. They also do not model hair strands directly but, instead, use a smaller number of guide strands and then upsample these to generate a hairstyle. Additionally, several methods use variational autoencoding to compress the guide strands across the scalp into a low-dimensional representation. All of these approaches are designed to cope with limtied training data but have two effects: (1) they limit the ability to model the complex spatial relationships between individual strands, and (2) they limit realism by working with low-dimensional representations. Effectively, they work in a compressed low-dimensional space and then need to upsample the results and post-process them to increase realism." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 281, + 296, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 296, + 460 + ], + "type": "text", + "content": "We take a different approach and focus on creating a sufficient amount of training data that we can remove the simplifying assumptions of previous methods. To that end, we present a novel 3D synthetic hair dataset consisting of 40K samples covering a wide variety of hairstyles; see Fig. 3. Each sample consists of 3D hair strands and a realistic RGB image rendered in Blender through path-tracing. We achieve this by automating the creation of the data using a variety of artist-inspired techniques. Traditional approaches are designed to create a single hairstyle using a small geometry node network tailored-made for that hairstyle. In contrast, we design a large and very general geometry node network in Blender that allows us to automatically create a large number of realistic hairstyles by changing the different parameters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 462, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 296, + 713 + ], + "type": "text", + "content": "We then leverage our dataset to train a novel hair diffusion framework, called DiffLocks, that is optionally conditioned on single RGB image in order to create highly detailed 3D strands; see Fig. 1. Specifically, we use Hourglass Diffusion Transformers (HDiT) [6] as a diffusion architecture and exploit features from a pretrained DINOv2 [30] model as a conditioning input to guide and control the generated results; see Fig. 2. The DINOv2 features are richer than the oriented filters used in many previous methods. Note that we directly regress the latent code for individual hair strands (instead of guide strands) enabling the transformer to learn detailed spatial relationships between strands across the scalp. With sufficient training data, there is no longer a need to first embed the hairstyle in a low-D scalp representation. We also model a density map that defines the probability of a strand being generated at each location on the scalp. All of these changes lead to increased realism, particularly for curly and balding hairstyles. Finally, our strand-based hair can be directly used in real-time game engines like Unreal Engine (Fig. 6) without additional heuristics to densify the hair or add fine-grained detail." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 203 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 203 + ], + "type": "text", + "content": "A key takeaway from our work is that, with sufficient training data, many of the key components of previous methods are no longer needed. For example, in contrast to the " + }, + { + "bbox": [ + 313, + 72, + 553, + 203 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 313, + 72, + 553, + 203 + ], + "type": "text", + "content": " scalp map used by HAAR, our diffusion model predicts a scalp texture of size " + }, + { + "bbox": [ + 313, + 72, + 553, + 203 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 72, + 553, + 203 + ], + "type": "text", + "content": " (each pixel containing a latent code for a single strand) from which DiffLocks directly decodes 3D strands. No post-processing is needed, such as hair upsampling or the addition of random noise (cf. [56]). The dataset already contains realistic hairstyles with flyaway strands, so the diffusion model learns to create them." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 326, + 205, + 489, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 205, + 489, + 216 + ], + "spans": [ + { + "bbox": [ + 326, + 205, + 489, + 216 + ], + "type": "text", + "content": "In summary, our main contributions are:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 218, + 553, + 384 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 314, + 218, + 553, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 218, + 553, + 266 + ], + "spans": [ + { + "bbox": [ + 314, + 218, + 553, + 266 + ], + "type": "text", + "content": "- a novel 3D hair dataset containing 40K diverse and realistic 3D hairstyles with corresponding RGB images. We make the dataset public in order to support future research in hair modeling and synthesis," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 266, + 553, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 266, + 553, + 301 + ], + "spans": [ + { + "bbox": [ + 313, + 266, + 553, + 301 + ], + "type": "text", + "content": "- an improved scalp representation that facilitates the reconstruction of hair styles with different hair density (bald spots, male pattern baldness, etc.)," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 301, + 553, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 553, + 384 + ], + "type": "text", + "content": "- a novel conditional scalp diffusion framework for robustly generating 3D hair directly from a single RGB image, bypassing a 2D orientation map. This framework can effectively create a variety of challenging hairstyles, while achieving the state-of-the-art performance and enable, for the first time, reconstruction of Afro-like and bald hairstyles. The model will be available for research." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 399, + 405, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 405, + 412 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 405, + 412 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 421, + 555, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 421, + 555, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 421, + 555, + 685 + ], + "type": "text", + "content": "3D Hair Reconstruction. The pioneering hair reconstruction work of Paris et al. [31] set the stage for numerous multi-view-based hair reconstruction methods. Since then, various methods [17, 25, 26, 29, 57] reconstruct the 3D geometric features of hair constrained by a 2D orientation map. In many cases this requires specialized hardware or multicamera rigs. In contrast, monocular video based methods [24, 41, 44, 49] sacrifice some accuracy to avoid expensive and specialized equipment. While achieving impressive results, such methods still require carefully captured data. To relax the capture conditions, single-view-based methods [3, 37, 48, 51, 53, 53] employ deep neural networks to infer volumetric fields by exploiting data priors learned from 3D synthetic datasets. Such methods enable rapid 3D hair reconstruction but typically generate low fidelity hair and can handle only a limited range of hairstyles due to the significant lack of diversity in existing 3D hair datasets. Similar to these methods, our approach also reconstructs hair from a single image. However, our work focuses on fast and robust reconstruction of diverse hairstyles, including challenging types such as balding and tightly curled (afro-like) styles; such hairstyles have received relatively little attention." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "type": "text", + "content": "3D Hair Generation. In addition to hair reconstruction, hair generation is another challenge, which, if solved, could" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10848" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 545, + 186 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 545, + 186 + ], + "type": "image", + "image_path": "11b00eeec5a8d13730cab3f5fda39811fc2edccd56d75fb8d9a08cace937f089.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "lines": [ + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "text", + "content": "Figure 2. Method. Given a single RGB image, we use a pretrained DINOv2 model to extract local and global features, which are used to guide a scalp diffusion model. The scalp diffusion model denoises a density map and a scalp texture containing latent codes for strand geometry. Finally, we probabilistically sample texels from the scalp texture and decode the latent code " + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 55, + 190, + 555, + 236 + ], + "type": "text", + "content": " into strands of 256 points. Decoding in parallel 100K strands yields the final hairstyle." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 251, + 297, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 251, + 297, + 529 + ], + "spans": [ + { + "bbox": [ + 54, + 251, + 297, + 529 + ], + "type": "text", + "content": "provide synthetic data for learning high-quality hair reconstruction. Ren et al. [34] propose a heuristic example-based hair generation method that is significantly limited by the reference hair models. Saito et al. [37] encode a 3D hair dataset with a Variational autoencoder (VAE), enabling them to generate plausible yet overly smooth hairstyles. To achieve high-quality and diverse hairstyles, Perm [9] leverages existing public 3D datasets, disentangling the global shape and local details of hair strands. Despite progress, the scale and diversity of synthetic 3D hair datasets is still far from what is needed. GroomGen [56] and HAAR [42] incorporate parametrized variations based on high-quality hairstyles crafted by artists, further enhancing the diversity of 3D hair datasets. They also train generative models to produce 3D hairstyles from noisy inputs or text prompts. Recently, Curly-Cue [47] focuses on the principles behind curly, afro-style, hair and provides tools for animators to create realistic hairstyles. In our work, we propose a low-cost synthetic 3D hair generation pipeline and use it to construct a new dataset that is more diverse than previous ones, containing 40K 3D synthetic hairstyles. Additionally, we use this dataset to train a generative hair model that is conditioned on a single input image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 534, + 298, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 298, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 298, + 714 + ], + "type": "text", + "content": "Image-To-3D via Diffusion Models. Early work on neural reconstruction of 3D objects from images [7, 28, 50] distills information from pretrained 2D diffusion models, such as Stable Diffusion [35], using techniques like Score Distillation Sampling (SDS) [33]. However, these pretrained models lack the multi-view information essential for accurate 3D reconstruction. To address this, later approaches [20, 21, 40] train custom 2D diffusion models to generate multi-view images from a given input, enabling more accurate 3D object reconstruction by integrating this multi-view data [13, 23]. While effective, this approach can be time-intensive due to the sampling and reconstruction processes, which has led to an alternative line of research focused on training diffusion models to generate 3D representations directly, such as meshes [22] or triplane repre" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 251, + 556, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 251, + 556, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 251, + 556, + 324 + ], + "type": "text", + "content": "sentations [4]. However, these methods often demand significant computational resources for 3D processing. In contrast, our method produces a 2D representation that contains 3D hair information, enabling direct decoding into 3D hair without the need for extensive multi-view generation or resource-intensive training of 3D diffusion models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 333, + 370, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 333, + 370, + 345 + ], + "spans": [ + { + "bbox": [ + 313, + 333, + 370, + 345 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 353, + 556, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 353, + 556, + 462 + ], + "spans": [ + { + "bbox": [ + 313, + 353, + 556, + 462 + ], + "type": "text", + "content": "In this section, we present our pipeline for 3D hair reconstruction from a single image, consisting of three key stages: 1) A data generation pipeline using Blender's geometry nodes to create a large, diverse, image-3D paired synthetic hair dataset (Sec. 3.1); 2) Parameterization of hair strands and hairstyles into a canonical scalp space to obtain scalp textures (Sec. 3.2); And 3) training a conditional diffusion model, DiffLocks, using the generated synthetic images and the scalp textures as shown in Fig. 2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 467, + 416, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 416, + 478 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 416, + 478 + ], + "type": "text", + "content": "3.1. Data Generation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 483, + 556, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 556, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 556, + 592 + ], + "type": "text", + "content": "A key bottleneck in the field of 3D hair reconstruction is the limited availability of public datasets, with only 343 hairstyles for USC-HairSalon [11] and 10 for CT2Hair [39]. Additionally, these datasets lack corresponding 2D images, which limits their usability. Thus, here we propose a novel data generation pipeline, which uses Blender geometry nodes to add variation to a small set of manually defined guide strands as shown in Fig. 4. Next, we will describe the main steps of the pipeline." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 594, + 557, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 557, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 557, + 715 + ], + "type": "text", + "content": "Scalp creation. The first step in creating the new dataset is defining a scalp mesh onto which to build the hairstyles. Due to its wide applicability in the human-reconstruction field, we use the SMPL-X model [32] to define our scalp. We create a SMPL-X neutral body with mean body shape from which we manually select the vertices corresponding to the scalp and extract a mesh of 513 vertices as seen in Fig. 2. The scalp mesh is then UV-unwrapped into a single chart using an As-Rigid-As-Possible (ARAP) parametrization [43] in order to minimize distortions. This" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10849" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 69, + 138, + 152 + ], + "blocks": [ + { + "bbox": [ + 57, + 69, + 138, + 152 + ], + "lines": [ + { + "bbox": [ + 57, + 69, + 138, + 152 + ], + "spans": [ + { + "bbox": [ + 57, + 69, + 138, + 152 + ], + "type": "image", + "image_path": "bf09dc3d1d7dc770e866fdca3b9cf68fa4dcba423c63eebe63b9a80c7200fe08.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 155, + 555, + 177 + ], + "lines": [ + { + "bbox": [ + 55, + 155, + 555, + 177 + ], + "spans": [ + { + "bbox": [ + 55, + 155, + 555, + 177 + ], + "type": "text", + "content": "Figure 3. Synthetic data. Sample RGB images from our synthetic hair dataset. Each sample from the dataset contains an image at " + }, + { + "bbox": [ + 55, + 155, + 555, + 177 + ], + "type": "inline_equation", + "content": "768 \\times 768" + }, + { + "bbox": [ + 55, + 155, + 555, + 177 + ], + "type": "text", + "content": " resolution together with the corresponding 3D strand geometry of " + }, + { + "bbox": [ + 55, + 155, + 555, + 177 + ], + "type": "inline_equation", + "content": "\\approx 100\\mathrm{K}" + }, + { + "bbox": [ + 55, + 155, + 555, + 177 + ], + "type": "text", + "content": " strands." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 139, + 70, + 220, + 152 + ], + "blocks": [ + { + "bbox": [ + 139, + 70, + 220, + 152 + ], + "lines": [ + { + "bbox": [ + 139, + 70, + 220, + 152 + ], + "spans": [ + { + "bbox": [ + 139, + 70, + 220, + 152 + ], + "type": "image", + "image_path": "86f18bcb6d6fb40e8be568ab4b605b7b5b4a14a3a5d3cbf1b6400f4107944404.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 221, + 70, + 303, + 152 + ], + "blocks": [ + { + "bbox": [ + 221, + 70, + 303, + 152 + ], + "lines": [ + { + "bbox": [ + 221, + 70, + 303, + 152 + ], + "spans": [ + { + "bbox": [ + 221, + 70, + 303, + 152 + ], + "type": "image", + "image_path": "46556d4d30d62af92354bf4e34454212b7efb36d0a0177db0ec06a76ba2d862f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 304, + 70, + 386, + 152 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 386, + 152 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 386, + 152 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 386, + 152 + ], + "type": "image", + "image_path": "be984e13daaa5becb3b5d841e5be95cc70632b5579896500c66d6bc4eb5f21a2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 386, + 70, + 468, + 152 + ], + "blocks": [ + { + "bbox": [ + 386, + 70, + 468, + 152 + ], + "lines": [ + { + "bbox": [ + 386, + 70, + 468, + 152 + ], + "spans": [ + { + "bbox": [ + 386, + 70, + 468, + 152 + ], + "type": "image", + "image_path": "5e9ef72ab27a9ea82de13d34626aca378d67ec8f8a813d6d0fa3279c92dda0ab.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 469, + 70, + 551, + 152 + ], + "blocks": [ + { + "bbox": [ + 469, + 70, + 551, + 152 + ], + "lines": [ + { + "bbox": [ + 469, + 70, + 551, + 152 + ], + "spans": [ + { + "bbox": [ + 469, + 70, + 551, + 152 + ], + "type": "image", + "image_path": "9c6256f2749fded413ca15c16b15dcb513be9fe6510081a2557d19dc086b3ee8.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 65, + 198, + 289, + 308 + ], + "blocks": [ + { + "bbox": [ + 65, + 198, + 289, + 308 + ], + "lines": [ + { + "bbox": [ + 65, + 198, + 289, + 308 + ], + "spans": [ + { + "bbox": [ + 65, + 198, + 289, + 308 + ], + "type": "image", + "image_path": "6d188e4c76e1d5a0ee2d640fcb1f050618e3e7db1a85f5d0a57c33c8725a3658.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 314, + 295, + 357 + ], + "lines": [ + { + "bbox": [ + 55, + 314, + 295, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 295, + 357 + ], + "type": "text", + "content": "Figure 4. Base hairstyles. Starting from a coarse set of guide strands, our Blender pipeline is able to generate a wide variety of hairstyles, covering different lengths, curliness and density patterns. Best viewed zoomed in." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 380, + 295, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 380, + 295, + 417 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 295, + 417 + ], + "type": "text", + "content": "operation is done only once and need not be repeated for each subject since they all share the same SMPL-X body topology." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 422, + 295, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 295, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 295, + 540 + ], + "type": "text", + "content": "Base hairstyle creation. The scalp mesh is imported into Blender and a series of hairstyles is manually created in the form of coarsely defined guide strands (Fig. 4). The base hairstyles define a starting point for the randomization process and therefore do not need to contain fine details, rather defining just the overall shape and direction of the hair. We manually create 75 base hairstyles, each represented by " + }, + { + "bbox": [ + 55, + 422, + 295, + 540 + ], + "type": "inline_equation", + "content": "\\approx 50" + }, + { + "bbox": [ + 55, + 422, + 295, + 540 + ], + "type": "text", + "content": " strands. We note that this is not a labour intensive process, as each base hairstyle takes only a few minutes to create." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 546, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 546, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 546, + 295, + 713 + ], + "type": "text", + "content": "Randomization pipeline. The guide strands are passed through a series of transformations defined as geometry nodes in Blender that gradually add more detail to the hair. The guide strands are first interpolated to 100K strands, after which clumping, curling and noise are applied. These operations are repeated multiple times with various intensities. Special attention must be given to prevent the hair from penetrating the scalp or intersecting with the body for which we apply shrinkwrap modifiers at various stages in the pipeline. In total the pipeline consists of 58 geometry nodes that transform the hair together with 349 auxiliary nodes that help feed parameters into the main nodes. We also define a hair BSDF using the Chiang model [5] for the strands material. Lastly we apply physics simulation to" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 198, + 554, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 198, + 554, + 258 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 554, + 258 + ], + "type": "text", + "content": "the strands using Blender's cloth simulation and randomize wind direction and gravity strength. A total of 110 parameters govern the whole Blender generation pipeline (geometry+material) and we select them at random with minimum and maximum ranges chosen empirically." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "spans": [ + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "type": "text", + "content": "Scene setup. In order to render realistic images, it is crucial to match the lighting of real scenes. For this, we use 255 HDRIs from Poly Haven1 and randomize their exposure and azimuthal angle. Additionally, we randomly select albedo, normal and roughness textures for the bodies from a library of artist-created SMPL-X textures. Furthermore, we also randomly change the face expression coefficients within the range " + }, + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "type": "text", + "content": ". We keep the jaw closed since we observed it can cause issues with strands physics. To train our network for robustness to different camera parameters, we also randomize camera position (maintaining the look-at direction towards the head) and focal length in the range " + }, + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "type": "inline_equation", + "content": "40\\mathrm{mm}" + }, + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "type": "inline_equation", + "content": "150\\mathrm{mm}" + }, + { + "bbox": [ + 313, + 262, + 554, + 429 + ], + "type": "text", + "content": ". For a study on network robustness to camera parameters please refer to the SupMat." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 431, + 554, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 554, + 527 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 554, + 527 + ], + "type": "text", + "content": "Full dataset. The full dataset contains 40K samples each containing 3D strands with " + }, + { + "bbox": [ + 313, + 431, + 554, + 527 + ], + "type": "inline_equation", + "content": "\\approx 100\\mathrm{K}" + }, + { + "bbox": [ + 313, + 431, + 554, + 527 + ], + "type": "text", + "content": " strands and a corresponding RGB image rendered through path tracing at " + }, + { + "bbox": [ + 313, + 431, + 554, + 527 + ], + "type": "inline_equation", + "content": "768 \\times 768" + }, + { + "bbox": [ + 313, + 431, + 554, + 527 + ], + "type": "text", + "content": " resolution. We additionally save a density map that defines the probability of a strand being generated at each texel of the scalp as shown in Fig. 5. The density map is especially useful for modelling hairstyles with balding patterns." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 534, + 464, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 464, + 547 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 464, + 547 + ], + "type": "text", + "content": "3.2. Hairstyle Parameterization" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": "Strand Parameterization. Formally, we represent a 3D strand as a set of " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": " 3D points " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{S} = \\{\\mathbf{p}_1,\\mathbf{p}_2,\\dots ,\\mathbf{p}_L\\}" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "L = 256" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": ". A full hairstyle consists of a set of " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "\\approx 100\\mathrm{K}" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": " strands " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{H} = \\{\\mathbf{S}_j\\}_{0}^{100\\mathrm{K}}" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": ". Similar to Neural Strands [36], we train a strand VAE to compress individual strands into a compact latent code " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{z}\\in \\mathbb{R}^{64}" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": ". The encoder of the VAE denoted by " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "\\mathcal{E}()" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": " is modeled as a series of 1D convolutions and the decoder denoted by " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "\\mathcal{G}()" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": " is a modulated SIREN [27] that maps the latent code " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": " back to a series of 3D points " + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 313, + 552, + 554, + 659 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 659, + 554, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 659, + 554, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 659, + 554, + 696 + ], + "type": "text", + "content": "In addition to the position and direction loss proposed by Neural Strands [36], we incorporate a curvature loss " + }, + { + "bbox": [ + 313, + 659, + 554, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cur}}" + }, + { + "bbox": [ + 313, + 659, + 554, + 696 + ], + "type": "text", + "content": ". This is motivated by the observation that, for highly coiled" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 325, + 702, + 421, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 702, + 421, + 712 + ], + "spans": [ + { + "bbox": [ + 325, + 702, + 421, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 325, + 702, + 421, + 712 + ], + "type": "text", + "content": "https://polyhaven.com/hdris" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10850" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "text", + "content": "hair, it is more perceptually impactful to match the curvature of the strand rather than matching the position of every point along the strand (i.e., as long as the strand looks curvy, it is acceptable to commit errors in per-point position). For an evaluation of this observation please refer to the SupMat. We define the local curvature as the instantaneous change in direction: " + }, + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "inline_equation", + "content": "\\kappa_{i} = \\mathbf{d}_{i + 1} - \\mathbf{d}_{i}" + }, + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "text", + "content": " where the direction is defined as the change in position: " + }, + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i = \\mathbf{p}_{i + 1} - \\mathbf{p}_i" + }, + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "text", + "content": ". Therefore, the new curvature loss is defined as the L1 distance between the ground-truth and the prediction: " + }, + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cur}} = \\sum_{0}^{L}|\\kappa_{i} - \\tilde{\\kappa}_{i}|" + }, + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "inline_equation", + "content": "\\hat{\\kappa}_i" + }, + { + "bbox": [ + 55, + 72, + 296, + 214 + ], + "type": "text", + "content": " is the curvature of the predicted strand." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 216, + 296, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 216, + 296, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 216, + 296, + 264 + ], + "type": "text", + "content": "The final training loss of our strands VAE is a weighted combination of a data term consisting of positional, directional and curvature losses together with a KL regularization term:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 268, + 295, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 268, + 295, + 300 + ], + "spans": [ + { + "bbox": [ + 67, + 268, + 295, + 300 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {d a t a}} = \\sum_ {0} ^ {L} | \\mathbf {p} _ {i} - \\tilde {\\mathbf {p}} _ {i} | + \\lambda_ {1} | \\mathbf {d} _ {i} - \\tilde {\\mathbf {d}} _ {i} | + \\lambda_ {2} | \\boldsymbol {\\kappa} _ {i} - \\tilde {\\boldsymbol {\\kappa}} _ {i} | \\tag {1}", + "image_path": "e6f29468431ef0a07a3544166627a00fa4eec919285b29fe060f7f61716ce9b8.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 303, + 295, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 303, + 295, + 316 + ], + "spans": [ + { + "bbox": [ + 66, + 303, + 295, + 316 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {V A E}} = \\mathcal {L} _ {\\mathrm {d a t a}} + \\lambda_ {\\mathrm {K L}} \\mathcal {L} _ {\\mathrm {K L}}. \\tag {2}", + "image_path": "cfde1a13022c953716c44901f01a4f7c6dd133a1681891d8dd7f80e360343102.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 322, + 296, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 322, + 296, + 346 + ], + "spans": [ + { + "bbox": [ + 55, + 322, + 296, + 346 + ], + "type": "text", + "content": "For more details on the hyperparameters please refer to the SupMat." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "spans": [ + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "text", + "content": "Neural Scalp Texture. Each 3D hairstyle generated from the Blender pipeline is parametrized onto the scalp surface using a regular 2D texture. Specifically, each strand " + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "text", + "content": " is encoded to a latent code " + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "text", + "content": " by the strand encoder " + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathcal{E}(\\mathbf{S})" + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "text", + "content": " and directly assigned to the texel corresponding to the root of the strand. If two strands are so close together that they are assigned the same texel on the scalp, one of them is chosen at random. This produces a raw scalp texture " + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\text{raw}} \\in \\mathbb{R}^{256 \\times 256 \\times 64}" + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "text", + "content": ", as shown in Fig. 5c where each texel contains a latent strand code. Since not all regions of the scalp have an equal hair density, we introduce a density map " + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{D} \\in \\mathbb{R}^{256 \\times 256 \\times 1}" + }, + { + "bbox": [ + 55, + 360, + 296, + 538 + ], + "type": "text", + "content": " with values in the range [0, 1] that defines the probability of a strand being present at each texel. For more discussion on the properties of the density map please refer to the SupMat." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 539, + 295, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 539, + 295, + 658 + ], + "spans": [ + { + "bbox": [ + 55, + 539, + 295, + 658 + ], + "type": "text", + "content": "The aforementioned creation of the scalp texture can create sparse regions with no latent codes since not every texel will correspond to a strand. This sparsity is particularly evident for hairstyles with balding patterns and can cause issues when decoding the texture back to 3D since sampling a texel with no assigned latent code would yield undefined strand geometry. To avoid this issue, we interpolate the sparsely assigned latent codes by using a push-pull algorithm [16] that ensures that every texel on the scalp has a valid strand latent code as shown in Fig. 5d." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "type": "text", + "content": "With the interpolated scalp texture " + }, + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "type": "text", + "content": ", we can sample at UV-positions according to the density " + }, + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "type": "text", + "content": ", and produce a full hairstyle " + }, + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 55, + 658, + 296, + 694 + ], + "type": "text", + "content": " by decoding each latent code:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 124, + 700, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 700, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 124, + 700, + 295, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {H} = \\mathcal {G} (\\text {S a m p l e} (\\mathbf {T}, \\mathbf {D})) \\tag {3}", + "image_path": "2877ee65f80a5a16f4a8d3f5d460d11a715eba435338ce9b133b57116fc1aa97.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\text{Sample}(\\cdot)" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": " performs probabilistic sampling in UV space such that regions with high density are sampled more often, allowing us to represent hairstyles with varying density of hair. To create a full hairstyle we sample 100K positions on the scalp and extract strand latent codes " + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 313, + 72, + 553, + 144 + ], + "type": "text", + "content": " using bilinear interpolation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 150, + 467, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 150, + 467, + 163 + ], + "spans": [ + { + "bbox": [ + 313, + 150, + 467, + 163 + ], + "type": "text", + "content": "3.3. Conditional Scalp Diffusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": "Diffusion framework. Similar to previous methods [42, 56] we train a generative model of scalp textures " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": " to learn the prior distribution over hairstyles. Furthermore, we condition the model on image data, enabling high-quality 3D hair generation from a single image. Specifically, we train a denoiser model " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": " using a Hourglass Diffusion Transformer [6] architecture, which is particularly efficient for pixel-space diffusion tasks. We denote the clean training sample for the diffusion as the concatenation of scalp texture and density map: " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{y} = [\\mathbf{T},\\mathbf{D}]" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": " and the noised input " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = \\mathbf{y} + \\mathbf{n}" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": " as a combination of the clean data " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": " and noise " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{n} \\sim \\mathcal{N}(0,\\sigma^2\\mathbf{I})" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": " with noise level " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": ". Following EDM [14], we parametrize the denoiser to allow it to predict " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 313, + 167, + 555, + 335 + ], + "type": "text", + "content": ", or something in between:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 319, + 342, + 555, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 342, + 555, + 357 + ], + "spans": [ + { + "bbox": [ + 319, + 342, + 555, + 357 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {\\theta} (\\mathbf {x}; \\sigma) = c _ {\\text {s k i p}} (\\sigma) \\mathbf {x} + c _ {\\text {o u t}} (\\sigma) \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\sigma) \\mathbf {x}; c _ {\\text {n o i s e}} (\\sigma)\\right) \\tag {4}", + "image_path": "003c418fd1768dde2779294fafac96d1fdd9849af937031167f57aefdfa8955a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\theta}" + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "text", + "content": " is the network to train, " + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{skip}}" + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "text", + "content": " is as a skip connection modulator, " + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}}" + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{out}}" + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "text", + "content": " scale the input and output magnitude, and " + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{noise}}" + }, + { + "bbox": [ + 313, + 361, + 554, + 409 + ], + "type": "text", + "content": " is the time condition of the network. Please refer to the EDM paper [14] for more details." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 410, + 554, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 554, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 554, + 433 + ], + "type": "text", + "content": "The training loss for each spatial element and each noise level is defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 351, + 440, + 553, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 440, + 553, + 453 + ], + "spans": [ + { + "bbox": [ + 351, + 440, + 553, + 453 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, \\mathbf {y}, \\mathbf {n}, \\sigma\\right) = \\left\\| \\mathcal {D} _ {\\theta} (\\mathbf {y} + \\mathbf {n}; \\sigma) - \\mathbf {y} \\right\\| _ {2} ^ {2}. \\tag {5}", + "image_path": "471a7df06c5a53bf12c998e5e526620a1e752aad6c89a9d248876155000aa186.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "text", + "content": "Loss scaling. The denoising network outputs a clean scalp texture " + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "text", + "content": " and a density map " + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "text", + "content": ". However, we observe that not all channels of the scalp texture are equally significant, some encode relevant information such as length or curliness, while others are noisy and have little impact on the decoded strand. We propose to down-weight the loss of the channels of the scalp textures based on their perceptual change to the strand shape. Since we have no direct metric to evaluate perceptual change, we reuse the data term from the loss " + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{data}}" + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "text", + "content": " used to train the StrandVAE. More specifically, we first define the mean strand predicted by the VAE as " + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_0 = \\mathcal{G}(\\mathbf{z}_0)" + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "text", + "content": " by decoding from a zero latent vector " + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0 = [0]^{64}" + }, + { + "bbox": [ + 313, + 467, + 555, + 693 + ], + "type": "text", + "content": ". Following that, we individually perturb each dimension of the latent code, decode a strand, and calculate the distance to the mean strand as measured by the loss. This can be seen as a metric that quantifies perceptual changes as a result of individual changes to the latent code dimensions. Therefore, the weight associated with each dimension of the latent code is:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 368, + 701, + 553, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 701, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 368, + 701, + 553, + 714 + ], + "type": "interline_equation", + "content": "w _ {i} = \\mathcal {L} _ {\\text {s t r a n d}} \\left(S _ {0}, \\mathcal {G} \\left(\\mathbf {z} _ {0} + \\epsilon \\cdot \\mathbf {j} _ {i}\\right)\\right), \\tag {6}", + "image_path": "bb2e44d89996f37de7eb08430c893ed75094e91f56692006bf933863fb3fbcb0.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10851" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{j}_i" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " is vector of zeros with a 1 at the i-th position and " + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 72, + 295, + 109 + ], + "type": "text", + "content": " is the perturbation strength which we empirically set to 0.8. We obtain a final weight vector by normalizing:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 116, + 295, + 143 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 116, + 295, + 143 + ], + "spans": [ + { + "bbox": [ + 145, + 116, + 295, + 143 + ], + "type": "interline_equation", + "content": "\\mathbf {w} = \\frac {w _ {i}}{\\sum_ {0} ^ {6 4} w _ {i}}. \\tag {7}", + "image_path": "047c1530b5b48008c0a8f061faa2322d81232a3d9bb2740e9dfffe87fc8f9d1d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 149, + 295, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 149, + 295, + 173 + ], + "spans": [ + { + "bbox": [ + 55, + 149, + 295, + 173 + ], + "type": "text", + "content": "For an evaluation and discussion of the proposed weighting scheme, please see SupMat." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 174, + 296, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 174, + 296, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 174, + 296, + 281 + ], + "type": "text", + "content": "In addition, we also incorporate a weighting term in order to equalize the error contribution across noise levels by taking the approach of EDM2 [15], which treats denoising as a form of multi-task learning and lets the network predict a log-variance of the uncertainty " + }, + { + "bbox": [ + 55, + 174, + 296, + 281 + ], + "type": "inline_equation", + "content": "u(\\sigma)" + }, + { + "bbox": [ + 55, + 174, + 296, + 281 + ], + "type": "text", + "content": " for a certain noise level. Combining the per-channel weighting with the per-noise level weighting we obtain our final formulation for the diffusion loss as an expectation over noise levels and spatial dimensions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 64, + 289, + 295, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 289, + 295, + 312 + ], + "spans": [ + { + "bbox": [ + 64, + 289, + 295, + 312 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, u\\right) = \\mathbb {E} _ {\\mathbf {y}, \\mathbf {n}, \\sigma} \\left[ \\frac {\\mathbf {w}}{e ^ {u (\\sigma)}} \\mathcal {L} \\left(\\mathcal {D} _ {\\theta}, \\mathbf {y}, \\mathbf {n}, \\sigma\\right) + u (\\sigma) \\right]. \\tag {8}", + "image_path": "da9f7ba78f3c83be63b53d6dafd83363310b12451cd83be893832926c3088086.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 323, + 295, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 323, + 295, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 323, + 295, + 491 + ], + "type": "text", + "content": "RGB conditioning. Previous approaches have primarily relied on 2D orientation maps [31, 55] extracted using Gabor filters in order to align the generated strands with the image. However, orientation maps cannot infer the hair growth direction and tend to be noisy for heavily occluded hairstyles. In our work, we forego the need to compute orientation maps and instead condition our diffusion network using robust DINOv2 [30] features extracted from the image. Specifically, we use the pre-trained DINOv2-large model to encode the RGB image into a feature map " + }, + { + "bbox": [ + 55, + 323, + 295, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{map} \\in \\mathbb{R}^{55 \\times 55 \\times 1024}" + }, + { + "bbox": [ + 55, + 323, + 295, + 491 + ], + "type": "text", + "content": " and a global CLS token " + }, + { + "bbox": [ + 55, + 323, + 295, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{cls} \\in \\mathbb{R}^{1024}" + }, + { + "bbox": [ + 55, + 323, + 295, + 491 + ], + "type": "text", + "content": ". Additionally, our rendered images are sufficiently realistic such that the network trained only on synthetic data, can generalize to in-the-wild images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "type": "text", + "content": "Since the scalp texture and the RGB image are not spatially aligned, we add cross-attention layers before each downsampling layer of the denoiser and let the network learn which regions of the feature map " + }, + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{map}" + }, + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "type": "text", + "content": " it should attend to. The CLS token " + }, + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{cls}" + }, + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "type": "text", + "content": " is used to globally condition the network similar to the time condition " + }, + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 491, + 295, + 574 + ], + "type": "text", + "content": " as described in HDiT [6]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 574, + 295, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 574, + 295, + 623 + ], + "spans": [ + { + "bbox": [ + 55, + 574, + 295, + 623 + ], + "type": "text", + "content": "Furthermore, in order to use the same network both conditionally and unconditionally, we train the denoiser using Classifier-Free Guidance [10] by randomly dropping the conditioning signal with " + }, + { + "bbox": [ + 55, + 574, + 295, + 623 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 55, + 574, + 295, + 623 + ], + "type": "text", + "content": " probability (Fig. 8)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 623, + 295, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 623, + 295, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 623, + 295, + 647 + ], + "type": "text", + "content": "For experiments on conditioning using DINOv2 features vs orientation maps, please refer to SupMat." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 657, + 136, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 657, + 136, + 671 + ], + "spans": [ + { + "bbox": [ + 55, + 657, + 136, + 671 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 713 + ], + "type": "text", + "content": "We evaluate DiffLocks using both synthetic data and in-the-wild images. We also perform ablation studies to assess the importance of the different components of our method" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 322, + 71, + 376, + 125 + ], + "blocks": [ + { + "bbox": [ + 322, + 71, + 376, + 125 + ], + "lines": [ + { + "bbox": [ + 322, + 71, + 376, + 125 + ], + "spans": [ + { + "bbox": [ + 322, + 71, + 376, + 125 + ], + "type": "image", + "image_path": "dd0e895f013d52904ef1681656a41255e8646fa764a8102ca0b7718a45f4e257.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 128, + 371, + 147 + ], + "lines": [ + { + "bbox": [ + 328, + 128, + 371, + 147 + ], + "spans": [ + { + "bbox": [ + 328, + 128, + 371, + 147 + ], + "type": "text", + "content": "(a) Synthetic Image" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 377, + 71, + 433, + 125 + ], + "blocks": [ + { + "bbox": [ + 377, + 71, + 433, + 125 + ], + "lines": [ + { + "bbox": [ + 377, + 71, + 433, + 125 + ], + "spans": [ + { + "bbox": [ + 377, + 71, + 433, + 125 + ], + "type": "image", + "image_path": "64e3f621fa06331ec53edb1ac3461d19abc0072a32e3f182e29112dd5c79065b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 378, + 128, + 433, + 138 + ], + "lines": [ + { + "bbox": [ + 378, + 128, + 433, + 138 + ], + "spans": [ + { + "bbox": [ + 378, + 128, + 433, + 138 + ], + "type": "text", + "content": "(b) Scalp density" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 434, + 71, + 490, + 125 + ], + "blocks": [ + { + "bbox": [ + 434, + 71, + 490, + 125 + ], + "lines": [ + { + "bbox": [ + 434, + 71, + 490, + 125 + ], + "spans": [ + { + "bbox": [ + 434, + 71, + 490, + 125 + ], + "type": "image", + "image_path": "02d8c2cd6ac17284d3fcb7dcd1f579e71dc8df34866411f968e5b8f06012677e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 438, + 128, + 489, + 146 + ], + "lines": [ + { + "bbox": [ + 438, + 128, + 489, + 146 + ], + "spans": [ + { + "bbox": [ + 438, + 128, + 489, + 146 + ], + "type": "text", + "content": "(c) Raw scalp texture" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 490, + 71, + 545, + 125 + ], + "blocks": [ + { + "bbox": [ + 490, + 71, + 545, + 125 + ], + "lines": [ + { + "bbox": [ + 490, + 71, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 490, + 71, + 545, + 125 + ], + "type": "image", + "image_path": "8fc377919fb412952e6cf3cb37189fe35f84b60da667958e87a1226f083f42bf.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 491, + 128, + 543, + 146 + ], + "lines": [ + { + "bbox": [ + 491, + 128, + 543, + 146 + ], + "spans": [ + { + "bbox": [ + 491, + 128, + 543, + 146 + ], + "type": "text", + "content": "(d) Interpolated texture" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 315, + 217, + 362, + 273 + ], + "blocks": [ + { + "bbox": [ + 313, + 151, + 555, + 207 + ], + "lines": [ + { + "bbox": [ + 313, + 151, + 555, + 207 + ], + "spans": [ + { + "bbox": [ + 313, + 151, + 555, + 207 + ], + "type": "text", + "content": "Figure 5. Scalp interpolation. Embedding each strand onto a the scalp texture can leave gaps where no strand is present. In order to enable probabilistic sampling of strands, we interpolate the sparse strand embeddings to achieve a smooth scalp texture that can be sampled at any position according to the density." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 315, + 217, + 362, + 273 + ], + "lines": [ + { + "bbox": [ + 315, + 217, + 362, + 273 + ], + "spans": [ + { + "bbox": [ + 315, + 217, + 362, + 273 + ], + "type": "image", + "image_path": "3664be4a609d78747f38714d5e88fa0f19d6e743f468cdfc4db6cce08f81b2b7.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 274, + 358, + 284 + ], + "lines": [ + { + "bbox": [ + 320, + 274, + 358, + 284 + ], + "spans": [ + { + "bbox": [ + 320, + 274, + 358, + 284 + ], + "type": "text", + "content": "RGB Input" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 299, + 554, + 344 + ], + "lines": [ + { + "bbox": [ + 313, + 299, + 554, + 344 + ], + "spans": [ + { + "bbox": [ + 313, + 299, + 554, + 344 + ], + "type": "text", + "content": "Figure 6. Rendering/Simulation. Our generated hair can be directly imported into Blender or Unreal Engine as an Alembic file. In Unreal Engine, the hair can be rendered in real-time with high-quality physics simulation (see Supplemental Video)." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 367, + 222, + 415, + 273 + ], + "blocks": [ + { + "bbox": [ + 367, + 222, + 415, + 273 + ], + "lines": [ + { + "bbox": [ + 367, + 222, + 415, + 273 + ], + "spans": [ + { + "bbox": [ + 367, + 222, + 415, + 273 + ], + "type": "image", + "image_path": "b7dcbe045408ecd716fca43d09329ac96c5fa75c7925186d88e2a5f5368eafd7.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 371, + 274, + 412, + 293 + ], + "lines": [ + { + "bbox": [ + 371, + 274, + 412, + 293 + ], + "spans": [ + { + "bbox": [ + 371, + 274, + 412, + 293 + ], + "type": "text", + "content": "Blender offline(40 s)" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 417, + 221, + 509, + 273 + ], + "blocks": [ + { + "bbox": [ + 417, + 221, + 509, + 273 + ], + "lines": [ + { + "bbox": [ + 417, + 221, + 509, + 273 + ], + "spans": [ + { + "bbox": [ + 417, + 221, + 509, + 273 + ], + "type": "image", + "image_path": "fc2b9c8e9139e9e36c9dc6b36281fbafd0bac781693a6a2ee6bc72f1ca280f23.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 419, + 274, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 419, + 274, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 419, + 274, + 547, + 293 + ], + "type": "text", + "content": "Unreal Engine real-time(16 ms)" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 509, + 221, + 546, + 273 + ], + "blocks": [ + { + "bbox": [ + 509, + 221, + 546, + 273 + ], + "lines": [ + { + "bbox": [ + 509, + 221, + 546, + 273 + ], + "spans": [ + { + "bbox": [ + 509, + 221, + 546, + 273 + ], + "type": "image", + "image_path": "d5d8eef7de70f5e02ce1b6b75651b29ca3f1ee2155c27bf897dc86346a424681.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 365, + 553, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 553, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 553, + 388 + ], + "type": "text", + "content": "(Sec. 4.4). For implementation details and additional experiments, please refer to SupMat." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 388, + 554, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 554, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 554, + 449 + ], + "type": "text", + "content": "We compare our method with Hairstep [55] and NeuralHDHair [48] as they are both state-of-the-art methods for reconstructing 3D hair from a single image. We also compare with the conditional 3D hair generation method of HAAR [42] although it is mainly designed for text-to-hair." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 456, + 389, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 389, + 468 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 389, + 468 + ], + "type": "text", + "content": "4.1. Qualitative" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 473, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 473, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 473, + 555, + 629 + ], + "type": "text", + "content": "The qualitative comparison with Hairstep, NeuralHDHair and HAAR is shown in Fig. 7. NeuralHDHair and HairStep tend to create hair that matches the overall shape from the image but that lacks fine-grained detail and curls, reconstructing strands that run parallel to each other. Furthermore, they cannot correctly reconstruct balding and afrolike hairstyles. In contrast, our method produces high-quality and realistic hair strands for a wide variety of images. Despite being a method designed for text-to-hair, we also compare with HAAR since they have released a pipeline for image-to-hairstyle by leveraging LLaVA to obtain text descriptions. We observe that their method often cannot match the hairstyle in the image." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 635, + 395, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 395, + 648 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 395, + 648 + ], + "type": "text", + "content": "4.2.Quantitative" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 554, + 713 + ], + "type": "text", + "content": "Quantitative evaluation is performed using the synthetic dataset of Yuksel et al. [52] from which we use two medium-length hairstyles: straight and curly. To render RGB images of the dataset we use Unreal Engine instead of Blender in order to remove possible bias our method might" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10852" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 105, + 70, + 504, + 517 + ], + "blocks": [ + { + "bbox": [ + 105, + 70, + 504, + 517 + ], + "lines": [ + { + "bbox": [ + 105, + 70, + 504, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 70, + 504, + 517 + ], + "type": "image", + "image_path": "b16c3056d429e98e19eb69f5c70e040e7cd99c4e1f1639f6b96e2b0a087d5ced.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 517, + 555, + 562 + ], + "lines": [ + { + "bbox": [ + 55, + 517, + 555, + 562 + ], + "spans": [ + { + "bbox": [ + 55, + 517, + 555, + 562 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison. We compare our method with HairStep [55], NeuralHDHair [48] and HAAR [42] on real images. Our method can robustly reconstruct a large variety of hairstyles with significantly more detail than previous approaches. We note that HAAR was designed to reconstruct hair given text captions, so we use LLaVA [19] to obtain text description of hair, followed by applying their text-to-3D method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 579, + 295, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 579, + 295, + 604 + ], + "spans": [ + { + "bbox": [ + 55, + 579, + 295, + 604 + ], + "type": "text", + "content": "have towards the path-traced images. The accuracy and precision results are reported in Tab. 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 604, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 604, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 604, + 295, + 700 + ], + "type": "text", + "content": "Additionally, we note that current synthetic datasets do not contain enough variety of hairstyles and propose a new synthetic dataset containing 10 representative hairstyles created by our Blender pipeline. We also evaluate our method and the baselines on this dataset and report the results in Tab. 2 although we recognize that our method has an advantage because it is trained on data created by the same Blender pipeline." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 701, + 295, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 295, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 295, + 712 + ], + "type": "text", + "content": "Across the two datasets we observe that our method can" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 579, + 555, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 579, + 555, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 579, + 555, + 628 + ], + "type": "text", + "content": "reconstruct the backside of the hair more faithfully, reinforcing the importance of varied data from which to learn a powerful prior. For the backside reconstruction, robustness to viewpoint, and more visualizations see SupMat." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 635, + 441, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 441, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 441, + 647 + ], + "type": "text", + "content": "4.3. Runtime Performance" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 653, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 555, + 713 + ], + "type": "text", + "content": "We evaluate the runtime performance in Tab. 3 by first dividing the hair reconstruction pipeline into three parts, 1) extraction of RGB features (DINOv2 features or in the case of the baseline methods: orientation maps, hair segmentation, etc.), 2) generation of the hair model, which in our" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10853" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 72, + 292, + 215 + ], + "blocks": [ + { + "bbox": [ + 62, + 72, + 292, + 215 + ], + "lines": [ + { + "bbox": [ + 62, + 72, + 292, + 215 + ], + "spans": [ + { + "bbox": [ + 62, + 72, + 292, + 215 + ], + "type": "image", + "image_path": "4c3afe6db211e070478ec85f792ab024b144c3494b7b51d10e82d1f45c570045.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 218, + 296, + 275 + ], + "lines": [ + { + "bbox": [ + 55, + 218, + 296, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 218, + 296, + 275 + ], + "type": "text", + "content": "Figure 8. Unconditional generation. We train our diffusion model with Classifier-free Guidance [10] so that the same model can be evaluated both conditionally and unconditionally. Here we show unconditionally generated results where we observe a range of high-quality and diverse hairstyles." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 291, + 105, + 342 + ], + "blocks": [ + { + "bbox": [ + 59, + 291, + 105, + 342 + ], + "lines": [ + { + "bbox": [ + 59, + 291, + 105, + 342 + ], + "spans": [ + { + "bbox": [ + 59, + 291, + 105, + 342 + ], + "type": "image", + "image_path": "e66f72d74bc1b1fe65edbd64de74d4cb375b0ecec0b2b753accbc4d991c5c775.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 343, + 100, + 352 + ], + "lines": [ + { + "bbox": [ + 64, + 343, + 100, + 352 + ], + "spans": [ + { + "bbox": [ + 64, + 343, + 100, + 352 + ], + "type": "text", + "content": "RGB Input" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 105, + 343, + 130, + 351 + ], + "lines": [ + { + "bbox": [ + 105, + 343, + 130, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 130, + 351 + ], + "type": "text", + "content": "Model:" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 105, + 354, + 141, + 362 + ], + "lines": [ + { + "bbox": [ + 105, + 354, + 141, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 141, + 362 + ], + "type": "text", + "content": "Condition:" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 369, + 296, + 437 + ], + "lines": [ + { + "bbox": [ + 55, + 369, + 296, + 437 + ], + "spans": [ + { + "bbox": [ + 55, + 369, + 296, + 437 + ], + "type": "text", + "content": "Figure 9. Ablation of conditioning signal and model architecture. Removing the local conditioning in the form of feature map " + }, + { + "bbox": [ + 55, + 369, + 296, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{map}" + }, + { + "bbox": [ + 55, + 369, + 296, + 437 + ], + "type": "text", + "content": " and relying only on the global CLS token severely affects the ability to reconstruct hair. Also generating scalp textures using a VAE yields overly smooth reconstructions. The combination of diffusion and local+global conditioning captures the most detail." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 147, + 289, + 191, + 342 + ], + "blocks": [ + { + "bbox": [ + 147, + 289, + 191, + 342 + ], + "lines": [ + { + "bbox": [ + 147, + 289, + 191, + 342 + ], + "spans": [ + { + "bbox": [ + 147, + 289, + 191, + 342 + ], + "type": "image", + "image_path": "44b79440f0ea3544fce4b83f503eaf3d011f31c18b67be64c13e69fd33f18572.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 160, + 343, + 177, + 350 + ], + "lines": [ + { + "bbox": [ + 160, + 343, + 177, + 350 + ], + "spans": [ + { + "bbox": [ + 160, + 343, + 177, + 350 + ], + "type": "text", + "content": "VAE" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 147, + 354, + 191, + 362 + ], + "lines": [ + { + "bbox": [ + 147, + 354, + 191, + 362 + ], + "spans": [ + { + "bbox": [ + 147, + 354, + 191, + 362 + ], + "type": "text", + "content": "Global+Local" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 196, + 293, + 237, + 342 + ], + "blocks": [ + { + "bbox": [ + 196, + 293, + 237, + 342 + ], + "lines": [ + { + "bbox": [ + 196, + 293, + 237, + 342 + ], + "spans": [ + { + "bbox": [ + 196, + 293, + 237, + 342 + ], + "type": "image", + "image_path": "d6fa5e34fcdb03a427c5ec0e40e2ce310b699bc0c324abf554c4ca5384eb1d6b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 201, + 343, + 230, + 351 + ], + "lines": [ + { + "bbox": [ + 201, + 343, + 230, + 351 + ], + "spans": [ + { + "bbox": [ + 201, + 343, + 230, + 351 + ], + "type": "text", + "content": "Diffusion" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 205, + 354, + 228, + 361 + ], + "lines": [ + { + "bbox": [ + 205, + 354, + 228, + 361 + ], + "spans": [ + { + "bbox": [ + 205, + 354, + 228, + 361 + ], + "type": "text", + "content": "Global" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 244, + 286, + 288, + 342 + ], + "blocks": [ + { + "bbox": [ + 244, + 286, + 288, + 342 + ], + "lines": [ + { + "bbox": [ + 244, + 286, + 288, + 342 + ], + "spans": [ + { + "bbox": [ + 244, + 286, + 288, + 342 + ], + "type": "image", + "image_path": "0f371eac801f9e385cc859fc44d24e5758ca52956503211f7445db9ded8afd5c.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 249, + 343, + 281, + 351 + ], + "lines": [ + { + "bbox": [ + 249, + 343, + 281, + 351 + ], + "spans": [ + { + "bbox": [ + 249, + 343, + 281, + 351 + ], + "type": "text", + "content": "Diffusion" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 242, + 354, + 288, + 362 + ], + "lines": [ + { + "bbox": [ + 242, + 354, + 288, + 362 + ], + "spans": [ + { + "bbox": [ + 242, + 354, + 288, + 362 + ], + "type": "text", + "content": "Global+Local" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 458, + 296, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 458, + 296, + 578 + ], + "spans": [ + { + "bbox": [ + 55, + 458, + 296, + 578 + ], + "type": "text", + "content": "case is the scalp texture while baseline methods create a 3D orientation field, 3) strand generation, which is the final step to either decode or grow the strands. All results are obtained on an NVIDIA H100 GPU. We observe that our method is overall the fastest as we do not need pre- or post-processing steps like head fitting, hair segmentation or hair growth and refinement. Note that our generated hair can be directly imported into Unreal Engine and rendered in real-time (60FPS) as shown in Fig. 6; see Supplemental Video." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 55, + 587, + 149, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 149, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 149, + 601 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": "We perform an ablation study on the architecture and the importance of the conditioning signal in Fig. 9. Changing the scalp generation model to a VAE model similar to GroomGen [56] causes the hair to be overly smooth and lack local detail. Our proposed diffusion model conditioned with global and local features in the form of " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{map}" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{cls}" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " manages to capture the most detail. However, the local feature map is crucial and removing it causes the generated hair to deviate significantly from the input image." + } + ] + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 317, + 77, + 553, + 114 + ], + "blocks": [ + { + "bbox": [ + 427, + 70, + 495, + 77 + ], + "lines": [ + { + "bbox": [ + 427, + 70, + 495, + 77 + ], + "spans": [ + { + "bbox": [ + 427, + 70, + 495, + 77 + ], + "type": "text", + "content": "Thresholds: mm / degrees" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 77, + 553, + 114 + ], + "lines": [ + { + "bbox": [ + 317, + 77, + 553, + 114 + ], + "spans": [ + { + "bbox": [ + 317, + 77, + 553, + 114 + ], + "type": "table", + "html": "
    Method2/203/304/402/203/304/402/203/304/40
    Precision(↑)Recall(↑)F-score(↑)
    NeuralHDHair [48]47.9165.0773.7631.5951.1064.6338.0057.1268.73
    HairStep[55]40.8855.9964.0732.1644.9653.1535.5049.0657.20
    Ours43.6068.3081.7934.9758.2771.7938.3562.4176.20
    ", + "image_path": "178a60dc34851ac8cd5f8c595748d7bede468727b73b65a1ecd62e03e99b44db.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "type": "table", + "bbox": [ + 317, + 152, + 553, + 196 + ], + "blocks": [ + { + "bbox": [ + 313, + 116, + 553, + 148 + ], + "lines": [ + { + "bbox": [ + 313, + 116, + 553, + 148 + ], + "spans": [ + { + "bbox": [ + 313, + 116, + 553, + 148 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with [48, 55] on [52]. It includes straight and curly hairstyles, please refer to the SupMat for more visualizations." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 152, + 553, + 196 + ], + "lines": [ + { + "bbox": [ + 317, + 152, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 317, + 152, + 553, + 196 + ], + "type": "table", + "html": "
    MethodThresholds: mm / degrees
    2/203/304/402/203/304/402/203/304/40
    Precision(↑)Recall(↑)F-score(↑)
    NeuralHDHair [48]18.6536.2149.4619.2637.3351.6018.5535.7649.30
    HairStep[55]20.2235.5445.7320.8038.5352.8219.4234.3845.48
    Ours63.0684.1692.7857.9179.7189.8160.1381.6891.17
    ", + "image_path": "1d2dd0e876e5704971af68c0ed019a3f277770c12ac7843f41fab5dcd0dd93a3.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + } + ], + "index": 22 + }, + { + "type": "table", + "bbox": [ + 342, + 251, + 525, + 294 + ], + "blocks": [ + { + "bbox": [ + 313, + 198, + 555, + 243 + ], + "lines": [ + { + "bbox": [ + 313, + 198, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 555, + 243 + ], + "type": "text", + "content": "Table 2. Quantitative comparison with [48, 55] on the DiffLocks evaluation set. Our results show substantial improvement over the baseline, particularly when reconstructing the backside of the hair due to our model's ability to learn a powerful prior over hairstyles." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 342, + 251, + 525, + 294 + ], + "lines": [ + { + "bbox": [ + 342, + 251, + 525, + 294 + ], + "spans": [ + { + "bbox": [ + 342, + 251, + 525, + 294 + ], + "type": "table", + "html": "
    HairStepNeuralHDHairOurs
    RGB features (↓)3.174.860.10
    hair model (↓)0.454.991.83
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    ", + "image_path": "500b4ae1ff73edf37dd2871fef74fdec193142117bfb8f33a6b4531f6ffa484d.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "table_body" + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 295, + 555, + 319 + ], + "lines": [ + { + "bbox": [ + 313, + 295, + 555, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 295, + 555, + 319 + ], + "type": "text", + "content": "Table 3. Timing. Comparison of the time in seconds needed for each part of the hair creation pipeline." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 314, + 342, + 476, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 342, + 476, + 355 + ], + "spans": [ + { + "bbox": [ + 314, + 342, + 476, + 355 + ], + "type": "text", + "content": "5. Limitations and future work" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 365, + 554, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 554, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 554, + 437 + ], + "type": "text", + "content": "Despite the large amount of data, there are still gaps in the synthetic dataset; e.g. it lacks hairstyles with braids, accessories, ponytails, and buns. However, we believe that further improvements to the pipeline will allow such details to be created. Furthermore, the generation pipeline can also be easily extended to beards and eyebrows." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 438, + 554, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 438, + 554, + 510 + ], + "spans": [ + { + "bbox": [ + 313, + 438, + 554, + 510 + ], + "type": "text", + "content": "We also note that DiffLocks prioritizes local hair details over perfect image alignment. However, for many tasks, generation or reconstruction is just the first step. When hair is animated with physics, the precise initial strand alignment is not critical, as the dynamic nature of hair makes the initial configuration transient." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 314, + 528, + 388, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 528, + 388, + 540 + ], + "spans": [ + { + "bbox": [ + 314, + 528, + 388, + 540 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 550, + 554, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 550, + 554, + 644 + ], + "spans": [ + { + "bbox": [ + 313, + 550, + 554, + 644 + ], + "type": "text", + "content": "We proposed a novel approach for generating 3D hair strands from a single image by first creating the largest dataset to date of synthetic hair paired with RGB images, and then by proposing an image-conditioned diffusion model based on scalp textures. Our method can create highly intricate 3D strands, surpassing previous methods and without requiring heuristic-based methods to increase the realism." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 647, + 554, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 647, + 554, + 704 + ], + "spans": [ + { + "bbox": [ + 313, + 647, + 554, + 704 + ], + "type": "text", + "content": "Acknowledgments and Disclosures. We give thanks to Nathan Bajandas for all the Unreal images and videos. While MJB is a co-founder and Chief Scientist at Meshcapade, his research in this project was performed solely at, and funded solely by, the Max Planck Society." + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10854" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 123 + ], + "type": "text", + "content": "[1] Mengei Chai, Changxi Zheng, and Kun Zhou. 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Groomcap: High-fidelity prior-free hair capture. arXiv preprint arXiv:2409.00831, 2024. 1, 2" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10857" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_content_list.json b/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1bf43593fcacf396de785f7fd793c6172277e82c --- /dev/null +++ b/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_content_list.json @@ -0,0 +1,1190 @@ +[ + { + "type": "text", + "text": "DiffPortrait360: Consistent Portrait Diffusion for 360 View Synthesis", + "text_level": 1, + "bbox": [ + 148, + 130, + 846, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yuming Gu $^{1,2}$ , Phong Tran $^{2}$ , Yujian Zheng $^{2}$ , Hongyi Xu $^{3}$ , Heyuan Li $^{4}$ , Adilbek Karmanov $^{2}$ , Hao Li $^{2,5}$", + "bbox": [ + 99, + 178, + 897, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Southern California, 2MBZUAI, 3ByteDance Inc.", + "bbox": [ + 246, + 196, + 751, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "4The Chinese University of Hong Kong, Shenzhen, 5Pinscreen Inc.", + "bbox": [ + 236, + 215, + 761, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://freedomgu.github.io/DiffPortrait360", + "bbox": [ + 328, + 234, + 671, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "yuminggu@usc.edu,{the.tran, yujian.zheng, adilbek.karmanov}@mbzuai.ac.ae", + "bbox": [ + 181, + 253, + 818, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "heyuanli@link.cuhk.edu.cn, hao@hao-li.com", + "bbox": [ + 318, + 272, + 684, + 286 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/74b8faaedb543445f336a37270b68acc61316c6b266ef4681be19f41e7fde1ad.jpg", + "image_caption": [ + "Figure 1. Our DiffPortrait360 enables $360^{\\circ}$ view-consistent full-head image synthesis. It is universally effective across a diverse range of facial portraits, allowing for the creation of 3D-aware head portraits from single-view images." + ], + "image_footnote": [], + "bbox": [ + 93, + 321, + 906, + 577 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 627, + 326, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generating high-quality 360-degree views of human heads from single-view images is essential for enabling accessible immersive telepresence applications and scalable personalized content creation. While cutting-edge methods for full head generation are limited to modeling realistic human heads, the latest diffusion-based approaches for style-omniscient head synthesis can produce only frontal views and struggle with view consistency, preventing their conversion into true 3D models for rendering from arbitrary angles. We introduce a novel approach that generates fully consistent 360-degree head views, accommodating human, stylized, and anthropomorphic forms, including accessories like glasses and hats. Our method builds on the DiffPortrait3D framework, incorporating a custom ControlNet for back-of-head detail generation and a dual appearance module to ensure global front-back consistency. By training on", + "bbox": [ + 86, + 659, + 485, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "continuous view sequences and integrating a back reference image, our approach achieves robust, locally continuous view synthesis. Our model can be used to produce high-quality neural radiance fields (NeRFs) for real-time, free-viewpoint rendering, outperforming state-of-the-art methods in object synthesis and 360-degree head generation for very challenging input portraits.", + "bbox": [ + 511, + 628, + 908, + 737 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 753, + 645, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In game, film, and animation production, CG characters are central to the content creation pipeline, meticulously designed with the right balance of realism and stylization to align with the narrative. Multi-view stereo systems and 3D scanners are commonly used to streamline the tedious manual process of creating realistic human characters. However, stylized characters are still often 3D modeled from scratch. Alongside the growing demand for efficient and", + "bbox": [ + 511, + 779, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26263", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "scalable 3D content production pipelines, immersive telepresence and virtual world applications are fueling interest in embodying personalized or imaginary characters created directly by end-users. In this context, highly accessible 3D modeling tools that can generate characters from a single photograph or drawing are becoming increasingly relevant.", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The most widely adopted approaches for image-based full 3D head reconstruction combine parametric models, like 3D Morphable Models (3DMMs) [10, 19, 20, 29, 34, 35, 48, 50, 57], with data-driven hair modeling or generate a single textured 3D mesh that includes both the face and hair. These methods often struggle with diverse hairstyles and capturing detailed appearance textures for the back of the head. Cutting-edge 3D head reconstruction, utilizing transformer-based networks [8, 9, 45-47] to estimate triplane representation, have shown success in capturing complex portraits of human heads with diverse hairstyles and accessories. However, tri-plane introduces strong projection ambiguity for extreme non-frontal poses and therefore fails to model 360-degree head. To facilitate the novel synthesis of full 360-degree views, tri-grid [1] neural volume representations have been introduced. While these methods have demonstrated impressive results, they are limited to realistic human heads and cannot handle stylized or other anthropomorphic shapes.", + "bbox": [ + 91, + 184, + 483, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The latest diffusion-based image-to-3D generation methods [27, 40, 51] are designed to model a wide range of 3D objects. However, they struggle to capture detailed, domain-specific appearances, such as those of human heads and are prone to severe, unpredictable artifacts. A recent diffusion model, DiffPortrait3D [14], demonstrates the capability to generate novel views of style-omniscient heads by incorporating 3D-aware noise for inference, and finetuning the model on a large 3D head dataset. In addition to being limited to frontal views, this approach also displays noticeable inconsistencies between angles.", + "bbox": [ + 89, + 473, + 482, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We present the first method capable of generating consistent 360-degree views from a single portrait of a head, accommodating human, stylized, or animal anthropomorphic forms, as well as accessories like glasses, jewelry, or masks. Our novel views can be computed offline (5.6 sec per view) and transformed into a high-quality neural radiance field (NeRF) [30], enabling free-viewpoint rendering in real-time. Our method is particularly robust, capable of handling a wide range of subjects, complex hairstyles, varied head poses, and expressive facial features, including detailed elements like tongues.", + "bbox": [ + 89, + 642, + 482, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Building on the state-of-the-art DiffPortrait3D framework, we introduce key innovations to support back-view renderings and achieve locally continuous view consistency. We begin by generating the back of the head from the input image using a custom ControlNet [55], trained specifically to infer back-of-head details from a front-facing im", + "bbox": [ + 89, + 810, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "age. This model is trained on a carefully curated dataset featuring diverse, realistic, and stylized heads. The front and back images are then passed into a dual appearance module (stable diffusion UNet), which extracts appearance information from both perspectives to condition our main image generator (stable diffusion denoising network) through attention layers. Unlike DiffPortrait3D, our approach incorporates an additional back reference image to improve global appearance consistency. Furthermore, we ensure locally continuous view consistency by using continuous view sequences (8 views) as conditions during training. Unlike DiffPortrait3D, which is trained only on frontal 3D-aware head generations, our approach utilizes a dataset comprising full 360-degree views of human heads, with data that is both captured and synthetically generated. Finally, our denoising process also uses a 3D-aware noise which is initialized using a fine-tuned inversion process-based a StyleGAN-based 360 head generator [1].", + "bbox": [ + 511, + 90, + 903, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate that diffusion models can generate highly detailed and consistent 360-degree head views from in-the-wild images across an extensive range of styles and complex portraits, handling challenging lighting conditions, intricate hairstyles, diverse appearances, and varying head poses. Our approach significantly outperforms all the latest generative methods for our challenge human head benchmarks generation, w.r.t. key metrics. More importantly, our method produces globally consistent appearances for the back of the head and locally view consistent synthesis when generating 360-degree views, which enables us to reconstruct true 3D representations (e.g., NeRFs) for free-view point rendering. We present the following contributions:", + "bbox": [ + 511, + 363, + 903, + 559 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a novel method for $360^{\\circ}$ view synthesis from a single style-omniscient portrait, which leverages priors from pre-trained stable diffusion models to generate view-consistent content.", + "- We propose a dual appearance control module, supported by a diffusion-based back-view generator, that ensures global consistency in novel view synthesis around the subject.", + "- We introduce a novel training strategy that employs view-consistent sequence generation to enhance continuity and smoothness, utilizing a 3D head dataset composed of both captured and synthetic subjects." + ], + "bbox": [ + 513, + 560, + 903, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 753, + 653, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Numerous research methods and commercial solutions [20, 35] have been developed for reconstructing full 3D avatar heads from a single input photo, as opposed to using a multi-view capture approach [2, 12, 23, 28, 37]. These capabilities enable applications such as consumer-accessible immersive telepresence, personalized avatars for 3D games, and scalable approaches to content creation. Despite their wide adoption, regression-based face modeling techniques", + "bbox": [ + 511, + 780, + 903, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26264", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/74a6d3e6d4c469e45cd0f1114dd237db5eaf636e51b7dcb993d1f67b77f354cd.jpg", + "image_caption": [ + "Figure 2. For the task of full-range 360-degree novel view synthesis, DiffPortrait360 employs a frozen pre-trained Latent Diffusion Model (LDM) as a rendering backbone and incorporates three auxiliary trainable modules for disentangled control of dual appearance $\\mathcal{R}$ , camera control $\\mathcal{C}$ , and U-Nets with view consistency $\\mathcal{V}$ . Specifically, $\\mathcal{R}$ extracts appearance information from $I_{\\mathrm{ref}}$ and $I_{\\mathrm{back}}$ , and $\\mathcal{C}$ derives the camera pose, which is rendered using an off-the-shelf 3D GAN. During training, we utilize a continuous sampling training strategy to better preserve the continuity of the camera trajectory. We enhance attention to continuity between frames to maintain the appearance information without changes due to turning angles. For inference, we employ our tailored back-view image generation network $\\mathcal{F}$ to generate a back-view image, enabling us to generate a 360-degree full range of camera trajectories using a single image portrait. Note that $z$ stands for latent space noise rather than image." + ], + "image_footnote": [], + "bbox": [ + 138, + 92, + 867, + 375 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "from a single input image [10, 19, 29, 34, 48, 50, 57] using parametric 3D Morphable Models (3DMM) [3] are increasingly being complemented in many applications by neural rendering techniques, as surveyed in [44].", + "bbox": [ + 88, + 525, + 486, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D-Aware GAN-Based Full-Head Synthesis. Recent advancements on 3D-aware GANs [1, 5-7, 13, 24, 31, 41, 52, 53], often leveraging StyleGAN2 [21] as backbone, are capable of generating novel views from a single input photograph through fine-tuned GAN inversion while ensuring view-consistency using a volumetric neural radiance field representation based on tri-planes [6] or signed distance function, such as StyleSDF [31]. While most of them can only generate frontal faces due their training data and their 3D representation, two recent methods have demonstrated how the generation of consistent 360-degree views are possible, namely, PanoHead [1] and SphereHead [24]. These methods generate a reasonable back head region using enhanced tri-plane representations by incorporating multiple depth layers or spherical coordinate system. However, their back-view synthesis often appear unnatural and mismatching the front view, especially when single-view inversion is applied. Most importantly, all of these methods are domain specific and only work on realistic human heads. They often fail for unknown accessories or complex hairstyles, and", + "bbox": [ + 89, + 598, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "generating novel views for stylized avatars is not possible.", + "bbox": [ + 513, + 525, + 898, + 541 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Model Based 360-Degree View Synthesis. Diffusion-based models [18, 42, 43], particularly latent diffusion models (LDM) [39], have recently gained significant attention for their unmatched performance in generating highly diverse and high-fidelity images across various domains. A number of diffusion-based methods have been introduced for the task of novel view synthesis [14, 26, 27, 40] for general objects, and several methods [14, 40] demonstrate the effectiveness of fusing features of a reference image into self-attention blocks in the LDM UNets, facilitating high-quality novel view generation while preserved appearance context effectively. The notable work, ControlNet [55], extends the LDM framework to controllable image generation with additive structural conditions from signals such as 3D-aware GAN-synthesized camera viewpoints or rendered 3DMM condition [36]. The work, Diff-Portrait3D [14] achieves the state-of-the-art portrait novel view synthesis results by seamlessly integrating the appearance and camera view attentions with pre-trained UNets. Despite the impressive results, especially for stylized input portraits, only frontal views are possible to generate, and unwanted local inconsistencies between the model from", + "bbox": [ + 511, + 568, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26265", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5ab9bb691d1075674a753028020a0c95b8de25a3557707e00763d37ce27ac848.jpg", + "image_caption": [ + "Figure 3. Qualitative comparisons with existing methods on in the wild portraits. Compared to the baselines, our method shows superior generalization capability to novel view synthesis of wild portraits with unseen appearances, expressions, and styles, even without any reliance on fine-tuning." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 906, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "being converted into a 3D representation, such as textured Meshes, NeRFs or 3D Gaussian Splats, which is needed for free-viewpoint rendering. Another recent diffusion-based technique, called Portrait3D [16], generates compelling views from all angles, achieving superior results to GAN-based approaches [1, 24] but is restricted to realistic heads only. Our proposed solution is particularly effective in generating globally consistent and plausible back views of the head, while also ensuring locally view-consistent renderings for full $360^{\\circ}$ style-omniscient portraits.", + "bbox": [ + 88, + 510, + 483, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 676, + 181, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a single RGB portrait image with arbitrary style, $I_{\\mathrm{ref}}$ , our approach aims to synthesize a new image, $I_{\\mathrm{tar}}$ , from any camera perspective within a $360^{\\circ}$ range using an $I_{\\mathrm{cam}}$ image. The novel view $I_{\\mathrm{tar}}$ must maintain consistent appearance information with $I_{\\mathrm{ref}}$ , with the camera view controlled by $I_{\\mathrm{cam}}$ . It is crucial to note that this includes not only positions near $I_{\\mathrm{ref}}$ but also areas with minimal overlap and previously unobserved regions from the given view.", + "bbox": [ + 89, + 703, + 482, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, DiffPortrait360 leverages powerful latent diffusion models, enabling disentangled control of appearance and camera views, as detailed in Section 3.1. Building upon this foundation, we propose a tailored dual-appearscence module that incorporates additional appearance", + "bbox": [ + 89, + 825, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "information from both the front and back of the head, $I_{\\mathrm{back}}$ outlined in Section 3.2. We introduce an additional Control-Net [55] based synthesizing network designed to generate a plausible back view in $I_{\\mathrm{back}}$ from $I_{\\mathrm{ref}}$ , and to correct biases due to limited 3D head training data, as detailed in Section 3.3. Finally, Section 3.4 introduces a novel training strategy that leverages sequence priors to distill fine-grained structural information, ensuring consistency and smooth view transitions while maintaining high synthesis quality.", + "bbox": [ + 511, + 510, + 906, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Background", + "text_level": 1, + "bbox": [ + 511, + 656, + 643, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Latent Diffusion Model. Diffusion models [18, 42, 43] are generative models designed to synthesize desired data samples from Gaussian noise $z_0$ by iteratively denoising across $T$ time steps. Latent diffusion models (LDMs) [39] extend this framework by operating in an encoded latent space $\\mathcal{E}(I)$ where $I$ is an input image, facilitated by a pretrained auto-encoder $\\mathcal{D} \\circ \\mathcal{E}(\\cdot)$ . Specifically, the model is trained to learn the denoising process from $z_T \\sim \\mathcal{N}(0,1)$ to $z_0 = \\mathcal{E}(I)$ with the objective,", + "bbox": [ + 511, + 678, + 908, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {l d m} = \\mathbb {E} _ {z _ {0}, t, \\epsilon \\sim \\mathcal {N} (0, 1)} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t) \\right\\| _ {2} ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 825, + 906, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_{t}$ is the noise map at timestep $t$ and $\\epsilon_{\\theta}$ is a trainable UNet equipped with layers of convolutions and self-/cross-", + "bbox": [ + 511, + 869, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26266", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6a161a8d8289b4b3ed7138b9ed458a51cb9cf138f6b6687fc6c9ed988769bef6.jpg", + "image_caption": [ + "Figure 4. Qualitative comparisons of novel view synterhisis on RenderMe360 [32]. Our method achieves effective appearance control for novel synthesis under substantial change of camera view for synthesis." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 906, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cf2cd0576589ebfa42ac49ab1b31e6e03bac5cc377defd23f6f8ff66ca2e5b64.jpg", + "image_caption": [ + "Figure 5. Ablation Study on Dual Appearance Control." + ], + "image_footnote": [], + "bbox": [ + 96, + 483, + 477, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": " attentions (TransBlock). Finally, the output image is calculated by mapping the denoised latent feature map back to the image domain $I = \\mathcal{D}(z_0)$ . Unlike traditional Text-to-Image (T2I) diffusion models, which rely on textual inputs to guide image synthesis, our approach directly extracts portrait appearance context and camera information from $I_{\\mathrm{ref}}$ and $I_{\\mathrm{cam}}$ , respectively, without relying on text descriptions. Consequently, we use an empty prompt for text control and omit it from our formulations.", + "bbox": [ + 89, + 678, + 482, + 814 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Diffusion-Based Novel View Synthesis. Recent studies [25-27, 40] have leveraged pre-trained LDMs for novel view synthesis. These efforts largely employ latent diffusion as the backbone for novel view synthesis, incorporating", + "bbox": [ + 89, + 839, + 483, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "modules for appearance injection and camera information control. While most of this research focuses on general objects, our work follows a specific [14] designed for portrait novel view synthesis, which uses three main modules: 1) an Appearance Reference Module $\\mathcal{R}$ that captures identity attributes and background from $I_{\\mathrm{ref}}$ , 2) a Control Module $(C)$ typically a ControlNet [55], that adjusts camera perspectives based on $I_{\\mathrm{cam}}$ and 3) a View Consistency Module $\\mathcal{V}$ , intervened within UNet blocks using temporal cross-attention between features of multiple consecutive views to ensure view consistency. We follow the same network structure but innovate on enabling 360-degree and consistent novel view synthesis that preserves input appearance coherence across extensive viewpoint shifts, encompassing elements such as expressions, hairstyles, and head shapes.", + "bbox": [ + 511, + 487, + 906, + 714 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Dual Appearance Module", + "text_level": 1, + "bbox": [ + 511, + 726, + 746, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To ensure the preservation of appearance information characteristics, previous methods typically employ a ReferenceNet [4] to inject the reference image and guide the denoising process with $I_{\\mathrm{ref}}$ in order to extract sufficient information from $I_{\\mathrm{ref}}$ . The Appearance Control Module is trained to ensure meticulous transfer of referenced structure and appearance into the SD-UNet for the task of novel view synthesis of portrait views. While effective at reference control in front near face, such an appearance control scheme induces following problems: Firstly, the appearance", + "bbox": [ + 511, + 750, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "26267", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ae12753b51056a43934337ed78ed2d5dddf549a4874babe7dc45ba903b8891b4.jpg", + "image_caption": [ + "Figure 6. Ablation on Back-view Generation." + ], + "image_footnote": [], + "bbox": [ + 98, + 88, + 477, + 296 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "content is largely provided by the image of $I_{\\mathrm{ref}}$ . As the viewpoint shifts from the front of the face to the back of the head, the training dataset introduces randomly generated content such as different hairstyles, hats, and other features. Additionally, front face images contain only very limited information related to the back of the head, with very few pixels or even no pixels available for use. This leads to a significant misuse of most of the facial feature information from the reference image, causing leakage to the back of the head, which can be amplified to create a dual face or result in facial information appearing on the back of the head. Furthermore, these inaccuracies impact view control consistency, since the network, as a shortcut, tends to use other tailored modules, e.g., the view control module $\\mathcal{C}$ , to generate information when there is insufficient appearance information. As a result, system collapse occurs during the generation of larger views with only a single reference.", + "bbox": [ + 88, + 340, + 482, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To mitigate this issue, we require an appearance reference network that could take information that entirely covers areas not observed by the front appearance while minimizing the overlap with the front face, which enables the diffusion network to access sufficient appearance information. This motivation leads us to design a dual-appearance module. Specifically, during training, we allow the appearance module to access two images, $I_{\\mathrm{ref}}$ and $I_{\\mathrm{back}}$ . The rationale behind this modification is to reduce ambiguities caused by insufficient or erroneous information during viewpoint transitions, and to compel the network to autonomously decide which information from $I_{\\mathrm{ref}}$ and $I_{\\mathrm{back}}$ should be relied on more under different camera views. We note that in selecting $I_{\\mathrm{ref}}$ and $I_{\\mathrm{back}}$ , views should overlap as little as possible but not be fixed, as this could affect the generalization ability of the input images. Consequently, in our training dataset, we deliberately choose pairs with minimal overlap as inputs for $I_{\\mathrm{ref}}$ and $I_{\\mathrm{back}}$ , enabling our dual appearance module to leverage the information to its fullest extent. As a result, we observed consistent and sat", + "bbox": [ + 89, + 599, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/028c7d571f9eeb000cfb74c6a5fa68b1c800512afa93086ea6f2d08dfa3388cd.jpg", + "image_caption": [ + "Figure 7. Ablation Study on View-consistency Control. (a) Generated novel view. (b-c) Rendering and depth of fitted NeRFs." + ], + "image_footnote": [], + "bbox": [ + 521, + 88, + 901, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "isfactory appearance in areas not covered by the reference images, and between the 360-degree area of $I_{\\mathrm{back}}$ and $I_{\\mathrm{ref}}$ . This makes our model capable of generating consistent appearance information while changing the camera views (see Figure 5).", + "bbox": [ + 511, + 378, + 906, + 454 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Back-View Reference Generation", + "text_level": 1, + "bbox": [ + 511, + 467, + 805, + 482 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our trained dual appearance module, $\\mathcal{R}$ , significantly improves appearance consistency, especially during large changes in viewing angles. However, during inference, it is challenging to obtain a reasonable reference image context with a viewing angle drastically different from the input, such as obtaining a nearly opposite auxiliary image to the reference. Compromising to this difficulty will reduce the effectiveness of the disentangled appearance information determined by $I_{\\mathrm{back}}$ .", + "bbox": [ + 511, + 489, + 905, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To address this issue, we developed a generative network capable of producing an $I_{\\mathrm{back}}$ that has minimal overlap in appearance information with $I_{\\mathrm{ref}}$ while maintaining a consistent style, reasonable head shape, and hairstyle. This motivates the use of ControlNet [55] and the original $I_{\\mathrm{ref}}$ to generate a decoupled $I_{\\mathrm{back}}$ as our extra appearance condition input. This approach is practical for real-world applications, allowing the generation of additional appearance information without needing external inputs.", + "bbox": [ + 511, + 628, + 905, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "However, this generation model can exhibit a strong bias when using only realistic data, which is unsuitable for producing a broader range of artistic styles. To avoid an overreliance on a training dataset that could lead to the generation of unreasonable $I_{\\mathrm{back}}$ , we supplemented our dataset with a large collection of cartoon and stylized task images of back views produced by [11] and Unique3D [51], adjusting the distribution of our dataset to lessen the bias towards realistic backdrops. Notably, even with limited cam", + "bbox": [ + 511, + 763, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "26268", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "era views (only including front and back views), this is sufficient for the Generative Module to correct biases from real dataset training, enabling it to generate reasonable unobserved head regions consistent with the input portrait style. As demonstrated in our experiments, our trained $\\mathcal{F}$ , with a limited dataset of cartoon front and back faces, effectively resolves the challenge of sourcing additional appearance $I_{\\mathrm{back}}$ in practical applications and generalizes well to unseen portrait styles. (see Figure 6).", + "bbox": [ + 89, + 90, + 480, + 227 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.4. View-Consistency Module", + "text_level": 1, + "bbox": [ + 89, + 239, + 326, + 255 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given an arbitrary view portrait image $I_{\\mathrm{ref}}$ , our trained module has already been capable of generating a full 360-degree range of novel view syntheses $I_{\\mathrm{tar}}$ via above designs. Nevertheless, during inference, we occasionally observe our module failing to capture nuanced view consistency compared to 3D-aware GANs, such as appearance flickering and choppy transitions between views. These unwanted artifacts significantly impact the effectiveness of novel view synthesis in downstream applications, such as 3D reconstruction.", + "bbox": [ + 89, + 261, + 482, + 397 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Reviewing our above module, the view consistency module $\\mathcal{V}$ is primarily managed by a temporal transformer [15], integrated with 3D-aware noise [14]. However, given the heritage motion prior from [15], we note that view consistency is trained by focusing on cross-view attentions with randomly shuffled views. We argue this training approach does not fully utilize the advantages of the motion prior, which may lead to the observed choppy transitions and minor appearance changes, ultimately resulting in the loss of detail and collapse of downstream tasks.", + "bbox": [ + 89, + 398, + 482, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To alleviate this issue, we have revised the training approach of the temporal transformer to include data from continuous view transitions. Instead of randomly sampling sparse views from a sparse multi-view dataset, we controlled the 3D-aware GAN [1] to generate consistently sampled sequential view changes. In contrast to random view cross-attention, our sequential training scheme effectively instructs the view consistency module $\\mathcal{V}$ to maximize the benefits derived from the pretrained motion prior. Even when trained on only a limited synthetic dataset, our sequential training scheme is sufficient for $\\mathcal{V}$ to decipher higher multi-view consistency accuracy and smoother view-changing results, enabling the synthesis process to produce smoother results that better fit downstream applications.", + "bbox": [ + 89, + 549, + 482, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 777, + 220, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 89, + 803, + 191, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We train our model using a hybrid dataset comprised of photo-realistic full-head multi-view images dataset RenderMe360 [32] and synthetic ones by PanoHead [1] and SphereHead [24]. RenderMe360 consists of images from 500 individuals, each captured with 12 different expres", + "bbox": [ + 89, + 825, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sions and an extended animated sequence from 60 multiview camera positions. This setup offers a substantial amount of multi-view consistent appearance data for training. We manually separated the front and back camera information, selecting front and back images as inputs for dual-appearance control, while using the remaining camera views as training data. We randomly selected 1,000 frames of multi-view data from 150 subjects while using PanoHead and SphereHead to sample continuous views from 600 identities, specifically for training the sequential view consistency module due to the scarcity of sparse camera views of RenderMe360. For the back-head reference image generation network, we collected 1,000 manually chosen, stylized front-and-back image pairs to augment the back-head image generation network. High-quality stylized front images were generated using a state-of-the-art tool [11]; we then fed the images to Unique3D [51] to generate content consistent back head. It's important to note that this highly stylized dataset, containing only front and back views, was used solely as data augmentation to reduce bias in the backview generation and was not included in the training of $\\mathcal{R}$ .", + "bbox": [ + 511, + 90, + 903, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparisons", + "text_level": 1, + "bbox": [ + 511, + 417, + 651, + 431 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons on Stylized Portraits. To demonstrate the generalization capability of our approach on stylized input portraits, we conduct a qualitative comparison with existing methods, as shown in Fig. 3. We also include Rome [22] and Itseez3D1. Thanks to our back-view generator and view-consistency module, our method exhibits superior generalization to diverse styles. We achieve high-quality details and continuous views across the full range of head poses. In contrast, it is evident that other approaches struggle to reach this level of performance. Specifically, Rome fails to generate reasonable back-view textures and structures, especially for inputs with thick hair and unusual accessories. Similarly, Zero-1-to-3 [27] and Unique3D [51] continue to struggle with bridging the domain gap between general objects and human heads. Itseez3D appears to operate with templates that preserve only the facial textures from the reference image. Additionally, both PanoHead [1] and SphereHead [24] perform poorly on stylized portraits.", + "bbox": [ + 511, + 438, + 906, + 710 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons on Real Portraits. We then compare the novel view synthesis results of our method with existing approaches on the test split of RenderMe360 [32], as illustrated in Fig. 4 and Tab. 1. We additionally incorporate Diff-Portrait3D* [14], which has been finetuned using our full-head datasets, as the original model was limited to generating frontal views using the provided checkpoints. As shown in the qualitative comparisons in Fig. 4, the GAN-based methods, PanoHead and SphereHead, struggle to generate realistic details that align with the reference images. Their", + "bbox": [ + 511, + 728, + 908, + 878 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "1https://itseez3d.com/", + "bbox": [ + 531, + 886, + 651, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "26269", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/15537ca697bd3e942faf58f10e1cc79a59f50e65c4e52a8ccdcdfd80f80736d4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodFrontal ViewBack View
    PSNR ↑SSIM ↑LPIPS ↓CSIM ↑FID ↓PSNR ↑SSIM ↑LPIPS ↓FID ↓
    PanoHead + PTI28.350.5050.4950.47198.9328.390.4500.432169.52
    SphereHead + PTI28.620.5130.4320.55669.4128.630.4630.413106.21
    Zero123---0.431152.03---216.88
    Unique3D---0.483195.33---285.75
    DiffPortrait3D*28.960.5090.4250.70949.0228.470.3730.44691.37
    Ours29.440.5780.3840.74635.3430.920.6480.31339.40
    ", + "bbox": [ + 138, + 88, + 859, + 203 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparisons of novel view synthesis on RenderMe360 [32] with perceptual metrics PSNR, SSIM [49], LPIPS [56], FID [17] and an additional face recognition metric CSIM [54] for frontal views.", + "bbox": [ + 89, + 214, + 903, + 242 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "outputs fail to preserve identity due to the limitations of the PTI [38]. Zero-1-to-3 and Unique3D are trained on datasets of general synthetic 3D objects, and without specific domain knowledge, they cannot consistently produce reasonable novel views. Their results are often riddled with artifacts unrelated to heads. Although we fine-tuned DiffPortrait3D* on our full-head datasets, it still struggles to generate consistent novel views at the back, resulting in significant discrepancies from the reference images. These examples show artifacts such as multiple faces and misaligned hair color. In contrast, our specially designed method outperforms all others, demonstrating strong consistency across significantly different viewpoints. This conclusion is further supported by the quantitative comparisons detailed in Tab. 1. While existing methods reveal their shortcomings in evaluation statistics using perceptual metrics—especially for back views—our method performs nearly equally well for both frontal and back views.", + "bbox": [ + 88, + 268, + 485, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 556, + 243, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Back-view Generation. By assessing the multi-style frontal/back pairs augmented from outputs of Unique3D [51], we can clearly highlight their importance. As shown in Fig. 6, when training the back-view generator using only real data pairs, the generated views align with the distribution of actual hair. In contrast, any incorrect back-view generated due to biases can severely impact the consistency of the subsequent full head view synthesis.", + "bbox": [ + 89, + 580, + 483, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dual Appearance Control. As illustrated in the first row of Fig. 5, the generated near views (random view 1 and 2) can exhibit significant inconsistencies without leveraging our dual appearance control. Additionally, for the nearly opposite views 2 and 3, the generated hair accessories do not match, which occurs due to the limited reference information, as the target view has only a small overlap with the provided image. With the implementation of our dual control, enhanced by the generated back view, our method effectively addresses these issues, achieving excellent consistency in both textures and the underlying 3D shape, as demonstrated in the second row of Fig. 5.", + "bbox": [ + 89, + 719, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "View-Consistency Control. To assess the effectiveness of our strategy for view-consistency control, we conduct an ablation study with three configurations: 1) without 3D-aware noise, 2) without the sequential training strategy, and 3) our full method. In addition to comparing the synthesized views from diffusion, we also fit NeRF [33] on 36 generated views that are evenly distributed around the head to thoroughly evaluate multi-view consistency. As shown in Fig. 7, the absence of 3D-aware noise results in a failure to achieve visual alignment between the diffusion output and the camera-control image. Without the sequential training approach, the method can achieve some visual alignment for certain views, as demonstrated in the second row of Fig. 7. However, when we fit the generated full-range 36 views into a NeRF using the approach from [33], the textures in rendered view (b) from the NeRF (with the same camera as view (a)) become significantly messy due to the discrepancies across multiple views. In contrast, our complete method maintains good consistency among the generated views, which supports decent 3D fitting and shows ability to provide plausible depth.", + "bbox": [ + 511, + 268, + 906, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 513, + 613, + 627, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented the first framework for generating consistent, full $360^{\\circ}$ views from a single portrait, accommodating photorealistic and stylized humans, as well as anthropomorphic animals or statues. Our method is robust, handling particularly difficult input portraits with complex accessories, make-ups, hairstyles, expressive faces, and challenging lighting conditions. We demonstrate that our back-of-head generation approach, combined with our novel dual appearance module, is essential for achieving globally consistent appearance generation full head.", + "bbox": [ + 511, + 643, + 906, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgment", + "text_level": 1, + "bbox": [ + 511, + 810, + 684, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by the Metaverse Center Grant from the MBZUAI Research Office. We thank Egor Zakharov, Zhenhui Lin, Maksat Kengeskanov, and Yiming Chen for the early discussions, helpful suggestions, and feedback.", + "bbox": [ + 511, + 839, + 905, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "26270", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sizhe An, Hongyi Xu, Yichun Shi, Guoxian Song, Umit Y. Ogras, and Linjie Luo. Panohed: Geometry-aware 3d fullhead synthesis in 360deg. In CVPR, pages 20950-20959, 2023. 2, 3, 4, 7", + "[2] Thabo Beeler, Bernd Bickel, Paul Beardsley, Bob Sumner, and Markus Gross. 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Springer, 2022. 2, 3" + ], + "bbox": [ + 91, + 90, + 486, + 218 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "26273", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_model.json b/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..50a6f6310fabd96097fa2ed0f5ba2cac044c7df9 --- /dev/null +++ b/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_model.json @@ -0,0 +1,1839 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.15, + 0.131, + 0.848, + 0.154 + ], + "angle": 0, + "content": "DiffPortrait360: Consistent Portrait Diffusion for 360 View Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.179, + 0.898, + 0.2 + ], + "angle": 0, + "content": "Yuming Gu\\(^{1,2}\\), Phong Tran\\(^{2}\\), Yujian Zheng\\(^{2}\\), Hongyi Xu\\(^{3}\\), Heyuan Li\\(^{4}\\), Adilbek Karmanov\\(^{2}\\), Hao Li\\(^{2,5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.248, + 0.198, + 0.753, + 0.217 + ], + "angle": 0, + "content": "1University of Southern California, 2MBZUAI, 3ByteDance Inc." + }, + { + "type": "text", + "bbox": [ + 0.237, + 0.216, + 0.763, + 0.235 + ], + "angle": 0, + "content": "4The Chinese University of Hong Kong, Shenzhen, 5Pinscreen Inc." + }, + { + "type": "text", + "bbox": [ + 0.329, + 0.235, + 0.672, + 0.253 + ], + "angle": 0, + "content": "https://freedomgu.github.io/DiffPortrait360" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.255, + 0.819, + 0.27 + ], + "angle": 0, + "content": "yuminggu@usc.edu,{the.tran, yujian.zheng, adilbek.karmanov}@mbzuai.ac.ae" + }, + { + "type": "text", + "bbox": [ + 0.32, + 0.273, + 0.686, + 0.287 + ], + "angle": 0, + "content": "heyuanli@link.cuhk.edu.cn, hao@hao-li.com" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.322, + 0.907, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.587, + 0.908, + 0.617 + ], + "angle": 0, + "content": "Figure 1. Our DiffPortrait360 enables \\(360^{\\circ}\\) view-consistent full-head image synthesis. It is universally effective across a diverse range of facial portraits, allowing for the creation of 3D-aware head portraits from single-view images." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.628, + 0.327, + 0.643 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.66, + 0.486, + 0.902 + ], + "angle": 0, + "content": "Generating high-quality 360-degree views of human heads from single-view images is essential for enabling accessible immersive telepresence applications and scalable personalized content creation. While cutting-edge methods for full head generation are limited to modeling realistic human heads, the latest diffusion-based approaches for style-omniscient head synthesis can produce only frontal views and struggle with view consistency, preventing their conversion into true 3D models for rendering from arbitrary angles. We introduce a novel approach that generates fully consistent 360-degree head views, accommodating human, stylized, and anthropomorphic forms, including accessories like glasses and hats. Our method builds on the DiffPortrait3D framework, incorporating a custom ControlNet for back-of-head detail generation and a dual appearance module to ensure global front-back consistency. By training on" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.909, + 0.738 + ], + "angle": 0, + "content": "continuous view sequences and integrating a back reference image, our approach achieves robust, locally continuous view synthesis. Our model can be used to produce high-quality neural radiance fields (NeRFs) for real-time, free-viewpoint rendering, outperforming state-of-the-art methods in object synthesis and 360-degree head generation for very challenging input portraits." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.754, + 0.646, + 0.769 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "In game, film, and animation production, CG characters are central to the content creation pipeline, meticulously designed with the right balance of realism and stylization to align with the narrative. Multi-view stereo systems and 3D scanners are commonly used to streamline the tedious manual process of creating realistic human characters. However, stylized characters are still often 3D modeled from scratch. Alongside the growing demand for efficient and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26263" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.183 + ], + "angle": 0, + "content": "scalable 3D content production pipelines, immersive telepresence and virtual world applications are fueling interest in embodying personalized or imaginary characters created directly by end-users. In this context, highly accessible 3D modeling tools that can generate characters from a single photograph or drawing are becoming increasingly relevant." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.185, + 0.485, + 0.472 + ], + "angle": 0, + "content": "The most widely adopted approaches for image-based full 3D head reconstruction combine parametric models, like 3D Morphable Models (3DMMs) [10, 19, 20, 29, 34, 35, 48, 50, 57], with data-driven hair modeling or generate a single textured 3D mesh that includes both the face and hair. These methods often struggle with diverse hairstyles and capturing detailed appearance textures for the back of the head. Cutting-edge 3D head reconstruction, utilizing transformer-based networks [8, 9, 45-47] to estimate triplane representation, have shown success in capturing complex portraits of human heads with diverse hairstyles and accessories. However, tri-plane introduces strong projection ambiguity for extreme non-frontal poses and therefore fails to model 360-degree head. To facilitate the novel synthesis of full 360-degree views, tri-grid [1] neural volume representations have been introduced. While these methods have demonstrated impressive results, they are limited to realistic human heads and cannot handle stylized or other anthropomorphic shapes." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.474, + 0.483, + 0.64 + ], + "angle": 0, + "content": "The latest diffusion-based image-to-3D generation methods [27, 40, 51] are designed to model a wide range of 3D objects. However, they struggle to capture detailed, domain-specific appearances, such as those of human heads and are prone to severe, unpredictable artifacts. A recent diffusion model, DiffPortrait3D [14], demonstrates the capability to generate novel views of style-omniscient heads by incorporating 3D-aware noise for inference, and finetuning the model on a large 3D head dataset. In addition to being limited to frontal views, this approach also displays noticeable inconsistencies between angles." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.643, + 0.483, + 0.809 + ], + "angle": 0, + "content": "We present the first method capable of generating consistent 360-degree views from a single portrait of a head, accommodating human, stylized, or animal anthropomorphic forms, as well as accessories like glasses, jewelry, or masks. Our novel views can be computed offline (5.6 sec per view) and transformed into a high-quality neural radiance field (NeRF) [30], enabling free-viewpoint rendering in real-time. Our method is particularly robust, capable of handling a wide range of subjects, complex hairstyles, varied head poses, and expressive facial features, including detailed elements like tongues." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Building on the state-of-the-art DiffPortrait3D framework, we introduce key innovations to support back-view renderings and achieve locally continuous view consistency. We begin by generating the back of the head from the input image using a custom ControlNet [55], trained specifically to infer back-of-head details from a front-facing im" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.363 + ], + "angle": 0, + "content": "age. This model is trained on a carefully curated dataset featuring diverse, realistic, and stylized heads. The front and back images are then passed into a dual appearance module (stable diffusion UNet), which extracts appearance information from both perspectives to condition our main image generator (stable diffusion denoising network) through attention layers. Unlike DiffPortrait3D, our approach incorporates an additional back reference image to improve global appearance consistency. Furthermore, we ensure locally continuous view consistency by using continuous view sequences (8 views) as conditions during training. Unlike DiffPortrait3D, which is trained only on frontal 3D-aware head generations, our approach utilizes a dataset comprising full 360-degree views of human heads, with data that is both captured and synthetically generated. Finally, our denoising process also uses a 3D-aware noise which is initialized using a fine-tuned inversion process-based a StyleGAN-based 360 head generator [1]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.364, + 0.905, + 0.56 + ], + "angle": 0, + "content": "We demonstrate that diffusion models can generate highly detailed and consistent 360-degree head views from in-the-wild images across an extensive range of styles and complex portraits, handling challenging lighting conditions, intricate hairstyles, diverse appearances, and varying head poses. Our approach significantly outperforms all the latest generative methods for our challenge human head benchmarks generation, w.r.t. key metrics. More importantly, our method produces globally consistent appearances for the back of the head and locally view consistent synthesis when generating 360-degree views, which enables us to reconstruct true 3D representations (e.g., NeRFs) for free-view point rendering. We present the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.561, + 0.904, + 0.619 + ], + "angle": 0, + "content": "- We present a novel method for \\(360^{\\circ}\\) view synthesis from a single style-omniscient portrait, which leverages priors from pre-trained stable diffusion models to generate view-consistent content." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.622, + 0.904, + 0.68 + ], + "angle": 0, + "content": "- We propose a dual appearance control module, supported by a diffusion-based back-view generator, that ensures global consistency in novel view synthesis around the subject." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.682, + 0.904, + 0.741 + ], + "angle": 0, + "content": "- We introduce a novel training strategy that employs view-consistent sequence generation to enhance continuity and smoothness, utilizing a 3D head dataset composed of both captured and synthetic subjects." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.561, + 0.904, + 0.741 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.755, + 0.655, + 0.77 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.781, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Numerous research methods and commercial solutions [20, 35] have been developed for reconstructing full 3D avatar heads from a single input photo, as opposed to using a multi-view capture approach [2, 12, 23, 28, 37]. These capabilities enable applications such as consumer-accessible immersive telepresence, personalized avatars for 3D games, and scalable approaches to content creation. Despite their wide adoption, regression-based face modeling techniques" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26264" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.093, + 0.868, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.388, + 0.908, + 0.501 + ], + "angle": 0, + "content": "Figure 2. For the task of full-range 360-degree novel view synthesis, DiffPortrait360 employs a frozen pre-trained Latent Diffusion Model (LDM) as a rendering backbone and incorporates three auxiliary trainable modules for disentangled control of dual appearance \\(\\mathcal{R}\\), camera control \\(\\mathcal{C}\\), and U-Nets with view consistency \\(\\mathcal{V}\\). Specifically, \\(\\mathcal{R}\\) extracts appearance information from \\(I_{\\mathrm{ref}}\\) and \\(I_{\\mathrm{back}}\\), and \\(\\mathcal{C}\\) derives the camera pose, which is rendered using an off-the-shelf 3D GAN. During training, we utilize a continuous sampling training strategy to better preserve the continuity of the camera trajectory. We enhance attention to continuity between frames to maintain the appearance information without changes due to turning angles. For inference, we employ our tailored back-view image generation network \\(\\mathcal{F}\\) to generate a back-view image, enabling us to generate a 360-degree full range of camera trajectories using a single image portrait. Note that \\(z\\) stands for latent space noise rather than image." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.526, + 0.487, + 0.587 + ], + "angle": 0, + "content": "from a single input image [10, 19, 29, 34, 48, 50, 57] using parametric 3D Morphable Models (3DMM) [3] are increasingly being complemented in many applications by neural rendering techniques, as surveyed in [44]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.485, + 0.902 + ], + "angle": 0, + "content": "3D-Aware GAN-Based Full-Head Synthesis. Recent advancements on 3D-aware GANs [1, 5-7, 13, 24, 31, 41, 52, 53], often leveraging StyleGAN2 [21] as backbone, are capable of generating novel views from a single input photograph through fine-tuned GAN inversion while ensuring view-consistency using a volumetric neural radiance field representation based on tri-planes [6] or signed distance function, such as StyleSDF [31]. While most of them can only generate frontal faces due their training data and their 3D representation, two recent methods have demonstrated how the generation of consistent 360-degree views are possible, namely, PanoHead [1] and SphereHead [24]. These methods generate a reasonable back head region using enhanced tri-plane representations by incorporating multiple depth layers or spherical coordinate system. However, their back-view synthesis often appear unnatural and mismatching the front view, especially when single-view inversion is applied. Most importantly, all of these methods are domain specific and only work on realistic human heads. They often fail for unknown accessories or complex hairstyles, and" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.526, + 0.899, + 0.542 + ], + "angle": 0, + "content": "generating novel views for stylized avatars is not possible." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.908, + 0.903 + ], + "angle": 0, + "content": "Diffusion Model Based 360-Degree View Synthesis. Diffusion-based models [18, 42, 43], particularly latent diffusion models (LDM) [39], have recently gained significant attention for their unmatched performance in generating highly diverse and high-fidelity images across various domains. A number of diffusion-based methods have been introduced for the task of novel view synthesis [14, 26, 27, 40] for general objects, and several methods [14, 40] demonstrate the effectiveness of fusing features of a reference image into self-attention blocks in the LDM UNets, facilitating high-quality novel view generation while preserved appearance context effectively. The notable work, ControlNet [55], extends the LDM framework to controllable image generation with additive structural conditions from signals such as 3D-aware GAN-synthesized camera viewpoints or rendered 3DMM condition [36]. The work, Diff-Portrait3D [14] achieves the state-of-the-art portrait novel view synthesis results by seamlessly integrating the appearance and camera view attentions with pre-trained UNets. Despite the impressive results, especially for stylized input portraits, only frontal views are possible to generate, and unwanted local inconsistencies between the model from" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26265" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.907, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.442, + 0.908, + 0.486 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparisons with existing methods on in the wild portraits. Compared to the baselines, our method shows superior generalization capability to novel view synthesis of wild portraits with unseen appearances, expressions, and styles, even without any reliance on fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.511, + 0.484, + 0.664 + ], + "angle": 0, + "content": "being converted into a 3D representation, such as textured Meshes, NeRFs or 3D Gaussian Splats, which is needed for free-viewpoint rendering. Another recent diffusion-based technique, called Portrait3D [16], generates compelling views from all angles, achieving superior results to GAN-based approaches [1, 24] but is restricted to realistic heads only. Our proposed solution is particularly effective in generating globally consistent and plausible back views of the head, while also ensuring locally view-consistent renderings for full \\(360^{\\circ}\\) style-omniscient portraits." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.678, + 0.182, + 0.693 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.704, + 0.483, + 0.825 + ], + "angle": 0, + "content": "Given a single RGB portrait image with arbitrary style, \\( I_{\\mathrm{ref}} \\), our approach aims to synthesize a new image, \\( I_{\\mathrm{tar}} \\), from any camera perspective within a \\( 360^{\\circ} \\) range using an \\( I_{\\mathrm{cam}} \\) image. The novel view \\( I_{\\mathrm{tar}} \\) must maintain consistent appearance information with \\( I_{\\mathrm{ref}} \\), with the camera view controlled by \\( I_{\\mathrm{cam}} \\). It is crucial to note that this includes not only positions near \\( I_{\\mathrm{ref}} \\) but also areas with minimal overlap and previously unobserved regions from the given view." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.902 + ], + "angle": 0, + "content": "In this work, DiffPortrait360 leverages powerful latent diffusion models, enabling disentangled control of appearance and camera views, as detailed in Section 3.1. Building upon this foundation, we propose a tailored dual-appearscence module that incorporates additional appearance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.511, + 0.907, + 0.648 + ], + "angle": 0, + "content": "information from both the front and back of the head, \\( I_{\\mathrm{back}} \\) outlined in Section 3.2. We introduce an additional Control-Net [55] based synthesizing network designed to generate a plausible back view in \\( I_{\\mathrm{back}} \\) from \\( I_{\\mathrm{ref}} \\), and to correct biases due to limited 3D head training data, as detailed in Section 3.3. Finally, Section 3.4 introduces a novel training strategy that leverages sequence priors to distill fine-grained structural information, ensuring consistency and smooth view transitions while maintaining high synthesis quality." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.657, + 0.645, + 0.673 + ], + "angle": 0, + "content": "3.1. Background" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.679, + 0.909, + 0.817 + ], + "angle": 0, + "content": "Latent Diffusion Model. Diffusion models [18, 42, 43] are generative models designed to synthesize desired data samples from Gaussian noise \\( z_0 \\) by iteratively denoising across \\( T \\) time steps. Latent diffusion models (LDMs) [39] extend this framework by operating in an encoded latent space \\( \\mathcal{E}(I) \\) where \\( I \\) is an input image, facilitated by a pretrained auto-encoder \\( \\mathcal{D} \\circ \\mathcal{E}(\\cdot) \\). Specifically, the model is trained to learn the denoising process from \\( z_T \\sim \\mathcal{N}(0,1) \\) to \\( z_0 = \\mathcal{E}(I) \\) with the objective," + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.827, + 0.907, + 0.862 + ], + "angle": 0, + "content": "\\[\nL _ {l d m} = \\mathbb {E} _ {z _ {0}, t, \\epsilon \\sim \\mathcal {N} (0, 1)} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t) \\right\\| _ {2} ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.908, + 0.902 + ], + "angle": 0, + "content": "where \\( z_{t} \\) is the noise map at timestep \\( t \\) and \\( \\epsilon_{\\theta} \\) is a trainable UNet equipped with layers of convolutions and self-/cross-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26266" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.907, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.432, + 0.907, + 0.462 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparisons of novel view synterhisis on RenderMe360 [32]. Our method achieves effective appearance control for novel synthesis under substantial change of camera view for synthesis." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.484, + 0.478, + 0.635 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.637, + 0.46, + 0.65 + ], + "angle": 0, + "content": "Figure 5. Ablation Study on Dual Appearance Control." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.679, + 0.483, + 0.815 + ], + "angle": 0, + "content": " attentions (TransBlock). Finally, the output image is calculated by mapping the denoised latent feature map back to the image domain \\( I = \\mathcal{D}(z_0) \\). Unlike traditional Text-to-Image (T2I) diffusion models, which rely on textual inputs to guide image synthesis, our approach directly extracts portrait appearance context and camera information from \\( I_{\\mathrm{ref}} \\) and \\( I_{\\mathrm{cam}} \\), respectively, without relying on text descriptions. Consequently, we use an empty prompt for text control and omit it from our formulations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Diffusion-Based Novel View Synthesis. Recent studies [25-27, 40] have leveraged pre-trained LDMs for novel view synthesis. These efforts largely employ latent diffusion as the backbone for novel view synthesis, incorporating" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.488, + 0.907, + 0.715 + ], + "angle": 0, + "content": "modules for appearance injection and camera information control. While most of this research focuses on general objects, our work follows a specific [14] designed for portrait novel view synthesis, which uses three main modules: 1) an Appearance Reference Module \\(\\mathcal{R}\\) that captures identity attributes and background from \\(I_{\\mathrm{ref}}\\), 2) a Control Module \\((C)\\) typically a ControlNet [55], that adjusts camera perspectives based on \\(I_{\\mathrm{cam}}\\) and 3) a View Consistency Module \\(\\mathcal{V}\\), intervened within UNet blocks using temporal cross-attention between features of multiple consecutive views to ensure view consistency. We follow the same network structure but innovate on enabling 360-degree and consistent novel view synthesis that preserves input appearance coherence across extensive viewpoint shifts, encompassing elements such as expressions, hairstyles, and head shapes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.727, + 0.748, + 0.743 + ], + "angle": 0, + "content": "3.2. Dual Appearance Module" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.903 + ], + "angle": 0, + "content": "To ensure the preservation of appearance information characteristics, previous methods typically employ a ReferenceNet [4] to inject the reference image and guide the denoising process with \\( I_{\\mathrm{ref}} \\) in order to extract sufficient information from \\( I_{\\mathrm{ref}} \\). The Appearance Control Module is trained to ensure meticulous transfer of referenced structure and appearance into the SD-UNet for the task of novel view synthesis of portrait views. While effective at reference control in front near face, such an appearance control scheme induces following problems: Firstly, the appearance" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26267" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.089, + 0.478, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.3, + 0.429, + 0.313 + ], + "angle": 0, + "content": "Figure 6. Ablation on Back-view Generation." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.342, + 0.483, + 0.599 + ], + "angle": 0, + "content": "content is largely provided by the image of \\( I_{\\mathrm{ref}} \\). As the viewpoint shifts from the front of the face to the back of the head, the training dataset introduces randomly generated content such as different hairstyles, hats, and other features. Additionally, front face images contain only very limited information related to the back of the head, with very few pixels or even no pixels available for use. This leads to a significant misuse of most of the facial feature information from the reference image, causing leakage to the back of the head, which can be amplified to create a dual face or result in facial information appearing on the back of the head. Furthermore, these inaccuracies impact view control consistency, since the network, as a shortcut, tends to use other tailored modules, e.g., the view control module \\( \\mathcal{C} \\), to generate information when there is insufficient appearance information. As a result, system collapse occurs during the generation of larger views with only a single reference." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.6, + 0.483, + 0.901 + ], + "angle": 0, + "content": "To mitigate this issue, we require an appearance reference network that could take information that entirely covers areas not observed by the front appearance while minimizing the overlap with the front face, which enables the diffusion network to access sufficient appearance information. This motivation leads us to design a dual-appearance module. Specifically, during training, we allow the appearance module to access two images, \\( I_{\\mathrm{ref}} \\) and \\( I_{\\mathrm{back}} \\). The rationale behind this modification is to reduce ambiguities caused by insufficient or erroneous information during viewpoint transitions, and to compel the network to autonomously decide which information from \\( I_{\\mathrm{ref}} \\) and \\( I_{\\mathrm{back}} \\) should be relied on more under different camera views. We note that in selecting \\( I_{\\mathrm{ref}} \\) and \\( I_{\\mathrm{back}} \\), views should overlap as little as possible but not be fixed, as this could affect the generalization ability of the input images. Consequently, in our training dataset, we deliberately choose pairs with minimal overlap as inputs for \\( I_{\\mathrm{ref}} \\) and \\( I_{\\mathrm{back}} \\), enabling our dual appearance module to leverage the information to its fullest extent. As a result, we observed consistent and sat" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.089, + 0.902, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.321, + 0.907, + 0.351 + ], + "angle": 0, + "content": "Figure 7. Ablation Study on View-consistency Control. (a) Generated novel view. (b-c) Rendering and depth of fitted NeRFs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.379, + 0.907, + 0.455 + ], + "angle": 0, + "content": "isfactory appearance in areas not covered by the reference images, and between the 360-degree area of \\( I_{\\mathrm{back}} \\) and \\( I_{\\mathrm{ref}} \\). This makes our model capable of generating consistent appearance information while changing the camera views (see Figure 5)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.468, + 0.806, + 0.483 + ], + "angle": 0, + "content": "3.3. Back-View Reference Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.491, + 0.906, + 0.627 + ], + "angle": 0, + "content": "Our trained dual appearance module, \\(\\mathcal{R}\\), significantly improves appearance consistency, especially during large changes in viewing angles. However, during inference, it is challenging to obtain a reasonable reference image context with a viewing angle drastically different from the input, such as obtaining a nearly opposite auxiliary image to the reference. Compromising to this difficulty will reduce the effectiveness of the disentangled appearance information determined by \\(I_{\\mathrm{back}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.906, + 0.764 + ], + "angle": 0, + "content": "To address this issue, we developed a generative network capable of producing an \\( I_{\\mathrm{back}} \\) that has minimal overlap in appearance information with \\( I_{\\mathrm{ref}} \\) while maintaining a consistent style, reasonable head shape, and hairstyle. This motivates the use of ControlNet [55] and the original \\( I_{\\mathrm{ref}} \\) to generate a decoupled \\( I_{\\mathrm{back}} \\) as our extra appearance condition input. This approach is practical for real-world applications, allowing the generation of additional appearance information without needing external inputs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.909, + 0.903 + ], + "angle": 0, + "content": "However, this generation model can exhibit a strong bias when using only realistic data, which is unsuitable for producing a broader range of artistic styles. To avoid an overreliance on a training dataset that could lead to the generation of unreasonable \\( I_{\\mathrm{back}} \\), we supplemented our dataset with a large collection of cartoon and stylized task images of back views produced by [11] and Unique3D [51], adjusting the distribution of our dataset to lessen the bias towards realistic backdrops. Notably, even with limited cam" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26268" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.228 + ], + "angle": 0, + "content": "era views (only including front and back views), this is sufficient for the Generative Module to correct biases from real dataset training, enabling it to generate reasonable unobserved head regions consistent with the input portrait style. As demonstrated in our experiments, our trained \\(\\mathcal{F}\\), with a limited dataset of cartoon front and back faces, effectively resolves the challenge of sourcing additional appearance \\(I_{\\mathrm{back}}\\) in practical applications and generalizes well to unseen portrait styles. (see Figure 6)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.24, + 0.327, + 0.256 + ], + "angle": 0, + "content": "3.4. View-Consistency Module" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.262, + 0.483, + 0.398 + ], + "angle": 0, + "content": "Given an arbitrary view portrait image \\( I_{\\mathrm{ref}} \\), our trained module has already been capable of generating a full 360-degree range of novel view syntheses \\( I_{\\mathrm{tar}} \\) via above designs. Nevertheless, during inference, we occasionally observe our module failing to capture nuanced view consistency compared to 3D-aware GANs, such as appearance flickering and choppy transitions between views. These unwanted artifacts significantly impact the effectiveness of novel view synthesis in downstream applications, such as 3D reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.399, + 0.483, + 0.549 + ], + "angle": 0, + "content": "Reviewing our above module, the view consistency module \\(\\mathcal{V}\\) is primarily managed by a temporal transformer [15], integrated with 3D-aware noise [14]. However, given the heritage motion prior from [15], we note that view consistency is trained by focusing on cross-view attentions with randomly shuffled views. We argue this training approach does not fully utilize the advantages of the motion prior, which may lead to the observed choppy transitions and minor appearance changes, ultimately resulting in the loss of detail and collapse of downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.55, + 0.483, + 0.763 + ], + "angle": 0, + "content": "To alleviate this issue, we have revised the training approach of the temporal transformer to include data from continuous view transitions. Instead of randomly sampling sparse views from a sparse multi-view dataset, we controlled the 3D-aware GAN [1] to generate consistently sampled sequential view changes. In contrast to random view cross-attention, our sequential training scheme effectively instructs the view consistency module \\(\\mathcal{V}\\) to maximize the benefits derived from the pretrained motion prior. Even when trained on only a limited synthetic dataset, our sequential training scheme is sufficient for \\(\\mathcal{V}\\) to decipher higher multi-view consistency accuracy and smoother view-changing results, enabling the synthesis process to produce smoother results that better fit downstream applications." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.778, + 0.222, + 0.794 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.804, + 0.192, + 0.817 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.483, + 0.901 + ], + "angle": 0, + "content": "We train our model using a hybrid dataset comprised of photo-realistic full-head multi-view images dataset RenderMe360 [32] and synthetic ones by PanoHead [1] and SphereHead [24]. RenderMe360 consists of images from 500 individuals, each captured with 12 different expres" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.41 + ], + "angle": 0, + "content": "sions and an extended animated sequence from 60 multiview camera positions. This setup offers a substantial amount of multi-view consistent appearance data for training. We manually separated the front and back camera information, selecting front and back images as inputs for dual-appearance control, while using the remaining camera views as training data. We randomly selected 1,000 frames of multi-view data from 150 subjects while using PanoHead and SphereHead to sample continuous views from 600 identities, specifically for training the sequential view consistency module due to the scarcity of sparse camera views of RenderMe360. For the back-head reference image generation network, we collected 1,000 manually chosen, stylized front-and-back image pairs to augment the back-head image generation network. High-quality stylized front images were generated using a state-of-the-art tool [11]; we then fed the images to Unique3D [51] to generate content consistent back head. It's important to note that this highly stylized dataset, containing only front and back views, was used solely as data augmentation to reduce bias in the backview generation and was not included in the training of \\(\\mathcal{R}\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.418, + 0.652, + 0.433 + ], + "angle": 0, + "content": "4.2. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.439, + 0.907, + 0.711 + ], + "angle": 0, + "content": "Comparisons on Stylized Portraits. To demonstrate the generalization capability of our approach on stylized input portraits, we conduct a qualitative comparison with existing methods, as shown in Fig. 3. We also include Rome [22] and Itseez3D1. Thanks to our back-view generator and view-consistency module, our method exhibits superior generalization to diverse styles. We achieve high-quality details and continuous views across the full range of head poses. In contrast, it is evident that other approaches struggle to reach this level of performance. Specifically, Rome fails to generate reasonable back-view textures and structures, especially for inputs with thick hair and unusual accessories. Similarly, Zero-1-to-3 [27] and Unique3D [51] continue to struggle with bridging the domain gap between general objects and human heads. Itseez3D appears to operate with templates that preserve only the facial textures from the reference image. Additionally, both PanoHead [1] and SphereHead [24] perform poorly on stylized portraits." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.729, + 0.909, + 0.88 + ], + "angle": 0, + "content": "Comparisons on Real Portraits. We then compare the novel view synthesis results of our method with existing approaches on the test split of RenderMe360 [32], as illustrated in Fig. 4 and Tab. 1. We additionally incorporate Diff-Portrait3D* [14], which has been finetuned using our full-head datasets, as the original model was limited to generating frontal views using the provided checkpoints. As shown in the qualitative comparisons in Fig. 4, the GAN-based methods, PanoHead and SphereHead, struggle to generate realistic details that align with the reference images. Their" + }, + { + "type": "page_footnote", + "bbox": [ + 0.532, + 0.887, + 0.652, + 0.9 + ], + "angle": 0, + "content": "1https://itseez3d.com/" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26269" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.139, + 0.089, + 0.86, + 0.204 + ], + "angle": 0, + "content": "
    MethodFrontal ViewBack View
    PSNR ↑SSIM ↑LPIPS ↓CSIM ↑FID ↓PSNR ↑SSIM ↑LPIPS ↓FID ↓
    PanoHead + PTI28.350.5050.4950.47198.9328.390.4500.432169.52
    SphereHead + PTI28.620.5130.4320.55669.4128.630.4630.413106.21
    Zero123---0.431152.03---216.88
    Unique3D---0.483195.33---285.75
    DiffPortrait3D*28.960.5090.4250.70949.0228.470.3730.44691.37
    Ours29.440.5780.3840.74635.3430.920.6480.31339.40
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.215, + 0.905, + 0.243 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons of novel view synthesis on RenderMe360 [32] with perceptual metrics PSNR, SSIM [49], LPIPS [56], FID [17] and an additional face recognition metric CSIM [54] for frontal views." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.27, + 0.486, + 0.542 + ], + "angle": 0, + "content": "outputs fail to preserve identity due to the limitations of the PTI [38]. Zero-1-to-3 and Unique3D are trained on datasets of general synthetic 3D objects, and without specific domain knowledge, they cannot consistently produce reasonable novel views. Their results are often riddled with artifacts unrelated to heads. Although we fine-tuned DiffPortrait3D* on our full-head datasets, it still struggles to generate consistent novel views at the back, resulting in significant discrepancies from the reference images. These examples show artifacts such as multiple faces and misaligned hair color. In contrast, our specially designed method outperforms all others, demonstrating strong consistency across significantly different viewpoints. This conclusion is further supported by the quantitative comparisons detailed in Tab. 1. While existing methods reveal their shortcomings in evaluation statistics using perceptual metrics—especially for back views—our method performs nearly equally well for both frontal and back views." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.557, + 0.245, + 0.573 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.581, + 0.484, + 0.703 + ], + "angle": 0, + "content": "Back-view Generation. By assessing the multi-style frontal/back pairs augmented from outputs of Unique3D [51], we can clearly highlight their importance. As shown in Fig. 6, when training the back-view generator using only real data pairs, the generated views align with the distribution of actual hair. In contrast, any incorrect back-view generated due to biases can severely impact the consistency of the subsequent full head view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Dual Appearance Control. As illustrated in the first row of Fig. 5, the generated near views (random view 1 and 2) can exhibit significant inconsistencies without leveraging our dual appearance control. Additionally, for the nearly opposite views 2 and 3, the generated hair accessories do not match, which occurs due to the limited reference information, as the target view has only a small overlap with the provided image. With the implementation of our dual control, enhanced by the generated back view, our method effectively addresses these issues, achieving excellent consistency in both textures and the underlying 3D shape, as demonstrated in the second row of Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.27, + 0.908, + 0.589 + ], + "angle": 0, + "content": "View-Consistency Control. To assess the effectiveness of our strategy for view-consistency control, we conduct an ablation study with three configurations: 1) without 3D-aware noise, 2) without the sequential training strategy, and 3) our full method. In addition to comparing the synthesized views from diffusion, we also fit NeRF [33] on 36 generated views that are evenly distributed around the head to thoroughly evaluate multi-view consistency. As shown in Fig. 7, the absence of 3D-aware noise results in a failure to achieve visual alignment between the diffusion output and the camera-control image. Without the sequential training approach, the method can achieve some visual alignment for certain views, as demonstrated in the second row of Fig. 7. However, when we fit the generated full-range 36 views into a NeRF using the approach from [33], the textures in rendered view (b) from the NeRF (with the same camera as view (a)) become significantly messy due to the discrepancies across multiple views. In contrast, our complete method maintains good consistency among the generated views, which supports decent 3D fitting and shows ability to provide plausible depth." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.614, + 0.628, + 0.63 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.644, + 0.907, + 0.795 + ], + "angle": 0, + "content": "We have presented the first framework for generating consistent, full \\(360^{\\circ}\\) views from a single portrait, accommodating photorealistic and stylized humans, as well as anthropomorphic animals or statues. Our method is robust, handling particularly difficult input portraits with complex accessories, make-ups, hairstyles, expressive faces, and challenging lighting conditions. We demonstrate that our back-of-head generation approach, combined with our novel dual appearance module, is essential for achieving globally consistent appearance generation full head." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.811, + 0.686, + 0.829 + ], + "angle": 0, + "content": "6. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.903 + ], + "angle": 0, + "content": "This work is supported by the Metaverse Center Grant from the MBZUAI Research Office. We thank Egor Zakharov, Zhenhui Lin, Maksat Kengeskanov, and Yiming Chen for the early discussions, helpful suggestions, and feedback." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26270" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.115, + 0.484, + 0.17 + ], + "angle": 0, + "content": "[1] Sizhe An, Hongyi Xu, Yichun Shi, Guoxian Song, Umit Y. Ogras, and Linjie Luo. Panohed: Geometry-aware 3d fullhead synthesis in 360deg. 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Springer, 2022. 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.487, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26273" + } + ] +] \ No newline at end of file diff --git a/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_origin.pdf b/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..23b8e10b3c87c7900a216e7a7502041ba9d02c1b --- /dev/null +++ b/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/300f1ac6-d9a8-4527-94a8-d8a1857b23e6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1acbf35b442696dca8f22cce673a6a40672eb42b743e6a68bbf4d8a869112651 +size 2521117 diff --git a/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/full.md b/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0c4cb397ea1ae703e69b4b2323ed7481d4b11dad --- /dev/null +++ b/2025/DiffPortrait360_ Consistent Portrait Diffusion for 360 View Synthesis/full.md @@ -0,0 +1,229 @@ +# DiffPortrait360: Consistent Portrait Diffusion for 360 View Synthesis + +Yuming Gu $^{1,2}$ , Phong Tran $^{2}$ , Yujian Zheng $^{2}$ , Hongyi Xu $^{3}$ , Heyuan Li $^{4}$ , Adilbek Karmanov $^{2}$ , Hao Li $^{2,5}$ + +1University of Southern California, 2MBZUAI, 3ByteDance Inc. + +4The Chinese University of Hong Kong, Shenzhen, 5Pinscreen Inc. + +https://freedomgu.github.io/DiffPortrait360 + +yuminggu@usc.edu,{the.tran, yujian.zheng, adilbek.karmanov}@mbzuai.ac.ae + +heyuanli@link.cuhk.edu.cn, hao@hao-li.com + +![](images/74b8faaedb543445f336a37270b68acc61316c6b266ef4681be19f41e7fde1ad.jpg) +Figure 1. Our DiffPortrait360 enables $360^{\circ}$ view-consistent full-head image synthesis. It is universally effective across a diverse range of facial portraits, allowing for the creation of 3D-aware head portraits from single-view images. + +# Abstract + +Generating high-quality 360-degree views of human heads from single-view images is essential for enabling accessible immersive telepresence applications and scalable personalized content creation. While cutting-edge methods for full head generation are limited to modeling realistic human heads, the latest diffusion-based approaches for style-omniscient head synthesis can produce only frontal views and struggle with view consistency, preventing their conversion into true 3D models for rendering from arbitrary angles. We introduce a novel approach that generates fully consistent 360-degree head views, accommodating human, stylized, and anthropomorphic forms, including accessories like glasses and hats. Our method builds on the DiffPortrait3D framework, incorporating a custom ControlNet for back-of-head detail generation and a dual appearance module to ensure global front-back consistency. By training on + +continuous view sequences and integrating a back reference image, our approach achieves robust, locally continuous view synthesis. Our model can be used to produce high-quality neural radiance fields (NeRFs) for real-time, free-viewpoint rendering, outperforming state-of-the-art methods in object synthesis and 360-degree head generation for very challenging input portraits. + +# 1. Introduction + +In game, film, and animation production, CG characters are central to the content creation pipeline, meticulously designed with the right balance of realism and stylization to align with the narrative. Multi-view stereo systems and 3D scanners are commonly used to streamline the tedious manual process of creating realistic human characters. However, stylized characters are still often 3D modeled from scratch. Alongside the growing demand for efficient and + +scalable 3D content production pipelines, immersive telepresence and virtual world applications are fueling interest in embodying personalized or imaginary characters created directly by end-users. In this context, highly accessible 3D modeling tools that can generate characters from a single photograph or drawing are becoming increasingly relevant. + +The most widely adopted approaches for image-based full 3D head reconstruction combine parametric models, like 3D Morphable Models (3DMMs) [10, 19, 20, 29, 34, 35, 48, 50, 57], with data-driven hair modeling or generate a single textured 3D mesh that includes both the face and hair. These methods often struggle with diverse hairstyles and capturing detailed appearance textures for the back of the head. Cutting-edge 3D head reconstruction, utilizing transformer-based networks [8, 9, 45-47] to estimate triplane representation, have shown success in capturing complex portraits of human heads with diverse hairstyles and accessories. However, tri-plane introduces strong projection ambiguity for extreme non-frontal poses and therefore fails to model 360-degree head. To facilitate the novel synthesis of full 360-degree views, tri-grid [1] neural volume representations have been introduced. While these methods have demonstrated impressive results, they are limited to realistic human heads and cannot handle stylized or other anthropomorphic shapes. + +The latest diffusion-based image-to-3D generation methods [27, 40, 51] are designed to model a wide range of 3D objects. However, they struggle to capture detailed, domain-specific appearances, such as those of human heads and are prone to severe, unpredictable artifacts. A recent diffusion model, DiffPortrait3D [14], demonstrates the capability to generate novel views of style-omniscient heads by incorporating 3D-aware noise for inference, and finetuning the model on a large 3D head dataset. In addition to being limited to frontal views, this approach also displays noticeable inconsistencies between angles. + +We present the first method capable of generating consistent 360-degree views from a single portrait of a head, accommodating human, stylized, or animal anthropomorphic forms, as well as accessories like glasses, jewelry, or masks. Our novel views can be computed offline (5.6 sec per view) and transformed into a high-quality neural radiance field (NeRF) [30], enabling free-viewpoint rendering in real-time. Our method is particularly robust, capable of handling a wide range of subjects, complex hairstyles, varied head poses, and expressive facial features, including detailed elements like tongues. + +Building on the state-of-the-art DiffPortrait3D framework, we introduce key innovations to support back-view renderings and achieve locally continuous view consistency. We begin by generating the back of the head from the input image using a custom ControlNet [55], trained specifically to infer back-of-head details from a front-facing im + +age. This model is trained on a carefully curated dataset featuring diverse, realistic, and stylized heads. The front and back images are then passed into a dual appearance module (stable diffusion UNet), which extracts appearance information from both perspectives to condition our main image generator (stable diffusion denoising network) through attention layers. Unlike DiffPortrait3D, our approach incorporates an additional back reference image to improve global appearance consistency. Furthermore, we ensure locally continuous view consistency by using continuous view sequences (8 views) as conditions during training. Unlike DiffPortrait3D, which is trained only on frontal 3D-aware head generations, our approach utilizes a dataset comprising full 360-degree views of human heads, with data that is both captured and synthetically generated. Finally, our denoising process also uses a 3D-aware noise which is initialized using a fine-tuned inversion process-based a StyleGAN-based 360 head generator [1]. + +We demonstrate that diffusion models can generate highly detailed and consistent 360-degree head views from in-the-wild images across an extensive range of styles and complex portraits, handling challenging lighting conditions, intricate hairstyles, diverse appearances, and varying head poses. Our approach significantly outperforms all the latest generative methods for our challenge human head benchmarks generation, w.r.t. key metrics. More importantly, our method produces globally consistent appearances for the back of the head and locally view consistent synthesis when generating 360-degree views, which enables us to reconstruct true 3D representations (e.g., NeRFs) for free-view point rendering. We present the following contributions: + +- We present a novel method for $360^{\circ}$ view synthesis from a single style-omniscient portrait, which leverages priors from pre-trained stable diffusion models to generate view-consistent content. +- We propose a dual appearance control module, supported by a diffusion-based back-view generator, that ensures global consistency in novel view synthesis around the subject. +- We introduce a novel training strategy that employs view-consistent sequence generation to enhance continuity and smoothness, utilizing a 3D head dataset composed of both captured and synthetic subjects. + +# 2. Related Work + +Numerous research methods and commercial solutions [20, 35] have been developed for reconstructing full 3D avatar heads from a single input photo, as opposed to using a multi-view capture approach [2, 12, 23, 28, 37]. These capabilities enable applications such as consumer-accessible immersive telepresence, personalized avatars for 3D games, and scalable approaches to content creation. Despite their wide adoption, regression-based face modeling techniques + +![](images/74a6d3e6d4c469e45cd0f1114dd237db5eaf636e51b7dcb993d1f67b77f354cd.jpg) +Figure 2. For the task of full-range 360-degree novel view synthesis, DiffPortrait360 employs a frozen pre-trained Latent Diffusion Model (LDM) as a rendering backbone and incorporates three auxiliary trainable modules for disentangled control of dual appearance $\mathcal{R}$ , camera control $\mathcal{C}$ , and U-Nets with view consistency $\mathcal{V}$ . Specifically, $\mathcal{R}$ extracts appearance information from $I_{\mathrm{ref}}$ and $I_{\mathrm{back}}$ , and $\mathcal{C}$ derives the camera pose, which is rendered using an off-the-shelf 3D GAN. During training, we utilize a continuous sampling training strategy to better preserve the continuity of the camera trajectory. We enhance attention to continuity between frames to maintain the appearance information without changes due to turning angles. For inference, we employ our tailored back-view image generation network $\mathcal{F}$ to generate a back-view image, enabling us to generate a 360-degree full range of camera trajectories using a single image portrait. Note that $z$ stands for latent space noise rather than image. + +from a single input image [10, 19, 29, 34, 48, 50, 57] using parametric 3D Morphable Models (3DMM) [3] are increasingly being complemented in many applications by neural rendering techniques, as surveyed in [44]. + +3D-Aware GAN-Based Full-Head Synthesis. Recent advancements on 3D-aware GANs [1, 5-7, 13, 24, 31, 41, 52, 53], often leveraging StyleGAN2 [21] as backbone, are capable of generating novel views from a single input photograph through fine-tuned GAN inversion while ensuring view-consistency using a volumetric neural radiance field representation based on tri-planes [6] or signed distance function, such as StyleSDF [31]. While most of them can only generate frontal faces due their training data and their 3D representation, two recent methods have demonstrated how the generation of consistent 360-degree views are possible, namely, PanoHead [1] and SphereHead [24]. These methods generate a reasonable back head region using enhanced tri-plane representations by incorporating multiple depth layers or spherical coordinate system. However, their back-view synthesis often appear unnatural and mismatching the front view, especially when single-view inversion is applied. Most importantly, all of these methods are domain specific and only work on realistic human heads. They often fail for unknown accessories or complex hairstyles, and + +generating novel views for stylized avatars is not possible. + +Diffusion Model Based 360-Degree View Synthesis. Diffusion-based models [18, 42, 43], particularly latent diffusion models (LDM) [39], have recently gained significant attention for their unmatched performance in generating highly diverse and high-fidelity images across various domains. A number of diffusion-based methods have been introduced for the task of novel view synthesis [14, 26, 27, 40] for general objects, and several methods [14, 40] demonstrate the effectiveness of fusing features of a reference image into self-attention blocks in the LDM UNets, facilitating high-quality novel view generation while preserved appearance context effectively. The notable work, ControlNet [55], extends the LDM framework to controllable image generation with additive structural conditions from signals such as 3D-aware GAN-synthesized camera viewpoints or rendered 3DMM condition [36]. The work, Diff-Portrait3D [14] achieves the state-of-the-art portrait novel view synthesis results by seamlessly integrating the appearance and camera view attentions with pre-trained UNets. Despite the impressive results, especially for stylized input portraits, only frontal views are possible to generate, and unwanted local inconsistencies between the model from + +![](images/5ab9bb691d1075674a753028020a0c95b8de25a3557707e00763d37ce27ac848.jpg) +Figure 3. Qualitative comparisons with existing methods on in the wild portraits. Compared to the baselines, our method shows superior generalization capability to novel view synthesis of wild portraits with unseen appearances, expressions, and styles, even without any reliance on fine-tuning. + +being converted into a 3D representation, such as textured Meshes, NeRFs or 3D Gaussian Splats, which is needed for free-viewpoint rendering. Another recent diffusion-based technique, called Portrait3D [16], generates compelling views from all angles, achieving superior results to GAN-based approaches [1, 24] but is restricted to realistic heads only. Our proposed solution is particularly effective in generating globally consistent and plausible back views of the head, while also ensuring locally view-consistent renderings for full $360^{\circ}$ style-omniscient portraits. + +# 3. Method + +Given a single RGB portrait image with arbitrary style, $I_{\mathrm{ref}}$ , our approach aims to synthesize a new image, $I_{\mathrm{tar}}$ , from any camera perspective within a $360^{\circ}$ range using an $I_{\mathrm{cam}}$ image. The novel view $I_{\mathrm{tar}}$ must maintain consistent appearance information with $I_{\mathrm{ref}}$ , with the camera view controlled by $I_{\mathrm{cam}}$ . It is crucial to note that this includes not only positions near $I_{\mathrm{ref}}$ but also areas with minimal overlap and previously unobserved regions from the given view. + +In this work, DiffPortrait360 leverages powerful latent diffusion models, enabling disentangled control of appearance and camera views, as detailed in Section 3.1. Building upon this foundation, we propose a tailored dual-appearscence module that incorporates additional appearance + +information from both the front and back of the head, $I_{\mathrm{back}}$ outlined in Section 3.2. We introduce an additional Control-Net [55] based synthesizing network designed to generate a plausible back view in $I_{\mathrm{back}}$ from $I_{\mathrm{ref}}$ , and to correct biases due to limited 3D head training data, as detailed in Section 3.3. Finally, Section 3.4 introduces a novel training strategy that leverages sequence priors to distill fine-grained structural information, ensuring consistency and smooth view transitions while maintaining high synthesis quality. + +# 3.1. Background + +Latent Diffusion Model. Diffusion models [18, 42, 43] are generative models designed to synthesize desired data samples from Gaussian noise $z_0$ by iteratively denoising across $T$ time steps. Latent diffusion models (LDMs) [39] extend this framework by operating in an encoded latent space $\mathcal{E}(I)$ where $I$ is an input image, facilitated by a pretrained auto-encoder $\mathcal{D} \circ \mathcal{E}(\cdot)$ . Specifically, the model is trained to learn the denoising process from $z_T \sim \mathcal{N}(0,1)$ to $z_0 = \mathcal{E}(I)$ with the objective, + +$$ +L _ {l d m} = \mathbb {E} _ {z _ {0}, t, \epsilon \sim \mathcal {N} (0, 1)} \left[ \left\| \epsilon - \epsilon_ {\theta} (z _ {t}, t) \right\| _ {2} ^ {2} \right], \tag {1} +$$ + +where $z_{t}$ is the noise map at timestep $t$ and $\epsilon_{\theta}$ is a trainable UNet equipped with layers of convolutions and self-/cross- + +![](images/6a161a8d8289b4b3ed7138b9ed458a51cb9cf138f6b6687fc6c9ed988769bef6.jpg) +Figure 4. Qualitative comparisons of novel view synterhisis on RenderMe360 [32]. Our method achieves effective appearance control for novel synthesis under substantial change of camera view for synthesis. + +![](images/cf2cd0576589ebfa42ac49ab1b31e6e03bac5cc377defd23f6f8ff66ca2e5b64.jpg) +Figure 5. Ablation Study on Dual Appearance Control. + +attentions (TransBlock). Finally, the output image is calculated by mapping the denoised latent feature map back to the image domain $I = \mathcal{D}(z_0)$ . Unlike traditional Text-to-Image (T2I) diffusion models, which rely on textual inputs to guide image synthesis, our approach directly extracts portrait appearance context and camera information from $I_{\mathrm{ref}}$ and $I_{\mathrm{cam}}$ , respectively, without relying on text descriptions. Consequently, we use an empty prompt for text control and omit it from our formulations. + +Diffusion-Based Novel View Synthesis. Recent studies [25-27, 40] have leveraged pre-trained LDMs for novel view synthesis. These efforts largely employ latent diffusion as the backbone for novel view synthesis, incorporating + +modules for appearance injection and camera information control. While most of this research focuses on general objects, our work follows a specific [14] designed for portrait novel view synthesis, which uses three main modules: 1) an Appearance Reference Module $\mathcal{R}$ that captures identity attributes and background from $I_{\mathrm{ref}}$ , 2) a Control Module $(C)$ typically a ControlNet [55], that adjusts camera perspectives based on $I_{\mathrm{cam}}$ and 3) a View Consistency Module $\mathcal{V}$ , intervened within UNet blocks using temporal cross-attention between features of multiple consecutive views to ensure view consistency. We follow the same network structure but innovate on enabling 360-degree and consistent novel view synthesis that preserves input appearance coherence across extensive viewpoint shifts, encompassing elements such as expressions, hairstyles, and head shapes. + +# 3.2. Dual Appearance Module + +To ensure the preservation of appearance information characteristics, previous methods typically employ a ReferenceNet [4] to inject the reference image and guide the denoising process with $I_{\mathrm{ref}}$ in order to extract sufficient information from $I_{\mathrm{ref}}$ . The Appearance Control Module is trained to ensure meticulous transfer of referenced structure and appearance into the SD-UNet for the task of novel view synthesis of portrait views. While effective at reference control in front near face, such an appearance control scheme induces following problems: Firstly, the appearance + +![](images/ae12753b51056a43934337ed78ed2d5dddf549a4874babe7dc45ba903b8891b4.jpg) +Figure 6. Ablation on Back-view Generation. + +content is largely provided by the image of $I_{\mathrm{ref}}$ . As the viewpoint shifts from the front of the face to the back of the head, the training dataset introduces randomly generated content such as different hairstyles, hats, and other features. Additionally, front face images contain only very limited information related to the back of the head, with very few pixels or even no pixels available for use. This leads to a significant misuse of most of the facial feature information from the reference image, causing leakage to the back of the head, which can be amplified to create a dual face or result in facial information appearing on the back of the head. Furthermore, these inaccuracies impact view control consistency, since the network, as a shortcut, tends to use other tailored modules, e.g., the view control module $\mathcal{C}$ , to generate information when there is insufficient appearance information. As a result, system collapse occurs during the generation of larger views with only a single reference. + +To mitigate this issue, we require an appearance reference network that could take information that entirely covers areas not observed by the front appearance while minimizing the overlap with the front face, which enables the diffusion network to access sufficient appearance information. This motivation leads us to design a dual-appearance module. Specifically, during training, we allow the appearance module to access two images, $I_{\mathrm{ref}}$ and $I_{\mathrm{back}}$ . The rationale behind this modification is to reduce ambiguities caused by insufficient or erroneous information during viewpoint transitions, and to compel the network to autonomously decide which information from $I_{\mathrm{ref}}$ and $I_{\mathrm{back}}$ should be relied on more under different camera views. We note that in selecting $I_{\mathrm{ref}}$ and $I_{\mathrm{back}}$ , views should overlap as little as possible but not be fixed, as this could affect the generalization ability of the input images. Consequently, in our training dataset, we deliberately choose pairs with minimal overlap as inputs for $I_{\mathrm{ref}}$ and $I_{\mathrm{back}}$ , enabling our dual appearance module to leverage the information to its fullest extent. As a result, we observed consistent and sat + +![](images/028c7d571f9eeb000cfb74c6a5fa68b1c800512afa93086ea6f2d08dfa3388cd.jpg) +Figure 7. Ablation Study on View-consistency Control. (a) Generated novel view. (b-c) Rendering and depth of fitted NeRFs. + +isfactory appearance in areas not covered by the reference images, and between the 360-degree area of $I_{\mathrm{back}}$ and $I_{\mathrm{ref}}$ . This makes our model capable of generating consistent appearance information while changing the camera views (see Figure 5). + +# 3.3. Back-View Reference Generation + +Our trained dual appearance module, $\mathcal{R}$ , significantly improves appearance consistency, especially during large changes in viewing angles. However, during inference, it is challenging to obtain a reasonable reference image context with a viewing angle drastically different from the input, such as obtaining a nearly opposite auxiliary image to the reference. Compromising to this difficulty will reduce the effectiveness of the disentangled appearance information determined by $I_{\mathrm{back}}$ . + +To address this issue, we developed a generative network capable of producing an $I_{\mathrm{back}}$ that has minimal overlap in appearance information with $I_{\mathrm{ref}}$ while maintaining a consistent style, reasonable head shape, and hairstyle. This motivates the use of ControlNet [55] and the original $I_{\mathrm{ref}}$ to generate a decoupled $I_{\mathrm{back}}$ as our extra appearance condition input. This approach is practical for real-world applications, allowing the generation of additional appearance information without needing external inputs. + +However, this generation model can exhibit a strong bias when using only realistic data, which is unsuitable for producing a broader range of artistic styles. To avoid an overreliance on a training dataset that could lead to the generation of unreasonable $I_{\mathrm{back}}$ , we supplemented our dataset with a large collection of cartoon and stylized task images of back views produced by [11] and Unique3D [51], adjusting the distribution of our dataset to lessen the bias towards realistic backdrops. Notably, even with limited cam + +era views (only including front and back views), this is sufficient for the Generative Module to correct biases from real dataset training, enabling it to generate reasonable unobserved head regions consistent with the input portrait style. As demonstrated in our experiments, our trained $\mathcal{F}$ , with a limited dataset of cartoon front and back faces, effectively resolves the challenge of sourcing additional appearance $I_{\mathrm{back}}$ in practical applications and generalizes well to unseen portrait styles. (see Figure 6). + +# 3.4. View-Consistency Module + +Given an arbitrary view portrait image $I_{\mathrm{ref}}$ , our trained module has already been capable of generating a full 360-degree range of novel view syntheses $I_{\mathrm{tar}}$ via above designs. Nevertheless, during inference, we occasionally observe our module failing to capture nuanced view consistency compared to 3D-aware GANs, such as appearance flickering and choppy transitions between views. These unwanted artifacts significantly impact the effectiveness of novel view synthesis in downstream applications, such as 3D reconstruction. + +Reviewing our above module, the view consistency module $\mathcal{V}$ is primarily managed by a temporal transformer [15], integrated with 3D-aware noise [14]. However, given the heritage motion prior from [15], we note that view consistency is trained by focusing on cross-view attentions with randomly shuffled views. We argue this training approach does not fully utilize the advantages of the motion prior, which may lead to the observed choppy transitions and minor appearance changes, ultimately resulting in the loss of detail and collapse of downstream tasks. + +To alleviate this issue, we have revised the training approach of the temporal transformer to include data from continuous view transitions. Instead of randomly sampling sparse views from a sparse multi-view dataset, we controlled the 3D-aware GAN [1] to generate consistently sampled sequential view changes. In contrast to random view cross-attention, our sequential training scheme effectively instructs the view consistency module $\mathcal{V}$ to maximize the benefits derived from the pretrained motion prior. Even when trained on only a limited synthetic dataset, our sequential training scheme is sufficient for $\mathcal{V}$ to decipher higher multi-view consistency accuracy and smoother view-changing results, enabling the synthesis process to produce smoother results that better fit downstream applications. + +# 4. Experiments + +# 4.1. Datasets + +We train our model using a hybrid dataset comprised of photo-realistic full-head multi-view images dataset RenderMe360 [32] and synthetic ones by PanoHead [1] and SphereHead [24]. RenderMe360 consists of images from 500 individuals, each captured with 12 different expres + +sions and an extended animated sequence from 60 multiview camera positions. This setup offers a substantial amount of multi-view consistent appearance data for training. We manually separated the front and back camera information, selecting front and back images as inputs for dual-appearance control, while using the remaining camera views as training data. We randomly selected 1,000 frames of multi-view data from 150 subjects while using PanoHead and SphereHead to sample continuous views from 600 identities, specifically for training the sequential view consistency module due to the scarcity of sparse camera views of RenderMe360. For the back-head reference image generation network, we collected 1,000 manually chosen, stylized front-and-back image pairs to augment the back-head image generation network. High-quality stylized front images were generated using a state-of-the-art tool [11]; we then fed the images to Unique3D [51] to generate content consistent back head. It's important to note that this highly stylized dataset, containing only front and back views, was used solely as data augmentation to reduce bias in the backview generation and was not included in the training of $\mathcal{R}$ . + +# 4.2. Comparisons + +Comparisons on Stylized Portraits. To demonstrate the generalization capability of our approach on stylized input portraits, we conduct a qualitative comparison with existing methods, as shown in Fig. 3. We also include Rome [22] and Itseez3D1. Thanks to our back-view generator and view-consistency module, our method exhibits superior generalization to diverse styles. We achieve high-quality details and continuous views across the full range of head poses. In contrast, it is evident that other approaches struggle to reach this level of performance. Specifically, Rome fails to generate reasonable back-view textures and structures, especially for inputs with thick hair and unusual accessories. Similarly, Zero-1-to-3 [27] and Unique3D [51] continue to struggle with bridging the domain gap between general objects and human heads. Itseez3D appears to operate with templates that preserve only the facial textures from the reference image. Additionally, both PanoHead [1] and SphereHead [24] perform poorly on stylized portraits. + +Comparisons on Real Portraits. We then compare the novel view synthesis results of our method with existing approaches on the test split of RenderMe360 [32], as illustrated in Fig. 4 and Tab. 1. We additionally incorporate Diff-Portrait3D* [14], which has been finetuned using our full-head datasets, as the original model was limited to generating frontal views using the provided checkpoints. As shown in the qualitative comparisons in Fig. 4, the GAN-based methods, PanoHead and SphereHead, struggle to generate realistic details that align with the reference images. Their + +
    MethodFrontal ViewBack View
    PSNR ↑SSIM ↑LPIPS ↓CSIM ↑FID ↓PSNR ↑SSIM ↑LPIPS ↓FID ↓
    PanoHead + PTI28.350.5050.4950.47198.9328.390.4500.432169.52
    SphereHead + PTI28.620.5130.4320.55669.4128.630.4630.413106.21
    Zero123---0.431152.03---216.88
    Unique3D---0.483195.33---285.75
    DiffPortrait3D*28.960.5090.4250.70949.0228.470.3730.44691.37
    Ours29.440.5780.3840.74635.3430.920.6480.31339.40
    + +Table 1. Quantitative comparisons of novel view synthesis on RenderMe360 [32] with perceptual metrics PSNR, SSIM [49], LPIPS [56], FID [17] and an additional face recognition metric CSIM [54] for frontal views. + +outputs fail to preserve identity due to the limitations of the PTI [38]. Zero-1-to-3 and Unique3D are trained on datasets of general synthetic 3D objects, and without specific domain knowledge, they cannot consistently produce reasonable novel views. Their results are often riddled with artifacts unrelated to heads. Although we fine-tuned DiffPortrait3D* on our full-head datasets, it still struggles to generate consistent novel views at the back, resulting in significant discrepancies from the reference images. These examples show artifacts such as multiple faces and misaligned hair color. In contrast, our specially designed method outperforms all others, demonstrating strong consistency across significantly different viewpoints. This conclusion is further supported by the quantitative comparisons detailed in Tab. 1. While existing methods reveal their shortcomings in evaluation statistics using perceptual metrics—especially for back views—our method performs nearly equally well for both frontal and back views. + +# 4.3. Ablation Study + +Back-view Generation. By assessing the multi-style frontal/back pairs augmented from outputs of Unique3D [51], we can clearly highlight their importance. As shown in Fig. 6, when training the back-view generator using only real data pairs, the generated views align with the distribution of actual hair. In contrast, any incorrect back-view generated due to biases can severely impact the consistency of the subsequent full head view synthesis. + +Dual Appearance Control. As illustrated in the first row of Fig. 5, the generated near views (random view 1 and 2) can exhibit significant inconsistencies without leveraging our dual appearance control. Additionally, for the nearly opposite views 2 and 3, the generated hair accessories do not match, which occurs due to the limited reference information, as the target view has only a small overlap with the provided image. With the implementation of our dual control, enhanced by the generated back view, our method effectively addresses these issues, achieving excellent consistency in both textures and the underlying 3D shape, as demonstrated in the second row of Fig. 5. + +View-Consistency Control. To assess the effectiveness of our strategy for view-consistency control, we conduct an ablation study with three configurations: 1) without 3D-aware noise, 2) without the sequential training strategy, and 3) our full method. In addition to comparing the synthesized views from diffusion, we also fit NeRF [33] on 36 generated views that are evenly distributed around the head to thoroughly evaluate multi-view consistency. As shown in Fig. 7, the absence of 3D-aware noise results in a failure to achieve visual alignment between the diffusion output and the camera-control image. Without the sequential training approach, the method can achieve some visual alignment for certain views, as demonstrated in the second row of Fig. 7. However, when we fit the generated full-range 36 views into a NeRF using the approach from [33], the textures in rendered view (b) from the NeRF (with the same camera as view (a)) become significantly messy due to the discrepancies across multiple views. In contrast, our complete method maintains good consistency among the generated views, which supports decent 3D fitting and shows ability to provide plausible depth. + +# 5. Discussion + +We have presented the first framework for generating consistent, full $360^{\circ}$ views from a single portrait, accommodating photorealistic and stylized humans, as well as anthropomorphic animals or statues. 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Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456, 2020. 3, 4 +[44] Ayush Tewari, Ohad Fried, Justus Thies, Vincent Sitzmann, Stephen Lombardi, Kalyan Sunkavalli, Ricardo Martin-Brualla, Tomas Simon, Jason Saragih, Matthias Nießner, et al. State of the art on neural rendering. In Computer Graphics Forum, pages 701-727. Wiley Online Library, 2020. 3 +[45] Phong Tran, Egor Zakharov, Long-Nhat Ho, Liwen Hu, Adilbek Karmanov, Aviral Agarwal, McLean Goldwhite, Ariana Bermudez Venegas, Anh Tuan Tran, and Hao Li. Voodoo xp: Expressive one-shot head reenactment for vr telepresence. ACM Transactions on Graphics, Proceedings of the 17th ACM SIGGRAPH Conference and Exhibition in Asia 2024, (SIGGRAPH Asia 2024), 12/2024, 2024. 2 +[46] Phong Tran, Egor Zakharov, Long-Nhat Ho, Anh Tuan Tran, Liwen Hu, and Hao Li. Voodoo 3d: Volumetric portrait disentanglement for one-shot 3d head reenactment. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024. +[47] Alex Trevithick, Matthew Chan, Michael Stengel, Eric R. Chan, Chao Liu, Zhiding Yu, Sameh Khamis, Manmohan Chandraker, Ravi Ramamoorthi, and Koki Nagano. Realtime radiance fields for single-image portrait view synthesis. In SIGGRAPH, 2023. 2 +[48] Satoshi Tsutsui, Weijia Mao, Sijing Lin, Yunyi Zhu, Murong Ma, and Mike Zheng Shou. Novel view synthesis for high-fidelity headshot scenes. arXiv preprint arXiv:2205.15595, 2022. 2, 3 +[49] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600-612, 2004. 8 +[50] Fanzi Wu, Linchao Bao, Yajing Chen, Yonggen Ling, Yibing Song, Songnan Li, King Ngi Ngan, and Wei Liu. Mvf-net: Multi-view 3d face morphable model regression. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 959-968, 2019. 2, 3 +[51] Kailu Wu, Fangfu Liu, Zhihan Cai, Runjie Yan, Hanyang Wang, Yating Hu, Yueqi Duan, and Kaisheng Ma. Unique3d: High-quality and efficient 3d mesh generation from a single image. arXiv preprint arXiv:2405.20343, 2024. 2, 6, 7, 8 +[52] Xudong Xu, Xingang Pan, Dahua Lin, and Bo Dai. Generative occupancy fields for 3d surface-aware image synthesis. NeurIPS, 34:20683-20695, 2021. 3 +[53] Yang Xue, Yuheng Li, Krishna Kumar Singh, and Yong Jae Lee. Giraffe hd: A high-resolution 3d-aware generative model. In CVPR, 2022. 3 +[54] Egor Zakharov, Aliaksandra Shysheya, Egor Burkov, and Victor Lempitsky. Few-shot adversarial learning of realistic neural talking head models. In Proceedings of the IEEE/CVF international conference on computer vision, pages 9459-9468, 2019. 8 +[55] Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. In ICCV, pages 3836-3847, 2023. 2, 3, 4, 5, 6 + +[56] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 8 +[57] Yiyu Zhuang, Hao Zhu, Xusen Sun, and Xun Cao. Mofanerf: Morphable facial neural radiance field. In European Conference on Computer Vision, pages 268-285. 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While cutting-edge methods for full head generation are limited to modeling realistic human heads, the latest diffusion-based approaches for style-omniscient head synthesis can produce only frontal views and struggle with view consistency, preventing their conversion into true 3D models for rendering from arbitrary angles. We introduce a novel approach that generates fully consistent 360-degree head views, accommodating human, stylized, and anthropomorphic forms, including accessories like glasses and hats. Our method builds on the DiffPortrait3D framework, incorporating a custom ControlNet for back-of-head detail generation and a dual appearance module to ensure global front-back consistency. By training on" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 498, + 556, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 556, + 584 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 556, + 584 + ], + "type": "text", + "content": "continuous view sequences and integrating a back reference image, our approach achieves robust, locally continuous view synthesis. Our model can be used to produce high-quality neural radiance fields (NeRFs) for real-time, free-viewpoint rendering, outperforming state-of-the-art methods in object synthesis and 360-degree head generation for very challenging input portraits." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 597, + 395, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 597, + 395, + 609 + ], + "spans": [ + { + "bbox": [ + 314, + 597, + 395, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": "In game, film, and animation production, CG characters are central to the content creation pipeline, meticulously designed with the right balance of realism and stylization to align with the narrative. Multi-view stereo systems and 3D scanners are commonly used to streamline the tedious manual process of creating realistic human characters. However, stylized characters are still often 3D modeled from scratch. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26263" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "scalable 3D content production pipelines, immersive telepresence and virtual world applications are fueling interest in embodying personalized or imaginary characters created directly by end-users. In this context, highly accessible 3D modeling tools that can generate characters from a single photograph or drawing are becoming increasingly relevant." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 146, + 296, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 146, + 296, + 373 + ], + "spans": [ + { + "bbox": [ + 56, + 146, + 296, + 373 + ], + "type": "text", + "content": "The most widely adopted approaches for image-based full 3D head reconstruction combine parametric models, like 3D Morphable Models (3DMMs) [10, 19, 20, 29, 34, 35, 48, 50, 57], with data-driven hair modeling or generate a single textured 3D mesh that includes both the face and hair. These methods often struggle with diverse hairstyles and capturing detailed appearance textures for the back of the head. Cutting-edge 3D head reconstruction, utilizing transformer-based networks [8, 9, 45-47] to estimate triplane representation, have shown success in capturing complex portraits of human heads with diverse hairstyles and accessories. However, tri-plane introduces strong projection ambiguity for extreme non-frontal poses and therefore fails to model 360-degree head. To facilitate the novel synthesis of full 360-degree views, tri-grid [1] neural volume representations have been introduced. While these methods have demonstrated impressive results, they are limited to realistic human heads and cannot handle stylized or other anthropomorphic shapes." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 375, + 295, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 375, + 295, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 375, + 295, + 506 + ], + "type": "text", + "content": "The latest diffusion-based image-to-3D generation methods [27, 40, 51] are designed to model a wide range of 3D objects. However, they struggle to capture detailed, domain-specific appearances, such as those of human heads and are prone to severe, unpredictable artifacts. A recent diffusion model, DiffPortrait3D [14], demonstrates the capability to generate novel views of style-omniscient heads by incorporating 3D-aware noise for inference, and finetuning the model on a large 3D head dataset. In addition to being limited to frontal views, this approach also displays noticeable inconsistencies between angles." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 509, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 295, + 640 + ], + "type": "text", + "content": "We present the first method capable of generating consistent 360-degree views from a single portrait of a head, accommodating human, stylized, or animal anthropomorphic forms, as well as accessories like glasses, jewelry, or masks. Our novel views can be computed offline (5.6 sec per view) and transformed into a high-quality neural radiance field (NeRF) [30], enabling free-viewpoint rendering in real-time. Our method is particularly robust, capable of handling a wide range of subjects, complex hairstyles, varied head poses, and expressive facial features, including detailed elements like tongues." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "content": "Building on the state-of-the-art DiffPortrait3D framework, we introduce key innovations to support back-view renderings and achieve locally continuous view consistency. We begin by generating the back of the head from the input image using a custom ControlNet [55], trained specifically to infer back-of-head details from a front-facing im" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 287 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 287 + ], + "type": "text", + "content": "age. This model is trained on a carefully curated dataset featuring diverse, realistic, and stylized heads. The front and back images are then passed into a dual appearance module (stable diffusion UNet), which extracts appearance information from both perspectives to condition our main image generator (stable diffusion denoising network) through attention layers. Unlike DiffPortrait3D, our approach incorporates an additional back reference image to improve global appearance consistency. Furthermore, we ensure locally continuous view consistency by using continuous view sequences (8 views) as conditions during training. Unlike DiffPortrait3D, which is trained only on frontal 3D-aware head generations, our approach utilizes a dataset comprising full 360-degree views of human heads, with data that is both captured and synthetically generated. Finally, our denoising process also uses a 3D-aware noise which is initialized using a fine-tuned inversion process-based a StyleGAN-based 360 head generator [1]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 288, + 553, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 288, + 553, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 288, + 553, + 443 + ], + "type": "text", + "content": "We demonstrate that diffusion models can generate highly detailed and consistent 360-degree head views from in-the-wild images across an extensive range of styles and complex portraits, handling challenging lighting conditions, intricate hairstyles, diverse appearances, and varying head poses. Our approach significantly outperforms all the latest generative methods for our challenge human head benchmarks generation, w.r.t. key metrics. More importantly, our method produces globally consistent appearances for the back of the head and locally view consistent synthesis when generating 360-degree views, which enables us to reconstruct true 3D representations (e.g., NeRFs) for free-view point rendering. We present the following contributions:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 444, + 553, + 586 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 314, + 444, + 553, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 444, + 553, + 490 + ], + "spans": [ + { + "bbox": [ + 314, + 444, + 553, + 490 + ], + "type": "text", + "content": "- We present a novel method for " + }, + { + "bbox": [ + 314, + 444, + 553, + 490 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 314, + 444, + 553, + 490 + ], + "type": "text", + "content": " view synthesis from a single style-omniscient portrait, which leverages priors from pre-trained stable diffusion models to generate view-consistent content." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 492, + 553, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 492, + 553, + 538 + ], + "spans": [ + { + "bbox": [ + 314, + 492, + 553, + 538 + ], + "type": "text", + "content": "- We propose a dual appearance control module, supported by a diffusion-based back-view generator, that ensures global consistency in novel view synthesis around the subject." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 540, + 553, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 540, + 553, + 586 + ], + "spans": [ + { + "bbox": [ + 314, + 540, + 553, + 586 + ], + "type": "text", + "content": "- We introduce a novel training strategy that employs view-consistent sequence generation to enhance continuity and smoothness, utilizing a 3D head dataset composed of both captured and synthetic subjects." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 597, + 400, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 597, + 400, + 609 + ], + "spans": [ + { + "bbox": [ + 314, + 597, + 400, + 609 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 618, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 618, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 618, + 553, + 714 + ], + "type": "text", + "content": "Numerous research methods and commercial solutions [20, 35] have been developed for reconstructing full 3D avatar heads from a single input photo, as opposed to using a multi-view capture approach [2, 12, 23, 28, 37]. These capabilities enable applications such as consumer-accessible immersive telepresence, personalized avatars for 3D games, and scalable approaches to content creation. Despite their wide adoption, regression-based face modeling techniques" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "26264" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 73, + 531, + 297 + ], + "blocks": [ + { + "bbox": [ + 85, + 73, + 531, + 297 + ], + "lines": [ + { + "bbox": [ + 85, + 73, + 531, + 297 + ], + "spans": [ + { + "bbox": [ + 85, + 73, + 531, + 297 + ], + "type": "image", + "image_path": "74a6d3e6d4c469e45cd0f1114dd237db5eaf636e51b7dcb993d1f67b77f354cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "lines": [ + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "spans": [ + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": "Figure 2. For the task of full-range 360-degree novel view synthesis, DiffPortrait360 employs a frozen pre-trained Latent Diffusion Model (LDM) as a rendering backbone and incorporates three auxiliary trainable modules for disentangled control of dual appearance " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": ", camera control " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": ", and U-Nets with view consistency " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": " extracts appearance information from " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": " derives the camera pose, which is rendered using an off-the-shelf 3D GAN. During training, we utilize a continuous sampling training strategy to better preserve the continuity of the camera trajectory. We enhance attention to continuity between frames to maintain the appearance information without changes due to turning angles. For inference, we employ our tailored back-view image generation network " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": " to generate a back-view image, enabling us to generate a 360-degree full range of camera trajectories using a single image portrait. Note that " + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 54, + 307, + 555, + 396 + ], + "type": "text", + "content": " stands for latent space noise rather than image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 416, + 298, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 416, + 298, + 464 + ], + "spans": [ + { + "bbox": [ + 54, + 416, + 298, + 464 + ], + "type": "text", + "content": "from a single input image [10, 19, 29, 34, 48, 50, 57] using parametric 3D Morphable Models (3DMM) [3] are increasingly being complemented in many applications by neural rendering techniques, as surveyed in [44]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 474, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 296, + 714 + ], + "type": "text", + "content": "3D-Aware GAN-Based Full-Head Synthesis. Recent advancements on 3D-aware GANs [1, 5-7, 13, 24, 31, 41, 52, 53], often leveraging StyleGAN2 [21] as backbone, are capable of generating novel views from a single input photograph through fine-tuned GAN inversion while ensuring view-consistency using a volumetric neural radiance field representation based on tri-planes [6] or signed distance function, such as StyleSDF [31]. While most of them can only generate frontal faces due their training data and their 3D representation, two recent methods have demonstrated how the generation of consistent 360-degree views are possible, namely, PanoHead [1] and SphereHead [24]. These methods generate a reasonable back head region using enhanced tri-plane representations by incorporating multiple depth layers or spherical coordinate system. However, their back-view synthesis often appear unnatural and mismatching the front view, especially when single-view inversion is applied. Most importantly, all of these methods are domain specific and only work on realistic human heads. They often fail for unknown accessories or complex hairstyles, and" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 314, + 416, + 550, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 416, + 550, + 429 + ], + "spans": [ + { + "bbox": [ + 314, + 416, + 550, + 429 + ], + "type": "text", + "content": "generating novel views for stylized avatars is not possible." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "text", + "content": "Diffusion Model Based 360-Degree View Synthesis. Diffusion-based models [18, 42, 43], particularly latent diffusion models (LDM) [39], have recently gained significant attention for their unmatched performance in generating highly diverse and high-fidelity images across various domains. A number of diffusion-based methods have been introduced for the task of novel view synthesis [14, 26, 27, 40] for general objects, and several methods [14, 40] demonstrate the effectiveness of fusing features of a reference image into self-attention blocks in the LDM UNets, facilitating high-quality novel view generation while preserved appearance context effectively. The notable work, ControlNet [55], extends the LDM framework to controllable image generation with additive structural conditions from signals such as 3D-aware GAN-synthesized camera viewpoints or rendered 3DMM condition [36]. The work, Diff-Portrait3D [14] achieves the state-of-the-art portrait novel view synthesis results by seamlessly integrating the appearance and camera view attentions with pre-trained UNets. Despite the impressive results, especially for stylized input portraits, only frontal views are possible to generate, and unwanted local inconsistencies between the model from" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26265" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 555, + 340 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 555, + 340 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 555, + 340 + ], + "type": "image", + "image_path": "5ab9bb691d1075674a753028020a0c95b8de25a3557707e00763d37ce27ac848.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 350, + 555, + 384 + ], + "lines": [ + { + "bbox": [ + 54, + 350, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 54, + 350, + 555, + 384 + ], + "type": "text", + "content": "Figure 3. Qualitative comparisons with existing methods on in the wild portraits. Compared to the baselines, our method shows superior generalization capability to novel view synthesis of wild portraits with unseen appearances, expressions, and styles, even without any reliance on fine-tuning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 404, + 296, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 404, + 296, + 525 + ], + "spans": [ + { + "bbox": [ + 54, + 404, + 296, + 525 + ], + "type": "text", + "content": "being converted into a 3D representation, such as textured Meshes, NeRFs or 3D Gaussian Splats, which is needed for free-viewpoint rendering. Another recent diffusion-based technique, called Portrait3D [16], generates compelling views from all angles, achieving superior results to GAN-based approaches [1, 24] but is restricted to realistic heads only. Our proposed solution is particularly effective in generating globally consistent and plausible back views of the head, while also ensuring locally view-consistent renderings for full " + }, + { + "bbox": [ + 54, + 404, + 296, + 525 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 54, + 404, + 296, + 525 + ], + "type": "text", + "content": " style-omniscient portraits." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 536, + 111, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 111, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 111, + 548 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": "Given a single RGB portrait image with arbitrary style, " + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": ", our approach aims to synthesize a new image, " + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{tar}}" + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": ", from any camera perspective within a " + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": " range using an " + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{cam}}" + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": " image. The novel view " + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{tar}}" + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": " must maintain consistent appearance information with " + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": ", with the camera view controlled by " + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{cam}}" + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": ". It is crucial to note that this includes not only positions near " + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 557, + 295, + 653 + ], + "type": "text", + "content": " but also areas with minimal overlap and previously unobserved regions from the given view." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 714 + ], + "type": "text", + "content": "In this work, DiffPortrait360 leverages powerful latent diffusion models, enabling disentangled control of appearance and camera views, as detailed in Section 3.1. Building upon this foundation, we propose a tailored dual-appearscence module that incorporates additional appearance" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "spans": [ + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "type": "text", + "content": "information from both the front and back of the head, " + }, + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "type": "text", + "content": " outlined in Section 3.2. We introduce an additional Control-Net [55] based synthesizing network designed to generate a plausible back view in " + }, + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 313, + 404, + 555, + 513 + ], + "type": "text", + "content": ", and to correct biases due to limited 3D head training data, as detailed in Section 3.3. Finally, Section 3.4 introduces a novel training strategy that leverages sequence priors to distill fine-grained structural information, ensuring consistency and smooth view transitions while maintaining high synthesis quality." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 520, + 394, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 520, + 394, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 520, + 394, + 533 + ], + "type": "text", + "content": "3.1. Background" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "content": "Latent Diffusion Model. Diffusion models [18, 42, 43] are generative models designed to synthesize desired data samples from Gaussian noise " + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "content": " by iteratively denoising across " + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "content": " time steps. Latent diffusion models (LDMs) [39] extend this framework by operating in an encoded latent space " + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(I)" + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "content": " is an input image, facilitated by a pretrained auto-encoder " + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{D} \\circ \\mathcal{E}(\\cdot)" + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "content": ". Specifically, the model is trained to learn the denoising process from " + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "inline_equation", + "content": "z_T \\sim \\mathcal{N}(0,1)" + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "inline_equation", + "content": "z_0 = \\mathcal{E}(I)" + }, + { + "bbox": [ + 313, + 537, + 556, + 647 + ], + "type": "text", + "content": " with the objective," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 347, + 654, + 555, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 654, + 555, + 682 + ], + "spans": [ + { + "bbox": [ + 347, + 654, + 555, + 682 + ], + "type": "interline_equation", + "content": "L _ {l d m} = \\mathbb {E} _ {z _ {0}, t, \\epsilon \\sim \\mathcal {N} (0, 1)} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t) \\right\\| _ {2} ^ {2} \\right], \\tag {1}", + "image_path": "b9e36761b3d9c18df8ee7d596d71039fa78e74b01f85800487826de1f4627de8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " is the noise map at timestep " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 689, + 555, + 714 + ], + "type": "text", + "content": " is a trainable UNet equipped with layers of convolutions and self-/cross-" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26266" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 555, + 335 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 555, + 335 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 555, + 335 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 555, + 335 + ], + "type": "image", + "image_path": "6a161a8d8289b4b3ed7138b9ed458a51cb9cf138f6b6687fc6c9ed988769bef6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 342, + 555, + 365 + ], + "lines": [ + { + "bbox": [ + 55, + 342, + 555, + 365 + ], + "spans": [ + { + "bbox": [ + 55, + 342, + 555, + 365 + ], + "type": "text", + "content": "Figure 4. Qualitative comparisons of novel view synterhisis on RenderMe360 [32]. Our method achieves effective appearance control for novel synthesis under substantial change of camera view for synthesis." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 383, + 292, + 502 + ], + "blocks": [ + { + "bbox": [ + 59, + 383, + 292, + 502 + ], + "lines": [ + { + "bbox": [ + 59, + 383, + 292, + 502 + ], + "spans": [ + { + "bbox": [ + 59, + 383, + 292, + 502 + ], + "type": "image", + "image_path": "cf2cd0576589ebfa42ac49ab1b31e6e03bac5cc377defd23f6f8ff66ca2e5b64.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 504, + 281, + 514 + ], + "lines": [ + { + "bbox": [ + 69, + 504, + 281, + 514 + ], + "spans": [ + { + "bbox": [ + 69, + 504, + 281, + 514 + ], + "type": "text", + "content": "Figure 5. Ablation Study on Dual Appearance Control." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "spans": [ + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "type": "text", + "content": " attentions (TransBlock). Finally, the output image is calculated by mapping the denoised latent feature map back to the image domain " + }, + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "type": "inline_equation", + "content": "I = \\mathcal{D}(z_0)" + }, + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "type": "text", + "content": ". Unlike traditional Text-to-Image (T2I) diffusion models, which rely on textual inputs to guide image synthesis, our approach directly extracts portrait appearance context and camera information from " + }, + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{cam}}" + }, + { + "bbox": [ + 55, + 537, + 295, + 645 + ], + "type": "text", + "content": ", respectively, without relying on text descriptions. Consequently, we use an empty prompt for text control and omit it from our formulations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 715 + ], + "type": "text", + "content": "Diffusion-Based Novel View Synthesis. Recent studies [25-27, 40] have leveraged pre-trained LDMs for novel view synthesis. These efforts largely employ latent diffusion as the backbone for novel view synthesis, incorporating" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "spans": [ + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "text", + "content": "modules for appearance injection and camera information control. While most of this research focuses on general objects, our work follows a specific [14] designed for portrait novel view synthesis, which uses three main modules: 1) an Appearance Reference Module " + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "text", + "content": " that captures identity attributes and background from " + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "text", + "content": ", 2) a Control Module " + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "inline_equation", + "content": "(C)" + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "text", + "content": " typically a ControlNet [55], that adjusts camera perspectives based on " + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{cam}}" + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "text", + "content": " and 3) a View Consistency Module " + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 313, + 386, + 555, + 566 + ], + "type": "text", + "content": ", intervened within UNet blocks using temporal cross-attention between features of multiple consecutive views to ensure view consistency. We follow the same network structure but innovate on enabling 360-degree and consistent novel view synthesis that preserves input appearance coherence across extensive viewpoint shifts, encompassing elements such as expressions, hairstyles, and head shapes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 575, + 457, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 575, + 457, + 588 + ], + "spans": [ + { + "bbox": [ + 313, + 575, + 457, + 588 + ], + "type": "text", + "content": "3.2. Dual Appearance Module" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": "To ensure the preservation of appearance information characteristics, previous methods typically employ a ReferenceNet [4] to inject the reference image and guide the denoising process with " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": " in order to extract sufficient information from " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": ". The Appearance Control Module is trained to ensure meticulous transfer of referenced structure and appearance into the SD-UNet for the task of novel view synthesis of portrait views. While effective at reference control in front near face, such an appearance control scheme induces following problems: Firstly, the appearance" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26267" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 70, + 292, + 235 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 292, + 235 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 292, + 235 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 292, + 235 + ], + "type": "image", + "image_path": "ae12753b51056a43934337ed78ed2d5dddf549a4874babe7dc45ba903b8891b4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 237, + 262, + 247 + ], + "lines": [ + { + "bbox": [ + 88, + 237, + 262, + 247 + ], + "spans": [ + { + "bbox": [ + 88, + 237, + 262, + 247 + ], + "type": "text", + "content": "Figure 6. Ablation on Back-view Generation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 270, + 295, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 270, + 295, + 474 + ], + "spans": [ + { + "bbox": [ + 54, + 270, + 295, + 474 + ], + "type": "text", + "content": "content is largely provided by the image of " + }, + { + "bbox": [ + 54, + 270, + 295, + 474 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 54, + 270, + 295, + 474 + ], + "type": "text", + "content": ". As the viewpoint shifts from the front of the face to the back of the head, the training dataset introduces randomly generated content such as different hairstyles, hats, and other features. Additionally, front face images contain only very limited information related to the back of the head, with very few pixels or even no pixels available for use. This leads to a significant misuse of most of the facial feature information from the reference image, causing leakage to the back of the head, which can be amplified to create a dual face or result in facial information appearing on the back of the head. Furthermore, these inaccuracies impact view control consistency, since the network, as a shortcut, tends to use other tailored modules, e.g., the view control module " + }, + { + "bbox": [ + 54, + 270, + 295, + 474 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 54, + 270, + 295, + 474 + ], + "type": "text", + "content": ", to generate information when there is insufficient appearance information. As a result, system collapse occurs during the generation of larger views with only a single reference." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": "To mitigate this issue, we require an appearance reference network that could take information that entirely covers areas not observed by the front appearance while minimizing the overlap with the front face, which enables the diffusion network to access sufficient appearance information. This motivation leads us to design a dual-appearance module. Specifically, during training, we allow the appearance module to access two images, " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": ". The rationale behind this modification is to reduce ambiguities caused by insufficient or erroneous information during viewpoint transitions, and to compel the network to autonomously decide which information from " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": " should be relied on more under different camera views. We note that in selecting " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": ", views should overlap as little as possible but not be fixed, as this could affect the generalization ability of the input images. Consequently, in our training dataset, we deliberately choose pairs with minimal overlap as inputs for " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 55, + 475, + 295, + 713 + ], + "type": "text", + "content": ", enabling our dual appearance module to leverage the information to its fullest extent. As a result, we observed consistent and sat" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 319, + 70, + 552, + 246 + ], + "blocks": [ + { + "bbox": [ + 319, + 70, + 552, + 246 + ], + "lines": [ + { + "bbox": [ + 319, + 70, + 552, + 246 + ], + "spans": [ + { + "bbox": [ + 319, + 70, + 552, + 246 + ], + "type": "image", + "image_path": "028c7d571f9eeb000cfb74c6a5fa68b1c800512afa93086ea6f2d08dfa3388cd.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 254, + 555, + 277 + ], + "lines": [ + { + "bbox": [ + 313, + 254, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 254, + 555, + 277 + ], + "type": "text", + "content": "Figure 7. Ablation Study on View-consistency Control. (a) Generated novel view. (b-c) Rendering and depth of fitted NeRFs." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 300, + 555, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 555, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 555, + 360 + ], + "type": "text", + "content": "isfactory appearance in areas not covered by the reference images, and between the 360-degree area of " + }, + { + "bbox": [ + 313, + 300, + 555, + 360 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 313, + 300, + 555, + 360 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 300, + 555, + 360 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 313, + 300, + 555, + 360 + ], + "type": "text", + "content": ". This makes our model capable of generating consistent appearance information while changing the camera views (see Figure 5)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 370, + 493, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 370, + 493, + 382 + ], + "spans": [ + { + "bbox": [ + 313, + 370, + 493, + 382 + ], + "type": "text", + "content": "3.3. Back-View Reference Generation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 388, + 554, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 388, + 554, + 496 + ], + "spans": [ + { + "bbox": [ + 313, + 388, + 554, + 496 + ], + "type": "text", + "content": "Our trained dual appearance module, " + }, + { + "bbox": [ + 313, + 388, + 554, + 496 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 388, + 554, + 496 + ], + "type": "text", + "content": ", significantly improves appearance consistency, especially during large changes in viewing angles. However, during inference, it is challenging to obtain a reasonable reference image context with a viewing angle drastically different from the input, such as obtaining a nearly opposite auxiliary image to the reference. Compromising to this difficulty will reduce the effectiveness of the disentangled appearance information determined by " + }, + { + "bbox": [ + 313, + 388, + 554, + 496 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 313, + 388, + 554, + 496 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "text", + "content": "To address this issue, we developed a generative network capable of producing an " + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "text", + "content": " that has minimal overlap in appearance information with " + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "text", + "content": " while maintaining a consistent style, reasonable head shape, and hairstyle. This motivates the use of ControlNet [55] and the original " + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "text", + "content": " to generate a decoupled " + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 313, + 498, + 554, + 605 + ], + "type": "text", + "content": " as our extra appearance condition input. This approach is practical for real-world applications, allowing the generation of additional appearance information without needing external inputs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": "However, this generation model can exhibit a strong bias when using only realistic data, which is unsuitable for producing a broader range of artistic styles. To avoid an overreliance on a training dataset that could lead to the generation of unreasonable " + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 313, + 605, + 556, + 715 + ], + "type": "text", + "content": ", we supplemented our dataset with a large collection of cartoon and stylized task images of back views produced by [11] and Unique3D [51], adjusting the distribution of our dataset to lessen the bias towards realistic backdrops. Notably, even with limited cam" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26268" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "text", + "content": "era views (only including front and back views), this is sufficient for the Generative Module to correct biases from real dataset training, enabling it to generate reasonable unobserved head regions consistent with the input portrait style. As demonstrated in our experiments, our trained " + }, + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "text", + "content": ", with a limited dataset of cartoon front and back faces, effectively resolves the challenge of sourcing additional appearance " + }, + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{back}}" + }, + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "text", + "content": " in practical applications and generalizes well to unseen portrait styles. (see Figure 6)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 190, + 200, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 190, + 200, + 202 + ], + "spans": [ + { + "bbox": [ + 55, + 190, + 200, + 202 + ], + "type": "text", + "content": "3.4. View-Consistency Module" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 207, + 295, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 207, + 295, + 315 + ], + "spans": [ + { + "bbox": [ + 55, + 207, + 295, + 315 + ], + "type": "text", + "content": "Given an arbitrary view portrait image " + }, + { + "bbox": [ + 55, + 207, + 295, + 315 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{ref}}" + }, + { + "bbox": [ + 55, + 207, + 295, + 315 + ], + "type": "text", + "content": ", our trained module has already been capable of generating a full 360-degree range of novel view syntheses " + }, + { + "bbox": [ + 55, + 207, + 295, + 315 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{tar}}" + }, + { + "bbox": [ + 55, + 207, + 295, + 315 + ], + "type": "text", + "content": " via above designs. Nevertheless, during inference, we occasionally observe our module failing to capture nuanced view consistency compared to 3D-aware GANs, such as appearance flickering and choppy transitions between views. These unwanted artifacts significantly impact the effectiveness of novel view synthesis in downstream applications, such as 3D reconstruction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 316, + 295, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 316, + 295, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 316, + 295, + 434 + ], + "type": "text", + "content": "Reviewing our above module, the view consistency module " + }, + { + "bbox": [ + 55, + 316, + 295, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 55, + 316, + 295, + 434 + ], + "type": "text", + "content": " is primarily managed by a temporal transformer [15], integrated with 3D-aware noise [14]. However, given the heritage motion prior from [15], we note that view consistency is trained by focusing on cross-view attentions with randomly shuffled views. We argue this training approach does not fully utilize the advantages of the motion prior, which may lead to the observed choppy transitions and minor appearance changes, ultimately resulting in the loss of detail and collapse of downstream tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 435, + 295, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 435, + 295, + 604 + ], + "spans": [ + { + "bbox": [ + 55, + 435, + 295, + 604 + ], + "type": "text", + "content": "To alleviate this issue, we have revised the training approach of the temporal transformer to include data from continuous view transitions. Instead of randomly sampling sparse views from a sparse multi-view dataset, we controlled the 3D-aware GAN [1] to generate consistently sampled sequential view changes. In contrast to random view cross-attention, our sequential training scheme effectively instructs the view consistency module " + }, + { + "bbox": [ + 55, + 435, + 295, + 604 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 55, + 435, + 295, + 604 + ], + "type": "text", + "content": " to maximize the benefits derived from the pretrained motion prior. Even when trained on only a limited synthetic dataset, our sequential training scheme is sufficient for " + }, + { + "bbox": [ + 55, + 435, + 295, + 604 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 55, + 435, + 295, + 604 + ], + "type": "text", + "content": " to decipher higher multi-view consistency accuracy and smoother view-changing results, enabling the synthesis process to produce smoother results that better fit downstream applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 616, + 135, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 616, + 135, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 616, + 135, + 628 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 636, + 117, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 636, + 117, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 636, + 117, + 647 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 654, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 295, + 713 + ], + "type": "text", + "content": "We train our model using a hybrid dataset comprised of photo-realistic full-head multi-view images dataset RenderMe360 [32] and synthetic ones by PanoHead [1] and SphereHead [24]. RenderMe360 consists of images from 500 individuals, each captured with 12 different expres" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": "sions and an extended animated sequence from 60 multiview camera positions. This setup offers a substantial amount of multi-view consistent appearance data for training. We manually separated the front and back camera information, selecting front and back images as inputs for dual-appearance control, while using the remaining camera views as training data. We randomly selected 1,000 frames of multi-view data from 150 subjects while using PanoHead and SphereHead to sample continuous views from 600 identities, specifically for training the sequential view consistency module due to the scarcity of sparse camera views of RenderMe360. For the back-head reference image generation network, we collected 1,000 manually chosen, stylized front-and-back image pairs to augment the back-head image generation network. High-quality stylized front images were generated using a state-of-the-art tool [11]; we then fed the images to Unique3D [51] to generate content consistent back head. It's important to note that this highly stylized dataset, containing only front and back views, was used solely as data augmentation to reduce bias in the backview generation and was not included in the training of " + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 331, + 399, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 399, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 399, + 342 + ], + "type": "text", + "content": "4.2. Comparisons" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 347, + 555, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 347, + 555, + 563 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 555, + 563 + ], + "type": "text", + "content": "Comparisons on Stylized Portraits. To demonstrate the generalization capability of our approach on stylized input portraits, we conduct a qualitative comparison with existing methods, as shown in Fig. 3. We also include Rome [22] and Itseez3D1. Thanks to our back-view generator and view-consistency module, our method exhibits superior generalization to diverse styles. We achieve high-quality details and continuous views across the full range of head poses. In contrast, it is evident that other approaches struggle to reach this level of performance. Specifically, Rome fails to generate reasonable back-view textures and structures, especially for inputs with thick hair and unusual accessories. Similarly, Zero-1-to-3 [27] and Unique3D [51] continue to struggle with bridging the domain gap between general objects and human heads. Itseez3D appears to operate with templates that preserve only the facial textures from the reference image. Additionally, both PanoHead [1] and SphereHead [24] perform poorly on stylized portraits." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 577, + 556, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 577, + 556, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 577, + 556, + 696 + ], + "type": "text", + "content": "Comparisons on Real Portraits. We then compare the novel view synthesis results of our method with existing approaches on the test split of RenderMe360 [32], as illustrated in Fig. 4 and Tab. 1. We additionally incorporate Diff-Portrait3D* [14], which has been finetuned using our full-head datasets, as the original model was limited to generating frontal views using the provided checkpoints. As shown in the qualitative comparisons in Fig. 4, the GAN-based methods, PanoHead and SphereHead, struggle to generate realistic details that align with the reference images. Their" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 325, + 702, + 399, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 702, + 399, + 712 + ], + "spans": [ + { + "bbox": [ + 325, + 702, + 399, + 712 + ], + "type": "text", + "content": "1https://itseez3d.com/" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "26269" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 70, + 526, + 161 + ], + "blocks": [ + { + "bbox": [ + 85, + 70, + 526, + 161 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 526, + 161 + ], + "spans": [ + { + "bbox": [ + 85, + 70, + 526, + 161 + ], + "type": "table", + "html": "
    MethodFrontal ViewBack View
    PSNR ↑SSIM ↑LPIPS ↓CSIM ↑FID ↓PSNR ↑SSIM ↑LPIPS ↓FID ↓
    PanoHead + PTI28.350.5050.4950.47198.9328.390.4500.432169.52
    SphereHead + PTI28.620.5130.4320.55669.4128.630.4630.413106.21
    Zero123---0.431152.03---216.88
    Unique3D---0.483195.33---285.75
    DiffPortrait3D*28.960.5090.4250.70949.0228.470.3730.44691.37
    Ours29.440.5780.3840.74635.3430.920.6480.31339.40
    ", + "image_path": "15537ca697bd3e942faf58f10e1cc79a59f50e65c4e52a8ccdcdfd80f80736d4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 170, + 553, + 192 + ], + "lines": [ + { + "bbox": [ + 55, + 170, + 553, + 192 + ], + "spans": [ + { + "bbox": [ + 55, + 170, + 553, + 192 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons of novel view synthesis on RenderMe360 [32] with perceptual metrics PSNR, SSIM [49], LPIPS [56], FID [17] and an additional face recognition metric CSIM [54] for frontal views." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 213, + 297, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 213, + 297, + 429 + ], + "spans": [ + { + "bbox": [ + 54, + 213, + 297, + 429 + ], + "type": "text", + "content": "outputs fail to preserve identity due to the limitations of the PTI [38]. Zero-1-to-3 and Unique3D are trained on datasets of general synthetic 3D objects, and without specific domain knowledge, they cannot consistently produce reasonable novel views. Their results are often riddled with artifacts unrelated to heads. Although we fine-tuned DiffPortrait3D* on our full-head datasets, it still struggles to generate consistent novel views at the back, resulting in significant discrepancies from the reference images. These examples show artifacts such as multiple faces and misaligned hair color. In contrast, our specially designed method outperforms all others, demonstrating strong consistency across significantly different viewpoints. This conclusion is further supported by the quantitative comparisons detailed in Tab. 1. While existing methods reveal their shortcomings in evaluation statistics using perceptual metrics—especially for back views—our method performs nearly equally well for both frontal and back views." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 441, + 149, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 441, + 149, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 441, + 149, + 453 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 460, + 296, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 460, + 296, + 556 + ], + "spans": [ + { + "bbox": [ + 55, + 460, + 296, + 556 + ], + "type": "text", + "content": "Back-view Generation. By assessing the multi-style frontal/back pairs augmented from outputs of Unique3D [51], we can clearly highlight their importance. As shown in Fig. 6, when training the back-view generator using only real data pairs, the generated views align with the distribution of actual hair. In contrast, any incorrect back-view generated due to biases can severely impact the consistency of the subsequent full head view synthesis." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": "Dual Appearance Control. As illustrated in the first row of Fig. 5, the generated near views (random view 1 and 2) can exhibit significant inconsistencies without leveraging our dual appearance control. Additionally, for the nearly opposite views 2 and 3, the generated hair accessories do not match, which occurs due to the limited reference information, as the target view has only a small overlap with the provided image. With the implementation of our dual control, enhanced by the generated back view, our method effectively addresses these issues, achieving excellent consistency in both textures and the underlying 3D shape, as demonstrated in the second row of Fig. 5." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 213, + 555, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 555, + 466 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 555, + 466 + ], + "type": "text", + "content": "View-Consistency Control. To assess the effectiveness of our strategy for view-consistency control, we conduct an ablation study with three configurations: 1) without 3D-aware noise, 2) without the sequential training strategy, and 3) our full method. In addition to comparing the synthesized views from diffusion, we also fit NeRF [33] on 36 generated views that are evenly distributed around the head to thoroughly evaluate multi-view consistency. As shown in Fig. 7, the absence of 3D-aware noise results in a failure to achieve visual alignment between the diffusion output and the camera-control image. Without the sequential training approach, the method can achieve some visual alignment for certain views, as demonstrated in the second row of Fig. 7. However, when we fit the generated full-range 36 views into a NeRF using the approach from [33], the textures in rendered view (b) from the NeRF (with the same camera as view (a)) become significantly messy due to the discrepancies across multiple views. In contrast, our complete method maintains good consistency among the generated views, which supports decent 3D fitting and shows ability to provide plausible depth." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 486, + 384, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 486, + 384, + 498 + ], + "spans": [ + { + "bbox": [ + 314, + 486, + 384, + 498 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 510, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 510, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 510, + 555, + 629 + ], + "type": "text", + "content": "We have presented the first framework for generating consistent, full " + }, + { + "bbox": [ + 313, + 510, + 555, + 629 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 313, + 510, + 555, + 629 + ], + "type": "text", + "content": " views from a single portrait, accommodating photorealistic and stylized humans, as well as anthropomorphic animals or statues. Our method is robust, handling particularly difficult input portraits with complex accessories, make-ups, hairstyles, expressive faces, and challenging lighting conditions. We demonstrate that our back-of-head generation approach, combined with our novel dual appearance module, is essential for achieving globally consistent appearance generation full head." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 642, + 419, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 642, + 419, + 656 + ], + "spans": [ + { + "bbox": [ + 313, + 642, + 419, + 656 + ], + "type": "text", + "content": "6. Acknowledgment" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 715 + ], + "type": "text", + "content": "This work is supported by the Metaverse Center Grant from the MBZUAI Research Office. We thank Egor Zakharov, Zhenhui Lin, Maksat Kengeskanov, and Yiming Chen for the early discussions, helpful suggestions, and feedback." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26270" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 296, + 134 + ], + "type": "text", + "content": "[1] Sizhe An, Hongyi Xu, Yichun Shi, Guoxian Song, Umit Y. 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Results of DiffSensei. (a) Customized manga generation with controllable character images, panel captions, and layout conditions. Our DiffSensei successfully generates detailed character expressions and states following the panel captions. (b) Manga creation for real human images. The dialogues are post-edited by humans. The continuation is in the Appendix. We strongly recommend that the readers see the Appendix for more comprehensive results. Manga reading order: Right to left. Top to bottom." + ], + "image_footnote": [], + "bbox": [ + 676, + 296, + 900, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 614, + 326, + 630 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Story visualization, the task of creating visual narratives from textual descriptions, has seen progress with text-to-image generation models. However, these models often lack effective control over character appearances and interactions, particularly in multi-character scenes. To address these limitations, we propose a new task: customized manga generation and introduce DiffSensei, an innovative framework specifically designed for generating manga with dynamic multi-character control. DiffSensei integrates a diffusion-based image generator with a multimodal large language model (MLLM) that acts as a text-compatible identity adapter. Our approach employs masked cross-attention to seamlessly incorporate character features, enabling precise layout control without direct pixel transfer. Additionally, the MLLM-based adapter adjusts character features to align with panel-specific text cues, allowing flex", + "bbox": [ + 86, + 659, + 485, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ible adjustments in character expressions, poses, and actions. We also introduce MangaZero, a large-scale dataset tailored to this task, containing 43,264 manga pages and 427,147 annotated panels, supporting the visualization of varied character interactions and movements across sequential frames. Extensive experiments demonstrate that DiffSensei outperforms existing models, marking a significant advancement in manga generation by enabling text-adaptable character customization. The code, model, and dataset are open-sourced to the community.", + "bbox": [ + 511, + 614, + 908, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 777, + 645, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Story visualization, the process of generating visual narratives from textual descriptions, is a rapidly evolving field [5, 18, 21, 25, 37, 46, 53]. Among its various applications, manga generation holds particular significance due", + "bbox": [ + 511, + 804, + 906, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 808, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1The work is done in Shanghai AI Laboratory. Corresponding to: Xiangtai Li, Jingbo Wang.", + "bbox": [ + 511, + 875, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28684", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to its popularity and unique narrative requirements. Unlike traditional story visualization, manga demands consistent characters across panels, precise layout control for positioning multiple characters, and the seamless integration of dialogues in a coherent, visually engaging manner.", + "bbox": [ + 89, + 90, + 480, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Currently, manga generation remains an underexplored area. Most existing research focuses on low-level imagedto-image tasks, primarily converting general images to a manga style [20, 33, 48, 50]. While these tasks enhance the visual appeal of static images, they do not extend to generating fully customized manga content from scratch. In general story visualization, current approaches have demonstrated some success in generating coherent image sequences from text. Still, they cannot often customize the characters across scenes [21, 25, 46, 53], a critical requirement for manga generation. Additionally, they do not provide the necessary control over layouts and dialogue placements, which are also essential for manga. A likely reason for these limitations is that existing story visualization datasets typically lack character annotations and layout controls [15, 18, 21, 46]. Another research direction has explored zero-shot character customization, showing promise for achieving character customization across manga panels [4, 9, 19, 29, 36, 39, 47]. However, these approaches often result in rigid \"copy-pasting\" effects [4, 39, 47], which limit expressive character variation and detract from narrative depth. This limitation largely stems from the scarcity of datasets capturing multiple appearances of the same character in varied expressions and poses.", + "bbox": [ + 91, + 170, + 482, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these limitations, we propose a new task: customized manga generation. As illustrated in Fig. 1, this task focuses on creating manga images with multiple characters, each customized based on a character image and positioned according to user input. Characters must dynamically adapt to text prompts, altering their expressions, motions, and poses as the narrative unfolds. Dialog layout should also be managed to generate expressive manga panels. Compared to traditional story visualization tasks, this proposed task prioritizes essential manga-specific controllability, aiming to generate vivid manga panels that are both coherent and visually engaging while supporting the customization of multiple characters. To address the lack of a dedicated dataset for customized manga generation, we collect a dataset of Japanese black-and-white manga, forming the basis of the proposed task. The resulting dataset, MangaZero, is the first large-scale collection designed to support multi-character, multi-state manga generation.", + "bbox": [ + 89, + 535, + 482, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle this task, we introduce a novel framework, DiffSensei, which leverages a diffusion-based image generator to produce customized manga panels. However, we observe that, even with training on multiple appearances of the same character, the generated portraits often tend to rigidly follow the pixel distribution of the input character image, re", + "bbox": [ + 89, + 810, + 482, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sulting in limited variations in appearance, pose, and motion based on the text input. Inspired by recent advancements in image editing using Multimodal Large Language Models (MLLMs) [6, 8, 16, 34, 40-43, 46, 49], we propose using an MLLM as a text-compatible character adapter. This approach enables seamless, dynamic adjustments to characters in response to textual cues, thereby supporting coherent and expressive manga panel generation. Additionally, we incorporate masked attention injection to manage character layout, along with a dialog embedding technique tailored specifically for manga, allowing for precise control over dialog placement. Through extensive experimentation, we validate DiffSensei's capability to generate coherent, expressive manga panels that maintain narrative consistency and offer improved character control. This represents a significant advancement in story visualization.", + "bbox": [ + 511, + 90, + 903, + 332 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a new task: customized manga generation, focused on generating manga images with multiple characters, each dynamically adapting to text prompts and positioned according to layout specifications.", + "- We present MangaZero, the first large-scale dataset specifically designed for multi-character, multi-state manga generation, addressing a significant gap in story visualization training data. The dataset will be released for the image generation community.", + "- We propose DiffSensei. As far as we know, it is the first framework for customized manga generation that links diffusion models and MLLMs. The MLLM serves as an adaptable character feature adapter, enabling characters to respond dynamically to textual cues. Extensive experiments demonstrate the effectiveness of DiffSensei." + ], + "bbox": [ + 513, + 334, + 903, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 571, + 653, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Story visualization. Story visualization, the process of generating visual narratives based on given stories, is rapidly evolving. Many approaches can generate consistent image sequences derived from story content [5, 21, 25, 37, 46, 53]. Despite recent advancements, the field faces significant limitations. Most existing methods generate story images solely from text and image-level prompts [21, 25, 46, 53], which restricts control over individual characters. This limited control over characters reduces the flexibility and depth of story visualization. A key factor is that current training datasets [10, 15, 18, 21, 46] lack character-specific annotations. In response to the data limit, recent works [5, 37] explore multi-character control using training-free methods that leverage existing subject preservation techniques, such as IP-Adapter [47]. Other works [4, 7, 9, 11, 12, 19, 29, 32, 36, 39, 44, 47] try to train diffusion models for a multi-character customized generation. However, these approaches often result in a \"copy-pasting\" effect, restricting the diversity of expressions and actions needed for dynamic storytelling. For training-free", + "bbox": [ + 511, + 598, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28685", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/7f36507d26f5f56c7f354c3758887a6097a34929d1c637062c9735fac464d20e.jpg", + "table_caption": [ + "Table 1. Comparison between MangaZero and related publicly available datasets. A story is defined as a sequence of continuous images annotated consistently with character IDs. In MangaZero, a story means a manga page. A panel means a distinct story image, or called frame [21, 46]. Most series in MangaZero are still popular in 2024. Please see the Appendix for the dataset details." + ], + "table_footnote": [], + "table_body": "
    DatasetTypeResolution#Series#Stories#PanelsCaptionAnnotations CharacterDialogOrigin
    PororoSV [18]AnimationFix115,33673,665✓××2003-2016
    FlintstonesSV [10]AnimationFix125,184122,560✓✓×1960-1966
    StorySalon [21]AnimationFix44618,255159,778✓××YouTube
    StoryStream [46]AnimationFix312,614257,850✓××1939-2013
    Manga109 [2]B/W MangaVary10910,602103,850×✓✓1970-2010
    MangaZeroB/W MangaVary4843,264427,147✓✓✓1974-2024
    ", + "bbox": [ + 94, + 142, + 911, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "methods, combining multiple models can significantly slow down inference speeds. To address these challenges, we first introduce a large-scale manga generation dataset with finely curated character annotations and then develop a novel framework utilizing diffusion models and MLLMs that enables the dynamic generation of manga panels.", + "bbox": [ + 88, + 304, + 480, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Manga generation. The field of black-and-while manga generation has received limited exploration. Most existing researches focus on low-level image-to-image tasks, primarily transferring general images to a manga style [20, 33, 48, 50]. Recent works contribute to manga content understanding [30, 31, 35]. In contrast, we propose the customized manga generation task beyond style transfer to offer complete character and story-driven manga generation.", + "bbox": [ + 88, + 395, + 480, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "MLLMs for personalized image generation. MLLMs have shown remarkable potential in personalized image generation, particularly for tasks involving image editing and customization [3, 6, 8, 16, 34, 40-42, 46, 49]. Notably, CAFE [52] explores customizing subject appearances through textual instructions. However, MLLM-driven image generation for multi-character narratives remains an open challenge, primarily due to the difficulties in maintaining inter-character relationships and scene continuity. Our framework proposes an MLLM-based identity adapter that enhances dynamic story consistency in multi-character manga generation. In contrast to previous works, our framework takes multi-character features as input and edits these features collectively, following the text prompt, enabling flexible subject editing across multiple characters.", + "bbox": [ + 89, + 517, + 482, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The MangaZero Dataset", + "text_level": 1, + "bbox": [ + 89, + 753, + 318, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first define the problem in Sec. 3.1. Then, we introduce the dataset construction pipeline in Sec. 3.2.", + "bbox": [ + 89, + 779, + 482, + 810 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 89, + 816, + 294, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce a challenging new task: customized manga generation. This task focuses on generating manga images where multiple characters, each with their distinct image inputs, are customized and positioned by users. Importantly,", + "bbox": [ + 89, + 839, + 482, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "characters must adapt to the text prompts by modifying their expressions, motions, and poses dynamically, even when only a limited set of character images is available. To generate a manga story across $N$ panels (or frames), the inputs include: text prompts for each panel $T_{0}, T_{1}, \\ldots, T_{N-1}$ , character images $\\mathbf{I} = I_{0}, I_{1}, \\ldots, I_{K-1}$ , character bounding boxes for each panel $\\mathbf{B}_{0}^{c}, \\mathbf{B}_{1}^{c}, \\ldots, \\mathbf{B}_{N-1}^{c}$ , and dialogue bounding boxes for each panel $\\mathbf{B}_{0}^{d}, \\mathbf{B}_{1}^{d}, \\ldots, \\mathbf{B}_{N-1}^{d}$ . The visualization of a panel is represented as $P_{i} = \\Phi_{\\theta}(T_{i}, \\mathbf{I}, \\mathbf{B}_{i}^{c}, \\mathbf{B}_{i}^{d})$ , where $\\Phi$ is the overall model function and $\\theta$ represents the model's learned parameters.", + "bbox": [ + 511, + 304, + 903, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Discussion. This task diverges from existing story visualization and continuation tasks [21, 25]. Specifically, in story visualization tasks, a panel is produced using $P_{i} = \\Phi_{\\theta}(T_{i})$ , while in story continuation tasks, the panel generation depends on previous panels as $P_{i} = \\Phi_{\\theta}(T_{i}, T_{i-1}, P_{i-1})$ for $i > 0$ . Both lack explicit character control, a crucial element in storytelling. Furthermore, the proposed task differs from subject-driven image generation approaches [29, 39, 47], as it demands that models not only generate accurate character representations but also modify characters' attributes in response to panel captions and layouts, resulting in varied and coherent narrative visuals. Our experiments, detailed in Sec. 5, demonstrate that our model significantly surpasses baseline models in these critical aspects.", + "bbox": [ + 511, + 472, + 905, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Dataset Construction", + "text_level": 1, + "bbox": [ + 511, + 695, + 714, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the proposed large-scale manga story visualization dataset MangaZero.", + "bbox": [ + 511, + 718, + 903, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Comparison with related datasets. A comprehensive comparison with existing datasets is presented in Tab. 1. In contrast to current manga and story visualization datasets, the proposed MangaZero dataset stands out as being larger in size, newer in source, richer in annotations, diverse in manga series, and varied in panel resolutions. Compared to the well-known black-and-white manga dataset Manga109 [2], the MangaZero dataset encompasses more manga series published after the year 2000, which inspired its naming. Additionally, MangaZero includes famous se", + "bbox": [ + 511, + 750, + 905, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28686", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fb2c4ca29fad8bf9f19c3fd78412f1ce1cb1fbce39eeb7558ac2ac2d089ed158.jpg", + "image_caption": [ + "Figure 2. We construct MangaZero through three steps: 1) Download manga pages from the internet. 2) Annotate manga panels autonomously with pre-trained models. 3) Human calibration for the character ID annotation." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 457, + 300 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ries from before the year 2000 that are not featured in Manga109, such as Doraemon (1974).", + "bbox": [ + 89, + 393, + 482, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Construction pipeline. To build our dataset, we first download manga pages from the internet, explicitly sourcing images from MangaDex [1]. It is important to note that all data will be used solely for academic research, not commercial purposes. We select 48 manga series and download up to 1,000 pages per series, resulting in 43,264 double-page images. These images are then annotated using pretrained models. For manga-specific annotations, including panel bounding boxes, character bounding boxes, character IDs, and dialog bounding boxes, we employ the recent manga understanding model, Magi [30]. It should be noted that character ID labeling is consistent only within individual pages, which is sufficient for achieving coherent character cross-reference. Once the panel bounding boxes are obtained, we utilize LLaVA-v1.6-34B [22] to generate captions for each panel. However, we observe that character ID labeling has relatively low accuracy, which poses a significant challenge for training purposes. To address this, human annotators refine the machine-generated labels, resulting in accurate and clean annotations. Finally, we split 96 pages (2 for each series) as the evaluation set and the remaining 43,168 pages as the training set.", + "bbox": [ + 91, + 424, + 483, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 89, + 768, + 181, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce the architecture of the proposed framework, DiffSensei, which generates vivid manga panels with precise character and dialog layout control while adapting the characters' status flexibly.", + "bbox": [ + 89, + 794, + 482, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivation. There are two critical problems in customizing objects and layouts in image generation: 1) Preserving the subjects' intrinsic features while avoiding direct copy-paste", + "bbox": [ + 89, + 854, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "from source images, and 2) Ensuring reliable layout control with minimal computational cost during both training and inference. To avoid copy-pasting effects, our model converts character image features into tokens, preventing the direct transfer of fine-grained pixel details. Additionally, we integrate an MLLM as a character image feature adapter. The MLLM adapter receives source character features and panel captions as inputs, generating text-compatible target character features. Compared with previous customization work [39], this approach enables text-compatible character encoding and flexible character adaptation to captions. For layout control, we employ lightweight masked encoding techniques for both character and dialog layouts, significantly reducing computational costs compared with previous works [38, 45] while maintaining high accuracy in both training and inference phases. Experiment results in Sec. 5 demonstrate the effectiveness of our design.", + "bbox": [ + 511, + 90, + 906, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-character feature extraction. As illustrated in Fig. 3, we initially extract local image features using CLIP and image-level features from a manga image encoder. These two sets of features are then processed by a feature extractor, which is implemented as a resampler module [47]. This process can be formalized as follows:", + "bbox": [ + 511, + 354, + 906, + 446 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {i} = \\operatorname {R e s a m p l e r} ([ \\operatorname {C L I P} (\\mathbf {I}), \\psi (\\mathbf {I}) ], \\mathbf {q}, \\mathbf {q} _ {\\text {v o i d}}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 472, + 906, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\psi$ represents the manga image encoder. $\\mathbf{q}$ and $\\mathbf{q}_{\\text{void}}$ are trainable query vectors for character and non-character features, respectively. $\\mathbf{q}$ re-samples the image features into the U-Net's cross-attention dimension, while $\\mathbf{q}_{\\text{void}}$ guides the cross-attention in regions without characters in the layout. $\\mathbf{c}_i \\in \\mathbb{R}^{B \\times ((N_c + 1) \\times N_q) \\times C}$ is the output feature for all characters, where $B$ is the batch size, $N_c$ is the maximum number of characters per panel (padded with all-zero features as needed), $N_q$ is the number of query tokens per character, and $C$ is the cross-attention dimension of the U-Net. Through compressing the character images into a few tokens, DiffSensei avoids encoding fine-grained spatial features from reference images into the model [21, 51]. This enables focusing on the characters' semantic representations rather than rigid pixel distributions.", + "bbox": [ + 511, + 516, + 908, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Masked cross-attention injection. We replicate the key and value matrices in each cross-attention layer, creating separate character cross-attention layers. This allows the image query features to attend to text and character cross-attentions independently and combine the results from both attentions. In the character cross-attention, we apply a masked cross-attention injection mechanism to control the layout of each character. Here, each character feature only attends to query features within its designated bounding box region. In areas without characters, query features attend to", + "bbox": [ + 511, + 750, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28687", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/06fd9a85d5bdaef5ea1f712d6315e93734cf9495c217db5cdcf75dd5926de8e8.jpg", + "image_caption": [ + "Figure 3. The architecture of DiffSensei. In the first stage, we train a multi-character customized manga image generation model with layout control. The dialog embedding is added to the noised latent after the first convolution layer. All the parameters in the U-Net and feature extractor are trained. In the second stage, we finetune LoRA and resampler weights of an MLLM to adapt the source character features corresponding to the text prompt. We use the model in the first stage as the image generator and freeze its weights." + ], + "image_footnote": [], + "bbox": [ + 106, + 95, + 893, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "a placeholder vector, $\\mathbf{q}_{\\text{void}}$ . This can be formulated as:", + "bbox": [ + 89, + 446, + 452, + 464 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {z}} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} _ {t} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V} _ {t} + \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 468, + 482, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\alpha} \\cdot \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q K} _ {i} ^ {\\top}}{\\sqrt {d}} + \\mathbf {M}\\right) \\mathbf {V} _ {i},\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 505, + 400, + 540 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{Q} = \\mathbf{z}\\mathbf{W}_q$ , $\\mathbf{K}^t = \\mathbf{c}_t\\mathbf{W}_k^t$ , $\\mathbf{V}^t = \\mathbf{c}_t\\mathbf{W}_v^t$ , $\\mathbf{K}^i = \\mathbf{c}_i\\mathbf{W}_k^i$ , $\\mathbf{V}^i = \\mathbf{c}_i\\mathbf{W}_v^i$ . $\\mathbf{Q}$ is the query, $\\mathbf{W_q}$ , $\\mathbf{W_k^t}$ , $\\mathbf{W_v^t}$ are query, key, and value projection matrices for the text cross-attention. $\\mathbf{W_k^t}$ , $\\mathbf{W_v^t}$ are key and value projection matrices for the character cross-attention, initialized from $\\mathbf{W_k^t}$ and $\\mathbf{W_v^t}$ . $d$ is the key dimension. $\\mathbf{c}_t$ , $\\mathbf{c}_i$ are text and character features respectively. $\\mathbf{z}$ , $\\hat{\\mathbf{z}}$ are the input and output image features. $\\alpha$ is a hyperparameter that controls character attention weight. $\\mathbf{M}$ is an attention mask to manage the characters' layout. Its values are defined as follows:", + "bbox": [ + 89, + 544, + 483, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} [ i, j ] = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} j = N _ {c} \\text {a n d} i \\notin \\mathbf {B} ^ {c} \\text {o r} \\\\ & i \\in \\mathbf {B} ^ {c} [ j ] \\\\ - \\infty , & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 703, + 482, + 760 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $i$ denotes the position of query tokens, $j \\in \\{0,1,\\dots,N_c\\}$ is the character indices. The $N_{c}$ -th character feature represents the placeholder vector $\\mathbf{q}_{void}$ . $\\mathbf{B}^c [j]$ is the bounding box of the $j$ -th character. The masked attention injection mechanism ensures that each character attends only to its specified bounding box region, while areas without characters attend to the placeholder vector. This technique achieves efficient and precise layout control for each character with minimal computational overhead.", + "bbox": [ + 89, + 763, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dialog layout encoding. Panels with dialog are a distinctive feature of manga images. However, most current text-to-image models struggle to generate coherent, readable text [26, 28]. While some recent models can produce stable text, they remain limited in terms of text length [17]. Generating extended text, such as dialogues, continues to pose challenges. Therefore, we propose controlling the layout of dialogs rather than the content itself. In this approach, human artists can manually edit the text within dialog bubbles, leaving image generation to the models. Concretely, we introduce a trainable embedding to represent the dialog layout. The dialog embedding is first expanded to match the spatial shape of the noised latent and then masked with the dialog layout. By summing the masked dialog embedding with the noised latent, we can encode dialog positions within the image generator. This process is expressed as:", + "bbox": [ + 511, + 446, + 906, + 689 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {z}} _ {t} = \\operatorname {C o n v} \\left(\\mathbf {z} _ {t}\\right) + \\operatorname {E x p a n d} \\left(\\mathbf {e} _ {d}, \\mathbf {z} _ {t}\\right) \\cdot \\mathbf {M} _ {d}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 696, + 906, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{e}_d$ is the trainable dialog embedding, $\\mathbf{z}_t$ is the noised latent in time step $t$ , Expand is a function that expands $\\mathbf{e}_d$ to the latent shape, and $\\mathbf{M}_d$ is the dialog region mask derived from input dialog bounding boxes $\\mathbf{B}^d$ . The output, $\\hat{\\mathbf{z}}_t$ , serves as a dialog-Layout-aware latent representation. This is then input into the U-Net for noise prediction. The dialog embedding effectively encodes the dialog layout, adding minimal computational overhead in space and time.", + "bbox": [ + 511, + 719, + 906, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MLLM as text-compatible character feature adapter. After training the image generator, our model can effectively create manga panels that adhere to specified character appearances and layout conditions. However, the model", + "bbox": [ + 511, + 840, + 908, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28688", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "often rigidly follows the input character images, lacking flexibility in adjusting expressions, poses, or motions based on panel captions. We propose incorporating MLLM as a text-compatible character feature adapter. This approach allows dynamic modifications to character states based on text prompts. A training sample for MLLM is organized as [panel caption, source character image features, target character image features]. The image features are encapsulated by two special tokens, $\\langle \\mathrm{IMG} \\rangle$ and $\\langle \\mathrm{IMG} \\rangle$ . To achieve this, we compute Language Modeling (LM) Loss on the special tokens to constrain the output format and Mean Squared Error (MSE) Loss to guide the target character features based on the panel caption. To ensure that the edited character features align with the image generator, we further pass the generated features into U-Net's character cross-attention and compute diffusion loss. In this stage, only the LoRA and resampler weights in MLLM are updated. This process can be formalized as follows:", + "bbox": [ + 89, + 90, + 483, + 363 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {h}}, \\hat {\\mathbf {c}} _ {i} = \\operatorname {M L L M} (T, \\phi (\\mathbf {c} _ {i})),\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 373, + 323, + 390 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {l m} = \\operatorname {L M L o s s} (\\hat {\\mathbf {h}}, T), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 396, + 480, + 417 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m s e} = \\operatorname {M S E L o s s} \\left(\\phi^ {\\prime} (\\hat {\\mathbf {c}} _ {i}), \\tilde {\\mathbf {c}} _ {i}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 415, + 344, + 431 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i f f} = \\mathbb {E} _ {\\epsilon , t} | | \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, T, \\hat {\\mathbf {c}} _ {i}, \\mathbf {B} ^ {c}, \\mathbf {B} ^ {d}, t) | | ^ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 434, + 433, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $T$ is the text prompt. $\\phi$ and $\\phi^{\\prime}$ denote the input and output resamplers of MLLM, which consist of stacked attention layers to convert the embeddings between inner and outer dimensions. $\\hat{\\mathbf{h}}$ refers to the MLLM predicted special token embeddings. We calculate LM Loss on it. $\\hat{\\mathbf{c}}_i$ is the predicted character features. We compute MSE Loss between $\\hat{\\mathbf{c}}_i$ and $\\tilde{\\mathbf{c}}_i$ , the ground truth target character embedding extracted from the feature extractor. By leveraging the character ID annotations of MangaZero, we can obtain features from the same character across different panels, thus facilitating the training of the MLLM feature adapter. The adapted character feature $\\hat{\\mathbf{c}}_i$ is then passed to the image generator $\\epsilon$ , previously trained, to compute a diffusion loss. The total loss for training MLLM is expressed as follows:", + "bbox": [ + 89, + 460, + 483, + 674 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {l m} \\mathcal {L} _ {l m} + \\lambda_ {m s e} \\mathcal {L} _ {m s e} + \\lambda_ {d i f f} \\mathcal {L} _ {d i f f}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 684, + 480, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{lm}$ , $\\lambda_{mse}$ , and $\\lambda_{diff}$ are loss weights.", + "bbox": [ + 89, + 710, + 393, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 738, + 223, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we thoroughly evaluate DiffSensei and compare it with baseline models.", + "bbox": [ + 89, + 763, + 482, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 89, + 803, + 297, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. The image generator is constructed on top of SDXL [26]. The feature extractor's weights are initialized using the pre-trained IP-AdapterPlus-SDXL [47], while the MLLM (Multi-modal Large Language Model) is initialized from SEED-X [8]. Other", + "bbox": [ + 89, + 825, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "newly introduced parameters, including the LoRA and resampler weights of the MLLM, are initialized randomly. In stage 1, the image generator is optimized using a learning rate of 1e-5. Stage 2 training employs a learning rate of 1e-4 and a LoRA rank of 64 [14]. The optimizer is AdamW [23]. The loss function coefficients $\\lambda_{lm}$ , $\\lambda_{mse}$ , and $\\lambda_{diff}$ are set to 1.0, 6.0, and 1.0, respectively. We train 250k steps for the first stage and 20k for the second stage. The source character images are chosen randomly, with a $50\\%$ probability of being from the same page; otherwise, they are selected from the target image. To handle varying image resolutions during training, we adopt the bucket-based approach from prior works [26], grouping images into resolution-specific buckets. For each training batch, images are loaded from the same resolution bucket. The batch size varies between 8 and 64 in stage 1, and between 8 and 128 in stage 2. This dynamic batch sizing is necessary to prevent out-of-memory (OOM) issues, especially when processing large-resolution images. Please see more details in the Appendix.", + "bbox": [ + 511, + 90, + 906, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation datasets and metrics. We evaluate our model using the MangaZero and Manga109 [2] evaluation sets. Note that the model is only trained on MangaZero. Characters in Manga109 are unseen during training, serving as a benchmark for generalization. To assess the generation quality of individual images, we employ autonomous metrics, which include Fréchet Inception Distance score (FID) [13], CLIP image-text similarity (CLIP) [27], DINO image similarity (DINO-I) [24], DINO character image similarity (DINO-C), and the dialog bounding box F1 score (F1 score). The source character images are randomly sampled on the same page. The dialog bounding boxes in the generated images are predicted using Magi [30]. For evaluating the story visualization quality of image sequences, human preference study proves more effective. We recruit human volunteers to choose their preferred story pages from our model's output and baseline models in the MangaZero evaluation set. The evaluation criteria include five key aspects: text-image alignment, style consistency, character consistency, image quality, and overall preference.", + "bbox": [ + 511, + 378, + 908, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We select recent advanced story visualization models as our baselines, including StoryDiffusion [53], AR-LDM [25], StoryGen [21], SEED-Story [46], and MS-Diffusion [39]. StoryDiffusion [53] is a training-free method. We directly use an SDXL text-to-image model finetuned on MangaZero for evaluation. Despite that, we re-train other baselines on our dataset for a fair comparison.", + "bbox": [ + 511, + 681, + 908, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison to Baselines", + "text_level": 1, + "bbox": [ + 511, + 801, + 741, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative comparison. We quantitatively compare our DiffSensei model with baseline models using automatic evaluation metrics. The results on the MangaZero evaluation set are presented in Tab. 2a. The results highlight that DiffSensei consistently outperforms the baseline mod", + "bbox": [ + 511, + 825, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28689", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/207ea7c4231c6df9d6d868d69df99617beab3024df12958d86cec8c5a3e30988.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons on automatic metrics. Methods followed by “*” use reference images as input rather than characters. Methods marked by “†” means re-trained with dialog embedding.", + "(a) Comparison on MangaZero evaluation set." + ], + "table_footnote": [], + "table_body": "
    MethodFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    AR-LDM* [25]0.4090.2570.5480.5070.004
    StoryGen* [21]0.4110.2190.5360.4880.012
    SEED-Story* [46]0.4110.1690.4160.4050.006
    StoryDiffusion* [53]0.4090.2440.4610.3620.002
    MS-Diffusion† [39]0.4080.2290.6100.6410.720
    DiffSensei0.4070.2350.6180.6510.727
    ", + "bbox": [ + 101, + 143, + 496, + 243 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/776c5e578f03ec308a5b86e710d538b9c6011acb028affe49e832969ab3d25f4.jpg", + "table_caption": [ + "(b) Comparison on Manga109 evaluation set." + ], + "table_footnote": [], + "table_body": "
    MethodFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    AR-LDM* [25]0.4100.2540.5270.4910.005
    StoryGen* [21]0.4140.2140.5400.4930.004
    SEED-Story* [46]0.4130.1670.4420.4280.005
    StoryDiffusion* [53]0.4100.2380.4420.3550.001
    MS-Diffusion† [39]0.4100.2270.5840.6000.601
    DiffSensei0.4100.2370.5880.6000.648
    ", + "bbox": [ + 503, + 143, + 895, + 242 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Story Summary: A sailor hears a sound in the cabin, walks up to the deck, and discovers a beautiful ghost girl. He tries to embrace her...", + "bbox": [ + 102, + 263, + 289, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b52522b814fe01ec2c1235cb13cddf0648c4dfef23e5d9a3b2c6bb83394c0402.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 256, + 433, + 297 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/73158a2ec00a54e3ca91861aa9ede5438635d1336ba566f4a3bfad6cdc639d97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 434, + 257, + 562, + 297 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/731b398cce9e0c06f9d9cccb61e7230d5f373bc0948d37df36e6f4db4f1c97de.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 563, + 257, + 733, + 297 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ccd0859941344e6aa84e89136bdb1811cca4eb664bcc21f73bbbcdd54d3e8d86.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 263, + 888, + 297 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1a1622d7a3a8e1e29cb27a7f80a0c85683f37fbf33d3f826eabb169487d3c9a5.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison with baselines. Baselines followed by a \\*\\* use reference images as input rather than character images. Methods marked by \\*\\* means re-trained with dialog embedding. Our model excels at preserving the characters while following the text prompt. Our DiffSensei successively generates highlighted details in panel captions. Better viewed with zoom-in." + ], + "image_footnote": [], + "bbox": [ + 98, + 299, + 207, + 501 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/68a273d5b63c2d0199378b1a9429715aa4cee164fdbf8c981fc91e4619ec2a46.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 212, + 299, + 320, + 501 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f33bf9ec5f480c8d7dc21bd72f25f995ad3414d1b8709b5752862d4855f54979.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 326, + 300, + 431, + 501 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/103f437e3802a1df3b4c1a56b6e8a0706ee628571825b0cce1213df834d6cba7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 437, + 300, + 562, + 501 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0ef2cda4ff2c12928e809c0eae2a94f83f5de23e800d9673a0e9f865cee5ec19.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 300, + 671, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/daefc6b632c87351b7faea032792b4d451af6d4e760f4a259e690bbbceb4ade4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 676, + 300, + 782, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/73c5f6e27557f1c0dc647c64276221af2cb9a3aaaa6f52833973803bdcd5d495.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 300, + 895, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7a3d44ac14164cd495db218e1d1232c60def80c4340ed8cb10f3ffd87668309a.jpg", + "image_caption": [ + "Figure 5. Human preference study on MangaZero eval set." + ], + "image_footnote": [], + "bbox": [ + 93, + 582, + 473, + 694 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "els across five key metrics. Our model improves 0.06 in the CLIP metrics compared to the multi-subject customization baseline, MS-Diffusion [39], which struggles to modify characters' states effectively in response to textual prompts. Furthermore, DiffSensei demonstrates superior image quality and character preservation, as evidenced by higher DINO-I and DINO-C scores. Although AR-LDM [25] achieves higher CLIP metrics, it suffers from poor image quality and lacks the architectural capability to manage multiple characters, resulting in low DINO-C scores. In contrast, our method strikes a balance be", + "bbox": [ + 88, + 734, + 485, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tween maintaining character appearances and adapting to text prompts. We also compare the Manga109 evaluation set with the results shown in Tab. 2b. When using previously unseen characters as inputs, our model continues to outperform the baselines. These results underscore the strong generalization ability of DiffSensei, demonstrating effective adaptation to new characters.", + "bbox": [ + 511, + 582, + 906, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 5, we present the results of a human preference study comparing our model to the baselines across several dimensions. Our model receives the highest ratings from human evaluators, particularly in terms of overall preference, character consistency, and image quality. These findings confirm that DiffSensei excels in rendering vivid and engaging manga stories.", + "bbox": [ + 511, + 688, + 908, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparison. Fig. 4 shows a qualitative comparison between DiffSensei and baseline models. The results illustrate that our model significantly outperforms the baselines in generating an entire page of a manga story. SEED-Story [46] employs an MLLM to create captions for each panel, leading to unnatural narrative text and chaotic story generation that fails to form a coherent story. StoryD", + "bbox": [ + 511, + 795, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28690", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c568511057517d739b036a5742d2e2e6f7321a7c189e892e49c856c174ecfce1.jpg", + "image_caption": [ + "Figure 6. Qualitative results. Character images in red boxes are from Manga109 (The rightmost example). Our DiffSensei can generate vivid manga pages in various scenarios. Better viewed with zoom-in. More results can be found in the appendix." + ], + "image_footnote": [], + "bbox": [ + 98, + 90, + 228, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/36417586eb88ed32341cbd430925da138072c13423b40036e2b73176b462ff11.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 233, + 90, + 357, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e448fec9f30b666f3888d40d9e915b57544a7319513972892ccb1342932f1851.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 90, + 504, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4dd5be999682c362265ad4c254be95ac636c7fdd58a09b24b2ace0c5a473bcd8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 90, + 625, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d803408655b73ddbd1dd72088d3d646e0aaf21625f259d0ea702c4948108aab1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 90, + 761, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d85b594c21becd46280a58f8f1a717a89caa12d4a781ad1eda3f23bc5f1ce46.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 90, + 900, + 261 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5bd4ddc6be307921aaffaac44c1e9b95ea72411decaf32bf97d5e4fa21222fca.jpg", + "table_caption": [ + "Table 3. Ablation study. CM is character masked attention injection. DM is dialog masked encoding. Magi means using Magi [30] image encoder. MLLM means using MLLM for stage 2 training." + ], + "table_footnote": [], + "table_body": "
    CMDMMagiMLLMFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    0.4100.2300.5930.6100.361
    ✓0.4110.2250.5910.6370.364
    ✓✓0.4070.2280.6000.6350.653
    ✓✓✓0.4080.2310.6180.6480.718
    ✓✓✓✓0.4070.2350.6180.6510.727
    ", + "bbox": [ + 98, + 381, + 478, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "iffusion [53] is limited to producing fixed-resolution images due to its self-attention sharing mechanism, restricting its ability to generate diverse images. It shows inferior results, probably because the input reference panel has an unbalanced aspect ratio. MS-Diffusion [39] trains with source character images from the target panel and lacks the flexibility to modify characters' states effectively. In contrast, our method excels in text-following, character preservation, and overall story presentation.", + "bbox": [ + 89, + 474, + 483, + 612 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 89, + 619, + 272, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 6 shows several manga pages generated by DiffSensei. The results demonstrate that our method can generate vivid manga panels and provide visually plausible results for the customized manga generation task. Our model can also generalize to unseen characters, as illustrated in the rightmost example, with character images from Manga109 [2] as input. Please see more results in the Appendix.", + "bbox": [ + 89, + 642, + 482, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 757, + 243, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 3 presents the quantitative ablation study of DiffSensei, where we systematically remove components to assess their impact. Specifically, when the MLLM component, serving as the flexible character feature adapter, is excluded, the CLIP metrics decrease by $1.73\\%$ , and the DINO-C score also drops, underscoring its role in enhancing transferring character to the text-derived states. The absence of the Magi [30] image encoder results in a general decline in met-", + "bbox": [ + 89, + 779, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "rics, particularly in image quality and character similarity, highlighting the importance of the Magi encoder for effectively encoding manga characters. Magi is trained specifically on manga datasets, performing better at preserving manga characters. To investigate alternative methods for encoding character and dialog layout conditions, we experimented with replacing the dialog embedding technique by inputting the Fourier embeddings of dialog bounding boxes into the timestep embedding of SDXL [26]. This modification led to a significant decrease in layout control, evidenced by the F1 score plummeting from 0.653 to 0.364, demonstrating that directly incorporating dialog embeddings into the latent is a superior approach for encoding dialog layouts. Furthermore, we explored adding the Fourier embeddings of character bounding boxes to the character features as an alternative to masked attention injection. This change caused a marked drop in the DINO-C metric, reaffirming the effectiveness of our original masked attention strategy. For comprehensive effect showcases, please see the qualitative ablation study in the Appendix.", + "bbox": [ + 511, + 329, + 906, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 513, + 647, + 633, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces DiffSensei, a novel framework for multi-character customized story visualization that integrates a diffusion-based image generator with an MLLM as a text-compatible identity adapter. Key innovations include masked attention control for character layout management, dialog layout embedding, and an MLLM-based feature adapter for flexible character customization. Supported by the proposed MangaZero dataset, comprising 43,264 manga pages and 427,147 panels, DiffSensei achieves superior, character-consistent panels that dynamically respond to textual prompts, surpassing existing methods and advancing the field of story visualization.", + "bbox": [ + 511, + 672, + 906, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported by the National Key Research and Development Program of China (No. 2023YFC3807600).", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28691", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 90, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mangadex, 2024. 4", + "[2] Kiyoharu Aizawa, Azuma Fujimoto, Atsushi Otsubo, Toru Ogawa, Yusuke Matsui, Koki Tsubota, and Hikaru Ikuta. Building a manga dataset \"manga109\" with annotations for multimedia applications. TMM, 2020. 3, 6, 8", + "[3] Jinbin Bai, Tian Ye, Wei Chow, Enxin Song, Qing-Guo Chen, Xiangtai Li, Zhen Dong, Lei Zhu, and Shuicheng Yan. 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Boxdiff:" + ], + "bbox": [ + 91, + 92, + 480, + 900 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "Text-to-image synthesis with training-free box-constrained diffusion. In ICCV, 2023. 4", + "[46] Shuai Yang, Yuying Ge, Yang Li, Yukang Chen, Yixiao Ge, Ying Shan, and Yingcong Chen. Seed-story: Multimodal long story generation with large language model. arXiv preprint arXiv:2407.08683, 2024. 1, 2, 3, 6, 7", + "[47] Hu Ye, Jun Zhang, Sibo Liu, Xiao Han, and Wei Yang. Ip-adapter: Text compatible image prompt adapter for text-to-image diffusion models. arXiv preprint arXiv:2308.06721, 2023. 2, 3, 4, 6", + "[48] Zhang Yunqian. Ai-driven background generation for manga illustrations: A deep generative model approach. ORES, 2024. 2, 3", + "[49] Kai Zhang, Lingbo Mo, Wenhu Chen, Huan Sun, and Yu Su. Magicbrush: A manually annotated dataset for instruction-guided image editing. 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In NeurIPS, 2024. 1, 2, 6, 7, 8" + ], + "bbox": [ + 516, + 92, + 903, + 503 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "28693", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/fada47c4-9d9c-4ce9-8477-3cca25b37313_model.json b/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/fada47c4-9d9c-4ce9-8477-3cca25b37313_model.json new file mode 100644 index 0000000000000000000000000000000000000000..17e471da508c617228f58915a8e998d973f9532d --- /dev/null +++ b/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/fada47c4-9d9c-4ce9-8477-3cca25b37313_model.json @@ -0,0 +1,2167 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.809, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.182, + 0.13, + 0.819, + 0.177 + ], + "angle": 0, + "content": "DiffSensei: Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.203, + 0.892, + 0.223 + ], + "angle": 0, + "content": "Jianzong Wu\\(^{1,2}\\) Chao Tang\\(^{1}\\) Jingbo Wang\\(^{2}\\) Yanhong Zeng\\(^{2}\\) Xiangtai Li\\(^{3,4}\\) Yunhai Tong\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.138, + 0.223, + 0.856, + 0.24 + ], + "angle": 0, + "content": "1 Peking University 2 Shanghai AI Laboratory 3 Nanyang Technological University 4 Bytedance Seed" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.242, + 0.785, + 0.258 + ], + "angle": 0, + "content": "Project Page: https://jianzongwu.github.io/projects/diffsensei/" + }, + { + "type": "text", + "bbox": [ + 0.32, + 0.26, + 0.673, + 0.275 + ], + "angle": 0, + "content": "Email: jzwu@stu.pku.edu.cn, xiangtai94@gmail.com" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.296, + 0.673, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.293, + 0.516, + 0.473, + 0.528 + ], + "angle": 0, + "content": "(a) Customized manga generation" + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.297, + 0.901, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.516, + 0.874, + 0.528 + ], + "angle": 0, + "content": "(b) Real human manga creation" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.541, + 0.908, + 0.598 + ], + "angle": 0, + "content": "Figure 1. Results of DiffSensei. (a) Customized manga generation with controllable character images, panel captions, and layout conditions. Our DiffSensei successfully generates detailed character expressions and states following the panel captions. (b) Manga creation for real human images. The dialogues are post-edited by humans. The continuation is in the Appendix. We strongly recommend that the readers see the Appendix for more comprehensive results. Manga reading order: Right to left. Top to bottom." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.615, + 0.327, + 0.631 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.66, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Story visualization, the task of creating visual narratives from textual descriptions, has seen progress with text-to-image generation models. However, these models often lack effective control over character appearances and interactions, particularly in multi-character scenes. To address these limitations, we propose a new task: customized manga generation and introduce DiffSensei, an innovative framework specifically designed for generating manga with dynamic multi-character control. DiffSensei integrates a diffusion-based image generator with a multimodal large language model (MLLM) that acts as a text-compatible identity adapter. Our approach employs masked cross-attention to seamlessly incorporate character features, enabling precise layout control without direct pixel transfer. Additionally, the MLLM-based adapter adjusts character features to align with panel-specific text cues, allowing flex" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.616, + 0.909, + 0.768 + ], + "angle": 0, + "content": "ible adjustments in character expressions, poses, and actions. We also introduce MangaZero, a large-scale dataset tailored to this task, containing 43,264 manga pages and 427,147 annotated panels, supporting the visualization of varied character interactions and movements across sequential frames. Extensive experiments demonstrate that DiffSensei outperforms existing models, marking a significant advancement in manga generation by enabling text-adaptable character customization. The code, model, and dataset are open-sourced to the community." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.779, + 0.646, + 0.794 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.805, + 0.907, + 0.867 + ], + "angle": 0, + "content": "Story visualization, the process of generating visual narratives from textual descriptions, is a rapidly evolving field [5, 18, 21, 25, 37, 46, 53]. Among its various applications, manga generation holds particular significance due" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.875, + 0.907, + 0.901 + ], + "angle": 0, + "content": "1The work is done in Shanghai AI Laboratory. Corresponding to: Xiangtai Li, Jingbo Wang." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28684" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.168 + ], + "angle": 0, + "content": "to its popularity and unique narrative requirements. Unlike traditional story visualization, manga demands consistent characters across panels, precise layout control for positioning multiple characters, and the seamless integration of dialogues in a coherent, visually engaging manner." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.171, + 0.483, + 0.532 + ], + "angle": 0, + "content": "Currently, manga generation remains an underexplored area. Most existing research focuses on low-level imagedto-image tasks, primarily converting general images to a manga style [20, 33, 48, 50]. While these tasks enhance the visual appeal of static images, they do not extend to generating fully customized manga content from scratch. In general story visualization, current approaches have demonstrated some success in generating coherent image sequences from text. Still, they cannot often customize the characters across scenes [21, 25, 46, 53], a critical requirement for manga generation. Additionally, they do not provide the necessary control over layouts and dialogue placements, which are also essential for manga. A likely reason for these limitations is that existing story visualization datasets typically lack character annotations and layout controls [15, 18, 21, 46]. Another research direction has explored zero-shot character customization, showing promise for achieving character customization across manga panels [4, 9, 19, 29, 36, 39, 47]. However, these approaches often result in rigid \"copy-pasting\" effects [4, 39, 47], which limit expressive character variation and detract from narrative depth. This limitation largely stems from the scarcity of datasets capturing multiple appearances of the same character in varied expressions and poses." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.536, + 0.483, + 0.807 + ], + "angle": 0, + "content": "To address these limitations, we propose a new task: customized manga generation. As illustrated in Fig. 1, this task focuses on creating manga images with multiple characters, each customized based on a character image and positioned according to user input. Characters must dynamically adapt to text prompts, altering their expressions, motions, and poses as the narrative unfolds. Dialog layout should also be managed to generate expressive manga panels. Compared to traditional story visualization tasks, this proposed task prioritizes essential manga-specific controllability, aiming to generate vivid manga panels that are both coherent and visually engaging while supporting the customization of multiple characters. To address the lack of a dedicated dataset for customized manga generation, we collect a dataset of Japanese black-and-white manga, forming the basis of the proposed task. The resulting dataset, MangaZero, is the first large-scale collection designed to support multi-character, multi-state manga generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.902 + ], + "angle": 0, + "content": "To tackle this task, we introduce a novel framework, DiffSensei, which leverages a diffusion-based image generator to produce customized manga panels. However, we observe that, even with training on multiple appearances of the same character, the generated portraits often tend to rigidly follow the pixel distribution of the input character image, re" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.333 + ], + "angle": 0, + "content": "sulting in limited variations in appearance, pose, and motion based on the text input. Inspired by recent advancements in image editing using Multimodal Large Language Models (MLLMs) [6, 8, 16, 34, 40-43, 46, 49], we propose using an MLLM as a text-compatible character adapter. This approach enables seamless, dynamic adjustments to characters in response to textual cues, thereby supporting coherent and expressive manga panel generation. Additionally, we incorporate masked attention injection to manage character layout, along with a dialog embedding technique tailored specifically for manga, allowing for precise control over dialog placement. Through extensive experimentation, we validate DiffSensei's capability to generate coherent, expressive manga panels that maintain narrative consistency and offer improved character control. This represents a significant advancement in story visualization." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.335, + 0.905, + 0.395 + ], + "angle": 0, + "content": "- We introduce a new task: customized manga generation, focused on generating manga images with multiple characters, each dynamically adapting to text prompts and positioned according to layout specifications." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.396, + 0.905, + 0.47 + ], + "angle": 0, + "content": "- We present MangaZero, the first large-scale dataset specifically designed for multi-character, multi-state manga generation, addressing a significant gap in story visualization training data. The dataset will be released for the image generation community." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.471, + 0.905, + 0.56 + ], + "angle": 0, + "content": "- We propose DiffSensei. As far as we know, it is the first framework for customized manga generation that links diffusion models and MLLMs. The MLLM serves as an adaptable character feature adapter, enabling characters to respond dynamically to textual cues. Extensive experiments demonstrate the effectiveness of DiffSensei." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.335, + 0.905, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.573, + 0.655, + 0.589 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Story visualization. Story visualization, the process of generating visual narratives based on given stories, is rapidly evolving. Many approaches can generate consistent image sequences derived from story content [5, 21, 25, 37, 46, 53]. Despite recent advancements, the field faces significant limitations. Most existing methods generate story images solely from text and image-level prompts [21, 25, 46, 53], which restricts control over individual characters. This limited control over characters reduces the flexibility and depth of story visualization. A key factor is that current training datasets [10, 15, 18, 21, 46] lack character-specific annotations. In response to the data limit, recent works [5, 37] explore multi-character control using training-free methods that leverage existing subject preservation techniques, such as IP-Adapter [47]. Other works [4, 7, 9, 11, 12, 19, 29, 32, 36, 39, 44, 47] try to train diffusion models for a multi-character customized generation. However, these approaches often result in a \"copy-pasting\" effect, restricting the diversity of expressions and actions needed for dynamic storytelling. For training-free" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "28685" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.089, + 0.907, + 0.133 + ], + "angle": 0, + "content": "Table 1. Comparison between MangaZero and related publicly available datasets. A story is defined as a sequence of continuous images annotated consistently with character IDs. In MangaZero, a story means a manga page. A panel means a distinct story image, or called frame [21, 46]. Most series in MangaZero are still popular in 2024. Please see the Appendix for the dataset details." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.143, + 0.912, + 0.281 + ], + "angle": 0, + "content": "
    DatasetTypeResolution#Series#Stories#PanelsCaptionAnnotations CharacterDialogOrigin
    PororoSV [18]AnimationFix115,33673,665✓××2003-2016
    FlintstonesSV [10]AnimationFix125,184122,560✓✓×1960-1966
    StorySalon [21]AnimationFix44618,255159,778✓××YouTube
    StoryStream [46]AnimationFix312,614257,850✓××1939-2013
    Manga109 [2]B/W MangaVary10910,602103,850×✓✓1970-2010
    MangaZeroB/W MangaVary4843,264427,147✓✓✓1974-2024
    " + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.305, + 0.482, + 0.396 + ], + "angle": 0, + "content": "methods, combining multiple models can significantly slow down inference speeds. To address these challenges, we first introduce a large-scale manga generation dataset with finely curated character annotations and then develop a novel framework utilizing diffusion models and MLLMs that enables the dynamic generation of manga panels." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.396, + 0.482, + 0.517 + ], + "angle": 0, + "content": "Manga generation. The field of black-and-while manga generation has received limited exploration. Most existing researches focus on low-level image-to-image tasks, primarily transferring general images to a manga style [20, 33, 48, 50]. Recent works contribute to manga content understanding [30, 31, 35]. In contrast, we propose the customized manga generation task beyond style transfer to offer complete character and story-driven manga generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.518, + 0.483, + 0.743 + ], + "angle": 0, + "content": "MLLMs for personalized image generation. MLLMs have shown remarkable potential in personalized image generation, particularly for tasks involving image editing and customization [3, 6, 8, 16, 34, 40-42, 46, 49]. Notably, CAFE [52] explores customizing subject appearances through textual instructions. However, MLLM-driven image generation for multi-character narratives remains an open challenge, primarily due to the difficulties in maintaining inter-character relationships and scene continuity. Our framework proposes an MLLM-based identity adapter that enhances dynamic story consistency in multi-character manga generation. In contrast to previous works, our framework takes multi-character features as input and edits these features collectively, following the text prompt, enabling flexible subject editing across multiple characters." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.755, + 0.32, + 0.772 + ], + "angle": 0, + "content": "3. The MangaZero Dataset" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.811 + ], + "angle": 0, + "content": "In this section, we first define the problem in Sec. 3.1. Then, we introduce the dataset construction pipeline in Sec. 3.2." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.295, + 0.833 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "We introduce a challenging new task: customized manga generation. This task focuses on generating manga images where multiple characters, each with their distinct image inputs, are customized and positioned by users. Importantly," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.305, + 0.905, + 0.472 + ], + "angle": 0, + "content": "characters must adapt to the text prompts by modifying their expressions, motions, and poses dynamically, even when only a limited set of character images is available. To generate a manga story across \\(N\\) panels (or frames), the inputs include: text prompts for each panel \\(T_{0}, T_{1}, \\ldots, T_{N-1}\\), character images \\(\\mathbf{I} = I_{0}, I_{1}, \\ldots, I_{K-1}\\), character bounding boxes for each panel \\(\\mathbf{B}_{0}^{c}, \\mathbf{B}_{1}^{c}, \\ldots, \\mathbf{B}_{N-1}^{c}\\), and dialogue bounding boxes for each panel \\(\\mathbf{B}_{0}^{d}, \\mathbf{B}_{1}^{d}, \\ldots, \\mathbf{B}_{N-1}^{d}\\). The visualization of a panel is represented as \\(P_{i} = \\Phi_{\\theta}(T_{i}, \\mathbf{I}, \\mathbf{B}_{i}^{c}, \\mathbf{B}_{i}^{d})\\), where \\(\\Phi\\) is the overall model function and \\(\\theta\\) represents the model's learned parameters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.473, + 0.906, + 0.685 + ], + "angle": 0, + "content": "Discussion. This task diverges from existing story visualization and continuation tasks [21, 25]. Specifically, in story visualization tasks, a panel is produced using \\( P_{i} = \\Phi_{\\theta}(T_{i}) \\), while in story continuation tasks, the panel generation depends on previous panels as \\( P_{i} = \\Phi_{\\theta}(T_{i}, T_{i-1}, P_{i-1}) \\) for \\( i > 0 \\). Both lack explicit character control, a crucial element in storytelling. Furthermore, the proposed task differs from subject-driven image generation approaches [29, 39, 47], as it demands that models not only generate accurate character representations but also modify characters' attributes in response to panel captions and layouts, resulting in varied and coherent narrative visuals. Our experiments, detailed in Sec. 5, demonstrate that our model significantly surpasses baseline models in these critical aspects." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.696, + 0.715, + 0.71 + ], + "angle": 0, + "content": "3.2. Dataset Construction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.719, + 0.905, + 0.749 + ], + "angle": 0, + "content": "In this section, we introduce the proposed large-scale manga story visualization dataset MangaZero." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Comparison with related datasets. A comprehensive comparison with existing datasets is presented in Tab. 1. In contrast to current manga and story visualization datasets, the proposed MangaZero dataset stands out as being larger in size, newer in source, richer in annotations, diverse in manga series, and varied in panel resolutions. Compared to the well-known black-and-white manga dataset Manga109 [2], the MangaZero dataset encompasses more manga series published after the year 2000, which inspired its naming. Additionally, MangaZero includes famous se" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28686" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.089, + 0.459, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.311, + 0.487, + 0.368 + ], + "angle": 0, + "content": "Figure 2. We construct MangaZero through three steps: 1) Download manga pages from the internet. 2) Annotate manga panels autonomously with pre-trained models. 3) Human calibration for the character ID annotation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.394, + 0.483, + 0.424 + ], + "angle": 0, + "content": "ries from before the year 2000 that are not featured in Manga109, such as Doraemon (1974)." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.425, + 0.485, + 0.756 + ], + "angle": 0, + "content": "Construction pipeline. To build our dataset, we first download manga pages from the internet, explicitly sourcing images from MangaDex [1]. It is important to note that all data will be used solely for academic research, not commercial purposes. We select 48 manga series and download up to 1,000 pages per series, resulting in 43,264 double-page images. These images are then annotated using pretrained models. For manga-specific annotations, including panel bounding boxes, character bounding boxes, character IDs, and dialog bounding boxes, we employ the recent manga understanding model, Magi [30]. It should be noted that character ID labeling is consistent only within individual pages, which is sufficient for achieving coherent character cross-reference. Once the panel bounding boxes are obtained, we utilize LLaVA-v1.6-34B [22] to generate captions for each panel. However, we observe that character ID labeling has relatively low accuracy, which poses a significant challenge for training purposes. To address this, human annotators refine the machine-generated labels, resulting in accurate and clean annotations. Finally, we split 96 pages (2 for each series) as the evaluation set and the remaining 43,168 pages as the training set." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.77, + 0.183, + 0.785 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.483, + 0.856 + ], + "angle": 0, + "content": "In this section, we introduce the architecture of the proposed framework, DiffSensei, which generates vivid manga panels with precise character and dialog layout control while adapting the characters' status flexibly." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Motivation. There are two critical problems in customizing objects and layouts in image generation: 1) Preserving the subjects' intrinsic features while avoiding direct copy-paste" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.35 + ], + "angle": 0, + "content": "from source images, and 2) Ensuring reliable layout control with minimal computational cost during both training and inference. To avoid copy-pasting effects, our model converts character image features into tokens, preventing the direct transfer of fine-grained pixel details. Additionally, we integrate an MLLM as a character image feature adapter. The MLLM adapter receives source character features and panel captions as inputs, generating text-compatible target character features. Compared with previous customization work [39], this approach enables text-compatible character encoding and flexible character adaptation to captions. For layout control, we employ lightweight masked encoding techniques for both character and dialog layouts, significantly reducing computational costs compared with previous works [38, 45] while maintaining high accuracy in both training and inference phases. Experiment results in Sec. 5 demonstrate the effectiveness of our design." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.356, + 0.907, + 0.448 + ], + "angle": 0, + "content": "Multi-character feature extraction. As illustrated in Fig. 3, we initially extract local image features using CLIP and image-level features from a manga image encoder. These two sets of features are then processed by a feature extractor, which is implemented as a resampler module [47]. This process can be formalized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.473, + 0.907, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {i} = \\operatorname {R e s a m p l e r} ([ \\operatorname {C L I P} (\\mathbf {I}), \\psi (\\mathbf {I}) ], \\mathbf {q}, \\mathbf {q} _ {\\text {v o i d}}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.517, + 0.909, + 0.744 + ], + "angle": 0, + "content": "where \\(\\psi\\) represents the manga image encoder. \\(\\mathbf{q}\\) and \\(\\mathbf{q}_{\\text{void}}\\) are trainable query vectors for character and non-character features, respectively. \\(\\mathbf{q}\\) re-samples the image features into the U-Net's cross-attention dimension, while \\(\\mathbf{q}_{\\text{void}}\\) guides the cross-attention in regions without characters in the layout. \\(\\mathbf{c}_i \\in \\mathbb{R}^{B \\times ((N_c + 1) \\times N_q) \\times C}\\) is the output feature for all characters, where \\(B\\) is the batch size, \\(N_c\\) is the maximum number of characters per panel (padded with all-zero features as needed), \\(N_q\\) is the number of query tokens per character, and \\(C\\) is the cross-attention dimension of the U-Net. Through compressing the character images into a few tokens, DiffSensei avoids encoding fine-grained spatial features from reference images into the model [21, 51]. This enables focusing on the characters' semantic representations rather than rigid pixel distributions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Masked cross-attention injection. We replicate the key and value matrices in each cross-attention layer, creating separate character cross-attention layers. This allows the image query features to attend to text and character cross-attentions independently and combine the results from both attentions. In the character cross-attention, we apply a masked cross-attention injection mechanism to control the layout of each character. Here, each character feature only attends to query features within its designated bounding box region. In areas without characters, query features attend to" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28687" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.096, + 0.895, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.366, + 0.908, + 0.424 + ], + "angle": 0, + "content": "Figure 3. The architecture of DiffSensei. In the first stage, we train a multi-character customized manga image generation model with layout control. The dialog embedding is added to the noised latent after the first convolution layer. All the parameters in the U-Net and feature extractor are trained. In the second stage, we finetune LoRA and resampler weights of an MLLM to adapt the source character features corresponding to the text prompt. We use the model in the first stage as the image generator and freeze its weights." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.454, + 0.465 + ], + "angle": 0, + "content": "a placeholder vector, \\(\\mathbf{q}_{\\text{void}}\\). This can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.469, + 0.483, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {z}} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} _ {t} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V} _ {t} + \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.506, + 0.401, + 0.541 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\alpha} \\cdot \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q K} _ {i} ^ {\\top}}{\\sqrt {d}} + \\mathbf {M}\\right) \\mathbf {V} _ {i},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.545, + 0.484, + 0.698 + ], + "angle": 0, + "content": "where \\(\\mathbf{Q} = \\mathbf{z}\\mathbf{W}_q\\), \\(\\mathbf{K}^t = \\mathbf{c}_t\\mathbf{W}_k^t\\), \\(\\mathbf{V}^t = \\mathbf{c}_t\\mathbf{W}_v^t\\), \\(\\mathbf{K}^i = \\mathbf{c}_i\\mathbf{W}_k^i\\), \\(\\mathbf{V}^i = \\mathbf{c}_i\\mathbf{W}_v^i\\). \\(\\mathbf{Q}\\) is the query, \\(\\mathbf{W_q}\\), \\(\\mathbf{W_k^t}\\), \\(\\mathbf{W_v^t}\\) are query, key, and value projection matrices for the text cross-attention. \\(\\mathbf{W_k^t}\\), \\(\\mathbf{W_v^t}\\) are key and value projection matrices for the character cross-attention, initialized from \\(\\mathbf{W_k^t}\\) and \\(\\mathbf{W_v^t}\\). \\(d\\) is the key dimension. \\(\\mathbf{c}_t\\), \\(\\mathbf{c}_i\\) are text and character features respectively. \\(\\mathbf{z}\\), \\(\\hat{\\mathbf{z}}\\) are the input and output image features. \\(\\alpha\\) is a hyperparameter that controls character attention weight. \\(\\mathbf{M}\\) is an attention mask to manage the characters' layout. Its values are defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.704, + 0.483, + 0.761 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} [ i, j ] = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} j = N _ {c} \\text {a n d} i \\notin \\mathbf {B} ^ {c} \\text {o r} \\\\ & i \\in \\mathbf {B} ^ {c} [ j ] \\\\ - \\infty , & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.901 + ], + "angle": 0, + "content": "where \\(i\\) denotes the position of query tokens, \\(j \\in \\{0,1,\\dots,N_c\\}\\) is the character indices. The \\(N_{c}\\)-th character feature represents the placeholder vector \\(\\mathbf{q}_{void}\\). \\(\\mathbf{B}^c [j]\\) is the bounding box of the \\(j\\)-th character. The masked attention injection mechanism ensures that each character attends only to its specified bounding box region, while areas without characters attend to the placeholder vector. This technique achieves efficient and precise layout control for each character with minimal computational overhead." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.907, + 0.69 + ], + "angle": 0, + "content": "Dialog layout encoding. Panels with dialog are a distinctive feature of manga images. However, most current text-to-image models struggle to generate coherent, readable text [26, 28]. While some recent models can produce stable text, they remain limited in terms of text length [17]. Generating extended text, such as dialogues, continues to pose challenges. Therefore, we propose controlling the layout of dialogs rather than the content itself. In this approach, human artists can manually edit the text within dialog bubbles, leaving image generation to the models. Concretely, we introduce a trainable embedding to represent the dialog layout. The dialog embedding is first expanded to match the spatial shape of the noised latent and then masked with the dialog layout. By summing the masked dialog embedding with the noised latent, we can encode dialog positions within the image generator. This process is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.697, + 0.907, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {z}} _ {t} = \\operatorname {C o n v} \\left(\\mathbf {z} _ {t}\\right) + \\operatorname {E x p a n d} \\left(\\mathbf {e} _ {d}, \\mathbf {z} _ {t}\\right) \\cdot \\mathbf {M} _ {d}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.907, + 0.84 + ], + "angle": 0, + "content": "where \\(\\mathbf{e}_d\\) is the trainable dialog embedding, \\(\\mathbf{z}_t\\) is the noised latent in time step \\(t\\), Expand is a function that expands \\(\\mathbf{e}_d\\) to the latent shape, and \\(\\mathbf{M}_d\\) is the dialog region mask derived from input dialog bounding boxes \\(\\mathbf{B}^d\\). The output, \\(\\hat{\\mathbf{z}}_t\\), serves as a dialog-Layout-aware latent representation. This is then input into the U-Net for noise prediction. The dialog embedding effectively encodes the dialog layout, adding minimal computational overhead in space and time." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.909, + 0.902 + ], + "angle": 0, + "content": "MLLM as text-compatible character feature adapter. After training the image generator, our model can effectively create manga panels that adhere to specified character appearances and layout conditions. However, the model" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28688" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.364 + ], + "angle": 0, + "content": "often rigidly follows the input character images, lacking flexibility in adjusting expressions, poses, or motions based on panel captions. We propose incorporating MLLM as a text-compatible character feature adapter. This approach allows dynamic modifications to character states based on text prompts. A training sample for MLLM is organized as [panel caption, source character image features, target character image features]. The image features are encapsulated by two special tokens, \\( \\langle \\mathrm{IMG} \\rangle \\) and \\( \\langle \\mathrm{IMG} \\rangle \\). To achieve this, we compute Language Modeling (LM) Loss on the special tokens to constrain the output format and Mean Squared Error (MSE) Loss to guide the target character features based on the panel caption. To ensure that the edited character features align with the image generator, we further pass the generated features into U-Net's character cross-attention and compute diffusion loss. In this stage, only the LoRA and resampler weights in MLLM are updated. This process can be formalized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.374, + 0.324, + 0.391 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {h}}, \\hat {\\mathbf {c}} _ {i} = \\operatorname {M L L M} (T, \\phi (\\mathbf {c} _ {i})),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.397, + 0.482, + 0.419 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {l m} = \\operatorname {L M L o s s} (\\hat {\\mathbf {h}}, T), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.416, + 0.346, + 0.432 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m s e} = \\operatorname {M S E L o s s} \\left(\\phi^ {\\prime} (\\hat {\\mathbf {c}} _ {i}), \\tilde {\\mathbf {c}} _ {i}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.435, + 0.434, + 0.453 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i f f} = \\mathbb {E} _ {\\epsilon , t} | | \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, T, \\hat {\\mathbf {c}} _ {i}, \\mathbf {B} ^ {c}, \\mathbf {B} ^ {d}, t) | | ^ {2},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.462, + 0.484, + 0.675 + ], + "angle": 0, + "content": "where \\(T\\) is the text prompt. \\(\\phi\\) and \\(\\phi^{\\prime}\\) denote the input and output resamplers of MLLM, which consist of stacked attention layers to convert the embeddings between inner and outer dimensions. \\(\\hat{\\mathbf{h}}\\) refers to the MLLM predicted special token embeddings. We calculate LM Loss on it. \\(\\hat{\\mathbf{c}}_i\\) is the predicted character features. We compute MSE Loss between \\(\\hat{\\mathbf{c}}_i\\) and \\(\\tilde{\\mathbf{c}}_i\\), the ground truth target character embedding extracted from the feature extractor. By leveraging the character ID annotations of MangaZero, we can obtain features from the same character across different panels, thus facilitating the training of the MLLM feature adapter. The adapted character feature \\(\\hat{\\mathbf{c}}_i\\) is then passed to the image generator \\(\\epsilon\\), previously trained, to compute a diffusion loss. The total loss for training MLLM is expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.685, + 0.482, + 0.701 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {l m} \\mathcal {L} _ {l m} + \\lambda_ {m s e} \\mathcal {L} _ {m s e} + \\lambda_ {d i f f} \\mathcal {L} _ {d i f f}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.711, + 0.395, + 0.728 + ], + "angle": 0, + "content": "where \\(\\lambda_{lm}\\), \\(\\lambda_{mse}\\), and \\(\\lambda_{diff}\\) are loss weights." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.739, + 0.224, + 0.756 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.794 + ], + "angle": 0, + "content": "In this section, we thoroughly evaluate DiffSensei and compare it with baseline models." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.804, + 0.298, + 0.82 + ], + "angle": 0, + "content": "5.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Implementation details. The image generator is constructed on top of SDXL [26]. The feature extractor's weights are initialized using the pre-trained IP-AdapterPlus-SDXL [47], while the MLLM (Multi-modal Large Language Model) is initialized from SEED-X [8]. Other" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.379 + ], + "angle": 0, + "content": "newly introduced parameters, including the LoRA and resampler weights of the MLLM, are initialized randomly. In stage 1, the image generator is optimized using a learning rate of 1e-5. Stage 2 training employs a learning rate of 1e-4 and a LoRA rank of 64 [14]. The optimizer is AdamW [23]. The loss function coefficients \\(\\lambda_{lm}\\), \\(\\lambda_{mse}\\), and \\(\\lambda_{diff}\\) are set to 1.0, 6.0, and 1.0, respectively. We train 250k steps for the first stage and 20k for the second stage. The source character images are chosen randomly, with a \\(50\\%\\) probability of being from the same page; otherwise, they are selected from the target image. To handle varying image resolutions during training, we adopt the bucket-based approach from prior works [26], grouping images into resolution-specific buckets. For each training batch, images are loaded from the same resolution bucket. The batch size varies between 8 and 64 in stage 1, and between 8 and 128 in stage 2. This dynamic batch sizing is necessary to prevent out-of-memory (OOM) issues, especially when processing large-resolution images. Please see more details in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.38, + 0.909, + 0.682 + ], + "angle": 0, + "content": "Evaluation datasets and metrics. We evaluate our model using the MangaZero and Manga109 [2] evaluation sets. Note that the model is only trained on MangaZero. Characters in Manga109 are unseen during training, serving as a benchmark for generalization. To assess the generation quality of individual images, we employ autonomous metrics, which include Fréchet Inception Distance score (FID) [13], CLIP image-text similarity (CLIP) [27], DINO image similarity (DINO-I) [24], DINO character image similarity (DINO-C), and the dialog bounding box F1 score (F1 score). The source character images are randomly sampled on the same page. The dialog bounding boxes in the generated images are predicted using Magi [30]. For evaluating the story visualization quality of image sequences, human preference study proves more effective. We recruit human volunteers to choose their preferred story pages from our model's output and baseline models in the MangaZero evaluation set. The evaluation criteria include five key aspects: text-image alignment, style consistency, character consistency, image quality, and overall preference." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.683, + 0.909, + 0.789 + ], + "angle": 0, + "content": "Baselines. We select recent advanced story visualization models as our baselines, including StoryDiffusion [53], AR-LDM [25], StoryGen [21], SEED-Story [46], and MS-Diffusion [39]. StoryDiffusion [53] is a training-free method. We directly use an SDXL text-to-image model finetuned on MangaZero for evaluation. Despite that, we re-train other baselines on our dataset for a fair comparison." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.802, + 0.742, + 0.818 + ], + "angle": 0, + "content": "5.2. Comparison to Baselines" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.908, + 0.901 + ], + "angle": 0, + "content": "Quantitative comparison. We quantitatively compare our DiffSensei model with baseline models using automatic evaluation metrics. The results on the MangaZero evaluation set are presented in Tab. 2a. The results highlight that DiffSensei consistently outperforms the baseline mod" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28689" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.09, + 0.908, + 0.118 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on automatic metrics. Methods followed by “*” use reference images as input rather than characters. Methods marked by “†” means re-trained with dialog embedding." + }, + { + "type": "table_caption", + "bbox": [ + 0.177, + 0.13, + 0.42, + 0.142 + ], + "angle": 0, + "content": "(a) Comparison on MangaZero evaluation set." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.145, + 0.497, + 0.244 + ], + "angle": 0, + "content": "
    MethodFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    AR-LDM* [25]0.4090.2570.5480.5070.004
    StoryGen* [21]0.4110.2190.5360.4880.012
    SEED-Story* [46]0.4110.1690.4160.4050.006
    StoryDiffusion* [53]0.4090.2440.4610.3620.002
    MS-Diffusion† [39]0.4080.2290.6100.6410.720
    DiffSensei0.4070.2350.6180.6510.727
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.58, + 0.13, + 0.818, + 0.142 + ], + "angle": 0, + "content": "(b) Comparison on Manga109 evaluation set." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.145, + 0.897, + 0.243 + ], + "angle": 0, + "content": "
    MethodFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    AR-LDM* [25]0.4100.2540.5270.4910.005
    StoryGen* [21]0.4140.2140.5400.4930.004
    SEED-Story* [46]0.4130.1670.4420.4280.005
    StoryDiffusion* [53]0.4100.2380.4420.3550.001
    MS-Diffusion† [39]0.4100.2270.5840.6000.601
    DiffSensei0.4100.2370.5880.6000.648
    " + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.265, + 0.29, + 0.293 + ], + "angle": 0, + "content": "Story Summary: A sailor hears a sound in the cabin, walks up to the deck, and discovers a beautiful ghost girl. He tries to embrace her..." + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.257, + 0.434, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.435, + 0.258, + 0.563, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.258, + 0.735, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.264, + 0.89, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.3, + 0.208, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.3, + 0.321, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.301, + 0.432, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.438, + 0.301, + 0.563, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.301, + 0.673, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.301, + 0.784, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.301, + 0.896, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.514, + 0.908, + 0.557 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison with baselines. Baselines followed by a \\*\\* use reference images as input rather than character images. Methods marked by \\*\\* means re-trained with dialog embedding. Our model excels at preserving the characters while following the text prompt. Our DiffSensei successively generates highlighted details in panel captions. Better viewed with zoom-in." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.583, + 0.475, + 0.695 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.103, + 0.708, + 0.471, + 0.723 + ], + "angle": 0, + "content": "Figure 5. Human preference study on MangaZero eval set." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.735, + 0.486, + 0.901 + ], + "angle": 0, + "content": "els across five key metrics. Our model improves 0.06 in the CLIP metrics compared to the multi-subject customization baseline, MS-Diffusion [39], which struggles to modify characters' states effectively in response to textual prompts. Furthermore, DiffSensei demonstrates superior image quality and character preservation, as evidenced by higher DINO-I and DINO-C scores. Although AR-LDM [25] achieves higher CLIP metrics, it suffers from poor image quality and lacks the architectural capability to manage multiple characters, resulting in low DINO-C scores. In contrast, our method strikes a balance be" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.907, + 0.688 + ], + "angle": 0, + "content": "tween maintaining character appearances and adapting to text prompts. We also compare the Manga109 evaluation set with the results shown in Tab. 2b. When using previously unseen characters as inputs, our model continues to outperform the baselines. These results underscore the strong generalization ability of DiffSensei, demonstrating effective adaptation to new characters." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.909, + 0.795 + ], + "angle": 0, + "content": "In Fig. 5, we present the results of a human preference study comparing our model to the baselines across several dimensions. Our model receives the highest ratings from human evaluators, particularly in terms of overall preference, character consistency, and image quality. These findings confirm that DiffSensei excels in rendering vivid and engaging manga stories." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Qualitative comparison. Fig. 4 shows a qualitative comparison between DiffSensei and baseline models. The results illustrate that our model significantly outperforms the baselines in generating an entire page of a manga story. SEED-Story [46] employs an MLLM to create captions for each panel, leading to unnatural narrative text and chaotic story generation that fails to form a coherent story. StoryD" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "28690" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.091, + 0.23, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.235, + 0.091, + 0.358, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.091, + 0.505, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.091, + 0.626, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.091, + 0.762, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.092, + 0.901, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.276, + 0.908, + 0.307 + ], + "angle": 0, + "content": "Figure 6. Qualitative results. Character images in red boxes are from Manga109 (The rightmost example). Our DiffSensei can generate vivid manga pages in various scenarios. Better viewed with zoom-in. More results can be found in the appendix." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.329, + 0.483, + 0.372 + ], + "angle": 0, + "content": "Table 3. Ablation study. CM is character masked attention injection. DM is dialog masked encoding. Magi means using Magi [30] image encoder. MLLM means using MLLM for stage 2 training." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.382, + 0.48, + 0.451 + ], + "angle": 0, + "content": "
    CMDMMagiMLLMFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    0.4100.2300.5930.6100.361
    ✓0.4110.2250.5910.6370.364
    ✓✓0.4070.2280.6000.6350.653
    ✓✓✓0.4080.2310.6180.6480.718
    ✓✓✓✓0.4070.2350.6180.6510.727
    " + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.476, + 0.484, + 0.613 + ], + "angle": 0, + "content": "iffusion [53] is limited to producing fixed-resolution images due to its self-attention sharing mechanism, restricting its ability to generate diverse images. It shows inferior results, probably because the input reference panel has an unbalanced aspect ratio. MS-Diffusion [39] trains with source character images from the target panel and lacks the flexibility to modify characters' states effectively. In contrast, our method excels in text-following, character preservation, and overall story presentation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.621, + 0.274, + 0.637 + ], + "angle": 0, + "content": "5.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.643, + 0.483, + 0.75 + ], + "angle": 0, + "content": "Fig. 6 shows several manga pages generated by DiffSensei. The results demonstrate that our method can generate vivid manga panels and provide visually plausible results for the customized manga generation task. Our model can also generalize to unseen characters, as illustrated in the rightmost example, with character images from Manga109 [2] as input. Please see more results in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.758, + 0.245, + 0.774 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Tab. 3 presents the quantitative ablation study of DiffSensei, where we systematically remove components to assess their impact. Specifically, when the MLLM component, serving as the flexible character feature adapter, is excluded, the CLIP metrics decrease by \\(1.73\\%\\), and the DINO-C score also drops, underscoring its role in enhancing transferring character to the text-derived states. The absence of the Magi [30] image encoder results in a general decline in met-" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.33, + 0.908, + 0.633 + ], + "angle": 0, + "content": "rics, particularly in image quality and character similarity, highlighting the importance of the Magi encoder for effectively encoding manga characters. Magi is trained specifically on manga datasets, performing better at preserving manga characters. To investigate alternative methods for encoding character and dialog layout conditions, we experimented with replacing the dialog embedding technique by inputting the Fourier embeddings of dialog bounding boxes into the timestep embedding of SDXL [26]. This modification led to a significant decrease in layout control, evidenced by the F1 score plummeting from 0.653 to 0.364, demonstrating that directly incorporating dialog embeddings into the latent is a superior approach for encoding dialog layouts. Furthermore, we explored adding the Fourier embeddings of character bounding boxes to the character features as an alternative to masked attention injection. This change caused a marked drop in the DINO-C metric, reaffirming the effectiveness of our original masked attention strategy. For comprehensive effect showcases, please see the qualitative ablation study in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.648, + 0.634, + 0.664 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.907, + 0.854 + ], + "angle": 0, + "content": "This paper introduces DiffSensei, a novel framework for multi-character customized story visualization that integrates a diffusion-based image generator with an MLLM as a text-compatible identity adapter. Key innovations include masked attention control for character layout management, dialog layout embedding, and an MLLM-based feature adapter for flexible character customization. Supported by the proposed MangaZero dataset, comprising 43,264 manga pages and 427,147 panels, DiffSensei achieves superior, character-consistent panels that dynamically respond to textual prompts, surpassing existing methods and advancing the field of story visualization." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported by the National Key Research and Development Program of China (No. 2023YFC3807600)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28691" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.091, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.245, + 0.128 + ], + "angle": 0, + "content": "[1] Mangadex, 2024. 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.131, + 0.483, + 0.185 + ], + "angle": 0, + "content": "[2] Kiyoharu Aizawa, Azuma Fujimoto, Atsushi Otsubo, Toru Ogawa, Yusuke Matsui, Koki Tsubota, and Hikaru Ikuta. Building a manga dataset \"manga109\" with annotations for multimedia applications. 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In NeurIPS, 2024. 1, 2, 6, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28693" + } + ] +] \ No newline at end of file diff --git a/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/fada47c4-9d9c-4ce9-8477-3cca25b37313_origin.pdf b/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/fada47c4-9d9c-4ce9-8477-3cca25b37313_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..79ea8121daaa3a96c2e90da473a30c43fdafe927 --- /dev/null +++ b/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/fada47c4-9d9c-4ce9-8477-3cca25b37313_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:11e7d186c02a05c5685b0be8ca53e11653df6f40cee567507b61505c5982925a +size 2649726 diff --git a/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/full.md b/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2730a2223a5495c69317fb5bfeffcec1940736da --- /dev/null +++ b/2025/DiffSensei_ Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation/full.md @@ -0,0 +1,312 @@ +# DiffSensei: Bridging Multi-Modal LLMs and Diffusion Models for Customized Manga Generation + +Jianzong Wu $^{1,2}$ Chao Tang $^{1}$ Jingbo Wang $^{2}$ Yanhong Zeng $^{2}$ Xiangtai Li $^{3,4}$ Yunhai Tong $^{1}$ + +1 Peking University 2 Shanghai AI Laboratory 3 Nanyang Technological University 4 Bytedance Seed + +Project Page: https://jianzongwu.github.io/projects/diffsensei/ + +Email: jzwu@stu.pku.edu.cn, xiangtai94@gmail.com + +![](images/69509d966de2f697b0c2ee479491c82317e04a0b3797b9fa5d6acbbd606f1e9c.jpg) +(a) Customized manga generation + +![](images/85d664683d23a0cdc82b3f17b96aceb856c73931504cc303f37821a699f3eefe.jpg) +(b) Real human manga creation +Figure 1. Results of DiffSensei. (a) Customized manga generation with controllable character images, panel captions, and layout conditions. Our DiffSensei successfully generates detailed character expressions and states following the panel captions. (b) Manga creation for real human images. The dialogues are post-edited by humans. The continuation is in the Appendix. We strongly recommend that the readers see the Appendix for more comprehensive results. Manga reading order: Right to left. Top to bottom. + +# Abstract + +Story visualization, the task of creating visual narratives from textual descriptions, has seen progress with text-to-image generation models. However, these models often lack effective control over character appearances and interactions, particularly in multi-character scenes. To address these limitations, we propose a new task: customized manga generation and introduce DiffSensei, an innovative framework specifically designed for generating manga with dynamic multi-character control. DiffSensei integrates a diffusion-based image generator with a multimodal large language model (MLLM) that acts as a text-compatible identity adapter. Our approach employs masked cross-attention to seamlessly incorporate character features, enabling precise layout control without direct pixel transfer. Additionally, the MLLM-based adapter adjusts character features to align with panel-specific text cues, allowing flex + +ible adjustments in character expressions, poses, and actions. We also introduce MangaZero, a large-scale dataset tailored to this task, containing 43,264 manga pages and 427,147 annotated panels, supporting the visualization of varied character interactions and movements across sequential frames. Extensive experiments demonstrate that DiffSensei outperforms existing models, marking a significant advancement in manga generation by enabling text-adaptable character customization. The code, model, and dataset are open-sourced to the community. + +# 1. Introduction + +Story visualization, the process of generating visual narratives from textual descriptions, is a rapidly evolving field [5, 18, 21, 25, 37, 46, 53]. Among its various applications, manga generation holds particular significance due + +to its popularity and unique narrative requirements. Unlike traditional story visualization, manga demands consistent characters across panels, precise layout control for positioning multiple characters, and the seamless integration of dialogues in a coherent, visually engaging manner. + +Currently, manga generation remains an underexplored area. Most existing research focuses on low-level imagedto-image tasks, primarily converting general images to a manga style [20, 33, 48, 50]. While these tasks enhance the visual appeal of static images, they do not extend to generating fully customized manga content from scratch. In general story visualization, current approaches have demonstrated some success in generating coherent image sequences from text. Still, they cannot often customize the characters across scenes [21, 25, 46, 53], a critical requirement for manga generation. Additionally, they do not provide the necessary control over layouts and dialogue placements, which are also essential for manga. A likely reason for these limitations is that existing story visualization datasets typically lack character annotations and layout controls [15, 18, 21, 46]. Another research direction has explored zero-shot character customization, showing promise for achieving character customization across manga panels [4, 9, 19, 29, 36, 39, 47]. However, these approaches often result in rigid "copy-pasting" effects [4, 39, 47], which limit expressive character variation and detract from narrative depth. This limitation largely stems from the scarcity of datasets capturing multiple appearances of the same character in varied expressions and poses. + +To address these limitations, we propose a new task: customized manga generation. As illustrated in Fig. 1, this task focuses on creating manga images with multiple characters, each customized based on a character image and positioned according to user input. Characters must dynamically adapt to text prompts, altering their expressions, motions, and poses as the narrative unfolds. Dialog layout should also be managed to generate expressive manga panels. Compared to traditional story visualization tasks, this proposed task prioritizes essential manga-specific controllability, aiming to generate vivid manga panels that are both coherent and visually engaging while supporting the customization of multiple characters. To address the lack of a dedicated dataset for customized manga generation, we collect a dataset of Japanese black-and-white manga, forming the basis of the proposed task. The resulting dataset, MangaZero, is the first large-scale collection designed to support multi-character, multi-state manga generation. + +To tackle this task, we introduce a novel framework, DiffSensei, which leverages a diffusion-based image generator to produce customized manga panels. However, we observe that, even with training on multiple appearances of the same character, the generated portraits often tend to rigidly follow the pixel distribution of the input character image, re + +sulting in limited variations in appearance, pose, and motion based on the text input. Inspired by recent advancements in image editing using Multimodal Large Language Models (MLLMs) [6, 8, 16, 34, 40-43, 46, 49], we propose using an MLLM as a text-compatible character adapter. This approach enables seamless, dynamic adjustments to characters in response to textual cues, thereby supporting coherent and expressive manga panel generation. Additionally, we incorporate masked attention injection to manage character layout, along with a dialog embedding technique tailored specifically for manga, allowing for precise control over dialog placement. Through extensive experimentation, we validate DiffSensei's capability to generate coherent, expressive manga panels that maintain narrative consistency and offer improved character control. This represents a significant advancement in story visualization. + +- We introduce a new task: customized manga generation, focused on generating manga images with multiple characters, each dynamically adapting to text prompts and positioned according to layout specifications. +- We present MangaZero, the first large-scale dataset specifically designed for multi-character, multi-state manga generation, addressing a significant gap in story visualization training data. The dataset will be released for the image generation community. +- We propose DiffSensei. As far as we know, it is the first framework for customized manga generation that links diffusion models and MLLMs. The MLLM serves as an adaptable character feature adapter, enabling characters to respond dynamically to textual cues. Extensive experiments demonstrate the effectiveness of DiffSensei. + +# 2. Related Work + +Story visualization. Story visualization, the process of generating visual narratives based on given stories, is rapidly evolving. Many approaches can generate consistent image sequences derived from story content [5, 21, 25, 37, 46, 53]. Despite recent advancements, the field faces significant limitations. Most existing methods generate story images solely from text and image-level prompts [21, 25, 46, 53], which restricts control over individual characters. This limited control over characters reduces the flexibility and depth of story visualization. A key factor is that current training datasets [10, 15, 18, 21, 46] lack character-specific annotations. In response to the data limit, recent works [5, 37] explore multi-character control using training-free methods that leverage existing subject preservation techniques, such as IP-Adapter [47]. Other works [4, 7, 9, 11, 12, 19, 29, 32, 36, 39, 44, 47] try to train diffusion models for a multi-character customized generation. However, these approaches often result in a "copy-pasting" effect, restricting the diversity of expressions and actions needed for dynamic storytelling. For training-free + +Table 1. Comparison between MangaZero and related publicly available datasets. A story is defined as a sequence of continuous images annotated consistently with character IDs. In MangaZero, a story means a manga page. A panel means a distinct story image, or called frame [21, 46]. Most series in MangaZero are still popular in 2024. Please see the Appendix for the dataset details. + +
    DatasetTypeResolution#Series#Stories#PanelsCaptionAnnotations CharacterDialogOrigin
    PororoSV [18]AnimationFix115,33673,665✓××2003-2016
    FlintstonesSV [10]AnimationFix125,184122,560✓✓×1960-1966
    StorySalon [21]AnimationFix44618,255159,778✓××YouTube
    StoryStream [46]AnimationFix312,614257,850✓××1939-2013
    Manga109 [2]B/W MangaVary10910,602103,850×✓✓1970-2010
    MangaZeroB/W MangaVary4843,264427,147✓✓✓1974-2024
    + +methods, combining multiple models can significantly slow down inference speeds. To address these challenges, we first introduce a large-scale manga generation dataset with finely curated character annotations and then develop a novel framework utilizing diffusion models and MLLMs that enables the dynamic generation of manga panels. + +Manga generation. The field of black-and-while manga generation has received limited exploration. Most existing researches focus on low-level image-to-image tasks, primarily transferring general images to a manga style [20, 33, 48, 50]. Recent works contribute to manga content understanding [30, 31, 35]. In contrast, we propose the customized manga generation task beyond style transfer to offer complete character and story-driven manga generation. + +MLLMs for personalized image generation. MLLMs have shown remarkable potential in personalized image generation, particularly for tasks involving image editing and customization [3, 6, 8, 16, 34, 40-42, 46, 49]. Notably, CAFE [52] explores customizing subject appearances through textual instructions. However, MLLM-driven image generation for multi-character narratives remains an open challenge, primarily due to the difficulties in maintaining inter-character relationships and scene continuity. Our framework proposes an MLLM-based identity adapter that enhances dynamic story consistency in multi-character manga generation. In contrast to previous works, our framework takes multi-character features as input and edits these features collectively, following the text prompt, enabling flexible subject editing across multiple characters. + +# 3. The MangaZero Dataset + +In this section, we first define the problem in Sec. 3.1. Then, we introduce the dataset construction pipeline in Sec. 3.2. + +# 3.1. Problem Formulation + +We introduce a challenging new task: customized manga generation. This task focuses on generating manga images where multiple characters, each with their distinct image inputs, are customized and positioned by users. Importantly, + +characters must adapt to the text prompts by modifying their expressions, motions, and poses dynamically, even when only a limited set of character images is available. To generate a manga story across $N$ panels (or frames), the inputs include: text prompts for each panel $T_{0}, T_{1}, \ldots, T_{N-1}$ , character images $\mathbf{I} = I_{0}, I_{1}, \ldots, I_{K-1}$ , character bounding boxes for each panel $\mathbf{B}_{0}^{c}, \mathbf{B}_{1}^{c}, \ldots, \mathbf{B}_{N-1}^{c}$ , and dialogue bounding boxes for each panel $\mathbf{B}_{0}^{d}, \mathbf{B}_{1}^{d}, \ldots, \mathbf{B}_{N-1}^{d}$ . The visualization of a panel is represented as $P_{i} = \Phi_{\theta}(T_{i}, \mathbf{I}, \mathbf{B}_{i}^{c}, \mathbf{B}_{i}^{d})$ , where $\Phi$ is the overall model function and $\theta$ represents the model's learned parameters. + +Discussion. This task diverges from existing story visualization and continuation tasks [21, 25]. Specifically, in story visualization tasks, a panel is produced using $P_{i} = \Phi_{\theta}(T_{i})$ , while in story continuation tasks, the panel generation depends on previous panels as $P_{i} = \Phi_{\theta}(T_{i}, T_{i-1}, P_{i-1})$ for $i > 0$ . Both lack explicit character control, a crucial element in storytelling. Furthermore, the proposed task differs from subject-driven image generation approaches [29, 39, 47], as it demands that models not only generate accurate character representations but also modify characters' attributes in response to panel captions and layouts, resulting in varied and coherent narrative visuals. Our experiments, detailed in Sec. 5, demonstrate that our model significantly surpasses baseline models in these critical aspects. + +# 3.2. Dataset Construction + +In this section, we introduce the proposed large-scale manga story visualization dataset MangaZero. + +Comparison with related datasets. A comprehensive comparison with existing datasets is presented in Tab. 1. In contrast to current manga and story visualization datasets, the proposed MangaZero dataset stands out as being larger in size, newer in source, richer in annotations, diverse in manga series, and varied in panel resolutions. Compared to the well-known black-and-white manga dataset Manga109 [2], the MangaZero dataset encompasses more manga series published after the year 2000, which inspired its naming. Additionally, MangaZero includes famous se + +![](images/fb2c4ca29fad8bf9f19c3fd78412f1ce1cb1fbce39eeb7558ac2ac2d089ed158.jpg) +Figure 2. We construct MangaZero through three steps: 1) Download manga pages from the internet. 2) Annotate manga panels autonomously with pre-trained models. 3) Human calibration for the character ID annotation. + +ries from before the year 2000 that are not featured in Manga109, such as Doraemon (1974). + +Construction pipeline. To build our dataset, we first download manga pages from the internet, explicitly sourcing images from MangaDex [1]. It is important to note that all data will be used solely for academic research, not commercial purposes. We select 48 manga series and download up to 1,000 pages per series, resulting in 43,264 double-page images. These images are then annotated using pretrained models. For manga-specific annotations, including panel bounding boxes, character bounding boxes, character IDs, and dialog bounding boxes, we employ the recent manga understanding model, Magi [30]. It should be noted that character ID labeling is consistent only within individual pages, which is sufficient for achieving coherent character cross-reference. Once the panel bounding boxes are obtained, we utilize LLaVA-v1.6-34B [22] to generate captions for each panel. However, we observe that character ID labeling has relatively low accuracy, which poses a significant challenge for training purposes. To address this, human annotators refine the machine-generated labels, resulting in accurate and clean annotations. Finally, we split 96 pages (2 for each series) as the evaluation set and the remaining 43,168 pages as the training set. + +# 4. Method + +In this section, we introduce the architecture of the proposed framework, DiffSensei, which generates vivid manga panels with precise character and dialog layout control while adapting the characters' status flexibly. + +Motivation. There are two critical problems in customizing objects and layouts in image generation: 1) Preserving the subjects' intrinsic features while avoiding direct copy-paste + +from source images, and 2) Ensuring reliable layout control with minimal computational cost during both training and inference. To avoid copy-pasting effects, our model converts character image features into tokens, preventing the direct transfer of fine-grained pixel details. Additionally, we integrate an MLLM as a character image feature adapter. The MLLM adapter receives source character features and panel captions as inputs, generating text-compatible target character features. Compared with previous customization work [39], this approach enables text-compatible character encoding and flexible character adaptation to captions. For layout control, we employ lightweight masked encoding techniques for both character and dialog layouts, significantly reducing computational costs compared with previous works [38, 45] while maintaining high accuracy in both training and inference phases. Experiment results in Sec. 5 demonstrate the effectiveness of our design. + +Multi-character feature extraction. As illustrated in Fig. 3, we initially extract local image features using CLIP and image-level features from a manga image encoder. These two sets of features are then processed by a feature extractor, which is implemented as a resampler module [47]. This process can be formalized as follows: + +$$ +\mathbf {c} _ {i} = \operatorname {R e s a m p l e r} ([ \operatorname {C L I P} (\mathbf {I}), \psi (\mathbf {I}) ], \mathbf {q}, \mathbf {q} _ {\text {v o i d}}), \tag {1} +$$ + +where $\psi$ represents the manga image encoder. $\mathbf{q}$ and $\mathbf{q}_{\text{void}}$ are trainable query vectors for character and non-character features, respectively. $\mathbf{q}$ re-samples the image features into the U-Net's cross-attention dimension, while $\mathbf{q}_{\text{void}}$ guides the cross-attention in regions without characters in the layout. $\mathbf{c}_i \in \mathbb{R}^{B \times ((N_c + 1) \times N_q) \times C}$ is the output feature for all characters, where $B$ is the batch size, $N_c$ is the maximum number of characters per panel (padded with all-zero features as needed), $N_q$ is the number of query tokens per character, and $C$ is the cross-attention dimension of the U-Net. Through compressing the character images into a few tokens, DiffSensei avoids encoding fine-grained spatial features from reference images into the model [21, 51]. This enables focusing on the characters' semantic representations rather than rigid pixel distributions. + +Masked cross-attention injection. We replicate the key and value matrices in each cross-attention layer, creating separate character cross-attention layers. This allows the image query features to attend to text and character cross-attentions independently and combine the results from both attentions. In the character cross-attention, we apply a masked cross-attention injection mechanism to control the layout of each character. Here, each character feature only attends to query features within its designated bounding box region. In areas without characters, query features attend to + +![](images/06fd9a85d5bdaef5ea1f712d6315e93734cf9495c217db5cdcf75dd5926de8e8.jpg) +Figure 3. The architecture of DiffSensei. In the first stage, we train a multi-character customized manga image generation model with layout control. The dialog embedding is added to the noised latent after the first convolution layer. All the parameters in the U-Net and feature extractor are trained. In the second stage, we finetune LoRA and resampler weights of an MLLM to adapt the source character features corresponding to the text prompt. We use the model in the first stage as the image generator and freeze its weights. + +a placeholder vector, $\mathbf{q}_{\text{void}}$ . This can be formulated as: + +$$ +\hat {\mathbf {z}} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} \mathbf {K} _ {t} ^ {\top}}{\sqrt {d}}\right) \mathbf {V} _ {t} + \tag {2} +$$ + +$$ +\boldsymbol {\alpha} \cdot \operatorname {S o f t m a x} \left(\frac {\mathbf {Q K} _ {i} ^ {\top}}{\sqrt {d}} + \mathbf {M}\right) \mathbf {V} _ {i}, +$$ + +where $\mathbf{Q} = \mathbf{z}\mathbf{W}_q$ , $\mathbf{K}^t = \mathbf{c}_t\mathbf{W}_k^t$ , $\mathbf{V}^t = \mathbf{c}_t\mathbf{W}_v^t$ , $\mathbf{K}^i = \mathbf{c}_i\mathbf{W}_k^i$ , $\mathbf{V}^i = \mathbf{c}_i\mathbf{W}_v^i$ . $\mathbf{Q}$ is the query, $\mathbf{W_q}$ , $\mathbf{W_k^t}$ , $\mathbf{W_v^t}$ are query, key, and value projection matrices for the text cross-attention. $\mathbf{W_k^t}$ , $\mathbf{W_v^t}$ are key and value projection matrices for the character cross-attention, initialized from $\mathbf{W_k^t}$ and $\mathbf{W_v^t}$ . $d$ is the key dimension. $\mathbf{c}_t$ , $\mathbf{c}_i$ are text and character features respectively. $\mathbf{z}$ , $\hat{\mathbf{z}}$ are the input and output image features. $\alpha$ is a hyperparameter that controls character attention weight. $\mathbf{M}$ is an attention mask to manage the characters' layout. Its values are defined as follows: + +$$ +\mathbf {M} [ i, j ] = \left\{ \begin{array}{l l} 0, & \text {i f} j = N _ {c} \text {a n d} i \notin \mathbf {B} ^ {c} \text {o r} \\ & i \in \mathbf {B} ^ {c} [ j ] \\ - \infty , & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +where $i$ denotes the position of query tokens, $j \in \{0,1,\dots,N_c\}$ is the character indices. The $N_{c}$ -th character feature represents the placeholder vector $\mathbf{q}_{void}$ . $\mathbf{B}^c [j]$ is the bounding box of the $j$ -th character. The masked attention injection mechanism ensures that each character attends only to its specified bounding box region, while areas without characters attend to the placeholder vector. This technique achieves efficient and precise layout control for each character with minimal computational overhead. + +Dialog layout encoding. Panels with dialog are a distinctive feature of manga images. However, most current text-to-image models struggle to generate coherent, readable text [26, 28]. While some recent models can produce stable text, they remain limited in terms of text length [17]. Generating extended text, such as dialogues, continues to pose challenges. Therefore, we propose controlling the layout of dialogs rather than the content itself. In this approach, human artists can manually edit the text within dialog bubbles, leaving image generation to the models. Concretely, we introduce a trainable embedding to represent the dialog layout. The dialog embedding is first expanded to match the spatial shape of the noised latent and then masked with the dialog layout. By summing the masked dialog embedding with the noised latent, we can encode dialog positions within the image generator. This process is expressed as: + +$$ +\hat {\mathbf {z}} _ {t} = \operatorname {C o n v} \left(\mathbf {z} _ {t}\right) + \operatorname {E x p a n d} \left(\mathbf {e} _ {d}, \mathbf {z} _ {t}\right) \cdot \mathbf {M} _ {d}, \tag {4} +$$ + +where $\mathbf{e}_d$ is the trainable dialog embedding, $\mathbf{z}_t$ is the noised latent in time step $t$ , Expand is a function that expands $\mathbf{e}_d$ to the latent shape, and $\mathbf{M}_d$ is the dialog region mask derived from input dialog bounding boxes $\mathbf{B}^d$ . The output, $\hat{\mathbf{z}}_t$ , serves as a dialog-Layout-aware latent representation. This is then input into the U-Net for noise prediction. The dialog embedding effectively encodes the dialog layout, adding minimal computational overhead in space and time. + +MLLM as text-compatible character feature adapter. After training the image generator, our model can effectively create manga panels that adhere to specified character appearances and layout conditions. However, the model + +often rigidly follows the input character images, lacking flexibility in adjusting expressions, poses, or motions based on panel captions. We propose incorporating MLLM as a text-compatible character feature adapter. This approach allows dynamic modifications to character states based on text prompts. A training sample for MLLM is organized as [panel caption, source character image features, target character image features]. The image features are encapsulated by two special tokens, $\langle \mathrm{IMG} \rangle$ and $\langle \mathrm{IMG} \rangle$ . To achieve this, we compute Language Modeling (LM) Loss on the special tokens to constrain the output format and Mean Squared Error (MSE) Loss to guide the target character features based on the panel caption. To ensure that the edited character features align with the image generator, we further pass the generated features into U-Net's character cross-attention and compute diffusion loss. In this stage, only the LoRA and resampler weights in MLLM are updated. This process can be formalized as follows: + +$$ +\hat {\mathbf {h}}, \hat {\mathbf {c}} _ {i} = \operatorname {M L L M} (T, \phi (\mathbf {c} _ {i})), +$$ + +$$ +\mathcal {L} _ {l m} = \operatorname {L M L o s s} (\hat {\mathbf {h}}, T), \tag {5} +$$ + +$$ +\mathcal {L} _ {m s e} = \operatorname {M S E L o s s} \left(\phi^ {\prime} (\hat {\mathbf {c}} _ {i}), \tilde {\mathbf {c}} _ {i}\right), +$$ + +$$ +\mathcal {L} _ {d i f f} = \mathbb {E} _ {\epsilon , t} | | \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {t}, T, \hat {\mathbf {c}} _ {i}, \mathbf {B} ^ {c}, \mathbf {B} ^ {d}, t) | | ^ {2}, +$$ + +where $T$ is the text prompt. $\phi$ and $\phi^{\prime}$ denote the input and output resamplers of MLLM, which consist of stacked attention layers to convert the embeddings between inner and outer dimensions. $\hat{\mathbf{h}}$ refers to the MLLM predicted special token embeddings. We calculate LM Loss on it. $\hat{\mathbf{c}}_i$ is the predicted character features. We compute MSE Loss between $\hat{\mathbf{c}}_i$ and $\tilde{\mathbf{c}}_i$ , the ground truth target character embedding extracted from the feature extractor. By leveraging the character ID annotations of MangaZero, we can obtain features from the same character across different panels, thus facilitating the training of the MLLM feature adapter. The adapted character feature $\hat{\mathbf{c}}_i$ is then passed to the image generator $\epsilon$ , previously trained, to compute a diffusion loss. The total loss for training MLLM is expressed as follows: + +$$ +\mathcal {L} = \lambda_ {l m} \mathcal {L} _ {l m} + \lambda_ {m s e} \mathcal {L} _ {m s e} + \lambda_ {d i f f} \mathcal {L} _ {d i f f}, \tag {6} +$$ + +where $\lambda_{lm}$ , $\lambda_{mse}$ , and $\lambda_{diff}$ are loss weights. + +# 5. Experiments + +In this section, we thoroughly evaluate DiffSensei and compare it with baseline models. + +# 5.1. Experimental Settings + +Implementation details. The image generator is constructed on top of SDXL [26]. The feature extractor's weights are initialized using the pre-trained IP-AdapterPlus-SDXL [47], while the MLLM (Multi-modal Large Language Model) is initialized from SEED-X [8]. Other + +newly introduced parameters, including the LoRA and resampler weights of the MLLM, are initialized randomly. In stage 1, the image generator is optimized using a learning rate of 1e-5. Stage 2 training employs a learning rate of 1e-4 and a LoRA rank of 64 [14]. The optimizer is AdamW [23]. The loss function coefficients $\lambda_{lm}$ , $\lambda_{mse}$ , and $\lambda_{diff}$ are set to 1.0, 6.0, and 1.0, respectively. We train 250k steps for the first stage and 20k for the second stage. The source character images are chosen randomly, with a $50\%$ probability of being from the same page; otherwise, they are selected from the target image. To handle varying image resolutions during training, we adopt the bucket-based approach from prior works [26], grouping images into resolution-specific buckets. For each training batch, images are loaded from the same resolution bucket. The batch size varies between 8 and 64 in stage 1, and between 8 and 128 in stage 2. This dynamic batch sizing is necessary to prevent out-of-memory (OOM) issues, especially when processing large-resolution images. Please see more details in the Appendix. + +Evaluation datasets and metrics. We evaluate our model using the MangaZero and Manga109 [2] evaluation sets. Note that the model is only trained on MangaZero. Characters in Manga109 are unseen during training, serving as a benchmark for generalization. To assess the generation quality of individual images, we employ autonomous metrics, which include Fréchet Inception Distance score (FID) [13], CLIP image-text similarity (CLIP) [27], DINO image similarity (DINO-I) [24], DINO character image similarity (DINO-C), and the dialog bounding box F1 score (F1 score). The source character images are randomly sampled on the same page. The dialog bounding boxes in the generated images are predicted using Magi [30]. For evaluating the story visualization quality of image sequences, human preference study proves more effective. We recruit human volunteers to choose their preferred story pages from our model's output and baseline models in the MangaZero evaluation set. The evaluation criteria include five key aspects: text-image alignment, style consistency, character consistency, image quality, and overall preference. + +Baselines. We select recent advanced story visualization models as our baselines, including StoryDiffusion [53], AR-LDM [25], StoryGen [21], SEED-Story [46], and MS-Diffusion [39]. StoryDiffusion [53] is a training-free method. We directly use an SDXL text-to-image model finetuned on MangaZero for evaluation. Despite that, we re-train other baselines on our dataset for a fair comparison. + +# 5.2. Comparison to Baselines + +Quantitative comparison. We quantitatively compare our DiffSensei model with baseline models using automatic evaluation metrics. The results on the MangaZero evaluation set are presented in Tab. 2a. The results highlight that DiffSensei consistently outperforms the baseline mod + +Table 2. Quantitative comparisons on automatic metrics. Methods followed by “*” use reference images as input rather than characters. Methods marked by “†” means re-trained with dialog embedding. +(a) Comparison on MangaZero evaluation set. + +
    MethodFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    AR-LDM* [25]0.4090.2570.5480.5070.004
    StoryGen* [21]0.4110.2190.5360.4880.012
    SEED-Story* [46]0.4110.1690.4160.4050.006
    StoryDiffusion* [53]0.4090.2440.4610.3620.002
    MS-Diffusion† [39]0.4080.2290.6100.6410.720
    DiffSensei0.4070.2350.6180.6510.727
    + +(b) Comparison on Manga109 evaluation set. + +
    MethodFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    AR-LDM* [25]0.4100.2540.5270.4910.005
    StoryGen* [21]0.4140.2140.5400.4930.004
    SEED-Story* [46]0.4130.1670.4420.4280.005
    StoryDiffusion* [53]0.4100.2380.4420.3550.001
    MS-Diffusion† [39]0.4100.2270.5840.6000.601
    DiffSensei0.4100.2370.5880.6000.648
    + +Story Summary: A sailor hears a sound in the cabin, walks up to the deck, and discovers a beautiful ghost girl. He tries to embrace her... + +![](images/b52522b814fe01ec2c1235cb13cddf0648c4dfef23e5d9a3b2c6bb83394c0402.jpg) + +![](images/73158a2ec00a54e3ca91861aa9ede5438635d1336ba566f4a3bfad6cdc639d97.jpg) + +![](images/731b398cce9e0c06f9d9cccb61e7230d5f373bc0948d37df36e6f4db4f1c97de.jpg) + +![](images/ccd0859941344e6aa84e89136bdb1811cca4eb664bcc21f73bbbcdd54d3e8d86.jpg) + +![](images/1a1622d7a3a8e1e29cb27a7f80a0c85683f37fbf33d3f826eabb169487d3c9a5.jpg) +Figure 4. Qualitative comparison with baselines. Baselines followed by a \*\* use reference images as input rather than character images. Methods marked by \*\* means re-trained with dialog embedding. Our model excels at preserving the characters while following the text prompt. Our DiffSensei successively generates highlighted details in panel captions. Better viewed with zoom-in. + +![](images/68a273d5b63c2d0199378b1a9429715aa4cee164fdbf8c981fc91e4619ec2a46.jpg) + +![](images/f33bf9ec5f480c8d7dc21bd72f25f995ad3414d1b8709b5752862d4855f54979.jpg) + +![](images/103f437e3802a1df3b4c1a56b6e8a0706ee628571825b0cce1213df834d6cba7.jpg) + +![](images/0ef2cda4ff2c12928e809c0eae2a94f83f5de23e800d9673a0e9f865cee5ec19.jpg) + +![](images/daefc6b632c87351b7faea032792b4d451af6d4e760f4a259e690bbbceb4ade4.jpg) + +![](images/73c5f6e27557f1c0dc647c64276221af2cb9a3aaaa6f52833973803bdcd5d495.jpg) + +![](images/7a3d44ac14164cd495db218e1d1232c60def80c4340ed8cb10f3ffd87668309a.jpg) +Figure 5. Human preference study on MangaZero eval set. + +els across five key metrics. Our model improves 0.06 in the CLIP metrics compared to the multi-subject customization baseline, MS-Diffusion [39], which struggles to modify characters' states effectively in response to textual prompts. Furthermore, DiffSensei demonstrates superior image quality and character preservation, as evidenced by higher DINO-I and DINO-C scores. Although AR-LDM [25] achieves higher CLIP metrics, it suffers from poor image quality and lacks the architectural capability to manage multiple characters, resulting in low DINO-C scores. In contrast, our method strikes a balance be + +tween maintaining character appearances and adapting to text prompts. We also compare the Manga109 evaluation set with the results shown in Tab. 2b. When using previously unseen characters as inputs, our model continues to outperform the baselines. These results underscore the strong generalization ability of DiffSensei, demonstrating effective adaptation to new characters. + +In Fig. 5, we present the results of a human preference study comparing our model to the baselines across several dimensions. Our model receives the highest ratings from human evaluators, particularly in terms of overall preference, character consistency, and image quality. These findings confirm that DiffSensei excels in rendering vivid and engaging manga stories. + +Qualitative comparison. Fig. 4 shows a qualitative comparison between DiffSensei and baseline models. The results illustrate that our model significantly outperforms the baselines in generating an entire page of a manga story. SEED-Story [46] employs an MLLM to create captions for each panel, leading to unnatural narrative text and chaotic story generation that fails to form a coherent story. StoryD + +![](images/c568511057517d739b036a5742d2e2e6f7321a7c189e892e49c856c174ecfce1.jpg) +Figure 6. Qualitative results. Character images in red boxes are from Manga109 (The rightmost example). Our DiffSensei can generate vivid manga pages in various scenarios. Better viewed with zoom-in. More results can be found in the appendix. + +![](images/36417586eb88ed32341cbd430925da138072c13423b40036e2b73176b462ff11.jpg) + +![](images/e448fec9f30b666f3888d40d9e915b57544a7319513972892ccb1342932f1851.jpg) + +![](images/4dd5be999682c362265ad4c254be95ac636c7fdd58a09b24b2ace0c5a473bcd8.jpg) + +![](images/d803408655b73ddbd1dd72088d3d646e0aaf21625f259d0ea702c4948108aab1.jpg) + +![](images/0d85b594c21becd46280a58f8f1a717a89caa12d4a781ad1eda3f23bc5f1ce46.jpg) + +Table 3. Ablation study. CM is character masked attention injection. DM is dialog masked encoding. Magi means using Magi [30] image encoder. MLLM means using MLLM for stage 2 training. + +
    CMDMMagiMLLMFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    0.4100.2300.5930.6100.361
    ✓0.4110.2250.5910.6370.364
    ✓✓0.4070.2280.6000.6350.653
    ✓✓✓0.4080.2310.6180.6480.718
    ✓✓✓✓0.4070.2350.6180.6510.727
    + +iffusion [53] is limited to producing fixed-resolution images due to its self-attention sharing mechanism, restricting its ability to generate diverse images. It shows inferior results, probably because the input reference panel has an unbalanced aspect ratio. MS-Diffusion [39] trains with source character images from the target panel and lacks the flexibility to modify characters' states effectively. In contrast, our method excels in text-following, character preservation, and overall story presentation. + +# 5.3. Qualitative Results + +Fig. 6 shows several manga pages generated by DiffSensei. The results demonstrate that our method can generate vivid manga panels and provide visually plausible results for the customized manga generation task. Our model can also generalize to unseen characters, as illustrated in the rightmost example, with character images from Manga109 [2] as input. Please see more results in the Appendix. + +# 5.4. Ablation Study + +Tab. 3 presents the quantitative ablation study of DiffSensei, where we systematically remove components to assess their impact. Specifically, when the MLLM component, serving as the flexible character feature adapter, is excluded, the CLIP metrics decrease by $1.73\%$ , and the DINO-C score also drops, underscoring its role in enhancing transferring character to the text-derived states. The absence of the Magi [30] image encoder results in a general decline in met- + +rics, particularly in image quality and character similarity, highlighting the importance of the Magi encoder for effectively encoding manga characters. Magi is trained specifically on manga datasets, performing better at preserving manga characters. To investigate alternative methods for encoding character and dialog layout conditions, we experimented with replacing the dialog embedding technique by inputting the Fourier embeddings of dialog bounding boxes into the timestep embedding of SDXL [26]. This modification led to a significant decrease in layout control, evidenced by the F1 score plummeting from 0.653 to 0.364, demonstrating that directly incorporating dialog embeddings into the latent is a superior approach for encoding dialog layouts. Furthermore, we explored adding the Fourier embeddings of character bounding boxes to the character features as an alternative to masked attention injection. This change caused a marked drop in the DINO-C metric, reaffirming the effectiveness of our original masked attention strategy. For comprehensive effect showcases, please see the qualitative ablation study in the Appendix. + +# 6. Conclusion + +This paper introduces DiffSensei, a novel framework for multi-character customized story visualization that integrates a diffusion-based image generator with an MLLM as a text-compatible identity adapter. Key innovations include masked attention control for character layout management, dialog layout embedding, and an MLLM-based feature adapter for flexible character customization. Supported by the proposed MangaZero dataset, comprising 43,264 manga pages and 427,147 panels, DiffSensei achieves superior, character-consistent panels that dynamically respond to textual prompts, surpassing existing methods and advancing the field of story visualization. + +Acknowledgement. This work is supported by the National Key Research and Development Program of China (No. 2023YFC3807600). + +# References + +[1] Mangadex, 2024. 4 +[2] Kiyoharu Aizawa, Azuma Fujimoto, Atsushi Otsubo, Toru Ogawa, Yusuke Matsui, Koki Tsubota, and Hikaru Ikuta. Building a manga dataset "manga109" with annotations for multimedia applications. TMM, 2020. 3, 6, 8 +[3] Jinbin Bai, Tian Ye, Wei Chow, Enxin Song, Qing-Guo Chen, Xiangtai Li, Zhen Dong, Lei Zhu, and Shuicheng Yan. 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} + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 58, + 234, + 411, + 407 + ], + "blocks": [ + { + "bbox": [ + 58, + 234, + 411, + 407 + ], + "lines": [ + { + "bbox": [ + 58, + 234, + 411, + 407 + ], + "spans": [ + { + "bbox": [ + 58, + 234, + 411, + 407 + ], + "type": "image", + "image_path": "69509d966de2f697b0c2ee479491c82317e04a0b3797b9fa5d6acbbd606f1e9c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 179, + 408, + 289, + 418 + ], + "lines": [ + { + "bbox": [ + 179, + 408, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 179, + 408, + 289, + 418 + ], + "type": "text", + "content": "(a) Customized manga generation" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 414, + 235, + 551, + 407 + ], + "blocks": [ + { + "bbox": [ + 414, + 235, + 551, + 407 + ], + "lines": [ + { + "bbox": [ + 414, + 235, + 551, + 407 + ], + "spans": [ + { + "bbox": [ + 414, + 235, + 551, + 407 + ], + "type": "image", + "image_path": "85d664683d23a0cdc82b3f17b96aceb856c73931504cc303f37821a699f3eefe.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 408, + 534, + 418 + ], + "lines": [ + { + "bbox": [ + 432, + 408, + 534, + 418 + ], + "spans": [ + { + "bbox": [ + 432, + 408, + 534, + 418 + ], + "type": "text", + "content": "(b) Real human manga creation" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 428, + 555, + 473 + ], + "lines": [ + { + "bbox": [ + 54, + 428, + 555, + 473 + ], + "spans": [ + { + "bbox": [ + 54, + 428, + 555, + 473 + ], + "type": "text", + "content": "Figure 1. Results of DiffSensei. (a) Customized manga generation with controllable character images, panel captions, and layout conditions. Our DiffSensei successfully generates detailed character expressions and states following the panel captions. (b) Manga creation for real human images. The dialogues are post-edited by humans. The continuation is in the Appendix. We strongly recommend that the readers see the Appendix for more comprehensive results. Manga reading order: Right to left. Top to bottom." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 151, + 487, + 200, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 487, + 200, + 499 + ], + "spans": [ + { + "bbox": [ + 151, + 487, + 200, + 499 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 53, + 522, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 522, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 53, + 522, + 297, + 715 + ], + "type": "text", + "content": "Story visualization, the task of creating visual narratives from textual descriptions, has seen progress with text-to-image generation models. However, these models often lack effective control over character appearances and interactions, particularly in multi-character scenes. To address these limitations, we propose a new task: customized manga generation and introduce DiffSensei, an innovative framework specifically designed for generating manga with dynamic multi-character control. DiffSensei integrates a diffusion-based image generator with a multimodal large language model (MLLM) that acts as a text-compatible identity adapter. Our approach employs masked cross-attention to seamlessly incorporate character features, enabling precise layout control without direct pixel transfer. Additionally, the MLLM-based adapter adjusts character features to align with panel-specific text cues, allowing flex" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 487, + 556, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 556, + 608 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 556, + 608 + ], + "type": "text", + "content": "ible adjustments in character expressions, poses, and actions. We also introduce MangaZero, a large-scale dataset tailored to this task, containing 43,264 manga pages and 427,147 annotated panels, supporting the visualization of varied character interactions and movements across sequential frames. Extensive experiments demonstrate that DiffSensei outperforms existing models, marking a significant advancement in manga generation by enabling text-adaptable character customization. The code, model, and dataset are open-sourced to the community." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 616, + 395, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 616, + 395, + 628 + ], + "spans": [ + { + "bbox": [ + 314, + 616, + 395, + 628 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 637, + 555, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 637, + 555, + 686 + ], + "spans": [ + { + "bbox": [ + 313, + 637, + 555, + 686 + ], + "type": "text", + "content": "Story visualization, the process of generating visual narratives from textual descriptions, is a rapidly evolving field [5, 18, 21, 25, 37, 46, 53]. Among its various applications, manga generation holds particular significance due" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 555, + 713 + ], + "type": "text", + "content": "1The work is done in Shanghai AI Laboratory. Corresponding to: Xiangtai Li, Jingbo Wang." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28684" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": "to its popularity and unique narrative requirements. Unlike traditional story visualization, manga demands consistent characters across panels, precise layout control for positioning multiple characters, and the seamless integration of dialogues in a coherent, visually engaging manner." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 135, + 295, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 135, + 295, + 421 + ], + "spans": [ + { + "bbox": [ + 56, + 135, + 295, + 421 + ], + "type": "text", + "content": "Currently, manga generation remains an underexplored area. Most existing research focuses on low-level imagedto-image tasks, primarily converting general images to a manga style [20, 33, 48, 50]. While these tasks enhance the visual appeal of static images, they do not extend to generating fully customized manga content from scratch. In general story visualization, current approaches have demonstrated some success in generating coherent image sequences from text. Still, they cannot often customize the characters across scenes [21, 25, 46, 53], a critical requirement for manga generation. Additionally, they do not provide the necessary control over layouts and dialogue placements, which are also essential for manga. A likely reason for these limitations is that existing story visualization datasets typically lack character annotations and layout controls [15, 18, 21, 46]. Another research direction has explored zero-shot character customization, showing promise for achieving character customization across manga panels [4, 9, 19, 29, 36, 39, 47]. However, these approaches often result in rigid \"copy-pasting\" effects [4, 39, 47], which limit expressive character variation and detract from narrative depth. This limitation largely stems from the scarcity of datasets capturing multiple appearances of the same character in varied expressions and poses." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 424, + 295, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 424, + 295, + 639 + ], + "spans": [ + { + "bbox": [ + 55, + 424, + 295, + 639 + ], + "type": "text", + "content": "To address these limitations, we propose a new task: customized manga generation. As illustrated in Fig. 1, this task focuses on creating manga images with multiple characters, each customized based on a character image and positioned according to user input. Characters must dynamically adapt to text prompts, altering their expressions, motions, and poses as the narrative unfolds. Dialog layout should also be managed to generate expressive manga panels. Compared to traditional story visualization tasks, this proposed task prioritizes essential manga-specific controllability, aiming to generate vivid manga panels that are both coherent and visually engaging while supporting the customization of multiple characters. To address the lack of a dedicated dataset for customized manga generation, we collect a dataset of Japanese black-and-white manga, forming the basis of the proposed task. The resulting dataset, MangaZero, is the first large-scale collection designed to support multi-character, multi-state manga generation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "content": "To tackle this task, we introduce a novel framework, DiffSensei, which leverages a diffusion-based image generator to produce customized manga panels. However, we observe that, even with training on multiple appearances of the same character, the generated portraits often tend to rigidly follow the pixel distribution of the input character image, re" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 263 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 263 + ], + "type": "text", + "content": "sulting in limited variations in appearance, pose, and motion based on the text input. Inspired by recent advancements in image editing using Multimodal Large Language Models (MLLMs) [6, 8, 16, 34, 40-43, 46, 49], we propose using an MLLM as a text-compatible character adapter. This approach enables seamless, dynamic adjustments to characters in response to textual cues, thereby supporting coherent and expressive manga panel generation. Additionally, we incorporate masked attention injection to manage character layout, along with a dialog embedding technique tailored specifically for manga, allowing for precise control over dialog placement. Through extensive experimentation, we validate DiffSensei's capability to generate coherent, expressive manga panels that maintain narrative consistency and offer improved character control. This represents a significant advancement in story visualization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 265, + 553, + 443 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 265, + 553, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 265, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 314, + 265, + 553, + 312 + ], + "type": "text", + "content": "- We introduce a new task: customized manga generation, focused on generating manga images with multiple characters, each dynamically adapting to text prompts and positioned according to layout specifications." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 315, + 313, + 553, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 313, + 553, + 372 + ], + "spans": [ + { + "bbox": [ + 315, + 313, + 553, + 372 + ], + "type": "text", + "content": "- We present MangaZero, the first large-scale dataset specifically designed for multi-character, multi-state manga generation, addressing a significant gap in story visualization training data. The dataset will be released for the image generation community." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 373, + 553, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 373, + 553, + 443 + ], + "spans": [ + { + "bbox": [ + 315, + 373, + 553, + 443 + ], + "type": "text", + "content": "- We propose DiffSensei. As far as we know, it is the first framework for customized manga generation that links diffusion models and MLLMs. The MLLM serves as an adaptable character feature adapter, enabling characters to respond dynamically to textual cues. Extensive experiments demonstrate the effectiveness of DiffSensei." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 453, + 400, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 453, + 400, + 466 + ], + "spans": [ + { + "bbox": [ + 314, + 453, + 400, + 466 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 474, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 553, + 713 + ], + "type": "text", + "content": "Story visualization. Story visualization, the process of generating visual narratives based on given stories, is rapidly evolving. Many approaches can generate consistent image sequences derived from story content [5, 21, 25, 37, 46, 53]. Despite recent advancements, the field faces significant limitations. Most existing methods generate story images solely from text and image-level prompts [21, 25, 46, 53], which restricts control over individual characters. This limited control over characters reduces the flexibility and depth of story visualization. A key factor is that current training datasets [10, 15, 18, 21, 46] lack character-specific annotations. In response to the data limit, recent works [5, 37] explore multi-character control using training-free methods that leverage existing subject preservation techniques, such as IP-Adapter [47]. Other works [4, 7, 9, 11, 12, 19, 29, 32, 36, 39, 44, 47] try to train diffusion models for a multi-character customized generation. However, these approaches often result in a \"copy-pasting\" effect, restricting the diversity of expressions and actions needed for dynamic storytelling. For training-free" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28685" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 113, + 558, + 222 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 555, + 105 + ], + "type": "text", + "content": "Table 1. Comparison between MangaZero and related publicly available datasets. A story is defined as a sequence of continuous images annotated consistently with character IDs. In MangaZero, a story means a manga page. A panel means a distinct story image, or called frame [21, 46]. Most series in MangaZero are still popular in 2024. Please see the Appendix for the dataset details." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 113, + 558, + 222 + ], + "lines": [ + { + "bbox": [ + 58, + 113, + 558, + 222 + ], + "spans": [ + { + "bbox": [ + 58, + 113, + 558, + 222 + ], + "type": "table", + "html": "
    DatasetTypeResolution#Series#Stories#PanelsCaptionAnnotations CharacterDialogOrigin
    PororoSV [18]AnimationFix115,33673,665✓××2003-2016
    FlintstonesSV [10]AnimationFix125,184122,560✓✓×1960-1966
    StorySalon [21]AnimationFix44618,255159,778✓××YouTube
    StoryStream [46]AnimationFix312,614257,850✓××1939-2013
    Manga109 [2]B/W MangaVary10910,602103,850×✓✓1970-2010
    MangaZeroB/W MangaVary4843,264427,147✓✓✓1974-2024
    ", + "image_path": "7f36507d26f5f56c7f354c3758887a6097a34929d1c637062c9735fac464d20e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 241, + 294, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 241, + 294, + 313 + ], + "spans": [ + { + "bbox": [ + 54, + 241, + 294, + 313 + ], + "type": "text", + "content": "methods, combining multiple models can significantly slow down inference speeds. To address these challenges, we first introduce a large-scale manga generation dataset with finely curated character annotations and then develop a novel framework utilizing diffusion models and MLLMs that enables the dynamic generation of manga panels." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 313, + 294, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 313, + 294, + 409 + ], + "spans": [ + { + "bbox": [ + 54, + 313, + 294, + 409 + ], + "type": "text", + "content": "Manga generation. The field of black-and-while manga generation has received limited exploration. Most existing researches focus on low-level image-to-image tasks, primarily transferring general images to a manga style [20, 33, 48, 50]. Recent works contribute to manga content understanding [30, 31, 35]. In contrast, we propose the customized manga generation task beyond style transfer to offer complete character and story-driven manga generation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 410, + 295, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 410, + 295, + 588 + ], + "spans": [ + { + "bbox": [ + 55, + 410, + 295, + 588 + ], + "type": "text", + "content": "MLLMs for personalized image generation. MLLMs have shown remarkable potential in personalized image generation, particularly for tasks involving image editing and customization [3, 6, 8, 16, 34, 40-42, 46, 49]. Notably, CAFE [52] explores customizing subject appearances through textual instructions. However, MLLM-driven image generation for multi-character narratives remains an open challenge, primarily due to the difficulties in maintaining inter-character relationships and scene continuity. Our framework proposes an MLLM-based identity adapter that enhances dynamic story consistency in multi-character manga generation. In contrast to previous works, our framework takes multi-character features as input and edits these features collectively, following the text prompt, enabling flexible subject editing across multiple characters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 597, + 195, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 195, + 611 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 195, + 611 + ], + "type": "text", + "content": "3. The MangaZero Dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 617, + 295, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 642 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 642 + ], + "type": "text", + "content": "In this section, we first define the problem in Sec. 3.1. Then, we introduce the dataset construction pipeline in Sec. 3.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 647, + 180, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 180, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 180, + 659 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "We introduce a challenging new task: customized manga generation. This task focuses on generating manga images where multiple characters, each with their distinct image inputs, are customized and positioned by users. Importantly," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": "characters must adapt to the text prompts by modifying their expressions, motions, and poses dynamically, even when only a limited set of character images is available. To generate a manga story across " + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": " panels (or frames), the inputs include: text prompts for each panel " + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "inline_equation", + "content": "T_{0}, T_{1}, \\ldots, T_{N-1}" + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": ", character images " + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{I} = I_{0}, I_{1}, \\ldots, I_{K-1}" + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": ", character bounding boxes for each panel " + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_{0}^{c}, \\mathbf{B}_{1}^{c}, \\ldots, \\mathbf{B}_{N-1}^{c}" + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": ", and dialogue bounding boxes for each panel " + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_{0}^{d}, \\mathbf{B}_{1}^{d}, \\ldots, \\mathbf{B}_{N-1}^{d}" + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": ". The visualization of a panel is represented as " + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "inline_equation", + "content": "P_{i} = \\Phi_{\\theta}(T_{i}, \\mathbf{I}, \\mathbf{B}_{i}^{c}, \\mathbf{B}_{i}^{d})" + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": " is the overall model function and " + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 241, + 553, + 373 + ], + "type": "text", + "content": " represents the model's learned parameters." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "type": "text", + "content": "Discussion. This task diverges from existing story visualization and continuation tasks [21, 25]. Specifically, in story visualization tasks, a panel is produced using " + }, + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "type": "inline_equation", + "content": "P_{i} = \\Phi_{\\theta}(T_{i})" + }, + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "type": "text", + "content": ", while in story continuation tasks, the panel generation depends on previous panels as " + }, + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "type": "inline_equation", + "content": "P_{i} = \\Phi_{\\theta}(T_{i}, T_{i-1}, P_{i-1})" + }, + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "type": "inline_equation", + "content": "i > 0" + }, + { + "bbox": [ + 313, + 374, + 554, + 542 + ], + "type": "text", + "content": ". Both lack explicit character control, a crucial element in storytelling. Furthermore, the proposed task differs from subject-driven image generation approaches [29, 39, 47], as it demands that models not only generate accurate character representations but also modify characters' attributes in response to panel captions and layouts, resulting in varied and coherent narrative visuals. Our experiments, detailed in Sec. 5, demonstrate that our model significantly surpasses baseline models in these critical aspects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 551, + 437, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 551, + 437, + 562 + ], + "spans": [ + { + "bbox": [ + 313, + 551, + 437, + 562 + ], + "type": "text", + "content": "3.2. Dataset Construction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 569, + 553, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 569, + 553, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 569, + 553, + 593 + ], + "type": "text", + "content": "In this section, we introduce the proposed large-scale manga story visualization dataset MangaZero." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 594, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 554, + 713 + ], + "type": "text", + "content": "Comparison with related datasets. A comprehensive comparison with existing datasets is presented in Tab. 1. In contrast to current manga and story visualization datasets, the proposed MangaZero dataset stands out as being larger in size, newer in source, richer in annotations, diverse in manga series, and varied in panel resolutions. Compared to the well-known black-and-white manga dataset Manga109 [2], the MangaZero dataset encompasses more manga series published after the year 2000, which inspired its naming. Additionally, MangaZero includes famous se" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "28686" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 280, + 238 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 280, + 238 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 280, + 238 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 280, + 238 + ], + "type": "image", + "image_path": "fb2c4ca29fad8bf9f19c3fd78412f1ce1cb1fbce39eeb7558ac2ac2d089ed158.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 246, + 298, + 291 + ], + "lines": [ + { + "bbox": [ + 55, + 246, + 298, + 291 + ], + "spans": [ + { + "bbox": [ + 55, + 246, + 298, + 291 + ], + "type": "text", + "content": "Figure 2. We construct MangaZero through three steps: 1) Download manga pages from the internet. 2) Annotate manga panels autonomously with pre-trained models. 3) Human calibration for the character ID annotation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 312, + 295, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 312, + 295, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 312, + 295, + 335 + ], + "type": "text", + "content": "ries from before the year 2000 that are not featured in Manga109, such as Doraemon (1974)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 336, + 296, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 336, + 296, + 598 + ], + "spans": [ + { + "bbox": [ + 56, + 336, + 296, + 598 + ], + "type": "text", + "content": "Construction pipeline. To build our dataset, we first download manga pages from the internet, explicitly sourcing images from MangaDex [1]. It is important to note that all data will be used solely for academic research, not commercial purposes. We select 48 manga series and download up to 1,000 pages per series, resulting in 43,264 double-page images. These images are then annotated using pretrained models. For manga-specific annotations, including panel bounding boxes, character bounding boxes, character IDs, and dialog bounding boxes, we employ the recent manga understanding model, Magi [30]. It should be noted that character ID labeling is consistent only within individual pages, which is sufficient for achieving coherent character cross-reference. Once the panel bounding boxes are obtained, we utilize LLaVA-v1.6-34B [22] to generate captions for each panel. However, we observe that character ID labeling has relatively low accuracy, which poses a significant challenge for training purposes. To address this, human annotators refine the machine-generated labels, resulting in accurate and clean annotations. Finally, we split 96 pages (2 for each series) as the evaluation set and the remaining 43,168 pages as the training set." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 609, + 111, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 609, + 111, + 621 + ], + "spans": [ + { + "bbox": [ + 55, + 609, + 111, + 621 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 629, + 295, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 295, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 295, + 677 + ], + "type": "text", + "content": "In this section, we introduce the architecture of the proposed framework, DiffSensei, which generates vivid manga panels with precise character and dialog layout control while adapting the characters' status flexibly." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 714 + ], + "type": "text", + "content": "Motivation. There are two critical problems in customizing objects and layouts in image generation: 1) Preserving the subjects' intrinsic features while avoiding direct copy-paste" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 277 + ], + "type": "text", + "content": "from source images, and 2) Ensuring reliable layout control with minimal computational cost during both training and inference. To avoid copy-pasting effects, our model converts character image features into tokens, preventing the direct transfer of fine-grained pixel details. Additionally, we integrate an MLLM as a character image feature adapter. The MLLM adapter receives source character features and panel captions as inputs, generating text-compatible target character features. Compared with previous customization work [39], this approach enables text-compatible character encoding and flexible character adaptation to captions. For layout control, we employ lightweight masked encoding techniques for both character and dialog layouts, significantly reducing computational costs compared with previous works [38, 45] while maintaining high accuracy in both training and inference phases. Experiment results in Sec. 5 demonstrate the effectiveness of our design." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 281, + 555, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 281, + 555, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 281, + 555, + 354 + ], + "type": "text", + "content": "Multi-character feature extraction. As illustrated in Fig. 3, we initially extract local image features using CLIP and image-level features from a manga image encoder. These two sets of features are then processed by a feature extractor, which is implemented as a resampler module [47]. This process can be formalized as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 345, + 374, + 555, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 374, + 555, + 389 + ], + "spans": [ + { + "bbox": [ + 345, + 374, + 555, + 389 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {i} = \\operatorname {R e s a m p l e r} ([ \\operatorname {C L I P} (\\mathbf {I}), \\psi (\\mathbf {I}) ], \\mathbf {q}, \\mathbf {q} _ {\\text {v o i d}}), \\tag {1}", + "image_path": "b75c6978d895927a48c36b6edc454c01fde0257b107b738af5aa30e8c69dea21.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "spans": [ + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " represents the manga image encoder. " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{\\text{void}}" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " are trainable query vectors for character and non-character features, respectively. " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " re-samples the image features into the U-Net's cross-attention dimension, while " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{\\text{void}}" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " guides the cross-attention in regions without characters in the layout. " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i \\in \\mathbb{R}^{B \\times ((N_c + 1) \\times N_q) \\times C}" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " is the output feature for all characters, where " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " is the batch size, " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "N_c" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " is the maximum number of characters per panel (padded with all-zero features as needed), " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "N_q" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " is the number of query tokens per character, and " + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 409, + 556, + 589 + ], + "type": "text", + "content": " is the cross-attention dimension of the U-Net. Through compressing the character images into a few tokens, DiffSensei avoids encoding fine-grained spatial features from reference images into the model [21, 51]. This enables focusing on the characters' semantic representations rather than rigid pixel distributions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 556, + 715 + ], + "type": "text", + "content": "Masked cross-attention injection. We replicate the key and value matrices in each cross-attention layer, creating separate character cross-attention layers. This allows the image query features to attend to text and character cross-attentions independently and combine the results from both attentions. In the character cross-attention, we apply a masked cross-attention injection mechanism to control the layout of each character. Here, each character feature only attends to query features within its designated bounding box region. In areas without characters, query features attend to" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28687" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 76, + 547, + 277 + ], + "blocks": [ + { + "bbox": [ + 65, + 76, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 65, + 76, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 65, + 76, + 547, + 277 + ], + "type": "image", + "image_path": "06fd9a85d5bdaef5ea1f712d6315e93734cf9495c217db5cdcf75dd5926de8e8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 289, + 555, + 335 + ], + "lines": [ + { + "bbox": [ + 54, + 289, + 555, + 335 + ], + "spans": [ + { + "bbox": [ + 54, + 289, + 555, + 335 + ], + "type": "text", + "content": "Figure 3. The architecture of DiffSensei. In the first stage, we train a multi-character customized manga image generation model with layout control. The dialog embedding is added to the noised latent after the first convolution layer. All the parameters in the U-Net and feature extractor are trained. In the second stage, we finetune LoRA and resampler weights of an MLLM to adapt the source character features corresponding to the text prompt. We use the model in the first stage as the image generator and freeze its weights." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 354, + 277, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 277, + 368 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 277, + 368 + ], + "type": "text", + "content": "a placeholder vector, " + }, + { + "bbox": [ + 55, + 354, + 277, + 368 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{\\text{void}}" + }, + { + "bbox": [ + 55, + 354, + 277, + 368 + ], + "type": "text", + "content": ". This can be formulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 371, + 295, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 371, + 295, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 295, + 403 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {z}} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} _ {t} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V} _ {t} + \\tag {2}", + "image_path": "f87b3fb8499c97f86a3b412cec89e16513352f1fb8b0011cbc9c86feb8f1ef5b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 112, + 400, + 245, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 400, + 245, + 428 + ], + "spans": [ + { + "bbox": [ + 112, + 400, + 245, + 428 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\alpha} \\cdot \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q K} _ {i} ^ {\\top}}{\\sqrt {d}} + \\mathbf {M}\\right) \\mathbf {V} _ {i},", + "image_path": "65fb6ebb658462d325295a6625778bf01be2dad4776372a3e555c6174a4191f7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} = \\mathbf{z}\\mathbf{W}_q" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{K}^t = \\mathbf{c}_t\\mathbf{W}_k^t" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^t = \\mathbf{c}_t\\mathbf{W}_v^t" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{K}^i = \\mathbf{c}_i\\mathbf{W}_k^i" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^i = \\mathbf{c}_i\\mathbf{W}_v^i" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " is the query, " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{W_q}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{W_k^t}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{W_v^t}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " are query, key, and value projection matrices for the text cross-attention. " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{W_k^t}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{W_v^t}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " are key and value projection matrices for the character cross-attention, initialized from " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{W_k^t}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{W_v^t}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " is the key dimension. " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_t" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " are text and character features respectively. " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " are the input and output image features. " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " is a hyperparameter that controls character attention weight. " + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 55, + 431, + 296, + 552 + ], + "type": "text", + "content": " is an attention mask to manage the characters' layout. Its values are defined as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 82, + 557, + 295, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 557, + 295, + 602 + ], + "spans": [ + { + "bbox": [ + 82, + 557, + 295, + 602 + ], + "type": "interline_equation", + "content": "\\mathbf {M} [ i, j ] = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} j = N _ {c} \\text {a n d} i \\notin \\mathbf {B} ^ {c} \\text {o r} \\\\ & i \\in \\mathbf {B} ^ {c} [ j ] \\\\ - \\infty , & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}", + "image_path": "fc925c4254164b24eccc61e039bff4db746117952ab4b5f0520b2b3af878067e.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " denotes the position of query tokens, " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "j \\in \\{0,1,\\dots,N_c\\}" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " is the character indices. The " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "-th character feature represents the placeholder vector " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{void}" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^c [j]" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": " is the bounding box of the " + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 605, + 296, + 713 + ], + "type": "text", + "content": "-th character. The masked attention injection mechanism ensures that each character attends only to its specified bounding box region, while areas without characters attend to the placeholder vector. This technique achieves efficient and precise layout control for each character with minimal computational overhead." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 354, + 555, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 546 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 546 + ], + "type": "text", + "content": "Dialog layout encoding. Panels with dialog are a distinctive feature of manga images. However, most current text-to-image models struggle to generate coherent, readable text [26, 28]. While some recent models can produce stable text, they remain limited in terms of text length [17]. Generating extended text, such as dialogues, continues to pose challenges. Therefore, we propose controlling the layout of dialogs rather than the content itself. In this approach, human artists can manually edit the text within dialog bubbles, leaving image generation to the models. Concretely, we introduce a trainable embedding to represent the dialog layout. The dialog embedding is first expanded to match the spatial shape of the noised latent and then masked with the dialog layout. By summing the masked dialog embedding with the noised latent, we can encode dialog positions within the image generator. This process is expressed as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 347, + 552, + 555, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 552, + 555, + 564 + ], + "spans": [ + { + "bbox": [ + 347, + 552, + 555, + 564 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {z}} _ {t} = \\operatorname {C o n v} \\left(\\mathbf {z} _ {t}\\right) + \\operatorname {E x p a n d} \\left(\\mathbf {e} _ {d}, \\mathbf {z} _ {t}\\right) \\cdot \\mathbf {M} _ {d}, \\tag {4}", + "image_path": "998f2b6ac3e882ec755e479099040aea164a4822bf370c48cd181f731f49ad40.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_d" + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "content": " is the trainable dialog embedding, " + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "content": " is the noised latent in time step " + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "content": ", Expand is a function that expands " + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_d" + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "content": " to the latent shape, and " + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_d" + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "content": " is the dialog region mask derived from input dialog bounding boxes " + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^d" + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "content": ". The output, " + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_t" + }, + { + "bbox": [ + 313, + 570, + 555, + 665 + ], + "type": "text", + "content": ", serves as a dialog-Layout-aware latent representation. This is then input into the U-Net for noise prediction. The dialog embedding effectively encodes the dialog layout, adding minimal computational overhead in space and time." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 666, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 556, + 714 + ], + "type": "text", + "content": "MLLM as text-compatible character feature adapter. After training the image generator, our model can effectively create manga panels that adhere to specified character appearances and layout conditions. However, the model" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28688" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 288 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 288 + ], + "type": "text", + "content": "often rigidly follows the input character images, lacking flexibility in adjusting expressions, poses, or motions based on panel captions. We propose incorporating MLLM as a text-compatible character feature adapter. This approach allows dynamic modifications to character states based on text prompts. A training sample for MLLM is organized as [panel caption, source character image features, target character image features]. The image features are encapsulated by two special tokens, " + }, + { + "bbox": [ + 55, + 72, + 296, + 288 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{IMG} \\rangle" + }, + { + "bbox": [ + 55, + 72, + 296, + 288 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 288 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{IMG} \\rangle" + }, + { + "bbox": [ + 55, + 72, + 296, + 288 + ], + "type": "text", + "content": ". To achieve this, we compute Language Modeling (LM) Loss on the special tokens to constrain the output format and Mean Squared Error (MSE) Loss to guide the target character features based on the panel caption. To ensure that the edited character features align with the image generator, we further pass the generated features into U-Net's character cross-attention and compute diffusion loss. In this stage, only the LoRA and resampler weights in MLLM are updated. This process can be formalized as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 90, + 296, + 198, + 309 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 296, + 198, + 309 + ], + "spans": [ + { + "bbox": [ + 90, + 296, + 198, + 309 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {h}}, \\hat {\\mathbf {c}} _ {i} = \\operatorname {M L L M} (T, \\phi (\\mathbf {c} _ {i})),", + "image_path": "2f42c6504184bd2b913c8b501bb5fd2c9235c79f250a30c7f899cdddab79e1cf.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 93, + 314, + 294, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 314, + 294, + 331 + ], + "spans": [ + { + "bbox": [ + 93, + 314, + 294, + 331 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {l m} = \\operatorname {L M L o s s} (\\hat {\\mathbf {h}}, T), \\tag {5}", + "image_path": "90dd1b3ac51f0b90b6865fba60466b3e5bde4b2b3d8835d30248832a9eeca09c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 88, + 329, + 211, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 329, + 211, + 342 + ], + "spans": [ + { + "bbox": [ + 88, + 329, + 211, + 342 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m s e} = \\operatorname {M S E L o s s} \\left(\\phi^ {\\prime} (\\hat {\\mathbf {c}} _ {i}), \\tilde {\\mathbf {c}} _ {i}\\right),", + "image_path": "10486a27fc1ab886766ff1595df5ebb3cb99512e78e62a73b7cce3a9e370b6ca.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 344, + 265, + 358 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 344, + 265, + 358 + ], + "spans": [ + { + "bbox": [ + 86, + 344, + 265, + 358 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i f f} = \\mathbb {E} _ {\\epsilon , t} | | \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, T, \\hat {\\mathbf {c}} _ {i}, \\mathbf {B} ^ {c}, \\mathbf {B} ^ {d}, t) | | ^ {2},", + "image_path": "e3bf46a0349c3bfb49dc6cfd8c37d319c8c330530eb4ccfe575d2e62d5f12631.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": " is the text prompt. " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\phi^{\\prime}" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": " denote the input and output resamplers of MLLM, which consist of stacked attention layers to convert the embeddings between inner and outer dimensions. " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{h}}" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": " refers to the MLLM predicted special token embeddings. We calculate LM Loss on it. " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_i" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": " is the predicted character features. We compute MSE Loss between " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_i" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{c}}_i" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": ", the ground truth target character embedding extracted from the feature extractor. By leveraging the character ID annotations of MangaZero, we can obtain features from the same character across different panels, thus facilitating the training of the MLLM feature adapter. The adapted character feature " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_i" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": " is then passed to the image generator " + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 365, + 296, + 534 + ], + "type": "text", + "content": ", previously trained, to compute a diffusion loss. The total loss for training MLLM is expressed as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 84, + 542, + 294, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 542, + 294, + 555 + ], + "spans": [ + { + "bbox": [ + 84, + 542, + 294, + 555 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {l m} \\mathcal {L} _ {l m} + \\lambda_ {m s e} \\mathcal {L} _ {m s e} + \\lambda_ {d i f f} \\mathcal {L} _ {d i f f}, \\tag {6}", + "image_path": "2b56d1b391a48d1e695173bc11aa9a5b1c376e25682d30f1cab24de89043215a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "type": "inline_equation", + "content": "\\lambda_{lm}" + }, + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "type": "inline_equation", + "content": "\\lambda_{mse}" + }, + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "type": "inline_equation", + "content": "\\lambda_{diff}" + }, + { + "bbox": [ + 55, + 563, + 241, + 576 + ], + "type": "text", + "content": " are loss weights." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 585, + 137, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 585, + 137, + 598 + ], + "spans": [ + { + "bbox": [ + 55, + 585, + 137, + 598 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 628 + ], + "type": "text", + "content": "In this section, we thoroughly evaluate DiffSensei and compare it with baseline models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 636, + 182, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 636, + 182, + 649 + ], + "spans": [ + { + "bbox": [ + 55, + 636, + 182, + 649 + ], + "type": "text", + "content": "5.1. Experimental Settings" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": "Implementation details. The image generator is constructed on top of SDXL [26]. The feature extractor's weights are initialized using the pre-trained IP-AdapterPlus-SDXL [47], while the MLLM (Multi-modal Large Language Model) is initialized from SEED-X [8]. Other" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "text", + "content": "newly introduced parameters, including the LoRA and resampler weights of the MLLM, are initialized randomly. In stage 1, the image generator is optimized using a learning rate of 1e-5. Stage 2 training employs a learning rate of 1e-4 and a LoRA rank of 64 [14]. The optimizer is AdamW [23]. The loss function coefficients " + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "inline_equation", + "content": "\\lambda_{lm}" + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "inline_equation", + "content": "\\lambda_{mse}" + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "inline_equation", + "content": "\\lambda_{diff}" + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "text", + "content": " are set to 1.0, 6.0, and 1.0, respectively. We train 250k steps for the first stage and 20k for the second stage. The source character images are chosen randomly, with a " + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 313, + 72, + 555, + 300 + ], + "type": "text", + "content": " probability of being from the same page; otherwise, they are selected from the target image. To handle varying image resolutions during training, we adopt the bucket-based approach from prior works [26], grouping images into resolution-specific buckets. For each training batch, images are loaded from the same resolution bucket. The batch size varies between 8 and 64 in stage 1, and between 8 and 128 in stage 2. This dynamic batch sizing is necessary to prevent out-of-memory (OOM) issues, especially when processing large-resolution images. Please see more details in the Appendix." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 300, + 556, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 556, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 556, + 540 + ], + "type": "text", + "content": "Evaluation datasets and metrics. We evaluate our model using the MangaZero and Manga109 [2] evaluation sets. Note that the model is only trained on MangaZero. Characters in Manga109 are unseen during training, serving as a benchmark for generalization. To assess the generation quality of individual images, we employ autonomous metrics, which include Fréchet Inception Distance score (FID) [13], CLIP image-text similarity (CLIP) [27], DINO image similarity (DINO-I) [24], DINO character image similarity (DINO-C), and the dialog bounding box F1 score (F1 score). The source character images are randomly sampled on the same page. The dialog bounding boxes in the generated images are predicted using Magi [30]. For evaluating the story visualization quality of image sequences, human preference study proves more effective. We recruit human volunteers to choose their preferred story pages from our model's output and baseline models in the MangaZero evaluation set. The evaluation criteria include five key aspects: text-image alignment, style consistency, character consistency, image quality, and overall preference." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 540, + 556, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 540, + 556, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 540, + 556, + 624 + ], + "type": "text", + "content": "Baselines. We select recent advanced story visualization models as our baselines, including StoryDiffusion [53], AR-LDM [25], StoryGen [21], SEED-Story [46], and MS-Diffusion [39]. StoryDiffusion [53] is a training-free method. We directly use an SDXL text-to-image model finetuned on MangaZero for evaluation. Despite that, we re-train other baselines on our dataset for a fair comparison." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 635, + 454, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 454, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 454, + 647 + ], + "type": "text", + "content": "5.2. Comparison to Baselines" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "type": "text", + "content": "Quantitative comparison. We quantitatively compare our DiffSensei model with baseline models using automatic evaluation metrics. The results on the MangaZero evaluation set are presented in Tab. 2a. The results highlight that DiffSensei consistently outperforms the baseline mod" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28689" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 114, + 304, + 193 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 555, + 93 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 555, + 93 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 555, + 93 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on automatic metrics. Methods followed by “*” use reference images as input rather than characters. Methods marked by “†” means re-trained with dialog embedding." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 108, + 102, + 257, + 112 + ], + "lines": [ + { + "bbox": [ + 108, + 102, + 257, + 112 + ], + "spans": [ + { + "bbox": [ + 108, + 102, + 257, + 112 + ], + "type": "text", + "content": "(a) Comparison on MangaZero evaluation set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 62, + 114, + 304, + 193 + ], + "lines": [ + { + "bbox": [ + 62, + 114, + 304, + 193 + ], + "spans": [ + { + "bbox": [ + 62, + 114, + 304, + 193 + ], + "type": "table", + "html": "
    MethodFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    AR-LDM* [25]0.4090.2570.5480.5070.004
    StoryGen* [21]0.4110.2190.5360.4880.012
    SEED-Story* [46]0.4110.1690.4160.4050.006
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    MS-Diffusion† [39]0.4080.2290.6100.6410.720
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    ", + "image_path": "207ea7c4231c6df9d6d868d69df99617beab3024df12958d86cec8c5a3e30988.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 308, + 114, + 548, + 192 + ], + "blocks": [ + { + "bbox": [ + 354, + 102, + 500, + 112 + ], + "lines": [ + { + "bbox": [ + 354, + 102, + 500, + 112 + ], + "spans": [ + { + "bbox": [ + 354, + 102, + 500, + 112 + ], + "type": "text", + "content": "(b) Comparison on Manga109 evaluation set." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 114, + 548, + 192 + ], + "lines": [ + { + "bbox": [ + 308, + 114, + 548, + 192 + ], + "spans": [ + { + "bbox": [ + 308, + 114, + 548, + 192 + ], + "type": "table", + "html": "
    MethodFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    AR-LDM* [25]0.4100.2540.5270.4910.005
    StoryGen* [21]0.4140.2140.5400.4930.004
    SEED-Story* [46]0.4130.1670.4420.4280.005
    StoryDiffusion* [53]0.4100.2380.4420.3550.001
    MS-Diffusion† [39]0.4100.2270.5840.6000.601
    DiffSensei0.4100.2370.5880.6000.648
    ", + "image_path": "776c5e578f03ec308a5b86e710d538b9c6011acb028affe49e832969ab3d25f4.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 63, + 209, + 177, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 209, + 177, + 232 + ], + "spans": [ + { + "bbox": [ + 63, + 209, + 177, + 232 + ], + "type": "text", + "content": "Story Summary: A sailor hears a sound in the cabin, walks up to the deck, and discovers a beautiful ghost girl. He tries to embrace her..." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 181, + 203, + 265, + 236 + ], + "blocks": [ + { + "bbox": [ + 181, + 203, + 265, + 236 + ], + "lines": [ + { + "bbox": [ + 181, + 203, + 265, + 236 + ], + "spans": [ + { + "bbox": [ + 181, + 203, + 265, + 236 + ], + "type": "image", + "image_path": "b52522b814fe01ec2c1235cb13cddf0648c4dfef23e5d9a3b2c6bb83394c0402.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 266, + 204, + 344, + 236 + ], + "blocks": [ + { + "bbox": [ + 266, + 204, + 344, + 236 + ], + "lines": [ + { + "bbox": [ + 266, + 204, + 344, + 236 + ], + "spans": [ + { + "bbox": [ + 266, + 204, + 344, + 236 + ], + "type": "image", + "image_path": "73158a2ec00a54e3ca91861aa9ede5438635d1336ba566f4a3bfad6cdc639d97.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 345, + 204, + 449, + 236 + ], + "blocks": [ + { + "bbox": [ + 345, + 204, + 449, + 236 + ], + "lines": [ + { + "bbox": [ + 345, + 204, + 449, + 236 + ], + "spans": [ + { + "bbox": [ + 345, + 204, + 449, + 236 + ], + "type": "image", + "image_path": "731b398cce9e0c06f9d9cccb61e7230d5f373bc0948d37df36e6f4db4f1c97de.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 451, + 209, + 544, + 236 + ], + "blocks": [ + { + "bbox": [ + 451, + 209, + 544, + 236 + ], + "lines": [ + { + "bbox": [ + 451, + 209, + 544, + 236 + ], + "spans": [ + { + "bbox": [ + 451, + 209, + 544, + 236 + ], + "type": "image", + "image_path": "ccd0859941344e6aa84e89136bdb1811cca4eb664bcc21f73bbbcdd54d3e8d86.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 60, + 237, + 127, + 397 + ], + "blocks": [ + { + "bbox": [ + 60, + 237, + 127, + 397 + ], + "lines": [ + { + "bbox": [ + 60, + 237, + 127, + 397 + ], + "spans": [ + { + "bbox": [ + 60, + 237, + 127, + 397 + ], + "type": "image", + "image_path": "1a1622d7a3a8e1e29cb27a7f80a0c85683f37fbf33d3f826eabb169487d3c9a5.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 407, + 555, + 441 + ], + "lines": [ + { + "bbox": [ + 55, + 407, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 555, + 441 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison with baselines. Baselines followed by a \\*\\* use reference images as input rather than character images. Methods marked by \\*\\* means re-trained with dialog embedding. Our model excels at preserving the characters while following the text prompt. Our DiffSensei successively generates highlighted details in panel captions. Better viewed with zoom-in." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 130, + 237, + 196, + 397 + ], + "blocks": [ + { + "bbox": [ + 130, + 237, + 196, + 397 + ], + "lines": [ + { + "bbox": [ + 130, + 237, + 196, + 397 + ], + "spans": [ + { + "bbox": [ + 130, + 237, + 196, + 397 + ], + "type": "image", + "image_path": "68a273d5b63c2d0199378b1a9429715aa4cee164fdbf8c981fc91e4619ec2a46.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 200, + 238, + 264, + 397 + ], + "blocks": [ + { + "bbox": [ + 200, + 238, + 264, + 397 + ], + "lines": [ + { + "bbox": [ + 200, + 238, + 264, + 397 + ], + "spans": [ + { + "bbox": [ + 200, + 238, + 264, + 397 + ], + "type": "image", + "image_path": "f33bf9ec5f480c8d7dc21bd72f25f995ad3414d1b8709b5752862d4855f54979.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 268, + 238, + 344, + 397 + ], + "blocks": [ + { + "bbox": [ + 268, + 238, + 344, + 397 + ], + "lines": [ + { + "bbox": [ + 268, + 238, + 344, + 397 + ], + "spans": [ + { + "bbox": [ + 268, + 238, + 344, + 397 + ], + "type": "image", + "image_path": "103f437e3802a1df3b4c1a56b6e8a0706ee628571825b0cce1213df834d6cba7.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 347, + 238, + 411, + 396 + ], + "blocks": [ + { + "bbox": [ + 347, + 238, + 411, + 396 + ], + "lines": [ + { + "bbox": [ + 347, + 238, + 411, + 396 + ], + "spans": [ + { + "bbox": [ + 347, + 238, + 411, + 396 + ], + "type": "image", + "image_path": "0ef2cda4ff2c12928e809c0eae2a94f83f5de23e800d9673a0e9f865cee5ec19.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 414, + 238, + 479, + 396 + ], + "blocks": [ + { + "bbox": [ + 414, + 238, + 479, + 396 + ], + "lines": [ + { + "bbox": [ + 414, + 238, + 479, + 396 + ], + "spans": [ + { + "bbox": [ + 414, + 238, + 479, + 396 + ], + "type": "image", + "image_path": "daefc6b632c87351b7faea032792b4d451af6d4e760f4a259e690bbbceb4ade4.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 483, + 238, + 548, + 396 + ], + "blocks": [ + { + "bbox": [ + 483, + 238, + 548, + 396 + ], + "lines": [ + { + "bbox": [ + 483, + 238, + 548, + 396 + ], + "spans": [ + { + "bbox": [ + 483, + 238, + 548, + 396 + ], + "type": "image", + "image_path": "73c5f6e27557f1c0dc647c64276221af2cb9a3aaaa6f52833973803bdcd5d495.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 57, + 461, + 290, + 550 + ], + "blocks": [ + { + "bbox": [ + 57, + 461, + 290, + 550 + ], + "lines": [ + { + "bbox": [ + 57, + 461, + 290, + 550 + ], + "spans": [ + { + "bbox": [ + 57, + 461, + 290, + 550 + ], + "type": "image", + "image_path": "7a3d44ac14164cd495db218e1d1232c60def80c4340ed8cb10f3ffd87668309a.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 63, + 560, + 288, + 572 + ], + "lines": [ + { + "bbox": [ + 63, + 560, + 288, + 572 + ], + "spans": [ + { + "bbox": [ + 63, + 560, + 288, + 572 + ], + "type": "text", + "content": "Figure 5. Human preference study on MangaZero eval set." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 54, + 582, + 297, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 582, + 297, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 582, + 297, + 713 + ], + "type": "text", + "content": "els across five key metrics. Our model improves 0.06 in the CLIP metrics compared to the multi-subject customization baseline, MS-Diffusion [39], which struggles to modify characters' states effectively in response to textual prompts. Furthermore, DiffSensei demonstrates superior image quality and character preservation, as evidenced by higher DINO-I and DINO-C scores. Although AR-LDM [25] achieves higher CLIP metrics, it suffers from poor image quality and lacks the architectural capability to manage multiple characters, resulting in low DINO-C scores. In contrast, our method strikes a balance be" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 461, + 555, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 555, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 555, + 544 + ], + "type": "text", + "content": "tween maintaining character appearances and adapting to text prompts. We also compare the Manga109 evaluation set with the results shown in Tab. 2b. When using previously unseen characters as inputs, our model continues to outperform the baselines. These results underscore the strong generalization ability of DiffSensei, demonstrating effective adaptation to new characters." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 545, + 556, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 556, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 556, + 629 + ], + "type": "text", + "content": "In Fig. 5, we present the results of a human preference study comparing our model to the baselines across several dimensions. Our model receives the highest ratings from human evaluators, particularly in terms of overall preference, character consistency, and image quality. These findings confirm that DiffSensei excels in rendering vivid and engaging manga stories." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 556, + 715 + ], + "type": "text", + "content": "Qualitative comparison. Fig. 4 shows a qualitative comparison between DiffSensei and baseline models. The results illustrate that our model significantly outperforms the baselines in generating an entire page of a manga story. SEED-Story [46] employs an MLLM to create captions for each panel, leading to unnatural narrative text and chaotic story generation that fails to form a coherent story. StoryD" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28690" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 72, + 140, + 207 + ], + "blocks": [ + { + "bbox": [ + 60, + 72, + 140, + 207 + ], + "lines": [ + { + "bbox": [ + 60, + 72, + 140, + 207 + ], + "spans": [ + { + "bbox": [ + 60, + 72, + 140, + 207 + ], + "type": "image", + "image_path": "c568511057517d739b036a5742d2e2e6f7321a7c189e892e49c856c174ecfce1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 218, + 555, + 243 + ], + "lines": [ + { + "bbox": [ + 55, + 218, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 55, + 218, + 555, + 243 + ], + "type": "text", + "content": "Figure 6. Qualitative results. Character images in red boxes are from Manga109 (The rightmost example). Our DiffSensei can generate vivid manga pages in various scenarios. Better viewed with zoom-in. More results can be found in the appendix." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 143, + 72, + 219, + 207 + ], + "blocks": [ + { + "bbox": [ + 143, + 72, + 219, + 207 + ], + "lines": [ + { + "bbox": [ + 143, + 72, + 219, + 207 + ], + "spans": [ + { + "bbox": [ + 143, + 72, + 219, + 207 + ], + "type": "image", + "image_path": "36417586eb88ed32341cbd430925da138072c13423b40036e2b73176b462ff11.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 223, + 72, + 309, + 207 + ], + "blocks": [ + { + "bbox": [ + 223, + 72, + 309, + 207 + ], + "lines": [ + { + "bbox": [ + 223, + 72, + 309, + 207 + ], + "spans": [ + { + "bbox": [ + 223, + 72, + 309, + 207 + ], + "type": "image", + "image_path": "e448fec9f30b666f3888d40d9e915b57544a7319513972892ccb1342932f1851.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 383, + 207 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 383, + 207 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 383, + 207 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 383, + 207 + ], + "type": "image", + "image_path": "4dd5be999682c362265ad4c254be95ac636c7fdd58a09b24b2ace0c5a473bcd8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 385, + 72, + 466, + 207 + ], + "blocks": [ + { + "bbox": [ + 385, + 72, + 466, + 207 + ], + "lines": [ + { + "bbox": [ + 385, + 72, + 466, + 207 + ], + "spans": [ + { + "bbox": [ + 385, + 72, + 466, + 207 + ], + "type": "image", + "image_path": "d803408655b73ddbd1dd72088d3d646e0aaf21625f259d0ea702c4948108aab1.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 468, + 72, + 551, + 207 + ], + "blocks": [ + { + "bbox": [ + 468, + 72, + 551, + 207 + ], + "lines": [ + { + "bbox": [ + 468, + 72, + 551, + 207 + ], + "spans": [ + { + "bbox": [ + 468, + 72, + 551, + 207 + ], + "type": "image", + "image_path": "0d85b594c21becd46280a58f8f1a717a89caa12d4a781ad1eda3f23bc5f1ce46.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 60, + 302, + 293, + 357 + ], + "blocks": [ + { + "bbox": [ + 55, + 260, + 295, + 294 + ], + "lines": [ + { + "bbox": [ + 55, + 260, + 295, + 294 + ], + "spans": [ + { + "bbox": [ + 55, + 260, + 295, + 294 + ], + "type": "text", + "content": "Table 3. Ablation study. CM is character masked attention injection. DM is dialog masked encoding. Magi means using Magi [30] image encoder. MLLM means using MLLM for stage 2 training." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 302, + 293, + 357 + ], + "lines": [ + { + "bbox": [ + 60, + 302, + 293, + 357 + ], + "spans": [ + { + "bbox": [ + 60, + 302, + 293, + 357 + ], + "type": "table", + "html": "
    CMDMMagiMLLMFID ↓CLIP ↑DINO-I ↑DINO-C ↑F1 score ↑
    0.4100.2300.5930.6100.361
    ✓0.4110.2250.5910.6370.364
    ✓✓0.4070.2280.6000.6350.653
    ✓✓✓0.4080.2310.6180.6480.718
    ✓✓✓✓0.4070.2350.6180.6510.727
    ", + "image_path": "5bd4ddc6be307921aaffaac44c1e9b95ea72411decaf32bf97d5e4fa21222fca.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 376, + 296, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 296, + 485 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 296, + 485 + ], + "type": "text", + "content": "iffusion [53] is limited to producing fixed-resolution images due to its self-attention sharing mechanism, restricting its ability to generate diverse images. It shows inferior results, probably because the input reference panel has an unbalanced aspect ratio. MS-Diffusion [39] trains with source character images from the target panel and lacks the flexibility to modify characters' states effectively. In contrast, our method excels in text-following, character preservation, and overall story presentation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 491, + 167, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 167, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 167, + 504 + ], + "type": "text", + "content": "5.3. Qualitative Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 509, + 295, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 295, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 295, + 594 + ], + "type": "text", + "content": "Fig. 6 shows several manga pages generated by DiffSensei. The results demonstrate that our method can generate vivid manga panels and provide visually plausible results for the customized manga generation task. Our model can also generalize to unseen characters, as illustrated in the rightmost example, with character images from Manga109 [2] as input. Please see more results in the Appendix." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 600, + 149, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 600, + 149, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 600, + 149, + 613 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 617, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 295, + 714 + ], + "type": "text", + "content": "Tab. 3 presents the quantitative ablation study of DiffSensei, where we systematically remove components to assess their impact. Specifically, when the MLLM component, serving as the flexible character feature adapter, is excluded, the CLIP metrics decrease by " + }, + { + "bbox": [ + 55, + 617, + 295, + 714 + ], + "type": "inline_equation", + "content": "1.73\\%" + }, + { + "bbox": [ + 55, + 617, + 295, + 714 + ], + "type": "text", + "content": ", and the DINO-C score also drops, underscoring its role in enhancing transferring character to the text-derived states. The absence of the Magi [30] image encoder results in a general decline in met-" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 261, + 555, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 261, + 555, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 261, + 555, + 501 + ], + "type": "text", + "content": "rics, particularly in image quality and character similarity, highlighting the importance of the Magi encoder for effectively encoding manga characters. Magi is trained specifically on manga datasets, performing better at preserving manga characters. To investigate alternative methods for encoding character and dialog layout conditions, we experimented with replacing the dialog embedding technique by inputting the Fourier embeddings of dialog bounding boxes into the timestep embedding of SDXL [26]. This modification led to a significant decrease in layout control, evidenced by the F1 score plummeting from 0.653 to 0.364, demonstrating that directly incorporating dialog embeddings into the latent is a superior approach for encoding dialog layouts. Furthermore, we explored adding the Fourier embeddings of character bounding boxes to the character features as an alternative to masked attention injection. This change caused a marked drop in the DINO-C metric, reaffirming the effectiveness of our original masked attention strategy. For comprehensive effect showcases, please see the qualitative ablation study in the Appendix." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 513, + 388, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 513, + 388, + 525 + ], + "spans": [ + { + "bbox": [ + 314, + 513, + 388, + 525 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 533, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 676 + ], + "type": "text", + "content": "This paper introduces DiffSensei, a novel framework for multi-character customized story visualization that integrates a diffusion-based image generator with an MLLM as a text-compatible identity adapter. Key innovations include masked attention control for character layout management, dialog layout embedding, and an MLLM-based feature adapter for flexible character customization. Supported by the proposed MangaZero dataset, comprising 43,264 manga pages and 427,147 panels, DiffSensei achieves superior, character-consistent panels that dynamically respond to textual prompts, surpassing existing methods and advancing the field of story visualization." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "Acknowledgement. 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In NeurIPS, 2024. 1, 2, 6, 7, 8" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28693" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/5f1209e6-1544-45b7-80b5-0030e5048d70_content_list.json b/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/5f1209e6-1544-45b7-80b5-0030e5048d70_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..48838dbf92d9db693642a6a2c1d996a7ab88e82e --- /dev/null +++ b/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/5f1209e6-1544-45b7-80b5-0030e5048d70_content_list.json @@ -0,0 +1,1964 @@ +[ + { + "type": "text", + "text": "DIFFVSGG: Diffusion-Driven Online Video Scene Graph Generation", + "text_level": 1, + "bbox": [ + 151, + 130, + 844, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mu Chen1, Lulei Li2, Wenguan Wang1†, Yi Yang1 \n1ReLER, CCAI, Zhejiang University 2ReLER, AAI, University of Technology Sydney \nhttps://github.com/kagawa588/DiffVsgg", + "bbox": [ + 233, + 179, + 761, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 286, + 326, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Top-leading solutions for Video Scene Graph Generation (VSGG) typically adopt an offline pipeline. Though demonstrating promising performance, they remain unable to handle real-time video streams and consume large GPU memory. Moreover, these approaches fall short in temporal reasoning, merely aggregating frame-level predictions over a temporal context. In response, we introduce DIFFVSGG, an online VSGG solution that frames this task as an iterative scene graph update problem. Drawing inspiration from Latent Diffusion Models (LDMs) which generate images via denoising a latent feature embedding, we unify the decoding of object classification, bounding box regression, and graph generation three tasks using one shared feature embedding. Then, given an embedding containing unified features of object pairs, we conduct a step-wise Denoising on it within LDMs, so as to deliver a clean embedding which clearly indicates the relationships between objects. This embedding then serves as the input to task-specific heads for object classification, scene graph generation, etc. DIFFVSGG further facilitates continuous temporal reasoning, where predictions for subsequent frames leverage results of past frames as the conditional inputs of LDMs, to guide the reverse diffusion process for current frames. Extensive experiments on three setups of Action Genome demonstrate the superiority of DIFFVSGG.", + "bbox": [ + 89, + 318, + 483, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 727, + 220, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video Scene Graph Generation (VSGG) is receiving growing attention as it benefits a wide range of downstream tasks (e.g., video caption [34, 91], video retrieval [31, 50], and visual question answering [49, 87]). To deliver a holistic understanding of the underlying spatial-temporal dynamics within scenes, this task aims to construct a sequence of directed graphs where nodes represent objects and edges describe inter-object relationships (a.k.a., predicate).", + "bbox": [ + 89, + 753, + 482, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0a2bae8d608eb403a3157ebffe44468b891e594aba328f7232fbb53267d49602.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 527, + 290, + 893, + 431 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5c83770ea906bd7cae56b2c8ae9b8936d33f4d2fac574ac4856e2334c04e3662.jpg", + "image_caption": [ + "Figure 1. (a) Existing VSGG solutions typically adopt an offline training pipeline, dividing the problem into various components: object detection, temporal association, and contextual aggregation. (b) DIFFVSGG introduces a new paradigm that performs spatial-temporal reasoning directly as each frame is processed sequentially, enabling progressive, online updates to the scene graph." + ], + "image_footnote": [], + "bbox": [ + 527, + 422, + 893, + 569 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Top-leading VSGG approaches typically adopt an offline pipeline [30, 69, 94], where scene graphs are generated independently for each frame and then aggregated along the temporal dimension (i.e., Fig. 1(a)). Though demonstrating strong performance, they require full video sequences as inputs, which faces challenges in processing long videos containing hundreds of frames due to GPU memory constraints, and is unable to handle real-time video streams for applications like autonomous driving and augmented reality [100]. Moreover, the dealing of temporal cues focuses solely on the global aggregation of frame-level predictions via Transform blocks. This falls short in the reasoning over temporal space, which is essential for modeling the dynamic changes of interactions between subjects and objects, and", + "bbox": [ + 511, + 688, + 906, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 109, + 886, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "29161", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "potentially benefits predicate prediction. Though a surge of early work has sought to facilitate explicit reasoning over the temporal domain via messaging passing [90] or spatial-temporal graph [74], a large performance gap remains when compared to these offline temporal aggregation approaches.", + "bbox": [ + 89, + 90, + 480, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose DIFFVSGG, a high performance online approach for VSGG in leverage of Latent Diffusion Models (LDMs)[77, 81] (i.e., Fig.1(b)). In VSGG, the scene graph is dynamically evolved throughout the progression of video frames, with nodes and edges being continuously updated to precisely reflect the latest video content. Such an iterative update process shares a similar spirit of LDMs, which progressively remove noise to generate new samples from data distributions. Naturally, our motivation is to develop a VSGG model that aligns with the denoising principle of LDMs to iterative refine scene graphs along the temporal dimension, facilitating online temporal reasoning within this reverse diffusion process.", + "bbox": [ + 88, + 170, + 480, + 366 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve this, we tackle VSGG from a unified perspective, organizing the decoding of object classification, bounding box regression, and graph generation three tasks from a shared feature embedding, which serves as the input and output of the Denoising U-Net. Concretely, from the spatial perspective, given the object detection results from each frame, multiple object pairs can be constructed. Then, for each object pair, we integrate i) the visual feature of two objects, ii) the union feature between, and iii) the locations of two objects, into a unified embedding. This embedding serves as the input to the denoising U-Net, after steps of denoising, a clean embedding clearly describing the objects as well as their inter-object relationships can be delivered. From the temporal perspective, DIFFVSGG conducts frame-by-frame reasoning where the result for each subsequent frame is delivered by iteratively refining the predictions of previous frames via reverse diffusion. Specifically, object positions and contextual information from prior frames are leveraged as conditions to guide the denoising of the shared feature embeddings for current frames. This encourages continuous temporal reasoning as the video progresses, allowing DIFFVSGG to effectively capture long-term spatiotemporal dependencies and adapt to complex motion patterns in an online manner. To further unlock the potential of LDMs, we build a memory bank to store positions for each object. In this way, motion information including acceleration and deceleration of object can be explicitly calculated. These motion cues are integrated into conditional inputs for the reverse diffusion step, which can help infer relationships such as following or approaching between objects.", + "bbox": [ + 91, + 369, + 482, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DIFFVSGG distinguishes itself in several aspects: First, it tackles VSGG in an online manner to continuously address an unlimited number of frames, while being friendly to devices with limited GPU memory. Second, the prediction of each video is implemented as a reverse diffusion pro", + "bbox": [ + 89, + 824, + 480, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cess, which elegantly encodes spatial and temporal reasoning into the Denoising step. Third, the temporal cues (i.e., historic predictions) are propagated into subsequent frames as conditions and participating in the prediction, while prior work simply aggregates predictions of all frames along the temporal dimension. Fourth, the learning of object classification, bounding box regression, and graph generation three tasks are jointly optimized with a shared feature embedding. Such a unified learning paradigm allows for the solving of VSGG from a global view, and avoids error made in one task propagating to subsequent tasks. Fifth, this unified decoding simplifies the VSGG pipeline and eliminates cumbersome handcrafted modules such as non-maximum suppression (NMS), and entity matching across frames.", + "bbox": [ + 511, + 90, + 903, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To the best of our knowledge, DIFFVSGG is the first work that treats the VSGG task as an iterative denoising problem along the temporal dimension. Extensive experiments on Action Genome (AG) [40] demonstrate the superiority of our proposed method. Notably, DIFFVSGG achieves SOTA results across all three setups and surpasses the top-leading solutions (e.g., DSG-DETR [30]) by 3.3 in terms of R@10, highlighting the great potential of utilizing diffusion models for visual relation understanding in videos.", + "bbox": [ + 511, + 301, + 903, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 452, + 653, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scene Graph Generation (SGG). SGG involves detecting object instances and classifying their pairwise visual relations in an image, which is essential for comprehensive visual tasks [7, 8, 11, 53, 97, 98, 117, 118]. Recent SGG approaches seek to comprehend visual context by aggregating spatial context through various strategies, including explicit message passing [14, 20, 56, 57, 103, 112], graph structure modeling [83, 85, 99, 106, 110], external knowledge integration [3, 14, 33, 35, 109, 111], and transformer-based networks [12, 18, 23, 24, 43, 48, 55, 59, 64, 72, 79].", + "bbox": [ + 511, + 477, + 903, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Extended from SGG, Video Scene Graph Generation (VSGG) aims to ground visual relationships jointly in spatial and temporal dimensions. Prior research primarily concentrates on addressing the long-tail distribution problem observed in prominent benchmarks [40]. Numerous unbiased approaches [16, 21, 46, 51, 54, 68, 86, 105] have been devised to handle infrequent predicate classes arising from this distribution. Furthermore, recent VSGG methods underscore the importance of spatial-temporal learning, and make use of the sequence-processing ability of Transformer [2, 70, 84] to capture temporal continuity. Nonetheless, these approaches often depend on complex post-processing that decouples spatial and temporal learning into two independent steps, and simply emphasizes on the consistent matching between frames.", + "bbox": [ + 511, + 628, + 903, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, DIFFVSGG handles both spatial and temporal reasoning from a unified perspective, where the reasoning on temporal dimension is naturally achieved via utiliz", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "29162", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing the spatial reasoning results of prior frames as the conditions to guide predictions for the current frames.", + "bbox": [ + 89, + 90, + 482, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Models Beyond Image Generation. Diffusion Models (DMs) have surpassed many other generative models in image generation [6, 22, 37, 38, 92, 104] by successively denoising images. Beyond image generation, DMs inherently perform implicit discriminative reasoning while generating data, which proves highly effective in visual tasks that require complex relationship modeling and spatiotemporal reasoning. Therefore, a surge of work has adapted generative diffusion models for tasks including image segmentation [1, 4, 5, 15, 32, 44, 93], object detection [13, 76, 102], object tracking [65, 66, 101], and monocular depth estimation [25, 67, 78, 116]. Recent research has also utilizes DMs for more complex tasks that require high-level visual understanding abilities such as visual-linguistic understanding [47], scene generation [39], and human-object interaction detection [41, 52]. The potential of DMs in processing graph data has also been explored, encompassing a range of advanced tasks. This includes early work employing score-based methods for generating permutation-invariant graphs [42, 71], as well as recent approaches focused on enhancing graph neural networks [114, 115] and advancing graph generation techniques [107].", + "bbox": [ + 91, + 123, + 483, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we borrow the step-wise denoising ability of latent diffusion models to enable spatial reasoning within a single frame. This is achieved by iteratively refining the union embeddings of object pairs, which serve to inform the prediction for bounding boxes and predicate classes, etc. On the other hand, temporal reasoning across frames is facilitated via conditional prompting, i.e., using predictions of prior frames which contain rich location and inter-object relationship cues to guide the denoising of current frames.", + "bbox": [ + 89, + 458, + 483, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Temporal Reasoning in Videos. Reasoning within the temporal dimension poses significant challenges for achieving high-level comprehension in video-related tasks [9, 10, 27-29, 61, 73, 108]. Recent advancements in video question answering seek to tackle temporal reasoning by employing attention mechanisms [26, 82] or incorporating external memory modules [45, 75] across video frames. In addition, to accurately capture the start, progression, and end of an action, action recognition approaches [89, 95] model complex motion patterns and dependencies in sequence. Video object detection (VOD) [19, 62] focuses on accurately capturing object trajectories, even in the presence of occlusions and abrupt movements. The top-leading VSGG solutions [30, 69, 94] instead aggregate predictions across frames to maintain the temporal consistency of objects.", + "bbox": [ + 89, + 595, + 483, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In summary, although existing work facilitates temporal reasoning from different perspectives and demonstrates it effectiveness, the potential of diffusion models remains largely underexplored. In fact, the sequential denoising in time, where each step is informed by previous one, offers", + "bbox": [ + 89, + 825, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a suitable tool to reconstruct the states for current frames based on observations from past frames. This insight motivates the proposal of DIFFVSGG, which tackles the VSGG task via graph denoising over the temporal dimension.", + "bbox": [ + 511, + 90, + 905, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 511, + 169, + 648, + 186 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first give a brief introduction to the general background of latent Diffusion Models (§3.1), then elaborate on the overall design of our proposed DIFFVSGG (§3.2), and finally present the detailed information on the network architecture and training objectives (§3.3).", + "bbox": [ + 511, + 196, + 905, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary: Latent Diffusion Models", + "text_level": 1, + "bbox": [ + 511, + 286, + 843, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To begin, we give an illustration on how diffusion processes [81] are used to model data distributions and generate high-quality samples. Specifically, we consider a continuous-time Markov chain with $t \\in [0,T]$ :", + "bbox": [ + 511, + 309, + 905, + 369 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq (x _ {t} | x _ {t - 1}) = \\mathcal {N} (x _ {t}; \\sqrt {1 - \\beta_ {t}} x _ {t - 1}, \\beta_ {t} I), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 381, + 906, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\beta_{t}$ is a small noise variance term at timestep $t$ , and $\\mathcal{N}$ denotes a Gaussian distribution. The corrupted data at any intermediate time step $t$ can be derived recursively as:", + "bbox": [ + 511, + 411, + 905, + 455 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha}} \\epsilon , \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 467, + 906, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = 1 - \\beta_{t}$ and $\\overline{\\alpha}_t = \\prod_{s = 1}^t\\alpha_s$ is the cumulative product of $\\alpha_{t}$ over the timesteps, $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ represents the sampled noise. The reverse process essentially involves learning to reverse the noise addition at each step. The cleaned data at time step $t$ can be written recursively as:", + "bbox": [ + 511, + 498, + 905, + 575 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} \\left(x _ {t}, t\\right), \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 585, + 905, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where a time-conditioned denoising neural network $\\epsilon_{\\theta}(x,t)$ is trained to minimize the mean squared error between the true and predicted noise at each timestep:", + "bbox": [ + 511, + 626, + 905, + 672 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {D M}} := \\mathbb {E} _ {x _ {0}, \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| _ {2} ^ {2} \\right]. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 681, + 905, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Building on the diffusion process described above, latent diffusion models (LDMs) [77] first encode samples into a low-dimensional latent space $z = \\mathcal{E}(x)$ using an encoder $\\mathcal{E}$ , and then apply the diffusion process within this compressed space. Moreover, LDMs introduce the conditioning mechanisms which allow for control over the generated output based on additional input $y$ such as text, labels, or images. Consequently, the training objective for LDMs is given as:", + "bbox": [ + 511, + 718, + 905, + 839 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {L D M}} := \\mathbb {E} _ {\\mathcal {E} (x _ {0}), y, \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\boldsymbol {z} _ {t}, t, c _ {\\theta} (y)\\right) \\| _ {2} ^ {2} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 849, + 903, + 875 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $c_{\\theta}$ is a conditioning model to encode $y$", + "bbox": [ + 511, + 885, + 818, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "29163", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ba5ec8b663d8693eec909998f5d99a3dbb7d655bb55e5b3e6f369d1753caf50c.jpg", + "image_caption": [ + "Figure 2. Overview of our proposed inter-object relationship learning strategy using latent diffusion models." + ], + "image_footnote": [], + "bbox": [ + 99, + 99, + 888, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. DIFFVSGG: Diffusion Models for VSGG", + "text_level": 1, + "bbox": [ + 89, + 268, + 429, + 282 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Problem Definition. Considering a video sequence represented as $\\mathcal{I} = \\{I^1,\\dots ,I^T\\}$ containing $T$ frames, the objective of VSGG is to generate a sequence of scene graph $\\mathcal{G} = \\{G^{1},\\dots ,G^{T}\\}$ over time, where each element $\\mathcal{G}^t$ represents the corresponding scene graph for frame $I^t$ . Each graph $G^{t}$ is defined as $G^{t} = (\\mathcal{V}^{t},\\mathcal{E}^{t})$ , with $\\mathcal{V}^t$ and $\\mathcal{E}^t$ denoting the sets of graph nodes and edges, respectively. Each node $v_{i}^{t}\\in \\mathcal{V}^{t}$ includes attributes such as category and location for object $i$ , while each edge $e_{i,j}^{t}\\in \\mathcal{E}^{t}$ describes the inter-object relationship (a.k.a.predicate) between subject $i$ and object $j$ . In this manner, $\\mathcal{G}$ captures all objects (i.e., $\\mathcal{V}$ ), their interactions (i.e., $\\mathcal{E}$ ), and the dynamics as they evolve over time (i.e., from $t = 1$ to $t = T$ ) within the scene.", + "bbox": [ + 89, + 290, + 483, + 487 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Graph Construction. Given a video $\\mathcal{I} = \\{I^1,\\dots ,I^T\\}$ , we first employ an on-the-shelf object detector $\\mathcal{F}_{\\mathrm{det}}$ for each frame:", + "bbox": [ + 89, + 486, + 483, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {F} ^ {t}, \\mathcal {B} ^ {t}, \\mathcal {O} ^ {t} \\right\\} = \\mathcal {F} _ {\\det } \\left(I ^ {t}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 527, + 480, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{F}^{t}$ is the feature extracted by backbone, $\\mathcal{B}^t = \\{b_1^t,\\dots ,b_{N_t}^t\\}$ and $\\mathcal{O}^t = \\{o_1^t,\\dots ,o_{N_t}^t\\}$ are bounding box and class predictions for $N_{t}$ objects detected from frame $I^t$ respectively. This serves to initialize an adjacency matrix $\\pmb{A}^{t}\\in \\mathbb{R}^{N_{t}\\times N_{t}\\times D_{e}}$ , of which each element aims to represent the inter-object relationships between object $i$ and $j$ ..", + "bbox": [ + 89, + 546, + 483, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} _ {i, j} ^ {t} = \\left[ \\boldsymbol {F} _ {o _ {i}} ^ {t}; \\boldsymbol {F} _ {o _ {i}, o _ {j}} ^ {t}; \\boldsymbol {F} _ {b _ {i}} ^ {t} \\right] \\in \\mathbb {R} ^ {D _ {e}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 643, + 480, + 670 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} _ {j, i} ^ {t} = \\left[ \\boldsymbol {F} _ {o _ {j}} ^ {t}; \\boldsymbol {F} _ {o _ {j}, o _ {i}} ^ {t}; \\boldsymbol {F} _ {b _ {j}} ^ {t} \\right] \\in \\mathbb {R} ^ {D _ {e}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 666, + 395, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $[]$ refers to the concatenation of features, implemented as torch.cat(). $F_{o_i}^t = \\mathcal{F}_{\\mathrm{ROI}}(F^t,b_i^t)$ is the instance-level feature for object $i$ extracted via ROAlign [36] (i.e., $\\mathcal{F}_{\\mathrm{ROI}}), F_{o_i,o_j}^t = \\mathcal{F}_{\\mathrm{ROI}}(F^t,b_i^t\\cup b_j^t)$ is the feature mapped from the union box of object $i$ and $j$ (i.e., $b_{i}^{t}\\cup b_{j}^{t})$ ,and $F_{b_i}^t$ describes bounding box $b_{i}^{t}$ using a box-to-feature mapping function identical to that in [112]. $A_{i,j}^{t}$ represents the relationship predicted from subject $i$ , which differs from $A_{j,i}^{t}$ where $j$ is considered the subject. In this way, the matrix $A^t$ encodes both node features of each object and the edge features between any pair of them. Note that such subject-based encoding does not incorporate $Fo_{j}$ and $Fb_{j}$ into $A_{i,j}$ (i.e., $[F_{o_i};F_{b_i};F_{o_i,o_j};F_{o_j};F_{b_j}])$ , which hinders the neural network to distinguish between the subject $(i)$ and object", + "bbox": [ + 89, + 686, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$(j)$ . Additionally, as the number of instances $(i.e., N_{t})$ typically varies across frames due to the emergence or disappearance of some instances, we pad $\\mathbf{A}^{t}$ to a fixed size of $N \\times N$ where $N > \\max(N_{1}, \\dots, N_{T})$ , using randomly generated feature embedding from Gaussian distributions.", + "bbox": [ + 511, + 268, + 906, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inter-object Relationship Learning via LDMs. Next we aim to facilitate the learning of inter-object relationships within LDMs using ground truth scene graph (i.e., Fig. 2). Since we use an off-the-self object detector, the extracted feature $F^t$ remains static for each frame. Therefore, with access to the ground truth bounding box annotations, we can compute precise edge features via Eq.7 from $F^t$ . The adjacency matrix $\\hat{A}^t$ which exactly encodes the inter-object features can also be obtained. Here $\\hat{A}^t$ is the ground truth of inter-object relationships, initialized using features derived from ground-truth bounding boxes, where object pairs with no relations are represented as empty entries. $\\hat{A}^t$ instructs the learning of a LDM which is responsible for recovering object features and their relationships from random noise.", + "bbox": [ + 511, + 345, + 906, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- Forward Process. Let $\\hat{A}^{t,0}$ represent the clean adjacency matrix. The noise injection process to progressively perturb this matrix is defined following Eq.2, and expressed as:", + "bbox": [ + 511, + 556, + 905, + 602 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {A}} ^ {t, k} = \\sqrt {\\bar {\\alpha} _ {t}} x \\hat {\\boldsymbol {A}} ^ {t, 0} + \\sqrt {1 - \\bar {\\alpha}} \\epsilon , \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 604, + 903, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{A}^{t,k}$ denotes the noisy adjacency matrix at step $k$ . This enables the model to learn robust feature representations, through the exposure to degraded versions of $\\hat{A}^{t,0}$ .", + "bbox": [ + 511, + 628, + 905, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- **Reverse Process.** To recover the original adjacency matrix $\\hat{A}^{t,0}$ , we employ a denoising U-Net $\\epsilon_{\\theta}$ which is trained to iteratively remove noise starting from the initial noisy matrix $\\hat{A}^{t,K}$ . This process follows the denoising step defined in Eq.3 and proceeds as:", + "bbox": [ + 511, + 675, + 906, + 750 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {A}} ^ {t, k - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} (\\hat {\\boldsymbol {A}} ^ {t, k} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} (\\hat {\\boldsymbol {A}} ^ {t, k}, k), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 753, + 906, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}$ is optimized to recover meaningful inter-object relationships. Following Eq. 5, we define the training objective $\\mathcal{L}_{\\mathrm{VSGG}}$ by minimizing the spatial structure loss:", + "bbox": [ + 511, + 791, + 905, + 837 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {V S G G}} := \\mathbb {E} _ {\\hat {\\boldsymbol {A}} ^ {t, k}, \\epsilon , k} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\hat {\\boldsymbol {A}} ^ {t, k}, k) \\| _ {2} ^ {2} \\right]. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 840, + 903, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{\\mathrm{VSGG}}$ encourages $\\epsilon_{\\theta}$ to accurately predict and remove the noise at each step $k$ , so as to restore $\\hat{\\boldsymbol{A}}^t$ structured in the", + "bbox": [ + 511, + 869, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "29164", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fedb4341dd21e77d73c9959b6c8446b264a2d78e26eeec7d7f2dd91aaf159eda.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 93, + 148, + 140 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/34556366425ae63134e07560e753c299c2af6184f0ae918d88b2f02d147032cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 153, + 95, + 183, + 138 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8473a30f996bc1070ad7f86f4ea76a967477497b81963f41a1160b2e5bb24cc3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 95, + 235, + 138 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/05b86db6900c1a573fd87835e98a388c4be6f3f7ebaebf886086693f0debe8d6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 97, + 473, + 188 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e2835cfc1ab9d08d216ee548470c8a073c32c37f20282a0bf26ba3edd1ffd437.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 143, + 148, + 189 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ca6278ce9ce36864ffd2abb575eb7cfa298ba96717c98965891d21bc78ca100d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 153, + 143, + 184, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9f1ab44f787e4bd76b0d68c7f999faeb14919fccfd20ca774221136ba21d4719.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 187, + 143, + 236, + 188 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/46b743f1ae8513363d070d421394cdf8f4597766d7d800d860113209af249cc4.jpg", + "image_caption": [ + "Figure 3. Overview of our proposed temporal prompting strategy." + ], + "image_footnote": [], + "bbox": [ + 243, + 189, + 473, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "way that preserves spatial and relational coherence. During inference, given the adjacency matrix $\\mathbf{A}^t$ from an arbitrary frame $t$ , we consider it noisy and utilize the well-trained denoising U-Net above to refine it, so as to deliver an updated version that indicates the interaction between objects, as well as the location and category of objects: $\\mathbf{A}^{t,k - 1} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{A}^{t,k} - \\frac{\\beta_t}{\\sqrt{1 - \\overline{\\alpha}}}\\epsilon_\\theta (\\mathbf{A}^{t,k},k)$ . Unlike the training process which utilizes $\\hat{\\mathbf{A}}$ derived from ground truth bounding boxes, $\\mathbf{A}$ here is obtained from the predicated ones. Note that the main challenge of VSGG lies in modeling of the dynamic changes of relation between object and subject, and the diffusion models primarily focus on recovering object features and their relationships. Thus, the slight bias in predicated bounding boxes, especially after ROIAAlign, causes negligible impacts to relation predictions.", + "bbox": [ + 89, + 268, + 483, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Condition Based Temporal Reasoning. For a given video stream, we can infer future frames based on the content of preceding frames. This observation serves as the motivation for our temporal prompting strategy (i.e., Fig.3), where we condition the denoising process of $A^t$ on the denoised adjacency matrix of prior frames (i.e., $A^{t - 1,0}$ ), as follows:", + "bbox": [ + 89, + 500, + 483, + 590 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} ^ {t, k - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {A} ^ {t, k} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} \\left(\\boldsymbol {A} ^ {t, k}, k, \\boldsymbol {A} ^ {t - 1, 0}\\right), \\right. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 597, + 480, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the condition decoder $c_{\\theta}$ in Eq. 5 is discarded, as $\\pmb{A}^{t - 1,0}$ has already shared the same dimension as $\\pmb{A}^{t,k}$ . With this condition-based temporal association for denoising, the training objective for $\\epsilon_{\\theta}$ is updated as:", + "bbox": [ + 89, + 637, + 483, + 699 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {T . V S G G}} := \\mathbb {E} _ {\\boldsymbol {A} ^ {t, k}, \\boldsymbol {A} ^ {t - 1, 0}, \\epsilon , k} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\boldsymbol {A} ^ {t, k}, \\boldsymbol {A} ^ {t - 1, 0}, k) \\| _ {2} ^ {2} \\right]. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 708, + 480, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here $\\mathcal{L}_{\\mathrm{T.VSGG}}$ encourages $\\epsilon_{\\theta}$ to generate temporally consistent outputs, enabling a smooth and coherent denoising of adjacency matrix across frames. Moreover, since new instances keep emerging as the video progresses, we calculate similarities between ROIAngled features of the potential new object (i.e., $F_{o_p}^t$ ) and all other objects in the past frame (i.e., $F_{o_i}^{t - 1}$ ), and consider $o_p$ as new object if the similarities is smaller than 0.2 for all other objects. Then, the random padded features in $A$ during graph construction are replaced with union and instance features of these new instances.", + "bbox": [ + 89, + 747, + 483, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motion Enhanced Denoising for VSGG. Motion cues serve as indicators to describe object movements in a given scene. They provide essential context for understanding the position and duration of events. Moreover, the speed and direction of object movements can reveal intentions for interactions (e.g., approaching), which aids in temporal reasoning by inferring whether they might complete an action or reach a goal. Therefore, given a box prediction $b_{i}^{t} = \\{x_{i}^{t}, y_{i}^{t}, w_{i}^{t}, h_{i}^{t}\\}$ for object $i$ , we explicitly calculate the approaching speed between object $i$ and $j$ as follows:", + "bbox": [ + 511, + 90, + 906, + 243 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i, j} ^ {t} = \\sqrt {\\left(x _ {i} ^ {t} - x _ {j} ^ {t}\\right) ^ {2} + \\left(y _ {i} ^ {t} - y _ {j} ^ {t}\\right) ^ {2}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 248, + 903, + 277 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv _ {i, j} ^ {t} = (d _ {i, j} ^ {t} - d _ {i, j} ^ {t - \\Delta t}) / \\Delta t,\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 277, + 774, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Delta t$ is the interval of frame. Given $v^t\\in \\mathbb{R}^{N^t\\times N^t}$ we pad it into the same size with $\\pmb{A}^{t}$ (i.e., $v^{t}\\in \\mathbb{R}^{N\\times N})$ and inject it into $\\pmb{A}^{t,k}$ at each denoising step $k\\colon \\pmb{A}^{t,k} = \\pmb{A}^{t,k} + v^t$", + "bbox": [ + 511, + 301, + 906, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Graph Readout. Next we investigate how to deliver SGG predictions for each frame based on the denoised adjacency matrix $\\mathbf{A}^{t,0}$ . Specifically, the prediction for predicate of each subject-object pair is obtained as follows:", + "bbox": [ + 511, + 364, + 905, + 425 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i, j} ^ {t} = \\operatorname {s o f t m a x} \\left(\\mathcal {F} _ {\\text {p r e d}} \\left(\\boldsymbol {A} _ {i, j} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {N _ {\\text {p r e d , c l s}}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 433, + 903, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_{\\mathrm{pred}}$ is an MLP-based classifier and $N_{\\mathrm{pred\\_cls}}$ represents the number of predicate classes. For object classification and bounding box regression, to render a global view, we utilize the entire row $i$ of $\\mathbf{A}^{t,0}$ (i.e., $\\mathbf{A}_i^{t,0}$ ) where all elements consider $i$ as the subject, to deliver the prediction:", + "bbox": [ + 511, + 460, + 905, + 537 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\no _ {i} ^ {t} = \\operatorname {s o f t m a x} \\left(\\mathcal {F} _ {\\mathrm {o b j}} \\left(\\boldsymbol {A} _ {i} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {N _ {\\mathrm {o b j , c l s}}}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 545, + 903, + 564 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nb _ {i} ^ {t} = \\operatorname {s i g m o i d} \\left(\\mathcal {F} _ {\\text {b o x}} \\left(A _ {i} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {4}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 566, + 903, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{\\mathrm{obj\\_cls}}$ is the number of object classes, $\\mathcal{F}_{\\mathrm{obj}}$ and $\\mathcal{F}_{\\mathrm{box}}$ are the MLP-based classifier and projector, respectively.", + "bbox": [ + 511, + 594, + 903, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Implementation Details", + "text_level": 1, + "bbox": [ + 511, + 633, + 730, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Network Configuration. DIFFVSGG is an online VSGG framework built upon the iterative diffusion diagram. It comprises three components: one off-the-shelf detector to deliver object detection results, the LDMs for inter-object relationship denosing, and projector heads for object classification, predicate prediction, and bounding box regression. Training Objective. The training process of DIFFVSGG consists of two stages. In the first stage, we pre-train the denoising U-Net $\\epsilon_{\\theta}$ in Eq. 9, using $\\hat{A}^t$ constructed from ground truth bounding box annotations for objects. In the second stage, we optimize the MLP classifier and projector in Eq. 14-15, which generate the final VSGG predictions.", + "bbox": [ + 511, + 655, + 906, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, given relation prediction $p_r$ and ground truth $y_r$ , the relation classification loss is computed as:", + "bbox": [ + 511, + 837, + 905, + 867 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p r e d . c l s}} = - \\sum_ {i = 1} ^ {C _ {r}} y _ {r, i} \\log \\left(p _ {r, i}\\right). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 877, + 903, + 905 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "29165", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f874e656f33871f46773b48d10a9427dd0fc4120af0c643ccfb118d7ac2a39f0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodPredCLSSGCLSSGDET
    R@10 R@20 R@50 mR@10 mR@20 mR@50R@10 R@20 R@50 mR@10 mR@20 mR@50R@10 R@20 R@50 mR@10 mR@20 mR@50
    RelDN [113]20.320.320.36.26.26.211.011.011.03.43.43.49.19.19.13.33.33.3
    TRACE [88]27.527.527.515.215.215.214.814.814.88.98.98.913.914.514.58.28.28.2
    VRD [63]51.754.754.7---32.433.333.3---19.224.526.0---
    Motif Freq [112]62.465.165.1---40.841.941.9---23.731.433.3---
    MSDN [57]65.568.568.5---43.945.145.1---24.132.434.5---
    VCTREE [85]66.069.369.3---44.145.345.3---24.432.634.7---
    GPS-Net [60]66.869.969.9---45.346.546.5---24.733.135.1---
    STTran [17]68.671.871.837.840.140.246.447.547.527.228.028.025.234.137.016.620.822.2
    APT [58]69.473.873.8---47.248.948.9---26.336.138.3---
    STTran-TPI [96]69.772.672.637.340.640.647.248.348.328.329.329.326.234.637.415.620.221.8
    TR2 [94]70.973.873.8---47.748.748.7---26.835.538.3---
    TEMPURA [69]68.871.571.542.946.346.347.248.348.334.035.235.228.133.434.918.522.623.7
    DSG-DETR [30]------50.852.052.0---30.334.836.1---
    DIFFVSGG71.974.574.548.150.250.252.553.753.737.338.438.432.839.945.520.923.626.2
    ", + "bbox": [ + 101, + 88, + 903, + 311 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Comparison of state-of-the-art VSGG methods on Action Genome test [40] under the $w$ constraint setting.", + "bbox": [ + 147, + 311, + 846, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Similarly, given object class prediction $p_{o}$ and ground truth $y_{o}$ , the object classification loss is defined as:", + "bbox": [ + 89, + 345, + 482, + 376 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {o b j} \\cdot \\mathrm {c l s}} = - \\sum_ {j = 1} ^ {C _ {o}} y _ {o, j} \\log \\left(p _ {o, j}\\right). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 378, + 482, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For bounding box regression, given the ground truth bounding box $t_k$ (e.g., $(x, y, w, h)$ ) and the predicted bounding box $\\hat{t}_k$ , the regression loss is formulated as:", + "bbox": [ + 89, + 417, + 483, + 463 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {b o x - r e g}} = \\operatorname {S m o o t h} \\mathrm {L} 1 \\left(t _ {k} - \\hat {t} _ {k}\\right). \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 477, + 482, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The training objectives for each stage are formulated as:", + "bbox": [ + 89, + 501, + 460, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Stage 1: $\\mathcal{L} = \\mathcal{L}_{\\mathrm{T\\_VSGG}}$ (20)", + "bbox": [ + 112, + 534, + 482, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Stage 2: $\\mathcal{L} = \\mathcal{L}_{\\mathrm{pred\\_cls}} + \\mathcal{L}_{\\mathrm{obj\\_cls}} + 0.5\\mathcal{L}_{\\mathrm{box\\_reg}}$", + "bbox": [ + 112, + 553, + 431, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 89, + 580, + 215, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental setting", + "text_level": 1, + "bbox": [ + 89, + 606, + 287, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We evaluate DIFFVSGG on Action Genome (AG) [40], the largest video scene graph generation dataset comprising over 10K videos extended from the Charades dataset [80]. This dataset includes 1,715,568 predicate instances across 25 predicate classes, spanning 234,253 video frames, and features 476,229 bounding boxes across 35 object categories. The 1,715,568 instances for 25 predicate classes are divided into attention, spatial and contacting, three different types. Following prior work [17, 58], we use the same training/testing split.", + "bbox": [ + 89, + 628, + 482, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. In the first training stage which optimizes the LDMs with ground-truth bounding box annotations, we set the learning rate to $10^{-4}$ and use the Adam optimizer. The batch size is set to 2048, and the model is trained for 100 epochs. Each input clip consists of five frames sampled at random time intervals, enabling conditional temporal reasoning. The denoising U-Net $\\epsilon_{\\theta}$ remains frozen once after pre-training. In the second training stage, the classifiers and", + "bbox": [ + 89, + 780, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "projectors are trained for 10 epochs with a batch size of 8. We use the AdamW optimizer with a learning rate of $10^{-5}$ , which decays by a factor of 5 halfway through the training. Evaluation Setup. In line with previous studies[30, 40, 58, 63], three standard evaluation protocols are adopted:", + "bbox": [ + 511, + 338, + 903, + 412 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- PredCLS: With oracle-provided object labels and bounding boxes as well as grounding-truth subject-object pairs, PredCLS assesses the model capability to predict predicate labels for each subject-object pair.", + "- SGCLS: Building on PredCLS, SGCLS requires the simultaneous prediction of both predicate labels and the associated subject-object pairs for each predicate.", + "- SGDET: As the most challenging task, SGDET requires generating complete scene graphs from scratch, including object detection, subject-object pair selection, and predicate classification. Detection is considered accurate if the overlap between prediction and ground truth exceeds 0.5. Evaluation Metric. We employ the Recall@k where $k \\in 10,20,50$ as the evaluation metric, to measure the proportion of ground truth elements within the top-k predictions. Additionally, Mean-Recall@k is also adopted to ensure the evaluation is not biased toward high-frequency classes. The evaluation is performed under two different scenarios:", + "- $w$ constraint: Each subject-object pair is restricted to a maximum of one predicate.", + "- $w / o$ constraints: Each subject-object pair is allowed to have multiple predicates simultaneously." + ], + "bbox": [ + 511, + 414, + 905, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-arts", + "text_level": 1, + "bbox": [ + 511, + 757, + 813, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tables 1-2 present the main experimental results of DIF-FVSGG against several top-leading approaches on Action Genome test [40]. Following existing VSGG works [17, 58], we firstly select a few representative image-level SGG methods such as RelDN [113] and GPS-Net [60]. Then, we compare DIFFVSGG with existing video-level solutions such as STTran[17], APT[58], etc. In general, DIF-FVSGG outperform image-level SGG methods by a large", + "bbox": [ + 511, + 779, + 905, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "29166", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5667d18ba0d60a65d3137ee00da9aea31821ba6cb8330e1b93d527ee74cffbcf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodPredCLSSGCLSSGDET
    R@10R@20R@50mR@10mR@20mR@50R@10R@20R@50mR@10mR@20mR@50R@10R@20R@50mR@10mR@20mR@50
    RelDN [113]44.275.489.231.263.175.525.041.947.918.636.942.613.623.036.67.518.833.7
    VRD [63]51.754.754.7---32.433.333.3---19.224.526.0---
    Motif Freq [112]62.465.165.1---40.841.941.9---23.731.433.3---
    MSDN [57]65.568.568.5---43.945.145.1---24.132.434.5---
    VCTREE [85]66.069.369.3---44.145.345.3---24.432.634.7---
    TRACE [88]72.691.696.450.973.682.737.146.750.531.942.746.326.535.645.322.831.341.8
    GPS-Net [60]76.093.699.5---------24.535.747.3---
    STTran [17]77.994.299.151.467.782.754.063.766.440.750.158.524.636.248.820.929.739.2
    APT [58]78.595.199.2---55.165.168.7---25.737.950.1---
    TR2 [94]83.196.699.9---57.264.466.2---27.839.250.0---
    TEMPURA [69]80.494.299.461.585.198.056.364.767.948.361.166.429.838.146.424.733.943.7
    DSG-DETR [30]------59.269.172.4---32.140.948.3---
    DIFFVSGG83.194.599.166.390.598.460.570.574.451.064.268.835.442.551.027.237.045.6
    ", + "bbox": [ + 101, + 88, + 903, + 296 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison of state-of-the-art VSGG methods on Action Genome test [40] under the w/o constraint setting.", + "bbox": [ + 142, + 300, + 852, + 313 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3bc2e5a808311f3c1fc0782ec9aa22bec747406486faea231cbb706a9fcaaa9c.jpg", + "image_caption": [ + "Figure 4. Visualization results on Action Genome test [40]. All results are given under the SGDET setup. Predicates in red indicate relationships are transformed to another one." + ], + "image_footnote": [], + "bbox": [ + 101, + 325, + 897, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "margin in all metrics. Concretely, under the $w$ constraint setup, our proposed method achieves R@10/R@20/R50 scores of 32.8/39.9/45.5, surpassing GPS-Net which achieves 24.7/33.1/35.1 scores by 8.1/6.8/10.4 scores, respectively. Similar trends can be observed on the $w/o$ constraint setup. All of the above firmly demonstrates the effectiveness of incorporating temporal cues to tackle relation understanding in dynamic scene.", + "bbox": [ + 88, + 598, + 482, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Additionally, when compared to the video-level counterparts, DIFFVSGG can still deliver state-of-the-art performance. Specifically, though DSG-DETR[30] adopts a modern DETR-like architecture and uses a Transformer-based decoder with all frames as the inputs to aggregate temporal cues, our DIFFVSGG which conducts online inference still outperforms it by a solid gap (i.e., 35.4/42.5/51.0 vs. 32.1/40.9/48.3 under the w/o constraint). More importantly, when it comes to the comparison of mR metric which prevents the bias toward high-frequency classes, DIFFVSGG obtains significantly higher performance compared to existing work. This suggests that using latent dif", + "bbox": [ + 89, + 719, + 483, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fusion models (LDMs) to model the inter-object relationship is effective, and it successfully learned meaning distributions which can prevent overfitting to high-frequency classes. Similar conclusions can be drawn on PredCLS and SGCLS two evaluation protocols, where DIFFVSGG can still deliver SOTA performance under both $w$ constraint and $w / o$ constraint two setups.", + "bbox": [ + 511, + 598, + 906, + 704 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 511, + 710, + 694, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We provide visualization results of UNIALIGN in Fig.4. It can be seen that our proposed method is able to generate accurate scene graphs across various challenging scenarios, such as fast motion and occlusion.", + "bbox": [ + 511, + 733, + 906, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Diagnostic Experiment", + "text_level": 1, + "bbox": [ + 511, + 801, + 725, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To assess the effectiveness of the detailed designs of DIF-FVSGG and gain deeper insights, we conduct a series of experiments on the AG test [40]. All performance metrics are reported under the SGDET setup.", + "bbox": [ + 511, + 825, + 903, + 885 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Key Component Analysis. We first examine the efficacy", + "bbox": [ + 511, + 885, + 903, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "29167", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9d50e6738878384fa00ff430c794f8811b3657ac3ded69940dc4e948762aa598.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    #L VSGGL T.VSGG Motionw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    126.935.338.027.538.948.5
    2✓29.737.741.530.340.149.9
    3✓32.039.344.633.942.050.3
    4✓32.839.945.535.442.551.0
    ", + "bbox": [ + 101, + 88, + 480, + 179 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/506aab7055203601cb33f4f6095aa4c8aa4ee1b63b8c9daf992c792941764972.jpg", + "table_caption": [ + "Table 3. Analysis on key components of DIFFVSGG." + ], + "table_footnote": [], + "table_body": "
    #Union Box FeatureSubject FeatureSubject Locationw constraintsNo Constraints
    R@10R@20R@50R@10R@20R@50
    1✓29.536.742.032.339.247.5
    2✓✓31.038.243.633.740.848.7
    3✓✓✓32.839.945.535.442.551.0
    ", + "bbox": [ + 101, + 215, + 478, + 289 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e996653f49a96bf1738c1dcdd8bf1c4143e1f9f527f6b28787539f5f2415168a.jpg", + "table_caption": [ + "Table 4. Analysis on elements to construct adjacency matrix ${\\mathbf{A}}^{t}$ ." + ], + "table_footnote": [], + "table_body": "
    Step Tw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    1031.738.542.934.041.149.5
    2032.839.945.535.442.551.0
    5033.240.546.435.743.151.4
    10033.140.345.935.542.851.1
    ", + "bbox": [ + 101, + 325, + 478, + 414 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of essential components of DIFFVSGG in Table3, where the first row denotes the baseline model directly using bounding box predictions to construct scene graphs without denoising refinement. After integrating LDMs to model complex inter-object relationships within the scene (i.e., row #2), DIFFVSGG enjoys considerable improvement on both w and w/o constraint setups. Next, applying condition based temporal reasoning to capture long-term temporal dependencies further boosts the performance to 32.0 and 33.9 on two setups. Finally, upon the incorporation of motion enhanced denoising (i.e., row #4), DIFFVSGG obtains the best performance on both setups, suggesting that motion cues can effectively enhance the awareness of temporal cues through conditional promoting.", + "bbox": [ + 88, + 462, + 482, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Graph Construction. We study the impact of using various features to construct the adjacency matrix $\\mathbf{A}^t$ in Table 4. As shown, incorporating all three types of features, as described in Eq.7, achieves the best performance.", + "bbox": [ + 89, + 674, + 482, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Diffusion Step. Next we investigate the effect of different number of diffusion steps. As shown in Table 5, the best performance is achieved at $T = 50$ . However, to balance the performance and efficiency efficiency, we set $T = 20$ , which yields a slight reduction in performance.", + "bbox": [ + 89, + 734, + 482, + 810 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Layer in Denoising U-Net. We further analyze the impact of using different number of layers in the encoder and decoder of denoising U-Net. As shown in Table 6, DIFFVSGG achieves similar performance when the layer number exceeds 2. For efficiency, we set it to 3.", + "bbox": [ + 89, + 810, + 482, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Graph Readout. We explore different graph readout strate", + "bbox": [ + 89, + 885, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/00e19318e6918906dbe8e2c96edd0cf5160a1bbfdd4c3984d1f48b1ed7a239f9.jpg", + "table_caption": [ + "Table 5. Analysis on forward and reverse diffusion steps." + ], + "table_footnote": [], + "table_body": "
    # Layerw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    231.938.244.534.042.150.1
    332.839.945.535.442.551.0
    532.439.646.134.443.050.7
    632.639.346.334.744.050.9
    ", + "bbox": [ + 524, + 89, + 900, + 176 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/87d71b105b4cc30b6db90a822312140dd346c87275ca70b79e9dc626bbf2739b.jpg", + "table_caption": [ + "Table 6. Analysis of the layer configuration of the U-Net." + ], + "table_footnote": [], + "table_body": "
    Elementw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    At,i,032.839.945.535.442.551.0
    At,i,j31.737.743.533.641.249.6
    ", + "bbox": [ + 524, + 217, + 900, + 284 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bf756cd5f5abc3e7d90084750c968ebb89a857e1e957a612f433a9665cab1d94.jpg", + "table_caption": [ + "Table 7. Analysis on the elements used for graph readout." + ], + "table_footnote": [], + "table_body": "
    ModelParameter Inferencew constraintsw/o constraints
    NumberTimeR@10R@20R@50R@10R@20R@50
    TRACE [88]66.7 M8.4 FPS13.914.514.526.535.645.3
    STTran [17]51.1 M10.9 FPS25.234.137.024.636.248.8
    TEMPURA [69]53.5 M9.6 FPS28.133.434.929.838.146.4
    DSG-DETR [30]65.5 M7.3 FPS30.334.836.132.140.948.3
    DIFFVSGG46.7 M8.7 FPS32.839.945.535.442.551.0
    ", + "bbox": [ + 524, + 321, + 900, + 415 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Analysis on the trainable parameters and inference time.", + "bbox": [ + 514, + 422, + 901, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "gies in Table 7. Here $A_{i}^{t,0}$ refers to utilize the entire row $i$ of $A^{t,0}$ to deliver the predictions (i.e., Eq. 15-16), while $A_{i,j}^{t,0}$ denoting utilize one element at $(i,j)$ of $A^{t,0}$ to make prediction. It can be seen that aggregating all elements in a row that contains the same subject delivers higher performance.", + "bbox": [ + 511, + 465, + 906, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Running Efficiency. Finally we probe the running efficiency of DIFFVSGG. As seen in Table 8, our method requires the fewest trainable parameters among all competitors. Though inference speed is slightly slower than existing work due to step-wise denoising, the improvement in performance compensates for this limitation.", + "bbox": [ + 511, + 549, + 905, + 640 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 660, + 633, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented DIFFVSGG, a diffusion-based VSGG solution that makes contributions in three aspects. First, as an online approach, it effectively addresses challenges such as GPU memory constraints and real-time processing while delivering high performance, highlighting its potential for real-world application. Second, we propose a learning strategy for LDMs to generate inter-object relationships from random subject-object pairs, with ground-truth object locations as the annotations. Third, in leverage of LDMs, DIFFVSGG provides a new approach to enable temporal reasoning via dynamic, iterative refinement of scene graphs across frames, conditioned on predictions of prior frame. We hope this work could provide a new perspective for video analysis through reverse diffusion along the temporal dimension.", + "bbox": [ + 511, + 688, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "29168", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 91, + 90, + 240, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported in part by the Natural Science Foundation of Zhejiang Province (LDT23F02023F02), the Fundamental Research Funds for the Central Universities (226-2024-00058), and the National Natural Science Foundation of China (No. 62372405). The authors would like to thank [optional: specific individuals or institutions] for their valuable discussions and feedback. We also acknowledge the use of [optional: datasets, computational resources, or tools] that contributed to this research.", + "bbox": [ + 89, + 116, + 483, + 251 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 268, + 186, + 282 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tomer Amit, Tal Shaharbany, Eliya Nachmani, and Lior Wolf. Segdiff: Image segmentation with diffusion probabilistic models. arXiv preprint arXiv:2112.00390, 2021. 3", + "[2] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. In ICCV, 2021. 2", + "[3] Stephan Baier, Yunpu Ma, and Volker Tresp. Improving visual relationship detection using semantic modeling of scene descriptions. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(6):2827-2840, 2021. 2" + ], + "bbox": [ + 516, + 92, + 903, + 304 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "29172", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/5f1209e6-1544-45b7-80b5-0030e5048d70_model.json b/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/5f1209e6-1544-45b7-80b5-0030e5048d70_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a4ed2223e15f2c3dfb5a2eb667f2759065e0e144 --- /dev/null +++ b/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/5f1209e6-1544-45b7-80b5-0030e5048d70_model.json @@ -0,0 +1,3216 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.153, + 0.131, + 0.846, + 0.154 + ], + "angle": 0, + "content": "DIFFVSGG: Diffusion-Driven Online Video Scene Graph Generation" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.18, + 0.763, + 0.235 + ], + "angle": 0, + "content": "Mu Chen1, Lulei Li2, Wenguan Wang1†, Yi Yang1 \n1ReLER, CCAI, Zhejiang University 2ReLER, AAI, University of Technology Sydney \nhttps://github.com/kagawa588/DiffVsgg" + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.287, + 0.327, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.319, + 0.485, + 0.699 + ], + "angle": 0, + "content": "Top-leading solutions for Video Scene Graph Generation (VSGG) typically adopt an offline pipeline. Though demonstrating promising performance, they remain unable to handle real-time video streams and consume large GPU memory. Moreover, these approaches fall short in temporal reasoning, merely aggregating frame-level predictions over a temporal context. In response, we introduce DIFFVSGG, an online VSGG solution that frames this task as an iterative scene graph update problem. Drawing inspiration from Latent Diffusion Models (LDMs) which generate images via denoising a latent feature embedding, we unify the decoding of object classification, bounding box regression, and graph generation three tasks using one shared feature embedding. Then, given an embedding containing unified features of object pairs, we conduct a step-wise Denoising on it within LDMs, so as to deliver a clean embedding which clearly indicates the relationships between objects. This embedding then serves as the input to task-specific heads for object classification, scene graph generation, etc. DIFFVSGG further facilitates continuous temporal reasoning, where predictions for subsequent frames leverage results of past frames as the conditional inputs of LDMs, to guide the reverse diffusion process for current frames. Extensive experiments on three setups of Action Genome demonstrate the superiority of DIFFVSGG." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.728, + 0.222, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.754, + 0.483, + 0.876 + ], + "angle": 0, + "content": "Video Scene Graph Generation (VSGG) is receiving growing attention as it benefits a wide range of downstream tasks (e.g., video caption [34, 91], video retrieval [31, 50], and visual question answering [49, 87]). To deliver a holistic understanding of the underlying spatial-temporal dynamics within scenes, this task aims to construct a sequence of directed graphs where nodes represent objects and edges describe inter-object relationships (a.k.a., predicate)." + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.291, + 0.895, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.424, + 0.895, + 0.57 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.581, + 0.907, + 0.667 + ], + "angle": 0, + "content": "Figure 1. (a) Existing VSGG solutions typically adopt an offline training pipeline, dividing the problem into various components: object detection, temporal association, and contextual aggregation. (b) DIFFVSGG introduces a new paradigm that performs spatial-temporal reasoning directly as each frame is processed sequentially, enabling progressive, online updates to the scene graph." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Top-leading VSGG approaches typically adopt an offline pipeline [30, 69, 94], where scene graphs are generated independently for each frame and then aggregated along the temporal dimension (i.e., Fig. 1(a)). Though demonstrating strong performance, they require full video sequences as inputs, which faces challenges in processing long videos containing hundreds of frames due to GPU memory constraints, and is unable to handle real-time video streams for applications like autonomous driving and augmented reality [100]. Moreover, the dealing of temporal cues focuses solely on the global aggregation of frame-level predictions via Transform blocks. This falls short in the reasoning over temporal space, which is essential for modeling the dynamic changes of interactions between subjects and objects, and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.236, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "29161" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.168 + ], + "angle": 0, + "content": "potentially benefits predicate prediction. Though a surge of early work has sought to facilitate explicit reasoning over the temporal domain via messaging passing [90] or spatial-temporal graph [74], a large performance gap remains when compared to these offline temporal aggregation approaches." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.171, + 0.482, + 0.367 + ], + "angle": 0, + "content": "To address these challenges, we propose DIFFVSGG, a high performance online approach for VSGG in leverage of Latent Diffusion Models (LDMs)[77, 81] (i.e., Fig.1(b)). In VSGG, the scene graph is dynamically evolved throughout the progression of video frames, with nodes and edges being continuously updated to precisely reflect the latest video content. Such an iterative update process shares a similar spirit of LDMs, which progressively remove noise to generate new samples from data distributions. Naturally, our motivation is to develop a VSGG model that aligns with the denoising principle of LDMs to iterative refine scene graphs along the temporal dimension, facilitating online temporal reasoning within this reverse diffusion process." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.37, + 0.483, + 0.822 + ], + "angle": 0, + "content": "To achieve this, we tackle VSGG from a unified perspective, organizing the decoding of object classification, bounding box regression, and graph generation three tasks from a shared feature embedding, which serves as the input and output of the Denoising U-Net. Concretely, from the spatial perspective, given the object detection results from each frame, multiple object pairs can be constructed. Then, for each object pair, we integrate i) the visual feature of two objects, ii) the union feature between, and iii) the locations of two objects, into a unified embedding. This embedding serves as the input to the denoising U-Net, after steps of denoising, a clean embedding clearly describing the objects as well as their inter-object relationships can be delivered. From the temporal perspective, DIFFVSGG conducts frame-by-frame reasoning where the result for each subsequent frame is delivered by iteratively refining the predictions of previous frames via reverse diffusion. Specifically, object positions and contextual information from prior frames are leveraged as conditions to guide the denoising of the shared feature embeddings for current frames. This encourages continuous temporal reasoning as the video progresses, allowing DIFFVSGG to effectively capture long-term spatiotemporal dependencies and adapt to complex motion patterns in an online manner. To further unlock the potential of LDMs, we build a memory bank to store positions for each object. In this way, motion information including acceleration and deceleration of object can be explicitly calculated. These motion cues are integrated into conditional inputs for the reverse diffusion step, which can help infer relationships such as following or approaching between objects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.482, + 0.901 + ], + "angle": 0, + "content": "DIFFVSGG distinguishes itself in several aspects: First, it tackles VSGG in an online manner to continuously address an unlimited number of frames, while being friendly to devices with limited GPU memory. Second, the prediction of each video is implemented as a reverse diffusion pro" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.302 + ], + "angle": 0, + "content": "cess, which elegantly encodes spatial and temporal reasoning into the Denoising step. Third, the temporal cues (i.e., historic predictions) are propagated into subsequent frames as conditions and participating in the prediction, while prior work simply aggregates predictions of all frames along the temporal dimension. Fourth, the learning of object classification, bounding box regression, and graph generation three tasks are jointly optimized with a shared feature embedding. Such a unified learning paradigm allows for the solving of VSGG from a global view, and avoids error made in one task propagating to subsequent tasks. Fifth, this unified decoding simplifies the VSGG pipeline and eliminates cumbersome handcrafted modules such as non-maximum suppression (NMS), and entity matching across frames." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.303, + 0.905, + 0.439 + ], + "angle": 0, + "content": "To the best of our knowledge, DIFFVSGG is the first work that treats the VSGG task as an iterative denoising problem along the temporal dimension. Extensive experiments on Action Genome (AG) [40] demonstrate the superiority of our proposed method. Notably, DIFFVSGG achieves SOTA results across all three setups and surpasses the top-leading solutions (e.g., DSG-DETR [30]) by 3.3 in terms of R@10, highlighting the great potential of utilizing diffusion models for visual relation understanding in videos." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.453, + 0.655, + 0.469 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.478, + 0.905, + 0.629 + ], + "angle": 0, + "content": "Scene Graph Generation (SGG). SGG involves detecting object instances and classifying their pairwise visual relations in an image, which is essential for comprehensive visual tasks [7, 8, 11, 53, 97, 98, 117, 118]. Recent SGG approaches seek to comprehend visual context by aggregating spatial context through various strategies, including explicit message passing [14, 20, 56, 57, 103, 112], graph structure modeling [83, 85, 99, 106, 110], external knowledge integration [3, 14, 33, 35, 109, 111], and transformer-based networks [12, 18, 23, 24, 43, 48, 55, 59, 64, 72, 79]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.63, + 0.905, + 0.855 + ], + "angle": 0, + "content": "Extended from SGG, Video Scene Graph Generation (VSGG) aims to ground visual relationships jointly in spatial and temporal dimensions. Prior research primarily concentrates on addressing the long-tail distribution problem observed in prominent benchmarks [40]. Numerous unbiased approaches [16, 21, 46, 51, 54, 68, 86, 105] have been devised to handle infrequent predicate classes arising from this distribution. Furthermore, recent VSGG methods underscore the importance of spatial-temporal learning, and make use of the sequence-processing ability of Transformer [2, 70, 84] to capture temporal continuity. Nonetheless, these approaches often depend on complex post-processing that decouples spatial and temporal learning into two independent steps, and simply emphasizes on the consistent matching between frames." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "In contrast, DIFFVSGG handles both spatial and temporal reasoning from a unified perspective, where the reasoning on temporal dimension is naturally achieved via utiliz" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "29162" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.121 + ], + "angle": 0, + "content": "ing the spatial reasoning results of prior frames as the conditions to guide predictions for the current frames." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.124, + 0.484, + 0.457 + ], + "angle": 0, + "content": "Diffusion Models Beyond Image Generation. Diffusion Models (DMs) have surpassed many other generative models in image generation [6, 22, 37, 38, 92, 104] by successively denoising images. Beyond image generation, DMs inherently perform implicit discriminative reasoning while generating data, which proves highly effective in visual tasks that require complex relationship modeling and spatiotemporal reasoning. Therefore, a surge of work has adapted generative diffusion models for tasks including image segmentation [1, 4, 5, 15, 32, 44, 93], object detection [13, 76, 102], object tracking [65, 66, 101], and monocular depth estimation [25, 67, 78, 116]. Recent research has also utilizes DMs for more complex tasks that require high-level visual understanding abilities such as visual-linguistic understanding [47], scene generation [39], and human-object interaction detection [41, 52]. The potential of DMs in processing graph data has also been explored, encompassing a range of advanced tasks. This includes early work employing score-based methods for generating permutation-invariant graphs [42, 71], as well as recent approaches focused on enhancing graph neural networks [114, 115] and advancing graph generation techniques [107]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.459, + 0.484, + 0.595 + ], + "angle": 0, + "content": "In this work, we borrow the step-wise denoising ability of latent diffusion models to enable spatial reasoning within a single frame. This is achieved by iteratively refining the union embeddings of object pairs, which serve to inform the prediction for bounding boxes and predicate classes, etc. On the other hand, temporal reasoning across frames is facilitated via conditional prompting, i.e., using predictions of prior frames which contain rich location and inter-object relationship cues to guide the denoising of current frames." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.597, + 0.484, + 0.824 + ], + "angle": 0, + "content": "Temporal Reasoning in Videos. Reasoning within the temporal dimension poses significant challenges for achieving high-level comprehension in video-related tasks [9, 10, 27-29, 61, 73, 108]. Recent advancements in video question answering seek to tackle temporal reasoning by employing attention mechanisms [26, 82] or incorporating external memory modules [45, 75] across video frames. In addition, to accurately capture the start, progression, and end of an action, action recognition approaches [89, 95] model complex motion patterns and dependencies in sequence. Video object detection (VOD) [19, 62] focuses on accurately capturing object trajectories, even in the presence of occlusions and abrupt movements. The top-leading VSGG solutions [30, 69, 94] instead aggregate predictions across frames to maintain the temporal consistency of objects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.484, + 0.901 + ], + "angle": 0, + "content": "In summary, although existing work facilitates temporal reasoning from different perspectives and demonstrates it effectiveness, the potential of diffusion models remains largely underexplored. In fact, the sequential denoising in time, where each step is informed by previous one, offers" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.152 + ], + "angle": 0, + "content": "a suitable tool to reconstruct the states for current frames based on observations from past frames. This insight motivates the proposal of DIFFVSGG, which tackles the VSGG task via graph denoising over the temporal dimension." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.17, + 0.65, + 0.187 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.197, + 0.906, + 0.273 + ], + "angle": 0, + "content": "In this section, we first give a brief introduction to the general background of latent Diffusion Models (§3.1), then elaborate on the overall design of our proposed DIFFVSGG (§3.2), and finally present the detailed information on the network architecture and training objectives (§3.3)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.287, + 0.844, + 0.303 + ], + "angle": 0, + "content": "3.1. Preliminary: Latent Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.31, + 0.906, + 0.371 + ], + "angle": 0, + "content": "To begin, we give an illustration on how diffusion processes [81] are used to model data distributions and generate high-quality samples. Specifically, we consider a continuous-time Markov chain with \\( t \\in [0,T] \\):" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.382, + 0.907, + 0.401 + ], + "angle": 0, + "content": "\\[\nq (x _ {t} | x _ {t - 1}) = \\mathcal {N} (x _ {t}; \\sqrt {1 - \\beta_ {t}} x _ {t - 1}, \\beta_ {t} I), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.412, + 0.906, + 0.457 + ], + "angle": 0, + "content": "where \\(\\beta_{t}\\) is a small noise variance term at timestep \\(t\\), and \\(\\mathcal{N}\\) denotes a Gaussian distribution. The corrupted data at any intermediate time step \\(t\\) can be derived recursively as:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.468, + 0.907, + 0.485 + ], + "angle": 0, + "content": "\\[\nx _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha}} \\epsilon , \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.499, + 0.906, + 0.576 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = 1 - \\beta_{t}\\) and \\(\\overline{\\alpha}_t = \\prod_{s = 1}^t\\alpha_s\\) is the cumulative product of \\(\\alpha_{t}\\) over the timesteps, \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) represents the sampled noise. The reverse process essentially involves learning to reverse the noise addition at each step. The cleaned data at time step \\(t\\) can be written recursively as:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.586, + 0.906, + 0.62 + ], + "angle": 0, + "content": "\\[\nx _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} \\left(x _ {t}, t\\right), \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.906, + 0.673 + ], + "angle": 0, + "content": "where a time-conditioned denoising neural network \\(\\epsilon_{\\theta}(x,t)\\) is trained to minimize the mean squared error between the true and predicted noise at each timestep:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.683, + 0.906, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {D M}} := \\mathbb {E} _ {x _ {0}, \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| _ {2} ^ {2} \\right]. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.719, + 0.906, + 0.84 + ], + "angle": 0, + "content": "Building on the diffusion process described above, latent diffusion models (LDMs) [77] first encode samples into a low-dimensional latent space \\( z = \\mathcal{E}(x) \\) using an encoder \\( \\mathcal{E} \\), and then apply the diffusion process within this compressed space. Moreover, LDMs introduce the conditioning mechanisms which allow for control over the generated output based on additional input \\( y \\) such as text, labels, or images. Consequently, the training objective for LDMs is given as:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.85, + 0.905, + 0.876 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {L D M}} := \\mathbb {E} _ {\\mathcal {E} (x _ {0}), y, \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\boldsymbol {z} _ {t}, t, c _ {\\theta} (y)\\right) \\| _ {2} ^ {2} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.819, + 0.901 + ], + "angle": 0, + "content": "where \\(c_{\\theta}\\) is a conditioning model to encode \\(y\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "29163" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.1, + 0.89, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.178, + 0.244, + 0.818, + 0.259 + ], + "angle": 0, + "content": "Figure 2. Overview of our proposed inter-object relationship learning strategy using latent diffusion models." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.269, + 0.431, + 0.284 + ], + "angle": 0, + "content": "3.2. DIFFVSGG: Diffusion Models for VSGG" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.291, + 0.484, + 0.488 + ], + "angle": 0, + "content": "Problem Definition. Considering a video sequence represented as \\(\\mathcal{I} = \\{I^1,\\dots ,I^T\\}\\) containing \\(T\\) frames, the objective of VSGG is to generate a sequence of scene graph \\(\\mathcal{G} = \\{G^{1},\\dots ,G^{T}\\}\\) over time, where each element \\(\\mathcal{G}^t\\) represents the corresponding scene graph for frame \\(I^t\\). Each graph \\(G^{t}\\) is defined as \\(G^{t} = (\\mathcal{V}^{t},\\mathcal{E}^{t})\\), with \\(\\mathcal{V}^t\\) and \\(\\mathcal{E}^t\\) denoting the sets of graph nodes and edges, respectively. Each node \\(v_{i}^{t}\\in \\mathcal{V}^{t}\\) includes attributes such as category and location for object \\(i\\), while each edge \\(e_{i,j}^{t}\\in \\mathcal{E}^{t}\\) describes the inter-object relationship (a.k.a.predicate) between subject \\(i\\) and object \\(j\\). In this manner, \\(\\mathcal{G}\\) captures all objects (i.e., \\(\\mathcal{V}\\)), their interactions (i.e., \\(\\mathcal{E}\\)), and the dynamics as they evolve over time (i.e., from \\(t = 1\\) to \\(t = T\\)) within the scene." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.487, + 0.484, + 0.53 + ], + "angle": 0, + "content": "Graph Construction. Given a video \\(\\mathcal{I} = \\{I^1,\\dots ,I^T\\}\\), we first employ an on-the-shelf object detector \\(\\mathcal{F}_{\\mathrm{det}}\\) for each frame:" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.528, + 0.482, + 0.544 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {F} ^ {t}, \\mathcal {B} ^ {t}, \\mathcal {O} ^ {t} \\right\\} = \\mathcal {F} _ {\\det } \\left(I ^ {t}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.547, + 0.484, + 0.639 + ], + "angle": 0, + "content": "where \\(\\pmb{F}^{t}\\) is the feature extracted by backbone, \\(\\mathcal{B}^t = \\{b_1^t,\\dots ,b_{N_t}^t\\}\\) and \\(\\mathcal{O}^t = \\{o_1^t,\\dots ,o_{N_t}^t\\}\\) are bounding box and class predictions for \\(N_{t}\\) objects detected from frame \\(I^t\\) respectively. This serves to initialize an adjacency matrix \\(\\pmb{A}^{t}\\in \\mathbb{R}^{N_{t}\\times N_{t}\\times D_{e}}\\) , of which each element aims to represent the inter-object relationships between object \\(i\\) and \\(j\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.645, + 0.482, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} _ {i, j} ^ {t} = \\left[ \\boldsymbol {F} _ {o _ {i}} ^ {t}; \\boldsymbol {F} _ {o _ {i}, o _ {j}} ^ {t}; \\boldsymbol {F} _ {b _ {i}} ^ {t} \\right] \\in \\mathbb {R} ^ {D _ {e}}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.667, + 0.397, + 0.687 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} _ {j, i} ^ {t} = \\left[ \\boldsymbol {F} _ {o _ {j}} ^ {t}; \\boldsymbol {F} _ {o _ {j}, o _ {i}} ^ {t}; \\boldsymbol {F} _ {b _ {j}} ^ {t} \\right] \\in \\mathbb {R} ^ {D _ {e}}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.688, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Here \\([]\\) refers to the concatenation of features, implemented as torch.cat(). \\(F_{o_i}^t = \\mathcal{F}_{\\mathrm{ROI}}(F^t,b_i^t)\\) is the instance-level feature for object \\(i\\) extracted via ROAlign [36] (i.e., \\(\\mathcal{F}_{\\mathrm{ROI}}), F_{o_i,o_j}^t = \\mathcal{F}_{\\mathrm{ROI}}(F^t,b_i^t\\cup b_j^t)\\) is the feature mapped from the union box of object \\(i\\) and \\(j\\) (i.e., \\(b_{i}^{t}\\cup b_{j}^{t})\\) ,and \\(F_{b_i}^t\\) describes bounding box \\(b_{i}^{t}\\) using a box-to-feature mapping function identical to that in [112]. \\(A_{i,j}^{t}\\) represents the relationship predicted from subject \\(i\\) , which differs from \\(A_{j,i}^{t}\\) where \\(j\\) is considered the subject. In this way, the matrix \\(A^t\\) encodes both node features of each object and the edge features between any pair of them. Note that such subject-based encoding does not incorporate \\(Fo_{j}\\) and \\(Fb_{j}\\) into \\(A_{i,j}\\) (i.e., \\([F_{o_i};F_{b_i};F_{o_i,o_j};F_{o_j};F_{b_j}])\\) , which hinders the neural network to distinguish between the subject \\((i)\\) and object" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.27, + 0.907, + 0.346 + ], + "angle": 0, + "content": "\\((j)\\). Additionally, as the number of instances \\((i.e., N_{t})\\) typically varies across frames due to the emergence or disappearance of some instances, we pad \\(\\mathbf{A}^{t}\\) to a fixed size of \\(N \\times N\\) where \\(N > \\max(N_{1}, \\dots, N_{T})\\), using randomly generated feature embedding from Gaussian distributions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.346, + 0.908, + 0.557 + ], + "angle": 0, + "content": "Inter-object Relationship Learning via LDMs. Next we aim to facilitate the learning of inter-object relationships within LDMs using ground truth scene graph (i.e., Fig. 2). Since we use an off-the-self object detector, the extracted feature \\( F^t \\) remains static for each frame. Therefore, with access to the ground truth bounding box annotations, we can compute precise edge features via Eq.7 from \\( F^t \\). The adjacency matrix \\( \\hat{A}^t \\) which exactly encodes the inter-object features can also be obtained. Here \\( \\hat{A}^t \\) is the ground truth of inter-object relationships, initialized using features derived from ground-truth bounding boxes, where object pairs with no relations are represented as empty entries. \\( \\hat{A}^t \\) instructs the learning of a LDM which is responsible for recovering object features and their relationships from random noise." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.557, + 0.906, + 0.603 + ], + "angle": 0, + "content": "- Forward Process. Let \\(\\hat{A}^{t,0}\\) represent the clean adjacency matrix. The noise injection process to progressively perturb this matrix is defined following Eq.2, and expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.606, + 0.905, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {A}} ^ {t, k} = \\sqrt {\\bar {\\alpha} _ {t}} x \\hat {\\boldsymbol {A}} ^ {t, 0} + \\sqrt {1 - \\bar {\\alpha}} \\epsilon , \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.906, + 0.675 + ], + "angle": 0, + "content": "where \\(\\hat{A}^{t,k}\\) denotes the noisy adjacency matrix at step \\(k\\). This enables the model to learn robust feature representations, through the exposure to degraded versions of \\(\\hat{A}^{t,0}\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.676, + 0.907, + 0.751 + ], + "angle": 0, + "content": "- **Reverse Process.** To recover the original adjacency matrix \\(\\hat{A}^{t,0}\\), we employ a denoising U-Net \\(\\epsilon_{\\theta}\\) which is trained to iteratively remove noise starting from the initial noisy matrix \\(\\hat{A}^{t,K}\\). This process follows the denoising step defined in Eq.3 and proceeds as:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.755, + 0.907, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {A}} ^ {t, k - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} (\\hat {\\boldsymbol {A}} ^ {t, k} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} (\\hat {\\boldsymbol {A}} ^ {t, k}, k), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.792, + 0.906, + 0.838 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}\\) is optimized to recover meaningful inter-object relationships. Following Eq. 5, we define the training objective \\(\\mathcal{L}_{\\mathrm{VSGG}}\\) by minimizing the spatial structure loss:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.842, + 0.905, + 0.868 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {V S G G}} := \\mathbb {E} _ {\\hat {\\boldsymbol {A}} ^ {t, k}, \\epsilon , k} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\hat {\\boldsymbol {A}} ^ {t, k}, k) \\| _ {2} ^ {2} \\right]. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.907, + 0.901 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{\\mathrm{VSGG}}\\) encourages \\(\\epsilon_{\\theta}\\) to accurately predict and remove the noise at each step \\(k\\), so as to restore \\(\\hat{\\boldsymbol{A}}^t\\) structured in the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "29164" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.094, + 0.149, + 0.141 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.154, + 0.097, + 0.184, + 0.139 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.096, + 0.236, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.098, + 0.474, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.145, + 0.149, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.155, + 0.145, + 0.185, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.189, + 0.145, + 0.237, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.19, + 0.474, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.246, + 0.482, + 0.261 + ], + "angle": 0, + "content": "Figure 3. Overview of our proposed temporal prompting strategy." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.269, + 0.484, + 0.5 + ], + "angle": 0, + "content": "way that preserves spatial and relational coherence. During inference, given the adjacency matrix \\( \\mathbf{A}^t \\) from an arbitrary frame \\( t \\), we consider it noisy and utilize the well-trained denoising U-Net above to refine it, so as to deliver an updated version that indicates the interaction between objects, as well as the location and category of objects: \\( \\mathbf{A}^{t,k - 1} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{A}^{t,k} - \\frac{\\beta_t}{\\sqrt{1 - \\overline{\\alpha}}}\\epsilon_\\theta (\\mathbf{A}^{t,k},k) \\). Unlike the training process which utilizes \\( \\hat{\\mathbf{A}} \\) derived from ground truth bounding boxes, \\( \\mathbf{A} \\) here is obtained from the predicated ones. Note that the main challenge of VSGG lies in modeling of the dynamic changes of relation between object and subject, and the diffusion models primarily focus on recovering object features and their relationships. Thus, the slight bias in predicated bounding boxes, especially after ROIAAlign, causes negligible impacts to relation predictions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.5, + 0.484, + 0.591 + ], + "angle": 0, + "content": "Condition Based Temporal Reasoning. For a given video stream, we can infer future frames based on the content of preceding frames. This observation serves as the motivation for our temporal prompting strategy (i.e., Fig.3), where we condition the denoising process of \\( A^t \\) on the denoised adjacency matrix of prior frames (i.e., \\( A^{t - 1,0} \\)), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.598, + 0.482, + 0.631 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} ^ {t, k - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {A} ^ {t, k} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} \\left(\\boldsymbol {A} ^ {t, k}, k, \\boldsymbol {A} ^ {t - 1, 0}\\right), \\right. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.638, + 0.484, + 0.7 + ], + "angle": 0, + "content": "where the condition decoder \\(c_{\\theta}\\) in Eq. 5 is discarded, as \\(\\pmb{A}^{t - 1,0}\\) has already shared the same dimension as \\(\\pmb{A}^{t,k}\\). With this condition-based temporal association for denoising, the training objective for \\(\\epsilon_{\\theta}\\) is updated as:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.709, + 0.482, + 0.747 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {T . V S G G}} := \\mathbb {E} _ {\\boldsymbol {A} ^ {t, k}, \\boldsymbol {A} ^ {t - 1, 0}, \\epsilon , k} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\boldsymbol {A} ^ {t, k}, \\boldsymbol {A} ^ {t - 1, 0}, k) \\| _ {2} ^ {2} \\right]. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.748, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Here \\(\\mathcal{L}_{\\mathrm{T.VSGG}}\\) encourages \\(\\epsilon_{\\theta}\\) to generate temporally consistent outputs, enabling a smooth and coherent denoising of adjacency matrix across frames. Moreover, since new instances keep emerging as the video progresses, we calculate similarities between ROIAngled features of the potential new object (i.e., \\(F_{o_p}^t\\)) and all other objects in the past frame (i.e., \\(F_{o_i}^{t - 1}\\)), and consider \\(o_p\\) as new object if the similarities is smaller than 0.2 for all other objects. Then, the random padded features in \\(A\\) during graph construction are replaced with union and instance features of these new instances." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.244 + ], + "angle": 0, + "content": "Motion Enhanced Denoising for VSGG. Motion cues serve as indicators to describe object movements in a given scene. They provide essential context for understanding the position and duration of events. Moreover, the speed and direction of object movements can reveal intentions for interactions (e.g., approaching), which aids in temporal reasoning by inferring whether they might complete an action or reach a goal. Therefore, given a box prediction \\( b_{i}^{t} = \\{x_{i}^{t}, y_{i}^{t}, w_{i}^{t}, h_{i}^{t}\\} \\) for object \\( i \\), we explicitly calculate the approaching speed between object \\( i \\) and \\( j \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.249, + 0.905, + 0.278 + ], + "angle": 0, + "content": "\\[\nd _ {i, j} ^ {t} = \\sqrt {\\left(x _ {i} ^ {t} - x _ {j} ^ {t}\\right) ^ {2} + \\left(y _ {i} ^ {t} - y _ {j} ^ {t}\\right) ^ {2}}, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.278, + 0.776, + 0.297 + ], + "angle": 0, + "content": "\\[\nv _ {i, j} ^ {t} = (d _ {i, j} ^ {t} - d _ {i, j} ^ {t - \\Delta t}) / \\Delta t,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.303, + 0.907, + 0.365 + ], + "angle": 0, + "content": "where \\(\\Delta t\\) is the interval of frame. Given \\(v^t\\in \\mathbb{R}^{N^t\\times N^t}\\) we pad it into the same size with \\(\\pmb{A}^{t}\\) (i.e., \\(v^{t}\\in \\mathbb{R}^{N\\times N})\\) and inject it into \\(\\pmb{A}^{t,k}\\) at each denoising step \\(k\\colon \\pmb{A}^{t,k} = \\pmb{A}^{t,k} + v^t\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.365, + 0.906, + 0.426 + ], + "angle": 0, + "content": "Graph Readout. Next we investigate how to deliver SGG predictions for each frame based on the denoised adjacency matrix \\( \\mathbf{A}^{t,0} \\). Specifically, the prediction for predicate of each subject-object pair is obtained as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.434, + 0.905, + 0.455 + ], + "angle": 0, + "content": "\\[\nr _ {i, j} ^ {t} = \\operatorname {s o f t m a x} \\left(\\mathcal {F} _ {\\text {p r e d}} \\left(\\boldsymbol {A} _ {i, j} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {N _ {\\text {p r e d , c l s}}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.462, + 0.906, + 0.538 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_{\\mathrm{pred}}\\) is an MLP-based classifier and \\(N_{\\mathrm{pred\\_cls}}\\) represents the number of predicate classes. For object classification and bounding box regression, to render a global view, we utilize the entire row \\(i\\) of \\(\\mathbf{A}^{t,0}\\) (i.e., \\(\\mathbf{A}_i^{t,0}\\)) where all elements consider \\(i\\) as the subject, to deliver the prediction:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.546, + 0.905, + 0.565 + ], + "angle": 0, + "content": "\\[\no _ {i} ^ {t} = \\operatorname {s o f t m a x} \\left(\\mathcal {F} _ {\\mathrm {o b j}} \\left(\\boldsymbol {A} _ {i} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {N _ {\\mathrm {o b j , c l s}}}, \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.568, + 0.905, + 0.586 + ], + "angle": 0, + "content": "\\[\nb _ {i} ^ {t} = \\operatorname {s i g m o i d} \\left(\\mathcal {F} _ {\\text {b o x}} \\left(A _ {i} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {4}, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.595, + 0.904, + 0.626 + ], + "angle": 0, + "content": "where \\(N_{\\mathrm{obj\\_cls}}\\) is the number of object classes, \\(\\mathcal{F}_{\\mathrm{obj}}\\) and \\(\\mathcal{F}_{\\mathrm{box}}\\) are the MLP-based classifier and projector, respectively." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.634, + 0.731, + 0.649 + ], + "angle": 0, + "content": "3.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.656, + 0.907, + 0.837 + ], + "angle": 0, + "content": "Network Configuration. DIFFVSGG is an online VSGG framework built upon the iterative diffusion diagram. It comprises three components: one off-the-shelf detector to deliver object detection results, the LDMs for inter-object relationship denosing, and projector heads for object classification, predicate prediction, and bounding box regression. Training Objective. The training process of DIFFVSGG consists of two stages. In the first stage, we pre-train the denoising U-Net \\(\\epsilon_{\\theta}\\) in Eq. 9, using \\(\\hat{A}^t\\) constructed from ground truth bounding box annotations for objects. In the second stage, we optimize the MLP classifier and projector in Eq. 14-15, which generate the final VSGG predictions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.838, + 0.906, + 0.868 + ], + "angle": 0, + "content": "Specifically, given relation prediction \\( p_r \\) and ground truth \\( y_r \\), the relation classification loss is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.878, + 0.905, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p r e d . c l s}} = - \\sum_ {i = 1} ^ {C _ {r}} y _ {r, i} \\log \\left(p _ {r, i}\\right). \\tag {17}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29165" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.089, + 0.905, + 0.312 + ], + "angle": 0, + "content": "
    MethodPredCLSSGCLSSGDET
    R@10 R@20 R@50 mR@10 mR@20 mR@50R@10 R@20 R@50 mR@10 mR@20 mR@50R@10 R@20 R@50 mR@10 mR@20 mR@50
    RelDN [113]20.320.320.36.26.26.211.011.011.03.43.43.49.19.19.13.33.33.3
    TRACE [88]27.527.527.515.215.215.214.814.814.88.98.98.913.914.514.58.28.28.2
    VRD [63]51.754.754.7---32.433.333.3---19.224.526.0---
    Motif Freq [112]62.465.165.1---40.841.941.9---23.731.433.3---
    MSDN [57]65.568.568.5---43.945.145.1---24.132.434.5---
    VCTREE [85]66.069.369.3---44.145.345.3---24.432.634.7---
    GPS-Net [60]66.869.969.9---45.346.546.5---24.733.135.1---
    STTran [17]68.671.871.837.840.140.246.447.547.527.228.028.025.234.137.016.620.822.2
    APT [58]69.473.873.8---47.248.948.9---26.336.138.3---
    STTran-TPI [96]69.772.672.637.340.640.647.248.348.328.329.329.326.234.637.415.620.221.8
    TR2 [94]70.973.873.8---47.748.748.7---26.835.538.3---
    TEMPURA [69]68.871.571.542.946.346.347.248.348.334.035.235.228.133.434.918.522.623.7
    DSG-DETR [30]------50.852.052.0---30.334.836.1---
    DIFFVSGG71.974.574.548.150.250.252.553.753.737.338.438.432.839.945.520.923.626.2
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.148, + 0.313, + 0.848, + 0.327 + ], + "angle": 0, + "content": "Table 1. Comparison of state-of-the-art VSGG methods on Action Genome test [40] under the \\( w \\) constraint setting." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.346, + 0.483, + 0.377 + ], + "angle": 0, + "content": "Similarly, given object class prediction \\( p_{o} \\) and ground truth \\( y_{o} \\), the object classification loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.38, + 0.483, + 0.41 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {o b j} \\cdot \\mathrm {c l s}} = - \\sum_ {j = 1} ^ {C _ {o}} y _ {o, j} \\log \\left(p _ {o, j}\\right). \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.418, + 0.484, + 0.464 + ], + "angle": 0, + "content": "For bounding box regression, given the ground truth bounding box \\( t_k \\) (e.g., \\( (x, y, w, h) \\)) and the predicted bounding box \\( \\hat{t}_k \\), the regression loss is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.181, + 0.478, + 0.483, + 0.496 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {b o x - r e g}} = \\operatorname {S m o o t h} \\mathrm {L} 1 \\left(t _ {k} - \\hat {t} _ {k}\\right). \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.502, + 0.462, + 0.518 + ], + "angle": 0, + "content": "The training objectives for each stage are formulated as:" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.535, + 0.483, + 0.558 + ], + "angle": 0, + "content": "Stage 1: \\(\\mathcal{L} = \\mathcal{L}_{\\mathrm{T\\_VSGG}}\\) (20)" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.554, + 0.432, + 0.571 + ], + "angle": 0, + "content": "Stage 2: \\(\\mathcal{L} = \\mathcal{L}_{\\mathrm{pred\\_cls}} + \\mathcal{L}_{\\mathrm{obj\\_cls}} + 0.5\\mathcal{L}_{\\mathrm{box\\_reg}}\\)" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.582, + 0.216, + 0.599 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.607, + 0.289, + 0.623 + ], + "angle": 0, + "content": "4.1. Experimental setting" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.629, + 0.483, + 0.78 + ], + "angle": 0, + "content": "Dataset. We evaluate DIFFVSGG on Action Genome (AG) [40], the largest video scene graph generation dataset comprising over 10K videos extended from the Charades dataset [80]. This dataset includes 1,715,568 predicate instances across 25 predicate classes, spanning 234,253 video frames, and features 476,229 bounding boxes across 35 object categories. The 1,715,568 instances for 25 predicate classes are divided into attention, spatial and contacting, three different types. Following prior work [17, 58], we use the same training/testing split." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Training. In the first training stage which optimizes the LDMs with ground-truth bounding box annotations, we set the learning rate to \\(10^{-4}\\) and use the Adam optimizer. The batch size is set to 2048, and the model is trained for 100 epochs. Each input clip consists of five frames sampled at random time intervals, enabling conditional temporal reasoning. The denoising U-Net \\(\\epsilon_{\\theta}\\) remains frozen once after pre-training. In the second training stage, the classifiers and" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.339, + 0.905, + 0.414 + ], + "angle": 0, + "content": "projectors are trained for 10 epochs with a batch size of 8. We use the AdamW optimizer with a learning rate of \\(10^{-5}\\), which decays by a factor of 5 halfway through the training. Evaluation Setup. In line with previous studies[30, 40, 58, 63], three standard evaluation protocols are adopted:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.415, + 0.905, + 0.476 + ], + "angle": 0, + "content": "- PredCLS: With oracle-provided object labels and bounding boxes as well as grounding-truth subject-object pairs, PredCLS assesses the model capability to predict predicate labels for each subject-object pair." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.475, + 0.905, + 0.52 + ], + "angle": 0, + "content": "- SGCLS: Building on PredCLS, SGCLS requires the simultaneous prediction of both predicate labels and the associated subject-object pairs for each predicate." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.52, + 0.906, + 0.686 + ], + "angle": 0, + "content": "- SGDET: As the most challenging task, SGDET requires generating complete scene graphs from scratch, including object detection, subject-object pair selection, and predicate classification. Detection is considered accurate if the overlap between prediction and ground truth exceeds 0.5. Evaluation Metric. We employ the Recall@k where \\( k \\in 10,20,50 \\) as the evaluation metric, to measure the proportion of ground truth elements within the top-k predictions. Additionally, Mean-Recall@k is also adopted to ensure the evaluation is not biased toward high-frequency classes. The evaluation is performed under two different scenarios:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.687, + 0.905, + 0.717 + ], + "angle": 0, + "content": "- \\( w \\) constraint: Each subject-object pair is restricted to a maximum of one predicate." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.718, + 0.905, + 0.748 + ], + "angle": 0, + "content": "- \\( w / o \\) constraints: Each subject-object pair is allowed to have multiple predicates simultaneously." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.415, + 0.906, + 0.748 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.758, + 0.815, + 0.774 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Tables 1-2 present the main experimental results of DIF-FVSGG against several top-leading approaches on Action Genome test [40]. Following existing VSGG works [17, 58], we firstly select a few representative image-level SGG methods such as RelDN [113] and GPS-Net [60]. Then, we compare DIFFVSGG with existing video-level solutions such as STTran[17], APT[58], etc. In general, DIF-FVSGG outperform image-level SGG methods by a large" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "29166" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.089, + 0.905, + 0.297 + ], + "angle": 0, + "content": "
    MethodPredCLSSGCLSSGDET
    R@10R@20R@50mR@10mR@20mR@50R@10R@20R@50mR@10mR@20mR@50R@10R@20R@50mR@10mR@20mR@50
    RelDN [113]44.275.489.231.263.175.525.041.947.918.636.942.613.623.036.67.518.833.7
    VRD [63]51.754.754.7---32.433.333.3---19.224.526.0---
    Motif Freq [112]62.465.165.1---40.841.941.9---23.731.433.3---
    MSDN [57]65.568.568.5---43.945.145.1---24.132.434.5---
    VCTREE [85]66.069.369.3---44.145.345.3---24.432.634.7---
    TRACE [88]72.691.696.450.973.682.737.146.750.531.942.746.326.535.645.322.831.341.8
    GPS-Net [60]76.093.699.5---------24.535.747.3---
    STTran [17]77.994.299.151.467.782.754.063.766.440.750.158.524.636.248.820.929.739.2
    APT [58]78.595.199.2---55.165.168.7---25.737.950.1---
    TR2 [94]83.196.699.9---57.264.466.2---27.839.250.0---
    TEMPURA [69]80.494.299.461.585.198.056.364.767.948.361.166.429.838.146.424.733.943.7
    DSG-DETR [30]------59.269.172.4---32.140.948.3---
    DIFFVSGG83.194.599.166.390.598.460.570.574.451.064.268.835.442.551.027.237.045.6
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.143, + 0.301, + 0.854, + 0.314 + ], + "angle": 0, + "content": "Table 2. Comparison of state-of-the-art VSGG methods on Action Genome test [40] under the w/o constraint setting." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.326, + 0.898, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.566, + 0.908, + 0.595 + ], + "angle": 0, + "content": "Figure 4. Visualization results on Action Genome test [40]. All results are given under the SGDET setup. Predicates in red indicate relationships are transformed to another one." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.599, + 0.483, + 0.718 + ], + "angle": 0, + "content": "margin in all metrics. Concretely, under the \\( w \\) constraint setup, our proposed method achieves R@10/R@20/R50 scores of 32.8/39.9/45.5, surpassing GPS-Net which achieves 24.7/33.1/35.1 scores by 8.1/6.8/10.4 scores, respectively. Similar trends can be observed on the \\( w/o \\) constraint setup. All of the above firmly demonstrates the effectiveness of incorporating temporal cues to tackle relation understanding in dynamic scene." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Additionally, when compared to the video-level counterparts, DIFFVSGG can still deliver state-of-the-art performance. Specifically, though DSG-DETR[30] adopts a modern DETR-like architecture and uses a Transformer-based decoder with all frames as the inputs to aggregate temporal cues, our DIFFVSGG which conducts online inference still outperforms it by a solid gap (i.e., 35.4/42.5/51.0 vs. 32.1/40.9/48.3 under the w/o constraint). More importantly, when it comes to the comparison of mR metric which prevents the bias toward high-frequency classes, DIFFVSGG obtains significantly higher performance compared to existing work. This suggests that using latent dif" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.907, + 0.705 + ], + "angle": 0, + "content": "fusion models (LDMs) to model the inter-object relationship is effective, and it successfully learned meaning distributions which can prevent overfitting to high-frequency classes. Similar conclusions can be drawn on PredCLS and SGCLS two evaluation protocols, where DIFFVSGG can still deliver SOTA performance under both \\( w \\) constraint and \\( w / o \\) constraint two setups." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.712, + 0.696, + 0.729 + ], + "angle": 0, + "content": "4.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.734, + 0.907, + 0.795 + ], + "angle": 0, + "content": "We provide visualization results of UNIALIGN in Fig.4. It can be seen that our proposed method is able to generate accurate scene graphs across various challenging scenarios, such as fast motion and occlusion." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.727, + 0.82 + ], + "angle": 0, + "content": "4.4. Diagnostic Experiment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.886 + ], + "angle": 0, + "content": "To assess the effectiveness of the detailed designs of DIF-FVSGG and gain deeper insights, we conduct a series of experiments on the AG test [40]. All performance metrics are reported under the SGDET setup." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.905, + 0.902 + ], + "angle": 0, + "content": "Key Component Analysis. We first examine the efficacy" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "29167" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.089, + 0.481, + 0.18 + ], + "angle": 0, + "content": "
    #L VSGGL T.VSGG Motionw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    126.935.338.027.538.948.5
    2✓29.737.741.530.340.149.9
    3✓32.039.344.633.942.050.3
    4✓32.839.945.535.442.551.0
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.187, + 0.444, + 0.202 + ], + "angle": 0, + "content": "Table 3. Analysis on key components of DIFFVSGG." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.216, + 0.48, + 0.29 + ], + "angle": 0, + "content": "
    #Union Box FeatureSubject FeatureSubject Locationw constraintsNo Constraints
    R@10R@20R@50R@10R@20R@50
    1✓29.536.742.032.339.247.5
    2✓✓31.038.243.633.740.848.7
    3✓✓✓32.839.945.535.442.551.0
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.096, + 0.297, + 0.479, + 0.312 + ], + "angle": 0, + "content": "Table 4. Analysis on elements to construct adjacency matrix \\( {\\mathbf{A}}^{t} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.326, + 0.48, + 0.415 + ], + "angle": 0, + "content": "
    Step Tw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    1031.738.542.934.041.149.5
    2032.839.945.535.442.551.0
    5033.240.546.435.743.151.4
    10033.140.345.935.542.851.1
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.117, + 0.422, + 0.456, + 0.436 + ], + "angle": 0, + "content": "Table 5. Analysis on forward and reverse diffusion steps." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.463, + 0.483, + 0.674 + ], + "angle": 0, + "content": "of essential components of DIFFVSGG in Table3, where the first row denotes the baseline model directly using bounding box predictions to construct scene graphs without denoising refinement. After integrating LDMs to model complex inter-object relationships within the scene (i.e., row #2), DIFFVSGG enjoys considerable improvement on both w and w/o constraint setups. Next, applying condition based temporal reasoning to capture long-term temporal dependencies further boosts the performance to 32.0 and 33.9 on two setups. Finally, upon the incorporation of motion enhanced denoising (i.e., row #4), DIFFVSGG obtains the best performance on both setups, suggesting that motion cues can effectively enhance the awareness of temporal cues through conditional promoting." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.735 + ], + "angle": 0, + "content": "Graph Construction. We study the impact of using various features to construct the adjacency matrix \\( \\mathbf{A}^t \\) in Table 4. As shown, incorporating all three types of features, as described in Eq.7, achieves the best performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.811 + ], + "angle": 0, + "content": "Number of Diffusion Step. Next we investigate the effect of different number of diffusion steps. As shown in Table 5, the best performance is achieved at \\( T = 50 \\). However, to balance the performance and efficiency efficiency, we set \\( T = 20 \\), which yields a slight reduction in performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.886 + ], + "angle": 0, + "content": "Number of Layer in Denoising U-Net. We further analyze the impact of using different number of layers in the encoder and decoder of denoising U-Net. As shown in Table 6, DIFFVSGG achieves similar performance when the layer number exceeds 2. For efficiency, we set it to 3." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Graph Readout. We explore different graph readout strate" + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.09, + 0.901, + 0.178 + ], + "angle": 0, + "content": "
    # Layerw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    231.938.244.534.042.150.1
    332.839.945.535.442.551.0
    532.439.646.134.443.050.7
    632.639.346.334.744.050.9
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.539, + 0.184, + 0.88, + 0.199 + ], + "angle": 0, + "content": "Table 6. Analysis of the layer configuration of the U-Net." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.218, + 0.901, + 0.285 + ], + "angle": 0, + "content": "
    Elementw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    At,i,032.839.945.535.442.551.0
    At,i,j31.737.743.533.641.249.6
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.538, + 0.292, + 0.88, + 0.306 + ], + "angle": 0, + "content": "Table 7. Analysis on the elements used for graph readout." + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.322, + 0.901, + 0.416 + ], + "angle": 0, + "content": "
    ModelParameter Inferencew constraintsw/o constraints
    NumberTimeR@10R@20R@50R@10R@20R@50
    TRACE [88]66.7 M8.4 FPS13.914.514.526.535.645.3
    STTran [17]51.1 M10.9 FPS25.234.137.024.636.248.8
    TEMPURA [69]53.5 M9.6 FPS28.133.434.929.838.146.4
    DSG-DETR [30]65.5 M7.3 FPS30.334.836.132.140.948.3
    DIFFVSGG46.7 M8.7 FPS32.839.945.535.442.551.0
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.515, + 0.423, + 0.902, + 0.437 + ], + "angle": 0, + "content": "Table 8. Analysis on the trainable parameters and inference time." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.467, + 0.907, + 0.547 + ], + "angle": 0, + "content": "gies in Table 7. Here \\( A_{i}^{t,0} \\) refers to utilize the entire row \\( i \\) of \\( A^{t,0} \\) to deliver the predictions (i.e., Eq. 15-16), while \\( A_{i,j}^{t,0} \\) denoting utilize one element at \\( (i,j) \\) of \\( A^{t,0} \\) to make prediction. It can be seen that aggregating all elements in a row that contains the same subject delivers higher performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.55, + 0.906, + 0.641 + ], + "angle": 0, + "content": "Running Efficiency. Finally we probe the running efficiency of DIFFVSGG. As seen in Table 8, our method requires the fewest trainable parameters among all competitors. Though inference speed is slightly slower than existing work due to step-wise denoising, the improvement in performance compensates for this limitation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.661, + 0.634, + 0.677 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.907, + 0.901 + ], + "angle": 0, + "content": "We presented DIFFVSGG, a diffusion-based VSGG solution that makes contributions in three aspects. First, as an online approach, it effectively addresses challenges such as GPU memory constraints and real-time processing while delivering high performance, highlighting its potential for real-world application. Second, we propose a learning strategy for LDMs to generate inter-object relationships from random subject-object pairs, with ground-truth object locations as the annotations. Third, in leverage of LDMs, DIFFVSGG provides a new approach to enable temporal reasoning via dynamic, iterative refinement of scene graphs across frames, conditioned on predictions of prior frame. We hope this work could provide a new perspective for video analysis through reverse diffusion along the temporal dimension." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "29168" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.241, + 0.108 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.117, + 0.484, + 0.252 + ], + "angle": 0, + "content": "This work was supported in part by the Natural Science Foundation of Zhejiang Province (LDT23F02023F02), the Fundamental Research Funds for the Central Universities (226-2024-00058), and the National Natural Science Foundation of China (No. 62372405). The authors would like to thank [optional: specific individuals or institutions] for their valuable discussions and feedback. We also acknowledge the use of [optional: datasets, computational resources, or tools] that contributed to this research." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.269, + 0.187, + 0.284 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.108, + 0.295, + 0.484, + 0.336 + ], + "angle": 0, + "content": "[1] Tomer Amit, Tal Shaharbany, Eliya Nachmani, and Lior Wolf. Segdiff: Image segmentation with diffusion probabilistic models. arXiv preprint arXiv:2112.00390, 2021. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.109, + 0.339, + 0.483, + 0.379 + ], + "angle": 0, + "content": "[2] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. 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Though demonstrating promising performance, they remain unable to handle real-time video streams and consume large GPU memory. Moreover, these approaches fall short in temporal reasoning, merely aggregating frame-level predictions over a temporal context. In response, we introduce DIFFVSGG, an online VSGG solution that frames this task as an iterative scene graph update problem. Drawing inspiration from Latent Diffusion Models (LDMs) which generate images via denoising a latent feature embedding, we unify the decoding of object classification, bounding box regression, and graph generation three tasks using one shared feature embedding. Then, given an embedding containing unified features of object pairs, we conduct a step-wise Denoising on it within LDMs, so as to deliver a clean embedding which clearly indicates the relationships between objects. This embedding then serves as the input to task-specific heads for object classification, scene graph generation, etc. DIFFVSGG further facilitates continuous temporal reasoning, where predictions for subsequent frames leverage results of past frames as the conditional inputs of LDMs, to guide the reverse diffusion process for current frames. Extensive experiments on three setups of Action Genome demonstrate the superiority of DIFFVSGG. + +# 1. Introduction + +Video Scene Graph Generation (VSGG) is receiving growing attention as it benefits a wide range of downstream tasks (e.g., video caption [34, 91], video retrieval [31, 50], and visual question answering [49, 87]). To deliver a holistic understanding of the underlying spatial-temporal dynamics within scenes, this task aims to construct a sequence of directed graphs where nodes represent objects and edges describe inter-object relationships (a.k.a., predicate). + +![](images/0a2bae8d608eb403a3157ebffe44468b891e594aba328f7232fbb53267d49602.jpg) + +![](images/5c83770ea906bd7cae56b2c8ae9b8936d33f4d2fac574ac4856e2334c04e3662.jpg) +Figure 1. (a) Existing VSGG solutions typically adopt an offline training pipeline, dividing the problem into various components: object detection, temporal association, and contextual aggregation. (b) DIFFVSGG introduces a new paradigm that performs spatial-temporal reasoning directly as each frame is processed sequentially, enabling progressive, online updates to the scene graph. + +Top-leading VSGG approaches typically adopt an offline pipeline [30, 69, 94], where scene graphs are generated independently for each frame and then aggregated along the temporal dimension (i.e., Fig. 1(a)). Though demonstrating strong performance, they require full video sequences as inputs, which faces challenges in processing long videos containing hundreds of frames due to GPU memory constraints, and is unable to handle real-time video streams for applications like autonomous driving and augmented reality [100]. Moreover, the dealing of temporal cues focuses solely on the global aggregation of frame-level predictions via Transform blocks. This falls short in the reasoning over temporal space, which is essential for modeling the dynamic changes of interactions between subjects and objects, and + +potentially benefits predicate prediction. Though a surge of early work has sought to facilitate explicit reasoning over the temporal domain via messaging passing [90] or spatial-temporal graph [74], a large performance gap remains when compared to these offline temporal aggregation approaches. + +To address these challenges, we propose DIFFVSGG, a high performance online approach for VSGG in leverage of Latent Diffusion Models (LDMs)[77, 81] (i.e., Fig.1(b)). In VSGG, the scene graph is dynamically evolved throughout the progression of video frames, with nodes and edges being continuously updated to precisely reflect the latest video content. Such an iterative update process shares a similar spirit of LDMs, which progressively remove noise to generate new samples from data distributions. Naturally, our motivation is to develop a VSGG model that aligns with the denoising principle of LDMs to iterative refine scene graphs along the temporal dimension, facilitating online temporal reasoning within this reverse diffusion process. + +To achieve this, we tackle VSGG from a unified perspective, organizing the decoding of object classification, bounding box regression, and graph generation three tasks from a shared feature embedding, which serves as the input and output of the Denoising U-Net. Concretely, from the spatial perspective, given the object detection results from each frame, multiple object pairs can be constructed. Then, for each object pair, we integrate i) the visual feature of two objects, ii) the union feature between, and iii) the locations of two objects, into a unified embedding. This embedding serves as the input to the denoising U-Net, after steps of denoising, a clean embedding clearly describing the objects as well as their inter-object relationships can be delivered. From the temporal perspective, DIFFVSGG conducts frame-by-frame reasoning where the result for each subsequent frame is delivered by iteratively refining the predictions of previous frames via reverse diffusion. Specifically, object positions and contextual information from prior frames are leveraged as conditions to guide the denoising of the shared feature embeddings for current frames. This encourages continuous temporal reasoning as the video progresses, allowing DIFFVSGG to effectively capture long-term spatiotemporal dependencies and adapt to complex motion patterns in an online manner. To further unlock the potential of LDMs, we build a memory bank to store positions for each object. In this way, motion information including acceleration and deceleration of object can be explicitly calculated. These motion cues are integrated into conditional inputs for the reverse diffusion step, which can help infer relationships such as following or approaching between objects. + +DIFFVSGG distinguishes itself in several aspects: First, it tackles VSGG in an online manner to continuously address an unlimited number of frames, while being friendly to devices with limited GPU memory. Second, the prediction of each video is implemented as a reverse diffusion pro + +cess, which elegantly encodes spatial and temporal reasoning into the Denoising step. Third, the temporal cues (i.e., historic predictions) are propagated into subsequent frames as conditions and participating in the prediction, while prior work simply aggregates predictions of all frames along the temporal dimension. Fourth, the learning of object classification, bounding box regression, and graph generation three tasks are jointly optimized with a shared feature embedding. Such a unified learning paradigm allows for the solving of VSGG from a global view, and avoids error made in one task propagating to subsequent tasks. Fifth, this unified decoding simplifies the VSGG pipeline and eliminates cumbersome handcrafted modules such as non-maximum suppression (NMS), and entity matching across frames. + +To the best of our knowledge, DIFFVSGG is the first work that treats the VSGG task as an iterative denoising problem along the temporal dimension. Extensive experiments on Action Genome (AG) [40] demonstrate the superiority of our proposed method. Notably, DIFFVSGG achieves SOTA results across all three setups and surpasses the top-leading solutions (e.g., DSG-DETR [30]) by 3.3 in terms of R@10, highlighting the great potential of utilizing diffusion models for visual relation understanding in videos. + +# 2. Related Work + +Scene Graph Generation (SGG). SGG involves detecting object instances and classifying their pairwise visual relations in an image, which is essential for comprehensive visual tasks [7, 8, 11, 53, 97, 98, 117, 118]. Recent SGG approaches seek to comprehend visual context by aggregating spatial context through various strategies, including explicit message passing [14, 20, 56, 57, 103, 112], graph structure modeling [83, 85, 99, 106, 110], external knowledge integration [3, 14, 33, 35, 109, 111], and transformer-based networks [12, 18, 23, 24, 43, 48, 55, 59, 64, 72, 79]. + +Extended from SGG, Video Scene Graph Generation (VSGG) aims to ground visual relationships jointly in spatial and temporal dimensions. Prior research primarily concentrates on addressing the long-tail distribution problem observed in prominent benchmarks [40]. Numerous unbiased approaches [16, 21, 46, 51, 54, 68, 86, 105] have been devised to handle infrequent predicate classes arising from this distribution. Furthermore, recent VSGG methods underscore the importance of spatial-temporal learning, and make use of the sequence-processing ability of Transformer [2, 70, 84] to capture temporal continuity. Nonetheless, these approaches often depend on complex post-processing that decouples spatial and temporal learning into two independent steps, and simply emphasizes on the consistent matching between frames. + +In contrast, DIFFVSGG handles both spatial and temporal reasoning from a unified perspective, where the reasoning on temporal dimension is naturally achieved via utiliz + +ing the spatial reasoning results of prior frames as the conditions to guide predictions for the current frames. + +Diffusion Models Beyond Image Generation. Diffusion Models (DMs) have surpassed many other generative models in image generation [6, 22, 37, 38, 92, 104] by successively denoising images. Beyond image generation, DMs inherently perform implicit discriminative reasoning while generating data, which proves highly effective in visual tasks that require complex relationship modeling and spatiotemporal reasoning. Therefore, a surge of work has adapted generative diffusion models for tasks including image segmentation [1, 4, 5, 15, 32, 44, 93], object detection [13, 76, 102], object tracking [65, 66, 101], and monocular depth estimation [25, 67, 78, 116]. Recent research has also utilizes DMs for more complex tasks that require high-level visual understanding abilities such as visual-linguistic understanding [47], scene generation [39], and human-object interaction detection [41, 52]. The potential of DMs in processing graph data has also been explored, encompassing a range of advanced tasks. This includes early work employing score-based methods for generating permutation-invariant graphs [42, 71], as well as recent approaches focused on enhancing graph neural networks [114, 115] and advancing graph generation techniques [107]. + +In this work, we borrow the step-wise denoising ability of latent diffusion models to enable spatial reasoning within a single frame. This is achieved by iteratively refining the union embeddings of object pairs, which serve to inform the prediction for bounding boxes and predicate classes, etc. On the other hand, temporal reasoning across frames is facilitated via conditional prompting, i.e., using predictions of prior frames which contain rich location and inter-object relationship cues to guide the denoising of current frames. + +Temporal Reasoning in Videos. Reasoning within the temporal dimension poses significant challenges for achieving high-level comprehension in video-related tasks [9, 10, 27-29, 61, 73, 108]. Recent advancements in video question answering seek to tackle temporal reasoning by employing attention mechanisms [26, 82] or incorporating external memory modules [45, 75] across video frames. In addition, to accurately capture the start, progression, and end of an action, action recognition approaches [89, 95] model complex motion patterns and dependencies in sequence. Video object detection (VOD) [19, 62] focuses on accurately capturing object trajectories, even in the presence of occlusions and abrupt movements. The top-leading VSGG solutions [30, 69, 94] instead aggregate predictions across frames to maintain the temporal consistency of objects. + +In summary, although existing work facilitates temporal reasoning from different perspectives and demonstrates it effectiveness, the potential of diffusion models remains largely underexplored. In fact, the sequential denoising in time, where each step is informed by previous one, offers + +a suitable tool to reconstruct the states for current frames based on observations from past frames. This insight motivates the proposal of DIFFVSGG, which tackles the VSGG task via graph denoising over the temporal dimension. + +# 3. Methodology + +In this section, we first give a brief introduction to the general background of latent Diffusion Models (§3.1), then elaborate on the overall design of our proposed DIFFVSGG (§3.2), and finally present the detailed information on the network architecture and training objectives (§3.3). + +# 3.1. Preliminary: Latent Diffusion Models + +To begin, we give an illustration on how diffusion processes [81] are used to model data distributions and generate high-quality samples. Specifically, we consider a continuous-time Markov chain with $t \in [0,T]$ : + +$$ +q (x _ {t} | x _ {t - 1}) = \mathcal {N} (x _ {t}; \sqrt {1 - \beta_ {t}} x _ {t - 1}, \beta_ {t} I), \tag {1} +$$ + +where $\beta_{t}$ is a small noise variance term at timestep $t$ , and $\mathcal{N}$ denotes a Gaussian distribution. The corrupted data at any intermediate time step $t$ can be derived recursively as: + +$$ +x _ {t} = \sqrt {\bar {\alpha} _ {t}} x _ {0} + \sqrt {1 - \bar {\alpha}} \epsilon , \tag {2} +$$ + +where $\alpha_{t} = 1 - \beta_{t}$ and $\overline{\alpha}_t = \prod_{s = 1}^t\alpha_s$ is the cumulative product of $\alpha_{t}$ over the timesteps, $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ represents the sampled noise. The reverse process essentially involves learning to reverse the noise addition at each step. The cleaned data at time step $t$ can be written recursively as: + +$$ +x _ {t - 1} = \frac {1}{\sqrt {\alpha_ {t}}} \left(x _ {t} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha}}} \epsilon_ {\theta} \left(x _ {t}, t\right), \right. \tag {3} +$$ + +where a time-conditioned denoising neural network $\epsilon_{\theta}(x,t)$ is trained to minimize the mean squared error between the true and predicted noise at each timestep: + +$$ +\mathcal {L} _ {\mathrm {D M}} := \mathbb {E} _ {x _ {0}, \epsilon , t} \left[ \| \epsilon - \epsilon_ {\theta} (x _ {t}, t) \| _ {2} ^ {2} \right]. \tag {4} +$$ + +Building on the diffusion process described above, latent diffusion models (LDMs) [77] first encode samples into a low-dimensional latent space $z = \mathcal{E}(x)$ using an encoder $\mathcal{E}$ , and then apply the diffusion process within this compressed space. Moreover, LDMs introduce the conditioning mechanisms which allow for control over the generated output based on additional input $y$ such as text, labels, or images. Consequently, the training objective for LDMs is given as: + +$$ +\mathcal {L} _ {\mathrm {L D M}} := \mathbb {E} _ {\mathcal {E} (x _ {0}), y, \epsilon , t} \left[ \| \epsilon - \epsilon_ {\theta} \left(\boldsymbol {z} _ {t}, t, c _ {\theta} (y)\right) \| _ {2} ^ {2} \right], \tag {5} +$$ + +where $c_{\theta}$ is a conditioning model to encode $y$ + +![](images/ba5ec8b663d8693eec909998f5d99a3dbb7d655bb55e5b3e6f369d1753caf50c.jpg) +Figure 2. Overview of our proposed inter-object relationship learning strategy using latent diffusion models. + +# 3.2. DIFFVSGG: Diffusion Models for VSGG + +Problem Definition. Considering a video sequence represented as $\mathcal{I} = \{I^1,\dots ,I^T\}$ containing $T$ frames, the objective of VSGG is to generate a sequence of scene graph $\mathcal{G} = \{G^{1},\dots ,G^{T}\}$ over time, where each element $\mathcal{G}^t$ represents the corresponding scene graph for frame $I^t$ . Each graph $G^{t}$ is defined as $G^{t} = (\mathcal{V}^{t},\mathcal{E}^{t})$ , with $\mathcal{V}^t$ and $\mathcal{E}^t$ denoting the sets of graph nodes and edges, respectively. Each node $v_{i}^{t}\in \mathcal{V}^{t}$ includes attributes such as category and location for object $i$ , while each edge $e_{i,j}^{t}\in \mathcal{E}^{t}$ describes the inter-object relationship (a.k.a.predicate) between subject $i$ and object $j$ . In this manner, $\mathcal{G}$ captures all objects (i.e., $\mathcal{V}$ ), their interactions (i.e., $\mathcal{E}$ ), and the dynamics as they evolve over time (i.e., from $t = 1$ to $t = T$ ) within the scene. + +Graph Construction. Given a video $\mathcal{I} = \{I^1,\dots ,I^T\}$ , we first employ an on-the-shelf object detector $\mathcal{F}_{\mathrm{det}}$ for each frame: + +$$ +\left\{\boldsymbol {F} ^ {t}, \mathcal {B} ^ {t}, \mathcal {O} ^ {t} \right\} = \mathcal {F} _ {\det } \left(I ^ {t}\right), \tag {6} +$$ + +where $\pmb{F}^{t}$ is the feature extracted by backbone, $\mathcal{B}^t = \{b_1^t,\dots ,b_{N_t}^t\}$ and $\mathcal{O}^t = \{o_1^t,\dots ,o_{N_t}^t\}$ are bounding box and class predictions for $N_{t}$ objects detected from frame $I^t$ respectively. This serves to initialize an adjacency matrix $\pmb{A}^{t}\in \mathbb{R}^{N_{t}\times N_{t}\times D_{e}}$ , of which each element aims to represent the inter-object relationships between object $i$ and $j$ .. + +$$ +\boldsymbol {A} _ {i, j} ^ {t} = \left[ \boldsymbol {F} _ {o _ {i}} ^ {t}; \boldsymbol {F} _ {o _ {i}, o _ {j}} ^ {t}; \boldsymbol {F} _ {b _ {i}} ^ {t} \right] \in \mathbb {R} ^ {D _ {e}}, \tag {7} +$$ + +$$ +\boldsymbol {A} _ {j, i} ^ {t} = \left[ \boldsymbol {F} _ {o _ {j}} ^ {t}; \boldsymbol {F} _ {o _ {j}, o _ {i}} ^ {t}; \boldsymbol {F} _ {b _ {j}} ^ {t} \right] \in \mathbb {R} ^ {D _ {e}}. +$$ + +Here $[]$ refers to the concatenation of features, implemented as torch.cat(). $F_{o_i}^t = \mathcal{F}_{\mathrm{ROI}}(F^t,b_i^t)$ is the instance-level feature for object $i$ extracted via ROAlign [36] (i.e., $\mathcal{F}_{\mathrm{ROI}}), F_{o_i,o_j}^t = \mathcal{F}_{\mathrm{ROI}}(F^t,b_i^t\cup b_j^t)$ is the feature mapped from the union box of object $i$ and $j$ (i.e., $b_{i}^{t}\cup b_{j}^{t})$ ,and $F_{b_i}^t$ describes bounding box $b_{i}^{t}$ using a box-to-feature mapping function identical to that in [112]. $A_{i,j}^{t}$ represents the relationship predicted from subject $i$ , which differs from $A_{j,i}^{t}$ where $j$ is considered the subject. In this way, the matrix $A^t$ encodes both node features of each object and the edge features between any pair of them. Note that such subject-based encoding does not incorporate $Fo_{j}$ and $Fb_{j}$ into $A_{i,j}$ (i.e., $[F_{o_i};F_{b_i};F_{o_i,o_j};F_{o_j};F_{b_j}])$ , which hinders the neural network to distinguish between the subject $(i)$ and object + +$(j)$ . Additionally, as the number of instances $(i.e., N_{t})$ typically varies across frames due to the emergence or disappearance of some instances, we pad $\mathbf{A}^{t}$ to a fixed size of $N \times N$ where $N > \max(N_{1}, \dots, N_{T})$ , using randomly generated feature embedding from Gaussian distributions. + +Inter-object Relationship Learning via LDMs. Next we aim to facilitate the learning of inter-object relationships within LDMs using ground truth scene graph (i.e., Fig. 2). Since we use an off-the-self object detector, the extracted feature $F^t$ remains static for each frame. Therefore, with access to the ground truth bounding box annotations, we can compute precise edge features via Eq.7 from $F^t$ . The adjacency matrix $\hat{A}^t$ which exactly encodes the inter-object features can also be obtained. Here $\hat{A}^t$ is the ground truth of inter-object relationships, initialized using features derived from ground-truth bounding boxes, where object pairs with no relations are represented as empty entries. $\hat{A}^t$ instructs the learning of a LDM which is responsible for recovering object features and their relationships from random noise. + +- Forward Process. Let $\hat{A}^{t,0}$ represent the clean adjacency matrix. The noise injection process to progressively perturb this matrix is defined following Eq.2, and expressed as: + +$$ +\hat {\boldsymbol {A}} ^ {t, k} = \sqrt {\bar {\alpha} _ {t}} x \hat {\boldsymbol {A}} ^ {t, 0} + \sqrt {1 - \bar {\alpha}} \epsilon , \tag {8} +$$ + +where $\hat{A}^{t,k}$ denotes the noisy adjacency matrix at step $k$ . This enables the model to learn robust feature representations, through the exposure to degraded versions of $\hat{A}^{t,0}$ . + +- **Reverse Process.** To recover the original adjacency matrix $\hat{A}^{t,0}$ , we employ a denoising U-Net $\epsilon_{\theta}$ which is trained to iteratively remove noise starting from the initial noisy matrix $\hat{A}^{t,K}$ . This process follows the denoising step defined in Eq.3 and proceeds as: + +$$ +\hat {\boldsymbol {A}} ^ {t, k - 1} = \frac {1}{\sqrt {\alpha_ {t}}} (\hat {\boldsymbol {A}} ^ {t, k} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha}}} \epsilon_ {\theta} (\hat {\boldsymbol {A}} ^ {t, k}, k), \tag {9} +$$ + +where $\epsilon_{\theta}$ is optimized to recover meaningful inter-object relationships. Following Eq. 5, we define the training objective $\mathcal{L}_{\mathrm{VSGG}}$ by minimizing the spatial structure loss: + +$$ +\mathcal {L} _ {\mathrm {V S G G}} := \mathbb {E} _ {\hat {\boldsymbol {A}} ^ {t, k}, \epsilon , k} \left[ \| \epsilon - \epsilon_ {\theta} (\hat {\boldsymbol {A}} ^ {t, k}, k) \| _ {2} ^ {2} \right]. \tag {10} +$$ + +$\mathcal{L}_{\mathrm{VSGG}}$ encourages $\epsilon_{\theta}$ to accurately predict and remove the noise at each step $k$ , so as to restore $\hat{\boldsymbol{A}}^t$ structured in the + +![](images/fedb4341dd21e77d73c9959b6c8446b264a2d78e26eeec7d7f2dd91aaf159eda.jpg) + +![](images/34556366425ae63134e07560e753c299c2af6184f0ae918d88b2f02d147032cb.jpg) + +![](images/8473a30f996bc1070ad7f86f4ea76a967477497b81963f41a1160b2e5bb24cc3.jpg) + +![](images/05b86db6900c1a573fd87835e98a388c4be6f3f7ebaebf886086693f0debe8d6.jpg) + +![](images/e2835cfc1ab9d08d216ee548470c8a073c32c37f20282a0bf26ba3edd1ffd437.jpg) + +![](images/ca6278ce9ce36864ffd2abb575eb7cfa298ba96717c98965891d21bc78ca100d.jpg) + +![](images/9f1ab44f787e4bd76b0d68c7f999faeb14919fccfd20ca774221136ba21d4719.jpg) + +![](images/46b743f1ae8513363d070d421394cdf8f4597766d7d800d860113209af249cc4.jpg) +Figure 3. Overview of our proposed temporal prompting strategy. + +way that preserves spatial and relational coherence. During inference, given the adjacency matrix $\mathbf{A}^t$ from an arbitrary frame $t$ , we consider it noisy and utilize the well-trained denoising U-Net above to refine it, so as to deliver an updated version that indicates the interaction between objects, as well as the location and category of objects: $\mathbf{A}^{t,k - 1} = \frac{1}{\sqrt{\alpha_t}} (\mathbf{A}^{t,k} - \frac{\beta_t}{\sqrt{1 - \overline{\alpha}}}\epsilon_\theta (\mathbf{A}^{t,k},k)$ . Unlike the training process which utilizes $\hat{\mathbf{A}}$ derived from ground truth bounding boxes, $\mathbf{A}$ here is obtained from the predicated ones. Note that the main challenge of VSGG lies in modeling of the dynamic changes of relation between object and subject, and the diffusion models primarily focus on recovering object features and their relationships. Thus, the slight bias in predicated bounding boxes, especially after ROIAAlign, causes negligible impacts to relation predictions. + +Condition Based Temporal Reasoning. For a given video stream, we can infer future frames based on the content of preceding frames. This observation serves as the motivation for our temporal prompting strategy (i.e., Fig.3), where we condition the denoising process of $A^t$ on the denoised adjacency matrix of prior frames (i.e., $A^{t - 1,0}$ ), as follows: + +$$ +\boldsymbol {A} ^ {t, k - 1} = \frac {1}{\sqrt {\alpha_ {t}}} \left(\boldsymbol {A} ^ {t, k} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha}}} \epsilon_ {\theta} \left(\boldsymbol {A} ^ {t, k}, k, \boldsymbol {A} ^ {t - 1, 0}\right), \right. \tag {11} +$$ + +where the condition decoder $c_{\theta}$ in Eq. 5 is discarded, as $\pmb{A}^{t - 1,0}$ has already shared the same dimension as $\pmb{A}^{t,k}$ . With this condition-based temporal association for denoising, the training objective for $\epsilon_{\theta}$ is updated as: + +$$ +\mathcal {L} _ {\mathrm {T . V S G G}} := \mathbb {E} _ {\boldsymbol {A} ^ {t, k}, \boldsymbol {A} ^ {t - 1, 0}, \epsilon , k} \left[ \| \epsilon - \epsilon_ {\theta} (\boldsymbol {A} ^ {t, k}, \boldsymbol {A} ^ {t - 1, 0}, k) \| _ {2} ^ {2} \right]. \tag {12} +$$ + +Here $\mathcal{L}_{\mathrm{T.VSGG}}$ encourages $\epsilon_{\theta}$ to generate temporally consistent outputs, enabling a smooth and coherent denoising of adjacency matrix across frames. Moreover, since new instances keep emerging as the video progresses, we calculate similarities between ROIAngled features of the potential new object (i.e., $F_{o_p}^t$ ) and all other objects in the past frame (i.e., $F_{o_i}^{t - 1}$ ), and consider $o_p$ as new object if the similarities is smaller than 0.2 for all other objects. Then, the random padded features in $A$ during graph construction are replaced with union and instance features of these new instances. + +Motion Enhanced Denoising for VSGG. Motion cues serve as indicators to describe object movements in a given scene. They provide essential context for understanding the position and duration of events. Moreover, the speed and direction of object movements can reveal intentions for interactions (e.g., approaching), which aids in temporal reasoning by inferring whether they might complete an action or reach a goal. Therefore, given a box prediction $b_{i}^{t} = \{x_{i}^{t}, y_{i}^{t}, w_{i}^{t}, h_{i}^{t}\}$ for object $i$ , we explicitly calculate the approaching speed between object $i$ and $j$ as follows: + +$$ +d _ {i, j} ^ {t} = \sqrt {\left(x _ {i} ^ {t} - x _ {j} ^ {t}\right) ^ {2} + \left(y _ {i} ^ {t} - y _ {j} ^ {t}\right) ^ {2}}, \tag {13} +$$ + +$$ +v _ {i, j} ^ {t} = (d _ {i, j} ^ {t} - d _ {i, j} ^ {t - \Delta t}) / \Delta t, +$$ + +where $\Delta t$ is the interval of frame. Given $v^t\in \mathbb{R}^{N^t\times N^t}$ we pad it into the same size with $\pmb{A}^{t}$ (i.e., $v^{t}\in \mathbb{R}^{N\times N})$ and inject it into $\pmb{A}^{t,k}$ at each denoising step $k\colon \pmb{A}^{t,k} = \pmb{A}^{t,k} + v^t$ + +Graph Readout. Next we investigate how to deliver SGG predictions for each frame based on the denoised adjacency matrix $\mathbf{A}^{t,0}$ . Specifically, the prediction for predicate of each subject-object pair is obtained as follows: + +$$ +r _ {i, j} ^ {t} = \operatorname {s o f t m a x} \left(\mathcal {F} _ {\text {p r e d}} \left(\boldsymbol {A} _ {i, j} ^ {t, 0}\right)\right) \in \mathbb {R} ^ {N _ {\text {p r e d , c l s}}} \tag {14} +$$ + +where $\mathcal{F}_{\mathrm{pred}}$ is an MLP-based classifier and $N_{\mathrm{pred\_cls}}$ represents the number of predicate classes. For object classification and bounding box regression, to render a global view, we utilize the entire row $i$ of $\mathbf{A}^{t,0}$ (i.e., $\mathbf{A}_i^{t,0}$ ) where all elements consider $i$ as the subject, to deliver the prediction: + +$$ +o _ {i} ^ {t} = \operatorname {s o f t m a x} \left(\mathcal {F} _ {\mathrm {o b j}} \left(\boldsymbol {A} _ {i} ^ {t, 0}\right)\right) \in \mathbb {R} ^ {N _ {\mathrm {o b j , c l s}}}, \tag {15} +$$ + +$$ +b _ {i} ^ {t} = \operatorname {s i g m o i d} \left(\mathcal {F} _ {\text {b o x}} \left(A _ {i} ^ {t, 0}\right)\right) \in \mathbb {R} ^ {4}, \tag {16} +$$ + +where $N_{\mathrm{obj\_cls}}$ is the number of object classes, $\mathcal{F}_{\mathrm{obj}}$ and $\mathcal{F}_{\mathrm{box}}$ are the MLP-based classifier and projector, respectively. + +# 3.3. Implementation Details + +Network Configuration. DIFFVSGG is an online VSGG framework built upon the iterative diffusion diagram. It comprises three components: one off-the-shelf detector to deliver object detection results, the LDMs for inter-object relationship denosing, and projector heads for object classification, predicate prediction, and bounding box regression. Training Objective. The training process of DIFFVSGG consists of two stages. In the first stage, we pre-train the denoising U-Net $\epsilon_{\theta}$ in Eq. 9, using $\hat{A}^t$ constructed from ground truth bounding box annotations for objects. In the second stage, we optimize the MLP classifier and projector in Eq. 14-15, which generate the final VSGG predictions. + +Specifically, given relation prediction $p_r$ and ground truth $y_r$ , the relation classification loss is computed as: + +$$ +\mathcal {L} _ {\text {p r e d . c l s}} = - \sum_ {i = 1} ^ {C _ {r}} y _ {r, i} \log \left(p _ {r, i}\right). \tag {17} +$$ + +
    MethodPredCLSSGCLSSGDET
    R@10 R@20 R@50 mR@10 mR@20 mR@50R@10 R@20 R@50 mR@10 mR@20 mR@50R@10 R@20 R@50 mR@10 mR@20 mR@50
    RelDN [113]20.320.320.36.26.26.211.011.011.03.43.43.49.19.19.13.33.33.3
    TRACE [88]27.527.527.515.215.215.214.814.814.88.98.98.913.914.514.58.28.28.2
    VRD [63]51.754.754.7---32.433.333.3---19.224.526.0---
    Motif Freq [112]62.465.165.1---40.841.941.9---23.731.433.3---
    MSDN [57]65.568.568.5---43.945.145.1---24.132.434.5---
    VCTREE [85]66.069.369.3---44.145.345.3---24.432.634.7---
    GPS-Net [60]66.869.969.9---45.346.546.5---24.733.135.1---
    STTran [17]68.671.871.837.840.140.246.447.547.527.228.028.025.234.137.016.620.822.2
    APT [58]69.473.873.8---47.248.948.9---26.336.138.3---
    STTran-TPI [96]69.772.672.637.340.640.647.248.348.328.329.329.326.234.637.415.620.221.8
    TR2 [94]70.973.873.8---47.748.748.7---26.835.538.3---
    TEMPURA [69]68.871.571.542.946.346.347.248.348.334.035.235.228.133.434.918.522.623.7
    DSG-DETR [30]------50.852.052.0---30.334.836.1---
    DIFFVSGG71.974.574.548.150.250.252.553.753.737.338.438.432.839.945.520.923.626.2
    + +Table 1. Comparison of state-of-the-art VSGG methods on Action Genome test [40] under the $w$ constraint setting. + +Similarly, given object class prediction $p_{o}$ and ground truth $y_{o}$ , the object classification loss is defined as: + +$$ +\mathcal {L} _ {\mathrm {o b j} \cdot \mathrm {c l s}} = - \sum_ {j = 1} ^ {C _ {o}} y _ {o, j} \log \left(p _ {o, j}\right). \tag {18} +$$ + +For bounding box regression, given the ground truth bounding box $t_k$ (e.g., $(x, y, w, h)$ ) and the predicted bounding box $\hat{t}_k$ , the regression loss is formulated as: + +$$ +\mathcal {L} _ {\text {b o x - r e g}} = \operatorname {S m o o t h} \mathrm {L} 1 \left(t _ {k} - \hat {t} _ {k}\right). \tag {19} +$$ + +The training objectives for each stage are formulated as: + +Stage 1: $\mathcal{L} = \mathcal{L}_{\mathrm{T\_VSGG}}$ (20) + +Stage 2: $\mathcal{L} = \mathcal{L}_{\mathrm{pred\_cls}} + \mathcal{L}_{\mathrm{obj\_cls}} + 0.5\mathcal{L}_{\mathrm{box\_reg}}$ + +# 4. Experiment + +# 4.1. Experimental setting + +Dataset. We evaluate DIFFVSGG on Action Genome (AG) [40], the largest video scene graph generation dataset comprising over 10K videos extended from the Charades dataset [80]. This dataset includes 1,715,568 predicate instances across 25 predicate classes, spanning 234,253 video frames, and features 476,229 bounding boxes across 35 object categories. The 1,715,568 instances for 25 predicate classes are divided into attention, spatial and contacting, three different types. Following prior work [17, 58], we use the same training/testing split. + +Training. In the first training stage which optimizes the LDMs with ground-truth bounding box annotations, we set the learning rate to $10^{-4}$ and use the Adam optimizer. The batch size is set to 2048, and the model is trained for 100 epochs. Each input clip consists of five frames sampled at random time intervals, enabling conditional temporal reasoning. The denoising U-Net $\epsilon_{\theta}$ remains frozen once after pre-training. In the second training stage, the classifiers and + +projectors are trained for 10 epochs with a batch size of 8. We use the AdamW optimizer with a learning rate of $10^{-5}$ , which decays by a factor of 5 halfway through the training. Evaluation Setup. In line with previous studies[30, 40, 58, 63], three standard evaluation protocols are adopted: + +- PredCLS: With oracle-provided object labels and bounding boxes as well as grounding-truth subject-object pairs, PredCLS assesses the model capability to predict predicate labels for each subject-object pair. +- SGCLS: Building on PredCLS, SGCLS requires the simultaneous prediction of both predicate labels and the associated subject-object pairs for each predicate. +- SGDET: As the most challenging task, SGDET requires generating complete scene graphs from scratch, including object detection, subject-object pair selection, and predicate classification. Detection is considered accurate if the overlap between prediction and ground truth exceeds 0.5. Evaluation Metric. We employ the Recall@k where $k \in 10,20,50$ as the evaluation metric, to measure the proportion of ground truth elements within the top-k predictions. Additionally, Mean-Recall@k is also adopted to ensure the evaluation is not biased toward high-frequency classes. The evaluation is performed under two different scenarios: +- $w$ constraint: Each subject-object pair is restricted to a maximum of one predicate. +- $w / o$ constraints: Each subject-object pair is allowed to have multiple predicates simultaneously. + +# 4.2. Comparison with State-of-the-arts + +Tables 1-2 present the main experimental results of DIF-FVSGG against several top-leading approaches on Action Genome test [40]. Following existing VSGG works [17, 58], we firstly select a few representative image-level SGG methods such as RelDN [113] and GPS-Net [60]. Then, we compare DIFFVSGG with existing video-level solutions such as STTran[17], APT[58], etc. In general, DIF-FVSGG outperform image-level SGG methods by a large + +
    MethodPredCLSSGCLSSGDET
    R@10R@20R@50mR@10mR@20mR@50R@10R@20R@50mR@10mR@20mR@50R@10R@20R@50mR@10mR@20mR@50
    RelDN [113]44.275.489.231.263.175.525.041.947.918.636.942.613.623.036.67.518.833.7
    VRD [63]51.754.754.7---32.433.333.3---19.224.526.0---
    Motif Freq [112]62.465.165.1---40.841.941.9---23.731.433.3---
    MSDN [57]65.568.568.5---43.945.145.1---24.132.434.5---
    VCTREE [85]66.069.369.3---44.145.345.3---24.432.634.7---
    TRACE [88]72.691.696.450.973.682.737.146.750.531.942.746.326.535.645.322.831.341.8
    GPS-Net [60]76.093.699.5---------24.535.747.3---
    STTran [17]77.994.299.151.467.782.754.063.766.440.750.158.524.636.248.820.929.739.2
    APT [58]78.595.199.2---55.165.168.7---25.737.950.1---
    TR2 [94]83.196.699.9---57.264.466.2---27.839.250.0---
    TEMPURA [69]80.494.299.461.585.198.056.364.767.948.361.166.429.838.146.424.733.943.7
    DSG-DETR [30]------59.269.172.4---32.140.948.3---
    DIFFVSGG83.194.599.166.390.598.460.570.574.451.064.268.835.442.551.027.237.045.6
    + +Table 2. Comparison of state-of-the-art VSGG methods on Action Genome test [40] under the w/o constraint setting. + +![](images/3bc2e5a808311f3c1fc0782ec9aa22bec747406486faea231cbb706a9fcaaa9c.jpg) +Figure 4. Visualization results on Action Genome test [40]. All results are given under the SGDET setup. Predicates in red indicate relationships are transformed to another one. + +margin in all metrics. Concretely, under the $w$ constraint setup, our proposed method achieves R@10/R@20/R50 scores of 32.8/39.9/45.5, surpassing GPS-Net which achieves 24.7/33.1/35.1 scores by 8.1/6.8/10.4 scores, respectively. Similar trends can be observed on the $w/o$ constraint setup. All of the above firmly demonstrates the effectiveness of incorporating temporal cues to tackle relation understanding in dynamic scene. + +Additionally, when compared to the video-level counterparts, DIFFVSGG can still deliver state-of-the-art performance. Specifically, though DSG-DETR[30] adopts a modern DETR-like architecture and uses a Transformer-based decoder with all frames as the inputs to aggregate temporal cues, our DIFFVSGG which conducts online inference still outperforms it by a solid gap (i.e., 35.4/42.5/51.0 vs. 32.1/40.9/48.3 under the w/o constraint). More importantly, when it comes to the comparison of mR metric which prevents the bias toward high-frequency classes, DIFFVSGG obtains significantly higher performance compared to existing work. This suggests that using latent dif + +fusion models (LDMs) to model the inter-object relationship is effective, and it successfully learned meaning distributions which can prevent overfitting to high-frequency classes. Similar conclusions can be drawn on PredCLS and SGCLS two evaluation protocols, where DIFFVSGG can still deliver SOTA performance under both $w$ constraint and $w / o$ constraint two setups. + +# 4.3. Qualitative Results + +We provide visualization results of UNIALIGN in Fig.4. It can be seen that our proposed method is able to generate accurate scene graphs across various challenging scenarios, such as fast motion and occlusion. + +# 4.4. Diagnostic Experiment + +To assess the effectiveness of the detailed designs of DIF-FVSGG and gain deeper insights, we conduct a series of experiments on the AG test [40]. All performance metrics are reported under the SGDET setup. + +Key Component Analysis. We first examine the efficacy + +
    #L VSGGL T.VSGG Motionw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    126.935.338.027.538.948.5
    2✓29.737.741.530.340.149.9
    3✓32.039.344.633.942.050.3
    4✓32.839.945.535.442.551.0
    + +Table 3. Analysis on key components of DIFFVSGG. + +
    #Union Box FeatureSubject FeatureSubject Locationw constraintsNo Constraints
    R@10R@20R@50R@10R@20R@50
    1✓29.536.742.032.339.247.5
    2✓✓31.038.243.633.740.848.7
    3✓✓✓32.839.945.535.442.551.0
    + +Table 4. Analysis on elements to construct adjacency matrix ${\mathbf{A}}^{t}$ . + +
    Step Tw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    1031.738.542.934.041.149.5
    2032.839.945.535.442.551.0
    5033.240.546.435.743.151.4
    10033.140.345.935.542.851.1
    + +of essential components of DIFFVSGG in Table3, where the first row denotes the baseline model directly using bounding box predictions to construct scene graphs without denoising refinement. After integrating LDMs to model complex inter-object relationships within the scene (i.e., row #2), DIFFVSGG enjoys considerable improvement on both w and w/o constraint setups. Next, applying condition based temporal reasoning to capture long-term temporal dependencies further boosts the performance to 32.0 and 33.9 on two setups. Finally, upon the incorporation of motion enhanced denoising (i.e., row #4), DIFFVSGG obtains the best performance on both setups, suggesting that motion cues can effectively enhance the awareness of temporal cues through conditional promoting. + +Graph Construction. We study the impact of using various features to construct the adjacency matrix $\mathbf{A}^t$ in Table 4. As shown, incorporating all three types of features, as described in Eq.7, achieves the best performance. + +Number of Diffusion Step. Next we investigate the effect of different number of diffusion steps. As shown in Table 5, the best performance is achieved at $T = 50$ . However, to balance the performance and efficiency efficiency, we set $T = 20$ , which yields a slight reduction in performance. + +Number of Layer in Denoising U-Net. We further analyze the impact of using different number of layers in the encoder and decoder of denoising U-Net. As shown in Table 6, DIFFVSGG achieves similar performance when the layer number exceeds 2. For efficiency, we set it to 3. + +Graph Readout. We explore different graph readout strate + +Table 5. Analysis on forward and reverse diffusion steps. + +
    # Layerw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    231.938.244.534.042.150.1
    332.839.945.535.442.551.0
    532.439.646.134.443.050.7
    632.639.346.334.744.050.9
    + +Table 6. Analysis of the layer configuration of the U-Net. + +
    Elementw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    At,i,032.839.945.535.442.551.0
    At,i,j31.737.743.533.641.249.6
    + +Table 7. Analysis on the elements used for graph readout. + +
    ModelParameter Inferencew constraintsw/o constraints
    NumberTimeR@10R@20R@50R@10R@20R@50
    TRACE [88]66.7 M8.4 FPS13.914.514.526.535.645.3
    STTran [17]51.1 M10.9 FPS25.234.137.024.636.248.8
    TEMPURA [69]53.5 M9.6 FPS28.133.434.929.838.146.4
    DSG-DETR [30]65.5 M7.3 FPS30.334.836.132.140.948.3
    DIFFVSGG46.7 M8.7 FPS32.839.945.535.442.551.0
    + +Table 8. Analysis on the trainable parameters and inference time. + +gies in Table 7. Here $A_{i}^{t,0}$ refers to utilize the entire row $i$ of $A^{t,0}$ to deliver the predictions (i.e., Eq. 15-16), while $A_{i,j}^{t,0}$ denoting utilize one element at $(i,j)$ of $A^{t,0}$ to make prediction. It can be seen that aggregating all elements in a row that contains the same subject delivers higher performance. + +Running Efficiency. Finally we probe the running efficiency of DIFFVSGG. As seen in Table 8, our method requires the fewest trainable parameters among all competitors. Though inference speed is slightly slower than existing work due to step-wise denoising, the improvement in performance compensates for this limitation. + +# 5. Conclusion + +We presented DIFFVSGG, a diffusion-based VSGG solution that makes contributions in three aspects. First, as an online approach, it effectively addresses challenges such as GPU memory constraints and real-time processing while delivering high performance, highlighting its potential for real-world application. Second, we propose a learning strategy for LDMs to generate inter-object relationships from random subject-object pairs, with ground-truth object locations as the annotations. Third, in leverage of LDMs, DIFFVSGG provides a new approach to enable temporal reasoning via dynamic, iterative refinement of scene graphs across frames, conditioned on predictions of prior frame. We hope this work could provide a new perspective for video analysis through reverse diffusion along the temporal dimension. + +# Acknowledgment + +This work was supported in part by the Natural Science Foundation of Zhejiang Province (LDT23F02023F02), the Fundamental Research Funds for the Central Universities (226-2024-00058), and the National Natural Science Foundation of China (No. 62372405). 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(6):2827-2840, 2021. 2 \ No newline at end of file diff --git a/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/images.zip b/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e6359da3eb9e119ef0214bf26b96905aef19b110 --- /dev/null +++ b/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4a137ab60b7887c5dbdec5c1e3e5e3cd6b01d74316c540d932128b0203eb4a29 +size 710084 diff --git a/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/layout.json b/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..46af45c291b498b8b444a80750783e70ecea7541 --- /dev/null +++ b/2025/DiffVsgg_ Diffusion-Driven Online Video Scene Graph Generation/layout.json @@ -0,0 +1,12876 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 93, + 103, + 517, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 103, + 517, + 121 + ], + "spans": [ + { + "bbox": [ + 93, + 103, + 517, + 121 + ], + "type": "text", + "content": "DIFFVSGG: Diffusion-Driven Online Video Scene Graph Generation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 142, + 466, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 142, + 466, + 186 + ], + "spans": [ + { + "bbox": [ + 143, + 142, + 466, + 186 + ], + "type": "text", + "content": "Mu Chen1, Lulei Li2, Wenguan Wang1†, Yi Yang1 \n1ReLER, CCAI, Zhejiang University 2ReLER, AAI, University of Technology Sydney \nhttps://github.com/kagawa588/DiffVsgg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 152, + 227, + 200, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 227, + 200, + 239 + ], + "spans": [ + { + "bbox": [ + 152, + 227, + 200, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 252, + 296, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 252, + 296, + 553 + ], + "spans": [ + { + "bbox": [ + 55, + 252, + 296, + 553 + ], + "type": "text", + "content": "Top-leading solutions for Video Scene Graph Generation (VSGG) typically adopt an offline pipeline. Though demonstrating promising performance, they remain unable to handle real-time video streams and consume large GPU memory. Moreover, these approaches fall short in temporal reasoning, merely aggregating frame-level predictions over a temporal context. In response, we introduce DIFFVSGG, an online VSGG solution that frames this task as an iterative scene graph update problem. Drawing inspiration from Latent Diffusion Models (LDMs) which generate images via denoising a latent feature embedding, we unify the decoding of object classification, bounding box regression, and graph generation three tasks using one shared feature embedding. Then, given an embedding containing unified features of object pairs, we conduct a step-wise Denoising on it within LDMs, so as to deliver a clean embedding which clearly indicates the relationships between objects. This embedding then serves as the input to task-specific heads for object classification, scene graph generation, etc. DIFFVSGG further facilitates continuous temporal reasoning, where predictions for subsequent frames leverage results of past frames as the conditional inputs of LDMs, to guide the reverse diffusion process for current frames. Extensive experiments on three setups of Action Genome demonstrate the superiority of DIFFVSGG." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 576, + 135, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 576, + 135, + 588 + ], + "spans": [ + { + "bbox": [ + 56, + 576, + 135, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 597, + 295, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 597, + 295, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 597, + 295, + 693 + ], + "type": "text", + "content": "Video Scene Graph Generation (VSGG) is receiving growing attention as it benefits a wide range of downstream tasks (e.g., video caption [34, 91], video retrieval [31, 50], and visual question answering [49, 87]). To deliver a holistic understanding of the underlying spatial-temporal dynamics within scenes, this task aims to construct a sequence of directed graphs where nodes represent objects and edges describe inter-object relationships (a.k.a., predicate)." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 323, + 230, + 547, + 342 + ], + "blocks": [ + { + "bbox": [ + 323, + 230, + 547, + 342 + ], + "lines": [ + { + "bbox": [ + 323, + 230, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 323, + 230, + 547, + 342 + ], + "type": "image", + "image_path": "0a2bae8d608eb403a3157ebffe44468b891e594aba328f7232fbb53267d49602.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 323, + 335, + 547, + 451 + ], + "blocks": [ + { + "bbox": [ + 323, + 335, + 547, + 451 + ], + "lines": [ + { + "bbox": [ + 323, + 335, + 547, + 451 + ], + "spans": [ + { + "bbox": [ + 323, + 335, + 547, + 451 + ], + "type": "image", + "image_path": "5c83770ea906bd7cae56b2c8ae9b8936d33f4d2fac574ac4856e2334c04e3662.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 460, + 555, + 528 + ], + "lines": [ + { + "bbox": [ + 313, + 460, + 555, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 555, + 528 + ], + "type": "text", + "content": "Figure 1. (a) Existing VSGG solutions typically adopt an offline training pipeline, dividing the problem into various components: object detection, temporal association, and contextual aggregation. (b) DIFFVSGG introduces a new paradigm that performs spatial-temporal reasoning directly as each frame is processed sequentially, enabling progressive, online updates to the scene graph." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 545, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 715 + ], + "type": "text", + "content": "Top-leading VSGG approaches typically adopt an offline pipeline [30, 69, 94], where scene graphs are generated independently for each frame and then aggregated along the temporal dimension (i.e., Fig. 1(a)). Though demonstrating strong performance, they require full video sequences as inputs, which faces challenges in processing long videos containing hundreds of frames due to GPU memory constraints, and is unable to handle real-time video streams for applications like autonomous driving and augmented reality [100]. Moreover, the dealing of temporal cues focuses solely on the global aggregation of frame-level predictions via Transform blocks. This falls short in the reasoning over temporal space, which is essential for modeling the dynamic changes of interactions between subjects and objects, and" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 702, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 144, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29161" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 133 + ], + "type": "text", + "content": "potentially benefits predicate prediction. Though a surge of early work has sought to facilitate explicit reasoning over the temporal domain via messaging passing [90] or spatial-temporal graph [74], a large performance gap remains when compared to these offline temporal aggregation approaches." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 135, + 294, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 135, + 294, + 290 + ], + "spans": [ + { + "bbox": [ + 54, + 135, + 294, + 290 + ], + "type": "text", + "content": "To address these challenges, we propose DIFFVSGG, a high performance online approach for VSGG in leverage of Latent Diffusion Models (LDMs)[77, 81] (i.e., Fig.1(b)). In VSGG, the scene graph is dynamically evolved throughout the progression of video frames, with nodes and edges being continuously updated to precisely reflect the latest video content. Such an iterative update process shares a similar spirit of LDMs, which progressively remove noise to generate new samples from data distributions. Naturally, our motivation is to develop a VSGG model that aligns with the denoising principle of LDMs to iterative refine scene graphs along the temporal dimension, facilitating online temporal reasoning within this reverse diffusion process." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 293, + 295, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 293, + 295, + 651 + ], + "spans": [ + { + "bbox": [ + 56, + 293, + 295, + 651 + ], + "type": "text", + "content": "To achieve this, we tackle VSGG from a unified perspective, organizing the decoding of object classification, bounding box regression, and graph generation three tasks from a shared feature embedding, which serves as the input and output of the Denoising U-Net. Concretely, from the spatial perspective, given the object detection results from each frame, multiple object pairs can be constructed. Then, for each object pair, we integrate i) the visual feature of two objects, ii) the union feature between, and iii) the locations of two objects, into a unified embedding. This embedding serves as the input to the denoising U-Net, after steps of denoising, a clean embedding clearly describing the objects as well as their inter-object relationships can be delivered. From the temporal perspective, DIFFVSGG conducts frame-by-frame reasoning where the result for each subsequent frame is delivered by iteratively refining the predictions of previous frames via reverse diffusion. Specifically, object positions and contextual information from prior frames are leveraged as conditions to guide the denoising of the shared feature embeddings for current frames. This encourages continuous temporal reasoning as the video progresses, allowing DIFFVSGG to effectively capture long-term spatiotemporal dependencies and adapt to complex motion patterns in an online manner. To further unlock the potential of LDMs, we build a memory bank to store positions for each object. In this way, motion information including acceleration and deceleration of object can be explicitly calculated. These motion cues are integrated into conditional inputs for the reverse diffusion step, which can help infer relationships such as following or approaching between objects." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 653, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 294, + 713 + ], + "type": "text", + "content": "DIFFVSGG distinguishes itself in several aspects: First, it tackles VSGG in an online manner to continuously address an unlimited number of frames, while being friendly to devices with limited GPU memory. Second, the prediction of each video is implemented as a reverse diffusion pro" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 239 + ], + "type": "text", + "content": "cess, which elegantly encodes spatial and temporal reasoning into the Denoising step. Third, the temporal cues (i.e., historic predictions) are propagated into subsequent frames as conditions and participating in the prediction, while prior work simply aggregates predictions of all frames along the temporal dimension. Fourth, the learning of object classification, bounding box regression, and graph generation three tasks are jointly optimized with a shared feature embedding. Such a unified learning paradigm allows for the solving of VSGG from a global view, and avoids error made in one task propagating to subsequent tasks. Fifth, this unified decoding simplifies the VSGG pipeline and eliminates cumbersome handcrafted modules such as non-maximum suppression (NMS), and entity matching across frames." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 239, + 553, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 239, + 553, + 347 + ], + "spans": [ + { + "bbox": [ + 313, + 239, + 553, + 347 + ], + "type": "text", + "content": "To the best of our knowledge, DIFFVSGG is the first work that treats the VSGG task as an iterative denoising problem along the temporal dimension. Extensive experiments on Action Genome (AG) [40] demonstrate the superiority of our proposed method. Notably, DIFFVSGG achieves SOTA results across all three setups and surpasses the top-leading solutions (e.g., DSG-DETR [30]) by 3.3 in terms of R@10, highlighting the great potential of utilizing diffusion models for visual relation understanding in videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 358, + 400, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 358, + 400, + 371 + ], + "spans": [ + { + "bbox": [ + 314, + 358, + 400, + 371 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 378, + 553, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 553, + 498 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 553, + 498 + ], + "type": "text", + "content": "Scene Graph Generation (SGG). SGG involves detecting object instances and classifying their pairwise visual relations in an image, which is essential for comprehensive visual tasks [7, 8, 11, 53, 97, 98, 117, 118]. Recent SGG approaches seek to comprehend visual context by aggregating spatial context through various strategies, including explicit message passing [14, 20, 56, 57, 103, 112], graph structure modeling [83, 85, 99, 106, 110], external knowledge integration [3, 14, 33, 35, 109, 111], and transformer-based networks [12, 18, 23, 24, 43, 48, 55, 59, 64, 72, 79]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 498, + 553, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 553, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 553, + 677 + ], + "type": "text", + "content": "Extended from SGG, Video Scene Graph Generation (VSGG) aims to ground visual relationships jointly in spatial and temporal dimensions. Prior research primarily concentrates on addressing the long-tail distribution problem observed in prominent benchmarks [40]. Numerous unbiased approaches [16, 21, 46, 51, 54, 68, 86, 105] have been devised to handle infrequent predicate classes arising from this distribution. Furthermore, recent VSGG methods underscore the importance of spatial-temporal learning, and make use of the sequence-processing ability of Transformer [2, 70, 84] to capture temporal continuity. Nonetheless, these approaches often depend on complex post-processing that decouples spatial and temporal learning into two independent steps, and simply emphasizes on the consistent matching between frames." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "In contrast, DIFFVSGG handles both spatial and temporal reasoning from a unified perspective, where the reasoning on temporal dimension is naturally achieved via utiliz" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29162" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 95 + ], + "type": "text", + "content": "ing the spatial reasoning results of prior frames as the conditions to guide predictions for the current frames." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 98, + 296, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 98, + 296, + 361 + ], + "spans": [ + { + "bbox": [ + 56, + 98, + 296, + 361 + ], + "type": "text", + "content": "Diffusion Models Beyond Image Generation. Diffusion Models (DMs) have surpassed many other generative models in image generation [6, 22, 37, 38, 92, 104] by successively denoising images. Beyond image generation, DMs inherently perform implicit discriminative reasoning while generating data, which proves highly effective in visual tasks that require complex relationship modeling and spatiotemporal reasoning. Therefore, a surge of work has adapted generative diffusion models for tasks including image segmentation [1, 4, 5, 15, 32, 44, 93], object detection [13, 76, 102], object tracking [65, 66, 101], and monocular depth estimation [25, 67, 78, 116]. Recent research has also utilizes DMs for more complex tasks that require high-level visual understanding abilities such as visual-linguistic understanding [47], scene generation [39], and human-object interaction detection [41, 52]. The potential of DMs in processing graph data has also been explored, encompassing a range of advanced tasks. This includes early work employing score-based methods for generating permutation-invariant graphs [42, 71], as well as recent approaches focused on enhancing graph neural networks [114, 115] and advancing graph generation techniques [107]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 363, + 296, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 363, + 296, + 471 + ], + "spans": [ + { + "bbox": [ + 55, + 363, + 296, + 471 + ], + "type": "text", + "content": "In this work, we borrow the step-wise denoising ability of latent diffusion models to enable spatial reasoning within a single frame. This is achieved by iteratively refining the union embeddings of object pairs, which serve to inform the prediction for bounding boxes and predicate classes, etc. On the other hand, temporal reasoning across frames is facilitated via conditional prompting, i.e., using predictions of prior frames which contain rich location and inter-object relationship cues to guide the denoising of current frames." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 472, + 296, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 296, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 296, + 652 + ], + "type": "text", + "content": "Temporal Reasoning in Videos. Reasoning within the temporal dimension poses significant challenges for achieving high-level comprehension in video-related tasks [9, 10, 27-29, 61, 73, 108]. Recent advancements in video question answering seek to tackle temporal reasoning by employing attention mechanisms [26, 82] or incorporating external memory modules [45, 75] across video frames. In addition, to accurately capture the start, progression, and end of an action, action recognition approaches [89, 95] model complex motion patterns and dependencies in sequence. Video object detection (VOD) [19, 62] focuses on accurately capturing object trajectories, even in the presence of occlusions and abrupt movements. The top-leading VSGG solutions [30, 69, 94] instead aggregate predictions across frames to maintain the temporal consistency of objects." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 296, + 713 + ], + "type": "text", + "content": "In summary, although existing work facilitates temporal reasoning from different perspectives and demonstrates it effectiveness, the potential of diffusion models remains largely underexplored. In fact, the sequential denoising in time, where each step is informed by previous one, offers" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 120 + ], + "type": "text", + "content": "a suitable tool to reconstruct the states for current frames based on observations from past frames. This insight motivates the proposal of DIFFVSGG, which tackles the VSGG task via graph denoising over the temporal dimension." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 134, + 397, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 134, + 397, + 148 + ], + "spans": [ + { + "bbox": [ + 313, + 134, + 397, + 148 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 156, + 554, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 156, + 554, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 156, + 554, + 216 + ], + "type": "text", + "content": "In this section, we first give a brief introduction to the general background of latent Diffusion Models (§3.1), then elaborate on the overall design of our proposed DIFFVSGG (§3.2), and finally present the detailed information on the network architecture and training objectives (§3.3)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 227, + 516, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 227, + 516, + 239 + ], + "spans": [ + { + "bbox": [ + 313, + 227, + 516, + 239 + ], + "type": "text", + "content": "3.1. Preliminary: Latent Diffusion Models" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 245, + 554, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 245, + 554, + 293 + ], + "spans": [ + { + "bbox": [ + 313, + 245, + 554, + 293 + ], + "type": "text", + "content": "To begin, we give an illustration on how diffusion processes [81] are used to model data distributions and generate high-quality samples. Specifically, we consider a continuous-time Markov chain with " + }, + { + "bbox": [ + 313, + 245, + 554, + 293 + ], + "type": "inline_equation", + "content": "t \\in [0,T]" + }, + { + "bbox": [ + 313, + 245, + 554, + 293 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 350, + 302, + 555, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 302, + 555, + 317 + ], + "spans": [ + { + "bbox": [ + 350, + 302, + 555, + 317 + ], + "type": "interline_equation", + "content": "q (x _ {t} | x _ {t - 1}) = \\mathcal {N} (x _ {t}; \\sqrt {1 - \\beta_ {t}} x _ {t - 1}, \\beta_ {t} I), \\tag {1}", + "image_path": "1086e78af66c3b7115436798688a1357853008105c56e454cf73498e562186b7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "spans": [ + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "text", + "content": " is a small noise variance term at timestep " + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "text", + "content": " denotes a Gaussian distribution. The corrupted data at any intermediate time step " + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 326, + 554, + 361 + ], + "type": "text", + "content": " can be derived recursively as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 382, + 370, + 555, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 370, + 555, + 384 + ], + "spans": [ + { + "bbox": [ + 382, + 370, + 555, + 384 + ], + "type": "interline_equation", + "content": "x _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha}} \\epsilon , \\tag {2}", + "image_path": "4c0dbd62b14c372907309732278f432d5d88b8f222286731717ac44d07e0cbb4.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}_t = \\prod_{s = 1}^t\\alpha_s" + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "text", + "content": " is the cumulative product of " + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "text", + "content": " over the timesteps, " + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "text", + "content": " represents the sampled noise. The reverse process essentially involves learning to reverse the noise addition at each step. The cleaned data at time step " + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 395, + 554, + 456 + ], + "type": "text", + "content": " can be written recursively as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 464, + 554, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 464, + 554, + 491 + ], + "spans": [ + { + "bbox": [ + 359, + 464, + 554, + 491 + ], + "type": "interline_equation", + "content": "x _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} \\left(x _ {t}, t\\right), \\right. \\tag {3}", + "image_path": "15f02a4a41b873ab91dce96c4db1c780f3fa8702a2d1dc3fe70c3ca6fcd7e8ed.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 496, + 554, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 554, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 554, + 533 + ], + "type": "text", + "content": "where a time-conditioned denoising neural network " + }, + { + "bbox": [ + 313, + 496, + 554, + 533 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x,t)" + }, + { + "bbox": [ + 313, + 496, + 554, + 533 + ], + "type": "text", + "content": " is trained to minimize the mean squared error between the true and predicted noise at each timestep:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 364, + 540, + 554, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 540, + 554, + 562 + ], + "spans": [ + { + "bbox": [ + 364, + 540, + 554, + 562 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {D M}} := \\mathbb {E} _ {x _ {0}, \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| _ {2} ^ {2} \\right]. \\tag {4}", + "image_path": "fe34a1835c5c7ae7f1b05e969bdfce72caff33ec429668b58642d27d98034255.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": "Building on the diffusion process described above, latent diffusion models (LDMs) [77] first encode samples into a low-dimensional latent space " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "z = \\mathcal{E}(x)" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": " using an encoder " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": ", and then apply the diffusion process within this compressed space. Moreover, LDMs introduce the conditioning mechanisms which allow for control over the generated output based on additional input " + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 569, + 554, + 665 + ], + "type": "text", + "content": " such as text, labels, or images. Consequently, the training objective for LDMs is given as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 339, + 673, + 553, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 673, + 553, + 693 + ], + "spans": [ + { + "bbox": [ + 339, + 673, + 553, + 693 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {L D M}} := \\mathbb {E} _ {\\mathcal {E} (x _ {0}), y, \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\boldsymbol {z} _ {t}, t, c _ {\\theta} (y)\\right) \\| _ {2} ^ {2} \\right], \\tag {5}", + "image_path": "013e4504eefcbbaaed0f2572e018c944c8f9fc8860cc89b5cdbc67a75b28027f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 701, + 501, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 501, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 501, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 701, + 501, + 713 + ], + "type": "inline_equation", + "content": "c_{\\theta}" + }, + { + "bbox": [ + 313, + 701, + 501, + 713 + ], + "type": "text", + "content": " is a conditioning model to encode " + }, + { + "bbox": [ + 313, + 701, + 501, + 713 + ], + "type": "inline_equation", + "content": "y" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "29163" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 79, + 544, + 186 + ], + "blocks": [ + { + "bbox": [ + 61, + 79, + 544, + 186 + ], + "lines": [ + { + "bbox": [ + 61, + 79, + 544, + 186 + ], + "spans": [ + { + "bbox": [ + 61, + 79, + 544, + 186 + ], + "type": "image", + "image_path": "ba5ec8b663d8693eec909998f5d99a3dbb7d655bb55e5b3e6f369d1753caf50c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 108, + 193, + 500, + 205 + ], + "lines": [ + { + "bbox": [ + 108, + 193, + 500, + 205 + ], + "spans": [ + { + "bbox": [ + 108, + 193, + 500, + 205 + ], + "type": "text", + "content": "Figure 2. Overview of our proposed inter-object relationship learning strategy using latent diffusion models." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 213, + 263, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 213, + 263, + 224 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 263, + 224 + ], + "type": "text", + "content": "3.2. DIFFVSGG: Diffusion Models for VSGG" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "spans": [ + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": "Problem Definition. Considering a video sequence represented as " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\{I^1,\\dots ,I^T\\}" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " containing " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " frames, the objective of VSGG is to generate a sequence of scene graph " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = \\{G^{1},\\dots ,G^{T}\\}" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " over time, where each element " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^t" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " represents the corresponding scene graph for frame " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "I^t" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": ". Each graph " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "G^{t}" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " is defined as " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "G^{t} = (\\mathcal{V}^{t},\\mathcal{E}^{t})" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^t" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{E}^t" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " denoting the sets of graph nodes and edges, respectively. Each node " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "v_{i}^{t}\\in \\mathcal{V}^{t}" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " includes attributes such as category and location for object " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": ", while each edge " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "e_{i,j}^{t}\\in \\mathcal{E}^{t}" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " describes the inter-object relationship (a.k.a.predicate) between subject " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " and object " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": ". In this manner, " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " captures all objects (i.e., " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": "), their interactions (i.e., " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": "), and the dynamics as they evolve over time (i.e., from " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "inline_equation", + "content": "t = T" + }, + { + "bbox": [ + 55, + 230, + 296, + 386 + ], + "type": "text", + "content": ") within the scene." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 385, + 296, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 385, + 296, + 419 + ], + "spans": [ + { + "bbox": [ + 55, + 385, + 296, + 419 + ], + "type": "text", + "content": "Graph Construction. Given a video " + }, + { + "bbox": [ + 55, + 385, + 296, + 419 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\{I^1,\\dots ,I^T\\}" + }, + { + "bbox": [ + 55, + 385, + 296, + 419 + ], + "type": "text", + "content": ", we first employ an on-the-shelf object detector " + }, + { + "bbox": [ + 55, + 385, + 296, + 419 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{det}}" + }, + { + "bbox": [ + 55, + 385, + 296, + 419 + ], + "type": "text", + "content": " for each frame:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 418, + 294, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 418, + 294, + 430 + ], + "spans": [ + { + "bbox": [ + 123, + 418, + 294, + 430 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {F} ^ {t}, \\mathcal {B} ^ {t}, \\mathcal {O} ^ {t} \\right\\} = \\mathcal {F} _ {\\det } \\left(I ^ {t}\\right), \\tag {6}", + "image_path": "d90a0fd7b797f435fa1c6be1f87bfe847f2406ea3798bd0faed46c8a59756091.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\pmb{F}^{t}" + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": " is the feature extracted by backbone, " + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^t = \\{b_1^t,\\dots ,b_{N_t}^t\\}" + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{O}^t = \\{o_1^t,\\dots ,o_{N_t}^t\\}" + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": " are bounding box and class predictions for " + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "inline_equation", + "content": "N_{t}" + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": " objects detected from frame " + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "inline_equation", + "content": "I^t" + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": " respectively. This serves to initialize an adjacency matrix " + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "inline_equation", + "content": "\\pmb{A}^{t}\\in \\mathbb{R}^{N_{t}\\times N_{t}\\times D_{e}}" + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": " , of which each element aims to represent the inter-object relationships between object " + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 433, + 296, + 506 + ], + "type": "text", + "content": " .." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 108, + 510, + 294, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 510, + 294, + 531 + ], + "spans": [ + { + "bbox": [ + 108, + 510, + 294, + 531 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} _ {i, j} ^ {t} = \\left[ \\boldsymbol {F} _ {o _ {i}} ^ {t}; \\boldsymbol {F} _ {o _ {i}, o _ {j}} ^ {t}; \\boldsymbol {F} _ {b _ {i}} ^ {t} \\right] \\in \\mathbb {R} ^ {D _ {e}}, \\tag {7}", + "image_path": "05956f2a0a1293afad1a31a64bbde1c86d9d34429d5302d1914fcc40f1446252.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 108, + 528, + 242, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 528, + 242, + 544 + ], + "spans": [ + { + "bbox": [ + 108, + 528, + 242, + 544 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} _ {j, i} ^ {t} = \\left[ \\boldsymbol {F} _ {o _ {j}} ^ {t}; \\boldsymbol {F} _ {o _ {j}, o _ {i}} ^ {t}; \\boldsymbol {F} _ {b _ {j}} ^ {t} \\right] \\in \\mathbb {R} ^ {D _ {e}}.", + "image_path": "4873640a359dd7401acc231a40a21808824acc63303319d2ec160e791fff3476.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "[]" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " refers to the concatenation of features, implemented as torch.cat(). " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "F_{o_i}^t = \\mathcal{F}_{\\mathrm{ROI}}(F^t,b_i^t)" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " is the instance-level feature for object " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " extracted via ROAlign [36] (i.e., " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{ROI}}), F_{o_i,o_j}^t = \\mathcal{F}_{\\mathrm{ROI}}(F^t,b_i^t\\cup b_j^t)" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " is the feature mapped from the union box of object " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "b_{i}^{t}\\cup b_{j}^{t})" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " ,and " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "F_{b_i}^t" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " describes bounding box " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "b_{i}^{t}" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " using a box-to-feature mapping function identical to that in [112]. " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "A_{i,j}^{t}" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " represents the relationship predicted from subject " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " , which differs from " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "A_{j,i}^{t}" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " is considered the subject. In this way, the matrix " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "A^t" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " encodes both node features of each object and the edge features between any pair of them. Note that such subject-based encoding does not incorporate " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "Fo_{j}" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "Fb_{j}" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "A_{i,j}" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "[F_{o_i};F_{b_i};F_{o_i,o_j};F_{o_j};F_{b_j}])" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " , which hinders the neural network to distinguish between the subject " + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "inline_equation", + "content": "(i)" + }, + { + "bbox": [ + 55, + 544, + 296, + 713 + ], + "type": "text", + "content": " and object" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "inline_equation", + "content": "(j)" + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "text", + "content": ". Additionally, as the number of instances " + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "inline_equation", + "content": "(i.e., N_{t})" + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "text", + "content": " typically varies across frames due to the emergence or disappearance of some instances, we pad " + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{t}" + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "text", + "content": " to a fixed size of " + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "inline_equation", + "content": "N > \\max(N_{1}, \\dots, N_{T})" + }, + { + "bbox": [ + 313, + 213, + 555, + 274 + ], + "type": "text", + "content": ", using randomly generated feature embedding from Gaussian distributions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "text", + "content": "Inter-object Relationship Learning via LDMs. Next we aim to facilitate the learning of inter-object relationships within LDMs using ground truth scene graph (i.e., Fig. 2). Since we use an off-the-self object detector, the extracted feature " + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "inline_equation", + "content": "F^t" + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "text", + "content": " remains static for each frame. Therefore, with access to the ground truth bounding box annotations, we can compute precise edge features via Eq.7 from " + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "inline_equation", + "content": "F^t" + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "text", + "content": ". The adjacency matrix " + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "inline_equation", + "content": "\\hat{A}^t" + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "text", + "content": " which exactly encodes the inter-object features can also be obtained. Here " + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "inline_equation", + "content": "\\hat{A}^t" + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "text", + "content": " is the ground truth of inter-object relationships, initialized using features derived from ground-truth bounding boxes, where object pairs with no relations are represented as empty entries. " + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "inline_equation", + "content": "\\hat{A}^t" + }, + { + "bbox": [ + 313, + 274, + 555, + 441 + ], + "type": "text", + "content": " instructs the learning of a LDM which is responsible for recovering object features and their relationships from random noise." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 441, + 554, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 441, + 554, + 477 + ], + "spans": [ + { + "bbox": [ + 313, + 441, + 554, + 477 + ], + "type": "text", + "content": "- Forward Process. Let " + }, + { + "bbox": [ + 313, + 441, + 554, + 477 + ], + "type": "inline_equation", + "content": "\\hat{A}^{t,0}" + }, + { + "bbox": [ + 313, + 441, + 554, + 477 + ], + "type": "text", + "content": " represent the clean adjacency matrix. The noise injection process to progressively perturb this matrix is defined following Eq.2, and expressed as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 370, + 479, + 553, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 479, + 553, + 495 + ], + "spans": [ + { + "bbox": [ + 370, + 479, + 553, + 495 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {A}} ^ {t, k} = \\sqrt {\\bar {\\alpha} _ {t}} x \\hat {\\boldsymbol {A}} ^ {t, 0} + \\sqrt {1 - \\bar {\\alpha}} \\epsilon , \\tag {8}", + "image_path": "d7b173532b351f2dc7ca0947f0c592e9c53f78f50deeba441d5d9e23ccccbdf7.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "type": "inline_equation", + "content": "\\hat{A}^{t,k}" + }, + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "type": "text", + "content": " denotes the noisy adjacency matrix at step " + }, + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "type": "text", + "content": ". This enables the model to learn robust feature representations, through the exposure to degraded versions of " + }, + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "type": "inline_equation", + "content": "\\hat{A}^{t,0}" + }, + { + "bbox": [ + 313, + 498, + 554, + 534 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "type": "text", + "content": "- **Reverse Process.** To recover the original adjacency matrix " + }, + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\hat{A}^{t,0}" + }, + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "type": "text", + "content": ", we employ a denoising U-Net " + }, + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "type": "text", + "content": " which is trained to iteratively remove noise starting from the initial noisy matrix " + }, + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "type": "inline_equation", + "content": "\\hat{A}^{t,K}" + }, + { + "bbox": [ + 313, + 535, + 555, + 594 + ], + "type": "text", + "content": ". This process follows the denoising step defined in Eq.3 and proceeds as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 343, + 597, + 555, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 597, + 555, + 624 + ], + "spans": [ + { + "bbox": [ + 343, + 597, + 555, + 624 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {A}} ^ {t, k - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} (\\hat {\\boldsymbol {A}} ^ {t, k} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} (\\hat {\\boldsymbol {A}} ^ {t, k}, k), \\tag {9}", + "image_path": "3adc213d1b2a042d0bc96780fb5a111dab91f12ad5012c1debb4f4522f871962.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 627, + 554, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 627, + 554, + 663 + ], + "spans": [ + { + "bbox": [ + 313, + 627, + 554, + 663 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 627, + 554, + 663 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 627, + 554, + 663 + ], + "type": "text", + "content": " is optimized to recover meaningful inter-object relationships. Following Eq. 5, we define the training objective " + }, + { + "bbox": [ + 313, + 627, + 554, + 663 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{VSGG}}" + }, + { + "bbox": [ + 313, + 627, + 554, + 663 + ], + "type": "text", + "content": " by minimizing the spatial structure loss:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 349, + 666, + 553, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 666, + 553, + 687 + ], + "spans": [ + { + "bbox": [ + 349, + 666, + 553, + 687 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {V S G G}} := \\mathbb {E} _ {\\hat {\\boldsymbol {A}} ^ {t, k}, \\epsilon , k} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\hat {\\boldsymbol {A}} ^ {t, k}, k) \\| _ {2} ^ {2} \\right]. \\tag {10}", + "image_path": "3b4f20597efe4a56a6e84b533f32726feaf7619de0b3b50fbebc602d178eb2b2.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 689, + 555, + 713 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Overview of our proposed temporal prompting strategy." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "text", + "content": "way that preserves spatial and relational coherence. During inference, given the adjacency matrix " + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^t" + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "text", + "content": " from an arbitrary frame " + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "text", + "content": ", we consider it noisy and utilize the well-trained denoising U-Net above to refine it, so as to deliver an updated version that indicates the interaction between objects, as well as the location and category of objects: " + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{t,k - 1} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{A}^{t,k} - \\frac{\\beta_t}{\\sqrt{1 - \\overline{\\alpha}}}\\epsilon_\\theta (\\mathbf{A}^{t,k},k)" + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "text", + "content": ". Unlike the training process which utilizes " + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "text", + "content": " derived from ground truth bounding boxes, " + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 55, + 213, + 296, + 396 + ], + "type": "text", + "content": " here is obtained from the predicated ones. Note that the main challenge of VSGG lies in modeling of the dynamic changes of relation between object and subject, and the diffusion models primarily focus on recovering object features and their relationships. Thus, the slight bias in predicated bounding boxes, especially after ROIAAlign, causes negligible impacts to relation predictions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 396, + 296, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 468 + ], + "type": "text", + "content": "Condition Based Temporal Reasoning. For a given video stream, we can infer future frames based on the content of preceding frames. This observation serves as the motivation for our temporal prompting strategy (i.e., Fig.3), where we condition the denoising process of " + }, + { + "bbox": [ + 55, + 396, + 296, + 468 + ], + "type": "inline_equation", + "content": "A^t" + }, + { + "bbox": [ + 55, + 396, + 296, + 468 + ], + "type": "text", + "content": " on the denoised adjacency matrix of prior frames (i.e., " + }, + { + "bbox": [ + 55, + 396, + 296, + 468 + ], + "type": "inline_equation", + "content": "A^{t - 1,0}" + }, + { + "bbox": [ + 55, + 396, + 296, + 468 + ], + "type": "text", + "content": "), as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 64, + 473, + 294, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 473, + 294, + 499 + ], + "spans": [ + { + "bbox": [ + 64, + 473, + 294, + 499 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} ^ {t, k - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {A} ^ {t, k} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha}}} \\epsilon_ {\\theta} \\left(\\boldsymbol {A} ^ {t, k}, k, \\boldsymbol {A} ^ {t - 1, 0}\\right), \\right. \\tag {11}", + "image_path": "de2e12fa40798d09b200c3fd90009d714495c99593a0f9d68c1bc261cbdd015c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "text", + "content": "where the condition decoder " + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "inline_equation", + "content": "c_{\\theta}" + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "text", + "content": " in Eq. 5 is discarded, as " + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "inline_equation", + "content": "\\pmb{A}^{t - 1,0}" + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "text", + "content": " has already shared the same dimension as " + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "inline_equation", + "content": "\\pmb{A}^{t,k}" + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "text", + "content": ". With this condition-based temporal association for denoising, the training objective for " + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 505, + 296, + 554 + ], + "type": "text", + "content": " is updated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 58, + 561, + 294, + 591 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 561, + 294, + 591 + ], + "spans": [ + { + "bbox": [ + 58, + 561, + 294, + 591 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {T . V S G G}} := \\mathbb {E} _ {\\boldsymbol {A} ^ {t, k}, \\boldsymbol {A} ^ {t - 1, 0}, \\epsilon , k} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\boldsymbol {A} ^ {t, k}, \\boldsymbol {A} ^ {t - 1, 0}, k) \\| _ {2} ^ {2} \\right]. \\tag {12}", + "image_path": "317f03de627e33f3f4b279622035a1eb25011904d4a9903390f2d0f32e7a5084.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{T.VSGG}}" + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "text", + "content": " encourages " + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "text", + "content": " to generate temporally consistent outputs, enabling a smooth and coherent denoising of adjacency matrix across frames. Moreover, since new instances keep emerging as the video progresses, we calculate similarities between ROIAngled features of the potential new object (i.e., " + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "inline_equation", + "content": "F_{o_p}^t" + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "text", + "content": ") and all other objects in the past frame (i.e., " + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "inline_equation", + "content": "F_{o_i}^{t - 1}" + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "text", + "content": "), and consider " + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "inline_equation", + "content": "o_p" + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "text", + "content": " as new object if the similarities is smaller than 0.2 for all other objects. Then, the random padded features in " + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 592, + 296, + 713 + ], + "type": "text", + "content": " during graph construction are replaced with union and instance features of these new instances." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "text", + "content": "Motion Enhanced Denoising for VSGG. Motion cues serve as indicators to describe object movements in a given scene. They provide essential context for understanding the position and duration of events. Moreover, the speed and direction of object movements can reveal intentions for interactions (e.g., approaching), which aids in temporal reasoning by inferring whether they might complete an action or reach a goal. Therefore, given a box prediction " + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "inline_equation", + "content": "b_{i}^{t} = \\{x_{i}^{t}, y_{i}^{t}, w_{i}^{t}, h_{i}^{t}\\}" + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "text", + "content": " for object " + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "text", + "content": ", we explicitly calculate the approaching speed between object " + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 313, + 72, + 555, + 193 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 364, + 197, + 553, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 197, + 553, + 220 + ], + "spans": [ + { + "bbox": [ + 364, + 197, + 553, + 220 + ], + "type": "interline_equation", + "content": "d _ {i, j} ^ {t} = \\sqrt {\\left(x _ {i} ^ {t} - x _ {j} ^ {t}\\right) ^ {2} + \\left(y _ {i} ^ {t} - y _ {j} ^ {t}\\right) ^ {2}}, \\tag {13}", + "image_path": "4c296bedecdf1f75c7f721e74b59cc22dab37e161cb53067905a2e85843812c1.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 366, + 220, + 474, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 220, + 474, + 235 + ], + "spans": [ + { + "bbox": [ + 366, + 220, + 474, + 235 + ], + "type": "interline_equation", + "content": "v _ {i, j} ^ {t} = (d _ {i, j} ^ {t} - d _ {i, j} ^ {t - \\Delta t}) / \\Delta t,", + "image_path": "0514bbbc5fc60f9e1d01dabccee9dcff7cf8273079bc9af77e15f696161da6d9.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "spans": [ + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "text", + "content": " is the interval of frame. Given " + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "inline_equation", + "content": "v^t\\in \\mathbb{R}^{N^t\\times N^t}" + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "text", + "content": " we pad it into the same size with " + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "inline_equation", + "content": "\\pmb{A}^{t}" + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "inline_equation", + "content": "v^{t}\\in \\mathbb{R}^{N\\times N})" + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "text", + "content": " and inject it into " + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "inline_equation", + "content": "\\pmb{A}^{t,k}" + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "text", + "content": " at each denoising step " + }, + { + "bbox": [ + 313, + 239, + 555, + 289 + ], + "type": "inline_equation", + "content": "k\\colon \\pmb{A}^{t,k} = \\pmb{A}^{t,k} + v^t" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 289, + 554, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 289, + 554, + 337 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 554, + 337 + ], + "type": "text", + "content": "Graph Readout. Next we investigate how to deliver SGG predictions for each frame based on the denoised adjacency matrix " + }, + { + "bbox": [ + 313, + 289, + 554, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{t,0}" + }, + { + "bbox": [ + 313, + 289, + 554, + 337 + ], + "type": "text", + "content": ". Specifically, the prediction for predicate of each subject-object pair is obtained as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 353, + 343, + 553, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 343, + 553, + 360 + ], + "spans": [ + { + "bbox": [ + 353, + 343, + 553, + 360 + ], + "type": "interline_equation", + "content": "r _ {i, j} ^ {t} = \\operatorname {s o f t m a x} \\left(\\mathcal {F} _ {\\text {p r e d}} \\left(\\boldsymbol {A} _ {i, j} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {N _ {\\text {p r e d , c l s}}} \\tag {14}", + "image_path": "183ec88c12cbabbd0ae0338b5d9d437c6e47d00c2f377fb73abcd96833e57d3d.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{pred}}" + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "text", + "content": " is an MLP-based classifier and " + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{pred\\_cls}}" + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "text", + "content": " represents the number of predicate classes. For object classification and bounding box regression, to render a global view, we utilize the entire row " + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{t,0}" + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_i^{t,0}" + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "text", + "content": ") where all elements consider " + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 365, + 554, + 426 + ], + "type": "text", + "content": " as the subject, to deliver the prediction:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 358, + 432, + 553, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 432, + 553, + 447 + ], + "spans": [ + { + "bbox": [ + 358, + 432, + 553, + 447 + ], + "type": "interline_equation", + "content": "o _ {i} ^ {t} = \\operatorname {s o f t m a x} \\left(\\mathcal {F} _ {\\mathrm {o b j}} \\left(\\boldsymbol {A} _ {i} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {N _ {\\mathrm {o b j , c l s}}}, \\tag {15}", + "image_path": "aa37932478589ea36f65c8284ac6d0a626dc6de554e717ad3b4393088d7540a1.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 359, + 449, + 553, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 449, + 553, + 464 + ], + "spans": [ + { + "bbox": [ + 359, + 449, + 553, + 464 + ], + "type": "interline_equation", + "content": "b _ {i} ^ {t} = \\operatorname {s i g m o i d} \\left(\\mathcal {F} _ {\\text {b o x}} \\left(A _ {i} ^ {t, 0}\\right)\\right) \\in \\mathbb {R} ^ {4}, \\tag {16}", + "image_path": "669361526d2607b5ea1e0dc01239341fd057aa8a98737a1d12e7502b54593307.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{obj\\_cls}}" + }, + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "type": "text", + "content": " is the number of object classes, " + }, + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{obj}}" + }, + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{box}}" + }, + { + "bbox": [ + 313, + 471, + 553, + 495 + ], + "type": "text", + "content": " are the MLP-based classifier and projector, respectively." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 502, + 447, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 447, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 447, + 514 + ], + "type": "text", + "content": "3.3. Implementation Details" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 519, + 555, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 519, + 555, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 519, + 555, + 662 + ], + "type": "text", + "content": "Network Configuration. DIFFVSGG is an online VSGG framework built upon the iterative diffusion diagram. It comprises three components: one off-the-shelf detector to deliver object detection results, the LDMs for inter-object relationship denosing, and projector heads for object classification, predicate prediction, and bounding box regression. Training Objective. The training process of DIFFVSGG consists of two stages. In the first stage, we pre-train the denoising U-Net " + }, + { + "bbox": [ + 313, + 519, + 555, + 662 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 519, + 555, + 662 + ], + "type": "text", + "content": " in Eq. 9, using " + }, + { + "bbox": [ + 313, + 519, + 555, + 662 + ], + "type": "inline_equation", + "content": "\\hat{A}^t" + }, + { + "bbox": [ + 313, + 519, + 555, + 662 + ], + "type": "text", + "content": " constructed from ground truth bounding box annotations for objects. In the second stage, we optimize the MLP classifier and projector in Eq. 14-15, which generate the final VSGG predictions." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 663, + 554, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 663, + 554, + 687 + ], + "spans": [ + { + "bbox": [ + 313, + 663, + 554, + 687 + ], + "type": "text", + "content": "Specifically, given relation prediction " + }, + { + "bbox": [ + 313, + 663, + 554, + 687 + ], + "type": "inline_equation", + "content": "p_r" + }, + { + "bbox": [ + 313, + 663, + 554, + 687 + ], + "type": "text", + "content": " and ground truth " + }, + { + "bbox": [ + 313, + 663, + 554, + 687 + ], + "type": "inline_equation", + "content": "y_r" + }, + { + "bbox": [ + 313, + 663, + 554, + 687 + ], + "type": "text", + "content": ", the relation classification loss is computed as:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 364, + 695, + 553, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 695, + 553, + 717 + ], + "spans": [ + { + "bbox": [ + 364, + 695, + 553, + 717 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p r e d . c l s}} = - \\sum_ {i = 1} ^ {C _ {r}} y _ {r, i} \\log \\left(p _ {r, i}\\right). \\tag {17}", + "image_path": "9154fb92f14039f983014ad7344790258dddbdbaed59d37547cfc11e635a71c6.jpg" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29165" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 70, + 553, + 247 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 553, + 247 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 553, + 247 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 553, + 247 + ], + "type": "table", + "html": "
    MethodPredCLSSGCLSSGDET
    R@10 R@20 R@50 mR@10 mR@20 mR@50R@10 R@20 R@50 mR@10 mR@20 mR@50R@10 R@20 R@50 mR@10 mR@20 mR@50
    RelDN [113]20.320.320.36.26.26.211.011.011.03.43.43.49.19.19.13.33.33.3
    TRACE [88]27.527.527.515.215.215.214.814.814.88.98.98.913.914.514.58.28.28.2
    VRD [63]51.754.754.7---32.433.333.3---19.224.526.0---
    Motif Freq [112]62.465.165.1---40.841.941.9---23.731.433.3---
    MSDN [57]65.568.568.5---43.945.145.1---24.132.434.5---
    VCTREE [85]66.069.369.3---44.145.345.3---24.432.634.7---
    GPS-Net [60]66.869.969.9---45.346.546.5---24.733.135.1---
    STTran [17]68.671.871.837.840.140.246.447.547.527.228.028.025.234.137.016.620.822.2
    APT [58]69.473.873.8---47.248.948.9---26.336.138.3---
    STTran-TPI [96]69.772.672.637.340.640.647.248.348.328.329.329.326.234.637.415.620.221.8
    TR2 [94]70.973.873.8---47.748.748.7---26.835.538.3---
    TEMPURA [69]68.871.571.542.946.346.347.248.348.334.035.235.228.133.434.918.522.623.7
    DSG-DETR [30]------50.852.052.0---30.334.836.1---
    DIFFVSGG71.974.574.548.150.250.252.553.753.737.338.438.432.839.945.520.923.626.2
    ", + "image_path": "f874e656f33871f46773b48d10a9427dd0fc4120af0c643ccfb118d7ac2a39f0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 90, + 247, + 518, + 258 + ], + "lines": [ + { + "bbox": [ + 90, + 247, + 518, + 258 + ], + "spans": [ + { + "bbox": [ + 90, + 247, + 518, + 258 + ], + "type": "text", + "content": "Table 1. Comparison of state-of-the-art VSGG methods on Action Genome test [40] under the " + }, + { + "bbox": [ + 90, + 247, + 518, + 258 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 90, + 247, + 518, + 258 + ], + "type": "text", + "content": " constraint setting." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 274, + 295, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 274, + 295, + 298 + ], + "spans": [ + { + "bbox": [ + 55, + 274, + 295, + 298 + ], + "type": "text", + "content": "Similarly, given object class prediction " + }, + { + "bbox": [ + 55, + 274, + 295, + 298 + ], + "type": "inline_equation", + "content": "p_{o}" + }, + { + "bbox": [ + 55, + 274, + 295, + 298 + ], + "type": "text", + "content": " and ground truth " + }, + { + "bbox": [ + 55, + 274, + 295, + 298 + ], + "type": "inline_equation", + "content": "y_{o}" + }, + { + "bbox": [ + 55, + 274, + 295, + 298 + ], + "type": "text", + "content": ", the object classification loss is defined as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 300, + 295, + 324 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 300, + 295, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 295, + 324 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {o b j} \\cdot \\mathrm {c l s}} = - \\sum_ {j = 1} ^ {C _ {o}} y _ {o, j} \\log \\left(p _ {o, j}\\right). \\tag {18}", + "image_path": "cc72ba718ee50252f308c6e5a5ba2c965d36692156da0a1b68fcf00be59b735f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "spans": [ + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "type": "text", + "content": "For bounding box regression, given the ground truth bounding box " + }, + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "type": "text", + "content": " (e.g., " + }, + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "type": "inline_equation", + "content": "(x, y, w, h)" + }, + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "type": "text", + "content": ") and the predicted bounding box " + }, + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "type": "inline_equation", + "content": "\\hat{t}_k" + }, + { + "bbox": [ + 55, + 331, + 296, + 367 + ], + "type": "text", + "content": ", the regression loss is formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 110, + 378, + 295, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 378, + 295, + 392 + ], + "spans": [ + { + "bbox": [ + 110, + 378, + 295, + 392 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {b o x - r e g}} = \\operatorname {S m o o t h} \\mathrm {L} 1 \\left(t _ {k} - \\hat {t} _ {k}\\right). \\tag {19}", + "image_path": "8cc0affd33df31350960d4c3f7af52a1b80683e9da66d12c7efecff2207cc06e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 397, + 282, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 397, + 282, + 410 + ], + "spans": [ + { + "bbox": [ + 55, + 397, + 282, + 410 + ], + "type": "text", + "content": "The training objectives for each stage are formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 423, + 295, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 423, + 295, + 441 + ], + "spans": [ + { + "bbox": [ + 69, + 423, + 295, + 441 + ], + "type": "text", + "content": "Stage 1: " + }, + { + "bbox": [ + 69, + 423, + 295, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_{\\mathrm{T\\_VSGG}}" + }, + { + "bbox": [ + 69, + 423, + 295, + 441 + ], + "type": "text", + "content": " (20)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 438, + 264, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 438, + 264, + 452 + ], + "spans": [ + { + "bbox": [ + 69, + 438, + 264, + 452 + ], + "type": "text", + "content": "Stage 2: " + }, + { + "bbox": [ + 69, + 438, + 264, + 452 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_{\\mathrm{pred\\_cls}} + \\mathcal{L}_{\\mathrm{obj\\_cls}} + 0.5\\mathcal{L}_{\\mathrm{box\\_reg}}" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 460, + 132, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 460, + 132, + 474 + ], + "spans": [ + { + "bbox": [ + 55, + 460, + 132, + 474 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 480, + 176, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 480, + 176, + 493 + ], + "spans": [ + { + "bbox": [ + 55, + 480, + 176, + 493 + ], + "type": "text", + "content": "4.1. Experimental setting" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 498, + 295, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 295, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 295, + 617 + ], + "type": "text", + "content": "Dataset. We evaluate DIFFVSGG on Action Genome (AG) [40], the largest video scene graph generation dataset comprising over 10K videos extended from the Charades dataset [80]. This dataset includes 1,715,568 predicate instances across 25 predicate classes, spanning 234,253 video frames, and features 476,229 bounding boxes across 35 object categories. The 1,715,568 instances for 25 predicate classes are divided into attention, spatial and contacting, three different types. Following prior work [17, 58], we use the same training/testing split." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "content": "Training. In the first training stage which optimizes the LDMs with ground-truth bounding box annotations, we set the learning rate to " + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "content": " and use the Adam optimizer. The batch size is set to 2048, and the model is trained for 100 epochs. Each input clip consists of five frames sampled at random time intervals, enabling conditional temporal reasoning. The denoising U-Net " + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "content": " remains frozen once after pre-training. In the second training stage, the classifiers and" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 268, + 553, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 268, + 553, + 327 + ], + "spans": [ + { + "bbox": [ + 313, + 268, + 553, + 327 + ], + "type": "text", + "content": "projectors are trained for 10 epochs with a batch size of 8. We use the AdamW optimizer with a learning rate of " + }, + { + "bbox": [ + 313, + 268, + 553, + 327 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 313, + 268, + 553, + 327 + ], + "type": "text", + "content": ", which decays by a factor of 5 halfway through the training. Evaluation Setup. In line with previous studies[30, 40, 58, 63], three standard evaluation protocols are adopted:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 328, + 554, + 592 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 314, + 328, + 553, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 328, + 553, + 376 + ], + "spans": [ + { + "bbox": [ + 314, + 328, + 553, + 376 + ], + "type": "text", + "content": "- PredCLS: With oracle-provided object labels and bounding boxes as well as grounding-truth subject-object pairs, PredCLS assesses the model capability to predict predicate labels for each subject-object pair." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 376, + 553, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 376, + 553, + 411 + ], + "spans": [ + { + "bbox": [ + 314, + 376, + 553, + 411 + ], + "type": "text", + "content": "- SGCLS: Building on PredCLS, SGCLS requires the simultaneous prediction of both predicate labels and the associated subject-object pairs for each predicate." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 411, + 554, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 554, + 543 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 554, + 543 + ], + "type": "text", + "content": "- SGDET: As the most challenging task, SGDET requires generating complete scene graphs from scratch, including object detection, subject-object pair selection, and predicate classification. Detection is considered accurate if the overlap between prediction and ground truth exceeds 0.5. Evaluation Metric. We employ the Recall@k where " + }, + { + "bbox": [ + 313, + 411, + 554, + 543 + ], + "type": "inline_equation", + "content": "k \\in 10,20,50" + }, + { + "bbox": [ + 313, + 411, + 554, + 543 + ], + "type": "text", + "content": " as the evaluation metric, to measure the proportion of ground truth elements within the top-k predictions. Additionally, Mean-Recall@k is also adopted to ensure the evaluation is not biased toward high-frequency classes. The evaluation is performed under two different scenarios:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 544, + 553, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 544, + 553, + 567 + ], + "spans": [ + { + "bbox": [ + 314, + 544, + 553, + 567 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 314, + 544, + 553, + 567 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 314, + 544, + 553, + 567 + ], + "type": "text", + "content": " constraint: Each subject-object pair is restricted to a maximum of one predicate." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 568, + 553, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 553, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 553, + 592 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 313, + 568, + 553, + 592 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 313, + 568, + 553, + 592 + ], + "type": "text", + "content": " constraints: Each subject-object pair is allowed to have multiple predicates simultaneously." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 600, + 498, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 600, + 498, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 600, + 498, + 613 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-arts" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 617, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 554, + 714 + ], + "type": "text", + "content": "Tables 1-2 present the main experimental results of DIF-FVSGG against several top-leading approaches on Action Genome test [40]. Following existing VSGG works [17, 58], we firstly select a few representative image-level SGG methods such as RelDN [113] and GPS-Net [60]. Then, we compare DIFFVSGG with existing video-level solutions such as STTran[17], APT[58], etc. In general, DIF-FVSGG outperform image-level SGG methods by a large" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "29166" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 70, + 553, + 235 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 553, + 235 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 553, + 235 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 553, + 235 + ], + "type": "table", + "html": "
    MethodPredCLSSGCLSSGDET
    R@10R@20R@50mR@10mR@20mR@50R@10R@20R@50mR@10mR@20mR@50R@10R@20R@50mR@10mR@20mR@50
    RelDN [113]44.275.489.231.263.175.525.041.947.918.636.942.613.623.036.67.518.833.7
    VRD [63]51.754.754.7---32.433.333.3---19.224.526.0---
    Motif Freq [112]62.465.165.1---40.841.941.9---23.731.433.3---
    MSDN [57]65.568.568.5---43.945.145.1---24.132.434.5---
    VCTREE [85]66.069.369.3---44.145.345.3---24.432.634.7---
    TRACE [88]72.691.696.450.973.682.737.146.750.531.942.746.326.535.645.322.831.341.8
    GPS-Net [60]76.093.699.5---------24.535.747.3---
    STTran [17]77.994.299.151.467.782.754.063.766.440.750.158.524.636.248.820.929.739.2
    APT [58]78.595.199.2---55.165.168.7---25.737.950.1---
    TR2 [94]83.196.699.9---57.264.466.2---27.839.250.0---
    TEMPURA [69]80.494.299.461.585.198.056.364.767.948.361.166.429.838.146.424.733.943.7
    DSG-DETR [30]------59.269.172.4---32.140.948.3---
    DIFFVSGG83.194.599.166.390.598.460.570.574.451.064.268.835.442.551.027.237.045.6
    ", + "image_path": "5667d18ba0d60a65d3137ee00da9aea31821ba6cb8330e1b93d527ee74cffbcf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 87, + 238, + 522, + 248 + ], + "lines": [ + { + "bbox": [ + 87, + 238, + 522, + 248 + ], + "spans": [ + { + "bbox": [ + 87, + 238, + 522, + 248 + ], + "type": "text", + "content": "Table 2. Comparison of state-of-the-art VSGG methods on Action Genome test [40] under the w/o constraint setting." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 62, + 258, + 549, + 443 + ], + "blocks": [ + { + "bbox": [ + 62, + 258, + 549, + 443 + ], + "lines": [ + { + "bbox": [ + 62, + 258, + 549, + 443 + ], + "spans": [ + { + "bbox": [ + 62, + 258, + 549, + 443 + ], + "type": "image", + "image_path": "3bc2e5a808311f3c1fc0782ec9aa22bec747406486faea231cbb706a9fcaaa9c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 448, + 555, + 471 + ], + "lines": [ + { + "bbox": [ + 55, + 448, + 555, + 471 + ], + "spans": [ + { + "bbox": [ + 55, + 448, + 555, + 471 + ], + "type": "text", + "content": "Figure 4. Visualization results on Action Genome test [40]. All results are given under the SGDET setup. Predicates in red indicate relationships are transformed to another one." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 474, + 295, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 474, + 295, + 568 + ], + "spans": [ + { + "bbox": [ + 54, + 474, + 295, + 568 + ], + "type": "text", + "content": "margin in all metrics. Concretely, under the " + }, + { + "bbox": [ + 54, + 474, + 295, + 568 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 54, + 474, + 295, + 568 + ], + "type": "text", + "content": " constraint setup, our proposed method achieves R@10/R@20/R50 scores of 32.8/39.9/45.5, surpassing GPS-Net which achieves 24.7/33.1/35.1 scores by 8.1/6.8/10.4 scores, respectively. Similar trends can be observed on the " + }, + { + "bbox": [ + 54, + 474, + 295, + 568 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 54, + 474, + 295, + 568 + ], + "type": "text", + "content": " constraint setup. All of the above firmly demonstrates the effectiveness of incorporating temporal cues to tackle relation understanding in dynamic scene." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 714 + ], + "type": "text", + "content": "Additionally, when compared to the video-level counterparts, DIFFVSGG can still deliver state-of-the-art performance. Specifically, though DSG-DETR[30] adopts a modern DETR-like architecture and uses a Transformer-based decoder with all frames as the inputs to aggregate temporal cues, our DIFFVSGG which conducts online inference still outperforms it by a solid gap (i.e., 35.4/42.5/51.0 vs. 32.1/40.9/48.3 under the w/o constraint). More importantly, when it comes to the comparison of mR metric which prevents the bias toward high-frequency classes, DIFFVSGG obtains significantly higher performance compared to existing work. This suggests that using latent dif" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 474, + 555, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 555, + 558 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 555, + 558 + ], + "type": "text", + "content": "fusion models (LDMs) to model the inter-object relationship is effective, and it successfully learned meaning distributions which can prevent overfitting to high-frequency classes. Similar conclusions can be drawn on PredCLS and SGCLS two evaluation protocols, where DIFFVSGG can still deliver SOTA performance under both " + }, + { + "bbox": [ + 313, + 474, + 555, + 558 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 313, + 474, + 555, + 558 + ], + "type": "text", + "content": " constraint and " + }, + { + "bbox": [ + 313, + 474, + 555, + 558 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 313, + 474, + 555, + 558 + ], + "type": "text", + "content": " constraint two setups." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 563, + 425, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 563, + 425, + 577 + ], + "spans": [ + { + "bbox": [ + 313, + 563, + 425, + 577 + ], + "type": "text", + "content": "4.3. Qualitative Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 581, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 581, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 581, + 555, + 629 + ], + "type": "text", + "content": "We provide visualization results of UNIALIGN in Fig.4. It can be seen that our proposed method is able to generate accurate scene graphs across various challenging scenarios, such as fast motion and occlusion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 635, + 444, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 444, + 649 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 444, + 649 + ], + "type": "text", + "content": "4.4. Diagnostic Experiment" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 654, + 553, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 701 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 701 + ], + "type": "text", + "content": "To assess the effectiveness of the detailed designs of DIF-FVSGG and gain deeper insights, we conduct a series of experiments on the AG test [40]. All performance metrics are reported under the SGDET setup." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 701, + 553, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 553, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 553, + 714 + ], + "type": "text", + "content": "Key Component Analysis. We first examine the efficacy" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29167" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 70, + 294, + 142 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 294, + 142 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 294, + 142 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 294, + 142 + ], + "type": "table", + "html": "
    #L VSGGL T.VSGG Motionw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    126.935.338.027.538.948.5
    2✓29.737.741.530.340.149.9
    3✓32.039.344.633.942.050.3
    4✓32.839.945.535.442.551.0
    ", + "image_path": "9d50e6738878384fa00ff430c794f8811b3657ac3ded69940dc4e948762aa598.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 62, + 171, + 293, + 229 + ], + "blocks": [ + { + "bbox": [ + 79, + 148, + 271, + 159 + ], + "lines": [ + { + "bbox": [ + 79, + 148, + 271, + 159 + ], + "spans": [ + { + "bbox": [ + 79, + 148, + 271, + 159 + ], + "type": "text", + "content": "Table 3. Analysis on key components of DIFFVSGG." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 62, + 171, + 293, + 229 + ], + "lines": [ + { + "bbox": [ + 62, + 171, + 293, + 229 + ], + "spans": [ + { + "bbox": [ + 62, + 171, + 293, + 229 + ], + "type": "table", + "html": "
    #Union Box FeatureSubject FeatureSubject Locationw constraintsNo Constraints
    R@10R@20R@50R@10R@20R@50
    1✓29.536.742.032.339.247.5
    2✓✓31.038.243.633.740.848.7
    3✓✓✓32.839.945.535.442.551.0
    ", + "image_path": "506aab7055203601cb33f4f6095aa4c8aa4ee1b63b8c9daf992c792941764972.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 62, + 258, + 293, + 328 + ], + "blocks": [ + { + "bbox": [ + 58, + 235, + 293, + 247 + ], + "lines": [ + { + "bbox": [ + 58, + 235, + 293, + 247 + ], + "spans": [ + { + "bbox": [ + 58, + 235, + 293, + 247 + ], + "type": "text", + "content": "Table 4. Analysis on elements to construct adjacency matrix " + }, + { + "bbox": [ + 58, + 235, + 293, + 247 + ], + "type": "inline_equation", + "content": "{\\mathbf{A}}^{t}" + }, + { + "bbox": [ + 58, + 235, + 293, + 247 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 62, + 258, + 293, + 328 + ], + "lines": [ + { + "bbox": [ + 62, + 258, + 293, + 328 + ], + "spans": [ + { + "bbox": [ + 62, + 258, + 293, + 328 + ], + "type": "table", + "html": "
    Step Tw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    1031.738.542.934.041.149.5
    2032.839.945.535.442.551.0
    5033.240.546.435.743.151.4
    10033.140.345.935.542.851.1
    ", + "image_path": "e996653f49a96bf1738c1dcdd8bf1c4143e1f9f527f6b28787539f5f2415168a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 366, + 295, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 366, + 295, + 533 + ], + "spans": [ + { + "bbox": [ + 54, + 366, + 295, + 533 + ], + "type": "text", + "content": "of essential components of DIFFVSGG in Table3, where the first row denotes the baseline model directly using bounding box predictions to construct scene graphs without denoising refinement. After integrating LDMs to model complex inter-object relationships within the scene (i.e., row #2), DIFFVSGG enjoys considerable improvement on both w and w/o constraint setups. Next, applying condition based temporal reasoning to capture long-term temporal dependencies further boosts the performance to 32.0 and 33.9 on two setups. Finally, upon the incorporation of motion enhanced denoising (i.e., row #4), DIFFVSGG obtains the best performance on both setups, suggesting that motion cues can effectively enhance the awareness of temporal cues through conditional promoting." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 534, + 295, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 582 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 582 + ], + "type": "text", + "content": "Graph Construction. We study the impact of using various features to construct the adjacency matrix " + }, + { + "bbox": [ + 55, + 534, + 295, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^t" + }, + { + "bbox": [ + 55, + 534, + 295, + 582 + ], + "type": "text", + "content": " in Table 4. As shown, incorporating all three types of features, as described in Eq.7, achieves the best performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 582, + 295, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 642 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 642 + ], + "type": "text", + "content": "Number of Diffusion Step. Next we investigate the effect of different number of diffusion steps. As shown in Table 5, the best performance is achieved at " + }, + { + "bbox": [ + 55, + 582, + 295, + 642 + ], + "type": "inline_equation", + "content": "T = 50" + }, + { + "bbox": [ + 55, + 582, + 295, + 642 + ], + "type": "text", + "content": ". However, to balance the performance and efficiency efficiency, we set " + }, + { + "bbox": [ + 55, + 582, + 295, + 642 + ], + "type": "inline_equation", + "content": "T = 20" + }, + { + "bbox": [ + 55, + 582, + 295, + 642 + ], + "type": "text", + "content": ", which yields a slight reduction in performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 701 + ], + "type": "text", + "content": "Number of Layer in Denoising U-Net. We further analyze the impact of using different number of layers in the encoder and decoder of denoising U-Net. As shown in Table 6, DIFFVSGG achieves similar performance when the layer number exceeds 2. For efficiency, we set it to 3." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 714 + ], + "type": "text", + "content": "Graph Readout. We explore different graph readout strate" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 321, + 71, + 551, + 140 + ], + "blocks": [ + { + "bbox": [ + 71, + 334, + 279, + 345 + ], + "lines": [ + { + "bbox": [ + 71, + 334, + 279, + 345 + ], + "spans": [ + { + "bbox": [ + 71, + 334, + 279, + 345 + ], + "type": "text", + "content": "Table 5. Analysis on forward and reverse diffusion steps." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 71, + 551, + 140 + ], + "lines": [ + { + "bbox": [ + 321, + 71, + 551, + 140 + ], + "spans": [ + { + "bbox": [ + 321, + 71, + 551, + 140 + ], + "type": "table", + "html": "
    # Layerw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    231.938.244.534.042.150.1
    332.839.945.535.442.551.0
    532.439.646.134.443.050.7
    632.639.346.334.744.050.9
    ", + "image_path": "00e19318e6918906dbe8e2c96edd0cf5160a1bbfdd4c3984d1f48b1ed7a239f9.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 321, + 172, + 551, + 225 + ], + "blocks": [ + { + "bbox": [ + 329, + 145, + 538, + 157 + ], + "lines": [ + { + "bbox": [ + 329, + 145, + 538, + 157 + ], + "spans": [ + { + "bbox": [ + 329, + 145, + 538, + 157 + ], + "type": "text", + "content": "Table 6. Analysis of the layer configuration of the U-Net." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 172, + 551, + 225 + ], + "lines": [ + { + "bbox": [ + 321, + 172, + 551, + 225 + ], + "spans": [ + { + "bbox": [ + 321, + 172, + 551, + 225 + ], + "type": "table", + "html": "
    Elementw constraintsw/o constraints
    R@10R@20R@50R@10R@20R@50
    At,i,032.839.945.535.442.551.0
    At,i,j31.737.743.533.641.249.6
    ", + "image_path": "87d71b105b4cc30b6db90a822312140dd346c87275ca70b79e9dc626bbf2739b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 321, + 255, + 551, + 329 + ], + "blocks": [ + { + "bbox": [ + 329, + 231, + 538, + 242 + ], + "lines": [ + { + "bbox": [ + 329, + 231, + 538, + 242 + ], + "spans": [ + { + "bbox": [ + 329, + 231, + 538, + 242 + ], + "type": "text", + "content": "Table 7. Analysis on the elements used for graph readout." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 255, + 551, + 329 + ], + "lines": [ + { + "bbox": [ + 321, + 255, + 551, + 329 + ], + "spans": [ + { + "bbox": [ + 321, + 255, + 551, + 329 + ], + "type": "table", + "html": "
    ModelParameter Inferencew constraintsw/o constraints
    NumberTimeR@10R@20R@50R@10R@20R@50
    TRACE [88]66.7 M8.4 FPS13.914.514.526.535.645.3
    STTran [17]51.1 M10.9 FPS25.234.137.024.636.248.8
    TEMPURA [69]53.5 M9.6 FPS28.133.434.929.838.146.4
    DSG-DETR [30]65.5 M7.3 FPS30.334.836.132.140.948.3
    DIFFVSGG46.7 M8.7 FPS32.839.945.535.442.551.0
    ", + "image_path": "bf756cd5f5abc3e7d90084750c968ebb89a857e1e957a612f433a9665cab1d94.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 335, + 552, + 346 + ], + "lines": [ + { + "bbox": [ + 315, + 335, + 552, + 346 + ], + "spans": [ + { + "bbox": [ + 315, + 335, + 552, + 346 + ], + "type": "text", + "content": "Table 8. Analysis on the trainable parameters and inference time." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "text", + "content": "gies in Table 7. Here " + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "inline_equation", + "content": "A_{i}^{t,0}" + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "text", + "content": " refers to utilize the entire row " + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "inline_equation", + "content": "A^{t,0}" + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "text", + "content": " to deliver the predictions (i.e., Eq. 15-16), while " + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "inline_equation", + "content": "A_{i,j}^{t,0}" + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "text", + "content": " denoting utilize one element at " + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "inline_equation", + "content": "A^{t,0}" + }, + { + "bbox": [ + 313, + 369, + 555, + 433 + ], + "type": "text", + "content": " to make prediction. It can be seen that aggregating all elements in a row that contains the same subject delivers higher performance." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 435, + 554, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 435, + 554, + 507 + ], + "spans": [ + { + "bbox": [ + 313, + 435, + 554, + 507 + ], + "type": "text", + "content": "Running Efficiency. Finally we probe the running efficiency of DIFFVSGG. As seen in Table 8, our method requires the fewest trainable parameters among all competitors. Though inference speed is slightly slower than existing work due to step-wise denoising, the improvement in performance compensates for this limitation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 523, + 388, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 523, + 388, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 523, + 388, + 536 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 555, + 713 + ], + "type": "text", + "content": "We presented DIFFVSGG, a diffusion-based VSGG solution that makes contributions in three aspects. First, as an online approach, it effectively addresses challenges such as GPU memory constraints and real-time processing while delivering high performance, highlighting its potential for real-world application. Second, we propose a learning strategy for LDMs to generate inter-object relationships from random subject-object pairs, with ground-truth object locations as the annotations. Third, in leverage of LDMs, DIFFVSGG provides a new approach to enable temporal reasoning via dynamic, iterative refinement of scene graphs across frames, conditioned on predictions of prior frame. We hope this work could provide a new perspective for video analysis through reverse diffusion along the temporal dimension." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "29168" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 147, + 85 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 92, + 296, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 92, + 296, + 199 + ], + "spans": [ + { + "bbox": [ + 55, + 92, + 296, + 199 + ], + "type": "text", + "content": "This work was supported in part by the Natural Science Foundation of Zhejiang Province (LDT23F02023F02), the Fundamental Research Funds for the Central Universities (226-2024-00058), and the National Natural Science Foundation of China (No. 62372405). 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(6):2827-2840, 2021. 2" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "29172" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Difference Inversion_ Interpolate and Isolate the Difference with Token Consistency for Image Analogy Generation/7ebc23f8-a8e8-4361-9a63-f7a091962245_content_list.json b/2025/Difference Inversion_ Interpolate and Isolate the Difference with Token Consistency for Image Analogy Generation/7ebc23f8-a8e8-4361-9a63-f7a091962245_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..45abb9716634334c9ee82abd3ee25beb01010fc6 --- /dev/null +++ b/2025/Difference Inversion_ Interpolate and Isolate the Difference with Token Consistency for Image Analogy Generation/7ebc23f8-a8e8-4361-9a63-f7a091962245_content_list.json @@ -0,0 +1,1491 @@ +[ + { + "type": "text", + "text": "Difference Inversion: Interpolate and Isolate the Difference with Token Consistency for Image Analogy Generation", + "text_level": 1, + "bbox": [ + 140, + 92, + 854, + 137 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyunsoo Kim $^{1,2}$ , Donghyun Kim $^{\\dagger 1}$ , Suhyun Kim $^{\\dagger 3}$", + "bbox": [ + 295, + 164, + 699, + 184 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Korea University $^{2}$ Korea Institute of Science and Technology $^{3}$ Kyung Hee University {climba, d.kim}@korea.ac.kr, dr.suhyun.kim@gmail.com", + "bbox": [ + 209, + 184, + 787, + 219 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e52c0a927fde8686d3cf5a802bb4919822055910f583fca714f3cf61a7d0d5b2.jpg", + "image_caption": [ + "Figure 1. We propose Difference Inversion, a method that generates $B'$ conditioned on an image triplet $\\{A, A', B\\}$ that satisfies $A: A'::B: B'$ . Our method produces a significantly more plausible $B'$ than other baselines. Note that SDEdit and InstructPix2Pix take the text instruction as input, whereas DIA, Analogist, VISII, and our Difference Inversion only use the image triplet $A, A', B$ as input." + ], + "image_footnote": [], + "bbox": [ + 104, + 256, + 898, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 679, + 326, + 695 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "How can we generate an image $B'$ that satisfies $A: A':: B: B'$ , given the input images $A, A'$ and $B$ ? Recent works have tackled this challenge through approaches like visual in-context learning or visual instruction. However, these methods are typically limited to specific models (e.g. InstructPix2Pix. Inpainting models) rather than general diffusion models (e.g. Stable Diffusion, SDXL). This dependency may lead to inherited biases or lower editing capabilities. In this paper, we propose Difference Inversion, a method that isolates only the difference from $A$ and $A'$ and applies it to $B$ to generate a plausible $B'$ . To address model de", + "bbox": [ + 89, + 710, + 483, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pendency, it is crucial to structure prompts in the form of a \"Full Prompt\" suitable for input to stable diffusion models, rather than using an \"Instruction Prompt\". To this end, we accurately extract the Difference between $A$ and $A'$ and combine it with the prompt of $B$ , enabling a plug-and-play application of the difference. To extract a precise difference, we first identify it through 1) Delta Interpolation. Additionally, to ensure accurate training, we propose the 2) Token Consistency Loss and 3) Zero Initialization of Token Embeddings. Our extensive experiments demonstrate that Difference Inversion outperforms existing baselines both quantitatively and qualitatively, indicating its ability to generate more feasible $B'$ in a model-agnostic manner.", + "bbox": [ + 511, + 680, + 908, + 876 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Co-corresponding author.", + "bbox": [ + 114, + 886, + 258, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18250", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 89, + 222, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The goal of image analogy generation [39] is to create the target image $B'$ based on the image triplet $\\{A, A', B\\}$ , ensuring that it satisfies the image analogy [12, 19] formulation $A: A':: B: B'$ . With the huge advancement of large-scale diffusion models [5, 7, 16, 29, 32, 34], it is natural to consider leveraging these models for solving image analogy generation from the perspective of conditional image generation. Unlike existing conditional diffusion models [1, 2, 13, 22, 26, 31] that usually take text prompts as conditions, image analogy generation assumes that only an image triplet is provided as input. For example, consider the top example in Fig. 1, where the transformation is changing a cabin into a castle. Previous conditional diffusion models ((a) and (b)) use a text instruction (i.e. \"Make the cabin a castle\") as well as $B$ to generate the target image $B'$ . On the other hand, in image analogy generation, $B'$ is generated using only the image triplet without any text prompt.", + "bbox": [ + 89, + 114, + 483, + 372 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pioneered by DIA [39], several studies [10, 23, 25, 39, 45] have explored diffusion-based image analogy generation in terms of visual in-context learning or visual instruction. From the perspective of visual in-context learning, [10, 23, 45] treat the generation of $B'$ as an image inpainting task, where $A$ , $A'$ , $B$ and initial noise are concatenated into a grid-based input image, and $B'$ is denoised from noise (see Fig. 2 (b)). This approach is limited to pretrained inpainting models and often requires manual prompt engineering by human to obtain additional text prompts. Visual Instruction Inversion (VISII, Fig. 2 (c)) [25] inverts visual instructions from $A$ to $A'$ using instruction tokens but is also limited to InstructPix2Pix [2]. Moreover, to efficiently optimize the visual instruction, VISII initializes the instruction tokens with image $A'$ , which leaves residual information from $A'$ in the instruction, leading to unintended artifacts in $B'$ . For instance, in the fourth example of Fig. 1 (e), the transformation from $A$ to $A'$ involves adding a rainbow, so the desired transformation for $B$ to $B'$ would similarly involve adding only the rainbow. However, in the images generated by VISII, residual information from $A'$ (i.e. mountains) remains, leading to unintended elements in the output.", + "bbox": [ + 89, + 372, + 483, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we introduce Difference Inversion, which leverages \"Full Prompt\" with both prompt tokens representing the input image and Difference Tokens that exclusively encode difference information. Difference Tokens can focus on only the difference (Delta) between $A$ and $A'$ and the combined tokens are more appropriate as an input of Stable Diffusion models. This contrasts with VISII, which relies on an image-based \"Instruction Prompt\" that can only be applied as input to InstructPix2Pix. To accurately disentangle the difference, we propose Delta Interpolation to define a more precise Delta. Additionally, we introduce Token Consistency Loss, which ensures that the difference", + "bbox": [ + 89, + 719, + 483, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/aaaca4d77e1af2ce9417e9f1240c2e681ef95791b2b8212966729fa5d2a99743.jpg", + "image_caption": [ + "(a) DIA" + ], + "image_footnote": [], + "bbox": [ + 514, + 88, + 903, + 186 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/076c9cba41f2c1981bf3bf21c71c35ae1a4e5dbb8e2cef9408437d03b6d8600a.jpg", + "image_caption": [ + "(c) VISII", + "Figure 2. Architectural comparison of image analogy generation baselines. We compare our approach with three baseline methods: (a) DIA, (b) Analogist, and (c) VISII. Detailed descriptions can be found in Sec. 2. It is noteworthy that, unlike (b) and (c), which each depend on specific models, our method can be applied to general stable diffusion models." + ], + "image_footnote": [], + "bbox": [ + 516, + 198, + 696, + 285 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ec44239b444799e6ba40425814b2d42e7616d1b9473ba3400e2266b58d327be9.jpg", + "image_caption": [ + "(d) Ours" + ], + "image_footnote": [], + "bbox": [ + 717, + 198, + 895, + 276 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "information emerges when the token is present and disappears when it is absent. By using Token Consistency Loss, the Difference Tokens trained on the Interpolated Delta can be seamlessly concatenated with any query image prompt, enabling their use without introducing unwanted artifacts. Finally, we zero-initialize the Difference Tokens to ensure stable optimization of the differences and to reduce bias by preventing any initial preference from being introduced.", + "bbox": [ + 511, + 415, + 903, + 536 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of our paper are as follows:", + "bbox": [ + 532, + 537, + 870, + 551 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Difference Inversion, which inverts precise differences into Difference Tokens and applies them to any query $B$ to generate $B'$ within general stable diffusion frameworks.", + "- To extract the exact difference between images $A$ and $A'$ , we additionally introduce a Delta Interpolation, Token Consistency Loss and Zero-Initialization of Token Embeddings. These ensures that the extracted differences contain only the intended modifications, free from unwanted artifacts.", + "- Our extensive experiments demonstrate that Difference Inversion outperforms existing baselines both quantitatively and qualitatively, as well as in human and large-scale Vision Language Models (VLMs) evaluations." + ], + "bbox": [ + 513, + 551, + 903, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related works", + "text_level": 1, + "bbox": [ + 513, + 777, + 658, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image Analogy Generation via Diffusion Models", + "text_level": 1, + "bbox": [ + 511, + 801, + 903, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The goal of image analogy generation [10, 23, 25, 39, 45] is to produce $B'$ by conditioning on $A$ , $A'$ and $B$ in the form of $A: A' :: B: B'$ . DIA [39] attempts to invert images to obtain conditioning matrices for diffusion, enabling high-", + "bbox": [ + 511, + 839, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18251", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/371a56c6c3851f8afa9a08d8d57ae9ba93faf040ce0d811cb408c09562a80153.jpg", + "image_caption": [ + "(a) Overall Pipeline of Difference Inversion", + "(b) Visualization of Interpolated Delta", + "Figure 3. Overall pipeline of Difference Inversion. Given an image triplet $\\{A, A', B\\}$ , Difference Inversion extracts the difference between $A$ and $A'$ using DIFF tokens. The Difference is estimated as the Interpolated Delta, computed between $A$ and $A'$ by applying Spherical Linear Interpolation (Slerp) on the Image Delta and Text Delta, effectively capturing both visual and semantic information. The circled numbers in the figure correspond to the steps outlined in Algorithm 1." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 903, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "level analogy through semantic vector operations. However it fails to capture not only the desired editing changes but also the detailed image information accurately. Starting with ImageBrush [45], several studies combined $A, A', B$ , and $B'$ into a single grid-formatted image and used a pretrained inpainting model to denoise the $B'$ section from noise, generating a plausible image for $B'$ . However, relying solely on a pretrained inpainting model makes it challenging to generate a plausible $B'$ . Leveraging the knowledge of large language models (LLMs) or large-scale vision language model (VLMs) is often necessary, which consequently requires cumbersome prompt engineering. In a different approach, VISII [25] achieves $A \\rightarrow A'$ transformations by inverting visual instructions into text tokens and applying them to query image (e.g. $B$ ) without relying on an VLMs. However, this process leaves unwanted information from $A$ and $A'$ in $B'$ . As a result, $B'$ may be generated in an unintended direction as shown in Fig. 1 (c). Additionally, since the inverted instruction can only be used with InstructPix2Pix [2], it is challenging to apply this method to various Stable Diffusion models, resulting in low generalizability. In this paper, we introduce Difference Inversion that precisely extracts only the difference between $A$ and $A'$ and applies it to $B$ , avoiding unintended artifacts. Furthermore, since it forms a Full Prompt rather than an Instruction Prompt, it can be applied to a wide range of Stable Diffusion models.", + "bbox": [ + 91, + 396, + 483, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Diffusion based Inversion", + "text_level": 1, + "bbox": [ + 89, + 816, + 323, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the wide range of diffusion-based conditional generation methods, DDIM Inversion [24, 37], which identifies the initial noise corresponding to a given image, serves as a core component. Once the initial noise is identified by inver", + "bbox": [ + 89, + 839, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sion, it is well-known that better results can be generated from the inverted noise when applied to personalized editing [9, 17, 40] or image-to-image translation [4, 11]. Alongside this trend, DreamBooth [33] and Textual Inversion [8] focus on optimizing special text tokens to learn representations that capture personalized information. ReVersion [15] also optimizes specific text prompts to capture and represent the relationship between two images. These inversion methods utilize a soft prompt approach, optimizing continuous embeddings. In contrast, PEZ [42] proposes hard prompt optimization to generate interpretable prompts that effectively capture the concept of a specific image. Similarly, our work optimizes Difference Tokens in a hard prompt manner, making them plug-and-play with other prompts, thereby enhancing their suitability for general Stable Diffusion models.", + "bbox": [ + 511, + 395, + 906, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 511, + 657, + 653, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Denoising diffusion models [14, 36] are generative models that learn the reversal of the forward process using denoising autoencoders, enabling the iterative sampling of images from noise. In the early stages of diffusion models [5, 14, 38], the forward and reverse diffusion process operates directly in the pixel space. Latent diffusion models [32], also well known as Stable Diffusion, performs this process in latent space, enabling more efficient image generation. Given an input image $x$ and a text condition $y$ , the image encoder transforms $x$ into $z_0$ . The denoising model $\\epsilon_{\\theta}$ is then trained to predict a denoised version of its input $z_t$ , as shown in the following equation.", + "bbox": [ + 511, + 686, + 908, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathbb {E} _ {\\mathcal {E} (x), y, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\| \\epsilon - \\epsilon_ {\\theta} \\left(z _ {t}, t, \\tau_ {\\theta} (y)\\right) \\| _ {2} ^ {2} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 883, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18252", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $z_{t}$ is a noisy variant of the original input $z_{0}$ in time $t$ and $\\tau_{\\theta}$ is text encoder. Since Stable Diffusion accepts text prompts as input, there have been attempts to add special tokens to text prompts for tasks such as personalized editing. Textual Inversion [8], for example, learns to capture specific concepts or objects using special token $(s_{*})$ .", + "bbox": [ + 89, + 90, + 480, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similarly, VISII (Fig. 2 (c)) also utilizes instruction tokens $C_T$ to learn the instruction information necessary for generating $B'$ . Since VISII needs to learn the transformation instruction from image $A$ to $A'$ and apply them to $B$ , it leverages InstructPix2Pix [2]. Furthermore, to better capture the transformation, $C_T$ is initialized via discrete token optimization (PEZ [42]) on the image $A'$ . Since VISII relies on InstructPix2Pix, it learns $C_T$ in the form of an instruction prompt. In contrast, our Difference Inversion isolates only the difference information, enabling a plug-and-play approach with general stable diffusion prompts. Further details will be provided in the following section.", + "bbox": [ + 89, + 181, + 483, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 89, + 377, + 181, + 392 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an image triplet $\\{A, A', B\\}$ , our goal is to extract the difference between $(A, A')$ and apply it to $B$ . To capture the difference, we optimize DIFF tokens $(\\tilde{D})$ to effectively encode the extracted differences. We first introduce the basic concept of Difference Inversion in Sec. 4.1. In Sec. 4.2, we explain how we optimize the DIFF token using the Interpolated Delta. Then, in Sec. 4.3, we present the token consistency loss to enhance image consistency, followed by an introduction to token embedding initialization in Sec. 4.4.", + "bbox": [ + 89, + 402, + 483, + 540 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Difference Inversion", + "text_level": 1, + "bbox": [ + 89, + 549, + 282, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We start from the key observation in VISII, which is the similar concept with our work. As shown in Fig. 1 (e), generating $B'$ with VISII results in unwanted artifacts. This occurs because the optimized visual instruction contains not only the difference (e.g. rainbow) but also information specific to $A$ and $A'$ (e.g. mountains). Therefore, the key is to enable the inversion of only the precise difference.", + "bbox": [ + 89, + 571, + 483, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, we define the difference as \"Delta,\" which can be obtained as the difference between embedding vectors from the CLIP [30] encoder $\\mathcal{E}_I$ . Letting the CLIP image encoder be represented by $\\mathcal{E}_I$ , the Image Delta $\\mathcal{D}_{img}$ can be expressed as follows:", + "bbox": [ + 89, + 676, + 483, + 753 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {i m g} = \\mathcal {E} _ {I} (A _ {i m g} ^ {\\prime}) - \\mathcal {E} _ {I} (A _ {i m g}) \\qquad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 765, + 482, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To optimize DIFF tokens, we first initialize the text prompts of $A$ and $A'$ using PEZ. This step aims to fully anchoring the prompt of $A$ (or $A'$ ) and isolate the only difference, enabling more precise extraction of the difference with the DIFF token in place. As shown in Fig. 3 (a), we only optimize DIFF tokens while optimized prompt embedding is frozen. Note that while optimization with PEZ can", + "bbox": [ + 89, + 794, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Difference Inversion" + ], + "code_body": "Require: pretrained denoising model $\\epsilon_{\\theta}$ ; Image encoder $\\mathcal{E}$ ; CLIP Image, Text Encoder $\\mathcal{E}_I$ $\\mathcal{E}_T$ ; Captioning model BLIP2; interpolation rate $\\alpha$ ; Learning rate $\\gamma$ $t_{before}, t_{after} \\sim \\mathcal{U}(0,T)$ . $\\epsilon_{before}, \\epsilon_{after} \\sim \\mathcal{N}(0,1)$ . Input: Image pair $\\{A, A'\\}$ \nOutput: Difference Tokens $\\tilde{D} = \\{D_1^*, \\dots, D_n^*\\}$ \n// Extract the caption of $A$ and $A'$ .. $①$ $cap_A = \\mathrm{BLIP2}(A)$ . $cap_{A'} = \\mathrm{BLIP2}(A')$ \n// Calculate Image Delta $\\mathcal{D}_I$ and Text Delta $\\mathcal{D}_T$ $\\mathcal{D}_I = \\mathcal{E}_I(A') - \\mathcal{E}_I(A)$ . $\\mathcal{D}_T = \\mathcal{E}_T(cap_{A'}) - \\mathcal{E}_{txt}(cap_A)$ \n// Calculate Interpolated Delta $D_{inter}$ ... $②$ $\\mathcal{D}_{inter} = Slerp(\\mathcal{D}_I,\\mathcal{D}_T,\\alpha)$ \n// Optimize the prompt w.r.t. $A$ and $A'$ .. $③$ \nprompt $A = \\mathrm{PEZ}(A)$ . prompt $A' = \\mathrm{PEZ}(A')$ \nEncode $z_A = \\mathcal{E}(A)$ . $z_{A'} = \\mathcal{E}(A')$ \n// Zero-Initialization token embeddings ... $④$ \nInitialize $\\tilde{D}$ with Zero embeddings \nfor $i = 1$ to $N$ do \n// Prepare noisy latents $z_A$ and $z_{A'}$ .. $⑤$ $z_{A_t} \\gets$ add $\\epsilon_{before}$ to $z_A$ at timestep $t_{before}$ $z_{A'_t} \\gets$ add $\\epsilon_{after}$ to $z_{A'}$ at timestep $t_{after}$ \n// Predict each noise $\\hat{\\epsilon}_{before}, \\hat{\\epsilon}_{after}$ $\\hat{\\epsilon}_{before} = \\epsilon_{\\theta}(z_{A_t}, t_{before}, \\{prompt_{A'}, -\\tilde{D}\\})$ $\\hat{\\epsilon}_{after} = \\epsilon_{\\theta}(z_{A'_t}, t_{after}, \\{prompt_A, \\tilde{D}\\})$ \n// Compute Token Consistency loss ... $⑥$ $\\mathcal{L}_{tc} = \\| \\epsilon_{before} - \\hat{\\epsilon}_{before} \\|_2 + \\| \\epsilon_{after} - \\hat{\\epsilon}_{after} \\|_2$ \n// Compute Clip loss $\\mathcal{L}_{clip}$ ... $⑦$ $\\mathcal{L}_{clip} = \\cosine(\\tilde{D},\\mathcal{D}_{inter})$ $\\mathcal{L} = \\lambda_{tc} * \\mathcal{L}_{tc} + \\lambda_{clip} * \\mathcal{L}_{clip}$ \nUpdate $\\tilde{D} = \\tilde{D} -\\gamma \\nabla L$ \nend for \nReturn: $\\tilde{D}$", + "bbox": [ + 519, + 109, + 903, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "be time-consuming, it can be replaced with text captions generated by BLIP2 [18], trading off a slight performance drop for faster processing (Sec. 4.3)", + "bbox": [ + 511, + 627, + 903, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, simply optimizing the DIFF token only with the Image Delta did not sufficiently capture the Difference information. As shown in Fig. 3 (b), $B'$ with the Image Delta retains much of the original image's cabin features rather than fully transforming into the intended castle. We hypothesize that this is because the CLIP embedding space may not fully represent the intricate details of the images. In the following section, we introduce Delta Interpolation to extract a more refined difference.", + "bbox": [ + 511, + 672, + 906, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Delta Interpolation", + "text_level": 1, + "bbox": [ + 511, + 818, + 697, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the Image Delta effectively captures the visual difference, it still fails to fully reflect the specific semantic differences. To obtain more detailed semantic information, we use an image captioning model to extract cap", + "bbox": [ + 511, + 839, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18253", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tions for each of the images $A$ and $A'$ . We utilize BLIP2, but for more detailed captions, BLIP3 [44] or large-scale VLMs [3, 20, 21] can be also be considered. The extracted captions contain more specific details, such as \"cabin\" and \"castle,\" which were used to derive the Text Delta $D_{txt}$ that contains more semantic information than Image Delta.", + "bbox": [ + 89, + 90, + 483, + 183 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {t x t} = \\mathcal {E} _ {T} \\left(A _ {t x t} ^ {\\prime}\\right) - \\mathcal {E} _ {T} \\left(A _ {t x t}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 191, + 482, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{E}_T$ is CLIP text encoder.", + "bbox": [ + 89, + 218, + 302, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining both Image and Text Delta of $A$ and $A'$ with CLIP, we apply Spherical Linear Interpolation (Slerp) [35] to integrate both embeddings. Since CLIP learns image-text pairs to maximize their cosine similarity, we hypothesize that it would be possible to find a more refined Delta within the joint hypersphere of the CLIP space. Therefore, to identify the Interpolated Delta $D_{inter}$ on this hypersphere, we apply Slerp shown below.", + "bbox": [ + 89, + 233, + 483, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {D} _ {\\text {i n t e r}} = \\operatorname {S l e r p} \\left(\\mathcal {D} _ {\\text {i m g}}, \\mathcal {D} _ {\\text {t x t}}; \\alpha\\right) (4) \\\\ = \\frac {\\sin ((1 - \\alpha) \\theta)}{\\sin (\\theta)} \\mathcal {D} _ {i m g} + \\frac {\\sin (\\alpha \\theta)}{\\sin (\\theta)} \\mathcal {D} _ {t x t} (5) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 364, + 482, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ is interpolation ratio between Image and Text Delta. We set $\\alpha$ to 0.8, and the ablation results are in Fig. 7.", + "bbox": [ + 89, + 424, + 482, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we optimize the DIFF token to minimize cosine distance with this Interpolated Delta as:", + "bbox": [ + 89, + 454, + 483, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c l i p}} = \\operatorname {c o s i n e} (\\tilde {D}, \\mathcal {D} _ {\\text {i n t e r}}) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 494, + 482, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Token Consistency Loss", + "text_level": 1, + "bbox": [ + 89, + 520, + 312, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Using only the Interpolated Delta $\\mathcal{D}_{inter}$ may resemble obtaining a visual instruction from $A$ to $A^{\\prime}$ . However, in Difference Inversion, it is also important to preserve aspects that should remain unchanged when generating $B^{\\prime}$ . To achieve this, it is essential to accurately extract only the bidirectional difference between $A$ and $A^{\\prime}$ . Visual instruction considers only the transformation from $A\\rightarrow A^{\\prime}$ , whereas the difference must account for both $A\\to A^{\\prime}$ and $A^{\\prime}\\to A$ . For DIFF tokens $(\\tilde{D})$ , this implies that when $\\tilde{D}$ is present, the result should correspond to $A^{\\prime}$ ; otherwise, it should yield $A$ .", + "bbox": [ + 89, + 542, + 483, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Additionally, maintaining consistency in elements we do not intend to modify during this process is necessary. Inspired by Cycle Consistency Loss [43, 47], we introduce Token Consistency Loss, which ensures that $A'$ is generated when $\\tilde{D}$ is present and $A$ when $\\tilde{D}$ is absent. Specifically, the prompt concatenated with prompt $A$ and $\\tilde{D}$ should accurately reconstruct image $A$ , while the prompt concatenated with prompt $A'$ and $-\\tilde{D}$ (reverse direction of $\\tilde{D}$ ) should accurately reconstruct image $A'$ . This can be expressed as follows:", + "bbox": [ + 89, + 709, + 483, + 858 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m s e _ {b e f o r e}} = \\left\\| \\epsilon_ {b e f o r e} - \\epsilon_ {\\theta} \\left(z _ {A _ {t}}, t _ {b e f o r e}, \\{p r o m p t _ {A ^ {\\prime}}, - \\tilde {D} \\}\\right) \\right\\| _ {2} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 868, + 498, + 901 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m s e _ {a f t e r}} = \\left\\| \\epsilon_ {a f t e r} - \\epsilon_ {\\theta} \\left(z _ {A _ {t} ^ {\\prime}}, t _ {a f t e r}, \\{p r o m p t _ {A}, \\tilde {D} \\}\\right) \\right\\| _ {2} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 116, + 903, + 148 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $t_{before}, t_{after} \\sim N(0,1)$", + "bbox": [ + 513, + 148, + 727, + 164 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Token Consistency loss can be written as", + "bbox": [ + 532, + 164, + 834, + 178 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t c} = \\mathcal {L} _ {m s e _ {\\text {b e f o r e}}} + \\mathcal {L} _ {m s e _ {\\text {a f t e r}}} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 190, + 903, + 208 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, to optimize the DIFF tokens $\\tilde{D}$ , we utilized the following objective:", + "bbox": [ + 511, + 219, + 903, + 250 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {t c} * \\mathcal {L} _ {t c} + \\lambda_ {c l i p} * \\mathcal {L} _ {c l i p} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 262, + 903, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{tc}$ and $\\lambda_{tc}$ denotes weight parameter of each loss, respectively. We empirically set $\\lambda_{tc}$ to 0.01 and $\\lambda_{clip}$ to 6.", + "bbox": [ + 511, + 289, + 903, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Zero-Initialization of Token Embeddings", + "text_level": 1, + "bbox": [ + 511, + 329, + 862, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus far, we have discussed the optimization process for the DIFF tokens $(\\tilde{D})$ . Finally, we address the approach for initializing $\\tilde{D}$ . It is crucial for the $\\tilde{D}$ to capture accurate differences, making it essential to effectively disentangle the original image information from the difference. From this perspective, randomly initializing the $\\tilde{D}$ can lead to unintended information being embedded within $\\tilde{D}$ (see Config. C in Fig. 5). Motivated by ContorlNet [46], we initialize the token embeddings with zero to ensure that only the intended differences are captured within the $\\tilde{D}$ , minimizing unwanted artifacts. By initializing all $\\tilde{D}$ to zero, we ensure that each token robustly encapsulates only the distinguishing differences from the original image. Detailed experimental results are presented in Sec. 5.", + "bbox": [ + 511, + 349, + 906, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 511, + 575, + 648, + 593 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental and Implementation Detail", + "text_level": 1, + "bbox": [ + 511, + 599, + 867, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We used Stable Diffusion 2.1 as our baseline. All experiments were conducted on a single NVIDIA GeForce RTX 4090 GPU. For further details on the experimental setup, please refer to the supplementary materials.", + "bbox": [ + 511, + 622, + 905, + 684 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compared our methodology with four baselines on image analogy generation. These methods all generate $B'$ using only an image triplet $\\{A, A', B\\}$ . Note that, some grid-image-based approaches (ImageBrush [45] and InstructGIE [23]) are also close with our works but since their code is not publicly available, we did not include them in the comparison. The implementation details for each baseline are provided in the supplementary materials.", + "bbox": [ + 511, + 700, + 906, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We randomly sample 300 instruct pairs from the InstructPix2Pix dataset to measure quantitative and qualitative results. The InstructPix2Pix dataset is structured as", + "bbox": [ + 511, + 854, + 908, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18254", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3ae2deec6e44badb40cfc94e9d0a52aa5c5f273a640ea3afa44274ebc0fbdb19.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison to baseline methods. Given inputs $A$ , $A'$ and $B$ , we generate $B'$ without utilizing any text instructions." + ], + "image_footnote": [], + "bbox": [ + 176, + 89, + 823, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "triplets in the form of {before image, after image, text instruction}. We utilized the before image and after image as $A$ and $A'$ , respectively. $B$ was randomly selected from other before images with the same text instruction. Note that we do not use the text instruction included in the dataset.", + "bbox": [ + 89, + 571, + 486, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metric. We evaluate how well the difference is reflected using the Directional score using CLIP. We also measure the directional score using DINO-v2, which offers a more refined embedding space than CLIP. Additionally, we conduct a user study to verify the perceptual suitability of our results from a human perspective. And finally, leveraging the significant advancements in large-scale vision language models (VLMs), we perform prompt engineering to enable VLMs to evaluate our tasks, as shown in the figure 5. We adopt GPT-4o [27], Qwen2-72B [41] and Llama3.2-90B [6] for VLM evaluation, and the question prompts are provided in the supplementary materials. For human evaluation, we use a four-option multiple-choice format with randomized order of the options. On the other hand, for VLM evaluation, we employ a two-option format to minimize the", + "bbox": [ + 89, + 672, + 486, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "influence of numbering and enable a more precise comparison. Further details about human and LLM evaluations are in the supplementary materials.", + "bbox": [ + 511, + 571, + 906, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Qualitative Results", + "text_level": 1, + "bbox": [ + 511, + 630, + 697, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Fig. 4, our approach qualitatively generates significantly superior images compared to existing baselines. It not only accurately reflects the transformation from $A \\rightarrow A'$ but also preserves as much information from B as possible, resulting in a plausible $B'$ . In Fig. 1, (a), (b), and (c) depict results generated using only the images $A$ , $A'$ , and $B$ without text instructions, while (d) and (e) utilize text instructions. Across all baselines, our results produce a $B'$ that best captures the before-after differences.", + "bbox": [ + 511, + 652, + 908, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3.Quantitative Results", + "text_level": 1, + "bbox": [ + 511, + 801, + 707, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Directional score. As shown in Table 1, our model achieves the best performance among image-only baselines in terms of the directional score using CLIP. Note that VISII's CLIP score is nearly comparable to ours, which is attributable to the fact that the dataset used for evalua", + "bbox": [ + 511, + 824, + 906, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18255", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/be70bd0f170965334e9179b153cc4a20ba40b33c2fdc826868881c51e0c42190.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MetricImage + TextImage only
    SDEditInstructPix2PixDIAAnalogistVISIIOurs
    CLIP (↑)0.11050.20000.02940.03980.10070.1024
    DINO-v2 (↑)0.53740.57230.51140.50980.54140.5732
    ", + "bbox": [ + 91, + 88, + 482, + 146 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/34e0383752060ffa5735e5e9718b7470480bd567bf66438f0c1d5dde17d64d88.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison with ablation studies for each proposed method. Each column shows the results when the corresponding method is not applied." + ], + "image_footnote": [], + "bbox": [ + 94, + 224, + 480, + 388 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f43d8642c0e0dcd96bf04816671689e3b7ab7dd9f4652c4e10d4895665a7ef86.jpg", + "table_caption": [ + "Table 1. Directional Score of CLIP and DINO-v2. We conducted quantitative evaluation by measuring the directional score using CLIP and DINO-v2. The directional score represents the embedding similarity between $A \\rightarrow A'$ and $B \\rightarrow B'$ ." + ], + "table_footnote": [], + "table_body": "
    ModelDIAAnalogistVISIIOurs
    Percentage (%)4%15%9%72%
    ", + "bbox": [ + 109, + 454, + 465, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion was also utilized in training VISII's backbone, InstructPix2Pix. In other words, VISII operates on a dataset it has already been trained on, whereas our model is evaluated on previously unseen data. Despite using Stable Diffusion as backbone, our model still performed exceptionally well. This gap becomes even clearer when measured with DINO-v2 [28] rather than CLIP. Furthermore, our DINO-v2 score surpasses even SDEdit and InstructPix2Pix, both of which utilize text descriptions.", + "bbox": [ + 89, + 607, + 483, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Human evaluation. Although DINO-v2 offers a better directional score compared to CLIP, it still does not fully capture how plausible $B'$ is in the $A: A' :: B: B'$ relationship. To address this, we conduct human evaluations to assess which $B'$ generated by the various baselines was the most appropriate. We asked 60 participants to select the most suitable image analogy generation result $(B')$ from four baselines, including our method. The order of models is randomly assigned for each evaluation, and the images", + "bbox": [ + 89, + 763, + 483, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2450402e4cdfbe67ec68ae1fc97c9c7e04d35aa119f1036adc5fe0a80ceac0f5.jpg", + "table_caption": [ + "Table 2. Human evaluation for image analogy generation. In each question, participants were asked which $B'$ would best complete the analogy $A: A' :: B: B'$ . We report the percentage preference for Difference Inversion over 50 images evaluated by 60 people." + ], + "table_footnote": [], + "table_body": "
    Model (vs Ours)DIAAnalogistVISII
    GPT4o [27]90%76%74%
    Qwen2-VL-72B [41]92%70%80%
    Llama-3.2-90B [6]72%60%62%
    ", + "bbox": [ + 535, + 88, + 887, + 164 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. VLM evaluation for image analogy generation. We provide the large-scale VLM with a prompt explaining the image analogy generation task and ask it to select the most suitable image for $B'$ , similar to the human evaluation (see in Sec. 5.1). The results above reflect the win rate of Difference Inversion compared to each baseline in pairwise comparisons, evaluated using 50 examples for each model (a total of 150 evaluations each).", + "bbox": [ + 511, + 174, + 906, + 272 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a4f1fd944fc9a78b743c19c4719fb7872e23dac5a158e12a660052c1dc4bb904.jpg", + "image_caption": [ + "Figure 6. Ablation results on the number of Difference tokens $(\\tilde{D})$ . The fewer $\\tilde{D}$ used, the less effectively they capture the difference information; however, using too many $\\tilde{D}$ can lead to capturing additional, unrelated information. Experimentally, we found that using a total of 5 tokens strikes the right balance." + ], + "image_footnote": [], + "bbox": [ + 517, + 287, + 903, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "used in the survey are available in the supplementary materials. As shown in Table 2, our model significantly outperforms the other three baselines in the human evaluation.", + "bbox": [ + 511, + 507, + 905, + 553 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "VLM evaluation. We also conduct evaluation with large-scale VLMs known for their strong reasoning capabilities. We leverage GPT-4o *, Qwen2-VL-72B-Instruct†, and Llama-3.2-90B-Vision‡ for evaluation, and unlike human evaluation, we employed a two-option format to compare our model against the baselines. As shown in Table 3, the preference for our model is significantly higher compared to existing baselines. This indicates that our method not only extracts the exact difference but also can generate plausible $B'$ , fulfilling the primary goal of image analogy generation.", + "bbox": [ + 511, + 571, + 906, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Further Analysis", + "text_level": 1, + "bbox": [ + 511, + 732, + 681, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study. Lastly, we performed ablation experiments on each of our proposed methods. Fig. 5 presents the ablation results for Token Consistency Loss, Delta Interpolation, Zero Initialization and CLIP loss. When Token Consistency Loss is not used, we observed significant degr", + "bbox": [ + 511, + 753, + 905, + 830 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "\\*https://chatgpt.com/ \n $\\dagger$ https://huggingface.co/Qwen/Qwen2.5-72B-Instruct \n $\\ddagger$ https://huggingface.co/metac-llama/Llama-3.2- 90B-Vision", + "bbox": [ + 511, + 838, + 903, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18256", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b9b1812ce41dd7c0e36070741d2c0da7731f8613d1ab54b363a23e33bf96987a.jpg", + "image_caption": [ + "Figure 7. Ablation results of $\\alpha$ . Since our delta ultimately needs to be optimized into text tokens, assigning a higher weight to $\\alpha$ tends to better capture the desired differences. We finally set $\\alpha$ to 0.8 for all experiments." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 480, + 198 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6447a3d65bc68f5139b527454a2994b677284e4cf6e39fdf9730a7432af85ca0.jpg", + "image_caption": [ + "Figure 8. Transferability to other Stable Diffusion models. Our Difference Inversion can also be applied to other general Stable Diffusion models, such as SDXL." + ], + "image_footnote": [], + "bbox": [ + 94, + 280, + 480, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dation in consistency with the original image (B). Without Delta Interpolation and using only Image Delta, the method fails to capture the difference effectively. Similarly, Zero Initialization of Token Embedding shows that when initialized randomly, the difference information is not properly reflected. The ablation results for the number of difference tokens and the interpolation ratio alpha are shown in Fig. 6 and 7, respectively. Additional hyperparameter search results for each method, including lambda tc and lambda clip, can be found in the supplementary materials.", + "bbox": [ + 88, + 460, + 482, + 612 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Transferability. Since our Difference Inversion is an inference-based method that does not require access to the pretrained diffusion model weights, it can be applied even if the diffusion model is provided in an API form. Though instruction inversion models such as VISII are also inference-based, they depend solely on specific models (e.g. InstructPix2Pix). We test our method on SDXL, which possesses a stronger image prior and is capable of generating more complex and refined images. Fig. 8 demonstrates the application of Difference Inversion to SDXL.", + "bbox": [ + 88, + 632, + 482, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations and Discussions", + "text_level": 1, + "bbox": [ + 89, + 799, + 349, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Failure cases. Despite the strong performance of our model across various editing tasks compared to various baselines, there are still some failure cases. In Fig. 9, it is evident that Difference Inversion struggles to capture global differences (a) or detailed differences (b). For example,", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0afe2d69e95eb88b896b63a1f7342681c00b1bd70563d74ba9055b607982f847.jpg", + "image_caption": [ + "Figure 9. Failure cases. When the difference is complex or difficult to define precisely, Difference Inversion may struggle to capture it effectively." + ], + "image_footnote": [], + "bbox": [ + 516, + 89, + 707, + 195 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5d688d164d25edded7de1406bd33e634c011b41196b12ac9048e97b46b96cfb2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 89, + 903, + 195 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "global differences (a) such as weather shifts or transformations like image-to-sketch cannot be effectively applied to $B'$ when optimized through text tokens. Similarly, for detailed differences (b), as shown in the top example of changing a boy to a crying boy, the approach may result in changing a girl to another girl or fail to accurately capture the intended crying expression altogether. In cases like adding cherries to a cake (bottom example), such changes may also be poorly reflected in B', highlighting its limitations in capturing intended variations.", + "bbox": [ + 511, + 277, + 906, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inherent limitations of the CLIP space. We hypothesize that the primary reason for the aforementioned failure cases stems from the inherent limitations of the CLIP space. Although we attempt to derive finer Delta using Image and Text Delta within the CLIP space, it does not always align well with human perception, potentially making it unstable for providing precise directional guidance. In the supplementary materials, we illustrate this using a colorization analogy on MNIST data, showing the CLIP similarity for transitions from ground truth $A \\rightarrow A'$ and $B \\rightarrow B'$ . Notably, the CLIP similarity yields only around 0.5, indicating that optimization based on this directional signal is challenging. We anticipate that future approaches may involve using more refined embedding spaces from foundation models such as DINO-v2 or learning additional mapping networks to enhance similarity and stability.", + "bbox": [ + 511, + 460, + 906, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 720, + 633, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose Difference Inversion, a model-agnostic inversion method that applies only the differences to $B'$ without introducing unwanted artifacts. Difference Inversion captures precise differences from $A$ and $A'$ and can be applied to any query image $B$ . This approach aligns well with the goal of image analogy generation, resulting in the creation of feasible $B'$ . Additionally, our method can be applied to various diffusion models, paving the way for new opportunities not only in image editing but also across diverse computer vision tasks using analogy formulations.", + "bbox": [ + 511, + 750, + 906, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18257", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgements", + "text_level": 1, + "bbox": [ + 89, + 90, + 277, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research was supported by the MSIT(Ministry of Science and ICT), Korea, under the ITRC(Information Technology Research Center) support program(IITP-2024-RS-2023-00258649, $50\\%$ ) supervised by the IITP(Institute for Information Communications Technology Planning Evaluation). This research was also supported by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No. RS-2019-II190079, Artificial Intelligence Graduate School Program(Korea University), $1\\%$ ) and the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(No. RS-2025-00562437 $40\\%$ , No. RS-2024- 00341514, $9\\%$", + "bbox": [ + 89, + 113, + 485, + 309 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 323, + 187, + 338 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Schonlieb, and Christian Etmann. Conditional image generation with score-based diffusion models. arXiv preprint arXiv:2111.13606, 2021. 2", + "[2] Tim Brooks, Aleksander Holynski, and Alexei A Efros. Instructpix2pix: Learning to follow image editing instructions. 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In Proceedings of the IEEE international conference on computer vision, pages 2223-2232, 2017. 5" + ], + "bbox": [ + 516, + 92, + 903, + 810 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18259", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Difference Inversion_ Interpolate and Isolate the Difference with Token Consistency for Image Analogy Generation/7ebc23f8-a8e8-4361-9a63-f7a091962245_model.json b/2025/Difference Inversion_ Interpolate and Isolate the Difference with Token Consistency for Image Analogy Generation/7ebc23f8-a8e8-4361-9a63-f7a091962245_model.json new file mode 100644 index 0000000000000000000000000000000000000000..75d7e410fb7761900284471616eac95c2ddbfdff --- /dev/null +++ b/2025/Difference Inversion_ Interpolate and Isolate the Difference with Token Consistency for Image Analogy Generation/7ebc23f8-a8e8-4361-9a63-f7a091962245_model.json @@ -0,0 +1,2112 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.141, + 0.093, + 0.856, + 0.138 + ], + "angle": 0, + "content": "Difference Inversion: Interpolate and Isolate the Difference with Token Consistency for Image Analogy Generation" + }, + { + "type": "text", + "bbox": [ + 0.297, + 0.165, + 0.7, + 0.185 + ], + "angle": 0, + "content": "Hyunsoo Kim\\(^{1,2}\\), Donghyun Kim\\(^{\\dagger 1}\\), Suhyun Kim\\(^{\\dagger 3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.185, + 0.788, + 0.22 + ], + "angle": 0, + "content": "\\(^{1}\\) Korea University \\(^{2}\\) Korea Institute of Science and Technology \\(^{3}\\) Kyung Hee University {climba, d.kim}@korea.ac.kr, dr.suhyun.kim@gmail.com" + }, + { + "type": "image", + "bbox": [ + 0.106, + 0.257, + 0.9, + 0.604 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.618, + 0.908, + 0.661 + ], + "angle": 0, + "content": "Figure 1. We propose Difference Inversion, a method that generates \\( B' \\) conditioned on an image triplet \\( \\{A, A', B\\} \\) that satisfies \\( A: A'::B: B' \\). Our method produces a significantly more plausible \\( B' \\) than other baselines. Note that SDEdit and InstructPix2Pix take the text instruction as input, whereas DIA, Analogist, VISII, and our Difference Inversion only use the image triplet \\( A, A', B \\) as input." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.68, + 0.327, + 0.696 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.711, + 0.484, + 0.877 + ], + "angle": 0, + "content": "How can we generate an image \\( B' \\) that satisfies \\( A: A':: B: B' \\), given the input images \\( A, A' \\) and \\( B \\)? Recent works have tackled this challenge through approaches like visual in-context learning or visual instruction. However, these methods are typically limited to specific models (e.g. InstructPix2Pix. Inpainting models) rather than general diffusion models (e.g. Stable Diffusion, SDXL). This dependency may lead to inherited biases or lower editing capabilities. In this paper, we propose Difference Inversion, a method that isolates only the difference from \\( A \\) and \\( A' \\) and applies it to \\( B \\) to generate a plausible \\( B' \\). To address model de" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.681, + 0.909, + 0.877 + ], + "angle": 0, + "content": "pendency, it is crucial to structure prompts in the form of a \"Full Prompt\" suitable for input to stable diffusion models, rather than using an \"Instruction Prompt\". To this end, we accurately extract the Difference between \\( A \\) and \\( A' \\) and combine it with the prompt of \\( B \\), enabling a plug-and-play application of the difference. To extract a precise difference, we first identify it through 1) Delta Interpolation. Additionally, to ensure accurate training, we propose the 2) Token Consistency Loss and 3) Zero Initialization of Token Embeddings. Our extensive experiments demonstrate that Difference Inversion outperforms existing baselines both quantitatively and qualitatively, indicating its ability to generate more feasible \\( B' \\) in a model-agnostic manner." + }, + { + "type": "page_footnote", + "bbox": [ + 0.116, + 0.887, + 0.259, + 0.901 + ], + "angle": 0, + "content": "†Co-corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18250" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.09, + 0.223, + 0.106 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.115, + 0.484, + 0.373 + ], + "angle": 0, + "content": "The goal of image analogy generation [39] is to create the target image \\( B' \\) based on the image triplet \\( \\{A, A', B\\} \\), ensuring that it satisfies the image analogy [12, 19] formulation \\( A: A':: B: B' \\). With the huge advancement of large-scale diffusion models [5, 7, 16, 29, 32, 34], it is natural to consider leveraging these models for solving image analogy generation from the perspective of conditional image generation. Unlike existing conditional diffusion models [1, 2, 13, 22, 26, 31] that usually take text prompts as conditions, image analogy generation assumes that only an image triplet is provided as input. For example, consider the top example in Fig. 1, where the transformation is changing a cabin into a castle. Previous conditional diffusion models ((a) and (b)) use a text instruction (i.e. \"Make the cabin a castle\") as well as \\( B \\) to generate the target image \\( B' \\). On the other hand, in image analogy generation, \\( B' \\) is generated using only the image triplet without any text prompt." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.373, + 0.484, + 0.719 + ], + "angle": 0, + "content": "Pioneered by DIA [39], several studies [10, 23, 25, 39, 45] have explored diffusion-based image analogy generation in terms of visual in-context learning or visual instruction. From the perspective of visual in-context learning, [10, 23, 45] treat the generation of \\( B' \\) as an image inpainting task, where \\( A \\), \\( A' \\), \\( B \\) and initial noise are concatenated into a grid-based input image, and \\( B' \\) is denoised from noise (see Fig. 2 (b)). This approach is limited to pretrained inpainting models and often requires manual prompt engineering by human to obtain additional text prompts. Visual Instruction Inversion (VISII, Fig. 2 (c)) [25] inverts visual instructions from \\( A \\) to \\( A' \\) using instruction tokens but is also limited to InstructPix2Pix [2]. Moreover, to efficiently optimize the visual instruction, VISII initializes the instruction tokens with image \\( A' \\), which leaves residual information from \\( A' \\) in the instruction, leading to unintended artifacts in \\( B' \\). For instance, in the fourth example of Fig. 1 (e), the transformation from \\( A \\) to \\( A' \\) involves adding a rainbow, so the desired transformation for \\( B \\) to \\( B' \\) would similarly involve adding only the rainbow. However, in the images generated by VISII, residual information from \\( A' \\) (i.e. mountains) remains, leading to unintended elements in the output." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.901 + ], + "angle": 0, + "content": "In this paper, we introduce Difference Inversion, which leverages \"Full Prompt\" with both prompt tokens representing the input image and Difference Tokens that exclusively encode difference information. Difference Tokens can focus on only the difference (Delta) between \\( A \\) and \\( A' \\) and the combined tokens are more appropriate as an input of Stable Diffusion models. This contrasts with VISII, which relies on an image-based \"Instruction Prompt\" that can only be applied as input to InstructPix2Pix. To accurately disentangle the difference, we propose Delta Interpolation to define a more precise Delta. Additionally, we introduce Token Consistency Loss, which ensures that the difference" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.089, + 0.905, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.586, + 0.188, + 0.623, + 0.198 + ], + "angle": 0, + "content": "(a) DIA" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.199, + 0.697, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.587, + 0.283, + 0.63, + 0.294 + ], + "angle": 0, + "content": "(c) VISII" + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.199, + 0.896, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.283, + 0.825, + 0.293 + ], + "angle": 0, + "content": "(d) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.305, + 0.907, + 0.389 + ], + "angle": 0, + "content": "Figure 2. Architectural comparison of image analogy generation baselines. We compare our approach with three baseline methods: (a) DIA, (b) Analogist, and (c) VISII. Detailed descriptions can be found in Sec. 2. It is noteworthy that, unlike (b) and (c), which each depend on specific models, our method can be applied to general stable diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.416, + 0.905, + 0.537 + ], + "angle": 0, + "content": "information emerges when the token is present and disappears when it is absent. By using Token Consistency Loss, the Difference Tokens trained on the Interpolated Delta can be seamlessly concatenated with any query image prompt, enabling their use without introducing unwanted artifacts. Finally, we zero-initialize the Difference Tokens to ensure stable optimization of the differences and to reduce bias by preventing any initial preference from being introduced." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.538, + 0.872, + 0.552 + ], + "angle": 0, + "content": "The main contributions of our paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.553, + 0.905, + 0.611 + ], + "angle": 0, + "content": "- We propose Difference Inversion, which inverts precise differences into Difference Tokens and applies them to any query \\( B \\) to generate \\( B' \\) within general stable diffusion frameworks." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.613, + 0.905, + 0.702 + ], + "angle": 0, + "content": "- To extract the exact difference between images \\( A \\) and \\( A' \\), we additionally introduce a Delta Interpolation, Token Consistency Loss and Zero-Initialization of Token Embeddings. These ensures that the extracted differences contain only the intended modifications, free from unwanted artifacts." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.704, + 0.905, + 0.763 + ], + "angle": 0, + "content": "- Our extensive experiments demonstrate that Difference Inversion outperforms existing baselines both quantitatively and qualitatively, as well as in human and large-scale Vision Language Models (VLMs) evaluations." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.553, + 0.905, + 0.763 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.778, + 0.66, + 0.793 + ], + "angle": 0, + "content": "2. Related works" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.905, + 0.833 + ], + "angle": 0, + "content": "2.1. Image Analogy Generation via Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.901 + ], + "angle": 0, + "content": "The goal of image analogy generation [10, 23, 25, 39, 45] is to produce \\( B' \\) by conditioning on \\( A \\), \\( A' \\) and \\( B \\) in the form of \\( A: A' :: B: B' \\). DIA [39] attempts to invert images to obtain conditioning matrices for diffusion, enabling high-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18251" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.905, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.173, + 0.285, + 0.43, + 0.299 + ], + "angle": 0, + "content": "(a) Overall Pipeline of Difference Inversion" + }, + { + "type": "image_caption", + "bbox": [ + 0.579, + 0.285, + 0.804, + 0.299 + ], + "angle": 0, + "content": "(b) Visualization of Interpolated Delta" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.313, + 0.907, + 0.37 + ], + "angle": 0, + "content": "Figure 3. Overall pipeline of Difference Inversion. Given an image triplet \\(\\{A, A', B\\}\\), Difference Inversion extracts the difference between \\(A\\) and \\(A'\\) using DIFF tokens. The Difference is estimated as the Interpolated Delta, computed between \\(A\\) and \\(A'\\) by applying Spherical Linear Interpolation (Slerp) on the Image Delta and Text Delta, effectively capturing both visual and semantic information. The circled numbers in the figure correspond to the steps outlined in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.397, + 0.485, + 0.804 + ], + "angle": 0, + "content": "level analogy through semantic vector operations. However it fails to capture not only the desired editing changes but also the detailed image information accurately. Starting with ImageBrush [45], several studies combined \\( A, A', B \\), and \\( B' \\) into a single grid-formatted image and used a pretrained inpainting model to denoise the \\( B' \\) section from noise, generating a plausible image for \\( B' \\). However, relying solely on a pretrained inpainting model makes it challenging to generate a plausible \\( B' \\). Leveraging the knowledge of large language models (LLMs) or large-scale vision language model (VLMs) is often necessary, which consequently requires cumbersome prompt engineering. In a different approach, VISII [25] achieves \\( A \\rightarrow A' \\) transformations by inverting visual instructions into text tokens and applying them to query image (e.g. \\( B \\)) without relying on an VLMs. However, this process leaves unwanted information from \\( A \\) and \\( A' \\) in \\( B' \\). As a result, \\( B' \\) may be generated in an unintended direction as shown in Fig. 1 (c). Additionally, since the inverted instruction can only be used with InstructPix2Pix [2], it is challenging to apply this method to various Stable Diffusion models, resulting in low generalizability. In this paper, we introduce Difference Inversion that precisely extracts only the difference between \\( A \\) and \\( A' \\) and applies it to \\( B \\), avoiding unintended artifacts. Furthermore, since it forms a Full Prompt rather than an Instruction Prompt, it can be applied to a wide range of Stable Diffusion models." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.817, + 0.325, + 0.832 + ], + "angle": 0, + "content": "2.2. Diffusion based Inversion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.485, + 0.902 + ], + "angle": 0, + "content": "In the wide range of diffusion-based conditional generation methods, DDIM Inversion [24, 37], which identifies the initial noise corresponding to a given image, serves as a core component. Once the initial noise is identified by inver" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.396, + 0.908, + 0.637 + ], + "angle": 0, + "content": "sion, it is well-known that better results can be generated from the inverted noise when applied to personalized editing [9, 17, 40] or image-to-image translation [4, 11]. Alongside this trend, DreamBooth [33] and Textual Inversion [8] focus on optimizing special text tokens to learn representations that capture personalized information. ReVersion [15] also optimizes specific text prompts to capture and represent the relationship between two images. These inversion methods utilize a soft prompt approach, optimizing continuous embeddings. In contrast, PEZ [42] proposes hard prompt optimization to generate interpretable prompts that effectively capture the concept of a specific image. Similarly, our work optimizes Difference Tokens in a hard prompt manner, making them plug-and-play with other prompts, thereby enhancing their suitability for general Stable Diffusion models." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.659, + 0.655, + 0.674 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.687, + 0.909, + 0.87 + ], + "angle": 0, + "content": "Denoising diffusion models [14, 36] are generative models that learn the reversal of the forward process using denoising autoencoders, enabling the iterative sampling of images from noise. In the early stages of diffusion models [5, 14, 38], the forward and reverse diffusion process operates directly in the pixel space. Latent diffusion models [32], also well known as Stable Diffusion, performs this process in latent space, enabling more efficient image generation. Given an input image \\( x \\) and a text condition \\( y \\), the image encoder transforms \\( x \\) into \\( z_0 \\). The denoising model \\( \\epsilon_{\\theta} \\) is then trained to predict a denoised version of its input \\( z_t \\), as shown in the following equation." + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.885, + 0.907, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathbb {E} _ {\\mathcal {E} (x), y, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\| \\epsilon - \\epsilon_ {\\theta} \\left(z _ {t}, t, \\tau_ {\\theta} (y)\\right) \\| _ {2} ^ {2} \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18252" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "where \\( z_{t} \\) is a noisy variant of the original input \\( z_{0} \\) in time \\( t \\) and \\( \\tau_{\\theta} \\) is text encoder. Since Stable Diffusion accepts text prompts as input, there have been attempts to add special tokens to text prompts for tasks such as personalized editing. Textual Inversion [8], for example, learns to capture specific concepts or objects using special token \\( (s_{*}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.183, + 0.484, + 0.364 + ], + "angle": 0, + "content": "Similarly, VISII (Fig. 2 (c)) also utilizes instruction tokens \\( C_T \\) to learn the instruction information necessary for generating \\( B' \\). Since VISII needs to learn the transformation instruction from image \\( A \\) to \\( A' \\) and apply them to \\( B \\), it leverages InstructPix2Pix [2]. Furthermore, to better capture the transformation, \\( C_T \\) is initialized via discrete token optimization (PEZ [42]) on the image \\( A' \\). Since VISII relies on InstructPix2Pix, it learns \\( C_T \\) in the form of an instruction prompt. In contrast, our Difference Inversion isolates only the difference information, enabling a plug-and-play approach with general stable diffusion prompts. Further details will be provided in the following section." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.378, + 0.182, + 0.393 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.403, + 0.484, + 0.541 + ], + "angle": 0, + "content": "Given an image triplet \\(\\{A, A', B\\}\\), our goal is to extract the difference between \\((A, A')\\) and apply it to \\(B\\). To capture the difference, we optimize DIFF tokens \\((\\tilde{D})\\) to effectively encode the extracted differences. We first introduce the basic concept of Difference Inversion in Sec. 4.1. In Sec. 4.2, we explain how we optimize the DIFF token using the Interpolated Delta. Then, in Sec. 4.3, we present the token consistency loss to enhance image consistency, followed by an introduction to token embedding initialization in Sec. 4.4." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.55, + 0.284, + 0.565 + ], + "angle": 0, + "content": "4.1. Difference Inversion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.572, + 0.484, + 0.678 + ], + "angle": 0, + "content": "We start from the key observation in VISII, which is the similar concept with our work. As shown in Fig. 1 (e), generating \\( B' \\) with VISII results in unwanted artifacts. This occurs because the optimized visual instruction contains not only the difference (e.g. rainbow) but also information specific to \\( A \\) and \\( A' \\) (e.g. mountains). Therefore, the key is to enable the inversion of only the precise difference." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.678, + 0.484, + 0.754 + ], + "angle": 0, + "content": "In this paper, we define the difference as \"Delta,\" which can be obtained as the difference between embedding vectors from the CLIP [30] encoder \\(\\mathcal{E}_I\\). Letting the CLIP image encoder be represented by \\(\\mathcal{E}_I\\), the Image Delta \\(\\mathcal{D}_{img}\\) can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.766, + 0.483, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {i m g} = \\mathcal {E} _ {I} (A _ {i m g} ^ {\\prime}) - \\mathcal {E} _ {I} (A _ {i m g}) \\qquad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.901 + ], + "angle": 0, + "content": "To optimize DIFF tokens, we first initialize the text prompts of \\( A \\) and \\( A' \\) using PEZ. This step aims to fully anchoring the prompt of \\( A \\) (or \\( A' \\)) and isolate the only difference, enabling more precise extraction of the difference with the DIFF token in place. As shown in Fig. 3 (a), we only optimize DIFF tokens while optimized prompt embedding is frozen. Note that while optimization with PEZ can" + }, + { + "type": "code_caption", + "bbox": [ + 0.516, + 0.092, + 0.742, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Difference Inversion" + }, + { + "type": "algorithm", + "bbox": [ + 0.52, + 0.11, + 0.905, + 0.601 + ], + "angle": 0, + "content": "Require: pretrained denoising model \\(\\epsilon_{\\theta}\\) ; Image encoder \\(\\mathcal{E}\\) ; CLIP Image, Text Encoder \\(\\mathcal{E}_I\\) \\(\\mathcal{E}_T\\) ; Captioning model BLIP2; interpolation rate \\(\\alpha\\) ; Learning rate \\(\\gamma\\) \\(t_{before}, t_{after} \\sim \\mathcal{U}(0,T)\\) . \\(\\epsilon_{before}, \\epsilon_{after} \\sim \\mathcal{N}(0,1)\\) . Input: Image pair \\(\\{A, A'\\}\\) \nOutput: Difference Tokens \\(\\tilde{D} = \\{D_1^*, \\dots, D_n^*\\}\\) \n// Extract the caption of \\(A\\) and \\(A'\\) .. \\(①\\) \n\\(cap_A = \\mathrm{BLIP2}(A)\\) . \\(cap_{A'} = \\mathrm{BLIP2}(A')\\) \n// Calculate Image Delta \\(\\mathcal{D}_I\\) and Text Delta \\(\\mathcal{D}_T\\) \n\\(\\mathcal{D}_I = \\mathcal{E}_I(A') - \\mathcal{E}_I(A)\\) . \\(\\mathcal{D}_T = \\mathcal{E}_T(cap_{A'}) - \\mathcal{E}_{txt}(cap_A)\\) \n// Calculate Interpolated Delta \\(D_{inter}\\) ... \\(②\\) \n\\(\\mathcal{D}_{inter} = Slerp(\\mathcal{D}_I,\\mathcal{D}_T,\\alpha)\\) \n// Optimize the prompt w.r.t. \\(A\\) and \\(A'\\) .. \\(③\\) \nprompt \\(A = \\mathrm{PEZ}(A)\\) . prompt \\(A' = \\mathrm{PEZ}(A')\\) \nEncode \\(z_A = \\mathcal{E}(A)\\) . \\(z_{A'} = \\mathcal{E}(A')\\) \n// Zero-Initialization token embeddings ... \\(④\\) \nInitialize \\(\\tilde{D}\\) with Zero embeddings \nfor \\(i = 1\\) to \\(N\\) do \n// Prepare noisy latents \\(z_A\\) and \\(z_{A'}\\) .. \\(⑤\\) \n\\(z_{A_t} \\gets\\) add \\(\\epsilon_{before}\\) to \\(z_A\\) at timestep \\(t_{before}\\) \n\\(z_{A'_t} \\gets\\) add \\(\\epsilon_{after}\\) to \\(z_{A'}\\) at timestep \\(t_{after}\\) \n// Predict each noise \\(\\hat{\\epsilon}_{before}, \\hat{\\epsilon}_{after}\\) \n\\(\\hat{\\epsilon}_{before} = \\epsilon_{\\theta}(z_{A_t}, t_{before}, \\{prompt_{A'}, -\\tilde{D}\\})\\) \n\\(\\hat{\\epsilon}_{after} = \\epsilon_{\\theta}(z_{A'_t}, t_{after}, \\{prompt_A, \\tilde{D}\\})\\) \n// Compute Token Consistency loss ... \\(⑥\\) \n\\(\\mathcal{L}_{tc} = \\| \\epsilon_{before} - \\hat{\\epsilon}_{before} \\|_2 + \\| \\epsilon_{after} - \\hat{\\epsilon}_{after} \\|_2\\) \n// Compute Clip loss \\(\\mathcal{L}_{clip}\\) ... \\(⑦\\) \n\\(\\mathcal{L}_{clip} = \\cosine(\\tilde{D},\\mathcal{D}_{inter})\\) \n\\(\\mathcal{L} = \\lambda_{tc} * \\mathcal{L}_{tc} + \\lambda_{clip} * \\mathcal{L}_{clip}\\) \nUpdate \\(\\tilde{D} = \\tilde{D} -\\gamma \\nabla L\\) \nend for \nReturn: \\(\\tilde{D}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.628, + 0.905, + 0.673 + ], + "angle": 0, + "content": "be time-consuming, it can be replaced with text captions generated by BLIP2 [18], trading off a slight performance drop for faster processing (Sec. 4.3)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.907, + 0.809 + ], + "angle": 0, + "content": "However, simply optimizing the DIFF token only with the Image Delta did not sufficiently capture the Difference information. As shown in Fig. 3 (b), \\( B' \\) with the Image Delta retains much of the original image's cabin features rather than fully transforming into the intended castle. We hypothesize that this is because the CLIP embedding space may not fully represent the intricate details of the images. In the following section, we introduce Delta Interpolation to extract a more refined difference." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.819, + 0.698, + 0.835 + ], + "angle": 0, + "content": "4.2. Delta Interpolation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Although the Image Delta effectively captures the visual difference, it still fails to fully reflect the specific semantic differences. To obtain more detailed semantic information, we use an image captioning model to extract cap" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18253" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.184 + ], + "angle": 0, + "content": "tions for each of the images \\( A \\) and \\( A' \\). We utilize BLIP2, but for more detailed captions, BLIP3 [44] or large-scale VLMs [3, 20, 21] can be also be considered. The extracted captions contain more specific details, such as \"cabin\" and \"castle,\" which were used to derive the Text Delta \\( D_{txt} \\) that contains more semantic information than Image Delta." + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.192, + 0.483, + 0.21 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {t x t} = \\mathcal {E} _ {T} \\left(A _ {t x t} ^ {\\prime}\\right) - \\mathcal {E} _ {T} \\left(A _ {t x t}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.219, + 0.303, + 0.233 + ], + "angle": 0, + "content": "where \\(\\mathcal{E}_T\\) is CLIP text encoder." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.234, + 0.485, + 0.356 + ], + "angle": 0, + "content": "After obtaining both Image and Text Delta of \\( A \\) and \\( A' \\) with CLIP, we apply Spherical Linear Interpolation (Slerp) [35] to integrate both embeddings. Since CLIP learns image-text pairs to maximize their cosine similarity, we hypothesize that it would be possible to find a more refined Delta within the joint hypersphere of the CLIP space. Therefore, to identify the Interpolated Delta \\( D_{inter} \\) on this hypersphere, we apply Slerp shown below." + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.365, + 0.483, + 0.417 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {D} _ {\\text {i n t e r}} = \\operatorname {S l e r p} \\left(\\mathcal {D} _ {\\text {i m g}}, \\mathcal {D} _ {\\text {t x t}}; \\alpha\\right) (4) \\\\ = \\frac {\\sin ((1 - \\alpha) \\theta)}{\\sin (\\theta)} \\mathcal {D} _ {i m g} + \\frac {\\sin (\\alpha \\theta)}{\\sin (\\theta)} \\mathcal {D} _ {t x t} (5) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.425, + 0.483, + 0.455 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is interpolation ratio between Image and Text Delta. We set \\(\\alpha\\) to 0.8, and the ablation results are in Fig. 7." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.455, + 0.484, + 0.486 + ], + "angle": 0, + "content": "Finally, we optimize the DIFF token to minimize cosine distance with this Interpolated Delta as:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.495, + 0.483, + 0.513 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c l i p}} = \\operatorname {c o s i n e} (\\tilde {D}, \\mathcal {D} _ {\\text {i n t e r}}) \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.521, + 0.313, + 0.538 + ], + "angle": 0, + "content": "4.3. Token Consistency Loss" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.543, + 0.484, + 0.709 + ], + "angle": 0, + "content": "Using only the Interpolated Delta \\(\\mathcal{D}_{inter}\\) may resemble obtaining a visual instruction from \\(A\\) to \\(A^{\\prime}\\). However, in Difference Inversion, it is also important to preserve aspects that should remain unchanged when generating \\(B^{\\prime}\\). To achieve this, it is essential to accurately extract only the bidirectional difference between \\(A\\) and \\(A^{\\prime}\\). Visual instruction considers only the transformation from \\(A\\rightarrow A^{\\prime}\\), whereas the difference must account for both \\(A\\to A^{\\prime}\\) and \\(A^{\\prime}\\to A\\). For DIFF tokens \\((\\tilde{D})\\), this implies that when \\(\\tilde{D}\\) is present, the result should correspond to \\(A^{\\prime}\\); otherwise, it should yield \\(A\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.71, + 0.484, + 0.859 + ], + "angle": 0, + "content": "Additionally, maintaining consistency in elements we do not intend to modify during this process is necessary. Inspired by Cycle Consistency Loss [43, 47], we introduce Token Consistency Loss, which ensures that \\( A' \\) is generated when \\( \\tilde{D} \\) is present and \\( A \\) when \\( \\tilde{D} \\) is absent. Specifically, the prompt concatenated with prompt \\( A \\) and \\( \\tilde{D} \\) should accurately reconstruct image \\( A \\), while the prompt concatenated with prompt \\( A' \\) and \\( -\\tilde{D} \\) (reverse direction of \\( \\tilde{D} \\)) should accurately reconstruct image \\( A' \\). This can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.869, + 0.499, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m s e _ {b e f o r e}} = \\left\\| \\epsilon_ {b e f o r e} - \\epsilon_ {\\theta} \\left(z _ {A _ {t}}, t _ {b e f o r e}, \\{p r o m p t _ {A ^ {\\prime}}, - \\tilde {D} \\}\\right) \\right\\| _ {2} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.117, + 0.905, + 0.149 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m s e _ {a f t e r}} = \\left\\| \\epsilon_ {a f t e r} - \\epsilon_ {\\theta} \\left(z _ {A _ {t} ^ {\\prime}}, t _ {a f t e r}, \\{p r o m p t _ {A}, \\tilde {D} \\}\\right) \\right\\| _ {2} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.149, + 0.728, + 0.165 + ], + "angle": 0, + "content": "where \\(t_{before}, t_{after} \\sim N(0,1)\\)" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.165, + 0.836, + 0.179 + ], + "angle": 0, + "content": "The Token Consistency loss can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.191, + 0.905, + 0.209 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t c} = \\mathcal {L} _ {m s e _ {\\text {b e f o r e}}} + \\mathcal {L} _ {m s e _ {\\text {a f t e r}}} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.22, + 0.905, + 0.251 + ], + "angle": 0, + "content": "Finally, to optimize the DIFF tokens \\(\\tilde{D}\\), we utilized the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.263, + 0.905, + 0.28 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {t c} * \\mathcal {L} _ {t c} + \\lambda_ {c l i p} * \\mathcal {L} _ {c l i p} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.29, + 0.905, + 0.322 + ], + "angle": 0, + "content": "where \\(\\lambda_{tc}\\) and \\(\\lambda_{tc}\\) denotes weight parameter of each loss, respectively. We empirically set \\(\\lambda_{tc}\\) to 0.01 and \\(\\lambda_{clip}\\) to 6." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.33, + 0.864, + 0.346 + ], + "angle": 0, + "content": "4.4. Zero-Initialization of Token Embeddings" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.351, + 0.907, + 0.564 + ], + "angle": 0, + "content": "Thus far, we have discussed the optimization process for the DIFF tokens \\((\\tilde{D})\\). Finally, we address the approach for initializing \\(\\tilde{D}\\). It is crucial for the \\(\\tilde{D}\\) to capture accurate differences, making it essential to effectively disentangle the original image information from the difference. From this perspective, randomly initializing the \\(\\tilde{D}\\) can lead to unintended information being embedded within \\(\\tilde{D}\\) (see Config. C in Fig. 5). Motivated by ContorlNet [46], we initialize the token embeddings with zero to ensure that only the intended differences are captured within the \\(\\tilde{D}\\), minimizing unwanted artifacts. By initializing all \\(\\tilde{D}\\) to zero, we ensure that each token robustly encapsulates only the distinguishing differences from the original image. Detailed experimental results are presented in Sec. 5." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.576, + 0.649, + 0.594 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.601, + 0.868, + 0.617 + ], + "angle": 0, + "content": "5.1. Experimental and Implementation Detail" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.623, + 0.906, + 0.685 + ], + "angle": 0, + "content": "We used Stable Diffusion 2.1 as our baseline. All experiments were conducted on a single NVIDIA GeForce RTX 4090 GPU. For further details on the experimental setup, please refer to the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.701, + 0.907, + 0.837 + ], + "angle": 0, + "content": "Baselines. We compared our methodology with four baselines on image analogy generation. These methods all generate \\( B' \\) using only an image triplet \\( \\{A, A', B\\} \\). Note that, some grid-image-based approaches (ImageBrush [45] and InstructGIE [23]) are also close with our works but since their code is not publicly available, we did not include them in the comparison. The implementation details for each baseline are provided in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Dataset. We randomly sample 300 instruct pairs from the InstructPix2Pix dataset to measure quantitative and qualitative results. The InstructPix2Pix dataset is structured as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18254" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.178, + 0.09, + 0.825, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.531, + 0.907, + 0.547 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison to baseline methods. Given inputs \\( A \\), \\( A' \\) and \\( B \\), we generate \\( B' \\) without utilizing any text instructions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.573, + 0.487, + 0.649 + ], + "angle": 0, + "content": "triplets in the form of {before image, after image, text instruction}. We utilized the before image and after image as \\( A \\) and \\( A' \\), respectively. \\( B \\) was randomly selected from other before images with the same text instruction. Note that we do not use the text instruction included in the dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.674, + 0.487, + 0.903 + ], + "angle": 0, + "content": "Evaluation Metric. We evaluate how well the difference is reflected using the Directional score using CLIP. We also measure the directional score using DINO-v2, which offers a more refined embedding space than CLIP. Additionally, we conduct a user study to verify the perceptual suitability of our results from a human perspective. And finally, leveraging the significant advancements in large-scale vision language models (VLMs), we perform prompt engineering to enable VLMs to evaluate our tasks, as shown in the figure 5. We adopt GPT-4o [27], Qwen2-72B [41] and Llama3.2-90B [6] for VLM evaluation, and the question prompts are provided in the supplementary materials. For human evaluation, we use a four-option multiple-choice format with randomized order of the options. On the other hand, for VLM evaluation, we employ a two-option format to minimize the" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.573, + 0.907, + 0.618 + ], + "angle": 0, + "content": "influence of numbering and enable a more precise comparison. Further details about human and LLM evaluations are in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.631, + 0.698, + 0.646 + ], + "angle": 0, + "content": "5.2. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.654, + 0.909, + 0.79 + ], + "angle": 0, + "content": "As shown in Fig. 4, our approach qualitatively generates significantly superior images compared to existing baselines. It not only accurately reflects the transformation from \\( A \\rightarrow A' \\) but also preserves as much information from B as possible, resulting in a plausible \\( B' \\). In Fig. 1, (a), (b), and (c) depict results generated using only the images \\( A \\), \\( A' \\), and \\( B \\) without text instructions, while (d) and (e) utilize text instructions. Across all baselines, our results produce a \\( B' \\) that best captures the before-after differences." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.803, + 0.709, + 0.818 + ], + "angle": 0, + "content": "5.3.Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.908, + 0.9 + ], + "angle": 0, + "content": "Directional score. As shown in Table 1, our model achieves the best performance among image-only baselines in terms of the directional score using CLIP. Note that VISII's CLIP score is nearly comparable to ours, which is attributable to the fact that the dataset used for evalua" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18255" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.483, + 0.147 + ], + "angle": 0, + "content": "
    MetricImage + TextImage only
    SDEditInstructPix2PixDIAAnalogistVISIIOurs
    CLIP (↑)0.11050.20000.02940.03980.10070.1024
    DINO-v2 (↑)0.53740.57230.51140.50980.54140.5732
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.156, + 0.483, + 0.213 + ], + "angle": 0, + "content": "Table 1. Directional Score of CLIP and DINO-v2. We conducted quantitative evaluation by measuring the directional score using CLIP and DINO-v2. The directional score represents the embedding similarity between \\( A \\rightarrow A' \\) and \\( B \\rightarrow B' \\)." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.226, + 0.482, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.398, + 0.483, + 0.44 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison with ablation studies for each proposed method. Each column shows the results when the corresponding method is not applied." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.455, + 0.466, + 0.5 + ], + "angle": 0, + "content": "
    ModelDIAAnalogistVISIIOurs
    Percentage (%)4%15%9%72%
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.51, + 0.484, + 0.581 + ], + "angle": 0, + "content": "Table 2. Human evaluation for image analogy generation. In each question, participants were asked which \\( B' \\) would best complete the analogy \\( A: A' :: B: B' \\). We report the percentage preference for Difference Inversion over 50 images evaluated by 60 people." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.608, + 0.484, + 0.745 + ], + "angle": 0, + "content": "tion was also utilized in training VISII's backbone, InstructPix2Pix. In other words, VISII operates on a dataset it has already been trained on, whereas our model is evaluated on previously unseen data. Despite using Stable Diffusion as backbone, our model still performed exceptionally well. This gap becomes even clearer when measured with DINO-v2 [28] rather than CLIP. Furthermore, our DINO-v2 score surpasses even SDEdit and InstructPix2Pix, both of which utilize text descriptions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Human evaluation. Although DINO-v2 offers a better directional score compared to CLIP, it still does not fully capture how plausible \\( B' \\) is in the \\( A: A' :: B: B' \\) relationship. To address this, we conduct human evaluations to assess which \\( B' \\) generated by the various baselines was the most appropriate. We asked 60 participants to select the most suitable image analogy generation result \\( (B') \\) from four baselines, including our method. The order of models is randomly assigned for each evaluation, and the images" + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.089, + 0.888, + 0.165 + ], + "angle": 0, + "content": "
    Model (vs Ours)DIAAnalogistVISII
    GPT4o [27]90%76%74%
    Qwen2-VL-72B [41]92%70%80%
    Llama-3.2-90B [6]72%60%62%
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.175, + 0.907, + 0.273 + ], + "angle": 0, + "content": "Table 3. VLM evaluation for image analogy generation. We provide the large-scale VLM with a prompt explaining the image analogy generation task and ask it to select the most suitable image for \\( B' \\), similar to the human evaluation (see in Sec. 5.1). The results above reflect the win rate of Difference Inversion compared to each baseline in pairwise comparisons, evaluated using 50 examples for each model (a total of 150 evaluations each)." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.288, + 0.905, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.412, + 0.907, + 0.482 + ], + "angle": 0, + "content": "Figure 6. Ablation results on the number of Difference tokens \\((\\tilde{D})\\). The fewer \\(\\tilde{D}\\) used, the less effectively they capture the difference information; however, using too many \\(\\tilde{D}\\) can lead to capturing additional, unrelated information. Experimentally, we found that using a total of 5 tokens strikes the right balance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.508, + 0.906, + 0.554 + ], + "angle": 0, + "content": "used in the survey are available in the supplementary materials. As shown in Table 2, our model significantly outperforms the other three baselines in the human evaluation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.572, + 0.907, + 0.725 + ], + "angle": 0, + "content": "VLM evaluation. We also conduct evaluation with large-scale VLMs known for their strong reasoning capabilities. We leverage GPT-4o *, Qwen2-VL-72B-Instruct†, and Llama-3.2-90B-Vision‡ for evaluation, and unlike human evaluation, we employed a two-option format to compare our model against the baselines. As shown in Table 3, the preference for our model is significantly higher compared to existing baselines. This indicates that our method not only extracts the exact difference but also can generate plausible \\( B' \\), fulfilling the primary goal of image analogy generation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.733, + 0.682, + 0.749 + ], + "angle": 0, + "content": "5.4. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.754, + 0.906, + 0.831 + ], + "angle": 0, + "content": "Ablation study. Lastly, we performed ablation experiments on each of our proposed methods. Fig. 5 presents the ablation results for Token Consistency Loss, Delta Interpolation, Zero Initialization and CLIP loss. When Token Consistency Loss is not used, we observed significant degr" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.839, + 0.905, + 0.9 + ], + "angle": 0, + "content": "\\*https://chatgpt.com/ \n\\(\\dagger\\) https://huggingface.co/Qwen/Qwen2.5-72B-Instruct \n\\(\\ddagger\\) https://huggingface.co/metac-llama/Llama-3.2- 90B-Vision" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18256" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.482, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.21, + 0.483, + 0.267 + ], + "angle": 0, + "content": "Figure 7. Ablation results of \\(\\alpha\\). Since our delta ultimately needs to be optimized into text tokens, assigning a higher weight to \\(\\alpha\\) tends to better capture the desired differences. We finally set \\(\\alpha\\) to 0.8 for all experiments." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.281, + 0.481, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.391, + 0.483, + 0.434 + ], + "angle": 0, + "content": "Figure 8. Transferability to other Stable Diffusion models. Our Difference Inversion can also be applied to other general Stable Diffusion models, such as SDXL." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.461, + 0.483, + 0.613 + ], + "angle": 0, + "content": "dation in consistency with the original image (B). Without Delta Interpolation and using only Image Delta, the method fails to capture the difference effectively. Similarly, Zero Initialization of Token Embedding shows that when initialized randomly, the difference information is not properly reflected. The ablation results for the number of difference tokens and the interpolation ratio alpha are shown in Fig. 6 and 7, respectively. Additional hyperparameter search results for each method, including lambda tc and lambda clip, can be found in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.633, + 0.483, + 0.784 + ], + "angle": 0, + "content": "Transferability. Since our Difference Inversion is an inference-based method that does not require access to the pretrained diffusion model weights, it can be applied even if the diffusion model is provided in an API form. Though instruction inversion models such as VISII are also inference-based, they depend solely on specific models (e.g. InstructPix2Pix). We test our method on SDXL, which possesses a stronger image prior and is capable of generating more complex and refined images. Fig. 8 demonstrates the application of Difference Inversion to SDXL." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.8, + 0.35, + 0.815 + ], + "angle": 0, + "content": "6. Limitations and Discussions" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Failure cases. Despite the strong performance of our model across various editing tasks compared to various baselines, there are still some failure cases. In Fig. 9, it is evident that Difference Inversion struggles to capture global differences (a) or detailed differences (b). For example," + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.09, + 0.708, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.714, + 0.09, + 0.905, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.206, + 0.905, + 0.248 + ], + "angle": 0, + "content": "Figure 9. Failure cases. When the difference is complex or difficult to define precisely, Difference Inversion may struggle to capture it effectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.279, + 0.907, + 0.43 + ], + "angle": 0, + "content": "global differences (a) such as weather shifts or transformations like image-to-sketch cannot be effectively applied to \\( B' \\) when optimized through text tokens. Similarly, for detailed differences (b), as shown in the top example of changing a boy to a crying boy, the approach may result in changing a girl to another girl or fail to accurately capture the intended crying expression altogether. In cases like adding cherries to a cake (bottom example), such changes may also be poorly reflected in B', highlighting its limitations in capturing intended variations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.461, + 0.907, + 0.703 + ], + "angle": 0, + "content": "Inherent limitations of the CLIP space. We hypothesize that the primary reason for the aforementioned failure cases stems from the inherent limitations of the CLIP space. Although we attempt to derive finer Delta using Image and Text Delta within the CLIP space, it does not always align well with human perception, potentially making it unstable for providing precise directional guidance. In the supplementary materials, we illustrate this using a colorization analogy on MNIST data, showing the CLIP similarity for transitions from ground truth \\( A \\rightarrow A' \\) and \\( B \\rightarrow B' \\). Notably, the CLIP similarity yields only around 0.5, indicating that optimization based on this directional signal is challenging. We anticipate that future approaches may involve using more refined embedding spaces from foundation models such as DINO-v2 or learning additional mapping networks to enhance similarity and stability." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.722, + 0.634, + 0.739 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose Difference Inversion, a model-agnostic inversion method that applies only the differences to \\( B' \\) without introducing unwanted artifacts. Difference Inversion captures precise differences from \\( A \\) and \\( A' \\) and can be applied to any query image \\( B \\). This approach aligns well with the goal of image analogy generation, resulting in the creation of feasible \\( B' \\). Additionally, our method can be applied to various diffusion models, paving the way for new opportunities not only in image editing but also across diverse computer vision tasks using analogy formulations." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18257" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.279, + 0.108 + ], + "angle": 0, + "content": "8. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.114, + 0.486, + 0.31 + ], + "angle": 0, + "content": "This research was supported by the MSIT(Ministry of Science and ICT), Korea, under the ITRC(Information Technology Research Center) support program(IITP-2024-RS-2023-00258649, \\(50\\%\\) ) supervised by the IITP(Institute for Information Communications Technology Planning Evaluation). This research was also supported by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No. RS-2019-II190079, Artificial Intelligence Graduate School Program(Korea University), \\(1\\%\\) ) and the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(No. RS-2025-00562437 \\(40\\%\\) , No. RS-2024- 00341514, \\(9\\%\\)" + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.324, + 0.188, + 0.339 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.348, + 0.484, + 0.404 + ], + "angle": 0, + "content": "[1] Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Schonlieb, and Christian Etmann. 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We propose Difference Inversion, a method that generates $B'$ conditioned on an image triplet $\{A, A', B\}$ that satisfies $A: A'::B: B'$ . Our method produces a significantly more plausible $B'$ than other baselines. Note that SDEdit and InstructPix2Pix take the text instruction as input, whereas DIA, Analogist, VISII, and our Difference Inversion only use the image triplet $A, A', B$ as input. + +# Abstract + +How can we generate an image $B'$ that satisfies $A: A':: B: B'$ , given the input images $A, A'$ and $B$ ? Recent works have tackled this challenge through approaches like visual in-context learning or visual instruction. However, these methods are typically limited to specific models (e.g. InstructPix2Pix. Inpainting models) rather than general diffusion models (e.g. Stable Diffusion, SDXL). This dependency may lead to inherited biases or lower editing capabilities. In this paper, we propose Difference Inversion, a method that isolates only the difference from $A$ and $A'$ and applies it to $B$ to generate a plausible $B'$ . To address model de + +pendency, it is crucial to structure prompts in the form of a "Full Prompt" suitable for input to stable diffusion models, rather than using an "Instruction Prompt". To this end, we accurately extract the Difference between $A$ and $A'$ and combine it with the prompt of $B$ , enabling a plug-and-play application of the difference. To extract a precise difference, we first identify it through 1) Delta Interpolation. Additionally, to ensure accurate training, we propose the 2) Token Consistency Loss and 3) Zero Initialization of Token Embeddings. Our extensive experiments demonstrate that Difference Inversion outperforms existing baselines both quantitatively and qualitatively, indicating its ability to generate more feasible $B'$ in a model-agnostic manner. + +# 1. Introduction + +The goal of image analogy generation [39] is to create the target image $B'$ based on the image triplet $\{A, A', B\}$ , ensuring that it satisfies the image analogy [12, 19] formulation $A: A':: B: B'$ . With the huge advancement of large-scale diffusion models [5, 7, 16, 29, 32, 34], it is natural to consider leveraging these models for solving image analogy generation from the perspective of conditional image generation. Unlike existing conditional diffusion models [1, 2, 13, 22, 26, 31] that usually take text prompts as conditions, image analogy generation assumes that only an image triplet is provided as input. For example, consider the top example in Fig. 1, where the transformation is changing a cabin into a castle. Previous conditional diffusion models ((a) and (b)) use a text instruction (i.e. "Make the cabin a castle") as well as $B$ to generate the target image $B'$ . On the other hand, in image analogy generation, $B'$ is generated using only the image triplet without any text prompt. + +Pioneered by DIA [39], several studies [10, 23, 25, 39, 45] have explored diffusion-based image analogy generation in terms of visual in-context learning or visual instruction. From the perspective of visual in-context learning, [10, 23, 45] treat the generation of $B'$ as an image inpainting task, where $A$ , $A'$ , $B$ and initial noise are concatenated into a grid-based input image, and $B'$ is denoised from noise (see Fig. 2 (b)). This approach is limited to pretrained inpainting models and often requires manual prompt engineering by human to obtain additional text prompts. Visual Instruction Inversion (VISII, Fig. 2 (c)) [25] inverts visual instructions from $A$ to $A'$ using instruction tokens but is also limited to InstructPix2Pix [2]. Moreover, to efficiently optimize the visual instruction, VISII initializes the instruction tokens with image $A'$ , which leaves residual information from $A'$ in the instruction, leading to unintended artifacts in $B'$ . For instance, in the fourth example of Fig. 1 (e), the transformation from $A$ to $A'$ involves adding a rainbow, so the desired transformation for $B$ to $B'$ would similarly involve adding only the rainbow. However, in the images generated by VISII, residual information from $A'$ (i.e. mountains) remains, leading to unintended elements in the output. + +In this paper, we introduce Difference Inversion, which leverages "Full Prompt" with both prompt tokens representing the input image and Difference Tokens that exclusively encode difference information. Difference Tokens can focus on only the difference (Delta) between $A$ and $A'$ and the combined tokens are more appropriate as an input of Stable Diffusion models. This contrasts with VISII, which relies on an image-based "Instruction Prompt" that can only be applied as input to InstructPix2Pix. To accurately disentangle the difference, we propose Delta Interpolation to define a more precise Delta. Additionally, we introduce Token Consistency Loss, which ensures that the difference + +![](images/aaaca4d77e1af2ce9417e9f1240c2e681ef95791b2b8212966729fa5d2a99743.jpg) +(a) DIA + +![](images/076c9cba41f2c1981bf3bf21c71c35ae1a4e5dbb8e2cef9408437d03b6d8600a.jpg) +(c) VISII +Figure 2. Architectural comparison of image analogy generation baselines. We compare our approach with three baseline methods: (a) DIA, (b) Analogist, and (c) VISII. Detailed descriptions can be found in Sec. 2. It is noteworthy that, unlike (b) and (c), which each depend on specific models, our method can be applied to general stable diffusion models. + +![](images/ec44239b444799e6ba40425814b2d42e7616d1b9473ba3400e2266b58d327be9.jpg) +(d) Ours + +information emerges when the token is present and disappears when it is absent. By using Token Consistency Loss, the Difference Tokens trained on the Interpolated Delta can be seamlessly concatenated with any query image prompt, enabling their use without introducing unwanted artifacts. Finally, we zero-initialize the Difference Tokens to ensure stable optimization of the differences and to reduce bias by preventing any initial preference from being introduced. + +The main contributions of our paper are as follows: + +- We propose Difference Inversion, which inverts precise differences into Difference Tokens and applies them to any query $B$ to generate $B'$ within general stable diffusion frameworks. +- To extract the exact difference between images $A$ and $A'$ , we additionally introduce a Delta Interpolation, Token Consistency Loss and Zero-Initialization of Token Embeddings. These ensures that the extracted differences contain only the intended modifications, free from unwanted artifacts. +- Our extensive experiments demonstrate that Difference Inversion outperforms existing baselines both quantitatively and qualitatively, as well as in human and large-scale Vision Language Models (VLMs) evaluations. + +# 2. Related works + +# 2.1. Image Analogy Generation via Diffusion Models + +The goal of image analogy generation [10, 23, 25, 39, 45] is to produce $B'$ by conditioning on $A$ , $A'$ and $B$ in the form of $A: A' :: B: B'$ . DIA [39] attempts to invert images to obtain conditioning matrices for diffusion, enabling high- + +![](images/371a56c6c3851f8afa9a08d8d57ae9ba93faf040ce0d811cb408c09562a80153.jpg) +(a) Overall Pipeline of Difference Inversion +(b) Visualization of Interpolated Delta +Figure 3. Overall pipeline of Difference Inversion. Given an image triplet $\{A, A', B\}$ , Difference Inversion extracts the difference between $A$ and $A'$ using DIFF tokens. The Difference is estimated as the Interpolated Delta, computed between $A$ and $A'$ by applying Spherical Linear Interpolation (Slerp) on the Image Delta and Text Delta, effectively capturing both visual and semantic information. The circled numbers in the figure correspond to the steps outlined in Algorithm 1. + +level analogy through semantic vector operations. However it fails to capture not only the desired editing changes but also the detailed image information accurately. Starting with ImageBrush [45], several studies combined $A, A', B$ , and $B'$ into a single grid-formatted image and used a pretrained inpainting model to denoise the $B'$ section from noise, generating a plausible image for $B'$ . However, relying solely on a pretrained inpainting model makes it challenging to generate a plausible $B'$ . Leveraging the knowledge of large language models (LLMs) or large-scale vision language model (VLMs) is often necessary, which consequently requires cumbersome prompt engineering. In a different approach, VISII [25] achieves $A \rightarrow A'$ transformations by inverting visual instructions into text tokens and applying them to query image (e.g. $B$ ) without relying on an VLMs. However, this process leaves unwanted information from $A$ and $A'$ in $B'$ . As a result, $B'$ may be generated in an unintended direction as shown in Fig. 1 (c). Additionally, since the inverted instruction can only be used with InstructPix2Pix [2], it is challenging to apply this method to various Stable Diffusion models, resulting in low generalizability. In this paper, we introduce Difference Inversion that precisely extracts only the difference between $A$ and $A'$ and applies it to $B$ , avoiding unintended artifacts. Furthermore, since it forms a Full Prompt rather than an Instruction Prompt, it can be applied to a wide range of Stable Diffusion models. + +# 2.2. Diffusion based Inversion + +In the wide range of diffusion-based conditional generation methods, DDIM Inversion [24, 37], which identifies the initial noise corresponding to a given image, serves as a core component. Once the initial noise is identified by inver + +sion, it is well-known that better results can be generated from the inverted noise when applied to personalized editing [9, 17, 40] or image-to-image translation [4, 11]. Alongside this trend, DreamBooth [33] and Textual Inversion [8] focus on optimizing special text tokens to learn representations that capture personalized information. ReVersion [15] also optimizes specific text prompts to capture and represent the relationship between two images. These inversion methods utilize a soft prompt approach, optimizing continuous embeddings. In contrast, PEZ [42] proposes hard prompt optimization to generate interpretable prompts that effectively capture the concept of a specific image. Similarly, our work optimizes Difference Tokens in a hard prompt manner, making them plug-and-play with other prompts, thereby enhancing their suitability for general Stable Diffusion models. + +# 3. Preliminaries + +Denoising diffusion models [14, 36] are generative models that learn the reversal of the forward process using denoising autoencoders, enabling the iterative sampling of images from noise. In the early stages of diffusion models [5, 14, 38], the forward and reverse diffusion process operates directly in the pixel space. Latent diffusion models [32], also well known as Stable Diffusion, performs this process in latent space, enabling more efficient image generation. Given an input image $x$ and a text condition $y$ , the image encoder transforms $x$ into $z_0$ . The denoising model $\epsilon_{\theta}$ is then trained to predict a denoised version of its input $z_t$ , as shown in the following equation. + +$$ +\mathcal {L} = \mathbb {E} _ {\mathcal {E} (x), y, \epsilon \sim \mathcal {N} (0, 1), t} \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, \tau_ {\theta} (y)\right) \| _ {2} ^ {2} \tag {1} +$$ + +where $z_{t}$ is a noisy variant of the original input $z_{0}$ in time $t$ and $\tau_{\theta}$ is text encoder. Since Stable Diffusion accepts text prompts as input, there have been attempts to add special tokens to text prompts for tasks such as personalized editing. Textual Inversion [8], for example, learns to capture specific concepts or objects using special token $(s_{*})$ . + +Similarly, VISII (Fig. 2 (c)) also utilizes instruction tokens $C_T$ to learn the instruction information necessary for generating $B'$ . Since VISII needs to learn the transformation instruction from image $A$ to $A'$ and apply them to $B$ , it leverages InstructPix2Pix [2]. Furthermore, to better capture the transformation, $C_T$ is initialized via discrete token optimization (PEZ [42]) on the image $A'$ . Since VISII relies on InstructPix2Pix, it learns $C_T$ in the form of an instruction prompt. In contrast, our Difference Inversion isolates only the difference information, enabling a plug-and-play approach with general stable diffusion prompts. Further details will be provided in the following section. + +# 4. Method + +Given an image triplet $\{A, A', B\}$ , our goal is to extract the difference between $(A, A')$ and apply it to $B$ . To capture the difference, we optimize DIFF tokens $(\tilde{D})$ to effectively encode the extracted differences. We first introduce the basic concept of Difference Inversion in Sec. 4.1. In Sec. 4.2, we explain how we optimize the DIFF token using the Interpolated Delta. Then, in Sec. 4.3, we present the token consistency loss to enhance image consistency, followed by an introduction to token embedding initialization in Sec. 4.4. + +# 4.1. Difference Inversion + +We start from the key observation in VISII, which is the similar concept with our work. As shown in Fig. 1 (e), generating $B'$ with VISII results in unwanted artifacts. This occurs because the optimized visual instruction contains not only the difference (e.g. rainbow) but also information specific to $A$ and $A'$ (e.g. mountains). Therefore, the key is to enable the inversion of only the precise difference. + +In this paper, we define the difference as "Delta," which can be obtained as the difference between embedding vectors from the CLIP [30] encoder $\mathcal{E}_I$ . Letting the CLIP image encoder be represented by $\mathcal{E}_I$ , the Image Delta $\mathcal{D}_{img}$ can be expressed as follows: + +$$ +\mathcal {D} _ {i m g} = \mathcal {E} _ {I} (A _ {i m g} ^ {\prime}) - \mathcal {E} _ {I} (A _ {i m g}) \qquad (2) +$$ + +To optimize DIFF tokens, we first initialize the text prompts of $A$ and $A'$ using PEZ. This step aims to fully anchoring the prompt of $A$ (or $A'$ ) and isolate the only difference, enabling more precise extraction of the difference with the DIFF token in place. As shown in Fig. 3 (a), we only optimize DIFF tokens while optimized prompt embedding is frozen. Note that while optimization with PEZ can + +Algorithm 1 Difference Inversion +Require: pretrained denoising model $\epsilon_{\theta}$ ; Image encoder $\mathcal{E}$ ; CLIP Image, Text Encoder $\mathcal{E}_I$ $\mathcal{E}_T$ ; Captioning model BLIP2; interpolation rate $\alpha$ ; Learning rate $\gamma$ $t_{before}, t_{after} \sim \mathcal{U}(0,T)$ . $\epsilon_{before}, \epsilon_{after} \sim \mathcal{N}(0,1)$ . Input: Image pair $\{A, A'\}$ +Output: Difference Tokens $\tilde{D} = \{D_1^*, \dots, D_n^*\}$ +// Extract the caption of $A$ and $A'$ .. $①$ $cap_A = \mathrm{BLIP2}(A)$ . $cap_{A'} = \mathrm{BLIP2}(A')$ +// Calculate Image Delta $\mathcal{D}_I$ and Text Delta $\mathcal{D}_T$ $\mathcal{D}_I = \mathcal{E}_I(A') - \mathcal{E}_I(A)$ . $\mathcal{D}_T = \mathcal{E}_T(cap_{A'}) - \mathcal{E}_{txt}(cap_A)$ +// Calculate Interpolated Delta $D_{inter}$ ... $②$ $\mathcal{D}_{inter} = Slerp(\mathcal{D}_I,\mathcal{D}_T,\alpha)$ +// Optimize the prompt w.r.t. $A$ and $A'$ .. $③$ +prompt $A = \mathrm{PEZ}(A)$ . prompt $A' = \mathrm{PEZ}(A')$ +Encode $z_A = \mathcal{E}(A)$ . $z_{A'} = \mathcal{E}(A')$ +// Zero-Initialization token embeddings ... $④$ +Initialize $\tilde{D}$ with Zero embeddings +for $i = 1$ to $N$ do +// Prepare noisy latents $z_A$ and $z_{A'}$ .. $⑤$ $z_{A_t} \gets$ add $\epsilon_{before}$ to $z_A$ at timestep $t_{before}$ $z_{A'_t} \gets$ add $\epsilon_{after}$ to $z_{A'}$ at timestep $t_{after}$ +// Predict each noise $\hat{\epsilon}_{before}, \hat{\epsilon}_{after}$ $\hat{\epsilon}_{before} = \epsilon_{\theta}(z_{A_t}, t_{before}, \{prompt_{A'}, -\tilde{D}\})$ $\hat{\epsilon}_{after} = \epsilon_{\theta}(z_{A'_t}, t_{after}, \{prompt_A, \tilde{D}\})$ +// Compute Token Consistency loss ... $⑥$ $\mathcal{L}_{tc} = \| \epsilon_{before} - \hat{\epsilon}_{before} \|_2 + \| \epsilon_{after} - \hat{\epsilon}_{after} \|_2$ +// Compute Clip loss $\mathcal{L}_{clip}$ ... $⑦$ $\mathcal{L}_{clip} = \cosine(\tilde{D},\mathcal{D}_{inter})$ $\mathcal{L} = \lambda_{tc} * \mathcal{L}_{tc} + \lambda_{clip} * \mathcal{L}_{clip}$ +Update $\tilde{D} = \tilde{D} -\gamma \nabla L$ +end for +Return: $\tilde{D}$ + +be time-consuming, it can be replaced with text captions generated by BLIP2 [18], trading off a slight performance drop for faster processing (Sec. 4.3) + +However, simply optimizing the DIFF token only with the Image Delta did not sufficiently capture the Difference information. As shown in Fig. 3 (b), $B'$ with the Image Delta retains much of the original image's cabin features rather than fully transforming into the intended castle. We hypothesize that this is because the CLIP embedding space may not fully represent the intricate details of the images. In the following section, we introduce Delta Interpolation to extract a more refined difference. + +# 4.2. Delta Interpolation + +Although the Image Delta effectively captures the visual difference, it still fails to fully reflect the specific semantic differences. To obtain more detailed semantic information, we use an image captioning model to extract cap + +tions for each of the images $A$ and $A'$ . We utilize BLIP2, but for more detailed captions, BLIP3 [44] or large-scale VLMs [3, 20, 21] can be also be considered. The extracted captions contain more specific details, such as "cabin" and "castle," which were used to derive the Text Delta $D_{txt}$ that contains more semantic information than Image Delta. + +$$ +\mathcal {D} _ {t x t} = \mathcal {E} _ {T} \left(A _ {t x t} ^ {\prime}\right) - \mathcal {E} _ {T} \left(A _ {t x t}\right) \tag {3} +$$ + +where $\mathcal{E}_T$ is CLIP text encoder. + +After obtaining both Image and Text Delta of $A$ and $A'$ with CLIP, we apply Spherical Linear Interpolation (Slerp) [35] to integrate both embeddings. Since CLIP learns image-text pairs to maximize their cosine similarity, we hypothesize that it would be possible to find a more refined Delta within the joint hypersphere of the CLIP space. Therefore, to identify the Interpolated Delta $D_{inter}$ on this hypersphere, we apply Slerp shown below. + +$$ +\begin{array}{l} \mathcal {D} _ {\text {i n t e r}} = \operatorname {S l e r p} \left(\mathcal {D} _ {\text {i m g}}, \mathcal {D} _ {\text {t x t}}; \alpha\right) (4) \\ = \frac {\sin ((1 - \alpha) \theta)}{\sin (\theta)} \mathcal {D} _ {i m g} + \frac {\sin (\alpha \theta)}{\sin (\theta)} \mathcal {D} _ {t x t} (5) \\ \end{array} +$$ + +where $\alpha$ is interpolation ratio between Image and Text Delta. We set $\alpha$ to 0.8, and the ablation results are in Fig. 7. + +Finally, we optimize the DIFF token to minimize cosine distance with this Interpolated Delta as: + +$$ +\mathcal {L} _ {\text {c l i p}} = \operatorname {c o s i n e} (\tilde {D}, \mathcal {D} _ {\text {i n t e r}}) \tag {6} +$$ + +# 4.3. Token Consistency Loss + +Using only the Interpolated Delta $\mathcal{D}_{inter}$ may resemble obtaining a visual instruction from $A$ to $A^{\prime}$ . However, in Difference Inversion, it is also important to preserve aspects that should remain unchanged when generating $B^{\prime}$ . To achieve this, it is essential to accurately extract only the bidirectional difference between $A$ and $A^{\prime}$ . Visual instruction considers only the transformation from $A\rightarrow A^{\prime}$ , whereas the difference must account for both $A\to A^{\prime}$ and $A^{\prime}\to A$ . For DIFF tokens $(\tilde{D})$ , this implies that when $\tilde{D}$ is present, the result should correspond to $A^{\prime}$ ; otherwise, it should yield $A$ . + +Additionally, maintaining consistency in elements we do not intend to modify during this process is necessary. Inspired by Cycle Consistency Loss [43, 47], we introduce Token Consistency Loss, which ensures that $A'$ is generated when $\tilde{D}$ is present and $A$ when $\tilde{D}$ is absent. Specifically, the prompt concatenated with prompt $A$ and $\tilde{D}$ should accurately reconstruct image $A$ , while the prompt concatenated with prompt $A'$ and $-\tilde{D}$ (reverse direction of $\tilde{D}$ ) should accurately reconstruct image $A'$ . This can be expressed as follows: + +$$ +\mathcal {L} _ {m s e _ {b e f o r e}} = \left\| \epsilon_ {b e f o r e} - \epsilon_ {\theta} \left(z _ {A _ {t}}, t _ {b e f o r e}, \{p r o m p t _ {A ^ {\prime}}, - \tilde {D} \}\right) \right\| _ {2} \tag {7} +$$ + +$$ +\mathcal {L} _ {m s e _ {a f t e r}} = \left\| \epsilon_ {a f t e r} - \epsilon_ {\theta} \left(z _ {A _ {t} ^ {\prime}}, t _ {a f t e r}, \{p r o m p t _ {A}, \tilde {D} \}\right) \right\| _ {2} \tag {8} +$$ + +where $t_{before}, t_{after} \sim N(0,1)$ + +The Token Consistency loss can be written as + +$$ +\mathcal {L} _ {t c} = \mathcal {L} _ {m s e _ {\text {b e f o r e}}} + \mathcal {L} _ {m s e _ {\text {a f t e r}}} \tag {9} +$$ + +Finally, to optimize the DIFF tokens $\tilde{D}$ , we utilized the following objective: + +$$ +\mathcal {L} = \lambda_ {t c} * \mathcal {L} _ {t c} + \lambda_ {c l i p} * \mathcal {L} _ {c l i p} \tag {10} +$$ + +where $\lambda_{tc}$ and $\lambda_{tc}$ denotes weight parameter of each loss, respectively. We empirically set $\lambda_{tc}$ to 0.01 and $\lambda_{clip}$ to 6. + +# 4.4. Zero-Initialization of Token Embeddings + +Thus far, we have discussed the optimization process for the DIFF tokens $(\tilde{D})$ . Finally, we address the approach for initializing $\tilde{D}$ . It is crucial for the $\tilde{D}$ to capture accurate differences, making it essential to effectively disentangle the original image information from the difference. From this perspective, randomly initializing the $\tilde{D}$ can lead to unintended information being embedded within $\tilde{D}$ (see Config. C in Fig. 5). Motivated by ContorlNet [46], we initialize the token embeddings with zero to ensure that only the intended differences are captured within the $\tilde{D}$ , minimizing unwanted artifacts. By initializing all $\tilde{D}$ to zero, we ensure that each token robustly encapsulates only the distinguishing differences from the original image. Detailed experimental results are presented in Sec. 5. + +# 5. Experiments + +# 5.1. Experimental and Implementation Detail + +We used Stable Diffusion 2.1 as our baseline. All experiments were conducted on a single NVIDIA GeForce RTX 4090 GPU. For further details on the experimental setup, please refer to the supplementary materials. + +Baselines. We compared our methodology with four baselines on image analogy generation. These methods all generate $B'$ using only an image triplet $\{A, A', B\}$ . Note that, some grid-image-based approaches (ImageBrush [45] and InstructGIE [23]) are also close with our works but since their code is not publicly available, we did not include them in the comparison. The implementation details for each baseline are provided in the supplementary materials. + +Dataset. We randomly sample 300 instruct pairs from the InstructPix2Pix dataset to measure quantitative and qualitative results. The InstructPix2Pix dataset is structured as + +![](images/3ae2deec6e44badb40cfc94e9d0a52aa5c5f273a640ea3afa44274ebc0fbdb19.jpg) +Figure 4. Qualitative comparison to baseline methods. Given inputs $A$ , $A'$ and $B$ , we generate $B'$ without utilizing any text instructions. + +triplets in the form of {before image, after image, text instruction}. We utilized the before image and after image as $A$ and $A'$ , respectively. $B$ was randomly selected from other before images with the same text instruction. Note that we do not use the text instruction included in the dataset. + +Evaluation Metric. We evaluate how well the difference is reflected using the Directional score using CLIP. We also measure the directional score using DINO-v2, which offers a more refined embedding space than CLIP. Additionally, we conduct a user study to verify the perceptual suitability of our results from a human perspective. And finally, leveraging the significant advancements in large-scale vision language models (VLMs), we perform prompt engineering to enable VLMs to evaluate our tasks, as shown in the figure 5. We adopt GPT-4o [27], Qwen2-72B [41] and Llama3.2-90B [6] for VLM evaluation, and the question prompts are provided in the supplementary materials. For human evaluation, we use a four-option multiple-choice format with randomized order of the options. On the other hand, for VLM evaluation, we employ a two-option format to minimize the + +influence of numbering and enable a more precise comparison. Further details about human and LLM evaluations are in the supplementary materials. + +# 5.2. Qualitative Results + +As shown in Fig. 4, our approach qualitatively generates significantly superior images compared to existing baselines. It not only accurately reflects the transformation from $A \rightarrow A'$ but also preserves as much information from B as possible, resulting in a plausible $B'$ . In Fig. 1, (a), (b), and (c) depict results generated using only the images $A$ , $A'$ , and $B$ without text instructions, while (d) and (e) utilize text instructions. Across all baselines, our results produce a $B'$ that best captures the before-after differences. + +# 5.3.Quantitative Results + +Directional score. As shown in Table 1, our model achieves the best performance among image-only baselines in terms of the directional score using CLIP. Note that VISII's CLIP score is nearly comparable to ours, which is attributable to the fact that the dataset used for evalua + +
    MetricImage + TextImage only
    SDEditInstructPix2PixDIAAnalogistVISIIOurs
    CLIP (↑)0.11050.20000.02940.03980.10070.1024
    DINO-v2 (↑)0.53740.57230.51140.50980.54140.5732
    + +![](images/34e0383752060ffa5735e5e9718b7470480bd567bf66438f0c1d5dde17d64d88.jpg) +Figure 5. Qualitative comparison with ablation studies for each proposed method. Each column shows the results when the corresponding method is not applied. + +Table 1. Directional Score of CLIP and DINO-v2. We conducted quantitative evaluation by measuring the directional score using CLIP and DINO-v2. The directional score represents the embedding similarity between $A \rightarrow A'$ and $B \rightarrow B'$ . + +
    ModelDIAAnalogistVISIIOurs
    Percentage (%)4%15%9%72%
    + +tion was also utilized in training VISII's backbone, InstructPix2Pix. In other words, VISII operates on a dataset it has already been trained on, whereas our model is evaluated on previously unseen data. Despite using Stable Diffusion as backbone, our model still performed exceptionally well. This gap becomes even clearer when measured with DINO-v2 [28] rather than CLIP. Furthermore, our DINO-v2 score surpasses even SDEdit and InstructPix2Pix, both of which utilize text descriptions. + +Human evaluation. Although DINO-v2 offers a better directional score compared to CLIP, it still does not fully capture how plausible $B'$ is in the $A: A' :: B: B'$ relationship. To address this, we conduct human evaluations to assess which $B'$ generated by the various baselines was the most appropriate. We asked 60 participants to select the most suitable image analogy generation result $(B')$ from four baselines, including our method. The order of models is randomly assigned for each evaluation, and the images + +Table 2. Human evaluation for image analogy generation. In each question, participants were asked which $B'$ would best complete the analogy $A: A' :: B: B'$ . We report the percentage preference for Difference Inversion over 50 images evaluated by 60 people. + +
    Model (vs Ours)DIAAnalogistVISII
    GPT4o [27]90%76%74%
    Qwen2-VL-72B [41]92%70%80%
    Llama-3.2-90B [6]72%60%62%
    + +Table 3. VLM evaluation for image analogy generation. We provide the large-scale VLM with a prompt explaining the image analogy generation task and ask it to select the most suitable image for $B'$ , similar to the human evaluation (see in Sec. 5.1). The results above reflect the win rate of Difference Inversion compared to each baseline in pairwise comparisons, evaluated using 50 examples for each model (a total of 150 evaluations each). + +![](images/a4f1fd944fc9a78b743c19c4719fb7872e23dac5a158e12a660052c1dc4bb904.jpg) +Figure 6. Ablation results on the number of Difference tokens $(\tilde{D})$ . The fewer $\tilde{D}$ used, the less effectively they capture the difference information; however, using too many $\tilde{D}$ can lead to capturing additional, unrelated information. Experimentally, we found that using a total of 5 tokens strikes the right balance. + +used in the survey are available in the supplementary materials. As shown in Table 2, our model significantly outperforms the other three baselines in the human evaluation. + +VLM evaluation. We also conduct evaluation with large-scale VLMs known for their strong reasoning capabilities. We leverage GPT-4o *, Qwen2-VL-72B-Instruct†, and Llama-3.2-90B-Vision‡ for evaluation, and unlike human evaluation, we employed a two-option format to compare our model against the baselines. As shown in Table 3, the preference for our model is significantly higher compared to existing baselines. This indicates that our method not only extracts the exact difference but also can generate plausible $B'$ , fulfilling the primary goal of image analogy generation. + +# 5.4. Further Analysis + +Ablation study. Lastly, we performed ablation experiments on each of our proposed methods. Fig. 5 presents the ablation results for Token Consistency Loss, Delta Interpolation, Zero Initialization and CLIP loss. When Token Consistency Loss is not used, we observed significant degr + +![](images/b9b1812ce41dd7c0e36070741d2c0da7731f8613d1ab54b363a23e33bf96987a.jpg) +Figure 7. Ablation results of $\alpha$ . Since our delta ultimately needs to be optimized into text tokens, assigning a higher weight to $\alpha$ tends to better capture the desired differences. We finally set $\alpha$ to 0.8 for all experiments. + +![](images/6447a3d65bc68f5139b527454a2994b677284e4cf6e39fdf9730a7432af85ca0.jpg) +Figure 8. Transferability to other Stable Diffusion models. Our Difference Inversion can also be applied to other general Stable Diffusion models, such as SDXL. + +dation in consistency with the original image (B). Without Delta Interpolation and using only Image Delta, the method fails to capture the difference effectively. Similarly, Zero Initialization of Token Embedding shows that when initialized randomly, the difference information is not properly reflected. The ablation results for the number of difference tokens and the interpolation ratio alpha are shown in Fig. 6 and 7, respectively. Additional hyperparameter search results for each method, including lambda tc and lambda clip, can be found in the supplementary materials. + +Transferability. Since our Difference Inversion is an inference-based method that does not require access to the pretrained diffusion model weights, it can be applied even if the diffusion model is provided in an API form. Though instruction inversion models such as VISII are also inference-based, they depend solely on specific models (e.g. InstructPix2Pix). We test our method on SDXL, which possesses a stronger image prior and is capable of generating more complex and refined images. Fig. 8 demonstrates the application of Difference Inversion to SDXL. + +# 6. Limitations and Discussions + +Failure cases. Despite the strong performance of our model across various editing tasks compared to various baselines, there are still some failure cases. In Fig. 9, it is evident that Difference Inversion struggles to capture global differences (a) or detailed differences (b). For example, + +![](images/0afe2d69e95eb88b896b63a1f7342681c00b1bd70563d74ba9055b607982f847.jpg) +Figure 9. Failure cases. When the difference is complex or difficult to define precisely, Difference Inversion may struggle to capture it effectively. + +![](images/5d688d164d25edded7de1406bd33e634c011b41196b12ac9048e97b46b96cfb2.jpg) + +global differences (a) such as weather shifts or transformations like image-to-sketch cannot be effectively applied to $B'$ when optimized through text tokens. Similarly, for detailed differences (b), as shown in the top example of changing a boy to a crying boy, the approach may result in changing a girl to another girl or fail to accurately capture the intended crying expression altogether. In cases like adding cherries to a cake (bottom example), such changes may also be poorly reflected in B', highlighting its limitations in capturing intended variations. + +Inherent limitations of the CLIP space. We hypothesize that the primary reason for the aforementioned failure cases stems from the inherent limitations of the CLIP space. Although we attempt to derive finer Delta using Image and Text Delta within the CLIP space, it does not always align well with human perception, potentially making it unstable for providing precise directional guidance. In the supplementary materials, we illustrate this using a colorization analogy on MNIST data, showing the CLIP similarity for transitions from ground truth $A \rightarrow A'$ and $B \rightarrow B'$ . Notably, the CLIP similarity yields only around 0.5, indicating that optimization based on this directional signal is challenging. We anticipate that future approaches may involve using more refined embedding spaces from foundation models such as DINO-v2 or learning additional mapping networks to enhance similarity and stability. + +# 7. Conclusion + +In this paper, we propose Difference Inversion, a model-agnostic inversion method that applies only the differences to $B'$ without introducing unwanted artifacts. Difference Inversion captures precise differences from $A$ and $A'$ and can be applied to any query image $B$ . This approach aligns well with the goal of image analogy generation, resulting in the creation of feasible $B'$ . Additionally, our method can be applied to various diffusion models, paving the way for new opportunities not only in image editing but also across diverse computer vision tasks using analogy formulations. + +# 8. Acknowledgements + +This research was supported by the MSIT(Ministry of Science and ICT), Korea, under the ITRC(Information Technology Research Center) support program(IITP-2024-RS-2023-00258649, $50\%$ ) supervised by the IITP(Institute for Information Communications Technology Planning Evaluation). This research was also supported by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No. RS-2019-II190079, Artificial Intelligence Graduate School Program(Korea University), $1\%$ ) and the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(No. RS-2025-00562437 $40\%$ , No. RS-2024- 00341514, $9\%$ + +# References + +[1] Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Schonlieb, and Christian Etmann. Conditional image generation with score-based diffusion models. arXiv preprint arXiv:2111.13606, 2021. 2 +[2] Tim Brooks, Aleksander Holynski, and Alexei A Efros. 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We propose Difference Inversion, a method that generates " + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "text", + "content": " conditioned on an image triplet " + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "inline_equation", + "content": "\\{A, A', B\\}" + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "text", + "content": " that satisfies " + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "inline_equation", + "content": "A: A'::B: B'" + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "text", + "content": ". Our method produces a significantly more plausible " + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "text", + "content": " than other baselines. Note that SDEdit and InstructPix2Pix take the text instruction as input, whereas DIA, Analogist, VISII, and our Difference Inversion only use the image triplet " + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "inline_equation", + "content": "A, A', B" + }, + { + "bbox": [ + 55, + 489, + 555, + 523 + ], + "type": "text", + "content": " as input." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 151, + 538, + 200, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 538, + 200, + 551 + ], + "spans": [ + { + "bbox": [ + 151, + 538, + 200, + 551 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": "How can we generate an image " + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": " that satisfies " + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "inline_equation", + "content": "A: A':: B: B'" + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": ", given the input images " + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "inline_equation", + "content": "A, A'" + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": "? Recent works have tackled this challenge through approaches like visual in-context learning or visual instruction. However, these methods are typically limited to specific models (e.g. InstructPix2Pix. Inpainting models) rather than general diffusion models (e.g. Stable Diffusion, SDXL). This dependency may lead to inherited biases or lower editing capabilities. In this paper, we propose Difference Inversion, a method that isolates only the difference from " + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": " and applies it to " + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": " to generate a plausible " + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 563, + 296, + 694 + ], + "type": "text", + "content": ". To address model de" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "spans": [ + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "text", + "content": "pendency, it is crucial to structure prompts in the form of a \"Full Prompt\" suitable for input to stable diffusion models, rather than using an \"Instruction Prompt\". To this end, we accurately extract the Difference between " + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "text", + "content": " and combine it with the prompt of " + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "text", + "content": ", enabling a plug-and-play application of the difference. To extract a precise difference, we first identify it through 1) Delta Interpolation. Additionally, to ensure accurate training, we propose the 2) Token Consistency Loss and 3) Zero Initialization of Token Embeddings. Our extensive experiments demonstrate that Difference Inversion outperforms existing baselines both quantitatively and qualitatively, indicating its ability to generate more feasible " + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 539, + 556, + 694 + ], + "type": "text", + "content": " in a model-agnostic manner." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 702, + 158, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 702, + 158, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 702, + 158, + 713 + ], + "type": "text", + "content": "†Co-corresponding author." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18250" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 136, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 136, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 136, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "text", + "content": "The goal of image analogy generation [39] is to create the target image " + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "text", + "content": " based on the image triplet " + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "inline_equation", + "content": "\\{A, A', B\\}" + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "text", + "content": ", ensuring that it satisfies the image analogy [12, 19] formulation " + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "inline_equation", + "content": "A: A':: B: B'" + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "text", + "content": ". With the huge advancement of large-scale diffusion models [5, 7, 16, 29, 32, 34], it is natural to consider leveraging these models for solving image analogy generation from the perspective of conditional image generation. Unlike existing conditional diffusion models [1, 2, 13, 22, 26, 31] that usually take text prompts as conditions, image analogy generation assumes that only an image triplet is provided as input. For example, consider the top example in Fig. 1, where the transformation is changing a cabin into a castle. Previous conditional diffusion models ((a) and (b)) use a text instruction (i.e. \"Make the cabin a castle\") as well as " + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "text", + "content": " to generate the target image " + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "text", + "content": ". On the other hand, in image analogy generation, " + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 91, + 296, + 295 + ], + "type": "text", + "content": " is generated using only the image triplet without any text prompt." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": "Pioneered by DIA [39], several studies [10, 23, 25, 39, 45] have explored diffusion-based image analogy generation in terms of visual in-context learning or visual instruction. From the perspective of visual in-context learning, [10, 23, 45] treat the generation of " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " as an image inpainting task, where " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " and initial noise are concatenated into a grid-based input image, and " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " is denoised from noise (see Fig. 2 (b)). This approach is limited to pretrained inpainting models and often requires manual prompt engineering by human to obtain additional text prompts. Visual Instruction Inversion (VISII, Fig. 2 (c)) [25] inverts visual instructions from " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " using instruction tokens but is also limited to InstructPix2Pix [2]. Moreover, to efficiently optimize the visual instruction, VISII initializes the instruction tokens with image " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": ", which leaves residual information from " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " in the instruction, leading to unintended artifacts in " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": ". For instance, in the fourth example of Fig. 1 (e), the transformation from " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " involves adding a rainbow, so the desired transformation for " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " would similarly involve adding only the rainbow. However, in the images generated by VISII, residual information from " + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 295, + 296, + 569 + ], + "type": "text", + "content": " (i.e. mountains) remains, leading to unintended elements in the output." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "content": "In this paper, we introduce Difference Inversion, which leverages \"Full Prompt\" with both prompt tokens representing the input image and Difference Tokens that exclusively encode difference information. Difference Tokens can focus on only the difference (Delta) between " + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "content": " and the combined tokens are more appropriate as an input of Stable Diffusion models. This contrasts with VISII, which relies on an image-based \"Instruction Prompt\" that can only be applied as input to InstructPix2Pix. To accurately disentangle the difference, we propose Delta Interpolation to define a more precise Delta. Additionally, we introduce Token Consistency Loss, which ensures that the difference" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 315, + 70, + 553, + 148 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 553, + 148 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 553, + 148 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 553, + 148 + ], + "type": "image", + "image_path": "aaaca4d77e1af2ce9417e9f1240c2e681ef95791b2b8212966729fa5d2a99743.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 358, + 148, + 381, + 156 + ], + "lines": [ + { + "bbox": [ + 358, + 148, + 381, + 156 + ], + "spans": [ + { + "bbox": [ + 358, + 148, + 381, + 156 + ], + "type": "text", + "content": "(a) DIA" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 316, + 157, + 426, + 226 + ], + "blocks": [ + { + "bbox": [ + 316, + 157, + 426, + 226 + ], + "lines": [ + { + "bbox": [ + 316, + 157, + 426, + 226 + ], + "spans": [ + { + "bbox": [ + 316, + 157, + 426, + 226 + ], + "type": "image", + "image_path": "076c9cba41f2c1981bf3bf21c71c35ae1a4e5dbb8e2cef9408437d03b6d8600a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 359, + 224, + 385, + 232 + ], + "lines": [ + { + "bbox": [ + 359, + 224, + 385, + 232 + ], + "spans": [ + { + "bbox": [ + 359, + 224, + 385, + 232 + ], + "type": "text", + "content": "(c) VISII" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 241, + 555, + 308 + ], + "lines": [ + { + "bbox": [ + 313, + 241, + 555, + 308 + ], + "spans": [ + { + "bbox": [ + 313, + 241, + 555, + 308 + ], + "type": "text", + "content": "Figure 2. Architectural comparison of image analogy generation baselines. We compare our approach with three baseline methods: (a) DIA, (b) Analogist, and (c) VISII. Detailed descriptions can be found in Sec. 2. It is noteworthy that, unlike (b) and (c), which each depend on specific models, our method can be applied to general stable diffusion models." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 439, + 157, + 548, + 219 + ], + "blocks": [ + { + "bbox": [ + 439, + 157, + 548, + 219 + ], + "lines": [ + { + "bbox": [ + 439, + 157, + 548, + 219 + ], + "spans": [ + { + "bbox": [ + 439, + 157, + 548, + 219 + ], + "type": "image", + "image_path": "ec44239b444799e6ba40425814b2d42e7616d1b9473ba3400e2266b58d327be9.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 480, + 224, + 504, + 232 + ], + "lines": [ + { + "bbox": [ + 480, + 224, + 504, + 232 + ], + "spans": [ + { + "bbox": [ + 480, + 224, + 504, + 232 + ], + "type": "text", + "content": "(d) Ours" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 329, + 553, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 329, + 553, + 425 + ], + "spans": [ + { + "bbox": [ + 313, + 329, + 553, + 425 + ], + "type": "text", + "content": "information emerges when the token is present and disappears when it is absent. By using Token Consistency Loss, the Difference Tokens trained on the Interpolated Delta can be seamlessly concatenated with any query image prompt, enabling their use without introducing unwanted artifacts. Finally, we zero-initialize the Difference Tokens to ensure stable optimization of the differences and to reduce bias by preventing any initial preference from being introduced." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 326, + 426, + 533, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 426, + 533, + 437 + ], + "spans": [ + { + "bbox": [ + 326, + 426, + 533, + 437 + ], + "type": "text", + "content": "The main contributions of our paper are as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 437, + 553, + 604 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 314, + 437, + 553, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 437, + 553, + 483 + ], + "spans": [ + { + "bbox": [ + 314, + 437, + 553, + 483 + ], + "type": "text", + "content": "- We propose Difference Inversion, which inverts precise differences into Difference Tokens and applies them to any query " + }, + { + "bbox": [ + 314, + 437, + 553, + 483 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 314, + 437, + 553, + 483 + ], + "type": "text", + "content": " to generate " + }, + { + "bbox": [ + 314, + 437, + 553, + 483 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 314, + 437, + 553, + 483 + ], + "type": "text", + "content": " within general stable diffusion frameworks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 485, + 553, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 485, + 553, + 555 + ], + "spans": [ + { + "bbox": [ + 314, + 485, + 553, + 555 + ], + "type": "text", + "content": "- To extract the exact difference between images " + }, + { + "bbox": [ + 314, + 485, + 553, + 555 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 314, + 485, + 553, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 314, + 485, + 553, + 555 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 314, + 485, + 553, + 555 + ], + "type": "text", + "content": ", we additionally introduce a Delta Interpolation, Token Consistency Loss and Zero-Initialization of Token Embeddings. These ensures that the extracted differences contain only the intended modifications, free from unwanted artifacts." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 557, + 553, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 557, + 553, + 604 + ], + "spans": [ + { + "bbox": [ + 314, + 557, + 553, + 604 + ], + "type": "text", + "content": "- Our extensive experiments demonstrate that Difference Inversion outperforms existing baselines both quantitatively and qualitatively, as well as in human and large-scale Vision Language Models (VLMs) evaluations." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 616, + 403, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 616, + 403, + 628 + ], + "spans": [ + { + "bbox": [ + 314, + 616, + 403, + 628 + ], + "type": "text", + "content": "2. Related works" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 635, + 553, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 553, + 659 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 553, + 659 + ], + "type": "text", + "content": "2.1. Image Analogy Generation via Diffusion Models" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": "The goal of image analogy generation [10, 23, 25, 39, 45] is to produce " + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": " by conditioning on " + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": " in the form of " + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "inline_equation", + "content": "A: A' :: B: B'" + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": ". DIA [39] attempts to invert images to obtain conditioning matrices for diffusion, enabling high-" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18251" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 553, + 223 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 553, + 223 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 553, + 223 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 553, + 223 + ], + "type": "image", + "image_path": "371a56c6c3851f8afa9a08d8d57ae9ba93faf040ce0d811cb408c09562a80153.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 105, + 225, + 263, + 236 + ], + "lines": [ + { + "bbox": [ + 105, + 225, + 263, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 225, + 263, + 236 + ], + "type": "text", + "content": "(a) Overall Pipeline of Difference Inversion" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 354, + 225, + 492, + 236 + ], + "lines": [ + { + "bbox": [ + 354, + 225, + 492, + 236 + ], + "spans": [ + { + "bbox": [ + 354, + 225, + 492, + 236 + ], + "type": "text", + "content": "(b) Visualization of Interpolated Delta" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "lines": [ + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "spans": [ + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "text", + "content": "Figure 3. Overall pipeline of Difference Inversion. Given an image triplet " + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "inline_equation", + "content": "\\{A, A', B\\}" + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "text", + "content": ", Difference Inversion extracts the difference between " + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "text", + "content": " using DIFF tokens. The Difference is estimated as the Interpolated Delta, computed between " + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 54, + 247, + 555, + 293 + ], + "type": "text", + "content": " by applying Spherical Linear Interpolation (Slerp) on the Image Delta and Text Delta, effectively capturing both visual and semantic information. The circled numbers in the figure correspond to the steps outlined in Algorithm 1." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "spans": [ + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": "level analogy through semantic vector operations. However it fails to capture not only the desired editing changes but also the detailed image information accurately. Starting with ImageBrush [45], several studies combined " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "A, A', B" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": " into a single grid-formatted image and used a pretrained inpainting model to denoise the " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": " section from noise, generating a plausible image for " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": ". However, relying solely on a pretrained inpainting model makes it challenging to generate a plausible " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": ". Leveraging the knowledge of large language models (LLMs) or large-scale vision language model (VLMs) is often necessary, which consequently requires cumbersome prompt engineering. In a different approach, VISII [25] achieves " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "A \\rightarrow A'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": " transformations by inverting visual instructions into text tokens and applying them to query image (e.g. " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": ") without relying on an VLMs. However, this process leaves unwanted information from " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": ". As a result, " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": " may be generated in an unintended direction as shown in Fig. 1 (c). Additionally, since the inverted instruction can only be used with InstructPix2Pix [2], it is challenging to apply this method to various Stable Diffusion models, resulting in low generalizability. In this paper, we introduce Difference Inversion that precisely extracts only the difference between " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": " and applies it to " + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 56, + 314, + 296, + 636 + ], + "type": "text", + "content": ", avoiding unintended artifacts. Furthermore, since it forms a Full Prompt rather than an Instruction Prompt, it can be applied to a wide range of Stable Diffusion models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 647, + 198, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 198, + 658 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 198, + 658 + ], + "type": "text", + "content": "2.2. Diffusion based Inversion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 714 + ], + "type": "text", + "content": "In the wide range of diffusion-based conditional generation methods, DDIM Inversion [24, 37], which identifies the initial noise corresponding to a given image, serves as a core component. Once the initial noise is identified by inver" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 313, + 555, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 313, + 555, + 504 + ], + "spans": [ + { + "bbox": [ + 313, + 313, + 555, + 504 + ], + "type": "text", + "content": "sion, it is well-known that better results can be generated from the inverted noise when applied to personalized editing [9, 17, 40] or image-to-image translation [4, 11]. Alongside this trend, DreamBooth [33] and Textual Inversion [8] focus on optimizing special text tokens to learn representations that capture personalized information. ReVersion [15] also optimizes specific text prompts to capture and represent the relationship between two images. These inversion methods utilize a soft prompt approach, optimizing continuous embeddings. In contrast, PEZ [42] proposes hard prompt optimization to generate interpretable prompts that effectively capture the concept of a specific image. Similarly, our work optimizes Difference Tokens in a hard prompt manner, making them plug-and-play with other prompts, thereby enhancing their suitability for general Stable Diffusion models." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 521, + 400, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 400, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 400, + 533 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "text", + "content": "Denoising diffusion models [14, 36] are generative models that learn the reversal of the forward process using denoising autoencoders, enabling the iterative sampling of images from noise. In the early stages of diffusion models [5, 14, 38], the forward and reverse diffusion process operates directly in the pixel space. Latent diffusion models [32], also well known as Stable Diffusion, performs this process in latent space, enabling more efficient image generation. Given an input image " + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "text", + "content": " and a text condition " + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "text", + "content": ", the image encoder transforms " + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "text", + "content": ". The denoising model " + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "text", + "content": " is then trained to predict a denoised version of its input " + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "inline_equation", + "content": "z_t" + }, + { + "bbox": [ + 313, + 544, + 556, + 689 + ], + "type": "text", + "content": ", as shown in the following equation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 342, + 700, + 555, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 700, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 342, + 700, + 555, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathbb {E} _ {\\mathcal {E} (x), y, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\| \\epsilon - \\epsilon_ {\\theta} \\left(z _ {t}, t, \\tau_ {\\theta} (y)\\right) \\| _ {2} ^ {2} \\tag {1}", + "image_path": "d6d1236af7519af0fd9abdff64f00067be6718adca250b2d76541324c68592db.jpg" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18252" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " is a noisy variant of the original input " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "z_{0}" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " in time " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": " is text encoder. Since Stable Diffusion accepts text prompts as input, there have been attempts to add special tokens to text prompts for tasks such as personalized editing. Textual Inversion [8], for example, learns to capture specific concepts or objects using special token " + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "inline_equation", + "content": "(s_{*})" + }, + { + "bbox": [ + 55, + 72, + 294, + 144 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "spans": [ + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": "Similarly, VISII (Fig. 2 (c)) also utilizes instruction tokens " + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "inline_equation", + "content": "C_T" + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": " to learn the instruction information necessary for generating " + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": ". Since VISII needs to learn the transformation instruction from image " + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": " and apply them to " + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": ", it leverages InstructPix2Pix [2]. Furthermore, to better capture the transformation, " + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "inline_equation", + "content": "C_T" + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": " is initialized via discrete token optimization (PEZ [42]) on the image " + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": ". Since VISII relies on InstructPix2Pix, it learns " + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "inline_equation", + "content": "C_T" + }, + { + "bbox": [ + 55, + 144, + 296, + 288 + ], + "type": "text", + "content": " in the form of an instruction prompt. In contrast, our Difference Inversion isolates only the difference information, enabling a plug-and-play approach with general stable diffusion prompts. Further details will be provided in the following section." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 299, + 111, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 299, + 111, + 311 + ], + "spans": [ + { + "bbox": [ + 55, + 299, + 111, + 311 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "spans": [ + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "text", + "content": "Given an image triplet " + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "inline_equation", + "content": "\\{A, A', B\\}" + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "text", + "content": ", our goal is to extract the difference between " + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "inline_equation", + "content": "(A, A')" + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "text", + "content": " and apply it to " + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "text", + "content": ". To capture the difference, we optimize DIFF tokens " + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "inline_equation", + "content": "(\\tilde{D})" + }, + { + "bbox": [ + 55, + 319, + 296, + 428 + ], + "type": "text", + "content": " to effectively encode the extracted differences. We first introduce the basic concept of Difference Inversion in Sec. 4.1. In Sec. 4.2, we explain how we optimize the DIFF token using the Interpolated Delta. Then, in Sec. 4.3, we present the token consistency loss to enhance image consistency, followed by an introduction to token embedding initialization in Sec. 4.4." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 435, + 173, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 435, + 173, + 447 + ], + "spans": [ + { + "bbox": [ + 55, + 435, + 173, + 447 + ], + "type": "text", + "content": "4.1. Difference Inversion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "spans": [ + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "type": "text", + "content": "We start from the key observation in VISII, which is the similar concept with our work. As shown in Fig. 1 (e), generating " + }, + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "type": "text", + "content": " with VISII results in unwanted artifacts. This occurs because the optimized visual instruction contains not only the difference (e.g. rainbow) but also information specific to " + }, + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 453, + 296, + 536 + ], + "type": "text", + "content": " (e.g. mountains). Therefore, the key is to enable the inversion of only the precise difference." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "type": "text", + "content": "In this paper, we define the difference as \"Delta,\" which can be obtained as the difference between embedding vectors from the CLIP [30] encoder " + }, + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_I" + }, + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "type": "text", + "content": ". Letting the CLIP image encoder be represented by " + }, + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_I" + }, + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "type": "text", + "content": ", the Image Delta " + }, + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{img}" + }, + { + "bbox": [ + 55, + 536, + 296, + 597 + ], + "type": "text", + "content": " can be expressed as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 110, + 606, + 295, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 606, + 295, + 622 + ], + "spans": [ + { + "bbox": [ + 110, + 606, + 295, + 622 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {i m g} = \\mathcal {E} _ {I} (A _ {i m g} ^ {\\prime}) - \\mathcal {E} _ {I} (A _ {i m g}) \\qquad (2)", + "image_path": "3e795797d1a021c06838f9693a3ca1baada6cf49966f0908735ce5fbf0a26735.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": "To optimize DIFF tokens, we first initialize the text prompts of " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " using PEZ. This step aims to fully anchoring the prompt of " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": ") and isolate the only difference, enabling more precise extraction of the difference with the DIFF token in place. As shown in Fig. 3 (a), we only optimize DIFF tokens while optimized prompt embedding is frozen. Note that while optimization with PEZ can" + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 318, + 87, + 553, + 475 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 454, + 83 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 454, + 83 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 454, + 83 + ], + "type": "text", + "content": "Algorithm 1 Difference Inversion" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "lines": [ + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "spans": [ + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": "Require: pretrained denoising model " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " ; Image encoder " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " ; CLIP Image, Text Encoder " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_I" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_T" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " ; Captioning model BLIP2; interpolation rate " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " ; Learning rate " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "t_{before}, t_{after} \\sim \\mathcal{U}(0,T)" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\epsilon_{before}, \\epsilon_{after} \\sim \\mathcal{N}(0,1)" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " . Input: Image pair " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\{A, A'\\}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \nOutput: Difference Tokens " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\tilde{D} = \\{D_1^*, \\dots, D_n^*\\}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \n// Extract the caption of " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " .. " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "①" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "cap_A = \\mathrm{BLIP2}(A)" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "cap_{A'} = \\mathrm{BLIP2}(A')" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \n// Calculate Image Delta " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_I" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " and Text Delta " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_I = \\mathcal{E}_I(A') - \\mathcal{E}_I(A)" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T = \\mathcal{E}_T(cap_{A'}) - \\mathcal{E}_{txt}(cap_A)" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \n// Calculate Interpolated Delta " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "D_{inter}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " ... " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "②" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{inter} = Slerp(\\mathcal{D}_I,\\mathcal{D}_T,\\alpha)" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \n// Optimize the prompt w.r.t. " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " .. " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "③" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \nprompt " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "A = \\mathrm{PEZ}(A)" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " . prompt " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "A' = \\mathrm{PEZ}(A')" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \nEncode " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "z_A = \\mathcal{E}(A)" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "z_{A'} = \\mathcal{E}(A')" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \n// Zero-Initialization token embeddings ... " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "④" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \nInitialize " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " with Zero embeddings \nfor " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " do \n// Prepare noisy latents " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "z_A" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "z_{A'}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " .. " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "⑤" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "z_{A_t} \\gets" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " add " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\epsilon_{before}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "z_A" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "t_{before}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "z_{A'_t} \\gets" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " add " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\epsilon_{after}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "z_{A'}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "t_{after}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \n// Predict each noise " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{before}, \\hat{\\epsilon}_{after}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{before} = \\epsilon_{\\theta}(z_{A_t}, t_{before}, \\{prompt_{A'}, -\\tilde{D}\\})" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{after} = \\epsilon_{\\theta}(z_{A'_t}, t_{after}, \\{prompt_A, \\tilde{D}\\})" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \n// Compute Token Consistency loss ... " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "⑥" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tc} = \\| \\epsilon_{before} - \\hat{\\epsilon}_{before} \\|_2 + \\| \\epsilon_{after} - \\hat{\\epsilon}_{after} \\|_2" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \n// Compute Clip loss " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{clip}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " ... " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "⑦" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{clip} = \\cosine(\\tilde{D},\\mathcal{D}_{inter})" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\lambda_{tc} * \\mathcal{L}_{tc} + \\lambda_{clip} * \\mathcal{L}_{clip}" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \nUpdate " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\tilde{D} = \\tilde{D} -\\gamma \\nabla L" + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "text", + "content": " \nend for \nReturn: " + }, + { + "bbox": [ + 318, + 87, + 553, + 475 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 313, + 497, + 553, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 497, + 553, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 497, + 553, + 533 + ], + "type": "text", + "content": "be time-consuming, it can be replaced with text captions generated by BLIP2 [18], trading off a slight performance drop for faster processing (Sec. 4.3)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 533, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 640 + ], + "type": "text", + "content": "However, simply optimizing the DIFF token only with the Image Delta did not sufficiently capture the Difference information. As shown in Fig. 3 (b), " + }, + { + "bbox": [ + 313, + 533, + 555, + 640 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 533, + 555, + 640 + ], + "type": "text", + "content": " with the Image Delta retains much of the original image's cabin features rather than fully transforming into the intended castle. We hypothesize that this is because the CLIP embedding space may not fully represent the intricate details of the images. In the following section, we introduce Delta Interpolation to extract a more refined difference." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 648, + 427, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 427, + 661 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 427, + 661 + ], + "type": "text", + "content": "4.2. Delta Interpolation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 554, + 714 + ], + "type": "text", + "content": "Although the Image Delta effectively captures the visual difference, it still fails to fully reflect the specific semantic differences. To obtain more detailed semantic information, we use an image captioning model to extract cap" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18253" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "text", + "content": "tions for each of the images " + }, + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "text", + "content": ". We utilize BLIP2, but for more detailed captions, BLIP3 [44] or large-scale VLMs [3, 20, 21] can be also be considered. The extracted captions contain more specific details, such as \"cabin\" and \"castle,\" which were used to derive the Text Delta " + }, + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "inline_equation", + "content": "D_{txt}" + }, + { + "bbox": [ + 55, + 72, + 296, + 145 + ], + "type": "text", + "content": " that contains more semantic information than Image Delta." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 113, + 152, + 295, + 166 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 152, + 295, + 166 + ], + "spans": [ + { + "bbox": [ + 113, + 152, + 295, + 166 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {t x t} = \\mathcal {E} _ {T} \\left(A _ {t x t} ^ {\\prime}\\right) - \\mathcal {E} _ {T} \\left(A _ {t x t}\\right) \\tag {3}", + "image_path": "0e187a2eb00075e6e9d9b513ee7b4ab4f4093cf3ee451c7d81eee2d84e37c93f.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 173, + 185, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 173, + 185, + 184 + ], + "spans": [ + { + "bbox": [ + 55, + 173, + 185, + 184 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 173, + 185, + 184 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_T" + }, + { + "bbox": [ + 55, + 173, + 185, + 184 + ], + "type": "text", + "content": " is CLIP text encoder." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "text", + "content": "After obtaining both Image and Text Delta of " + }, + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "text", + "content": " with CLIP, we apply Spherical Linear Interpolation (Slerp) [35] to integrate both embeddings. Since CLIP learns image-text pairs to maximize their cosine similarity, we hypothesize that it would be possible to find a more refined Delta within the joint hypersphere of the CLIP space. Therefore, to identify the Interpolated Delta " + }, + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "inline_equation", + "content": "D_{inter}" + }, + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "text", + "content": " on this hypersphere, we apply Slerp shown below." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 79, + 289, + 295, + 330 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 289, + 295, + 330 + ], + "spans": [ + { + "bbox": [ + 79, + 289, + 295, + 330 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {D} _ {\\text {i n t e r}} = \\operatorname {S l e r p} \\left(\\mathcal {D} _ {\\text {i m g}}, \\mathcal {D} _ {\\text {t x t}}; \\alpha\\right) (4) \\\\ = \\frac {\\sin ((1 - \\alpha) \\theta)}{\\sin (\\theta)} \\mathcal {D} _ {i m g} + \\frac {\\sin (\\alpha \\theta)}{\\sin (\\theta)} \\mathcal {D} _ {t x t} (5) \\\\ \\end{array}", + "image_path": "dbde01b844b74402f0ce5d4b601e9e684f8c8007532b63cc59c03ac782169373.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 336, + 295, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 336, + 295, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 336, + 295, + 360 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 336, + 295, + 360 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 336, + 295, + 360 + ], + "type": "text", + "content": " is interpolation ratio between Image and Text Delta. We set " + }, + { + "bbox": [ + 55, + 336, + 295, + 360 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 336, + 295, + 360 + ], + "type": "text", + "content": " to 0.8, and the ablation results are in Fig. 7." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 360, + 296, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 360, + 296, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 360, + 296, + 384 + ], + "type": "text", + "content": "Finally, we optimize the DIFF token to minimize cosine distance with this Interpolated Delta as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 120, + 392, + 295, + 406 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 392, + 295, + 406 + ], + "spans": [ + { + "bbox": [ + 120, + 392, + 295, + 406 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c l i p}} = \\operatorname {c o s i n e} (\\tilde {D}, \\mathcal {D} _ {\\text {i n t e r}}) \\tag {6}", + "image_path": "895ee0745dbb06a98be88e1db47b09283d94d1627d4f8b1bebb947ffd6f31a97.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 412, + 191, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 412, + 191, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 412, + 191, + 426 + ], + "type": "text", + "content": "4.3. Token Consistency Loss" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "spans": [ + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": "Using only the Interpolated Delta " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{inter}" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": " may resemble obtaining a visual instruction from " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A^{\\prime}" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": ". However, in Difference Inversion, it is also important to preserve aspects that should remain unchanged when generating " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "B^{\\prime}" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": ". To achieve this, it is essential to accurately extract only the bidirectional difference between " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A^{\\prime}" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": ". Visual instruction considers only the transformation from " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A\\rightarrow A^{\\prime}" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": ", whereas the difference must account for both " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A\\to A^{\\prime}" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A^{\\prime}\\to A" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": ". For DIFF tokens " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "(\\tilde{D})" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": ", this implies that when " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": " is present, the result should correspond to " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A^{\\prime}" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": "; otherwise, it should yield " + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 430, + 296, + 561 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": "Additionally, maintaining consistency in elements we do not intend to modify during this process is necessary. Inspired by Cycle Consistency Loss [43, 47], we introduce Token Consistency Loss, which ensures that " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": " is generated when " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": " is present and " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": " is absent. Specifically, the prompt concatenated with prompt " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": " should accurately reconstruct image " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": ", while the prompt concatenated with prompt " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "-\\tilde{D}" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": " (reverse direction of " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": ") should accurately reconstruct image " + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 562, + 296, + 680 + ], + "type": "text", + "content": ". This can be expressed as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 688, + 305, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 688, + 305, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 688, + 305, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m s e _ {b e f o r e}} = \\left\\| \\epsilon_ {b e f o r e} - \\epsilon_ {\\theta} \\left(z _ {A _ {t}}, t _ {b e f o r e}, \\{p r o m p t _ {A ^ {\\prime}}, - \\tilde {D} \\}\\right) \\right\\| _ {2} \\tag {7}", + "image_path": "bfa6f733c040128bc003141ea433d4c9f1d8bf2fdf35cc77579f78e04e2f83e1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 92, + 553, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 92, + 553, + 118 + ], + "spans": [ + { + "bbox": [ + 318, + 92, + 553, + 118 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m s e _ {a f t e r}} = \\left\\| \\epsilon_ {a f t e r} - \\epsilon_ {\\theta} \\left(z _ {A _ {t} ^ {\\prime}}, t _ {a f t e r}, \\{p r o m p t _ {A}, \\tilde {D} \\}\\right) \\right\\| _ {2} \\tag {8}", + "image_path": "73a225e981ace0d70b55a5ace1fe1967183085c34f2bbfbee6a234c20ae1a9e5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 118, + 445, + 130 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 118, + 445, + 130 + ], + "spans": [ + { + "bbox": [ + 314, + 118, + 445, + 130 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 314, + 118, + 445, + 130 + ], + "type": "inline_equation", + "content": "t_{before}, t_{after} \\sim N(0,1)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 130, + 511, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 130, + 511, + 141 + ], + "spans": [ + { + "bbox": [ + 326, + 130, + 511, + 141 + ], + "type": "text", + "content": "The Token Consistency loss can be written as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 371, + 151, + 553, + 165 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 151, + 553, + 165 + ], + "spans": [ + { + "bbox": [ + 371, + 151, + 553, + 165 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t c} = \\mathcal {L} _ {m s e _ {\\text {b e f o r e}}} + \\mathcal {L} _ {m s e _ {\\text {a f t e r}}} \\tag {9}", + "image_path": "15c0c7c81a5e42ce63c60d094a323b79bbd99536b0ea4924c66039f9a6066e2c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 174, + 553, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 174, + 553, + 198 + ], + "spans": [ + { + "bbox": [ + 313, + 174, + 553, + 198 + ], + "type": "text", + "content": "Finally, to optimize the DIFF tokens " + }, + { + "bbox": [ + 313, + 174, + 553, + 198 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 174, + 553, + 198 + ], + "type": "text", + "content": ", we utilized the following objective:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 373, + 208, + 553, + 221 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 208, + 553, + 221 + ], + "spans": [ + { + "bbox": [ + 373, + 208, + 553, + 221 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {t c} * \\mathcal {L} _ {t c} + \\lambda_ {c l i p} * \\mathcal {L} _ {c l i p} \\tag {10}", + "image_path": "7636772eb041d5206cdf93b722b752589f195dc556baad092f2959ad0e13cebf.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "spans": [ + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "inline_equation", + "content": "\\lambda_{tc}" + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "inline_equation", + "content": "\\lambda_{tc}" + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "text", + "content": " denotes weight parameter of each loss, respectively. We empirically set " + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "inline_equation", + "content": "\\lambda_{tc}" + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "text", + "content": " to 0.01 and " + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "inline_equation", + "content": "\\lambda_{clip}" + }, + { + "bbox": [ + 313, + 229, + 553, + 255 + ], + "type": "text", + "content": " to 6." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 261, + 528, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 261, + 528, + 274 + ], + "spans": [ + { + "bbox": [ + 313, + 261, + 528, + 274 + ], + "type": "text", + "content": "4.4. Zero-Initialization of Token Embeddings" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "content": "Thus far, we have discussed the optimization process for the DIFF tokens " + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "inline_equation", + "content": "(\\tilde{D})" + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "content": ". Finally, we address the approach for initializing " + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "content": ". It is crucial for the " + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "content": " to capture accurate differences, making it essential to effectively disentangle the original image information from the difference. From this perspective, randomly initializing the " + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "content": " can lead to unintended information being embedded within " + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "content": " (see Config. C in Fig. 5). Motivated by ContorlNet [46], we initialize the token embeddings with zero to ensure that only the intended differences are captured within the " + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "content": ", minimizing unwanted artifacts. By initializing all " + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 277, + 555, + 446 + ], + "type": "text", + "content": " to zero, we ensure that each token robustly encapsulates only the distinguishing differences from the original image. Detailed experimental results are presented in Sec. 5." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 456, + 397, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 456, + 397, + 470 + ], + "spans": [ + { + "bbox": [ + 313, + 456, + 397, + 470 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 475, + 531, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 531, + 488 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 531, + 488 + ], + "type": "text", + "content": "5.1. Experimental and Implementation Detail" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 493, + 554, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 493, + 554, + 542 + ], + "spans": [ + { + "bbox": [ + 313, + 493, + 554, + 542 + ], + "type": "text", + "content": "We used Stable Diffusion 2.1 as our baseline. All experiments were conducted on a single NVIDIA GeForce RTX 4090 GPU. For further details on the experimental setup, please refer to the supplementary materials." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 555, + 555, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 555, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 555, + 662 + ], + "type": "text", + "content": "Baselines. We compared our methodology with four baselines on image analogy generation. These methods all generate " + }, + { + "bbox": [ + 313, + 555, + 555, + 662 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 555, + 555, + 662 + ], + "type": "text", + "content": " using only an image triplet " + }, + { + "bbox": [ + 313, + 555, + 555, + 662 + ], + "type": "inline_equation", + "content": "\\{A, A', B\\}" + }, + { + "bbox": [ + 313, + 555, + 555, + 662 + ], + "type": "text", + "content": ". Note that, some grid-image-based approaches (ImageBrush [45] and InstructGIE [23]) are also close with our works but since their code is not publicly available, we did not include them in the comparison. The implementation details for each baseline are provided in the supplementary materials." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "type": "text", + "content": "Dataset. We randomly sample 300 instruct pairs from the InstructPix2Pix dataset to measure quantitative and qualitative results. The InstructPix2Pix dataset is structured as" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18254" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 71, + 504, + 411 + ], + "blocks": [ + { + "bbox": [ + 108, + 71, + 504, + 411 + ], + "lines": [ + { + "bbox": [ + 108, + 71, + 504, + 411 + ], + "spans": [ + { + "bbox": [ + 108, + 71, + 504, + 411 + ], + "type": "image", + "image_path": "3ae2deec6e44badb40cfc94e9d0a52aa5c5f273a640ea3afa44274ebc0fbdb19.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "lines": [ + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison to baseline methods. Given inputs " + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "text", + "content": ", we generate " + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 420, + 555, + 433 + ], + "type": "text", + "content": " without utilizing any text instructions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "type": "text", + "content": "triplets in the form of {before image, after image, text instruction}. We utilized the before image and after image as " + }, + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 453, + 298, + 514 + ], + "type": "text", + "content": " was randomly selected from other before images with the same text instruction. Note that we do not use the text instruction included in the dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 533, + 298, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 533, + 298, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 533, + 298, + 715 + ], + "type": "text", + "content": "Evaluation Metric. We evaluate how well the difference is reflected using the Directional score using CLIP. We also measure the directional score using DINO-v2, which offers a more refined embedding space than CLIP. Additionally, we conduct a user study to verify the perceptual suitability of our results from a human perspective. And finally, leveraging the significant advancements in large-scale vision language models (VLMs), we perform prompt engineering to enable VLMs to evaluate our tasks, as shown in the figure 5. We adopt GPT-4o [27], Qwen2-72B [41] and Llama3.2-90B [6] for VLM evaluation, and the question prompts are provided in the supplementary materials. For human evaluation, we use a four-option multiple-choice format with randomized order of the options. On the other hand, for VLM evaluation, we employ a two-option format to minimize the" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 453, + 555, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 555, + 489 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 555, + 489 + ], + "type": "text", + "content": "influence of numbering and enable a more precise comparison. Further details about human and LLM evaluations are in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 499, + 427, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 499, + 427, + 511 + ], + "spans": [ + { + "bbox": [ + 313, + 499, + 427, + 511 + ], + "type": "text", + "content": "5.2. Qualitative Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "content": "As shown in Fig. 4, our approach qualitatively generates significantly superior images compared to existing baselines. It not only accurately reflects the transformation from " + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "inline_equation", + "content": "A \\rightarrow A'" + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "content": " but also preserves as much information from B as possible, resulting in a plausible " + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "content": ". In Fig. 1, (a), (b), and (c) depict results generated using only the images " + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "content": " without text instructions, while (d) and (e) utilize text instructions. Across all baselines, our results produce a " + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 517, + 556, + 625 + ], + "type": "text", + "content": " that best captures the before-after differences." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 635, + 433, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 635, + 433, + 647 + ], + "spans": [ + { + "bbox": [ + 313, + 635, + 433, + 647 + ], + "type": "text", + "content": "5.3.Quantitative Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 653, + 555, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 555, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 555, + 712 + ], + "type": "text", + "content": "Directional score. As shown in Table 1, our model achieves the best performance among image-only baselines in terms of the directional score using CLIP. Note that VISII's CLIP score is nearly comparable to ours, which is attributable to the fact that the dataset used for evalua" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18255" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 295, + 116 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 295, + 116 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 295, + 116 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 295, + 116 + ], + "type": "table", + "html": "
    MetricImage + TextImage only
    SDEditInstructPix2PixDIAAnalogistVISIIOurs
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    DINO-v2 (↑)0.53740.57230.51140.50980.54140.5732
    ", + "image_path": "be70bd0f170965334e9179b153cc4a20ba40b33c2fdc826868881c51e0c42190.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 178, + 294, + 308 + ], + "blocks": [ + { + "bbox": [ + 58, + 178, + 294, + 308 + ], + "lines": [ + { + "bbox": [ + 58, + 178, + 294, + 308 + ], + "spans": [ + { + "bbox": [ + 58, + 178, + 294, + 308 + ], + "type": "image", + "image_path": "34e0383752060ffa5735e5e9718b7470480bd567bf66438f0c1d5dde17d64d88.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 315, + 295, + 348 + ], + "lines": [ + { + "bbox": [ + 55, + 315, + 295, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 315, + 295, + 348 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison with ablation studies for each proposed method. Each column shows the results when the corresponding method is not applied." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 67, + 360, + 285, + 396 + ], + "blocks": [ + { + "bbox": [ + 55, + 123, + 295, + 168 + ], + "lines": [ + { + "bbox": [ + 55, + 123, + 295, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 123, + 295, + 168 + ], + "type": "text", + "content": "Table 1. Directional Score of CLIP and DINO-v2. We conducted quantitative evaluation by measuring the directional score using CLIP and DINO-v2. The directional score represents the embedding similarity between " + }, + { + "bbox": [ + 55, + 123, + 295, + 168 + ], + "type": "inline_equation", + "content": "A \\rightarrow A'" + }, + { + "bbox": [ + 55, + 123, + 295, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 123, + 295, + 168 + ], + "type": "inline_equation", + "content": "B \\rightarrow B'" + }, + { + "bbox": [ + 55, + 123, + 295, + 168 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 360, + 285, + 396 + ], + "lines": [ + { + "bbox": [ + 67, + 360, + 285, + 396 + ], + "spans": [ + { + "bbox": [ + 67, + 360, + 285, + 396 + ], + "type": "table", + "html": "
    ModelDIAAnalogistVISIIOurs
    Percentage (%)4%15%9%72%
    ", + "image_path": "f43d8642c0e0dcd96bf04816671689e3b7ab7dd9f4652c4e10d4895665a7ef86.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 481, + 296, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 481, + 296, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 481, + 296, + 590 + ], + "type": "text", + "content": "tion was also utilized in training VISII's backbone, InstructPix2Pix. In other words, VISII operates on a dataset it has already been trained on, whereas our model is evaluated on previously unseen data. Despite using Stable Diffusion as backbone, our model still performed exceptionally well. This gap becomes even clearer when measured with DINO-v2 [28] rather than CLIP. Furthermore, our DINO-v2 score surpasses even SDEdit and InstructPix2Pix, both of which utilize text descriptions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": "Human evaluation. Although DINO-v2 offers a better directional score compared to CLIP, it still does not fully capture how plausible " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " is in the " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "A: A' :: B: B'" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " relationship. To address this, we conduct human evaluations to assess which " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " generated by the various baselines was the most appropriate. We asked 60 participants to select the most suitable image analogy generation result " + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "inline_equation", + "content": "(B')" + }, + { + "bbox": [ + 55, + 605, + 296, + 715 + ], + "type": "text", + "content": " from four baselines, including our method. The order of models is randomly assigned for each evaluation, and the images" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 328, + 70, + 543, + 130 + ], + "blocks": [ + { + "bbox": [ + 55, + 403, + 296, + 460 + ], + "lines": [ + { + "bbox": [ + 55, + 403, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 403, + 296, + 460 + ], + "type": "text", + "content": "Table 2. Human evaluation for image analogy generation. In each question, participants were asked which " + }, + { + "bbox": [ + 55, + 403, + 296, + 460 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 55, + 403, + 296, + 460 + ], + "type": "text", + "content": " would best complete the analogy " + }, + { + "bbox": [ + 55, + 403, + 296, + 460 + ], + "type": "inline_equation", + "content": "A: A' :: B: B'" + }, + { + "bbox": [ + 55, + 403, + 296, + 460 + ], + "type": "text", + "content": ". We report the percentage preference for Difference Inversion over 50 images evaluated by 60 people." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 70, + 543, + 130 + ], + "lines": [ + { + "bbox": [ + 328, + 70, + 543, + 130 + ], + "spans": [ + { + "bbox": [ + 328, + 70, + 543, + 130 + ], + "type": "table", + "html": "
    Model (vs Ours)DIAAnalogistVISII
    GPT4o [27]90%76%74%
    Qwen2-VL-72B [41]92%70%80%
    Llama-3.2-90B [6]72%60%62%
    ", + "image_path": "2450402e4cdfbe67ec68ae1fc97c9c7e04d35aa119f1036adc5fe0a80ceac0f5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 138, + 555, + 216 + ], + "lines": [ + { + "bbox": [ + 313, + 138, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 313, + 138, + 555, + 216 + ], + "type": "text", + "content": "Table 3. VLM evaluation for image analogy generation. We provide the large-scale VLM with a prompt explaining the image analogy generation task and ask it to select the most suitable image for " + }, + { + "bbox": [ + 313, + 138, + 555, + 216 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 138, + 555, + 216 + ], + "type": "text", + "content": ", similar to the human evaluation (see in Sec. 5.1). The results above reflect the win rate of Difference Inversion compared to each baseline in pairwise comparisons, evaluated using 50 examples for each model (a total of 150 evaluations each)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 317, + 228, + 553, + 316 + ], + "blocks": [ + { + "bbox": [ + 317, + 228, + 553, + 316 + ], + "lines": [ + { + "bbox": [ + 317, + 228, + 553, + 316 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 553, + 316 + ], + "type": "image", + "image_path": "a4f1fd944fc9a78b743c19c4719fb7872e23dac5a158e12a660052c1dc4bb904.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "lines": [ + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "spans": [ + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "type": "text", + "content": "Figure 6. Ablation results on the number of Difference tokens " + }, + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "type": "inline_equation", + "content": "(\\tilde{D})" + }, + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "type": "text", + "content": ". The fewer " + }, + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "type": "text", + "content": " used, the less effectively they capture the difference information; however, using too many " + }, + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "type": "inline_equation", + "content": "\\tilde{D}" + }, + { + "bbox": [ + 313, + 326, + 555, + 381 + ], + "type": "text", + "content": " can lead to capturing additional, unrelated information. Experimentally, we found that using a total of 5 tokens strikes the right balance." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 402, + 554, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 402, + 554, + 438 + ], + "spans": [ + { + "bbox": [ + 313, + 402, + 554, + 438 + ], + "type": "text", + "content": "used in the survey are available in the supplementary materials. As shown in Table 2, our model significantly outperforms the other three baselines in the human evaluation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 453, + 555, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 453, + 555, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 453, + 555, + 574 + ], + "type": "text", + "content": "VLM evaluation. We also conduct evaluation with large-scale VLMs known for their strong reasoning capabilities. We leverage GPT-4o *, Qwen2-VL-72B-Instruct†, and Llama-3.2-90B-Vision‡ for evaluation, and unlike human evaluation, we employed a two-option format to compare our model against the baselines. As shown in Table 3, the preference for our model is significantly higher compared to existing baselines. This indicates that our method not only extracts the exact difference but also can generate plausible " + }, + { + "bbox": [ + 313, + 453, + 555, + 574 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 453, + 555, + 574 + ], + "type": "text", + "content": ", fulfilling the primary goal of image analogy generation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 580, + 417, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 580, + 417, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 580, + 417, + 593 + ], + "type": "text", + "content": "5.4. Further Analysis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 597, + 554, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 597, + 554, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 597, + 554, + 658 + ], + "type": "text", + "content": "Ablation study. Lastly, we performed ablation experiments on each of our proposed methods. Fig. 5 presents the ablation results for Token Consistency Loss, Delta Interpolation, Zero Initialization and CLIP loss. When Token Consistency Loss is not used, we observed significant degr" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 313, + 664, + 553, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 664, + 553, + 712 + ], + "spans": [ + { + "bbox": [ + 313, + 664, + 553, + 712 + ], + "type": "text", + "content": "\\*https://chatgpt.com/ \n" + }, + { + "bbox": [ + 313, + 664, + 553, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 313, + 664, + 553, + 712 + ], + "type": "text", + "content": " https://huggingface.co/Qwen/Qwen2.5-72B-Instruct \n" + }, + { + "bbox": [ + 313, + 664, + 553, + 712 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 313, + 664, + 553, + 712 + ], + "type": "text", + "content": " https://huggingface.co/metac-llama/Llama-3.2- 90B-Vision" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18256" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 294, + 157 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 294, + 157 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 294, + 157 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 294, + 157 + ], + "type": "image", + "image_path": "b9b1812ce41dd7c0e36070741d2c0da7731f8613d1ab54b363a23e33bf96987a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "lines": [ + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "spans": [ + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "type": "text", + "content": "Figure 7. Ablation results of " + }, + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "type": "text", + "content": ". Since our delta ultimately needs to be optimized into text tokens, assigning a higher weight to " + }, + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "type": "text", + "content": " tends to better capture the desired differences. We finally set " + }, + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 166, + 295, + 211 + ], + "type": "text", + "content": " to 0.8 for all experiments." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 222, + 294, + 300 + ], + "blocks": [ + { + "bbox": [ + 58, + 222, + 294, + 300 + ], + "lines": [ + { + "bbox": [ + 58, + 222, + 294, + 300 + ], + "spans": [ + { + "bbox": [ + 58, + 222, + 294, + 300 + ], + "type": "image", + "image_path": "6447a3d65bc68f5139b527454a2994b677284e4cf6e39fdf9730a7432af85ca0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 309, + 295, + 343 + ], + "lines": [ + { + "bbox": [ + 55, + 309, + 295, + 343 + ], + "spans": [ + { + "bbox": [ + 55, + 309, + 295, + 343 + ], + "type": "text", + "content": "Figure 8. Transferability to other Stable Diffusion models. Our Difference Inversion can also be applied to other general Stable Diffusion models, such as SDXL." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 365, + 295, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 365, + 295, + 485 + ], + "spans": [ + { + "bbox": [ + 54, + 365, + 295, + 485 + ], + "type": "text", + "content": "dation in consistency with the original image (B). Without Delta Interpolation and using only Image Delta, the method fails to capture the difference effectively. Similarly, Zero Initialization of Token Embedding shows that when initialized randomly, the difference information is not properly reflected. The ablation results for the number of difference tokens and the interpolation ratio alpha are shown in Fig. 6 and 7, respectively. Additional hyperparameter search results for each method, including lambda tc and lambda clip, can be found in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 501, + 295, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 501, + 295, + 620 + ], + "spans": [ + { + "bbox": [ + 54, + 501, + 295, + 620 + ], + "type": "text", + "content": "Transferability. Since our Difference Inversion is an inference-based method that does not require access to the pretrained diffusion model weights, it can be applied even if the diffusion model is provided in an API form. Though instruction inversion models such as VISII are also inference-based, they depend solely on specific models (e.g. InstructPix2Pix). We test our method on SDXL, which possesses a stronger image prior and is capable of generating more complex and refined images. Fig. 8 demonstrates the application of Difference Inversion to SDXL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 633, + 214, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 633, + 214, + 645 + ], + "spans": [ + { + "bbox": [ + 55, + 633, + 214, + 645 + ], + "type": "text", + "content": "6. Limitations and Discussions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "Failure cases. Despite the strong performance of our model across various editing tasks compared to various baselines, there are still some failure cases. In Fig. 9, it is evident that Difference Inversion struggles to capture global differences (a) or detailed differences (b). For example," + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 71, + 433, + 155 + ], + "blocks": [ + { + "bbox": [ + 316, + 71, + 433, + 155 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 433, + 155 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 433, + 155 + ], + "type": "image", + "image_path": "0afe2d69e95eb88b896b63a1f7342681c00b1bd70563d74ba9055b607982f847.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 163, + 553, + 196 + ], + "lines": [ + { + "bbox": [ + 313, + 163, + 553, + 196 + ], + "spans": [ + { + "bbox": [ + 313, + 163, + 553, + 196 + ], + "type": "text", + "content": "Figure 9. Failure cases. When the difference is complex or difficult to define precisely, Difference Inversion may struggle to capture it effectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 436, + 71, + 553, + 155 + ], + "blocks": [ + { + "bbox": [ + 436, + 71, + 553, + 155 + ], + "lines": [ + { + "bbox": [ + 436, + 71, + 553, + 155 + ], + "spans": [ + { + "bbox": [ + 436, + 71, + 553, + 155 + ], + "type": "image", + "image_path": "5d688d164d25edded7de1406bd33e634c011b41196b12ac9048e97b46b96cfb2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "spans": [ + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "text", + "content": "global differences (a) such as weather shifts or transformations like image-to-sketch cannot be effectively applied to " + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 220, + 555, + 340 + ], + "type": "text", + "content": " when optimized through text tokens. Similarly, for detailed differences (b), as shown in the top example of changing a boy to a crying boy, the approach may result in changing a girl to another girl or fail to accurately capture the intended crying expression altogether. In cases like adding cherries to a cake (bottom example), such changes may also be poorly reflected in B', highlighting its limitations in capturing intended variations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 365, + 555, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 555, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 555, + 556 + ], + "type": "text", + "content": "Inherent limitations of the CLIP space. We hypothesize that the primary reason for the aforementioned failure cases stems from the inherent limitations of the CLIP space. Although we attempt to derive finer Delta using Image and Text Delta within the CLIP space, it does not always align well with human perception, potentially making it unstable for providing precise directional guidance. In the supplementary materials, we illustrate this using a colorization analogy on MNIST data, showing the CLIP similarity for transitions from ground truth " + }, + { + "bbox": [ + 313, + 365, + 555, + 556 + ], + "type": "inline_equation", + "content": "A \\rightarrow A'" + }, + { + "bbox": [ + 313, + 365, + 555, + 556 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 365, + 555, + 556 + ], + "type": "inline_equation", + "content": "B \\rightarrow B'" + }, + { + "bbox": [ + 313, + 365, + 555, + 556 + ], + "type": "text", + "content": ". Notably, the CLIP similarity yields only around 0.5, indicating that optimization based on this directional signal is challenging. We anticipate that future approaches may involve using more refined embedding spaces from foundation models such as DINO-v2 or learning additional mapping networks to enhance similarity and stability." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 571, + 388, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 571, + 388, + 585 + ], + "spans": [ + { + "bbox": [ + 313, + 571, + 388, + 585 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": "In this paper, we propose Difference Inversion, a model-agnostic inversion method that applies only the differences to " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": " without introducing unwanted artifacts. Difference Inversion captures precise differences from " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": " and can be applied to any query image " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": ". This approach aligns well with the goal of image analogy generation, resulting in the creation of feasible " + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 313, + 594, + 555, + 715 + ], + "type": "text", + "content": ". Additionally, our method can be applied to various diffusion models, paving the way for new opportunities not only in image editing but also across diverse computer vision tasks using analogy formulations." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18257" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 170, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 170, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 170, + 85 + ], + "type": "text", + "content": "8. Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "spans": [ + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "text", + "content": "This research was supported by the MSIT(Ministry of Science and ICT), Korea, under the ITRC(Information Technology Research Center) support program(IITP-2024-RS-2023-00258649, " + }, + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "text", + "content": " ) supervised by the IITP(Institute for Information Communications Technology Planning Evaluation). This research was also supported by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No. RS-2019-II190079, Artificial Intelligence Graduate School Program(Korea University), " + }, + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "text", + "content": " ) and the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(No. RS-2025-00562437 " + }, + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "text", + "content": " , No. RS-2024- 00341514, " + }, + { + "bbox": [ + 55, + 90, + 297, + 245 + ], + "type": "inline_equation", + "content": "9\\%" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 256, + 115, + 268 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 256, + 115, + 268 + ], + "spans": [ + { + "bbox": [ + 56, + 256, + 115, + 268 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 275, + 296, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 61, + 275, + 296, + 319 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 275, + 296, + 319 + ], + "spans": [ + { + "bbox": [ + 61, + 275, + 296, + 319 + ], + "type": "text", + "content": "[1] Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Schonlieb, and Christian Etmann. 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We propose a differentiable inverse rendering method with (a) multi-view flash photography inputs. Our analysis-by-synthesis method achieves not only (b) novel-view relighting and accurate geometry reconstruction, but also (c) interpretable basis BRDFs and their spatially-separated weights. This allows for (d) intuitive scene editing." + ], + "image_footnote": [], + "bbox": [ + 411, + 390, + 645, + 457 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/99a3fb3115c2ef2b1cbfc31835b950f7e615c0c859d51c3fb2c48c2d709c6f9f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 661, + 239, + 844, + 349 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/aed52b066ac36716b8cd2c1376f347038de4efb1487e3688cd51d45baf35887a.jpg", + "image_caption": [ + "(d) Reflectance editing with environment relighting" + ], + "image_footnote": [], + "bbox": [ + 661, + 349, + 844, + 457 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7a49492bbf2da34c3acc2a579a8d5517689da89a794051bce05ba856d15a6077.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 844, + 253, + 890, + 335 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4bd9bd5016b6c39a5e0595801a31f1dd667c8ef4d88c82df6b261c8293a046e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 844, + 359, + 890, + 441 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 544, + 310, + 559 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inverse rendering seeks to reconstruct both geometry and spatially varying BRDFs (SVBRDFs) from captured images. To address the inherent ill-posedness of inverse rendering, basis BRDF representations are commonly used, modeling SVBRDFs as spatially varying blends of a set of basis BRDFs. However, existing methods often yield basis BRDFs that lack intuitive separation and have limited scalability to scenes of varying complexity. In this paper, we introduce a differentiable inverse rendering method that produces interpretable basis BRDFs. Our approach models a scene using 2D Gaussians, where the reflectance of each Gaussian is defined by a weighted blend of basis BRDFs. We efficiently render an image from the 2D Gaussians and basis BRDFs using differentiable rasterization and impose a specular-weighted rendering loss with the input flash photography images. During this analysis-by-synthesis optimization process of differentiable inverse rendering, we dynamically adjust the number of basis BRDFs to fit the target scene while encouraging sparsity in the basis weights. This ensures that the reflectance of each Gaussian is represented by only a few basis BRDFs. This approach enables", + "bbox": [ + 75, + 583, + 472, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the reconstruction of accurate geometry and interpretable basis BRDFs that are spatially separated. Consequently, the resulting scene representation, comprising basis BRDFs and 2D Gaussians, supports physically-based novel-view relighting and intuitive scene editing.", + "bbox": [ + 498, + 545, + 892, + 621 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 646, + 630, + 661 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inverse rendering aims to reconstruct geometry and reflectance from captured images, a fundamental problem in computer vision and computer graphics. Recent advances in differentiable rendering methods [18, 29] have facilitated analysis-by-synthesis differentiable inverse rendering. These methods enable the optimization of scene parameters by minimizing the discrepancy between captured and synthesized images [2, 8, 12, 45, 47]. However, achieving accurate inverse rendering remains challenging, especially when the available lighting and viewing angles are limited. A promising approach to mitigate this problem is to exploit the spatial coherence of SVBRDFs using basis BRDF representations [1, 19, 27, 28, 32]. Representing the BRDF at each point as a spatially varying blend of basis BRDFs allows gathering multiple points to accurately fit basis BRDFs", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "475", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and their per-point weights.", + "bbox": [ + 76, + 90, + 261, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Early methods often focus solely on estimating basis BRDFs and their weights for objects with known 3D geometry [20, 21, 50]. Moreover, they typically require excessive optimization time and suffer from low accuracy. Recent methods jointly optimize geometry and basis BRDFs [2, 8, 30]. These approaches often result in non-interpretable basis BRDFs which are spatially entangled: each scene point is represented by many basis BRDFs with high weights and those basis BRDFs are often non-interpretable. Thus, their results are impractical to use for downstream tasks such as scene editing. Additionally, they are often limited to using a fixed number of basis BRDFs, regardless of scene complexity.", + "bbox": [ + 75, + 106, + 467, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a differentiable inverse rendering method that jointly estimates geometry and reflectance. We represent geometry as a set of 2D Gaussians [9, 14], each with shape parameters and basis BRDF weights. The reflectance of each Gaussian is modeled as a spatially varying blend of basis BRDFs. We dynamically adjust the number of basis BRDFs during the analysis-by-synthesis optimization, promoting sparsity in the basis BRDF weights. To enhance training stability, we employ a weighted photometric loss that focuses on potentially specular regions. We demonstrate that our method obtains not only accurate geometry but also scalable and interpretable basis BRDFs which sparsely represent SVBRDFs as shown in Figure 1. In summary, we make the following contributions:", + "bbox": [ + 75, + 301, + 467, + 513 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs, obtaining interpretable basis BRDFs.", + "- A basis BRDF control method and sparsity regularizer that dynamically adjust the number of basis BRDFs during analysis-by-synthesis optimization, promoting interpretability through sparse blending.", + "- Extensive evaluation compared with existing methods, and demonstration of intuitive scene editing." + ], + "bbox": [ + 76, + 513, + 467, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 662, + 217, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inverse Rendering Learning-based inverse rendering methods train neural networks such as CNNs [22, 23, 33, 34, 38, 43], transformers [51], and diffusion models [25, 31, 40] on datasets, enabling efficient inference by exploiting prior distributions in the training data. They often suffer from out-of-distribution inputs, resulting in physically inaccurate results.", + "bbox": [ + 75, + 688, + 467, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The analysis-by-synthesis framework enables inverse rendering by inverting the forward rendering process. Recent advancements have been particularly sparked by differentiable rendering techniques using volumetric rendering [3-7, 10, 11, 17, 26, 36, 37, 39, 41, 44-48] and rasterization [2, 12, 16, 24, 35, 52]. Recent rasterization-based methods using isotropic points [8], 2D Gaussians [49], and", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Gaussians [2, 12, 16, 24, 35, 52] exhibit both efficiency and accuracy. However, they suffer when insufficient light-view angular samples are provided. Incorporating basis BRDFs into the modern analysis-by-synthesis framework has shown promising performance, however the reconstructed basis BRDFs are often non-interpretable, limiting their usefulness in downstream tasks such as scene editing [2, 8]. In contrast, our novel method obtains 2D Gaussians with accurate geometry and interpretable basis BRDFs.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Basis BRDF Basis BRDFs have often been used as a representation of SVBRDFs, decomposing the SVBRDF into a blend of basis BRDFs. This approach is based on the spatial coherence of reflectance, assuming that the BRDFs of many pixels are similar in real-world scenes [27, 28]. Using basis BRDFs helps reduce the ill-posedness of inverse rendering because it enables gathering many light-angular observations for each basis BRDF reconstruction. Existing methods jointly optimize basis BRDFs and spatially varying weights for planar [19, 32] and non-planar objects [1, 13, 15, 30]. Recently, two methods [2, 8] demonstrated the effectiveness of basis BRDFs in modern differentiable analysis-by-synthesis frameworks. While they showed promising results, the estimated basis BRDFs are non-interpretable as shown in Figure 6, which limits their utility in downstream tasks such as scene editing. Moreover, generalizing their methods to varying degrees of scene complexity is challenging because the number of basis BRDFs is fixed. To overcome these problems, we are inspired by the decade ago work of Zhou et al. [50], which proposed adjusting the number of basis BRDFs during optimization. Their method assumes known geometry, does not exploit a differentiable rendering pipeline, and suffers from low reconstruction accuracy and efficiency. We address these challenges by developing a differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs to obtain interpretable basis BRDFs, where the number of basis BRDFs are automatically controlled.", + "bbox": [ + 496, + 244, + 890, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 679, + 589, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our method consists of two parts. In Section 3.1, we focus on optimizing 2D Gaussians and basis BRDFs without concerning the interpretability of basis BRDFs. Next, we extend the method to obtaining interpretable basis BRDFs in Section 3.2. Figure 2 shows the process of our method over analysis-by-synthesis iterations. We obtain not only accurate geometry but also interpretable basis BRDFs whose number adapts to the scene and the basis BRDFs represent SVBRDFs with spatially-separated basis-BRDF weights.", + "bbox": [ + 496, + 704, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Gaussian Inverse Rendering with Basis BRDFs", + "text_level": 1, + "bbox": [ + 500, + 847, + 890, + 862 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce our method that jointly estimates geometry and a fixed number of basis BRDFs in a differentiable man", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "476", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8045f4104dd6ae281e5d215a87fbc4cdd92de7ac563666385961970a52533e97.jpg", + "image_caption": [ + "Figure 2. The process of our analysis-by-synthesis iterations. Given a set of multi-view photometric images, we initialize point cloud and extract base color for basis BRDFs. We jointly optimize 2D Gaussians and basis BRDFs by comparing the differentiably-rendered images and the input images. Our method enables obtaining interpretable basis BRDFs with spatially-separated basis-BRDF weights and the number of basis BRDFs adapts to the scene." + ], + "image_footnote": [], + "bbox": [ + 78, + 85, + 897, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ner from multi-view flash-photography images.", + "bbox": [ + 76, + 477, + 392, + 493 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Geometry We use 2D Gaussians as geometric primitives [14], where each Gaussian $g \\in G$ is an elliptical disk, and $G$ is the set of all Gaussians. Each Gaussian $g$ is parameterized by its center location $\\mathbf{p} \\in \\mathbb{R}^{3 \\times 1}$ , principal vectors $\\mathbf{t} \\in \\mathbb{R}^{3 \\times 2}$ , and scaling factors $\\mathbf{s} \\in \\mathbb{R}^{2 \\times 1}$ . The Gaussian surface normal $\\mathbf{n}$ is computed as the cross product of the principal vectors.", + "bbox": [ + 75, + 511, + 468, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Basis BRDFs We use a basis BRDF representation, where we define $N$ basis BRDFs. We model the $i$ -th basis $\\mathrm{BRDF}f_{i}$ with base color $\\mathbf{b}_i$ , roughness $\\sigma_{i}$ , and metallic parameter $m_{i}$ using the simplified Disney BRDF model [42]:", + "bbox": [ + 75, + 636, + 470, + 699 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} f _ {i} (\\mathbf {i}, \\mathbf {o}) = \\frac {1 - m _ {i}}{\\pi} \\mathbf {b} _ {i} \\\\ + \\frac {D (\\mathbf {h} ; \\sigma_ {i}) F (\\mathbf {o} , \\mathbf {h} ; \\mathbf {b} _ {i} , m _ {i}) G (\\mathbf {i} , \\mathbf {o} , \\mathbf {n} ; \\sigma_ {i})}{4 (\\mathbf {n} \\cdot \\mathbf {i}) (\\mathbf {n} \\cdot \\mathbf {o})}, \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 720, + 468, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{i}$ and $\\mathbf{o}$ are the incident and outgoing directions, and $\\mathbf{h} = (\\mathbf{i} + \\mathbf{o}) / 2$ is the half-way vector. $D$ is the normal distribution function, $F$ is the Fresnel term, and $G$ is the geometric attenuation. Details of these terms are provided in the Supplemental Document.", + "bbox": [ + 75, + 794, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We assign blending weights $w_{i}(g)$ for every $i$ -th basis BRDF per each Gaussian $g$ , and represent the BRDF $f$ of", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the Gaussian $g$ as:", + "bbox": [ + 500, + 477, + 624, + 492 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\mathbf {i}, \\mathbf {o}; g) = \\sum_ {i = 1} ^ {N} w _ {i} (g) f _ {i} (\\mathbf {i}, \\mathbf {o}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 500, + 890, + 541 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene Representations In summary, our scene representation consists of per-Gaussian parameters $G$ and basis BRDF parameters $R$ :", + "bbox": [ + 498, + 559, + 892, + 604 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ng = \\underbrace{\\{\\mathbf{p},\\mathbf{t},\\mathbf{s}\\}}_{\\text{geometric}}\\cup \\underbrace{\\{\\{w_{i}(g)\\}_{i = 1}^{N},\\alpha\\}}_{\\text{photometric}},\\text{where} g\\in G,\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 611, + 854, + 648 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nR = \\left\\{m _ {i}, \\mathbf {b} _ {i}, \\sigma_ {i} \\right\\} _ {i = 1} ^ {N}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 651, + 890, + 670 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\alpha$ is the Gaussian opacity. To initialize the basis BRDF parameters $R$ , we perform k-means clustering with a fixed number $N$ on the input multi-view flash photography images $I'$ . The base colors $\\{\\mathbf{b}_i\\}_{i=1}^N$ are initialized as the mean values of the clusters. The roughness $\\{\\sigma_i\\}_{i=1}^N$ and metallic parameters $\\{m_i\\}_{i=1}^N$ are set to initial values: $\\sigma_i = 0.5$ and $m_i = 0.0$ . We initialize the weights $w_i(g)$ uniformly and set $\\alpha$ following Huang et al. [14].", + "bbox": [ + 496, + 676, + 892, + 799 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Differentiable Rendering We render an image under the flash light, modeled as a point light source, using differentiable rasterization. Specifically, we compute the radiance $L$ of each Gaussian $g$ as:", + "bbox": [ + 498, + 815, + 890, + 876 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL (\\mathbf {i}, \\mathbf {o}; g) = (\\mathbf {n} \\cdot \\mathbf {i}) f (\\mathbf {i}, \\mathbf {o}; g) E (g), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 883, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "477", + "bbox": [ + 485, + 944, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $E(g)$ is the incident light intensity on Gaussian $g$ .", + "bbox": [ + 76, + 90, + 450, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After computing the radiance, we rasterize the Gaussians onto the image plane, sort them by depth, and accumulate radiance values using alpha blending [14] to produce the final pixel value of the rendered image $I$ . We define this rendering as a function $\\operatorname{render}(\\cdot)$ :", + "bbox": [ + 75, + 106, + 468, + 183 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} I (u) = \\operatorname {r e n d e r} \\left(\\left\\{L _ {i} \\right\\} _ {i = 1} ^ {M}\\right) \\\\ = \\sum_ {i = 1} ^ {M} L _ {i} \\alpha_ {i} \\mathcal {G} _ {i} (\\mathbf {r} (u)) \\prod_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j} \\mathcal {G} _ {j} (\\mathbf {r} (u))\\right), \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 188, + 468, + 252 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $u \\in U$ is a pixel, $M$ is the number of Gaussians projected onto pixel $u$ . $\\{L_i\\}_{i=1}^M$ and $\\{\\alpha_i\\}_{i=1}^M$ are the radiance and opacity values of the depth-sorted $i$ -th Gaussian, respectively. The vector $\\mathbf{r}(u)$ is the ray coming from corresponding pixel $u$ , and $\\mathcal{G}_i(\\mathbf{r}(u))$ is the Gaussian-filtered distance between the center of $i$ -th Gaussian and the intersection point between the ray $\\mathbf{r}(u)$ and the $i$ -th Gaussian. Details are provided in the Supplemental Document.", + "bbox": [ + 75, + 258, + 468, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Optimization We optimize the Gaussian parameters $G$ and the basis BRDF parameters $R$ by minimizing the loss function $\\mathcal{L}$ in an analysis-by-synthesis manner:", + "bbox": [ + 76, + 398, + 468, + 444 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {r e n d e r}} + \\lambda_ {\\text {g e o m}} \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {m a s k}} \\mathcal {L} _ {\\text {m a s k}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 452, + 468, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{render}}$ penalizes the difference between the rendered image $I$ and the input image $I^{\\prime}$ across all input views. $\\mathcal{L}_{\\mathrm{geom}}$ is a geometric regularization term for depth distortion and normal consistency [14], and $\\mathcal{L}_{\\mathrm{mask}}$ is the cross-entropy loss between the rendered mask and the ground-truth mask. $\\lambda_{\\mathrm{geom}}$ and $\\lambda_{\\mathrm{mask}}$ are the balancing weights. Details are provided in the Supplemental Document.", + "bbox": [ + 76, + 476, + 468, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specular-weighted Rendering Loss Multi-view flash photography typically generates fewer observations of specular-dominant pixels compared to diffuse-dominant pixels. To address this imbalance, we weight specular observations by using the potentially-specular weight map:", + "bbox": [ + 75, + 599, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH (u) = 1 + \\lambda_ {\\theta_ {h}} (\\cos \\theta_ {h} (u)) ^ {k}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 683, + 468, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta_h$ is the rendered half-way angle map as $\\theta_h(u) =$ render $\\left(\\{\\arccos (\\mathbf{n}_i\\cdot \\mathbf{h}_i)\\}_{i = 1}^M\\right)$ . $\\mathbf{n}_i$ and $\\mathbf{h}_i$ are the normal and half-way vector of Gaussian $i$ , respectively. We set the scalar $\\lambda_{\\theta_h} = 5$ and $k = 10$ to strongly weight specular regions.", + "bbox": [ + 76, + 708, + 468, + 782 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use the potentially-specular weight map $H$ for calculating the final rendering loss:", + "bbox": [ + 76, + 782, + 468, + 814 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e n d e r}} = \\frac {1}{| U |} \\sum_ {u \\in U} H (u) \\left((1 - \\lambda_ {s}) \\mathcal {L} _ {1} (u) + \\lambda_ {s} \\mathcal {L} _ {\\mathrm {S S I M}} (u)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 820, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_1(u) = \\| I(u) - I'(u)\\|_1$ , $\\mathcal{L}_{\\mathrm{SSIM}}(u)$ is the SSIM loss between $I(u)$ and $I'(u)$ , and $\\lambda_s$ is a balancing weight.", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/725d627019aad0029f75f40064115a70930be9c53f4ec7716ca5f302361bf08e.jpg", + "image_caption": [ + "Figure 3. Basis BRDFs with varying scene complexity. We adjust the number of basis BRDFs during optimization to adapt to the scene complexity. We initialize the same number of basis BRDFs for both scenes in this example." + ], + "image_footnote": [], + "bbox": [ + 501, + 85, + 890, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Interpretable Basis BRDFs", + "text_level": 1, + "bbox": [ + 500, + 436, + 743, + 452 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While our method in Section 3.1 offers accurate inverse rendering, the reconstructed basis BRDFs lack of interpretability. Here, we extend the method to obtain interpretable basis BRDFs whose number adapts to the scene as shown in Figure 3. We develop basis BRDF control method of merge and removal in addition to impose sparsity on basis BRDF weights.", + "bbox": [ + 498, + 467, + 890, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sparsity of Basis BRDF Weights For obtaining interpretable basis BRDF, each scene point needs to be represented with only few basis BRDFs with high weights. This enables spatially separating SVBRDFs with sparse basis BRDFs. We impose sparsity on the basis BRDF weights $\\{w_{i}(g)\\}_{i = 1}^{N}$ for each Gaussian $g$ , making each Gaussian represented by only a few basis BRDFs.", + "bbox": [ + 498, + 623, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, we apply a softmax function with a low temperature $T = 0.0125$ to the weights, promoting sparse per-Gaussian weights:", + "bbox": [ + 498, + 737, + 890, + 782 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} (g) \\leftarrow \\frac {\\exp \\left(w _ {i} (g) / T\\right)}{\\sum_ {i ^ {\\prime} = 1} ^ {N} \\exp \\left(w _ {i ^ {\\prime}} (g) / T\\right)}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 808, + 890, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Second, we apply an entropy-based sparsity regularizer on the Gaussian weight $w_{i}$ and rendered weight image $W_{i}$ for", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "478", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/128eb20158ed538f396b53c408be0bda6d7dce6db115734b416288d99a388cc7.jpg", + "image_caption": [ + "Figure 4. Basis BRDF control. During the optimization, we compute the values of each basis BRDF for sampled half-way angles $\\theta_h$ from which radiometric difference is obtained. We compute the geometric difference between point clouds of basis BRDFs. If two basis BRDFs are radiometrically and geometrically similar, we merge them. If the rendered weight map $W_i$ has few valid pixels, we remove the basis BRDF." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 895, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "each $i$ -th basis BRDF:", + "bbox": [ + 76, + 513, + 228, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {s p a r s e}} = - \\frac {1}{| G |} \\sum_ {g \\in G} \\sum_ {i = 1} ^ {N} w _ {i} (g) \\log w _ {i} (g) \\\\ - \\frac {1}{| U |} \\sum_ {u \\in U} \\sum_ {i = 1} ^ {N} W _ {i} (u) \\log W _ {i} (u), \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 532, + 468, + 619 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nW _ {i} = \\operatorname {r e n d e r} \\left(\\left\\{w _ {i} (g) \\right\\} _ {g \\in G}\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 623, + 468, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Basis BRDF Merge Basis BRDFs often become similar during optimization, making the resulting basis BRDFs non-intuitive with duplicates. We address this by merging similar basis BRDFs during analysis-by-synthesis optimization, as shown in Figure 4. We compute the values of each basis BRDF $f_{i}$ at uniformly-sampled halfway angles $\\theta_{h}$ for the RGB channels, resulting in a matrix $\\mathbf{f}_i\\in \\mathbb{R}^{C\\times 3}$ . $C$ is the number of halfway angles. We then compute the radiometric difference between pairs of basis BRDFs, represented as a matrix $\\mathbf{D}_{\\mathrm{radio}}\\in \\mathbb{R}^{N\\times N}$ , which is defined as:", + "bbox": [ + 75, + 678, + 472, + 830 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {D} _ {\\text {r a d i o}} (i, j) = \\frac {1}{C} \\| \\mathbf {f} _ {i} - \\mathbf {f} _ {j} \\| _ {2}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 839, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also compute the geometric difference between the every pair of basis BRDFs, represented as a matrix $\\mathbf{D}_{\\mathrm{point}} \\in$", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathbb{R}^{N\\times N}$ using the Chamfer distance between point clouds represented by each basis BRDF:", + "bbox": [ + 498, + 512, + 890, + 544 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {D} _ {\\text {p o i n t}} (i, j) = \\frac {1}{| P _ {i} |} \\sum_ {\\mathbf {p} \\in P _ {i}} \\min _ {\\mathbf {q} \\in P _ {j}} \\| \\mathbf {p} - \\mathbf {q} \\| _ {2} ^ {2} \\\\ + \\frac {1}{\\left| P _ {j} \\right|} \\sum_ {\\mathbf {q} \\in P _ {j}} \\min _ {\\mathbf {p} \\in P _ {i}} \\| \\mathbf {q} - \\mathbf {p} \\| _ {2} ^ {2}, \\tag {13} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 556, + 890, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P_{i}$ and $P_{j}$ are the point clouds for the $i$ -th and $j$ -th basis BRDFs, consisting of the center locations of Gaussians where the $i$ -th or $j$ -th basis BRDF has the highest weight.", + "bbox": [ + 498, + 647, + 890, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "If the radiometric difference $\\mathbf{D}_{\\mathrm{radio}}(i,j)$ is below a threshold $\\tau_{\\mathrm{merge}}$ and $\\mathbf{D}_{\\mathrm{point}}(i,j)$ is minimal among all $\\forall j$ , we merge the two basis BRDFs by deleting the basis BRDF with fewer associated Gaussians and reassigning the per-Gaussian basis BRDF weights as", + "bbox": [ + 496, + 693, + 890, + 768 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {j} (g) \\leftarrow w _ {i} (g) + w _ {j} (g), \\quad \\forall g \\in G. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 784, + 890, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Basis BRDF Removal To obtain meaningful basis BRDFs only, we remove $i$ -th basis BRDF if it contributes to only a few pixels during optimization as shown in Figure 4. We evaluate this using the rendered weight image $W_{i}$", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "479", + "bbox": [ + 485, + 944, + 511, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/470faa1752544a0026f279f3201b4879732ff9771dabe3abebdbaa5179b2b448.jpg", + "image_caption": [ + "Figure 5. Normal reconstruction. Our method successfully recovers the detailed surface normal, outperforming other state-of-the-art inverse rendering methods: IRON [45], DPIR [8], GS³ [2]." + ], + "image_footnote": [], + "bbox": [ + 80, + 85, + 349, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/abdf114cd4c4954a437455666a963281e500b646c319ebce255f66713c9bda6e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 85, + 485, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9ba739addaa04c9ca7251207b8e2fe0057d17d002d00a4da0d2597717e11c97c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 85, + 620, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f200ddf5e1121800a39f25407707f2c6b6734e32bd315cea34fd6cd872aa13cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 85, + 753, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c5dfd8e6db340811253473b1ea218673f1ed389a95b258ee0a2a53a42b24c104.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 85, + 892, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "from Equation (11) as:", + "bbox": [ + 76, + 321, + 230, + 335 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\left| \\left\\{u \\in U \\mid W _ {i} (u) > \\tau_ {\\text {r e m o v a l - w e i g h t}} \\right\\} \\right|}{\\left| U \\right|} < \\tau_ {\\text {r e m o v a l - n u m b e r}}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 345, + 468, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\tau_{\\mathrm{removal - weight}} = 0.1$ is the threshold determining whether the $i$ -th basis BRDF significantly contributes to that pixel $u$ , and $\\tau_{\\mathrm{removal - number}} = 0.005$ is the threshold for the normalized number of such pixels.", + "bbox": [ + 75, + 388, + 468, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Scheduling For a warm start, we first run our inverse rendering described in Section 3.1. After a predefined number of iterations, 6000 in our experiments, we perform basis BRDF merge and removal at predefined intervals 500 during iterations to refine the basis BRDFs. We incorporate the sparsity loss $\\mathcal{L}_{\\mathrm{sparse}}$ and optimize the scene parameters by minimizing:", + "bbox": [ + 75, + 457, + 468, + 563 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {r e n d e r}} + \\lambda_ {\\text {g e o m}} \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {m a s k}} \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {\\text {s p a r s e}} \\mathcal {L} _ {\\text {s p a r s e}}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 574, + 468, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{\\mathrm{sparse}}$ is the balancing weight. Refer to the Supplemental Document for the details on the optimization.", + "bbox": [ + 76, + 602, + 468, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Results", + "text_level": 1, + "bbox": [ + 76, + 646, + 163, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets We evaluate our approach on both synthetic and real-world photometric dataset. For the synthetic dataset, we render four complex scenes containing multiple objects, following the co-located flash photography. Each scene includes multiple objects. The dataset consists of 200 training images and 100 test images per scene. For the real-world photometric dataset, we capture one multi-object scene using a mobile phone with flash at 200/40 training/testing images. We conduct geometric and radiometric calibrations of the light and the camera.", + "bbox": [ + 75, + 671, + 468, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Validation and Comparison", + "text_level": 1, + "bbox": [ + 76, + 832, + 326, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Geometry We assess our method in comparison with state-of-the-art analysis-by-synthesis inverse rendering methods: IRON [45], DPIR [8] and $\\mathrm{GS}^3$ [2]. Figure 5", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/49385010c4977bd46a8a6ea2e417ff13ded020f155e2827b82e255717ca2fa97.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    IRONDPIRGS3Ours
    MAE ↓15.7117.0415.289.81
    Train ↓12h2h1h0.5h
    ", + "bbox": [ + 562, + 318, + 834, + 369 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Normal reconstruction and training time. Our method outperforms IRON [45], DPIR [8], and $\\mathrm{GS}^3$ [2] in quantitative numbers evaluated on the synthetic dataset.", + "bbox": [ + 498, + 380, + 892, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and Table 1 show the results for geometry reconstruction, demonstrating the highest accuracy in normal reconstruction with mean angular error (MAE). IRON and DPIR employ neural signed distance functions to recover smooth surface normal, not only resulting in loss of details but also requiring extended training times for optimization as shown in Table 1. $\\mathrm{GS}^3$ , which is based on 3D Gaussian splatting with anisotropic spherical Gaussians, exhibits limited accuracy in shape reconstruction. Our method accurately models surface geometry and reflectance using 2D Gaussians and interpretable basis BRDFs, achieving the highest accuracy of normal reconstruction, especially for thin and convex objects. Moreover, we outperform the others in terms of training speed.", + "bbox": [ + 496, + 428, + 892, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Basis BRDF Figure 6 shows the estimated basis BRDFs and weight maps, comparing modern inverse-rendering methods using basis BRDFs: $\\mathrm{GS}^3$ , DPIR, our method without interpretable basis BRDFs (Section 3.1), and our method with interpretable basis BRDFs (Section 3.2). Both DPIR and $\\mathrm{GS}^3$ use basis BRDFs to leverage spatial coherence of specular reflectance. These methods yield non-interpretable basis BRDFs, as evident from the rendered weight maps and basis BRDF renderings. Our method introduced in Section 3.1 improves the interpretability of the basis BRDFs by jointly optimizing base colors. However, the resulting basis BRDFs are still often duplicated and non-intuitively classified. Moreover, all the methods have a fixed number of basis BRDFs, limited to modeling different complexity of scenes. In contrast, our full method (Section 3.2) obtains interpretable basis BRDFs whose number fits the target scene, as shown in Figure 3.", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "480", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3aba177f7a6066582e1fc2def283490cc35a0b60880c9e6e013fdfdfee2e9a71.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 89, + 893, + 400 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3b2ffe749a6065a3179b29f1206265b1d567c30434ca5e329c2b7bb9b14c3575.jpg", + "image_caption": [ + "Figure 6. Basis BRDFs and weight maps. Our inverse-rendering methods (Section 3.1 and Section 3.2) obtain basis BRDFs that are explainable with spatially separated weight maps and intuitive basis BRDFs, compared to $\\mathrm{GS}^3$ [2] and DPIR [8].", + "Figure 7. Novel-view relighting. Our method enables high quality novel-view relighting with the accurate surface normal. We achieve physically-valid relighting with accurate normal and basis BRDFs." + ], + "image_footnote": [], + "bbox": [ + 78, + 436, + 890, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Applications", + "text_level": 1, + "bbox": [ + 76, + 625, + 210, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Novel-view Relighting Figure 7 shows novel-view relighting and estimated normals, compared with IRON, DPIR, $\\mathrm{GS}^3$ . They suffer from inaccurate estimation of geometry. Despite inaccurate normals, $\\mathrm{GS}^3$ manages to render high-quality relighting results. This is because neural networks compensate for such imperfection by learning residuals, as relighting is the main goal of $\\mathrm{GS}^3$ . In contrast, our method reconstructs accurate geometry and interpretable basis BRDFs that enable not only novel-view relighting but also downstream tasks such as intuitive scene editing. For more results, refer to the Supplemental Document.", + "bbox": [ + 75, + 648, + 472, + 815 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Scene Editing Our inverse rendering method enables selective editing based on basis BRDFs and weight images. Figure 8 shows that our interpretable basis BRDFs facilitate reflectance editing. Interpretable basis BRDFs enable prac", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tical material editing by adjusting desired BRDF parameters of base color, roughness, metallic based on their sparse weight maps. We then obtain a single object from the entire scene by selecting basis BRDFs that are utilized to represent the corresponding object. Next, we delete other basis BRDFs and Gaussians that have the highest weight for other basis BRDFs. We also filter out Gaussians based on Gaussian positions. This allows for extracting object mesh [14] and relighting it under an environment map. Figure 9 shows additional material-editing results on a real-world scene.", + "bbox": [ + 496, + 625, + 893, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 787, + 653, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sparsity Regularizer $\\mathcal{L}_{\\mathrm{sparse}}$ Figure 10 shows that the sparsity regularizer and the basis BRDF control enable obtaining interpretable basis BRDFs.", + "bbox": [ + 496, + 810, + 892, + 857 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Specular-weighted Rendering Loss We test the impact of the specular-weighted rendering loss that prioritizes", + "bbox": [ + 496, + 869, + 892, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "481", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f7aec45f78e3b5222d1a04210da25b1433abc2c19580bf32bd7ce66a64594c04.jpg", + "image_caption": [ + "Estimated image and basis BRDFs" + ], + "image_footnote": [], + "bbox": [ + 80, + 85, + 468, + 198 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d28bcb77663995c68478d9bbf5dfd430021a835b812c4a14a6929985414ecf57.jpg", + "image_caption": [ + "Point cloud for basis BRDF" + ], + "image_footnote": [], + "bbox": [ + 81, + 205, + 225, + 318 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d00a7595a30c1d4ac2562b3bc7d5e72849365378037cc1170f92e2e5ad5e77fd.jpg", + "image_caption": [ + "Mesh extraction" + ], + "image_footnote": [], + "bbox": [ + 228, + 209, + 336, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f8f735e0375b71662b16560f0dc49ec6c47a437944ea6a35bfc8b0e73875e6e.jpg", + "image_caption": [ + "Environment relighting" + ], + "image_footnote": [], + "bbox": [ + 354, + 208, + 460, + 318 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bda3b30dd6cee9ace18049fcae506b8c566218244c13194a0d6521d0d06a12b8.jpg", + "image_caption": [ + "Figure 8. Intuitive scene editing. We modify our basis BRDF parameters to edit the reflectance. We also selectively extract mesh and relight it under the environment map.", + "Novel view relighting" + ], + "image_footnote": [], + "bbox": [ + 80, + 393, + 289, + 483 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/babf3c1e0e78e41d07e8d793feaf26fb5fcdb541d24266f39d4dd7b0e241aad9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 393, + 468, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d44a9320fde5d759681afbbca882817d8c5248e1202795ef7d8ff0cb0f0eed43.jpg", + "image_caption": [ + "Material editing with white lightings", + "Material editing with colorful lightings", + "Figure 9. Material editing and relighting on real-world objects. We obtain high-quality novel-view relighting for a real-world scene, where interpretable basis BRDFs are reconstructed with their sparse weight maps. We edit basis BRDFs and relight the scene under novel illumination conditions." + ], + "image_footnote": [], + "bbox": [ + 80, + 489, + 287, + 578 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/061d5ee2138d4d6bd2fa1ee5390adf9718fd5da68ffd436e7be065e890a94ec2.jpg", + "image_caption": [ + "Basis BRDFs and weight maps" + ], + "image_footnote": [], + "bbox": [ + 295, + 489, + 468, + 578 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "potentially-specular areas using the rendered half-way angle map. Figure 11 shows that specular-weighted rendering loss produces a more stable reconstruction compared to not using the weighting.", + "bbox": [ + 75, + 681, + 468, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 753, + 194, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have introduced a differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs. Our method obtains interpretable basis BRDFs that can represent SVBRDFs in a spatially-separable manner, enabling accurate geometry and SVBRDF reconstruction. Also, the number of basis BRDFs automatically adjusts to a target scene. We demonstrate the effectiveness of our method compared to state-of-the", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a1f38dea73faad2c0d905caaf91b8fb59a840432661f080e24253919383ad319.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 640, + 234 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5022f0ecb408223ea0884a10865c925943dde71eb7e9bb83a0892491662b9df1.jpg", + "image_caption": [ + "With sparsity and basis control" + ], + "image_footnote": [], + "bbox": [ + 640, + 88, + 764, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/727817af93538d602176f098e25b618d6d96cbc66031cfae2fb06a8933daf61b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 89, + 890, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a9264f18796ed9133c5248facdc4a5286b3b7268e796d8020ff9cb9f7908a7ec.jpg", + "image_caption": [ + "Without sparsity and basis control" + ], + "image_footnote": [], + "bbox": [ + 640, + 188, + 764, + 275 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cd723bc44511fd5486c83091dd8ee8e80b88f8d1780dbe533f2818c8cfa057ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 766, + 188, + 890, + 275 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2e03aaaf67bc472bfdb0f12b53182161a6fc6cbd6f9f330cd9797d2855260d8c.jpg", + "image_caption": [ + "Figure 10. Impact of sparsity regularizer and basis BRDF control. Without sparsity loss and basis BRDF control of merge and removal, the resulting basis BRDFs are blended each other as shown in the corresponding images, making them non-interpretable for downstream tasks.", + "GT image" + ], + "image_footnote": [], + "bbox": [ + 501, + 369, + 687, + 515 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a94cdbae2b05ddc38aa7aed56013b505387afdc317c485933c4f193d618b352d.jpg", + "image_caption": [ + "Specular weight map" + ], + "image_footnote": [], + "bbox": [ + 687, + 371, + 870, + 513 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2d529f9d2135ac2dd1c5cec2813275cf1311d3926ae87f203f4fe61faf4c72ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 523, + 629, + 571 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e374f566130c2d394e41e489ce9d669d4262c7fe05e029b9747c7c0147bb60eb.jpg", + "image_caption": [ + "Without specular weight", + "Figure 11. Impact of specular-weighted loss. Using specular-weighted rendering loss improves geometry and reflectance reconstruction quality by recovering high frequency features from specularity, which is emphasized by the specular weight map." + ], + "image_footnote": [], + "bbox": [ + 504, + 571, + 630, + 622 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4cdb5770a6022cd051b43fd3c5299dc67e329f631f4ec74ebd2bf6e64d3d6b83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 523, + 756, + 571 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/805d98973449b3329b258aab08aae9b35daf766ea39373ed81293ff803e25897.jpg", + "image_caption": [ + "With specular weight" + ], + "image_footnote": [], + "bbox": [ + 630, + 571, + 756, + 622 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/907ae77864f8145dcfe095019c6b949f9aee953cfb32ba8d8be79600fd1a0e1d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 758, + 523, + 888, + 571 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/def55d2dbc94e646ada2516d8126d3f90a5c89f2118584dac220a8af4243d22b.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 759, + 571, + 888, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "art approaches. Using the interpretable basis BRDFs, our method also facilitates downstream tasks such as intuitive scene editing.", + "bbox": [ + 498, + 714, + 890, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations Our basis BRDF representation assumes opaque objects, leaving modeling non-surface objects as a future work. Combining semantic information from a large vision model is also an interesting future work.", + "bbox": [ + 498, + 768, + 890, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, RS-2024-00438532, RS-2025-00518643), and Korea IITP MSIT (RS-2023-00215700).", + "bbox": [ + 498, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "482", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Neil Alldrin, Todd Zickler, and David Kriegman. Photometric stereo with non-parametric and spatially-varying reflectance. In 2008 IEEE Conference on Computer Vision and Pattern Recognition, pages 1-8. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.155, + 0.131, + 0.816, + 0.152 + ], + "angle": 0, + "content": "Differentiable Inverse Rendering with Interpretable Basis BRDFs" + }, + { + "type": "text", + "bbox": [ + 0.251, + 0.181, + 0.72, + 0.216 + ], + "angle": 0, + "content": "Hoon-Gyu Chung Seokjun Choi Seung-Hwan Baek POSTECH" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.24, + 0.227, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.344, + 0.225, + 0.458 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.459, + 0.206, + 0.482 + ], + "angle": 0, + "content": "(a) Input multi-view flash images" + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.24, + 0.411, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.348, + 0.411, + 0.458 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.24, + 0.459, + 0.399, + 0.482 + ], + "angle": 0, + "content": "(b) Image and normals under novel view and lighting" + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.24, + 0.647, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.391, + 0.647, + 0.458 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.44, + 0.459, + 0.624, + 0.482 + ], + "angle": 0, + "content": "(c) Our interpretable basis BRDFs and weight maps" + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.315, + 0.658, + 0.393 + ], + "angle": 0, + "content": "1.C 0.C" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.24, + 0.846, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.351, + 0.846, + 0.458 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.459, + 0.831, + 0.481 + ], + "angle": 0, + "content": "(d) Reflectance editing with environment relighting" + }, + { + "type": "image", + "bbox": [ + 0.846, + 0.255, + 0.892, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.846, + 0.361, + 0.892, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.49, + 0.893, + 0.532 + ], + "angle": 0, + "content": "Figure 1. We propose a differentiable inverse rendering method with (a) multi-view flash photography inputs. Our analysis-by-synthesis method achieves not only (b) novel-view relighting and accurate geometry reconstruction, but also (c) interpretable basis BRDFs and their spatially-separated weights. This allows for (d) intuitive scene editing." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.545, + 0.312, + 0.56 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Inverse rendering seeks to reconstruct both geometry and spatially varying BRDFs (SVBRDFs) from captured images. To address the inherent ill-posedness of inverse rendering, basis BRDF representations are commonly used, modeling SVBRDFs as spatially varying blends of a set of basis BRDFs. However, existing methods often yield basis BRDFs that lack intuitive separation and have limited scalability to scenes of varying complexity. In this paper, we introduce a differentiable inverse rendering method that produces interpretable basis BRDFs. Our approach models a scene using 2D Gaussians, where the reflectance of each Gaussian is defined by a weighted blend of basis BRDFs. We efficiently render an image from the 2D Gaussians and basis BRDFs using differentiable rasterization and impose a specular-weighted rendering loss with the input flash photography images. During this analysis-by-synthesis optimization process of differentiable inverse rendering, we dynamically adjust the number of basis BRDFs to fit the target scene while encouraging sparsity in the basis weights. This ensures that the reflectance of each Gaussian is represented by only a few basis BRDFs. This approach enables" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.546, + 0.893, + 0.622 + ], + "angle": 0, + "content": "the reconstruction of accurate geometry and interpretable basis BRDFs that are spatially separated. Consequently, the resulting scene representation, comprising basis BRDFs and 2D Gaussians, supports physically-based novel-view relighting and intuitive scene editing." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.647, + 0.631, + 0.662 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Inverse rendering aims to reconstruct geometry and reflectance from captured images, a fundamental problem in computer vision and computer graphics. Recent advances in differentiable rendering methods [18, 29] have facilitated analysis-by-synthesis differentiable inverse rendering. These methods enable the optimization of scene parameters by minimizing the discrepancy between captured and synthesized images [2, 8, 12, 45, 47]. However, achieving accurate inverse rendering remains challenging, especially when the available lighting and viewing angles are limited. A promising approach to mitigate this problem is to exploit the spatial coherence of SVBRDFs using basis BRDF representations [1, 19, 27, 28, 32]. Representing the BRDF at each point as a spatially varying blend of basis BRDFs allows gathering multiple points to accurately fit basis BRDFs" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "475" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.262, + 0.106 + ], + "angle": 0, + "content": "and their per-point weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.468, + 0.302 + ], + "angle": 0, + "content": "Early methods often focus solely on estimating basis BRDFs and their weights for objects with known 3D geometry [20, 21, 50]. Moreover, they typically require excessive optimization time and suffer from low accuracy. Recent methods jointly optimize geometry and basis BRDFs [2, 8, 30]. These approaches often result in non-interpretable basis BRDFs which are spatially entangled: each scene point is represented by many basis BRDFs with high weights and those basis BRDFs are often non-interpretable. Thus, their results are impractical to use for downstream tasks such as scene editing. Additionally, they are often limited to using a fixed number of basis BRDFs, regardless of scene complexity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.468, + 0.514 + ], + "angle": 0, + "content": "In this paper, we propose a differentiable inverse rendering method that jointly estimates geometry and reflectance. We represent geometry as a set of 2D Gaussians [9, 14], each with shape parameters and basis BRDF weights. The reflectance of each Gaussian is modeled as a spatially varying blend of basis BRDFs. We dynamically adjust the number of basis BRDFs during the analysis-by-synthesis optimization, promoting sparsity in the basis BRDF weights. To enhance training stability, we employ a weighted photometric loss that focuses on potentially specular regions. We demonstrate that our method obtains not only accurate geometry but also scalable and interpretable basis BRDFs which sparsely represent SVBRDFs as shown in Figure 1. In summary, we make the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.515, + 0.468, + 0.559 + ], + "angle": 0, + "content": "- A differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs, obtaining interpretable basis BRDFs." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.56, + 0.468, + 0.62 + ], + "angle": 0, + "content": "- A basis BRDF control method and sparsity regularizer that dynamically adjust the number of basis BRDFs during analysis-by-synthesis optimization, promoting interpretability through sparse blending." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.62, + 0.468, + 0.651 + ], + "angle": 0, + "content": "- Extensive evaluation compared with existing methods, and demonstration of intuitive scene editing." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.515, + 0.468, + 0.651 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.218, + 0.68 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.468, + 0.794 + ], + "angle": 0, + "content": "Inverse Rendering Learning-based inverse rendering methods train neural networks such as CNNs [22, 23, 33, 34, 38, 43], transformers [51], and diffusion models [25, 31, 40] on datasets, enabling efficient inference by exploiting prior distributions in the training data. They often suffer from out-of-distribution inputs, resulting in physically inaccurate results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The analysis-by-synthesis framework enables inverse rendering by inverting the forward rendering process. Recent advancements have been particularly sparked by differentiable rendering techniques using volumetric rendering [3-7, 10, 11, 17, 26, 36, 37, 39, 41, 44-48] and rasterization [2, 12, 16, 24, 35, 52]. Recent rasterization-based methods using isotropic points [8], 2D Gaussians [49], and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "3D Gaussians [2, 12, 16, 24, 35, 52] exhibit both efficiency and accuracy. However, they suffer when insufficient light-view angular samples are provided. Incorporating basis BRDFs into the modern analysis-by-synthesis framework has shown promising performance, however the reconstructed basis BRDFs are often non-interpretable, limiting their usefulness in downstream tasks such as scene editing [2, 8]. In contrast, our novel method obtains 2D Gaussians with accurate geometry and interpretable basis BRDFs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.668 + ], + "angle": 0, + "content": "Basis BRDF Basis BRDFs have often been used as a representation of SVBRDFs, decomposing the SVBRDF into a blend of basis BRDFs. This approach is based on the spatial coherence of reflectance, assuming that the BRDFs of many pixels are similar in real-world scenes [27, 28]. Using basis BRDFs helps reduce the ill-posedness of inverse rendering because it enables gathering many light-angular observations for each basis BRDF reconstruction. Existing methods jointly optimize basis BRDFs and spatially varying weights for planar [19, 32] and non-planar objects [1, 13, 15, 30]. Recently, two methods [2, 8] demonstrated the effectiveness of basis BRDFs in modern differentiable analysis-by-synthesis frameworks. While they showed promising results, the estimated basis BRDFs are non-interpretable as shown in Figure 6, which limits their utility in downstream tasks such as scene editing. Moreover, generalizing their methods to varying degrees of scene complexity is challenging because the number of basis BRDFs is fixed. To overcome these problems, we are inspired by the decade ago work of Zhou et al. [50], which proposed adjusting the number of basis BRDFs during optimization. Their method assumes known geometry, does not exploit a differentiable rendering pipeline, and suffers from low reconstruction accuracy and efficiency. We address these challenges by developing a differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs to obtain interpretable basis BRDFs, where the number of basis BRDFs are automatically controlled." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.591, + 0.695 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Our method consists of two parts. In Section 3.1, we focus on optimizing 2D Gaussians and basis BRDFs without concerning the interpretability of basis BRDFs. Next, we extend the method to obtaining interpretable basis BRDFs in Section 3.2. Figure 2 shows the process of our method over analysis-by-synthesis iterations. We obtain not only accurate geometry but also interpretable basis BRDFs whose number adapts to the scene and the basis BRDFs represent SVBRDFs with spatially-separated basis-BRDF weights." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.891, + 0.863 + ], + "angle": 0, + "content": "3.1. Gaussian Inverse Rendering with Basis BRDFs" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.891, + 0.899 + ], + "angle": 0, + "content": "We introduce our method that jointly estimates geometry and a fixed number of basis BRDFs in a differentiable man" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "476" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.086, + 0.898, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.403, + 0.895, + 0.46 + ], + "angle": 0, + "content": "Figure 2. The process of our analysis-by-synthesis iterations. Given a set of multi-view photometric images, we initialize point cloud and extract base color for basis BRDFs. We jointly optimize 2D Gaussians and basis BRDFs by comparing the differentiably-rendered images and the input images. Our method enables obtaining interpretable basis BRDFs with spatially-separated basis-BRDF weights and the number of basis BRDFs adapts to the scene." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.478, + 0.393, + 0.494 + ], + "angle": 0, + "content": "ner from multi-view flash-photography images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.619 + ], + "angle": 0, + "content": "Geometry We use 2D Gaussians as geometric primitives [14], where each Gaussian \\( g \\in G \\) is an elliptical disk, and \\( G \\) is the set of all Gaussians. Each Gaussian \\( g \\) is parameterized by its center location \\( \\mathbf{p} \\in \\mathbb{R}^{3 \\times 1} \\), principal vectors \\( \\mathbf{t} \\in \\mathbb{R}^{3 \\times 2} \\), and scaling factors \\( \\mathbf{s} \\in \\mathbb{R}^{2 \\times 1} \\). The Gaussian surface normal \\( \\mathbf{n} \\) is computed as the cross product of the principal vectors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.471, + 0.7 + ], + "angle": 0, + "content": "Basis BRDFs We use a basis BRDF representation, where we define \\(N\\) basis BRDFs. We model the \\(i\\)-th basis \\(\\mathrm{BRDF}f_{i}\\) with base color \\(\\mathbf{b}_i\\), roughness \\(\\sigma_{i}\\), and metallic parameter \\(m_{i}\\) using the simplified Disney BRDF model [42]:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.721, + 0.469, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} f _ {i} (\\mathbf {i}, \\mathbf {o}) = \\frac {1 - m _ {i}}{\\pi} \\mathbf {b} _ {i} \\\\ + \\frac {D (\\mathbf {h} ; \\sigma_ {i}) F (\\mathbf {o} , \\mathbf {h} ; \\mathbf {b} _ {i} , m _ {i}) G (\\mathbf {i} , \\mathbf {o} , \\mathbf {n} ; \\sigma_ {i})}{4 (\\mathbf {n} \\cdot \\mathbf {i}) (\\mathbf {n} \\cdot \\mathbf {o})}, \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.87 + ], + "angle": 0, + "content": "where \\(\\mathbf{i}\\) and \\(\\mathbf{o}\\) are the incident and outgoing directions, and \\(\\mathbf{h} = (\\mathbf{i} + \\mathbf{o}) / 2\\) is the half-way vector. \\(D\\) is the normal distribution function, \\(F\\) is the Fresnel term, and \\(G\\) is the geometric attenuation. Details of these terms are provided in the Supplemental Document." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We assign blending weights \\( w_{i}(g) \\) for every \\( i \\)-th basis BRDF per each Gaussian \\( g \\), and represent the BRDF \\( f \\) of" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.478, + 0.625, + 0.493 + ], + "angle": 0, + "content": "the Gaussian \\(g\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.501, + 0.892, + 0.542 + ], + "angle": 0, + "content": "\\[\nf (\\mathbf {i}, \\mathbf {o}; g) = \\sum_ {i = 1} ^ {N} w _ {i} (g) f _ {i} (\\mathbf {i}, \\mathbf {o}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.56, + 0.893, + 0.605 + ], + "angle": 0, + "content": "Scene Representations In summary, our scene representation consists of per-Gaussian parameters \\(G\\) and basis BRDF parameters \\(R\\):" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.612, + 0.855, + 0.65 + ], + "angle": 0, + "content": "\\[\ng = \\underbrace{\\{\\mathbf{p},\\mathbf{t},\\mathbf{s}\\}}_{\\text{geometric}}\\cup \\underbrace{\\{\\{w_{i}(g)\\}_{i = 1}^{N},\\alpha\\}}_{\\text{photometric}},\\text{where} g\\in G,\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.652, + 0.892, + 0.671 + ], + "angle": 0, + "content": "\\[\nR = \\left\\{m _ {i}, \\mathbf {b} _ {i}, \\sigma_ {i} \\right\\} _ {i = 1} ^ {N}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.678, + 0.893, + 0.8 + ], + "angle": 0, + "content": "\\(\\alpha\\) is the Gaussian opacity. To initialize the basis BRDF parameters \\(R\\), we perform k-means clustering with a fixed number \\(N\\) on the input multi-view flash photography images \\(I'\\). The base colors \\(\\{\\mathbf{b}_i\\}_{i=1}^N\\) are initialized as the mean values of the clusters. The roughness \\(\\{\\sigma_i\\}_{i=1}^N\\) and metallic parameters \\(\\{m_i\\}_{i=1}^N\\) are set to initial values: \\(\\sigma_i = 0.5\\) and \\(m_i = 0.0\\). We initialize the weights \\(w_i(g)\\) uniformly and set \\(\\alpha\\) following Huang et al. [14]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.816, + 0.892, + 0.877 + ], + "angle": 0, + "content": "Differentiable Rendering We render an image under the flash light, modeled as a point light source, using differentiable rasterization. Specifically, we compute the radiance \\( L \\) of each Gaussian \\( g \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\nL (\\mathbf {i}, \\mathbf {o}; g) = (\\mathbf {n} \\cdot \\mathbf {i}) f (\\mathbf {i}, \\mathbf {o}; g) E (g), \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.945, + 0.511, + 0.956 + ], + "angle": 0, + "content": "477" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.452, + 0.107 + ], + "angle": 0, + "content": "where \\( E(g) \\) is the incident light intensity on Gaussian \\( g \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.47, + 0.184 + ], + "angle": 0, + "content": "After computing the radiance, we rasterize the Gaussians onto the image plane, sort them by depth, and accumulate radiance values using alpha blending [14] to produce the final pixel value of the rendered image \\(I\\). We define this rendering as a function \\(\\operatorname{render}(\\cdot)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.189, + 0.469, + 0.253 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} I (u) = \\operatorname {r e n d e r} \\left(\\left\\{L _ {i} \\right\\} _ {i = 1} ^ {M}\\right) \\\\ = \\sum_ {i = 1} ^ {M} L _ {i} \\alpha_ {i} \\mathcal {G} _ {i} (\\mathbf {r} (u)) \\prod_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j} \\mathcal {G} _ {j} (\\mathbf {r} (u))\\right), \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.26, + 0.47, + 0.381 + ], + "angle": 0, + "content": "where \\( u \\in U \\) is a pixel, \\( M \\) is the number of Gaussians projected onto pixel \\( u \\). \\( \\{L_i\\}_{i=1}^M \\) and \\( \\{\\alpha_i\\}_{i=1}^M \\) are the radiance and opacity values of the depth-sorted \\( i \\)-th Gaussian, respectively. The vector \\( \\mathbf{r}(u) \\) is the ray coming from corresponding pixel \\( u \\), and \\( \\mathcal{G}_i(\\mathbf{r}(u)) \\) is the Gaussian-filtered distance between the center of \\( i \\)-th Gaussian and the intersection point between the ray \\( \\mathbf{r}(u) \\) and the \\( i \\)-th Gaussian. Details are provided in the Supplemental Document." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.399, + 0.47, + 0.445 + ], + "angle": 0, + "content": "Optimization We optimize the Gaussian parameters \\( G \\) and the basis BRDF parameters \\( R \\) by minimizing the loss function \\( \\mathcal{L} \\) in an analysis-by-synthesis manner:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.453, + 0.469, + 0.47 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {r e n d e r}} + \\lambda_ {\\text {g e o m}} \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {m a s k}} \\mathcal {L} _ {\\text {m a s k}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.477, + 0.469, + 0.584 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{render}}\\) penalizes the difference between the rendered image \\(I\\) and the input image \\(I^{\\prime}\\) across all input views. \\(\\mathcal{L}_{\\mathrm{geom}}\\) is a geometric regularization term for depth distortion and normal consistency [14], and \\(\\mathcal{L}_{\\mathrm{mask}}\\) is the cross-entropy loss between the rendered mask and the ground-truth mask. \\(\\lambda_{\\mathrm{geom}}\\) and \\(\\lambda_{\\mathrm{mask}}\\) are the balancing weights. Details are provided in the Supplemental Document." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.47, + 0.678 + ], + "angle": 0, + "content": "Specular-weighted Rendering Loss Multi-view flash photography typically generates fewer observations of specular-dominant pixels compared to diffuse-dominant pixels. To address this imbalance, we weight specular observations by using the potentially-specular weight map:" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.684, + 0.469, + 0.703 + ], + "angle": 0, + "content": "\\[\nH (u) = 1 + \\lambda_ {\\theta_ {h}} (\\cos \\theta_ {h} (u)) ^ {k}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.709, + 0.469, + 0.784 + ], + "angle": 0, + "content": "where \\(\\theta_h\\) is the rendered half-way angle map as \\(\\theta_h(u) =\\) render \\(\\left(\\{\\arccos (\\mathbf{n}_i\\cdot \\mathbf{h}_i)\\}_{i = 1}^M\\right)\\). \\(\\mathbf{n}_i\\) and \\(\\mathbf{h}_i\\) are the normal and half-way vector of Gaussian \\(i\\), respectively. We set the scalar \\(\\lambda_{\\theta_h} = 5\\) and \\(k = 10\\) to strongly weight specular regions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.784, + 0.469, + 0.815 + ], + "angle": 0, + "content": "We use the potentially-specular weight map \\( H \\) for calculating the final rendering loss:" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.821, + 0.469, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e n d e r}} = \\frac {1}{| U |} \\sum_ {u \\in U} H (u) \\left((1 - \\lambda_ {s}) \\mathcal {L} _ {1} (u) + \\lambda_ {s} \\mathcal {L} _ {\\mathrm {S S I M}} (u)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_1(u) = \\| I(u) - I'(u)\\|_1\\), \\(\\mathcal{L}_{\\mathrm{SSIM}}(u)\\) is the SSIM loss between \\(I(u)\\) and \\(I'(u)\\), and \\(\\lambda_s\\) is a balancing weight." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.087, + 0.892, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.357, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Figure 3. Basis BRDFs with varying scene complexity. We adjust the number of basis BRDFs during optimization to adapt to the scene complexity. We initialize the same number of basis BRDFs for both scenes in this example." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.744, + 0.453 + ], + "angle": 0, + "content": "3.2. Interpretable Basis BRDFs" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.468, + 0.892, + 0.574 + ], + "angle": 0, + "content": "While our method in Section 3.1 offers accurate inverse rendering, the reconstructed basis BRDFs lack of interpretability. Here, we extend the method to obtain interpretable basis BRDFs whose number adapts to the scene as shown in Figure 3. We develop basis BRDF control method of merge and removal in addition to impose sparsity on basis BRDF weights." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.624, + 0.892, + 0.731 + ], + "angle": 0, + "content": "Sparsity of Basis BRDF Weights For obtaining interpretable basis BRDF, each scene point needs to be represented with only few basis BRDFs with high weights. This enables spatially separating SVBRDFs with sparse basis BRDFs. We impose sparsity on the basis BRDF weights \\(\\{w_{i}(g)\\}_{i = 1}^{N}\\) for each Gaussian \\(g\\), making each Gaussian represented by only a few basis BRDFs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.738, + 0.892, + 0.784 + ], + "angle": 0, + "content": "First, we apply a softmax function with a low temperature \\( T = 0.0125 \\) to the weights, promoting sparse per-Gaussian weights:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.809, + 0.892, + 0.847 + ], + "angle": 0, + "content": "\\[\nw _ {i} (g) \\leftarrow \\frac {\\exp \\left(w _ {i} (g) / T\\right)}{\\sum_ {i ^ {\\prime} = 1} ^ {N} \\exp \\left(w _ {i ^ {\\prime}} (g) / T\\right)}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Second, we apply an entropy-based sparsity regularizer on the Gaussian weight \\( w_{i} \\) and rendered weight image \\( W_{i} \\) for" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "478" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.086, + 0.896, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.449, + 0.895, + 0.507 + ], + "angle": 0, + "content": "Figure 4. Basis BRDF control. During the optimization, we compute the values of each basis BRDF for sampled half-way angles \\(\\theta_h\\) from which radiometric difference is obtained. We compute the geometric difference between point clouds of basis BRDFs. If two basis BRDFs are radiometrically and geometrically similar, we merge them. If the rendered weight map \\(W_i\\) has few valid pixels, we remove the basis BRDF." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.514, + 0.229, + 0.529 + ], + "angle": 0, + "content": "each \\(i\\)-th basis BRDF:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.533, + 0.469, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {s p a r s e}} = - \\frac {1}{| G |} \\sum_ {g \\in G} \\sum_ {i = 1} ^ {N} w _ {i} (g) \\log w _ {i} (g) \\\\ - \\frac {1}{| U |} \\sum_ {u \\in U} \\sum_ {i = 1} ^ {N} W _ {i} (u) \\log W _ {i} (u), \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.624, + 0.469, + 0.643 + ], + "angle": 0, + "content": "\\[\nW _ {i} = \\operatorname {r e n d e r} \\left(\\left\\{w _ {i} (g) \\right\\} _ {g \\in G}\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.473, + 0.831 + ], + "angle": 0, + "content": "Basis BRDF Merge Basis BRDFs often become similar during optimization, making the resulting basis BRDFs non-intuitive with duplicates. We address this by merging similar basis BRDFs during analysis-by-synthesis optimization, as shown in Figure 4. We compute the values of each basis BRDF \\( f_{i} \\) at uniformly-sampled halfway angles \\( \\theta_{h} \\) for the RGB channels, resulting in a matrix \\( \\mathbf{f}_i\\in \\mathbb{R}^{C\\times 3} \\). \\( C \\) is the number of halfway angles. We then compute the radiometric difference between pairs of basis BRDFs, represented as a matrix \\( \\mathbf{D}_{\\mathrm{radio}}\\in \\mathbb{R}^{N\\times N} \\), which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.84, + 0.47, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\mathbf {D} _ {\\text {r a d i o}} (i, j) = \\frac {1}{C} \\| \\mathbf {f} _ {i} - \\mathbf {f} _ {j} \\| _ {2}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We also compute the geometric difference between the every pair of basis BRDFs, represented as a matrix \\(\\mathbf{D}_{\\mathrm{point}} \\in\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.513, + 0.892, + 0.545 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^{N\\times N}\\) using the Chamfer distance between point clouds represented by each basis BRDF:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.557, + 0.892, + 0.636 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {D} _ {\\text {p o i n t}} (i, j) = \\frac {1}{| P _ {i} |} \\sum_ {\\mathbf {p} \\in P _ {i}} \\min _ {\\mathbf {q} \\in P _ {j}} \\| \\mathbf {p} - \\mathbf {q} \\| _ {2} ^ {2} \\\\ + \\frac {1}{\\left| P _ {j} \\right|} \\sum_ {\\mathbf {q} \\in P _ {j}} \\min _ {\\mathbf {p} \\in P _ {i}} \\| \\mathbf {q} - \\mathbf {p} \\| _ {2} ^ {2}, \\tag {13} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.648, + 0.892, + 0.693 + ], + "angle": 0, + "content": "where \\( P_{i} \\) and \\( P_{j} \\) are the point clouds for the \\( i \\)-th and \\( j \\)-th basis BRDFs, consisting of the center locations of Gaussians where the \\( i \\)-th or \\( j \\)-th basis BRDF has the highest weight." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.77 + ], + "angle": 0, + "content": "If the radiometric difference \\(\\mathbf{D}_{\\mathrm{radio}}(i,j)\\) is below a threshold \\(\\tau_{\\mathrm{merge}}\\) and \\(\\mathbf{D}_{\\mathrm{point}}(i,j)\\) is minimal among all \\(\\forall j\\), we merge the two basis BRDFs by deleting the basis BRDF with fewer associated Gaussians and reassigning the per-Gaussian basis BRDF weights as" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.785, + 0.892, + 0.802 + ], + "angle": 0, + "content": "\\[\nw _ {j} (g) \\leftarrow w _ {i} (g) + w _ {j} (g), \\quad \\forall g \\in G. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Basis BRDF Removal To obtain meaningful basis BRDFs only, we remove \\(i\\)-th basis BRDF if it contributes to only a few pixels during optimization as shown in Figure 4. We evaluate this using the rendered weight image \\(W_{i}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.945, + 0.512, + 0.957 + ], + "angle": 0, + "content": "479" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.087, + 0.351, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.087, + 0.486, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.087, + 0.621, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.087, + 0.754, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.755, + 0.087, + 0.893, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.893, + 0.317 + ], + "angle": 0, + "content": "Figure 5. Normal reconstruction. Our method successfully recovers the detailed surface normal, outperforming other state-of-the-art inverse rendering methods: IRON [45], DPIR [8], GS³ [2]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.322, + 0.232, + 0.337 + ], + "angle": 0, + "content": "from Equation (11) as:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.346, + 0.47, + 0.38 + ], + "angle": 0, + "content": "\\[\n\\frac {\\left| \\left\\{u \\in U \\mid W _ {i} (u) > \\tau_ {\\text {r e m o v a l - w e i g h t}} \\right\\} \\right|}{\\left| U \\right|} < \\tau_ {\\text {r e m o v a l - n u m b e r}}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.47, + 0.451 + ], + "angle": 0, + "content": "where \\(\\tau_{\\mathrm{removal - weight}} = 0.1\\) is the threshold determining whether the \\(i\\)-th basis BRDF significantly contributes to that pixel \\(u\\), and \\(\\tau_{\\mathrm{removal - number}} = 0.005\\) is the threshold for the normalized number of such pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.47, + 0.564 + ], + "angle": 0, + "content": "Scheduling For a warm start, we first run our inverse rendering described in Section 3.1. After a predefined number of iterations, 6000 in our experiments, we perform basis BRDF merge and removal at predefined intervals 500 during iterations to refine the basis BRDFs. We incorporate the sparsity loss \\(\\mathcal{L}_{\\mathrm{sparse}}\\) and optimize the scene parameters by minimizing:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.575, + 0.469, + 0.593 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {r e n d e r}} + \\lambda_ {\\text {g e o m}} \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {m a s k}} \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {\\text {s p a r s e}} \\mathcal {L} _ {\\text {s p a r s e}}, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.603, + 0.469, + 0.634 + ], + "angle": 0, + "content": "where \\(\\lambda_{\\mathrm{sparse}}\\) is the balancing weight. Refer to the Supplemental Document for the details on the optimization." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.647, + 0.164, + 0.663 + ], + "angle": 0, + "content": "4. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.824 + ], + "angle": 0, + "content": "Datasets We evaluate our approach on both synthetic and real-world photometric dataset. For the synthetic dataset, we render four complex scenes containing multiple objects, following the co-located flash photography. Each scene includes multiple objects. The dataset consists of 200 training images and 100 test images per scene. For the real-world photometric dataset, we capture one multi-object scene using a mobile phone with flash at 200/40 training/testing images. We conduct geometric and radiometric calibrations of the light and the camera." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.327, + 0.849 + ], + "angle": 0, + "content": "4.1. Validation and Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Geometry We assess our method in comparison with state-of-the-art analysis-by-synthesis inverse rendering methods: IRON [45], DPIR [8] and \\(\\mathrm{GS}^3\\) [2]. Figure 5" + }, + { + "type": "table", + "bbox": [ + 0.563, + 0.319, + 0.835, + 0.37 + ], + "angle": 0, + "content": "
    IRONDPIRGS3Ours
    MAE ↓15.7117.0415.289.81
    Train ↓12h2h1h0.5h
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.381, + 0.893, + 0.424 + ], + "angle": 0, + "content": "Table 1. Normal reconstruction and training time. Our method outperforms IRON [45], DPIR [8], and \\(\\mathrm{GS}^3\\) [2] in quantitative numbers evaluated on the synthetic dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.893, + 0.641 + ], + "angle": 0, + "content": "and Table 1 show the results for geometry reconstruction, demonstrating the highest accuracy in normal reconstruction with mean angular error (MAE). IRON and DPIR employ neural signed distance functions to recover smooth surface normal, not only resulting in loss of details but also requiring extended training times for optimization as shown in Table 1. \\(\\mathrm{GS}^3\\), which is based on 3D Gaussian splatting with anisotropic spherical Gaussians, exhibits limited accuracy in shape reconstruction. Our method accurately models surface geometry and reflectance using 2D Gaussians and interpretable basis BRDFs, achieving the highest accuracy of normal reconstruction, especially for thin and convex objects. Moreover, we outperform the others in terms of training speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Basis BRDF Figure 6 shows the estimated basis BRDFs and weight maps, comparing modern inverse-rendering methods using basis BRDFs: \\(\\mathrm{GS}^3\\), DPIR, our method without interpretable basis BRDFs (Section 3.1), and our method with interpretable basis BRDFs (Section 3.2). Both DPIR and \\(\\mathrm{GS}^3\\) use basis BRDFs to leverage spatial coherence of specular reflectance. These methods yield non-interpretable basis BRDFs, as evident from the rendered weight maps and basis BRDF renderings. Our method introduced in Section 3.1 improves the interpretability of the basis BRDFs by jointly optimizing base colors. However, the resulting basis BRDFs are still often duplicated and non-intuitively classified. Moreover, all the methods have a fixed number of basis BRDFs, limited to modeling different complexity of scenes. In contrast, our full method (Section 3.2) obtains interpretable basis BRDFs whose number fits the target scene, as shown in Figure 3." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "480" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.894, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.411, + 0.893, + 0.438 + ], + "angle": 0, + "content": "Figure 6. Basis BRDFs and weight maps. Our inverse-rendering methods (Section 3.1 and Section 3.2) obtain basis BRDFs that are explainable with spatially separated weight maps and intuitive basis BRDFs, compared to \\(\\mathrm{GS}^3\\) [2] and DPIR [8]." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.438, + 0.891, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.592, + 0.893, + 0.621 + ], + "angle": 0, + "content": "Figure 7. Novel-view relighting. Our method enables high quality novel-view relighting with the accurate surface normal. We achieve physically-valid relighting with accurate normal and basis BRDFs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.625, + 0.212, + 0.642 + ], + "angle": 0, + "content": "4.2. Applications" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.649, + 0.473, + 0.816 + ], + "angle": 0, + "content": "Novel-view Relighting Figure 7 shows novel-view relighting and estimated normals, compared with IRON, DPIR, \\(\\mathrm{GS}^3\\). They suffer from inaccurate estimation of geometry. Despite inaccurate normals, \\(\\mathrm{GS}^3\\) manages to render high-quality relighting results. This is because neural networks compensate for such imperfection by learning residuals, as relighting is the main goal of \\(\\mathrm{GS}^3\\). In contrast, our method reconstructs accurate geometry and interpretable basis BRDFs that enable not only novel-view relighting but also downstream tasks such as intuitive scene editing. For more results, refer to the Supplemental Document." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Scene Editing Our inverse rendering method enables selective editing based on basis BRDFs and weight images. Figure 8 shows that our interpretable basis BRDFs facilitate reflectance editing. Interpretable basis BRDFs enable prac" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.895, + 0.779 + ], + "angle": 0, + "content": "tical material editing by adjusting desired BRDF parameters of base color, roughness, metallic based on their sparse weight maps. We then obtain a single object from the entire scene by selecting basis BRDFs that are utilized to represent the corresponding object. Next, we delete other basis BRDFs and Gaussians that have the highest weight for other basis BRDFs. We also filter out Gaussians based on Gaussian positions. This allows for extracting object mesh [14] and relighting it under an environment map. Figure 9 shows additional material-editing results on a real-world scene." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.788, + 0.655, + 0.804 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.858 + ], + "angle": 0, + "content": "Sparsity Regularizer \\(\\mathcal{L}_{\\mathrm{sparse}}\\) Figure 10 shows that the sparsity regularizer and the basis BRDF control enable obtaining interpretable basis BRDFs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Specular-weighted Rendering Loss We test the impact of the specular-weighted rendering loss that prioritizes" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "481" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.087, + 0.47, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.198, + 0.266, + 0.207 + ], + "angle": 0, + "content": "Estimated image and basis BRDFs" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.207, + 0.227, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.32, + 0.222, + 0.33 + ], + "angle": 0, + "content": "Point cloud for basis BRDF" + }, + { + "type": "image", + "bbox": [ + 0.23, + 0.21, + 0.338, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.319, + 0.346, + 0.328 + ], + "angle": 0, + "content": "Mesh extraction" + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.209, + 0.461, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.32, + 0.465, + 0.33 + ], + "angle": 0, + "content": "Environment relighting" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.342, + 0.47, + 0.384 + ], + "angle": 0, + "content": "Figure 8. Intuitive scene editing. We modify our basis BRDF parameters to edit the reflectance. We also selectively extract mesh and relight it under the environment map." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.394, + 0.29, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.483, + 0.235, + 0.492 + ], + "angle": 0, + "content": "Novel view relighting" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.394, + 0.469, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.483, + 0.459, + 0.491 + ], + "angle": 0, + "content": "Basis BRDFs and weight maps" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.491, + 0.288, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.579, + 0.269, + 0.59 + ], + "angle": 0, + "content": "Material editing with white lightings" + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.491, + 0.469, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.579, + 0.467, + 0.59 + ], + "angle": 0, + "content": "Material editing with colorful lightings" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.6, + 0.47, + 0.67 + ], + "angle": 0, + "content": "Figure 9. Material editing and relighting on real-world objects. We obtain high-quality novel-view relighting for a real-world scene, where interpretable basis BRDFs are reconstructed with their sparse weight maps. We edit basis BRDFs and relight the scene under novel illumination conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.682, + 0.47, + 0.743 + ], + "angle": 0, + "content": "potentially-specular areas using the rendered half-way angle map. Figure 11 shows that specular-weighted rendering loss produces a more stable reconstruction compared to not using the weighting." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.754, + 0.196, + 0.769 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this paper, we have introduced a differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs. Our method obtains interpretable basis BRDFs that can represent SVBRDFs in a spatially-separable manner, enabling accurate geometry and SVBRDF reconstruction. Also, the number of basis BRDFs automatically adjusts to a target scene. We demonstrate the effectiveness of our method compared to state-of-the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.641, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.563, + 0.233, + 0.58, + 0.243 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.641, + 0.089, + 0.765, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.681, + 0.178, + 0.852, + 0.189 + ], + "angle": 0, + "content": "With sparsity and basis control" + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.09, + 0.891, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.189, + 0.765, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.189, + 0.891, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.276, + 0.865, + 0.287 + ], + "angle": 0, + "content": "Without sparsity and basis control" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.298, + 0.893, + 0.367 + ], + "angle": 0, + "content": "Figure 10. Impact of sparsity regularizer and basis BRDF control. Without sparsity loss and basis BRDF control of merge and removal, the resulting basis BRDFs are blended each other as shown in the corresponding images, making them non-interpretable for downstream tasks." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.37, + 0.688, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.513, + 0.614, + 0.524 + ], + "angle": 0, + "content": "GT image" + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.372, + 0.872, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.514, + 0.83, + 0.524 + ], + "angle": 0, + "content": "Specular weight map" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.524, + 0.63, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.572, + 0.631, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.623, + 0.633, + 0.635 + ], + "angle": 0, + "content": "Without specular weight" + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.524, + 0.758, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.572, + 0.758, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.646, + 0.623, + 0.755, + 0.634 + ], + "angle": 0, + "content": "With specular weight" + }, + { + "type": "image", + "bbox": [ + 0.759, + 0.524, + 0.889, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.572, + 0.889, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.817, + 0.624, + 0.835, + 0.633 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.653, + 0.892, + 0.709 + ], + "angle": 0, + "content": "Figure 11. Impact of specular-weighted loss. Using specular-weighted rendering loss improves geometry and reflectance reconstruction quality by recovering high frequency features from specularity, which is emphasized by the specular weight map." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.715, + 0.892, + 0.761 + ], + "angle": 0, + "content": "art approaches. Using the interpretable basis BRDFs, our method also facilitates downstream tasks such as intuitive scene editing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.77, + 0.892, + 0.831 + ], + "angle": 0, + "content": "Limitations Our basis BRDF representation assumes opaque objects, leaving modeling non-surface objects as a future work. Combining semantic information from a large vision model is also an interesting future work." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, RS-2024-00438532, RS-2025-00518643), and Korea IITP MSIT (RS-2023-00215700)." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "482" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Neil Alldrin, Todd Zickler, and David Kriegman. Photometric stereo with non-parametric and spatially-varying reflectance. In 2008 IEEE Conference on Computer Vision and Pattern Recognition, pages 1-8. 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We propose a differentiable inverse rendering method with (a) multi-view flash photography inputs. Our analysis-by-synthesis method achieves not only (b) novel-view relighting and accurate geometry reconstruction, but also (c) interpretable basis BRDFs and their spatially-separated weights. This allows for (d) intuitive scene editing. + +![](images/99a3fb3115c2ef2b1cbfc31835b950f7e615c0c859d51c3fb2c48c2d709c6f9f.jpg) + +![](images/aed52b066ac36716b8cd2c1376f347038de4efb1487e3688cd51d45baf35887a.jpg) +(d) Reflectance editing with environment relighting + +![](images/7a49492bbf2da34c3acc2a579a8d5517689da89a794051bce05ba856d15a6077.jpg) + +![](images/4bd9bd5016b6c39a5e0595801a31f1dd667c8ef4d88c82df6b261c8293a046e0.jpg) + +# Abstract + +Inverse rendering seeks to reconstruct both geometry and spatially varying BRDFs (SVBRDFs) from captured images. To address the inherent ill-posedness of inverse rendering, basis BRDF representations are commonly used, modeling SVBRDFs as spatially varying blends of a set of basis BRDFs. However, existing methods often yield basis BRDFs that lack intuitive separation and have limited scalability to scenes of varying complexity. In this paper, we introduce a differentiable inverse rendering method that produces interpretable basis BRDFs. Our approach models a scene using 2D Gaussians, where the reflectance of each Gaussian is defined by a weighted blend of basis BRDFs. We efficiently render an image from the 2D Gaussians and basis BRDFs using differentiable rasterization and impose a specular-weighted rendering loss with the input flash photography images. During this analysis-by-synthesis optimization process of differentiable inverse rendering, we dynamically adjust the number of basis BRDFs to fit the target scene while encouraging sparsity in the basis weights. This ensures that the reflectance of each Gaussian is represented by only a few basis BRDFs. This approach enables + +the reconstruction of accurate geometry and interpretable basis BRDFs that are spatially separated. Consequently, the resulting scene representation, comprising basis BRDFs and 2D Gaussians, supports physically-based novel-view relighting and intuitive scene editing. + +# 1. Introduction + +Inverse rendering aims to reconstruct geometry and reflectance from captured images, a fundamental problem in computer vision and computer graphics. Recent advances in differentiable rendering methods [18, 29] have facilitated analysis-by-synthesis differentiable inverse rendering. These methods enable the optimization of scene parameters by minimizing the discrepancy between captured and synthesized images [2, 8, 12, 45, 47]. However, achieving accurate inverse rendering remains challenging, especially when the available lighting and viewing angles are limited. A promising approach to mitigate this problem is to exploit the spatial coherence of SVBRDFs using basis BRDF representations [1, 19, 27, 28, 32]. Representing the BRDF at each point as a spatially varying blend of basis BRDFs allows gathering multiple points to accurately fit basis BRDFs + +and their per-point weights. + +Early methods often focus solely on estimating basis BRDFs and their weights for objects with known 3D geometry [20, 21, 50]. Moreover, they typically require excessive optimization time and suffer from low accuracy. Recent methods jointly optimize geometry and basis BRDFs [2, 8, 30]. These approaches often result in non-interpretable basis BRDFs which are spatially entangled: each scene point is represented by many basis BRDFs with high weights and those basis BRDFs are often non-interpretable. Thus, their results are impractical to use for downstream tasks such as scene editing. Additionally, they are often limited to using a fixed number of basis BRDFs, regardless of scene complexity. + +In this paper, we propose a differentiable inverse rendering method that jointly estimates geometry and reflectance. We represent geometry as a set of 2D Gaussians [9, 14], each with shape parameters and basis BRDF weights. The reflectance of each Gaussian is modeled as a spatially varying blend of basis BRDFs. We dynamically adjust the number of basis BRDFs during the analysis-by-synthesis optimization, promoting sparsity in the basis BRDF weights. To enhance training stability, we employ a weighted photometric loss that focuses on potentially specular regions. We demonstrate that our method obtains not only accurate geometry but also scalable and interpretable basis BRDFs which sparsely represent SVBRDFs as shown in Figure 1. In summary, we make the following contributions: + +- A differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs, obtaining interpretable basis BRDFs. +- A basis BRDF control method and sparsity regularizer that dynamically adjust the number of basis BRDFs during analysis-by-synthesis optimization, promoting interpretability through sparse blending. +- Extensive evaluation compared with existing methods, and demonstration of intuitive scene editing. + +# 2. Related Work + +Inverse Rendering Learning-based inverse rendering methods train neural networks such as CNNs [22, 23, 33, 34, 38, 43], transformers [51], and diffusion models [25, 31, 40] on datasets, enabling efficient inference by exploiting prior distributions in the training data. They often suffer from out-of-distribution inputs, resulting in physically inaccurate results. + +The analysis-by-synthesis framework enables inverse rendering by inverting the forward rendering process. Recent advancements have been particularly sparked by differentiable rendering techniques using volumetric rendering [3-7, 10, 11, 17, 26, 36, 37, 39, 41, 44-48] and rasterization [2, 12, 16, 24, 35, 52]. Recent rasterization-based methods using isotropic points [8], 2D Gaussians [49], and + +3D Gaussians [2, 12, 16, 24, 35, 52] exhibit both efficiency and accuracy. However, they suffer when insufficient light-view angular samples are provided. Incorporating basis BRDFs into the modern analysis-by-synthesis framework has shown promising performance, however the reconstructed basis BRDFs are often non-interpretable, limiting their usefulness in downstream tasks such as scene editing [2, 8]. In contrast, our novel method obtains 2D Gaussians with accurate geometry and interpretable basis BRDFs. + +Basis BRDF Basis BRDFs have often been used as a representation of SVBRDFs, decomposing the SVBRDF into a blend of basis BRDFs. This approach is based on the spatial coherence of reflectance, assuming that the BRDFs of many pixels are similar in real-world scenes [27, 28]. Using basis BRDFs helps reduce the ill-posedness of inverse rendering because it enables gathering many light-angular observations for each basis BRDF reconstruction. Existing methods jointly optimize basis BRDFs and spatially varying weights for planar [19, 32] and non-planar objects [1, 13, 15, 30]. Recently, two methods [2, 8] demonstrated the effectiveness of basis BRDFs in modern differentiable analysis-by-synthesis frameworks. While they showed promising results, the estimated basis BRDFs are non-interpretable as shown in Figure 6, which limits their utility in downstream tasks such as scene editing. Moreover, generalizing their methods to varying degrees of scene complexity is challenging because the number of basis BRDFs is fixed. To overcome these problems, we are inspired by the decade ago work of Zhou et al. [50], which proposed adjusting the number of basis BRDFs during optimization. Their method assumes known geometry, does not exploit a differentiable rendering pipeline, and suffers from low reconstruction accuracy and efficiency. We address these challenges by developing a differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs to obtain interpretable basis BRDFs, where the number of basis BRDFs are automatically controlled. + +# 3. Method + +Our method consists of two parts. In Section 3.1, we focus on optimizing 2D Gaussians and basis BRDFs without concerning the interpretability of basis BRDFs. Next, we extend the method to obtaining interpretable basis BRDFs in Section 3.2. Figure 2 shows the process of our method over analysis-by-synthesis iterations. We obtain not only accurate geometry but also interpretable basis BRDFs whose number adapts to the scene and the basis BRDFs represent SVBRDFs with spatially-separated basis-BRDF weights. + +# 3.1. Gaussian Inverse Rendering with Basis BRDFs + +We introduce our method that jointly estimates geometry and a fixed number of basis BRDFs in a differentiable man + +![](images/8045f4104dd6ae281e5d215a87fbc4cdd92de7ac563666385961970a52533e97.jpg) +Figure 2. The process of our analysis-by-synthesis iterations. Given a set of multi-view photometric images, we initialize point cloud and extract base color for basis BRDFs. We jointly optimize 2D Gaussians and basis BRDFs by comparing the differentiably-rendered images and the input images. Our method enables obtaining interpretable basis BRDFs with spatially-separated basis-BRDF weights and the number of basis BRDFs adapts to the scene. + +ner from multi-view flash-photography images. + +Geometry We use 2D Gaussians as geometric primitives [14], where each Gaussian $g \in G$ is an elliptical disk, and $G$ is the set of all Gaussians. Each Gaussian $g$ is parameterized by its center location $\mathbf{p} \in \mathbb{R}^{3 \times 1}$ , principal vectors $\mathbf{t} \in \mathbb{R}^{3 \times 2}$ , and scaling factors $\mathbf{s} \in \mathbb{R}^{2 \times 1}$ . The Gaussian surface normal $\mathbf{n}$ is computed as the cross product of the principal vectors. + +Basis BRDFs We use a basis BRDF representation, where we define $N$ basis BRDFs. We model the $i$ -th basis $\mathrm{BRDF}f_{i}$ with base color $\mathbf{b}_i$ , roughness $\sigma_{i}$ , and metallic parameter $m_{i}$ using the simplified Disney BRDF model [42]: + +$$ +\begin{array}{l} f _ {i} (\mathbf {i}, \mathbf {o}) = \frac {1 - m _ {i}}{\pi} \mathbf {b} _ {i} \\ + \frac {D (\mathbf {h} ; \sigma_ {i}) F (\mathbf {o} , \mathbf {h} ; \mathbf {b} _ {i} , m _ {i}) G (\mathbf {i} , \mathbf {o} , \mathbf {n} ; \sigma_ {i})}{4 (\mathbf {n} \cdot \mathbf {i}) (\mathbf {n} \cdot \mathbf {o})}, \tag {1} \\ \end{array} +$$ + +where $\mathbf{i}$ and $\mathbf{o}$ are the incident and outgoing directions, and $\mathbf{h} = (\mathbf{i} + \mathbf{o}) / 2$ is the half-way vector. $D$ is the normal distribution function, $F$ is the Fresnel term, and $G$ is the geometric attenuation. Details of these terms are provided in the Supplemental Document. + +We assign blending weights $w_{i}(g)$ for every $i$ -th basis BRDF per each Gaussian $g$ , and represent the BRDF $f$ of + +the Gaussian $g$ as: + +$$ +f (\mathbf {i}, \mathbf {o}; g) = \sum_ {i = 1} ^ {N} w _ {i} (g) f _ {i} (\mathbf {i}, \mathbf {o}). \tag {2} +$$ + +Scene Representations In summary, our scene representation consists of per-Gaussian parameters $G$ and basis BRDF parameters $R$ : + +$$ +g = \underbrace{\{\mathbf{p},\mathbf{t},\mathbf{s}\}}_{\text{geometric}}\cup \underbrace{\{\{w_{i}(g)\}_{i = 1}^{N},\alpha\}}_{\text{photometric}},\text{where} g\in G, +$$ + +$$ +R = \left\{m _ {i}, \mathbf {b} _ {i}, \sigma_ {i} \right\} _ {i = 1} ^ {N}. \tag {3} +$$ + +$\alpha$ is the Gaussian opacity. To initialize the basis BRDF parameters $R$ , we perform k-means clustering with a fixed number $N$ on the input multi-view flash photography images $I'$ . The base colors $\{\mathbf{b}_i\}_{i=1}^N$ are initialized as the mean values of the clusters. The roughness $\{\sigma_i\}_{i=1}^N$ and metallic parameters $\{m_i\}_{i=1}^N$ are set to initial values: $\sigma_i = 0.5$ and $m_i = 0.0$ . We initialize the weights $w_i(g)$ uniformly and set $\alpha$ following Huang et al. [14]. + +Differentiable Rendering We render an image under the flash light, modeled as a point light source, using differentiable rasterization. Specifically, we compute the radiance $L$ of each Gaussian $g$ as: + +$$ +L (\mathbf {i}, \mathbf {o}; g) = (\mathbf {n} \cdot \mathbf {i}) f (\mathbf {i}, \mathbf {o}; g) E (g), \tag {4} +$$ + +where $E(g)$ is the incident light intensity on Gaussian $g$ . + +After computing the radiance, we rasterize the Gaussians onto the image plane, sort them by depth, and accumulate radiance values using alpha blending [14] to produce the final pixel value of the rendered image $I$ . We define this rendering as a function $\operatorname{render}(\cdot)$ : + +$$ +\begin{array}{l} I (u) = \operatorname {r e n d e r} \left(\left\{L _ {i} \right\} _ {i = 1} ^ {M}\right) \\ = \sum_ {i = 1} ^ {M} L _ {i} \alpha_ {i} \mathcal {G} _ {i} (\mathbf {r} (u)) \prod_ {j = 1} ^ {i - 1} \left(1 - \alpha_ {j} \mathcal {G} _ {j} (\mathbf {r} (u))\right), \tag {5} \\ \end{array} +$$ + +where $u \in U$ is a pixel, $M$ is the number of Gaussians projected onto pixel $u$ . $\{L_i\}_{i=1}^M$ and $\{\alpha_i\}_{i=1}^M$ are the radiance and opacity values of the depth-sorted $i$ -th Gaussian, respectively. The vector $\mathbf{r}(u)$ is the ray coming from corresponding pixel $u$ , and $\mathcal{G}_i(\mathbf{r}(u))$ is the Gaussian-filtered distance between the center of $i$ -th Gaussian and the intersection point between the ray $\mathbf{r}(u)$ and the $i$ -th Gaussian. Details are provided in the Supplemental Document. + +Optimization We optimize the Gaussian parameters $G$ and the basis BRDF parameters $R$ by minimizing the loss function $\mathcal{L}$ in an analysis-by-synthesis manner: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {r e n d e r}} + \lambda_ {\text {g e o m}} \mathcal {L} _ {\text {g e o m}} + \lambda_ {\text {m a s k}} \mathcal {L} _ {\text {m a s k}}, \tag {6} +$$ + +where $\mathcal{L}_{\mathrm{render}}$ penalizes the difference between the rendered image $I$ and the input image $I^{\prime}$ across all input views. $\mathcal{L}_{\mathrm{geom}}$ is a geometric regularization term for depth distortion and normal consistency [14], and $\mathcal{L}_{\mathrm{mask}}$ is the cross-entropy loss between the rendered mask and the ground-truth mask. $\lambda_{\mathrm{geom}}$ and $\lambda_{\mathrm{mask}}$ are the balancing weights. Details are provided in the Supplemental Document. + +Specular-weighted Rendering Loss Multi-view flash photography typically generates fewer observations of specular-dominant pixels compared to diffuse-dominant pixels. To address this imbalance, we weight specular observations by using the potentially-specular weight map: + +$$ +H (u) = 1 + \lambda_ {\theta_ {h}} (\cos \theta_ {h} (u)) ^ {k}, \tag {7} +$$ + +where $\theta_h$ is the rendered half-way angle map as $\theta_h(u) =$ render $\left(\{\arccos (\mathbf{n}_i\cdot \mathbf{h}_i)\}_{i = 1}^M\right)$ . $\mathbf{n}_i$ and $\mathbf{h}_i$ are the normal and half-way vector of Gaussian $i$ , respectively. We set the scalar $\lambda_{\theta_h} = 5$ and $k = 10$ to strongly weight specular regions. + +We use the potentially-specular weight map $H$ for calculating the final rendering loss: + +$$ +\mathcal {L} _ {\text {r e n d e r}} = \frac {1}{| U |} \sum_ {u \in U} H (u) \left((1 - \lambda_ {s}) \mathcal {L} _ {1} (u) + \lambda_ {s} \mathcal {L} _ {\mathrm {S S I M}} (u)\right), \tag {8} +$$ + +where $\mathcal{L}_1(u) = \| I(u) - I'(u)\|_1$ , $\mathcal{L}_{\mathrm{SSIM}}(u)$ is the SSIM loss between $I(u)$ and $I'(u)$ , and $\lambda_s$ is a balancing weight. + +![](images/725d627019aad0029f75f40064115a70930be9c53f4ec7716ca5f302361bf08e.jpg) +Figure 3. Basis BRDFs with varying scene complexity. We adjust the number of basis BRDFs during optimization to adapt to the scene complexity. We initialize the same number of basis BRDFs for both scenes in this example. + +# 3.2. Interpretable Basis BRDFs + +While our method in Section 3.1 offers accurate inverse rendering, the reconstructed basis BRDFs lack of interpretability. Here, we extend the method to obtain interpretable basis BRDFs whose number adapts to the scene as shown in Figure 3. We develop basis BRDF control method of merge and removal in addition to impose sparsity on basis BRDF weights. + +Sparsity of Basis BRDF Weights For obtaining interpretable basis BRDF, each scene point needs to be represented with only few basis BRDFs with high weights. This enables spatially separating SVBRDFs with sparse basis BRDFs. We impose sparsity on the basis BRDF weights $\{w_{i}(g)\}_{i = 1}^{N}$ for each Gaussian $g$ , making each Gaussian represented by only a few basis BRDFs. + +First, we apply a softmax function with a low temperature $T = 0.0125$ to the weights, promoting sparse per-Gaussian weights: + +$$ +w _ {i} (g) \leftarrow \frac {\exp \left(w _ {i} (g) / T\right)}{\sum_ {i ^ {\prime} = 1} ^ {N} \exp \left(w _ {i ^ {\prime}} (g) / T\right)}. \tag {9} +$$ + +Second, we apply an entropy-based sparsity regularizer on the Gaussian weight $w_{i}$ and rendered weight image $W_{i}$ for + +![](images/128eb20158ed538f396b53c408be0bda6d7dce6db115734b416288d99a388cc7.jpg) +Figure 4. Basis BRDF control. During the optimization, we compute the values of each basis BRDF for sampled half-way angles $\theta_h$ from which radiometric difference is obtained. We compute the geometric difference between point clouds of basis BRDFs. If two basis BRDFs are radiometrically and geometrically similar, we merge them. If the rendered weight map $W_i$ has few valid pixels, we remove the basis BRDF. + +each $i$ -th basis BRDF: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {s p a r s e}} = - \frac {1}{| G |} \sum_ {g \in G} \sum_ {i = 1} ^ {N} w _ {i} (g) \log w _ {i} (g) \\ - \frac {1}{| U |} \sum_ {u \in U} \sum_ {i = 1} ^ {N} W _ {i} (u) \log W _ {i} (u), \tag {10} \\ \end{array} +$$ + +$$ +W _ {i} = \operatorname {r e n d e r} \left(\left\{w _ {i} (g) \right\} _ {g \in G}\right). \tag {11} +$$ + +Basis BRDF Merge Basis BRDFs often become similar during optimization, making the resulting basis BRDFs non-intuitive with duplicates. We address this by merging similar basis BRDFs during analysis-by-synthesis optimization, as shown in Figure 4. We compute the values of each basis BRDF $f_{i}$ at uniformly-sampled halfway angles $\theta_{h}$ for the RGB channels, resulting in a matrix $\mathbf{f}_i\in \mathbb{R}^{C\times 3}$ . $C$ is the number of halfway angles. We then compute the radiometric difference between pairs of basis BRDFs, represented as a matrix $\mathbf{D}_{\mathrm{radio}}\in \mathbb{R}^{N\times N}$ , which is defined as: + +$$ +\mathbf {D} _ {\text {r a d i o}} (i, j) = \frac {1}{C} \| \mathbf {f} _ {i} - \mathbf {f} _ {j} \| _ {2}. \tag {12} +$$ + +We also compute the geometric difference between the every pair of basis BRDFs, represented as a matrix $\mathbf{D}_{\mathrm{point}} \in$ + +$\mathbb{R}^{N\times N}$ using the Chamfer distance between point clouds represented by each basis BRDF: + +$$ +\begin{array}{l} \mathbf {D} _ {\text {p o i n t}} (i, j) = \frac {1}{| P _ {i} |} \sum_ {\mathbf {p} \in P _ {i}} \min _ {\mathbf {q} \in P _ {j}} \| \mathbf {p} - \mathbf {q} \| _ {2} ^ {2} \\ + \frac {1}{\left| P _ {j} \right|} \sum_ {\mathbf {q} \in P _ {j}} \min _ {\mathbf {p} \in P _ {i}} \| \mathbf {q} - \mathbf {p} \| _ {2} ^ {2}, \tag {13} \\ \end{array} +$$ + +where $P_{i}$ and $P_{j}$ are the point clouds for the $i$ -th and $j$ -th basis BRDFs, consisting of the center locations of Gaussians where the $i$ -th or $j$ -th basis BRDF has the highest weight. + +If the radiometric difference $\mathbf{D}_{\mathrm{radio}}(i,j)$ is below a threshold $\tau_{\mathrm{merge}}$ and $\mathbf{D}_{\mathrm{point}}(i,j)$ is minimal among all $\forall j$ , we merge the two basis BRDFs by deleting the basis BRDF with fewer associated Gaussians and reassigning the per-Gaussian basis BRDF weights as + +$$ +w _ {j} (g) \leftarrow w _ {i} (g) + w _ {j} (g), \quad \forall g \in G. \tag {14} +$$ + +Basis BRDF Removal To obtain meaningful basis BRDFs only, we remove $i$ -th basis BRDF if it contributes to only a few pixels during optimization as shown in Figure 4. We evaluate this using the rendered weight image $W_{i}$ + +![](images/470faa1752544a0026f279f3201b4879732ff9771dabe3abebdbaa5179b2b448.jpg) +Figure 5. Normal reconstruction. Our method successfully recovers the detailed surface normal, outperforming other state-of-the-art inverse rendering methods: IRON [45], DPIR [8], GS³ [2]. + +![](images/abdf114cd4c4954a437455666a963281e500b646c319ebce255f66713c9bda6e.jpg) + +![](images/9ba739addaa04c9ca7251207b8e2fe0057d17d002d00a4da0d2597717e11c97c.jpg) + +![](images/f200ddf5e1121800a39f25407707f2c6b6734e32bd315cea34fd6cd872aa13cc.jpg) + +![](images/c5dfd8e6db340811253473b1ea218673f1ed389a95b258ee0a2a53a42b24c104.jpg) + +from Equation (11) as: + +$$ +\frac {\left| \left\{u \in U \mid W _ {i} (u) > \tau_ {\text {r e m o v a l - w e i g h t}} \right\} \right|}{\left| U \right|} < \tau_ {\text {r e m o v a l - n u m b e r}}, \tag {15} +$$ + +where $\tau_{\mathrm{removal - weight}} = 0.1$ is the threshold determining whether the $i$ -th basis BRDF significantly contributes to that pixel $u$ , and $\tau_{\mathrm{removal - number}} = 0.005$ is the threshold for the normalized number of such pixels. + +Scheduling For a warm start, we first run our inverse rendering described in Section 3.1. After a predefined number of iterations, 6000 in our experiments, we perform basis BRDF merge and removal at predefined intervals 500 during iterations to refine the basis BRDFs. We incorporate the sparsity loss $\mathcal{L}_{\mathrm{sparse}}$ and optimize the scene parameters by minimizing: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {r e n d e r}} + \lambda_ {\text {g e o m}} \mathcal {L} _ {\text {g e o m}} + \lambda_ {\text {m a s k}} \mathcal {L} _ {\text {m a s k}} + \lambda_ {\text {s p a r s e}} \mathcal {L} _ {\text {s p a r s e}}, \tag {16} +$$ + +where $\lambda_{\mathrm{sparse}}$ is the balancing weight. Refer to the Supplemental Document for the details on the optimization. + +# 4. Results + +Datasets We evaluate our approach on both synthetic and real-world photometric dataset. For the synthetic dataset, we render four complex scenes containing multiple objects, following the co-located flash photography. Each scene includes multiple objects. The dataset consists of 200 training images and 100 test images per scene. For the real-world photometric dataset, we capture one multi-object scene using a mobile phone with flash at 200/40 training/testing images. We conduct geometric and radiometric calibrations of the light and the camera. + +# 4.1. Validation and Comparison + +Geometry We assess our method in comparison with state-of-the-art analysis-by-synthesis inverse rendering methods: IRON [45], DPIR [8] and $\mathrm{GS}^3$ [2]. Figure 5 + +
    IRONDPIRGS3Ours
    MAE ↓15.7117.0415.289.81
    Train ↓12h2h1h0.5h
    + +Table 1. Normal reconstruction and training time. Our method outperforms IRON [45], DPIR [8], and $\mathrm{GS}^3$ [2] in quantitative numbers evaluated on the synthetic dataset. + +and Table 1 show the results for geometry reconstruction, demonstrating the highest accuracy in normal reconstruction with mean angular error (MAE). IRON and DPIR employ neural signed distance functions to recover smooth surface normal, not only resulting in loss of details but also requiring extended training times for optimization as shown in Table 1. $\mathrm{GS}^3$ , which is based on 3D Gaussian splatting with anisotropic spherical Gaussians, exhibits limited accuracy in shape reconstruction. Our method accurately models surface geometry and reflectance using 2D Gaussians and interpretable basis BRDFs, achieving the highest accuracy of normal reconstruction, especially for thin and convex objects. Moreover, we outperform the others in terms of training speed. + +Basis BRDF Figure 6 shows the estimated basis BRDFs and weight maps, comparing modern inverse-rendering methods using basis BRDFs: $\mathrm{GS}^3$ , DPIR, our method without interpretable basis BRDFs (Section 3.1), and our method with interpretable basis BRDFs (Section 3.2). Both DPIR and $\mathrm{GS}^3$ use basis BRDFs to leverage spatial coherence of specular reflectance. These methods yield non-interpretable basis BRDFs, as evident from the rendered weight maps and basis BRDF renderings. Our method introduced in Section 3.1 improves the interpretability of the basis BRDFs by jointly optimizing base colors. However, the resulting basis BRDFs are still often duplicated and non-intuitively classified. Moreover, all the methods have a fixed number of basis BRDFs, limited to modeling different complexity of scenes. In contrast, our full method (Section 3.2) obtains interpretable basis BRDFs whose number fits the target scene, as shown in Figure 3. + +![](images/3aba177f7a6066582e1fc2def283490cc35a0b60880c9e6e013fdfdfee2e9a71.jpg) + +![](images/3b2ffe749a6065a3179b29f1206265b1d567c30434ca5e329c2b7bb9b14c3575.jpg) +Figure 6. Basis BRDFs and weight maps. Our inverse-rendering methods (Section 3.1 and Section 3.2) obtain basis BRDFs that are explainable with spatially separated weight maps and intuitive basis BRDFs, compared to $\mathrm{GS}^3$ [2] and DPIR [8]. +Figure 7. Novel-view relighting. Our method enables high quality novel-view relighting with the accurate surface normal. We achieve physically-valid relighting with accurate normal and basis BRDFs. + +# 4.2. Applications + +Novel-view Relighting Figure 7 shows novel-view relighting and estimated normals, compared with IRON, DPIR, $\mathrm{GS}^3$ . They suffer from inaccurate estimation of geometry. Despite inaccurate normals, $\mathrm{GS}^3$ manages to render high-quality relighting results. This is because neural networks compensate for such imperfection by learning residuals, as relighting is the main goal of $\mathrm{GS}^3$ . In contrast, our method reconstructs accurate geometry and interpretable basis BRDFs that enable not only novel-view relighting but also downstream tasks such as intuitive scene editing. For more results, refer to the Supplemental Document. + +Scene Editing Our inverse rendering method enables selective editing based on basis BRDFs and weight images. Figure 8 shows that our interpretable basis BRDFs facilitate reflectance editing. Interpretable basis BRDFs enable prac + +tical material editing by adjusting desired BRDF parameters of base color, roughness, metallic based on their sparse weight maps. We then obtain a single object from the entire scene by selecting basis BRDFs that are utilized to represent the corresponding object. Next, we delete other basis BRDFs and Gaussians that have the highest weight for other basis BRDFs. We also filter out Gaussians based on Gaussian positions. This allows for extracting object mesh [14] and relighting it under an environment map. Figure 9 shows additional material-editing results on a real-world scene. + +# 4.3. Ablation Study + +Sparsity Regularizer $\mathcal{L}_{\mathrm{sparse}}$ Figure 10 shows that the sparsity regularizer and the basis BRDF control enable obtaining interpretable basis BRDFs. + +Specular-weighted Rendering Loss We test the impact of the specular-weighted rendering loss that prioritizes + +![](images/f7aec45f78e3b5222d1a04210da25b1433abc2c19580bf32bd7ce66a64594c04.jpg) +Estimated image and basis BRDFs + +![](images/d28bcb77663995c68478d9bbf5dfd430021a835b812c4a14a6929985414ecf57.jpg) +Point cloud for basis BRDF + +![](images/d00a7595a30c1d4ac2562b3bc7d5e72849365378037cc1170f92e2e5ad5e77fd.jpg) +Mesh extraction + +![](images/3f8f735e0375b71662b16560f0dc49ec6c47a437944ea6a35bfc8b0e73875e6e.jpg) +Environment relighting + +![](images/bda3b30dd6cee9ace18049fcae506b8c566218244c13194a0d6521d0d06a12b8.jpg) +Figure 8. Intuitive scene editing. We modify our basis BRDF parameters to edit the reflectance. We also selectively extract mesh and relight it under the environment map. +Novel view relighting + +![](images/babf3c1e0e78e41d07e8d793feaf26fb5fcdb541d24266f39d4dd7b0e241aad9.jpg) + +![](images/d44a9320fde5d759681afbbca882817d8c5248e1202795ef7d8ff0cb0f0eed43.jpg) +Material editing with white lightings +Material editing with colorful lightings +Figure 9. Material editing and relighting on real-world objects. We obtain high-quality novel-view relighting for a real-world scene, where interpretable basis BRDFs are reconstructed with their sparse weight maps. We edit basis BRDFs and relight the scene under novel illumination conditions. + +![](images/061d5ee2138d4d6bd2fa1ee5390adf9718fd5da68ffd436e7be065e890a94ec2.jpg) +Basis BRDFs and weight maps + +potentially-specular areas using the rendered half-way angle map. Figure 11 shows that specular-weighted rendering loss produces a more stable reconstruction compared to not using the weighting. + +# 5. Conclusion + +In this paper, we have introduced a differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs. Our method obtains interpretable basis BRDFs that can represent SVBRDFs in a spatially-separable manner, enabling accurate geometry and SVBRDF reconstruction. Also, the number of basis BRDFs automatically adjusts to a target scene. We demonstrate the effectiveness of our method compared to state-of-the + +![](images/a1f38dea73faad2c0d905caaf91b8fb59a840432661f080e24253919383ad319.jpg) +GT + +![](images/5022f0ecb408223ea0884a10865c925943dde71eb7e9bb83a0892491662b9df1.jpg) +With sparsity and basis control + +![](images/727817af93538d602176f098e25b618d6d96cbc66031cfae2fb06a8933daf61b.jpg) + +![](images/a9264f18796ed9133c5248facdc4a5286b3b7268e796d8020ff9cb9f7908a7ec.jpg) +Without sparsity and basis control + +![](images/cd723bc44511fd5486c83091dd8ee8e80b88f8d1780dbe533f2818c8cfa057ee.jpg) + +![](images/2e03aaaf67bc472bfdb0f12b53182161a6fc6cbd6f9f330cd9797d2855260d8c.jpg) +Figure 10. Impact of sparsity regularizer and basis BRDF control. Without sparsity loss and basis BRDF control of merge and removal, the resulting basis BRDFs are blended each other as shown in the corresponding images, making them non-interpretable for downstream tasks. +GT image + +![](images/a94cdbae2b05ddc38aa7aed56013b505387afdc317c485933c4f193d618b352d.jpg) +Specular weight map + +![](images/2d529f9d2135ac2dd1c5cec2813275cf1311d3926ae87f203f4fe61faf4c72ec.jpg) + +![](images/e374f566130c2d394e41e489ce9d669d4262c7fe05e029b9747c7c0147bb60eb.jpg) +Without specular weight +Figure 11. Impact of specular-weighted loss. Using specular-weighted rendering loss improves geometry and reflectance reconstruction quality by recovering high frequency features from specularity, which is emphasized by the specular weight map. + +![](images/4cdb5770a6022cd051b43fd3c5299dc67e329f631f4ec74ebd2bf6e64d3d6b83.jpg) + +![](images/805d98973449b3329b258aab08aae9b35daf766ea39373ed81293ff803e25897.jpg) +With specular weight + +![](images/907ae77864f8145dcfe095019c6b949f9aee953cfb32ba8d8be79600fd1a0e1d.jpg) + +![](images/def55d2dbc94e646ada2516d8126d3f90a5c89f2118584dac220a8af4243d22b.jpg) +GT + +art approaches. Using the interpretable basis BRDFs, our method also facilitates downstream tasks such as intuitive scene editing. + +Limitations Our basis BRDF representation assumes opaque objects, leaving modeling non-surface objects as a future work. Combining semantic information from a large vision model is also an interesting future work. + +Acknowledgments Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, RS-2024-00438532, RS-2025-00518643), and Korea IITP MSIT (RS-2023-00215700). + +# References + +[1] Neil Alldrin, Todd Zickler, and David Kriegman. Photometric stereo with non-parametric and spatially-varying reflectance. In 2008 IEEE Conference on Computer Vision and Pattern Recognition, pages 1-8. IEEE, 2008. 1, 2 +[2] Zoubin Bi, Yixin Zeng, Chong Zeng, Fan Pei, Xiang Feng, Kun Zhou, and Hongzhi Wu. $\mathrm{Gs}^3$ : Efficient relighting with triple gaussian splatting. In SIGGRAPH Asia 2024 Conference Papers, 2024. 1, 2, 6, 7 +[3] Mark Boss, Raphael Braun, Varun Jampani, Jonathan T Barron, Ce Liu, and Hendrik Lensch. Nerd: Neural reflectance decomposition from image collections. In Int. Conf. Comput. 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To address the inherent ill-posedness of inverse rendering, basis BRDF representations are commonly used, modeling SVBRDFs as spatially varying blends of a set of basis BRDFs. However, existing methods often yield basis BRDFs that lack intuitive separation and have limited scalability to scenes of varying complexity. In this paper, we introduce a differentiable inverse rendering method that produces interpretable basis BRDFs. Our approach models a scene using 2D Gaussians, where the reflectance of each Gaussian is defined by a weighted blend of basis BRDFs. We efficiently render an image from the 2D Gaussians and basis BRDFs using differentiable rasterization and impose a specular-weighted rendering loss with the input flash photography images. During this analysis-by-synthesis optimization process of differentiable inverse rendering, we dynamically adjust the number of basis BRDFs to fit the target scene while encouraging sparsity in the basis weights. This ensures that the reflectance of each Gaussian is represented by only a few basis BRDFs. This approach enables" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 432, + 546, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 432, + 546, + 492 + ], + "spans": [ + { + "bbox": [ + 305, + 432, + 546, + 492 + ], + "type": "text", + "content": "the reconstruction of accurate geometry and interpretable basis BRDFs that are spatially separated. Consequently, the resulting scene representation, comprising basis BRDFs and 2D Gaussians, supports physically-based novel-view relighting and intuitive scene editing." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 512, + 386, + 524 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 386, + 524 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 386, + 524 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Inverse rendering aims to reconstruct geometry and reflectance from captured images, a fundamental problem in computer vision and computer graphics. Recent advances in differentiable rendering methods [18, 29] have facilitated analysis-by-synthesis differentiable inverse rendering. These methods enable the optimization of scene parameters by minimizing the discrepancy between captured and synthesized images [2, 8, 12, 45, 47]. However, achieving accurate inverse rendering remains challenging, especially when the available lighting and viewing angles are limited. A promising approach to mitigate this problem is to exploit the spatial coherence of SVBRDFs using basis BRDF representations [1, 19, 27, 28, 32]. Representing the BRDF at each point as a spatially varying blend of basis BRDFs allows gathering multiple points to accurately fit basis BRDFs" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "475" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "type": "text", + "content": "and their per-point weights." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 286, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 286, + 239 + ], + "type": "text", + "content": "Early methods often focus solely on estimating basis BRDFs and their weights for objects with known 3D geometry [20, 21, 50]. Moreover, they typically require excessive optimization time and suffer from low accuracy. Recent methods jointly optimize geometry and basis BRDFs [2, 8, 30]. These approaches often result in non-interpretable basis BRDFs which are spatially entangled: each scene point is represented by many basis BRDFs with high weights and those basis BRDFs are often non-interpretable. Thus, their results are impractical to use for downstream tasks such as scene editing. Additionally, they are often limited to using a fixed number of basis BRDFs, regardless of scene complexity." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 239, + 286, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 286, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 286, + 407 + ], + "type": "text", + "content": "In this paper, we propose a differentiable inverse rendering method that jointly estimates geometry and reflectance. We represent geometry as a set of 2D Gaussians [9, 14], each with shape parameters and basis BRDF weights. The reflectance of each Gaussian is modeled as a spatially varying blend of basis BRDFs. We dynamically adjust the number of basis BRDFs during the analysis-by-synthesis optimization, promoting sparsity in the basis BRDF weights. To enhance training stability, we employ a weighted photometric loss that focuses on potentially specular regions. We demonstrate that our method obtains not only accurate geometry but also scalable and interpretable basis BRDFs which sparsely represent SVBRDFs as shown in Figure 1. In summary, we make the following contributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 407, + 286, + 515 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 407, + 286, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 286, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 286, + 442 + ], + "type": "text", + "content": "- A differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs, obtaining interpretable basis BRDFs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 443, + 286, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 286, + 491 + ], + "type": "text", + "content": "- A basis BRDF control method and sparsity regularizer that dynamically adjust the number of basis BRDFs during analysis-by-synthesis optimization, promoting interpretability through sparse blending." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 491, + 286, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 286, + 515 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 286, + 515 + ], + "type": "text", + "content": "- Extensive evaluation compared with existing methods, and demonstration of intuitive scene editing." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 525, + 133, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 133, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 133, + 538 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 286, + 628 + ], + "type": "text", + "content": "Inverse Rendering Learning-based inverse rendering methods train neural networks such as CNNs [22, 23, 33, 34, 38, 43], transformers [51], and diffusion models [25, 31, 40] on datasets, enabling efficient inference by exploiting prior distributions in the training data. They often suffer from out-of-distribution inputs, resulting in physically inaccurate results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "The analysis-by-synthesis framework enables inverse rendering by inverting the forward rendering process. Recent advancements have been particularly sparked by differentiable rendering techniques using volumetric rendering [3-7, 10, 11, 17, 26, 36, 37, 39, 41, 44-48] and rasterization [2, 12, 16, 24, 35, 52]. Recent rasterization-based methods using isotropic points [8], 2D Gaussians [49], and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "3D Gaussians [2, 12, 16, 24, 35, 52] exhibit both efficiency and accuracy. However, they suffer when insufficient light-view angular samples are provided. Incorporating basis BRDFs into the modern analysis-by-synthesis framework has shown promising performance, however the reconstructed basis BRDFs are often non-interpretable, limiting their usefulness in downstream tasks such as scene editing [2, 8]. In contrast, our novel method obtains 2D Gaussians with accurate geometry and interpretable basis BRDFs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 194, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 529 + ], + "type": "text", + "content": "Basis BRDF Basis BRDFs have often been used as a representation of SVBRDFs, decomposing the SVBRDF into a blend of basis BRDFs. This approach is based on the spatial coherence of reflectance, assuming that the BRDFs of many pixels are similar in real-world scenes [27, 28]. Using basis BRDFs helps reduce the ill-posedness of inverse rendering because it enables gathering many light-angular observations for each basis BRDF reconstruction. Existing methods jointly optimize basis BRDFs and spatially varying weights for planar [19, 32] and non-planar objects [1, 13, 15, 30]. Recently, two methods [2, 8] demonstrated the effectiveness of basis BRDFs in modern differentiable analysis-by-synthesis frameworks. While they showed promising results, the estimated basis BRDFs are non-interpretable as shown in Figure 6, which limits their utility in downstream tasks such as scene editing. Moreover, generalizing their methods to varying degrees of scene complexity is challenging because the number of basis BRDFs is fixed. To overcome these problems, we are inspired by the decade ago work of Zhou et al. [50], which proposed adjusting the number of basis BRDFs during optimization. Their method assumes known geometry, does not exploit a differentiable rendering pipeline, and suffers from low reconstruction accuracy and efficiency. We address these challenges by developing a differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs to obtain interpretable basis BRDFs, where the number of basis BRDFs are automatically controlled." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 538, + 361, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 361, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 361, + 550 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "type": "text", + "content": "Our method consists of two parts. In Section 3.1, we focus on optimizing 2D Gaussians and basis BRDFs without concerning the interpretability of basis BRDFs. Next, we extend the method to obtaining interpretable basis BRDFs in Section 3.2. Figure 2 shows the process of our method over analysis-by-synthesis iterations. We obtain not only accurate geometry but also interpretable basis BRDFs whose number adapts to the scene and the basis BRDFs represent SVBRDFs with spatially-separated basis-BRDF weights." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 671, + 545, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 545, + 683 + ], + "type": "text", + "content": "3.1. Gaussian Inverse Rendering with Basis BRDFs" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "We introduce our method that jointly estimates geometry and a fixed number of basis BRDFs in a differentiable man" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "476" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 549, + 312 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 549, + 312 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 549, + 312 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 549, + 312 + ], + "type": "image", + "image_path": "8045f4104dd6ae281e5d215a87fbc4cdd92de7ac563666385961970a52533e97.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 319, + 547, + 364 + ], + "lines": [ + { + "bbox": [ + 46, + 319, + 547, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 547, + 364 + ], + "type": "text", + "content": "Figure 2. The process of our analysis-by-synthesis iterations. Given a set of multi-view photometric images, we initialize point cloud and extract base color for basis BRDFs. We jointly optimize 2D Gaussians and basis BRDFs by comparing the differentiably-rendered images and the input images. Our method enables obtaining interpretable basis BRDFs with spatially-separated basis-BRDF weights and the number of basis BRDFs adapts to the scene." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 378, + 240, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 240, + 391 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 240, + 391 + ], + "type": "text", + "content": "ner from multi-view flash-photography images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "content": "Geometry We use 2D Gaussians as geometric primitives [14], where each Gaussian " + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "inline_equation", + "content": "g \\in G" + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "content": " is an elliptical disk, and " + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "content": " is the set of all Gaussians. Each Gaussian " + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "content": " is parameterized by its center location " + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbb{R}^{3 \\times 1}" + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "content": ", principal vectors " + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{t} \\in \\mathbb{R}^{3 \\times 2}" + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "content": ", and scaling factors " + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{s} \\in \\mathbb{R}^{2 \\times 1}" + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "content": ". The Gaussian surface normal " + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 46, + 405, + 287, + 490 + ], + "type": "text", + "content": " is computed as the cross product of the principal vectors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "text", + "content": "Basis BRDFs We use a basis BRDF representation, where we define " + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "text", + "content": " basis BRDFs. We model the " + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "text", + "content": "-th basis " + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "inline_equation", + "content": "\\mathrm{BRDF}f_{i}" + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "text", + "content": " with base color " + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_i" + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "text", + "content": ", roughness " + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "text", + "content": ", and metallic parameter " + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "inline_equation", + "content": "m_{i}" + }, + { + "bbox": [ + 46, + 504, + 288, + 554 + ], + "type": "text", + "content": " using the simplified Disney BRDF model [42]:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 571, + 287, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 571, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 55, + 571, + 287, + 622 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} f _ {i} (\\mathbf {i}, \\mathbf {o}) = \\frac {1 - m _ {i}}{\\pi} \\mathbf {b} _ {i} \\\\ + \\frac {D (\\mathbf {h} ; \\sigma_ {i}) F (\\mathbf {o} , \\mathbf {h} ; \\mathbf {b} _ {i} , m _ {i}) G (\\mathbf {i} , \\mathbf {o} , \\mathbf {n} ; \\sigma_ {i})}{4 (\\mathbf {n} \\cdot \\mathbf {i}) (\\mathbf {n} \\cdot \\mathbf {o})}, \\tag {1} \\\\ \\end{array}", + "image_path": "4b9bfaa564fe6c0305fb7a68ba0d12585627617bf3158dc5aa5d5597d46fd19a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{i}" + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{o}" + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "content": " are the incident and outgoing directions, and " + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{h} = (\\mathbf{i} + \\mathbf{o}) / 2" + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "content": " is the half-way vector. " + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "content": " is the normal distribution function, " + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "content": " is the Fresnel term, and " + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "content": " is the geometric attenuation. Details of these terms are provided in the Supplemental Document." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "We assign blending weights " + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "w_{i}(g)" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": " for every " + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "-th basis BRDF per each Gaussian " + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": ", and represent the BRDF " + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": " of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 378, + 382, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 378, + 382, + 390 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 382, + 390 + ], + "type": "text", + "content": "the Gaussian " + }, + { + "bbox": [ + 306, + 378, + 382, + 390 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 306, + 378, + 382, + 390 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 363, + 396, + 545, + 429 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 396, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 363, + 396, + 545, + 429 + ], + "type": "interline_equation", + "content": "f (\\mathbf {i}, \\mathbf {o}; g) = \\sum_ {i = 1} ^ {N} w _ {i} (g) f _ {i} (\\mathbf {i}, \\mathbf {o}). \\tag {2}", + "image_path": "b4b6417fde2b7b0d77c73af3ba5cf937ff351fc542d0b6d74f8026589432790e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 443, + 546, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 443, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 443, + 546, + 479 + ], + "type": "text", + "content": "Scene Representations In summary, our scene representation consists of per-Gaussian parameters " + }, + { + "bbox": [ + 305, + 443, + 546, + 479 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 443, + 546, + 479 + ], + "type": "text", + "content": " and basis BRDF parameters " + }, + { + "bbox": [ + 305, + 443, + 546, + 479 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 443, + 546, + 479 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 330, + 484, + 523, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 484, + 523, + 514 + ], + "spans": [ + { + "bbox": [ + 330, + 484, + 523, + 514 + ], + "type": "interline_equation", + "content": "g = \\underbrace{\\{\\mathbf{p},\\mathbf{t},\\mathbf{s}\\}}_{\\text{geometric}}\\cup \\underbrace{\\{\\{w_{i}(g)\\}_{i = 1}^{N},\\alpha\\}}_{\\text{photometric}},\\text{where} g\\in G,", + "image_path": "f9519f08ff0c49299b8afcc54eb0666380b0d39e41fdd8686d94e1a44f1cae2a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 516, + 545, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 516, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 329, + 516, + 545, + 531 + ], + "type": "interline_equation", + "content": "R = \\left\\{m _ {i}, \\mathbf {b} _ {i}, \\sigma_ {i} \\right\\} _ {i = 1} ^ {N}. \\tag {3}", + "image_path": "6ed42bf028678b4464114496e4b4bdd56258ab23a8c5503575e1548b4cd993aa.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": " is the Gaussian opacity. To initialize the basis BRDF parameters " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": ", we perform k-means clustering with a fixed number " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": " on the input multi-view flash photography images " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "I'" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": ". The base colors " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{b}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": " are initialized as the mean values of the clusters. The roughness " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "\\{\\sigma_i\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": " and metallic parameters " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "\\{m_i\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": " are set to initial values: " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "\\sigma_i = 0.5" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "m_i = 0.0" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": ". We initialize the weights " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "w_i(g)" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": " uniformly and set " + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 536, + 546, + 633 + ], + "type": "text", + "content": " following Huang et al. [14]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 646, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 646, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 305, + 646, + 545, + 694 + ], + "type": "text", + "content": "Differentiable Rendering We render an image under the flash light, modeled as a point light source, using differentiable rasterization. Specifically, we compute the radiance " + }, + { + "bbox": [ + 305, + 646, + 545, + 694 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 646, + 545, + 694 + ], + "type": "text", + "content": " of each Gaussian " + }, + { + "bbox": [ + 305, + 646, + 545, + 694 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 305, + 646, + 545, + 694 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 356, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 356, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "L (\\mathbf {i}, \\mathbf {o}; g) = (\\mathbf {n} \\cdot \\mathbf {i}) f (\\mathbf {i}, \\mathbf {o}; g) E (g), \\tag {4}", + "image_path": "139274ea22b77bf8444e923dfab8308059908ea03ca425d609c98dd87631eddd.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "text", + "content": "477" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 276, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 276, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 276, + 84 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 276, + 84 + ], + "type": "inline_equation", + "content": "E(g)" + }, + { + "bbox": [ + 47, + 72, + 276, + 84 + ], + "type": "text", + "content": " is the incident light intensity on Gaussian " + }, + { + "bbox": [ + 47, + 72, + 276, + 84 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 47, + 72, + 276, + 84 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 287, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 287, + 145 + ], + "type": "text", + "content": "After computing the radiance, we rasterize the Gaussians onto the image plane, sort them by depth, and accumulate radiance values using alpha blending [14] to produce the final pixel value of the rendered image " + }, + { + "bbox": [ + 46, + 84, + 287, + 145 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 84, + 287, + 145 + ], + "type": "text", + "content": ". We define this rendering as a function " + }, + { + "bbox": [ + 46, + 84, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\operatorname{render}(\\cdot)" + }, + { + "bbox": [ + 46, + 84, + 287, + 145 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 149, + 287, + 200 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 149, + 287, + 200 + ], + "spans": [ + { + "bbox": [ + 61, + 149, + 287, + 200 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} I (u) = \\operatorname {r e n d e r} \\left(\\left\\{L _ {i} \\right\\} _ {i = 1} ^ {M}\\right) \\\\ = \\sum_ {i = 1} ^ {M} L _ {i} \\alpha_ {i} \\mathcal {G} _ {i} (\\mathbf {r} (u)) \\prod_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j} \\mathcal {G} _ {j} (\\mathbf {r} (u))\\right), \\tag {5} \\\\ \\end{array}", + "image_path": "e0f9caa20962e1f03c330c98346c092d937dad6ed76939bc5121bb93452cbb10.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "u \\in U" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": " is a pixel, " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": " is the number of Gaussians projected onto pixel " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\{L_i\\}_{i=1}^M" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\{\\alpha_i\\}_{i=1}^M" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": " are the radiance and opacity values of the depth-sorted " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": "-th Gaussian, respectively. The vector " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(u)" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": " is the ray coming from corresponding pixel " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i(\\mathbf{r}(u))" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": " is the Gaussian-filtered distance between the center of " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": "-th Gaussian and the intersection point between the ray " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(u)" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 205, + 287, + 301 + ], + "type": "text", + "content": "-th Gaussian. Details are provided in the Supplemental Document." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": "Optimization We optimize the Gaussian parameters " + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": " and the basis BRDF parameters " + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": " by minimizing the loss function " + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": " in an analysis-by-synthesis manner:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 85, + 358, + 287, + 372 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 358, + 287, + 372 + ], + "spans": [ + { + "bbox": [ + 85, + 358, + 287, + 372 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {r e n d e r}} + \\lambda_ {\\text {g e o m}} \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {m a s k}} \\mathcal {L} _ {\\text {m a s k}}, \\tag {6}", + "image_path": "22c5a6fe7c5c3682625c03b59d99983c05e42400f4b2a120899881aa79f9a7c6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{render}}" + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "content": " penalizes the difference between the rendered image " + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "content": " and the input image " + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "inline_equation", + "content": "I^{\\prime}" + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "content": " across all input views. " + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{geom}}" + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "content": " is a geometric regularization term for depth distortion and normal consistency [14], and " + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mask}}" + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "content": " is the cross-entropy loss between the rendered mask and the ground-truth mask. " + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{geom}}" + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{mask}}" + }, + { + "bbox": [ + 47, + 377, + 287, + 462 + ], + "type": "text", + "content": " are the balancing weights. Details are provided in the Supplemental Document." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 475, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 536 + ], + "type": "text", + "content": "Specular-weighted Rendering Loss Multi-view flash photography typically generates fewer observations of specular-dominant pixels compared to diffuse-dominant pixels. To address this imbalance, we weight specular observations by using the potentially-specular weight map:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 541, + 287, + 556 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 541, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 104, + 541, + 287, + 556 + ], + "type": "interline_equation", + "content": "H (u) = 1 + \\lambda_ {\\theta_ {h}} (\\cos \\theta_ {h} (u)) ^ {k}, \\tag {7}", + "image_path": "71c883580ebaa55b5c77aee640bba7ffa31a0703587f819e2882845d43628afc.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": " is the rendered half-way angle map as " + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\theta_h(u) =" + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": " render " + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\left(\\{\\arccos (\\mathbf{n}_i\\cdot \\mathbf{h}_i)\\}_{i = 1}^M\\right)" + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_i" + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_i" + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": " are the normal and half-way vector of Gaussian " + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": ", respectively. We set the scalar " + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\lambda_{\\theta_h} = 5" + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "inline_equation", + "content": "k = 10" + }, + { + "bbox": [ + 47, + 561, + 287, + 620 + ], + "type": "text", + "content": " to strongly weight specular regions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 620, + 287, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 287, + 645 + ], + "type": "text", + "content": "We use the potentially-specular weight map " + }, + { + "bbox": [ + 47, + 620, + 287, + 645 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 620, + 287, + 645 + ], + "type": "text", + "content": " for calculating the final rendering loss:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 50, + 650, + 287, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 650, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 50, + 650, + 287, + 689 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e n d e r}} = \\frac {1}{| U |} \\sum_ {u \\in U} H (u) \\left((1 - \\lambda_ {s}) \\mathcal {L} _ {1} (u) + \\lambda_ {s} \\mathcal {L} _ {\\mathrm {S S I M}} (u)\\right), \\tag {8}", + "image_path": "811c9b659e15943c8f74e61e676e3626b0093c821a104ca2736535516dd2449a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1(u) = \\| I(u) - I'(u)\\|_1" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SSIM}}(u)" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " is the SSIM loss between " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "I(u)" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "I'(u)" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_s" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " is a balancing weight." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 68, + 545, + 276 + ], + "blocks": [ + { + "bbox": [ + 307, + 68, + 545, + 276 + ], + "lines": [ + { + "bbox": [ + 307, + 68, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 307, + 68, + 545, + 276 + ], + "type": "image", + "image_path": "725d627019aad0029f75f40064115a70930be9c53f4ec7716ca5f302361bf08e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 282, + 545, + 327 + ], + "lines": [ + { + "bbox": [ + 305, + 282, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 282, + 545, + 327 + ], + "type": "text", + "content": "Figure 3. Basis BRDFs with varying scene complexity. We adjust the number of basis BRDFs during optimization to adapt to the scene complexity. We initialize the same number of basis BRDFs for both scenes in this example." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 346, + 455, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 455, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 455, + 358 + ], + "type": "text", + "content": "3.2. Interpretable Basis BRDFs" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 370, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 370, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 545, + 454 + ], + "type": "text", + "content": "While our method in Section 3.1 offers accurate inverse rendering, the reconstructed basis BRDFs lack of interpretability. Here, we extend the method to obtain interpretable basis BRDFs whose number adapts to the scene as shown in Figure 3. We develop basis BRDF control method of merge and removal in addition to impose sparsity on basis BRDF weights." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 494, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 494, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 305, + 494, + 545, + 578 + ], + "type": "text", + "content": "Sparsity of Basis BRDF Weights For obtaining interpretable basis BRDF, each scene point needs to be represented with only few basis BRDFs with high weights. This enables spatially separating SVBRDFs with sparse basis BRDFs. We impose sparsity on the basis BRDF weights " + }, + { + "bbox": [ + 305, + 494, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\{w_{i}(g)\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 305, + 494, + 545, + 578 + ], + "type": "text", + "content": " for each Gaussian " + }, + { + "bbox": [ + 305, + 494, + 545, + 578 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 305, + 494, + 545, + 578 + ], + "type": "text", + "content": ", making each Gaussian represented by only a few basis BRDFs." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 584, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 584, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 305, + 584, + 545, + 620 + ], + "type": "text", + "content": "First, we apply a softmax function with a low temperature " + }, + { + "bbox": [ + 305, + 584, + 545, + 620 + ], + "type": "inline_equation", + "content": "T = 0.0125" + }, + { + "bbox": [ + 305, + 584, + 545, + 620 + ], + "type": "text", + "content": " to the weights, promoting sparse per-Gaussian weights:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 356, + 640, + 545, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 640, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 356, + 640, + 545, + 670 + ], + "type": "interline_equation", + "content": "w _ {i} (g) \\leftarrow \\frac {\\exp \\left(w _ {i} (g) / T\\right)}{\\sum_ {i ^ {\\prime} = 1} ^ {N} \\exp \\left(w _ {i ^ {\\prime}} (g) / T\\right)}. \\tag {9}", + "image_path": "09761ac86e70a82459ec88219795d23dd9eb5d9ebb4ee4e718cb22b8ebc23476.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Second, we apply an entropy-based sparsity regularizer on the Gaussian weight " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " and rendered weight image " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "W_{i}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " for" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "478" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 548, + 350 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 548, + 350 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 548, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 548, + 350 + ], + "type": "image", + "image_path": "128eb20158ed538f396b53c408be0bda6d7dce6db115734b416288d99a388cc7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 355, + 547, + 401 + ], + "lines": [ + { + "bbox": [ + 46, + 355, + 547, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 547, + 401 + ], + "type": "text", + "content": "Figure 4. Basis BRDF control. During the optimization, we compute the values of each basis BRDF for sampled half-way angles " + }, + { + "bbox": [ + 46, + 355, + 547, + 401 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 46, + 355, + 547, + 401 + ], + "type": "text", + "content": " from which radiometric difference is obtained. We compute the geometric difference between point clouds of basis BRDFs. If two basis BRDFs are radiometrically and geometrically similar, we merge them. If the rendered weight map " + }, + { + "bbox": [ + 46, + 355, + 547, + 401 + ], + "type": "inline_equation", + "content": "W_i" + }, + { + "bbox": [ + 46, + 355, + 547, + 401 + ], + "type": "text", + "content": " has few valid pixels, we remove the basis BRDF." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 407, + 140, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 140, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 140, + 418 + ], + "type": "text", + "content": "each " + }, + { + "bbox": [ + 47, + 407, + 140, + 418 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 407, + 140, + 418 + ], + "type": "text", + "content": "-th basis BRDF:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 422, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 422, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 71, + 422, + 287, + 491 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {s p a r s e}} = - \\frac {1}{| G |} \\sum_ {g \\in G} \\sum_ {i = 1} ^ {N} w _ {i} (g) \\log w _ {i} (g) \\\\ - \\frac {1}{| U |} \\sum_ {u \\in U} \\sum_ {i = 1} ^ {N} W _ {i} (u) \\log W _ {i} (u), \\tag {10} \\\\ \\end{array}", + "image_path": "9ed5ee4d2d287c810e1b17b454f161a3d21e5d2e3c8ba10747fe7caa874ea36a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 84, + 494, + 287, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 494, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 84, + 494, + 287, + 509 + ], + "type": "interline_equation", + "content": "W _ {i} = \\operatorname {r e n d e r} \\left(\\left\\{w _ {i} (g) \\right\\} _ {g \\in G}\\right). \\tag {11}", + "image_path": "fc84f50cfa09b0ce173e22d544fce47da694500de4ec3738ce40ed8d63380f76.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "text", + "content": "Basis BRDF Merge Basis BRDFs often become similar during optimization, making the resulting basis BRDFs non-intuitive with duplicates. We address this by merging similar basis BRDFs during analysis-by-synthesis optimization, as shown in Figure 4. We compute the values of each basis BRDF " + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "text", + "content": " at uniformly-sampled halfway angles " + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "inline_equation", + "content": "\\theta_{h}" + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "text", + "content": " for the RGB channels, resulting in a matrix " + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i\\in \\mathbb{R}^{C\\times 3}" + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "text", + "content": " is the number of halfway angles. We then compute the radiometric difference between pairs of basis BRDFs, represented as a matrix " + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{\\mathrm{radio}}\\in \\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 46, + 537, + 289, + 658 + ], + "type": "text", + "content": ", which is defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 665, + 287, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 665, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 107, + 665, + 287, + 689 + ], + "type": "interline_equation", + "content": "\\mathbf {D} _ {\\text {r a d i o}} (i, j) = \\frac {1}{C} \\| \\mathbf {f} _ {i} - \\mathbf {f} _ {j} \\| _ {2}. \\tag {12}", + "image_path": "a9fa01df6fcbdf98c5d196b7a416f19e2029ef694ea96336cc5967b7a0c9bcf2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "We also compute the geometric difference between the every pair of basis BRDFs, represented as a matrix " + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{\\mathrm{point}} \\in" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 406, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 406, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 305, + 406, + 545, + 431 + ], + "type": "text", + "content": " using the Chamfer distance between point clouds represented by each basis BRDF:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 338, + 441, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 441, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 338, + 441, + 545, + 503 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {D} _ {\\text {p o i n t}} (i, j) = \\frac {1}{| P _ {i} |} \\sum_ {\\mathbf {p} \\in P _ {i}} \\min _ {\\mathbf {q} \\in P _ {j}} \\| \\mathbf {p} - \\mathbf {q} \\| _ {2} ^ {2} \\\\ + \\frac {1}{\\left| P _ {j} \\right|} \\sum_ {\\mathbf {q} \\in P _ {j}} \\min _ {\\mathbf {p} \\in P _ {i}} \\| \\mathbf {q} - \\mathbf {p} \\| _ {2} ^ {2}, \\tag {13} \\\\ \\end{array}", + "image_path": "fef27959d18afc112b5f78f44a2b471abb5b899556a487437d0e64be4fcc3965.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "P_{j}" + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "text", + "content": " are the point clouds for the " + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "text", + "content": "-th and " + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "text", + "content": "-th basis BRDFs, consisting of the center locations of Gaussians where the " + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "text", + "content": "-th or " + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 513, + 545, + 548 + ], + "type": "text", + "content": "-th basis BRDF has the highest weight." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "text", + "content": "If the radiometric difference " + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{\\mathrm{radio}}(i,j)" + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "text", + "content": " is below a threshold " + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{merge}}" + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{\\mathrm{point}}(i,j)" + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "text", + "content": " is minimal among all " + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\forall j" + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "text", + "content": ", we merge the two basis BRDFs by deleting the basis BRDF with fewer associated Gaussians and reassigning the per-Gaussian basis BRDF weights as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 350, + 621, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 621, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 350, + 621, + 545, + 635 + ], + "type": "interline_equation", + "content": "w _ {j} (g) \\leftarrow w _ {i} (g) + w _ {j} (g), \\quad \\forall g \\in G. \\tag {14}", + "image_path": "baffa5c628a70eb997c00495dcadf307efce0f0cfadeae8e0903d2b9b7297188.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Basis BRDF Removal To obtain meaningful basis BRDFs only, we remove " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "-th basis BRDF if it contributes to only a few pixels during optimization as shown in Figure 4. We evaluate this using the rendered weight image " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "W_{i}" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 748, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 748, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 748, + 313, + 757 + ], + "type": "text", + "content": "479" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 68, + 214, + 220 + ], + "blocks": [ + { + "bbox": [ + 49, + 68, + 214, + 220 + ], + "lines": [ + { + "bbox": [ + 49, + 68, + 214, + 220 + ], + "spans": [ + { + "bbox": [ + 49, + 68, + 214, + 220 + ], + "type": "image", + "image_path": "470faa1752544a0026f279f3201b4879732ff9771dabe3abebdbaa5179b2b448.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "type": "text", + "content": "Figure 5. Normal reconstruction. Our method successfully recovers the detailed surface normal, outperforming other state-of-the-art inverse rendering methods: IRON [45], DPIR [8], GS³ [2]." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 68, + 297, + 220 + ], + "blocks": [ + { + "bbox": [ + 215, + 68, + 297, + 220 + ], + "lines": [ + { + "bbox": [ + 215, + 68, + 297, + 220 + ], + "spans": [ + { + "bbox": [ + 215, + 68, + 297, + 220 + ], + "type": "image", + "image_path": "abdf114cd4c4954a437455666a963281e500b646c319ebce255f66713c9bda6e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 298, + 68, + 380, + 220 + ], + "blocks": [ + { + "bbox": [ + 298, + 68, + 380, + 220 + ], + "lines": [ + { + "bbox": [ + 298, + 68, + 380, + 220 + ], + "spans": [ + { + "bbox": [ + 298, + 68, + 380, + 220 + ], + "type": "image", + "image_path": "9ba739addaa04c9ca7251207b8e2fe0057d17d002d00a4da0d2597717e11c97c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 380, + 68, + 461, + 220 + ], + "blocks": [ + { + "bbox": [ + 380, + 68, + 461, + 220 + ], + "lines": [ + { + "bbox": [ + 380, + 68, + 461, + 220 + ], + "spans": [ + { + "bbox": [ + 380, + 68, + 461, + 220 + ], + "type": "image", + "image_path": "f200ddf5e1121800a39f25407707f2c6b6734e32bd315cea34fd6cd872aa13cc.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 462, + 68, + 546, + 220 + ], + "blocks": [ + { + "bbox": [ + 462, + 68, + 546, + 220 + ], + "lines": [ + { + "bbox": [ + 462, + 68, + 546, + 220 + ], + "spans": [ + { + "bbox": [ + 462, + 68, + 546, + 220 + ], + "type": "image", + "image_path": "c5dfd8e6db340811253473b1ea218673f1ed389a95b258ee0a2a53a42b24c104.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 255, + 141, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 141, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 141, + 266 + ], + "type": "text", + "content": "from Equation (11) as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 274, + 287, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 274, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 56, + 274, + 287, + 300 + ], + "type": "interline_equation", + "content": "\\frac {\\left| \\left\\{u \\in U \\mid W _ {i} (u) > \\tau_ {\\text {r e m o v a l - w e i g h t}} \\right\\} \\right|}{\\left| U \\right|} < \\tau_ {\\text {r e m o v a l - n u m b e r}}, \\tag {15}", + "image_path": "7fe329242383639d0ebd05383ea93e5a748f0d21055c3b8d586843b34402495c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{removal - weight}} = 0.1" + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "text", + "content": " is the threshold determining whether the " + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "text", + "content": "-th basis BRDF significantly contributes to that pixel " + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{removal - number}} = 0.005" + }, + { + "bbox": [ + 46, + 308, + 287, + 357 + ], + "type": "text", + "content": " is the threshold for the normalized number of such pixels." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 362, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 287, + 446 + ], + "type": "text", + "content": "Scheduling For a warm start, we first run our inverse rendering described in Section 3.1. After a predefined number of iterations, 6000 in our experiments, we perform basis BRDF merge and removal at predefined intervals 500 during iterations to refine the basis BRDFs. We incorporate the sparsity loss " + }, + { + "bbox": [ + 46, + 362, + 287, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{sparse}}" + }, + { + "bbox": [ + 46, + 362, + 287, + 446 + ], + "type": "text", + "content": " and optimize the scene parameters by minimizing:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 52, + 455, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 455, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 52, + 455, + 287, + 469 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {r e n d e r}} + \\lambda_ {\\text {g e o m}} \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {m a s k}} \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {\\text {s p a r s e}} \\mathcal {L} _ {\\text {s p a r s e}}, \\tag {16}", + "image_path": "a032b34fec66e065e51315b9dd3f80bac1b7a3dd85813542406a66d996c76305.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 477, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 287, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 477, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{sparse}}" + }, + { + "bbox": [ + 47, + 477, + 287, + 502 + ], + "type": "text", + "content": " is the balancing weight. Refer to the Supplemental Document for the details on the optimization." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 512, + 100, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 512, + 100, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 512, + 100, + 525 + ], + "type": "text", + "content": "4. Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 532, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 652 + ], + "type": "text", + "content": "Datasets We evaluate our approach on both synthetic and real-world photometric dataset. For the synthetic dataset, we render four complex scenes containing multiple objects, following the co-located flash photography. Each scene includes multiple objects. The dataset consists of 200 training images and 100 test images per scene. For the real-world photometric dataset, we capture one multi-object scene using a mobile phone with flash at 200/40 training/testing images. We conduct geometric and radiometric calibrations of the light and the camera." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 659, + 200, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 200, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 200, + 672 + ], + "type": "text", + "content": "4.1. Validation and Comparison" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Geometry We assess our method in comparison with state-of-the-art analysis-by-synthesis inverse rendering methods: IRON [45], DPIR [8] and " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " [2]. Figure 5" + } + ] + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 344, + 252, + 511, + 293 + ], + "blocks": [ + { + "bbox": [ + 344, + 252, + 511, + 293 + ], + "lines": [ + { + "bbox": [ + 344, + 252, + 511, + 293 + ], + "spans": [ + { + "bbox": [ + 344, + 252, + 511, + 293 + ], + "type": "table", + "html": "
    IRONDPIRGS3Ours
    MAE ↓15.7117.0415.289.81
    Train ↓12h2h1h0.5h
    ", + "image_path": "49385010c4977bd46a8a6ea2e417ff13ded020f155e2827b82e255717ca2fa97.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 301, + 546, + 335 + ], + "lines": [ + { + "bbox": [ + 305, + 301, + 546, + 335 + ], + "spans": [ + { + "bbox": [ + 305, + 301, + 546, + 335 + ], + "type": "text", + "content": "Table 1. Normal reconstruction and training time. Our method outperforms IRON [45], DPIR [8], and " + }, + { + "bbox": [ + 305, + 301, + 546, + 335 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 305, + 301, + 546, + 335 + ], + "type": "text", + "content": " [2] in quantitative numbers evaluated on the synthetic dataset." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 339, + 546, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 546, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 546, + 507 + ], + "type": "text", + "content": "and Table 1 show the results for geometry reconstruction, demonstrating the highest accuracy in normal reconstruction with mean angular error (MAE). IRON and DPIR employ neural signed distance functions to recover smooth surface normal, not only resulting in loss of details but also requiring extended training times for optimization as shown in Table 1. " + }, + { + "bbox": [ + 304, + 339, + 546, + 507 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 304, + 339, + 546, + 507 + ], + "type": "text", + "content": ", which is based on 3D Gaussian splatting with anisotropic spherical Gaussians, exhibits limited accuracy in shape reconstruction. Our method accurately models surface geometry and reflectance using 2D Gaussians and interpretable basis BRDFs, achieving the highest accuracy of normal reconstruction, especially for thin and convex objects. Moreover, we outperform the others in terms of training speed." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "Basis BRDF Figure 6 shows the estimated basis BRDFs and weight maps, comparing modern inverse-rendering methods using basis BRDFs: " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": ", DPIR, our method without interpretable basis BRDFs (Section 3.1), and our method with interpretable basis BRDFs (Section 3.2). Both DPIR and " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " use basis BRDFs to leverage spatial coherence of specular reflectance. These methods yield non-interpretable basis BRDFs, as evident from the rendered weight maps and basis BRDF renderings. Our method introduced in Section 3.1 improves the interpretability of the basis BRDFs by jointly optimizing base colors. However, the resulting basis BRDFs are still often duplicated and non-intuitively classified. Moreover, all the methods have a fixed number of basis BRDFs, limited to modeling different complexity of scenes. In contrast, our full method (Section 3.2) obtains interpretable basis BRDFs whose number fits the target scene, as shown in Figure 3." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "480" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 547, + 317 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 547, + 317 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 547, + 317 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 547, + 317 + ], + "type": "image", + "image_path": "3aba177f7a6066582e1fc2def283490cc35a0b60880c9e6e013fdfdfee2e9a71.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 346, + 545, + 460 + ], + "blocks": [ + { + "bbox": [ + 46, + 325, + 546, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 325, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 546, + 346 + ], + "type": "text", + "content": "Figure 6. Basis BRDFs and weight maps. Our inverse-rendering methods (Section 3.1 and Section 3.2) obtain basis BRDFs that are explainable with spatially separated weight maps and intuitive basis BRDFs, compared to " + }, + { + "bbox": [ + 46, + 325, + 546, + 346 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 46, + 325, + 546, + 346 + ], + "type": "text", + "content": " [2] and DPIR [8]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 346, + 545, + 460 + ], + "lines": [ + { + "bbox": [ + 48, + 346, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 48, + 346, + 545, + 460 + ], + "type": "image", + "image_path": "3b2ffe749a6065a3179b29f1206265b1d567c30434ca5e329c2b7bb9b14c3575.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 468, + 546, + 491 + ], + "lines": [ + { + "bbox": [ + 46, + 468, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 546, + 491 + ], + "type": "text", + "content": "Figure 7. Novel-view relighting. Our method enables high quality novel-view relighting with the accurate surface normal. We achieve physically-valid relighting with accurate normal and basis BRDFs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 495, + 129, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 129, + 508 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 129, + 508 + ], + "type": "text", + "content": "4.2. Applications" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": "Novel-view Relighting Figure 7 shows novel-view relighting and estimated normals, compared with IRON, DPIR, " + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": ". They suffer from inaccurate estimation of geometry. Despite inaccurate normals, " + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": " manages to render high-quality relighting results. This is because neural networks compensate for such imperfection by learning residuals, as relighting is the main goal of " + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{GS}^3" + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": ". In contrast, our method reconstructs accurate geometry and interpretable basis BRDFs that enable not only novel-view relighting but also downstream tasks such as intuitive scene editing. For more results, refer to the Supplemental Document." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Scene Editing Our inverse rendering method enables selective editing based on basis BRDFs and weight images. Figure 8 shows that our interpretable basis BRDFs facilitate reflectance editing. Interpretable basis BRDFs enable prac" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 495, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 616 + ], + "type": "text", + "content": "tical material editing by adjusting desired BRDF parameters of base color, roughness, metallic based on their sparse weight maps. We then obtain a single object from the entire scene by selecting basis BRDFs that are utilized to represent the corresponding object. Next, we delete other basis BRDFs and Gaussians that have the highest weight for other basis BRDFs. We also filter out Gaussians based on Gaussian positions. This allows for extracting object mesh [14] and relighting it under an environment map. Figure 9 shows additional material-editing results on a real-world scene." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 624, + 400, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 624, + 400, + 636 + ], + "spans": [ + { + "bbox": [ + 306, + 624, + 400, + 636 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 642, + 546, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 546, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 546, + 679 + ], + "type": "text", + "content": "Sparsity Regularizer " + }, + { + "bbox": [ + 304, + 642, + 546, + 679 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{sparse}}" + }, + { + "bbox": [ + 304, + 642, + 546, + 679 + ], + "type": "text", + "content": " Figure 10 shows that the sparsity regularizer and the basis BRDF control enable obtaining interpretable basis BRDFs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 546, + 715 + ], + "type": "text", + "content": "Specular-weighted Rendering Loss We test the impact of the specular-weighted rendering loss that prioritizes" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "481" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 68, + 287, + 157 + ], + "blocks": [ + { + "bbox": [ + 49, + 68, + 287, + 157 + ], + "lines": [ + { + "bbox": [ + 49, + 68, + 287, + 157 + ], + "spans": [ + { + "bbox": [ + 49, + 68, + 287, + 157 + ], + "type": "image", + "image_path": "f7aec45f78e3b5222d1a04210da25b1433abc2c19580bf32bd7ce66a64594c04.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 156, + 162, + 163 + ], + "lines": [ + { + "bbox": [ + 56, + 156, + 162, + 163 + ], + "spans": [ + { + "bbox": [ + 56, + 156, + 162, + 163 + ], + "type": "text", + "content": "Estimated image and basis BRDFs" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 163, + 138, + 252 + ], + "blocks": [ + { + "bbox": [ + 50, + 163, + 138, + 252 + ], + "lines": [ + { + "bbox": [ + 50, + 163, + 138, + 252 + ], + "spans": [ + { + "bbox": [ + 50, + 163, + 138, + 252 + ], + "type": "image", + "image_path": "d28bcb77663995c68478d9bbf5dfd430021a835b812c4a14a6929985414ecf57.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 53, + 253, + 135, + 261 + ], + "lines": [ + { + "bbox": [ + 53, + 253, + 135, + 261 + ], + "spans": [ + { + "bbox": [ + 53, + 253, + 135, + 261 + ], + "type": "text", + "content": "Point cloud for basis BRDF" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 140, + 166, + 206, + 247 + ], + "blocks": [ + { + "bbox": [ + 140, + 166, + 206, + 247 + ], + "lines": [ + { + "bbox": [ + 140, + 166, + 206, + 247 + ], + "spans": [ + { + "bbox": [ + 140, + 166, + 206, + 247 + ], + "type": "image", + "image_path": "d00a7595a30c1d4ac2562b3bc7d5e72849365378037cc1170f92e2e5ad5e77fd.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 162, + 252, + 211, + 259 + ], + "lines": [ + { + "bbox": [ + 162, + 252, + 211, + 259 + ], + "spans": [ + { + "bbox": [ + 162, + 252, + 211, + 259 + ], + "type": "text", + "content": "Mesh extraction" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 217, + 165, + 282, + 252 + ], + "blocks": [ + { + "bbox": [ + 217, + 165, + 282, + 252 + ], + "lines": [ + { + "bbox": [ + 217, + 165, + 282, + 252 + ], + "spans": [ + { + "bbox": [ + 217, + 165, + 282, + 252 + ], + "type": "image", + "image_path": "3f8f735e0375b71662b16560f0dc49ec6c47a437944ea6a35bfc8b0e73875e6e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 216, + 253, + 284, + 261 + ], + "lines": [ + { + "bbox": [ + 216, + 253, + 284, + 261 + ], + "spans": [ + { + "bbox": [ + 216, + 253, + 284, + 261 + ], + "type": "text", + "content": "Environment relighting" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 49, + 312, + 177, + 383 + ], + "blocks": [ + { + "bbox": [ + 47, + 270, + 287, + 304 + ], + "lines": [ + { + "bbox": [ + 47, + 270, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 287, + 304 + ], + "type": "text", + "content": "Figure 8. Intuitive scene editing. We modify our basis BRDF parameters to edit the reflectance. We also selectively extract mesh and relight it under the environment map." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 312, + 177, + 383 + ], + "lines": [ + { + "bbox": [ + 49, + 312, + 177, + 383 + ], + "spans": [ + { + "bbox": [ + 49, + 312, + 177, + 383 + ], + "type": "image", + "image_path": "bda3b30dd6cee9ace18049fcae506b8c566218244c13194a0d6521d0d06a12b8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 78, + 382, + 143, + 389 + ], + "lines": [ + { + "bbox": [ + 78, + 382, + 143, + 389 + ], + "spans": [ + { + "bbox": [ + 78, + 382, + 143, + 389 + ], + "type": "text", + "content": "Novel view relighting" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 178, + 312, + 287, + 380 + ], + "blocks": [ + { + "bbox": [ + 178, + 312, + 287, + 380 + ], + "lines": [ + { + "bbox": [ + 178, + 312, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 178, + 312, + 287, + 380 + ], + "type": "image", + "image_path": "babf3c1e0e78e41d07e8d793feaf26fb5fcdb541d24266f39d4dd7b0e241aad9.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 49, + 388, + 176, + 458 + ], + "blocks": [ + { + "bbox": [ + 49, + 388, + 176, + 458 + ], + "lines": [ + { + "bbox": [ + 49, + 388, + 176, + 458 + ], + "spans": [ + { + "bbox": [ + 49, + 388, + 176, + 458 + ], + "type": "image", + "image_path": "d44a9320fde5d759681afbbca882817d8c5248e1202795ef7d8ff0cb0f0eed43.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 458, + 164, + 467 + ], + "lines": [ + { + "bbox": [ + 54, + 458, + 164, + 467 + ], + "spans": [ + { + "bbox": [ + 54, + 458, + 164, + 467 + ], + "type": "text", + "content": "Material editing with white lightings" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 169, + 458, + 285, + 467 + ], + "lines": [ + { + "bbox": [ + 169, + 458, + 285, + 467 + ], + "spans": [ + { + "bbox": [ + 169, + 458, + 285, + 467 + ], + "type": "text", + "content": "Material editing with colorful lightings" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 475, + 287, + 530 + ], + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 530 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 530 + ], + "type": "text", + "content": "Figure 9. Material editing and relighting on real-world objects. We obtain high-quality novel-view relighting for a real-world scene, where interpretable basis BRDFs are reconstructed with their sparse weight maps. We edit basis BRDFs and relight the scene under novel illumination conditions." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 181, + 388, + 287, + 458 + ], + "blocks": [ + { + "bbox": [ + 182, + 382, + 280, + 388 + ], + "lines": [ + { + "bbox": [ + 182, + 382, + 280, + 388 + ], + "spans": [ + { + "bbox": [ + 182, + 382, + 280, + 388 + ], + "type": "text", + "content": "Basis BRDFs and weight maps" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 181, + 388, + 287, + 458 + ], + "lines": [ + { + "bbox": [ + 181, + 388, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 181, + 388, + 287, + 458 + ], + "type": "image", + "image_path": "061d5ee2138d4d6bd2fa1ee5390adf9718fd5da68ffd436e7be065e890a94ec2.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 540, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 588 + ], + "type": "text", + "content": "potentially-specular areas using the rendered half-way angle map. Figure 11 shows that specular-weighted rendering loss produces a more stable reconstruction compared to not using the weighting." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "In this paper, we have introduced a differentiable inverse rendering method that jointly estimates 2D Gaussians and basis BRDFs. Our method obtains interpretable basis BRDFs that can represent SVBRDFs in a spatially-separable manner, enabling accurate geometry and SVBRDF reconstruction. Also, the number of basis BRDFs automatically adjusts to a target scene. We demonstrate the effectiveness of our method compared to state-of-the" + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 392, + 186 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 392, + 186 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 392, + 186 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 392, + 186 + ], + "type": "image", + "image_path": "a1f38dea73faad2c0d905caaf91b8fb59a840432661f080e24253919383ad319.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 344, + 184, + 354, + 192 + ], + "lines": [ + { + "bbox": [ + 344, + 184, + 354, + 192 + ], + "spans": [ + { + "bbox": [ + 344, + 184, + 354, + 192 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 392, + 70, + 468, + 140 + ], + "blocks": [ + { + "bbox": [ + 392, + 70, + 468, + 140 + ], + "lines": [ + { + "bbox": [ + 392, + 70, + 468, + 140 + ], + "spans": [ + { + "bbox": [ + 392, + 70, + 468, + 140 + ], + "type": "image", + "image_path": "5022f0ecb408223ea0884a10865c925943dde71eb7e9bb83a0892491662b9df1.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 416, + 140, + 521, + 149 + ], + "lines": [ + { + "bbox": [ + 416, + 140, + 521, + 149 + ], + "spans": [ + { + "bbox": [ + 416, + 140, + 521, + 149 + ], + "type": "text", + "content": "With sparsity and basis control" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 468, + 71, + 545, + 140 + ], + "blocks": [ + { + "bbox": [ + 468, + 71, + 545, + 140 + ], + "lines": [ + { + "bbox": [ + 468, + 71, + 545, + 140 + ], + "spans": [ + { + "bbox": [ + 468, + 71, + 545, + 140 + ], + "type": "image", + "image_path": "727817af93538d602176f098e25b618d6d96cbc66031cfae2fb06a8933daf61b.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 392, + 149, + 468, + 218 + ], + "blocks": [ + { + "bbox": [ + 392, + 149, + 468, + 218 + ], + "lines": [ + { + "bbox": [ + 392, + 149, + 468, + 218 + ], + "spans": [ + { + "bbox": [ + 392, + 149, + 468, + 218 + ], + "type": "image", + "image_path": "a9264f18796ed9133c5248facdc4a5286b3b7268e796d8020ff9cb9f7908a7ec.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 413, + 218, + 529, + 227 + ], + "lines": [ + { + "bbox": [ + 413, + 218, + 529, + 227 + ], + "spans": [ + { + "bbox": [ + 413, + 218, + 529, + 227 + ], + "type": "text", + "content": "Without sparsity and basis control" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 469, + 149, + 545, + 218 + ], + "blocks": [ + { + "bbox": [ + 469, + 149, + 545, + 218 + ], + "lines": [ + { + "bbox": [ + 469, + 149, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 469, + 149, + 545, + 218 + ], + "type": "image", + "image_path": "cd723bc44511fd5486c83091dd8ee8e80b88f8d1780dbe533f2818c8cfa057ee.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 307, + 293, + 421, + 408 + ], + "blocks": [ + { + "bbox": [ + 305, + 236, + 546, + 290 + ], + "lines": [ + { + "bbox": [ + 305, + 236, + 546, + 290 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 546, + 290 + ], + "type": "text", + "content": "Figure 10. Impact of sparsity regularizer and basis BRDF control. Without sparsity loss and basis BRDF control of merge and removal, the resulting basis BRDFs are blended each other as shown in the corresponding images, making them non-interpretable for downstream tasks." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 293, + 421, + 408 + ], + "lines": [ + { + "bbox": [ + 307, + 293, + 421, + 408 + ], + "spans": [ + { + "bbox": [ + 307, + 293, + 421, + 408 + ], + "type": "image", + "image_path": "2e03aaaf67bc472bfdb0f12b53182161a6fc6cbd6f9f330cd9797d2855260d8c.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 406, + 375, + 415 + ], + "lines": [ + { + "bbox": [ + 345, + 406, + 375, + 415 + ], + "spans": [ + { + "bbox": [ + 345, + 406, + 375, + 415 + ], + "type": "text", + "content": "GT image" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 421, + 294, + 533, + 407 + ], + "blocks": [ + { + "bbox": [ + 421, + 294, + 533, + 407 + ], + "lines": [ + { + "bbox": [ + 421, + 294, + 533, + 407 + ], + "spans": [ + { + "bbox": [ + 421, + 294, + 533, + 407 + ], + "type": "image", + "image_path": "a94cdbae2b05ddc38aa7aed56013b505387afdc317c485933c4f193d618b352d.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 441, + 407, + 507, + 415 + ], + "lines": [ + { + "bbox": [ + 441, + 407, + 507, + 415 + ], + "spans": [ + { + "bbox": [ + 441, + 407, + 507, + 415 + ], + "type": "text", + "content": "Specular weight map" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 309, + 415, + 385, + 453 + ], + "blocks": [ + { + "bbox": [ + 309, + 415, + 385, + 453 + ], + "lines": [ + { + "bbox": [ + 309, + 415, + 385, + 453 + ], + "spans": [ + { + "bbox": [ + 309, + 415, + 385, + 453 + ], + "type": "image", + "image_path": "2d529f9d2135ac2dd1c5cec2813275cf1311d3926ae87f203f4fe61faf4c72ec.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_body" + } + ], + "index": 34 + }, + { + "type": "image", + "bbox": [ + 309, + 453, + 386, + 493 + ], + "blocks": [ + { + "bbox": [ + 309, + 453, + 386, + 493 + ], + "lines": [ + { + "bbox": [ + 309, + 453, + 386, + 493 + ], + "spans": [ + { + "bbox": [ + 309, + 453, + 386, + 493 + ], + "type": "image", + "image_path": "e374f566130c2d394e41e489ce9d669d4262c7fe05e029b9747c7c0147bb60eb.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 493, + 387, + 502 + ], + "lines": [ + { + "bbox": [ + 310, + 493, + 387, + 502 + ], + "spans": [ + { + "bbox": [ + 310, + 493, + 387, + 502 + ], + "type": "text", + "content": "Without specular weight" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 517, + 545, + 561 + ], + "lines": [ + { + "bbox": [ + 305, + 517, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 305, + 517, + 545, + 561 + ], + "type": "text", + "content": "Figure 11. 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Using specular-weighted rendering loss improves geometry and reflectance reconstruction quality by recovering high frequency features from specularity, which is emphasized by the specular weight map." + } + ] + } + ], + "index": 43, + "angle": 0, + "type": "image_caption" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 386, + 415, + 463, + 453 + ], + "blocks": [ + { + "bbox": [ + 386, + 415, + 463, + 453 + ], + "lines": [ + { + "bbox": [ + 386, + 415, + 463, + 453 + ], + "spans": [ + { + "bbox": [ + 386, + 415, + 463, + 453 + ], + "type": "image", + "image_path": "4cdb5770a6022cd051b43fd3c5299dc67e329f631f4ec74ebd2bf6e64d3d6b83.jpg" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_body" + } + ], + "index": 37 + }, + { + "type": "image", + "bbox": [ + 386, + 453, + 463, + 493 + ], + "blocks": [ + { + "bbox": [ + 386, + 453, + 463, + 493 + ], + "lines": [ + { + "bbox": [ + 386, + 453, + 463, + 493 + ], + "spans": [ + { + "bbox": [ + 386, + 453, + 463, + 493 + ], + "type": "image", + "image_path": "805d98973449b3329b258aab08aae9b35daf766ea39373ed81293ff803e25897.jpg" + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 395, + 493, + 462, + 502 + ], + "lines": [ + { + "bbox": [ + 395, + 493, + 462, + 502 + ], + "spans": [ + { + "bbox": [ + 395, + 493, + 462, + 502 + ], + "type": "text", + "content": "With specular weight" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_caption" + } + ], + "index": 38 + }, + { + "type": "image", + "bbox": [ + 464, + 415, + 544, + 453 + ], + "blocks": [ + { + "bbox": [ + 464, + 415, + 544, + 453 + ], + "lines": [ + { + "bbox": [ + 464, + 415, + 544, + 453 + ], + "spans": [ + { + "bbox": [ + 464, + 415, + 544, + 453 + ], + "type": "image", + "image_path": "907ae77864f8145dcfe095019c6b949f9aee953cfb32ba8d8be79600fd1a0e1d.jpg" + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "image_body" + } + ], + "index": 40 + }, + { + "type": "image", + "bbox": [ + 465, + 453, + 544, + 493 + ], + "blocks": [ + { + "bbox": [ + 465, + 453, + 544, + 493 + ], + "lines": [ + { + "bbox": [ + 465, + 453, + 544, + 493 + ], + "spans": [ + { + "bbox": [ + 465, + 453, + 544, + 493 + ], + "type": "image", + "image_path": "def55d2dbc94e646ada2516d8126d3f90a5c89f2118584dac220a8af4243d22b.jpg" + } + ] + } + ], + "index": 41, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 500, + 494, + 511, + 501 + ], + "lines": [ + { + "bbox": [ + 500, + 494, + 511, + 501 + ], + "spans": [ + { + "bbox": [ + 500, + 494, + 511, + 501 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 42, + "angle": 0, + "type": "image_caption" + } + ], + "index": 41 + }, + { + "bbox": [ + 305, + 566, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 566, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 305, + 566, + 545, + 602 + ], + "type": "text", + "content": "art approaches. Using the interpretable basis BRDFs, our method also facilitates downstream tasks such as intuitive scene editing." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 305, + 609, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 545, + 658 + ], + "type": "text", + "content": "Limitations Our basis BRDF representation assumes opaque objects, leaving modeling non-surface objects as a future work. Combining semantic information from a large vision model is also an interesting future work." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, RS-2024-00438532, RS-2025-00518643), and Korea IITP MSIT (RS-2023-00215700)." + } + ] + } + ], + "index": 46 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "482" + } + ] + } + ], + "index": 47 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 704 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Neil Alldrin, Todd Zickler, and David Kriegman. 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Gs-ror: 3d gaussian splatting for reflective object relighting via sdf priors. arXiv preprint arXiv:2406.18544, 2024. 2" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "484" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_content_list.json b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dbcb5f3b9839b18d04ebae66fc788598406a7047 --- /dev/null +++ b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_content_list.json @@ -0,0 +1,1491 @@ +[ + { + "type": "text", + "text": "Diffusion Bridge: Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning", + "text_level": 1, + "bbox": [ + 120, + 128, + 875, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jeong Ryong Lee1 Yejee Shin1 Geonhui Son1 Dosik Hwang1,2* \n1Yonsei University 2 Korea Institute of Science and Technology {emaker, yejeeshin, higun2, dosik.hwang}@yonsei.ac.kr", + "bbox": [ + 192, + 202, + 810, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 291, + 326, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The modality gap between vision and text embeddings in CLIP presents a significant challenge for zero-shot image captioning, limiting effective cross-modal representation. Traditional approaches, such as noise injection and memory-based similarity matching, attempt to address this gap, yet these methods either rely on indirect alignment or relatively naive solutions with heavy computation. Diffusion Bridge introduces a novel approach to directly reduce this modality gap by leveraging Denoising Diffusion Probabilistic Models (DDPM), trained exclusively on text embeddings to model their distribution. Our approach is motivated by the observation that, while paired vision and text embeddings are relatively close, a modality gap still exists due to stable regions created by the contrastive loss. This gap can be interpreted as noise in cross-modal mappings, which we approximate as Gaussian noise. To bridge this gap, we employ a reverse diffusion process, where image embeddings are strategically introduced at an intermediate step in the reverse process, allowing them to be refined progressively toward the text embedding distribution. This process transforms vision embeddings into textlike representations closely aligned with paired text embeddings, effectively minimizing discrepancies between modalities. Experimental results demonstrate that these textlike vision embeddings significantly enhance alignment with their paired text embeddings, leading to improved zero-shot captioning performance on MSCOCO and Flickr30K. Diffusion Bridge achieves competitive results without reliance on memory banks or entity-driven methods, offering a novel pathway for cross-modal alignment and opening new possibilities for the application of diffusion models in multimodal tasks. The source code is available at: https://github.com/mongeoroo/diffusion-bridge", + "bbox": [ + 88, + 330, + 485, + 832 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1d6ba72032eff4cc5e5dc6eca67f64ff2f253b8f55a20ee3a6c63dae4f9e77b0.jpg", + "image_caption": [ + "Figure 1. Overview of Diffusion Bridge for zero-shot image captioning. Diffusion Bridge utilizes a diffusion model trained on text embeddings to bridge the modality gap in CLIP. During inference, vision embeddings are introduced into the reverse diffusion process at an intermediate timestep, progressively aligned with the text embedding space. This alignment facilitates improved zero-shot image captioning performance by producing embeddings that closely match the text distribution" + ], + "image_footnote": [], + "bbox": [ + 550, + 292, + 861, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 750, + 645, + 766 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large-scale pre-trained vision-language models have garnered significant attention in recent research, demonstrating impressive performance across various multi-modal tasks [3, 8, 11, 31]. Among these models, CLIP [31] (Contrastive Language-Image Pretraining) stands out, leveraging a powerful joint embedding space for visual and textual data, which has paved the way for advancements in cross-modal tasks [6, 13, 26, 26, 38, 40]. With its powerful", + "bbox": [ + 511, + 779, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 109, + 886, + 236, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4050", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pretraining on a large-scale, diverse set of image-text pairs, CLIP enables impressive zero-shot performance across numerous downstream tasks, from classification to complex retrieval tasks [23, 35, 42]. Among these applications, zero-shot image captioning stands out, where models are required to generate descriptive captions for images without having seen any paired image-caption data during training [7, 15, 28, 35, 43]. In zero-shot captioning, a model's ability to bridge visual content to meaningful language representations is critical. CLIP's inherent cross-modal alignment has made it a central model for such endeavors.", + "bbox": [ + 89, + 90, + 480, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, a persistent challenge within CLIP is the modality gap between its vision and text embeddings, a structural separation within the embedding space that limits the effectiveness of cross-modal alignment [17, 45]. This gap, caused by the contrastive learning dynamics and model initialization, results in visual and textual representations occupying distinct regions within the shared embedding space. Consequently, this gap restricts direct transfer and alignment for zero-shot captioning, where precise semantic alignment is essential for high-quality caption generation.", + "bbox": [ + 89, + 258, + 480, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Previous zero-shot image captioning methods have addressed the modality gap challenge through various techniques. Notably, noise injection methods [28, 45] seek to enhance the decoder's robustness by introducing Gaussian noise into text embeddings during training, thereby promoting generalization across the inherent discrepancies between vision and text embeddings. However, these approaches do not fundamentally align vision and text embeddings, leaving modality mismatches that can hinder zero-shot performance.", + "bbox": [ + 89, + 412, + 480, + 563 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On the other hand, recent advancements in diffusion-based models have shown considerable promise within multi-modal domains, particularly in tasks such as image synthesis and text-guided image manipulation [5, 21, 27]. At the core of these advancements is Denoising Diffusion Probabilistic Models (DDPM) [10], which iteratively refine noisy vectors to capture the intrinsic data distribution with high fidelity. This ability to model complex, nuanced distributions renders diffusion models powerful tools for novel applications across a range of multi-modal settings. However, their application in bridging the modality gap for zero-shot image captioning remains an area yet to be thoroughly explored.", + "bbox": [ + 89, + 566, + 480, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we introduce Diffusion Bridge, an innovative approach that leverages diffusion models to directly address the modality gap within CLIP's embedding space for zero-shot image captioning. Diffusion Bridge models the distribution of text embeddings through the diffusion model, effectively capturing the intricate structure of the text embedding space. Given that paired vision and text embeddings remain relatively close despite their inherent differences, our method strategically inserts vision embed", + "bbox": [ + 89, + 763, + 480, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "dings at an intermediate step of the diffusion reverse process. The gradual refinement of reverse process allows vision embeddings to transform into text-like representations, incrementally reducing residual discrepancies stemming from the intrinsic characteristics of each modality.", + "bbox": [ + 511, + 90, + 903, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Through comprehensive experiments, we demonstrate that Diffusion Bridge significantly reduces the modality gap, resulting in enhanced cross-modal similarity and improved captioning performance. Importantly, Diffusion Bridge achieves robust zero-shot captioning without reliance on large memory banks or external knowledge modules. Our findings indicate that Diffusion Bridge not only advances zero-shot captioning but also opens novel potentials for the application of diffusion models in cross-modal alignment tasks.", + "bbox": [ + 511, + 167, + 905, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 330, + 653, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-modal contrastive learning has been fundamental in aligning visual and textual data within a shared embedding space, enabling cross-modal applications without paired data. Pioneering frameworks such as CLIP [31] and Image-Bind [8] achieve this alignment by training on large-scale image-text datasets, aiming to encode paired data from different modalities closer together in the embedding space. However, the modality gap [17], which keeps visual and textual embeddings in distinct regions, remains a persistent challenge. This separation limits the interchangeability of embeddings and diminishes the effectiveness of zero-shot multi-modal tasks. Studies such as Mind the Gap [17] and C3 [45] provide an in-depth examination of the modality gap in multi-modal models like CLIP, emphasizing that the contrastive loss function and model initialization result in the separation between image and text embeddings.", + "bbox": [ + 511, + 356, + 905, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Efforts to bridge this gap in zero-shot image captioning can be categorized into three main strategies: Late-Guidance Decoding, Early-Guidance Decoding, and Keywords-Guidance Decoding. These approaches represent parallel research directions that tackle zero-shot captioning challenges from distinct perspectives. Our work contributes specifically to the Early-Guidance Decoding category.", + "bbox": [ + 511, + 599, + 905, + 719 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Late-Guidance Decoding: Methods such as MAGIC [34] and ZeroCap [36] apply guidance at a later stage of the decoding process, often by leveraging language models to generate captions that reflect visual content. While this strategy can produce visually grounded captions, it typically relies on indirect adjustments and does not fully address the modality gap between vision and text embeddings, resulting in less precise alignment.", + "bbox": [ + 511, + 719, + 905, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Early-Guidance Decoding: Several studies [9, 15, 28, 45] aim to address the modality gap earlier in the caption generation process by employing techniques such as noise-injected decoder training and memory-based simi", + "bbox": [ + 511, + 839, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4051", + "bbox": [ + 482, + 944, + 511, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "larity matching. For instance, CapDec [28] and C3 [45] employ noise injection to improve the decoder's robustness to variability in vision embeddings, helping it generalize across the modality gap. DeCap [15] takes a different approach by using a memory-based projection method that maps vision embeddings into the text space through similarity-based projections. However, it requires a large memory bank, which can introduce computational challenges and limit scalability. Additionally, the direct projection relies on similarity matching, which may lack adaptability for handling inputs beyond the training distribution.", + "bbox": [ + 89, + 90, + 480, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Keywords-Guidance Decoding: Approaches such as ViECap [7] and MeaCap [43] focus on enhancing caption relevance and specificity by extracting entities or keywords from visual content to guide the caption generation process. Unlike Early-Guidance Decoding, these methods do not address the modality gap at the embedding level but instead operate at the sentence level, using keyword-based prompts to improve linguistic and contextual alignment. This approach is particularly beneficial for out-of-domain scenarios through explicit guidance.", + "bbox": [ + 89, + 257, + 480, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Models for Multi-Modal Generation. Recent advancements in diffusion models have had a substantial impact on generative modeling, particularly in tasks such as image synthesis and text generation [14, 16, 27, 44]. DDPM is prominent in this field, iteratively refining Gaussian noise to produce structured, high-quality outputs. Extensions such as Guided Diffusion [25] introduce controlled generation, enabling zero-shot and conditional tasks with enhanced specificity. In image captioning, diffusion models like SCD-Net [22] and Prefix-Diffusion [20] enhance alignment between image embeddings and textual descriptions, improving caption accuracy and diversity. SCD-Net uses semantic priors for better visual-linguistic coherence, while Prefix-Diffusion employs image-derived prefix embeddings to generate varied and contextually rich captions. Despite these advancements, the potential of diffusion models to directly address the modality gap in embedding alignment tasks, particularly in zero-shot captioning with CLIP, remains underexplored.", + "bbox": [ + 89, + 407, + 482, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 709, + 181, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Bridge presents an innovative solution to address the modality gap by utilizing only text embeddings. Our approach is motivated by the analysis in C3 [45], which reveals that even paired vision and text embeddings, while close, still exhibit a modality gap. This gap arises due to stable regions produced by the contrastive loss, resulting in a constant offset, or 'alignment noise', between embeddings from different modalities. This alignment noise persists in the shared embedding space and can be approximated as Gaussian noise.", + "bbox": [ + 89, + 734, + 480, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our proposed method employs the diffusion model's", + "bbox": [ + 109, + 885, + 480, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dual strengths: its capacity as a generative model to learn the intrinsic distribution of text embeddings and its ability to incorporate conditional inputs during the reverse process.", + "bbox": [ + 511, + 90, + 903, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By training the diffusion model on text embeddings, the model learns the distributional characteristics of the text embedding space. During inference, we initiate the reverse diffusion process with vision embeddings at an intermediate step. Guided by the learned text distribution, the diffusion model progressively refines these vision embeddings into text-like representations. This conditioned reverse mapping effectively minimizes residual discrepancies, aligning vision embeddings more closely with the text embedding space and thereby mitigating the modality gap.", + "bbox": [ + 511, + 136, + 903, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following sections, we describe the mechanisms and architecture of Diffusion Bridge, detailing each component's role in enabling efficient and scalable zero-shot captioning. Fig. 2 visualizes the overall pipeline of Diffusion Bridge.", + "bbox": [ + 511, + 287, + 903, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background on Denoising Diffusion Probabilistic Models", + "text_level": 1, + "bbox": [ + 511, + 369, + 903, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DDPM is the generative model that creates data by iteratively refining Gaussian noise through a controlled denoising process. The model learns a sequence of transformations that progressively reduces noise in sampled data to generate structured representations. DDPM operates in two main stages: the forward diffusion process and the reverse diffusion process.", + "bbox": [ + 511, + 407, + 903, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Forward Diffusion Process: Starting from an initial sample $\\mathbf{z}_0$ , the forward process generates a series of increasingly noisy samples $\\mathbf{z}_t$ by applying a Gaussian noise schedule over $T$ time steps. This process is defined as:", + "bbox": [ + 511, + 513, + 903, + 574 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}\\right) := \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {z} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 582, + 903, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\beta_{t}$ represents a variance schedule that determines the amount of noise added at each step. In the last step, the data $\\mathbf{z}_T$ becomes nearly indistinguishable from pure Gaussian noise $\\mathbf{z}_T\\sim \\mathcal{N}(0,\\mathbf{I})$", + "bbox": [ + 511, + 608, + 903, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By defining $\\alpha_{t} := 1 - \\beta_{t}$ and $\\bar{\\alpha}_{t} := \\prod_{s=1}^{t} \\alpha_{s}$ , the forward process from $\\mathbf{z}_0$ to $\\mathbf{z}_{t}$ can be expressed as:", + "bbox": [ + 511, + 667, + 903, + 699 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 707, + 903, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reverse Diffusion Process: A network estimates the mean $\\pmb{\\mu}_{\\theta}(\\mathbf{z}_t,t)$ of the distribution $p_{\\theta}(\\mathbf{z}_{t - 1}\\mid \\mathbf{z}_t)$ in the reverse process. This process denoises the data step-by-step to generate structured samples from noise, defined as:", + "bbox": [ + 511, + 732, + 903, + 792 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N} \\left(\\mathbf {z} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {z} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 800, + 903, + 818 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sigma_t^2$ represents time-dependent variance. The predicted mean $\\pmb{\\mu}_{\\theta}(z_{t},t)$ can be expressed as:", + "bbox": [ + 511, + 825, + 903, + 856 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {\\theta} (\\mathbf {z} _ {t}, t) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {z} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {z} _ {t}, t)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 864, + 903, + 897 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4052", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9c372eea1e5987f54b99b1be6fcb43e0bb0e1affa64be2cafc2e423a1a8f45eb.jpg", + "image_caption": [ + "Figure 2. Detailed model pipeline of Diffusion Bridge, illustrating the three stages of the method. First, the diffusion model is trained exclusively on text embeddings, capturing their intrinsic distribution. Next, the decoder is trained using diffusion-augmented text embeddings, preparing it to handle variations during caption generation. In the final inference stage, vision embeddings are mapped into the text embedding space via the reverse diffusion process and then the decoder generates a caption with the transformed embedding. This pipeline enables zero-shot caption generation by aligning vision embeddings with the text distribution, achieving effective cross-modal alignment without relying on paired image-text data." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 906, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}(z_t,t)$ represents the noise predicted by the model.", + "bbox": [ + 89, + 583, + 482, + 597 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To train the diffusion model, the objective is to minimize the difference between the true noise $\\epsilon$ and the predicted noise $\\epsilon_{\\theta}(\\mathbf{z}_t,t)$ across all diffusion steps, which is expressed by the following loss function:", + "bbox": [ + 89, + 598, + 483, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {D D P M}} (\\theta) = \\mathbb {E} _ {t, \\mathbf {z} _ {0}, \\epsilon} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) \\right\\| ^ {2} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 667, + 483, + 708 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon$ is standard Gaussian noise, $\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})$ . This objective enables the model to accurately estimate the noise added at each diffusion step, allowing for precise reconstruction during the reverse process.", + "bbox": [ + 89, + 718, + 483, + 780 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Diffusion Training with Text Embeddings", + "text_level": 1, + "bbox": [ + 89, + 787, + 446, + 804 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After encoding the training text dataset into embeddings using the CLIP text encoder, several preprocessing steps are applied to condition the embeddings for diffusion model training. Initially, each text embedding, $\\mathbf{e}^{text}$ , is an L2-normalized vector to ensure a consistent magnitude. Subsequently, following previous works [9, 28, 45], we subtract", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the mean vector, $\\bar{\\mathbf{e}}^{text}$ , computed across the training set embeddings to center the embeddings.", + "bbox": [ + 511, + 582, + 906, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following mean-centering, we apply a second normalization step to further enhance uniformity. However, we observe that the L2 normalized embeddings have a relatively low average scale, which may obscure the distinction between signal and noise during DDPM training. To address this, we amplify the embeddings by a scalar factor of $C$ , yielding the final processed embedding:", + "bbox": [ + 511, + 613, + 905, + 719 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {0} = C \\times \\frac {\\mathbf {e} ^ {t e x t} - \\bar {\\mathbf {e}} ^ {t e x t}}{\\left| \\left| \\mathbf {e} ^ {t e x t} - \\bar {\\mathbf {e}} ^ {t e x t} \\right| \\right| _ {2}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 724, + 903, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The model trained with this processed set of embeddings, $\\mathbf{z}_0$ , through Eq. 5, allows the diffusion model to learn the score function of the text embedding distribution [33], denoted as $\\nabla_{\\mathbf{z}^{\\mathrm{ext}}}\\log p(\\mathbf{z}^{\\mathrm{ext}})$ . This score function encodes gradient directions toward high-density regions of the text manifold. While the model is trained exclusively on text, the learned text manifold serves as a semantic prior that defines plausible regions for cross-modal alignment. Following findings in C3 [45], the modality gap between vision and", + "bbox": [ + 511, + 763, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4053", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "text embeddings in CLIP is approximated as Gaussian noise $(\\mathbf{z}^{\\mathrm{vision}} = \\mathbf{z}^{\\mathrm{text}} + \\epsilon, \\epsilon \\sim \\mathcal{N}(0, \\sigma^2 \\mathbf{I}))$ . During inference, the score function guides vision embeddings along the gradient of the text distribution, iteratively shifting them toward the nearest high-density regions of the text manifold. This process effectively denoises the modality gap, aligning vision embeddings with the text manifold.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Decoder Training", + "text_level": 1, + "bbox": [ + 89, + 207, + 264, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The decoder in Diffusion Bridge is trained exclusively on text embeddings to generate coherent captions, using these embeddings as prefix inputs with an autoregressive loss. This section details the training process of the decoder.", + "bbox": [ + 89, + 229, + 480, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Diffusion-Augmented Text Embeddings: The text embeddings are applied centering and normalization, following the approach used in C3 [45]. While it is possible to train the decoder directly on these preprocessed text embeddings, it is essential to account for the non-unique mapping between vision and text embeddings. The inherent variability can arise in reverse-diffused vision embeddings, introducing subtle randomness to the alignment. Specifically, if a text embedding undergoes forward diffusion to an intermediate step and is then reverse-diffused, the resulting embedding may not perfectly match the original due to the randomness. To prepare the decoder to handle these practical variations, we incorporate diffusion-augmented embeddings into the training data. The augmentation process involves two main steps.", + "bbox": [ + 89, + 290, + 482, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each text embedding $\\mathbf{z}_0$ , we select an intermediate step $t = A$ , where $(T > A > 0)$ and apply the forward diffusion process, producing a noisy version:", + "bbox": [ + 89, + 517, + 482, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {z} _ {A} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {A}; \\sqrt {\\bar {\\alpha} _ {A}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {A}) \\mathbf {I}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 575, + 482, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then we denoise the noise vector, $\\mathbf{z}_A$ , through the reverse process to obtain the augmented embedding $\\mathrm{e}^{\\mathrm{aug}}$ . For faster inference, we utilized DDIM [32] for denoising.", + "bbox": [ + 89, + 604, + 482, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By utilizing diffusion-augmented embeddings $\\mathbf{e}^{\\mathrm{aug}}$ as prefix inputs, we train the decoder to be resilient to the inherent randomness that arises from the fact that a single vision embedding does not map uniquely to a specific text embedding. The decoder learns to predict the caption y based on these augmented embeddings, using the autoregressive loss:", + "bbox": [ + 89, + 650, + 482, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {A R}} = - \\sum_ {t = 1} ^ {L} \\log p \\left(y _ {t} \\mid y _ {< t}, \\mathbf {e} ^ {\\text {a u g}}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 765, + 482, + 805 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Inference Process", + "text_level": 1, + "bbox": [ + 89, + 816, + 263, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During inference, the vision embedding, $\\mathbf{e}^{img}$ , is strategically introduced into the reverse diffusion process at a predefined intermediate timestep $t = M$ , where $T > M > 0$ . This conditioned reverse process leverages our core insight:", + "bbox": [ + 89, + 839, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "while vision and text embeddings are inherently different, they remain relatively proximate in the shared embedding space. By initiating the reverse diffusion from this intermediate step $M$ , we enable the model to map the vision embedding into a text-like vision embedding, $\\tilde{\\mathbf{e}}^{\\mathrm{img}}$ , that closely aligns with the learned distribution of text embeddings. We refer to this alignment process as diffusion-bridging.", + "bbox": [ + 511, + 90, + 903, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The transformed vision embedding, $\\tilde{\\mathbf{e}}^{\\mathrm{img}}$ , is then fed as a prefix input to the decoder trained on text embeddings. This setup ensures that the decoder receives an embedding in a familiar distribution, enhancing its capacity to generate accurate and contextually relevant captions without the need for paired data.", + "bbox": [ + 511, + 200, + 903, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 318, + 645, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate the effectiveness of Diffusion Bridge in mitigating the modality gap for zero-shot image captioning. Our experiments aim to assess how well our method aligns vision embeddings with the text embedding space. We conduct evaluations on standard image captioning datasets under both in-domain and cross-domain setups to comprehensively test the generalization capabilities of Diffusion Bridge.", + "bbox": [ + 511, + 348, + 905, + 469 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and Metrics: We assess Diffusion Bridge on two widely used image captioning datasets: MSCOCO [4, 19] and Flickr30K [39]. For dataset partitioning, we utilize the standard Karpathy split [12], which is commonly adopted in captioning benchmarks. For quantitative evaluation, we employ a suite of established metrics to gauge caption quality, including BLEU (B@n) [29], METEOR (M) [2], ROUGE-L (R-L) [18], CIDEr (C) [37], and SPICE (S) [1].", + "bbox": [ + 511, + 473, + 905, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details: For the DDPM training, we employ a 1-D UNet architecture with four layers, where each layer successively doubles in dimensionality. The model is trained using a batch size of 64, a learning rate of $8 \\times 10^{-5}$ , and a total of 3,000,000 steps. The number of diffusion timesteps is set to $T = 1000$ and we set $C$ in Eqt. 6 as 5 in all experiments. For experiments on the MSCOCO dataset, we set the intermediate and augmentation steps to $M = 600$ and $A = 400$ , respectively, whereas for Flickr30K, these values are configured to $M = 400$ and $A = 300$ . For decoder training, we use CLIP-ViT-B/32 [31] as the encoding backbone and adopt GPT-2 [30] as the base decoder. The prefix projector consists of two fully connected layers with a hidden dimensionality of 768. The learnable soft prompts are defined with a length of 10. The projection layer projects the CLIP embedding from 512 to 768 dimensions. Training is conducted for 10 epochs with a batch size of 40 and a learning rate of $2 \\times 10^{-5}$ , using the AdamW optimizer following the setup in [28, 45].", + "bbox": [ + 511, + 613, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4054", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a45e1bd1d8f1fb9e7d36a21587608261dfa02d12c686c7e5c8282d786f20867f.jpg", + "image_caption": [ + "Figure 3. UMAP visualization of COCO validation set embeddings. Red points represent image embeddings $\\hat{\\mathbf{e}}^{\\mathrm{img}}$ , blue points denote text embeddings $\\hat{\\mathbf{e}}^{\\mathrm{text}}$ , and green points show mapped embeddings $\\tilde{\\mathbf{e}}^{\\mathrm{img}}$ produced by Diffusion Bridge from image embeddings." + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 478, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation on Modality Gap", + "text_level": 1, + "bbox": [ + 89, + 436, + 344, + 454 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the following sections, we evaluate the effectiveness of Diffusion Bridge in reducing the modality gap. Specifically, we conduct UMAP-based visualization and similarity assessments on embeddings from the MSCOCO validation set. To facilitate this analysis, we denote $\\hat{\\mathbf{e}}$ as the centered embedding, representing aligned embeddings in a unified space.", + "bbox": [ + 89, + 460, + 482, + 565 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visual Experiment on Modality Gap. To evaluate the effectiveness of Diffusion Bridge in reducing the modality gap, we conducted a UMAP [24] visualization experiment using the validation set of the COCO dataset. This visualization provides insight into the alignment of vision embeddings with text embeddings in a shared embedding space. Fig. 3 displays three types of embeddings: centered image embeddings $\\hat{\\mathbf{e}}^{\\mathrm{img}}$ (red), centered text embeddings $\\hat{\\mathbf{e}}^{\\mathrm{text}}$ (blue), and diffusion-mapped embeddings from image embeddings $\\tilde{\\mathbf{e}}^{\\mathrm{img}}$ (green). In Fig. 3, distinct clusters for image embeddings and text embeddings illustrate the inherent modality gap between visual and textual data. However, the overlap of mapped embeddings to the text cluster suggests that Diffusion Bridge significantly reduces the modality gap. This alignment allows the decoder, which is trained in text embeddings, to effectively process text-like vision embeddings as inputs, thereby enhancing the model's captioning performance.", + "bbox": [ + 89, + 566, + 482, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cosine Similarity Analysis of Modality Alignment. In the previous analysis, we visually examine the reduction in the modality gap. Herein, we use cosine similarity to provide a more quantitative assessment of this reduction. Tab.", + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/40119153db0bfb57d543ba727e05b357caddaead02a7a134586f0aeecf50b1f3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Comparison PairCosine Similarity
    EmbeddingProjector
    (a) e text · e img(∼)0.3060.714
    (b) e text · {e text + N(0,0.016)}(∼)0.2350.684
    (c) e text · e text(∼)0.6520.833
    (d) e text · e img(∼)0.6060.826
    (e) e text · e text(∼)0.0030.588
    (f) e text · e img(∼)0.0520.604
    ", + "bbox": [ + 526, + 88, + 893, + 198 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Average cosine similarity scores for various embedding pairs. $\\sim$ and $\\nVdash$ denote corresponding pairs and non-corresponding pairs. 'Embedding' shows the direct similarity between embeddings, while 'Projector' represents the similarity of projected embeddings through a prefix projector.", + "bbox": [ + 511, + 208, + 903, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1 presents cosine similarity scores for different embedding sets, offering a clearer view of how effectively Diffusion Bridge brings vision embeddings closer to text embeddings in the shared space.", + "bbox": [ + 511, + 306, + 903, + 366 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(a) shows the similarity between text and image embeddings within the paired set, which is only 0.306. Although a 0.3 cosine similarity can indicate a certain level of similarity in high-dimensional spaces [17], it remains noticeably lower compared to the similarity between text embeddings for the same image in (c), which has a much higher score of 0.652. This discrepancy highlights the inherent modality gap between visual and textual embeddings, which can hinder zero-shot image captioning performance.", + "bbox": [ + 511, + 368, + 903, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(b) represents the cosine similarity between a text embedding and a noise-injected version of itself, with a similarity score of 0.235. This setup mirrors the noise injection process used in models like CapDec [28] and C3 [45]. Adding Gaussian noise creates a broader distribution around the original text embedding, allowing the decoder to generalize by encompassing the range where vision embeddings are likely to fall. This approach helps the decoder manage variability in vision embeddings, supporting zero-shot captioning. However, noise injection may also introduce certain limitations. If the noise range is too broad, captions could become overly generic, lacking specific details. Consequently, finding an optimal level of noise is crucial.", + "bbox": [ + 511, + 506, + 903, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(d) examines the similarity between a text embedding and its paired vision embedding mapped by Diffusion Bridge. The similarity score of 0.606 shows a substantial increase from the original score of 0.306 in (a), approaching the high similarity observed within the text embeddings in the paired set in (c). This result demonstrates that Diffusion Bridge effectively reduces the modality gap, aligning vision embeddings closer to the paired text embeddings.", + "bbox": [ + 511, + 703, + 903, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The effect of the prefix projector is also noteworthy. Across all embedding sets, we observe a trend similar to that of the plain embeddings; however, the absolute similarity scores increase substantially. For instance, the similarity between vision and text embeddings in the paired set", + "bbox": [ + 511, + 825, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4055", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "rises from 0.306 to 0.714 when passed through the projector. This boost in similarity helps reduce the modality gap and facilitates zero-shot captioning by making embeddings more compatible. However, as seen in (e) and (f), the projector also increases the similarity between embeddings in the unpaired set (0.003 to 0.588 for text and unpaired text, and 0.052 to 0.604 for text and unpaired mapped vision embeddings). This unintended increase can lead to hallucination issues, where the model generates plausible but irrelevant captions that do not accurately reflect the image content.", + "bbox": [ + 89, + 90, + 480, + 256 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In contrast, Diffusion Bridge maintains a selective alignment, as shown by (c) and (d). It aligns paired vision and text embeddings to a level close to that of paired text embeddings within the paired set (0.833 in (c) vs. 0.826 in (d)). This selective mapping ensures that Diffusion Bridge effectively reduces the modality gap without indiscriminately increasing similarity, thereby avoiding the hallucination problem and enabling accurate cross-modal alignment.", + "bbox": [ + 89, + 258, + 480, + 380 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In summary, these cosine similarity scores confirm that Diffusion Bridge significantly reduces the modality gap, aligning vision embeddings closely with their corresponding text embeddings while preserving distinctions within the unpaired set. This selective alignment, achieved through Diffusion Bridge, enhances zero-shot image captioning performance by reducing the risk of hallucination.", + "bbox": [ + 89, + 380, + 480, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Zero-shot Image Captioning", + "text_level": 1, + "bbox": [ + 89, + 500, + 344, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In-Domain Captioning. Tab. 2 presents the indomain zero-shot image captioning performance of Diffusion Bridge compared to existing methods on the MSCOCO and Flickr30K datasets. On MSCOCO, Diffusion Bridge achieves state-of-the-art results across all metrics, demonstrating its effectiveness in aligning vision embeddings with the text space and generating accurate, contextually relevant captions for a large and diverse dataset.", + "bbox": [ + 89, + 521, + 480, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On the Flickr30K dataset, while Diffusion Bridge does not consistently achieve the highest score across all metrics, it performs competitively, securing the second-highest results in several categories. Due to the smaller size of the Flickr30K dataset, the diffusion model in Diffusion Bridge may not fully capture the intrinsic distribution of text embeddings, resulting in lower scores compared to MSCOCO. In contrast, methods like DeCap, which leverage a memory bank to access the entire training text dataset, gain a performance advantage on this relatively smaller dataset by retrieving relevant text embeddings. This memory-based similarity-matching mechanism allows DeCap to excel in capturing context, benefiting from direct references to memorized captions. Nonetheless, Diffusion Bridge achieves near state-of-the-art performance without relying on memory banks unlike DeCap, and MeaCap. Notably, Diffusion Bridge outperforms all methods except DeCap,", + "bbox": [ + 89, + 643, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cd40b19c30b7a9668db51e061a15added5a566d6e5e9b5c421f8163932e5bed4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodB@1B@4MR-LCS
    ZeroCap [36]49.87.015.431.834.5-
    MAGIC [34]56.812.917.439.947.311.3
    ESPER [41]-21.921.9-78.2-
    CLIPRe [15]-4.613.3-25.69.2
    DeCap [15]-24.725.0-91.218.7
    CapDec [28]69.226.425.151.891.8-
    ViECap [7]-27.224.8-92.918.2
    MeaCap [43]-17.724.3-84.818.7
    C3 [45]71.027.725.052.093.318.3
    Diffusion Bridge72.328.725.152.496.418.7
    ", + "bbox": [ + 516, + 89, + 924, + 251 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/523747a62491283bae4d785acd06974831a42bdf636593ffce2ea08a95405c6e.jpg", + "table_caption": [ + "(a) MSCOCO" + ], + "table_footnote": [], + "table_body": "
    MethodB@1B@4MR-LCS
    ZeroCap [36]44.75.411.827.316.8-
    MAGIC [34]44.56.413.131.620.4-
    CLIPRe [15]-9.818.2-31.712.0
    DeCap [15]-21.221.8-56.715.2
    CapDec [28]55.517.720.027.339.1-
    ViECap [7]-21.420.1-47.913.6
    MeaCap [43]-15.320.6-50.214.5
    Diffusion Bridge66.921.421.146.853.014.5
    ", + "bbox": [ + 516, + 277, + 924, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(b) Flickr30K", + "bbox": [ + 681, + 415, + 756, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Performance comparison on (a) MSCOCO and (b) Flickr30K datasets. The metrics include BLEU@1 (B@1), BLEU@4 (B@4), METEOR (M), ROUGE-L (R-L), CIDEr (C), and SPICE (S).", + "bbox": [ + 511, + 439, + 906, + 496 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "demonstrating its effectiveness and efficiency in zero-shot settings by achieving competitive results without additional resources.", + "bbox": [ + 511, + 523, + 903, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Cross-Domain Captioning. Tab. 3 presents the cross-domain captioning performance of Diffusion Bridge in comparison to other methods on the MSCOCO and Flickr30K test sets. In the MSCOCO $\\rightarrow$ Flickr30K setting, Diffusion Bridge demonstrates performance on par with other leading methods, achieving the highest scores in BLEU@4 and METEOR, as well as the second-highest scores in CIDEr and SPICE. This competitive performance on a large, diverse dataset like MSCOCO underscores the robustness of our approach, as it effectively learns generalized representations that transfer well to smaller, cross-domain datasets. In the Flickr30K $\\rightarrow$ MSCOCO setting, Diffusion Bridge continues to deliver comparable performance, though it falls behind methods such as ViECAP in CIDEr and SPICE—metrics that capture fine-grained linguistic and content alignment. This slight gap suggests that the use of entity-driven hard prompts, as employed by ViECap and MeaCap, may provide an advantage in maintaining relevance and contextual accuracy during out-of-domain transfers. Nevertheless, Diffusion Bridge achieves comparable results in BLEU@4 and METEOR, demonstrating that its diffusion-based alignment can generalize", + "bbox": [ + 511, + 568, + 906, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4056", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b9c5988b56617994530dca519bdab6f24fae01d616d9e777c839dd18f54701c0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodMSCOCO → Flickr30KFlickr30K → MSCOCO
    B@4MCSB@4MCS
    DeCap [15]16.317.935.711.112.118.044.410.9
    CapDec [28]17.318.635.7-9.216.327.3-
    ViECap [7]17.418.038.411.212.618.354.212.5
    MeaCap [43]13.418.540.312.19.817.451.712.0
    Diffusion Bridge17.418.638.511.214.718.047.111.1
    ", + "bbox": [ + 91, + 88, + 500, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "without reliance on external modules such as grammar parser or visual-related large textual memory. Furthermore, as a complementary approach, Diffusion Bridge could be enhanced with entity-aware techniques in a 'plug-and-play' manner, further extending its adaptability and potential in diverse cross-domain applications. We conducted the 'plug-and-play' experiment in", + "bbox": [ + 89, + 247, + 483, + 353 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation studies", + "text_level": 1, + "bbox": [ + 89, + 363, + 251, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this subsection, we conduct ablation studies to evaluate the influence of each component of Diffusion Bridge and the intermediate inference step. In all ablation studies, we experiment with our model on the COCO test set.", + "bbox": [ + 89, + 385, + 482, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of each component. To examine the effectiveness of each component in Diffusion Bridge, we conduct an ablation study comparing three setups: (1) a baseline model trained solely on plain text embeddings, referred to as 'Plain Embed', corresponding to the baseline model $C_1^2$ [45], (2) the same model with diffusion-bridging applied to the vision embeddings at inference, and (3) the model incorporating both diffusion-bridging and Diffusion-Augmented embeddings, denoted as $^+$ Diffusion-augmented'.", + "bbox": [ + 89, + 446, + 482, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Tab 4, the performance improves significantly when diffusion-bridging is applied to the vision embeddings across all metrics. This improvement indicates that Diffusion Bridging effectively reduces the modality gap, aligning vision embeddings more closely with the text embedding space, which allows the decoder to generate more accurate and contextually relevant captions.", + "bbox": [ + 89, + 598, + 482, + 703 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With the addition of Diffusion-Augmented embeddings, the model achieves the highest scores across all metrics, demonstrating that the decoder effectively learns to bridge the modality gap. This augmentation not only allows the model to adapt to nuanced discrepancies between vision and text embeddings but also boosts the zero-shot captioning performance of Diffusion Bridge.", + "bbox": [ + 89, + 704, + 482, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Effect of Inference Steps. To effectively evaluate the modality gap reduction achieved by Diffusion Bridging, we used the baseline model described in Section 4.3.1, which is trained without diffusion-augmented text embeddings. Tab. 5 presents the performance of Diffusion Bridge across varying numbers of inference steps, illustrating how", + "bbox": [ + 89, + 810, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/361bb49a6ca8786cccbd8008be142cee76230d3c7a49c9fdc5ca5634040aa52d.jpg", + "table_caption": [ + "Table 3. Cross-domain captioning performance on the MSCOCO test and Flickr30K test set." + ], + "table_footnote": [], + "table_body": "
    MethodB@1B@4MR-LCS
    Plain Embed [45]44.46.115.533.625.29.2
    + Diffusion-bridging70.225.424.350.588.818.2
    + Diffusion-augmented72.028.525.152.395.718.7
    ", + "bbox": [ + 526, + 88, + 893, + 143 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/80b2670f5877f2e59431e2e91db276f9c649d9252e1603c0af6a131601be69c0.jpg", + "table_caption": [ + "Table 4. Ablation study evaluating the effects of Diffusion-bridging and Diffusion-augmented embeddings on zero-shot image captioning performance." + ], + "table_footnote": [], + "table_body": "
    Inference stepB@1B@4MR-LCS
    044.46.115.533.625.29.2
    20061.016.922.344.865.916.4
    40067.422.924.449.483.318.2
    60070.225.524.350.588.818.2
    80069.624.524.250.286.118.0
    ", + "bbox": [ + 526, + 209, + 893, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation study on various inference steps.", + "bbox": [ + 557, + 308, + 859, + 323 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "different step sizes influence the alignment quality between modalities.", + "bbox": [ + 511, + 348, + 903, + 377 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "When inference steps are increased from 0 to 600, there is a clear improvement across all metrics. This trend suggests that a moderate number of steps helps to refine the vision embeddings, allowing them to align more closely with the text embedding space, which leads to improved caption quality. However, in the 800 step, performance declines slightly, as observed in metrics like B@1 and CIDEr. This decline indicates that excessive inference steps may add unnecessary noise, which disrupts the precision of the embedding mapping.", + "bbox": [ + 511, + 378, + 903, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "These results suggest that an optimal range of inference steps exists, balancing alignment quality and noise levels. Selecting an appropriate inference step size, such as 600 in this case, ensures effective modality alignment while avoiding over-processing that could negatively impact mapping accuracy. This balance is essential for leveraging Diffusion Bridge to achieve high-quality zero-shot image captioning results.", + "bbox": [ + 511, + 530, + 905, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 664, + 633, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Diffusion Bridge introduces an innovative solution to the modality gap in CLIP-based zero-shot image captioning by leveraging diffusion models to bring vision embeddings into closer alignment with the text embedding space. Through the integration of diffusion-bridging and diffusion-augmented text embeddings, our approach effectively reduces the modality gap, achieving strong performance across multiple captioning metrics without reliance on noise injection, memory-intensive methods, or entity-driven hard prompts. Ablation studies further emphasize the significance of each component in Diffusion Bridge and intermediate diffusion steps in enhancing robustness and alignment precision. Our work opens up new directions for research and practical applications in cross-modal understanding.", + "bbox": [ + 511, + 688, + 905, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4057", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 226, + 187, + 242 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Spice: Semantic propositional image caption evaluation. In Computer Vision-ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part V 14, pages 382-398. Springer, 2016. 5", + "[2] Satanjeev Banerjee and Alon Lavie. Meteor: An automatic metric for mt evaluation with improved correlation with human judgments. 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Connect, collapse, corrupt: Learning cross-modal tasks with unimodal data. arXiv preprint arXiv:2401.08567, 2024. 2, 3, 4, 5, 6, 7, 8" + ], + "bbox": [ + 516, + 92, + 905, + 654 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "4059", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_model.json b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4026b454a20023ce8279497494d3d00fcb209fe6 --- /dev/null +++ b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_model.json @@ -0,0 +1,1980 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.122, + 0.13, + 0.877, + 0.177 + ], + "angle": 0, + "content": "Diffusion Bridge: Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning" + }, + { + "type": "text", + "bbox": [ + 0.193, + 0.203, + 0.812, + 0.257 + ], + "angle": 0, + "content": "Jeong Ryong Lee1 Yejee Shin1 Geonhui Son1 Dosik Hwang1,2* \n1Yonsei University 2 Korea Institute of Science and Technology {emaker, yejeeshin, higun2, dosik.hwang}@yonsei.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.292, + 0.327, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.332, + 0.486, + 0.833 + ], + "angle": 0, + "content": "The modality gap between vision and text embeddings in CLIP presents a significant challenge for zero-shot image captioning, limiting effective cross-modal representation. Traditional approaches, such as noise injection and memory-based similarity matching, attempt to address this gap, yet these methods either rely on indirect alignment or relatively naive solutions with heavy computation. Diffusion Bridge introduces a novel approach to directly reduce this modality gap by leveraging Denoising Diffusion Probabilistic Models (DDPM), trained exclusively on text embeddings to model their distribution. Our approach is motivated by the observation that, while paired vision and text embeddings are relatively close, a modality gap still exists due to stable regions created by the contrastive loss. This gap can be interpreted as noise in cross-modal mappings, which we approximate as Gaussian noise. To bridge this gap, we employ a reverse diffusion process, where image embeddings are strategically introduced at an intermediate step in the reverse process, allowing them to be refined progressively toward the text embedding distribution. This process transforms vision embeddings into textlike representations closely aligned with paired text embeddings, effectively minimizing discrepancies between modalities. Experimental results demonstrate that these textlike vision embeddings significantly enhance alignment with their paired text embeddings, leading to improved zero-shot captioning performance on MSCOCO and Flickr30K. Diffusion Bridge achieves competitive results without reliance on memory banks or entity-driven methods, offering a novel pathway for cross-modal alignment and opening new possibilities for the application of diffusion models in multimodal tasks. The source code is available at: https://github.com/mongeoroo/diffusion-bridge" + }, + { + "type": "image", + "bbox": [ + 0.552, + 0.293, + 0.862, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.605, + 0.909, + 0.718 + ], + "angle": 0, + "content": "Figure 1. Overview of Diffusion Bridge for zero-shot image captioning. Diffusion Bridge utilizes a diffusion model trained on text embeddings to bridge the modality gap in CLIP. During inference, vision embeddings are introduced into the reverse diffusion process at an intermediate timestep, progressively aligned with the text embedding space. This alignment facilitates improved zero-shot image captioning performance by producing embeddings that closely match the text distribution" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.751, + 0.646, + 0.767 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Large-scale pre-trained vision-language models have garnered significant attention in recent research, demonstrating impressive performance across various multi-modal tasks [3, 8, 11, 31]. Among these models, CLIP [31] (Contrastive Language-Image Pretraining) stands out, leveraging a powerful joint embedding space for visual and textual data, which has paved the way for advancements in cross-modal tasks [6, 13, 26, 26, 38, 40]. With its powerful" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.237, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "4050" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.257 + ], + "angle": 0, + "content": "pretraining on a large-scale, diverse set of image-text pairs, CLIP enables impressive zero-shot performance across numerous downstream tasks, from classification to complex retrieval tasks [23, 35, 42]. Among these applications, zero-shot image captioning stands out, where models are required to generate descriptive captions for images without having seen any paired image-caption data during training [7, 15, 28, 35, 43]. In zero-shot captioning, a model's ability to bridge visual content to meaningful language representations is critical. CLIP's inherent cross-modal alignment has made it a central model for such endeavors." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.26, + 0.482, + 0.412 + ], + "angle": 0, + "content": "However, a persistent challenge within CLIP is the modality gap between its vision and text embeddings, a structural separation within the embedding space that limits the effectiveness of cross-modal alignment [17, 45]. This gap, caused by the contrastive learning dynamics and model initialization, results in visual and textual representations occupying distinct regions within the shared embedding space. Consequently, this gap restricts direct transfer and alignment for zero-shot captioning, where precise semantic alignment is essential for high-quality caption generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.413, + 0.482, + 0.564 + ], + "angle": 0, + "content": "Previous zero-shot image captioning methods have addressed the modality gap challenge through various techniques. Notably, noise injection methods [28, 45] seek to enhance the decoder's robustness by introducing Gaussian noise into text embeddings during training, thereby promoting generalization across the inherent discrepancies between vision and text embeddings. However, these approaches do not fundamentally align vision and text embeddings, leaving modality mismatches that can hinder zero-shot performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.567, + 0.482, + 0.763 + ], + "angle": 0, + "content": "On the other hand, recent advancements in diffusion-based models have shown considerable promise within multi-modal domains, particularly in tasks such as image synthesis and text-guided image manipulation [5, 21, 27]. At the core of these advancements is Denoising Diffusion Probabilistic Models (DDPM) [10], which iteratively refine noisy vectors to capture the intrinsic data distribution with high fidelity. This ability to model complex, nuanced distributions renders diffusion models powerful tools for novel applications across a range of multi-modal settings. However, their application in bridging the modality gap for zero-shot image captioning remains an area yet to be thoroughly explored." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.482, + 0.901 + ], + "angle": 0, + "content": "In this paper, we introduce Diffusion Bridge, an innovative approach that leverages diffusion models to directly address the modality gap within CLIP's embedding space for zero-shot image captioning. Diffusion Bridge models the distribution of text embeddings through the diffusion model, effectively capturing the intricate structure of the text embedding space. Given that paired vision and text embeddings remain relatively close despite their inherent differences, our method strategically inserts vision embed" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.168 + ], + "angle": 0, + "content": "dings at an intermediate step of the diffusion reverse process. The gradual refinement of reverse process allows vision embeddings to transform into text-like representations, incrementally reducing residual discrepancies stemming from the intrinsic characteristics of each modality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.168, + 0.906, + 0.318 + ], + "angle": 0, + "content": "Through comprehensive experiments, we demonstrate that Diffusion Bridge significantly reduces the modality gap, resulting in enhanced cross-modal similarity and improved captioning performance. Importantly, Diffusion Bridge achieves robust zero-shot captioning without reliance on large memory banks or external knowledge modules. Our findings indicate that Diffusion Bridge not only advances zero-shot captioning but also opens novel potentials for the application of diffusion models in cross-modal alignment tasks." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.332, + 0.655, + 0.348 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.357, + 0.906, + 0.599 + ], + "angle": 0, + "content": "Multi-modal contrastive learning has been fundamental in aligning visual and textual data within a shared embedding space, enabling cross-modal applications without paired data. Pioneering frameworks such as CLIP [31] and Image-Bind [8] achieve this alignment by training on large-scale image-text datasets, aiming to encode paired data from different modalities closer together in the embedding space. However, the modality gap [17], which keeps visual and textual embeddings in distinct regions, remains a persistent challenge. This separation limits the interchangeability of embeddings and diminishes the effectiveness of zero-shot multi-modal tasks. Studies such as Mind the Gap [17] and C3 [45] provide an in-depth examination of the modality gap in multi-modal models like CLIP, emphasizing that the contrastive loss function and model initialization result in the separation between image and text embeddings." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.6, + 0.906, + 0.72 + ], + "angle": 0, + "content": "Efforts to bridge this gap in zero-shot image captioning can be categorized into three main strategies: Late-Guidance Decoding, Early-Guidance Decoding, and Keywords-Guidance Decoding. These approaches represent parallel research directions that tackle zero-shot captioning challenges from distinct perspectives. Our work contributes specifically to the Early-Guidance Decoding category." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.906, + 0.84 + ], + "angle": 0, + "content": "Late-Guidance Decoding: Methods such as MAGIC [34] and ZeroCap [36] apply guidance at a later stage of the decoding process, often by leveraging language models to generate captions that reflect visual content. While this strategy can produce visually grounded captions, it typically relies on indirect adjustments and does not fully address the modality gap between vision and text embeddings, resulting in less precise alignment." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Early-Guidance Decoding: Several studies [9, 15, 28, 45] aim to address the modality gap earlier in the caption generation process by employing techniques such as noise-injected decoder training and memory-based simi" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.513, + 0.956 + ], + "angle": 0, + "content": "4051" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.257 + ], + "angle": 0, + "content": "larity matching. For instance, CapDec [28] and C3 [45] employ noise injection to improve the decoder's robustness to variability in vision embeddings, helping it generalize across the modality gap. DeCap [15] takes a different approach by using a memory-based projection method that maps vision embeddings into the text space through similarity-based projections. However, it requires a large memory bank, which can introduce computational challenges and limit scalability. Additionally, the direct projection relies on similarity matching, which may lack adaptability for handling inputs beyond the training distribution." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.258, + 0.482, + 0.408 + ], + "angle": 0, + "content": "Keywords-Guidance Decoding: Approaches such as ViECap [7] and MeaCap [43] focus on enhancing caption relevance and specificity by extracting entities or keywords from visual content to guide the caption generation process. Unlike Early-Guidance Decoding, these methods do not address the modality gap at the embedding level but instead operate at the sentence level, using keyword-based prompts to improve linguistic and contextual alignment. This approach is particularly beneficial for out-of-domain scenarios through explicit guidance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.409, + 0.483, + 0.695 + ], + "angle": 0, + "content": "Diffusion Models for Multi-Modal Generation. Recent advancements in diffusion models have had a substantial impact on generative modeling, particularly in tasks such as image synthesis and text generation [14, 16, 27, 44]. DDPM is prominent in this field, iteratively refining Gaussian noise to produce structured, high-quality outputs. Extensions such as Guided Diffusion [25] introduce controlled generation, enabling zero-shot and conditional tasks with enhanced specificity. In image captioning, diffusion models like SCD-Net [22] and Prefix-Diffusion [20] enhance alignment between image embeddings and textual descriptions, improving caption accuracy and diversity. SCD-Net uses semantic priors for better visual-linguistic coherence, while Prefix-Diffusion employs image-derived prefix embeddings to generate varied and contextually rich captions. Despite these advancements, the potential of diffusion models to directly address the modality gap in embedding alignment tasks, particularly in zero-shot captioning with CLIP, remains underexplored." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.71, + 0.182, + 0.725 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.482, + 0.884 + ], + "angle": 0, + "content": "Diffusion Bridge presents an innovative solution to address the modality gap by utilizing only text embeddings. Our approach is motivated by the analysis in C3 [45], which reveals that even paired vision and text embeddings, while close, still exhibit a modality gap. This gap arises due to stable regions produced by the contrastive loss, resulting in a constant offset, or 'alignment noise', between embeddings from different modalities. This alignment noise persists in the shared embedding space and can be approximated as Gaussian noise." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.886, + 0.482, + 0.901 + ], + "angle": 0, + "content": "Our proposed method employs the diffusion model's" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.137 + ], + "angle": 0, + "content": "dual strengths: its capacity as a generative model to learn the intrinsic distribution of text embeddings and its ability to incorporate conditional inputs during the reverse process." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.137, + 0.905, + 0.288 + ], + "angle": 0, + "content": "By training the diffusion model on text embeddings, the model learns the distributional characteristics of the text embedding space. During inference, we initiate the reverse diffusion process with vision embeddings at an intermediate step. Guided by the learned text distribution, the diffusion model progressively refines these vision embeddings into text-like representations. This conditioned reverse mapping effectively minimizes residual discrepancies, aligning vision embeddings more closely with the text embedding space and thereby mitigating the modality gap." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.905, + 0.363 + ], + "angle": 0, + "content": "In the following sections, we describe the mechanisms and architecture of Diffusion Bridge, detailing each component's role in enabling efficient and scalable zero-shot captioning. Fig. 2 visualizes the overall pipeline of Diffusion Bridge." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.371, + 0.905, + 0.401 + ], + "angle": 0, + "content": "3.1. Background on Denoising Diffusion Probabilistic Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.409, + 0.905, + 0.514 + ], + "angle": 0, + "content": "DDPM is the generative model that creates data by iteratively refining Gaussian noise through a controlled denoising process. The model learns a sequence of transformations that progressively reduces noise in sampled data to generate structured representations. DDPM operates in two main stages: the forward diffusion process and the reverse diffusion process." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.514, + 0.905, + 0.575 + ], + "angle": 0, + "content": "Forward Diffusion Process: Starting from an initial sample \\(\\mathbf{z}_0\\), the forward process generates a series of increasingly noisy samples \\(\\mathbf{z}_t\\) by applying a Gaussian noise schedule over \\(T\\) time steps. This process is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.583, + 0.905, + 0.601 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}\\right) := \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {z} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.609, + 0.905, + 0.669 + ], + "angle": 0, + "content": "where \\(\\beta_{t}\\) represents a variance schedule that determines the amount of noise added at each step. In the last step, the data \\(\\mathbf{z}_T\\) becomes nearly indistinguishable from pure Gaussian noise \\(\\mathbf{z}_T\\sim \\mathcal{N}(0,\\mathbf{I})\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.669, + 0.905, + 0.7 + ], + "angle": 0, + "content": "By defining \\(\\alpha_{t} := 1 - \\beta_{t}\\) and \\(\\bar{\\alpha}_{t} := \\prod_{s=1}^{t} \\alpha_{s}\\), the forward process from \\(\\mathbf{z}_0\\) to \\(\\mathbf{z}_{t}\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.708, + 0.905, + 0.725 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.733, + 0.905, + 0.793 + ], + "angle": 0, + "content": "Reverse Diffusion Process: A network estimates the mean \\(\\pmb{\\mu}_{\\theta}(\\mathbf{z}_t,t)\\) of the distribution \\(p_{\\theta}(\\mathbf{z}_{t - 1}\\mid \\mathbf{z}_t)\\) in the reverse process. This process denoises the data step-by-step to generate structured samples from noise, defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.801, + 0.905, + 0.819 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N} \\left(\\mathbf {z} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {z} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.857 + ], + "angle": 0, + "content": "where \\(\\sigma_t^2\\) represents time-dependent variance. The predicted mean \\(\\pmb{\\mu}_{\\theta}(z_{t},t)\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.865, + 0.905, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mu_ {\\theta} (\\mathbf {z} _ {t}, t) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {z} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {z} _ {t}, t)\\right), \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4052" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.907, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.473, + 0.907, + 0.557 + ], + "angle": 0, + "content": "Figure 2. Detailed model pipeline of Diffusion Bridge, illustrating the three stages of the method. First, the diffusion model is trained exclusively on text embeddings, capturing their intrinsic distribution. Next, the decoder is trained using diffusion-augmented text embeddings, preparing it to handle variations during caption generation. In the final inference stage, vision embeddings are mapped into the text embedding space via the reverse diffusion process and then the decoder generates a caption with the transformed embedding. This pipeline enables zero-shot caption generation by aligning vision embeddings with the text distribution, achieving effective cross-modal alignment without relying on paired image-text data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.483, + 0.598 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}(z_t,t)\\) represents the noise predicted by the model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.484, + 0.659 + ], + "angle": 0, + "content": "To train the diffusion model, the objective is to minimize the difference between the true noise \\(\\epsilon\\) and the predicted noise \\(\\epsilon_{\\theta}(\\mathbf{z}_t,t)\\) across all diffusion steps, which is expressed by the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.668, + 0.484, + 0.709 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {D D P M}} (\\theta) = \\mathbb {E} _ {t, \\mathbf {z} _ {0}, \\epsilon} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) \\right\\| ^ {2} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.719, + 0.484, + 0.781 + ], + "angle": 0, + "content": "where \\(\\epsilon\\) is standard Gaussian noise, \\(\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})\\). This objective enables the model to accurately estimate the noise added at each diffusion step, allowing for precise reconstruction during the reverse process." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.789, + 0.447, + 0.805 + ], + "angle": 0, + "content": "3.2. Diffusion Training with Text Embeddings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "After encoding the training text dataset into embeddings using the CLIP text encoder, several preprocessing steps are applied to condition the embeddings for diffusion model training. Initially, each text embedding, \\(\\mathbf{e}^{text}\\), is an L2-normalized vector to ensure a consistent magnitude. Subsequently, following previous works [9, 28, 45], we subtract" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.583, + 0.907, + 0.614 + ], + "angle": 0, + "content": "the mean vector, \\(\\bar{\\mathbf{e}}^{text}\\), computed across the training set embeddings to center the embeddings." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.906, + 0.72 + ], + "angle": 0, + "content": "Following mean-centering, we apply a second normalization step to further enhance uniformity. However, we observe that the L2 normalized embeddings have a relatively low average scale, which may obscure the distinction between signal and noise during DDPM training. To address this, we amplify the embeddings by a scalar factor of \\( C \\), yielding the final processed embedding:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.725, + 0.905, + 0.76 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {0} = C \\times \\frac {\\mathbf {e} ^ {t e x t} - \\bar {\\mathbf {e}} ^ {t e x t}}{\\left| \\left| \\mathbf {e} ^ {t e x t} - \\bar {\\mathbf {e}} ^ {t e x t} \\right| \\right| _ {2}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.902 + ], + "angle": 0, + "content": "The model trained with this processed set of embeddings, \\(\\mathbf{z}_0\\), through Eq. 5, allows the diffusion model to learn the score function of the text embedding distribution [33], denoted as \\(\\nabla_{\\mathbf{z}^{\\mathrm{ext}}}\\log p(\\mathbf{z}^{\\mathrm{ext}})\\). This score function encodes gradient directions toward high-density regions of the text manifold. While the model is trained exclusively on text, the learned text manifold serves as a semantic prior that defines plausible regions for cross-modal alignment. Following findings in C3 [45], the modality gap between vision and" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4053" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "text embeddings in CLIP is approximated as Gaussian noise \\((\\mathbf{z}^{\\mathrm{vision}} = \\mathbf{z}^{\\mathrm{text}} + \\epsilon, \\epsilon \\sim \\mathcal{N}(0, \\sigma^2 \\mathbf{I}))\\). During inference, the score function guides vision embeddings along the gradient of the text distribution, iteratively shifting them toward the nearest high-density regions of the text manifold. This process effectively denoises the modality gap, aligning vision embeddings with the text manifold." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.208, + 0.265, + 0.224 + ], + "angle": 0, + "content": "3.3. Decoder Training" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.23, + 0.482, + 0.291 + ], + "angle": 0, + "content": "The decoder in Diffusion Bridge is trained exclusively on text embeddings to generate coherent captions, using these embeddings as prefix inputs with an autoregressive loss. This section details the training process of the decoder." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.291, + 0.483, + 0.518 + ], + "angle": 0, + "content": "Diffusion-Augmented Text Embeddings: The text embeddings are applied centering and normalization, following the approach used in C3 [45]. While it is possible to train the decoder directly on these preprocessed text embeddings, it is essential to account for the non-unique mapping between vision and text embeddings. The inherent variability can arise in reverse-diffused vision embeddings, introducing subtle randomness to the alignment. Specifically, if a text embedding undergoes forward diffusion to an intermediate step and is then reverse-diffused, the resulting embedding may not perfectly match the original due to the randomness. To prepare the decoder to handle these practical variations, we incorporate diffusion-augmented embeddings into the training data. The augmentation process involves two main steps." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.518, + 0.483, + 0.563 + ], + "angle": 0, + "content": "For each text embedding \\(\\mathbf{z}_0\\), we select an intermediate step \\(t = A\\), where \\((T > A > 0)\\) and apply the forward diffusion process, producing a noisy version:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.576, + 0.483, + 0.593 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {z} _ {A} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {A}; \\sqrt {\\bar {\\alpha} _ {A}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {A}) \\mathbf {I}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.606, + 0.483, + 0.65 + ], + "angle": 0, + "content": "Then we denoise the noise vector, \\(\\mathbf{z}_A\\), through the reverse process to obtain the augmented embedding \\(\\mathrm{e}^{\\mathrm{aug}}\\). For faster inference, we utilized DDIM [32] for denoising." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.651, + 0.483, + 0.755 + ], + "angle": 0, + "content": "By utilizing diffusion-augmented embeddings \\(\\mathbf{e}^{\\mathrm{aug}}\\) as prefix inputs, we train the decoder to be resilient to the inherent randomness that arises from the fact that a single vision embedding does not map uniquely to a specific text embedding. The decoder learns to predict the caption y based on these augmented embeddings, using the autoregressive loss:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.766, + 0.483, + 0.806 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {A R}} = - \\sum_ {t = 1} ^ {L} \\log p \\left(y _ {t} \\mid y _ {< t}, \\mathbf {e} ^ {\\text {a u g}}\\right). \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.818, + 0.264, + 0.833 + ], + "angle": 0, + "content": "3.4. Inference Process" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.902 + ], + "angle": 0, + "content": "During inference, the vision embedding, \\(\\mathbf{e}^{img}\\), is strategically introduced into the reverse diffusion process at a predefined intermediate timestep \\(t = M\\), where \\(T > M > 0\\). This conditioned reverse process leverages our core insight:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.198 + ], + "angle": 0, + "content": "while vision and text embeddings are inherently different, they remain relatively proximate in the shared embedding space. By initiating the reverse diffusion from this intermediate step \\(M\\), we enable the model to map the vision embedding into a text-like vision embedding, \\(\\tilde{\\mathbf{e}}^{\\mathrm{img}}\\), that closely aligns with the learned distribution of text embeddings. We refer to this alignment process as diffusion-bridging." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.202, + 0.905, + 0.293 + ], + "angle": 0, + "content": "The transformed vision embedding, \\(\\tilde{\\mathbf{e}}^{\\mathrm{img}}\\), is then fed as a prefix input to the decoder trained on text embeddings. This setup ensures that the decoder receives an embedding in a familiar distribution, enhancing its capacity to generate accurate and contextually relevant captions without the need for paired data." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.319, + 0.646, + 0.336 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.349, + 0.906, + 0.47 + ], + "angle": 0, + "content": "In this section, we evaluate the effectiveness of Diffusion Bridge in mitigating the modality gap for zero-shot image captioning. Our experiments aim to assess how well our method aligns vision embeddings with the text embedding space. We conduct evaluations on standard image captioning datasets under both in-domain and cross-domain setups to comprehensively test the generalization capabilities of Diffusion Bridge." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.474, + 0.906, + 0.61 + ], + "angle": 0, + "content": "Datasets and Metrics: We assess Diffusion Bridge on two widely used image captioning datasets: MSCOCO [4, 19] and Flickr30K [39]. For dataset partitioning, we utilize the standard Karpathy split [12], which is commonly adopted in captioning benchmarks. For quantitative evaluation, we employ a suite of established metrics to gauge caption quality, including BLEU (B@n) [29], METEOR (M) [2], ROUGE-L (R-L) [18], CIDEr (C) [37], and SPICE (S) [1]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Implementation details: For the DDPM training, we employ a 1-D UNet architecture with four layers, where each layer successively doubles in dimensionality. The model is trained using a batch size of 64, a learning rate of \\(8 \\times 10^{-5}\\), and a total of 3,000,000 steps. The number of diffusion timesteps is set to \\(T = 1000\\) and we set \\(C\\) in Eqt. 6 as 5 in all experiments. For experiments on the MSCOCO dataset, we set the intermediate and augmentation steps to \\(M = 600\\) and \\(A = 400\\), respectively, whereas for Flickr30K, these values are configured to \\(M = 400\\) and \\(A = 300\\). For decoder training, we use CLIP-ViT-B/32 [31] as the encoding backbone and adopt GPT-2 [30] as the base decoder. The prefix projector consists of two fully connected layers with a hidden dimensionality of 768. The learnable soft prompts are defined with a length of 10. The projection layer projects the CLIP embedding from 512 to 768 dimensions. Training is conducted for 10 epochs with a batch size of 40 and a learning rate of \\(2 \\times 10^{-5}\\), using the AdamW optimizer following the setup in [28, 45]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4054" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.09, + 0.48, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.34, + 0.483, + 0.41 + ], + "angle": 0, + "content": "Figure 3. UMAP visualization of COCO validation set embeddings. Red points represent image embeddings \\(\\hat{\\mathbf{e}}^{\\mathrm{img}}\\), blue points denote text embeddings \\(\\hat{\\mathbf{e}}^{\\mathrm{text}}\\), and green points show mapped embeddings \\(\\tilde{\\mathbf{e}}^{\\mathrm{img}}\\) produced by Diffusion Bridge from image embeddings." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.438, + 0.346, + 0.455 + ], + "angle": 0, + "content": "4.1. Evaluation on Modality Gap" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.461, + 0.483, + 0.566 + ], + "angle": 0, + "content": "In the following sections, we evaluate the effectiveness of Diffusion Bridge in reducing the modality gap. Specifically, we conduct UMAP-based visualization and similarity assessments on embeddings from the MSCOCO validation set. To facilitate this analysis, we denote \\(\\hat{\\mathbf{e}}\\) as the centered embedding, representing aligned embeddings in a unified space." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.568, + 0.483, + 0.839 + ], + "angle": 0, + "content": "Visual Experiment on Modality Gap. To evaluate the effectiveness of Diffusion Bridge in reducing the modality gap, we conducted a UMAP [24] visualization experiment using the validation set of the COCO dataset. This visualization provides insight into the alignment of vision embeddings with text embeddings in a shared embedding space. Fig. 3 displays three types of embeddings: centered image embeddings \\(\\hat{\\mathbf{e}}^{\\mathrm{img}}\\) (red), centered text embeddings \\(\\hat{\\mathbf{e}}^{\\mathrm{text}}\\) (blue), and diffusion-mapped embeddings from image embeddings \\(\\tilde{\\mathbf{e}}^{\\mathrm{img}}\\) (green). In Fig. 3, distinct clusters for image embeddings and text embeddings illustrate the inherent modality gap between visual and textual data. However, the overlap of mapped embeddings to the text cluster suggests that Diffusion Bridge significantly reduces the modality gap. This alignment allows the decoder, which is trained in text embeddings, to effectively process text-like vision embeddings as inputs, thereby enhancing the model's captioning performance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Cosine Similarity Analysis of Modality Alignment. In the previous analysis, we visually examine the reduction in the modality gap. Herein, we use cosine similarity to provide a more quantitative assessment of this reduction. Tab." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.089, + 0.895, + 0.199 + ], + "angle": 0, + "content": "
    Comparison PairCosine Similarity
    EmbeddingProjector
    (a) e text · e img(∼)0.3060.714
    (b) e text · {e text + N(0,0.016)}(∼)0.2350.684
    (c) e text · e text(∼)0.6520.833
    (d) e text · e img(∼)0.6060.826
    (e) e text · e text(∼)0.0030.588
    (f) e text · e img(∼)0.0520.604
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.209, + 0.905, + 0.279 + ], + "angle": 0, + "content": "Table 1. Average cosine similarity scores for various embedding pairs. \\(\\sim\\) and \\(\\nVdash\\) denote corresponding pairs and non-corresponding pairs. 'Embedding' shows the direct similarity between embeddings, while 'Projector' represents the similarity of projected embeddings through a prefix projector." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.307, + 0.905, + 0.367 + ], + "angle": 0, + "content": "1 presents cosine similarity scores for different embedding sets, offering a clearer view of how effectively Diffusion Bridge brings vision embeddings closer to text embeddings in the shared space." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.369, + 0.905, + 0.505 + ], + "angle": 0, + "content": "(a) shows the similarity between text and image embeddings within the paired set, which is only 0.306. Although a 0.3 cosine similarity can indicate a certain level of similarity in high-dimensional spaces [17], it remains noticeably lower compared to the similarity between text embeddings for the same image in (c), which has a much higher score of 0.652. This discrepancy highlights the inherent modality gap between visual and textual embeddings, which can hinder zero-shot image captioning performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.507, + 0.905, + 0.702 + ], + "angle": 0, + "content": "(b) represents the cosine similarity between a text embedding and a noise-injected version of itself, with a similarity score of 0.235. This setup mirrors the noise injection process used in models like CapDec [28] and C3 [45]. Adding Gaussian noise creates a broader distribution around the original text embedding, allowing the decoder to generalize by encompassing the range where vision embeddings are likely to fall. This approach helps the decoder manage variability in vision embeddings, supporting zero-shot captioning. However, noise injection may also introduce certain limitations. If the noise range is too broad, captions could become overly generic, lacking specific details. Consequently, finding an optimal level of noise is crucial." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.905, + 0.824 + ], + "angle": 0, + "content": "(d) examines the similarity between a text embedding and its paired vision embedding mapped by Diffusion Bridge. The similarity score of 0.606 shows a substantial increase from the original score of 0.306 in (a), approaching the high similarity observed within the text embeddings in the paired set in (c). This result demonstrates that Diffusion Bridge effectively reduces the modality gap, aligning vision embeddings closer to the paired text embeddings." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.901 + ], + "angle": 0, + "content": "The effect of the prefix projector is also noteworthy. Across all embedding sets, we observe a trend similar to that of the plain embeddings; however, the absolute similarity scores increase substantially. For instance, the similarity between vision and text embeddings in the paired set" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4055" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.257 + ], + "angle": 0, + "content": "rises from 0.306 to 0.714 when passed through the projector. This boost in similarity helps reduce the modality gap and facilitates zero-shot captioning by making embeddings more compatible. However, as seen in (e) and (f), the projector also increases the similarity between embeddings in the unpaired set (0.003 to 0.588 for text and unpaired text, and 0.052 to 0.604 for text and unpaired mapped vision embeddings). This unintended increase can lead to hallucination issues, where the model generates plausible but irrelevant captions that do not accurately reflect the image content." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.259, + 0.482, + 0.381 + ], + "angle": 0, + "content": "In contrast, Diffusion Bridge maintains a selective alignment, as shown by (c) and (d). It aligns paired vision and text embeddings to a level close to that of paired text embeddings within the paired set (0.833 in (c) vs. 0.826 in (d)). This selective mapping ensures that Diffusion Bridge effectively reduces the modality gap without indiscriminately increasing similarity, thereby avoiding the hallucination problem and enabling accurate cross-modal alignment." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.381, + 0.482, + 0.486 + ], + "angle": 0, + "content": "In summary, these cosine similarity scores confirm that Diffusion Bridge significantly reduces the modality gap, aligning vision embeddings closely with their corresponding text embeddings while preserving distinctions within the unpaired set. This selective alignment, achieved through Diffusion Bridge, enhances zero-shot image captioning performance by reducing the risk of hallucination." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.5, + 0.345, + 0.516 + ], + "angle": 0, + "content": "4.2. Zero-shot Image Captioning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.522, + 0.482, + 0.643 + ], + "angle": 0, + "content": "In-Domain Captioning. Tab. 2 presents the indomain zero-shot image captioning performance of Diffusion Bridge compared to existing methods on the MSCOCO and Flickr30K datasets. On MSCOCO, Diffusion Bridge achieves state-of-the-art results across all metrics, demonstrating its effectiveness in aligning vision embeddings with the text space and generating accurate, contextually relevant captions for a large and diverse dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.644, + 0.483, + 0.901 + ], + "angle": 0, + "content": "On the Flickr30K dataset, while Diffusion Bridge does not consistently achieve the highest score across all metrics, it performs competitively, securing the second-highest results in several categories. Due to the smaller size of the Flickr30K dataset, the diffusion model in Diffusion Bridge may not fully capture the intrinsic distribution of text embeddings, resulting in lower scores compared to MSCOCO. In contrast, methods like DeCap, which leverage a memory bank to access the entire training text dataset, gain a performance advantage on this relatively smaller dataset by retrieving relevant text embeddings. This memory-based similarity-matching mechanism allows DeCap to excel in capturing context, benefiting from direct references to memorized captions. Nonetheless, Diffusion Bridge achieves near state-of-the-art performance without relying on memory banks unlike DeCap, and MeaCap. Notably, Diffusion Bridge outperforms all methods except DeCap," + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.09, + 0.925, + 0.252 + ], + "angle": 0, + "content": "
    MethodB@1B@4MR-LCS
    ZeroCap [36]49.87.015.431.834.5-
    MAGIC [34]56.812.917.439.947.311.3
    ESPER [41]-21.921.9-78.2-
    CLIPRe [15]-4.613.3-25.69.2
    DeCap [15]-24.725.0-91.218.7
    CapDec [28]69.226.425.151.891.8-
    ViECap [7]-27.224.8-92.918.2
    MeaCap [43]-17.724.3-84.818.7
    C3 [45]71.027.725.052.093.318.3
    Diffusion Bridge72.328.725.152.496.418.7
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.682, + 0.254, + 0.758, + 0.266 + ], + "angle": 0, + "content": "(a) MSCOCO" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.279, + 0.925, + 0.415 + ], + "angle": 0, + "content": "
    MethodB@1B@4MR-LCS
    ZeroCap [36]44.75.411.827.316.8-
    MAGIC [34]44.56.413.131.620.4-
    CLIPRe [15]-9.818.2-31.712.0
    DeCap [15]-21.221.8-56.715.2
    CapDec [28]55.517.720.027.339.1-
    ViECap [7]-21.420.1-47.913.6
    MeaCap [43]-15.320.6-50.214.5
    Diffusion Bridge66.921.421.146.853.014.5
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.682, + 0.416, + 0.757, + 0.428 + ], + "angle": 0, + "content": "(b) Flickr30K" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.44, + 0.907, + 0.497 + ], + "angle": 0, + "content": "Table 2. Performance comparison on (a) MSCOCO and (b) Flickr30K datasets. The metrics include BLEU@1 (B@1), BLEU@4 (B@4), METEOR (M), ROUGE-L (R-L), CIDEr (C), and SPICE (S)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.524, + 0.905, + 0.568 + ], + "angle": 0, + "content": "demonstrating its effectiveness and efficiency in zero-shot settings by achieving competitive results without additional resources." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Cross-Domain Captioning. Tab. 3 presents the cross-domain captioning performance of Diffusion Bridge in comparison to other methods on the MSCOCO and Flickr30K test sets. In the MSCOCO \\(\\rightarrow\\) Flickr30K setting, Diffusion Bridge demonstrates performance on par with other leading methods, achieving the highest scores in BLEU@4 and METEOR, as well as the second-highest scores in CIDEr and SPICE. This competitive performance on a large, diverse dataset like MSCOCO underscores the robustness of our approach, as it effectively learns generalized representations that transfer well to smaller, cross-domain datasets. In the Flickr30K \\(\\rightarrow\\) MSCOCO setting, Diffusion Bridge continues to deliver comparable performance, though it falls behind methods such as ViECAP in CIDEr and SPICE—metrics that capture fine-grained linguistic and content alignment. This slight gap suggests that the use of entity-driven hard prompts, as employed by ViECap and MeaCap, may provide an advantage in maintaining relevance and contextual accuracy during out-of-domain transfers. Nevertheless, Diffusion Bridge achieves comparable results in BLEU@4 and METEOR, demonstrating that its diffusion-based alignment can generalize" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4056" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.5, + 0.182 + ], + "angle": 0, + "content": "
    MethodMSCOCO → Flickr30KFlickr30K → MSCOCO
    B@4MCSB@4MCS
    DeCap [15]16.317.935.711.112.118.044.410.9
    CapDec [28]17.318.635.7-9.216.327.3-
    ViECap [7]17.418.038.411.212.618.354.212.5
    MeaCap [43]13.418.540.312.19.817.451.712.0
    Diffusion Bridge17.418.638.511.214.718.047.111.1
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.192, + 0.483, + 0.22 + ], + "angle": 0, + "content": "Table 3. Cross-domain captioning performance on the MSCOCO test and Flickr30K test set." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.248, + 0.484, + 0.354 + ], + "angle": 0, + "content": "without reliance on external modules such as grammar parser or visual-related large textual memory. Furthermore, as a complementary approach, Diffusion Bridge could be enhanced with entity-aware techniques in a 'plug-and-play' manner, further extending its adaptability and potential in diverse cross-domain applications. We conducted the 'plug-and-play' experiment in" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.364, + 0.253, + 0.379 + ], + "angle": 0, + "content": "4.3. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.386, + 0.483, + 0.446 + ], + "angle": 0, + "content": "In this subsection, we conduct ablation studies to evaluate the influence of each component of Diffusion Bridge and the intermediate inference step. In all ablation studies, we experiment with our model on the COCO test set." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.448, + 0.483, + 0.598 + ], + "angle": 0, + "content": "Effectiveness of each component. To examine the effectiveness of each component in Diffusion Bridge, we conduct an ablation study comparing three setups: (1) a baseline model trained solely on plain text embeddings, referred to as 'Plain Embed', corresponding to the baseline model \\( C_1^2 \\) [45], (2) the same model with diffusion-bridging applied to the vision embeddings at inference, and (3) the model incorporating both diffusion-bridging and Diffusion-Augmented embeddings, denoted as \\( ^+ \\) Diffusion-augmented'." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.599, + 0.483, + 0.704 + ], + "angle": 0, + "content": "As shown in Tab 4, the performance improves significantly when diffusion-bridging is applied to the vision embeddings across all metrics. This improvement indicates that Diffusion Bridging effectively reduces the modality gap, aligning vision embeddings more closely with the text embedding space, which allows the decoder to generate more accurate and contextually relevant captions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.483, + 0.81 + ], + "angle": 0, + "content": "With the addition of Diffusion-Augmented embeddings, the model achieves the highest scores across all metrics, demonstrating that the decoder effectively learns to bridge the modality gap. This augmentation not only allows the model to adapt to nuanced discrepancies between vision and text embeddings but also boosts the zero-shot captioning performance of Diffusion Bridge." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.483, + 0.902 + ], + "angle": 0, + "content": "The Effect of Inference Steps. To effectively evaluate the modality gap reduction achieved by Diffusion Bridging, we used the baseline model described in Section 4.3.1, which is trained without diffusion-augmented text embeddings. Tab. 5 presents the performance of Diffusion Bridge across varying numbers of inference steps, illustrating how" + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.089, + 0.895, + 0.144 + ], + "angle": 0, + "content": "
    MethodB@1B@4MR-LCS
    Plain Embed [45]44.46.115.533.625.29.2
    + Diffusion-bridging70.225.424.350.588.818.2
    + Diffusion-augmented72.028.525.152.395.718.7
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.154, + 0.905, + 0.197 + ], + "angle": 0, + "content": "Table 4. Ablation study evaluating the effects of Diffusion-bridging and Diffusion-augmented embeddings on zero-shot image captioning performance." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.21, + 0.895, + 0.298 + ], + "angle": 0, + "content": "
    Inference stepB@1B@4MR-LCS
    044.46.115.533.625.29.2
    20061.016.922.344.865.916.4
    40067.422.924.449.483.318.2
    60070.225.524.350.588.818.2
    80069.624.524.250.286.118.0
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.558, + 0.309, + 0.86, + 0.324 + ], + "angle": 0, + "content": "Table 5. Ablation study on various inference steps." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.349, + 0.905, + 0.378 + ], + "angle": 0, + "content": "different step sizes influence the alignment quality between modalities." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.379, + 0.905, + 0.53 + ], + "angle": 0, + "content": "When inference steps are increased from 0 to 600, there is a clear improvement across all metrics. This trend suggests that a moderate number of steps helps to refine the vision embeddings, allowing them to align more closely with the text embedding space, which leads to improved caption quality. However, in the 800 step, performance declines slightly, as observed in metrics like B@1 and CIDEr. This decline indicates that excessive inference steps may add unnecessary noise, which disrupts the precision of the embedding mapping." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.531, + 0.906, + 0.65 + ], + "angle": 0, + "content": "These results suggest that an optimal range of inference steps exists, balancing alignment quality and noise levels. Selecting an appropriate inference step size, such as 600 in this case, ensures effective modality alignment while avoiding over-processing that could negatively impact mapping accuracy. This balance is essential for leveraging Diffusion Bridge to achieve high-quality zero-shot image captioning results." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.665, + 0.634, + 0.68 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.689, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Diffusion Bridge introduces an innovative solution to the modality gap in CLIP-based zero-shot image captioning by leveraging diffusion models to bring vision embeddings into closer alignment with the text embedding space. Through the integration of diffusion-bridging and diffusion-augmented text embeddings, our approach effectively reduces the modality gap, achieving strong performance across multiple captioning metrics without reliance on noise injection, memory-intensive methods, or entity-driven hard prompts. Ablation studies further emphasize the significance of each component in Diffusion Bridge and intermediate diffusion steps in enhancing robustness and alignment precision. Our work opens up new directions for research and practical applications in cross-modal understanding." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4057" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.213 + ], + "angle": 0, + "content": "Acknowledgements. This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2022R1A2C2008983), Artificial Intelligence Graduate School Program at Yonsei University (RS-2020-II201361), the KIST Institutional Program (2E33801, 2E33800), and Yonsei Signature Research Cluster Program of 2024 (2024-22-0161)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.227, + 0.188, + 0.243 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.251, + 0.486, + 0.336 + ], + "angle": 0, + "content": "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Spice: Semantic propositional image caption evaluation. In Computer Vision-ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part V 14, pages 382-398. 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Connect, collapse, corrupt: Learning cross-modal tasks with unimodal data. arXiv preprint arXiv:2401.08567, 2024. 2, 3, 4, 5, 6, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.906, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4059" + } + ] +] \ No newline at end of file diff --git a/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_origin.pdf b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e13c14ab1279b2014f3333a3e39f3f7d8dcef2b9 --- /dev/null +++ b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/a385942f-3738-4670-9bc4-4dd50307bb7c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a4d7e9d6dc6edd31719f6b83cfef8a78a3c13cb7257f4a201e5e19e828073bae +size 3275946 diff --git a/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/full.md b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..748515f8dde56ff4a954638172c372753cdb40ee --- /dev/null +++ b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/full.md @@ -0,0 +1,292 @@ +# Diffusion Bridge: Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning + +Jeong Ryong Lee1 Yejee Shin1 Geonhui Son1 Dosik Hwang1,2* +1Yonsei University 2 Korea Institute of Science and Technology {emaker, yejeeshin, higun2, dosik.hwang}@yonsei.ac.kr + +# Abstract + +The modality gap between vision and text embeddings in CLIP presents a significant challenge for zero-shot image captioning, limiting effective cross-modal representation. Traditional approaches, such as noise injection and memory-based similarity matching, attempt to address this gap, yet these methods either rely on indirect alignment or relatively naive solutions with heavy computation. Diffusion Bridge introduces a novel approach to directly reduce this modality gap by leveraging Denoising Diffusion Probabilistic Models (DDPM), trained exclusively on text embeddings to model their distribution. Our approach is motivated by the observation that, while paired vision and text embeddings are relatively close, a modality gap still exists due to stable regions created by the contrastive loss. This gap can be interpreted as noise in cross-modal mappings, which we approximate as Gaussian noise. To bridge this gap, we employ a reverse diffusion process, where image embeddings are strategically introduced at an intermediate step in the reverse process, allowing them to be refined progressively toward the text embedding distribution. This process transforms vision embeddings into textlike representations closely aligned with paired text embeddings, effectively minimizing discrepancies between modalities. Experimental results demonstrate that these textlike vision embeddings significantly enhance alignment with their paired text embeddings, leading to improved zero-shot captioning performance on MSCOCO and Flickr30K. Diffusion Bridge achieves competitive results without reliance on memory banks or entity-driven methods, offering a novel pathway for cross-modal alignment and opening new possibilities for the application of diffusion models in multimodal tasks. The source code is available at: https://github.com/mongeoroo/diffusion-bridge + +![](images/1d6ba72032eff4cc5e5dc6eca67f64ff2f253b8f55a20ee3a6c63dae4f9e77b0.jpg) +Figure 1. Overview of Diffusion Bridge for zero-shot image captioning. Diffusion Bridge utilizes a diffusion model trained on text embeddings to bridge the modality gap in CLIP. During inference, vision embeddings are introduced into the reverse diffusion process at an intermediate timestep, progressively aligned with the text embedding space. This alignment facilitates improved zero-shot image captioning performance by producing embeddings that closely match the text distribution + +# 1. Introduction + +Large-scale pre-trained vision-language models have garnered significant attention in recent research, demonstrating impressive performance across various multi-modal tasks [3, 8, 11, 31]. Among these models, CLIP [31] (Contrastive Language-Image Pretraining) stands out, leveraging a powerful joint embedding space for visual and textual data, which has paved the way for advancements in cross-modal tasks [6, 13, 26, 26, 38, 40]. With its powerful + +pretraining on a large-scale, diverse set of image-text pairs, CLIP enables impressive zero-shot performance across numerous downstream tasks, from classification to complex retrieval tasks [23, 35, 42]. Among these applications, zero-shot image captioning stands out, where models are required to generate descriptive captions for images without having seen any paired image-caption data during training [7, 15, 28, 35, 43]. In zero-shot captioning, a model's ability to bridge visual content to meaningful language representations is critical. CLIP's inherent cross-modal alignment has made it a central model for such endeavors. + +However, a persistent challenge within CLIP is the modality gap between its vision and text embeddings, a structural separation within the embedding space that limits the effectiveness of cross-modal alignment [17, 45]. This gap, caused by the contrastive learning dynamics and model initialization, results in visual and textual representations occupying distinct regions within the shared embedding space. Consequently, this gap restricts direct transfer and alignment for zero-shot captioning, where precise semantic alignment is essential for high-quality caption generation. + +Previous zero-shot image captioning methods have addressed the modality gap challenge through various techniques. Notably, noise injection methods [28, 45] seek to enhance the decoder's robustness by introducing Gaussian noise into text embeddings during training, thereby promoting generalization across the inherent discrepancies between vision and text embeddings. However, these approaches do not fundamentally align vision and text embeddings, leaving modality mismatches that can hinder zero-shot performance. + +On the other hand, recent advancements in diffusion-based models have shown considerable promise within multi-modal domains, particularly in tasks such as image synthesis and text-guided image manipulation [5, 21, 27]. At the core of these advancements is Denoising Diffusion Probabilistic Models (DDPM) [10], which iteratively refine noisy vectors to capture the intrinsic data distribution with high fidelity. This ability to model complex, nuanced distributions renders diffusion models powerful tools for novel applications across a range of multi-modal settings. However, their application in bridging the modality gap for zero-shot image captioning remains an area yet to be thoroughly explored. + +In this paper, we introduce Diffusion Bridge, an innovative approach that leverages diffusion models to directly address the modality gap within CLIP's embedding space for zero-shot image captioning. Diffusion Bridge models the distribution of text embeddings through the diffusion model, effectively capturing the intricate structure of the text embedding space. Given that paired vision and text embeddings remain relatively close despite their inherent differences, our method strategically inserts vision embed + +dings at an intermediate step of the diffusion reverse process. The gradual refinement of reverse process allows vision embeddings to transform into text-like representations, incrementally reducing residual discrepancies stemming from the intrinsic characteristics of each modality. + +Through comprehensive experiments, we demonstrate that Diffusion Bridge significantly reduces the modality gap, resulting in enhanced cross-modal similarity and improved captioning performance. Importantly, Diffusion Bridge achieves robust zero-shot captioning without reliance on large memory banks or external knowledge modules. Our findings indicate that Diffusion Bridge not only advances zero-shot captioning but also opens novel potentials for the application of diffusion models in cross-modal alignment tasks. + +# 2. Related Work + +Multi-modal contrastive learning has been fundamental in aligning visual and textual data within a shared embedding space, enabling cross-modal applications without paired data. Pioneering frameworks such as CLIP [31] and Image-Bind [8] achieve this alignment by training on large-scale image-text datasets, aiming to encode paired data from different modalities closer together in the embedding space. However, the modality gap [17], which keeps visual and textual embeddings in distinct regions, remains a persistent challenge. This separation limits the interchangeability of embeddings and diminishes the effectiveness of zero-shot multi-modal tasks. Studies such as Mind the Gap [17] and C3 [45] provide an in-depth examination of the modality gap in multi-modal models like CLIP, emphasizing that the contrastive loss function and model initialization result in the separation between image and text embeddings. + +Efforts to bridge this gap in zero-shot image captioning can be categorized into three main strategies: Late-Guidance Decoding, Early-Guidance Decoding, and Keywords-Guidance Decoding. These approaches represent parallel research directions that tackle zero-shot captioning challenges from distinct perspectives. Our work contributes specifically to the Early-Guidance Decoding category. + +Late-Guidance Decoding: Methods such as MAGIC [34] and ZeroCap [36] apply guidance at a later stage of the decoding process, often by leveraging language models to generate captions that reflect visual content. While this strategy can produce visually grounded captions, it typically relies on indirect adjustments and does not fully address the modality gap between vision and text embeddings, resulting in less precise alignment. + +Early-Guidance Decoding: Several studies [9, 15, 28, 45] aim to address the modality gap earlier in the caption generation process by employing techniques such as noise-injected decoder training and memory-based simi + +larity matching. For instance, CapDec [28] and C3 [45] employ noise injection to improve the decoder's robustness to variability in vision embeddings, helping it generalize across the modality gap. DeCap [15] takes a different approach by using a memory-based projection method that maps vision embeddings into the text space through similarity-based projections. However, it requires a large memory bank, which can introduce computational challenges and limit scalability. Additionally, the direct projection relies on similarity matching, which may lack adaptability for handling inputs beyond the training distribution. + +Keywords-Guidance Decoding: Approaches such as ViECap [7] and MeaCap [43] focus on enhancing caption relevance and specificity by extracting entities or keywords from visual content to guide the caption generation process. Unlike Early-Guidance Decoding, these methods do not address the modality gap at the embedding level but instead operate at the sentence level, using keyword-based prompts to improve linguistic and contextual alignment. This approach is particularly beneficial for out-of-domain scenarios through explicit guidance. + +Diffusion Models for Multi-Modal Generation. Recent advancements in diffusion models have had a substantial impact on generative modeling, particularly in tasks such as image synthesis and text generation [14, 16, 27, 44]. DDPM is prominent in this field, iteratively refining Gaussian noise to produce structured, high-quality outputs. Extensions such as Guided Diffusion [25] introduce controlled generation, enabling zero-shot and conditional tasks with enhanced specificity. In image captioning, diffusion models like SCD-Net [22] and Prefix-Diffusion [20] enhance alignment between image embeddings and textual descriptions, improving caption accuracy and diversity. SCD-Net uses semantic priors for better visual-linguistic coherence, while Prefix-Diffusion employs image-derived prefix embeddings to generate varied and contextually rich captions. Despite these advancements, the potential of diffusion models to directly address the modality gap in embedding alignment tasks, particularly in zero-shot captioning with CLIP, remains underexplored. + +# 3. Method + +Diffusion Bridge presents an innovative solution to address the modality gap by utilizing only text embeddings. Our approach is motivated by the analysis in C3 [45], which reveals that even paired vision and text embeddings, while close, still exhibit a modality gap. This gap arises due to stable regions produced by the contrastive loss, resulting in a constant offset, or 'alignment noise', between embeddings from different modalities. This alignment noise persists in the shared embedding space and can be approximated as Gaussian noise. + +Our proposed method employs the diffusion model's + +dual strengths: its capacity as a generative model to learn the intrinsic distribution of text embeddings and its ability to incorporate conditional inputs during the reverse process. + +By training the diffusion model on text embeddings, the model learns the distributional characteristics of the text embedding space. During inference, we initiate the reverse diffusion process with vision embeddings at an intermediate step. Guided by the learned text distribution, the diffusion model progressively refines these vision embeddings into text-like representations. This conditioned reverse mapping effectively minimizes residual discrepancies, aligning vision embeddings more closely with the text embedding space and thereby mitigating the modality gap. + +In the following sections, we describe the mechanisms and architecture of Diffusion Bridge, detailing each component's role in enabling efficient and scalable zero-shot captioning. Fig. 2 visualizes the overall pipeline of Diffusion Bridge. + +# 3.1. Background on Denoising Diffusion Probabilistic Models + +DDPM is the generative model that creates data by iteratively refining Gaussian noise through a controlled denoising process. The model learns a sequence of transformations that progressively reduces noise in sampled data to generate structured representations. DDPM operates in two main stages: the forward diffusion process and the reverse diffusion process. + +Forward Diffusion Process: Starting from an initial sample $\mathbf{z}_0$ , the forward process generates a series of increasingly noisy samples $\mathbf{z}_t$ by applying a Gaussian noise schedule over $T$ time steps. This process is defined as: + +$$ +q \left(\mathbf {z} _ {t} \mid \mathbf {z} _ {t - 1}\right) := \mathcal {N} \left(\mathbf {z} _ {t}; \sqrt {1 - \beta_ {t}} \mathbf {z} _ {t - 1}, \beta_ {t} \mathbf {I}\right), \tag {1} +$$ + +where $\beta_{t}$ represents a variance schedule that determines the amount of noise added at each step. In the last step, the data $\mathbf{z}_T$ becomes nearly indistinguishable from pure Gaussian noise $\mathbf{z}_T\sim \mathcal{N}(0,\mathbf{I})$ + +By defining $\alpha_{t} := 1 - \beta_{t}$ and $\bar{\alpha}_{t} := \prod_{s=1}^{t} \alpha_{s}$ , the forward process from $\mathbf{z}_0$ to $\mathbf{z}_{t}$ can be expressed as: + +$$ +q \left(\mathbf {z} _ {t} \mid \mathbf {z} _ {0}\right) = \mathcal {N} \left(\mathbf {z} _ {t}; \sqrt {\bar {\alpha} _ {t}} \mathbf {z} _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right). \tag {2} +$$ + +Reverse Diffusion Process: A network estimates the mean $\pmb{\mu}_{\theta}(\mathbf{z}_t,t)$ of the distribution $p_{\theta}(\mathbf{z}_{t - 1}\mid \mathbf{z}_t)$ in the reverse process. This process denoises the data step-by-step to generate structured samples from noise, defined as: + +$$ +p _ {\theta} \left(\mathbf {z} _ {t - 1} \mid \mathbf {z} _ {t}\right) := \mathcal {N} \left(\mathbf {z} _ {t - 1}; \mu_ {\theta} \left(\mathbf {z} _ {t}, t\right), \sigma_ {t} ^ {2} \mathbf {I}\right), \tag {3} +$$ + +where $\sigma_t^2$ represents time-dependent variance. The predicted mean $\pmb{\mu}_{\theta}(z_{t},t)$ can be expressed as: + +$$ +\mu_ {\theta} (\mathbf {z} _ {t}, t) = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {z} _ {t} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} _ {\theta} (\mathbf {z} _ {t}, t)\right), \tag {4} +$$ + +![](images/9c372eea1e5987f54b99b1be6fcb43e0bb0e1affa64be2cafc2e423a1a8f45eb.jpg) +Figure 2. Detailed model pipeline of Diffusion Bridge, illustrating the three stages of the method. First, the diffusion model is trained exclusively on text embeddings, capturing their intrinsic distribution. Next, the decoder is trained using diffusion-augmented text embeddings, preparing it to handle variations during caption generation. In the final inference stage, vision embeddings are mapped into the text embedding space via the reverse diffusion process and then the decoder generates a caption with the transformed embedding. This pipeline enables zero-shot caption generation by aligning vision embeddings with the text distribution, achieving effective cross-modal alignment without relying on paired image-text data. + +where $\epsilon_{\theta}(z_t,t)$ represents the noise predicted by the model. + +To train the diffusion model, the objective is to minimize the difference between the true noise $\epsilon$ and the predicted noise $\epsilon_{\theta}(\mathbf{z}_t,t)$ across all diffusion steps, which is expressed by the following loss function: + +$$ +L _ {\mathrm {D D P M}} (\theta) = \mathbb {E} _ {t, \mathbf {z} _ {0}, \epsilon} \left[ \left\| \epsilon - \epsilon_ {\theta} \left(\sqrt {\bar {\alpha} _ {t}} \mathbf {z} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , t\right) \right\| ^ {2} \right], \tag {5} +$$ + +where $\epsilon$ is standard Gaussian noise, $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ . This objective enables the model to accurately estimate the noise added at each diffusion step, allowing for precise reconstruction during the reverse process. + +# 3.2. Diffusion Training with Text Embeddings + +After encoding the training text dataset into embeddings using the CLIP text encoder, several preprocessing steps are applied to condition the embeddings for diffusion model training. Initially, each text embedding, $\mathbf{e}^{text}$ , is an L2-normalized vector to ensure a consistent magnitude. Subsequently, following previous works [9, 28, 45], we subtract + +the mean vector, $\bar{\mathbf{e}}^{text}$ , computed across the training set embeddings to center the embeddings. + +Following mean-centering, we apply a second normalization step to further enhance uniformity. However, we observe that the L2 normalized embeddings have a relatively low average scale, which may obscure the distinction between signal and noise during DDPM training. To address this, we amplify the embeddings by a scalar factor of $C$ , yielding the final processed embedding: + +$$ +\mathbf {z} _ {0} = C \times \frac {\mathbf {e} ^ {t e x t} - \bar {\mathbf {e}} ^ {t e x t}}{\left| \left| \mathbf {e} ^ {t e x t} - \bar {\mathbf {e}} ^ {t e x t} \right| \right| _ {2}}. \tag {6} +$$ + +The model trained with this processed set of embeddings, $\mathbf{z}_0$ , through Eq. 5, allows the diffusion model to learn the score function of the text embedding distribution [33], denoted as $\nabla_{\mathbf{z}^{\mathrm{ext}}}\log p(\mathbf{z}^{\mathrm{ext}})$ . This score function encodes gradient directions toward high-density regions of the text manifold. While the model is trained exclusively on text, the learned text manifold serves as a semantic prior that defines plausible regions for cross-modal alignment. Following findings in C3 [45], the modality gap between vision and + +text embeddings in CLIP is approximated as Gaussian noise $(\mathbf{z}^{\mathrm{vision}} = \mathbf{z}^{\mathrm{text}} + \epsilon, \epsilon \sim \mathcal{N}(0, \sigma^2 \mathbf{I}))$ . During inference, the score function guides vision embeddings along the gradient of the text distribution, iteratively shifting them toward the nearest high-density regions of the text manifold. This process effectively denoises the modality gap, aligning vision embeddings with the text manifold. + +# 3.3. Decoder Training + +The decoder in Diffusion Bridge is trained exclusively on text embeddings to generate coherent captions, using these embeddings as prefix inputs with an autoregressive loss. This section details the training process of the decoder. + +Diffusion-Augmented Text Embeddings: The text embeddings are applied centering and normalization, following the approach used in C3 [45]. While it is possible to train the decoder directly on these preprocessed text embeddings, it is essential to account for the non-unique mapping between vision and text embeddings. The inherent variability can arise in reverse-diffused vision embeddings, introducing subtle randomness to the alignment. Specifically, if a text embedding undergoes forward diffusion to an intermediate step and is then reverse-diffused, the resulting embedding may not perfectly match the original due to the randomness. To prepare the decoder to handle these practical variations, we incorporate diffusion-augmented embeddings into the training data. The augmentation process involves two main steps. + +For each text embedding $\mathbf{z}_0$ , we select an intermediate step $t = A$ , where $(T > A > 0)$ and apply the forward diffusion process, producing a noisy version: + +$$ +q \left(\mathbf {z} _ {A} \mid \mathbf {z} _ {0}\right) = \mathcal {N} \left(\mathbf {z} _ {A}; \sqrt {\bar {\alpha} _ {A}} \mathbf {z} _ {0}, (1 - \bar {\alpha} _ {A}) \mathbf {I}\right). \tag {7} +$$ + +Then we denoise the noise vector, $\mathbf{z}_A$ , through the reverse process to obtain the augmented embedding $\mathrm{e}^{\mathrm{aug}}$ . For faster inference, we utilized DDIM [32] for denoising. + +By utilizing diffusion-augmented embeddings $\mathbf{e}^{\mathrm{aug}}$ as prefix inputs, we train the decoder to be resilient to the inherent randomness that arises from the fact that a single vision embedding does not map uniquely to a specific text embedding. The decoder learns to predict the caption y based on these augmented embeddings, using the autoregressive loss: + +$$ +L _ {\mathrm {A R}} = - \sum_ {t = 1} ^ {L} \log p \left(y _ {t} \mid y _ {< t}, \mathbf {e} ^ {\text {a u g}}\right). \tag {8} +$$ + +# 3.4. Inference Process + +During inference, the vision embedding, $\mathbf{e}^{img}$ , is strategically introduced into the reverse diffusion process at a predefined intermediate timestep $t = M$ , where $T > M > 0$ . This conditioned reverse process leverages our core insight: + +while vision and text embeddings are inherently different, they remain relatively proximate in the shared embedding space. By initiating the reverse diffusion from this intermediate step $M$ , we enable the model to map the vision embedding into a text-like vision embedding, $\tilde{\mathbf{e}}^{\mathrm{img}}$ , that closely aligns with the learned distribution of text embeddings. We refer to this alignment process as diffusion-bridging. + +The transformed vision embedding, $\tilde{\mathbf{e}}^{\mathrm{img}}$ , is then fed as a prefix input to the decoder trained on text embeddings. This setup ensures that the decoder receives an embedding in a familiar distribution, enhancing its capacity to generate accurate and contextually relevant captions without the need for paired data. + +# 4. Experiments + +In this section, we evaluate the effectiveness of Diffusion Bridge in mitigating the modality gap for zero-shot image captioning. Our experiments aim to assess how well our method aligns vision embeddings with the text embedding space. We conduct evaluations on standard image captioning datasets under both in-domain and cross-domain setups to comprehensively test the generalization capabilities of Diffusion Bridge. + +Datasets and Metrics: We assess Diffusion Bridge on two widely used image captioning datasets: MSCOCO [4, 19] and Flickr30K [39]. For dataset partitioning, we utilize the standard Karpathy split [12], which is commonly adopted in captioning benchmarks. For quantitative evaluation, we employ a suite of established metrics to gauge caption quality, including BLEU (B@n) [29], METEOR (M) [2], ROUGE-L (R-L) [18], CIDEr (C) [37], and SPICE (S) [1]. + +Implementation details: For the DDPM training, we employ a 1-D UNet architecture with four layers, where each layer successively doubles in dimensionality. The model is trained using a batch size of 64, a learning rate of $8 \times 10^{-5}$ , and a total of 3,000,000 steps. The number of diffusion timesteps is set to $T = 1000$ and we set $C$ in Eqt. 6 as 5 in all experiments. For experiments on the MSCOCO dataset, we set the intermediate and augmentation steps to $M = 600$ and $A = 400$ , respectively, whereas for Flickr30K, these values are configured to $M = 400$ and $A = 300$ . For decoder training, we use CLIP-ViT-B/32 [31] as the encoding backbone and adopt GPT-2 [30] as the base decoder. The prefix projector consists of two fully connected layers with a hidden dimensionality of 768. The learnable soft prompts are defined with a length of 10. The projection layer projects the CLIP embedding from 512 to 768 dimensions. Training is conducted for 10 epochs with a batch size of 40 and a learning rate of $2 \times 10^{-5}$ , using the AdamW optimizer following the setup in [28, 45]. + +![](images/a45e1bd1d8f1fb9e7d36a21587608261dfa02d12c686c7e5c8282d786f20867f.jpg) +Figure 3. UMAP visualization of COCO validation set embeddings. Red points represent image embeddings $\hat{\mathbf{e}}^{\mathrm{img}}$ , blue points denote text embeddings $\hat{\mathbf{e}}^{\mathrm{text}}$ , and green points show mapped embeddings $\tilde{\mathbf{e}}^{\mathrm{img}}$ produced by Diffusion Bridge from image embeddings. + +# 4.1. Evaluation on Modality Gap + +In the following sections, we evaluate the effectiveness of Diffusion Bridge in reducing the modality gap. Specifically, we conduct UMAP-based visualization and similarity assessments on embeddings from the MSCOCO validation set. To facilitate this analysis, we denote $\hat{\mathbf{e}}$ as the centered embedding, representing aligned embeddings in a unified space. + +Visual Experiment on Modality Gap. To evaluate the effectiveness of Diffusion Bridge in reducing the modality gap, we conducted a UMAP [24] visualization experiment using the validation set of the COCO dataset. This visualization provides insight into the alignment of vision embeddings with text embeddings in a shared embedding space. Fig. 3 displays three types of embeddings: centered image embeddings $\hat{\mathbf{e}}^{\mathrm{img}}$ (red), centered text embeddings $\hat{\mathbf{e}}^{\mathrm{text}}$ (blue), and diffusion-mapped embeddings from image embeddings $\tilde{\mathbf{e}}^{\mathrm{img}}$ (green). In Fig. 3, distinct clusters for image embeddings and text embeddings illustrate the inherent modality gap between visual and textual data. However, the overlap of mapped embeddings to the text cluster suggests that Diffusion Bridge significantly reduces the modality gap. This alignment allows the decoder, which is trained in text embeddings, to effectively process text-like vision embeddings as inputs, thereby enhancing the model's captioning performance. + +Cosine Similarity Analysis of Modality Alignment. In the previous analysis, we visually examine the reduction in the modality gap. Herein, we use cosine similarity to provide a more quantitative assessment of this reduction. Tab. + +
    Comparison PairCosine Similarity
    EmbeddingProjector
    (a) e text · e img(∼)0.3060.714
    (b) e text · {e text + N(0,0.016)}(∼)0.2350.684
    (c) e text · e text(∼)0.6520.833
    (d) e text · e img(∼)0.6060.826
    (e) e text · e text(∼)0.0030.588
    (f) e text · e img(∼)0.0520.604
    + +Table 1. Average cosine similarity scores for various embedding pairs. $\sim$ and $\nVdash$ denote corresponding pairs and non-corresponding pairs. 'Embedding' shows the direct similarity between embeddings, while 'Projector' represents the similarity of projected embeddings through a prefix projector. + +1 presents cosine similarity scores for different embedding sets, offering a clearer view of how effectively Diffusion Bridge brings vision embeddings closer to text embeddings in the shared space. + +(a) shows the similarity between text and image embeddings within the paired set, which is only 0.306. Although a 0.3 cosine similarity can indicate a certain level of similarity in high-dimensional spaces [17], it remains noticeably lower compared to the similarity between text embeddings for the same image in (c), which has a much higher score of 0.652. This discrepancy highlights the inherent modality gap between visual and textual embeddings, which can hinder zero-shot image captioning performance. + +(b) represents the cosine similarity between a text embedding and a noise-injected version of itself, with a similarity score of 0.235. This setup mirrors the noise injection process used in models like CapDec [28] and C3 [45]. Adding Gaussian noise creates a broader distribution around the original text embedding, allowing the decoder to generalize by encompassing the range where vision embeddings are likely to fall. This approach helps the decoder manage variability in vision embeddings, supporting zero-shot captioning. However, noise injection may also introduce certain limitations. If the noise range is too broad, captions could become overly generic, lacking specific details. Consequently, finding an optimal level of noise is crucial. + +(d) examines the similarity between a text embedding and its paired vision embedding mapped by Diffusion Bridge. The similarity score of 0.606 shows a substantial increase from the original score of 0.306 in (a), approaching the high similarity observed within the text embeddings in the paired set in (c). This result demonstrates that Diffusion Bridge effectively reduces the modality gap, aligning vision embeddings closer to the paired text embeddings. + +The effect of the prefix projector is also noteworthy. Across all embedding sets, we observe a trend similar to that of the plain embeddings; however, the absolute similarity scores increase substantially. For instance, the similarity between vision and text embeddings in the paired set + +rises from 0.306 to 0.714 when passed through the projector. This boost in similarity helps reduce the modality gap and facilitates zero-shot captioning by making embeddings more compatible. However, as seen in (e) and (f), the projector also increases the similarity between embeddings in the unpaired set (0.003 to 0.588 for text and unpaired text, and 0.052 to 0.604 for text and unpaired mapped vision embeddings). This unintended increase can lead to hallucination issues, where the model generates plausible but irrelevant captions that do not accurately reflect the image content. + +In contrast, Diffusion Bridge maintains a selective alignment, as shown by (c) and (d). It aligns paired vision and text embeddings to a level close to that of paired text embeddings within the paired set (0.833 in (c) vs. 0.826 in (d)). This selective mapping ensures that Diffusion Bridge effectively reduces the modality gap without indiscriminately increasing similarity, thereby avoiding the hallucination problem and enabling accurate cross-modal alignment. + +In summary, these cosine similarity scores confirm that Diffusion Bridge significantly reduces the modality gap, aligning vision embeddings closely with their corresponding text embeddings while preserving distinctions within the unpaired set. This selective alignment, achieved through Diffusion Bridge, enhances zero-shot image captioning performance by reducing the risk of hallucination. + +# 4.2. Zero-shot Image Captioning + +In-Domain Captioning. Tab. 2 presents the indomain zero-shot image captioning performance of Diffusion Bridge compared to existing methods on the MSCOCO and Flickr30K datasets. On MSCOCO, Diffusion Bridge achieves state-of-the-art results across all metrics, demonstrating its effectiveness in aligning vision embeddings with the text space and generating accurate, contextually relevant captions for a large and diverse dataset. + +On the Flickr30K dataset, while Diffusion Bridge does not consistently achieve the highest score across all metrics, it performs competitively, securing the second-highest results in several categories. Due to the smaller size of the Flickr30K dataset, the diffusion model in Diffusion Bridge may not fully capture the intrinsic distribution of text embeddings, resulting in lower scores compared to MSCOCO. In contrast, methods like DeCap, which leverage a memory bank to access the entire training text dataset, gain a performance advantage on this relatively smaller dataset by retrieving relevant text embeddings. This memory-based similarity-matching mechanism allows DeCap to excel in capturing context, benefiting from direct references to memorized captions. Nonetheless, Diffusion Bridge achieves near state-of-the-art performance without relying on memory banks unlike DeCap, and MeaCap. Notably, Diffusion Bridge outperforms all methods except DeCap, + +
    MethodB@1B@4MR-LCS
    ZeroCap [36]49.87.015.431.834.5-
    MAGIC [34]56.812.917.439.947.311.3
    ESPER [41]-21.921.9-78.2-
    CLIPRe [15]-4.613.3-25.69.2
    DeCap [15]-24.725.0-91.218.7
    CapDec [28]69.226.425.151.891.8-
    ViECap [7]-27.224.8-92.918.2
    MeaCap [43]-17.724.3-84.818.7
    C3 [45]71.027.725.052.093.318.3
    Diffusion Bridge72.328.725.152.496.418.7
    + +(a) MSCOCO + +
    MethodB@1B@4MR-LCS
    ZeroCap [36]44.75.411.827.316.8-
    MAGIC [34]44.56.413.131.620.4-
    CLIPRe [15]-9.818.2-31.712.0
    DeCap [15]-21.221.8-56.715.2
    CapDec [28]55.517.720.027.339.1-
    ViECap [7]-21.420.1-47.913.6
    MeaCap [43]-15.320.6-50.214.5
    Diffusion Bridge66.921.421.146.853.014.5
    + +(b) Flickr30K + +Table 2. Performance comparison on (a) MSCOCO and (b) Flickr30K datasets. The metrics include BLEU@1 (B@1), BLEU@4 (B@4), METEOR (M), ROUGE-L (R-L), CIDEr (C), and SPICE (S). + +demonstrating its effectiveness and efficiency in zero-shot settings by achieving competitive results without additional resources. + +Cross-Domain Captioning. Tab. 3 presents the cross-domain captioning performance of Diffusion Bridge in comparison to other methods on the MSCOCO and Flickr30K test sets. In the MSCOCO $\rightarrow$ Flickr30K setting, Diffusion Bridge demonstrates performance on par with other leading methods, achieving the highest scores in BLEU@4 and METEOR, as well as the second-highest scores in CIDEr and SPICE. This competitive performance on a large, diverse dataset like MSCOCO underscores the robustness of our approach, as it effectively learns generalized representations that transfer well to smaller, cross-domain datasets. In the Flickr30K $\rightarrow$ MSCOCO setting, Diffusion Bridge continues to deliver comparable performance, though it falls behind methods such as ViECAP in CIDEr and SPICE—metrics that capture fine-grained linguistic and content alignment. This slight gap suggests that the use of entity-driven hard prompts, as employed by ViECap and MeaCap, may provide an advantage in maintaining relevance and contextual accuracy during out-of-domain transfers. Nevertheless, Diffusion Bridge achieves comparable results in BLEU@4 and METEOR, demonstrating that its diffusion-based alignment can generalize + +
    MethodMSCOCO → Flickr30KFlickr30K → MSCOCO
    B@4MCSB@4MCS
    DeCap [15]16.317.935.711.112.118.044.410.9
    CapDec [28]17.318.635.7-9.216.327.3-
    ViECap [7]17.418.038.411.212.618.354.212.5
    MeaCap [43]13.418.540.312.19.817.451.712.0
    Diffusion Bridge17.418.638.511.214.718.047.111.1
    + +without reliance on external modules such as grammar parser or visual-related large textual memory. Furthermore, as a complementary approach, Diffusion Bridge could be enhanced with entity-aware techniques in a 'plug-and-play' manner, further extending its adaptability and potential in diverse cross-domain applications. We conducted the 'plug-and-play' experiment in + +# 4.3. Ablation studies + +In this subsection, we conduct ablation studies to evaluate the influence of each component of Diffusion Bridge and the intermediate inference step. In all ablation studies, we experiment with our model on the COCO test set. + +Effectiveness of each component. To examine the effectiveness of each component in Diffusion Bridge, we conduct an ablation study comparing three setups: (1) a baseline model trained solely on plain text embeddings, referred to as 'Plain Embed', corresponding to the baseline model $C_1^2$ [45], (2) the same model with diffusion-bridging applied to the vision embeddings at inference, and (3) the model incorporating both diffusion-bridging and Diffusion-Augmented embeddings, denoted as $^+$ Diffusion-augmented'. + +As shown in Tab 4, the performance improves significantly when diffusion-bridging is applied to the vision embeddings across all metrics. This improvement indicates that Diffusion Bridging effectively reduces the modality gap, aligning vision embeddings more closely with the text embedding space, which allows the decoder to generate more accurate and contextually relevant captions. + +With the addition of Diffusion-Augmented embeddings, the model achieves the highest scores across all metrics, demonstrating that the decoder effectively learns to bridge the modality gap. This augmentation not only allows the model to adapt to nuanced discrepancies between vision and text embeddings but also boosts the zero-shot captioning performance of Diffusion Bridge. + +The Effect of Inference Steps. To effectively evaluate the modality gap reduction achieved by Diffusion Bridging, we used the baseline model described in Section 4.3.1, which is trained without diffusion-augmented text embeddings. Tab. 5 presents the performance of Diffusion Bridge across varying numbers of inference steps, illustrating how + +Table 3. Cross-domain captioning performance on the MSCOCO test and Flickr30K test set. + +
    MethodB@1B@4MR-LCS
    Plain Embed [45]44.46.115.533.625.29.2
    + Diffusion-bridging70.225.424.350.588.818.2
    + Diffusion-augmented72.028.525.152.395.718.7
    + +Table 4. Ablation study evaluating the effects of Diffusion-bridging and Diffusion-augmented embeddings on zero-shot image captioning performance. + +
    Inference stepB@1B@4MR-LCS
    044.46.115.533.625.29.2
    20061.016.922.344.865.916.4
    40067.422.924.449.483.318.2
    60070.225.524.350.588.818.2
    80069.624.524.250.286.118.0
    + +Table 5. Ablation study on various inference steps. + +different step sizes influence the alignment quality between modalities. + +When inference steps are increased from 0 to 600, there is a clear improvement across all metrics. This trend suggests that a moderate number of steps helps to refine the vision embeddings, allowing them to align more closely with the text embedding space, which leads to improved caption quality. However, in the 800 step, performance declines slightly, as observed in metrics like B@1 and CIDEr. This decline indicates that excessive inference steps may add unnecessary noise, which disrupts the precision of the embedding mapping. + +These results suggest that an optimal range of inference steps exists, balancing alignment quality and noise levels. Selecting an appropriate inference step size, such as 600 in this case, ensures effective modality alignment while avoiding over-processing that could negatively impact mapping accuracy. This balance is essential for leveraging Diffusion Bridge to achieve high-quality zero-shot image captioning results. + +# 5. Conclusion + +Diffusion Bridge introduces an innovative solution to the modality gap in CLIP-based zero-shot image captioning by leveraging diffusion models to bring vision embeddings into closer alignment with the text embedding space. Through the integration of diffusion-bridging and diffusion-augmented text embeddings, our approach effectively reduces the modality gap, achieving strong performance across multiple captioning metrics without reliance on noise injection, memory-intensive methods, or entity-driven hard prompts. Ablation studies further emphasize the significance of each component in Diffusion Bridge and intermediate diffusion steps in enhancing robustness and alignment precision. 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Multimodal knowledge alignment with reinforcement learning. arXiv preprint arXiv:2205.12630, 2022. 7 +[42] Zequn Zeng, Hao Zhang, Ruiying Lu, Dongsheng Wang, Bo Chen, and Zhengjue Wang. Conzic: Controllable zero-shot image captioning by sampling-based polishing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 23465-23476, 2023. 2 +[43] Zequn Zeng, Yan Xie, Hao Zhang, Chiyu Chen, Bo Chen, and Zhengjue Wang. Meacap: Memory-augmented zero-shot image captioning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14100-14110, 2024. 2, 3, 7, 8 +[44] Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3836-3847, 2023. 3 +[45] Yuhui Zhang, Elaine Sui, and Serena Yeung-Levy. Connect, collapse, corrupt: Learning cross-modal tasks with unimodal data. arXiv preprint arXiv:2401.08567, 2024. 2, 3, 4, 5, 6, 7, 8 \ No newline at end of file diff --git a/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/images.zip b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2cd3ddcee9dd08d94ef35a5309f97123b72d40ea --- /dev/null +++ b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2d034cba856a8de9ce49f71b40fd2ad2c55e9c6ae6e7f1187249221351bd43a6 +size 365393 diff --git a/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/layout.json b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..66916580703639112e58e4dc09c6c5db9d433e2c --- /dev/null +++ b/2025/Diffusion Bridge_ Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning/layout.json @@ -0,0 +1,7186 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 74, + 102, + 536, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 102, + 536, + 140 + ], + "spans": [ + { + "bbox": [ + 74, + 102, + 536, + 140 + ], + "type": "text", + "content": "Diffusion Bridge: Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 118, + 160, + 496, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 160, + 496, + 203 + ], + "spans": [ + { + "bbox": [ + 118, + 160, + 496, + 203 + ], + "type": "text", + "content": "Jeong Ryong Lee1 Yejee Shin1 Geonhui Son1 Dosik Hwang1,2* \n1Yonsei University 2 Korea Institute of Science and Technology {emaker, yejeeshin, higun2, dosik.hwang}@yonsei.ac.kr" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "spans": [ + { + "bbox": [ + 151, + 231, + 200, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 262, + 297, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 262, + 297, + 659 + ], + "spans": [ + { + "bbox": [ + 54, + 262, + 297, + 659 + ], + "type": "text", + "content": "The modality gap between vision and text embeddings in CLIP presents a significant challenge for zero-shot image captioning, limiting effective cross-modal representation. Traditional approaches, such as noise injection and memory-based similarity matching, attempt to address this gap, yet these methods either rely on indirect alignment or relatively naive solutions with heavy computation. Diffusion Bridge introduces a novel approach to directly reduce this modality gap by leveraging Denoising Diffusion Probabilistic Models (DDPM), trained exclusively on text embeddings to model their distribution. Our approach is motivated by the observation that, while paired vision and text embeddings are relatively close, a modality gap still exists due to stable regions created by the contrastive loss. This gap can be interpreted as noise in cross-modal mappings, which we approximate as Gaussian noise. To bridge this gap, we employ a reverse diffusion process, where image embeddings are strategically introduced at an intermediate step in the reverse process, allowing them to be refined progressively toward the text embedding distribution. This process transforms vision embeddings into textlike representations closely aligned with paired text embeddings, effectively minimizing discrepancies between modalities. Experimental results demonstrate that these textlike vision embeddings significantly enhance alignment with their paired text embeddings, leading to improved zero-shot captioning performance on MSCOCO and Flickr30K. Diffusion Bridge achieves competitive results without reliance on memory banks or entity-driven methods, offering a novel pathway for cross-modal alignment and opening new possibilities for the application of diffusion models in multimodal tasks. The source code is available at: https://github.com/mongeoroo/diffusion-bridge" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 337, + 232, + 527, + 469 + ], + "blocks": [ + { + "bbox": [ + 337, + 232, + 527, + 469 + ], + "lines": [ + { + "bbox": [ + 337, + 232, + 527, + 469 + ], + "spans": [ + { + "bbox": [ + 337, + 232, + 527, + 469 + ], + "type": "image", + "image_path": "1d6ba72032eff4cc5e5dc6eca67f64ff2f253b8f55a20ee3a6c63dae4f9e77b0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 479, + 556, + 568 + ], + "lines": [ + { + "bbox": [ + 313, + 479, + 556, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 556, + 568 + ], + "type": "text", + "content": "Figure 1. Overview of Diffusion Bridge for zero-shot image captioning. Diffusion Bridge utilizes a diffusion model trained on text embeddings to bridge the modality gap in CLIP. During inference, vision embeddings are introduced into the reverse diffusion process at an intermediate timestep, progressively aligned with the text embedding space. This alignment facilitates improved zero-shot image captioning performance by producing embeddings that closely match the text distribution" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 594, + 395, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 594, + 395, + 607 + ], + "spans": [ + { + "bbox": [ + 314, + 594, + 395, + 607 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 556, + 715 + ], + "type": "text", + "content": "Large-scale pre-trained vision-language models have garnered significant attention in recent research, demonstrating impressive performance across various multi-modal tasks [3, 8, 11, 31]. Among these models, CLIP [31] (Contrastive Language-Image Pretraining) stands out, leveraging a powerful joint embedding space for visual and textual data, which has paved the way for advancements in cross-modal tasks [6, 13, 26, 26, 38, 40]. With its powerful" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 702, + 145, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 145, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 145, + 713 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "4050" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "content": "pretraining on a large-scale, diverse set of image-text pairs, CLIP enables impressive zero-shot performance across numerous downstream tasks, from classification to complex retrieval tasks [23, 35, 42]. Among these applications, zero-shot image captioning stands out, where models are required to generate descriptive captions for images without having seen any paired image-caption data during training [7, 15, 28, 35, 43]. In zero-shot captioning, a model's ability to bridge visual content to meaningful language representations is critical. CLIP's inherent cross-modal alignment has made it a central model for such endeavors." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 205, + 294, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 205, + 294, + 326 + ], + "spans": [ + { + "bbox": [ + 55, + 205, + 294, + 326 + ], + "type": "text", + "content": "However, a persistent challenge within CLIP is the modality gap between its vision and text embeddings, a structural separation within the embedding space that limits the effectiveness of cross-modal alignment [17, 45]. This gap, caused by the contrastive learning dynamics and model initialization, results in visual and textual representations occupying distinct regions within the shared embedding space. Consequently, this gap restricts direct transfer and alignment for zero-shot captioning, where precise semantic alignment is essential for high-quality caption generation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 327, + 294, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 294, + 446 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 294, + 446 + ], + "type": "text", + "content": "Previous zero-shot image captioning methods have addressed the modality gap challenge through various techniques. Notably, noise injection methods [28, 45] seek to enhance the decoder's robustness by introducing Gaussian noise into text embeddings during training, thereby promoting generalization across the inherent discrepancies between vision and text embeddings. However, these approaches do not fundamentally align vision and text embeddings, leaving modality mismatches that can hinder zero-shot performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 449, + 294, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 294, + 604 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 294, + 604 + ], + "type": "text", + "content": "On the other hand, recent advancements in diffusion-based models have shown considerable promise within multi-modal domains, particularly in tasks such as image synthesis and text-guided image manipulation [5, 21, 27]. At the core of these advancements is Denoising Diffusion Probabilistic Models (DDPM) [10], which iteratively refine noisy vectors to capture the intrinsic data distribution with high fidelity. This ability to model complex, nuanced distributions renders diffusion models powerful tools for novel applications across a range of multi-modal settings. However, their application in bridging the modality gap for zero-shot image captioning remains an area yet to be thoroughly explored." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 605, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 294, + 713 + ], + "type": "text", + "content": "In this paper, we introduce Diffusion Bridge, an innovative approach that leverages diffusion models to directly address the modality gap within CLIP's embedding space for zero-shot image captioning. Diffusion Bridge models the distribution of text embeddings through the diffusion model, effectively capturing the intricate structure of the text embedding space. Given that paired vision and text embeddings remain relatively close despite their inherent differences, our method strategically inserts vision embed" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 133 + ], + "type": "text", + "content": "dings at an intermediate step of the diffusion reverse process. The gradual refinement of reverse process allows vision embeddings to transform into text-like representations, incrementally reducing residual discrepancies stemming from the intrinsic characteristics of each modality." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 133, + 554, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 554, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 554, + 251 + ], + "type": "text", + "content": "Through comprehensive experiments, we demonstrate that Diffusion Bridge significantly reduces the modality gap, resulting in enhanced cross-modal similarity and improved captioning performance. Importantly, Diffusion Bridge achieves robust zero-shot captioning without reliance on large memory banks or external knowledge modules. Our findings indicate that Diffusion Bridge not only advances zero-shot captioning but also opens novel potentials for the application of diffusion models in cross-modal alignment tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 262, + 400, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 262, + 400, + 275 + ], + "spans": [ + { + "bbox": [ + 314, + 262, + 400, + 275 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 282, + 554, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 282, + 554, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 282, + 554, + 474 + ], + "type": "text", + "content": "Multi-modal contrastive learning has been fundamental in aligning visual and textual data within a shared embedding space, enabling cross-modal applications without paired data. Pioneering frameworks such as CLIP [31] and Image-Bind [8] achieve this alignment by training on large-scale image-text datasets, aiming to encode paired data from different modalities closer together in the embedding space. However, the modality gap [17], which keeps visual and textual embeddings in distinct regions, remains a persistent challenge. This separation limits the interchangeability of embeddings and diminishes the effectiveness of zero-shot multi-modal tasks. Studies such as Mind the Gap [17] and C3 [45] provide an in-depth examination of the modality gap in multi-modal models like CLIP, emphasizing that the contrastive loss function and model initialization result in the separation between image and text embeddings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 475, + 554, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 475, + 554, + 570 + ], + "spans": [ + { + "bbox": [ + 313, + 475, + 554, + 570 + ], + "type": "text", + "content": "Efforts to bridge this gap in zero-shot image captioning can be categorized into three main strategies: Late-Guidance Decoding, Early-Guidance Decoding, and Keywords-Guidance Decoding. These approaches represent parallel research directions that tackle zero-shot captioning challenges from distinct perspectives. Our work contributes specifically to the Early-Guidance Decoding category." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 570, + 554, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 554, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 554, + 665 + ], + "type": "text", + "content": "Late-Guidance Decoding: Methods such as MAGIC [34] and ZeroCap [36] apply guidance at a later stage of the decoding process, often by leveraging language models to generate captions that reflect visual content. While this strategy can produce visually grounded captions, it typically relies on indirect adjustments and does not fully address the modality gap between vision and text embeddings, resulting in less precise alignment." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 553, + 713 + ], + "type": "text", + "content": "Early-Guidance Decoding: Several studies [9, 15, 28, 45] aim to address the modality gap earlier in the caption generation process by employing techniques such as noise-injected decoder training and memory-based simi" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 313, + 757 + ], + "type": "text", + "content": "4051" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "content": "larity matching. For instance, CapDec [28] and C3 [45] employ noise injection to improve the decoder's robustness to variability in vision embeddings, helping it generalize across the modality gap. DeCap [15] takes a different approach by using a memory-based projection method that maps vision embeddings into the text space through similarity-based projections. However, it requires a large memory bank, which can introduce computational challenges and limit scalability. Additionally, the direct projection relies on similarity matching, which may lack adaptability for handling inputs beyond the training distribution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 204, + 294, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 204, + 294, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 204, + 294, + 323 + ], + "type": "text", + "content": "Keywords-Guidance Decoding: Approaches such as ViECap [7] and MeaCap [43] focus on enhancing caption relevance and specificity by extracting entities or keywords from visual content to guide the caption generation process. Unlike Early-Guidance Decoding, these methods do not address the modality gap at the embedding level but instead operate at the sentence level, using keyword-based prompts to improve linguistic and contextual alignment. This approach is particularly beneficial for out-of-domain scenarios through explicit guidance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 323, + 295, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 323, + 295, + 550 + ], + "spans": [ + { + "bbox": [ + 55, + 323, + 295, + 550 + ], + "type": "text", + "content": "Diffusion Models for Multi-Modal Generation. Recent advancements in diffusion models have had a substantial impact on generative modeling, particularly in tasks such as image synthesis and text generation [14, 16, 27, 44]. DDPM is prominent in this field, iteratively refining Gaussian noise to produce structured, high-quality outputs. Extensions such as Guided Diffusion [25] introduce controlled generation, enabling zero-shot and conditional tasks with enhanced specificity. In image captioning, diffusion models like SCD-Net [22] and Prefix-Diffusion [20] enhance alignment between image embeddings and textual descriptions, improving caption accuracy and diversity. SCD-Net uses semantic priors for better visual-linguistic coherence, while Prefix-Diffusion employs image-derived prefix embeddings to generate varied and contextually rich captions. Despite these advancements, the potential of diffusion models to directly address the modality gap in embedding alignment tasks, particularly in zero-shot captioning with CLIP, remains underexplored." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 562, + 111, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 111, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 111, + 574 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 582, + 294, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 294, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 294, + 700 + ], + "type": "text", + "content": "Diffusion Bridge presents an innovative solution to address the modality gap by utilizing only text embeddings. Our approach is motivated by the analysis in C3 [45], which reveals that even paired vision and text embeddings, while close, still exhibit a modality gap. This gap arises due to stable regions produced by the contrastive loss, resulting in a constant offset, or 'alignment noise', between embeddings from different modalities. This alignment noise persists in the shared embedding space and can be approximated as Gaussian noise." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 701, + 294, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 701, + 294, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 701, + 294, + 713 + ], + "type": "text", + "content": "Our proposed method employs the diffusion model's" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": "dual strengths: its capacity as a generative model to learn the intrinsic distribution of text embeddings and its ability to incorporate conditional inputs during the reverse process." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 108, + 553, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 108, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 108, + 553, + 228 + ], + "type": "text", + "content": "By training the diffusion model on text embeddings, the model learns the distributional characteristics of the text embedding space. During inference, we initiate the reverse diffusion process with vision embeddings at an intermediate step. Guided by the learned text distribution, the diffusion model progressively refines these vision embeddings into text-like representations. This conditioned reverse mapping effectively minimizes residual discrepancies, aligning vision embeddings more closely with the text embedding space and thereby mitigating the modality gap." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 228, + 553, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 287 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 287 + ], + "type": "text", + "content": "In the following sections, we describe the mechanisms and architecture of Diffusion Bridge, detailing each component's role in enabling efficient and scalable zero-shot captioning. Fig. 2 visualizes the overall pipeline of Diffusion Bridge." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 293, + 553, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 293, + 553, + 317 + ], + "spans": [ + { + "bbox": [ + 313, + 293, + 553, + 317 + ], + "type": "text", + "content": "3.1. Background on Denoising Diffusion Probabilistic Models" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 323, + 553, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 323, + 553, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 323, + 553, + 407 + ], + "type": "text", + "content": "DDPM is the generative model that creates data by iteratively refining Gaussian noise through a controlled denoising process. The model learns a sequence of transformations that progressively reduces noise in sampled data to generate structured representations. DDPM operates in two main stages: the forward diffusion process and the reverse diffusion process." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "type": "text", + "content": "Forward Diffusion Process: Starting from an initial sample " + }, + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "type": "text", + "content": ", the forward process generates a series of increasingly noisy samples " + }, + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "type": "text", + "content": " by applying a Gaussian noise schedule over " + }, + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 407, + 553, + 455 + ], + "type": "text", + "content": " time steps. This process is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 347, + 461, + 553, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 461, + 553, + 475 + ], + "spans": [ + { + "bbox": [ + 347, + 461, + 553, + 475 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}\\right) := \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {z} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {1}", + "image_path": "f82afa4d90dfa788c2f48ade558395b49127f8e325d69f9fd162077f7a2b9d1d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 482, + 553, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 482, + 553, + 529 + ], + "spans": [ + { + "bbox": [ + 313, + 482, + 553, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 482, + 553, + 529 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 313, + 482, + 553, + 529 + ], + "type": "text", + "content": " represents a variance schedule that determines the amount of noise added at each step. In the last step, the data " + }, + { + "bbox": [ + 313, + 482, + 553, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 313, + 482, + 553, + 529 + ], + "type": "text", + "content": " becomes nearly indistinguishable from pure Gaussian noise " + }, + { + "bbox": [ + 313, + 482, + 553, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T\\sim \\mathcal{N}(0,\\mathbf{I})" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "text", + "content": "By defining " + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "inline_equation", + "content": "\\alpha_{t} := 1 - \\beta_{t}" + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} := \\prod_{s=1}^{t} \\alpha_{s}" + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "text", + "content": ", the forward process from " + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t}" + }, + { + "bbox": [ + 313, + 529, + 553, + 554 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 353, + 560, + 553, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 560, + 553, + 574 + ], + "spans": [ + { + "bbox": [ + 353, + 560, + 553, + 574 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right). \\tag {2}", + "image_path": "987a42d5084251a152ec0c33cb9f1383c59ecf79da002e91079cd11b8a34e13c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 580, + 553, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 580, + 553, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 580, + 553, + 628 + ], + "type": "text", + "content": "Reverse Diffusion Process: A network estimates the mean " + }, + { + "bbox": [ + 313, + 580, + 553, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{\\theta}(\\mathbf{z}_t,t)" + }, + { + "bbox": [ + 313, + 580, + 553, + 628 + ], + "type": "text", + "content": " of the distribution " + }, + { + "bbox": [ + 313, + 580, + 553, + 628 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}_{t - 1}\\mid \\mathbf{z}_t)" + }, + { + "bbox": [ + 313, + 580, + 553, + 628 + ], + "type": "text", + "content": " in the reverse process. This process denoises the data step-by-step to generate structured samples from noise, defined as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 348, + 634, + 553, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 634, + 553, + 648 + ], + "spans": [ + { + "bbox": [ + 348, + 634, + 553, + 648 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N} \\left(\\mathbf {z} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {z} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {3}", + "image_path": "3cb2dc3d958d4471e1cd3263992f8dfc27a00a003700b965c420257e8c886b97.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 654, + 553, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 678 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 678 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 654, + 553, + 678 + ], + "type": "inline_equation", + "content": "\\sigma_t^2" + }, + { + "bbox": [ + 313, + 654, + 553, + 678 + ], + "type": "text", + "content": " represents time-dependent variance. The predicted mean " + }, + { + "bbox": [ + 313, + 654, + 553, + 678 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{\\theta}(z_{t},t)" + }, + { + "bbox": [ + 313, + 654, + 553, + 678 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 341, + 685, + 553, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 685, + 553, + 711 + ], + "spans": [ + { + "bbox": [ + 341, + 685, + 553, + 711 + ], + "type": "interline_equation", + "content": "\\mu_ {\\theta} (\\mathbf {z} _ {t}, t) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {z} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {z} _ {t}, t)\\right), \\tag {4}", + "image_path": "a59515abb12fafdb74866de27b1028ba9d757ea2047300b496bf8b3dc00b0527.jpg" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4052" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 555, + 365 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 555, + 365 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 555, + 365 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 555, + 365 + ], + "type": "image", + "image_path": "9c372eea1e5987f54b99b1be6fcb43e0bb0e1affa64be2cafc2e423a1a8f45eb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 374, + 555, + 441 + ], + "lines": [ + { + "bbox": [ + 54, + 374, + 555, + 441 + ], + "spans": [ + { + "bbox": [ + 54, + 374, + 555, + 441 + ], + "type": "text", + "content": "Figure 2. Detailed model pipeline of Diffusion Bridge, illustrating the three stages of the method. First, the diffusion model is trained exclusively on text embeddings, capturing their intrinsic distribution. Next, the decoder is trained using diffusion-augmented text embeddings, preparing it to handle variations during caption generation. In the final inference stage, vision embeddings are mapped into the text embedding space via the reverse diffusion process and then the decoder generates a caption with the transformed embedding. This pipeline enables zero-shot caption generation by aligning vision embeddings with the text distribution, achieving effective cross-modal alignment without relying on paired image-text data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 462, + 295, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 295, + 473 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 295, + 473 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 462, + 295, + 473 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(z_t,t)" + }, + { + "bbox": [ + 55, + 462, + 295, + 473 + ], + "type": "text", + "content": " represents the noise predicted by the model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 474, + 296, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 296, + 521 + ], + "type": "text", + "content": "To train the diffusion model, the objective is to minimize the difference between the true noise " + }, + { + "bbox": [ + 55, + 474, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 474, + 296, + 521 + ], + "type": "text", + "content": " and the predicted noise " + }, + { + "bbox": [ + 55, + 474, + 296, + 521 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t,t)" + }, + { + "bbox": [ + 55, + 474, + 296, + 521 + ], + "type": "text", + "content": " across all diffusion steps, which is expressed by the following loss function:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 529, + 296, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 529, + 296, + 561 + ], + "spans": [ + { + "bbox": [ + 55, + 529, + 296, + 561 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {D D P M}} (\\theta) = \\mathbb {E} _ {t, \\mathbf {z} _ {0}, \\epsilon} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) \\right\\| ^ {2} \\right], \\tag {5}", + "image_path": "b1baf60b3ad5f5d052beb3c14a96db18e29313f7b46f80a077476862f306b4d7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 569, + 296, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 569, + 296, + 618 + ], + "spans": [ + { + "bbox": [ + 55, + 569, + 296, + 618 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 569, + 296, + 618 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 569, + 296, + 618 + ], + "type": "text", + "content": " is standard Gaussian noise, " + }, + { + "bbox": [ + 55, + 569, + 296, + 618 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 55, + 569, + 296, + 618 + ], + "type": "text", + "content": ". This objective enables the model to accurately estimate the noise added at each diffusion step, allowing for precise reconstruction during the reverse process." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 624, + 273, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 273, + 637 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 273, + 637 + ], + "type": "text", + "content": "3.2. Diffusion Training with Text Embeddings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "After encoding the training text dataset into embeddings using the CLIP text encoder, several preprocessing steps are applied to condition the embeddings for diffusion model training. Initially, each text embedding, " + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{e}^{text}" + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": ", is an L2-normalized vector to ensure a consistent magnitude. Subsequently, following previous works [9, 28, 45], we subtract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 461, + 555, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 461, + 555, + 486 + ], + "spans": [ + { + "bbox": [ + 313, + 461, + 555, + 486 + ], + "type": "text", + "content": "the mean vector, " + }, + { + "bbox": [ + 313, + 461, + 555, + 486 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{e}}^{text}" + }, + { + "bbox": [ + 313, + 461, + 555, + 486 + ], + "type": "text", + "content": ", computed across the training set embeddings to center the embeddings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 486, + 554, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 554, + 570 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 554, + 570 + ], + "type": "text", + "content": "Following mean-centering, we apply a second normalization step to further enhance uniformity. However, we observe that the L2 normalized embeddings have a relatively low average scale, which may obscure the distinction between signal and noise during DDPM training. To address this, we amplify the embeddings by a scalar factor of " + }, + { + "bbox": [ + 313, + 486, + 554, + 570 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 486, + 554, + 570 + ], + "type": "text", + "content": ", yielding the final processed embedding:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 374, + 574, + 553, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 574, + 553, + 601 + ], + "spans": [ + { + "bbox": [ + 374, + 574, + 553, + 601 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {0} = C \\times \\frac {\\mathbf {e} ^ {t e x t} - \\bar {\\mathbf {e}} ^ {t e x t}}{\\left| \\left| \\mathbf {e} ^ {t e x t} - \\bar {\\mathbf {e}} ^ {t e x t} \\right| \\right| _ {2}}. \\tag {6}", + "image_path": "42cfcb3068a9950e15ea422bd8332b67d3dbae1c074b49b1ad5c48d5e3ab1b8c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": "The model trained with this processed set of embeddings, " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": ", through Eq. 5, allows the diffusion model to learn the score function of the text embedding distribution [33], denoted as " + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{z}^{\\mathrm{ext}}}\\log p(\\mathbf{z}^{\\mathrm{ext}})" + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": ". This score function encodes gradient directions toward high-density regions of the text manifold. While the model is trained exclusively on text, the learned text manifold serves as a semantic prior that defines plausible regions for cross-modal alignment. Following findings in C3 [45], the modality gap between vision and" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4053" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "text embeddings in CLIP is approximated as Gaussian noise " + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "inline_equation", + "content": "(\\mathbf{z}^{\\mathrm{vision}} = \\mathbf{z}^{\\mathrm{text}} + \\epsilon, \\epsilon \\sim \\mathcal{N}(0, \\sigma^2 \\mathbf{I}))" + }, + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": ". During inference, the score function guides vision embeddings along the gradient of the text distribution, iteratively shifting them toward the nearest high-density regions of the text manifold. This process effectively denoises the modality gap, aligning vision embeddings with the text manifold." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 164, + 162, + 177 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 164, + 162, + 177 + ], + "spans": [ + { + "bbox": [ + 55, + 164, + 162, + 177 + ], + "type": "text", + "content": "3.3. Decoder Training" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 182, + 294, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 182, + 294, + 230 + ], + "spans": [ + { + "bbox": [ + 55, + 182, + 294, + 230 + ], + "type": "text", + "content": "The decoder in Diffusion Bridge is trained exclusively on text embeddings to generate coherent captions, using these embeddings as prefix inputs with an autoregressive loss. This section details the training process of the decoder." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 230, + 295, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 230, + 295, + 410 + ], + "spans": [ + { + "bbox": [ + 55, + 230, + 295, + 410 + ], + "type": "text", + "content": "Diffusion-Augmented Text Embeddings: The text embeddings are applied centering and normalization, following the approach used in C3 [45]. While it is possible to train the decoder directly on these preprocessed text embeddings, it is essential to account for the non-unique mapping between vision and text embeddings. The inherent variability can arise in reverse-diffused vision embeddings, introducing subtle randomness to the alignment. Specifically, if a text embedding undergoes forward diffusion to an intermediate step and is then reverse-diffused, the resulting embedding may not perfectly match the original due to the randomness. To prepare the decoder to handle these practical variations, we incorporate diffusion-augmented embeddings into the training data. The augmentation process involves two main steps." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "type": "text", + "content": "For each text embedding " + }, + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "type": "text", + "content": ", we select an intermediate step " + }, + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "type": "inline_equation", + "content": "t = A" + }, + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "type": "inline_equation", + "content": "(T > A > 0)" + }, + { + "bbox": [ + 55, + 410, + 295, + 445 + ], + "type": "text", + "content": " and apply the forward diffusion process, producing a noisy version:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 89, + 456, + 295, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 456, + 295, + 469 + ], + "spans": [ + { + "bbox": [ + 89, + 456, + 295, + 469 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {z} _ {A} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {A}; \\sqrt {\\bar {\\alpha} _ {A}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {A}) \\mathbf {I}\\right). \\tag {7}", + "image_path": "593916ca6e31c1c688a53bdd15977221abf48e08a24194971c0d3f6f992795dc.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 479, + 295, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 479, + 295, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 479, + 295, + 514 + ], + "type": "text", + "content": "Then we denoise the noise vector, " + }, + { + "bbox": [ + 55, + 479, + 295, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_A" + }, + { + "bbox": [ + 55, + 479, + 295, + 514 + ], + "type": "text", + "content": ", through the reverse process to obtain the augmented embedding " + }, + { + "bbox": [ + 55, + 479, + 295, + 514 + ], + "type": "inline_equation", + "content": "\\mathrm{e}^{\\mathrm{aug}}" + }, + { + "bbox": [ + 55, + 479, + 295, + 514 + ], + "type": "text", + "content": ". For faster inference, we utilized DDIM [32] for denoising." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 515, + 295, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 515, + 295, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 515, + 295, + 597 + ], + "type": "text", + "content": "By utilizing diffusion-augmented embeddings " + }, + { + "bbox": [ + 55, + 515, + 295, + 597 + ], + "type": "inline_equation", + "content": "\\mathbf{e}^{\\mathrm{aug}}" + }, + { + "bbox": [ + 55, + 515, + 295, + 597 + ], + "type": "text", + "content": " as prefix inputs, we train the decoder to be resilient to the inherent randomness that arises from the fact that a single vision embedding does not map uniquely to a specific text embedding. The decoder learns to predict the caption y based on these augmented embeddings, using the autoregressive loss:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 606, + 295, + 638 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 606, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 295, + 638 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {A R}} = - \\sum_ {t = 1} ^ {L} \\log p \\left(y _ {t} \\mid y _ {< t}, \\mathbf {e} ^ {\\text {a u g}}\\right). \\tag {8}", + "image_path": "ea867ccb78a8d1b113e22f8d5fe0e482c52770d82e4477c1bf95b097ef7432f1.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 647, + 161, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 647, + 161, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 647, + 161, + 659 + ], + "type": "text", + "content": "3.4. Inference Process" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": "During inference, the vision embedding, " + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{e}^{img}" + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": ", is strategically introduced into the reverse diffusion process at a predefined intermediate timestep " + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "inline_equation", + "content": "t = M" + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "inline_equation", + "content": "T > M > 0" + }, + { + "bbox": [ + 55, + 665, + 295, + 714 + ], + "type": "text", + "content": ". This conditioned reverse process leverages our core insight:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": "while vision and text embeddings are inherently different, they remain relatively proximate in the shared embedding space. By initiating the reverse diffusion from this intermediate step " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": ", we enable the model to map the vision embedding into a text-like vision embedding, " + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{e}}^{\\mathrm{img}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 156 + ], + "type": "text", + "content": ", that closely aligns with the learned distribution of text embeddings. We refer to this alignment process as diffusion-bridging." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 159, + 553, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 159, + 553, + 232 + ], + "spans": [ + { + "bbox": [ + 313, + 159, + 553, + 232 + ], + "type": "text", + "content": "The transformed vision embedding, " + }, + { + "bbox": [ + 313, + 159, + 553, + 232 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{e}}^{\\mathrm{img}}" + }, + { + "bbox": [ + 313, + 159, + 553, + 232 + ], + "type": "text", + "content": ", is then fed as a prefix input to the decoder trained on text embeddings. This setup ensures that the decoder receives an embedding in a familiar distribution, enhancing its capacity to generate accurate and contextually relevant captions without the need for paired data." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 252, + 395, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 252, + 395, + 266 + ], + "spans": [ + { + "bbox": [ + 313, + 252, + 395, + 266 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 276, + 554, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 554, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 554, + 372 + ], + "type": "text", + "content": "In this section, we evaluate the effectiveness of Diffusion Bridge in mitigating the modality gap for zero-shot image captioning. Our experiments aim to assess how well our method aligns vision embeddings with the text embedding space. We conduct evaluations on standard image captioning datasets under both in-domain and cross-domain setups to comprehensively test the generalization capabilities of Diffusion Bridge." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 375, + 554, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 375, + 554, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 375, + 554, + 483 + ], + "type": "text", + "content": "Datasets and Metrics: We assess Diffusion Bridge on two widely used image captioning datasets: MSCOCO [4, 19] and Flickr30K [39]. For dataset partitioning, we utilize the standard Karpathy split [12], which is commonly adopted in captioning benchmarks. For quantitative evaluation, we employ a suite of established metrics to gauge caption quality, including BLEU (B@n) [29], METEOR (M) [2], ROUGE-L (R-L) [18], CIDEr (C) [37], and SPICE (S) [1]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": "Implementation details: For the DDPM training, we employ a 1-D UNet architecture with four layers, where each layer successively doubles in dimensionality. The model is trained using a batch size of 64, a learning rate of " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "8 \\times 10^{-5}" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": ", and a total of 3,000,000 steps. The number of diffusion timesteps is set to " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "T = 1000" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": " and we set " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": " in Eqt. 6 as 5 in all experiments. For experiments on the MSCOCO dataset, we set the intermediate and augmentation steps to " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "M = 600" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "A = 400" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": ", respectively, whereas for Flickr30K, these values are configured to " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "M = 400" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "A = 300" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": ". For decoder training, we use CLIP-ViT-B/32 [31] as the encoding backbone and adopt GPT-2 [30] as the base decoder. The prefix projector consists of two fully connected layers with a hidden dimensionality of 768. The learnable soft prompts are defined with a length of 10. The projection layer projects the CLIP embedding from 512 to 768 dimensions. Training is conducted for 10 epochs with a batch size of 40 and a learning rate of " + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-5}" + }, + { + "bbox": [ + 313, + 486, + 555, + 713 + ], + "type": "text", + "content": ", using the AdamW optimizer following the setup in [28, 45]." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4054" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 293, + 259 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 293, + 259 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 293, + 259 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 293, + 259 + ], + "type": "image", + "image_path": "a45e1bd1d8f1fb9e7d36a21587608261dfa02d12c686c7e5c8282d786f20867f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "lines": [ + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "spans": [ + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "type": "text", + "content": "Figure 3. UMAP visualization of COCO validation set embeddings. Red points represent image embeddings " + }, + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{e}}^{\\mathrm{img}}" + }, + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "type": "text", + "content": ", blue points denote text embeddings " + }, + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{e}}^{\\mathrm{text}}" + }, + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "type": "text", + "content": ", and green points show mapped embeddings " + }, + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{e}}^{\\mathrm{img}}" + }, + { + "bbox": [ + 55, + 269, + 295, + 324 + ], + "type": "text", + "content": " produced by Diffusion Bridge from image embeddings." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 346, + 211, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 346, + 211, + 360 + ], + "spans": [ + { + "bbox": [ + 55, + 346, + 211, + 360 + ], + "type": "text", + "content": "4.1. Evaluation on Modality Gap" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 365, + 295, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 295, + 448 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 295, + 448 + ], + "type": "text", + "content": "In the following sections, we evaluate the effectiveness of Diffusion Bridge in reducing the modality gap. Specifically, we conduct UMAP-based visualization and similarity assessments on embeddings from the MSCOCO validation set. To facilitate this analysis, we denote " + }, + { + "bbox": [ + 55, + 365, + 295, + 448 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{e}}" + }, + { + "bbox": [ + 55, + 365, + 295, + 448 + ], + "type": "text", + "content": " as the centered embedding, representing aligned embeddings in a unified space." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "type": "text", + "content": "Visual Experiment on Modality Gap. To evaluate the effectiveness of Diffusion Bridge in reducing the modality gap, we conducted a UMAP [24] visualization experiment using the validation set of the COCO dataset. This visualization provides insight into the alignment of vision embeddings with text embeddings in a shared embedding space. Fig. 3 displays three types of embeddings: centered image embeddings " + }, + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{e}}^{\\mathrm{img}}" + }, + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "type": "text", + "content": " (red), centered text embeddings " + }, + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{e}}^{\\mathrm{text}}" + }, + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "type": "text", + "content": " (blue), and diffusion-mapped embeddings from image embeddings " + }, + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{e}}^{\\mathrm{img}}" + }, + { + "bbox": [ + 55, + 449, + 295, + 664 + ], + "type": "text", + "content": " (green). In Fig. 3, distinct clusters for image embeddings and text embeddings illustrate the inherent modality gap between visual and textual data. However, the overlap of mapped embeddings to the text cluster suggests that Diffusion Bridge significantly reduces the modality gap. This alignment allows the decoder, which is trained in text embeddings, to effectively process text-like vision embeddings as inputs, thereby enhancing the model's captioning performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "content": "Cosine Similarity Analysis of Modality Alignment. In the previous analysis, we visually examine the reduction in the modality gap. Herein, we use cosine similarity to provide a more quantitative assessment of this reduction. Tab." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 322, + 70, + 547, + 157 + ], + "blocks": [ + { + "bbox": [ + 322, + 70, + 547, + 157 + ], + "lines": [ + { + "bbox": [ + 322, + 70, + 547, + 157 + ], + "spans": [ + { + "bbox": [ + 322, + 70, + 547, + 157 + ], + "type": "table", + "html": "
    Comparison PairCosine Similarity
    EmbeddingProjector
    (a) e text · e img(∼)0.3060.714
    (b) e text · {e text + N(0,0.016)}(∼)0.2350.684
    (c) e text · e text(∼)0.6520.833
    (d) e text · e img(∼)0.6060.826
    (e) e text · e text(∼)0.0030.588
    (f) e text · e img(∼)0.0520.604
    ", + "image_path": "40119153db0bfb57d543ba727e05b357caddaead02a7a134586f0aeecf50b1f3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 165, + 553, + 220 + ], + "lines": [ + { + "bbox": [ + 313, + 165, + 553, + 220 + ], + "spans": [ + { + "bbox": [ + 313, + 165, + 553, + 220 + ], + "type": "text", + "content": "Table 1. Average cosine similarity scores for various embedding pairs. " + }, + { + "bbox": [ + 313, + 165, + 553, + 220 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 313, + 165, + 553, + 220 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 165, + 553, + 220 + ], + "type": "inline_equation", + "content": "\\nVdash" + }, + { + "bbox": [ + 313, + 165, + 553, + 220 + ], + "type": "text", + "content": " denote corresponding pairs and non-corresponding pairs. 'Embedding' shows the direct similarity between embeddings, while 'Projector' represents the similarity of projected embeddings through a prefix projector." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 243, + 553, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 553, + 290 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 553, + 290 + ], + "type": "text", + "content": "1 presents cosine similarity scores for different embedding sets, offering a clearer view of how effectively Diffusion Bridge brings vision embeddings closer to text embeddings in the shared space." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 292, + 553, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 292, + 553, + 399 + ], + "spans": [ + { + "bbox": [ + 313, + 292, + 553, + 399 + ], + "type": "text", + "content": "(a) shows the similarity between text and image embeddings within the paired set, which is only 0.306. Although a 0.3 cosine similarity can indicate a certain level of similarity in high-dimensional spaces [17], it remains noticeably lower compared to the similarity between text embeddings for the same image in (c), which has a much higher score of 0.652. This discrepancy highlights the inherent modality gap between visual and textual embeddings, which can hinder zero-shot image captioning performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 401, + 553, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 401, + 553, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 401, + 553, + 555 + ], + "type": "text", + "content": "(b) represents the cosine similarity between a text embedding and a noise-injected version of itself, with a similarity score of 0.235. This setup mirrors the noise injection process used in models like CapDec [28] and C3 [45]. Adding Gaussian noise creates a broader distribution around the original text embedding, allowing the decoder to generalize by encompassing the range where vision embeddings are likely to fall. This approach helps the decoder manage variability in vision embeddings, supporting zero-shot captioning. However, noise injection may also introduce certain limitations. If the noise range is too broad, captions could become overly generic, lacking specific details. Consequently, finding an optimal level of noise is crucial." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 557, + 553, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 553, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 553, + 652 + ], + "type": "text", + "content": "(d) examines the similarity between a text embedding and its paired vision embedding mapped by Diffusion Bridge. The similarity score of 0.606 shows a substantial increase from the original score of 0.306 in (a), approaching the high similarity observed within the text embeddings in the paired set in (c). This result demonstrates that Diffusion Bridge effectively reduces the modality gap, aligning vision embeddings closer to the paired text embeddings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": "The effect of the prefix projector is also noteworthy. Across all embedding sets, we observe a trend similar to that of the plain embeddings; however, the absolute similarity scores increase substantially. For instance, the similarity between vision and text embeddings in the paired set" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4055" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "content": "rises from 0.306 to 0.714 when passed through the projector. This boost in similarity helps reduce the modality gap and facilitates zero-shot captioning by making embeddings more compatible. However, as seen in (e) and (f), the projector also increases the similarity between embeddings in the unpaired set (0.003 to 0.588 for text and unpaired text, and 0.052 to 0.604 for text and unpaired mapped vision embeddings). This unintended increase can lead to hallucination issues, where the model generates plausible but irrelevant captions that do not accurately reflect the image content." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 205, + 294, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 205, + 294, + 301 + ], + "spans": [ + { + "bbox": [ + 55, + 205, + 294, + 301 + ], + "type": "text", + "content": "In contrast, Diffusion Bridge maintains a selective alignment, as shown by (c) and (d). It aligns paired vision and text embeddings to a level close to that of paired text embeddings within the paired set (0.833 in (c) vs. 0.826 in (d)). This selective mapping ensures that Diffusion Bridge effectively reduces the modality gap without indiscriminately increasing similarity, thereby avoiding the hallucination problem and enabling accurate cross-modal alignment." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 301, + 294, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 301, + 294, + 384 + ], + "spans": [ + { + "bbox": [ + 55, + 301, + 294, + 384 + ], + "type": "text", + "content": "In summary, these cosine similarity scores confirm that Diffusion Bridge significantly reduces the modality gap, aligning vision embeddings closely with their corresponding text embeddings while preserving distinctions within the unpaired set. This selective alignment, achieved through Diffusion Bridge, enhances zero-shot image captioning performance by reducing the risk of hallucination." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 396, + 211, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 211, + 408 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 211, + 408 + ], + "type": "text", + "content": "4.2. Zero-shot Image Captioning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 413, + 294, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 413, + 294, + 509 + ], + "spans": [ + { + "bbox": [ + 55, + 413, + 294, + 509 + ], + "type": "text", + "content": "In-Domain Captioning. Tab. 2 presents the indomain zero-shot image captioning performance of Diffusion Bridge compared to existing methods on the MSCOCO and Flickr30K datasets. On MSCOCO, Diffusion Bridge achieves state-of-the-art results across all metrics, demonstrating its effectiveness in aligning vision embeddings with the text space and generating accurate, contextually relevant captions for a large and diverse dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 295, + 713 + ], + "type": "text", + "content": "On the Flickr30K dataset, while Diffusion Bridge does not consistently achieve the highest score across all metrics, it performs competitively, securing the second-highest results in several categories. Due to the smaller size of the Flickr30K dataset, the diffusion model in Diffusion Bridge may not fully capture the intrinsic distribution of text embeddings, resulting in lower scores compared to MSCOCO. In contrast, methods like DeCap, which leverage a memory bank to access the entire training text dataset, gain a performance advantage on this relatively smaller dataset by retrieving relevant text embeddings. This memory-based similarity-matching mechanism allows DeCap to excel in capturing context, benefiting from direct references to memorized captions. Nonetheless, Diffusion Bridge achieves near state-of-the-art performance without relying on memory banks unlike DeCap, and MeaCap. Notably, Diffusion Bridge outperforms all methods except DeCap," + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 316, + 71, + 566, + 199 + ], + "blocks": [ + { + "bbox": [ + 316, + 71, + 566, + 199 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 566, + 199 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 566, + 199 + ], + "type": "table", + "html": "
    MethodB@1B@4MR-LCS
    ZeroCap [36]49.87.015.431.834.5-
    MAGIC [34]56.812.917.439.947.311.3
    ESPER [41]-21.921.9-78.2-
    CLIPRe [15]-4.613.3-25.69.2
    DeCap [15]-24.725.0-91.218.7
    CapDec [28]69.226.425.151.891.8-
    ViECap [7]-27.224.8-92.918.2
    MeaCap [43]-17.724.3-84.818.7
    C3 [45]71.027.725.052.093.318.3
    Diffusion Bridge72.328.725.152.496.418.7
    ", + "image_path": "cd40b19c30b7a9668db51e061a15added5a566d6e5e9b5c421f8163932e5bed4.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 316, + 220, + 566, + 328 + ], + "blocks": [ + { + "bbox": [ + 417, + 201, + 463, + 210 + ], + "lines": [ + { + "bbox": [ + 417, + 201, + 463, + 210 + ], + "spans": [ + { + "bbox": [ + 417, + 201, + 463, + 210 + ], + "type": "text", + "content": "(a) MSCOCO" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 220, + 566, + 328 + ], + "lines": [ + { + "bbox": [ + 316, + 220, + 566, + 328 + ], + "spans": [ + { + "bbox": [ + 316, + 220, + 566, + 328 + ], + "type": "table", + "html": "
    MethodB@1B@4MR-LCS
    ZeroCap [36]44.75.411.827.316.8-
    MAGIC [34]44.56.413.131.620.4-
    CLIPRe [15]-9.818.2-31.712.0
    DeCap [15]-21.221.8-56.715.2
    CapDec [28]55.517.720.027.339.1-
    ViECap [7]-21.420.1-47.913.6
    MeaCap [43]-15.320.6-50.214.5
    Diffusion Bridge66.921.421.146.853.014.5
    ", + "image_path": "523747a62491283bae4d785acd06974831a42bdf636593ffce2ea08a95405c6e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 417, + 329, + 463, + 338 + ], + "lines": [ + { + "bbox": [ + 417, + 329, + 463, + 338 + ], + "spans": [ + { + "bbox": [ + 417, + 329, + 463, + 338 + ], + "type": "text", + "content": "(b) Flickr30K" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 348, + 555, + 393 + ], + "lines": [ + { + "bbox": [ + 313, + 348, + 555, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 348, + 555, + 393 + ], + "type": "text", + "content": "Table 2. Performance comparison on (a) MSCOCO and (b) Flickr30K datasets. The metrics include BLEU@1 (B@1), BLEU@4 (B@4), METEOR (M), ROUGE-L (R-L), CIDEr (C), and SPICE (S)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 415, + 553, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 415, + 553, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 415, + 553, + 449 + ], + "type": "text", + "content": "demonstrating its effectiveness and efficiency in zero-shot settings by achieving competitive results without additional resources." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "text", + "content": "Cross-Domain Captioning. Tab. 3 presents the cross-domain captioning performance of Diffusion Bridge in comparison to other methods on the MSCOCO and Flickr30K test sets. In the MSCOCO " + }, + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "text", + "content": " Flickr30K setting, Diffusion Bridge demonstrates performance on par with other leading methods, achieving the highest scores in BLEU@4 and METEOR, as well as the second-highest scores in CIDEr and SPICE. This competitive performance on a large, diverse dataset like MSCOCO underscores the robustness of our approach, as it effectively learns generalized representations that transfer well to smaller, cross-domain datasets. In the Flickr30K " + }, + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 313, + 450, + 555, + 715 + ], + "type": "text", + "content": " MSCOCO setting, Diffusion Bridge continues to deliver comparable performance, though it falls behind methods such as ViECAP in CIDEr and SPICE—metrics that capture fine-grained linguistic and content alignment. This slight gap suggests that the use of entity-driven hard prompts, as employed by ViECap and MeaCap, may provide an advantage in maintaining relevance and contextual accuracy during out-of-domain transfers. Nevertheless, Diffusion Bridge achieves comparable results in BLEU@4 and METEOR, demonstrating that its diffusion-based alignment can generalize" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4056" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 306, + 144 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 306, + 144 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 306, + 144 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 306, + 144 + ], + "type": "table", + "html": "
    MethodMSCOCO → Flickr30KFlickr30K → MSCOCO
    B@4MCSB@4MCS
    DeCap [15]16.317.935.711.112.118.044.410.9
    CapDec [28]17.318.635.7-9.216.327.3-
    ViECap [7]17.418.038.411.212.618.354.212.5
    MeaCap [43]13.418.540.312.19.817.451.712.0
    Diffusion Bridge17.418.638.511.214.718.047.111.1
    ", + "image_path": "b9c5988b56617994530dca519bdab6f24fae01d616d9e777c839dd18f54701c0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 196, + 296, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 196, + 296, + 280 + ], + "spans": [ + { + "bbox": [ + 55, + 196, + 296, + 280 + ], + "type": "text", + "content": "without reliance on external modules such as grammar parser or visual-related large textual memory. Furthermore, as a complementary approach, Diffusion Bridge could be enhanced with entity-aware techniques in a 'plug-and-play' manner, further extending its adaptability and potential in diverse cross-domain applications. We conducted the 'plug-and-play' experiment in" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 288, + 154, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 288, + 154, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 288, + 154, + 300 + ], + "type": "text", + "content": "4.3. Ablation studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 305, + 295, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 305, + 295, + 353 + ], + "spans": [ + { + "bbox": [ + 55, + 305, + 295, + 353 + ], + "type": "text", + "content": "In this subsection, we conduct ablation studies to evaluate the influence of each component of Diffusion Bridge and the intermediate inference step. In all ablation studies, we experiment with our model on the COCO test set." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 354, + 295, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 354, + 295, + 473 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 295, + 473 + ], + "type": "text", + "content": "Effectiveness of each component. To examine the effectiveness of each component in Diffusion Bridge, we conduct an ablation study comparing three setups: (1) a baseline model trained solely on plain text embeddings, referred to as 'Plain Embed', corresponding to the baseline model " + }, + { + "bbox": [ + 55, + 354, + 295, + 473 + ], + "type": "inline_equation", + "content": "C_1^2" + }, + { + "bbox": [ + 55, + 354, + 295, + 473 + ], + "type": "text", + "content": " [45], (2) the same model with diffusion-bridging applied to the vision embeddings at inference, and (3) the model incorporating both diffusion-bridging and Diffusion-Augmented embeddings, denoted as " + }, + { + "bbox": [ + 55, + 354, + 295, + 473 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 55, + 354, + 295, + 473 + ], + "type": "text", + "content": " Diffusion-augmented'." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 474, + 295, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 474, + 295, + 557 + ], + "spans": [ + { + "bbox": [ + 55, + 474, + 295, + 557 + ], + "type": "text", + "content": "As shown in Tab 4, the performance improves significantly when diffusion-bridging is applied to the vision embeddings across all metrics. This improvement indicates that Diffusion Bridging effectively reduces the modality gap, aligning vision embeddings more closely with the text embedding space, which allows the decoder to generate more accurate and contextually relevant captions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 558, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 295, + 641 + ], + "type": "text", + "content": "With the addition of Diffusion-Augmented embeddings, the model achieves the highest scores across all metrics, demonstrating that the decoder effectively learns to bridge the modality gap. This augmentation not only allows the model to adapt to nuanced discrepancies between vision and text embeddings but also boosts the zero-shot captioning performance of Diffusion Bridge." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 295, + 714 + ], + "type": "text", + "content": "The Effect of Inference Steps. To effectively evaluate the modality gap reduction achieved by Diffusion Bridging, we used the baseline model described in Section 4.3.1, which is trained without diffusion-augmented text embeddings. Tab. 5 presents the performance of Diffusion Bridge across varying numbers of inference steps, illustrating how" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 322, + 70, + 547, + 114 + ], + "blocks": [ + { + "bbox": [ + 55, + 152, + 295, + 174 + ], + "lines": [ + { + "bbox": [ + 55, + 152, + 295, + 174 + ], + "spans": [ + { + "bbox": [ + 55, + 152, + 295, + 174 + ], + "type": "text", + "content": "Table 3. Cross-domain captioning performance on the MSCOCO test and Flickr30K test set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 70, + 547, + 114 + ], + "lines": [ + { + "bbox": [ + 322, + 70, + 547, + 114 + ], + "spans": [ + { + "bbox": [ + 322, + 70, + 547, + 114 + ], + "type": "table", + "html": "
    MethodB@1B@4MR-LCS
    Plain Embed [45]44.46.115.533.625.29.2
    + Diffusion-bridging70.225.424.350.588.818.2
    + Diffusion-augmented72.028.525.152.395.718.7
    ", + "image_path": "361bb49a6ca8786cccbd8008be142cee76230d3c7a49c9fdc5ca5634040aa52d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 322, + 166, + 547, + 236 + ], + "blocks": [ + { + "bbox": [ + 313, + 121, + 553, + 156 + ], + "lines": [ + { + "bbox": [ + 313, + 121, + 553, + 156 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 553, + 156 + ], + "type": "text", + "content": "Table 4. Ablation study evaluating the effects of Diffusion-bridging and Diffusion-augmented embeddings on zero-shot image captioning performance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 166, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 322, + 166, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 322, + 166, + 547, + 236 + ], + "type": "table", + "html": "
    Inference stepB@1B@4MR-LCS
    044.46.115.533.625.29.2
    20061.016.922.344.865.916.4
    40067.422.924.449.483.318.2
    60070.225.524.350.588.818.2
    80069.624.524.250.286.118.0
    ", + "image_path": "80b2670f5877f2e59431e2e91db276f9c649d9252e1603c0af6a131601be69c0.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 341, + 244, + 526, + 256 + ], + "lines": [ + { + "bbox": [ + 341, + 244, + 526, + 256 + ], + "spans": [ + { + "bbox": [ + 341, + 244, + 526, + 256 + ], + "type": "text", + "content": "Table 5. Ablation study on various inference steps." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 276, + 553, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 553, + 299 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 553, + 299 + ], + "type": "text", + "content": "different step sizes influence the alignment quality between modalities." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 300, + 553, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 553, + 419 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 553, + 419 + ], + "type": "text", + "content": "When inference steps are increased from 0 to 600, there is a clear improvement across all metrics. This trend suggests that a moderate number of steps helps to refine the vision embeddings, allowing them to align more closely with the text embedding space, which leads to improved caption quality. However, in the 800 step, performance declines slightly, as observed in metrics like B@1 and CIDEr. This decline indicates that excessive inference steps may add unnecessary noise, which disrupts the precision of the embedding mapping." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 420, + 554, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 420, + 554, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 420, + 554, + 514 + ], + "type": "text", + "content": "These results suggest that an optimal range of inference steps exists, balancing alignment quality and noise levels. Selecting an appropriate inference step size, such as 600 in this case, ensures effective modality alignment while avoiding over-processing that could negatively impact mapping accuracy. This balance is essential for leveraging Diffusion Bridge to achieve high-quality zero-shot image captioning results." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 526, + 388, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 526, + 388, + 538 + ], + "spans": [ + { + "bbox": [ + 313, + 526, + 388, + 538 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 545, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 554, + 713 + ], + "type": "text", + "content": "Diffusion Bridge introduces an innovative solution to the modality gap in CLIP-based zero-shot image captioning by leveraging diffusion models to bring vision embeddings into closer alignment with the text embedding space. Through the integration of diffusion-bridging and diffusion-augmented text embeddings, our approach effectively reduces the modality gap, achieving strong performance across multiple captioning metrics without reliance on noise injection, memory-intensive methods, or entity-driven hard prompts. Ablation studies further emphasize the significance of each component in Diffusion Bridge and intermediate diffusion steps in enhancing robustness and alignment precision. Our work opens up new directions for research and practical applications in cross-modal understanding." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4057" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 179, + 115, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 179, + 115, + 192 + ], + "spans": [ + { + "bbox": [ + 56, + 179, + 115, + 192 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 198, + 297, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 61, + 198, + 297, + 266 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 198, + 297, + 266 + ], + "spans": [ + { + "bbox": [ + 61, + 198, + 297, + 266 + ], + "type": "text", + "content": "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14100-14110, 2024. 2, 3, 7, 8" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 316, + 431, + 553, + 474 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 431, + 553, + 474 + ], + "spans": [ + { + "bbox": [ + 316, + 431, + 553, + 474 + ], + "type": "text", + "content": "[44] Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3836-3847, 2023. 3" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 316, + 476, + 553, + 518 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 476, + 553, + 518 + ], + "spans": [ + { + "bbox": [ + 316, + 476, + 553, + 518 + ], + "type": "text", + "content": "[45] Yuhui Zhang, Elaine Sui, and Serena Yeung-Levy. Connect, collapse, corrupt: Learning cross-modal tasks with unimodal data. arXiv preprint arXiv:2401.08567, 2024. 2, 3, 4, 5, 6, 7, 8" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4059" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Diffusion Model is Effectively Its Own Teacher/0fc82481-a954-458e-b9b5-30892d3cb276_content_list.json b/2025/Diffusion Model is Effectively Its Own Teacher/0fc82481-a954-458e-b9b5-30892d3cb276_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..279ff7e56772a3149f18898397277a81b72e8a53 --- /dev/null +++ b/2025/Diffusion Model is Effectively Its Own Teacher/0fc82481-a954-458e-b9b5-30892d3cb276_content_list.json @@ -0,0 +1,1607 @@ +[ + { + "type": "text", + "text": "Diffusion Model is Effectively Its Own Teacher", + "text_level": 1, + "bbox": [ + 261, + 130, + 736, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xinyin Ma Runpeng Yu Songhua Liu Gongfan Fang Xinchao Wang\\* National University of Singapore", + "text_level": 1, + "bbox": [ + 171, + 179, + 825, + 218 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "maxinyin@u.nus.edu, xinchao@nus.edu.sg", + "bbox": [ + 328, + 220, + 666, + 233 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/da1b25071d7ff31928b52cc4c1701d362de1c303bfcd937da6ce70bf3e1ab544.jpg", + "image_caption": [ + "(a) DiT-XL/2 For ImageNet $512 \\times 512$", + "(b) Stable Diffusion v1.5", + "Figure 1. Generated Images before (left) and after (right) our proposed self-distillation framework on DiT-XL/2 for ImageNet $512 \\times 512$ and Stable Diffusion v1.5 with 10 DDIM sampling steps." + ], + "image_footnote": [], + "bbox": [ + 94, + 270, + 901, + 501 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 579, + 326, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we introduce a novel self-distillation paradigm for improving the performance of diffusion models. Previous studies have shown that introducing a teacher to distill the diffusion model can enhance its sampling efficiency. We raise an intriguing question: can the diffusion model itself serve as its teacher to further improve the performance of itself? To this end, we propose a new paradigm called Self Step-Distillation (SSD). The core idea of SSD is to integrate the predictions or the intermediate activations of the diffusion model at each timestep with its preceding timestep through a fusion mechanism. We propose two forms, explicit SSD and implicit SSD (iSSD), to perform $N$ -step to $N$ -step distillation from the diffusion model itself to achieve improved image quality. We further elucidate the relationship between SSD and high-order solver, highlighting their underlying relationship. The effectiveness of SSD is validated through extensive experiments on diffu", + "bbox": [ + 88, + 614, + 485, + 872 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sion transformers of various sizes and across different sampling steps. Our results show that this novel self-distillation paradigm can significantly enhance performance. Additionally, our method is compatible with the distillation method designed for few-step inference. Notably, with iSSD trained less than one epoch, we obtain a 32-step DiT-XL/2 achieving an FID of 1.99, outperforming the original 250-step DiT-XL/2 with an FID of 2.26. We further validate the effectiveness of our method on text-to-image diffusion models, such as Stable Diffusion, and also observe notable improvement in image quality.", + "bbox": [ + 511, + 566, + 906, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 767, + 645, + 782 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion-based generative models [5, 16, 51] have gained significant attention for their remarkable capability to generate diverse, high-fidelity outputs across various domains. It has been proven effective in tasks such as image synthesis [42, 44, 46], video generation [1, 17, 18] and natural language processing [27, 33]. Unlike previous generative approaches like VAEs [24] and GANs [12], Diffusion Mod-", + "bbox": [ + 511, + 794, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author", + "bbox": [ + 114, + 886, + 240, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12901", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "els (DMs) rely on a unique process where noise is gradually refined into meaningful data by reversing a specified noise pathway [20]. This iterative noise-to-data transformation gives DMs exceptional versatility, allowing them to be applied successfully in image editing [21], inpainting [35], super-resolution [11], object detection [3], 3D generation [43], etc.", + "bbox": [ + 89, + 90, + 480, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent studies have emphasized the effectiveness of knowledge distillation [15] as a tool for enhancing inference efficiency or accelerating pre-training for diffusion models [38, 50]. These methods typically achieve distillation through the use of an external teacher model or a teacher with more sampling steps. To improve inference efficiency, approaches such as progressive distillation and consistency distillation [23, 36, 47, 52] employ an extensive multi-step sampling process as a teacher model to distill the student model with fewer steps. These teacher models more accurately approximate the denoising trajectory, thereby guiding the student model to enable the few-step generation or even one-step generation [7]. Other studies [13, 19, 22] focus on distilling compact diffusion models by training smaller models under the supervision of larger, high-capacity models. Besides, [60] demonstrates that aligning model representations using guidance from an external pre-trained vision encoder can facilitate faster convergence.", + "bbox": [ + 91, + 200, + 483, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The aforementioned methods can significantly enhance the sampling efficiency of diffusion models through distillation. However, the student models are constrained by the performance of the teacher model, with their training aimed at matching, but not surpassing, the teacher's performance. This raises an intriguing question: Can distillation be leveraged to improve the generation quality of the diffusion model itself, potentially exceeding the performance of the teacher model? This shifts the focus from traditional $N$ -to- $M$ step distillation or model compression for speed to a form of $N$ -to- $N$ step self-distillation aimed at enhancing the generation quality of the original diffusion model.", + "bbox": [ + 89, + 474, + 482, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We thereby explore the unique form of self-distillation within diffusion models. While self-distillation has been studied extensively in conventional architectures [10, 39, 61, 62], its application to diffusion models remains unexplored. explore the special way that self-distillation operates in diffusion models by utilizing the properties of diffusion models. Given the temporal relationships between steps that form a sequence of predictions, we introduce Self Step-Distillation in both explicit and implicit forms. The core idea is that, with careful design, the model can enhance its performance by mimicking the next-step prediction. To achieve this, we propose a fusion of predictions and features across different steps, and redefine the computational flow for the student model. Once the student model is trained, it can be reverted to the original computational pipeline. We also illustrate how this fusion mechanism relates to high-", + "bbox": [ + 89, + 659, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "order solvers.", + "bbox": [ + 513, + 92, + 607, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We mainly conduct our experiments on diffusion transformers [40] due to their exceptional performance. We conduct experiments on DiT models ranging from DiT-S/2 to DiT-XL/2 and sampling steps from 4 to 250. With our method, a self-distilled DiT-XL/2 with 50 sampling steps surpasses the performance of the pre-trained DiT-XL/2 with 250 sampling steps (2.02 vs 2.14 in FID). To further examine the $N$ -to- $N$ distillation setting and show that our method is complementary to the few-step distillation, we applied our method on a progressively distilled DiT-XL/2. This resulted in an enhanced generation quality, with an FID of 1.99 achieved using 32 sampling steps. Additionally, we tested the generalizability of our method by applying it to Stable Diffusion, confirming its effectiveness in the text-to-image setting. All experiments require fewer than 10k optimization steps and a short training duration—approximately 40 minutes for DiT-XL/2 and 3 hours for Stable Diffusion. Consequently, our method can be considered a quick self-improvement technique for diffusion models, which we further show that it can operate without dependence on training data.", + "bbox": [ + 511, + 106, + 903, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, the contributions of our work are:", + "bbox": [ + 532, + 424, + 857, + 436 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We demonstrate for the first time that self-distillation can enhance the performance of diffusion models itself, significantly surpassing the original model.", + "- We introduce a novel self-distillation framework for diffusion models, termed Self Step-Distillation. By corrupting and fusing predictions and intermediate activations, we redefine the computational flow of the teacher and student diffusion model to facilitate self-distillation.", + "- We analyze the underlying mechanisms of this unique self-distillation approach and reveal its connection to high-order solvers.", + "- Experimental results demonstrate that our self-distillation method significantly enhances the performance of diffusion models, including both DiT and Stable Diffusion, as well as distilled few-step diffusion models." + ], + "bbox": [ + 513, + 439, + 903, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 679, + 653, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Distillation in Diffusion Models. knowledge distillation [15] becomes a popular paradigm to improve the efficiency of diffusion models. Progressive Distillation [47] proposes to half the steps of sampling by matching the samples generated by N deterministic steps with 2N steps. Consistency distillation [52] enforces the self-consistency between any pair of steps and makes the boundary condition avoid trivial solutions. [36] extends it into the latent space, and [23, 54] divides the whole trajectory consistency into subphase consistency. SFD [64] solves the accumulative errors in local distillation by sampling and imitating the whole trajectory. [59] distills the diffusion model into a one-step generator by matching at the distribution level with adversarial", + "bbox": [ + 511, + 703, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12902", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7c9252b37f1c5bd7bb593c9de27984e43383682c7d67562f7ff861e8bca7a261.jpg", + "image_caption": [ + "Figure 2. The overall framework of Self Step-Distillation. Here $\\theta^{-}$ means that the weight of the model is frozen." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 480, + 305 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "loss. [6] shows that the high-order term, jacobian-vector products, can be distilled into a separate neural network. Guided diffusion [38] matches the combined output of the classifier-free guidance with a single model, and reduces the sampling steps for unconditional generation and conditional generation. The adversarial objective can also be incorporated in diffusion training to stabilize the training process [30, 48]. Apart from this, another line of work uses knowledge distillation to make the diffusion model small and efficient [8, 58]. Feature-level knowledge distillation is widely adopted in those works to accelerate the post-training of these compressed diffusion models [8, 13, 22].", + "bbox": [ + 88, + 375, + 486, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Efficiency in Diffusion Models. Balancing the image quality and the sampling speed is a challenging topic in diffusion models [20, 55]. (1) Fast solver for sampling. One common way to reduce the sampling steps is to employ a training-free solver to off-the-shelf pre-trained diffusion models. Those methods approximate the true trajectory of probability flow ODE, such as Euler's method [50], Heun's method [20], the exponential integrator with Taylor expansion [34], the unified predictor-corrector framework [63] and numerical methods [32]. (2) Structural Efficiency. Besides of optimizing the number of model evaluations, another way is to encourage structural efficiency. Redesign the model architectures [58], pruning [8, 29, 65] and quantization [14, 28] constructs lightweight diffusion model. Cache-based methods [37, 56] leverage the similarity between steps to reduce calculations. (3) Pipeline Efficiency. Breaking the sequential nature of denoising is another way to improve the efficiency of diffusion models. [49] uses Picard iteration to iteratively refine until convergence. [4, 25] decouples the images or models into multiple components and assigns them to different devices.", + "bbox": [ + 91, + 583, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-Distillation Knowledge distillation is widely used for compressing compact networks, while self-distillation focuses on improving the performance of networks. [10] investigate distillation with a student network parameterized identically to its teacher, demonstrating that the student could significantly outperform the teacher. [61] explores distilling knowledge from deeper network layers into shallower ones. Several works [2, 39, 57] examine the underlying reasons for this phenomenon, commonly attributing it to the \"dark knowledge\" encoded in soft labels. [62] highlight the importance of predictive diversity, while [41] systematically investigates self-distillation carefully and interprets self-distillation as a process of learning previously unlearned perspectives of input data. Unlike these prior works, our focus is not on leveraging soft labels from teacher predictions to guide student network training. Instead, we explore a unique mechanism in diffusion models to enhance their performance.", + "bbox": [ + 511, + 90, + 906, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 375, + 604, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we elaborate on the design of our self-distillation framework. We first show our proposed framework of the self-distillation paradigm in Section 3.2, and then give the explanation about why it works in Section 3.3 and Section 3.4.", + "bbox": [ + 511, + 401, + 906, + 476 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 511, + 484, + 643, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We begin from the forward and reverse processes in diffusion probabilistic models. Let $q_{\\mathrm{data}}(x)$ represent the data distribution. The forward process entails adding noise incrementally to a clean image $x_0 \\sim q_{\\mathrm{data}}(x)$ . At a given timestep $t$ , the distribution of $x_t$ , which includes the noise added up to that point, is defined by:", + "bbox": [ + 511, + 507, + 908, + 599 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, \\left(1 - \\bar {\\alpha} _ {t}\\right) \\mathbf {I}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 608, + 906, + 627 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t}$ is a time-dependent function that controls the noise scheduling. As $t$ approaches a sufficiently large value, the final state $x_{T}$ becomes nearly the same as a Gaussian noise. For denoising, starting from a noise input $x_{T} \\sim \\mathcal{N}(0, \\mathbf{I})$ , an image can be progressively reconstructed through iterative sampling from the conditional distribution $q(x_{t-1} | x_{t})$ . This conditional probability is typically approximated by a parameterized distribution, given as $p_{\\theta}(x_{t-1} | x_{t}) = \\mathcal{N}(x_{t-1}; \\mu_{\\theta}(x_{t}, t), \\Sigma_{\\theta}(x_{t}, t))$ . Here, $\\mu_{\\theta}(x_{t}, t)$ is parameterized by $\\theta$ , and it follows:", + "bbox": [ + 511, + 635, + 908, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {\\theta} \\left(x _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(x _ {t}, t\\right)\\right) \\quad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 796, + 906, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}(x_t,t)$ represents the noise estimation function at timestep $t$ given input $x_{t}$ . The training objective for diffusion models is to minimize the difference between the predicted noise and the ground-truth noise $\\epsilon_{t}$ added during", + "bbox": [ + 511, + 840, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12903", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the forward process. This is typically framed as a simplified version of the variational bound on the negative log-likelihood of $x_0$ . The objective can be written as:", + "bbox": [ + 89, + 90, + 483, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t} = \\mathbb {E} _ {t \\sim [ 1, T ], \\mathbf {x} _ {0} \\sim q _ {\\text {d a t a}} (x)} \\left[ \\| \\boldsymbol {\\epsilon} _ {t} - \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}, t) \\| ^ {2} \\right] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 148, + 482, + 172 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overall Framework", + "text_level": 1, + "bbox": [ + 89, + 184, + 279, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we introduce the design of this unique form of self-distillation within diffusion models. To achieve self-distillation, three essential components must be defined: the construction of the teacher model, the formulation of the student model, and the definition of the training objective. Given that we have only a single pre-trained model without any external supervision. This poses a critical challenge: how can a single pre-trained diffusion model be used to construct both a teacher and a student model, with the teacher model designed to be more capable than the student?", + "bbox": [ + 89, + 205, + 483, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We focus on the timesteps of diffusion models, which inherently give us a sequence of predictions for one sample. Denote the model to have $L$ layers. $x^{(l)}$ denotes the input for layer $l$ , where $l \\in \\{1, 2, \\dots, L\\}$ . $x_{t}^{(1)} = x_{t}$ represents the input to the network at timestep $t$ . Each layer $l$ applies a function $f_{\\theta_l}$ parameterized by $\\theta_{l}$ , which includes operations such as multi-head self-attention and pointwise feedforward module in Transformer [53], and residual or convolution blocks in U-Net [45]. Thus, for each layer, the layer-wise computation at timestep $t$ can be formulated as:", + "bbox": [ + 89, + 358, + 483, + 511 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} ^ {(l)} = f _ {\\theta_ {l - 1}} \\left(x _ {t} ^ {(l - 1)}, t\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 521, + 482, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here the calculation is conditioned on the timestep $t$ , although not all blocks in diffusion model use $t$ as a conditional input. After all $L$ layers have been processed, the final output of the model is the predicted noise, represented as $\\epsilon(x_{t}, t) = x_{t}^{(L + 1)}$ .", + "bbox": [ + 89, + 559, + 483, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To construct the teacher and student models, we require the outputs for two timesteps, $t$ and $s$ , where $s$ represents the preceding denoising step of $t$ under a pre-defined solver, satisfying $s > t$ . We denote the predictions of the teacher and the student model as $\\epsilon^{\\mathcal{T}}(x_t,x_s,t,s)$ and $\\epsilon^S (x_t,x_s,t,s)$ , respectively. Our approach to building the teacher and student models is based on a core principle: using the predictions from a later step as stronger supervision to guide the prediction at an earlier step. The rationale behind this principle will be discussed in detail later. Based on this guideline, we develop the below two distinct forms for self-distillation.", + "bbox": [ + 89, + 637, + 483, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Explicit Form: For the explicit self step-distillation, we build a teacher model by fusing the predicted noise:", + "bbox": [ + 89, + 837, + 482, + 868 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\epsilon} ^ {\\mathcal {T}} \\left(x _ {t}, x _ {s}, t, s\\right) = \\lambda \\boldsymbol {\\epsilon} _ {\\theta^ {-}} \\left(x _ {t}, t\\right) + (1 - \\lambda) \\boldsymbol {\\epsilon} _ {\\theta^ {-}} \\left(x _ {s}, s\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 878, + 482, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The student prediction use the predicted noise at timestep $s$ : $\\epsilon^{\\mathcal{S}}(x_t,x_s,t,s) = \\epsilon_\\theta (x_s,s)$ . Here, $\\theta^{-}$ represents the model would be frozen during training.", + "bbox": [ + 511, + 90, + 905, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Implicit Form: For the implicit self step-distillation, we redefine the computation flow in the model. We fuse the outputs at the same intermediate layer but different timesteps $t$ and $s$ , denoted $x_{t}^{(l)}$ and $x_{s}^{(l)}$ respectively. The fused output at this layer is now calculated as:", + "bbox": [ + 511, + 157, + 906, + 236 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {t} ^ {(l)} = \\lambda f _ {\\theta_ {l - 1} ^ {-}} \\left(x _ {s} ^ {(l - 1)}, s\\right) + (1 - \\lambda) f _ {\\theta_ {l - 1}} \\left(\\tilde {x} _ {t} ^ {(l - 1)}, t\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 247, + 906, + 273 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{x}_t^{(l-1)}$ represents the fused output from the previous layer, and $\\tilde{x}_t^{(l)}$ serves as the input for the next layer, replacing the original $x_t^{(l)}$ . The above equation serves as a weighted fusion of layer output in two timesteps. The final prediction $\\epsilon^S(x_t, x_s, t, s) = \\tilde{x}_t^{(L+1)}$ is obtained from these fused features, forming the prediction for the student model. With this, the computation flow of the student model is changed. In constraint, the teacher model functions as the original denoising predictor at timestep $t$ , with its prediction output expressed as $\\epsilon^T(x_t, x_s, t, s) = \\epsilon_{\\theta^{-}}(x_t, t)$", + "bbox": [ + 511, + 286, + 906, + 449 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training Objective. We take the pre-trained model as both the initialization for the teacher and the student model. The teacher $\\theta_T$ model remained frozen while the update of parameters is performed on the student side. The self-distillation objective here is the matching between the student $\\epsilon^S(x_t, x_s, t, s)$ and the teacher $\\epsilon^T(x_t, x_s, t, s)$ . The distillation objective would be:", + "bbox": [ + 511, + 469, + 905, + 575 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathbb {E} _ {s \\sim [ 1, T ], x _ {0} \\sim q _ {\\mathrm {d a t a}} (x)} \\left[ \\left\\| \\boldsymbol {\\epsilon} ^ {\\mathcal {T}} \\left(x _ {t}, x _ {s}, t, s\\right) - \\boldsymbol {\\epsilon} ^ {\\mathcal {S}} \\left(x _ {t}, x _ {s}, t, s\\right) \\right\\| ^ {2} \\right] \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 585, + 903, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $x_{s}$ represents $x_{0}$ with added noise, and $x_{t}$ is obtained by performing one step from $x_{s}$ in the ODE solver. After the training phase is completed, no fusion operations are applied during the inference stage. The model's computation remains identical to its original configuration but benefits from the enhancements gained through the self-distillation process.", + "bbox": [ + 511, + 625, + 905, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Distill from High-Order Solver", + "text_level": 1, + "bbox": [ + 511, + 741, + 787, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we explain why this self-distillation framework works. In order to reduce the discretization error for the first-order ODE solver, such as Euler [20], one straightforward way is to use the higher-order solver for the diffusion ODEs. The cost for this is that it needs twice or third or even more times of function evaluation. We show that our self-distillation framework serves as an approximated form for distilling it into the same network without introducing additional parameters.", + "bbox": [ + 511, + 763, + 906, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12904", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We perform a single step forward from timestep $s$ to timestep $t$ . We compare the formulation of DPM-Solver-1 and DPM-Solver-2 [34].", + "bbox": [ + 89, + 90, + 482, + 136 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {D P M - S o l v e r - 1 :} x _ {t} = \\frac {\\alpha_ {t}}{\\alpha_ {s}} x _ {s} - w _ {t} \\epsilon_ {\\theta} (x _ {s}, s) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 147, + 482, + 175 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {D P M - S o l v e r - 2 :} x _ {t} = \\frac {\\alpha_ {t}}{\\alpha_ {s}} x _ {s} - w _ {t} \\epsilon_ {\\theta} (x _ {u}, u) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 176, + 482, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here the timestep $u$ is an intermediate timestep between $t$ and $s$ . As defined in DPM-Solver-2, timestep $u$ has $\\lambda_u \\coloneqq \\log \\left( \\frac{\\alpha_u}{\\sigma_u} \\right)$ which is the average of those for timestep $t$ and timestep $s$ , and $x_u$ denotes the state one step forward from $s$ to $u$ . The term $w_t$ is a weight factor that depends only on the timestep. Using DPM-Solver-2, which is more accurate than DPM-Solver-1, the following training objective can be interpreted as encouraging the predictions of the first-order solver to align more closely with those of the second-order solver:", + "bbox": [ + 89, + 215, + 483, + 366 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathbb {E} _ {s \\sim [ 1, T ], \\mathbf {x} _ {0} \\sim q _ {\\text {d a t a}} (x)} \\left[ w _ {t} \\| \\boldsymbol {\\epsilon} _ {\\theta} \\left(x _ {s}, s\\right) - \\boldsymbol {\\epsilon} _ {\\theta} \\left(x _ {u}, u\\right) \\| ^ {2} \\right] \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 376, + 482, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Building on the above equation, if the goal is to approximate a higher-order solver using a first-order solver, the training objective simplifies to: matching the prediction at the current step with the prediction at a subsequent step.", + "bbox": [ + 89, + 419, + 483, + 481 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Ways to approximate $\\epsilon_{\\theta}(x_u,u)$", + "text_level": 1, + "bbox": [ + 89, + 491, + 356, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, this method requires the prediction at the intermediate step between timestep $s$ and $t$ , which is not always feasible in $N$ -step to $N$ -step distillation. A feasible scenario involves using a linear interpolant noise scheduler, where $x_{s} = (1 - s / T)x_{0} + (s / T)\\epsilon$ , and the model predicts the velocity instead of the noise $\\epsilon$ . Under these conditions, the objective can be reformulated to align $\\epsilon_{\\theta}(x_s,s)$ with $\\epsilon_{\\theta}(x_t,t)$ . The corresponding results are presented in Table 1, with detailed proofs provided in the Appendix. With 10 and 250 sampling steps, consistent improvements in sample quality are observed, validating the effectiveness of Eq.10. However, as expected, performance declined in both cases when using $\\epsilon$ -prediction without incorporating these properties into the noise scheduler and the specific model prediction type.", + "bbox": [ + 89, + 513, + 483, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The question now arises: how we can approximate $\\epsilon_{\\theta}(x_u,u)$ given $\\epsilon_{\\theta}(x_s,s)$ and $\\epsilon_{\\theta}(x_t,t)$ . One straightforward way is to get the approximation of $\\epsilon_{\\theta}(x_u,u)$ by Taylor Expansion, whose results turned to be the interpolating between $\\epsilon_{\\theta}(x_s,s)$ and $\\epsilon_{\\theta}(x_t,t)$ . Following the assumption in [34] that $\\epsilon_{\\theta}(x_s,s)$ is Lipschitz w.r.t $x_{s}$ , we have:", + "bbox": [ + 89, + 741, + 483, + 832 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\epsilon_ {\\theta} \\left(x _ {u}, u\\right) = \\epsilon_ {\\theta} \\left(x _ {s}, u\\right) + \\left(\\epsilon_ {\\theta} \\left(x _ {u}, u\\right) - \\epsilon_ {\\theta} \\left(x _ {s}, u\\right)\\right) \\\\ = \\epsilon_ {\\theta} (x _ {s}, s) + \\epsilon_ {\\theta} ^ {(1)} (x _ {s}, s) (u - s) + \\mathcal {O} ((u - s) ^ {2}) \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 844, + 482, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5695d6d6a40fca42b8282d6034378892e105b9e79acf981f45ce8cc01c6a06a9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelSamplerNFEsISFIDsFID
    v-prediction with linear interpolant noise scheduler
    REPA - SiT-XL/2SDE250305.71.424.70
    REPA - SiT-XL/2° w/ Eq.10SDE250306.31.414.68
    REPA - SiT-XL/2°ODE10233.95.857.82
    REPA - SiT-XL/2° w/ Eq.10ODE10238.45.117.48
    ε-prediction
    DiT-XL/2ODE50238.62.264.29
    DiT-XL/2 w/ Eq.10ODE50230.82.816.41
    DiT-XL/2 w/ Eq.12ODE50239.92.214.41
    DiT-XI/2ODE10158.312.3811.22
    DiT-XL/2 w/ Eq.10ODE1051.845.9926.95
    DiT-XL/2 w/ Eq.12ODE10184.77.999.91
    ", + "bbox": [ + 517, + 88, + 903, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Results on $v$ -prediction and $\\epsilon$ -prediction diffusion models. For the experiments on REPA, we use the EMA model as the teacher for the experiments with 250 steps.", + "bbox": [ + 511, + 281, + 903, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}^{(1)}(x_s,s)$ is the first-order derivative w.r.t $s$ . As above, we derive $\\epsilon_{\\theta}^{(1)}(x_s,s)$ the same way between two different timesteps $t$ and $s$ , and we have:", + "bbox": [ + 511, + 327, + 903, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {\\theta} \\left(x _ {u}, u\\right) = (1 - \\lambda) \\epsilon_ {\\theta} \\left(x _ {s}, s\\right) + \\lambda \\epsilon_ {\\theta} \\left(x _ {t}, t\\right) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 386, + 903, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda = (u - s) / (t - s)$ . We get the same form as the explicit self step-distillation. The results with this equation are also shown in Table 1.", + "bbox": [ + 511, + 410, + 903, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While the aforementioned method can approximate $\\epsilon_{\\theta}(x_u,u)$ to some extent, it remains suboptimal. An alternative approach is the implicit form of interpolation, which approximates $\\epsilon_{\\theta}(x_u,u)$ by interpolating on features rather than on the output. This one shares the same form with implicit self step-distillation. This idea is inspired by previous works [26, 37], which demonstrated that certain intermediate activations in timestep $s$ can be reused in later timestep $u$ to produce an approximated output for timestep $u$ , with minimal effect on image quality. Consequently, we interpolate on the intermediate layers, and experimental results indicate that this method yields better performance than interpolation on predictions.", + "bbox": [ + 511, + 455, + 906, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 511, + 664, + 638, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we demonstrate the effectiveness of our proposed method. In Section 4.2, we present empirical evidence that both SSD and iSSD consistently enhance the performance of a pre-trained DiT across various image resolutions, model sizes, and sampling steps. Additionally, Section 4.3 provides the results of applying these methods to text-to-image generation. Section 4.4 highlights how iSSD can be applied to distilled models, yielding further performance improvements. Finally, Section 4.5 offers an in-depth analysis.", + "bbox": [ + 511, + 689, + 906, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 511, + 848, + 702, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Models. For the conditional generation on ImageNet, we take all four DiT models: DiT-S/2, DiT-B/2, DiT-L/2, and", + "bbox": [ + 511, + 869, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12905", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/748179db7ed5a998502539735fca3008b53983431a2495f8ceef33829256ef2e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodNFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑NFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    -256×256--512×512-
    DiT-XL/2250(ODE)1400243.42.144.560.810.61250(SDE)600240.83.045.020.840.54
    SiT-XL/2250(SDE)1400277.52.064.490.830.59250(SDE)600252.22.624.180.840.57
    DiT-XL/2501400238.62.264.290.800.6050600204.13.284.500.830.55
    + SSD501400 + 0.8239.92.214.410.800.6050600 + 0.4205.23.184.590.830.57
    + iSSD501400 + 0.8250.02.024.220.810.6050600 + 0.4210.22.864.060.840.54
    DiT-XL/2201400223.53.484.890.790.5720600186.35.105.730.820.55
    + SSD201400 + 0.8228.62.824.630.790.6020600 + 0.4194.74.015.330.830.56
    + iSSD201400 + 0.8227.52.674.850.790.6020600 + 0.4200.83.694.410.840.54
    DiT-XL/2101400158.312.3811.220.670.5310600128.415.1911.580.740.49
    + SSD101400 + 0.8184.77.999.910.710.5610600 + 0.4158.59.6111.090.780.54
    + iSSD101400 + 0.8209.64.927.620.790.5310600 + 0.4164.96.977.050.830.51
    ", + "bbox": [ + 94, + 89, + 903, + 268 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8d7f30b723dc2d2c34f6d4c7788965b7763cb2be8e69835928a13071494e4ce7.jpg", + "table_caption": [ + "Table 2. Image quality on ImageNet ${256} \\times {256}$ and ${512} \\times {512}$ ,with DiT-XL/2 as the base model. Prec. and Rec. denotes Precision and Recall. We adopt CFG=1.5 in all the experiments for ImageNet." + ], + "table_footnote": [], + "table_body": "
    ModelNFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    -DiT-S/2-
    DiT-S/225040059.426.517.310.590.56
    DiT-S/2+ iSSD5040053.529.215.890.570.58
    50400 + 0.254.627.755.730.580.58
    DiT-S/2+ iSSD2040052.032.627.430.550.55
    20400 + 0.252.530.628.230.560.55
    DiT-S/2+ iSSD1040040.149.5018.330.430.48
    10400 + 0.240.746.1718.890.450.48
    -DiT-B/2-
    DiT-B/2250200119.610.125.390.730.55
    DiT-B/2+ iSSD50200101.812.844.810.710.56
    50200 + 0.2104.911.774.990.710.56
    DiT-B/2+ iSSD2020097.515.406.110.680.54
    20200 + 0.2100.613.848.630.710.52
    DiT-B/2+ iSSD1020072.128.9915.540.560.48
    10200 + 0.277.921.4013.370.610.53
    -DiT-L/2-
    DiT-L/2250200196.33.734.620.820.54
    DiT-L/2+ iSSD50200168.84.774.410.780.55
    50200 + 0.2172.74.414.440.800.56
    DiT-L/2+ iSSD20200160.56.425.260.770.53
    20200 + 0.2172.34.924.870.800.53
    DiT-L/2+ iSSD10200118.516.0112.630.670.47
    10200 + 0.2143.77.754.990.750.55
    ", + "bbox": [ + 94, + 330, + 480, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Image quality on ImageNet ${256} \\times {256}$ with DiT-S/2,DiT-B/2 and DiT-L/2", + "bbox": [ + 89, + 680, + 482, + 708 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DiT-XL/2. For DiT-XL/2, we utilize the official pre-trained model, whereas for the other three models, we train them for 1 million to 2 million steps. For the text-to-image generation experiments, we employ Stable Diffusion v1.5 [44] as our base model.", + "bbox": [ + 89, + 732, + 483, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation. We follow previous work [40] to use IS, FID, sFID, Precision and Recall as the evaluation metric. For text-to-image generation, we test the FID on the validation set of COCO2014 and COCO2017 [31].", + "bbox": [ + 89, + 839, + 483, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training and Sampling Details. For training, the teacher and student models are both initialized from the base model, with the teacher remaining fixed during training. We use DDIM [50] as our base ODE solver and only utilize N-step predictions during training if the fine-tuned model would be evaluated under N-step. For DiT, we set a learning rate of 5e-6, a batch size of 128. The training epochs for each experiment are listed in the tables. Exponential Moving Average (EMA) is not used due to the short training period. We follow the original DiT setup without weight decay, warm-up, or learning rate schedulers. Models were evaluated with 10, 20, and 50 numbers of function evaluations (NFEs), and we show that even the basic ODE algorithms outperformed many advanced samplers with our algorithms. More details, especially for text-to-image generation, are in the Appendix.", + "bbox": [ + 511, + 334, + 906, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Conditional Generation", + "text_level": 1, + "bbox": [ + 511, + 585, + 732, + 602 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on DiT-XL. We show the results of DiT-XL/2 in Table 2. With less than 1 epoch for optimizing DiT-XL/2, our method achieves consistent performance improvement upon the base models. Notably, our method with 50 NFEs can exceed the performance of the base DiT-XL/2 sampled 250 times by a large margin (2.02 vs 2.14), both under the same ODE sampler. Also this improvement can be observed in the resolution of 512, where the base DiT achieves the FID of 3.04, while our method can improve it to 2.86. We also notice improvement compared with the 250-step SiT, with our method sampled with only 50 steps. Besides, we found the implicit SSD performs better than the explicit SSD in most cases, and sometimes the implicit SSD outperforms the explicit SSD by a large margin. We show the qualitative results on ImageNet in the Appendix.", + "bbox": [ + 511, + 608, + 906, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on small-scale DiTs. We also apply our method under smaller DiT models, showing that the method can be generalized to models with different sizes. Since in the ex", + "bbox": [ + 511, + 854, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12906", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4a2f54b7038ca5db70708a795514840ed0c103a1d361b876b47f07f0cf5f7c79.jpg", + "image_caption": [ + "Figure 3. Visualization of generated images using various sampling algorithms with NFEs=10. From left to right, the algorithms shown are: PLMS, DDIM, DPM-Solver-2, and SSD." + ], + "image_footnote": [], + "bbox": [ + 94, + 90, + 478, + 241 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cc9d539a8d2f349f0db48f82121be6a8cc93ebe8b00f9ccf61aad11e3dce90e2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    DatasetNFEsDDIMPLMSDPM-Solver-2Ours
    COCO20141012.7817.7115.2310.94
    2012.6812.6514.6310.56
    COCO20171022.7929.5124.4620.85
    2022.4322.1424.0220.69
    ", + "bbox": [ + 94, + 309, + 478, + 391 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "periment in DiT-XL/2, we found iSSD consistently outperforms SSD, we here test the performance of iSSD on these DiT models. From Table 3, with only 0.2 epoch for training, we observe a large improvement upon the base model. It would only take several minutes to finish the training, and thus, can be seen as a cheap way to improve the performance of the trained models.", + "bbox": [ + 89, + 457, + 483, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Text-to-Image Generation", + "text_level": 1, + "bbox": [ + 89, + 573, + 326, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We apply SSD to Stable Diffusion v1.5. The experimental details are outlined in Appendix. Our method is compared against DDIM [50], DPM-Solver-2 [34] and PLMS [32] on COCO2014 and COCO2017, as shown in Table 4. Our approach demonstrates significant improvements in FID, outperforming other methods. Notably, our results with 10 NFEs surpass those achieved with 20 NFEs by competing samplers. Visualization results further highlight that images enhanced by our algorithm exhibit more detailed features.", + "bbox": [ + 89, + 595, + 482, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Results on Distilled Models", + "text_level": 1, + "bbox": [ + 89, + 742, + 334, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we apply our method to a distilled model obtained through progressive distillation (PD). Notably, this implies that predictions at intermediate steps that are not explicitly part of the PD process are not trained, resulting in suboptimal performance at these steps. This experiment aims to demonstrate that our method is effective that distills from N steps to enhance performance across those N steps, since using the results from intermediate steps other than these N steps would harm the performance.", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/835cae22bb6e1d64a0f7a755571a9d23dba7e532d809b1ea10e1d2e27d3549c1.jpg", + "table_caption": [ + "Table 4. FID Comparison with different samplers on the validation set of COCO2014 and COCO2017" + ], + "table_footnote": [], + "table_body": "
    ModelNFEsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    DiT-XL/2250243.42.144.560.810.61
    PD 64 → 3232239.82.244.330.800.60
    + iSSD32246.21.994.330.810.60
    PD 20 → 1010209.94.195.240.760.57
    + iSSD10233.93.567.080.810.55
    PD 20 → 10 → 55173.07.006.590.730.58
    + iSSD5186.75.416.480.760.56
    PD 16 → 8 → 44152.68.757.900.700.59
    + iSSD4168.586.107.530.720.57
    ", + "bbox": [ + 517, + 88, + 903, + 233 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8671725a1998a959e0f75d6274c9475279cf6852d5c89d4854c99fa408119b14.jpg", + "table_caption": [ + "Table 5. Results of building iSSD upon diffusion models being distilled for few-step generation." + ], + "table_footnote": [], + "table_body": "
    ModelIS ↑FID ↓sFID ↓Prec.↑Rec.↑
    DiT-XL/213.4107.7594.570.110.36
    PD [47]158.37.847.110.700.60
    Shortcut Model [9]-7.8---
    PD + Ours168.66.117.530.720.57
    ", + "bbox": [ + 517, + 284, + 901, + 362 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Comparison with training-based method on ImageNet $256\\times 256$ . We set NFEs $= 4$ and use DiT-XL/2 for sampling.", + "bbox": [ + 511, + 372, + 903, + 401 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Orthogonal to distillation methods. Table 5 presents the results for models distilled through two-stage and three-stage progressive distillation (PD), and Figure 4(a) illustrates the results on a chain of models distilled from progressive distillation. The results indicate that our method can significantly enhance performance. Specifically, when applied to a 32-step distilled model, our approach achieves an FID of 1.99 with minimal additional computational cost, representing a substantial improvement over the distilled model and even the pre-trained DiT-XL/2. However, when comparing our method to the model directly distilled from PD, the performance at 10-step NFE is slightly lower (4.19 vs. 4.92). We position our method as an auxiliary step that complements and further refines the performance of distilled models, providing an orthogonal improvement.", + "bbox": [ + 511, + 426, + 906, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with training-based methods. We evaluated our model against flow-matching algorithms designed for training diffusion models to enable few-step generation. The experiments are performed using 4 steps to generate images, and the backbone for diffusion models is DiT-XL/2. The results, summarized in Table 6, indicate that our method surpasses the performance of competing algorithms. Specifically, when compared to the ShortCut Model [9], an enhanced variant of the flow matching model adapted for DiT, our approach achieves superior results (FID: 6.1 v.s. 7.8).", + "bbox": [ + 511, + 672, + 906, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Analysis", + "text_level": 1, + "bbox": [ + 511, + 848, + 616, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with continual training. To demonstrate that the observed performance improvements are not merely", + "bbox": [ + 511, + 869, + 903, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12907", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d36e4565dcd98a0184a8776964638e3fe4d68032ec55568922d2de68f0b3ea51.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 310, + 188 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9fe056c2a0654486fef4678df07ce01c2bb070f3e50b5b8ff125c8761dd78ffc.jpg", + "image_caption": [ + "(b)", + "Figure 4. Analysis of our proposed self-distillation framework includes: (a) iSSD consistently enhancing the quality of distilled DMs, (b) significant improvements in sample quality achieved by training only one step in the ODE trajectory, (c) evaluation of the performance of the teacher, student, and the final model, and (d) a substantial impact observed with variations in $\\lambda$" + ], + "image_footnote": [], + "bbox": [ + 316, + 90, + 532, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/62fa50bb81eb032820405d04cf2f4233bcaee3abf780ef3a6a2b2cc28f3295b6.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 535, + 90, + 715, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d47b928843002a2c9038ccbbf9c716c22a0d039c1215cf40a5eb00aa3cd24601.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 720, + 93, + 901, + 185 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8db48615f44c55e84e15aecf477a25428fffb09744f90a40afb72e117ba92f7c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelNFETrain EpochsIS↑FID↓
    DiT-XL/2101400158.312.38
    DiT-XL/2°101400 + 0.8156.712.97
    DiT-XL/2 + iSSD101400 + 0.8209.64.92
    DiT-S°25040027.651.55
    DiT-S°25042027.951.13
    DiT-S° + iSSD250400 + 228.748.38
    ", + "bbox": [ + 94, + 271, + 478, + 390 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "due to additional training iterations, we conducted experiments on DiT-XL/2 (officially pre-trained and only have the EMA model) and DiT-S/2 ( has both the EMA and the base model). The results in Table 7 show that even with fewer training epochs, our method significantly outperforms models trained for 20 epochs on DiT-S/2. This confirms that the performance gains stem from the proposed self-distillation approach rather than extended training iterations.", + "bbox": [ + 89, + 453, + 483, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Synthetic Data v.s. Real Data. An additional exploration involves assessing whether a model's performance can be improved when only the model itself is available, without any supplementary training data or external models. We conducted experiments under this setting, and the results are presented in Table 8. The findings indicate that, while real data remains the optimal choice for achieving the highest performance, the use of synthetic data can still result in substantial improvements in generation quality, albeit with a slight performance trade-off compared to using real data.", + "bbox": [ + 89, + 592, + 483, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Distill upon only one step. In Figure 4(b), we show the results of applying iSSD to a single step. This process yields two models; here, our focus is on determining which step has the greatest impact on images. The results indicate that applying self-distillation in the later stages of denoising provides the most significant benefit to image quality.", + "bbox": [ + 89, + 761, + 483, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Training dynamics for the teacher and the student in iSSD. Figure 4(c) presents the training dynamics ob", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/508f244d4c882d90c12f6f56d20a0fe6f46da0c068f821a725b57de337f570ab.jpg", + "table_caption": [ + "Table 7. Comparison with Continual Training. The superscript $\\diamond$ means we train these models from the official codebase." + ], + "table_footnote": [], + "table_body": "
    ModelData SourceISFIDsFIDPrecisionRecall
    DiT-XL/2-158.312.3811.220.670.53
    iSSDOriginal Data209.64.927.620.790.53
    iSSDSynthetic - 10 step206.25.079.030.790.52
    iSSDSynthetic - 20 step207.95.028.990.790.53
    ", + "bbox": [ + 516, + 271, + 903, + 342 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Results on Synthetic Data on ImageNet $256 \\times 256$ . The experiments are based on DDIM with 10 sampling steps.", + "bbox": [ + 511, + 352, + 906, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "served during our experiments. It is crucial to note that the student model used in training differs from the one used for inference. The student model with fused activations starts with lower performance compared to the teacher model and remains inferior after training. In contrast, the unfused one, which maintains the same architecture and computation way for each layer, shows consistent improvement throughout training and eventually achieves significantly better performance than the teacher model.", + "bbox": [ + 511, + 406, + 906, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of gradient influential term $\\lambda$ . We show the effect of $\\lambda$ , as defined in Eq.5 and Eq.6. Though in Eq.12, we can directly calculate $\\lambda$ if we adopt the same intermediate step as in DPM-Solver, we also put this timestep scheduler in this hyper-parameter, and search the best $\\lambda$ for our approach. Figure 4(d) show for iSSD, with $\\lambda$ equals a small value, the model would get poor results. We show the $\\lambda$ used in each of our experiments in Appendix.", + "bbox": [ + 511, + 560, + 908, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 694, + 633, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel self-distillation approach named Self Step-Distillation. We introduce two forms for Self Step-Distillation. Furthermore, we explain this approach by analyzing it through the lens of distillation with high-order samplers. Experimental results demonstrate that our method significantly outperforms the performance of the teacher model, achieving substantial improvements in both conditional generation and text-to-image generation. However, our method also has certain limitations. For instance, we still rely on suboptimal approaches to approximate the prediction of the intermediate step. Additionally, our method is relatively sensitive to hyperparameters.", + "bbox": [ + 511, + 719, + 908, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12908", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006).", + "bbox": [ + 89, + 114, + 483, + 160 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 172, + 187, + 188 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. 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Knowledge distillation in generations: More tolerant teachers educate better students. arXiv preprint arXiv:1805.05551, 2018. 3", + "[58] Xingyi Yang, Daquan Zhou, Jiashi Feng, and Xinchao Wang. Diffusion probabilistic model made slim. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22552-22562, 2023. 3", + "[59] Tianwei Yin, Michael Gharbi, Richard Zhang, Eli Shechtman, Fredo Durand, William T Freeman, and Taesung Park. One-step diffusion with distribution matching distillation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6613-6623, 2024. 2", + "[60] Sihyun Yu, Sangkyung Kwak, Huiwon Jang, Jongheon Jeong, Jonathan Huang, Jinwoo Shin, and Saining Xie. Representation alignment for generation: Training diffusion transformers is easier than you think. arXiv preprint arXiv:2410.06940, 2024. 2", + "[61] Linfeng Zhang, Jiebo Song, Anni Gao, Jingwei Chen, Chenglong Bao, and Kaisheng Ma. Be your own teacher: Improve the performance of convolutional neural networks via self distillation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 3713-3722, 2019. 2, 3", + "[62] Zhilu Zhang and Mert Sabuncu. Self-distillation as instancespecific label smoothing. Advances in Neural Information Processing Systems, 33:2184-2195, 2020. 2, 3", + "[63] Wenliang Zhao, Lujia Bai, Yongming Rao, Jie Zhou, and Jiwen Lu. Unipc: A unified predictor-corrector framework for fast sampling of diffusion models. arXiv preprint arXiv:2302.04867, 2023. 3", + "[64] Zhenyu Zhou, Defang Chen, Can Wang, Chun Chen, and Siwei Lyu. Simple and fast distillation of diffusion models. arXiv preprint arXiv:2409.19681, 2024. 2", + "[65] Haowei Zhu, Dehua Tang, Ji Liu, Mingjie Lu, Jintu Zheng, Jinzhang Peng, Dong Li, Yu Wang, Fan Jiang, Lu Tian, et al. Dip-go: A diffusion pruner via few-step gradient optimization. arXiv preprint arXiv:2410.16942, 2024. 3" + ], + "bbox": [ + 91, + 92, + 480, + 753 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12911", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Diffusion Model is Effectively Its Own Teacher/0fc82481-a954-458e-b9b5-30892d3cb276_model.json b/2025/Diffusion Model is Effectively Its Own Teacher/0fc82481-a954-458e-b9b5-30892d3cb276_model.json new file mode 100644 index 0000000000000000000000000000000000000000..70bcc0f566eb7c09b629b986111590f3606ece8e --- /dev/null +++ b/2025/Diffusion Model is Effectively Its Own Teacher/0fc82481-a954-458e-b9b5-30892d3cb276_model.json @@ -0,0 +1,2367 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.263, + 0.131, + 0.738, + 0.154 + ], + "angle": 0, + "content": "Diffusion Model is Effectively Its Own Teacher" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.18, + 0.826, + 0.219 + ], + "angle": 0, + "content": "Xinyin Ma Runpeng Yu Songhua Liu Gongfan Fang Xinchao Wang\\* National University of Singapore" + }, + { + "type": "text", + "bbox": [ + 0.33, + 0.221, + 0.668, + 0.234 + ], + "angle": 0, + "content": "maxinyin@u.nus.edu, xinchao@nus.edu.sg" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.271, + 0.903, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.505, + 0.403, + 0.518 + ], + "angle": 0, + "content": "(a) DiT-XL/2 For ImageNet \\(512 \\times 512\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.627, + 0.505, + 0.768, + 0.518 + ], + "angle": 0, + "content": "(b) Stable Diffusion v1.5" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.524, + 0.908, + 0.553 + ], + "angle": 0, + "content": "Figure 1. Generated Images before (left) and after (right) our proposed self-distillation framework on DiT-XL/2 for ImageNet \\(512 \\times 512\\) and Stable Diffusion v1.5 with 10 DDIM sampling steps." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.58, + 0.327, + 0.597 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.615, + 0.486, + 0.873 + ], + "angle": 0, + "content": "In this paper, we introduce a novel self-distillation paradigm for improving the performance of diffusion models. Previous studies have shown that introducing a teacher to distill the diffusion model can enhance its sampling efficiency. We raise an intriguing question: can the diffusion model itself serve as its teacher to further improve the performance of itself? To this end, we propose a new paradigm called Self Step-Distillation (SSD). The core idea of SSD is to integrate the predictions or the intermediate activations of the diffusion model at each timestep with its preceding timestep through a fusion mechanism. We propose two forms, explicit SSD and implicit SSD (iSSD), to perform \\(N\\)-step to \\(N\\)-step distillation from the diffusion model itself to achieve improved image quality. We further elucidate the relationship between SSD and high-order solver, highlighting their underlying relationship. The effectiveness of SSD is validated through extensive experiments on diffu" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.907, + 0.734 + ], + "angle": 0, + "content": "sion transformers of various sizes and across different sampling steps. Our results show that this novel self-distillation paradigm can significantly enhance performance. Additionally, our method is compatible with the distillation method designed for few-step inference. Notably, with iSSD trained less than one epoch, we obtain a 32-step DiT-XL/2 achieving an FID of 1.99, outperforming the original 250-step DiT-XL/2 with an FID of 2.26. We further validate the effectiveness of our method on text-to-image diffusion models, such as Stable Diffusion, and also observe notable improvement in image quality." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.768, + 0.646, + 0.784 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Diffusion-based generative models [5, 16, 51] have gained significant attention for their remarkable capability to generate diverse, high-fidelity outputs across various domains. It has been proven effective in tasks such as image synthesis [42, 44, 46], video generation [1, 17, 18] and natural language processing [27, 33]. Unlike previous generative approaches like VAEs [24] and GANs [12], Diffusion Mod-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.116, + 0.887, + 0.241, + 0.901 + ], + "angle": 0, + "content": "* Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12901" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.198 + ], + "angle": 0, + "content": "els (DMs) rely on a unique process where noise is gradually refined into meaningful data by reversing a specified noise pathway [20]. This iterative noise-to-data transformation gives DMs exceptional versatility, allowing them to be applied successfully in image editing [21], inpainting [35], super-resolution [11], object detection [3], 3D generation [43], etc." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.201, + 0.485, + 0.473 + ], + "angle": 0, + "content": "Recent studies have emphasized the effectiveness of knowledge distillation [15] as a tool for enhancing inference efficiency or accelerating pre-training for diffusion models [38, 50]. These methods typically achieve distillation through the use of an external teacher model or a teacher with more sampling steps. To improve inference efficiency, approaches such as progressive distillation and consistency distillation [23, 36, 47, 52] employ an extensive multi-step sampling process as a teacher model to distill the student model with fewer steps. These teacher models more accurately approximate the denoising trajectory, thereby guiding the student model to enable the few-step generation or even one-step generation [7]. Other studies [13, 19, 22] focus on distilling compact diffusion models by training smaller models under the supervision of larger, high-capacity models. Besides, [60] demonstrates that aligning model representations using guidance from an external pre-trained vision encoder can facilitate faster convergence." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.476, + 0.483, + 0.656 + ], + "angle": 0, + "content": "The aforementioned methods can significantly enhance the sampling efficiency of diffusion models through distillation. However, the student models are constrained by the performance of the teacher model, with their training aimed at matching, but not surpassing, the teacher's performance. This raises an intriguing question: Can distillation be leveraged to improve the generation quality of the diffusion model itself, potentially exceeding the performance of the teacher model? This shifts the focus from traditional \\(N\\)-to-\\(M\\) step distillation or model compression for speed to a form of \\(N\\)-to-\\(N\\) step self-distillation aimed at enhancing the generation quality of the original diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.483, + 0.901 + ], + "angle": 0, + "content": "We thereby explore the unique form of self-distillation within diffusion models. While self-distillation has been studied extensively in conventional architectures [10, 39, 61, 62], its application to diffusion models remains unexplored. explore the special way that self-distillation operates in diffusion models by utilizing the properties of diffusion models. Given the temporal relationships between steps that form a sequence of predictions, we introduce Self Step-Distillation in both explicit and implicit forms. The core idea is that, with careful design, the model can enhance its performance by mimicking the next-step prediction. To achieve this, we propose a fusion of predictions and features across different steps, and redefine the computational flow for the student model. Once the student model is trained, it can be reverted to the original computational pipeline. We also illustrate how this fusion mechanism relates to high-" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.093, + 0.608, + 0.106 + ], + "angle": 0, + "content": "order solvers." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.107, + 0.905, + 0.424 + ], + "angle": 0, + "content": "We mainly conduct our experiments on diffusion transformers [40] due to their exceptional performance. We conduct experiments on DiT models ranging from DiT-S/2 to DiT-XL/2 and sampling steps from 4 to 250. With our method, a self-distilled DiT-XL/2 with 50 sampling steps surpasses the performance of the pre-trained DiT-XL/2 with 250 sampling steps (2.02 vs 2.14 in FID). To further examine the \\(N\\)-to-\\(N\\) distillation setting and show that our method is complementary to the few-step distillation, we applied our method on a progressively distilled DiT-XL/2. This resulted in an enhanced generation quality, with an FID of 1.99 achieved using 32 sampling steps. Additionally, we tested the generalizability of our method by applying it to Stable Diffusion, confirming its effectiveness in the text-to-image setting. All experiments require fewer than 10k optimization steps and a short training duration—approximately 40 minutes for DiT-XL/2 and 3 hours for Stable Diffusion. Consequently, our method can be considered a quick self-improvement technique for diffusion models, which we further show that it can operate without dependence on training data." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.425, + 0.858, + 0.438 + ], + "angle": 0, + "content": "To summarize, the contributions of our work are:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.44, + 0.905, + 0.484 + ], + "angle": 0, + "content": "- We demonstrate for the first time that self-distillation can enhance the performance of diffusion models itself, significantly surpassing the original model." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.485, + 0.905, + 0.559 + ], + "angle": 0, + "content": "- We introduce a novel self-distillation framework for diffusion models, termed Self Step-Distillation. By corrupting and fusing predictions and intermediate activations, we redefine the computational flow of the teacher and student diffusion model to facilitate self-distillation." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.561, + 0.905, + 0.605 + ], + "angle": 0, + "content": "- We analyze the underlying mechanisms of this unique self-distillation approach and reveal its connection to high-order solvers." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.606, + 0.905, + 0.665 + ], + "angle": 0, + "content": "- Experimental results demonstrate that our self-distillation method significantly enhances the performance of diffusion models, including both DiT and Stable Diffusion, as well as distilled few-step diffusion models." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.44, + 0.905, + 0.665 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.68, + 0.655, + 0.695 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Distillation in Diffusion Models. knowledge distillation [15] becomes a popular paradigm to improve the efficiency of diffusion models. Progressive Distillation [47] proposes to half the steps of sampling by matching the samples generated by N deterministic steps with 2N steps. Consistency distillation [52] enforces the self-consistency between any pair of steps and makes the boundary condition avoid trivial solutions. [36] extends it into the latent space, and [23, 54] divides the whole trajectory consistency into subphase consistency. SFD [64] solves the accumulative errors in local distillation by sampling and imitating the whole trajectory. [59] distills the diffusion model into a one-step generator by matching at the distribution level with adversarial" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12902" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.482, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.318, + 0.485, + 0.348 + ], + "angle": 0, + "content": "Figure 2. The overall framework of Self Step-Distillation. Here \\(\\theta^{-}\\) means that the weight of the model is frozen." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.376, + 0.487, + 0.558 + ], + "angle": 0, + "content": "loss. [6] shows that the high-order term, jacobian-vector products, can be distilled into a separate neural network. Guided diffusion [38] matches the combined output of the classifier-free guidance with a single model, and reduces the sampling steps for unconditional generation and conditional generation. The adversarial objective can also be incorporated in diffusion training to stabilize the training process [30, 48]. Apart from this, another line of work uses knowledge distillation to make the diffusion model small and efficient [8, 58]. Feature-level knowledge distillation is widely adopted in those works to accelerate the post-training of these compressed diffusion models [8, 13, 22]." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.584, + 0.485, + 0.902 + ], + "angle": 0, + "content": "Efficiency in Diffusion Models. Balancing the image quality and the sampling speed is a challenging topic in diffusion models [20, 55]. (1) Fast solver for sampling. One common way to reduce the sampling steps is to employ a training-free solver to off-the-shelf pre-trained diffusion models. Those methods approximate the true trajectory of probability flow ODE, such as Euler's method [50], Heun's method [20], the exponential integrator with Taylor expansion [34], the unified predictor-corrector framework [63] and numerical methods [32]. (2) Structural Efficiency. Besides of optimizing the number of model evaluations, another way is to encourage structural efficiency. Redesign the model architectures [58], pruning [8, 29, 65] and quantization [14, 28] constructs lightweight diffusion model. Cache-based methods [37, 56] leverage the similarity between steps to reduce calculations. (3) Pipeline Efficiency. Breaking the sequential nature of denoising is another way to improve the efficiency of diffusion models. [49] uses Picard iteration to iteratively refine until convergence. [4, 25] decouples the images or models into multiple components and assigns them to different devices." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.091, + 0.908, + 0.364 + ], + "angle": 0, + "content": "Self-Distillation Knowledge distillation is widely used for compressing compact networks, while self-distillation focuses on improving the performance of networks. [10] investigate distillation with a student network parameterized identically to its teacher, demonstrating that the student could significantly outperform the teacher. [61] explores distilling knowledge from deeper network layers into shallower ones. Several works [2, 39, 57] examine the underlying reasons for this phenomenon, commonly attributing it to the \"dark knowledge\" encoded in soft labels. [62] highlight the importance of predictive diversity, while [41] systematically investigates self-distillation carefully and interprets self-distillation as a process of learning previously unlearned perspectives of input data. Unlike these prior works, our focus is not on leveraging soft labels from teacher predictions to guide student network training. Instead, we explore a unique mechanism in diffusion models to enhance their performance." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.376, + 0.606, + 0.391 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.402, + 0.907, + 0.477 + ], + "angle": 0, + "content": "In this section, we elaborate on the design of our self-distillation framework. We first show our proposed framework of the self-distillation paradigm in Section 3.2, and then give the explanation about why it works in Section 3.3 and Section 3.4." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.486, + 0.644, + 0.503 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.508, + 0.909, + 0.6 + ], + "angle": 0, + "content": "We begin from the forward and reverse processes in diffusion probabilistic models. Let \\( q_{\\mathrm{data}}(x) \\) represent the data distribution. The forward process entails adding noise incrementally to a clean image \\( x_0 \\sim q_{\\mathrm{data}}(x) \\). At a given timestep \\( t \\), the distribution of \\( x_t \\), which includes the noise added up to that point, is defined by:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.609, + 0.907, + 0.628 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, \\left(1 - \\bar {\\alpha} _ {t}\\right) \\mathbf {I}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.636, + 0.909, + 0.789 + ], + "angle": 0, + "content": "where \\(\\alpha_{t}\\) is a time-dependent function that controls the noise scheduling. As \\(t\\) approaches a sufficiently large value, the final state \\(x_{T}\\) becomes nearly the same as a Gaussian noise. For denoising, starting from a noise input \\(x_{T} \\sim \\mathcal{N}(0, \\mathbf{I})\\), an image can be progressively reconstructed through iterative sampling from the conditional distribution \\(q(x_{t-1} | x_{t})\\). This conditional probability is typically approximated by a parameterized distribution, given as \\(p_{\\theta}(x_{t-1} | x_{t}) = \\mathcal{N}(x_{t-1}; \\mu_{\\theta}(x_{t}, t), \\Sigma_{\\theta}(x_{t}, t))\\). Here, \\(\\mu_{\\theta}(x_{t}, t)\\) is parameterized by \\(\\theta\\), and it follows:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.797, + 0.907, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\mu_ {\\theta} \\left(x _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(x _ {t}, t\\right)\\right) \\quad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.909, + 0.903 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}(x_t,t)\\) represents the noise estimation function at timestep \\(t\\) given input \\(x_{t}\\). The training objective for diffusion models is to minimize the difference between the predicted noise and the ground-truth noise \\(\\epsilon_{t}\\) added during" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12903" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.485, + 0.138 + ], + "angle": 0, + "content": "the forward process. This is typically framed as a simplified version of the variational bound on the negative log-likelihood of \\( x_0 \\). The objective can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.149, + 0.483, + 0.174 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t} = \\mathbb {E} _ {t \\sim [ 1, T ], \\mathbf {x} _ {0} \\sim q _ {\\text {d a t a}} (x)} \\left[ \\| \\boldsymbol {\\epsilon} _ {t} - \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}, t) \\| ^ {2} \\right] \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.185, + 0.281, + 0.2 + ], + "angle": 0, + "content": "3.2. Overall Framework" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.207, + 0.484, + 0.357 + ], + "angle": 0, + "content": "Next, we introduce the design of this unique form of self-distillation within diffusion models. To achieve self-distillation, three essential components must be defined: the construction of the teacher model, the formulation of the student model, and the definition of the training objective. Given that we have only a single pre-trained model without any external supervision. This poses a critical challenge: how can a single pre-trained diffusion model be used to construct both a teacher and a student model, with the teacher model designed to be more capable than the student?" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.359, + 0.484, + 0.512 + ], + "angle": 0, + "content": "We focus on the timesteps of diffusion models, which inherently give us a sequence of predictions for one sample. Denote the model to have \\(L\\) layers. \\(x^{(l)}\\) denotes the input for layer \\(l\\), where \\(l \\in \\{1, 2, \\dots, L\\}\\). \\(x_{t}^{(1)} = x_{t}\\) represents the input to the network at timestep \\(t\\). Each layer \\(l\\) applies a function \\(f_{\\theta_l}\\) parameterized by \\(\\theta_{l}\\), which includes operations such as multi-head self-attention and pointwise feedforward module in Transformer [53], and residual or convolution blocks in U-Net [45]. Thus, for each layer, the layer-wise computation at timestep \\(t\\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.522, + 0.483, + 0.549 + ], + "angle": 0, + "content": "\\[\nx _ {t} ^ {(l)} = f _ {\\theta_ {l - 1}} \\left(x _ {t} ^ {(l - 1)}, t\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.56, + 0.484, + 0.636 + ], + "angle": 0, + "content": "Here the calculation is conditioned on the timestep \\( t \\), although not all blocks in diffusion model use \\( t \\) as a conditional input. After all \\( L \\) layers have been processed, the final output of the model is the predicted noise, represented as \\( \\epsilon(x_{t}, t) = x_{t}^{(L + 1)} \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.638, + 0.484, + 0.818 + ], + "angle": 0, + "content": "To construct the teacher and student models, we require the outputs for two timesteps, \\(t\\) and \\(s\\), where \\(s\\) represents the preceding denoising step of \\(t\\) under a pre-defined solver, satisfying \\(s > t\\). We denote the predictions of the teacher and the student model as \\(\\epsilon^{\\mathcal{T}}(x_t,x_s,t,s)\\) and \\(\\epsilon^S (x_t,x_s,t,s)\\), respectively. Our approach to building the teacher and student models is based on a core principle: using the predictions from a later step as stronger supervision to guide the prediction at an earlier step. The rationale behind this principle will be discussed in detail later. Based on this guideline, we develop the below two distinct forms for self-distillation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.838, + 0.483, + 0.869 + ], + "angle": 0, + "content": "Explicit Form: For the explicit self step-distillation, we build a teacher model by fusing the predicted noise:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.879, + 0.483, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\epsilon} ^ {\\mathcal {T}} \\left(x _ {t}, x _ {s}, t, s\\right) = \\lambda \\boldsymbol {\\epsilon} _ {\\theta^ {-}} \\left(x _ {t}, t\\right) + (1 - \\lambda) \\boldsymbol {\\epsilon} _ {\\theta^ {-}} \\left(x _ {s}, s\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.906, + 0.138 + ], + "angle": 0, + "content": "The student prediction use the predicted noise at timestep \\(s\\): \\(\\epsilon^{\\mathcal{S}}(x_t,x_s,t,s) = \\epsilon_\\theta (x_s,s)\\). Here, \\(\\theta^{-}\\) represents the model would be frozen during training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.159, + 0.907, + 0.237 + ], + "angle": 0, + "content": "Implicit Form: For the implicit self step-distillation, we redefine the computation flow in the model. We fuse the outputs at the same intermediate layer but different timesteps \\(t\\) and \\(s\\), denoted \\(x_{t}^{(l)}\\) and \\(x_{s}^{(l)}\\) respectively. The fused output at this layer is now calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.248, + 0.907, + 0.275 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {t} ^ {(l)} = \\lambda f _ {\\theta_ {l - 1} ^ {-}} \\left(x _ {s} ^ {(l - 1)}, s\\right) + (1 - \\lambda) f _ {\\theta_ {l - 1}} \\left(\\tilde {x} _ {t} ^ {(l - 1)}, t\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.287, + 0.907, + 0.45 + ], + "angle": 0, + "content": "where \\(\\tilde{x}_t^{(l-1)}\\) represents the fused output from the previous layer, and \\(\\tilde{x}_t^{(l)}\\) serves as the input for the next layer, replacing the original \\(x_t^{(l)}\\). The above equation serves as a weighted fusion of layer output in two timesteps. The final prediction \\(\\epsilon^S(x_t, x_s, t, s) = \\tilde{x}_t^{(L+1)}\\) is obtained from these fused features, forming the prediction for the student model. With this, the computation flow of the student model is changed. In constraint, the teacher model functions as the original denoising predictor at timestep \\(t\\), with its prediction output expressed as \\(\\epsilon^T(x_t, x_s, t, s) = \\epsilon_{\\theta^{-}}(x_t, t)\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.906, + 0.576 + ], + "angle": 0, + "content": "Training Objective. We take the pre-trained model as both the initialization for the teacher and the student model. The teacher \\(\\theta_T\\) model remained frozen while the update of parameters is performed on the student side. The self-distillation objective here is the matching between the student \\(\\epsilon^S(x_t, x_s, t, s)\\) and the teacher \\(\\epsilon^T(x_t, x_s, t, s)\\). The distillation objective would be:" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.587, + 0.905, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathbb {E} _ {s \\sim [ 1, T ], x _ {0} \\sim q _ {\\mathrm {d a t a}} (x)} \\left[ \\left\\| \\boldsymbol {\\epsilon} ^ {\\mathcal {T}} \\left(x _ {t}, x _ {s}, t, s\\right) - \\boldsymbol {\\epsilon} ^ {\\mathcal {S}} \\left(x _ {t}, x _ {s}, t, s\\right) \\right\\| ^ {2} \\right] \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.626, + 0.906, + 0.732 + ], + "angle": 0, + "content": "Here, \\( x_{s} \\) represents \\( x_{0} \\) with added noise, and \\( x_{t} \\) is obtained by performing one step from \\( x_{s} \\) in the ODE solver. After the training phase is completed, no fusion operations are applied during the inference stage. The model's computation remains identical to its original configuration but benefits from the enhancements gained through the self-distillation process." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.742, + 0.788, + 0.759 + ], + "angle": 0, + "content": "3.3. Distill from High-Order Solver" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.902 + ], + "angle": 0, + "content": "In this section, we explain why this self-distillation framework works. In order to reduce the discretization error for the first-order ODE solver, such as Euler [20], one straightforward way is to use the higher-order solver for the diffusion ODEs. The cost for this is that it needs twice or third or even more times of function evaluation. We show that our self-distillation framework serves as an approximated form for distilling it into the same network without introducing additional parameters." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12904" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.483, + 0.137 + ], + "angle": 0, + "content": "We perform a single step forward from timestep \\( s \\) to timestep \\( t \\). We compare the formulation of DPM-Solver-1 and DPM-Solver-2 [34]." + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.148, + 0.483, + 0.176 + ], + "angle": 0, + "content": "\\[\n\\text {D P M - S o l v e r - 1 :} x _ {t} = \\frac {\\alpha_ {t}}{\\alpha_ {s}} x _ {s} - w _ {t} \\epsilon_ {\\theta} (x _ {s}, s) \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.178, + 0.483, + 0.207 + ], + "angle": 0, + "content": "\\[\n\\text {D P M - S o l v e r - 2 :} x _ {t} = \\frac {\\alpha_ {t}}{\\alpha_ {s}} x _ {s} - w _ {t} \\epsilon_ {\\theta} (x _ {u}, u) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.217, + 0.484, + 0.367 + ], + "angle": 0, + "content": "Here the timestep \\( u \\) is an intermediate timestep between \\( t \\) and \\( s \\). As defined in DPM-Solver-2, timestep \\( u \\) has \\( \\lambda_u \\coloneqq \\log \\left( \\frac{\\alpha_u}{\\sigma_u} \\right) \\) which is the average of those for timestep \\( t \\) and timestep \\( s \\), and \\( x_u \\) denotes the state one step forward from \\( s \\) to \\( u \\). The term \\( w_t \\) is a weight factor that depends only on the timestep. Using DPM-Solver-2, which is more accurate than DPM-Solver-1, the following training objective can be interpreted as encouraging the predictions of the first-order solver to align more closely with those of the second-order solver:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.377, + 0.483, + 0.418 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathbb {E} _ {s \\sim [ 1, T ], \\mathbf {x} _ {0} \\sim q _ {\\text {d a t a}} (x)} \\left[ w _ {t} \\| \\boldsymbol {\\epsilon} _ {\\theta} \\left(x _ {s}, s\\right) - \\boldsymbol {\\epsilon} _ {\\theta} \\left(x _ {u}, u\\right) \\| ^ {2} \\right] \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.42, + 0.484, + 0.482 + ], + "angle": 0, + "content": "Building on the above equation, if the goal is to approximate a higher-order solver using a first-order solver, the training objective simplifies to: matching the prediction at the current step with the prediction at a subsequent step." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.492, + 0.357, + 0.509 + ], + "angle": 0, + "content": "3.4. Ways to approximate \\(\\epsilon_{\\theta}(x_u,u)\\)" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.514, + 0.484, + 0.741 + ], + "angle": 0, + "content": "However, this method requires the prediction at the intermediate step between timestep \\( s \\) and \\( t \\), which is not always feasible in \\( N \\)-step to \\( N \\)-step distillation. A feasible scenario involves using a linear interpolant noise scheduler, where \\( x_{s} = (1 - s / T)x_{0} + (s / T)\\epsilon \\), and the model predicts the velocity instead of the noise \\( \\epsilon \\). Under these conditions, the objective can be reformulated to align \\( \\epsilon_{\\theta}(x_s,s) \\) with \\( \\epsilon_{\\theta}(x_t,t) \\). The corresponding results are presented in Table 1, with detailed proofs provided in the Appendix. With 10 and 250 sampling steps, consistent improvements in sample quality are observed, validating the effectiveness of Eq.10. However, as expected, performance declined in both cases when using \\( \\epsilon \\)-prediction without incorporating these properties into the noise scheduler and the specific model prediction type." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.742, + 0.484, + 0.833 + ], + "angle": 0, + "content": "The question now arises: how we can approximate \\(\\epsilon_{\\theta}(x_u,u)\\) given \\(\\epsilon_{\\theta}(x_s,s)\\) and \\(\\epsilon_{\\theta}(x_t,t)\\). One straightforward way is to get the approximation of \\(\\epsilon_{\\theta}(x_u,u)\\) by Taylor Expansion, whose results turned to be the interpolating between \\(\\epsilon_{\\theta}(x_s,s)\\) and \\(\\epsilon_{\\theta}(x_t,t)\\). Following the assumption in [34] that \\(\\epsilon_{\\theta}(x_s,s)\\) is Lipschitz w.r.t \\(x_{s}\\), we have:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.845, + 0.483, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\epsilon_ {\\theta} \\left(x _ {u}, u\\right) = \\epsilon_ {\\theta} \\left(x _ {s}, u\\right) + \\left(\\epsilon_ {\\theta} \\left(x _ {u}, u\\right) - \\epsilon_ {\\theta} \\left(x _ {s}, u\\right)\\right) \\\\ = \\epsilon_ {\\theta} (x _ {s}, s) + \\epsilon_ {\\theta} ^ {(1)} (x _ {s}, s) (u - s) + \\mathcal {O} ((u - s) ^ {2}) \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.089, + 0.905, + 0.272 + ], + "angle": 0, + "content": "
    ModelSamplerNFEsISFIDsFID
    v-prediction with linear interpolant noise scheduler
    REPA - SiT-XL/2SDE250305.71.424.70
    REPA - SiT-XL/2° w/ Eq.10SDE250306.31.414.68
    REPA - SiT-XL/2°ODE10233.95.857.82
    REPA - SiT-XL/2° w/ Eq.10ODE10238.45.117.48
    ε-prediction
    DiT-XL/2ODE50238.62.264.29
    DiT-XL/2 w/ Eq.10ODE50230.82.816.41
    DiT-XL/2 w/ Eq.12ODE50239.92.214.41
    DiT-XI/2ODE10158.312.3811.22
    DiT-XL/2 w/ Eq.10ODE1051.845.9926.95
    DiT-XL/2 w/ Eq.12ODE10184.77.999.91
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.282, + 0.905, + 0.325 + ], + "angle": 0, + "content": "Table 1. Results on \\( v \\)-prediction and \\( \\epsilon \\)-prediction diffusion models. For the experiments on REPA, we use the EMA model as the teacher for the experiments with 250 steps." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.328, + 0.905, + 0.379 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}^{(1)}(x_s,s)\\) is the first-order derivative w.r.t \\(s\\). As above, we derive \\(\\epsilon_{\\theta}^{(1)}(x_s,s)\\) the same way between two different timesteps \\(t\\) and \\(s\\), and we have:" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.387, + 0.905, + 0.404 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {\\theta} \\left(x _ {u}, u\\right) = (1 - \\lambda) \\epsilon_ {\\theta} \\left(x _ {s}, s\\right) + \\lambda \\epsilon_ {\\theta} \\left(x _ {t}, t\\right) \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.411, + 0.905, + 0.455 + ], + "angle": 0, + "content": "where \\(\\lambda = (u - s) / (t - s)\\). We get the same form as the explicit self step-distillation. The results with this equation are also shown in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.457, + 0.907, + 0.653 + ], + "angle": 0, + "content": "While the aforementioned method can approximate \\(\\epsilon_{\\theta}(x_u,u)\\) to some extent, it remains suboptimal. An alternative approach is the implicit form of interpolation, which approximates \\(\\epsilon_{\\theta}(x_u,u)\\) by interpolating on features rather than on the output. This one shares the same form with implicit self step-distillation. This idea is inspired by previous works [26, 37], which demonstrated that certain intermediate activations in timestep \\(s\\) can be reused in later timestep \\(u\\) to produce an approximated output for timestep \\(u\\), with minimal effect on image quality. Consequently, we interpolate on the intermediate layers, and experimental results indicate that this method yields better performance than interpolation on predictions." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.665, + 0.64, + 0.682 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.907, + 0.842 + ], + "angle": 0, + "content": "In this section, we demonstrate the effectiveness of our proposed method. In Section 4.2, we present empirical evidence that both SSD and iSSD consistently enhance the performance of a pre-trained DiT across various image resolutions, model sizes, and sampling steps. Additionally, Section 4.3 provides the results of applying these methods to text-to-image generation. Section 4.4 highlights how iSSD can be applied to distilled models, yielding further performance improvements. Finally, Section 4.5 offers an in-depth analysis." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.849, + 0.704, + 0.866 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Models. For the conditional generation on ImageNet, we take all four DiT models: DiT-S/2, DiT-B/2, DiT-L/2, and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12905" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.09, + 0.904, + 0.27 + ], + "angle": 0, + "content": "
    MethodNFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑NFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    -256×256--512×512-
    DiT-XL/2250(ODE)1400243.42.144.560.810.61250(SDE)600240.83.045.020.840.54
    SiT-XL/2250(SDE)1400277.52.064.490.830.59250(SDE)600252.22.624.180.840.57
    DiT-XL/2501400238.62.264.290.800.6050600204.13.284.500.830.55
    + SSD501400 + 0.8239.92.214.410.800.6050600 + 0.4205.23.184.590.830.57
    + iSSD501400 + 0.8250.02.024.220.810.6050600 + 0.4210.22.864.060.840.54
    DiT-XL/2201400223.53.484.890.790.5720600186.35.105.730.820.55
    + SSD201400 + 0.8228.62.824.630.790.6020600 + 0.4194.74.015.330.830.56
    + iSSD201400 + 0.8227.52.674.850.790.6020600 + 0.4200.83.694.410.840.54
    DiT-XL/2101400158.312.3811.220.670.5310600128.415.1911.580.740.49
    + SSD101400 + 0.8184.77.999.910.710.5610600 + 0.4158.59.6111.090.780.54
    + iSSD101400 + 0.8209.64.927.620.790.5310600 + 0.4164.96.977.050.830.51
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.28, + 0.907, + 0.31 + ], + "angle": 0, + "content": "Table 2. Image quality on ImageNet \\( {256} \\times {256} \\) and \\( {512} \\times {512} \\) ,with DiT-XL/2 as the base model. Prec. and Rec. denotes Precision and Recall. We adopt CFG=1.5 in all the experiments for ImageNet." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.332, + 0.481, + 0.671 + ], + "angle": 0, + "content": "
    ModelNFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    -DiT-S/2-
    DiT-S/225040059.426.517.310.590.56
    DiT-S/2+ iSSD5040053.529.215.890.570.58
    50400 + 0.254.627.755.730.580.58
    DiT-S/2+ iSSD2040052.032.627.430.550.55
    20400 + 0.252.530.628.230.560.55
    DiT-S/2+ iSSD1040040.149.5018.330.430.48
    10400 + 0.240.746.1718.890.450.48
    -DiT-B/2-
    DiT-B/2250200119.610.125.390.730.55
    DiT-B/2+ iSSD50200101.812.844.810.710.56
    50200 + 0.2104.911.774.990.710.56
    DiT-B/2+ iSSD2020097.515.406.110.680.54
    20200 + 0.2100.613.848.630.710.52
    DiT-B/2+ iSSD1020072.128.9915.540.560.48
    10200 + 0.277.921.4013.370.610.53
    -DiT-L/2-
    DiT-L/2250200196.33.734.620.820.54
    DiT-L/2+ iSSD50200168.84.774.410.780.55
    50200 + 0.2172.74.414.440.800.56
    DiT-L/2+ iSSD20200160.56.425.260.770.53
    20200 + 0.2172.34.924.870.800.53
    DiT-L/2+ iSSD10200118.516.0112.630.670.47
    10200 + 0.2143.77.754.990.750.55
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.681, + 0.483, + 0.709 + ], + "angle": 0, + "content": "Table 3. Image quality on ImageNet \\( {256} \\times {256} \\) with DiT-S/2,DiT-B/2 and DiT-L/2" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.733, + 0.484, + 0.809 + ], + "angle": 0, + "content": "DiT-XL/2. For DiT-XL/2, we utilize the official pre-trained model, whereas for the other three models, we train them for 1 million to 2 million steps. For the text-to-image generation experiments, we employ Stable Diffusion v1.5 [44] as our base model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Evaluation. We follow previous work [40] to use IS, FID, sFID, Precision and Recall as the evaluation metric. For text-to-image generation, we test the FID on the validation set of COCO2014 and COCO2017 [31]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.335, + 0.907, + 0.577 + ], + "angle": 0, + "content": "Training and Sampling Details. For training, the teacher and student models are both initialized from the base model, with the teacher remaining fixed during training. We use DDIM [50] as our base ODE solver and only utilize N-step predictions during training if the fine-tuned model would be evaluated under N-step. For DiT, we set a learning rate of 5e-6, a batch size of 128. The training epochs for each experiment are listed in the tables. Exponential Moving Average (EMA) is not used due to the short training period. We follow the original DiT setup without weight decay, warm-up, or learning rate schedulers. Models were evaluated with 10, 20, and 50 numbers of function evaluations (NFEs), and we show that even the basic ODE algorithms outperformed many advanced samplers with our algorithms. More details, especially for text-to-image generation, are in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.587, + 0.733, + 0.603 + ], + "angle": 0, + "content": "4.2. Conditional Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.609, + 0.907, + 0.837 + ], + "angle": 0, + "content": "Results on DiT-XL. We show the results of DiT-XL/2 in Table 2. With less than 1 epoch for optimizing DiT-XL/2, our method achieves consistent performance improvement upon the base models. Notably, our method with 50 NFEs can exceed the performance of the base DiT-XL/2 sampled 250 times by a large margin (2.02 vs 2.14), both under the same ODE sampler. Also this improvement can be observed in the resolution of 512, where the base DiT achieves the FID of 3.04, while our method can improve it to 2.86. We also notice improvement compared with the 250-step SiT, with our method sampled with only 50 steps. Besides, we found the implicit SSD performs better than the explicit SSD in most cases, and sometimes the implicit SSD outperforms the explicit SSD by a large margin. We show the qualitative results on ImageNet in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Results on small-scale DiTs. We also apply our method under smaller DiT models, showing that the method can be generalized to models with different sizes. Since in the ex" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12906" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.091, + 0.48, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.254, + 0.483, + 0.296 + ], + "angle": 0, + "content": "Figure 3. Visualization of generated images using various sampling algorithms with NFEs=10. From left to right, the algorithms shown are: PLMS, DDIM, DPM-Solver-2, and SSD." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.31, + 0.48, + 0.392 + ], + "angle": 0, + "content": "
    DatasetNFEsDDIMPLMSDPM-Solver-2Ours
    COCO20141012.7817.7115.2310.94
    2012.6812.6514.6310.56
    COCO20171022.7929.5124.4620.85
    2022.4322.1424.0220.69
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.402, + 0.483, + 0.43 + ], + "angle": 0, + "content": "Table 4. FID Comparison with different samplers on the validation set of COCO2014 and COCO2017" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.458, + 0.484, + 0.563 + ], + "angle": 0, + "content": "periment in DiT-XL/2, we found iSSD consistently outperforms SSD, we here test the performance of iSSD on these DiT models. From Table 3, with only 0.2 epoch for training, we observe a large improvement upon the base model. It would only take several minutes to finish the training, and thus, can be seen as a cheap way to improve the performance of the trained models." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.574, + 0.328, + 0.59 + ], + "angle": 0, + "content": "4.3. Text-to-Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.596, + 0.483, + 0.732 + ], + "angle": 0, + "content": "We apply SSD to Stable Diffusion v1.5. The experimental details are outlined in Appendix. Our method is compared against DDIM [50], DPM-Solver-2 [34] and PLMS [32] on COCO2014 and COCO2017, as shown in Table 4. Our approach demonstrates significant improvements in FID, outperforming other methods. Notably, our results with 10 NFEs surpass those achieved with 20 NFEs by competing samplers. Visualization results further highlight that images enhanced by our algorithm exhibit more detailed features." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.743, + 0.336, + 0.758 + ], + "angle": 0, + "content": "4.4. Results on Distilled Models" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this section, we apply our method to a distilled model obtained through progressive distillation (PD). Notably, this implies that predictions at intermediate steps that are not explicitly part of the PD process are not trained, resulting in suboptimal performance at these steps. This experiment aims to demonstrate that our method is effective that distills from N steps to enhance performance across those N steps, since using the results from intermediate steps other than these N steps would harm the performance." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.089, + 0.905, + 0.234 + ], + "angle": 0, + "content": "
    ModelNFEsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    DiT-XL/2250243.42.144.560.810.61
    PD 64 → 3232239.82.244.330.800.60
    + iSSD32246.21.994.330.810.60
    PD 20 → 1010209.94.195.240.760.57
    + iSSD10233.93.567.080.810.55
    PD 20 → 10 → 55173.07.006.590.730.58
    + iSSD5186.75.416.480.760.56
    PD 16 → 8 → 44152.68.757.900.700.59
    + iSSD4168.586.107.530.720.57
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.243, + 0.905, + 0.271 + ], + "angle": 0, + "content": "Table 5. Results of building iSSD upon diffusion models being distilled for few-step generation." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.285, + 0.903, + 0.363 + ], + "angle": 0, + "content": "
    ModelIS ↑FID ↓sFID ↓Prec.↑Rec.↑
    DiT-XL/213.4107.7594.570.110.36
    PD [47]158.37.847.110.700.60
    Shortcut Model [9]-7.8---
    PD + Ours168.66.117.530.720.57
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.373, + 0.905, + 0.402 + ], + "angle": 0, + "content": "Table 6. Comparison with training-based method on ImageNet \\(256\\times 256\\) . We set NFEs \\(= 4\\) and use DiT-XL/2 for sampling." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.428, + 0.907, + 0.655 + ], + "angle": 0, + "content": "Orthogonal to distillation methods. Table 5 presents the results for models distilled through two-stage and three-stage progressive distillation (PD), and Figure 4(a) illustrates the results on a chain of models distilled from progressive distillation. The results indicate that our method can significantly enhance performance. Specifically, when applied to a 32-step distilled model, our approach achieves an FID of 1.99 with minimal additional computational cost, representing a substantial improvement over the distilled model and even the pre-trained DiT-XL/2. However, when comparing our method to the model directly distilled from PD, the performance at 10-step NFE is slightly lower (4.19 vs. 4.92). We position our method as an auxiliary step that complements and further refines the performance of distilled models, providing an orthogonal improvement." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.907, + 0.84 + ], + "angle": 0, + "content": "Comparison with training-based methods. We evaluated our model against flow-matching algorithms designed for training diffusion models to enable few-step generation. The experiments are performed using 4 steps to generate images, and the backbone for diffusion models is DiT-XL/2. The results, summarized in Table 6, indicate that our method surpasses the performance of competing algorithms. Specifically, when compared to the ShortCut Model [9], an enhanced variant of the flow matching model adapted for DiT, our approach achieves superior results (FID: 6.1 v.s. 7.8)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.849, + 0.617, + 0.865 + ], + "angle": 0, + "content": "4.5. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Comparison with continual training. To demonstrate that the observed performance improvements are not merely" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12907" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.312, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.195, + 0.192, + 0.214, + 0.203 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.317, + 0.091, + 0.534, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.417, + 0.192, + 0.435, + 0.203 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.092, + 0.716, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.192, + 0.638, + 0.203 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.094, + 0.903, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.804, + 0.192, + 0.822, + 0.203 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.206, + 0.907, + 0.248 + ], + "angle": 0, + "content": "Figure 4. Analysis of our proposed self-distillation framework includes: (a) iSSD consistently enhancing the quality of distilled DMs, (b) significant improvements in sample quality achieved by training only one step in the ODE trajectory, (c) evaluation of the performance of the teacher, student, and the final model, and (d) a substantial impact observed with variations in \\(\\lambda\\)" + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.272, + 0.48, + 0.391 + ], + "angle": 0, + "content": "
    ModelNFETrain EpochsIS↑FID↓
    DiT-XL/2101400158.312.38
    DiT-XL/2°101400 + 0.8156.712.97
    DiT-XL/2 + iSSD101400 + 0.8209.64.92
    DiT-S°25040027.651.55
    DiT-S°25042027.951.13
    DiT-S° + iSSD250400 + 228.748.38
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.401, + 0.483, + 0.43 + ], + "angle": 0, + "content": "Table 7. Comparison with Continual Training. The superscript \\(\\diamond\\) means we train these models from the official codebase." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.454, + 0.484, + 0.576 + ], + "angle": 0, + "content": "due to additional training iterations, we conducted experiments on DiT-XL/2 (officially pre-trained and only have the EMA model) and DiT-S/2 ( has both the EMA and the base model). The results in Table 7 show that even with fewer training epochs, our method significantly outperforms models trained for 20 epochs on DiT-S/2. This confirms that the performance gains stem from the proposed self-distillation approach rather than extended training iterations." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.593, + 0.484, + 0.745 + ], + "angle": 0, + "content": "Synthetic Data v.s. Real Data. An additional exploration involves assessing whether a model's performance can be improved when only the model itself is available, without any supplementary training data or external models. We conducted experiments under this setting, and the results are presented in Table 8. The findings indicate that, while real data remains the optimal choice for achieving the highest performance, the use of synthetic data can still result in substantial improvements in generation quality, albeit with a slight performance trade-off compared to using real data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.762, + 0.484, + 0.854 + ], + "angle": 0, + "content": "Distill upon only one step. In Figure 4(b), we show the results of applying iSSD to a single step. This process yields two models; here, our focus is on determining which step has the greatest impact on images. The results indicate that applying self-distillation in the later stages of denoising provides the most significant benefit to image quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "Training dynamics for the teacher and the student in iSSD. Figure 4(c) presents the training dynamics ob" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.272, + 0.905, + 0.343 + ], + "angle": 0, + "content": "
    ModelData SourceISFIDsFIDPrecisionRecall
    DiT-XL/2-158.312.3811.220.670.53
    iSSDOriginal Data209.64.927.620.790.53
    iSSDSynthetic - 10 step206.25.079.030.790.52
    iSSDSynthetic - 20 step207.95.028.990.790.53
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.353, + 0.907, + 0.382 + ], + "angle": 0, + "content": "Table 8. Results on Synthetic Data on ImageNet \\(256 \\times 256\\). The experiments are based on DDIM with 10 sampling steps." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.407, + 0.907, + 0.542 + ], + "angle": 0, + "content": "served during our experiments. It is crucial to note that the student model used in training differs from the one used for inference. The student model with fused activations starts with lower performance compared to the teacher model and remains inferior after training. In contrast, the unfused one, which maintains the same architecture and computation way for each layer, shows consistent improvement throughout training and eventually achieves significantly better performance than the teacher model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.561, + 0.909, + 0.683 + ], + "angle": 0, + "content": "Effect of gradient influential term \\(\\lambda\\). We show the effect of \\(\\lambda\\), as defined in Eq.5 and Eq.6. Though in Eq.12, we can directly calculate \\(\\lambda\\) if we adopt the same intermediate step as in DPM-Solver, we also put this timestep scheduler in this hyper-parameter, and search the best \\(\\lambda\\) for our approach. Figure 4(d) show for iSSD, with \\(\\lambda\\) equals a small value, the model would get poor results. We show the \\(\\lambda\\) used in each of our experiments in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.695, + 0.634, + 0.71 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.909, + 0.902 + ], + "angle": 0, + "content": "In this paper, we propose a novel self-distillation approach named Self Step-Distillation. We introduce two forms for Self Step-Distillation. Furthermore, we explain this approach by analyzing it through the lens of distillation with high-order samplers. Experimental results demonstrate that our method significantly outperforms the performance of the teacher model, achieving substantial improvements in both conditional generation and text-to-image generation. However, our method also has certain limitations. For instance, we still rely on suboptimal approaches to approximate the prediction of the intermediate step. Additionally, our method is relatively sensitive to hyperparameters." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12908" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.484, + 0.161 + ], + "angle": 0, + "content": "This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006)." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.173, + 0.188, + 0.189 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.199, + 0.484, + 0.282 + ], + "angle": 0, + "content": "[1] Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. Align your latents: High-resolution video synthesis with latent diffusion models. 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Generated Images before (left) and after (right) our proposed self-distillation framework on DiT-XL/2 for ImageNet $512 \times 512$ and Stable Diffusion v1.5 with 10 DDIM sampling steps. + +# Abstract + +In this paper, we introduce a novel self-distillation paradigm for improving the performance of diffusion models. Previous studies have shown that introducing a teacher to distill the diffusion model can enhance its sampling efficiency. We raise an intriguing question: can the diffusion model itself serve as its teacher to further improve the performance of itself? To this end, we propose a new paradigm called Self Step-Distillation (SSD). The core idea of SSD is to integrate the predictions or the intermediate activations of the diffusion model at each timestep with its preceding timestep through a fusion mechanism. We propose two forms, explicit SSD and implicit SSD (iSSD), to perform $N$ -step to $N$ -step distillation from the diffusion model itself to achieve improved image quality. We further elucidate the relationship between SSD and high-order solver, highlighting their underlying relationship. The effectiveness of SSD is validated through extensive experiments on diffu + +sion transformers of various sizes and across different sampling steps. Our results show that this novel self-distillation paradigm can significantly enhance performance. Additionally, our method is compatible with the distillation method designed for few-step inference. Notably, with iSSD trained less than one epoch, we obtain a 32-step DiT-XL/2 achieving an FID of 1.99, outperforming the original 250-step DiT-XL/2 with an FID of 2.26. We further validate the effectiveness of our method on text-to-image diffusion models, such as Stable Diffusion, and also observe notable improvement in image quality. + +# 1. Introduction + +Diffusion-based generative models [5, 16, 51] have gained significant attention for their remarkable capability to generate diverse, high-fidelity outputs across various domains. It has been proven effective in tasks such as image synthesis [42, 44, 46], video generation [1, 17, 18] and natural language processing [27, 33]. Unlike previous generative approaches like VAEs [24] and GANs [12], Diffusion Mod- + +els (DMs) rely on a unique process where noise is gradually refined into meaningful data by reversing a specified noise pathway [20]. This iterative noise-to-data transformation gives DMs exceptional versatility, allowing them to be applied successfully in image editing [21], inpainting [35], super-resolution [11], object detection [3], 3D generation [43], etc. + +Recent studies have emphasized the effectiveness of knowledge distillation [15] as a tool for enhancing inference efficiency or accelerating pre-training for diffusion models [38, 50]. These methods typically achieve distillation through the use of an external teacher model or a teacher with more sampling steps. To improve inference efficiency, approaches such as progressive distillation and consistency distillation [23, 36, 47, 52] employ an extensive multi-step sampling process as a teacher model to distill the student model with fewer steps. These teacher models more accurately approximate the denoising trajectory, thereby guiding the student model to enable the few-step generation or even one-step generation [7]. Other studies [13, 19, 22] focus on distilling compact diffusion models by training smaller models under the supervision of larger, high-capacity models. Besides, [60] demonstrates that aligning model representations using guidance from an external pre-trained vision encoder can facilitate faster convergence. + +The aforementioned methods can significantly enhance the sampling efficiency of diffusion models through distillation. However, the student models are constrained by the performance of the teacher model, with their training aimed at matching, but not surpassing, the teacher's performance. This raises an intriguing question: Can distillation be leveraged to improve the generation quality of the diffusion model itself, potentially exceeding the performance of the teacher model? This shifts the focus from traditional $N$ -to- $M$ step distillation or model compression for speed to a form of $N$ -to- $N$ step self-distillation aimed at enhancing the generation quality of the original diffusion model. + +We thereby explore the unique form of self-distillation within diffusion models. While self-distillation has been studied extensively in conventional architectures [10, 39, 61, 62], its application to diffusion models remains unexplored. explore the special way that self-distillation operates in diffusion models by utilizing the properties of diffusion models. Given the temporal relationships between steps that form a sequence of predictions, we introduce Self Step-Distillation in both explicit and implicit forms. The core idea is that, with careful design, the model can enhance its performance by mimicking the next-step prediction. To achieve this, we propose a fusion of predictions and features across different steps, and redefine the computational flow for the student model. Once the student model is trained, it can be reverted to the original computational pipeline. We also illustrate how this fusion mechanism relates to high- + +order solvers. + +We mainly conduct our experiments on diffusion transformers [40] due to their exceptional performance. We conduct experiments on DiT models ranging from DiT-S/2 to DiT-XL/2 and sampling steps from 4 to 250. With our method, a self-distilled DiT-XL/2 with 50 sampling steps surpasses the performance of the pre-trained DiT-XL/2 with 250 sampling steps (2.02 vs 2.14 in FID). To further examine the $N$ -to- $N$ distillation setting and show that our method is complementary to the few-step distillation, we applied our method on a progressively distilled DiT-XL/2. This resulted in an enhanced generation quality, with an FID of 1.99 achieved using 32 sampling steps. Additionally, we tested the generalizability of our method by applying it to Stable Diffusion, confirming its effectiveness in the text-to-image setting. All experiments require fewer than 10k optimization steps and a short training duration—approximately 40 minutes for DiT-XL/2 and 3 hours for Stable Diffusion. Consequently, our method can be considered a quick self-improvement technique for diffusion models, which we further show that it can operate without dependence on training data. + +To summarize, the contributions of our work are: + +- We demonstrate for the first time that self-distillation can enhance the performance of diffusion models itself, significantly surpassing the original model. +- We introduce a novel self-distillation framework for diffusion models, termed Self Step-Distillation. By corrupting and fusing predictions and intermediate activations, we redefine the computational flow of the teacher and student diffusion model to facilitate self-distillation. +- We analyze the underlying mechanisms of this unique self-distillation approach and reveal its connection to high-order solvers. +- Experimental results demonstrate that our self-distillation method significantly enhances the performance of diffusion models, including both DiT and Stable Diffusion, as well as distilled few-step diffusion models. + +# 2. Related Work + +Distillation in Diffusion Models. knowledge distillation [15] becomes a popular paradigm to improve the efficiency of diffusion models. Progressive Distillation [47] proposes to half the steps of sampling by matching the samples generated by N deterministic steps with 2N steps. Consistency distillation [52] enforces the self-consistency between any pair of steps and makes the boundary condition avoid trivial solutions. [36] extends it into the latent space, and [23, 54] divides the whole trajectory consistency into subphase consistency. SFD [64] solves the accumulative errors in local distillation by sampling and imitating the whole trajectory. [59] distills the diffusion model into a one-step generator by matching at the distribution level with adversarial + +![](images/7c9252b37f1c5bd7bb593c9de27984e43383682c7d67562f7ff861e8bca7a261.jpg) +Figure 2. The overall framework of Self Step-Distillation. Here $\theta^{-}$ means that the weight of the model is frozen. + +loss. [6] shows that the high-order term, jacobian-vector products, can be distilled into a separate neural network. Guided diffusion [38] matches the combined output of the classifier-free guidance with a single model, and reduces the sampling steps for unconditional generation and conditional generation. The adversarial objective can also be incorporated in diffusion training to stabilize the training process [30, 48]. Apart from this, another line of work uses knowledge distillation to make the diffusion model small and efficient [8, 58]. Feature-level knowledge distillation is widely adopted in those works to accelerate the post-training of these compressed diffusion models [8, 13, 22]. + +Efficiency in Diffusion Models. Balancing the image quality and the sampling speed is a challenging topic in diffusion models [20, 55]. (1) Fast solver for sampling. One common way to reduce the sampling steps is to employ a training-free solver to off-the-shelf pre-trained diffusion models. Those methods approximate the true trajectory of probability flow ODE, such as Euler's method [50], Heun's method [20], the exponential integrator with Taylor expansion [34], the unified predictor-corrector framework [63] and numerical methods [32]. (2) Structural Efficiency. Besides of optimizing the number of model evaluations, another way is to encourage structural efficiency. Redesign the model architectures [58], pruning [8, 29, 65] and quantization [14, 28] constructs lightweight diffusion model. Cache-based methods [37, 56] leverage the similarity between steps to reduce calculations. (3) Pipeline Efficiency. Breaking the sequential nature of denoising is another way to improve the efficiency of diffusion models. [49] uses Picard iteration to iteratively refine until convergence. [4, 25] decouples the images or models into multiple components and assigns them to different devices. + +Self-Distillation Knowledge distillation is widely used for compressing compact networks, while self-distillation focuses on improving the performance of networks. [10] investigate distillation with a student network parameterized identically to its teacher, demonstrating that the student could significantly outperform the teacher. [61] explores distilling knowledge from deeper network layers into shallower ones. Several works [2, 39, 57] examine the underlying reasons for this phenomenon, commonly attributing it to the "dark knowledge" encoded in soft labels. [62] highlight the importance of predictive diversity, while [41] systematically investigates self-distillation carefully and interprets self-distillation as a process of learning previously unlearned perspectives of input data. Unlike these prior works, our focus is not on leveraging soft labels from teacher predictions to guide student network training. Instead, we explore a unique mechanism in diffusion models to enhance their performance. + +# 3. Method + +In this section, we elaborate on the design of our self-distillation framework. We first show our proposed framework of the self-distillation paradigm in Section 3.2, and then give the explanation about why it works in Section 3.3 and Section 3.4. + +# 3.1. Preliminary + +We begin from the forward and reverse processes in diffusion probabilistic models. Let $q_{\mathrm{data}}(x)$ represent the data distribution. The forward process entails adding noise incrementally to a clean image $x_0 \sim q_{\mathrm{data}}(x)$ . At a given timestep $t$ , the distribution of $x_t$ , which includes the noise added up to that point, is defined by: + +$$ +q \left(x _ {t} \mid x _ {0}\right) = \mathcal {N} \left(x _ {t}; \sqrt {\bar {\alpha} _ {t}} x _ {0}, \left(1 - \bar {\alpha} _ {t}\right) \mathbf {I}\right) \tag {1} +$$ + +where $\alpha_{t}$ is a time-dependent function that controls the noise scheduling. As $t$ approaches a sufficiently large value, the final state $x_{T}$ becomes nearly the same as a Gaussian noise. For denoising, starting from a noise input $x_{T} \sim \mathcal{N}(0, \mathbf{I})$ , an image can be progressively reconstructed through iterative sampling from the conditional distribution $q(x_{t-1} | x_{t})$ . This conditional probability is typically approximated by a parameterized distribution, given as $p_{\theta}(x_{t-1} | x_{t}) = \mathcal{N}(x_{t-1}; \mu_{\theta}(x_{t}, t), \Sigma_{\theta}(x_{t}, t))$ . Here, $\mu_{\theta}(x_{t}, t)$ is parameterized by $\theta$ , and it follows: + +$$ +\mu_ {\theta} \left(x _ {t}, t\right) = \frac {1}{\sqrt {\alpha_ {t}}} \left(x _ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} \left(x _ {t}, t\right)\right) \quad (2) +$$ + +where $\epsilon_{\theta}(x_t,t)$ represents the noise estimation function at timestep $t$ given input $x_{t}$ . The training objective for diffusion models is to minimize the difference between the predicted noise and the ground-truth noise $\epsilon_{t}$ added during + +the forward process. This is typically framed as a simplified version of the variational bound on the negative log-likelihood of $x_0$ . The objective can be written as: + +$$ +\mathcal {L} _ {t} = \mathbb {E} _ {t \sim [ 1, T ], \mathbf {x} _ {0} \sim q _ {\text {d a t a}} (x)} \left[ \| \boldsymbol {\epsilon} _ {t} - \boldsymbol {\epsilon} _ {\theta} (\mathbf {x} _ {t}, t) \| ^ {2} \right] \tag {3} +$$ + +# 3.2. Overall Framework + +Next, we introduce the design of this unique form of self-distillation within diffusion models. To achieve self-distillation, three essential components must be defined: the construction of the teacher model, the formulation of the student model, and the definition of the training objective. Given that we have only a single pre-trained model without any external supervision. This poses a critical challenge: how can a single pre-trained diffusion model be used to construct both a teacher and a student model, with the teacher model designed to be more capable than the student? + +We focus on the timesteps of diffusion models, which inherently give us a sequence of predictions for one sample. Denote the model to have $L$ layers. $x^{(l)}$ denotes the input for layer $l$ , where $l \in \{1, 2, \dots, L\}$ . $x_{t}^{(1)} = x_{t}$ represents the input to the network at timestep $t$ . Each layer $l$ applies a function $f_{\theta_l}$ parameterized by $\theta_{l}$ , which includes operations such as multi-head self-attention and pointwise feedforward module in Transformer [53], and residual or convolution blocks in U-Net [45]. Thus, for each layer, the layer-wise computation at timestep $t$ can be formulated as: + +$$ +x _ {t} ^ {(l)} = f _ {\theta_ {l - 1}} \left(x _ {t} ^ {(l - 1)}, t\right) \tag {4} +$$ + +Here the calculation is conditioned on the timestep $t$ , although not all blocks in diffusion model use $t$ as a conditional input. After all $L$ layers have been processed, the final output of the model is the predicted noise, represented as $\epsilon(x_{t}, t) = x_{t}^{(L + 1)}$ . + +To construct the teacher and student models, we require the outputs for two timesteps, $t$ and $s$ , where $s$ represents the preceding denoising step of $t$ under a pre-defined solver, satisfying $s > t$ . We denote the predictions of the teacher and the student model as $\epsilon^{\mathcal{T}}(x_t,x_s,t,s)$ and $\epsilon^S (x_t,x_s,t,s)$ , respectively. Our approach to building the teacher and student models is based on a core principle: using the predictions from a later step as stronger supervision to guide the prediction at an earlier step. The rationale behind this principle will be discussed in detail later. Based on this guideline, we develop the below two distinct forms for self-distillation. + +Explicit Form: For the explicit self step-distillation, we build a teacher model by fusing the predicted noise: + +$$ +\boldsymbol {\epsilon} ^ {\mathcal {T}} \left(x _ {t}, x _ {s}, t, s\right) = \lambda \boldsymbol {\epsilon} _ {\theta^ {-}} \left(x _ {t}, t\right) + (1 - \lambda) \boldsymbol {\epsilon} _ {\theta^ {-}} \left(x _ {s}, s\right) \tag {5} +$$ + +The student prediction use the predicted noise at timestep $s$ : $\epsilon^{\mathcal{S}}(x_t,x_s,t,s) = \epsilon_\theta (x_s,s)$ . Here, $\theta^{-}$ represents the model would be frozen during training. + +Implicit Form: For the implicit self step-distillation, we redefine the computation flow in the model. We fuse the outputs at the same intermediate layer but different timesteps $t$ and $s$ , denoted $x_{t}^{(l)}$ and $x_{s}^{(l)}$ respectively. The fused output at this layer is now calculated as: + +$$ +\tilde {x} _ {t} ^ {(l)} = \lambda f _ {\theta_ {l - 1} ^ {-}} \left(x _ {s} ^ {(l - 1)}, s\right) + (1 - \lambda) f _ {\theta_ {l - 1}} \left(\tilde {x} _ {t} ^ {(l - 1)}, t\right) \tag {6} +$$ + +where $\tilde{x}_t^{(l-1)}$ represents the fused output from the previous layer, and $\tilde{x}_t^{(l)}$ serves as the input for the next layer, replacing the original $x_t^{(l)}$ . The above equation serves as a weighted fusion of layer output in two timesteps. The final prediction $\epsilon^S(x_t, x_s, t, s) = \tilde{x}_t^{(L+1)}$ is obtained from these fused features, forming the prediction for the student model. With this, the computation flow of the student model is changed. In constraint, the teacher model functions as the original denoising predictor at timestep $t$ , with its prediction output expressed as $\epsilon^T(x_t, x_s, t, s) = \epsilon_{\theta^{-}}(x_t, t)$ + +Training Objective. We take the pre-trained model as both the initialization for the teacher and the student model. The teacher $\theta_T$ model remained frozen while the update of parameters is performed on the student side. The self-distillation objective here is the matching between the student $\epsilon^S(x_t, x_s, t, s)$ and the teacher $\epsilon^T(x_t, x_s, t, s)$ . The distillation objective would be: + +$$ +\min _ {\theta} \mathbb {E} _ {s \sim [ 1, T ], x _ {0} \sim q _ {\mathrm {d a t a}} (x)} \left[ \left\| \boldsymbol {\epsilon} ^ {\mathcal {T}} \left(x _ {t}, x _ {s}, t, s\right) - \boldsymbol {\epsilon} ^ {\mathcal {S}} \left(x _ {t}, x _ {s}, t, s\right) \right\| ^ {2} \right] \tag {7} +$$ + +Here, $x_{s}$ represents $x_{0}$ with added noise, and $x_{t}$ is obtained by performing one step from $x_{s}$ in the ODE solver. After the training phase is completed, no fusion operations are applied during the inference stage. The model's computation remains identical to its original configuration but benefits from the enhancements gained through the self-distillation process. + +# 3.3. Distill from High-Order Solver + +In this section, we explain why this self-distillation framework works. In order to reduce the discretization error for the first-order ODE solver, such as Euler [20], one straightforward way is to use the higher-order solver for the diffusion ODEs. The cost for this is that it needs twice or third or even more times of function evaluation. We show that our self-distillation framework serves as an approximated form for distilling it into the same network without introducing additional parameters. + +We perform a single step forward from timestep $s$ to timestep $t$ . We compare the formulation of DPM-Solver-1 and DPM-Solver-2 [34]. + +$$ +\text {D P M - S o l v e r - 1 :} x _ {t} = \frac {\alpha_ {t}}{\alpha_ {s}} x _ {s} - w _ {t} \epsilon_ {\theta} (x _ {s}, s) \tag {8} +$$ + +$$ +\text {D P M - S o l v e r - 2 :} x _ {t} = \frac {\alpha_ {t}}{\alpha_ {s}} x _ {s} - w _ {t} \epsilon_ {\theta} (x _ {u}, u) \tag {9} +$$ + +Here the timestep $u$ is an intermediate timestep between $t$ and $s$ . As defined in DPM-Solver-2, timestep $u$ has $\lambda_u \coloneqq \log \left( \frac{\alpha_u}{\sigma_u} \right)$ which is the average of those for timestep $t$ and timestep $s$ , and $x_u$ denotes the state one step forward from $s$ to $u$ . The term $w_t$ is a weight factor that depends only on the timestep. Using DPM-Solver-2, which is more accurate than DPM-Solver-1, the following training objective can be interpreted as encouraging the predictions of the first-order solver to align more closely with those of the second-order solver: + +$$ +\min _ {\theta} \mathbb {E} _ {s \sim [ 1, T ], \mathbf {x} _ {0} \sim q _ {\text {d a t a}} (x)} \left[ w _ {t} \| \boldsymbol {\epsilon} _ {\theta} \left(x _ {s}, s\right) - \boldsymbol {\epsilon} _ {\theta} \left(x _ {u}, u\right) \| ^ {2} \right] \tag {10} +$$ + +Building on the above equation, if the goal is to approximate a higher-order solver using a first-order solver, the training objective simplifies to: matching the prediction at the current step with the prediction at a subsequent step. + +# 3.4. Ways to approximate $\epsilon_{\theta}(x_u,u)$ + +However, this method requires the prediction at the intermediate step between timestep $s$ and $t$ , which is not always feasible in $N$ -step to $N$ -step distillation. A feasible scenario involves using a linear interpolant noise scheduler, where $x_{s} = (1 - s / T)x_{0} + (s / T)\epsilon$ , and the model predicts the velocity instead of the noise $\epsilon$ . Under these conditions, the objective can be reformulated to align $\epsilon_{\theta}(x_s,s)$ with $\epsilon_{\theta}(x_t,t)$ . The corresponding results are presented in Table 1, with detailed proofs provided in the Appendix. With 10 and 250 sampling steps, consistent improvements in sample quality are observed, validating the effectiveness of Eq.10. However, as expected, performance declined in both cases when using $\epsilon$ -prediction without incorporating these properties into the noise scheduler and the specific model prediction type. + +The question now arises: how we can approximate $\epsilon_{\theta}(x_u,u)$ given $\epsilon_{\theta}(x_s,s)$ and $\epsilon_{\theta}(x_t,t)$ . One straightforward way is to get the approximation of $\epsilon_{\theta}(x_u,u)$ by Taylor Expansion, whose results turned to be the interpolating between $\epsilon_{\theta}(x_s,s)$ and $\epsilon_{\theta}(x_t,t)$ . Following the assumption in [34] that $\epsilon_{\theta}(x_s,s)$ is Lipschitz w.r.t $x_{s}$ , we have: + +$$ +\begin{array}{l} \epsilon_ {\theta} \left(x _ {u}, u\right) = \epsilon_ {\theta} \left(x _ {s}, u\right) + \left(\epsilon_ {\theta} \left(x _ {u}, u\right) - \epsilon_ {\theta} \left(x _ {s}, u\right)\right) \\ = \epsilon_ {\theta} (x _ {s}, s) + \epsilon_ {\theta} ^ {(1)} (x _ {s}, s) (u - s) + \mathcal {O} ((u - s) ^ {2}) \tag {11} \\ \end{array} +$$ + +
    ModelSamplerNFEsISFIDsFID
    v-prediction with linear interpolant noise scheduler
    REPA - SiT-XL/2SDE250305.71.424.70
    REPA - SiT-XL/2° w/ Eq.10SDE250306.31.414.68
    REPA - SiT-XL/2°ODE10233.95.857.82
    REPA - SiT-XL/2° w/ Eq.10ODE10238.45.117.48
    ε-prediction
    DiT-XL/2ODE50238.62.264.29
    DiT-XL/2 w/ Eq.10ODE50230.82.816.41
    DiT-XL/2 w/ Eq.12ODE50239.92.214.41
    DiT-XI/2ODE10158.312.3811.22
    DiT-XL/2 w/ Eq.10ODE1051.845.9926.95
    DiT-XL/2 w/ Eq.12ODE10184.77.999.91
    + +Table 1. Results on $v$ -prediction and $\epsilon$ -prediction diffusion models. For the experiments on REPA, we use the EMA model as the teacher for the experiments with 250 steps. + +where $\epsilon_{\theta}^{(1)}(x_s,s)$ is the first-order derivative w.r.t $s$ . As above, we derive $\epsilon_{\theta}^{(1)}(x_s,s)$ the same way between two different timesteps $t$ and $s$ , and we have: + +$$ +\epsilon_ {\theta} \left(x _ {u}, u\right) = (1 - \lambda) \epsilon_ {\theta} \left(x _ {s}, s\right) + \lambda \epsilon_ {\theta} \left(x _ {t}, t\right) \tag {12} +$$ + +where $\lambda = (u - s) / (t - s)$ . We get the same form as the explicit self step-distillation. The results with this equation are also shown in Table 1. + +While the aforementioned method can approximate $\epsilon_{\theta}(x_u,u)$ to some extent, it remains suboptimal. An alternative approach is the implicit form of interpolation, which approximates $\epsilon_{\theta}(x_u,u)$ by interpolating on features rather than on the output. This one shares the same form with implicit self step-distillation. This idea is inspired by previous works [26, 37], which demonstrated that certain intermediate activations in timestep $s$ can be reused in later timestep $u$ to produce an approximated output for timestep $u$ , with minimal effect on image quality. Consequently, we interpolate on the intermediate layers, and experimental results indicate that this method yields better performance than interpolation on predictions. + +# 4. Experiment + +In this section, we demonstrate the effectiveness of our proposed method. In Section 4.2, we present empirical evidence that both SSD and iSSD consistently enhance the performance of a pre-trained DiT across various image resolutions, model sizes, and sampling steps. Additionally, Section 4.3 provides the results of applying these methods to text-to-image generation. Section 4.4 highlights how iSSD can be applied to distilled models, yielding further performance improvements. Finally, Section 4.5 offers an in-depth analysis. + +# 4.1. Experimental Setup + +Models. For the conditional generation on ImageNet, we take all four DiT models: DiT-S/2, DiT-B/2, DiT-L/2, and + +
    MethodNFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑NFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    -256×256--512×512-
    DiT-XL/2250(ODE)1400243.42.144.560.810.61250(SDE)600240.83.045.020.840.54
    SiT-XL/2250(SDE)1400277.52.064.490.830.59250(SDE)600252.22.624.180.840.57
    DiT-XL/2501400238.62.264.290.800.6050600204.13.284.500.830.55
    + SSD501400 + 0.8239.92.214.410.800.6050600 + 0.4205.23.184.590.830.57
    + iSSD501400 + 0.8250.02.024.220.810.6050600 + 0.4210.22.864.060.840.54
    DiT-XL/2201400223.53.484.890.790.5720600186.35.105.730.820.55
    + SSD201400 + 0.8228.62.824.630.790.6020600 + 0.4194.74.015.330.830.56
    + iSSD201400 + 0.8227.52.674.850.790.6020600 + 0.4200.83.694.410.840.54
    DiT-XL/2101400158.312.3811.220.670.5310600128.415.1911.580.740.49
    + SSD101400 + 0.8184.77.999.910.710.5610600 + 0.4158.59.6111.090.780.54
    + iSSD101400 + 0.8209.64.927.620.790.5310600 + 0.4164.96.977.050.830.51
    + +Table 2. Image quality on ImageNet ${256} \times {256}$ and ${512} \times {512}$ ,with DiT-XL/2 as the base model. Prec. and Rec. denotes Precision and Recall. We adopt CFG=1.5 in all the experiments for ImageNet. + +
    ModelNFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    -DiT-S/2-
    DiT-S/225040059.426.517.310.590.56
    DiT-S/2+ iSSD5040053.529.215.890.570.58
    50400 + 0.254.627.755.730.580.58
    DiT-S/2+ iSSD2040052.032.627.430.550.55
    20400 + 0.252.530.628.230.560.55
    DiT-S/2+ iSSD1040040.149.5018.330.430.48
    10400 + 0.240.746.1718.890.450.48
    -DiT-B/2-
    DiT-B/2250200119.610.125.390.730.55
    DiT-B/2+ iSSD50200101.812.844.810.710.56
    50200 + 0.2104.911.774.990.710.56
    DiT-B/2+ iSSD2020097.515.406.110.680.54
    20200 + 0.2100.613.848.630.710.52
    DiT-B/2+ iSSD1020072.128.9915.540.560.48
    10200 + 0.277.921.4013.370.610.53
    -DiT-L/2-
    DiT-L/2250200196.33.734.620.820.54
    DiT-L/2+ iSSD50200168.84.774.410.780.55
    50200 + 0.2172.74.414.440.800.56
    DiT-L/2+ iSSD20200160.56.425.260.770.53
    20200 + 0.2172.34.924.870.800.53
    DiT-L/2+ iSSD10200118.516.0112.630.670.47
    10200 + 0.2143.77.754.990.750.55
    + +Table 3. Image quality on ImageNet ${256} \times {256}$ with DiT-S/2,DiT-B/2 and DiT-L/2 + +DiT-XL/2. For DiT-XL/2, we utilize the official pre-trained model, whereas for the other three models, we train them for 1 million to 2 million steps. For the text-to-image generation experiments, we employ Stable Diffusion v1.5 [44] as our base model. + +Evaluation. We follow previous work [40] to use IS, FID, sFID, Precision and Recall as the evaluation metric. For text-to-image generation, we test the FID on the validation set of COCO2014 and COCO2017 [31]. + +Training and Sampling Details. For training, the teacher and student models are both initialized from the base model, with the teacher remaining fixed during training. We use DDIM [50] as our base ODE solver and only utilize N-step predictions during training if the fine-tuned model would be evaluated under N-step. For DiT, we set a learning rate of 5e-6, a batch size of 128. The training epochs for each experiment are listed in the tables. Exponential Moving Average (EMA) is not used due to the short training period. We follow the original DiT setup without weight decay, warm-up, or learning rate schedulers. Models were evaluated with 10, 20, and 50 numbers of function evaluations (NFEs), and we show that even the basic ODE algorithms outperformed many advanced samplers with our algorithms. More details, especially for text-to-image generation, are in the Appendix. + +# 4.2. Conditional Generation + +Results on DiT-XL. We show the results of DiT-XL/2 in Table 2. With less than 1 epoch for optimizing DiT-XL/2, our method achieves consistent performance improvement upon the base models. Notably, our method with 50 NFEs can exceed the performance of the base DiT-XL/2 sampled 250 times by a large margin (2.02 vs 2.14), both under the same ODE sampler. Also this improvement can be observed in the resolution of 512, where the base DiT achieves the FID of 3.04, while our method can improve it to 2.86. We also notice improvement compared with the 250-step SiT, with our method sampled with only 50 steps. Besides, we found the implicit SSD performs better than the explicit SSD in most cases, and sometimes the implicit SSD outperforms the explicit SSD by a large margin. We show the qualitative results on ImageNet in the Appendix. + +Results on small-scale DiTs. We also apply our method under smaller DiT models, showing that the method can be generalized to models with different sizes. Since in the ex + +![](images/4a2f54b7038ca5db70708a795514840ed0c103a1d361b876b47f07f0cf5f7c79.jpg) +Figure 3. Visualization of generated images using various sampling algorithms with NFEs=10. From left to right, the algorithms shown are: PLMS, DDIM, DPM-Solver-2, and SSD. + +
    DatasetNFEsDDIMPLMSDPM-Solver-2Ours
    COCO20141012.7817.7115.2310.94
    2012.6812.6514.6310.56
    COCO20171022.7929.5124.4620.85
    2022.4322.1424.0220.69
    + +periment in DiT-XL/2, we found iSSD consistently outperforms SSD, we here test the performance of iSSD on these DiT models. From Table 3, with only 0.2 epoch for training, we observe a large improvement upon the base model. It would only take several minutes to finish the training, and thus, can be seen as a cheap way to improve the performance of the trained models. + +# 4.3. Text-to-Image Generation + +We apply SSD to Stable Diffusion v1.5. The experimental details are outlined in Appendix. Our method is compared against DDIM [50], DPM-Solver-2 [34] and PLMS [32] on COCO2014 and COCO2017, as shown in Table 4. Our approach demonstrates significant improvements in FID, outperforming other methods. Notably, our results with 10 NFEs surpass those achieved with 20 NFEs by competing samplers. Visualization results further highlight that images enhanced by our algorithm exhibit more detailed features. + +# 4.4. Results on Distilled Models + +In this section, we apply our method to a distilled model obtained through progressive distillation (PD). Notably, this implies that predictions at intermediate steps that are not explicitly part of the PD process are not trained, resulting in suboptimal performance at these steps. This experiment aims to demonstrate that our method is effective that distills from N steps to enhance performance across those N steps, since using the results from intermediate steps other than these N steps would harm the performance. + +Table 4. FID Comparison with different samplers on the validation set of COCO2014 and COCO2017 + +
    ModelNFEsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    DiT-XL/2250243.42.144.560.810.61
    PD 64 → 3232239.82.244.330.800.60
    + iSSD32246.21.994.330.810.60
    PD 20 → 1010209.94.195.240.760.57
    + iSSD10233.93.567.080.810.55
    PD 20 → 10 → 55173.07.006.590.730.58
    + iSSD5186.75.416.480.760.56
    PD 16 → 8 → 44152.68.757.900.700.59
    + iSSD4168.586.107.530.720.57
    + +Table 5. Results of building iSSD upon diffusion models being distilled for few-step generation. + +
    ModelIS ↑FID ↓sFID ↓Prec.↑Rec.↑
    DiT-XL/213.4107.7594.570.110.36
    PD [47]158.37.847.110.700.60
    Shortcut Model [9]-7.8---
    PD + Ours168.66.117.530.720.57
    + +Table 6. Comparison with training-based method on ImageNet $256\times 256$ . We set NFEs $= 4$ and use DiT-XL/2 for sampling. + +Orthogonal to distillation methods. Table 5 presents the results for models distilled through two-stage and three-stage progressive distillation (PD), and Figure 4(a) illustrates the results on a chain of models distilled from progressive distillation. The results indicate that our method can significantly enhance performance. Specifically, when applied to a 32-step distilled model, our approach achieves an FID of 1.99 with minimal additional computational cost, representing a substantial improvement over the distilled model and even the pre-trained DiT-XL/2. However, when comparing our method to the model directly distilled from PD, the performance at 10-step NFE is slightly lower (4.19 vs. 4.92). We position our method as an auxiliary step that complements and further refines the performance of distilled models, providing an orthogonal improvement. + +Comparison with training-based methods. We evaluated our model against flow-matching algorithms designed for training diffusion models to enable few-step generation. The experiments are performed using 4 steps to generate images, and the backbone for diffusion models is DiT-XL/2. The results, summarized in Table 6, indicate that our method surpasses the performance of competing algorithms. Specifically, when compared to the ShortCut Model [9], an enhanced variant of the flow matching model adapted for DiT, our approach achieves superior results (FID: 6.1 v.s. 7.8). + +# 4.5. Analysis + +Comparison with continual training. To demonstrate that the observed performance improvements are not merely + +![](images/d36e4565dcd98a0184a8776964638e3fe4d68032ec55568922d2de68f0b3ea51.jpg) +(a) + +![](images/9fe056c2a0654486fef4678df07ce01c2bb070f3e50b5b8ff125c8761dd78ffc.jpg) +(b) +Figure 4. Analysis of our proposed self-distillation framework includes: (a) iSSD consistently enhancing the quality of distilled DMs, (b) significant improvements in sample quality achieved by training only one step in the ODE trajectory, (c) evaluation of the performance of the teacher, student, and the final model, and (d) a substantial impact observed with variations in $\lambda$ + +![](images/62fa50bb81eb032820405d04cf2f4233bcaee3abf780ef3a6a2b2cc28f3295b6.jpg) +(c) + +![](images/d47b928843002a2c9038ccbbf9c716c22a0d039c1215cf40a5eb00aa3cd24601.jpg) +(d) + +
    ModelNFETrain EpochsIS↑FID↓
    DiT-XL/2101400158.312.38
    DiT-XL/2°101400 + 0.8156.712.97
    DiT-XL/2 + iSSD101400 + 0.8209.64.92
    DiT-S°25040027.651.55
    DiT-S°25042027.951.13
    DiT-S° + iSSD250400 + 228.748.38
    + +due to additional training iterations, we conducted experiments on DiT-XL/2 (officially pre-trained and only have the EMA model) and DiT-S/2 ( has both the EMA and the base model). The results in Table 7 show that even with fewer training epochs, our method significantly outperforms models trained for 20 epochs on DiT-S/2. This confirms that the performance gains stem from the proposed self-distillation approach rather than extended training iterations. + +Synthetic Data v.s. Real Data. An additional exploration involves assessing whether a model's performance can be improved when only the model itself is available, without any supplementary training data or external models. We conducted experiments under this setting, and the results are presented in Table 8. The findings indicate that, while real data remains the optimal choice for achieving the highest performance, the use of synthetic data can still result in substantial improvements in generation quality, albeit with a slight performance trade-off compared to using real data. + +Distill upon only one step. In Figure 4(b), we show the results of applying iSSD to a single step. This process yields two models; here, our focus is on determining which step has the greatest impact on images. The results indicate that applying self-distillation in the later stages of denoising provides the most significant benefit to image quality. + +Training dynamics for the teacher and the student in iSSD. Figure 4(c) presents the training dynamics ob + +Table 7. Comparison with Continual Training. The superscript $\diamond$ means we train these models from the official codebase. + +
    ModelData SourceISFIDsFIDPrecisionRecall
    DiT-XL/2-158.312.3811.220.670.53
    iSSDOriginal Data209.64.927.620.790.53
    iSSDSynthetic - 10 step206.25.079.030.790.52
    iSSDSynthetic - 20 step207.95.028.990.790.53
    + +Table 8. Results on Synthetic Data on ImageNet $256 \times 256$ . The experiments are based on DDIM with 10 sampling steps. + +served during our experiments. It is crucial to note that the student model used in training differs from the one used for inference. The student model with fused activations starts with lower performance compared to the teacher model and remains inferior after training. In contrast, the unfused one, which maintains the same architecture and computation way for each layer, shows consistent improvement throughout training and eventually achieves significantly better performance than the teacher model. + +Effect of gradient influential term $\lambda$ . We show the effect of $\lambda$ , as defined in Eq.5 and Eq.6. Though in Eq.12, we can directly calculate $\lambda$ if we adopt the same intermediate step as in DPM-Solver, we also put this timestep scheduler in this hyper-parameter, and search the best $\lambda$ for our approach. Figure 4(d) show for iSSD, with $\lambda$ equals a small value, the model would get poor results. We show the $\lambda$ used in each of our experiments in Appendix. + +# 5. Conclusion + +In this paper, we propose a novel self-distillation approach named Self Step-Distillation. We introduce two forms for Self Step-Distillation. Furthermore, we explain this approach by analyzing it through the lens of distillation with high-order samplers. Experimental results demonstrate that our method significantly outperforms the performance of the teacher model, achieving substantial improvements in both conditional generation and text-to-image generation. However, our method also has certain limitations. For instance, we still rely on suboptimal approaches to approximate the prediction of the intermediate step. Additionally, our method is relatively sensitive to hyperparameters. + +# Acknowledgement + +This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006). + +# References + +[1] Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. Align your latents: High-resolution video synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22563-22575, 2023. 1 +[2] Kenneth Borup and Lars N Andersen. Even your teacher needs guidance: Ground-truth targets dampen regularization imposed by self-distillation. Advances in Neural Information Processing Systems, 34:5316-5327, 2021. 3 +[3] Shoufa Chen, Peize Sun, Yibing Song, and Ping Luo. Diffusionnet: Diffusion model for object detection. 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Previous studies have shown that introducing a teacher to distill the diffusion model can enhance its sampling efficiency. We raise an intriguing question: can the diffusion model itself serve as its teacher to further improve the performance of itself? To this end, we propose a new paradigm called Self Step-Distillation (SSD). The core idea of SSD is to integrate the predictions or the intermediate activations of the diffusion model at each timestep with its preceding timestep through a fusion mechanism. 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It has been proven effective in tasks such as image synthesis [42, 44, 46], video generation [1, 17, 18] and natural language processing [27, 33]. Unlike previous generative approaches like VAEs [24] and GANs [12], Diffusion Mod-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 702, + 147, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 702, + 147, + 713 + ], + "spans": [ + { + "bbox": [ + 70, + 702, + 147, + 713 + ], + "type": "text", + "content": "* Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12901" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 156 + ], + "type": "text", + "content": "els (DMs) rely on a unique process where noise is gradually refined into meaningful data by reversing a specified noise pathway [20]. This iterative noise-to-data transformation gives DMs exceptional versatility, allowing them to be applied successfully in image editing [21], inpainting [35], super-resolution [11], object detection [3], 3D generation [43], etc." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 159, + 296, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 159, + 296, + 374 + ], + "spans": [ + { + "bbox": [ + 56, + 159, + 296, + 374 + ], + "type": "text", + "content": "Recent studies have emphasized the effectiveness of knowledge distillation [15] as a tool for enhancing inference efficiency or accelerating pre-training for diffusion models [38, 50]. These methods typically achieve distillation through the use of an external teacher model or a teacher with more sampling steps. To improve inference efficiency, approaches such as progressive distillation and consistency distillation [23, 36, 47, 52] employ an extensive multi-step sampling process as a teacher model to distill the student model with fewer steps. These teacher models more accurately approximate the denoising trajectory, thereby guiding the student model to enable the few-step generation or even one-step generation [7]. Other studies [13, 19, 22] focus on distilling compact diffusion models by training smaller models under the supervision of larger, high-capacity models. Besides, [60] demonstrates that aligning model representations using guidance from an external pre-trained vision encoder can facilitate faster convergence." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "spans": [ + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "text", + "content": "The aforementioned methods can significantly enhance the sampling efficiency of diffusion models through distillation. However, the student models are constrained by the performance of the teacher model, with their training aimed at matching, but not surpassing, the teacher's performance. This raises an intriguing question: Can distillation be leveraged to improve the generation quality of the diffusion model itself, potentially exceeding the performance of the teacher model? This shifts the focus from traditional " + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "text", + "content": "-to-" + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "text", + "content": " step distillation or model compression for speed to a form of " + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "text", + "content": "-to-" + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 376, + 295, + 519 + ], + "type": "text", + "content": " step self-distillation aimed at enhancing the generation quality of the original diffusion model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 295, + 713 + ], + "type": "text", + "content": "We thereby explore the unique form of self-distillation within diffusion models. While self-distillation has been studied extensively in conventional architectures [10, 39, 61, 62], its application to diffusion models remains unexplored. explore the special way that self-distillation operates in diffusion models by utilizing the properties of diffusion models. Given the temporal relationships between steps that form a sequence of predictions, we introduce Self Step-Distillation in both explicit and implicit forms. The core idea is that, with careful design, the model can enhance its performance by mimicking the next-step prediction. To achieve this, we propose a fusion of predictions and features across different steps, and redefine the computational flow for the student model. Once the student model is trained, it can be reverted to the original computational pipeline. We also illustrate how this fusion mechanism relates to high-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 314, + 73, + 372, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 73, + 372, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 73, + 372, + 83 + ], + "type": "text", + "content": "order solvers." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 84, + 553, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 84, + 553, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 84, + 553, + 335 + ], + "type": "text", + "content": "We mainly conduct our experiments on diffusion transformers [40] due to their exceptional performance. We conduct experiments on DiT models ranging from DiT-S/2 to DiT-XL/2 and sampling steps from 4 to 250. With our method, a self-distilled DiT-XL/2 with 50 sampling steps surpasses the performance of the pre-trained DiT-XL/2 with 250 sampling steps (2.02 vs 2.14 in FID). To further examine the " + }, + { + "bbox": [ + 313, + 84, + 553, + 335 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 84, + 553, + 335 + ], + "type": "text", + "content": "-to-" + }, + { + "bbox": [ + 313, + 84, + 553, + 335 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 84, + 553, + 335 + ], + "type": "text", + "content": " distillation setting and show that our method is complementary to the few-step distillation, we applied our method on a progressively distilled DiT-XL/2. This resulted in an enhanced generation quality, with an FID of 1.99 achieved using 32 sampling steps. Additionally, we tested the generalizability of our method by applying it to Stable Diffusion, confirming its effectiveness in the text-to-image setting. All experiments require fewer than 10k optimization steps and a short training duration—approximately 40 minutes for DiT-XL/2 and 3 hours for Stable Diffusion. Consequently, our method can be considered a quick self-improvement technique for diffusion models, which we further show that it can operate without dependence on training data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 326, + 336, + 525, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 336, + 525, + 346 + ], + "spans": [ + { + "bbox": [ + 326, + 336, + 525, + 346 + ], + "type": "text", + "content": "To summarize, the contributions of our work are:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 348, + 553, + 526 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 314, + 348, + 553, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 348, + 553, + 383 + ], + "spans": [ + { + "bbox": [ + 314, + 348, + 553, + 383 + ], + "type": "text", + "content": "- We demonstrate for the first time that self-distillation can enhance the performance of diffusion models itself, significantly surpassing the original model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 384, + 553, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 384, + 553, + 442 + ], + "spans": [ + { + "bbox": [ + 314, + 384, + 553, + 442 + ], + "type": "text", + "content": "- We introduce a novel self-distillation framework for diffusion models, termed Self Step-Distillation. By corrupting and fusing predictions and intermediate activations, we redefine the computational flow of the teacher and student diffusion model to facilitate self-distillation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 444, + 553, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 444, + 553, + 479 + ], + "spans": [ + { + "bbox": [ + 314, + 444, + 553, + 479 + ], + "type": "text", + "content": "- We analyze the underlying mechanisms of this unique self-distillation approach and reveal its connection to high-order solvers." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 479, + 553, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 479, + 553, + 526 + ], + "spans": [ + { + "bbox": [ + 314, + 479, + 553, + 526 + ], + "type": "text", + "content": "- Experimental results demonstrate that our self-distillation method significantly enhances the performance of diffusion models, including both DiT and Stable Diffusion, as well as distilled few-step diffusion models." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 538, + 400, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 538, + 400, + 550 + ], + "spans": [ + { + "bbox": [ + 314, + 538, + 400, + 550 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 555, + 713 + ], + "type": "text", + "content": "Distillation in Diffusion Models. knowledge distillation [15] becomes a popular paradigm to improve the efficiency of diffusion models. Progressive Distillation [47] proposes to half the steps of sampling by matching the samples generated by N deterministic steps with 2N steps. Consistency distillation [52] enforces the self-consistency between any pair of steps and makes the boundary condition avoid trivial solutions. [36] extends it into the latent space, and [23, 54] divides the whole trajectory consistency into subphase consistency. SFD [64] solves the accumulative errors in local distillation by sampling and imitating the whole trajectory. [59] distills the diffusion model into a one-step generator by matching at the distribution level with adversarial" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12902" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 294, + 242 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 294, + 242 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 294, + 242 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 294, + 242 + ], + "type": "image", + "image_path": "7c9252b37f1c5bd7bb593c9de27984e43383682c7d67562f7ff861e8bca7a261.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "lines": [ + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "type": "text", + "content": "Figure 2. The overall framework of Self Step-Distillation. Here " + }, + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "type": "inline_equation", + "content": "\\theta^{-}" + }, + { + "bbox": [ + 55, + 251, + 296, + 275 + ], + "type": "text", + "content": " means that the weight of the model is frozen." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 297, + 298, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 297, + 298, + 441 + ], + "spans": [ + { + "bbox": [ + 54, + 297, + 298, + 441 + ], + "type": "text", + "content": "loss. [6] shows that the high-order term, jacobian-vector products, can be distilled into a separate neural network. Guided diffusion [38] matches the combined output of the classifier-free guidance with a single model, and reduces the sampling steps for unconditional generation and conditional generation. The adversarial objective can also be incorporated in diffusion training to stabilize the training process [30, 48]. Apart from this, another line of work uses knowledge distillation to make the diffusion model small and efficient [8, 58]. Feature-level knowledge distillation is widely adopted in those works to accelerate the post-training of these compressed diffusion models [8, 13, 22]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 462, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 462, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 462, + 296, + 714 + ], + "type": "text", + "content": "Efficiency in Diffusion Models. Balancing the image quality and the sampling speed is a challenging topic in diffusion models [20, 55]. (1) Fast solver for sampling. One common way to reduce the sampling steps is to employ a training-free solver to off-the-shelf pre-trained diffusion models. Those methods approximate the true trajectory of probability flow ODE, such as Euler's method [50], Heun's method [20], the exponential integrator with Taylor expansion [34], the unified predictor-corrector framework [63] and numerical methods [32]. (2) Structural Efficiency. Besides of optimizing the number of model evaluations, another way is to encourage structural efficiency. Redesign the model architectures [58], pruning [8, 29, 65] and quantization [14, 28] constructs lightweight diffusion model. Cache-based methods [37, 56] leverage the similarity between steps to reduce calculations. (3) Pipeline Efficiency. Breaking the sequential nature of denoising is another way to improve the efficiency of diffusion models. [49] uses Picard iteration to iteratively refine until convergence. [4, 25] decouples the images or models into multiple components and assigns them to different devices." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 555, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 288 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 288 + ], + "type": "text", + "content": "Self-Distillation Knowledge distillation is widely used for compressing compact networks, while self-distillation focuses on improving the performance of networks. [10] investigate distillation with a student network parameterized identically to its teacher, demonstrating that the student could significantly outperform the teacher. [61] explores distilling knowledge from deeper network layers into shallower ones. Several works [2, 39, 57] examine the underlying reasons for this phenomenon, commonly attributing it to the \"dark knowledge\" encoded in soft labels. [62] highlight the importance of predictive diversity, while [41] systematically investigates self-distillation carefully and interprets self-distillation as a process of learning previously unlearned perspectives of input data. Unlike these prior works, our focus is not on leveraging soft labels from teacher predictions to guide student network training. Instead, we explore a unique mechanism in diffusion models to enhance their performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 314, + 297, + 370, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 297, + 370, + 309 + ], + "spans": [ + { + "bbox": [ + 314, + 297, + 370, + 309 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 318, + 555, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 318, + 555, + 377 + ], + "spans": [ + { + "bbox": [ + 313, + 318, + 555, + 377 + ], + "type": "text", + "content": "In this section, we elaborate on the design of our self-distillation framework. We first show our proposed framework of the self-distillation paradigm in Section 3.2, and then give the explanation about why it works in Section 3.3 and Section 3.4." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 384, + 394, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 394, + 398 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 394, + 398 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "text", + "content": "We begin from the forward and reverse processes in diffusion probabilistic models. Let " + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{data}}(x)" + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "text", + "content": " represent the data distribution. The forward process entails adding noise incrementally to a clean image " + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "inline_equation", + "content": "x_0 \\sim q_{\\mathrm{data}}(x)" + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "text", + "content": ". At a given timestep " + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "text", + "content": ", the distribution of " + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 313, + 402, + 556, + 475 + ], + "type": "text", + "content": ", which includes the noise added up to that point, is defined by:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 350, + 482, + 555, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 482, + 555, + 497 + ], + "spans": [ + { + "bbox": [ + 350, + 482, + 555, + 497 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, \\left(1 - \\bar {\\alpha} _ {t}\\right) \\mathbf {I}\\right) \\tag {1}", + "image_path": "5eab141e97d0ed71b9fdc70c29ae8005fdcf548324c009182a507497f4bedf3b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": " is a time-dependent function that controls the noise scheduling. As " + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": " approaches a sufficiently large value, the final state " + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": " becomes nearly the same as a Gaussian noise. For denoising, starting from a noise input " + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "inline_equation", + "content": "x_{T} \\sim \\mathcal{N}(0, \\mathbf{I})" + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": ", an image can be progressively reconstructed through iterative sampling from the conditional distribution " + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "inline_equation", + "content": "q(x_{t-1} | x_{t})" + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": ". This conditional probability is typically approximated by a parameterized distribution, given as " + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_{t-1} | x_{t}) = \\mathcal{N}(x_{t-1}; \\mu_{\\theta}(x_{t}, t), \\Sigma_{\\theta}(x_{t}, t))" + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}(x_{t}, t)" + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": " is parameterized by " + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 503, + 556, + 624 + ], + "type": "text", + "content": ", and it follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 340, + 631, + 555, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 631, + 555, + 658 + ], + "spans": [ + { + "bbox": [ + 340, + 631, + 555, + 658 + ], + "type": "interline_equation", + "content": "\\mu_ {\\theta} \\left(x _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(x _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(x _ {t}, t\\right)\\right) \\quad (2)", + "image_path": "3ef1962a374b21d1b92b7105359562c480bf3040fc7d145599804c0aff076a89.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "text", + "content": " represents the noise estimation function at timestep " + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "text", + "content": " given input " + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "text", + "content": ". The training objective for diffusion models is to minimize the difference between the predicted noise and the ground-truth noise " + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 313, + 666, + 556, + 715 + ], + "type": "text", + "content": " added during" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12903" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "content": "the forward process. This is typically framed as a simplified version of the variational bound on the negative log-likelihood of " + }, + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 55, + 72, + 296, + 109 + ], + "type": "text", + "content": ". The objective can be written as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 83, + 118, + 295, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 118, + 295, + 137 + ], + "spans": [ + { + "bbox": [ + 83, + 118, + 295, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t} = \\mathbb {E} _ {t \\sim [ 1, T ], \\mathbf {x} _ {0} \\sim q _ {\\text {d a t a}} (x)} \\left[ \\| \\boldsymbol {\\epsilon} _ {t} - \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}, t) \\| ^ {2} \\right] \\tag {3}", + "image_path": "2d9a34bbd6859d9409d5e250f4c740966d5dc5d145787d0dfe5da0c399c535e7.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 146, + 171, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 146, + 171, + 158 + ], + "spans": [ + { + "bbox": [ + 55, + 146, + 171, + 158 + ], + "type": "text", + "content": "3.2. Overall Framework" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 163, + 296, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 163, + 296, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 296, + 282 + ], + "type": "text", + "content": "Next, we introduce the design of this unique form of self-distillation within diffusion models. To achieve self-distillation, three essential components must be defined: the construction of the teacher model, the formulation of the student model, and the definition of the training objective. Given that we have only a single pre-trained model without any external supervision. This poses a critical challenge: how can a single pre-trained diffusion model be used to construct both a teacher and a student model, with the teacher model designed to be more capable than the student?" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "spans": [ + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": "We focus on the timesteps of diffusion models, which inherently give us a sequence of predictions for one sample. Denote the model to have " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": " layers. " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "x^{(l)}" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": " denotes the input for layer " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "l \\in \\{1, 2, \\dots, L\\}" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "x_{t}^{(1)} = x_{t}" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": " represents the input to the network at timestep " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": ". Each layer " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": " applies a function " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "f_{\\theta_l}" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "\\theta_{l}" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": ", which includes operations such as multi-head self-attention and pointwise feedforward module in Transformer [53], and residual or convolution blocks in U-Net [45]. Thus, for each layer, the layer-wise computation at timestep " + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 284, + 296, + 405 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 125, + 413, + 295, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 413, + 295, + 434 + ], + "spans": [ + { + "bbox": [ + 125, + 413, + 295, + 434 + ], + "type": "interline_equation", + "content": "x _ {t} ^ {(l)} = f _ {\\theta_ {l - 1}} \\left(x _ {t} ^ {(l - 1)}, t\\right) \\tag {4}", + "image_path": "9a479ed591a15a3a7516c2a138fc5f1a89de5d4d40a091f23c214777ed9e96b4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "spans": [ + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "text", + "content": "Here the calculation is conditioned on the timestep " + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "text", + "content": ", although not all blocks in diffusion model use " + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "text", + "content": " as a conditional input. After all " + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "text", + "content": " layers have been processed, the final output of the model is the predicted noise, represented as " + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "inline_equation", + "content": "\\epsilon(x_{t}, t) = x_{t}^{(L + 1)}" + }, + { + "bbox": [ + 55, + 443, + 296, + 503 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "content": "To construct the teacher and student models, we require the outputs for two timesteps, " + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "content": " represents the preceding denoising step of " + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "content": " under a pre-defined solver, satisfying " + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "inline_equation", + "content": "s > t" + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "content": ". We denote the predictions of the teacher and the student model as " + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "inline_equation", + "content": "\\epsilon^{\\mathcal{T}}(x_t,x_s,t,s)" + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "inline_equation", + "content": "\\epsilon^S (x_t,x_s,t,s)" + }, + { + "bbox": [ + 55, + 505, + 296, + 647 + ], + "type": "text", + "content": ", respectively. Our approach to building the teacher and student models is based on a core principle: using the predictions from a later step as stronger supervision to guide the prediction at an earlier step. The rationale behind this principle will be discussed in detail later. Based on this guideline, we develop the below two distinct forms for self-distillation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 663, + 295, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 663, + 295, + 688 + ], + "spans": [ + { + "bbox": [ + 55, + 663, + 295, + 688 + ], + "type": "text", + "content": "Explicit Form: For the explicit self step-distillation, we build a teacher model by fusing the predicted noise:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 63, + 696, + 295, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 696, + 295, + 711 + ], + "spans": [ + { + "bbox": [ + 63, + 696, + 295, + 711 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\epsilon} ^ {\\mathcal {T}} \\left(x _ {t}, x _ {s}, t, s\\right) = \\lambda \\boldsymbol {\\epsilon} _ {\\theta^ {-}} \\left(x _ {t}, t\\right) + (1 - \\lambda) \\boldsymbol {\\epsilon} _ {\\theta^ {-}} \\left(x _ {s}, s\\right) \\tag {5}", + "image_path": "6daa7c5ae79dc945b5ec341f8ddad5695890ec1491b42526686a53ecfcb1ce27.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": "The student prediction use the predicted noise at timestep " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "\\epsilon^{\\mathcal{S}}(x_t,x_s,t,s) = \\epsilon_\\theta (x_s,s)" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "inline_equation", + "content": "\\theta^{-}" + }, + { + "bbox": [ + 313, + 72, + 554, + 109 + ], + "type": "text", + "content": " represents the model would be frozen during training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "spans": [ + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "text", + "content": "Implicit Form: For the implicit self step-distillation, we redefine the computation flow in the model. We fuse the outputs at the same intermediate layer but different timesteps " + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "text", + "content": ", denoted " + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "inline_equation", + "content": "x_{t}^{(l)}" + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "inline_equation", + "content": "x_{s}^{(l)}" + }, + { + "bbox": [ + 313, + 125, + 555, + 187 + ], + "type": "text", + "content": " respectively. The fused output at this layer is now calculated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 319, + 196, + 555, + 217 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 196, + 555, + 217 + ], + "spans": [ + { + "bbox": [ + 319, + 196, + 555, + 217 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {t} ^ {(l)} = \\lambda f _ {\\theta_ {l - 1} ^ {-}} \\left(x _ {s} ^ {(l - 1)}, s\\right) + (1 - \\lambda) f _ {\\theta_ {l - 1}} \\left(\\tilde {x} _ {t} ^ {(l - 1)}, t\\right) \\tag {6}", + "image_path": "18b3970760440cd0f1433d98750efb2743933b664f5d8bb813880e1c08057bcf.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "spans": [ + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\tilde{x}_t^{(l-1)}" + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "text", + "content": " represents the fused output from the previous layer, and " + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\tilde{x}_t^{(l)}" + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "text", + "content": " serves as the input for the next layer, replacing the original " + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "inline_equation", + "content": "x_t^{(l)}" + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "text", + "content": ". The above equation serves as a weighted fusion of layer output in two timesteps. The final prediction " + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\epsilon^S(x_t, x_s, t, s) = \\tilde{x}_t^{(L+1)}" + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "text", + "content": " is obtained from these fused features, forming the prediction for the student model. With this, the computation flow of the student model is changed. In constraint, the teacher model functions as the original denoising predictor at timestep " + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "text", + "content": ", with its prediction output expressed as " + }, + { + "bbox": [ + 313, + 227, + 555, + 356 + ], + "type": "inline_equation", + "content": "\\epsilon^T(x_t, x_s, t, s) = \\epsilon_{\\theta^{-}}(x_t, t)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "type": "text", + "content": "Training Objective. We take the pre-trained model as both the initialization for the teacher and the student model. The teacher " + }, + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "type": "inline_equation", + "content": "\\theta_T" + }, + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "type": "text", + "content": " model remained frozen while the update of parameters is performed on the student side. The self-distillation objective here is the matching between the student " + }, + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "type": "inline_equation", + "content": "\\epsilon^S(x_t, x_s, t, s)" + }, + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "type": "text", + "content": " and the teacher " + }, + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "type": "inline_equation", + "content": "\\epsilon^T(x_t, x_s, t, s)" + }, + { + "bbox": [ + 313, + 372, + 554, + 456 + ], + "type": "text", + "content": ". The distillation objective would be:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 464, + 553, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 553, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 553, + 495 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathbb {E} _ {s \\sim [ 1, T ], x _ {0} \\sim q _ {\\mathrm {d a t a}} (x)} \\left[ \\left\\| \\boldsymbol {\\epsilon} ^ {\\mathcal {T}} \\left(x _ {t}, x _ {s}, t, s\\right) - \\boldsymbol {\\epsilon} ^ {\\mathcal {S}} \\left(x _ {t}, x _ {s}, t, s\\right) \\right\\| ^ {2} \\right] \\tag {7}", + "image_path": "1f2ceace390257a1c5ad01cb0dfff28c3f9bfc0fceaac60768367e2af0f6c451.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "inline_equation", + "content": "x_{s}" + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "text", + "content": " represents " + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "inline_equation", + "content": "x_{0}" + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "text", + "content": " with added noise, and " + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "text", + "content": " is obtained by performing one step from " + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "inline_equation", + "content": "x_{s}" + }, + { + "bbox": [ + 313, + 495, + 554, + 579 + ], + "type": "text", + "content": " in the ODE solver. After the training phase is completed, no fusion operations are applied during the inference stage. The model's computation remains identical to its original configuration but benefits from the enhancements gained through the self-distillation process." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 587, + 482, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 587, + 482, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 587, + 482, + 601 + ], + "type": "text", + "content": "3.3. Distill from High-Order Solver" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": "In this section, we explain why this self-distillation framework works. In order to reduce the discretization error for the first-order ODE solver, such as Euler [20], one straightforward way is to use the higher-order solver for the diffusion ODEs. The cost for this is that it needs twice or third or even more times of function evaluation. We show that our self-distillation framework serves as an approximated form for distilling it into the same network without introducing additional parameters." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12904" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "content": "We perform a single step forward from timestep " + }, + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "content": " to timestep " + }, + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "content": ". We compare the formulation of DPM-Solver-1 and DPM-Solver-2 [34]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 88, + 117, + 295, + 139 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 117, + 295, + 139 + ], + "spans": [ + { + "bbox": [ + 88, + 117, + 295, + 139 + ], + "type": "interline_equation", + "content": "\\text {D P M - S o l v e r - 1 :} x _ {t} = \\frac {\\alpha_ {t}}{\\alpha_ {s}} x _ {s} - w _ {t} \\epsilon_ {\\theta} (x _ {s}, s) \\tag {8}", + "image_path": "ca7cdead7b965e9c5b2ec69cbd1c184bbccedf8b1683451c34e678f146f34422.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 89, + 140, + 295, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 140, + 295, + 163 + ], + "spans": [ + { + "bbox": [ + 89, + 140, + 295, + 163 + ], + "type": "interline_equation", + "content": "\\text {D P M - S o l v e r - 2 :} x _ {t} = \\frac {\\alpha_ {t}}{\\alpha_ {s}} x _ {s} - w _ {t} \\epsilon_ {\\theta} (x _ {u}, u) \\tag {9}", + "image_path": "29cd0f297592f9202aa322034a4dafcd0dd9ffc88ef806b5e685caf45fda8a0b.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "spans": [ + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": "Here the timestep " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": " is an intermediate timestep between " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": ". As defined in DPM-Solver-2, timestep " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": " has " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "\\lambda_u \\coloneqq \\log \\left( \\frac{\\alpha_u}{\\sigma_u} \\right)" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": " which is the average of those for timestep " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": " and timestep " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "x_u" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": " denotes the state one step forward from " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": ". The term " + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "inline_equation", + "content": "w_t" + }, + { + "bbox": [ + 55, + 171, + 296, + 290 + ], + "type": "text", + "content": " is a weight factor that depends only on the timestep. Using DPM-Solver-2, which is more accurate than DPM-Solver-1, the following training objective can be interpreted as encouraging the predictions of the first-order solver to align more closely with those of the second-order solver:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 298, + 295, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 298, + 295, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 298, + 295, + 331 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathbb {E} _ {s \\sim [ 1, T ], \\mathbf {x} _ {0} \\sim q _ {\\text {d a t a}} (x)} \\left[ w _ {t} \\| \\boldsymbol {\\epsilon} _ {\\theta} \\left(x _ {s}, s\\right) - \\boldsymbol {\\epsilon} _ {\\theta} \\left(x _ {u}, u\\right) \\| ^ {2} \\right] \\tag {10}", + "image_path": "1ace8b56fca9d76e574cb14c7af31dbacca6b75922cc8ea4d24f6e3e2538beca.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 332, + 296, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 332, + 296, + 381 + ], + "spans": [ + { + "bbox": [ + 55, + 332, + 296, + 381 + ], + "type": "text", + "content": "Building on the above equation, if the goal is to approximate a higher-order solver using a first-order solver, the training objective simplifies to: matching the prediction at the current step with the prediction at a subsequent step." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 389, + 218, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 389, + 218, + 403 + ], + "spans": [ + { + "bbox": [ + 55, + 389, + 218, + 403 + ], + "type": "text", + "content": "3.4. Ways to approximate " + }, + { + "bbox": [ + 55, + 389, + 218, + 403 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_u,u)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "spans": [ + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": "However, this method requires the prediction at the intermediate step between timestep " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": ", which is not always feasible in " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": "-step to " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": "-step distillation. A feasible scenario involves using a linear interpolant noise scheduler, where " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "x_{s} = (1 - s / T)x_{0} + (s / T)\\epsilon" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": ", and the model predicts the velocity instead of the noise " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": ". Under these conditions, the objective can be reformulated to align " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_s,s)" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": ". The corresponding results are presented in Table 1, with detailed proofs provided in the Appendix. With 10 and 250 sampling steps, consistent improvements in sample quality are observed, validating the effectiveness of Eq.10. However, as expected, performance declined in both cases when using " + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 407, + 296, + 586 + ], + "type": "text", + "content": "-prediction without incorporating these properties into the noise scheduler and the specific model prediction type." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "spans": [ + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": "The question now arises: how we can approximate " + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_u,u)" + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_s,s)" + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": ". One straightforward way is to get the approximation of " + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_u,u)" + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": " by Taylor Expansion, whose results turned to be the interpolating between " + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_s,s)" + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": ". Following the assumption in [34] that " + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_s,s)" + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": " is Lipschitz w.r.t " + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "inline_equation", + "content": "x_{s}" + }, + { + "bbox": [ + 55, + 587, + 296, + 659 + ], + "type": "text", + "content": ", we have:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 669, + 295, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 295, + 713 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\epsilon_ {\\theta} \\left(x _ {u}, u\\right) = \\epsilon_ {\\theta} \\left(x _ {s}, u\\right) + \\left(\\epsilon_ {\\theta} \\left(x _ {u}, u\\right) - \\epsilon_ {\\theta} \\left(x _ {s}, u\\right)\\right) \\\\ = \\epsilon_ {\\theta} (x _ {s}, s) + \\epsilon_ {\\theta} ^ {(1)} (x _ {s}, s) (u - s) + \\mathcal {O} ((u - s) ^ {2}) \\tag {11} \\\\ \\end{array}", + "image_path": "8b6029c13a20b730cf2233a9d74a40df56a9327fd32352fa5aa34a34f293692b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 317, + 70, + 553, + 215 + ], + "blocks": [ + { + "bbox": [ + 317, + 70, + 553, + 215 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 553, + 215 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 553, + 215 + ], + "type": "table", + "html": "
    ModelSamplerNFEsISFIDsFID
    v-prediction with linear interpolant noise scheduler
    REPA - SiT-XL/2SDE250305.71.424.70
    REPA - SiT-XL/2° w/ Eq.10SDE250306.31.414.68
    REPA - SiT-XL/2°ODE10233.95.857.82
    REPA - SiT-XL/2° w/ Eq.10ODE10238.45.117.48
    ε-prediction
    DiT-XL/2ODE50238.62.264.29
    DiT-XL/2 w/ Eq.10ODE50230.82.816.41
    DiT-XL/2 w/ Eq.12ODE50239.92.214.41
    DiT-XI/2ODE10158.312.3811.22
    DiT-XL/2 w/ Eq.10ODE1051.845.9926.95
    DiT-XL/2 w/ Eq.12ODE10184.77.999.91
    ", + "image_path": "5695d6d6a40fca42b8282d6034378892e105b9e79acf981f45ce8cc01c6a06a9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 223, + 553, + 257 + ], + "lines": [ + { + "bbox": [ + 313, + 223, + 553, + 257 + ], + "spans": [ + { + "bbox": [ + 313, + 223, + 553, + 257 + ], + "type": "text", + "content": "Table 1. Results on " + }, + { + "bbox": [ + 313, + 223, + 553, + 257 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 313, + 223, + 553, + 257 + ], + "type": "text", + "content": "-prediction and " + }, + { + "bbox": [ + 313, + 223, + 553, + 257 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 223, + 553, + 257 + ], + "type": "text", + "content": "-prediction diffusion models. For the experiments on REPA, we use the EMA model as the teacher for the experiments with 250 steps." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{(1)}(x_s,s)" + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "text", + "content": " is the first-order derivative w.r.t " + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "text", + "content": ". As above, we derive " + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{(1)}(x_s,s)" + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "text", + "content": " the same way between two different timesteps " + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 259, + 553, + 300 + ], + "type": "text", + "content": ", and we have:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 335, + 306, + 553, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 306, + 553, + 319 + ], + "spans": [ + { + "bbox": [ + 335, + 306, + 553, + 319 + ], + "type": "interline_equation", + "content": "\\epsilon_ {\\theta} \\left(x _ {u}, u\\right) = (1 - \\lambda) \\epsilon_ {\\theta} \\left(x _ {s}, s\\right) + \\lambda \\epsilon_ {\\theta} \\left(x _ {t}, t\\right) \\tag {12}", + "image_path": "e0839d51138c2f57d79cc1c090f9e4bf8efe4bc68be765d057d76df45e53b980.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 325, + 553, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 325, + 553, + 360 + ], + "spans": [ + { + "bbox": [ + 313, + 325, + 553, + 360 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 325, + 553, + 360 + ], + "type": "inline_equation", + "content": "\\lambda = (u - s) / (t - s)" + }, + { + "bbox": [ + 313, + 325, + 553, + 360 + ], + "type": "text", + "content": ". We get the same form as the explicit self step-distillation. The results with this equation are also shown in Table 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "spans": [ + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "text", + "content": "While the aforementioned method can approximate " + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_u,u)" + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "text", + "content": " to some extent, it remains suboptimal. An alternative approach is the implicit form of interpolation, which approximates " + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_u,u)" + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "text", + "content": " by interpolating on features rather than on the output. This one shares the same form with implicit self step-distillation. This idea is inspired by previous works [26, 37], which demonstrated that certain intermediate activations in timestep " + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "text", + "content": " can be reused in later timestep " + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "text", + "content": " to produce an approximated output for timestep " + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 313, + 361, + 555, + 517 + ], + "type": "text", + "content": ", with minimal effect on image quality. Consequently, we interpolate on the intermediate layers, and experimental results indicate that this method yields better performance than interpolation on predictions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 526, + 391, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 526, + 391, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 526, + 391, + 540 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 546, + 555, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 555, + 666 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 555, + 666 + ], + "type": "text", + "content": "In this section, we demonstrate the effectiveness of our proposed method. In Section 4.2, we present empirical evidence that both SSD and iSSD consistently enhance the performance of a pre-trained DiT across various image resolutions, model sizes, and sampling steps. Additionally, Section 4.3 provides the results of applying these methods to text-to-image generation. Section 4.4 highlights how iSSD can be applied to distilled models, yielding further performance improvements. Finally, Section 4.5 offers an in-depth analysis." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 672, + 430, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 672, + 430, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 672, + 430, + 685 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 555, + 713 + ], + "type": "text", + "content": "Models. For the conditional generation on ImageNet, we take all four DiT models: DiT-S/2, DiT-B/2, DiT-L/2, and" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12905" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 71, + 553, + 213 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 553, + 213 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 553, + 213 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 553, + 213 + ], + "type": "table", + "html": "
    MethodNFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑NFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    -256×256--512×512-
    DiT-XL/2250(ODE)1400243.42.144.560.810.61250(SDE)600240.83.045.020.840.54
    SiT-XL/2250(SDE)1400277.52.064.490.830.59250(SDE)600252.22.624.180.840.57
    DiT-XL/2501400238.62.264.290.800.6050600204.13.284.500.830.55
    + SSD501400 + 0.8239.92.214.410.800.6050600 + 0.4205.23.184.590.830.57
    + iSSD501400 + 0.8250.02.024.220.810.6050600 + 0.4210.22.864.060.840.54
    DiT-XL/2201400223.53.484.890.790.5720600186.35.105.730.820.55
    + SSD201400 + 0.8228.62.824.630.790.6020600 + 0.4194.74.015.330.830.56
    + iSSD201400 + 0.8227.52.674.850.790.6020600 + 0.4200.83.694.410.840.54
    DiT-XL/2101400158.312.3811.220.670.5310600128.415.1911.580.740.49
    + SSD101400 + 0.8184.77.999.910.710.5610600 + 0.4158.59.6111.090.780.54
    + iSSD101400 + 0.8209.64.927.620.790.5310600 + 0.4164.96.977.050.830.51
    ", + "image_path": "748179db7ed5a998502539735fca3008b53983431a2495f8ceef33829256ef2e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 262, + 294, + 531 + ], + "blocks": [ + { + "bbox": [ + 55, + 221, + 555, + 245 + ], + "lines": [ + { + "bbox": [ + 55, + 221, + 555, + 245 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 555, + 245 + ], + "type": "text", + "content": "Table 2. Image quality on ImageNet " + }, + { + "bbox": [ + 55, + 221, + 555, + 245 + ], + "type": "inline_equation", + "content": "{256} \\times {256}" + }, + { + "bbox": [ + 55, + 221, + 555, + 245 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 221, + 555, + 245 + ], + "type": "inline_equation", + "content": "{512} \\times {512}" + }, + { + "bbox": [ + 55, + 221, + 555, + 245 + ], + "type": "text", + "content": " ,with DiT-XL/2 as the base model. Prec. and Rec. denotes Precision and Recall. We adopt CFG=1.5 in all the experiments for ImageNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 262, + 294, + 531 + ], + "lines": [ + { + "bbox": [ + 58, + 262, + 294, + 531 + ], + "spans": [ + { + "bbox": [ + 58, + 262, + 294, + 531 + ], + "type": "table", + "html": "
    ModelNFEsTrain EpochsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    -DiT-S/2-
    DiT-S/225040059.426.517.310.590.56
    DiT-S/2+ iSSD5040053.529.215.890.570.58
    50400 + 0.254.627.755.730.580.58
    DiT-S/2+ iSSD2040052.032.627.430.550.55
    20400 + 0.252.530.628.230.560.55
    DiT-S/2+ iSSD1040040.149.5018.330.430.48
    10400 + 0.240.746.1718.890.450.48
    -DiT-B/2-
    DiT-B/2250200119.610.125.390.730.55
    DiT-B/2+ iSSD50200101.812.844.810.710.56
    50200 + 0.2104.911.774.990.710.56
    DiT-B/2+ iSSD2020097.515.406.110.680.54
    20200 + 0.2100.613.848.630.710.52
    DiT-B/2+ iSSD1020072.128.9915.540.560.48
    10200 + 0.277.921.4013.370.610.53
    -DiT-L/2-
    DiT-L/2250200196.33.734.620.820.54
    DiT-L/2+ iSSD50200168.84.774.410.780.55
    50200 + 0.2172.74.414.440.800.56
    DiT-L/2+ iSSD20200160.56.425.260.770.53
    20200 + 0.2172.34.924.870.800.53
    DiT-L/2+ iSSD10200118.516.0112.630.670.47
    10200 + 0.2143.77.754.990.750.55
    ", + "image_path": "8d7f30b723dc2d2c34f6d4c7788965b7763cb2be8e69835928a13071494e4ce7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 539, + 295, + 561 + ], + "lines": [ + { + "bbox": [ + 55, + 539, + 295, + 561 + ], + "spans": [ + { + "bbox": [ + 55, + 539, + 295, + 561 + ], + "type": "text", + "content": "Table 3. Image quality on ImageNet " + }, + { + "bbox": [ + 55, + 539, + 295, + 561 + ], + "type": "inline_equation", + "content": "{256} \\times {256}" + }, + { + "bbox": [ + 55, + 539, + 295, + 561 + ], + "type": "text", + "content": " with DiT-S/2,DiT-B/2 and DiT-L/2" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 580, + 296, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 580, + 296, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 580, + 296, + 640 + ], + "type": "text", + "content": "DiT-XL/2. For DiT-XL/2, we utilize the official pre-trained model, whereas for the other three models, we train them for 1 million to 2 million steps. For the text-to-image generation experiments, we employ Stable Diffusion v1.5 [44] as our base model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 296, + 713 + ], + "type": "text", + "content": "Evaluation. We follow previous work [40] to use IS, FID, sFID, Precision and Recall as the evaluation metric. For text-to-image generation, we test the FID on the validation set of COCO2014 and COCO2017 [31]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 265, + 555, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 265, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 265, + 555, + 456 + ], + "type": "text", + "content": "Training and Sampling Details. For training, the teacher and student models are both initialized from the base model, with the teacher remaining fixed during training. We use DDIM [50] as our base ODE solver and only utilize N-step predictions during training if the fine-tuned model would be evaluated under N-step. For DiT, we set a learning rate of 5e-6, a batch size of 128. The training epochs for each experiment are listed in the tables. Exponential Moving Average (EMA) is not used due to the short training period. We follow the original DiT setup without weight decay, warm-up, or learning rate schedulers. Models were evaluated with 10, 20, and 50 numbers of function evaluations (NFEs), and we show that even the basic ODE algorithms outperformed many advanced samplers with our algorithms. More details, especially for text-to-image generation, are in the Appendix." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 464, + 448, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 448, + 477 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 448, + 477 + ], + "type": "text", + "content": "4.2. Conditional Generation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 482, + 555, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 482, + 555, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 482, + 555, + 662 + ], + "type": "text", + "content": "Results on DiT-XL. We show the results of DiT-XL/2 in Table 2. With less than 1 epoch for optimizing DiT-XL/2, our method achieves consistent performance improvement upon the base models. Notably, our method with 50 NFEs can exceed the performance of the base DiT-XL/2 sampled 250 times by a large margin (2.02 vs 2.14), both under the same ODE sampler. Also this improvement can be observed in the resolution of 512, where the base DiT achieves the FID of 3.04, while our method can improve it to 2.86. We also notice improvement compared with the 250-step SiT, with our method sampled with only 50 steps. Besides, we found the implicit SSD performs better than the explicit SSD in most cases, and sometimes the implicit SSD outperforms the explicit SSD by a large margin. We show the qualitative results on ImageNet in the Appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 715 + ], + "type": "text", + "content": "Results on small-scale DiTs. We also apply our method under smaller DiT models, showing that the method can be generalized to models with different sizes. Since in the ex" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "12906" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 72, + 293, + 191 + ], + "blocks": [ + { + "bbox": [ + 58, + 72, + 293, + 191 + ], + "lines": [ + { + "bbox": [ + 58, + 72, + 293, + 191 + ], + "spans": [ + { + "bbox": [ + 58, + 72, + 293, + 191 + ], + "type": "image", + "image_path": "4a2f54b7038ca5db70708a795514840ed0c103a1d361b876b47f07f0cf5f7c79.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 201, + 295, + 234 + ], + "lines": [ + { + "bbox": [ + 55, + 201, + 295, + 234 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 295, + 234 + ], + "type": "text", + "content": "Figure 3. Visualization of generated images using various sampling algorithms with NFEs=10. From left to right, the algorithms shown are: PLMS, DDIM, DPM-Solver-2, and SSD." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 245, + 293, + 310 + ], + "blocks": [ + { + "bbox": [ + 58, + 245, + 293, + 310 + ], + "lines": [ + { + "bbox": [ + 58, + 245, + 293, + 310 + ], + "spans": [ + { + "bbox": [ + 58, + 245, + 293, + 310 + ], + "type": "table", + "html": "
    DatasetNFEsDDIMPLMSDPM-Solver-2Ours
    COCO20141012.7817.7115.2310.94
    2012.6812.6514.6310.56
    COCO20171022.7929.5124.4620.85
    2022.4322.1424.0220.69
    ", + "image_path": "cc9d539a8d2f349f0db48f82121be6a8cc93ebe8b00f9ccf61aad11e3dce90e2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 362, + 296, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 362, + 296, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 362, + 296, + 445 + ], + "type": "text", + "content": "periment in DiT-XL/2, we found iSSD consistently outperforms SSD, we here test the performance of iSSD on these DiT models. From Table 3, with only 0.2 epoch for training, we observe a large improvement upon the base model. It would only take several minutes to finish the training, and thus, can be seen as a cheap way to improve the performance of the trained models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 454, + 200, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 454, + 200, + 467 + ], + "spans": [ + { + "bbox": [ + 55, + 454, + 200, + 467 + ], + "type": "text", + "content": "4.3. Text-to-Image Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 472, + 295, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 295, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 295, + 579 + ], + "type": "text", + "content": "We apply SSD to Stable Diffusion v1.5. The experimental details are outlined in Appendix. Our method is compared against DDIM [50], DPM-Solver-2 [34] and PLMS [32] on COCO2014 and COCO2017, as shown in Table 4. Our approach demonstrates significant improvements in FID, outperforming other methods. Notably, our results with 10 NFEs surpass those achieved with 20 NFEs by competing samplers. Visualization results further highlight that images enhanced by our algorithm exhibit more detailed features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 588, + 205, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 588, + 205, + 600 + ], + "spans": [ + { + "bbox": [ + 55, + 588, + 205, + 600 + ], + "type": "text", + "content": "4.4. Results on Distilled Models" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "In this section, we apply our method to a distilled model obtained through progressive distillation (PD). Notably, this implies that predictions at intermediate steps that are not explicitly part of the PD process are not trained, resulting in suboptimal performance at these steps. This experiment aims to demonstrate that our method is effective that distills from N steps to enhance performance across those N steps, since using the results from intermediate steps other than these N steps would harm the performance." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 317, + 70, + 553, + 185 + ], + "blocks": [ + { + "bbox": [ + 55, + 318, + 295, + 340 + ], + "lines": [ + { + "bbox": [ + 55, + 318, + 295, + 340 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 295, + 340 + ], + "type": "text", + "content": "Table 4. FID Comparison with different samplers on the validation set of COCO2014 and COCO2017" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 70, + 553, + 185 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 553, + 185 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 553, + 185 + ], + "type": "table", + "html": "
    ModelNFEsIS ↑FID ↓sFID ↓Prec. ↑Rec. ↑
    DiT-XL/2250243.42.144.560.810.61
    PD 64 → 3232239.82.244.330.800.60
    + iSSD32246.21.994.330.810.60
    PD 20 → 1010209.94.195.240.760.57
    + iSSD10233.93.567.080.810.55
    PD 20 → 10 → 55173.07.006.590.730.58
    + iSSD5186.75.416.480.760.56
    PD 16 → 8 → 44152.68.757.900.700.59
    + iSSD4168.586.107.530.720.57
    ", + "image_path": "835cae22bb6e1d64a0f7a755571a9d23dba7e532d809b1ea10e1d2e27d3549c1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 317, + 225, + 552, + 287 + ], + "blocks": [ + { + "bbox": [ + 313, + 192, + 553, + 214 + ], + "lines": [ + { + "bbox": [ + 313, + 192, + 553, + 214 + ], + "spans": [ + { + "bbox": [ + 313, + 192, + 553, + 214 + ], + "type": "text", + "content": "Table 5. Results of building iSSD upon diffusion models being distilled for few-step generation." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 225, + 552, + 287 + ], + "lines": [ + { + "bbox": [ + 317, + 225, + 552, + 287 + ], + "spans": [ + { + "bbox": [ + 317, + 225, + 552, + 287 + ], + "type": "table", + "html": "
    ModelIS ↑FID ↓sFID ↓Prec.↑Rec.↑
    DiT-XL/213.4107.7594.570.110.36
    PD [47]158.37.847.110.700.60
    Shortcut Model [9]-7.8---
    PD + Ours168.66.117.530.720.57
    ", + "image_path": "8671725a1998a959e0f75d6274c9475279cf6852d5c89d4854c99fa408119b14.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 295, + 553, + 318 + ], + "lines": [ + { + "bbox": [ + 313, + 295, + 553, + 318 + ], + "spans": [ + { + "bbox": [ + 313, + 295, + 553, + 318 + ], + "type": "text", + "content": "Table 6. Comparison with training-based method on ImageNet " + }, + { + "bbox": [ + 313, + 295, + 553, + 318 + ], + "type": "inline_equation", + "content": "256\\times 256" + }, + { + "bbox": [ + 313, + 295, + 553, + 318 + ], + "type": "text", + "content": " . We set NFEs " + }, + { + "bbox": [ + 313, + 295, + 553, + 318 + ], + "type": "inline_equation", + "content": "= 4" + }, + { + "bbox": [ + 313, + 295, + 553, + 318 + ], + "type": "text", + "content": " and use DiT-XL/2 for sampling." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 338, + 555, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 555, + 518 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 555, + 518 + ], + "type": "text", + "content": "Orthogonal to distillation methods. Table 5 presents the results for models distilled through two-stage and three-stage progressive distillation (PD), and Figure 4(a) illustrates the results on a chain of models distilled from progressive distillation. The results indicate that our method can significantly enhance performance. Specifically, when applied to a 32-step distilled model, our approach achieves an FID of 1.99 with minimal additional computational cost, representing a substantial improvement over the distilled model and even the pre-trained DiT-XL/2. However, when comparing our method to the model directly distilled from PD, the performance at 10-step NFE is slightly lower (4.19 vs. 4.92). We position our method as an auxiliary step that complements and further refines the performance of distilled models, providing an orthogonal improvement." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 533, + 555, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 665 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 665 + ], + "type": "text", + "content": "Comparison with training-based methods. We evaluated our model against flow-matching algorithms designed for training diffusion models to enable few-step generation. The experiments are performed using 4 steps to generate images, and the backbone for diffusion models is DiT-XL/2. The results, summarized in Table 6, indicate that our method surpasses the performance of competing algorithms. Specifically, when compared to the ShortCut Model [9], an enhanced variant of the flow matching model adapted for DiT, our approach achieves superior results (FID: 6.1 v.s. 7.8)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 672, + 377, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 672, + 377, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 672, + 377, + 685 + ], + "type": "text", + "content": "4.5. Analysis" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 553, + 713 + ], + "type": "text", + "content": "Comparison with continual training. To demonstrate that the observed performance improvements are not merely" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12907" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 190, + 149 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 190, + 149 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 190, + 149 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 190, + 149 + ], + "type": "image", + "image_path": "d36e4565dcd98a0184a8776964638e3fe4d68032ec55568922d2de68f0b3ea51.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 119, + 152, + 130, + 160 + ], + "lines": [ + { + "bbox": [ + 119, + 152, + 130, + 160 + ], + "spans": [ + { + "bbox": [ + 119, + 152, + 130, + 160 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 194, + 72, + 326, + 148 + ], + "blocks": [ + { + "bbox": [ + 194, + 72, + 326, + 148 + ], + "lines": [ + { + "bbox": [ + 194, + 72, + 326, + 148 + ], + "spans": [ + { + "bbox": [ + 194, + 72, + 326, + 148 + ], + "type": "image", + "image_path": "9fe056c2a0654486fef4678df07ce01c2bb070f3e50b5b8ff125c8761dd78ffc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 255, + 152, + 266, + 160 + ], + "lines": [ + { + "bbox": [ + 255, + 152, + 266, + 160 + ], + "spans": [ + { + "bbox": [ + 255, + 152, + 266, + 160 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 163, + 555, + 196 + ], + "lines": [ + { + "bbox": [ + 55, + 163, + 555, + 196 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 555, + 196 + ], + "type": "text", + "content": "Figure 4. 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    ModelNFETrain EpochsIS↑FID↓
    DiT-XL/2101400158.312.38
    DiT-XL/2°101400 + 0.8156.712.97
    DiT-XL/2 + iSSD101400 + 0.8209.64.92
    DiT-S°25040027.651.55
    DiT-S°25042027.951.13
    DiT-S° + iSSD250400 + 228.748.38
    ", + "image_path": "8db48615f44c55e84e15aecf477a25428fffb09744f90a40afb72e117ba92f7c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 359, + 296, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 359, + 296, + 456 + ], + "spans": [ + { + "bbox": [ + 55, + 359, + 296, + 456 + ], + "type": "text", + "content": "due to additional training iterations, we conducted experiments on DiT-XL/2 (officially pre-trained and only have the EMA model) and DiT-S/2 ( has both the EMA and the base model). The results in Table 7 show that even with fewer training epochs, our method significantly outperforms models trained for 20 epochs on DiT-S/2. This confirms that the performance gains stem from the proposed self-distillation approach rather than extended training iterations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 469, + 296, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 469, + 296, + 590 + ], + "spans": [ + { + "bbox": [ + 55, + 469, + 296, + 590 + ], + "type": "text", + "content": "Synthetic Data v.s. Real Data. An additional exploration involves assessing whether a model's performance can be improved when only the model itself is available, without any supplementary training data or external models. We conducted experiments under this setting, and the results are presented in Table 8. The findings indicate that, while real data remains the optimal choice for achieving the highest performance, the use of synthetic data can still result in substantial improvements in generation quality, albeit with a slight performance trade-off compared to using real data." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 603, + 296, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 603, + 296, + 676 + ], + "spans": [ + { + "bbox": [ + 55, + 603, + 296, + 676 + ], + "type": "text", + "content": "Distill upon only one step. In Figure 4(b), we show the results of applying iSSD to a single step. This process yields two models; here, our focus is on determining which step has the greatest impact on images. The results indicate that applying self-distillation in the later stages of denoising provides the most significant benefit to image quality." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "Training dynamics for the teacher and the student in iSSD. Figure 4(c) presents the training dynamics ob" + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 316, + 215, + 553, + 271 + ], + "blocks": [ + { + "bbox": [ + 55, + 317, + 295, + 340 + ], + "lines": [ + { + "bbox": [ + 55, + 317, + 295, + 340 + ], + "spans": [ + { + "bbox": [ + 55, + 317, + 295, + 340 + ], + "type": "text", + "content": "Table 7. Comparison with Continual Training. The superscript " + }, + { + "bbox": [ + 55, + 317, + 295, + 340 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 55, + 317, + 295, + 340 + ], + "type": "text", + "content": " means we train these models from the official codebase." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 215, + 553, + 271 + ], + "lines": [ + { + "bbox": [ + 316, + 215, + 553, + 271 + ], + "spans": [ + { + "bbox": [ + 316, + 215, + 553, + 271 + ], + "type": "table", + "html": "
    ModelData SourceISFIDsFIDPrecisionRecall
    DiT-XL/2-158.312.3811.220.670.53
    iSSDOriginal Data209.64.927.620.790.53
    iSSDSynthetic - 10 step206.25.079.030.790.52
    iSSDSynthetic - 20 step207.95.028.990.790.53
    ", + "image_path": "508f244d4c882d90c12f6f56d20a0fe6f46da0c068f821a725b57de337f570ab.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 279, + 555, + 302 + ], + "lines": [ + { + "bbox": [ + 313, + 279, + 555, + 302 + ], + "spans": [ + { + "bbox": [ + 313, + 279, + 555, + 302 + ], + "type": "text", + "content": "Table 8. Results on Synthetic Data on ImageNet " + }, + { + "bbox": [ + 313, + 279, + 555, + 302 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 279, + 555, + 302 + ], + "type": "text", + "content": ". The experiments are based on DDIM with 10 sampling steps." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 322, + 555, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 322, + 555, + 429 + ], + "spans": [ + { + "bbox": [ + 313, + 322, + 555, + 429 + ], + "type": "text", + "content": "served during our experiments. It is crucial to note that the student model used in training differs from the one used for inference. The student model with fused activations starts with lower performance compared to the teacher model and remains inferior after training. In contrast, the unfused one, which maintains the same architecture and computation way for each layer, shows consistent improvement throughout training and eventually achieves significantly better performance than the teacher model." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "spans": [ + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "text", + "content": "Effect of gradient influential term " + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "text", + "content": ". We show the effect of " + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "text", + "content": ", as defined in Eq.5 and Eq.6. Though in Eq.12, we can directly calculate " + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "text", + "content": " if we adopt the same intermediate step as in DPM-Solver, we also put this timestep scheduler in this hyper-parameter, and search the best " + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "text", + "content": " for our approach. Figure 4(d) show for iSSD, with " + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "text", + "content": " equals a small value, the model would get poor results. We show the " + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 313, + 444, + 556, + 540 + ], + "type": "text", + "content": " used in each of our experiments in Appendix." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 550, + 388, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 550, + 388, + 562 + ], + "spans": [ + { + "bbox": [ + 313, + 550, + 388, + 562 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 556, + 714 + ], + "type": "text", + "content": "In this paper, we propose a novel self-distillation approach named Self Step-Distillation. We introduce two forms for Self Step-Distillation. Furthermore, we explain this approach by analyzing it through the lens of distillation with high-order samplers. Experimental results demonstrate that our method significantly outperforms the performance of the teacher model, achieving substantial improvements in both conditional generation and text-to-image generation. However, our method also has certain limitations. For instance, we still rely on suboptimal approaches to approximate the prediction of the intermediate step. Additionally, our method is relatively sensitive to hyperparameters." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12908" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 127 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 127 + ], + "type": "text", + "content": "This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 137, + 115, + 149 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 137, + 115, + 149 + ], + "spans": [ + { + "bbox": [ + 56, + 137, + 115, + 149 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 157, + 296, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 61, + 157, + 296, + 223 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 157, + 296, + 223 + ], + "spans": [ + { + "bbox": [ + 61, + 157, + 296, + 223 + ], + "type": "text", + "content": "[1] Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. 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We present DIFFUSIONRENDERER, a general-purpose method for both neural inverse and forward rendering. From input images or videos, it accurately estimates geometry and material buffers, and generates photorealistic images under specified lighting conditions, offering fundamental tools for image editing applications." + ], + "image_footnote": [], + "bbox": [ + 111, + 280, + 883, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 589, + 326, + 604 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding and modeling lighting effects are fundamental tasks in computer vision and graphics. Classic physically-based rendering (PBR) accurately simulates the light transport, but relies on precise scene representations—explicit 3D geometry, high-quality material properties, and lighting conditions—that are often impractical to obtain in real-world scenarios. Therefore, we introduce DIFFUSIONRENDERER, a neural approach that addresses the dual problem of inverse and forward rendering within a holistic framework. Leveraging powerful video diffusion model priors, the inverse rendering model accurately estimates $G$ -filters from real-world videos, providing an interface for image editing tasks, and training data for the rendering model. Conversely, our rendering model generates photorealistic images from $G$ -filters without explicit light transport simulation. Specifically, we first train a video diffusion model for inverse rendering on synthetic data, which generalizes well to real-world videos and allows us to auto-label diverse real-world videos. We", + "bbox": [ + 88, + 628, + 485, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "then co-train our rendering model using both synthetic and auto-labeled real-world data. Experiments demonstrate that DIFFUSIONRENDERER effectively approximates inverse and forwards rendering, consistently outperforming the state-of-the-art. Our model enables practical applications from a single video input—including relighting, material editing, and realistic object insertion.", + "bbox": [ + 511, + 590, + 908, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 712, + 645, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding and modeling light transport forms the basis of Physically Based Rendering (PBR) [59]. Modern path tracing algorithms, as regularly used in the gaming and movie industries, simulate light transport to render images that cannot be distinguished from photographs. The quality of such PBR-rendered images heavily depends on the accuracy and realism of the scene's surface geometry, material properties, and lighting representations. Such a scene description is either designed by artists (synthetic scenes) or reconstructed from data—also known as the inverse rendering problem [2, 3]. Inverse rendering has been extensively stud", + "bbox": [ + 509, + 734, + 910, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26069", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ied, particularly for applications like relighting and object insertion into real-world scenes [20, 41, 75, 88]. However, acquiring high quality surface and material representations is challenging in real-world scenarios, limiting the practicality of PBR methods (Fig. 2).", + "bbox": [ + 89, + 90, + 482, + 166 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While physically-based rendering and inverse rendering are usually considered separately, we propose to consider them jointly. Our approach draws inspiration from the success of large-scale generative models [8, 65], which \"render\" photorealistic images from simple text prompts without any explicit understanding of PBR. These models learn the underlying distribution of real-world images from a vast amounts of data, implicitly capturing the complex lighting effects.", + "bbox": [ + 89, + 167, + 482, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we propose DIFFUSIONRENDERER, a general-purpose neural rendering engine that can synthesize light transport simulation—such as shadows and reflections—by leveraging the powerful priors of video diffusion models. Conditioned on input geometry, material buffers, and environment map light source, DIFFUSIONRENDERER acts as a neural approximation of path-traced shading. DIFFUSIONRENDERER is designed to remain faithful to the conditioning signals, while adhering to the distribution of real-world images. As a result, we bypass the need for precise scene representations and description, as our model learns to handle imperfections in the input data.", + "bbox": [ + 89, + 289, + 483, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Training such a model requires some amount of high quality and diverse data, including data with noisy conditions to ensure robustness. Therefore, we first train an inverse renderer, a video diffusion model to map input RGB videos to intrinsic properties. Although trained solely on synthetic data, the inverse rendering model generalizes robustly to real-world scenarios. We then use it to generate \"pseudo-labels\" for diverse real-world videos. Combining both real-world auto-labeled data and synthetic data, we train our forward renderer video diffusion model.", + "bbox": [ + 89, + 470, + 483, + 621 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DIFFUSIONRENDERER outperforms state-of-the-art methods and effectively approximates the complex functionalities of inverse and forward rendering, allowing us to relight images and videos across diverse scenes and to synthesize consistent shadows and reflections without explicit path tracing and 3D scene representation. Our model can relight any scene from only a single video input, and provides fundamental tools for editing tasks such as material editing and realistic object insertion. To summarize:", + "bbox": [ + 89, + 623, + 482, + 758 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We develop a state-of-the-art inverse rendering method for videos of synthetic and real-world scenes.", + "- We repurpose a video diffusion model as a neural rendering engine that can synthesize photorealistic images and videos conditioned on noisy G-buffers.", + "- From a single video input, DIFFUSIONRENDERER enables relighting, material editing, and virtual object insertion in a unified framework, expanding the possibilities for real-world neural rendering applications." + ], + "bbox": [ + 93, + 761, + 482, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5d0cfc677626576635c6ab1bf27d25e8761528674cb87fc407cfa33ad0089ece.jpg", + "image_caption": [ + "Reference" + ], + "image_footnote": [], + "bbox": [ + 517, + 80, + 612, + 147 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6c394bd814112e04d6fd7257038ff820df912bfdbb46a095b7a099ab250a74c7.jpg", + "image_caption": [ + "SSRT" + ], + "image_footnote": [], + "bbox": [ + 616, + 80, + 712, + 147 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/25d3d0afe4bfcce680a303b953df84fa47f16478febdb5bacb51bf84c13676ed.jpg", + "image_caption": [ + "SSRT side view" + ], + "image_footnote": [], + "bbox": [ + 717, + 80, + 812, + 147 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/552653e7f881c57fc6585235e1f2a3c402fdc04d613b8e3be3bf2ba83fabda36.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 813, + 80, + 906, + 147 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b5986799a749f7fedcca1d6d2c80c56af1ea4b706bb0b96fc28a42c4c8a78bd5.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 517, + 157, + 612, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e5738f5ac4f8ec5c17c711cdcad0a2fc9688ea27aae6c7d84e0fb29b6d3614fb.jpg", + "image_caption": [ + "Estimated G-buffer" + ], + "image_footnote": [], + "bbox": [ + 616, + 157, + 712, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c7be291c11567a082c6b59da92a14159fbb5ecdc8d282f65f23d206a64b18243.jpg", + "image_caption": [ + "SSRT relit" + ], + "image_footnote": [], + "bbox": [ + 717, + 157, + 812, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9845dc399d41bb69f2f826e856c6bca3256858beeea7bfee5b20ea3bb8f320d2.jpg", + "image_caption": [ + "Ours relit", + "Figure 2. Classic PBR relies on explicit 3D geometry, e.g., meshes. When it is not available, screen space ray tracing (SSRT) struggles to accurately represent shadows and reflections (top). PBR is also sensitive to errors in G-buffers – SSRT with estimated G-buffers from inverse rendering models often fails to deliver quality results (bottom). DIFFUSIONRENDERER bypasses these issues, producing photorealistic results without 3D geometry or perfect G-buffers." + ], + "image_footnote": [], + "bbox": [ + 813, + 157, + 906, + 229 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 356, + 653, + 371 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural rendering refers to methods that replace or extend traditional rendering pipelines by neural networks. For example, Deep Shading [56] replaces traditional deferred shading [15] by a CNN to render images with ambient occlusion, global illumination, and depth-of-field from G-buffers. More recently, RGB $\\leftrightarrow$ X [83] trains image diffusion models to both estimate a G-buffer from an image and to render an image from a G-buffer. We extend this approach to video diffusion models and provide a novel approach for neural relighting that does not require an irradiance estimate. Other approaches fit rendered data using neural models or introduce neural components into an existing renderer with focus on approximating light transport [28, 31] or radiance caching [25, 53]. A plethora of works on neural and inverse rendering involve volumetric 3D scene representations in the form of NeRF [52] or 3D Gaussian Splats [35]. We refer to [70] for an overview. While providing photo-real view interpolation, these approaches typically bake radiance, and have limited editing capabilities. In contrast, we explicitly target an intermediate scene representation in the form of traditional, easy-to-edit, G-buffers with separate lighting.", + "bbox": [ + 511, + 380, + 906, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inverse rendering is a fundamental task first formalized in the 1970s [4], aiming to estimate intrinsic scene properties, like geometry, materials, and lighting from input images. Early methods designed hand-crafted priors within an optimization framework [2, 4, 11, 23, 39, 89], typically focusing on low-order effects. These methods lead to errors when the hand-crafted priors do not match reality. Recently, supervised and self-supervised learning has been extensively studied [5, 6, 9, 38, 40-42, 67, 73, 74, 76, 80]. The resulting algorithms are often data-hungry and specific to a certain task or domain. Acquiring sufficient and diverse training data poses a challenge. Recent advances in large image generative models provide new deep learning tools for inverse", + "bbox": [ + 511, + 703, + 908, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26070", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "rendering [19, 36, 44, 61, 83] resulting in much higher reconstruction quality. Still, the quality is not enough to power physically based rendering pipelines.", + "bbox": [ + 89, + 90, + 485, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Relighting focuses on modifying the lighting conditions of a scene given captured images or videos. Recent methods reconstruct 3D scene representations from multi-view images, performing explicit inverse rendering to recover material properties and enable relighting [10, 13, 24, 29, 43, 45, 54, 66, 68, 75, 78, 84, 85, 87]. These methods often optimize for each scene individually, and their quality may be affected by practical issues such as single-illumination capture, large scene scale, and dynamic content. Learning-based methods that train across multiple scenes have explored latent feature learning [7, 48, 90] and often incorporate neural rendering modules that utilize PBR buffers as inductive priors [22, 37, 57, 60, 79]. To improve relighting quality, recent approaches [30, 37, 62, 82] leverage diffusion models. With very few multi-illumination datasets [55], existing methods often are specialized to a domain, such as portraits, objects, and outdoor scenes, and remain data-hungry.", + "bbox": [ + 89, + 138, + 485, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 409, + 230, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Physically-based rendering (PBR) is concerned with the simulation of how the incoming radiance contributes to the outgoing radiance", + "bbox": [ + 89, + 430, + 483, + 477 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {o} (\\mathbf {p}, \\boldsymbol {\\omega} _ {o}) = \\int_ {\\Omega} f _ {r} (\\mathbf {p}, \\boldsymbol {\\omega} _ {o}, \\boldsymbol {\\omega} _ {i}) L _ {i} (\\mathbf {p}, \\boldsymbol {\\omega} _ {i}) | \\mathbf {n} \\cdot \\boldsymbol {\\omega} _ {i} | d \\boldsymbol {\\omega} _ {i}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 488, + 483, + 520 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "at a surface point $\\mathbf{p}$ in direction $\\omega_{o}$ . The integral over the hemisphere $\\Omega$ considers the BRDF $f_{r}(\\mathbf{p},\\omega_{o},\\omega_{i})$ , incoming radiance $L_{i}(\\mathbf{p},\\omega_{i})$ , and a cosine factor $|\\mathbf{n}\\cdot \\boldsymbol{\\omega}_i|$ for the angle between the normal $\\mathbf{n}$ and incoming light. It is evaluated by Monte Carlo methods [59, 71], with meticulously designed BRDF models [12, 14, 72] that approximate real surfaces.", + "bbox": [ + 89, + 532, + 483, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video diffusion models (VDMs). A diffusion model learns to approximate a data distribution $p_{\\mathrm{data}}(\\mathbf{I})$ via iterative denoising [18, 26, 69]. Most VDMs operate in a compressed, lower-dimensional latent space [1, 8]. Given an RGB video $\\mathbf{I} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}$ , consisting of $F$ frames at resolution $H \\times W$ , a pre-trained VAE encoder $\\mathcal{E}$ first encodes the video into a latent representation $\\mathbf{z} = \\mathcal{E}(\\mathbf{I}) \\in \\mathbb{R}^{F' \\times h \\times w \\times C}$ . The final video $\\hat{\\mathbf{I}}$ is then reconstructed by decoding $\\mathbf{z}$ with a pre-trained VAE decoder $\\mathcal{D}$ . Both training and inference stages of the VDM are conducted in this latent space. In this work, we build on Stable Video Diffusion [8], which compresses the video only along the spatial dimensions: $F' = F$ , $C = 4$ , $h = \\frac{H}{8}$ , and $w = \\frac{W}{8}$ .", + "bbox": [ + 89, + 626, + 485, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To train the VDM, noisy versions $\\mathbf{z}_{\\tau} = \\alpha_{\\tau}\\mathbf{z}_0 + \\sigma_{\\tau}\\epsilon$ are constructed by adding a Gaussian noise $\\epsilon$ with the noise schedule provided by $\\alpha_{\\tau}$ and $\\sigma_{\\tau}$ following EDM [33]. The diffusion model parameters $\\theta$ of the denoising function $\\mathbf{f}_{\\theta}$ are optimized using the denoising score matching objective [33].", + "bbox": [ + 89, + 825, + 485, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Once trained, iteratively applying $\\mathbf{f}_{\\theta}$ to a sample of Gaussian noise will produce a sample of $p_{\\mathrm{data}}(\\mathbf{I})$", + "bbox": [ + 511, + 90, + 906, + 122 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Conditioning in VDMs. Two common approaches to inject conditions into VDMs are: (i) concatenating condition channels with image latents $\\mathbf{z}_{\\tau}$ , which is often used for pixelwise conditions [8, 34, 36, 83], and (ii) injecting conditions through cross-attention layers [8, 65], which is often used for semantic features such as the CLIP embedding [63]. Note that our method is compatible with any standard VDMs and does not depend on specific architectural details.", + "bbox": [ + 511, + 123, + 908, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 511, + 253, + 604, + 270 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DIFFUSIONRENDERER is a unified framework comprising two video diffusion models designed for the dual tasks of neural forward and inverse rendering. As illustrated in Fig. 3, the neural forward renderer (Sec. 4.1) approximates physically based light transport (Eq. 1), transforming G-buffers [56] and lighting into a photorealistic video. The neural inverse renderer (Sec. 4.2) reconstructs geometry and material buffers from input video. The neural forward and inverse renderers are based on pre-trained video diffusion models and fine-tuned for conditional generation [34, 36, 83].", + "bbox": [ + 511, + 276, + 908, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Data is a critical aspect of learning-based methods. We describe our data curation workflow and synthetic-real joint training strategies in Sec. 4.3 and Sec. 4.4. Finally, we discuss image editing applications in Sec. 4.5.", + "bbox": [ + 511, + 428, + 906, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Neural Forward Rendering", + "text_level": 1, + "bbox": [ + 511, + 497, + 761, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We formulate neural forward rendering as a conditional generation task, producing photorealistic images given geometry, materials, and lighting as conditions. By approximating light transport simulation in a data-driven manner, the model requires neither classic 3D geometry nor explicit path tracing, thus reducing the constraints in real-world applications.", + "bbox": [ + 511, + 518, + 908, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Geometry and material conditions. Similar to the G-buffers in rendering system based on deferred shading [15], we use per-pixel scene attribute maps to represent scene geometry and materials. Specifically, we use surface normals $\\mathbf{n} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}$ in camera space and relative depth $\\mathbf{d} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}$ normalized to $[-1,1]$ to represent scene geometry. For materials, we use base color $\\mathbf{a} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}$ , roughness $\\mathbf{r} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}$ , and metallic $\\mathbf{m} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}$ following the Disney BRDF [12].", + "bbox": [ + 511, + 611, + 908, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Lighting conditions. Lighting is represented by environment maps $\\mathbf{E} \\in \\mathbb{R}^{F \\times H_{\\mathrm{env}} \\times W_{\\mathrm{env}} \\times 3}$ , which are panoramic images that capture the lighting intensity from all directions over the sphere. These environment maps are encoded in high dynamic range (HDR), while the VAEs used in typical latent diffusion models are designed for pixel values between -1 and 1. To address this discrepancy, similar to the light representation in Neural Gaffer [30], we first apply Reinhard tonemapping to convert HDR environment map into an LDR image $\\mathbf{E}_{\\mathrm{ldr}}$ . To more effectively represent HDR values,", + "bbox": [ + 511, + 750, + 910, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26071", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/51284f8fd23fe3ba4f2e7b768272ea460fd9ed1f628578a3ee166ecf80d6bc7a.jpg", + "image_caption": [ + "Figure 3. Method overview. Given an input video, the neural inverse renderer estimates geometry and material properties per pixel. It generates one scene attribute at a time, with the domain embedding indicating the target attributes to generate (Sec. 4.2). Conversely, the neural forward renderer produces photorealistic images given lighting information, geometry, and material buffers. The lighting condition is injected into the base video diffusion model through cross-attention layers (Sec. 4.1). During joint training with both synthetic and real data, we use an estimizable LoRA for real data sources (Sec. 4.4)." + ], + "image_footnote": [], + "bbox": [ + 112, + 70, + 883, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "particularly for light sources with high-intensity peaks, we compute $\\mathbf{E}_{\\mathrm{log}} = \\log (\\mathbf{E} + 1) / E_{\\mathrm{max}}$ where the light intensity values are mapped to logarithm space that is closer to human perception and normalized by max log intensity $E_{\\mathrm{max}}$ . Additionally, we also compute a directional encoding image, $\\mathbf{E}_{\\mathrm{dir}} \\in \\mathbb{R}^{F \\times H_{\\mathrm{env}} \\times W_{\\mathrm{env}} \\times 3}$ , where each pixel is represented by a unit vector indicating its direction in the camera coordinate system. The resulting lighting encodings used by the model consist of three panoramic images: $\\{\\mathbf{E}_{\\mathrm{ldr}}, \\mathbf{E}_{\\mathrm{log}}, \\mathbf{E}_{\\mathrm{dir}}\\}$ .", + "bbox": [ + 89, + 335, + 483, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model architecture. Our models are based on Stable Video Diffusion [8], an image-to-video diffusion model with its core architecture including a VAE encoder-decoder pair $\\{\\mathcal{E},\\mathcal{D}\\}$ , and a UNet-based denoising function $\\mathbf{f}_{\\theta}$ .", + "bbox": [ + 89, + 482, + 483, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use the VAE encoder $\\mathcal{E}$ to separately encode each G-buffer from $\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}$ into the latent space and concatenate them to produce the pixel-aligned scene attribute latent map $\\mathbf{g} = \\{\\mathcal{E}(\\mathbf{n}),\\mathcal{E}(\\mathbf{d}),\\mathcal{E}(\\mathbf{a}),\\mathcal{E}(\\mathbf{r}),\\mathcal{E}(\\mathbf{m})\\} \\in \\mathbb{R}^{F\\times h\\times w\\times 20}$ .", + "bbox": [ + 89, + 551, + 483, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Environment maps are usually in equi-rectangular projection and are not pixel-aligned with the generated images, thus requiring extra consideration. Prior works explored directly concatenating environment maps to the image latents [30] or concatenate split-sum shading buffers [17], which we also experimented with, but found suboptimal (Table 1). Instead, we take the cross-attention layers which originally operate on the text/image CLIP features, and re-purpose them for lighting conditions. To preserve spatial details of the environment maps, we generalize the conditional signals to a list of multi-resolution feature maps.", + "bbox": [ + 89, + 619, + 483, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we first pass the environment map information through VAE encoder $\\mathcal{E}$ to obtain $\\mathbf{h}_{\\mathbf{E}} = \\{\\mathcal{E}(\\mathbf{E}_{\\mathrm{ldr}}),\\mathcal{E}(\\mathbf{E}_{\\mathrm{log}}),\\mathcal{E}(\\mathbf{E}_{\\mathrm{dir}})\\} \\in \\mathbb{R}^{F\\times h_{\\mathrm{env}}\\times w_{\\mathrm{env}}\\times 12}$ . We additionally use an environment map encoder $\\mathcal{E}_{\\mathrm{env}}$ to further operate on $\\mathbf{h}_{\\mathbf{E}}$ . $\\mathcal{E}_{\\mathrm{env}}$ is the simplified encoder part of diffusion UNet with attention and temporal layers removed. It contains several convolutional layers to downsample and extract", + "bbox": [ + 89, + 794, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$K$ levels of multi-resolution features as lighting conditions:", + "bbox": [ + 513, + 335, + 898, + 351 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {\\text {e n v}} := \\left\\{\\mathbf {h} _ {\\text {e n v}} ^ {i} \\right\\} _ {i = 1} ^ {K} = \\mathcal {E} _ {\\text {e n v}} \\left(\\mathbf {h} _ {\\mathbf {E}}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 359, + 906, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As a result, the diffusion UNet $\\mathbf{f}_{\\theta}$ takes the noisy latent $\\mathbf{z}_{\\tau}$ and G-buffer latent $\\mathbf{g}$ as pixel-wise input. At each UNet level $k$ , the diffusion UNet queries the latent environment map features at the corresponding level $\\mathbf{h}_{\\mathrm{env}}^k$ , and aggregates based on its keys and values. Through the multi-level self-attention and cross-attention layers, the diffusion model is given the capacity to learn to shade G-buffers with lighting. During inference, the diffusion target can be computed as $\\mathbf{f}_{\\theta}(\\mathbf{z}_{\\tau}; \\mathbf{g}, \\mathbf{c}_{\\mathrm{env}}, \\tau)$ to produce photorealistic images with iterative denoising.", + "bbox": [ + 511, + 386, + 906, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Neural Inverse Rendering", + "text_level": 1, + "bbox": [ + 511, + 546, + 750, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We similarly formulate inverse rendering as a conditional generation task. Given an input video $\\mathbf{I}$ as a condition, the inverse renderer estimates scene attribute maps $\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}$ which are the G-buffers used by the forward renderer.", + "bbox": [ + 511, + 565, + 906, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model architecture. The input video $\\mathbf{I}$ is encoded into latent space $\\mathbf{z} = \\mathcal{E}(\\mathbf{I})$ , and concatenated with the noisy G-buffer latent, which we denote as $\\mathbf{g}_{\\tau} = \\alpha_{\\tau}\\mathbf{g}_0 + \\sigma_{\\tau}\\epsilon$ .", + "bbox": [ + 511, + 628, + 905, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an input video, the inverse renderer generates all five attributes $\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}$ using the same model. To preserve the high-quality generation and maximally leverage the diffusion model pre-trained knowledge, each attribute is generated in a dedicated pass, instead of generating all at once. We follow prior works [21, 49, 83] and use a domain embedding to indicate to the model which attribute should be generated. Specifically, we introduce an estimizable domain embedding $\\mathbf{c}_{\\mathrm{emb}}\\in \\mathbb{R}^{K_{\\mathrm{emb}}\\times C_{\\mathrm{emb}}}$ , where $K_{\\mathrm{emb}} = 5$ is the number of buffers and $C_\\mathrm{emb}$ is the dimension of the embedding vector. We re-purpose the cross-attention layers with image CLIP features to take domain embeddings. When estimating an attribute indexed by $P$ , we feed its embedding $\\mathbf{c}_{\\mathrm{emb}}^P$ as a condition and predict the diffusion target with $\\mathbf{f}_{\\theta}(\\mathbf{g}_{\\tau}^{P};\\mathbf{z},\\mathbf{c}_{\\mathrm{emb}}^{P},\\tau)$ .", + "bbox": [ + 511, + 674, + 906, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26072", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Data Strategy", + "text_level": 1, + "bbox": [ + 89, + 90, + 235, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Synthetic data curation. To train our models, we require high-quality video data with paired ground-truth for material, geometry, and lighting information. Specifically, each video data sample should include paired frames of RGB, base color, roughness, metallic, normals, depth, and environment map: $\\{\\mathbf{I},\\mathbf{a},\\mathbf{r},\\mathbf{m},\\mathbf{n},\\mathbf{d},\\mathbf{E}\\}$ . These buffers are typically only available in synthetic data, and most existing public datasets contain only a subset of them.", + "bbox": [ + 89, + 112, + 483, + 233 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address the data scarcity, we designed a synthetic data generation workflow to produce a large amount of high-quality data covering diverse and complex lighting effects. We start by curating a collection of 3D assets, PBR materials, and HDR environment maps. We use 36,500 3D assets from Objaverse LVIS split. For materials and lighting, we collected 4,260 high-quality PBR material maps, and 766 HDR environment maps from publicly available resources.", + "bbox": [ + 89, + 233, + 483, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In each scene, we place a plane with a randomly selected PBR material, and sample up to three 3D objects, and place them on the plane. We perform collision detection to avoid intersecting objects. We also place up to three primitives (cube, sphere, and cylinder) with randomized shape and materials to cover complex lighting effects such as inter-reflections. A randomly selected HDR environment map illuminates the scene. We generate motions including camera orbits, camera oscillation, lighting rotation, object rotation and translation.", + "bbox": [ + 89, + 354, + 483, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use a custom path tracer based on OptiX [58] to render the videos. In total, we generate 150,000 videos with paired ground-truth G-buffers and environment maps, at 24 frames per video in $512 \\times 512$ resolution. This dataset can be used to train both rendering and inverse rendering models.", + "bbox": [ + 89, + 505, + 483, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Real world auto-labeling. Synthetic data provides accurate supervision signals, and when combined with powerful image diffusion models, it demonstrates impressive generalization to unseen domains for inverse rendering tasks [21, 34]. However, when it comes to training the forward rendering model, synthetic data alone is insufficient. Since the output of the forward renderer is an RGB video, training only on synthetic renderings biases the model toward synthetic visual styles. Compared to inverse rendering, we observe a much more significant domain gap in complex real-world scenes for forward rendering tasks (Fig. 7).", + "bbox": [ + 89, + 583, + 483, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Acquiring real-world data with paired geometry, material, and lighting ground truth requires complex and impractical capturing setups. Based on the observation that our inverse rendering model generalizes to real-world videos, we apply it to automatically label real-world videos. Specifically, we use the DL3DV10k [47] dataset, which is a large-scale dataset consisting of 10,510 videos featuring diverse real-world environments. We use our inverse rendering model (Sec. 4.2) to generate G-buffer labels and use an off-the-shelf method DiffusionLight [61] to estimate environment", + "bbox": [ + 89, + 750, + 485, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "maps. Each video is divided into 15 segments, resulting in around 150,000 real-world video samples with auto-labeled geometry, material, and lighting attributes.", + "bbox": [ + 511, + 90, + 906, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Training pipeline", + "text_level": 1, + "bbox": [ + 511, + 147, + 684, + 162 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Neural inverse renderer. We first co-train the inverse rendering model on the combination of the curated synthetic video dataset and public image intrinsic datasets Interior-Verse [91] and HyperSim [64]. For image datasets, we treat images as single-frame videos. Each data sample consists of a video $\\mathbf{I}$ , an attribute index $P$ , and the scene attribute map $\\mathbf{s}^P$ . The target latent variable is the latents of the scene attribute $\\mathbf{g}_0^P \\coloneqq \\mathcal{E}(\\mathbf{s}^P)$ , and noise is added to $\\mathbf{g}_0^P$ to produce $\\mathbf{g}_{\\tau}^P$ . The model is trained using the objective function [33]:", + "bbox": [ + 511, + 170, + 906, + 306 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\theta , \\mathbf {c} _ {\\mathrm {e m b}}) = \\| \\mathbf {f} _ {\\theta} \\left(\\mathbf {g} _ {\\tau} ^ {P}; \\mathbf {z}, \\mathbf {c} _ {\\mathrm {e m b}} ^ {P}, \\tau\\right) - \\mathbf {g} _ {0} ^ {P} \\| _ {2} ^ {2}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 316, + 906, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We fine-tune the diffusion model parameters $\\theta$ and domain embeddings $\\mathbf{c}_{\\mathrm{emb}}$ , while keeping the latent encoder $\\mathcal{E}$ and decoder $\\mathcal{D}$ frozen. Once trained, the inverse renderer is used to auto-label real-world videos, generating training data for the forward renderer.", + "bbox": [ + 511, + 349, + 906, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Environment map encoder pre-training. Following the approach of latent diffusion models [65], we pre-train the environment map encoder $\\mathcal{E}_{\\mathrm{env}}$ along with a decoder $\\mathcal{D}_{\\mathrm{env}}$ using an L2 image reconstruction objective on environment maps, similar to an auto-encoder. The decoder architecture is based on the UNet decoder, containing a set of upsampling layers. After training, we discard the decoder $\\mathcal{D}_{\\mathrm{env}}$ and freeze the environment map encoder $\\mathcal{E}_{\\mathrm{env}}$ while training the neural forward rendering model.", + "bbox": [ + 511, + 426, + 905, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Neural forward renderer. We train our rendering model on a combination of a synthetic video dataset and real-world auto-labeled data, using paired G-buffer, lighting, and RGB videos. Although the auto-labeled real-world data is of sufficient quality, it may still contain inaccuracies. To address discrepancies between the synthetic and real-world data sources, we introduce an additional LoRA [27] with a small set of estimizable parameters $\\Delta \\theta$ during training on real data. We empirically find it improves the rendering quality (Fig. 7).", + "bbox": [ + 511, + 566, + 908, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During training, for an RGB video $\\mathbf{I}$ , the target latent variable is defined as $\\mathbf{z}_0 \\coloneqq \\mathcal{E}(\\mathbf{I})$ . Noise is added to $\\mathbf{z}_0$ to produce noisy image latent $\\mathbf{z}_{\\tau}$ . The training objective is:", + "bbox": [ + 511, + 703, + 908, + 750 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} (\\boldsymbol {\\theta}, \\Delta \\boldsymbol {\\theta}) = \\| \\mathbf {f} _ {\\boldsymbol {\\theta}} \\left(\\mathbf {z} _ {\\tau} ^ {\\mathrm {s y n t h}}; \\mathbf {g} ^ {\\mathrm {s y n t h}}, \\mathbf {c} _ {\\mathrm {e n v}} ^ {\\mathrm {s y n t h}}, \\boldsymbol {\\tau}\\right) - \\mathbf {z} _ {0} ^ {\\mathrm {s y n t h}} \\| _ {2} ^ {2} + \\\\ \\left\\| \\mathbf {f} _ {\\theta + \\Delta \\theta} \\left(\\mathbf {z} _ {\\tau} ^ {\\text {r e a l}}; \\mathbf {g} ^ {\\text {r e a l}}, \\mathbf {c} _ {\\text {e n v}} ^ {\\text {r e a l}}, \\tau\\right) - \\mathbf {z} _ {0} ^ {\\text {r e a l}} \\right\\| _ {2} ^ {2} \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 753, + 906, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5. Editing Applications", + "text_level": 1, + "bbox": [ + 511, + 819, + 709, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our proposed framework provides fundamental solutions for inverse and forward rendering, enabling photorealistic image editing applications through a three-step process: neural inverse rendering, G-buffer and lighting editing, and neural", + "bbox": [ + 511, + 840, + 906, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "26073", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/73bf3dfe358823a2c5cb1dc438eb71024636f530bef42633895fde0405d50152.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    SyntheticObjectsSyntheticScenes
    PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
    SSRT29.40.9510.03724.80.8990.113
    SplitSum [32]28.70.9510.03823.10.8830.116
    RGB↔X [83]25.20.8960.07718.50.6450.302
    DiLightNet [82]26.60.9140.06720.70.6300.300
    Ours28.30.9350.04826.00.7800.201
    Ours (image)27.40.9160.06225.40.7600.215
    Ours (w/o env. encoder)27.80.9270.05725.30.7560.237
    Ours (+ shading cond.)28.70.9300.05625.60.7610.245
    ", + "bbox": [ + 94, + 80, + 493, + 215 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9a0a7b69ed3ef700978bb6305ece0cd3a83cabcfef98d8c4508f338f55b1d440.jpg", + "table_caption": [ + "Table 1. Quantitative evaluation of neural rendering." + ], + "table_footnote": [], + "table_body": "
    SyntheticObjectsSyntheticScenes
    PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
    DiLightNet [82]23.790.8720.08718.880.5760.344
    Neural Gaffer [30]26.390.9030.08620.750.6330.343
    Ours27.500.9180.06724.630.7560.257
    ", + "bbox": [ + 94, + 234, + 488, + 311 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative evaluation of relighting.", + "bbox": [ + 148, + 314, + 421, + 329 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "rendering. For the example of relighting, given a video I as input, the inverse rendering model estimates the G-buffers", + "bbox": [ + 89, + 338, + 482, + 369 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\{\\hat {\\mathbf {n}}, \\hat {\\mathbf {d}}, \\hat {\\mathbf {a}}, \\hat {\\mathbf {r}}, \\hat {\\mathbf {m}} \\} = \\operatorname {I n v e r s e R e n d e r e r} (\\mathbf {I}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 380, + 483, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "With a user-specified target environment map $\\mathbf{E}_{\\mathrm{tgt}}$ , the rendering model produces relit videos", + "bbox": [ + 89, + 409, + 483, + 440 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {I}} _ {\\mathrm {t g t}} = \\text {F o r w a r d R e n d e r e r} \\left(\\left\\{\\hat {\\mathbf {n}}, \\hat {\\mathbf {d}}, \\hat {\\mathbf {a}}, \\hat {\\mathbf {r}}, \\hat {\\mathbf {m}}, \\mathbf {E} _ {\\mathrm {t g t}} \\right\\}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 450, + 483, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Similarly, editing the G-buffers and rendering the videos can enable material editing and virtual object insertion.", + "bbox": [ + 89, + 481, + 482, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 89, + 526, + 223, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We extensively evaluate DIFFUSIONRENDERER on a diverse range of synthetic and real-world datasets. Sec. 5.1 details our experimental settings. We compare and ablate across three main tasks: image generation from G-buffers (Sec. 5.2), inverse rendering (Sec. 5.3), and relighting (Sec. 5.4). Finally, we show applications of our method in Sec. 5.5.", + "bbox": [ + 89, + 547, + 483, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 89, + 648, + 282, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We refer to model implementation details in the Supplement.", + "bbox": [ + 89, + 669, + 483, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Task definitions. We evaluate our method on three fundamental tasks: forward rendering, inverse rendering, and relighting. For forward rendering, the methods take the G-buffers and lighting information $\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m},\\mathbf{E}\\}$ as input, and output rendered images $\\hat{\\mathbf{l}}$ . We evaluate the consistency between the rendered outputs and the ground-truth images $\\mathbf{l}$ .", + "bbox": [ + 89, + 686, + 483, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For inverse rendering, each method uses RGB images $\\mathbf{I}$ as input to estimate scene attributes $\\{\\hat{\\mathbf{a}},\\hat{\\mathbf{r}},\\hat{\\mathbf{m}},\\hat{\\mathbf{n}}\\}$ , and compare against ground truth values. Our focus is primarily on the attributes related to PBR - specifically, base color, roughness, and metallic properties. We recognize dedicated works on normal and depth estimation [21, 34] and do not aim to provide an exhaustive evaluation. For relighting, each method takes RGB images and target lighting conditions $\\{\\mathbf{I}^{\\mathrm{src}},\\mathbf{E}^{\\mathrm{tgt}}\\}$", + "bbox": [ + 89, + 780, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "as input, output re-lit image sequence $\\hat{\\mathbf{I}}^{\\mathrm{gt}}$ under the target lighting conditions, and compare with ground truth $\\mathbf{I}^{\\mathrm{gt}}$ .", + "bbox": [ + 511, + 90, + 903, + 121 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. For forward rendering, we compare with Split Sum [32] and Screen Space Ray Tracing (SSRT). For SSRT, we extract a mesh from the depth buffer and render the mesh with material parameters from the G-buffers and a provided HDR probe in a path tracer. We additionally compare against the neural rendering components of recent state-of-the-art methods RGB $\\leftrightarrow$ X [83] and DiLightNet [82]. For inverse rendering, we compare with recent diffusion-based methods Kocsis et al. [36], RGB $\\leftrightarrow$ X [83] and earlier methods [5, 41, 91]. For relighting, we compare with 2D methods DiLightNet [82], Neural Gaffer [30]. We also compare with 3D reconstruction-based methods [46, 75] in supplement.", + "bbox": [ + 511, + 123, + 906, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We use PSNR, SSIM, and LPIPS [86] for forward rendering and relighting. For inverse rendering, we evaluate albedo with PSNR and LPIPS following [36, 83]. Since albedo estimation involves scale ambiguity [23], we additionally solve and apply a three-channel scaling factor using least-squares error minimization before computing metrics, referred to as si-PSNR and si-LPIPS. We use root mean square error (RMSE) for metallic and roughness evaluation, and mean angular error for normals.", + "bbox": [ + 511, + 306, + 905, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We curate two high-quality synthetic datasets for quantitative evaluation, named SyntheticScenes and SyntheticObjects. The datasets consist of 3D assets from PolyHaven [81] and Objaverse [16] that are not included in the training data of our method or the baseline methods. SyntheticScenes contains 40 scenes, each featuring multiple objects arranged on a plane textured with high-quality PBR materials. Each scene is rendered into 24-frame videos under four lighting conditions, with motions such as camera orbiting and oscillation. As some baseline methods perform best with object-centric setups, we also create SyntheticObjects, a dataset of 30 individual objects. For each object, we render 24-frame videos under four different lighting conditions, with lighting rotated across frames.", + "bbox": [ + 511, + 446, + 908, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For inverse rendering, we also evaluate on the indoor scene benchmark InteriorVerse [91]. We include qualitative comparisons on the DL3DV10k [47] dataset.", + "bbox": [ + 511, + 657, + 903, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Evaluation of Forward Rendering", + "text_level": 1, + "bbox": [ + 511, + 714, + 810, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method with baseline methods in Table 1 and Fig. 4. For the neural methods RGB $\\leftrightarrow$ X [83] and DiLightNet [82], we use their rendering models with ground-truth G-buffers to generate the images.", + "bbox": [ + 511, + 734, + 906, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Both classic PBR and neural methods perform well on the SyntheticObjects dataset in single-object settings but show significant quality drops on the SyntheticScenes dataset due to complex inter-reflections and occlusions. For example, our method exhibits a minor PSNR decrease of 2.3 dB from SyntheticObjects to SyntheticScenes, while other baselines show more substantial drops.", + "bbox": [ + 511, + 795, + 905, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "26074", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8024706fdb5be8ef6e638774bfd9673b1bf1d76c10243af3710bd3e36c1ea977.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    AlbedoMetallic RMSE↓Roughness RMSE↓Normals Angular Error↓
    PSNR ↑LPIPS ↓si-PSNR ↑si-LPIPS ↓
    RGB↔X [83]14.30.32319.60.2860.4410.32123.80°
    Ours25.00.20526.70.2040.0390.0785.97°
    Ours (det.)26.00.21927.70.2170.0280.0605.85°
    Ours (image)23.40.21326.00.2090.0660.0986.67°
    Ours (image, det.)24.80.23127.20.2280.0430.0696.17°
    ", + "bbox": [ + 94, + 71, + 620, + 167 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/477a00d9bc12bce5ddb8658706c9bdb2449cee62121f3ea3fc926550bcfa2dd5.jpg", + "table_caption": [ + "Table 3. Quantitative evaluation of inverse rendering on SyntheticScenes video dataset. image: per-frame inference as image model. det.: 1-step deterministic inference." + ], + "table_footnote": [], + "table_body": "
    PSNR ↑SSIM ↑LPIPS ↓
    IIW [5]9.70.620.47
    Li et al. [41]12.30.680.52
    Zhu et al. [91]15.90.780.34
    Kocsis et al. [36]17.40.800.22
    RGB↔X [83]16.40.780.19
    Ours (image)21.90.870.17
    Ours (image, det.)22.40.870.19
    ", + "bbox": [ + 640, + 66, + 903, + 175 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Quantitative benchmark of albedo estimation on InteriorVerse dataset [91].", + "bbox": [ + 635, + 178, + 906, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f714e5c96958dca31ce42806fef31763c606255598a754ebef022cc7cc1b1b2c.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of forward rendering. Our method generates high-quality inter-reflections (top) and shadows (bottom), producing more accurate results than the neural baselines." + ], + "image_footnote": [], + "bbox": [ + 101, + 213, + 893, + 393 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b14b7179cca42db2aef87be3f0e99cb8b8ab22cb5448ed147d8516e39e30cade.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison of inverse rendering. We compare with RGB $\\leftrightarrow$ X [83] on DL3DV10k dataset. Both methods work well on indoor scenes, while our method predicts finer details in thin structures and more accurate metallic and roughness channels (top), likely benefiting from our curated training data. As compared to RGB $\\leftrightarrow$ X, our method generalizes better to outdoor scenes (bottom row)." + ], + "image_footnote": [], + "bbox": [ + 101, + 425, + 890, + 592 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method consistently outperforms all neural methods on both datasets and performs comparably to classic methods. In real-world editing applications, however, these PBR techniques often face significant limitations due to missing 3D geometry and noisy G-buffers (Fig. 2). Furthermore, SplitSum does not model shadows and inter-reflections.", + "bbox": [ + 89, + 647, + 485, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study. We ablate our model design choices in Table 1. While our method generalizes from images to videos, it can treat images as a special case of single-frame videos. To evaluate the benefits introduced by the video model, we compare with an ablated version of our method that performs per-frame inference (Ours, image). The video model consistently improves rendering quality across both datasets. In the ablated variant Ours (w/o env. encoder), we concatenate the VAE encoded environment maps directly to the image channels [30] rather than using a separate environment map", + "bbox": [ + 88, + 750, + 485, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "encoder. We demonstrate that a dedicated environment map encoder improves performance. For Ours (+ shading cond.), we include split-sum shading buffers as a conditioning input, following [17]. However, we observed no significant improvement with this addition and chose to exclude it from our final method for simplicity.", + "bbox": [ + 511, + 647, + 908, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Evaluation of Inverse Rendering", + "text_level": 1, + "bbox": [ + 511, + 742, + 802, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We quantitatively compare our method with baseline methods on SyntheticScenes in Table 3 and InteriorVerse [91] benchmark in Table 4. Our methods consistently outperforms baseline methods in both datasets, indicating the effectiveness of our data curation workflow and method designs. We show a qualitative comparison with RGB $\\leftrightarrow$ X [83] on DL3DV10k [47] dataset in Fig. 5.", + "bbox": [ + 511, + 762, + 908, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image vs. video model. Comparing Ours (image) and Ours, the video model consistently enhances the quality of", + "bbox": [ + 511, + 869, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "26075", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67baf571f70d4722d12966a2e377b1b8a32707f395a7b0067a0ceec66ee609c6.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison of relighting. Our method produces more accurate specular reflections compared to the baselines." + ], + "image_footnote": [], + "bbox": [ + 96, + 70, + 477, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7893d232d0e018fb50523c0347a7da5957fa6de6bf90c204c13c6440f2d4e06e.jpg", + "image_caption": [ + "Input Image & Tgt. Light Ours Ours (Synth.) Ours (w/o LoRA)", + "Figure 7. Qualitative ablation of relighting. Joint training with real-world data and adding LoRA during training significantly improve relighting quality for real-world scenes." + ], + "image_footnote": [], + "bbox": [ + 96, + 261, + 473, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "inverse rendering across all attributes. Notably, for properties associated with specular materials, the video model reduces RMSE by $41\\%$ for metallic (from 0.066 to 0.039) and $20\\%$ for roughness (from 0.098 to 0.078) compared to the image model. This suggests that the model learns to leverage view changes in video data, effectively capturing view-dependent effects to predict specular properties more accurately.", + "bbox": [ + 88, + 385, + 482, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "One-step deterministic fine-tuning. We also ablate the design choice of 1-step deterministic fine-tuning in Table 3 and 4. By default, the inverse renderer performs 20 denoising steps during inference. Building on recent findings in image diffusion models [51], we demonstrate that strongly conditioned video diffusion models can also be fine-tuned as 1-step deterministic models. Despite the significantly reduced computational cost, we observe that 1-step models consistently produce more \"accurate\" predictions and outperform multi-step stochastic models in photometric evaluations such as PSNR scores. However, the 1-step model enforces deterministic output, which can result in blurrier predictions for ambiguous regions with high-frequency details, thus yielding lower perceptual metrics, such as LPIPS. For neural forward rendering and relighting tasks, we use multi-step stochastic models to capture more realistic details, though we note that 1-step models can be a competitive choice for error-sensitive tasks and enhancing runtime efficiency.", + "bbox": [ + 89, + 493, + 482, + 766 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Evaluation of Relighting", + "text_level": 1, + "bbox": [ + 89, + 771, + 316, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 2 and Fig. 6, we compare with recent state-of-the-art relighting methods DiLightNet [82] and Neural Gaffer [30]. Our method outperforms these baselines, particularly in scenes with complex shadows and inter-reflections. Overall, it produces high-quality lighting effects and more accurate color and scale.", + "bbox": [ + 89, + 792, + 482, + 881 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation study. We ablate the design choices of synthetic-", + "bbox": [ + 89, + 885, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9aad6c557ab31133cfe695913fe5de772221640af3e1db222e44cc677cdbe4df.jpg", + "image_caption": [ + "Figure 8. Image editing applications. Top: Realistic material editing, adjusting the sphere's roughness and the horse's metallic. Bottom: Object insertion of a bathtub and table into scene images." + ], + "image_footnote": [], + "bbox": [ + 516, + 70, + 901, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "real joint training in Fig. 7. While synthetic data provides accurate supervision signals, it is limited to a specific domain and lacks the diversity and complexity found in real-world data. When training exclusively on synthetic data (Ours Synth.), the model struggles with complex structures, such as trees, which are rarely represented in synthetic datasets. Since the real-world auto-labels are estimated using inverse rendering models and contain imperfections, we find that incorporating a LoRA [27] during training with real data consistently improves visual quality.", + "bbox": [ + 511, + 234, + 906, + 387 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Applications", + "text_level": 1, + "bbox": [ + 511, + 393, + 648, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We show material editing and object insertion applications in Fig. 8. In the top row, we adjust the sphere's roughness from 0.15 to 0.6 and increase the horse's metallic property from 0 to 1, achieving photorealistic material edits. In the bottom row, we insert a bathtub and table in the G-buffer space of the input image, and use our forward renderer to produce the edited result. The inserted objects blend naturally into the scene, generating realistic reflections and shadows.", + "bbox": [ + 511, + 414, + 906, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 511, + 542, + 627, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DIFFUSIONRENDERER provides a scalable, data-driven approach to inverse and forward rendering, achieving high-quality G-buffer estimation and photorealistic image generation without relying on explicit path tracing or precise 3D scene representations. Jointly trained on synthetic and auto-labeled real-world data, DIFFUSIONRENDERER consistently outperforms state-of-the-art methods.", + "bbox": [ + 511, + 565, + 908, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. Our method is based on Stable Video Diffusion, which operates offline and would benefit from distillation techniques to improve inference speed. For editing tasks, the inverse and forward rendering models preserve most of the original content but may introduce slight variations in color or texture. Future work could explore task-specific fine-tuning [37] and develop neural intrinsic features to enhance content consistency and handle more complex visual effects. Additionally, our real-world auto-labeling currently adopts off-the-shelf lighting estimation model [61] which could benefit from better accuracy and robustness. With rapid advancements in video diffusion models [1] toward higher quality and faster inference speeds, we are optimistic that DIFFUSIONRENDERER will inspire future research in high-quality image synthesis and editing.", + "bbox": [ + 511, + 674, + 908, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "26076", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. The authors thank Shiqiu Liu, Yichen Sheng, and Michael Kass for their insightful discussions that contributed to this project. 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ACM, 2022. 5, 6, 7" + ], + "bbox": [ + 91, + 92, + 486, + 386 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "26080", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/65119a53-c0fc-4b0a-9ea3-a2e6c2c9c1d5_model.json b/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/65119a53-c0fc-4b0a-9ea3-a2e6c2c9c1d5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f511c06ab9189298b4a17f80090569cbc6d72ca9 --- /dev/null +++ b/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/65119a53-c0fc-4b0a-9ea3-a2e6c2c9c1d5_model.json @@ -0,0 +1,2853 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.175, + 0.131, + 0.825, + 0.175 + ], + "angle": 0, + "content": "DIFFUSIONRENDERER: Neural Inverse and Forward Rendering with Video Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.203, + 0.899, + 0.258 + ], + "angle": 0, + "content": "Ruofan Liang\\(^{1,2,3*}\\), Zan Gojcic\\(^{1}\\), Huan Ling\\(^{1,2,3}\\), Jacob Munkberg\\(^{1}\\), Jon Hasselgren\\(^{1}\\), Chih-Hao Lin\\(^{1,4}\\), Jun Gao\\(^{1,2,3}\\), Alexander Keller\\(^{1}\\), Nandita Vijaykumar\\(^{2,3}\\), Sanja Fidler\\(^{1,2,3}\\), Zian Wang\\(^{1,2,3*}\\) \n\\(^{1}\\)NVIDIA \\(^{2}\\)University of Toronto \\(^{3}\\)Vector Institute \\(^{4}\\)University of Illinois Urbana-Champaign" + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.281, + 0.885, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.535, + 0.908, + 0.58 + ], + "angle": 0, + "content": "Figure 1. We present DIFFUSIONRENDERER, a general-purpose method for both neural inverse and forward rendering. From input images or videos, it accurately estimates geometry and material buffers, and generates photorealistic images under specified lighting conditions, offering fundamental tools for image editing applications." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.59, + 0.327, + 0.605 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.629, + 0.486, + 0.901 + ], + "angle": 0, + "content": "Understanding and modeling lighting effects are fundamental tasks in computer vision and graphics. Classic physically-based rendering (PBR) accurately simulates the light transport, but relies on precise scene representations—explicit 3D geometry, high-quality material properties, and lighting conditions—that are often impractical to obtain in real-world scenarios. Therefore, we introduce DIFFUSIONRENDERER, a neural approach that addresses the dual problem of inverse and forward rendering within a holistic framework. Leveraging powerful video diffusion model priors, the inverse rendering model accurately estimates \\(G\\)-filters from real-world videos, providing an interface for image editing tasks, and training data for the rendering model. Conversely, our rendering model generates photorealistic images from \\(G\\)-filters without explicit light transport simulation. Specifically, we first train a video diffusion model for inverse rendering on synthetic data, which generalizes well to real-world videos and allows us to auto-label diverse real-world videos. We" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.591, + 0.909, + 0.698 + ], + "angle": 0, + "content": "then co-train our rendering model using both synthetic and auto-labeled real-world data. Experiments demonstrate that DIFFUSIONRENDERER effectively approximates inverse and forwards rendering, consistently outperforming the state-of-the-art. Our model enables practical applications from a single video input—including relighting, material editing, and realistic object insertion." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.713, + 0.646, + 0.728 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.735, + 0.911, + 0.903 + ], + "angle": 0, + "content": "Understanding and modeling light transport forms the basis of Physically Based Rendering (PBR) [59]. Modern path tracing algorithms, as regularly used in the gaming and movie industries, simulate light transport to render images that cannot be distinguished from photographs. The quality of such PBR-rendered images heavily depends on the accuracy and realism of the scene's surface geometry, material properties, and lighting representations. Such a scene description is either designed by artists (synthetic scenes) or reconstructed from data—also known as the inverse rendering problem [2, 3]. Inverse rendering has been extensively stud" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26069" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.167 + ], + "angle": 0, + "content": "ied, particularly for applications like relighting and object insertion into real-world scenes [20, 41, 75, 88]. However, acquiring high quality surface and material representations is challenging in real-world scenarios, limiting the practicality of PBR methods (Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.168, + 0.483, + 0.289 + ], + "angle": 0, + "content": "While physically-based rendering and inverse rendering are usually considered separately, we propose to consider them jointly. Our approach draws inspiration from the success of large-scale generative models [8, 65], which \"render\" photorealistic images from simple text prompts without any explicit understanding of PBR. These models learn the underlying distribution of real-world images from a vast amounts of data, implicitly capturing the complex lighting effects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.29, + 0.484, + 0.472 + ], + "angle": 0, + "content": "Specifically, we propose DIFFUSIONRENDERER, a general-purpose neural rendering engine that can synthesize light transport simulation—such as shadows and reflections—by leveraging the powerful priors of video diffusion models. Conditioned on input geometry, material buffers, and environment map light source, DIFFUSIONRENDERER acts as a neural approximation of path-traced shading. DIFFUSIONRENDERER is designed to remain faithful to the conditioning signals, while adhering to the distribution of real-world images. As a result, we bypass the need for precise scene representations and description, as our model learns to handle imperfections in the input data." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.472, + 0.484, + 0.622 + ], + "angle": 0, + "content": "Training such a model requires some amount of high quality and diverse data, including data with noisy conditions to ensure robustness. Therefore, we first train an inverse renderer, a video diffusion model to map input RGB videos to intrinsic properties. Although trained solely on synthetic data, the inverse rendering model generalizes robustly to real-world scenarios. We then use it to generate \"pseudo-labels\" for diverse real-world videos. Combining both real-world auto-labeled data and synthetic data, we train our forward renderer video diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.624, + 0.483, + 0.76 + ], + "angle": 0, + "content": "DIFFUSIONRENDERER outperforms state-of-the-art methods and effectively approximates the complex functionalities of inverse and forward rendering, allowing us to relight images and videos across diverse scenes and to synthesize consistent shadows and reflections without explicit path tracing and 3D scene representation. Our model can relight any scene from only a single video input, and provides fundamental tools for editing tasks such as material editing and realistic object insertion. To summarize:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.762, + 0.483, + 0.792 + ], + "angle": 0, + "content": "- We develop a state-of-the-art inverse rendering method for videos of synthetic and real-world scenes." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.793, + 0.483, + 0.837 + ], + "angle": 0, + "content": "- We repurpose a video diffusion model as a neural rendering engine that can synthesize photorealistic images and videos conditioned on noisy G-buffers." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.838, + 0.483, + 0.898 + ], + "angle": 0, + "content": "- From a single video input, DIFFUSIONRENDERER enables relighting, material editing, and virtual object insertion in a unified framework, expanding the possibilities for real-world neural rendering applications." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.762, + 0.483, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.082, + 0.614, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.149, + 0.593, + 0.157 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.082, + 0.713, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.148, + 0.681, + 0.157 + ], + "angle": 0, + "content": "SSRT" + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.082, + 0.813, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.723, + 0.148, + 0.807, + 0.157 + ], + "angle": 0, + "content": "SSRT side view" + }, + { + "type": "image", + "bbox": [ + 0.815, + 0.082, + 0.908, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.847, + 0.148, + 0.875, + 0.157 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.158, + 0.613, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.232, + 0.581, + 0.242 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.158, + 0.713, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.615, + 0.232, + 0.716, + 0.242 + ], + "angle": 0, + "content": "Estimated G-buffer" + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.158, + 0.813, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.737, + 0.231, + 0.794, + 0.241 + ], + "angle": 0, + "content": "SSRT relit" + }, + { + "type": "image", + "bbox": [ + 0.815, + 0.158, + 0.908, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.835, + 0.232, + 0.887, + 0.241 + ], + "angle": 0, + "content": "Ours relit" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.245, + 0.907, + 0.343 + ], + "angle": 0, + "content": "Figure 2. Classic PBR relies on explicit 3D geometry, e.g., meshes. When it is not available, screen space ray tracing (SSRT) struggles to accurately represent shadows and reflections (top). PBR is also sensitive to errors in G-buffers – SSRT with estimated G-buffers from inverse rendering models often fails to deliver quality results (bottom). DIFFUSIONRENDERER bypasses these issues, producing photorealistic results without 3D geometry or perfect G-buffers." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.357, + 0.655, + 0.372 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.381, + 0.908, + 0.699 + ], + "angle": 0, + "content": "Neural rendering refers to methods that replace or extend traditional rendering pipelines by neural networks. For example, Deep Shading [56] replaces traditional deferred shading [15] by a CNN to render images with ambient occlusion, global illumination, and depth-of-field from G-buffers. More recently, RGB \\(\\leftrightarrow\\) X [83] trains image diffusion models to both estimate a G-buffer from an image and to render an image from a G-buffer. We extend this approach to video diffusion models and provide a novel approach for neural relighting that does not require an irradiance estimate. Other approaches fit rendered data using neural models or introduce neural components into an existing renderer with focus on approximating light transport [28, 31] or radiance caching [25, 53]. A plethora of works on neural and inverse rendering involve volumetric 3D scene representations in the form of NeRF [52] or 3D Gaussian Splats [35]. We refer to [70] for an overview. While providing photo-real view interpolation, these approaches typically bake radiance, and have limited editing capabilities. In contrast, we explicitly target an intermediate scene representation in the form of traditional, easy-to-edit, G-buffers with separate lighting." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Inverse rendering is a fundamental task first formalized in the 1970s [4], aiming to estimate intrinsic scene properties, like geometry, materials, and lighting from input images. Early methods designed hand-crafted priors within an optimization framework [2, 4, 11, 23, 39, 89], typically focusing on low-order effects. These methods lead to errors when the hand-crafted priors do not match reality. Recently, supervised and self-supervised learning has been extensively studied [5, 6, 9, 38, 40-42, 67, 73, 74, 76, 80]. The resulting algorithms are often data-hungry and specific to a certain task or domain. Acquiring sufficient and diverse training data poses a challenge. Recent advances in large image generative models provide new deep learning tools for inverse" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26070" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.138 + ], + "angle": 0, + "content": "rendering [19, 36, 44, 61, 83] resulting in much higher reconstruction quality. Still, the quality is not enough to power physically based rendering pipelines." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.14, + 0.486, + 0.399 + ], + "angle": 0, + "content": "Relighting focuses on modifying the lighting conditions of a scene given captured images or videos. Recent methods reconstruct 3D scene representations from multi-view images, performing explicit inverse rendering to recover material properties and enable relighting [10, 13, 24, 29, 43, 45, 54, 66, 68, 75, 78, 84, 85, 87]. These methods often optimize for each scene individually, and their quality may be affected by practical issues such as single-illumination capture, large scene scale, and dynamic content. Learning-based methods that train across multiple scenes have explored latent feature learning [7, 48, 90] and often incorporate neural rendering modules that utilize PBR buffers as inductive priors [22, 37, 57, 60, 79]. To improve relighting quality, recent approaches [30, 37, 62, 82] leverage diffusion models. With very few multi-illumination datasets [55], existing methods often are specialized to a domain, such as portraits, objects, and outdoor scenes, and remain data-hungry." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.41, + 0.231, + 0.426 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.431, + 0.485, + 0.478 + ], + "angle": 0, + "content": "Physically-based rendering (PBR) is concerned with the simulation of how the incoming radiance contributes to the outgoing radiance" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.489, + 0.484, + 0.521 + ], + "angle": 0, + "content": "\\[\nL _ {o} (\\mathbf {p}, \\boldsymbol {\\omega} _ {o}) = \\int_ {\\Omega} f _ {r} (\\mathbf {p}, \\boldsymbol {\\omega} _ {o}, \\boldsymbol {\\omega} _ {i}) L _ {i} (\\mathbf {p}, \\boldsymbol {\\omega} _ {i}) | \\mathbf {n} \\cdot \\boldsymbol {\\omega} _ {i} | d \\boldsymbol {\\omega} _ {i}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.533, + 0.484, + 0.625 + ], + "angle": 0, + "content": "at a surface point \\(\\mathbf{p}\\) in direction \\(\\omega_{o}\\). The integral over the hemisphere \\(\\Omega\\) considers the BRDF \\(f_{r}(\\mathbf{p},\\omega_{o},\\omega_{i})\\), incoming radiance \\(L_{i}(\\mathbf{p},\\omega_{i})\\), and a cosine factor \\(|\\mathbf{n}\\cdot \\boldsymbol{\\omega}_i|\\) for the angle between the normal \\(\\mathbf{n}\\) and incoming light. It is evaluated by Monte Carlo methods [59, 71], with meticulously designed BRDF models [12, 14, 72] that approximate real surfaces." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.627, + 0.486, + 0.825 + ], + "angle": 0, + "content": "Video diffusion models (VDMs). A diffusion model learns to approximate a data distribution \\( p_{\\mathrm{data}}(\\mathbf{I}) \\) via iterative denoising [18, 26, 69]. Most VDMs operate in a compressed, lower-dimensional latent space [1, 8]. Given an RGB video \\( \\mathbf{I} \\in \\mathbb{R}^{F \\times H \\times W \\times 3} \\), consisting of \\( F \\) frames at resolution \\( H \\times W \\), a pre-trained VAE encoder \\( \\mathcal{E} \\) first encodes the video into a latent representation \\( \\mathbf{z} = \\mathcal{E}(\\mathbf{I}) \\in \\mathbb{R}^{F' \\times h \\times w \\times C} \\). The final video \\( \\hat{\\mathbf{I}} \\) is then reconstructed by decoding \\( \\mathbf{z} \\) with a pre-trained VAE decoder \\( \\mathcal{D} \\). Both training and inference stages of the VDM are conducted in this latent space. In this work, we build on Stable Video Diffusion [8], which compresses the video only along the spatial dimensions: \\( F' = F \\), \\( C = 4 \\), \\( h = \\frac{H}{8} \\), and \\( w = \\frac{W}{8} \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.826, + 0.486, + 0.903 + ], + "angle": 0, + "content": "To train the VDM, noisy versions \\(\\mathbf{z}_{\\tau} = \\alpha_{\\tau}\\mathbf{z}_0 + \\sigma_{\\tau}\\epsilon\\) are constructed by adding a Gaussian noise \\(\\epsilon\\) with the noise schedule provided by \\(\\alpha_{\\tau}\\) and \\(\\sigma_{\\tau}\\) following EDM [33]. The diffusion model parameters \\(\\theta\\) of the denoising function \\(\\mathbf{f}_{\\theta}\\) are optimized using the denoising score matching objective [33]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.907, + 0.123 + ], + "angle": 0, + "content": "Once trained, iteratively applying \\(\\mathbf{f}_{\\theta}\\) to a sample of Gaussian noise will produce a sample of \\(p_{\\mathrm{data}}(\\mathbf{I})\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.124, + 0.909, + 0.246 + ], + "angle": 0, + "content": "Conditioning in VDMs. Two common approaches to inject conditions into VDMs are: (i) concatenating condition channels with image latents \\(\\mathbf{z}_{\\tau}\\), which is often used for pixelwise conditions [8, 34, 36, 83], and (ii) injecting conditions through cross-attention layers [8, 65], which is often used for semantic features such as the CLIP embedding [63]. Note that our method is compatible with any standard VDMs and does not depend on specific architectural details." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.255, + 0.606, + 0.271 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.277, + 0.909, + 0.429 + ], + "angle": 0, + "content": "DIFFUSIONRENDERER is a unified framework comprising two video diffusion models designed for the dual tasks of neural forward and inverse rendering. As illustrated in Fig. 3, the neural forward renderer (Sec. 4.1) approximates physically based light transport (Eq. 1), transforming G-buffers [56] and lighting into a photorealistic video. The neural inverse renderer (Sec. 4.2) reconstructs geometry and material buffers from input video. The neural forward and inverse renderers are based on pre-trained video diffusion models and fine-tuned for conditional generation [34, 36, 83]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.429, + 0.908, + 0.49 + ], + "angle": 0, + "content": "Data is a critical aspect of learning-based methods. We describe our data curation workflow and synthetic-real joint training strategies in Sec. 4.3 and Sec. 4.4. Finally, we discuss image editing applications in Sec. 4.5." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.498, + 0.763, + 0.515 + ], + "angle": 0, + "content": "4.1. Neural Forward Rendering" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.519, + 0.909, + 0.61 + ], + "angle": 0, + "content": "We formulate neural forward rendering as a conditional generation task, producing photorealistic images given geometry, materials, and lighting as conditions. By approximating light transport simulation in a data-driven manner, the model requires neither classic 3D geometry nor explicit path tracing, thus reducing the constraints in real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.612, + 0.909, + 0.748 + ], + "angle": 0, + "content": "Geometry and material conditions. Similar to the G-buffers in rendering system based on deferred shading [15], we use per-pixel scene attribute maps to represent scene geometry and materials. Specifically, we use surface normals \\(\\mathbf{n} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}\\) in camera space and relative depth \\(\\mathbf{d} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}\\) normalized to \\([-1,1]\\) to represent scene geometry. For materials, we use base color \\(\\mathbf{a} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}\\), roughness \\(\\mathbf{r} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}\\), and metallic \\(\\mathbf{m} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}\\) following the Disney BRDF [12]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.911, + 0.902 + ], + "angle": 0, + "content": "Lighting conditions. Lighting is represented by environment maps \\(\\mathbf{E} \\in \\mathbb{R}^{F \\times H_{\\mathrm{env}} \\times W_{\\mathrm{env}} \\times 3}\\), which are panoramic images that capture the lighting intensity from all directions over the sphere. These environment maps are encoded in high dynamic range (HDR), while the VAEs used in typical latent diffusion models are designed for pixel values between -1 and 1. To address this discrepancy, similar to the light representation in Neural Gaffer [30], we first apply Reinhard tonemapping to convert HDR environment map into an LDR image \\(\\mathbf{E}_{\\mathrm{ldr}}\\). To more effectively represent HDR values," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26071" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.071, + 0.885, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.255, + 0.908, + 0.325 + ], + "angle": 0, + "content": "Figure 3. Method overview. Given an input video, the neural inverse renderer estimates geometry and material properties per pixel. It generates one scene attribute at a time, with the domain embedding indicating the target attributes to generate (Sec. 4.2). Conversely, the neural forward renderer produces photorealistic images given lighting information, geometry, and material buffers. The lighting condition is injected into the base video diffusion model through cross-attention layers (Sec. 4.1). During joint training with both synthetic and real data, we use an estimizable LoRA for real data sources (Sec. 4.4)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.337, + 0.484, + 0.474 + ], + "angle": 0, + "content": "particularly for light sources with high-intensity peaks, we compute \\(\\mathbf{E}_{\\mathrm{log}} = \\log (\\mathbf{E} + 1) / E_{\\mathrm{max}}\\) where the light intensity values are mapped to logarithm space that is closer to human perception and normalized by max log intensity \\(E_{\\mathrm{max}}\\). Additionally, we also compute a directional encoding image, \\(\\mathbf{E}_{\\mathrm{dir}} \\in \\mathbb{R}^{F \\times H_{\\mathrm{env}} \\times W_{\\mathrm{env}} \\times 3}\\), where each pixel is represented by a unit vector indicating its direction in the camera coordinate system. The resulting lighting encodings used by the model consist of three panoramic images: \\(\\{\\mathbf{E}_{\\mathrm{ldr}}, \\mathbf{E}_{\\mathrm{log}}, \\mathbf{E}_{\\mathrm{dir}}\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.483, + 0.484, + 0.545 + ], + "angle": 0, + "content": "Model architecture. Our models are based on Stable Video Diffusion [8], an image-to-video diffusion model with its core architecture including a VAE encoder-decoder pair \\(\\{\\mathcal{E},\\mathcal{D}\\}\\), and a UNet-based denoising function \\(\\mathbf{f}_{\\theta}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.552, + 0.484, + 0.613 + ], + "angle": 0, + "content": "We use the VAE encoder \\(\\mathcal{E}\\) to separately encode each G-buffer from \\(\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}\\) into the latent space and concatenate them to produce the pixel-aligned scene attribute latent map \\(\\mathbf{g} = \\{\\mathcal{E}(\\mathbf{n}),\\mathcal{E}(\\mathbf{d}),\\mathcal{E}(\\mathbf{a}),\\mathcal{E}(\\mathbf{r}),\\mathcal{E}(\\mathbf{m})\\} \\in \\mathbb{R}^{F\\times h\\times w\\times 20}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.621, + 0.484, + 0.788 + ], + "angle": 0, + "content": "Environment maps are usually in equi-rectangular projection and are not pixel-aligned with the generated images, thus requiring extra consideration. Prior works explored directly concatenating environment maps to the image latents [30] or concatenate split-sum shading buffers [17], which we also experimented with, but found suboptimal (Table 1). Instead, we take the cross-attention layers which originally operate on the text/image CLIP features, and re-purpose them for lighting conditions. To preserve spatial details of the environment maps, we generalize the conditional signals to a list of multi-resolution feature maps." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Specifically, we first pass the environment map information through VAE encoder \\(\\mathcal{E}\\) to obtain \\(\\mathbf{h}_{\\mathbf{E}} = \\{\\mathcal{E}(\\mathbf{E}_{\\mathrm{ldr}}),\\mathcal{E}(\\mathbf{E}_{\\mathrm{log}}),\\mathcal{E}(\\mathbf{E}_{\\mathrm{dir}})\\} \\in \\mathbb{R}^{F\\times h_{\\mathrm{env}}\\times w_{\\mathrm{env}}\\times 12}\\). We additionally use an environment map encoder \\(\\mathcal{E}_{\\mathrm{env}}\\) to further operate on \\(\\mathbf{h}_{\\mathbf{E}}\\). \\(\\mathcal{E}_{\\mathrm{env}}\\) is the simplified encoder part of diffusion UNet with attention and temporal layers removed. It contains several convolutional layers to downsample and extract" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.337, + 0.9, + 0.352 + ], + "angle": 0, + "content": "\\(K\\) levels of multi-resolution features as lighting conditions:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.36, + 0.907, + 0.379 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {\\text {e n v}} := \\left\\{\\mathbf {h} _ {\\text {e n v}} ^ {i} \\right\\} _ {i = 1} ^ {K} = \\mathcal {E} _ {\\text {e n v}} \\left(\\mathbf {h} _ {\\mathbf {E}}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.387, + 0.907, + 0.538 + ], + "angle": 0, + "content": "As a result, the diffusion UNet \\(\\mathbf{f}_{\\theta}\\) takes the noisy latent \\(\\mathbf{z}_{\\tau}\\) and G-buffer latent \\(\\mathbf{g}\\) as pixel-wise input. At each UNet level \\(k\\), the diffusion UNet queries the latent environment map features at the corresponding level \\(\\mathbf{h}_{\\mathrm{env}}^k\\), and aggregates based on its keys and values. Through the multi-level self-attention and cross-attention layers, the diffusion model is given the capacity to learn to shade G-buffers with lighting. During inference, the diffusion target can be computed as \\(\\mathbf{f}_{\\theta}(\\mathbf{z}_{\\tau}; \\mathbf{g}, \\mathbf{c}_{\\mathrm{env}}, \\tau)\\) to produce photorealistic images with iterative denoising." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.547, + 0.75, + 0.563 + ], + "angle": 0, + "content": "4.2. Neural Inverse Rendering" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.566, + 0.907, + 0.627 + ], + "angle": 0, + "content": "We similarly formulate inverse rendering as a conditional generation task. Given an input video \\(\\mathbf{I}\\) as a condition, the inverse renderer estimates scene attribute maps \\(\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}\\) which are the G-buffers used by the forward renderer." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.906, + 0.674 + ], + "angle": 0, + "content": "Model architecture. The input video \\(\\mathbf{I}\\) is encoded into latent space \\(\\mathbf{z} = \\mathcal{E}(\\mathbf{I})\\), and concatenated with the noisy G-buffer latent, which we denote as \\(\\mathbf{g}_{\\tau} = \\alpha_{\\tau}\\mathbf{g}_0 + \\sigma_{\\tau}\\epsilon\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.907, + 0.903 + ], + "angle": 0, + "content": "Given an input video, the inverse renderer generates all five attributes \\(\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}\\) using the same model. To preserve the high-quality generation and maximally leverage the diffusion model pre-trained knowledge, each attribute is generated in a dedicated pass, instead of generating all at once. We follow prior works [21, 49, 83] and use a domain embedding to indicate to the model which attribute should be generated. Specifically, we introduce an estimizable domain embedding \\(\\mathbf{c}_{\\mathrm{emb}}\\in \\mathbb{R}^{K_{\\mathrm{emb}}\\times C_{\\mathrm{emb}}}\\), where \\(K_{\\mathrm{emb}} = 5\\) is the number of buffers and \\(C_\\mathrm{emb}\\) is the dimension of the embedding vector. We re-purpose the cross-attention layers with image CLIP features to take domain embeddings. When estimating an attribute indexed by \\(P\\), we feed its embedding \\(\\mathbf{c}_{\\mathrm{emb}}^P\\) as a condition and predict the diffusion target with \\(\\mathbf{f}_{\\theta}(\\mathbf{g}_{\\tau}^{P};\\mathbf{z},\\mathbf{c}_{\\mathrm{emb}}^{P},\\tau)\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26072" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.236, + 0.108 + ], + "angle": 0, + "content": "4.3. Data Strategy" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.484, + 0.234 + ], + "angle": 0, + "content": "Synthetic data curation. To train our models, we require high-quality video data with paired ground-truth for material, geometry, and lighting information. Specifically, each video data sample should include paired frames of RGB, base color, roughness, metallic, normals, depth, and environment map: \\(\\{\\mathbf{I},\\mathbf{a},\\mathbf{r},\\mathbf{m},\\mathbf{n},\\mathbf{d},\\mathbf{E}\\}\\). These buffers are typically only available in synthetic data, and most existing public datasets contain only a subset of them." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.234, + 0.484, + 0.355 + ], + "angle": 0, + "content": "To address the data scarcity, we designed a synthetic data generation workflow to produce a large amount of high-quality data covering diverse and complex lighting effects. We start by curating a collection of 3D assets, PBR materials, and HDR environment maps. We use 36,500 3D assets from Objaverse LVIS split. For materials and lighting, we collected 4,260 high-quality PBR material maps, and 766 HDR environment maps from publicly available resources." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.356, + 0.484, + 0.505 + ], + "angle": 0, + "content": "In each scene, we place a plane with a randomly selected PBR material, and sample up to three 3D objects, and place them on the plane. We perform collision detection to avoid intersecting objects. We also place up to three primitives (cube, sphere, and cylinder) with randomized shape and materials to cover complex lighting effects such as inter-reflections. A randomly selected HDR environment map illuminates the scene. We generate motions including camera orbits, camera oscillation, lighting rotation, object rotation and translation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.506, + 0.484, + 0.582 + ], + "angle": 0, + "content": "We use a custom path tracer based on OptiX [58] to render the videos. In total, we generate 150,000 videos with paired ground-truth G-buffers and environment maps, at 24 frames per video in \\(512 \\times 512\\) resolution. This dataset can be used to train both rendering and inverse rendering models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.584, + 0.484, + 0.75 + ], + "angle": 0, + "content": "Real world auto-labeling. Synthetic data provides accurate supervision signals, and when combined with powerful image diffusion models, it demonstrates impressive generalization to unseen domains for inverse rendering tasks [21, 34]. However, when it comes to training the forward rendering model, synthetic data alone is insufficient. Since the output of the forward renderer is an RGB video, training only on synthetic renderings biases the model toward synthetic visual styles. Compared to inverse rendering, we observe a much more significant domain gap in complex real-world scenes for forward rendering tasks (Fig. 7)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.486, + 0.902 + ], + "angle": 0, + "content": "Acquiring real-world data with paired geometry, material, and lighting ground truth requires complex and impractical capturing setups. Based on the observation that our inverse rendering model generalizes to real-world videos, we apply it to automatically label real-world videos. Specifically, we use the DL3DV10k [47] dataset, which is a large-scale dataset consisting of 10,510 videos featuring diverse real-world environments. We use our inverse rendering model (Sec. 4.2) to generate G-buffer labels and use an off-the-shelf method DiffusionLight [61] to estimate environment" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.907, + 0.138 + ], + "angle": 0, + "content": "maps. Each video is divided into 15 segments, resulting in around 150,000 real-world video samples with auto-labeled geometry, material, and lighting attributes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.148, + 0.685, + 0.164 + ], + "angle": 0, + "content": "4.4. Training pipeline" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.171, + 0.908, + 0.308 + ], + "angle": 0, + "content": "Neural inverse renderer. We first co-train the inverse rendering model on the combination of the curated synthetic video dataset and public image intrinsic datasets Interior-Verse [91] and HyperSim [64]. For image datasets, we treat images as single-frame videos. Each data sample consists of a video \\(\\mathbf{I}\\), an attribute index \\(P\\), and the scene attribute map \\(\\mathbf{s}^P\\). The target latent variable is the latents of the scene attribute \\(\\mathbf{g}_0^P \\coloneqq \\mathcal{E}(\\mathbf{s}^P)\\), and noise is added to \\(\\mathbf{g}_0^P\\) to produce \\(\\mathbf{g}_{\\tau}^P\\). The model is trained using the objective function [33]:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.318, + 0.907, + 0.339 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\theta , \\mathbf {c} _ {\\mathrm {e m b}}) = \\| \\mathbf {f} _ {\\theta} \\left(\\mathbf {g} _ {\\tau} ^ {P}; \\mathbf {z}, \\mathbf {c} _ {\\mathrm {e m b}} ^ {P}, \\tau\\right) - \\mathbf {g} _ {0} ^ {P} \\| _ {2} ^ {2}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.35, + 0.907, + 0.424 + ], + "angle": 0, + "content": "We fine-tune the diffusion model parameters \\(\\theta\\) and domain embeddings \\(\\mathbf{c}_{\\mathrm{emb}}\\), while keeping the latent encoder \\(\\mathcal{E}\\) and decoder \\(\\mathcal{D}\\) frozen. Once trained, the inverse renderer is used to auto-label real-world videos, generating training data for the forward renderer." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.428, + 0.906, + 0.564 + ], + "angle": 0, + "content": "Environment map encoder pre-training. Following the approach of latent diffusion models [65], we pre-train the environment map encoder \\(\\mathcal{E}_{\\mathrm{env}}\\) along with a decoder \\(\\mathcal{D}_{\\mathrm{env}}\\) using an L2 image reconstruction objective on environment maps, similar to an auto-encoder. The decoder architecture is based on the UNet decoder, containing a set of upsampling layers. After training, we discard the decoder \\(\\mathcal{D}_{\\mathrm{env}}\\) and freeze the environment map encoder \\(\\mathcal{E}_{\\mathrm{env}}\\) while training the neural forward rendering model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.567, + 0.909, + 0.703 + ], + "angle": 0, + "content": "Neural forward renderer. We train our rendering model on a combination of a synthetic video dataset and real-world auto-labeled data, using paired G-buffer, lighting, and RGB videos. Although the auto-labeled real-world data is of sufficient quality, it may still contain inaccuracies. To address discrepancies between the synthetic and real-world data sources, we introduce an additional LoRA [27] with a small set of estimizable parameters \\(\\Delta \\theta\\) during training on real data. We empirically find it improves the rendering quality (Fig. 7)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.909, + 0.75 + ], + "angle": 0, + "content": "During training, for an RGB video \\(\\mathbf{I}\\), the target latent variable is defined as \\(\\mathbf{z}_0 \\coloneqq \\mathcal{E}(\\mathbf{I})\\). Noise is added to \\(\\mathbf{z}_0\\) to produce noisy image latent \\(\\mathbf{z}_{\\tau}\\). The training objective is:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.754, + 0.907, + 0.807 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} (\\boldsymbol {\\theta}, \\Delta \\boldsymbol {\\theta}) = \\| \\mathbf {f} _ {\\boldsymbol {\\theta}} \\left(\\mathbf {z} _ {\\tau} ^ {\\mathrm {s y n t h}}; \\mathbf {g} ^ {\\mathrm {s y n t h}}, \\mathbf {c} _ {\\mathrm {e n v}} ^ {\\mathrm {s y n t h}}, \\boldsymbol {\\tau}\\right) - \\mathbf {z} _ {0} ^ {\\mathrm {s y n t h}} \\| _ {2} ^ {2} + \\\\ \\left\\| \\mathbf {f} _ {\\theta + \\Delta \\theta} \\left(\\mathbf {z} _ {\\tau} ^ {\\text {r e a l}}; \\mathbf {g} ^ {\\text {r e a l}}, \\mathbf {c} _ {\\text {e n v}} ^ {\\text {r e a l}}, \\tau\\right) - \\mathbf {z} _ {0} ^ {\\text {r e a l}} \\right\\| _ {2} ^ {2} \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.82, + 0.71, + 0.837 + ], + "angle": 0, + "content": "4.5. Editing Applications" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.841, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Our proposed framework provides fundamental solutions for inverse and forward rendering, enabling photorealistic image editing applications through a three-step process: neural inverse rendering, G-buffer and lighting editing, and neural" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26073" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.082, + 0.495, + 0.216 + ], + "angle": 0, + "content": "
    SyntheticObjectsSyntheticScenes
    PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
    SSRT29.40.9510.03724.80.8990.113
    SplitSum [32]28.70.9510.03823.10.8830.116
    RGB↔X [83]25.20.8960.07718.50.6450.302
    DiLightNet [82]26.60.9140.06720.70.6300.300
    Ours28.30.9350.04826.00.7800.201
    Ours (image)27.40.9160.06225.40.7600.215
    Ours (w/o env. encoder)27.80.9270.05725.30.7560.237
    Ours (+ shading cond.)28.70.9300.05625.60.7610.245
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.131, + 0.218, + 0.442, + 0.232 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation of neural rendering." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.235, + 0.49, + 0.312 + ], + "angle": 0, + "content": "
    SyntheticObjectsSyntheticScenes
    PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
    DiLightNet [82]23.790.8720.08718.880.5760.344
    Neural Gaffer [30]26.390.9030.08620.750.6330.343
    Ours27.500.9180.06724.630.7560.257
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.15, + 0.315, + 0.422, + 0.33 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluation of relighting." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.339, + 0.483, + 0.37 + ], + "angle": 0, + "content": "rendering. For the example of relighting, given a video I as input, the inverse rendering model estimates the G-buffers" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.381, + 0.484, + 0.4 + ], + "angle": 0, + "content": "\\[\n\\{\\hat {\\mathbf {n}}, \\hat {\\mathbf {d}}, \\hat {\\mathbf {a}}, \\hat {\\mathbf {r}}, \\hat {\\mathbf {m}} \\} = \\operatorname {I n v e r s e R e n d e r e r} (\\mathbf {I}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.41, + 0.485, + 0.441 + ], + "angle": 0, + "content": "With a user-specified target environment map \\(\\mathbf{E}_{\\mathrm{tgt}}\\), the rendering model produces relit videos" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.452, + 0.484, + 0.471 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {I}} _ {\\mathrm {t g t}} = \\text {F o r w a r d R e n d e r e r} \\left(\\left\\{\\hat {\\mathbf {n}}, \\hat {\\mathbf {d}}, \\hat {\\mathbf {a}}, \\hat {\\mathbf {r}}, \\hat {\\mathbf {m}}, \\mathbf {E} _ {\\mathrm {t g t}} \\right\\}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.482, + 0.483, + 0.513 + ], + "angle": 0, + "content": "Similarly, editing the G-buffers and rendering the videos can enable material editing and virtual object insertion." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.527, + 0.224, + 0.544 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.549, + 0.484, + 0.64 + ], + "angle": 0, + "content": "We extensively evaluate DIFFUSIONRENDERER on a diverse range of synthetic and real-world datasets. Sec. 5.1 details our experimental settings. We compare and ablate across three main tasks: image generation from G-buffers (Sec. 5.2), inverse rendering (Sec. 5.3), and relighting (Sec. 5.4). Finally, we show applications of our method in Sec. 5.5." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.65, + 0.284, + 0.667 + ], + "angle": 0, + "content": "5.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.67, + 0.485, + 0.685 + ], + "angle": 0, + "content": "We refer to model implementation details in the Supplement." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.687, + 0.484, + 0.78 + ], + "angle": 0, + "content": "Task definitions. We evaluate our method on three fundamental tasks: forward rendering, inverse rendering, and relighting. For forward rendering, the methods take the G-buffers and lighting information \\(\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m},\\mathbf{E}\\}\\) as input, and output rendered images \\(\\hat{\\mathbf{l}}\\). We evaluate the consistency between the rendered outputs and the ground-truth images \\(\\mathbf{l}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.484, + 0.902 + ], + "angle": 0, + "content": "For inverse rendering, each method uses RGB images \\(\\mathbf{I}\\) as input to estimate scene attributes \\(\\{\\hat{\\mathbf{a}},\\hat{\\mathbf{r}},\\hat{\\mathbf{m}},\\hat{\\mathbf{n}}\\}\\), and compare against ground truth values. Our focus is primarily on the attributes related to PBR - specifically, base color, roughness, and metallic properties. We recognize dedicated works on normal and depth estimation [21, 34] and do not aim to provide an exhaustive evaluation. For relighting, each method takes RGB images and target lighting conditions \\(\\{\\mathbf{I}^{\\mathrm{src}},\\mathbf{E}^{\\mathrm{tgt}}\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.091, + 0.905, + 0.122 + ], + "angle": 0, + "content": "as input, output re-lit image sequence \\(\\hat{\\mathbf{I}}^{\\mathrm{gt}}\\) under the target lighting conditions, and compare with ground truth \\(\\mathbf{I}^{\\mathrm{gt}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.124, + 0.907, + 0.306 + ], + "angle": 0, + "content": "Baselines. For forward rendering, we compare with Split Sum [32] and Screen Space Ray Tracing (SSRT). For SSRT, we extract a mesh from the depth buffer and render the mesh with material parameters from the G-buffers and a provided HDR probe in a path tracer. We additionally compare against the neural rendering components of recent state-of-the-art methods RGB \\(\\leftrightarrow\\) X [83] and DiLightNet [82]. For inverse rendering, we compare with recent diffusion-based methods Kocsis et al. [36], RGB \\(\\leftrightarrow\\) X [83] and earlier methods [5, 41, 91]. For relighting, we compare with 2D methods DiLightNet [82], Neural Gaffer [30]. We also compare with 3D reconstruction-based methods [46, 75] in supplement." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.308, + 0.906, + 0.444 + ], + "angle": 0, + "content": "Metrics. We use PSNR, SSIM, and LPIPS [86] for forward rendering and relighting. For inverse rendering, we evaluate albedo with PSNR and LPIPS following [36, 83]. Since albedo estimation involves scale ambiguity [23], we additionally solve and apply a three-channel scaling factor using least-squares error minimization before computing metrics, referred to as si-PSNR and si-LPIPS. We use root mean square error (RMSE) for metallic and roughness evaluation, and mean angular error for normals." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.447, + 0.909, + 0.658 + ], + "angle": 0, + "content": "Datasets. We curate two high-quality synthetic datasets for quantitative evaluation, named SyntheticScenes and SyntheticObjects. The datasets consist of 3D assets from PolyHaven [81] and Objaverse [16] that are not included in the training data of our method or the baseline methods. SyntheticScenes contains 40 scenes, each featuring multiple objects arranged on a plane textured with high-quality PBR materials. Each scene is rendered into 24-frame videos under four lighting conditions, with motions such as camera orbiting and oscillation. As some baseline methods perform best with object-centric setups, we also create SyntheticObjects, a dataset of 30 individual objects. For each object, we render 24-frame videos under four different lighting conditions, with lighting rotated across frames." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.905, + 0.704 + ], + "angle": 0, + "content": "For inverse rendering, we also evaluate on the indoor scene benchmark InteriorVerse [91]. We include qualitative comparisons on the DL3DV10k [47] dataset." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.715, + 0.812, + 0.731 + ], + "angle": 0, + "content": "5.2. Evaluation of Forward Rendering" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.908, + 0.795 + ], + "angle": 0, + "content": "We compare our method with baseline methods in Table 1 and Fig. 4. For the neural methods RGB \\(\\leftrightarrow\\) X [83] and DiLightNet [82], we use their rendering models with ground-truth G-buffers to generate the images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.796, + 0.906, + 0.901 + ], + "angle": 0, + "content": "Both classic PBR and neural methods perform well on the SyntheticObjects dataset in single-object settings but show significant quality drops on the SyntheticScenes dataset due to complex inter-reflections and occlusions. For example, our method exhibits a minor PSNR decrease of 2.3 dB from SyntheticObjects to SyntheticScenes, while other baselines show more substantial drops." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26074" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.073, + 0.622, + 0.169 + ], + "angle": 0, + "content": "
    AlbedoMetallic RMSE↓Roughness RMSE↓Normals Angular Error↓
    PSNR ↑LPIPS ↓si-PSNR ↑si-LPIPS ↓
    RGB↔X [83]14.30.32319.60.2860.4410.32123.80°
    Ours25.00.20526.70.2040.0390.0785.97°
    Ours (det.)26.00.21927.70.2170.0280.0605.85°
    Ours (image)23.40.21326.00.2090.0660.0986.67°
    Ours (image, det.)24.80.23127.20.2280.0430.0696.17°
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.173, + 0.625, + 0.201 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation of inverse rendering on SyntheticScenes video dataset. image: per-frame inference as image model. det.: 1-step deterministic inference." + }, + { + "type": "table", + "bbox": [ + 0.642, + 0.068, + 0.905, + 0.176 + ], + "angle": 0, + "content": "
    PSNR ↑SSIM ↑LPIPS ↓
    IIW [5]9.70.620.47
    Li et al. [41]12.30.680.52
    Zhu et al. [91]15.90.780.34
    Kocsis et al. [36]17.40.800.22
    RGB↔X [83]16.40.780.19
    Ours (image)21.90.870.17
    Ours (image, det.)22.40.870.19
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.637, + 0.179, + 0.907, + 0.207 + ], + "angle": 0, + "content": "Table 4. Quantitative benchmark of albedo estimation on InteriorVerse dataset [91]." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.214, + 0.895, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.397, + 0.908, + 0.424 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of forward rendering. Our method generates high-quality inter-reflections (top) and shadows (bottom), producing more accurate results than the neural baselines." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.426, + 0.891, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.595, + 0.908, + 0.639 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison of inverse rendering. We compare with RGB \\(\\leftrightarrow\\) X [83] on DL3DV10k dataset. Both methods work well on indoor scenes, while our method predicts finer details in thin structures and more accurate metallic and roughness channels (top), likely benefiting from our curated training data. As compared to RGB \\(\\leftrightarrow\\) X, our method generalizes better to outdoor scenes (bottom row)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.648, + 0.486, + 0.74 + ], + "angle": 0, + "content": "Our method consistently outperforms all neural methods on both datasets and performs comparably to classic methods. In real-world editing applications, however, these PBR techniques often face significant limitations due to missing 3D geometry and noisy G-buffers (Fig. 2). Furthermore, SplitSum does not model shadows and inter-reflections." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.75, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Ablation study. We ablate our model design choices in Table 1. While our method generalizes from images to videos, it can treat images as a special case of single-frame videos. To evaluate the benefits introduced by the video model, we compare with an ablated version of our method that performs per-frame inference (Ours, image). The video model consistently improves rendering quality across both datasets. In the ablated variant Ours (w/o env. encoder), we concatenate the VAE encoded environment maps directly to the image channels [30] rather than using a separate environment map" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.648, + 0.909, + 0.74 + ], + "angle": 0, + "content": "encoder. We demonstrate that a dedicated environment map encoder improves performance. For Ours (+ shading cond.), we include split-sum shading buffers as a conditioning input, following [17]. However, we observed no significant improvement with this addition and chose to exclude it from our final method for simplicity." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.743, + 0.803, + 0.76 + ], + "angle": 0, + "content": "5.3. Evaluation of Inverse Rendering" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.763, + 0.909, + 0.869 + ], + "angle": 0, + "content": "We quantitatively compare our method with baseline methods on SyntheticScenes in Table 3 and InteriorVerse [91] benchmark in Table 4. Our methods consistently outperforms baseline methods in both datasets, indicating the effectiveness of our data curation workflow and method designs. We show a qualitative comparison with RGB \\(\\leftrightarrow\\) X [83] on DL3DV10k [47] dataset in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Image vs. video model. Comparing Ours (image) and Ours, the video model consistently enhances the quality of" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26075" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.071, + 0.478, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.218, + 0.483, + 0.245 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison of relighting. Our method produces more accurate specular reflections compared to the baselines." + }, + { + "type": "image_caption", + "bbox": [ + 0.094, + 0.249, + 0.478, + 0.261 + ], + "angle": 0, + "content": "Input Image & Tgt. Light Ours Ours (Synth.) Ours (w/o LoRA)" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.262, + 0.475, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.329, + 0.483, + 0.371 + ], + "angle": 0, + "content": "Figure 7. Qualitative ablation of relighting. Joint training with real-world data and adding LoRA during training significantly improve relighting quality for real-world scenes." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.386, + 0.483, + 0.492 + ], + "angle": 0, + "content": "inverse rendering across all attributes. Notably, for properties associated with specular materials, the video model reduces RMSE by \\(41\\%\\) for metallic (from 0.066 to 0.039) and \\(20\\%\\) for roughness (from 0.098 to 0.078) compared to the image model. This suggests that the model learns to leverage view changes in video data, effectively capturing view-dependent effects to predict specular properties more accurately." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.494, + 0.483, + 0.767 + ], + "angle": 0, + "content": "One-step deterministic fine-tuning. We also ablate the design choice of 1-step deterministic fine-tuning in Table 3 and 4. By default, the inverse renderer performs 20 denoising steps during inference. Building on recent findings in image diffusion models [51], we demonstrate that strongly conditioned video diffusion models can also be fine-tuned as 1-step deterministic models. Despite the significantly reduced computational cost, we observe that 1-step models consistently produce more \"accurate\" predictions and outperform multi-step stochastic models in photometric evaluations such as PSNR scores. However, the 1-step model enforces deterministic output, which can result in blurrier predictions for ambiguous regions with high-frequency details, thus yielding lower perceptual metrics, such as LPIPS. For neural forward rendering and relighting tasks, we use multi-step stochastic models to capture more realistic details, though we note that 1-step models can be a competitive choice for error-sensitive tasks and enhancing runtime efficiency." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.772, + 0.317, + 0.789 + ], + "angle": 0, + "content": "5.4. Evaluation of Relighting" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.793, + 0.483, + 0.882 + ], + "angle": 0, + "content": "In Table 2 and Fig. 6, we compare with recent state-of-the-art relighting methods DiLightNet [82] and Neural Gaffer [30]. Our method outperforms these baselines, particularly in scenes with complex shadows and inter-reflections. Overall, it produces high-quality lighting effects and more accurate color and scale." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.484, + 0.901 + ], + "angle": 0, + "content": "Ablation study. We ablate the design choices of synthetic-" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.071, + 0.903, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.185, + 0.907, + 0.227 + ], + "angle": 0, + "content": "Figure 8. Image editing applications. Top: Realistic material editing, adjusting the sphere's roughness and the horse's metallic. Bottom: Object insertion of a bathtub and table into scene images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.236, + 0.907, + 0.388 + ], + "angle": 0, + "content": "real joint training in Fig. 7. While synthetic data provides accurate supervision signals, it is limited to a specific domain and lacks the diversity and complexity found in real-world data. When training exclusively on synthetic data (Ours Synth.), the model struggles with complex structures, such as trees, which are rarely represented in synthetic datasets. Since the real-world auto-labels are estimated using inverse rendering models and contain imperfections, we find that incorporating a LoRA [27] during training with real data consistently improves visual quality." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.395, + 0.649, + 0.41 + ], + "angle": 0, + "content": "5.5. Applications" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.415, + 0.907, + 0.536 + ], + "angle": 0, + "content": "We show material editing and object insertion applications in Fig. 8. In the top row, we adjust the sphere's roughness from 0.15 to 0.6 and increase the horse's metallic property from 0 to 1, achieving photorealistic material edits. In the bottom row, we insert a bathtub and table in the G-buffer space of the input image, and use our forward renderer to produce the edited result. The inserted objects blend naturally into the scene, generating realistic reflections and shadows." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.544, + 0.628, + 0.558 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.566, + 0.909, + 0.672 + ], + "angle": 0, + "content": "DIFFUSIONRENDERER provides a scalable, data-driven approach to inverse and forward rendering, achieving high-quality G-buffer estimation and photorealistic image generation without relying on explicit path tracing or precise 3D scene representations. Jointly trained on synthetic and auto-labeled real-world data, DIFFUSIONRENDERER consistently outperforms state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Limitations and future work. Our method is based on Stable Video Diffusion, which operates offline and would benefit from distillation techniques to improve inference speed. For editing tasks, the inverse and forward rendering models preserve most of the original content but may introduce slight variations in color or texture. Future work could explore task-specific fine-tuning [37] and develop neural intrinsic features to enhance content consistency and handle more complex visual effects. Additionally, our real-world auto-labeling currently adopts off-the-shelf lighting estimation model [61] which could benefit from better accuracy and robustness. With rapid advancements in video diffusion models [1] toward higher quality and faster inference speeds, we are optimistic that DIFFUSIONRENDERER will inspire future research in high-quality image synthesis and editing." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "26076" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.168 + ], + "angle": 0, + "content": "Acknowledgments. The authors thank Shiqiu Liu, Yichen Sheng, and Michael Kass for their insightful discussions that contributed to this project. We also appreciate the discussions with Xuanchi Ren, Tianchang Shen and Zheng Zeng during the model development process." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.181, + 0.188, + 0.196 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.206, + 0.484, + 0.274 + ], + "angle": 0, + "content": "[1] Niket Agarwal, Arslan Ali, Maciej Bala, Yogesh Balaji, Erik Barker, Tiffany Cai, Prithvijit Chattopadhyay, Yongxin Chen, Yin Cui, Yifan Ding, et al. Cosmos world foundation model platform for physical ai. arXiv preprint arXiv:2501.03575, 2025. 3, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.277, + 0.484, + 0.33 + ], + "angle": 0, + "content": "[2] Jonathan T. Barron and Jitendra Malik. Shape, illumination, and reflectance from shading. 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ACM, 2022. 5, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.093, + 0.487, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "26080" + } + ] +] \ No newline at end of file diff --git a/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/65119a53-c0fc-4b0a-9ea3-a2e6c2c9c1d5_origin.pdf b/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/65119a53-c0fc-4b0a-9ea3-a2e6c2c9c1d5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d79a8870a81539a415e678091873ecf82ddf1856 --- /dev/null +++ b/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/65119a53-c0fc-4b0a-9ea3-a2e6c2c9c1d5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3c0cdcef30cc03e660d0885c14cba52cb594cd6c9fa1515a060d0517f2903626 +size 5268794 diff --git a/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/full.md b/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..51f7b3379340ae887eddccc14dedd4e53398571b --- /dev/null +++ b/2025/Diffusion Renderer_ Neural Inverse and Forward Rendering with Video Diffusion Models/full.md @@ -0,0 +1,377 @@ +# DIFFUSIONRENDERER: Neural Inverse and Forward Rendering with Video Diffusion Models + +Ruofan Liang $^{1,2,3*}$ , Zan Gojcic $^{1}$ , Huan Ling $^{1,2,3}$ , Jacob Munkberg $^{1}$ , Jon Hasselgren $^{1}$ , Chih-Hao Lin $^{1,4}$ , Jun Gao $^{1,2,3}$ , Alexander Keller $^{1}$ , Nandita Vijaykumar $^{2,3}$ , Sanja Fidler $^{1,2,3}$ , Zian Wang $^{1,2,3*}$ $^{1}$ NVIDIA $^{2}$ University of Toronto $^{3}$ Vector Institute $^{4}$ University of Illinois Urbana-Champaign + +![](images/f02ed007288a0fad9b2038c9f4d8e8e6cebd96d2e7ca1852247ccc17f68043c7.jpg) +Figure 1. We present DIFFUSIONRENDERER, a general-purpose method for both neural inverse and forward rendering. From input images or videos, it accurately estimates geometry and material buffers, and generates photorealistic images under specified lighting conditions, offering fundamental tools for image editing applications. + +# Abstract + +Understanding and modeling lighting effects are fundamental tasks in computer vision and graphics. Classic physically-based rendering (PBR) accurately simulates the light transport, but relies on precise scene representations—explicit 3D geometry, high-quality material properties, and lighting conditions—that are often impractical to obtain in real-world scenarios. Therefore, we introduce DIFFUSIONRENDERER, a neural approach that addresses the dual problem of inverse and forward rendering within a holistic framework. Leveraging powerful video diffusion model priors, the inverse rendering model accurately estimates $G$ -filters from real-world videos, providing an interface for image editing tasks, and training data for the rendering model. Conversely, our rendering model generates photorealistic images from $G$ -filters without explicit light transport simulation. Specifically, we first train a video diffusion model for inverse rendering on synthetic data, which generalizes well to real-world videos and allows us to auto-label diverse real-world videos. We + +then co-train our rendering model using both synthetic and auto-labeled real-world data. Experiments demonstrate that DIFFUSIONRENDERER effectively approximates inverse and forwards rendering, consistently outperforming the state-of-the-art. Our model enables practical applications from a single video input—including relighting, material editing, and realistic object insertion. + +# 1. Introduction + +Understanding and modeling light transport forms the basis of Physically Based Rendering (PBR) [59]. Modern path tracing algorithms, as regularly used in the gaming and movie industries, simulate light transport to render images that cannot be distinguished from photographs. The quality of such PBR-rendered images heavily depends on the accuracy and realism of the scene's surface geometry, material properties, and lighting representations. Such a scene description is either designed by artists (synthetic scenes) or reconstructed from data—also known as the inverse rendering problem [2, 3]. Inverse rendering has been extensively stud + +ied, particularly for applications like relighting and object insertion into real-world scenes [20, 41, 75, 88]. However, acquiring high quality surface and material representations is challenging in real-world scenarios, limiting the practicality of PBR methods (Fig. 2). + +While physically-based rendering and inverse rendering are usually considered separately, we propose to consider them jointly. Our approach draws inspiration from the success of large-scale generative models [8, 65], which "render" photorealistic images from simple text prompts without any explicit understanding of PBR. These models learn the underlying distribution of real-world images from a vast amounts of data, implicitly capturing the complex lighting effects. + +Specifically, we propose DIFFUSIONRENDERER, a general-purpose neural rendering engine that can synthesize light transport simulation—such as shadows and reflections—by leveraging the powerful priors of video diffusion models. Conditioned on input geometry, material buffers, and environment map light source, DIFFUSIONRENDERER acts as a neural approximation of path-traced shading. DIFFUSIONRENDERER is designed to remain faithful to the conditioning signals, while adhering to the distribution of real-world images. As a result, we bypass the need for precise scene representations and description, as our model learns to handle imperfections in the input data. + +Training such a model requires some amount of high quality and diverse data, including data with noisy conditions to ensure robustness. Therefore, we first train an inverse renderer, a video diffusion model to map input RGB videos to intrinsic properties. Although trained solely on synthetic data, the inverse rendering model generalizes robustly to real-world scenarios. We then use it to generate "pseudo-labels" for diverse real-world videos. Combining both real-world auto-labeled data and synthetic data, we train our forward renderer video diffusion model. + +DIFFUSIONRENDERER outperforms state-of-the-art methods and effectively approximates the complex functionalities of inverse and forward rendering, allowing us to relight images and videos across diverse scenes and to synthesize consistent shadows and reflections without explicit path tracing and 3D scene representation. Our model can relight any scene from only a single video input, and provides fundamental tools for editing tasks such as material editing and realistic object insertion. To summarize: + +- We develop a state-of-the-art inverse rendering method for videos of synthetic and real-world scenes. +- We repurpose a video diffusion model as a neural rendering engine that can synthesize photorealistic images and videos conditioned on noisy G-buffers. +- From a single video input, DIFFUSIONRENDERER enables relighting, material editing, and virtual object insertion in a unified framework, expanding the possibilities for real-world neural rendering applications. + +![](images/5d0cfc677626576635c6ab1bf27d25e8761528674cb87fc407cfa33ad0089ece.jpg) +Reference + +![](images/6c394bd814112e04d6fd7257038ff820df912bfdbb46a095b7a099ab250a74c7.jpg) +SSRT + +![](images/25d3d0afe4bfcce680a303b953df84fa47f16478febdb5bacb51bf84c13676ed.jpg) +SSRT side view + +![](images/552653e7f881c57fc6585235e1f2a3c402fdc04d613b8e3be3bf2ba83fabda36.jpg) +Ours + +![](images/b5986799a749f7fedcca1d6d2c80c56af1ea4b706bb0b96fc28a42c4c8a78bd5.jpg) +Input + +![](images/e5738f5ac4f8ec5c17c711cdcad0a2fc9688ea27aae6c7d84e0fb29b6d3614fb.jpg) +Estimated G-buffer + +![](images/c7be291c11567a082c6b59da92a14159fbb5ecdc8d282f65f23d206a64b18243.jpg) +SSRT relit + +![](images/9845dc399d41bb69f2f826e856c6bca3256858beeea7bfee5b20ea3bb8f320d2.jpg) +Ours relit +Figure 2. Classic PBR relies on explicit 3D geometry, e.g., meshes. When it is not available, screen space ray tracing (SSRT) struggles to accurately represent shadows and reflections (top). PBR is also sensitive to errors in G-buffers – SSRT with estimated G-buffers from inverse rendering models often fails to deliver quality results (bottom). DIFFUSIONRENDERER bypasses these issues, producing photorealistic results without 3D geometry or perfect G-buffers. + +# 2. Related Work + +Neural rendering refers to methods that replace or extend traditional rendering pipelines by neural networks. For example, Deep Shading [56] replaces traditional deferred shading [15] by a CNN to render images with ambient occlusion, global illumination, and depth-of-field from G-buffers. More recently, RGB $\leftrightarrow$ X [83] trains image diffusion models to both estimate a G-buffer from an image and to render an image from a G-buffer. We extend this approach to video diffusion models and provide a novel approach for neural relighting that does not require an irradiance estimate. Other approaches fit rendered data using neural models or introduce neural components into an existing renderer with focus on approximating light transport [28, 31] or radiance caching [25, 53]. A plethora of works on neural and inverse rendering involve volumetric 3D scene representations in the form of NeRF [52] or 3D Gaussian Splats [35]. We refer to [70] for an overview. While providing photo-real view interpolation, these approaches typically bake radiance, and have limited editing capabilities. In contrast, we explicitly target an intermediate scene representation in the form of traditional, easy-to-edit, G-buffers with separate lighting. + +Inverse rendering is a fundamental task first formalized in the 1970s [4], aiming to estimate intrinsic scene properties, like geometry, materials, and lighting from input images. Early methods designed hand-crafted priors within an optimization framework [2, 4, 11, 23, 39, 89], typically focusing on low-order effects. These methods lead to errors when the hand-crafted priors do not match reality. Recently, supervised and self-supervised learning has been extensively studied [5, 6, 9, 38, 40-42, 67, 73, 74, 76, 80]. The resulting algorithms are often data-hungry and specific to a certain task or domain. Acquiring sufficient and diverse training data poses a challenge. Recent advances in large image generative models provide new deep learning tools for inverse + +rendering [19, 36, 44, 61, 83] resulting in much higher reconstruction quality. Still, the quality is not enough to power physically based rendering pipelines. + +Relighting focuses on modifying the lighting conditions of a scene given captured images or videos. Recent methods reconstruct 3D scene representations from multi-view images, performing explicit inverse rendering to recover material properties and enable relighting [10, 13, 24, 29, 43, 45, 54, 66, 68, 75, 78, 84, 85, 87]. These methods often optimize for each scene individually, and their quality may be affected by practical issues such as single-illumination capture, large scene scale, and dynamic content. Learning-based methods that train across multiple scenes have explored latent feature learning [7, 48, 90] and often incorporate neural rendering modules that utilize PBR buffers as inductive priors [22, 37, 57, 60, 79]. To improve relighting quality, recent approaches [30, 37, 62, 82] leverage diffusion models. With very few multi-illumination datasets [55], existing methods often are specialized to a domain, such as portraits, objects, and outdoor scenes, and remain data-hungry. + +# 3. Preliminaries + +Physically-based rendering (PBR) is concerned with the simulation of how the incoming radiance contributes to the outgoing radiance + +$$ +L _ {o} (\mathbf {p}, \boldsymbol {\omega} _ {o}) = \int_ {\Omega} f _ {r} (\mathbf {p}, \boldsymbol {\omega} _ {o}, \boldsymbol {\omega} _ {i}) L _ {i} (\mathbf {p}, \boldsymbol {\omega} _ {i}) | \mathbf {n} \cdot \boldsymbol {\omega} _ {i} | d \boldsymbol {\omega} _ {i}, \tag {1} +$$ + +at a surface point $\mathbf{p}$ in direction $\omega_{o}$ . The integral over the hemisphere $\Omega$ considers the BRDF $f_{r}(\mathbf{p},\omega_{o},\omega_{i})$ , incoming radiance $L_{i}(\mathbf{p},\omega_{i})$ , and a cosine factor $|\mathbf{n}\cdot \boldsymbol{\omega}_i|$ for the angle between the normal $\mathbf{n}$ and incoming light. It is evaluated by Monte Carlo methods [59, 71], with meticulously designed BRDF models [12, 14, 72] that approximate real surfaces. + +Video diffusion models (VDMs). A diffusion model learns to approximate a data distribution $p_{\mathrm{data}}(\mathbf{I})$ via iterative denoising [18, 26, 69]. Most VDMs operate in a compressed, lower-dimensional latent space [1, 8]. Given an RGB video $\mathbf{I} \in \mathbb{R}^{F \times H \times W \times 3}$ , consisting of $F$ frames at resolution $H \times W$ , a pre-trained VAE encoder $\mathcal{E}$ first encodes the video into a latent representation $\mathbf{z} = \mathcal{E}(\mathbf{I}) \in \mathbb{R}^{F' \times h \times w \times C}$ . The final video $\hat{\mathbf{I}}$ is then reconstructed by decoding $\mathbf{z}$ with a pre-trained VAE decoder $\mathcal{D}$ . Both training and inference stages of the VDM are conducted in this latent space. In this work, we build on Stable Video Diffusion [8], which compresses the video only along the spatial dimensions: $F' = F$ , $C = 4$ , $h = \frac{H}{8}$ , and $w = \frac{W}{8}$ . + +To train the VDM, noisy versions $\mathbf{z}_{\tau} = \alpha_{\tau}\mathbf{z}_0 + \sigma_{\tau}\epsilon$ are constructed by adding a Gaussian noise $\epsilon$ with the noise schedule provided by $\alpha_{\tau}$ and $\sigma_{\tau}$ following EDM [33]. The diffusion model parameters $\theta$ of the denoising function $\mathbf{f}_{\theta}$ are optimized using the denoising score matching objective [33]. + +Once trained, iteratively applying $\mathbf{f}_{\theta}$ to a sample of Gaussian noise will produce a sample of $p_{\mathrm{data}}(\mathbf{I})$ + +Conditioning in VDMs. Two common approaches to inject conditions into VDMs are: (i) concatenating condition channels with image latents $\mathbf{z}_{\tau}$ , which is often used for pixelwise conditions [8, 34, 36, 83], and (ii) injecting conditions through cross-attention layers [8, 65], which is often used for semantic features such as the CLIP embedding [63]. Note that our method is compatible with any standard VDMs and does not depend on specific architectural details. + +# 4. Method + +DIFFUSIONRENDERER is a unified framework comprising two video diffusion models designed for the dual tasks of neural forward and inverse rendering. As illustrated in Fig. 3, the neural forward renderer (Sec. 4.1) approximates physically based light transport (Eq. 1), transforming G-buffers [56] and lighting into a photorealistic video. The neural inverse renderer (Sec. 4.2) reconstructs geometry and material buffers from input video. The neural forward and inverse renderers are based on pre-trained video diffusion models and fine-tuned for conditional generation [34, 36, 83]. + +Data is a critical aspect of learning-based methods. We describe our data curation workflow and synthetic-real joint training strategies in Sec. 4.3 and Sec. 4.4. Finally, we discuss image editing applications in Sec. 4.5. + +# 4.1. Neural Forward Rendering + +We formulate neural forward rendering as a conditional generation task, producing photorealistic images given geometry, materials, and lighting as conditions. By approximating light transport simulation in a data-driven manner, the model requires neither classic 3D geometry nor explicit path tracing, thus reducing the constraints in real-world applications. + +Geometry and material conditions. Similar to the G-buffers in rendering system based on deferred shading [15], we use per-pixel scene attribute maps to represent scene geometry and materials. Specifically, we use surface normals $\mathbf{n} \in \mathbb{R}^{F \times H \times W \times 3}$ in camera space and relative depth $\mathbf{d} \in \mathbb{R}^{F \times H \times W \times 1}$ normalized to $[-1,1]$ to represent scene geometry. For materials, we use base color $\mathbf{a} \in \mathbb{R}^{F \times H \times W \times 3}$ , roughness $\mathbf{r} \in \mathbb{R}^{F \times H \times W \times 1}$ , and metallic $\mathbf{m} \in \mathbb{R}^{F \times H \times W \times 1}$ following the Disney BRDF [12]. + +Lighting conditions. Lighting is represented by environment maps $\mathbf{E} \in \mathbb{R}^{F \times H_{\mathrm{env}} \times W_{\mathrm{env}} \times 3}$ , which are panoramic images that capture the lighting intensity from all directions over the sphere. These environment maps are encoded in high dynamic range (HDR), while the VAEs used in typical latent diffusion models are designed for pixel values between -1 and 1. To address this discrepancy, similar to the light representation in Neural Gaffer [30], we first apply Reinhard tonemapping to convert HDR environment map into an LDR image $\mathbf{E}_{\mathrm{ldr}}$ . To more effectively represent HDR values, + +![](images/51284f8fd23fe3ba4f2e7b768272ea460fd9ed1f628578a3ee166ecf80d6bc7a.jpg) +Figure 3. Method overview. Given an input video, the neural inverse renderer estimates geometry and material properties per pixel. It generates one scene attribute at a time, with the domain embedding indicating the target attributes to generate (Sec. 4.2). Conversely, the neural forward renderer produces photorealistic images given lighting information, geometry, and material buffers. The lighting condition is injected into the base video diffusion model through cross-attention layers (Sec. 4.1). During joint training with both synthetic and real data, we use an estimizable LoRA for real data sources (Sec. 4.4). + +particularly for light sources with high-intensity peaks, we compute $\mathbf{E}_{\mathrm{log}} = \log (\mathbf{E} + 1) / E_{\mathrm{max}}$ where the light intensity values are mapped to logarithm space that is closer to human perception and normalized by max log intensity $E_{\mathrm{max}}$ . Additionally, we also compute a directional encoding image, $\mathbf{E}_{\mathrm{dir}} \in \mathbb{R}^{F \times H_{\mathrm{env}} \times W_{\mathrm{env}} \times 3}$ , where each pixel is represented by a unit vector indicating its direction in the camera coordinate system. The resulting lighting encodings used by the model consist of three panoramic images: $\{\mathbf{E}_{\mathrm{ldr}}, \mathbf{E}_{\mathrm{log}}, \mathbf{E}_{\mathrm{dir}}\}$ . + +Model architecture. Our models are based on Stable Video Diffusion [8], an image-to-video diffusion model with its core architecture including a VAE encoder-decoder pair $\{\mathcal{E},\mathcal{D}\}$ , and a UNet-based denoising function $\mathbf{f}_{\theta}$ . + +We use the VAE encoder $\mathcal{E}$ to separately encode each G-buffer from $\{\mathbf{n},\mathbf{d},\mathbf{a},\mathbf{r},\mathbf{m}\}$ into the latent space and concatenate them to produce the pixel-aligned scene attribute latent map $\mathbf{g} = \{\mathcal{E}(\mathbf{n}),\mathcal{E}(\mathbf{d}),\mathcal{E}(\mathbf{a}),\mathcal{E}(\mathbf{r}),\mathcal{E}(\mathbf{m})\} \in \mathbb{R}^{F\times h\times w\times 20}$ . + +Environment maps are usually in equi-rectangular projection and are not pixel-aligned with the generated images, thus requiring extra consideration. Prior works explored directly concatenating environment maps to the image latents [30] or concatenate split-sum shading buffers [17], which we also experimented with, but found suboptimal (Table 1). Instead, we take the cross-attention layers which originally operate on the text/image CLIP features, and re-purpose them for lighting conditions. To preserve spatial details of the environment maps, we generalize the conditional signals to a list of multi-resolution feature maps. + +Specifically, we first pass the environment map information through VAE encoder $\mathcal{E}$ to obtain $\mathbf{h}_{\mathbf{E}} = \{\mathcal{E}(\mathbf{E}_{\mathrm{ldr}}),\mathcal{E}(\mathbf{E}_{\mathrm{log}}),\mathcal{E}(\mathbf{E}_{\mathrm{dir}})\} \in \mathbb{R}^{F\times h_{\mathrm{env}}\times w_{\mathrm{env}}\times 12}$ . We additionally use an environment map encoder $\mathcal{E}_{\mathrm{env}}$ to further operate on $\mathbf{h}_{\mathbf{E}}$ . $\mathcal{E}_{\mathrm{env}}$ is the simplified encoder part of diffusion UNet with attention and temporal layers removed. It contains several convolutional layers to downsample and extract + +$K$ levels of multi-resolution features as lighting conditions: + +$$ +\mathbf {c} _ {\text {e n v}} := \left\{\mathbf {h} _ {\text {e n v}} ^ {i} \right\} _ {i = 1} ^ {K} = \mathcal {E} _ {\text {e n v}} \left(\mathbf {h} _ {\mathbf {E}}\right) \tag {2} +$$ + +As a result, the diffusion UNet $\mathbf{f}_{\theta}$ takes the noisy latent $\mathbf{z}_{\tau}$ and G-buffer latent $\mathbf{g}$ as pixel-wise input. At each UNet level $k$ , the diffusion UNet queries the latent environment map features at the corresponding level $\mathbf{h}_{\mathrm{env}}^k$ , and aggregates based on its keys and values. Through the multi-level self-attention and cross-attention layers, the diffusion model is given the capacity to learn to shade G-buffers with lighting. During inference, the diffusion target can be computed as $\mathbf{f}_{\theta}(\mathbf{z}_{\tau}; \mathbf{g}, \mathbf{c}_{\mathrm{env}}, \tau)$ to produce photorealistic images with iterative denoising. + +# 4.2. Neural Inverse Rendering + +We similarly formulate inverse rendering as a conditional generation task. Given an input video $\mathbf{I}$ as a condition, the inverse renderer estimates scene attribute maps $\{\mathbf{n},\mathbf{d},\mathbf{a},\mathbf{r},\mathbf{m}\}$ which are the G-buffers used by the forward renderer. + +Model architecture. The input video $\mathbf{I}$ is encoded into latent space $\mathbf{z} = \mathcal{E}(\mathbf{I})$ , and concatenated with the noisy G-buffer latent, which we denote as $\mathbf{g}_{\tau} = \alpha_{\tau}\mathbf{g}_0 + \sigma_{\tau}\epsilon$ . + +Given an input video, the inverse renderer generates all five attributes $\{\mathbf{n},\mathbf{d},\mathbf{a},\mathbf{r},\mathbf{m}\}$ using the same model. To preserve the high-quality generation and maximally leverage the diffusion model pre-trained knowledge, each attribute is generated in a dedicated pass, instead of generating all at once. We follow prior works [21, 49, 83] and use a domain embedding to indicate to the model which attribute should be generated. Specifically, we introduce an estimizable domain embedding $\mathbf{c}_{\mathrm{emb}}\in \mathbb{R}^{K_{\mathrm{emb}}\times C_{\mathrm{emb}}}$ , where $K_{\mathrm{emb}} = 5$ is the number of buffers and $C_\mathrm{emb}$ is the dimension of the embedding vector. We re-purpose the cross-attention layers with image CLIP features to take domain embeddings. When estimating an attribute indexed by $P$ , we feed its embedding $\mathbf{c}_{\mathrm{emb}}^P$ as a condition and predict the diffusion target with $\mathbf{f}_{\theta}(\mathbf{g}_{\tau}^{P};\mathbf{z},\mathbf{c}_{\mathrm{emb}}^{P},\tau)$ . + +# 4.3. Data Strategy + +Synthetic data curation. To train our models, we require high-quality video data with paired ground-truth for material, geometry, and lighting information. Specifically, each video data sample should include paired frames of RGB, base color, roughness, metallic, normals, depth, and environment map: $\{\mathbf{I},\mathbf{a},\mathbf{r},\mathbf{m},\mathbf{n},\mathbf{d},\mathbf{E}\}$ . These buffers are typically only available in synthetic data, and most existing public datasets contain only a subset of them. + +To address the data scarcity, we designed a synthetic data generation workflow to produce a large amount of high-quality data covering diverse and complex lighting effects. We start by curating a collection of 3D assets, PBR materials, and HDR environment maps. We use 36,500 3D assets from Objaverse LVIS split. For materials and lighting, we collected 4,260 high-quality PBR material maps, and 766 HDR environment maps from publicly available resources. + +In each scene, we place a plane with a randomly selected PBR material, and sample up to three 3D objects, and place them on the plane. We perform collision detection to avoid intersecting objects. We also place up to three primitives (cube, sphere, and cylinder) with randomized shape and materials to cover complex lighting effects such as inter-reflections. A randomly selected HDR environment map illuminates the scene. We generate motions including camera orbits, camera oscillation, lighting rotation, object rotation and translation. + +We use a custom path tracer based on OptiX [58] to render the videos. In total, we generate 150,000 videos with paired ground-truth G-buffers and environment maps, at 24 frames per video in $512 \times 512$ resolution. This dataset can be used to train both rendering and inverse rendering models. + +Real world auto-labeling. Synthetic data provides accurate supervision signals, and when combined with powerful image diffusion models, it demonstrates impressive generalization to unseen domains for inverse rendering tasks [21, 34]. However, when it comes to training the forward rendering model, synthetic data alone is insufficient. Since the output of the forward renderer is an RGB video, training only on synthetic renderings biases the model toward synthetic visual styles. Compared to inverse rendering, we observe a much more significant domain gap in complex real-world scenes for forward rendering tasks (Fig. 7). + +Acquiring real-world data with paired geometry, material, and lighting ground truth requires complex and impractical capturing setups. Based on the observation that our inverse rendering model generalizes to real-world videos, we apply it to automatically label real-world videos. Specifically, we use the DL3DV10k [47] dataset, which is a large-scale dataset consisting of 10,510 videos featuring diverse real-world environments. We use our inverse rendering model (Sec. 4.2) to generate G-buffer labels and use an off-the-shelf method DiffusionLight [61] to estimate environment + +maps. Each video is divided into 15 segments, resulting in around 150,000 real-world video samples with auto-labeled geometry, material, and lighting attributes. + +# 4.4. Training pipeline + +Neural inverse renderer. We first co-train the inverse rendering model on the combination of the curated synthetic video dataset and public image intrinsic datasets Interior-Verse [91] and HyperSim [64]. For image datasets, we treat images as single-frame videos. Each data sample consists of a video $\mathbf{I}$ , an attribute index $P$ , and the scene attribute map $\mathbf{s}^P$ . The target latent variable is the latents of the scene attribute $\mathbf{g}_0^P \coloneqq \mathcal{E}(\mathbf{s}^P)$ , and noise is added to $\mathbf{g}_0^P$ to produce $\mathbf{g}_{\tau}^P$ . The model is trained using the objective function [33]: + +$$ +\mathcal {L} (\theta , \mathbf {c} _ {\mathrm {e m b}}) = \| \mathbf {f} _ {\theta} \left(\mathbf {g} _ {\tau} ^ {P}; \mathbf {z}, \mathbf {c} _ {\mathrm {e m b}} ^ {P}, \tau\right) - \mathbf {g} _ {0} ^ {P} \| _ {2} ^ {2}. \tag {3} +$$ + +We fine-tune the diffusion model parameters $\theta$ and domain embeddings $\mathbf{c}_{\mathrm{emb}}$ , while keeping the latent encoder $\mathcal{E}$ and decoder $\mathcal{D}$ frozen. Once trained, the inverse renderer is used to auto-label real-world videos, generating training data for the forward renderer. + +Environment map encoder pre-training. Following the approach of latent diffusion models [65], we pre-train the environment map encoder $\mathcal{E}_{\mathrm{env}}$ along with a decoder $\mathcal{D}_{\mathrm{env}}$ using an L2 image reconstruction objective on environment maps, similar to an auto-encoder. The decoder architecture is based on the UNet decoder, containing a set of upsampling layers. After training, we discard the decoder $\mathcal{D}_{\mathrm{env}}$ and freeze the environment map encoder $\mathcal{E}_{\mathrm{env}}$ while training the neural forward rendering model. + +Neural forward renderer. We train our rendering model on a combination of a synthetic video dataset and real-world auto-labeled data, using paired G-buffer, lighting, and RGB videos. Although the auto-labeled real-world data is of sufficient quality, it may still contain inaccuracies. To address discrepancies between the synthetic and real-world data sources, we introduce an additional LoRA [27] with a small set of estimizable parameters $\Delta \theta$ during training on real data. We empirically find it improves the rendering quality (Fig. 7). + +During training, for an RGB video $\mathbf{I}$ , the target latent variable is defined as $\mathbf{z}_0 \coloneqq \mathcal{E}(\mathbf{I})$ . Noise is added to $\mathbf{z}_0$ to produce noisy image latent $\mathbf{z}_{\tau}$ . The training objective is: + +$$ +\begin{array}{l} \mathcal {L} (\boldsymbol {\theta}, \Delta \boldsymbol {\theta}) = \| \mathbf {f} _ {\boldsymbol {\theta}} \left(\mathbf {z} _ {\tau} ^ {\mathrm {s y n t h}}; \mathbf {g} ^ {\mathrm {s y n t h}}, \mathbf {c} _ {\mathrm {e n v}} ^ {\mathrm {s y n t h}}, \boldsymbol {\tau}\right) - \mathbf {z} _ {0} ^ {\mathrm {s y n t h}} \| _ {2} ^ {2} + \\ \left\| \mathbf {f} _ {\theta + \Delta \theta} \left(\mathbf {z} _ {\tau} ^ {\text {r e a l}}; \mathbf {g} ^ {\text {r e a l}}, \mathbf {c} _ {\text {e n v}} ^ {\text {r e a l}}, \tau\right) - \mathbf {z} _ {0} ^ {\text {r e a l}} \right\| _ {2} ^ {2} \tag {4} \\ \end{array} +$$ + +# 4.5. Editing Applications + +Our proposed framework provides fundamental solutions for inverse and forward rendering, enabling photorealistic image editing applications through a three-step process: neural inverse rendering, G-buffer and lighting editing, and neural + +
    SyntheticObjectsSyntheticScenes
    PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
    SSRT29.40.9510.03724.80.8990.113
    SplitSum [32]28.70.9510.03823.10.8830.116
    RGB↔X [83]25.20.8960.07718.50.6450.302
    DiLightNet [82]26.60.9140.06720.70.6300.300
    Ours28.30.9350.04826.00.7800.201
    Ours (image)27.40.9160.06225.40.7600.215
    Ours (w/o env. encoder)27.80.9270.05725.30.7560.237
    Ours (+ shading cond.)28.70.9300.05625.60.7610.245
    + +Table 1. Quantitative evaluation of neural rendering. + +
    SyntheticObjectsSyntheticScenes
    PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
    DiLightNet [82]23.790.8720.08718.880.5760.344
    Neural Gaffer [30]26.390.9030.08620.750.6330.343
    Ours27.500.9180.06724.630.7560.257
    + +Table 2. Quantitative evaluation of relighting. + +rendering. For the example of relighting, given a video I as input, the inverse rendering model estimates the G-buffers + +$$ +\{\hat {\mathbf {n}}, \hat {\mathbf {d}}, \hat {\mathbf {a}}, \hat {\mathbf {r}}, \hat {\mathbf {m}} \} = \operatorname {I n v e r s e R e n d e r e r} (\mathbf {I}). \tag {5} +$$ + +With a user-specified target environment map $\mathbf{E}_{\mathrm{tgt}}$ , the rendering model produces relit videos + +$$ +\hat {\mathbf {I}} _ {\mathrm {t g t}} = \text {F o r w a r d R e n d e r e r} \left(\left\{\hat {\mathbf {n}}, \hat {\mathbf {d}}, \hat {\mathbf {a}}, \hat {\mathbf {r}}, \hat {\mathbf {m}}, \mathbf {E} _ {\mathrm {t g t}} \right\}\right). \tag {6} +$$ + +Similarly, editing the G-buffers and rendering the videos can enable material editing and virtual object insertion. + +# 5. Experiments + +We extensively evaluate DIFFUSIONRENDERER on a diverse range of synthetic and real-world datasets. Sec. 5.1 details our experimental settings. We compare and ablate across three main tasks: image generation from G-buffers (Sec. 5.2), inverse rendering (Sec. 5.3), and relighting (Sec. 5.4). Finally, we show applications of our method in Sec. 5.5. + +# 5.1. Experiment Settings + +We refer to model implementation details in the Supplement. + +Task definitions. We evaluate our method on three fundamental tasks: forward rendering, inverse rendering, and relighting. For forward rendering, the methods take the G-buffers and lighting information $\{\mathbf{n},\mathbf{d},\mathbf{a},\mathbf{r},\mathbf{m},\mathbf{E}\}$ as input, and output rendered images $\hat{\mathbf{l}}$ . We evaluate the consistency between the rendered outputs and the ground-truth images $\mathbf{l}$ . + +For inverse rendering, each method uses RGB images $\mathbf{I}$ as input to estimate scene attributes $\{\hat{\mathbf{a}},\hat{\mathbf{r}},\hat{\mathbf{m}},\hat{\mathbf{n}}\}$ , and compare against ground truth values. Our focus is primarily on the attributes related to PBR - specifically, base color, roughness, and metallic properties. We recognize dedicated works on normal and depth estimation [21, 34] and do not aim to provide an exhaustive evaluation. For relighting, each method takes RGB images and target lighting conditions $\{\mathbf{I}^{\mathrm{src}},\mathbf{E}^{\mathrm{tgt}}\}$ + +as input, output re-lit image sequence $\hat{\mathbf{I}}^{\mathrm{gt}}$ under the target lighting conditions, and compare with ground truth $\mathbf{I}^{\mathrm{gt}}$ . + +Baselines. For forward rendering, we compare with Split Sum [32] and Screen Space Ray Tracing (SSRT). For SSRT, we extract a mesh from the depth buffer and render the mesh with material parameters from the G-buffers and a provided HDR probe in a path tracer. We additionally compare against the neural rendering components of recent state-of-the-art methods RGB $\leftrightarrow$ X [83] and DiLightNet [82]. For inverse rendering, we compare with recent diffusion-based methods Kocsis et al. [36], RGB $\leftrightarrow$ X [83] and earlier methods [5, 41, 91]. For relighting, we compare with 2D methods DiLightNet [82], Neural Gaffer [30]. We also compare with 3D reconstruction-based methods [46, 75] in supplement. + +Metrics. We use PSNR, SSIM, and LPIPS [86] for forward rendering and relighting. For inverse rendering, we evaluate albedo with PSNR and LPIPS following [36, 83]. Since albedo estimation involves scale ambiguity [23], we additionally solve and apply a three-channel scaling factor using least-squares error minimization before computing metrics, referred to as si-PSNR and si-LPIPS. We use root mean square error (RMSE) for metallic and roughness evaluation, and mean angular error for normals. + +Datasets. We curate two high-quality synthetic datasets for quantitative evaluation, named SyntheticScenes and SyntheticObjects. The datasets consist of 3D assets from PolyHaven [81] and Objaverse [16] that are not included in the training data of our method or the baseline methods. SyntheticScenes contains 40 scenes, each featuring multiple objects arranged on a plane textured with high-quality PBR materials. Each scene is rendered into 24-frame videos under four lighting conditions, with motions such as camera orbiting and oscillation. As some baseline methods perform best with object-centric setups, we also create SyntheticObjects, a dataset of 30 individual objects. For each object, we render 24-frame videos under four different lighting conditions, with lighting rotated across frames. + +For inverse rendering, we also evaluate on the indoor scene benchmark InteriorVerse [91]. We include qualitative comparisons on the DL3DV10k [47] dataset. + +# 5.2. Evaluation of Forward Rendering + +We compare our method with baseline methods in Table 1 and Fig. 4. For the neural methods RGB $\leftrightarrow$ X [83] and DiLightNet [82], we use their rendering models with ground-truth G-buffers to generate the images. + +Both classic PBR and neural methods perform well on the SyntheticObjects dataset in single-object settings but show significant quality drops on the SyntheticScenes dataset due to complex inter-reflections and occlusions. For example, our method exhibits a minor PSNR decrease of 2.3 dB from SyntheticObjects to SyntheticScenes, while other baselines show more substantial drops. + +
    AlbedoMetallic RMSE↓Roughness RMSE↓Normals Angular Error↓
    PSNR ↑LPIPS ↓si-PSNR ↑si-LPIPS ↓
    RGB↔X [83]14.30.32319.60.2860.4410.32123.80°
    Ours25.00.20526.70.2040.0390.0785.97°
    Ours (det.)26.00.21927.70.2170.0280.0605.85°
    Ours (image)23.40.21326.00.2090.0660.0986.67°
    Ours (image, det.)24.80.23127.20.2280.0430.0696.17°
    + +Table 3. Quantitative evaluation of inverse rendering on SyntheticScenes video dataset. image: per-frame inference as image model. det.: 1-step deterministic inference. + +
    PSNR ↑SSIM ↑LPIPS ↓
    IIW [5]9.70.620.47
    Li et al. [41]12.30.680.52
    Zhu et al. [91]15.90.780.34
    Kocsis et al. [36]17.40.800.22
    RGB↔X [83]16.40.780.19
    Ours (image)21.90.870.17
    Ours (image, det.)22.40.870.19
    + +Table 4. Quantitative benchmark of albedo estimation on InteriorVerse dataset [91]. + +![](images/f714e5c96958dca31ce42806fef31763c606255598a754ebef022cc7cc1b1b2c.jpg) +Figure 4. Qualitative comparison of forward rendering. Our method generates high-quality inter-reflections (top) and shadows (bottom), producing more accurate results than the neural baselines. + +![](images/b14b7179cca42db2aef87be3f0e99cb8b8ab22cb5448ed147d8516e39e30cade.jpg) +Figure 5. Qualitative comparison of inverse rendering. We compare with RGB $\leftrightarrow$ X [83] on DL3DV10k dataset. Both methods work well on indoor scenes, while our method predicts finer details in thin structures and more accurate metallic and roughness channels (top), likely benefiting from our curated training data. As compared to RGB $\leftrightarrow$ X, our method generalizes better to outdoor scenes (bottom row). + +Our method consistently outperforms all neural methods on both datasets and performs comparably to classic methods. In real-world editing applications, however, these PBR techniques often face significant limitations due to missing 3D geometry and noisy G-buffers (Fig. 2). Furthermore, SplitSum does not model shadows and inter-reflections. + +Ablation study. We ablate our model design choices in Table 1. While our method generalizes from images to videos, it can treat images as a special case of single-frame videos. To evaluate the benefits introduced by the video model, we compare with an ablated version of our method that performs per-frame inference (Ours, image). The video model consistently improves rendering quality across both datasets. In the ablated variant Ours (w/o env. encoder), we concatenate the VAE encoded environment maps directly to the image channels [30] rather than using a separate environment map + +encoder. We demonstrate that a dedicated environment map encoder improves performance. For Ours (+ shading cond.), we include split-sum shading buffers as a conditioning input, following [17]. However, we observed no significant improvement with this addition and chose to exclude it from our final method for simplicity. + +# 5.3. Evaluation of Inverse Rendering + +We quantitatively compare our method with baseline methods on SyntheticScenes in Table 3 and InteriorVerse [91] benchmark in Table 4. Our methods consistently outperforms baseline methods in both datasets, indicating the effectiveness of our data curation workflow and method designs. We show a qualitative comparison with RGB $\leftrightarrow$ X [83] on DL3DV10k [47] dataset in Fig. 5. + +Image vs. video model. Comparing Ours (image) and Ours, the video model consistently enhances the quality of + +![](images/67baf571f70d4722d12966a2e377b1b8a32707f395a7b0067a0ceec66ee609c6.jpg) +Figure 6. Qualitative comparison of relighting. Our method produces more accurate specular reflections compared to the baselines. + +![](images/7893d232d0e018fb50523c0347a7da5957fa6de6bf90c204c13c6440f2d4e06e.jpg) +Input Image & Tgt. Light Ours Ours (Synth.) Ours (w/o LoRA) +Figure 7. Qualitative ablation of relighting. Joint training with real-world data and adding LoRA during training significantly improve relighting quality for real-world scenes. + +inverse rendering across all attributes. Notably, for properties associated with specular materials, the video model reduces RMSE by $41\%$ for metallic (from 0.066 to 0.039) and $20\%$ for roughness (from 0.098 to 0.078) compared to the image model. This suggests that the model learns to leverage view changes in video data, effectively capturing view-dependent effects to predict specular properties more accurately. + +One-step deterministic fine-tuning. We also ablate the design choice of 1-step deterministic fine-tuning in Table 3 and 4. By default, the inverse renderer performs 20 denoising steps during inference. Building on recent findings in image diffusion models [51], we demonstrate that strongly conditioned video diffusion models can also be fine-tuned as 1-step deterministic models. Despite the significantly reduced computational cost, we observe that 1-step models consistently produce more "accurate" predictions and outperform multi-step stochastic models in photometric evaluations such as PSNR scores. However, the 1-step model enforces deterministic output, which can result in blurrier predictions for ambiguous regions with high-frequency details, thus yielding lower perceptual metrics, such as LPIPS. For neural forward rendering and relighting tasks, we use multi-step stochastic models to capture more realistic details, though we note that 1-step models can be a competitive choice for error-sensitive tasks and enhancing runtime efficiency. + +# 5.4. Evaluation of Relighting + +In Table 2 and Fig. 6, we compare with recent state-of-the-art relighting methods DiLightNet [82] and Neural Gaffer [30]. Our method outperforms these baselines, particularly in scenes with complex shadows and inter-reflections. Overall, it produces high-quality lighting effects and more accurate color and scale. + +Ablation study. We ablate the design choices of synthetic- + +![](images/9aad6c557ab31133cfe695913fe5de772221640af3e1db222e44cc677cdbe4df.jpg) +Figure 8. Image editing applications. Top: Realistic material editing, adjusting the sphere's roughness and the horse's metallic. Bottom: Object insertion of a bathtub and table into scene images. + +real joint training in Fig. 7. While synthetic data provides accurate supervision signals, it is limited to a specific domain and lacks the diversity and complexity found in real-world data. When training exclusively on synthetic data (Ours Synth.), the model struggles with complex structures, such as trees, which are rarely represented in synthetic datasets. Since the real-world auto-labels are estimated using inverse rendering models and contain imperfections, we find that incorporating a LoRA [27] during training with real data consistently improves visual quality. + +# 5.5. Applications + +We show material editing and object insertion applications in Fig. 8. In the top row, we adjust the sphere's roughness from 0.15 to 0.6 and increase the horse's metallic property from 0 to 1, achieving photorealistic material edits. In the bottom row, we insert a bathtub and table in the G-buffer space of the input image, and use our forward renderer to produce the edited result. The inserted objects blend naturally into the scene, generating realistic reflections and shadows. + +# 6. Discussion + +DIFFUSIONRENDERER provides a scalable, data-driven approach to inverse and forward rendering, achieving high-quality G-buffer estimation and photorealistic image generation without relying on explicit path tracing or precise 3D scene representations. Jointly trained on synthetic and auto-labeled real-world data, DIFFUSIONRENDERER consistently outperforms state-of-the-art methods. + +Limitations and future work. Our method is based on Stable Video Diffusion, which operates offline and would benefit from distillation techniques to improve inference speed. For editing tasks, the inverse and forward rendering models preserve most of the original content but may introduce slight variations in color or texture. Future work could explore task-specific fine-tuning [37] and develop neural intrinsic features to enhance content consistency and handle more complex visual effects. Additionally, our real-world auto-labeling currently adopts off-the-shelf lighting estimation model [61] which could benefit from better accuracy and robustness. With rapid advancements in video diffusion models [1] toward higher quality and faster inference speeds, we are optimistic that DIFFUSIONRENDERER will inspire future research in high-quality image synthesis and editing. + +Acknowledgments. The authors thank Shiqiu Liu, Yichen Sheng, and Michael Kass for their insightful discussions that contributed to this project. We also appreciate the discussions with Xuanchi Ren, Tianchang Shen and Zheng Zeng during the model development process. + +# References + +[1] Niket Agarwal, Arslan Ali, Maciej Bala, Yogesh Balaji, Erik Barker, Tiffany Cai, Prithvijit Chattopadhyay, Yongxin Chen, Yin Cui, Yifan Ding, et al. 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"^{1}" + }, + { + "bbox": [ + 61, + 160, + 550, + 204 + ], + "type": "text", + "content": "NVIDIA " + }, + { + "bbox": [ + 61, + 160, + 550, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 61, + 160, + 550, + 204 + ], + "type": "text", + "content": "University of Toronto " + }, + { + "bbox": [ + 61, + 160, + 550, + 204 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 61, + 160, + 550, + 204 + ], + "type": "text", + "content": "Vector Institute " + }, + { + "bbox": [ + 61, + 160, + 550, + 204 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 61, + 160, + 550, + 204 + ], + "type": "text", + "content": "University of Illinois Urbana-Champaign" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 68, + 222, + 541, + 422 + ], + "blocks": [ + { + "bbox": [ + 68, + 222, + 541, + 422 + ], + "lines": [ + { + "bbox": [ + 68, + 222, + 541, + 422 + ], + "spans": [ + { + "bbox": [ + 68, + 222, + 541, + 422 + ], + "type": "image", + "image_path": "f02ed007288a0fad9b2038c9f4d8e8e6cebd96d2e7ca1852247ccc17f68043c7.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 423, + 555, + 459 + ], + "lines": [ + { + "bbox": [ + 54, + 423, + 555, + 459 + ], + "spans": [ + { + "bbox": [ + 54, + 423, + 555, + 459 + ], + "type": "text", + "content": "Figure 1. We present DIFFUSIONRENDERER, a general-purpose method for both neural inverse and forward rendering. From input images or videos, it accurately estimates geometry and material buffers, and generates photorealistic images under specified lighting conditions, offering fundamental tools for image editing applications." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 467, + 200, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 467, + 200, + 479 + ], + "spans": [ + { + "bbox": [ + 151, + 467, + 200, + 479 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 498, + 297, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 498, + 297, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 498, + 297, + 713 + ], + "type": "text", + "content": "Understanding and modeling lighting effects are fundamental tasks in computer vision and graphics. Classic physically-based rendering (PBR) accurately simulates the light transport, but relies on precise scene representations—explicit 3D geometry, high-quality material properties, and lighting conditions—that are often impractical to obtain in real-world scenarios. Therefore, we introduce DIFFUSIONRENDERER, a neural approach that addresses the dual problem of inverse and forward rendering within a holistic framework. Leveraging powerful video diffusion model priors, the inverse rendering model accurately estimates " + }, + { + "bbox": [ + 54, + 498, + 297, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 54, + 498, + 297, + 713 + ], + "type": "text", + "content": "-filters from real-world videos, providing an interface for image editing tasks, and training data for the rendering model. Conversely, our rendering model generates photorealistic images from " + }, + { + "bbox": [ + 54, + 498, + 297, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 54, + 498, + 297, + 713 + ], + "type": "text", + "content": "-filters without explicit light transport simulation. Specifically, we first train a video diffusion model for inverse rendering on synthetic data, which generalizes well to real-world videos and allows us to auto-label diverse real-world videos. We" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 468, + 556, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 556, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 556, + 552 + ], + "type": "text", + "content": "then co-train our rendering model using both synthetic and auto-labeled real-world data. Experiments demonstrate that DIFFUSIONRENDERER effectively approximates inverse and forwards rendering, consistently outperforming the state-of-the-art. Our model enables practical applications from a single video input—including relighting, material editing, and realistic object insertion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 564, + 395, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 564, + 395, + 576 + ], + "spans": [ + { + "bbox": [ + 314, + 564, + 395, + 576 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 582, + 557, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 582, + 557, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 582, + 557, + 715 + ], + "type": "text", + "content": "Understanding and modeling light transport forms the basis of Physically Based Rendering (PBR) [59]. Modern path tracing algorithms, as regularly used in the gaming and movie industries, simulate light transport to render images that cannot be distinguished from photographs. The quality of such PBR-rendered images heavily depends on the accuracy and realism of the scene's surface geometry, material properties, and lighting representations. Such a scene description is either designed by artists (synthetic scenes) or reconstructed from data—also known as the inverse rendering problem [2, 3]. Inverse rendering has been extensively stud" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26069" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 132 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 132 + ], + "type": "text", + "content": "ied, particularly for applications like relighting and object insertion into real-world scenes [20, 41, 75, 88]. However, acquiring high quality surface and material representations is challenging in real-world scenarios, limiting the practicality of PBR methods (Fig. 2)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 133, + 295, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 133, + 295, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 133, + 295, + 228 + ], + "type": "text", + "content": "While physically-based rendering and inverse rendering are usually considered separately, we propose to consider them jointly. Our approach draws inspiration from the success of large-scale generative models [8, 65], which \"render\" photorealistic images from simple text prompts without any explicit understanding of PBR. These models learn the underlying distribution of real-world images from a vast amounts of data, implicitly capturing the complex lighting effects." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 229, + 296, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 229, + 296, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 229, + 296, + 373 + ], + "type": "text", + "content": "Specifically, we propose DIFFUSIONRENDERER, a general-purpose neural rendering engine that can synthesize light transport simulation—such as shadows and reflections—by leveraging the powerful priors of video diffusion models. Conditioned on input geometry, material buffers, and environment map light source, DIFFUSIONRENDERER acts as a neural approximation of path-traced shading. DIFFUSIONRENDERER is designed to remain faithful to the conditioning signals, while adhering to the distribution of real-world images. As a result, we bypass the need for precise scene representations and description, as our model learns to handle imperfections in the input data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 373, + 296, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 373, + 296, + 492 + ], + "spans": [ + { + "bbox": [ + 55, + 373, + 296, + 492 + ], + "type": "text", + "content": "Training such a model requires some amount of high quality and diverse data, including data with noisy conditions to ensure robustness. Therefore, we first train an inverse renderer, a video diffusion model to map input RGB videos to intrinsic properties. Although trained solely on synthetic data, the inverse rendering model generalizes robustly to real-world scenarios. We then use it to generate \"pseudo-labels\" for diverse real-world videos. Combining both real-world auto-labeled data and synthetic data, we train our forward renderer video diffusion model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 494, + 295, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 494, + 295, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 494, + 295, + 601 + ], + "type": "text", + "content": "DIFFUSIONRENDERER outperforms state-of-the-art methods and effectively approximates the complex functionalities of inverse and forward rendering, allowing us to relight images and videos across diverse scenes and to synthesize consistent shadows and reflections without explicit path tracing and 3D scene representation. Our model can relight any scene from only a single video input, and provides fundamental tools for editing tasks such as material editing and realistic object insertion. To summarize:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 603, + 295, + 711 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 57, + 603, + 295, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 603, + 295, + 627 + ], + "spans": [ + { + "bbox": [ + 57, + 603, + 295, + 627 + ], + "type": "text", + "content": "- We develop a state-of-the-art inverse rendering method for videos of synthetic and real-world scenes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 628, + 295, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 628, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 57, + 628, + 295, + 662 + ], + "type": "text", + "content": "- We repurpose a video diffusion model as a neural rendering engine that can synthesize photorealistic images and videos conditioned on noisy G-buffers." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 57, + 663, + 295, + 711 + ], + 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Classic PBR relies on explicit 3D geometry, e.g., meshes. When it is not available, screen space ray tracing (SSRT) struggles to accurately represent shadows and reflections (top). PBR is also sensitive to errors in G-buffers – SSRT with estimated G-buffers from inverse rendering models often fails to deliver quality results (bottom). DIFFUSIONRENDERER bypasses these issues, producing photorealistic results without 3D geometry or perfect G-buffers." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 314, + 282, + 400, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 282, + 400, + 294 + ], + "spans": [ + { + "bbox": [ + 314, + 282, + 400, + 294 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 301, + 555, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 301, + 555, + 553 + ], + "spans": [ + { + "bbox": [ + 313, + 301, + 555, + 553 + ], + "type": "text", + "content": "Neural rendering refers to methods that replace or extend traditional rendering pipelines by neural networks. For example, Deep Shading [56] replaces traditional deferred shading [15] by a CNN to render images with ambient occlusion, global illumination, and depth-of-field from G-buffers. More recently, RGB " + }, + { + "bbox": [ + 313, + 301, + 555, + 553 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 313, + 301, + 555, + 553 + ], + "type": "text", + "content": " X [83] trains image diffusion models to both estimate a G-buffer from an image and to render an image from a G-buffer. We extend this approach to video diffusion models and provide a novel approach for neural relighting that does not require an irradiance estimate. Other approaches fit rendered data using neural models or introduce neural components into an existing renderer with focus on approximating light transport [28, 31] or radiance caching [25, 53]. A plethora of works on neural and inverse rendering involve volumetric 3D scene representations in the form of NeRF [52] or 3D Gaussian Splats [35]. We refer to [70] for an overview. While providing photo-real view interpolation, these approaches typically bake radiance, and have limited editing capabilities. In contrast, we explicitly target an intermediate scene representation in the form of traditional, easy-to-edit, G-buffers with separate lighting." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 557, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 556, + 713 + ], + "type": "text", + "content": "Inverse rendering is a fundamental task first formalized in the 1970s [4], aiming to estimate intrinsic scene properties, like geometry, materials, and lighting from input images. Early methods designed hand-crafted priors within an optimization framework [2, 4, 11, 23, 39, 89], typically focusing on low-order effects. These methods lead to errors when the hand-crafted priors do not match reality. Recently, supervised and self-supervised learning has been extensively studied [5, 6, 9, 38, 40-42, 67, 73, 74, 76, 80]. The resulting algorithms are often data-hungry and specific to a certain task or domain. Acquiring sufficient and diverse training data poses a challenge. Recent advances in large image generative models provide new deep learning tools for inverse" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26070" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 109 + ], + "type": "text", + "content": "rendering [19, 36, 44, 61, 83] resulting in much higher reconstruction quality. Still, the quality is not enough to power physically based rendering pipelines." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 110, + 297, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 110, + 297, + 316 + ], + "spans": [ + { + "bbox": [ + 55, + 110, + 297, + 316 + ], + "type": "text", + "content": "Relighting focuses on modifying the lighting conditions of a scene given captured images or videos. Recent methods reconstruct 3D scene representations from multi-view images, performing explicit inverse rendering to recover material properties and enable relighting [10, 13, 24, 29, 43, 45, 54, 66, 68, 75, 78, 84, 85, 87]. These methods often optimize for each scene individually, and their quality may be affected by practical issues such as single-illumination capture, large scene scale, and dynamic content. Learning-based methods that train across multiple scenes have explored latent feature learning [7, 48, 90] and often incorporate neural rendering modules that utilize PBR buffers as inductive priors [22, 37, 57, 60, 79]. To improve relighting quality, recent approaches [30, 37, 62, 82] leverage diffusion models. With very few multi-illumination datasets [55], existing methods often are specialized to a domain, such as portraits, objects, and outdoor scenes, and remain data-hungry." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 324, + 141, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 141, + 337 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 141, + 337 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 341, + 296, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 341, + 296, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 341, + 296, + 378 + ], + "type": "text", + "content": "Physically-based rendering (PBR) is concerned with the simulation of how the incoming radiance contributes to the outgoing radiance" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 387, + 296, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 387, + 296, + 412 + ], + "spans": [ + { + "bbox": [ + 62, + 387, + 296, + 412 + ], + "type": "interline_equation", + "content": "L _ {o} (\\mathbf {p}, \\boldsymbol {\\omega} _ {o}) = \\int_ {\\Omega} f _ {r} (\\mathbf {p}, \\boldsymbol {\\omega} _ {o}, \\boldsymbol {\\omega} _ {i}) L _ {i} (\\mathbf {p}, \\boldsymbol {\\omega} _ {i}) | \\mathbf {n} \\cdot \\boldsymbol {\\omega} _ {i} | d \\boldsymbol {\\omega} _ {i}, \\tag {1}", + "image_path": "850abbae5417d5d3bf8ebb338ceb25521bf0f6a5ad3521d329a151007be4ee2b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "content": "at a surface point " + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "content": " in direction " + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\omega_{o}" + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "content": ". The integral over the hemisphere " + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "content": " considers the BRDF " + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "inline_equation", + "content": "f_{r}(\\mathbf{p},\\omega_{o},\\omega_{i})" + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "content": ", incoming radiance " + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "inline_equation", + "content": "L_{i}(\\mathbf{p},\\omega_{i})" + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "content": ", and a cosine factor " + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "inline_equation", + "content": "|\\mathbf{n}\\cdot \\boldsymbol{\\omega}_i|" + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "content": " for the angle between the normal " + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 55, + 422, + 296, + 495 + ], + "type": "text", + "content": " and incoming light. It is evaluated by Monte Carlo methods [59, 71], with meticulously designed BRDF models [12, 14, 72] that approximate real surfaces." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": "Video diffusion models (VDMs). A diffusion model learns to approximate a data distribution " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}(\\mathbf{I})" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": " via iterative denoising [18, 26, 69]. Most VDMs operate in a compressed, lower-dimensional latent space [1, 8]. Given an RGB video " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": ", consisting of " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": " frames at resolution " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": ", a pre-trained VAE encoder " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": " first encodes the video into a latent representation " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathcal{E}(\\mathbf{I}) \\in \\mathbb{R}^{F' \\times h \\times w \\times C}" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": ". The final video " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": " is then reconstructed by decoding " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": " with a pre-trained VAE decoder " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": ". Both training and inference stages of the VDM are conducted in this latent space. In this work, we build on Stable Video Diffusion [8], which compresses the video only along the spatial dimensions: " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "F' = F" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "C = 4" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "h = \\frac{H}{8}" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "inline_equation", + "content": "w = \\frac{W}{8}" + }, + { + "bbox": [ + 55, + 496, + 297, + 653 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": "To train the VDM, noisy versions " + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\tau} = \\alpha_{\\tau}\\mathbf{z}_0 + \\sigma_{\\tau}\\epsilon" + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": " are constructed by adding a Gaussian noise " + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": " with the noise schedule provided by " + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{\\tau}" + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\sigma_{\\tau}" + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": " following EDM [33]. The diffusion model parameters " + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": " of the denoising function " + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\theta}" + }, + { + "bbox": [ + 55, + 654, + 297, + 715 + ], + "type": "text", + "content": " are optimized using the denoising score matching objective [33]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "content": "Once trained, iteratively applying " + }, + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\theta}" + }, + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "text", + "content": " to a sample of Gaussian noise will produce a sample of " + }, + { + "bbox": [ + 313, + 72, + 555, + 97 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}(\\mathbf{I})" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 98, + 556, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 98, + 556, + 194 + ], + "spans": [ + { + "bbox": [ + 313, + 98, + 556, + 194 + ], + "type": "text", + "content": "Conditioning in VDMs. Two common approaches to inject conditions into VDMs are: (i) concatenating condition channels with image latents " + }, + { + "bbox": [ + 313, + 98, + 556, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\tau}" + }, + { + "bbox": [ + 313, + 98, + 556, + 194 + ], + "type": "text", + "content": ", which is often used for pixelwise conditions [8, 34, 36, 83], and (ii) injecting conditions through cross-attention layers [8, 65], which is often used for semantic features such as the CLIP embedding [63]. Note that our method is compatible with any standard VDMs and does not depend on specific architectural details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 201, + 370, + 214 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 201, + 370, + 214 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 370, + 214 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 219, + 556, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 219, + 556, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 556, + 339 + ], + "type": "text", + "content": "DIFFUSIONRENDERER is a unified framework comprising two video diffusion models designed for the dual tasks of neural forward and inverse rendering. As illustrated in Fig. 3, the neural forward renderer (Sec. 4.1) approximates physically based light transport (Eq. 1), transforming G-buffers [56] and lighting into a photorealistic video. The neural inverse renderer (Sec. 4.2) reconstructs geometry and material buffers from input video. The neural forward and inverse renderers are based on pre-trained video diffusion models and fine-tuned for conditional generation [34, 36, 83]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 339, + 555, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 555, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 555, + 388 + ], + "type": "text", + "content": "Data is a critical aspect of learning-based methods. We describe our data curation workflow and synthetic-real joint training strategies in Sec. 4.3 and Sec. 4.4. Finally, we discuss image editing applications in Sec. 4.5." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 394, + 466, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 466, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 466, + 407 + ], + "type": "text", + "content": "4.1. Neural Forward Rendering" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 411, + 556, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 556, + 483 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 556, + 483 + ], + "type": "text", + "content": "We formulate neural forward rendering as a conditional generation task, producing photorealistic images given geometry, materials, and lighting as conditions. By approximating light transport simulation in a data-driven manner, the model requires neither classic 3D geometry nor explicit path tracing, thus reducing the constraints in real-world applications." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "text", + "content": "Geometry and material conditions. Similar to the G-buffers in rendering system based on deferred shading [15], we use per-pixel scene attribute maps to represent scene geometry and materials. Specifically, we use surface normals " + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{n} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}" + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "text", + "content": " in camera space and relative depth " + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{d} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}" + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "text", + "content": " normalized to " + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "inline_equation", + "content": "[-1,1]" + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "text", + "content": " to represent scene geometry. For materials, we use base color " + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{a} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}" + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "text", + "content": ", roughness " + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{r} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}" + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "text", + "content": ", and metallic " + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{m} \\in \\mathbb{R}^{F \\times H \\times W \\times 1}" + }, + { + "bbox": [ + 313, + 484, + 556, + 592 + ], + "type": "text", + "content": " following the Disney BRDF [12]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": "Lighting conditions. Lighting is represented by environment maps " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E} \\in \\mathbb{R}^{F \\times H_{\\mathrm{env}} \\times W_{\\mathrm{env}} \\times 3}" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": ", which are panoramic images that capture the lighting intensity from all directions over the sphere. These environment maps are encoded in high dynamic range (HDR), while the VAEs used in typical latent diffusion models are designed for pixel values between -1 and 1. To address this discrepancy, similar to the light representation in Neural Gaffer [30], we first apply Reinhard tonemapping to convert HDR environment map into an LDR image " + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\mathrm{ldr}}" + }, + { + "bbox": [ + 313, + 594, + 557, + 714 + ], + "type": "text", + "content": ". To more effectively represent HDR values," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26071" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 56, + 541, + 199 + ], + "blocks": [ + { + "bbox": [ + 69, + 56, + 541, + 199 + ], + "lines": [ + { + "bbox": [ + 69, + 56, + 541, + 199 + ], + "spans": [ + { + "bbox": [ + 69, + 56, + 541, + 199 + ], + "type": "image", + "image_path": "51284f8fd23fe3ba4f2e7b768272ea460fd9ed1f628578a3ee166ecf80d6bc7a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 201, + 555, + 257 + ], + "lines": [ + { + "bbox": [ + 54, + 201, + 555, + 257 + ], + "spans": [ + { + "bbox": [ + 54, + 201, + 555, + 257 + ], + "type": "text", + "content": "Figure 3. Method overview. Given an input video, the neural inverse renderer estimates geometry and material properties per pixel. It generates one scene attribute at a time, with the domain embedding indicating the target attributes to generate (Sec. 4.2). Conversely, the neural forward renderer produces photorealistic images given lighting information, geometry, and material buffers. The lighting condition is injected into the base video diffusion model through cross-attention layers (Sec. 4.1). During joint training with both synthetic and real data, we use an estimizable LoRA for real data sources (Sec. 4.4)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "text", + "content": "particularly for light sources with high-intensity peaks, we compute " + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\mathrm{log}} = \\log (\\mathbf{E} + 1) / E_{\\mathrm{max}}" + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "text", + "content": " where the light intensity values are mapped to logarithm space that is closer to human perception and normalized by max log intensity " + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{max}}" + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "text", + "content": ". Additionally, we also compute a directional encoding image, " + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\mathrm{dir}} \\in \\mathbb{R}^{F \\times H_{\\mathrm{env}} \\times W_{\\mathrm{env}} \\times 3}" + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "text", + "content": ", where each pixel is represented by a unit vector indicating its direction in the camera coordinate system. The resulting lighting encodings used by the model consist of three panoramic images: " + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{E}_{\\mathrm{ldr}}, \\mathbf{E}_{\\mathrm{log}}, \\mathbf{E}_{\\mathrm{dir}}\\}" + }, + { + "bbox": [ + 55, + 266, + 296, + 375 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 382, + 296, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 382, + 296, + 431 + ], + "spans": [ + { + "bbox": [ + 55, + 382, + 296, + 431 + ], + "type": "text", + "content": "Model architecture. Our models are based on Stable Video Diffusion [8], an image-to-video diffusion model with its core architecture including a VAE encoder-decoder pair " + }, + { + "bbox": [ + 55, + 382, + 296, + 431 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{E},\\mathcal{D}\\}" + }, + { + "bbox": [ + 55, + 382, + 296, + 431 + ], + "type": "text", + "content": ", and a UNet-based denoising function " + }, + { + "bbox": [ + 55, + 382, + 296, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\theta}" + }, + { + "bbox": [ + 55, + 382, + 296, + 431 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "type": "text", + "content": "We use the VAE encoder " + }, + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "type": "text", + "content": " to separately encode each G-buffer from " + }, + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}" + }, + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "type": "text", + "content": " into the latent space and concatenate them to produce the pixel-aligned scene attribute latent map " + }, + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{g} = \\{\\mathcal{E}(\\mathbf{n}),\\mathcal{E}(\\mathbf{d}),\\mathcal{E}(\\mathbf{a}),\\mathcal{E}(\\mathbf{r}),\\mathcal{E}(\\mathbf{m})\\} \\in \\mathbb{R}^{F\\times h\\times w\\times 20}" + }, + { + "bbox": [ + 55, + 437, + 296, + 485 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 491, + 296, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 296, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 296, + 624 + ], + "type": "text", + "content": "Environment maps are usually in equi-rectangular projection and are not pixel-aligned with the generated images, thus requiring extra consideration. Prior works explored directly concatenating environment maps to the image latents [30] or concatenate split-sum shading buffers [17], which we also experimented with, but found suboptimal (Table 1). Instead, we take the cross-attention layers which originally operate on the text/image CLIP features, and re-purpose them for lighting conditions. To preserve spatial details of the environment maps, we generalize the conditional signals to a list of multi-resolution feature maps." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": "Specifically, we first pass the environment map information through VAE encoder " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{\\mathbf{E}} = \\{\\mathcal{E}(\\mathbf{E}_{\\mathrm{ldr}}),\\mathcal{E}(\\mathbf{E}_{\\mathrm{log}}),\\mathcal{E}(\\mathbf{E}_{\\mathrm{dir}})\\} \\in \\mathbb{R}^{F\\times h_{\\mathrm{env}}\\times w_{\\mathrm{env}}\\times 12}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": ". We additionally use an environment map encoder " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathrm{env}}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " to further operate on " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{\\mathbf{E}}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathrm{env}}" + }, + { + "bbox": [ + 55, + 629, + 296, + 713 + ], + "type": "text", + "content": " is the simplified encoder part of diffusion UNet with attention and temporal layers removed. It contains several convolutional layers to downsample and extract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 266, + 550, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 266, + 550, + 278 + ], + "spans": [ + { + "bbox": [ + 314, + 266, + 550, + 278 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 314, + 266, + 550, + 278 + ], + "type": "text", + "content": " levels of multi-resolution features as lighting conditions:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 371, + 285, + 555, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 285, + 555, + 300 + ], + "spans": [ + { + "bbox": [ + 371, + 285, + 555, + 300 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {\\text {e n v}} := \\left\\{\\mathbf {h} _ {\\text {e n v}} ^ {i} \\right\\} _ {i = 1} ^ {K} = \\mathcal {E} _ {\\text {e n v}} \\left(\\mathbf {h} _ {\\mathbf {E}}\\right) \\tag {2}", + "image_path": "d8b9e7db57b1a8fd762fb8fd9a1027eab130fc9c4eefc83e3b92b420af3e2045.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "text", + "content": "As a result, the diffusion UNet " + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\theta}" + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "text", + "content": " takes the noisy latent " + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\tau}" + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "text", + "content": " and G-buffer latent " + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "text", + "content": " as pixel-wise input. At each UNet level " + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "text", + "content": ", the diffusion UNet queries the latent environment map features at the corresponding level " + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{\\mathrm{env}}^k" + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "text", + "content": ", and aggregates based on its keys and values. Through the multi-level self-attention and cross-attention layers, the diffusion model is given the capacity to learn to shade G-buffers with lighting. During inference, the diffusion target can be computed as " + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\theta}(\\mathbf{z}_{\\tau}; \\mathbf{g}, \\mathbf{c}_{\\mathrm{env}}, \\tau)" + }, + { + "bbox": [ + 313, + 306, + 555, + 426 + ], + "type": "text", + "content": " to produce photorealistic images with iterative denoising." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 433, + 459, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 433, + 459, + 445 + ], + "spans": [ + { + "bbox": [ + 313, + 433, + 459, + 445 + ], + "type": "text", + "content": "4.2. Neural Inverse Rendering" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 448, + 555, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 448, + 555, + 496 + ], + "spans": [ + { + "bbox": [ + 313, + 448, + 555, + 496 + ], + "type": "text", + "content": "We similarly formulate inverse rendering as a conditional generation task. Given an input video " + }, + { + "bbox": [ + 313, + 448, + 555, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 313, + 448, + 555, + 496 + ], + "type": "text", + "content": " as a condition, the inverse renderer estimates scene attribute maps " + }, + { + "bbox": [ + 313, + 448, + 555, + 496 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}" + }, + { + "bbox": [ + 313, + 448, + 555, + 496 + ], + "type": "text", + "content": " which are the G-buffers used by the forward renderer." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "type": "text", + "content": "Model architecture. The input video " + }, + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "type": "text", + "content": " is encoded into latent space " + }, + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathcal{E}(\\mathbf{I})" + }, + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "type": "text", + "content": ", and concatenated with the noisy G-buffer latent, which we denote as " + }, + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\tau} = \\alpha_{\\tau}\\mathbf{g}_0 + \\sigma_{\\tau}\\epsilon" + }, + { + "bbox": [ + 313, + 498, + 554, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": "Given an input video, the inverse renderer generates all five attributes " + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m}\\}" + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": " using the same model. To preserve the high-quality generation and maximally leverage the diffusion model pre-trained knowledge, each attribute is generated in a dedicated pass, instead of generating all at once. We follow prior works [21, 49, 83] and use a domain embedding to indicate to the model which attribute should be generated. Specifically, we introduce an estimizable domain embedding " + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{emb}}\\in \\mathbb{R}^{K_{\\mathrm{emb}}\\times C_{\\mathrm{emb}}}" + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "inline_equation", + "content": "K_{\\mathrm{emb}} = 5" + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": " is the number of buffers and " + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "inline_equation", + "content": "C_\\mathrm{emb}" + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": " is the dimension of the embedding vector. We re-purpose the cross-attention layers with image CLIP features to take domain embeddings. When estimating an attribute indexed by " + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": ", we feed its embedding " + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{emb}}^P" + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": " as a condition and predict the diffusion target with " + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\theta}(\\mathbf{g}_{\\tau}^{P};\\mathbf{z},\\mathbf{c}_{\\mathrm{emb}}^{P},\\tau)" + }, + { + "bbox": [ + 313, + 534, + 555, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26072" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 144, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 144, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 144, + 85 + ], + "type": "text", + "content": "4.3. Data Strategy" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "text", + "content": "Synthetic data curation. To train our models, we require high-quality video data with paired ground-truth for material, geometry, and lighting information. Specifically, each video data sample should include paired frames of RGB, base color, roughness, metallic, normals, depth, and environment map: " + }, + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I},\\mathbf{a},\\mathbf{r},\\mathbf{m},\\mathbf{n},\\mathbf{d},\\mathbf{E}\\}" + }, + { + "bbox": [ + 55, + 89, + 296, + 185 + ], + "type": "text", + "content": ". These buffers are typically only available in synthetic data, and most existing public datasets contain only a subset of them." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 185, + 296, + 281 + ], + "type": "text", + "content": "To address the data scarcity, we designed a synthetic data generation workflow to produce a large amount of high-quality data covering diverse and complex lighting effects. We start by curating a collection of 3D assets, PBR materials, and HDR environment maps. We use 36,500 3D assets from Objaverse LVIS split. For materials and lighting, we collected 4,260 high-quality PBR material maps, and 766 HDR environment maps from publicly available resources." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 281, + 296, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 296, + 399 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 296, + 399 + ], + "type": "text", + "content": "In each scene, we place a plane with a randomly selected PBR material, and sample up to three 3D objects, and place them on the plane. We perform collision detection to avoid intersecting objects. We also place up to three primitives (cube, sphere, and cylinder) with randomized shape and materials to cover complex lighting effects such as inter-reflections. A randomly selected HDR environment map illuminates the scene. We generate motions including camera orbits, camera oscillation, lighting rotation, object rotation and translation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 400, + 296, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 400, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 400, + 296, + 460 + ], + "type": "text", + "content": "We use a custom path tracer based on OptiX [58] to render the videos. In total, we generate 150,000 videos with paired ground-truth G-buffers and environment maps, at 24 frames per video in " + }, + { + "bbox": [ + 55, + 400, + 296, + 460 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 400, + 296, + 460 + ], + "type": "text", + "content": " resolution. This dataset can be used to train both rendering and inverse rendering models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 462, + 296, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 462, + 296, + 594 + ], + "spans": [ + { + "bbox": [ + 55, + 462, + 296, + 594 + ], + "type": "text", + "content": "Real world auto-labeling. Synthetic data provides accurate supervision signals, and when combined with powerful image diffusion models, it demonstrates impressive generalization to unseen domains for inverse rendering tasks [21, 34]. However, when it comes to training the forward rendering model, synthetic data alone is insufficient. Since the output of the forward renderer is an RGB video, training only on synthetic renderings biases the model toward synthetic visual styles. Compared to inverse rendering, we observe a much more significant domain gap in complex real-world scenes for forward rendering tasks (Fig. 7)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 297, + 714 + ], + "type": "text", + "content": "Acquiring real-world data with paired geometry, material, and lighting ground truth requires complex and impractical capturing setups. Based on the observation that our inverse rendering model generalizes to real-world videos, we apply it to automatically label real-world videos. Specifically, we use the DL3DV10k [47] dataset, which is a large-scale dataset consisting of 10,510 videos featuring diverse real-world environments. We use our inverse rendering model (Sec. 4.2) to generate G-buffer labels and use an off-the-shelf method DiffusionLight [61] to estimate environment" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 555, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 109 + ], + "type": "text", + "content": "maps. Each video is divided into 15 segments, resulting in around 150,000 real-world video samples with auto-labeled geometry, material, and lighting attributes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 117, + 419, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 117, + 419, + 129 + ], + "spans": [ + { + "bbox": [ + 313, + 117, + 419, + 129 + ], + "type": "text", + "content": "4.4. Training pipeline" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "text", + "content": "Neural inverse renderer. We first co-train the inverse rendering model on the combination of the curated synthetic video dataset and public image intrinsic datasets Interior-Verse [91] and HyperSim [64]. For image datasets, we treat images as single-frame videos. Each data sample consists of a video " + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "text", + "content": ", an attribute index " + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "text", + "content": ", and the scene attribute map " + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{s}^P" + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "text", + "content": ". The target latent variable is the latents of the scene attribute " + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_0^P \\coloneqq \\mathcal{E}(\\mathbf{s}^P)" + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "text", + "content": ", and noise is added to " + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_0^P" + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "text", + "content": " to produce " + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\tau}^P" + }, + { + "bbox": [ + 313, + 135, + 555, + 243 + ], + "type": "text", + "content": ". The model is trained using the objective function [33]:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 347, + 251, + 555, + 268 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 251, + 555, + 268 + ], + "spans": [ + { + "bbox": [ + 347, + 251, + 555, + 268 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\theta , \\mathbf {c} _ {\\mathrm {e m b}}) = \\| \\mathbf {f} _ {\\theta} \\left(\\mathbf {g} _ {\\tau} ^ {P}; \\mathbf {z}, \\mathbf {c} _ {\\mathrm {e m b}} ^ {P}, \\tau\\right) - \\mathbf {g} _ {0} ^ {P} \\| _ {2} ^ {2}. \\tag {3}", + "image_path": "84a2999caee5e7ea7a5ef461137eaf74e811fadf4f722e364c8ccb0b8795ca53.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "text", + "content": "We fine-tune the diffusion model parameters " + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "text", + "content": " and domain embeddings " + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{emb}}" + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "text", + "content": ", while keeping the latent encoder " + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "text", + "content": " and decoder " + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 277, + 555, + 335 + ], + "type": "text", + "content": " frozen. Once trained, the inverse renderer is used to auto-label real-world videos, generating training data for the forward renderer." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "text", + "content": "Environment map encoder pre-training. Following the approach of latent diffusion models [65], we pre-train the environment map encoder " + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathrm{env}}" + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "text", + "content": " along with a decoder " + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{env}}" + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "text", + "content": " using an L2 image reconstruction objective on environment maps, similar to an auto-encoder. The decoder architecture is based on the UNet decoder, containing a set of upsampling layers. After training, we discard the decoder " + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{env}}" + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "text", + "content": " and freeze the environment map encoder " + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathrm{env}}" + }, + { + "bbox": [ + 313, + 338, + 554, + 446 + ], + "type": "text", + "content": " while training the neural forward rendering model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 449, + 556, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 449, + 556, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 449, + 556, + 556 + ], + "type": "text", + "content": "Neural forward renderer. We train our rendering model on a combination of a synthetic video dataset and real-world auto-labeled data, using paired G-buffer, lighting, and RGB videos. Although the auto-labeled real-world data is of sufficient quality, it may still contain inaccuracies. To address discrepancies between the synthetic and real-world data sources, we introduce an additional LoRA [27] with a small set of estimizable parameters " + }, + { + "bbox": [ + 313, + 449, + 556, + 556 + ], + "type": "inline_equation", + "content": "\\Delta \\theta" + }, + { + "bbox": [ + 313, + 449, + 556, + 556 + ], + "type": "text", + "content": " during training on real data. We empirically find it improves the rendering quality (Fig. 7)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "text", + "content": "During training, for an RGB video " + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "text", + "content": ", the target latent variable is defined as " + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0 \\coloneqq \\mathcal{E}(\\mathbf{I})" + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "text", + "content": ". Noise is added to " + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "text", + "content": " to produce noisy image latent " + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\tau}" + }, + { + "bbox": [ + 313, + 557, + 556, + 594 + ], + "type": "text", + "content": ". The training objective is:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 597, + 555, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 597, + 555, + 639 + ], + "spans": [ + { + "bbox": [ + 317, + 597, + 555, + 639 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} (\\boldsymbol {\\theta}, \\Delta \\boldsymbol {\\theta}) = \\| \\mathbf {f} _ {\\boldsymbol {\\theta}} \\left(\\mathbf {z} _ {\\tau} ^ {\\mathrm {s y n t h}}; \\mathbf {g} ^ {\\mathrm {s y n t h}}, \\mathbf {c} _ {\\mathrm {e n v}} ^ {\\mathrm {s y n t h}}, \\boldsymbol {\\tau}\\right) - \\mathbf {z} _ {0} ^ {\\mathrm {s y n t h}} \\| _ {2} ^ {2} + \\\\ \\left\\| \\mathbf {f} _ {\\theta + \\Delta \\theta} \\left(\\mathbf {z} _ {\\tau} ^ {\\text {r e a l}}; \\mathbf {g} ^ {\\text {r e a l}}, \\mathbf {c} _ {\\text {e n v}} ^ {\\text {r e a l}}, \\tau\\right) - \\mathbf {z} _ {0} ^ {\\text {r e a l}} \\right\\| _ {2} ^ {2} \\tag {4} \\\\ \\end{array}", + "image_path": "5b47e520090ef9521ce880eabdfac343ec923ad87e5e4e5e714eb2f266c7dc41.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 649, + 434, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 649, + 434, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 649, + 434, + 662 + ], + "type": "text", + "content": "4.5. Editing Applications" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 555, + 714 + ], + "type": "text", + "content": "Our proposed framework provides fundamental solutions for inverse and forward rendering, enabling photorealistic image editing applications through a three-step process: neural inverse rendering, G-buffer and lighting editing, and neural" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "26073" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 64, + 302, + 171 + ], + "blocks": [ + { + "bbox": [ + 58, + 64, + 302, + 171 + ], + "lines": [ + { + "bbox": [ + 58, + 64, + 302, + 171 + ], + "spans": [ + { + "bbox": [ + 58, + 64, + 302, + 171 + ], + "type": "table", + "html": "
    SyntheticObjectsSyntheticScenes
    PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
    SSRT29.40.9510.03724.80.8990.113
    SplitSum [32]28.70.9510.03823.10.8830.116
    RGB↔X [83]25.20.8960.07718.50.6450.302
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    Ours28.30.9350.04826.00.7800.201
    Ours (image)27.40.9160.06225.40.7600.215
    Ours (w/o env. encoder)27.80.9270.05725.30.7560.237
    Ours (+ shading cond.)28.70.9300.05625.60.7610.245
    ", + "image_path": "73bf3dfe358823a2c5cb1dc438eb71024636f530bef42633895fde0405d50152.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 186, + 299, + 247 + ], + "blocks": [ + { + "bbox": [ + 80, + 172, + 270, + 183 + ], + "lines": [ + { + "bbox": [ + 80, + 172, + 270, + 183 + ], + "spans": [ + { + "bbox": [ + 80, + 172, + 270, + 183 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation of neural rendering." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 186, + 299, + 247 + ], + "lines": [ + { + "bbox": [ + 58, + 186, + 299, + 247 + ], + "spans": [ + { + "bbox": [ + 58, + 186, + 299, + 247 + ], + "type": "table", + "html": "
    SyntheticObjectsSyntheticScenes
    PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
    DiLightNet [82]23.790.8720.08718.880.5760.344
    Neural Gaffer [30]26.390.9030.08620.750.6330.343
    Ours27.500.9180.06724.630.7560.257
    ", + "image_path": "9a0a7b69ed3ef700978bb6305ece0cd3a83cabcfef98d8c4508f338f55b1d440.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 249, + 258, + 261 + ], + "lines": [ + { + "bbox": [ + 91, + 249, + 258, + 261 + ], + "spans": [ + { + "bbox": [ + 91, + 249, + 258, + 261 + ], + "type": "text", + "content": "Table 2. Quantitative evaluation of relighting." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 268, + 295, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 268, + 295, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 268, + 295, + 293 + ], + "type": "text", + "content": "rendering. For the example of relighting, given a video I as input, the inverse rendering model estimates the G-buffers" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 85, + 301, + 296, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 301, + 296, + 316 + ], + "spans": [ + { + "bbox": [ + 85, + 301, + 296, + 316 + ], + "type": "interline_equation", + "content": "\\{\\hat {\\mathbf {n}}, \\hat {\\mathbf {d}}, \\hat {\\mathbf {a}}, \\hat {\\mathbf {r}}, \\hat {\\mathbf {m}} \\} = \\operatorname {I n v e r s e R e n d e r e r} (\\mathbf {I}). \\tag {5}", + "image_path": "c5e6f1c9191cfe03b2b6fbec698ba228f43dbe19aad11111f93c2e086e34b0b3.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 324, + 296, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 324, + 296, + 349 + ], + "spans": [ + { + "bbox": [ + 55, + 324, + 296, + 349 + ], + "type": "text", + "content": "With a user-specified target environment map " + }, + { + "bbox": [ + 55, + 324, + 296, + 349 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\mathrm{tgt}}" + }, + { + "bbox": [ + 55, + 324, + 296, + 349 + ], + "type": "text", + "content": ", the rendering model produces relit videos" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 65, + 357, + 296, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 357, + 296, + 373 + ], + "spans": [ + { + "bbox": [ + 65, + 357, + 296, + 373 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {I}} _ {\\mathrm {t g t}} = \\text {F o r w a r d R e n d e r e r} \\left(\\left\\{\\hat {\\mathbf {n}}, \\hat {\\mathbf {d}}, \\hat {\\mathbf {a}}, \\hat {\\mathbf {r}}, \\hat {\\mathbf {m}}, \\mathbf {E} _ {\\mathrm {t g t}} \\right\\}\\right). \\tag {6}", + "image_path": "7af393de2b81d04023aa974fe8993caf3a8ea24b8c7d522ccf6bb56b4c5ea35a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 381, + 295, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 381, + 295, + 406 + ], + "spans": [ + { + "bbox": [ + 55, + 381, + 295, + 406 + ], + "type": "text", + "content": "Similarly, editing the G-buffers and rendering the videos can enable material editing and virtual object insertion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 417, + 137, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 417, + 137, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 417, + 137, + 430 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 434, + 296, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 434, + 296, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 434, + 296, + 506 + ], + "type": "text", + "content": "We extensively evaluate DIFFUSIONRENDERER on a diverse range of synthetic and real-world datasets. Sec. 5.1 details our experimental settings. We compare and ablate across three main tasks: image generation from G-buffers (Sec. 5.2), inverse rendering (Sec. 5.3), and relighting (Sec. 5.4). Finally, we show applications of our method in Sec. 5.5." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 514, + 173, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 173, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 173, + 528 + ], + "type": "text", + "content": "5.1. Experiment Settings" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 530, + 296, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 530, + 296, + 542 + ], + "spans": [ + { + "bbox": [ + 55, + 530, + 296, + 542 + ], + "type": "text", + "content": "We refer to model implementation details in the Supplement." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "type": "text", + "content": "Task definitions. We evaluate our method on three fundamental tasks: forward rendering, inverse rendering, and relighting. For forward rendering, the methods take the G-buffers and lighting information " + }, + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{n},\\mathbf{d},\\mathbf{a},\\mathbf{r},\\mathbf{m},\\mathbf{E}\\}" + }, + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "type": "text", + "content": " as input, and output rendered images " + }, + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{l}}" + }, + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "type": "text", + "content": ". We evaluate the consistency between the rendered outputs and the ground-truth images " + }, + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 55, + 544, + 296, + 617 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "content": "For inverse rendering, each method uses RGB images " + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "content": " as input to estimate scene attributes " + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\mathbf{a}},\\hat{\\mathbf{r}},\\hat{\\mathbf{m}},\\hat{\\mathbf{n}}\\}" + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "text", + "content": ", and compare against ground truth values. Our focus is primarily on the attributes related to PBR - specifically, base color, roughness, and metallic properties. We recognize dedicated works on normal and depth estimation [21, 34] and do not aim to provide an exhaustive evaluation. For relighting, each method takes RGB images and target lighting conditions " + }, + { + "bbox": [ + 55, + 618, + 296, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}^{\\mathrm{src}},\\mathbf{E}^{\\mathrm{tgt}}\\}" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "as input, output re-lit image sequence " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}^{\\mathrm{gt}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": " under the target lighting conditions, and compare with ground truth " + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{\\mathrm{gt}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 96 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 98, + 555, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 98, + 555, + 242 + ], + "spans": [ + { + "bbox": [ + 313, + 98, + 555, + 242 + ], + "type": "text", + "content": "Baselines. For forward rendering, we compare with Split Sum [32] and Screen Space Ray Tracing (SSRT). For SSRT, we extract a mesh from the depth buffer and render the mesh with material parameters from the G-buffers and a provided HDR probe in a path tracer. We additionally compare against the neural rendering components of recent state-of-the-art methods RGB " + }, + { + "bbox": [ + 313, + 98, + 555, + 242 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 313, + 98, + 555, + 242 + ], + "type": "text", + "content": " X [83] and DiLightNet [82]. For inverse rendering, we compare with recent diffusion-based methods Kocsis et al. [36], RGB " + }, + { + "bbox": [ + 313, + 98, + 555, + 242 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 313, + 98, + 555, + 242 + ], + "type": "text", + "content": " X [83] and earlier methods [5, 41, 91]. For relighting, we compare with 2D methods DiLightNet [82], Neural Gaffer [30]. We also compare with 3D reconstruction-based methods [46, 75] in supplement." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 243, + 554, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 243, + 554, + 351 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 554, + 351 + ], + "type": "text", + "content": "Metrics. We use PSNR, SSIM, and LPIPS [86] for forward rendering and relighting. For inverse rendering, we evaluate albedo with PSNR and LPIPS following [36, 83]. Since albedo estimation involves scale ambiguity [23], we additionally solve and apply a three-channel scaling factor using least-squares error minimization before computing metrics, referred to as si-PSNR and si-LPIPS. We use root mean square error (RMSE) for metallic and roughness evaluation, and mean angular error for normals." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 354, + 556, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 556, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 556, + 521 + ], + "type": "text", + "content": "Datasets. We curate two high-quality synthetic datasets for quantitative evaluation, named SyntheticScenes and SyntheticObjects. The datasets consist of 3D assets from PolyHaven [81] and Objaverse [16] that are not included in the training data of our method or the baseline methods. SyntheticScenes contains 40 scenes, each featuring multiple objects arranged on a plane textured with high-quality PBR materials. Each scene is rendered into 24-frame videos under four lighting conditions, with motions such as camera orbiting and oscillation. As some baseline methods perform best with object-centric setups, we also create SyntheticObjects, a dataset of 30 individual objects. For each object, we render 24-frame videos under four different lighting conditions, with lighting rotated across frames." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 521, + 553, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 553, + 557 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 553, + 557 + ], + "type": "text", + "content": "For inverse rendering, we also evaluate on the indoor scene benchmark InteriorVerse [91]. We include qualitative comparisons on the DL3DV10k [47] dataset." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 566, + 496, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 566, + 496, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 496, + 578 + ], + "type": "text", + "content": "5.2. Evaluation of Forward Rendering" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 582, + 555, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 629 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 629 + ], + "type": "text", + "content": "We compare our method with baseline methods in Table 1 and Fig. 4. For the neural methods RGB " + }, + { + "bbox": [ + 313, + 582, + 555, + 629 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 313, + 582, + 555, + 629 + ], + "type": "text", + "content": " X [83] and DiLightNet [82], we use their rendering models with ground-truth G-buffers to generate the images." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 630, + 554, + 713 + ], + "type": "text", + "content": "Both classic PBR and neural methods perform well on the SyntheticObjects dataset in single-object settings but show significant quality drops on the SyntheticScenes dataset due to complex inter-reflections and occlusions. For example, our method exhibits a minor PSNR decrease of 2.3 dB from SyntheticObjects to SyntheticScenes, while other baselines show more substantial drops." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26074" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 57, + 380, + 133 + ], + "blocks": [ + { + "bbox": [ + 58, + 57, + 380, + 133 + ], + "lines": [ + { + "bbox": [ + 58, + 57, + 380, + 133 + ], + "spans": [ + { + "bbox": [ + 58, + 57, + 380, + 133 + ], + "type": "table", + "html": "
    AlbedoMetallic RMSE↓Roughness RMSE↓Normals Angular Error↓
    PSNR ↑LPIPS ↓si-PSNR ↑si-LPIPS ↓
    RGB↔X [83]14.30.32319.60.2860.4410.32123.80°
    Ours25.00.20526.70.2040.0390.0785.97°
    Ours (det.)26.00.21927.70.2170.0280.0605.85°
    Ours (image)23.40.21326.00.2090.0660.0986.67°
    Ours (image, det.)24.80.23127.20.2280.0430.0696.17°
    ", + "image_path": "8024706fdb5be8ef6e638774bfd9673b1bf1d76c10243af3710bd3e36c1ea977.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 392, + 53, + 553, + 139 + ], + "blocks": [ + { + "bbox": [ + 55, + 137, + 382, + 159 + ], + "lines": [ + { + "bbox": [ + 55, + 137, + 382, + 159 + ], + "spans": [ + { + "bbox": [ + 55, + 137, + 382, + 159 + ], + "type": "text", + "content": "Table 3. Quantitative evaluation of inverse rendering on SyntheticScenes video dataset. image: per-frame inference as image model. det.: 1-step deterministic inference." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 392, + 53, + 553, + 139 + ], + "lines": [ + { + "bbox": [ + 392, + 53, + 553, + 139 + ], + "spans": [ + { + "bbox": [ + 392, + 53, + 553, + 139 + ], + "type": "table", + "html": "
    PSNR ↑SSIM ↑LPIPS ↓
    IIW [5]9.70.620.47
    Li et al. [41]12.30.680.52
    Zhu et al. [91]15.90.780.34
    Kocsis et al. [36]17.40.800.22
    RGB↔X [83]16.40.780.19
    Ours (image)21.90.870.17
    Ours (image, det.)22.40.870.19
    ", + "image_path": "477a00d9bc12bce5ddb8658706c9bdb2449cee62121f3ea3fc926550bcfa2dd5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 389, + 141, + 555, + 163 + ], + "lines": [ + { + "bbox": [ + 389, + 141, + 555, + 163 + ], + "spans": [ + { + "bbox": [ + 389, + 141, + 555, + 163 + ], + "type": "text", + "content": "Table 4. Quantitative benchmark of albedo estimation on InteriorVerse dataset [91]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 62, + 169, + 547, + 312 + ], + "blocks": [ + { + "bbox": [ + 62, + 169, + 547, + 312 + ], + "lines": [ + { + "bbox": [ + 62, + 169, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 62, + 169, + 547, + 312 + ], + "type": "image", + "image_path": "f714e5c96958dca31ce42806fef31763c606255598a754ebef022cc7cc1b1b2c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 314, + 555, + 335 + ], + "lines": [ + { + "bbox": [ + 55, + 314, + 555, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 555, + 335 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of forward rendering. Our method generates high-quality inter-reflections (top) and shadows (bottom), producing more accurate results than the neural baselines." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 62, + 337, + 545, + 469 + ], + "blocks": [ + { + "bbox": [ + 62, + 337, + 545, + 469 + ], + "lines": [ + { + "bbox": [ + 62, + 337, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 62, + 337, + 545, + 469 + ], + "type": "image", + "image_path": "b14b7179cca42db2aef87be3f0e99cb8b8ab22cb5448ed147d8516e39e30cade.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 471, + 555, + 506 + ], + "lines": [ + { + "bbox": [ + 55, + 471, + 555, + 506 + ], + "spans": [ + { + "bbox": [ + 55, + 471, + 555, + 506 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison of inverse rendering. We compare with RGB " + }, + { + "bbox": [ + 55, + 471, + 555, + 506 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 55, + 471, + 555, + 506 + ], + "type": "text", + "content": " X [83] on DL3DV10k dataset. Both methods work well on indoor scenes, while our method predicts finer details in thin structures and more accurate metallic and roughness channels (top), likely benefiting from our curated training data. As compared to RGB " + }, + { + "bbox": [ + 55, + 471, + 555, + 506 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 55, + 471, + 555, + 506 + ], + "type": "text", + "content": " X, our method generalizes better to outdoor scenes (bottom row)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 513, + 297, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 513, + 297, + 586 + ], + "spans": [ + { + "bbox": [ + 55, + 513, + 297, + 586 + ], + "type": "text", + "content": "Our method consistently outperforms all neural methods on both datasets and performs comparably to classic methods. In real-world editing applications, however, these PBR techniques often face significant limitations due to missing 3D geometry and noisy G-buffers (Fig. 2). Furthermore, SplitSum does not model shadows and inter-reflections." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 594, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 594, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 594, + 297, + 715 + ], + "type": "text", + "content": "Ablation study. We ablate our model design choices in Table 1. While our method generalizes from images to videos, it can treat images as a special case of single-frame videos. To evaluate the benefits introduced by the video model, we compare with an ablated version of our method that performs per-frame inference (Ours, image). The video model consistently improves rendering quality across both datasets. In the ablated variant Ours (w/o env. encoder), we concatenate the VAE encoded environment maps directly to the image channels [30] rather than using a separate environment map" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 513, + 556, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 513, + 556, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 513, + 556, + 586 + ], + "type": "text", + "content": "encoder. We demonstrate that a dedicated environment map encoder improves performance. For Ours (+ shading cond.), we include split-sum shading buffers as a conditioning input, following [17]. However, we observed no significant improvement with this addition and chose to exclude it from our final method for simplicity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 588, + 491, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 588, + 491, + 601 + ], + "spans": [ + { + "bbox": [ + 313, + 588, + 491, + 601 + ], + "type": "text", + "content": "5.3. Evaluation of Inverse Rendering" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 604, + 556, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 604, + 556, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 604, + 556, + 688 + ], + "type": "text", + "content": "We quantitatively compare our method with baseline methods on SyntheticScenes in Table 3 and InteriorVerse [91] benchmark in Table 4. Our methods consistently outperforms baseline methods in both datasets, indicating the effectiveness of our data curation workflow and method designs. We show a qualitative comparison with RGB " + }, + { + "bbox": [ + 313, + 604, + 556, + 688 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 313, + 604, + 556, + 688 + ], + "type": "text", + "content": " X [83] on DL3DV10k [47] dataset in Fig. 5." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 556, + 715 + ], + "type": "text", + "content": "Image vs. video model. Comparing Ours (image) and Ours, the video model consistently enhances the quality of" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26075" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 56, + 292, + 171 + ], + "blocks": [ + { + "bbox": [ + 59, + 56, + 292, + 171 + ], + "lines": [ + { + "bbox": [ + 59, + 56, + 292, + 171 + ], + "spans": [ + { + "bbox": [ + 59, + 56, + 292, + 171 + ], + "type": "image", + "image_path": "67baf571f70d4722d12966a2e377b1b8a32707f395a7b0067a0ceec66ee609c6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 172, + 295, + 194 + ], + "lines": [ + { + "bbox": [ + 55, + 172, + 295, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 172, + 295, + 194 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison of relighting. Our method produces more accurate specular reflections compared to the baselines." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 207, + 290, + 258 + ], + "blocks": [ + { + "bbox": [ + 57, + 197, + 292, + 206 + ], + "lines": [ + { + "bbox": [ + 57, + 197, + 292, + 206 + ], + "spans": [ + { + "bbox": [ + 57, + 197, + 292, + 206 + ], + "type": "text", + "content": "Input Image & Tgt. Light Ours Ours (Synth.) Ours (w/o LoRA)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 59, + 207, + 290, + 258 + ], + "lines": [ + { + "bbox": [ + 59, + 207, + 290, + 258 + ], + "spans": [ + { + "bbox": [ + 59, + 207, + 290, + 258 + ], + "type": "image", + "image_path": "7893d232d0e018fb50523c0347a7da5957fa6de6bf90c204c13c6440f2d4e06e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 260, + 295, + 293 + ], + "lines": [ + { + "bbox": [ + 55, + 260, + 295, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 260, + 295, + 293 + ], + "type": "text", + "content": "Figure 7. Qualitative ablation of relighting. Joint training with real-world data and adding LoRA during training significantly improve relighting quality for real-world scenes." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 305, + 295, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 305, + 295, + 389 + ], + "spans": [ + { + "bbox": [ + 54, + 305, + 295, + 389 + ], + "type": "text", + "content": "inverse rendering across all attributes. Notably, for properties associated with specular materials, the video model reduces RMSE by " + }, + { + "bbox": [ + 54, + 305, + 295, + 389 + ], + "type": "inline_equation", + "content": "41\\%" + }, + { + "bbox": [ + 54, + 305, + 295, + 389 + ], + "type": "text", + "content": " for metallic (from 0.066 to 0.039) and " + }, + { + "bbox": [ + 54, + 305, + 295, + 389 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 54, + 305, + 295, + 389 + ], + "type": "text", + "content": " for roughness (from 0.098 to 0.078) compared to the image model. This suggests that the model learns to leverage view changes in video data, effectively capturing view-dependent effects to predict specular properties more accurately." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 391, + 295, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 391, + 295, + 607 + ], + "spans": [ + { + "bbox": [ + 55, + 391, + 295, + 607 + ], + "type": "text", + "content": "One-step deterministic fine-tuning. We also ablate the design choice of 1-step deterministic fine-tuning in Table 3 and 4. By default, the inverse renderer performs 20 denoising steps during inference. Building on recent findings in image diffusion models [51], we demonstrate that strongly conditioned video diffusion models can also be fine-tuned as 1-step deterministic models. Despite the significantly reduced computational cost, we observe that 1-step models consistently produce more \"accurate\" predictions and outperform multi-step stochastic models in photometric evaluations such as PSNR scores. However, the 1-step model enforces deterministic output, which can result in blurrier predictions for ambiguous regions with high-frequency details, thus yielding lower perceptual metrics, such as LPIPS. For neural forward rendering and relighting tasks, we use multi-step stochastic models to capture more realistic details, though we note that 1-step models can be a competitive choice for error-sensitive tasks and enhancing runtime efficiency." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 611, + 194, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 611, + 194, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 611, + 194, + 624 + ], + "type": "text", + "content": "5.4. Evaluation of Relighting" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 628, + 295, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 295, + 698 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 295, + 698 + ], + "type": "text", + "content": "In Table 2 and Fig. 6, we compare with recent state-of-the-art relighting methods DiLightNet [82] and Neural Gaffer [30]. Our method outperforms these baselines, particularly in scenes with complex shadows and inter-reflections. Overall, it produces high-quality lighting effects and more accurate color and scale." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 701, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 296, + 713 + ], + "type": "text", + "content": "Ablation study. We ablate the design choices of synthetic-" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 316, + 56, + 552, + 144 + ], + "blocks": [ + { + "bbox": [ + 316, + 56, + 552, + 144 + ], + "lines": [ + { + "bbox": [ + 316, + 56, + 552, + 144 + ], + "spans": [ + { + "bbox": [ + 316, + 56, + 552, + 144 + ], + "type": "image", + "image_path": "9aad6c557ab31133cfe695913fe5de772221640af3e1db222e44cc677cdbe4df.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 146, + 555, + 179 + ], + "lines": [ + { + "bbox": [ + 313, + 146, + 555, + 179 + ], + "spans": [ + { + "bbox": [ + 313, + 146, + 555, + 179 + ], + "type": "text", + "content": "Figure 8. Image editing applications. Top: Realistic material editing, adjusting the sphere's roughness and the horse's metallic. Bottom: Object insertion of a bathtub and table into scene images." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 186, + 555, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 186, + 555, + 307 + ], + "spans": [ + { + "bbox": [ + 313, + 186, + 555, + 307 + ], + "type": "text", + "content": "real joint training in Fig. 7. While synthetic data provides accurate supervision signals, it is limited to a specific domain and lacks the diversity and complexity found in real-world data. When training exclusively on synthetic data (Ours Synth.), the model struggles with complex structures, such as trees, which are rarely represented in synthetic datasets. Since the real-world auto-labels are estimated using inverse rendering models and contain imperfections, we find that incorporating a LoRA [27] during training with real data consistently improves visual quality." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 312, + 397, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 312, + 397, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 312, + 397, + 324 + ], + "type": "text", + "content": "5.5. Applications" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 328, + 555, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 328, + 555, + 424 + ], + "spans": [ + { + "bbox": [ + 313, + 328, + 555, + 424 + ], + "type": "text", + "content": "We show material editing and object insertion applications in Fig. 8. In the top row, we adjust the sphere's roughness from 0.15 to 0.6 and increase the horse's metallic property from 0 to 1, achieving photorealistic material edits. In the bottom row, we insert a bathtub and table in the G-buffer space of the input image, and use our forward renderer to produce the edited result. The inserted objects blend naturally into the scene, generating realistic reflections and shadows." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 430, + 384, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 430, + 384, + 441 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 384, + 441 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 448, + 556, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 448, + 556, + 532 + ], + "spans": [ + { + "bbox": [ + 313, + 448, + 556, + 532 + ], + "type": "text", + "content": "DIFFUSIONRENDERER provides a scalable, data-driven approach to inverse and forward rendering, achieving high-quality G-buffer estimation and photorealistic image generation without relying on explicit path tracing or precise 3D scene representations. Jointly trained on synthetic and auto-labeled real-world data, DIFFUSIONRENDERER consistently outperforms state-of-the-art methods." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 534, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 556, + 713 + ], + "type": "text", + "content": "Limitations and future work. Our method is based on Stable Video Diffusion, which operates offline and would benefit from distillation techniques to improve inference speed. For editing tasks, the inverse and forward rendering models preserve most of the original content but may introduce slight variations in color or texture. Future work could explore task-specific fine-tuning [37] and develop neural intrinsic features to enhance content consistency and handle more complex visual effects. Additionally, our real-world auto-labeling currently adopts off-the-shelf lighting estimation model [61] which could benefit from better accuracy and robustness. With rapid advancements in video diffusion models [1] toward higher quality and faster inference speeds, we are optimistic that DIFFUSIONRENDERER will inspire future research in high-quality image synthesis and editing." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "26076" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 133 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 133 + ], + "type": "text", + "content": "Acknowledgments. The authors thank Shiqiu Liu, Yichen Sheng, and Michael Kass for their insightful discussions that contributed to this project. 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ACM, 2022. 5, 6, 7" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "26080" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/a8e48178-d4e9-44cb-a83c-4fab97048f04_content_list.json b/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/a8e48178-d4e9-44cb-a83c-4fab97048f04_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f88cadb944556b799e1a2be067f4a08c5a37dc17 --- /dev/null +++ b/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/a8e48178-d4e9-44cb-a83c-4fab97048f04_content_list.json @@ -0,0 +1,1228 @@ +[ + { + "type": "text", + "text": "Diffusion Self-Distillation for Zero-Shot Customized Image Generation", + "text_level": 1, + "bbox": [ + 140, + 130, + 854, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shengqu Cai Eric Ryan Chan Yunzhi Zhang Leonidas Guibas Jiajun Wu Gordon Wetzstein Stanford University", + "bbox": [ + 303, + 180, + 710, + 233 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c0e9c5235eff5600f63d275d09620e3107a1bcea982d6a77f3d5fffc369c0769.jpg", + "image_caption": [ + "Figure 1. Given an input image, Diffusion Self-Distillation is a novel diffusion-based approach that generates diverse images that maintain the input's identity across various contexts. Unlike prior approaches that require fine-tuning or are limited to specific domains, Diffusion Self-Distillation offers instant customization without any additional inference-stage training, enabling precise control and editability in text-to-image diffusion models. This ability makes Diffusion Self-Distillation a valuable tool for general AI content creation." + ], + "image_footnote": [], + "bbox": [ + 94, + 261, + 901, + 472 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 556, + 326, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-image diffusion models produce impressive results but are frustrating tools for artists who desire fine-grained control. For example, a common use case is to create images of a specific concept in novel contexts, i.e., \"identity-preserving generation\". This setting, along with many other tasks (e.g., relighting), is a natural fit for image+text-conditional generative models. However, there is insufficient high-quality paired data to train such a model directly. We propose Diffusion Self-Distillation, a method for using a pre-trained text-to-image model to generate its own dataset for text-conditioned image-to-image tasks. We first leverage a text-to-image diffusion model's in-context generation ability to create grids of images and curate a large paired dataset with the help of a vision-language model. We then fine-tune the text-to-image model into a text+image-to-image model using the curated paired dataset. We demonstrate that Diffusion Self-Distillation outperforms existing zero-shot methods and is competitive with per-instance tuning techniques on a wide range of identity-preserving generation tasks, without requiring test-time optimization. Project page: primecai.github.io/dsd.", + "bbox": [ + 86, + 584, + 485, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 514, + 556, + 643, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, text-to-image diffusion models [26, 31, 32, 35] have set new standards in image synthesis, generating high-quality and diverse images from textual prompts. However, while their ability to generate images from text is impressive, these models often fall short in offering precise control, editability, and consistency—key features that are crucial for real-world applications. Text input alone can be insufficient to convey specific details, leading to variations that may not fully align with the user's intent, especially in scenarios that require faithful adaptation of a character or asset's identity across different contexts.", + "bbox": [ + 509, + 582, + 906, + 747 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Maintaining the instance's identity is challenging, however. We distinguish structure-preserving edits, in which the target and source image share the general layout, but may differ in style, texture, or other local features, and identity-preserving edits, where assets are recognizably the same across target and source images despite potentially largescale changes in image structure (Fig. 3). The latter task is a superset of the former and requires the model to have a significantly more profound understanding of the input image and concepts to extract and customize the desired", + "bbox": [ + 509, + 750, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 808, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18434", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/861fbabdfbbdffe49dc66f1a12947b257de75a6fd9895de1d5cf4c445db23030.jpg", + "image_caption": [ + "Figure 2. Overview of our pipeline. Left: the top shows our vanilla paired data generation wheel (Sec. 3.1). We first sample reference image captions from the LAION [36] dataset. These reference captions are parsed through an LLM to be translated into identity-preserved grid generation prompts (Sec. 3.1.2). We feed these enhanced prompts to a pretrained text-to-image diffusion model to sample potentially identity-preserved grids of images, which are then cropped and composed into vanilla image pairs (Sec. 3.1.1). On the bottom, we show our data curation pipeline (Sec. 3.1.3), where the vanilla image paired are fed into a VLM to classify whether they depict identical main subjects. This process mimics a human annotation/curation process while being fully automatic; we use the curated data as our final training data. Right: we extend the diffusion transformer model into an image-conditioned framework by treating the input image as the first frame of a two-frame sequence. The model generates both frames simultaneously—the first reconstructs the input, while the second is the edited output—allowing effective information exchange between the conditioning image and the desired output." + ], + "image_footnote": [], + "bbox": [ + 96, + 87, + 604, + 340 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b0389e6cdac94a7b94869f8a14d148ed65bc1b75fe78c43f16d144d4d95744d8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 612, + 87, + 901, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "identity. For example, image editing [3, 24, 48], such as local content editing, re-lighting, and semantic image synthesis, etc. are all structure-preserving and identity-preserving edits, but novel-view synthesis and character-consistent generation under pose variations, are identity-preserving but not structure-preserving. We aim to address the general case, maintaining identity without constraining structure.", + "bbox": [ + 89, + 479, + 482, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For structure-preserving edits, adding layers, as in ControlNet [48], introduces spatial conditioning controls but is limited to structure guidance and does not address consistent identity adaptation across diverse contexts. For identity-preserving edits, fine-tuning methods such as Dream-Booth [34] and LoRA [15] can improve consistency using a few reference samples but are time consuming and computationally intensive, requiring training for each reference. Zero-shot alternatives like IP-Adapter [46] and InstantID [41] offer faster solutions without the need for retraining but fall short in providing the desired level of consistency and customization; IP-Adapter [46] lacks full customization capabilities, and InstantID [41] is restricted to facial identity.", + "bbox": [ + 89, + 592, + 482, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel approach called Diffusion Self-Distillation, designed to address the core challenge of zero-shot instant customization and adaptation of any character or asset in text-to-image diffusion models. We identify the primary obstacle that hinders prior methods, such as IP-Adapter [46] and InstantID [41], from achieving better identity preservation or generalizing beyond facial", + "bbox": [ + 89, + 795, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "contexts: the absence of large-scale paired datasets and corresponding supervised identity-preserving training pipelines. With recent advancements in foundational model capabilities, we are now positioned to exploit these strengths further. Specifically, we can generate consistent grids of identical characters or assets, opening a new pathway for customization that eliminates the need for pre-existing, handcrafted paired datasets—which are expensive and time consuming to collect. The ability to generate these consistent grids likely emerged from foundational model training on diverse datasets, including photo albums, mangas, and comics. Our approach harnesses Vision-Language Models (VLMs) to automatically curate many generated grids, producing a diverse set of grid images with consistent identity features across various contexts. This curated synthetic dataset then serves as the foundation for fine-tuning and adapting any identity, transforming the task of zero-shot customized image generation from unsupervised to supervised. Diffusion Self-Distillation offers transformative potential for applications like consistent character generation, camera control, relighting, and asset customization in fields such as comics and digital art. This flexibility allows artists to rapidly iterate and adapt their work, reducing effort and enhancing creative freedom, making Diffusion Self-Distillation a valuable tool for AI-generated content.", + "bbox": [ + 511, + 479, + 906, + 857 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions as follows:", + "bbox": [ + 532, + 864, + 823, + 878 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose Diffusion Self-Distillation, a zero-shot", + "bbox": [ + 513, + 885, + 906, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18435", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f46eaefb23afdf189a7ede14e6c86c99c86a5896c27045a36d662f3759e94b5e.jpg", + "image_caption": [ + "Figure 3. Difference between structure-preserving and identity-preserving edits. In structure-preserving editing, the main structures of the image are preserved, and only local edits or stylizations are performed. In identity-preserving editing, the global structure of the image may change radically." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 480, + 170 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "identity-preserving customized image generation model that scales to any instance under any context, with performances on par with inference-stage tuning methods;", + "bbox": [ + 102, + 277, + 483, + 321 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We provide a self-distillation pipeline to obtain identity-preserving data pairs purely from pretrained text-to-image diffusion models, LLMs, and VLMs, without any human effort involved in the entire data creation wheel;", + "- We correspondingly design a unified architecture for image-to-image translation tasks involving both identity- and structure-preserving edits, including personalization, relighting, depth controls, and instruction following." + ], + "bbox": [ + 89, + 321, + 483, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 89, + 457, + 228, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent advancements in diffusion models have underscored the need for enhanced control and customization in image-generation tasks. Various methods have been proposed to address these challenges through additional conditioning mechanisms, personalization, and rapid adaptation [28].", + "bbox": [ + 89, + 482, + 483, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Control Mechanisms in Diffusion Models. To move beyond purely text-based controls, approaches like ControlNet [48] introduce spatial conditioning via inputs such as sketches, depth maps, and segmentation masks, enabling fine-grained structure control. ControlNet++ [21] refines this by enhancing the integration of spatial inputs for more nuanced control. Uni-ControlNet [49] unifies various control types within a single framework, standardizing the handling of diverse signals. T2I-Adapter [25] employs lightweight adapters to align pretrained models with external control signals without altering the core architecture. While these methods offer increased flexibility, they often focus on structural conditioning types such as depths and lack capabilities for concept extraction or identity preservation.", + "bbox": [ + 89, + 570, + 483, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Personalization and Fine-Tuning. Techniques like Dream-Booth [34] and LoRA [15] enhance the consistency and relevance of generated images by fine-tuning models with small sets of reference images. DreamBooth [34] personalizes models to maintain a subject's identity across different contexts, while LoRA [15] provides an efficient approach to fine-tuning large models without extensive retraining. How", + "bbox": [ + 89, + 794, + 485, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ever, these methods require multiple images and test-time optimization for each reference, which can be computationally expensive—especially with the exponential growth in model sizes (12 billion parameters for FLUX).", + "bbox": [ + 511, + 90, + 906, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Zero-Shot and Fast Adaptation. IP-Adapter [46] incorporates image prompts into diffusion models using image embeddings, allowing for generations that align closely with reference visuals. InstantID [41] ensures zero-shot face preservation, maintaining a subject's key features across various contexts. While effective as zero-shot methods without user training, IP-Adapter [46] struggles to adapt specific targets like unique characters or assets, and InstantID [41] is limited to facial identity preservation. IPAdapter-Instruct [33] enhances image-based conditioning with instruct prompts but relies heavily on specific instructions and task-specific pretrained models. Other methods, such as SuTI [8] and GDT [17], handcrafted corresponding datasets, which are expensive and challenging to collect and scale. Another work along this line is Subject-Diffusion [23], which uses segmentation masks to create synthetic data for training but is bounded by achieving only simple attributes and accessories copying and editing within input images. Other methods [1, 11, 29, 40, 47] also investigated synthetic pairwise data generation but often fell short in scale because of the manual effort involved.", + "bbox": [ + 511, + 167, + 908, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing methods contribute valuable advancements but often target specific domains or require user-stage tuning. Diffusion Self-Distillation bridges these gaps by offering a unified, zero-shot approach for consistent customization of characters and assets using minimal input. By leveraging self-distillation assisted by vision-language models, Diffusion Self-Distillation provides a comprehensive and adaptable solution for a wide range of creative applications.", + "bbox": [ + 511, + 487, + 908, + 608 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Diffusion Self-Distillation", + "text_level": 1, + "bbox": [ + 511, + 630, + 751, + 646 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We discover that recent text-to-image generation models offer the surprising ability to generate in-context, consistent image grids (see Fig. 2, left). Motivated by this insight, we develop a zero-shot adaptation network that offers fast, diverse, high-quality, and identity-preserving, i.e., consistent image generation conditioned on a reference image. For this purpose, we first generate and curate sets of images that exhibit the desired consistency using pretrained text-to-image diffusion models, large language models (LLMs), and vision-language models (VLMs) (Sec. 3.1). Then, we finetune the same pretrained diffusion model with these consistent image sets, employing our newly proposed parallel processing architecture (Sec. 3.2) to create a conditional model. By this end, Diffusion Self-Distillation finetunes a pretrained text-to-image diffusion model into a zero-shot customized image generator in a supervised manner.", + "bbox": [ + 511, + 659, + 908, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18436", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Generating a Pairwise Dataset", + "text_level": 1, + "bbox": [ + 89, + 90, + 359, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To create a pairwise dataset for supervised Diffusion Self-Distillation training, we leverage the emerging multi-image generation capabilities of pretrained text-to-image diffusion models to produce potentially consistent vanilla images (Sec. 3.1.1) created by LLM-generated prompts (Sec. 3.1.2). We then use VLMs to curate these vanilla samples, obtaining clean sets of images that share the desired identity consistency (Sec. 3.1.3). The data generation and curation pipeline is shown in Fig. 2, left.", + "bbox": [ + 89, + 112, + 483, + 248 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.1. Vanilla Data Generation via Teacher Model", + "text_level": 1, + "bbox": [ + 89, + 255, + 439, + 270 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To generate sets of images that fulfill the desired identity preservation, we prompt the teacher pretrained text-to-image diffusion model to create images containing multiple panels featuring the same subject with variations in expression, pose, lighting conditions, and more, for training purposes. Such prompting can be as simple as specifying the desired identity preservation in the output, such as \"a grid of 4 images representing the same $<$ object/character/scene/etc. >\", \"an evenly separated 4 panels, depicting identical $<$ object/character/scene/etc. >\", etc. We additionally specify the expected content in each sub-image/panel. The full set of prompts is provided in our supplemental material Sec. A. Our analysis shows that current state-of-the-art text-to-image diffusion models (e.g., SD3 [9], DALL-E 3, FLUX) demonstrate this identity-preserving capability, likely emerging from their training data, which includes comics, mangas, photo albums, and video frames. Such in-context generation ability is crucial to our data generation wheel.", + "bbox": [ + 91, + 273, + 483, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.2. Prompt Generation via LLMs", + "text_level": 1, + "bbox": [ + 89, + 568, + 344, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We rely on an LLM to \"brainstorm\" a large dataset of diverse prompts, from which we derive our image grid dataset. By defining a prompt structure, we prompt the LLM to produce text prompts that describe image grids. A challenge we encountered is that when prompted to create large sets of prompts, LLMs tend to produce prompts of low diversity. For example, we noticed that without additional guidance, GPT-4o has a strong preference for prompts with cars and robots, resulting in highly repetitive outputs. To address this issue, we utilize the available image captions in the LAION [36] dataset, feeding them into the LLM as content references. These references from real image captions dramatically improve the diversity of generated prompts. Optionally, we also use the LLM to filter these reference captions, ensuring they contain a clear target for identity preservation. We find that this significantly improves the hit rate of generating consistent multi-image outputs.", + "bbox": [ + 89, + 587, + 483, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.3. Dataset Curation and Caption with VLMs", + "text_level": 1, + "bbox": [ + 89, + 851, + 429, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the aforementioned data generation scheme provides identity-preserving multi-image samples of decent quality", + "bbox": [ + 89, + 869, + 483, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and quantity, these initial \"uncurated\" images tend to be noisy and unsuitable for direct use. Therefore, we leverage the strong capabilities of VLMs to curate a clean dataset. We extract pairs of images from the generated samples intended to preserve the identity and ask the VLM whether the two images depict the same object, character, scene, etc. We find that employing Chain-of-Thought prompting [42] is particularly helpful in this context. Specifically, we first prompt the VLM to identify the common object, character, or scene present in both images, then have it describe each one in detail, and finally analyze whether they are identical, providing a conclusive response. This process yields pairs of images that share the same identity.", + "bbox": [ + 511, + 90, + 906, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Parallel Processing Architecture", + "text_level": 1, + "bbox": [ + 511, + 297, + 797, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We desire a conditional architecture suitable for general image-to-image tasks, including transformations in which structure is preserved, and transformations in which concepts/identities are preserved but image structure is not. This is a challenging problem because it may necessitate the transfer of fine details without guaranteeing spatial correspondences. While the ControlNet [48] architecture is excellent at structure-preserving edits, such as depth-to-image or segmentation-map-to-image, it struggles to preserve details under more complex identity-preserving edits, where the source and target images are not pixel-aligned. On the other hand, IP-Adapter [46] can extract certain concepts, such as styles, from the input image. Still, it strongly relies on a task-specific image encoder and often fails to preserve more complex concepts and identities. Drawing inspiration from the success of multi-view and video diffusion models [2, 4–6, 12–14, 16, 18, 20, 37, 38, 43, 45], we propose a simple yet effective method to extend the vanilla diffusion transformer model into an image-conditioned diffusion model. Specifically, we treat the input image as the first frame of a video and produce a two-frame video as output. The final loss is computed over the two-frame video, establishing an identity mapping for the first frame and a conditionally editing target for the second frame. Our architecture design allows generality for generic image-to-image translation tasks, since it enables effective information exchange between the two frames, allowing the model to capture complex semantics and perform sophisticated edits, as shown in Fig. 2, right.", + "bbox": [ + 511, + 320, + 908, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 756, + 643, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Implementation details. We use FLUX1.0 DEV as both our teacher and student models, achieving self-distillation. For prompt generation, we use GPT-4o; for dataset curation and captioning, we use Gemini-1.5. We train all models on 8 NVIDIA H100 80GB GPUs with an effective batch size of 160 for 100k iterations, using AdamW optimizer [22] with a learning rate $10^{-4}$ . Our parallel processing architecture uses", + "bbox": [ + 511, + 794, + 908, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18437", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/63af7ebf150e84f622cad33d6277aa4c319ea15202177de26bb810679c0c29ea.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison. Overall, our method achieves high subject identity preservation and prompt-aligned diversity while not suffering from a \"copy-paste\" effect, such as the results of IP-Adapter+ [46]. This is largely thanks to our supervised training pipeline, which alleviates the base model's in-context generation ability." + ], + "image_footnote": [], + "bbox": [ + 96, + 88, + 901, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LoRAs with rank 512 on the base model.", + "bbox": [ + 89, + 544, + 364, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Our final training dataset contains $\\sim 400\\mathrm{k}$ subject-consistent image pairs generated from our teacher model, FLUX1.0 DEV. Generating and curating the dataset is fully automated and requires no human effort, so its size could be further scaled. We use the publicly available DreamBench++ [27] dataset and follow their protocols for evaluation. DreamBench++ [27] is a comprehensive and diverse dataset for evaluating personalized image generation, consisting of 150 high-quality images and 1,350 prompts—significantly more than previous benchmarks like DreamBench [34]. The dataset covers various categories such as animals, humans, objects, etc., including photorealistic and non-photorealistic images, with prompts designed to span different difficulty levels (simple/imaginative). In contrast, prompts are generated using GPT-4o and refined by human annotators to ensure diversity and ethical compliance.", + "bbox": [ + 89, + 579, + 485, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We follow the setups in DreamBench++ [27] and compare our model with two classes of baselines: inference-stage tuning models and zero-shot models. For inference-stage models, we compare against Textual Inversion [10],", + "bbox": [ + 89, + 839, + 485, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DreamBooth [34] and its LoRA [15] version. For zero-shot models, we compare with BLIP-Diffusion [19], Emu2 [39], IP-Adapter [46], IP-Adapter+ [46].", + "bbox": [ + 511, + 544, + 908, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. The evaluation protocol of prior works [8, 33, 34, 46] typically involves comparing the CLIP [30] and DINO [7] feature similarities. However, we note that the metrics mentioned above capture only global semantic similarity, are extremely noisy, and are biased towards \"copy-pasting\" the input image. This is especially troublesome when the input image or the prompt is complex. We refer to DreamBench++ [27] for a detailed analysis of their limitations. Therefore, we follow the metrics designed in DreamBench++ [27] and report GPT-4o scores on the more diverse DreamBench++ [27] benchmark for both concept preservation (CP) with different categories of subjects and prompt following (PF) with photorealistic (Real.) and Imaginative (Imag.) prompts, then use their product as a final evaluation score. This evaluation protocol emulates a human user study using VLMs. We additionally slightly modify the GPT evaluation prompts so that penalization can be applied if the generated contents show no internal understanding and creative output but instead naively copy over", + "bbox": [ + 511, + 613, + 908, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18438", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e7186bc7d9913c78370951b459575d4b7408ed2410ffd4d996b8575f5b58501b.jpg", + "image_caption": [ + "Character Preservation", + "Figure 5. Qualitative result. Our Diffusion Self-Distillation is capable of various customization targets across different tasks and styles, for instance, characters or objects, photorealistic or animated. Diffusion Self-Distillation can also take instruction types of prompts as input, similar to InstructPix2Pix [3]. Further, our model exhibits relighting capabilities without significantly altering the scene's content." + ], + "image_footnote": [], + "bbox": [ + 96, + 102, + 901, + 714 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "components from the reference image. The modified metrics are named \"de-biased concept preservation (Debiased CP)\" and \"de-biased prompt following (Debiased PF)\". The full set of GPT evaluation prompts will be provided in our supplementary Sec. B.", + "bbox": [ + 89, + 767, + 485, + 843 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative results. Fig. 4 presents our qualitative comparison results, demonstrating that our model significantly outperforms all baselines in subject adaptation and concept", + "bbox": [ + 89, + 854, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "consistency while exhibiting excellent prompt alignment and diversity in the outputs. Textual Inversion [10], as an early concept extraction method, captures only vague semantics from the input image, making it unsuitable for zero-shot customization tasks that require precise subject adaptation. DreamBooth [34] and DreamBooth-LoRA [15, 34] face challenges in maintaining consistency, primarily because they perform better with multiple input images. This dependency", + "bbox": [ + 511, + 767, + 908, + 890 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18439", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f6da2918db03a5e39408b53e448c3e5ed1165e1e30f57e57923936634a086839.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Quantitative result. On the human-aligned GPT score metrics, our method is only inferior to IP-Adapter+ [46] for concept preservation (largely because of IP-Adapter families' \"copy-pasting\" effect) and the tuning-base DreamBooth-LoRA [15, 34] for prompt following, but outperforms every other baseline, achieving the best overall performance considering both concept preservation and prompt following. We also note that on the de-biased GPT evaluation, which penalizes \"copy-pasting\" the reference image without significant creative interpretation or transformation, the advantages of IP-Adaper+ [46] no longer hold. This can also be partly observed by their bad prompt following scores, meaning they are biased towards the reference input and are not accommodating the input prompt. The first, second, and third values are highlighted, where Diffusion Self-Distillation is the best overall performing model." + ], + "table_body": "
    MethodConcept PreservationPrompt FollowingDebiased Concept PreservationDebiased Prompt Following
    Z-S?Animal↑Human↑Object↑Overall↑Real.↑Imag.↑Overall↑CP-PF↑Animal↑Human↑Object↑Overall↑Real.↑Imag.↑Overall↑
    Textual Inversion✘0.5020.3580.3050.3880.6710.4370.5980.2320.7410.6940.7170.7220.6190.3850.541
    DreamBooth✘0.6400.1990.4880.4420.7980.5040.6920.3060.6700.3620.6760.6260.7500.4670.656
    DreamBooth LoRA✘0.7510.3110.5430.5350.8980.7540.8490.4500.6810.6750.7610.7200.8650.7180.816
    BLIP-Diffusion✓0.6370.5570.4690.5540.5810.3030.4640.2570.7710.7330.7450.7500.5290.2660.442
    Emu2✓0.6700.5460.4470.5540.7320.5600.6700.3710.6520.6830.7010.6810.6860.4940.622
    IP-Adapter✓0.6670.5580.5040.5760.7430.4460.6070.3500.7900.7640.7430.7660.6950.3770.589
    IP-Adapter+✓0.9000.8450.7590.8340.5020.2790.3880.3240.4810.4730.5300.5040.4420.2290.371
    Ours✓0.6470.5670.6400.6310.7770.6250.7260.4580.8520.7740.7500.7890.8080.6810.757
    ", + "bbox": [ + 91, + 89, + 906, + 212 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "limits their effectiveness when only a single reference image is available. In contrast, our method achieves robust results even with just one input image, highlighting its efficiency and practicality. BLIP-Diffusion [19], operating as a self-supervised representation learning framework, can extract concepts from the input in a zero-shot manner but is confined to capturing overall semantic concepts without the ability to customize specific subjects. Similarly, Emu2 [39], a multimodal foundation model, excels at extracting semantic concepts but lacks mechanisms for specific subject customization, limiting its utility in personalized image generation. IP-Adapter [46] and IP-Adapter+ [46] employ self-supervised learning schemes aimed at reconstructing the input from encoded signals. While effective in extracting global concepts, they suffer from a pronounced \"copy-paste\" effect, where the generated images closely resemble the input without meaningful transformation. Notably, IP-Adapter+ [46], which utilizes a stronger input image encoder, exacerbates this issue, leading to less diversity and adaptability in the outputs. In contrast, our approach effectively preserves the subject's core identity while enabling diverse and contextually appropriate transformations. As illustrated in Fig. 5, our Diffusion Self-Distillation demonstrates remarkable versatility, adeptly handling various customization targets across different targets (characters, objects, etc.) and styles (photorealistic, animated, etc.). Moreover, Diffusion Self-Distillation generalizes well to a wide range of prompts, including instructions similar to InstructPix2Pix [3], underscoring its robustness and adaptability in diverse customization tasks.", + "bbox": [ + 91, + 323, + 485, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative results. Quantitative comparison with the baselines are shown in Tab. 1, where we report GPT evaluation following DreamBench++ [27]. Such an evaluation protocol is similar to human score but uses automatic multimodal LLMs. Our method achieves the best overall performances accommodating both concept preservation and prompt following, while only being inferior to IP-Adapter+ [46] for the former (mainly because of", + "bbox": [ + 89, + 780, + 485, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the \"copy-paste\" effect again), and the per-instance tuning DreamBooth-LoRA [15, 34] for the latter. We note that the concept preservation evaluation of DreamBench++ [27] is still biased towards favoring a \"copy-paste\" effect, especially on more challenging and diverse prompts. For instance, the outstanding concept preservation performances of the IP-Adapter family [46] are primarily because of their strong \"copy-paste\" effect, which copies over the input image without considering relevant essential changes in the prompts. This can also be partly observed by their underperforming prompt following scores, which means they are biased towards the reference input and do not accommodate the input prompt. Therefore, we also present our \"de-biased\" version of GPT scores, which are as simple as telling GPT to penalize if the generated image resembles a direct copy of the reference image. We observe that the advantages of IP-Adaper+ [46] no longer hold. Overall, Diffusion Self-Distillation is the best-performing model.", + "bbox": [ + 511, + 323, + 908, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation studies. (1) Data curation: During dataset generation, we first synthesize grids using a frozen pre-trained FLUX model and then filter the images via VLM curation. Why not fine-tune the FLUX model on image grids to improve the hit rate? To study this, we fit a LoRA [15] using $>7000$ consistent grids (Fig. 6, left). Though a more significant proportion of samples are consistent grids, we find that the teacher model loses diversity in its output. Therefore, we choose to rely entirely on VLMs to help us curate from large numbers of diverse but potentially noisy grids. (2) Parallel processing architecture: We compare the parallel processing architecture to three alternative image-to-image architectures: 1) concatenating the source image to the noise image (\"concatenation\"); 2) a ControlNet [48]-based design, and 3) an IP-Adapter [46]-based design. We train each architecture using the same data as our parallel processing model (Fig. 6, middle). For ControlNet [48], we draw the same conclusion as prior work [16], in that it works best for structure-aligned edits, but generally strug", + "bbox": [ + 511, + 613, + 908, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18440", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4f6ee5730564c79ace5c64222ddd5f2541362561202fb08fbe1fd0ccebd90353.jpg", + "image_caption": [ + "Effect of LoRA for Data Generation", + "No LoRA" + ], + "image_footnote": [], + "bbox": [ + 98, + 103, + 176, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4b1711c89a594c6e04614ee8636175ec65a6f057bd5a5f291e3ba403cd95454f.jpg", + "image_caption": [ + "No LoRA" + ], + "image_footnote": [], + "bbox": [ + 99, + 172, + 173, + 228 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8d6d3d5639c31401c5433b13e505b774a4008b6470c42603d1c6a758a92a10f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 104, + 267, + 160 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b61c2a90aa89c9d5494efbf5e314ee72459b6c1f0032969ce773796fb76cb814.jpg", + "image_caption": [ + "LoRA fitting", + "LoRA fitting" + ], + "image_footnote": [], + "bbox": [ + 191, + 172, + 264, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1813be7e965ecec070425930bbb9982923b2c4f3d1fd7b4eac28557b7f3eed42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 107, + 364, + 160 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3cc92c487c4b482247911edeef4a3d81d08b3d707bfb7f5404b91d96db933dc1.jpg", + "image_caption": [ + "reference" + ], + "image_footnote": [], + "bbox": [ + 276, + 164, + 364, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/71158be9e04e643365263cf4900e18fa555e2011b885227cfb1689e1e1e6593a.jpg", + "image_caption": [ + "Figure 6. Ablation study. Left: We compare the base model's in-context sampling ability with a consistent grid LoRA-overfitted model. We observe that although applying LoRA to the base model can increase the likelihood of outputs being consistent grids, it may adversely affect output diversity. Therefore, we rely on vision-language models (VLMs) to curate from a large number of diverse but potentially noisy grids. Right: We compare our architectural design with a vanilla conditional model (by adding a few input channels), ControlNet [48], and IP-Adapter [46]. Our architecture learns the input concepts and identities significantly better. We also demonstrate that our architecture can effectively scale to depth-conditioned image generation similar to ControlNet [48]." + ], + "image_footnote": [ + "A young woman with brown eyes, shoulder-length dark brown wavy hair, rosy cheeks, wearing a yellow-brown coat over a green sweater and black pants, with a brown backpack, standing in a rainy alleyway with blurred figures in the background." + ], + "bbox": [ + 369, + 107, + 586, + 241 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/82be34914c8e2e83f3284644708d4580ea1c77f4b554729d01b1500d16b1a41f.jpg", + "image_caption": [ + "Comparison of Different Architectures" + ], + "image_footnote": [], + "bbox": [ + 374, + 99, + 578, + 162 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 369, + 191, + 584, + 241 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/db13d74a782a3f963d4ea6e7ae29f34cb12a3406771fe4a271be404114326e60.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 593, + 121, + 648, + 162 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 594, + 179, + 650, + 222 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/62867113117156a8e21204a697f87ce1870cb9943c7f6b35750dc5de38dc2569.jpg", + "image_caption": [], + "image_footnote": [ + "A regal, elderly man with a long white beard and hair, wearing ornate gold and red formal attire, plays a grand piano in a richly decorated room, lit by warm, natural light, camera angle low, focusing on the man's hands on the keys." + ], + "bbox": [ + 655, + 121, + 738, + 164 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 594, + 179, + 650, + 222 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/80f8c6c74cc8bc352b60fbd17e0b85eb0edac2b0d69f43fbb8afa51a0749b26e.jpg", + "image_caption": [], + "image_footnote": [ + "A red four-door sedan parked in front of a brightly lit storefront, with the camera angled slightly towards the driver's side." + ], + "bbox": [ + 655, + 179, + 738, + 222 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/25396dae6244689970b8d7ab5f46eaeee3b152908120540f8d9746e3dd1052ff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodCP ↑PF ↑Creativity ↑
    Textual Inversion [10]1.6931.9242.850
    DreamBooth [34]2.3292.8833.597
    DreamBooth LoRA [15, 34]2.5763.3864.247
    BLIP-Diffusion [19]1.8542.2810.286
    Emu2 [39]1.8432.0962.965
    IP-Adapter [46]2.2742.3073.481
    IP-Adapter+ [46]3.7331.9592.428
    Ours3.6613.3284.453
    ", + "bbox": [ + 94, + 339, + 478, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. User study. “CP” refers to concept preservation scores and “PF” refers to prompt following scores. The first, second, and third values are highlighted. Our user study results mostly align with our GPT evaluation, where our Diffusion Self-Distillation is the best overall performing model.", + "bbox": [ + 89, + 484, + 482, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "gles to preserve details when the source image and target image differ in camera pose. IP-Adapter [46] struggles to effectively transfer details and styles from the source image due to the limited capacity of its image encoder. (3) Other image-to-image tasks: Although not \"self-distillation\", since it requires an externally-sourced paired dataset (generated with Depth Anything [44]), we additionally train our architecture on depth-to-image to demonstrate its utility for more general image-to-image tasks (Fig. 6, right).", + "bbox": [ + 89, + 566, + 483, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "User study. To evaluate the fidelity and prompt consistency of our generated images, we conducted a user study on a random subset of the DreamBench++ [27] test cases, selecting 20 samples. A total of 25 female and 29 male annotators, aged from 22 to 78 (average 34), independently scored each image from 1 to 5 based on three criteria: (1) concept preservation—the consistency with the reference image, (2) prompt alignment—the consistency with the given prompt, and (3) creativity—the level of internal understanding and transformation. The average scores are presented in Tab. 2. Our human annotations closely align with the GPT evaluation, demonstrating that our Diffusion Self-Distillation is slightly", + "bbox": [ + 89, + 719, + 483, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "behind IP-Adapter+[46] in concept preservation and the inference-stage tuning method DreamBooth-LoRA [15, 34] in prompt alignment. Notably, our model achieved the highest creativity score, while IP-Adapter+ [46] scored lower in this metric due to its \"copy-paste\" effect. These results further confirm that our Diffusion Self-Distillation offers the most balanced and superior overall performance.", + "bbox": [ + 511, + 342, + 906, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 511, + 467, + 625, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present Diffusion Self-Distillation, a zero-shot approach designed to achieve identity adaptation across a wide range of contexts using text-to-image diffusion models without any human effort. Our method effectively transforms zero-shot customized image generation into a supervised task, substantially reducing its difficulty. Empirical evaluations demonstrate that Diffusion Self-Distillation performs comparably to inference-stage tuning techniques while retaining the efficiency of zero-shot methods.", + "bbox": [ + 511, + 494, + 906, + 630 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. Our work focuses on identity-preserving edits of characters, objects, and scene relighting. Future directions could explore additional tasks and use cases. Integration with ControlNet [48], for example, could provide fine-grained and independent control of identity and structure. Additionally, extending our approach from image to video generation is a promising avenue of future work.", + "bbox": [ + 511, + 645, + 908, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethics. We are mindful of the potential misuse, particularly in deepfakes. We oppose exploiting our work for purposes that infringe upon ethical standards or privacy.", + "bbox": [ + 511, + 765, + 905, + 810 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. Our Diffusion Self-Distillation democratizes content creation, enabling identity-preserving, high-quality, and fast customized image generation that adapts seamlessly to evolving foundational models, significantly expanding the creative boundaries of art, design, and digital storytelling.", + "bbox": [ + 511, + 825, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18441", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This project was in part supported by Google, Kaiber AI, 3bodylabs, ONR N00014-23-1-2355, and NSF RI #2211258. ERC was supported by the Nvidia Graduate Fellowship and the Snap Research Fellowship. 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In NeurIPS, 2023. 3" + ], + "bbox": [ + 516, + 92, + 906, + 742 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18443", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/a8e48178-d4e9-44cb-a83c-4fab97048f04_model.json b/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/a8e48178-d4e9-44cb-a83c-4fab97048f04_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f4bb8370af5cb231e0da00d6e741be3f63db619a --- /dev/null +++ b/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/a8e48178-d4e9-44cb-a83c-4fab97048f04_model.json @@ -0,0 +1,1881 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.809, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.142, + 0.131, + 0.856, + 0.152 + ], + "angle": 0, + "content": "Diffusion Self-Distillation for Zero-Shot Customized Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.304, + 0.181, + 0.711, + 0.234 + ], + "angle": 0, + "content": "Shengqu Cai Eric Ryan Chan Yunzhi Zhang Leonidas Guibas Jiajun Wu Gordon Wetzstein Stanford University" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.262, + 0.903, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.478, + 0.907, + 0.534 + ], + "angle": 0, + "content": "Figure 1. Given an input image, Diffusion Self-Distillation is a novel diffusion-based approach that generates diverse images that maintain the input's identity across various contexts. Unlike prior approaches that require fine-tuning or are limited to specific domains, Diffusion Self-Distillation offers instant customization without any additional inference-stage training, enabling precise control and editability in text-to-image diffusion models. This ability makes Diffusion Self-Distillation a valuable tool for general AI content creation." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.558, + 0.327, + 0.573 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.585, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Text-to-image diffusion models produce impressive results but are frustrating tools for artists who desire fine-grained control. For example, a common use case is to create images of a specific concept in novel contexts, i.e., \"identity-preserving generation\". This setting, along with many other tasks (e.g., relighting), is a natural fit for image+text-conditional generative models. However, there is insufficient high-quality paired data to train such a model directly. We propose Diffusion Self-Distillation, a method for using a pre-trained text-to-image model to generate its own dataset for text-conditioned image-to-image tasks. We first leverage a text-to-image diffusion model's in-context generation ability to create grids of images and curate a large paired dataset with the help of a vision-language model. We then fine-tune the text-to-image model into a text+image-to-image model using the curated paired dataset. We demonstrate that Diffusion Self-Distillation outperforms existing zero-shot methods and is competitive with per-instance tuning techniques on a wide range of identity-preserving generation tasks, without requiring test-time optimization. Project page: primecai.github.io/dsd." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.557, + 0.645, + 0.573 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.583, + 0.907, + 0.748 + ], + "angle": 0, + "content": "In recent years, text-to-image diffusion models [26, 31, 32, 35] have set new standards in image synthesis, generating high-quality and diverse images from textual prompts. However, while their ability to generate images from text is impressive, these models often fall short in offering precise control, editability, and consistency—key features that are crucial for real-world applications. Text input alone can be insufficient to convey specific details, leading to variations that may not fully align with the user's intent, especially in scenarios that require faithful adaptation of a character or asset's identity across different contexts." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.75, + 0.909, + 0.901 + ], + "angle": 0, + "content": "Maintaining the instance's identity is challenging, however. We distinguish structure-preserving edits, in which the target and source image share the general layout, but may differ in style, texture, or other local features, and identity-preserving edits, where assets are recognizably the same across target and source images despite potentially largescale changes in image structure (Fig. 3). The latter task is a superset of the former and requires the model to have a significantly more profound understanding of the input image and concepts to extract and customize the desired" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18434" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.088, + 0.605, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.088, + 0.902, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.347, + 0.907, + 0.472 + ], + "angle": 0, + "content": "Figure 2. Overview of our pipeline. Left: the top shows our vanilla paired data generation wheel (Sec. 3.1). We first sample reference image captions from the LAION [36] dataset. These reference captions are parsed through an LLM to be translated into identity-preserved grid generation prompts (Sec. 3.1.2). We feed these enhanced prompts to a pretrained text-to-image diffusion model to sample potentially identity-preserved grids of images, which are then cropped and composed into vanilla image pairs (Sec. 3.1.1). On the bottom, we show our data curation pipeline (Sec. 3.1.3), where the vanilla image paired are fed into a VLM to classify whether they depict identical main subjects. This process mimics a human annotation/curation process while being fully automatic; we use the curated data as our final training data. Right: we extend the diffusion transformer model into an image-conditioned framework by treating the input image as the first frame of a two-frame sequence. The model generates both frames simultaneously—the first reconstructs the input, while the second is the edited output—allowing effective information exchange between the conditioning image and the desired output." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.48, + 0.483, + 0.587 + ], + "angle": 0, + "content": "identity. For example, image editing [3, 24, 48], such as local content editing, re-lighting, and semantic image synthesis, etc. are all structure-preserving and identity-preserving edits, but novel-view synthesis and character-consistent generation under pose variations, are identity-preserving but not structure-preserving. We aim to address the general case, maintaining identity without constraining structure." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.593, + 0.483, + 0.789 + ], + "angle": 0, + "content": "For structure-preserving edits, adding layers, as in ControlNet [48], introduces spatial conditioning controls but is limited to structure guidance and does not address consistent identity adaptation across diverse contexts. For identity-preserving edits, fine-tuning methods such as Dream-Booth [34] and LoRA [15] can improve consistency using a few reference samples but are time consuming and computationally intensive, requiring training for each reference. Zero-shot alternatives like IP-Adapter [46] and InstantID [41] offer faster solutions without the need for retraining but fall short in providing the desired level of consistency and customization; IP-Adapter [46] lacks full customization capabilities, and InstantID [41] is restricted to facial identity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose a novel approach called Diffusion Self-Distillation, designed to address the core challenge of zero-shot instant customization and adaptation of any character or asset in text-to-image diffusion models. We identify the primary obstacle that hinders prior methods, such as IP-Adapter [46] and InstantID [41], from achieving better identity preservation or generalizing beyond facial" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.48, + 0.907, + 0.858 + ], + "angle": 0, + "content": "contexts: the absence of large-scale paired datasets and corresponding supervised identity-preserving training pipelines. With recent advancements in foundational model capabilities, we are now positioned to exploit these strengths further. Specifically, we can generate consistent grids of identical characters or assets, opening a new pathway for customization that eliminates the need for pre-existing, handcrafted paired datasets—which are expensive and time consuming to collect. The ability to generate these consistent grids likely emerged from foundational model training on diverse datasets, including photo albums, mangas, and comics. Our approach harnesses Vision-Language Models (VLMs) to automatically curate many generated grids, producing a diverse set of grid images with consistent identity features across various contexts. This curated synthetic dataset then serves as the foundation for fine-tuning and adapting any identity, transforming the task of zero-shot customized image generation from unsupervised to supervised. Diffusion Self-Distillation offers transformative potential for applications like consistent character generation, camera control, relighting, and asset customization in fields such as comics and digital art. This flexibility allows artists to rapidly iterate and adapt their work, reducing effort and enhancing creative freedom, making Diffusion Self-Distillation a valuable tool for AI-generated content." + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.865, + 0.825, + 0.879 + ], + "angle": 0, + "content": "We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.886, + 0.907, + 0.901 + ], + "angle": 0, + "content": "- We propose Diffusion Self-Distillation, a zero-shot" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18435" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.482, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.18, + 0.486, + 0.252 + ], + "angle": 0, + "content": "Figure 3. Difference between structure-preserving and identity-preserving edits. In structure-preserving editing, the main structures of the image are preserved, and only local edits or stylizations are performed. In identity-preserving editing, the global structure of the image may change radically." + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.278, + 0.484, + 0.322 + ], + "angle": 0, + "content": "identity-preserving customized image generation model that scales to any instance under any context, with performances on par with inference-stage tuning methods;" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.323, + 0.483, + 0.38 + ], + "angle": 0, + "content": "- We provide a self-distillation pipeline to obtain identity-preserving data pairs purely from pretrained text-to-image diffusion models, LLMs, and VLMs, without any human effort involved in the entire data creation wheel;" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.383, + 0.484, + 0.443 + ], + "angle": 0, + "content": "- We correspondingly design a unified architecture for image-to-image translation tasks involving both identity- and structure-preserving edits, including personalization, relighting, depth controls, and instruction following." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.323, + 0.484, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.458, + 0.229, + 0.473 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.483, + 0.484, + 0.559 + ], + "angle": 0, + "content": "Recent advancements in diffusion models have underscored the need for enhanced control and customization in image-generation tasks. Various methods have been proposed to address these challenges through additional conditioning mechanisms, personalization, and rapid adaptation [28]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.571, + 0.484, + 0.783 + ], + "angle": 0, + "content": "Control Mechanisms in Diffusion Models. To move beyond purely text-based controls, approaches like ControlNet [48] introduce spatial conditioning via inputs such as sketches, depth maps, and segmentation masks, enabling fine-grained structure control. ControlNet++ [21] refines this by enhancing the integration of spatial inputs for more nuanced control. Uni-ControlNet [49] unifies various control types within a single framework, standardizing the handling of diverse signals. T2I-Adapter [25] employs lightweight adapters to align pretrained models with external control signals without altering the core architecture. While these methods offer increased flexibility, they often focus on structural conditioning types such as depths and lack capabilities for concept extraction or identity preservation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.795, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Personalization and Fine-Tuning. Techniques like Dream-Booth [34] and LoRA [15] enhance the consistency and relevance of generated images by fine-tuning models with small sets of reference images. DreamBooth [34] personalizes models to maintain a subject's identity across different contexts, while LoRA [15] provides an efficient approach to fine-tuning large models without extensive retraining. How" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.152 + ], + "angle": 0, + "content": "ever, these methods require multiple images and test-time optimization for each reference, which can be computationally expensive—especially with the exponential growth in model sizes (12 billion parameters for FLUX)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.168, + 0.909, + 0.485 + ], + "angle": 0, + "content": "Zero-Shot and Fast Adaptation. IP-Adapter [46] incorporates image prompts into diffusion models using image embeddings, allowing for generations that align closely with reference visuals. InstantID [41] ensures zero-shot face preservation, maintaining a subject's key features across various contexts. While effective as zero-shot methods without user training, IP-Adapter [46] struggles to adapt specific targets like unique characters or assets, and InstantID [41] is limited to facial identity preservation. IPAdapter-Instruct [33] enhances image-based conditioning with instruct prompts but relies heavily on specific instructions and task-specific pretrained models. Other methods, such as SuTI [8] and GDT [17], handcrafted corresponding datasets, which are expensive and challenging to collect and scale. Another work along this line is Subject-Diffusion [23], which uses segmentation masks to create synthetic data for training but is bounded by achieving only simple attributes and accessories copying and editing within input images. Other methods [1, 11, 29, 40, 47] also investigated synthetic pairwise data generation but often fell short in scale because of the manual effort involved." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.488, + 0.909, + 0.609 + ], + "angle": 0, + "content": "Existing methods contribute valuable advancements but often target specific domains or require user-stage tuning. Diffusion Self-Distillation bridges these gaps by offering a unified, zero-shot approach for consistent customization of characters and assets using minimal input. By leveraging self-distillation assisted by vision-language models, Diffusion Self-Distillation provides a comprehensive and adaptable solution for a wide range of creative applications." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.631, + 0.753, + 0.647 + ], + "angle": 0, + "content": "3. Diffusion Self-Distillation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.909, + 0.901 + ], + "angle": 0, + "content": "We discover that recent text-to-image generation models offer the surprising ability to generate in-context, consistent image grids (see Fig. 2, left). Motivated by this insight, we develop a zero-shot adaptation network that offers fast, diverse, high-quality, and identity-preserving, i.e., consistent image generation conditioned on a reference image. For this purpose, we first generate and curate sets of images that exhibit the desired consistency using pretrained text-to-image diffusion models, large language models (LLMs), and vision-language models (VLMs) (Sec. 3.1). Then, we finetune the same pretrained diffusion model with these consistent image sets, employing our newly proposed parallel processing architecture (Sec. 3.2) to create a conditional model. By this end, Diffusion Self-Distillation finetunes a pretrained text-to-image diffusion model into a zero-shot customized image generator in a supervised manner." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18436" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.091, + 0.091, + 0.361, + 0.108 + ], + "angle": 0, + "content": "3.1. Generating a Pairwise Dataset" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.113, + 0.484, + 0.249 + ], + "angle": 0, + "content": "To create a pairwise dataset for supervised Diffusion Self-Distillation training, we leverage the emerging multi-image generation capabilities of pretrained text-to-image diffusion models to produce potentially consistent vanilla images (Sec. 3.1.1) created by LLM-generated prompts (Sec. 3.1.2). We then use VLMs to curate these vanilla samples, obtaining clean sets of images that share the desired identity consistency (Sec. 3.1.3). The data generation and curation pipeline is shown in Fig. 2, left." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.256, + 0.441, + 0.271 + ], + "angle": 0, + "content": "3.1.1. Vanilla Data Generation via Teacher Model" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.275, + 0.485, + 0.562 + ], + "angle": 0, + "content": "To generate sets of images that fulfill the desired identity preservation, we prompt the teacher pretrained text-to-image diffusion model to create images containing multiple panels featuring the same subject with variations in expression, pose, lighting conditions, and more, for training purposes. Such prompting can be as simple as specifying the desired identity preservation in the output, such as \"a grid of 4 images representing the same \\(<\\) object/character/scene/etc. >\", \"an evenly separated 4 panels, depicting identical \\(<\\) object/character/scene/etc. >\", etc. We additionally specify the expected content in each sub-image/panel. The full set of prompts is provided in our supplemental material Sec. A. Our analysis shows that current state-of-the-art text-to-image diffusion models (e.g., SD3 [9], DALL-E 3, FLUX) demonstrate this identity-preserving capability, likely emerging from their training data, which includes comics, mangas, photo albums, and video frames. Such in-context generation ability is crucial to our data generation wheel." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.569, + 0.345, + 0.584 + ], + "angle": 0, + "content": "3.1.2. Prompt Generation via LLMs" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.588, + 0.484, + 0.845 + ], + "angle": 0, + "content": "We rely on an LLM to \"brainstorm\" a large dataset of diverse prompts, from which we derive our image grid dataset. By defining a prompt structure, we prompt the LLM to produce text prompts that describe image grids. A challenge we encountered is that when prompted to create large sets of prompts, LLMs tend to produce prompts of low diversity. For example, we noticed that without additional guidance, GPT-4o has a strong preference for prompts with cars and robots, resulting in highly repetitive outputs. To address this issue, we utilize the available image captions in the LAION [36] dataset, feeding them into the LLM as content references. These references from real image captions dramatically improve the diversity of generated prompts. Optionally, we also use the LLM to filter these reference captions, ensuring they contain a clear target for identity preservation. We find that this significantly improves the hit rate of generating consistent multi-image outputs." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.852, + 0.431, + 0.867 + ], + "angle": 0, + "content": "3.1.3. Dataset Curation and Caption with VLMs" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.903 + ], + "angle": 0, + "content": "While the aforementioned data generation scheme provides identity-preserving multi-image samples of decent quality" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.908, + 0.289 + ], + "angle": 0, + "content": "and quantity, these initial \"uncurated\" images tend to be noisy and unsuitable for direct use. Therefore, we leverage the strong capabilities of VLMs to curate a clean dataset. We extract pairs of images from the generated samples intended to preserve the identity and ask the VLM whether the two images depict the same object, character, scene, etc. We find that employing Chain-of-Thought prompting [42] is particularly helpful in this context. Specifically, we first prompt the VLM to identify the common object, character, or scene present in both images, then have it describe each one in detail, and finally analyze whether they are identical, providing a conclusive response. This process yields pairs of images that share the same identity." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.298, + 0.798, + 0.314 + ], + "angle": 0, + "content": "3.2. Parallel Processing Architecture" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.321, + 0.909, + 0.744 + ], + "angle": 0, + "content": "We desire a conditional architecture suitable for general image-to-image tasks, including transformations in which structure is preserved, and transformations in which concepts/identities are preserved but image structure is not. This is a challenging problem because it may necessitate the transfer of fine details without guaranteeing spatial correspondences. While the ControlNet [48] architecture is excellent at structure-preserving edits, such as depth-to-image or segmentation-map-to-image, it struggles to preserve details under more complex identity-preserving edits, where the source and target images are not pixel-aligned. On the other hand, IP-Adapter [46] can extract certain concepts, such as styles, from the input image. Still, it strongly relies on a task-specific image encoder and often fails to preserve more complex concepts and identities. Drawing inspiration from the success of multi-view and video diffusion models [2, 4–6, 12–14, 16, 18, 20, 37, 38, 43, 45], we propose a simple yet effective method to extend the vanilla diffusion transformer model into an image-conditioned diffusion model. Specifically, we treat the input image as the first frame of a video and produce a two-frame video as output. The final loss is computed over the two-frame video, establishing an identity mapping for the first frame and a conditionally editing target for the second frame. Our architecture design allows generality for generic image-to-image translation tasks, since it enables effective information exchange between the two frames, allowing the model to capture complex semantics and perform sophisticated edits, as shown in Fig. 2, right." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.757, + 0.645, + 0.774 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Implementation details. We use FLUX1.0 DEV as both our teacher and student models, achieving self-distillation. For prompt generation, we use GPT-4o; for dataset curation and captioning, we use Gemini-1.5. We train all models on 8 NVIDIA H100 80GB GPUs with an effective batch size of 160 for 100k iterations, using AdamW optimizer [22] with a learning rate \\(10^{-4}\\). Our parallel processing architecture uses" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18437" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.089, + 0.903, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.495, + 0.908, + 0.539 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison. Overall, our method achieves high subject identity preservation and prompt-aligned diversity while not suffering from a \"copy-paste\" effect, such as the results of IP-Adapter+ [46]. This is largely thanks to our supervised training pipeline, which alleviates the base model's in-context generation ability." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.545, + 0.365, + 0.559 + ], + "angle": 0, + "content": "LoRAs with rank 512 on the base model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.58, + 0.486, + 0.822 + ], + "angle": 0, + "content": "Datasets. Our final training dataset contains \\(\\sim 400\\mathrm{k}\\) subject-consistent image pairs generated from our teacher model, FLUX1.0 DEV. Generating and curating the dataset is fully automated and requires no human effort, so its size could be further scaled. We use the publicly available DreamBench++ [27] dataset and follow their protocols for evaluation. DreamBench++ [27] is a comprehensive and diverse dataset for evaluating personalized image generation, consisting of 150 high-quality images and 1,350 prompts—significantly more than previous benchmarks like DreamBench [34]. The dataset covers various categories such as animals, humans, objects, etc., including photorealistic and non-photorealistic images, with prompts designed to span different difficulty levels (simple/imaginative). In contrast, prompts are generated using GPT-4o and refined by human annotators to ensure diversity and ethical compliance." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Baselines. We follow the setups in DreamBench++ [27] and compare our model with two classes of baselines: inference-stage tuning models and zero-shot models. For inference-stage models, we compare against Textual Inversion [10]," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.545, + 0.909, + 0.592 + ], + "angle": 0, + "content": "DreamBooth [34] and its LoRA [15] version. For zero-shot models, we compare with BLIP-Diffusion [19], Emu2 [39], IP-Adapter [46], IP-Adapter+ [46]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Evaluation metrics. The evaluation protocol of prior works [8, 33, 34, 46] typically involves comparing the CLIP [30] and DINO [7] feature similarities. However, we note that the metrics mentioned above capture only global semantic similarity, are extremely noisy, and are biased towards \"copy-pasting\" the input image. This is especially troublesome when the input image or the prompt is complex. We refer to DreamBench++ [27] for a detailed analysis of their limitations. Therefore, we follow the metrics designed in DreamBench++ [27] and report GPT-4o scores on the more diverse DreamBench++ [27] benchmark for both concept preservation (CP) with different categories of subjects and prompt following (PF) with photorealistic (Real.) and Imaginative (Imag.) prompts, then use their product as a final evaluation score. This evaluation protocol emulates a human user study using VLMs. We additionally slightly modify the GPT evaluation prompts so that penalization can be applied if the generated contents show no internal understanding and creative output but instead naively copy over" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18438" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.422, + 0.091, + 0.572, + 0.103 + ], + "angle": 0, + "content": "Character Preservation" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.103, + 0.903, + 0.715 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.718, + 0.907, + 0.761 + ], + "angle": 0, + "content": "Figure 5. Qualitative result. Our Diffusion Self-Distillation is capable of various customization targets across different tasks and styles, for instance, characters or objects, photorealistic or animated. Diffusion Self-Distillation can also take instruction types of prompts as input, similar to InstructPix2Pix [3]. Further, our model exhibits relighting capabilities without significantly altering the scene's content." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.768, + 0.486, + 0.844 + ], + "angle": 0, + "content": "components from the reference image. The modified metrics are named \"de-biased concept preservation (Debiased CP)\" and \"de-biased prompt following (Debiased PF)\". The full set of GPT evaluation prompts will be provided in our supplementary Sec. B." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.485, + 0.903 + ], + "angle": 0, + "content": "Qualitative results. Fig. 4 presents our qualitative comparison results, demonstrating that our model significantly outperforms all baselines in subject adaptation and concept" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.768, + 0.909, + 0.891 + ], + "angle": 0, + "content": "consistency while exhibiting excellent prompt alignment and diversity in the outputs. Textual Inversion [10], as an early concept extraction method, captures only vague semantics from the input image, making it unsuitable for zero-shot customization tasks that require precise subject adaptation. DreamBooth [34] and DreamBooth-LoRA [15, 34] face challenges in maintaining consistency, primarily because they perform better with multiple input images. This dependency" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18439" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.09, + 0.907, + 0.213 + ], + "angle": 0, + "content": "
    MethodConcept PreservationPrompt FollowingDebiased Concept PreservationDebiased Prompt Following
    Z-S?Animal↑Human↑Object↑Overall↑Real.↑Imag.↑Overall↑CP-PF↑Animal↑Human↑Object↑Overall↑Real.↑Imag.↑Overall↑
    Textual Inversion✘0.5020.3580.3050.3880.6710.4370.5980.2320.7410.6940.7170.7220.6190.3850.541
    DreamBooth✘0.6400.1990.4880.4420.7980.5040.6920.3060.6700.3620.6760.6260.7500.4670.656
    DreamBooth LoRA✘0.7510.3110.5430.5350.8980.7540.8490.4500.6810.6750.7610.7200.8650.7180.816
    BLIP-Diffusion✓0.6370.5570.4690.5540.5810.3030.4640.2570.7710.7330.7450.7500.5290.2660.442
    Emu2✓0.6700.5460.4470.5540.7320.5600.6700.3710.6520.6830.7010.6810.6860.4940.622
    IP-Adapter✓0.6670.5580.5040.5760.7430.4460.6070.3500.7900.7640.7430.7660.6950.3770.589
    IP-Adapter+✓0.9000.8450.7590.8340.5020.2790.3880.3240.4810.4730.5300.5040.4420.2290.371
    Ours✓0.6470.5670.6400.6310.7770.6250.7260.4580.8520.7740.7500.7890.8080.6810.757
    " + }, + { + "type": "table_footnote", + "bbox": [ + 0.09, + 0.218, + 0.907, + 0.318 + ], + "angle": 0, + "content": "Table 1. Quantitative result. On the human-aligned GPT score metrics, our method is only inferior to IP-Adapter+ [46] for concept preservation (largely because of IP-Adapter families' \"copy-pasting\" effect) and the tuning-base DreamBooth-LoRA [15, 34] for prompt following, but outperforms every other baseline, achieving the best overall performance considering both concept preservation and prompt following. We also note that on the de-biased GPT evaluation, which penalizes \"copy-pasting\" the reference image without significant creative interpretation or transformation, the advantages of IP-Adaper+ [46] no longer hold. This can also be partly observed by their bad prompt following scores, meaning they are biased towards the reference input and are not accommodating the input prompt. The first, second, and third values are highlighted, where Diffusion Self-Distillation is the best overall performing model." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.324, + 0.486, + 0.761 + ], + "angle": 0, + "content": "limits their effectiveness when only a single reference image is available. In contrast, our method achieves robust results even with just one input image, highlighting its efficiency and practicality. BLIP-Diffusion [19], operating as a self-supervised representation learning framework, can extract concepts from the input in a zero-shot manner but is confined to capturing overall semantic concepts without the ability to customize specific subjects. Similarly, Emu2 [39], a multimodal foundation model, excels at extracting semantic concepts but lacks mechanisms for specific subject customization, limiting its utility in personalized image generation. IP-Adapter [46] and IP-Adapter+ [46] employ self-supervised learning schemes aimed at reconstructing the input from encoded signals. While effective in extracting global concepts, they suffer from a pronounced \"copy-paste\" effect, where the generated images closely resemble the input without meaningful transformation. Notably, IP-Adapter+ [46], which utilizes a stronger input image encoder, exacerbates this issue, leading to less diversity and adaptability in the outputs. In contrast, our approach effectively preserves the subject's core identity while enabling diverse and contextually appropriate transformations. As illustrated in Fig. 5, our Diffusion Self-Distillation demonstrates remarkable versatility, adeptly handling various customization targets across different targets (characters, objects, etc.) and styles (photorealistic, animated, etc.). Moreover, Diffusion Self-Distillation generalizes well to a wide range of prompts, including instructions similar to InstructPix2Pix [3], underscoring its robustness and adaptability in diverse customization tasks." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.486, + 0.903 + ], + "angle": 0, + "content": "Quantitative results. Quantitative comparison with the baselines are shown in Tab. 1, where we report GPT evaluation following DreamBench++ [27]. Such an evaluation protocol is similar to human score but uses automatic multimodal LLMs. Our method achieves the best overall performances accommodating both concept preservation and prompt following, while only being inferior to IP-Adapter+ [46] for the former (mainly because of" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.324, + 0.909, + 0.596 + ], + "angle": 0, + "content": "the \"copy-paste\" effect again), and the per-instance tuning DreamBooth-LoRA [15, 34] for the latter. We note that the concept preservation evaluation of DreamBench++ [27] is still biased towards favoring a \"copy-paste\" effect, especially on more challenging and diverse prompts. For instance, the outstanding concept preservation performances of the IP-Adapter family [46] are primarily because of their strong \"copy-paste\" effect, which copies over the input image without considering relevant essential changes in the prompts. This can also be partly observed by their underperforming prompt following scores, which means they are biased towards the reference input and do not accommodate the input prompt. Therefore, we also present our \"de-biased\" version of GPT scores, which are as simple as telling GPT to penalize if the generated image resembles a direct copy of the reference image. We observe that the advantages of IP-Adaper+ [46] no longer hold. Overall, Diffusion Self-Distillation is the best-performing model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Ablation studies. (1) Data curation: During dataset generation, we first synthesize grids using a frozen pre-trained FLUX model and then filter the images via VLM curation. Why not fine-tune the FLUX model on image grids to improve the hit rate? To study this, we fit a LoRA [15] using \\(>7000\\) consistent grids (Fig. 6, left). Though a more significant proportion of samples are consistent grids, we find that the teacher model loses diversity in its output. Therefore, we choose to rely entirely on VLMs to help us curate from large numbers of diverse but potentially noisy grids. (2) Parallel processing architecture: We compare the parallel processing architecture to three alternative image-to-image architectures: 1) concatenating the source image to the noise image (\"concatenation\"); 2) a ControlNet [48]-based design, and 3) an IP-Adapter [46]-based design. We train each architecture using the same data as our parallel processing model (Fig. 6, middle). For ControlNet [48], we draw the same conclusion as prior work [16], in that it works best for structure-aligned edits, but generally strug" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18440" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.091, + 0.269, + 0.102 + ], + "angle": 0, + "content": "Effect of LoRA for Data Generation" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.104, + 0.177, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.166, + 0.158, + 0.174 + ], + "angle": 0, + "content": "No LoRA" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.174, + 0.174, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.23, + 0.158, + 0.239 + ], + "angle": 0, + "content": "No LoRA" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.106, + 0.268, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.2, + 0.165, + 0.258, + 0.173 + ], + "angle": 0, + "content": "LoRA fitting" + }, + { + "type": "image", + "bbox": [ + 0.192, + 0.174, + 0.266, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.2, + 0.231, + 0.258, + 0.24 + ], + "angle": 0, + "content": "LoRA fitting" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.108, + 0.365, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.165, + 0.365, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.28, + 0.233, + 0.329, + 0.242 + ], + "angle": 0, + "content": "reference" + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.108, + 0.587, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.493, + 0.09, + 0.684, + 0.099 + ], + "angle": 0, + "content": "Comparison of Different Architectures" + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.101, + 0.58, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.37, + 0.166, + 0.586, + 0.192 + ], + "angle": 0, + "content": "A young woman with brown eyes, shoulder-length dark brown wavy hair, rosy cheeks, wearing a yellow-brown coat over a green sweater and black pants, with a brown backpack, standing in a rainy alleyway with blurred figures in the background." + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.192, + 0.586, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.594, + 0.122, + 0.65, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.595, + 0.18, + 0.651, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.656, + 0.122, + 0.74, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.595, + 0.18, + 0.651, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.656, + 0.18, + 0.74, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.743, + 0.127, + 0.901, + 0.162 + ], + "angle": 0, + "content": "A regal, elderly man with a long white beard and hair, wearing ornate gold and red formal attire, plays a grand piano in a richly decorated room, lit by warm, natural light, camera angle low, focusing on the man's hands on the keys." + }, + { + "type": "image_footnote", + "bbox": [ + 0.761, + 0.192, + 0.883, + 0.212 + ], + "angle": 0, + "content": "A red four-door sedan parked in front of a brightly lit storefront, with the camera angled slightly towards the driver's side." + }, + { + "type": "list", + "bbox": [ + 0.743, + 0.127, + 0.901, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.245, + 0.907, + 0.329 + ], + "angle": 0, + "content": "Figure 6. Ablation study. Left: We compare the base model's in-context sampling ability with a consistent grid LoRA-overfitted model. We observe that although applying LoRA to the base model can increase the likelihood of outputs being consistent grids, it may adversely affect output diversity. Therefore, we rely on vision-language models (VLMs) to curate from a large number of diverse but potentially noisy grids. Right: We compare our architectural design with a vanilla conditional model (by adding a few input channels), ControlNet [48], and IP-Adapter [46]. Our architecture learns the input concepts and identities significantly better. We also demonstrate that our architecture can effectively scale to depth-conditioned image generation similar to ControlNet [48]." + }, + { + "type": "table", + "bbox": [ + 0.096, + 0.34, + 0.48, + 0.48 + ], + "angle": 0, + "content": "
    MethodCP ↑PF ↑Creativity ↑
    Textual Inversion [10]1.6931.9242.850
    DreamBooth [34]2.3292.8833.597
    DreamBooth LoRA [15, 34]2.5763.3864.247
    BLIP-Diffusion [19]1.8542.2810.286
    Emu2 [39]1.8432.0962.965
    IP-Adapter [46]2.2742.3073.481
    IP-Adapter+ [46]3.7331.9592.428
    Ours3.6613.3284.453
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.486, + 0.483, + 0.556 + ], + "angle": 0, + "content": "Table 2. User study. “CP” refers to concept preservation scores and “PF” refers to prompt following scores. The first, second, and third values are highlighted. Our user study results mostly align with our GPT evaluation, where our Diffusion Self-Distillation is the best overall performing model." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.568, + 0.484, + 0.705 + ], + "angle": 0, + "content": "gles to preserve details when the source image and target image differ in camera pose. IP-Adapter [46] struggles to effectively transfer details and styles from the source image due to the limited capacity of its image encoder. (3) Other image-to-image tasks: Although not \"self-distillation\", since it requires an externally-sourced paired dataset (generated with Depth Anything [44]), we additionally train our architecture on depth-to-image to demonstrate its utility for more general image-to-image tasks (Fig. 6, right)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.901 + ], + "angle": 0, + "content": "User study. To evaluate the fidelity and prompt consistency of our generated images, we conducted a user study on a random subset of the DreamBench++ [27] test cases, selecting 20 samples. A total of 25 female and 29 male annotators, aged from 22 to 78 (average 34), independently scored each image from 1 to 5 based on three criteria: (1) concept preservation—the consistency with the reference image, (2) prompt alignment—the consistency with the given prompt, and (3) creativity—the level of internal understanding and transformation. The average scores are presented in Tab. 2. Our human annotations closely align with the GPT evaluation, demonstrating that our Diffusion Self-Distillation is slightly" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.343, + 0.907, + 0.449 + ], + "angle": 0, + "content": "behind IP-Adapter+[46] in concept preservation and the inference-stage tuning method DreamBooth-LoRA [15, 34] in prompt alignment. Notably, our model achieved the highest creativity score, while IP-Adapter+ [46] scored lower in this metric due to its \"copy-paste\" effect. These results further confirm that our Diffusion Self-Distillation offers the most balanced and superior overall performance." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.468, + 0.627, + 0.484 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.495, + 0.907, + 0.631 + ], + "angle": 0, + "content": "We present Diffusion Self-Distillation, a zero-shot approach designed to achieve identity adaptation across a wide range of contexts using text-to-image diffusion models without any human effort. Our method effectively transforms zero-shot customized image generation into a supervised task, substantially reducing its difficulty. Empirical evaluations demonstrate that Diffusion Self-Distillation performs comparably to inference-stage tuning techniques while retaining the efficiency of zero-shot methods." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.646, + 0.909, + 0.751 + ], + "angle": 0, + "content": "Limitations and future work. Our work focuses on identity-preserving edits of characters, objects, and scene relighting. Future directions could explore additional tasks and use cases. Integration with ControlNet [48], for example, could provide fine-grained and independent control of identity and structure. Additionally, extending our approach from image to video generation is a promising avenue of future work." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.766, + 0.906, + 0.811 + ], + "angle": 0, + "content": "Ethics. We are mindful of the potential misuse, particularly in deepfakes. We oppose exploiting our work for purposes that infringe upon ethical standards or privacy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Conclusion. Our Diffusion Self-Distillation democratizes content creation, enabling identity-preserving, high-quality, and fast customized image generation that adapts seamlessly to evolving foundational models, significantly expanding the creative boundaries of art, design, and digital storytelling." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18441" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.486, + 0.184 + ], + "angle": 0, + "content": "Acknowledgements. This project was in part supported by Google, Kaiber AI, 3bodylabs, ONR N00014-23-1-2355, and NSF RI #2211258. ERC was supported by the Nvidia Graduate Fellowship and the Snap Research Fellowship. YZ was in part supported by the Stanford Interdisciplinary Graduate Fellowship." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.196, + 0.188, + 0.212 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.221, + 0.484, + 0.262 + ], + "angle": 0, + "content": "[1] Kiymet Akdemir and Pinar Yanardag. Oracle: Leveraging mutual information for consistent character generation with loras in diffusion models. In ICC, 2024. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.264, + 0.484, + 0.332 + ], + "angle": 0, + "content": "[2] Andreas Blattmann, Tim Dockhorn, Sumith Kulal, Daniel Mendelevitch, Maciej Kilian, Dominik Lorenz, Yam Levi, Zion English, Vikram Voleti, Adam Letts, Varun Jampani, and Robin Rombach. Stable video diffusion: Scaling latent video diffusion models to large datasets. 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Given an input image, Diffusion Self-Distillation is a novel diffusion-based approach that generates diverse images that maintain the input's identity across various contexts. Unlike prior approaches that require fine-tuning or are limited to specific domains, Diffusion Self-Distillation offers instant customization without any additional inference-stage training, enabling precise control and editability in text-to-image diffusion models. This ability makes Diffusion Self-Distillation a valuable tool for general AI content creation. + +# Abstract + +Text-to-image diffusion models produce impressive results but are frustrating tools for artists who desire fine-grained control. For example, a common use case is to create images of a specific concept in novel contexts, i.e., "identity-preserving generation". This setting, along with many other tasks (e.g., relighting), is a natural fit for image+text-conditional generative models. However, there is insufficient high-quality paired data to train such a model directly. We propose Diffusion Self-Distillation, a method for using a pre-trained text-to-image model to generate its own dataset for text-conditioned image-to-image tasks. We first leverage a text-to-image diffusion model's in-context generation ability to create grids of images and curate a large paired dataset with the help of a vision-language model. We then fine-tune the text-to-image model into a text+image-to-image model using the curated paired dataset. We demonstrate that Diffusion Self-Distillation outperforms existing zero-shot methods and is competitive with per-instance tuning techniques on a wide range of identity-preserving generation tasks, without requiring test-time optimization. Project page: primecai.github.io/dsd. + +# 1. Introduction + +In recent years, text-to-image diffusion models [26, 31, 32, 35] have set new standards in image synthesis, generating high-quality and diverse images from textual prompts. However, while their ability to generate images from text is impressive, these models often fall short in offering precise control, editability, and consistency—key features that are crucial for real-world applications. Text input alone can be insufficient to convey specific details, leading to variations that may not fully align with the user's intent, especially in scenarios that require faithful adaptation of a character or asset's identity across different contexts. + +Maintaining the instance's identity is challenging, however. We distinguish structure-preserving edits, in which the target and source image share the general layout, but may differ in style, texture, or other local features, and identity-preserving edits, where assets are recognizably the same across target and source images despite potentially largescale changes in image structure (Fig. 3). The latter task is a superset of the former and requires the model to have a significantly more profound understanding of the input image and concepts to extract and customize the desired + +![](images/861fbabdfbbdffe49dc66f1a12947b257de75a6fd9895de1d5cf4c445db23030.jpg) +Figure 2. Overview of our pipeline. Left: the top shows our vanilla paired data generation wheel (Sec. 3.1). We first sample reference image captions from the LAION [36] dataset. These reference captions are parsed through an LLM to be translated into identity-preserved grid generation prompts (Sec. 3.1.2). We feed these enhanced prompts to a pretrained text-to-image diffusion model to sample potentially identity-preserved grids of images, which are then cropped and composed into vanilla image pairs (Sec. 3.1.1). On the bottom, we show our data curation pipeline (Sec. 3.1.3), where the vanilla image paired are fed into a VLM to classify whether they depict identical main subjects. This process mimics a human annotation/curation process while being fully automatic; we use the curated data as our final training data. Right: we extend the diffusion transformer model into an image-conditioned framework by treating the input image as the first frame of a two-frame sequence. The model generates both frames simultaneously—the first reconstructs the input, while the second is the edited output—allowing effective information exchange between the conditioning image and the desired output. + +![](images/b0389e6cdac94a7b94869f8a14d148ed65bc1b75fe78c43f16d144d4d95744d8.jpg) + +identity. For example, image editing [3, 24, 48], such as local content editing, re-lighting, and semantic image synthesis, etc. are all structure-preserving and identity-preserving edits, but novel-view synthesis and character-consistent generation under pose variations, are identity-preserving but not structure-preserving. We aim to address the general case, maintaining identity without constraining structure. + +For structure-preserving edits, adding layers, as in ControlNet [48], introduces spatial conditioning controls but is limited to structure guidance and does not address consistent identity adaptation across diverse contexts. For identity-preserving edits, fine-tuning methods such as Dream-Booth [34] and LoRA [15] can improve consistency using a few reference samples but are time consuming and computationally intensive, requiring training for each reference. Zero-shot alternatives like IP-Adapter [46] and InstantID [41] offer faster solutions without the need for retraining but fall short in providing the desired level of consistency and customization; IP-Adapter [46] lacks full customization capabilities, and InstantID [41] is restricted to facial identity. + +In this paper, we propose a novel approach called Diffusion Self-Distillation, designed to address the core challenge of zero-shot instant customization and adaptation of any character or asset in text-to-image diffusion models. We identify the primary obstacle that hinders prior methods, such as IP-Adapter [46] and InstantID [41], from achieving better identity preservation or generalizing beyond facial + +contexts: the absence of large-scale paired datasets and corresponding supervised identity-preserving training pipelines. With recent advancements in foundational model capabilities, we are now positioned to exploit these strengths further. Specifically, we can generate consistent grids of identical characters or assets, opening a new pathway for customization that eliminates the need for pre-existing, handcrafted paired datasets—which are expensive and time consuming to collect. The ability to generate these consistent grids likely emerged from foundational model training on diverse datasets, including photo albums, mangas, and comics. Our approach harnesses Vision-Language Models (VLMs) to automatically curate many generated grids, producing a diverse set of grid images with consistent identity features across various contexts. This curated synthetic dataset then serves as the foundation for fine-tuning and adapting any identity, transforming the task of zero-shot customized image generation from unsupervised to supervised. Diffusion Self-Distillation offers transformative potential for applications like consistent character generation, camera control, relighting, and asset customization in fields such as comics and digital art. This flexibility allows artists to rapidly iterate and adapt their work, reducing effort and enhancing creative freedom, making Diffusion Self-Distillation a valuable tool for AI-generated content. + +We summarize our contributions as follows: + +- We propose Diffusion Self-Distillation, a zero-shot + +![](images/f46eaefb23afdf189a7ede14e6c86c99c86a5896c27045a36d662f3759e94b5e.jpg) +Figure 3. Difference between structure-preserving and identity-preserving edits. In structure-preserving editing, the main structures of the image are preserved, and only local edits or stylizations are performed. In identity-preserving editing, the global structure of the image may change radically. + +identity-preserving customized image generation model that scales to any instance under any context, with performances on par with inference-stage tuning methods; + +- We provide a self-distillation pipeline to obtain identity-preserving data pairs purely from pretrained text-to-image diffusion models, LLMs, and VLMs, without any human effort involved in the entire data creation wheel; +- We correspondingly design a unified architecture for image-to-image translation tasks involving both identity- and structure-preserving edits, including personalization, relighting, depth controls, and instruction following. + +# 2. Related work + +Recent advancements in diffusion models have underscored the need for enhanced control and customization in image-generation tasks. Various methods have been proposed to address these challenges through additional conditioning mechanisms, personalization, and rapid adaptation [28]. + +Control Mechanisms in Diffusion Models. To move beyond purely text-based controls, approaches like ControlNet [48] introduce spatial conditioning via inputs such as sketches, depth maps, and segmentation masks, enabling fine-grained structure control. ControlNet++ [21] refines this by enhancing the integration of spatial inputs for more nuanced control. Uni-ControlNet [49] unifies various control types within a single framework, standardizing the handling of diverse signals. T2I-Adapter [25] employs lightweight adapters to align pretrained models with external control signals without altering the core architecture. While these methods offer increased flexibility, they often focus on structural conditioning types such as depths and lack capabilities for concept extraction or identity preservation. + +Personalization and Fine-Tuning. Techniques like Dream-Booth [34] and LoRA [15] enhance the consistency and relevance of generated images by fine-tuning models with small sets of reference images. DreamBooth [34] personalizes models to maintain a subject's identity across different contexts, while LoRA [15] provides an efficient approach to fine-tuning large models without extensive retraining. How + +ever, these methods require multiple images and test-time optimization for each reference, which can be computationally expensive—especially with the exponential growth in model sizes (12 billion parameters for FLUX). + +Zero-Shot and Fast Adaptation. IP-Adapter [46] incorporates image prompts into diffusion models using image embeddings, allowing for generations that align closely with reference visuals. InstantID [41] ensures zero-shot face preservation, maintaining a subject's key features across various contexts. While effective as zero-shot methods without user training, IP-Adapter [46] struggles to adapt specific targets like unique characters or assets, and InstantID [41] is limited to facial identity preservation. IPAdapter-Instruct [33] enhances image-based conditioning with instruct prompts but relies heavily on specific instructions and task-specific pretrained models. Other methods, such as SuTI [8] and GDT [17], handcrafted corresponding datasets, which are expensive and challenging to collect and scale. Another work along this line is Subject-Diffusion [23], which uses segmentation masks to create synthetic data for training but is bounded by achieving only simple attributes and accessories copying and editing within input images. Other methods [1, 11, 29, 40, 47] also investigated synthetic pairwise data generation but often fell short in scale because of the manual effort involved. + +Existing methods contribute valuable advancements but often target specific domains or require user-stage tuning. Diffusion Self-Distillation bridges these gaps by offering a unified, zero-shot approach for consistent customization of characters and assets using minimal input. By leveraging self-distillation assisted by vision-language models, Diffusion Self-Distillation provides a comprehensive and adaptable solution for a wide range of creative applications. + +# 3. Diffusion Self-Distillation + +We discover that recent text-to-image generation models offer the surprising ability to generate in-context, consistent image grids (see Fig. 2, left). Motivated by this insight, we develop a zero-shot adaptation network that offers fast, diverse, high-quality, and identity-preserving, i.e., consistent image generation conditioned on a reference image. For this purpose, we first generate and curate sets of images that exhibit the desired consistency using pretrained text-to-image diffusion models, large language models (LLMs), and vision-language models (VLMs) (Sec. 3.1). Then, we finetune the same pretrained diffusion model with these consistent image sets, employing our newly proposed parallel processing architecture (Sec. 3.2) to create a conditional model. By this end, Diffusion Self-Distillation finetunes a pretrained text-to-image diffusion model into a zero-shot customized image generator in a supervised manner. + +# 3.1. Generating a Pairwise Dataset + +To create a pairwise dataset for supervised Diffusion Self-Distillation training, we leverage the emerging multi-image generation capabilities of pretrained text-to-image diffusion models to produce potentially consistent vanilla images (Sec. 3.1.1) created by LLM-generated prompts (Sec. 3.1.2). We then use VLMs to curate these vanilla samples, obtaining clean sets of images that share the desired identity consistency (Sec. 3.1.3). The data generation and curation pipeline is shown in Fig. 2, left. + +# 3.1.1. Vanilla Data Generation via Teacher Model + +To generate sets of images that fulfill the desired identity preservation, we prompt the teacher pretrained text-to-image diffusion model to create images containing multiple panels featuring the same subject with variations in expression, pose, lighting conditions, and more, for training purposes. Such prompting can be as simple as specifying the desired identity preservation in the output, such as "a grid of 4 images representing the same $<$ object/character/scene/etc. >", "an evenly separated 4 panels, depicting identical $<$ object/character/scene/etc. >", etc. We additionally specify the expected content in each sub-image/panel. The full set of prompts is provided in our supplemental material Sec. A. Our analysis shows that current state-of-the-art text-to-image diffusion models (e.g., SD3 [9], DALL-E 3, FLUX) demonstrate this identity-preserving capability, likely emerging from their training data, which includes comics, mangas, photo albums, and video frames. Such in-context generation ability is crucial to our data generation wheel. + +# 3.1.2. Prompt Generation via LLMs + +We rely on an LLM to "brainstorm" a large dataset of diverse prompts, from which we derive our image grid dataset. By defining a prompt structure, we prompt the LLM to produce text prompts that describe image grids. A challenge we encountered is that when prompted to create large sets of prompts, LLMs tend to produce prompts of low diversity. For example, we noticed that without additional guidance, GPT-4o has a strong preference for prompts with cars and robots, resulting in highly repetitive outputs. To address this issue, we utilize the available image captions in the LAION [36] dataset, feeding them into the LLM as content references. These references from real image captions dramatically improve the diversity of generated prompts. Optionally, we also use the LLM to filter these reference captions, ensuring they contain a clear target for identity preservation. We find that this significantly improves the hit rate of generating consistent multi-image outputs. + +# 3.1.3. Dataset Curation and Caption with VLMs + +While the aforementioned data generation scheme provides identity-preserving multi-image samples of decent quality + +and quantity, these initial "uncurated" images tend to be noisy and unsuitable for direct use. Therefore, we leverage the strong capabilities of VLMs to curate a clean dataset. We extract pairs of images from the generated samples intended to preserve the identity and ask the VLM whether the two images depict the same object, character, scene, etc. We find that employing Chain-of-Thought prompting [42] is particularly helpful in this context. Specifically, we first prompt the VLM to identify the common object, character, or scene present in both images, then have it describe each one in detail, and finally analyze whether they are identical, providing a conclusive response. This process yields pairs of images that share the same identity. + +# 3.2. Parallel Processing Architecture + +We desire a conditional architecture suitable for general image-to-image tasks, including transformations in which structure is preserved, and transformations in which concepts/identities are preserved but image structure is not. This is a challenging problem because it may necessitate the transfer of fine details without guaranteeing spatial correspondences. While the ControlNet [48] architecture is excellent at structure-preserving edits, such as depth-to-image or segmentation-map-to-image, it struggles to preserve details under more complex identity-preserving edits, where the source and target images are not pixel-aligned. On the other hand, IP-Adapter [46] can extract certain concepts, such as styles, from the input image. Still, it strongly relies on a task-specific image encoder and often fails to preserve more complex concepts and identities. Drawing inspiration from the success of multi-view and video diffusion models [2, 4–6, 12–14, 16, 18, 20, 37, 38, 43, 45], we propose a simple yet effective method to extend the vanilla diffusion transformer model into an image-conditioned diffusion model. Specifically, we treat the input image as the first frame of a video and produce a two-frame video as output. The final loss is computed over the two-frame video, establishing an identity mapping for the first frame and a conditionally editing target for the second frame. Our architecture design allows generality for generic image-to-image translation tasks, since it enables effective information exchange between the two frames, allowing the model to capture complex semantics and perform sophisticated edits, as shown in Fig. 2, right. + +# 4. Experiments + +Implementation details. We use FLUX1.0 DEV as both our teacher and student models, achieving self-distillation. For prompt generation, we use GPT-4o; for dataset curation and captioning, we use Gemini-1.5. We train all models on 8 NVIDIA H100 80GB GPUs with an effective batch size of 160 for 100k iterations, using AdamW optimizer [22] with a learning rate $10^{-4}$ . Our parallel processing architecture uses + +![](images/63af7ebf150e84f622cad33d6277aa4c319ea15202177de26bb810679c0c29ea.jpg) +Figure 4. Qualitative comparison. Overall, our method achieves high subject identity preservation and prompt-aligned diversity while not suffering from a "copy-paste" effect, such as the results of IP-Adapter+ [46]. This is largely thanks to our supervised training pipeline, which alleviates the base model's in-context generation ability. + +LoRAs with rank 512 on the base model. + +Datasets. Our final training dataset contains $\sim 400\mathrm{k}$ subject-consistent image pairs generated from our teacher model, FLUX1.0 DEV. Generating and curating the dataset is fully automated and requires no human effort, so its size could be further scaled. We use the publicly available DreamBench++ [27] dataset and follow their protocols for evaluation. DreamBench++ [27] is a comprehensive and diverse dataset for evaluating personalized image generation, consisting of 150 high-quality images and 1,350 prompts—significantly more than previous benchmarks like DreamBench [34]. The dataset covers various categories such as animals, humans, objects, etc., including photorealistic and non-photorealistic images, with prompts designed to span different difficulty levels (simple/imaginative). In contrast, prompts are generated using GPT-4o and refined by human annotators to ensure diversity and ethical compliance. + +Baselines. We follow the setups in DreamBench++ [27] and compare our model with two classes of baselines: inference-stage tuning models and zero-shot models. For inference-stage models, we compare against Textual Inversion [10], + +DreamBooth [34] and its LoRA [15] version. For zero-shot models, we compare with BLIP-Diffusion [19], Emu2 [39], IP-Adapter [46], IP-Adapter+ [46]. + +Evaluation metrics. The evaluation protocol of prior works [8, 33, 34, 46] typically involves comparing the CLIP [30] and DINO [7] feature similarities. However, we note that the metrics mentioned above capture only global semantic similarity, are extremely noisy, and are biased towards "copy-pasting" the input image. This is especially troublesome when the input image or the prompt is complex. We refer to DreamBench++ [27] for a detailed analysis of their limitations. Therefore, we follow the metrics designed in DreamBench++ [27] and report GPT-4o scores on the more diverse DreamBench++ [27] benchmark for both concept preservation (CP) with different categories of subjects and prompt following (PF) with photorealistic (Real.) and Imaginative (Imag.) prompts, then use their product as a final evaluation score. This evaluation protocol emulates a human user study using VLMs. We additionally slightly modify the GPT evaluation prompts so that penalization can be applied if the generated contents show no internal understanding and creative output but instead naively copy over + +![](images/e7186bc7d9913c78370951b459575d4b7408ed2410ffd4d996b8575f5b58501b.jpg) +Character Preservation +Figure 5. Qualitative result. Our Diffusion Self-Distillation is capable of various customization targets across different tasks and styles, for instance, characters or objects, photorealistic or animated. Diffusion Self-Distillation can also take instruction types of prompts as input, similar to InstructPix2Pix [3]. Further, our model exhibits relighting capabilities without significantly altering the scene's content. + +components from the reference image. The modified metrics are named "de-biased concept preservation (Debiased CP)" and "de-biased prompt following (Debiased PF)". The full set of GPT evaluation prompts will be provided in our supplementary Sec. B. + +Qualitative results. Fig. 4 presents our qualitative comparison results, demonstrating that our model significantly outperforms all baselines in subject adaptation and concept + +consistency while exhibiting excellent prompt alignment and diversity in the outputs. Textual Inversion [10], as an early concept extraction method, captures only vague semantics from the input image, making it unsuitable for zero-shot customization tasks that require precise subject adaptation. DreamBooth [34] and DreamBooth-LoRA [15, 34] face challenges in maintaining consistency, primarily because they perform better with multiple input images. This dependency + +
    MethodConcept PreservationPrompt FollowingDebiased Concept PreservationDebiased Prompt Following
    Z-S?Animal↑Human↑Object↑Overall↑Real.↑Imag.↑Overall↑CP-PF↑Animal↑Human↑Object↑Overall↑Real.↑Imag.↑Overall↑
    Textual Inversion✘0.5020.3580.3050.3880.6710.4370.5980.2320.7410.6940.7170.7220.6190.3850.541
    DreamBooth✘0.6400.1990.4880.4420.7980.5040.6920.3060.6700.3620.6760.6260.7500.4670.656
    DreamBooth LoRA✘0.7510.3110.5430.5350.8980.7540.8490.4500.6810.6750.7610.7200.8650.7180.816
    BLIP-Diffusion✓0.6370.5570.4690.5540.5810.3030.4640.2570.7710.7330.7450.7500.5290.2660.442
    Emu2✓0.6700.5460.4470.5540.7320.5600.6700.3710.6520.6830.7010.6810.6860.4940.622
    IP-Adapter✓0.6670.5580.5040.5760.7430.4460.6070.3500.7900.7640.7430.7660.6950.3770.589
    IP-Adapter+✓0.9000.8450.7590.8340.5020.2790.3880.3240.4810.4730.5300.5040.4420.2290.371
    Ours✓0.6470.5670.6400.6310.7770.6250.7260.4580.8520.7740.7500.7890.8080.6810.757
    + +Table 1. Quantitative result. On the human-aligned GPT score metrics, our method is only inferior to IP-Adapter+ [46] for concept preservation (largely because of IP-Adapter families' "copy-pasting" effect) and the tuning-base DreamBooth-LoRA [15, 34] for prompt following, but outperforms every other baseline, achieving the best overall performance considering both concept preservation and prompt following. We also note that on the de-biased GPT evaluation, which penalizes "copy-pasting" the reference image without significant creative interpretation or transformation, the advantages of IP-Adaper+ [46] no longer hold. This can also be partly observed by their bad prompt following scores, meaning they are biased towards the reference input and are not accommodating the input prompt. The first, second, and third values are highlighted, where Diffusion Self-Distillation is the best overall performing model. + +limits their effectiveness when only a single reference image is available. In contrast, our method achieves robust results even with just one input image, highlighting its efficiency and practicality. BLIP-Diffusion [19], operating as a self-supervised representation learning framework, can extract concepts from the input in a zero-shot manner but is confined to capturing overall semantic concepts without the ability to customize specific subjects. Similarly, Emu2 [39], a multimodal foundation model, excels at extracting semantic concepts but lacks mechanisms for specific subject customization, limiting its utility in personalized image generation. IP-Adapter [46] and IP-Adapter+ [46] employ self-supervised learning schemes aimed at reconstructing the input from encoded signals. While effective in extracting global concepts, they suffer from a pronounced "copy-paste" effect, where the generated images closely resemble the input without meaningful transformation. Notably, IP-Adapter+ [46], which utilizes a stronger input image encoder, exacerbates this issue, leading to less diversity and adaptability in the outputs. In contrast, our approach effectively preserves the subject's core identity while enabling diverse and contextually appropriate transformations. As illustrated in Fig. 5, our Diffusion Self-Distillation demonstrates remarkable versatility, adeptly handling various customization targets across different targets (characters, objects, etc.) and styles (photorealistic, animated, etc.). Moreover, Diffusion Self-Distillation generalizes well to a wide range of prompts, including instructions similar to InstructPix2Pix [3], underscoring its robustness and adaptability in diverse customization tasks. + +Quantitative results. Quantitative comparison with the baselines are shown in Tab. 1, where we report GPT evaluation following DreamBench++ [27]. Such an evaluation protocol is similar to human score but uses automatic multimodal LLMs. Our method achieves the best overall performances accommodating both concept preservation and prompt following, while only being inferior to IP-Adapter+ [46] for the former (mainly because of + +the "copy-paste" effect again), and the per-instance tuning DreamBooth-LoRA [15, 34] for the latter. We note that the concept preservation evaluation of DreamBench++ [27] is still biased towards favoring a "copy-paste" effect, especially on more challenging and diverse prompts. For instance, the outstanding concept preservation performances of the IP-Adapter family [46] are primarily because of their strong "copy-paste" effect, which copies over the input image without considering relevant essential changes in the prompts. This can also be partly observed by their underperforming prompt following scores, which means they are biased towards the reference input and do not accommodate the input prompt. Therefore, we also present our "de-biased" version of GPT scores, which are as simple as telling GPT to penalize if the generated image resembles a direct copy of the reference image. We observe that the advantages of IP-Adaper+ [46] no longer hold. Overall, Diffusion Self-Distillation is the best-performing model. + +Ablation studies. (1) Data curation: During dataset generation, we first synthesize grids using a frozen pre-trained FLUX model and then filter the images via VLM curation. Why not fine-tune the FLUX model on image grids to improve the hit rate? To study this, we fit a LoRA [15] using $>7000$ consistent grids (Fig. 6, left). Though a more significant proportion of samples are consistent grids, we find that the teacher model loses diversity in its output. Therefore, we choose to rely entirely on VLMs to help us curate from large numbers of diverse but potentially noisy grids. (2) Parallel processing architecture: We compare the parallel processing architecture to three alternative image-to-image architectures: 1) concatenating the source image to the noise image ("concatenation"); 2) a ControlNet [48]-based design, and 3) an IP-Adapter [46]-based design. We train each architecture using the same data as our parallel processing model (Fig. 6, middle). For ControlNet [48], we draw the same conclusion as prior work [16], in that it works best for structure-aligned edits, but generally strug + +![](images/4f6ee5730564c79ace5c64222ddd5f2541362561202fb08fbe1fd0ccebd90353.jpg) +Effect of LoRA for Data Generation +No LoRA + +![](images/4b1711c89a594c6e04614ee8636175ec65a6f057bd5a5f291e3ba403cd95454f.jpg) +No LoRA + +![](images/8d6d3d5639c31401c5433b13e505b774a4008b6470c42603d1c6a758a92a10f4.jpg) + +![](images/b61c2a90aa89c9d5494efbf5e314ee72459b6c1f0032969ce773796fb76cb814.jpg) +LoRA fitting +LoRA fitting + +![](images/1813be7e965ecec070425930bbb9982923b2c4f3d1fd7b4eac28557b7f3eed42.jpg) + +![](images/3cc92c487c4b482247911edeef4a3d81d08b3d707bfb7f5404b91d96db933dc1.jpg) +reference + +Figure 6. Ablation study. Left: We compare the base model's in-context sampling ability with a consistent grid LoRA-overfitted model. We observe that although applying LoRA to the base model can increase the likelihood of outputs being consistent grids, it may adversely affect output diversity. Therefore, we rely on vision-language models (VLMs) to curate from a large number of diverse but potentially noisy grids. Right: We compare our architectural design with a vanilla conditional model (by adding a few input channels), ControlNet [48], and IP-Adapter [46]. Our architecture learns the input concepts and identities significantly better. We also demonstrate that our architecture can effectively scale to depth-conditioned image generation similar to ControlNet [48]. +![](images/71158be9e04e643365263cf4900e18fa555e2011b885227cfb1689e1e1e6593a.jpg) +A young woman with brown eyes, shoulder-length dark brown wavy hair, rosy cheeks, wearing a yellow-brown coat over a green sweater and black pants, with a brown backpack, standing in a rainy alleyway with blurred figures in the background. + +![](images/82be34914c8e2e83f3284644708d4580ea1c77f4b554729d01b1500d16b1a41f.jpg) +Comparison of Different Architectures + +![](images/db13d74a782a3f963d4ea6e7ae29f34cb12a3406771fe4a271be404114326e60.jpg) + +![](images/62867113117156a8e21204a697f87ce1870cb9943c7f6b35750dc5de38dc2569.jpg) +A regal, elderly man with a long white beard and hair, wearing ornate gold and red formal attire, plays a grand piano in a richly decorated room, lit by warm, natural light, camera angle low, focusing on the man's hands on the keys. + +![](images/80f8c6c74cc8bc352b60fbd17e0b85eb0edac2b0d69f43fbb8afa51a0749b26e.jpg) +A red four-door sedan parked in front of a brightly lit storefront, with the camera angled slightly towards the driver's side. + +
    MethodCP ↑PF ↑Creativity ↑
    Textual Inversion [10]1.6931.9242.850
    DreamBooth [34]2.3292.8833.597
    DreamBooth LoRA [15, 34]2.5763.3864.247
    BLIP-Diffusion [19]1.8542.2810.286
    Emu2 [39]1.8432.0962.965
    IP-Adapter [46]2.2742.3073.481
    IP-Adapter+ [46]3.7331.9592.428
    Ours3.6613.3284.453
    + +Table 2. User study. “CP” refers to concept preservation scores and “PF” refers to prompt following scores. The first, second, and third values are highlighted. Our user study results mostly align with our GPT evaluation, where our Diffusion Self-Distillation is the best overall performing model. + +gles to preserve details when the source image and target image differ in camera pose. IP-Adapter [46] struggles to effectively transfer details and styles from the source image due to the limited capacity of its image encoder. (3) Other image-to-image tasks: Although not "self-distillation", since it requires an externally-sourced paired dataset (generated with Depth Anything [44]), we additionally train our architecture on depth-to-image to demonstrate its utility for more general image-to-image tasks (Fig. 6, right). + +User study. To evaluate the fidelity and prompt consistency of our generated images, we conducted a user study on a random subset of the DreamBench++ [27] test cases, selecting 20 samples. A total of 25 female and 29 male annotators, aged from 22 to 78 (average 34), independently scored each image from 1 to 5 based on three criteria: (1) concept preservation—the consistency with the reference image, (2) prompt alignment—the consistency with the given prompt, and (3) creativity—the level of internal understanding and transformation. The average scores are presented in Tab. 2. Our human annotations closely align with the GPT evaluation, demonstrating that our Diffusion Self-Distillation is slightly + +behind IP-Adapter+[46] in concept preservation and the inference-stage tuning method DreamBooth-LoRA [15, 34] in prompt alignment. Notably, our model achieved the highest creativity score, while IP-Adapter+ [46] scored lower in this metric due to its "copy-paste" effect. These results further confirm that our Diffusion Self-Distillation offers the most balanced and superior overall performance. + +# 5. Discussion + +We present Diffusion Self-Distillation, a zero-shot approach designed to achieve identity adaptation across a wide range of contexts using text-to-image diffusion models without any human effort. Our method effectively transforms zero-shot customized image generation into a supervised task, substantially reducing its difficulty. Empirical evaluations demonstrate that Diffusion Self-Distillation performs comparably to inference-stage tuning techniques while retaining the efficiency of zero-shot methods. + +Limitations and future work. Our work focuses on identity-preserving edits of characters, objects, and scene relighting. Future directions could explore additional tasks and use cases. Integration with ControlNet [48], for example, could provide fine-grained and independent control of identity and structure. Additionally, extending our approach from image to video generation is a promising avenue of future work. + +Ethics. We are mindful of the potential misuse, particularly in deepfakes. We oppose exploiting our work for purposes that infringe upon ethical standards or privacy. + +Conclusion. Our Diffusion Self-Distillation democratizes content creation, enabling identity-preserving, high-quality, and fast customized image generation that adapts seamlessly to evolving foundational models, significantly expanding the creative boundaries of art, design, and digital storytelling. + +Acknowledgements. This project was in part supported by Google, Kaiber AI, 3bodylabs, ONR N00014-23-1-2355, and NSF RI #2211258. ERC was supported by the Nvidia Graduate Fellowship and the Snap Research Fellowship. YZ was in part supported by the Stanford Interdisciplinary Graduate Fellowship. + +# References + +[1] Kiymet Akdemir and Pinar Yanardag. 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In NeurIPS, 2023. 3 \ No newline at end of file diff --git a/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/images.zip b/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..100f94baef3dfb3d6a81fde8a79d18d565da89b6 --- /dev/null +++ b/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7e3803d06cc7f278fd2ed534098900668477c4864b9751c49129fc8acc5d2c17 +size 1239596 diff --git a/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/layout.json b/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..3fac4021173d399aa9593f36fa92c3fc31b72555 --- /dev/null +++ b/2025/Diffusion Self-Distillation for Zero-Shot Customized Image Generation/layout.json @@ -0,0 +1,5895 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 86, + 103, + 523, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 103, + 523, + 120 + ], + "spans": [ + { + "bbox": [ + 86, + 103, + 523, + 120 + ], + "type": "text", + "content": "Diffusion Self-Distillation for Zero-Shot Customized Image Generation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 186, + 143, + 435, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 186, + 143, + 435, + 185 + ], + "spans": [ + { + "bbox": [ + 186, + 143, + 435, + 185 + ], + "type": "text", + "content": "Shengqu Cai Eric Ryan Chan Yunzhi Zhang Leonidas Guibas Jiajun Wu Gordon Wetzstein Stanford University" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 58, + 207, + 552, + 374 + ], + "blocks": [ + { + "bbox": [ + 58, + 207, + 552, + 374 + ], + "lines": [ + { + "bbox": [ + 58, + 207, + 552, + 374 + ], + "spans": [ + { + "bbox": [ + 58, + 207, + 552, + 374 + ], + "type": "image", + "image_path": "c0e9c5235eff5600f63d275d09620e3107a1bcea982d6a77f3d5fffc369c0769.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 378, + 555, + 422 + ], + "lines": [ + { + "bbox": [ + 55, + 378, + 555, + 422 + ], + "spans": [ + { + "bbox": [ + 55, + 378, + 555, + 422 + ], + "type": "text", + "content": "Figure 1. Given an input image, Diffusion Self-Distillation is a novel diffusion-based approach that generates diverse images that maintain the input's identity across various contexts. Unlike prior approaches that require fine-tuning or are limited to specific domains, Diffusion Self-Distillation offers instant customization without any additional inference-stage training, enabling precise control and editability in text-to-image diffusion models. This ability makes Diffusion Self-Distillation a valuable tool for general AI content creation." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 152, + 441, + 200, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 441, + 200, + 453 + ], + "spans": [ + { + "bbox": [ + 152, + 441, + 200, + 453 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 463, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 463, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 53, + 463, + 297, + 715 + ], + "type": "text", + "content": "Text-to-image diffusion models produce impressive results but are frustrating tools for artists who desire fine-grained control. For example, a common use case is to create images of a specific concept in novel contexts, i.e., \"identity-preserving generation\". This setting, along with many other tasks (e.g., relighting), is a natural fit for image+text-conditional generative models. However, there is insufficient high-quality paired data to train such a model directly. We propose Diffusion Self-Distillation, a method for using a pre-trained text-to-image model to generate its own dataset for text-conditioned image-to-image tasks. We first leverage a text-to-image diffusion model's in-context generation ability to create grids of images and curate a large paired dataset with the help of a vision-language model. We then fine-tune the text-to-image model into a text+image-to-image model using the curated paired dataset. We demonstrate that Diffusion Self-Distillation outperforms existing zero-shot methods and is competitive with per-instance tuning techniques on a wide range of identity-preserving generation tasks, without requiring test-time optimization. Project page: primecai.github.io/dsd." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 441, + 394, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 441, + 394, + 453 + ], + "spans": [ + { + "bbox": [ + 315, + 441, + 394, + 453 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 461, + 555, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 461, + 555, + 592 + ], + "spans": [ + { + "bbox": [ + 312, + 461, + 555, + 592 + ], + "type": "text", + "content": "In recent years, text-to-image diffusion models [26, 31, 32, 35] have set new standards in image synthesis, generating high-quality and diverse images from textual prompts. However, while their ability to generate images from text is impressive, these models often fall short in offering precise control, editability, and consistency—key features that are crucial for real-world applications. Text input alone can be insufficient to convey specific details, leading to variations that may not fully align with the user's intent, especially in scenarios that require faithful adaptation of a character or asset's identity across different contexts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 594, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 594, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 312, + 594, + 556, + 713 + ], + "type": "text", + "content": "Maintaining the instance's identity is challenging, however. We distinguish structure-preserving edits, in which the target and source image share the general layout, but may differ in style, texture, or other local features, and identity-preserving edits, where assets are recognizably the same across target and source images despite potentially largescale changes in image structure (Fig. 3). The latter task is a superset of the former and requires the model to have a significantly more profound understanding of the input image and concepts to extract and customize the desired" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "18434" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 69, + 370, + 270 + ], + "blocks": [ + { + "bbox": [ + 59, + 69, + 370, + 270 + ], + "lines": [ + { + "bbox": [ + 59, + 69, + 370, + 270 + ], + "spans": [ + { + "bbox": [ + 59, + 69, + 370, + 270 + ], + "type": "image", + "image_path": "861fbabdfbbdffe49dc66f1a12947b257de75a6fd9895de1d5cf4c445db23030.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 274, + 555, + 373 + ], + "lines": [ + { + "bbox": [ + 55, + 274, + 555, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 274, + 555, + 373 + ], + "type": "text", + "content": "Figure 2. Overview of our pipeline. Left: the top shows our vanilla paired data generation wheel (Sec. 3.1). We first sample reference image captions from the LAION [36] dataset. These reference captions are parsed through an LLM to be translated into identity-preserved grid generation prompts (Sec. 3.1.2). We feed these enhanced prompts to a pretrained text-to-image diffusion model to sample potentially identity-preserved grids of images, which are then cropped and composed into vanilla image pairs (Sec. 3.1.1). On the bottom, we show our data curation pipeline (Sec. 3.1.3), where the vanilla image paired are fed into a VLM to classify whether they depict identical main subjects. This process mimics a human annotation/curation process while being fully automatic; we use the curated data as our final training data. Right: we extend the diffusion transformer model into an image-conditioned framework by treating the input image as the first frame of a two-frame sequence. The model generates both frames simultaneously—the first reconstructs the input, while the second is the edited output—allowing effective information exchange between the conditioning image and the desired output." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 375, + 69, + 552, + 270 + ], + "blocks": [ + { + "bbox": [ + 375, + 69, + 552, + 270 + ], + "lines": [ + { + "bbox": [ + 375, + 69, + 552, + 270 + ], + "spans": [ + { + "bbox": [ + 375, + 69, + 552, + 270 + ], + "type": "image", + "image_path": "b0389e6cdac94a7b94869f8a14d148ed65bc1b75fe78c43f16d144d4d95744d8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 380, + 295, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 380, + 295, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 380, + 295, + 464 + ], + "type": "text", + "content": "identity. For example, image editing [3, 24, 48], such as local content editing, re-lighting, and semantic image synthesis, etc. are all structure-preserving and identity-preserving edits, but novel-view synthesis and character-consistent generation under pose variations, are identity-preserving but not structure-preserving. We aim to address the general case, maintaining identity without constraining structure." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 469, + 295, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 469, + 295, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 469, + 295, + 624 + ], + "type": "text", + "content": "For structure-preserving edits, adding layers, as in ControlNet [48], introduces spatial conditioning controls but is limited to structure guidance and does not address consistent identity adaptation across diverse contexts. For identity-preserving edits, fine-tuning methods such as Dream-Booth [34] and LoRA [15] can improve consistency using a few reference samples but are time consuming and computationally intensive, requiring training for each reference. Zero-shot alternatives like IP-Adapter [46] and InstantID [41] offer faster solutions without the need for retraining but fall short in providing the desired level of consistency and customization; IP-Adapter [46] lacks full customization capabilities, and InstantID [41] is restricted to facial identity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": "In this paper, we propose a novel approach called Diffusion Self-Distillation, designed to address the core challenge of zero-shot instant customization and adaptation of any character or asset in text-to-image diffusion models. We identify the primary obstacle that hinders prior methods, such as IP-Adapter [46] and InstantID [41], from achieving better identity preservation or generalizing beyond facial" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 380, + 555, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 380, + 555, + 679 + ], + "spans": [ + { + "bbox": [ + 313, + 380, + 555, + 679 + ], + "type": "text", + "content": "contexts: the absence of large-scale paired datasets and corresponding supervised identity-preserving training pipelines. With recent advancements in foundational model capabilities, we are now positioned to exploit these strengths further. Specifically, we can generate consistent grids of identical characters or assets, opening a new pathway for customization that eliminates the need for pre-existing, handcrafted paired datasets—which are expensive and time consuming to collect. The ability to generate these consistent grids likely emerged from foundational model training on diverse datasets, including photo albums, mangas, and comics. Our approach harnesses Vision-Language Models (VLMs) to automatically curate many generated grids, producing a diverse set of grid images with consistent identity features across various contexts. This curated synthetic dataset then serves as the foundation for fine-tuning and adapting any identity, transforming the task of zero-shot customized image generation from unsupervised to supervised. Diffusion Self-Distillation offers transformative potential for applications like consistent character generation, camera control, relighting, and asset customization in fields such as comics and digital art. This flexibility allows artists to rapidly iterate and adapt their work, reducing effort and enhancing creative freedom, making Diffusion Self-Distillation a valuable tool for AI-generated content." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 326, + 685, + 504, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 685, + 504, + 696 + ], + "spans": [ + { + "bbox": [ + 326, + 685, + 504, + 696 + ], + "type": "text", + "content": "We summarize our contributions as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 701, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 701, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 314, + 701, + 555, + 713 + ], + "type": "text", + "content": "- We propose Diffusion Self-Distillation, a zero-shot" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "18435" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 294, + 135 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 294, + 135 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 294, + 135 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 294, + 135 + ], + "type": "image", + "image_path": "f46eaefb23afdf189a7ede14e6c86c99c86a5896c27045a36d662f3759e94b5e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 142, + 297, + 199 + ], + "lines": [ + { + "bbox": [ + 54, + 142, + 297, + 199 + ], + "spans": [ + { + "bbox": [ + 54, + 142, + 297, + 199 + ], + "type": "text", + "content": "Figure 3. Difference between structure-preserving and identity-preserving edits. In structure-preserving editing, the main structures of the image are preserved, and only local edits or stylizations are performed. In identity-preserving editing, the global structure of the image may change radically." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 63, + 220, + 296, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 220, + 296, + 255 + ], + "spans": [ + { + "bbox": [ + 63, + 220, + 296, + 255 + ], + "type": "text", + "content": "identity-preserving customized image generation model that scales to any instance under any context, with performances on par with inference-stage tuning methods;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 255, + 296, + 350 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 255, + 295, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 255, + 295, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 255, + 295, + 300 + ], + "type": "text", + "content": "- We provide a self-distillation pipeline to obtain identity-preserving data pairs purely from pretrained text-to-image diffusion models, LLMs, and VLMs, without any human effort involved in the entire data creation wheel;" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 303, + 296, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 303, + 296, + 350 + ], + "spans": [ + { + "bbox": [ + 56, + 303, + 296, + 350 + ], + "type": "text", + "content": "- We correspondingly design a unified architecture for image-to-image translation tasks involving both identity- and structure-preserving edits, including personalization, relighting, depth controls, and instruction following." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 362, + 140, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 362, + 140, + 374 + ], + "spans": [ + { + "bbox": [ + 55, + 362, + 140, + 374 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 382, + 296, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 382, + 296, + 442 + ], + "spans": [ + { + "bbox": [ + 55, + 382, + 296, + 442 + ], + "type": "text", + "content": "Recent advancements in diffusion models have underscored the need for enhanced control and customization in image-generation tasks. Various methods have been proposed to address these challenges through additional conditioning mechanisms, personalization, and rapid adaptation [28]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 452, + 296, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 452, + 296, + 620 + ], + "spans": [ + { + "bbox": [ + 55, + 452, + 296, + 620 + ], + "type": "text", + "content": "Control Mechanisms in Diffusion Models. To move beyond purely text-based controls, approaches like ControlNet [48] introduce spatial conditioning via inputs such as sketches, depth maps, and segmentation masks, enabling fine-grained structure control. ControlNet++ [21] refines this by enhancing the integration of spatial inputs for more nuanced control. Uni-ControlNet [49] unifies various control types within a single framework, standardizing the handling of diverse signals. T2I-Adapter [25] employs lightweight adapters to align pretrained models with external control signals without altering the core architecture. While these methods offer increased flexibility, they often focus on structural conditioning types such as depths and lack capabilities for concept extraction or identity preservation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 629, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 629, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 297, + 715 + ], + "type": "text", + "content": "Personalization and Fine-Tuning. Techniques like Dream-Booth [34] and LoRA [15] enhance the consistency and relevance of generated images by fine-tuning models with small sets of reference images. DreamBooth [34] personalizes models to maintain a subject's identity across different contexts, while LoRA [15] provides an efficient approach to fine-tuning large models without extensive retraining. How" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 120 + ], + "type": "text", + "content": "ever, these methods require multiple images and test-time optimization for each reference, which can be computationally expensive—especially with the exponential growth in model sizes (12 billion parameters for FLUX)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 133, + 556, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 133, + 556, + 384 + ], + "spans": [ + { + "bbox": [ + 313, + 133, + 556, + 384 + ], + "type": "text", + "content": "Zero-Shot and Fast Adaptation. IP-Adapter [46] incorporates image prompts into diffusion models using image embeddings, allowing for generations that align closely with reference visuals. InstantID [41] ensures zero-shot face preservation, maintaining a subject's key features across various contexts. While effective as zero-shot methods without user training, IP-Adapter [46] struggles to adapt specific targets like unique characters or assets, and InstantID [41] is limited to facial identity preservation. IPAdapter-Instruct [33] enhances image-based conditioning with instruct prompts but relies heavily on specific instructions and task-specific pretrained models. Other methods, such as SuTI [8] and GDT [17], handcrafted corresponding datasets, which are expensive and challenging to collect and scale. Another work along this line is Subject-Diffusion [23], which uses segmentation masks to create synthetic data for training but is bounded by achieving only simple attributes and accessories copying and editing within input images. Other methods [1, 11, 29, 40, 47] also investigated synthetic pairwise data generation but often fell short in scale because of the manual effort involved." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 386, + 556, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 386, + 556, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 386, + 556, + 482 + ], + "type": "text", + "content": "Existing methods contribute valuable advancements but often target specific domains or require user-stage tuning. Diffusion Self-Distillation bridges these gaps by offering a unified, zero-shot approach for consistent customization of characters and assets using minimal input. By leveraging self-distillation assisted by vision-language models, Diffusion Self-Distillation provides a comprehensive and adaptable solution for a wide range of creative applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 499, + 460, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 499, + 460, + 512 + ], + "spans": [ + { + "bbox": [ + 313, + 499, + 460, + 512 + ], + "type": "text", + "content": "3. Diffusion Self-Distillation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 522, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 556, + 713 + ], + "type": "text", + "content": "We discover that recent text-to-image generation models offer the surprising ability to generate in-context, consistent image grids (see Fig. 2, left). Motivated by this insight, we develop a zero-shot adaptation network that offers fast, diverse, high-quality, and identity-preserving, i.e., consistent image generation conditioned on a reference image. For this purpose, we first generate and curate sets of images that exhibit the desired consistency using pretrained text-to-image diffusion models, large language models (LLMs), and vision-language models (VLMs) (Sec. 3.1). Then, we finetune the same pretrained diffusion model with these consistent image sets, employing our newly proposed parallel processing architecture (Sec. 3.2) to create a conditional model. By this end, Diffusion Self-Distillation finetunes a pretrained text-to-image diffusion model into a zero-shot customized image generator in a supervised manner." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18436" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 220, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 220, + 85 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 220, + 85 + ], + "type": "text", + "content": "3.1. Generating a Pairwise Dataset" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 89, + 296, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 89, + 296, + 197 + ], + "spans": [ + { + "bbox": [ + 55, + 89, + 296, + 197 + ], + "type": "text", + "content": "To create a pairwise dataset for supervised Diffusion Self-Distillation training, we leverage the emerging multi-image generation capabilities of pretrained text-to-image diffusion models to produce potentially consistent vanilla images (Sec. 3.1.1) created by LLM-generated prompts (Sec. 3.1.2). We then use VLMs to curate these vanilla samples, obtaining clean sets of images that share the desired identity consistency (Sec. 3.1.3). The data generation and curation pipeline is shown in Fig. 2, left." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 202, + 269, + 214 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 202, + 269, + 214 + ], + "spans": [ + { + "bbox": [ + 55, + 202, + 269, + 214 + ], + "type": "text", + "content": "3.1.1. Vanilla Data Generation via Teacher Model" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 217, + 296, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 217, + 296, + 445 + ], + "spans": [ + { + "bbox": [ + 56, + 217, + 296, + 445 + ], + "type": "text", + "content": "To generate sets of images that fulfill the desired identity preservation, we prompt the teacher pretrained text-to-image diffusion model to create images containing multiple panels featuring the same subject with variations in expression, pose, lighting conditions, and more, for training purposes. Such prompting can be as simple as specifying the desired identity preservation in the output, such as \"a grid of 4 images representing the same " + }, + { + "bbox": [ + 56, + 217, + 296, + 445 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 56, + 217, + 296, + 445 + ], + "type": "text", + "content": " object/character/scene/etc. >\", \"an evenly separated 4 panels, depicting identical " + }, + { + "bbox": [ + 56, + 217, + 296, + 445 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 56, + 217, + 296, + 445 + ], + "type": "text", + "content": " object/character/scene/etc. >\", etc. We additionally specify the expected content in each sub-image/panel. The full set of prompts is provided in our supplemental material Sec. A. Our analysis shows that current state-of-the-art text-to-image diffusion models (e.g., SD3 [9], DALL-E 3, FLUX) demonstrate this identity-preserving capability, likely emerging from their training data, which includes comics, mangas, photo albums, and video frames. Such in-context generation ability is crucial to our data generation wheel." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 450, + 211, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 211, + 462 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 211, + 462 + ], + "type": "text", + "content": "3.1.2. Prompt Generation via LLMs" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 465, + 296, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 465, + 296, + 669 + ], + "spans": [ + { + "bbox": [ + 55, + 465, + 296, + 669 + ], + "type": "text", + "content": "We rely on an LLM to \"brainstorm\" a large dataset of diverse prompts, from which we derive our image grid dataset. By defining a prompt structure, we prompt the LLM to produce text prompts that describe image grids. A challenge we encountered is that when prompted to create large sets of prompts, LLMs tend to produce prompts of low diversity. For example, we noticed that without additional guidance, GPT-4o has a strong preference for prompts with cars and robots, resulting in highly repetitive outputs. To address this issue, we utilize the available image captions in the LAION [36] dataset, feeding them into the LLM as content references. These references from real image captions dramatically improve the diversity of generated prompts. Optionally, we also use the LLM to filter these reference captions, ensuring they contain a clear target for identity preservation. We find that this significantly improves the hit rate of generating consistent multi-image outputs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 674, + 263, + 686 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 674, + 263, + 686 + ], + "spans": [ + { + "bbox": [ + 55, + 674, + 263, + 686 + ], + "type": "text", + "content": "3.1.3. Dataset Curation and Caption with VLMs" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 715 + ], + "type": "text", + "content": "While the aforementioned data generation scheme provides identity-preserving multi-image samples of decent quality" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 555, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 555, + 228 + ], + "type": "text", + "content": "and quantity, these initial \"uncurated\" images tend to be noisy and unsuitable for direct use. Therefore, we leverage the strong capabilities of VLMs to curate a clean dataset. We extract pairs of images from the generated samples intended to preserve the identity and ask the VLM whether the two images depict the same object, character, scene, etc. We find that employing Chain-of-Thought prompting [42] is particularly helpful in this context. Specifically, we first prompt the VLM to identify the common object, character, or scene present in both images, then have it describe each one in detail, and finally analyze whether they are identical, providing a conclusive response. This process yields pairs of images that share the same identity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 236, + 488, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 488, + 248 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 488, + 248 + ], + "type": "text", + "content": "3.2. Parallel Processing Architecture" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 254, + 556, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 254, + 556, + 589 + ], + "spans": [ + { + "bbox": [ + 313, + 254, + 556, + 589 + ], + "type": "text", + "content": "We desire a conditional architecture suitable for general image-to-image tasks, including transformations in which structure is preserved, and transformations in which concepts/identities are preserved but image structure is not. This is a challenging problem because it may necessitate the transfer of fine details without guaranteeing spatial correspondences. While the ControlNet [48] architecture is excellent at structure-preserving edits, such as depth-to-image or segmentation-map-to-image, it struggles to preserve details under more complex identity-preserving edits, where the source and target images are not pixel-aligned. On the other hand, IP-Adapter [46] can extract certain concepts, such as styles, from the input image. Still, it strongly relies on a task-specific image encoder and often fails to preserve more complex concepts and identities. Drawing inspiration from the success of multi-view and video diffusion models [2, 4–6, 12–14, 16, 18, 20, 37, 38, 43, 45], we propose a simple yet effective method to extend the vanilla diffusion transformer model into an image-conditioned diffusion model. Specifically, we treat the input image as the first frame of a video and produce a two-frame video as output. The final loss is computed over the two-frame video, establishing an identity mapping for the first frame and a conditionally editing target for the second frame. Our architecture design allows generality for generic image-to-image translation tasks, since it enables effective information exchange between the two frames, allowing the model to capture complex semantics and perform sophisticated edits, as shown in Fig. 2, right." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 599, + 394, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 599, + 394, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 599, + 394, + 613 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": "Implementation details. We use FLUX1.0 DEV as both our teacher and student models, achieving self-distillation. For prompt generation, we use GPT-4o; for dataset curation and captioning, we use Gemini-1.5. We train all models on 8 NVIDIA H100 80GB GPUs with an effective batch size of 160 for 100k iterations, using AdamW optimizer [22] with a learning rate " + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 313, + 629, + 556, + 715 + ], + "type": "text", + "content": ". Our parallel processing architecture uses" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18437" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 552, + 388 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 552, + 388 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 552, + 388 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 552, + 388 + ], + "type": "image", + "image_path": "63af7ebf150e84f622cad33d6277aa4c319ea15202177de26bb810679c0c29ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 392, + 555, + 426 + ], + "lines": [ + { + "bbox": [ + 55, + 392, + 555, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 392, + 555, + 426 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison. Overall, our method achieves high subject identity preservation and prompt-aligned diversity while not suffering from a \"copy-paste\" effect, such as the results of IP-Adapter+ [46]. This is largely thanks to our supervised training pipeline, which alleviates the base model's in-context generation ability." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 431, + 223, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 431, + 223, + 442 + ], + "spans": [ + { + "bbox": [ + 55, + 431, + 223, + 442 + ], + "type": "text", + "content": "LoRAs with rank 512 on the base model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 459, + 297, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 459, + 297, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 459, + 297, + 651 + ], + "type": "text", + "content": "Datasets. Our final training dataset contains " + }, + { + "bbox": [ + 55, + 459, + 297, + 651 + ], + "type": "inline_equation", + "content": "\\sim 400\\mathrm{k}" + }, + { + "bbox": [ + 55, + 459, + 297, + 651 + ], + "type": "text", + "content": " subject-consistent image pairs generated from our teacher model, FLUX1.0 DEV. Generating and curating the dataset is fully automated and requires no human effort, so its size could be further scaled. We use the publicly available DreamBench++ [27] dataset and follow their protocols for evaluation. DreamBench++ [27] is a comprehensive and diverse dataset for evaluating personalized image generation, consisting of 150 high-quality images and 1,350 prompts—significantly more than previous benchmarks like DreamBench [34]. The dataset covers various categories such as animals, humans, objects, etc., including photorealistic and non-photorealistic images, with prompts designed to span different difficulty levels (simple/imaginative). In contrast, prompts are generated using GPT-4o and refined by human annotators to ensure diversity and ethical compliance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 665, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 297, + 715 + ], + "type": "text", + "content": "Baselines. We follow the setups in DreamBench++ [27] and compare our model with two classes of baselines: inference-stage tuning models and zero-shot models. For inference-stage models, we compare against Textual Inversion [10]," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 431, + 556, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 431, + 556, + 468 + ], + "spans": [ + { + "bbox": [ + 313, + 431, + 556, + 468 + ], + "type": "text", + "content": "DreamBooth [34] and its LoRA [15] version. For zero-shot models, we compare with BLIP-Diffusion [19], Emu2 [39], IP-Adapter [46], IP-Adapter+ [46]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "content": "Evaluation metrics. The evaluation protocol of prior works [8, 33, 34, 46] typically involves comparing the CLIP [30] and DINO [7] feature similarities. However, we note that the metrics mentioned above capture only global semantic similarity, are extremely noisy, and are biased towards \"copy-pasting\" the input image. This is especially troublesome when the input image or the prompt is complex. We refer to DreamBench++ [27] for a detailed analysis of their limitations. Therefore, we follow the metrics designed in DreamBench++ [27] and report GPT-4o scores on the more diverse DreamBench++ [27] benchmark for both concept preservation (CP) with different categories of subjects and prompt following (PF) with photorealistic (Real.) and Imaginative (Imag.) prompts, then use their product as a final evaluation score. This evaluation protocol emulates a human user study using VLMs. We additionally slightly modify the GPT evaluation prompts so that penalization can be applied if the generated contents show no internal understanding and creative output but instead naively copy over" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18438" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 81, + 552, + 566 + ], + "blocks": [ + { + "bbox": [ + 258, + 72, + 350, + 81 + ], + "lines": [ + { + "bbox": [ + 258, + 72, + 350, + 81 + ], + "spans": [ + { + "bbox": [ + 258, + 72, + 350, + 81 + ], + "type": "text", + "content": "Character Preservation" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 59, + 81, + 552, + 566 + ], + "lines": [ + { + "bbox": [ + 59, + 81, + 552, + 566 + ], + "spans": [ + { + "bbox": [ + 59, + 81, + 552, + 566 + ], + "type": "image", + "image_path": "e7186bc7d9913c78370951b459575d4b7408ed2410ffd4d996b8575f5b58501b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 568, + 555, + 602 + ], + "lines": [ + { + "bbox": [ + 55, + 568, + 555, + 602 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 555, + 602 + ], + "type": "text", + "content": "Figure 5. Qualitative result. Our Diffusion Self-Distillation is capable of various customization targets across different tasks and styles, for instance, characters or objects, photorealistic or animated. Diffusion Self-Distillation can also take instruction types of prompts as input, similar to InstructPix2Pix [3]. Further, our model exhibits relighting capabilities without significantly altering the scene's content." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 608, + 297, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 608, + 297, + 668 + ], + "spans": [ + { + "bbox": [ + 55, + 608, + 297, + 668 + ], + "type": "text", + "content": "components from the reference image. The modified metrics are named \"de-biased concept preservation (Debiased CP)\" and \"de-biased prompt following (Debiased PF)\". The full set of GPT evaluation prompts will be provided in our supplementary Sec. B." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 296, + 715 + ], + "type": "text", + "content": "Qualitative results. Fig. 4 presents our qualitative comparison results, demonstrating that our model significantly outperforms all baselines in subject adaptation and concept" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 608, + 556, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 608, + 556, + 705 + ], + "spans": [ + { + "bbox": [ + 313, + 608, + 556, + 705 + ], + "type": "text", + "content": "consistency while exhibiting excellent prompt alignment and diversity in the outputs. Textual Inversion [10], as an early concept extraction method, captures only vague semantics from the input image, making it unsuitable for zero-shot customization tasks that require precise subject adaptation. DreamBooth [34] and DreamBooth-LoRA [15, 34] face challenges in maintaining consistency, primarily because they perform better with multiple input images. This dependency" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18439" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 71, + 555, + 168 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 555, + 168 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 555, + 168 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 555, + 168 + ], + "type": "table", + "html": "
    MethodConcept PreservationPrompt FollowingDebiased Concept PreservationDebiased Prompt Following
    Z-S?Animal↑Human↑Object↑Overall↑Real.↑Imag.↑Overall↑CP-PF↑Animal↑Human↑Object↑Overall↑Real.↑Imag.↑Overall↑
    Textual Inversion✘0.5020.3580.3050.3880.6710.4370.5980.2320.7410.6940.7170.7220.6190.3850.541
    DreamBooth✘0.6400.1990.4880.4420.7980.5040.6920.3060.6700.3620.6760.6260.7500.4670.656
    DreamBooth LoRA✘0.7510.3110.5430.5350.8980.7540.8490.4500.6810.6750.7610.7200.8650.7180.816
    BLIP-Diffusion✓0.6370.5570.4690.5540.5810.3030.4640.2570.7710.7330.7450.7500.5290.2660.442
    Emu2✓0.6700.5460.4470.5540.7320.5600.6700.3710.6520.6830.7010.6810.6860.4940.622
    IP-Adapter✓0.6670.5580.5040.5760.7430.4460.6070.3500.7900.7640.7430.7660.6950.3770.589
    IP-Adapter+✓0.9000.8450.7590.8340.5020.2790.3880.3240.4810.4730.5300.5040.4420.2290.371
    Ours✓0.6470.5670.6400.6310.7770.6250.7260.4580.8520.7740.7500.7890.8080.6810.757
    ", + "image_path": "f6da2918db03a5e39408b53e448c3e5ed1165e1e30f57e57923936634a086839.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 172, + 555, + 251 + ], + "lines": [ + { + "bbox": [ + 55, + 172, + 555, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 172, + 555, + 251 + ], + "type": "text", + "content": "Table 1. Quantitative result. On the human-aligned GPT score metrics, our method is only inferior to IP-Adapter+ [46] for concept preservation (largely because of IP-Adapter families' \"copy-pasting\" effect) and the tuning-base DreamBooth-LoRA [15, 34] for prompt following, but outperforms every other baseline, achieving the best overall performance considering both concept preservation and prompt following. We also note that on the de-biased GPT evaluation, which penalizes \"copy-pasting\" the reference image without significant creative interpretation or transformation, the advantages of IP-Adaper+ [46] no longer hold. This can also be partly observed by their bad prompt following scores, meaning they are biased towards the reference input and are not accommodating the input prompt. The first, second, and third values are highlighted, where Diffusion Self-Distillation is the best overall performing model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 256, + 297, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 256, + 297, + 602 + ], + "spans": [ + { + "bbox": [ + 56, + 256, + 297, + 602 + ], + "type": "text", + "content": "limits their effectiveness when only a single reference image is available. In contrast, our method achieves robust results even with just one input image, highlighting its efficiency and practicality. BLIP-Diffusion [19], operating as a self-supervised representation learning framework, can extract concepts from the input in a zero-shot manner but is confined to capturing overall semantic concepts without the ability to customize specific subjects. Similarly, Emu2 [39], a multimodal foundation model, excels at extracting semantic concepts but lacks mechanisms for specific subject customization, limiting its utility in personalized image generation. IP-Adapter [46] and IP-Adapter+ [46] employ self-supervised learning schemes aimed at reconstructing the input from encoded signals. While effective in extracting global concepts, they suffer from a pronounced \"copy-paste\" effect, where the generated images closely resemble the input without meaningful transformation. Notably, IP-Adapter+ [46], which utilizes a stronger input image encoder, exacerbates this issue, leading to less diversity and adaptability in the outputs. In contrast, our approach effectively preserves the subject's core identity while enabling diverse and contextually appropriate transformations. As illustrated in Fig. 5, our Diffusion Self-Distillation demonstrates remarkable versatility, adeptly handling various customization targets across different targets (characters, objects, etc.) and styles (photorealistic, animated, etc.). Moreover, Diffusion Self-Distillation generalizes well to a wide range of prompts, including instructions similar to InstructPix2Pix [3], underscoring its robustness and adaptability in diverse customization tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 618, + 297, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 297, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 297, + 715 + ], + "type": "text", + "content": "Quantitative results. Quantitative comparison with the baselines are shown in Tab. 1, where we report GPT evaluation following DreamBench++ [27]. Such an evaluation protocol is similar to human score but uses automatic multimodal LLMs. Our method achieves the best overall performances accommodating both concept preservation and prompt following, while only being inferior to IP-Adapter+ [46] for the former (mainly because of" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 256, + 556, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 256, + 556, + 472 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 556, + 472 + ], + "type": "text", + "content": "the \"copy-paste\" effect again), and the per-instance tuning DreamBooth-LoRA [15, 34] for the latter. We note that the concept preservation evaluation of DreamBench++ [27] is still biased towards favoring a \"copy-paste\" effect, especially on more challenging and diverse prompts. For instance, the outstanding concept preservation performances of the IP-Adapter family [46] are primarily because of their strong \"copy-paste\" effect, which copies over the input image without considering relevant essential changes in the prompts. This can also be partly observed by their underperforming prompt following scores, which means they are biased towards the reference input and do not accommodate the input prompt. Therefore, we also present our \"de-biased\" version of GPT scores, which are as simple as telling GPT to penalize if the generated image resembles a direct copy of the reference image. We observe that the advantages of IP-Adaper+ [46] no longer hold. Overall, Diffusion Self-Distillation is the best-performing model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "content": "Ablation studies. (1) Data curation: During dataset generation, we first synthesize grids using a frozen pre-trained FLUX model and then filter the images via VLM curation. Why not fine-tune the FLUX model on image grids to improve the hit rate? To study this, we fit a LoRA [15] using " + }, + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "inline_equation", + "content": ">7000" + }, + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "content": " consistent grids (Fig. 6, left). Though a more significant proportion of samples are consistent grids, we find that the teacher model loses diversity in its output. Therefore, we choose to rely entirely on VLMs to help us curate from large numbers of diverse but potentially noisy grids. (2) Parallel processing architecture: We compare the parallel processing architecture to three alternative image-to-image architectures: 1) concatenating the source image to the noise image (\"concatenation\"); 2) a ControlNet [48]-based design, and 3) an IP-Adapter [46]-based design. We train each architecture using the same data as our parallel processing model (Fig. 6, middle). For ControlNet [48], we draw the same conclusion as prior work [16], in that it works best for structure-aligned edits, but generally strug" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "18440" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 82, + 108, + 131 + ], + "blocks": [ + { + "bbox": [ + 59, + 72, + 164, + 80 + ], + "lines": [ + { + "bbox": [ + 59, + 72, + 164, + 80 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 164, + 80 + ], + "type": "text", + "content": "Effect of LoRA for Data Generation" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 60, + 82, + 108, + 131 + ], 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Ablation study. Left: We compare the base model's in-context sampling ability with a consistent grid LoRA-overfitted model. We observe that although applying LoRA to the base model can increase the likelihood of outputs being consistent grids, it may adversely affect output diversity. Therefore, we rely on vision-language models (VLMs) to curate from a large number of diverse but potentially noisy grids. Right: We compare our architectural design with a vanilla conditional model (by adding a few input channels), ControlNet [48], and IP-Adapter [46]. Our architecture learns the input concepts and identities significantly better. We also demonstrate that our architecture can effectively scale to depth-conditioned image generation similar to ControlNet [48]." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 229, + 79, + 354, + 129 + ], + "blocks": [ + { + "bbox": [ + 301, + 71, + 418, + 78 + ], + "lines": [ + { + "bbox": [ + 301, + 71, + 418, + 78 + ], + "spans": [ + { + "bbox": [ + 301, + 71, + 418, + 78 + ], + "type": "text", + "content": "Comparison of Different Architectures" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 229, + 79, + 354, + 129 + ], + "lines": [ + { + "bbox": [ + 229, + 79, + 354, + 129 + ], + "spans": [ + { + "bbox": [ + 229, + 79, + 354, + 129 + ], + "type": "image", + "image_path": "82be34914c8e2e83f3284644708d4580ea1c77f4b554729d01b1500d16b1a41f.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 226, + 152, + 358, + 191 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 226, + 152, + 358, + 191 + ], + "spans": [ + { + "bbox": [ + 226, + 152, + 358, + 191 + ], + "type": "image", + "image_path": "916d239f83bb47e454e665302cbedf4aeebc3fff55be0751041ffdfcd8debdf9.jpg" + } + ] + } + ], + "index": 16, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 363, + 96, + 397, + 129 + ], + "blocks": [ + { + "bbox": [ + 363, + 96, + 397, + 129 + ], + "lines": [ + { + "bbox": [ + 363, + 96, + 397, + 129 + ], + "spans": [ + { + "bbox": [ + 363, + 96, + 397, + 129 + ], + "type": "image", + "image_path": "db13d74a782a3f963d4ea6e7ae29f34cb12a3406771fe4a271be404114326e60.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 364, + 142, + 398, + 176 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 142, + 398, + 176 + ], + "spans": [ + { + "bbox": [ + 364, + 142, + 398, + 176 + ], + "type": "image", + "image_path": "f742df35b83647d5f67d12270ff7a95de6f75f676e0fcd6666a3ee48e71027bb.jpg" + } + ] + } + ], + "index": 18, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 401, + 96, + 452, + 130 + ], + "blocks": [ + { + "bbox": [ + 401, + 96, + 452, + 130 + ], + "lines": [ + { + "bbox": [ + 401, + 96, + 452, + 130 + ], + "spans": [ + { + "bbox": [ + 401, + 96, + 452, + 130 + ], + "type": "image", + "image_path": "62867113117156a8e21204a697f87ce1870cb9943c7f6b35750dc5de38dc2569.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 454, + 100, + 551, + 128 + ], + "lines": [ + { + "bbox": [ + 454, + 100, + 551, + 128 + ], + "spans": [ + { + "bbox": [ + 454, + 100, + 551, + 128 + ], + "type": "text", + "content": "A regal, elderly man with a long white beard and hair, wearing ornate gold and red formal attire, plays a grand piano in a richly decorated room, lit by warm, natural light, camera angle low, focusing on the man's hands on the keys." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 19 + }, + { + "bbox": [ + 364, + 142, + 398, + 176 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 142, + 398, + 176 + ], + "spans": [ + { + "bbox": [ + 364, + 142, + 398, + 176 + ], + "type": "image", + "image_path": "f742df35b83647d5f67d12270ff7a95de6f75f676e0fcd6666a3ee48e71027bb.jpg" + } + ] + } + ], + "index": 20, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 401, + 142, + 452, + 176 + ], + "blocks": [ + { + "bbox": [ + 401, + 142, + 452, + 176 + ], + "lines": [ + { + "bbox": [ + 401, + 142, + 452, + 176 + ], + "spans": [ + { + "bbox": [ + 401, + 142, + 452, + 176 + ], + "type": "image", + "image_path": "80f8c6c74cc8bc352b60fbd17e0b85eb0edac2b0d69f43fbb8afa51a0749b26e.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 465, + 152, + 540, + 167 + ], + "lines": [ + { + "bbox": [ + 465, + 152, + 540, + 167 + ], + "spans": [ + { + "bbox": [ + 465, + 152, + 540, + 167 + ], + "type": "text", + "content": "A red four-door sedan parked in front of a brightly lit storefront, with the camera angled slightly towards the driver's side." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 58, + 269, + 293, + 380 + ], + "blocks": [ + { + "bbox": [ + 58, + 269, + 293, + 380 + ], + "lines": [ + { + "bbox": [ + 58, + 269, + 293, + 380 + ], + "spans": [ + { + "bbox": [ + 58, + 269, + 293, + 380 + ], + "type": "table", + "html": "
    MethodCP ↑PF ↑Creativity ↑
    Textual Inversion [10]1.6931.9242.850
    DreamBooth [34]2.3292.8833.597
    DreamBooth LoRA [15, 34]2.5763.3864.247
    BLIP-Diffusion [19]1.8542.2810.286
    Emu2 [39]1.8432.0962.965
    IP-Adapter [46]2.2742.3073.481
    IP-Adapter+ [46]3.7331.9592.428
    Ours3.6613.3284.453
    ", + "image_path": "25396dae6244689970b8d7ab5f46eaeee3b152908120540f8d9746e3dd1052ff.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "table_body" + } + ], + "index": 26 + }, + { + "bbox": [ + 55, + 384, + 295, + 440 + ], + "lines": [ + { + "bbox": [ + 55, + 384, + 295, + 440 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 295, + 440 + ], + "type": "text", + "content": "Table 2. User study. “CP” refers to concept preservation scores and “PF” refers to prompt following scores. The first, second, and third values are highlighted. Our user study results mostly align with our GPT evaluation, where our Diffusion Self-Distillation is the best overall performing model." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 55, + 449, + 296, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 296, + 558 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 296, + 558 + ], + "type": "text", + "content": "gles to preserve details when the source image and target image differ in camera pose. IP-Adapter [46] struggles to effectively transfer details and styles from the source image due to the limited capacity of its image encoder. (3) Other image-to-image tasks: Although not \"self-distillation\", since it requires an externally-sourced paired dataset (generated with Depth Anything [44]), we additionally train our architecture on depth-to-image to demonstrate its utility for more general image-to-image tasks (Fig. 6, right)." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "content": "User study. To evaluate the fidelity and prompt consistency of our generated images, we conducted a user study on a random subset of the DreamBench++ [27] test cases, selecting 20 samples. A total of 25 female and 29 male annotators, aged from 22 to 78 (average 34), independently scored each image from 1 to 5 based on three criteria: (1) concept preservation—the consistency with the reference image, (2) prompt alignment—the consistency with the given prompt, and (3) creativity—the level of internal understanding and transformation. The average scores are presented in Tab. 2. Our human annotations closely align with the GPT evaluation, demonstrating that our Diffusion Self-Distillation is slightly" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 271, + 555, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 271, + 555, + 355 + ], + "spans": [ + { + "bbox": [ + 313, + 271, + 555, + 355 + ], + "type": "text", + "content": "behind IP-Adapter+[46] in concept preservation and the inference-stage tuning method DreamBooth-LoRA [15, 34] in prompt alignment. Notably, our model achieved the highest creativity score, while IP-Adapter+ [46] scored lower in this metric due to its \"copy-paste\" effect. These results further confirm that our Diffusion Self-Distillation offers the most balanced and superior overall performance." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 370, + 383, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 370, + 383, + 383 + ], + "spans": [ + { + "bbox": [ + 313, + 370, + 383, + 383 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 313, + 392, + 555, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 392, + 555, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 392, + 555, + 499 + ], + "type": "text", + "content": "We present Diffusion Self-Distillation, a zero-shot approach designed to achieve identity adaptation across a wide range of contexts using text-to-image diffusion models without any human effort. Our method effectively transforms zero-shot customized image generation into a supervised task, substantially reducing its difficulty. Empirical evaluations demonstrate that Diffusion Self-Distillation performs comparably to inference-stage tuning techniques while retaining the efficiency of zero-shot methods." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 511, + 556, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 556, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 556, + 594 + ], + "type": "text", + "content": "Limitations and future work. Our work focuses on identity-preserving edits of characters, objects, and scene relighting. Future directions could explore additional tasks and use cases. Integration with ControlNet [48], for example, could provide fine-grained and independent control of identity and structure. Additionally, extending our approach from image to video generation is a promising avenue of future work." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 313, + 606, + 554, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 606, + 554, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 606, + 554, + 642 + ], + "type": "text", + "content": "Ethics. We are mindful of the potential misuse, particularly in deepfakes. We oppose exploiting our work for purposes that infringe upon ethical standards or privacy." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 555, + 713 + ], + "type": "text", + "content": "Conclusion. Our Diffusion Self-Distillation democratizes content creation, enabling identity-preserving, high-quality, and fast customized image generation that adapts seamlessly to evolving foundational models, significantly expanding the creative boundaries of art, design, and digital storytelling." + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18441" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 297, + 145 + ], + "type": "text", + "content": "Acknowledgements. This project was in part supported by Google, Kaiber AI, 3bodylabs, ONR N00014-23-1-2355, and NSF RI #2211258. ERC was supported by the Nvidia Graduate Fellowship and the Snap Research Fellowship. YZ was in part supported by the Stanford Interdisciplinary Graduate Fellowship." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 155, + 115, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 155, + 115, + 167 + ], + "spans": [ + { + "bbox": [ + 56, + 155, + 115, + 167 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 175, + 296, + 710 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 61, + 175, + 296, + 207 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 175, + 296, + 207 + ], + "spans": [ + { + "bbox": [ + 61, + 175, + 296, + 207 + ], + "type": "text", + "content": "[1] Kiymet Akdemir and Pinar Yanardag. 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Example results synthesized by our Diffusion-4K, emphasizing exceptional fine details in generated 4K images." + ], + "image_footnote": [], + "bbox": [ + 112, + 473, + 250, + 638 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/be0576bfef8283e279bd86ce49a08751eae2b47bbd2ea85664026931f4c4bcf6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 250, + 332, + 385, + 473 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b69dc306a8369ce044083b869baeece947185457efb54619436171d454df33bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 250, + 473, + 385, + 638 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4a75be8d3d29b90058430fad9496fb30b3ea64fca3c490045f12e32bea59d46d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 332, + 521, + 473 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a698ab0d24c7a42d888ff8a5637560a4f4155d44d4982f77ddf18b3d9ca71c62.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 473, + 521, + 638 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c049cffe824c09f89845351bc26ad1a521d8707a29d2a8bde55776711fbb19c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 332, + 702, + 473 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9d8df44b69aafa635e14a64275e63f65974b7d8d2309904a68809007703de3fc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 473, + 702, + 638 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/92ed28402298af9a017caefc59ab24d7cb033ae5bad0dbff5abfc386b90ded24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 333, + 883, + 473 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1ce4561b0ae947e7c6c6c09bf3d3796fa56824677bdde9ffdb87787d21fa10bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 473, + 883, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 676, + 326, + 693 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present Diffusion-4K, a novel framework for direct ultra-high-resolution image synthesis using text-to-image diffusion models. The core advancements include: (1) Aesthetic-4K Benchmark: addressing the absence of a publicly available 4K image synthesis dataset, we construct Aesthetic-4K, a comprehensive benchmark for ultra-high-resolution image generation. We curated a high-quality 4K dataset with carefully selected images and captions generated by GPT-4o. Additionally, we introduce GLCM Score and Compression Ratio metrics to evaluate fine details, combined with holis", + "bbox": [ + 89, + 709, + 483, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tic measures such as FID, Aesthetics and CLIPScore for a comprehensive assessment of ultra-high-resolution images. (2) Wavelet-based Fine-tuning: we propose a wavelet-based fine-tuning approach for direct training with photorealistic 4K images, applicable to various latent diffusion models, demonstrating its effectiveness in synthesizing highly detailed 4K images. Consequently, Diffusion-4K achieves impressive performance in high-quality image synthesis and text prompt adherence, especially when powered by modern large-scale diffusion models (e.g., SD3-2B and Flux-12B). Extensive experimental results from our benchmark demonstrate the superiority of Diffusion-4K in ultra-high-resolution image synthesis. Code is available at", + "bbox": [ + 511, + 679, + 906, + 875 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 109, + 887, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23464", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 135, + 222, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models have proven to be highly effective for modeling high-dimensional, perceptual data such as images [18, 21, 29, 31, 46]. In recent years, latent diffusion models have made significant advancements in text-to-image synthesis, demonstrating impressive generalization capabilities at high resolutions [9, 12, 23, 25, 34, 41]. Replacing convolutional U-Net with a transformer architecture shows promising improvements as model scalability increases, e.g., Stable Diffusion 3 (SD3) at 8B [12], Flux at 12B [5], and Playground v3 at 24B [25]. Alternatively, flow-based formulations, using data or velocity prediction, have emerged as an viable choice due to their faster convergence and enhanced performance [1, 21, 24, 26, 28].", + "bbox": [ + 89, + 160, + 482, + 356 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite substantial progress, most latent diffusion models focus on training and generating images at $1024 \\times 1024$ , leaving direct ultra-high-resolution image synthesis largely unexplored. Direct training and generating 4K images is valuable in realistic applications, but require considerable computational resources, especially as model parameters increase. Concurrent approaches such as PixArt- $\\Sigma$ [9] and Sana [49] address direct ultra-high-resolution image synthesis at 4K, showcasing the potentials of scalable latent diffusion transformer architectures. Both PixArt- $\\Sigma$ at 0.6B and Sana at 0.6/1.6B primarily focus on the efficiency of ultra-high-resolution image generation, however, the intrinsic advantages of 4K images, such as high-frequency details and rich textures, are neglected. Furthermore, due to the scarcity of photorealistic 4K images, there is currently no publicly available benchmark for 4K image synthesis, hindering further research on this valuable topic.", + "bbox": [ + 89, + 357, + 482, + 613 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose Diffusion-4K, a novel framework designed for direct ultra-high-resolution image synthesis using latent diffusion models. Specifically, we introduce Aesthetic-4K, including a high-quality dataset of curated ultra-high-resolution images, with corresponding captions generated by GPT-4o [19]. Additionally, most automated evaluation metrics, such as Frechet Inception Distance (FID) [17], Aesthetics [45] and CLIPScore [16], offer only holistic measures at low resolutions, which are insufficient for the comprehensive benchmarking in high-resolution image synthesis, particularly for 4K images. To address the limitations, we introduce Gray Level Cooccurrence Matrix (GLCM) Score and Compression Ratio metrics, focusing on assessment of fine details in ultra-high-resolution images which has not yet been explored, with the goal of establishing a comprehensive benchmark for 4K image synthesis. Additionally, we propose a wavelet-based fine-tuning method that emphasizes high-frequency components while preserving low-frequent approximation in ultra", + "bbox": [ + 89, + 614, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "high-resolution image synthesis. Notably, our method is compatible with various latent diffusion models. We conduct experiments with open-sourced latent diffusion models including SD3-2B [12] and Flux-12B [5], capable of training and generating photorealistic images at $4096 \\times 4096$ resolution. Consequently, our method demonstrates superior performance in 4K image synthesis, underscoring the effectiveness of the Diffusion-4K framework.", + "bbox": [ + 511, + 90, + 903, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions are summarized as follows:", + "bbox": [ + 532, + 212, + 872, + 224 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We establish Aesthetic-4k, a comprehensive benchmark for 4K image synthesis, including a high-quality dataset of ultra-high-resolution images with corresponding precise captions, and elaborated evaluation metrics for ultra-high-resolution images generation.", + "- We propose a wavelet-based fine-tuning approach for latent diffusion model, focusing on generating ultra-high-resolution images with fine details.", + "- Extensive experiment results demonstrate the effectiveness and generalization of our proposed method in 4K image synthesis, particularly when powered by large-scale diffusion transformers, e.g. SD3 and Flux." + ], + "bbox": [ + 511, + 227, + 903, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 513, + 422, + 650, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Latent Diffusion Models. Stable Diffusion (SD) [41] proposes latent diffusion models to operate diffusion process in compressed latent space using Variational AutoEncoder (VAE). Widely used VAEs [7, 12, 31] employ a down-sampling factor of $F = 8$ , compressing pixel space $\\mathbb{R}^{H\\times W\\times 3}$ into latent space $\\mathbb{R}^{\\frac{H}{F}\\times \\frac{W}{F}\\times C}$ , where $H$ and $W$ represent height and width respectively, and $C$ denotes the channel of latent space. In the field of latent diffusion models, Diffusion Transformer (DiT) [31] has made significant progress in the past year. Typically, the patch size of DiT is set to $P = 2$ , resulting in $\\frac{H}{FP}\\times \\frac{H}{FP}$ tokens. The transformer architecture demonstrates excellent scalability in latent diffusion models, as evidenced by PixArt [7, 9], SD3 [12], Flux [5], Playground [23, 25], etc.", + "bbox": [ + 511, + 446, + 906, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In text-to-image synthesis, the text encoder plays a crucial role in prompt coherence. SD employs CLIP [35] as its text encoder, while subsequent diffusion models, such as Imagen [42] and PixArt [7, 9], utilize T5-XXL [36] for text feature extraction. Recent approaches, such as SD3 [12] and Flux [5], combine both CLIP and T5-XXL for enhanced text understanding. DALL-E 3 [4] demonstrates that training with descriptive image captions can significantly enhance the prompt coherence of text-to-image models. Sana [49] utilizes the latest decoder-only Large Language Model (LLM), Gemma 2 [48], as its text encoder to improve understanding and reasoning capabilities related to text prompts.", + "bbox": [ + 511, + 659, + 905, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "High-Resolution Image Synthesis. High-resolution image generation is valuable in various practical applications such as industry and entertainment [6, 11]. Currently, advanced", + "bbox": [ + 511, + 854, + 905, + 900 + ], + "page_idx": 1 + }, + { + "type": "header", + "text": "https://github.com/zhangOjhon/diffusion-4k.", + "bbox": [ + 91, + 90, + 379, + 104 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23465", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "latent diffusion models typically train and synthesize images at $1024 \\times 1024$ for high-resolution image generation due to computational complexity [34, 38, 39, 41, 43, 44]. However, increasing image resolution introduces quadratic computational costs, posing challenges particularly for 4K image synthesis. Several training-free fusion approaches for 4K image generation have been developed based on existing latent diffusion models [2, 10]. Additionally, Stable Cascade [32] employs multiple diffusion networks to increase resolution progressively. However, such ensemble methods can introduce cumulative errors.", + "bbox": [ + 89, + 90, + 480, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PixArt- $\\Sigma$ [9] pioneers to direct image generation close to 4K (3840 × 2160) with efficient token compression for DiT, significantly improving efficiency and enabling ultra-high-resolution image generation. Sana [49], a pipeline designed to efficiently and cost-effectively train and synthesize 4K images, is capable of generating images at resolutions ranging from $1024\\times 1024$ to $4096\\times 4096$ . Sana introduces a deep compression VAE [8] that compresses images with an aggressive down-sampling factor of $F = 32$ , enabling content creation at low cost. Despite significant improvements in resolution, both PixArt- $\\Sigma$ -0.6B and Sana-0.6B/1.6B ignore the intrinsic high-frequency details and rich textures in 4K image synthesis. Furthermore, the potential for scalable DiT in 4K image generation remains unexplored.", + "bbox": [ + 89, + 257, + 482, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 89, + 481, + 191, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we elaborate on the details of Diffusion-4K, illustrating how it facilitates photorealistic 4K image synthesis. In Sec. 3.1, we introduce Aesthetic-4K, outlining the design principles and the process of constructing our human-centric benchmark with ultra-high-resolution images. Subsequently, we present a wavelet-based fine-tuning approach for direct training with photorealistic 4K images, applicable to various latent diffusion models, in Sec. 3.2.", + "bbox": [ + 89, + 507, + 482, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Aesthetic-4K Benchmark", + "text_level": 1, + "bbox": [ + 89, + 637, + 321, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing benchmarks for advanced latent diffusion models generally conduct experiments with images at $1024 \\times 1024$ resolution [7, 12, 23, 34], however, direct training and assessing with 4K images has not been thoroughly addressed yet. In this section, we construct Aesthetic-4K, a comprehensive benchmark for ultra-high-resolution image synthesis. The details are outlined as follows.", + "bbox": [ + 89, + 659, + 482, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Design Principles. Emphasis on human-centric perceptual cognition: To design a benchmark centered on human-level perceptual cognition, our primary goal is to explore the key factors of human perception on 4K images and formulate quantifiable indicators, while evaluating the general abilities of the generative model in these key factors. However, most automated evaluation metrics, such as FID [17], Aesthetics [45], and CLIPScore [16], provide only holistic measures at lower resolutions, which are insufficient for", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8ed412471c0e8cab02d65ced7cc7e0bd06bd24c83b283dfbee7ccf86141dcfd2.jpg", + "image_caption": [ + "Figure 2. Analysis of GLCM Score↑ / Compression Ratio↓. Our indicators demonstrate strong alignment with human-centric perceptual cognition at the level of local patches." + ], + "image_footnote": [], + "bbox": [ + 516, + 88, + 903, + 284 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/08016fc27aef3d106958bbfd6003db059f034667630cda517ff2b62120c9396c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MetricGLCM ScoreCompression RatioMUSIQMANIQA
    SRCC0.750.530.360.20
    PLCC0.770.560.410.26
    ", + "bbox": [ + 521, + 353, + 898, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Correlation with human evaluation.", + "bbox": [ + 576, + 417, + 841, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "comprehensive assessment, particularly lacking the ability of evaluating fine details in 4K images.", + "bbox": [ + 511, + 460, + 903, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by relevant literature in perceptual psychology, we found that highly structured textures play a decisive role in human perceptual cognition [3, 20, 47]. Therefore, we proposed additional indicators that accurately measure the richness of highly structured textures, including the commonly used quantitative indicators for texture analysis GLCM and the image compression ratio with discrete cosine transform (DCT). Considering human visual sensitivities, the GLCM, which captures the varying textural patterns, optical flow, and distortion through comprehensive spatial interactions of neighboring pixels, enables the creation of a truly representative characterization of human visual perception [13]. Simultaneously, the image compression ratio with DCT serves as an important reference for assessing the preservation of fine details in 4K images. To demonstrate alignment with human preferences, we conduct quantitative analysis of our indicators with adequate images, and present examples in Fig. 2. Moreover, as depicted in Tab. 1, we compute the Spearman Rank-order Correlation Coefficient (SRCC) and Pearson Linear Correlation Coefficient (PLCC) with human evaluations using various patches sampled from generated images, demonstrating the superior alignment with human ratings compared to no-reference image quality assessment metrics such as MUSIQ [22] and MANIQA [50]. Our benchmark design ensures that the model performance assessment is directly relevant to human decision-making and cognitive abilities.", + "bbox": [ + 511, + 493, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23466", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f8afdd4db2c4e4ef10e8e42debe2f99c2463239e6fb9476274104e165aea3a29.jpg", + "image_caption": [ + "Prompt: A vast colony of king penguins densely populates a rocky shore, with numerous individuals standing closely together against a backdrop of ocean waves." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 287, + 180 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/418f1901629cc925249c357062c56764c2c45a94ec332078b00b3b4b5c64e083.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 289, + 88, + 491, + 180 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8e779aa6776563cdc07483dcf3309d1e5383f7087284bbc4b82384ad59f6b768.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 198, + 287, + 290 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4e4a316ff619105b49cd720a8cdffd9bbf144065975985e97d3b6470aab448a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 289, + 198, + 491, + 290 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/85f2403418dfa62b2a7b8bede8508d505acf65409cf55b0ef4812f1f15d7f2b1.jpg", + "image_caption": [ + "Prompt: A sea turtle glides gracefully through crystal-clear turquoise water above a school of small fish, with sunlight reflecting off the surface.", + "Prompt: A close-up of a fox's face, partially covered in snow, with sharp ears and bright, alert eyes. The snowy backdrop adds a serene atmosphere to the scene.", + "(a) Image-text samples in training set.", + "Figure 3. Illustration of image-text samples in the Aesthetic-4K dataset, which includes high-quality images and precise text prompts generated by GPT-4o, distinguished by high aesthetics and fine details." + ], + "image_footnote": [], + "bbox": [ + 94, + 306, + 287, + 479 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/58389e8f04e24b2cd42d746dcbec95c353e53c867fb5df56c7edc3b5cddcfd1f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 289, + 306, + 490, + 479 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e66eb6b8c92ccd8d98e49a86552840a6cff03da06db1431a379b4b89ec1e9919.jpg", + "image_caption": [ + "Prompt: A picturesque riverside scene featuring a medieval castle atop a hill, surrounded by vibrant autumn foliage, with colorful homes lining the waterfront and several boats docked along the river." + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 697, + 180 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cb5e4bc63fada8b5b80e5a44404aaad455aa17d60119ea4749907d9ee4459f9e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 89, + 901, + 180 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/31e014e633c3dbc8156d4b93de06a6eac6ff3e4c5b5ce09ba00d56caa0c66f85.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 198, + 699, + 290 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c339301352df9423f57407b160d627423045f878208363c86f71bf8e03ee9318.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 198, + 901, + 290 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fc1351c83007173ed97044d3707a916ab0d3715b9ed695a463f2b24cc471d408.jpg", + "image_caption": [ + "Prompt: A lone astronaut floats in space, gazing at a swirling black hole surrounded by vibrant landscapes, rivers, and clouds below.", + "Prompt: A majestic polar bear sits near a rocky shore, reflecting in calm waters under a full moon amid a dramatic, cloudy sky filled with flying birds. A small figure stands in the distance, observing the scene.", + "(b) Image-text samples in evaluation set." + ], + "image_footnote": [], + "bbox": [ + 506, + 306, + 699, + 479 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/306f479833c7c79d8f3fa220ba2a465da082c3c3e5b3fbbf68ed5f2736f557b8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 306, + 901, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Aesthetic-4K Dataset. Addressing the absence of a publicly available 4K dataset, we propose the Aesthetic-4K dataset that includes a well-curated training and evaluation set for in-depth study. For the Aesthetic-4K training set, we collect high-quality images from the Internet, distinguished by exceptional aesthetics and fine details. Notably, the Aesthetic-4K training set consists of 12,015 high-quality images with a median height of 4128 and median width of 4640, representing a significant improvement in training data for ultra-high-resolution image synthesis. Additionally, we provide precise and detailed image captions generated by powerful GPT-4o [19], demonstrating strong alignment between vision and language. These curated images and corresponding captions comprise Aesthetic-Train, the training set of Aesthetic-4K.", + "bbox": [ + 88, + 579, + 482, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the evaluation set, Aesthetic-Eval, we select imag-text pairs from the LAION-Aesthetics V2 6.5+ dataset, following the criterion of a short image side greater than 2048. The LAION-Aesthetics dataset includes 625,000 imag-text pairs with predicted aesthetic scores of 6.5 or higher in LAION-5B [45]. Notably, the Aesthetic-4K evaluation set", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "consists of 2,781 high-quality images with a median height of 2983 and median width of 3613. We do not sample the evaluation set from the collected images sourced from the Internet, to mitigate the risk of overfitting in comprehensive assessments. Within the evaluation set, 195 images have a short side greater than 4096, which we refer to as Aesthetic-Eval@4096. Instead of evaluating with images at $1024 \\times 1024$ resolution [49], the proposed Aesthetic-4K evaluation set provides a suitable benchmark for ultra-high-resolution image synthesis.", + "bbox": [ + 511, + 579, + 906, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In summary, the proposed dataset encompasses common categories in realistic scenarios, including nature, travel, fashion, animals, film, art, food, sports, street photography, etc. As illustrated in Fig. 3, we present several image-text pairs from both the training and evaluation sets of Aesthetic-4K, clearly demonstrating their exceptional quality. For more details about the Aesthetic-4K dataset, please refer to the supplementary materials.", + "bbox": [ + 511, + 732, + 906, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Comprehensive Evaluation Metrics. To construct a comprehensive human-centric benchmark for 4K image synthesis, we provide conventional evaluation metrics in genera", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23467", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tive models, such as FID [17], Aesthetics [45], and CLIP-Score [16], for an intuitive understanding of image synthesis from a holistic perspective.", + "bbox": [ + 89, + 90, + 482, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, we report quantitative results for the proposed metrics assessing fine details in 4K images, including the GLCM Score and Compression Ratio, as significant complements to human-centric perceptual cognition in 4K images, which have not been addressed previously. The GLCM Score is formulated as follows: $s = -\\frac{1}{P}\\sum_{p=1}^{P}H(g_p)$ , where $H$ represents entropy, and $g_p$ is the GLCM [15] derived from local patch $p$ in the original image with 64 gray levels, defined by radius $\\delta = [1,2,3,4]$ and orientation $\\theta = [0^{\\circ},45^{\\circ},90^{\\circ},135^{\\circ}]$ . In practice, we divide the gray image into local patches of size 64, and compute the average GLCM Score based on the partitioned local patches. Regrading the Compression Ratio, it is calculated as the ratio of the original image size in memory to the compressed image size using the JPEG algorithm at a quality of 95. Qualitative and quantitative assessments constitute the comprehensive benchmark, Aesthetic-4K.", + "bbox": [ + 89, + 137, + 483, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Wavelet-based Fine-tuning", + "text_level": 1, + "bbox": [ + 89, + 401, + 334, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we propose a WaveLet-based Fine-tuning (WLF) method suitable for various latent diffusion models, enabling direct training with photorealistic images at $4096 \\times 4096$ resolution. The core improvements consist of two components:", + "bbox": [ + 89, + 422, + 483, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Partitioned VAE. The most commonly used VAEs [5, 12] with $F = 8$ encounter out-of-memory (OOM) issues during direct training and inference at $4096 \\times 4096$ . To address this issue, we propose an efficient partitioned VAE, a simple yet effective method that compresses images with $F = 16$ , significantly reducing memory consumption. Specifically, we use a dilation rate of 2 in the first convolutional layer of the VAE's encoder. In the last convolutional layer of the VAE's decoder, we partition the input feature map, up-sample by a factor of 2, apply the same convolution operator to each partitioned feature map, and then reorganize the final output. Notably, our method maintains consistency in the latent space of pre-trained latent diffusion models, eliminating the need for retraining or fine-tuning VAEs, which prevents distribution shifts in the latent space and ensures compatibility with various diffusion models.", + "bbox": [ + 89, + 500, + 483, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Wavelet-based Latent Enhancement. Wavelet transform has achieved significant success in image processing and is widely used to decompose low-frequency approximations and high-frequency details from images or features [14, 33]. In this section, we propose wavelet-based latent enhancement, which emphasizes high-frequency components while preserving low-frequency information, thereby significantly enhancing fine details and rich textures in 4K image generation. Consider the diffusion process, i.e.", + "bbox": [ + 89, + 739, + 483, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {z} _ {t} = \\alpha_ {t} \\cdot \\boldsymbol {x} _ {0} + \\sigma_ {t} \\cdot \\epsilon , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 886, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x_0$ and $\\epsilon$ represent data distribution and standard normal distribution, respectively, and $\\alpha_{t}$ and $\\sigma_t$ are hyperparameters in the diffusion formulation. The original training objective in latent diffusion models is noise prediction [18, 41], defined as:", + "bbox": [ + 511, + 90, + 905, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\epsilon_ {t}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 176, + 906, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Theta$ denotes the neural network, e.g., convolutional UNet or DiT. Recent approaches, such as SD3 [12] and Flux [5], adopt rectified flows to predict velocity $\\mathbf{v}$ parameterized by $\\Theta$ , with the objective as follows:", + "bbox": [ + 511, + 200, + 906, + 261 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {v} _ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\epsilon - \\boldsymbol {x} _ {0}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 270, + 906, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our method decomposes the low-frequency approximation and high-frequency details of latent features using wavelet transform, defining the training objective as follows:", + "bbox": [ + 511, + 294, + 906, + 340 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {W L F} = \\mathbb {E} \\left[ w _ {t} \\| f \\left(\\boldsymbol {v} _ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) - \\epsilon\\right) - f \\left(\\boldsymbol {x} _ {0}\\right) \\| ^ {2} \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 348, + 906, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{t}$ is the loss weight, and $f(\\cdot)$ denotes discrete wavelet transform (DWT). Notably, we use the Haar wavelet, widely adopted in real-world applications due to its efficiency. Specifically, $L = \\frac{1}{\\sqrt{2}} [1,1]$ and $H = \\frac{1}{\\sqrt{2}} [-1,1]$ denote the low-pass and high-pass filters, used to construct four kernels in DWT with stride 2, namely $LL^{T}, LHT, HLT, HH^{T}$ . The DWT kernels are then used to decompose the input features into four sub-bands, the low-frequency approximation $x_{ll}$ and high-frequency components $x_{lh}, x_{hl}, x_{hh}$ . As a result, both low-frequency information and high-frequency details are incorporated in Eq. (4), contributing to a comprehensive optimization in 4K image synthesis. In addition, our method supports various diffusion models by simply substituting the reconstruction objective, enabling seamless integration with conventional noise prediction approaches.", + "bbox": [ + 511, + 375, + 906, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 633, + 645, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of our method, we conduct experiments with the state-of-the-art latent diffusion models at various scales, including open-source SD3-2B [12] and Flux-12B [5]. Specifically, mainstream evaluation metrics, such as FID [17], Aesthetics [45] and CLIPScore [16], as well as the proposed GLCM Score and Compression Ratio metrics, are reported for comprehensive assessments. Additionally, we present quantitative and qualitative results that showcase the high-resolution image reconstruction and generation capabilities of partitioned VAE and WLF, respectively.", + "bbox": [ + 511, + 659, + 905, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 511, + 833, + 720, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Regrading the VAEs in both SD3 [12] and Flux [5], we encapsulate them using partitioned VAE with $F = 16$ , ensuring the direct training at", + "bbox": [ + 511, + 854, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23468", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a90a8fb5ac5e31bc557c3210d260573d909ffbebabab7e39ca5a8160a0bbcf78.jpg", + "image_caption": [ + "Figure 4. Reconstruction results of 4K images with partitioned VAEs of $F = 16$ ." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 222, + 314 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d683df6963aba897a0dcf660d68d8e72527ecd7e507bf18b967a49153a88c448.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 222, + 88, + 352, + 314 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/54b0daf059c3676cdc898ee9f292c154d07c989a0c190ea26d07cc54d36e8c74.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 88, + 480, + 314 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$4096 \\times 4096$ resolution without OOM issues. Notably, WLF is used for fine-tuning diffusion models, while the partitioned VAE and text encoder in pre-trained models are kept frozen, significantly improving the training efficiency. In practice, we use the AdamW [27] optimizer with a constant learning rate of 1e-6 and weight decay of 1e-4. We employ mixed-precision training with a batch size of 32 and use ZeRO Stage 2 with CPU offload techniques [37, 40]. The fine-tuning of SD3-2B and Flux-12B is conducted on 2 A800-80G GPUs and 8 A100-80G GPUs, respectively.", + "bbox": [ + 89, + 383, + 483, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experiment Results", + "text_level": 1, + "bbox": [ + 89, + 545, + 277, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis of partitioned VAEs. In Tab. 2, we report the evaluation results, including rFID, Normalized Mean Square Error (NMSE), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and LPIPS [51], to assess the reconstruction ability of partitioned VAEs on Aesthetic-4K at $4096 \\times 4096$ resolution. We provide detailed results for VAEs in SD3 and Flux, enhanced by our partition techniques with $F = 16$ . Notably, our partitioned VAE resolves the OOM issue encountered by the original VAE without requiring retraining or fine-tuning, thereby avoiding potential distribution shifts in the latent space. In addition, we present visualizations of original and reconstruction images in Fig. 4. The qualitative results demonstrate the effectiveness of the partitioned VAEs in 4K image reconstruction, ensuring consistency in the latent space for subsequent fine-tuning with 4K images.", + "bbox": [ + 89, + 568, + 482, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image Quality Assessment. Regarding image quality assessment, we conduct comprehensive comparisons using mainstream evaluation metrics, such as FID [17], Aesthetics [45] and CLIPScore [16], to provide an intuitive understanding of image quality and text prompt adherence. In Tab. 3, we report experimental results with SD3-2B and", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/19faf9e506f4699ab7c9e5bf716a58d925eeb4c7225086c507f2e3018c379abc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelrFIDNMSEPSNRSSIMLPIPS
    SD3-VAE-F161.400.0928.820.760.15
    Flux-VAE-F161.690.0829.220.790.16
    ", + "bbox": [ + 529, + 88, + 890, + 142 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/53e89fb6840bd9b9831ba50da52295b4e09613894a71dc68155f76ed3591addd.jpg", + "table_caption": [ + "Table 2. Quantitative reconstruction results of VAEs with down-sampling factor of $F = 16$ on our Aesthetic-4K training set at $4096 \\times 4096$ ." + ], + "table_footnote": [], + "table_body": "
    ModelFID ↓CLIPScore ↑Aesthetics ↑
    SD3-F16@204843.8231.505.91
    SD3-F16-WLF@204840.1834.045.96
    Flux-F16@204850.5730.416.36
    Flux-F16-WLF@204839.4934.416.37
    ", + "bbox": [ + 527, + 210, + 893, + 295 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d06bbb22b591cac0e349f657290c74ad2cbccf9d04f40ceb353c1fa0f312528d.jpg", + "table_caption": [ + "Table 3. Quantitative benchmarks of latent diffusion models on Aesthetic-Eval@2048 at $2048 \\times 2048$ resolution." + ], + "table_footnote": [], + "table_body": "
    ModelGLCM Score ↑Compression Ratio ↓
    SD3-F16@20480.7511.23
    SD3-F16-WLF@20480.7910.51
    Flux-F16@20480.5814.80
    Flux-F16-WLF@20480.6113.60
    ", + "bbox": [ + 517, + 349, + 903, + 435 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. GLCM Score and Compression Ratio of latent diffusion models on Aesthetic-Eval@2048 at $2048 \\times 2048$ resolution.", + "bbox": [ + 511, + 446, + 906, + 472 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Flux-12B on Aesthetic-Eval@2048 in Tab. 3, demonstrating the effectiveness of our method.", + "bbox": [ + 511, + 503, + 903, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As aforementioned, these conventional evaluation metrics are insufficient for comprehensive assessment in ultra-high-resolution image synthesis, particularly in evaluating the fine details of 4K images. In addition to commonly used benchmarks, we also compare the GLCM Score, which aims to assess the texture richness in ultra-high-resolution images. Simultaneously, we also report the Compression Ratio using the JPEG algorithm at a quality setting of 95, which can serve as an important reference for assessing image quality with fine details. As depicted in Tab. 4, experimental results highlight the advantages of WLF in these metrics, distinctly demonstrating our method's ability to generate 4K images with fine details.", + "bbox": [ + 509, + 536, + 906, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative 4K Image Synthesis. As illustrated in Fig. 5, we present qualitative high-resolution images synthesized with Diffusion-4K, powered by the state-of-the-art latent diffusion model, Flux-12B. Although WLF fine-tunes at $4096 \\times 4096$ resolution, our method can synthesize ultra-high-resolution images at various aspect ratios, and even supports direct photorealistic image generation at higher resolutions. In addition, we report the inference details in Tab. 5, highlighting the time and memory consumption of our method for directly generating 4K images. For sampling, images are generated by discretizing the ordinary", + "bbox": [ + 511, + 734, + 908, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23469", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4ca29c6722a3b0f250afc4436e7bff9b02792d4bb62a6fd1f77fc2d0bf4a1e75.jpg", + "image_caption": [], + "image_footnote": [ + "A stylish woman walks down a Tokyo street filled with warm glowing neon and animated city signage. She wears a black leather jacket, a long red dress, and black boots, and carries a black purse. She wears sunglasses and red lipstick. She walks confidently and casually. The street is damp and reflective, creating a mirror effect of the colorful lights. Many pedestrians walk about.", + "A gorgeously rendered papercraft world of a coral reef, rife with colorful fish and sea creatures." + ], + "bbox": [ + 119, + 87, + 877, + 382 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0bbeaea64b312f0295f59740b15644650e034249ba59456c1c3f9a9468e6d522.jpg", + "image_caption": [], + "image_footnote": [ + "A litter of golden retriever puppies playing in the snow. Their heads pop out of the snow, covered in." + ], + "bbox": [ + 119, + 414, + 475, + 618 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1304aa533ee6f8a0282bda4f301b6b931f336d88150739eb2fd19d18bd5a432e.jpg", + "image_caption": [], + "image_footnote": [ + "A petri dish with a bamboo forest growing within it that has tiny red pandas running around." + ], + "bbox": [ + 477, + 414, + 676, + 619 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9b8cb73681bb1183d8f32726ced2c7abbc9fc4f09fda3947c2198dded292eec7.jpg", + "image_caption": [], + "image_footnote": [ + "A young man at his 20s is sitting on a piece of cloud in the sky, reading a book." + ], + "bbox": [ + 676, + 414, + 875, + 619 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/61e3ee3274046f1b67eb8eb0720f4783ffda5a136df594b9d436769676647690.jpg", + "image_caption": [ + "Figure 5. Qualitative 4K images synthesis of Diffusion-4K. Prompts are from Sora [30]." + ], + "image_footnote": [ + "Extreme close up of a 24 year old woman's eye blinking, standing in Marrakech during magic hour, cinematic film shot in $70\\mathrm{mm}$ depth of field, vivid colors, cinematic" + ], + "bbox": [ + 119, + 645, + 496, + 864 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a3782a474e6af4901e6fd92a500f0a67191ad6ab2eea1e5f765dc9fb319ff70a.jpg", + "image_caption": [], + "image_footnote": [ + "3D animation of a small, round, fluffy creature with big, expressive eyes explores a vibrant, enchanted forest. The creature, a whimsical blend of a rabbit and a squirrel, has soft blue fur and a bushy, striped tail. It hops along a sparkling stream, its eyes wide with wonder. The forest is alive with magical elements: flowing water and small floating lights that resemble fireflies. The creature stops to interact playfully with a group of tiny, fairy-like beings dancing around a mushroom ring. The creature looks up in awe at a large, glowing tree that seems to be the heart of the forest." + ], + "bbox": [ + 500, + 645, + 877, + 864 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23470", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a9d258c02ec6cfa51d479a19a542308ca90ed2ecc5b0f0bf45f14d991e90475b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    ModelMemoryTime (s/step)
    SD3-F8@4096OOM-
    SD3-F16-WLF@409631.3GB1.16
    SD3-F16-WLF@4096 (CPU offload)16.1GB1.22
    Flux-F8@4096OOM-
    Flux-F16-WLF@409650.4 GB2.42
    Flux-F16-WLF@4096 (CPU offload)26.9 GB3.16
    ", + "bbox": [ + 94, + 88, + 482, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/366caeacd72239d9968b18b7bb8a284e25dc1c2db676663d67c71b62a849c4c7.jpg", + "image_caption": [ + "Figure 6. Human and GPT-4o preference evaluation." + ], + "image_footnote": [], + "bbox": [ + 106, + 266, + 465, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "differential equation (ODE) process using an Euler solver. Please refer to the supplementary materials for more comparisons and details.", + "bbox": [ + 89, + 483, + 482, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Preference Study. Human preference is assessed by rating the pairwise outputs from two models, i.e. Flux with and without WLF. Additionally, we employ the advanced multi-modal model, GPT-4o [19], as the evaluator for the preference study. The following questions are asked:", + "bbox": [ + 89, + 529, + 483, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visual Aesthetics: Given the prompt, which image is of higher-quality and aesthetically more pleasing?", + "bbox": [ + 89, + 606, + 483, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Prompt Adherence: Which image looks more representative to the text shown above and faithfully follows it?", + "bbox": [ + 89, + 637, + 482, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fine Details: Which image more accurately represents the fine visual details? Focus on clarity, sharpness, and texture. Assess the fidelity of fine elements such as edges, patterns, and nuances in color. The more precise representation of these details is preferred! Ignore other aspects.", + "bbox": [ + 88, + 667, + 483, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Fig. 6, our method demonstrates a superior win rate in both human and AI preference, highlighting the effectiveness of our WLF method in various aspects, including visual aesthetics, prompt adherence and fine details performance in 4K images.", + "bbox": [ + 89, + 744, + 483, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 89, + 832, + 254, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on Quality of Image Captions. We compare 4K image synthesis using original captions from LAION-5B [45] and captions generated by GPT-4o. As shown", + "bbox": [ + 89, + 854, + 482, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a3eb5a8d9fd027bb6f088d230cd2789f1b063f5a7c62c6f39cc21f57a74f9c1c.jpg", + "table_caption": [ + "Table 5. Memory consumption and inference speed of direct image synthesis at $4096 \\times 4096$ . The result is tested on one A100 GPU with BF16 Precision." + ], + "table_footnote": [], + "table_body": "
    CaptionsModelCLIPScore ↑Aesthetics ↑
    LAION-5BSD3-F16@409629.375.90
    GPT-4oSD3-F16@409633.125.97
    LAION-5BFlux-F16@409629.126.02
    GPT-4oFlux-F16@409633.676.11
    ", + "bbox": [ + 529, + 88, + 890, + 171 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/24c8d1f07ad33bc71bc20cf8869a299986c083b5f9fc55642a81f682b7b3bd74.jpg", + "table_caption": [ + "Table 6. Ablation study on quality of image captions on Aesthetic-Eval@4096 at $4096 \\times 4096$ ." + ], + "table_footnote": [], + "table_body": "
    ModelCLIPScore ↑Aesthetics ↑
    SD3-F16@409633.125.97
    SD3-F16-finetune@409634.145.99
    SD3-F16-WLF@409634.406.07
    ", + "bbox": [ + 529, + 228, + 890, + 299 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/abbe948a1d3f1c4ea0e8d8fc87880bf0a78420cabc996ebeccaf00cfc2012958.jpg", + "table_caption": [ + "Table 7. Ablation on CLIPScore and Aesthetics of SD3 on Aesthetic-Eval@4096 at $4096 \\times 4096$ . SD3-F16-finetune@4096 represents fine-tuning without WLF." + ], + "table_footnote": [], + "table_body": "
    ModelGLCM Score ↑Compression Ratio ↓
    SD3-F16@40960.7311.97
    SD3-F16-finetune@40960.7411.41
    SD3-F16-WLF@40960.7710.50
    ", + "bbox": [ + 517, + 369, + 903, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Ablation on GLCM Score and Compression Ratio of SD3 on Aesthetic-Eval@4096 at $4096 \\times 4096$ . SD3-F16-finetune@4096 denotes fine-tuning without WLF.", + "bbox": [ + 511, + 444, + 905, + 487 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in Tab. 6, both SD3 and Flux exhibit enhanced results in Aesthetic-Eval@4096 with captions from GPT-4o. Quantitative results indicate that prompts generated by GPT-4o improve image synthesis and prompt coherence, demonstrating the significance of high-quality prompts in 4K image generation.", + "bbox": [ + 511, + 517, + 905, + 608 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on WLF. To demonstrate the effectiveness of WLF, we conduct ablation studies with SD3, comparing fine-tuning diffusion models with and without WLF, and report the experiment results of Aesthetic-Eval@4096 in Tab. 7 and Tab. 8. Compared to fine-tuning without WLF, our WLF method demonstrates superior performance in CLIPScore, Aesthetics, GLCM Score and Compression Ratio, significantly showcasing its effectiveness in visual aesthetics, prompt adherence, and high-frequency details.", + "bbox": [ + 511, + 609, + 905, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 767, + 633, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present Diffusion-4K, a novel framework for ultra-high-resolution text-to-image generation. We introduce Aesthetic-4K benchmark and wavelet-based fine-tuning, capable of training with the state-of-the-art latent diffusion models, such as SD3 and Flux. Qualitative and quantitative results demonstrate the effectiveness of our approach in training and generating photorealistic 4K images.", + "bbox": [ + 511, + 794, + 905, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23471", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 269, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is partly supported by the National Natural Science Foundation of China (82441024), the Research Program of State Key Laboratory of Critical Software Environment, and the Fundamental Research Funds for the Central Universities.", + "bbox": [ + 89, + 114, + 483, + 189 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 203, + 187, + 218 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Michael S Albergo and Eric Vanden-Eijnden. Building normalizing flows with stochastic interpolants. arXiv preprint arXiv:2209.15571, 2022. 2", + "[2] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. Multidiffusion: Fusing diffusion paths for controlled image generation. 2023. 3", + "[3] James R Bergen and Edward H Adelson. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 6" + ], + "bbox": [ + 516, + 90, + 905, + 767 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23473", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/4935daf0-51e8-442b-8d44-f641c7d877f3_model.json b/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/4935daf0-51e8-442b-8d44-f641c7d877f3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9892be6ddd9ee855d2fc89fdb013dafb7cba4c80 --- /dev/null +++ b/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/4935daf0-51e8-442b-8d44-f641c7d877f3_model.json @@ -0,0 +1,2398 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.118, + 0.13, + 0.882, + 0.175 + ], + "angle": 0, + "content": "Diffusion-4K: Ultra-High-Resolution Image Synthesis with Latent Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.203, + 0.806, + 0.223 + ], + "angle": 0, + "content": "Jinjin Zhang\\(^{1,2}\\) Qiuyu Huang\\(^{3}\\) Junjie Liu\\(^{3}\\) Xiefan Guo\\(^{1,2}\\) Di Huang\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.222, + 0.778, + 0.257 + ], + "angle": 0, + "content": "\\(^{1}\\)State Key Laboratory of Complex and Critical Software Environment, Beihang University, Beijing 100191, China" + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.257, + 0.857, + 0.275 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Computer Science and Engineering, Beihang University, Beijing 100191, China" + }, + { + "type": "text", + "bbox": [ + 0.461, + 0.274, + 0.537, + 0.291 + ], + "angle": 0, + "content": "3Meituan" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.295, + 0.844, + 0.31 + ], + "angle": 0, + "content": "{jinjin.zhang, xfguo, dhuang}@buaa.edu.cn {huangqiuyu, liujunjiel0}@meituan.com" + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.332, + 0.249, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.474, + 0.25, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.251, + 0.333, + 0.386, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.251, + 0.474, + 0.386, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.333, + 0.522, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.474, + 0.522, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.333, + 0.704, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.474, + 0.703, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.334, + 0.885, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.474, + 0.885, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.137, + 0.651, + 0.86, + 0.666 + ], + "angle": 0, + "content": "Figure 1. Example results synthesized by our Diffusion-4K, emphasizing exceptional fine details in generated 4K images." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.678, + 0.327, + 0.694 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.71, + 0.484, + 0.876 + ], + "angle": 0, + "content": "In this paper, we present Diffusion-4K, a novel framework for direct ultra-high-resolution image synthesis using text-to-image diffusion models. The core advancements include: (1) Aesthetic-4K Benchmark: addressing the absence of a publicly available 4K image synthesis dataset, we construct Aesthetic-4K, a comprehensive benchmark for ultra-high-resolution image generation. We curated a high-quality 4K dataset with carefully selected images and captions generated by GPT-4o. Additionally, we introduce GLCM Score and Compression Ratio metrics to evaluate fine details, combined with holis" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.68, + 0.908, + 0.876 + ], + "angle": 0, + "content": "tic measures such as FID, Aesthetics and CLIPScore for a comprehensive assessment of ultra-high-resolution images. (2) Wavelet-based Fine-tuning: we propose a wavelet-based fine-tuning approach for direct training with photorealistic 4K images, applicable to various latent diffusion models, demonstrating its effectiveness in synthesizing highly detailed 4K images. Consequently, Diffusion-4K achieves impressive performance in high-quality image synthesis and text prompt adherence, especially when powered by modern large-scale diffusion models (e.g., SD3-2B and Flux-12B). Extensive experimental results from our benchmark demonstrate the superiority of Diffusion-4K in ultra-high-resolution image synthesis. Code is available at" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.236, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23464" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.092, + 0.092, + 0.38, + 0.106 + ], + "angle": 0, + "content": "https://github.com/zhangOjhon/diffusion-4k." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.136, + 0.223, + 0.151 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.161, + 0.483, + 0.357 + ], + "angle": 0, + "content": "Diffusion models have proven to be highly effective for modeling high-dimensional, perceptual data such as images [18, 21, 29, 31, 46]. In recent years, latent diffusion models have made significant advancements in text-to-image synthesis, demonstrating impressive generalization capabilities at high resolutions [9, 12, 23, 25, 34, 41]. Replacing convolutional U-Net with a transformer architecture shows promising improvements as model scalability increases, e.g., Stable Diffusion 3 (SD3) at 8B [12], Flux at 12B [5], and Playground v3 at 24B [25]. Alternatively, flow-based formulations, using data or velocity prediction, have emerged as an viable choice due to their faster convergence and enhanced performance [1, 21, 24, 26, 28]." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.358, + 0.483, + 0.614 + ], + "angle": 0, + "content": "Despite substantial progress, most latent diffusion models focus on training and generating images at \\(1024 \\times 1024\\), leaving direct ultra-high-resolution image synthesis largely unexplored. Direct training and generating 4K images is valuable in realistic applications, but require considerable computational resources, especially as model parameters increase. Concurrent approaches such as PixArt-\\(\\Sigma\\) [9] and Sana [49] address direct ultra-high-resolution image synthesis at 4K, showcasing the potentials of scalable latent diffusion transformer architectures. Both PixArt-\\(\\Sigma\\) at 0.6B and Sana at 0.6/1.6B primarily focus on the efficiency of ultra-high-resolution image generation, however, the intrinsic advantages of 4K images, such as high-frequency details and rich textures, are neglected. Furthermore, due to the scarcity of photorealistic 4K images, there is currently no publicly available benchmark for 4K image synthesis, hindering further research on this valuable topic." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.615, + 0.483, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose Diffusion-4K, a novel framework designed for direct ultra-high-resolution image synthesis using latent diffusion models. Specifically, we introduce Aesthetic-4K, including a high-quality dataset of curated ultra-high-resolution images, with corresponding captions generated by GPT-4o [19]. Additionally, most automated evaluation metrics, such as Frechet Inception Distance (FID) [17], Aesthetics [45] and CLIPScore [16], offer only holistic measures at low resolutions, which are insufficient for the comprehensive benchmarking in high-resolution image synthesis, particularly for 4K images. To address the limitations, we introduce Gray Level Cooccurrence Matrix (GLCM) Score and Compression Ratio metrics, focusing on assessment of fine details in ultra-high-resolution images which has not yet been explored, with the goal of establishing a comprehensive benchmark for 4K image synthesis. Additionally, we propose a wavelet-based fine-tuning method that emphasizes high-frequency components while preserving low-frequent approximation in ultra" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.212 + ], + "angle": 0, + "content": "high-resolution image synthesis. Notably, our method is compatible with various latent diffusion models. We conduct experiments with open-sourced latent diffusion models including SD3-2B [12] and Flux-12B [5], capable of training and generating photorealistic images at \\(4096 \\times 4096\\) resolution. Consequently, our method demonstrates superior performance in 4K image synthesis, underscoring the effectiveness of the Diffusion-4K framework." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.213, + 0.874, + 0.226 + ], + "angle": 0, + "content": "The main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.228, + 0.905, + 0.303 + ], + "angle": 0, + "content": "- We establish Aesthetic-4k, a comprehensive benchmark for 4K image synthesis, including a high-quality dataset of ultra-high-resolution images with corresponding precise captions, and elaborated evaluation metrics for ultra-high-resolution images generation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.304, + 0.905, + 0.348 + ], + "angle": 0, + "content": "- We propose a wavelet-based fine-tuning approach for latent diffusion model, focusing on generating ultra-high-resolution images with fine details." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.348, + 0.905, + 0.409 + ], + "angle": 0, + "content": "- Extensive experiment results demonstrate the effectiveness and generalization of our proposed method in 4K image synthesis, particularly when powered by large-scale diffusion transformers, e.g. SD3 and Flux." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.228, + 0.905, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.423, + 0.651, + 0.438 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.448, + 0.907, + 0.659 + ], + "angle": 0, + "content": "Latent Diffusion Models. Stable Diffusion (SD) [41] proposes latent diffusion models to operate diffusion process in compressed latent space using Variational AutoEncoder (VAE). Widely used VAEs [7, 12, 31] employ a down-sampling factor of \\( F = 8 \\), compressing pixel space \\( \\mathbb{R}^{H\\times W\\times 3} \\) into latent space \\( \\mathbb{R}^{\\frac{H}{F}\\times \\frac{W}{F}\\times C} \\), where \\( H \\) and \\( W \\) represent height and width respectively, and \\( C \\) denotes the channel of latent space. In the field of latent diffusion models, Diffusion Transformer (DiT) [31] has made significant progress in the past year. Typically, the patch size of DiT is set to \\( P = 2 \\), resulting in \\( \\frac{H}{FP}\\times \\frac{H}{FP} \\) tokens. The transformer architecture demonstrates excellent scalability in latent diffusion models, as evidenced by PixArt [7, 9], SD3 [12], Flux [5], Playground [23, 25], etc." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.906, + 0.856 + ], + "angle": 0, + "content": "In text-to-image synthesis, the text encoder plays a crucial role in prompt coherence. SD employs CLIP [35] as its text encoder, while subsequent diffusion models, such as Imagen [42] and PixArt [7, 9], utilize T5-XXL [36] for text feature extraction. Recent approaches, such as SD3 [12] and Flux [5], combine both CLIP and T5-XXL for enhanced text understanding. DALL-E 3 [4] demonstrates that training with descriptive image captions can significantly enhance the prompt coherence of text-to-image models. Sana [49] utilizes the latest decoder-only Large Language Model (LLM), Gemma 2 [48], as its text encoder to improve understanding and reasoning capabilities related to text prompts." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.906, + 0.901 + ], + "angle": 0, + "content": "High-Resolution Image Synthesis. High-resolution image generation is valuable in various practical applications such as industry and entertainment [6, 11]. Currently, advanced" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23465" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.257 + ], + "angle": 0, + "content": "latent diffusion models typically train and synthesize images at \\(1024 \\times 1024\\) for high-resolution image generation due to computational complexity [34, 38, 39, 41, 43, 44]. However, increasing image resolution introduces quadratic computational costs, posing challenges particularly for 4K image synthesis. Several training-free fusion approaches for 4K image generation have been developed based on existing latent diffusion models [2, 10]. Additionally, Stable Cascade [32] employs multiple diffusion networks to increase resolution progressively. However, such ensemble methods can introduce cumulative errors." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.258, + 0.483, + 0.471 + ], + "angle": 0, + "content": "PixArt- \\(\\Sigma\\) [9] pioneers to direct image generation close to 4K (3840 × 2160) with efficient token compression for DiT, significantly improving efficiency and enabling ultra-high-resolution image generation. Sana [49], a pipeline designed to efficiently and cost-effectively train and synthesize 4K images, is capable of generating images at resolutions ranging from \\(1024\\times 1024\\) to \\(4096\\times 4096\\). Sana introduces a deep compression VAE [8] that compresses images with an aggressive down-sampling factor of \\(F = 32\\), enabling content creation at low cost. Despite significant improvements in resolution, both PixArt- \\(\\Sigma\\) -0.6B and Sana-0.6B/1.6B ignore the intrinsic high-frequency details and rich textures in 4K image synthesis. Furthermore, the potential for scalable DiT in 4K image generation remains unexplored." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.482, + 0.192, + 0.497 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.508, + 0.483, + 0.629 + ], + "angle": 0, + "content": "In this section, we elaborate on the details of Diffusion-4K, illustrating how it facilitates photorealistic 4K image synthesis. In Sec. 3.1, we introduce Aesthetic-4K, outlining the design principles and the process of constructing our human-centric benchmark with ultra-high-resolution images. Subsequently, we present a wavelet-based fine-tuning approach for direct training with photorealistic 4K images, applicable to various latent diffusion models, in Sec. 3.2." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.638, + 0.323, + 0.653 + ], + "angle": 0, + "content": "3.1. Aesthetic-4K Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.483, + 0.764 + ], + "angle": 0, + "content": "Existing benchmarks for advanced latent diffusion models generally conduct experiments with images at \\(1024 \\times 1024\\) resolution [7, 12, 23, 34], however, direct training and assessing with 4K images has not been thoroughly addressed yet. In this section, we construct Aesthetic-4K, a comprehensive benchmark for ultra-high-resolution image synthesis. The details are outlined as follows." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Design Principles. Emphasis on human-centric perceptual cognition: To design a benchmark centered on human-level perceptual cognition, our primary goal is to explore the key factors of human perception on 4K images and formulate quantifiable indicators, while evaluating the general abilities of the generative model in these key factors. However, most automated evaluation metrics, such as FID [17], Aesthetics [45], and CLIPScore [16], provide only holistic measures at lower resolutions, which are insufficient for" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.089, + 0.905, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.296, + 0.908, + 0.339 + ], + "angle": 0, + "content": "Figure 2. Analysis of GLCM Score↑ / Compression Ratio↓. Our indicators demonstrate strong alignment with human-centric perceptual cognition at the level of local patches." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.354, + 0.899, + 0.408 + ], + "angle": 0, + "content": "
    MetricGLCM ScoreCompression RatioMUSIQMANIQA
    SRCC0.750.530.360.20
    PLCC0.770.560.410.26
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.577, + 0.419, + 0.842, + 0.432 + ], + "angle": 0, + "content": "Table 1. Correlation with human evaluation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.462, + 0.905, + 0.492 + ], + "angle": 0, + "content": "comprehensive assessment, particularly lacking the ability of evaluating fine details in 4K images." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.494, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Inspired by relevant literature in perceptual psychology, we found that highly structured textures play a decisive role in human perceptual cognition [3, 20, 47]. Therefore, we proposed additional indicators that accurately measure the richness of highly structured textures, including the commonly used quantitative indicators for texture analysis GLCM and the image compression ratio with discrete cosine transform (DCT). Considering human visual sensitivities, the GLCM, which captures the varying textural patterns, optical flow, and distortion through comprehensive spatial interactions of neighboring pixels, enables the creation of a truly representative characterization of human visual perception [13]. Simultaneously, the image compression ratio with DCT serves as an important reference for assessing the preservation of fine details in 4K images. To demonstrate alignment with human preferences, we conduct quantitative analysis of our indicators with adequate images, and present examples in Fig. 2. Moreover, as depicted in Tab. 1, we compute the Spearman Rank-order Correlation Coefficient (SRCC) and Pearson Linear Correlation Coefficient (PLCC) with human evaluations using various patches sampled from generated images, demonstrating the superior alignment with human ratings compared to no-reference image quality assessment metrics such as MUSIQ [22] and MANIQA [50]. Our benchmark design ensures that the model performance assessment is directly relevant to human decision-making and cognitive abilities." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23466" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.289, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.089, + 0.492, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.182, + 0.456, + 0.198 + ], + "angle": 0, + "content": "Prompt: A vast colony of king penguins densely populates a rocky shore, with numerous individuals standing closely together against a backdrop of ocean waves." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.199, + 0.289, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.199, + 0.492, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.292, + 0.476, + 0.307 + ], + "angle": 0, + "content": "Prompt: A sea turtle glides gracefully through crystal-clear turquoise water above a school of small fish, with sunlight reflecting off the surface." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.308, + 0.289, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.308, + 0.491, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.482, + 0.475, + 0.498 + ], + "angle": 0, + "content": "Prompt: A close-up of a fox's face, partially covered in snow, with sharp ears and bright, alert eyes. The snowy backdrop adds a serene atmosphere to the scene." + }, + { + "type": "image_caption", + "bbox": [ + 0.193, + 0.501, + 0.393, + 0.513 + ], + "angle": 0, + "content": "(a) Image-text samples in training set." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.089, + 0.699, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.09, + 0.902, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.183, + 0.89, + 0.198 + ], + "angle": 0, + "content": "Prompt: A picturesque riverside scene featuring a medieval castle atop a hill, surrounded by vibrant autumn foliage, with colorful homes lining the waterfront and several boats docked along the river." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.199, + 0.7, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.199, + 0.903, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.292, + 0.865, + 0.308 + ], + "angle": 0, + "content": "Prompt: A lone astronaut floats in space, gazing at a swirling black hole surrounded by vibrant landscapes, rivers, and clouds below." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.308, + 0.7, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.308, + 0.902, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.482, + 0.9, + 0.498 + ], + "angle": 0, + "content": "Prompt: A majestic polar bear sits near a rocky shore, reflecting in calm waters under a full moon amid a dramatic, cloudy sky filled with flying birds. A small figure stands in the distance, observing the scene." + }, + { + "type": "image_caption", + "bbox": [ + 0.598, + 0.501, + 0.812, + 0.513 + ], + "angle": 0, + "content": "(b) Image-text samples in evaluation set." + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.525, + 0.907, + 0.555 + ], + "angle": 0, + "content": "Figure 3. Illustration of image-text samples in the Aesthetic-4K dataset, which includes high-quality images and precise text prompts generated by GPT-4o, distinguished by high aesthetics and fine details." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.58, + 0.483, + 0.807 + ], + "angle": 0, + "content": "Aesthetic-4K Dataset. Addressing the absence of a publicly available 4K dataset, we propose the Aesthetic-4K dataset that includes a well-curated training and evaluation set for in-depth study. For the Aesthetic-4K training set, we collect high-quality images from the Internet, distinguished by exceptional aesthetics and fine details. Notably, the Aesthetic-4K training set consists of 12,015 high-quality images with a median height of 4128 and median width of 4640, representing a significant improvement in training data for ultra-high-resolution image synthesis. Additionally, we provide precise and detailed image captions generated by powerful GPT-4o [19], demonstrating strong alignment between vision and language. These curated images and corresponding captions comprise Aesthetic-Train, the training set of Aesthetic-4K." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "For the evaluation set, Aesthetic-Eval, we select imag-text pairs from the LAION-Aesthetics V2 6.5+ dataset, following the criterion of a short image side greater than 2048. The LAION-Aesthetics dataset includes 625,000 imag-text pairs with predicted aesthetic scores of 6.5 or higher in LAION-5B [45]. Notably, the Aesthetic-4K evaluation set" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.58, + 0.907, + 0.732 + ], + "angle": 0, + "content": "consists of 2,781 high-quality images with a median height of 2983 and median width of 3613. We do not sample the evaluation set from the collected images sourced from the Internet, to mitigate the risk of overfitting in comprehensive assessments. Within the evaluation set, 195 images have a short side greater than 4096, which we refer to as Aesthetic-Eval@4096. Instead of evaluating with images at \\(1024 \\times 1024\\) resolution [49], the proposed Aesthetic-4K evaluation set provides a suitable benchmark for ultra-high-resolution image synthesis." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.733, + 0.907, + 0.854 + ], + "angle": 0, + "content": "In summary, the proposed dataset encompasses common categories in realistic scenarios, including nature, travel, fashion, animals, film, art, food, sports, street photography, etc. As illustrated in Fig. 3, we present several image-text pairs from both the training and evaluation sets of Aesthetic-4K, clearly demonstrating their exceptional quality. For more details about the Aesthetic-4K dataset, please refer to the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Comprehensive Evaluation Metrics. To construct a comprehensive human-centric benchmark for 4K image synthesis, we provide conventional evaluation metrics in genera" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23467" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.483, + 0.137 + ], + "angle": 0, + "content": "tive models, such as FID [17], Aesthetics [45], and CLIP-Score [16], for an intuitive understanding of image synthesis from a holistic perspective." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.138, + 0.484, + 0.394 + ], + "angle": 0, + "content": "In addition, we report quantitative results for the proposed metrics assessing fine details in 4K images, including the GLCM Score and Compression Ratio, as significant complements to human-centric perceptual cognition in 4K images, which have not been addressed previously. The GLCM Score is formulated as follows: \\( s = -\\frac{1}{P}\\sum_{p=1}^{P}H(g_p) \\), where \\( H \\) represents entropy, and \\( g_p \\) is the GLCM [15] derived from local patch \\( p \\) in the original image with 64 gray levels, defined by radius \\( \\delta = [1,2,3,4] \\) and orientation \\( \\theta = [0^{\\circ},45^{\\circ},90^{\\circ},135^{\\circ}] \\). In practice, we divide the gray image into local patches of size 64, and compute the average GLCM Score based on the partitioned local patches. Regrading the Compression Ratio, it is calculated as the ratio of the original image size in memory to the compressed image size using the JPEG algorithm at a quality of 95. Qualitative and quantitative assessments constitute the comprehensive benchmark, Aesthetic-4K." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.402, + 0.336, + 0.418 + ], + "angle": 0, + "content": "3.2. Wavelet-based Fine-tuning" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.424, + 0.484, + 0.498 + ], + "angle": 0, + "content": "In this section, we propose a WaveLet-based Fine-tuning (WLF) method suitable for various latent diffusion models, enabling direct training with photorealistic images at \\(4096 \\times 4096\\) resolution. The core improvements consist of two components:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.5, + 0.484, + 0.739 + ], + "angle": 0, + "content": "Partitioned VAE. The most commonly used VAEs [5, 12] with \\( F = 8 \\) encounter out-of-memory (OOM) issues during direct training and inference at \\( 4096 \\times 4096 \\). To address this issue, we propose an efficient partitioned VAE, a simple yet effective method that compresses images with \\( F = 16 \\), significantly reducing memory consumption. Specifically, we use a dilation rate of 2 in the first convolutional layer of the VAE's encoder. In the last convolutional layer of the VAE's decoder, we partition the input feature map, up-sample by a factor of 2, apply the same convolution operator to each partitioned feature map, and then reorganize the final output. Notably, our method maintains consistency in the latent space of pre-trained latent diffusion models, eliminating the need for retraining or fine-tuning VAEs, which prevents distribution shifts in the latent space and ensures compatibility with various diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.741, + 0.484, + 0.877 + ], + "angle": 0, + "content": "Wavelet-based Latent Enhancement. Wavelet transform has achieved significant success in image processing and is widely used to decompose low-frequency approximations and high-frequency details from images or features [14, 33]. In this section, we propose wavelet-based latent enhancement, which emphasizes high-frequency components while preserving low-frequency information, thereby significantly enhancing fine details and rich textures in 4K image generation. Consider the diffusion process, i.e." + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.887, + 0.483, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {z} _ {t} = \\alpha_ {t} \\cdot \\boldsymbol {x} _ {0} + \\sigma_ {t} \\cdot \\epsilon , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.906, + 0.168 + ], + "angle": 0, + "content": "where \\(x_0\\) and \\(\\epsilon\\) represent data distribution and standard normal distribution, respectively, and \\(\\alpha_{t}\\) and \\(\\sigma_t\\) are hyperparameters in the diffusion formulation. The original training objective in latent diffusion models is noise prediction [18, 41], defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.177, + 0.907, + 0.193 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\epsilon_ {t}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.201, + 0.907, + 0.262 + ], + "angle": 0, + "content": "where \\(\\Theta\\) denotes the neural network, e.g., convolutional UNet or DiT. Recent approaches, such as SD3 [12] and Flux [5], adopt rectified flows to predict velocity \\(\\mathbf{v}\\) parameterized by \\(\\Theta\\), with the objective as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.271, + 0.907, + 0.288 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {v} _ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\epsilon - \\boldsymbol {x} _ {0}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.295, + 0.907, + 0.342 + ], + "angle": 0, + "content": "Our method decomposes the low-frequency approximation and high-frequency details of latent features using wavelet transform, defining the training objective as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.349, + 0.907, + 0.368 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {W L F} = \\mathbb {E} \\left[ w _ {t} \\| f \\left(\\boldsymbol {v} _ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) - \\epsilon\\right) - f \\left(\\boldsymbol {x} _ {0}\\right) \\| ^ {2} \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.375, + 0.907, + 0.623 + ], + "angle": 0, + "content": "where \\( w_{t} \\) is the loss weight, and \\( f(\\cdot) \\) denotes discrete wavelet transform (DWT). Notably, we use the Haar wavelet, widely adopted in real-world applications due to its efficiency. Specifically, \\( L = \\frac{1}{\\sqrt{2}} [1,1] \\) and \\( H = \\frac{1}{\\sqrt{2}} [-1,1] \\) denote the low-pass and high-pass filters, used to construct four kernels in DWT with stride 2, namely \\( LL^{T}, LHT, HLT, HH^{T} \\). The DWT kernels are then used to decompose the input features into four sub-bands, the low-frequency approximation \\( x_{ll} \\) and high-frequency components \\( x_{lh}, x_{hl}, x_{hh} \\). As a result, both low-frequency information and high-frequency details are incorporated in Eq. (4), contributing to a comprehensive optimization in 4K image synthesis. In addition, our method supports various diffusion models by simply substituting the reconstruction objective, enabling seamless integration with conventional noise prediction approaches." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.634, + 0.646, + 0.651 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.906, + 0.827 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of our method, we conduct experiments with the state-of-the-art latent diffusion models at various scales, including open-source SD3-2B [12] and Flux-12B [5]. Specifically, mainstream evaluation metrics, such as FID [17], Aesthetics [45] and CLIPScore [16], as well as the proposed GLCM Score and Compression Ratio metrics, are reported for comprehensive assessments. Additionally, we present quantitative and qualitative results that showcase the high-resolution image reconstruction and generation capabilities of partitioned VAE and WLF, respectively." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.834, + 0.722, + 0.85 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. Regrading the VAEs in both SD3 [12] and Flux [5], we encapsulate them using partitioned VAE with \\( F = 16 \\), ensuring the direct training at" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23468" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.223, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.089, + 0.353, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.089, + 0.482, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.33, + 0.483, + 0.357 + ], + "angle": 0, + "content": "Figure 4. Reconstruction results of 4K images with partitioned VAEs of \\( F = 16 \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.385, + 0.484, + 0.537 + ], + "angle": 0, + "content": "\\(4096 \\times 4096\\) resolution without OOM issues. Notably, WLF is used for fine-tuning diffusion models, while the partitioned VAE and text encoder in pre-trained models are kept frozen, significantly improving the training efficiency. In practice, we use the AdamW [27] optimizer with a constant learning rate of 1e-6 and weight decay of 1e-4. We employ mixed-precision training with a batch size of 32 and use ZeRO Stage 2 with CPU offload techniques [37, 40]. The fine-tuning of SD3-2B and Flux-12B is conducted on 2 A800-80G GPUs and 8 A100-80G GPUs, respectively." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.546, + 0.279, + 0.563 + ], + "angle": 0, + "content": "4.2. Experiment Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.569, + 0.483, + 0.81 + ], + "angle": 0, + "content": "Analysis of partitioned VAEs. In Tab. 2, we report the evaluation results, including rFID, Normalized Mean Square Error (NMSE), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and LPIPS [51], to assess the reconstruction ability of partitioned VAEs on Aesthetic-4K at \\(4096 \\times 4096\\) resolution. We provide detailed results for VAEs in SD3 and Flux, enhanced by our partition techniques with \\(F = 16\\). Notably, our partitioned VAE resolves the OOM issue encountered by the original VAE without requiring retraining or fine-tuning, thereby avoiding potential distribution shifts in the latent space. In addition, we present visualizations of original and reconstruction images in Fig. 4. The qualitative results demonstrate the effectiveness of the partitioned VAEs in 4K image reconstruction, ensuring consistency in the latent space for subsequent fine-tuning with 4K images." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Image Quality Assessment. Regarding image quality assessment, we conduct comprehensive comparisons using mainstream evaluation metrics, such as FID [17], Aesthetics [45] and CLIPScore [16], to provide an intuitive understanding of image quality and text prompt adherence. In Tab. 3, we report experimental results with SD3-2B and" + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.089, + 0.892, + 0.143 + ], + "angle": 0, + "content": "
    ModelrFIDNMSEPSNRSSIMLPIPS
    SD3-VAE-F161.400.0928.820.760.15
    Flux-VAE-F161.690.0829.220.790.16
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.153, + 0.907, + 0.194 + ], + "angle": 0, + "content": "Table 2. Quantitative reconstruction results of VAEs with down-sampling factor of \\( F = 16 \\) on our Aesthetic-4K training set at \\( 4096 \\times 4096 \\)." + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.212, + 0.895, + 0.296 + ], + "angle": 0, + "content": "
    ModelFID ↓CLIPScore ↑Aesthetics ↑
    SD3-F16@204843.8231.505.91
    SD3-F16-WLF@204840.1834.045.96
    Flux-F16@204850.5730.416.36
    Flux-F16-WLF@204839.4934.416.37
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.306, + 0.907, + 0.334 + ], + "angle": 0, + "content": "Table 3. Quantitative benchmarks of latent diffusion models on Aesthetic-Eval@2048 at \\(2048 \\times 2048\\) resolution." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.351, + 0.905, + 0.436 + ], + "angle": 0, + "content": "
    ModelGLCM Score ↑Compression Ratio ↓
    SD3-F16@20480.7511.23
    SD3-F16-WLF@20480.7910.51
    Flux-F16@20480.5814.80
    Flux-F16-WLF@20480.6113.60
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.447, + 0.907, + 0.473 + ], + "angle": 0, + "content": "Table 4. GLCM Score and Compression Ratio of latent diffusion models on Aesthetic-Eval@2048 at \\(2048 \\times 2048\\) resolution." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.505, + 0.905, + 0.535 + ], + "angle": 0, + "content": "Flux-12B on Aesthetic-Eval@2048 in Tab. 3, demonstrating the effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.537, + 0.907, + 0.734 + ], + "angle": 0, + "content": "As aforementioned, these conventional evaluation metrics are insufficient for comprehensive assessment in ultra-high-resolution image synthesis, particularly in evaluating the fine details of 4K images. In addition to commonly used benchmarks, we also compare the GLCM Score, which aims to assess the texture richness in ultra-high-resolution images. Simultaneously, we also report the Compression Ratio using the JPEG algorithm at a quality setting of 95, which can serve as an important reference for assessing image quality with fine details. As depicted in Tab. 4, experimental results highlight the advantages of WLF in these metrics, distinctly demonstrating our method's ability to generate 4K images with fine details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Qualitative 4K Image Synthesis. As illustrated in Fig. 5, we present qualitative high-resolution images synthesized with Diffusion-4K, powered by the state-of-the-art latent diffusion model, Flux-12B. Although WLF fine-tunes at \\(4096 \\times 4096\\) resolution, our method can synthesize ultra-high-resolution images at various aspect ratios, and even supports direct photorealistic image generation at higher resolutions. In addition, we report the inference details in Tab. 5, highlighting the time and memory consumption of our method for directly generating 4K images. For sampling, images are generated by discretizing the ordinary" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23469" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.088, + 0.878, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.129, + 0.384, + 0.482, + 0.411 + ], + "angle": 0, + "content": "A stylish woman walks down a Tokyo street filled with warm glowing neon and animated city signage. She wears a black leather jacket, a long red dress, and black boots, and carries a black purse. She wears sunglasses and red lipstick. She walks confidently and casually. The street is damp and reflective, creating a mirror effect of the colorful lights. Many pedestrians walk about." + }, + { + "type": "image_footnote", + "bbox": [ + 0.526, + 0.385, + 0.851, + 0.404 + ], + "angle": 0, + "content": "A gorgeously rendered papercraft world of a coral reef, rife with colorful fish and sea creatures." + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.415, + 0.477, + 0.619 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.16, + 0.624, + 0.436, + 0.642 + ], + "angle": 0, + "content": "A litter of golden retriever puppies playing in the snow. Their heads pop out of the snow, covered in." + }, + { + "type": "image", + "bbox": [ + 0.478, + 0.415, + 0.677, + 0.62 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.481, + 0.625, + 0.672, + 0.642 + ], + "angle": 0, + "content": "A petri dish with a bamboo forest growing within it that has tiny red pandas running around." + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.415, + 0.877, + 0.62 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.693, + 0.625, + 0.861, + 0.641 + ], + "angle": 0, + "content": "A young man at his 20s is sitting on a piece of cloud in the sky, reading a book." + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.646, + 0.497, + 0.866 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.147, + 0.867, + 0.458, + 0.894 + ], + "angle": 0, + "content": "Extreme close up of a 24 year old woman's eye blinking, standing in Marrakech during magic hour, cinematic film shot in \\(70\\mathrm{mm}\\) depth of field, vivid colors, cinematic" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.646, + 0.878, + 0.866 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.504, + 0.867, + 0.875, + 0.894 + ], + "angle": 0, + "content": "3D animation of a small, round, fluffy creature with big, expressive eyes explores a vibrant, enchanted forest. The creature, a whimsical blend of a rabbit and a squirrel, has soft blue fur and a bushy, striped tail. It hops along a sparkling stream, its eyes wide with wonder. The forest is alive with magical elements: flowing water and small floating lights that resemble fireflies. The creature stops to interact playfully with a group of tiny, fairy-like beings dancing around a mushroom ring. The creature looks up in awe at a large, glowing tree that seems to be the heart of the forest." + }, + { + "type": "image_caption", + "bbox": [ + 0.237, + 0.907, + 0.759, + 0.921 + ], + "angle": 0, + "content": "Figure 5. Qualitative 4K images synthesis of Diffusion-4K. Prompts are from Sora [30]." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23470" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.483, + 0.201 + ], + "angle": 0, + "content": "
    ModelMemoryTime (s/step)
    SD3-F8@4096OOM-
    SD3-F16-WLF@409631.3GB1.16
    SD3-F16-WLF@4096 (CPU offload)16.1GB1.22
    Flux-F8@4096OOM-
    Flux-F16-WLF@409650.4 GB2.42
    Flux-F16-WLF@4096 (CPU offload)26.9 GB3.16
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.21, + 0.483, + 0.252 + ], + "angle": 0, + "content": "Table 5. Memory consumption and inference speed of direct image synthesis at \\(4096 \\times 4096\\). The result is tested on one A100 GPU with BF16 Precision." + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.267, + 0.466, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.442, + 0.443, + 0.456 + ], + "angle": 0, + "content": "Figure 6. Human and GPT-4o preference evaluation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.484, + 0.483, + 0.529 + ], + "angle": 0, + "content": "differential equation (ODE) process using an Euler solver. Please refer to the supplementary materials for more comparisons and details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.53, + 0.484, + 0.606 + ], + "angle": 0, + "content": "Preference Study. Human preference is assessed by rating the pairwise outputs from two models, i.e. Flux with and without WLF. Additionally, we employ the advanced multi-modal model, GPT-4o [19], as the evaluator for the preference study. The following questions are asked:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.607, + 0.485, + 0.637 + ], + "angle": 0, + "content": "Visual Aesthetics: Given the prompt, which image is of higher-quality and aesthetically more pleasing?" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.638, + 0.483, + 0.669 + ], + "angle": 0, + "content": "Prompt Adherence: Which image looks more representative to the text shown above and faithfully follows it?" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.669, + 0.484, + 0.745 + ], + "angle": 0, + "content": "Fine Details: Which image more accurately represents the fine visual details? Focus on clarity, sharpness, and texture. Assess the fidelity of fine elements such as edges, patterns, and nuances in color. The more precise representation of these details is preferred! Ignore other aspects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.746, + 0.484, + 0.822 + ], + "angle": 0, + "content": "As shown in Fig. 6, our method demonstrates a superior win rate in both human and AI preference, highlighting the effectiveness of our WLF method in various aspects, including visual aesthetics, prompt adherence and fine details performance in 4K images." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.833, + 0.255, + 0.848 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.902 + ], + "angle": 0, + "content": "Ablation on Quality of Image Captions. We compare 4K image synthesis using original captions from LAION-5B [45] and captions generated by GPT-4o. As shown" + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.089, + 0.892, + 0.172 + ], + "angle": 0, + "content": "
    CaptionsModelCLIPScore ↑Aesthetics ↑
    LAION-5BSD3-F16@409629.375.90
    GPT-4oSD3-F16@409633.125.97
    LAION-5BFlux-F16@409629.126.02
    GPT-4oFlux-F16@409633.676.11
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.182, + 0.905, + 0.21 + ], + "angle": 0, + "content": "Table 6. Ablation study on quality of image captions on Aesthetic-Eval@4096 at \\(4096 \\times 4096\\)." + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.229, + 0.892, + 0.3 + ], + "angle": 0, + "content": "
    ModelCLIPScore ↑Aesthetics ↑
    SD3-F16@409633.125.97
    SD3-F16-finetune@409634.145.99
    SD3-F16-WLF@409634.406.07
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.31, + 0.906, + 0.355 + ], + "angle": 0, + "content": "Table 7. Ablation on CLIPScore and Aesthetics of SD3 on Aesthetic-Eval@4096 at \\(4096 \\times 4096\\). SD3-F16-finetune@4096 represents fine-tuning without WLF." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.371, + 0.905, + 0.435 + ], + "angle": 0, + "content": "
    ModelGLCM Score ↑Compression Ratio ↓
    SD3-F16@40960.7311.97
    SD3-F16-finetune@40960.7411.41
    SD3-F16-WLF@40960.7710.50
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.445, + 0.906, + 0.488 + ], + "angle": 0, + "content": "Table 8. Ablation on GLCM Score and Compression Ratio of SD3 on Aesthetic-Eval@4096 at \\(4096 \\times 4096\\). SD3-F16-finetune@4096 denotes fine-tuning without WLF." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.518, + 0.906, + 0.609 + ], + "angle": 0, + "content": "in Tab. 6, both SD3 and Flux exhibit enhanced results in Aesthetic-Eval@4096 with captions from GPT-4o. Quantitative results indicate that prompts generated by GPT-4o improve image synthesis and prompt coherence, demonstrating the significance of high-quality prompts in 4K image generation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.611, + 0.906, + 0.749 + ], + "angle": 0, + "content": "Ablation on WLF. To demonstrate the effectiveness of WLF, we conduct ablation studies with SD3, comparing fine-tuning diffusion models with and without WLF, and report the experiment results of Aesthetic-Eval@4096 in Tab. 7 and Tab. 8. Compared to fine-tuning without WLF, our WLF method demonstrates superior performance in CLIPScore, Aesthetics, GLCM Score and Compression Ratio, significantly showcasing its effectiveness in visual aesthetics, prompt adherence, and high-frequency details." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.768, + 0.634, + 0.783 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.795, + 0.906, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present Diffusion-4K, a novel framework for ultra-high-resolution text-to-image generation. We introduce Aesthetic-4K benchmark and wavelet-based fine-tuning, capable of training with the state-of-the-art latent diffusion models, such as SD3 and Flux. Qualitative and quantitative results demonstrate the effectiveness of our approach in training and generating photorealistic 4K images." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23471" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.271, + 0.108 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.484, + 0.19 + ], + "angle": 0, + "content": "This work is partly supported by the National Natural Science Foundation of China (82441024), the Research Program of State Key Laboratory of Critical Software Environment, and the Fundamental Research Funds for the Central Universities." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.204, + 0.188, + 0.219 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.228, + 0.484, + 0.27 + ], + "angle": 0, + "content": "[1] Michael S Albergo and Eric Vanden-Eijnden. Building normalizing flows with stochastic interpolants. arXiv preprint arXiv:2209.15571, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.272, + 0.484, + 0.312 + ], + "angle": 0, + "content": "[2] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 6" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.092, + 0.906, + 0.768 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23473" + } + ] +] \ No newline at end of file diff --git a/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/4935daf0-51e8-442b-8d44-f641c7d877f3_origin.pdf b/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/4935daf0-51e8-442b-8d44-f641c7d877f3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c9df528326e0b4c01a245a8ed19f2b83a57b8753 --- /dev/null +++ b/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/4935daf0-51e8-442b-8d44-f641c7d877f3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:475f1cf409c6760e24012c8785e8e35307e5aaf817e70014d5144fddfbe2aec2 +size 10010852 diff --git a/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/full.md b/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..820361b0edd64424f351e00d8c8e452d587375ab --- /dev/null +++ b/2025/Diffusion-4K_ Ultra-High-Resolution Image Synthesis with Latent Diffusion Models/full.md @@ -0,0 +1,331 @@ +# Diffusion-4K: Ultra-High-Resolution Image Synthesis with Latent Diffusion Models + +Jinjin Zhang $^{1,2}$ Qiuyu Huang $^{3}$ Junjie Liu $^{3}$ Xiefan Guo $^{1,2}$ Di Huang $^{1,2*}$ + +$^{1}$ State Key Laboratory of Complex and Critical Software Environment, Beihang University, Beijing 100191, China + +$^{2}$ School of Computer Science and Engineering, Beihang University, Beijing 100191, China + +3Meituan + +{jinjin.zhang, xfguo, dhuang}@buaa.edu.cn {huangqiuyu, liujunjiel0}@meituan.com + +![](images/5e2da6d280840e999c6eb141e656f192a3545f5ea811f415cece507f868f6960.jpg) + +![](images/4ebc73ce42706a3f053a512101897841c586671a33cfc4d7d0ef89ac74b9cd03.jpg) +Figure 1. Example results synthesized by our Diffusion-4K, emphasizing exceptional fine details in generated 4K images. + +![](images/be0576bfef8283e279bd86ce49a08751eae2b47bbd2ea85664026931f4c4bcf6.jpg) + +![](images/b69dc306a8369ce044083b869baeece947185457efb54619436171d454df33bc.jpg) + +![](images/4a75be8d3d29b90058430fad9496fb30b3ea64fca3c490045f12e32bea59d46d.jpg) + +![](images/a698ab0d24c7a42d888ff8a5637560a4f4155d44d4982f77ddf18b3d9ca71c62.jpg) + +![](images/c049cffe824c09f89845351bc26ad1a521d8707a29d2a8bde55776711fbb19c1.jpg) + +![](images/9d8df44b69aafa635e14a64275e63f65974b7d8d2309904a68809007703de3fc.jpg) + +![](images/92ed28402298af9a017caefc59ab24d7cb033ae5bad0dbff5abfc386b90ded24.jpg) + +![](images/1ce4561b0ae947e7c6c6c09bf3d3796fa56824677bdde9ffdb87787d21fa10bc.jpg) + +# Abstract + +In this paper, we present Diffusion-4K, a novel framework for direct ultra-high-resolution image synthesis using text-to-image diffusion models. The core advancements include: (1) Aesthetic-4K Benchmark: addressing the absence of a publicly available 4K image synthesis dataset, we construct Aesthetic-4K, a comprehensive benchmark for ultra-high-resolution image generation. We curated a high-quality 4K dataset with carefully selected images and captions generated by GPT-4o. Additionally, we introduce GLCM Score and Compression Ratio metrics to evaluate fine details, combined with holis + +tic measures such as FID, Aesthetics and CLIPScore for a comprehensive assessment of ultra-high-resolution images. (2) Wavelet-based Fine-tuning: we propose a wavelet-based fine-tuning approach for direct training with photorealistic 4K images, applicable to various latent diffusion models, demonstrating its effectiveness in synthesizing highly detailed 4K images. Consequently, Diffusion-4K achieves impressive performance in high-quality image synthesis and text prompt adherence, especially when powered by modern large-scale diffusion models (e.g., SD3-2B and Flux-12B). Extensive experimental results from our benchmark demonstrate the superiority of Diffusion-4K in ultra-high-resolution image synthesis. Code is available at + +# 1. Introduction + +Diffusion models have proven to be highly effective for modeling high-dimensional, perceptual data such as images [18, 21, 29, 31, 46]. In recent years, latent diffusion models have made significant advancements in text-to-image synthesis, demonstrating impressive generalization capabilities at high resolutions [9, 12, 23, 25, 34, 41]. Replacing convolutional U-Net with a transformer architecture shows promising improvements as model scalability increases, e.g., Stable Diffusion 3 (SD3) at 8B [12], Flux at 12B [5], and Playground v3 at 24B [25]. Alternatively, flow-based formulations, using data or velocity prediction, have emerged as an viable choice due to their faster convergence and enhanced performance [1, 21, 24, 26, 28]. + +Despite substantial progress, most latent diffusion models focus on training and generating images at $1024 \times 1024$ , leaving direct ultra-high-resolution image synthesis largely unexplored. Direct training and generating 4K images is valuable in realistic applications, but require considerable computational resources, especially as model parameters increase. Concurrent approaches such as PixArt- $\Sigma$ [9] and Sana [49] address direct ultra-high-resolution image synthesis at 4K, showcasing the potentials of scalable latent diffusion transformer architectures. Both PixArt- $\Sigma$ at 0.6B and Sana at 0.6/1.6B primarily focus on the efficiency of ultra-high-resolution image generation, however, the intrinsic advantages of 4K images, such as high-frequency details and rich textures, are neglected. Furthermore, due to the scarcity of photorealistic 4K images, there is currently no publicly available benchmark for 4K image synthesis, hindering further research on this valuable topic. + +In this paper, we propose Diffusion-4K, a novel framework designed for direct ultra-high-resolution image synthesis using latent diffusion models. Specifically, we introduce Aesthetic-4K, including a high-quality dataset of curated ultra-high-resolution images, with corresponding captions generated by GPT-4o [19]. Additionally, most automated evaluation metrics, such as Frechet Inception Distance (FID) [17], Aesthetics [45] and CLIPScore [16], offer only holistic measures at low resolutions, which are insufficient for the comprehensive benchmarking in high-resolution image synthesis, particularly for 4K images. To address the limitations, we introduce Gray Level Cooccurrence Matrix (GLCM) Score and Compression Ratio metrics, focusing on assessment of fine details in ultra-high-resolution images which has not yet been explored, with the goal of establishing a comprehensive benchmark for 4K image synthesis. Additionally, we propose a wavelet-based fine-tuning method that emphasizes high-frequency components while preserving low-frequent approximation in ultra + +high-resolution image synthesis. Notably, our method is compatible with various latent diffusion models. We conduct experiments with open-sourced latent diffusion models including SD3-2B [12] and Flux-12B [5], capable of training and generating photorealistic images at $4096 \times 4096$ resolution. Consequently, our method demonstrates superior performance in 4K image synthesis, underscoring the effectiveness of the Diffusion-4K framework. + +The main contributions are summarized as follows: + +- We establish Aesthetic-4k, a comprehensive benchmark for 4K image synthesis, including a high-quality dataset of ultra-high-resolution images with corresponding precise captions, and elaborated evaluation metrics for ultra-high-resolution images generation. +- We propose a wavelet-based fine-tuning approach for latent diffusion model, focusing on generating ultra-high-resolution images with fine details. +- Extensive experiment results demonstrate the effectiveness and generalization of our proposed method in 4K image synthesis, particularly when powered by large-scale diffusion transformers, e.g. SD3 and Flux. + +# 2. Related work + +Latent Diffusion Models. Stable Diffusion (SD) [41] proposes latent diffusion models to operate diffusion process in compressed latent space using Variational AutoEncoder (VAE). Widely used VAEs [7, 12, 31] employ a down-sampling factor of $F = 8$ , compressing pixel space $\mathbb{R}^{H\times W\times 3}$ into latent space $\mathbb{R}^{\frac{H}{F}\times \frac{W}{F}\times C}$ , where $H$ and $W$ represent height and width respectively, and $C$ denotes the channel of latent space. In the field of latent diffusion models, Diffusion Transformer (DiT) [31] has made significant progress in the past year. Typically, the patch size of DiT is set to $P = 2$ , resulting in $\frac{H}{FP}\times \frac{H}{FP}$ tokens. The transformer architecture demonstrates excellent scalability in latent diffusion models, as evidenced by PixArt [7, 9], SD3 [12], Flux [5], Playground [23, 25], etc. + +In text-to-image synthesis, the text encoder plays a crucial role in prompt coherence. SD employs CLIP [35] as its text encoder, while subsequent diffusion models, such as Imagen [42] and PixArt [7, 9], utilize T5-XXL [36] for text feature extraction. Recent approaches, such as SD3 [12] and Flux [5], combine both CLIP and T5-XXL for enhanced text understanding. DALL-E 3 [4] demonstrates that training with descriptive image captions can significantly enhance the prompt coherence of text-to-image models. Sana [49] utilizes the latest decoder-only Large Language Model (LLM), Gemma 2 [48], as its text encoder to improve understanding and reasoning capabilities related to text prompts. + +High-Resolution Image Synthesis. High-resolution image generation is valuable in various practical applications such as industry and entertainment [6, 11]. Currently, advanced + +latent diffusion models typically train and synthesize images at $1024 \times 1024$ for high-resolution image generation due to computational complexity [34, 38, 39, 41, 43, 44]. However, increasing image resolution introduces quadratic computational costs, posing challenges particularly for 4K image synthesis. Several training-free fusion approaches for 4K image generation have been developed based on existing latent diffusion models [2, 10]. Additionally, Stable Cascade [32] employs multiple diffusion networks to increase resolution progressively. However, such ensemble methods can introduce cumulative errors. + +PixArt- $\Sigma$ [9] pioneers to direct image generation close to 4K (3840 × 2160) with efficient token compression for DiT, significantly improving efficiency and enabling ultra-high-resolution image generation. Sana [49], a pipeline designed to efficiently and cost-effectively train and synthesize 4K images, is capable of generating images at resolutions ranging from $1024\times 1024$ to $4096\times 4096$ . Sana introduces a deep compression VAE [8] that compresses images with an aggressive down-sampling factor of $F = 32$ , enabling content creation at low cost. Despite significant improvements in resolution, both PixArt- $\Sigma$ -0.6B and Sana-0.6B/1.6B ignore the intrinsic high-frequency details and rich textures in 4K image synthesis. Furthermore, the potential for scalable DiT in 4K image generation remains unexplored. + +# 3. Methods + +In this section, we elaborate on the details of Diffusion-4K, illustrating how it facilitates photorealistic 4K image synthesis. In Sec. 3.1, we introduce Aesthetic-4K, outlining the design principles and the process of constructing our human-centric benchmark with ultra-high-resolution images. Subsequently, we present a wavelet-based fine-tuning approach for direct training with photorealistic 4K images, applicable to various latent diffusion models, in Sec. 3.2. + +# 3.1. Aesthetic-4K Benchmark + +Existing benchmarks for advanced latent diffusion models generally conduct experiments with images at $1024 \times 1024$ resolution [7, 12, 23, 34], however, direct training and assessing with 4K images has not been thoroughly addressed yet. In this section, we construct Aesthetic-4K, a comprehensive benchmark for ultra-high-resolution image synthesis. The details are outlined as follows. + +Design Principles. Emphasis on human-centric perceptual cognition: To design a benchmark centered on human-level perceptual cognition, our primary goal is to explore the key factors of human perception on 4K images and formulate quantifiable indicators, while evaluating the general abilities of the generative model in these key factors. However, most automated evaluation metrics, such as FID [17], Aesthetics [45], and CLIPScore [16], provide only holistic measures at lower resolutions, which are insufficient for + +![](images/8ed412471c0e8cab02d65ced7cc7e0bd06bd24c83b283dfbee7ccf86141dcfd2.jpg) +Figure 2. Analysis of GLCM Score↑ / Compression Ratio↓. Our indicators demonstrate strong alignment with human-centric perceptual cognition at the level of local patches. + +
    MetricGLCM ScoreCompression RatioMUSIQMANIQA
    SRCC0.750.530.360.20
    PLCC0.770.560.410.26
    + +Table 1. Correlation with human evaluation. + +comprehensive assessment, particularly lacking the ability of evaluating fine details in 4K images. + +Inspired by relevant literature in perceptual psychology, we found that highly structured textures play a decisive role in human perceptual cognition [3, 20, 47]. Therefore, we proposed additional indicators that accurately measure the richness of highly structured textures, including the commonly used quantitative indicators for texture analysis GLCM and the image compression ratio with discrete cosine transform (DCT). Considering human visual sensitivities, the GLCM, which captures the varying textural patterns, optical flow, and distortion through comprehensive spatial interactions of neighboring pixels, enables the creation of a truly representative characterization of human visual perception [13]. Simultaneously, the image compression ratio with DCT serves as an important reference for assessing the preservation of fine details in 4K images. To demonstrate alignment with human preferences, we conduct quantitative analysis of our indicators with adequate images, and present examples in Fig. 2. Moreover, as depicted in Tab. 1, we compute the Spearman Rank-order Correlation Coefficient (SRCC) and Pearson Linear Correlation Coefficient (PLCC) with human evaluations using various patches sampled from generated images, demonstrating the superior alignment with human ratings compared to no-reference image quality assessment metrics such as MUSIQ [22] and MANIQA [50]. Our benchmark design ensures that the model performance assessment is directly relevant to human decision-making and cognitive abilities. + +![](images/f8afdd4db2c4e4ef10e8e42debe2f99c2463239e6fb9476274104e165aea3a29.jpg) +Prompt: A vast colony of king penguins densely populates a rocky shore, with numerous individuals standing closely together against a backdrop of ocean waves. + +![](images/418f1901629cc925249c357062c56764c2c45a94ec332078b00b3b4b5c64e083.jpg) + +![](images/8e779aa6776563cdc07483dcf3309d1e5383f7087284bbc4b82384ad59f6b768.jpg) + +![](images/4e4a316ff619105b49cd720a8cdffd9bbf144065975985e97d3b6470aab448a6.jpg) + +![](images/85f2403418dfa62b2a7b8bede8508d505acf65409cf55b0ef4812f1f15d7f2b1.jpg) +Prompt: A sea turtle glides gracefully through crystal-clear turquoise water above a school of small fish, with sunlight reflecting off the surface. +Prompt: A close-up of a fox's face, partially covered in snow, with sharp ears and bright, alert eyes. The snowy backdrop adds a serene atmosphere to the scene. +(a) Image-text samples in training set. +Figure 3. Illustration of image-text samples in the Aesthetic-4K dataset, which includes high-quality images and precise text prompts generated by GPT-4o, distinguished by high aesthetics and fine details. + +![](images/58389e8f04e24b2cd42d746dcbec95c353e53c867fb5df56c7edc3b5cddcfd1f.jpg) + +![](images/e66eb6b8c92ccd8d98e49a86552840a6cff03da06db1431a379b4b89ec1e9919.jpg) +Prompt: A picturesque riverside scene featuring a medieval castle atop a hill, surrounded by vibrant autumn foliage, with colorful homes lining the waterfront and several boats docked along the river. + +![](images/cb5e4bc63fada8b5b80e5a44404aaad455aa17d60119ea4749907d9ee4459f9e.jpg) + +![](images/31e014e633c3dbc8156d4b93de06a6eac6ff3e4c5b5ce09ba00d56caa0c66f85.jpg) + +![](images/c339301352df9423f57407b160d627423045f878208363c86f71bf8e03ee9318.jpg) + +![](images/fc1351c83007173ed97044d3707a916ab0d3715b9ed695a463f2b24cc471d408.jpg) +Prompt: A lone astronaut floats in space, gazing at a swirling black hole surrounded by vibrant landscapes, rivers, and clouds below. +Prompt: A majestic polar bear sits near a rocky shore, reflecting in calm waters under a full moon amid a dramatic, cloudy sky filled with flying birds. A small figure stands in the distance, observing the scene. +(b) Image-text samples in evaluation set. + +![](images/306f479833c7c79d8f3fa220ba2a465da082c3c3e5b3fbbf68ed5f2736f557b8.jpg) + +Aesthetic-4K Dataset. Addressing the absence of a publicly available 4K dataset, we propose the Aesthetic-4K dataset that includes a well-curated training and evaluation set for in-depth study. For the Aesthetic-4K training set, we collect high-quality images from the Internet, distinguished by exceptional aesthetics and fine details. Notably, the Aesthetic-4K training set consists of 12,015 high-quality images with a median height of 4128 and median width of 4640, representing a significant improvement in training data for ultra-high-resolution image synthesis. Additionally, we provide precise and detailed image captions generated by powerful GPT-4o [19], demonstrating strong alignment between vision and language. These curated images and corresponding captions comprise Aesthetic-Train, the training set of Aesthetic-4K. + +For the evaluation set, Aesthetic-Eval, we select imag-text pairs from the LAION-Aesthetics V2 6.5+ dataset, following the criterion of a short image side greater than 2048. The LAION-Aesthetics dataset includes 625,000 imag-text pairs with predicted aesthetic scores of 6.5 or higher in LAION-5B [45]. Notably, the Aesthetic-4K evaluation set + +consists of 2,781 high-quality images with a median height of 2983 and median width of 3613. We do not sample the evaluation set from the collected images sourced from the Internet, to mitigate the risk of overfitting in comprehensive assessments. Within the evaluation set, 195 images have a short side greater than 4096, which we refer to as Aesthetic-Eval@4096. Instead of evaluating with images at $1024 \times 1024$ resolution [49], the proposed Aesthetic-4K evaluation set provides a suitable benchmark for ultra-high-resolution image synthesis. + +In summary, the proposed dataset encompasses common categories in realistic scenarios, including nature, travel, fashion, animals, film, art, food, sports, street photography, etc. As illustrated in Fig. 3, we present several image-text pairs from both the training and evaluation sets of Aesthetic-4K, clearly demonstrating their exceptional quality. For more details about the Aesthetic-4K dataset, please refer to the supplementary materials. + +Comprehensive Evaluation Metrics. To construct a comprehensive human-centric benchmark for 4K image synthesis, we provide conventional evaluation metrics in genera + +tive models, such as FID [17], Aesthetics [45], and CLIP-Score [16], for an intuitive understanding of image synthesis from a holistic perspective. + +In addition, we report quantitative results for the proposed metrics assessing fine details in 4K images, including the GLCM Score and Compression Ratio, as significant complements to human-centric perceptual cognition in 4K images, which have not been addressed previously. The GLCM Score is formulated as follows: $s = -\frac{1}{P}\sum_{p=1}^{P}H(g_p)$ , where $H$ represents entropy, and $g_p$ is the GLCM [15] derived from local patch $p$ in the original image with 64 gray levels, defined by radius $\delta = [1,2,3,4]$ and orientation $\theta = [0^{\circ},45^{\circ},90^{\circ},135^{\circ}]$ . In practice, we divide the gray image into local patches of size 64, and compute the average GLCM Score based on the partitioned local patches. Regrading the Compression Ratio, it is calculated as the ratio of the original image size in memory to the compressed image size using the JPEG algorithm at a quality of 95. Qualitative and quantitative assessments constitute the comprehensive benchmark, Aesthetic-4K. + +# 3.2. Wavelet-based Fine-tuning + +In this section, we propose a WaveLet-based Fine-tuning (WLF) method suitable for various latent diffusion models, enabling direct training with photorealistic images at $4096 \times 4096$ resolution. The core improvements consist of two components: + +Partitioned VAE. The most commonly used VAEs [5, 12] with $F = 8$ encounter out-of-memory (OOM) issues during direct training and inference at $4096 \times 4096$ . To address this issue, we propose an efficient partitioned VAE, a simple yet effective method that compresses images with $F = 16$ , significantly reducing memory consumption. Specifically, we use a dilation rate of 2 in the first convolutional layer of the VAE's encoder. In the last convolutional layer of the VAE's decoder, we partition the input feature map, up-sample by a factor of 2, apply the same convolution operator to each partitioned feature map, and then reorganize the final output. Notably, our method maintains consistency in the latent space of pre-trained latent diffusion models, eliminating the need for retraining or fine-tuning VAEs, which prevents distribution shifts in the latent space and ensures compatibility with various diffusion models. + +Wavelet-based Latent Enhancement. Wavelet transform has achieved significant success in image processing and is widely used to decompose low-frequency approximations and high-frequency details from images or features [14, 33]. In this section, we propose wavelet-based latent enhancement, which emphasizes high-frequency components while preserving low-frequency information, thereby significantly enhancing fine details and rich textures in 4K image generation. Consider the diffusion process, i.e. + +$$ +\boldsymbol {z} _ {t} = \alpha_ {t} \cdot \boldsymbol {x} _ {0} + \sigma_ {t} \cdot \epsilon , \tag {1} +$$ + +where $x_0$ and $\epsilon$ represent data distribution and standard normal distribution, respectively, and $\alpha_{t}$ and $\sigma_t$ are hyperparameters in the diffusion formulation. The original training objective in latent diffusion models is noise prediction [18, 41], defined as: + +$$ +\epsilon_ {\Theta} \left(\boldsymbol {z} _ {t}, t\right) = \epsilon_ {t}, \tag {2} +$$ + +where $\Theta$ denotes the neural network, e.g., convolutional UNet or DiT. Recent approaches, such as SD3 [12] and Flux [5], adopt rectified flows to predict velocity $\mathbf{v}$ parameterized by $\Theta$ , with the objective as follows: + +$$ +\boldsymbol {v} _ {\Theta} \left(\boldsymbol {z} _ {t}, t\right) = \epsilon - \boldsymbol {x} _ {0}. \tag {3} +$$ + +Our method decomposes the low-frequency approximation and high-frequency details of latent features using wavelet transform, defining the training objective as follows: + +$$ +\mathcal {L} _ {W L F} = \mathbb {E} \left[ w _ {t} \| f \left(\boldsymbol {v} _ {\Theta} \left(\boldsymbol {z} _ {t}, t\right) - \epsilon\right) - f \left(\boldsymbol {x} _ {0}\right) \| ^ {2} \right], \tag {4} +$$ + +where $w_{t}$ is the loss weight, and $f(\cdot)$ denotes discrete wavelet transform (DWT). Notably, we use the Haar wavelet, widely adopted in real-world applications due to its efficiency. Specifically, $L = \frac{1}{\sqrt{2}} [1,1]$ and $H = \frac{1}{\sqrt{2}} [-1,1]$ denote the low-pass and high-pass filters, used to construct four kernels in DWT with stride 2, namely $LL^{T}, LHT, HLT, HH^{T}$ . The DWT kernels are then used to decompose the input features into four sub-bands, the low-frequency approximation $x_{ll}$ and high-frequency components $x_{lh}, x_{hl}, x_{hh}$ . As a result, both low-frequency information and high-frequency details are incorporated in Eq. (4), contributing to a comprehensive optimization in 4K image synthesis. In addition, our method supports various diffusion models by simply substituting the reconstruction objective, enabling seamless integration with conventional noise prediction approaches. + +# 4. Experiments + +To demonstrate the effectiveness of our method, we conduct experiments with the state-of-the-art latent diffusion models at various scales, including open-source SD3-2B [12] and Flux-12B [5]. Specifically, mainstream evaluation metrics, such as FID [17], Aesthetics [45] and CLIPScore [16], as well as the proposed GLCM Score and Compression Ratio metrics, are reported for comprehensive assessments. Additionally, we present quantitative and qualitative results that showcase the high-resolution image reconstruction and generation capabilities of partitioned VAE and WLF, respectively. + +# 4.1. Experimental Settings + +Implementation Details. Regrading the VAEs in both SD3 [12] and Flux [5], we encapsulate them using partitioned VAE with $F = 16$ , ensuring the direct training at + +![](images/a90a8fb5ac5e31bc557c3210d260573d909ffbebabab7e39ca5a8160a0bbcf78.jpg) +Figure 4. Reconstruction results of 4K images with partitioned VAEs of $F = 16$ . + +![](images/d683df6963aba897a0dcf660d68d8e72527ecd7e507bf18b967a49153a88c448.jpg) + +![](images/54b0daf059c3676cdc898ee9f292c154d07c989a0c190ea26d07cc54d36e8c74.jpg) + +$4096 \times 4096$ resolution without OOM issues. Notably, WLF is used for fine-tuning diffusion models, while the partitioned VAE and text encoder in pre-trained models are kept frozen, significantly improving the training efficiency. In practice, we use the AdamW [27] optimizer with a constant learning rate of 1e-6 and weight decay of 1e-4. We employ mixed-precision training with a batch size of 32 and use ZeRO Stage 2 with CPU offload techniques [37, 40]. The fine-tuning of SD3-2B and Flux-12B is conducted on 2 A800-80G GPUs and 8 A100-80G GPUs, respectively. + +# 4.2. Experiment Results + +Analysis of partitioned VAEs. In Tab. 2, we report the evaluation results, including rFID, Normalized Mean Square Error (NMSE), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and LPIPS [51], to assess the reconstruction ability of partitioned VAEs on Aesthetic-4K at $4096 \times 4096$ resolution. We provide detailed results for VAEs in SD3 and Flux, enhanced by our partition techniques with $F = 16$ . Notably, our partitioned VAE resolves the OOM issue encountered by the original VAE without requiring retraining or fine-tuning, thereby avoiding potential distribution shifts in the latent space. In addition, we present visualizations of original and reconstruction images in Fig. 4. The qualitative results demonstrate the effectiveness of the partitioned VAEs in 4K image reconstruction, ensuring consistency in the latent space for subsequent fine-tuning with 4K images. + +Image Quality Assessment. Regarding image quality assessment, we conduct comprehensive comparisons using mainstream evaluation metrics, such as FID [17], Aesthetics [45] and CLIPScore [16], to provide an intuitive understanding of image quality and text prompt adherence. In Tab. 3, we report experimental results with SD3-2B and + +
    ModelrFIDNMSEPSNRSSIMLPIPS
    SD3-VAE-F161.400.0928.820.760.15
    Flux-VAE-F161.690.0829.220.790.16
    + +Table 2. Quantitative reconstruction results of VAEs with down-sampling factor of $F = 16$ on our Aesthetic-4K training set at $4096 \times 4096$ . + +
    ModelFID ↓CLIPScore ↑Aesthetics ↑
    SD3-F16@204843.8231.505.91
    SD3-F16-WLF@204840.1834.045.96
    Flux-F16@204850.5730.416.36
    Flux-F16-WLF@204839.4934.416.37
    + +Table 3. Quantitative benchmarks of latent diffusion models on Aesthetic-Eval@2048 at $2048 \times 2048$ resolution. + +
    ModelGLCM Score ↑Compression Ratio ↓
    SD3-F16@20480.7511.23
    SD3-F16-WLF@20480.7910.51
    Flux-F16@20480.5814.80
    Flux-F16-WLF@20480.6113.60
    + +Table 4. GLCM Score and Compression Ratio of latent diffusion models on Aesthetic-Eval@2048 at $2048 \times 2048$ resolution. + +Flux-12B on Aesthetic-Eval@2048 in Tab. 3, demonstrating the effectiveness of our method. + +As aforementioned, these conventional evaluation metrics are insufficient for comprehensive assessment in ultra-high-resolution image synthesis, particularly in evaluating the fine details of 4K images. In addition to commonly used benchmarks, we also compare the GLCM Score, which aims to assess the texture richness in ultra-high-resolution images. Simultaneously, we also report the Compression Ratio using the JPEG algorithm at a quality setting of 95, which can serve as an important reference for assessing image quality with fine details. As depicted in Tab. 4, experimental results highlight the advantages of WLF in these metrics, distinctly demonstrating our method's ability to generate 4K images with fine details. + +Qualitative 4K Image Synthesis. As illustrated in Fig. 5, we present qualitative high-resolution images synthesized with Diffusion-4K, powered by the state-of-the-art latent diffusion model, Flux-12B. Although WLF fine-tunes at $4096 \times 4096$ resolution, our method can synthesize ultra-high-resolution images at various aspect ratios, and even supports direct photorealistic image generation at higher resolutions. In addition, we report the inference details in Tab. 5, highlighting the time and memory consumption of our method for directly generating 4K images. For sampling, images are generated by discretizing the ordinary + +![](images/4ca29c6722a3b0f250afc4436e7bff9b02792d4bb62a6fd1f77fc2d0bf4a1e75.jpg) +A stylish woman walks down a Tokyo street filled with warm glowing neon and animated city signage. She wears a black leather jacket, a long red dress, and black boots, and carries a black purse. She wears sunglasses and red lipstick. She walks confidently and casually. The street is damp and reflective, creating a mirror effect of the colorful lights. Many pedestrians walk about. +A gorgeously rendered papercraft world of a coral reef, rife with colorful fish and sea creatures. + +![](images/0bbeaea64b312f0295f59740b15644650e034249ba59456c1c3f9a9468e6d522.jpg) +A litter of golden retriever puppies playing in the snow. Their heads pop out of the snow, covered in. + +![](images/1304aa533ee6f8a0282bda4f301b6b931f336d88150739eb2fd19d18bd5a432e.jpg) +A petri dish with a bamboo forest growing within it that has tiny red pandas running around. + +![](images/9b8cb73681bb1183d8f32726ced2c7abbc9fc4f09fda3947c2198dded292eec7.jpg) +A young man at his 20s is sitting on a piece of cloud in the sky, reading a book. + +Figure 5. Qualitative 4K images synthesis of Diffusion-4K. Prompts are from Sora [30]. +![](images/61e3ee3274046f1b67eb8eb0720f4783ffda5a136df594b9d436769676647690.jpg) +Extreme close up of a 24 year old woman's eye blinking, standing in Marrakech during magic hour, cinematic film shot in $70\mathrm{mm}$ depth of field, vivid colors, cinematic + +![](images/a3782a474e6af4901e6fd92a500f0a67191ad6ab2eea1e5f765dc9fb319ff70a.jpg) +3D animation of a small, round, fluffy creature with big, expressive eyes explores a vibrant, enchanted forest. The creature, a whimsical blend of a rabbit and a squirrel, has soft blue fur and a bushy, striped tail. It hops along a sparkling stream, its eyes wide with wonder. The forest is alive with magical elements: flowing water and small floating lights that resemble fireflies. The creature stops to interact playfully with a group of tiny, fairy-like beings dancing around a mushroom ring. The creature looks up in awe at a large, glowing tree that seems to be the heart of the forest. + +
    ModelMemoryTime (s/step)
    SD3-F8@4096OOM-
    SD3-F16-WLF@409631.3GB1.16
    SD3-F16-WLF@4096 (CPU offload)16.1GB1.22
    Flux-F8@4096OOM-
    Flux-F16-WLF@409650.4 GB2.42
    Flux-F16-WLF@4096 (CPU offload)26.9 GB3.16
    + +![](images/366caeacd72239d9968b18b7bb8a284e25dc1c2db676663d67c71b62a849c4c7.jpg) +Figure 6. Human and GPT-4o preference evaluation. + +differential equation (ODE) process using an Euler solver. Please refer to the supplementary materials for more comparisons and details. + +Preference Study. Human preference is assessed by rating the pairwise outputs from two models, i.e. Flux with and without WLF. Additionally, we employ the advanced multi-modal model, GPT-4o [19], as the evaluator for the preference study. The following questions are asked: + +Visual Aesthetics: Given the prompt, which image is of higher-quality and aesthetically more pleasing? + +Prompt Adherence: Which image looks more representative to the text shown above and faithfully follows it? + +Fine Details: Which image more accurately represents the fine visual details? Focus on clarity, sharpness, and texture. Assess the fidelity of fine elements such as edges, patterns, and nuances in color. The more precise representation of these details is preferred! Ignore other aspects. + +As shown in Fig. 6, our method demonstrates a superior win rate in both human and AI preference, highlighting the effectiveness of our WLF method in various aspects, including visual aesthetics, prompt adherence and fine details performance in 4K images. + +# 4.3. Ablation Studies + +Ablation on Quality of Image Captions. We compare 4K image synthesis using original captions from LAION-5B [45] and captions generated by GPT-4o. As shown + +Table 5. Memory consumption and inference speed of direct image synthesis at $4096 \times 4096$ . The result is tested on one A100 GPU with BF16 Precision. + +
    CaptionsModelCLIPScore ↑Aesthetics ↑
    LAION-5BSD3-F16@409629.375.90
    GPT-4oSD3-F16@409633.125.97
    LAION-5BFlux-F16@409629.126.02
    GPT-4oFlux-F16@409633.676.11
    + +Table 6. Ablation study on quality of image captions on Aesthetic-Eval@4096 at $4096 \times 4096$ . + +
    ModelCLIPScore ↑Aesthetics ↑
    SD3-F16@409633.125.97
    SD3-F16-finetune@409634.145.99
    SD3-F16-WLF@409634.406.07
    + +Table 7. Ablation on CLIPScore and Aesthetics of SD3 on Aesthetic-Eval@4096 at $4096 \times 4096$ . SD3-F16-finetune@4096 represents fine-tuning without WLF. + +
    ModelGLCM Score ↑Compression Ratio ↓
    SD3-F16@40960.7311.97
    SD3-F16-finetune@40960.7411.41
    SD3-F16-WLF@40960.7710.50
    + +Table 8. Ablation on GLCM Score and Compression Ratio of SD3 on Aesthetic-Eval@4096 at $4096 \times 4096$ . SD3-F16-finetune@4096 denotes fine-tuning without WLF. + +in Tab. 6, both SD3 and Flux exhibit enhanced results in Aesthetic-Eval@4096 with captions from GPT-4o. Quantitative results indicate that prompts generated by GPT-4o improve image synthesis and prompt coherence, demonstrating the significance of high-quality prompts in 4K image generation. + +Ablation on WLF. To demonstrate the effectiveness of WLF, we conduct ablation studies with SD3, comparing fine-tuning diffusion models with and without WLF, and report the experiment results of Aesthetic-Eval@4096 in Tab. 7 and Tab. 8. Compared to fine-tuning without WLF, our WLF method demonstrates superior performance in CLIPScore, Aesthetics, GLCM Score and Compression Ratio, significantly showcasing its effectiveness in visual aesthetics, prompt adherence, and high-frequency details. + +# 5. Conclusion + +In this paper, we present Diffusion-4K, a novel framework for ultra-high-resolution text-to-image generation. We introduce Aesthetic-4K benchmark and wavelet-based fine-tuning, capable of training with the state-of-the-art latent diffusion models, such as SD3 and Flux. Qualitative and quantitative results demonstrate the effectiveness of our approach in training and generating photorealistic 4K images. + +# 6. Acknowledgement + +This work is partly supported by the National Natural Science Foundation of China (82441024), the Research Program of State Key Laboratory of Critical Software Environment, and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Michael S Albergo and Eric Vanden-Eijnden. Building normalizing flows with stochastic interpolants. arXiv preprint arXiv:2209.15571, 2022. 2 +[2] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. 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Example results synthesized by our Diffusion-4K, emphasizing exceptional fine details in generated 4K images." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 153, + 263, + 236, + 375 + ], + "blocks": [ + { + "bbox": [ + 153, + 263, + 236, + 375 + ], + "lines": [ + { + "bbox": [ + 153, + 263, + 236, + 375 + ], + "spans": [ + { + "bbox": [ + 153, + 263, + 236, + 375 + ], + "type": "image", + "image_path": "be0576bfef8283e279bd86ce49a08751eae2b47bbd2ea85664026931f4c4bcf6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 153, + 375, + 236, + 506 + ], + "blocks": [ + { + "bbox": [ + 153, + 375, + 236, + 506 + ], + "lines": [ + { + "bbox": [ + 153, + 375, + 236, + 506 + ], + "spans": [ + { + "bbox": [ + 153, + 375, + 236, + 506 + ], + "type": "image", + "image_path": "b69dc306a8369ce044083b869baeece947185457efb54619436171d454df33bc.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 236, + 263, + 319, + 375 + ], + "blocks": [ + { + "bbox": [ + 236, + 263, + 319, + 375 + ], + "lines": [ + { + "bbox": [ + 236, + 263, + 319, + 375 + ], + "spans": [ + { + "bbox": [ + 236, + 263, + 319, + 375 + ], + "type": "image", + "image_path": "4a75be8d3d29b90058430fad9496fb30b3ea64fca3c490045f12e32bea59d46d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 236, + 375, + 319, + 506 + ], + "blocks": [ + { + "bbox": [ + 236, + 375, + 319, + 506 + ], + "lines": [ + { + "bbox": [ + 236, + 375, + 319, + 506 + ], + "spans": [ + { + "bbox": [ + 236, + 375, + 319, + 506 + ], + "type": "image", + "image_path": "a698ab0d24c7a42d888ff8a5637560a4f4155d44d4982f77ddf18b3d9ca71c62.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 319, + 263, + 430, + 375 + ], + "blocks": [ + { + "bbox": [ + 319, + 263, + 430, + 375 + ], + "lines": [ + { + "bbox": [ + 319, + 263, + 430, + 375 + ], + "spans": [ + { + "bbox": [ + 319, + 263, + 430, + 375 + ], + "type": "image", + "image_path": "c049cffe824c09f89845351bc26ad1a521d8707a29d2a8bde55776711fbb19c1.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 319, + 375, + 430, + 506 + ], + "blocks": [ + { + "bbox": [ + 319, + 375, + 430, + 506 + ], + "lines": [ + { + "bbox": [ + 319, + 375, + 430, + 506 + ], + "spans": [ + { + "bbox": [ + 319, + 375, + 430, + 506 + ], + "type": "image", + "image_path": "9d8df44b69aafa635e14a64275e63f65974b7d8d2309904a68809007703de3fc.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 430, + 264, + 541, + 375 + ], + "blocks": [ + { + "bbox": [ + 430, + 264, + 541, + 375 + ], + "lines": [ + { + "bbox": [ + 430, + 264, + 541, + 375 + ], + "spans": [ + { + "bbox": [ + 430, + 264, + 541, + 375 + ], + "type": "image", + "image_path": "92ed28402298af9a017caefc59ab24d7cb033ae5bad0dbff5abfc386b90ded24.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 430, + 375, + 541, + 506 + ], + "blocks": [ + { + "bbox": [ + 430, + 375, + 541, + 506 + ], + "lines": [ + { + "bbox": [ + 430, + 375, + 541, + 506 + ], + "spans": [ + { + "bbox": [ + 430, + 375, + 541, + 506 + ], + "type": "image", + "image_path": "1ce4561b0ae947e7c6c6c09bf3d3796fa56824677bdde9ffdb87787d21fa10bc.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 151, + 536, + 200, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 536, + 200, + 549 + ], + "spans": [ + { + "bbox": [ + 151, + 536, + 200, + 549 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 55, + 562, + 296, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 562, + 296, + 693 + ], + "spans": [ + { + "bbox": [ + 55, + 562, + 296, + 693 + ], + "type": "text", + "content": "In this paper, we present Diffusion-4K, a novel framework for direct ultra-high-resolution image synthesis using text-to-image diffusion models. The core advancements include: (1) Aesthetic-4K Benchmark: addressing the absence of a publicly available 4K image synthesis dataset, we construct Aesthetic-4K, a comprehensive benchmark for ultra-high-resolution image generation. We curated a high-quality 4K dataset with carefully selected images and captions generated by GPT-4o. Additionally, we introduce GLCM Score and Compression Ratio metrics to evaluate fine details, combined with holis" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 538, + 555, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 538, + 555, + 693 + ], + "spans": [ + { + "bbox": [ + 313, + 538, + 555, + 693 + ], + "type": "text", + "content": "tic measures such as FID, Aesthetics and CLIPScore for a comprehensive assessment of ultra-high-resolution images. (2) Wavelet-based Fine-tuning: we propose a wavelet-based fine-tuning approach for direct training with photorealistic 4K images, applicable to various latent diffusion models, demonstrating its effectiveness in synthesizing highly detailed 4K images. Consequently, Diffusion-4K achieves impressive performance in high-quality image synthesis and text prompt adherence, especially when powered by modern large-scale diffusion models (e.g., SD3-2B and Flux-12B). Extensive experimental results from our benchmark demonstrate the superiority of Diffusion-4K in ultra-high-resolution image synthesis. Code is available at" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23464" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 107, + 136, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 107, + 136, + 119 + ], + "spans": [ + { + "bbox": [ + 56, + 107, + 136, + 119 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 127, + 295, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 127, + 295, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 127, + 295, + 282 + ], + "type": "text", + "content": "Diffusion models have proven to be highly effective for modeling high-dimensional, perceptual data such as images [18, 21, 29, 31, 46]. In recent years, latent diffusion models have made significant advancements in text-to-image synthesis, demonstrating impressive generalization capabilities at high resolutions [9, 12, 23, 25, 34, 41]. Replacing convolutional U-Net with a transformer architecture shows promising improvements as model scalability increases, e.g., Stable Diffusion 3 (SD3) at 8B [12], Flux at 12B [5], and Playground v3 at 24B [25]. Alternatively, flow-based formulations, using data or velocity prediction, have emerged as an viable choice due to their faster convergence and enhanced performance [1, 21, 24, 26, 28]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "spans": [ + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "type": "text", + "content": "Despite substantial progress, most latent diffusion models focus on training and generating images at " + }, + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "type": "text", + "content": ", leaving direct ultra-high-resolution image synthesis largely unexplored. Direct training and generating 4K images is valuable in realistic applications, but require considerable computational resources, especially as model parameters increase. Concurrent approaches such as PixArt-" + }, + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "type": "text", + "content": " [9] and Sana [49] address direct ultra-high-resolution image synthesis at 4K, showcasing the potentials of scalable latent diffusion transformer architectures. Both PixArt-" + }, + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 283, + 295, + 486 + ], + "type": "text", + "content": " at 0.6B and Sana at 0.6/1.6B primarily focus on the efficiency of ultra-high-resolution image generation, however, the intrinsic advantages of 4K images, such as high-frequency details and rich textures, are neglected. Furthermore, due to the scarcity of photorealistic 4K images, there is currently no publicly available benchmark for 4K image synthesis, hindering further research on this valuable topic." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 487, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 295, + 713 + ], + "type": "text", + "content": "In this paper, we propose Diffusion-4K, a novel framework designed for direct ultra-high-resolution image synthesis using latent diffusion models. Specifically, we introduce Aesthetic-4K, including a high-quality dataset of curated ultra-high-resolution images, with corresponding captions generated by GPT-4o [19]. Additionally, most automated evaluation metrics, such as Frechet Inception Distance (FID) [17], Aesthetics [45] and CLIPScore [16], offer only holistic measures at low resolutions, which are insufficient for the comprehensive benchmarking in high-resolution image synthesis, particularly for 4K images. To address the limitations, we introduce Gray Level Cooccurrence Matrix (GLCM) Score and Compression Ratio metrics, focusing on assessment of fine details in ultra-high-resolution images which has not yet been explored, with the goal of establishing a comprehensive benchmark for 4K image synthesis. Additionally, we propose a wavelet-based fine-tuning method that emphasizes high-frequency components while preserving low-frequent approximation in ultra" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": "high-resolution image synthesis. Notably, our method is compatible with various latent diffusion models. We conduct experiments with open-sourced latent diffusion models including SD3-2B [12] and Flux-12B [5], capable of training and generating photorealistic images at " + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 313, + 72, + 553, + 167 + ], + "type": "text", + "content": " resolution. Consequently, our method demonstrates superior performance in 4K image synthesis, underscoring the effectiveness of the Diffusion-4K framework." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 326, + 168, + 534, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 168, + 534, + 178 + ], + "spans": [ + { + "bbox": [ + 326, + 168, + 534, + 178 + ], + "type": "text", + "content": "The main contributions are summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 180, + 553, + 323 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 314, + 180, + 553, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 180, + 553, + 239 + ], + "spans": [ + { + "bbox": [ + 314, + 180, + 553, + 239 + ], + "type": "text", + "content": "- We establish Aesthetic-4k, a comprehensive benchmark for 4K image synthesis, including a high-quality dataset of ultra-high-resolution images with corresponding precise captions, and elaborated evaluation metrics for ultra-high-resolution images generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 240, + 553, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 240, + 553, + 275 + ], + "spans": [ + { + "bbox": [ + 313, + 240, + 553, + 275 + ], + "type": "text", + "content": "- We propose a wavelet-based fine-tuning approach for latent diffusion model, focusing on generating ultra-high-resolution images with fine details." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 275, + 553, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 275, + 553, + 323 + ], + "spans": [ + { + "bbox": [ + 313, + 275, + 553, + 323 + ], + "type": "text", + "content": "- Extensive experiment results demonstrate the effectiveness and generalization of our proposed method in 4K image synthesis, particularly when powered by large-scale diffusion transformers, e.g. SD3 and Flux." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 335, + 398, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 335, + 398, + 346 + ], + "spans": [ + { + "bbox": [ + 314, + 335, + 398, + 346 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": "Latent Diffusion Models. Stable Diffusion (SD) [41] proposes latent diffusion models to operate diffusion process in compressed latent space using Variational AutoEncoder (VAE). Widely used VAEs [7, 12, 31] employ a down-sampling factor of " + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "inline_equation", + "content": "F = 8" + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": ", compressing pixel space " + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H\\times W\\times 3}" + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": " into latent space " + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{\\frac{H}{F}\\times \\frac{W}{F}\\times C}" + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": " represent height and width respectively, and " + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": " denotes the channel of latent space. In the field of latent diffusion models, Diffusion Transformer (DiT) [31] has made significant progress in the past year. Typically, the patch size of DiT is set to " + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "inline_equation", + "content": "P = 2" + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": ", resulting in " + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "inline_equation", + "content": "\\frac{H}{FP}\\times \\frac{H}{FP}" + }, + { + "bbox": [ + 313, + 354, + 555, + 521 + ], + "type": "text", + "content": " tokens. The transformer architecture demonstrates excellent scalability in latent diffusion models, as evidenced by PixArt [7, 9], SD3 [12], Flux [5], Playground [23, 25], etc." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 522, + 554, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 554, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 554, + 677 + ], + "type": "text", + "content": "In text-to-image synthesis, the text encoder plays a crucial role in prompt coherence. SD employs CLIP [35] as its text encoder, while subsequent diffusion models, such as Imagen [42] and PixArt [7, 9], utilize T5-XXL [36] for text feature extraction. Recent approaches, such as SD3 [12] and Flux [5], combine both CLIP and T5-XXL for enhanced text understanding. DALL-E 3 [4] demonstrates that training with descriptive image captions can significantly enhance the prompt coherence of text-to-image models. Sana [49] utilizes the latest decoder-only Large Language Model (LLM), Gemma 2 [48], as its text encoder to improve understanding and reasoning capabilities related to text prompts." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 554, + 713 + ], + "type": "text", + "content": "High-Resolution Image Synthesis. High-resolution image generation is valuable in various practical applications such as industry and entertainment [6, 11]. Currently, advanced" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 56, + 72, + 232, + 83 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 232, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 232, + 83 + ], + "type": "text", + "content": "https://github.com/zhangOjhon/diffusion-4k." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23465" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "content": "latent diffusion models typically train and synthesize images at " + }, + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 55, + 72, + 294, + 203 + ], + "type": "text", + "content": " for high-resolution image generation due to computational complexity [34, 38, 39, 41, 43, 44]. However, increasing image resolution introduces quadratic computational costs, posing challenges particularly for 4K image synthesis. Several training-free fusion approaches for 4K image generation have been developed based on existing latent diffusion models [2, 10]. Additionally, Stable Cascade [32] employs multiple diffusion networks to increase resolution progressively. However, such ensemble methods can introduce cumulative errors." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "text", + "content": "PixArt- " + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "text", + "content": " [9] pioneers to direct image generation close to 4K (3840 × 2160) with efficient token compression for DiT, significantly improving efficiency and enabling ultra-high-resolution image generation. Sana [49], a pipeline designed to efficiently and cost-effectively train and synthesize 4K images, is capable of generating images at resolutions ranging from " + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "inline_equation", + "content": "1024\\times 1024" + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "inline_equation", + "content": "4096\\times 4096" + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "text", + "content": ". Sana introduces a deep compression VAE [8] that compresses images with an aggressive down-sampling factor of " + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "inline_equation", + "content": "F = 32" + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "text", + "content": ", enabling content creation at low cost. Despite significant improvements in resolution, both PixArt- " + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 55, + 204, + 295, + 373 + ], + "type": "text", + "content": " -0.6B and Sana-0.6B/1.6B ignore the intrinsic high-frequency details and rich textures in 4K image synthesis. Furthermore, the potential for scalable DiT in 4K image generation remains unexplored." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 381, + 117, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 381, + 117, + 393 + ], + "spans": [ + { + "bbox": [ + 55, + 381, + 117, + 393 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 402, + 295, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 402, + 295, + 498 + ], + "spans": [ + { + "bbox": [ + 55, + 402, + 295, + 498 + ], + "type": "text", + "content": "In this section, we elaborate on the details of Diffusion-4K, illustrating how it facilitates photorealistic 4K image synthesis. In Sec. 3.1, we introduce Aesthetic-4K, outlining the design principles and the process of constructing our human-centric benchmark with ultra-high-resolution images. Subsequently, we present a wavelet-based fine-tuning approach for direct training with photorealistic 4K images, applicable to various latent diffusion models, in Sec. 3.2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 505, + 197, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 197, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 197, + 517 + ], + "type": "text", + "content": "3.1. Aesthetic-4K Benchmark" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 522, + 295, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 295, + 605 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 295, + 605 + ], + "type": "text", + "content": "Existing benchmarks for advanced latent diffusion models generally conduct experiments with images at " + }, + { + "bbox": [ + 55, + 522, + 295, + 605 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 55, + 522, + 295, + 605 + ], + "type": "text", + "content": " resolution [7, 12, 23, 34], however, direct training and assessing with 4K images has not been thoroughly addressed yet. In this section, we construct Aesthetic-4K, a comprehensive benchmark for ultra-high-resolution image synthesis. The details are outlined as follows." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "Design Principles. Emphasis on human-centric perceptual cognition: To design a benchmark centered on human-level perceptual cognition, our primary goal is to explore the key factors of human perception on 4K images and formulate quantifiable indicators, while evaluating the general abilities of the generative model in these key factors. However, most automated evaluation metrics, such as FID [17], Aesthetics [45], and CLIPScore [16], provide only holistic measures at lower resolutions, which are insufficient for" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 316, + 70, + 553, + 225 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 553, + 225 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 553, + 225 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 553, + 225 + ], + "type": "image", + "image_path": "8ed412471c0e8cab02d65ced7cc7e0bd06bd24c83b283dfbee7ccf86141dcfd2.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 234, + 555, + 268 + ], + "lines": [ + { + "bbox": [ + 313, + 234, + 555, + 268 + ], + "spans": [ + { + "bbox": [ + 313, + 234, + 555, + 268 + ], + "type": "text", + "content": "Figure 2. Analysis of GLCM Score↑ / Compression Ratio↓. Our indicators demonstrate strong alignment with human-centric perceptual cognition at the level of local patches." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 319, + 280, + 550, + 323 + ], + "blocks": [ + { + "bbox": [ + 319, + 280, + 550, + 323 + ], + "lines": [ + { + "bbox": [ + 319, + 280, + 550, + 323 + ], + "spans": [ + { + "bbox": [ + 319, + 280, + 550, + 323 + ], + "type": "table", + "html": "
    MetricGLCM ScoreCompression RatioMUSIQMANIQA
    SRCC0.750.530.360.20
    PLCC0.770.560.410.26
    ", + "image_path": "08016fc27aef3d106958bbfd6003db059f034667630cda517ff2b62120c9396c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 353, + 331, + 515, + 342 + ], + "lines": [ + { + "bbox": [ + 353, + 331, + 515, + 342 + ], + "spans": [ + { + "bbox": [ + 353, + 331, + 515, + 342 + ], + "type": "text", + "content": "Table 1. Correlation with human evaluation." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 365, + 553, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 365, + 553, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 365, + 553, + 389 + ], + "type": "text", + "content": "comprehensive assessment, particularly lacking the ability of evaluating fine details in 4K images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 391, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 555, + 713 + ], + "type": "text", + "content": "Inspired by relevant literature in perceptual psychology, we found that highly structured textures play a decisive role in human perceptual cognition [3, 20, 47]. Therefore, we proposed additional indicators that accurately measure the richness of highly structured textures, including the commonly used quantitative indicators for texture analysis GLCM and the image compression ratio with discrete cosine transform (DCT). Considering human visual sensitivities, the GLCM, which captures the varying textural patterns, optical flow, and distortion through comprehensive spatial interactions of neighboring pixels, enables the creation of a truly representative characterization of human visual perception [13]. Simultaneously, the image compression ratio with DCT serves as an important reference for assessing the preservation of fine details in 4K images. To demonstrate alignment with human preferences, we conduct quantitative analysis of our indicators with adequate images, and present examples in Fig. 2. Moreover, as depicted in Tab. 1, we compute the Spearman Rank-order Correlation Coefficient (SRCC) and Pearson Linear Correlation Coefficient (PLCC) with human evaluations using various patches sampled from generated images, demonstrating the superior alignment with human ratings compared to no-reference image quality assessment metrics such as MUSIQ [22] and MANIQA [50]. Our benchmark design ensures that the model performance assessment is directly relevant to human decision-making and cognitive abilities." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23466" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 176, + 143 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 176, + 143 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 176, + 143 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 176, + 143 + ], + "type": "image", + "image_path": "f8afdd4db2c4e4ef10e8e42debe2f99c2463239e6fb9476274104e165aea3a29.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 144, + 279, + 156 + ], + "lines": [ + { + "bbox": [ + 64, + 144, + 279, + 156 + ], + "spans": [ + { + "bbox": [ + 64, + 144, + 279, + 156 + ], + "type": "text", + "content": "Prompt: A vast colony of king penguins densely populates a rocky shore, with numerous individuals standing closely together against a backdrop of ocean waves." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 177, + 70, + 301, + 143 + ], + "blocks": [ + { + "bbox": [ + 177, + 70, + 301, + 143 + ], + "lines": [ + { + "bbox": [ + 177, + 70, + 301, + 143 + ], + "spans": [ + { + "bbox": [ + 177, + 70, + 301, + 143 + ], + "type": "image", + "image_path": "418f1901629cc925249c357062c56764c2c45a94ec332078b00b3b4b5c64e083.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 58, + 157, + 176, + 230 + ], + "blocks": [ + { + "bbox": [ + 58, + 157, + 176, + 230 + ], + "lines": [ + { + "bbox": [ + 58, + 157, + 176, + 230 + ], + "spans": [ + { + "bbox": [ + 58, + 157, + 176, + 230 + ], + "type": "image", + "image_path": "8e779aa6776563cdc07483dcf3309d1e5383f7087284bbc4b82384ad59f6b768.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 177, + 157, + 301, + 230 + ], + "blocks": [ + { + "bbox": [ + 177, + 157, + 301, + 230 + ], + "lines": [ + { + "bbox": [ + 177, + 157, + 301, + 230 + ], + "spans": [ + { + "bbox": [ + 177, + 157, + 301, + 230 + ], + "type": "image", + "image_path": "4e4a316ff619105b49cd720a8cdffd9bbf144065975985e97d3b6470aab448a6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 58, + 243, + 176, + 380 + ], + "blocks": [ + { + "bbox": [ + 64, + 231, + 291, + 243 + ], + "lines": [ + { + "bbox": [ + 64, + 231, + 291, + 243 + ], + "spans": [ + { + "bbox": [ + 64, + 231, + 291, + 243 + ], + "type": "text", + "content": "Prompt: A sea turtle glides gracefully through crystal-clear turquoise water above a school of small fish, with sunlight reflecting off the surface." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 243, + 176, + 380 + ], + "lines": [ + { + "bbox": [ + 58, + 243, + 176, + 380 + ], + "spans": [ + { + "bbox": [ + 58, + 243, + 176, + 380 + ], + "type": "image", + "image_path": "85f2403418dfa62b2a7b8bede8508d505acf65409cf55b0ef4812f1f15d7f2b1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 381, + 290, + 394 + ], + "lines": [ + { + "bbox": [ + 64, + 381, + 290, + 394 + ], + "spans": [ + { + "bbox": [ + 64, + 381, + 290, + 394 + ], + "type": "text", + "content": "Prompt: A close-up of a fox's face, partially covered in snow, with sharp ears and bright, alert eyes. The snowy backdrop adds a serene atmosphere to the scene." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 118, + 396, + 240, + 406 + ], + "lines": [ + { + "bbox": [ + 118, + 396, + 240, + 406 + ], + "spans": [ + { + "bbox": [ + 118, + 396, + 240, + 406 + ], + "type": "text", + "content": "(a) Image-text samples in training set." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 415, + 555, + 439 + ], + "lines": [ + { + "bbox": [ + 55, + 415, + 555, + 439 + ], + "spans": [ + { + "bbox": [ + 55, + 415, + 555, + 439 + ], + "type": "text", + "content": "Figure 3. Illustration of image-text samples in the Aesthetic-4K dataset, which includes high-quality images and precise text prompts generated by GPT-4o, distinguished by high aesthetics and fine details." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 177, + 243, + 300, + 380 + ], + "blocks": [ + { + "bbox": [ + 177, + 243, + 300, + 380 + ], + "lines": [ + { + "bbox": [ + 177, + 243, + 300, + 380 + ], + "spans": [ + { + "bbox": [ + 177, + 243, + 300, + 380 + ], + "type": "image", + "image_path": "58389e8f04e24b2cd42d746dcbec95c353e53c867fb5df56c7edc3b5cddcfd1f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 427, + 143 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 427, + 143 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 427, + 143 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 427, + 143 + ], + "type": "image", + "image_path": "e66eb6b8c92ccd8d98e49a86552840a6cff03da06db1431a379b4b89ec1e9919.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 144, + 544, + 156 + ], + "lines": [ + { + "bbox": [ + 318, + 144, + 544, + 156 + ], + "spans": [ + { + "bbox": [ + 318, + 144, + 544, + 156 + ], + "type": "text", + "content": "Prompt: A picturesque riverside scene featuring a medieval castle atop a hill, surrounded by vibrant autumn foliage, with colorful homes lining the waterfront and several boats docked along the river." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 427, + 71, + 552, + 143 + ], + "blocks": [ + { + "bbox": [ + 427, + 71, + 552, + 143 + ], + "lines": [ + { + "bbox": [ + 427, + 71, + 552, + 143 + ], + "spans": [ + { + "bbox": [ + 427, + 71, + 552, + 143 + ], + "type": "image", + "image_path": "cb5e4bc63fada8b5b80e5a44404aaad455aa17d60119ea4749907d9ee4459f9e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 157, + 428, + 230 + ], + "blocks": [ + { + "bbox": [ + 310, + 157, + 428, + 230 + ], + "lines": [ + { + "bbox": [ + 310, + 157, + 428, + 230 + ], + "spans": [ + { + "bbox": [ + 310, + 157, + 428, + 230 + ], + "type": "image", + "image_path": "31e014e633c3dbc8156d4b93de06a6eac6ff3e4c5b5ce09ba00d56caa0c66f85.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 429, + 157, + 552, + 230 + ], + "blocks": [ + { + "bbox": [ + 429, + 157, + 552, + 230 + ], + "lines": [ + { + "bbox": [ + 429, + 157, + 552, + 230 + ], + "spans": [ + { + "bbox": [ + 429, + 157, + 552, + 230 + ], + "type": "image", + "image_path": "c339301352df9423f57407b160d627423045f878208363c86f71bf8e03ee9318.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 310, + 243, + 428, + 380 + ], + "blocks": [ + { + "bbox": [ + 318, + 231, + 529, + 243 + ], + "lines": [ + { + "bbox": [ + 318, + 231, + 529, + 243 + ], + "spans": [ + { + "bbox": [ + 318, + 231, + 529, + 243 + ], + "type": "text", + "content": "Prompt: A lone astronaut floats in space, gazing at a swirling black hole surrounded by vibrant landscapes, rivers, and clouds below." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 243, + 428, + 380 + ], + "lines": [ + { + "bbox": [ + 310, + 243, + 428, + 380 + ], + "spans": [ + { + "bbox": [ + 310, + 243, + 428, + 380 + ], + "type": "image", + "image_path": "fc1351c83007173ed97044d3707a916ab0d3715b9ed695a463f2b24cc471d408.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 381, + 550, + 394 + ], + "lines": [ + { + "bbox": [ + 315, + 381, + 550, + 394 + ], + "spans": [ + { + "bbox": [ + 315, + 381, + 550, + 394 + ], + "type": "text", + "content": "Prompt: A majestic polar bear sits near a rocky shore, reflecting in calm waters under a full moon amid a dramatic, cloudy sky filled with flying birds. A small figure stands in the distance, observing the scene." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 365, + 396, + 496, + 406 + ], + "lines": [ + { + "bbox": [ + 365, + 396, + 496, + 406 + ], + "spans": [ + { + "bbox": [ + 365, + 396, + 496, + 406 + ], + "type": "text", + "content": "(b) Image-text samples in evaluation set." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 428, + 243, + 552, + 380 + ], + "blocks": [ + { + "bbox": [ + 428, + 243, + 552, + 380 + ], + "lines": [ + { + "bbox": [ + 428, + 243, + 552, + 380 + ], + "spans": [ + { + "bbox": [ + 428, + 243, + 552, + 380 + ], + "type": "image", + "image_path": "306f479833c7c79d8f3fa220ba2a465da082c3c3e5b3fbbf68ed5f2736f557b8.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 54, + 459, + 295, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 459, + 295, + 639 + ], + "spans": [ + { + "bbox": [ + 54, + 459, + 295, + 639 + ], + "type": "text", + "content": "Aesthetic-4K Dataset. Addressing the absence of a publicly available 4K dataset, we propose the Aesthetic-4K dataset that includes a well-curated training and evaluation set for in-depth study. For the Aesthetic-4K training set, we collect high-quality images from the Internet, distinguished by exceptional aesthetics and fine details. Notably, the Aesthetic-4K training set consists of 12,015 high-quality images with a median height of 4128 and median width of 4640, representing a significant improvement in training data for ultra-high-resolution image synthesis. Additionally, we provide precise and detailed image captions generated by powerful GPT-4o [19], demonstrating strong alignment between vision and language. These curated images and corresponding captions comprise Aesthetic-Train, the training set of Aesthetic-4K." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "For the evaluation set, Aesthetic-Eval, we select imag-text pairs from the LAION-Aesthetics V2 6.5+ dataset, following the criterion of a short image side greater than 2048. The LAION-Aesthetics dataset includes 625,000 imag-text pairs with predicted aesthetic scores of 6.5 or higher in LAION-5B [45]. Notably, the Aesthetic-4K evaluation set" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 459, + 555, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 459, + 555, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 459, + 555, + 579 + ], + "type": "text", + "content": "consists of 2,781 high-quality images with a median height of 2983 and median width of 3613. We do not sample the evaluation set from the collected images sourced from the Internet, to mitigate the risk of overfitting in comprehensive assessments. Within the evaluation set, 195 images have a short side greater than 4096, which we refer to as Aesthetic-Eval@4096. Instead of evaluating with images at " + }, + { + "bbox": [ + 313, + 459, + 555, + 579 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 313, + 459, + 555, + 579 + ], + "type": "text", + "content": " resolution [49], the proposed Aesthetic-4K evaluation set provides a suitable benchmark for ultra-high-resolution image synthesis." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 580, + 555, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 580, + 555, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 580, + 555, + 676 + ], + "type": "text", + "content": "In summary, the proposed dataset encompasses common categories in realistic scenarios, including nature, travel, fashion, animals, film, art, food, sports, street photography, etc. As illustrated in Fig. 3, we present several image-text pairs from both the training and evaluation sets of Aesthetic-4K, clearly demonstrating their exceptional quality. For more details about the Aesthetic-4K dataset, please refer to the supplementary materials." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "Comprehensive Evaluation Metrics. To construct a comprehensive human-centric benchmark for 4K image synthesis, we provide conventional evaluation metrics in genera" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23467" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 295, + 108 + ], + "type": "text", + "content": "tive models, such as FID [17], Aesthetics [45], and CLIP-Score [16], for an intuitive understanding of image synthesis from a holistic perspective." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "text", + "content": "In addition, we report quantitative results for the proposed metrics assessing fine details in 4K images, including the GLCM Score and Compression Ratio, as significant complements to human-centric perceptual cognition in 4K images, which have not been addressed previously. The GLCM Score is formulated as follows: " + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "inline_equation", + "content": "s = -\\frac{1}{P}\\sum_{p=1}^{P}H(g_p)" + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "text", + "content": " represents entropy, and " + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "inline_equation", + "content": "g_p" + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "text", + "content": " is the GLCM [15] derived from local patch " + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "text", + "content": " in the original image with 64 gray levels, defined by radius " + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "inline_equation", + "content": "\\delta = [1,2,3,4]" + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "text", + "content": " and orientation " + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "inline_equation", + "content": "\\theta = [0^{\\circ},45^{\\circ},90^{\\circ},135^{\\circ}]" + }, + { + "bbox": [ + 55, + 109, + 296, + 312 + ], + "type": "text", + "content": ". In practice, we divide the gray image into local patches of size 64, and compute the average GLCM Score based on the partitioned local patches. Regrading the Compression Ratio, it is calculated as the ratio of the original image size in memory to the compressed image size using the JPEG algorithm at a quality of 95. Qualitative and quantitative assessments constitute the comprehensive benchmark, Aesthetic-4K." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 318, + 205, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 318, + 205, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 205, + 331 + ], + "type": "text", + "content": "3.2. Wavelet-based Fine-tuning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 335, + 296, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 335, + 296, + 394 + ], + "spans": [ + { + "bbox": [ + 55, + 335, + 296, + 394 + ], + "type": "text", + "content": "In this section, we propose a WaveLet-based Fine-tuning (WLF) method suitable for various latent diffusion models, enabling direct training with photorealistic images at " + }, + { + "bbox": [ + 55, + 335, + 296, + 394 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 55, + 335, + 296, + 394 + ], + "type": "text", + "content": " resolution. The core improvements consist of two components:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "spans": [ + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "type": "text", + "content": "Partitioned VAE. The most commonly used VAEs [5, 12] with " + }, + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "type": "inline_equation", + "content": "F = 8" + }, + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "type": "text", + "content": " encounter out-of-memory (OOM) issues during direct training and inference at " + }, + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "type": "text", + "content": ". To address this issue, we propose an efficient partitioned VAE, a simple yet effective method that compresses images with " + }, + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "type": "inline_equation", + "content": "F = 16" + }, + { + "bbox": [ + 55, + 396, + 296, + 585 + ], + "type": "text", + "content": ", significantly reducing memory consumption. Specifically, we use a dilation rate of 2 in the first convolutional layer of the VAE's encoder. In the last convolutional layer of the VAE's decoder, we partition the input feature map, up-sample by a factor of 2, apply the same convolution operator to each partitioned feature map, and then reorganize the final output. Notably, our method maintains consistency in the latent space of pre-trained latent diffusion models, eliminating the need for retraining or fine-tuning VAEs, which prevents distribution shifts in the latent space and ensures compatibility with various diffusion models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 586, + 296, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 296, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 296, + 694 + ], + "type": "text", + "content": "Wavelet-based Latent Enhancement. Wavelet transform has achieved significant success in image processing and is widely used to decompose low-frequency approximations and high-frequency details from images or features [14, 33]. In this section, we propose wavelet-based latent enhancement, which emphasizes high-frequency components while preserving low-frequency information, thereby significantly enhancing fine details and rich textures in 4K image generation. Consider the diffusion process, i.e." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 130, + 702, + 295, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 702, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 130, + 702, + 295, + 714 + ], + "type": "interline_equation", + "content": "\\boldsymbol {z} _ {t} = \\alpha_ {t} \\cdot \\boldsymbol {x} _ {0} + \\sigma_ {t} \\cdot \\epsilon , \\tag {1}", + "image_path": "305559b60011a6d1c2f26c1c113d394a2bd4ee4b4e47cdbbdd23c5d3fdfbee43.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": " represent data distribution and standard normal distribution, respectively, and " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "inline_equation", + "content": "\\sigma_t" + }, + { + "bbox": [ + 313, + 72, + 554, + 133 + ], + "type": "text", + "content": " are hyperparameters in the diffusion formulation. The original training objective in latent diffusion models is noise prediction [18, 41], defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 402, + 140, + 555, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 140, + 555, + 152 + ], + "spans": [ + { + "bbox": [ + 402, + 140, + 555, + 152 + ], + "type": "interline_equation", + "content": "\\epsilon_ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\epsilon_ {t}, \\tag {2}", + "image_path": "b71df1e038d453b1cc965ef3edc670a1b3d304e423bf3968d094a9e87492bf8a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "spans": [ + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "type": "text", + "content": " denotes the neural network, e.g., convolutional UNet or DiT. Recent approaches, such as SD3 [12] and Flux [5], adopt rectified flows to predict velocity " + }, + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 313, + 159, + 555, + 207 + ], + "type": "text", + "content": ", with the objective as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 392, + 214, + 555, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 214, + 555, + 228 + ], + "spans": [ + { + "bbox": [ + 392, + 214, + 555, + 228 + ], + "type": "interline_equation", + "content": "\\boldsymbol {v} _ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) = \\epsilon - \\boldsymbol {x} _ {0}. \\tag {3}", + "image_path": "f95d62d0a5c209cd929665db39d4050335122433461b99b7ec322101c4b19c67.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 233, + 555, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 233, + 555, + 270 + ], + "spans": [ + { + "bbox": [ + 313, + 233, + 555, + 270 + ], + "type": "text", + "content": "Our method decomposes the low-frequency approximation and high-frequency details of latent features using wavelet transform, defining the training objective as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 331, + 276, + 555, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 276, + 555, + 291 + ], + "spans": [ + { + "bbox": [ + 331, + 276, + 555, + 291 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {W L F} = \\mathbb {E} \\left[ w _ {t} \\| f \\left(\\boldsymbol {v} _ {\\Theta} \\left(\\boldsymbol {z} _ {t}, t\\right) - \\epsilon\\right) - f \\left(\\boldsymbol {x} _ {0}\\right) \\| ^ {2} \\right], \\tag {4}", + "image_path": "db113504b7f544abffcf70d75c02c64c2bea6dac7a7e9ce91c5a8cb5974d9e58.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "spans": [ + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "content": " is the loss weight, and " + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "content": " denotes discrete wavelet transform (DWT). Notably, we use the Haar wavelet, widely adopted in real-world applications due to its efficiency. Specifically, " + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "inline_equation", + "content": "L = \\frac{1}{\\sqrt{2}} [1,1]" + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "inline_equation", + "content": "H = \\frac{1}{\\sqrt{2}} [-1,1]" + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "content": " denote the low-pass and high-pass filters, used to construct four kernels in DWT with stride 2, namely " + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "inline_equation", + "content": "LL^{T}, LHT, HLT, HH^{T}" + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "content": ". The DWT kernels are then used to decompose the input features into four sub-bands, the low-frequency approximation " + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "inline_equation", + "content": "x_{ll}" + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "content": " and high-frequency components " + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "inline_equation", + "content": "x_{lh}, x_{hl}, x_{hh}" + }, + { + "bbox": [ + 313, + 297, + 555, + 493 + ], + "type": "text", + "content": ". As a result, both low-frequency information and high-frequency details are incorporated in Eq. (4), contributing to a comprehensive optimization in 4K image synthesis. In addition, our method supports various diffusion models by simply substituting the reconstruction objective, enabling seamless integration with conventional noise prediction approaches." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 502, + 395, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 395, + 515 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 395, + 515 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 522, + 554, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 554, + 654 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 554, + 654 + ], + "type": "text", + "content": "To demonstrate the effectiveness of our method, we conduct experiments with the state-of-the-art latent diffusion models at various scales, including open-source SD3-2B [12] and Flux-12B [5]. Specifically, mainstream evaluation metrics, such as FID [17], Aesthetics [45] and CLIPScore [16], as well as the proposed GLCM Score and Compression Ratio metrics, are reported for comprehensive assessments. Additionally, we present quantitative and qualitative results that showcase the high-resolution image reconstruction and generation capabilities of partitioned VAE and WLF, respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 660, + 441, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 660, + 441, + 673 + ], + "spans": [ + { + "bbox": [ + 313, + 660, + 441, + 673 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": "Implementation Details. Regrading the VAEs in both SD3 [12] and Flux [5], we encapsulate them using partitioned VAE with " + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "inline_equation", + "content": "F = 16" + }, + { + "bbox": [ + 313, + 677, + 555, + 713 + ], + "type": "text", + "content": ", ensuring the direct training at" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23468" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 136, + 249 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 136, + 249 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 136, + 249 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 136, + 249 + ], + "type": "image", + "image_path": "a90a8fb5ac5e31bc557c3210d260573d909ffbebabab7e39ca5a8160a0bbcf78.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 261, + 295, + 282 + ], + "lines": [ + { + "bbox": [ + 55, + 261, + 295, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 261, + 295, + 282 + ], + "type": "text", + "content": "Figure 4. Reconstruction results of 4K images with partitioned VAEs of " + }, + { + "bbox": [ + 55, + 261, + 295, + 282 + ], + "type": "inline_equation", + "content": "F = 16" + }, + { + "bbox": [ + 55, + 261, + 295, + 282 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 136, + 70, + 216, + 249 + ], + "blocks": [ + { + "bbox": [ + 136, + 70, + 216, + 249 + ], + "lines": [ + { + "bbox": [ + 136, + 70, + 216, + 249 + ], + "spans": [ + { + "bbox": [ + 136, + 70, + 216, + 249 + ], + "type": "image", + "image_path": "d683df6963aba897a0dcf660d68d8e72527ecd7e507bf18b967a49153a88c448.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 216, + 70, + 294, + 249 + ], + "blocks": [ + { + "bbox": [ + 216, + 70, + 294, + 249 + ], + "lines": [ + { + "bbox": [ + 216, + 70, + 294, + 249 + ], + "spans": [ + { + "bbox": [ + 216, + 70, + 294, + 249 + ], + "type": "image", + "image_path": "54b0daf059c3676cdc898ee9f292c154d07c989a0c190ea26d07cc54d36e8c74.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 304, + 296, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 304, + 296, + 425 + ], + "spans": [ + { + "bbox": [ + 55, + 304, + 296, + 425 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 55, + 304, + 296, + 425 + ], + "type": "text", + "content": " resolution without OOM issues. Notably, WLF is used for fine-tuning diffusion models, while the partitioned VAE and text encoder in pre-trained models are kept frozen, significantly improving the training efficiency. In practice, we use the AdamW [27] optimizer with a constant learning rate of 1e-6 and weight decay of 1e-4. We employ mixed-precision training with a batch size of 32 and use ZeRO Stage 2 with CPU offload techniques [37, 40]. The fine-tuning of SD3-2B and Flux-12B is conducted on 2 A800-80G GPUs and 8 A100-80G GPUs, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 432, + 170, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 432, + 170, + 445 + ], + "spans": [ + { + "bbox": [ + 55, + 432, + 170, + 445 + ], + "type": "text", + "content": "4.2. Experiment Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 450, + 295, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 295, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 295, + 641 + ], + "type": "text", + "content": "Analysis of partitioned VAEs. In Tab. 2, we report the evaluation results, including rFID, Normalized Mean Square Error (NMSE), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and LPIPS [51], to assess the reconstruction ability of partitioned VAEs on Aesthetic-4K at " + }, + { + "bbox": [ + 55, + 450, + 295, + 641 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 55, + 450, + 295, + 641 + ], + "type": "text", + "content": " resolution. We provide detailed results for VAEs in SD3 and Flux, enhanced by our partition techniques with " + }, + { + "bbox": [ + 55, + 450, + 295, + 641 + ], + "type": "inline_equation", + "content": "F = 16" + }, + { + "bbox": [ + 55, + 450, + 295, + 641 + ], + "type": "text", + "content": ". Notably, our partitioned VAE resolves the OOM issue encountered by the original VAE without requiring retraining or fine-tuning, thereby avoiding potential distribution shifts in the latent space. In addition, we present visualizations of original and reconstruction images in Fig. 4. The qualitative results demonstrate the effectiveness of the partitioned VAEs in 4K image reconstruction, ensuring consistency in the latent space for subsequent fine-tuning with 4K images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "Image Quality Assessment. Regarding image quality assessment, we conduct comprehensive comparisons using mainstream evaluation metrics, such as FID [17], Aesthetics [45] and CLIPScore [16], to provide an intuitive understanding of image quality and text prompt adherence. In Tab. 3, we report experimental results with SD3-2B and" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 324, + 70, + 545, + 113 + ], + "blocks": [ + { + "bbox": [ + 324, + 70, + 545, + 113 + ], + "lines": [ + { + "bbox": [ + 324, + 70, + 545, + 113 + ], + "spans": [ + { + "bbox": [ + 324, + 70, + 545, + 113 + ], + "type": "table", + "html": "
    ModelrFIDNMSEPSNRSSIMLPIPS
    SD3-VAE-F161.400.0928.820.760.15
    Flux-VAE-F161.690.0829.220.790.16
    ", + "image_path": "19faf9e506f4699ab7c9e5bf716a58d925eeb4c7225086c507f2e3018c379abc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 323, + 167, + 547, + 234 + ], + "blocks": [ + { + "bbox": [ + 313, + 121, + 555, + 153 + ], + "lines": [ + { + "bbox": [ + 313, + 121, + 555, + 153 + ], + "spans": [ + { + "bbox": [ + 313, + 121, + 555, + 153 + ], + "type": "text", + "content": "Table 2. Quantitative reconstruction results of VAEs with down-sampling factor of " + }, + { + "bbox": [ + 313, + 121, + 555, + 153 + ], + "type": "inline_equation", + "content": "F = 16" + }, + { + "bbox": [ + 313, + 121, + 555, + 153 + ], + "type": "text", + "content": " on our Aesthetic-4K training set at " + }, + { + "bbox": [ + 313, + 121, + 555, + 153 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 313, + 121, + 555, + 153 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 323, + 167, + 547, + 234 + ], + "lines": [ + { + "bbox": [ + 323, + 167, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 323, + 167, + 547, + 234 + ], + "type": "table", + "html": "
    ModelFID ↓CLIPScore ↑Aesthetics ↑
    SD3-F16@204843.8231.505.91
    SD3-F16-WLF@204840.1834.045.96
    Flux-F16@204850.5730.416.36
    Flux-F16-WLF@204839.4934.416.37
    ", + "image_path": "53e89fb6840bd9b9831ba50da52295b4e09613894a71dc68155f76ed3591addd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 317, + 277, + 553, + 345 + ], + "blocks": [ + { + "bbox": [ + 313, + 242, + 555, + 264 + ], + "lines": [ + { + "bbox": [ + 313, + 242, + 555, + 264 + ], + "spans": [ + { + "bbox": [ + 313, + 242, + 555, + 264 + ], + "type": "text", + "content": "Table 3. Quantitative benchmarks of latent diffusion models on Aesthetic-Eval@2048 at " + }, + { + "bbox": [ + 313, + 242, + 555, + 264 + ], + "type": "inline_equation", + "content": "2048 \\times 2048" + }, + { + "bbox": [ + 313, + 242, + 555, + 264 + ], + "type": "text", + "content": " resolution." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 277, + 553, + 345 + ], + "lines": [ + { + "bbox": [ + 317, + 277, + 553, + 345 + ], + "spans": [ + { + "bbox": [ + 317, + 277, + 553, + 345 + ], + "type": "table", + "html": "
    ModelGLCM Score ↑Compression Ratio ↓
    SD3-F16@20480.7511.23
    SD3-F16-WLF@20480.7910.51
    Flux-F16@20480.5814.80
    Flux-F16-WLF@20480.6113.60
    ", + "image_path": "d06bbb22b591cac0e349f657290c74ad2cbccf9d04f40ceb353c1fa0f312528d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 354, + 555, + 374 + ], + "lines": [ + { + "bbox": [ + 313, + 354, + 555, + 374 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 555, + 374 + ], + "type": "text", + "content": "Table 4. GLCM Score and Compression Ratio of latent diffusion models on Aesthetic-Eval@2048 at " + }, + { + "bbox": [ + 313, + 354, + 555, + 374 + ], + "type": "inline_equation", + "content": "2048 \\times 2048" + }, + { + "bbox": [ + 313, + 354, + 555, + 374 + ], + "type": "text", + "content": " resolution." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 399, + 553, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 553, + 423 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 553, + 423 + ], + "type": "text", + "content": "Flux-12B on Aesthetic-Eval@2048 in Tab. 3, demonstrating the effectiveness of our method." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 425, + 555, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 425, + 555, + 581 + ], + "spans": [ + { + "bbox": [ + 312, + 425, + 555, + 581 + ], + "type": "text", + "content": "As aforementioned, these conventional evaluation metrics are insufficient for comprehensive assessment in ultra-high-resolution image synthesis, particularly in evaluating the fine details of 4K images. In addition to commonly used benchmarks, we also compare the GLCM Score, which aims to assess the texture richness in ultra-high-resolution images. Simultaneously, we also report the Compression Ratio using the JPEG algorithm at a quality setting of 95, which can serve as an important reference for assessing image quality with fine details. As depicted in Tab. 4, experimental results highlight the advantages of WLF in these metrics, distinctly demonstrating our method's ability to generate 4K images with fine details." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": "Qualitative 4K Image Synthesis. As illustrated in Fig. 5, we present qualitative high-resolution images synthesized with Diffusion-4K, powered by the state-of-the-art latent diffusion model, Flux-12B. Although WLF fine-tunes at " + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 313, + 582, + 556, + 715 + ], + "type": "text", + "content": " resolution, our method can synthesize ultra-high-resolution images at various aspect ratios, and even supports direct photorealistic image generation at higher resolutions. In addition, we report the inference details in Tab. 5, highlighting the time and memory consumption of our method for directly generating 4K images. 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Qualitative 4K images synthesis of Diffusion-4K. Prompts are from Sora [30]." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 306, + 511, + 537, + 685 + ], + "blocks": [ + { + "bbox": [ + 306, + 511, + 537, + 685 + ], + "lines": [ + { + "bbox": [ + 306, + 511, + 537, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 511, + 537, + 685 + ], + "type": "image", + "image_path": "a3782a474e6af4901e6fd92a500f0a67191ad6ab2eea1e5f765dc9fb319ff70a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 308, + 686, + 535, + 708 + ], + "lines": [ + { + "bbox": [ + 308, + 686, + 535, + 708 + ], + "spans": [ + { + "bbox": [ + 308, + 686, + 535, + 708 + ], + "type": "text", + "content": "3D animation of a small, round, fluffy creature with big, expressive eyes explores a vibrant, enchanted forest. The creature, a whimsical blend of a rabbit and a squirrel, has soft blue fur and a bushy, striped tail. It hops along a sparkling stream, its eyes wide with wonder. The forest is alive with magical elements: flowing water and small floating lights that resemble fireflies. The creature stops to interact playfully with a group of tiny, fairy-like beings dancing around a mushroom ring. The creature looks up in awe at a large, glowing tree that seems to be the heart of the forest." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23470" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 295, + 159 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 295, + 159 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 295, + 159 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 295, + 159 + ], + "type": "table", + "html": "
    ModelMemoryTime (s/step)
    SD3-F8@4096OOM-
    SD3-F16-WLF@409631.3GB1.16
    SD3-F16-WLF@4096 (CPU offload)16.1GB1.22
    Flux-F8@4096OOM-
    Flux-F16-WLF@409650.4 GB2.42
    Flux-F16-WLF@4096 (CPU offload)26.9 GB3.16
    ", + "image_path": "a9d258c02ec6cfa51d479a19a542308ca90ed2ecc5b0f0bf45f14d991e90475b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 65, + 211, + 285, + 342 + ], + "blocks": [ + { + "bbox": [ + 65, + 211, + 285, + 342 + ], + "lines": [ + { + "bbox": [ + 65, + 211, + 285, + 342 + ], + "spans": [ + { + "bbox": [ + 65, + 211, + 285, + 342 + ], + "type": "image", + "image_path": "366caeacd72239d9968b18b7bb8a284e25dc1c2db676663d67c71b62a849c4c7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 79, + 350, + 271, + 361 + ], + "lines": [ + { + "bbox": [ + 79, + 350, + 271, + 361 + ], + "spans": [ + { + "bbox": [ + 79, + 350, + 271, + 361 + ], + "type": "text", + "content": "Figure 6. Human and GPT-4o preference evaluation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 383, + 295, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 383, + 295, + 418 + ], + "spans": [ + { + "bbox": [ + 55, + 383, + 295, + 418 + ], + "type": "text", + "content": "differential equation (ODE) process using an Euler solver. Please refer to the supplementary materials for more comparisons and details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 419, + 296, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 419, + 296, + 479 + ], + "spans": [ + { + "bbox": [ + 55, + 419, + 296, + 479 + ], + "type": "text", + "content": "Preference Study. Human preference is assessed by rating the pairwise outputs from two models, i.e. Flux with and without WLF. Additionally, we employ the advanced multi-modal model, GPT-4o [19], as the evaluator for the preference study. The following questions are asked:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 480, + 296, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 480, + 296, + 504 + ], + "spans": [ + { + "bbox": [ + 55, + 480, + 296, + 504 + ], + "type": "text", + "content": "Visual Aesthetics: Given the prompt, which image is of higher-quality and aesthetically more pleasing?" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 505, + 295, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 505, + 295, + 529 + ], + "spans": [ + { + "bbox": [ + 55, + 505, + 295, + 529 + ], + "type": "text", + "content": "Prompt Adherence: Which image looks more representative to the text shown above and faithfully follows it?" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 529, + 296, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 529, + 296, + 590 + ], + "spans": [ + { + "bbox": [ + 54, + 529, + 296, + 590 + ], + "type": "text", + "content": "Fine Details: Which image more accurately represents the fine visual details? Focus on clarity, sharpness, and texture. Assess the fidelity of fine elements such as edges, patterns, and nuances in color. The more precise representation of these details is preferred! Ignore other aspects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 590, + 296, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 590, + 296, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 590, + 296, + 651 + ], + "type": "text", + "content": "As shown in Fig. 6, our method demonstrates a superior win rate in both human and AI preference, highlighting the effectiveness of our WLF method in various aspects, including visual aesthetics, prompt adherence and fine details performance in 4K images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 659, + 156, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 659, + 156, + 671 + ], + "spans": [ + { + "bbox": [ + 55, + 659, + 156, + 671 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 714 + ], + "type": "text", + "content": "Ablation on Quality of Image Captions. We compare 4K image synthesis using original captions from LAION-5B [45] and captions generated by GPT-4o. As shown" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 324, + 70, + 545, + 136 + ], + "blocks": [ + { + "bbox": [ + 55, + 166, + 295, + 199 + ], + "lines": [ + { + "bbox": [ + 55, + 166, + 295, + 199 + ], + "spans": [ + { + "bbox": [ + 55, + 166, + 295, + 199 + ], + "type": "text", + "content": "Table 5. Memory consumption and inference speed of direct image synthesis at " + }, + { + "bbox": [ + 55, + 166, + 295, + 199 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 55, + 166, + 295, + 199 + ], + "type": "text", + "content": ". The result is tested on one A100 GPU with BF16 Precision." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 324, + 70, + 545, + 136 + ], + "lines": [ + { + "bbox": [ + 324, + 70, + 545, + 136 + ], + "spans": [ + { + "bbox": [ + 324, + 70, + 545, + 136 + ], + "type": "table", + "html": "
    CaptionsModelCLIPScore ↑Aesthetics ↑
    LAION-5BSD3-F16@409629.375.90
    GPT-4oSD3-F16@409633.125.97
    LAION-5BFlux-F16@409629.126.02
    GPT-4oFlux-F16@409633.676.11
    ", + "image_path": "a3eb5a8d9fd027bb6f088d230cd2789f1b063f5a7c62c6f39cc21f57a74f9c1c.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 324, + 181, + 545, + 237 + ], + "blocks": [ + { + "bbox": [ + 313, + 144, + 553, + 166 + ], + "lines": [ + { + "bbox": [ + 313, + 144, + 553, + 166 + ], + "spans": [ + { + "bbox": [ + 313, + 144, + 553, + 166 + ], + "type": "text", + "content": "Table 6. Ablation study on quality of image captions on Aesthetic-Eval@4096 at " + }, + { + "bbox": [ + 313, + 144, + 553, + 166 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 313, + 144, + 553, + 166 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 324, + 181, + 545, + 237 + ], + "lines": [ + { + "bbox": [ + 324, + 181, + 545, + 237 + ], + "spans": [ + { + "bbox": [ + 324, + 181, + 545, + 237 + ], + "type": "table", + "html": "
    ModelCLIPScore ↑Aesthetics ↑
    SD3-F16@409633.125.97
    SD3-F16-finetune@409634.145.99
    SD3-F16-WLF@409634.406.07
    ", + "image_path": "24c8d1f07ad33bc71bc20cf8869a299986c083b5f9fc55642a81f682b7b3bd74.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 317, + 293, + 553, + 344 + ], + "blocks": [ + { + "bbox": [ + 313, + 245, + 554, + 281 + ], + "lines": [ + { + "bbox": [ + 313, + 245, + 554, + 281 + ], + "spans": [ + { + "bbox": [ + 313, + 245, + 554, + 281 + ], + "type": "text", + "content": "Table 7. Ablation on CLIPScore and Aesthetics of SD3 on Aesthetic-Eval@4096 at " + }, + { + "bbox": [ + 313, + 245, + 554, + 281 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 313, + 245, + 554, + 281 + ], + "type": "text", + "content": ". SD3-F16-finetune@4096 represents fine-tuning without WLF." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 293, + 553, + 344 + ], + "lines": [ + { + "bbox": [ + 317, + 293, + 553, + 344 + ], + "spans": [ + { + "bbox": [ + 317, + 293, + 553, + 344 + ], + "type": "table", + "html": "
    ModelGLCM Score ↑Compression Ratio ↓
    SD3-F16@40960.7311.97
    SD3-F16-finetune@40960.7411.41
    SD3-F16-WLF@40960.7710.50
    ", + "image_path": "abbe948a1d3f1c4ea0e8d8fc87880bf0a78420cabc996ebeccaf00cfc2012958.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 352, + 554, + 386 + ], + "lines": [ + { + "bbox": [ + 313, + 352, + 554, + 386 + ], + "spans": [ + { + "bbox": [ + 313, + 352, + 554, + 386 + ], + "type": "text", + "content": "Table 8. Ablation on GLCM Score and Compression Ratio of SD3 on Aesthetic-Eval@4096 at " + }, + { + "bbox": [ + 313, + 352, + 554, + 386 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 313, + 352, + 554, + 386 + ], + "type": "text", + "content": ". SD3-F16-finetune@4096 denotes fine-tuning without WLF." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 410, + 554, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 554, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 554, + 482 + ], + "type": "text", + "content": "in Tab. 6, both SD3 and Flux exhibit enhanced results in Aesthetic-Eval@4096 with captions from GPT-4o. Quantitative results indicate that prompts generated by GPT-4o improve image synthesis and prompt coherence, demonstrating the significance of high-quality prompts in 4K image generation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 483, + 554, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 483, + 554, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 483, + 554, + 593 + ], + "type": "text", + "content": "Ablation on WLF. To demonstrate the effectiveness of WLF, we conduct ablation studies with SD3, comparing fine-tuning diffusion models with and without WLF, and report the experiment results of Aesthetic-Eval@4096 in Tab. 7 and Tab. 8. Compared to fine-tuning without WLF, our WLF method demonstrates superior performance in CLIPScore, Aesthetics, GLCM Score and Compression Ratio, significantly showcasing its effectiveness in visual aesthetics, prompt adherence, and high-frequency details." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 608, + 388, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 608, + 388, + 620 + ], + "spans": [ + { + "bbox": [ + 313, + 608, + 388, + 620 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 629, + 554, + 715 + ], + "type": "text", + "content": "In this paper, we present Diffusion-4K, a novel framework for ultra-high-resolution text-to-image generation. We introduce Aesthetic-4K benchmark and wavelet-based fine-tuning, capable of training with the state-of-the-art latent diffusion models, such as SD3 and Flux. Qualitative and quantitative results demonstrate the effectiveness of our approach in training and generating photorealistic 4K images." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23471" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 165, + 85 + ], + "type": "text", + "content": "6. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 6" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23473" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/d2f268e0-066c-441a-8577-0e87bbf4c0b9_content_list.json b/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/d2f268e0-066c-441a-8577-0e87bbf4c0b9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..09fc3a27a654782be95da880f2644f2e91fbf8e1 --- /dev/null +++ b/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/d2f268e0-066c-441a-8577-0e87bbf4c0b9_content_list.json @@ -0,0 +1,2095 @@ +[ + { + "type": "text", + "text": "Diffusion-based Event Generation for High-Quality Image Deblurring", + "text_level": 1, + "bbox": [ + 143, + 130, + 852, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xinan Xie $^{1}$ Qing Zhang $^{1,2*}$ Wei-Shi Zheng $^{1,2}$ $^{1}$ School of Computer Science and Engineering, Sun Yat-sen University, China \n $^{2}$ Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, China \nxiexn9@mail2.sysu.edu.cn zhangq93@mail.sysu.edu.cn wszheng@ieee.org", + "bbox": [ + 109, + 179, + 887, + 252 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4fa114d03f93af72e8694da821c2fe0778ec896ec244ae64f267a9c7b7910c31.jpg", + "image_caption": [ + "Figure 1. Comparison with previous methods on image blurring. As shown, by leveraging event guidance generated by a diffusion model, our method allows to produce high-quality deblurring results for images with complex motion blur, which are comparable to results of EFNet [43], a recent event-based deblurring method using GT event as input, and clearly better than results produced by HI-Diff [5]), a state-of-the-art image-only deblurring method." + ], + "image_footnote": [], + "bbox": [ + 101, + 289, + 259, + 536 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eb963d74a5a4adb25f3b12d485c6faf004e10d3989287272691a19ba61c67b4c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 261, + 290, + 419, + 536 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1942ee8584818511cdfe87670c8f410a26355430848f030bdbd48a99c4404f1c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 290, + 576, + 535 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/65e409a4e44abf250d64043e7e41960ac7e6bbca5375e6d888ae78d3bd25e503.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 580, + 290, + 736, + 534 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/537b3c5a1c750b7a298854c16b9261b41a965a5a7f18277bc758ce1e21d8f568.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 738, + 290, + 897, + 534 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 617, + 326, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While event-based deblurring have demonstrated impressive results, they are impractical for consumer photos captured by cell phones and digital cameras that are not equipped with the event sensor. To address this problem, we in this paper propose a novel deblurring framework called Event Generation Deblurring (EGDeblurring), which allows to effectively deblur an image by generating event guidance describing the motion information using a diffusion model. Specifically, we design a motion prior generation diffusion model and a feature extractor to produce prior information beneficial for deblurring, rather than generating the raw event representation. In order to achieve effective fusion of motion prior information with blurry images and produce high-quality results, we develop a regression deblurring network embedded with a dual-attention channel fusion block. Experiments on multiple", + "bbox": [ + 88, + 633, + 485, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "datasets demonstrate that our method outperforms state-of-the-art image deblurring methods. Our code is available at https://github.com/XinanXie/EGDeblurring.", + "bbox": [ + 511, + 618, + 906, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 513, + 693, + 645, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image deblurring is an important problem in computer vision, aiming to recover a sharp image from the original blurred input. Traditional methods primarily address the problem by formulating an optimization that incorporates various hand-crafted priors and assumptions [2, 3, 7, 11, 21, 24, 32, 39, 54]. In recent years, learning-based methods [4, 8, 31, 42, 45, 47, 56] have made significant progress. However, they are often less effective for images with complex motion blur, as shown in Figure 1.", + "bbox": [ + 509, + 718, + 906, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To enhance the robustness to complex blurry images, event-based deblurring methods [17, 27, 33, 40, 53, 60] have been developed, where the motion information cap", + "bbox": [ + 511, + 854, + 908, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 109, + 887, + 235, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2194", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tured by event camera is utilized to achieve high-quality image deblurring. Although these methods demonstrate impressive results, they require events as additional inference input, which cannot be recorded by most consumer cameras, thereby having relatively limited practicability. Diffusion models [15] have recently gained widespread attention due to its powerful generation capability. This motivates us to explore the possibility of using diffusion models to generate event guidance for blurred images.", + "bbox": [ + 89, + 90, + 480, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present EGDeblurring, a method that allows high-quality image deblurring by utilizing motion information from event guidance generated by a diffusion model. EGDeblurring consists of a motion prior generation diffusion model (MPG-Diff) and a regression deblurring network (RDNet), where MPG-Diff is a diffusion model used for generating event recording the motion information of a blurry image, while RDNet aims to recover a sharp image from the blurry image and the associated events. Note, we design MPG-Diff to generate event-based motion prior features instead of raw events. The reason behind is that raw event usually appears in terms of sparse representation, while diffusion models excel at generating dense representation with rich details. To ensure that MPG-diff generates reliable event guidance, we instead choose to predict motion prior feature rather than raw event. To effectively utilize the motion information recorded by events, we embed dual-attention channel fusion block (DACFB) at multiple levels of the RDNet, which enables aligning and fusing motion information features with image features. To enable better performance, a multi-stage training strategy is further introduced. During inference, our method receives only blurry images as input as it can generate event guidance by itself.", + "bbox": [ + 91, + 228, + 486, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we make the following main contributions:", + "bbox": [ + 109, + 575, + 480, + 589 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a method that allows high-quality image deblurring by generating event guidance describing the motion information using a diffusion model.", + "- We develop a diffusion model for generating event guidance and a network to produce sharp image from a blurry image and its predicted event. Besides, we introduce an effective multi-stage training strategy.", + "- We compare our method with various state-of-the-art image deblurring methods on benchmark datasets. Results show that our method significantly outperforms existing image-only methods, and can produce comparable results to event-based methods with ground truth event as inference input." + ], + "bbox": [ + 109, + 590, + 480, + 799 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 89, + 814, + 232, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image-only methods. Early image deblurring methods typically work by estimating the blur kernel using various natural image priors and assumptions [2, 3, 11, 21, 22, 25, 54]. However, these methods are mostly less effective for im", + "bbox": [ + 89, + 839, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ages with complex motion blur, as their leveraged priors and assumptions may not always hold in real-world scenarios. In the past decade, numerous deep learning based methods are developed for image deblurring [1, 4, 8, 16, 31, 38, 42, 45, 47, 56, 58] from different perspectives including multi-scale [31, 45], coarse-to-fine [8], and multistage [4]. More recently, transformer [20, 46, 57] and frequency analysis [10, 20] have been applied to image deblurring, which demonstrates promising results. However, due to lack of reliable modeling of the motion information, existing learning-based methods basically struggle to recover sharp images with clear and well-preserved details, especially when facing with blurry images incurred by complex object and camera motion.", + "bbox": [ + 511, + 90, + 903, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event-based methods. As event carries the motion information beneficial to image deblurring, there are various event-based methods [6, 14, 17, 19, 27, 33, 34, 40, 53, 60, 61] in the literature. Pan et al. [33] proposed an event-based double integral (EDI) model that integrates blurred images and events for deblurring. Shang et al. [40] developed a event fusion module that can be incorporated into existing image and video deblurring networks. RED-Net [53] proposes to combine optical flow estimation and for self-supervised deblurring. EFNet [43] designs an event-image cross-modal attention module to fuse event and image features. Although event-based methods achieve superior deblurring performance by leveraging motion information, to our knowledge, all of them require ground truth event as addition inference input, which limits their practicability.", + "bbox": [ + 511, + 309, + 903, + 536 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion-based methods. Recently, diffusion models have demonstrated impressive performance in various low-level vision tasks including image/video deblurring [13, 26, 37, 51]. DvSR [51] presents a framework for stochastic blind image deblurring with a focus on perceptual quality using a conditional diffusion model. Ren et al. [36] proposed to improve the performance by leveraging multiscale structure guidance. DiffIR [52] achieves efficient diffusion-based image restoration. HI-Diff [5] applies diffusion model in a highly compacted latent space to generate the prior feature for the deblurring process. There is also attempt towards integrating event information into diffusion models. Diffevent [50] formulates event-based image deblurring as an image generation problem by designing diffusion priors for both the image and residuals.", + "bbox": [ + 511, + 542, + 906, + 770 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 782, + 604, + 799 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Figure 2 presents the overview of the proposed EGDeblurring. As shown, during inference, our method only receives single blurry image as input. The EGDeblurring encompasses two key modules: the RDNet and the MPGDiff. The RDNet embed the DACFB is designed to restore a blurred image into the corresponding sharp one, guided", + "bbox": [ + 511, + 809, + 903, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2195", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2de3b3dce4bdee3ee5dbfad43aeff8efcd494b652bbacc94092e6118c50456ae.jpg", + "image_caption": [ + "Training Stage 1: Training of Regression Deblurring Network (RDNet)" + ], + "image_footnote": [], + "bbox": [ + 99, + 119, + 450, + 238 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cc4d0ccfe95bf26776633bf8900ccfab2b92424de1f56630b7139009745bfc75.jpg", + "image_caption": [ + "Training Stage 3: Joint training of MPG-Diff and RDNet" + ], + "image_footnote": [], + "bbox": [ + 506, + 113, + 883, + 239 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6434c2f235a0246a466fb5b733260cb99156309a016e5830ec8a74c35e946bec.jpg", + "image_caption": [ + "Training Stage 2: Training of Motion Prior Generation Diffusion Model (MPG-Diff)" + ], + "image_footnote": [], + "bbox": [ + 117, + 267, + 444, + 411 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/88d66eb711bf254bf25104f89555667c9fbe0d54988cb732b1f32579ca8eb28c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 535, + 250, + 854, + 369 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c824de5fc430ac840bfbd672141239998cf2e98d545982dbb24d9f14c1356683.jpg", + "image_caption": [ + "Figure 2. Overview of EGDeblurring. The EGDeblurring incorporates events during the training process, while it does not require event input during the inference stage, which is consistent with the image-only approach. The EGDeblurring are trained with a multi-stage training strategy. In Stage 1, the FE transforms the event representation $E$ into the motion prior feature representation $M$ which guides the RDNet to restore the sharp image $S$ from the blurred image $B$ . In Stage 2, the MPG-Diff is trained to generate motion prior feature $M'$ conditioned on the blurred image $B$ and the detail guidance $P$ . In Stage 3, the MPG-Diff and the RDNet are jointly trained to achieve optimal deblurring performance. During inference, given a blurry image $B$ , the MPG-Diff generates the corresponding motion prior feature $M'$ , guiding the RDNet to output the final sharp result $S$ ." + ], + "image_footnote": [], + "bbox": [ + 517, + 375, + 872, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "by motion prior features from events or the MPG-Diff. The MPG-Diff accepts the blurred image and the corresponding detail guidance as conditions, generating motion prior features. We adopt a multi-stage training strategy. In training stage 1 and training stage 2, the RDNet and MPG-Diff are trained respectively. Subsequently, in training stage 3, both are jointly trained to achieve coordination between the modules. During the inference process, given a blurred image, the MPG-Diff generates the corresponding motion prior features. The RDNet then utilizes these prior features to achieve high-quality image deblurring, eliminating the need for event assistance. Therefore, during inference, the EGDeblurring method is consistent with the image-only approach.", + "bbox": [ + 88, + 565, + 482, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Regression Deblurring Network", + "text_level": 1, + "bbox": [ + 89, + 787, + 372, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To avoid undesired artifacts and achieve better results, we design the RDNet to perform image deblurring. The RDNet consists of a motion prior encoder, an image encoder, and an image decoder. Meanwhile, in order to match the generation of the subsequent diffusion model, we employ a Feature Extractor (FE) composed of a deep neural", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "network to convert the event representation $E \\in \\mathbb{R}^{C_e \\times H \\times W}$ into a feature representation $M \\in \\mathbb{R}^{C_m \\times H \\times W}$ . The motion prior encoder encodes $M$ from the FE in training stage 1 (or $M'$ from the MPG-Diff in training stage 3 and inference) into multi-scale motion prior features $F_{m}^{k} \\in \\mathbb{R}^{C' \\times H' \\times W'}$ , where $k = 0, 1, 2$ and $C' = 2^k C_b$ , $H' = H / 2^k$ , $W' = W / 2^k$ . $C_b$ denotes the base number of channels. The blurred image $B \\in \\mathbb{R}^{3 \\times H \\times W}$ is encoded by the image encoder into image features $F_{i}^{k}$ . $F_{i}^{k}$ and $F_{m}^{k}$ at the same scale are fused through the DACFB embedded in the image encoder. The image features are processed through the image decoder to produce the sharp image $S \\in \\mathbb{R}^{3 \\times H \\times W}$ , which serves as the final output of the framework.", + "bbox": [ + 511, + 564, + 906, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Details of DACFB. We propose a DACFB as the modal information regulator for the network. The utilization of a multi-branch structure enables the network to learn multiple sets of cross-modal values to modulate the image features. As shown in Figure 3, layer normalization and $1 \\times 1$ convolutional layers process $F_{m}^{k}$ and $F_{i}^{k}$ to obtain $K \\in \\mathbb{R}^{H'W' \\times C'}$ and $Q \\in \\mathbb{R}^{H'W' \\times C'}$ respectively. The cross-channel attention map $A$ is computed from $K$ and $Q$ . To ensure suf", + "bbox": [ + 511, + 777, + 908, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2196", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2ba9a61daabea251924c3d135aa8069f20c3a4c4fc7516bc0d596c398d82f8b7.jpg", + "image_caption": [ + "Figure 3. Network architecture of DACFB. The DACFB is embedded within the image encoder of the RDNet, aiming to fuse the motion feature $F_{m}^{k}$ and the image feature $F_{i}^{k}$ ." + ], + "image_footnote": [], + "bbox": [ + 102, + 97, + 478, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ficient modulation of features, we extract $V_{1}$ and $V_{2}$ from $F_{m}^{k}$ , where $V_{1}, V_{2} \\in \\mathbb{R}^{H'W' \\times C'}$ . The vectors $V_{1}$ and $V_{2}$ are respectively taken to compute the outer products with $A$ , resulting in $A_{1}$ and $A_{2}$ . Then the outputs of the attention operation are separately multiplied and added to $F_{i}^{k}$ to obtain the output feature $F_{out}'$ . $F_{out}'$ is passed to the feed forward network and outputs the final result $F_{out}$ . It can be represented by the following formula:", + "bbox": [ + 89, + 354, + 483, + 477 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA = \\operatorname {s o f t m a x} (\\frac {Q ^ {T} K}{\\sqrt {d}}),\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 483, + 351, + 517 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {1} = V _ {1} \\times A,\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 518, + 289, + 535 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {2} = V _ {2} \\times A, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 534, + 480, + 554 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {o u t} ^ {\\prime} = L N \\left(F _ {i} ^ {k}\\right) \\cdot A _ {1} + A _ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 558, + 380, + 577 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {o u t} = F F N \\left(F _ {o u t} ^ {\\prime}\\right) + F _ {o u t} ^ {\\prime},\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 578, + 383, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $LN(\\cdot)$ represents layer normalization and $FFN(\\cdot)$ represents the feed forward network.", + "bbox": [ + 89, + 603, + 482, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Motion Prior Generation Diffusion Model", + "text_level": 1, + "bbox": [ + 89, + 642, + 449, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We employ the MPG-Diff to generate the motion prior feature $M'$ as a substitute for the motion information features $M$ from events. We employ a conditional denoising diffusion probabilistic model [9, 15] to guide the generation of the corresponding motion prior information. We perform the forward diffusion process and the reverse denoising process on the motion prior features $M$ instead of the events $E$ .", + "bbox": [ + 89, + 664, + 482, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the forward diffusion process, $M$ transformed from $E$ by the FE is considered as the starting point of the forward Markov process (i.e., $M = M_0$ ). The diffusion model learns a Markov chain by progressively corrupting the target feature $M_0$ with Gaussian noise at each time step $t$ , thereby transforming it into a Gaussian distribution (referred to as $\\mathcal{N}$ ). The forward diffusion process is formulated as:", + "bbox": [ + 89, + 770, + 483, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(M _ {t} \\mid M _ {t - 1}\\right) = \\mathcal {N} \\left(M _ {t}; \\sqrt {1 - \\beta_ {t}} M _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 883, + 482, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M_{t}$ is the feature at time step $t$ , $\\beta_{t}$ is the predefined variance, and $\\mathbf{I}$ represents the identity matrix for ensuring isotropic of the noise. After reparameterization [15], we obtain $M_{t}$ from $M_0$ in a single step by:", + "bbox": [ + 511, + 90, + 905, + 152 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} M _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 164, + 906, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{\\alpha}_t = \\prod_{i=0}^t \\alpha_i$ is the cumulative product of forward noise weight parameters $\\alpha_i = 1 - \\beta_i$ , while $\\epsilon \\sim \\mathcal{N}(0, I)$ denotes random Gaussian noise.", + "bbox": [ + 511, + 198, + 905, + 256 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the reverse denoising process, Gaussian noise is iteratively denoised into the motion prior feature $M'$ . We adopt the DDIM [41] sampling strategy. To synthesize the corresponding motion prior features, we utilize the blurred image $B$ and detail guidance $P$ as conditions. The reverse denoising process is defined as follows:", + "bbox": [ + 511, + 258, + 906, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} (\\frac {M _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\cdot \\mathbf {e} _ {t}}{\\sqrt {\\bar {\\alpha} _ {t}}}) + \\sqrt {1 - \\bar {\\alpha} _ {t - 1}} \\cdot \\mathbf {e} _ {t},\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 361, + 901, + 396 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {t} = \\epsilon_ {\\theta} (M _ {t}, B, P, t), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 398, + 903, + 428 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{e}_t$ is the noise estimated by the neural network $\\epsilon_{\\theta}$ .", + "bbox": [ + 511, + 428, + 888, + 443 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Detail guidance. To better constrain the diffusion model to output highly relevant information, we explore extracting details from the blurred image. We observed that when the image is downsampled, further detail information is lost. Thus, the difference between the downsampled image and the original image can serve as a guidance for the image details. We propose $P = B - \\mathcal{T}(B)$ as the detail guidance, where $\\mathcal{T}$ represents the operation of downsampling the image and then upsampling it back to its original size.", + "bbox": [ + 511, + 450, + 905, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Multi-Stage Training Strategy", + "text_level": 1, + "bbox": [ + 511, + 597, + 782, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We adopt a three-stage joint training strategy to achieve synchronization between the modules.", + "bbox": [ + 511, + 621, + 905, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stage 1: training of RDNet. During the first stage of training, our goal is to introduce events and train a high-performance deblurring network. The training process at this stage is similar to that of event-based deblurring. We concatenate the FE and the RDNet in series and perform joint training. The event representation $E$ is transformed into the feature representation $M$ through the FE. Next, the RDNet accepts the $M$ and the blurred image $B$ and outputs the sharp image $S$ . The overall process of training stage 1 can be expressed as follows:", + "bbox": [ + 511, + 657, + 906, + 808 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} M = F E (E), \\\\ S _ {m} = \\text {P D N t} (R, M) \\end{array} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 821, + 903, + 845 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS = R D N e t (B, M).\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 840, + 782, + 857 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At this stage, we aim for the network to achieve optimal deblurring performance. We employ $L_{1}$ loss to constrain the", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2197", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "network output and jointly optimize the FE and the RDNet. The loss function is defined as follows:", + "bbox": [ + 89, + 90, + 480, + 119 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s t a g e 1}} = \\left\\| S - G \\right\\| _ {1}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 133, + 482, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $G$ represents the corresponding ground truth.", + "bbox": [ + 89, + 164, + 434, + 179 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage 2: Training of MPG-Diff. We train the MPG-Diff using the basic training strategy of diffusion models. Given the event $E$ , we first use the FE trained in the first stage to synthesize the $M$ . Subsequently, $M_{t}$ is generated using Equation 3. In the reverse denoising process, the blurred image $B$ and detail guidance $P$ serve as conditions, and the denoising network predicts the noise $\\mathbf{e}_t$ . We train the denoising network $\\epsilon_{\\theta}$ using the following loss function:", + "bbox": [ + 89, + 185, + 483, + 306 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s t a g e 2} = E _ {M _ {t}, t, B, P, \\epsilon \\sim \\mathcal {N} (0, I)} \\| \\mathbf {e} _ {t} - \\epsilon \\| _ {2} ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 318, + 482, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that the parameters of FE are frozen in this stage.", + "bbox": [ + 89, + 349, + 452, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage 3: Joint training of MPG-Diff and RDNet. Since in training stage 2, we only trained the MPG-Diff without training the FE and the RDNet, the output $M'$ from the MPG-Diff exhibits slight differences compared to the output $M$ generated by the FE. As a result, directly using $M'$ to guide the RDNet will not achieve optimal deblurring performance. To address this, we perform joint training of the MPG-Diff and the RDNet. Specifically, the MPG-Diff performs a complete iterative denoising process to obtain the predicted motion prior $M'$ . Then we input both $M'$ and the blurred image $B$ into the RDNet to generate the deblurred result $S$ . By constraining the final result, we jointly optimize the MPG-Diff and the RDNet. The loss function is defined as follows:", + "bbox": [ + 89, + 369, + 483, + 580 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s t a g e 3}} = \\left\\| S - G \\right\\| _ {1} + \\lambda \\cdot \\left\\| M ^ {\\prime} - M \\right\\| _ {1}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 595, + 482, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is the weight factor and $M$ is the output of the FE. Since the denoising process is iterated multiple times, to reduce memory usage, we only record the gradients of the self-attention modules in the network $\\epsilon_{\\theta}$ and update the weights of that specific part of the network.", + "bbox": [ + 89, + 625, + 483, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Inference", + "text_level": 1, + "bbox": [ + 89, + 710, + 200, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a blurred image $B$ , the MPG-Diff generates the corresponding motion prior features $M'$ . The RDNet takes $B$ and $M'$ as inputs and outputs the sharp image $S$ as the final result. The overall process is represented by the following equation:", + "bbox": [ + 89, + 733, + 483, + 809 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM ^ {\\prime} = D i f f (B), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 209, + 821, + 482, + 845 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS = R D N e t (B, M ^ {\\prime}),\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 840, + 362, + 857 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Diff(\\cdot)$ represents the complete iterative denoising process of the MPG-Diff using the network $\\epsilon_{\\theta}$ .", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/af3c7e3915724ad4ec2af3e576932babdb56a1ac6cdc2dfdadf94115bbd7ebe6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Image-only methodSSIM↑PSNR↑Param.(M)
    DeepDeblur [31]0.91429.0811.7
    DeblurGAN-v2 [23]0.93429.5560.9
    SRN [45]0.93430.266.8
    DBGAN [59]0.94231.1011.6
    DMPHN [58]0.94031.2021.7
    Ren et al. [36]0.95432.1152.0
    MIMO-UNet+ [8]0.95732.4516.1
    HINet [4]0.95932.9188.7
    Restormer [57]0.96132.9226.1
    Stripformer [46]0.96233.0820.0
    HI-Diff [5]0.96433.3328.49
    MLWNet [12]0.96833.8395.1
    LoFormer [30]0.96934.0949.0
    MISC Filter [28]0.96934.1016.0
    FFTformer [20]0.96834.2116.6
    SegFFTformer [18]0.97034.38-
    AdaRevD [29]0.97234.60220.8
    Ours0.97334.6280.3
    D²Net [40]0.94031.6032.63
    eSL-Net [49]0.95433.520.19
    MADANET+ [55]0.96433.8416.9
    Vitoria et al. [48]0.94434.335.7
    EFNet [43]0.97235.468.47
    Ours Stage 10.97435.5020.7
    ", + "bbox": [ + 519, + 80, + 903, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison with state-of-the-art deblurring methods on synthetic GoPro dataset. Red background represents the best performance. Orange background represents the second best. yellow box represents the third best. Ours Stage 1 represents the framework trained in Stage 1 with events. The underline denotes event-based method.", + "bbox": [ + 511, + 493, + 906, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Implementation Details", + "text_level": 1, + "bbox": [ + 511, + 589, + 730, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the RDNet, we set $C_b = 64$ and concatenate two DACFB modules at each scale of the image encoder. In the MPG-Diff, we use 1000 diffusion steps and a nosie schedule $\\beta_t$ linearly increasing from 1e-6 to 1e-2 for training, and 5 steps for inference. During training, we set the batch size to 4 and use the ADAM optimizer with an initial learning rate of $1 \\times 10^{-4}$ . We implement the algorithm in PyTorch and run it on the NVIDIA RTX 4090 GPU.", + "bbox": [ + 511, + 611, + 906, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 511, + 748, + 645, + 765 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 511, + 773, + 710, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GoPro Dataset. We evaluate the effectiveness of the method on the GoPro dataset [31], which is widely used in both image-only and event-based deblurring research. We use ESIM [35] to construct synthetic event data and create an image-like representation from the events [43].", + "bbox": [ + 511, + 803, + 905, + 878 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "REBlur Dataset. To reflect the performance on real-world", + "bbox": [ + 511, + 885, + 906, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2198", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/19a59963a8fe678173208c48415a3d2027e28bb1bbe023c425fc6c4d54ef59d5.jpg", + "image_caption": [ + "(a) Input (0.638, 21.31)" + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 295, + 175 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bb3ef0e6e589e4b59c9439120afe7442fa6700a5976997f1a481445a4fdac6e3.jpg", + "image_caption": [ + "(b) HINet[4] (0.730, 23.74)" + ], + "image_footnote": [], + "bbox": [ + 295, + 88, + 500, + 175 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ade364f59f088d89d87def00dad5c3a0403fe9a2d00024fde5e116444c9849f7.jpg", + "image_caption": [ + "(c) FFTformer[20] (0.882, 29.37)" + ], + "image_footnote": [], + "bbox": [ + 500, + 88, + 700, + 175 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3da60e790083472f61923db57d6a938ff2435447f72bda6f5c553df57797325a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 88, + 903, + 175 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c34f68e69ce403926d9c466c598746d89d986d63485a29c1621acc8a284c7240.jpg", + "image_caption": [ + "(e) HI-Diff[5] (0.836, 27.02)" + ], + "image_footnote": [], + "bbox": [ + 91, + 191, + 295, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6f8e9618da778ead0c8cbbae9ceb514ccda08656ef4ab0624d426cfff2c93698.jpg", + "image_caption": [ + "(f) Restomer [57] (0.793, 25.39)" + ], + "image_footnote": [], + "bbox": [ + 295, + 191, + 500, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/759085e64242bd8f1c9604f8f2148275e912b1423531cbbdb57c4500f5d357f6.jpg", + "image_caption": [ + "(g) Ours (0.889, 30.91)" + ], + "image_footnote": [], + "bbox": [ + 500, + 191, + 700, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/64b673ab26aa4e01b26b2ecbd4391687e574c92bbd5377e25aedb7142db33891.jpg", + "image_caption": [ + "(d) AdaRevD[29] (0.842, 27.53)", + "(h) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 700, + 191, + 903, + 277 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ff1a2f40d21257a4fd4e02d44592a0bf75bccc0ddd59c4472039344c3f285bd4.jpg", + "image_caption": [ + "Figure 4. Qualitative results on the GoPro dataset. The values in parentheses represent (SSIM, PSNR)." + ], + "image_footnote": [], + "bbox": [ + 91, + 333, + 295, + 421 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/91fa3705139e8bbf6f719beefc802dd59e31ff615a205b2cd059d987251e0cab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 333, + 500, + 421 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/60536e1fa356d14c607a8b59699ffc4e2ec2f71492f6807c2a5bd2f28030bae3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 333, + 700, + 421 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4cf54bb1e9a34213e3885d7c0bc28c7892fe04f8f7721466386edac4e551806b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 333, + 903, + 421 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/887282609ab1c3918760ef7a310534304cb430173319da92cf8b27a7bfb740ff.jpg", + "image_caption": [ + "(a) Input (0.833, 25.90)", + "(e) HI-Diff[5] (0.929, 32.91)" + ], + "image_footnote": [], + "bbox": [ + 91, + 435, + 295, + 522 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/afd094efbadf5ab7e335a6823da39c6cfe8af42696ed533f1674ca3d46dbdd34.jpg", + "image_caption": [ + "(b) HINet[4] (0.923, 32.51)", + "(f) Restomer [57] (0.924, 32.52)", + "Figure 5. Qualitative results on the GoPro dataset." + ], + "image_footnote": [], + "bbox": [ + 295, + 435, + 500, + 522 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7ff8d5fb272ab2335c2ac91ee48eb739065eb10a48265455a60cb512adbca6fe.jpg", + "image_caption": [ + "(c) FFTformer[20] (0.934, 33.64)", + "(g) Ours (0.944, 35.24)" + ], + "image_footnote": [], + "bbox": [ + 500, + 435, + 700, + 522 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2dba3e94f4cd6e3c1e7b7a4fb063706655e1942345bea36237fa446e8896f1dc.jpg", + "image_caption": [ + "(d) AdaRevD[29] (0.935, 33.57)", + "(h) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 700, + 435, + 903, + 522 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "event datasets, we validate our approach on the REBlur dataset [43], which contains 1,469 group of blurred-sharp image pairs with the associated events captured by event cameras.", + "bbox": [ + 89, + 590, + 482, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We adopt two common metrics to quantitatively evaluate the performance of our method, including SSIM and PSNR, which are used to measure the similarity between the predicted results and the corresponding ground truth sharp images.", + "bbox": [ + 89, + 657, + 482, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison on Synthetic Datasets", + "text_level": 1, + "bbox": [ + 89, + 742, + 390, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results on GoPro datasets are presented in Table 1, while visual results are shown in Figures 1, 4 and 5. We compare the model trained in stage 1 with event-based methods, while comparing the final EGDeblurring with image-only methods, as it only inputs the blurred image during inference. As shown in Table 1, the performance of our method in Stage 1 is better than that of other event-based methods, showing that our RDNet enables effective event-based image deblurring. In quantitative re", + "bbox": [ + 89, + 763, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ee594927c093d6f15a74877557956bba22d874e74ca63a1277f0f7238575cee2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    Image-only methodSSIM↑PSNR↑
    SRN [45]0.96135.10
    FFTformer [20]0.96035.44
    Restormer [57]0.95935.50
    HINet [4]0.96535.58
    Stripformer [46]0.96035.66
    HI-Diff [5]0.96335.91
    Ours0.96936.21
    EDI [33]0.96436.52
    EFNet [43]0.97538.12
    REFID [44]0.97538.34
    Ours Stage 10.97738.51
    ", + "bbox": [ + 568, + 580, + 854, + 784 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison with state-of-the-art methods for deblurring task on real world dataset: REBlur.", + "bbox": [ + 511, + 794, + 906, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sults, EGDeblurring outperforms all image-only deblurring methods. Even though our method has a relatively modest improvement compared to high-performance methods such as AdaRevD [29], we have achieved performance at the", + "bbox": [ + 511, + 839, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2199", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3b5f33881dd9e19485f5d6a47346c33e38b2f0049369f04b05552e34a3a69266.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    methodSSIM↑PSNR↑
    w/ raw event0.92132.33
    w/o MPG-Diff0.92432.47
    w/o DACFB0.96733.91
    w/o the detail guidance0.96333.84
    Ours0.97334.62
    ", + "bbox": [ + 133, + 80, + 441, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "same level while the scale of our model is much smaller than theirs. This is attributed to the combination of the diffusion model and the regression network, which demonstrates advantages in distortion-based quantitative results. As shown in the visual results in Figure 4 and 5, under complex motion blur, other methods struggle to fully remove the blur due to the absence of motion information guidance. In contrast, our approach leveraging generated event guidance allows to recover high-quality sharp image. This indicates that utilizing the diffusion model to generate motion prior information can clearly enhance the overall deblurring performance and the robustness to deal with images with complex motion blur.", + "bbox": [ + 89, + 220, + 483, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparison on Real-world Dataset", + "text_level": 1, + "bbox": [ + 89, + 428, + 398, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative results are presented in Table 2, while visual results are shown in Figure 6. In the quantitative results, our models from Stage 1 and Stage 3 perform the best among event-based methods and image-only methods, respectively. Our method achieves superior quantitative results, with a $0.3\\mathrm{dB}$ improvement in PSNR compared to the second best method. The visual results in Figure 6 demonstrate that other methods leave residual blur along the edges of moving objects and exhibit noticeable ghosting artifacts, whereas our method restores sharp edge details. This validates the advantage of using the diffusion model to incorporate motion information into our approach.", + "bbox": [ + 89, + 450, + 483, + 632 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 643, + 243, + 660 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results of the ablation studies are presented in Table 3 and Figure 7, where we investigate the contribution of each our design to our method.", + "bbox": [ + 89, + 667, + 482, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of MPG-Diff. MPG-Diff is responsible for generating motion prior information. To validate the effectiveness of the diffusion model, we replace it with a convolutional neural network and train it using the same training strategy. Compared to the complete method, the framework without the MPG-Diff shows a decrease in PSNR by $1.64\\mathrm{dB}$ . This indicates that the motion information prior generated by the convolutional neural network is insufficient to provide adequate guidance for the deblurring task. In contrast, the introduction of the diffusion model enhances the robustness of the generated information, leading to improved overall performance of the method.", + "bbox": [ + 89, + 719, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7ba9bb8cbd33643aba5a7a6e98aa5feb4b586cd88647adcaef386e0f6922e309.jpg", + "table_caption": [ + "Table 3. Ablation studies on the GoPro dataset." + ], + "table_footnote": [], + "table_body": "
    Metric1 tensor2 tensors (ours)3 tensors4 tensors5 tensors
    SSIM↑0.9690.9730.9710.9730.972
    PSNR↑34.1034.6234.6134.6134.59
    ", + "bbox": [ + 517, + 80, + 903, + 128 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5a6891b2a3fe8c4a4a695b145bf03624e5234a7644f17fc246db40c4e7bfa254.jpg", + "table_caption": [ + "Table 4. Ablation study on different numbers of value tensors in DACFB." + ], + "table_footnote": [], + "table_body": "
    Metric1× dimension2× dimension4× dimensionOurs with two-value
    SSIM↑0.9690.9700.9710.973
    PSNR↑34.1034.1234.2334.62
    ", + "bbox": [ + 517, + 183, + 903, + 227 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Ablation study on feature dimensions of the vanilla cross-modal attention block.", + "bbox": [ + 511, + 234, + 903, + 263 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of motion prior feature generation. FE is designed to convert the raw event representation into the feature representation, which is the generation target of the diffusion model. Dense features represent motion information similar to event representations while ensuring that the diffusion model can generate corresponding prior features robustly. To validate that dense features is superior to directly generating event representation, we remove the FE and train the diffusion model to directly generate events (as shown in \"w/ raw event\" in Table 3 and 7). Both quantitative and qualitative results indicate a substantial decline in the framework's deblurring performance. This indicates that introducing dense feature representation is more beneficial to the generation of the diffusion model and the performance of the overall framework.", + "bbox": [ + 511, + 294, + 906, + 521 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of detail guidance. The detail guidance $P$ , along with the blurred image, constrain the generation process of the diffusion model. We remove the detail guidance and only use the blurred image to constrain the output of the diffusion model. The deblurring results are negatively impacted, showing a 0.78 dB decrease in PSNR compared to the complete method. This indicates that the detail guidance constrain the output of the diffusion model, leading to the generation of more effective guiding features for deblurring.", + "bbox": [ + 511, + 529, + 905, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of DACFB. The DACFB embedded in the RDNet fuses motion information features and image features through a cross-modal attention mechanism. We replace the DACFB in the RDNet with simple feature concatenation and convolutional layers, and train the model according to the original strategy. Quantitative results indicate a reduction in deblurring performance, with a decrease of $0.71\\mathrm{dB}$ in PSNR. This demonstrates that, compared to simple concatenation, the DACFB effectively aligns and fuses the two different modalities. We verify the effectiveness of our scheme by adjusting the number of value tensors in the attention mechanism. As shown in Table 4, two value tensors we employ in our DACFB design produces best results, while either decrease or increase in the number of the tensors will lead to performance drop. Note, we show in", + "bbox": [ + 511, + 672, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2200", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b62ae53788f7963cd721f2290e71df6da36931f01cca9d7fdbcea48681fa73b.jpg", + "image_caption": [ + "(a) Input (0.916, 28.55)" + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 295, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9a1ff05d389f1bd8b92b42eb627bc25300527f0be92cbf16a3a9f5113d2b3e0a.jpg", + "image_caption": [ + "(b) HINet[4] (0.913, 30.43)" + ], + "image_footnote": [], + "bbox": [ + 295, + 88, + 496, + 214 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1a2885416fd3419b1e90173b1cceef69e39c35d9376fe46fd361bcb1d0563d16.jpg", + "image_caption": [ + "(c) FFTformer[20] (0.946, 30.87)" + ], + "image_footnote": [], + "bbox": [ + 496, + 88, + 700, + 214 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/41b787467fcb78f24fe7db62a2505df6f0ff85c405f61b12808e0f0bdf6a9b1a.jpg", + "image_caption": [ + "(d) Stripformer[46] (0.925, 30.72)" + ], + "image_footnote": [], + "bbox": [ + 700, + 88, + 903, + 214 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e81c682a361b0471cda4cf0fa6cb6e9dc00842d78155e68e30d7f6e7738b15e.jpg", + "image_caption": [ + "(e) HI-Diff[5] (0.913, 30.43)" + ], + "image_footnote": [], + "bbox": [ + 91, + 236, + 295, + 362 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f7ed37ca2ff36775573efb1b923251f59ff53664486c2e118b7b6579b98fbdfa.jpg", + "image_caption": [ + "(f) Restormer [57] (0.926, 30.96)" + ], + "image_footnote": [], + "bbox": [ + 295, + 236, + 496, + 362 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4282189e412b52ca138bdc16c11b5f79b1a1df5253fc9e3264bac0c37190fceb.jpg", + "image_caption": [ + "(g) Ours (0.968, 34.78)" + ], + "image_footnote": [], + "bbox": [ + 500, + 236, + 700, + 362 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bd69deb70aec3d1b3ff99c02662be2ee378cc2bd7ba5f5ee83be28119a4c82ad.jpg", + "image_caption": [ + "(h) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 700, + 236, + 905, + 362 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5d01cc89544b9070d5f561e57c63fb4d0fff40fff864439b2a9ab5c4ac5f1c59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 417, + 207, + 521 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/40aaf00d72562eed230468cc17e6d337a73e48bc11ed2336a09c40dd76917213.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 94, + 521, + 209, + 656 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4cacee3d6281bd3c1c175219dc7753dace7ccb520564017d48e3a34c8e6cb4b1.jpg", + "image_caption": [ + "Figure 6. Qualitative results on the REBlur dataset." + ], + "image_footnote": [], + "bbox": [ + 209, + 417, + 325, + 521 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a7c6102f9851e358db2c527083e452812a9fccdd96b53a21fc0f42f754fbaa0a.jpg", + "image_caption": [ + "w/o MPG-Diff" + ], + "image_footnote": [], + "bbox": [ + 209, + 521, + 325, + 657 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/91a30c11b682378f7434101586d92a93dd736ef4eeed8e3dae992c10615c74c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 326, + 417, + 439, + 521 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/16d78d9f6c5d90a3524111afb82a5e15fb628d6cf73e5d7e9ef5005d229cdf66.jpg", + "image_caption": [ + "w/ raw event" + ], + "image_footnote": [], + "bbox": [ + 326, + 521, + 439, + 657 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/23ed82345f526220dbfbea8663111722a61e28f55261dbde40918eae990176f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 441, + 417, + 555, + 521 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7e725f8a0c55a804e26b600c71328bc7f07b913d280f34d1797d11ebbe71a130.jpg", + "image_caption": [ + "w/o DACFB" + ], + "image_footnote": [], + "bbox": [ + 441, + 521, + 553, + 657 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/de1b98241769500bf5398c73f68a64a49c0edfd26999d5d78cb94c727d8285b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 555, + 417, + 671, + 521 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ad29478e767472070784ac5a52ec5a8459c62e945eab9a4bb1ae732ef27776f5.jpg", + "image_caption": [ + "w/o detail guidance" + ], + "image_footnote": [], + "bbox": [ + 557, + 521, + 671, + 657 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a5d327100db076fa4fd1c405d58e7b8fd6337b54bfa7acee6b1763724c605a27.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 671, + 417, + 787, + 521 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/333c3711cecdae2d638892760620a35de0ff91536b5e5ff692507fc838483176.jpg", + "image_caption": [ + "Ours", + "Figure 7. Visual results of ablation experiments." + ], + "image_footnote": [], + "bbox": [ + 671, + 521, + 787, + 657 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e4548f0888871c3617b6a9c2ea8d2c96485609a40d76e6d3e90e6b57bc7fd46a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 417, + 903, + 521 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9aad458e09a16d4484fa7a29b1236d73ddda0592697df30015df0c698107f569.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 789, + 521, + 903, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the Table 5 that our two-value design cannot be replaced by simple feature dimension increase with single-value motion prior feature (see 2nd, 3rd, and 4th columns).", + "bbox": [ + 89, + 724, + 482, + 770 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 784, + 209, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented EGDeblurring, a method that allows to achieve high-quality image deblurring by generating event guidance carrying the desired motion prior information using a diffusion model. Specifically, we design a motion prior generation diffusion model to generate event guidance from a single blurry image, and a regression de", + "bbox": [ + 89, + 809, + 483, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "blurring network that can effectively utilize the motion prior information in the event guidance for image deblurring. Unlike existing event-based methods, our method can test with a single blurry image, without using ground truth event as input. Extensive experiments on both synthetic and real-world blur datasets demonstrate that our proposed method outperforms current state-of-the-art approaches.", + "bbox": [ + 511, + 724, + 906, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work was supported by the National Natural Science Foundation of China (62471499), the Guangdong Basic and Applied Basic Research Foundation (2023A1515030002).", + "bbox": [ + 511, + 839, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2201", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 89, + 187, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdullah Abuolaim and Michael S Brown. Defocus deblurring using dual-pixel data. In ECCV, 2020. 2", + "[2] Yuval Bahat, Netalee Efrat, and Michal Irani. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.145, + 0.131, + 0.853, + 0.154 + ], + "angle": 0, + "content": "Diffusion-based Event Generation for High-Quality Image Deblurring" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.18, + 0.888, + 0.253 + ], + "angle": 0, + "content": "Xinan Xie\\(^{1}\\) Qing Zhang\\(^{1,2*}\\) Wei-Shi Zheng\\(^{1,2}\\) \n\\(^{1}\\)School of Computer Science and Engineering, Sun Yat-sen University, China \n\\(^{2}\\)Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, China \nxiexn9@mail2.sysu.edu.cn zhangq93@mail.sysu.edu.cn wszheng@ieee.org" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.29, + 0.261, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.291, + 0.42, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.422, + 0.291, + 0.578, + 0.536 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.291, + 0.738, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.74, + 0.291, + 0.898, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.547, + 0.908, + 0.603 + ], + "angle": 0, + "content": "Figure 1. Comparison with previous methods on image blurring. As shown, by leveraging event guidance generated by a diffusion model, our method allows to produce high-quality deblurring results for images with complex motion blur, which are comparable to results of EFNet [43], a recent event-based deblurring method using GT event as input, and clearly better than results produced by HI-Diff [5]), a state-of-the-art image-only deblurring method." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.618, + 0.327, + 0.633 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.635, + 0.486, + 0.877 + ], + "angle": 0, + "content": "While event-based deblurring have demonstrated impressive results, they are impractical for consumer photos captured by cell phones and digital cameras that are not equipped with the event sensor. To address this problem, we in this paper propose a novel deblurring framework called Event Generation Deblurring (EGDeblurring), which allows to effectively deblur an image by generating event guidance describing the motion information using a diffusion model. Specifically, we design a motion prior generation diffusion model and a feature extractor to produce prior information beneficial for deblurring, rather than generating the raw event representation. In order to achieve effective fusion of motion prior information with blurry images and produce high-quality results, we develop a regression deblurring network embedded with a dual-attention channel fusion block. Experiments on multiple" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.619, + 0.908, + 0.665 + ], + "angle": 0, + "content": "datasets demonstrate that our method outperforms state-of-the-art image deblurring methods. Our code is available at https://github.com/XinanXie/EGDeblurring." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.694, + 0.646, + 0.71 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.719, + 0.907, + 0.856 + ], + "angle": 0, + "content": "Image deblurring is an important problem in computer vision, aiming to recover a sharp image from the original blurred input. Traditional methods primarily address the problem by formulating an optimization that incorporates various hand-crafted priors and assumptions [2, 3, 7, 11, 21, 24, 32, 39, 54]. In recent years, learning-based methods [4, 8, 31, 42, 45, 47, 56] have made significant progress. However, they are often less effective for images with complex motion blur, as shown in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.909, + 0.901 + ], + "angle": 0, + "content": "To enhance the robustness to complex blurry images, event-based deblurring methods [17, 27, 33, 40, 53, 60] have been developed, where the motion information cap" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.888, + 0.236, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2194" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.228 + ], + "angle": 0, + "content": "tured by event camera is utilized to achieve high-quality image deblurring. Although these methods demonstrate impressive results, they require events as additional inference input, which cannot be recorded by most consumer cameras, thereby having relatively limited practicability. Diffusion models [15] have recently gained widespread attention due to its powerful generation capability. This motivates us to explore the possibility of using diffusion models to generate event guidance for blurred images." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.229, + 0.487, + 0.575 + ], + "angle": 0, + "content": "In this paper, we present EGDeblurring, a method that allows high-quality image deblurring by utilizing motion information from event guidance generated by a diffusion model. EGDeblurring consists of a motion prior generation diffusion model (MPG-Diff) and a regression deblurring network (RDNet), where MPG-Diff is a diffusion model used for generating event recording the motion information of a blurry image, while RDNet aims to recover a sharp image from the blurry image and the associated events. Note, we design MPG-Diff to generate event-based motion prior features instead of raw events. The reason behind is that raw event usually appears in terms of sparse representation, while diffusion models excel at generating dense representation with rich details. To ensure that MPG-diff generates reliable event guidance, we instead choose to predict motion prior feature rather than raw event. To effectively utilize the motion information recorded by events, we embed dual-attention channel fusion block (DACFB) at multiple levels of the RDNet, which enables aligning and fusing motion information features with image features. To enable better performance, a multi-stage training strategy is further introduced. During inference, our method receives only blurry images as input as it can generate event guidance by itself." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.577, + 0.481, + 0.59 + ], + "angle": 0, + "content": "In summary, we make the following main contributions:" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.592, + 0.481, + 0.637 + ], + "angle": 0, + "content": "- We present a method that allows high-quality image deblurring by generating event guidance describing the motion information using a diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.643, + 0.481, + 0.703 + ], + "angle": 0, + "content": "- We develop a diffusion model for generating event guidance and a network to produce sharp image from a blurry image and its predicted event. Besides, we introduce an effective multi-stage training strategy." + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.71, + 0.481, + 0.8 + ], + "angle": 0, + "content": "- We compare our method with various state-of-the-art image deblurring methods on benchmark datasets. Results show that our method significantly outperforms existing image-only methods, and can produce comparable results to event-based methods with ground truth event as inference input." + }, + { + "type": "list", + "bbox": [ + 0.11, + 0.592, + 0.481, + 0.8 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.815, + 0.233, + 0.831 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.84, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Image-only methods. Early image deblurring methods typically work by estimating the blur kernel using various natural image priors and assumptions [2, 3, 11, 21, 22, 25, 54]. However, these methods are mostly less effective for im" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.304 + ], + "angle": 0, + "content": "ages with complex motion blur, as their leveraged priors and assumptions may not always hold in real-world scenarios. In the past decade, numerous deep learning based methods are developed for image deblurring [1, 4, 8, 16, 31, 38, 42, 45, 47, 56, 58] from different perspectives including multi-scale [31, 45], coarse-to-fine [8], and multistage [4]. More recently, transformer [20, 46, 57] and frequency analysis [10, 20] have been applied to image deblurring, which demonstrates promising results. However, due to lack of reliable modeling of the motion information, existing learning-based methods basically struggle to recover sharp images with clear and well-preserved details, especially when facing with blurry images incurred by complex object and camera motion." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.31, + 0.905, + 0.537 + ], + "angle": 0, + "content": "Event-based methods. As event carries the motion information beneficial to image deblurring, there are various event-based methods [6, 14, 17, 19, 27, 33, 34, 40, 53, 60, 61] in the literature. Pan et al. [33] proposed an event-based double integral (EDI) model that integrates blurred images and events for deblurring. Shang et al. [40] developed a event fusion module that can be incorporated into existing image and video deblurring networks. RED-Net [53] proposes to combine optical flow estimation and for self-supervised deblurring. EFNet [43] designs an event-image cross-modal attention module to fuse event and image features. Although event-based methods achieve superior deblurring performance by leveraging motion information, to our knowledge, all of them require ground truth event as addition inference input, which limits their practicability." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.543, + 0.907, + 0.771 + ], + "angle": 0, + "content": "Diffusion-based methods. Recently, diffusion models have demonstrated impressive performance in various low-level vision tasks including image/video deblurring [13, 26, 37, 51]. DvSR [51] presents a framework for stochastic blind image deblurring with a focus on perceptual quality using a conditional diffusion model. Ren et al. [36] proposed to improve the performance by leveraging multiscale structure guidance. DiffIR [52] achieves efficient diffusion-based image restoration. HI-Diff [5] applies diffusion model in a highly compacted latent space to generate the prior feature for the deblurring process. There is also attempt towards integrating event information into diffusion models. Diffevent [50] formulates event-based image deblurring as an image generation problem by designing diffusion priors for both the image and residuals." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.784, + 0.605, + 0.8 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.905, + 0.903 + ], + "angle": 0, + "content": "Figure 2 presents the overview of the proposed EGDeblurring. As shown, during inference, our method only receives single blurry image as input. The EGDeblurring encompasses two key modules: the RDNet and the MPGDiff. The RDNet embed the DACFB is designed to restore a blurred image into the corresponding sharp one, guided" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2195" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.103, + 0.437, + 0.112 + ], + "angle": 0, + "content": "Training Stage 1: Training of Regression Deblurring Network (RDNet)" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.121, + 0.452, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.103, + 0.807, + 0.112 + ], + "angle": 0, + "content": "Training Stage 3: Joint training of MPG-Diff and RDNet" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.114, + 0.884, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.139, + 0.249, + 0.465, + 0.259 + ], + "angle": 0, + "content": "Training Stage 2: Training of Motion Prior Generation Diffusion Model (MPG-Diff)" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.268, + 0.445, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.251, + 0.856, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.376, + 0.874, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.442, + 0.907, + 0.54 + ], + "angle": 0, + "content": "Figure 2. Overview of EGDeblurring. The EGDeblurring incorporates events during the training process, while it does not require event input during the inference stage, which is consistent with the image-only approach. The EGDeblurring are trained with a multi-stage training strategy. In Stage 1, the FE transforms the event representation \\( E \\) into the motion prior feature representation \\( M \\) which guides the RDNet to restore the sharp image \\( S \\) from the blurred image \\( B \\). In Stage 2, the MPG-Diff is trained to generate motion prior feature \\( M' \\) conditioned on the blurred image \\( B \\) and the detail guidance \\( P \\). In Stage 3, the MPG-Diff and the RDNet are jointly trained to achieve optimal deblurring performance. During inference, given a blurry image \\( B \\), the MPG-Diff generates the corresponding motion prior feature \\( M' \\), guiding the RDNet to output the final sharp result \\( S \\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.566, + 0.483, + 0.779 + ], + "angle": 0, + "content": "by motion prior features from events or the MPG-Diff. The MPG-Diff accepts the blurred image and the corresponding detail guidance as conditions, generating motion prior features. We adopt a multi-stage training strategy. In training stage 1 and training stage 2, the RDNet and MPG-Diff are trained respectively. Subsequently, in training stage 3, both are jointly trained to achieve coordination between the modules. During the inference process, given a blurred image, the MPG-Diff generates the corresponding motion prior features. The RDNet then utilizes these prior features to achieve high-quality image deblurring, eliminating the need for event assistance. Therefore, during inference, the EGDeblurring method is consistent with the image-only approach." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.788, + 0.373, + 0.804 + ], + "angle": 0, + "content": "3.1. Regression Deblurring Network" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "To avoid undesired artifacts and achieve better results, we design the RDNet to perform image deblurring. The RDNet consists of a motion prior encoder, an image encoder, and an image decoder. Meanwhile, in order to match the generation of the subsequent diffusion model, we employ a Feature Extractor (FE) composed of a deep neural" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.565, + 0.907, + 0.765 + ], + "angle": 0, + "content": "network to convert the event representation \\( E \\in \\mathbb{R}^{C_e \\times H \\times W} \\) into a feature representation \\( M \\in \\mathbb{R}^{C_m \\times H \\times W} \\). The motion prior encoder encodes \\( M \\) from the FE in training stage 1 (or \\( M' \\) from the MPG-Diff in training stage 3 and inference) into multi-scale motion prior features \\( F_{m}^{k} \\in \\mathbb{R}^{C' \\times H' \\times W'} \\), where \\( k = 0, 1, 2 \\) and \\( C' = 2^k C_b \\), \\( H' = H / 2^k \\), \\( W' = W / 2^k \\). \\( C_b \\) denotes the base number of channels. The blurred image \\( B \\in \\mathbb{R}^{3 \\times H \\times W} \\) is encoded by the image encoder into image features \\( F_{i}^{k} \\). \\( F_{i}^{k} \\) and \\( F_{m}^{k} \\) at the same scale are fused through the DACFB embedded in the image encoder. The image features are processed through the image decoder to produce the sharp image \\( S \\in \\mathbb{R}^{3 \\times H \\times W} \\), which serves as the final output of the framework." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.779, + 0.909, + 0.903 + ], + "angle": 0, + "content": "Details of DACFB. We propose a DACFB as the modal information regulator for the network. The utilization of a multi-branch structure enables the network to learn multiple sets of cross-modal values to modulate the image features. As shown in Figure 3, layer normalization and \\(1 \\times 1\\) convolutional layers process \\(F_{m}^{k}\\) and \\(F_{i}^{k}\\) to obtain \\(K \\in \\mathbb{R}^{H'W' \\times C'}\\) and \\(Q \\in \\mathbb{R}^{H'W' \\times C'}\\) respectively. The cross-channel attention map \\(A\\) is computed from \\(K\\) and \\(Q\\). To ensure suf" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2196" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.098, + 0.48, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.29, + 0.485, + 0.334 + ], + "angle": 0, + "content": "Figure 3. Network architecture of DACFB. The DACFB is embedded within the image encoder of the RDNet, aiming to fuse the motion feature \\( F_{m}^{k} \\) and the image feature \\( F_{i}^{k} \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.356, + 0.484, + 0.478 + ], + "angle": 0, + "content": "ficient modulation of features, we extract \\( V_{1} \\) and \\( V_{2} \\) from \\( F_{m}^{k} \\), where \\( V_{1}, V_{2} \\in \\mathbb{R}^{H'W' \\times C'} \\). The vectors \\( V_{1} \\) and \\( V_{2} \\) are respectively taken to compute the outer products with \\( A \\), resulting in \\( A_{1} \\) and \\( A_{2} \\). Then the outputs of the attention operation are separately multiplied and added to \\( F_{i}^{k} \\) to obtain the output feature \\( F_{out}' \\). \\( F_{out}' \\) is passed to the feed forward network and outputs the final result \\( F_{out} \\). It can be represented by the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.189, + 0.484, + 0.352, + 0.518 + ], + "angle": 0, + "content": "\\[\nA = \\operatorname {s o f t m a x} (\\frac {Q ^ {T} K}{\\sqrt {d}}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.52, + 0.29, + 0.536 + ], + "angle": 0, + "content": "\\[\nA _ {1} = V _ {1} \\times A,\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.535, + 0.482, + 0.555 + ], + "angle": 0, + "content": "\\[\nA _ {2} = V _ {2} \\times A, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.559, + 0.381, + 0.578 + ], + "angle": 0, + "content": "\\[\nF _ {o u t} ^ {\\prime} = L N \\left(F _ {i} ^ {k}\\right) \\cdot A _ {1} + A _ {2},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.579, + 0.384, + 0.597 + ], + "angle": 0, + "content": "\\[\nF _ {o u t} = F F N \\left(F _ {o u t} ^ {\\prime}\\right) + F _ {o u t} ^ {\\prime},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.604, + 0.483, + 0.636 + ], + "angle": 0, + "content": "where \\( LN(\\cdot) \\) represents layer normalization and \\( FFN(\\cdot) \\) represents the feed forward network." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.643, + 0.45, + 0.658 + ], + "angle": 0, + "content": "3.2. Motion Prior Generation Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.665, + 0.483, + 0.77 + ], + "angle": 0, + "content": "We employ the MPG-Diff to generate the motion prior feature \\( M' \\) as a substitute for the motion information features \\( M \\) from events. We employ a conditional denoising diffusion probabilistic model [9, 15] to guide the generation of the corresponding motion prior information. We perform the forward diffusion process and the reverse denoising process on the motion prior features \\( M \\) instead of the events \\( E \\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.771, + 0.484, + 0.877 + ], + "angle": 0, + "content": "In the forward diffusion process, \\( M \\) transformed from \\( E \\) by the FE is considered as the starting point of the forward Markov process (i.e., \\( M = M_0 \\)). The diffusion model learns a Markov chain by progressively corrupting the target feature \\( M_0 \\) with Gaussian noise at each time step \\( t \\), thereby transforming it into a Gaussian distribution (referred to as \\( \\mathcal{N} \\)). The forward diffusion process is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.884, + 0.483, + 0.904 + ], + "angle": 0, + "content": "\\[\nq \\left(M _ {t} \\mid M _ {t - 1}\\right) = \\mathcal {N} \\left(M _ {t}; \\sqrt {1 - \\beta_ {t}} M _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.906, + 0.153 + ], + "angle": 0, + "content": "where \\(M_{t}\\) is the feature at time step \\(t\\), \\(\\beta_{t}\\) is the predefined variance, and \\(\\mathbf{I}\\) represents the identity matrix for ensuring isotropic of the noise. After reparameterization [15], we obtain \\(M_{t}\\) from \\(M_0\\) in a single step by:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.165, + 0.907, + 0.183 + ], + "angle": 0, + "content": "\\[\nM _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} M _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.199, + 0.906, + 0.257 + ], + "angle": 0, + "content": "where \\(\\bar{\\alpha}_t = \\prod_{i=0}^t \\alpha_i\\) is the cumulative product of forward noise weight parameters \\(\\alpha_i = 1 - \\beta_i\\), while \\(\\epsilon \\sim \\mathcal{N}(0, I)\\) denotes random Gaussian noise." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.259, + 0.907, + 0.35 + ], + "angle": 0, + "content": "In the reverse denoising process, Gaussian noise is iteratively denoised into the motion prior feature \\( M' \\). We adopt the DDIM [41] sampling strategy. To synthesize the corresponding motion prior features, we utilize the blurred image \\( B \\) and detail guidance \\( P \\) as conditions. The reverse denoising process is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.362, + 0.903, + 0.397 + ], + "angle": 0, + "content": "\\[\nM _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} (\\frac {M _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\cdot \\mathbf {e} _ {t}}{\\sqrt {\\bar {\\alpha} _ {t}}}) + \\sqrt {1 - \\bar {\\alpha} _ {t - 1}} \\cdot \\mathbf {e} _ {t},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.399, + 0.905, + 0.429 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {t} = \\epsilon_ {\\theta} (M _ {t}, B, P, t), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.429, + 0.89, + 0.444 + ], + "angle": 0, + "content": "where \\(\\mathbf{e}_t\\) is the noise estimated by the neural network \\(\\epsilon_{\\theta}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.451, + 0.906, + 0.587 + ], + "angle": 0, + "content": "Detail guidance. To better constrain the diffusion model to output highly relevant information, we explore extracting details from the blurred image. We observed that when the image is downsampled, further detail information is lost. Thus, the difference between the downsampled image and the original image can serve as a guidance for the image details. We propose \\( P = B - \\mathcal{T}(B) \\) as the detail guidance, where \\( \\mathcal{T} \\) represents the operation of downsampling the image and then upsampling it back to its original size." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.598, + 0.783, + 0.615 + ], + "angle": 0, + "content": "3.3. Multi-Stage Training Strategy" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.622, + 0.906, + 0.652 + ], + "angle": 0, + "content": "We adopt a three-stage joint training strategy to achieve synchronization between the modules." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.659, + 0.907, + 0.809 + ], + "angle": 0, + "content": "Stage 1: training of RDNet. During the first stage of training, our goal is to introduce events and train a high-performance deblurring network. The training process at this stage is similar to that of event-based deblurring. We concatenate the FE and the RDNet in series and perform joint training. The event representation \\( E \\) is transformed into the feature representation \\( M \\) through the FE. Next, the RDNet accepts the \\( M \\) and the blurred image \\( B \\) and outputs the sharp image \\( S \\). The overall process of training stage 1 can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.823, + 0.905, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} M = F E (E), \\\\ S _ {m} = \\text {P D N t} (R, M) \\end{array} \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.842, + 0.783, + 0.858 + ], + "angle": 0, + "content": "\\[\nS = R D N e t (B, M).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "At this stage, we aim for the network to achieve optimal deblurring performance. We employ \\( L_{1} \\) loss to constrain the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2197" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.121 + ], + "angle": 0, + "content": "network output and jointly optimize the FE and the RDNet. The loss function is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.135, + 0.483, + 0.153 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s t a g e 1}} = \\left\\| S - G \\right\\| _ {1}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.165, + 0.435, + 0.18 + ], + "angle": 0, + "content": "where \\(G\\) represents the corresponding ground truth." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.186, + 0.485, + 0.307 + ], + "angle": 0, + "content": "Stage 2: Training of MPG-Diff. We train the MPG-Diff using the basic training strategy of diffusion models. Given the event \\( E \\), we first use the FE trained in the first stage to synthesize the \\( M \\). Subsequently, \\( M_{t} \\) is generated using Equation 3. In the reverse denoising process, the blurred image \\( B \\) and detail guidance \\( P \\) serve as conditions, and the denoising network predicts the noise \\( \\mathbf{e}_t \\). We train the denoising network \\( \\epsilon_{\\theta} \\) using the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.319, + 0.483, + 0.339 + ], + "angle": 0, + "content": "\\[\nL _ {s t a g e 2} = E _ {M _ {t}, t, B, P, \\epsilon \\sim \\mathcal {N} (0, I)} \\| \\mathbf {e} _ {t} - \\epsilon \\| _ {2} ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.35, + 0.454, + 0.365 + ], + "angle": 0, + "content": "Note that the parameters of FE are frozen in this stage." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.371, + 0.484, + 0.581 + ], + "angle": 0, + "content": "Stage 3: Joint training of MPG-Diff and RDNet. Since in training stage 2, we only trained the MPG-Diff without training the FE and the RDNet, the output \\( M' \\) from the MPG-Diff exhibits slight differences compared to the output \\( M \\) generated by the FE. As a result, directly using \\( M' \\) to guide the RDNet will not achieve optimal deblurring performance. To address this, we perform joint training of the MPG-Diff and the RDNet. Specifically, the MPG-Diff performs a complete iterative denoising process to obtain the predicted motion prior \\( M' \\). Then we input both \\( M' \\) and the blurred image \\( B \\) into the RDNet to generate the deblurred result \\( S \\). By constraining the final result, we jointly optimize the MPG-Diff and the RDNet. The loss function is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.596, + 0.483, + 0.613 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s t a g e 3}} = \\left\\| S - G \\right\\| _ {1} + \\lambda \\cdot \\left\\| M ^ {\\prime} - M \\right\\| _ {1}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.625, + 0.485, + 0.701 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the weight factor and \\(M\\) is the output of the FE. Since the denoising process is iterated multiple times, to reduce memory usage, we only record the gradients of the self-attention modules in the network \\(\\epsilon_{\\theta}\\) and update the weights of that specific part of the network." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.712, + 0.201, + 0.726 + ], + "angle": 0, + "content": "3.4. Inference" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.734, + 0.484, + 0.81 + ], + "angle": 0, + "content": "Given a blurred image \\( B \\), the MPG-Diff generates the corresponding motion prior features \\( M' \\). The RDNet takes \\( B \\) and \\( M' \\) as inputs and outputs the sharp image \\( S \\) as the final result. The overall process is represented by the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.822, + 0.483, + 0.846 + ], + "angle": 0, + "content": "\\[\nM ^ {\\prime} = D i f f (B), \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.842, + 0.363, + 0.858 + ], + "angle": 0, + "content": "\\[\nS = R D N e t (B, M ^ {\\prime}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "where \\(Diff(\\cdot)\\) represents the complete iterative denoising process of the MPG-Diff using the network \\(\\epsilon_{\\theta}\\)." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.082, + 0.905, + 0.485 + ], + "angle": 0, + "content": "
    Image-only methodSSIM↑PSNR↑Param.(M)
    DeepDeblur [31]0.91429.0811.7
    DeblurGAN-v2 [23]0.93429.5560.9
    SRN [45]0.93430.266.8
    DBGAN [59]0.94231.1011.6
    DMPHN [58]0.94031.2021.7
    Ren et al. [36]0.95432.1152.0
    MIMO-UNet+ [8]0.95732.4516.1
    HINet [4]0.95932.9188.7
    Restormer [57]0.96132.9226.1
    Stripformer [46]0.96233.0820.0
    HI-Diff [5]0.96433.3328.49
    MLWNet [12]0.96833.8395.1
    LoFormer [30]0.96934.0949.0
    MISC Filter [28]0.96934.1016.0
    FFTformer [20]0.96834.2116.6
    SegFFTformer [18]0.97034.38-
    AdaRevD [29]0.97234.60220.8
    Ours0.97334.6280.3
    D²Net [40]0.94031.6032.63
    eSL-Net [49]0.95433.520.19
    MADANET+ [55]0.96433.8416.9
    Vitoria et al. [48]0.94434.335.7
    EFNet [43]0.97235.468.47
    Ours Stage 10.97435.5020.7
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.494, + 0.907, + 0.577 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with state-of-the-art deblurring methods on synthetic GoPro dataset. Red background represents the best performance. Orange background represents the second best. yellow box represents the third best. Ours Stage 1 represents the framework trained in Stage 1 with events. The underline denotes event-based method." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.59, + 0.731, + 0.606 + ], + "angle": 0, + "content": "3.5. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.612, + 0.907, + 0.732 + ], + "angle": 0, + "content": "In the RDNet, we set \\( C_b = 64 \\) and concatenate two DACFB modules at each scale of the image encoder. In the MPG-Diff, we use 1000 diffusion steps and a nosie schedule \\( \\beta_t \\) linearly increasing from 1e-6 to 1e-2 for training, and 5 steps for inference. During training, we set the batch size to 4 and use the ADAM optimizer with an initial learning rate of \\( 1 \\times 10^{-4} \\). We implement the algorithm in PyTorch and run it on the NVIDIA RTX 4090 GPU." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.749, + 0.646, + 0.766 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.774, + 0.712, + 0.789 + ], + "angle": 0, + "content": "4.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.804, + 0.906, + 0.879 + ], + "angle": 0, + "content": "GoPro Dataset. We evaluate the effectiveness of the method on the GoPro dataset [31], which is widely used in both image-only and event-based deblurring research. We use ESIM [35] to construct synthetic event data and create an image-like representation from the events [43]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.886, + 0.907, + 0.901 + ], + "angle": 0, + "content": "REBlur Dataset. To reflect the performance on real-world" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2198" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.297, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.179, + 0.258, + 0.191 + ], + "angle": 0, + "content": "(a) Input (0.638, 21.31)" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.089, + 0.5, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.179, + 0.471, + 0.191 + ], + "angle": 0, + "content": "(b) HINet[4] (0.730, 23.74)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.089, + 0.702, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.179, + 0.69, + 0.191 + ], + "angle": 0, + "content": "(c) FFTformer[20] (0.882, 29.37)" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.089, + 0.905, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.179, + 0.889, + 0.191 + ], + "angle": 0, + "content": "(d) AdaRevD[29] (0.842, 27.53)" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.192, + 0.296, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.281, + 0.271, + 0.293 + ], + "angle": 0, + "content": "(e) HI-Diff[5] (0.836, 27.02)" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.192, + 0.5, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.311, + 0.281, + 0.486, + 0.293 + ], + "angle": 0, + "content": "(f) Restomer [57] (0.793, 25.39)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.192, + 0.702, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.281, + 0.662, + 0.293 + ], + "angle": 0, + "content": "(g) Ours (0.889, 30.91)" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.192, + 0.905, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.281, + 0.849, + 0.292 + ], + "angle": 0, + "content": "(h) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.194, + 0.305, + 0.802, + 0.32 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on the GoPro dataset. The values in parentheses represent (SSIM, PSNR)." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.334, + 0.296, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.424, + 0.257, + 0.435 + ], + "angle": 0, + "content": "(a) Input (0.833, 25.90)" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.334, + 0.5, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.424, + 0.471, + 0.436 + ], + "angle": 0, + "content": "(b) HINet[4] (0.923, 32.51)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.334, + 0.702, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.424, + 0.69, + 0.436 + ], + "angle": 0, + "content": "(c) FFTformer[20] (0.934, 33.64)" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.334, + 0.905, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.424, + 0.889, + 0.436 + ], + "angle": 0, + "content": "(d) AdaRevD[29] (0.935, 33.57)" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.436, + 0.296, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.526, + 0.271, + 0.538 + ], + "angle": 0, + "content": "(e) HI-Diff[5] (0.929, 32.91)" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.436, + 0.5, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.31, + 0.526, + 0.486, + 0.538 + ], + "angle": 0, + "content": "(f) Restomer [57] (0.924, 32.52)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.436, + 0.702, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.526, + 0.662, + 0.538 + ], + "angle": 0, + "content": "(g) Ours (0.944, 35.24)" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.436, + 0.905, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.526, + 0.849, + 0.537 + ], + "angle": 0, + "content": "(h) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.348, + 0.55, + 0.647, + 0.564 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on the GoPro dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.592, + 0.483, + 0.651 + ], + "angle": 0, + "content": "event datasets, we validate our approach on the REBlur dataset [43], which contains 1,469 group of blurred-sharp image pairs with the associated events captured by event cameras." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.658, + 0.483, + 0.734 + ], + "angle": 0, + "content": "Metrics. We adopt two common metrics to quantitatively evaluate the performance of our method, including SSIM and PSNR, which are used to measure the similarity between the predicted results and the corresponding ground truth sharp images." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.743, + 0.391, + 0.759 + ], + "angle": 0, + "content": "4.2. Comparison on Synthetic Datasets" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Quantitative results on GoPro datasets are presented in Table 1, while visual results are shown in Figures 1, 4 and 5. We compare the model trained in stage 1 with event-based methods, while comparing the final EGDeblurring with image-only methods, as it only inputs the blurred image during inference. As shown in Table 1, the performance of our method in Stage 1 is better than that of other event-based methods, showing that our RDNet enables effective event-based image deblurring. In quantitative re" + }, + { + "type": "table", + "bbox": [ + 0.569, + 0.581, + 0.855, + 0.785 + ], + "angle": 0, + "content": "
    Image-only methodSSIM↑PSNR↑
    SRN [45]0.96135.10
    FFTformer [20]0.96035.44
    Restormer [57]0.95935.50
    HINet [4]0.96535.58
    Stripformer [46]0.96035.66
    HI-Diff [5]0.96335.91
    Ours0.96936.21
    EDI [33]0.96436.52
    EFNet [43]0.97538.12
    REFID [44]0.97538.34
    Ours Stage 10.97738.51
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.795, + 0.907, + 0.823 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison with state-of-the-art methods for deblurring task on real world dataset: REBlur." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.901 + ], + "angle": 0, + "content": "sults, EGDeblurring outperforms all image-only deblurring methods. Even though our method has a relatively modest improvement compared to high-performance methods such as AdaRevD [29], we have achieved performance at the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2199" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.134, + 0.081, + 0.442, + 0.183 + ], + "angle": 0, + "content": "
    methodSSIM↑PSNR↑
    w/ raw event0.92132.33
    w/o MPG-Diff0.92432.47
    w/o DACFB0.96733.91
    w/o the detail guidance0.96333.84
    Ours0.97334.62
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.146, + 0.194, + 0.427, + 0.207 + ], + "angle": 0, + "content": "Table 3. Ablation studies on the GoPro dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.221, + 0.484, + 0.417 + ], + "angle": 0, + "content": "same level while the scale of our model is much smaller than theirs. This is attributed to the combination of the diffusion model and the regression network, which demonstrates advantages in distortion-based quantitative results. As shown in the visual results in Figure 4 and 5, under complex motion blur, other methods struggle to fully remove the blur due to the absence of motion information guidance. In contrast, our approach leveraging generated event guidance allows to recover high-quality sharp image. This indicates that utilizing the diffusion model to generate motion prior information can clearly enhance the overall deblurring performance and the robustness to deal with images with complex motion blur." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.429, + 0.399, + 0.445 + ], + "angle": 0, + "content": "4.3. Comparison on Real-world Dataset" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.452, + 0.484, + 0.633 + ], + "angle": 0, + "content": "Quantitative results are presented in Table 2, while visual results are shown in Figure 6. In the quantitative results, our models from Stage 1 and Stage 3 perform the best among event-based methods and image-only methods, respectively. Our method achieves superior quantitative results, with a \\(0.3\\mathrm{dB}\\) improvement in PSNR compared to the second best method. The visual results in Figure 6 demonstrate that other methods leave residual blur along the edges of moving objects and exhibit noticeable ghosting artifacts, whereas our method restores sharp edge details. This validates the advantage of using the diffusion model to incorporate motion information into our approach." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.645, + 0.245, + 0.661 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.668, + 0.483, + 0.713 + ], + "angle": 0, + "content": "The results of the ablation studies are presented in Table 3 and Figure 7, where we investigate the contribution of each our design to our method." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Effect of MPG-Diff. MPG-Diff is responsible for generating motion prior information. To validate the effectiveness of the diffusion model, we replace it with a convolutional neural network and train it using the same training strategy. Compared to the complete method, the framework without the MPG-Diff shows a decrease in PSNR by \\(1.64\\mathrm{dB}\\). This indicates that the motion information prior generated by the convolutional neural network is insufficient to provide adequate guidance for the deblurring task. In contrast, the introduction of the diffusion model enhances the robustness of the generated information, leading to improved overall performance of the method." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.081, + 0.905, + 0.13 + ], + "angle": 0, + "content": "
    Metric1 tensor2 tensors (ours)3 tensors4 tensors5 tensors
    SSIM↑0.9690.9730.9710.9730.972
    PSNR↑34.1034.6234.6134.6134.59
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.138, + 0.905, + 0.165 + ], + "angle": 0, + "content": "Table 4. Ablation study on different numbers of value tensors in DACFB." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.184, + 0.905, + 0.228 + ], + "angle": 0, + "content": "
    Metric1× dimension2× dimension4× dimensionOurs with two-value
    SSIM↑0.9690.9700.9710.973
    PSNR↑34.1034.1234.2334.62
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.236, + 0.905, + 0.264 + ], + "angle": 0, + "content": "Table 5. Ablation study on feature dimensions of the vanilla cross-modal attention block." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.295, + 0.907, + 0.522 + ], + "angle": 0, + "content": "Effect of motion prior feature generation. FE is designed to convert the raw event representation into the feature representation, which is the generation target of the diffusion model. Dense features represent motion information similar to event representations while ensuring that the diffusion model can generate corresponding prior features robustly. To validate that dense features is superior to directly generating event representation, we remove the FE and train the diffusion model to directly generate events (as shown in \"w/ raw event\" in Table 3 and 7). Both quantitative and qualitative results indicate a substantial decline in the framework's deblurring performance. This indicates that introducing dense feature representation is more beneficial to the generation of the diffusion model and the performance of the overall framework." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.53, + 0.906, + 0.667 + ], + "angle": 0, + "content": "Effect of detail guidance. The detail guidance \\( P \\), along with the blurred image, constrain the generation process of the diffusion model. We remove the detail guidance and only use the blurred image to constrain the output of the diffusion model. The deblurring results are negatively impacted, showing a 0.78 dB decrease in PSNR compared to the complete method. This indicates that the detail guidance constrain the output of the diffusion model, leading to the generation of more effective guiding features for deblurring." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Effect of DACFB. The DACFB embedded in the RDNet fuses motion information features and image features through a cross-modal attention mechanism. We replace the DACFB in the RDNet with simple feature concatenation and convolutional layers, and train the model according to the original strategy. Quantitative results indicate a reduction in deblurring performance, with a decrease of \\(0.71\\mathrm{dB}\\) in PSNR. This demonstrates that, compared to simple concatenation, the DACFB effectively aligns and fuses the two different modalities. We verify the effectiveness of our scheme by adjusting the number of value tensors in the attention mechanism. As shown in Table 4, two value tensors we employ in our DACFB design produces best results, while either decrease or increase in the number of the tensors will lead to performance drop. Note, we show in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2200" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.296, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.132, + 0.218, + 0.258, + 0.23 + ], + "angle": 0, + "content": "(a) Input (0.916, 28.55)" + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.089, + 0.498, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.218, + 0.47, + 0.23 + ], + "angle": 0, + "content": "(b) HINet[4] (0.913, 30.43)" + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.089, + 0.701, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.218, + 0.688, + 0.23 + ], + "angle": 0, + "content": "(c) FFTformer[20] (0.946, 30.87)" + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.089, + 0.905, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.218, + 0.892, + 0.23 + ], + "angle": 0, + "content": "(d) Stripformer[46] (0.925, 30.72)" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.237, + 0.296, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.365, + 0.271, + 0.378 + ], + "angle": 0, + "content": "(e) HI-Diff[5] (0.913, 30.43)" + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.237, + 0.498, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.31, + 0.365, + 0.486, + 0.378 + ], + "angle": 0, + "content": "(f) Restormer [57] (0.926, 30.96)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.237, + 0.702, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.365, + 0.662, + 0.378 + ], + "angle": 0, + "content": "(g) Ours (0.968, 34.78)" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.237, + 0.906, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.365, + 0.849, + 0.377 + ], + "angle": 0, + "content": "(h) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.39, + 0.651, + 0.404 + ], + "angle": 0, + "content": "Figure 6. Qualitative results on the REBlur dataset." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.418, + 0.209, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.522, + 0.21, + 0.657 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.137, + 0.659, + 0.168, + 0.671 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.418, + 0.326, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.522, + 0.326, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.66, + 0.308, + 0.671 + ], + "angle": 0, + "content": "w/o MPG-Diff" + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.418, + 0.441, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.522, + 0.441, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.349, + 0.66, + 0.419, + 0.671 + ], + "angle": 0, + "content": "w/ raw event" + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.418, + 0.556, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.522, + 0.555, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.66, + 0.533, + 0.671 + ], + "angle": 0, + "content": "w/o DACFB" + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.418, + 0.672, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.522, + 0.672, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.563, + 0.66, + 0.667, + 0.672 + ], + "angle": 0, + "content": "w/o detail guidance" + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.418, + 0.788, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.673, + 0.522, + 0.788, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.717, + 0.66, + 0.744, + 0.671 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.418, + 0.904, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.522, + 0.904, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.809, + 0.66, + 0.884, + 0.671 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.684, + 0.642, + 0.699 + ], + "angle": 0, + "content": "Figure 7. Visual results of ablation experiments." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.725, + 0.483, + 0.771 + ], + "angle": 0, + "content": "the Table 5 that our two-value design cannot be replaced by simple feature dimension increase with single-value motion prior feature (see 2nd, 3rd, and 4th columns)." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.785, + 0.21, + 0.801 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.484, + 0.902 + ], + "angle": 0, + "content": "We have presented EGDeblurring, a method that allows to achieve high-quality image deblurring by generating event guidance carrying the desired motion prior information using a diffusion model. Specifically, we design a motion prior generation diffusion model to generate event guidance from a single blurry image, and a regression de" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.725, + 0.907, + 0.832 + ], + "angle": 0, + "content": "blurring network that can effectively utilize the motion prior information in the event guidance for image deblurring. Unlike existing event-based methods, our method can test with a single blurry image, without using ground truth event as input. Extensive experiments on both synthetic and real-world blur datasets demonstrate that our proposed method outperforms current state-of-the-art approaches." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Acknowledgment. This work was supported by the National Natural Science Foundation of China (62471499), the Guangdong Basic and Applied Basic Research Foundation (2023A1515030002)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2201" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.093, + 0.09, + 0.188, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.101, + 0.116, + 0.482, + 0.143 + ], + "angle": 0, + "content": "[1] Abdullah Abuolaim and Michael S Brown. Defocus deblurring using dual-pixel data. In ECCV, 2020. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.102, + 0.145, + 0.483, + 0.171 + ], + "angle": 0, + "content": "[2] Yuval Bahat, Netalee Efrat, and Michal Irani. Non-uniform blind deblurring by reblurring. 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Comparison with previous methods on image blurring. As shown, by leveraging event guidance generated by a diffusion model, our method allows to produce high-quality deblurring results for images with complex motion blur, which are comparable to results of EFNet [43], a recent event-based deblurring method using GT event as input, and clearly better than results produced by HI-Diff [5]), a state-of-the-art image-only deblurring method. + +![](images/eb963d74a5a4adb25f3b12d485c6faf004e10d3989287272691a19ba61c67b4c.jpg) + +![](images/1942ee8584818511cdfe87670c8f410a26355430848f030bdbd48a99c4404f1c.jpg) + +![](images/65e409a4e44abf250d64043e7e41960ac7e6bbca5375e6d888ae78d3bd25e503.jpg) + +![](images/537b3c5a1c750b7a298854c16b9261b41a965a5a7f18277bc758ce1e21d8f568.jpg) + +# Abstract + +While event-based deblurring have demonstrated impressive results, they are impractical for consumer photos captured by cell phones and digital cameras that are not equipped with the event sensor. To address this problem, we in this paper propose a novel deblurring framework called Event Generation Deblurring (EGDeblurring), which allows to effectively deblur an image by generating event guidance describing the motion information using a diffusion model. Specifically, we design a motion prior generation diffusion model and a feature extractor to produce prior information beneficial for deblurring, rather than generating the raw event representation. In order to achieve effective fusion of motion prior information with blurry images and produce high-quality results, we develop a regression deblurring network embedded with a dual-attention channel fusion block. Experiments on multiple + +datasets demonstrate that our method outperforms state-of-the-art image deblurring methods. Our code is available at https://github.com/XinanXie/EGDeblurring. + +# 1. Introduction + +Image deblurring is an important problem in computer vision, aiming to recover a sharp image from the original blurred input. Traditional methods primarily address the problem by formulating an optimization that incorporates various hand-crafted priors and assumptions [2, 3, 7, 11, 21, 24, 32, 39, 54]. In recent years, learning-based methods [4, 8, 31, 42, 45, 47, 56] have made significant progress. However, they are often less effective for images with complex motion blur, as shown in Figure 1. + +To enhance the robustness to complex blurry images, event-based deblurring methods [17, 27, 33, 40, 53, 60] have been developed, where the motion information cap + +tured by event camera is utilized to achieve high-quality image deblurring. Although these methods demonstrate impressive results, they require events as additional inference input, which cannot be recorded by most consumer cameras, thereby having relatively limited practicability. Diffusion models [15] have recently gained widespread attention due to its powerful generation capability. This motivates us to explore the possibility of using diffusion models to generate event guidance for blurred images. + +In this paper, we present EGDeblurring, a method that allows high-quality image deblurring by utilizing motion information from event guidance generated by a diffusion model. EGDeblurring consists of a motion prior generation diffusion model (MPG-Diff) and a regression deblurring network (RDNet), where MPG-Diff is a diffusion model used for generating event recording the motion information of a blurry image, while RDNet aims to recover a sharp image from the blurry image and the associated events. Note, we design MPG-Diff to generate event-based motion prior features instead of raw events. The reason behind is that raw event usually appears in terms of sparse representation, while diffusion models excel at generating dense representation with rich details. To ensure that MPG-diff generates reliable event guidance, we instead choose to predict motion prior feature rather than raw event. To effectively utilize the motion information recorded by events, we embed dual-attention channel fusion block (DACFB) at multiple levels of the RDNet, which enables aligning and fusing motion information features with image features. To enable better performance, a multi-stage training strategy is further introduced. During inference, our method receives only blurry images as input as it can generate event guidance by itself. + +In summary, we make the following main contributions: + +- We present a method that allows high-quality image deblurring by generating event guidance describing the motion information using a diffusion model. +- We develop a diffusion model for generating event guidance and a network to produce sharp image from a blurry image and its predicted event. Besides, we introduce an effective multi-stage training strategy. +- We compare our method with various state-of-the-art image deblurring methods on benchmark datasets. Results show that our method significantly outperforms existing image-only methods, and can produce comparable results to event-based methods with ground truth event as inference input. + +# 2. Related Work + +Image-only methods. Early image deblurring methods typically work by estimating the blur kernel using various natural image priors and assumptions [2, 3, 11, 21, 22, 25, 54]. However, these methods are mostly less effective for im + +ages with complex motion blur, as their leveraged priors and assumptions may not always hold in real-world scenarios. In the past decade, numerous deep learning based methods are developed for image deblurring [1, 4, 8, 16, 31, 38, 42, 45, 47, 56, 58] from different perspectives including multi-scale [31, 45], coarse-to-fine [8], and multistage [4]. More recently, transformer [20, 46, 57] and frequency analysis [10, 20] have been applied to image deblurring, which demonstrates promising results. However, due to lack of reliable modeling of the motion information, existing learning-based methods basically struggle to recover sharp images with clear and well-preserved details, especially when facing with blurry images incurred by complex object and camera motion. + +Event-based methods. As event carries the motion information beneficial to image deblurring, there are various event-based methods [6, 14, 17, 19, 27, 33, 34, 40, 53, 60, 61] in the literature. Pan et al. [33] proposed an event-based double integral (EDI) model that integrates blurred images and events for deblurring. Shang et al. [40] developed a event fusion module that can be incorporated into existing image and video deblurring networks. RED-Net [53] proposes to combine optical flow estimation and for self-supervised deblurring. EFNet [43] designs an event-image cross-modal attention module to fuse event and image features. Although event-based methods achieve superior deblurring performance by leveraging motion information, to our knowledge, all of them require ground truth event as addition inference input, which limits their practicability. + +Diffusion-based methods. Recently, diffusion models have demonstrated impressive performance in various low-level vision tasks including image/video deblurring [13, 26, 37, 51]. DvSR [51] presents a framework for stochastic blind image deblurring with a focus on perceptual quality using a conditional diffusion model. Ren et al. [36] proposed to improve the performance by leveraging multiscale structure guidance. DiffIR [52] achieves efficient diffusion-based image restoration. HI-Diff [5] applies diffusion model in a highly compacted latent space to generate the prior feature for the deblurring process. There is also attempt towards integrating event information into diffusion models. Diffevent [50] formulates event-based image deblurring as an image generation problem by designing diffusion priors for both the image and residuals. + +# 3. Method + +Figure 2 presents the overview of the proposed EGDeblurring. As shown, during inference, our method only receives single blurry image as input. The EGDeblurring encompasses two key modules: the RDNet and the MPGDiff. The RDNet embed the DACFB is designed to restore a blurred image into the corresponding sharp one, guided + +![](images/2de3b3dce4bdee3ee5dbfad43aeff8efcd494b652bbacc94092e6118c50456ae.jpg) +Training Stage 1: Training of Regression Deblurring Network (RDNet) + +![](images/cc4d0ccfe95bf26776633bf8900ccfab2b92424de1f56630b7139009745bfc75.jpg) +Training Stage 3: Joint training of MPG-Diff and RDNet + +![](images/6434c2f235a0246a466fb5b733260cb99156309a016e5830ec8a74c35e946bec.jpg) +Training Stage 2: Training of Motion Prior Generation Diffusion Model (MPG-Diff) + +![](images/88d66eb711bf254bf25104f89555667c9fbe0d54988cb732b1f32579ca8eb28c.jpg) + +![](images/c824de5fc430ac840bfbd672141239998cf2e98d545982dbb24d9f14c1356683.jpg) +Figure 2. Overview of EGDeblurring. The EGDeblurring incorporates events during the training process, while it does not require event input during the inference stage, which is consistent with the image-only approach. The EGDeblurring are trained with a multi-stage training strategy. In Stage 1, the FE transforms the event representation $E$ into the motion prior feature representation $M$ which guides the RDNet to restore the sharp image $S$ from the blurred image $B$ . In Stage 2, the MPG-Diff is trained to generate motion prior feature $M'$ conditioned on the blurred image $B$ and the detail guidance $P$ . In Stage 3, the MPG-Diff and the RDNet are jointly trained to achieve optimal deblurring performance. During inference, given a blurry image $B$ , the MPG-Diff generates the corresponding motion prior feature $M'$ , guiding the RDNet to output the final sharp result $S$ . + +by motion prior features from events or the MPG-Diff. The MPG-Diff accepts the blurred image and the corresponding detail guidance as conditions, generating motion prior features. We adopt a multi-stage training strategy. In training stage 1 and training stage 2, the RDNet and MPG-Diff are trained respectively. Subsequently, in training stage 3, both are jointly trained to achieve coordination between the modules. During the inference process, given a blurred image, the MPG-Diff generates the corresponding motion prior features. The RDNet then utilizes these prior features to achieve high-quality image deblurring, eliminating the need for event assistance. Therefore, during inference, the EGDeblurring method is consistent with the image-only approach. + +# 3.1. Regression Deblurring Network + +To avoid undesired artifacts and achieve better results, we design the RDNet to perform image deblurring. The RDNet consists of a motion prior encoder, an image encoder, and an image decoder. Meanwhile, in order to match the generation of the subsequent diffusion model, we employ a Feature Extractor (FE) composed of a deep neural + +network to convert the event representation $E \in \mathbb{R}^{C_e \times H \times W}$ into a feature representation $M \in \mathbb{R}^{C_m \times H \times W}$ . The motion prior encoder encodes $M$ from the FE in training stage 1 (or $M'$ from the MPG-Diff in training stage 3 and inference) into multi-scale motion prior features $F_{m}^{k} \in \mathbb{R}^{C' \times H' \times W'}$ , where $k = 0, 1, 2$ and $C' = 2^k C_b$ , $H' = H / 2^k$ , $W' = W / 2^k$ . $C_b$ denotes the base number of channels. The blurred image $B \in \mathbb{R}^{3 \times H \times W}$ is encoded by the image encoder into image features $F_{i}^{k}$ . $F_{i}^{k}$ and $F_{m}^{k}$ at the same scale are fused through the DACFB embedded in the image encoder. The image features are processed through the image decoder to produce the sharp image $S \in \mathbb{R}^{3 \times H \times W}$ , which serves as the final output of the framework. + +Details of DACFB. We propose a DACFB as the modal information regulator for the network. The utilization of a multi-branch structure enables the network to learn multiple sets of cross-modal values to modulate the image features. As shown in Figure 3, layer normalization and $1 \times 1$ convolutional layers process $F_{m}^{k}$ and $F_{i}^{k}$ to obtain $K \in \mathbb{R}^{H'W' \times C'}$ and $Q \in \mathbb{R}^{H'W' \times C'}$ respectively. The cross-channel attention map $A$ is computed from $K$ and $Q$ . To ensure suf + +![](images/2ba9a61daabea251924c3d135aa8069f20c3a4c4fc7516bc0d596c398d82f8b7.jpg) +Figure 3. Network architecture of DACFB. The DACFB is embedded within the image encoder of the RDNet, aiming to fuse the motion feature $F_{m}^{k}$ and the image feature $F_{i}^{k}$ . + +ficient modulation of features, we extract $V_{1}$ and $V_{2}$ from $F_{m}^{k}$ , where $V_{1}, V_{2} \in \mathbb{R}^{H'W' \times C'}$ . The vectors $V_{1}$ and $V_{2}$ are respectively taken to compute the outer products with $A$ , resulting in $A_{1}$ and $A_{2}$ . Then the outputs of the attention operation are separately multiplied and added to $F_{i}^{k}$ to obtain the output feature $F_{out}'$ . $F_{out}'$ is passed to the feed forward network and outputs the final result $F_{out}$ . It can be represented by the following formula: + +$$ +A = \operatorname {s o f t m a x} (\frac {Q ^ {T} K}{\sqrt {d}}), +$$ + +$$ +A _ {1} = V _ {1} \times A, +$$ + +$$ +A _ {2} = V _ {2} \times A, \tag {1} +$$ + +$$ +F _ {o u t} ^ {\prime} = L N \left(F _ {i} ^ {k}\right) \cdot A _ {1} + A _ {2}, +$$ + +$$ +F _ {o u t} = F F N \left(F _ {o u t} ^ {\prime}\right) + F _ {o u t} ^ {\prime}, +$$ + +where $LN(\cdot)$ represents layer normalization and $FFN(\cdot)$ represents the feed forward network. + +# 3.2. Motion Prior Generation Diffusion Model + +We employ the MPG-Diff to generate the motion prior feature $M'$ as a substitute for the motion information features $M$ from events. We employ a conditional denoising diffusion probabilistic model [9, 15] to guide the generation of the corresponding motion prior information. We perform the forward diffusion process and the reverse denoising process on the motion prior features $M$ instead of the events $E$ . + +In the forward diffusion process, $M$ transformed from $E$ by the FE is considered as the starting point of the forward Markov process (i.e., $M = M_0$ ). The diffusion model learns a Markov chain by progressively corrupting the target feature $M_0$ with Gaussian noise at each time step $t$ , thereby transforming it into a Gaussian distribution (referred to as $\mathcal{N}$ ). The forward diffusion process is formulated as: + +$$ +q \left(M _ {t} \mid M _ {t - 1}\right) = \mathcal {N} \left(M _ {t}; \sqrt {1 - \beta_ {t}} M _ {t - 1}, \beta_ {t} \mathbf {I}\right), \tag {2} +$$ + +where $M_{t}$ is the feature at time step $t$ , $\beta_{t}$ is the predefined variance, and $\mathbf{I}$ represents the identity matrix for ensuring isotropic of the noise. After reparameterization [15], we obtain $M_{t}$ from $M_0$ in a single step by: + +$$ +M _ {t} = \sqrt {\bar {\alpha} _ {t}} M _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \tag {3} +$$ + +where $\bar{\alpha}_t = \prod_{i=0}^t \alpha_i$ is the cumulative product of forward noise weight parameters $\alpha_i = 1 - \beta_i$ , while $\epsilon \sim \mathcal{N}(0, I)$ denotes random Gaussian noise. + +In the reverse denoising process, Gaussian noise is iteratively denoised into the motion prior feature $M'$ . We adopt the DDIM [41] sampling strategy. To synthesize the corresponding motion prior features, we utilize the blurred image $B$ and detail guidance $P$ as conditions. The reverse denoising process is defined as follows: + +$$ +M _ {t - 1} = \sqrt {\bar {\alpha} _ {t - 1}} (\frac {M _ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \cdot \mathbf {e} _ {t}}{\sqrt {\bar {\alpha} _ {t}}}) + \sqrt {1 - \bar {\alpha} _ {t - 1}} \cdot \mathbf {e} _ {t}, +$$ + +$$ +\mathbf {e} _ {t} = \epsilon_ {\theta} (M _ {t}, B, P, t), \tag {4} +$$ + +where $\mathbf{e}_t$ is the noise estimated by the neural network $\epsilon_{\theta}$ . + +Detail guidance. To better constrain the diffusion model to output highly relevant information, we explore extracting details from the blurred image. We observed that when the image is downsampled, further detail information is lost. Thus, the difference between the downsampled image and the original image can serve as a guidance for the image details. We propose $P = B - \mathcal{T}(B)$ as the detail guidance, where $\mathcal{T}$ represents the operation of downsampling the image and then upsampling it back to its original size. + +# 3.3. Multi-Stage Training Strategy + +We adopt a three-stage joint training strategy to achieve synchronization between the modules. + +Stage 1: training of RDNet. During the first stage of training, our goal is to introduce events and train a high-performance deblurring network. The training process at this stage is similar to that of event-based deblurring. We concatenate the FE and the RDNet in series and perform joint training. The event representation $E$ is transformed into the feature representation $M$ through the FE. Next, the RDNet accepts the $M$ and the blurred image $B$ and outputs the sharp image $S$ . The overall process of training stage 1 can be expressed as follows: + +$$ +\begin{array}{l} M = F E (E), \\ S _ {m} = \text {P D N t} (R, M) \end{array} \tag {5} +$$ + +$$ +S = R D N e t (B, M). +$$ + +At this stage, we aim for the network to achieve optimal deblurring performance. We employ $L_{1}$ loss to constrain the + +network output and jointly optimize the FE and the RDNet. The loss function is defined as follows: + +$$ +L _ {\text {s t a g e 1}} = \left\| S - G \right\| _ {1}, \tag {6} +$$ + +where $G$ represents the corresponding ground truth. + +Stage 2: Training of MPG-Diff. We train the MPG-Diff using the basic training strategy of diffusion models. Given the event $E$ , we first use the FE trained in the first stage to synthesize the $M$ . Subsequently, $M_{t}$ is generated using Equation 3. In the reverse denoising process, the blurred image $B$ and detail guidance $P$ serve as conditions, and the denoising network predicts the noise $\mathbf{e}_t$ . We train the denoising network $\epsilon_{\theta}$ using the following loss function: + +$$ +L _ {s t a g e 2} = E _ {M _ {t}, t, B, P, \epsilon \sim \mathcal {N} (0, I)} \| \mathbf {e} _ {t} - \epsilon \| _ {2} ^ {2}. \tag {7} +$$ + +Note that the parameters of FE are frozen in this stage. + +Stage 3: Joint training of MPG-Diff and RDNet. Since in training stage 2, we only trained the MPG-Diff without training the FE and the RDNet, the output $M'$ from the MPG-Diff exhibits slight differences compared to the output $M$ generated by the FE. As a result, directly using $M'$ to guide the RDNet will not achieve optimal deblurring performance. To address this, we perform joint training of the MPG-Diff and the RDNet. Specifically, the MPG-Diff performs a complete iterative denoising process to obtain the predicted motion prior $M'$ . Then we input both $M'$ and the blurred image $B$ into the RDNet to generate the deblurred result $S$ . By constraining the final result, we jointly optimize the MPG-Diff and the RDNet. The loss function is defined as follows: + +$$ +L _ {\text {s t a g e 3}} = \left\| S - G \right\| _ {1} + \lambda \cdot \left\| M ^ {\prime} - M \right\| _ {1}, \tag {8} +$$ + +where $\lambda$ is the weight factor and $M$ is the output of the FE. Since the denoising process is iterated multiple times, to reduce memory usage, we only record the gradients of the self-attention modules in the network $\epsilon_{\theta}$ and update the weights of that specific part of the network. + +# 3.4. Inference + +Given a blurred image $B$ , the MPG-Diff generates the corresponding motion prior features $M'$ . The RDNet takes $B$ and $M'$ as inputs and outputs the sharp image $S$ as the final result. The overall process is represented by the following equation: + +$$ +M ^ {\prime} = D i f f (B), \tag {9} +$$ + +$$ +S = R D N e t (B, M ^ {\prime}), +$$ + +where $Diff(\cdot)$ represents the complete iterative denoising process of the MPG-Diff using the network $\epsilon_{\theta}$ . + +
    Image-only methodSSIM↑PSNR↑Param.(M)
    DeepDeblur [31]0.91429.0811.7
    DeblurGAN-v2 [23]0.93429.5560.9
    SRN [45]0.93430.266.8
    DBGAN [59]0.94231.1011.6
    DMPHN [58]0.94031.2021.7
    Ren et al. [36]0.95432.1152.0
    MIMO-UNet+ [8]0.95732.4516.1
    HINet [4]0.95932.9188.7
    Restormer [57]0.96132.9226.1
    Stripformer [46]0.96233.0820.0
    HI-Diff [5]0.96433.3328.49
    MLWNet [12]0.96833.8395.1
    LoFormer [30]0.96934.0949.0
    MISC Filter [28]0.96934.1016.0
    FFTformer [20]0.96834.2116.6
    SegFFTformer [18]0.97034.38-
    AdaRevD [29]0.97234.60220.8
    Ours0.97334.6280.3
    D²Net [40]0.94031.6032.63
    eSL-Net [49]0.95433.520.19
    MADANET+ [55]0.96433.8416.9
    Vitoria et al. [48]0.94434.335.7
    EFNet [43]0.97235.468.47
    Ours Stage 10.97435.5020.7
    + +Table 1. Quantitative comparison with state-of-the-art deblurring methods on synthetic GoPro dataset. Red background represents the best performance. Orange background represents the second best. yellow box represents the third best. Ours Stage 1 represents the framework trained in Stage 1 with events. The underline denotes event-based method. + +# 3.5. Implementation Details + +In the RDNet, we set $C_b = 64$ and concatenate two DACFB modules at each scale of the image encoder. In the MPG-Diff, we use 1000 diffusion steps and a nosie schedule $\beta_t$ linearly increasing from 1e-6 to 1e-2 for training, and 5 steps for inference. During training, we set the batch size to 4 and use the ADAM optimizer with an initial learning rate of $1 \times 10^{-4}$ . We implement the algorithm in PyTorch and run it on the NVIDIA RTX 4090 GPU. + +# 4. Experiments + +# 4.1. Datasets and Metrics + +GoPro Dataset. We evaluate the effectiveness of the method on the GoPro dataset [31], which is widely used in both image-only and event-based deblurring research. We use ESIM [35] to construct synthetic event data and create an image-like representation from the events [43]. + +REBlur Dataset. To reflect the performance on real-world + +![](images/19a59963a8fe678173208c48415a3d2027e28bb1bbe023c425fc6c4d54ef59d5.jpg) +(a) Input (0.638, 21.31) + +![](images/bb3ef0e6e589e4b59c9439120afe7442fa6700a5976997f1a481445a4fdac6e3.jpg) +(b) HINet[4] (0.730, 23.74) + +![](images/ade364f59f088d89d87def00dad5c3a0403fe9a2d00024fde5e116444c9849f7.jpg) +(c) FFTformer[20] (0.882, 29.37) + +![](images/3da60e790083472f61923db57d6a938ff2435447f72bda6f5c553df57797325a.jpg) + +![](images/c34f68e69ce403926d9c466c598746d89d986d63485a29c1621acc8a284c7240.jpg) +(e) HI-Diff[5] (0.836, 27.02) + +![](images/6f8e9618da778ead0c8cbbae9ceb514ccda08656ef4ab0624d426cfff2c93698.jpg) +(f) Restomer [57] (0.793, 25.39) + +![](images/759085e64242bd8f1c9604f8f2148275e912b1423531cbbdb57c4500f5d357f6.jpg) +(g) Ours (0.889, 30.91) + +![](images/64b673ab26aa4e01b26b2ecbd4391687e574c92bbd5377e25aedb7142db33891.jpg) +(d) AdaRevD[29] (0.842, 27.53) +(h) Ground Truth + +![](images/ff1a2f40d21257a4fd4e02d44592a0bf75bccc0ddd59c4472039344c3f285bd4.jpg) +Figure 4. Qualitative results on the GoPro dataset. The values in parentheses represent (SSIM, PSNR). + +![](images/91fa3705139e8bbf6f719beefc802dd59e31ff615a205b2cd059d987251e0cab.jpg) + +![](images/60536e1fa356d14c607a8b59699ffc4e2ec2f71492f6807c2a5bd2f28030bae3.jpg) + +![](images/4cf54bb1e9a34213e3885d7c0bc28c7892fe04f8f7721466386edac4e551806b.jpg) + +![](images/887282609ab1c3918760ef7a310534304cb430173319da92cf8b27a7bfb740ff.jpg) +(a) Input (0.833, 25.90) +(e) HI-Diff[5] (0.929, 32.91) + +![](images/afd094efbadf5ab7e335a6823da39c6cfe8af42696ed533f1674ca3d46dbdd34.jpg) +(b) HINet[4] (0.923, 32.51) +(f) Restomer [57] (0.924, 32.52) +Figure 5. Qualitative results on the GoPro dataset. + +![](images/7ff8d5fb272ab2335c2ac91ee48eb739065eb10a48265455a60cb512adbca6fe.jpg) +(c) FFTformer[20] (0.934, 33.64) +(g) Ours (0.944, 35.24) + +![](images/2dba3e94f4cd6e3c1e7b7a4fb063706655e1942345bea36237fa446e8896f1dc.jpg) +(d) AdaRevD[29] (0.935, 33.57) +(h) Ground Truth + +event datasets, we validate our approach on the REBlur dataset [43], which contains 1,469 group of blurred-sharp image pairs with the associated events captured by event cameras. + +Metrics. We adopt two common metrics to quantitatively evaluate the performance of our method, including SSIM and PSNR, which are used to measure the similarity between the predicted results and the corresponding ground truth sharp images. + +# 4.2. Comparison on Synthetic Datasets + +Quantitative results on GoPro datasets are presented in Table 1, while visual results are shown in Figures 1, 4 and 5. We compare the model trained in stage 1 with event-based methods, while comparing the final EGDeblurring with image-only methods, as it only inputs the blurred image during inference. As shown in Table 1, the performance of our method in Stage 1 is better than that of other event-based methods, showing that our RDNet enables effective event-based image deblurring. In quantitative re + +
    Image-only methodSSIM↑PSNR↑
    SRN [45]0.96135.10
    FFTformer [20]0.96035.44
    Restormer [57]0.95935.50
    HINet [4]0.96535.58
    Stripformer [46]0.96035.66
    HI-Diff [5]0.96335.91
    Ours0.96936.21
    EDI [33]0.96436.52
    EFNet [43]0.97538.12
    REFID [44]0.97538.34
    Ours Stage 10.97738.51
    + +Table 2. Quantitative comparison with state-of-the-art methods for deblurring task on real world dataset: REBlur. + +sults, EGDeblurring outperforms all image-only deblurring methods. Even though our method has a relatively modest improvement compared to high-performance methods such as AdaRevD [29], we have achieved performance at the + +
    methodSSIM↑PSNR↑
    w/ raw event0.92132.33
    w/o MPG-Diff0.92432.47
    w/o DACFB0.96733.91
    w/o the detail guidance0.96333.84
    Ours0.97334.62
    + +same level while the scale of our model is much smaller than theirs. This is attributed to the combination of the diffusion model and the regression network, which demonstrates advantages in distortion-based quantitative results. As shown in the visual results in Figure 4 and 5, under complex motion blur, other methods struggle to fully remove the blur due to the absence of motion information guidance. In contrast, our approach leveraging generated event guidance allows to recover high-quality sharp image. This indicates that utilizing the diffusion model to generate motion prior information can clearly enhance the overall deblurring performance and the robustness to deal with images with complex motion blur. + +# 4.3. Comparison on Real-world Dataset + +Quantitative results are presented in Table 2, while visual results are shown in Figure 6. In the quantitative results, our models from Stage 1 and Stage 3 perform the best among event-based methods and image-only methods, respectively. Our method achieves superior quantitative results, with a $0.3\mathrm{dB}$ improvement in PSNR compared to the second best method. The visual results in Figure 6 demonstrate that other methods leave residual blur along the edges of moving objects and exhibit noticeable ghosting artifacts, whereas our method restores sharp edge details. This validates the advantage of using the diffusion model to incorporate motion information into our approach. + +# 4.4. Ablation Study + +The results of the ablation studies are presented in Table 3 and Figure 7, where we investigate the contribution of each our design to our method. + +Effect of MPG-Diff. MPG-Diff is responsible for generating motion prior information. To validate the effectiveness of the diffusion model, we replace it with a convolutional neural network and train it using the same training strategy. Compared to the complete method, the framework without the MPG-Diff shows a decrease in PSNR by $1.64\mathrm{dB}$ . This indicates that the motion information prior generated by the convolutional neural network is insufficient to provide adequate guidance for the deblurring task. In contrast, the introduction of the diffusion model enhances the robustness of the generated information, leading to improved overall performance of the method. + +Table 3. Ablation studies on the GoPro dataset. + +
    Metric1 tensor2 tensors (ours)3 tensors4 tensors5 tensors
    SSIM↑0.9690.9730.9710.9730.972
    PSNR↑34.1034.6234.6134.6134.59
    + +Table 4. Ablation study on different numbers of value tensors in DACFB. + +
    Metric1× dimension2× dimension4× dimensionOurs with two-value
    SSIM↑0.9690.9700.9710.973
    PSNR↑34.1034.1234.2334.62
    + +Table 5. Ablation study on feature dimensions of the vanilla cross-modal attention block. + +Effect of motion prior feature generation. FE is designed to convert the raw event representation into the feature representation, which is the generation target of the diffusion model. Dense features represent motion information similar to event representations while ensuring that the diffusion model can generate corresponding prior features robustly. To validate that dense features is superior to directly generating event representation, we remove the FE and train the diffusion model to directly generate events (as shown in "w/ raw event" in Table 3 and 7). Both quantitative and qualitative results indicate a substantial decline in the framework's deblurring performance. This indicates that introducing dense feature representation is more beneficial to the generation of the diffusion model and the performance of the overall framework. + +Effect of detail guidance. The detail guidance $P$ , along with the blurred image, constrain the generation process of the diffusion model. We remove the detail guidance and only use the blurred image to constrain the output of the diffusion model. The deblurring results are negatively impacted, showing a 0.78 dB decrease in PSNR compared to the complete method. This indicates that the detail guidance constrain the output of the diffusion model, leading to the generation of more effective guiding features for deblurring. + +Effect of DACFB. The DACFB embedded in the RDNet fuses motion information features and image features through a cross-modal attention mechanism. We replace the DACFB in the RDNet with simple feature concatenation and convolutional layers, and train the model according to the original strategy. Quantitative results indicate a reduction in deblurring performance, with a decrease of $0.71\mathrm{dB}$ in PSNR. This demonstrates that, compared to simple concatenation, the DACFB effectively aligns and fuses the two different modalities. We verify the effectiveness of our scheme by adjusting the number of value tensors in the attention mechanism. As shown in Table 4, two value tensors we employ in our DACFB design produces best results, while either decrease or increase in the number of the tensors will lead to performance drop. Note, we show in + +![](images/5b62ae53788f7963cd721f2290e71df6da36931f01cca9d7fdbcea48681fa73b.jpg) +(a) Input (0.916, 28.55) + +![](images/9a1ff05d389f1bd8b92b42eb627bc25300527f0be92cbf16a3a9f5113d2b3e0a.jpg) +(b) HINet[4] (0.913, 30.43) + +![](images/1a2885416fd3419b1e90173b1cceef69e39c35d9376fe46fd361bcb1d0563d16.jpg) +(c) FFTformer[20] (0.946, 30.87) + +![](images/41b787467fcb78f24fe7db62a2505df6f0ff85c405f61b12808e0f0bdf6a9b1a.jpg) +(d) Stripformer[46] (0.925, 30.72) + +![](images/6e81c682a361b0471cda4cf0fa6cb6e9dc00842d78155e68e30d7f6e7738b15e.jpg) +(e) HI-Diff[5] (0.913, 30.43) + +![](images/f7ed37ca2ff36775573efb1b923251f59ff53664486c2e118b7b6579b98fbdfa.jpg) +(f) Restormer [57] (0.926, 30.96) + +![](images/4282189e412b52ca138bdc16c11b5f79b1a1df5253fc9e3264bac0c37190fceb.jpg) +(g) Ours (0.968, 34.78) + +![](images/bd69deb70aec3d1b3ff99c02662be2ee378cc2bd7ba5f5ee83be28119a4c82ad.jpg) +(h) Ground Truth + +![](images/5d01cc89544b9070d5f561e57c63fb4d0fff40fff864439b2a9ab5c4ac5f1c59.jpg) + +![](images/40aaf00d72562eed230468cc17e6d337a73e48bc11ed2336a09c40dd76917213.jpg) +Input + +![](images/4cacee3d6281bd3c1c175219dc7753dace7ccb520564017d48e3a34c8e6cb4b1.jpg) +Figure 6. Qualitative results on the REBlur dataset. + +![](images/a7c6102f9851e358db2c527083e452812a9fccdd96b53a21fc0f42f754fbaa0a.jpg) +w/o MPG-Diff + +![](images/91a30c11b682378f7434101586d92a93dd736ef4eeed8e3dae992c10615c74c6.jpg) + +![](images/16d78d9f6c5d90a3524111afb82a5e15fb628d6cf73e5d7e9ef5005d229cdf66.jpg) +w/ raw event + +![](images/23ed82345f526220dbfbea8663111722a61e28f55261dbde40918eae990176f1.jpg) + +![](images/7e725f8a0c55a804e26b600c71328bc7f07b913d280f34d1797d11ebbe71a130.jpg) +w/o DACFB + +![](images/de1b98241769500bf5398c73f68a64a49c0edfd26999d5d78cb94c727d8285b9.jpg) + +![](images/ad29478e767472070784ac5a52ec5a8459c62e945eab9a4bb1ae732ef27776f5.jpg) +w/o detail guidance + +![](images/a5d327100db076fa4fd1c405d58e7b8fd6337b54bfa7acee6b1763724c605a27.jpg) + +![](images/333c3711cecdae2d638892760620a35de0ff91536b5e5ff692507fc838483176.jpg) +Ours +Figure 7. Visual results of ablation experiments. + +![](images/e4548f0888871c3617b6a9c2ea8d2c96485609a40d76e6d3e90e6b57bc7fd46a.jpg) + +![](images/9aad458e09a16d4484fa7a29b1236d73ddda0592697df30015df0c698107f569.jpg) +Ground Truth + +the Table 5 that our two-value design cannot be replaced by simple feature dimension increase with single-value motion prior feature (see 2nd, 3rd, and 4th columns). + +# 5. Conclusion + +We have presented EGDeblurring, a method that allows to achieve high-quality image deblurring by generating event guidance carrying the desired motion prior information using a diffusion model. Specifically, we design a motion prior generation diffusion model to generate event guidance from a single blurry image, and a regression de + +blurring network that can effectively utilize the motion prior information in the event guidance for image deblurring. Unlike existing event-based methods, our method can test with a single blurry image, without using ground truth event as input. 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In ECCV, 2022. 1, 2, 5, 6 +[44] Lei Sun, Christos Sakaridis, Jingyun Liang, Peng Sun, Jiezhang Cao, Kai Zhang, Qi Jiang, Kaiwei Wang, and Luc Van Gool. Event-based frame interpolation with ad-hoc deblurring. In CVPR, 2023. 6 +[45] Xin Tao, Hongyun Gao, Xiaoyong Shen, Jue Wang, and Jiaya Jia. Scale-recurrent network for deep image deblurring. In CVPR, 2018. 1, 2, 5, 6 +[46] Fu-Jen Tsai, Yan-Tsung Peng, Yen-Yu Lin, Chung-Chi Tsai, and Chia-Wen Lin. Stripformer: Strip transformer for fast image deblurring. In ECCV, 2022. 2, 5, 6, 8 +[47] Fu-Jen Tsai, Yan-Tsung Peng, Chung-Chi Tsai, Yen-Yu Lin, and Chia-Wen Lin. Banet: A blur-aware attention network for dynamic scene deblurring. IEEE Transactions on Image Processing, 31:6789-6799, 2022. 1, 2 +[48] Patricia Vitoria, Stamatios Georgoulis, Stepan Tulyakov, Alfredo Bochicchio, Julius Erbach, and Yuanyou Li. Event-based image deblurring with dynamic motion awareness. In ECCV, 2022. 5 +[49] Bishan Wang, Jingwei He, Lei Yu, Gui-Song Xia, and Wen Yang. Event enhanced high-quality image recovery. In ECCV, 2020. 5 +[50] Pei Wang, Jiumei He, Qingsen Yan, Yu Zhu, Jinqiu Sun, and Yanning Zhang. Diffevent: Event residual diffusion for image deblurring. In ICASSP. IEEE, 2024. 2 +[51] Jay Whang, Maurizio Delbracio, Hossein Talebi, Chitwan Sahara, Alexandros G Dimakis, and Peyman Milanfar. Deblurring via stochastic refinement. In CVPR, 2022. 2 +[52] Bin Xia, Yulun Zhang, Shiyin Wang, Yitong Wang, Xinglong Wu, Yapeng Tian, Wenming Yang, and Luc Van Gool. + +Diffir: Efficient diffusion model for image restoration. In ICCV, 2023. 2 +[53] Fang Xu, Lei Yu, Bishan Wang, Wen Yang, Gui-Song Xia, Xu Jia, Zhendong Qiao, and Jianzhuang Liu. Motion deblurring with real events. In ICCV, 2021. 1, 2 +[54] Li Xu, Shicheng Zheng, and Jiaya Jia. Unnatural 10 sparse representation for natural image deblurring. In CVPR, 2013. 1, 2 +[55] Dan Yang and Mehmet Yamac. Motion aware double attention network for dynamic scene deblurring. In CVPR, 2022. 5 +[56] Syed Waqas Zamir, Aditya Arora, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, Ming-Hsuan Yang, and Ling Shao. Multi-stage progressive image restoration. In CVPR, 2021. 1, 2 +[57] Syed Waqas Zamir, Aditya Arora, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, and Ming-Hsuan Yang. Restormer: Efficient transformer for high-resolution image restoration. In CVPR, 2022. 2, 5, 6, 8 +[58] Hongguang Zhang, Yuchao Dai, Hongdong Li, and Piotr Koniusz. Deep stacked hierarchical multi-patch network for image deblurring. In CVPR, 2019. 2, 5 +[59] Kaihao Zhang, Wenhan Luo, Yiran Zhong, Lin Ma, Bjorn Stenger, Wei Liu, and Hongdong Li. Deblurring by realistic blurring. In CVPR, 2020. 5 +[60] Xiang Zhang and Lei Yu. Unifying motion deblurring and frame interpolation with events. In CVPR, 2022. 1, 2 +[61] Xiang Zhang, Lei Yu, Wen Yang, Jianzhuang Liu, and GuiSong Xia. Generalizing event-based motion deblurring in real-world scenarios. In ICCV, 2023. 2 \ No newline at end of file diff --git a/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/images.zip b/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..29339c2ba7ad1ad9d56af5a79494c3c3d26fe36c --- /dev/null +++ b/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7d1c342f2401e0241b1a6e120cacc52965adede93582852736e72950680031cd +size 877634 diff --git a/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/layout.json b/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..9c02b7c6f70de7652a0435c0d9fb062d2369de2a --- /dev/null +++ b/2025/Diffusion-based Event Generation for High-Quality Image Deblurring/layout.json @@ -0,0 +1,12003 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 88, + 103, + 522, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 103, + 522, + 121 + ], + "spans": [ + { + "bbox": [ + 88, + 103, + 522, + 121 + ], + "type": "text", + "content": "Diffusion-based Event Generation for High-Quality Image Deblurring" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "spans": [ + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "text", + "content": "Xinan Xie" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "text", + "content": " Qing Zhang" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "text", + "content": " Wei-Shi Zheng" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "text", + "content": "School of Computer Science and Engineering, Sun Yat-sen University, China \n" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 67, + 142, + 543, + 200 + ], + "type": "text", + "content": "Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, China \nxiexn9@mail2.sysu.edu.cn zhangq93@mail.sysu.edu.cn wszheng@ieee.org" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 62, + 229, + 159, + 425 + ], + "blocks": [ + { + "bbox": [ + 62, + 229, + 159, + 425 + ], + "lines": [ + { + "bbox": [ + 62, + 229, + 159, + 425 + ], + "spans": [ + { + "bbox": [ + 62, + 229, + 159, + 425 + ], + "type": "image", + "image_path": "4fa114d03f93af72e8694da821c2fe0778ec896ec244ae64f267a9c7b7910c31.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 433, + 555, + 477 + ], + "lines": [ + { + "bbox": [ + 54, + 433, + 555, + 477 + ], + "spans": [ + { + "bbox": [ + 54, + 433, + 555, + 477 + ], + "type": "text", + "content": "Figure 1. 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As shown, by leveraging event guidance generated by a diffusion model, our method allows to produce high-quality deblurring results for images with complex motion blur, which are comparable to results of EFNet [43], a recent event-based deblurring method using GT event as input, and clearly better than results produced by HI-Diff [5]), a state-of-the-art image-only deblurring method." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 160, + 230, + 257, + 425 + ], + "blocks": [ + { + "bbox": [ + 160, + 230, + 257, + 425 + ], + "lines": [ + { + "bbox": [ + 160, + 230, + 257, + 425 + ], + "spans": [ + { + "bbox": [ + 160, + 230, + 257, + 425 + ], + "type": "image", + "image_path": "eb963d74a5a4adb25f3b12d485c6faf004e10d3989287272691a19ba61c67b4c.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 258, + 230, + 353, + 424 + ], + "blocks": [ + { + "bbox": [ + 258, + 230, + 353, + 424 + ], + "lines": [ + { + "bbox": [ + 258, + 230, + 353, + 424 + ], + "spans": [ + { + "bbox": [ + 258, + 230, + 353, + 424 + ], + "type": "image", + "image_path": "1942ee8584818511cdfe87670c8f410a26355430848f030bdbd48a99c4404f1c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 355, + 230, + 451, + 423 + ], + "blocks": [ + { + "bbox": [ + 355, + 230, + 451, + 423 + ], + "lines": [ + { + "bbox": [ + 355, + 230, + 451, + 423 + ], + "spans": [ + { + "bbox": [ + 355, + 230, + 451, + 423 + ], + "type": "image", + "image_path": "65e409a4e44abf250d64043e7e41960ac7e6bbca5375e6d888ae78d3bd25e503.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 452, + 230, + 549, + 423 + ], + "blocks": [ + { + "bbox": [ + 452, + 230, + 549, + 423 + ], + "lines": [ + { + "bbox": [ + 452, + 230, + 549, + 423 + ], + "spans": [ + { + "bbox": [ + 452, + 230, + 549, + 423 + ], + "type": "image", + "image_path": "537b3c5a1c750b7a298854c16b9261b41a965a5a7f18277bc758ce1e21d8f568.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 151, + 489, + 200, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 489, + 200, + 501 + ], + "spans": [ + { + "bbox": [ + 151, + 489, + 200, + 501 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 54, + 502, + 297, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 502, + 297, + 694 + ], + "spans": [ + { + "bbox": [ + 54, + 502, + 297, + 694 + ], + "type": "text", + "content": "While event-based deblurring have demonstrated impressive results, they are impractical for consumer photos captured by cell phones and digital cameras that are not equipped with the event sensor. To address this problem, we in this paper propose a novel deblurring framework called Event Generation Deblurring (EGDeblurring), which allows to effectively deblur an image by generating event guidance describing the motion information using a diffusion model. Specifically, we design a motion prior generation diffusion model and a feature extractor to produce prior information beneficial for deblurring, rather than generating the raw event representation. In order to achieve effective fusion of motion prior information with blurry images and produce high-quality results, we develop a regression deblurring network embedded with a dual-attention channel fusion block. Experiments on multiple" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 490, + 555, + 526 + ], + "type": "text", + "content": "datasets demonstrate that our method outperforms state-of-the-art image deblurring methods. Our code is available at https://github.com/XinanXie/EGDeblurring." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 549, + 395, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 549, + 395, + 562 + ], + "spans": [ + { + "bbox": [ + 314, + 549, + 395, + 562 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 569, + 555, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 569, + 555, + 677 + ], + "spans": [ + { + "bbox": [ + 312, + 569, + 555, + 677 + ], + "type": "text", + "content": "Image deblurring is an important problem in computer vision, aiming to recover a sharp image from the original blurred input. Traditional methods primarily address the problem by formulating an optimization that incorporates various hand-crafted priors and assumptions [2, 3, 7, 11, 21, 24, 32, 39, 54]. In recent years, learning-based methods [4, 8, 31, 42, 45, 47, 56] have made significant progress. However, they are often less effective for images with complex motion blur, as shown in Figure 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 556, + 713 + ], + "type": "text", + "content": "To enhance the robustness to complex blurry images, event-based deblurring methods [17, 27, 33, 40, 53, 60] have been developed, where the motion information cap" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 144, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2194" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 180 + ], + "type": "text", + "content": "tured by event camera is utilized to achieve high-quality image deblurring. Although these methods demonstrate impressive results, they require events as additional inference input, which cannot be recorded by most consumer cameras, thereby having relatively limited practicability. Diffusion models [15] have recently gained widespread attention due to its powerful generation capability. This motivates us to explore the possibility of using diffusion models to generate event guidance for blurred images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 181, + 298, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 181, + 298, + 455 + ], + "spans": [ + { + "bbox": [ + 56, + 181, + 298, + 455 + ], + "type": "text", + "content": "In this paper, we present EGDeblurring, a method that allows high-quality image deblurring by utilizing motion information from event guidance generated by a diffusion model. EGDeblurring consists of a motion prior generation diffusion model (MPG-Diff) and a regression deblurring network (RDNet), where MPG-Diff is a diffusion model used for generating event recording the motion information of a blurry image, while RDNet aims to recover a sharp image from the blurry image and the associated events. Note, we design MPG-Diff to generate event-based motion prior features instead of raw events. The reason behind is that raw event usually appears in terms of sparse representation, while diffusion models excel at generating dense representation with rich details. To ensure that MPG-diff generates reliable event guidance, we instead choose to predict motion prior feature rather than raw event. To effectively utilize the motion information recorded by events, we embed dual-attention channel fusion block (DACFB) at multiple levels of the RDNet, which enables aligning and fusing motion information features with image features. To enable better performance, a multi-stage training strategy is further introduced. During inference, our method receives only blurry images as input as it can generate event guidance by itself." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 456, + 294, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 456, + 294, + 467 + ], + "spans": [ + { + "bbox": [ + 67, + 456, + 294, + 467 + ], + "type": "text", + "content": "In summary, we make the following main contributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 468, + 294, + 633 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 67, + 468, + 294, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 468, + 294, + 504 + ], + "spans": [ + { + "bbox": [ + 67, + 468, + 294, + 504 + ], + "type": "text", + "content": "- We present a method that allows high-quality image deblurring by generating event guidance describing the motion information using a diffusion model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 509, + 294, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 509, + 294, + 556 + ], + "spans": [ + { + "bbox": [ + 67, + 509, + 294, + 556 + ], + "type": "text", + "content": "- We develop a diffusion model for generating event guidance and a network to produce sharp image from a blurry image and its predicted event. Besides, we introduce an effective multi-stage training strategy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 562, + 294, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 562, + 294, + 633 + ], + "spans": [ + { + "bbox": [ + 67, + 562, + 294, + 633 + ], + "type": "text", + "content": "- We compare our method with various state-of-the-art image deblurring methods on benchmark datasets. Results show that our method significantly outperforms existing image-only methods, and can produce comparable results to event-based methods with ground truth event as inference input." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 645, + 142, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 645, + 142, + 658 + ], + "spans": [ + { + "bbox": [ + 55, + 645, + 142, + 658 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 665, + 295, + 713 + ], + "type": "text", + "content": "Image-only methods. Early image deblurring methods typically work by estimating the blur kernel using various natural image priors and assumptions [2, 3, 11, 21, 22, 25, 54]. However, these methods are mostly less effective for im" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 72, + 553, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 240 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 240 + ], + "type": "text", + "content": "ages with complex motion blur, as their leveraged priors and assumptions may not always hold in real-world scenarios. In the past decade, numerous deep learning based methods are developed for image deblurring [1, 4, 8, 16, 31, 38, 42, 45, 47, 56, 58] from different perspectives including multi-scale [31, 45], coarse-to-fine [8], and multistage [4]. More recently, transformer [20, 46, 57] and frequency analysis [10, 20] have been applied to image deblurring, which demonstrates promising results. However, due to lack of reliable modeling of the motion information, existing learning-based methods basically struggle to recover sharp images with clear and well-preserved details, especially when facing with blurry images incurred by complex object and camera motion." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 245, + 553, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 245, + 553, + 425 + ], + "spans": [ + { + "bbox": [ + 313, + 245, + 553, + 425 + ], + "type": "text", + "content": "Event-based methods. As event carries the motion information beneficial to image deblurring, there are various event-based methods [6, 14, 17, 19, 27, 33, 34, 40, 53, 60, 61] in the literature. Pan et al. [33] proposed an event-based double integral (EDI) model that integrates blurred images and events for deblurring. Shang et al. [40] developed a event fusion module that can be incorporated into existing image and video deblurring networks. RED-Net [53] proposes to combine optical flow estimation and for self-supervised deblurring. EFNet [43] designs an event-image cross-modal attention module to fuse event and image features. Although event-based methods achieve superior deblurring performance by leveraging motion information, to our knowledge, all of them require ground truth event as addition inference input, which limits their practicability." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 430, + 555, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 430, + 555, + 610 + ], + "spans": [ + { + "bbox": [ + 313, + 430, + 555, + 610 + ], + "type": "text", + "content": "Diffusion-based methods. Recently, diffusion models have demonstrated impressive performance in various low-level vision tasks including image/video deblurring [13, 26, 37, 51]. DvSR [51] presents a framework for stochastic blind image deblurring with a focus on perceptual quality using a conditional diffusion model. Ren et al. [36] proposed to improve the performance by leveraging multiscale structure guidance. DiffIR [52] achieves efficient diffusion-based image restoration. HI-Diff [5] applies diffusion model in a highly compacted latent space to generate the prior feature for the deblurring process. There is also attempt towards integrating event information into diffusion models. Diffevent [50] formulates event-based image deblurring as an image generation problem by designing diffusion priors for both the image and residuals." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 620, + 370, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 620, + 370, + 633 + ], + "spans": [ + { + "bbox": [ + 314, + 620, + 370, + 633 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 641, + 553, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 553, + 715 + ], + "type": "text", + "content": "Figure 2 presents the overview of the proposed EGDeblurring. As shown, during inference, our method only receives single blurry image as input. The EGDeblurring encompasses two key modules: the RDNet and the MPGDiff. The RDNet embed the DACFB is designed to restore a blurred image into the corresponding sharp one, guided" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "2195" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 95, + 276, + 189 + ], + "blocks": [ + { + "bbox": [ + 99, + 81, + 267, + 88 + ], + "lines": [ + { + "bbox": [ + 99, + 81, + 267, + 88 + ], + "spans": [ + { + "bbox": [ + 99, + 81, + 267, + 88 + ], + "type": "text", + "content": "Training Stage 1: Training of Regression Deblurring Network (RDNet)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 95, + 276, + 189 + ], + "lines": [ + { + "bbox": [ + 61, + 95, + 276, + 189 + ], + "spans": [ + { + "bbox": [ + 61, + 95, + 276, + 189 + ], + "type": "image", + "image_path": "2de3b3dce4bdee3ee5dbfad43aeff8efcd494b652bbacc94092e6118c50456ae.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 310, + 90, + 541, + 190 + ], + "blocks": [ + { + "bbox": [ + 359, + 81, + 493, + 88 + ], + "lines": [ + { + "bbox": [ + 359, + 81, + 493, + 88 + ], + "spans": [ + { + "bbox": [ + 359, + 81, + 493, + 88 + ], + "type": "text", + "content": "Training Stage 3: Joint training of MPG-Diff and RDNet" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 90, + 541, + 190 + ], + "lines": [ + { + "bbox": [ + 310, + 90, + 541, + 190 + ], + "spans": [ + { + "bbox": [ + 310, + 90, + 541, + 190 + ], + "type": "image", + "image_path": "cc4d0ccfe95bf26776633bf8900ccfab2b92424de1f56630b7139009745bfc75.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 72, + 212, + 272, + 326 + ], + "blocks": [ + { + "bbox": [ + 85, + 197, + 284, + 205 + ], + "lines": [ + { + "bbox": [ + 85, + 197, + 284, + 205 + ], + "spans": [ + { + "bbox": [ + 85, + 197, + 284, + 205 + ], + "type": "text", + "content": "Training Stage 2: Training of Motion Prior Generation Diffusion Model (MPG-Diff)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 72, + 212, + 272, + 326 + ], + "lines": [ + { + "bbox": [ + 72, + 212, + 272, + 326 + ], + "spans": [ + { + "bbox": [ + 72, + 212, + 272, + 326 + ], + "type": "image", + "image_path": "6434c2f235a0246a466fb5b733260cb99156309a016e5830ec8a74c35e946bec.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 328, + 198, + 523, + 293 + ], + "blocks": [ + { + "bbox": [ + 328, + 198, + 523, + 293 + ], + "lines": [ + { + "bbox": [ + 328, + 198, + 523, + 293 + ], + "spans": [ + { + "bbox": [ + 328, + 198, + 523, + 293 + ], + "type": "image", + "image_path": "88d66eb711bf254bf25104f89555667c9fbe0d54988cb732b1f32579ca8eb28c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 297, + 534, + 338 + ], + "blocks": [ + { + "bbox": [ + 317, + 297, + 534, + 338 + ], + "lines": [ + { + "bbox": [ + 317, + 297, + 534, + 338 + ], + "spans": [ + { + "bbox": [ + 317, + 297, + 534, + 338 + ], + "type": "image", + "image_path": "c824de5fc430ac840bfbd672141239998cf2e98d545982dbb24d9f14c1356683.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "lines": [ + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "spans": [ + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": "Figure 2. Overview of EGDeblurring. The EGDeblurring incorporates events during the training process, while it does not require event input during the inference stage, which is consistent with the image-only approach. The EGDeblurring are trained with a multi-stage training strategy. In Stage 1, the FE transforms the event representation " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": " into the motion prior feature representation " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": " which guides the RDNet to restore the sharp image " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": " from the blurred image " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": ". In Stage 2, the MPG-Diff is trained to generate motion prior feature " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": " conditioned on the blurred image " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": " and the detail guidance " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": ". In Stage 3, the MPG-Diff and the RDNet are jointly trained to achieve optimal deblurring performance. During inference, given a blurry image " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": ", the MPG-Diff generates the corresponding motion prior feature " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": ", guiding the RDNet to output the final sharp result " + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 350, + 555, + 427 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 448, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 448, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 54, + 448, + 295, + 616 + ], + "type": "text", + "content": "by motion prior features from events or the MPG-Diff. The MPG-Diff accepts the blurred image and the corresponding detail guidance as conditions, generating motion prior features. We adopt a multi-stage training strategy. In training stage 1 and training stage 2, the RDNet and MPG-Diff are trained respectively. Subsequently, in training stage 3, both are jointly trained to achieve coordination between the modules. During the inference process, given a blurred image, the MPG-Diff generates the corresponding motion prior features. The RDNet then utilizes these prior features to achieve high-quality image deblurring, eliminating the need for event assistance. Therefore, during inference, the EGDeblurring method is consistent with the image-only approach." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 624, + 228, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 228, + 636 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 228, + 636 + ], + "type": "text", + "content": "3.1. Regression Deblurring Network" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "To avoid undesired artifacts and achieve better results, we design the RDNet to perform image deblurring. The RDNet consists of a motion prior encoder, an image encoder, and an image decoder. Meanwhile, in order to match the generation of the subsequent diffusion model, we employ a Feature Extractor (FE) composed of a deep neural" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": "network to convert the event representation " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "E \\in \\mathbb{R}^{C_e \\times H \\times W}" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": " into a feature representation " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{R}^{C_m \\times H \\times W}" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": ". The motion prior encoder encodes " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": " from the FE in training stage 1 (or " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": " from the MPG-Diff in training stage 3 and inference) into multi-scale motion prior features " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "F_{m}^{k} \\in \\mathbb{R}^{C' \\times H' \\times W'}" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "k = 0, 1, 2" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "C' = 2^k C_b" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "H' = H / 2^k" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "W' = W / 2^k" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "C_b" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": " denotes the base number of channels. The blurred image " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "B \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": " is encoded by the image encoder into image features " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "F_{i}^{k}" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "F_{i}^{k}" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "F_{m}^{k}" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": " at the same scale are fused through the DACFB embedded in the image encoder. The image features are processed through the image decoder to produce the sharp image " + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 313, + 447, + 555, + 605 + ], + "type": "text", + "content": ", which serves as the final output of the framework." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": "Details of DACFB. We propose a DACFB as the modal information regulator for the network. The utilization of a multi-branch structure enables the network to learn multiple sets of cross-modal values to modulate the image features. As shown in Figure 3, layer normalization and " + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": " convolutional layers process " + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "inline_equation", + "content": "F_{m}^{k}" + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "inline_equation", + "content": "F_{i}^{k}" + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "inline_equation", + "content": "K \\in \\mathbb{R}^{H'W' \\times C'}" + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{H'W' \\times C'}" + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": " respectively. The cross-channel attention map " + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": " is computed from " + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 313, + 616, + 556, + 715 + ], + "type": "text", + "content": ". To ensure suf" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2196" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 77, + 293, + 219 + ], + "blocks": [ + { + "bbox": [ + 63, + 77, + 293, + 219 + ], + "lines": [ + { + "bbox": [ + 63, + 77, + 293, + 219 + ], + "spans": [ + { + "bbox": [ + 63, + 77, + 293, + 219 + ], + "type": "image", + "image_path": "2ba9a61daabea251924c3d135aa8069f20c3a4c4fc7516bc0d596c398d82f8b7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 229, + 296, + 264 + ], + "lines": [ + { + "bbox": [ + 55, + 229, + 296, + 264 + ], + "spans": [ + { + "bbox": [ + 55, + 229, + 296, + 264 + ], + "type": "text", + "content": "Figure 3. Network architecture of DACFB. The DACFB is embedded within the image encoder of the RDNet, aiming to fuse the motion feature " + }, + { + "bbox": [ + 55, + 229, + 296, + 264 + ], + "type": "inline_equation", + "content": "F_{m}^{k}" + }, + { + "bbox": [ + 55, + 229, + 296, + 264 + ], + "type": "text", + "content": " and the image feature " + }, + { + "bbox": [ + 55, + 229, + 296, + 264 + ], + "type": "inline_equation", + "content": "F_{i}^{k}" + }, + { + "bbox": [ + 55, + 229, + 296, + 264 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "spans": [ + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": "ficient modulation of features, we extract " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "V_{1}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "V_{2}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "F_{m}^{k}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "V_{1}, V_{2} \\in \\mathbb{R}^{H'W' \\times C'}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": ". The vectors " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "V_{1}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "V_{2}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": " are respectively taken to compute the outer products with " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": ", resulting in " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "A_{1}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "A_{2}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": ". Then the outputs of the attention operation are separately multiplied and added to " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "F_{i}^{k}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": " to obtain the output feature " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "F_{out}'" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "F_{out}'" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": " is passed to the feed forward network and outputs the final result " + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "inline_equation", + "content": "F_{out}" + }, + { + "bbox": [ + 55, + 281, + 296, + 378 + ], + "type": "text", + "content": ". It can be represented by the following formula:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 383, + 215, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 383, + 215, + 410 + ], + "spans": [ + { + "bbox": [ + 115, + 383, + 215, + 410 + ], + "type": "interline_equation", + "content": "A = \\operatorname {s o f t m a x} (\\frac {Q ^ {T} K}{\\sqrt {d}}),", + "image_path": "3ce556242856c75b3f80f46ea5965f4d32e4a8188c7b423e2b17f0981ea11515.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 116, + 411, + 177, + 424 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 411, + 177, + 424 + ], + "spans": [ + { + "bbox": [ + 116, + 411, + 177, + 424 + ], + "type": "interline_equation", + "content": "A _ {1} = V _ {1} \\times A,", + "image_path": "469a740c01903aa42a4ab125df60188caf1d56632853fecb82a58de114665d71.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 423, + 294, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 423, + 294, + 439 + ], + "spans": [ + { + "bbox": [ + 116, + 423, + 294, + 439 + ], + "type": "interline_equation", + "content": "A _ {2} = V _ {2} \\times A, \\tag {1}", + "image_path": "5519fe5df2482537bff7eb894677373e1a119f55d5180cd590cda4fc63fb0bae.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 442, + 233, + 457 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 442, + 233, + 457 + ], + "spans": [ + { + "bbox": [ + 116, + 442, + 233, + 457 + ], + "type": "interline_equation", + "content": "F _ {o u t} ^ {\\prime} = L N \\left(F _ {i} ^ {k}\\right) \\cdot A _ {1} + A _ {2},", + "image_path": "3c838d853a83898fb3769325cf4af6f946f9d5673a7e3ae78841156c4b480473.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 458, + 235, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 458, + 235, + 472 + ], + "spans": [ + { + "bbox": [ + 116, + 458, + 235, + 472 + ], + "type": "interline_equation", + "content": "F _ {o u t} = F F N \\left(F _ {o u t} ^ {\\prime}\\right) + F _ {o u t} ^ {\\prime},", + "image_path": "3db401c52e43b242300f81b35043f9eca73c896180ecc805c16a66e69e7c97b5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 478, + 295, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 478, + 295, + 503 + ], + "spans": [ + { + "bbox": [ + 55, + 478, + 295, + 503 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 478, + 295, + 503 + ], + "type": "inline_equation", + "content": "LN(\\cdot)" + }, + { + "bbox": [ + 55, + 478, + 295, + 503 + ], + "type": "text", + "content": " represents layer normalization and " + }, + { + "bbox": [ + 55, + 478, + 295, + 503 + ], + "type": "inline_equation", + "content": "FFN(\\cdot)" + }, + { + "bbox": [ + 55, + 478, + 295, + 503 + ], + "type": "text", + "content": " represents the feed forward network." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 509, + 275, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 509, + 275, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 509, + 275, + 521 + ], + "type": "text", + "content": "3.2. Motion Prior Generation Diffusion Model" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "spans": [ + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "text", + "content": "We employ the MPG-Diff to generate the motion prior feature " + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "text", + "content": " as a substitute for the motion information features " + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "text", + "content": " from events. We employ a conditional denoising diffusion probabilistic model [9, 15] to guide the generation of the corresponding motion prior information. We perform the forward diffusion process and the reverse denoising process on the motion prior features " + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "text", + "content": " instead of the events " + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 526, + 295, + 609 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "spans": [ + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "text", + "content": "In the forward diffusion process, " + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "text", + "content": " transformed from " + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "text", + "content": " by the FE is considered as the starting point of the forward Markov process (i.e., " + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "inline_equation", + "content": "M = M_0" + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "text", + "content": "). The diffusion model learns a Markov chain by progressively corrupting the target feature " + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "inline_equation", + "content": "M_0" + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "text", + "content": " with Gaussian noise at each time step " + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "text", + "content": ", thereby transforming it into a Gaussian distribution (referred to as " + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 55, + 610, + 296, + 694 + ], + "type": "text", + "content": "). The forward diffusion process is formulated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 83, + 700, + 295, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 700, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 83, + 700, + 295, + 715 + ], + "type": "interline_equation", + "content": "q \\left(M _ {t} \\mid M _ {t - 1}\\right) = \\mathcal {N} \\left(M _ {t}; \\sqrt {1 - \\beta_ {t}} M _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {2}", + "image_path": "a60ebc9149acf7fdbc31a8f254a4b4338e25568baa1c6633731fbdbc9562fe68.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " is the feature at time step " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " is the predefined variance, and " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " represents the identity matrix for ensuring isotropic of the noise. After reparameterization [15], we obtain " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "inline_equation", + "content": "M_0" + }, + { + "bbox": [ + 313, + 72, + 554, + 121 + ], + "type": "text", + "content": " in a single step by:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 376, + 130, + 555, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 130, + 555, + 144 + ], + "spans": [ + { + "bbox": [ + 376, + 130, + 555, + 144 + ], + "type": "interline_equation", + "content": "M _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} M _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {3}", + "image_path": "0f96c0bcbadc8a91cbb2219dcbaf395dc9213641499005ff5113b62141e5b0c1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "spans": [ + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_t = \\prod_{i=0}^t \\alpha_i" + }, + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "type": "text", + "content": " is the cumulative product of forward noise weight parameters " + }, + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "type": "inline_equation", + "content": "\\alpha_i = 1 - \\beta_i" + }, + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 313, + 157, + 554, + 203 + ], + "type": "text", + "content": " denotes random Gaussian noise." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "spans": [ + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "type": "text", + "content": "In the reverse denoising process, Gaussian noise is iteratively denoised into the motion prior feature " + }, + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "type": "text", + "content": ". We adopt the DDIM [41] sampling strategy. To synthesize the corresponding motion prior features, we utilize the blurred image " + }, + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "type": "text", + "content": " and detail guidance " + }, + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 205, + 555, + 277 + ], + "type": "text", + "content": " as conditions. The reverse denoising process is defined as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 286, + 552, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 286, + 552, + 314 + ], + "spans": [ + { + "bbox": [ + 317, + 286, + 552, + 314 + ], + "type": "interline_equation", + "content": "M _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} (\\frac {M _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\cdot \\mathbf {e} _ {t}}{\\sqrt {\\bar {\\alpha} _ {t}}}) + \\sqrt {1 - \\bar {\\alpha} _ {t - 1}} \\cdot \\mathbf {e} _ {t},", + "image_path": "c6bc74f7be4bfe90fa07bca5324f37107994afde796be8c655ec85a5ffc7d94c.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 316, + 553, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 316, + 553, + 339 + ], + "spans": [ + { + "bbox": [ + 317, + 316, + 553, + 339 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {t} = \\epsilon_ {\\theta} (M _ {t}, B, P, t), \\tag {4}", + "image_path": "7cdcdf992a2d726c4ba5be35ddde39fbdd14e9a57af24b6c5b101d648e10a980.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 339, + 544, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 339, + 544, + 351 + ], + "spans": [ + { + "bbox": [ + 313, + 339, + 544, + 351 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 339, + 544, + 351 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_t" + }, + { + "bbox": [ + 313, + 339, + 544, + 351 + ], + "type": "text", + "content": " is the noise estimated by the neural network " + }, + { + "bbox": [ + 313, + 339, + 544, + 351 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 339, + 544, + 351 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 357, + 554, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 357, + 554, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 357, + 554, + 464 + ], + "type": "text", + "content": "Detail guidance. To better constrain the diffusion model to output highly relevant information, we explore extracting details from the blurred image. We observed that when the image is downsampled, further detail information is lost. Thus, the difference between the downsampled image and the original image can serve as a guidance for the image details. We propose " + }, + { + "bbox": [ + 313, + 357, + 554, + 464 + ], + "type": "inline_equation", + "content": "P = B - \\mathcal{T}(B)" + }, + { + "bbox": [ + 313, + 357, + 554, + 464 + ], + "type": "text", + "content": " as the detail guidance, where " + }, + { + "bbox": [ + 313, + 357, + 554, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 313, + 357, + 554, + 464 + ], + "type": "text", + "content": " represents the operation of downsampling the image and then upsampling it back to its original size." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 473, + 479, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 473, + 479, + 487 + ], + "spans": [ + { + "bbox": [ + 313, + 473, + 479, + 487 + ], + "type": "text", + "content": "3.3. Multi-Stage Training Strategy" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 492, + 554, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 492, + 554, + 516 + ], + "spans": [ + { + "bbox": [ + 313, + 492, + 554, + 516 + ], + "type": "text", + "content": "We adopt a three-stage joint training strategy to achieve synchronization between the modules." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "spans": [ + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "text", + "content": "Stage 1: training of RDNet. During the first stage of training, our goal is to introduce events and train a high-performance deblurring network. The training process at this stage is similar to that of event-based deblurring. We concatenate the FE and the RDNet in series and perform joint training. The event representation " + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "text", + "content": " is transformed into the feature representation " + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "text", + "content": " through the FE. Next, the RDNet accepts the " + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "text", + "content": " and the blurred image " + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "text", + "content": " and outputs the sharp image " + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 521, + 555, + 640 + ], + "type": "text", + "content": ". The overall process of training stage 1 can be expressed as follows:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 389, + 651, + 553, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 651, + 553, + 670 + ], + "spans": [ + { + "bbox": [ + 389, + 651, + 553, + 670 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} M = F E (E), \\\\ S _ {m} = \\text {P D N t} (R, M) \\end{array} \\tag {5}", + "image_path": "9c9df4e8bb5dbde7d5945fc04564c6528e47569a6683b3903bd26d120d217568.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 389, + 666, + 479, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 666, + 479, + 679 + ], + "spans": [ + { + "bbox": [ + 389, + 666, + 479, + 679 + ], + "type": "interline_equation", + "content": "S = R D N e t (B, M).", + "image_path": "4cbc06033337c051174790068d68bb3eabd0264e5f1cebbf6dec0513da8d7eca.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "At this stage, we aim for the network to achieve optimal deblurring performance. We employ " + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": " loss to constrain the" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2197" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 95 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 95 + ], + "type": "text", + "content": "network output and jointly optimize the FE and the RDNet. The loss function is defined as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 129, + 106, + 295, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 106, + 295, + 121 + ], + "spans": [ + { + "bbox": [ + 129, + 106, + 295, + 121 + ], + "type": "interline_equation", + "content": "L _ {\\text {s t a g e 1}} = \\left\\| S - G \\right\\| _ {1}, \\tag {6}", + "image_path": "5bbccf61021211204f890bf906be1e39a0e701368a33e3783b0e61275d1c80db.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 130, + 266, + 142 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 130, + 266, + 142 + ], + "spans": [ + { + "bbox": [ + 55, + 130, + 266, + 142 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 130, + 266, + 142 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 55, + 130, + 266, + 142 + ], + "type": "text", + "content": " represents the corresponding ground truth." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "spans": [ + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "content": "Stage 2: Training of MPG-Diff. We train the MPG-Diff using the basic training strategy of diffusion models. Given the event " + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "content": ", we first use the FE trained in the first stage to synthesize the " + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "content": ". Subsequently, " + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "content": " is generated using Equation 3. In the reverse denoising process, the blurred image " + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "content": " and detail guidance " + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "content": " serve as conditions, and the denoising network predicts the noise " + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_t" + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "content": ". We train the denoising network " + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 147, + 296, + 243 + ], + "type": "text", + "content": " using the following loss function:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 252, + 295, + 268 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 252, + 295, + 268 + ], + "spans": [ + { + "bbox": [ + 91, + 252, + 295, + 268 + ], + "type": "interline_equation", + "content": "L _ {s t a g e 2} = E _ {M _ {t}, t, B, P, \\epsilon \\sim \\mathcal {N} (0, I)} \\| \\mathbf {e} _ {t} - \\epsilon \\| _ {2} ^ {2}. \\tag {7}", + "image_path": "e4940f9277128a52c06767e67611031d6ca5e9480a438f12264595f3b4be9943.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 277, + 277, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 277, + 277, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 277, + 289 + ], + "type": "text", + "content": "Note that the parameters of FE are frozen in this stage." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "content": "Stage 3: Joint training of MPG-Diff and RDNet. Since in training stage 2, we only trained the MPG-Diff without training the FE and the RDNet, the output " + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "content": " from the MPG-Diff exhibits slight differences compared to the output " + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "content": " generated by the FE. As a result, directly using " + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "content": " to guide the RDNet will not achieve optimal deblurring performance. To address this, we perform joint training of the MPG-Diff and the RDNet. Specifically, the MPG-Diff performs a complete iterative denoising process to obtain the predicted motion prior " + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "content": ". Then we input both " + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "content": " and the blurred image " + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "content": " into the RDNet to generate the deblurred result " + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 293, + 296, + 460 + ], + "type": "text", + "content": ". By constraining the final result, we jointly optimize the MPG-Diff and the RDNet. The loss function is defined as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 91, + 472, + 295, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 472, + 295, + 485 + ], + "spans": [ + { + "bbox": [ + 91, + 472, + 295, + 485 + ], + "type": "interline_equation", + "content": "L _ {\\text {s t a g e 3}} = \\left\\| S - G \\right\\| _ {1} + \\lambda \\cdot \\left\\| M ^ {\\prime} - M \\right\\| _ {1}, \\tag {8}", + "image_path": "e83245e575dbb5ce1392bd95141b56febe31b1c64e7648ec068afa15c661eeca.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "type": "text", + "content": " is the weight factor and " + }, + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "type": "text", + "content": " is the output of the FE. Since the denoising process is iterated multiple times, to reduce memory usage, we only record the gradients of the self-attention modules in the network " + }, + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 495, + 296, + 555 + ], + "type": "text", + "content": " and update the weights of that specific part of the network." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 563, + 123, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 123, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 123, + 574 + ], + "type": "text", + "content": "3.4. Inference" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "content": "Given a blurred image " + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "content": ", the MPG-Diff generates the corresponding motion prior features " + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "content": ". The RDNet takes " + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "content": " as inputs and outputs the sharp image " + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 581, + 296, + 641 + ], + "type": "text", + "content": " as the final result. The overall process is represented by the following equation:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 128, + 651, + 295, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 651, + 295, + 670 + ], + "spans": [ + { + "bbox": [ + 128, + 651, + 295, + 670 + ], + "type": "interline_equation", + "content": "M ^ {\\prime} = D i f f (B), \\tag {9}", + "image_path": "8e2dbf8acd0af56d4afcaf3c5c093ec7b374b6c79ba9fdf9f800ae3c586c876b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 129, + 666, + 222, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 666, + 222, + 679 + ], + "spans": [ + { + "bbox": [ + 129, + 666, + 222, + 679 + ], + "type": "interline_equation", + "content": "S = R D N e t (B, M ^ {\\prime}),", + "image_path": "5b3f73f7b6ce9285c65cddba13fdc2feaf6d2ced4de099029d00ac08afabed8d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "inline_equation", + "content": "Diff(\\cdot)" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": " represents the complete iterative denoising process of the MPG-Diff using the network " + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 318, + 64, + 553, + 384 + ], + "blocks": [ + { + "bbox": [ + 318, + 64, + 553, + 384 + ], + "lines": [ + { + "bbox": [ + 318, + 64, + 553, + 384 + ], + "spans": [ + { + "bbox": [ + 318, + 64, + 553, + 384 + ], + "type": "table", + "html": "
    Image-only methodSSIM↑PSNR↑Param.(M)
    DeepDeblur [31]0.91429.0811.7
    DeblurGAN-v2 [23]0.93429.5560.9
    SRN [45]0.93430.266.8
    DBGAN [59]0.94231.1011.6
    DMPHN [58]0.94031.2021.7
    Ren et al. [36]0.95432.1152.0
    MIMO-UNet+ [8]0.95732.4516.1
    HINet [4]0.95932.9188.7
    Restormer [57]0.96132.9226.1
    Stripformer [46]0.96233.0820.0
    HI-Diff [5]0.96433.3328.49
    MLWNet [12]0.96833.8395.1
    LoFormer [30]0.96934.0949.0
    MISC Filter [28]0.96934.1016.0
    FFTformer [20]0.96834.2116.6
    SegFFTformer [18]0.97034.38-
    AdaRevD [29]0.97234.60220.8
    Ours0.97334.6280.3
    D²Net [40]0.94031.6032.63
    eSL-Net [49]0.95433.520.19
    MADANET+ [55]0.96433.8416.9
    Vitoria et al. [48]0.94434.335.7
    EFNet [43]0.97235.468.47
    Ours Stage 10.97435.5020.7
    ", + "image_path": "af3c7e3915724ad4ec2af3e576932babdb56a1ac6cdc2dfdadf94115bbd7ebe6.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 391, + 555, + 456 + ], + "lines": [ + { + "bbox": [ + 313, + 391, + 555, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 555, + 456 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with state-of-the-art deblurring methods on synthetic GoPro dataset. Red background represents the best performance. Orange background represents the second best. yellow box represents the third best. Ours Stage 1 represents the framework trained in Stage 1 with events. The underline denotes event-based method." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 467, + 447, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 467, + 447, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 467, + 447, + 479 + ], + "type": "text", + "content": "3.5. Implementation Details" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "type": "text", + "content": "In the RDNet, we set " + }, + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "type": "inline_equation", + "content": "C_b = 64" + }, + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "type": "text", + "content": " and concatenate two DACFB modules at each scale of the image encoder. In the MPG-Diff, we use 1000 diffusion steps and a nosie schedule " + }, + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "type": "inline_equation", + "content": "\\beta_t" + }, + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "type": "text", + "content": " linearly increasing from 1e-6 to 1e-2 for training, and 5 steps for inference. During training, we set the batch size to 4 and use the ADAM optimizer with an initial learning rate of " + }, + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 313, + 484, + 555, + 579 + ], + "type": "text", + "content": ". We implement the algorithm in PyTorch and run it on the NVIDIA RTX 4090 GPU." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 593, + 395, + 606 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 395, + 606 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 395, + 606 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 613, + 435, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 435, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 435, + 624 + ], + "type": "text", + "content": "4.1. Datasets and Metrics" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 636, + 554, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 636, + 554, + 696 + ], + "spans": [ + { + "bbox": [ + 313, + 636, + 554, + 696 + ], + "type": "text", + "content": "GoPro Dataset. We evaluate the effectiveness of the method on the GoPro dataset [31], which is widely used in both image-only and event-based deblurring research. We use ESIM [35] to construct synthetic event data and create an image-like representation from the events [43]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 701, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 555, + 713 + ], + "type": "text", + "content": "REBlur Dataset. 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Qualitative results on the GoPro dataset. 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We adopt two common metrics to quantitatively evaluate the performance of our method, including SSIM and PSNR, which are used to measure the similarity between the predicted results and the corresponding ground truth sharp images." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 55, + 588, + 239, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 588, + 239, + 601 + ], + "spans": [ + { + "bbox": [ + 55, + 588, + 239, + 601 + ], + "type": "text", + "content": "4.2. Comparison on Synthetic Datasets" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 295, + 713 + ], + "type": "text", + "content": "Quantitative results on GoPro datasets are presented in Table 1, while visual results are shown in Figures 1, 4 and 5. We compare the model trained in stage 1 with event-based methods, while comparing the final EGDeblurring with image-only methods, as it only inputs the blurred image during inference. As shown in Table 1, the performance of our method in Stage 1 is better than that of other event-based methods, showing that our RDNet enables effective event-based image deblurring. In quantitative re" + } + ] + } + ], + "index": 37 + }, + { + "type": "table", + "bbox": [ + 348, + 460, + 523, + 621 + ], + "blocks": [ + { + "bbox": [ + 348, + 460, + 523, + 621 + ], + "lines": [ + { + "bbox": [ + 348, + 460, + 523, + 621 + ], + "spans": [ + { + "bbox": [ + 348, + 460, + 523, + 621 + ], + "type": "table", + "html": "
    Image-only methodSSIM↑PSNR↑
    SRN [45]0.96135.10
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    EDI [33]0.96436.52
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    REFID [44]0.97538.34
    Ours Stage 10.97738.51
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    methodSSIM↑PSNR↑
    w/ raw event0.92132.33
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This indicates that utilizing the diffusion model to generate motion prior information can clearly enhance the overall deblurring performance and the robustness to deal with images with complex motion blur." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 339, + 244, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 339, + 244, + 352 + ], + "spans": [ + { + "bbox": [ + 55, + 339, + 244, + 352 + ], + "type": "text", + "content": "4.3. Comparison on Real-world Dataset" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 357, + 296, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 296, + 501 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 296, + 501 + ], + "type": "text", + "content": "Quantitative results are presented in Table 2, while visual results are shown in Figure 6. In the quantitative results, our models from Stage 1 and Stage 3 perform the best among event-based methods and image-only methods, respectively. Our method achieves superior quantitative results, with a " + }, + { + "bbox": [ + 55, + 357, + 296, + 501 + ], + "type": "inline_equation", + "content": "0.3\\mathrm{dB}" + }, + { + "bbox": [ + 55, + 357, + 296, + 501 + ], + "type": "text", + "content": " improvement in PSNR compared to the second best method. The visual results in Figure 6 demonstrate that other methods leave residual blur along the edges of moving objects and exhibit noticeable ghosting artifacts, whereas our method restores sharp edge details. This validates the advantage of using the diffusion model to incorporate motion information into our approach." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 510, + 149, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 149, + 523 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 149, + 523 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 529, + 295, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 529, + 295, + 564 + ], + "spans": [ + { + "bbox": [ + 55, + 529, + 295, + 564 + ], + "type": "text", + "content": "The results of the ablation studies are presented in Table 3 and Figure 7, where we investigate the contribution of each our design to our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 570, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 295, + 713 + ], + "type": "text", + "content": "Effect of MPG-Diff. MPG-Diff is responsible for generating motion prior information. To validate the effectiveness of the diffusion model, we replace it with a convolutional neural network and train it using the same training strategy. Compared to the complete method, the framework without the MPG-Diff shows a decrease in PSNR by " + }, + { + "bbox": [ + 55, + 570, + 295, + 713 + ], + "type": "inline_equation", + "content": "1.64\\mathrm{dB}" + }, + { + "bbox": [ + 55, + 570, + 295, + 713 + ], + "type": "text", + "content": ". This indicates that the motion information prior generated by the convolutional neural network is insufficient to provide adequate guidance for the deblurring task. In contrast, the introduction of the diffusion model enhances the robustness of the generated information, leading to improved overall performance of the method." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 64, + 553, + 102 + ], + "blocks": [ + { + "bbox": [ + 89, + 153, + 261, + 163 + ], + "lines": [ + { + "bbox": [ + 89, + 153, + 261, + 163 + ], + "spans": [ + { + "bbox": [ + 89, + 153, + 261, + 163 + ], + "type": "text", + "content": "Table 3. Ablation studies on the GoPro dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 64, + 553, + 102 + ], + "lines": [ + { + "bbox": [ + 317, + 64, + 553, + 102 + ], + "spans": [ + { + "bbox": [ + 317, + 64, + 553, + 102 + ], + "type": "table", + "html": "
    Metric1 tensor2 tensors (ours)3 tensors4 tensors5 tensors
    SSIM↑0.9690.9730.9710.9730.972
    PSNR↑34.1034.6234.6134.6134.59
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    Metric1× dimension2× dimension4× dimensionOurs with two-value
    SSIM↑0.9690.9700.9710.973
    PSNR↑34.1034.1234.2334.62
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Dense features represent motion information similar to event representations while ensuring that the diffusion model can generate corresponding prior features robustly. To validate that dense features is superior to directly generating event representation, we remove the FE and train the diffusion model to directly generate events (as shown in \"w/ raw event\" in Table 3 and 7). Both quantitative and qualitative results indicate a substantial decline in the framework's deblurring performance. This indicates that introducing dense feature representation is more beneficial to the generation of the diffusion model and the performance of the overall framework." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 419, + 554, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 419, + 554, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 554, + 528 + ], + "type": "text", + "content": "Effect of detail guidance. The detail guidance " + }, + { + "bbox": [ + 313, + 419, + 554, + 528 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 313, + 419, + 554, + 528 + ], + "type": "text", + "content": ", along with the blurred image, constrain the generation process of the diffusion model. We remove the detail guidance and only use the blurred image to constrain the output of the diffusion model. The deblurring results are negatively impacted, showing a 0.78 dB decrease in PSNR compared to the complete method. This indicates that the detail guidance constrain the output of the diffusion model, leading to the generation of more effective guiding features for deblurring." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 533, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 713 + ], + "type": "text", + "content": "Effect of DACFB. The DACFB embedded in the RDNet fuses motion information features and image features through a cross-modal attention mechanism. We replace the DACFB in the RDNet with simple feature concatenation and convolutional layers, and train the model according to the original strategy. Quantitative results indicate a reduction in deblurring performance, with a decrease of " + }, + { + "bbox": [ + 313, + 533, + 555, + 713 + ], + "type": "inline_equation", + "content": "0.71\\mathrm{dB}" + }, + { + "bbox": [ + 313, + 533, + 555, + 713 + ], + "type": "text", + "content": " in PSNR. This demonstrates that, compared to simple concatenation, the DACFB effectively aligns and fuses the two different modalities. We verify the effectiveness of our scheme by adjusting the number of value tensors in the attention mechanism. 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Conclusion" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 296, + 714 + ], + "type": "text", + "content": "We have presented EGDeblurring, a method that allows to achieve high-quality image deblurring by generating event guidance carrying the desired motion prior information using a diffusion model. Specifically, we design a motion prior generation diffusion model to generate event guidance from a single blurry image, and a regression de" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 313, + 574, + 555, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 555, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 555, + 658 + ], + "type": "text", + "content": "blurring network that can effectively utilize the motion prior information in the event guidance for image deblurring. Unlike existing event-based methods, our method can test with a single blurry image, without using ground truth event as input. Extensive experiments on both synthetic and real-world blur datasets demonstrate that our proposed method outperforms current state-of-the-art approaches." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 555, + 713 + ], + "type": "text", + "content": "Acknowledgment. This work was supported by the National Natural Science Foundation of China (62471499), the Guangdong Basic and Applied Basic Research Foundation (2023A1515030002)." + } + ] + } + ], + "index": 43 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2201" + } + ] + } + ], + "index": 44 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 91, + 295, + 712 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 61, + 91, + 294, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 294, + 113 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 294, + 113 + ], + "type": "text", + "content": "[1] Abdullah Abuolaim and Michael S Brown. 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In ICCV, 2023. 2" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2203" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_content_list.json b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d7bb657d1865a48101caa793a719e7e16d04ddd5 --- /dev/null +++ b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_content_list.json @@ -0,0 +1,1458 @@ +[ + { + "type": "text", + "text": "Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling", + "text_level": 1, + "bbox": [ + 135, + 128, + 864, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yinuo Wang $^{1,*,‡}$ , Yanbo Fan $^{2,*,†}$ , Xuan Wang $^{2}$ , Guo Yu $^{1,†}$ , Fei Wang $^{1}$ $^{1}$ National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University", + "bbox": [ + 183, + 202, + 815, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Ant Group\nnuolwang.github.io/DiffListener", + "bbox": [ + 357, + 273, + 633, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 246, + 344, + 328, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Listening head generation aims to synthesize non-verbal responsive listening head videos that naturally react to a certain speaker, for which, both realistic head movements, expressive facial expressions, and high visual qualities are expected. Previous approaches typically follow a two-stage pipeline that first generates intermediate 3D motion signals such as 3DMM coefficients, and then synthesizes the videos by deterministic rendering, suffering from limited motion expressiveness and low visual quality (e.g. $256 \\times 256$ ). In this work, we propose a novel listening head generation method that harnesses the generative capabilities of the diffusion model for both motion generation and high-quality rendering. Crucially, we propose an effective hybrid motion modeling module that addresses training difficulties caused by the scarcity of listening head data while preserving the intricate details that may be lost in explicit motion representations. We further develop a tailored control guidance for head pose and facial expression, by integrating their intrinsic motion characteristics. Our method enables high-fidelity video generation with $512 \\times 512$ resolution and delivers vivid listener motion feedback. We conduct comprehensive experiments and obtain superior performance in terms of both visual quality and motion expressiveness compared with existing methods.", + "bbox": [ + 86, + 376, + 485, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 91, + 767, + 223, + 782 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Listening head generation aims to generate responsive listener videos that react to the corresponding speaker [46]. Unlike talking head videos, the listener's response mainly consists of non-verbal behaviors, such as nodding, smil", + "bbox": [ + 89, + 792, + 483, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing, frowning, head shaking, etc. The realism and vividness of the listener feedback are vital to the success of speaker and listener communication. Being a crucial part of digital avatar generation, listening head generation has many potential applications, such as movie production, online customer service, and human-computer interaction.", + "bbox": [ + 511, + 345, + 906, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While most works focus on speaker-centric talking head generation [16, 17, 26-28, 37, 44], only a few study listening head generation [21, 24, 25, 46]. It is a non-trivial problem as given a certain speaker video, there can be many reasonable listener reactions. Such a one-to-many mapping problem makes it challenging for the model to learn to generate proper yet diverse listener motions. In addition, since the generated listening head mostly contains non-verbal reactions, the audience may focus more on the listeners' facial expressions, requiring that the generated reaction videos be high-fidelity to manifest detailed and subtle expressions.", + "bbox": [ + 511, + 441, + 908, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The state-of-the-art works of listening head generation follow a two-stage design that first generates intermediate listener motion signals and then synthesizes the RGB videos with post-rendering [20, 21, 35, 46]. For motion generation, explicit 3D motion signals, such as 3DMM [3] coefficients are used as motion descriptions. Existing works developed different models to generate the listener's 3D motion coefficients, including LSTM [46], VQ-VAE [35], and diffusion-based models [20, 21]. As for the video rendering, PIRenderer [29] is used to generate the RGB frames conditioned on the generated 3DMM coefficients. Though promising, they still fall short of generating expressive and natural listening head motions, as well as photorealistic rendering. For instance, 1) the intermediate parametric 3D motion signals, such as the 3DMM expression coefficients, are characterized in a low-dimensional generalizable subspace and lack facial details and subtle expressions, which limits the richness and naturalness of the learned facial expressions, 2) while focusing more on motion generation, the determinis", + "bbox": [ + 511, + 613, + 908, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 107, + 862, + 217, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors", + "bbox": [ + 109, + 875, + 238, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "This work was done during Yinuo Wang's internship at Ant Group", + "bbox": [ + 109, + 887, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15885", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tic rendering used in existing works is of low visual quality, suffering from low resolution (e.g. $256 \\times 256$ ), identity inconsistency, improper head motions, and facial artifacts.", + "bbox": [ + 89, + 90, + 480, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a novel listening head generation framework that enables both highly expressive head motions and photorealistic rendering. Our motivation is to fully leverage the generative ability of the diffusion model for both motion generation and video synthesis. Recently, the latent diffusion model (LDM) [30] has shown superior ability in high-resolution and vivid video generation, largely promoting the speaker-centric talking head generation performance [7, 34, 41]. Nevertheless, it is not feasible to directly apply these methods to listening head generation. Firstly, they require hundreds of hours of talking head videos for training the audio-to-visual correspondence, which does not apply to listening head generation, where only a few hours of training data are available. Secondly, due to the high computational and memory cost, these methods can only model the context information in a small window size (e.g. 16 frames in [34]). This is acceptable for talking head generation since talking heads have a strong correlation with the audio. However, for listening head generation, the listener feedback may be related to an even longer duration of the speaker's content. To generate a reasonable reaction, it may require long-term modeling of audio conditions and motion. Based on these, it is nontrivial to unleash the diffusion generative ability for listening head generation.", + "bbox": [ + 91, + 140, + 482, + 516 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose a novel hybrid motion modeling method, which consists of an explicit and explainable 3D motion representation and a learnable implicit latent representation. Specifically, instead of utilizing the LDM-based rendering to generate listening video directly from the speaker's input, we first learn explicit 3D motion signals by a diffusion-based motion generation module. The explicit motions are later used as guiding conditions to train the rendering module. To facilitate controllability, we propose distinct control strategies considering the different intrinsic natures of head poses and facial expressions. The explicit motion generation module is expected to generate feasible and diverse listener motions but may lack facial details, as analyzed above. We further develop an implicit motion refinement module to complement the potentially missing facial details. With these designs, we successfully train the LDM-based rendering model on the small-scale listening dataset, enabling high-fidelity rendering (e.g. $512 \\times 512$ ) and vivid and expressive listener motion generation. Compared with the existing methods, we significantly boost listening head generation performance in both visual and motion quality.", + "bbox": [ + 89, + 520, + 482, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The hybrid motion design brings several advantages, 1) the explicit motion generation module is lightweight and takes much less computational resources than directly mod", + "bbox": [ + 89, + 854, + 482, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "eling audio-to-visual correspondence, making it possible to learn the long-term relations between speaker and listener, which is essential for listener motion modeling. 2) The learning of the hybrid motion representation is much easier than the pure latent motion modeling, especially on limited training data. In addition, with the intermediate explicit representation, we can better utilize talking videos to pre-train the rendering module. We conduct thorough ablation studies and verify the necessity of the hybrid motion modeling. Our contributions are as follows,", + "bbox": [ + 511, + 90, + 903, + 239 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel diffusion-based method for motion generation and visual rendering, resulting in realistic and vivid listening head generation.", + "- We introduce an effective hybrid motion modeling module that overcomes training challenges while enhancing both motion dynamics and visual quality.", + "- We conduct comprehensive experiments and significantly improve listening head generation in both visual quality and motion quality compared with existing methods." + ], + "bbox": [ + 511, + 242, + 903, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 513, + 392, + 661, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Non-verbal Listening Head Generation. Non-verbal listening head generation is an important part of digital avatar generation, and has drawn increasing research interests in recent years. Earlier works [4, 5, 10, 15, 32] use rule-based methods to generate the listener response. Such methods require specifically designed rules and pre-defined reaction motion sequences. Thus they have very limited motion diversity and expressiveness.", + "bbox": [ + 511, + 417, + 903, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning-based methods alleviate the problem by using data-driven approaches to automatically learn to generate proper reactions given speaker conditions. Zhou et al. [46] propose an LSTM-based network RLHG that predicts the listener's head poses and 3DMM expression coefficients given speaker's audio and motions. Later, several works are proposed to improve the performance of RLHG by refining the conditional features [6, 45] or improving visual quality [14]. However, these works are deterministic models and are inefficient in addressing the one-to-many mapping problems in listener motion generation, resulting in unnatural motions. To alleviate this, the work of [25] models the listener motion with VQ-VAE. Song et al. [31] proposes a more fine-grained codebook that supports emotion control. Liu et al. [20] further improves the diversity of the generated motion by a diffusion model. In addition, the work of Liu et al. [21] improves the controllability of the diffusion-based motion generation model by aggregating the user-specified expression and pose labels. Focusing on intermediate motion generation, these methods suffer from limited expressiveness and naturalness in the generated videos.", + "bbox": [ + 511, + 537, + 903, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion Generative Models on Head Generation. Denoising diffusion probabilistic models [13] have shown remarkable results on image generation tasks. An iconic work", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15886", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4b60f0904798e2a909ef3e9570f4b7ced397e5822a692fb20ec2e00c5b0cc4d0.jpg", + "image_caption": [ + "Figure 1. Overview of the proposed framework. Given one listener portrait image and speaker's audio and head motion as input, we generate realistic and vivid listening head video. (a) is a lightweight diffusion transformer to generate the explicit motion representation, (b) is a reference net to extract the listener identity feature, (c) is our generation backbone, (d) is the implicit motion refinement module." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 901, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "is Stable Diffusion (SD), which is based on latent diffusion model (LDM) [30] and can generate high-resolution images. Guo et al. [11] propose a plug-in motion module and a lightweight fine-tuning technique that enables Stable Diffusion to generate animated clips. Based on these works, Tian et al. [34] propose EMO, a direct audio to talking head video generation framework that discards intermediate 3DMM representations. Benefiting from the capability of Stable Diffusion, EMO outperforms previous talking head generation methods in terms of expressiveness and realism. Several other diffusion-based audio driven works are proposed after EMO, and achieve promising results [7, 18, 41], proving the powerful generative capabilities of diffusion models in talking head generations. Nevertheless, these models require hundreds of hours training data. This can be an obstacle for training the listening head generation model, where only a few hours of data are available.", + "bbox": [ + 88, + 469, + 485, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 89, + 739, + 183, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a single listener portrait image and a speaker's audio and video, we aim to generate a non-verbal responsive listening head video that synchronizes with the speaker, with detailed facial expressions and natural head movements. Our overall framework is shown in Fig. 1.", + "bbox": [ + 89, + 763, + 483, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 89, + 848, + 232, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first introduce the preliminaries of the diffusion model [13, 30], which is a key component of our frame", + "bbox": [ + 89, + 869, + 483, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "work. The diffusion model defines a Markov chain of adding random noise to data samples and then trains the network to learn the reverse process, so that it can generate desired data from random noise. The forward diffusion process is defined as,", + "bbox": [ + 511, + 469, + 906, + 546 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 556, + 906, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ , and $\\overline{\\alpha}_t$ is a hyper-parameter that controls the diffusion rate. With Eq. (1), we can sample at arbitrary step $t$ to get the noised sample. Then the reverse diffusion process trains a neural network to predict the noise $\\epsilon_t$ added to the samples at step $t$ , and the overall training objective is simplified as [13]:", + "bbox": [ + 511, + 585, + 905, + 676 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t} = \\mathbb {E} _ {t \\sim [ 1, T ], \\mathbf {x} _ {0}, \\epsilon_ {t}} [ | | \\epsilon_ {t} - \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t, \\mathbf {c}) | | ^ {2} ], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 688, + 906, + 707 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}$ is predicted using a neural network with parameters $\\theta, T$ is the max step, and $\\mathbf{c}$ is the additional condition.", + "bbox": [ + 511, + 717, + 905, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Network Pipeline", + "text_level": 1, + "bbox": [ + 511, + 757, + 684, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathbf{A} \\in \\mathbb{R}^{N \\times d_a}$ and $\\mathbf{S} \\in \\mathbb{R}^{N \\times d}$ denote the speaker's audio and 3D head motion features, where $N$ is the number of frames, $d_a$ and $d$ are dimensionality of audio and speaker's motion features respectively. Let $\\mathbf{I} \\in \\mathbb{R}^{h \\times w \\times c}$ be the listener portrait for identity reference. As shown in Fig. 1, to enable high-fidelity rendering and vivid responsive head motion generation, 1) we adopt an LDM-based high-fidelity rendering module to harness the power of diffusion models,", + "bbox": [ + 511, + 777, + 906, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15887", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "so the visual qualities of the generated videos can be greatly improved. 2) We propose a novel hybrid motion modeling module that consists of a lightweight explicit motion generation module to generate explicit guiding motions, i.e. head poses and facial expressions, a tailored control strategy for the rigid head poses and non-rigid facial expressions, and an implicit and learnable motion refinement module to complement the motion details. 3) To enhance the identity consistency of the generated video, a parallel reference net with similar structure as the rendering module is used to integrate the listener identity features. We introduce each part next.", + "bbox": [ + 89, + 90, + 480, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "High-fidelity Rendering Module. One major limitation of the existing listening head generation methods is the deterministic rendering module such as PIRenderer [29], which suffers from low resolution, identity inconsistency, and visual artifacts. Inspired by the recent advance in diffusion-based talking head generation works [34, 36, 39], we design a high-fidelity rendering module based on SD 1.5. To enable the video generation capability of SD 1.5, we follow the motion module design [11, 19] that applies self attention along the temporal dimension of the network's intermediate features, ensuring the continuity and consistency along the generated video frames. Benefiting from the probabilistic nature and the great generative capabilities, the proposed rendering module can generate photorealistic videos with detailed visuals and expressive motions.", + "bbox": [ + 89, + 257, + 482, + 483 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conditioned on reference image $\\mathbf{I}$ , and speaker features $\\mathbf{A}$ and $\\mathbf{S}$ , the rendering module $\\mathcal{R}$ takes noised latent $\\mathbf{V}_t \\in \\mathbb{R}^{N \\times h \\times w \\times c}$ at step $t$ as inputs, and predicts the denoised latent $\\hat{\\mathbf{V}}_0$ :", + "bbox": [ + 89, + 484, + 482, + 544 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {V}} _ {0} = \\mathcal {R} \\left(\\mathbf {V} _ {t}, t, \\mathbf {c}\\right), \\mathbf {c} = \\{\\mathbf {A}, \\mathbf {S}, \\mathbf {I} \\}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 556, + 482, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, facing the scarcity of the listening head data, it's not feasible to train the rendering module directly from speaker features alone. So we propose a novel hybrid motion modeling method where we use explicit listener motion $\\hat{\\mathbf{L}}$ as an additional guiding signal to ease the training of the rendering module. $\\hat{\\mathbf{L}}$ is set to 51-dim facial expression coefficient and 6-dim head pose coefficients extracted by MediaPipe [23]. The generation procedure becomes:", + "bbox": [ + 89, + 585, + 482, + 707 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {V}} _ {0} = \\mathcal {R} \\left(\\mathbf {V} _ {t}, t, \\mathbf {c}\\right), \\mathbf {c} = \\{\\hat {\\mathbf {L}}, \\mathbf {A}, \\mathbf {S}, \\mathbf {I} \\}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 718, + 482, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{L}}$ is generated by a lightweight motion generation module, given the speaker features $\\mathbf{A}$ and $\\mathbf{S}$ .", + "bbox": [ + 89, + 750, + 482, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Explicit Motion Generation. We design a transformer diffusion-based explicit motion generation module, inspired by the successful applications of diffusion models on various human motion generations [1, 21, 33, 42]. The motion generation module generates both listener's facial expressions and head poses with a lightweight diffusion network, addressing the one-to-many mapping problem as well as enabling us to model motions in larger time window.", + "bbox": [ + 89, + 780, + 482, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a noised motion sequence $\\mathbf{L}_t\\in \\mathbb{R}^{M\\times d}$ at step $t$ the explicit motion generation module $\\mathcal{G}$ aims to predict the clean sample $\\hat{\\mathbf{L}}$ condition on speaker features A and S:", + "bbox": [ + 511, + 90, + 903, + 136 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {L}} = \\mathcal {G} (\\mathbf {L} _ {t}, t, \\mathbf {c}), \\mathbf {c} = \\{\\mathbf {A}, \\mathbf {S} \\}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 148, + 903, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 1 (a), the noised motion sequence $\\mathbf{L}_t$ is mapped to the latent space and then encoded by a transformer encoder. In the meantime, the speaker features, i.e. speakers facial expression features and audio features are integrated by a cross-modal transformer, where we use a pretrained speech model wav2vec 2.0 [2] to encode the raw audio. Then a transformer decoder is used to generate denoised sequence, where the integrated speaker features are used as keys and values.", + "bbox": [ + 511, + 176, + 906, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Explicit Motion Guidance. $\\hat{\\mathbf{L}}$ generated by Eq. (5) contains the learned explicit 3D head poses and facial expression coefficients. It serves as a explicit motion guidance in our design. There are other options for explicit motion representation such as mesh, normal maps etc. We choose expression coefficients because it's more compact and semantic meaningful. The ways to inject conditional information are crucial in diffusion models. An intuitive way to add controllability of head poses and facial expressions might be concatenating these features and injecting to the layers of the rendering module via cross-attention operator, which is a common practice in existing methods. However, in practice, such an operation leads to sub-optimal head pose and expression controllability. Considering the different intrinsic nature of head poses and facial expressions, i.e. head pose is a global rigid transformation that decides the position of the generated head while facial expression is a local non-rigid transformation that focuses more on the visual details, we opt to use distinct conditional strategies for head pose and facial expressions accordingly.", + "bbox": [ + 511, + 311, + 906, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, for pose control, we generate explicit pose images $\\mathbf{P}$ as guidance. We use three facial key points (the inner corners of the eyes and nose tip) and synthesize the pose guidance images by connecting them. Then, a pose guidance net consists of multiple convolutional layers is designed to extract multi-resolution features of the pose guidance images, and the extracted features are added to the latent features of the same resolution in the downsample blocks of the rendering module:", + "bbox": [ + 511, + 614, + 905, + 750 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {h}} _ {d} ^ {(i)} = C o n v _ {i} (\\mathbf {P}) + \\mathbf {h} _ {d} ^ {(i)} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 761, + 903, + 782 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Conv_{i}$ is the $i$ -th convolutional layer in the pose guidance net, its output has the same dimensionality as the latent features $\\mathbf{h}_{d}^{(i)}$ in the downsample blocks of rendering module.", + "bbox": [ + 511, + 792, + 903, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As for the facial expression control, we adopt more fine-grained control where we inject the facial expression features $\\mathbf{F}$ into the rendering module through additional cross", + "bbox": [ + 511, + 854, + 903, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15888", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c54b41eeeba2a34d2a35c9d982f1f82dddc87db2f535805efc9e8f1d65008c6b.jpg", + "image_caption": [ + "Figure 2. Visualization of the compared methods. Our method exhibits highly detailed visuals, accurate motion, and identity consistency." + ], + "image_footnote": [], + "bbox": [ + 96, + 87, + 903, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "attention layers, one after each reference layer, and the facial expression features $\\mathbf{F}$ are use as keys and values, as follows", + "bbox": [ + 89, + 508, + 482, + 551 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} _ {e} ^ {(l)} = \\operatorname {C r o s s A t t n} \\left(\\mathbf {h} _ {r} ^ {(l)}, \\mathbf {F}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 551, + 482, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{h}_r^{(l)}$ is the output of the $l$ -th reference layer.", + "bbox": [ + 89, + 574, + 423, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implicit Motion Refinement. Though the explicit motion guidance introduced above eases the training difficulty, the explicit motion representation $\\hat{\\mathbf{L}}$ has limitations in depicting the facial details and subtle expressions, restricting the overall generation quality. We further propose an implicit motion refinement module to complement the explicit motion representation. Concretely, during the motion refining process, the speaker features (i.e. audio features $\\mathbf{A}$ and facial expression features $\\mathbf{S}$ ) are first integrated, then injected into a cross-attention layer as keys and values, and the latent feature map generated after the explicit motion modeling serving as the query, the motion refinement is", + "bbox": [ + 88, + 592, + 482, + 773 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} _ {i} ^ {(l)} = C r o s s A t t n _ {s} [ \\mathbf {h} _ {e} ^ {(l)}, C r o s s A t t n _ {i} (\\mathbf {S}, \\mathbf {A}) ] + \\mathbf {h} _ {e} ^ {(l)}. (8)\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 781, + 482, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We add this refinement module after each explicit facial expression cross-attention layer by residual connections.", + "bbox": [ + 89, + 809, + 482, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reference Net. Inspired by [34], we adopt a parallel network that has a similar structure as the rendering module to inject the identity features. Since the reference net and the rendering module both inherit structures and weights from", + "bbox": [ + 89, + 840, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SD 1.5, the corresponding layers of the two networks share certain similarities. We feed the reference image $\\mathbf{I}$ to the reference net and use its intermediate UNet block features to guide the denoising process of the rendering module. Concretely, the features $\\mathbf{r}_s^{(l)}$ from self-attention layers of the reference net are first concatenated with the corresponding layers' features $\\mathbf{h}_s^{(l)}$ from the rendering module, then undergo a cross-attention layer to inject the identity information into the denoising process:", + "bbox": [ + 511, + 508, + 906, + 648 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} _ {r} ^ {(l)} = \\operatorname {C r o s s A t t n} \\left[ \\mathbf {h} _ {s} ^ {(l)}, \\left(\\mathbf {h} _ {s} ^ {(l)} \\oplus \\mathbf {r} _ {s} ^ {(l)}\\right) \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 657, + 906, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the concatenated features are used as keys and values.", + "bbox": [ + 511, + 688, + 903, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Training Strategy", + "text_level": 1, + "bbox": [ + 511, + 712, + 687, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training of our method has two stages. In the first stage, the motion generation module is trained on listening head datasets while the rendering module is pretrained on listening head dataset together with a large scale talking head dataset VFHQ [40]. For the rendering module pretrain, we do not incorporate the speaker information, and the ground truth head poses and facial expression coefficients are used as guidance signals. In the second stage, we train the implicit motion refinement part in the rendering backbone. In this stage, we incorporate the explicit motion generated by the motion generation module as guidance.", + "bbox": [ + 511, + 734, + 906, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15889", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a1a1d42fc07b3cb4d3e0d4093c4b2cc16f6505a89429ee3a654b08567ec99f11.jpg", + "image_caption": [ + "Figure 3. Visualization of the ablation study on explicit motion guidance. We highlight the artifacts of the compared method with red boxes." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 473, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/41420fbb0750454dfa309594f59f0ec7148d31d9477afe324b239bec150cf576.jpg", + "image_caption": [ + "Figure 4. Visualization of the ablation study on different motion control schemes. We highlight the inaccurate head poses and facial expressions, as well as visual artifacts with red boxes." + ], + "image_footnote": [], + "bbox": [ + 99, + 290, + 475, + 428 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 89, + 505, + 220, + 522 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 89, + 530, + 279, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We conduct experiments on the widely used ViCo dataset [46] and RealTalk dataset [9]. Both ViCo and RealTalk consist of videos of face-to-face daily conversations between two individuals of diverse ages, genders, and ethnicity. We follow the training and testing split provided in their original papers. ViCo contains 398 clips of total 1.3 hours for training, 43 clips for testing, and 42 clips for out-of-distribution (OOD) testing. RealTalk contains 1489 clips of total 6.4 hours for training and 407 clips for testing. Additionally, VFHQ dataset [40], a large-scale high-quality talking head video dataset containing over 16k clips, is used to pretrain the rendering module.", + "bbox": [ + 89, + 551, + 482, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. For both datasets, we crop the original videos into $512 \\times 512$ face videos for training and testing, and use MediaPipe [23] to extract 51-dim facial expression coefficients and 6-dim head pose. For the motion generation module, we train it with the input sequence of 50 frames and a batch size of 64. The diffusion step is set to 1000 for training and inference. For the high-fidelity rendering, we set the input to 16 frames with a batch size of 8. The diffusion step is 1000 for training and 25 for inference. Both modules are trained with AdamW [22] optimizer.", + "bbox": [ + 89, + 734, + 482, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared Methods. We compare the proposed method", + "bbox": [ + 89, + 885, + 482, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ed4e16e5eb40d9a27244ceabe8d07512250ca78a1e3fdbbedc9ffa4e18950d50.jpg", + "image_caption": [ + "Figure 5. Visualization of the ablation study on implicit motion refinement. We highlight the inaccurate motion with red boxes and the improved facial details with green box." + ], + "image_footnote": [], + "bbox": [ + 524, + 87, + 897, + 224 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with several state-of-the-art listening head generation methods, including RLHG [46], PCH [14], L2L [25], MFR-Net [20] and CustomListener [21]. We retrain RLHG, PCH and L2L on both ViCo and RealTalk dataset. Since MFR-Net and CustomListener are not open-sourced, we list their results on ViCo dataset from the original papers for reference. We also conduct thorough ablation studies to verify the effectiveness of the proposed method.", + "bbox": [ + 511, + 305, + 903, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. We compare both visual and motion quality for evaluation. The visual quality is evaluated by Fréchet Inception Distance (FID) [12], Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity (SSIM) [38]. For the motion quality evaluation, we adopt 1) Feature Distance (FD), the $L_{1}$ distance between the generated motion and the ground truth motion, 2) $\\mathrm{FID}_{\\Delta \\mathrm{fm}}$ [43], the FID score of motion difference between consecutive frames, and 3) Sequence Naturalness Distance (SND) [43], the summarization of $\\mathrm{FID}_{\\Delta \\mathrm{fm}}$ and FID score of motion. For $\\mathrm{FID}_{\\Delta \\mathrm{fm}}$ and SND, we concatenate the angle and translation to compute the overall pose metrics. To compare with existing works, we extract the 3DMM coefficients by [8], to compute the motion quality metrics.", + "bbox": [ + 511, + 426, + 905, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Quantitative Results", + "text_level": 1, + "bbox": [ + 511, + 648, + 705, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The quantitative results on RealTalk and ViCo are listed in Table 1 and Table 2, respectively.", + "bbox": [ + 511, + 672, + 903, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the visual quality, our proposed method obtains significantly better visual quality in terms of SSIM, PSNR and FID on both Realtalk and ViCo datasets. For instance, on RealTalk dataset, the relative performance improvements are $14\\%$ for SSIM, $14\\%$ for PSNR, and $33\\%$ for FID. On ViCo dataset, the improvements are $12\\%$ for SSIM, $15\\%$ for PSNR, and $5\\%$ for FID. These demonstrate the superior high-fidelity generative capability of our proposed method. This is due to the proposed rendering module is much more powerful than the deterministic PIRenderer, and that the hybrid motion modeling further enhances the visual quality of the rendering module.", + "bbox": [ + 511, + 703, + 905, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the motion quality, our method also achieves the", + "bbox": [ + 531, + 885, + 903, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15890", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7b1d05818c64ddc66ec8ec87955f5ef8d73a135ee73c09cc50fa1d1353cbb1a9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodsSSIM↑PSNR↑FID↓FD↓FIDΔfm ↓SND↓
    expangletransexpposeexppose
    RLHG [46]0.5717.8720.7913.095.916.0212.010.742.090.04
    PCH [14]0.5717.7820.0513.805.695.9911.360.722.110.04
    L2L [25]0.5015.6127.2822.9211.779.1910.930.587.810.14
    Ours0.6520.3413.3810.493.955.126.000.051.490.02
    ", + "bbox": [ + 171, + 88, + 826, + 195 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1125068ff4c6162a47d42527b88a5a1300a345655e77a07be638bef250dff7ae.jpg", + "table_caption": [ + "Table 1. Quantitative results on RealTalk dataset, where the values of FD and $\\mathrm{FID}_{\\Delta \\mathrm{fm}}$ are multiplied by 100. The $\\uparrow$ indicates the higher the better while $\\downarrow$ indicates the lower the better. The best and the second best results are in bold and underlined, respectively." + ], + "table_footnote": [], + "table_body": "
    MethodsTest setSSIM↑PSNR↑FID↓FD ↓FIDΔfm ↓SND ↓
    expangletransexpposeexppose
    RLHG [46]Dtest0.5817.8838.6916.439.056.759.540.763.450.09
    Dood26.709.7510.617.360.559.380.14
    PCH [14]Dtest0.6017.9231.6215.488.845.958.910.733.010.09
    Dood24.117.2710.056.070.477.790.11
    L2L [25]Dtest0.5817.7538.3920.3612.528.8812.060.606.610.19
    Dood23.828.107.438.670.518.160.07
    MFR-Net* [20]Dtest0.5917.8220.0813.376.826.02////
    Dood14.708.126.37////
    CustomListener* [21]Dtest0.6017.9820.0611.546.125.903.120.062.400.07
    Dood12.677.496.013.590.075.940.05
    OursDtest0.6720.6018.9912.547.575.685.130.082.360.08
    Dood11.893.835.435.050.052.060.02
    ", + "bbox": [ + 112, + 247, + 885, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative results on ViCo dataset, where the values of FD and $\\mathrm{FID}_{\\Delta \\mathrm{fm}}$ are multiplied by 100. The $\\uparrow$ indicates higher is better for the corresponding metric while $\\downarrow$ indicates lower is better. The * denotes we report the results from their papers. The best and the second best results are in bold and underlined respectively.", + "bbox": [ + 89, + 482, + 906, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "best overall performance on both datasets. Specifically, for RealTalk, we achieve the best results on all motion metrics. In terms of FD, we obtain $20\\%$ , $31\\%$ , and $15\\%$ performance improvement for the expression, angle, and translations, respectively. In terms of $\\mathrm{FID}_{\\Delta \\mathrm{fm}}$ , the performance improvements are $45\\%$ for expression and $91\\%$ for head pose. On ViCo dataset, we also obtain the best motion quality on the OOD set and the second-best results on the test set. For ViCo, the motion of the test set is much more intense and random than that of the OOD set. The one-to-many characteristic makes it more difficult to generate the exact motion as the ground truth on the test set. In such cases, CustomListener that additionally incorporates the ground-truth motion text description leads to more similar motions to the ground-truth. Nevertheless, the superior performance on the OOD set demonstrates our better generalization ability. These results verify that our method can largely promote the visual and motion quality, enabling realistic and vivid listening head generation.", + "bbox": [ + 88, + 551, + 482, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 89, + 848, + 274, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare the visualization result with RLHG, L2L and PCH. MFR-Net and CustomListener are not open-sourced", + "bbox": [ + 89, + 869, + 482, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and their visualization is not available. As shown in Fig 2, our method surpasses the baseline methods in terms of visual quality, motion accuracy, and identity consistency. To be specific, 1) in Fig. 2 (a), our method generates a proper reaction video while the baseline methods show inappropriate facial expressions. 2) in Fig. 2 (b, c), we obtain much better identity preservation, even under more drastic facial expressions, e.g. laughing. 3) in Fig. 2 (b, c, d), our method retains better facial details, such as realistic teeth, wrinkles, and natural complexities.", + "bbox": [ + 511, + 551, + 906, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 511, + 712, + 666, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct ablations to demonstrate the necessities of each part of the proposed hybrid motion modeling.", + "bbox": [ + 511, + 734, + 905, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Explicit Motion Modeling. We remove the intermediate explicit motion guidance and train a diffusion UNet that learns the listener motion purely from implicit motion modeling, i.e. the rendering module in Section 3.2 without pose guidance net and expression attention layers. The network is first pretrained on VFHQ and Realtalk dataset for unconditioned image generation, then trained on Realtalk dataset for listening head generation conditioned on speaker features. As shown in Table 3, without the motion guidance,", + "bbox": [ + 511, + 763, + 906, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15891", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dd71fc8fe5e7bbde5743db5f38b1613889635399a406f3d92f3b77b96b1b7508.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
    MethodsSSIM↑PSNR↑FID↓FD↓FIDΔfm ↓SND↓
    expangletransexpposeexppose
    w/o motion guidance0.6319.7514.3711.024.285.009.050.121.670.02
    w/o implicit motion refinement0.6420.1713.5811.004.055.176.840.061.610.02
    Ours0.6520.3413.3810.483.945.126.000.051.480.02
    ", + "bbox": [ + 132, + 88, + 866, + 176 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6927e5c1a7eb6c33a9044fdd0f49388fb9e4b68a67db627f05363adf242d7098.jpg", + "table_caption": [ + "Table 3. Ablation study on motion modeling, tested on Realtalk dataset, the values of FD and $\\mathrm{{FID}}_{{\\Delta }_{\\mathrm{{fm}}}}$ are multiplied by 100 ." + ], + "table_footnote": [], + "table_body": "
    SettingsFD↓FIDΔfm ↓
    expangletransexppose
    Concatenate pose7.813.034.369.870.10
    Separate control7.482.014.284.690.10
    ", + "bbox": [ + 102, + 224, + 470, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study on different motion control schemes, tested on Realtalk dataset, the values of FD and $\\mathrm{FID}_{\\Delta \\mathrm{fm}}$ are multiplied by 100.", + "bbox": [ + 89, + 308, + 482, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "both the visual quality and the motion quality of the generated listening head degrades. It can be observed that $\\mathrm{FID}_{\\Delta \\mathrm{fm}}$ has significantly degrades, indicating there are unnatural transitions of expression and head poses. As shown in Fig. 3, without motion guidance, the network struggles to generate continuous head poses and expressions, often resulting in serious artifacts in faces. Such result proves that the explicit motion guidance can effectively ease the training of LDM-based models on small scale datasets.", + "bbox": [ + 88, + 382, + 482, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Distinct Controls of Pose and Expressions. In Section 3.2, we propose to use separate controls of head pose and facial expression according to the intrinsics of these two types of motion signals. To validate the effectiveness of the proposed control strategies, we remove the pose images in the rendering module, and concatenate the head pose coefficients with the facial expression coefficients. The concatenated motion signal is injected into the rendering module through the expression cross-attention layer. The results in Table 4 show that using concatenated motion as the control signal leads to a degeneration in both motion accuracy and naturalness, especially on expression metrics. We also present some visualizations in Fig. 4. From the visualization, there exists inaccurate pose control and visual artifacts when using concatenated motion signals (the left example), and poor expression controllability (the right example). These results verify the effectiveness of the proposed pose and expression controls.", + "bbox": [ + 91, + 520, + 482, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Implicit Motion Refinement. Furthermore, we validate the effectiveness of the proposed implicit motion refinement method. As shown in Table 3, without the refinement module, the motion quality and visual quality of the generated video both degrade. As shown in Fig. 5, we observe mainly two effects of the implicit motion refinement. The first is that the refinement fixes some wrong facial expressions (the", + "bbox": [ + 89, + 795, + 482, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "left example), and the second is that it tends to add more facial details to the generated videos, such as more realistic wrinkles (the right example). As a result, we can observe more stable and detailed facial expressions after refinement. This implies that the implicit motion refinement helps the rendering module learn to revise the details of the generated videos given additional conditions, further improving the visual qualities.", + "bbox": [ + 511, + 227, + 903, + 348 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "**Discussions.** Our proposed framework can generate high fidelity listening head videos with accurate motion, vivid facial details and expressive motions. Nevertheless, there are still some limitations. 1) The condition used to generate listening heads is restricted within the speaker's audio and facial expressions. But more flexible conditions such as text description, motion styles etc. are always appreciated. The proposed hybrid motion generation has the potential of integrating diverse control signals, we will study this in the future. 2) Time complexities. The motion generation module in our framework is lightweight and can generate motions at 15 fps, the computational bottleneck lies in the rendering module. This is a common limitation of the LDM-based methods and can be alleviated by model quantization or distillation, and we will explore more in the future.", + "bbox": [ + 511, + 348, + 906, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Supplementary Materials. We provide user study, details of network, training objectives, experimental setups, ethics, and more visual results in supplementary materials.", + "bbox": [ + 511, + 574, + 903, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 511, + 633, + 633, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a diffusion-based listening head generation framework that generates photorealistic listening head videos up to $512 \\times 512$ resolution, with highly expressive motions and fine facial details. A hybrid motion modeling method that consists of an explicit motion generation module, a specially designed motion control strategy and an implicit motion refining process eases the training of the LDM-based framework, making the learning on a small scale dataset feasible. Comprehensive experiments on Realtalk and ViCo dataset demonstrate that our framework achieves superior results in terms of visual quality and motion expressiveness compared with several state-of-the-art methods. And a thorough ablation study proves the effectiveness and necessity of the proposed hybrid motion modeling method. In the future, we will study further to improve the controllability and the generating speed of our model.", + "bbox": [ + 511, + 659, + 906, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15892", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 91, + 90, + 250, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research was funded by Key R&D Program of Shaanxi Province under Grant 2024GX-YBXM-141. This work was also supported by Ant Group Research Intern Program.", + "bbox": [ + 89, + 114, + 483, + 159 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 91, + 188, + 187, + 204 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tenglong Ao, Zeyi Zhang, and Libin Liu. Gesture diffuclip: Gesture diffusion model with clip latents. ACM Trans. Graph., 42(4), 2023. 4", + "[2] Alexei Baevski, Henry Zhou, Abdelrahman Mohamed, and Michael Auli. wav2vec 2.0: a framework for self-supervised learning of speech representations. In Proceedings of the 34th International Conference on Neural Information Processing Systems, Red Hook, NY, USA, 2020. Curran Associates Inc. 4", + "[3] Volker Blanz and Thomas Vetter. A morphable model for the synthesis of 3d faces. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, page 187-194, USA, 1999. 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In European Conference on Computer Vision, 2021. 1, 2, 6, 7" + ], + "bbox": [ + 91, + 90, + 482, + 246 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15895", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_model.json b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d39330593569f1fcfd36b5546cf068af2d8f5c17 --- /dev/null +++ b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_model.json @@ -0,0 +1,2015 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.137, + 0.13, + 0.865, + 0.178 + ], + "angle": 0, + "content": "Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.203, + 0.816, + 0.274 + ], + "angle": 0, + "content": "Yinuo Wang\\(^{1,*,‡}\\), Yanbo Fan\\(^{2,*,†}\\), Xuan Wang\\(^{2}\\), Guo Yu\\(^{1,†}\\), Fei Wang\\(^{1}\\) \n\\(^{1}\\)National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University" + }, + { + "type": "text", + "bbox": [ + 0.358, + 0.275, + 0.634, + 0.31 + ], + "angle": 0, + "content": "\\(^{2}\\)Ant Group\nnuolwang.github.io/DiffListener" + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.345, + 0.329, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.377, + 0.486, + 0.739 + ], + "angle": 0, + "content": "Listening head generation aims to synthesize non-verbal responsive listening head videos that naturally react to a certain speaker, for which, both realistic head movements, expressive facial expressions, and high visual qualities are expected. Previous approaches typically follow a two-stage pipeline that first generates intermediate 3D motion signals such as 3DMM coefficients, and then synthesizes the videos by deterministic rendering, suffering from limited motion expressiveness and low visual quality (e.g. \\(256 \\times 256\\)). In this work, we propose a novel listening head generation method that harnesses the generative capabilities of the diffusion model for both motion generation and high-quality rendering. Crucially, we propose an effective hybrid motion modeling module that addresses training difficulties caused by the scarcity of listening head data while preserving the intricate details that may be lost in explicit motion representations. We further develop a tailored control guidance for head pose and facial expression, by integrating their intrinsic motion characteristics. Our method enables high-fidelity video generation with \\(512 \\times 512\\) resolution and delivers vivid listener motion feedback. We conduct comprehensive experiments and obtain superior performance in terms of both visual quality and motion expressiveness compared with existing methods." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.768, + 0.224, + 0.784 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.793, + 0.484, + 0.855 + ], + "angle": 0, + "content": "Listening head generation aims to generate responsive listener videos that react to the corresponding speaker [46]. Unlike talking head videos, the listener's response mainly consists of non-verbal behaviors, such as nodding, smil" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.346, + 0.907, + 0.438 + ], + "angle": 0, + "content": "ing, frowning, head shaking, etc. The realism and vividness of the listener feedback are vital to the success of speaker and listener communication. Being a crucial part of digital avatar generation, listening head generation has many potential applications, such as movie production, online customer service, and human-computer interaction." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.442, + 0.909, + 0.609 + ], + "angle": 0, + "content": "While most works focus on speaker-centric talking head generation [16, 17, 26-28, 37, 44], only a few study listening head generation [21, 24, 25, 46]. It is a non-trivial problem as given a certain speaker video, there can be many reasonable listener reactions. Such a one-to-many mapping problem makes it challenging for the model to learn to generate proper yet diverse listener motions. In addition, since the generated listening head mostly contains non-verbal reactions, the audience may focus more on the listeners' facial expressions, requiring that the generated reaction videos be high-fidelity to manifest detailed and subtle expressions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.614, + 0.909, + 0.903 + ], + "angle": 0, + "content": "The state-of-the-art works of listening head generation follow a two-stage design that first generates intermediate listener motion signals and then synthesizes the RGB videos with post-rendering [20, 21, 35, 46]. For motion generation, explicit 3D motion signals, such as 3DMM [3] coefficients are used as motion descriptions. Existing works developed different models to generate the listener's 3D motion coefficients, including LSTM [46], VQ-VAE [35], and diffusion-based models [20, 21]. As for the video rendering, PIRenderer [29] is used to generate the RGB frames conditioned on the generated 3DMM coefficients. Though promising, they still fall short of generating expressive and natural listening head motions, as well as photorealistic rendering. For instance, 1) the intermediate parametric 3D motion signals, such as the 3DMM expression coefficients, are characterized in a low-dimensional generalizable subspace and lack facial details and subtle expressions, which limits the richness and naturalness of the learned facial expressions, 2) while focusing more on motion generation, the determinis" + }, + { + "type": "page_footnote", + "bbox": [ + 0.109, + 0.863, + 0.218, + 0.876 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.876, + 0.239, + 0.888 + ], + "angle": 0, + "content": "† Corresponding authors" + }, + { + "type": "page_footnote", + "bbox": [ + 0.111, + 0.888, + 0.468, + 0.901 + ], + "angle": 0, + "content": "This work was done during Yinuo Wang's internship at Ant Group" + }, + { + "type": "list", + "bbox": [ + 0.109, + 0.863, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15885" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.137 + ], + "angle": 0, + "content": "tic rendering used in existing works is of low visual quality, suffering from low resolution (e.g. \\(256 \\times 256\\)), identity inconsistency, improper head motions, and facial artifacts." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.141, + 0.483, + 0.517 + ], + "angle": 0, + "content": "In this work, we propose a novel listening head generation framework that enables both highly expressive head motions and photorealistic rendering. Our motivation is to fully leverage the generative ability of the diffusion model for both motion generation and video synthesis. Recently, the latent diffusion model (LDM) [30] has shown superior ability in high-resolution and vivid video generation, largely promoting the speaker-centric talking head generation performance [7, 34, 41]. Nevertheless, it is not feasible to directly apply these methods to listening head generation. Firstly, they require hundreds of hours of talking head videos for training the audio-to-visual correspondence, which does not apply to listening head generation, where only a few hours of training data are available. Secondly, due to the high computational and memory cost, these methods can only model the context information in a small window size (e.g. 16 frames in [34]). This is acceptable for talking head generation since talking heads have a strong correlation with the audio. However, for listening head generation, the listener feedback may be related to an even longer duration of the speaker's content. To generate a reasonable reaction, it may require long-term modeling of audio conditions and motion. Based on these, it is nontrivial to unleash the diffusion generative ability for listening head generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.521, + 0.483, + 0.853 + ], + "angle": 0, + "content": "To address these challenges, we propose a novel hybrid motion modeling method, which consists of an explicit and explainable 3D motion representation and a learnable implicit latent representation. Specifically, instead of utilizing the LDM-based rendering to generate listening video directly from the speaker's input, we first learn explicit 3D motion signals by a diffusion-based motion generation module. The explicit motions are later used as guiding conditions to train the rendering module. To facilitate controllability, we propose distinct control strategies considering the different intrinsic natures of head poses and facial expressions. The explicit motion generation module is expected to generate feasible and diverse listener motions but may lack facial details, as analyzed above. We further develop an implicit motion refinement module to complement the potentially missing facial details. With these designs, we successfully train the LDM-based rendering model on the small-scale listening dataset, enabling high-fidelity rendering (e.g. \\(512 \\times 512\\)) and vivid and expressive listener motion generation. Compared with the existing methods, we significantly boost listening head generation performance in both visual and motion quality." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.856, + 0.483, + 0.901 + ], + "angle": 0, + "content": "The hybrid motion design brings several advantages, 1) the explicit motion generation module is lightweight and takes much less computational resources than directly mod" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.241 + ], + "angle": 0, + "content": "eling audio-to-visual correspondence, making it possible to learn the long-term relations between speaker and listener, which is essential for listener motion modeling. 2) The learning of the hybrid motion representation is much easier than the pure latent motion modeling, especially on limited training data. In addition, with the intermediate explicit representation, we can better utilize talking videos to pre-train the rendering module. We conduct thorough ablation studies and verify the necessity of the hybrid motion modeling. Our contributions are as follows," + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.243, + 0.905, + 0.287 + ], + "angle": 0, + "content": "- We propose a novel diffusion-based method for motion generation and visual rendering, resulting in realistic and vivid listening head generation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.288, + 0.904, + 0.332 + ], + "angle": 0, + "content": "- We introduce an effective hybrid motion modeling module that overcomes training challenges while enhancing both motion dynamics and visual quality." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.334, + 0.904, + 0.379 + ], + "angle": 0, + "content": "- We conduct comprehensive experiments and significantly improve listening head generation in both visual quality and motion quality compared with existing methods." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.243, + 0.905, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.393, + 0.663, + 0.408 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.418, + 0.905, + 0.538 + ], + "angle": 0, + "content": "Non-verbal Listening Head Generation. Non-verbal listening head generation is an important part of digital avatar generation, and has drawn increasing research interests in recent years. Earlier works [4, 5, 10, 15, 32] use rule-based methods to generate the listener response. Such methods require specifically designed rules and pre-defined reaction motion sequences. Thus they have very limited motion diversity and expressiveness." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.539, + 0.905, + 0.854 + ], + "angle": 0, + "content": "Learning-based methods alleviate the problem by using data-driven approaches to automatically learn to generate proper reactions given speaker conditions. Zhou et al. [46] propose an LSTM-based network RLHG that predicts the listener's head poses and 3DMM expression coefficients given speaker's audio and motions. Later, several works are proposed to improve the performance of RLHG by refining the conditional features [6, 45] or improving visual quality [14]. However, these works are deterministic models and are inefficient in addressing the one-to-many mapping problems in listener motion generation, resulting in unnatural motions. To alleviate this, the work of [25] models the listener motion with VQ-VAE. Song et al. [31] proposes a more fine-grained codebook that supports emotion control. Liu et al. [20] further improves the diversity of the generated motion by a diffusion model. In addition, the work of Liu et al. [21] improves the controllability of the diffusion-based motion generation model by aggregating the user-specified expression and pose labels. Focusing on intermediate motion generation, these methods suffer from limited expressiveness and naturalness in the generated videos." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Diffusion Generative Models on Head Generation. Denoising diffusion probabilistic models [13] have shown remarkable results on image generation tasks. An iconic work" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "15886" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.903, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.402, + 0.907, + 0.446 + ], + "angle": 0, + "content": "Figure 1. Overview of the proposed framework. Given one listener portrait image and speaker's audio and head motion as input, we generate realistic and vivid listening head video. (a) is a lightweight diffusion transformer to generate the explicit motion representation, (b) is a reference net to extract the listener identity feature, (c) is our generation backbone, (d) is the implicit motion refinement module." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.47, + 0.486, + 0.729 + ], + "angle": 0, + "content": "is Stable Diffusion (SD), which is based on latent diffusion model (LDM) [30] and can generate high-resolution images. Guo et al. [11] propose a plug-in motion module and a lightweight fine-tuning technique that enables Stable Diffusion to generate animated clips. Based on these works, Tian et al. [34] propose EMO, a direct audio to talking head video generation framework that discards intermediate 3DMM representations. Benefiting from the capability of Stable Diffusion, EMO outperforms previous talking head generation methods in terms of expressiveness and realism. Several other diffusion-based audio driven works are proposed after EMO, and achieve promising results [7, 18, 41], proving the powerful generative capabilities of diffusion models in talking head generations. Nevertheless, these models require hundreds of hours training data. This can be an obstacle for training the listening head generation model, where only a few hours of data are available." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.74, + 0.184, + 0.755 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.765, + 0.484, + 0.841 + ], + "angle": 0, + "content": "Given a single listener portrait image and a speaker's audio and video, we aim to generate a non-verbal responsive listening head video that synchronizes with the speaker, with detailed facial expressions and natural head movements. Our overall framework is shown in Fig. 1." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.233, + 0.863 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We first introduce the preliminaries of the diffusion model [13, 30], which is a key component of our frame" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.907, + 0.547 + ], + "angle": 0, + "content": "work. The diffusion model defines a Markov chain of adding random noise to data samples and then trains the network to learn the reverse process, so that it can generate desired data from random noise. The forward diffusion process is defined as," + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.558, + 0.907, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.587, + 0.906, + 0.678 + ], + "angle": 0, + "content": "where \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\), and \\(\\overline{\\alpha}_t\\) is a hyper-parameter that controls the diffusion rate. With Eq. (1), we can sample at arbitrary step \\(t\\) to get the noised sample. Then the reverse diffusion process trains a neural network to predict the noise \\(\\epsilon_t\\) added to the samples at step \\(t\\), and the overall training objective is simplified as [13]:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.689, + 0.907, + 0.708 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t} = \\mathbb {E} _ {t \\sim [ 1, T ], \\mathbf {x} _ {0}, \\epsilon_ {t}} [ | | \\epsilon_ {t} - \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t, \\mathbf {c}) | | ^ {2} ], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.906, + 0.749 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}\\) is predicted using a neural network with parameters \\(\\theta, T\\) is the max step, and \\(\\mathbf{c}\\) is the additional condition." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.758, + 0.685, + 0.774 + ], + "angle": 0, + "content": "3.2. Network Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.779, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Let \\(\\mathbf{A} \\in \\mathbb{R}^{N \\times d_a}\\) and \\(\\mathbf{S} \\in \\mathbb{R}^{N \\times d}\\) denote the speaker's audio and 3D head motion features, where \\(N\\) is the number of frames, \\(d_a\\) and \\(d\\) are dimensionality of audio and speaker's motion features respectively. Let \\(\\mathbf{I} \\in \\mathbb{R}^{h \\times w \\times c}\\) be the listener portrait for identity reference. As shown in Fig. 1, to enable high-fidelity rendering and vivid responsive head motion generation, 1) we adopt an LDM-based high-fidelity rendering module to harness the power of diffusion models," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15887" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.258 + ], + "angle": 0, + "content": "so the visual qualities of the generated videos can be greatly improved. 2) We propose a novel hybrid motion modeling module that consists of a lightweight explicit motion generation module to generate explicit guiding motions, i.e. head poses and facial expressions, a tailored control strategy for the rigid head poses and non-rigid facial expressions, and an implicit and learnable motion refinement module to complement the motion details. 3) To enhance the identity consistency of the generated video, a parallel reference net with similar structure as the rendering module is used to integrate the listener identity features. We introduce each part next." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.258, + 0.483, + 0.484 + ], + "angle": 0, + "content": "High-fidelity Rendering Module. One major limitation of the existing listening head generation methods is the deterministic rendering module such as PIRenderer [29], which suffers from low resolution, identity inconsistency, and visual artifacts. Inspired by the recent advance in diffusion-based talking head generation works [34, 36, 39], we design a high-fidelity rendering module based on SD 1.5. To enable the video generation capability of SD 1.5, we follow the motion module design [11, 19] that applies self attention along the temporal dimension of the network's intermediate features, ensuring the continuity and consistency along the generated video frames. Benefiting from the probabilistic nature and the great generative capabilities, the proposed rendering module can generate photorealistic videos with detailed visuals and expressive motions." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.485, + 0.483, + 0.545 + ], + "angle": 0, + "content": "Conditioned on reference image \\(\\mathbf{I}\\), and speaker features \\(\\mathbf{A}\\) and \\(\\mathbf{S}\\), the rendering module \\(\\mathcal{R}\\) takes noised latent \\(\\mathbf{V}_t \\in \\mathbb{R}^{N \\times h \\times w \\times c}\\) at step \\(t\\) as inputs, and predicts the denoised latent \\(\\hat{\\mathbf{V}}_0\\):" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.557, + 0.483, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {V}} _ {0} = \\mathcal {R} \\left(\\mathbf {V} _ {t}, t, \\mathbf {c}\\right), \\mathbf {c} = \\{\\mathbf {A}, \\mathbf {S}, \\mathbf {I} \\}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.587, + 0.483, + 0.708 + ], + "angle": 0, + "content": "However, facing the scarcity of the listening head data, it's not feasible to train the rendering module directly from speaker features alone. So we propose a novel hybrid motion modeling method where we use explicit listener motion \\(\\hat{\\mathbf{L}}\\) as an additional guiding signal to ease the training of the rendering module. \\(\\hat{\\mathbf{L}}\\) is set to 51-dim facial expression coefficient and 6-dim head pose coefficients extracted by MediaPipe [23]. The generation procedure becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.719, + 0.483, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {V}} _ {0} = \\mathcal {R} \\left(\\mathbf {V} _ {t}, t, \\mathbf {c}\\right), \\mathbf {c} = \\{\\hat {\\mathbf {L}}, \\mathbf {A}, \\mathbf {S}, \\mathbf {I} \\}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.75, + 0.483, + 0.779 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{L}}\\) is generated by a lightweight motion generation module, given the speaker features \\(\\mathbf{A}\\) and \\(\\mathbf{S}\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.781, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Explicit Motion Generation. We design a transformer diffusion-based explicit motion generation module, inspired by the successful applications of diffusion models on various human motion generations [1, 21, 33, 42]. The motion generation module generates both listener's facial expressions and head poses with a lightweight diffusion network, addressing the one-to-many mapping problem as well as enabling us to model motions in larger time window." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.091, + 0.905, + 0.137 + ], + "angle": 0, + "content": "Given a noised motion sequence \\(\\mathbf{L}_t\\in \\mathbb{R}^{M\\times d}\\) at step \\(t\\) the explicit motion generation module \\(\\mathcal{G}\\) aims to predict the clean sample \\(\\hat{\\mathbf{L}}\\) condition on speaker features A and S:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.149, + 0.905, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {L}} = \\mathcal {G} (\\mathbf {L} _ {t}, t, \\mathbf {c}), \\mathbf {c} = \\{\\mathbf {A}, \\mathbf {S} \\}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.177, + 0.907, + 0.312 + ], + "angle": 0, + "content": "As shown in Fig. 1 (a), the noised motion sequence \\(\\mathbf{L}_t\\) is mapped to the latent space and then encoded by a transformer encoder. In the meantime, the speaker features, i.e. speakers facial expression features and audio features are integrated by a cross-modal transformer, where we use a pretrained speech model wav2vec 2.0 [2] to encode the raw audio. Then a transformer decoder is used to generate denoised sequence, where the integrated speaker features are used as keys and values." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.313, + 0.907, + 0.617 + ], + "angle": 0, + "content": "Explicit Motion Guidance. \\(\\hat{\\mathbf{L}}\\) generated by Eq. (5) contains the learned explicit 3D head poses and facial expression coefficients. It serves as a explicit motion guidance in our design. There are other options for explicit motion representation such as mesh, normal maps etc. We choose expression coefficients because it's more compact and semantic meaningful. The ways to inject conditional information are crucial in diffusion models. An intuitive way to add controllability of head poses and facial expressions might be concatenating these features and injecting to the layers of the rendering module via cross-attention operator, which is a common practice in existing methods. However, in practice, such an operation leads to sub-optimal head pose and expression controllability. Considering the different intrinsic nature of head poses and facial expressions, i.e. head pose is a global rigid transformation that decides the position of the generated head while facial expression is a local non-rigid transformation that focuses more on the visual details, we opt to use distinct conditional strategies for head pose and facial expressions accordingly." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.616, + 0.906, + 0.751 + ], + "angle": 0, + "content": "Specifically, for pose control, we generate explicit pose images \\(\\mathbf{P}\\) as guidance. We use three facial key points (the inner corners of the eyes and nose tip) and synthesize the pose guidance images by connecting them. Then, a pose guidance net consists of multiple convolutional layers is designed to extract multi-resolution features of the pose guidance images, and the extracted features are added to the latent features of the same resolution in the downsample blocks of the rendering module:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.762, + 0.905, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {h}} _ {d} ^ {(i)} = C o n v _ {i} (\\mathbf {P}) + \\mathbf {h} _ {d} ^ {(i)} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.793, + 0.905, + 0.854 + ], + "angle": 0, + "content": "where \\( Conv_{i} \\) is the \\( i \\)-th convolutional layer in the pose guidance net, its output has the same dimensionality as the latent features \\( \\mathbf{h}_{d}^{(i)} \\) in the downsample blocks of rendering module." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.905, + 0.901 + ], + "angle": 0, + "content": "As for the facial expression control, we adopt more fine-grained control where we inject the facial expression features \\(\\mathbf{F}\\) into the rendering module through additional cross" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "15888" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.088, + 0.905, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.467, + 0.903, + 0.484 + ], + "angle": 0, + "content": "Figure 2. Visualization of the compared methods. Our method exhibits highly detailed visuals, accurate motion, and identity consistency." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.509, + 0.483, + 0.553 + ], + "angle": 0, + "content": "attention layers, one after each reference layer, and the facial expression features \\(\\mathbf{F}\\) are use as keys and values, as follows" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.552, + 0.483, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} _ {e} ^ {(l)} = \\operatorname {C r o s s A t t n} \\left(\\mathbf {h} _ {r} ^ {(l)}, \\mathbf {F}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.575, + 0.424, + 0.593 + ], + "angle": 0, + "content": "where \\(\\mathbf{h}_r^{(l)}\\) is the output of the \\(l\\)-th reference layer." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.593, + 0.483, + 0.775 + ], + "angle": 0, + "content": "Implicit Motion Refinement. Though the explicit motion guidance introduced above eases the training difficulty, the explicit motion representation \\(\\hat{\\mathbf{L}}\\) has limitations in depicting the facial details and subtle expressions, restricting the overall generation quality. We further propose an implicit motion refinement module to complement the explicit motion representation. Concretely, during the motion refining process, the speaker features (i.e. audio features \\(\\mathbf{A}\\) and facial expression features \\(\\mathbf{S}\\)) are first integrated, then injected into a cross-attention layer as keys and values, and the latent feature map generated after the explicit motion modeling serving as the query, the motion refinement is" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.782, + 0.483, + 0.803 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} _ {i} ^ {(l)} = C r o s s A t t n _ {s} [ \\mathbf {h} _ {e} ^ {(l)}, C r o s s A t t n _ {i} (\\mathbf {S}, \\mathbf {A}) ] + \\mathbf {h} _ {e} ^ {(l)}. (8)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.81, + 0.483, + 0.841 + ], + "angle": 0, + "content": "We add this refinement module after each explicit facial expression cross-attention layer by residual connections." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.841, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Reference Net. Inspired by [34], we adopt a parallel network that has a similar structure as the rendering module to inject the identity features. Since the reference net and the rendering module both inherit structures and weights from" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.509, + 0.907, + 0.65 + ], + "angle": 0, + "content": "SD 1.5, the corresponding layers of the two networks share certain similarities. We feed the reference image \\(\\mathbf{I}\\) to the reference net and use its intermediate UNet block features to guide the denoising process of the rendering module. Concretely, the features \\(\\mathbf{r}_s^{(l)}\\) from self-attention layers of the reference net are first concatenated with the corresponding layers' features \\(\\mathbf{h}_s^{(l)}\\) from the rendering module, then undergo a cross-attention layer to inject the identity information into the denoising process:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.658, + 0.907, + 0.679 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} _ {r} ^ {(l)} = \\operatorname {C r o s s A t t n} \\left[ \\mathbf {h} _ {s} ^ {(l)}, \\left(\\mathbf {h} _ {s} ^ {(l)} \\oplus \\mathbf {r} _ {s} ^ {(l)}\\right) \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.689, + 0.905, + 0.705 + ], + "angle": 0, + "content": "where the concatenated features are used as keys and values." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.713, + 0.688, + 0.73 + ], + "angle": 0, + "content": "3.3. Training Strategy" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.907, + 0.903 + ], + "angle": 0, + "content": "The training of our method has two stages. In the first stage, the motion generation module is trained on listening head datasets while the rendering module is pretrained on listening head dataset together with a large scale talking head dataset VFHQ [40]. For the rendering module pretrain, we do not incorporate the speaker information, and the ground truth head poses and facial expression coefficients are used as guidance signals. In the second stage, we train the implicit motion refinement part in the rendering backbone. In this stage, we incorporate the explicit motion generated by the motion generation module as guidance." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15889" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.475, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.235, + 0.483, + 0.276 + ], + "angle": 0, + "content": "Figure 3. Visualization of the ablation study on explicit motion guidance. We highlight the artifacts of the compared method with red boxes." + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.291, + 0.476, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.439, + 0.483, + 0.482 + ], + "angle": 0, + "content": "Figure 4. Visualization of the ablation study on different motion control schemes. We highlight the inaccurate head poses and facial expressions, as well as visual artifacts with red boxes." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.506, + 0.222, + 0.523 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.531, + 0.281, + 0.548 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.553, + 0.483, + 0.734 + ], + "angle": 0, + "content": "Dataset. We conduct experiments on the widely used ViCo dataset [46] and RealTalk dataset [9]. Both ViCo and RealTalk consist of videos of face-to-face daily conversations between two individuals of diverse ages, genders, and ethnicity. We follow the training and testing split provided in their original papers. ViCo contains 398 clips of total 1.3 hours for training, 43 clips for testing, and 42 clips for out-of-distribution (OOD) testing. RealTalk contains 1489 clips of total 6.4 hours for training and 407 clips for testing. Additionally, VFHQ dataset [40], a large-scale high-quality talking head video dataset containing over 16k clips, is used to pretrain the rendering module." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.885 + ], + "angle": 0, + "content": "Implementation Details. For both datasets, we crop the original videos into \\(512 \\times 512\\) face videos for training and testing, and use MediaPipe [23] to extract 51-dim facial expression coefficients and 6-dim head pose. For the motion generation module, we train it with the input sequence of 50 frames and a batch size of 64. The diffusion step is set to 1000 for training and inference. For the high-fidelity rendering, we set the input to 16 frames with a batch size of 8. The diffusion step is 1000 for training and 25 for inference. Both modules are trained with AdamW [22] optimizer." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.886, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Compared Methods. We compare the proposed method" + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.088, + 0.898, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.235, + 0.905, + 0.278 + ], + "angle": 0, + "content": "Figure 5. Visualization of the ablation study on implicit motion refinement. We highlight the inaccurate motion with red boxes and the improved facial details with green box." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.306, + 0.905, + 0.427 + ], + "angle": 0, + "content": "with several state-of-the-art listening head generation methods, including RLHG [46], PCH [14], L2L [25], MFR-Net [20] and CustomListener [21]. We retrain RLHG, PCH and L2L on both ViCo and RealTalk dataset. Since MFR-Net and CustomListener are not open-sourced, we list their results on ViCo dataset from the original papers for reference. We also conduct thorough ablation studies to verify the effectiveness of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.428, + 0.906, + 0.64 + ], + "angle": 0, + "content": "Evaluation Metrics. We compare both visual and motion quality for evaluation. The visual quality is evaluated by Fréchet Inception Distance (FID) [12], Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity (SSIM) [38]. For the motion quality evaluation, we adopt 1) Feature Distance (FD), the \\( L_{1} \\) distance between the generated motion and the ground truth motion, 2) \\( \\mathrm{FID}_{\\Delta \\mathrm{fm}} \\) [43], the FID score of motion difference between consecutive frames, and 3) Sequence Naturalness Distance (SND) [43], the summarization of \\( \\mathrm{FID}_{\\Delta \\mathrm{fm}} \\) and FID score of motion. For \\( \\mathrm{FID}_{\\Delta \\mathrm{fm}} \\) and SND, we concatenate the angle and translation to compute the overall pose metrics. To compare with existing works, we extract the 3DMM coefficients by [8], to compute the motion quality metrics." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.65, + 0.707, + 0.667 + ], + "angle": 0, + "content": "4.2. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.905, + 0.703 + ], + "angle": 0, + "content": "The quantitative results on RealTalk and ViCo are listed in Table 1 and Table 2, respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.704, + 0.906, + 0.885 + ], + "angle": 0, + "content": "For the visual quality, our proposed method obtains significantly better visual quality in terms of SSIM, PSNR and FID on both Realtalk and ViCo datasets. For instance, on RealTalk dataset, the relative performance improvements are \\(14\\%\\) for SSIM, \\(14\\%\\) for PSNR, and \\(33\\%\\) for FID. On ViCo dataset, the improvements are \\(12\\%\\) for SSIM, \\(15\\%\\) for PSNR, and \\(5\\%\\) for FID. These demonstrate the superior high-fidelity generative capability of our proposed method. This is due to the proposed rendering module is much more powerful than the deterministic PIRenderer, and that the hybrid motion modeling further enhances the visual quality of the rendering module." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.886, + 0.905, + 0.901 + ], + "angle": 0, + "content": "For the motion quality, our method also achieves the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15890" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.172, + 0.089, + 0.827, + 0.196 + ], + "angle": 0, + "content": "
    MethodsSSIM↑PSNR↑FID↓FD↓FIDΔfm ↓SND↓
    expangletransexpposeexppose
    RLHG [46]0.5717.8720.7913.095.916.0212.010.742.090.04
    PCH [14]0.5717.7820.0513.805.695.9911.360.722.110.04
    L2L [25]0.5015.6127.2822.9211.779.1910.930.587.810.14
    Ours0.6520.3413.3810.493.955.126.000.051.490.02
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.206, + 0.907, + 0.237 + ], + "angle": 0, + "content": "Table 1. Quantitative results on RealTalk dataset, where the values of FD and \\(\\mathrm{FID}_{\\Delta \\mathrm{fm}}\\) are multiplied by 100. The \\(\\uparrow\\) indicates the higher the better while \\(\\downarrow\\) indicates the lower the better. The best and the second best results are in bold and underlined, respectively." + }, + { + "type": "table", + "bbox": [ + 0.113, + 0.248, + 0.887, + 0.472 + ], + "angle": 0, + "content": "
    MethodsTest setSSIM↑PSNR↑FID↓FD ↓FIDΔfm ↓SND ↓
    expangletransexpposeexppose
    RLHG [46]Dtest0.5817.8838.6916.439.056.759.540.763.450.09
    Dood26.709.7510.617.360.559.380.14
    PCH [14]Dtest0.6017.9231.6215.488.845.958.910.733.010.09
    Dood24.117.2710.056.070.477.790.11
    L2L [25]Dtest0.5817.7538.3920.3612.528.8812.060.606.610.19
    Dood23.828.107.438.670.518.160.07
    MFR-Net* [20]Dtest0.5917.8220.0813.376.826.02////
    Dood14.708.126.37////
    CustomListener* [21]Dtest0.6017.9820.0611.546.125.903.120.062.400.07
    Dood12.677.496.013.590.075.940.05
    OursDtest0.6720.6018.9912.547.575.685.130.082.360.08
    Dood11.893.835.435.050.052.060.02
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.483, + 0.907, + 0.527 + ], + "angle": 0, + "content": "Table 2. Quantitative results on ViCo dataset, where the values of FD and \\( \\mathrm{FID}_{\\Delta \\mathrm{fm}} \\) are multiplied by 100. The \\( \\uparrow \\) indicates higher is better for the corresponding metric while \\( \\downarrow \\) indicates lower is better. The * denotes we report the results from their papers. The best and the second best results are in bold and underlined respectively." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.552, + 0.483, + 0.839 + ], + "angle": 0, + "content": "best overall performance on both datasets. Specifically, for RealTalk, we achieve the best results on all motion metrics. In terms of FD, we obtain \\(20\\%\\), \\(31\\%\\), and \\(15\\%\\) performance improvement for the expression, angle, and translations, respectively. In terms of \\(\\mathrm{FID}_{\\Delta \\mathrm{fm}}\\), the performance improvements are \\(45\\%\\) for expression and \\(91\\%\\) for head pose. On ViCo dataset, we also obtain the best motion quality on the OOD set and the second-best results on the test set. For ViCo, the motion of the test set is much more intense and random than that of the OOD set. The one-to-many characteristic makes it more difficult to generate the exact motion as the ground truth on the test set. In such cases, CustomListener that additionally incorporates the ground-truth motion text description leads to more similar motions to the ground-truth. Nevertheless, the superior performance on the OOD set demonstrates our better generalization ability. These results verify that our method can largely promote the visual and motion quality, enabling realistic and vivid listening head generation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.849, + 0.275, + 0.866 + ], + "angle": 0, + "content": "4.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.903 + ], + "angle": 0, + "content": "We compare the visualization result with RLHG, L2L and PCH. MFR-Net and CustomListener are not open-sourced" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.552, + 0.907, + 0.704 + ], + "angle": 0, + "content": "and their visualization is not available. As shown in Fig 2, our method surpasses the baseline methods in terms of visual quality, motion accuracy, and identity consistency. To be specific, 1) in Fig. 2 (a), our method generates a proper reaction video while the baseline methods show inappropriate facial expressions. 2) in Fig. 2 (b, c), we obtain much better identity preservation, even under more drastic facial expressions, e.g. laughing. 3) in Fig. 2 (b, c, d), our method retains better facial details, such as realistic teeth, wrinkles, and natural complexities." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.713, + 0.667, + 0.729 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.906, + 0.765 + ], + "angle": 0, + "content": "We conduct ablations to demonstrate the necessities of each part of the proposed hybrid motion modeling." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.907, + 0.902 + ], + "angle": 0, + "content": "Explicit Motion Modeling. We remove the intermediate explicit motion guidance and train a diffusion UNet that learns the listener motion purely from implicit motion modeling, i.e. the rendering module in Section 3.2 without pose guidance net and expression attention layers. The network is first pretrained on VFHQ and Realtalk dataset for unconditioned image generation, then trained on Realtalk dataset for listening head generation conditioned on speaker features. As shown in Table 3, without the motion guidance," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15891" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.133, + 0.089, + 0.867, + 0.177 + ], + "angle": 0, + "content": "
    MethodsSSIM↑PSNR↑FID↓FD↓FIDΔfm ↓SND↓
    expangletransexpposeexppose
    w/o motion guidance0.6319.7514.3711.024.285.009.050.121.670.02
    w/o implicit motion refinement0.6420.1713.5811.004.055.176.840.061.610.02
    Ours0.6520.3413.3810.483.945.126.000.051.480.02
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.128, + 0.187, + 0.868, + 0.202 + ], + "angle": 0, + "content": "Table 3. Ablation study on motion modeling, tested on Realtalk dataset, the values of FD and \\( \\mathrm{{FID}}_{{\\Delta }_{\\mathrm{{fm}}}} \\) are multiplied by 100 ." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.225, + 0.472, + 0.298 + ], + "angle": 0, + "content": "
    SettingsFD↓FIDΔfm ↓
    expangletransexppose
    Concatenate pose7.813.034.369.870.10
    Separate control7.482.014.284.690.10
    " + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.309, + 0.483, + 0.351 + ], + "angle": 0, + "content": "Table 4. Ablation study on different motion control schemes, tested on Realtalk dataset, the values of FD and \\(\\mathrm{FID}_{\\Delta \\mathrm{fm}}\\) are multiplied by 100." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.383, + 0.483, + 0.518 + ], + "angle": 0, + "content": "both the visual quality and the motion quality of the generated listening head degrades. It can be observed that \\(\\mathrm{FID}_{\\Delta \\mathrm{fm}}\\) has significantly degrades, indicating there are unnatural transitions of expression and head poses. As shown in Fig. 3, without motion guidance, the network struggles to generate continuous head poses and expressions, often resulting in serious artifacts in faces. Such result proves that the explicit motion guidance can effectively ease the training of LDM-based models on small scale datasets." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.521, + 0.483, + 0.793 + ], + "angle": 0, + "content": "The Distinct Controls of Pose and Expressions. In Section 3.2, we propose to use separate controls of head pose and facial expression according to the intrinsics of these two types of motion signals. To validate the effectiveness of the proposed control strategies, we remove the pose images in the rendering module, and concatenate the head pose coefficients with the facial expression coefficients. The concatenated motion signal is injected into the rendering module through the expression cross-attention layer. The results in Table 4 show that using concatenated motion as the control signal leads to a degeneration in both motion accuracy and naturalness, especially on expression metrics. We also present some visualizations in Fig. 4. From the visualization, there exists inaccurate pose control and visual artifacts when using concatenated motion signals (the left example), and poor expression controllability (the right example). These results verify the effectiveness of the proposed pose and expression controls." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.796, + 0.483, + 0.901 + ], + "angle": 0, + "content": "Implicit Motion Refinement. Furthermore, we validate the effectiveness of the proposed implicit motion refinement method. As shown in Table 3, without the refinement module, the motion quality and visual quality of the generated video both degrade. As shown in Fig. 5, we observe mainly two effects of the implicit motion refinement. The first is that the refinement fixes some wrong facial expressions (the" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.228, + 0.905, + 0.349 + ], + "angle": 0, + "content": "left example), and the second is that it tends to add more facial details to the generated videos, such as more realistic wrinkles (the right example). As a result, we can observe more stable and detailed facial expressions after refinement. This implies that the implicit motion refinement helps the rendering module learn to revise the details of the generated videos given additional conditions, further improving the visual qualities." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.349, + 0.907, + 0.575 + ], + "angle": 0, + "content": "**Discussions.** Our proposed framework can generate high fidelity listening head videos with accurate motion, vivid facial details and expressive motions. Nevertheless, there are still some limitations. 1) The condition used to generate listening heads is restricted within the speaker's audio and facial expressions. But more flexible conditions such as text description, motion styles etc. are always appreciated. The proposed hybrid motion generation has the potential of integrating diverse control signals, we will study this in the future. 2) Time complexities. The motion generation module in our framework is lightweight and can generate motions at 15 fps, the computational bottleneck lies in the rendering module. This is a common limitation of the LDM-based methods and can be alleviated by model quantization or distillation, and we will explore more in the future." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.575, + 0.905, + 0.621 + ], + "angle": 0, + "content": "Supplementary Materials. We provide user study, details of network, training objectives, experimental setups, ethics, and more visual results in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.634, + 0.634, + 0.65 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.66, + 0.907, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose a diffusion-based listening head generation framework that generates photorealistic listening head videos up to \\(512 \\times 512\\) resolution, with highly expressive motions and fine facial details. A hybrid motion modeling method that consists of an explicit motion generation module, a specially designed motion control strategy and an implicit motion refining process eases the training of the LDM-based framework, making the learning on a small scale dataset feasible. Comprehensive experiments on Realtalk and ViCo dataset demonstrate that our framework achieves superior results in terms of visual quality and motion expressiveness compared with several state-of-the-art methods. And a thorough ablation study proves the effectiveness and necessity of the proposed hybrid motion modeling method. In the future, we will study further to improve the controllability and the generating speed of our model." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15892" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.092, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.115, + 0.484, + 0.16 + ], + "angle": 0, + "content": "This research was funded by Key R&D Program of Shaanxi Province under Grant 2024GX-YBXM-141. 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In European Conference on Computer Vision, 2021. 1, 2, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.092, + 0.483, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "15895" + } + ] +] \ No newline at end of file diff --git a/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_origin.pdf b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8a53a009d4e0273bad318a9bccc34df4b02ab638 --- /dev/null +++ b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/54547168-012b-4a96-999b-4f0bfc23f076_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:298dbb345f18669e37a969cc5bd6faf367107d0e92792f7d64faad6a1e01295f +size 2181355 diff --git a/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/full.md b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/full.md new file mode 100644 index 0000000000000000000000000000000000000000..72a68ac113e1ee5c945be61f59c945bef203b660 --- /dev/null +++ b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/full.md @@ -0,0 +1,283 @@ +# Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling + +Yinuo Wang $^{1,*,‡}$ , Yanbo Fan $^{2,*,†}$ , Xuan Wang $^{2}$ , Guo Yu $^{1,†}$ , Fei Wang $^{1}$ $^{1}$ National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University + +$^{2}$ Ant Group +nuolwang.github.io/DiffListener + +# Abstract + +Listening head generation aims to synthesize non-verbal responsive listening head videos that naturally react to a certain speaker, for which, both realistic head movements, expressive facial expressions, and high visual qualities are expected. Previous approaches typically follow a two-stage pipeline that first generates intermediate 3D motion signals such as 3DMM coefficients, and then synthesizes the videos by deterministic rendering, suffering from limited motion expressiveness and low visual quality (e.g. $256 \times 256$ ). In this work, we propose a novel listening head generation method that harnesses the generative capabilities of the diffusion model for both motion generation and high-quality rendering. Crucially, we propose an effective hybrid motion modeling module that addresses training difficulties caused by the scarcity of listening head data while preserving the intricate details that may be lost in explicit motion representations. We further develop a tailored control guidance for head pose and facial expression, by integrating their intrinsic motion characteristics. Our method enables high-fidelity video generation with $512 \times 512$ resolution and delivers vivid listener motion feedback. We conduct comprehensive experiments and obtain superior performance in terms of both visual quality and motion expressiveness compared with existing methods. + +# 1. Introduction + +Listening head generation aims to generate responsive listener videos that react to the corresponding speaker [46]. Unlike talking head videos, the listener's response mainly consists of non-verbal behaviors, such as nodding, smil + +ing, frowning, head shaking, etc. The realism and vividness of the listener feedback are vital to the success of speaker and listener communication. Being a crucial part of digital avatar generation, listening head generation has many potential applications, such as movie production, online customer service, and human-computer interaction. + +While most works focus on speaker-centric talking head generation [16, 17, 26-28, 37, 44], only a few study listening head generation [21, 24, 25, 46]. It is a non-trivial problem as given a certain speaker video, there can be many reasonable listener reactions. Such a one-to-many mapping problem makes it challenging for the model to learn to generate proper yet diverse listener motions. In addition, since the generated listening head mostly contains non-verbal reactions, the audience may focus more on the listeners' facial expressions, requiring that the generated reaction videos be high-fidelity to manifest detailed and subtle expressions. + +The state-of-the-art works of listening head generation follow a two-stage design that first generates intermediate listener motion signals and then synthesizes the RGB videos with post-rendering [20, 21, 35, 46]. For motion generation, explicit 3D motion signals, such as 3DMM [3] coefficients are used as motion descriptions. Existing works developed different models to generate the listener's 3D motion coefficients, including LSTM [46], VQ-VAE [35], and diffusion-based models [20, 21]. As for the video rendering, PIRenderer [29] is used to generate the RGB frames conditioned on the generated 3DMM coefficients. Though promising, they still fall short of generating expressive and natural listening head motions, as well as photorealistic rendering. For instance, 1) the intermediate parametric 3D motion signals, such as the 3DMM expression coefficients, are characterized in a low-dimensional generalizable subspace and lack facial details and subtle expressions, which limits the richness and naturalness of the learned facial expressions, 2) while focusing more on motion generation, the determinis + +tic rendering used in existing works is of low visual quality, suffering from low resolution (e.g. $256 \times 256$ ), identity inconsistency, improper head motions, and facial artifacts. + +In this work, we propose a novel listening head generation framework that enables both highly expressive head motions and photorealistic rendering. Our motivation is to fully leverage the generative ability of the diffusion model for both motion generation and video synthesis. Recently, the latent diffusion model (LDM) [30] has shown superior ability in high-resolution and vivid video generation, largely promoting the speaker-centric talking head generation performance [7, 34, 41]. Nevertheless, it is not feasible to directly apply these methods to listening head generation. Firstly, they require hundreds of hours of talking head videos for training the audio-to-visual correspondence, which does not apply to listening head generation, where only a few hours of training data are available. Secondly, due to the high computational and memory cost, these methods can only model the context information in a small window size (e.g. 16 frames in [34]). This is acceptable for talking head generation since talking heads have a strong correlation with the audio. However, for listening head generation, the listener feedback may be related to an even longer duration of the speaker's content. To generate a reasonable reaction, it may require long-term modeling of audio conditions and motion. Based on these, it is nontrivial to unleash the diffusion generative ability for listening head generation. + +To address these challenges, we propose a novel hybrid motion modeling method, which consists of an explicit and explainable 3D motion representation and a learnable implicit latent representation. Specifically, instead of utilizing the LDM-based rendering to generate listening video directly from the speaker's input, we first learn explicit 3D motion signals by a diffusion-based motion generation module. The explicit motions are later used as guiding conditions to train the rendering module. To facilitate controllability, we propose distinct control strategies considering the different intrinsic natures of head poses and facial expressions. The explicit motion generation module is expected to generate feasible and diverse listener motions but may lack facial details, as analyzed above. We further develop an implicit motion refinement module to complement the potentially missing facial details. With these designs, we successfully train the LDM-based rendering model on the small-scale listening dataset, enabling high-fidelity rendering (e.g. $512 \times 512$ ) and vivid and expressive listener motion generation. Compared with the existing methods, we significantly boost listening head generation performance in both visual and motion quality. + +The hybrid motion design brings several advantages, 1) the explicit motion generation module is lightweight and takes much less computational resources than directly mod + +eling audio-to-visual correspondence, making it possible to learn the long-term relations between speaker and listener, which is essential for listener motion modeling. 2) The learning of the hybrid motion representation is much easier than the pure latent motion modeling, especially on limited training data. In addition, with the intermediate explicit representation, we can better utilize talking videos to pre-train the rendering module. We conduct thorough ablation studies and verify the necessity of the hybrid motion modeling. Our contributions are as follows, + +- We propose a novel diffusion-based method for motion generation and visual rendering, resulting in realistic and vivid listening head generation. +- We introduce an effective hybrid motion modeling module that overcomes training challenges while enhancing both motion dynamics and visual quality. +- We conduct comprehensive experiments and significantly improve listening head generation in both visual quality and motion quality compared with existing methods. + +# 2. Related Works + +Non-verbal Listening Head Generation. Non-verbal listening head generation is an important part of digital avatar generation, and has drawn increasing research interests in recent years. Earlier works [4, 5, 10, 15, 32] use rule-based methods to generate the listener response. Such methods require specifically designed rules and pre-defined reaction motion sequences. Thus they have very limited motion diversity and expressiveness. + +Learning-based methods alleviate the problem by using data-driven approaches to automatically learn to generate proper reactions given speaker conditions. Zhou et al. [46] propose an LSTM-based network RLHG that predicts the listener's head poses and 3DMM expression coefficients given speaker's audio and motions. Later, several works are proposed to improve the performance of RLHG by refining the conditional features [6, 45] or improving visual quality [14]. However, these works are deterministic models and are inefficient in addressing the one-to-many mapping problems in listener motion generation, resulting in unnatural motions. To alleviate this, the work of [25] models the listener motion with VQ-VAE. Song et al. [31] proposes a more fine-grained codebook that supports emotion control. Liu et al. [20] further improves the diversity of the generated motion by a diffusion model. In addition, the work of Liu et al. [21] improves the controllability of the diffusion-based motion generation model by aggregating the user-specified expression and pose labels. Focusing on intermediate motion generation, these methods suffer from limited expressiveness and naturalness in the generated videos. + +Diffusion Generative Models on Head Generation. Denoising diffusion probabilistic models [13] have shown remarkable results on image generation tasks. An iconic work + +![](images/4b60f0904798e2a909ef3e9570f4b7ced397e5822a692fb20ec2e00c5b0cc4d0.jpg) +Figure 1. Overview of the proposed framework. Given one listener portrait image and speaker's audio and head motion as input, we generate realistic and vivid listening head video. (a) is a lightweight diffusion transformer to generate the explicit motion representation, (b) is a reference net to extract the listener identity feature, (c) is our generation backbone, (d) is the implicit motion refinement module. + +is Stable Diffusion (SD), which is based on latent diffusion model (LDM) [30] and can generate high-resolution images. Guo et al. [11] propose a plug-in motion module and a lightweight fine-tuning technique that enables Stable Diffusion to generate animated clips. Based on these works, Tian et al. [34] propose EMO, a direct audio to talking head video generation framework that discards intermediate 3DMM representations. Benefiting from the capability of Stable Diffusion, EMO outperforms previous talking head generation methods in terms of expressiveness and realism. Several other diffusion-based audio driven works are proposed after EMO, and achieve promising results [7, 18, 41], proving the powerful generative capabilities of diffusion models in talking head generations. Nevertheless, these models require hundreds of hours training data. This can be an obstacle for training the listening head generation model, where only a few hours of data are available. + +# 3. Method + +Given a single listener portrait image and a speaker's audio and video, we aim to generate a non-verbal responsive listening head video that synchronizes with the speaker, with detailed facial expressions and natural head movements. Our overall framework is shown in Fig. 1. + +# 3.1. Preliminaries + +We first introduce the preliminaries of the diffusion model [13, 30], which is a key component of our frame + +work. The diffusion model defines a Markov chain of adding random noise to data samples and then trains the network to learn the reverse process, so that it can generate desired data from random noise. The forward diffusion process is defined as, + +$$ +\mathbf {x} _ {t} = \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \tag {1} +$$ + +where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ , and $\overline{\alpha}_t$ is a hyper-parameter that controls the diffusion rate. With Eq. (1), we can sample at arbitrary step $t$ to get the noised sample. Then the reverse diffusion process trains a neural network to predict the noise $\epsilon_t$ added to the samples at step $t$ , and the overall training objective is simplified as [13]: + +$$ +\mathcal {L} _ {t} = \mathbb {E} _ {t \sim [ 1, T ], \mathbf {x} _ {0}, \epsilon_ {t}} [ | | \epsilon_ {t} - \epsilon_ {\theta} (\mathbf {x} _ {t}, t, \mathbf {c}) | | ^ {2} ], \tag {2} +$$ + +where $\epsilon_{\theta}$ is predicted using a neural network with parameters $\theta, T$ is the max step, and $\mathbf{c}$ is the additional condition. + +# 3.2. Network Pipeline + +Let $\mathbf{A} \in \mathbb{R}^{N \times d_a}$ and $\mathbf{S} \in \mathbb{R}^{N \times d}$ denote the speaker's audio and 3D head motion features, where $N$ is the number of frames, $d_a$ and $d$ are dimensionality of audio and speaker's motion features respectively. Let $\mathbf{I} \in \mathbb{R}^{h \times w \times c}$ be the listener portrait for identity reference. As shown in Fig. 1, to enable high-fidelity rendering and vivid responsive head motion generation, 1) we adopt an LDM-based high-fidelity rendering module to harness the power of diffusion models, + +so the visual qualities of the generated videos can be greatly improved. 2) We propose a novel hybrid motion modeling module that consists of a lightweight explicit motion generation module to generate explicit guiding motions, i.e. head poses and facial expressions, a tailored control strategy for the rigid head poses and non-rigid facial expressions, and an implicit and learnable motion refinement module to complement the motion details. 3) To enhance the identity consistency of the generated video, a parallel reference net with similar structure as the rendering module is used to integrate the listener identity features. We introduce each part next. + +High-fidelity Rendering Module. One major limitation of the existing listening head generation methods is the deterministic rendering module such as PIRenderer [29], which suffers from low resolution, identity inconsistency, and visual artifacts. Inspired by the recent advance in diffusion-based talking head generation works [34, 36, 39], we design a high-fidelity rendering module based on SD 1.5. To enable the video generation capability of SD 1.5, we follow the motion module design [11, 19] that applies self attention along the temporal dimension of the network's intermediate features, ensuring the continuity and consistency along the generated video frames. Benefiting from the probabilistic nature and the great generative capabilities, the proposed rendering module can generate photorealistic videos with detailed visuals and expressive motions. + +Conditioned on reference image $\mathbf{I}$ , and speaker features $\mathbf{A}$ and $\mathbf{S}$ , the rendering module $\mathcal{R}$ takes noised latent $\mathbf{V}_t \in \mathbb{R}^{N \times h \times w \times c}$ at step $t$ as inputs, and predicts the denoised latent $\hat{\mathbf{V}}_0$ : + +$$ +\hat {\mathbf {V}} _ {0} = \mathcal {R} \left(\mathbf {V} _ {t}, t, \mathbf {c}\right), \mathbf {c} = \{\mathbf {A}, \mathbf {S}, \mathbf {I} \}. \tag {3} +$$ + +However, facing the scarcity of the listening head data, it's not feasible to train the rendering module directly from speaker features alone. So we propose a novel hybrid motion modeling method where we use explicit listener motion $\hat{\mathbf{L}}$ as an additional guiding signal to ease the training of the rendering module. $\hat{\mathbf{L}}$ is set to 51-dim facial expression coefficient and 6-dim head pose coefficients extracted by MediaPipe [23]. The generation procedure becomes: + +$$ +\hat {\mathbf {V}} _ {0} = \mathcal {R} \left(\mathbf {V} _ {t}, t, \mathbf {c}\right), \mathbf {c} = \{\hat {\mathbf {L}}, \mathbf {A}, \mathbf {S}, \mathbf {I} \}, \tag {4} +$$ + +where $\hat{\mathbf{L}}$ is generated by a lightweight motion generation module, given the speaker features $\mathbf{A}$ and $\mathbf{S}$ . + +Explicit Motion Generation. We design a transformer diffusion-based explicit motion generation module, inspired by the successful applications of diffusion models on various human motion generations [1, 21, 33, 42]. The motion generation module generates both listener's facial expressions and head poses with a lightweight diffusion network, addressing the one-to-many mapping problem as well as enabling us to model motions in larger time window. + +Given a noised motion sequence $\mathbf{L}_t\in \mathbb{R}^{M\times d}$ at step $t$ the explicit motion generation module $\mathcal{G}$ aims to predict the clean sample $\hat{\mathbf{L}}$ condition on speaker features A and S: + +$$ +\hat {\mathbf {L}} = \mathcal {G} (\mathbf {L} _ {t}, t, \mathbf {c}), \mathbf {c} = \{\mathbf {A}, \mathbf {S} \}. \tag {5} +$$ + +As shown in Fig. 1 (a), the noised motion sequence $\mathbf{L}_t$ is mapped to the latent space and then encoded by a transformer encoder. In the meantime, the speaker features, i.e. speakers facial expression features and audio features are integrated by a cross-modal transformer, where we use a pretrained speech model wav2vec 2.0 [2] to encode the raw audio. Then a transformer decoder is used to generate denoised sequence, where the integrated speaker features are used as keys and values. + +Explicit Motion Guidance. $\hat{\mathbf{L}}$ generated by Eq. (5) contains the learned explicit 3D head poses and facial expression coefficients. It serves as a explicit motion guidance in our design. There are other options for explicit motion representation such as mesh, normal maps etc. We choose expression coefficients because it's more compact and semantic meaningful. The ways to inject conditional information are crucial in diffusion models. An intuitive way to add controllability of head poses and facial expressions might be concatenating these features and injecting to the layers of the rendering module via cross-attention operator, which is a common practice in existing methods. However, in practice, such an operation leads to sub-optimal head pose and expression controllability. Considering the different intrinsic nature of head poses and facial expressions, i.e. head pose is a global rigid transformation that decides the position of the generated head while facial expression is a local non-rigid transformation that focuses more on the visual details, we opt to use distinct conditional strategies for head pose and facial expressions accordingly. + +Specifically, for pose control, we generate explicit pose images $\mathbf{P}$ as guidance. We use three facial key points (the inner corners of the eyes and nose tip) and synthesize the pose guidance images by connecting them. Then, a pose guidance net consists of multiple convolutional layers is designed to extract multi-resolution features of the pose guidance images, and the extracted features are added to the latent features of the same resolution in the downsample blocks of the rendering module: + +$$ +\hat {\mathbf {h}} _ {d} ^ {(i)} = C o n v _ {i} (\mathbf {P}) + \mathbf {h} _ {d} ^ {(i)} \tag {6} +$$ + +where $Conv_{i}$ is the $i$ -th convolutional layer in the pose guidance net, its output has the same dimensionality as the latent features $\mathbf{h}_{d}^{(i)}$ in the downsample blocks of rendering module. + +As for the facial expression control, we adopt more fine-grained control where we inject the facial expression features $\mathbf{F}$ into the rendering module through additional cross + +![](images/c54b41eeeba2a34d2a35c9d982f1f82dddc87db2f535805efc9e8f1d65008c6b.jpg) +Figure 2. Visualization of the compared methods. Our method exhibits highly detailed visuals, accurate motion, and identity consistency. + +attention layers, one after each reference layer, and the facial expression features $\mathbf{F}$ are use as keys and values, as follows + +$$ +\mathbf {h} _ {e} ^ {(l)} = \operatorname {C r o s s A t t n} \left(\mathbf {h} _ {r} ^ {(l)}, \mathbf {F}\right), \tag {7} +$$ + +where $\mathbf{h}_r^{(l)}$ is the output of the $l$ -th reference layer. + +Implicit Motion Refinement. Though the explicit motion guidance introduced above eases the training difficulty, the explicit motion representation $\hat{\mathbf{L}}$ has limitations in depicting the facial details and subtle expressions, restricting the overall generation quality. We further propose an implicit motion refinement module to complement the explicit motion representation. Concretely, during the motion refining process, the speaker features (i.e. audio features $\mathbf{A}$ and facial expression features $\mathbf{S}$ ) are first integrated, then injected into a cross-attention layer as keys and values, and the latent feature map generated after the explicit motion modeling serving as the query, the motion refinement is + +$$ +\mathbf {h} _ {i} ^ {(l)} = C r o s s A t t n _ {s} [ \mathbf {h} _ {e} ^ {(l)}, C r o s s A t t n _ {i} (\mathbf {S}, \mathbf {A}) ] + \mathbf {h} _ {e} ^ {(l)}. (8) +$$ + +We add this refinement module after each explicit facial expression cross-attention layer by residual connections. + +Reference Net. Inspired by [34], we adopt a parallel network that has a similar structure as the rendering module to inject the identity features. Since the reference net and the rendering module both inherit structures and weights from + +SD 1.5, the corresponding layers of the two networks share certain similarities. We feed the reference image $\mathbf{I}$ to the reference net and use its intermediate UNet block features to guide the denoising process of the rendering module. Concretely, the features $\mathbf{r}_s^{(l)}$ from self-attention layers of the reference net are first concatenated with the corresponding layers' features $\mathbf{h}_s^{(l)}$ from the rendering module, then undergo a cross-attention layer to inject the identity information into the denoising process: + +$$ +\mathbf {h} _ {r} ^ {(l)} = \operatorname {C r o s s A t t n} \left[ \mathbf {h} _ {s} ^ {(l)}, \left(\mathbf {h} _ {s} ^ {(l)} \oplus \mathbf {r} _ {s} ^ {(l)}\right) \right], \tag {9} +$$ + +where the concatenated features are used as keys and values. + +# 3.3. Training Strategy + +The training of our method has two stages. In the first stage, the motion generation module is trained on listening head datasets while the rendering module is pretrained on listening head dataset together with a large scale talking head dataset VFHQ [40]. For the rendering module pretrain, we do not incorporate the speaker information, and the ground truth head poses and facial expression coefficients are used as guidance signals. In the second stage, we train the implicit motion refinement part in the rendering backbone. In this stage, we incorporate the explicit motion generated by the motion generation module as guidance. + +![](images/a1a1d42fc07b3cb4d3e0d4093c4b2cc16f6505a89429ee3a654b08567ec99f11.jpg) +Figure 3. Visualization of the ablation study on explicit motion guidance. We highlight the artifacts of the compared method with red boxes. + +![](images/41420fbb0750454dfa309594f59f0ec7148d31d9477afe324b239bec150cf576.jpg) +Figure 4. Visualization of the ablation study on different motion control schemes. We highlight the inaccurate head poses and facial expressions, as well as visual artifacts with red boxes. + +# 4. Experiments + +# 4.1. Experimental Setup + +Dataset. We conduct experiments on the widely used ViCo dataset [46] and RealTalk dataset [9]. Both ViCo and RealTalk consist of videos of face-to-face daily conversations between two individuals of diverse ages, genders, and ethnicity. We follow the training and testing split provided in their original papers. ViCo contains 398 clips of total 1.3 hours for training, 43 clips for testing, and 42 clips for out-of-distribution (OOD) testing. RealTalk contains 1489 clips of total 6.4 hours for training and 407 clips for testing. Additionally, VFHQ dataset [40], a large-scale high-quality talking head video dataset containing over 16k clips, is used to pretrain the rendering module. + +Implementation Details. For both datasets, we crop the original videos into $512 \times 512$ face videos for training and testing, and use MediaPipe [23] to extract 51-dim facial expression coefficients and 6-dim head pose. For the motion generation module, we train it with the input sequence of 50 frames and a batch size of 64. The diffusion step is set to 1000 for training and inference. For the high-fidelity rendering, we set the input to 16 frames with a batch size of 8. The diffusion step is 1000 for training and 25 for inference. Both modules are trained with AdamW [22] optimizer. + +Compared Methods. We compare the proposed method + +![](images/ed4e16e5eb40d9a27244ceabe8d07512250ca78a1e3fdbbedc9ffa4e18950d50.jpg) +Figure 5. Visualization of the ablation study on implicit motion refinement. We highlight the inaccurate motion with red boxes and the improved facial details with green box. + +with several state-of-the-art listening head generation methods, including RLHG [46], PCH [14], L2L [25], MFR-Net [20] and CustomListener [21]. We retrain RLHG, PCH and L2L on both ViCo and RealTalk dataset. Since MFR-Net and CustomListener are not open-sourced, we list their results on ViCo dataset from the original papers for reference. We also conduct thorough ablation studies to verify the effectiveness of the proposed method. + +Evaluation Metrics. We compare both visual and motion quality for evaluation. The visual quality is evaluated by Fréchet Inception Distance (FID) [12], Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity (SSIM) [38]. For the motion quality evaluation, we adopt 1) Feature Distance (FD), the $L_{1}$ distance between the generated motion and the ground truth motion, 2) $\mathrm{FID}_{\Delta \mathrm{fm}}$ [43], the FID score of motion difference between consecutive frames, and 3) Sequence Naturalness Distance (SND) [43], the summarization of $\mathrm{FID}_{\Delta \mathrm{fm}}$ and FID score of motion. For $\mathrm{FID}_{\Delta \mathrm{fm}}$ and SND, we concatenate the angle and translation to compute the overall pose metrics. To compare with existing works, we extract the 3DMM coefficients by [8], to compute the motion quality metrics. + +# 4.2. Quantitative Results + +The quantitative results on RealTalk and ViCo are listed in Table 1 and Table 2, respectively. + +For the visual quality, our proposed method obtains significantly better visual quality in terms of SSIM, PSNR and FID on both Realtalk and ViCo datasets. For instance, on RealTalk dataset, the relative performance improvements are $14\%$ for SSIM, $14\%$ for PSNR, and $33\%$ for FID. On ViCo dataset, the improvements are $12\%$ for SSIM, $15\%$ for PSNR, and $5\%$ for FID. These demonstrate the superior high-fidelity generative capability of our proposed method. This is due to the proposed rendering module is much more powerful than the deterministic PIRenderer, and that the hybrid motion modeling further enhances the visual quality of the rendering module. + +For the motion quality, our method also achieves the + +
    MethodsSSIM↑PSNR↑FID↓FD↓FIDΔfm ↓SND↓
    expangletransexpposeexppose
    RLHG [46]0.5717.8720.7913.095.916.0212.010.742.090.04
    PCH [14]0.5717.7820.0513.805.695.9911.360.722.110.04
    L2L [25]0.5015.6127.2822.9211.779.1910.930.587.810.14
    Ours0.6520.3413.3810.493.955.126.000.051.490.02
    + +Table 1. Quantitative results on RealTalk dataset, where the values of FD and $\mathrm{FID}_{\Delta \mathrm{fm}}$ are multiplied by 100. The $\uparrow$ indicates the higher the better while $\downarrow$ indicates the lower the better. The best and the second best results are in bold and underlined, respectively. + +
    MethodsTest setSSIM↑PSNR↑FID↓FD ↓FIDΔfm ↓SND ↓
    expangletransexpposeexppose
    RLHG [46]Dtest0.5817.8838.6916.439.056.759.540.763.450.09
    Dood26.709.7510.617.360.559.380.14
    PCH [14]Dtest0.6017.9231.6215.488.845.958.910.733.010.09
    Dood24.117.2710.056.070.477.790.11
    L2L [25]Dtest0.5817.7538.3920.3612.528.8812.060.606.610.19
    Dood23.828.107.438.670.518.160.07
    MFR-Net* [20]Dtest0.5917.8220.0813.376.826.02////
    Dood14.708.126.37////
    CustomListener* [21]Dtest0.6017.9820.0611.546.125.903.120.062.400.07
    Dood12.677.496.013.590.075.940.05
    OursDtest0.6720.6018.9912.547.575.685.130.082.360.08
    Dood11.893.835.435.050.052.060.02
    + +Table 2. Quantitative results on ViCo dataset, where the values of FD and $\mathrm{FID}_{\Delta \mathrm{fm}}$ are multiplied by 100. The $\uparrow$ indicates higher is better for the corresponding metric while $\downarrow$ indicates lower is better. The * denotes we report the results from their papers. The best and the second best results are in bold and underlined respectively. + +best overall performance on both datasets. Specifically, for RealTalk, we achieve the best results on all motion metrics. In terms of FD, we obtain $20\%$ , $31\%$ , and $15\%$ performance improvement for the expression, angle, and translations, respectively. In terms of $\mathrm{FID}_{\Delta \mathrm{fm}}$ , the performance improvements are $45\%$ for expression and $91\%$ for head pose. On ViCo dataset, we also obtain the best motion quality on the OOD set and the second-best results on the test set. For ViCo, the motion of the test set is much more intense and random than that of the OOD set. The one-to-many characteristic makes it more difficult to generate the exact motion as the ground truth on the test set. In such cases, CustomListener that additionally incorporates the ground-truth motion text description leads to more similar motions to the ground-truth. Nevertheless, the superior performance on the OOD set demonstrates our better generalization ability. These results verify that our method can largely promote the visual and motion quality, enabling realistic and vivid listening head generation. + +# 4.3. Qualitative Results + +We compare the visualization result with RLHG, L2L and PCH. MFR-Net and CustomListener are not open-sourced + +and their visualization is not available. As shown in Fig 2, our method surpasses the baseline methods in terms of visual quality, motion accuracy, and identity consistency. To be specific, 1) in Fig. 2 (a), our method generates a proper reaction video while the baseline methods show inappropriate facial expressions. 2) in Fig. 2 (b, c), we obtain much better identity preservation, even under more drastic facial expressions, e.g. laughing. 3) in Fig. 2 (b, c, d), our method retains better facial details, such as realistic teeth, wrinkles, and natural complexities. + +# 4.4. Ablation Study + +We conduct ablations to demonstrate the necessities of each part of the proposed hybrid motion modeling. + +Explicit Motion Modeling. We remove the intermediate explicit motion guidance and train a diffusion UNet that learns the listener motion purely from implicit motion modeling, i.e. the rendering module in Section 3.2 without pose guidance net and expression attention layers. The network is first pretrained on VFHQ and Realtalk dataset for unconditioned image generation, then trained on Realtalk dataset for listening head generation conditioned on speaker features. As shown in Table 3, without the motion guidance, + +
    MethodsSSIM↑PSNR↑FID↓FD↓FIDΔfm ↓SND↓
    expangletransexpposeexppose
    w/o motion guidance0.6319.7514.3711.024.285.009.050.121.670.02
    w/o implicit motion refinement0.6420.1713.5811.004.055.176.840.061.610.02
    Ours0.6520.3413.3810.483.945.126.000.051.480.02
    + +Table 3. Ablation study on motion modeling, tested on Realtalk dataset, the values of FD and $\mathrm{{FID}}_{{\Delta }_{\mathrm{{fm}}}}$ are multiplied by 100 . + +
    SettingsFD↓FIDΔfm ↓
    expangletransexppose
    Concatenate pose7.813.034.369.870.10
    Separate control7.482.014.284.690.10
    + +Table 4. Ablation study on different motion control schemes, tested on Realtalk dataset, the values of FD and $\mathrm{FID}_{\Delta \mathrm{fm}}$ are multiplied by 100. + +both the visual quality and the motion quality of the generated listening head degrades. It can be observed that $\mathrm{FID}_{\Delta \mathrm{fm}}$ has significantly degrades, indicating there are unnatural transitions of expression and head poses. As shown in Fig. 3, without motion guidance, the network struggles to generate continuous head poses and expressions, often resulting in serious artifacts in faces. Such result proves that the explicit motion guidance can effectively ease the training of LDM-based models on small scale datasets. + +The Distinct Controls of Pose and Expressions. In Section 3.2, we propose to use separate controls of head pose and facial expression according to the intrinsics of these two types of motion signals. To validate the effectiveness of the proposed control strategies, we remove the pose images in the rendering module, and concatenate the head pose coefficients with the facial expression coefficients. The concatenated motion signal is injected into the rendering module through the expression cross-attention layer. The results in Table 4 show that using concatenated motion as the control signal leads to a degeneration in both motion accuracy and naturalness, especially on expression metrics. We also present some visualizations in Fig. 4. From the visualization, there exists inaccurate pose control and visual artifacts when using concatenated motion signals (the left example), and poor expression controllability (the right example). These results verify the effectiveness of the proposed pose and expression controls. + +Implicit Motion Refinement. Furthermore, we validate the effectiveness of the proposed implicit motion refinement method. As shown in Table 3, without the refinement module, the motion quality and visual quality of the generated video both degrade. As shown in Fig. 5, we observe mainly two effects of the implicit motion refinement. The first is that the refinement fixes some wrong facial expressions (the + +left example), and the second is that it tends to add more facial details to the generated videos, such as more realistic wrinkles (the right example). As a result, we can observe more stable and detailed facial expressions after refinement. This implies that the implicit motion refinement helps the rendering module learn to revise the details of the generated videos given additional conditions, further improving the visual qualities. + +**Discussions.** Our proposed framework can generate high fidelity listening head videos with accurate motion, vivid facial details and expressive motions. Nevertheless, there are still some limitations. 1) The condition used to generate listening heads is restricted within the speaker's audio and facial expressions. But more flexible conditions such as text description, motion styles etc. are always appreciated. The proposed hybrid motion generation has the potential of integrating diverse control signals, we will study this in the future. 2) Time complexities. The motion generation module in our framework is lightweight and can generate motions at 15 fps, the computational bottleneck lies in the rendering module. This is a common limitation of the LDM-based methods and can be alleviated by model quantization or distillation, and we will explore more in the future. + +Supplementary Materials. We provide user study, details of network, training objectives, experimental setups, ethics, and more visual results in supplementary materials. + +# 5. Conclusion + +In this paper, we propose a diffusion-based listening head generation framework that generates photorealistic listening head videos up to $512 \times 512$ resolution, with highly expressive motions and fine facial details. A hybrid motion modeling method that consists of an explicit motion generation module, a specially designed motion control strategy and an implicit motion refining process eases the training of the LDM-based framework, making the learning on a small scale dataset feasible. Comprehensive experiments on Realtalk and ViCo dataset demonstrate that our framework achieves superior results in terms of visual quality and motion expressiveness compared with several state-of-the-art methods. And a thorough ablation study proves the effectiveness and necessity of the proposed hybrid motion modeling method. 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In European Conference on Computer Vision, 2021. 1, 2, 6, 7 \ No newline at end of file diff --git a/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/images.zip b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..12bb4fa962c773b45f260a3394d40b0d1fc821bb --- /dev/null +++ b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:85825c93f115226fd7f1dc0c08e2bc51a5e8587a79b847485757d979c2ee3cda +size 625023 diff --git a/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/layout.json b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..22c867a28f8860118816e195d7a75234e3f10062 --- /dev/null +++ b/2025/Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling/layout.json @@ -0,0 +1,7734 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 83, + 102, + 529, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 102, + 529, + 140 + ], + "spans": [ + { + "bbox": [ + 83, + 102, + 529, + 140 + ], + "type": "text", + "content": "Diffusion-based Realistic Listening Head Generation via Hybrid Motion Modeling" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "spans": [ + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "text", + "content": "Yinuo Wang" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1,*,‡}" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "text", + "content": ", Yanbo Fan" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{2,*,†}" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "text", + "content": ", Xuan Wang" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "text", + "content": ", Guo Yu" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1,†}" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "text", + "content": ", Fei Wang" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 112, + 160, + 499, + 217 + ], + "type": "text", + "content": "National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 219, + 217, + 388, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 219, + 217, + 388, + 245 + ], + "spans": [ + { + "bbox": [ + 219, + 217, + 388, + 245 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 219, + 217, + 388, + 245 + ], + "type": "text", + "content": "Ant Group\nnuolwang.github.io/DiffListener" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 273, + 201, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 273, + 201, + 285 + ], + "spans": [ + { + "bbox": [ + 151, + 273, + 201, + 285 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 298, + 297, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 298, + 297, + 585 + ], + "spans": [ + { + "bbox": [ + 53, + 298, + 297, + 585 + ], + "type": "text", + "content": "Listening head generation aims to synthesize non-verbal responsive listening head videos that naturally react to a certain speaker, for which, both realistic head movements, expressive facial expressions, and high visual qualities are expected. Previous approaches typically follow a two-stage pipeline that first generates intermediate 3D motion signals such as 3DMM coefficients, and then synthesizes the videos by deterministic rendering, suffering from limited motion expressiveness and low visual quality (e.g. " + }, + { + "bbox": [ + 53, + 298, + 297, + 585 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 53, + 298, + 297, + 585 + ], + "type": "text", + "content": "). In this work, we propose a novel listening head generation method that harnesses the generative capabilities of the diffusion model for both motion generation and high-quality rendering. Crucially, we propose an effective hybrid motion modeling module that addresses training difficulties caused by the scarcity of listening head data while preserving the intricate details that may be lost in explicit motion representations. We further develop a tailored control guidance for head pose and facial expression, by integrating their intrinsic motion characteristics. Our method enables high-fidelity video generation with " + }, + { + "bbox": [ + 53, + 298, + 297, + 585 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 53, + 298, + 297, + 585 + ], + "type": "text", + "content": " resolution and delivers vivid listener motion feedback. We conduct comprehensive experiments and obtain superior performance in terms of both visual quality and motion expressiveness compared with existing methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 608, + 137, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 608, + 137, + 620 + ], + "spans": [ + { + "bbox": [ + 56, + 608, + 137, + 620 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 628, + 296, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 296, + 677 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 296, + 677 + ], + "type": "text", + "content": "Listening head generation aims to generate responsive listener videos that react to the corresponding speaker [46]. Unlike talking head videos, the listener's response mainly consists of non-verbal behaviors, such as nodding, smil" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 274, + 555, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 274, + 555, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 555, + 346 + ], + "type": "text", + "content": "ing, frowning, head shaking, etc. The realism and vividness of the listener feedback are vital to the success of speaker and listener communication. Being a crucial part of digital avatar generation, listening head generation has many potential applications, such as movie production, online customer service, and human-computer interaction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 350, + 556, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 350, + 556, + 482 + ], + "spans": [ + { + "bbox": [ + 313, + 350, + 556, + 482 + ], + "type": "text", + "content": "While most works focus on speaker-centric talking head generation [16, 17, 26-28, 37, 44], only a few study listening head generation [21, 24, 25, 46]. It is a non-trivial problem as given a certain speaker video, there can be many reasonable listener reactions. Such a one-to-many mapping problem makes it challenging for the model to learn to generate proper yet diverse listener motions. In addition, since the generated listening head mostly contains non-verbal reactions, the audience may focus more on the listeners' facial expressions, requiring that the generated reaction videos be high-fidelity to manifest detailed and subtle expressions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 486, + 556, + 715 + ], + "type": "text", + "content": "The state-of-the-art works of listening head generation follow a two-stage design that first generates intermediate listener motion signals and then synthesizes the RGB videos with post-rendering [20, 21, 35, 46]. For motion generation, explicit 3D motion signals, such as 3DMM [3] coefficients are used as motion descriptions. Existing works developed different models to generate the listener's 3D motion coefficients, including LSTM [46], VQ-VAE [35], and diffusion-based models [20, 21]. As for the video rendering, PIRenderer [29] is used to generate the RGB frames conditioned on the generated 3DMM coefficients. Though promising, they still fall short of generating expressive and natural listening head motions, as well as photorealistic rendering. For instance, 1) the intermediate parametric 3D motion signals, such as the 3DMM expression coefficients, are characterized in a low-dimensional generalizable subspace and lack facial details and subtle expressions, which limits the richness and naturalness of the learned facial expressions, 2) while focusing more on motion generation, the determinis" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 683, + 133, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 683, + 133, + 693 + ], + "spans": [ + { + "bbox": [ + 66, + 683, + 133, + 693 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 67, + 693, + 146, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 693, + 146, + 703 + ], + "spans": [ + { + "bbox": [ + 67, + 693, + 146, + 703 + ], + "type": "text", + "content": "† Corresponding authors" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 67, + 703, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 703, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 67, + 703, + 286, + 713 + ], + "type": "text", + "content": "This work was done during Yinuo Wang's internship at Ant Group" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15885" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "tic rendering used in existing works is of low visual quality, suffering from low resolution (e.g. " + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 55, + 72, + 294, + 108 + ], + "type": "text", + "content": "), identity inconsistency, improper head motions, and facial artifacts." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 111, + 295, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 111, + 295, + 409 + ], + "spans": [ + { + "bbox": [ + 56, + 111, + 295, + 409 + ], + "type": "text", + "content": "In this work, we propose a novel listening head generation framework that enables both highly expressive head motions and photorealistic rendering. Our motivation is to fully leverage the generative ability of the diffusion model for both motion generation and video synthesis. Recently, the latent diffusion model (LDM) [30] has shown superior ability in high-resolution and vivid video generation, largely promoting the speaker-centric talking head generation performance [7, 34, 41]. Nevertheless, it is not feasible to directly apply these methods to listening head generation. Firstly, they require hundreds of hours of talking head videos for training the audio-to-visual correspondence, which does not apply to listening head generation, where only a few hours of training data are available. Secondly, due to the high computational and memory cost, these methods can only model the context information in a small window size (e.g. 16 frames in [34]). This is acceptable for talking head generation since talking heads have a strong correlation with the audio. However, for listening head generation, the listener feedback may be related to an even longer duration of the speaker's content. To generate a reasonable reaction, it may require long-term modeling of audio conditions and motion. Based on these, it is nontrivial to unleash the diffusion generative ability for listening head generation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 412, + 295, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 412, + 295, + 675 + ], + "spans": [ + { + "bbox": [ + 55, + 412, + 295, + 675 + ], + "type": "text", + "content": "To address these challenges, we propose a novel hybrid motion modeling method, which consists of an explicit and explainable 3D motion representation and a learnable implicit latent representation. Specifically, instead of utilizing the LDM-based rendering to generate listening video directly from the speaker's input, we first learn explicit 3D motion signals by a diffusion-based motion generation module. The explicit motions are later used as guiding conditions to train the rendering module. To facilitate controllability, we propose distinct control strategies considering the different intrinsic natures of head poses and facial expressions. The explicit motion generation module is expected to generate feasible and diverse listener motions but may lack facial details, as analyzed above. We further develop an implicit motion refinement module to complement the potentially missing facial details. With these designs, we successfully train the LDM-based rendering model on the small-scale listening dataset, enabling high-fidelity rendering (e.g. " + }, + { + "bbox": [ + 55, + 412, + 295, + 675 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 412, + 295, + 675 + ], + "type": "text", + "content": ") and vivid and expressive listener motion generation. Compared with the existing methods, we significantly boost listening head generation performance in both visual and motion quality." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 295, + 713 + ], + "type": "text", + "content": "The hybrid motion design brings several advantages, 1) the explicit motion generation module is lightweight and takes much less computational resources than directly mod" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 553, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 190 + ], + "type": "text", + "content": "eling audio-to-visual correspondence, making it possible to learn the long-term relations between speaker and listener, which is essential for listener motion modeling. 2) The learning of the hybrid motion representation is much easier than the pure latent motion modeling, especially on limited training data. In addition, with the intermediate explicit representation, we can better utilize talking videos to pre-train the rendering module. We conduct thorough ablation studies and verify the necessity of the hybrid motion modeling. Our contributions are as follows," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 192, + 553, + 300 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 314, + 192, + 553, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 192, + 553, + 227 + ], + "spans": [ + { + "bbox": [ + 314, + 192, + 553, + 227 + ], + "type": "text", + "content": "- We propose a novel diffusion-based method for motion generation and visual rendering, resulting in realistic and vivid listening head generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 228, + 553, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 262 + ], + "type": "text", + "content": "- We introduce an effective hybrid motion modeling module that overcomes training challenges while enhancing both motion dynamics and visual quality." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 264, + 553, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 264, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 264, + 553, + 300 + ], + "type": "text", + "content": "- We conduct comprehensive experiments and significantly improve listening head generation in both visual quality and motion quality compared with existing methods." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 311, + 405, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 311, + 405, + 323 + ], + "spans": [ + { + "bbox": [ + 314, + 311, + 405, + 323 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 331, + 553, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 553, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 553, + 426 + ], + "type": "text", + "content": "Non-verbal Listening Head Generation. Non-verbal listening head generation is an important part of digital avatar generation, and has drawn increasing research interests in recent years. Earlier works [4, 5, 10, 15, 32] use rule-based methods to generate the listener response. Such methods require specifically designed rules and pre-defined reaction motion sequences. Thus they have very limited motion diversity and expressiveness." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 426, + 553, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 426, + 553, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 426, + 553, + 676 + ], + "type": "text", + "content": "Learning-based methods alleviate the problem by using data-driven approaches to automatically learn to generate proper reactions given speaker conditions. Zhou et al. [46] propose an LSTM-based network RLHG that predicts the listener's head poses and 3DMM expression coefficients given speaker's audio and motions. Later, several works are proposed to improve the performance of RLHG by refining the conditional features [6, 45] or improving visual quality [14]. However, these works are deterministic models and are inefficient in addressing the one-to-many mapping problems in listener motion generation, resulting in unnatural motions. To alleviate this, the work of [25] models the listener motion with VQ-VAE. Song et al. [31] proposes a more fine-grained codebook that supports emotion control. Liu et al. [20] further improves the diversity of the generated motion by a diffusion model. In addition, the work of Liu et al. [21] improves the controllability of the diffusion-based motion generation model by aggregating the user-specified expression and pose labels. Focusing on intermediate motion generation, these methods suffer from limited expressiveness and naturalness in the generated videos." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "Diffusion Generative Models on Head Generation. Denoising diffusion probabilistic models [13] have shown remarkable results on image generation tasks. An iconic work" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "15886" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 552, + 309 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 552, + 309 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 552, + 309 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 552, + 309 + ], + "type": "image", + "image_path": "4b60f0904798e2a909ef3e9570f4b7ced397e5822a692fb20ec2e00c5b0cc4d0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 318, + 555, + 353 + ], + "lines": [ + { + "bbox": [ + 55, + 318, + 555, + 353 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 555, + 353 + ], + "type": "text", + "content": "Figure 1. Overview of the proposed framework. Given one listener portrait image and speaker's audio and head motion as input, we generate realistic and vivid listening head video. (a) is a lightweight diffusion transformer to generate the explicit motion representation, (b) is a reference net to extract the listener identity feature, (c) is our generation backbone, (d) is the implicit motion refinement module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 372, + 297, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 372, + 297, + 577 + ], + "spans": [ + { + "bbox": [ + 54, + 372, + 297, + 577 + ], + "type": "text", + "content": "is Stable Diffusion (SD), which is based on latent diffusion model (LDM) [30] and can generate high-resolution images. Guo et al. [11] propose a plug-in motion module and a lightweight fine-tuning technique that enables Stable Diffusion to generate animated clips. Based on these works, Tian et al. [34] propose EMO, a direct audio to talking head video generation framework that discards intermediate 3DMM representations. Benefiting from the capability of Stable Diffusion, EMO outperforms previous talking head generation methods in terms of expressiveness and realism. Several other diffusion-based audio driven works are proposed after EMO, and achieve promising results [7, 18, 41], proving the powerful generative capabilities of diffusion models in talking head generations. Nevertheless, these models require hundreds of hours training data. This can be an obstacle for training the listening head generation model, where only a few hours of data are available." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 586, + 112, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 586, + 112, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 586, + 112, + 597 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 605, + 296, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 605, + 296, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 605, + 296, + 666 + ], + "type": "text", + "content": "Given a single listener portrait image and a speaker's audio and video, we aim to generate a non-verbal responsive listening head video that synchronizes with the speaker, with detailed facial expressions and natural head movements. Our overall framework is shown in Fig. 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 672, + 142, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 142, + 683 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 142, + 683 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 296, + 713 + ], + "type": "text", + "content": "We first introduce the preliminaries of the diffusion model [13, 30], which is a key component of our frame" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 372, + 555, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 555, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 555, + 433 + ], + "type": "text", + "content": "work. The diffusion model defines a Markov chain of adding random noise to data samples and then trains the network to learn the reverse process, so that it can generate desired data from random noise. The forward diffusion process is defined as," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 378, + 441, + 555, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 441, + 555, + 455 + ], + "spans": [ + { + "bbox": [ + 378, + 441, + 555, + 455 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}", + "image_path": "e870888da0d7498c8b247241dd8ae337f334517f4e5802a8c9d3cb8a184f79a8.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "spans": [ + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}_t" + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "text", + "content": " is a hyper-parameter that controls the diffusion rate. With Eq. (1), we can sample at arbitrary step " + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "text", + "content": " to get the noised sample. Then the reverse diffusion process trains a neural network to predict the noise " + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "inline_equation", + "content": "\\epsilon_t" + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "text", + "content": " added to the samples at step " + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 464, + 554, + 536 + ], + "type": "text", + "content": ", and the overall training objective is simplified as [13]:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 350, + 545, + 555, + 560 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 545, + 555, + 560 + ], + "spans": [ + { + "bbox": [ + 350, + 545, + 555, + 560 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t} = \\mathbb {E} _ {t \\sim [ 1, T ], \\mathbf {x} _ {0}, \\epsilon_ {t}} [ | | \\epsilon_ {t} - \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t, \\mathbf {c}) | | ^ {2} ], \\tag {2}", + "image_path": "a2372d6ac2ee209fc49d8c6b5ba98f49a4f72f8e2ca1012a9acccf32246710a7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "type": "text", + "content": " is predicted using a neural network with parameters " + }, + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\theta, T" + }, + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "type": "text", + "content": " is the max step, and " + }, + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 313, + 568, + 554, + 593 + ], + "type": "text", + "content": " is the additional condition." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 600, + 419, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 600, + 419, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 600, + 419, + 613 + ], + "type": "text", + "content": "3.2. Network Pipeline" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{N \\times d_a}" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": " denote the speaker's audio and 3D head motion features, where " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": " is the number of frames, " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "d_a" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": " are dimensionality of audio and speaker's motion features respectively. Let " + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{h \\times w \\times c}" + }, + { + "bbox": [ + 313, + 616, + 555, + 713 + ], + "type": "text", + "content": " be the listener portrait for identity reference. As shown in Fig. 1, to enable high-fidelity rendering and vivid responsive head motion generation, 1) we adopt an LDM-based high-fidelity rendering module to harness the power of diffusion models," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15887" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 204 + ], + "type": "text", + "content": "so the visual qualities of the generated videos can be greatly improved. 2) We propose a novel hybrid motion modeling module that consists of a lightweight explicit motion generation module to generate explicit guiding motions, i.e. head poses and facial expressions, a tailored control strategy for the rigid head poses and non-rigid facial expressions, and an implicit and learnable motion refinement module to complement the motion details. 3) To enhance the identity consistency of the generated video, a parallel reference net with similar structure as the rendering module is used to integrate the listener identity features. We introduce each part next." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 204, + 295, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 204, + 295, + 383 + ], + "spans": [ + { + "bbox": [ + 55, + 204, + 295, + 383 + ], + "type": "text", + "content": "High-fidelity Rendering Module. One major limitation of the existing listening head generation methods is the deterministic rendering module such as PIRenderer [29], which suffers from low resolution, identity inconsistency, and visual artifacts. Inspired by the recent advance in diffusion-based talking head generation works [34, 36, 39], we design a high-fidelity rendering module based on SD 1.5. To enable the video generation capability of SD 1.5, we follow the motion module design [11, 19] that applies self attention along the temporal dimension of the network's intermediate features, ensuring the continuity and consistency along the generated video frames. Benefiting from the probabilistic nature and the great generative capabilities, the proposed rendering module can generate photorealistic videos with detailed visuals and expressive motions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "content": "Conditioned on reference image " + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "content": ", and speaker features " + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "content": ", the rendering module " + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "content": " takes noised latent " + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_t \\in \\mathbb{R}^{N \\times h \\times w \\times c}" + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "content": " at step " + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "content": " as inputs, and predicts the denoised latent " + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{V}}_0" + }, + { + "bbox": [ + 55, + 384, + 295, + 431 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 441, + 295, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 441, + 295, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 295, + 455 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {V}} _ {0} = \\mathcal {R} \\left(\\mathbf {V} _ {t}, t, \\mathbf {c}\\right), \\mathbf {c} = \\{\\mathbf {A}, \\mathbf {S}, \\mathbf {I} \\}. \\tag {3}", + "image_path": "dfb895b1a4f657063c1be150243266f7e356fe0d7d0aae22982c5cb152c13731.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 464, + 295, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 464, + 295, + 560 + ], + "spans": [ + { + "bbox": [ + 55, + 464, + 295, + 560 + ], + "type": "text", + "content": "However, facing the scarcity of the listening head data, it's not feasible to train the rendering module directly from speaker features alone. So we propose a novel hybrid motion modeling method where we use explicit listener motion " + }, + { + "bbox": [ + 55, + 464, + 295, + 560 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}" + }, + { + "bbox": [ + 55, + 464, + 295, + 560 + ], + "type": "text", + "content": " as an additional guiding signal to ease the training of the rendering module. " + }, + { + "bbox": [ + 55, + 464, + 295, + 560 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}" + }, + { + "bbox": [ + 55, + 464, + 295, + 560 + ], + "type": "text", + "content": " is set to 51-dim facial expression coefficient and 6-dim head pose coefficients extracted by MediaPipe [23]. The generation procedure becomes:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 100, + 569, + 295, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 569, + 295, + 583 + ], + "spans": [ + { + "bbox": [ + 100, + 569, + 295, + 583 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {V}} _ {0} = \\mathcal {R} \\left(\\mathbf {V} _ {t}, t, \\mathbf {c}\\right), \\mathbf {c} = \\{\\hat {\\mathbf {L}}, \\mathbf {A}, \\mathbf {S}, \\mathbf {I} \\}, \\tag {4}", + "image_path": "be0dd64e6a65d2cc0b8c82ff83841813ba31ed4cd235c2c841d22c7c33ce1120.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}" + }, + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "text", + "content": " is generated by a lightweight motion generation module, given the speaker features " + }, + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 55, + 594, + 295, + 616 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 295, + 713 + ], + "type": "text", + "content": "Explicit Motion Generation. We design a transformer diffusion-based explicit motion generation module, inspired by the successful applications of diffusion models on various human motion generations [1, 21, 33, 42]. The motion generation module generates both listener's facial expressions and head poses with a lightweight diffusion network, addressing the one-to-many mapping problem as well as enabling us to model motions in larger time window." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": "Given a noised motion sequence " + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_t\\in \\mathbb{R}^{M\\times d}" + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": " at step " + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": " the explicit motion generation module " + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": " aims to predict the clean sample " + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}" + }, + { + "bbox": [ + 313, + 72, + 553, + 108 + ], + "type": "text", + "content": " condition on speaker features A and S:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 373, + 118, + 553, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 118, + 553, + 131 + ], + "spans": [ + { + "bbox": [ + 373, + 118, + 553, + 131 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {L}} = \\mathcal {G} (\\mathbf {L} _ {t}, t, \\mathbf {c}), \\mathbf {c} = \\{\\mathbf {A}, \\mathbf {S} \\}. \\tag {5}", + "image_path": "3dce19b868bbdb2c47811323099a32470b20d05168a2c31b17299f4679a72168.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 140, + 555, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 140, + 555, + 247 + ], + "spans": [ + { + "bbox": [ + 313, + 140, + 555, + 247 + ], + "type": "text", + "content": "As shown in Fig. 1 (a), the noised motion sequence " + }, + { + "bbox": [ + 313, + 140, + 555, + 247 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_t" + }, + { + "bbox": [ + 313, + 140, + 555, + 247 + ], + "type": "text", + "content": " is mapped to the latent space and then encoded by a transformer encoder. In the meantime, the speaker features, i.e. speakers facial expression features and audio features are integrated by a cross-modal transformer, where we use a pretrained speech model wav2vec 2.0 [2] to encode the raw audio. Then a transformer decoder is used to generate denoised sequence, where the integrated speaker features are used as keys and values." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 247, + 555, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 247, + 555, + 488 + ], + "spans": [ + { + "bbox": [ + 313, + 247, + 555, + 488 + ], + "type": "text", + "content": "Explicit Motion Guidance. " + }, + { + "bbox": [ + 313, + 247, + 555, + 488 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}" + }, + { + "bbox": [ + 313, + 247, + 555, + 488 + ], + "type": "text", + "content": " generated by Eq. (5) contains the learned explicit 3D head poses and facial expression coefficients. It serves as a explicit motion guidance in our design. There are other options for explicit motion representation such as mesh, normal maps etc. We choose expression coefficients because it's more compact and semantic meaningful. The ways to inject conditional information are crucial in diffusion models. An intuitive way to add controllability of head poses and facial expressions might be concatenating these features and injecting to the layers of the rendering module via cross-attention operator, which is a common practice in existing methods. However, in practice, such an operation leads to sub-optimal head pose and expression controllability. Considering the different intrinsic nature of head poses and facial expressions, i.e. head pose is a global rigid transformation that decides the position of the generated head while facial expression is a local non-rigid transformation that focuses more on the visual details, we opt to use distinct conditional strategies for head pose and facial expressions accordingly." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 487, + 554, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 487, + 554, + 594 + ], + "spans": [ + { + "bbox": [ + 313, + 487, + 554, + 594 + ], + "type": "text", + "content": "Specifically, for pose control, we generate explicit pose images " + }, + { + "bbox": [ + 313, + 487, + 554, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 313, + 487, + 554, + 594 + ], + "type": "text", + "content": " as guidance. We use three facial key points (the inner corners of the eyes and nose tip) and synthesize the pose guidance images by connecting them. Then, a pose guidance net consists of multiple convolutional layers is designed to extract multi-resolution features of the pose guidance images, and the extracted features are added to the latent features of the same resolution in the downsample blocks of the rendering module:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 382, + 603, + 553, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 603, + 553, + 620 + ], + "spans": [ + { + "bbox": [ + 382, + 603, + 553, + 620 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {h}} _ {d} ^ {(i)} = C o n v _ {i} (\\mathbf {P}) + \\mathbf {h} _ {d} ^ {(i)} \\tag {6}", + "image_path": "6f97c6438e5ab7e1465c900a66ac641388a1d4399941b28abc01dee2090d0a26.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "spans": [ + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "type": "inline_equation", + "content": "Conv_{i}" + }, + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "type": "text", + "content": "-th convolutional layer in the pose guidance net, its output has the same dimensionality as the latent features " + }, + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{d}^{(i)}" + }, + { + "bbox": [ + 313, + 628, + 553, + 676 + ], + "type": "text", + "content": " in the downsample blocks of rendering module." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": "As for the facial expression control, we adopt more fine-grained control where we inject the facial expression features " + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 313, + 677, + 553, + 713 + ], + "type": "text", + "content": " into the rendering module through additional cross" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15888" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 69, + 553, + 361 + ], + "blocks": [ + { + "bbox": [ + 59, + 69, + 553, + 361 + ], + "lines": [ + { + "bbox": [ + 59, + 69, + 553, + 361 + ], + "spans": [ + { + "bbox": [ + 59, + 69, + 553, + 361 + ], + "type": "image", + "image_path": "c54b41eeeba2a34d2a35c9d982f1f82dddc87db2f535805efc9e8f1d65008c6b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 369, + 552, + 383 + ], + "lines": [ + { + "bbox": [ + 56, + 369, + 552, + 383 + ], + "spans": [ + { + "bbox": [ + 56, + 369, + 552, + 383 + ], + "type": "text", + "content": "Figure 2. Visualization of the compared methods. Our method exhibits highly detailed visuals, accurate motion, and identity consistency." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 403, + 295, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 403, + 295, + 437 + ], + "spans": [ + { + "bbox": [ + 55, + 403, + 295, + 437 + ], + "type": "text", + "content": "attention layers, one after each reference layer, and the facial expression features " + }, + { + "bbox": [ + 55, + 403, + 295, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 55, + 403, + 295, + 437 + ], + "type": "text", + "content": " are use as keys and values, as follows" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 437, + 295, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 437, + 295, + 452 + ], + "spans": [ + { + "bbox": [ + 116, + 437, + 295, + 452 + ], + "type": "interline_equation", + "content": "\\mathbf {h} _ {e} ^ {(l)} = \\operatorname {C r o s s A t t n} \\left(\\mathbf {h} _ {r} ^ {(l)}, \\mathbf {F}\\right), \\tag {7}", + "image_path": "90185249c6660d95460b21c75036dfc9b5d57bc444b6e1781809d0489bfa2f12.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 455, + 259, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 259, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 259, + 469 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 455, + 259, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_r^{(l)}" + }, + { + "bbox": [ + 55, + 455, + 259, + 469 + ], + "type": "text", + "content": " is the output of the " + }, + { + "bbox": [ + 55, + 455, + 259, + 469 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 55, + 455, + 259, + 469 + ], + "type": "text", + "content": "-th reference layer." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "spans": [ + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "type": "text", + "content": "Implicit Motion Refinement. Though the explicit motion guidance introduced above eases the training difficulty, the explicit motion representation " + }, + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}" + }, + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "type": "text", + "content": " has limitations in depicting the facial details and subtle expressions, restricting the overall generation quality. We further propose an implicit motion refinement module to complement the explicit motion representation. Concretely, during the motion refining process, the speaker features (i.e. audio features " + }, + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "type": "text", + "content": " and facial expression features " + }, + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 54, + 469, + 295, + 613 + ], + "type": "text", + "content": ") are first integrated, then injected into a cross-attention layer as keys and values, and the latent feature map generated after the explicit motion modeling serving as the query, the motion refinement is" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 619, + 295, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 619, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 59, + 619, + 295, + 635 + ], + "type": "interline_equation", + "content": "\\mathbf {h} _ {i} ^ {(l)} = C r o s s A t t n _ {s} [ \\mathbf {h} _ {e} ^ {(l)}, C r o s s A t t n _ {i} (\\mathbf {S}, \\mathbf {A}) ] + \\mathbf {h} _ {e} ^ {(l)}. (8)", + "image_path": "1d9030f3941b53d181c4949aba97b94625c4d6aef6f95ce8678e73d850333914.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "spans": [ + { + "bbox": [ + 55, + 641, + 295, + 666 + ], + "type": "text", + "content": "We add this refinement module after each explicit facial expression cross-attention layer by residual connections." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 666, + 296, + 714 + ], + "type": "text", + "content": "Reference Net. Inspired by [34], we adopt a parallel network that has a similar structure as the rendering module to inject the identity features. Since the reference net and the rendering module both inherit structures and weights from" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "type": "text", + "content": "SD 1.5, the corresponding layers of the two networks share certain similarities. We feed the reference image " + }, + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "type": "text", + "content": " to the reference net and use its intermediate UNet block features to guide the denoising process of the rendering module. Concretely, the features " + }, + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_s^{(l)}" + }, + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "type": "text", + "content": " from self-attention layers of the reference net are first concatenated with the corresponding layers' features " + }, + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_s^{(l)}" + }, + { + "bbox": [ + 313, + 403, + 555, + 514 + ], + "type": "text", + "content": " from the rendering module, then undergo a cross-attention layer to inject the identity information into the denoising process:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 354, + 521, + 555, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 521, + 555, + 537 + ], + "spans": [ + { + "bbox": [ + 354, + 521, + 555, + 537 + ], + "type": "interline_equation", + "content": "\\mathbf {h} _ {r} ^ {(l)} = \\operatorname {C r o s s A t t n} \\left[ \\mathbf {h} _ {s} ^ {(l)}, \\left(\\mathbf {h} _ {s} ^ {(l)} \\oplus \\mathbf {r} _ {s} ^ {(l)}\\right) \\right], \\tag {9}", + "image_path": "3a39da936cabac89bfd437d621b83132f533fe7d68f0b41cb46ad1e7247097fa.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 545, + 553, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 553, + 558 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 553, + 558 + ], + "type": "text", + "content": "where the concatenated features are used as keys and values." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 564, + 421, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 421, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 421, + 578 + ], + "type": "text", + "content": "3.3. Training Strategy" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": "The training of our method has two stages. In the first stage, the motion generation module is trained on listening head datasets while the rendering module is pretrained on listening head dataset together with a large scale talking head dataset VFHQ [40]. For the rendering module pretrain, we do not incorporate the speaker information, and the ground truth head poses and facial expression coefficients are used as guidance signals. In the second stage, we train the implicit motion refinement part in the rendering backbone. In this stage, we incorporate the explicit motion generated by the motion generation module as guidance." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15889" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 290, + 178 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 290, + 178 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 290, + 178 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 290, + 178 + ], + "type": "image", + "image_path": "a1a1d42fc07b3cb4d3e0d4093c4b2cc16f6505a89429ee3a654b08567ec99f11.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 186, + 295, + 218 + ], + "lines": [ + { + "bbox": [ + 55, + 186, + 295, + 218 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 295, + 218 + ], + "type": "text", + "content": "Figure 3. Visualization of the ablation study on explicit motion guidance. We highlight the artifacts of the compared method with red boxes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 61, + 230, + 291, + 339 + ], + "blocks": [ + { + "bbox": [ + 61, + 230, + 291, + 339 + ], + "lines": [ + { + "bbox": [ + 61, + 230, + 291, + 339 + ], + "spans": [ + { + "bbox": [ + 61, + 230, + 291, + 339 + ], + "type": "image", + "image_path": "41420fbb0750454dfa309594f59f0ec7148d31d9477afe324b239bec150cf576.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 347, + 295, + 381 + ], + "lines": [ + { + "bbox": [ + 55, + 347, + 295, + 381 + ], + "spans": [ + { + "bbox": [ + 55, + 347, + 295, + 381 + ], + "type": "text", + "content": "Figure 4. Visualization of the ablation study on different motion control schemes. We highlight the inaccurate head poses and facial expressions, as well as visual artifacts with red boxes." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 400, + 135, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 400, + 135, + 414 + ], + "spans": [ + { + "bbox": [ + 55, + 400, + 135, + 414 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 420, + 171, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 420, + 171, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 171, + 434 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 437, + 295, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 295, + 581 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 295, + 581 + ], + "type": "text", + "content": "Dataset. We conduct experiments on the widely used ViCo dataset [46] and RealTalk dataset [9]. Both ViCo and RealTalk consist of videos of face-to-face daily conversations between two individuals of diverse ages, genders, and ethnicity. We follow the training and testing split provided in their original papers. ViCo contains 398 clips of total 1.3 hours for training, 43 clips for testing, and 42 clips for out-of-distribution (OOD) testing. RealTalk contains 1489 clips of total 6.4 hours for training and 407 clips for testing. Additionally, VFHQ dataset [40], a large-scale high-quality talking head video dataset containing over 16k clips, is used to pretrain the rendering module." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 582, + 295, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 295, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 295, + 700 + ], + "type": "text", + "content": "Implementation Details. For both datasets, we crop the original videos into " + }, + { + "bbox": [ + 55, + 582, + 295, + 700 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 582, + 295, + 700 + ], + "type": "text", + "content": " face videos for training and testing, and use MediaPipe [23] to extract 51-dim facial expression coefficients and 6-dim head pose. For the motion generation module, we train it with the input sequence of 50 frames and a batch size of 64. The diffusion step is set to 1000 for training and inference. For the high-fidelity rendering, we set the input to 16 frames with a batch size of 8. The diffusion step is 1000 for training and 25 for inference. Both modules are trained with AdamW [22] optimizer." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 295, + 713 + ], + "type": "text", + "content": "Compared Methods. We compare the proposed method" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 321, + 69, + 549, + 178 + ], + "blocks": [ + { + "bbox": [ + 321, + 69, + 549, + 178 + ], + "lines": [ + { + "bbox": [ + 321, + 69, + 549, + 178 + ], + "spans": [ + { + "bbox": [ + 321, + 69, + 549, + 178 + ], + "type": "image", + "image_path": "ed4e16e5eb40d9a27244ceabe8d07512250ca78a1e3fdbbedc9ffa4e18950d50.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 186, + 553, + 220 + ], + "lines": [ + { + "bbox": [ + 313, + 186, + 553, + 220 + ], + "spans": [ + { + "bbox": [ + 313, + 186, + 553, + 220 + ], + "type": "text", + "content": "Figure 5. Visualization of the ablation study on implicit motion refinement. We highlight the inaccurate motion with red boxes and the improved facial details with green box." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 242, + 553, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 242, + 553, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 242, + 553, + 338 + ], + "type": "text", + "content": "with several state-of-the-art listening head generation methods, including RLHG [46], PCH [14], L2L [25], MFR-Net [20] and CustomListener [21]. We retrain RLHG, PCH and L2L on both ViCo and RealTalk dataset. Since MFR-Net and CustomListener are not open-sourced, we list their results on ViCo dataset from the original papers for reference. We also conduct thorough ablation studies to verify the effectiveness of the proposed method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "text", + "content": "Evaluation Metrics. We compare both visual and motion quality for evaluation. The visual quality is evaluated by Fréchet Inception Distance (FID) [12], Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity (SSIM) [38]. For the motion quality evaluation, we adopt 1) Feature Distance (FD), the " + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "text", + "content": " distance between the generated motion and the ground truth motion, 2) " + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{\\Delta \\mathrm{fm}}" + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "text", + "content": " [43], the FID score of motion difference between consecutive frames, and 3) Sequence Naturalness Distance (SND) [43], the summarization of " + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{\\Delta \\mathrm{fm}}" + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "text", + "content": " and FID score of motion. For " + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{\\Delta \\mathrm{fm}}" + }, + { + "bbox": [ + 313, + 338, + 554, + 506 + ], + "type": "text", + "content": " and SND, we concatenate the angle and translation to compute the overall pose metrics. To compare with existing works, we extract the 3DMM coefficients by [8], to compute the motion quality metrics." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 514, + 432, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 514, + 432, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 514, + 432, + 528 + ], + "type": "text", + "content": "4.2. Quantitative Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 533, + 553, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 553, + 556 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 553, + 556 + ], + "type": "text", + "content": "The quantitative results on RealTalk and ViCo are listed in Table 1 and Table 2, respectively." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "spans": [ + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "text", + "content": "For the visual quality, our proposed method obtains significantly better visual quality in terms of SSIM, PSNR and FID on both Realtalk and ViCo datasets. For instance, on RealTalk dataset, the relative performance improvements are " + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "inline_equation", + "content": "14\\%" + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "text", + "content": " for SSIM, " + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "inline_equation", + "content": "14\\%" + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "text", + "content": " for PSNR, and " + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "text", + "content": " for FID. On ViCo dataset, the improvements are " + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "inline_equation", + "content": "12\\%" + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "text", + "content": " for SSIM, " + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "text", + "content": " for PSNR, and " + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 313, + 557, + 554, + 700 + ], + "type": "text", + "content": " for FID. These demonstrate the superior high-fidelity generative capability of our proposed method. This is due to the proposed rendering module is much more powerful than the deterministic PIRenderer, and that the hybrid motion modeling further enhances the visual quality of the rendering module." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 325, + 701, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 701, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 325, + 701, + 553, + 713 + ], + "type": "text", + "content": "For the motion quality, our method also achieves the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15890" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 105, + 70, + 506, + 155 + ], + "blocks": [ + { + "bbox": [ + 105, + 70, + 506, + 155 + ], + "lines": [ + { + "bbox": [ + 105, + 70, + 506, + 155 + ], + "spans": [ + { + "bbox": [ + 105, + 70, + 506, + 155 + ], + "type": "table", + "html": "
    MethodsSSIM↑PSNR↑FID↓FD↓FIDΔfm ↓SND↓
    expangletransexpposeexppose
    RLHG [46]0.5717.8720.7913.095.916.0212.010.742.090.04
    PCH [14]0.5717.7820.0513.805.695.9911.360.722.110.04
    L2L [25]0.5015.6127.2822.9211.779.1910.930.587.810.14
    Ours0.6520.3413.3810.493.955.126.000.051.490.02
    ", + "image_path": "7b1d05818c64ddc66ec8ec87955f5ef8d73a135ee73c09cc50fa1d1353cbb1a9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 69, + 196, + 542, + 373 + ], + "blocks": [ + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "lines": [ + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "type": "text", + "content": "Table 1. Quantitative results on RealTalk dataset, where the values of FD and " + }, + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{\\Delta \\mathrm{fm}}" + }, + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "type": "text", + "content": " are multiplied by 100. The " + }, + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "type": "text", + "content": " indicates the higher the better while " + }, + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 55, + 163, + 555, + 187 + ], + "type": "text", + "content": " indicates the lower the better. The best and the second best results are in bold and underlined, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 196, + 542, + 373 + ], + "lines": [ + { + "bbox": [ + 69, + 196, + 542, + 373 + ], + "spans": [ + { + "bbox": [ + 69, + 196, + 542, + 373 + ], + "type": "table", + "html": "
    MethodsTest setSSIM↑PSNR↑FID↓FD ↓FIDΔfm ↓SND ↓
    expangletransexpposeexppose
    RLHG [46]Dtest0.5817.8838.6916.439.056.759.540.763.450.09
    Dood26.709.7510.617.360.559.380.14
    PCH [14]Dtest0.6017.9231.6215.488.845.958.910.733.010.09
    Dood24.117.2710.056.070.477.790.11
    L2L [25]Dtest0.5817.7538.3920.3612.528.8812.060.606.610.19
    Dood23.828.107.438.670.518.160.07
    MFR-Net* [20]Dtest0.5917.8220.0813.376.826.02////
    Dood14.708.126.37////
    CustomListener* [21]Dtest0.6017.9820.0611.546.125.903.120.062.400.07
    Dood12.677.496.013.590.075.940.05
    OursDtest0.6720.6018.9912.547.575.685.130.082.360.08
    Dood11.893.835.435.050.052.060.02
    ", + "image_path": "1125068ff4c6162a47d42527b88a5a1300a345655e77a07be638bef250dff7ae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "lines": [ + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "spans": [ + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "type": "text", + "content": "Table 2. Quantitative results on ViCo dataset, where the values of FD and " + }, + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{\\Delta \\mathrm{fm}}" + }, + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "type": "text", + "content": " are multiplied by 100. The " + }, + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "type": "text", + "content": " indicates higher is better for the corresponding metric while " + }, + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 55, + 382, + 555, + 417 + ], + "type": "text", + "content": " indicates lower is better. The * denotes we report the results from their papers. The best and the second best results are in bold and underlined respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "spans": [ + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "text", + "content": "best overall performance on both datasets. Specifically, for RealTalk, we achieve the best results on all motion metrics. In terms of FD, we obtain " + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "inline_equation", + "content": "31\\%" + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "text", + "content": " performance improvement for the expression, angle, and translations, respectively. In terms of " + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{\\Delta \\mathrm{fm}}" + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "text", + "content": ", the performance improvements are " + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "text", + "content": " for expression and " + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "inline_equation", + "content": "91\\%" + }, + { + "bbox": [ + 54, + 437, + 295, + 664 + ], + "type": "text", + "content": " for head pose. On ViCo dataset, we also obtain the best motion quality on the OOD set and the second-best results on the test set. For ViCo, the motion of the test set is much more intense and random than that of the OOD set. The one-to-many characteristic makes it more difficult to generate the exact motion as the ground truth on the test set. In such cases, CustomListener that additionally incorporates the ground-truth motion text description leads to more similar motions to the ground-truth. Nevertheless, the superior performance on the OOD set demonstrates our better generalization ability. These results verify that our method can largely promote the visual and motion quality, enabling realistic and vivid listening head generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 672, + 168, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 168, + 685 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 168, + 685 + ], + "type": "text", + "content": "4.3. Qualitative Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 715 + ], + "type": "text", + "content": "We compare the visualization result with RLHG, L2L and PCH. MFR-Net and CustomListener are not open-sourced" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 437, + 555, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 555, + 557 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 555, + 557 + ], + "type": "text", + "content": "and their visualization is not available. As shown in Fig 2, our method surpasses the baseline methods in terms of visual quality, motion accuracy, and identity consistency. To be specific, 1) in Fig. 2 (a), our method generates a proper reaction video while the baseline methods show inappropriate facial expressions. 2) in Fig. 2 (b, c), we obtain much better identity preservation, even under more drastic facial expressions, e.g. laughing. 3) in Fig. 2 (b, c, d), our method retains better facial details, such as realistic teeth, wrinkles, and natural complexities." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 564, + 408, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 564, + 408, + 577 + ], + "spans": [ + { + "bbox": [ + 313, + 564, + 408, + 577 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 582, + 554, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 554, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 554, + 605 + ], + "type": "text", + "content": "We conduct ablations to demonstrate the necessities of each part of the proposed hybrid motion modeling." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 555, + 714 + ], + "type": "text", + "content": "Explicit Motion Modeling. We remove the intermediate explicit motion guidance and train a diffusion UNet that learns the listener motion purely from implicit motion modeling, i.e. the rendering module in Section 3.2 without pose guidance net and expression attention layers. The network is first pretrained on VFHQ and Realtalk dataset for unconditioned image generation, then trained on Realtalk dataset for listening head generation conditioned on speaker features. As shown in Table 3, without the motion guidance," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15891" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 81, + 70, + 530, + 140 + ], + "blocks": [ + { + "bbox": [ + 81, + 70, + 530, + 140 + ], + "lines": [ + { + "bbox": [ + 81, + 70, + 530, + 140 + ], + "spans": [ + { + "bbox": [ + 81, + 70, + 530, + 140 + ], + "type": "table", + "html": "
    MethodsSSIM↑PSNR↑FID↓FD↓FIDΔfm ↓SND↓
    expangletransexpposeexppose
    w/o motion guidance0.6319.7514.3711.024.285.009.050.121.670.02
    w/o implicit motion refinement0.6420.1713.5811.004.055.176.840.061.610.02
    Ours0.6520.3413.3810.483.945.126.000.051.480.02
    ", + "image_path": "dd71fc8fe5e7bbde5743db5f38b1613889635399a406f3d92f3b77b96b1b7508.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 63, + 178, + 288, + 236 + ], + "blocks": [ + { + "bbox": [ + 78, + 148, + 531, + 159 + ], + "lines": [ + { + "bbox": [ + 78, + 148, + 531, + 159 + ], + "spans": [ + { + "bbox": [ + 78, + 148, + 531, + 159 + ], + "type": "text", + "content": "Table 3. Ablation study on motion modeling, tested on Realtalk dataset, the values of FD and " + }, + { + "bbox": [ + 78, + 148, + 531, + 159 + ], + "type": "inline_equation", + "content": "\\mathrm{{FID}}_{{\\Delta }_{\\mathrm{{fm}}}}" + }, + { + "bbox": [ + 78, + 148, + 531, + 159 + ], + "type": "text", + "content": " are multiplied by 100 ." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 178, + 288, + 236 + ], + "lines": [ + { + "bbox": [ + 63, + 178, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 63, + 178, + 288, + 236 + ], + "type": "table", + "html": "
    SettingsFD↓FIDΔfm ↓
    expangletransexppose
    Concatenate pose7.813.034.369.870.10
    Separate control7.482.014.284.690.10
    ", + "image_path": "6927e5c1a7eb6c33a9044fdd0f49388fb9e4b68a67db627f05363adf242d7098.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 244, + 295, + 277 + ], + "lines": [ + { + "bbox": [ + 55, + 244, + 295, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 244, + 295, + 277 + ], + "type": "text", + "content": "Table 4. Ablation study on different motion control schemes, tested on Realtalk dataset, the values of FD and " + }, + { + "bbox": [ + 55, + 244, + 295, + 277 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{\\Delta \\mathrm{fm}}" + }, + { + "bbox": [ + 55, + 244, + 295, + 277 + ], + "type": "text", + "content": " are multiplied by 100." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 54, + 303, + 295, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 303, + 295, + 410 + ], + "spans": [ + { + "bbox": [ + 54, + 303, + 295, + 410 + ], + "type": "text", + "content": "both the visual quality and the motion quality of the generated listening head degrades. It can be observed that " + }, + { + "bbox": [ + 54, + 303, + 295, + 410 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{\\Delta \\mathrm{fm}}" + }, + { + "bbox": [ + 54, + 303, + 295, + 410 + ], + "type": "text", + "content": " has significantly degrades, indicating there are unnatural transitions of expression and head poses. As shown in Fig. 3, without motion guidance, the network struggles to generate continuous head poses and expressions, often resulting in serious artifacts in faces. Such result proves that the explicit motion guidance can effectively ease the training of LDM-based models on small scale datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 412, + 295, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 412, + 295, + 628 + ], + "spans": [ + { + "bbox": [ + 56, + 412, + 295, + 628 + ], + "type": "text", + "content": "The Distinct Controls of Pose and Expressions. In Section 3.2, we propose to use separate controls of head pose and facial expression according to the intrinsics of these two types of motion signals. To validate the effectiveness of the proposed control strategies, we remove the pose images in the rendering module, and concatenate the head pose coefficients with the facial expression coefficients. The concatenated motion signal is injected into the rendering module through the expression cross-attention layer. The results in Table 4 show that using concatenated motion as the control signal leads to a degeneration in both motion accuracy and naturalness, especially on expression metrics. We also present some visualizations in Fig. 4. From the visualization, there exists inaccurate pose control and visual artifacts when using concatenated motion signals (the left example), and poor expression controllability (the right example). These results verify the effectiveness of the proposed pose and expression controls." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 630, + 295, + 713 + ], + "type": "text", + "content": "Implicit Motion Refinement. Furthermore, we validate the effectiveness of the proposed implicit motion refinement method. As shown in Table 3, without the refinement module, the motion quality and visual quality of the generated video both degrade. As shown in Fig. 5, we observe mainly two effects of the implicit motion refinement. The first is that the refinement fixes some wrong facial expressions (the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 180, + 553, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 180, + 553, + 276 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 553, + 276 + ], + "type": "text", + "content": "left example), and the second is that it tends to add more facial details to the generated videos, such as more realistic wrinkles (the right example). As a result, we can observe more stable and detailed facial expressions after refinement. This implies that the implicit motion refinement helps the rendering module learn to revise the details of the generated videos given additional conditions, further improving the visual qualities." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 276, + 555, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 555, + 455 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 555, + 455 + ], + "type": "text", + "content": "**Discussions.** Our proposed framework can generate high fidelity listening head videos with accurate motion, vivid facial details and expressive motions. Nevertheless, there are still some limitations. 1) The condition used to generate listening heads is restricted within the speaker's audio and facial expressions. But more flexible conditions such as text description, motion styles etc. are always appreciated. The proposed hybrid motion generation has the potential of integrating diverse control signals, we will study this in the future. 2) Time complexities. The motion generation module in our framework is lightweight and can generate motions at 15 fps, the computational bottleneck lies in the rendering module. This is a common limitation of the LDM-based methods and can be alleviated by model quantization or distillation, and we will explore more in the future." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 455, + 553, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 455, + 553, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 455, + 553, + 491 + ], + "type": "text", + "content": "Supplementary Materials. We provide user study, details of network, training objectives, experimental setups, ethics, and more visual results in supplementary materials." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 388, + 514 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "content": "In this paper, we propose a diffusion-based listening head generation framework that generates photorealistic listening head videos up to " + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 313, + 522, + 555, + 713 + ], + "type": "text", + "content": " resolution, with highly expressive motions and fine facial details. A hybrid motion modeling method that consists of an explicit motion generation module, a specially designed motion control strategy and an implicit motion refining process eases the training of the LDM-based framework, making the learning on a small scale dataset feasible. Comprehensive experiments on Realtalk and ViCo dataset demonstrate that our framework achieves superior results in terms of visual quality and motion expressiveness compared with several state-of-the-art methods. And a thorough ablation study proves the effectiveness and necessity of the proposed hybrid motion modeling method. In the future, we will study further to improve the controllability and the generating speed of our model." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15892" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 153, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 91, + 296, + 126 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 91, + 296, + 126 + ], + "spans": [ + { + "bbox": [ + 55, + 91, + 296, + 126 + ], + "type": "text", + "content": "This research was funded by Key R&D Program of Shaanxi Province under Grant 2024GX-YBXM-141. 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